1>>> Level = conductor = 11 <<<
2Minimal curve = [0,-1,1,-10,-20]
3
4Enter sign (1,-1,0 for both):Newform information:
5
61 newform(s) at level 11:
7p0=2
8#ap=	500
91:	aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
10aq = [ -1 ]
11ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
12SFE = 1,	L/P = 2/5
13lplus = 1, mplus = 1
14lminus = 3, mminus = 2
15[(4,1;1,3),-1,1;1]
16
17Modular symbol map (+,-)
18(0:1) = {0,oo} -> (-2/5,0)
19(1:1) = {0,1} -> (0,0)
20(2:1) = {0,1/2} -> (-2,0)
21(3:1) = {0,1/3} -> (-1,1)
22(4:1) = {0,1/4} -> (1,1)
23(5:1) = {0,1/5} -> (2,0)
24(6:1) = {0,1/6} -> (2,0)
25(7:1) = {0,1/7} -> (1,-1)
26(8:1) = {0,1/8} -> (-1,-1)
27(9:1) = {0,1/9} -> (-2,0)
28(10:1) = {0,1/10} -> (0,0)
29(1:0) = {oo,0} -> (2/5,0)
30
31Computation of further modular symbols
32
33Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
34Enter numerator and denominator of r:
35All modular symbols with bounded denominator
36
37Enter maximum denominator (0 for none): {0,0} -> (0,0)
38{0,1/2} -> (-2,0)
39{0,1/3} -> (-1,1)
40{0,2/3} -> (-1,-1)
41{0,1/4} -> (1,1)
42{0,3/4} -> (1,-1)
43{0,1/5} -> (2,0)
44{0,2/5} -> (-3,1)
45{0,3/5} -> (-3,-1)
46{0,4/5} -> (2,0)
47>>> Level = conductor = 11 <<<
48Minimal curve = [0,-1,1,-10,-20]
49
50Enter sign (1,-1,0 for both):Newform information:
51
521 newform(s) at level 11:
53p0=2
54#ap=	500
551:	aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
56aq = [ -1 ]
57ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
58SFE = 1,	L/P = 2/5
59lplus = 1, mplus = 1
60[(-5,1;-1,2),-2,0;?]
61
62Modular symbol map (+)
63(0:1) = {0,oo} -> -2/5
64(1:1) = {0,1} -> 0
65(2:1) = {0,1/2} -> -2
66(3:1) = {0,1/3} -> -1
67(4:1) = {0,1/4} -> 1
68(5:1) = {0,1/5} -> 2
69(6:1) = {0,1/6} -> 2
70(7:1) = {0,1/7} -> 1
71(8:1) = {0,1/8} -> -1
72(9:1) = {0,1/9} -> -2
73(10:1) = {0,1/10} -> 0
74(1:0) = {oo,0} -> 2/5
75
76Computation of further modular symbols
77
78Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
79Enter numerator and denominator of r:
80All modular symbols with bounded denominator
81
82Enter maximum denominator (0 for none): {0,0} -> 0
83{0,1/2} -> -2
84{0,1/3} -> -1
85{0,2/3} -> -1
86{0,1/4} -> 1
87{0,3/4} -> 1
88{0,1/5} -> 2
89{0,2/5} -> -3
90{0,3/5} -> -3
91{0,4/5} -> 2
92>>> Level = conductor = 11 <<<
93Minimal curve = [0,-1,1,-10,-20]
94
95Enter sign (1,-1,0 for both):Newform information:
96
971 newform(s) at level 11:
98p0=2
99#ap=	500
1001:	aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
101aq = [ -1 ]
102ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
103SFE = 1,	L/P = 2/5
104lplus = 1, mplus = 1
105lminus = 3, mminus = 2
106[(4,1;1,3),-1,1;1]
107
108Modular symbol map (+,-)
109(0:1) = {0,oo} -> (-2/5,0)
110(1:1) = {0,1} -> (0,0)
111(2:1) = {0,1/2} -> (-2,0)
112(3:1) = {0,1/3} -> (-1,1)
113(4:1) = {0,1/4} -> (1,1)
114(5:1) = {0,1/5} -> (2,0)
115(6:1) = {0,1/6} -> (2,0)
116(7:1) = {0,1/7} -> (1,-1)
117(8:1) = {0,1/8} -> (-1,-1)
118(9:1) = {0,1/9} -> (-2,0)
119(10:1) = {0,1/10} -> (0,0)
120(1:0) = {oo,0} -> (2/5,0)
121
122Computation of further modular symbols
123
124Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
125Enter numerator and denominator of r:
126All modular symbols with bounded denominator
127
128Enter maximum denominator (0 for none): {oo,0} -> (2/5,0)
129{oo,1/2} -> (-8/5,0)
130{oo,1/3} -> (-3/5,1)
131{oo,2/3} -> (-3/5,-1)
132{oo,1/4} -> (7/5,1)
133{oo,3/4} -> (7/5,-1)
134{oo,1/5} -> (12/5,0)
135{oo,2/5} -> (-13/5,1)
136{oo,3/5} -> (-13/5,-1)
137{oo,4/5} -> (12/5,0)
138>>> Level = conductor = 11 <<<
139Minimal curve = [0,-1,1,-10,-20]
140
141Enter sign (1,-1,0 for both):Newform information:
142
1431 newform(s) at level 11:
144p0=2
145#ap=	500
1461:	aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
147aq = [ -1 ]
148ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
149SFE = 1,	L/P = 2/5
150lplus = 1, mplus = 1
151[(-5,1;-1,2),-2,0;?]
