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

$R= 24.6372905679$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.664122812
4 0.5
5 -0.447213595
6 0.469605744
7 0.628202392
8 0.353553390
9 -0.558940889
10 -0.316227766
11 0.299138614
12 0.332061406
13 -0.859296148
14 0.444206172
15 -0.297004751
16 0.250000000
17 -1.328004699
18 -0.395230893
19 1.893285210
20 -0.223606797
21 0.417203540
22 0.211522943
23 0.706602569
24 0.234802872
25 0.200000000
26 -0.607614133
27 -1.035328208
28 0.314101196
29 0.614189391
30 -0.210014073
31 0.709264766
32 0.176776695
33 0.198664778
34 -0.939041128
35 -0.280940650
36 -0.279470444
37 -0.167197654
38 1.338754811
39 -0.570678175
40 -0.158113883
41 -0.196959354
42 0.295007452
43 1.908244203
44 0.149569307
45 0.249965964
46 0.499643468
47 0.873188804
48 0.166030703
49 -0.605361753
50 0.141421356
51 -0.881958216
52 -0.429648074
53 0.186268927
54 -0.732087597
55 -0.133778855
56 0.222103086
57 1.257373899
58 0.434297483
59 -0.236102311
60 -0.148502375
61 1.143388711
62 0.501525925
63 -0.351128004
64 0.125000000
65 0.384288920
66 0.140477211
67 1.054103407
68 -0.664002349
69 0.469270885
70 -0.198655039
71 -1.617727120
72 -0.197615446
73 1.705295549
74 -0.118226595
75 0.132824562
76 0.946642605
77 0.187919593
78 -0.403530407
79 1.240996309
80 -0.111803398
81 -0.128644192
82 -0.139271294
83 -0.538119637
84 0.208601770
85 0.593901756
86 1.349332416
87 0.407897186
88 0.105761471
89 0.640534610
90 0.176752628
91 -0.539811896
92 0.353301284
93 0.471038911
94 0.617437724
95 -0.846702886
96 0.117401436
97 -0.804301456
98 -0.428055400
99 -0.167200803
100 0.100000000
101 -0.0168395472
102 -0.623638635
103 -1.298747828
104 -0.303807066
105 -0.186579095
106 0.131712021
107 0.281208980
108 -0.517664104
109 -0.589622860
110 -0.0945959359
111 -0.111039776
112 0.157050598
113 0.269194682
114 0.889097611
115 -0.316002275
116 0.307094695
117 0.480295753
118 -0.166949545
119 -0.834255729
120 -0.105007036
121 -0.910516088
122 0.808497911
123 -0.130805200
124 0.354632383
125 -0.0894427190
126 -0.248284992
127 0.407738106
128 0.0883883476
129 1.267308505
130 0.271733301
131 0.900018647
132 0.0993323891
133 1.189366300
134 0.745363667
135 0.463012850
136 -0.469520564
137 1.556642729
138 0.331824625
139 1.252480921
140 -0.140470325
141 0.579904590
142 -1.143905816
143 -0.257048656
144 -0.139735222
145 -0.274673846
146 1.205826046
147 -0.402034615
148 -0.0835988273
149 0.364630887
150 0.0939211489
151 1.108647304
152 0.669377405
153 0.742276173
154 0.132879219
155 -0.317192846
156 -0.285339087
157 1.624760295
158 0.877516905
159 0.123705512
160 -0.0790569415
161 0.443888866
162 -0.0909651810
163 0.230191230
164 -0.0984796771
165 -0.0888455898
166 -0.380508044
167 0.709997880
168 0.147503726
169 -0.261604120
170 0.419951959
171 -1.058229390
172 0.954122101
173 -0.142787916
174 0.288426866
175 0.125640478
176 0.0747846537
177 -0.156783564
178 0.452926366
179 -1.436153554
180 0.124982982
181 0.727927041
182 -0.381704652
183 0.759372960
184 0.249821734
185 0.0747730643
186 0.333074808
187 -0.397115978
188 0.436594402
189 -0.649979275
190 -0.598709352
191 1.328083656
192 0.0830153516
193 0.281839948
194 -0.568727014
195 0.255215038
196 -0.302680876
197 0.468544431
198 -0.118228821
199 0.292879156
200 0.0707106781
201 0.700211543
202 -0.0119073580
203 0.390941964
204 -0.440979108
205 0.0880829009
206 -0.918353396
207 -0.376391462
208 -0.214824037
209 0.585034252
210 -0.131931343
211 -0.222593577
212 0.0931344635
213 -1.013986934
214 0.198844777
215 -0.853392751
216 -0.366043798
217 0.443331760
218 -0.416926323
219 1.177908895
220 -0.0668894277
221 1.117425819
222 -0.0785169791