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

$R= 29.868898766$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.676533092
4 0.5
5 -0.447213595
6 0.478381137
7 -1.328416191
8 -0.353553390
9 -0.542302974
10 0.316227766
11 1.219594562
12 -0.338266546
13 -1.549725222
14 0.939332097
15 0.302554796
16 0.250000000
17 -0.299431691
18 0.383466110
19 -0.724687435
20 -0.223606797
21 0.898717514
22 -0.862383585
23 -1.312003664
24 0.239190568
25 0.200000000
26 1.095821214
27 1.043419001
28 -0.664208095
29 1.371287321
30 -0.213938548
31 1.470714165
32 -0.176776695
33 -0.825096081
34 0.211730179
35 0.594085781
36 -0.271151487
37 -1.276863489
38 0.512431400
39 1.048440397
40 0.158113883
41 0.636859228
42 -0.635489248
43 -0.132931118
44 0.609797281
45 0.242525263
46 0.927726687
47 -1.449656700
48 -0.169133273
49 0.764689578
50 -0.141421356
51 0.202575448
52 -0.774862611
53 0.173082040
54 -0.737808651
55 -0.545419269
56 0.469666048
57 0.490275032
58 -0.969646564
59 -1.730291425
60 0.151277398
61 0.539399143
62 -1.039951959
63 0.720404052
64 0.125000000
65 0.693058188
66 0.583431034
67 1.871316762
68 -0.149715845
69 0.887613896
70 -0.420082084
71 0.101693570
72 0.191733055
73 -0.00827505496
74 0.902878832
75 -0.135306618
76 -0.362343717
77 -1.620129164
78 -0.741359314
79 1.030820136
80 -0.111803398
81 -0.163604509
82 -0.450327478
83 1.305190742
84 0.449358757
85 0.133909923
86 0.0939964956
87 -0.927721252
88 -0.431191792
89 0.601075378
90 -0.171491258
91 2.058680079
92 -0.656001832
93 -0.994986802
94 1.025062083
95 0.324090073
96 0.119595284
97 -0.0159563498
98 -0.540717186
99 -0.661389759
100 0.100000000
101 1.258258966
102 -0.143242473
103 0.722409806
104 0.547910607
105 -0.401918691
106 -0.122387484
107 -0.00764920969
108 0.521709500
109 -0.694789280
110 0.385669664
111 0.863840405
112 -0.332104047
113 1.221070581
114 -0.346676799
115 0.586745876
116 0.685643660
117 0.840420598
118 1.223500800
119 0.397769907
120 -0.106969274
121 0.487410897
122 -0.381412791
123 -0.430856343
124 0.735357082
125 -0.0894427190
126 -0.509402590
127 -1.095370219
128 -0.0883883476
129 0.0899323010
130 -0.490066145
131 -0.638773373
132 -0.412548040
133 0.962686523
134 -1.323220772
135 -0.466631163
136 0.105865089
137 1.531051613
138 -0.627637805
139 0.859993645
140 0.297042890
141 0.980740730
142 -0.0719082132
143 -1.890036455
144 -0.135575743
145 -0.613258333
146 0.00585134747
147 -0.517337805
148 -0.638431744
149 -0.790639601
150 0.0956762274
151 1.785165664
152 0.256215700
153 0.162382697
154 1.145604318
155 -0.657723369
156 0.524220198
157 1.287375159
158 -0.728899908
159 -0.117095730
160 0.0790569415
161 1.742886905
162 0.115685857
163 1.438354329
164 0.318429614
165 0.368994185
166 -0.922909224
167 -0.862983241
168 -0.317744624
169 1.401648265
170 -0.0946886148
171 0.393000104
172 -0.0664655594
173 -1.060140460
174 0.655997988
175 -0.265683238
176 0.304898640
177 1.170599273
178 -0.425024476
179 -1.524004045
180 0.121262631
181 0.837397441
182 -1.455706644
183 -0.364921052
184 0.463863343
185 0.571030712
186 0.703561915
187 -0.365186571
188 -0.724828350
189 -1.386094222
190 -0.229166288
191 0.0177072237
192 -0.0845666365
193 0.248307783
194 0.0112828431
195 -0.468876799
196 0.382344789
197 0.134467236
198 0.467673183
199 -1.754038527
200 -0.0707106781
201 -1.265999059
202 -0.889723447
203 -1.821652970
204 0.101287724
205 -0.284812105
206 -0.510820872
207 0.711453070
208 -0.387431305
209 -0.883791197
210 0.284199431
211 -0.946639734
212 0.0865410202
213 -0.0690696966
214 0.00540880804
215 0.0594486036
216 -0.368904325
217 -1.953804668
218 0.491290211
219 0.00558281457
220 -0.272709634
221 0.464236086
222 -0.610827408
223 -0.274756448
224 0.234833024
225 -0.108460594
226 -0.863427288
227 -0.751511989
228 0.245137516
229 0.135722986
230 -0.414891987
231 1.098469791
232 -0.484823282
233 -0.318950155
234 -0.594267104
235 0.648306185
236 -0.865145712
237 -0.685107356
238 -0.281265798