Properties

Label 25.3.f.a.13.3
Level $25$
Weight $3$
Character 25.13
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 13.3
Character \(\chi\) \(=\) 25.13
Dual form 25.3.f.a.2.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.287585 - 0.0455490i) q^{2} +(1.72787 - 3.39113i) q^{3} +(-3.72360 + 1.20987i) q^{4} +(2.36408 + 4.40581i) q^{5} +(0.342446 - 1.05394i) q^{6} +(-2.38950 + 2.38950i) q^{7} +(-2.05348 + 1.04630i) q^{8} +(-3.22416 - 4.43767i) q^{9} +O(q^{10})\) \(q+(0.287585 - 0.0455490i) q^{2} +(1.72787 - 3.39113i) q^{3} +(-3.72360 + 1.20987i) q^{4} +(2.36408 + 4.40581i) q^{5} +(0.342446 - 1.05394i) q^{6} +(-2.38950 + 2.38950i) q^{7} +(-2.05348 + 1.04630i) q^{8} +(-3.22416 - 4.43767i) q^{9} +(0.880552 + 1.15936i) q^{10} +(-15.4985 - 11.2603i) q^{11} +(-2.33105 + 14.7177i) q^{12} +(16.2234 + 2.56953i) q^{13} +(-0.578344 + 0.796023i) q^{14} +(19.0255 - 0.404238i) q^{15} +(12.1270 - 8.81080i) q^{16} +(-2.10364 - 4.12863i) q^{17} +(-1.12935 - 1.12935i) q^{18} +(1.02742 + 0.333828i) q^{19} +(-14.1333 - 13.5452i) q^{20} +(3.97436 + 12.2318i) q^{21} +(-4.97001 - 2.53235i) q^{22} +(-1.81434 - 11.4553i) q^{23} +8.77147i q^{24} +(-13.8223 + 20.8313i) q^{25} +4.78263 q^{26} +(13.2122 - 2.09261i) q^{27} +(6.00654 - 11.7885i) q^{28} +(-17.5664 + 5.70767i) q^{29} +(5.45302 - 0.982843i) q^{30} +(-6.76718 + 20.8272i) q^{31} +(9.60482 - 9.60482i) q^{32} +(-64.9643 + 33.1010i) q^{33} +(-0.793031 - 1.09151i) q^{34} +(-16.1766 - 4.87872i) q^{35} +(17.3745 + 12.6233i) q^{36} +(7.13692 - 45.0607i) q^{37} +(0.310675 + 0.0492062i) q^{38} +(36.7454 - 50.5757i) q^{39} +(-9.46437 - 6.57370i) q^{40} +(-13.3733 + 9.71629i) q^{41} +(1.70011 + 3.33666i) q^{42} +(41.9589 + 41.9589i) q^{43} +(71.3335 + 23.1776i) q^{44} +(11.9294 - 24.6960i) q^{45} +(-1.04356 - 3.21173i) q^{46} +(20.1364 + 10.2600i) q^{47} +(-8.92468 - 56.3482i) q^{48} +37.5806i q^{49} +(-3.02624 + 6.62037i) q^{50} -17.6355 q^{51} +(-63.5180 + 10.0603i) q^{52} +(-21.6364 + 42.4637i) q^{53} +(3.70431 - 1.20360i) q^{54} +(12.9711 - 94.9034i) q^{55} +(2.40665 - 7.40691i) q^{56} +(2.90730 - 2.90730i) q^{57} +(-4.79186 + 2.44157i) q^{58} +(-27.2616 - 37.5224i) q^{59} +(-70.3541 + 24.5235i) q^{60} +(45.3825 + 32.9723i) q^{61} +(-0.997479 + 6.29783i) q^{62} +(18.3079 + 2.89969i) q^{63} +(-32.9185 + 45.3084i) q^{64} +(27.0324 + 77.5516i) q^{65} +(-17.1750 + 12.4784i) q^{66} +(2.50707 + 4.92040i) q^{67} +(12.8282 + 12.8282i) q^{68} +(-41.9814 - 13.6406i) q^{69} +(-4.87437 - 0.666216i) q^{70} +(-20.2891 - 62.4433i) q^{71} +(11.2639 + 5.73923i) q^{72} +(-16.1217 - 101.788i) q^{73} -13.2839i q^{74} +(46.7586 + 82.8669i) q^{75} -4.22958 q^{76} +(63.9400 - 10.1271i) q^{77} +(8.26375 - 16.2185i) q^{78} +(-81.7963 + 26.5772i) q^{79} +(67.4879 + 32.6000i) q^{80} +(30.9880 - 95.3712i) q^{81} +(-3.40340 + 3.40340i) q^{82} +(19.1762 - 9.77074i) q^{83} +(-29.5978 - 40.7379i) q^{84} +(13.2168 - 19.0286i) q^{85} +(13.9779 + 10.1556i) q^{86} +(-10.9970 + 69.4320i) q^{87} +(43.6074 + 6.90673i) q^{88} +(52.7361 - 72.5850i) q^{89} +(2.30583 - 7.64557i) q^{90} +(-44.9056 + 32.6258i) q^{91} +(20.6153 + 40.4599i) q^{92} +(58.9350 + 58.9350i) q^{93} +(6.25825 + 2.03343i) q^{94} +(0.958111 + 5.31580i) q^{95} +(-15.9753 - 49.1670i) q^{96} +(-83.7126 - 42.6537i) q^{97} +(1.71176 + 10.8076i) q^{98} +105.082i 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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{19}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.287585 0.0455490i 0.143792 0.0227745i −0.0841233 0.996455i \(-0.526809\pi\)
0.227916 + 0.973681i \(0.426809\pi\)
\(3\) 1.72787 3.39113i 0.575955 1.13038i −0.400829 0.916153i \(-0.631278\pi\)
0.976785 0.214223i \(-0.0687220\pi\)
\(4\) −3.72360 + 1.20987i −0.930899 + 0.302467i
\(5\) 2.36408 + 4.40581i 0.472815 + 0.881162i
\(6\) 0.342446 1.05394i 0.0570743 0.175657i
\(7\) −2.38950 + 2.38950i −0.341357 + 0.341357i −0.856877 0.515520i \(-0.827599\pi\)
0.515520 + 0.856877i \(0.327599\pi\)
\(8\) −2.05348 + 1.04630i −0.256685 + 0.130787i
\(9\) −3.22416 4.43767i −0.358240 0.493075i
\(10\) 0.880552 + 1.15936i 0.0880552 + 0.115936i
\(11\) −15.4985 11.2603i −1.40895 1.02366i −0.993474 0.114058i \(-0.963615\pi\)
−0.415476 0.909604i \(-0.636385\pi\)
\(12\) −2.33105 + 14.7177i −0.194254 + 1.22647i
\(13\) 16.2234 + 2.56953i 1.24795 + 0.197656i 0.745239 0.666798i \(-0.232336\pi\)
0.502712 + 0.864454i \(0.332336\pi\)
\(14\) −0.578344 + 0.796023i −0.0413103 + 0.0568588i
\(15\) 19.0255 0.404238i 1.26836 0.0269492i
\(16\) 12.1270 8.81080i 0.757939 0.550675i
\(17\) −2.10364 4.12863i −0.123744 0.242861i 0.820821 0.571185i \(-0.193516\pi\)
−0.944565 + 0.328324i \(0.893516\pi\)
\(18\) −1.12935 1.12935i −0.0627417 0.0627417i
\(19\) 1.02742 + 0.333828i 0.0540747 + 0.0175699i 0.335929 0.941887i \(-0.390950\pi\)
−0.281855 + 0.959457i \(0.590950\pi\)
\(20\) −14.1333 13.5452i −0.706666 0.677261i
\(21\) 3.97436 + 12.2318i 0.189255 + 0.582468i
\(22\) −4.97001 2.53235i −0.225910 0.115107i
\(23\) −1.81434 11.4553i −0.0788845 0.498057i −0.995221 0.0976482i \(-0.968868\pi\)
0.916336 0.400409i \(-0.131132\pi\)
\(24\) 8.77147i 0.365478i
\(25\) −13.8223 + 20.8313i −0.552892 + 0.833253i
\(26\) 4.78263 0.183947
\(27\) 13.2122 2.09261i 0.489341 0.0775040i
\(28\) 6.00654 11.7885i 0.214519 0.421018i
\(29\) −17.5664 + 5.70767i −0.605738 + 0.196816i −0.595798 0.803134i \(-0.703164\pi\)
−0.00994032 + 0.999951i \(0.503164\pi\)
\(30\) 5.45302 0.982843i 0.181767 0.0327614i
\(31\) −6.76718 + 20.8272i −0.218296 + 0.671846i 0.780607 + 0.625022i \(0.214910\pi\)
−0.998903 + 0.0468241i \(0.985090\pi\)
\(32\) 9.60482 9.60482i 0.300151 0.300151i
\(33\) −64.9643 + 33.1010i −1.96862 + 1.00306i
\(34\) −0.793031 1.09151i −0.0233244 0.0321033i
\(35\) −16.1766 4.87872i −0.462189 0.139392i
\(36\) 17.3745 + 12.6233i 0.482624 + 0.350647i
\(37\) 7.13692 45.0607i 0.192890 1.21786i −0.681201 0.732096i \(-0.738542\pi\)
0.874091 0.485762i \(-0.161458\pi\)
\(38\) 0.310675 + 0.0492062i 0.00817567 + 0.00129490i
\(39\) 36.7454 50.5757i 0.942190 1.29681i
\(40\) −9.46437 6.57370i −0.236609 0.164342i
\(41\) −13.3733 + 9.71629i −0.326179 + 0.236983i −0.738807 0.673917i \(-0.764611\pi\)
0.412629 + 0.910899i \(0.364611\pi\)
\(42\) 1.70011 + 3.33666i 0.0404789 + 0.0794443i
\(43\) 41.9589 + 41.9589i 0.975789 + 0.975789i 0.999714 0.0239244i \(-0.00761609\pi\)
−0.0239244 + 0.999714i \(0.507616\pi\)
\(44\) 71.3335 + 23.1776i 1.62121 + 0.526765i
\(45\) 11.9294 24.6960i 0.265097 0.548801i
\(46\) −1.04356 3.21173i −0.0226860 0.0698203i
\(47\) 20.1364 + 10.2600i 0.428434 + 0.218298i 0.654891 0.755723i \(-0.272714\pi\)
−0.226457 + 0.974021i \(0.572714\pi\)
\(48\) −8.92468 56.3482i −0.185931 1.17392i
\(49\) 37.5806i 0.766951i
\(50\) −3.02624 + 6.62037i −0.0605247 + 0.132407i
\(51\) −17.6355 −0.345795
\(52\) −63.5180 + 10.0603i −1.22150 + 0.193467i
\(53\) −21.6364 + 42.4637i −0.408233 + 0.801203i −0.999988 0.00491533i \(-0.998435\pi\)
0.591755 + 0.806118i \(0.298435\pi\)
\(54\) 3.70431 1.20360i 0.0685984 0.0222890i
\(55\) 12.9711 94.9034i 0.235839 1.72552i
\(56\) 2.40665 7.40691i 0.0429759 0.132266i
\(57\) 2.90730 2.90730i 0.0510052 0.0510052i
\(58\) −4.79186 + 2.44157i −0.0826182 + 0.0420961i
\(59\) −27.2616 37.5224i −0.462062 0.635973i 0.512873 0.858464i \(-0.328581\pi\)
−0.974935 + 0.222491i \(0.928581\pi\)
\(60\) −70.3541 + 24.5235i −1.17257 + 0.408726i
\(61\) 45.3825 + 32.9723i 0.743975 + 0.540529i 0.893953 0.448160i \(-0.147920\pi\)
−0.149979 + 0.988689i \(0.547920\pi\)
\(62\) −0.997479 + 6.29783i −0.0160884 + 0.101578i
\(63\) 18.3079 + 2.89969i 0.290602 + 0.0460269i
\(64\) −32.9185 + 45.3084i −0.514351 + 0.707944i
\(65\) 27.0324 + 77.5516i 0.415883 + 1.19310i
\(66\) −17.1750 + 12.4784i −0.260228 + 0.189067i
\(67\) 2.50707 + 4.92040i 0.0374190 + 0.0734388i 0.908959 0.416885i \(-0.136878\pi\)
−0.871540 + 0.490324i \(0.836878\pi\)
\(68\) 12.8282 + 12.8282i 0.188650 + 0.188650i
