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

$R= 23.6301398227$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.536438016
4 0.5
5 -0.447213595
6 -1.086425740
7 -1.607143809
8 -0.353553390
9 1.360641777
10 0.316227766
11 -1.774488593
12 0.768219008
13 0.395386062
14 1.136422285
15 -0.687115969
16 0.250000000
17 0.590866844
18 -0.962119027
19 -0.609504645
20 -0.223606797
21 -2.469276845
22 1.254752917
23 -1.909570455
24 -0.543212870
25 0.200000000
26 -0.279580166
27 0.554103737
28 -0.803571904
29 -1.040599004
30 0.485864361
31 1.788556732
32 -0.176776695
33 -2.726391733
34 -0.417805952
35 0.718736561
36 0.680320888
37 0.454885359
38 0.430984868
39 0.607486178
40 0.158113883
41 0.227705608
42 1.746042402
43 0.998952824
44 -0.887244296
45 -0.608497501
46 1.350270217
47 0.633873559
48 0.384109504
49 1.582911223
50 -0.141421356
51 0.907830282
52 0.197693031
53 -0.149703343
54 -0.391810509
55 0.793575423
56 0.568211142
57 -0.936466108
58 0.735814612
59 -0.760649745
60 -0.343557984
61 0.788084318
62 -1.264700593
63 -2.186747009
64 0.125000000
65 -0.176822022
66 1.927850083
67 -1.078076322
68 0.295433422
69 -2.933936641
70 -0.508223496
71 0.666865121
72 -0.481059513
73 0.977784571
74 -0.321652522
75 0.307287603
76 -0.304752322
77 2.851858357
78 -0.429557596
79 0.447725892
80 -0.111803398
81 -0.509295730
82 -0.161012179
83 0.763392342
84 -1.234638422
85 -0.264243686
86 -0.706366316
87 -1.598815870
88 0.627376458
89 0.226117089
90 0.430272709
91 -0.635442263
92 -0.954785227
93 2.748006557
94 -0.448216292
95 0.272578764
96 -0.271606435
97 -0.512872281
98 -1.119287260
99 -2.414443313
100 0.100000000
101 -0.406901248
102 -0.641932949
103 0.190371910
104 -0.139790083
105 1.104294176
106 0.105856249
107 0.374584377
108 0.277051868
109 0.324920022
110 -0.561142563
111 0.698903158
112 -0.401785952
113 0.361889719
114 0.662181535
115 0.853985869
116 -0.520299502
117 0.537978795
118 0.537860593
119 -0.949607992
120 0.242932180
121 2.148809767
122 -0.557259765
123 0.349855551
124 0.894278366
125 -0.0894427190
126 1.546263638
127 -0.536411134
128 -0.0883883476
129 1.534829095
130 0.125032051
131 -0.598654148
132 -1.363195866
133 0.979561613
134 0.762315078
135 -0.247802724
136 -0.208902976
137 1.127169423
138 2.074606494
139 0.411065224
140 0.359368280
141 0.973907477
142 -0.471544849
143 -0.701608056
144 0.340160444
145 0.465370022
146 -0.691398101
147 2.432045079
148 0.227442679
149 -0.931236167
150 -0.217285148
151 0.166774492
152 0.215492434
153 0.803957862
154 -2.016568383
155 -0.799866886
156 0.303743089
157 0.775412060
158 -0.316590014
159 -0.230009942
160 0.0790569415
161 3.068956062
162 0.360126464
163 -1.973352883
164 0.113852804
165 1.219279449
166 -0.539799902
167 0.526088682
168 0.873021201
169 -0.843656517
170 0.186848502
171 -0.829316202
172 0.499476412
173 0.940008916
174 1.130533543
175 -0.321428761
176 -0.443622148
177 -1.168688564
178 -0.159888927
179 -1.188541379
180 -0.304248750
181 1.520637043
182 0.449325533
183 1.210898003
184 0.675135108
185 -0.203430917
186 -1.943134071
187 -1.048317792
188 0.316936779
189 -0.890385354
190 -0.192742292
191 0.878186599
192 0.192054752
193 -1.336658019
194 0.362655467
195 -0.271676077
196 0.791455611
197 -0.0389620796
198 1.707269239
199 1.683715362
200 -0.0707106781
201 -1.658954756
202 0.287722632
203 1.667503196
204 0.453915141
205 -0.101833043
206 -0.134613268
207 -2.619753367
208 0.0988465157
209 1.106455370
210 -0.780853900
211 0.483246800
212 -0.0748516716
213 0.983923579
214 -0.264871153
215 -0.446745284
216 -0.195905254
217 -2.908675851
218 -0.229753151