Properties

Label 2550.2.a.bc.1.1
Level 25502550
Weight 22
Character 2550.1
Self dual yes
Analytic conductor 20.36220.362
Analytic rank 11
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2550,2,Mod(1,2550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2550, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2550.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2550=235217 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2550.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,0,1,-2,1,1,0,-4,1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 20.361852515420.3618525154
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 510)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 2550.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q2+1.00000q3+1.00000q4+1.00000q62.00000q7+1.00000q8+1.00000q94.00000q11+1.00000q124.00000q132.00000q14+1.00000q161.00000q17+1.00000q184.00000q192.00000q214.00000q228.00000q23+1.00000q244.00000q26+1.00000q272.00000q28+2.00000q29+4.00000q31+1.00000q324.00000q331.00000q34+1.00000q366.00000q374.00000q384.00000q39+8.00000q412.00000q426.00000q434.00000q448.00000q468.00000q47+1.00000q483.00000q491.00000q514.00000q52+2.00000q53+1.00000q542.00000q564.00000q57+2.00000q586.00000q59+14.0000q61+4.00000q622.00000q63+1.00000q644.00000q66+2.00000q671.00000q688.00000q69+2.00000q71+1.00000q724.00000q736.00000q744.00000q76+8.00000q774.00000q78+1.00000q81+8.00000q82+16.0000q832.00000q846.00000q86+2.00000q874.00000q882.00000q89+8.00000q918.00000q92+4.00000q938.00000q94+1.00000q963.00000q984.00000q99+O(q100)q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} -2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -4.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} -2.00000 q^{14} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -2.00000 q^{21} -4.00000 q^{22} -8.00000 q^{23} +1.00000 q^{24} -4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} +2.00000 q^{29} +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} -4.00000 q^{39} +8.00000 q^{41} -2.00000 q^{42} -6.00000 q^{43} -4.00000 q^{44} -8.00000 q^{46} -8.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{51} -4.00000 q^{52} +2.00000 q^{53} +1.00000 q^{54} -2.00000 q^{56} -4.00000 q^{57} +2.00000 q^{58} -6.00000 q^{59} +14.0000 q^{61} +4.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} +2.00000 q^{67} -1.00000 q^{68} -8.00000 q^{69} +2.00000 q^{71} +1.00000 q^{72} -4.00000 q^{73} -6.00000 q^{74} -4.00000 q^{76} +8.00000 q^{77} -4.00000 q^{78} +1.00000 q^{81} +8.00000 q^{82} +16.0000 q^{83} -2.00000 q^{84} -6.00000 q^{86} +2.00000 q^{87} -4.00000 q^{88} -2.00000 q^{89} +8.00000 q^{91} -8.00000 q^{92} +4.00000 q^{93} -8.00000 q^{94} +1.00000 q^{96} -3.00000 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 0 0
66 1.00000 0.408248
77 −2.00000 −0.755929 −0.377964 0.925820i 0.623376π-0.623376\pi
−0.377964 + 0.925820i 0.623376π0.623376\pi
88 1.00000 0.353553
99 1.00000 0.333333
1010 0 0
1111 −4.00000 −1.20605 −0.603023 0.797724i 0.706037π-0.706037\pi
−0.603023 + 0.797724i 0.706037π0.706037\pi
1212 1.00000 0.288675
1313 −4.00000 −1.10940 −0.554700 0.832050i 0.687167π-0.687167\pi
−0.554700 + 0.832050i 0.687167π0.687167\pi
1414 −2.00000 −0.534522
1515 0 0
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 0 0
2121 −2.00000 −0.436436
2222 −4.00000 −0.852803
2323 −8.00000 −1.66812 −0.834058 0.551677i 0.813988π-0.813988\pi
−0.834058 + 0.551677i 0.813988π0.813988\pi
2424 1.00000 0.204124
2525 0 0
2626 −4.00000 −0.784465
2727 1.00000 0.192450
2828 −2.00000 −0.377964
2929 2.00000 0.371391 0.185695 0.982607i 0.440546π-0.440546\pi
0.185695 + 0.982607i 0.440546π0.440546\pi
3030 0 0
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\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 −4.00000 −0.640513
4040 0 0
4141 8.00000 1.24939 0.624695 0.780869i 0.285223π-0.285223\pi
0.624695 + 0.780869i 0.285223π0.285223\pi
4242 −2.00000 −0.308607
4343 −6.00000 −0.914991 −0.457496 0.889212i 0.651253π-0.651253\pi
−0.457496 + 0.889212i 0.651253π0.651253\pi
4444 −4.00000 −0.603023
4545 0 0
4646 −8.00000 −1.17954
4747 −8.00000 −1.16692 −0.583460 0.812142i 0.698301π-0.698301\pi
−0.583460 + 0.812142i 0.698301π0.698301\pi
4848 1.00000 0.144338
4949 −3.00000 −0.428571
5050 0 0
5151 −1.00000 −0.140028
5252 −4.00000 −0.554700
5353 2.00000 0.274721 0.137361 0.990521i 0.456138π-0.456138\pi
0.137361 + 0.990521i 0.456138π0.456138\pi
5454 1.00000 0.136083
5555 0 0
5656 −2.00000 −0.267261
5757 −4.00000 −0.529813
5858 2.00000 0.262613
5959 −6.00000 −0.781133 −0.390567 0.920575i 0.627721π-0.627721\pi
−0.390567 + 0.920575i 0.627721π0.627721\pi
6060 0 0
6161 14.0000 1.79252 0.896258 0.443533i 0.146275π-0.146275\pi
