Properties

Label 25.3.f.a.2.2
Level $25$
Weight $3$
Character 25.2
Analytic conductor $0.681$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,3,Mod(2,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.f (of order \(20\), degree \(8\), minimal)

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: no
Analytic conductor: \(0.681200660901\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 2.2
Character \(\chi\) \(=\) 25.2
Dual form 25.3.f.a.13.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.86717 - 0.295731i) q^{2} +(-2.19472 - 4.30737i) q^{3} +(-0.405347 - 0.131705i) q^{4} +(4.99561 + 0.209511i) q^{5} +(2.82409 + 8.69166i) q^{6} +(-3.57009 - 3.57009i) q^{7} +(7.45551 + 3.79877i) q^{8} +(-8.44662 + 11.6258i) q^{9} +O(q^{10})\) \(q+(-1.86717 - 0.295731i) q^{2} +(-2.19472 - 4.30737i) q^{3} +(-0.405347 - 0.131705i) q^{4} +(4.99561 + 0.209511i) q^{5} +(2.82409 + 8.69166i) q^{6} +(-3.57009 - 3.57009i) q^{7} +(7.45551 + 3.79877i) q^{8} +(-8.44662 + 11.6258i) q^{9} +(-9.26571 - 1.86855i) q^{10} +(11.7507 - 8.53735i) q^{11} +(0.322318 + 2.03504i) q^{12} +(1.48281 - 0.234854i) q^{13} +(5.61018 + 7.72176i) q^{14} +(-10.0615 - 21.9778i) q^{15} +(-11.4181 - 8.29572i) q^{16} +(0.980634 - 1.92460i) q^{17} +(19.2094 - 19.2094i) q^{18} +(-0.665919 + 0.216370i) q^{19} +(-1.99736 - 0.742872i) q^{20} +(-7.54237 + 23.2130i) q^{21} +(-24.4653 + 12.4657i) q^{22} +(-5.44617 + 34.3858i) q^{23} -40.4509i q^{24} +(24.9122 + 2.09327i) q^{25} -2.83811 q^{26} +(25.6417 + 4.06124i) q^{27} +(0.976924 + 1.91732i) q^{28} +(23.5192 + 7.64185i) q^{29} +(12.2871 + 44.0118i) q^{30} +(-0.269813 - 0.830398i) q^{31} +(-4.80067 - 4.80067i) q^{32} +(-62.5629 - 31.8774i) q^{33} +(-2.40018 + 3.30356i) q^{34} +(-17.0868 - 18.5827i) q^{35} +(4.95498 - 3.60001i) q^{36} +(3.63763 + 22.9671i) q^{37} +(1.30737 - 0.207068i) q^{38} +(-4.26594 - 5.87157i) q^{39} +(36.4489 + 20.5392i) q^{40} +(-17.9244 - 13.0228i) q^{41} +(20.9477 - 41.1122i) q^{42} +(7.47137 - 7.47137i) q^{43} +(-5.88750 + 1.91297i) q^{44} +(-44.6317 + 56.3082i) q^{45} +(20.3379 - 62.5936i) q^{46} +(69.0671 - 35.1914i) q^{47} +(-10.6733 + 67.3887i) q^{48} -23.5090i q^{49} +(-45.8964 - 11.2758i) q^{50} -10.4422 q^{51} +(-0.631983 - 0.100096i) q^{52} +(11.3757 + 22.3261i) q^{53} +(-46.6764 - 15.1661i) q^{54} +(60.4904 - 40.1874i) q^{55} +(-13.0549 - 40.1788i) q^{56} +(2.39349 + 2.39349i) q^{57} +(-41.6545 - 21.2240i) q^{58} +(-38.5765 + 53.0960i) q^{59} +(1.18381 + 10.2338i) q^{60} +(-71.2176 + 51.7426i) q^{61} +(0.258213 + 1.63029i) q^{62} +(71.6602 - 11.3499i) q^{63} +(40.7269 + 56.0557i) q^{64} +(7.45673 - 0.862573i) q^{65} +(107.389 + 78.0225i) q^{66} +(-40.4707 + 79.4283i) q^{67} +(-0.650977 + 0.650977i) q^{68} +(160.065 - 52.0084i) q^{69} +(26.4085 + 39.7503i) q^{70} +(-8.73781 + 26.8922i) q^{71} +(-107.138 + 54.5893i) q^{72} +(13.1161 - 82.8116i) q^{73} -43.9593i q^{74} +(-45.6588 - 111.900i) q^{75} +0.298425 q^{76} +(-72.4300 - 11.4718i) q^{77} +(6.22885 + 12.2248i) q^{78} +(-102.728 - 33.3782i) q^{79} +(-55.3022 - 43.8344i) q^{80} +(1.18297 + 3.64080i) q^{81} +(29.6167 + 29.6167i) q^{82} +(-22.5540 - 11.4919i) q^{83} +(6.11455 - 8.41596i) q^{84} +(5.30209 - 9.40911i) q^{85} +(-16.1599 + 11.7408i) q^{86} +(-18.7017 - 118.078i) q^{87} +(120.039 - 19.0122i) q^{88} +(21.8651 + 30.0947i) q^{89} +(99.9873 - 91.9381i) q^{90} +(-6.13220 - 4.45530i) q^{91} +(6.73637 - 13.2209i) q^{92} +(-2.98467 + 2.98467i) q^{93} +(-139.367 + 45.2832i) q^{94} +(-3.37200 + 0.941384i) q^{95} +(-10.1422 + 31.2144i) q^{96} +(53.1853 - 27.0993i) q^{97} +(-6.95233 + 43.8953i) q^{98} +208.722i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{20}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86717 0.295731i −0.933587 0.147866i −0.328932 0.944354i \(-0.606689\pi\)
−0.604654 + 0.796488i \(0.706689\pi\)
\(3\) −2.19472 4.30737i −0.731572 1.43579i −0.893535 0.448994i \(-0.851782\pi\)
0.161962 0.986797i \(-0.448218\pi\)
\(4\) −0.405347 0.131705i −0.101337 0.0329263i
\(5\) 4.99561 + 0.209511i 0.999122 + 0.0419021i
\(6\) 2.82409 + 8.69166i 0.470682 + 1.44861i
\(7\) −3.57009 3.57009i −0.510012 0.510012i 0.404518 0.914530i \(-0.367439\pi\)
−0.914530 + 0.404518i \(0.867439\pi\)
\(8\) 7.45551 + 3.79877i 0.931939 + 0.474846i
\(9\) −8.44662 + 11.6258i −0.938513 + 1.29175i
\(10\) −9.26571 1.86855i −0.926571 0.186855i
\(11\) 11.7507 8.53735i 1.06824 0.776123i 0.0926463 0.995699i \(-0.470467\pi\)
0.975595 + 0.219576i \(0.0704674\pi\)
\(12\) 0.322318 + 2.03504i 0.0268598 + 0.169586i
\(13\) 1.48281 0.234854i 0.114062 0.0180657i −0.0991424 0.995073i \(-0.531610\pi\)
0.213205 + 0.977008i \(0.431610\pi\)
\(14\) 5.61018 + 7.72176i 0.400727 + 0.551554i
\(15\) −10.0615 21.9778i −0.670767 1.46518i
\(16\) −11.4181 8.29572i −0.713630 0.518482i
\(17\) 0.980634 1.92460i 0.0576844 0.113212i −0.860364 0.509679i \(-0.829764\pi\)
0.918049 + 0.396467i \(0.129764\pi\)
\(18\) 19.2094 19.2094i 1.06719 1.06719i
\(19\) −0.665919 + 0.216370i −0.0350484 + 0.0113879i −0.326489 0.945201i \(-0.605866\pi\)
0.291440 + 0.956589i \(0.405866\pi\)
\(20\) −1.99736 0.742872i −0.0998680 0.0371436i
\(21\) −7.54237 + 23.2130i −0.359160 + 1.10538i
\(22\) −24.4653 + 12.4657i −1.11206 + 0.566622i
\(23\) −5.44617 + 34.3858i −0.236790 + 1.49503i 0.527164 + 0.849764i \(0.323255\pi\)
−0.763954 + 0.645271i \(0.776745\pi\)
\(24\) 40.4509i 1.68545i
\(25\) 24.9122 + 2.09327i 0.996488 + 0.0837306i
\(26\) −2.83811 −0.109158
\(27\) 25.6417 + 4.06124i 0.949691 + 0.150416i
\(28\) 0.976924 + 1.91732i 0.0348901 + 0.0684758i
\(29\) 23.5192 + 7.64185i 0.811007 + 0.263512i 0.685024 0.728520i \(-0.259792\pi\)
0.125983 + 0.992032i \(0.459792\pi\)
\(30\) 12.2871 + 44.0118i 0.409569 + 1.46706i
\(31\) −0.269813 0.830398i −0.00870364 0.0267870i 0.946610 0.322380i \(-0.104483\pi\)
−0.955314 + 0.295593i \(0.904483\pi\)
\(32\) −4.80067 4.80067i −0.150021 0.150021i
\(33\) −62.5629 31.8774i −1.89585 0.965982i
\(34\) −2.40018 + 3.30356i −0.0705935 + 0.0971636i
\(35\) −17.0868 18.5827i −0.488194 0.530935i
\(36\) 4.95498 3.60001i 0.137638 0.100000i
\(37\) 3.63763 + 22.9671i 0.0983144 + 0.620732i 0.986814 + 0.161856i \(0.0517480\pi\)
−0.888500 + 0.458877i \(0.848252\pi\)
\(38\) 1.30737 0.207068i 0.0344046 0.00544915i
\(39\) −4.26594 5.87157i −0.109383 0.150553i
\(40\) 36.4489 + 20.5392i 0.911223 + 0.513480i
\(41\) −17.9244 13.0228i −0.437180 0.317630i 0.347333 0.937742i \(-0.387087\pi\)
−0.784514 + 0.620112i \(0.787087\pi\)
\(42\) 20.9477 41.1122i 0.498755 0.978863i
\(43\) 7.47137 7.47137i 0.173753 0.173753i −0.614873 0.788626i \(-0.710793\pi\)
0.788626 + 0.614873i \(0.210793\pi\)
\(44\) −5.88750 + 1.91297i −0.133807 + 0.0434765i
\(45\) −44.6317 + 56.3082i −0.991816 + 1.25129i
\(46\) 20.3379 62.5936i 0.442128 1.36073i
\(47\) 69.0671 35.1914i 1.46951 0.748754i 0.477951 0.878387i \(-0.341380\pi\)
0.991562 + 0.129633i \(0.0413798\pi\)
\(48\) −10.6733 + 67.3887i −0.222361 + 1.40393i
\(49\) 23.5090i 0.479775i
\(50\) −45.8964 11.2758i −0.917927 0.225516i
\(51\) −10.4422 −0.204749
\(52\) −0.631983 0.100096i −0.0121535 0.00192493i
\(53\) 11.3757 + 22.3261i 0.214636 + 0.421246i 0.973072 0.230501i \(-0.0740364\pi\)
−0.758436 + 0.651747i \(0.774036\pi\)
\(54\) −46.6764 15.1661i −0.864378 0.280853i
\(55\) 60.4904 40.1874i 1.09982 0.730680i
\(56\) −13.0549 40.1788i −0.233123 0.717478i
\(57\) 2.39349 + 2.39349i 0.0419911 + 0.0419911i
\(58\) −41.6545 21.2240i −0.718181 0.365931i
\(59\) −38.5765 + 53.0960i −0.653839 + 0.899932i −0.999258 0.0385168i \(-0.987737\pi\)
0.345419 + 0.938448i \(0.387737\pi\)
\(60\) 1.18381 + 10.2338i 0.0197302 + 0.170563i
\(61\) −71.2176 + 51.7426i −1.16750 + 0.848239i −0.990708 0.136008i \(-0.956573\pi\)
−0.176794 + 0.984248i \(0.556573\pi\)
\(62\) 0.258213 + 1.63029i 0.00416472 + 0.0262950i
\(63\) 71.6602 11.3499i 1.13746 0.180157i
\(64\) 40.7269 + 56.0557i 0.636357 + 0.875870i
\(65\) 7.45673 0.862573i 0.114719 0.0132704i
