Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 5e-13
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues 1,-1,0,0

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Spectral parameter

$R= 6.37879720849$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.7071067811
3 0.2238840325
4 0.5000000000
5 0.4472135955
6 -0.1583099175
7 -0.4987278333
8 -0.3535533905
9 -0.9498759399
10 -0.3162277660
11 -0.6460633312
12 0.1119420162
13 -0.08714684192
14 0.3526538329
15 0.1001239831
16 0.2500000000
17 -1.623448822
18 0.6716637184
19 -1.085541190
20 0.2236067977
21 -0.1116571984
22 0.4568357626
23 1.036729303
24 -0.07915495878
25 0.1999999999
26 0.06162212286
27 -0.4365460883
28 -0.2493639166 + 1.030069130e-13i
29 0.3472112886 + 2.232878771e-13i
30 -0.07079834754 - 7.076706132e-13i
31 -1.640102194 + 1.525430087e-13i
32 -0.1767766953 + 1.730828684e-12i
33 -0.1446432645 - 1.587589140e-12i
34 1.147951672 - 3.031948503e-12i
35 -0.2230378673 + 5.406802460e-12i
36 -0.4749379760 + 2.875357326e-12i
37 1.582737179 - 1.640528250e-11i
38 0.7675935448 + 1.556593744e-11i
39 -0.01951081664 + 1.671897771e-11i
40 -0.1581138775 - 6.654484200e-11i
41 -0.9661109023 + 6.541240495e-11i
42 0.07895356220
43 0.2971028756
44 -0.3230316656
45 -0.4247974343
46 -0.7330783206
47 1.363025737
48 0.05597100812
49 -0.7512705481
50 -0.1414213562
51 -0.3634642688
52 -0.04357342100
53 0.2488960836
54 0.3086846993
55 -0.2889283051
56 0.1763269163
57 -0.2430353389
58 -0.2455154569 + 1.019445176e-13i
59 1.956825683 - 1.116052861e-13i
60 0.05006199105 + 1.200436618e-13i
61 -1.617834089 + 1.322080425e-13i
62 1.159727383 - 3.822369724e-13i
63 0.4737295701
64 0.1249999990 + 3.109736990e-13i
65 -0.03897325113 + 1.661088336e-13i
66 0.1022782312 - 7.893736709e-13i
67 -0.8204754956 + 1.260535086e-13i
68 -0.8117244125 + 1.512180135e-12i
69 0.2321071390 - 1.216381929e-12i
70 0.1577115873 - 9.430829477e-13i
71 -0.2050663822 + 4.323938377e-13i
72 0.3358318573 + 1.626548588e-12i
73 -0.6319806844
74 -1.119164185 - 2.001369807e-12i
75 0.04477679812 + 2.690816402e-12i
76 -0.5427705861 - 5.709282408e-12i
77 0.3222097628 + 8.867253992e-12i
78 0.01379621729 + 9.062545928e-13i
79 0.4794372052 - 3.070255199e-11i
80 0.1118034416 + 3.689744611e-11i
81 0.8521401637 + 1.296234513e-11i
82 0.6831436561
83 1.424909741
84 -0.05582859927
85 -0.7260283848
86 -0.2100834580 + 1.781473923e-13i
87 0.07773506343
88 0.2284178812
89 -0.3981039911
90 0.3003771462
91 0.04346255570 - 2.449909535e-13i
92 0.5183646516
93 -0.3671926933 + 8.004469882e-13i
94 -0.9638047417 - 1.422469956e-13i
95 -0.4854687785 - 6.533883734e-13i
96 -0.03957747929
97 -1.937198487 + 1.730149511e-13i
98 0.5312285002 - 7.606303693e-13i
99 0.6136800129 + 1.317927785e-12i
100 0.1000000018 + 1.309897625e-12i
101 -0.1971560133 - 1.444011647e-12i
102 0.2570080509
103 -0.05677522667 - 1.204652491e-12i
104 0.03081106398 - 1.334014343e-12i
