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

$R= 25.0775787865$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.109630858
4 0.5
5 0.447213595
6 0.784627504
7 0.955470795
8 -0.353553390
9 0.231280642
10 -0.316227766
11 -1.585850532
12 -0.554815429
13 -1.343658101
14 -0.675619878
15 -0.496242006
16 0.250000000
17 -1.460572437
18 -0.163540110
19 1.132513090
20 0.223606797
21 -1.060219878
22 1.121365665
23 0.440839937
24 0.392313752
25 0.200000000
26 0.950109754
27 0.852994720
28 0.477735397
29 -1.268826561
30 0.350896087
31 -1.208131002
32 -0.176776695
33 1.759708688
34 1.032780674
35 0.427299529
36 0.115640321
37 1.066893359
38 -0.800807685
39 1.490964492
40 -0.158113883
41 -0.436012858
42 0.749688665
43 -1.091989888
44 -0.792925266
45 0.103431847
46 -0.311720909
47 -1.097137494
48 -0.277407714
49 -0.0870755596
50 -0.141421356
51 1.620696248
52 -0.671829050
53 -0.987835702
54 -0.603158351
55 -0.709213918
56 -0.337809939
57 -1.256671472
58 0.897195865
59 1.416361470
60 -0.248121003
61 -0.173587323
62 0.854277624
63 0.220981899
64 0.125000000
65 -0.600902170
66 -1.244301946
67 0.775850674
68 -0.730286218
69 -0.489169598
70 -0.302146395
71 -1.108154099
72 -0.0817700554
73 -0.153193408
74 -0.754407529
75 -0.221926171
76 0.566256545
77 -1.515233869
78 -1.054271103
79 1.803586048
80 0.111803398
81 -1.177789907
82 0.308307648
83 -0.866395523
84 -0.530109939
85 -0.653187851
86 0.772153455
87 1.407929106
88 0.560682832
89 -0.0571580702
90 -0.0731373610
91 -1.283826074
92 0.220419968
93 1.340579441
94 0.775793362
95 0.506475251
96 0.196156876
97 -0.674566536
98 0.0615717186
99 -0.366776530
100 0.100000000
101 -1.422915418
102 -1.146005307
103 -0.0692208827
104 0.475054877
105 -0.474144744
106 0.698505324
107 -1.574121296
108 0.426497360
109 -0.933080596
110 0.501489971
111 -1.183857795
112 0.238867698
113 0.399273600
114 0.888600920
115 0.197149613
116 -0.634413280
117 -0.310762109
118 -1.001518800
119 -1.395534307
120 0.175448043
121 1.514921912
122 0.122744773
123 0.483813321
124 -0.604065501
125 0.0894427190
126 -0.156257799
127 -0.910879251
128 -0.0883883476
129 1.211705680
130 0.424901999
131 0.732692721
132 0.879854344
133 1.082083182
134 -0.548609273
135 0.381470835
136 0.516390337
137 -0.720054760
138 0.345895140
139 -0.220045706
140 0.213649764
141 1.217417609
142 0.783583278
143 2.130840911
144 0.0578201607
145 -0.567436488
146 0.108324098
147 0.0966217546
148 0.533446679
149 1.296748076
150 0.156925500
151 -0.0954190857
152 -0.400403842
153 -0.337802257
154 1.071432144
155 -0.540292609
156 0.745482246
157 -0.259331458
158 -1.275327925
159 1.096133093
160 -0.0790569415
161 0.421209020
162 0.832823230
163 0.711325935
164 -0.218006429
165 0.786965649
166 0.612634149
167 1.714099942
168 0.374844332
169 0.805417552
170 0.461873559
171 0.261924216
172 -0.545994944
173 -0.339033745
174 -0.995556218
175 0.191094159
176 -0.396462633
177 -1.571629941
178 0.0404168591
179 -0.896659365
180 0.0517159239
181 0.553693873
182 0.907802122
183 0.192571011
184 -0.155860454
185 0.477129215
186 -0.947932813
187 2.316293215
188 -0.548568747
189 0.815009142
190 -0.358132084
191 -0.0279826926
192 -0.138703857
193 0.146417201
194 0.476990572
195 0.666779591
196 -0.0435377798
197 -0.960713931
198 0.259350172
199 1.121954172
200 -0.0707106781
201 -0.863348473
202 1.006153141
203 -1.215649325
204 0.810348124
205 -0.194990877
206 0.0489465556
207 0.104395394
208 -0.335914525
209 -1.800849606
210 0.335270963
211 -0.493412252
212 -0.493917851
213 1.215864496
214 1.113071843
215 -0.488352724
216 -0.301579175
217 -1.148701245
218 0.659787617
219 0.193744638
220 -0.354606959
221 1.739744906
222 0.837113875