Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 3e-13
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues 1,1,0,0

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Spectral parameter

$R= 8.58191066592$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.7071067811
3 -0.6710118531
4 0.4999999999
5 -0.4472135954
6 0.4744770316
7 -1.601546461
8 -0.3535533905
9 -0.5497430928
10 0.3162277660
11 -1.300924025
12 -0.3355059265
13 1.640227838
14 1.132464363
15 0.3000856234
16 0.2500000000
17 0.4907925758
18 0.3887270688
19 -0.9286522040
20 -0.2236067977
21 1.074656659
22 0.9198922001
23 0.7069282982
24 0.2372385158
25 0.1999999999
26 -1.159816227
27 1.039895984
28 -0.8007732308
29 -0.2130332687
30 -0.2121925792 - 1.316857295e-13i
31 -0.03096148164
32 -0.1767766952 + 1.717146755e-13i
33 0.8729354412 - 3.469674342e-13i
34 -0.3470427589
35 0.7162333515 + 4.683612120e-13i
36 -0.2748715458 - 5.042344475e-13i
37 0.2325721140 + 1.506410688e-13i
38 0.6566562676 + 7.303649524e-13i
39 -1.100612318 - 2.689400789e-12i
40 0.1581138903 - 1.266931384e-12i
41 0.8557252173 + 9.940418120e-12i
42 -0.7598970287 - 6.344144015e-13i
43 0.7445043414 - 1.449599276e-11i
44 -0.6504619572 - 4.405389895e-12i
45 0.2458525851
46 -0.4998737935
47 -1.409783877
48 -0.1677529633
49 1.564951068
50 -0.1414213562
51 -0.3293276358
52 0.8201139193
53 -0.4055686701
54 -0.7353175025
55 0.5817909108
56 0.5662321816
57 0.6231366364
58 0.1506372689
59 0.3064430306 - 1.082861574e-13i
60 0.1500428116
61 -1.754867961 + 3.761213918e-13i
62 0.02189307356 - 3.903568457e-13i
63 0.8804391053
64 0.1249999999 - 1.794784787e-13i
65 -0.7335321890
66 -0.6172585704 + 1.396324804e-12i
67 0.4306586611 - 1.351176332e-12i
68 0.2453962875 - 3.208306425e-13i
69 -0.4743572669 + 8.761563388e-13i
70 -0.5064534590 - 1.176082701e-12i
71 -0.5888982288 + 3.007103936e-12i
72 0.1943635363 - 3.217718026e-12i
73 0.07242982570 - 1.188450318e-12i
74 -0.1644533200 + 5.142543194e-12i
75 -0.1342023703 - 1.456685908e-12i
76 -0.4643261055 + 3.756212691e-12i
77 2.083490277 - 1.790569377e-11i
78 0.7782504444 + 4.642903461e-12i
79 1.589410564 + 2.540732203e-11i
80 -0.1118033794 - 1.133641462e-11i
81 -0.1480394347 + 1.271197355e-11i
82 -0.6050890708 - 6.986495366e-11i
83 -1.007654192 + 2.016655825e-11i
84 0.5373283194 + 9.762972000e-11i
85 -0.2194891595 - 8.366494884e-11i
86 -0.5264440494 + 1.421859130e-13i
87 0.1429478484
88 0.4599460999
89 -0.9871607842
90 -0.1738440298 - 2.627338495e-13i
91 -2.626901091
92 0.3534641491 + 4.489964547e-13i
93 0.02077552029 + 3.124570029e-13i
94 0.9968677399
95 0.4153058918 - 5.473232146e-13i
96 0.1186192576 - 7.136167463e-13i
97 1.580473730 + 1.799810472e-13i
98 -1.106587512 + 8.988766319e-13i
99 0.7151739961 + 5.890803750e-13i
100 0.09999999952 + 5.454220882e-13i
101 -0.3158217541 - 1.471208117e-12i
102 0.2328698066 - 2.557656098e-12i
103 0.2215867232 + 1.386705660e-12i
