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

$R= 26.444565745$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.695997263
4 0.5
5 -0.447213595
6 1.199251165
7 -1.491320377
8 0.353553390
9 1.876406717
10 -0.316227766
11 -0.429384933
12 0.847998631
13 -1.156128633
14 -1.054522751
15 -0.758473034
16 0.250000000
17 1.120542294
18 1.326819914
19 1.529822568
20 -0.223606797
21 -2.529275279
22 -0.303620998
23 1.120053866
24 0.599625582
25 0.200000000
26 -0.817506396
27 1.486383394
28 -0.745660188
29 -0.387824780
30 -0.536321425
31 0.600095807
32 0.176776695
33 -0.728235672
34 0.792343055
35 0.666938748
36 0.938203358
37 -1.298177502
38 1.081747912
39 -1.960790999
40 -0.158113883
41 1.961916645
42 -1.788467701
43 0.0156780062
44 -0.214692466
45 -0.839154594
46 0.791997684
47 -0.100488501
48 0.423999315
49 1.224036468
50 0.141421356
51 1.900436665
52 -0.578064316
53 1.802395099
54 1.051031777
55 0.192026780
56 -0.527261375
57 2.594574889
58 -0.274233532
59 -0.0856431003
60 -0.379236517
61 1.231120042
62 0.424331814
63 -2.798323574
64 0.125000000
65 0.517036443
66 -0.514940382
67 -0.361147051
68 0.560271147
69 1.899608291
70 0.471596911
71 0.751194183
72 0.663409957
73 0.228379287
74 -0.917950115
75 0.339199452
76 0.764911284
77 0.640350501
78 -1.386488611
79 0.344625849
80 -0.111803398
81 0.644495451
82 1.387284563
83 1.568270770
84 -1.264637639
85 -0.501121748
86 0.0110860245
87 -0.657749766
88 -0.151810499
89 -0.388381304
90 -0.593371904
91 1.724158190
92 0.560026933
93 1.017760847
94 -0.0710561008
95 -0.684157451
96 0.299812791
97 -0.724160251
98 0.865524487
99 -0.805700773
100 0.100000000
101 1.030144305
102 1.343811653
103 0.896958456
104 -0.408753198
105 1.131126291
106 1.274485797
107 -0.950923881
108 0.743191697
109 -1.118998751
110 0.135783438
111 -2.201705491
112 -0.372830094
113 0.774036433
114 1.834641498
115 -0.500903316
116 -0.193912390
117 -2.169367534
118 -0.0605588170
119 -1.671087558
120 -0.268160712
121 -0.815628578
122 0.870533330
123 3.327405261
124 0.300047903
125 -0.0894427190
126 -1.978713575
127 -0.0222509155
128 0.0883883476
129 0.0265898555
130 0.365599975
131 -1.701202311
132 -0.364117836
133 -2.281455570
134 -0.255369529
135 -0.664730862
136 0.396171527
137 0.953374860
138 1.343225904
139 0.274690721
140 0.333469374
141 -0.170428223
142 0.531174501
143 0.496424222
144 0.469101679
145 0.173440514
146 0.161488542
147 2.075962500
148 -0.649088751
149 -0.987503996
150 0.239850233
151 -0.559682949
152 0.540873956
153 2.102593072
154 0.452796181
155 -0.268371003
156 -0.980395499
157 0.0497034845
158 0.243687275
159 3.056857208
160 -0.0790569415
161 -1.670359220
162 0.455727104
163 1.180590426
164 0.980958322
165 0.325676893
166 1.108934896
167 -0.906935611
168 -0.894233850
169 0.336632932
170 -0.354346586
171 2.870570196
172 0.00783900310
173 0.701952253
174 -0.465099319
175 -0.298264075
176 -0.107346233
177 -0.145247814
178 -0.274627054
179 1.815293417
180 -0.419577297
181 -0.178466209
182 1.219163948
183 2.087972494
184 0.395998842
185 0.580562628
186 0.719665596
187 -0.481107793
188 -0.0502442507
189 -2.216649262
190 -0.483772373
191 -0.476679370
192 0.211999657
193 -0.313016630
194 -0.512058624
195 0.876892392
196 0.612018234
197 1.624204567
198 -0.569716480
199 -1.080795697
200 0.0707106781
201 -0.612705650
202 0.728422024
203 0.580170833
204 0.950218332
205 -0.877395796
206 0.634245407
207 2.101136967
208 -0.289032158
209 -0.657045786
210 0.799827071
211 -1.187918012
212 0.901197549
213 1.271326481
214 -0.672404724
215 -0.00701141752
216 0.525515888
217 -0.920387927
218 -0.791251605
219 0.383848804
220 0.0960133900
221 -1.339030412
222 -1.556840883