\(66\) 107.389 + 78.0225i 1.62710 + 1.18216i
\(67\) −40.4707 + 79.4283i −0.604041 + 1.18550i 0.363218 + 0.931704i \(0.381678\pi\)
−0.967259 + 0.253793i \(0.918322\pi\)
\(68\) −0.650977 + 0.650977i −0.00957319 + 0.00957319i
\(69\) 160.065 52.0084i 2.31979 0.753744i
\(70\) 26.4085 + 39.7503i 0.377264 + 0.567861i
\(71\) −8.73781 + 26.8922i −0.123068 + 0.378763i −0.993544 0.113447i \(-0.963811\pi\)
0.870476 + 0.492210i \(0.163811\pi\)
\(72\) −107.138 + 54.5893i −1.48802 + 0.758185i
\(73\) 13.1161 82.8116i 0.179672 1.13441i −0.718749 0.695270i \(-0.755285\pi\)
0.898421 0.439136i \(-0.144715\pi\)
\(74\) 43.9593i 0.594045i
\(75\) −45.6588 111.900i −0.608784 1.49200i
\(76\) 0.298425 0.00392665
\(77\) −72.4300 11.4718i −0.940649 0.148984i
\(78\) 6.22885 + 12.2248i 0.0798571 + 0.156728i
\(79\) −102.728 33.3782i −1.30035 0.422509i −0.424646 0.905359i \(-0.639602\pi\)
−0.875703 + 0.482850i \(0.839602\pi\)
\(80\) −55.3022 43.8344i −0.691278 0.547930i
\(81\) 1.18297 + 3.64080i 0.0146045 + 0.0449481i
\(82\) 29.6167 + 29.6167i 0.361179 + 0.361179i
\(83\) −22.5540 11.4919i −0.271735 0.138456i 0.312813 0.949815i \(-0.398729\pi\)
−0.584549 + 0.811358i \(0.698729\pi\)
\(84\) 6.11455 8.41596i 0.0727923 0.100190i
\(85\) 5.30209 9.40911i 0.0623775 0.110695i
\(86\) −16.1599 + 11.7408i −0.187905 + 0.136521i
\(87\) −18.7017 118.078i −0.214962 1.35721i
\(88\) 120.039 19.0122i 1.36407 0.216048i
\(89\) 21.8651 + 30.0947i 0.245675 + 0.338143i 0.913991 0.405735i \(-0.132984\pi\)
−0.668316 + 0.743878i \(0.732984\pi\)
\(90\) 99.9873 91.9381i 1.11097 1.02153i
\(91\) −6.13220 4.45530i −0.0673868 0.0489594i
\(92\) 6.73637 13.2209i 0.0732215 0.143705i
\(93\) −2.98467 + 2.98467i −0.0320933 + 0.0320933i
\(94\) −139.367 + 45.2832i −1.48263 + 0.481736i
\(95\) −3.37200 + 0.941384i −0.0354948 + 0.00990930i
\(96\) −10.1422 + 31.2144i −0.105648 + 0.325150i
\(97\) 53.1853 27.0993i 0.548302 0.279374i −0.157815 0.987469i \(-0.550445\pi\)
0.706117 + 0.708095i \(0.250445\pi\)
\(98\) −6.95233 + 43.8953i −0.0709422 + 0.447911i
\(99\) 208.722i 2.10831i
\(100\) −9.82239 4.12956i −0.0982239 0.0412956i
\(101\) 125.096 1.23857 0.619287 0.785164i \(-0.287422\pi\)
0.619287 + 0.785164i \(0.287422\pi\)
\(102\) 19.4974 + 3.08808i 0.191151 + 0.0302753i
\(103\) 10.0578 + 19.7396i 0.0976487 + 0.191646i 0.934663 0.355534i \(-0.115701\pi\)
−0.837015 + 0.547181i \(0.815701\pi\)
\(104\) 11.9472 + 3.88189i 0.114877 + 0.0373259i
\(105\) −42.5421 + 114.383i −0.405163 + 1.08936i
\(106\) −14.6379 45.0508i −0.138093 0.425007i
\(107\) −35.6587 35.6587i −0.333259 0.333259i 0.520564 0.853823i \(-0.325722\pi\)
−0.853823 + 0.520564i \(0.825722\pi\)
\(108\) −9.85888 5.02335i −0.0912859 0.0465125i
\(109\) 16.9971 23.3945i 0.155937 0.214628i −0.723900 0.689905i \(-0.757652\pi\)
0.879836 + 0.475277i \(0.157652\pi\)
\(110\) −124.831 + 57.1479i −1.13482 + 0.519527i
\(111\) 90.9443 66.0749i 0.819318 0.595269i
\(112\) 11.1471 + 70.3800i 0.0995276 + 0.628393i
\(113\) −85.3823 + 13.5232i −0.755596 + 0.119675i −0.522336 0.852740i \(-0.674939\pi\)
−0.233260 + 0.972414i \(0.574939\pi\)
\(114\) −3.76123 5.17689i −0.0329933 0.0454113i
\(115\) −34.4111 + 170.637i −0.299227 + 1.48380i
\(116\) −8.52696 6.19520i −0.0735082 0.0534069i
\(117\) −9.79436 + 19.2225i −0.0837124 + 0.164295i
\(118\) 87.7311 87.7311i 0.743484 0.743484i
\(119\) −10.3719 + 3.37005i −0.0871592 + 0.0283198i
\(120\) 8.47489 202.077i 0.0706241 1.68397i
\(121\) 27.8005 85.5612i 0.229756 0.707117i
\(122\) 148.277 75.5511i 1.21539 0.619272i
\(123\) −16.7553 + 105.789i −0.136222 + 0.860069i
\(124\) 0.372135i 0.00300109i
\(125\) 124.013 + 15.6765i 0.992105 + 0.125412i
\(126\) −137.159 −1.08856
\(127\) −41.0976 6.50923i −0.323603 0.0512538i −0.00748062 0.999972i \(-0.502381\pi\)
−0.316123 + 0.948718i \(0.602381\pi\)
\(128\) −47.1378 92.5131i −0.368264 0.722759i
\(129\) −48.5795 15.7844i −0.376585 0.122360i
\(130\) −14.1781 0.594614i −0.109062 0.00457396i
\(131\) 71.9522 + 221.446i 0.549253 + 1.69043i 0.710657 + 0.703539i \(0.248398\pi\)
−0.161403 + 0.986889i \(0.551602\pi\)
\(132\) 21.1613 + 21.1613i 0.160313 + 0.160313i
\(133\) 3.14985 + 1.60493i 0.0236831 + 0.0120671i
\(134\) 99.0553 136.338i 0.739219 1.01745i
\(135\) 127.245 + 25.6606i 0.942554 + 0.190078i
\(136\) 14.6223 10.6237i 0.107517 0.0781154i
\(137\) 1.52175 + 9.60794i 0.0111076 + 0.0701309i 0.992620 0.121270i \(-0.0386968\pi\)
−0.981512 + 0.191401i \(0.938697\pi\)
\(138\) −314.250 + 49.7723i −2.27717 + 0.360669i
\(139\) −97.0770 133.615i −0.698395 0.961259i −0.999969 0.00781597i \(-0.997512\pi\)
0.301574 0.953443i \(-0.402488\pi\)
\(140\) 4.47863 + 9.78286i 0.0319902 + 0.0698776i
\(141\) −303.165 220.263i −2.15011 1.56215i
\(142\) 24.2679 47.6284i 0.170900 0.335411i
\(143\) 15.4189 15.4189i 0.107825 0.107825i
\(144\) 192.888 62.6732i 1.33950 0.435231i
\(145\) 115.892 + 43.1032i 0.799253 + 0.297263i
\(146\) −48.9800 + 150.745i −0.335479 + 1.03250i
\(147\) −101.262 + 51.5955i −0.688856 + 0.350990i
\(148\) 1.55038 9.78873i 0.0104756 0.0661401i
\(149\) 182.741i 1.22645i −0.789908 0.613225i \(-0.789872\pi\)
0.789908 0.613225i \(-0.210128\pi\)
\(150\) 52.1604 + 222.440i 0.347736 + 1.48293i
\(151\) −46.5918 −0.308555 −0.154277 0.988028i \(-0.549305\pi\)
−0.154277 + 0.988028i \(0.549305\pi\)
\(152\) −5.78671 0.916524i −0.0380704 0.00602976i
\(153\) 14.0920 + 27.6570i 0.0921043 + 0.180765i
\(154\) 131.847 + 42.8396i 0.856148 + 0.278179i
\(155\) −1.17390 4.20487i −0.00757356 0.0271282i
\(156\) 0.955871 + 2.94187i 0.00612738 + 0.0188581i
\(157\) 113.507 + 113.507i 0.722972 + 0.722972i 0.969210 0.246237i \(-0.0791943\pi\)
−0.246237 + 0.969210i \(0.579194\pi\)
\(158\) 181.939 + 92.7027i 1.15151 + 0.586726i
\(159\) 71.2003 97.9987i 0.447800 0.616344i
\(160\) −22.9765 24.9881i −0.143603 0.156175i
\(161\) 142.204 103.317i 0.883252 0.641720i
\(162\) −1.13211 7.14784i −0.00698832 0.0441225i
\(163\) 51.9393 8.22637i 0.318646 0.0504685i 0.00493714 0.999988i \(-0.498428\pi\)
0.313709 + 0.949519i \(0.398428\pi\)
\(164\) 5.55042 + 7.63950i 0.0338440 + 0.0465823i
\(165\) −305.861 172.355i −1.85370 1.04457i
\(166\) 38.7138 + 28.1272i 0.233216 + 0.169441i
\(167\) −80.6381 + 158.261i −0.482863 + 0.947672i 0.513136 + 0.858307i \(0.328484\pi\)
−0.995999 + 0.0893646i \(0.971516\pi\)
\(168\) −144.413 + 144.413i −0.859602 + 0.859602i
\(169\) −158.585 + 51.5274i −0.938373 + 0.304896i
\(170\) −12.6825 + 16.0004i −0.0746029 + 0.0941203i
\(171\) 3.10929 9.56942i 0.0181830 0.0559615i
\(172\) −4.01251 + 2.04448i −0.0233286 + 0.0118865i
\(173\) 14.6263 92.3468i 0.0845450 0.533796i −0.908671 0.417513i \(-0.862902\pi\)
0.993216 0.116283i \(-0.0370981\pi\)
\(174\) 226.002i 1.29886i
\(175\) −81.4656 96.4119i −0.465518 0.550925i
\(176\) −204.993 −1.16474
\(177\) 313.369 + 49.6327i 1.77044 + 0.280411i
\(178\) −31.9260 62.6582i −0.179359 0.352013i
\(179\) 148.821 + 48.3547i 0.831400 + 0.270138i 0.693635 0.720327i \(-0.256008\pi\)
0.137765 + 0.990465i \(0.456008\pi\)
\(180\) 25.5074 16.9461i 0.141708 0.0941450i
\(181\) −78.4020 241.296i −0.433160 1.33313i −0.894960 0.446146i \(-0.852796\pi\)
0.461800 0.886984i \(-0.347204\pi\)
\(182\) 10.1323 + 10.1323i 0.0556720 + 0.0556720i
\(183\) 379.177 + 193.200i 2.07201 + 1.05574i
\(184\) −171.228 + 235.675i −0.930586 + 1.28084i
\(185\) 13.3603 + 115.497i 0.0722180 + 0.624307i
\(186\) 6.45556 4.69024i 0.0347073 0.0252164i
\(187\) −4.90792 30.9874i −0.0262456 0.165708i
\(188\) −32.6310 + 5.16825i −0.173569 + 0.0274907i
\(189\) −77.0440 106.042i −0.407640 0.561068i
\(190\) 6.57451 0.760520i 0.0346027 0.00400274i
\(191\) 122.790 + 89.2124i 0.642881 + 0.467081i 0.860839 0.508878i \(-0.169939\pi\)
−0.217958 + 0.975958i \(0.569939\pi\)
\(192\) 152.069 298.452i 0.792026 1.55444i
\(193\) −235.980 + 235.980i −1.22269 + 1.22269i −0.256021 + 0.966671i \(0.582412\pi\)
−0.966671 + 0.256021i \(0.917588\pi\)
\(194\) −107.320 + 34.8705i −0.553198 + 0.179745i