152
153Modular symbol map (+)
154(0:1) = {0,oo} -> -2/5
155(1:1) = {0,1} -> 0
156(2:1) = {0,1/2} -> -2
157(3:1) = {0,1/3} -> -1
158(4:1) = {0,1/4} -> 1
159(5:1) = {0,1/5} -> 2
160(6:1) = {0,1/6} -> 2
161(7:1) = {0,1/7} -> 1
162(8:1) = {0,1/8} -> -1
163(9:1) = {0,1/9} -> -2
164(10:1) = {0,1/10} -> 0
165(1:0) = {oo,0} -> 2/5
166
167Computation of further modular symbols
168
169Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
170Enter numerator and denominator of r:
171All modular symbols with bounded denominator
172
173Enter maximum denominator (0 for none): {oo,0} -> 2/5
174{oo,1/2} -> -8/5
175{oo,1/3} -> -3/5
176{oo,2/3} -> -3/5
177{oo,1/4} -> 7/5
178{oo,3/4} -> 7/5
179{oo,1/5} -> 12/5
180{oo,2/5} -> -13/5
181{oo,3/5} -> -13/5
182{oo,4/5} -> 12/5
183>>> Level = conductor = 11 <<<
184Minimal curve = [0,-1,1,0,0]
185
186Enter sign (1,-1,0 for both):Newform information:
187
1881 newform(s) at level 11:
189p0=2
190#ap=	500
1911:	aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
192aq = [ -1 ]
193ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
194SFE = 1,	L/P = 2/5
195lplus = 1, mplus = 1
196lminus = 3, mminus = 2
197[(4,1;1,3),-1,1;1]
198
199Modular symbol map (+,-)
200(0:1) = {0,oo} -> (-2/25,0)
201(1:1) = {0,1} -> (0,0)
202(2:1) = {0,1/2} -> (-2/5,0)
203(3:1) = {0,1/3} -> (-1/5,1)
204(4:1) = {0,1/4} -> (1/5,1)
205(5:1) = {0,1/5} -> (2/5,0)
206(6:1) = {0,1/6} -> (2/5,0)
207(7:1) = {0,1/7} -> (1/5,-1)
208(8:1) = {0,1/8} -> (-1/5,-1)
209(9:1) = {0,1/9} -> (-2/5,0)
210(10:1) = {0,1/10} -> (0,0)
211(1:0) = {oo,0} -> (2/25,0)
212
213Computation of further modular symbols
214
215Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
216Enter numerator and denominator of r:
217All modular symbols with bounded denominator
218
219Enter maximum denominator (0 for none): {0,0} -> (0,0)
220{0,1/2} -> (-2/5,0)
221{0,1/3} -> (-1/5,1)
222{0,2/3} -> (-1/5,-1)
223{0,1/4} -> (1/5,1)
224{0,3/4} -> (1/5,-1)
225{0,1/5} -> (2/5,0)
226{0,2/5} -> (-3/5,1)
227{0,3/5} -> (-3/5,-1)
228{0,4/5} -> (2/5,0)
229>>> Level = conductor = 11 <<<
230Minimal curve = [0,-1,1,-7820,-263580]
231
232Enter sign (1,-1,0 for both):Newform information:
233
2341 newform(s) at level 11:
235p0=2
236#ap=	500
2371:	aplist = [ -2 -1 1 -2 1 4 -2 0 -1 0 7 3 -8 -6 8 -6 5 12 -7 -3 ...]
238aq = [ -1 ]
239ap0 = -2, dp0 = 2, np0 = 5, pdot = -10
240SFE = 1,	L/P = 2/5
241lplus = 1, mplus = 1
242lminus = 3, mminus = 2
243[(4,1;1,3),-1,1;1]
244
245Modular symbol map (+,-)
246(0:1) = {0,oo} -> (-2,0)
247(1:1) = {0,1} -> (0,0)
248(2:1) = {0,1/2} -> (-10,0)
249(3:1) = {0,1/3} -> (-5,1)
250(4:1) = {0,1/4} -> (5,1)
251(5:1) = {0,1/5} -> (10,0)
252(6:1) = {0,1/6} -> (10,0)
253(7:1) = {0,1/7} -> (5,-1)
254(8:1) = {0,1/8} -> (-5,-1)
255(9:1) = {0,1/9} -> (-10,0)
256(10:1) = {0,1/10} -> (0,0)
257(1:0) = {oo,0} -> (2,0)
258
259Computation of further modular symbols
260
261Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
262Enter numerator and denominator of r:
263All modular symbols with bounded denominator
264
265Enter maximum denominator (0 for none): {0,0} -> (0,0)
266{0,1/2} -> (-10,0)
267{0,1/3} -> (-5,1)
268{0,2/3} -> (-5,-1)
269{0,1/4} -> (5,1)
270{0,3/4} -> (5,-1)
271{0,1/5} -> (10,0)
272{0,2/5} -> (-15,1)
273{0,3/5} -> (-15,-1)
274{0,4/5} -> (10,0)
275>>> Level = conductor = 37 <<<
276Minimal curve = [0,0,1,-1,0]
277
278Enter sign (1,-1,0 for both):Newform information:
279
2801 newform(s) at level 37:
281p0=2
282#ap=	608
2831:	aplist = [ -2 -3 -2 -1 -5 -2 0 0 2 6 -4 -1 -9 2 -9 1 8 -8 8 9 ...]
