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

$R= 15.5019918437$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.579648465
4 0.5
5 0.447213595
6 -1.116980141
7 -0.442116437
8 0.353553390
9 1.495289274
10 0.316227766
11 -1.085189792
12 -0.789824232
13 0.484488101
14 -0.312623531
15 -0.706440269
16 0.250000000
17 0.788909495
18 1.057329185
19 1.769729765
20 0.223606797
21 0.698388552
22 -0.767345060
23 0.384147628
24 -0.558490070
25 0.200000000
26 0.342584822
27 -0.782382942
28 -0.221058218
29 -1.651728897
30 -0.499528705
31 -0.544474500
32 0.176776695
33 1.714218389
34 0.557843253
35 -0.197720481
36 0.747644637
37 -1.338215347
38 1.251387917
39 -0.765320886
40 0.158113883
41 0.860534634
42 0.493835281
43 -1.600655542
44 -0.542594896
45 0.668713692
46 0.271633393
47 -1.418267493
48 -0.394912116
49 -0.804533055
50 0.141421356
51 -1.246199673
52 0.242244050
53 1.495574480
54 -0.553228284
55 -0.485311628
56 -0.156311765
57 -2.795550907
58 -1.167948703
59 -0.0557645684
60 -0.353220134
61 0.804408272
62 -0.385001611
63 -0.661091967
64 0.125000000
65 0.216669665
66 1.212135447
67 -0.648872563
68 0.394454747
69 -0.606818212
70 -0.139809493
71 -1.761539892
72 0.528664592
73 0.510785817
74 -0.946261146
75 -0.315929693
76 0.884864882
77 0.479780245
78 -0.541163588
79 -1.559316485
80 0.111803398
81 -0.259399260
82 0.608489875
83 -0.205954938
84 0.349194276
85 0.352811051
86 -1.131834388
87 2.609151017
88 -0.383672530
89 -0.966971895
90 0.472851986
91 -0.214200153
92 0.192073814
93 0.860078308
94 -1.002866562
95 0.791447211
96 -0.279245035
97 0.113335373
98 -0.568890779
99 -1.622672659
100 0.100000000
101 -0.505346502
102 -0.881196239
103 -0.282556032
104 0.171292411
105 0.312328855
106 1.057530857
107 1.741105466
108 -0.391191471
109 0.511440022
110 -0.343167143
111 2.113909973
112 -0.110529109
113 -0.140438156
114 -1.976753004
115 0.171796042
116 -0.825864448
117 0.724449714
118 -0.0394315045
119 -0.348790024
120 -0.249764352
121 0.177636657
122 0.568802544
123 -1.359343399
124 -0.272237250
125 0.0894427190
126 -0.467462613
127 0.267365900
128 0.0883883476
129 2.528474467
130 0.153208590
131 -1.945002490
132 0.857109194
133 -0.782429350
134 -0.458822189
135 -0.349892288
136 0.278921626
137 1.241830041
138 -0.429085272
139 -0.649299327
140 -0.0988602409
141 2.240442463
142 -1.245596803
143 -0.525715948
144 0.373822318
145 -0.738675618
146 0.361180115
147 1.270856506
148 -0.669107673
149 0.479015149
150 -0.223396028
151 -0.0945504365
152 0.625693958
153 1.180362209
154 0.339255865
155 -0.243496398
156 -0.382660443
157 -0.810598560
158 -1.102603260
159 -2.358212516
160 0.0790569415
161 -0.159364907
162 -0.183422975
163 -0.0504613789
164 0.430267317
165 0.766621769
166 -0.145632133
167 0.202208958
168 0.246917640
169 -0.798606633
170 0.249475087
171 2.651521426
172 -0.800327771