0.896258 + 0.443533i 0.146275π0.146275\pi
6262 4.00000 0.508001
6363 −2.00000 −0.251976
6464 1.00000 0.125000
6565 0 0
6666 −4.00000 −0.492366
6767 2.00000 0.244339 0.122169 0.992509i 0.461015π-0.461015\pi
0.122169 + 0.992509i 0.461015π0.461015\pi
6868 −1.00000 −0.121268
6969 −8.00000 −0.963087
7070 0 0
7171 2.00000 0.237356 0.118678 0.992933i 0.462134π-0.462134\pi
0.118678 + 0.992933i 0.462134π0.462134\pi
7272 1.00000 0.117851
7373 −4.00000 −0.468165 −0.234082 0.972217i 0.575209π-0.575209\pi
−0.234082 + 0.972217i 0.575209π0.575209\pi
7474 −6.00000 −0.697486
7575 0 0
7676 −4.00000 −0.458831
7777 8.00000 0.911685
7878 −4.00000 −0.452911
7979 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8080 0 0
8181 1.00000 0.111111
8282 8.00000 0.883452
8383 16.0000 1.75623 0.878114 0.478451i 0.158802π-0.158802\pi
0.878114 + 0.478451i 0.158802π0.158802\pi
8484 −2.00000 −0.218218
8585 0 0
8686 −6.00000 −0.646997
8787 2.00000 0.214423
8888 −4.00000 −0.426401
8989 −2.00000 −0.212000 −0.106000 0.994366i 0.533804π-0.533804\pi
−0.106000 + 0.994366i 0.533804π0.533804\pi
9090 0 0
9191 8.00000 0.838628
9292 −8.00000 −0.834058
9393 4.00000 0.414781
9494 −8.00000 −0.825137
9595 0 0
9696 1.00000 0.102062
9797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9898 −3.00000 −0.303046
9999 −4.00000 −0.402015
100100 0 0
101101 8.00000 0.796030 0.398015 0.917379i 0.369699π-0.369699\pi
0.398015 + 0.917379i 0.369699π0.369699\pi
102102 −1.00000 −0.0990148
103103 12.0000 1.18240 0.591198 0.806527i 0.298655π-0.298655\pi
0.591198 + 0.806527i 0.298655π0.298655\pi
104104 −4.00000 −0.392232
105105 0 0
106106 2.00000 0.194257
107107 −12.0000 −1.16008 −0.580042 0.814587i 0.696964π-0.696964\pi
−0.580042 + 0.814587i 0.696964π0.696964\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 0 0
111111 −6.00000 −0.569495
112112 −2.00000 −0.188982
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 −4.00000 −0.374634
115115 0 0
116116 2.00000 0.185695
117117 −4.00000 −0.369800
118118 −6.00000 −0.552345
119119 2.00000 0.183340
120120 0 0
121121 5.00000 0.454545
122122 14.0000 1.26750
123123 8.00000 0.721336
124124 4.00000 0.359211
125125 0 0
126126 −2.00000 −0.178174
127127 4.00000 0.354943 0.177471 0.984126i 0.443208π-0.443208\pi
0.177471 + 0.984126i 0.443208π0.443208\pi
128128 1.00000 0.0883883
129129 −6.00000 −0.528271
130130 0 0
131131 −16.0000 −1.39793 −0.698963 0.715158i 0.746355π-0.746355\pi
−0.698963 + 0.715158i 0.746355π0.746355\pi
132132 −4.00000 −0.348155
133133 8.00000 0.693688
134134 2.00000 0.172774
135135 0 0
136136 −1.00000 −0.0857493
137137 6.00000 0.512615 0.256307 0.966595i 0.417494π-0.417494\pi
0.256307 + 0.966595i 0.417494π0.417494\pi
138138 −8.00000 −0.681005
139139 −20.0000 −1.69638 −0.848189 0.529694i 0.822307π-0.822307\pi
−0.848189 + 0.529694i 0.822307π0.822307\pi
140140 0 0
141141 −8.00000 −0.673722
142142 2.00000 0.167836
143143 16.0000 1.33799
144144 1.00000 0.0833333
145145 0 0
146146 −4.00000 −0.331042
147147 −3.00000 −0.247436
148148 −6.00000 −0.493197
149149 16.0000 1.31077 0.655386 0.755295i 0.272506π-0.272506\pi
0.655386 + 0.755295i 0.272506π0.272506\pi
150150 0 0
151151 −8.00000 −0.651031 −0.325515 0.945537i 0.605538π-0.605538\pi
−0.325515 + 0.945537i 0.605538π0.605538\pi
152152 −4.00000 −0.324443
153153 −1.00000 −0.0808452
154154 8.00000 0.644658
155155 0 0
156156 −4.00000 −0.320256
157157 4.00000 0.319235 0.159617 0.987179i 0.448974π-0.448974\pi
0.159617 + 0.987179i 0.448974π0.448974\pi
158158 0 0
159159 2.00000 0.158610
160160 0 0
161161 16.0000 1.26098
162162 1.00000 0.0785674
163163 8.00000 0.626608 0.313304 0.949653i 0.398564π-0.398564\pi
0.313304 + 0.949653i 0.398564π0.398564\pi
164164 8.00000 0.624695
165165 0 0
166166 16.0000 1.24184
167167 12.0000 0.928588 0.464294 0.885681i 0.346308π-0.346308\pi
0.464294 + 0.885681i 0.346308π0.346308\pi
168168 −2.00000 −0.154303
169169 3.00000 0.230769
170170 0 0
171171 −4.00000 −0.305888
172172 −6.00000 −0.457496
173173 −22.0000 −1.67263 −0.836315 0.548250i 0.815294π-0.815294\pi
−0.836315 + 0.548250i 0.815294π0.815294\pi
174174 2.00000 0.151620
175175 0 0
176176 −4.00000 −0.301511
177177 −6.00000 −0.450988
178178 −2.00000 −0.149906
179179 6.00000 0.448461 0.224231 0.974536i 0.428013π-0.428013\pi
0.224231 + 0.974536i 0.428013π0.428013\pi
180180 0 0
181181 26.0000 1.93256 0.966282 0.257485i 0.0828937π-0.0828937\pi
0.966282 + 0.257485i 0.0828937π0.0828937\pi
182182 8.00000 0.592999
183183 14.0000 1.03491
184184 −8.00000 −0.589768
185185 0 0
186186 4.00000 0.293294
187187 4.00000 0.292509
188188 −8.00000 −0.583460
189189 −2.00000 −0.145479
190190 0 0
191191 4.00000 0.289430 0.144715 0.989473i 0.453773π-0.453773\pi
