Properties

Label 510.2.a.f.1.1
Level 510510
Weight 22
Character 510.1
Self dual yes
Analytic conductor 4.0724.072
Analytic rank 00
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [510,2,Mod(1,510)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(510, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("510.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 510=23517 510 = 2 \cdot 3 \cdot 5 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 510.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 4.072370503094.07237050309
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 510.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q2+1.00000q3+1.00000q41.00000q5+1.00000q6+1.00000q8+1.00000q91.00000q10+4.00000q11+1.00000q12+2.00000q131.00000q15+1.00000q16+1.00000q17+1.00000q184.00000q191.00000q20+4.00000q22+4.00000q23+1.00000q24+1.00000q25+2.00000q26+1.00000q27+2.00000q291.00000q304.00000q31+1.00000q32+4.00000q33+1.00000q34+1.00000q366.00000q374.00000q38+2.00000q391.00000q4010.0000q418.00000q43+4.00000q441.00000q45+4.00000q46+1.00000q487.00000q49+1.00000q50+1.00000q51+2.00000q52+6.00000q53+1.00000q544.00000q554.00000q57+2.00000q588.00000q591.00000q60+10.0000q614.00000q62+1.00000q642.00000q65+4.00000q668.00000q67+1.00000q68+4.00000q69+8.00000q71+1.00000q722.00000q736.00000q74+1.00000q754.00000q76+2.00000q78+4.00000q791.00000q80+1.00000q8110.0000q82+4.00000q831.00000q858.00000q86+2.00000q87+4.00000q8814.0000q891.00000q90+4.00000q924.00000q93+4.00000q95+1.00000q9610.0000q977.00000q98+4.00000q99+O(q100)q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} +4.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} +2.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +4.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} -10.0000 q^{41} -8.00000 q^{43} +4.00000 q^{44} -1.00000 q^{45} +4.00000 q^{46} +1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +2.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} -4.00000 q^{55} -4.00000 q^{57} +2.00000 q^{58} -8.00000 q^{59} -1.00000 q^{60} +10.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} +4.00000 q^{66} -8.00000 q^{67} +1.00000 q^{68} +4.00000 q^{69} +8.00000 q^{71} +1.00000 q^{72} -2.00000 q^{73} -6.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} +2.00000 q^{78} +4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} -1.00000 q^{85} -8.00000 q^{86} +2.00000 q^{87} +4.00000 q^{88} -14.0000 q^{89} -1.00000 q^{90} +4.00000 q^{92} -4.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000 0.707107
33 1.00000 0.577350
44 1.00000 0.500000
55 −1.00000 −0.447214
66 1.00000 0.408248
77 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
88 1.00000 0.353553
99 1.00000 0.333333
1010 −1.00000 −0.316228
1111 4.00000 1.20605 0.603023 0.797724i 0.293963π-0.293963\pi
0.603023 + 0.797724i 0.293963π0.293963\pi
1212 1.00000 0.288675
1313 2.00000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 0 0
1515 −1.00000 −0.258199
1616 1.00000 0.250000
1717 1.00000 0.242536
1818 1.00000 0.235702
1919 −4.00000 −0.917663 −0.458831 0.888523i 0.651732π-0.651732\pi
−0.458831 + 0.888523i 0.651732π0.651732\pi
2020 −1.00000 −0.223607
2121 0 0
2222 4.00000 0.852803
2323 4.00000 0.834058 0.417029 0.908893i 0.363071π-0.363071\pi
0.417029 + 0.908893i 0.363071π0.363071\pi
2424 1.00000 0.204124
2525 1.00000 0.200000
2626 2.00000 0.392232
2727 1.00000 0.192450
2828 0 0
2929 2.00000 0.371391 0.185695 0.982607i 0.440546π-0.440546\pi
0.185695 + 0.982607i 0.440546π0.440546\pi
3030 −1.00000 −0.182574
3131 −4.00000 −0.718421 −0.359211 0.933257i 0.616954π-0.616954\pi
−0.359211 + 0.933257i 0.616954π0.616954\pi
3232 1.00000 0.176777
3333 4.00000 0.696311
3434 1.00000 0.171499
3535 0 0
3636 1.00000 0.166667
3737 −6.00000 −0.986394 −0.493197 0.869918i 0.664172π-0.664172\pi
−0.493197 + 0.869918i 0.664172π0.664172\pi
3838 −4.00000 −0.648886
3939 2.00000 0.320256
4040 −1.00000 −0.158114
4141 −10.0000 −1.56174 −0.780869 0.624695i 0.785223π-0.785223\pi
−0.780869 + 0.624695i 0.785223π0.785223\pi
4242 0 0
4343 −8.00000 −1.21999 −0.609994 0.792406i 0.708828π-0.708828\pi
−0.609994 + 0.792406i 0.708828π0.708828\pi
4444 4.00000 0.603023
4545 −1.00000 −0.149071
4646 4.00000 0.589768
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 1.00000 0.144338
4949 −7.00000 −1.00000
5050 1.00000 0.141421
5151 1.00000 0.140028
5252 2.00000 0.277350
5353 6.00000 0.824163 0.412082 0.911147i 0.364802π-0.364802\pi
0.412082 + 0.911147i 0.364802π0.364802\pi
5454 1.00000 0.136083
5555 −4.00000 −0.539360
5656 0 0
5757 −4.00000 −0.529813
5858 2.00000 0.262613
5959 −8.00000 −1.04151 −0.520756 0.853706i 0.674350π-0.674350\pi
−0.520756 + 0.853706i 0.674350π0.674350\pi
6060 −1.00000 −0.129099
6161 10.0000 1.28037 0.640184 0.768221i 0.278858π-0.278858\pi
0.640184 + 0.768221i 0.278858π0.278858\pi
6262 −4.00000 −0.508001
6363 0 0
6464 1.00000 0.125000
