Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

Related objects

Downloads

Learn more about

Spectral parameter

$R= 25.8810477463$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.453684226
4 0.5
5 0.447213595
6 -0.320803192
7 0.710689115
8 -0.353553390
9 -0.794170622
10 -0.316227766
11 1.826091742
12 0.226842113
13 -1.296446398
14 -0.502533093
15 0.202893754
16 0.250000000
17 -0.172202542
18 0.561563432
19 0.167607009
20 0.223606797
21 0.322428441
22 -1.291241854
23 0.336240410
24 -0.160401596
25 0.200000000
26 0.916726039
27 -0.813986910
28 0.355344557
29 0.196753060
30 -0.143467549
31 -1.360050447
32 -0.176776695
33 0.828469019
34 0.121765585
35 0.317829834
36 -0.397085311
37 -0.629859642
38 -0.118516053
39 -0.588177281
40 -0.158113883
41 -1.061290099
42 -0.227991337
43 1.167745818
44 0.913045871
45 -0.355163899
46 -0.237757874
47 -0.520924746
48 0.113421056
49 -0.494920980
50 -0.141421356
51 -0.0781255773
52 -0.648223199
53 -1.137523222
54 0.575575664
55 0.816653053
56 -0.251266546
57 0.0760406565
58 -0.139125423
59 -1.665982014
60 0.101446877
61 -0.383671067
62 0.961700894
63 -0.564408417
64 0.125000000
65 -0.579788455
66 -0.585816061
67 1.720089468
68 -0.0861012713
69 0.152546970
70 -0.224739631
71 -1.460089290
72 0.280781716
73 -0.132716662
74 0.445378024
75 0.0907368452
76 0.0838035048
77 1.297783525
78 0.415904144
79 1.482102519
80 0.111803398
81 0.424877600
82 0.750445426
83 0.932031662
84 0.161214220
85 -0.0770113182
86 -0.825720987
87 0.0892637598
88 -0.645620927
89 0.883772176
90 0.251138801
91 -0.921370344
92 0.168120205
93 -0.617033435
94 0.368349420
95 0.0749561334
96 -0.0802007982
97 0.440702059
98 0.349961981
99 -1.450228416
100 0.100000000
101 0.0186426226
102 0.0552431255
103 -1.530830608
104 0.458363019
105 0.144194382
106 0.804350384
107 0.473559993
108 -0.406993455
109 1.638673537
110 -0.577460912
111 -0.285757384
112 0.177672278
113 -0.316505780
114 -0.0537688639
115 0.150371282
116 0.0983765300
117 1.029599643
118 1.178027180
119 -0.122382472
120 -0.0717337746
121 2.334611051
122 0.271296413
123 -0.481490577
124 -0.680025223
125 0.0894427190
126 0.399097019
127 -0.821704763
128 -0.0883883476
129 0.529787857
130 0.409972348
131 -0.786633512
132 0.414234509
133 0.119116477
134 -1.216286927
135 -0.364026013
136 0.0608827928
137 -1.446109652
138 -0.107866997
139 0.913044366
140 0.158914917
141 -0.236335345
142 1.032439038
143 -2.367430066
144 -0.198542655
145 0.0879906434
146 0.0938448523
147 -0.224537849
148 -0.314929821
149 -0.0696052845
150 -0.0641606385
151 -0.953367941
152 -0.0592580266
153 0.136758171
154 -0.917671531
155 -0.608233050
156 -0.294088640
157 -1.764016431
158 -1.048004742
159 -0.516076513
160 -0.0790569415
161 0.238962008
162 -0.300433832
163 0.278050470
164 -0.530645049
165 0.370502608
166 -0.659045909
167 -1.542159889
168 -0.113995668
169 0.680771426
170 0.0544552253
171 -0.133111297
172 0.583872909
173 0.572269934
174 -0.0631190098
175 0.142137823
176 0.456522935
177 -0.755835867
178 -0.624921299
179 -1.687484906
180 -0.177581949
181 -1.128763089
182 0.651507218
183 -0.174075565
184 -0.118878937
185 -0.281681795
186 0.436308526
187 -0.314472036
188 -0.260462373
189 -0.578554704
190 -0.0530019902
191 -0.855726258
192 0.0567105282
193 -0.0913510087
194 -0.311623414
195 -0.263040876
196 -0.247460490
197 1.797308199
198 1.025466347
199 -0.956076364
200 -0.0707106781
201 0.779225987
202 -0.0131823248
203 0.139852267
204 -0.0390627886
205 -0.474623361
206 1.082460703
207 -0.267370282
208 -0.324111599
209 0.303407542
210 -0.101960825
211 -0.667927898
212 -0.568761611
213 -0.665825356
214 -0.334857482
215 0.522231806
216 0.287787832
217 -0.953222419
218 -1.158717170
219 -0.0757213824
220 0.408326526
221 0.176547186
222 0.202060984