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

$R= 14.6341180002$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.167648796
4 0.5
5 0.447213595
6 0.118545600
7 0.0157472699
8 0.353553390
9 -0.971893881
10 0.316227766
11 -0.259243269
12 0.0838243981
13 -1.679191975
14 0.0111350013
15 0.0749748209
16 0.250000000
17 1.692619073
18 -0.687232753
19 -1.293226863
20 0.223606797
21 0.00264001085
22 -0.183312673
23 -1.522497483
24 0.0592728003
25 0.200000000
26 -1.187368032
27 -0.330585635
28 0.00787363499
29 0.0273156403
30 0.0530152043
31 1.111639400
32 0.176776695
33 -0.0434618220
34 1.196862424
35 0.00704239323
36 -0.485946940
37 -0.524752499
38 -0.914449485
39 -0.281514513
40 0.158113883
41 -0.692198024
42 0.00186676957
43 0.135997118
44 -0.129621634
45 -0.434644157
46 -1.076568294
47 -0.553626218
48 0.0419121990
49 -0.999752023
50 0.141421356
51 0.283765550
52 -0.839595987
53 -1.363031660
54 -0.233759344
55 -0.115937114
56 0.00556750069
57 -0.216807926
58 0.0193150745
59 -1.160292644
60 0.0374874104
61 0.159962459
62 0.786047758
63 -0.0153046753
64 0.125000000
65 -0.750957480
66 -0.0307321490
67 -0.338900873
68 0.846309536
69 -0.255244870
70 0.00497972401
71 -1.006687845
72 -0.343616376
73 0.250547829
74 -0.371056050
75 0.0335297592
76 -0.646613431
77 -0.00408237373
78 -0.199060821
79 0.538553717
80 0.111803398
81 0.916471597
82 -0.489457917
83 0.667094149
84 0.00132000542
85 0.756962261
86 0.0961644847
87 0.00457943473
88 -0.0916563367
89 -0.526806188
90 -0.307339830
91 -0.0264426891
92 -0.761248741
93 0.186365008
94 -0.391472853
95 -0.578348635
96 0.0296364001
97 -0.393020355
98 -0.706931435
99 0.251956945
100 0.100000000
101 1.711815210
102 0.200652544
103 0.904372795
104 -0.593684016
105 0.00118064874
106 -0.963808929
107 1.009560046
108 -0.165292817
109 1.602192691
110 -0.0819799198
111 -0.0879740874
112 0.00393681749
113 -1.858864146
114 -0.153306355
115 -0.680881573
116 0.0136578201
117 1.631996667
118 -0.820450796
119 0.0266544047
120 0.0265076021
121 -0.932792826
122 0.113110540
123 -0.116046342
124 0.555819700
125 0.0894427190
126 -0.0108220397
127 -0.694999574
128 0.0883883476
129 0.0228021142
130 -0.531007127
131 1.790596974
132 -0.0217309110
133 -0.0203654801
134 -0.239639105
135 -0.147842390
136 0.598431212
137 0.788297532
138 -0.180485378
139 -0.201379578
140 0.00352119661
141 -0.0928120307
142 -0.711835801
143 0.435304735
144 -0.242973470
145 0.0122159257
146 0.177164069
147 -0.167606579
148 -0.262376249
149 -0.655401477
150 0.0237091201
151 1.736984454
152 -0.457224742
153 -1.644324006
154 -0.00288667415
155 0.497140253
156 -0.140757256
157 -0.233506910
158 0.380814985
159 -0.226679411
160 0.0790569415
161 -0.0216774430
162 0.648043281
163 -0.964666012
164 -0.346099012
165 -0.0194367176
166 0.471706797
167 -1.361718371
168 0.000933384789
169 1.798465570
170 0.535253148
171 1.221523157
172 0.0679985592