6565 −2.00000 −0.248069
6666 4.00000 0.492366
6767 −8.00000 −0.977356 −0.488678 0.872464i 0.662521π-0.662521\pi
−0.488678 + 0.872464i 0.662521π0.662521\pi
6868 1.00000 0.121268
6969 4.00000 0.481543
7070 0 0
7171 8.00000 0.949425 0.474713 0.880141i 0.342552π-0.342552\pi
0.474713 + 0.880141i 0.342552π0.342552\pi
7272 1.00000 0.117851
7373 −2.00000 −0.234082 −0.117041 0.993127i 0.537341π-0.537341\pi
−0.117041 + 0.993127i 0.537341π0.537341\pi
7474 −6.00000 −0.697486
7575 1.00000 0.115470
7676 −4.00000 −0.458831
7777 0 0
7878 2.00000 0.226455
7979 4.00000 0.450035 0.225018 0.974355i 0.427756π-0.427756\pi
0.225018 + 0.974355i 0.427756π0.427756\pi
8080 −1.00000 −0.111803
8181 1.00000 0.111111
8282 −10.0000 −1.10432
8383 4.00000 0.439057 0.219529 0.975606i 0.429548π-0.429548\pi
0.219529 + 0.975606i 0.429548π0.429548\pi
8484 0 0
8585 −1.00000 −0.108465
8686 −8.00000 −0.862662
8787 2.00000 0.214423
8888 4.00000 0.426401
8989 −14.0000 −1.48400 −0.741999 0.670402i 0.766122π-0.766122\pi
−0.741999 + 0.670402i 0.766122π0.766122\pi
9090 −1.00000 −0.105409
9191 0 0
9292 4.00000 0.417029
9393 −4.00000 −0.414781
9494 0 0
9595 4.00000 0.410391
9696 1.00000 0.102062
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 −7.00000 −0.707107
9999 4.00000 0.402015
100100 1.00000 0.100000
101101 −6.00000 −0.597022 −0.298511 0.954406i 0.596490π-0.596490\pi
−0.298511 + 0.954406i 0.596490π0.596490\pi
102102 1.00000 0.0990148
103103 16.0000 1.57653 0.788263 0.615338i 0.210980π-0.210980\pi
0.788263 + 0.615338i 0.210980π0.210980\pi
104104 2.00000 0.196116
105105 0 0
106106 6.00000 0.582772
107107 12.0000 1.16008 0.580042 0.814587i 0.303036π-0.303036\pi
0.580042 + 0.814587i 0.303036π0.303036\pi
108108 1.00000 0.0962250
109109 −14.0000 −1.34096 −0.670478 0.741929i 0.733911π-0.733911\pi
−0.670478 + 0.741929i 0.733911π0.733911\pi
110110 −4.00000 −0.381385
111111 −6.00000 −0.569495
112112 0 0
113113 18.0000 1.69330 0.846649 0.532152i 0.178617π-0.178617\pi
0.846649 + 0.532152i 0.178617π0.178617\pi
114114 −4.00000 −0.374634
115115 −4.00000 −0.373002
116116 2.00000 0.185695
117117 2.00000 0.184900
118118 −8.00000 −0.736460
119119 0 0
120120 −1.00000 −0.0912871
121121 5.00000 0.454545
122122 10.0000 0.905357
123123 −10.0000 −0.901670
124124 −4.00000 −0.359211
125125 −1.00000 −0.0894427
126126 0 0
127127 −16.0000 −1.41977 −0.709885 0.704317i 0.751253π-0.751253\pi
−0.709885 + 0.704317i 0.751253π0.751253\pi
128128 1.00000 0.0883883
129129 −8.00000 −0.704361
130130 −2.00000 −0.175412
131131 4.00000 0.349482 0.174741 0.984614i 0.444091π-0.444091\pi
0.174741 + 0.984614i 0.444091π0.444091\pi
132132 4.00000 0.348155
133133 0 0
134134 −8.00000 −0.691095
135135 −1.00000 −0.0860663
136136 1.00000 0.0857493
137137 −6.00000 −0.512615 −0.256307 0.966595i 0.582506π-0.582506\pi
−0.256307 + 0.966595i 0.582506π0.582506\pi
138138 4.00000 0.340503
139139 −4.00000 −0.339276 −0.169638 0.985506i 0.554260π-0.554260\pi
−0.169638 + 0.985506i 0.554260π0.554260\pi
140140 0 0
141141 0 0
142142 8.00000 0.671345
143143 8.00000 0.668994
144144 1.00000 0.0833333
145145 −2.00000 −0.166091
146146 −2.00000 −0.165521
147147 −7.00000 −0.577350
148148 −6.00000 −0.493197
149149 2.00000 0.163846 0.0819232 0.996639i 0.473894π-0.473894\pi
0.0819232 + 0.996639i 0.473894π0.473894\pi
150150 1.00000 0.0816497
151151 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
152152 −4.00000 −0.324443
153153 1.00000 0.0808452
154154 0 0
155155 4.00000 0.321288
156156 2.00000 0.160128
157157 −6.00000 −0.478852 −0.239426 0.970915i 0.576959π-0.576959\pi
−0.239426 + 0.970915i 0.576959π0.576959\pi
158158 4.00000 0.318223
159159 6.00000 0.475831
160160 −1.00000 −0.0790569
161161 0 0
162162 1.00000 0.0785674
163163 12.0000 0.939913 0.469956 0.882690i 0.344270π-0.344270\pi
0.469956 + 0.882690i 0.344270π0.344270\pi
164164 −10.0000 −0.780869
165165 −4.00000 −0.311400
166166 4.00000 0.310460
167167 12.0000 0.928588 0.464294 0.885681i 0.346308π-0.346308\pi
0.464294 + 0.885681i 0.346308π0.346308\pi
168168 0 0
169169 −9.00000 −0.692308
170170 −1.00000 −0.0766965
171171 −4.00000 −0.305888
172172 −8.00000 −0.609994
173173 2.00000 0.152057 0.0760286 0.997106i 0.475776π-0.475776\pi
0.0760286 + 0.997106i 0.475776π0.475776\pi
174174 2.00000 0.151620
175175 0 0
176176 4.00000 0.301511
177177 −8.00000 −0.601317
178178 −14.0000 −1.04934
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 −1.00000 −0.0745356
181181 −14.0000 −1.04061 −0.520306 0.853980i 0.674182π-0.674182\pi
−0.520306 + 0.853980i 0.674182π0.674182\pi
182182 0 0
183183 10.0000 0.739221
184184 4.00000 0.294884
185185 6.00000 0.441129
186186 −4.00000 −0.293294
187187 4.00000 0.292509
188188 0 0
189189 0 0
190190 4.00000 0.290191
191191 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
192192 1.00000 0.0721688
193193 6.00000 0.431889 0.215945 0.976406i 0.430717π-0.430717\pi
0.215945 + 0.976406i 0.430717π0.430717\pi
