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

$R= 21.2155846326$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.740318863
4 0.5
5 0.447213595
6 0.523484488
7 -0.732756677
8 -0.353553390
9 -0.451927980
10 -0.316227766
11 0.643660424
12 -0.370159431
13 -1.917572835
14 0.518137215
15 -0.331080660
16 0.250000000
17 -0.444153553
18 0.319561339
19 -0.379200737
20 0.223606797
21 0.542473590
22 -0.455136650
23 0.699597178
24 0.261742244
25 0.200000000
26 1.355928755
27 1.074889672
28 -0.366378338
29 -1.337505507
30 0.234109380
31 -0.181755861
32 -0.176776695
33 -0.476513953
34 0.314063989
35 -0.327698748
36 -0.225963990
37 -1.249336043
38 0.268135412
39 1.419615342
40 -0.158113883
41 1.042232306
42 -0.383586754
43 -0.808228529
44 0.321830212
45 -0.202108337
46 -0.494689909
47 -1.678400914
48 -0.185079715
49 -0.463067652
50 -0.141421356
51 0.328815253
52 -0.958786417
53 -0.533632301
54 -0.760061776
55 0.287853692
56 0.259068607
57 0.280729458
58 0.945759214
59 0.249771312
60 -0.165540330
61 -0.674938948
62 0.128520802
63 0.331153245
64 0.125000000
65 -0.857564642
66 0.336946247
67 -0.921665973
68 -0.222076776
69 -0.517924988
70 0.231718007
71 0.956286209
72 0.159780669
73 -1.857066057
74 0.883413988
75 -0.148063772
76 -0.189600368
77 -0.471646473
78 -1.003819635
79 -1.496918895
80 0.111803398
81 -0.343833119
82 -0.736969531
83 1.328657709
84 0.271236795
85 -0.198631507
86 0.571503874
87 0.990180557
88 -0.227568325
89 -0.380414575
90 0.142912175
91 1.405114299
92 0.349798589
93 0.134557292
94 1.186808668
95 -0.169583725
96 0.130871122
97 -0.647226695
98 0.327438276
99 -0.290888155
100 0.100000000
101 1.641496597
102 -0.232507495
103 0.0912907192
104 0.677964377
105 0.242601564
106 0.377335018
107 1.057340341
108 0.537444836
109 0.984721476
110 -0.203543298
111 0.924907039
112 -0.183189169
113 1.098443172
114 -0.198505704
115 0.312869369
116 -0.668752753
117 0.866604818
118 -0.176614988
119 0.325456479
120 0.117054690
121 -0.585701259
122 0.477253907
123 -0.771584234
124 -0.0908779306
125 0.0894427190
126 -0.234160705
127 1.183689171
128 -0.0883883476
129 0.598346835
130 0.606389773
131 -0.0845194853
132 -0.238256976
133 0.277861875
134 0.651716260
135 0.480705275
136 0.157031994
137 -0.673267823
138 0.366228271
139 0.173862095
140 -0.163849374
141 1.242552031
142 -0.676196463
143 -1.234265834
144 -0.112981995
145 -0.598150647
146 1.313144002
147 0.342817528
148 -0.624668021
149 -0.164754569
150 0.104696897
151 -1.320000736
152 0.134067706
153 0.200724538
154 0.333504419
155 -0.0812836922
156 0.709807671
157 -0.0857901861
158 1.058481501
159 0.395049102
160 -0.0790569415
161 -0.512643566
162 0.243126730
163 -0.998743358
164 0.521116153
165 -0.213103518
166 -0.939502875
167 -0.941669028
168 -0.191793377
169 2.677108077
170 0.140453685
171 0.171326242
172 -0.404114264
173 1.297560759
174 -0.700163386
175 -0.146551335
176 0.160915106
177 -0.184644976
178 0.268993725
179 0.420432093
180 -0.101054168
181 -1.331499791
182 -0.993565849
183 0.499381902
184 -0.247344954
185 -0.558720063
186 -0.0951463740
187 -0.286993384
188 -0.839200457
189 -0.790719965
190 0.119913802
191 1.353930002
192 -0.0925398579
193 1.630712447
194 0.457658385
195 0.634871281
196 -0.231533826
197 -0.232056558
198 0.205688987
199 0.254599350
200 -0.0707106781
201 0.626583373
202 -1.160713375
203 0.978818017
204 0.164407626
205 0.466100457
206 -0.0645522866