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

$R= 26.8954926454$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.737771248
4 0.5
5 0.447213595
6 -1.228789834
7 1.943660613
8 0.353553390
9 2.019848912
10 0.316227766
11 -0.934475317
12 -0.868885624
13 0.488303658
14 1.374375600
15 -0.777154928
16 0.250000000
17 -0.515430386
18 1.428248862
19 -1.027271655
20 0.223606797
21 -3.377637531
22 -0.660773833
23 -0.551336382
24 -0.614394917
25 0.200000000
26 0.345282828
27 -1.772264117
28 0.971830306
29 0.954052982
30 -0.549531519
31 -1.422045596
32 0.176776695
33 1.623904339
34 -0.364464321
35 0.869231451
36 1.009924456
37 -0.889078110
38 -0.726390753
39 -0.848560058
40 0.158113883
41 0.448300855
42 -2.388350402
43 -0.290362827
44 -0.467237658
45 0.903303894
46 -0.389853695
47 -1.976156850
48 -0.434442812
49 2.777816581
50 0.141421356
51 0.895700105
52 0.244151829
53 0.780714750
54 -1.253179975
55 -0.417910066
56 0.687187800
57 1.785163146
58 0.674617333
59 0.742739682
60 -0.388577464
61 0.102558438
62 -1.005538084
63 3.925900776
64 0.125000000
65 0.218376034
66 1.148273770
67 -0.156398666
68 -0.257715193
69 0.958096514
70 0.614639453
71 -0.454158256
72 0.714124431
73 -0.878424568
74 -0.628673160
75 -0.347554249
76 -0.513635827
77 -1.816302868
78 -0.600022571
79 0.278608427
80 0.111803398
81 1.059940716
82 0.316996575
83 1.692529941
84 -1.688818765
85 -0.230507476
86 -0.205317523
87 -1.657925843
88 -0.330386916
89 -1.065145231
90 0.638732309
91 0.949096589
92 -0.275668191
93 2.471189951
94 -1.397353909
95 -0.459409850
96 -0.307197458
97 0.286218345
98 1.964212941
99 -1.887498953
100 0.100000000
101 -1.596024797
102 0.633355618
103 -1.031231414
104 0.172641414
105 -1.510525424
106 0.552048694
107 -1.678677893
108 -0.886132058
109 0.184334905
110 -0.295507042
111 1.545014378
112 0.485915153
113 -1.217181942
114 1.262300966
115 -0.246565126
116 0.477026491
117 0.986299614
118 0.525196265
119 -1.001821740
120 -0.274765759
121 -0.126755881
122 0.0725197674
123 -0.779044337
124 -0.711022798
125 0.0894427190
126 2.776031061
127 0.478683143
128 0.0883883476
129 0.504584172
130 0.154415175
131 1.208646198
132 0.811952169
133 -1.996667454
134 -0.110590557
135 -0.792580608
136 -0.182232160
137 0.757704121
138 0.677476542
139 -0.990849042
140 0.434615725
141 3.434108558
142 -0.321138383
143 -0.456307721
144 0.504962228
145 0.426665464
146 -0.621139969
147 -4.827209786
148 -0.444539055
149 1.775441994
150 -0.245757966
151 1.097331276
152 -0.363195376
153 -1.041091519
154 -1.284320075
155 -0.635958124
156 -0.424280029
157 0.415793868
158 0.197005908
159 -1.356703721
160 0.0790569415
161 -1.071610826
162 0.749491268
163 -0.605252209
164 0.224150427
165 0.726232098
166 1.196799399
167 -0.515342471
168 -1.194175201
169 -0.761559730
170 -0.162993399
171 -2.074933664
172 -0.145181413
173 -0.288093868
174 -1.172330606
175 0.388732122
176 -0.233618829
177 -1.290712814
178 -0.753171416
179 0.530721861
180 0.451651947
181 -0.983319165
182 0.671112634
183 -0.178233105
184 -0.194926847
185 -0.397607818
186 1.747395172
187 0.481660443
188 -0.988078425
189 -3.444679212
190 -0.324851820
191 -0.169830621
192 -0.217221406
193 0.542151635
194 0.202386933
195 -0.379487594
196 1.388908290
197 -0.346854056
198 -1.334663309
199 0.629752098
200 0.0707106781
201 0.271738145
202 -1.128559957
203 1.854489367
204 0.447850052
205 0.200486237
206 -0.729190726
207 -1.112948650
208 0.122075914
209 0.960011149
210 -1.068102770
211 -1.335432639
212 0.390357375
213 0.790960309
214 -1.187004521
215 -0.129854203
216 -0.626589987
217 -2.760746589
218 0.130344461
219 1.526782930
220 -0.208955033
221 -0.247180991
222 1.092490143
223 0.623452812
224 0.343593900
225 0.403969782
226 -0.860677605