Properties

Label 189.2.w.a.25.8
Level $189$
Weight $2$
Character 189.25
Analytic conductor $1.509$
Analytic rank $0$
Dimension $132$
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] = [189,2,Mod(25,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([10, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.w (of order \(9\), degree \(6\), 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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 25.8
Character \(\chi\) \(=\) 189.25
Dual form 189.2.w.a.121.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.928908 + 0.338095i) q^{2} +(-1.69366 + 0.362654i) q^{3} +(-0.783527 + 0.657458i) q^{4} +(-3.08847 - 1.12411i) q^{5} +(1.45064 - 0.909490i) q^{6} +(2.54716 + 0.715520i) q^{7} +(1.49406 - 2.58780i) q^{8} +(2.73696 - 1.22843i) q^{9} +O(q^{10})\) \(q+(-0.928908 + 0.338095i) q^{2} +(-1.69366 + 0.362654i) q^{3} +(-0.783527 + 0.657458i) q^{4} +(-3.08847 - 1.12411i) q^{5} +(1.45064 - 0.909490i) q^{6} +(2.54716 + 0.715520i) q^{7} +(1.49406 - 2.58780i) q^{8} +(2.73696 - 1.22843i) q^{9} +3.24896 q^{10} +(3.23909 - 1.17893i) q^{11} +(1.08860 - 1.39766i) q^{12} +(-0.176997 - 1.00380i) q^{13} +(-2.60799 + 0.196530i) q^{14} +(5.63848 + 0.783815i) q^{15} +(-0.157705 + 0.894392i) q^{16} -0.671106 q^{17} +(-2.12706 + 2.06645i) q^{18} -2.12460 q^{19} +(3.15896 - 1.14977i) q^{20} +(-4.57351 - 0.288108i) q^{21} +(-2.61023 + 2.19024i) q^{22} +(-0.996522 - 5.65156i) q^{23} +(-1.59196 + 4.92467i) q^{24} +(4.44481 + 3.72964i) q^{25} +(0.503792 + 0.872594i) q^{26} +(-4.18999 + 3.07311i) q^{27} +(-2.46619 + 1.11402i) q^{28} +(0.678506 - 3.84800i) q^{29} +(-5.50263 + 1.17825i) q^{30} +(7.91115 - 6.63825i) q^{31} +(0.881871 + 5.00134i) q^{32} +(-5.05837 + 3.17138i) q^{33} +(0.623395 - 0.226897i) q^{34} +(-7.06251 - 5.07316i) q^{35} +(-1.33685 + 2.76194i) q^{36} +(4.55770 - 7.89416i) q^{37} +(1.97356 - 0.718318i) q^{38} +(0.663803 + 1.63590i) q^{39} +(-7.52335 + 6.31284i) q^{40} +(0.857967 + 4.86577i) q^{41} +(4.34578 - 1.27865i) q^{42} +(-2.16071 - 1.81305i) q^{43} +(-1.76282 + 3.05329i) q^{44} +(-9.83392 + 0.717305i) q^{45} +(2.83644 + 4.91286i) q^{46} +(-0.379189 - 0.318177i) q^{47} +(-0.0572559 - 1.57199i) q^{48} +(5.97606 + 3.64509i) q^{49} +(-5.38979 - 1.96172i) q^{50} +(1.13662 - 0.243379i) q^{51} +(0.798636 + 0.670135i) q^{52} +(-4.04846 + 7.01214i) q^{53} +(2.85311 - 4.27125i) q^{54} -11.3291 q^{55} +(5.65724 - 5.52250i) q^{56} +(3.59836 - 0.770497i) q^{57} +(0.670718 + 3.80383i) q^{58} +(-1.67822 - 9.51765i) q^{59} +(-4.93323 + 3.09292i) q^{60} +(6.71058 + 5.63085i) q^{61} +(-5.10438 + 8.84104i) q^{62} +(7.85045 - 1.17065i) q^{63} +(-3.41829 - 5.92066i) q^{64} +(-0.581732 + 3.29916i) q^{65} +(3.62653 - 4.65613i) q^{66} +(-9.15746 - 3.33304i) q^{67} +(0.525830 - 0.441223i) q^{68} +(3.73733 + 9.21042i) q^{69} +(8.27563 + 2.32470i) q^{70} +(4.72319 + 8.18081i) q^{71} +(0.910285 - 