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

$R= 22.3041595536$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.334248997
4 0.5
5 0.447213595
6 0.943456513
7 0.577841096
8 0.353553390
9 0.780220386
10 0.316227766
11 1.634075763
12 0.667124498
13 -0.0594466849
14 0.408595357
15 0.596694291
16 0.250000000
17 1.180106958
18 0.551699126
19 -0.851025273
20 0.223606797
21 0.770983903
22 1.155466053
23 0.511672394
24 0.471728256
25 0.200000000
26 -0.0420351540
27 -0.293240728
28 0.288920548
29 -1.803195325
30 0.421926579
31 0.291724139
32 0.176776695
33 2.180263949
34 0.834461632
35 0.258418394
36 0.390110193
37 0.785008071
38 -0.601765741
39 -0.0793166797
40 0.158113883
41 -0.623190680
42 0.545167946
43 1.569604425
44 0.817037881
45 0.348925164
46 0.361807019
47 -1.097751398
48 0.333562249
49 -0.666099667
50 0.141421356
51 1.574556525
52 -0.0297233424
53 0.882909349
54 -0.207352507
55 0.730780897
56 0.204297678
57 -1.135479617
58 -1.275051642
59 1.205483708
60 0.298347145
61 0.511977237
62 0.206280116
63 0.450843403
64 0.125000000
65 -0.0265853657
66 1.541679423
67 0.643610249
68 0.590053479
69 0.682698379
70 0.182729399
71 -1.327089929
72 0.275849563
73 -0.403483720
74 0.555084530
75 0.266849799
76 -0.425512636
77 0.944236130
78 -0.0560853621
79 -1.509626820
80 0.111803398
81 -1.171476534
82 -0.440662356
83 -0.595804248
84 0.385491951
85 0.527759875
86 1.109877932
87 -2.405911555
88 0.577733026
89 -0.151129876
90 0.246727349
91 -0.0343507376
92 0.255836197
93 0.389232640
94 -0.776227457
95 -0.380590072
96 0.235864128
97 -1.447792346
98 -0.471003591
99 1.274939224
100 0.100000000
101 0.999117805
102 1.113379596
103 0.581568426
104 -0.0210175770
105 0.344794483
106 0.624311188
107 1.308388635
108 -0.146620364
109 -0.880609761
110 0.516740128
111 1.047396233
112 0.144460274
113 1.882560275
114 -0.802905337
115 0.228826851
116 -0.901597662
117 -0.0463815156
118 0.852405704
119 0.681914298
120 0.210963289
121 1.670203600
122 0.362022576
123 -0.831491543
124 0.145862069
125 0.0894427190
126 0.318794428
127 -0.997823724
128 0.0883883476
129 2.094243147
130 -0.0187986923
131 0.594069553
132 1.090131974
133 -0.491757401
134 0.455101171
135 -0.131141240
136 0.417230816
137 0.350101755
138 0.482740653
139 1.187614015
140 0.129209197
141 -1.464673674
142 -0.938394288
143 -0.0971405422
144 0.195055096
145 -0.806413465
146 -0.285306075
147 -0.888742172
148 0.392504035
149 -0.124938329
150 0.188691302
151 1.514265666
152 -0.300882870
153 0.920744052
154 0.667675771
155 0.130463001
156 -0.0396583398
157 1.561266199
158 -1.067467361
159 1.178017580
160 0.0790569415
161 0.295668895
162 -0.828359001
163 -0.935007926
164 -0.311595340
165 0.975043679
166 -0.421297224
167 -0.853604065
168 0.272583973
169 -0.996532718
170 0.373182587
171 -0.664089954
172 0.784802212
173 0.162612943
174 -1.701236375
175 0.115568219
176 0.408518940
177 1.608357153
178 -0.106864960
179 0.274583002
180 0.174462582
181 -1.603623361
182 -0.0242896395
183 0.681704066
184 0.180903509
185 0.351066282
186 0.275229039
187 1.928724787
188 -0.548875699
189 -0.174853893
190 -0.269117820
191 0.280607634
192 0.166781124
193 -1.889904570
194 -1.023743785
195 -0.0354714975
196 -0.333049833
197 1.571035908
198 0.901518171
199 -1.217675636
200 0.0707106781
201 0.872813344
202 0.706482975
203 -0.985687157
204 0.787278262
205 -0.278699344
206 0.411230978
207 0.381479147
208 -0.0148616712
209 -1.382924254
210 0.243806517