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

$R= 23.0718574707$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -0.741488780
4 0.5
5 -0.447213595
6 0.524311744
7 0.600114760
8 -0.353553390
9 -0.450194388
10 0.316227766
11 -0.611565664
12 -0.370744390
13 1.456877721
14 -0.424345216
15 0.331603863
16 0.250000000
17 0.0692914650
18 0.318335504
19 -1.852947710
20 -0.223606797
21 -0.444978361
22 0.432442228
23 0.833614372
24 0.262155872
25 0.200000000
26 -1.030168115
27 1.075302868
28 0.300057380
29 -1.691390760
30 -0.234479340
31 -0.374819939
32 -0.176776695
33 0.453469078
34 -0.0489964648
35 -0.268379479
36 -0.225097194
37 0.327163390
38 1.310231891
39 -1.080258484
40 0.158113883
41 1.584375190
42 0.314647217
43 -0.208276834
44 -0.305782832
45 0.201333051
46 -0.589454375
47 1.075884310
48 -0.185372195
49 -0.639862274
50 -0.141421356
51 -0.0513788439
52 0.728438860
53 -0.614216661
54 -0.760353950
55 0.273500479
56 -0.212172608
57 1.373939938
58 1.195993876
59 1.179240808
60 0.165801931
61 1.269898857
62 0.265037720
63 -0.270168297
64 0.125000000
65 -0.651535523
66 -0.320651060
67 0.719942069
68 0.0346457325
69 -0.618115704
70 0.189772949
71 0.670774299
72 0.159167752
73 0.121731550
74 -0.231339452
75 -0.148297756
76 -0.926473855
77 -0.367009582
78 0.763858100
79 0.468684426
80 -0.111803398
81 -0.347130624
82 -1.120322440
83 0.952798345
84 -0.222489180
85 -0.0309880852
86 0.147273961
87 1.254147272
88 0.216221114
89 1.591902062
90 -0.142363965
91 0.874293824
92 0.416807186
93 0.277924779
94 -0.760765091
95 0.828663407
96 0.131077936
97 -1.408198837
98 0.452450953
99 0.275323430
100 0.100000000
101 -0.276592668
102 0.0363303289
103 -0.630004548
104 -0.515084057
105 0.199000373
106 0.434316766
107 -0.550162486
108 0.537651434
109 -0.802685175
110 -0.193394043
111 -0.242587983
112 0.150028690
113 0.787627375
114 -0.971522247
115 -0.372803680
116 -0.845695380
117 -0.655878174
118 -0.833849172
119 0.0415828309
120 -0.117239670
121 -0.625987437
122 -0.897954093
123 -1.174796428
124 -0.187409969
125 -0.0894427190
126 0.191037835
127 -1.728245196
128 -0.0883883476
129 0.154434935
130 0.460705187
131 0.622255380
132 0.226734539
133 -1.111981269
134 -0.509075919
135 -0.480890062
136 -0.0244982324
137 -0.0867406996
138 0.437073806
139 -0.466801550
140 -0.134189739
141 -0.797756128
142 -0.474309055
143 -0.890976353
144 -0.112548597
145 0.756412943
146 -0.0860772049
147 0.474450692
148 0.163581695
149 -0.886176523
150 0.104862348
151 -1.864495451
152 0.655115945
153 -0.0311947484
154 0.259514964
155 0.167624572
156 -0.540129242
157 -0.585009492
158 -0.331409936
159 0.455434675
160 0.0790569415
161 0.500262790
162 0.245458418
163 -1.167296131
164 0.792187595
165 -0.202797537
166 -0.673730171
167 0.372256835
168 0.157323608
169 1.122497369
170 0.0219118851
171 0.834191418
172 -0.104138417
173 0.488312256
174 -0.886816040
175 0.120022952
176 -0.152891416
177 -0.874398853
178 -1.125644743
179 -0.765398407
180 0.100666525
181 1.044386154
182 -0.618219091
183 -0.941722901
184 -0.294727187
185 -0.146311916
186 -0.196522496
187 -0.0422016187
188 0.537942155
189 0.645628571
190 -0.585953515
191 1.201123231
192 -0.0926860975
193 1.357197856
194 0.995746947
195 0.483106281
196 -0.319931137
197 -1.083368288
198 -0.194683064
199 1.150374606
200 -0.0707106781
201 -0.528392708
202 0.195580551
203 -1.007536614
204 -0.0256894219
205 -0.708554125
206 0.445480488
207 -0.399504786
208 0.364219430
209 1.134084504
210 -0.140714513