Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 4e-14
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues 1,1,0,0

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Spectral parameter

$R= 6.99327291741$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.7071067811
3 1.518345576 - 1.013024797e-13i
4 0.4999999999
5 0.4472135955
6 1.073632453
7 -0.6243197430
8 0.3535533905
9 1.305373290
10 0.3162277660
11 1.596496810
12 0.7591727883
13 -1.289415232
14 -0.4414607239
15 0.6790247845
16 0.2499999999
17 0.8884062689
18 0.9230383055
19 -0.9379932322
20 0.2236067977 - 1.155916124e-13i
21 -0.9479331203 + 3.001818631e-13i
22 1.128893720
23 -0.5769617040 - 5.072853551e-13i
24 0.5368162267 + 4.418998611e-13i
25 0.1999999999
26 -0.9117542552 - 1.794056663e-12i
27 0.4636621849 + 2.545277108e-12i
28 -0.3121598711 + 2.376531693e-12i
29 -0.6936141043 - 7.898490251e-12i
30 0.4801430299 + 1.636575538e-13i
31 -1.052641751 + 1.531631291e-11i
32 0.1767766939 - 8.164177109e-12i
33 2.424033867 - 2.335249879e-11i
34 0.6281980990 + 1.670893304e-11i
35 -0.2792042696 + 4.568480664e-11i
36 0.6526866443 + 4.650231570e-12i
37 -1.073363070 - 2.089512917e-10i
38 -0.6632613749 + 7.486233316e-12i
39 -1.957777794 + 7.800976634e-10i
40 0.1581138830
41 1.640924159 - 2.144959236e-13i
42 -0.6702899374 + 4.368117224e-13i
43 -0.9764650768 - 2.267539584e-13i
44 0.7982484051 - 1.958019241e-13i
45 0.5837806826 + 3.997520125e-13i
46 -0.4079735334 - 4.768682942e-13i
47 0.2436443506 + 4.116761977e-13i
48 0.3795863940 - 9.462727728e-13i
49 -0.6102248583 + 4.669926258e-13i
50 0.1414213565 + 1.878996768e-12i
51 1.348907728 - 1.908028096e-12i
52 -0.6447076161 + 1.976992372e-12i
53 0.4679025913 - 3.165193031e-12i
54 0.3278586745 - 1.710330492e-12i
55 0.7139750795 + 5.081235897e-12i
56 -0.2207303622 - 2.154544746e-12i
57 -1.424197873 + 8.487843550e-12i
58 -0.4904592379 - 1.315887413e-11i
59 -0.2786266066 - 4.363475463e-12i
60 0.3395123963 + 2.310388782e-11i
61 0.05633536659 - 2.236334712e-11i
62 -0.7443301208 + 1.018343217e-11i
63 -0.8149703197 - 1.397493797e-11i
64 0.1250000035 + 1.643655894e-11i
65 -0.5766440166 + 4.864664879e-11i
66 1.714050772 - 1.010911421e-10i
67 0.07680164987 + 7.095192336e-11i
68 0.4442031282 - 7.131931355e-11i
69 -0.8760272595 - 2.050730530e-11i
70 -0.1974271993 + 2.390131948e-10i
71 1.477895510 - 2.375504914e-10i
72 0.4615191940 + 1.968510330e-10i
73 1.488386034 - 3.322110671e-10i
74 -0.7589822486 + 1.463543468e-10i
75 0.3036692130 + 7.541296916e-10i
76 -0.4689966165 - 2.754336033e-12i
77 -0.9967244781 + 2.491275941e-12i
78 -1.384358040 + 1.294792740e-13i
79 0.1807717746 - 5.299150142e-12i
80 0.1118033989 + 7.712612230e-13i
81 -0.6013738629 + 1.229392174e-12i
82 1.160308602 + 1.029346842e-11i
83 0.7751427184 - 3.082079944e-13i
84 -0.4739665612 - 4.085224531e-12i
85 0.3973073590 - 1.903405798e-11i
86 -0.6904650792 - 1.080367465e-11i
