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

$R= 30.610412682$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.683002998
4 0.5
5 -0.447213595
6 -0.482956051
7 -0.283834597
8 0.353553390
9 -0.533506904
10 -0.316227766
11 0.652241746
12 -0.341501499
13 -1.842725037
14 -0.200701368
15 0.305448226
16 0.250000000
17 1.396322196
18 -0.377246349
19 0.312680146
20 -0.223606797
21 0.193859880
22 0.461204561
23 0.757785069
24 -0.241478025
25 0.200000000
26 -1.303003369
27 1.047389813
28 -0.141917298
29 0.525080071
30 0.215984512
31 -0.878757545
32 0.176776695
33 -0.445483068
34 0.987348894
35 0.126934690
36 -0.266753452
37 0.313691013
38 0.221098252
39 1.258586725
40 -0.158113883
41 -1.850223191
42 0.137079636
43 1.405024817
44 0.326120873
45 0.238591540
46 0.535834961
47 1.983730625
48 -0.170750749
49 -0.919437921
50 0.141421356
51 -0.953692247
52 -0.921362518
53 -0.268202095
54 0.740616439
55 -0.291691376
56 -0.100350684
57 -0.213561477
58 0.371287679
59 -0.595995951
60 0.152724113
61 -0.788880761
62 -0.621375419
63 0.151427717
64 0.125000000
65 0.824091689
66 -0.315004098
67 0.403548562
68 0.698161098
69 -0.517569474
70 0.0897563805
71 -0.126080550
72 -0.188623174
73 0.636546007
74 0.221813042
75 -0.136600599
76 0.156340073
77 -0.185128773
78 0.889955208
79 1.536929631
80 -0.111803398
81 -0.181863479
82 -1.308305365
83 0.683970237
84 0.0969299404
85 -0.624454270
86 0.993502576
87 -0.358631263
88 0.230602280
89 0.660228517
90 0.168709696
91 0.523029118
92 0.378892534
93 0.600194038
94 1.402709377
95 -0.139834812
96 -0.120739012
97 -1.170580371
98 -0.650140789
99 -0.347975474
100 0.100000000
101 0.885304659
102 -0.674362255
103 -1.063477740
104 -0.651501684
105 -0.0866967743
106 -0.189647520
107 -1.946011192
108 0.523694906
109 -0.302718734
110 -0.206256950
111 -0.214251902
112 -0.0709586492
113 -0.323444292
114 -0.151010769
115 -0.338891785
116 0.262540035
117 0.983106529
118 -0.421432778
119 -0.396324548
120 0.107992256
121 -0.574580704
122 -0.557822936
123 1.263707987
124 -0.439378772
125 -0.0894427190
126 0.107075565
127 0.570851230
128 0.0883883476
129 -0.959636163
130 0.582720821
131 0.499995447
132 -0.222741534
133 -0.0887494434
134 0.285351924
135 -0.468406964
136 0.493674447
137 -0.932054109
138 -0.365976885
139 -0.0929103764
140 0.0634673453
141 -1.354893965
142 -0.0891524124
143 -1.201902195
144 -0.133376726
145 -0.234822946
146 0.450105998
147 0.627978856
148 0.156845506
149 -1.669726263
150 -0.0965912103
151 0.227742101
152 0.110549126
153 -0.744947531
154 -0.130905810
155 0.392992321
156 0.629293362
157 0.342273428
158 1.086773364
159 0.183182834
160 -0.0790569415
161 -0.215085618
162 -0.128596899
163 0.871259815
164 -0.925111595
165 0.199226084
166 0.483639992
167 0.320610073
168 0.0685398181
169 2.395635568
170 -0.441555848
171 -0.166817035
172 0.702512408
173 -1.818136973
174 -0.253590598
175 -0.0567669194
176 0.163060436
177 0.407066995
178 0.466852061
179 1.310941844
180 0.119295770
181 -0.431891826
182 0.369837436
183 0.538808046
184 0.267917480
185 -0.140286885
186 0.424401274
187 0.910739192
188 0.991865312
189 -0.297285988
190 -0.0988781442
191 -0.668728053
192 -0.0853753748
193 -1.306824760
194 -0.827725318
195 -0.562857094
196 -0.459718960
197 -1.577036942
198 -0.246055817
199 -0.447172051
200 0.0707106781
201 -0.275625922
202 0.626004928
203 -0.149033017
204 -0.476846123
205 0.827444966
206 -0.751992321
207 -0.404269840
208 -0.460681259
209 0.203950643
210 -0.0613038770
211 0.166941970
212 -0.134101047
213 0.0860544863
214 -1.376037710
215 -0.628346200
216 0.370308219
217 0.249471396
218 -0.214054469
219 -0.434534392
220 -0.145845688
221 -2.573154309
222 -0.151498973
223 -0.362248715
224 -0.0501753420
225 -0.106701380
226 -0.228709652
227 -0.746702328
228 -0.106780738
229 -1.718006283
230 -0.239632679
231 0.125532022
232 0.185643839
233 -0.506710021
234 0.695161293
235 -0.887151305
236 -0.297997975
237 -1.055273352
238 -0.280243775
239 1.346528634
240 0.0763620566
241 0.708279256
242 -0.406289912
243 -0.949285420
244 -0.394440380
245 0.411185138
246 0.893576487
247 -0.518183787
248 -0.310687709
249 -0.342363156
250 -0.0632455532
251 -2.110949045
252 0.0757138585