284aq = [ 1 ]
285ap0 = -2, dp0 = 0, np0 = 5
286SFE = -1,	L/P = 0
287lplus = 5, mplus = 4
288lminus = 3, mminus = 2
289[(14,1;3,8),1,-1;2]
290
291Modular symbol map (+,-)
292(0:1) = {0,oo} -> (0,0)
293(1:1) = {0,1} -> (0,0)
294(2:1) = {0,1/2} -> (0,0)
295(3:1) = {0,1/3} -> (0,1)
296(4:1) = {0,1/4} -> (0,1)
297(5:1) = {0,1/5} -> (1,0)
298(6:1) = {0,1/6} -> (0,0)
299(7:1) = {0,1/7} -> (1,0)
300(8:1) = {0,1/8} -> (1,-1)
301(9:1) = {0,1/9} -> (0,-1)
302(10:1) = {0,1/10} -> (0,0)
303(11:1) = {0,1/11} -> (0,0)
304(12:1) = {0,1/12} -> (0,-1)
305(13:1) = {0,1/13} -> (0,-1)
306(14:1) = {0,1/14} -> (-1,-1)
307(15:1) = {0,1/15} -> (-1,0)
308(16:1) = {0,1/16} -> (-1,0)
309(17:1) = {0,1/17} -> (0,1)
310(18:1) = {0,1/18} -> (0,0)
311(19:1) = {0,1/19} -> (0,0)
312(20:1) = {0,1/20} -> (0,-1)
313(21:1) = {0,1/21} -> (-1,0)
314(22:1) = {0,1/22} -> (-1,0)
315(23:1) = {0,1/23} -> (-1,1)
316(24:1) = {0,1/24} -> (0,1)
317(25:1) = {0,1/25} -> (0,1)
318(26:1) = {0,1/26} -> (0,0)
319(27:1) = {0,1/27} -> (0,0)
320(28:1) = {0,1/28} -> (0,1)
321(29:1) = {0,1/29} -> (1,1)
322(30:1) = {0,1/30} -> (1,0)
323(31:1) = {0,1/31} -> (0,0)
324(32:1) = {0,1/32} -> (1,0)
325(33:1) = {0,1/33} -> (0,-1)
326(34:1) = {0,1/34} -> (0,-1)
327(35:1) = {0,1/35} -> (0,0)
328(36:1) = {0,1/36} -> (0,0)
329(1:0) = {oo,0} -> (0,0)
330
331Computation of further modular symbols
332
333Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
334Enter numerator and denominator of r:
335All modular symbols with bounded denominator
336
337Enter maximum denominator (0 for none): >>> Level = conductor = 37 <<<
338Minimal curve = [0,0,1,-1,0]
339
340Enter sign (1,-1,0 for both):Newform information:
341
3421 newform(s) at level 37:
343p0=2
344#ap=	608
3451:	aplist = [ -2 -3 -2 -1 -5 -2 0 0 2 6 -4 -1 -9 2 -9 1 8 -8 8 9 ...]
346aq = [ 1 ]
347ap0 = -2, dp0 = 0, np0 = 5
348SFE = -1,	L/P = 0
349lplus = 5, mplus = 4
350[(15,1;2,5),1,0;?]
