Properties

Level 10
Symmetry odd
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

$R= 9.30018385212$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.7071067811
3 1.689879837
4 0.4999999999
5 -0.4472135954
6 -1.194925492
7 -1.423096875
8 -0.3535533905
9 1.855693865
10 0.3162277660
11 -0.4352566226
12 0.8449399187
13 -1.059563716
14 1.006281450
15 -0.7557372380
16 0.2500000000
17 -0.8900610616
18 -1.312173715
19 0.8022360500
20 -0.2236067977
21 -2.404862716
22 0.3077729094
23 -0.2608606495
24 -0.5974627462
25 0.2000000000
26 0.7492246886
27 1.446019809 - 1.034565800e-13i
28 -0.7115484375 + 2.829795935e-13i
29 -1.597965056 - 1.768751825e-13i
30 0.5343869256 - 3.717255406e-13i
31 -1.427355875 + 1.022711998e-12i
32 -0.1767766955 - 1.645326390e-13i
33 -0.7355313922 - 2.877887233e-12i
34 0.6293682146 + 2.590396776e-12i
35 0.6364282720 + 6.162490191e-12i
36 0.9278469255 - 1.020340780e-11i
37 0.8652056872 - 7.367391830e-12i
38 -0.5672665384 + 2.253589258e-11i
39 -1.790535381 - 3.933697459e-13i
40 0.1581138833 - 2.253476929e-11i
41 0.7035402753 + 2.977772207e-12i
42 1.700494689 + 1.066988258e-11i
43 -1.492315795
44 -0.2176283113
45 -0.8298915256 - 1.025333109e-13i
46 0.1844563342
47 0.6187323571
48 0.4224699593 - 1.739445089e-13i
49 1.025204716 + 1.523356132e-13i
50 -0.1414213561 + 2.565092274e-13i
51 -1.504096242 - 3.388135641e-13i
52 -0.5297818580 - 1.580363603e-13i
53 -0.6279320186 + 3.223180625e-13i
54 -1.022490413
55 0.1946526792 - 1.265281744e-13i
56 0.5031407252 + 3.486240289e-13i
57 1.355682526
58 1.129931927 - 6.732836718e-13i
59 1.247906631 + 8.065532901e-13i
60 -0.3778686185 + 5.654120391e-13i
61 -0.1389032820 - 2.564668020e-12i
62 1.009293019 + 1.931276531e-12i
63 -2.640832140 + 3.040719640e-12i
64 0.1249999971 - 8.532988734e-12i
65 0.4738513004 + 4.043822126e-12i
66 0.5200992381 + 1.390694124e-11i
67 -1.075253045 - 1.809217625e-11i
68 -0.4450305301 - 2.797407387e-12i
69 -0.4408231557 + 1.618222181e-11i
70 -0.4500227462 - 2.952473540e-11i
71 0.6688318969 + 2.484585100e-11i
72 -0.6560868555 + 5.720137791e-11i
73 0.3537956950 - 7.296822460e-11i
74 -0.6117928033 - 4.955070197e-11i
75 0.3379759751 + 8.406394917e-11i
76 0.4011180296 - 3.912878432e-11i
77 0.6194122835 - 1.318332218e-10i
78 1.266099781 + 3.385264210e-10i
79 -0.2662953750 + 2.711746646e-10i
80 -0.1118035699 - 8.081720604e-10i
81 0.5879057471 - 2.139222451e-10i
82 -0.4974778970 + 6.969242040e-10i
83 0.6965392847 + 9.942591090e-13i
84 -1.202431358 - 2.828236947e-13i
85 0.3980474076 - 1.286961088e-13i
86 1.055226618 - 5.025192357e-13i
87 -2.700368930 - 2.797706985e-12i
88 0.1538864541 - 1.733440911e-12i
89 1.057665735 + 3.045656591e-12i
90 0.5868219258 + 2.730431723e-12i
91 1.507861814 + 1.365880751e-12i
92 -0.1304303238 + 3.320195578e-12i
93 -2.412059915 + 5.331353774e-13i
94 -0.4375098480 - 6.363371412e-12i