\(69\) −41.9814 13.6406i −0.608426 0.197690i
\(70\) −4.87437 0.666216i −0.0696339 0.00951737i
\(71\) −20.2891 62.4433i −0.285761 0.879483i −0.986169 0.165740i \(-0.946999\pi\)
0.700408 0.713743i \(-0.253001\pi\)
\(72\) 11.2639 + 5.73923i 0.156443 + 0.0797115i
\(73\) −16.1217 101.788i −0.220845 1.39436i −0.810044 0.586370i \(-0.800557\pi\)
0.589199 0.807988i \(-0.299443\pi\)
\(74\) 13.2839i 0.179512i
\(75\) 46.7586 + 82.8669i 0.623449 + 1.10489i
\(76\) −4.22958 −0.0556524
\(77\) 63.9400 10.1271i 0.830389 0.131521i
\(78\) 8.26375 16.2185i 0.105945 0.207930i
\(79\) −81.7963 + 26.5772i −1.03540 + 0.336421i −0.776922 0.629597i \(-0.783220\pi\)
−0.258475 + 0.966018i \(0.583220\pi\)
\(80\) 67.4879 + 32.6000i 0.843599 + 0.407499i
\(81\) 30.9880 95.3712i 0.382568 1.17742i
\(82\) −3.40340 + 3.40340i −0.0415048 + 0.0415048i
\(83\) 19.1762 9.77074i 0.231038 0.117720i −0.334640 0.942346i \(-0.608615\pi\)
0.565678 + 0.824626i \(0.308615\pi\)
\(84\) −29.5978 40.7379i −0.352355 0.484975i
\(85\) 13.2168 19.0286i 0.155492 0.223866i
\(86\) 13.9779 + 10.1556i 0.162534 + 0.118088i
\(87\) −10.9970 + 69.4320i −0.126402 + 0.798070i
\(88\) 43.6074 + 6.90673i 0.495538 + 0.0784855i
\(89\) 52.7361 72.5850i 0.592541 0.815562i −0.402459 0.915438i \(-0.631844\pi\)
0.995000 + 0.0998756i \(0.0318445\pi\)
\(90\) 2.30583 7.64557i 0.0256204 0.0849508i
\(91\) −44.9056 + 32.6258i −0.493468 + 0.358525i
\(92\) 20.6153 + 40.4599i 0.224080 + 0.439781i
\(93\) 58.9350 + 58.9350i 0.633710 + 0.633710i
\(94\) 6.25825 + 2.03343i 0.0665772 + 0.0216322i
\(95\) 0.958111 + 5.31580i 0.0100854 + 0.0559558i
\(96\) −15.9753 49.1670i −0.166410 0.512156i
\(97\) −83.7126 42.6537i −0.863017 0.439729i −0.0343096 0.999411i \(-0.510923\pi\)
−0.828707 + 0.559682i \(0.810923\pi\)
\(98\) 1.71176 + 10.8076i 0.0174669 + 0.110282i
\(99\) 105.082i 1.06143i
\(100\) 26.2654 94.2906i 0.262654 0.942906i
\(101\) 14.4367 0.142938 0.0714690 0.997443i \(-0.477231\pi\)
0.0714690 + 0.997443i \(0.477231\pi\)
\(102\) −5.07171 + 0.803280i −0.0497227 + 0.00787530i
\(103\) 39.3351 77.1995i 0.381894 0.749510i −0.617416 0.786637i \(-0.711821\pi\)
0.999311 + 0.0371269i \(0.0118206\pi\)
\(104\) −36.0028 + 11.6980i −0.346181 + 0.112481i
\(105\) −44.4954 + 46.4272i −0.423766 + 0.442164i
\(106\) −4.28811 + 13.1974i −0.0404539 + 0.124504i
\(107\) −120.842 + 120.842i −1.12937 + 1.12937i −0.139087 + 0.990280i \(0.544417\pi\)
−0.990280 + 0.139087i \(0.955583\pi\)
\(108\) −46.6651 + 23.7771i −0.432085 + 0.220158i
\(109\) 19.5764 + 26.9446i 0.179600 + 0.247198i 0.889320 0.457286i \(-0.151178\pi\)
−0.709720 + 0.704484i \(0.751178\pi\)
\(110\) −0.592449 27.8836i −0.00538590 0.253487i
\(111\) −140.475 102.061i −1.26554 0.919470i
\(112\) −7.92412 + 50.0309i −0.0707510 + 0.446705i
\(113\) −25.8428 4.09310i −0.228697 0.0362221i 0.0410338 0.999158i \(-0.486935\pi\)
−0.269731 + 0.962936i \(0.586935\pi\)
\(114\) 0.703670 0.968519i 0.00617254 0.00849578i
\(115\) 46.1807 35.0749i 0.401571 0.304999i
\(116\) 58.5047 42.5061i 0.504351 0.366432i
\(117\) −40.9040 80.2786i −0.349607 0.686142i
\(118\) −9.54914 9.54914i −0.0809249 0.0809249i
\(119\) 14.8920 + 4.83871i 0.125143 + 0.0406614i
\(120\) −38.6454 + 20.7364i −0.322045 + 0.172803i
\(121\) 76.0170 + 233.956i 0.628240 + 1.93352i
\(122\) 14.5532 + 7.41521i 0.119288 + 0.0607804i
\(123\) 9.84186 + 62.1391i 0.0800151 + 0.505196i
\(124\) 85.7396i 0.691448i
\(125\) −124.456 11.6515i −0.995646 0.0932121i
\(126\) 5.39716 0.0428346
\(127\) 73.7930 11.6877i 0.581047 0.0920289i 0.141010 0.990008i \(-0.454965\pi\)
0.440038 + 0.897979i \(0.354965\pi\)
\(128\) −32.0698 + 62.9405i −0.250545 + 0.491723i
\(129\) 214.788 69.7887i 1.66502 0.540998i
\(130\) 11.3065 + 21.0714i 0.0869731 + 0.162087i
\(131\) −25.0313 + 77.0383i −0.191078 + 0.588078i 0.808922 + 0.587916i \(0.200052\pi\)
−1.00000 0.000162070i \(0.999948\pi\)
\(132\) 201.853 201.853i 1.52919 1.52919i
\(133\) −3.25270 + 1.65733i −0.0244564 + 0.0124611i
\(134\) 0.945114 + 1.30084i 0.00705309 + 0.00970775i
\(135\) 40.4543 + 53.2634i 0.299661 + 0.394544i
\(136\) 8.63957 + 6.27701i 0.0635262 + 0.0461545i
\(137\) 24.7567 156.308i 0.180706 1.14093i −0.715932 0.698170i \(-0.753998\pi\)
0.896638 0.442763i \(-0.146002\pi\)
\(138\) −12.6945 2.01062i −0.0919893 0.0145697i
\(139\) −92.2598 + 126.985i −0.663739 + 0.913559i −0.999598 0.0283536i \(-0.990974\pi\)
0.335859 + 0.941912i \(0.390974\pi\)
\(140\) 66.1378 1.40524i 0.472413 0.0100375i
\(141\) 69.5860 50.5572i 0.493518 0.358561i
\(142\) −8.67905 17.0336i −0.0611201 0.119955i
\(143\) −222.503 222.503i −1.55597 1.55597i
\(144\) −78.1989 25.4084i −0.543048 0.176447i
\(145\) −66.6753 63.9009i −0.459829 0.440696i
\(146\) −9.27269 28.5384i −0.0635115 0.195468i
\(147\) 127.441 + 64.9342i 0.866943 + 0.441729i
\(148\) 27.9426 + 176.423i 0.188801 + 1.19205i
\(149\) 87.4028i 0.586596i −0.956021 0.293298i \(-0.905247\pi\)
0.956021 0.293298i \(-0.0947529\pi\)
\(150\) 17.2216 + 21.7015i 0.114811 + 0.144676i
\(151\) 172.239 1.14066 0.570328 0.821417i \(-0.306816\pi\)
0.570328 + 0.821417i \(0.306816\pi\)
\(152\) −2.45906 + 0.389478i −0.0161781 + 0.00256235i
\(153\) −11.5390 + 22.6467i −0.0754186 + 0.148017i
\(154\) 17.9269 5.82480i 0.116408 0.0378234i
\(155\) −107.759 + 19.4223i −0.695219 + 0.125305i
\(156\) −75.6350 + 232.781i −0.484840 + 1.49218i
\(157\) −53.0884 + 53.0884i −0.338143 + 0.338143i −0.855668 0.517525i \(-0.826853\pi\)
0.517525 + 0.855668i \(0.326853\pi\)
\(158\) −22.3128 + 11.3689i −0.141220 + 0.0719553i
\(159\) 106.615 + 146.743i 0.670536 + 0.922914i
\(160\) 65.0235 + 19.6105i 0.406397 + 0.122565i
\(161\) 31.7078 + 23.0371i 0.196943 + 0.143088i
\(162\) 4.56762 28.8388i 0.0281952 0.178017i
\(163\) 1.91719 + 0.303653i 0.0117619 + 0.00186290i 0.162313 0.986739i \(-0.448105\pi\)
−0.150551 + 0.988602i \(0.548105\pi\)
\(164\) 38.0414 52.3595i 0.231960 0.319265i
\(165\) −299.417 207.967i −1.81465 1.26041i
\(166\) 5.06973 3.68337i 0.0305405 0.0221890i
\(167\) −5.17831 10.1630i −0.0310078 0.0608563i 0.874983 0.484154i \(-0.160872\pi\)
−0.905991 + 0.423298i \(0.860872\pi\)
\(168\) −20.9594 20.9594i −0.124758 0.124758i
\(169\) 95.8665 + 31.1489i 0.567257 + 0.184313i
\(170\) 2.93421 6.07436i 0.0172601 0.0357315i
\(171\) −1.83114 5.63567i −0.0107084 0.0329571i
\(172\) −207.003 105.473i −1.20351 0.613217i
\(173\) 31.2522 + 197.319i 0.180649 + 1.14057i 0.896738 + 0.442562i \(0.145930\pi\)
−0.716089 + 0.698009i \(0.754070\pi\)
\(174\) 20.4685i 0.117635i
\(175\) −16.7481 82.8048i −0.0957034 0.473170i
\(176\) −287.162 −1.63160
\(177\) −174.348 + 27.6140i −0.985016 + 0.156011i
\(178\) 11.8599 23.2764i 0.0666288 0.130766i
\(179\) −51.8588 + 16.8499i −0.289714 + 0.0941338i −0.450269 0.892893i \(-0.648672\pi\)
0.160555 + 0.987027i \(0.448672\pi\)
\(180\) −14.5412 + 106.391i −0.0807846 + 0.591061i
\(181\) 42.0315 129.360i 0.232218 0.714694i −0.765260 0.643721i \(-0.777390\pi\)
0.997478 0.0709726i \(-0.0226103\pi\)
\(182\) −11.4281 + 11.4281i −0.0627917 + 0.0627917i
\(183\) 190.228 96.9260i 1.03950 0.529650i
\(184\) 15.7114 + 21.6249i 0.0853881 + 0.117527i
\(185\) 215.401 75.0831i 1.16433 0.405855i
\(186\) 19.6332 + 14.2644i 0.105555 + 0.0766903i
\(187\) −13.8864 + 87.6750i −0.0742586 + 0.468850i
\(188\) −87.3931 13.8417i −0.464857 0.0736261i
\(189\) −26.5703 + 36.5708i −0.140583 + 0.193496i
\(190\) 0.517668 + 1.48510i 0.00272457 + 0.00781634i
\(191\) 73.9512 53.7287i 0.387179 0.281302i −0.377119 0.926165i \(-0.623085\pi\)
0.764299 + 0.644863i \(0.223085\pi\)
\(192\) 96.7679 + 189.918i 0.503999 + 0.989155i
\(193\) 62.2572 + 62.2572i 0.322576 + 0.322576i 0.849755 0.527178i \(-0.176750\pi\)
−0.527178 + 0.849755i \(0.676750\pi\)
\(194\) −26.0173 8.45354i −0.134110 0.0435749i
\(195\) 309.696 + 42.3284i 1.58818 + 0.217069i
\(196\) −45.4676 139.935i −0.231978 0.713954i
\(197\) 232.265 + 118.345i 1.17901 + 0.600736i 0.929926 0.367746i \(-0.119870\pi\)
