Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 6e-15
Fricke Eigenvalue 1
Atkin-Lehner Eigenvalues 1,1,0,0

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Spectral parameter

$R= 2.73410555925$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.7071067811
3 1.379492817
4 0.5000000000
5 -0.4472135954
6 -0.9754487261
7 0.4536216109
8 -0.3535533905
9 0.9030004345
10 0.3162277660
11 -1.249643909
12 0.6897464089
13 0.9852325226
14 -0.3207589172
15 -0.6169279429
16 0.2500000000
17 -0.6156629616
18 -0.6385177306
19 -0.08304725124
20 -0.2236067984
21 0.6257677528 + 2.267915677e-13i
22 0.8836316861
23 0.9335943787 - 5.043075203e-13i
24 -0.4877243751 + 2.151606236e-13i
25 0.2000000072 + 1.537145252e-12i
26 -0.6966645663 - 1.615175566e-12i
27 -0.1338102558 - 4.380859133e-12i
28 0.2268107559 + 6.675625346e-12i
29 0.3684943342 + 7.480021262e-12i
30 0.4362338914 - 1.997884327e-11i
31 -1.045601365 - 2.566581821e-12i
32 -0.1767766952
33 -1.723874798
34 0.4353394549
35 -0.2028657516
36 0.4515002172
37 0.2702372295
38 0.05872327500
39 1.359121188
40 0.1581138830
41 1.280300176
42 -0.4424846225
43 0.1712181284
44 -0.6248219547
45 -0.4038340710
46 -0.6601509143 - 1.259077832e-13i
47 -0.2816377922
48 0.3448732036 + 1.378866704e-13i
49 -0.7942274349 + 1.323585282e-13i
50 -0.1414213557 - 1.588158999e-13i
51 -0.8493026241 - 2.929229077e-13i
52 0.4926162664 + 1.901787529e-13i
53 1.183504188 + 1.446629455e-13i
54 0.09461812652
55 0.5588576126 - 3.411765377e-13i
56 -0.1603793580 + 3.937284694e-13i
57 -0.1145631982 + 5.657323732e-13i
58 -0.2605647648 - 8.277413581e-13i
59 -1.846303162
60 -0.3084650716 - 4.892314628e-13i
61 1.162882375 + 5.818963203e-13i
62 0.7393509756 + 1.167520555e-12i
63 0.4096220039 - 1.167101409e-12i
64 0.1249995337 + 1.662089231e-12i
65 -0.4406141630 - 3.551729140e-12i
66 1.218961840 + 1.368033067e-12i
67 0.1440661137 + 1.160476198e-12i
68 -0.3078157043 - 9.803289788e-12i
69 1.287932364 + 6.124376074e-12i
70 0.1434547649 + 1.541715066e-11i
71 -1.196364025 + 8.367236666e-12i
72 -0.3190288873 - 3.772033887e-11i
73 -1.235235551 - 3.489535987e-11i
74 -0.1910865756
75 0.2758985494 + 2.350117388e-13i
76 -0.04152365203 - 1.253545666e-13i
77 -0.5668654792
78 -0.9610437933 - 1.510510908e-13i
79 1.019953680
80 -0.1118033700
81 -1.087590555 + 1.208532687e-13i
82 -0.9053089018 + 4.617393635e-13i
83 1.830933183 - 4.452788885e-13i
84 0.3128840137
85 0.2753339805 - 2.355980350e-13i
86 -0.1210693084
87 0.5083349224 + 1.744652027e-13i
88 0.4418162573 + 5.877874294e-13i
89 0.5968133027 + 1.270982426e-12i
90 0.2855536219 - 2.587316079e-12i
91 0.4469229880 - 1.318383889e-12i
92 0.4667979912 + 9.024062684e-13i
93 -1.442398560 + 2.412992049e-12i
94 0.1991497148 + 1.013018863e-12i
95 0.03714620980 - 3.245132109e-12i
96 -0.2438431531 + 9.997761494e-13i
97 -0.2618560663 - 1.710978287e-12i
98 0.5615858357 + 8.501258872e-13i