105 -0.04993462095 + 1.055544012e-12i
106 -0.1759961074 + 3.259932363e-12i
107 0.5661198951
108 -0.2182730476 + 9.526405193e-13i
109 0.7433447396 - 1.826490627e-12i
110 0.2043031593 - 9.434868289e-12i
111 0.3543496025 + 4.310417489e-12i
112 -0.1246819770 + 5.370240357e-12i
113 0.06416219152 + 5.100022557e-12i
114 0.1718519255 - 7.180605860e-13i
115 0.4636394334 + 1.268541826e-11i
116 0.1736056315 - 1.491071866e-11i
117 0.08277875539 - 4.380001202e-11i
118 -1.383684730 + 2.555131806e-11i
119 0.8096592316 + 1.541235624e-11i
120 -0.03539912691 + 8.528074654e-12i
121 -0.5826021700 - 2.403760592e-13i
122 1.143981457 + 6.503993817e-13i
123 -0.2162968315
124 -0.8200510998 - 5.943654394e-13i
125 0.08944271699 - 1.684130625e-13i
126 -0.3349773923 - 2.800339812e-13i
127 -0.2798747646 + 1.170312447e-12i
128 -0.08838834400 - 1.318560661e-13i
129 0.06651659422 + 1.292021582e-12i
130 0.02755825156 - 2.763980442e-13i
131 -0.7383162777 - 1.327537472e-12i
132 -0.07232163959
133 0.5413896035 + 5.459026557e-13i
134 0.5801637914 + 1.805888836e-12i
135 -0.1952293379 - 4.528214408e-12i
136 0.5739758477 - 1.488112776e-12i
137 -1.156551095 - 6.603975785e-13i
138 -0.1641245454 + 3.240851290e-12i
139 -0.5228781509 + 2.586026927e-12i
140 -0.1115189517 + 6.851248499e-12i
141 0.3051597064 + 4.234139695e-12i
142 0.1450038580 - 1.933416663e-11i
143 0.05630240928
144 -0.2374689690 + 5.868420917e-12i
145 0.1552775830 + 1.063278716e-11i
146 0.4468777725 + 6.435825219e-13i
147 -0.1681975179 - 6.386417571e-12i
148 0.7913686173 - 1.681723701e-11i
149 -0.08500338390 - 3.284613459e-11i
150 -0.03166185717 + 2.436666648e-11i
151 0.7439830849 + 3.369250741e-11i
152 0.3837966606 + 5.022685172e-11i
153 1.542074964 + 2.367182807e-13i
154 -0.2278367358 - 6.283479737e-13i
155 -0.7334760343 + 1.254729665e-12i
156 -0.009755397715 + 1.295732759e-12i
157 0.7870921924 - 8.414263236e-13i
158 -0.3390132723 + 2.808392183e-12i
159 0.05572389338 + 1.769110059e-12i
160 -0.07905695185 - 2.042867258e-12i
161 -0.5170458185 - 7.088425445e-13i
162 -0.6025542152 - 4.551776784e-12i
163 -0.4306611350 - 1.175122241e-12i
164 -0.4830554641 + 2.483771243e-12i
165 -0.06468639551 + 5.460485555e-12i
166 -1.007563312 + 3.638044300e-12i
167 -0.3338020773 + 8.302320312e-12i
168 0.03947673773 - 5.952127643e-12i
169 -0.9924055011 - 1.271158313e-12i
170 0.5133795858 + 2.569303666e-13i
171 1.031129457 + 9.017472800e-13i
172 0.1485514399 - 2.465394285e-13i
173 -1.023504865 + 1.491445666e-12i
174 -0.05496698821 - 2.120830299e-12i
175 -0.09974556894 - 3.871212272e-12i
176 -0.1615158328 - 1.080422999e-12i
177 0.4381020225 - 1.949316597e-13i
178 0.2815020345 + 3.401319565e-12i
179 1.225717668 + 2.585736680e-12i
180 -0.2123987144 - 1.177378169e-12i
181 -0.1609758740 + 1.471713330e-12i
182 -0.03073266896 - 2.286808052e-12i
183 -0.3622072254 - 3.338931619e-12i
184 -0.3665391613 + 6.254403222e-12i
185 0.7078215829 + 3.539667046e-12i