87 -1.053145900 + 3.089243952e-11i
88 0.5644468604 + 2.606553889e-12i
89 0.007113581896 + 1.708915749e-11i
90 0.4127952755 - 2.442251627e-11i
91 0.8050073864 - 4.407498361e-12i
92 -0.2884808479 + 3.516950570e-11i
93 -1.598273962 - 8.063151152e-11i
94 0.1722825762 + 3.005834849e-11i
95 -0.4194833235 - 5.355139309e-12i
96 0.2684081152 + 4.368858848e-11i
97 -0.8442550095 + 8.386012629e-11i
98 -0.4314941577 - 1.224936509e-10i
99 2.084024291 - 2.594656206e-11i
100 0.09999997890 - 1.034552226e-10i
101 0.8032819310 + 2.138230895e-10i
102 0.9538218069 - 1.495897684e-12i
103 0.1607775824 - 1.640913190e-11i
104 -0.4558771285 - 6.094899522e-12i
105 -0.4239285805 - 1.098384695e-11i
106 0.3308570995 + 2.782491936e-11i
107 0.5085363849 - 2.970838781e-12i
108 0.2318310898 - 1.764435216e-11i
109 0.5187106291 + 4.654874272e-11i
110 0.5048566164 - 2.144854436e-11i
111 -1.629736026 - 6.941462150e-12i
112 -0.1560799453 - 6.033039317e-11i
113 -0.6633869166 + 3.544494444e-11i
114 -1.007059964 + 7.606555052e-11i
115 -0.2580251151 + 1.811693371e-11i
116 -0.3468070480 + 1.924722284e-11i
117 -1.683168254 - 3.243826750e-10i
118 -0.1970187706 - 3.979111688e-11i
119 -0.5546495299 + 2.692564203e-10i
120 0.2400715731 + 3.887588506e-10i
121 1.548802063 - 2.524417609e-11i
122 0.03983502859 - 5.986981776e-10i
123 2.491489945 + 3.290132552e-11i
124 -0.5263208767 + 1.731127742e-11i
125 0.08944278445 + 3.932213779e-10i
126 -0.5762710605 - 1.067478049e-10i
127 1.408316003 - 7.969445010e-12i
128 0.08838835708 + 5.819209238e-11i
129 -1.482611433 - 1.844361021e-11i
130 -0.4077488958 + 1.362673244e-11i
131 0.06375400288 - 6.844284282e-11i
132 1.212016939 + 3.139203908e-11i
133 0.5856076862 - 5.326035057e-11i
134 0.05430696554 + 4.247308138e-11i
135 0.2073560384 + 4.075745034e-11i
136 0.3140990327 - 9.826637124e-11i
137 -1.524644982 + 2.308277526e-10i
138 -0.6194448224 - 8.592693659e-11i
139 1.281632008 - 4.849671705e-11i
140 -0.1396021767 - 2.439554044e-10i
141 0.3699363494 + 1.968909793e-10i
142 1.045030046 + 5.198739341e-10i
143 -2.058547403 - 5.992006822e-10i
144 0.3263433231 - 4.658695400e-11i
145 -0.3101937007 - 3.259792427e-10i
146 1.052447912 + 2.206887723e-11i
147 -0.9265322025 + 2.829354841e-11i
148 -0.5366815197 + 2.507065519e-11i
149 0.4339021097 - 6.462954821e-11i
150 0.2147264851 + 5.582042704e-11i
151 -1.273991981 - 8.108200536e-11i
152 -0.3316306950 - 1.033424804e-10i
153 1.159701851 + 8.906538479e-11i
154 -0.7047905975 + 1.377830628e-10i
155 -0.4707556747 + 1.894339865e-10i
156 -0.9788889968 - 3.187969703e-11i
157 -0.3263953954 - 2.217051798e-10i
158 0.1278248746 - 3.942895321e-10i
159 0.7104378527 - 5.165111504e-11i
160 0.07905704451 + 3.257205208e-10i
161 0.3602086558 + 1.757098928e-10i
162 -0.4252355198 + 1.615836751e-10i
163 0.3761214705 + 1.844826317e-10i
164 0.8204619981 + 8.080192665e-11i
165 1.084060907 + 2.435949812e-11i
166 0.5481086645 - 1.583686638e-11i
