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

$R= 25.2347442706$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.0984305642
4 0.5
5 0.447213595
6 0.0696009194
7 -1.245260930
8 -0.353553390
9 -0.990311424
10 -0.316227766
11 -1.167556539
12 -0.0492152821
13 0.371141814
14 0.880532448
15 -0.0440194865
16 0.250000000
17 0.387856699
18 0.700255923
19 1.093450136
20 0.223606797
21 0.122571736
22 0.825587146
23 0.896104447
24 0.0348004597
25 0.200000000
26 -0.262436894
27 0.195907476
28 -0.622630465
29 0.0897852250
30 0.0311264774
31 0.455674593
32 -0.176776695
33 0.114923249
34 -0.274256102
35 -0.556897617
36 -0.495155712
37 -0.812384048
38 -0.773186006
39 -0.0365316982
40 -0.158113883
41 1.272370301
42 -0.0866713057
43 0.762557800
44 -0.583778269
45 -0.442880732
46 -0.633641531
47 0.0948302861
48 -0.0246076410
49 0.550674784
50 -0.141421356
51 -0.0381769537
52 0.185570907
53 0.285193362
54 -0.138527505
55 -0.522147158
56 0.440266224
57 -0.107628913
58 -0.0634877414
59 -1.401253021
60 -0.0220097432
61 0.455205796
62 -0.322210595
63 1.233196125
64 0.125000000
65 0.165979665
66 -0.0812630087
67 -1.668675254
68 0.193928349
69 -0.0882040664
70 0.393786082
71 1.654583833
72 0.350127961
73 -0.0899663624
74 0.574442269
75 -0.0196861128
76 0.546725068
77 1.453912542
78 0.0258318115
79 1.607442707
80 0.111803398
81 0.971028140
82 -0.899701668
83 -1.666882485
84 0.0612858680
85 0.173454789
86 -0.539209791
87 -0.00883761036
88 0.412793573
89 -0.637358757
90 0.313163969
91 -0.462168401
92 0.448052223
93 -0.0448523073
94 -0.0670551384
95 0.489005766
96 0.0174002298
97 -1.027196905
98 -0.389385874
99 1.156244579
100 0.100000000
101 -1.190501409
102 0.0269951828
103 1.197013654
104 -0.131218447
105 0.0548157467
106 -0.201662160
107 1.447133407
108 0.0979537382
109 -0.159448851
110 0.369213796
111 0.0799634204
112 -0.311315232
113 1.898205437
114 0.0761051348
115 0.400750092
116 0.0448926125
117 -0.367545979
118 0.990835514
119 -0.482982794
120 0.0155632387
121 0.363188273
122 -0.321879105
123 -0.125240126
124 0.227837296
125 0.0894427190
126 -0.872001342
127 -0.220294453
128 -0.0883883476
129 -0.0750589961
130 -0.117365346
131 -1.503527577
132 0.0574616245
133 -1.361630731
134 1.179931587
135 0.0876124869
136 -0.137128051
137 0.332173741
138 0.0623696934
139 -1.453035964
140 -0.278448808
141 -0.00933416712
142 -1.169967448
143 -0.433329022
144 -0.247577856
145 0.0401531733
146 0.0636158249
147 -0.0542033532
148 -0.406192024
149 -0.522355322
150 0.0139201838
151 -1.214703093
152 -0.386593003
153 -0.384098760
154 -1.028071418
155 0.203783873
156 -0.0182658491
157 -1.282050288
158 -1.136633638
159 -0.0280720416
160 -0.0790569415
161 -1.115882073
162 -0.686620582
163 1.568254774
164 0.636185150
165 0.0513952394
166 1.178663909
167 0.306500831
168 -0.0433356528
169 -0.862256607
170 -0.122651057
171 -1.082845766
172 0.381278900
173 -0.922399047
174 0.00624913421
175 -0.249052186
176 -0.291889134
177 0.137880420
178 0.450680699
179 -1.683360659
180 -0.221440366
181 -0.581720300
182 0.326802410
183 -0.0446800962
184 -0.316820765
185 -0.363309191
186 0.0317153706
187 -0.453267488
188 0.0474151430
189 -0.244023904
190 -0.345779293
191 1.607355059
192 -0.0123038205
193 0.646263744
194 0.726337897
195 -0.0163374721
196 0.275337392
197 -0.798717976
198 -0.817588382
199 0.323181072
200 -0.0707106781
201 0.167088977
202 0.841811619
203 -0.105919891
204 -0.0190884768
205 0.569021297
206 -0.846416472
207 -0.902426245
208 0.0927854536
209 -1.279226430
210 -0.0387605862
211 0.892825316
212 0.142596681
213 -0.117959897
214 -1.023277845
215 0.341026215
216 -0.0692637525
217 -0.693814531
218 0.112747364
219 -0.0561960329
220 -0.261073579
221 0.196878221
222 -0.0565426768