351
352Modular symbol map (+)
353(0:1) = {0,oo} -> 0
354(1:1) = {0,1} -> 0
355(2:1) = {0,1/2} -> 0
356(3:1) = {0,1/3} -> 0
357(4:1) = {0,1/4} -> 0
358(5:1) = {0,1/5} -> 1
359(6:1) = {0,1/6} -> 0
360(7:1) = {0,1/7} -> 1
361(8:1) = {0,1/8} -> 1
362(9:1) = {0,1/9} -> 0
363(10:1) = {0,1/10} -> 0
364(11:1) = {0,1/11} -> 0
365(12:1) = {0,1/12} -> 0
366(13:1) = {0,1/13} -> 0
367(14:1) = {0,1/14} -> -1
368(15:1) = {0,1/15} -> -1
369(16:1) = {0,1/16} -> -1
370(17:1) = {0,1/17} -> 0
371(18:1) = {0,1/18} -> 0
372(19:1) = {0,1/19} -> 0
373(20:1) = {0,1/20} -> 0
374(21:1) = {0,1/21} -> -1
375(22:1) = {0,1/22} -> -1
376(23:1) = {0,1/23} -> -1
377(24:1) = {0,1/24} -> 0
378(25:1) = {0,1/25} -> 0
379(26:1) = {0,1/26} -> 0
380(27:1) = {0,1/27} -> 0
381(28:1) = {0,1/28} -> 0
382(29:1) = {0,1/29} -> 1
383(30:1) = {0,1/30} -> 1
384(31:1) = {0,1/31} -> 0
385(32:1) = {0,1/32} -> 1
386(33:1) = {0,1/33} -> 0
387(34:1) = {0,1/34} -> 0
388(35:1) = {0,1/35} -> 0
389(36:1) = {0,1/36} -> 0
390(1:0) = {oo,0} -> 0
391
392Computation of further modular symbols
393
394Base point? (enter 0 for 0, or 1 for oo) Values of {0,r} for rational r:
395Enter numerator and denominator of r:
396All modular symbols with bounded denominator
397
398Enter maximum denominator (0 for none): >>> Level = conductor = 389 <<<
399Minimal curve = [0,1,1,-2,0]
400
401Enter sign (1,-1,0 for both):Newform information:
402
4031 newform(s) at level 389:
404p0=2
405#ap=	1972
4061:	aplist = [ -2 -2 -3 -5 -4 -3 -6 5 -4 -6 4 -8 -3 12 -2 -6 3 -8 -5 -10 ...]
407aq = [ -1 ]
408ap0 = -2, dp0 = 0, np0 = 5
409SFE = 1,	L/P = 0
410lplus = 5, mplus = 8
411lminus = 3, mminus = 4
412[(-111,1;-2,7),1,-1;2]
413
414Modular symbol map (+,-)
415(0:1) = {0,oo} -> (0,0)
416(1:1) = {0,1} -> (0,0)
417(2:1) = {0,1/2} -> (0,0)
418(3:1) = {0,1/3} -> (0,2)
419(4:1) = {0,1/4} -> (0,0)
420(5:1) = {0,1/5} -> (2,0)
421(6:1) = {0,1/6} -> (0,0)
422(7:1) = {0,1/7} -> (1,-1)
423(8:1) = {0,1/8} -> (0,1)
424(9:1) = {0,1/9} -> (-1,-1)
425(10:1) = {0,1/10} -> (0,0)
426(11:1) = {0,1/11} -> (1,0)
427(12:1) = {0,1/12} -> (0,-1)
428(13:1) = {0,1/13} -> (0,-2)
429(14:1) = {0,1/14} -> (-1,1)
430(15:1) = {0,1/15} -> (0,0)
431(16:1) = {0,1/16} -> (1,-1)
432(17:1) = {0,1/17} -> (0,1)
433(18:1) = {0,1/18} -> (1,-1)
434(19:1) = {0,1/19} -> (0,-1)
435(20:1) = {0,1/20} -> (-1,0)
436(21:1) = {0,1/21} -> (0,-1)
437(22:1) = {0,1/22} -> (0,0)
438(23:1) = {0,1/23} -> (0,1)
439(24:1) = {0,1/24} -> (1,-1)
440(25:1) = {0,1/25} -> (-1,-1)
441(26:1) = {0,1/26} -> (0,0)
442(27:1) = {0,1/27} -> (1,1)
443(28:1) = {0,1/28} -> (1,-1)
444(29:1) = {0,1/29} -> (0,-1)
445(30:1) = {0,1/30} -> (0,-2)
446(31:1) = {0,1/31} -> (-1,-3)
447(32:1) = {0,1/32} -> (-2,-1)
448(33:1) = {0,1/33} -> (-2,-1)
449(34:1) = {0,1/34} -> (-1,0)
450(35:1) = {0,1/35} -> (-1,0)
451(36:1) = {0,1/36} -> (0,1)
452(37:1) = {0,1/37} -> (0,1)
453(38:1) = {0,1/38} -> (-1,1)
454(39:1) = {0,1/39} -> (0,0)
455(40:1) = {0,1/40} -> (1,0)
456(41:1) = {0,1/41} -> (0,-1)
457(42:1) = {0,1/42} -> (-1,-1)
