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

$R= 30.546564283$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 0.387731548
4 0.5
5 -0.447213595
6 0.274167607
7 0.392039865
8 0.353553390
9 -0.849664246
10 -0.316227766
11 0.577606175
12 0.193865774
13 0.912818868
14 0.277214047
15 -0.173398819
16 0.250000000
17 1.286089793
18 -0.600803350
19 1.787955296
20 -0.223606797
21 0.152006224
22 0.408429243
23 -1.805988041
24 0.137083803
25 0.200000000
26 0.645460411
27 -0.717173182
28 0.196019932
29 -0.976692090
30 -0.122611481
31 1.057521757
32 0.176776695
33 0.223956137
34 0.909402814
35 -0.175325557
36 -0.424832123
37 -0.188776591
38 1.264275314
39 0.353928673
40 -0.158113883
41 -0.645723159
42 0.107484631
43 -1.509961721
44 0.288803087
45 0.379981402
46 -1.277026390
47 1.130176015
48 0.0969328871
49 -0.846304743
50 0.141421356
51 0.498657587
52 0.456409434
53 1.169169419
54 -0.507118020
55 -0.258313334
56 0.138607023
57 0.693246675
58 -0.690625600
59 -1.641972142
60 -0.0866994099
61 1.025056053
62 0.747780806
63 -0.333102257
64 0.125000000
65 -0.408225008
66 0.158360903
67 1.816360890
68 0.643044896
69 -0.700238540
70 -0.123973890
71 0.399723967
72 -0.300401675
73 -0.500299280
74 -0.133485208
75 0.0775463097
76 0.893977648
77 0.226444647
78 0.250265365
79 1.045245196
80 -0.111803398
81 0.571593577
82 -0.456595225
83 0.0181036763
84 0.0760031121
85 -0.575156840
86 -1.067704172
87 -0.378694336
88 0.204214621
89 -0.490282467
90 0.268687426
91 0.357861386
92 -0.902994020
93 0.410034548
94 0.799155124
95 -0.799597916
96 0.0685419018
97 0.936326816
98 -0.598427823
99 -0.490771316
100 0.100000000
101 -0.0330012915
102 0.352604161
103 1.378724691
104 0.322730205
105 -0.0679792500
106 0.826727624
107 1.227384462
108 -0.358586591
109 1.388288100
110 -0.182655110
111 -0.0731946401
112 0.0980099664
113 0.751730157
114 0.490199425
115 0.807662405
116 -0.488346045
117 -0.775589555
118 -1.161049636
119 0.504198470
120 -0.0613057407
121 -0.666371105
122 0.724824086
123 -0.250367240
124 0.528760878
125 -0.0894427190
126 -0.235538864
127 -0.141484496
128 0.0883883476
129 -0.585459796
130 -0.288658671
131 0.221794409
132 0.111978068
133 0.700949754
134 1.284361102
135 0.320729597
136 0.454701407
137 -0.806445006
138 -0.495143420
139 1.285134338
140 -0.0876627789
141 0.438204896
142 0.282647527
143 0.527249815
144 -0.212416061
145 0.436789981
146 -0.353765013
147 -0.328139048
148 -0.0943882957
149 0.141188583
150 0.0548335214
151 1.147279877
152 0.632137657
153 -1.092744515
154 0.160120545
155 -0.472938107
156 0.176964336
157 0.0814432857
158 0.739099966
159 0.453323869
160 -0.0790569415
161 -0.708019305
162 0.404177694
163 -1.804892411
164 -0.322861579
165 -0.100156229
166 0.0128012323
167 -0.617906687
168 0.0537423159
169 -0.166761713
170 -0.406697302
171 -1.519161706
172 -0.754980860
173 0.0695306943
174 -0.267777333
175 0.0784079731
176 0.144401543
177 -0.636644356
178 -0.346682057
179 -0.0686252834
180 0.189990701
181 1.295032346
182 0.253046213
183 0.397446800
184 -0.638513195
185 0.0844234582
186 0.289938209
187 0.742853791
188 0.565088007
189 -0.281160130
190 -0.565401109
191 -1.362873649
192 0.0484664435
193 0.127612274
194 0.662083041
195 -0.158281714
196 -0.423152371
197 0.564154429
198 -0.347027725
199 0.933623366
200 0.0707106781
201 0.704266740
202 -0.0233354370
203 -0.382891691
204 0.249328793
205 0.288776176
206 0.974905578
207 1.534493833
208 0.228204717
209 1.032729956
210 -0.0480685887
211 0.0912822510
212 0.584584709
213 0.154943132
214 0.867891876
215 0.675275410
216 -0.253559010
217 0.414668368
218 0.981667930
219 -0.193855858
220 -0.129156667
221 1.174610106
222 -0.0517564264
223 -0.395984888
224 0.0693035118
225 -0.169932849
226 0.531553491
227 -0.231185720
228 0.346623337
229 0.588190145
230 0.571103563
231 0.0870938442
232 -0.345312800
233 1.518815083
234 -0.548424634
235 -0.505430079
236 -0.820986071
237 0.403000705
238 0.356522157
239 1.498790598
240 -0.0433497049