0.144715 + 0.989473i 0.453773π0.453773\pi
192192 1.00000 0.0721688
193193 −24.0000 −1.72756 −0.863779 0.503871i 0.831909π-0.831909\pi
−0.863779 + 0.503871i 0.831909π0.831909\pi
194194 0 0
195195 0 0
196196 −3.00000 −0.214286
197197 26.0000 1.85242 0.926212 0.377004i 0.123046π-0.123046\pi
0.926212 + 0.377004i 0.123046π0.123046\pi
198198 −4.00000 −0.284268
199199 −20.0000 −1.41776 −0.708881 0.705328i 0.750800π-0.750800\pi
−0.708881 + 0.705328i 0.750800π0.750800\pi
200200 0 0
201201 2.00000 0.141069
202202 8.00000 0.562878
203203 −4.00000 −0.280745
204204 −1.00000 −0.0700140
205205 0 0
206206 12.0000 0.836080
207207 −8.00000 −0.556038
208208 −4.00000 −0.277350
209209 16.0000 1.10674
210210 0 0
211211 4.00000 0.275371 0.137686 0.990476i 0.456034π-0.456034\pi
0.137686 + 0.990476i 0.456034π0.456034\pi
212212 2.00000 0.137361
213213 2.00000 0.137038
214214 −12.0000 −0.820303
215215 0 0
216216 1.00000 0.0680414
217217 −8.00000 −0.543075
218218 −14.0000 −0.948200
219219 −4.00000 −0.270295
220220 0 0
221221 4.00000 0.269069
222222 −6.00000 −0.402694
223223 −28.0000 −1.87502 −0.937509 0.347960i 0.886874π-0.886874\pi
−0.937509 + 0.347960i 0.886874π0.886874\pi
224224 −2.00000 −0.133631
225225 0 0
226226 −6.00000 −0.399114
227227 −28.0000 −1.85843 −0.929213 0.369546i 0.879513π-0.879513\pi
−0.929213 + 0.369546i 0.879513π0.879513\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 0 0
231231 8.00000 0.526361
232232 2.00000 0.131306
233233 −18.0000 −1.17922 −0.589610 0.807688i 0.700718π-0.700718\pi
−0.589610 + 0.807688i 0.700718π0.700718\pi
234234 −4.00000 −0.261488
235235 0 0
236236 −6.00000 −0.390567
237237 0 0
238238 2.00000 0.129641
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 −14.0000 −0.901819 −0.450910 0.892570i 0.648900π-0.648900\pi
−0.450910 + 0.892570i 0.648900π0.648900\pi
242242 5.00000 0.321412
243243 1.00000 0.0641500
244244 14.0000 0.896258
245245 0 0
246246 8.00000 0.510061
247247 16.0000 1.01806
248248 4.00000 0.254000
249249 16.0000 1.01396
250250 0 0
251251 26.0000 1.64111 0.820553 0.571571i 0.193666π-0.193666\pi
0.820553 + 0.571571i 0.193666π0.193666\pi
252252 −2.00000 −0.125988
253253 32.0000 2.01182
254254 4.00000 0.250982
255255 0 0
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 −6.00000 −0.373544
259259 12.0000 0.745644
260260 0 0
261261 2.00000 0.123797
262262 −16.0000 −0.988483
263263 −8.00000 −0.493301 −0.246651 0.969104i 0.579330π-0.579330\pi
−0.246651 + 0.969104i 0.579330π0.579330\pi
264264 −4.00000 −0.246183
265265 0 0
266266 8.00000 0.490511
267267 −2.00000 −0.122398
268268 2.00000 0.122169
269269 −30.0000 −1.82913 −0.914566 0.404436i 0.867468π-0.867468\pi
−0.914566 + 0.404436i 0.867468π0.867468\pi
270270 0 0
271271 −24.0000 −1.45790 −0.728948 0.684569i 0.759990π-0.759990\pi
−0.728948 + 0.684569i 0.759990π0.759990\pi
272272 −1.00000 −0.0606339
273273 8.00000 0.484182
274274 6.00000 0.362473
275275 0 0
276276 −8.00000 −0.481543
277277 −2.00000 −0.120168 −0.0600842 0.998193i 0.519137π-0.519137\pi
−0.0600842 + 0.998193i 0.519137π0.519137\pi
278278 −20.0000 −1.19952
279279 4.00000 0.239474
280280 0 0
281281 −2.00000 −0.119310 −0.0596550 0.998219i 0.519000π-0.519000\pi
−0.0596550 + 0.998219i 0.519000π0.519000\pi
282282 −8.00000 −0.476393
283283 20.0000 1.18888 0.594438 0.804141i 0.297374π-0.297374\pi
0.594438 + 0.804141i 0.297374π0.297374\pi
284284 2.00000 0.118678
285285 0 0
286286 16.0000 0.946100
287287 −16.0000 −0.944450
288288 1.00000 0.0589256
289289 1.00000 0.0588235
290290 0 0
291291 0 0
292292 −4.00000 −0.234082
293293 14.0000 0.817889 0.408944 0.912559i 0.365897π-0.365897\pi
0.408944 + 0.912559i 0.365897π0.365897\pi
294294 −3.00000 −0.174964
295295 0 0
296296 −6.00000 −0.348743
297297 −4.00000 −0.232104
298298 16.0000 0.926855
299299 32.0000 1.85061
300300 0 0
301301 12.0000 0.691669
302302 −8.00000 −0.460348
303303 8.00000 0.459588
304304 −4.00000 −0.229416
305305 0 0
306306 −1.00000 −0.0571662
307307 10.0000 0.570730 0.285365 0.958419i 0.407885π-0.407885\pi
0.285365 + 0.958419i 0.407885π0.407885\pi
308308 8.00000 0.455842
309309 12.0000 0.682656
310310 0 0
311311 14.0000 0.793867 0.396934 0.917847i 0.370074π-0.370074\pi
0.396934 + 0.917847i 0.370074π0.370074\pi
312312 −4.00000 −0.226455
313313 −16.0000 −0.904373 −0.452187 0.891923i 0.649356π-0.649356\pi
−0.452187 + 0.891923i 0.649356π0.649356\pi
314314 4.00000 0.225733
315315 0 0
316316 0 0
317317 2.00000 0.112331 0.0561656 0.998421i 0.482113π-0.482113\pi
0.0561656 + 0.998421i 0.482113π0.482113\pi
318318 2.00000 0.112154
319319 −8.00000 −0.447914
320320 0 0
321321 −12.0000 −0.669775
322322 16.0000 0.891645
323323 4.00000 0.222566
324324 1.00000 0.0555556
325325 0 0
