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

$R= 14.7336237927$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.128270163
4 0.5
5 0.447213595
6 -0.797807483
7 -1.916800762
8 -0.353553390
9 0.272993561
10 -0.316227766
11 -1.498234422
12 0.564135081
13 0.599853099
14 1.355382817
15 0.504577756
16 0.250000000
17 0.690406966
18 -0.193035598
19 1.150665789
20 0.223606797
21 -2.162669109
22 1.059411719
23 0.927870131
24 -0.398903741
25 0.200000000
26 -0.424160194
27 -0.820259673
28 -0.958400381
29 1.018132533
30 -0.356790353
31 -0.0633195511
32 -0.176776695
33 -1.690413195
34 -0.488191448
35 -0.857219360
36 0.136496780
37 1.273687715
38 -0.813643582
39 0.676796354
40 -0.158113883
41 1.264895844
42 1.529237992
43 0.327899543
44 -0.749117211
45 0.122086432
46 -0.656103262
47 -0.478307987
48 0.282067540
49 2.674125163
50 -0.141421356
51 0.778965581
52 0.299926549
53 0.846076505
54 0.580011177
55 -0.670030802
56 0.677691408
57 1.298261878
58 -0.719928418
59 0.391411095
60 0.252288878
61 -0.961563708
62 0.0447736840
63 -0.523274266
64 0.125000000
65 0.268262461
66 1.195302633
67 -0.696690315
68 0.345203483
69 1.046888184
70 0.606145623
71 -0.488785483
72 -0.0965177991
73 -0.392173774
74 -0.900633220
75 0.225654032
76 0.575332894
77 2.871816883
78 -0.478567291
79 -1.257810663
80 0.111803398
81 -1.198468076
82 -0.894416429
83 0.528765490
84 -1.081334554
85 0.308759382
86 -0.231859990
87 1.148728558
88 0.529705859
89 0.705648467
90 -0.0863281439
91 -1.149798878
92 0.463935065
93 -0.0714415669
94 0.338214821
95 0.514593385
96 -0.199451870
97 1.494018108
98 -1.890892036
99 -0.409008362
100 0.100000000
101 1.240413784
102 -0.550811844
103 0.412574205
104 -0.212080097
105 -0.967175028
106 -0.598266434
107 0.387729757
108 -0.410129836
109 0.421561429
110 0.473783324
111 1.437064070
112 -0.479200190
113 -1.481192609
114 -0.918009777
115 0.414956137
116 0.509066266
117 0.163756648
118 -0.276769440
119 -1.323374034
120 -0.178395176
121 1.244704960
122 0.679928218
123 1.427148081
124 -0.0316597755
125 0.0894427190
126 0.370010782
127 0.270719340
128 -0.0883883476
129 0.369959036
130 -0.189690205
131 0.519180687
132 -0.845206597
133 -2.205635117
134 0.492634446
135 -0.366831277
136 -0.244095724
137 -0.852525498
138 -0.740261734
139 1.098193133
140 -0.428609680
141 -0.539734648
142 0.345623529
143 -0.898440602
144 0.0682483902
145 0.455322710
146 0.277308735
147 3.016789227
148 0.636843857
149 0.675407326
150 -0.159561496
151 -0.266062954
152 -0.406821791
153 0.186233237
154 -2.030681192
155 -0.0283173641
156 0.338398177
157 -0.210472422
158 0.889406449
159 0.957216400
160 -0.0790569415
161 -1.775634836
162 0.847444904
163 -0.707016959
164 0.632447922
165 -0.755975763
166 -0.373893664