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

$R= 22.3042312641$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.902537950
4 0.5
5 -0.447213595
6 1.345297486
7 -1.019354700
8 -0.353553390
9 2.619650652
10 0.316227766
11 -0.364912904
12 -0.951268975
13 -1.794570474
14 0.720792621
15 0.850840837
16 0.250000000
17 -0.458324110
18 -1.852372740
19 -0.275660989
20 -0.223606797
21 1.939361003
22 0.258032389
23 -1.317524785
24 0.672648743
25 0.200000000
26 1.268952951
27 -3.081446831
28 -0.509677350
29 -0.536067964
30 -0.601635325
31 0.680656219
32 -0.176776695
33 0.694260649
34 0.324084086
35 0.455869280
36 1.309825326
37 -0.526899671
38 0.194921755
39 3.414238431
40 0.158113883
41 0.503809548
42 -1.371335316
43 0.916823481
44 -0.182456452
45 -1.171543387
46 0.931630710
47 1.326159285
48 -0.475634487
49 0.0390840062
50 -0.141421356
51 0.871979012
52 -0.897285237
53 0.497650202
54 2.178911950
55 0.163194012
56 0.360396310
57 0.524455494
58 0.379057292
59 1.918790414
60 0.425420418
61 -0.665072794
62 -0.481296628
63 -2.670353206
64 0.125000000
65 0.802556314
66 -0.490916413
67 1.069407227
68 -0.229162055
69 2.506640905
70 -0.322348259
71 -1.616307171
72 -0.926186370
73 0.773946161
74 0.372574330
75 -0.380507590
76 -0.137830494
77 0.371975684
78 -2.414231147
79 1.711580551
80 -0.111803398
81 3.242918886
82 -0.356247148
83 -0.239478198
84 0.969680501
85 0.204968773
86 -0.648292101
87 1.019889645
88 0.129016194
89 -0.701849483
90 0.828406273
91 1.829303849
92 -0.658762392
93 -1.294974288
94 -0.937736223
95 0.123279342
96 0.336324371
97 -0.566517334
98 -0.0276365658
99 -0.955944328
100 0.100000000
101 0.486582549
102 -0.616582273
103 0.445281453
104 0.634476475
105 -0.867308607
106 -0.351891832
107 -0.681179982
108 -1.540723415
109 -0.885354326
110 -0.115395592
111 1.002446621
112 -0.254838675
113 0.931690596
114 -0.370846036
115 0.589214996
116 -0.268033982
117 -4.701147709
118 -1.356789713
119 0.467194838
120 -0.300817662
121 -0.866838576
122 0.470277483
123 -0.958516796
124 0.340328109
125 -0.0894427190
126 1.888224860
127 1.566248746
128 -0.0883883476
129 -1.744291450
130 -0.567493012
131 -1.623493315
132 0.347130324
133 0.280996247
134 -0.756185102
135 1.378064916
136 0.162042043
137 -0.0748169680
138 -1.772462782
139 -1.007319692
140 0.227934640
141 -2.523068538
142 1.142901761
143 0.654861925
144 0.654912663
145 0.239736881
146 -0.547262578
147 -0.0743591647
148 -0.263449835
149 0.938542379
150 0.269059497
151 -0.358599939
152 0.0974608775
153 -1.200649030
154 -0.263026529
155 -0.304398715
156 1.707119215
157 0.395799990
158 -1.210270214
159 -0.946801536
160 0.0790569415
161 1.343026298
162 -2.293089935
163 1.505012854
164 0.251904774
165 -0.310482801
166 0.169336658
167 0.830355584
168 -0.685667658
169 2.220462480
170 -0.144934809
171 -0.722046108
172 0.458411740
173 -0.415779558
174 -0.721170884
175 -0.203870940
176 -0.0912282261
177 -3.650510763
178 0.496282529
179 0.981336497
180 -0.585771693
181 -0.414685162
182 -1.293513156
183 1.267395480
184 0.465815355
185 0.235636696
186 0.915685100
187 0.172375044
188 0.663079642
189 3.143915256
190 -0.0871716589
191 0.00149023882
192 -0.237817243
193 -1.016578566
194 0.400588248
195 -1.526893844
196 0.0195420031