0.249084 + 0.968482i \(0.419870\pi\)
\(198\) 4.78638 + 30.2200i 0.0241736 + 0.152626i
\(199\) 198.360i 0.996782i −0.866952 0.498391i \(-0.833924\pi\)
0.866952 0.498391i \(-0.166076\pi\)
\(200\) 6.58796 57.2389i 0.0329398 0.286195i
\(201\) 21.0176 0.104565
\(202\) 4.15178 0.657578i 0.0205534 0.00325534i
\(203\) 28.3364 55.6134i 0.139588 0.273958i
\(204\) 65.6676 21.3367i 0.321900 0.104592i
\(205\) −74.4236 35.9502i −0.363042 0.175367i
\(206\) 7.79582 23.9931i 0.0378438 0.116471i
\(207\) −44.9853 + 44.9853i −0.217320 + 0.217320i
\(208\) 219.381 111.780i 1.05472 0.537404i
\(209\) −12.1644 16.7429i −0.0582028 0.0801093i
\(210\) −10.6815 + 15.3785i −0.0508642 + 0.0732309i
\(211\) −32.1898 23.3872i −0.152558 0.110840i 0.508888 0.860833i \(-0.330057\pi\)
−0.661446 + 0.749993i \(0.730057\pi\)
\(212\) 29.1895 184.295i 0.137686 0.869316i
\(213\) −246.810 39.0909i −1.15873 0.183525i
\(214\) −29.2482 + 40.2566i −0.136674 + 0.188115i
\(215\) −85.6689 + 284.057i −0.398460 + 1.32120i
\(216\) −24.9415 + 18.1210i −0.115470 + 0.0838937i
\(217\) −33.5965 65.9368i −0.154822 0.303856i
\(218\) 6.85717 + 6.85717i 0.0314549 + 0.0314549i
\(219\) −373.033 121.206i −1.70334 0.553450i
\(220\) 66.5215 + 369.075i 0.302370 + 1.67761i
\(221\) −23.5195 72.3857i −0.106423 0.327537i
\(222\) −45.0473 22.9527i −0.202916 0.103391i
\(223\) −10.9708 69.2671i −0.0491966 0.310615i −1.00000 0.000819017i \(-0.999739\pi\)
0.950803 0.309796i \(-0.100261\pi\)
\(224\) 45.9014i 0.204917i
\(225\) 137.008 5.82470i 0.608924 0.0258876i
\(226\) −7.61844 −0.0337099
\(227\) −46.0077 + 7.28690i −0.202677 + 0.0321009i −0.256947 0.966425i \(-0.582717\pi\)
0.0542703 + 0.998526i \(0.482717\pi\)
\(228\) −7.30815 + 14.3430i −0.0320533 + 0.0629081i
\(229\) −17.5687 + 5.70843i −0.0767194 + 0.0249276i −0.347125 0.937819i \(-0.612842\pi\)
0.270406 + 0.962746i \(0.412842\pi\)
\(230\) 11.6832 12.1905i 0.0507967 0.0530021i
\(231\) 76.1374 234.327i 0.329599 1.01440i
\(232\) 30.1003 30.1003i 0.129743 0.129743i
\(233\) 364.992 185.972i 1.56649 0.798165i 0.566817 0.823844i \(-0.308175\pi\)
0.999670 + 0.0256786i \(0.00817466\pi\)
\(234\) −15.4200 21.2238i −0.0658973 0.0906999i
\(235\) 2.40035 + 112.973i 0.0102143 + 0.480734i
\(236\) 146.909 + 106.735i 0.622494 + 0.452268i
\(237\) −51.2063 + 323.304i −0.216060 + 1.36415i
\(238\) 4.50311 + 0.713223i 0.0189206 + 0.00299674i
\(239\) −241.175 + 331.949i −1.00910 + 1.38891i −0.0895301 + 0.995984i \(0.528537\pi\)
−0.919571 + 0.392924i \(0.871463\pi\)
\(240\) 227.161 172.532i 0.946503 0.718882i
\(241\) −284.923 + 207.009i −1.18225 + 0.858958i −0.992424 0.122859i \(-0.960794\pi\)
−0.189830 + 0.981817i \(0.560794\pi\)
\(242\) 32.5178 + 63.8198i 0.134371 + 0.263718i
\(243\) −184.743 184.743i −0.760259 0.760259i
\(244\) −208.878 67.8686i −0.856058 0.278150i
\(245\) −165.573 + 88.8434i −0.675808 + 0.362626i
\(246\) 5.66074 + 17.4220i 0.0230111 + 0.0708210i
\(247\) 15.8104 + 8.05580i 0.0640097 + 0.0326146i
\(248\) −7.89526 49.8487i −0.0318357 0.201003i
\(249\) 81.9114i 0.328961i
\(250\) −36.3223 + 2.31803i −0.145289 + 0.00927214i
\(251\) 99.8650 0.397869 0.198934 0.980013i \(-0.436252\pi\)
0.198934 + 0.980013i \(0.436252\pi\)
\(252\) −71.6796 + 11.3529i −0.284443 + 0.0450513i
\(253\) −100.871 + 197.970i −0.398698 + 0.782489i
\(254\) 20.6894 6.72239i 0.0814543 0.0264661i
\(255\) −41.6917 77.6988i −0.163497 0.304701i
\(256\) 62.8692 193.491i 0.245583 0.755826i
\(257\) −138.476 + 138.476i −0.538818 + 0.538818i −0.923182 0.384363i \(-0.874421\pi\)
0.384363 + 0.923182i \(0.374421\pi\)
\(258\) 58.5908 29.8535i 0.227096 0.115711i
\(259\) 90.6189 + 124.726i 0.349880 + 0.481568i
\(260\) −194.485 256.065i −0.748020 0.984866i
\(261\) 81.9657 + 59.5516i 0.314045 + 0.228167i
\(262\) −3.68959 + 23.2952i −0.0140824 + 0.0889129i
\(263\) 208.637 + 33.0448i 0.793296 + 0.125646i 0.539914 0.841720i \(-0.318457\pi\)
0.253382 + 0.967366i \(0.418457\pi\)
\(264\) 98.7692 135.944i 0.374126 0.514940i
\(265\) −238.237 + 5.06187i −0.899008 + 0.0191014i
\(266\) −0.859937 + 0.624781i −0.00323284 + 0.00234880i
\(267\) −155.024 304.252i −0.580615 1.13952i
\(268\) −15.2884 15.2884i −0.0570461 0.0570461i
\(269\) 326.227 + 105.998i 1.21274 + 0.394043i 0.844433 0.535661i \(-0.179938\pi\)
0.368307 + 0.929704i \(0.379938\pi\)
\(270\) 14.0601 + 13.4751i 0.0520746 + 0.0499077i
\(271\) −71.5216 220.121i −0.263918 0.812255i −0.991941 0.126702i \(-0.959561\pi\)
0.728023 0.685552i \(-0.240439\pi\)
\(272\) −61.8875 31.5333i −0.227528 0.115931i
\(273\) 33.0475 + 208.654i 0.121053 + 0.764299i
\(274\) 46.0794i 0.168173i
\(275\) 448.791 167.210i 1.63197 0.608038i
\(276\) 172.825 0.626178
\(277\) 395.109 62.5791i 1.42639 0.225917i 0.604971 0.796247i \(-0.293185\pi\)
0.821416 + 0.570330i \(0.193185\pi\)
\(278\) −20.7485 + 40.7212i −0.0746348 + 0.146479i
\(279\) 114.243 37.1198i 0.409473 0.133046i
\(280\) 38.3229 6.90726i 0.136868 0.0246688i
\(281\) −41.2543 + 126.968i −0.146813 + 0.451843i −0.997240 0.0742504i \(-0.976344\pi\)
0.850427 + 0.526093i \(0.176344\pi\)
\(282\) 17.7090 17.7090i 0.0627980 0.0627980i
\(283\) −222.492 + 113.365i −0.786190 + 0.400584i −0.800515 0.599313i \(-0.795440\pi\)
0.0143241 + 0.999897i \(0.495440\pi\)
\(284\) 151.096 + 207.966i 0.532030 + 0.732276i
\(285\) 19.6821 + 5.93592i 0.0690599 + 0.0208278i
\(286\) −74.1234 53.8538i −0.259173 0.188300i
\(287\) 8.73848 55.1726i 0.0304477 0.192239i
\(288\) −73.5905 11.6556i −0.255523 0.0404708i
\(289\) 157.250 216.436i 0.544116 0.748912i
\(290\) −22.0854 15.3399i −0.0761566 0.0528963i
\(291\) −289.288 + 210.180i −0.994118 + 0.722269i
\(292\) 183.181 + 359.513i 0.627332 + 1.23121i
\(293\) 279.769 + 279.769i 0.954844 + 0.954844i 0.999024 0.0441800i \(-0.0140675\pi\)
−0.0441800 + 0.999024i \(0.514068\pi\)
\(294\) 39.6077 + 12.8693i 0.134720 + 0.0437732i
\(295\) 100.868 208.815i 0.341925 0.707849i
\(296\) 32.4915 + 99.9986i 0.109769 + 0.337833i
\(297\) −228.332 116.341i −0.768795 0.391721i
\(298\) −3.98111 25.1357i −0.0133594 0.0843481i
\(299\) 190.506i 0.637143i
\(300\) −274.368 251.991i −0.914561 0.839970i
\(301\) −200.522 −0.666185
\(302\) 49.5333 7.84531i 0.164018 0.0259779i
\(303\) 24.9447 48.9568i 0.0823258 0.161574i
\(304\) 15.4008 5.00403i 0.0506606 0.0164606i
\(305\) −37.9820 + 277.895i −0.124531 + 0.911133i
\(306\) −2.28692 + 7.03842i −0.00747360 + 0.0230014i
\(307\) 292.963 292.963i 0.954277 0.954277i −0.0447226 0.998999i \(-0.514240\pi\)
0.998999 + 0.0447226i \(0.0142404\pi\)
\(308\) −225.834 + 115.068i −0.733228 + 0.373598i
\(309\) −193.828 266.781i −0.627274 0.863368i
\(310\) −30.1052 + 10.4939i −0.0971134 + 0.0338511i
\(311\) −56.9351 41.3658i −0.183071 0.133009i 0.492475 0.870326i \(-0.336092\pi\)
−0.675546 + 0.737318i \(0.736092\pi\)
\(312\) −22.5385 + 142.303i −0.0722389 + 0.456098i
\(313\) −551.569 87.3599i −1.76220 0.279105i −0.810412 0.585860i \(-0.800757\pi\)
−0.951788 + 0.306755i \(0.900757\pi\)
\(314\) −12.8493 + 17.6855i −0.0409213 + 0.0563234i
\(315\) 30.5059 + 87.5164i 0.0968440 + 0.277830i
\(316\) 272.421 197.926i 0.862093 0.626347i
\(317\) −283.718 556.827i −0.895008 1.75655i −0.597581 0.801808i \(-0.703871\pi\)
−0.297427 0.954744i \(-0.596129\pi\)
\(318\) 37.3449 + 37.3449i 0.117437 + 0.117437i
\(319\) 336.522 + 109.343i 1.05493 + 0.342767i
\(320\) −277.442 37.9200i −0.867006 0.118500i
\(321\) 200.992 + 618.591i 0.626144 + 1.92707i
\(322\) 10.1680 + 5.18086i 0.0315777 + 0.0160896i
\(323\) −0.783067 4.94409i −0.00242436 0.0153068i
\(324\) 392.615i 1.21178i
\(325\) −277.771 + 302.437i −0.854679 + 0.930577i
\(326\) 0.565186 0.00173370
\(327\) 125.198 19.8294i 0.382868 0.0606403i
\(328\) 17.2957 33.9447i 0.0527307 0.103490i
\(329\) −72.6321 + 23.5996i −0.220766 + 0.0717314i
\(330\) −95.5805 46.1700i −0.289638 0.139909i
\(331\) −98.3145 + 302.581i −0.297023 + 0.914142i 0.685512 + 0.728062i \(0.259579\pi\)
−0.982535 + 0.186080i \(0.940421\pi\)
