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

$R= 20.7236246695$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.00263189915
4 0.5
5 0.447213595
6 0.00186103374
7 -1.663091064
8 -0.353553390
9 -0.999993073
10 -0.316227766
11 0.707061421
12 -0.00131594957
13 1.383807718
14 1.175982969
15 -0.00117702108
16 0.250000000
17 0.723251457
18 0.707101883
19 -1.003332043
20 0.223606797
21 0.00437708796
22 -0.499967926
23 -0.457177476
24 0.000930516870
25 0.200000000
26 -0.978499821
27 0.00526378007
28 -0.831545532
29 0.789664601
30 0.000832279590
31 1.085338091
32 -0.176776695
33 -0.00186091435
34 -0.511416010
35 -0.743756934
36 -0.499996536
37 -1.200269097
38 0.709462891
39 -0.00364204237
40 -0.158113883
41 0.0734091497
42 -0.00309506858
43 1.434303773
44 0.353530710
45 -0.447210497
46 0.323273293
47 0.543737547
48 -0.000657974789
49 1.765871890
50 -0.141421356
51 -0.00190352488
52 0.691903859
53 -1.548804805
54 -0.00372205458
55 0.316207480
56 0.587991484
57 0.00264066874
58 -0.558377194
59 0.585510996
60 -0.000588510542
61 -1.645096875
62 -0.767449924
63 1.663079544
64 0.125000000
65 0.618857625
66 0.00131586516
67 1.116844731
68 0.361625728
69 0.00120324501
70 0.525915572
71 -0.851625246
72 0.353550941
73 1.849780687
74 0.848718418
75 -0.000526379831
76 -0.501666021
77 -1.175907533
78 0.00257531286
79 -1.042300409
80 0.111803398
81 0.999979219
82 -0.0519081075
83 0.119178348
84 0.00218854398
85 0.323447884
86 -1.014205924
87 -0.00207831761
88 -0.249983963
89 0.432310589
90 0.316225575
91 -2.301398251
92 -0.228588738
93 -0.00285650046
94 -0.384480506
95 -0.448703730
96 0.000465258435
97 -1.393581967
98 -1.248659988
99 -0.707056524
100 0.100000000
101 -1.190437689
102 0.00134599535
103 0.795832945
104 -0.489249910
105 0.00195749324
106 1.095170380
107 -0.0992269753
108 0.00263189003
109 -0.970095052
110 -0.223592453
111 0.00315898727
112 -0.415772766
113 -0.966481330
114 -0.00186723477
115 -0.204455982
116 0.394832300
117 -1.383798130
118 -0.414018796
119 -1.202833036
120 0.000416139795
121 -0.500064148
122 1.163259156
123 -0.000193209736
124 0.542669045
125 0.0894427190
126 -1.175974823
127 0.658403277
128 -0.0883883476
129 -0.00377492461
130 -0.437598423
131 0.663784481
132 -0.000930457177
133 1.668632547
134 -0.789728483
135 0.00235403401
136 -0.255708005
137 -1.558083437
138 -0.000850822706
139 0.0564056042
140 -0.371878467
141 -0.00143107163
142 0.602189986
143 0.978436765
144 -0.249998268
145 0.353148745
146 -1.307992468
147 -0.00464587320
148 -0.600134548
149 -1.502077562
150 0.000372206748
151 1.266148905
152 0.354731445
153 -0.723244159
154 0.831492190
155 0.485377950
156 -0.00182102118
157 -0.172506628
158 0.737017687
159 0.00406322122
160 -0.0790569415
161 0.760327170
162 -0.707092087
163 -0.555579814
164 0.0367045748
165 -0.000832226199
166 -0.0842718184
167 -0.864615369
168 -0.00154753429
169 0.914995295
170 -0.228712192
171 1.003473727
172 0.717151886
173 -0.460432458
174 0.00146959247
175 -0.332618212
176 0.176765355
177 -0.00185228570
178 -0.305689749
179 -1.722946157
180 -0.223605248
181 -1.483115922
182 1.627334310
183 0.00495401873
184 0.161636646
185 -0.536776658
186 0.00201985085
187 0.505039770
188 0.271868773
189 -0.00998902706
190 0.317281450
191 -0.0508610618
192 -0.000328987394
193 -0.0982732090
194 0.985411259
195 -0.00162877086
196 0.882935945