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

$R= 19.3181145352$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.261644963
4 0.5
5 -0.447213595
6 -0.185010928
7 1.410994376
8 -0.353553390
9 -0.931541913
10 0.316227766
11 -0.0204655527
12 0.130822481
13 1.674179912
14 -0.997723691
15 -0.117011184
16 0.250000000
17 -0.887409579
18 0.658699603
19 -0.0463636626
20 -0.223606797
21 0.369179572
22 0.0144713311
23 0.504224028
24 -0.0925054640
25 0.200000000
26 -1.183823969
27 -0.505378213
28 0.705497188
29 1.940578748
30 0.0827394023
31 0.922672256
32 -0.176776695
33 -0.00535470881
34 0.627493331
35 -0.631015868
36 -0.465770956
37 -1.635100183
38 0.0327840602
39 0.438040742
40 0.158113883
41 -0.634715405
42 -0.261049379
43 -0.522240533
44 -0.0102327763
45 0.416598208
46 -0.356540230
47 -0.607994073
48 0.0654112408
49 0.990905130
50 -0.141421356
51 -0.232186247
52 0.837089956
53 -1.157515970
54 0.357356361
55 0.00915247344
56 -0.498861845
57 -0.0121308188
58 -1.372196392
59 -1.422238441
60 -0.0585055924
61 1.707980600
62 -0.652427809
63 -1.314400400
64 0.125000000
65 -0.748716018
66 0.00378635091
67 0.903577888
68 -0.443704789
69 0.131927677
70 0.446195599
71 0.368694405
72 0.329349801
73 -0.197203403
74 1.156190427
75 0.0523289927
76 -0.0231818313
77 -0.0288767798
78 -0.309741579
79 0.430478031
80 -0.111803398
81 0.799312248
82 0.448811567
83 1.460568554
84 0.184589786
85 0.396861628
86 0.369279822
87 0.507742655
88 0.00723566557
89 0.0906754808
90 -0.294579418
91 2.362258442
92 0.252112014
93 0.241412548
94 0.429916732
95 0.0207344602
96 -0.0462527320
97 0.312457949
98 -0.700675737
99 0.0190645201
100 0.100000000
101 -1.106082024
102 0.164180469
103 1.269358683
104 -0.591911984
105 -0.165102123
106 0.818487391
107 1.819302717
108 -0.252689106
109 0.400219178
110 -0.00647177603
111 -0.427815726
112 0.352748594
113 1.250125495
114 0.00857778425
115 -0.225495840
116 0.970289374
117 -1.559568759
118 1.005674446
119 -1.252129935
120 0.0413697011
121 -0.999581178
122 -1.207724664
123 -0.166070097
124 0.461336128
125 -0.0894427190
126 0.929421436
127 0.987987419
128 -0.0883883476
129 -0.136641646
130 0.529422173
131 0.284807315
132 -0.00267735440
133 -0.0654186981
134 -0.638926052
135 0.226012007
136 0.313746665
137 -0.195508188
138 -0.0932869555
139 1.770870980
140 -0.315507934
141 -0.159079237
142 -0.260706314
143 -0.0342645253
144 -0.232885478
145 -0.867853199
146 0.139443864
147 0.259267062
148 -0.817550091
149 -0.202260143
150 -0.0370021856
151 -0.270263882
152 0.0163920301
153 0.826671089
154 0.0204189668
155 -0.412631577
156 0.219020371
157 0.530067111
158 -0.304393935
159 -0.302858346
160 0.0790569415
161 0.711359587
162 -0.565199111
163 0.297134197
164 -0.317357702
165 0.00239469858
166 -1.032777929
167 1.393293274
168 -0.130524689
169 1.802731444
170 -0.280623548
171 0.0436179778
172 -0.261120266
173 -0.501901465
174 -0.359028275
175 0.282198875
176 -0.00511638819
177 -0.373009196
178 -0.0641172474
179 -0.178818910
180 0.208299104
181 0.610664506
182 -1.670368963
183 0.437786804
184 -0.178270115
185 0.731239031
186 -0.170704450
187 0.0145973571
188 -0.303997036
189 -0.693661809
190 -0.0146614774