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

$R= 27.7280415236$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.155962807
4 0.5
5 -0.447213595
6 0.817389140
7 -0.0725691798
8 0.353553390
9 0.336250012
10 -0.316227766
11 0.367830072
12 0.577981403
13 -0.219317402
14 -0.0513141591
15 -0.516962283
16 0.250000000
17 0.185616043
18 0.237764664
19 -1.047390076
20 -0.223606797
21 -0.0838872728
22 0.260095138
23 -0.108308663
24 0.408694570
25 0.200000000
26 -0.155080822
27 -0.767270298
28 -0.0362845899
29 -1.896557541
30 -0.365547536
31 0.926157993
32 0.176776695
33 0.425197883
34 0.131250362
35 0.0324539238
36 0.168125006
37 -0.138306331
38 -0.740616625
39 -0.253522760
40 -0.158113883
41 -0.0581287626
42 -0.0593172594
43 0.772075138
44 0.183915036
45 -0.150375577
46 -0.0765857905
47 0.416944125
48 0.288990701
49 -0.994733714
50 0.141421356
51 0.214565242
52 -0.109658701
53 0.401504166
54 -0.542542031
55 -0.164498609
56 -0.0256570795
57 -1.210743973
58 -1.341068698
59 -1.075464934
60 -0.258481141
61 -1.422987197
62 0.654892597
63 -0.0244013876
64 0.125000000
65 0.0980817242
66 0.300660306
67 -1.342959272
68 0.0928080215
69 -0.125200786
70 0.0229483896
71 0.506618716
72 0.118882332
73 1.102082889
74 -0.0977973446
75 0.231192561
76 -0.523695038
77 -0.0266931266
78 -0.179267663
79 -0.537002157
80 -0.111803398
81 -1.223185941
82 -0.0411032422
83 -1.026402697
84 -0.0419436364
85 -0.0830100179
86 0.545939565
87 -2.192349980
88 0.130047569
89 -0.673396896
90 -0.106331590
91 0.0159156840
92 -0.0541543318
93 1.070604195
94 0.294824018
95 0.468407081
96 0.204347285
97 0.200835018
98 -0.703382954
99 0.123682866
100 0.100000000
101 -1.018209741
102 0.151720537
103 -1.535872128
104 -0.0775404114
105 0.0375155289
106 0.283906318
107 0.104515409
108 -0.383635149
109 -0.239742105
110 -0.116318082
111 -0.159876974
112 -0.0181422949
113 1.070889430
114 -0.856125273
115 0.0484371068
116 -0.948278770
117 -0.0737454795
118 -0.760468548
119 -0.0134700040
120 -0.182773768
121 -0.864701037
122 -1.006203897
123 -0.0671946878
124 0.463078996
125 -0.0894427190
126 -0.0172543866
127 1.505814784
128 0.0883883476
129 0.892490144
130 0.0693542523
131 1.803804654
132 0.212598941
133 0.0760082386
134 -0.949615608
135 0.343133708
136 0.0656251813
137 0.457761813
138 -0.0885303254
139 -0.0971118399
140 0.0162269619
141 0.481971900
142 0.358233529
143 -0.0806715365
144 0.0840625032
145 0.848166317
146 0.779290284
147 -1.149875179
148 -0.0691531655
149 0.0262953786
150 0.163477828
151 0.562588190
152 -0.370308312
153 0.0624133915
154 -0.0188748908
155 -0.414190446
156 -0.126761380
157 -0.729710291
158 -0.379717867
159 0.464123877
160 -0.0790569415
161 0.00785986090
162 -0.864923074
163 0.592079026
164 -0.0290643813
165 -0.190154274
166 -0.725776307
167 -0.741854603
168 -0.0296586297
169 -0.951899729
170 -0.0586969466
171 -0.352184689
172 0.386037569
173 -0.622684315
174 -1.550225537
175 -0.0145138359
176 0.0919575181
177 -1.243196475
178 -0.476163511
179 -1.601350194
180 -0.0751877886
181 0.814827285
182 0.0112540881
183 -1.644917548
184 -0.0382928952
185 0.0618524716
186 0.757031486
187 0.0682695045
188 0.208472062
189 0.0556931174
190 0.331213823
191 -1.019674431
192 0.144495350
193 -1.245490832
194 0.142011803
195 0.113378825
196 -0.497366857
197 -0.331823878
198 0.0874569937
199 -1.094276965
200 0.0707106781
201 -1.552424335
202 -0.719983012
203 0.137928639
204 0.107282621
205 0.0259959729
206 -1.086025596
207 -0.0366158013
208 -0.0548293507
209 -0.384944037
210 0.0265274848
211 0.571005269
212 0.200752083
213 0.584996784
214 0.0739035545
215 -0.345282498
216 -0.271271015
217 -0.0669328866
218 -0.169523268
219 1.264890065
220 -0.0822493046
221 -0.0467417941
222 -0.113050093
223 -0.720852441
224 -0.0128285397
225 0.0672500025
226 0.757233178
227 -1.921274623
228 -0.605371986