99 -1.128422244 + 3.753851783e-12i
100 0.09995968909 - 2.933910645e-12i
101 1.203614603 - 2.868827254e-12i
102 0.6005398257 - 5.339809023e-12i
103 -1.338471217 + 1.516675780e-11i
104 -0.3481974517 - 2.459019964e-12i
105 -0.2803019636 - 9.950316049e-12i
106 -0.8371038004 + 2.219525064e-12i
107 0.01363181239 - 6.197553290e-12i
108 -0.06717242000 + 8.942908326e-12i
109 -0.7051027687 - 1.901654638e-11i
110 -0.3951720686 + 7.495221068e-13i
111 0.3727907508 + 4.378293307e-13i
112 0.1134057414 - 2.813684388e-13i
113 0.5088901959 - 7.152163145e-13i
114 0.08100845663 + 3.022254410e-13i
115 -0.4175171299 - 5.698091782e-13i
116 0.1842477062 - 5.737014904e-13i
117 0.8896673008 + 1.170360761e-12i
118 1.305532471 + 9.168599660e-13i
119 -0.2792692934 + 6.746033431e-13i
120 0.2181137158 - 1.650853445e-12i
121 0.5616138533 - 7.360410227e-13i
122 -0.8222833828
123 1.766165923 - 4.798116646e-13i
124 -0.5228004364 - 7.673758468e-13i
125 -0.08944586432 + 1.940909476e-13i
126 -0.2896460168 + 2.478687613e-13i
127 -0.8486060681 + 1.178909458e-12i
128 -0.08838534707 + 1.056251283e-12i
129 0.2361931146 - 1.074342434e-12i
130 0.3115557151 - 1.990408248e-12i
131 -0.6602712184 + 3.216760080e-13i
132 -0.8619350992 + 1.329700665e-13i
133 -0.03768297590 + 1.910750984e-12i
134 -0.1018752530 + 2.417276427e-13i
135 0.05984091974 - 1.133209466e-12i
136 0.2176669831 + 4.134745581e-12i
137 0.6691991454 - 5.036874025e-12i
138 -0.9106535525 - 1.549847510e-12i
139 1.358823696 + 1.044789070e-12i
140 -0.1014118694 + 5.410860024e-13i
141 -0.3885604481 + 5.856400835e-12i
142 0.8459621734 - 2.130089397e-12i
143 -1.231139407 + 1.492014421e-12i
144 0.2257264148 - 1.480418181e-12i
145 -0.1648203271 - 4.311976073e-12i
146 0.8735386801 - 5.782420932e-12i
147 -1.095539493 + 4.111515894e-12i
148 0.1351880341 + 1.309170697e-12i
149 -1.480791930 + 9.402474363e-12i
150 -0.1950657761 + 1.482930250e-11i
151 -0.8725483537 - 2.592796163e-11i
152 0.02948398827 - 4.766673589e-12i
153 -0.5555934352 - 1.038020386e-11i
154 0.4006334471 + 1.198217339e-11i
155 0.4691333993 + 2.792000644e-11i
156 0.6790039781 - 1.876058568e-11i
157 1.752389478 + 3.165474871e-11i
158 -0.7212171972 + 2.351023106e-12i
159 1.632635379 - 3.475157676e-13i
160 0.07905663078 + 6.841036516e-13i
161 0.4234960926 - 9.268171389e-13i
162 0.7690393033 - 2.477648498e-12i
163 -0.1769115592 - 4.573173030e-13i
164 0.6401505416 - 5.426964351e-13i
165 0.7709355403 + 3.521832310e-12i
166 -1.294670452 + 2.384910254e-12i
167 -0.5936829029 - 1.439788715e-12i
168 -0.2212361596 - 2.883138076e-12i
169 -0.02931254837 - 2.940798589e-12i
170 -0.1946914006 + 2.245728253e-12i
171 -0.07498092539 + 5.945556704e-13i
172 0.08561240520 + 1.795271910e-12i
173 0.9666070220 - 2.172376240e-12i
174 -0.3594735355 - 1.878954221e-12i
175 0.09072245308 + 2.846653293e-12i
176 -0.3123846630 - 6.049263308e-13i
177 -2.546929969 - 5.261398759e-13i
