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

$R= 31.7376827649$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.429149143
4 0.5
5 -0.447213595
6 0.303454269
7 -1.550145031
8 0.353553390
9 -0.815831012
10 -0.316227766
11 1.060998268
12 0.214574571
13 0.530357788
14 -1.096118063
15 -0.191921331
16 0.250000000
17 1.841248912
18 -0.576879641
19 -1.237917241
20 -0.223606797
21 -0.665243412
22 0.750239070
23 -0.467674506
24 0.151727134
25 0.200000000
26 0.375019588
27 -0.779262324
28 -0.775072515
29 0.696414661
30 -0.135708875
31 1.260437493
32 0.176776695
33 0.455326498
34 1.301959592
35 0.693245932
36 -0.407915506
37 -0.248966007
38 -0.875339675
39 0.227602590
40 -0.158113883
41 1.736145885
42 -0.470398128
43 -0.333352023
44 0.530499134
45 0.364850720
46 -0.330695814
47 -0.595027280
48 0.107287285
49 1.402949617
50 0.141421356
51 0.790170394
52 0.265178894
53 -0.483375021
54 -0.551021673
55 -0.474492850
56 -0.548059031
57 -0.531251124
58 0.492439529
59 -0.394428997
60 -0.0959606658
61 -0.878697315
62 0.891263899
63 1.264656390
64 0.125000000
65 -0.237183213
66 0.321964454
67 -1.802532461
68 0.920624456
69 -0.200702113
70 0.490198900
71 -1.288189350
72 -0.288439820
73 1.045065813
74 -0.176045552
75 0.0858298287
76 -0.618958620
77 -1.644701194
78 0.160939335
79 -1.283629356
80 -0.111803398
81 0.481411252
82 1.227640528
83 0.598972339
84 -0.332621706
85 -0.823431546
86 -0.235715476
87 0.298865755
88 0.375119535
89 -0.819039574
90 0.257988418
91 -0.822131490
92 -0.233837253
93 0.540915671
94 -0.420747824
95 0.553613420
96 0.0758635674
97 -0.0664731706
98 0.992035188
99 -0.865595291
100 0.100000000
101 1.707072105
102 0.558734844
103 -0.658116018
104 0.187509794
105 0.297505898
106 -0.341797755
107 -1.256017168
108 -0.389631162
109 0.557925258
110 -0.335517112
111 -0.106843549
112 -0.387536257
113 -1.298312288
114 -0.375651272
115 0.209150397
116 0.348207330
117 -0.432682331
118 -0.278903419
119 -2.854202853
120 -0.0678544375
121 0.125717326
122 -0.621332830
123 0.745065520
124 0.630218746
125 -0.0894427190
126 0.894247109
127 -1.090507203
128 0.0883883476
129 -0.143057735
130 -0.167713858
131 -1.832104372
132 0.227663249
133 1.918951260
134 -1.274582926
135 0.348496705
136 0.650979796
137 0.911990070
138 -0.141917825
139 -0.189495908
140 0.346622966
141 -0.255355447
142 -0.910887425
143 0.562708695
144 -0.203957753
145 -0.311446104
146 0.738973123
147 0.602074627
148 -0.124483003
149 -0.343518142
150 0.0606908539
151 -0.736729550
152 -0.437669837
153 -1.502147964
154 -1.162979367
155 -0.563684783
156 0.113801295
157 0.559272923
158 -0.907663022
159 -0.207439978
160 -0.0790569415
161 0.724963310
162 0.340409161
163 -1.428244746
164 0.868072942
165 -0.203628200
166 0.423537402
167 1.338549340
168 -0.235199064
169 -0.718720618
170 -0.582254030
171 1.009931265
172 -0.166676011
173 0.651042805
174 0.211330002
175 -0.310029006
176 0.265249567
177 -0.169268859
178 -0.579148437
179 0.0446675321
180 0.182425360
181 1.226801220
182 -0.581334751
183 -0.377092266
184 -0.165347907
185 0.111340983
186 0.382485139
187 1.953561989
188 -0.297513640
189 1.207969537
190 0.391463803
191 1.537846965
192 0.0536436429
193 -0.243550880
194 -0.0470036297
195 -0.101786973
196 0.701474808
197 -0.740304228
198 -0.612068300
199 0.525379876
200 0.0707106781
201 -0.773553499
202 1.207082261
203 -1.079542220
204 0.395085197
205 -0.776428043
206 -0.465358299
207 0.381552583
208 0.132589447
209 -1.313415264
210 0.210368438
211 0.541498688
212 -0.241687510
213 -0.552804799
214 -0.888138257
215 0.149079557
216 -0.275510836
217 -1.953798177
218 0.394512733
219 0.448593591
220 -0.237246425
221 0.976629986
222 -0.0755497981
223 0.868622834
224 -0.274029515
225 -0.163166202
226 -0.918045423
227 -1.536650082
228 -0.265625562
229 -0.447850577
230 0.147891664
231 -0.704577512
232 0.246219764
233 -1.202568822
234 -0.305952610
235 0.266104289
236 -0.197214498
237 -0.552025558
238 -2.018226192
239 -1.733894188
240 -0.0479803329
241 -0.196915039
242 0.0888955740
243 0.996506609
244 -0.439348657
245 -0.627418142
246 0.526840881
247 -0.650423345
248 0.445631949
249 0.271563773
250 -0.0632455532