458(43:1) = {0,1/43} -> (1,-1)
459(44:1) = {0,1/44} -> (-1,-1)
460(45:1) = {0,1/45} -> (0,-2)
461(46:1) = {0,1/46} -> (-1,-3)
462(47:1) = {0,1/47} -> (-2,1)
463(48:1) = {0,1/48} -> (-2,1)
464(49:1) = {0,1/49} -> (0,-1)
465(50:1) = {0,1/50} -> (0,1)
466(51:1) = {0,1/51} -> (0,-1)
467(52:1) = {0,1/52} -> (0,1)
468(53:1) = {0,1/53} -> (0,0)
469(54:1) = {0,1/54} -> (0,-1)
470(55:1) = {0,1/55} -> (-1,-1)
471(56:1) = {0,1/56} -> (-1,1)
472(57:1) = {0,1/57} -> (-1,-1)
473(58:1) = {0,1/58} -> (-1,-1)
474(59:1) = {0,1/59} -> (-2,2)
475(60:1) = {0,1/60} -> (0,2)
476(61:1) = {0,1/61} -> (0,1)
477(62:1) = {0,1/62} -> (0,2)
478(63:1) = {0,1/63} -> (0,0)
479(64:1) = {0,1/64} -> (2,0)
480(65:1) = {0,1/65} -> (0,0)
481(66:1) = {0,1/66} -> (1,1)
482(67:1) = {0,1/67} -> (0,-2)
483(68:1) = {0,1/68} -> (0,-2)
484(69:1) = {0,1/69} -> (0,-2)
485(70:1) = {0,1/70} -> (0,-1)
486(71:1) = {0,1/71} -> (0,-2)
487(72:1) = {0,1/72} -> (-1,-1)
488(73:1) = {0,1/73} -> (-1,-1)
489(74:1) = {0,1/74} -> (-1,-2)
490(75:1) = {0,1/75} -> (0,0)
491(76:1) = {0,1/76} -> (0,-2)
492(77:1) = {0,1/77} -> (-2,0)
493(78:1) = {0,1/78} -> (-2,0)
494(79:1) = {0,1/79} -> (-2,0)
495(80:1) = {0,1/80} -> (-2,0)
496(81:1) = {0,1/81} -> (-1,1)
497(82:1) = {0,1/82} -> (-1,2)
498(83:1) = {0,1/83} -> (0,0)
499(84:1) = {0,1/84} -> (0,2)
500(85:1) = {0,1/85} -> (-1,1)
501(86:1) = {0,1/86} -> (-2,2)
502(87:1) = {0,1/87} -> (0,2)
503(88:1) = {0,1/88} -> (0,2)
504(89:1) = {0,1/89} -> (-1,1)
505(90:1) = {0,1/90} -> (-1,3)
506(91:1) = {0,1/91} -> (-2,2)
507(92:1) = {0,1/92} -> (-1,4)
508(93:1) = {0,1/93} -> (1,3)
509(94:1) = {0,1/94} -> (1,1)
510(95:1) = {0,1/95} -> (2,2)
511(96:1) = {0,1/96} -> (2,0)
512(97:1) = {0,1/97} -> (0,0)
513(98:1) = {0,1/98} -> (0,2)
514(99:1) = {0,1/99} -> (1,1)
515(100:1) = {0,1/100} -> (1,0)
516(101:1) = {0,1/101} -> (0,0)
517(102:1) = {0,1/102} -> (-1,1)
518(103:1) = {0,1/103} -> (1,0)
519(104:1) = {0,1/104} -> (0,0)
520(105:1) = {0,1/105} -> (-1,-1)
521(106:1) = {0,1/106} -> (-1,0)
522(107:1) = {0,1/107} -> (-1,0)
523(108:1) = {0,1/108} -> (-1,1)
524(109:1) = {0,1/109} -> (-1,2)
525(110:1) = {0,1/110} -> (-1,2)
526(111:1) = {0,1/111} -> (-1,1)
527(112:1) = {0,1/112} -> (-1,1)
528(113:1) = {0,1/113} -> (-1,3)
529(114:1) = {0,1/114} -> (1,1)
530(115:1) = {0,1/115} -> (0,0)
531(116:1) = {0,1/116} -> (1,1)
532(117:1) = {0,1/117} -> (0,2)
533(118:1) = {0,1/118} -> (1,-1)
534(119:1) = {0,1/119} -> (1,1)
535(120:1) = {0,1/120} -> (-1,-1)
536(121:1) = {0,1/121} -> (0,2)
537(122:1) = {0,1/122} -> (-1,1)
538(123:1) = {0,1/123} -> (0,2)
539(124:1) = {0,1/124} -> (-1,0)
540(125:1) = {0,1/125} -> (-1,1)
541(126:1) = {0,1/126} -> (0,2)
542(127:1) = {0,1/127} -> (0,1)
543(128:1) = {0,1/128} -> (-2,2)
544(129:1) = {0,1/129} -> (0,2)
545(130:1) = {0,1/130} -> (0,2)
546(131:1) = {0,1/131} -> (0,2)
547(132:1) = {0,1/132} -> (1,1)
548(133:1) = {0,1/133} -> (0,2)
549(134:1) = {0,1/134} -> (1,3)
550(135:1) = {0,1/135} -> (-1,1)
551(136:1) = {0,1/136} -> (0,2)
552(137:1) = {0,1/137} -> (-1,2)
