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

$R= 14.2889756764$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.524966100
4 0.5
5 -0.447213595
6 1.078313870
7 -1.518993008
8 0.353553390
9 1.325521606
10 -0.316227766
11 -0.926068865
12 0.762483050
13 -0.941576124
14 -1.074090256
15 -0.681985572
16 0.250000000
17 -0.806468489
18 0.937285316
19 -0.930661902
20 -0.223606797
21 -2.316412844
22 -0.654829574
23 -0.670638832
24 0.539156935
25 0.200000000
26 -0.665794862
27 0.496409414
28 -0.759496504
29 1.379714834
30 -0.482236623
31 0.963770805
32 0.176776695
33 -1.412223626
34 -0.570259337
35 0.679314324
36 0.662760803
37 0.620019664
38 -0.658077342
39 -1.435871670
40 -0.158113883
41 1.574165050
42 -1.637951230
43 -1.769246360
44 -0.463034432
45 -0.592791283
46 -0.474213265
47 -1.018376440
48 0.381241525
49 1.307339760
50 0.141421356
51 -1.229837106
52 -0.470788062
53 -0.966923181
54 0.351014463
55 0.414150586
56 -0.537045128
57 -1.419227852
58 0.975605715
59 -1.325170167
60 -0.340992786
61 1.461249323
62 0.681488872
63 -2.013458053
64 0.125000000
65 0.421085643
66 -0.998592902
67 0.875321535
68 -0.403234244
69 -1.022701484
70 0.480347765
71 0.745098081
72 0.468642658
73 -0.137900673
74 0.438420109
75 0.304993220
76 -0.465330951
77 1.406692132
78 -1.015314594
79 -1.174931224
80 -0.111803398
81 -0.568514077
82 1.113102782
83 -1.326394092
84 -1.158206422
85 0.360663672
86 -1.251046098
87 2.104018349
88 -0.327414787
89 0.947336530
90 -0.419166736
91 1.430247547
92 -0.335319416
93 1.469717802
94 -0.720100886
95 0.416204655
96 0.269578467
97 -0.713847901
98 0.924428809
99 -1.227524261
100 0.100000000
101 -1.494000286
102 -0.869626158
103 -0.639058032
104 -0.332897431
105 1.035931316
106 -0.683717938
107 1.138069092
108 0.248204707
109 0.521104766
110 0.292848688
111 0.945510335
112 -0.379748252
113 -0.335823198
114 -1.003545638
115 0.299918803
116 0.689857417
117 -1.248077666
118 -0.937036811
119 1.225011210
120 -0.241118311
121 -0.142400189
122 1.033259305
123 2.400546957
124 0.481885402
125 -0.0894427190
126 -1.423729842
127 -0.155174064
128 0.0883883476
129 -2.698003970
130 0.297752514
131 -0.114522539
132 -0.706111813
133 1.413724589
134 0.618945793
135 -0.222001039
136 -0.285129668
137 -0.282882915
138 -0.723159154
139 0.309964452
140 0.339657162
141 -1.551836052
142 0.526863906
143 0.872107319
144 0.331380401
145 -0.617027231
146 -0.0975105016
147 1.996120435
148 0.310009832
149 0.648632810
150 0.215662774
151 -0.569354697
152 -0.329038671
153 -1.070672997
154 0.994681545
155 -0.431011407
156 -0.717935835
157 1.152989266
158 -0.830801836
159 -1.443676842
160 -0.0790569415
161 0.990219106
162 -0.402000159