326326 8.00000 0.443079
327327 −14.0000 −0.774202
328328 8.00000 0.441726
329329 16.0000 0.882109
330330 0 0
331331 −8.00000 −0.439720 −0.219860 0.975531i 0.570560π-0.570560\pi
−0.219860 + 0.975531i 0.570560π0.570560\pi
332332 16.0000 0.878114
333333 −6.00000 −0.328798
334334 12.0000 0.656611
335335 0 0
336336 −2.00000 −0.109109
337337 −20.0000 −1.08947 −0.544735 0.838608i 0.683370π-0.683370\pi
−0.544735 + 0.838608i 0.683370π0.683370\pi
338338 3.00000 0.163178
339339 −6.00000 −0.325875
340340 0 0
341341 −16.0000 −0.866449
342342 −4.00000 −0.216295
343343 20.0000 1.07990
344344 −6.00000 −0.323498
345345 0 0
346346 −22.0000 −1.18273
347347 28.0000 1.50312 0.751559 0.659665i 0.229302π-0.229302\pi
0.751559 + 0.659665i 0.229302π0.229302\pi
348348 2.00000 0.107211
349349 −14.0000 −0.749403 −0.374701 0.927146i 0.622255π-0.622255\pi
−0.374701 + 0.927146i 0.622255π0.622255\pi
350350 0 0
351351 −4.00000 −0.213504
352352 −4.00000 −0.213201
353353 10.0000 0.532246 0.266123 0.963939i 0.414257π-0.414257\pi
0.266123 + 0.963939i 0.414257π0.414257\pi
354354 −6.00000 −0.318896
355355 0 0
356356 −2.00000 −0.106000
357357 2.00000 0.105851
358358 6.00000 0.317110
359359 36.0000 1.90001 0.950004 0.312239i 0.101079π-0.101079\pi
0.950004 + 0.312239i 0.101079π0.101079\pi
360360 0 0
361361 −3.00000 −0.157895
362362 26.0000 1.36653
363363 5.00000 0.262432
364364 8.00000 0.419314
365365 0 0
366366 14.0000 0.731792
367367 −22.0000 −1.14839 −0.574195 0.818718i 0.694685π-0.694685\pi
−0.574195 + 0.818718i 0.694685π0.694685\pi
368368 −8.00000 −0.417029
369369 8.00000 0.416463
370370 0 0
371371 −4.00000 −0.207670
372372 4.00000 0.207390
373373 16.0000 0.828449 0.414224 0.910175i 0.364053π-0.364053\pi
0.414224 + 0.910175i 0.364053π0.364053\pi
374374 4.00000 0.206835
375375 0 0
376376 −8.00000 −0.412568
377377 −8.00000 −0.412021
378378 −2.00000 −0.102869
379379 −4.00000 −0.205466 −0.102733 0.994709i 0.532759π-0.532759\pi
−0.102733 + 0.994709i 0.532759π0.532759\pi
380380 0 0
381381 4.00000 0.204926
382382 4.00000 0.204658
383383 −8.00000 −0.408781 −0.204390 0.978889i 0.565521π-0.565521\pi
−0.204390 + 0.978889i 0.565521π0.565521\pi
384384 1.00000 0.0510310
385385 0 0
386386 −24.0000 −1.22157
387387 −6.00000 −0.304997
388388 0 0
389389 24.0000 1.21685 0.608424 0.793612i 0.291802π-0.291802\pi
0.608424 + 0.793612i 0.291802π0.291802\pi
390390 0 0
391391 8.00000 0.404577
392392 −3.00000 −0.151523
393393 −16.0000 −0.807093
394394 26.0000 1.30986
395395 0 0
396396 −4.00000 −0.201008
397397 −6.00000 −0.301131 −0.150566 0.988600i 0.548110π-0.548110\pi
−0.150566 + 0.988600i 0.548110π0.548110\pi
398398 −20.0000 −1.00251
399399 8.00000 0.400501
400400 0 0
401401 −12.0000 −0.599251 −0.299626 0.954057i 0.596862π-0.596862\pi
−0.299626 + 0.954057i 0.596862π0.596862\pi
402402 2.00000 0.0997509
403403 −16.0000 −0.797017
404404 8.00000 0.398015
405405 0 0
406406 −4.00000 −0.198517
407407 24.0000 1.18964
408408 −1.00000 −0.0495074
409409 −26.0000 −1.28562 −0.642809 0.766027i 0.722231π-0.722231\pi
−0.642809 + 0.766027i 0.722231π0.722231\pi
410410 0 0
411411 6.00000 0.295958
412412 12.0000 0.591198
413413 12.0000 0.590481
414414 −8.00000 −0.393179
415415 0 0
416416 −4.00000 −0.196116
417417 −20.0000 −0.979404
418418 16.0000 0.782586
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 −18.0000 −0.877266 −0.438633 0.898666i 0.644537π-0.644537\pi
−0.438633 + 0.898666i 0.644537π0.644537\pi
422422 4.00000 0.194717
423423 −8.00000 −0.388973
424424 2.00000 0.0971286
425425 0 0
426426 2.00000 0.0969003
427427 −28.0000 −1.35501
428428 −12.0000 −0.580042
429429 16.0000 0.772487
430430 0 0
431431 14.0000 0.674356 0.337178 0.941441i 0.390528π-0.390528\pi
0.337178 + 0.941441i 0.390528π0.390528\pi
432432 1.00000 0.0481125
433433 26.0000 1.24948 0.624740 0.780833i 0.285205π-0.285205\pi
0.624740 + 0.780833i 0.285205π0.285205\pi
434434 −8.00000 −0.384012
435435 0 0
436436 −14.0000 −0.670478
437437 32.0000 1.53077
438438 −4.00000 −0.191127
439439 −24.0000 −1.14546 −0.572729 0.819745i 0.694115π-0.694115\pi
−0.572729 + 0.819745i 0.694115π0.694115\pi
440440 0 0
441441 −3.00000 −0.142857
442442 4.00000 0.190261
443443 −24.0000 −1.14027 −0.570137 0.821549i 0.693110π-0.693110\pi
−0.570137 + 0.821549i 0.693110π0.693110\pi
444444 −6.00000 −0.284747
445445 0 0
446446 −28.0000 −1.32584
447447 16.0000 0.756774
448448 −2.00000 −0.0944911
449449 −12.0000 −0.566315 −0.283158 0.959073i 0.591382π-0.591382\pi
−0.283158 + 0.959073i 0.591382π0.591382\pi
450450 0 0
451451 −32.0000 −1.50682
452452 −6.00000 −0.282216
453453 −8.00000 −0.375873
454454 −28.0000 −1.31411
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 0 0
461461 −28.0000 −1.30409 −0.652045 0.758180i 0.726089π-0.726089\pi
