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

$R= 25.9030999676$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.047524141
4 0.5
5 0.447213595
6 0.740711423
7 -1.364690413
8 0.353553390
9 0.0973068261
10 0.316227766
11 -0.162475179
12 0.523762070
13 0.171129132
14 -0.964981845
15 0.468467037
16 0.250000000
17 1.281764176
18 0.0688063166
19 -0.479092547
20 0.223606797
21 -1.429546152
22 -0.114887301
23 -0.0879156652
24 0.370355711
25 0.200000000
26 0.121006570
27 -0.945592891
28 -0.682345206
29 1.101218991
30 0.331256218
31 0.662855904
32 0.176776695
33 -0.170196673
34 0.906344140
35 -0.610308106
36 0.0486534130
37 1.431608820
38 -0.338769588
39 0.179261897
40 0.158113883
41 -1.312729641
42 -1.010841778
43 1.336010605
44 -0.0812375898
45 0.0435169356
46 -0.0621657630
47 1.395072324
48 0.261881035
49 0.862379923
50 0.141421356
51 1.342678917
52 0.0855645663
53 1.765605930
54 -0.668635145
55 -0.0726611093
56 -0.482490922
57 -0.501861009
58 0.778679416
59 -0.877291126
60 0.234233518
61 -0.181920024
62 0.468709905
63 -0.132793692
64 0.125000000
65 0.0765312747
66 -0.120347221
67 0.692946488
68 0.640882088
69 -0.0920937816
70 -0.431553000
71 1.158449146
72 0.0344031583
73 0.892918372
74 1.012300304
75 0.209504828
76 -0.239546273
77 0.221728320
78 0.126757303
79 -0.0612652573
80 0.111803398
81 -1.087838207
82 -0.928240031
83 0.544724121
84 -0.714773076
85 0.573222365
86 0.944702159
87 1.153553477
88 -0.0574436506
89 0.343210493
90 0.0307711202
91 -0.233538286
92 -0.0439578326
93 0.694357562
94 0.986465100
95 -0.214256700
96 0.185177855
97 0.765928787
98 0.609794691
99 -0.0158099440
100 0.100000000
101 -0.821018725
102 0.949417367
103 -1.236991517
104 0.0605032850
105 -0.639312474
106 1.248471926
107 0.451580933
108 -0.472796445
109 -0.0724159056
110 -0.0513791631
111 1.499644799
112 -0.341172603
113 -1.930360677
114 -0.354869322
115 -0.0393170807
116 0.550609495
117 0.0166520328
118 -0.620338504
119 -1.749211283
120 0.165628109
121 -0.973601815
122 -0.128636882
123 -1.375115990
124 0.331427952
125 0.0894427190
126 -0.0938993206
127 -0.184089467
128 0.0883883476
129 1.399503362
130 0.0541157833
131 1.514977111
132 -0.0850983365
133 0.653813005
134 0.489987160
135 -0.422881996
136 0.453172070
137 -1.645504121
138 -0.0651201375
139 -1.089851518
140 -0.305154053
141 1.461371938
142 0.819147246
143 -0.0278042357
144 0.0243267065
145 0.492480104
146 0.631388636
147 0.903363788
148 0.715804410
149 -0.176233869
150 0.148142284
151 1.377693213
152 -0.169384794
153 0.124724407
154 0.156785598
155 0.296438172
156 0.0896309488
157 1.693071746
158 -0.0433210788
159 1.849514826
160 0.0790569415
161 0.119977654
162 -0.769217773
163 0.555558459
164 -0.656364820
165 -0.0761142661
166 0.385178120
167 1.852634058
168 -0.505420889
169 -0.970715267
170 0.405329422
171 -0.0466186883
172 0.668005302
173 1.530414925
174 0.815685486
175 -0.272938082
176 -0.0406187949
177 -0.918984885
178 0.242686467
179 1.039484389
180 0.0217584678
181 -0.784051246
182 -0.165136506
183 -0.190564433
184 -0.0310828815
185 0.640234927
186 0.490984940
187 -0.208247260
188 0.697536162
189 1.290443761
190 -0.151502365
191 1.320645016
192 0.130940517
193 -1.221010421
194 0.541593439
195 0.0801683578
196 0.431189961
197 -1.283594017
198 -0.0111793186
199 0.666890892
200 0.0707106781
201 0.726096130
202 -0.580547908
203 -1.503144813
204 0.671339458
205 -0.587070543
206 -0.874685089
207 -0.00733109617
208 0.0427822831
209 0.0778014042
210 -0.452062186
211 -0.00325585663
212 0.882802965
213 1.215058040
214 0.319315940
215 0.597482106
216 -0.334317572
217 -0.908778286
218 -0.0512057779
219 0.931322105
220 -0.0363305546
221 0.212545476
222 1.060409007