Properties

Level 10
Symmetry odd
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

$R= 21.7875095659$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.392322570
4 0.5
5 0.447213595
6 -0.984520731
7 0.286359808
8 -0.353553390
9 0.938562141
10 -0.316227766
11 -0.186449671
12 0.696161285
13 0.360908310
14 -0.202486962
15 0.622665582
16 0.250000000
17 -1.210191301
18 -0.663663654
19 -0.273789162
20 0.223606797
21 0.398705225
22 0.131839826
23 0.379959777
24 -0.492260365
25 0.200000000
26 -0.255200713
27 -0.0855413175
28 0.143179904
29 0.0678912336
30 -0.440291056
31 1.740684314
32 -0.176776695
33 -0.259598085
34 0.855734476
35 0.128063999
36 0.469281070
37 1.442688960
38 0.193598173
39 0.502500786
40 -0.158113883
41 1.521298930
42 -0.281927168
43 1.591722157
44 -0.0932248355
45 0.419737749
46 -0.268672135
47 0.483982483
48 0.348080642
49 -0.917998059
50 -0.141421356
51 -1.684976664
52 0.180454155
53 -1.544566081
54 0.0604868457
55 -0.0833828278
56 -0.101243481
57 -0.381202830
58 -0.0480063517
59 1.044111127
60 0.311332791
61 0.0494920304
62 -1.230849682
63 0.268766475
64 0.125000000
65 0.161403102
66 0.183563566
67 0.386293270
68 -0.605095650
69 0.529026574
70 -0.0905549226
71 -0.414097587
72 -0.331831827
73 0.0154684425
74 -1.020135147
75 0.278464514
76 -0.136894581
77 -0.0533916922
78 -0.355321713
79 0.699914013
80 0.111803398
81 -1.057663248
82 -1.075720789
83 -0.829457106
84 0.199352612
85 -0.541214003
86 -1.125517531
87 0.0945264969
88 0.0659199134
89 1.257898300
90 -0.296799409
91 0.103349634
92 0.189979888
93 2.423594059
94 -0.342227295
95 -0.122442235
96 -0.246130182
97 1.405632912
98 0.649122653
99 -0.174994602
100 0.100000000
101 -1.361565264
102 1.191458425
103 -1.390073768
104 -0.127600356
105 0.178306397
106 1.092173150
107 1.415162511
108 -0.0427706587
109 1.173697507
110 0.0589605629
111 2.008688402
112 0.0715899522
113 1.385693493
114 0.269551106
115 0.169923178
116 0.0339456168
117 0.338734877
118 -0.738298058
119 -0.346550147
120 -0.220145528
121 -0.965236518
122 -0.0349961503
123 2.118138839
124 0.870342157
125 0.0894427190
126 -0.190046597
127 -0.226868176
128 -0.0883883476
129 2.216190685
130 -0.114129228
131 -0.837669467
132 -0.129799042
133 -0.0784022259
134 -0.273150590
135 -0.0382552401
136 0.427867238
137 -0.388914103
138 -0.374078278
139 1.837574363
140 0.0640319998
141 0.673859754
142 0.292811212
143 -0.0672913515
144 0.234640535
145 0.0303618827
146 -0.0109378406
147 -1.278149090
148 0.721344480
149 0.117273607
150 -0.196904146
151 0.154739261
152 0.0967990866
153 -1.135838808
154 0.0377536276
155 0.778457690
156 0.251250393
157 0.403572389
158 -0.494913944
159 -2.150547612
160 -0.0790569415
161 0.108795342
162 0.747880855
163 -0.0605430792
164 0.760649465
165 -0.116095793
166 0.586514744
167 1.767905412
168 -0.140963584
169 -0.869641630
170 0.382696091
171 -0.256893227
172 0.795861078
173 -1.219731918
174 -0.0668403270
175 0.0572719617
176 -0.0466124177
177 1.453264751
178 -0.889468418
179 -0.122794961
180 0.209868874
181 -0.750585950
182 -0.0730792275
183 0.0694089133
184 -0.134336067
185 0.645190117
186 -1.713739794
187 0.227819455
188 0.241991241
189 -0.0209839898
190 0.0865797352
191 -0.675947166
192 0.174040321
193 1.117575000
194 -0.993932563
195 0.224725183
196 -0.458999029
197 1.365989430
198 0.123739870
199 -1.391971840
200 -0.0707106781
201 0.665801432
202 0.962772031
203 0.0414989282
204 -0.842488332
205 0.680345564
206 0.982930588
207 0.458281736
208 0.0902270775
209 -0.133008326