\(195\) −20.0808 30.2258i −0.102979 0.155004i
\(196\) −3.09625 + 9.52928i −0.0157972 + 0.0486188i
\(197\) −29.8286 + 15.1984i −0.151414 + 0.0771494i −0.528056 0.849210i \(-0.677079\pi\)
0.376642 + 0.926359i \(0.377079\pi\)
\(198\) 61.7257 389.721i 0.311746 1.96829i
\(199\) 169.710i 0.852815i −0.904531 0.426407i \(-0.859779\pi\)
0.904531 0.426407i \(-0.140221\pi\)
\(200\) 177.781 + 110.242i 0.888907 + 0.551211i
\(201\) 430.949 2.14403
\(202\) −233.576 36.9948i −1.15632 0.183143i
\(203\) −56.6835 111.248i −0.279229 0.548018i
\(204\) 4.23271 + 1.37529i 0.0207486 + 0.00674162i
\(205\) −86.8148 68.8123i −0.423487 0.335670i
\(206\) −12.9421 39.8316i −0.0628256 0.193357i
\(207\) −353.760 353.760i −1.70898 1.70898i
\(208\) −18.8791 9.61938i −0.0907649 0.0462470i
\(209\) −5.97776 + 8.22768i −0.0286017 + 0.0393669i
\(210\) 113.260 200.992i 0.539334 0.957104i
\(211\) −258.395 + 187.735i −1.22462 + 0.889739i −0.996475 0.0838886i \(-0.973266\pi\)
−0.228145 + 0.973627i \(0.573266\pi\)
\(212\) −1.67064 10.5480i −0.00788040 0.0497549i
\(213\) 135.012 21.3838i 0.633858 0.100393i
\(214\) 56.0357 + 77.1265i 0.261849 + 0.360404i
\(215\) 38.8894 35.7587i 0.180881 0.166320i
\(216\) 175.744 + 127.685i 0.813629 + 0.591136i
\(217\) −2.00134 + 3.92785i −0.00922276 + 0.0181007i
\(218\) −38.6550 + 38.6550i −0.177316 + 0.177316i
\(219\) −385.487 + 125.252i −1.76021 + 0.571928i
\(220\) −29.8125 + 8.32294i −0.135511 + 0.0378315i
\(221\) 1.00209 3.08412i 0.00453435 0.0139553i
\(222\) −189.349 + 96.4782i −0.852924 + 0.434587i
\(223\) 45.5256 287.438i 0.204151 1.28896i −0.646373 0.763021i \(-0.723715\pi\)
0.850524 0.525936i \(-0.176285\pi\)
\(224\) 34.2776i 0.153025i
\(225\) −234.760 + 271.943i −1.04338 + 1.20863i
\(226\) 163.423 0.723110
\(227\) −69.1857 10.9579i −0.304783 0.0482728i 0.00216992 0.999998i \(-0.499309\pi\)
−0.306953 + 0.951725i \(0.599309\pi\)
\(228\) −0.654959 1.28543i −0.00287263 0.00563785i
\(229\) 308.912 + 100.371i 1.34896 + 0.438303i 0.892342 0.451360i \(-0.149061\pi\)
0.456617 + 0.889663i \(0.349061\pi\)
\(230\) 114.714 308.432i 0.498757 1.34101i
\(231\) 109.550 + 337.160i 0.474242 + 1.45957i
\(232\) 146.318 + 146.318i 0.630681 + 0.630681i
\(233\) −252.995 128.908i −1.08582 0.553252i −0.182929 0.983126i \(-0.558558\pi\)
−0.902889 + 0.429875i \(0.858558\pi\)
\(234\) 23.9725 32.9953i 0.102446 0.141005i
\(235\) 352.405 161.332i 1.49960 0.686521i
\(236\) 22.6299 16.4416i 0.0958892 0.0696676i
\(237\) 81.6855 + 515.742i 0.344665 + 2.17613i
\(238\) 20.3629 3.22516i 0.0855582 0.0135511i
\(239\) 94.5343 + 130.115i 0.395541 + 0.544416i 0.959618 0.281307i \(-0.0907678\pi\)
−0.564077 + 0.825722i \(0.690768\pi\)
\(240\) −67.4384 + 334.411i −0.280993 + 1.39338i
\(241\) 215.316 + 156.436i 0.893427 + 0.649113i 0.936769 0.349948i \(-0.113801\pi\)
−0.0433422 + 0.999060i \(0.513801\pi\)
\(242\) −77.2115 + 151.536i −0.319056 + 0.626182i
\(243\) 178.303 178.303i 0.733756 0.733756i
\(244\) 35.6826 11.5940i 0.146240 0.0475163i
\(245\) 4.92538 117.442i 0.0201036 0.479353i
\(246\) 62.5699 192.570i 0.254349 0.782807i
\(247\) −0.936614 + 0.477229i −0.00379196 + 0.00193210i
\(248\) 1.14290 7.21600i 0.00460848 0.0290968i
\(249\) 122.370i 0.491446i
\(250\) −226.918 65.9453i −0.907672 0.263781i
\(251\) −304.349 −1.21255 −0.606273 0.795257i \(-0.707336\pi\)
−0.606273 + 0.795257i \(0.707336\pi\)
\(252\) −30.5421 4.83739i −0.121199 0.0191960i
\(253\) 229.567 + 450.552i 0.907381 + 1.78084i
\(254\) 74.8114 + 24.3077i 0.294533 + 0.0956996i
\(255\) −52.1651 2.18775i −0.204569 0.00857941i
\(256\) −24.9901 76.9116i −0.0976176 0.300436i
\(257\) −328.140 328.140i −1.27681 1.27681i −0.942444 0.334364i \(-0.891478\pi\)
−0.334364 0.942444i \(-0.608522\pi\)
\(258\) 86.0384 + 43.8388i 0.333482 + 0.169918i
\(259\) 69.0079 94.9812i 0.266440 0.366723i
\(260\) −3.13617 0.632448i −0.0120622 0.00243249i
\(261\) −287.500 + 208.881i −1.10153 + 0.800311i
\(262\) −68.8587 434.757i −0.262819 1.65938i
\(263\) −98.9066 + 15.6653i −0.376071 + 0.0595638i −0.341609 0.939842i \(-0.610972\pi\)
−0.0344620 + 0.999406i \(0.510972\pi\)
\(264\) −345.344 475.325i −1.30812 1.80047i
\(265\) 52.1510 + 113.916i 0.196796 + 0.429870i
\(266\) −5.40669 3.92819i −0.0203259 0.0147676i
\(267\) 81.6415 160.230i 0.305773 0.600114i
\(268\) 26.8658 26.8658i 0.100246 0.100246i
\(269\) −104.699 + 34.0186i −0.389214 + 0.126463i −0.497085 0.867702i \(-0.665596\pi\)
0.107872 + 0.994165i \(0.465596\pi\)
\(270\) −230.000 85.5430i −0.851850 0.316826i
\(271\) 86.7259 266.915i 0.320022 0.984926i −0.653616 0.756826i \(-0.726749\pi\)
0.973638 0.228100i \(-0.0732512\pi\)
\(272\) −27.1629 + 13.8402i −0.0998637 + 0.0508831i
\(273\) −5.73222 + 36.1918i −0.0209971 + 0.132571i
\(274\) 18.3897i 0.0671157i
\(275\) 310.606 188.087i 1.12948 0.683953i
\(276\) −71.7317 −0.259897
\(277\) 278.815 + 44.1599i 1.00655 + 0.159422i 0.637878 0.770137i \(-0.279812\pi\)
0.368673 + 0.929559i \(0.379812\pi\)
\(278\) 141.745 + 278.191i 0.509875 + 1.00069i
\(279\) 11.9330 + 3.87728i 0.0427707 + 0.0138971i
\(280\) −56.7991 203.452i −0.202854 0.726616i
\(281\) −168.715 519.250i −0.600408 1.84786i −0.525720 0.850658i \(-0.676204\pi\)
−0.0746877 0.997207i \(-0.523796\pi\)
\(282\) 500.924 + 500.924i 1.77633 + 1.77633i
\(283\) 53.0066 + 27.0082i 0.187302 + 0.0954353i 0.545127 0.838353i \(-0.316481\pi\)
−0.357825 + 0.933789i \(0.616481\pi\)
\(284\) 7.08368 9.74985i 0.0249425 0.0343305i
\(285\) 11.4555 + 12.4584i 0.0401947 + 0.0437137i
\(286\) −33.3497 + 24.2300i −0.116607 + 0.0847201i
\(287\) 17.4990 + 110.484i 0.0609721 + 0.384963i
\(288\) 96.3610 15.2621i 0.334587 0.0529934i
\(289\) 167.127 + 230.031i 0.578296 + 0.795956i
\(290\) −203.643 114.754i −0.702217 0.395703i
\(291\) −233.453 169.614i −0.802245 0.582865i
\(292\) −16.2233 + 31.8400i −0.0555591 + 0.109041i
\(293\) −83.9701 + 83.9701i −0.286587 + 0.286587i −0.835729 0.549142i \(-0.814955\pi\)
0.549142 + 0.835729i \(0.314955\pi\)
\(294\) 204.332 66.3915i 0.695007 0.225821i
\(295\) −203.837 + 257.164i −0.690973 + 0.871744i
\(296\) −60.1264 + 185.050i −0.203130 + 0.625169i
\(297\) 335.979 171.190i 1.13124 0.576396i
\(298\) −54.0422 + 341.209i −0.181350 + 1.14500i
\(299\) 52.2666i 0.174805i
\(300\) 3.76978 + 51.3719i 0.0125659 + 0.171240i
\(301\) −53.3469 −0.177232
\(302\) 86.9949 + 13.7786i 0.288063 + 0.0456247i
\(303\) −274.550 538.836i −0.906107 1.77834i
\(304\) 9.39846 + 3.05375i 0.0309160 + 0.0100452i
\(305\) −366.616 + 243.565i −1.20202 + 0.798574i
\(306\) −18.1331 55.8079i −0.0592585 0.182379i
\(307\) 28.0098 + 28.0098i 0.0912370 + 0.0912370i 0.751252 0.660015i \(-0.229450\pi\)
−0.660015 + 0.751252i \(0.729450\pi\)
\(308\) 27.8484 + 14.1894i 0.0904167 + 0.0460696i
\(309\) 62.9517 86.6456i 0.203727 0.280406i
\(310\) 0.948366 + 8.19839i 0.00305924 + 0.0264464i
\(311\) 286.986 208.507i 0.922784 0.670442i −0.0214313 0.999770i \(-0.506822\pi\)
0.944215 + 0.329328i \(0.106822\pi\)
\(312\) −9.50004 59.9809i −0.0304488 0.192246i
\(313\) −250.103 + 39.6125i −0.799052 + 0.126557i −0.542591 0.839997i \(-0.682557\pi\)
−0.256461 + 0.966554i \(0.582557\pi\)
\(314\) −178.369 245.504i −0.568055 0.781860i
\(315\) 360.364 41.6859i 1.14401 0.132336i
\(316\) 37.2442 + 27.0595i 0.117861 + 0.0856314i
\(317\) −125.982 + 247.254i −0.397420 + 0.779980i −0.999834 0.0182030i \(-0.994205\pi\)
0.602414 + 0.798183i \(0.294205\pi\)
\(318\) −161.925 + 161.925i −0.509197 + 0.509197i
\(319\) 341.607 110.995i 1.07087 0.347946i
\(320\) 191.711 + 288.565i 0.599097 + 0.901766i
\(321\) −75.3347 + 231.856i −0.234688 + 0.722294i
\(322\) −296.073 + 150.857i −0.919480 + 0.468499i
\(323\) −0.236596 + 1.49381i −0.000732496 + 0.00462480i
\(324\) 1.63159i 0.00503577i
\(325\) 37.4316 2.74681i 0.115174 0.00845173i
\(326\) −99.4124 −0.304946
\(327\) −138.073 21.8685i −0.422240 0.0668763i
\(328\) −84.1647 165.183i −0.256600 0.503605i
\(329\) −372.212 120.939i −1.13134 0.367596i
\(330\) 520.125 + 412.269i 1.57614 + 1.24930i
