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

$R= 14.9238928466$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.580788631
4 0.5
5 0.447213595
6 1.117786360
7 -0.798040638
8 -0.353553390
9 1.498892697
10 -0.316227766
11 1.993303430
12 -0.790394315
13 0.221361958
14 0.564299947
15 -0.706950167
16 0.250000000
17 -0.651028374
18 -1.059877190
19 -1.579774565
20 0.223606797
21 1.261533568
22 -1.409478372
23 -1.255200879
24 0.558893180
25 0.200000000
26 -0.156526541
27 -0.788643903
28 -0.399020319
29 0.188115278
30 0.499889257
31 -0.411069172
32 -0.176776695
33 -3.150991401
34 0.460346578
35 -0.356894623
36 0.749446348
37 -0.929530286
38 1.117069307
39 -0.349926466
40 -0.158113883
41 1.573215209
42 -0.892038941
43 -0.0210574225
44 0.996651715
45 0.670325192
46 0.887561053
47 0.372508351
48 -0.395197157
49 -0.363131139
50 -0.141421356
51 1.029138253
52 0.110680979
53 0.846911548
54 0.557655452
55 0.891432394
56 0.282149973
57 2.497289672
58 -0.133017589
59 -0.300331417
60 -0.353475083
61 -1.239738901
62 0.290669799
63 -1.196177284
64 0.125000000
65 0.0989960771
66 2.228087387
67 -1.406856104
68 -0.325514187
69 1.984207280
70 0.252362608
71 0.256726082
72 -0.529938595
73 1.186360609
74 0.657277168
75 -0.316157726
76 -0.789887282
77 -1.590737142
78 0.247435377
79 0.342871470
80 0.111803398
81 -0.252213379
82 -1.112431142
83 1.807519092
84 0.630766784
85 -0.291148740
86 0.0148898462
87 -0.297370494
88 -0.704739186
89 0.845439206
90 -0.473991489
91 -0.176655839
92 -0.627600439
93 0.649813475
94 -0.263403181
95 -0.706496663
96 0.279446590
97 0.380548249
98 0.256772491
99 2.987747955
100 0.100000000
101 -0.777201029
102 -0.727710637
103 -0.524260285
104 -0.0782632708
105 0.564174963
106 -0.598856899
107 -1.238248423
108 -0.394321951
109 0.362122317
110 -0.630337890
111 1.469390959
112 -0.199510159
113 0.413125503
114 -1.765850462
115 -0.561342898
116 0.0940576393
117 0.331798116
118 0.212366382
119 0.519547071
120 0.249944628
121 2.973258514
122 0.876627784
123 -2.486920940
124 -0.205534586
125 0.0894427190
126 0.845825069
127 -0.552589971
128 -0.0883883476
129 0.0332992364
130 -0.0700007974
131 -0.628114063
132 -1.575495700
133 1.260738380
134 0.994797491
135 -0.352692275
136 0.230173289
137 0.526429139
138 -1.403046423
139 -0.595074968
140 -0.178447311
141 -0.588776576
142 -0.181532754
143 0.441267876
144 0.374723174
145 0.0841277101
146 -0.838883632
147 0.574192183
148 -0.464765143
149 0.636156925
150 0.223557272
151 1.117406196
152 0.558534653
153 -0.974268951
154 1.124821020
155 -0.183835722
156 -0.174963233
157 1.315243332
158 -0.242446742
159 -1.343824505
160 -0.0790569415
161 1.002703845
162 0.178341791
163 0.164156310
164 0.786607604
165 -1.409166194
166 -1.278109007
167 0.587746112
168 -0.446019470
169 -1.010483668
170 0.205873248
171 -2.457200593
172 -0.0105287112