194194 −10.0000 −0.717958
195195 −2.00000 −0.143223
196196 −7.00000 −0.500000
197197 18.0000 1.28245 0.641223 0.767354i 0.278427π-0.278427\pi
0.641223 + 0.767354i 0.278427π0.278427\pi
198198 4.00000 0.284268
199199 −4.00000 −0.283552 −0.141776 0.989899i 0.545281π-0.545281\pi
−0.141776 + 0.989899i 0.545281π0.545281\pi
200200 1.00000 0.0707107
201201 −8.00000 −0.564276
202202 −6.00000 −0.422159
203203 0 0
204204 1.00000 0.0700140
205205 10.0000 0.698430
206206 16.0000 1.11477
207207 4.00000 0.278019
208208 2.00000 0.138675
209209 −16.0000 −1.10674
210210 0 0
211211 12.0000 0.826114 0.413057 0.910705i 0.364461π-0.364461\pi
0.413057 + 0.910705i 0.364461π0.364461\pi
212212 6.00000 0.412082
213213 8.00000 0.548151
214214 12.0000 0.820303
215215 8.00000 0.545595
216216 1.00000 0.0680414
217217 0 0
218218 −14.0000 −0.948200
219219 −2.00000 −0.135147
220220 −4.00000 −0.269680
221221 2.00000 0.134535
222222 −6.00000 −0.402694
223223 24.0000 1.60716 0.803579 0.595198i 0.202926π-0.202926\pi
0.803579 + 0.595198i 0.202926π0.202926\pi
224224 0 0
225225 1.00000 0.0666667
226226 18.0000 1.19734
227227 12.0000 0.796468 0.398234 0.917284i 0.369623π-0.369623\pi
0.398234 + 0.917284i 0.369623π0.369623\pi
228228 −4.00000 −0.264906
229229 6.00000 0.396491 0.198246 0.980152i 0.436476π-0.436476\pi
0.198246 + 0.980152i 0.436476π0.436476\pi
230230 −4.00000 −0.263752
231231 0 0
232232 2.00000 0.131306
233233 −30.0000 −1.96537 −0.982683 0.185296i 0.940675π-0.940675\pi
−0.982683 + 0.185296i 0.940675π0.940675\pi
234234 2.00000 0.130744
235235 0 0
236236 −8.00000 −0.520756
237237 4.00000 0.259828
238238 0 0
239239 8.00000 0.517477 0.258738 0.965947i 0.416693π-0.416693\pi
0.258738 + 0.965947i 0.416693π0.416693\pi
240240 −1.00000 −0.0645497
241241 10.0000 0.644157 0.322078 0.946713i 0.395619π-0.395619\pi
0.322078 + 0.946713i 0.395619π0.395619\pi
242242 5.00000 0.321412
243243 1.00000 0.0641500
244244 10.0000 0.640184
245245 7.00000 0.447214
246246 −10.0000 −0.637577
247247 −8.00000 −0.509028
248248 −4.00000 −0.254000
249249 4.00000 0.253490
250250 −1.00000 −0.0632456
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 16.0000 1.00591
254254 −16.0000 −1.00393
255255 −1.00000 −0.0626224
256256 1.00000 0.0625000
257257 18.0000 1.12281 0.561405 0.827541i 0.310261π-0.310261\pi
0.561405 + 0.827541i 0.310261π0.310261\pi
258258 −8.00000 −0.498058
259259 0 0
260260 −2.00000 −0.124035
261261 2.00000 0.123797
262262 4.00000 0.247121
263263 16.0000 0.986602 0.493301 0.869859i 0.335790π-0.335790\pi
0.493301 + 0.869859i 0.335790π0.335790\pi
264264 4.00000 0.246183
265265 −6.00000 −0.368577
266266 0 0
267267 −14.0000 −0.856786
268268 −8.00000 −0.488678
269269 −14.0000 −0.853595 −0.426798 0.904347i 0.640358π-0.640358\pi
−0.426798 + 0.904347i 0.640358π0.640358\pi
270270 −1.00000 −0.0608581
271271 −8.00000 −0.485965 −0.242983 0.970031i 0.578126π-0.578126\pi
−0.242983 + 0.970031i 0.578126π0.578126\pi
272272 1.00000 0.0606339
273273 0 0
274274 −6.00000 −0.362473
275275 4.00000 0.241209
276276 4.00000 0.240772
277277 10.0000 0.600842 0.300421 0.953807i 0.402873π-0.402873\pi
0.300421 + 0.953807i 0.402873π0.402873\pi
278278 −4.00000 −0.239904
279279 −4.00000 −0.239474
280280 0 0
281281 −30.0000 −1.78965 −0.894825 0.446417i 0.852700π-0.852700\pi
−0.894825 + 0.446417i 0.852700π0.852700\pi
282282 0 0
283283 20.0000 1.18888 0.594438 0.804141i 0.297374π-0.297374\pi
0.594438 + 0.804141i 0.297374π0.297374\pi
284284 8.00000 0.474713
285285 4.00000 0.236940
286286 8.00000 0.473050
287287 0 0
288288 1.00000 0.0589256
289289 1.00000 0.0588235
290290 −2.00000 −0.117444
291291 −10.0000 −0.586210
292292 −2.00000 −0.117041
293293 6.00000 0.350524 0.175262 0.984522i 0.443923π-0.443923\pi
0.175262 + 0.984522i 0.443923π0.443923\pi
294294 −7.00000 −0.408248
295295 8.00000 0.465778
296296 −6.00000 −0.348743
297297 4.00000 0.232104
298298 2.00000 0.115857
299299 8.00000 0.462652
300300 1.00000 0.0577350
301301 0 0
302302 0 0
303303 −6.00000 −0.344691
304304 −4.00000 −0.229416
305305 −10.0000 −0.572598
306306 1.00000 0.0571662
307307 16.0000 0.913168 0.456584 0.889680i 0.349073π-0.349073\pi
0.456584 + 0.889680i 0.349073π0.349073\pi
308308 0 0
309309 16.0000 0.910208
310310 4.00000 0.227185
311311 −8.00000 −0.453638 −0.226819 0.973937i 0.572833π-0.572833\pi
−0.226819 + 0.973937i 0.572833π0.572833\pi
312312 2.00000 0.113228
313313 −2.00000 −0.113047 −0.0565233 0.998401i 0.518002π-0.518002\pi
−0.0565233 + 0.998401i 0.518002π0.518002\pi
314314 −6.00000 −0.338600
315315 0 0
316316 4.00000 0.225018
317317 26.0000 1.46031 0.730153 0.683284i 0.239449π-0.239449\pi
0.730153 + 0.683284i 0.239449π0.239449\pi
318318 6.00000 0.336463
319319 8.00000 0.447914
320320 −1.00000 −0.0559017
321321 12.0000 0.669775
322322 0 0
323323 −4.00000 −0.222566
324324 1.00000 0.0555556
325325 2.00000 0.110940
326326 12.0000 0.664619