\(331\) 142.165 + 437.539i 0.429501 + 1.32187i 0.898618 + 0.438733i \(0.144573\pi\)
−0.469116 + 0.883136i \(0.655427\pi\)
\(332\) 7.62867 + 7.62867i 0.0229779 + 0.0229779i
\(333\) −297.736 151.704i −0.894102 0.455568i
\(334\) 197.368 271.654i 0.590923 0.813335i
\(335\) −218.817 + 388.314i −0.653185 + 1.15915i
\(336\) 278.688 202.479i 0.829429 0.602615i
\(337\) −95.9825 606.010i −0.284815 1.79825i −0.551190 0.834380i \(-0.685826\pi\)
0.266376 0.963869i \(-0.414174\pi\)
\(338\) 311.344 49.3120i 0.921136 0.145894i
\(339\) 245.640 + 338.094i 0.724601 + 0.997327i
\(340\) −3.38841 + 3.11564i −0.00996592 + 0.00916365i
\(341\) −10.2599 7.45424i −0.0300876 0.0218599i
\(342\) −8.63557 + 16.9483i −0.0252502 + 0.0495563i
\(343\) −258.863 + 258.863i −0.754703 + 0.754703i
\(344\) 84.0849 27.3208i 0.244433 0.0794210i
\(345\) 810.520 226.278i 2.34933 0.655878i
\(346\) −54.6196 + 168.102i −0.157860 + 0.485844i
\(347\) 471.200 240.088i 1.35792 0.691897i 0.384977 0.922926i \(-0.374209\pi\)
0.972947 + 0.231029i \(0.0742093\pi\)
\(348\) −7.97077 + 50.3255i −0.0229045 + 0.144613i
\(349\) 189.896i 0.544113i −0.962281 0.272057i \(-0.912296\pi\)
0.962281 0.272057i \(-0.0877038\pi\)
\(350\) 123.598 + 204.110i 0.353138 + 0.583170i
\(351\) 38.9754 0.111041
\(352\) −97.3961 15.4260i −0.276694 0.0438239i
\(353\) −103.285 202.708i −0.292591 0.574242i 0.697182 0.716894i \(-0.254437\pi\)
−0.989773 + 0.142652i \(0.954437\pi\)
\(354\) −570.436 185.346i −1.61140 0.523576i
\(355\) −49.2849 + 132.512i −0.138831 + 0.373274i
\(356\) −4.89931 15.0785i −0.0137621 0.0423554i
\(357\) 37.2796 + 37.2796i 0.104425 + 0.104425i
\(358\) −263.574 134.298i −0.736239 0.375133i
\(359\) −177.619 + 244.471i −0.494760 + 0.680979i −0.981257 0.192703i \(-0.938274\pi\)
0.486497 + 0.873682i \(0.338274\pi\)
\(360\) −546.654 + 250.260i −1.51848 + 0.695168i
\(361\) −291.659 + 211.902i −0.807918 + 0.586987i
\(362\) 75.0312 + 473.728i 0.207268 + 1.30864i
\(363\) −429.558 + 68.0354i −1.18336 + 0.187425i
\(364\) 1.89888 + 2.61358i 0.00521670 + 0.00718018i
\(365\) 82.8727 410.946i 0.227048 1.12588i
\(366\) −650.854 472.873i −1.77829 1.29200i
\(367\) 114.708 225.127i 0.312556 0.613425i −0.680275 0.732957i \(-0.738140\pi\)
0.992830 + 0.119532i \(0.0381395\pi\)
\(368\) 347.440 347.440i 0.944130 0.944130i
\(369\) 302.801 98.3861i 0.820599 0.266629i
\(370\) 9.20994 219.604i 0.0248917 0.593523i
\(371\) 39.0937 120.318i 0.105374 0.324308i
\(372\) 1.60292 0.816731i 0.00430894 0.00219551i
\(373\) −20.8557 + 131.678i −0.0559135 + 0.353024i 0.943831 + 0.330428i \(0.107193\pi\)
−0.999745 + 0.0225959i \(0.992807\pi\)
\(374\) 59.3102i 0.158583i
\(375\) −204.649 568.576i −0.545731 1.51620i
\(376\) 648.615 1.72504
\(377\) 36.6691 + 5.80782i 0.0972656 + 0.0154054i
\(378\) 112.495 + 220.783i 0.297605 + 0.584082i
\(379\) −210.936 68.5373i −0.556560 0.180837i 0.0172129 0.999852i \(-0.494521\pi\)
−0.573773 + 0.819015i \(0.694521\pi\)
\(380\) 1.49082 + 0.0625232i 0.00392320 + 0.000164535i
\(381\) 62.1600 + 191.309i 0.163150 + 0.502123i
\(382\) −202.888 202.888i −0.531120 0.531120i
\(383\) 636.506 + 324.316i 1.66190 + 0.846778i 0.994805 + 0.101802i \(0.0324608\pi\)
0.667091 + 0.744976i \(0.267539\pi\)
\(384\) −295.035 + 406.080i −0.768319 + 1.05750i
\(385\) −359.428 72.4833i −0.933580 0.188268i
\(386\) 510.401 370.828i 1.32228 0.960695i
\(387\) 23.7526 + 149.968i 0.0613763 + 0.387515i
\(388\) −25.1276 + 3.97982i −0.0647619 + 0.0102573i
\(389\) 225.276 + 310.066i 0.579116 + 0.797085i 0.993598 0.112973i \(-0.0360373\pi\)
−0.414482 + 0.910057i \(0.636037\pi\)
\(390\) 28.5557 + 62.3754i 0.0732197 + 0.159937i
\(391\) 60.8383 + 44.2016i 0.155597 + 0.113048i
\(392\) 89.3052 175.271i 0.227819 0.447121i
\(393\) 795.936 795.936i 2.02528 2.02528i
\(394\) 60.1898 19.5569i 0.152766 0.0496367i
\(395\) −506.194 188.267i −1.28150 0.476625i
\(396\) 27.4898 84.6049i 0.0694187 0.213649i
\(397\) −179.280 + 91.3478i −0.451587 + 0.230095i −0.664965 0.746875i \(-0.731554\pi\)
0.213378 + 0.976970i \(0.431554\pi\)
\(398\) −50.1886 + 316.878i −0.126102 + 0.796176i
\(399\) 17.0899i 0.0428319i
\(400\) −267.084 230.566i −0.667711 0.576414i
\(401\) −334.385 −0.833878 −0.416939 0.908935i \(-0.636897\pi\)
−0.416939 + 0.908935i \(0.636897\pi\)
\(402\) −804.657 127.445i −2.00163 0.317028i
\(403\) −0.595102 1.16795i −0.00147668 0.00289815i
\(404\) −50.7073 16.4758i −0.125513 0.0407817i
\(405\) 5.14686 + 18.4359i 0.0127083 + 0.0455206i
\(406\) 72.9385 + 224.482i 0.179651 + 0.552910i
\(407\) 238.823 + 238.823i 0.586788 + 0.586788i
\(408\) −77.8519 39.6675i −0.190814 0.0972243i
\(409\) 89.2243 122.807i 0.218152 0.300261i −0.685889 0.727706i \(-0.740586\pi\)
0.904041 + 0.427445i \(0.140586\pi\)
\(410\) 141.748 + 154.158i 0.345728 + 0.375996i
\(411\) 38.0452 27.6414i 0.0925673 0.0672541i
\(412\) −1.47710 9.32604i −0.00358519 0.0226360i
\(413\) 327.279 51.8358i 0.792442 0.125510i
\(414\) 555.913 + 765.148i 1.34278 + 1.84818i
\(415\) −110.264 62.1341i −0.265695 0.149721i
\(416\) −8.24593 5.99102i −0.0198219 0.0144015i
\(417\) −362.473 + 711.394i −0.869240 + 1.70598i
\(418\) 13.5947 13.5947i 0.0325232 0.0325232i
\(419\) −245.486 + 79.7632i −0.585885 + 0.190366i −0.586935 0.809634i \(-0.699666\pi\)
0.00105020 + 0.999999i \(0.499666\pi\)
\(420\) 32.3091 40.7618i 0.0769265 0.0970518i
\(421\) −67.3265 + 207.210i −0.159920 + 0.492184i −0.998626 0.0524005i \(-0.983313\pi\)
0.838706 + 0.544585i \(0.183313\pi\)
\(422\) 537.987 274.118i 1.27485 0.649569i
\(423\) −174.256 + 1100.21i −0.411952 + 2.60096i
\(424\) 209.666i 0.494495i
\(425\) 28.4585 45.8934i 0.0669611 0.107984i
\(426\) −258.414 −0.606606
\(427\) 438.979 + 69.5274i 1.02805 + 0.162828i
\(428\) 9.75772 + 19.1506i 0.0227984 + 0.0447444i
\(429\) −100.255 32.5749i −0.233695 0.0759322i
\(430\) −83.1882 + 55.2669i −0.193461 + 0.128528i
\(431\) 61.9145 + 190.553i 0.143653 + 0.442119i 0.996835 0.0794942i \(-0.0253305\pi\)
−0.853182 + 0.521613i \(0.825331\pi\)
\(432\) −259.088 259.088i −0.599740 0.599740i
\(433\) −424.969 216.532i −0.981452 0.500075i −0.111795 0.993731i \(-0.535660\pi\)
−0.869657 + 0.493657i \(0.835660\pi\)
\(434\) 4.89843 6.74212i 0.0112867 0.0155348i
\(435\) −68.6877 593.788i −0.157903 1.36503i
\(436\) −9.97089 + 7.24427i −0.0228690 + 0.0166153i
\(437\) −3.81335 24.0765i −0.00872620 0.0550951i
\(438\) 756.811 119.867i 1.72788 0.273669i
\(439\) −444.956 612.429i −1.01357 1.39506i −0.916617 0.399766i \(-0.869091\pi\)
−0.0969494 0.995289i \(-0.530909\pi\)
\(440\) 603.649 69.8284i 1.37193 0.158701i
\(441\) 273.310 + 198.571i 0.619751 + 0.450275i
\(442\) −2.78315 + 5.46224i −0.00629672 + 0.0123580i
\(443\) 243.432 243.432i 0.549509 0.549509i −0.376790 0.926299i \(-0.622972\pi\)
0.926299 + 0.376790i \(0.122972\pi\)
\(444\) −45.5664 + 14.8054i −0.102627 + 0.0333455i
\(445\) 102.924 + 154.922i 0.231290 + 0.348140i
\(446\) −170.008 + 523.232i −0.381185 + 1.17317i
\(447\) −787.134 + 401.065i −1.76093 + 0.897237i
\(448\) 54.7253 345.522i 0.122155 0.771255i
\(449\) 404.772i 0.901496i 0.892651 + 0.450748i \(0.148843\pi\)
−0.892651 + 0.450748i \(0.851157\pi\)
\(450\) 518.759 438.338i 1.15280 0.974086i
\(451\) −321.804 −0.713534
\(452\) 36.3905 + 5.76369i 0.0805100 + 0.0127515i
\(453\) 102.256 + 200.688i 0.225730 + 0.443020i
\(454\) 125.941 + 40.9207i 0.277403 + 0.0901337i
\(455\) −29.7006 23.5417i −0.0652761 0.0517400i
\(456\) 8.75237 + 26.9370i 0.0191938 + 0.0590724i
\(457\) 166.102 + 166.102i 0.363461 + 0.363461i 0.865085 0.501625i \(-0.167264\pi\)
−0.501625 + 0.865085i \(0.667264\pi\)
\(458\) −547.109 278.766i −1.19456 0.608659i
\(459\) 32.9614 45.3674i 0.0718113 0.0988397i
\(460\) 36.4222 64.6350i 0.0791787 0.140511i
\(461\) 88.2257 64.0997i 0.191379 0.139045i −0.487970 0.872861i \(-0.662262\pi\)
0.679349 + 0.733816i \(0.262262\pi\)
\(462\) −104.840 661.934i −0.226926 1.43276i
\(463\) 413.975 65.5672i 0.894114 0.141614i 0.307565 0.951527i \(-0.400486\pi\)
