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

$R= 30.2650176797$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.226550670
4 0.5
5 0.447213595
6 0.867302296
7 0.133887811
8 -0.353553390
9 0.504426547
10 -0.316227766
11 -0.106318716
12 -0.613275335
13 0.610721884
14 -0.0946729791
15 -0.548530135
16 0.250000000
17 0.155983011
18 -0.356683432
19 0.882833905
20 0.223606797
21 -0.164220184
22 0.0751786854
23 -0.726253914
24 0.433651148
25 0.200000000
26 -0.431845585
27 0.607845950
28 0.0669439055
29 0.145554244
30 0.387869378
31 -0.780858031
32 -0.176776695
33 0.130405293
34 -0.110296644
35 0.0598764493
36 0.252213273
37 -1.044415784
38 -0.624257841
39 -0.749081336
40 -0.158113883
41 -0.0533611053
42 0.116121206
43 -0.306302172
44 -0.0531593582
45 0.225586409
46 0.513539067
47 -0.130274940
48 -0.306637667
49 -0.982074054
50 -0.141421356
51 -0.191321066
52 0.305360942
53 -0.106106921
54 -0.429811993
55 -0.0475471755
56 -0.0473364895
57 -1.082840518
58 -0.102922393
59 -1.886881663
60 -0.274265067
61 -0.178501430
62 0.552150009
63 0.0675365662
64 0.125000000
65 0.273123129
66 -0.0922104670
67 1.837527655
68 0.0779915055
69 0.890787225
70 -0.0423390433
71 1.629147926
72 -0.178341716
73 0.801638802
74 0.738513483
75 -0.245310134
76 0.441416952
77 -0.0142347802
78 0.529680492
79 -0.307064472
80 0.111803398
81 -1.249980405
82 0.0377319994
83 -0.0122594854
84 -0.0821100922
85 0.0697577232
86 0.216588343
87 -0.178529656
88 0.0375893427
89 1.397511060
90 -0.159513680
91 0.0817682162
92 -0.363126957
93 0.957761942
94 0.0921182940
95 0.394815325
96 0.216825574
97 -0.330516396
98 0.694431223
99 -0.0536299831
100 0.100000000
101 -0.221053357
102 0.135284423
103 -0.638031383
104 -0.215922792
105 -0.0734414991
106 0.0750289236
107 0.235837245
108 0.303922975
109 0.358963411
110 0.0336209302
111 1.281028880
112 0.0334719527
113 0.970921000
114 0.765683873
115 -0.324790624
116 0.0727771223
117 0.308064331
118 1.334226819
119 0.0208842239
120 0.193934689
121 -0.988696330
122 0.126219571
123 0.0654500995
124 -0.390429015
125 0.0894427190
126 -0.0477555639
127 1.678240555
128 -0.0883883476
129 0.375695135
130 -0.193127217
131 1.673356293
132 0.0652026465
133 0.118200699
134 -1.299328266
135 0.271836973
136 -0.0551483224
137 -1.117294451
138 -0.629881687
139 -1.979680880
140 0.0299382246
141 0.159788816
142 -1.151981546
143 -0.0649311669
144 0.126106636
145 0.0650938371
146 -0.566844233
147 1.204563589
148 -0.522207892
149 1.919992194
150 0.173460459
151 0.546895366
152 -0.312128920
153 0.0786819710
154 0.0100655096
155 -0.349210327
156 -0.374540668
157 -0.187235405
158 0.217127370
159 0.130145514
160 -0.0790569415
161 -0.0972365494
162 0.883869621
163 1.251029822
164 -0.0266805526
165 0.0583190200
166 0.00866876532
167 1.295564549
168 0.0580606030
169 -0.627018788
170 -0.0493261591
171 0.445324849
172 -0.153151086
173 0.139797085
174 0.126239530
175 0.0267775622
176 -0.0265796791
177 2.314355954
178 -0.988189547
179 0.322304847
180 0.112793204
181 0.0881667498
182 -0.0578188601
183 0.218941150
184 0.256769533
185 -0.467076938
186 -0.677239964
187 -0.0165840223
188 -0.0651374703
189 0.0813834163
190 -0.279176593
191 -1.192924515
192 -0.153318833
193 0.349196835
194 0.233710385
195 -0.334999357
196 -0.491037027
197 -1.767972717
198 0.0379221247
199 0.169573750
200 -0.0707106781
201 -2.253812769
202 0.156308327
203 0.0194999754
204 -0.0956605334
205 -0.0238638117
206 0.451156318
207 -0.366329471
208 0.152680471
209 -0.0938161147
210 0.0519309820
211 -0.160835033
212 -0.0530534606
213 -1.998252753
214 -0.166762115
215 -0.136982495
216 -0.214905996
217 -0.104399150
218 -0.253825462
219 -0.982799687
220 -0.0237735877
221 0.0957433663
222 -0.905824208
223 -1.628316121
224 -0.0236682447
225 0.100885309
226 -0.686544823
227 0.344279419
228 -0.541420259
229 -0.523867517
230 0.229661652
231 0.0168770749
232 -0.0514611967
233 -0.173764826
234 -0.217834377
235 -0.0582607246
236 -0.943440831
237 0.382866106
238 -0.0147673763
239 -1.529652701
240 -0.137132533
241 -0.767288801
242 0.699113879
243 0.893373729
244 -0.0892507151
245 -0.439196868
246 -0.0462802092
247 0.612220249
248 0.276075004
249 -0.0461143360
250 -0.0632455532
251 -0.0223024306