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

$R= 22.106362656$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.940314624
4 0.5
5 0.447213595
6 0.664902847
7 1.045275838
8 -0.353553390
9 -0.115808407
10 -0.316227766
11 -1.286136927
12 -0.470157312
13 0.328829515
14 -0.739121633
15 -0.420521483
16 0.250000000
17 1.689285137
18 0.0818889104
19 0.566367215
20 0.223606797
21 -0.982888157
22 0.909436143
23 0.293551674
24 0.332451423
25 0.200000000
26 -0.232517579
27 1.049210963
28 0.522637919
29 1.644128917
30 0.297353592
31 -1.893336704
32 -0.176776695
33 1.209373361
34 -1.194504975
35 0.467461566
36 -0.0579042038
37 -1.514280728
38 -0.400482098
39 -0.309203201
40 -0.158113883
41 -0.112350609
42 0.695006881
43 0.785620363
44 -0.643068463
45 -0.0517910944
46 -0.207572379
47 0.576810603
48 -0.235078656
49 0.0926015786
50 -0.141421356
51 -1.588459518
52 0.164414757
53 -0.520065443
54 -0.741904187
55 -0.575177919
56 -0.369560816
57 -0.532563375
58 -1.162574706
59 0.0456497984
60 -0.210260741
61 0.817281354
62 1.338791222
63 -0.121051730
64 0.125000000
65 0.147057029
66 -0.855156105
67 -0.466410097
68 0.844642568
69 -0.276030932
70 -0.330545243
71 -1.171389230
72 0.0409444552
73 1.002260467
74 1.070758171
75 -0.188062924
76 0.283183607
77 -1.344367855
78 0.218639680
79 -0.764971627
80 0.111803398
81 -0.870780004
82 0.0794438781
83 -1.357200600
84 -0.491444078
85 0.755471279
86 -0.555517486
87 -1.545998464
88 0.454718071
89 -0.197915385
90 0.0366218340
91 0.343717547
92 0.146775837
93 1.780332191
94 -0.407866689
95 0.253287118
96 0.166225711
97 -0.126164771
98 -0.0654792042
99 0.148945469
100 0.100000000
101 0.362950239
102 1.123210497
103 0.500971772
104 -0.116258789
105 -0.439560946
106 0.367741801
107 -1.063974556
108 0.524605481
109 1.020406184
110 0.406712207
111 1.423900314
112 0.261318959
113 0.838002922
114 0.376579174
115 0.131280299
116 0.822064458
117 -0.0380812206
118 -0.0322792820
119 1.765768935
120 0.148676796
121 0.654148194
122 -0.577905188
123 0.105644929
124 -0.946668352
125 0.0894427190
126 0.0855964995
127 1.779592847
128 -0.0883883476
129 -0.738730294
130 -0.103985022
131 -0.543550352
132 0.604686680
133 0.592009927
134 0.329801742
135 0.469221407
136 -0.597252487
137 0.197390616
138 0.195183344
139 1.836215368
140 0.233730783
141 -0.542383497
142 0.828297268
143 -0.422919439
144 -0.0289521019
145 0.735276804
146 -0.708705172
147 -0.0870755058
148 -0.757140364
149 -0.952459011
150 0.132980569
151 1.936694968
152 -0.200241049
153 -0.195636845
154 0.950611627
155 -0.846725915
156 -0.154601600
157 -0.957682609
158 0.540916625
159 0.489014501
160 -0.0790569415
161 0.306838855
162 0.615734446
163 -1.530489209
164 -0.0561753049
165 0.540848209
166 0.959685748
167 -1.168657292
168 0.347503440
169 -0.891818933
170 -0.534198865
171 -0.0655170190
172 0.392810181
173 0.974126472
174 1.093185998
175 0.209055167
176 -0.321534231
177 -0.0425259602
178 0.139947311
179 1.861290506
180 -0.0258955472
181 0.459749755
182 -0.243045008
183 -0.766512673
184 -0.103786189
185 -0.677206928
186 -1.258884965
187 -2.175683512
188 0.288405301
189 1.097985690
190 -0.179101039
191 -1.003868331
192 -0.117539328
193 0.441027962
194 0.0892119652
195 -0.138279875
196 0.0463007893
197 0.544962270
198 -0.105320351
199 1.517767133
200 -0.0707106781
201 0.397423153
202 -0.256644575
203 1.799161490
204 -0.794229759
205 -0.0502447202
206 -0.354240537
207 -0.103512868
208 0.0822073787
209 -0.797926386
210 0.310816526