327327 −14.0000 −0.774202
328328 −10.0000 −0.552158
329329 0 0
330330 −4.00000 −0.220193
331331 20.0000 1.09930 0.549650 0.835395i 0.314761π-0.314761\pi
0.549650 + 0.835395i 0.314761π0.314761\pi
332332 4.00000 0.219529
333333 −6.00000 −0.328798
334334 12.0000 0.656611
335335 8.00000 0.437087
336336 0 0
337337 6.00000 0.326841 0.163420 0.986557i 0.447747π-0.447747\pi
0.163420 + 0.986557i 0.447747π0.447747\pi
338338 −9.00000 −0.489535
339339 18.0000 0.977626
340340 −1.00000 −0.0542326
341341 −16.0000 −0.866449
342342 −4.00000 −0.216295
343343 0 0
344344 −8.00000 −0.431331
345345 −4.00000 −0.215353
346346 2.00000 0.107521
347347 4.00000 0.214731 0.107366 0.994220i 0.465758π-0.465758\pi
0.107366 + 0.994220i 0.465758π0.465758\pi
348348 2.00000 0.107211
349349 −34.0000 −1.81998 −0.909989 0.414632i 0.863910π-0.863910\pi
−0.909989 + 0.414632i 0.863910π0.863910\pi
350350 0 0
351351 2.00000 0.106752
352352 4.00000 0.213201
353353 −30.0000 −1.59674 −0.798369 0.602168i 0.794304π-0.794304\pi
−0.798369 + 0.602168i 0.794304π0.794304\pi
354354 −8.00000 −0.425195
355355 −8.00000 −0.424596
356356 −14.0000 −0.741999
357357 0 0
358358 0 0
359359 32.0000 1.68890 0.844448 0.535638i 0.179929π-0.179929\pi
0.844448 + 0.535638i 0.179929π0.179929\pi
360360 −1.00000 −0.0527046
361361 −3.00000 −0.157895
362362 −14.0000 −0.735824
363363 5.00000 0.262432
364364 0 0
365365 2.00000 0.104685
366366 10.0000 0.522708
367367 8.00000 0.417597 0.208798 0.977959i 0.433045π-0.433045\pi
0.208798 + 0.977959i 0.433045π0.433045\pi
368368 4.00000 0.208514
369369 −10.0000 −0.520579
370370 6.00000 0.311925
371371 0 0
372372 −4.00000 −0.207390
373373 18.0000 0.932005 0.466002 0.884783i 0.345694π-0.345694\pi
0.466002 + 0.884783i 0.345694π0.345694\pi
374374 4.00000 0.206835
375375 −1.00000 −0.0516398
376376 0 0
377377 4.00000 0.206010
378378 0 0
379379 20.0000 1.02733 0.513665 0.857991i 0.328287π-0.328287\pi
0.513665 + 0.857991i 0.328287π0.328287\pi
380380 4.00000 0.205196
381381 −16.0000 −0.819705
382382 0 0
383383 −24.0000 −1.22634 −0.613171 0.789950i 0.710106π-0.710106\pi
−0.613171 + 0.789950i 0.710106π0.710106\pi
384384 1.00000 0.0510310
385385 0 0
386386 6.00000 0.305392
387387 −8.00000 −0.406663
388388 −10.0000 −0.507673
389389 −30.0000 −1.52106 −0.760530 0.649303i 0.775061π-0.775061\pi
−0.760530 + 0.649303i 0.775061π0.775061\pi
390390 −2.00000 −0.101274
391391 4.00000 0.202289
392392 −7.00000 −0.353553
393393 4.00000 0.201773
394394 18.0000 0.906827
395395 −4.00000 −0.201262
396396 4.00000 0.201008
397397 18.0000 0.903394 0.451697 0.892171i 0.350819π-0.350819\pi
0.451697 + 0.892171i 0.350819π0.350819\pi
398398 −4.00000 −0.200502
399399 0 0
400400 1.00000 0.0500000
401401 6.00000 0.299626 0.149813 0.988714i 0.452133π-0.452133\pi
0.149813 + 0.988714i 0.452133π0.452133\pi
402402 −8.00000 −0.399004
403403 −8.00000 −0.398508
404404 −6.00000 −0.298511
405405 −1.00000 −0.0496904
406406 0 0
407407 −24.0000 −1.18964
408408 1.00000 0.0495074
409409 10.0000 0.494468 0.247234 0.968956i 0.420478π-0.420478\pi
0.247234 + 0.968956i 0.420478π0.420478\pi
410410 10.0000 0.493865
411411 −6.00000 −0.295958
412412 16.0000 0.788263
413413 0 0
414414 4.00000 0.196589
415415 −4.00000 −0.196352
416416 2.00000 0.0980581
417417 −4.00000 −0.195881
418418 −16.0000 −0.782586
419419 28.0000 1.36789 0.683945 0.729534i 0.260263π-0.260263\pi
0.683945 + 0.729534i 0.260263π0.260263\pi
420420 0 0
421421 30.0000 1.46211 0.731055 0.682318i 0.239028π-0.239028\pi
0.731055 + 0.682318i 0.239028π0.239028\pi
422422 12.0000 0.584151
423423 0 0
424424 6.00000 0.291386
425425 1.00000 0.0485071
426426 8.00000 0.387601
427427 0 0
428428 12.0000 0.580042
429429 8.00000 0.386244
430430 8.00000 0.385794
431431 −16.0000 −0.770693 −0.385346 0.922772i 0.625918π-0.625918\pi
−0.385346 + 0.922772i 0.625918π0.625918\pi
432432 1.00000 0.0481125
433433 −6.00000 −0.288342 −0.144171 0.989553i 0.546051π-0.546051\pi
−0.144171 + 0.989553i 0.546051π0.546051\pi
434434 0 0
435435 −2.00000 −0.0958927
436436 −14.0000 −0.670478
437437 −16.0000 −0.765384
438438 −2.00000 −0.0955637
439439 20.0000 0.954548 0.477274 0.878755i 0.341625π-0.341625\pi
0.477274 + 0.878755i 0.341625π0.341625\pi
440440 −4.00000 −0.190693
441441 −7.00000 −0.333333
442442 2.00000 0.0951303
443443 −28.0000 −1.33032 −0.665160 0.746701i 0.731637π-0.731637\pi
−0.665160 + 0.746701i 0.731637π0.731637\pi
444444 −6.00000 −0.284747
445445 14.0000 0.663664
446446 24.0000 1.13643
447447 2.00000 0.0945968
448448 0 0
449449 −26.0000 −1.22702 −0.613508 0.789689i 0.710242π-0.710242\pi
−0.613508 + 0.789689i 0.710242π0.710242\pi
450450 1.00000 0.0471405
451451 −40.0000 −1.88353
452452 18.0000 0.846649
453453 0 0
454454 12.0000 0.563188
455455 0 0
456456 −4.00000 −0.187317
457457 2.00000 0.0935561 0.0467780 0.998905i 0.485105π-0.485105\pi
0.0467780 + 0.998905i 0.485105π0.485105\pi
458458 6.00000 0.280362
459459 1.00000 0.0466760
