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

$R= 12.0150070407$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.505075638
4 0.5
5 -0.447213595
6 1.064249190
7 -1.564071732
8 -0.353553390
9 1.265252677
10 0.316227766
11 1.242956793
12 -0.752537819
13 0.0218116580
14 1.105965728
15 0.673090287
16 0.250000000
17 0.775103937
18 -0.894668748
19 1.549663754
20 -0.223606797
21 2.354046262
22 -0.878903177
23 -0.824733724
24 0.532124595
25 0.200000000
26 -0.0154231712
27 -0.399225342
28 -0.782035866
29 -1.405887307
30 -0.475946706
31 0.532443418
32 -0.176776695
33 -1.870743989
34 -0.548081250
35 0.699474143
36 0.632626338
37 0.0270012623
38 -1.095777749
39 -0.0328281950
40 0.158113883
41 -1.391224231
42 -1.664562075
43 0.851446278
44 0.621478396
45 -0.565838199
46 0.583174809
47 -0.668496874
48 -0.376268909
49 1.446320385
50 -0.141421356
51 -1.166590053
52 0.0109058290
53 1.206791579
54 0.282294947
55 -0.555867176
56 0.552982864
57 -2.332361164
58 0.994112448
59 0.902244675
60 0.336545143
61 -1.001160630
62 -0.376494352
63 -1.978945948
64 0.125000000
65 -0.00975446999
66 1.322815760
67 0.111558909
68 0.387551968
69 1.241286637
70 -0.494602909
71 1.902004604
72 -0.447334374
73 -0.521703378
74 -0.0190927756
75 -0.301015127
76 0.774831877
77 -1.944073583
78 0.0232130393
79 -1.679075684
80 -0.111803398
81 -0.664388335
82 0.983744088
83 0.171954656
84 1.177023131
85 -0.346637018
86 -0.602063437
87 2.115966729
88 -0.439451588
89 0.144597439
90 0.400108027
91 -0.0341150188
92 -0.412366862
93 -0.801367722
94 0.472698673
95 -0.693030699
96 0.266062297
97 -0.126102379
98 -1.022702952
99 1.572654500
100 0.100000000
101 0.154490879
102 0.824903737
103 0.261342007
104 -0.00771158564
105 -1.052761492
106 -0.853330509
107 0.239191730
108 -0.199612671
109 -1.692055226
110 0.393057450
111 -0.0406367867
112 -0.391017933
113 0.725051888
114 1.649228395
115 0.368832134
116 -0.702943653
117 0.0275657105
118 -0.637983328
119 -1.212355541
120 -0.237973353
121 0.544864957
122 0.707927470
123 2.093814819
124 0.266221709
125 -0.0894427190
126 1.399326099
127 -0.551003525
128 -0.0883883476
129 -1.281391257
130 0.00689745188
131 0.980569866
132 -0.935371994
133 -2.423652219
134 -0.0788840617
135 0.178539001
136 -0.274040625
137 1.169918879
138 -0.877722198
139 0.271149367
140 0.349737071
141 1.007918427
142 -1.344920353
143 0.0255215637
144 0.316313169
145 0.628731917
146 0.368899996
147 -2.211577637
148 0.0135006311