104 -0.5799081157 + 1.625477600e-12i
105 -0.4806010714 + 1.270111932e-12i
106 0.2867803588 + 1.428566413e-12i
107 0.1695892782 - 3.350855291e-12i
108 0.5199479900 - 1.877916923e-12i
109 0.9289248635 - 7.441464234e-13i
110 -0.4113883089 + 3.307409451e-13i
111 -0.1560586321 + 6.731379507e-12i
112 -0.4003866193 - 7.240888607e-13i
113 1.219164653 - 9.125192278e-12i
114 -0.4406241526 + 6.639812776e-12i
115 -0.3161479255 + 5.845610537e-12i
116 -0.1065166598 - 1.159609281e-11i
117 -0.9017038832 + 4.570699980e-12i
118 -0.2166879998 - 9.665395938e-12i
119 -0.7860270362 - 1.168699413e-11i
120 -0.1060963413 + 3.951777963e-11i
121 0.6924032910 + 1.287442784e-11i
122 1.240879035 + 1.871981081e-13i
123 -0.5742017700 - 1.214925774e-13i
124 -0.01548074085 - 1.618887136e-13i
125 -0.08944271879 - 6.435033041e-13i
126 -0.6225644619 + 6.766831978e-13i
127 -0.1612695008 + 1.349758630e-12i
128 -0.08838834749 - 5.890274976e-13i
129 -0.4995712190 - 2.311129158e-13i
130 0.5186855867 - 9.907116788e-13i
131 -1.370722831 - 2.674169237e-13i
132 0.4364677192 + 1.305421819e-13i
133 1.487279650 + 1.506002367e-12i
134 -0.3045216603 + 2.235064118e-12i
135 -0.4650556201 - 3.118076905e-12i
136 -0.1735213797 - 2.190100839e-12i
137 0.4827684726 + 1.520545402e-13i
138 0.3354212413 + 1.991720619e-12i
139 1.822724436 + 4.354980307e-13i
140 0.3581166733 + 2.172416768e-12i
141 0.9459816860 + 4.737677589e-12i
142 0.4164139348 - 9.455976599e-12i
143 -2.133811801 - 1.328082001e-12i
144 -0.1374357661 + 1.656867797e-12i
145 0.09527136738 + 4.585839108e-12i
146 -0.05121562026 + 1.246736191e-12i
147 -1.050100712 - 1.635698934e-11i
148 0.1162860550 + 1.439120725e-11i
149 0.9631724149
150 0.09489539034 + 2.908828537e-12i
151 0.2422555435 + 1.276665371e-11i
152 0.3283281753 - 1.156231928e-11i
153 -0.2698098279 - 2.405712671e-11i
154 -1.473250106 - 1.589727739e-11i
155 0.01384639522 + 1.436695820e-12i
156 -0.5503061596 + 5.290856039e-13i
157 0.3501531057 - 4.525470197e-13i
158 -1.123883012 + 4.313300680e-13i
159 0.2721413856 - 5.037130888e-13i
160 0.07905694188 - 1.559435483e-12i
161 -1.132178519 - 4.037458073e-13i
162 0.1046796914 + 1.677941511e-12i
163 0.7304433564 - 5.984490679e-13i
164 0.4278626121 + 5.572097475e-12i
165 -0.3903885935 - 4.320073118e-12i
166 0.7125190787 - 3.085960900e-12i
167 -1.644958091 + 1.745332540e-12i
168 -0.3799485046 - 8.571387921e-12i
169 1.690347347 + 1.296250880e-11i
170 0.1552022515 - 1.152280839e-12i
171 0.5105201460 + 3.356478986e-12i
172 0.3722521509 + 3.578905894e-12i
173 1.492162429 - 1.927475521e-11i
174 -0.1010794032 + 6.608645997e-12i
175 -0.3203092930 - 7.382081168e-12i
176 -0.3252310094 + 7.838817458e-12i
177 -0.2056269236 + 1.073249218e-11i
178 0.6980281143 + 4.676586771e-12i
179 -1.377124985 - 1.195338716e-11i
180 0.1229262686 - 1.402648459e-11i
181 0.2086419071 + 1.047979401e-11i
182 1.857499555 - 1.907205674e-11i