460460 −4.00000 −0.186501
461461 −38.0000 −1.76984 −0.884918 0.465746i 0.845786π-0.845786\pi
−0.884918 + 0.465746i 0.845786π0.845786\pi
462462 0 0
463463 −24.0000 −1.11537 −0.557687 0.830051i 0.688311π-0.688311\pi
−0.557687 + 0.830051i 0.688311π0.688311\pi
464464 2.00000 0.0928477
465465 4.00000 0.185496
466466 −30.0000 −1.38972
467467 −12.0000 −0.555294 −0.277647 0.960683i 0.589555π-0.589555\pi
−0.277647 + 0.960683i 0.589555π0.589555\pi
468468 2.00000 0.0924500
469469 0 0
470470 0 0
471471 −6.00000 −0.276465
472472 −8.00000 −0.368230
473473 −32.0000 −1.47136
474474 4.00000 0.183726
475475 −4.00000 −0.183533
476476 0 0
477477 6.00000 0.274721
478478 8.00000 0.365911
479479 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
480480 −1.00000 −0.0456435
481481 −12.0000 −0.547153
482482 10.0000 0.455488
483483 0 0
484484 5.00000 0.227273
485485 10.0000 0.454077
486486 1.00000 0.0453609
487487 −40.0000 −1.81257 −0.906287 0.422664i 0.861095π-0.861095\pi
−0.906287 + 0.422664i 0.861095π0.861095\pi
488488 10.0000 0.452679
489489 12.0000 0.542659
490490 7.00000 0.316228
491491 24.0000 1.08310 0.541552 0.840667i 0.317837π-0.317837\pi
0.541552 + 0.840667i 0.317837π0.317837\pi
492492 −10.0000 −0.450835
493493 2.00000 0.0900755
494494 −8.00000 −0.359937
495495 −4.00000 −0.179787
496496 −4.00000 −0.179605
497497 0 0
498498 4.00000 0.179244
499499 28.0000 1.25345 0.626726 0.779240i 0.284395π-0.284395\pi
0.626726 + 0.779240i 0.284395π0.284395\pi
500500 −1.00000 −0.0447214
501501 12.0000 0.536120
502502 0 0
503503 −28.0000 −1.24846 −0.624229 0.781241i 0.714587π-0.714587\pi
−0.624229 + 0.781241i 0.714587π0.714587\pi
504504 0 0
505505 6.00000 0.266996
506506 16.0000 0.711287
507507 −9.00000 −0.399704
508508 −16.0000 −0.709885
509509 −6.00000 −0.265945 −0.132973 0.991120i 0.542452π-0.542452\pi
−0.132973 + 0.991120i 0.542452π0.542452\pi
510510 −1.00000 −0.0442807
511511 0 0
512512 1.00000 0.0441942
513513 −4.00000 −0.176604
514514 18.0000 0.793946
515515 −16.0000 −0.705044
516516 −8.00000 −0.352180
517517 0 0
518518 0 0
519519 2.00000 0.0877903
520520 −2.00000 −0.0877058
521521 30.0000 1.31432 0.657162 0.753749i 0.271757π-0.271757\pi
0.657162 + 0.753749i 0.271757π0.271757\pi
522522 2.00000 0.0875376
523523 −40.0000 −1.74908 −0.874539 0.484955i 0.838836π-0.838836\pi
−0.874539 + 0.484955i 0.838836π0.838836\pi
524524 4.00000 0.174741
525525 0 0
526526 16.0000 0.697633
527527 −4.00000 −0.174243
528528 4.00000 0.174078
529529 −7.00000 −0.304348
530530 −6.00000 −0.260623
531531 −8.00000 −0.347170
532532 0 0
533533 −20.0000 −0.866296
534534 −14.0000 −0.605839
535535 −12.0000 −0.518805
536536 −8.00000 −0.345547
537537 0 0
538538 −14.0000 −0.603583
539539 −28.0000 −1.20605
540540 −1.00000 −0.0430331
541541 −22.0000 −0.945854 −0.472927 0.881102i 0.656803π-0.656803\pi
−0.472927 + 0.881102i 0.656803π0.656803\pi
542542 −8.00000 −0.343629
543543 −14.0000 −0.600798
544544 1.00000 0.0428746
545545 14.0000 0.599694
546546 0 0
547547 −20.0000 −0.855138 −0.427569 0.903983i 0.640630π-0.640630\pi
−0.427569 + 0.903983i 0.640630π0.640630\pi
548548 −6.00000 −0.256307
549549 10.0000 0.426790
550550 4.00000 0.170561
551551 −8.00000 −0.340811
552552 4.00000 0.170251
553553 0 0
554554 10.0000 0.424859
555555 6.00000 0.254686
556556 −4.00000 −0.169638
557557 30.0000 1.27114 0.635570 0.772043i 0.280765π-0.280765\pi
0.635570 + 0.772043i 0.280765π0.280765\pi
558558 −4.00000 −0.169334
559559 −16.0000 −0.676728
560560 0 0
561561 4.00000 0.168880
562562 −30.0000 −1.26547
563563 20.0000 0.842900 0.421450 0.906852i 0.361521π-0.361521\pi
0.421450 + 0.906852i 0.361521π0.361521\pi
564564 0 0
565565 −18.0000 −0.757266
566566 20.0000 0.840663
567567 0 0
568568 8.00000 0.335673
569569 26.0000 1.08998 0.544988 0.838444i 0.316534π-0.316534\pi
0.544988 + 0.838444i 0.316534π0.316534\pi
570570 4.00000 0.167542
571571 −44.0000 −1.84134 −0.920671 0.390339i 0.872358π-0.872358\pi
−0.920671 + 0.390339i 0.872358π0.872358\pi
572572 8.00000 0.334497
573573 0 0
574574 0 0
575575 4.00000 0.166812
576576 1.00000 0.0416667
577577 −6.00000 −0.249783 −0.124892 0.992170i 0.539858π-0.539858\pi
−0.124892 + 0.992170i 0.539858π0.539858\pi
578578 1.00000 0.0415945
579579 6.00000 0.249351
580580 −2.00000 −0.0830455
581581 0 0
582582 −10.0000 −0.414513
583583 24.0000 0.993978
584584 −2.00000 −0.0827606
585585 −2.00000 −0.0826898
586586 6.00000 0.247858
587587 −12.0000 −0.495293 −0.247647 0.968850i 0.579657π-0.579657\pi
−0.247647 + 0.968850i 0.579657π0.579657\pi
588588 −7.00000 −0.288675
589589 16.0000 0.659269
590590 8.00000 0.329355
591591 18.0000 0.740421
592592 −6.00000 −0.246598
593593 −30.0000 −1.23195 −0.615976 0.787765i 0.711238π-0.711238\pi
−0.615976 + 0.787765i 0.711238π0.711238\pi
594594 4.00000 0.164122
595595 0 0
596596 2.00000 0.0819232
597597 −4.00000 −0.163709
598598 8.00000 0.327144