0.586549 + 0.809913i \(0.300486\pi\)
\(464\) −205.149 282.364i −0.442132 0.608543i
\(465\) −15.5356 + 14.2849i −0.0334099 + 0.0307203i
\(466\) 434.264 + 315.512i 0.931898 + 0.677063i
\(467\) 33.4938 65.7354i 0.0717213 0.140761i −0.852362 0.522952i \(-0.824831\pi\)
0.924083 + 0.382191i \(0.124831\pi\)
\(468\) 6.50181 6.50181i 0.0138928 0.0138928i
\(469\) 428.050 139.082i 0.912686 0.296550i
\(470\) −705.713 + 197.018i −1.50152 + 0.419188i
\(471\) 239.801 738.030i 0.509131 1.56694i
\(472\) −489.307 + 249.314i −1.03667 + 0.528208i
\(473\) 24.0078 151.579i 0.0507564 0.320464i
\(474\) 987.137i 2.08257i
\(475\) −17.0424 + 3.99631i −0.0358788 + 0.00841329i
\(476\) 4.64809 0.00976489
\(477\) −355.644 56.3285i −0.745585 0.118089i
\(478\) −138.033 270.905i −0.288772 0.566746i
\(479\) 133.246 + 43.2942i 0.278175 + 0.0903846i 0.444782 0.895639i \(-0.353281\pi\)
−0.166607 + 0.986023i \(0.553281\pi\)
\(480\) −57.2061 + 153.810i −0.119179 + 0.320438i
\(481\) 10.7878 + 33.2015i 0.0224279 + 0.0690259i
\(482\) −355.769 355.769i −0.738110 0.738110i
\(483\) −757.121 385.772i −1.56754 0.798701i
\(484\) −22.5377 + 31.0205i −0.0465655 + 0.0640919i
\(485\) 271.371 124.234i 0.559527 0.256154i
\(486\) −385.652 + 280.192i −0.793522 + 0.576527i
\(487\) 19.9189 + 125.763i 0.0409012 + 0.258240i 0.999663 0.0259720i \(-0.00826807\pi\)
−0.958761 + 0.284212i \(0.908268\pi\)
\(488\) −727.522 + 115.228i −1.49082 + 0.236123i
\(489\) −149.426 205.667i −0.305575 0.420588i
\(490\) −43.9277 + 217.827i −0.0896483 + 0.444545i
\(491\) 242.641 + 176.289i 0.494178 + 0.359041i 0.806789 0.590840i \(-0.201204\pi\)
−0.312611 + 0.949881i \(0.601204\pi\)
\(492\) 20.7246 40.6743i 0.0421231 0.0826713i
\(493\) 37.7713 37.7713i 0.0766151 0.0766151i
\(494\) 1.88995 0.614083i 0.00382581 0.00124308i
\(495\) −43.7295 + 1042.69i −0.0883425 + 2.10645i
\(496\) −3.80801 + 11.7198i −0.00767744 + 0.0236287i
\(497\) 127.202 64.8128i 0.255940 0.130408i
\(498\) 36.1887 228.486i 0.0726680 0.458808i
\(499\) 438.153i 0.878063i 0.898472 + 0.439031i \(0.144678\pi\)
−0.898472 + 0.439031i \(0.855322\pi\)
\(500\) −48.2036 22.6876i −0.0964073 0.0453752i
\(501\) 858.668 1.71391
\(502\) 568.272 + 90.0055i 1.13202 + 0.179294i
\(503\) 21.9783 + 43.1348i 0.0436944 + 0.0857550i 0.911821 0.410587i \(-0.134676\pi\)
−0.868127 + 0.496342i \(0.834676\pi\)
\(504\) 577.379 + 187.602i 1.14559 + 0.372226i
\(505\) 624.931 + 26.2089i 1.23749 + 0.0518989i
\(506\) −295.400 909.148i −0.583795 1.79674i
\(507\) 569.997 + 569.997i 1.12425 + 1.12425i
\(508\) 15.8015 + 8.05126i 0.0311053 + 0.0158489i
\(509\) −380.749 + 524.056i −0.748034 + 1.02958i 0.250082 + 0.968225i \(0.419542\pi\)
−0.998116 + 0.0613557i \(0.980458\pi\)
\(510\) 96.7544 + 19.5118i 0.189714 + 0.0382584i
\(511\) −342.470 + 248.819i −0.670196 + 0.486926i
\(512\) 88.8860 + 561.204i 0.173605 + 1.09610i
\(513\) −17.9540 + 2.84363i −0.0349980 + 0.00554315i
\(514\) 515.653 + 709.735i 1.00322 + 1.38081i
\(515\) 46.1093 + 100.718i 0.0895326 + 0.195570i
\(516\) 17.6127 + 12.7963i 0.0341331 + 0.0247991i
\(517\) 511.142 1003.17i 0.988669 1.94037i
\(518\) −156.939 + 156.939i −0.302970 + 0.302970i
\(519\) −429.873 + 139.674i −0.828271 + 0.269122i
\(520\) 58.8704 + 21.8955i 0.113212 + 0.0421067i
\(521\) 32.4116 99.7526i 0.0622103 0.191464i −0.915121 0.403179i \(-0.867905\pi\)
0.977331 + 0.211716i \(0.0679051\pi\)
\(522\) 598.585 304.994i 1.14671 0.584280i
\(523\) −55.9046 + 352.968i −0.106892 + 0.674891i 0.874810 + 0.484467i \(0.160986\pi\)
−0.981702 + 0.190424i \(0.939014\pi\)
\(524\) 99.2389i 0.189387i
\(525\) −236.488 + 562.500i −0.450454 + 1.07143i
\(526\) 189.309 0.359902
\(527\) −1.86278 0.295035i −0.00353468 0.000559838i
\(528\) 449.902 + 882.983i 0.852088 + 1.67232i
\(529\) −649.613 211.072i −1.22800 0.399002i
\(530\) −63.6865 228.123i −0.120163 0.430420i
\(531\) −291.441 896.963i −0.548853 1.68920i
\(532\) −1.06540 1.06540i −0.00200264 0.00200264i
\(533\) −29.6369 15.1007i −0.0556039 0.0283316i
\(534\) −199.824 + 275.034i −0.374202 + 0.515045i
\(535\) −170.666 185.608i −0.319002 0.346931i
\(536\) −603.460 + 438.439i −1.12586 + 0.817984i
\(537\) −118.337 747.151i −0.220367 1.39134i
\(538\) 205.551 32.5560i 0.382064 0.0605131i
\(539\) −200.704 276.246i −0.372364 0.512515i
\(540\) −48.1986 27.1602i −0.0892567 0.0502967i
\(541\) −221.720 161.089i −0.409834 0.297762i 0.363700 0.931516i \(-0.381513\pi\)
−0.773535 + 0.633754i \(0.781513\pi\)
\(542\) −240.867 + 472.729i −0.444405 + 0.872193i
\(543\) −867.284 + 867.284i −1.59721 + 1.59721i
\(544\) −13.9471 + 4.53169i −0.0256380 + 0.00833031i
\(545\) 89.8122 113.309i 0.164793 0.207906i
\(546\) 21.4061 65.8812i 0.0392053 0.120661i
\(547\) 559.689 285.176i 1.02320 0.521345i 0.139904 0.990165i \(-0.455321\pi\)
0.883294 + 0.468820i \(0.155321\pi\)
\(548\) 0.648579 4.09497i 0.00118354 0.00747257i
\(549\) 1265.01i 2.30421i
\(550\) −635.578 + 259.335i −1.15560 + 0.471519i
\(551\) −17.3153 −0.0314253
\(552\) 1390.94 + 220.303i 2.51981 + 0.399099i
\(553\) 247.583 + 485.910i 0.447709 + 0.878679i
\(554\) −507.536 164.908i −0.916130 0.297669i
\(555\) 468.166 311.031i 0.843542 0.560416i
\(556\) 21.7520 + 66.9459i 0.0391224 + 0.120406i
\(557\) −770.632 770.632i −1.38354 1.38354i −0.838241 0.545300i \(-0.816416\pi\)
−0.545300 0.838241i \(-0.683584\pi\)
\(558\) −21.1344 10.7685i −0.0378753 0.0192984i
\(559\) 9.32392 12.8333i 0.0166796 0.0229576i
\(560\) 40.9412 + 353.926i 0.0731092 + 0.632011i
\(561\) −122.703 + 89.1487i −0.218721 + 0.158910i
\(562\) 161.461 + 1019.42i 0.287297 + 1.81392i
\(563\) 479.058 75.8754i 0.850903 0.134770i 0.284274 0.958743i \(-0.408247\pi\)
0.566629 + 0.823973i \(0.308247\pi\)
\(564\) 93.8774 + 129.211i 0.166449 + 0.229098i
\(565\) −429.370 + 49.6683i −0.759947 + 0.0879085i
\(566\) −90.9853 66.1047i −0.160751 0.116793i
\(567\) 8.77467 17.2213i 0.0154756 0.0303726i
\(568\) −167.302 + 167.302i −0.294546 + 0.294546i
\(569\) 862.709 280.311i 1.51619 0.492638i 0.571496 0.820605i \(-0.306363\pi\)
0.944689 + 0.327967i \(0.106363\pi\)
\(570\) −17.7050 26.6497i −0.0310615 0.0467539i
\(571\) 298.299 918.071i 0.522416 1.60783i −0.246955 0.969027i \(-0.579430\pi\)
0.769371 0.638803i \(-0.220570\pi\)
\(572\) −8.28077 + 4.21926i −0.0144769 + 0.00737633i
\(573\) 114.781 724.700i 0.200316 1.26475i
\(574\) 211.468i 0.368412i
\(575\) −207.655 + 845.226i −0.361139 + 1.46996i
\(576\) −995.696 −1.72864
\(577\) −1072.44 169.858i −1.85865 0.294381i −0.876348 0.481679i \(-0.840027\pi\)
−0.982303 + 0.187298i \(0.940027\pi\)
\(578\) −244.029 478.933i −0.422195 0.828604i
\(579\) 1534.36 + 498.544i 2.65002 + 0.861043i
\(580\) −41.2994 32.7353i −0.0712058 0.0564401i
\(581\) 39.4930 + 121.547i 0.0679741 + 0.209203i
\(582\) 385.738 + 385.738i 0.662780 + 0.662780i
\(583\) 324.277 + 165.228i 0.556222 + 0.283409i
\(584\) 412.369 567.578i 0.706112 0.971880i
\(585\) −52.9561 + 93.9761i −0.0905232 + 0.160643i
\(586\) 181.619 131.954i 0.309930 0.225178i
\(587\) 126.992 + 801.794i 0.216340 + 1.36592i 0.821679 + 0.569950i \(0.193037\pi\)
−0.605339 + 0.795968i \(0.706963\pi\)
\(588\) 47.8416 7.57736i 0.0813632 0.0128867i
\(589\) 0.359347 + 0.494599i 0.000610097 + 0.000839726i
\(590\) 456.651 419.890i 0.773984 0.711677i
\(591\) 130.931 + 95.1267i 0.221541 + 0.160959i
\(592\) 148.994 292.417i 0.251679 0.493947i
\(593\) −104.789 + 104.789i −0.176710 + 0.176710i −0.789920 0.613210i \(-0.789878\pi\)
0.613210 + 0.789920i \(0.289878\pi\)
\(594\) −677.956 + 220.281i −1.14134 + 0.370844i
\(595\) −52.5203 + 14.6624i −0.0882693 + 0.0246427i
\(596\) −24.0679 + 74.0735i −0.0403824 + 0.124284i
\(597\) −731.005 + 372.466i −1.22446 + 0.623896i
\(598\) 15.4568 97.5907i 0.0258476 0.163195i
\(599\) 683.205i 1.14058i −0.821445 0.570288i \(-0.806832\pi\)
0.821445 0.570288i \(-0.193168\pi\)
\(600\) 84.6744 1007.72i 0.141124 1.67954i
\(601\) −227.072 −0.377823 −0.188912 0.981994i \(-0.560496\pi\)
