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

$R= 19.4246337363$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.122156858
4 0.5
5 -0.447213595
6 0.0863779431
7 1.788721884
8 0.353553390
9 -0.985077701
10 -0.316227766
11 1.899404373
12 0.0610784293
13 0.0793645709
14 1.264817374
15 -0.0546302079
16 0.250000000
17 -0.349519813
18 -0.696555122
19 0.325662781
20 -0.223606797
21 0.218504646
22 1.343081712
23 -0.477793150
24 0.0431889715
25 0.200000000
26 0.0561192263
27 -0.242490856
28 0.894360942
29 -1.190251116
30 -0.0386293905
31 0.644334086
32 0.176776695
33 0.232025271
34 -0.247147830
35 -0.799940745
36 -0.492538850
37 1.695017865
38 0.230278361
39 0.00969492668
40 -0.158113883
41 -1.501725649
42 0.154506117
43 1.357084658
44 0.949702186
45 0.440540140
46 -0.337850776
47 0.961467448
48 0.0305392146
49 2.199525981
50 0.141421356
51 -0.0426962424
52 0.0396822854
53 -0.959472682
54 -0.171466928
55 -0.849439459
56 0.632408687
57 0.0397819424
58 -0.841634635
59 0.0849541959
60 -0.0273151039
61 0.632714297
62 0.455613001
63 -1.762030043
64 0.125000000
65 -0.0354929151
66 0.164066642
67 -0.650421355
68 -0.174759906
69 -0.0583657103
70 -0.565643525
71 0.540351028
72 -0.348277561
73 -0.604894510
74 1.198558627
75 0.0244313717
76 0.162831390
77 3.397506170
78 0.00685534839
79 0.440234116
80 -0.111803398
81 0.955455780
82 -1.061880390
83 -0.129383710
84 0.109252323
85 0.156310012
86 0.959603764
87 -0.145397337
88 0.671540856
89 1.140505231
90 0.311508921
91 0.141961144
92 -0.238896575
93 0.0787098278
94 0.679860152
95 -0.145640823
96 0.0215944857
97 1.910193226
98 1.555299736
99 -1.871060895
100 0.100000000
101 0.991869965
102 -0.0301908025
103 0.665979985
104 0.0280596131
105 -0.0977182486
106 -0.678449640
107 0.134455477
108 -0.121245428
109 0.886033933
110 -0.600644401
111 0.207058055
112 0.447180471
113 -0.270138430
114 0.0281300812
115 0.213675592
116 -0.595125558
117 -0.0781802641
118 0.0600716880
119 -0.625193738
120 -0.0193146952
121 2.607736969
122 0.447396570
123 -0.183446104
124 0.322167043
125 -0.0894427190
126 -1.245943392
127 -0.662524433
128 0.0883883476
129 0.165777210
130 -0.0250972809
131 1.340134779
132 0.116012635
133 0.582519893
134 -0.459917351
135 0.108445207
136 -0.123573915
137 -0.867730752
138 -0.0412707895
139 -1.427148526
140 -0.399970372
141 0.117450154
142 0.382085876
143 0.150743630
144 -0.246269425
145 0.532296481
146 -0.427725010
147 0.268686661
148 0.847508932
149 0.771212802
150 0.0172755886
151 -1.404829291
152 0.115139180
153 0.344294887
154 2.402399652
155 -0.288154963
156 0.00484746334
157 -0.691822547
158 0.311292529
159 -0.117190993
160 -0.0790569415
161 -0.854704848
162 0.675609261
163 -0.155271266
164 -0.750862824
165 -0.103764855
166 -0.0914880987
167 -0.613805019
168 0.0772530586
169 -0.993039580
170 0.110527869
171 -0.320660080
172 0.678542329
173 -0.832299049
174 -0.102811443
175 0.357744376
176 0.474851093
177 0.00905218839
178 0.806458983
179 0.193825780
180 0.220270070
181 1.591690029
182 0.100381688
183 0.0814498157
184 -0.168925388
185 -0.758035034
186 0.0556562530
187 -0.643519393
188 0.480733724
189 -0.368558849
190 -0.102983614
191 0.330591893
192 0.0152696073