186 0.2596444445 + 4.602401515e-12i
187 1.048850756 + 1.207420858e-12i
188 0.6815128669 - 1.357096385e-11i
189 0.2177176951 - 1.230507188e-11i
190 0.3432782462 - 9.897906479e-12i
191 -0.1889176394 + 2.793702116e-13i
192 0.02798550110 + 2.421674054e-11i
193 -0.6837976911 + 1.299088920e-11i
194 1.369806170 + 5.189082621e-12i
195 -0.008725473580 + 1.378389998e-11i
196 -0.3756352888 - 2.210022644e-11i
197 -1.507614849 - 1.808388607e-11i
198 -0.4339373363 - 3.528048364e-12i
199 0.3282652884 - 6.475315536e-12i
200 -0.07071065950 + 3.039773620e-11i
201 -0.1836913385 - 4.174033560e-12i
202 0.1394103353 - 2.348216377e-11i
203 -0.1731639496 - 1.374010321e-11i
204 -0.1817321280 - 3.412415927e-12i
205 -0.4320579889 + 1.804135485e-12i
206 0.04014614951 - 1.323333517e-12i
207 -0.9847642273 - 1.576690912e-12i
208 -0.02178670881 - 1.654361001e-12i
209 0.7013283590 + 1.430028325e-12i
210 0.03530911848 + 7.518029109e-12i
211 -0.4138953186 + 4.445567060e-12i
212 0.1244480433 - 1.403141252e-13i
213 -0.04591109285 + 6.602254679e-13i
214 -0.4003072174 + 1.023042172e-12i
215 0.1328684441 - 1.162860348e-11i
216 0.1543423546 - 7.105575538e-12i
217 0.8179646239 - 1.379341898e-11i
218 -0.5256241210 + 3.748540140e-12i
219 -0.1414903738 + 2.044794576e-11i
220 -0.1444641552 + 4.704333100e-12i
221 0.1414784505 + 1.209791468e-11i
222 -0.2505630037 - 2.035252745e-11i
223 0.8327361865 + 3.366816570e-12i
224 0.08816341639 + 9.052245365e-12i
225 -0.1899751625 - 1.320506808e-11i
226 -0.04536953280 + 1.205187083e-11i
227 0.2792258257 + 1.159757687e-11i
228 -0.1215176868 + 2.653312651e-11i
229 -0.3601187360 - 3.613752928e-11i
230 -0.3278426407 - 7.172122697e-11i
231 0.07213762348 - 7.583323063e-12i
232 -0.1227577255 + 2.559915616e-12i
233 1.512828819 + 5.736781751e-12i
234 -0.05853336904 + 1.394394154e-12i
235 0.6095636495 + 6.180812785e-13i
236 0.9784128442 - 9.992889305e-12i
237 0.1073383263 + 1.732482384e-12i
238 -0.5725154507 - 5.178163756e-12i
239 -1.622397120 + 4.404924970e-12i
240 0.02503099118 + 1.754617625e-13i
241 0.9215020517 + 1.515013329e-11i
242 0.4119619354 + 1.542732369e-11i
243 0.6273266933 - 1.461655823e-11i
244 -0.8089170637 - 5.333399286e-12i
245 -0.3359784346 - 2.214503385e-11i
246 0.1529449360 + 5.883015231e-12i
247 0.09460151244 - 2.996193304e-12i
248 0.5798636748 + 7.610121513e-12i
249 0.3190145447 + 1.156196894e-11i
250 -0.06324555614 + 2.313867567e-13i
251 -1.521251295 + 1.214840284e-11i
252 0.2368647754 - 2.970556850e-11i
253 -0.6697928135 + 6.700132138e-13i
254 0.1979013198 - 1.527857930e-11i
255 -0.1625461573 - 3.333329791e-12i
256 0.06249999872 - 1.790353705e-12i
257 -0.2095174575 - 3.562541748e-13i
258 -0.04703434103 - 1.678591241e-12i
259 -0.7893550791 + 8.702531713e-12i
260 -0.01948662932 + 7.112692198e-13i
261 -0.3298076379 - 5.230977171e-12i
262 0.5220684347 - 2.143488487e-12i
263 -0.1477743799 - 4.955296076e-12i
