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

$R= 31.097569992$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.781581304
4 0.5
5 0.447213595
6 -1.259768221
7 1.142714020
8 0.353553390
9 2.174031945
10 0.316227766
11 1.008476526
12 -0.890790652
13 -0.602927298
14 0.808020832
15 -0.796747381
16 0.250000000
17 -0.884165627
18 1.537272731
19 1.164638450
20 0.223606797
21 -2.035837935
22 0.713100590
23 -0.859120062
24 -0.629884110
25 0.200000000
26 -0.426333981
27 -2.091633366
28 0.571357010
29 -1.585567045
30 -0.563385476
31 -0.803343234
32 0.176776695
33 -1.796682926
34 -0.625199511
35 0.511037245
36 1.087015972
37 0.577096104
38 0.823523745
39 1.074164002
40 0.158113883
41 -1.672313495
42 -1.439554809
43 0.299718103
44 0.504238263
45 0.972256643
46 -0.607489621
47 1.016229330
48 -0.445395326
49 0.305795331
50 0.141421356
51 1.575212952
52 -0.301463649
53 -0.874779845
54 -1.479008137
55 0.451004413
56 0.404010416
57 -2.074898089
58 -1.121165210
59 -1.190196690
60 -0.398373690
61 0.739456516
62 -0.568049448
63 2.484296784
64 0.125000000
65 -0.269637284
66 -1.270446681
67 -1.514448035
68 -0.442082813
69 1.530592241
70 0.361357901
71 1.124461419
72 0.768636365
73 1.363283470
74 0.408068569
75 -0.356316260
76 0.582319225
77 1.152400266
78 0.759548650
79 -0.171158892
80 0.111803398
81 1.552382956
82 -1.182504213
83 1.670650904
84 -1.017918967
85 -0.395410889
86 0.211932703
87 2.824816606
88 0.356550295
89 -0.534736702
90 0.687489265
91 -0.688973476
92 -0.429560031
93 1.431221288
94 0.718582650
95 0.520842148
96 -0.314942055
97 -1.076831895
98 0.216229952
99 2.192460186
100 0.100000000
101 -1.276480408
102 1.113843760
103 -1.186167798
104 -0.213166990
105 -0.910454402
106 -0.618562760
107 1.337916712
108 -1.045816683
109 -1.335538202
110 0.318908279
111 -1.028143631
112 0.285678505
113 1.649265510
114 -1.467174509
115 -0.384210172
116 -0.792783522
117 -1.310783207
118 -0.841596150
119 -1.010348458
120 -0.281692738
121 0.0170249053
122 0.522874717
123 2.979362460
124 -0.401671617
125 0.0894427190
126 1.756663103
127 -1.147519811
128 0.0883883476
129 -0.533972170
130 -0.190662352
131 0.132604587
132 -0.898341463
133 1.330848685
134 -1.070876475
135 -0.935406878
136 -0.312599755
137 1.610971266
138 1.082292153
139 -1.659398437
140 0.255518622
141 -1.810495176
142 0.795114294
143 -0.608038027
144 0.543507986
145 -0.709087139
146 0.963986986
147 -0.544799246
148 0.288548052
149 -1.568433963
150 -0.251953644
151 0.126692022
152 0.411761872
153 -1.922204320
154 0.814870042
155 -0.359266016
156 0.537082001
157 -1.292613287
158 -0.121027613
159 1.558491418
160 0.0790569415
161 -0.981728540
162 1.097700515
163 0.874899866
164 -0.836156747
165 -0.803501031
166 1.181328583
167 -1.147750249
168 -0.719777404
169 -0.636478671
170 -0.279597721
171 2.531961193
172 0.149859051
173 0.0348865881
174 1.997446977
175 0.228542804
176 0.252119131
177 2.120432178
178 -0.378115948
179 -0.307804012
180 0.486128321
181 1.309113006
182 -0.487177817
183 -1.317401930
184 -0.303744810
185 0.258085223
186 1.012026278
187 -0.891660492
188 0.508114665
189 -2.390138399
190 0.368291015
191 0.0653930434
192 -0.222697663
193 0.404267605
194 -0.761435135
195 0.480380745
196 0.152897665
197 0.293531782
198 1.550303465
199 -0.127145356
200 0.0707106781
201 2.698111978
202 -0.902607953
203 -1.811853547
204 0.787606476
205 -0.747881331
206 -0.838747294
207 -1.867758676
208 -0.150731824
209 1.174514135
210 -0.643788482
211 -0.736037693
212 -0.437389922
213 -2.003363242
214 0.946049980
215 0.134038010
216 -0.739504068
217 -0.917905244
218 -0.944368119
219 -2.428679684
220 0.225502206
221 0.533013438
222 -0.727007333
223 1.125891903
224 0.202005208
225 0.434806389
226 1.166206826
227 -0.625655447
228 -1.037449044
229 0.416711173
230 -0.271677618
231 -2.053036542
232 -0.560582605
233 0.392715369
234 -0.926863694
235 0.454471572
236 -0.595098345
237 0.308518028
238 -0.714424246
239 -1.139817366
240 -0.199186845
241 -0.610159903
242 0.0120384260
243 -0.666161004
244 0.369728258
245 0.136755829
246 2.106727399
247 -0.767598297
248 -0.284024724
249 -2.856314261
250 0.0632455532
251 -0.415933782
252 1.242148392
253 -0.573823665
254 -0.811419040
255 0.704456648