−0.652045 + 0.758180i 0.726089π0.726089\pi
462462 8.00000 0.372194
463463 −4.00000 −0.185896 −0.0929479 0.995671i 0.529629π-0.529629\pi
−0.0929479 + 0.995671i 0.529629π0.529629\pi
464464 2.00000 0.0928477
465465 0 0
466466 −18.0000 −0.833834
467467 12.0000 0.555294 0.277647 0.960683i 0.410445π-0.410445\pi
0.277647 + 0.960683i 0.410445π0.410445\pi
468468 −4.00000 −0.184900
469469 −4.00000 −0.184703
470470 0 0
471471 4.00000 0.184310
472472 −6.00000 −0.276172
473473 24.0000 1.10352
474474 0 0
475475 0 0
476476 2.00000 0.0916698
477477 2.00000 0.0915737
478478 0 0
479479 −22.0000 −1.00521 −0.502603 0.864517i 0.667624π-0.667624\pi
−0.502603 + 0.864517i 0.667624π0.667624\pi
480480 0 0
481481 24.0000 1.09431
482482 −14.0000 −0.637683
483483 16.0000 0.728025
484484 5.00000 0.227273
485485 0 0
486486 1.00000 0.0453609
487487 22.0000 0.996915 0.498458 0.866914i 0.333900π-0.333900\pi
0.498458 + 0.866914i 0.333900π0.333900\pi
488488 14.0000 0.633750
489489 8.00000 0.361773
490490 0 0
491491 −18.0000 −0.812329 −0.406164 0.913800i 0.633134π-0.633134\pi
−0.406164 + 0.913800i 0.633134π0.633134\pi
492492 8.00000 0.360668
493493 −2.00000 −0.0900755
494494 16.0000 0.719874
495495 0 0
496496 4.00000 0.179605
497497 −4.00000 −0.179425
498498 16.0000 0.716977
499499 4.00000 0.179065 0.0895323 0.995984i 0.471463π-0.471463\pi
0.0895323 + 0.995984i 0.471463π0.471463\pi
500500 0 0
501501 12.0000 0.536120
502502 26.0000 1.16044
503503 16.0000 0.713405 0.356702 0.934218i 0.383901π-0.383901\pi
0.356702 + 0.934218i 0.383901π0.383901\pi
504504 −2.00000 −0.0890871
505505 0 0
506506 32.0000 1.42257
507507 3.00000 0.133235
508508 4.00000 0.177471
509509 8.00000 0.354594 0.177297 0.984157i 0.443265π-0.443265\pi
0.177297 + 0.984157i 0.443265π0.443265\pi
510510 0 0
511511 8.00000 0.353899
512512 1.00000 0.0441942
513513 −4.00000 −0.176604
514514 18.0000 0.793946
515515 0 0
516516 −6.00000 −0.264135
517517 32.0000 1.40736
518518 12.0000 0.527250
519519 −22.0000 −0.965693
520520 0 0
521521 −36.0000 −1.57719 −0.788594 0.614914i 0.789191π-0.789191\pi
−0.788594 + 0.614914i 0.789191π0.789191\pi
522522 2.00000 0.0875376
523523 14.0000 0.612177 0.306089 0.952003i 0.400980π-0.400980\pi
0.306089 + 0.952003i 0.400980π0.400980\pi
524524 −16.0000 −0.698963
525525 0 0
526526 −8.00000 −0.348817
527527 −4.00000 −0.174243
528528 −4.00000 −0.174078
529529 41.0000 1.78261
530530 0 0
531531 −6.00000 −0.260378
532532 8.00000 0.346844
533533 −32.0000 −1.38607
534534 −2.00000 −0.0865485
535535 0 0
536536 2.00000 0.0863868
537537 6.00000 0.258919
538538 −30.0000 −1.29339
539539 12.0000 0.516877
540540 0 0
541541 30.0000 1.28980 0.644900 0.764267i 0.276899π-0.276899\pi
0.644900 + 0.764267i 0.276899π0.276899\pi
542542 −24.0000 −1.03089
543543 26.0000 1.11577
544544 −1.00000 −0.0428746
545545 0 0
546546 8.00000 0.342368
547547 −44.0000 −1.88130 −0.940652 0.339372i 0.889785π-0.889785\pi
−0.940652 + 0.339372i 0.889785π0.889785\pi
548548 6.00000 0.256307
549549 14.0000 0.597505
550550 0 0
551551 −8.00000 −0.340811
552552 −8.00000 −0.340503
553553 0 0
554554 −2.00000 −0.0849719
555555 0 0
556556 −20.0000 −0.848189
557557 2.00000 0.0847427 0.0423714 0.999102i 0.486509π-0.486509\pi
0.0423714 + 0.999102i 0.486509π0.486509\pi
558558 4.00000 0.169334
559559 24.0000 1.01509
560560 0 0
561561 4.00000 0.168880
562562 −2.00000 −0.0843649
563563 24.0000 1.01148 0.505740 0.862686i 0.331220π-0.331220\pi
0.505740 + 0.862686i 0.331220π0.331220\pi
564564 −8.00000 −0.336861
565565 0 0
566566 20.0000 0.840663
567567 −2.00000 −0.0839921
568568 2.00000 0.0839181
569569 42.0000 1.76073 0.880366 0.474295i 0.157297π-0.157297\pi
0.880366 + 0.474295i 0.157297π0.157297\pi
570570 0 0
571571 28.0000 1.17176 0.585882 0.810397i 0.300748π-0.300748\pi
0.585882 + 0.810397i 0.300748π0.300748\pi
572572 16.0000 0.668994
573573 4.00000 0.167102
574574 −16.0000 −0.667827
575575 0 0
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 −24.0000 −0.997406
580580 0 0
581581 −32.0000 −1.32758
582582 0 0
583583 −8.00000 −0.331326
584584 −4.00000 −0.165521
585585 0 0
586586 14.0000 0.578335
587587 −8.00000 −0.330195 −0.165098 0.986277i 0.552794π-0.552794\pi
−0.165098 + 0.986277i 0.552794π0.552794\pi
588588 −3.00000 −0.123718
589589 −16.0000 −0.659269
590590 0 0
591591 26.0000 1.06950
592592 −6.00000 −0.246598
593593 18.0000 0.739171 0.369586 0.929197i 0.379500π-0.379500\pi
0.369586 + 0.929197i 0.379500π0.379500\pi
594594 −4.00000 −0.164122
595595 0 0
596596 16.0000 0.655386
597597 −20.0000 −0.818546
598598 32.0000 1.30858
599599 12.0000 0.490307 0.245153 0.969484i 0.421162π-0.421162\pi
0.245153 + 0.969484i 0.421162π0.421162\pi
600600 0 0
