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

$R= 15.9382784617$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.524544017
4 0.5
5 0.447213595
6 -0.370908631
7 0.0626611080
8 -0.353553390
9 -0.724853573
10 -0.316227766
11 1.173934620
12 0.262272008
13 -0.771201722
14 -0.0443080943
15 0.234583215
16 0.250000000
17 0.798685436
18 0.512548877
19 1.021174462
20 0.223606797
21 0.0328685093
22 -0.830097131
23 0.156308331
24 -0.185454315
25 0.200000000
26 0.545321967
27 -0.904761622
28 0.0313305540
29 -0.652147930
30 -0.165875382
31 0.613278818
32 -0.176776695
33 0.615780381
34 -0.564755887
35 0.0280228994
36 -0.362426786
37 -1.712917066
38 -0.722079387
39 -0.404529249
40 -0.158113883
41 -0.252094126
42 -0.0232415458
43 0.360471044
44 0.586967310
45 -0.324164373
46 -0.110526681
47 1.686399293
48 0.131136004
49 -0.996073585
50 -0.141421356
51 0.418945667
52 -0.385600861
53 1.161375554
54 0.639763078
55 0.524999522
56 -0.0221540471
57 0.535650955
58 0.461138224
59 1.854077391
60 0.117291607
61 1.124128931
62 -0.433653611
63 -0.0454201280
64 0.125000000
65 -0.344891895
66 -0.435422483
67 1.204664381
68 0.399342718
69 0.0819906001
70 -0.0198151821
71 -0.245592261
72 0.256274438
73 -0.765468546
74 1.211215273
75 0.104908803
76 0.510587231
77 0.0735600440
78 0.286045375
79 0.261450553
80 0.111803398
81 0.250266277
82 0.178257466
83 -0.610734664
84 0.0164342546
85 0.357182985
86 -0.254891520
87 -0.342080295
88 -0.415048565
89 0.116193007
90 0.229218826
91 -0.0483243537
92 0.0781541657
93 0.321691736
94 -1.192464376
95 0.456683103
96 -0.0927271579
97 0.674672473
98 0.704330386
99 -0.850930702
100 0.100000000
101 0.217158864
102 -0.296239322
103 0.651463001
104 0.272660983
105 0.0146992442
106 -0.821216530
107 1.173338098
108 -0.452380811
109 1.109246875
110 -0.371230722
111 -0.898500355
112 0.0156652770
113 -0.170953308
114 -0.378762422
115 0.0699032109
116 -0.326073965
117 0.559008273
118 -1.311030696
119 0.0500463827
120 -0.0829376913
121 0.378123028
122 -0.794879190
123 -0.132232767
124 0.306639409
125 0.0894427190
126 0.0321168805
127 1.769195971
128 -0.0883883476
129 0.189081545
130 0.243875397
131 1.822921383
132 0.307890190
133 0.0639872804
134 -0.851826352
135 -0.404621698
136 -0.282377943
137 -1.220717000
138 -0.0579761093
139 -1.276349427
140 0.0140114497
141 0.884622585
142 0.173659953
143 -0.905485654
144 -0.181213393
145 -0.291649421
146 0.541267999
147 -0.522483237
148 -0.856458533
149 1.198657124
150 -0.0741817263
151 1.773767460
152 -0.361039693
153 -0.578117455
154 -0.0520148059
155 0.274266625
156 -0.202264624
157 0.647967081
158 -0.184873459
159 0.607133612
160 -0.0790569415
161 0.00124883511
162 -0.176964982
163 0.127623697
164 -0.126047063
165 0.275385358
166 0.431854622
167 0.290897764
168 -0.0116207729
169 -0.356920979
170 -0.252566511
171 -0.795887607
172 0.180235522