553(138:1) = {0,1/138} -> (1,3)
554(139:1) = {0,1/139} -> (1,1)
555(140:1) = {0,1/140} -> (1,1)
556(141:1) = {0,1/141} -> (2,0)
557(142:1) = {0,1/142} -> (0,0)
558(143:1) = {0,1/143} -> (0,2)
559(144:1) = {0,1/144} -> (0,0)
560(145:1) = {0,1/145} -> (1,2)
561(146:1) = {0,1/146} -> (0,1)
562(147:1) = {0,1/147} -> (-1,2)
563(148:1) = {0,1/148} -> (1,4)
564(149:1) = {0,1/149} -> (2,1)
565(150:1) = {0,1/150} -> (0,0)
566(151:1) = {0,1/151} -> (0,2)
567(152:1) = {0,1/152} -> (0,2)
568(153:1) = {0,1/153} -> (0,0)
569(154:1) = {0,1/154} -> (2,1)
570(155:1) = {0,1/155} -> (2,2)
571(156:1) = {0,1/156} -> (2,0)
572(157:1) = {0,1/157} -> (0,0)
573(158:1) = {0,1/158} -> (2,1)
574(159:1) = {0,1/159} -> (1,-2)
575(160:1) = {0,1/160} -> (1,0)
576(161:1) = {0,1/161} -> (0,-1)
577(162:1) = {0,1/162} -> (0,1)
578(163:1) = {0,1/163} -> (1,1)
579(164:1) = {0,1/164} -> (1,1)
580(165:1) = {0,1/165} -> (2,1)
581(166:1) = {0,1/166} -> (0,0)
582(167:1) = {0,1/167} -> (2,0)
583(168:1) = {0,1/168} -> (1,-1)
584(169:1) = {0,1/169} -> (1,1)
585(170:1) = {0,1/170} -> (1,-1)
586(171:1) = {0,1/171} -> (2,2)
587(172:1) = {0,1/172} -> (1,-2)
588(173:1) = {0,1/173} -> (1,-1)
589(174:1) = {0,1/174} -> (1,-1)
590(175:1) = {0,1/175} -> (1,0)
591(176:1) = {0,1/176} -> (1,-1)
592(177:1) = {0,1/177} -> (2,0)
593(178:1) = {0,1/178} -> (2,-2)
594(179:1) = {0,1/179} -> (1,-3)
595(180:1) = {0,1/180} -> (0,-2)
596(181:1) = {0,1/181} -> (0,0)
597(182:1) = {0,1/182} -> (1,-2)
598(183:1) = {0,1/183} -> (0,-1)
599(184:1) = {0,1/184} -> (1,-2)
600(185:1) = {0,1/185} -> (1,-2)
601(186:1) = {0,1/186} -> (0,-1)
602(187:1) = {0,1/187} -> (0,-1)
603(188:1) = {0,1/188} -> (0,-2)
604(189:1) = {0,1/189} -> (-2,0)
605(190:1) = {0,1/190} -> (-1,-1)
606(191:1) = {0,1/191} -> (-2,0)
607(192:1) = {0,1/192} -> (-2,0)
608(193:1) = {0,1/193} -> (0,2)
609(194:1) = {0,1/194} -> (0,0)
610(195:1) = {0,1/195} -> (0,0)
611(196:1) = {0,1/196} -> (0,-2)
612(197:1) = {0,1/197} -> (-2,0)
613(198:1) = {0,1/198} -> (-2,0)
614(199:1) = {0,1/199} -> (-1,1)
615(200:1) = {0,1/200} -> (-2,0)
616(201:1) = {0,1/201} -> (0,2)
617(202:1) = {0,1/202} -> (0,1)
618(203:1) = {0,1/203} -> (0,1)
619(204:1) = {0,1/204} -> (1,2)
620(205:1) = {0,1/205} -> (1,2)
621(206:1) = {0,1/206} -> (0,1)
622(207:1) = {0,1/207} -> (1,2)
623(208:1) = {0,1/208} -> (0,0)
624(209:1) = {0,1/209} -> (0,2)
625(210:1) = {0,1/210} -> (1,3)
626(211:1) = {0,1/211} -> (2,2)
627(212:1) = {0,1/212} -> (2,0)
628(213:1) = {0,1/213} -> (1,1)
629(214:1) = {0,1/214} -> (1,0)
630(215:1) = {0,1/215} -> (1,1)
631(216:1) = {0,1/216} -> (1,1)
632(217:1) = {0,1/217} -> (1,2)
633(218:1) = {0,1/218} -> (2,-2)
634(219:1) = {0,1/219} -> (1,1)
635(220:1) = {0,1/220} -> (1,-1)
636(221:1) = {0,1/221} -> (1,1)
637(222:1) = {0,1/222} -> (2,0)
638(223:1) = {0,1/223} -> (0,0)
639(224:1) = {0,1/224} -> (2,-1)
640(225:1) = {0,1/225} -> (1,-1)
641(226:1) = {0,1/226} -> (1,-1)
642(227:1) = {0,1/227} -> (0,-1)
643(228:1) = {0,1/228} -> (0,1)
644(229:1) = {0,1/229} -> (1,0)
