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

$R= 20.8248391133$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.335812086
4 0.5
5 -0.447213595
6 -0.237455003
7 1.284574847
8 0.353553390
9 -0.887230242
10 -0.316227766
11 -1.566797354
12 -0.167906043
13 0.948010385
14 0.908331585
15 0.150179730
16 0.250000000
17 -0.490007778
18 -0.627366521
19 1.128241612
20 -0.223606797
21 -0.431375759
22 -1.107893033
23 0.837516591
24 -0.118727501
25 0.200000000
26 0.670344572
27 0.633754725
28 0.642287423
29 -0.760208116
30 0.106193105
31 -0.996995580
32 0.176776695
33 0.526149488
34 -0.346487823
35 -0.574479336
36 -0.443615121
37 -0.845781979
38 0.797787295
39 -0.318353345
40 -0.158113883
41 1.616645743
42 -0.305028724
43 0.0827313707
44 -0.783398677
45 0.396781426
46 0.592213661
47 -1.471934069
48 -0.0839530215
49 0.650132539
50 0.141421356
51 0.164550534
52 0.474005192
53 1.500432317
54 0.448132263
55 0.700693078
56 0.454165792
57 -0.378877169
58 -0.537548314
59 1.668301531
60 0.0750898652
61 0.493674676
62 -0.704982335
63 -1.139713653
64 0.125000000
65 -0.423963133
66 0.372043871
67 1.452239401
68 -0.245003889
69 -0.281248194
70 -0.406218234
71 0.112805963
72 -0.313683260
73 -1.461966493
74 -0.598058172
75 -0.0671624172
76 0.564120806
77 -2.012668472
78 -0.225109809
79 0.897560508
80 -0.111803398
81 0.674407746
82 1.143141167
83 -0.0691504475
84 -0.215687879
85 0.219138140
86 0.0584999132
87 0.255287073
88 -0.553946516
89 1.466099826
90 0.280566837
91 1.217790296
92 0.418758295
93 0.334803165
94 -1.040814561
95 -0.504564988
96 -0.0593637508
97 1.385395994
98 0.459713127
99 1.390109996
100 0.100000000
101 0.543781915
102 0.116354798
103 -0.268222913
104 0.335172286
105 0.192917104
106 1.060965866
107 -0.134793692
108 0.316877362
109 0.627414120
110 0.495464827
111 0.284023810
112 0.321143711
113 1.456341637
114 -0.267906616
115 -0.374548806
116 -0.380104058
117 -0.841103483
118 1.179667325
119 -0.629451668
120 0.0530965529
121 1.454853949
122 0.349080711
123 -0.542889178
124 -0.498497790
125 -0.0894427190
126 -0.805899253
127 0.689740099
128 0.0883883476
129 -0.0277821932
130 -0.299787206
131 0.409388162
132 0.263074744
133 1.449310801
134 1.026888328
135 -0.283423729
136 -0.173243911
137 0.372079294
138 -0.198872505
139 0.365554999
140 -0.287239668
141 0.494293283
142 0.0797658618
143 -1.485340078
144 -0.221807560
145 0.339975405
146 -1.033766421
147 -0.218322501
148 -0.422890989
149 -0.739829822
150 -0.0474910006
151 1.782452514
152 0.398893647
153 0.434748024
154 -1.423171525
155 0.445869978
156 -0.159176672
157 0.202829714
158 0.634671121
159 -0.503862213
160 -0.0790569415
161 1.075841120
162 0.476878290
163 0.492865684
164 0.808322871
165 -0.235301204
166 -0.0488967503
167 -0.873420845
168 -0.152514362
169 -0.101285341
170 0.154954065
171 -1.000982119
172 0.0413656853
173 -0.247447508
174 0.180515221
175 0.256914969
176 -0.391699338
177 -0.560334197
178 1.036689129
179 -1.468457863
180 0.198390713
181 -0.894487849
182 0.861107776
183 -0.165049372
184 0.296106830
185 0.378245199
186 0.236741588
187 0.766542174
188 -0.735967034
189 0.811762896
190 -0.356781324
191 -1.377025531
192 -0.0419765107
193 0.576011930
194 0.979622902
195 0.142371944
196 0.325066269
197 0.849641390
198 0.982956205