Properties

Level 10
Symmetry even
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

$R= 25.1274344211$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 1.719674159
4 0.5
5 0.447213595
6 1.215993259
7 1.820848222
8 0.353553390
9 1.957279215
10 0.316227766
11 -0.202573479
12 0.859837079
13 -1.701367803
14 1.287534125
15 0.769061664
16 0.250000000
17 0.187030192
18 1.384005405
19 -0.368523453
20 0.223606797
21 3.131265636
22 -0.143241080
23 1.486428856
24 0.607996629
25 0.200000000
26 -1.203048711
27 1.646208330
28 0.910424111
29 0.379048760
30 0.543808717
31 0.598835226
32 0.176776695
33 -0.348360377
34 0.132250317
35 0.814308080
36 0.978639607
37 -1.194455660
38 -0.260585433
39 -2.925798248
40 0.158113883
41 0.945143126
42 2.214139165
43 0.416096688
44 -0.101286739
45 0.875321875
46 1.051063924
47 0.600857515
48 0.429918539
49 2.315488249
50 0.141421356
51 0.321630989
52 -0.850683901
53 -0.774480327
54 1.164045073
55 -0.0905936140
56 0.643767062
57 -0.633740260
58 0.268027948
59 0.171218087
60 0.384530832
61 -1.121458781
62 0.423440449
63 3.563908380
64 0.125000000
65 -0.760874812
66 -0.246327985
67 -1.505202894
68 0.0935150963
69 2.556173294
70 0.575802765
71 0.598355625
72 0.692002702
73 -0.706260807
74 -0.844607697
75 0.343934831
76 -0.184261726
77 -0.368855559
78 -2.068851781
79 1.518295083
80 0.111803398
81 0.873662711
82 0.668317113
83 -0.587666821
84 1.565632818
85 0.0836424449
86 0.294224790
87 0.651840358
88 -0.0716205404
89 1.562422914
90 0.618946033
91 -3.097932541
92 0.743214428
93 1.029801464
94 0.424870423
95 -0.164808698
96 0.303998314
97 -1.110675839
98 1.637297442
99 -0.396492860
100 0.100000000
101 -0.229735062
102 0.227427453
103 -1.755482936
104 -0.601524355
105 1.400344563
106 -0.547640291
107 -0.282256574
108 0.823104165
109 -0.746778508
110 -0.0640593588
111 -2.054074534
112 0.455212055
113 0.479671929
114 -0.448122035
115 0.664751193
116 0.189524380
117 -3.330051840
118 0.121069470
119 0.340553594
120 0.271904358
121 -0.958963985
122 -0.792991108
123 1.625338211
124 0.299417613
125 0.0894427190
126 2.520063783
127 0.310854253
128 0.0883883476
129 0.715550722
130 -0.538019739
131 1.388746159
132 -0.174180188
133 -0.671025272
134 -1.064339173
135 0.736206746
136 0.0661251587
137 -1.485380347
138 1.807487470
139 -0.640420226
140 0.407154040
141 1.033279137
142 0.423101320
143 0.344652006
144 0.489319803
145 0.169515759
146 -0.499401805
147 3.981885329
148 -0.597227830
149 1.044086406
150 0.243198651
151 1.004801417
152 -0.130292716
153 0.366070253
154 -0.260820267
155 0.267807254
156 -1.462899124
157 -0.252200659
158 1.073596749
159 -1.331853603
160 0.0790569415
161 2.706561187
162 0.617772828
163 -0.252303807
164 0.472571563
165 -0.155791497
166 -0.415543194
167 -1.385787910
168 1.107069582
169 1.894652660
170 0.0591441400
171 -0.721303963
172 0.208048344
173 -0.722289197
174 0.460920737
175 0.364169644
176 -0.0506433698
177 0.294439326
178 1.104799837
179 0.707958835
180 0.437660937
181 1.026077208
182 -2.190569107
183 -1.928567713
184 0.525531962
185 -0.534176810
186 0.728179598
187 -0.0378606193
188 0.300428757
189 2.997517622
190 -0.116537348
191 0.492506702
192 0.214959269
193 0.0534632569
194 -0.785366417
195 -1.308456754
196 1.157744124
197 -1.123164759
198 -0.280362790
199 -0.161575427
200 0.0707106781
201 -2.590048865
202 -0.162447220
203 0.689931183
204 0.160815494
205 0.422680855
206 -1.241313888
207 2.910678538
208 -0.425341950
209 0.0704759982
210 0.990193137
211 0.398261326
212 -0.387240163
213 1.023219283
214 -0.199585537
215 0.186084096
216 0.582022536
217 1.053207703
218 -0.528052147
219 -1.219466676
220 -0.0452968070
221 -0.239841849
222 -1.452450032