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

$R= 21.6514464961$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.407671501
4 0.5
5 0.447213595
6 -0.995374064
7 -0.886152580
8 -0.353553390
9 0.981539055
10 -0.316227766
11 -0.419932674
12 0.703835750
13 -1.644448452
14 0.626604498
15 0.629529833
16 0.250000000
17 1.692225006
18 -0.694052922
19 1.547080030
20 0.223606797
21 -1.247411732
22 0.296937242
23 -0.105619770
24 -0.497687032
25 0.200000000
26 1.162800652
27 -0.0259869452
28 -0.443076290
29 -0.601297357
30 -0.445144814
31 0.217779866
32 -0.176776695
33 -0.591127259
34 -1.196583777
35 -0.396299481
36 0.490769527
37 0.360614002
38 -1.093950780
39 -2.314843222
40 -0.158113883
41 -1.134209591
42 0.882053295
43 -1.684566336
44 -0.209966337
45 0.438957610
46 0.0746844556
47 0.566785150
48 0.351917875
49 -0.214733604
50 -0.141421356
51 2.382096914
52 -0.822224226
53 0.242387432
54 0.0183755452
55 -0.187799601
56 0.313302249
57 2.177780468
58 0.425181439
59 -1.458932616
60 0.314764916
61 -0.403143547
62 -0.153993620
63 -0.869793366
64 0.125000000
65 -0.735419705
66 0.417990093
67 0.160256395
68 0.846112503
69 -0.148677940
70 0.280226050
71 -0.751948104
72 -0.347026461
73 1.646699663
74 -0.254992606
75 0.281534300
76 0.773540015
77 0.372124423
78 1.636841340
79 0.128324119
80 0.111803398
81 -1.018120137
82 0.802007293
83 -1.194113340
84 -0.623705866
85 0.756786029
86 1.191168279
87 -0.846429154
88 0.148468621
89 -0.672825787
90 -0.310389902
91 1.457232239
92 -0.0528098850
93 0.306562510
94 -0.400777623
95 0.691875222
96 -0.248843516
97 -1.776728365
98 0.151839588
99 -0.412180321
100 0.100000000
101 -1.928546024
102 -1.684396881
103 -1.539343329
104 0.581400326
105 -0.557859486
106 -0.171393797
107 -0.00227713602
108 -0.0129934726
109 0.813597092
110 0.132794371
111 0.507626055
112 -0.221538145
113 0.0254973126
114 -1.539923337
115 -0.0472345971
116 -0.300648678
117 -1.614090382
118 1.031621146
119 -1.499569555
120 -0.222572407
121 -0.823656543
122 0.285065536
123 -1.596594515
124 0.108889933
125 0.0894427190
126 0.615036787
127 1.519869026
128 -0.0883883476
129 -2.371316032
130 0.520020260
131 0.937382416
132 -0.295563629
133 -1.370948934
134 -0.113318384
135 -0.0116217152
136 -0.598291888
137 0.397547893
138 0.105131179
139 -0.174106507
140 -0.198149740
141 0.797847312
142 0.531707603
143 0.690557617
144 0.245384763
145 -0.268908353
146 -1.164392498
147 -0.302274863
148 0.180307001
149 -0.462921821
150 -0.199074812
151 -0.446715223
152 -0.546975390
153 1.660985964
154 -0.263131703
155 0.0973941169
156 -1.157421611
157 -0.888480090
158 -0.0907388552
159 0.341207692
160 -0.0790569415
161 0.0936084209
162 0.719919653
163 0.730033185
164 -0.567104795
165 -0.264360146
166 0.844365640
167 -1.191645456
168 0.441026647
169 1.704211041
170 -0.535128533
171 1.518449170
172 -0.842283168
173 -0.751541815
174 0.598515794
175 -0.177230516
176 -0.104983168
177 -2.053332683
178 0.475759677
179 1.135318941
180 0.219478805
181 0.225892812
182 -1.030418798
183 -0.571152344
184 0.0373422278
185 0.161271484
186 -0.216772430
187 -0.705890989
188 0.283392575
189 0.0259096887
190 -0.489229661
191 0.533423363
192 0.175958937
193 0.624317162
194 1.256336675
195 -1.035229360
196 -0.107366802