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

$R= 18.172577593$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.498023981
4 0.5
5 -0.447213595
6 0.352156134
7 0.314171014
8 -0.353553390
9 -0.751972114
10 0.316227766
11 0.980166353
12 -0.249011990
13 -0.770170399
14 -0.222152454
15 0.222723095
16 0.250000000
17 0.235926187
18 0.531724581
19 0.183292338
20 -0.223606797
21 -0.156464699
22 -0.693082275
23 -0.269042431
24 0.176078067
25 0.200000000
26 0.544592712
27 0.872524127
28 0.157085507
29 -0.588378264
30 -0.157489011
31 -1.540712525
32 -0.176776695
33 -0.488146349
34 -0.166825006
35 -0.140501548
36 -0.375986057
37 0.425069956
38 -0.129607255
39 0.383563328
40 0.158113883
41 -1.317254570
42 0.110637249
43 -0.776070621
44 0.490083176
45 0.336292152
46 0.190241727
47 0.0899904396
48 -0.124505995
49 -0.901296573
50 -0.141421356
51 -0.117496899
52 -0.385085199
53 -1.476446147
54 -0.616967727
55 -0.438343719
56 -0.111076227
57 -0.0912839802
58 0.416046260
59 1.314987430
60 0.111361547
61 -1.207536721
62 1.089448274
63 -0.236247841
64 0.125000000
65 0.344430673
66 0.345171594
67 0.501937487
68 0.117963093
69 0.133989582
70 0.0993495979
71 1.366482143
72 0.265862290
73 0.922548613
74 -0.300569848
75 -0.0996047962
76 0.0916461693
77 0.307939857
78 -0.271220230
79 1.970060309
80 -0.111803398
81 0.317434174
82 0.931439639
83 1.143608482
84 -0.0782323495
85 -0.105509398
86 0.548764798
87 0.293026485
88 -0.346541137
89 -0.00987672221
90 -0.237794461
91 -0.241965215
92 -0.134521215
93 0.767311785
94 -0.0636328501
95 -0.0819708258
96 0.0880390335
97 0.148917349
98 0.637312919
99 -0.737057764
100 0.100000000
101 0.112538104
102 0.0830828541
103 1.468176354
104 0.272296356
105 0.0699731406
106 1.044005082
107 -0.695446676
108 0.436262063
109 -0.883978790
110 0.309955816
111 -0.211695026
112 0.0785427535
113 -1.497829226
114 0.0645475214
115 0.120319433
116 -0.294189132
117 0.579146664
118 -0.929836529
119 0.0741211722
120 -0.0787445055
121 -0.0392739229
122 0.853857404
123 0.656024382
124 -0.770356262
125 -0.0894427190
126 0.167052450
127 1.638593928
128 -0.0883883476
129 0.386501446
130 -0.243549264
131 0.127329628
132 -0.244073174
133 0.0575849258
134 -0.354923400
135 -0.390204652
136 -0.0834125034
137 0.817810708
138 -0.0947449426
139 -0.359995613
140 -0.0702507743
141 -0.0448176849
142 -0.966248790
143 -0.754897264
144 -0.187993028
145 0.263130759
146 -0.652340380
147 0.448874887
148 0.212534978
149 -0.0758932539
150 0.0704312268
151 1.532296173
152 -0.0648036278
153 -0.177385457
154 -0.217746361
155 0.689027587
156 0.191781664
157 0.509558816
158 -1.393043003
159 0.735102808
160 0.0790569415
161 -0.0846293810
162 -0.224459857
163 1.633914642
164 -0.658627285
165 0.218305684
166 -0.808653312
167 -0.955003545
168 0.0553186249
169 -0.409459164
170 0.0746064111
171 -0.135405465
172 -0.388035310
173 1.279882359
174 -0.207201015
175 0.0628342028
176 0.245041588
177 -0.662074267
178 0.00698389725
179 -0.614662082
180 0.168146076
181 -0.00482833801
182 0.171095244
183 0.640056889
184 0.0951208638
185 -0.190097063
186 -0.542571366
187 0.319134921
188 0.0449952198
189 0.147030705
190 0.0579621268