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

$R= 27.6399081653$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.949613472
4 0.5
5 0.447213595
6 -1.378584907
7 -0.912654027
8 0.353553390
9 2.800992693
10 0.316227766
11 1.337435766
12 -0.974806736
13 0.963720049
14 -0.645343851
15 -0.871893651
16 0.250000000
17 0.105504669
18 1.980600927
19 0.792262889
20 0.223606797
21 1.779322587
22 0.945709900
23 1.730947575
24 -0.689292453
25 0.200000000
26 0.681452982
27 -3.511239620
28 -0.456327013
29 0.244908930
30 -0.616521913
31 1.493186801
32 0.176776695
33 -2.607482790
34 0.0746030671
35 -0.408151288
36 1.400496346
37 -1.221948163
38 0.560214461
39 -1.878881593
40 0.158113883
41 0.800219198
42 1.258171067
43 -0.353569945
44 0.668717883
45 1.252642013
46 1.223964768
47 0.675063777
48 -0.487403368
49 -0.167062626
50 0.141421356
51 -0.205693324
52 0.481860024
53 -0.255165919
54 -2.482821345
55 0.598119458
56 -0.322671925
57 -1.544606403
58 0.173176765
59 0.125752441
60 -0.435946825
61 -0.984048303
62 1.055842513
63 -2.556337261
64 0.125000000
65 0.430988708
66 -1.843768762
67 -0.495139401
68 0.0527523346
69 -3.374678715
70 -0.288606544
71 1.118386290
72 0.990300463
73 0.245830002
74 -0.864047832
75 -0.389922694
76 0.396131444
77 -1.220616138
78 -1.328569915
79 -0.934261127
80 0.111803398
81 4.044567376
82 0.565840421
83 0.756154041
84 0.889661293
85 0.0471831225
86 -0.250011705
87 -0.477477749
88 0.472854950
89 0.144008212
90 0.885751662
91 -0.879542984
92 0.865473787
93 -2.911137106
94 0.477342174
95 0.354310735
96 -0.344646226
97 -0.510324764
98 -0.118131116
99 3.746147811
100 0.100000000
101 -1.109228584
102 -0.145447144
103 0.242716615
104 0.340726491
105 0.795737251
106 -0.180429552
107 -0.989962445
108 -1.755619810
109 1.550827470
110 0.422934324
111 2.382326602
112 -0.228163506
113 -0.694518024
114 -1.092201662
115 0.774103289
116 0.122454465
117 2.699372818
118 0.0889204043
119 -0.0962892613
120 -0.308260956
121 0.788734430
122 -0.695827228
123 -1.560118130
124 0.746593400
125 0.0894427190
126 -1.807603412
127 0.359526310
128 0.0883883476
129 0.689324729
130 0.304755038
131 0.807116679
132 -1.303741395
133 -0.723061917
134 -0.350116428
135 -1.570274095
136 0.0373015335
137 0.476840950
138 -2.386258203
139 0.458439903
140 -0.204075644
141 -1.316113434
142 0.790818529
143 1.288913665
144 0.700248173
145 0.109526603
146 0.173828061
147 0.325707546
148 -0.610974081
149 0.396046828
150 -0.275716981
151 -0.972641465
152 0.280107230
153 0.295517800
154 -0.863105948
155 0.667773438
156 -0.939440796
157 0.919561532
158 -0.660622378
159 0.497474916
160 0.0790569415
161 -1.579756229
162 2.859941018
163 1.147561142
164 0.400109599
165 -1.166101753
166 0.534681650
167 1.700976059
168 0.629085533
169 -0.0712432889
170 0.0333635059
171 2.219123045
172 -0.176784972
173 -0.230519575
174 -0.337627754
175 -0.182530805
176 0.334358941
177 -0.245168227
178 0.101829183
179 1.032706051
180 0.626321006
181 1.184310443
182 -0.621930808
183 1.918513481
184 0.611982384
185 -0.546471831
186 -2.058484788
187 0.141109488
188 0.337531888
189 3.204560765
190 0.250535523
191 1.094856176
192 -0.243701684
193 -1.411543961
194 -0.360854101
195 -0.840261392
196 -0.0835313134
197 -1.067841289
198 2.648926520
199 0.307665684
200 0.0707106781
201 0.965376731
202 -0.784343053
203 -0.223322943
204 -0.102846662
205 0.357868904
206 0.171626564
207 4.848018935
208 0.240930012
209 1.059884554
210 0.562671206
211 -1.238428313
212 -0.127582959
213 -2.178656755
214 -0.700009158
215 -0.158121286
216 -1.241410672
217 -1.363291970
218 1.096600620
219 -0.482706278
220 0.299059729
221 0.103457668
222 1.684559295
223 0.274928239
224 -0.161335962
225 0.560198538
226 -0.491098405
227 -0.110873438
228 -0.772303201