167 0.9875513262 - 2.233384878e-11i
168 -0.3351449865 - 9.237254560e-11i
169 0.6625916460 - 3.784419297e-11i
170 0.2809387622 + 2.266122568e-10i
171 -1.224431292 + 9.841736116e-11i
172 -0.4882325473 - 7.480830081e-12i
173 -0.3736839665 - 1.185358625e-10i
174 -0.7446866928 - 4.920897715e-10i
175 -0.1248639360 + 2.032564391e-11i
176 0.3991242853 + 4.580953978e-10i
177 -0.4230514381 + 2.156068758e-10i
178 0.005030087768 + 1.903341514e-10i
179 0.01120402407 + 3.464969698e-11i
180 0.2918903575 + 1.010022336e-10i
181 0.3245215146 + 7.906637574e-11i
182 0.5692261819 - 9.171403514e-12i
183 0.08553654608 - 9.388655722e-11i
184 -0.2039867788 - 7.817295632e-11i
185 -0.4800225641 - 1.211560398e-10i
186 -1.130150337 + 6.132777952e-11i
187 1.418337799 + 1.504853781e-10i
188 0.1218221997 + 1.693250671e-10i
189 -0.2894734467 + 7.244420012e-11i
190 -0.2966195474 - 2.892488971e-10i
191 1.774667046 - 1.853154040e-10i
192 0.1897931820 - 7.268925316e-11i
193 -1.957909029 + 2.149346572e-10i
194 -0.5969784141 + 2.719474349e-10i
195 -0.8755449088 - 7.254410198e-11i
196 -0.3051124571 - 1.694203504e-10i
197 -1.257714947 + 4.195432188e-11i
198 1.473627767 + 3.309308466e-10i
199 -1.084752939 - 2.867365698e-10i
200 0.07071058192 - 5.891929011e-10i
201 0.1166114281 + 4.689270664e-11i
202 0.5680061688 + 6.107710067e-10i
203 0.4330370421 + 2.972611016e-10i
204 0.6744538746 + 6.548809963e-11i
205 0.7338435296 - 4.039202617e-10i
206 0.1136867979 - 6.981208086e-10i
207 -0.7531503224 + 4.481392199e-10i
208 -0.3223537807 + 1.324970523e-10i
209 -1.497503209 - 3.256366496e-11i
210 -0.2997627761 - 2.252076970e-11i
211 1.228459649 + 2.215932200e-10i
212 0.2339513071 + 7.303375042e-11i
213 2.243956137 - 2.404020442e-10i
214 0.3595894948 - 2.306287158e-10i
215 -0.4366884399 + 1.014000550e-10i
216 0.1639294061 + 4.332886711e-10i
217 0.6571850273 + 2.270308005e-11i
218 0.3667837419 - 3.685883380e-10i
219 2.259884397 - 2.765768976e-10i
220 0.3569875895 + 3.013975279e-10i
221 -1.145524529 + 3.037333775e-10i
222 -1.152397407 - 9.282698466e-11i
223 -0.2610239370 - 2.415865332e-10i
224 -0.1103652625 - 3.899676317e-10i
225 0.2610747661 + 6.232244087e-10i
226 -0.4690852902 + 6.461549345e-10i
227 -0.7644424606 + 2.163891844e-10i
228 -0.7120989568 - 1.083928258e-10i
229 -0.1746365362 - 1.321785773e-11i
230 -0.1824513077 + 3.039571323e-11i
231 -1.513372191 + 7.645305160e-11i
232 -0.2452296102 + 3.552408104e-11i
233 0.4898006596 - 1.207918030e-11i
234 -1.190179654 + 1.054071931e-11i
235 0.1089610414 - 1.398392958e-10i
236 -0.1393133158 - 6.379495348e-11i
237 0.2744740362 + 1.036435531e-11i
238 -0.3921964409 + 2.004451939e-10i
239 -0.4145139375 + 1.250358331e-10i
240 0.1697561813 - 1.044000859e-10i
241 0.9742157835 - 1.020573288e-10i
242 1.095168413 - 1.832810852e-10i
243 -1.376755526 + 1.039967634e-10i
244 0.02816768862 + 1.325801142e-11i
245 -0.2729008168 + 1.719147599e-10i
