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

$R= 22.1410716544$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.306619557
4 0.5
5 0.447213595
6 -0.216812768
7 0.280019311
8 0.353553390
9 -0.905984446
10 0.316227766
11 0.263935320
12 -0.153309778
13 0.0595898011
14 0.198003553
15 -0.137124434
16 0.250000000
17 -0.633820179
18 -0.640627745
19 1.237693940
20 0.223606797
21 -0.0858593974
22 0.186630454
23 -1.607197131
24 -0.108406384
25 0.200000000
26 0.0421363524
27 0.584412108
28 0.140009655
29 -1.789109537
30 -0.0969616178
31 -0.338207953
32 0.176776695
33 -0.0809277311
34 -0.448178547
35 0.125228443
36 -0.452992223
37 0.527544550
38 0.875181778
39 -0.0182713984
40 0.158113883
41 1.035922666
42 -0.0607117621
43 0.412570540
44 0.131967660
45 -0.405168561
46 -1.136459990
47 0.279385392
48 -0.0766548894
49 -0.921589185
50 0.141421356
51 0.194341663
52 0.0297949005
53 0.466454554
54 0.413241764
55 0.118035463
56 0.0990017769
57 -0.379501168
58 -1.265091486
59 0.141902462
60 -0.0685622174
61 -1.690264392
62 -0.239149137
63 -0.253693140
64 0.125000000
65 0.0266493692
66 -0.0572245474
67 -0.808750158
68 -0.316910089
69 0.492798074
70 0.0885498812
71 -0.715554201
72 -0.320313872
73 -0.852446378
74 0.373030329
75 -0.0613239115
76 0.618846970
77 0.0739069865
78 -0.0129198297
79 0.454769949
80 0.111803398
81 0.726792264
82 0.732507942
83 0.654214806
84 -0.0429296987
85 -0.283453001
86 0.291731426
87 0.548575975
88 0.0933152272
89 0.345360913
90 -0.286497437
91 0.0166862950
92 -0.803598565
93 0.103701173
94 0.197555305
95 0.553513557
96 -0.0542031921
97 -1.180162786
98 -0.651661962
99 -0.239121294
100 0.100000000
101 -0.641128289
102 0.137420308
103 -1.109072041
104 0.0210681762
105 -0.0383974898
106 0.329833178
107 -0.404450723
108 0.292206054
109 -1.296723886
110 0.0834636766
111 -0.161755476
112 0.0700048278
113 -1.711326482
114 -0.268347850
115 -0.718760408
116 -0.894554768
117 -0.0539874333
118 0.100340193
119 -0.177481890
120 -0.0484808089
121 -0.930338145
122 -1.195197413
123 -0.317634150
124 -0.169103976
125 0.0894427190
126 -0.179388140
127 0.174739341
128 0.0883883476
129 -0.126502194
130 0.0188439497
131 0.876127248
132 -0.0404638655
133 0.346578212
134 -0.571872721
135 0.261357040
136 -0.224089273
137 -1.344928927
138 0.348460859
139 -1.496617806
140 0.0626142215
141 -0.0856650169
142 -0.505973228
143 0.0157278370
144 -0.226496111
145 -0.800114108
146 -0.602770614
147 0.282577237
148 0.263772275
149 0.219128400
150 -0.0433625537
151 0.805933046
152 0.437590889
153 0.574231571
154 0.0522601313
155 -0.151251195
156 -0.00913569924
157 -0.156642684
158 0.321570915
159 -0.143023601
160 0.0790569415
161 -0.450048892
162 0.513919738
163 -1.652931408
164 0.517961333
165 -0.0361919816
166 0.462599725
167 0.732929476
168 -0.0303558810
169 -0.996457639
170 -0.200431539
171 -1.121312694
172 0.206285270
173 -0.633328807
174 0.387901792
175 0.0560038622
176 0.0659838300
177 -0.0435906409
178 0.244207043
179 -0.789688196
180 -0.202584280
181 1.794324781
182 0.0117989924
183 0.518169793
184 -0.568229995
185 0.235925095
186 0.0733278028
187 -0.167671548
188 0.139692696
189 0.163656983
190 0.391393189
191 0.158399898
192 -0.0383274447
193 1.171547698
194 -0.834501109
195 -0.00817121781
196 -0.460794592
197 -1.033200487
198 -0.169084289
199 -0.122973080
200 0.0707106781
201 0.248392266
202 -0.453346160
203 -0.480178169
204 0.0971708316
205 0.463278700
206 -0.784232361
207 1.406371782
208 0.0148974502
209 0.238505576
210 -0.0271511254
211 -1.359850067