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

$R= 25.3582309994$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.00351939657
4 0.5
5 -0.447213595
6 -0.00248858918
7 -1.571802235
8 0.353553390
9 -0.999987613
10 -0.316227766
11 -0.274681255
12 -0.00175969828
13 -0.377653582
14 -1.111432019
15 0.00157392199
16 0.250000000
17 0.248539932
18 -0.707098022
19 -1.247128383
20 -0.223606797
21 0.00553179540
22 -0.194228978
23 -1.096298558
24 -0.00124429459
25 0.200000000
26 -0.267041409
27 0.00703874955
28 -0.785901117
29 -0.973949931
30 0.00111293091
31 -0.0626273287
32 0.176776695
33 0.000966712270
34 0.175744271
35 0.702931329
36 -0.499993806
37 0.852457826
38 -0.881852936
39 0.00132911272
40 -0.158113883
41 0.643792232
42 0.00391157004
43 0.0525882048
44 -0.137340627
45 0.447208056
46 -0.775200144
47 1.049906231
48 -0.000879849144
49 1.470562268
50 0.141421356
51 -0.000874710590
52 -0.188826791
53 -1.922908233
54 0.00497714754
55 0.122841192
56 -0.555716009
57 0.00438913936
58 -0.688686600
59 -0.291751797
60 0.000786960998
61 -0.0341479735
62 -0.0442842088
63 1.571782767
64 0.125000000
65 0.168891816
66 0.000683568802
67 0.713975523
68 0.124269966
69 0.00385830939
70 0.497047509
71 0.926803332
72 -0.353549011
73 -1.131379302
74 0.602778709
75 -0.000703879315
76 -0.623564191
77 0.431744611
78 0.000939824619
79 0.820010327
80 -0.111803398
81 0.999962841
82 0.455229852
83 -0.799635903
84 0.00276589770
85 -0.111150436
86 0.0371854762
87 0.00342771604
88 -0.0971144893
89 1.641821722
90 0.316223849
91 0.593596745
92 -0.548149279
93 0.000220410411
94 0.742395815
95 0.557732768
96 -0.000622147296
97 0.219922804
98 1.039844551
99 0.274677853
100 0.100000000
101 -1.820335255
102 -0.000618513789
103 1.258125596
104 -0.133520704
105 -0.00247389411
106 -1.359701451
107 -1.929767161
108 0.00351937477
109 -0.811938072
110 0.0868618398
111 -0.00300013708
112 -0.392950558
113 0.887144903
114 0.00310359020
115 0.490279620
116 -0.486974965
117 0.377648904
118 -0.206299674
119 -0.390655621
120 0.000556465458
121 -0.924550207
122 -0.0241462636
123 -0.00226576002
124 -0.0313136643
125 -0.0894427190
126 1.111418253
127 -1.468688182
128 0.0883883476
129 -0.000185077938
130 0.119424548
131 -0.865400828
132 0.000483356135
133 1.960239180
134 0.504856934
135 -0.00314782449
136 0.0878721358
137 1.910153006
138 0.00272823673
139 1.353270348
140 0.351465664
141 -0.00369503895
142 0.655348920
143 0.103734353
144 -0.249996903
145 0.435563650
146 -0.800005976
147 -0.00517549737
148 0.426228913
149 1.170566589
150 -0.000497717836
151 1.952954217
152 -0.440926468
153 -0.248536921
154 0.305289542
155 0.0280077928
156 0.000664556361
157 -0.366184114
158 0.579834863
159 0.00676750811
160 -0.0790569415
161 1.723164449
162 0.707080506
163 0.958303159
164 0.321896116
165 -0.000432326870
166 -0.565427969
167 1.470037942
168 0.00195578502
169 -0.857377189
170 -0.0785952275
171 1.247113523
172 0.0262941024
173 -0.275387688
174 0.00242376126
175 -0.314360447
176 -0.0686703139
177 0.00102869086
178 1.160943273
179 0.953494285
180 0.223604028
181 -1.619331656
182 0.419736283
183 0.000103439129
184 -0.387600072
185 -0.381230729
186 0.000155853696
187 -0.0683062380
188 0.524953115
189 -0.0110594851
190 0.394376622
191 0.312804702
192 -0.000439924572
193 0.253100436
194 0.155508906
195 -0.000594397279
196 0.735281134
197 0.272114088
198 0.194226572
199 -1.173932111
200 0.0707106781
201 -0.00230113426
202 -1.287171403
203 1.530566084
204 -0.000437355295
205 -0.287912638
206 0.889629140
207 1.089715947
208 -0.0944133955
209 0.336489395
210 -0.00174930730
211 0.0324655516
212 -0.961454116
213 -0.00220151713
214 -1.364551446
215 -0.0235181601
216 0.00248857377
217 0.0659400958
218 -0.574126917
219 -0.0474468895
220 0.0614205960
221 -0.160700588
222 -0.00212141727