178 -0.4220293440 - 6.395140967e-12i
179 -0.7971578362 - 1.450659944e-12i
180 -0.2019236672 + 4.987679451e-12i
181 -0.7517057918 + 1.627874283e-12i
182 -0.3158932916 - 4.221104566e-12i
183 1.604420390 - 9.045294438e-13i
184 -0.3302006462 + 6.406133217e-12i
185 -0.1208606415 - 5.833483096e-13i
186 1.019934015 - 2.104163773e-13i
187 0.7693606025 - 1.820386580e-13i
188 -0.1408141789 - 9.497520431e-13i
189 -0.06068724362 + 1.077173221e-12i
190 -0.02626365929 - 1.551414765e-13i
191 0.7548728268 - 7.482734414e-13i
192 0.1724475185 - 2.171754583e-12i
193 -0.3285884094 + 7.226600671e-12i
194 0.1851575350 - 4.102601539e-12i
195 -0.6078180986 + 9.402821634e-13i
196 -0.3971115535 - 2.438493752e-12i
197 1.099600799 - 4.222770792e-12i
198 0.7979817479 + 1.508886608e-11i
199 -0.0009779808152 - 7.525207530e-12i
200 -0.07074865416 - 1.203818764e-12i
201 0.1987669245 - 5.907025493e-12i
202 -0.8509775811 - 1.597627968e-12i
203 0.1670690450 + 1.223766391e-11i
204 -0.4245823734 + 6.067859387e-12i
205 -0.5723369009 - 2.653381556e-12i
206 0.9463508436 - 1.381238667e-12i
207 0.8434690974 - 1.124957908e-12i
208 0.2463864359 - 2.170150784e-11i
209 0.1037929416
210 0.1978828914 - 5.394875312e-12i
211 0.6279042466 + 4.336971246e-12i
212 0.5917402098 + 1.854937882e-13i
213 -1.650362919 - 1.178054575e-12i
214 -0.009808039688 + 7.778296394e-12i
215 -0.07658863247 - 5.670263921e-12i
216 0.04724057032 + 2.959514918e-12i
217 -0.4742658606 - 3.880552148e-12i
218 0.4989319804 - 8.863159145e-12i
219 -1.704162630 + 2.711107738e-12i
220 0.2794332687 + 1.930407391e-12i
221 -0.6065430539 + 8.141808160e-12i
222 -0.2636259813 + 3.735249451e-12i
223 0.5313503330 - 5.101237853e-12i
224 -0.08010514560 - 8.627636030e-12i
225 0.1806826822 + 1.084929713e-11i
226 -0.3598298054 - 1.831393827e-11i
227 -0.5904547620 + 5.554163239e-12i
228 -0.05729338753 + 2.076799351e-13i
229 0.2474294343 + 7.117345905e-12i
230 0.2951872264 + 3.144409413e-11i
231 -0.7819861174 - 3.191351933e-12i
232 -0.1302823574 + 1.710207714e-12i
233 1.037001355 - 3.994315844e-12i
234 -0.6290763689 - 4.878866241e-12i
235 0.1259633889 + 1.528714658e-12i
236 -0.9231299658 - 5.341512368e-13i
237 1.407047937 + 1.223243614e-11i
238 0.1974691660 - 4.350473972e-13i
239 0.07309190959 - 3.698439999e-12i
240 -0.1542523725 - 6.022865108e-12i
241 1.520867203 - 3.232510243e-12i
242 -0.3971100690 + 4.527520993e-13i
243 -1.366524210 + 8.711928677e-12i
244 0.5814230589 + 4.165648817e-13i
245 0.3551659559 - 3.243608982e-12i
246 -1.248854355 + 6.284344413e-12i
247 -0.08179232083 - 6.643515088e-12i
248 0.3697489079 + 7.966871655e-12i
249 2.525942268 - 1.335424193e-11i
250 0.06324222914 + 2.089319422e-12i
251 0.2205987186 + 4.437475932e-12i
252 0.2048002465 - 5.913586468e-12i
253 -1.166757218 + 7.818744599e-13i
254 0.6000249089 + 5.451399576e-12i
255 0.3798625489 + 1.393993759e-11i
