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

$R= 26.12318927$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.574785299
4 0.5
5 -0.447213595
6 -1.113541364
7 -0.178062980
8 0.353553390
9 1.479948738
10 -0.316227766
11 1.480394905
12 -0.787392649
13 0.375216536
14 -0.125909540
15 0.704265395
16 0.250000000
17 -0.108475631
18 1.046481789
19 1.497619387
20 -0.223606797
21 0.280410963
22 1.046797276
23 -1.018941317
24 -0.556770682
25 0.200000000
26 0.265318157
27 -0.755816218
28 -0.0890314900
29 -0.646330146
30 0.497990837
31 -1.540040899
32 0.176776695
33 -2.331304134
34 -0.0767038543
35 0.0796321855
36 0.739974369
37 0.963258319
38 1.058976824
39 -0.590885486
40 -0.158113883
41 0.843610665
42 0.198280493
43 0.674485140
44 0.740197452
45 -0.661853196
46 -0.720500315
47 -0.423308933
48 -0.393696324
49 -0.968293575
50 0.141421356
51 0.170825829
52 0.187608268
53 -0.0842847593
54 -0.534442773
55 -0.662052728
56 -0.0629547703
57 -2.358428995
58 -0.457024429
59 -0.773395543
60 0.352132697
61 -0.806451893
62 -1.088973363
63 -0.263524082
64 0.125000000
65 -0.167801936
66 -1.648480962
67 1.723997181
68 -0.0542378155
69 1.604613807
70 0.0563084584
71 -1.624161465
72 0.523240894
73 1.739528520
74 0.681126490
75 -0.314957059
76 0.748809693
77 -0.263603528
78 -0.417819134
79 -0.962673358
80 -0.111803398
81 -0.289700468
82 0.596522822
83 0.908780337
84 0.140205481
85 0.0485117770
86 0.476933016
87 1.017831212
88 0.523398638
89 -1.777073557
90 -0.468000883
91 -0.0668121747
92 -0.509470658
93 2.425233769
94 -0.299324617
95 -0.669755751
96 -0.278385341
97 1.212241927
98 -0.684686953
99 2.190908574
100 0.100000000
101 1.199619063
102 0.120792102
103 0.859004072
104 0.132659078
105 -0.125403595
106 -0.0595983249
107 -0.994736410
108 -0.377908109
109 -0.444824710
110 -0.468141973
111 -1.516925041
112 -0.0445157450
113 1.683559310
114 -1.667661135
115 0.455684410
116 -0.323165073
117 0.555301240
118 -0.546873233
119 0.0193154941
120 0.248995418
121 1.191569077
122 -0.570247602
123 -1.328505675
124 -0.770020449
125 -0.0894427190
126 -0.186339666
127 -0.633747766
128 0.0883883476
129 -1.062169283
130 -0.118653887
131 1.793728165
132 -1.165652067
133 -0.266670571
134 1.219050097
135 0.338011288
136 -0.0383519271
137 -1.374378575
138 1.134633304
139 0.271721927
140 0.0398160927
141 0.666620686
142 -1.148455585
143 0.555468650
144 0.369987184
145 0.289047628
146 1.230032412
147 1.524854479
148 0.481629159
149 0.862779580
150 -0.222708272
151 -0.00669180357
152 0.529488412
153 -0.160538373
154 -0.186395842
155 0.688727227
156 -0.295442743
157 1.451276001
158 -0.680712859
159 0.132730349
160 -0.0790569415
161 0.181435675
162 -0.204849166
163 0.863249491
164 0.421805332
165 1.042590904
166 0.642604739
167 0.102836077
168 0.0991402469
169 -0.859213138
170 0.0343030065
171 2.216399765
172 0.337242570
173 1.018723447
174 0.719715352
175 -0.0356125960
176 0.370098726
177 1.217929563
178 -1.256580763
179 -0.446013171
180 -0.330926598
181 -0.985003638
182 -0.0472433418
183 1.269993927
184 -0.360250157
185 -0.430782216
186 1.714899244
187 -0.160591473
188 -0.211654466
189 0.134557150
190 -0.473588833
191 0.794064371
192 -0.196848162
193 0.616133338
194 0.857184487
195 0.264252022
196 -0.484146787
197 -1.574465455
198 1.549206309
199 0.833210414
200 0.0707106781
201 -2.715044326
202 0.848258774
203 0.114976433
204 0.0854129146
205 -0.377274159
206 0.607407604
207 -1.508849715
208 0.0938041342
209 2.215627869
210 -0.0886737325
211 1.661227905
212 -0.0421423796
213 2.559065434
214 -0.703384861
215 -0.301638924
216 -0.267221386
217 0.268793226
218 -0.314538569
219 -2.750412242
220 -0.331026364
221 -0.0230252920
222 -1.072627983
223 -0.677486314
224 -0.0314773851
225 0.295989747
226 1.190456205