Properties

Level 10
Symmetry even
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

$R= 25.7889209812$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.435001809
4 0.5
5 -0.447213595
6 -1.014699510
7 -0.835511719
8 0.353553390
9 1.059230192
10 -0.316227766
11 -0.560085518
12 -0.717500904
13 1.538986233
14 -0.590796002
15 0.641752318
16 0.250000000
17 -1.344575699
18 0.748988852
19 -1.757439325
20 -0.223606797
21 1.198960829
22 -0.396040268
23 1.166174342
24 -0.507349755
25 0.200000000
26 1.088227601
27 -0.0849954339
28 -0.417755859
29 1.412334494
30 0.453787416
31 1.099286370
32 0.176776695
33 0.803723732
34 -0.950758594
35 0.373652200
36 0.529615096
37 -0.530462834
38 -1.242697264
39 -2.208448029
40 -0.158113883
41 0.875711627
42 0.847793333
43 0.570923766
44 -0.280042759
45 -0.473702143
46 0.824609785
47 -0.398822448
48 -0.358750452
49 -0.301920165
50 0.141421356
51 1.929468561
52 0.769493116
53 0.304778129
54 -0.0601008477
55 0.250477858
56 -0.295398001
57 2.521928611
58 0.998671298
59 -0.759768273
60 0.320876159
61 1.431714138
62 0.777312846
63 -0.884999240
64 0.125000000
65 -0.688255566
66 0.568318501
67 0.286284214
68 -0.672287849
69 -1.673462291
70 0.264212004
71 -0.535103322
72 0.374494426
73 0.361399337
74 -0.375093867
75 -0.287000361
76 -0.878719662
77 0.467958014
78 -1.561608577
79 1.712780141
80 -0.111803398
81 -0.937261591
82 0.619221630
83 0.401675291
84 0.599480414
85 0.601312532
86 0.403704066
87 -2.026702555
88 -0.198020134
89 -0.599004670
90 -0.334957997
91 -1.285841034
92 0.583087171
93 -1.577477930
94 -0.282010057
95 0.785950759
96 -0.253674877
97 -0.0403608207
98 -0.213489796
99 -0.593259491
100 0.100000000
101 0.974095107
102 1.364340303
103 -1.542284995
104 0.544113800
105 -0.536191583
106 0.215510681
107 -1.329980464
108 -0.0424977169
109 -0.795321561
110 0.177114592
111 0.761215127
112 -0.208877929
113 0.895588717
114 1.783272822
115 -0.521529020
116 0.706167247
117 1.630140685
118 -0.537237298
119 1.123408754
120 0.226893708
121 -0.686304212
122 1.012374776
123 -1.256647770
124 0.549643185
125 -0.0894427190
126 -0.625788964
127 0.784664723
128 0.0883883476
129 -0.819276638
130 -0.486670178
131 -1.417250346
132 0.401861866
133 1.468361153
134 0.202433509
135 0.0380111136
136 -0.475379297
137 0.532904925
138 -1.183316534
139 -1.804883238
140 0.186826100
141 0.572310935
142 -0.378375188
143 -0.861963904
144 0.264807548
145 -0.631615187
146 0.255547922
147 0.433255983
148 -0.265231417
149 -0.487795224
150 -0.202939902
151 -0.803430473
152 -0.621348632
153 -1.424215168
154 0.330896285
155 -0.491615810
156 -1.104224014
157 -1.565037370
158 1.211118452
159 -0.437357102
160 -0.0790569415
161 -0.974352303
162 -0.662744027
163 -0.423029994
164 0.437855813
165 -0.359436180
166 0.284027322
167 -0.813770433
168 0.423896666
169 1.368478170
170 0.425192169
171 -1.861533436
172 0.285461883
173 0.232490936
174 -1.433095120
175 -0.167102343
176 -0.140021379
177 1.090265985
178 -0.423560264
179 -1.305664647
180 -0.236851071
181 0.977388419
182 -0.909226915
183 -2.054517360
184 0.412304892
185 0.237230191
186 -1.115445341
187 0.753078590
188 -0.199411224
189 0.0710571582
190 0.555751111
191 0.869582809
192 -0.179375226
193 -0.768260769
194 -0.0285394100
195 0.987647983
196 -0.150960082
197 -0.0916097519
198 -0.419497809
199 -1.261056027
200 0.0707106781
201 -0.411178136
202 0.688789256
203 -1.180361779
204 0.964734280
205 -0.391630145
206 -1.090560178
207 1.235363081
208 0.384746558
209 0.983275126
210 -0.379144704
211 1.637924274
212 0.152389064
213 0.774557732
214 -0.940438205
215 -0.255324870
216 -0.0300504238
217 -0.919190037
218 -0.562377269
219 -0.522141752
220 0.125238929
221 -2.127154354
222 0.538260378