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

$R= 27.3725417397$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.153599189
4 0.5
5 0.447213595
6 -0.108611028
7 0.653560814
8 0.353553390
9 -0.976407288
10 0.316227766
11 0.0725055093
12 -0.0767995949
13 -0.932766440
14 0.462137283
15 -0.0686916459
16 0.250000000
17 0.0967262571
18 -0.690424215
19 -0.808579197
20 0.223606797
21 -0.100386411
22 0.0512691373
23 0.770112959
24 -0.0543055143
25 0.200000000
26 -0.659565475
27 0.303574558
28 0.326780407
29 1.041572724
30 -0.0485723286
31 -0.901569733
32 0.176776695
33 -0.0111367875
34 0.0683957923
35 0.292281281
36 -0.488203644
37 1.430912270
38 -0.571751833
39 0.143272169
40 0.158113883
41 0.0194672875
42 -0.0709839124
43 1.430825648
44 0.0362527546
45 -0.436662614
46 0.544552095
47 0.539189304
48 -0.0383997974
49 -0.572858262
50 0.141421356
51 -0.0148570747
52 -0.466383220
53 0.206495838
54 0.214659628
55 0.0324254495
56 0.231068641
57 0.124197109
58 0.736503136
59 0.424084129
60 -0.0343458229
61 0.00485353605
62 -0.637506072
63 -0.638141542
64 0.125000000
65 -0.417145833
66 -0.00787489796
67 -0.993802555
68 0.0483631285
69 -0.118288726
70 0.206674076
71 -0.350609959
72 -0.345212107
73 -0.795613381
74 1.011807769
75 -0.0307198379
76 -0.404289598
77 0.0473867597
78 0.101308722
79 1.304112497
80 0.111803398
81 0.929778482
82 0.0137654510
83 1.619317123
84 -0.0501932058
85 0.0432572972
86 1.011746518
87 -0.159984726
88 0.0256345686
89 -1.118404432
90 -0.308767095
91 -0.609619594
92 0.385056479
93 0.138480380
94 0.381264413
95 -0.361607609
96 -0.0271527571
97 0.691611866
98 -0.405071961
99 -0.0707949078
100 0.100000000
101 1.684293994
102 -0.0105055382
103 0.931585508
104 -0.329782737
105 -0.0448941680
106 0.146014607
107 0.350034557
108 0.151787279
109 -0.941661427
110 0.0229282552
111 -0.219786965
112 0.163390203
113 1.489395283
114 0.0878206184
115 0.344404985
116 0.520786362
117 0.910759951
118 0.299872763
119 0.0632164914
120 -0.0242861643
121 -0.994742951
122 0.00343196826
123 -0.00299015951
124 -0.450784866
125 0.0894427190
126 -0.451234212
127 -1.266682647
128 0.0883883476
129 -0.219773660
130 -0.294966647
131 -0.492675292
132 -0.00556839375
133 -0.528455678
134 -0.702724526
135 0.135762669
136 0.0341978961
137 -0.146665854
138 -0.0836427607
139 -0.107878793
140 0.146140640
141 -0.0828190411
142 -0.247918679
143 -0.0676307055
144 -0.244101822
145 0.465805482
146 -0.562583617
147 0.0879905656
148 0.715456135
149 1.054973765
150 -0.0217222057
151 -0.891613135
152 -0.285875916
153 -0.0944442129
154 0.0335074991
155 -0.403194242
156 0.0716360848
157 0.794340733
158 0.922146790
159 -0.0317176012
160 0.0790569415
161 0.503315648
162 0.657452670
163 0.647857849
164 0.00973364379
165 -0.00498052278
166 1.145030118
167 0.734325650
168 -0.0354919562
169 -0.129946763
170 0.0305875282
171 0.789502176
172 0.715412824
173 1.565232935
174 -0.113126285
175 0.130712162
176 0.0181263773
177 -0.0651380965
178 -0.790831358
179 1.537771299
180 -0.218331307
181 1.730457105
182 -0.431066148
183 -0.000744857720
184 0.272276047
185 0.639923421
186 0.0979204162
187 0.00701505694
188 0.269594652
189 0.198408015
190 -0.255695193
191 -1.214294595
192 -0.0191998987
193 1.275138735
194 0.489043441
195 0.0640732621
196 -0.286429131
197 1.429143420
198 -0.0500595594
199 0.820758801
200 0.0707106781
201 0.152757341
202 1.190975704
203 0.680878351
204 -0.00742853736
205 0.00870603568
206 0.658730430
207 -0.751560184
208 -0.233191610
209 -0.0584417782
210 -0.0317449706
211 -0.767418619
212 0.103247919
213 0.0567847620
214 0.247511809
215 0.639884682
216 0.107329814
217 -0.589925824
218 -0.665855180
219 0.128996753
220 0.0162127247
221 -0.0925563101
222 -0.155412853
223 -1.046387649
224 0.115534320
225 -0.195281457
226 1.053161504
227 0.477914469
228 0.0620985548
229 1.612194936
230 0.243531100
231 0.0245199426
232 0.368251568