Properties

Level 10
Symmetry odd
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

$R= 31.7315288843$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.437913315
4 0.5
5 0.447213595
6 1.016758255
7 1.620057690
8 -0.353553390
9 1.067594701
10 -0.316227766
11 -1.485940942
12 -0.718956657
13 1.031795476
14 -1.145553778
15 -0.643054383
16 0.250000000
17 1.429854577
18 -0.754903453
19 -0.926118539
20 0.223606797
21 -2.329502524
22 1.050718916
23 -1.289547622
24 0.508379127
25 0.200000000
26 -0.729589578
27 -0.0971953217
28 0.810028845
29 -1.105289277
30 0.454708115
31 0.211398515
32 -0.176776695
33 2.136654266
34 -1.011059867
35 0.724511824
36 0.533797350
37 1.910935978
38 0.654864699
39 -1.483632454
40 -0.158113883
41 1.026073542
42 1.647207031
43 0.924290941
44 -0.742970471
45 0.477442865
46 0.911847868
47 -0.518292051
48 -0.359478328
49 1.624586920
50 -0.141421356
51 -2.056006935
52 0.515897738
53 0.939877121
54 0.0687274710
55 -0.664532991
56 -0.572776889
57 1.331678178
58 0.781557543
59 0.942305755
60 -0.321527191
61 0.295849132
62 -0.149481324
63 1.729565006
64 0.125000000
65 0.461432964
66 -1.510842720
67 0.109580384
68 0.714927288
69 1.854257696
70 -0.512307224
71 -0.505031128
72 -0.377451726
73 0.478470386
74 -1.351235789
75 -0.287582663
76 -0.463059269
77 -2.407310050
78 1.049086569
79 -1.904691786
80 0.111803398
81 -0.927836254
82 -0.725543560
83 -0.929772021
84 -1.164751262
85 0.639450406
86 -0.653572392
87 1.589310169
88 0.525359458
89 -0.651922910
90 -0.337603087
91 1.671568196
92 -0.644773811
93 -0.303972740
94 0.366487824
95 -0.414172801
96 0.254189563
97 0.724776936
98 -1.148756427
99 -1.586382676
100 0.100000000
101 -0.271053570
102 1.453816446
103 0.574630682
104 -0.364794789
105 -1.041785199
106 -0.664593486
107 0.267197640
108 -0.0485976608
109 -0.118560190
110 0.469895784
111 -2.747760288
112 0.405014422
113 0.570093710
114 -0.941638670
115 -0.576703228
116 -0.552644638
117 1.101539384
118 -0.666310789
119 2.316446904
120 0.227354057
121 1.208020483
122 -0.209196928
123 -1.475404809
124 0.105699257
125 0.0894427190
126 -1.222987144
127 -1.833388089
128 -0.0883883476
129 -1.329050251
130 -0.326282378
131 0.00364787863
132 1.068327133
133 -1.500365461
134 -0.0774850331
135 -0.0434670692
136 -0.505529933
137 0.492548306
138 -1.311158191
139 1.337648789
140 0.362255912
141 0.745259042
142 0.357110935
143 -1.533187142
144 0.266898675
145 -0.494300391
146 -0.338329655
147 -2.336015163
148 0.955467989
149 1.210614953
150 0.203351651
151 -0.668944108
152 0.327432349
153 1.526505170
154 1.702225261
155 0.0945402903
156 -0.741816227
157 0.198745626
158 1.346820478
159 -1.351461825
160 -0.0790569415
161 -2.089141542
162 0.656079307
163 0.685099674
164 0.513036771
165 0.955540836
166 0.657448101
167 -0.130756587
168 0.823603515
169 0.0646019104
170 -0.452159718
171 -0.988719237
172 0.462145470
173 -0.259038178
174 -1.123811998
175 0.324011538
176 -0.371485235
177 -1.354953964
178 0.460979110
179 -0.904192465
180 0.238721432
181 -0.171192454
182 -1.181977207
183 -0.425405436
184 0.455923934
185 0.854596549
186 0.214941186
187 -2.124679496
188 -0.259146025
189 -0.157462093
190 0.292864396
191 -0.746005744
192 -0.179739164
193 1.578131365
194 -0.512494686
195 -0.663500604
196 0.812293460
197 -0.983229237
198 1.121741948
199 0.795653197
200 -0.0707106781
201 -0.157569565
202 0.191663817
203 -1.790639441
204 -1.028003467
205 0.458874038
206 -0.406325252
207 -1.376711175
208 0.257948869
209 1.376174879
210 0.736653379
211 0.740479548
212 0.469938560
213 0.726168290
214 -0.188937263
215 0.413355475
216 0.0343637355
217 0.342422628
218 0.0838347145
219 -0.687766105
220 -0.332266495
221 1.475275879
222 1.942959932
223 0.662236342
224 -0.286388444
225 0.213518940
226 -0.403117128
227 -1.223393522
228 0.665839089
229 0.217334500
230 0.407790763
231 3.464642006
232 0.390778771
233 0.711942540
234 -0.778905968
235 -0.231787251
236 0.471152877
237 2.733486629
238 -1.637975314
239 -0.242938109
240 -0.160763595