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

$R= 30.2223231519$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.532180172
4 0.5
5 0.447213595
6 0.376308208
7 -1.376558912
8 0.353553390
9 -0.716784263
10 0.316227766
11 -0.484182385
12 0.266090086
13 0.890670567
14 -0.973374141
15 0.237998208
16 0.250000000
17 0.733400253
18 -0.506843013
19 0.338092229
20 0.223606797
21 -0.732577359
22 -0.342368648
23 0.424407197
24 0.188154104
25 0.200000000
26 0.629799197
27 -0.913638546
28 -0.688279456
29 -0.294361814
30 0.168290147
31 -1.549600262
32 0.176776695
33 -0.257672265
34 0.518592292
35 -0.615615860
36 -0.358392131
37 0.0488053469
38 0.239067308
39 0.473997216
40 0.158113883
41 0.662318294
42 -0.518010418
43 -0.543739691
44 -0.242091192
45 -0.320555667
46 0.300101207
47 1.281581797
48 0.133045043
49 0.894914438
50 0.141421356
51 0.390301073
52 0.445335283
53 -0.289481785
54 -0.646040011
55 -0.216532945
56 -0.486687070
57 0.179925981
58 -0.208145235
59 1.687168489
60 0.118999104
61 -0.456928467
62 -1.095732853
63 0.986695766
64 0.125000000
65 0.398319986
66 -0.182201806
67 0.548550480
68 0.366700126
69 0.225861095
70 -0.435306149
71 1.221208247
72 -0.253421506
73 0.557209254
74 0.0345105917
75 0.106436034
76 0.169046114
77 0.666505578
78 0.335166645
79 -1.702077541
80 0.111803398
81 0.230563944
82 0.468329757
83 0.916120117
84 -0.366288679
85 0.327986564
86 -0.384482023
87 -0.156653521
88 -0.171184324
89 -0.951344904
90 -0.226667086
91 -1.226060507
92 0.212203598
93 -0.824666535
94 0.906215179
95 0.151199441
96 0.0940770522
97 1.069860046
98 0.632800068
99 0.347054314
100 0.100000000
101 1.407183577
102 0.275984535
103 0.622495037
104 0.314899598
105 -0.327618555
106 -0.204694533
107 1.351645989
108 -0.456819273
109 0.0276418582
110 -0.153111914
111 0.0259732380
112 -0.344139728
113 1.567008773
114 0.127226881
115 0.189800668
116 -0.147180907
117 -0.638418646
118 1.193008280
119 -1.009568655
120 0.0841450735
121 -0.765567417
122 -0.323097217
123 0.352472664
124 -0.774800131
125 0.0894427190
126 0.697699267
127 1.092730564
128 0.0883883476
129 -0.289367483
130 0.281654763
131 -0.152974860
132 -0.128836132
133 -0.465403872
134 0.387883764
135 -0.408591579
136 0.259296146
137 1.486579359
138 0.159707912
139 1.254106299
140 -0.307807930
141 0.682032422
142 0.863524633
143 -0.431247000
144 -0.179196065
145 -0.131642605
146 0.394006442
147 0.476255720
148 0.0244026734
149 -1.820844830
150 0.0752616417
151 1.585864464
152 0.119533654
153 -0.525689762
154 0.471290614
155 -0.693002304
156 0.236998608
157 -1.468589639
158 -1.203550571
159 -0.154056466
160 0.0790569415
161 -0.584221506
162 0.163033328
163 -0.913640614
164 0.331159147
165 -0.115234540
166 0.647794747
167 0.810837244
168 -0.259005209
169 -0.206705940
170 0.231921523
171 -0.242339180
172 -0.271869845
173 -1.741487976
174 -0.110770767
175 -0.275311782
176 -0.121045596
177 0.897877608
178 -0.672702433
179 -1.455046511
180 -0.160277833
181 1.533766939
182 -0.866955698
183 -0.243168477
184 0.150050603
185 0.0218264146
186 -0.583127299
187 -0.355099667
188 0.640790898
189 1.257677360
190 0.106914150
191 1.283132392
192 0.0665225215
193 1.041239364
194 0.756505293
195 0.211977999
196 0.447457219
197 -0.323164614
198 0.245404459
199 -0.479853358
200 0.0707106781
201 0.291925748
202 0.995029049
203 0.405194887
204 0.195150536
205 0.296197745
206 0.440170461
207 -0.304215227
208 0.222667641
209 -0.163698281
210 -0.231661301
211 0.677516213
212 -0.144740892
213 0.649890322
214 0.955758044
215 -0.243167782
216 -0.323020005
217 2.133129613
218 0.0195457453
219 0.296764841
220 -0.108266472
221 0.653444755
222 0.0183658527
223 1.081840899
224 -0.243343535
225 -0.143356852
226 1.108042530
227 1.834478322
228 0.0899629906
229 0.351789711
230 0.134209340
231 0.354532241
232 -0.104072617
233 -0.430535690
234 -0.451430154
235 0.573140803
236 0.843584244
237 -0.910451616
238 -0.713872842
239 1.273031180
240 0.0594995521