Properties

Level 10
Symmetry odd
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

$R= 24.6159903788$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.845335196
4 0.5
5 -0.447213595
6 -1.304849031
7 0.0429217633
8 0.353553390
9 2.405261987
10 -0.316227766
11 -0.884249346
12 -0.922667598
13 -1.272808309
14 0.0303502699
15 0.825258988
16 0.250000000
17 1.223294234
18 1.700777061
19 -0.544867883
20 -0.223606797
21 -0.0792050405
22 -0.625258709
23 1.130286070
24 -0.652424515
25 0.200000000
26 -0.900011386
27 -2.593179406
28 0.0214608816
29 -0.367765308
30 0.583546226
31 -1.108056579
32 0.176776695
33 1.631736441
34 0.864999648
35 -0.0191951960
36 1.202630993
37 -1.937489055
38 -0.385279775
39 2.348757972
40 -0.158113883
41 -0.569101864
42 -0.0560064212
43 -1.008722969
44 -0.442124673
45 -1.075665861
46 0.799232945
47 -0.729900208
48 -0.461333799
49 -0.998157722
50 0.141421356
51 -2.257387907
52 -0.636404154
53 -1.264700433
54 -1.833654742
55 0.395448329
56 0.0151751349
57 1.005463883
58 -0.260049343
59 1.622099663
60 0.412629494
61 -0.919754840
62 -0.783514321
63 0.103238085
64 0.125000000
65 0.569217180
66 1.153811902
67 -0.339360905
68 0.611647117
69 -2.085756668
70 -0.0135730533
71 1.101744644
72 0.850388530
73 1.052751487
74 -1.370011649
75 -0.369067039
76 -0.272433941
77 -0.0379535411
78 1.660822689
79 -0.956020089
80 -0.111803398
81 2.380023241
82 -0.402415787
83 1.481966495
84 -0.0396025202
85 -0.547073813
86 -0.713274852
87 0.678650268
88 -0.312629354
89 1.230380285
90 -0.760610625
91 -0.0546311770
92 0.565143035
93 2.044735806
94 -0.516117387
95 0.243672325
96 -0.326212257
97 0.421426697
98 -0.705804094
99 -2.126851340
100 0.100000000
101 0.366550211
102 -1.596214297
103 0.132466101
104 -0.450005693
105 0.0354215709
106 -0.894278252
107 0.179862369
108 -1.296589703
109 -0.647626562
110 0.279624195
111 3.575316747
112 0.0107304408
113 -0.386710785
114 0.710970330
115 -0.505479297
116 -0.183882654
117 -3.061437444
118 1.146997672
119 0.0525059456
120 0.291773113
121 -0.218103093
122 -0.650364885
123 1.050183699
124 -0.554028289
125 -0.0894427190
126 0.0730003505
127 0.920790679
128 0.0883883476
129 1.861431999
130 0.402497328
131 1.556241040
132 0.815868220
133 -0.0233866913
134 -0.239964397
135 1.159705086
136 0.432499824
137 -0.215815439
138 -1.474852683
139 -0.287298565
140 -0.00959759804
141 1.346910551
142 0.779051109
143 1.125479920
144 0.601315496
145 0.164469646
146 0.744407715
147 1.841935582
148 -0.968744527
149 -1.982765614
150 -0.260969806
151 -0.466759823
152 -0.192639887
153 2.942343053
154 -0.0268372063
155 0.495537967
156 1.174378986
157 -1.609015571
158 -0.676008288
159 2.333796157
160 -0.0790569415
161 0.0485139597
162 1.682930573
163 -0.147082254
164 -0.284550932
165 -0.729734720
166 1.047908558
167 0.665528584
168 -0.0280032106
169 0.620041430
170 -0.386839603
171 -1.310545890
172 -0.504361484
173 1.383213507
174 0.479878206
175 0.00858435266
176 -0.221062336
177 -2.993303355
178 0.870010243
179 -0.188737648
180 -0.537832930
181 0.474486416
182 -0.0386300757
183 1.697252678
184 0.399616472
185 0.866471446
186 1.445846554
187 -1.081584923
188 -0.364950104
189 -0.111150536
190 0.172302353
191 0.185507588
192 -0.230666899
193 1.356618663
194 0.297993675
195 -1.050396497
196 -0.499078861
197 1.299032704
198 -1.503911005
199 -1.535442136
200 0.0707106781
201 0.629271403
202 0.259190139
203 -0.0144868706
204 -1.128693953
205 0.254510090
206 0.0936676788
207 2.723096140
208 -0.318202077
209 0.485595288
210 0.0250468330
211 0.986031030
212 -0.632350216
213 -2.051674580
214 0.127181900
215 0.451114626
216 -0.916827371
217 -0.0683211709
218 -0.457941134
219 -1.858472353
220 0.197724164
221 -1.613439481
222 2.528130717