645(230:1) = {0,1/230} -> (1,2)
646(231:1) = {0,1/231} -> (2,-1)
647(232:1) = {0,1/232} -> (0,0)
648(233:1) = {0,1/233} -> (2,0)
649(234:1) = {0,1/234} -> (2,-2)
650(235:1) = {0,1/235} -> (2,-1)
651(236:1) = {0,1/236} -> (0,0)
652(237:1) = {0,1/237} -> (0,-2)
653(238:1) = {0,1/238} -> (0,-2)
654(239:1) = {0,1/239} -> (0,0)
655(240:1) = {0,1/240} -> (2,-1)
656(241:1) = {0,1/241} -> (1,-4)
657(242:1) = {0,1/242} -> (-1,-2)
658(243:1) = {0,1/243} -> (0,-1)
659(244:1) = {0,1/244} -> (1,-2)
660(245:1) = {0,1/245} -> (0,0)
661(246:1) = {0,1/246} -> (0,-2)
662(247:1) = {0,1/247} -> (0,0)
663(248:1) = {0,1/248} -> (2,0)
664(249:1) = {0,1/249} -> (1,-1)
665(250:1) = {0,1/250} -> (1,-1)
666(251:1) = {0,1/251} -> (1,-3)
667(252:1) = {0,1/252} -> (-1,-2)
668(253:1) = {0,1/253} -> (0,-2)
669(254:1) = {0,1/254} -> (-1,-1)
670(255:1) = {0,1/255} -> (1,-3)
671(256:1) = {0,1/256} -> (0,-2)
672(257:1) = {0,1/257} -> (1,-1)
673(258:1) = {0,1/258} -> (0,-2)
674(259:1) = {0,1/259} -> (0,-2)
675(260:1) = {0,1/260} -> (0,-2)
676(261:1) = {0,1/261} -> (-2,-2)
677(262:1) = {0,1/262} -> (0,-1)
678(263:1) = {0,1/263} -> (0,-2)
679(264:1) = {0,1/264} -> (-1,-1)
680(265:1) = {0,1/265} -> (-1,0)
681(266:1) = {0,1/266} -> (0,-2)
682(267:1) = {0,1/267} -> (-1,-1)
683(268:1) = {0,1/268} -> (0,-2)
684(269:1) = {0,1/269} -> (-1,1)
685(270:1) = {0,1/270} -> (1,-1)
686(271:1) = {0,1/271} -> (1,1)
687(272:1) = {0,1/272} -> (0,-2)
688(273:1) = {0,1/273} -> (1,-1)
689(274:1) = {0,1/274} -> (0,0)
690(275:1) = {0,1/275} -> (1,-1)
691(276:1) = {0,1/276} -> (-1,-3)
692(277:1) = {0,1/277} -> (-1,-1)
693(278:1) = {0,1/278} -> (-1,-1)
694(279:1) = {0,1/279} -> (-1,-2)
695(280:1) = {0,1/280} -> (-1,-2)
696(281:1) = {0,1/281} -> (-1,-1)
697(282:1) = {0,1/282} -> (-1,0)
698(283:1) = {0,1/283} -> (-1,0)
699(284:1) = {0,1/284} -> (-1,1)
700(285:1) = {0,1/285} -> (0,0)
701(286:1) = {0,1/286} -> (1,0)
702(287:1) = {0,1/287} -> (-1,-1)
703(288:1) = {0,1/288} -> (0,0)
704(289:1) = {0,1/289} -> (1,0)
705(290:1) = {0,1/290} -> (1,-1)
706(291:1) = {0,1/291} -> (0,-2)
707(292:1) = {0,1/292} -> (0,0)
708(293:1) = {0,1/293} -> (2,0)
709(294:1) = {0,1/294} -> (2,-2)
710(295:1) = {0,1/295} -> (1,-1)
711(296:1) = {0,1/296} -> (1,-3)
712(297:1) = {0,1/297} -> (-1,-4)
713(298:1) = {0,1/298} -> (-2,-2)
714(299:1) = {0,1/299} -> (-1,-3)
715(300:1) = {0,1/300} -> (-1,-1)
716(301:1) = {0,1/301} -> (0,-2)
717(302:1) = {0,1/302} -> (0,-2)
718(303:1) = {0,1/303} -> (-2,-2)
719(304:1) = {0,1/304} -> (-1,-1)
720(305:1) = {0,1/305} -> (0,-2)
721(306:1) = {0,1/306} -> (0,0)
722(307:1) = {0,1/307} -> (-1,-2)
723(308:1) = {0,1/308} -> (-1,-1)
724(309:1) = {0,1/309} -> (-2,0)
725(310:1) = {0,1/310} -> (-2,0)
726(311:1) = {0,1/311} -> (-2,0)
727(312:1) = {0,1/312} -> (-2,0)
728(313:1) = {0,1/313} -> (0,2)
729(314:1) = {0,1/314} -> (0,0)
730(315:1) = {0,1/315} -> (-1,2)
731(316:1) = {0,1/316} -> (-1,1)
732(317:1) = {0,1/317} -> (-1,1)
733(318:1) = {0,1/318} -> (0,2)
734(319:1) = {0,1/319} -> (0,1)
