Properties

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

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Spectral parameter

$R= 3.20437245526$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.7071067794 - 1.593222817e-12i
3 1.974932982 + 1.029796244e-11i
4 0.4999999914 - 8.742063075e-12i
5 0.4472135985 + 3.144308931e-12i
6 1.396488517 + 2.155636666e-11i
7 -0.9731243573 - 4.075647591e-12i
8 0.3535533799 - 1.096065783e-11i
9 -0.5203240050 - 1.121572337e-12i
10 0.3162277689 + 2.689801826e-12i
11 1.259007895 + 4.824570100e-12i
12 0.9874664949 + 9.121865026e-12i
13 0.3892901014 + 2.755354829e-12i
14 -0.6881028339 - 4.402299448e-12i
15 0.8832168786 + 3.298613295e-12i
16 0.2499999900 - 1.061860333e-11i
17 -1.741707925 - 7.015845892e-12i
18 -0.3679246343 - 3.279612362e-12i
19 1.160170989 + 4.666928645e-12i
20 0.2236068030 + 5.776919326e-12i
21 -1.921855381 - 8.751790694e-12i
22 0.8902530240 + 7.015571047e-12i
23 0.08747353065
24 0.6982442614 + 1.327593615e-11i
25 0.2000000007 + 1.389178802e-13i
26 0.2752696723 + 3.728208801e-12i
27 -2.101310400 - 8.008406191e-12i
28 -0.4865621797 - 2.889961615e-12i
29 -0.3965470347 - 4.806621247e-12i
30 0.6245286388 - 1.693522926e-12i
31 0.4720104454 + 1.088870225e-13i
32 0.1767766845 - 1.109342947e-11i
33 2.486456205 + 8.606246920e-12i
34 -1.231573481 - 2.833991065e-12i
35 -0.4351944327 + 9.430432509e-12i
36 -0.2601620028 - 2.424869328e-12i
37 0.2157466398 + 1.253985373e-11i
38 0.8203647699 - 3.676850082e-12i
39 0.7688218434 - 6.313831112e-12i
40 0.1581138842 + 6.148887422e-13i
41 0.7006904667 - 1.017049869e-11i
42 -1.358956977 - 8.878085458e-12i
43 0.5116445591 - 1.266389703e-11i
44 0.6295039508 + 1.502880800e-11i
45 -0.2326959541 + 5.780980453e-12i
46 0.06185312357 + 1.005310462e-11i
47 -0.7070633771 + 1.715360907e-11i
48 0.4937333157 + 7.784583928e-11i
49 -0.05302897680 + 1.191709959e-11i
50 0.1414213462 - 4.734484630e-11i
51 -3.439756448 - 1.821179368e-11i
52 0.1946450409 - 1.886787230e-11i
53 -1.800313276 + 2.100218255e-11i
54 -1.485850891 - 7.728017180e-11i
55 0.5630453907 - 5.066011165e-11i
56 -0.3440514328 - 5.860359565e-12i
57 2.291259942 - 1.259733358e-11i
58 -0.2804010791 + 1.768916804e-11i
59 1.151346919 + 1.235683095e-11i
60 0.4416084214 + 1.592331213e-11i
61 0.1764507144 + 2.522736335e-11i
62 0.3337617994 + 2.125316411e-11i
63 0.5063399703 + 1.291146628e-11i
64 0.1249999893 - 1.617363268e-11i
65 0.1740958032 - 3.217179222e-11i
66 1.758190041 - 1.376930723e-11i
67 0.4071939758 - 4.326247988e-13i
68 -0.8708540094 - 3.970313758e-11i
69 0.1727543481 + 2.111932790e-11i
70 -0.3077289187 + 1.372509191e-11i
71 -1.142711153 + 6.047648142e-12i
72 -0.1839623374 - 2.887996862e-11i
73 0.3822187397 - 1.238676957e-11i
74 0.1525559158 - 1.383194846e-13i
75 0.3949866367 + 3.394811836e-11i
76 0.5800855060 + 5.318263907e-11i
77 -1.225171248
78 0.5436391221 - 2.649918115e-11i
