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

$R= 23.4039248757$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.508738190
4 0.5
5 0.447213595
6 -0.359732224
7 1.543283905
8 0.353553390
9 -0.741185453
10 0.316227766
11 0.909538681
12 -0.254369095
13 -1.490485324
14 1.091266515
15 -0.227514635
16 0.250000000
17 0.852819980
18 -0.524097260
19 1.770909038
20 0.223606797
21 -0.785127461
22 0.643140969
23 0.0209556249
24 -0.179866112
25 0.200000000
26 -1.053932280
27 0.885807537
28 0.771641952
29 1.321776947
30 -0.160877141
31 -0.649452866
32 0.176776695
33 -0.462717062
34 0.603034791
35 0.690177544
36 -0.370592726
37 -0.0350495567
38 1.252221790
39 0.758266807
40 0.158113883
41 -1.233519769
42 -0.555168952
43 -1.547544687
44 0.454769340
45 -0.331468211
46 0.0148178644
47 -1.448845749
48 -0.127184547
49 1.381725214
50 0.141421356
51 -0.433862093
52 -0.745242662
53 -0.0375348145
54 0.626360516
55 0.406758063
56 0.545633257
57 -0.900929059
58 0.934637443
59 0.174361815
60 -0.113757317
61 1.693994846
62 -0.459232525
63 -1.143859581
64 0.125000000
65 -0.666565301
66 -0.327190372
67 0.975944981
68 0.426409990
69 -0.0106609267
70 0.488029221
71 1.317097171
72 -0.262048630
73 0.606414930
74 -0.0247837792
75 -0.101747638
76 0.885454519
77 1.403676408
78 0.536175601
79 -1.232649254
80 0.111803398
81 0.290541329
82 -0.872230193
83 1.175426445
84 -0.392563730
85 0.381392689
86 -1.094279342
87 -0.672438412
88 0.321570484
89 1.075713061
90 -0.234383420
91 -2.300242014
92 0.0104778124
93 0.330401475
94 -1.024488654
95 0.791974598
96 -0.0899330561
97 -0.235846391
98 0.977027268
99 -0.674136839
100 0.100000000
101 -0.890106360
102 -0.306786828
103 -0.348269070
104 -0.526966140
105 -0.351119675
106 -0.0265411218
107 0.0843875638
108 0.442903768
109 1.227921768
110 0.287621385
111 0.0178310478
112 0.385820976
113 1.240514628
114 -0.637053047
115 0.00937164036
116 0.660888473
117 1.104726041
118 0.123292422
119 1.316143350
120 -0.0804385707
121 -0.172739387
122 1.197835243
123 0.627538615
124 -0.324726433
125 0.0894427190
126 -0.808830866
127 -0.823372565
128 0.0883883476
129 0.787295084
130 -0.471332844
131 1.224180992
132 -0.231358531
133 2.733015414
134 0.690097314
135 0.396145173
136 0.301517395
137 0.448322843
138 -0.00753841359
139 0.119567739
140 0.345088772
141 0.737083168
142 0.931328341
143 -1.355654058
144 -0.185296363
145 0.591116621
146 0.428800109
147 -0.702936424
148 -0.0175247783
149 0.790234410
150 -0.0719464448
151 -1.223387498
152 0.626110895
153 -0.632097373
154 0.992549107
155 -0.290444151
156 0.379133403
157 1.278339591
158 -0.871614647
159 0.0190950835
160 0.0790569415
161 0.0323391215
162 0.205443744
163 0.902800457
164 -0.616759884
165 -0.206933361
166 0.831152010
167 0.938506592
168 -0.277584476
169 1.221547090
170 0.269685357
171 -1.312579352
172 -0.773772343
173 0.199745558
174 -0.475485761
175 0.308656781
176 0.227384670
177 -0.0887274740
178 0.760644000
179 0.142162879
180 -0.165734105
181 -0.201254116
182 -1.626516726
183 -0.861801552
184 0.00740893224
185 -0.0156746383
186 0.233629124
187 0.775752262
188 -0.724422874
189 1.366771456
190 0.560010609
191 -0.141105845
192 -0.0635922738
193 0.860363985
194 -0.166768582
195 0.339107225
196 0.690862607
197 -0.888566648
198 -0.476686730
199 -0.347164495
200 0.0707106781
201 -0.497405048
202 -0.629400243
203 2.043556406
204 -0.216931046
205 -0.551646811
206 -0.246263421
207 -0.0298476399
208 -0.372621331
209 1.607027784
210 -0.248279103
211 0.319154144
212 -0.0187674072
213 -0.667610498
214 0.0596710186
215 -0.692083023
216 0.313180258
217 -1.003061068