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

$R= 19.1674767534$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.102003939
4 0.5
5 -0.447213595
6 0.779234458
7 -0.528289596
8 0.353553390
9 0.214412682
10 -0.316227766
11 -0.216692742
12 0.551001969
13 -0.217811951
14 -0.373557156
15 -0.492831144
16 0.250000000
17 -0.165945378
18 0.151612661
19 1.329556326
20 -0.223606797
21 -0.582177216
22 -0.153224907
23 -1.328768310
24 0.389617229
25 0.200000000
26 -0.154016308
27 -0.865720318
28 -0.264144798
29 -0.644519342
30 -0.348484243
31 -0.664714029
32 0.176776695
33 -0.238796256
34 -0.117341102
35 0.236258290
36 0.107206341
37 -1.008226439
38 0.940138294
39 -0.240029628
40 -0.158113883
41 -0.912519402
42 -0.411661457
43 -1.213931586
44 -0.108346371
45 -0.0958882667
46 -0.939581083
47 0.0864336626
48 0.275500984
49 -0.720910101
50 0.141421356
51 -0.182872461
52 -0.108905975
53 -0.464373345
54 -0.612156707
55 0.0969079406
56 -0.186778578
57 1.465176309
58 -0.455743998
59 1.900718429
60 -0.246415572
61 1.753473755
62 -0.470023797
63 -0.113271989
64 0.125000000
65 0.0974084661
66 -0.168854452
67 -1.068220761
68 -0.0829726894
69 -1.464307913
70 0.167059839
71 0.727487820
72 0.0758063309
73 -0.358233791
74 -0.712923752
75 0.220400787
76 0.664778163
77 0.114476521
78 -0.169726578
79 -1.300883805
80 -0.111803398
81 -1.168439884
82 -0.645248657
83 -1.308401684
84 -0.291088608
85 0.0742130295
86 -0.858379256
87 -0.710262854
88 -0.0766124539
89 0.606305122
90 -0.0678032436
91 0.115067788
92 -0.664384155
93 -0.732517478
94 0.0611178290
95 -0.594595665
96 0.194808614
97 -0.651510785
98 -0.509760421
99 -0.0464616725
100 0.100000000
101 0.784913338
102 -0.129310357
103 0.134603971
104 -0.0770081540
105 0.260357566
106 -0.328361541
107 -1.722815995
108 -0.432860159
109 0.211245383
110 0.0685242619
111 -1.111069496
112 -0.132072399
113 -0.656219196
114 1.036036104
115 0.594243253
116 -0.322259671
117 -0.0467016023
118 1.344010890
119 0.0876672325
120 -0.174242121
121 -0.953044284
122 1.239893182
123 -1.005599845
124 -0.332357014
125 -0.0894427190
126 -0.0800953920
127 1.687061169
128 0.0883883476
129 -1.337757344
130 0.0688781869
131 0.355160803
132 -0.119398128
133 -0.702391985
134 -0.755346144
135 0.387161896
136 -0.0586705513
137 0.975814994
138 -1.035422055
139 -0.385704929
140 0.118129145
141 0.0952517619
142 0.514411571
143 0.0472007624
144 0.0536031706
145 0.288237812
146 -0.253309542
147 -0.794425577
148 -0.504113219
149 -0.131614746
150 0.155846891
151 1.698864807
152 0.470069147
153 -0.0354742138
154 0.0809471248
155 0.297269150
156 -0.120014814
157 1.876331329
158 -0.919863760
159 -0.511621688
160 -0.0790569415
161 0.702171213
162 -0.826211765
163 -1.520816998
164 -0.456259701
165 0.106792932
166 -0.925179703
167 0.520111729
168 -0.205830728
169 -0.955063947
170 0.0524765364
171 0.287443090
172 -0.606965793
173 1.326556569
174 -0.502231681
175 -0.105657919
176 -0.0541731857
177 2.106692473
178 0.428722463
179 0.733789435
180 -0.0479441333
181 -1.475901499
182 0.0813652133
183 1.953079445
184 -0.469790541
185 0.450892571
186 -0.517968076
187 0.144526109
188 0.0432168313
189 0.681026787
190 -0.420442626