\(332\) −59.5830 + 59.5830i −0.179467 + 0.179467i
\(333\) −222.975 + 113.612i −0.669596 + 0.341176i
\(334\) −1.95212 2.68686i −0.00584466 0.00804448i
\(335\) −15.7514 + 22.6779i −0.0470192 + 0.0676951i
\(336\) 155.969 + 113.318i 0.464195 + 0.337257i
\(337\) 52.4267 331.009i 0.155569 0.982223i −0.779151 0.626837i \(-0.784349\pi\)
0.934719 0.355387i \(-0.115651\pi\)
\(338\) 28.9885 + 4.59133i 0.0857649 + 0.0135838i
\(339\) −58.5331 + 80.5640i −0.172664 + 0.237652i
\(340\) −26.1918 + 86.8456i −0.0770347 + 0.255428i
\(341\) 339.401 246.590i 0.995312 0.723136i
\(342\) −0.783306 1.53733i −0.00229037 0.00449510i
\(343\) −206.884 206.884i −0.603161 0.603161i
\(344\) −130.063 42.2601i −0.378091 0.122849i
\(345\) −39.1494 217.209i −0.113477 0.629592i
\(346\) 17.9753 + 55.3224i 0.0519518 + 0.159891i
\(347\) 368.200 + 187.607i 1.06110 + 0.540655i 0.895281 0.445501i \(-0.146975\pi\)
0.165815 + 0.986157i \(0.446975\pi\)
\(348\) −43.0555 271.842i −0.123723 0.781154i
\(349\) 234.141i 0.670891i 0.942060 + 0.335445i \(0.108887\pi\)
−0.942060 + 0.335445i \(0.891113\pi\)
\(350\) −8.58817 23.0505i −0.0245376 0.0658587i
\(351\) 219.723 0.625993
\(352\) −257.013 + 40.7069i −0.730150 + 0.115644i
\(353\) 93.3076 183.126i 0.264327 0.518772i −0.720251 0.693713i \(-0.755974\pi\)
0.984579 + 0.174941i \(0.0559736\pi\)
\(354\) −48.8820 + 15.8827i −0.138085 + 0.0448664i
\(355\) 227.148 237.010i 0.639854 0.667635i
\(356\) −108.550 + 334.081i −0.304914 + 0.938430i
\(357\) 42.1401 42.1401i 0.118039 0.118039i
\(358\) −14.1463 + 7.20790i −0.0395148 + 0.0201338i
\(359\) −203.218 279.706i −0.566068 0.779126i 0.426014 0.904717i \(-0.359917\pi\)
−0.992082 + 0.125591i \(0.959917\pi\)
\(360\) 1.34271 + 63.1944i 0.00372974 + 0.175540i
\(361\) −291.111 211.505i −0.806402 0.585885i
\(362\) 6.19542 39.1163i 0.0171144 0.108056i
\(363\) 924.723 + 146.462i 2.54745 + 0.403476i
\(364\) 127.737 175.815i 0.350927 0.483009i
\(365\) 410.346 311.664i 1.12424 0.853873i
\(366\) 50.2918 36.5391i 0.137409 0.0998337i
\(367\) 241.897 + 474.749i 0.659119 + 1.29359i 0.942378 + 0.334551i \(0.108585\pi\)
−0.283258 + 0.959044i \(0.591415\pi\)
\(368\) −122.933 122.933i −0.334058 0.334058i
\(369\) 86.2354 + 28.0196i 0.233700 + 0.0759338i
\(370\) 58.5262 31.4041i 0.158179 0.0848759i
\(371\) −49.7670 153.167i −0.134143 0.412849i
\(372\) −290.754 148.146i −0.781596 0.398243i
\(373\) −9.51134 60.0522i −0.0254996 0.160998i 0.971653 0.236413i \(-0.0759718\pi\)
−0.997152 + 0.0754151i \(0.975972\pi\)
\(374\) 25.8465i 0.0691083i
\(375\) −254.555 + 401.913i −0.678812 + 1.07177i
\(376\) −52.0847 −0.138523
\(377\) −299.652 + 47.4603i −0.794834 + 0.125889i
\(378\) −5.97544 + 11.7275i −0.0158080 + 0.0310250i
\(379\) 185.112 60.1464i 0.488421 0.158698i −0.0544453 0.998517i \(-0.517339\pi\)
0.542866 + 0.839819i \(0.317339\pi\)
\(380\) −9.99905 18.6347i −0.0263133 0.0490387i
\(381\) 87.8701 270.436i 0.230630 0.709807i
\(382\) 18.8200 18.8200i 0.0492669 0.0492669i
\(383\) −446.637 + 227.573i −1.16615 + 0.594186i −0.926361 0.376638i \(-0.877080\pi\)
−0.239794 + 0.970824i \(0.577080\pi\)
\(384\) 158.027 + 217.506i 0.411529 + 0.566421i
\(385\) 195.777 + 257.766i 0.508512 + 0.669522i
\(386\) 20.7400 + 15.0685i 0.0537305 + 0.0390375i
\(387\) 50.9178 321.482i 0.131571 0.830704i
\(388\) 363.317 + 57.5438i 0.936385 + 0.148309i
\(389\) 96.3944 132.676i 0.247801 0.341068i −0.666939 0.745112i \(-0.732396\pi\)
0.914739 + 0.404044i \(0.132396\pi\)
\(390\) 90.9918 1.93332i 0.233312 0.00495724i
\(391\) −43.4781 + 31.5887i −0.111197 + 0.0807894i
\(392\) −39.3205 77.1709i −0.100307 0.196865i
\(393\) 217.996 + 217.996i 0.554697 + 0.554697i
\(394\) 72.1864 + 23.4548i 0.183214 + 0.0595299i
\(395\) −310.467 297.548i −0.785992 0.753287i
\(396\) −127.136 391.283i −0.321049 0.988089i
\(397\) 306.180 + 156.006i 0.771234 + 0.392963i 0.794887 0.606757i \(-0.207530\pi\)
−0.0236537 + 0.999720i \(0.507530\pi\)
\(398\) −9.03507 57.0452i −0.0227012 0.143330i
\(399\) 13.8940i 0.0348220i
\(400\) 15.9174 + 374.408i 0.0397936 + 0.936019i
\(401\) −355.216 −0.885825 −0.442912 0.896565i \(-0.646055\pi\)
−0.442912 + 0.896565i \(0.646055\pi\)
\(402\) 6.04434 0.957329i 0.0150357 0.00238142i
\(403\) −163.303 + 320.499i −0.405217 + 0.795283i
\(404\) −53.7565 + 17.4666i −0.133061 + 0.0432341i
\(405\) 493.445 88.9377i 1.21838 0.219599i
\(406\) 5.61600 17.2843i 0.0138325 0.0425721i
\(407\) −618.008 + 618.008i −1.51845 + 1.51845i
\(408\) 36.2142 18.4520i 0.0887602 0.0452256i
\(409\) −221.160 304.400i −0.540733 0.744255i 0.447986 0.894041i \(-0.352142\pi\)
−0.988718 + 0.149786i \(0.952142\pi\)
\(410\) −23.0406 6.94882i −0.0561966 0.0169484i
\(411\) −487.283 354.032i −1.18560 0.861392i
\(412\) −53.0667 + 335.050i −0.128803 + 0.813228i
\(413\) 154.801 + 24.5181i 0.374822 + 0.0593659i
\(414\) −10.8880 + 14.9861i −0.0262996 + 0.0361983i
\(415\) 88.3819 + 61.3877i 0.212969 + 0.147922i
\(416\) 180.502 131.143i 0.433900 0.315247i
\(417\) 271.209 + 532.277i 0.650381 + 1.27644i
\(418\) −4.26091 4.26091i −0.0101936 0.0101936i
\(419\) −581.123 188.818i −1.38693 0.450640i −0.481987 0.876178i \(-0.660085\pi\)
−0.904941 + 0.425538i \(0.860085\pi\)
\(420\) 109.512 226.710i 0.260743 0.539785i
\(421\) −63.7783 196.289i −0.151492 0.466245i 0.846296 0.532712i \(-0.178827\pi\)
−0.997789 + 0.0664671i \(0.978827\pi\)
\(422\) −10.3226 5.25960i −0.0244610 0.0124635i
\(423\) −19.3924 122.439i −0.0458449 0.289453i
\(424\) 109.836i 0.259048i
\(425\) 115.082 + 13.2455i 0.270781 + 0.0311658i
\(426\) −72.7593 −0.170797
\(427\) −187.229 + 29.6541i −0.438474 + 0.0694475i
\(428\) 303.764 596.171i 0.709730 1.39292i
\(429\) −1138.99 + 370.081i −2.65500 + 0.862661i
\(430\) −11.6986 + 85.5927i −0.0272060 + 0.199053i
\(431\) −75.3165 + 231.800i −0.174748 + 0.537820i −0.999622 0.0274974i \(-0.991246\pi\)
0.824874 + 0.565317i \(0.191246\pi\)
\(432\) 141.787 141.787i 0.328211 0.328211i
\(433\) −347.221 + 176.918i −0.801896 + 0.408586i −0.806376 0.591404i \(-0.798574\pi\)
0.00447992 + 0.999990i \(0.498574\pi\)
\(434\) −12.6652 17.4321i −0.0291825 0.0401662i
\(435\) −331.902 + 115.692i −0.762993 + 0.265959i
\(436\) −105.494 76.6458i −0.241959 0.175793i
\(437\) 1.96002 12.3751i 0.00448517 0.0283183i
\(438\) −112.799 17.8657i −0.257533 0.0407892i
\(439\) 213.132 293.351i 0.485494 0.668225i −0.494055 0.869430i \(-0.664486\pi\)
0.979549 + 0.201206i \(0.0644860\pi\)
\(440\) 72.6614 + 208.454i 0.165140 + 0.473758i
\(441\) 166.770 121.166i 0.378164 0.274752i
\(442\) −10.0610 19.7457i −0.0227623 0.0446736i
\(443\) 464.820 + 464.820i 1.04926 + 1.04926i 0.998722 + 0.0505328i \(0.0160920\pi\)
0.0505328 + 0.998722i \(0.483908\pi\)
\(444\) 646.553 + 210.078i 1.45620 + 0.473148i
\(445\) 444.468 + 60.7487i 0.998804 + 0.136514i
\(446\) −6.31009 19.4205i −0.0141482 0.0435436i
\(447\) −296.394 151.020i −0.663074 0.337853i
\(448\) −29.6057 186.923i −0.0660842 0.417239i
\(449\) 516.794i 1.15099i 0.817806 + 0.575495i \(0.195190\pi\)
−0.817806 + 0.575495i \(0.804810\pi\)
\(450\) 39.1361 7.91567i 0.0869691 0.0175904i
\(451\) 316.674 0.702160
\(452\) 101.180 16.0254i 0.223850 0.0354544i
\(453\) 297.606 584.085i 0.656967 1.28937i
\(454\) −12.8992 + 4.19121i −0.0284123 + 0.00923173i
\(455\) −249.903 120.715i −0.549238 0.265309i
\(456\) −2.92817 + 9.01197i −0.00642142 + 0.0197631i
\(457\) 276.799 276.799i 0.605687 0.605687i −0.336129 0.941816i \(-0.609118\pi\)
0.941816 + 0.336129i \(0.109118\pi\)
\(458\) −4.79249 + 2.44190i −0.0104640 + 0.00533165i
\(459\) −36.4334 50.1463i −0.0793756 0.109251i
\(460\) −129.522 + 186.477i −0.281570 + 0.405386i
\(461\) 692.843 + 503.380i 1.50291 + 1.09193i 0.969203 + 0.246264i \(0.0792029\pi\)
0.533711 + 0.845667i \(0.320797\pi\)
\(462\) 11.2226 70.8568i 0.0242914 0.153370i
\(463\) −138.978 22.0119i −0.300168 0.0475419i 0.00453395 0.999990i \(-0.498557\pi\)
−0.304702 + 0.952448i \(0.598557\pi\)
\(464\) −162.739 + 223.991i −0.350731 + 0.482740i