183 1.177537183 + 4.036138455e-11i
184 -0.2499368680 - 3.057907102e-11i
185 -0.1040094476 + 2.676790102e-11i
186 -0.01469045117 + 8.356755089e-12i
187 -0.6384838342 - 6.927353466e-11i
188 -0.7048919323 - 1.746626840e-12i
189 -1.665441740 - 3.445569039e-13i
190 -0.2936656074 - 1.762973539e-12i
191 -0.1970043910 - 7.873964958e-13i
192 -0.08387647532 + 2.175356553e-12i
193 -1.099245807 - 2.093241654e-12i
194 -1.117563682 + 6.960543942e-12i
195 0.4922087801 + 1.896150886e-12i
196 0.7824755513 - 1.083971559e-11i
197 0.3200782382 + 9.387088001e-12i
198 -0.5057043630 - 1.252081912e-11i
199 1.151085432 + 1.501975628e-12i
200 -0.07071065790 + 1.010425233e-11i
201 -0.2889770830 - 4.686066258e-12i
202 0.2233197266 + 1.263692822e-11i
203 0.3411826608 - 1.618167086e-11i
204 -0.1646638021 - 4.467228179e-13i
205 -0.3826919835 + 3.874233397e-12i
206 -0.1566854722 - 3.748434142e-12i
207 -0.3886289495 - 6.666802164e-12i
208 0.4100569779 + 1.729408402e-11i
209 1.208105969 + 1.441670298e-12i
210 0.3398362878 - 1.581529684e-11i
211 0.4107069004 + 2.113830668e-11i
212 -0.2027843435 - 3.010143426e-11i
213 0.3951576860 + 4.095458230e-12i
214 -0.1199177224 - 6.679808110e-12i
215 -0.3329524474 + 1.043312501e-12i
216 -0.3676587546 + 6.170682672e-12i
217 0.04958625044 - 3.638193511e-12i
218 -0.6568490786 + 6.695621032e-12i
219 -0.04860125393 - 6.240799506e-12i
220 0.2908954488 + 3.927950249e-13i
221 0.8050116549 - 6.419215581e-12i
222 0.1103501169 + 4.631027260e-12i
223 -0.5802787786 + 8.753306208e-12i
224 0.2831160907 - 2.297098503e-12i
225 -0.1099486103 + 1.388987272e-12i
226 -0.8620795987 - 9.132298091e-12i
227 0.4170562092 + 8.602962688e-12i
228 0.3115683156 - 1.672513793e-11i
229 1.622196491 + 2.197057144e-12i
230 0.2235503677 + 6.665085976e-12i
231 -1.398046675 + 1.874995563e-11i
232 0.07531863389 - 1.342403840e-12i
233 -0.09728149827 - 2.008661049e-11i
234 0.6376009429 + 1.696100174e-11i
235 0.6304745448 - 4.382442080e-11i
236 0.1532215285 + 2.083768588e-11i
237 -1.066513341 - 1.066203787e-12i
238 0.5558050902 + 6.791547021e-12i
239 -0.6481473247
240 0.07502140783 - 4.258397837e-12i
241 -0.06552626220
242 -0.4896030814 - 3.441257002e-12i
243 -0.9405597644 + 6.304637588e-12i
244 -0.8774339891 - 4.116531868e-12i
245 -0.6998673995 + 6.815896984e-13i
246 0.4060219712 - 2.747396309e-12i
247 -1.523201204 + 7.199913856e-12i
248 0.01094655206 + 2.920767794e-12i
249 0.6761478727 - 8.749408351e-12i
250 0.06324555650 + 3.497266471e-12i
251 0.8095499750 - 5.873224899e-12i
252 0.4402195667 + 1.563631960e-11i
253 -0.9196600361 - 1.509186149e-11i
254 0.1140348254 - 1.218550896e-11i
255 0.1472797342 + 1.367400804e-11i
256 0.06250000038
257 1.698310352 + 1.672036512e-12i
258 0.3532501949 - 1.439999444e-12i
259 -0.3724750461 - 1.045549876e-13i
260 -0.3667660949 + 2.316910058e-12i
261 0.1171135625 + 1.195020405e-12i
262 0.9692474148 - 3.827056019e-12i