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 1.00000 0.0408248
601601 34.0000 1.38689 0.693444 0.720510i 0.256092π-0.256092\pi
0.693444 + 0.720510i 0.256092π0.256092\pi
602602 0 0
603603 −8.00000 −0.325785
604604 0 0
605605 −5.00000 −0.203279
606606 −6.00000 −0.243733
607607 −32.0000 −1.29884 −0.649420 0.760430i 0.724988π-0.724988\pi
−0.649420 + 0.760430i 0.724988π0.724988\pi
608608 −4.00000 −0.162221
609609 0 0
610610 −10.0000 −0.404888
611611 0 0
612612 1.00000 0.0404226
613613 10.0000 0.403896 0.201948 0.979396i 0.435273π-0.435273\pi
0.201948 + 0.979396i 0.435273π0.435273\pi
614614 16.0000 0.645707
615615 10.0000 0.403239
616616 0 0
617617 2.00000 0.0805170 0.0402585 0.999189i 0.487182π-0.487182\pi
0.0402585 + 0.999189i 0.487182π0.487182\pi
618618 16.0000 0.643614
619619 44.0000 1.76851 0.884255 0.467005i 0.154667π-0.154667\pi
0.884255 + 0.467005i 0.154667π0.154667\pi
620620 4.00000 0.160644
621621 4.00000 0.160514
622622 −8.00000 −0.320771
623623 0 0
624624 2.00000 0.0800641
625625 1.00000 0.0400000
626626 −2.00000 −0.0799361
627627 −16.0000 −0.638978
628628 −6.00000 −0.239426
629629 −6.00000 −0.239236
630630 0 0
631631 32.0000 1.27390 0.636950 0.770905i 0.280196π-0.280196\pi
0.636950 + 0.770905i 0.280196π0.280196\pi
632632 4.00000 0.159111
633633 12.0000 0.476957
634634 26.0000 1.03259
635635 16.0000 0.634941
636636 6.00000 0.237915
637637 −14.0000 −0.554700
638638 8.00000 0.316723
639639 8.00000 0.316475
640640 −1.00000 −0.0395285
641641 −42.0000 −1.65890 −0.829450 0.558581i 0.811346π-0.811346\pi
−0.829450 + 0.558581i 0.811346π0.811346\pi
642642 12.0000 0.473602
643643 −20.0000 −0.788723 −0.394362 0.918955i 0.629034π-0.629034\pi
−0.394362 + 0.918955i 0.629034π0.629034\pi
644644 0 0
645645 8.00000 0.315000
646646 −4.00000 −0.157378
647647 −32.0000 −1.25805 −0.629025 0.777385i 0.716546π-0.716546\pi
−0.629025 + 0.777385i 0.716546π0.716546\pi
648648 1.00000 0.0392837
649649 −32.0000 −1.25611
650650 2.00000 0.0784465
651651 0 0
652652 12.0000 0.469956
653653 34.0000 1.33052 0.665261 0.746611i 0.268320π-0.268320\pi
0.665261 + 0.746611i 0.268320π0.268320\pi
654654 −14.0000 −0.547443
655655 −4.00000 −0.156293
656656 −10.0000 −0.390434
657657 −2.00000 −0.0780274
658658 0 0
659659 24.0000 0.934907 0.467454 0.884018i 0.345171π-0.345171\pi
0.467454 + 0.884018i 0.345171π0.345171\pi
660660 −4.00000 −0.155700
661661 22.0000 0.855701 0.427850 0.903850i 0.359271π-0.359271\pi
0.427850 + 0.903850i 0.359271π0.359271\pi
662662 20.0000 0.777322
663663 2.00000 0.0776736
664664 4.00000 0.155230
665665 0 0
666666 −6.00000 −0.232495
667667 8.00000 0.309761
668668 12.0000 0.464294
669669 24.0000 0.927894
670670 8.00000 0.309067
671671 40.0000 1.54418
672672 0 0
673673 −10.0000 −0.385472 −0.192736 0.981251i 0.561736π-0.561736\pi
−0.192736 + 0.981251i 0.561736π0.561736\pi
674674 6.00000 0.231111
675675 1.00000 0.0384900
676676 −9.00000 −0.346154
677677 18.0000 0.691796 0.345898 0.938272i 0.387574π-0.387574\pi
0.345898 + 0.938272i 0.387574π0.387574\pi
678678 18.0000 0.691286
679679 0 0
680680 −1.00000 −0.0383482
681681 12.0000 0.459841
682682 −16.0000 −0.612672
683683 44.0000 1.68361 0.841807 0.539779i 0.181492π-0.181492\pi
0.841807 + 0.539779i 0.181492π0.181492\pi
684684 −4.00000 −0.152944
685685 6.00000 0.229248
686686 0 0
687687 6.00000 0.228914
688688 −8.00000 −0.304997
689689 12.0000 0.457164
690690 −4.00000 −0.152277
691691 −36.0000 −1.36950 −0.684752 0.728776i 0.740090π-0.740090\pi
−0.684752 + 0.728776i 0.740090π0.740090\pi
692692 2.00000 0.0760286
693693 0 0
694694 4.00000 0.151838
695695 4.00000 0.151729
696696 2.00000 0.0758098
697697 −10.0000 −0.378777
698698 −34.0000 −1.28692
699699 −30.0000 −1.13470
700700 0 0
701701 10.0000 0.377695 0.188847 0.982006i 0.439525π-0.439525\pi
0.188847 + 0.982006i 0.439525π0.439525\pi
702702 2.00000 0.0754851
703703 24.0000 0.905177
704704 4.00000 0.150756
705705 0 0
706706 −30.0000 −1.12906
707707 0 0
708708 −8.00000 −0.300658
709709 10.0000 0.375558 0.187779 0.982211i 0.439871π-0.439871\pi
0.187779 + 0.982211i 0.439871π0.439871\pi
710710 −8.00000 −0.300235
711711 4.00000 0.150012
712712 −14.0000 −0.524672
713713 −16.0000 −0.599205
714714 0 0
715715 −8.00000 −0.299183
716716 0 0
717717 8.00000 0.298765
718718 32.0000 1.19423
719719 −48.0000 −1.79010 −0.895049 0.445968i 0.852860π-0.852860\pi
−0.895049 + 0.445968i 0.852860π0.852860\pi
720720 −1.00000 −0.0372678
721721 0 0
722722 −3.00000 −0.111648
723723 10.0000 0.371904
724724 −14.0000 −0.520306
725725 2.00000 0.0742781
726726 5.00000 0.185567
727727 40.0000 1.48352 0.741759 0.670667i 0.233992π-0.233992\pi
0.741759 + 0.670667i 0.233992π0.233992\pi
728728 0 0
729729 1.00000 0.0370370
730730 2.00000 0.0740233
731731 −8.00000 −0.295891
732732 10.0000 0.369611
733733 26.0000 0.960332 0.480166 0.877178i 0.340576π-0.340576\pi
0.480166 + 0.877178i 0.340576π0.340576\pi
734734 8.00000 0.295285
735735 7.00000 0.258199