8.91805i) q^{72} +(-5.56377 - 9.63672i) q^{73} +(-1.56470 + 8.87388i) q^{74} +(-8.88056 - 4.70481i) q^{75} +(1.66469 - 1.39684i) q^{76} +(9.09404 - 0.685297i) q^{77} +(-1.16970 - 1.29517i) q^{78} +(0.194091 - 0.0706432i) q^{79} +(1.49247 - 2.58503i) q^{80} +(5.98194 - 6.72431i) q^{81} +(-2.44206 - 4.22978i) q^{82} +(2.37994 - 13.4973i) q^{83} +(3.77289 - 2.78115i) q^{84} +(2.07269 + 0.754398i) q^{85} +(2.62008 + 0.953630i) q^{86} +(0.246335 + 6.76326i) q^{87} +(1.78857 - 10.1435i) q^{88} +11.9916 q^{89} +(8.89229 - 3.99111i) q^{90} +(0.267399 - 2.68348i) q^{91} +(4.49646 + 3.77298i) q^{92} +(-10.9914 + 14.1119i) q^{93} +(0.459806 + 0.167356i) q^{94} +(6.56178 + 2.38829i) q^{95} +(-3.30735 - 8.15075i) q^{96} +(0.577101 + 0.484245i) q^{97} +(-6.78360 - 1.36548i) q^{98} +(7.41704 - 7.20568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.928908 + 0.338095i −0.656837 + 0.239069i −0.648870 0.760899i \(-0.724758\pi\)
−0.00796681 + 0.999968i \(0.502536\pi\)
\(3\) −1.69366 + 0.362654i −0.977835 + 0.209379i
\(4\) −0.783527 + 0.657458i −0.391764 + 0.328729i
\(5\) −3.08847 1.12411i −1.38121 0.502718i −0.458663 0.888610i \(-0.651671\pi\)
−0.922544 + 0.385892i \(0.873894\pi\)
\(6\) 1.45064 0.909490i 0.592222 0.371298i
\(7\) 2.54716 + 0.715520i 0.962736 + 0.270441i
\(8\) 1.49406 2.58780i 0.528232 0.914924i
\(9\) 2.73696 1.22843i 0.912321 0.409475i
\(10\) 3.24896 1.02741
\(11\) 3.23909 1.17893i 0.976622 0.355462i 0.196096 0.980585i \(-0.437173\pi\)
0.780526 + 0.625123i \(0.214951\pi\)
\(12\) 1.08860 1.39766i 0.314251 0.403469i
\(13\) −0.176997 1.00380i −0.0490900 0.278403i 0.950375 0.311106i \(-0.100700\pi\)
−0.999465 + 0.0327031i \(0.989588\pi\)
\(14\) −2.60799 + 0.196530i −0.697015 + 0.0525248i
\(15\) 5.63848 + 0.783815i 1.45585 + 0.202380i
\(16\) −0.157705 + 0.894392i −0.0394264 + 0.223598i
\(17\) −0.671106 −0.162767 −0.0813835 0.996683i \(-0.525934\pi\)
−0.0813835 + 0.996683i \(0.525934\pi\)
\(18\) −2.12706 + 2.06645i −0.501353 + 0.487066i
\(19\) −2.12460 −0.487418 −0.243709 0.969848i \(-0.578364\pi\)
−0.243709 + 0.969848i \(0.578364\pi\)
\(20\) 3.15896 1.14977i 0.706365 0.257096i
\(21\) −4.57351 0.288108i −0.998022 0.0628704i
\(22\) −2.61023 + 2.19024i −0.556502 + 0.466961i
\(23\) −0.996522 5.65156i −0.207789 1.17843i −0.892990 0.450077i \(-0.851397\pi\)
0.685201 0.728354i \(-0.259714\pi\)
\(24\) −1.59196 + 4.92467i −0.324958 + 1.00524i
\(25\) 4.44481 + 3.72964i 0.888962 + 0.745928i
\(26\) 0.503792 + 0.872594i 0.0988018 + 0.171130i
\(27\) −4.18999 + 3.07311i −0.806364 + 0.591420i
\(28\) −2.46619 + 1.11402i −0.466067 + 0.210530i
\(29\) 0.678506 3.84800i 0.125995 0.714555i −0.854716 0.519095i \(-0.826269\pi\)
0.980712 0.195460i \(-0.0626199\pi\)
\(30\) −5.50263 + 1.17825i −1.00464 + 0.215118i
\(31\) 7.91115 6.63825i 1.42089 1.19226i 0.470021 0.882655i \(-0.344246\pi\)
0.950864 0.309609i \(-0.100198\pi\)
\(32\) 0.881871 + 5.00134i 0.155894 + 0.884120i