601601 30.0000 1.22373 0.611863 0.790964i 0.290420π-0.290420\pi
0.611863 + 0.790964i 0.290420π0.290420\pi
602602 12.0000 0.489083
603603 2.00000 0.0814463
604604 −8.00000 −0.325515
605605 0 0
606606 8.00000 0.324978
607607 −34.0000 −1.38002 −0.690009 0.723801i 0.742393π-0.742393\pi
−0.690009 + 0.723801i 0.742393π0.742393\pi
608608 −4.00000 −0.162221
609609 −4.00000 −0.162088
610610 0 0
611611 32.0000 1.29458
612612 −1.00000 −0.0404226
613613 −16.0000 −0.646234 −0.323117 0.946359i 0.604731π-0.604731\pi
−0.323117 + 0.946359i 0.604731π0.604731\pi
614614 10.0000 0.403567
615615 0 0
616616 8.00000 0.322329
617617 6.00000 0.241551 0.120775 0.992680i 0.461462π-0.461462\pi
0.120775 + 0.992680i 0.461462π0.461462\pi
618618 12.0000 0.482711
619619 −4.00000 −0.160774 −0.0803868 0.996764i 0.525616π-0.525616\pi
−0.0803868 + 0.996764i 0.525616π0.525616\pi
620620 0 0
621621 −8.00000 −0.321029
622622 14.0000 0.561349
623623 4.00000 0.160257
624624 −4.00000 −0.160128
625625 0 0
626626 −16.0000 −0.639489
627627 16.0000 0.638978
628628 4.00000 0.159617
629629 6.00000 0.239236
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 0 0
633633 4.00000 0.158986
634634 2.00000 0.0794301
635635 0 0
636636 2.00000 0.0793052
637637 12.0000 0.475457
638638 −8.00000 −0.316723
639639 2.00000 0.0791188
640640 0 0
641641 12.0000 0.473972 0.236986 0.971513i 0.423841π-0.423841\pi
0.236986 + 0.971513i 0.423841π0.423841\pi
642642 −12.0000 −0.473602
643643 −16.0000 −0.630978 −0.315489 0.948929i 0.602169π-0.602169\pi
−0.315489 + 0.948929i 0.602169π0.602169\pi
644644 16.0000 0.630488
645645 0 0
646646 4.00000 0.157378
647647 16.0000 0.629025 0.314512 0.949253i 0.398159π-0.398159\pi
0.314512 + 0.949253i 0.398159π0.398159\pi
648648 1.00000 0.0392837
649649 24.0000 0.942082
650650 0 0
651651 −8.00000 −0.313545
652652 8.00000 0.313304
653653 30.0000 1.17399 0.586995 0.809590i 0.300311π-0.300311\pi
0.586995 + 0.809590i 0.300311π0.300311\pi
654654 −14.0000 −0.547443
655655 0 0
656656 8.00000 0.312348
657657 −4.00000 −0.156055
658658 16.0000 0.623745
659659 14.0000 0.545363 0.272681 0.962104i 0.412090π-0.412090\pi
0.272681 + 0.962104i 0.412090π0.412090\pi
660660 0 0
661661 2.00000 0.0777910 0.0388955 0.999243i 0.487616π-0.487616\pi
0.0388955 + 0.999243i 0.487616π0.487616\pi
662662 −8.00000 −0.310929
663663 4.00000 0.155347
664664 16.0000 0.620920
665665 0 0
666666 −6.00000 −0.232495
667667 −16.0000 −0.619522
668668 12.0000 0.464294
669669 −28.0000 −1.08254
670670 0 0
671671 −56.0000 −2.16186
672672 −2.00000 −0.0771517
673673 8.00000 0.308377 0.154189 0.988041i 0.450724π-0.450724\pi
0.154189 + 0.988041i 0.450724π0.450724\pi
674674 −20.0000 −0.770371
675675 0 0
676676 3.00000 0.115385
677677 −6.00000 −0.230599 −0.115299 0.993331i 0.536783π-0.536783\pi
−0.115299 + 0.993331i 0.536783π0.536783\pi
678678 −6.00000 −0.230429
679679 0 0
680680 0 0
681681 −28.0000 −1.07296
682682 −16.0000 −0.612672
683683 −36.0000 −1.37750 −0.688751 0.724998i 0.741841π-0.741841\pi
−0.688751 + 0.724998i 0.741841π0.741841\pi
684684 −4.00000 −0.152944
685685 0 0
686686 20.0000 0.763604
687687 6.00000 0.228914
688688 −6.00000 −0.228748
689689 −8.00000 −0.304776
690690 0 0
691691 −20.0000 −0.760836 −0.380418 0.924815i 0.624220π-0.624220\pi
−0.380418 + 0.924815i 0.624220π0.624220\pi
692692 −22.0000 −0.836315
693693 8.00000 0.303895
694694 28.0000 1.06287
695695 0 0
696696 2.00000 0.0758098
697697 −8.00000 −0.303022
698698 −14.0000 −0.529908
699699 −18.0000 −0.680823
700700 0 0
701701 36.0000 1.35970 0.679851 0.733351i 0.262045π-0.262045\pi
0.679851 + 0.733351i 0.262045π0.262045\pi
702702 −4.00000 −0.150970
703703 24.0000 0.905177
704704 −4.00000 −0.150756
705705 0 0
706706 10.0000 0.376355
707707 −16.0000 −0.601742
708708 −6.00000 −0.225494
709709 22.0000 0.826227 0.413114 0.910679i 0.364441π-0.364441\pi
0.413114 + 0.910679i 0.364441π0.364441\pi
710710 0 0
711711 0 0
712712 −2.00000 −0.0749532
713713 −32.0000 −1.19841
714714 2.00000 0.0748481
715715 0 0
716716 6.00000 0.224231
717717 0 0
718718 36.0000 1.34351
719719 10.0000 0.372937 0.186469 0.982461i 0.440296π-0.440296\pi
0.186469 + 0.982461i 0.440296π0.440296\pi
720720 0 0
721721 −24.0000 −0.893807
722722 −3.00000 −0.111648
723723 −14.0000 −0.520666
724724 26.0000 0.966282
725725 0 0
726726 5.00000 0.185567
727727 −44.0000 −1.63187 −0.815935 0.578144i 0.803777π-0.803777\pi
−0.815935 + 0.578144i 0.803777π0.803777\pi
728728 8.00000 0.296500
729729 1.00000 0.0370370
730730 0 0
731731 6.00000 0.221918
732732 14.0000 0.517455
733733 −48.0000 −1.77292 −0.886460 0.462805i 0.846843π-0.846843\pi
−0.886460 + 0.462805i 0.846843π0.846843\pi
734734 −22.0000 −0.812035
735735 0 0
736736 −8.00000 −0.294884
