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

$R= 11.0009604498$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.863089481
4 0.5
5 -0.447213595
6 1.317403206
7 -0.752339590
8 0.353553390
9 2.471102414
10 -0.316227766
11 1.229867699
12 0.931544740
13 1.147711166
14 -0.531984426
15 -0.833198945
16 0.250000000
17 -0.424722456
18 1.747333274
19 -0.0141527986
20 -0.223606797
21 -1.401675977
22 0.869647790
23 0.937103461
24 0.658701603
25 0.200000000
26 0.811554348
27 2.740795434
28 -0.376169795
29 -0.432680617
30 -0.589160624
31 -0.910979748
32 0.176776695
33 2.291353575
34 -0.300324129
35 0.336456493
36 1.235551207
37 -1.773247845
38 -0.0100075399
39 2.138288601
40 -0.158113883
41 -0.233521758
42 -0.991134588
43 0.947700521
44 0.614933849
45 -1.105110595
46 0.662632212
47 -1.558931365
48 0.465772370
49 -0.433985140
50 0.141421356
51 -0.791295941
52 0.573855583
53 1.054451400
54 1.938035037
55 -0.550013556
56 -0.265992213
57 -0.0263679303
58 -0.305951398
59 0.0340083331
60 -0.416599472
61 0.828426570
62 -0.644159957
63 -1.859108178
64 0.125000000
65 -0.513272037
66 1.620231650
67 -0.801626939
68 -0.212361228
69 1.745907601
70 0.237910667
71 -0.613527256
72 0.873666637
73 -0.511441834
74 -1.253875576
75 0.372617896
76 -0.00707639934
77 -0.925278162
78 1.511998370
79 -0.652834902
80 -0.111803398
81 2.635244730
82 -0.165124818
83 -1.149353731
84 -0.700837988
85 0.189941656
86 0.670125465
87 -0.806122706
88 0.434823895
89 0.485763237
90 -0.781431196
91 -0.863468526
92 0.468551730
93 -1.697236805
94 -1.102330939
95 0.00632932398
96 0.329350801
97 0.888106013
98 -0.306873835
99 3.039129029
100 0.100000000
101 -0.285414108
102 -0.559530725
103 0.518427265
104 0.405777174
105 0.626848553
106 0.745609735
107 -0.120513064
108 1.370397717
109 -1.409253799
110 -0.388918315
111 -3.303720625
112 -0.188084897
113 -0.927128884
114 -0.0186449423
115 -0.419085408
116 -0.216340308
117 2.836108279
118 0.0240475230
119 0.319538158
120 -0.294580312
121 0.512587349
122 0.585786045
123 -0.435027972
124 -0.455489874
125 -0.0894427190
126 -1.314588000
127 -0.948741418
128 0.0883883476
129 1.765845017
130 -0.362938138
131 1.254133801
132 1.145676787
133 0.0107099497
134 -0.566835845
135 -1.225720980
136 -0.150162064
137 1.664656645
138 1.234543104
139 -0.386043769
140 0.168228246
141 -2.903118711
142 -0.433829283
143 1.413270055
144 0.617775603
145 0.193500654
146 -0.361643989
147 -0.814155074
148 -0.886623922
149 0.700157625
150 0.263480641
151 -1.644010781
152 -0.00500376996
153 -1.009059512
154 -0.654270462
155 0.407402528
156 1.069144300
157 0.567909791
158 -0.461623986
159 1.996200210
160 -0.0790569415
161 -0.516741739
162 1.863399419