95 -0.3587708700 - 7.268010738e-12i
96 -0.2987313731 - 5.821191996e-12i
97 0.6209451349 - 8.811814343e-12i
98 -0.7249292056 + 7.925728361e-12i
99 -0.8077030398 + 2.687168435e-11i
100 0.1000000072 + 2.137459955e-11i
101 0.6733943021 + 2.016242779e-11i
102 1.063556651 - 1.116378310e-11i
103 -0.1253615198 - 6.072489053e-11i
104 0.3746123351 - 6.017609468e-11i
105 1.075487284 - 4.759361615e-11i
106 0.4440149851 - 1.211493040e-11i
107 -1.878459272 + 1.312547764e-10i
108 0.7230099556 + 2.364246443e-10i
109 0.5008225251 + 6.546381584e-11i
110 -0.1376402623 - 1.066982666e-10i
111 1.462093632 - 1.563705650e-10i
112 -0.3557743085 - 3.562212618e-10i
113 0.8875687326 - 3.035907911e-10i
114 -0.9586122864 + 2.077544741e-10i
115 0.1166604280 - 2.769789750e-12i
116 -0.7989825273 + 2.873537369e-12i
117 -1.966225885 + 4.976041733e-12i
118 -0.8824032403 - 7.680957436e-13i
119 1.266643111 - 1.543180575e-11i
120 0.2671934599 - 6.884589900e-12i
121 -0.8105516730 + 3.284648789e-12i
122 0.09821944853 - 1.184602566e-11i
123 1.188898458 + 2.491569500e-11i
124 -0.7136779322 + 1.854543885e-11i
125 -0.08944271623 - 4.272994908e-12i
126 1.867350316 + 3.495074361e-12i
127 0.9906937800 + 1.594923620e-11i
128 -0.08838836534 - 4.423513250e-11i
129 -2.521834381 - 3.289150652e-11i
130 -0.3350634422 + 6.718075765e-11i
131 0.6178617826 - 5.037109302e-11i
132 -0.3677656966 - 1.604712888e-11i
133 -1.141659604 + 3.878189348e-11i
134 0.7603187018 - 7.061526748e-11i
135 -0.6466797387 - 4.014443114e-11i
136 0.3146841479 + 1.859140760e-10i
137 -0.1386130932 + 1.139615849e-10i
138 0.3117090332 - 9.959355118e-11i
139 -0.3979564757 + 1.712702607e-10i
140 0.3182140628 - 1.120519631e-10i
141 1.045583236 - 3.936522023e-10i
142 -0.4729355807 - 1.359485772e-10i
143 0.4611821875 + 1.319958764e-10i
144 0.4639234632 - 1.239674084e-10i
145 0.7146317356 + 2.596955741e-10i
146 -0.2501711337 + 7.265634090e-10i
147 1.732472785 + 6.726674947e-12i
148 0.4326028375 - 1.003381671e-11i
149 1.175776714 - 1.965180216e-11i
150 -0.2389851184 - 2.391753998e-11i
151 -0.9946203160 - 6.368651905e-12i
152 -0.2836332529 + 4.084983001e-11i
153 -1.651680815 + 4.719429291e-11i
154 -0.4379906499 + 1.943705643e-11i
155 0.6383329454 - 1.615225947e-11i
156 -0.8952677338 - 1.013462540e-10i
157 -1.722042572 - 6.582078410e-11i
158 0.1882992950 - 1.980669253e-11i
159 -1.061129605 + 8.349137002e-11i
160 0.07905703427 + 1.689113547e-10i
161 0.3712300370 + 5.217233630e-11i
162 -0.4157122296 - 4.626257024e-11i
163 0.2390191110 - 1.237657062e-10i
164 0.3517700094 - 1.264569435e-10i
165 0.3289395619 - 8.112947113e-11i
166 -0.4925275718 + 1.334937318e-10i
167 0.01484350561 + 1.546224916e-10i
168 0.8502475240 + 1.548541380e-10i
169 0.1226752690 - 1.509441914e-11i
170 -0.2814623201 - 4.620670941e-10i
171 1.488704319 - 1.583994598e-10i
172 -0.7461580155 - 5.034127760e-11i
173 -0.5374537132 + 7.151994765e-12i