264 0.05113910902 + 1.075859625e-11i
265 0.1113097235 - 9.857979445e-12i
266 -0.3828202803 + 5.030781872e-12i
267 -0.08912912193 + 1.467848722e-11i
268 -0.4102377510 - 1.608998741e-12i
269 -0.3520788422 - 6.899692225e-12i
270 0.1380479653 - 7.008399459e-12i
271 0.03590367085 - 7.374107198e-12i
272 -0.4058622189 - 1.203349080e-11i
273 0.009730585091 + 2.031660536e-11i
274 0.8178050992 - 4.042420872e-12i
275 -0.1292126747 + 2.182843870e-11i
276 0.1160535418 - 2.488394435e-12i
277 -0.7054143430 - 2.417681910e-11i
278 0.3697306794 + 8.623962189e-12i
279 1.557893678 - 2.710360703e-11i
280 0.07885586426 + 3.042456629e-11i
281 1.587642437 + 2.502634716e-11i
282 -0.2157805422 + 3.360080858e-11i
283 0.3536099342 - 5.565368364e-12i
284 -0.1025331970 + 2.514651694e-12i
285 -0.1086887092 - 1.431369944e-12i
286 -0.03981178175 + 8.295062237e-12i
287 0.4818264539 - 9.144677763e-12i
288 0.1679159207 + 2.973467693e-12i
289 1.635586081 + 8.185044726e-12i
290 -0.1097978433 - 1.295264012e-11i
291 -0.4337078077 + 6.721552243e-12i
292 -0.3159903525 - 1.951986005e-13i
293 -1.916625509 - 5.015715659e-12i
294 0.1189335859 - 2.151202575e-12i
295 0.8751190423 + 6.475510174e-12i
296 -0.5595821102 - 2.873385484e-12i
297 0.2820364413 + 4.238758834e-12i
298 0.06010652387 - 1.135383893e-13i
299 -0.09034768581 - 3.590805238e-12i
300 0.02238839401 + 1.083602440e-12i
301 -0.1481734603 - 1.874807525e-11i
302 -0.5260754809 + 1.666762456e-11i
303 -0.04414008975 + 7.141974296e-12i
304 -0.2713852908 - 9.616472216e-12i
305 -0.7235173734 + 1.563234433e-12i
306 -1.090411672 + 5.656163231e-12i
307 -0.6435526005 + 1.074257128e-11i
308 0.1611048776 - 8.692340591e-12i
309 -0.01271105815 - 3.250046687e-11i
310 0.5186458379 + 6.385168950e-12i
311 0.08350877895 + 2.142760195e-11i
312 0.006898151738 - 7.093778944e-12i
313 -1.350172813 + 2.235668247e-11i
314 -0.5565582082 + 4.977826100e-12i
315 0.2118583038 - 1.445804829e-12i
316 0.2397186278 - 7.621751357e-12i
317 0.7133468955 + 9.268140182e-12i
318 -0.03940271668 - 1.334179037e-12i
319 -0.2243204838 - 4.939932944e-12i
320 0.05590169889 + 1.625203676e-13i
321 0.1267452054 + 3.372225286e-12i
322 0.3656065731 - 2.723794186e-12i
323 1.762320560 + 3.315416654e-12i
324 0.4260701104 - 4.948231730e-12i
325 -0.01742936941 - 4.521677550e-12i
326 0.3045234018 + 6.431450138e-12i
327 0.1664230091 - 1.272962249e-11i
328 0.3415718244 + 1.293520133e-11i
329 -0.6797788630 + 1.002714292e-11i
330 0.04574023220 - 2.866178338e-13i
331 -0.6948366896 - 1.330057144e-13i
332 0.7124548646 - 6.374557598e-12i
333 -1.503403930 + 1.036112558e-12i
334 0.2360337304 - 6.608327661e-12i
335 -0.3669278255 + 9.605341010e-13i
336 -0.02791433347 - 6.528522800e-13i
337 0.9700995756 + 1.914106451e-12i
338 0.7017366459 - 1.698185518e-11i
339 0.01436484078 + 2.567423213e-11i
340 -0.3630141977 + 1.129239880e-11i
341 1.059609894 - 3.666214440e-11i
342 -0.7291185792 + 1.179976789e-11i