\(465\) −120.330 + 398.983i −0.258773 + 0.858028i
\(466\) 96.4952 70.1078i 0.207071 0.150446i
\(467\) −164.433 322.718i −0.352105 0.691045i 0.645231 0.763987i \(-0.276761\pi\)
−0.997336 + 0.0729424i \(0.976761\pi\)
\(468\) 249.436 + 249.436i 0.532984 + 0.532984i
\(469\) −17.7479 5.76665i −0.0378421 0.0122956i
\(470\) 5.83609 + 32.3798i 0.0124172 + 0.0688933i
\(471\) 88.2999 + 271.759i 0.187473 + 0.576983i
\(472\) 95.2408 + 48.5276i 0.201781 + 0.102813i
\(473\) −177.829 1122.77i −0.375960 2.37372i
\(474\) 95.3096i 0.201075i
\(475\) −21.1554 + 16.7882i −0.0445376 + 0.0353436i
\(476\) −61.3060 −0.128794
\(477\) 258.199 40.8948i 0.541298 0.0857333i
\(478\) −54.2384 + 106.449i −0.113469 + 0.222696i
\(479\) 326.819 106.190i 0.682293 0.221691i 0.0526943 0.998611i \(-0.483219\pi\)
0.629599 + 0.776920i \(0.283219\pi\)
\(480\) 178.854 186.619i 0.372612 0.388789i
\(481\) 231.570 712.698i 0.481434 1.48170i
\(482\) −72.5106 + 72.5106i −0.150437 + 0.150437i
\(483\) 132.909 67.7203i 0.275173 0.140208i
\(484\) −566.113 779.188i −1.16966 1.60989i
\(485\) −9.97893 469.658i −0.0205751 0.968368i
\(486\) −61.5441 44.7144i −0.126634 0.0920049i
\(487\) −109.417 + 690.831i −0.224675 + 1.41854i 0.575021 + 0.818139i \(0.304994\pi\)
−0.799696 + 0.600405i \(0.795006\pi\)
\(488\) −127.691 20.2242i −0.261661 0.0414431i
\(489\) 4.34237 5.97676i 0.00888011 0.0122224i
\(490\) −43.5695 + 33.0917i −0.0889174 + 0.0675340i
\(491\) −281.430 + 204.471i −0.573177 + 0.416438i −0.836258 0.548336i \(-0.815261\pi\)
0.263081 + 0.964774i \(0.415261\pi\)
\(492\) −111.827 219.473i −0.227291 0.446084i
\(493\) 60.5184 + 60.5184i 0.122755 + 0.122755i
\(494\) 4.91376 + 1.59658i 0.00994689 + 0.00323194i
\(495\) −462.971 + 248.422i −0.935296 + 0.501863i
\(496\) 101.439 + 312.197i 0.204514 + 0.629429i
\(497\) 197.689 + 100.727i 0.397764 + 0.202671i
\(498\) −3.73098 23.5565i −0.00749192 0.0473021i
\(499\) 90.5909i 0.181545i 0.995872 + 0.0907724i \(0.0289336\pi\)
−0.995872 + 0.0907724i \(0.971066\pi\)
\(500\) 477.520 107.190i 0.955040 0.214380i
\(501\) −43.4114 −0.0866496
\(502\) 28.7197 4.54875i 0.0572105 0.00906125i
\(503\) −360.023 + 706.585i −0.715751 + 1.40474i 0.190365 + 0.981713i \(0.439033\pi\)
−0.906117 + 0.423028i \(0.860967\pi\)
\(504\) −40.6289 + 13.2011i −0.0806129 + 0.0261927i
\(505\) 34.1295 + 63.6055i 0.0675832 + 0.125951i
\(506\) −19.9916 + 61.5277i −0.0395090 + 0.121596i
\(507\) 271.274 271.274i 0.535058 0.535058i
\(508\) −260.635 + 132.800i −0.513061 + 0.261417i
\(509\) 361.411 + 497.439i 0.710041 + 0.977287i 0.999796 + 0.0201863i \(0.00642593\pi\)
−0.289756 + 0.957101i \(0.593574\pi\)
\(510\) −15.5290 20.4460i −0.0304490 0.0400901i
\(511\) 281.745 + 204.700i 0.551360 + 0.400587i
\(512\) 53.4689 337.589i 0.104431 0.659354i
\(513\) 14.2730 + 2.26063i 0.0278227 + 0.00440668i
\(514\) −33.5162 + 46.1311i −0.0652067 + 0.0897493i
\(515\) 433.117 9.20254i 0.841004 0.0178690i
\(516\) −715.347 + 519.730i −1.38633 + 1.00723i
\(517\) −196.552 385.756i −0.380179 0.746143i
\(518\) 31.7418 + 31.7418i 0.0612776 + 0.0612776i
\(519\) 723.133 + 234.960i 1.39332 + 0.452717i
\(520\) −136.653 130.966i −0.262793 0.251859i
\(521\) −204.980 630.864i −0.393436 1.21087i −0.930173 0.367121i \(-0.880343\pi\)
0.536737 0.843749i \(-0.319657\pi\)
\(522\) 26.2846 + 13.3927i 0.0503537 + 0.0256565i
\(523\) 37.7042 + 238.055i 0.0720921 + 0.455172i 0.997156 + 0.0753609i \(0.0240109\pi\)
−0.925064 + 0.379811i \(0.875989\pi\)
\(524\) 317.144i 0.605237i
\(525\) −309.740 86.2806i −0.589981 0.164344i
\(526\) 61.5059 0.116931
\(527\) 100.224 15.8739i 0.190178 0.0301212i
\(528\) −496.178 + 973.804i −0.939731 + 1.84433i
\(529\) 375.176 121.902i 0.709218 0.230439i
\(530\) −68.2828 + 12.3072i −0.128835 + 0.0232211i
\(531\) −78.6164 + 241.957i −0.148054 + 0.455662i
\(532\) 10.1066 10.1066i 0.0189973 0.0189973i
\(533\) −241.926 + 123.268i −0.453896 + 0.231271i
\(534\) −58.4410 80.4371i −0.109440 0.150631i
\(535\) −818.088 246.728i −1.52914 0.461173i
\(536\) −10.2964 7.48079i −0.0192097 0.0139567i
\(537\) −32.4647 + 204.974i −0.0604557 + 0.381703i
\(538\) 98.6460 + 15.6240i 0.183357 + 0.0290409i
\(539\) 423.168 582.441i 0.785099 1.08060i
\(540\) −215.077 149.387i −0.398291 0.276642i
\(541\) −755.213 + 548.694i −1.39596 + 1.01422i −0.400776 + 0.916176i \(0.631259\pi\)
−0.995182 + 0.0980465i \(0.968741\pi\)
\(542\) −30.5948 60.0457i −0.0564480 0.110785i
\(543\) −366.050 366.050i −0.674125 0.674125i
\(544\) −59.8599 19.4497i −0.110037 0.0357530i
\(545\) −72.4326 + 149.949i −0.132904 + 0.275135i
\(546\) 19.0079 + 58.5003i 0.0348130 + 0.107143i
\(547\) −926.420 472.034i −1.69364 0.862951i −0.988014 0.154364i \(-0.950667\pi\)
−0.705623 0.708587i \(-0.749333\pi\)
\(548\) 96.9280 + 611.980i 0.176876 + 1.11675i
\(549\) 307.701i 0.560475i
\(550\) 121.449 68.5292i 0.220817 0.124598i
\(551\) −19.9534 −0.0362131
\(552\) 100.480 15.9145i 0.182029 0.0288306i
\(553\) 131.946 258.958i 0.238600 0.468279i
\(554\) 110.777 35.9936i 0.199958 0.0649704i
\(555\) 117.568 860.187i 0.211834 1.54989i
\(556\) 189.903 584.462i 0.341552 1.05119i
\(557\) −162.407 + 162.407i −0.291575 + 0.291575i −0.837702 0.546127i \(-0.816102\pi\)
0.546127 + 0.837702i \(0.316102\pi\)
\(558\) 31.1638 15.8787i 0.0558490 0.0284565i
\(559\) 572.900 + 788.530i 1.02487 + 1.41061i
\(560\) −239.160 + 83.3647i −0.427071 + 0.148866i
\(561\) 273.323 + 198.581i 0.487208 + 0.353977i
\(562\) −6.08087 + 38.3931i −0.0108201 + 0.0683151i
\(563\) −228.223 36.1470i −0.405370 0.0642043i −0.0495798 0.998770i \(-0.515788\pi\)
−0.355790 + 0.934566i \(0.615788\pi\)
\(564\) −197.942 + 272.444i −0.350962 + 0.483057i
\(565\) −43.0610 123.535i −0.0762141 0.218646i
\(566\) −58.8216 + 42.7364i −0.103925 + 0.0755060i
\(567\) 153.844 + 301.935i 0.271329 + 0.532513i
\(568\) 106.997 + 106.997i 0.188376 + 0.188376i
\(569\) −124.308 40.3900i −0.218467 0.0709842i 0.197739 0.980255i \(-0.436640\pi\)
−0.416205 + 0.909271i \(0.636640\pi\)
\(570\) 5.93064 + 0.810583i 0.0104046 + 0.00142208i
\(571\) 154.922 + 476.802i 0.271318 + 0.835030i 0.990170 + 0.139867i \(0.0446677\pi\)
−0.718853 + 0.695163i \(0.755332\pi\)
\(572\) 1097.71 + 559.313i 1.91908 + 0.977819i
\(573\) −54.4231 343.614i −0.0949793 0.599675i
\(574\) 16.2648i 0.0283359i
\(575\) 263.708 + 120.544i 0.458623 + 0.209641i
\(576\) 307.199 0.533331
\(577\) 372.888 59.0596i 0.646252 0.102356i 0.175300 0.984515i \(-0.443910\pi\)
0.470952 + 0.882159i \(0.343910\pi\)
\(578\) 35.3642 69.4061i 0.0611837 0.120080i
\(579\) 318.694 103.550i 0.550422 0.178843i
\(580\) 325.583 + 157.273i 0.561351 + 0.271160i
\(581\) −22.4742 + 69.1686i −0.0386820 + 0.119051i
\(582\) −73.6215 + 73.6215i −0.126497 + 0.126497i
\(583\) 813.484 414.491i 1.39534 0.710962i
\(584\) 139.606 + 192.152i 0.239052 + 0.329027i
\(585\) 256.992 370.000i 0.439302 0.632478i
\(586\) 93.2006 + 67.7142i 0.159045 + 0.115553i
\(587\) 138.085 871.835i 0.235239 1.48524i −0.533568 0.845757i \(-0.679149\pi\)
0.768807 0.639481i \(-0.220851\pi\)
\(588\) −553.099 87.6023i −0.940645 0.148984i
\(589\) −13.9054 + 19.1392i −0.0236086 + 0.0324944i
\(590\) 19.4968 64.6466i 0.0330454 0.109570i
\(591\) 802.646 583.156i 1.35811 0.986728i
\(592\) −310.472 609.335i −0.524445 1.02928i
\(593\) 128.291 + 128.291i 0.216342 + 0.216342i 0.806955 0.590613i \(-0.201114\pi\)
−0.590613 + 0.806955i \(0.701114\pi\)
\(594\) −70.9641 23.0576i −0.119468 0.0388176i
\(595\) 13.8874 + 77.0504i 0.0233402 + 0.129496i
\(596\) 105.746 + 325.453i 0.177426 + 0.546062i
\(597\) −672.663 342.739i −1.12674 0.574102i
\(598\) −8.67734 54.7866i −0.0145106 0.0916164i
\(599\) 543.188i 0.906825i 0.891301 + 0.453412i \(0.149793\pi\)
−0.891301 + 0.453412i \(0.850207\pi\)
\(600\) −182.721 121.242i −0.304536 0.202070i
\(601\) 228.860 0.380799 0.190399 0.981707i \(-0.439022\pi\)
0.190399 + 0.981707i \(0.439022\pi\)
\(602\) −57.6670 + 9.13355i −0.0957923 + 0.0151720i
