Properties

Level 10
Symmetry odd
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 13.8721865958$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.835362067
4 0.5
5 0.447213595
6 -0.590690182
7 1.442301480
8 -0.353553390
9 -0.302170215
10 -0.316227766
11 0.972345870
12 0.417681033
13 1.762608323
14 -1.019861157
15 0.373585273
16 0.250000000
17 1.193182237
18 0.213666608
19 -1.681027127
20 0.223606797
21 1.204843947
22 -0.687552358
23 -0.307376327
24 -0.295345091
25 0.200000000
26 -1.246352298
27 -1.087783603
28 0.721150740
29 -0.428235328
30 -0.264164680
31 -0.794710950
32 -0.176776695
33 0.812260856
34 -0.843707251
35 0.645016830
36 -0.151085107
37 1.188805294
38 1.188665680
39 1.472416134
40 -0.158113883
41 -0.584888379
42 -0.851953325
43 1.028181167
44 0.486172935
45 -0.135134628
46 0.217347885
47 1.142440765
48 0.208840516
49 1.080233560
50 -0.141421356
51 0.996739181
52 0.881304161
53 -0.873143217
54 0.769179162
55 0.434846292
56 -0.509930578
57 -1.404266297
58 0.302808104
59 -0.383693084
60 0.186792636
61 0.499472344
62 0.561945502
63 -0.435820549
64 0.125000000
65 0.788262405
66 -0.574355159
67 1.227128997
68 0.596591118
69 -0.256770524
70 -0.456095775
71 -0.197686541
72 0.106833304
73 0.509624246
74 -0.840612285
75 0.167072413
76 -0.840513563
77 1.402415887
78 -1.041155433
79 -0.478993592
80 0.111803398
81 -0.606522945
82 0.413578539
83 0.157741733
84 0.602421973
85 0.533607318
86 -0.727033875
87 -0.357731548
88 -0.343776179
89 0.742093672
90 0.0955546121
91 2.542212596
92 -0.153688163
93 -0.663871385
94 -0.807827612
95 -0.751778185
96 -0.147672545
97 0.718567615
98 -0.763840475
99 -0.293813950
100 0.100000000
101 0.831541917
102 -0.704801034
103 -0.123971439
104 -0.623176149
105 0.538822593
106 0.617405490
107 0.711436551
108 -0.543891801
109 -1.656141352
110 -0.307482762
111 0.993082886
112 0.360575370
113 -0.433977283
114 0.992966221
115 -0.137462872
116 -0.214117664
117 -0.532609119
118 0.271311982
119 1.720928420
120 -0.132082340
121 -0.0545442678
122 -0.353180281
123 -0.488591996
124 -0.397355475
125 0.0894427190
126 0.308171665
127 1.602765944
128 -0.0883883476
129 0.858919394
130 -0.557385692
131 -1.600017056
132 0.406130428
133 -2.424570122
134 -0.867711235
135 -0.486471616
136 -0.421853625
137 0.170757125
138 0.181564178
139 0.849195050
140 0.322508415
141 0.954253468
142 0.139785493
143 1.714054960
144 -0.0755425538
145 -0.191512660
146 -0.360358760
147 0.902834094
148 0.594402647
149 0.148164149
150 -0.118138036
151 -0.950858169
152 0.594332840
153 -0.365672657
154 -0.991657784
155 -0.355405541
156 0.736208067
157 -0.0864658244
158 0.338699617
159 -0.749166824
160 -0.0790569415
161 -0.464869640
162 0.428876487
163 -0.716677050
164 -0.292444189
165 0.363254098
166 -0.111540249
167 -1.612000151
168 -0.425976662
169 2.163463616