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

$R= 21.0684479685$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 -0.707106781
3 1.074511104
4 0.5
5 -0.447213595
6 -0.759794088
7 1.337939998
8 -0.353553390
9 0.154574113
10 0.316227766
11 -0.123047403
12 0.537255552
13 -0.821838971
14 -0.946066445
15 -0.480535974
16 0.250000000
17 1.136449536
18 -0.109300404
19 -0.664394326
20 -0.223606797
21 1.437631385
22 0.0870076535
23 -0.0193337441
24 -0.379897044
25 0.200000000
26 0.581127909
27 -0.908419502
28 0.668969999
29 -0.984025535
30 0.339790246
31 -0.526000487
32 -0.176776695
33 -0.132215801
34 -0.803591173
35 -0.598344957
36 0.0772870569
37 -1.852337874
38 0.469797733
39 -0.883075100
40 0.158113883
41 -1.083764353
42 -1.016558901
43 1.299307530
44 -0.0615237018
45 -0.0691276452
46 0.0136710215
47 1.748274336
48 0.268627776
49 0.790083439
50 -0.141421356
51 1.221127646
52 -0.410919485
53 -0.673310264
54 0.642349590
55 0.0550284718
56 -0.473033222
57 -0.713899081
58 0.695811129
59 -0.438120327
60 -0.240267987
61 0.162151615
62 0.371938511
63 0.206810889
64 0.125000000
65 0.367537561
66 0.0934906899
67 -0.497297589
68 0.568224768
69 -0.0207743227
70 0.423093776
71 -0.533658070
72 -0.0546502020
73 1.219113628
74 1.309800671
75 0.214902220
76 -0.332197163
77 -0.164630043
78 0.624428391
79 0.326991504
80 -0.111803398
81 -1.130680957
82 0.766337123
83 1.486325391
84 0.718815692
85 -0.508235683
86 -0.918749165
87 -1.057346365
88 0.0435038267
89 -1.278577329
90 0.0488806266
91 -1.099571231
92 -0.00966687207
93 -0.565193365
94 -1.236216638
95 0.297126175
96 -0.189948522
97 1.673035292
98 -0.558673357
99 -0.0190199433
100 0.100000000
101 -0.413866249
102 -0.863467639
103 -1.175972195
104 0.290563954
105 -0.642928300
106 0.476102253
107 -1.663018805
108 -0.454209751
109 -1.862295446
110 -0.0389110055
111 -1.990357615
112 0.334484999
113 1.091521116
114 0.504802881
115 0.00864631323
116 -0.492012767
117 -0.127035030
118 0.309797854
119 1.520501291
120 0.169895123
121 -0.984859336
122 -0.114658506
123 -1.164516832
124 -0.263000243
125 -0.0894427190
126 -0.146237382
127 -1.643255730
128 -0.0883883476
129 1.396120370
130 -0.259888301
131 0.494450863
132 -0.0661079008
133 -0.888919771
134 0.351642497
135 0.406257552
136 -0.401795586
137 -0.925246996
138 0.0146896645
139 -1.529913240
140 -0.299172478
141 1.878540138
142 0.377353240
143 0.101125237
144 0.0386435284
145 0.440069597
146 -0.862043513
147 0.848953048
148 -0.926168937
149 0.203780627
150 -0.151958817
151 -0.0539731836
152 0.234898866
153 0.175664312
154 0.116411019
155 0.235234569
156 -0.441537550
157 1.326598576
158 -0.231217910
159 -0.723480744
160 0.0790569415
161 -0.0258775334
162 0.799512172
163 -1.761016542
164 -0.541882176
165 0.0591287040
166 -1.050990763
167 0.692187315
168 -0.508279450
169 -0.324660193
170 0.359376898
171 -0.102753479
172 0.649653765
173 0.740609277
174 0.747656785
175 0.267587999
176 -0.0307618509
177 -0.470701268
178 0.904090699
179 -0.887881580
180 -0.0345638226
181 -1.226894722
182 0.777514274
183 0.174774621
184 0.00683551079
185 0.828390680
186 0.399652061
187 -0.141835788
188 0.874137168
189 -1.216965369
190 -0.210099933
191 0.471603149
192 0.134313888
193 -0.533736037
194 -1.183014600
195 0.394923190
196 0.395041719
197 0.304944030
198 0.0134491309
199 -1.360766643
200 -0.0707106781
201 -0.473529640
202 0.292647631
203 -1.256829776
204 0.610563823
205 0.484674153
206 0.831537913