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

$R= 27.299702759$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.724768977
4 0.5
5 -0.447213595
6 -0.512489058
7 -0.514916310
8 -0.353553390
9 -0.474709929
10 0.316227766
11 -0.793333250
12 0.362384488
13 -0.314645564
14 0.364100814
15 -0.324126540
16 0.250000000
17 0.0972255073
18 0.335670610
19 0.155888614
20 -0.223606797
21 -0.373195367
22 0.560971321
23 1.535386130
24 -0.256244529
25 0.200000000
26 0.222488012
27 -1.068824007
28 -0.257458155
29 1.478971193
30 0.229192074
31 1.927674013
32 -0.176776695
33 -0.574983328
34 -0.0687488155
35 0.230277574
36 -0.237354964
37 0.911571066
38 -0.110229896
39 -0.228045344
40 0.158113883
41 0.285829238
42 0.263888975
43 -0.170469707
44 -0.396666625
45 0.212296734
46 -1.085681944
47 0.483360717
48 0.181192244
49 -0.734861193
50 -0.141421356
51 0.0704660315
52 -0.157322782
53 -0.347892970
54 0.755772703
55 0.354789415
56 0.182050407
57 0.112983231
58 -1.045790560
59 -1.530966761
60 -0.162063270
61 -0.663284190
62 -1.363071366
63 0.244435885
64 0.125000000
65 0.140713774
66 0.406574610
67 -0.393188954
68 0.0486127536
69 1.112800234
70 -0.162830834
71 -1.540853396
72 0.167835305
73 -0.450469784
74 -0.644578082
75 0.144953795
76 0.0779443070
77 0.408500230
78 0.161252409
79 0.769741209
80 -0.111803398
81 -0.299940552
82 -0.202111792
83 0.465080608
84 -0.186597683
85 -0.0434805687
86 0.120540286
87 1.071912439
88 0.280485660
89 0.944423933
90 -0.150116460
91 0.162016133
92 0.767693065
93 1.397118322
94 -0.341787641
95 -0.0697155076
96 -0.128122264
97 0.414736741
98 0.519625332
99 0.376603171
100 0.100000000
101 -0.303459715
102 -0.0498270087
103 0.334115576
104 0.111244006
105 0.166898042
106 0.245997478
107 -1.495986874
108 -0.534412003
109 -0.739363619
110 -0.250874001
111 0.660678429
112 -0.128729077
113 -1.030993722
114 -0.0798912091
115 -0.686645551
116 0.739485596
117 0.149365373
118 1.082556978
119 -0.0500629995
120 0.114596037
121 -0.370622353
122 0.469012748
123 0.207160164
124 0.963837006
125 -0.0894427190
126 -0.172842272
127 0.461913816
128 -0.0883883476
129 -0.123551155
130 -0.0994996640
131 0.875486151
132 -0.287491664
133 -0.0802695902
134 0.278026575
135 0.477992627
136 -0.0343744077
137 1.025765475
138 -0.786868592
139 0.927522137
140 0.115138787
141 0.350324851
142 1.089547885
143 0.249618787
144 -0.118677482
145 -0.661416025
146 0.318530239
147 -0.532604593
148 0.455785533
149 0.303734287
150 -0.102497811
151 -1.402573132
152 -0.0551149480
153 -0.0461539284
154 -0.288853283
155 -0.862082026
156 -0.114022672
157 -0.834339900
158 -0.544289229
159 -0.252142047
160 0.0790569415
161 -0.790595405
162 0.212089998
163 -0.967000946
164 0.142914619
165 0.257140361
166 -0.328861651
167 -0.153832432
168 0.131944487
169 -0.900998149
170 0.0307454049
171 -0.0740017436
172 -0.0852348538
173 0.529258313
174 -0.757956554
175 -0.102983262
176 -0.198333312
177 -1.109598760
178 -0.667808568
179 -1.681699278
180 0.106148367
181 -0.823237236
182 -0.114562706
183 -0.480729919
184 -0.542840972
185 -0.407666974
186 -0.987911840
187 -0.0771274846
188 0.241680358
189 0.550354416
190 0.0492963082
191 0.651629535
192 0.0905961221
193 -1.695397662
194 -0.293263162
195 0.101984978
196 -0.367430596
197 0.648967237
198 -0.266298656
199 1.038472979
200 -0.0707106781
201 -0.284943881
202 0.214578422
203 -0.761669029
204 0.0352330157
205 -0.127826721
206 -0.236255389
207 -0.728481924
208 -0.0786613911
209 -0.122752544
210 -0.118014737
211 -1.343867664
212 -0.173946485
213 -1.116822601
214 1.057822463
215 0.0762363708
216 0.377886351
217 -0.995582134
218 0.522809028
219 -0.329763431
220 0.177394707
221 -0.0286005943
222 -0.467170197
223 1.665176178
224 0.0910252037
225 -0.0949419859
226 0.729022652
227 -1.383327572
228 0.0564916157