737737 −8.00000 −0.294684
738738 8.00000 0.294484
739739 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
740740 0 0
741741 16.0000 0.587775
742742 −4.00000 −0.146845
743743 20.0000 0.733729 0.366864 0.930274i 0.380431π-0.380431\pi
0.366864 + 0.930274i 0.380431π0.380431\pi
744744 4.00000 0.146647
745745 0 0
746746 16.0000 0.585802
747747 16.0000 0.585409
748748 4.00000 0.146254
749749 24.0000 0.876941
750750 0 0
751751 −24.0000 −0.875772 −0.437886 0.899030i 0.644273π-0.644273\pi
−0.437886 + 0.899030i 0.644273π0.644273\pi
752752 −8.00000 −0.291730
753753 26.0000 0.947493
754754 −8.00000 −0.291343
755755 0 0
756756 −2.00000 −0.0727393
757757 28.0000 1.01768 0.508839 0.860862i 0.330075π-0.330075\pi
0.508839 + 0.860862i 0.330075π0.330075\pi
758758 −4.00000 −0.145287
759759 32.0000 1.16153
760760 0 0
761761 −6.00000 −0.217500 −0.108750 0.994069i 0.534685π-0.534685\pi
−0.108750 + 0.994069i 0.534685π0.534685\pi
762762 4.00000 0.144905
763763 28.0000 1.01367
764764 4.00000 0.144715
765765 0 0
766766 −8.00000 −0.289052
767767 24.0000 0.866590
768768 1.00000 0.0360844
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 18.0000 0.648254
772772 −24.0000 −0.863779
773773 42.0000 1.51064 0.755318 0.655359i 0.227483π-0.227483\pi
0.755318 + 0.655359i 0.227483π0.227483\pi
774774 −6.00000 −0.215666
775775 0 0
776776 0 0
777777 12.0000 0.430498
778778 24.0000 0.860442
779779 −32.0000 −1.14652
780780 0 0
781781 −8.00000 −0.286263
782782 8.00000 0.286079
783783 2.00000 0.0714742
784784 −3.00000 −0.107143
785785 0 0
786786 −16.0000 −0.570701
787787 −24.0000 −0.855508 −0.427754 0.903895i 0.640695π-0.640695\pi
−0.427754 + 0.903895i 0.640695π0.640695\pi
788788 26.0000 0.926212
789789 −8.00000 −0.284808
790790 0 0
791791 12.0000 0.426671
792792 −4.00000 −0.142134
793793 −56.0000 −1.98862
794794 −6.00000 −0.212932
795795 0 0
796796 −20.0000 −0.708881
797797 14.0000 0.495905 0.247953 0.968772i 0.420242π-0.420242\pi
0.247953 + 0.968772i 0.420242π0.420242\pi
798798 8.00000 0.283197
799799 8.00000 0.283020
800800 0 0
801801 −2.00000 −0.0706665
802802 −12.0000 −0.423735
803803 16.0000 0.564628
804804 2.00000 0.0705346
805805 0 0
806806 −16.0000 −0.563576
807807 −30.0000 −1.05605
808808 8.00000 0.281439
809809 −48.0000 −1.68759 −0.843795 0.536666i 0.819684π-0.819684\pi
−0.843795 + 0.536666i 0.819684π0.819684\pi
810810 0 0
811811 20.0000 0.702295 0.351147 0.936320i 0.385792π-0.385792\pi
0.351147 + 0.936320i 0.385792π0.385792\pi
812812 −4.00000 −0.140372
813813 −24.0000 −0.841717
814814 24.0000 0.841200
815815 0 0
816816 −1.00000 −0.0350070
817817 24.0000 0.839654
818818 −26.0000 −0.909069
819819 8.00000 0.279543
820820 0 0
821821 −18.0000 −0.628204 −0.314102 0.949389i 0.601703π-0.601703\pi
−0.314102 + 0.949389i 0.601703π0.601703\pi
822822 6.00000 0.209274
823823 −14.0000 −0.488009 −0.244005 0.969774i 0.578461π-0.578461\pi
−0.244005 + 0.969774i 0.578461π0.578461\pi
824824 12.0000 0.418040
825825 0 0
826826 12.0000 0.417533
827827 −44.0000 −1.53003 −0.765015 0.644013i 0.777268π-0.777268\pi
−0.765015 + 0.644013i 0.777268π0.777268\pi
828828 −8.00000 −0.278019
829829 −46.0000 −1.59765 −0.798823 0.601566i 0.794544π-0.794544\pi
−0.798823 + 0.601566i 0.794544π0.794544\pi
830830 0 0
831831 −2.00000 −0.0693792
832832 −4.00000 −0.138675
833833 3.00000 0.103944
834834 −20.0000 −0.692543
835835 0 0
836836 16.0000 0.553372
837837 4.00000 0.138260
838838 0 0
839839 6.00000 0.207143 0.103572 0.994622i 0.466973π-0.466973\pi
0.103572 + 0.994622i 0.466973π0.466973\pi
840840 0 0
841841 −25.0000 −0.862069
842842 −18.0000 −0.620321
843843 −2.00000 −0.0688837
844844 4.00000 0.137686
845845 0 0
846846 −8.00000 −0.275046
847847 −10.0000 −0.343604
848848 2.00000 0.0686803
849849 20.0000 0.686398
850850 0 0
851851 48.0000 1.64542
852852 2.00000 0.0685189
853853 −2.00000 −0.0684787 −0.0342393 0.999414i 0.510901π-0.510901\pi
−0.0342393 + 0.999414i 0.510901π0.510901\pi
854854 −28.0000 −0.958140
855855 0 0
856856 −12.0000 −0.410152
857857 22.0000 0.751506 0.375753 0.926720i 0.377384π-0.377384\pi
0.375753 + 0.926720i 0.377384π0.377384\pi
858858 16.0000 0.546231
859859 −32.0000 −1.09183 −0.545913 0.837842i 0.683817π-0.683817\pi
−0.545913 + 0.837842i 0.683817π0.683817\pi
860860 0 0
861861 −16.0000 −0.545279
862862 14.0000 0.476842
863863 16.0000 0.544646 0.272323 0.962206i 0.412208π-0.412208\pi
0.272323 + 0.962206i 0.412208π0.412208\pi
864864 1.00000 0.0340207
865865 0 0
866866 26.0000 0.883516
867867 1.00000 0.0339618
868868 −8.00000 −0.271538
869869 0 0
870870 0 0
871871 −8.00000 −0.271070
872872 −14.0000 −0.474100
873873 0 0
874874 32.0000 1.08242
875875 0 0
876876 −4.00000 −0.135147
877877 −50.0000 −1.68838 −0.844190 0.536044i 0.819918π-0.819918\pi