79 -1.455319928 - 5.811406077e-11i
80 0.1118033418 - 7.016305961e-11i
81 0.009953138644 - 5.254122889e-11i
82 0.4954630619 + 7.842937457e-11i
83 0.9046598228 + 7.722836317e-11i
84 -0.9609276750 + 1.163334313e-11i
85 -0.7789154732 - 1.364030163e-11i
86 0.3617874005 + 6.181627669e-11i
87 -0.7831538350 - 3.272502432e-11i
88 0.4451265322 + 3.367662180e-11i
89 0.8250828188 + 2.571400313e-12i
90 -0.1645408779 + 1.572192547e-11i
91 -0.3788276330 + 4.657345602e-11i
92 0.04373674012 - 1.894010248e-11i
93 0.9321890435 + 2.897039462e-11i
94 -0.4999693846 - 6.285523595e-11i
95 0.5188442223 - 1.616065932e-11i
96 0.3491220699 - 4.757343747e-11i
97 1.290450179 + 7.702233528e-12i
98 -0.03749712641 + 2.843140132e-11i
99 -0.6550919896 + 4.930356221e-11i
100 0.1000001041 + 1.091422810e-10i
101 0.5037900316 + 1.253311538e-11i
102 -2.432275065 + 6.129362475e-12i
103 -0.1942778971 - 2.330362272e-11i
104 0.1376348510 + 2.120550459e-11i
105 -0.8594798691 - 2.036655450e-11i
106 -1.273013797 - 6.747801029e-11i
107 -0.2030888267 - 2.520496155e-11i
108 -1.050655259 - 2.920066388e-11i
109 0.3709620600 + 1.230478283e-11i
110 0.3981331435 - 1.074137635e-10i
111 0.4260851494 + 3.408926785e-11i
112 -0.2432810976 - 3.364784266e-11i
113 -1.710487914 - 4.822398494e-12i
114 1.620165456 + 4.361402950e-11i
115 0.03911930925 - 7.385617453e-11i
116 -0.1982735182 + 3.584176105e-12i
117 -0.2025570400 - 7.854903128e-11i
118 0.8141252971 + 1.385744264e-10i
119 1.694898411 + 1.237423553e-11i
120 0.3122644448 + 1.477223582e-10i
121 0.5851009185 + 3.020483965e-11i
122 0.1247694539 - 4.164425700e-11i
123 1.383816700 - 1.315575470e-12i
124 0.2360051851 - 4.008040399e-11i
125 0.08944268764 - 5.021791499e-11i
126 0.3580364088 - 8.033973483e-13i
127 0.06741273709 + 1.343938537e-11i
128 0.08838837102 + 2.900342512e-11i
129 1.010463771 + 3.951559103e-11i
130 0.1231043289 + 4.143082598e-12i
131 -0.9073808099 + 3.204496723e-11i
132 1.243228129 + 3.383554224e-11i
133 -1.128990610 + 3.660529387e-11i
134 0.2879296502 + 2.811387398e-11i
135 -0.9397346057 - 3.674101412e-11i
136 -0.6157868039 - 8.087938799e-11i
137 -0.2542319698 - 3.039836030e-11i
138 0.1221557106 - 8.432556465e-11i
139 0.06002101070 - 2.370087525e-11i
140 -0.2175972160 + 4.958500415e-12i
141 -1.396402807 - 6.965376703e-12i
142 -0.8080188048 + 5.422978196e-12i
143 0.4901193347 + 2.570603669e-11i
144 -0.1300810126 - 2.221355065e-12i
145 -0.1773411654 + 5.615990179e-11i
146 0.2702694676 + 1.995791276e-11i
147 -0.1047287014 - 9.950473790e-12i
148 0.1078733420 + 3.645519487e-11i
149 -1.256493996 - 3.506102351e-11i
150 0.2792976765 - 2.650457273e-11i
151 1.130240717 - 1.010267546e-11i
152 0.4101824301 + 3.391369541e-11i
153 0.9062523992 - 4.240521237e-11i
154 -0.8663269361 - 5.420481182e-11i
155 0.2110894266 - 5.386933826e-11i
156 0.3844109539 + 1.369176376e-11i
157 0.9947405719 + 1.359808632e-11i
158 -1.029066586 - 4.101113356e-11i