\(33\) −5.05837 + 3.17138i −0.880549 + 0.552066i
\(34\) 0.623395 0.226897i 0.106911 0.0389126i
\(35\) −7.06251 5.07316i −1.19378 0.857520i
\(36\) −1.33685 + 2.76194i −0.222808 + 0.460324i
\(37\) 4.55770 7.89416i 0.749281 1.29779i −0.198887 0.980022i \(-0.563733\pi\)
0.948168 0.317770i \(-0.102934\pi\)
\(38\) 1.97356 0.718318i 0.320154 0.116527i
\(39\) 0.663803 + 1.63590i 0.106294 + 0.261954i
\(40\) −7.52335 + 6.31284i −1.18955 + 0.998148i
\(41\) 0.857967 + 4.86577i 0.133992 + 0.759906i 0.975556 + 0.219749i \(0.0705239\pi\)
−0.841564 + 0.540157i \(0.818365\pi\)
\(42\) 4.34578 1.27865i 0.670568 0.197301i
\(43\) −2.16071 1.81305i −0.329504 0.276487i 0.462993 0.886362i \(-0.346775\pi\)
−0.792498 + 0.609875i \(0.791220\pi\)
\(44\) −1.76282 + 3.05329i −0.265755 + 0.460301i
\(45\) −9.83392 + 0.717305i −1.46595 + 0.106930i
\(46\) 2.83644 + 4.91286i 0.418210 + 0.724361i
\(47\) −0.379189 0.318177i −0.0553104 0.0464109i 0.614713 0.788751i \(-0.289272\pi\)
−0.670024 + 0.742340i \(0.733716\pi\)
\(48\) −0.0572559 1.57199i −0.00826417 0.226897i
\(49\) 5.97606 + 3.64509i 0.853723 + 0.520727i
\(50\) −5.38979 1.96172i −0.762231 0.277429i
\(51\) 1.13662 0.243379i 0.159159 0.0340799i
\(52\) 0.798636 + 0.670135i 0.110751 + 0.0929310i
\(53\) −4.04846 + 7.01214i −0.556099 + 0.963191i 0.441718 + 0.897154i \(0.354369\pi\)
−0.997817 + 0.0660375i \(0.978964\pi\)
\(54\) 2.85311 4.27125i 0.388259 0.581243i
\(55\) −11.3291 −1.52761
\(56\) 5.65724 5.52250i 0.755981 0.737975i
\(57\) 3.59836 0.770497i 0.476614 0.102055i
\(58\) 0.670718 + 3.80383i 0.0880696 + 0.499468i
\(59\) −1.67822 9.51765i −0.218485 1.23909i −0.874755 0.484566i \(-0.838978\pi\)
0.656269 0.754527i \(-0.272134\pi\)
\(60\) −4.93323 + 3.09292i −0.636877 + 0.399295i
\(61\) 6.71058 + 5.63085i 0.859202 + 0.720956i 0.961796 0.273767i \(-0.0882698\pi\)
−0.102594 + 0.994723i \(0.532714\pi\)
\(62\) −5.10438 + 8.84104i −0.648256 + 1.12281i
\(63\) 7.85045 1.17065i 0.989064 0.147488i
\(64\) −3.41829 5.92066i −0.427287 0.740082i
\(65\) −0.581732 + 3.29916i −0.0721549 + 0.409211i
\(66\) 3.62653 4.65613i 0.446395 0.573130i
\(67\) −9.15746 3.33304i −1.11876 0.407196i −0.284562 0.958658i \(-0.591848\pi\)
−0.834200 + 0.551462i \(0.814070\pi\)
\(68\) 0.525830 0.441223i 0.0637662 0.0535062i
\(69\) 3.73733 + 9.21042i 0.449922 + 1.10880i
\(70\) 8.27563 + 2.32470i 0.989127 + 0.277855i
\(71\) 4.72319 + 8.18081i 0.560540 + 0.970883i 0.997449 + 0.0713778i \(0.0227396\pi\)
−0.436910 + 0.899505i \(0.643927\pi\)
\(72\) 0.910285 8.91805i 0.107278 1.05100i
\(73\) −5.56377 9.63672i −0.651189 1.12789i −0.982835 0.184489i \(-0.940937\pi\)
0.331645 0.943404i \(-0.392396\pi\)
\(74\) −1.56470 + 8.87388i −0.181893 + 1.03157i
\(75\) −8.88056 4.70481i −1.02544 0.543264i
\(76\) 1.66469 1.39684i 0.190953 0.160228i
\(77\) 9.09404 0.685297i 1.03636 0.0780968i
\(78\) −1.16970 1.29517i −0.132443 0.146650i
