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

$R= 31.0493228289$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.956804207
4 0.5
5 -0.447213595
6 1.383669524
7 -0.148586844
8 0.353553390
9 2.829082707
10 -0.316227766
11 0.565275638
12 0.978402103
13 0.558131309
14 -0.105066765
15 -0.875109445
16 0.250000000
17 0.383180555
18 2.000463566
19 -1.177336146
20 -0.223606797
21 -0.290755363
22 0.399710237
23 1.820851460
24 0.691834762
25 0.200000000
26 0.394658433
27 3.579156737
28 -0.0742934224
29 -0.449602152
30 -0.618795823
31 -0.888143640
32 0.176776695
33 1.106133747
34 0.270949569
35 0.0664500571
36 1.414541353
37 1.449144298
38 -0.832502373
39 1.092153695
40 -0.158113883
41 1.094351302
42 -0.205595089
43 -1.906086713
44 0.282637819
45 -1.265204249
46 1.287536415
47 0.487304983
48 0.489201051
49 -0.977921949
50 0.141421356
51 0.749809323
52 0.279065654
53 -0.404097012
54 2.530846000
55 -0.252798950
56 -0.0525333828
57 -2.303816325
58 -0.317916730
59 -0.0322878701
60 -0.437554722
61 0.110797672
62 -0.628012390
63 -0.420364473
64 0.125000000
65 -0.249603909
66 0.782154673
67 -0.300971488
68 0.191590277
69 3.563049799
70 0.0469872860
71 -0.0917304764
72 1.000231783
73 1.050962234
74 1.024699760
75 0.391360841
76 -0.588668073
77 -0.0839925236
78 0.772269284
79 -0.424858854
80 -0.111803398
81 4.174626256
82 0.773823226
83 1.245996518
84 -0.145377681
85 -0.171363553
86 -1.347806840
87 -0.879783383
88 0.199855118
89 1.777776850
90 -0.894634504
91 -0.0829309703
92 0.910425730
93 -1.737923212
94 0.344576658
95 0.526520731
96 0.345917381
97 -0.318924924
98 -0.691495241
99 1.599211533
100 0.100000000
101 -0.441551332
102 0.530195257
103 -1.669841421
104 0.197329216
105 0.130029751
106 -0.285739737
107 0.521350368
108 1.789578368
109 1.031023422
110 -0.178755852
111 2.835691661
112 -0.0371467112
113 1.396846461
114 -1.629044146
115 -0.814309528
116 -0.224801076
117 1.578999636
118 -0.0228309719
119 -0.0569355897
120 -0.309397911
121 -0.680463452
122 0.0783457856
123 2.141431232
124 -0.444071820
125 -0.0894427190
126 -0.297242569
127 0.728250780
128 0.0883883476
129 -3.729838500
130 -0.176496617
131 1.787918665
132 0.553066873
133 0.174936663
134 -0.212818980
135 -1.600647553
136 0.135474784
137 -0.531724058
138 2.519456675
139 0.394188754
140 0.0332250285
141 0.953560441
142 -0.0648632419
143 0.315498033
144 0.707270676
145 0.201068195
146 0.743142522
147 -1.913601785
148 0.724572149
149 -1.344539528
150 0.276733904
151 0.720779043
152 -0.416251186
153 1.084049481
154 -0.0593916830
155 0.397189910
156 0.546076847
157 0.438230158
158 -0.300420577
159 -0.790738734
160 -0.0790569415
161 -0.270554569
162 2.951906535
163 -1.054040546
164 0.547175651
165 -0.494678050
166 0.881052587
167 -0.957115990
168 -0.102797544
169 -0.688489420
170 -0.121172331
171 -3.330781338
172 -0.953043356
173 -0.300491075
174 -0.622100796
175 -0.0297173689
176 0.141318909
177 -0.0631809843
178 1.257078066
179 1.346464415
180 -0.632602124
181 -1.210805042
182 -0.0586410515
183 0.216809293
184 0.643768207
185 -0.648077032
186 -1.228897288
187 0.216602258
188 0.243652491
189 -0.531815425
190 0.372306379
191 1.142226859
192 0.244600525
193 -0.769122232
194 -0.225513976
195 -0.488425980
196 -0.488960974
197 -0.261443858
198 1.130813319
199 0.743300652
200 0.0707106781
201 -0.588938883
202 -0.312223941
203 0.0668229659
204 0.374904661
205 -0.489408780
206 -1.180756192
207 5.151360246
208 0.139532827
209 -0.665526247
210 0.0919449189
211 -1.046566473
212 -0.202048506
213 -0.179676351
214 0.368650381
215 0.852427892
216 1.265423000
217 0.132106838
218 0.729043653
219 2.056559623
220 -0.126399475
221 0.213281301
222 2.005136802
223 -0.905952340
224 -0.0262666914
225 0.565816541
226 0.987719605
227 0.363351194
228 -1.151908162
229 0.0911897132
230 -0.575803789
231 -0.171201866
232 -0.158958365
233 1.489230517
234 1.116521350
235 -0.217929413
236 -0.0161439350
237 -0.830550084
238 -0.0402595416
239 -0.227862689
240 -0.218777361
241 -0.628869093
242 -0.481160321
243 4.588553124
244 0.0553988363
245 0.437339991
246 1.514220546
247 -0.751797002
248 -0.314006195
249 2.442098218
250 -0.0632455532