159 -3.555497996 + 4.596072214e-11i
160 0.07905694620 + 5.559406046e-12i
161 -0.08512261267 + 1.526146845e-11i
162 0.007037982095 + 2.675998168e-11i
163 1.208496585 + 1.254674675e-11i
164 0.3503452068 - 2.632380056e-11i
165 1.111977013 - 1.240572033e-11i
166 0.6396910462 + 1.402931450e-12i
167 -0.4537985681 - 7.545735506e-11i
168 -0.6794785283 - 3.930427887e-11i
169 -0.8484532247 - 7.532558782e-12i
170 -0.5507764089 - 7.936886723e-12i
171 -0.6036647766 + 4.159262493e-11i
172 0.2558222999 + 1.435756871e-11i
173 -0.8081955958 + 2.075847307e-11i
174 -0.5537732956 + 7.240406770e-11i
175 -0.1946248760 - 3.943594171e-12i
176 0.3147520053 + 3.411432056e-11i
177 2.273832930 - 1.839719271e-11i
178 0.5834216714 + 1.696319508e-11i
179 0.4210354454 - 2.858143294e-11i
180 -0.1163480000 - 2.166980950e-11i
181 0.2717595066 - 2.648366431e-11i
182 -0.2678716458 - 2.753636605e-11i
183 0.3484782631 - 2.542509896e-11i
184 0.03092650375 - 6.192925100e-11i
185 0.09648488476 + 6.719638588e-11i
186 0.6591570880 - 7.017567500e-11i
187 -2.192824014 - 1.634321913e-12i
188 -0.3535317043 - 9.084122608e-12i
189 2.044836341 + 2.295233037e-11i
190 0.3668782724 + 3.459139575e-12i
191 -0.7156417343 + 7.202890193e-12i
192 0.2468667347 + 1.186012711e-10i
193 -0.1857029446 + 4.273754077e-11i
194 0.9124860570 - 1.850053951e-11i
195 0.3438276088 + 2.565214138e-11i
196 -0.02651444796 + 4.476401270e-11i
197 1.268344181 + 3.748595836e-11i
198 -0.4632200156 - 7.253373400e-12i
199 0.4924195047 + 1.956295374e-11i
200 0.07071063611 - 5.138191003e-11i
201 0.8041807731 - 6.562797843e-11i
202 0.3562333308 + 5.649262163e-12i
203 0.3858895712 - 5.346712262e-12i
204 -1.719878167 + 3.253957252e-11i
205 0.3133582911 - 5.046004582e-12i
206 -0.1373751561 + 4.835373885e-11i
207 -0.04551459355 - 6.300256024e-12i
208 0.09732245162 - 7.919476159e-11i
209 1.460664390 - 3.623252312e-11i
210 -0.6077440072 + 2.654929261e-11i
211 0.7417493201 + 1.948620007e-12i
212 -0.9001566452 - 5.510352258e-12i
213 -2.256777904 + 4.364814893e-11i
214 -0.1436054359 + 5.269313136e-11i
215 0.2288144155 + 2.033925775e-11i
216 -0.7429254260 - 1.614908707e-12i
217 -0.4593247723 + 6.827509581e-11i
218 0.2623098215 + 6.515497016e-11i
219 0.7548563594 - 2.182945726e-11i
220 0.2815226940 - 2.543987665e-11i
221 -0.6780296569 - 2.225440864e-11i
222 0.3012877075 + 1.315207426e-11i
223 -1.867195524 + 9.000007960e-11i
224 -0.1720257109 - 1.624061294e-11i
225 -0.1040648143 - 1.458308691e-11i
226 -1.209497574 + 6.255753404e-12i
227 1.853432009 - 2.956380034e-11i
228 1.145629956 - 9.102634129e-12i
229 -1.092869435 - 1.598112779e-11i
230 0.02766155816 + 4.332292538e-12i
231 -2.419631147 - 6.712885045e-11i
232 -0.1402006389 - 1.068399849e-10i
233 -0.4154495494 - 3.356882231e-11i
234 -0.1432294532 - 4.368602699e-11i
235 -0.3162083733 - 2.041914518e-11i
236 0.5756734707 + 3.379370494e-11i
237 -2.874159078 + 1.001199114e-10i
