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

$R= 26.3274378838$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.270411734
4 0.5
5 0.447213595
6 -0.898316752
7 -0.663820993
8 0.353553390
9 0.613945975
10 0.316227766
11 -0.524879008
12 -0.635205867
13 -1.656262041
14 -0.469392326
15 -0.568145399
16 0.250000000
17 -0.657032390
18 0.434125362
19 1.044108369
20 0.223606797
21 0.843325980
22 -0.371145506
23 -1.078337146
24 -0.449158376
25 0.200000000
26 -1.171154120
27 0.490447563
28 -0.331910496
29 0.337664577
30 -0.401739464
31 -1.179622253
32 0.176776695
33 0.666812452
34 -0.464592058
35 -0.296869773
36 0.306972987
37 -0.963041986
38 0.738296108
39 2.104134732
40 0.158113883
41 1.268291585
42 0.596321519
43 -1.161055686
44 -0.262439504
45 0.274564986
46 -0.762499508
47 0.720890734
48 -0.317602933
49 -0.559341688
50 0.141421356
51 0.834701658
52 -0.828131020
53 -1.038586859
54 0.346798797
55 -0.234733028
56 -0.234696163
57 -1.326447524
58 0.238764912
59 -0.958630842
60 -0.284072699
61 -0.942002728
62 -0.834118894
63 -0.407550227
64 0.125000000
65 -0.740702902
66 0.471507606
67 -0.758682945
68 -0.328516195
69 1.369932164
70 -0.209918629
71 1.100054485
72 0.217062681
73 0.238653253
74 -0.680973519
75 -0.254082346
76 0.522054184
77 0.348425705
78 1.487847937
79 1.228866977
80 0.111803398
81 -1.237016314
82 0.896817580
83 -1.528766801
84 0.421662990
85 -0.293833817
86 -0.820990349
87 -0.428973041
88 -0.185572753
89 0.871476530
90 0.194146764
91 1.099461514
92 -0.539168573
93 1.498605952
94 0.509746727
95 0.466939458
96 -0.224579188
97 0.860155563
98 -0.395514300
99 -0.322247354
100 0.100000000
101 1.160950678
102 0.590223203
103 -1.218725402
104 -0.585577060
105 0.377146843
106 -0.734391811
107 0.969999305
108 0.245223781
109 1.135850446
110 -0.165981316
111 1.223459840
112 -0.165955248
113 -0.0726681154
114 -0.937940039
115 -0.482247032
116 0.168832288
117 -1.016855413
118 -0.677854369
119 0.436151894
120 -0.200869732
121 -0.724502025
122 -0.666096517
123 -1.611252512
124 -0.589811126
125 0.0894427190
126 -0.288181529
127 1.362987952
128 0.0883883476
129 1.475018768
130 -0.523756045
131 -1.181415547
132 0.333406226
133 -0.693101055
134 -0.536469855
135 0.219334818
136 -0.232296029
137 0.953804282
138 0.968688323
139 0.0926809955
140 -0.148434886
141 -0.915828048
142 0.777855986
143 0.869337177
144 0.153486493
145 0.151008189
146 0.168753333
147 0.710594243
148 -0.481520993
149 -0.633546275
150 -0.179663350
151 1.422662860
152 0.369148054
153 -0.403382415
154 0.246374178
155 -0.527543109
156 1.052067366
157 1.771106649
158 0.868940173
159 1.319432871
160 0.0790569415
161 0.715822767
162 -0.874702624
163 1.425598865
164 0.634145792
165 0.298207594
166 -1.081001372
167 -0.488809786
168 0.298160759
169 1.743203414
170 -0.207771885
171 0.641026062
172 -0.580527843
173 -0.123234957
174 -0.303329746
175 -0.132764198
176 -0.131219752
177 1.217855528
178 0.616226964
179 1.142834625
180 0.137282493
181 -1.409934343
182 0.777436692
183 1.196726536
184 -0.381249754
185 -0.430685469
186 1.059674431
187 0.344851947
188 0.360445367
189 -0.325561472
190 0.330176057
191 0.594456507
192 -0.158801466
193 -1.950393014
194 0.608221831
195 0.940997659
196 -0.279670844
197 1.075853933
198 -0.227863289
199 -0.302064844
200 0.0707106781
201 0.963737594
202 0.820916097
203 -0.224230962
204 0.417350829
205 0.567197240
206 -0.861768996
207 -0.661087781
208 -0.414065510
209 -0.547893163
210 0.266683090
211 -0.187506395
212 -0.519293429
213 -1.392285956
214 0.685893086
215 -0.519239888
216 0.173399398
217 0.789895097
218 0.803167552
219 -0.293448225
220 -0.117366514
221 1.107609955
222 0.865116749
223 -0.0646772826
224 -0.117348081
225 0.122789195
226 -0.0513841172
227 1.377051761
228 -0.663223762
229 1.175087034
230 -0.341000146
231 -0.107311130
232 0.119382456