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

$R= 18.2771231012$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.0557137732
4 0.5
5 0.447213595
6 -0.0393955868
7 -0.799718603
8 0.353553390
9 -0.996895975
10 0.316227766
11 -1.176934349
12 -0.0278568866
13 0.456433438
14 -0.565486447
15 -0.0249159568
16 0.250000000
17 0.499950449
18 -0.704911904
19 1.867712140
20 0.223606797
21 0.0445553409
22 -0.832218259
23 0.196552961
24 -0.0196977934
25 0.200000000
26 0.322747179
27 0.111254609
28 -0.399859301
29 -0.0521456676
30 -0.0176182420
31 -0.710216964
32 0.176776695
33 0.0655714534
34 0.353518352
35 -0.357645032
36 -0.498447987
37 1.578392875
38 1.320671919
39 -0.0254296290
40 0.158113883
41 0.707657276
42 0.0315053837
43 1.073697390
44 -0.588467174
45 -0.445825433
46 0.138983932
47 1.011519858
48 -0.0139284433
49 -0.360450154
50 0.141421356
51 -0.0278541259
52 0.228216719
53 -1.903934335
54 0.0786688888
55 -0.526341041
56 -0.282743223
57 -0.104057290
58 -0.0368725552
59 -0.766093964
60 -0.0124579784
61 1.587583245
62 -0.502199231
63 0.797236257
64 0.125000000
65 0.204123239
66 0.0463660193
67 1.875522341
68 0.249975224
69 -0.0109507071
70 -0.252893227
71 -0.532742703
72 -0.352455952
73 0.307848285
74 1.116092305
75 -0.0111427546
76 0.933856070
77 0.941216294
78 -0.0179814631
79 0.928448461
80 0.111803398
81 0.990697561
82 0.500389258
83 0.548736627
84 0.0222776704
85 0.223584637
86 0.759218705
87 0.00290523185
88 -0.416109129
89 -0.326775801
90 -0.315246187
91 -0.365018312
92 0.0982764808
93 0.0395688667
94 0.715252551
95 0.835266261
96 -0.00984889671
97 -0.163204579
98 -0.254876748
99 1.173281115
100 0.100000000
101 0.122130710
102 -0.0196958413
103 0.615717286
104 0.161373589
105 0.0199257542
106 -1.346284879
107 0.734588129
108 0.0556273047
109 0.550990014
110 -0.372179319
111 -0.0879382222
112 -0.199929650
113 0.244155116
114 -0.0735796158
115 0.0879011566
116 -0.0260728338
117 -0.455016667
118 -0.541710237
119 -0.399819685
120 -0.00880912102
121 0.385174453
122 1.122590878
123 -0.0394262649
124 -0.355108482
125 0.0894427190
126 0.563731164
127 -0.731601856
128 0.0883883476
129 -0.0598196127
130 0.144336926
131 1.193564141
132 0.0327857267
133 -1.493643902
134 1.326194566
135 0.0497545739
136 0.176759176
137 -0.721714044
138 -0.00774331927
139 0.540738784
140 -0.178822516
141 -0.0563562184
142 -0.376705978
143 -0.537194936
144 -0.249223993
145 -0.0233202515
146 0.217681610
147 0.0201020271
148 0.789196437
149 -1.457083209
150 -0.00787911736
151 -1.011364601
152 0.660335959
153 -0.498349073
154 0.665540424
155 -0.317618682
156 -0.0127148145
157 1.266136467
158 0.656512203
159 0.106053198
160 0.0790569415
161 -0.157321735
162 0.700528963
163 1.066562021
164 0.353828638
165 0.0293244454
166 0.388015390
167 -1.882998552
168 0.0157526918
169 -0.791079685
170 0.158098213
171 -1.860629358
172 0.536848695
173 0.415071601
174 0.00205430914
175 -0.159943720
176 -0.294233587
177 0.0435425512
178 -0.231065385
179 1.385567910
180 -0.222912716
181 -1.525306380
182 -0.258106924
183 -0.0757828675
184 0.0694919660
185 0.705878752
186 0.0279794139
187 -0.698802652
188 0.505759929
189 -0.183395643
190 0.590622437