238 1.198474172 + 5.632309005e-11i
239 -0.6194736644 - 1.057621683e-11i
240 0.2208043755 + 1.751417065e-10i
241 1.234745130 + 5.584992688e-11i
242 0.4137288203 + 2.783946197e-11i
243 2.103727806 - 4.476005814e-11i
244 0.08822531777 - 2.053390815e-11i
245 -0.02371532901 - 5.329106996e-11i
246 0.9785061089 - 7.481446381e-11i
247 0.4516430625 - 1.016387605e-11i
248 0.1668808816 - 1.693289247e-11i
249 1.786642395 + 2.945846937e-11i
250 0.06324550405 - 7.383092754e-11i
251 0.6630691940 + 5.098197663e-11i
252 0.2531699689 - 1.053028145e-11i
253 0.1101299163 + 3.375196561e-11i
254 0.04766803653 + 4.909071115e-11i
255 -1.538305828 + 2.256289482e-13i
256 0.06250002213 + 3.274554129e-11i
257 -1.988605610 - 3.321846142e-11i
258 0.7145057917 + 4.303984554e-11i
259 -0.2099482912 + 7.552056701e-12i
260 0.08704791319 + 1.228903568e-11i
261 0.2063329425 - 6.493040196e-12i
262 -0.6416150915 + 7.678531000e-11i
263 1.409258484 - 3.969614872e-12i
264 0.8790949812 - 3.812155646e-11i
265 -0.8051245893 - 2.721749546e-11i
266 -0.7983169786 - 7.015342736e-11i
267 1.629483246 + 9.317355538e-12i
268 0.2035969645 - 2.448245673e-11i
269 -1.083792935 - 9.415405937e-11i
270 -0.6644927158 - 1.296394422e-11i
271 -0.06100922033 - 2.903003340e-12i
272 -0.4354269627 + 2.237679009e-11i
273 -0.7481592423 + 2.512313130e-11i
274 -0.1797691258 - 2.081272826e-11i
275 0.2518015769 - 4.676023610e-12i
276 0.08637718117 - 1.438705193e-11i
277 1.723459517 - 1.809935938e-11i
278 0.04244121946 - 4.403180770e-11i
279 -0.2455983430 + 2.399007764e-11i
280 -0.1538644577 + 3.684723200e-11i
281 -0.7029596154 + 2.385087763e-11i
282 -0.9874058940 - 7.223358348e-12i
283 -0.6912222762 - 3.783071771e-11i
284 -0.5713555584 + 2.421982746e-11i
285 1.024682621 + 3.191438801e-11i
286 0.3465666572 - 2.808343675e-11i
287 -0.6818589578 + 5.913496000e-13i
288 -0.09198113061 + 3.097455294e-11i
289 2.033546455 - 1.508733269e-11i
290 -0.1253991390 + 3.980791831e-11i
291 2.548552654 + 4.449598000e-11i
292 0.1911093991 + 2.384825394e-11i
293 0.2505379612 + 1.042730420e-11i
294 -0.07405435331 + 2.088281919e-11i
295 0.5148980038 + 2.414871566e-11i
296 0.07627799022 + 3.873904298e-11i
297 -2.645566401 - 3.558834655e-11i
298 -0.8884754200 - 1.826776122e-11i
299 0.03405255393 - 2.375852997e-11i
300 0.1974932202 - 8.819381279e-11i
301 -0.4978938178 - 3.057566206e-11i
302 0.7992008553 - 3.453824104e-11i
303 0.9949514764 - 3.606600951e-11i
304 0.2900427431 - 8.401622788e-12i
305 0.07891116419 + 1.662301571e-11i
306 0.6408172703 + 4.498664145e-11i
307 0.9362025059 + 3.156159735e-11i
308 -0.6125856177 - 2.186069166e-12i
309 -0.3836857606 + 4.451273699e-11i
310 0.1492628665 + 4.820562778e-11i
311 -0.6709878380 - 3.082613771e-11i
312 0.2718195945 + 3.090198896e-11i
313 0.7207093556 + 3.862211254e-11i
314 0.7033877883 - 2.642490125e-11i
315 0.2264421113 + 7.942543238e-12i
316 -0.7276599122 + 2.669386098e-11i