174 1.909449189 + 6.602900174e-13i
175 -0.2846193833 - 1.957575304e-12i
176 -0.1088141418 + 5.033002022e-11i
177 2.108812248 + 2.809392597e-11i
178 -0.7478826058 + 1.506507780e-11i
179 0.6571772433 + 8.826804502e-11i
180 -0.4149457556 - 2.179809403e-11i
181 -1.106135569 - 6.378535405e-11i
182 -1.066219313 + 2.261248666e-11i
183 -0.2347299255 - 1.639486057e-10i
184 0.09222813680 - 1.152991415e-10i
185 -0.3869317207 + 2.903346561e-11i
186 1.705583928 - 1.134726928e-11i
187 0.3874050165 + 7.148488218e-11i
188 0.3093661692 + 6.612362090e-11i
189 -2.057826248 + 8.655654289e-11i
190 0.2536893532 + 1.927494697e-10i
191 0.4357809073 + 1.745341397e-10i
192 0.2112350358 + 1.376619456e-10i
193 -0.8263812108 - 8.450999042e-11i
194 -0.4390744859 + 5.310123678e-11i
195 0.8007517724 + 5.072950681e-11i
196 0.5126023435 - 1.411385911e-11i
197 0.1788567794 - 6.725309459e-11i
198 0.5711322554 - 8.953880922e-11i
199 -1.258245402 - 5.834493275e-11i
200 -0.07071064611 + 4.032574127e-11i
201 -1.817048387 + 8.312980345e-11i
202 -0.4761616459 + 1.697946656e-11i
203 2.274059055 - 1.071440826e-11i
204 -0.7520481571 - 3.098622810e-11i
205 -0.3146328434 - 1.140296954e-10i
206 0.08864398323 + 4.595029463e-11i
207 -0.4840774107 + 2.497481544e-10i
208 -0.2648908126 + 1.759116931e-10i
209 -0.3491784992 + 3.162394274e-11i
210 -0.7604844159 - 1.495904952e-10i
211 -0.002071097580 - 1.487198349e-11i
212 -0.3139660139 + 8.495194269e-12i
213 1.130245520 + 3.726810029e-12i
214 1.328271322 - 1.900796775e-11i
215 0.6673839305 + 3.679969126e-11i
216 -0.5112451977 + 1.873380657e-11i
217 2.031265674 - 2.137511100e-11i
218 -0.3541350079 + 5.920361065e-12i
219 0.5978722242 - 2.346902196e-11i
220 0.09732634187 - 1.383362074e-12i
221 0.9430764234 + 2.338588924e-11i
222 -1.033856306 - 1.837593785e-11i
223 -1.623862703 - 1.148393905e-11i
224 0.2515703446 - 2.206391077e-11i
225 0.3711387487 - 1.102272837e-11i
226 -0.6276059159 + 6.202365467e-11i
227 -0.3566750348 - 5.733981441e-12i
228 0.6778412790 - 1.255761530e-12i
229 -0.5119135688 + 9.848802221e-11i
230 -0.08249137135 - 4.246853007e-11i
231 1.046732387 - 8.434279735e-11i
232 0.5649658833 - 4.351206842e-11i
233 -1.416248626 - 2.384920653e-11i
234 1.390331698 + 1.534031498e-10i
235 -0.2767054590 + 2.271954324e-11i
236 0.6239533477 - 1.445510128e-10i
237 -0.4500072819 + 7.284670642e-11i
238 -0.8956519768 - 7.188435738e-11i
239 0.2645309585 - 1.979749151e-10i
240 -0.1889343685 + 1.521546230e-10i
241 -1.237012780 + 1.631066828e-10i
242 0.5731467534 + 2.062486516e-10i
243 -0.4525295583 + 8.417793942e-12i
244 -0.06945163085 + 2.774491166e-11i
245 -0.4584854858 - 3.350715180e-11i
246 -0.8406781930 - 9.438854866e-11i
247 -0.8500202040 - 3.483255608e-12i
248 0.5046464819 - 5.028701126e-11i
249 1.177067700 + 1.018543685e-11i
250 0.06324556599 + 2.855227263e-11i
251 1.863817506 + 1.215777917e-10i
