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

$R= 27.4132128948$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.318945763
4 0.5
5 0.447213595
6 0.932635493
7 -1.453956585
8 0.353553390
9 0.739617927
10 0.316227766
11 1.055540279
12 0.659472881
13 0.111212710
14 -1.028102561
15 0.589850477
16 0.250000000
17 -1.782973605
18 0.522988852
19 -1.980258687
20 0.223606797
21 -1.917689879
22 0.746379689
23 1.373571026
24 0.466317746
25 0.200000000
26 0.0786392620
27 -0.343429831
28 -0.726978292
29 0.469194527
30 0.417087272
31 -0.855312126
32 0.176776695
33 1.392200380
34 -1.260752727
35 -0.650229152
36 0.369808963
37 -0.988309629
38 -1.400254346
39 0.146683533
40 0.158113883
41 1.284620368
42 -1.356011517
43 -0.533513739
44 0.527770139
45 0.330767192
46 0.971261387
47 -1.122973853
48 0.329736440
49 1.113989752
50 0.141421356
51 -2.351645483
52 0.0556063554
53 -0.356362353
54 -0.242841562
55 0.472051963
56 -0.514051280
57 -2.611853806
58 0.331770631
59 -0.506122990
60 0.294925238
61 -1.714092642
62 -0.604797004
63 -1.075372356
64 0.125000000
65 0.0497358362
66 0.984434329
67 1.007720686
68 -0.891486802
69 1.811665686
70 -0.459781442
71 -0.290993810
72 0.261494426
73 -0.255657760
74 -0.698840440
75 0.263789152
76 -0.990129343
77 -1.534709741
78 0.103720921
79 0.849684244
80 0.111803398
81 -1.192583248
82 0.908363773
83 -1.238557546
84 -0.958844939
85 -0.797370036
86 -0.377251182
87 0.618842134
88 0.373189844
89 -0.0198061890
90 0.233887724
91 -0.161698453
92 0.686785513
93 -1.128110305
94 -0.794062426
95 -0.885598607
96 0.233158873
97 0.404781159
98 0.787709708
99 0.780696514
100 0.100000000
101 0.893902499
102 -1.662864468
103 0.0265152163
104 0.0393196310
105 -0.857616985
106 -0.251986236
107 -0.0731116509
108 -0.171714915
109 -1.675015111
110 0.333791144
111 -1.303526798
112 -0.363489146
113 0.543507309
114 -1.846859537
115 0.614279637
116 0.234597263
117 0.0822549147
118 -0.357882998
119 2.592366215
120 0.208543636
121 0.114165282
122 -1.212046530
123 1.694344593
124 -0.427656063
125 0.0894427190
126 -0.760403085
127 -0.605986710
128 0.0883883476
129 -0.703675686
130 0.0351685471
131 -0.533416217
132 0.696100190
133 2.879210159
134 0.712566130
135 -0.153586489
136 -0.630376363
137 0.580628721
138 1.281041091
139 1.129667117
140 -0.325114576
141 -1.481141606
142 -0.205763696
143 0.117389495
144 0.184904481
145 0.209830171
146 -0.180777335
147 1.469292068
148 -0.494154814
149 -0.150528537
150 0.186527098
151 0.170464824
152 -0.700127173
153 -1.318719233
154 -1.085203665
155 -0.382507211
156 0.0733417669
157 1.059347044
158 0.600817491
159 -0.470022633
160 0.0790569415
161 -1.997112679
162 -0.843283702
163 -0.412566403
164 0.642310184
165 0.622610937
166 -0.875792439
167 -0.0311400824
168 -0.678005758
169 -0.987631839
170 -0.563825760
171 -1.464634636
172 -0.266756869
173 1.175234766
174 0.437587469
175 -0.290791317
176 0.263885069
177 -0.667548288
178 -0.0140050905
179 -0.319190898
180 0.165383596
181 -0.732335201
182 -0.114338072
183 -2.260793976
184 0.485630693
185 -0.441985502
186 -0.797694446
187 -1.882005962
188 -0.561486926
189 0.499327867
190 -0.626212780
191 -0.684800293
192 0.164868220
193 1.117814775
194 0.286223502
195 0.0655988705
196 0.556994876
197 -1.398623114
198 0.552035799
199 -1.016471320
200 0.0707106781
201 1.329152225
202 0.632084519
203 -0.682235196
204 -1.175822741
205 0.574499693
206 0.0187490892
207 1.015939662
208 0.0278031777
209 -2.088411626
210 -0.606426786
211 -0.569444366
212 -0.178181176
213 -0.382665268
214 -0.0516977441
215 -0.238594597
216 -0.121420781
217 1.253063370
218 -1.184414543
219 -0.344524258
220 0.236025981
221 -0.202664802
222 -0.921732638
223 1.335641856
224 -0.257025640
225 0.147923585
226 0.384317704
227 1.045795708
228 -1.305926903