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

$R= 27.8530777214$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.112004391
4 0.5
5 0.447213595
6 0.0791990650
7 0.209422098
8 -0.353553390
9 -0.987455016
10 -0.316227766
11 -0.319088987
12 -0.0560021959
13 0.155097362
14 -0.148083786
15 -0.0500898868
16 0.250000000
17 -0.797503441
18 0.698236138
19 1.322180436
20 0.223606797
21 -0.0234561948
22 0.225629987
23 0.745465902
24 0.0395995325
25 0.200000000
26 -0.109670397
27 0.222603690
28 0.104711049
29 -0.558778569
30 0.0354188986
31 0.0376894833
32 -0.176776695
33 0.0357393680
34 0.563920091
35 0.0936564096
36 -0.493727508
37 -0.477609528
38 -0.934922752
39 -0.0173715858
40 -0.158113883
41 0.749384734
42 0.0165860344
43 0.415116746
44 -0.159544493
45 -0.441603308
46 -0.527123994
47 -1.355392704
48 -0.0280010979
49 -0.956142384
50 -0.141421356
51 0.0893238880
52 0.0775486814
53 1.547004574
54 -0.157404579
55 -0.142700933
56 -0.0740418930
57 -0.148090015
58 0.395116115
59 0.466423955
60 -0.0250449434
61 -0.490656888
62 -0.0266504892
63 -0.206794901
64 0.125000000
65 0.0693616493
66 -0.0252715495
67 -0.548220834
68 -0.398751720
69 -0.0834954551
70 -0.0662250823
71 -0.827265212
72 0.349118069
73 0.892532637
74 0.337720936
75 -0.0224008783
76 0.661090218
77 -0.0668242855
78 0.0122835661
79 -1.173840804
80 0.111803398
81 0.962522425
82 -0.529895027
83 0.0317578307
84 -0.0117280974
85 -0.356654381
86 -0.293531866
87 0.0625856539
88 0.112814993
89 1.570716890
90 0.312260693
91 0.0324808152
92 0.372732951
93 -0.00422138765
94 0.958407372
95 0.591297066
96 0.0197997662
97 0.427420108
98 0.676094763
99 0.315086021
100 0.100000000
101 1.420464085
102 -0.0631615269
103 -0.777378662
104 -0.0548351985
105 -0.0104899292
106 -1.093897425
107 0.276230264
108 0.111301845
109 0.550208144
110 0.100904797
111 0.0534943647
112 0.0523555246
113 -1.158255508
114 0.104715454
115 0.333382486
116 -0.279389284
117 -0.153151669
118 -0.329811541
119 -0.167014844
120 0.0177094493
121 -0.898182217
122 0.346946812
123 -0.0839343815
124 0.0188447416
125 0.0894427190
126 0.146226077
127 -0.417623737
128 -0.0883883476
129 -0.0464948988
130 -0.0490460926
131 1.636005832
132 0.0178696840
133 0.276893801
134 0.387650669
135 0.0995513968
136 0.281960045
137 1.402020557
138 0.0590402025
139 0.896811502
140 0.0468282048
141 0.151809935
142 0.584964841
143 -0.0494898603
144 -0.246863754
145 -0.249893373
146 -0.631115880
147 0.107092147
148 -0.238804764
149 -0.406656866
150 0.0158398130
151 0.0293803311
152 -0.467461376
153 0.787498775
154 0.0472519054
155 0.0168552493
156 -0.00868579291
157 0.703679734
158 0.830030792
159 -0.173271303
160 -0.0790569415
161 0.156117037
162 -0.680606133
163 -1.377119161
164 0.374692367
165 0.0159831312
166 -0.0224561774
167 -1.825096937
168 0.00829301720
169 -0.975944836
170 0.252192731
171 -1.305593693
172 0.207558373
173 -1.655775075
174 -0.0442547403
175 0.0418844197
176 -0.0797722469
177 -0.0522413016
178 -1.110664564
179 0.0264998032
180 -0.220801654
181 -0.677893553
182 -0.0229674047
183 0.0549564186
184 -0.263561997
185 -0.213593474
186 0.00298497184
187 0.254473278
188 -0.677696352
189 0.0466151522
190 -0.418110165
191 -0.879032472
192 -0.0140005489
193 0.598903699
194 -0.302231657
195 -0.00776880936
196 -0.478071192
197 -0.857985595
198 -0.222799462
199 -1.738933984
200 -0.0707106781
201 0.0613627836
202 -1.004419787
203 -0.117043902
204 0.0446619440
205 0.335135041
206 0.549689723
207 -0.736060624
208 0.0387743407
209 -0.421784523
210 0.00741750008
211 -0.854758093
212 0.773502287
213 0.0924948035
214 -0.195324293
215 0.185645852
216 -0.0787022895
217 0.00733471985
218 -0.389055910
219 -0.100421034
220 -0.0713504667
221 -0.126274630
222 -0.0378262280
223 0.824824702
224 -0.0370209465
225 -0.197491003
226 0.819010324
227 -0.977336323
228 -0.0740450079
229 -0.966527699
230 -0.235737016
231 0.0240512426
232 0.197558057
233 0.317628669
234 0.108294583
235 -0.606150044
236 0.233211977
237 0.128647732
238 0.118097329