252 -1.320416057 + 9.449237819e-11i
253 0.1135413229 - 1.741601324e-11i
254 -0.7005263002 + 5.861585300e-11i
255 0.6726522554 - 1.088472299e-10i
256 0.06250001903 + 1.593575936e-11i
257 0.4203055184 - 6.547283478e-11i
258 1.783206164 - 1.511782533e-10i
259 -1.231271501 + 1.593172438e-11i
260 0.2369255776 - 3.808081739e-11i
261 -2.965333947 - 6.842447174e-11i
262 -0.4368942987 - 7.743391284e-11i
263 -1.969378288 + 2.140348180e-10i
264 0.2600496669 + 7.271146617e-11i
265 0.2808198097 + 2.981720246e-10i
266 0.8072753238 + 3.790716462e-10i
267 1.787327871 - 1.994633502e-10i
268 -0.5376265990 - 1.978540524e-10i
269 1.362726306 - 2.660890997e-10i
270 0.4572717524 - 7.387634550e-11i
271 1.218878501 - 4.859642901e-10i
272 -0.2225153041 - 6.479634026e-11i
273 2.548105351 + 4.671618072e-10i
274 0.09801419777 - 3.495502635e-10i
275 -0.08705132881 - 7.107209910e-11i
276 -0.2204115925 - 2.059056257e-11i
277 1.953848553 - 5.838328361e-11i
278 0.2813977415 + 7.340674871e-12i
279 -2.648735559 - 3.834728693e-11i
280 -0.2250113783 + 2.920103378e-11i
281 -0.9534476267 + 1.285328983e-10i
282 -0.7393390278 + 1.355124508e-10i
283 0.8856347489 + 1.502453184e-10i
284 0.3344159033 - 5.100558567e-11i
285 -0.6062796833 + 8.610422166e-12i
286 -0.3261050361 - 1.707451889e-10i
287 -1.001205932 - 1.207717961e-10i
288 -0.3280434443 - 7.513400295e-11i
289 -0.2077913272 - 2.091390307e-10i
290 -0.5053208800 + 2.454015709e-11i
291 1.049322684 + 1.158492233e-11i
292 0.1768978465 + 1.517061042e-10i
293 -1.831228026 - 1.059435529e-10i
294 -1.225043252 + 2.343792575e-11i
295 -0.5580808138 + 2.329471343e-11i
296 -0.3058963995 + 2.531632684e-11i
297 -0.6293896956 - 3.405824115e-12i
298 -0.8313996921 - 6.328831286e-12i
299 0.2763984773 + 1.707195748e-11i
300 0.1689879723 - 2.985652034e-11i
301 2.123709964 + 1.338249790e-11i
302 0.7033027384 - 5.641205493e-11i
303 1.137955450 + 1.088109045e-12i
304 0.2005589939 - 5.638615615e-11i
305 0.06211945422 + 4.257958699e-12i
306 1.167914763 + 3.037404624e-11i
307 -1.287352696 - 2.161898091e-11i
308 0.3097061746 + 1.168722750e-10i
309 -0.2118458677 + 2.933420891e-11i
310 -0.4513695451 + 7.259645455e-11i
311 -0.1149531050 - 8.344547324e-11i
312 0.6330498622 + 1.631315773e-11i
313 -0.1005402203 - 5.043197352e-11i
314 1.217667975 - 4.655405593e-11i
315 1.181016027 + 2.809315444e-11i
316 -0.1331478206 - 1.603682297e-10i
317 0.1415139691 + 5.299041800e-11i
318 0.7503319630 - 1.090940225e-10i
319 0.6955248928 + 3.566795944e-11i
320 -0.05590169444 + 6.113498801e-11i
321 -3.174370507 + 2.101700066e-10i
322 -0.2624991913 + 1.282394242e-10i
323 -0.7140390903 + 1.870680202e-11i
324 0.2939529086 + 4.457173079e-11i
325 -0.2119127874 - 2.382223087e-10i
326 -0.1690120481 + 7.049056579e-11i
327 0.8463298692 - 3.031415439e-12i
328 -0.2487390273 + 1.566160042e-11i
329 -0.8805160983 - 2.243864873e-11i