256 0.06250107701 - 1.683751987e-12i
257 -1.559232626 - 4.576021572e-12i
258 -0.1670133612 + 1.635006392e-13i
259 0.1225917741 - 1.116439747e-12i
260 -0.2203050254 + 5.487372103e-12i
261 0.3327522205 + 4.057798371e-12i
262 0.4668823629 - 1.281645307e-12i
263 -0.8594404297 - 5.969522085e-12i
264 0.6094783978 + 1.549617690e-12i
265 -0.5292552105
266 0.02664029043 + 2.714870275e-12i
267 0.8233266292
268 0.07203642706 - 6.021265381e-12i
269 0.2709468102 + 5.573701990e-12i
270 -0.04230427189 - 1.011869932e-11i
271 0.09895278873 + 2.801751407e-12i
272 -0.1539221523 + 3.072748946e-12i
273 0.6164703475 + 4.407915440e-12i
274 -0.4732312531 + 3.235746834e-13i
275 -0.2498933305 - 2.948728528e-12i
276 0.6439543561 + 1.785497748e-12i
277 -1.429775968 - 8.069586504e-12i
278 -0.9609210849 + 1.011082503e-11i
279 -0.9441717338 - 8.251677461e-12i
280 0.07175553880 + 5.107376195e-12i
281 -1.172556335 - 1.062731929e-11i
282 0.2746849379 + 6.970265450e-12i
283 -0.6077178864 + 1.129978287e-11i
284 -0.5981806042 + 6.412363221e-13i
285 0.05123407332 - 5.137772676e-13i
286 0.8705832104 - 7.255703047e-13i
287 0.5807720378
288 -0.1596296946 + 6.138654675e-13i
289 -0.6209581291 - 2.018231656e-13i
290 0.1165278774 - 5.359354409e-13i
291 -0.3612077432 + 4.334419151e-13i
292 -0.6176799969 + 2.908501126e-13i
293 1.499829094 + 2.259772029e-13i
294 0.7747276626 + 6.595910011e-13i
295 0.8256929912 - 1.355320819e-12i
296 -0.09554344733 - 7.618504294e-13i
297 0.1672148473 + 6.529678658e-13i
298 1.047047953 + 5.581212477e-13i
299 0.9198057115 + 5.266541512e-13i
300 0.1379504890 - 9.631246015e-13i
301 0.07766846210 + 4.496317736e-13i
302 0.6168449864 + 3.221147477e-13i
303 1.660423277 - 2.012793933e-12i
304 -0.02076301714 + 2.766766209e-13i
305 -0.5200558048 + 3.294349696e-12i
306 0.3931102414 + 1.277782538e-12i
307 1.145182583 - 1.765539697e-12i
308 -0.2834319323 - 2.599031554e-12i
309 -1.846111004 - 1.198136021e-12i
310 -0.3306522202 + 2.372177772e-12i
311 -1.365458688 + 1.772879112e-12i
312 -0.4805216247 + 5.439479497e-13i
313 0.7214293668 + 6.021049903e-13i
314 -1.238665661 - 2.620784731e-12i
315 -0.1831975713 - 8.750656314e-13i
316 0.5099707795 + 1.138814286e-12i
317 0.9272606730 - 3.199130081e-12i
318 -1.154458756 + 2.060925459e-12i
319 -0.4604920441 + 3.602040004e-12i
320 -0.05589560554 + 2.638541394e-12i
321 0.01911842172 - 1.833496668e-12i
322 -0.2994615479 - 5.169557860e-12i
323 0.05111038843 + 1.622579153e-12i
324 -0.5438019397 - 8.320903642e-13i
325 0.1970740264 - 3.842294570e-12i
326 0.1251051825 + 8.258876708e-13i
327 -0.9733953459 + 7.517373857e-12i
328 -0.4526576220 + 2.111908860e-12i
329 -0.1277239886 - 4.624859258e-12i
330 -0.5451345939 - 3.717919010e-12i
331 1.078891178 - 2.661708707e-12i
332 0.9154652266 + 3.723014426e-12i
333 0.2439777637 + 1.292597719e-12i
334 0.4197983753 + 2.273700732e-13i
335 -0.06436992095 - 2.822694654e-13i
