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

$R= 31.2255274723$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.529405526
4 0.5
5 -0.447213595
6 -1.081453019
7 -1.409426961
8 -0.353553390
9 1.339081265
10 0.316227766
11 -1.531594263
12 0.764702763
13 -1.423619258
14 0.996615362
15 -0.683970944
16 0.250000000
17 1.263871576
18 -0.946873443
19 -0.574630845
20 -0.223606797
21 -2.155585384
22 1.083000689
23 0.811192758
24 -0.540726509
25 0.200000000
26 1.006650831
27 0.518592761
28 -0.704713480
29 1.453621418
30 0.483640493
31 -1.297330960
32 -0.176776695
33 -2.342428731
34 -0.893692162
35 0.630314899
36 0.669540632
37 -0.468166474
38 0.406325367
39 -2.177291161
40 0.158113883
41 -1.475689149
42 1.524229042
43 -1.726741058
44 -0.765797131
45 -0.598855347
46 -0.573599900
47 -0.811725550
48 0.382351381
49 0.986484360
50 -0.141421356
51 1.932972174
52 -0.711809629
53 -0.187710382
54 -0.366700457
55 0.684949777
56 0.498307681
57 -0.878843590
58 -1.027865562
59 -0.439605000
60 -0.341985472
61 0.0224006167
62 0.917351519
63 -1.887337238
64 0.125000000
65 0.636661887
66 1.656347240
67 0.132479792
68 0.631935788
69 1.240642688
70 -0.445699939
71 1.395274424
72 -0.473436721
73 -1.166806694
74 0.331043689
75 0.305881105
76 -0.287315422
77 2.158670249
78 1.539577345
79 -0.430396711
80 -0.111803398
81 -0.545942630
82 1.043469804
83 1.218009833
84 -1.077792692
85 -0.565220552
86 1.220990311
87 2.223176631
88 0.541500344
89 0.0219987325
90 0.423454677
91 2.006487366
92 0.405596379
93 -1.984145141
94 0.573976641
95 0.256982726
96 -0.270363254
97 0.303573562
98 -0.697549780
99 -2.050929184
100 0.100000000
101 1.317253264
102 -1.366817732
103 -0.614758782
104 0.503325415
105 0.964007090
106 0.132731284
107 0.486971302
108 0.259296380
109 -0.815617672
110 -0.484332632
111 -0.716016394
112 -0.352356740
113 0.840039336
114 0.621436262
115 -0.362776430
116 0.726810709
117 -1.906341877
118 0.310847677
119 -1.781334676
120 0.241820246
121 1.345780988
122 -0.0158396280
123 -2.256927141
124 -0.648665480
125 -0.0894427190
126 1.334548960
127 1.034423784
128 -0.0883883476
129 -2.640887318
130 -0.450187937
131 0.235653049
132 -1.171214365
133 0.809900206
134 -0.0936773593
135 -0.231921733
136 -0.446846081
137 1.009987490
138 -0.877266858
139 -0.686342184
140 0.315157449
141 -1.241457543
142 -0.986608007
143 2.180407089
144 0.334770316
145 -0.650079261
146 0.825056925
147 1.508734632
148 -0.234083237
149 1.243529486
150 -0.216290603
151 0.573521016
152 0.203162683
153 1.692426750
154 -1.526410371
155 0.580184043
156 -1.088645580
157 -0.211622403
158 0.304336433
159 -0.287085297
160 0.0790569415
161 -1.143316944
162 0.386039736
163 -0.285557371
164 -0.737844574
165 1.047565975
166 -0.861263012
167 0.0387906244
168 0.762114521
169 1.026691795
170 0.399671285
171 -0.769477409
172 -0.863370529
173 0.907515916
174 -1.572023271
175 -0.281885392
176 -0.382898565
177 -0.672334316
178 -0.0155554529
179 -0.284508789
180 -0.299427673
181 0.394337085
182 -1.418800822
183 0.0342596201
184 -0.286799950
185 0.209370412
186 1.403002484
187 -1.935738631
188 -0.405862775
189 -0.730919029
190 -0.181714228
191 -0.350357440
192 0.191175690
193 0.908013980
194 -0.214658924
195 0.973714208
196 0.493242180
197 -0.493305585
198 1.450225934
199 -0.478685089
200 -0.0707106781
201 0.202620622
202 -0.931438715
203 -2.048774393
204 0.966486087
205 0.659948250
206 0.434700103
207 1.086241007
208 -0.355904814
209 0.880094045
210 -0.681655950
211 1.955924612
212 -0.0938551913
213 2.133876329
214 -0.344340710
215 0.772222077
216 -0.183350228
217 1.828608350
218 0.576728786
219 -1.784617931
220 0.342474888
221 -1.799409424
222 0.506300047
223 -0.701797445
224 0.249153840
225 0.267816253
226 -0.593997511
227 0.720813470
228 -0.439421795
229 1.625891406
230 0.256521673
231 3.301815043
232 -0.513932781
233 1.512718009
234 1.347987269
235 0.363014701
236 -0.219802500
237 -0.656149821
238 1.259593829
239 0.204712525
240 -0.170992736
241 1.723044856
242 -0.951610863
243 -1.365782423
244 0.0112003083
245 -0.441169217
246 1.595888486
247 0.851296212
248 0.458675759
249 1.810458034
250 0.0632455532