330 -0.2325954357 + 2.325712705e-11i
331 0.5962610168 + 2.314897611e-11i
332 0.3482696220 - 5.013499824e-11i
333 1.605556891 + 1.036505245e-11i
334 -0.01049582595 + 9.840764323e-12i
335 0.4808677747 - 1.273844530e-11i
336 -0.6012156910 + 2.788001721e-11i
337 -1.062982136 + 4.570276514e-11i
338 -0.08674452245 - 2.524607865e-11i
339 1.499884612 - 1.573476219e-11i
340 0.1990236921 - 9.816105494e-12i
341 0.6212660787 - 7.244633379e-11i
342 -1.052673039 + 1.346748911e-11i
343 -0.03586875697 + 4.260147030e-11i
344 0.5276133269 + 3.824223109e-11i
345 0.1971420832 - 2.232612987e-11i
346 0.3800371883 - 2.294282021e-12i
347 -0.6070105734 + 1.742767337e-11i
348 -1.350184499 - 8.004995238e-11i
349 -0.5924177980 + 5.873777989e-11i
350 0.2012563162 + 7.674408623e-11i
351 -1.532150115 - 4.784421843e-11i
352 0.07694321294 + 2.845283762e-11i
353 -0.4038838088 + 4.816206270e-11i
354 -1.491155507 - 2.156676331e-10i
355 -0.2991106694 - 3.910740007e-11i
356 0.5288328959 + 1.522528934e-10i
357 2.140474607 - 1.068581850e-10i
358 -0.4646944323 + 1.253499045e-10i
359 -0.2392022856 + 8.695290387e-11i
360 0.2934109184 - 1.041308076e-10i
361 -0.3564173150 - 1.162065957e-11i
362 0.7821559601 + 4.256186422e-11i
363 -1.369734938 - 1.410972758e-11i
364 0.7539309065 - 1.493584195e-11i
365 -0.1582222501 + 4.817586947e-12i
366 0.1659790643 - 3.883761688e-11i
367 0.3991288072 - 3.143333963e-11i
368 -0.06521515445 + 4.616036907e-11i
369 1.305555312 + 4.404719091e-11i
370 0.2736020679 + 3.428219050e-11i
371 0.8936080829 + 2.913062213e-11i
372 -1.206029956 - 3.757053933e-11i
373 -1.507430431 - 6.793326890e-11i
374 -0.2739366924 - 3.940024588e-11i
375 -0.1511474459 + 2.505381302e-11i
376 -0.2187549078 + 4.163546225e-11i
377 1.693145812 + 3.640624888e-11i
378 1.455102914 + 1.662208228e-11i
379 0.5614137320 - 5.829896783e-11i
380 -0.1793854600 - 1.589426088e-10i
381 1.674153449 + 1.362679411e-11i
382 -0.3081436238 + 1.091773987e-10i
383 0.7890995541 + 5.975270475e-11i
384 -0.1493656447 + 1.834857141e-10i
385 -0.2770096034 - 4.719235390e-12i
386 0.5843397097 - 1.995176816e-10i
387 -2.769281299 - 6.716041708e-11i
388 0.3104725916 + 2.030376318e-11i
389 -0.6485439416 - 9.406406375e-11i
390 -0.5662169737 + 1.833895256e-10i
391 0.2321819607 + 1.232361227e-10i
392 -0.3624646415 - 2.184282745e-10i
393 1.044112185 - 4.438627974e-11i
394 -0.1264708804 - 1.034875614e-10i
395 0.1190909067 - 7.024855086e-11i
396 -0.4038514636 + 1.767736788e-10i
397 0.4083592506 + 3.702486133e-10i
398 0.8897138212 - 4.887491398e-12i
399 -1.929267569 - 1.812408321e-11i
400 0.05000001234 - 5.007417012e-11i
401 -1.307092468 - 3.727202710e-10i
402 1.284847255 + 1.459298709e-11i
403 1.512374521 + 5.126114398e-11i
404 0.3366971437 + 8.038892606e-12i
405 -0.2629194889 + 1.981421233e-11i
406 -1.608002589 - 2.155653653e-11i
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