−0.188912 + 0.981994i \(0.560496\pi\)
\(602\) 99.6079 + 15.7763i 0.165462 + 0.0262065i
\(603\) −581.575 1141.40i −0.964469 1.89288i
\(604\) 18.8858 + 6.13638i 0.0312679 + 0.0101596i
\(605\) 156.806 421.606i 0.259184 0.696869i
\(606\) 353.283 + 1087.29i 0.582975 + 1.79421i
\(607\) −65.4899 65.4899i −0.107891 0.107891i 0.651101 0.758992i \(-0.274308\pi\)
−0.758992 + 0.651101i \(0.774308\pi\)
\(608\) 4.23558 + 2.15814i 0.00696642 + 0.00354957i
\(609\) −354.781 + 488.314i −0.582563 + 0.801829i
\(610\) 756.565 346.358i 1.24027 0.567800i
\(611\) 94.1484 68.4028i 0.154089 0.111952i
\(612\) −2.06956 13.0667i −0.00338163 0.0213508i
\(613\) −522.470 + 82.7511i −0.852316 + 0.134994i −0.567282 0.823524i \(-0.692005\pi\)
−0.285034 + 0.958517i \(0.592005\pi\)
\(614\) −44.0157 60.5824i −0.0716868 0.0986685i
\(615\) −105.866 + 524.968i −0.172141 + 0.853606i
\(616\) −496.424 360.673i −0.805882 0.585508i
\(617\) −126.641 + 248.548i −0.205254 + 0.402833i −0.970569 0.240822i \(-0.922583\pi\)
0.765316 + 0.643655i \(0.222583\pi\)
\(618\) −143.166 + 143.166i −0.231659 + 0.231659i
\(619\) 81.1742 26.3751i 0.131138 0.0426092i −0.242713 0.970098i \(-0.578037\pi\)
0.373851 + 0.927489i \(0.378037\pi\)
\(620\) −0.0779662 + 1.85904i −0.000125752 + 0.00299845i
\(621\) −279.298 + 859.590i −0.449755 + 1.38420i
\(622\) −597.515 + 304.449i −0.960634 + 0.489468i
\(623\) 29.3805 185.501i 0.0471597 0.297754i
\(624\) 102.431i 0.164152i
\(625\) 616.236 + 104.296i 0.985978 + 0.166873i
\(626\) 478.701 0.764698
\(627\) 48.5592 + 7.69102i 0.0774468 + 0.0122664i
\(628\) −31.0601 60.9590i −0.0494588 0.0970684i
\(629\) 47.7697 + 15.5213i 0.0759455 + 0.0246762i
\(630\) −685.190 28.7362i −1.08760 0.0456129i
\(631\) −124.769 384.001i −0.197733 0.608559i −0.999934 0.0115048i \(-0.996338\pi\)
0.802201 0.597054i \(-0.203662\pi\)
\(632\) −639.090 639.090i −1.01122 1.01122i
\(633\) 1375.75 + 700.978i 2.17338 + 1.10739i
\(634\) 308.351 424.409i 0.486358 0.669415i
\(635\) −203.944 41.1279i −0.321172 0.0647684i
\(636\) −41.7677 + 30.3460i −0.0656725 + 0.0477139i
\(637\) −5.52117 34.8593i −0.00866745 0.0547241i
\(638\) −670.664 + 106.223i −1.05120 + 0.166493i
\(639\) −238.838 328.732i −0.373768 0.514448i
\(640\) −216.099 472.035i −0.337655 0.737555i
\(641\) 418.717 + 304.216i 0.653225 + 0.474596i 0.864368 0.502859i \(-0.167719\pi\)
−0.211143 + 0.977455i \(0.567719\pi\)
\(642\) 209.230 410.637i 0.325904 0.639622i
\(643\) 435.521 435.521i 0.677326 0.677326i −0.282068 0.959394i \(-0.591020\pi\)
0.959394 + 0.282068i \(0.0910204\pi\)
\(644\) −71.2491 + 23.1502i −0.110635 + 0.0359476i
\(645\) −239.377 89.0308i −0.371128 0.138032i
\(646\) 0.883532 2.71923i 0.00136770 0.00420934i
\(647\) −182.235 + 92.8532i −0.281661 + 0.143513i −0.589114 0.808050i \(-0.700523\pi\)
0.307453 + 0.951563i \(0.400523\pi\)
\(648\) −5.01094 + 31.6378i −0.00773293 + 0.0488238i
\(649\) 953.254i 1.46880i
\(650\) −70.7036 5.94092i −0.108775 0.00913988i
\(651\) 21.3111 0.0327359
\(652\) −22.1369 3.50614i −0.0339523 0.00537751i
\(653\) 366.165 + 718.639i 0.560743 + 1.10052i 0.981161 + 0.193189i \(0.0618832\pi\)
−0.420419 + 0.907330i \(0.638117\pi\)
\(654\) 251.338 + 81.6647i 0.384309 + 0.124870i
\(655\) 313.050 + 1121.33i 0.477938 + 1.71196i
\(656\) 96.6284 + 297.392i 0.147299 + 0.453341i
\(657\) 851.963 + 851.963i 1.29675 + 1.29675i
\(658\) 659.219 + 335.889i 1.00185 + 0.510469i
\(659\) 426.426 586.925i 0.647081 0.890630i −0.351888 0.936042i \(-0.614460\pi\)
0.998968 + 0.0454122i \(0.0144601\pi\)
\(660\) 101.280 + 110.147i 0.153454 + 0.166889i
\(661\) 562.862 408.943i 0.851531 0.618674i −0.0740365 0.997256i \(-0.523588\pi\)
0.925568 + 0.378582i \(0.123588\pi\)
\(662\) −136.053 859.003i −0.205518 1.29759i
\(663\) −15.4838 + 2.45239i −0.0233541 + 0.00369893i
\(664\) −124.497 171.355i −0.187495 0.258065i
\(665\) 15.3992 + 8.67752i 0.0231566 + 0.0130489i
\(666\) 511.061 + 371.308i 0.767359 + 0.557519i
\(667\) −390.861 + 767.107i −0.585998 + 1.15009i
\(668\) 53.5302 53.5302i 0.0801350 0.0801350i
\(669\) −1338.02 + 434.748i −2.00003 + 0.649848i
\(670\) 523.406 660.338i 0.781203 0.985579i
\(671\) −395.109 + 1216.02i −0.588836 + 1.81225i
\(672\) 147.647 75.2297i 0.219712 0.111949i
\(673\) −6.25856 + 39.5150i −0.00929950 + 0.0587147i −0.991902 0.127008i \(-0.959463\pi\)
0.982602 + 0.185723i \(0.0594626\pi\)
\(674\) 1159.91i 1.72094i
\(675\) 630.289 + 154.849i 0.933762 + 0.229406i
\(676\) 71.0683 0.105131
\(677\) 32.0421 + 5.07497i 0.0473296 + 0.00749627i 0.180054 0.983657i \(-0.442373\pi\)
−0.132725 + 0.991153i \(0.542373\pi\)
\(678\) −358.667 703.923i −0.529007 1.03824i
\(679\) −286.623 93.1294i −0.422125 0.137157i
\(680\) 75.2728 50.0083i 0.110695 0.0735416i
\(681\) 104.643 + 322.058i 0.153661 + 0.472919i
\(682\) 16.9525 + 16.9525i 0.0248571 + 0.0248571i
\(683\) −245.294 124.983i −0.359142 0.182992i 0.265104 0.964220i \(-0.414594\pi\)
−0.624246 + 0.781228i \(0.714594\pi\)
\(684\) −2.52068 + 3.46942i −0.00368521 + 0.00507226i
\(685\) 5.58909 + 48.3163i 0.00815926 + 0.0705348i
\(686\) 559.897 406.789i 0.816176 0.592986i
\(687\) −245.636 1550.88i −0.357549 2.25747i
\(688\) −147.289 + 23.3283i −0.214083 + 0.0339074i
\(689\) 22.1113 + 30.4336i 0.0320919 + 0.0441707i
\(690\) −1580.30 + 182.804i −2.29029 + 0.264934i
\(691\) −825.186 599.532i −1.19419 0.867630i −0.200490 0.979696i \(-0.564253\pi\)
−0.993701 + 0.112066i \(0.964253\pi\)
\(692\) −18.0913 + 35.5061i −0.0261434 + 0.0513094i
\(693\) 745.157 745.157i 1.07526 1.07526i
\(694\) −950.813 + 308.938i −1.37005 + 0.445155i
\(695\) −456.965 687.827i −0.657503 0.989679i
\(696\) 309.120 951.372i 0.444137 1.36691i
\(697\) −42.6411 + 21.7267i −0.0611780 + 0.0311718i
\(698\) −56.1580 + 354.568i −0.0804556 + 0.507977i
\(699\) 1372.66i 1.96375i
\(700\) 20.3239 + 49.8097i 0.0290341 + 0.0711567i
\(701\) −356.349 −0.508344 −0.254172 0.967159i \(-0.581803\pi\)
−0.254172 + 0.967159i \(0.581803\pi\)
\(702\) −72.7739 11.5263i −0.103667 0.0164192i
\(703\) −7.39176 14.5072i −0.0105146 0.0206361i
\(704\) 957.135 + 310.992i 1.35957 + 0.441750i
\(705\) −1468.35 1163.86i −2.08276 1.65087i
\(706\) 132.903 + 409.035i 0.188248 + 0.579369i
\(707\) −446.604 446.604i −0.631689 0.631689i
\(708\) −120.486 61.3907i −0.170178 0.0867100i
\(709\) −672.951 + 926.237i −0.949155 + 1.30640i 0.00274737 + 0.999996i \(0.499125\pi\)
−0.951902 + 0.306403i \(0.900875\pi\)
\(710\) 131.211 232.848i 0.184805 0.327955i
\(711\) 1255.75 912.355i 1.76617 1.28320i
\(712\) 48.6924 + 307.432i 0.0683882 + 0.431786i
\(713\) 30.0233 4.75523i 0.0421085 0.00666933i
\(714\) −58.5827 80.6321i −0.0820486 0.112930i
\(715\) 80.2574 73.7965i 0.112248 0.103212i
\(716\) −53.9553 39.2009i −0.0753566 0.0547498i
\(717\) 352.979 692.761i 0.492300 0.966194i
\(718\) 403.943 403.943i 0.562595 0.562595i
\(719\) 876.169 284.685i 1.21859 0.395945i 0.372024 0.928223i \(-0.378664\pi\)
0.846570 + 0.532278i \(0.178664\pi\)
\(720\) 976.725 272.679i 1.35656 0.378721i
\(721\) 34.5647 106.379i 0.0479400 0.147544i
\(722\) 607.243 309.406i 0.841057 0.428540i
\(723\) 201.272 1270.78i 0.278384 1.75765i
\(724\) 108.135i 0.149357i
\(725\) 569.919 + 239.607i 0.786095 + 0.330493i
\(726\) 822.180 1.13248
\(727\) −321.634 50.9418i −0.442413 0.0700713i −0.0687456 0.997634i \(-0.521900\pi\)
−0.373667 + 0.927563i \(0.621900\pi\)
\(728\) −28.7940 56.5114i −0.0395522 0.0776255i
\(729\) −1126.57 366.046i −1.54537 0.502120i
\(730\) −276.267 + 742.800i −0.378448 + 1.01753i
\(731\) −7.05274 21.7061i −0.00964807 0.0296937i
\(732\) −128.253 128.253i −0.175209 0.175209i
\(733\) 46.2214 + 23.5510i 0.0630579 + 0.0321296i 0.485235 0.874384i \(-0.338734\pi\)
−0.422177 + 0.906513i \(0.638734\pi\)
\(734\) −280.757 + 386.428i −0.382502 + 0.526469i
\(735\) −516.675 + 236.536i −0.702959 + 0.321817i
\(736\) 191.220 138.930i 0.259810 0.188763i
\(737\) 202.550 + 1278.85i 0.274830 + 1.73521i
\(738\) −594.478 + 94.1561i −0.805526 + 0.127583i
