Properties

Level 10
Symmetry odd
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

$R= 28.2148889919$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.019186501
4 0.5
5 0.447213595
6 -0.720673686
7 -0.855137701
8 -0.353553390
9 0.0387411247
10 -0.316227766
11 -1.827057176
12 0.509593250
13 1.877586846
14 0.604673667
15 0.455794059
16 0.250000000
17 -0.527273357
18 -0.0273941120
19 -0.969308943
20 0.223606797
21 -0.871544802
22 1.291924519
23 -0.436754125
24 -0.360336843
25 0.200000000
26 -1.327654391
27 -0.979702070
28 -0.427568850
29 1.292159482
30 -0.322295070
31 -0.877078643
32 -0.176776695
33 -1.862112011
34 0.372838566
35 -0.382429206
36 0.0193705623
37 0.0457611932
38 0.685404927
39 1.913611169
40 -0.158113883
41 -1.647255160
42 0.616275239
43 0.948974749
44 -0.913528588
45 0.0173255577
46 0.308831804
47 -0.107871712
48 0.254796625
49 -0.268739511
50 -0.141421356
51 -0.537389888
52 0.938793423
53 1.849084078
54 0.692753977
55 -0.817084809
56 0.302336833
57 -0.987906591
58 -0.913694732
59 0.233078713
60 0.227897029
61 1.374002399
62 0.620188256
63 -0.0331289963
64 0.125000000
65 0.839682364
66 1.316712030
67 1.618283465
68 -0.263636678
69 -0.445133909
70 0.270418284
71 -0.952810387
72 -0.0136970560
73 1.310249780
74 -0.0323580500
75 0.203837300
76 -0.484654471
77 1.562385473
78 -1.353127434
79 0.229234665
80 0.111803398
81 -1.037240250
82 1.164785294
83 0.0337123800
84 -0.435772401
85 -0.235803814
86 -0.671026480
87 1.316951502
88 0.645962259
89 -0.174378564
90 -0.0122510193
91 -1.605595300
92 -0.218377062
93 -0.893906714
94 0.0762768197
95 -0.433488137
96 -0.180168421
97 -0.383203139
98 0.190027531
99 -0.0707822500
100 0.100000000
101 -1.496534011
102 0.379992034
103 -0.147605844
104 -0.663827195
105 -0.389766684
106 -1.307499890
107 -0.170182768
108 -0.489851035
109 0.0509444103
110 0.577766209
111 0.0466391905
112 -0.213784425
113 1.484818191
114 0.698555449
115 -0.195322382
116 0.646079741
117 0.0727398262
118 -0.164811538
119 0.450891326
120 -0.161147535
121 2.338137925
122 -0.971566414
123 -1.678860223
124 -0.438539321
125 0.0894427190
126 0.0234257379
127 0.885361790
128 -0.0883883476
129 0.967182255
130 -0.593745094
131 -0.764522899
132 -0.931056005
133 0.828892622
134 -1.144299212
135 -0.438136085
136 0.186419283
137 0.586089841
138 0.314757205
139 0.358234937
140 -0.191214603
141 -0.109941393
142 0.673738685
143 -3.430458524
144 0.00968528119
145 0.577871288
146 -0.926486504
147 -0.273895683
148 0.0228805966
149 0.0781498261
150 -0.144134737
151 -1.105194757
152 0.342702463
153 -0.0204271674
154 -1.104773363
155 -0.392241493
156 0.956805584
157 -0.314740150
158 -0.162093386
159 1.884561506
160 -0.0790569415
161 0.373484883
162 0.733439614
163 1.123530534
164 -0.823627580
165 -0.832761807
166 -0.0238382525
167 0.279152094
168 0.308137619
169 2.525332307
170 0.166738475
171 -0.0375521982
172 0.474487374
173 -0.170803006
174 -0.931225337
175 -0.171027540
176 -0.456764294
177 0.237550376
178 0.123304265
179 0.376537433
180 0.00866277885
181 0.748773158
182 1.135327324
183 1.400364107
184 0.154415902
185 0.0204650277
186 0.632087499
187 0.963358996
188 -0.0539358564
189 0.837780154
190 0.306522401
191 -0.204416799
192 0.127398312
193 1.845583996
194 0.270965538
195 0.855792931
196 -0.134369755
197 -0.183151140
198 0.0500506089
199 -1.579080053
200 -0.0707106781
201 1.649346026
202 1.058209347
203 -1.104938440
204 -0.268694944
205 -0.736674902
206 0.104373093
207 -0.0167838874
208 0.469396711
209 1.771399612
210 0.275606665
211 0.00267182163
212 0.924542039
213 -0.970923137
214 0.120337389
215 0.424394409
216 0.346376988
217 0.752826897
218 -0.0360231379
219 1.340686998
220 -0.408542404
221 -0.984627312
222 -0.0329788878
223 0.248587665
224 0.151168416
225 0.00774822495
226 -1.049925011
227 -0.361284969
228 -0.493953295
229 1.479995926
230 0.138113781
231 1.615229542
232 -0.456847366