\(603\) 13.7519 26.9897i 0.0228059 0.0447591i
\(604\) −641.349 + 208.387i −1.06184 + 0.345011i
\(605\) −851.056 + 888.007i −1.40670 + 1.46778i
\(606\) 4.94380 15.2154i 0.00815808 0.0251080i
\(607\) 241.898 241.898i 0.398514 0.398514i −0.479195 0.877709i \(-0.659071\pi\)
0.877709 + 0.479195i \(0.159071\pi\)
\(608\) 13.0745 6.66181i 0.0215042 0.0109569i
\(609\) −139.631 192.185i −0.229278 0.315575i
\(610\) 1.73480 + 81.6485i 0.00284394 + 0.133850i
\(611\) 300.317 + 218.193i 0.491517 + 0.357108i
\(612\) 15.5672 98.2877i 0.0254367 0.160601i
\(613\) −58.4076 9.25086i −0.0952816 0.0150911i 0.108612 0.994084i \(-0.465360\pi\)
−0.203893 + 0.978993i \(0.565360\pi\)
\(614\) 70.9075 97.5959i 0.115485 0.158951i
\(615\) −250.506 + 190.263i −0.407327 + 0.309370i
\(616\) −120.703 + 87.6961i −0.195947 + 0.142364i
\(617\) 352.094 + 691.024i 0.570656 + 1.11997i 0.978370 + 0.206865i \(0.0663260\pi\)
−0.407714 + 0.913110i \(0.633674\pi\)
\(618\) −67.8934 67.8934i −0.109860 0.109860i
\(619\) −537.492 174.642i −0.868323 0.282135i −0.159222 0.987243i \(-0.550899\pi\)
−0.709100 + 0.705108i \(0.750899\pi\)
\(620\) 377.752 202.695i 0.609278 0.326927i
\(621\) −47.9430 147.553i −0.0772029 0.237606i
\(622\) −18.2578 9.30283i −0.0293534 0.0149563i
\(623\) 47.4290 + 299.455i 0.0761300 + 0.480666i
\(624\) 937.089i 1.50175i
\(625\) −242.889 575.873i −0.388622 0.921397i
\(626\) −162.602 −0.259748
\(627\) −77.7956 + 12.3216i −0.124076 + 0.0196517i
\(628\) 133.450 261.910i 0.212500 0.417054i
\(629\) −201.053 + 65.3260i −0.319639 + 0.103857i
\(630\) 12.7593 + 23.7789i 0.0202529 + 0.0377442i
\(631\) −187.092 + 575.810i −0.296501 + 0.912536i 0.686212 + 0.727401i \(0.259272\pi\)
−0.982713 + 0.185134i \(0.940728\pi\)
\(632\) 140.159 140.159i 0.221771 0.221771i
\(633\) −134.929 + 68.7496i −0.213158 + 0.108609i
\(634\) −106.956 147.212i −0.168700 0.232196i
\(635\) 225.946 + 297.487i 0.355820 + 0.468484i
\(636\) −574.532 417.422i −0.903353 0.656324i
\(637\) −96.5644 + 609.684i −0.151592 + 0.957117i
\(638\) 101.759 + 16.1171i 0.159497 + 0.0252619i
\(639\) −211.688 + 291.363i −0.331280 + 0.455968i
\(640\) −353.119 + 7.50280i −0.551749 + 0.0117231i
\(641\) 621.687 451.682i 0.969870 0.704652i 0.0144481 0.999896i \(-0.495401\pi\)
0.955422 + 0.295244i \(0.0954009\pi\)
\(642\) 85.9785 + 168.742i 0.133923 + 0.262839i
\(643\) −485.126 485.126i −0.754472 0.754472i 0.220838 0.975310i \(-0.429121\pi\)
−0.975310 + 0.220838i \(0.929121\pi\)
\(644\) −145.939 47.4185i −0.226613 0.0736312i
\(645\) 815.250 + 781.327i 1.26395 + 1.21136i
\(646\) −0.450396 1.38618i −0.000697208 0.00214578i
\(647\) 438.563 + 223.459i 0.677840 + 0.345377i 0.758785 0.651342i \(-0.225794\pi\)
−0.0809441 + 0.996719i \(0.525794\pi\)
\(648\) 36.1537 + 228.265i 0.0557927 + 0.352261i
\(649\) 888.513i 1.36905i
\(650\) −66.1069 + 99.6286i −0.101703 + 0.153275i
\(651\) −281.650 −0.432642
\(652\) −7.50622 + 1.18887i −0.0115126 + 0.00182342i
\(653\) 330.468 648.579i 0.506076 0.993230i −0.486736 0.873549i \(-0.661813\pi\)
0.992812 0.119681i \(-0.0381873\pi\)
\(654\) 35.1018 11.4053i 0.0536725 0.0174392i
\(655\) −398.592 + 71.8414i −0.608537 + 0.109682i
\(656\) −76.5704 + 235.659i −0.116723 + 0.359237i
\(657\) −399.724 + 399.724i −0.608408 + 0.608408i
\(658\) −19.8130 + 10.0952i −0.0301109 + 0.0153423i
\(659\) −285.023 392.301i −0.432509 0.595297i 0.536018 0.844206i \(-0.319928\pi\)
−0.968527 + 0.248909i \(0.919928\pi\)
\(660\) 1366.52 + 412.130i 2.07049 + 0.624439i
\(661\) −837.490 608.472i −1.26700 0.920533i −0.267925 0.963440i \(-0.586338\pi\)
−0.999079 + 0.0429071i \(0.986338\pi\)
\(662\) −14.4915 + 91.4958i −0.0218905 + 0.138211i
\(663\) −286.108 45.3150i −0.431535 0.0683484i
\(664\) −29.1547 + 40.1280i −0.0439077 + 0.0604337i
\(665\) −14.9915 10.4127i −0.0225436 0.0156582i
\(666\) −58.9495 + 42.8293i −0.0885127 + 0.0643083i
\(667\) 97.2548 + 190.873i 0.145809 + 0.286167i
\(668\) 31.5778 + 31.5778i 0.0472722 + 0.0472722i
\(669\) −253.850 82.4808i −0.379447 0.123290i
\(670\) −3.49692 + 7.23927i −0.00521929 + 0.0108049i
\(671\) −332.081 1022.04i −0.494904 1.52316i
\(672\) 155.658 + 79.3115i 0.231633 + 0.118023i
\(673\) 143.361 + 905.147i 0.213018 + 1.34494i 0.829910 + 0.557897i \(0.188391\pi\)
−0.616892 + 0.787048i \(0.711609\pi\)
\(674\) 97.5812i 0.144779i
\(675\) −139.031 + 304.153i −0.205972 + 0.450596i
\(676\) −394.654 −0.583808
\(677\) −1316.25 + 208.473i −1.94424 + 0.307937i −0.999785 0.0207152i \(-0.993406\pi\)
−0.944451 + 0.328652i \(0.893406\pi\)
\(678\) −13.1636 + 25.8351i −0.0194154 + 0.0381049i
\(679\) 301.952 98.1102i 0.444701 0.144492i
\(680\) −7.23072 + 52.9036i −0.0106334 + 0.0777994i
\(681\) −54.7843 + 168.609i −0.0804469 + 0.247590i
\(682\) 86.3748 86.3748i 0.126649 0.126649i
\(683\) 553.314 281.927i 0.810123 0.412778i 0.000696453 1.00000i \(-0.499778\pi\)
0.809426 + 0.587222i \(0.199778\pi\)
\(684\) 13.6368 + 18.7695i 0.0199369 + 0.0274408i
\(685\) 747.189 260.450i 1.09079 0.380219i
\(686\) −68.9201 50.0734i −0.100467 0.0729933i
\(687\) −10.9984 + 69.4413i −0.0160093 + 0.101079i
\(688\) 878.529 + 139.145i 1.27693 + 0.202246i
\(689\) −460.126 + 633.310i −0.667818 + 0.919172i
\(690\) −21.1524 60.6829i −0.0306557 0.0879462i
\(691\) 651.607 473.420i 0.942992 0.685123i −0.00614739 0.999981i \(-0.501957\pi\)
0.949139 + 0.314858i \(0.101957\pi\)
\(692\) −355.101 696.924i −0.513151 1.00712i
\(693\) −251.093 251.093i −0.362328 0.362328i
\(694\) 114.434 + 37.1819i 0.164891 + 0.0535762i
\(695\) −777.579 106.277i −1.11882 0.152917i
\(696\) −50.0647 154.083i −0.0719320 0.221384i
\(697\) 68.2477 + 34.7739i 0.0979163 + 0.0498908i
\(698\) 10.6649 + 67.3354i 0.0152792 + 0.0964690i
\(699\) 1559.07i 2.23043i
\(700\) 162.546 + 288.068i 0.232209 + 0.411526i
\(701\) −570.439 −0.813751 −0.406876 0.913484i \(-0.633382\pi\)
−0.406876 + 0.913484i \(0.633382\pi\)
\(702\) 63.1891 10.0082i 0.0900130 0.0142567i
\(703\) 22.3752 43.9137i 0.0318281 0.0624662i
\(704\) 1020.37 331.539i 1.44939 0.470936i
\(705\) 387.252 + 187.061i 0.549293 + 0.265335i
\(706\) 18.4926 56.9144i 0.0261935 0.0806154i
\(707\) −34.4965 + 34.4965i −0.0487928 + 0.0487928i
\(708\) 615.791 313.761i 0.869762 0.443166i
\(709\) 341.238 + 469.674i 0.481295 + 0.662445i 0.978753 0.205043i \(-0.0657333\pi\)
−0.497458 + 0.867488i \(0.665733\pi\)
\(710\) 54.5288 78.5070i 0.0768012 0.110573i
\(711\) 381.665 + 277.296i 0.536801 + 0.390009i
\(712\) −32.3468 + 204.229i −0.0454309 + 0.286839i
\(713\) 250.861 + 39.7324i 0.351838 + 0.0557257i
\(714\) 10.1994 14.0383i 0.0142849 0.0196615i
\(715\) 454.292 1506.32i 0.635374 2.10674i
\(716\) 172.715 125.485i 0.241222 0.175258i
\(717\) 708.963 + 1391.42i 0.988791 + 1.94061i
\(718\) −71.1829 71.1829i −0.0991405 0.0991405i
\(719\) −497.061 161.505i −0.691322 0.224624i −0.0577767 0.998330i \(-0.518401\pi\)
−0.633546 + 0.773705i \(0.718401\pi\)
\(720\) −72.9238 404.597i −0.101283 0.561940i
\(721\) 90.4769 + 278.459i 0.125488 + 0.386213i
\(722\) −93.3529 47.5657i −0.129298 0.0658804i
\(723\) 209.684 + 1323.89i 0.290020 + 1.83111i
\(724\) 532.535i 0.735546i
\(725\) 123.910 444.825i 0.170910 0.613552i
\(726\) 272.607 0.375492
\(727\) −412.828 + 65.3856i −0.567852 + 0.0899389i −0.433757 0.901030i \(-0.642813\pi\)
−0.134094 + 0.990969i \(0.542813\pi\)
\(728\) 58.0762 113.981i 0.0797751 0.156567i
\(729\) −87.3564 + 28.3838i −0.119830 + 0.0389353i
\(730\) 103.813 108.321i 0.142210 0.148384i
\(731\) 84.9664 261.500i 0.116233 0.357729i
\(732\) −591.065 + 591.065i −0.807465 + 0.807465i
\(733\) 641.297 326.757i 0.874894 0.445781i 0.0419378 0.999120i \(-0.486647\pi\)
0.832956 + 0.553340i \(0.186647\pi\)
\(734\) 91.1902 + 125.513i 0.124237 + 0.170998i
\(735\) 15.1915 + 714.988i 0.0206687 + 0.972773i
\(736\) −127.453 92.5999i −0.173170 0.125815i
\(737\) 16.5494 104.489i 0.0224551 0.141776i
\(738\) 26.0763 + 4.13007i 0.0353337 + 0.00559631i