\(739\) −513.049 706.151i −0.694247 0.955550i −0.999994 0.00343667i \(-0.998906\pi\)
0.305747 0.952113i \(-0.401094\pi\)
\(740\) 9.79595 48.5759i 0.0132378 0.0656431i
\(741\) 4.11121 + 2.98697i 0.00554819 + 0.00403099i
\(742\) −108.577 + 213.094i −0.146330 + 0.287188i
\(743\) −739.686 + 739.686i −0.995540 + 0.995540i −0.999990 0.00444973i \(-0.998584\pi\)
0.00444973 + 0.999990i \(0.498584\pi\)
\(744\) −33.5904 + 10.9142i −0.0451483 + 0.0146696i
\(745\) 38.2862 912.903i 0.0513908 1.22537i
\(746\) 77.8826 239.698i 0.104400 0.321311i
\(747\) 324.107 165.141i 0.433879 0.221072i
\(748\) −2.09179 + 13.2070i −0.00279651 + 0.0176565i
\(749\) 254.610i 0.339933i
\(750\) 213.969 + 1122.15i 0.285293 + 1.49620i
\(751\) 95.9204 0.127724 0.0638618 0.997959i \(-0.479658\pi\)
0.0638618 + 0.997959i \(0.479658\pi\)
\(752\) −1080.55 171.143i −1.43690 0.227583i
\(753\) 667.960 + 1310.94i 0.887064 + 1.74096i
\(754\) −66.7501 21.6884i −0.0885280 0.0287645i
\(755\) −232.754 9.76147i −0.308284 0.0129291i
\(756\) 17.2633 + 53.1308i 0.0228350 + 0.0702789i
\(757\) 475.737 + 475.737i 0.628451 + 0.628451i 0.947678 0.319227i \(-0.103423\pi\)
−0.319227 + 0.947678i \(0.603423\pi\)
\(758\) 373.586 + 190.351i 0.492857 + 0.251123i
\(759\) 1436.86 1977.67i 1.89309 2.60562i
\(760\) −28.7161 5.79097i −0.0377843 0.00761970i
\(761\) −491.896 + 357.383i −0.646381 + 0.469623i −0.862036 0.506846i \(-0.830811\pi\)
0.215655 + 0.976470i \(0.430811\pi\)
\(762\) −59.4875 375.589i −0.0780676 0.492899i
\(763\) −144.201 + 22.8393i −0.188993 + 0.0299335i
\(764\) −38.0229 52.3341i −0.0497682 0.0685001i
\(765\) 64.6035 + 141.116i 0.0844490 + 0.184466i
\(766\) −1092.56 793.789i −1.42631 1.03628i
\(767\) −44.7317 + 87.7909i −0.0583203 + 0.114460i
\(768\) −276.441 + 276.441i −0.359949 + 0.359949i
\(769\) 805.996 261.884i 1.04811 0.340551i 0.266183 0.963923i \(-0.414238\pi\)
0.781926 + 0.623371i \(0.214238\pi\)
\(770\) 649.679 + 241.633i 0.843739 + 0.313809i
\(771\) −693.247 + 2133.59i −0.899153 + 2.76731i
\(772\) 126.733 64.5738i 0.164162 0.0836448i
\(773\) 34.6368 218.688i 0.0448083 0.282909i −0.955102 0.296276i \(-0.904255\pi\)
0.999911 + 0.0133675i \(0.00425513\pi\)
\(774\) 287.041i 0.370854i
\(775\) −4.98339 21.2518i −0.00643018 0.0274217i
\(776\) 499.468 0.643644
\(777\) −560.572 88.7859i −0.721457 0.114268i
\(778\) −328.933 645.568i −0.422794 0.829779i
\(779\) 14.7539 + 4.79385i 0.0189396 + 0.00615385i
\(780\) 4.15880 + 14.8967i 0.00533180 + 0.0190983i
\(781\) 126.913 + 390.599i 0.162501 + 0.500127i
\(782\) −100.524 100.524i −0.128547 0.128547i
\(783\) 572.036 + 291.467i 0.730569 + 0.372244i
\(784\) −195.024 + 268.427i −0.248755 + 0.342382i
\(785\) 543.254 + 590.816i 0.692043 + 0.752631i
\(786\) −1721.53 + 1250.77i −2.19025 + 1.59131i
\(787\) 32.8697 + 207.531i 0.0417658 + 0.263699i 0.999731 0.0231849i \(-0.00738066\pi\)
−0.957965 + 0.286884i \(0.907381\pi\)
\(788\) 14.0926 2.23206i 0.0178841 0.00283256i
\(789\) 284.548 + 391.647i 0.360644 + 0.496384i
\(790\) 889.475 + 501.225i 1.12592 + 0.634461i
\(791\) 353.101 + 256.543i 0.446399 + 0.324328i
\(792\) −792.888 + 1556.13i −1.00112 + 1.96481i
\(793\) −93.4500 + 93.4500i −0.117844 + 0.117844i
\(794\) 361.761 117.543i 0.455619 0.148040i
\(795\) 376.220 474.646i 0.473233 0.597039i
\(796\) −22.3517 + 68.7915i −0.0280800 + 0.0864214i
\(797\) 533.202 271.680i 0.669011 0.340878i −0.0862771 0.996271i \(-0.527497\pi\)
0.755288 + 0.655393i \(0.227497\pi\)
\(798\) −5.05403 + 31.9099i −0.00633337 + 0.0399873i
\(799\) 167.437i 0.209558i
\(800\) −109.546 129.644i −0.136933 0.162056i
\(801\) −534.561 −0.667366
\(802\) 624.355 + 98.8880i 0.778497 + 0.123302i
\(803\) −552.869 1085.07i −0.688505 1.35127i
\(804\) −174.684 56.7582i −0.217268 0.0705948i
\(805\) 732.039 486.338i 0.909366 0.604146i
\(806\) 0.765759 + 2.35676i 0.000950073 + 0.00292402i
\(807\) 376.314 + 376.314i 0.466313 + 0.466313i
\(808\) 932.655 + 475.211i 1.15428 + 0.588133i
\(809\) 668.464 920.062i 0.826285 1.13728i −0.162318 0.986738i \(-0.551897\pi\)
0.988603 0.150545i \(-0.0481028\pi\)
\(810\) −4.15802 35.9450i −0.00513335 0.0443766i
\(811\) 193.105 140.299i 0.238108 0.172995i −0.462332 0.886707i \(-0.652987\pi\)
0.700440 + 0.713711i \(0.252987\pi\)
\(812\) 8.32459 + 52.5594i 0.0102520 + 0.0647283i
\(813\) −1340.04 + 212.242i −1.64827 + 0.261060i
\(814\) −375.296 516.551i −0.461052 0.634583i
\(815\) 261.192 30.2139i 0.320481 0.0370723i
\(816\) 119.230 + 86.6256i 0.146115 + 0.106159i
\(817\) −3.35875 + 6.59191i −0.00411107 + 0.00806843i
\(818\) −202.915 + 202.915i −0.248062 + 0.248062i
\(819\) 103.593 33.6593i 0.126487 0.0410981i
\(820\) 26.1272 + 39.3268i 0.0318624 + 0.0479595i
\(821\) 413.541 1272.75i 0.503704 1.55024i −0.299234 0.954180i \(-0.596731\pi\)
0.802938 0.596062i \(-0.203269\pi\)
\(822\) −79.2114 + 40.3602i −0.0963642 + 0.0491000i
\(823\) 100.444 634.180i 0.122046 0.770571i −0.848418 0.529327i \(-0.822445\pi\)
0.970464 0.241244i \(-0.0775554\pi\)
\(824\) 185.376i 0.224971i
\(825\) −1491.85 925.098i −1.80831 1.12133i
\(826\) −626.415 −0.758372
\(827\) 677.919 + 107.372i 0.819732 + 0.129833i 0.552195 0.833715i \(-0.313790\pi\)
0.267537 + 0.963548i \(0.413790\pi\)
\(828\) 96.8034 + 189.987i 0.116912 + 0.229453i
\(829\) 466.331 + 151.520i 0.562522 + 0.182774i 0.576456 0.817129i \(-0.304435\pi\)
−0.0139337 + 0.999903i \(0.504435\pi\)
\(830\) 187.506 + 148.624i 0.225911 + 0.179065i
\(831\) −421.706 1297.88i −0.507468 1.56183i
\(832\) 73.5550 + 73.5550i 0.0884074 + 0.0884074i
\(833\) −45.2454 23.0537i −0.0543162 0.0276755i
\(834\) 887.182 1221.10i 1.06377 1.46415i
\(835\) −435.994 + 773.717i −0.522148 + 0.926607i
\(836\) 3.50669 2.54776i 0.00419461 0.00304756i
\(837\) −3.54600 22.3886i −0.00423656 0.0267486i
\(838\) 481.953 76.3339i 0.575123 0.0910905i
\(839\) 351.074 + 483.211i 0.418443 + 0.575937i 0.965252 0.261320i \(-0.0841578\pi\)
−0.546809 + 0.837257i \(0.684158\pi\)
\(840\) −751.688 + 691.176i −0.894866 + 0.822828i
\(841\) −185.629 134.867i −0.220724 0.160365i
\(842\) 186.989 366.986i 0.222077 0.435850i
\(843\) −1866.32 + 1866.32i −2.21391 + 2.21391i
\(844\) 129.465 42.0658i 0.153395 0.0498410i
\(845\) −803.024 + 224.185i −0.950324 + 0.265308i
\(846\) 650.731 2002.74i 0.769186 2.36731i
\(847\) −404.711 + 206.211i −0.477817 + 0.243460i
\(848\) 55.3221 349.290i 0.0652384 0.411899i
\(849\) 287.594i 0.338745i
\(850\) −66.7090 + 77.2749i −0.0784812 + 0.0909116i
\(851\) −809.553 −0.951296
\(852\) −57.5429 9.11391i −0.0675387 0.0106971i
\(853\) −361.364 709.217i −0.423639 0.831438i −0.999900 0.0141723i \(-0.995489\pi\)
0.576261 0.817266i \(-0.304511\pi\)
\(854\) −799.088 259.639i −0.935700 0.304027i
\(855\) 17.5377 47.1537i 0.0205119 0.0551505i
\(856\) −130.395 401.314i −0.152330 0.468824i
\(857\) 574.113 + 574.113i 0.669910 + 0.669910i 0.957695 0.287785i \(-0.0929188\pi\)
−0.287785 + 0.957695i \(0.592919\pi\)
\(858\) 177.561 + 90.4716i 0.206947 + 0.105445i
\(859\) −478.848 + 659.078i −0.557448 + 0.767262i −0.990999 0.133867i \(-0.957260\pi\)
0.433551 + 0.901129i \(0.357260\pi\)
\(860\) −20.4733 + 9.37275i −0.0238061 + 0.0108985i
\(861\) 437.492 317.856i 0.508121 0.369171i
\(862\) −59.2525 374.106i −0.0687384 0.433997i
\(863\) 813.474 128.842i 0.942611 0.149295i 0.333830 0.942633i \(-0.391659\pi\)
0.608781 + 0.793338i \(0.291659\pi\)
\(864\) −103.601 142.594i −0.119908 0.165039i
\(865\) 92.4148 458.264i 0.106838 0.529785i
\(866\) 729.455 + 529.980i 0.842326 + 0.611986i
\(867\) 624.033 1224.73i 0.719761 1.41261i
\(868\) 1.32855 1.32855i 0.00153059 0.00153059i
\(869\) −1492.08 + 484.806i −1.71701 + 0.557889i
\(870\) −47.3498 + 1129.02i −0.0544251 + 1.29772i
\(871\) −41.3563 + 127.282i −0.0474814 + 0.146133i
\(872\) 215.592 109.850i 0.247239 0.125974i
\(873\) −134.186 + 847.218i −0.153707 + 0.970467i
\(874\) 46.0828i 0.0527263i
\(875\) −386.771 498.704i −0.442024 0.569947i
\(876\) 172.752 0.197206