263 0.5067408147 - 1.721851577e-12i
264 -0.3086292773 + 1.318334462e-12i
265 0.1813758216 + 2.537823591e-12i
266 -1.051665525 + 3.163055528e-12i
267 0.6623965793 - 6.531383037e-12i
268 0.2153293359 + 9.211560530e-13i
269 -1.369690255 + 5.274275447e-12i
270 0.3288439956 - 1.928816645e-12i
271 1.748929223 - 2.190566020e-12i
272 0.1226981602 - 4.762546886e-12i
273 1.762681759 + 5.033385890e-13i
274 -0.3413688517 + 8.950688513e-12i
275 -0.2601848328 + 1.051579033e-12i
276 -0.2371786129 - 6.974263182e-12i
277 0.4725374318 + 1.769511044e-12i
278 -1.288860786 + 7.718639474e-13i
279 0.01702082841 + 4.155635724e-12i
280 -0.2532266948 - 6.670454729e-12i
281 -1.012879567 - 1.722973776e-11i
282 -0.6689100567 + 1.526257090e-11i
283 0.4757435559 + 1.673667722e-11i
284 -0.2944490921 - 1.189615492e-11i
285 -0.2786751527 - 2.874269150e-12i
286 1.508832787 - 8.426434325e-12i
287 -1.370483707 + 8.544749962e-12i
288 0.09718173111 + 2.325813093e-11i
289 -0.7591225721 - 3.526273835e-11i
290 -0.06736706878 - 3.551613597e-12i
291 -1.060516607 + 2.183272168e-11i
292 0.03621483330 + 1.717153597e-12i
293 0.7490558530 - 5.299041402e-12i
294 0.7425333360 + 1.403957203e-12i
295 -0.1370454804 - 5.343013343e-12i
296 -0.08222666186 + 4.381026233e-12i
297 -1.352825672 + 5.859712345e-12i
298 -0.6810657599 + 2.131095933e-13i
299 1.159523491 - 4.027842201e-12i
300 -0.06710119404 - 4.184377983e-12i
301 -1.192358252 + 4.332605089e-12i
302 -0.1713005432 + 1.077603317e-12i
303 0.2119201714 + 6.604334126e-13i
304 -0.2321630510 - 6.948396441e-12i
305 0.7848008043 + 7.367464148e-12i
306 0.1907843374 + 1.579109463e-12i
307 1.116184732 - 4.902966786e-12i
308 1.041745137 + 4.103964758e-12i
309 -0.1486873206 - 6.984798245e-12i
310 -0.009790889761 + 6.985935566e-12i
311 1.562054938 - 1.269298440e-12i
312 0.3891252254 - 7.089200195e-12i
313 -1.036825832 - 3.589485525e-12i
314 -0.2475956608 + 5.963213579e-12i
315 -0.3937443415 + 1.191236212e-13i
316 0.7947052962 + 2.730452417e-12i
317 -0.07227562089 - 6.298059538e-13i
318 -0.1924330185 + 1.024128795e-12i
319 0.2771400970 - 8.543994446e-13i
320 -0.05590169727
321 -0.1137964128 - 3.267480136e-12i
322 0.8005711037 - 2.165673621e-12i
323 -0.4557756125 + 2.007762711e-12i
324 -0.07401972240 + 1.567439680e-12i
325 0.3280455701 + 4.572213654e-12i
326 -0.5165014400 - 5.641780737e-13i
327 -0.6233195980 + 3.259689033e-13i
328 -0.3025445476 - 4.499995627e-12i
329 2.257834372 - 3.641988773e-12i
330 0.2760464253 - 1.926268912e-12i
331 -1.643460466
332 -0.5038270743 + 7.281942889e-12i
333 -0.1278549179 + 6.772587475e-12i
334 1.163161025 + 3.393287414e-12i
335 -0.1925964157 - 7.182499981e-12i
336 0.2686641813 - 1.194554721e-11i
337 0.4096836774 - 3.947480581e-12i
338 -1.195256091 + 7.409314200e-13i
339 -0.8180739352 + 8.405486336e-12i
340 -0.1097445607 + 6.834049024e-12i
341 0.04027852697 + 8.570042496e-12i
342 -0.3609922320 + 6.240943770e-13i