736736 4.00000 0.147442
737737 −32.0000 −1.17874
738738 −10.0000 −0.368105
739739 −44.0000 −1.61857 −0.809283 0.587419i 0.800144π-0.800144\pi
−0.809283 + 0.587419i 0.800144π0.800144\pi
740740 6.00000 0.220564
741741 −8.00000 −0.293887
742742 0 0
743743 28.0000 1.02722 0.513610 0.858024i 0.328308π-0.328308\pi
0.513610 + 0.858024i 0.328308π0.328308\pi
744744 −4.00000 −0.146647
745745 −2.00000 −0.0732743
746746 18.0000 0.659027
747747 4.00000 0.146352
748748 4.00000 0.146254
749749 0 0
750750 −1.00000 −0.0365148
751751 −4.00000 −0.145962 −0.0729810 0.997333i 0.523251π-0.523251\pi
−0.0729810 + 0.997333i 0.523251π0.523251\pi
752752 0 0
753753 0 0
754754 4.00000 0.145671
755755 0 0
756756 0 0
757757 −14.0000 −0.508839 −0.254419 0.967094i 0.581884π-0.581884\pi
−0.254419 + 0.967094i 0.581884π0.581884\pi
758758 20.0000 0.726433
759759 16.0000 0.580763
760760 4.00000 0.145095
761761 42.0000 1.52250 0.761249 0.648459i 0.224586π-0.224586\pi
0.761249 + 0.648459i 0.224586π0.224586\pi
762762 −16.0000 −0.579619
763763 0 0
764764 0 0
765765 −1.00000 −0.0361551
766766 −24.0000 −0.867155
767767 −16.0000 −0.577727
768768 1.00000 0.0360844
769769 2.00000 0.0721218 0.0360609 0.999350i 0.488519π-0.488519\pi
0.0360609 + 0.999350i 0.488519π0.488519\pi
770770 0 0
771771 18.0000 0.648254
772772 6.00000 0.215945
773773 14.0000 0.503545 0.251773 0.967786i 0.418987π-0.418987\pi
0.251773 + 0.967786i 0.418987π0.418987\pi
774774 −8.00000 −0.287554
775775 −4.00000 −0.143684
776776 −10.0000 −0.358979
777777 0 0
778778 −30.0000 −1.07555
779779 40.0000 1.43315
780780 −2.00000 −0.0716115
781781 32.0000 1.14505
782782 4.00000 0.143040
783783 2.00000 0.0714742
784784 −7.00000 −0.250000
785785 6.00000 0.214149
786786 4.00000 0.142675
787787 4.00000 0.142585 0.0712923 0.997455i 0.477288π-0.477288\pi
0.0712923 + 0.997455i 0.477288π0.477288\pi
788788 18.0000 0.641223
789789 16.0000 0.569615
790790 −4.00000 −0.142314
791791 0 0
792792 4.00000 0.142134
793793 20.0000 0.710221
794794 18.0000 0.638796
795795 −6.00000 −0.212798
796796 −4.00000 −0.141776
797797 6.00000 0.212531 0.106265 0.994338i 0.466111π-0.466111\pi
0.106265 + 0.994338i 0.466111π0.466111\pi
798798 0 0
799799 0 0
800800 1.00000 0.0353553
801801 −14.0000 −0.494666
802802 6.00000 0.211867
803803 −8.00000 −0.282314
804804 −8.00000 −0.282138
805805 0 0
806806 −8.00000 −0.281788
807807 −14.0000 −0.492823
808808 −6.00000 −0.211079
809809 54.0000 1.89854 0.949269 0.314464i 0.101825π-0.101825\pi
0.949269 + 0.314464i 0.101825π0.101825\pi
810810 −1.00000 −0.0351364
811811 −28.0000 −0.983213 −0.491606 0.870817i 0.663590π-0.663590\pi
−0.491606 + 0.870817i 0.663590π0.663590\pi
812812 0 0
813813 −8.00000 −0.280572
814814 −24.0000 −0.841200
815815 −12.0000 −0.420342
816816 1.00000 0.0350070
817817 32.0000 1.11954
818818 10.0000 0.349642
819819 0 0
820820 10.0000 0.349215
821821 −6.00000 −0.209401 −0.104701 0.994504i 0.533388π-0.533388\pi
−0.104701 + 0.994504i 0.533388π0.533388\pi
822822 −6.00000 −0.209274
823823 16.0000 0.557725 0.278862 0.960331i 0.410043π-0.410043\pi
0.278862 + 0.960331i 0.410043π0.410043\pi
824824 16.0000 0.557386
825825 4.00000 0.139262
826826 0 0
827827 36.0000 1.25184 0.625921 0.779886i 0.284723π-0.284723\pi
0.625921 + 0.779886i 0.284723π0.284723\pi
828828 4.00000 0.139010
829829 54.0000 1.87550 0.937749 0.347314i 0.112906π-0.112906\pi
0.937749 + 0.347314i 0.112906π0.112906\pi
830830 −4.00000 −0.138842
831831 10.0000 0.346896
832832 2.00000 0.0693375
833833 −7.00000 −0.242536
834834 −4.00000 −0.138509
835835 −12.0000 −0.415277
836836 −16.0000 −0.553372
837837 −4.00000 −0.138260
838838 28.0000 0.967244
839839 16.0000 0.552381 0.276191 0.961103i 0.410928π-0.410928\pi
0.276191 + 0.961103i 0.410928π0.410928\pi
840840 0 0
841841 −25.0000 −0.862069
842842 30.0000 1.03387
843843 −30.0000 −1.03325
844844 12.0000 0.413057
845845 9.00000 0.309609
846846 0 0
847847 0 0
848848 6.00000 0.206041
849849 20.0000 0.686398
850850 1.00000 0.0342997
851851 −24.0000 −0.822709
852852 8.00000 0.274075
853853 −54.0000 −1.84892 −0.924462 0.381273i 0.875486π-0.875486\pi
−0.924462 + 0.381273i 0.875486π0.875486\pi
854854 0 0
855855 4.00000 0.136797
856856 12.0000 0.410152
857857 26.0000 0.888143 0.444072 0.895991i 0.353534π-0.353534\pi
0.444072 + 0.895991i 0.353534π0.353534\pi
858858 8.00000 0.273115
859859 20.0000 0.682391 0.341196 0.939992i 0.389168π-0.389168\pi
0.341196 + 0.939992i 0.389168π0.389168\pi
860860 8.00000 0.272798
861861 0 0
862862 −16.0000 −0.544962
863863 −8.00000 −0.272323 −0.136162 0.990687i 0.543477π-0.543477\pi
−0.136162 + 0.990687i 0.543477π0.543477\pi
864864 1.00000 0.0340207
865865 −2.00000 −0.0680020
866866 −6.00000 −0.203888
867867 1.00000 0.0339618
868868 0 0
869869 16.0000 0.542763
870870 −2.00000 −0.0678064
871871 −16.0000 −0.542139
872872 −14.0000 −0.474100
873873 −10.0000 −0.338449
874874 −16.0000 −0.541208
875875 0 0
