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

$R= 19.7360025488$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.150835840
4 0.5
5 0.447213595
6 0.813763826
7 0.750037516
8 -0.353553390
9 0.324423131
10 -0.316227766
11 0.981569086
12 -0.575417920
13 -0.809284269
14 -0.530356614
15 -0.514669433
16 0.250000000
17 0.239940930
18 -0.229401796
19 -1.435269980
20 0.223606797
21 -0.863170055
22 -0.694074157
23 -1.062618134
24 0.406881913
25 0.200000000
26 0.572250394
27 0.777478073
28 0.375018758
29 0.681670356
30 0.363926246
31 -0.202675107
32 -0.176776695
33 -1.129624884
34 -0.169663859
35 0.335426974
36 0.162211565
37 1.670286985
38 1.014889136
39 0.931353342
40 -0.158113883
41 -1.593003703
42 0.610353399
43 1.121690507
44 0.490784543
45 0.145086434
46 0.751384489
47 0.344576610
48 -0.287708960
49 -0.437443723
50 -0.141421356
51 -0.276132622
52 -0.404642134
53 0.464485752
54 -0.549760017
55 0.438971040
56 -0.265178307
57 1.651760134
58 -0.482013731
59 0.251990961
60 -0.257334716
61 1.410227488
62 0.143312942
63 0.243329519
64 0.125000000
65 -0.361922927
66 0.798765415
67 0.559984891
68 0.119970465
69 1.222899034
70 -0.237182688
71 -0.679322420
72 -0.114700898
73 -0.450614247
74 -1.181071254
75 -0.230167168
76 -0.717634990
77 0.736213639
78 -0.658566264
79 1.062682979
80 0.111803398
81 -1.219172763
82 1.126423721
83 -1.113360145
84 -0.431585027
85 0.107304846
86 -0.793154964
87 -0.784490677
88 -0.347037078
89 -1.850476855
90 -0.102591602
91 -0.606993563
92 -0.531309067
93 0.233245777
94 -0.243652458
95 -0.641872248
96 0.203440956
97 -1.210736368
98 0.309319423
99 0.318443716
100 0.100000000
101 1.071387440
102 0.195255249
103 -1.884911153
104 0.286125197
105 -0.386021384
106 -0.328441025
107 -0.566590173
108 0.388739036
109 0.194947897
110 -0.310399399
111 -1.922226126
112 0.187509379
113 1.136326627
114 -1.167970791
115 -0.475217276
116 0.340835178
117 -0.262550539
118 -0.178184517
119 0.179964699
120 0.181963123
121 -0.0365221422
122 -0.997181420
123 1.833285766
124 -0.101337553
125 0.0894427190
126 -0.172059953
127 1.386366212
128 -0.0883883476
129 -1.290881608
130 0.255918156
131 0.886228068
132 -0.564812442
133 -1.076506370
134 -0.395969113
135 0.347698764
136 -0.0848319295
137 1.130539897
138 -0.864720199
139 -1.457772928
140 0.167713487
141 -0.396551289
142 0.480353490
143 -0.794368671
144 0.0811057827
145 0.304852250
146 0.318632390
147 0.503424253
148 0.835143492
149 0.0521133275
150 0.162752765
151 -0.120439627
152 0.507444568
153 0.0778372292
154 -0.520581656
155 -0.0906390634
156 0.465676671
157 1.040198165
158 -0.751430341
159 -0.534552477
160 -0.0790569415
161 -0.796995193
162 0.862085328
163 -1.149850114
164 -0.796501851
165 -0.505183605
166 0.787264509
167 1.326023635
168 0.305176699
169 -0.344898319
170 -0.0758759844
171 -0.465871140
172 0.560845253
173 -0.963919307
174 0.554718677
175 0.150007503
176 0.245392271
177 -0.289752163
178 1.308484732
179 -1.322467296
180 0.0725432174
181 -1.236715871
182 0.429209264
183 -1.628431995
184 0.375692244
185 0.746975048
186 -0.164929670
187 0.240681484
188 0.172288305
189 0.609806047
190 0.453872219