317 -0.5932424939 + 4.366902684e-11i
318 -2.514116744 + 8.738057210e-12i
319 -0.4992558824 - 3.721445296e-11i
320 0.05590165056 - 6.350722389e-11i
321 -0.4010869150 - 5.808472288e-11i
322 -0.06019084657 - 6.227845559e-11i
323 -2.020679012 - 1.839705924e-11i
324 0.004976592151 - 5.766498552e-12i
325 0.07785793814 - 1.021140302e-10i
326 0.8545361186 - 2.439534830e-11i
327 0.7326251912 - 8.641851934e-12i
328 0.2477314939 + 1.060230673e-11i
329 0.6880607099 + 1.189835683e-10i
330 0.7862865596 + 8.623843018e-11i
331 -1.529449305 + 4.566996522e-11i
332 0.4523299445 + 9.178557103e-11i
333 -0.1122581606 - 7.921563824e-12i
334 -0.3208840321 - 2.136359733e-11i
335 0.1821027170 + 3.406025364e-11i
336 -0.4804638246 + 1.319495492e-11i
337 -0.9644137302 - 7.097582165e-12i
338 -0.5999470427 - 1.753050478e-11i
339 -3.378098995 - 2.795180651e-11i
340 -0.3894577408 - 1.498265065e-11i
341 0.5942648082 - 7.803760236e-11i
342 -0.4268554991 - 3.335319481e-11i
343 1.024728186 + 3.341059009e-11i
344 0.1808936458 - 1.967357643e-11i
345 0.07725807472 - 2.108793321e-11i
346 -0.5714805972 + 9.965311893e-12i
347 -0.2425534335 - 3.384699396e-11i
348 -0.3915769197 - 1.095759783e-11i
349 0.5656712232 + 2.136188749e-11i
350 -0.1376205166 + 6.841861729e-11i
351 -0.8180192714 + 6.587893769e-11i
352 0.2225632238 - 5.534589597e-11i
353 1.720172531 - 7.685954664e-11i
354 1.607842705 + 2.159969940e-11i
355 -0.5110359521 + 1.742140129e-11i
356 0.4125414266 + 2.983792020e-11i
357 3.347310817 + 1.045675983e-10i
358 0.2977171002 + 5.944893559e-11i
359 1.282279661 - 5.109803996e-12i
360 -0.08227046681 - 1.934849647e-11i
361 0.3459967417 + 3.668426167e-11i
362 0.1921630443 + 4.448414942e-11i
363 1.155534979 - 2.926814757e-11i
364 -0.1894138431 - 3.961952888e-12i
365 0.1709334571 + 4.826890902e-11i
366 0.2464113027 - 5.756843672e-11i
367 0.3978033047 - 3.781719617e-11i
368 0.02186837732 + 7.069836777e-13i
369 -0.3645860940 - 2.148908315e-11i
370 0.06822506104 - 9.981229626e-12i
371 1.751928682 + 7.939505494e-12i
372 0.4660945510 + 5.490906418e-11i
373 -1.051053966 - 8.252423474e-12i
374 -1.550560738 - 1.195200734e-11i
375 0.1766433508 - 4.230201851e-11i
376 -0.2499846496 + 1.728827590e-11i
377 -0.1543718541 - 3.668590370e-11i
378 1.445917647 + 1.173177565e-11i
379 -1.453753488 + 2.900677994e-11i
380 0.2594220936 - 3.584707904e-11i
381 0.1331355779 - 1.838158513e-11i
382 -0.5060351352 + 5.684281679e-12i
383 0.3763068133 + 9.731339759e-11i
384 0.1745610477 - 3.955216321e-13i
385 -0.5479132188 + 2.020529079e-11i
386 -0.1313118522 - 1.212286679e-11i
387 -0.2662209197 + 3.436904322e-11i
388 0.6452250637 - 4.628781405e-11i
389 -1.601991999 - 2.875234371e-12i
390 0.2431228608 + 3.951828336e-11i
391 -0.1523533897 - 6.752021818e-11i
392 -0.01874863100 - 4.116975974e-11i
393 -1.792016327 + 1.403528523e-11i
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