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

$R= 23.0057216741$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.790243017
4 0.5
5 -0.447213595
6 0.558786196
7 1.394915581
8 0.353553390
9 -0.375515972
10 -0.316227766
11 -0.170009149
12 0.395121508
13 0.0546378784
14 0.986354267
15 -0.353407421
16 0.250000000
17 -1.734532435
18 -0.265529890
19 -1.551378202
20 -0.223606797
21 1.102322299
22 -0.120214622
23 -1.080512575
24 0.279393098
25 0.200000000
26 0.0386348143
27 -1.086991893
28 0.697457790
29 -0.216786140
30 -0.249896784
31 1.924365972
32 0.176776695
33 -0.134348543
34 -1.226499647
35 -0.623825212
36 -0.187757986
37 -1.297617473
38 -1.096990047
39 0.0431772019
40 -0.158113883
41 1.597090861
42 0.779459572
43 -1.333397384
44 -0.0850045746
45 0.167935848
46 -0.764037769
47 -0.701749793
48 0.197560754
49 0.945789480
50 0.141421356
51 -1.370702146
52 0.0273189392
53 -0.0818349522
54 -0.768619338
55 0.0760304029
56 0.493177133
57 -1.225965792
58 -0.153290950
59 0.0395229444
60 -0.176703710
61 -0.224935118
62 1.360732228
63 -0.523813081
64 0.125000000
65 -0.0244348020
66 -0.0949987659
67 -0.956099274
68 -0.867266217
69 -0.853867518
70 -0.441111038
71 -0.0967319973
72 -0.132764945
73 0.431163774
74 -0.917554115
75 0.158048603
76 -0.775689101
77 -0.237148411
78 0.0305308923
79 -0.565890708
80 -0.111803398
81 -0.483471781
82 1.129313778
83 1.497460274
84 0.551161149
85 0.775706487
86 -0.942854332
87 -0.171313733
88 -0.0601073111
89 0.268402908
90 0.118748577
91 0.0762152280
92 -0.540256287
93 1.520716773
94 -0.496212037
95 0.693797423
96 0.139696549
97 -0.257073663
98 0.668774155
99 0.0638411511
100 0.100000000
101 0.741342531
102 -0.969232782
103 0.334134980
104 0.0193174071
105 -0.492973518
106 -0.0578660496
107 -0.828787922
108 -0.543495946
109 -0.224942781
110 0.0537616134
111 -1.025433148
112 0.348728895
113 -1.260603279
114 -0.866888725
115 0.483219913
116 -0.108393070
117 -0.0205173968
118 0.0279469420
119 -2.419526321
120 -0.124948392
121 -0.971096888
122 -0.159053147
123 1.262089901
124 0.962182986
125 -0.0894427190
126 -0.370391782
127 -1.440355899
128 0.0883883476
129 -1.053707984
130 -0.0172780142
131 0.731263026
132 -0.0671742716
133 -2.164041643
134 -0.676064280
135 0.486117552
136 -0.613249823
137 -1.419643431
138 -0.603775512
139 0.886949166
140 -0.311912606
141 -0.554552865
142 -0.0683998513
143 -0.00928884667
144 -0.0938789931
145 0.0969497094
146 0.304878828
147 0.747403464
148 -0.648808736
149 1.643503169
150 0.111757239
151 -0.525524691
152 -0.548495023
153 0.651343002
154 -0.167689249
155 -0.860602625
156 0.0215886009
157 -0.585370886
158 -0.400145157
159 -0.0646689373
160 -0.0790569415
161 -1.507226038
162 -0.341866175
163 -1.107558008
164 0.798545430
165 0.0600824950
166 1.058864314
167 0.501396561
168 0.389729786
169 -0.997042474
170 0.548507317
171 0.582561308
172 -0.666698692
173 0.0715408937
174 -0.121137103
175 0.278983116
176 -0.0425022873
177 0.0311650228
178 0.189789516
179 1.294344264
180 0.0839679241
181 -1.705898737
182 0.0538923045
183 -0.176982434
184 -0.382018884
185 0.580312176
186 1.075309142
187 0.294767526
188 -0.350874896
189 -1.518553104
190 0.490588863
191 -0.939102100
192 0.0987803772
193 -0.209011478
194 -0.181778530
195 -0.0193094317
196 0.472894740
197 0.809089337
198 0.0451425108
199 0.126601627
200 0.0707106781
201 -0.736016560
202 0.524208331
203 -0.272603066
204 -0.685351073
205 -0.714240746
206 0.236269110
207 0.527031906
208 0.0136594696
209 0.222111336
210 -0.348584918