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

$R= 21.2190521412$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.195167389
4 0.5
5 -0.447213595
6 -0.138004184
7 -0.0864835174
8 -0.353553390
9 -0.961909690
10 0.316227766
11 -1.708479530
12 0.0975836947
13 -0.812751758
14 0.0611530816
15 -0.0872815100
16 0.250000000
17 -0.692606511
18 0.680172864
19 -1.483795639
20 -0.223606797
21 -0.0168787623
22 1.208077461
23 -1.150001324
24 -0.0690020923
25 0.200000000
26 0.574702280
27 -0.382900792
28 -0.0432417587
29 1.378953186
30 0.0617173476
31 -0.932806683
32 -0.176776695
33 -0.333439490
34 0.489746760
35 0.0386766047
36 -0.480954845
37 1.320481099
38 1.049201958
39 -0.158622639
40 0.158113883
41 0.928986663
42 0.0119350873
43 -0.847236438
44 -0.854239765
45 0.430179091
46 0.813173735
47 -1.736598924
48 0.0487918473
49 -0.992520601
50 -0.141421356
51 -0.135174204
52 -0.406375879
53 -1.083679282
54 0.270751747
55 0.764055273
56 0.0305765408
57 -0.289588521
58 -0.975067149
59 0.545076264
60 -0.0436407550
61 0.315224336
62 0.659593931
63 0.0831893334
64 0.125000000
65 0.363473636
66 0.235777324
67 -1.119969675
68 -0.346303255
69 -0.224442756
70 -0.0273484895
71 -1.313006196
72 0.340086432
73 -0.517439076
74 -0.933721139
75 0.0390334779
76 -0.741897819
77 0.147755319
78 0.112163143
79 0.287346171
80 -0.111803398
81 0.887179941
82 -0.656892769
83 -0.846350114
84 -0.00843938117
85 0.309743048
86 0.599086631
87 0.269126693
88 0.604038730
89 -0.764397525
90 -0.304182552
91 0.0702896309
92 -0.575000662
93 -0.182053445
94 1.227960875
95 0.663573583
96 -0.0345010461
97 1.770587104
98 0.701818047
99 1.643403015
100 0.100000000
101 -0.207253194
102 0.0955825968
103 0.891454582
104 0.287351140
105 0.00754841199
106 0.766276969
107 0.0406328397
108 -0.191450396
109 -0.625014433
110 -0.540268665
111 0.257714848
112 -0.0216208793
113 1.437068312
114 0.204770007
115 0.514296227
116 0.689476593
117 0.781793791
118 -0.385427123
119 0.0598990479
120 0.0308586738
121 1.918902304
122 -0.222897265
123 0.181307901
124 -0.466403341
125 -0.0894427190
126 -0.0588237418
127 1.374247274
128 -0.0883883476
129 -0.165352924
130 -0.257014673
131 -0.860174235
132 -0.166719745
133 0.128323824
134 0.791938152
135 0.171238440
136 0.244873380
137 -0.847479389
138 0.158704995
139 -0.577571051
140 0.0193383023
141 -0.338927787
142 0.928435585
143 1.388569176
144 -0.240477422
145 -0.616686612
146 0.365884680
147 -0.193708578
148 0.660240549
149 -0.263120536
150 -0.0276008369
151 -0.696671513
152 0.524600979
153 0.666221307
154 -0.104478788
155 0.417163830
156 -0.0793113195
157 -0.0443668444
158 -0.203184426
159 -0.211486783
160 0.0790569415
161 0.0994671427
162 -0.627330953
163 -0.668734282
164 0.464493331
165 0.149118673
166 0.598459904
167 -0.977105390
168 0.00596754365
169 -0.339418264
170 -0.219021409
171 1.427345454
172 -0.423618219
173 -0.664568699
174 -0.190301310
175 -0.0172967034
176 -0.427119882
177 0.106042669
178 0.540510674
179 1.030108695
180 0.215089545
181 0.106799169
182 -0.0497022747
183 0.0640275741
184 0.406586867
185 -0.590537100
186 0.128731225
187 1.188769896
188 -0.868299462
189 0.0438400069
190 -0.469217380
191 0.585102393
192 0.0243959236
193 1.309369629
194 -1.251994148
195 0.0709382007
196 -0.496260300
197 -0.132443924
198 -1.162061416
199 -0.797563317
200 -0.0707106781
201 -0.129671225
202 0.146550139
203 0.0323963252
204 -0.0675871023
205 -0.415455465
206 -0.630353580