246 1.761749451 + 3.969798958e-11i
247 1.209462709 - 2.193038100e-10i
248 -0.3721650073 + 3.113822340e-10i
249 1.176934495 - 7.205561102e-11i
250 0.06324547793 - 5.506012989e-10i
251 -0.8319612629 - 5.808397650e-11i
252 -0.4074851736 - 9.773685377e-11i
253 -0.9211175253 - 2.762104253e-11i
254 0.9958298094 + 6.768083292e-11i
255 0.6032498841 + 7.595760679e-11i
256 0.06250001645 + 8.160535336e-11i
257 -0.01159912192 - 1.063263232e-10i
258 -1.048364608 - 8.842703911e-11i
259 0.6701217354 + 7.380519414e-12i
260 -0.2883220116 - 9.413230232e-12i
261 -0.9054253065 + 9.859078297e-11i
262 0.04508089875 + 2.787878312e-11i
263 0.1767512711 - 7.843650748e-11i
264 0.8570253978 + 1.504121198e-11i
265 0.2092524007 + 8.529342156e-12i
266 0.4140871792 + 5.331999325e-11i
267 0.01080085334 - 8.068091683e-11i
268 0.03840080383 - 1.329804404e-10i
269 -0.3840828818 + 1.490413352e-10i
270 0.1466228649 + 5.742287201e-11i
271 0.05098798776 + 1.255947814e-10i
272 0.2221015426 - 1.385902141e-10i
273 1.222279369 - 2.617773278e-10i
274 -1.078086802 + 1.972029529e-10i
275 0.3192993280 - 2.031416696e-10i
276 -0.4380135656 + 3.713605567e-10i
277 -1.811576885 + 4.852485196e-10i
278 0.9062505741 - 6.258385775e-10i
279 -1.374090479 - 2.580928523e-10i
280 -0.09871368337 - 3.519597568e-10i
281 1.651973177 + 1.846070563e-11i
282 0.2615846456 + 1.071183604e-9i
283 0.4559184811 + 2.712357207e-10i
284 0.7389477701 - 6.852039403e-12i
285 -0.6369207352 - 5.906041634e-10i
286 -1.455612789 - 1.939355396e-10i
287 -1.024461336 + 1.154717303e-10i
288 0.2307595647 - 8.806443933e-11i
289 -0.2107342933 + 5.037966694e-11i
290 -0.2193400180 + 1.103084233e-10i
291 -1.281870913 - 1.568112144e-10i
292 0.7441930660 + 1.360659460e-10i
293 -0.1406634798 - 4.337706878e-12i
294 -0.6551572008 + 7.915199288e-11i
295 -0.1246056143 - 5.221841006e-11i
296 -0.3794911772 - 1.953044677e-10i
297 0.7402351760 - 1.806659927e-10i
298 0.3068151583 + 1.134840509e-10i
299 0.7439432502 + 2.910839046e-10i
300 0.1518345907 + 2.293241858e-10i
301 0.6096264311
302 -0.9008484170 - 3.518984854e-10i
303 1.219659483 - 1.959472429e-10i
304 -0.2344983367 - 1.714406408e-10i
305 0.02519395160 + 4.702039341e-11i
306 0.8200330059 - 5.728605108e-11i
307 1.329757230 - 1.908138648e-11i
308 -0.4983622308 + 3.198332815e-11i
309 0.2441159480 + 8.995133612e-11i
310 -0.3328745548 - 3.613239583e-12i
311 1.621539534 - 1.654245497e-11i
312 -0.6921790336 - 1.152122375e-10i
313 -0.9037627516 - 1.028543635e-10i
314 -0.2307963495 + 6.733731555e-12i
315 -0.3644657985 + 4.707036778e-11i
316 0.09038591581 + 1.527929446e-10i
317 0.07183398770 - 1.413234577e-10i
318 0.5023554060 + 1.876175319e-11i
319 -1.107352695 + 1.584256010e-11i
320 0.05590169807 - 2.667767303e-11i
321 0.7721340089 + 2.710095404e-10i
322 0.2547059237 - 3.061371457e-11i
323 -0.8333190696 - 4.474844914e-11i
324 -0.3006869515 - 1.444227945e-10i
325 -0.2578830674 - 1.089283720e-10i
