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

$R= 31.8329099691$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -1.474645239
4 0.5
5 -0.447213595
6 -1.042731648
7 -0.182247535
8 0.353553390
9 1.174578581
10 -0.316227766
11 0.788238469
12 -0.737322619
13 1.759367228
14 -0.128868468
15 0.659481399
16 0.250000000
17 1.146066095
18 0.830552480
19 0.172561157
20 -0.223606797
21 0.268750460
22 0.557368767
23 0.152359681
24 -0.521365824
25 0.200000000
26 1.244060498
27 -0.257441474
28 -0.0911237677
29 1.640612499
30 0.466323769
31 -0.0687708953
32 0.176776695
33 -1.162372106
34 0.810391107
35 0.0815035756
36 0.587289290
37 0.363798661
38 0.122019164
39 -2.594442508
40 -0.158113883
41 -1.012985273
42 0.190035273
43 0.456649020
44 0.394119234
45 -0.525287510
46 0.107734563
47 -0.223977152
48 -0.368661309
49 -0.966785835
50 0.141421356
51 -1.690040911
52 0.879683614
53 -0.973327864
54 -0.182038612
55 -0.352510960
56 -0.0644342341
57 -0.254466488
58 1.160088223
59 1.693681340
60 0.329740699
61 1.872047954
62 -0.0486283664
63 -0.214064051
64 0.125000000
65 -0.786812944
66 -0.821921198
67 0.401589237
68 0.573033047
69 -0.224676478
70 0.0576317310
71 0.525410892
72 0.415276240
73 -1.654289275
74 0.257244500
75 -0.294929047
76 0.0862805785
77 -0.143654518
78 -1.834547891
79 -0.722762048
80 -0.111803398
81 -0.794943736
82 -0.716288755
83 0.541127127
84 0.134375230
85 -0.512536339
86 0.322899618
87 -2.419321411
88 0.278684383
89 0.264539069
90 -0.371434360
91 -0.320640341
92 0.0761798406
93 0.101412673
94 -0.158375763
95 -0.0771716955
96 -0.260682912
97 -1.340619240
98 -0.683620820
99 0.925848023
100 0.100000000
101 -1.344438454
102 -1.195039388
103 1.280877801
104 0.622030249
105 -0.120188859
106 -0.688246733
107 0.241089024
108 -0.128720737
109 1.571206883
110 -0.249262890
111 -0.536473963
112 -0.0455618838
113 0.0269345908
114 -0.179934979
115 -0.0681373208
116 0.820306249
117 2.066515064
118 1.197613560
119 -0.208867721
120 0.233161884
121 -0.378680115
122 1.323737803
123 1.493793910
124 -0.0343854476
125 -0.0894427190
126 -0.151366142
127 -1.133993141
128 0.0883883476
129 -0.673395303
130 -0.556360768
131 1.382180937
132 -0.581186053
133 -0.0314488455
134 0.283966472
135 0.115131327
136 0.405195553
137 -0.988317559
138 -0.158870261
139 -0.909342877
140 0.0407517878
141 0.330286842
142 0.371521605
143 1.386800932
144 0.293644645
145 -0.733704214
146 -1.169759164
147 1.425666130
148 0.181899330
149 -0.881881767
150 -0.208546329
151 1.372916595
152 0.0610095821
153 1.346144688
154 -0.101579084
155 0.0307552793
156 -1.297221254
157 1.222757678
158 -0.511069945
159 1.435313300
160 -0.0790569415
161 -0.0277671758
162 -0.562110106
163 0.266974944
164 -0.506492636
165 0.519828609
166 0.382634661
167 -0.405763459
168 0.0950176365
169 2.095373039
170 -0.362417920
171 0.202686633
172 0.228324510
173 1.462832319
174 -1.710718575
175 -0.0364495070
176 0.197059617
177 -2.497579111
178 0.187057370
179 -0.440827573
180 -0.262643755
181 -0.893208415
182 -0.226726959
183 -2.760606608
184 0.0538672818
185 -0.162695707
186 0.0717095890
187 0.903373469
188 -0.111988576
189 0.0469183948
190 -0.0545686292
191 1.703980966
192 -0.184330654
193 0.517143629
194 -0.947960956
195 1.160269962
196 -0.483392917
197 -0.733937447
198 0.654673415
199 -1.714617163
200 0.0707106781
201 -0.592200425
202 -0.950661547
203 -0.298998455
204 -0.845020455
205 0.453020786
206 0.905717379
207 0.178965134
208 0.439841807
209 0.136009688
210 -0.0849863577
211 1.374744683
212 -0.486663932
213 -0.774787231
214 0.170475684
215 -0.204219650
216 -0.0910193062
217 0.0125269787
218 1.111011041
219 2.439334608
220 -0.176255480
221 2.016232226
222 -0.379344377
223 0.613816650
224 -0.0322171170
225 0.234915716
226 0.0190456318
227 -0.484216098
228 -0.127233244
229 0.364053853
230 -0.0481803616
231 0.213950219
232 0.580044111
233 -0.270296020
234 1.461246815
235 0.100165627
236 0.846840670
237 1.067102968
238 -0.147691782
239 0.516896007
240 0.164870349
241 -1.748560186
242 -0.267767277
243 1.408585682
244 0.936023977
245 0.432359769
246 1.056271803
247 0.269801560
248 -0.0243141832
249 -0.712758998
250 -0.0632455532