−0.844190 + 0.536044i 0.819918π0.819918\pi
878878 −24.0000 −0.809961
879879 14.0000 0.472208
880880 0 0
881881 36.0000 1.21287 0.606435 0.795133i 0.292599π-0.292599\pi
0.606435 + 0.795133i 0.292599π0.292599\pi
882882 −3.00000 −0.101015
883883 46.0000 1.54802 0.774012 0.633171i 0.218247π-0.218247\pi
0.774012 + 0.633171i 0.218247π0.218247\pi
884884 4.00000 0.134535
885885 0 0
886886 −24.0000 −0.806296
887887 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
888888 −6.00000 −0.201347
889889 −8.00000 −0.268311
890890 0 0
891891 −4.00000 −0.134005
892892 −28.0000 −0.937509
893893 32.0000 1.07084
894894 16.0000 0.535120
895895 0 0
896896 −2.00000 −0.0668153
897897 32.0000 1.06845
898898 −12.0000 −0.400445
899899 8.00000 0.266815
900900 0 0
901901 −2.00000 −0.0666297
902902 −32.0000 −1.06548
903903 12.0000 0.399335
904904 −6.00000 −0.199557
905905 0 0
906906 −8.00000 −0.265782
907907 32.0000 1.06254 0.531271 0.847202i 0.321714π-0.321714\pi
0.531271 + 0.847202i 0.321714π0.321714\pi
908908 −28.0000 −0.929213
909909 8.00000 0.265343
910910 0 0
911911 50.0000 1.65657 0.828287 0.560304i 0.189316π-0.189316\pi
0.828287 + 0.560304i 0.189316π0.189316\pi
912912 −4.00000 −0.132453
913913 −64.0000 −2.11809
914914 2.00000 0.0661541
915915 0 0
916916 6.00000 0.198246
917917 32.0000 1.05673
918918 −1.00000 −0.0330049
919919 −8.00000 −0.263896 −0.131948 0.991257i 0.542123π-0.542123\pi
−0.131948 + 0.991257i 0.542123π0.542123\pi
920920 0 0
921921 10.0000 0.329511
922922 −28.0000 −0.922131
923923 −8.00000 −0.263323
924924 8.00000 0.263181
925925 0 0
926926 −4.00000 −0.131448
927927 12.0000 0.394132
928928 2.00000 0.0656532
929929 −48.0000 −1.57483 −0.787414 0.616424i 0.788581π-0.788581\pi
−0.787414 + 0.616424i 0.788581π0.788581\pi
930930 0 0
931931 12.0000 0.393284
932932 −18.0000 −0.589610
933933 14.0000 0.458339
934934 12.0000 0.392652
935935 0 0
936936 −4.00000 −0.130744
937937 34.0000 1.11073 0.555366 0.831606i 0.312578π-0.312578\pi
0.555366 + 0.831606i 0.312578π0.312578\pi
938938 −4.00000 −0.130605
939939 −16.0000 −0.522140
940940 0 0
941941 −2.00000 −0.0651981 −0.0325991 0.999469i 0.510378π-0.510378\pi
−0.0325991 + 0.999469i 0.510378π0.510378\pi
942942 4.00000 0.130327
943943 −64.0000 −2.08413
944944 −6.00000 −0.195283
945945 0 0
946946 24.0000 0.780307
947947 4.00000 0.129983 0.0649913 0.997886i 0.479298π-0.479298\pi
0.0649913 + 0.997886i 0.479298π0.479298\pi
948948 0 0
949949 16.0000 0.519382
950950 0 0
951951 2.00000 0.0648544
952952 2.00000 0.0648204
953953 −42.0000 −1.36051 −0.680257 0.732974i 0.738132π-0.738132\pi
−0.680257 + 0.732974i 0.738132π0.738132\pi
954954 2.00000 0.0647524
955955 0 0
956956 0 0
957957 −8.00000 −0.258603
958958 −22.0000 −0.710788
959959 −12.0000 −0.387500
960960 0 0
961961 −15.0000 −0.483871
962962 24.0000 0.773791
963963 −12.0000 −0.386695
964964 −14.0000 −0.450910
965965 0 0
966966 16.0000 0.514792
967967 −56.0000 −1.80084 −0.900419 0.435023i 0.856740π-0.856740\pi
−0.900419 + 0.435023i 0.856740π0.856740\pi
968968 5.00000 0.160706
969969 4.00000 0.128499
970970 0 0
971971 −50.0000 −1.60458 −0.802288 0.596937i 0.796384π-0.796384\pi
−0.802288 + 0.596937i 0.796384π0.796384\pi
972972 1.00000 0.0320750
973973 40.0000 1.28234
974974 22.0000 0.704925
975975 0 0
976976 14.0000 0.448129
977977 42.0000 1.34370 0.671850 0.740688i 0.265500π-0.265500\pi
0.671850 + 0.740688i 0.265500π0.265500\pi
978978 8.00000 0.255812
979979 8.00000 0.255681
980980 0 0
981981 −14.0000 −0.446986
982982 −18.0000 −0.574403
983983 52.0000 1.65854 0.829271 0.558846i 0.188756π-0.188756\pi
0.829271 + 0.558846i 0.188756π0.188756\pi
984984 8.00000 0.255031
985985 0 0
986986 −2.00000 −0.0636930
987987 16.0000 0.509286
988988 16.0000 0.509028
989989 48.0000 1.52631
990990 0 0
991991 20.0000 0.635321 0.317660 0.948205i 0.397103π-0.397103\pi
0.317660 + 0.948205i 0.397103π0.397103\pi
992992 4.00000 0.127000
993993 −8.00000 −0.253872
994994 −4.00000 −0.126872
995995 0 0
996996 16.0000 0.506979
997997 50.0000 1.58352 0.791758 0.610835i 0.209166π-0.209166\pi
0.791758 + 0.610835i 0.209166π0.209166\pi
998998 4.00000 0.126618
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 2550.2.a.bc.1.1 1
3.2 odd 2 7650.2.a.k.1.1 1
5.2 odd 4 2550.2.d.n.2449.2 2
5.3 odd 4 2550.2.d.n.2449.1 2
5.4 even 2 510.2.a.a.1.1 1
15.14 odd 2 1530.2.a.p.1.1 1
20.19 odd 2 4080.2.a.s.1.1 1
85.84 even 2 8670.2.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
510.2.a.a.1.1 1 5.4 even 2
1530.2.a.p.1.1 1 15.14 odd 2
2550.2.a.bc.1.1 1 1.1 even 1 trivial
2550.2.d.n.2449.1 2 5.3 odd 4
2550.2.d.n.2449.2 2 5.2 odd 4
4080.2.a.s.1.1 1 20.19 odd 2
7650.2.a.k.1.1 1 3.2 odd 2
8670.2.a.k.1.1 1 85.84 even 2