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

$R= 23.4946353042$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.702512342
4 0.5
5 -0.447213595
6 1.203858022
7 1.299627771
8 0.353553390
9 1.898548276
10 -0.316227766
11 -0.340368231
12 0.851256171
13 0.394954290
14 0.918975610
15 -0.761386666
16 0.250000000
17 1.457145913
18 1.342476360
19 0.940889767
20 -0.223606797
21 2.212632321
22 -0.240676684
23 -1.019966227
24 0.601929011
25 0.200000000
26 0.279274857
27 1.529789530
28 0.649813885
29 -0.994986495
30 -0.538381674
31 -1.657590853
32 0.176776695
33 -0.579481115
34 1.030357756
35 -0.581211208
36 0.949274138
37 0.662718926
38 0.665309534
39 0.672414554
40 -0.158113883
41 1.423147356
42 1.564567318
43 1.542504473
44 -0.170184115
45 -0.849056600
46 -0.721225035
47 -0.704689143
48 0.425628085
49 0.689032344
50 0.141421356
51 2.480808902
52 0.197477145
53 -1.422844450
54 1.081724551
55 0.152217300
56 0.459487805
57 1.601876441
58 -0.703561698
59 -0.486791090
60 -0.380693333
61 0.219282781
62 -1.172093733
63 2.467406065
64 0.125000000
65 -0.176628928
66 -0.409755026
67 0.554814676
68 0.728572956
69 -1.736505090
70 -0.410978386
71 1.989727657
72 0.671238180
73 0.930138586
74 0.468613046
75 0.340502468
76 0.470444883
77 -0.442352006
78 0.475468891
79 -1.761021598
80 -0.111803398
81 0.705937281
82 1.006317146
83 0.619895282
84 1.106316160
85 -0.651655463
86 1.090715373
87 -1.693976789
88 -0.120338342
89 0.0233957753
90 -0.600373680
91 0.513293564
92 -0.509983113
93 -2.822068887
94 -0.498290471
95 -0.420778695
96 0.300964505
97 1.165951838
98 0.487219443
99 -0.646205519
100 0.100000000
101 -1.502228318
102 1.754196797
103 -0.0647647616
104 0.139637428
105 -0.989519256
106 -1.006102959
107 0.927084577
108 0.764894765
109 -0.0843666552
110 0.107633885
111 1.128287151
112 0.324906942
113 -1.639470912
114 1.132697694
115 0.456142763
116 -0.497493247
117 0.749839787
118 -0.344213281
119 1.893747295
120 -0.269190837
121 -0.884149466
122 0.155056341
123 2.422925938
124 -0.828795426
125 -0.0894427190
126 1.744719560
127 -0.235710560
128 0.0883883476
129 2.626132907
130 -0.124895512
131 0.584571911
132 -0.289740557
133 1.222806476
134 0.392313219
135 -0.684142676
136 0.515178878
137 0.718153023
138 -1.227894525
139 -0.606714074
140 -0.290605604
141 -1.199741948
142 1.406949919
143 -0.134429887
144 0.474637069
145 0.444971488
146 0.657707301
147 1.173086069
148 0.331359463
149 -0.401787268
150 0.240771604
151 0.229058157
152 0.332654767
153 2.766461877
154 -0.312790103
155 0.741297165
156 0.336207277
157 0.469404864
158 -1.245230314
159 -2.422410040
160 -0.0790569415
161 -1.325575940
162 0.499173038
163 -0.271295545
164 0.711573678
165 0.259151833
166 0.438332158
167 -0.0664407493
168 0.782283659
169 -0.844008061
170 -0.460789996
171 1.786333501
172 0.771252236
173 -0.134912531
174 -1.197822474
175 0.259925554
176 -0.0850920579
177 -0.828807447
178 0.0165433114
179 1.115326512
180 -0.424528300
181 1.711922707
182 0.362953360
183 0.373234215
184 -0.360612517
185 -0.296376913
186 -1.995504047
187 -0.495887970
188 -0.352344571
189 1.988154365
190 -0.297535469
191 -1.253854553
192 0.212814042
193 1.405870003
194 0.824452451
195 -0.300712930
196 0.344516172
197 -0.360265394
198 -0.456936305
199 -0.0550157492
200 0.0707106781
201 0.944598867
202 -1.062235831
203 -1.286490157
204 1.240404451
205 -0.636450846
206 -0.0457956021
207 -1.914614087
208 0.0987385726
209 -0.283778617
210 -0.699695776
211 1.507521348
212 -0.711422225
213 3.465674227
214 0.655547791
215 -0.689828971
216 0.540862275
217 -2.641333148
218 -0.0596562340