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

$R= 30.9513504138$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.387127413
4 0.5
5 0.447213595
6 0.980847200
7 1.492550127
8 0.353553390
9 0.924122460
10 0.316227766
11 0.689553368
12 0.693563706
13 0.549632305
14 1.055392316
15 0.620342237
16 0.250000000
17 1.750683087
18 0.653453258
19 -0.662337918
20 0.223606797
21 2.070357197
22 0.487587863
23 -0.518555114
24 0.490423600
25 0.200000000
26 0.388648730
27 -0.105251814
28 0.746275063
29 1.100220049
30 0.438648203
31 -0.768850508
32 0.176776695
33 0.956498380
34 1.237919882
35 0.667488709
36 0.462061230
37 1.335541420
38 -0.468343633
39 0.762410038
40 0.158113883
41 -0.697623190
42 1.463963614
43 -0.0359376251
44 0.344776684
45 0.413280128
46 -0.366673837
47 -1.365871393
48 0.346781853
49 1.227705883
50 0.141421356
51 2.428420502
52 0.274816152
53 -0.823192757
54 -0.0744242721
55 0.308377641
56 0.527696158
57 -0.918747084
58 0.777973057
59 -1.816872307
60 0.310171118
61 -1.099049206
62 -0.543659408
63 1.379299096
64 0.125000000
65 0.245803039
66 0.676346491
67 0.00775101798
68 0.875341543
69 -0.719302013
70 0.471985792
71 1.157795547
72 0.326726629
73 0.856333121
74 0.944370394
75 0.277425482
76 -0.331168959
77 1.029192968
78 0.539105308
79 1.500467486
80 0.111803398
81 -1.070120138
82 -0.493294088
83 -0.396622448
84 1.035178598
85 0.782929278
86 -0.0254117384
87 1.526145390
88 0.243793931
89 -1.067786899
90 0.292233181
91 0.820353767
92 -0.259277557
93 -1.066493617
94 -0.965816924
95 -0.296206522
96 0.245211800
97 -1.956918836
98 0.868119155
99 0.637231756
100 0.100000000
101 -0.869283005
102 1.717152604
103 1.882892403
104 0.194324365
105 0.925891886
106 -0.582085180
107 -0.690414328
108 -0.0526259074
109 0.333865539
110 0.218055921
111 1.852566115
112 0.373137531
113 0.851913602
114 -0.649652293
115 -0.231904897
116 0.550110024
117 0.507927558
118 -1.284722729
119 2.612982265
120 0.219324101
121 -0.524516151
122 -0.777145146
123 -0.967692252
124 -0.384425254
125 0.0894427190
126 0.975311744
127 -0.480087369
128 0.0883883476
129 -0.0498500650
130 0.173808996
131 0.171884211
132 0.478249190
133 -0.988572545
134 0.00548079738
135 -0.0470700426
136 0.618959941
137 0.318218204
138 -0.508623331
139 0.585698991
140 0.333744354
141 -1.894637652
142 0.818685082
143 0.379000808
144 0.231030615
145 0.492033364
146 0.605518957
147 1.702984486
148 0.667770710
149 0.662464984
150 0.196169440
151 -1.966055405
152 -0.234171816
153 1.617845562
154 0.727749327
155 -0.343840400
156 0.381205019
157 -1.014899690
158 1.060990734
159 -1.141873239
160 0.0790569415
161 -0.773969503
162 -0.756689206
163 -0.489472742
164 -0.348811595
165 0.427759080
166 -0.280454423
167 -0.771383497
168 0.731981807
169 -0.697904312
170 0.553614601
171 -0.612081324
172 -0.0179688125
173 1.497710812
174 1.079147754
175 0.298510025
176 0.172388342
177 -2.520233335
178 -0.755039357
179 -1.920640654
180 0.206640064
181 -0.665130648
182 0.580077712
183 -1.524521425
184 -0.183336918
185 0.597272280
186 -0.754124868
187 1.207189876
188 -0.682935696
189 -0.157092733
190 -0.209449640
191 1.360147147
192 0.173390926
193 0.694217385
194 -1.383750579
195 0.340960134
196 0.613852941
197 -1.471534380
198 0.450590895
199 1.460235644
200 0.0707106781
201 0.0107477262
202 -0.614675908
203 1.642129726
204 1.214210251
205 -0.311986575
206 1.331405987
207 -0.479197961
208 0.137408076
209 -0.456711490
210 0.654704431
211 0.299616620
212 -0.411596378
213 1.606008388
214 -0.488196653
215 -0.0160717945
216 -0.0372121360
217 -1.147610389
218 0.236078587
219 1.187643896
220 0.154188820
221 0.962125010
222 1.309962062
223 -0.486752877
224 0.263848079
225 0.184824492
226 0.602393885
227 1.317457266
228 -0.459373542
229 -0.0191791162
230 -0.163981525
231 1.427135847
232 0.388986528
233 1.446885286
234 0.359159021
235 -0.610836256
236 -0.908436153
237 2.069780321
238 1.847657479
239 -0.0397927544
240 0.155085559
241 0.601903575
242 -0.370888927
243 -1.376180713
244 -0.549524603
245 0.549046762
246 -0.684261753
247 -0.344263134
248 -0.271829704
249 -0.661402146
250 0.0632455532