\(739\) −560.278 + 771.157i −0.758158 + 1.04351i 0.239208 + 0.970968i \(0.423112\pi\)
−0.997365 + 0.0725458i \(0.976888\pi\)
\(740\) −711.226 + 540.187i −0.961117 + 0.729982i
\(741\) 54.6365 39.6957i 0.0737335 0.0535705i
\(742\) −21.2888 41.7817i −0.0286912 0.0563096i
\(743\) −973.452 973.452i −1.31016 1.31016i −0.921292 0.388872i \(-0.872865\pi\)
−0.388872 0.921292i \(-0.627135\pi\)
\(744\) −182.685 59.3581i −0.245545 0.0797824i
\(745\) 385.080 206.627i 0.516886 0.277352i
\(746\) −5.47063 16.8369i −0.00733329 0.0225695i
\(747\) −105.186 53.5951i −0.140812 0.0717472i
\(748\) −54.3682 343.267i −0.0726847 0.458913i
\(749\) 577.505i 0.771034i
\(750\) −54.8993 + 127.179i −0.0731991 + 0.169572i
\(751\) 815.196 1.08548 0.542740 0.839901i \(-0.317387\pi\)
0.542740 + 0.839901i \(0.317387\pi\)
\(752\) 334.593 52.9944i 0.444938 0.0704713i
\(753\) 172.553 338.655i 0.229155 0.449741i
\(754\) −84.0137 + 27.2977i −0.111424 + 0.0362039i
\(755\) 407.186 + 758.852i 0.539320 + 1.00510i
\(756\) 54.6910 168.322i 0.0723426 0.222648i
\(757\) 266.404 266.404i 0.351920 0.351920i −0.508903 0.860824i \(-0.669949\pi\)
0.860824 + 0.508903i \(0.169949\pi\)
\(758\) 50.4957 25.7288i 0.0666170 0.0339430i
\(759\) 497.050 + 684.131i 0.654875 + 0.901358i
\(760\) −7.52938 9.91341i −0.00990708 0.0130440i
\(761\) −875.638 636.188i −1.15064 0.835989i −0.162075 0.986778i \(-0.551819\pi\)
−0.988566 + 0.150789i \(0.951819\pi\)
\(762\) 12.9520 81.7758i 0.0169974 0.107317i
\(763\) −111.162 17.6063i −0.145690 0.0230751i
\(764\) −210.360 + 289.535i −0.275340 + 0.378973i
\(765\) −127.056 + 2.69959i −0.166086 + 0.00352887i
\(766\) −118.080 + 85.7904i −0.154152 + 0.111998i
\(767\) −345.860 678.789i −0.450926 0.884993i
\(768\) −547.525 547.525i −0.712923 0.712923i
\(769\) −749.913 243.662i −0.975180 0.316855i −0.222275 0.974984i \(-0.571348\pi\)
−0.752905 + 0.658129i \(0.771348\pi\)
\(770\) 68.0435 + 65.2121i 0.0883681 + 0.0846911i
\(771\) 230.322 + 708.860i 0.298732 + 0.919403i
\(772\) −307.144 156.498i −0.397855 0.202717i
\(773\) 56.0962 + 354.177i 0.0725694 + 0.458185i 0.997037 + 0.0769245i \(0.0245100\pi\)
−0.924467 + 0.381261i \(0.875490\pi\)
\(774\) 94.7727i 0.122445i
\(775\) −340.321 428.849i −0.439124 0.553354i
\(776\) 216.531 0.279034
\(777\) 579.540 91.7901i 0.745869 0.118134i
\(778\) 21.6783 42.5461i 0.0278642 0.0546866i
\(779\) −16.9836 + 5.51830i −0.0218018 + 0.00708382i
\(780\) −1204.39 + 217.078i −1.54409 + 0.278305i
\(781\) −388.680 + 1196.24i −0.497670 + 1.53167i
\(782\) −11.0648 + 11.0648i −0.0141494 + 0.0141494i
\(783\) −220.147 + 112.171i −0.281159 + 0.143257i
\(784\) 331.115 + 455.741i 0.422341 + 0.581302i
\(785\) −359.402 108.392i −0.457837 0.138079i
\(786\) 72.6218 + 52.7628i 0.0923942 + 0.0671283i
\(787\) 197.057 1244.17i 0.250390 1.58090i −0.467021 0.884246i \(-0.654673\pi\)
0.717410 0.696651i \(-0.245327\pi\)
\(788\) −1008.04 159.658i −1.27924 0.202612i
\(789\) 472.556 650.417i 0.598930 0.824356i
\(790\) −102.839 71.4289i −0.130175 0.0904163i
\(791\) 71.5318 51.9709i 0.0904321 0.0657028i
\(792\) −109.947 215.784i −0.138822 0.272454i
\(793\) 651.533 + 651.533i 0.821605 + 0.821605i
\(794\) 95.1586 + 30.9189i 0.119847 + 0.0389407i
\(795\) −394.476 + 816.639i −0.496197 + 1.02722i
\(796\) 239.989 + 738.611i 0.301494 + 0.927903i
\(797\) 748.686 + 381.474i 0.939380 + 0.478638i 0.855480 0.517836i \(-0.173262\pi\)
0.0839000 + 0.996474i \(0.473262\pi\)
\(798\) 0.632855 + 3.99569i 0.000793052 + 0.00500713i
\(799\) 104.719i 0.131063i
\(800\) 67.3206 + 332.842i 0.0841507 + 0.416052i
\(801\) −492.138 −0.614405
\(802\) −102.155 + 16.1797i −0.127375 + 0.0201742i
\(803\) −896.303 + 1759.09i −1.11619 + 2.19065i
\(804\) −78.2610 + 25.4285i −0.0973396 + 0.0316275i
\(805\) −26.5373 + 194.160i −0.0329656 + 0.241193i
\(806\) −32.3649 + 99.6090i −0.0401550 + 0.123584i
\(807\) 923.128 923.128i 1.14390 1.14390i
\(808\) −29.6455 + 15.1051i −0.0366900 + 0.0186945i
\(809\) −668.124 919.594i −0.825864 1.13670i −0.988679 0.150048i \(-0.952057\pi\)
0.162814 0.986657i \(-0.447943\pi\)
\(810\) 137.856 48.0531i 0.170193 0.0593248i
\(811\) 1006.65 + 731.378i 1.24125 + 0.901822i 0.997681 0.0680614i \(-0.0216814\pi\)
0.243570 + 0.969883i \(0.421681\pi\)
\(812\) −38.2285 + 241.365i −0.0470794 + 0.297248i
\(813\) −870.038 137.801i −1.07016 0.169496i
\(814\) −149.580 + 205.879i −0.183759 + 0.252923i
\(815\) 3.19454 + 9.16463i 0.00391969 + 0.0112449i
\(816\) −213.867 + 155.383i −0.262091 + 0.190421i
\(817\) 29.1023 + 57.1165i 0.0356209 + 0.0699100i
\(818\) −77.4673 77.4673i −0.0947033 0.0947033i
\(819\) 289.566 + 94.0855i 0.353560 + 0.114879i
\(820\) 320.619 + 43.8213i 0.390998 + 0.0534406i
\(821\) 3.49825 + 10.7665i 0.00426096 + 0.0131139i 0.953164 0.302453i \(-0.0978054\pi\)
−0.948903 + 0.315567i \(0.897805\pi\)
\(822\) −156.261 79.6190i −0.190099 0.0968601i
\(823\) −65.6724 414.639i −0.0797964 0.503815i −0.994922 0.100646i \(-0.967909\pi\)
0.915126 0.403168i \(-0.132091\pi\)
\(824\) 199.684i 0.242335i
\(825\) 208.418 1810.82i 0.252628 2.19494i
\(826\) 45.6353 0.0552485
\(827\) 1100.78 174.346i 1.33105 0.210817i 0.549936 0.835207i \(-0.314652\pi\)
0.781113 + 0.624390i \(0.214652\pi\)
\(828\) 113.081 221.933i 0.136571 0.268035i
\(829\) 494.260 160.595i 0.596213 0.193721i 0.00466205 0.999989i \(-0.498516\pi\)
0.591551 + 0.806268i \(0.298516\pi\)
\(830\) 28.2135 + 13.6285i 0.0339921 + 0.0164198i
\(831\) 470.482 1447.99i 0.566163 1.74247i
\(832\) −650.470 + 650.470i −0.781815 + 0.781815i
\(833\) 155.156 79.0562i 0.186262 0.0949054i
\(834\) 102.240 + 140.722i 0.122590 + 0.168731i
\(835\) 32.5343 46.8407i 0.0389632 0.0560967i
\(836\) 65.5520 + 47.6263i 0.0784114 + 0.0569692i
\(837\) −45.8261 + 289.335i −0.0547504 + 0.345681i
\(838\) −175.723 27.8317i −0.209693 0.0332121i
\(839\) 657.552 905.043i 0.783733 1.07872i −0.211127 0.977459i \(-0.567713\pi\)
0.994860 0.101257i \(-0.0322865\pi\)
\(840\) 42.7935 141.893i 0.0509446 0.168920i
\(841\) −404.382 + 293.801i −0.480835 + 0.349347i
\(842\) −27.2824 53.5448i −0.0324019 0.0635924i
\(843\) 359.282 + 359.282i 0.426194 + 0.426194i
\(844\) 148.157 + 48.1392i 0.175542 + 0.0570370i
\(845\) 89.3995 + 496.008i 0.105798 + 0.586991i
\(846\) −11.1539 34.3282i −0.0131843 0.0405771i
\(847\) −740.681 377.396i −0.874475 0.445567i
\(848\) 111.755 + 705.593i 0.131786 + 0.832067i
\(849\) 950.378i 1.11941i
\(850\) 33.6992 1.43267i 0.0396461 0.00168550i
\(851\) −529.134 −0.621779
\(852\) 966.315 153.049i 1.13417 0.179635i
\(853\) 281.083 551.657i 0.329523 0.646725i −0.665497 0.746401i \(-0.731780\pi\)
0.995020 + 0.0996751i \(0.0317803\pi\)
\(854\) −52.4934 + 17.0561i −0.0614677 + 0.0199721i
\(855\) 20.5007 21.3908i 0.0239774 0.0250185i
\(856\) 121.710 374.584i 0.142184 0.437598i
\(857\) 312.684 312.684i 0.364858 0.364858i −0.500740 0.865598i \(-0.666939\pi\)
0.865598 + 0.500740i \(0.166939\pi\)
\(858\) −310.700 + 158.310i −0.362122 + 0.184510i
\(859\) 59.1889 + 81.4665i 0.0689044 + 0.0948387i 0.842078 0.539355i \(-0.181332\pi\)
−0.773174 + 0.634194i \(0.781332\pi\)
\(860\) −24.6757 1161.36i −0.0286927 1.35042i
\(861\) −171.998 124.964i −0.199766 0.145138i
\(862\) −11.1016 + 70.0928i −0.0128789 + 0.0813142i
\(863\) −158.959 25.1766i −0.184194 0.0291734i 0.0636561 0.997972i \(-0.479724\pi\)
−0.247850 + 0.968798i \(0.579724\pi\)
\(864\) 106.802 147.000i 0.123613 0.170139i
\(865\) −795.466 + 604.168i −0.919614 + 0.698460i
\(866\) −91.7970 + 66.6944i −0.106001 + 0.0770144i
\(867\) −462.254 907.225i −0.533165 1.04640i
\(868\) 204.875 + 204.875i 0.236031 + 0.236031i
\(869\) 1566.98 + 509.144i 1.80320 + 0.585896i
\(870\) −90.1803 + 48.3891i −0.103656 + 0.0556197i
\(871\) 28.0300 + 86.2675i 0.0321814 + 0.0990442i
\(872\) −68.3917 34.8473i −0.0784309 0.0399625i
\(873\) 80.6196 + 509.012i 0.0923477 + 0.583061i
\(874\) 3.64816i 0.00417410i
\(875\) 325.228 269.546i 0.371689 0.308052i
\(876\) 1535.67 1.75304
