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

$R= 29.2898614134$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.189379667
4 0.5
5 0.447213595
6 0.133911647
7 -0.440081513
8 0.353553390
9 -0.964135341
10 0.316227766
11 -0.0577893130
12 0.0946898337
13 0.604354223
14 -0.311184622
15 0.0846931619
16 0.250000000
17 -0.860940585
18 -0.681746637
19 0.803920889
20 0.223606797
21 -0.0833424907
22 -0.0408632151
23 0.107410075
24 0.0669558235
25 0.200000000
26 0.427342969
27 -0.371967297
28 -0.220040756
29 0.729074185
30 0.0598871091
31 0.429105653
32 0.176776695
33 -0.0109441208
34 -0.608776926
35 -0.196810436
36 -0.482067670
37 0.262411534
38 0.568457912
39 0.114452401
40 0.158113883
41 -0.482519794
42 -0.0589320403
43 -0.520494235
44 -0.0288946565
45 -0.431174432
46 0.0759503925
47 -0.595578085
48 0.0473449168
49 -0.806328261
50 0.141421356
51 -0.163044641
52 0.302177111
53 0.259178771
54 -0.263020598
55 -0.0258441664
56 -0.155592311
57 0.152246270
58 0.515533300
59 -1.548894773
60 0.0423465809
61 -0.802149185
62 0.303423517
63 0.424298140
64 0.125000000
65 0.270275425
66 -0.00773866208
67 -0.278566402
68 -0.430470292
69 0.0203412843
70 -0.139165994
71 -1.173620897
72 -0.340873318
73 0.0257466411
74 0.185552975
75 0.0378759334
76 0.401960444
77 0.0254320083
78 0.0809300695
79 1.338947123
80 0.111803398
81 0.893692298
82 -0.341193018
83 0.584926336
84 -0.0416712453
85 -0.385024334
86 -0.368045003
87 0.138071826
88 -0.0204316075
89 -0.996190873
90 -0.304886365
91 -0.265965121
92 0.0537050376
93 0.0812638859
94 -0.421137303
95 0.359524351
96 0.0334779117
97 -1.674351984
98 -0.570160181
99 0.0557167190
100 0.100000000
101 -1.256953264
102 -0.115289971
103 -1.456764536
104 0.213671484
105 -0.0372718949
106 0.183267066
107 1.002177208
108 -0.185983648
109 1.011227364
110 -0.0182745853
111 0.0496954091
112 -0.110020378
113 0.183568660
114 0.107654370
115 0.0480352459
116 0.364537092
117 -0.582679265
118 -1.095233997
119 0.378884036
120 0.0299435545
121 -0.996660395
122 -0.567205128
123 -0.0913794382
124 0.214552826
125 0.0894427190
126 0.300024092
127 -1.456753087
128 0.0883883476
129 -0.0985710252
130 0.191113586
131 -0.971900098
132 -0.00547206043
133 -0.353790722
134 -0.196976192
135 -0.166348832
136 -0.304388463
137 1.026174736
138 0.0143834600
139 0.599521711
140 -0.0984052180
141 -0.112790379
142 -0.829875295
143 -0.0349252151
144 -0.241033835
145 0.326051887
146 0.0182056245
147 -0.152702177
148 0.131205767
149 1.293614112
150 0.0267823294
151 0.467694833
152 0.284228956
153 0.830063245
154 0.0179831455
155 0.191901882
156 0.0572262009
157 -0.316220271
158 0.946778591
159 0.0490831879
160 0.0790569415
161 -0.0472691923
162 0.631935884
163 1.126952493
164 -0.241259897
165 -0.00489435964
166 0.413605379
167 0.513498927
168 -0.0294660201
169 -0.634755951
170 -0.272253318
171 -0.775088544
172 -0.260247117
173 -0.630526355
174 0.0976315250
175 -0.0880163027
176 -0.0144473282
177 -0.293329218
178 -0.704413322
179 0.710691330
180 -0.215587216
181 -1.102281819
182 -0.188065741
183 -0.151910290
184 0.0379751962
185 0.117354005
186 0.0574622447
187 0.0497528648
188 -0.297789042
189 0.163694888
190 0.254222106
191 -0.0135117031
192 0.0236724584
193 -1.481231344
194 -1.183945642
195 0.0511846701
196 -0.403164130
197 -1.629493795
198 0.0393976698
199 -1.390959967
200 0.0707106781
201 -0.0527610624
202 -0.888800176
203 -0.320825464
204 -0.0815223208
205 -0.215789412
206 -1.030088082
207 -0.103489613
208 0.151088555
209 -0.0464211557
210 -0.0263552096
211 -1.161826130
212 0.129589385
213 -0.222470718
214 0.708646299
215 -0.232772098
216 -0.131510299
217 -0.188813669
218 0.715045726
219 0.00556732850
220 -0.0129220832
221 -0.520972134
222 0.0351399607
223 -1.343191516
224 -0.0777961556
225 -0.192827068
226 0.129802644
227 -0.800674296
228 0.0761231353
229 -1.042838969
230 0.0339660481
231 0.00203809435
232 0.257766650
233 -1.010586076
234 -0.412016460
235 -0.266350617
236 -0.774447386
237 0.255979766
238 0.267911471
239 -0.930216313
240 0.0211732904