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

$R= 25.4802073427$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.278477173
4 0.5
5 -0.447213595
6 0.904019879
7 -0.453209242
8 -0.353553390
9 0.634503884
10 0.316227766
11 0.0503577816
12 -0.639238586
13 -1.133591123
14 0.320467328
15 0.571752373
16 0.250000000
17 0.727231078
18 -0.448661999
19 -0.903974378
20 -0.223606797
21 0.579417671
22 -0.0356083289
23 -0.398819363
24 0.452009939
25 0.200000000
26 0.801569970
27 0.467278441
28 -0.226604621
29 -0.262169196
30 -0.404289980
31 -0.791243983
32 -0.176776695
33 -0.0643812743
34 -0.514230027
35 0.202681335
36 0.317251942
37 1.776237488
38 0.639206413
39 1.449270375
40 0.158113883
41 -0.454916999
42 -0.409710165
43 -1.569433838
44 0.0251788908
45 -0.283758763
46 0.282007876
47 0.353544320
48 -0.319619293
49 -0.794601382
50 -0.141421356
51 -0.929748333
52 -0.566795561
53 -0.959414142
54 -0.330415754
55 -0.0225206846
56 0.160233664
57 1.155710608
58 0.185381616
59 -1.599706990
60 0.285876186
61 -0.933136160
62 0.559493985
63 -0.287563024
64 0.125000000
65 0.506957362
66 0.0455244357
67 -0.969500917
68 0.363615539
69 0.509881453
70 -0.143317346
71 -0.615850778
72 -0.224330999
73 0.150239323
74 -1.255989572
75 -0.255695434
76 -0.451987189
77 -0.0228226121
78 -1.024788910
79 -1.318827631
80 -0.111803398
81 -1.231908705
82 0.321674895
83 0.158064494
84 0.289708835
85 -0.325227625
86 1.109757310
87 0.335177332
88 -0.0178041644
89 -0.869985623
90 0.200647745
91 0.513753974
92 -0.199409681
93 1.011587371
94 -0.249993586
95 0.404269632
96 0.226004969
97 -1.441930910
98 0.561868025
99 0.0319522080
100 0.100000000
101 -0.523764588
102 0.657431351
103 -1.087247625
104 0.400784985
105 -0.259123460
106 0.678408246
107 1.194547376
108 0.233639220
109 -1.317910057
110 0.0159245288
111 -2.270879084
112 -0.113302310
113 -0.665890840
114 -0.817210808
115 0.178357441
116 -0.131084598
117 -0.719267970
118 1.131163660
119 -0.329587846
120 -0.202144990
121 -0.997464094
122 0.659826906
123 0.581601000
124 -0.395621991
125 -0.0894427190
126 0.203337764
127 -0.748559485
128 -0.0883883476
129 2.006485337
130 -0.358472988
131 -0.363296867
132 -0.0321906371
133 0.409689542
134 0.685540672
135 -0.208973271
136 -0.257115013
137 1.854051435
138 -0.360540633
139 1.296435268
140 0.101340667
141 -0.451998348
142 0.435472261
143 -0.0570851413
144 0.158625971
145 0.117245628
146 -0.106235244
147 1.015879717
148 0.888118744
149 -0.913720793
150 0.180803975
151 1.098807265
152 0.319603206
153 0.461430887
154 0.0161380237
155 0.353855066
156 0.724635187
157 1.502020140
158 0.932551961
159 1.226588725
160 0.0790569415
161 0.180748741
162 0.871090999
163 -0.870558086
164 -0.227458499
165 0.0287921812
166 -0.111768476
167 -1.287891316
168 -0.204855082
169 0.285027835
170 0.229970659
171 -0.573575153
172 -0.784716919
173 1.784358639
174 -0.237006164
175 -0.0906418485
176 0.0125894454
177 2.045195750
178 0.615172733
179 0.457293227
180 -0.141879381
181 1.374245144
182 -0.363278919
183 1.193000639
184 0.141003938
185 -0.794357553
186 -0.715300289
187 0.0365981322
188 0.176772160
189 -0.211740842
190 -0.285861798
191 0.886467154
192 -0.159809646
193 -0.669878733
194 1.019599125
195 -0.648133415
196 -0.397300691
197 -1.549234401
198 -0.0225936230
199 0.374894815
200 -0.0707106781
201 1.242156997
202 0.370357491
203 0.120317887
204 -0.464874166
205 0.203445067
206 0.768800168
207 -0.253649454
208 -0.283397780
209 -0.0391169290
210 0.183227956
211 -0.128404735
212 -0.479707071
213 0.812111487
214 -0.844672550
215 0.701872149
216 -0.165207877
217 0.411439101
218 0.931903138
219 -0.152952529
220 -0.0112603423
221 -0.877889927
222 1.605753999
223 -0.422692609
224 0.0801168322
225 0.126900776
226 0.470855929