\(877\) −889.491 + 140.882i −1.01424 + 0.160640i −0.641362 0.767239i \(-0.721630\pi\)
−0.372882 + 0.927879i \(0.621630\pi\)
\(878\) 47.9316 94.0711i 0.0545918 0.107143i
\(879\) 1432.14 465.329i 1.62928 0.529385i
\(880\) −678.874 1265.18i −0.771447 1.43771i
\(881\) −310.239 + 954.819i −0.352145 + 1.08379i 0.605502 + 0.795844i \(0.292972\pi\)
−0.957647 + 0.287946i \(0.907028\pi\)
\(882\) 42.4417 42.4417i 0.0481198 0.0481198i
\(883\) 322.466 164.305i 0.365193 0.186075i −0.261758 0.965133i \(-0.584302\pi\)
0.626952 + 0.779058i \(0.284302\pi\)
\(884\) 175.154 + 241.079i 0.198139 + 0.272714i
\(885\) −533.833 702.861i −0.603201 0.794193i
\(886\) 154.847 + 112.503i 0.174771 + 0.126979i
\(887\) −172.488 + 1089.05i −0.194463 + 1.22779i 0.676501 + 0.736442i \(0.263495\pi\)
−0.870964 + 0.491347i \(0.836505\pi\)
\(888\) 395.249 + 62.6013i 0.445100 + 0.0704969i
\(889\) −148.401 + 204.256i −0.166930 + 0.229759i
\(890\) 130.589 2.77466i 0.146730 0.00311759i
\(891\) −1554.17 + 1129.17i −1.74430 + 1.26731i
\(892\) 124.655 + 244.649i 0.139748 + 0.274271i
\(893\) 17.2634 + 17.2634i 0.0193319 + 0.0193319i
\(894\) −92.1173 29.9307i −0.103039 0.0334796i
\(895\) −196.836 188.645i −0.219928 0.210777i
\(896\) −73.7656 227.027i −0.0823276 0.253378i
\(897\) −646.030 329.169i −0.720211 0.366966i
\(898\) 23.5394 + 148.622i 0.0262132 + 0.165503i
\(899\) 404.485i 0.449927i
\(900\) −503.115 + 187.451i −0.559017 + 0.208278i
\(901\) 220.832 0.245097
\(902\) 91.0706 14.4242i 0.100965 0.0159913i
\(903\) −346.475 + 679.995i −0.383693 + 0.753039i
\(904\) 57.3502 18.6342i 0.0634405 0.0206131i
\(905\) 669.299 120.633i 0.739557 0.133296i
\(906\) 58.9825 181.530i 0.0651021 0.200364i
\(907\) 183.638 183.638i 0.202468 0.202468i −0.598589 0.801056i \(-0.704272\pi\)
0.801056 + 0.598589i \(0.204272\pi\)
\(908\) 162.498 82.7968i 0.178962 0.0911859i
\(909\) −46.5463 64.0655i −0.0512061 0.0704791i
\(910\) −77.3669 23.3331i −0.0850185 0.0256408i
\(911\) 922.010 + 669.880i 1.01209 + 0.735323i 0.964646 0.263551i \(-0.0848936\pi\)
0.0474403 + 0.998874i \(0.484894\pi\)
\(912\) 9.64125 60.8725i 0.0105715 0.0667461i
\(913\) −407.222 64.4977i −0.446027 0.0706437i
\(914\) 66.9953 92.2111i 0.0732990 0.100887i
\(915\) 876.751 + 608.968i 0.958198 + 0.665539i
\(916\) 58.5124 42.5118i 0.0638782 0.0464102i
\(917\) −124.271 243.895i −0.135519 0.265971i
\(918\) −12.7618 12.7618i −0.0139017 0.0139017i
\(919\) −1036.37 336.736i −1.12771 0.366416i −0.315006 0.949090i \(-0.602007\pi\)
−0.812706 + 0.582674i \(0.802007\pi\)
\(920\) −58.1322 + 120.344i −0.0631872 + 0.130809i
\(921\) −487.274 1499.68i −0.529071 1.62831i
\(922\) 222.180 + 113.206i 0.240976 + 0.122783i
\(923\) −168.707 1065.17i −0.182781 1.15403i
\(924\) 964.655i 1.04400i
\(925\) 840.027 + 771.514i 0.908137 + 0.834069i
\(926\) −40.9705 −0.0442446
\(927\) −469.409 + 74.3471i −0.506374 + 0.0802018i
\(928\) −113.901 + 223.543i −0.122738 + 0.240887i
\(929\) −832.928 + 270.635i −0.896585 + 0.291318i −0.720827 0.693115i \(-0.756238\pi\)
−0.175758 + 0.984433i \(0.556238\pi\)
\(930\) −16.4317 + 120.222i −0.0176685 + 0.129271i
\(931\) −12.5455 + 38.6110i −0.0134753 + 0.0414726i
\(932\) −1134.08 + 1134.08i −1.21682 + 1.21682i
\(933\) −238.653 + 121.600i −0.255791 + 0.130332i
\(934\) −61.9879 85.3190i −0.0663682 0.0913480i
\(935\) −419.108 + 146.090i −0.448244 + 0.156246i
\(936\) 167.991 + 122.052i 0.179477 + 0.130398i
\(937\) 10.8140 68.2770i 0.0115411 0.0728676i −0.981246 0.192762i \(-0.938256\pi\)
0.992787 + 0.119894i \(0.0382555\pi\)
\(938\) −5.36670 0.850002i −0.00572143 0.000906185i
\(939\) −1249.29 + 1719.49i −1.33044 + 1.83120i
\(940\) −145.620 417.760i −0.154915 0.444425i
\(941\) −300.146 + 218.068i −0.318964 + 0.231741i −0.735733 0.677271i \(-0.763162\pi\)
0.416769 + 0.909012i \(0.363162\pi\)
\(942\) 37.7721 + 74.1318i 0.0400977 + 0.0786962i
\(943\) 135.567 + 135.567i 0.143761 + 0.143761i
\(944\) −661.205 214.839i −0.700429 0.227583i
\(945\) −223.938 30.6073i −0.236972 0.0323886i
\(946\) −102.282 314.791i −0.108120 0.332760i
\(947\) −47.7905 24.3505i −0.0504651 0.0257133i 0.428576 0.903506i \(-0.359015\pi\)
−0.479041 + 0.877793i \(0.659015\pi\)
\(948\) −200.484 1265.80i −0.211481 1.33524i
\(949\) 1692.77i 1.78374i
\(950\) −5.31928 + 5.79164i −0.00559924 + 0.00609647i
\(951\) −2378.50 −2.50105
\(952\) −35.6431 + 5.64532i −0.0374403 + 0.00592996i
\(953\) −62.8579 + 123.366i −0.0659580 + 0.129450i −0.921632 0.388066i \(-0.873143\pi\)
0.855674 + 0.517516i \(0.173143\pi\)
\(954\) 72.3915 23.5214i 0.0758821 0.0246556i
\(955\) 411.545 + 198.796i 0.430937 + 0.208163i
\(956\) 496.424 1527.83i 0.519272 1.59815i
\(957\) 952.261 952.261i 0.995048 0.995048i
\(958\) 89.1512 45.4248i 0.0930597 0.0474163i
\(959\) 314.341 + 432.653i 0.327780 + 0.451151i
\(960\) −607.974 + 875.321i −0.633307 + 0.911792i
\(961\) 389.487 + 282.979i 0.405293 + 0.294463i
\(962\) 34.1333 215.509i 0.0354816 0.224022i
\(963\) 925.873 + 146.644i 0.961447 + 0.152278i
\(964\) 810.485 1115.54i 0.840752 1.15720i
\(965\) −127.113 + 421.474i −0.131723 + 0.436761i
\(966\) 35.1379 25.5292i 0.0363747 0.0264277i
\(967\) 358.090 + 702.791i 0.370310 + 0.726775i 0.998692 0.0511303i \(-0.0162824\pi\)
−0.628382 + 0.777905i \(0.716282\pi\)
\(968\) −400.887 400.887i −0.414140 0.414140i
\(969\) −18.1191 5.88724i −0.0186987 0.00607559i
\(970\) −24.2622 134.612i −0.0250126 0.138775i
\(971\) 295.128 + 908.310i 0.303942 + 0.935438i 0.980070 + 0.198653i \(0.0636567\pi\)
−0.676128 + 0.736784i \(0.736343\pi\)
\(972\) 911.422 + 464.393i 0.937677 + 0.477771i
\(973\) −82.9751 523.884i −0.0852776 0.538422i
\(974\) 203.656i 0.209093i
\(975\) 545.654 + 1464.53i 0.559645 + 1.50208i
\(976\) 840.867 0.861544
\(977\) 699.516 110.792i 0.715984 0.113401i 0.212195 0.977227i \(-0.431939\pi\)
0.503789 + 0.863827i \(0.331939\pi\)
\(978\) 0.976565 1.91662i 0.000998533 0.00195973i
\(979\) −1634.66 + 531.132i −1.66972 + 0.542525i
\(980\) 509.038 531.138i 0.519426 0.541978i
\(981\) 56.4539 173.747i 0.0575473 0.177112i
\(982\) −71.6216 + 71.6216i −0.0729344 + 0.0729344i
\(983\) 375.050 191.097i 0.381536 0.194402i −0.252695 0.967546i \(-0.581317\pi\)
0.634231 + 0.773144i \(0.281317\pi\)
\(984\) −85.2261 117.304i −0.0866119 0.119211i
\(985\) 27.6871 + 1303.09i 0.0281087 + 1.32294i
\(986\) 20.1607 + 14.6476i 0.0204470 + 0.0148556i
\(987\) −45.4693 + 287.082i −0.0460682 + 0.290863i
\(988\) −68.6180 10.8680i −0.0694514 0.0110000i
\(989\) 404.525 556.781i 0.409024 0.562974i
\(990\) −121.828 + 92.5303i −0.123059 + 0.0934649i
\(991\) 984.068 714.967i 0.993005 0.721460i 0.0324279 0.999474i \(-0.489676\pi\)
0.960577 + 0.278014i \(0.0896761\pi\)
\(992\) 135.044 + 265.039i 0.136133 + 0.267177i
\(993\) 856.216 + 856.216i 0.862252 + 0.862252i
\(994\) 61.4403 + 19.9632i 0.0618112 + 0.0200837i
\(995\) 873.934 468.937i 0.878326 0.471294i
\(996\) 99.1021 + 305.005i 0.0995001 + 0.306230i
\(997\) 31.4577 + 16.0285i 0.0315523 + 0.0160767i 0.469695 0.882828i \(-0.344364\pi\)
−0.438143 + 0.898905i \(0.644364\pi\)
\(998\) 4.12632 + 26.0526i 0.00413459 + 0.0261048i
\(999\) 610.287i 0.610898i
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.13.3 yes 32
3.2 odd 2 225.3.r.a.163.2 32
4.3 odd 2 400.3.bg.c.113.1 32
5.2 odd 4 125.3.f.a.82.3 32
5.3 odd 4 125.3.f.b.82.2 32
5.4 even 2 125.3.f.c.43.2 32
25.2 odd 20 inner 25.3.f.a.2.3 32
25.11 even 5 125.3.f.a.93.3 32
25.14 even 10 125.3.f.b.93.2 32
25.23 odd 20 125.3.f.c.32.2 32
75.2 even 20 225.3.r.a.127.2 32
100.27 even 20 400.3.bg.c.177.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.3.f.a.2.3 32 25.2 odd 20 inner
25.3.f.a.13.3 yes 32 1.1 even 1 trivial
125.3.f.a.82.3 32 5.2 odd 4
125.3.f.a.93.3 32 25.11 even 5
125.3.f.b.82.2 32 5.3 odd 4
125.3.f.b.93.2 32 25.14 even 10
125.3.f.c.32.2 32 25.23 odd 20
125.3.f.c.43.2 32 5.4 even 2
225.3.r.a.127.2 32 75.2 even 20
225.3.r.a.163.2 32 3.2 odd 2
400.3.bg.c.113.1 32 4.3 odd 2
400.3.bg.c.177.1 32 100.27 even 20