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

$R= 31.4042589826$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.782419767
4 0.5
5 0.447213595
6 0.553254323
7 -0.165907234
8 0.353553390
9 -0.387819307
10 0.316227766
11 0.0357029694
12 0.391209883
13 1.602547338
14 -0.117314130
15 0.349908757
16 0.250000000
17 -0.831474497
18 -0.274229662
19 -1.499200791
20 0.223606797
21 -0.129809100
22 0.0252458117
23 -1.152507753
24 0.276627161
25 0.200000000
26 1.133172090
27 -1.085857259
28 -0.0829536174
29 -1.046080546
30 0.247422855
31 1.291370616
32 0.176776695
33 0.0279347090
34 -0.587941255
35 -0.0741959710
36 -0.193909653
37 0.106697568
38 -1.060095045
39 1.253864715
40 0.158113883
41 -1.868618888
42 -0.0917888949
43 0.634310642
44 0.0178514847
45 -0.173438067
46 -0.814946048
47 0.824542661
48 0.195604941
49 -0.972474789
50 0.141421356
51 -0.650562082
52 0.801273669
53 -0.791694851
54 -0.767817031
55 0.0159668533
56 -0.0586570654
57 -1.173004334
58 -0.739690648
59 1.415778059
60 0.174954378
61 -0.690152712
62 0.913136920
63 0.0643420290
64 0.125000000
65 0.716680957
66 0.0197528221
67 -0.0153339840
68 -0.415737248
69 -0.901744848
70 -0.0524644742
71 -1.512035459
72 -0.137114831
73 -0.705472302
74 0.0754465739
75 0.156483953
76 -0.749600395
77 -0.00592338093
78 0.886616242
79 -0.112999942
80 0.111803398
81 -0.461776876
82 -1.321313087
83 -0.894210693
84 -0.0649045500
85 -0.371846699
86 0.448525356
87 -0.818474098
88 0.0126229058
89 1.548244980
90 -0.122639233
91 -0.265874197
92 -0.576253876
93 1.010393897
94 0.583039707
95 -0.670462976
96 0.138313580
97 0.113565541
98 -0.687643518
99 -0.0138463008
100 0.100000000
101 0.840456385
102 -0.460016860
103 0.734986319
104 0.566586045
105 -0.0580523943
106 -0.559812798
107 -0.711613161
108 -0.542928629
109 -0.826627960
110 0.0112902702
111 0.0834822864
112 -0.0414768087
113 -1.448775090
114 -0.829439319
115 -0.515417136
116 -0.523040273
117 -0.621498799
118 1.001106266
119 0.137947634
120 0.123711427
121 -0.998725297
122 -0.488011663
123 -1.462044355
124 0.645685308
125 0.0894427190
126 0.0454966850
127 0.541148343
128 0.0883883476
129 0.496297185
130 0.506769964
131 0.381788124
132 0.0139673545
133 0.248728257
134 -0.0108427641
135 -0.485610129
136 -0.293970627
137 0.518806054
138 -0.637629897
139 -0.225731694
140 -0.0370979855
141 0.645138477
142 -1.069170526
143 0.0572156985
144 -0.0969548269
145 -0.467821442
146 -0.498844249
147 -0.760883498
148 0.0533487840
149 0.732344293
150 0.110650864
151 -1.003208851
152 -0.530047522
153 0.322461864
154 -0.00418846282
155 0.577518496
156 0.626932357
157 -1.013074640
158 -0.0799030255
159 -0.619437700
160 0.0790569415
161 0.191209378
162 -0.326525560
163 -1.388294285
164 -0.934309444
165 0.0124927816
166 -0.632302445
167 1.085352993
168 -0.0458944474
169 1.568157983
170 -0.262935322
171 0.581418998
172 0.317155321
173 1.227863089
174 -0.578748584
175 -0.0331814469
176 0.00892574235
177 1.107732795
178 1.094774524
179 1.968076494
180 -0.0867190335
181 -0.846756099
182 -0.188001448
183 -0.539989169
184 -0.407473024
185 0.0477166030
186 0.714456376
187 -0.0296858620
188 0.412271330
189 0.180151501
190 -0.474088917
191 -0.224807183
192 0.0978024709
193 0.788318782
194 0.0803029645
195 0.560745347
196 -0.486237394
197 -0.560053481
198 -0.00979081321
199 -0.000479070224
200 0.0707106781
201 -0.0120021028
202 0.594292409
203 0.173546117
204 -0.325281041
205 -0.835671771
206 0.519713810
207 0.446962030
208 0.400636834
209 -0.0535438614
210 -0.0410492417
211 -1.417197426
212 -0.395847425
213 -1.183002679
214 -0.503186491
215 0.283672343
216 -0.383908515
217 -0.214226048
218 -0.584514236
219 -0.552042837
220 0.00798342666
221 -1.332349958
222 0.0590308908
223 -1.479984549
224 -0.0293285327
225 -0.0775638615
226 -1.024438691
227 0.474092319
228 -0.586502167
229 0.794236139
230 -0.364454952
231 -0.00883052966
232 -0.369845324
233 -1.143411337
234 -0.439466015
235 0.368746688
236 0.707889029
237 -0.0853371183
238 0.0975437079
239 -0.877449975
240 0.0874771893
241 -0.371857345
242 -0.706205430
243 0.689163022
244 -0.345076356
245 -0.434903947
246 -1.033821478
247 -2.408317716
248 0.456568460
249 -0.902301725
250 0.0632455532