\(877\) 883.498 + 139.932i 1.00741 + 0.159558i 0.638267 0.769815i \(-0.279652\pi\)
0.369142 + 0.929373i \(0.379652\pi\)
\(878\) 649.695 + 1275.10i 0.739972 + 1.45228i
\(879\) 545.981 + 177.400i 0.621139 + 0.201820i
\(880\) −1024.07 42.9483i −1.16371 0.0488049i
\(881\) −34.0309 104.736i −0.0386276 0.118883i 0.929883 0.367855i \(-0.119908\pi\)
−0.968511 + 0.248971i \(0.919908\pi\)
\(882\) −451.593 451.593i −0.512011 0.512011i
\(883\) −375.623 191.389i −0.425394 0.216749i 0.228169 0.973622i \(-0.426726\pi\)
−0.653562 + 0.756873i \(0.726726\pi\)
\(884\) −0.812389 + 1.11816i −0.000918992 + 0.00126488i
\(885\) 1555.07 + 313.600i 1.75714 + 0.354350i
\(886\) −526.521 + 382.540i −0.594268 + 0.431761i
\(887\) −58.4169 368.830i −0.0658589 0.415817i −0.998488 0.0549791i \(-0.982491\pi\)
0.932629 0.360838i \(-0.117509\pi\)
\(888\) 929.040 147.145i 1.04622 0.165704i
\(889\) 123.484 + 169.961i 0.138902 + 0.191182i
\(890\) −146.362 319.705i −0.164452 0.359219i
\(891\) 44.9834 + 32.6824i 0.0504865 + 0.0366806i
\(892\) −56.3107 + 110.516i −0.0631286 + 0.123897i
\(893\) −38.3787 + 38.3787i −0.0429773 + 0.0429773i
\(894\) 1588.32 516.077i 1.77665 0.577268i
\(895\) 733.318 + 272.741i 0.819350 + 0.304738i
\(896\) −161.994 + 498.566i −0.180797 + 0.556435i
\(897\) 225.132 114.710i 0.250983 0.127882i
\(898\) 119.704 755.779i 0.133300 0.841624i
\(899\) 21.5922i 0.0240180i
\(900\) 130.975 79.3120i 0.145528 0.0881245i
\(901\) 54.1242 0.0600713
\(902\) 600.864 + 95.1675i 0.666146 + 0.105507i
\(903\) 117.081 + 229.785i 0.129658 + 0.254468i
\(904\) −687.940 223.525i −0.760996 0.247263i
\(905\) −341.111 1221.85i −0.376919 1.35011i
\(906\) −131.579 404.960i −0.145231 0.446976i
\(907\) 605.651 + 605.651i 0.667752 + 0.667752i 0.957195 0.289443i \(-0.0934701\pi\)
−0.289443 + 0.957195i \(0.593470\pi\)
\(908\) 26.6010 + 13.5539i 0.0292962 + 0.0149272i
\(909\) −1056.64 + 1454.34i −1.16242 + 1.59993i
\(910\) 48.4942 + 52.7399i 0.0532903 + 0.0579559i
\(911\) −457.690 + 332.532i −0.502404 + 0.365018i −0.809935 0.586520i \(-0.800497\pi\)
0.307530 + 0.951538i \(0.400497\pi\)
\(912\) −7.47334 47.1848i −0.00819445 0.0517377i
\(913\) −363.135 + 57.5149i −0.397738 + 0.0629955i
\(914\) −261.019 359.262i −0.285579 0.393065i
\(915\) 1853.74 + 1044.60i 2.02595 + 1.14163i
\(916\) −111.997 81.3705i −0.122267 0.0888324i
\(917\) 533.706 1047.46i 0.582013 1.14226i
\(918\) −74.9611 + 74.9611i −0.0816570 + 0.0816570i
\(919\) −1251.04 + 406.488i −1.36131 + 0.442315i −0.896479 0.443086i \(-0.853884\pi\)
−0.464827 + 0.885401i \(0.653884\pi\)
\(920\) −904.763 + 1141.46i −0.983438 + 1.24072i
\(921\) 59.1750 182.122i 0.0642508 0.197744i
\(922\) −183.689 + 93.5942i −0.199229 + 0.101512i
\(923\) −6.64075 + 41.9281i −0.00719475 + 0.0454259i
\(924\) 151.095i 0.163523i
\(925\) 42.5452 + 579.776i 0.0459948 + 0.626785i
\(926\) −792.353 −0.855673
\(927\) −314.443 49.8028i −0.339204 0.0537247i
\(928\) −76.2219 149.594i −0.0821357 0.161200i
\(929\) −743.446 241.560i −0.800265 0.260022i −0.119796 0.992799i \(-0.538224\pi\)
−0.680469 + 0.732777i \(0.738224\pi\)
\(930\) 33.2321 22.0781i 0.0357335 0.0237399i
\(931\) 5.08664 + 15.6551i 0.00546363 + 0.0168153i
\(932\) 85.5731 + 85.5731i 0.0918166 + 0.0918166i
\(933\) −1527.97 778.541i −1.63770 0.834449i
\(934\) −81.9788 + 112.834i −0.0877718 + 0.120807i
\(935\) −18.0259 155.829i −0.0192790 0.166662i
\(936\) −146.044 + 106.107i −0.156030 + 0.113362i
\(937\) −144.725 913.755i −0.154455 0.975193i −0.936168 0.351554i \(-0.885654\pi\)
0.781712 0.623639i \(-0.214346\pi\)
\(938\) −840.374 + 133.102i −0.895921 + 0.141900i
\(939\) 719.532 + 990.350i 0.766274 + 1.05469i
\(940\) −164.095 + 18.9820i −0.174569 + 0.0201936i
\(941\) 1236.27 + 898.202i 1.31378 + 0.954518i 0.999987 + 0.00502752i \(0.00160032\pi\)
0.313795 + 0.949491i \(0.398400\pi\)
\(942\) −666.008 + 1307.11i −0.707015 + 1.38759i
\(943\) 545.420 545.420i 0.578388 0.578388i
\(944\) 880.938 286.234i 0.933198 0.303214i
\(945\) −362.665 545.885i −0.383772 0.577657i
\(946\) −89.6534 + 275.925i −0.0947711 + 0.291675i
\(947\) −301.102 + 153.419i −0.317953 + 0.162005i −0.605682 0.795707i \(-0.707100\pi\)
0.287729 + 0.957712i \(0.407100\pi\)
\(948\) 34.8149 219.813i 0.0367246 0.231870i
\(949\) 125.874i 0.132639i
\(950\) 33.0030 2.42183i 0.0347400 0.00254930i
\(951\) 1341.51 1.41063
\(952\) −90.1302 14.2752i −0.0946746 0.0149950i
\(953\) 257.411 + 505.198i 0.270106 + 0.530114i 0.985722 0.168381i \(-0.0538538\pi\)
−0.715616 + 0.698494i \(0.753854\pi\)
\(954\) 647.391 + 210.350i 0.678607 + 0.220493i
\(955\) 594.721 + 471.396i 0.622745 + 0.493608i
\(956\) −21.1823 65.1925i −0.0221572 0.0681930i
\(957\) −1227.83 1227.83i −1.28300 1.28300i
\(958\) −235.990 120.243i −0.246336 0.125514i
\(959\) 28.8684 39.7339i 0.0301026 0.0414327i
\(960\) 822.206 1459.09i 0.856465 1.51989i
\(961\) 776.849 564.414i 0.808375 0.587319i
\(962\) −10.3240 65.1832i −0.0107318 0.0677580i
\(963\) 715.757 113.365i 0.743257 0.117720i
\(964\) −66.6742 91.7691i −0.0691641 0.0951962i
\(965\) −1228.30 + 1129.42i −1.27285 + 1.17038i
\(966\) 1299.59 + 944.208i 1.34533 + 0.977441i
\(967\) −497.530 + 976.458i −0.514509 + 1.00978i 0.476897 + 0.878959i \(0.341762\pi\)
−0.991406 + 0.130822i \(0.958238\pi\)
\(968\) 532.294 532.294i 0.549891 0.549891i
\(969\) 6.95366 2.25938i 0.00717612 0.00233166i
\(970\) −543.436 + 151.715i −0.560243 + 0.156407i
\(971\) 26.3844 81.2029i 0.0271724 0.0836281i −0.936551 0.350532i \(-0.886001\pi\)
0.963723 + 0.266904i \(0.0860007\pi\)
\(972\) −95.7578 + 48.7910i −0.0985162 + 0.0501965i
\(973\) −130.444 + 823.590i −0.134064 + 0.846444i
\(974\) 240.712i 0.247137i
\(975\) −93.9833 155.203i −0.0963932 0.159183i
\(976\) 1242.41 1.27296
\(977\) −599.515 94.9539i −0.613629 0.0971893i −0.158119 0.987420i \(-0.550543\pi\)
−0.455510 + 0.890231i \(0.650543\pi\)
\(978\) 218.182 + 428.206i 0.223090 + 0.437839i
\(979\) 513.858 + 166.963i 0.524881 + 0.170544i
\(980\) −17.4641 + 46.9559i −0.0178206 + 0.0479142i
\(981\) 128.411 + 395.209i 0.130898 + 0.402863i
\(982\) −400.919 400.919i −0.408268 0.408268i
\(983\) −1531.04 780.104i −1.55752 0.793595i −0.558170 0.829727i \(-0.688496\pi\)
−0.999347 + 0.0361319i \(0.988496\pi\)
\(984\) −526.785 + 725.058i −0.535351 + 0.736847i
\(985\) −152.196 + 69.6760i −0.154514 + 0.0707371i
\(986\) −81.6956 + 59.3553i −0.0828556 + 0.0601981i
\(987\) 295.970 + 1868.68i 0.299869 + 1.89330i
\(988\) 0.442507 0.0700862i 0.000447882 7.09375e-5i
\(989\) 216.219 + 297.599i 0.218623 + 0.300909i
\(990\) 390.008 1933.96i 0.393948 1.95350i
\(991\) 374.757 + 272.277i 0.378160 + 0.274749i 0.760587 0.649236i \(-0.224911\pi\)
−0.382426 + 0.923986i \(0.624911\pi\)
\(992\) −2.69119 + 5.28175i −0.00271289 + 0.00532435i
\(993\) 1572.63 1572.63i 1.58372 1.58372i
\(994\) −256.676 + 83.3990i −0.258225 + 0.0839024i
\(995\) 35.5561 847.805i 0.0357347 0.852066i
\(996\) 16.1168 49.6023i 0.0161815 0.0498015i
\(997\) −977.886 + 498.258i −0.980828 + 0.499757i −0.869450 0.494021i \(-0.835527\pi\)
−0.111379 + 0.993778i \(0.535527\pi\)
\(998\) 129.576 818.108i 0.129835 0.819748i
\(999\) 603.688i 0.604292i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 25.3.f.a.2.2 32
3.2 odd 2 225.3.r.a.127.3 32
4.3 odd 2 400.3.bg.c.177.4 32
5.2 odd 4 125.3.f.b.93.3 32
5.3 odd 4 125.3.f.a.93.2 32
5.4 even 2 125.3.f.c.32.3 32
25.9 even 10 125.3.f.b.82.3 32
25.12 odd 20 125.3.f.c.43.3 32
25.13 odd 20 inner 25.3.f.a.13.2 yes 32
25.16 even 5 125.3.f.a.82.2 32
75.38 even 20 225.3.r.a.163.3 32
100.63 even 20 400.3.bg.c.113.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.2.2 32 1.1 even 1 trivial
25.3.f.a.13.2 yes 32 25.13 odd 20 inner
125.3.f.a.82.2 32 25.16 even 5
125.3.f.a.93.2 32 5.3 odd 4
125.3.f.b.82.3 32 25.9 even 10
125.3.f.b.93.3 32 5.2 odd 4
125.3.f.c.32.3 32 5.4 even 2
125.3.f.c.43.3 32 25.12 odd 20
225.3.r.a.127.3 32 3.2 odd 2
225.3.r.a.163.3 32 75.38 even 20
400.3.bg.c.113.4 32 100.63 even 20
400.3.bg.c.177.4 32 4.3 odd 2