326 0.2659580891 + 1.922390198e-10i
327 0.7875820055 + 1.310391052e-10i
328 0.5801542587 - 2.731910804e-10i
329 -0.1521119962 - 8.447090369e-11i
330 0.7665468056 - 6.725814354e-11i
331 -0.4778321263 - 6.202843809e-11i
332 0.3875714110 + 3.713050744e-10i
333 -1.401139484 - 2.559173790e-10i
334 0.6983042640 + 1.925197084e-10i
335 0.03434673487 - 1.105740542e-10i
336 -0.2369832779 + 5.688704806e-11i
337 0.4529053349 + 7.015313836e-10i
338 0.4685230153 - 1.812649443e-10i
339 -1.007250633 - 2.749559366e-10i
340 0.1986536164 - 4.973405353e-10i
341 -1.680539213 - 1.064420017e-10i
342 -0.8658036859 - 1.737421302e-11i
343 1.005295161 - 3.924591830e-11i
344 -0.3452325346 + 3.780698407e-11i
345 -0.3917712886 + 2.160253574e-11i
346 -0.2642344566 - 3.984283854e-11i
347 -0.6971895865 - 7.379410692e-12i
348 -0.5265729429 + 8.161599942e-11i
349 0.9142568334 - 3.108480068e-11i
350 -0.08829214933 - 3.959500952e-11i
351 -0.5978530939 - 3.702907506e-11i
352 0.2822234293 + 9.799355004e-12i
353 -1.323909873 + 5.010159362e-11i
354 -0.2991425709 - 2.383242359e-11i
355 0.6609350002 + 1.240677362e-10i
356 0.003556780347 - 4.236435510e-11i
357 -0.8421497445 - 1.500054315e-10i
358 0.007922440012 - 1.915304060e-11i
359 1.798631481 + 7.150673731e-11i
360 0.2063976571 + 9.519317706e-11i
361 -0.1201686957 - 2.942379296e-11i
362 0.2294713656 + 7.269376348e-11i
363 2.351616749 - 6.554038313e-11i
364 0.4025036782 - 1.315361636e-10i
365 0.6656264879 - 3.924182312e-11i
366 0.06048352333 + 2.241091124e-10i
367 -0.1435251426 + 7.338791730e-12i
368 -0.1442404601 - 1.992425848e-10i
369 2.142018585 + 8.704612246e-11i
370 -0.3394272082 - 8.582483961e-11i
371 -0.2921208046 + 1.345605460e-10i
372 -0.7991369984 - 2.200771009e-10i
373 -0.9538607855 + 2.399494614e-10i
374 1.002916281 + 1.149710578e-10i
375 0.1358049126 - 2.389941608e-10i
376 0.08614131859 + 1.829313327e-10i
377 0.8943565762 - 8.037043309e-11i
378 -0.2046886164 + 1.343261126e-10i
379 -1.519902149 - 4.035994795e-10i
380 -0.2097416168 + 2.728695328e-10i
381 2.138310362 + 6.239177232e-11i
382 1.254879137 - 2.222535574e-11i
383 -1.349188115 - 1.773396899e-10i
384 0.1342040473 - 1.439426795e-11i
385 -0.4457487435 + 2.849760431e-11i
386 -1.384450775 - 3.356120643e-11i
387 -1.274651426 + 5.694262616e-11i
388 -0.4221275103 - 9.391120428e-12i
389 -1.379850226 - 2.214945949e-11i
390 -0.6191037494 - 4.328415307e-11i
391 -0.5125763840 + 1.345051026e-11i
392 -0.2157470591 + 1.196438840e-10i
393 0.09680062116 - 4.035815399e-11i
394 -0.8893387628 + 4.847270353e-11i
395 0.08084360685 + 1.162270332e-10i
396 1.042012126 - 1.661710867e-10i
397 0.2734626633 + 8.782703131e-11i
398 -0.7670361584 - 6.659993041e-11i
399 0.8891548611 + 3.339031933e-12i
400 0.04999998840 - 4.257034823e-11i
401 1.806717348 - 9.685611830e-11i
402 0.08245675942 + 1.020937749e-10i
403 1.357292293 - 8.780218612e-11i
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