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

$R= 26.2945508064$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 -1.024719207
4 0.5
5 -0.447213595
6 0.724585900
7 -1.749156195
8 -0.353553390
9 0.0500494540
10 0.316227766
11 -1.742231647
12 -0.512359603
13 0.300496356
14 1.236840207
15 0.458268361
16 0.250000000
17 -1.137242361
18 -0.0353903083
19 0.683055283
20 -0.223606797
21 1.792393950
22 1.231943812
23 -0.613399708
24 0.362292950
25 0.200000000
26 -0.212483011
27 0.973432570
28 -0.874578097
29 0.659775769
30 -0.324044665
31 -0.787574518
32 -0.176776695
33 1.785298232
34 0.804151785
35 0.782246431
36 0.0250247270
37 -1.613083912
38 -0.482993023
39 -0.307924387
40 0.158113883
41 -0.127759270
42 -1.267413916
43 -0.170472960
44 -0.871115823
45 -0.0223827962
46 0.433739093
47 0.603357280
48 -0.256179801
49 2.059547395
50 -0.141421356
51 1.165354091
52 0.150248178
53 -0.634877459
54 -0.688320771
55 0.779149679
56 0.618420103
57 -0.699939868
58 -0.466531920
59 1.463326210
60 0.229134180
61 0.483640653
62 0.556899282
63 -0.0875443126
64 0.125000000
65 -0.134386055
66 -1.262396486
67 1.176405094
68 -0.568621180
69 0.628562462
70 -0.553131756
71 -0.149651804
72 -0.0176951541
73 -1.128148962
74 1.140622573
75 -0.204943841
76 0.341527641
77 3.047435279
78 0.217735422
79 -0.726052652
80 -0.111803398
81 -1.047544506
82 0.0903394462
83 1.786108057
84 0.896196975
85 0.508590245
86 0.120542586
87 -0.676084903
88 0.615971906
89 1.524890328
90 0.0158270270
91 -0.525615062
92 -0.306699854
93 0.807042736
94 -0.426638024
95 -0.305471609
96 0.181146475
97 1.128371886
98 -1.456319929
99 -0.0871977427
100 0.100000000
101 -0.972939808
102 -0.824029780
103 -0.729605139
104 -0.106241505
105 -0.801582942
106 0.448926156
107 1.876038768
108 0.486716285
109 -0.0471825976
110 -0.550942021
111 1.652958068
112 -0.437289048
113 -1.186801461
114 0.494932227
115 0.274320689
116 0.329887884
117 0.0150396787
118 -1.034727886
119 1.989214522
120 -0.162022332
121 2.035371112
122 -0.341985585
123 0.130917378
124 -0.393787259
125 -0.0894427190
126 0.0619031771
127 -0.223090728
128 -0.0883883476
129 0.174686916
130 0.0950252913
131 1.773530799
132 0.892649116
133 -1.194770381
134 -0.831844019
135 -0.435332279
136 0.402075892
137 0.752845085
138 -0.444460779
139 0.146320464
140 0.391123215
141 -0.618271794
142 0.105819805
143 -0.523534262
144 0.0125123635
145 -0.295060693
146 0.797721781
147 -2.110457762
148 -0.806541956
149 -1.066838654
150 0.144917180
151 -0.725250637
152 -0.241496511
153 -0.0569183646
154 -2.154862151
155 0.352214032
156 -0.153962193
157 -1.260952774
158 0.513396754
159 0.650571194
160 0.0790569415
161 1.072931753
162 0.740725823
163 0.208717322
164 -0.0638796350
165 -0.798409641
166 -1.262969119
167 -1.822150166
168 -0.633706958
169 -0.909702861
170 -0.359627611
171 0.0341861513
172 -0.0852364800
173 -0.934469664
174 0.478064219
175 -0.349831239
176 -0.435557911
177 -1.499496836
178 -1.078260291
179 1.233675654
180 -0.0111913981
181 -0.474428908
182 0.371665975
183 -0.495594835
184 0.216869546
185 0.721393056
186 -0.570665391
187 1.981377485
188 0.301678640
189 -1.702694448
190 0.216001046
191 -0.0268206351
192 -0.128089900
193 -0.788927894
194 -0.797879412
195 0.137707972
196 1.029773697
197 -1.736308442
198 0.0616581152
199 0.811070177
200 -0.0707106781
201 -1.206106525
202 0.687972336
203 -1.154152215
204 0.582677045
205 0.0571356825
206 0.515908741
207 -0.0308563856
208 0.0751240890
209 -1.189382524
210 0.566804734
211 -0.504526240
212 -0.317438729
213 0.153175554
214 -1.326559735
215 0.0762378254
216 -0.344160385
217 1.394684922
218 0.0333631347
219 1.140100356
220 0.389574839
221 -0.439847772
222 -1.168817859