Properties

Level 10
Symmetry odd
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

$R= 18.570584434$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.201736403
4 0.5
5 -0.447213595
6 0.849755960
7 -1.714563336
8 -0.353553390
9 0.444170383
10 0.316227766
11 0.649833071
12 -0.600868201
13 0.161306126
14 1.212379361
15 0.537432857
16 0.250000000
17 -1.177537822
18 -0.314075889
19 -1.469469652
20 -0.223606797
21 2.060453177
22 -0.459501371
23 0.340103670
24 0.424877980
25 0.200000000
26 -0.114060656
27 0.667960684
28 -0.857281668
29 0.500773889
30 -0.380022418
31 1.903520188
32 -0.176776695
33 -0.780928058
34 0.832644979
35 0.766776034
36 0.222085191
37 1.096648315
38 1.039071956
39 -0.193847444
40 0.158113883
41 0.101068201
42 -1.456960413
43 -0.272612608
44 0.324916535
45 -0.198639034
46 -0.240489611
47 0.819045242
48 -0.300434100
49 1.939727434
50 -0.141421356
51 1.415090067
52 0.0806530634
53 -1.088177599
54 -0.472319529
55 -0.290614184
56 0.606189680
57 1.765915175
58 -0.354100613
59 0.272841683
60 0.268716428
61 1.736415638
62 -1.345992033
63 -0.761558254
64 0.125000000
65 -0.0721382929
66 0.552199525
67 -0.913924909
68 -0.588768911
69 -0.408714961
70 -0.542192533
71 1.199314281
72 -0.157037944
73 -1.261074071
74 -0.775447460
75 -0.240347280
76 -0.734734826
77 -1.114179959
78 0.137070842
79 -0.769354921
80 -0.111803398
81 -1.246883053
82 -0.0714660109
83 -0.0276378945
84 1.030226588
85 0.526610923
86 0.192766224
87 -0.601798213
88 -0.229750685
89 -1.754072634
90 0.140459007
91 -0.276569571
92 0.170051835
93 -2.287529505
94 -0.579152445
95 0.657166806
96 0.212438990
97 0.858141132
98 -1.371594422
99 0.288636603
100 0.100000000
101 -0.378817660
102 -1.000619782
103 1.523628064
104 -0.0570303280
105 -0.921462673
106 0.769457759
107 0.442227129
108 0.333980342
109 1.560242266
110 0.205495260
111 -1.317882205
112 -0.428640834
113 -1.365384393
114 -1.248690595
115 -0.152098985
116 0.250386944
117 0.0716473835
118 -0.192928204
119 2.018963141
120 -0.190011209
121 -0.577717011
122 -1.227831272
123 -0.121457357
124 0.951760094
125 -0.0894427190
126 0.538503005
127 -0.952933030
128 -0.0883883476
129 0.327608279
130 0.0510094761
131 0.0574248152
132 -0.390464029
133 2.519498462
134 0.646242500
135 -0.298721099
136 0.416322489
137 -1.251015238
138 0.289005121
139 -0.895879893
140 0.383388017
141 -0.984279290
142 -0.848043260
143 0.104823923
144 0.111042595
145 -0.223952891
146 0.891714027
147 -2.331048193
148 0.548324157
149 0.556117422
150 0.169951192
151 0.230324483
152 0.519535978
153 -0.523042049
154 0.787844204
155 -0.851280107
156 -0.0969237223
157 0.466465366
158 0.544016082
159 1.307501812
160 0.0790569415
161 -0.582949576
162 0.881679462
163 -0.999722433
164 0.0505341009
165 0.349241644
166 0.0195429426
167 0.238995432
168 -0.728480206
169 -0.975259430
170 -0.372370155
171 -0.653249376
172 -0.136306304
173 0.651865265
174 0.425535597
175 -0.342912667
176 0.162458267
177 -0.335493351
178 1.240316654
179 1.776025841
180 -0.0993195170
181 -1.145550888
182 0.195564219
183 -2.104829158
184 -0.120244805
185 -0.490436036
186 1.617527625
187 -0.849683277
188 0.409522621
189 -1.135360930
190 -0.464687105