735(320:1) = {0,1/320} -> (0,2)
736(321:1) = {0,1/321} -> (0,2)
737(322:1) = {0,1/322} -> (0,2)
738(323:1) = {0,1/323} -> (1,-1)
739(324:1) = {0,1/324} -> (0,0)
740(325:1) = {0,1/325} -> (2,0)
741(326:1) = {0,1/326} -> (0,0)
742(327:1) = {0,1/327} -> (0,-2)
743(328:1) = {0,1/328} -> (0,-1)
744(329:1) = {0,1/329} -> (0,-2)
745(330:1) = {0,1/330} -> (-2,-2)
746(331:1) = {0,1/331} -> (-1,1)
747(332:1) = {0,1/332} -> (-1,1)
748(333:1) = {0,1/333} -> (-1,-1)
749(334:1) = {0,1/334} -> (-1,1)
750(335:1) = {0,1/335} -> (0,1)
751(336:1) = {0,1/336} -> (0,0)
752(337:1) = {0,1/337} -> (0,-1)
753(338:1) = {0,1/338} -> (0,1)
754(339:1) = {0,1/339} -> (0,-1)
755(340:1) = {0,1/340} -> (0,1)
756(341:1) = {0,1/341} -> (-2,-1)
757(342:1) = {0,1/342} -> (-2,-1)
758(343:1) = {0,1/343} -> (-1,3)
759(344:1) = {0,1/344} -> (0,2)
760(345:1) = {0,1/345} -> (-1,1)
761(346:1) = {0,1/346} -> (1,1)
762(347:1) = {0,1/347} -> (-1,1)
763(348:1) = {0,1/348} -> (0,1)
764(349:1) = {0,1/349} -> (1,0)
765(350:1) = {0,1/350} -> (0,0)
766(351:1) = {0,1/351} -> (-1,-1)
767(352:1) = {0,1/352} -> (0,-1)
768(353:1) = {0,1/353} -> (0,-1)
769(354:1) = {0,1/354} -> (-1,0)
770(355:1) = {0,1/355} -> (-1,0)
771(356:1) = {0,1/356} -> (-2,1)
772(357:1) = {0,1/357} -> (-2,1)
773(358:1) = {0,1/358} -> (-1,3)
774(359:1) = {0,1/359} -> (0,2)
775(360:1) = {0,1/360} -> (0,1)
776(361:1) = {0,1/361} -> (1,1)
777(362:1) = {0,1/362} -> (1,-1)
778(363:1) = {0,1/363} -> (0,0)
779(364:1) = {0,1/364} -> (-1,1)
780(365:1) = {0,1/365} -> (1,1)
781(366:1) = {0,1/366} -> (0,-1)
782(367:1) = {0,1/367} -> (0,0)
783(368:1) = {0,1/368} -> (0,1)
784(369:1) = {0,1/369} -> (-1,0)
785(370:1) = {0,1/370} -> (0,1)
786(371:1) = {0,1/371} -> (1,1)
787(372:1) = {0,1/372} -> (0,-1)
788(373:1) = {0,1/373} -> (1,1)
789(374:1) = {0,1/374} -> (0,0)
790(375:1) = {0,1/375} -> (-1,-1)
791(376:1) = {0,1/376} -> (0,2)
792(377:1) = {0,1/377} -> (0,1)
793(378:1) = {0,1/378} -> (1,0)
794(379:1) = {0,1/379} -> (0,0)
795(380:1) = {0,1/380} -> (-1,1)
796(381:1) = {0,1/381} -> (0,-1)
797(382:1) = {0,1/382} -> (1,1)
798(383:1) = {0,1/383} -> (0,0)
799(384:1) = {0,1/384} -> (2,0)
800(385:1) = {0,1/385} -> (0,0)
801(386:1) = {0,1/386} -> (0,-2)
802(387:1) = {0,1/387} -> (0,0)
803(388:1) = {0,1/388} -> (0,0)
804(1:0) = {oo,0} -> (0,0)
805
806Computation of further modular symbols
807
808Base point? (enter 0 for 0, or 1 for oo) Values of {oo,r} for rational r:
809Enter numerator and denominator of r: {oo,355/113} -> (3,1)
810Enter numerator and denominator of r:
811All modular symbols with bounded denominator
812
813Enter maximum denominator (0 for none): {oo,0} -> (0,0)
814{oo,1/2} -> (0,0)
815{oo,1/3} -> (0,2)
816{oo,2/3} -> (0,-2)
817{oo,1/4} -> (0,0)
818{oo,3/4} -> (0,0)
819{oo,1/5} -> (2,0)
820{oo,2/5} -> (-2,0)
821{oo,3/5} -> (-2,0)
822{oo,4/5} -> (2,0)
823{oo,1/6} -> (0,0)
824{oo,5/6} -> (0,0)
825{oo,1/7} -> (1,-1)
826{oo,2/7} -> (1,1)
827{oo,3/7} -> (-2,0)
828{oo,4/7} -> (-2,0)
829{oo,5/7} -> (1,-1)
830{oo,6/7} -> (1,1)
831