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

$R= 25.7447796785$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 0.123394885
4 0.5
5 -0.447213595
6 -0.0872533603
7 0.474302819
8 -0.353553390
9 -0.984773702
10 0.316227766
11 1.305394814
12 0.0616974428
13 -0.923837776
14 -0.335382739
15 -0.0551838704
16 0.250000000
17 -0.705208548
18 0.696340162
19 1.251934665
20 -0.223606797
21 0.0585265421
22 -0.923053525
23 -0.214428818
24 -0.0436266801
25 0.200000000
26 0.653251956
27 -0.244910923
28 0.237151409
29 -0.854907226
30 0.0390208890
31 1.618121999
32 -0.176776695
33 0.161079043
34 0.498657746
35 -0.212114669
36 -0.492386851
37 -0.0398384288
38 -0.885251491
39 -0.113996856
40 0.158113883
41 0.522928049
42 -0.0413845148
43 -1.871477228
44 0.652697407
45 0.440404188
46 0.151624071
47 0.934095257
48 0.0308487214
49 -0.775036835
50 -0.141421356
51 -0.0870191281
52 -0.461918888
53 -0.481080874
54 0.173178175
55 -0.583790308
56 -0.167691369
57 0.154482334
58 0.604510697
59 0.416567356
60 -0.0275919352
61 0.481218640
62 -1.144185038
63 -0.467080943
64 0.125000000
65 0.413152813
66 -0.113900084
67 -1.526163237
68 -0.352604274
69 -0.0264594194
70 0.149987721
71 1.458438542
72 0.348170081
73 1.075580833
74 0.0281700231
75 0.0246789771
76 0.625967332
77 0.619152440
78 0.0806079504
79 -0.419118528
80 -0.111803398
81 0.954552946
82 -0.369765969
83 1.430999719
84 0.0292632710
85 0.315378850
86 1.323334239
87 -0.105491179
88 -0.461526762
89 0.202552280
90 -0.311412787
91 -0.438178862
92 -0.107214409
93 0.199667979
94 -0.660505090
95 -0.559882203
96 -0.0218133400
97 -0.397424523
98 0.548033802
99 -1.285518484
100 0.100000000
101 -0.107247936
102 0.0615318156
103 0.879096448
104 0.326625978
105 -0.0261738653
106 0.340175548
107 -0.806683730
108 -0.122455461
109 1.242167425
110 0.412802085
111 -0.00491585835
112 0.118575704
113 1.569343840
114 -0.109235506
115 0.0958954827
116 -0.427453613
117 0.909771147
118 -0.294557602
119 -0.334482402
120 0.0195104445
121 0.704055621
122 -0.340272964
123 0.0645266468
124 0.809060999
125 -0.0894427190
126 0.330276102
127 0.673549993
128 -0.0883883476
129 -0.230930718
130 -0.292143156
131 -1.530179695
132 0.0805395218
133 0.593796141
134 1.079160374
135 0.109527494
136 0.249328873
137 -0.978673899
138 0.0187096349
139 -1.679693846
140 -0.106057334
141 0.115262578
142 -1.031271783
143 -1.205973041
144 -0.246193425
145 0.382326134
146 -0.760550501
147 -0.0956355758
148 -0.0199192144
149 -1.582223014
150 -0.0174506720
151 -0.574528784
152 -0.442625745
153 0.694470830
154 -0.437806889
155 -0.723646157
156 -0.0569984283
157 0.325411544
158 0.296361553
159 -0.0593628855
160 0.0790569415
161 -0.101704161
162 -0.674970861
163 -1.870328631
164 0.261464024
165 -0.0720367383
166 -1.011869605
167 0.391568456
168 -0.0206922574
169 -0.146523658
170 -0.223006523
171 -1.232873047
172 -0.935738614
173 -1.720544994
174 0.0745935283
175 0.0948605638
176 0.326348703
177 0.0514037484
178 -0.143226090
179 -0.0334236649
180 0.220202094
181 0.939252946
182 0.309839244
183 0.0593693050
184 0.0758120356
185 0.0178162869
186 -0.141186581
187 -0.920580316
188 0.467047628
189 -0.116179249
190 0.395896502
191 -0.382241931
192 0.0154243607
193 -0.906724424
194 0.281021575
195 0.0509809441
196 -0.387518417
197 -1.249323915
198 0.908998837
199 -0.685269786
200 -0.0707106781
201 -0.189012793
202 0.0758357432
203 -0.406072360
204 -0.0435095640
205 -0.233860533
206 -0.621615060
207 0.210914543
208 -0.230959444
209 1.629936076
210 0.0185077176
211 -0.813229894
212 -0.240540437
213 0.177916281
214 0.570411535
215 0.836950060
216 0.0865890875
217 0.752277294
218 -0.878345010
219 0.113790832
220 -0.291895154
221 0.620854468
222 0.00347603677
223 -0.175918380
224 -0.0838456849
225 -0.196954740
226 -1.109693671
227 0.662710316
228 0.0772411674