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

$R= 26.6272055083$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.035526117
4 0.5
5 -0.447213595
6 0.732227539
7 0.899601514
8 -0.353553390
9 0.0723143404
10 0.316227766
11 0.110089753
12 -0.517763058
13 -0.299780870
14 -0.636114331
15 0.463101358
16 0.250000000
17 -0.255886736
18 -0.0511339604
19 0.281396969
20 -0.223606797
21 -0.931560864
22 -0.0778452112
23 1.256026072
24 0.366113769
25 0.200000000
26 0.211977086
27 0.960642729
28 0.449800757
29 0.262330894
30 -0.327462110
31 0.149414119
32 -0.176776695
33 -0.114000815
34 0.180939246
35 -0.402314027
36 0.0361571702
37 -1.373861529
38 -0.198977705
39 0.310430920
40 0.158113883
41 1.923527222
42 0.658713004
43 1.612877140
44 0.0550448767
45 -0.0323399561
46 -0.888144553
47 -0.788420252
48 -0.258881529
49 -0.190717114
50 -0.141421356
51 0.264977398
52 -0.149890435
53 -0.932994448
54 -0.679276988
55 -0.0492336345
56 -0.318057165
57 -0.291393911
58 -0.185495954
59 0.602132170
60 0.231550679
61 -1.432534531
62 -0.105651737
63 0.0650540901
64 0.125000000
65 0.134066080
66 0.0806107493
67 0.123822207
68 -0.127943368
69 -1.300647802
70 0.284478977
71 -0.103145266
72 -0.0255669802
73 -0.223678649
74 0.971466803
75 -0.207105223
76 0.140698484
77 0.0990369090
78 -0.219507809
79 0.169020998
80 -0.111803398
81 -1.067084976
82 -1.360139142
83 0.0237372172
84 -0.465780432
85 0.114436027
86 -1.140476362
87 -0.271650492
88 -0.0389226056
89 -1.790219921
90 0.0228678023
91 -0.269683325
92 0.628013036
93 -0.154722222
94 0.557497307
95 -0.125844550
96 0.183056884
97 0.189593671
98 0.134857364
99 0.00796106791
100 0.100000000
101 -0.165652342
102 -0.187367315
103 -0.185906434
104 0.105988543
105 0.416606683
106 0.659726701
107 -0.299168244
108 0.480321364
109 -0.384013206
110 0.0348134368
111 1.422669495
112 0.224900378
113 -1.307072381
114 0.206046610
115 -0.561711936
116 0.131165447
117 -0.0216784558
118 -0.425771740
119 -0.230196095
120 -0.163731055
121 -0.987880246
122 1.012954881
123 -1.991862676
124 0.0747070596
125 -0.0894427190
126 -0.0460001883
127 0.731843659
128 -0.0883883476
129 -1.670176403
130 -0.0947990349
131 -1.026006989
132 -0.0570004075
133 0.253145139
134 -0.0875555226
135 -0.429612489
136 0.0904696233
137 -0.253226179
138 0.919696881
139 1.158420632
140 -0.201157013
141 0.816429764
142 0.0729347170
143 -0.0330028021
144 0.0180785851
145 -0.117317942
146 0.158164689
147 0.197492553
148 -0.686930764
149 1.817801940
150 0.146445507
151 -1.058927825
152 -0.0994888525
153 -0.0185042803
154 -0.0700296699
155 -0.0668200255
156 0.155215460
157 1.591644818
158 -0.119515894
159 0.966140138
160 0.0790569415
161 1.129922971
162 0.754543023
163 1.635510721
164 0.961763611
165 0.0509827143
166 -0.0167847472
167 1.735379534
168 0.329356502
169 -0.910131407
170 -0.0809184910
171 0.0203491790
172 0.806438570
173 -1.933133943
174 0.192085905
175 0.179920302
176 0.0275224383
177 -0.623523220
178 1.265876646
179 0.155240985
180 -0.0161699780
181 1.110127533
182 0.190694907
183 1.483424793
184 -0.444072276
185 0.614409554
186 0.109405133
187 -0.0281701630
188 -0.394210126
189 0.864175191
190 0.0889855349
191 0.142399252
192 -0.129440764
193 1.508917059
194 -0.134062970
195 -0.138828928
196 -0.0953585572
197 0.333012710
198 -0.00562932510
199 0.136837335
200 -0.0707106781
201 -0.128261616
202 0.117133894
203 0.235903472
204 0.132488699
205 -0.860227525
206 0.131455700
207 0.0908562915
208 -0.0749452175
209 0.0310142574
210 -0.294585410
211 1.096027761
212 -0.466497224
213 0.108112976
214 0.211543894
215 -0.721300584
216 -0.339638494
217 0.137257303
218 0.271538342
219 0.237097374
220 -0.0246168172
221 0.0764513142
222 -1.005979247
223 1.647222212
224 -0.159028582
225 0.0144628680
226 0.924239744
227 0.797264444
228 -0.145696955