343 -0.9047953820 - 1.507398237e-11i
344 -0.2632220067 - 9.340285950e-12i
345 0.2121390011 - 7.476027018e-12i
346 -1.055118204 + 1.773863216e-11i
347 0.4116187787 + 3.329813059e-12i
348 0.07147392196 + 1.116040105e-11i
349 -1.283357000 - 9.339961448e-12i
350 0.2264928799 - 1.256012656e-11i
351 1.705666341 + 1.132665764e-11i
352 0.2299730230 - 1.684611539e-11i
353 0.5421244791 + 1.633541467e-11i
354 0.1454001495 - 1.772433997e-11i
355 0.2633633609 + 2.829151369e-11i
356 -0.4935803882 - 6.174713192e-12i
357 0.5274334910 - 8.233565236e-12i
358 0.9737744477 - 8.895881556e-12i
359 0.3856252017 - 4.427241068e-12i
360 -0.08692205281 + 3.729288917e-11i
361 -0.1376050682 - 3.628576741e-11i
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363 -0.4646108174 - 4.019113432e-12i
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367 -0.3305074783 - 3.429241478e-12i
368 0.1767320760 + 2.688139764e-12i
369 -0.4704290280 + 1.287553638e-12i
370 0.07354575632 + 4.509970438e-12i
371 0.6495370767 + 5.475425143e-12i
372 0.01038774351 - 1.228487381e-11i
373 1.088693953 - 2.261672187e-13i
374 0.4514762665 - 1.197867196e-11i
375 0.06001713416 - 5.819165223e-12i
376 0.4984338725 + 2.233401088e-12i
377 -0.3494231114 + 1.494982098e-12i
378 1.177645146 + 8.159385258e-12i
379 0.3185543010 - 8.420590290e-13i
380 0.2076529476 - 4.485814937e-13i
381 0.1082137498 + 1.375607913e-12i
382 0.1393031601 + 2.116091795e-11i
383 -1.147460065 + 2.847561288e-12i
384 0.05930962441 - 1.808511231e-13i
385 -0.9317651915 - 7.978120329e-12i
386 0.7772841866 - 1.354581755e-11i
387 -0.4092861319 + 1.998258295e-11i
388 0.7902368546 - 1.374891295e-11i
389 1.086642118 - 1.127733367e-11i
390 -0.3480441402 - 1.684057412e-11i
391 0.3469551242 - 9.916860979e-12i
392 -0.5532937545 + 9.860349757e-12i
393 0.9197712384 + 3.843906499e-13i
394 -0.2263295061 + 8.863498140e-13i
395 -0.7108060277 + 1.905503666e-12i
396 0.3575869999 - 2.539538676e-12i
397 0.8450433018 - 5.569683559e-13i
398 -0.8139403262 - 3.745492206e-12i
399 -0.9979822716 + 4.522840974e-12i
400 0.04999999497 + 2.757127030e-12i
401 -1.112033481 - 2.769183587e-12i
402 0.2043376460 - 2.801196183e-12i
403 -0.05078388218 - 2.654977964e-13i
404 -0.1579108898 + 9.227712438e-12i
405 0.06620524757 - 1.149567298e-13i
406 -0.2412525817 - 2.858800662e-12i
407 -0.3025586391 - 1.094277257e-11i
408 0.1164348956 + 3.712142091e-12i
409 -1.820165650 + 8.748488099e-12i
410 0.2706040775 - 5.768056683e-13i
411 -0.3239433580 + 7.980443274e-13i
412 0.1107933612 - 1.015496940e-11i
413 -0.4907827566 + 7.435558540e-12i
414 0.2748021740 - 6.542849403e-12i
415 0.4506366415 - 2.451736372e-12i
416 -0.2899540597 - 4.139928780e-12i
417 -1.223069719 + 9.280996843e-12i
418 -0.8542599190 + 7.738164475e-12i
419 -0.3234186107 - 7.784081077e-12i
420 -0.2403005530 + 4.452818635e-12i
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