336 0.1564452766 - 4.542401038e-12i
337 -0.8778794816 + 6.917048131e-12i
338 0.02077447583 + 5.990005348e-12i
339 0.7019050143 - 1.281739762e-11i
340 0.1376679900 - 7.661879467e-12i
341 1.306798369 + 2.696860093e-12i
342 0.05298510263 + 6.676665221e-12i
343 -0.8138844544 - 1.845707585e-13i
344 -0.06047613216 + 3.784713971e-12i
345 -0.5760568655 + 9.141352255e-12i
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347 -0.6496862295 - 1.872790235e-11i
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351 -0.1318343007
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353 -0.9358003288 - 1.006580161e-12i
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355 0.5350295199 - 1.435530889e-13i
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357 -0.3852616735 - 1.730846430e-12i
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364 0.2234613814 - 2.572720818e-13i
365 0.5524699946 - 2.580073958e-13i
366 -1.134333368
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368 0.2333985560 + 3.138348214e-13i
369 1.156111717
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371 0.5368631136 - 3.112115890e-13i
372 -0.7211994162 - 1.037191045e-13i
373 -0.4379138586 + 3.128632936e-13i
374 -0.5440192057 - 3.973387646e-13i
375 -0.1233857862 + 1.711418589e-13i
376 0.09957405013 + 3.004880584e-13i
377 0.3630523258
378 0.04292104081
379 -0.6495043214
380 0.01856996402
381 -1.170646220 + 3.916948368e-13i
382 -0.5337781300 - 6.353754429e-13i
383 -0.2375789408 + 9.419892785e-13i
384 -0.1219311298 + 4.168905527e-13i
385 0.2535097469
386 0.2323463661 - 6.373465120e-13i
387 0.1546096295 - 7.915569298e-13i
388 -0.1309200886
389 0.3703453167 - 7.606066001e-13i
390 0.4297915666 + 1.347332739e-13i
391 -0.5747793983 - 8.705077812e-13i
392 0.2808017466 + 9.792453727e-13i
393 -0.9108489671 - 6.222397600e-13i
394 -0.7775202307 + 1.279677788e-12i
395 -0.4561375553 + 7.914307405e-13i
396 -0.5642144849 - 5.302236624e-13i
397 0.7816916680 + 1.172769092e-12i
398 0.0006500431621 - 3.688680597e-13i
399 -0.05196962512 + 1.247180515e-12i
400 0.05000002555 - 5.570002667e-13i
401 0.3415049822 - 9.787157166e-13i
402 -0.1405375263 - 1.760132399e-13i
403 -1.030161071 - 2.084091842e-12i
404 0.6018221266 - 1.330327637e-12i
405 0.4863850366 - 4.628573431e-13i
406 -0.1181982289 + 1.932735757e-12i
407 -0.3376986471 + 2.102881194e-12i
408 0.3002729878 - 7.196647821e-13i
409 1.704007910 + 8.775195803e-13i
410 0.4048653177 - 7.219345573e-13i
411 0.9231904620 + 1.096033599e-12i
412 -0.6691241437 - 2.103788996e-13i
413 -0.8375229860
414 -0.5961174707 + 4.590332914e-13i
415 -0.8188217703 - 1.119853097e-12i
416 -0.1741653333 - 2.169131333e-13i
417 1.874492468 - 1.461003355e-12i
418 -0.07338236190 - 1.894121182e-13i
419 -0.2196452924 - 1.019936715e-12i
420 -0.1399263081 + 2.897600055e-12i
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