876876 −2.00000 −0.0675737
877877 50.0000 1.68838 0.844190 0.536044i 0.180082π-0.180082\pi
0.844190 + 0.536044i 0.180082π0.180082\pi
878878 20.0000 0.674967
879879 6.00000 0.202375
880880 −4.00000 −0.134840
881881 −2.00000 −0.0673817 −0.0336909 0.999432i 0.510726π-0.510726\pi
−0.0336909 + 0.999432i 0.510726π0.510726\pi
882882 −7.00000 −0.235702
883883 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
884884 2.00000 0.0672673
885885 8.00000 0.268917
886886 −28.0000 −0.940678
887887 12.0000 0.402921 0.201460 0.979497i 0.435431π-0.435431\pi
0.201460 + 0.979497i 0.435431π0.435431\pi
888888 −6.00000 −0.201347
889889 0 0
890890 14.0000 0.469281
891891 4.00000 0.134005
892892 24.0000 0.803579
893893 0 0
894894 2.00000 0.0668900
895895 0 0
896896 0 0
897897 8.00000 0.267112
898898 −26.0000 −0.867631
899899 −8.00000 −0.266815
900900 1.00000 0.0333333
901901 6.00000 0.199889
902902 −40.0000 −1.33185
903903 0 0
904904 18.0000 0.598671
905905 14.0000 0.465376
906906 0 0
907907 −36.0000 −1.19536 −0.597680 0.801735i 0.703911π-0.703911\pi
−0.597680 + 0.801735i 0.703911π0.703911\pi
908908 12.0000 0.398234
909909 −6.00000 −0.199007
910910 0 0
911911 48.0000 1.59031 0.795155 0.606406i 0.207389π-0.207389\pi
0.795155 + 0.606406i 0.207389π0.207389\pi
912912 −4.00000 −0.132453
913913 16.0000 0.529523
914914 2.00000 0.0661541
915915 −10.0000 −0.330590
916916 6.00000 0.198246
917917 0 0
918918 1.00000 0.0330049
919919 16.0000 0.527791 0.263896 0.964551i 0.414993π-0.414993\pi
0.263896 + 0.964551i 0.414993π0.414993\pi
920920 −4.00000 −0.131876
921921 16.0000 0.527218
922922 −38.0000 −1.25146
923923 16.0000 0.526646
924924 0 0
925925 −6.00000 −0.197279
926926 −24.0000 −0.788689
927927 16.0000 0.525509
928928 2.00000 0.0656532
929929 −50.0000 −1.64045 −0.820223 0.572043i 0.806151π-0.806151\pi
−0.820223 + 0.572043i 0.806151π0.806151\pi
930930 4.00000 0.131165
931931 28.0000 0.917663
932932 −30.0000 −0.982683
933933 −8.00000 −0.261908
934934 −12.0000 −0.392652
935935 −4.00000 −0.130814
936936 2.00000 0.0653720
937937 2.00000 0.0653372 0.0326686 0.999466i 0.489599π-0.489599\pi
0.0326686 + 0.999466i 0.489599π0.489599\pi
938938 0 0
939939 −2.00000 −0.0652675
940940 0 0
941941 −30.0000 −0.977972 −0.488986 0.872292i 0.662633π-0.662633\pi
−0.488986 + 0.872292i 0.662633π0.662633\pi
942942 −6.00000 −0.195491
943943 −40.0000 −1.30258
944944 −8.00000 −0.260378
945945 0 0
946946 −32.0000 −1.04041
947947 −28.0000 −0.909878 −0.454939 0.890523i 0.650339π-0.650339\pi
−0.454939 + 0.890523i 0.650339π0.650339\pi
948948 4.00000 0.129914
949949 −4.00000 −0.129845
950950 −4.00000 −0.129777
951951 26.0000 0.843108
952952 0 0
953953 −6.00000 −0.194359 −0.0971795 0.995267i 0.530982π-0.530982\pi
−0.0971795 + 0.995267i 0.530982π0.530982\pi
954954 6.00000 0.194257
955955 0 0
956956 8.00000 0.258738
957957 8.00000 0.258603
958958 0 0
959959 0 0
960960 −1.00000 −0.0322749
961961 −15.0000 −0.483871
962962 −12.0000 −0.386896
963963 12.0000 0.386695
964964 10.0000 0.322078
965965 −6.00000 −0.193147
966966 0 0
967967 24.0000 0.771788 0.385894 0.922543i 0.373893π-0.373893\pi
0.385894 + 0.922543i 0.373893π0.373893\pi
968968 5.00000 0.160706
969969 −4.00000 −0.128499
970970 10.0000 0.321081
971971 32.0000 1.02693 0.513464 0.858111i 0.328362π-0.328362\pi
0.513464 + 0.858111i 0.328362π0.328362\pi
972972 1.00000 0.0320750
973973 0 0
974974 −40.0000 −1.28168
975975 2.00000 0.0640513
976976 10.0000 0.320092
977977 18.0000 0.575871 0.287936 0.957650i 0.407031π-0.407031\pi
0.287936 + 0.957650i 0.407031π0.407031\pi
978978 12.0000 0.383718
979979 −56.0000 −1.78977
980980 7.00000 0.223607
981981 −14.0000 −0.446986
982982 24.0000 0.765871
983983 −44.0000 −1.40338 −0.701691 0.712481i 0.747571π-0.747571\pi
−0.701691 + 0.712481i 0.747571π0.747571\pi
984984 −10.0000 −0.318788
985985 −18.0000 −0.573528
986986 2.00000 0.0636930
987987 0 0
988988 −8.00000 −0.254514
989989 −32.0000 −1.01754
990990 −4.00000 −0.127128
991991 −44.0000 −1.39771 −0.698853 0.715265i 0.746306π-0.746306\pi
−0.698853 + 0.715265i 0.746306π0.746306\pi
992992 −4.00000 −0.127000
993993 20.0000 0.634681
994994 0 0
995995 4.00000 0.126809
996996 4.00000 0.126745
997997 10.0000 0.316703 0.158352 0.987383i 0.449382π-0.449382\pi
0.158352 + 0.987383i 0.449382π0.449382\pi
998998 28.0000 0.886325
999999 −6.00000 −0.189832
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 510.2.a.f.1.1 1
3.2 odd 2 1530.2.a.f.1.1 1
4.3 odd 2 4080.2.a.c.1.1 1
5.2 odd 4 2550.2.d.s.2449.2 2
5.3 odd 4 2550.2.d.s.2449.1 2
5.4 even 2 2550.2.a.d.1.1 1
15.14 odd 2 7650.2.a.bw.1.1 1
17.16 even 2 8670.2.a.r.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
510.2.a.f.1.1 1 1.1 even 1 trivial
1530.2.a.f.1.1 1 3.2 odd 2
2550.2.a.d.1.1 1 5.4 even 2
2550.2.d.s.2449.1 2 5.3 odd 4
2550.2.d.s.2449.2 2 5.2 odd 4
4080.2.a.c.1.1 1 4.3 odd 2
7650.2.a.bw.1.1 1 15.14 odd 2
8670.2.a.r.1.1 1 17.16 even 2