343 0.8734073617 + 1.949762178e-12i
344 -0.1050417154 - 9.510649370e-13i
345 0.1038014598 + 9.626603371e-13i
346 0.7237272326 + 1.075132802e-12i
347 -0.6277876088 - 4.476582859e-12i
348 0.03886752496 - 4.263206977e-12i
349 -1.530465519 + 3.272645410e-12i
350 0.07053076964 + 1.685040649e-12i
351 0.03804360866 + 1.323797972e-12i
352 0.1142089669 - 2.084720654e-12i
353 1.337027119 - 2.507354740e-12i
354 -0.3097849270 - 5.418054183e-12i
355 -0.09170847230 + 2.837859676e-12i
356 -0.1990519972 + 7.110640606e-12i
357 0.1812697401 + 1.495657283e-12i
358 -0.8667132633 + 1.003159312e-12i
359 -0.5903364375
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361 0.1783996732 - 5.732242052e-12i
362 0.1138270987 - 6.554673310e-12i
363 -0.1304352830 - 6.748581618e-12i
364 0.02173128765 + 8.790778723e-12i
365 -0.2826303737 + 7.601512066e-12i
366 0.2561191876 - 8.477360048e-12i
367 -1.432798123 + 3.299302460e-12i
368 0.2591823286 - 1.060953587e-12i
369 0.9176856364 - 4.117054098e-12i
370 -0.5005054341 - 9.653679392e-12i
371 -0.1241313955 + 1.021122332e-11i
372 -0.1835963528 + 6.867731912e-12i
373 -0.1131207235
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375 0.02002485038 - 3.209690708e-12i
376 -0.4819023964 - 2.344725779e-11i
377 -0.03025832927 - 3.072219517e-12i
378 -0.1539497153 + 2.703797647e-11i
379 1.033195739 - 2.137697752e-11i
380 -0.2427344218 - 7.180912120e-12i
381 -0.06265946228 + 8.443582441e-12i
382 0.1335849814 - 3.593751689e-13i
383 1.729670157 + 2.424259899e-13i
384 -0.01978872195 + 6.458600786e-12i
385 0.1440965844 - 3.634768981e-12i
386 0.4835179749 - 3.652184342e-12i
387 -0.2822108539 - 1.365766108e-12i
388 -0.9685992468 + 3.753819252e-12i
389 -0.6396590988 - 1.015688822e-12i
390 0.006169849909 + 5.422392995e-13i
391 -1.683076964 - 1.098192702e-12i
392 0.2656142484
393 -0.1652972235 + 2.649635811e-13i
394 1.066044687 - 1.203385943e-12i
395 0.2144108500 - 1.031258330e-12i
396 0.3068400122 + 2.283944163e-13i
397 1.636737470 + 1.406246778e-12i
398 -0.2321185861 - 4.056140811e-13i
399 0.1212084848 + 1.593861718e-12i
400 0.05000000133 - 1.697444316e-12i
401 1.137890916 + 3.421764407e-13i
402 0.1298894044 - 2.411672932e-13i
403 0.1429297314
404 -0.09857800992 + 1.069858151e-12i
405 0.3810887067 - 3.336879443e-13i
406 0.1224453845 + 9.323968868e-13i
407 -1.022548443 - 1.210528874e-12i
408 0.1285040208 - 2.831237869e-12i
409 1.078558714 - 5.186593116e-13i
410 0.3055111349 + 2.543687969e-12i
411 -0.2589333306 + 2.252507454e-12i
412 -0.02838760313 + 2.261159258e-12i
413 -0.9759234439 - 4.078118629e-13i
414 0.6963334660 - 1.622193845e-12i
415 0.6372390034 + 5.552093293e-13i
416 0.01540553351 - 2.629563104e-12i
417 -0.1170640636 - 2.583591488e-12i
418 -0.4959140407 + 2.050034470e-12i
419 -1.121286821 + 1.793610899e-12i
420 -0.02496732181 - 1.698286241e-13i
421 -0.7547743124 - 5.559490237e-12i
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