Properties

Level 10
Symmetry even
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

$R= 20.2392441753$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.857777403
4 0.5
5 0.447213595
6 1.313646999
7 -1.658018023
8 0.353553390
9 2.451336879
10 0.316227766
11 1.220619687
12 0.928888701
13 -0.652251599
14 -1.172395787
15 0.830823312
16 0.250000000
17 -0.128029368
18 1.733356930
19 1.195755863
20 0.223606797
21 -3.080228417
22 0.863108457
23 0.161576502
24 0.656823499
25 0.200000000
26 -0.461211529
27 2.696260859
28 -0.829009011
29 0.966065236
30 0.587480797
31 -0.0263554827
32 0.176776695
33 2.267639672
34 -0.0905304349
35 -0.741488201
36 1.225668439
37 1.300619739
38 0.845527079
39 -1.211738282
40 0.158113883
41 0.956511028
42 -2.178050401
43 0.908322784
44 0.610309843
45 1.096271179
46 0.114251840
47 -0.202335567
48 0.464444350
49 1.749023765
50 0.141421356
51 -0.237850068
52 -0.326125799
53 -1.346673988
54 1.906544337
55 0.545877718
56 -0.586197893
57 2.221448222
58 0.683111280
59 -0.00297221156
60 0.415411656
61 -0.192232739
62 -0.0186361405
63 -4.064360727
64 0.125000000
65 -0.291695783
66 1.603463389
67 -1.486711335
68 -0.0640146844
69 0.300173175
70 -0.524311335
71 0.354057841
72 0.866678465
73 -1.085847127
74 0.919677037
75 0.371555480
76 0.597877931
77 -2.023809440
78 -0.856828356
79 -0.184070041
80 0.111803398
81 2.557715617
82 0.676355434
83 0.364525741
84 -1.540114208
85 -0.0572564744
86 0.642281200
87 1.794734167
88 0.431554228
89 -0.571262647
90 0.775180785
91 1.081444907
92 0.0807882513
93 -0.0489626204
94 -0.143072852
95 0.534758279
96 0.328411749
97 -0.235324978
98 1.236746564
99 2.992150055
100 0.100000000
101 0.420859310
102 -0.168185396
103 -1.457676097
104 -0.230605764
105 -1.377520025
106 -0.952242309
107 0.637363760
108 1.348130429
109 0.592452151
110 0.385993836
111 2.416261961
112 -0.414504505
113 -0.876378556
114 1.570801102
115 0.0722592086
116 0.483032618
117 -1.598888403
118 -0.00210167095
119 0.212274999
120 0.293740398
121 0.489912421
122 -0.135929073
123 1.776984579
124 -0.0131777413
125 0.0894427190
126 -2.873937031
127 -1.277911118
128 0.0883883476
129 1.687461618
130 -0.206260066
131 1.495970445
132 1.133819836
133 -1.982584803
134 -1.051263666
135 1.205804513
136 -0.0452652174
137 1.554416078
138 0.212254487
139 -1.812550604
140 -0.370744100
141 -0.375895045
142 0.250356700
143 -0.796150347
144 0.612834219
145 0.432037508
146 -0.767809867
147 3.249298050
148 0.650309869
149 -0.176384462
150 0.262729399
151 -0.170852651
152 0.422763539
153 -0.313850940
154 -1.431049379
155 -0.0117865302
156 -0.605869141
157 -0.566150170
158 -0.130157174
159 -2.501747727
160 0.0790569415
161 -0.267964966
162 1.808578057
163 -1.277567373
164 0.478255514
165 1.014119291
166 0.257758623
167 1.342005234
168 -1.089025200
169 -0.574302336
170 -0.0404864413
171 2.931463748
172 0.454161392
173 -1.480851888
174 1.269068699
175 -0.331603604
176 0.305154921
177 -0.00824536080
178 -0.403943692
179 -0.665155106
180 0.548135589
181 -1.516028162
182 0.764697027
183 -0.369456479
184 0.0571259203
185 0.581654830
186 -0.0346218009
187 -0.141441996
188 -0.101167783
189 -4.445748622
190 0.378131205