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

$R= 24.293655303$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.186283654
4 0.5
5 0.447213595
6 -0.838829216
7 0.418169250
8 -0.353553390
9 0.407268907
10 -0.316227766
11 -0.488892412
12 0.593141827
13 -0.0245650013
14 -0.295690312
15 0.530522178
16 0.250000000
17 -0.461788734
18 -0.287982606
19 -0.450445062
20 0.223606797
21 0.496067346
22 0.345699140
23 0.865988830
24 -0.419414608
25 0.200000000
26 0.0173700790
27 -0.703147205
28 0.209084625
29 0.513582208
30 -0.375135829
31 -0.470133664
32 -0.176776695
33 -0.579965078
34 0.326533945
35 0.187010974
36 0.203634453
37 0.0251162015
38 0.318512758
39 -0.0291410595
40 -0.158113883
41 -1.470337370
42 -0.350772584
43 -0.842027205
44 -0.244446206
45 0.182136192
46 -0.612346574
47 -0.525167890
48 0.296570913
49 -0.825134477
50 -0.141421356
51 -0.547812427
52 -0.0122825006
53 -1.624536257
54 0.497200157
55 -0.218639333
56 -0.147845156
57 -0.534355615
58 -0.363157462
59 -0.406536710
60 0.265261089
61 0.743175149
62 0.332434702
63 0.170307334
64 0.125000000
65 -0.0109858025
66 0.410097239
67 0.191151222
68 -0.230894367
69 1.027308394
70 -0.132236727
71 1.826760778
72 -0.143991303
73 1.766029608
74 -0.0177598364
75 0.237256730
76 -0.225222531
77 -0.204439773
78 0.0206058408
79 -1.783565589
80 0.111803398
81 -1.241400944
82 1.039685525
83 -1.075964725
84 0.248033673
85 -0.206518200
86 0.595403147
87 0.609254178
88 0.172849570
89 0.465877395
90 -0.128789736
91 -0.0102723282
92 0.432994415
93 -0.557711881
94 0.371349776
95 -0.201445156
96 -0.209707304
97 -0.775247605
98 0.583458184
99 -0.199110679
100 0.100000000
101 1.847916981
102 0.387361881
103 1.043886823
104 0.00868503951
105 0.221848061
106 1.148720604
107 0.209566174
108 -0.351573602
109 -1.015510607
110 0.154601355
111 0.0297949393
112 0.104542312
113 -0.923386484
114 0.377846479
115 0.387281978
116 0.256791104
117 -0.0100045612
118 0.287464864
119 -0.193105848
120 -0.187567914
121 -0.760984208
122 -0.525504188
123 -1.744237188
124 -0.235066832
125 0.0894427190
126 -0.120425470
127 -0.769002442
128 -0.0883883476
129 -0.998883109
130 0.00776813549
131 1.145800098
132 -0.289982539
133 -0.188362275
134 -0.135164325
135 -0.314456990
136 0.163266972
137 -1.825848567
138 -0.726416732
139 0.179061602
140 0.0935054870
141 -0.622998083
142 -1.291714933
143 0.0120096469
144 0.101817226
145 0.229680945
146 -1.248771511
147 -0.978843562
148 0.0125581007
149 -0.452591936
150 -0.167765843
151 -0.840801797
152 0.159256379
153 -0.188072251
154 0.144560750
155 -0.210250166
156 -0.0145705297
157 1.078994115
158 1.261171322
159 -1.927160678
160 -0.0790569415
161 0.362129812
162 0.877803026
163 -1.773263338
164 -0.735168685
165 -0.259368267
166 0.760821953
167 0.764480890
168 -0.175386292
169 -0.999398250
170 0.146030419
171 -0.183456579
172 -0.421013602
173 -0.295470740
174 -0.430807761
175 0.0836338501
176 -0.122223103
177 -0.482268837
178 -0.329425065
179 -0.180788301
180 0.0910680963
181 -0.0375402463
182 0.00726363293
183 0.881600369
184 -0.306173287
185 0.0112323068
186 0.394361853
187 0.225761578
188 -0.262583945
189 -0.293977023
190 0.142443235
191 0.791911440
192 0.148285456
193 0.268196762
194 0.548182839
195 -0.0130322780
196 -0.412567238
197 -0.166879045
198 0.140792511
199 -0.182029014
200 -0.0707106781
201 0.225801841
202 -1.306674628
203 0.209904745
204 -0.273906213
205 -0.657554862
206 -0.738139451
207 0.344096120
208 -0.00614125033
209 0.223688124
210 -0.156870268