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

$R= 31.4195889828$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.123358492
4 0.5
5 -0.447213595
6 -0.794334407
7 0.00870270494
8 -0.353553390
9 0.261934303
10 0.316227766
11 1.268890540
12 0.561679246
13 -1.604457901
14 -0.00615374167
15 -0.502381190
16 0.250000000
17 1.464924366
18 -0.185215521
19 0.233312852
20 -0.223606797
21 0.00977625750
22 -0.897241105
23 -1.084975202
24 -0.397167203
25 0.200000000
26 1.134523062
27 -0.829112368
28 0.00435135247
29 -1.343273985
30 0.355237146
31 0.484538512
32 -0.176776695
33 1.425418964
34 -1.035857953
35 -0.00389196796
36 0.130967151
37 1.117380112
38 -0.164977100
39 -1.802381409
40 0.158113883
41 1.644541718
42 -0.00691285797
43 1.274179669
44 0.634445270
45 -0.117140581
46 0.767193323
47 0.0860360265
48 0.280839623
49 -0.999924262
50 -0.141421356
51 1.645635228
52 -0.802228950
53 -1.781931194
54 0.586270978
55 -0.567465100
56 -0.00307687083
57 0.262093974
58 0.949838144
59 0.754918372
60 -0.251190595
61 0.273562504
62 -0.342620468
63 0.00227953694
64 0.125000000
65 0.717535387
66 -1.007923415
67 -0.994172641
68 0.732462183
69 -1.218816108
70 0.00275203694
71 -0.471002340
72 -0.0926077609
73 -1.243270942
74 -0.790107054
75 0.224671698
76 0.116656426
77 0.0110427799
78 1.274476117
79 0.778316424
80 -0.111803398
81 -1.193324723
82 -1.162866600
83 -0.438420985
84 0.00488812875
85 -0.655134093
86 -0.900981085
87 -1.508978240
88 -0.448620552
89 0.169920406
90 0.0828308994
91 -0.0139631236
92 -0.542487601
93 0.544310453
94 -0.0608366577
95 -0.104340679
96 -0.198583601
97 -1.324169768
98 0.707053227
99 0.332365959
100 0.100000000
101 0.448921212
102 -1.163639829
103 1.135206422
104 0.567261531
105 -0.00437207527
106 1.260015631
107 -0.265417864
108 -0.414556184
109 -0.530954422
110 0.401258420
111 1.255218439
112 0.00217567623
113 -0.189634288
114 -0.185328426
115 0.485215661
116 -0.671636992
117 -0.420262562
118 -0.533807900
119 0.0127488045
120 0.177618573
121 0.610083202
122 -0.193437901
123 1.847409905
124 0.242269256
125 -0.0894427190
126 -0.00161187603
127 0.778033634
128 -0.0883883476
129 1.431360553
130 -0.507374137
131 1.000654097
132 0.712709482
133 0.00203045290
134 0.702986216
135 0.370790323
136 -0.517928976
137 -1.095053375
138 0.861833135
139 -0.436268514
140 -0.00194598398
141 0.0966493011
142 0.333048948
143 -2.035881453
144 0.0654835757
145 0.600730388
146 0.879125314
147 -1.123273412
148 0.558690056
149 0.265442224
150 -0.158866881
151 0.0781972466
152 -0.0824885500
153 0.383713943
154 -0.00780842459
155 -0.216692210
156 -0.901190704
157 -0.669399037
158 -0.550352821
159 -2.001747539
160 0.0790569415
161 -0.00944221944
162 0.843808004
163 0.689776191
164 0.822270859
165 -0.637466740
166 0.310010451
167 -1.784332429
168 -0.00345642898
169 1.574285160
170 0.463249759
171 0.0611126307
172 0.637089834
173 0.282812205
174 1.067008746
175 0.00174054098
176 0.317222635
177 0.848043968
178 -0.120151872
179 -1.005127831
180 -0.0585702907
181 1.183607813
182 0.00987341944
183 0.307308572
184 0.383596661
185 -0.499707577
186 -0.384885612
187 1.858828894
188 0.0430180132
189 -0.00721599761
190 0.0737800021
191 -1.877501219
192 0.140419811
193 0.694961991
194 0.936329422
195 0.806049470
196 -0.499962131
197 1.196748614
198 -0.235018223
199 -0.710928960
200 -0.0707106781
201 -1.116816689
202 -0.317435233
203 -0.0116882786
204 0.822817614
205 -0.735461414
206 -0.802712159
207 -0.284203359
208 -0.401114475
209 0.296048471
210 0.00309152407
211 1.732296394
212 -0.890965597
213 -0.529116465
214 0.187678772
215 -0.569830471
216 0.293135489
217 0.00407011185
218 0.375441472
219 -1.396758642
220 -0.283732550
221 -2.350546254
222 -0.887573470
223 -1.193202556
224 -0.00153843541
225 0.0523868606
226 0.134091691
227 -1.397342198
228 0.131046987
229 -1.603425873
230 -0.343099284
231 0.0131616380
232 0.474919072
233 0.351875606
234 0.297170507
235 -0.0384764807
236 0.377459186
237 0.869364422
238 -0.00901476613
239 -0.616429050
240 -0.125595297
241 -1.334850141
242 -0.431393969
243 -0.469899192
244 0.136781252
245 0.447179724
246 -1.306316072
247 -0.384654761
248 -0.171310234
249 -0.489225935
250 0.0632455532