\(79\) 0.194091 0.0706432i 0.0218369 0.00794798i −0.331079 0.943603i \(-0.607413\pi\)
0.352916 + 0.935655i \(0.385190\pi\)
\(80\) 1.49247 2.58503i 0.166863 0.289015i
\(81\) 5.98194 6.72431i 0.664660 0.747146i
\(82\) −2.44206 4.22978i −0.269681 0.467101i
\(83\) 2.37994 13.4973i 0.261232 1.48152i −0.518321 0.855186i \(-0.673443\pi\)
0.779553 0.626336i \(-0.215446\pi\)
\(84\) 3.77289 2.78115i 0.411656 0.303448i
\(85\) 2.07269 + 0.754398i 0.224815 + 0.0818259i
\(86\) 2.62008 + 0.953630i 0.282530 + 0.102833i
\(87\) 0.246335 + 6.76326i 0.0264099 + 0.725097i
\(88\) 1.78857 10.1435i 0.190663 1.08130i
\(89\) 11.9916 1.27111 0.635553 0.772057i \(-0.280772\pi\)
0.635553 + 0.772057i \(0.280772\pi\)
\(90\) 8.89229 3.99111i 0.937330 0.420700i
\(91\) 0.267399 2.68348i 0.0280310 0.281305i
\(92\) 4.49646 + 3.77298i 0.468788 + 0.393360i
\(93\) −10.9914 + 14.1119i −1.13976 + 1.46334i
\(94\) 0.459806 + 0.167356i 0.0474253 + 0.0172614i
\(95\) 6.56178 + 2.38829i 0.673225 + 0.245034i
\(96\) −3.30735 8.15075i −0.337555 0.831882i
\(97\) 0.577101 + 0.484245i 0.0585957 + 0.0491676i 0.671615 0.740900i \(-0.265601\pi\)
−0.613019 + 0.790068i \(0.710045\pi\)
\(98\) −6.78360 1.36548i −0.685247 0.137934i
\(99\) 7.41704 7.20568i 0.745441 0.724198i
\(100\) −5.93471 −0.593471
\(101\) −1.01306 + 5.74536i −0.100803 + 0.571684i 0.892010 + 0.452015i \(0.149295\pi\)
−0.992814 + 0.119669i \(0.961817\pi\)
\(102\) −0.973534 + 0.610364i −0.0963942 + 0.0604350i
\(103\) −9.79821 3.56626i −0.965447 0.351394i −0.189281 0.981923i \(-0.560616\pi\)
−0.776166 + 0.630529i \(0.782838\pi\)
\(104\) −2.86207 1.04171i −0.280649 0.102148i
\(105\) 13.8013 + 6.03095i 1.34687 + 0.588561i
\(106\) 1.38988 7.88239i 0.134997 0.765606i
\(107\) 3.21721 + 5.57237i 0.311019 + 0.538701i 0.978583 0.205851i \(-0.0659963\pi\)
−0.667564 + 0.744552i \(0.732663\pi\)
\(108\) 1.26253 5.16260i 0.121487 0.496772i
\(109\) 0.963502 1.66883i 0.0922868 0.159845i −0.816186 0.577789i \(-0.803916\pi\)
0.908473 + 0.417944i \(0.137249\pi\)
\(110\) 10.5237 3.83031i 1.00339 0.365205i
\(111\) −4.85633 + 15.0229i −0.460943 + 1.42591i
\(112\) −1.04166 + 2.16532i −0.0984273 + 0.204604i
\(113\) −12.2378 + 10.2688i −1.15124 + 0.966004i −0.999748 0.0224549i \(-0.992852\pi\)
−0.151491 + 0.988459i \(0.548407\pi\)
\(114\) −3.08204 + 1.93231i −0.288659 + 0.180977i
\(115\) −3.27525 + 18.5749i −0.305419 + 1.73212i
\(116\) 1.99827 + 3.46110i 0.185534 + 0.321355i
\(117\) −1.71752 2.52993i −0.158785 0.233892i
\(118\) 4.77678 + 8.27362i 0.439738 + 0.761649i
\(119\) −1.70941 0.480190i −0.156702 0.0440189i
\(120\) 10.4526 13.4202i 0.954188 1.22509i
\(121\) 0.675336 0.566674i 0.0613941 0.0515158i
\(122\) −8.13727 2.96172i −0.736714 0.268142i
\(123\) −3.21770 7.92981i −0.290130 0.715007i
\(124\) −1.83424 + 10.4025i −0.164720 + 0.934172i
\(125\) −1.31843 2.28359i −0.117924 0.204250i
\(126\) −6.89656 + 3.74162i −0.614394 + 0.333330i
\(127\) 10.3519 17.9300i 0.918584 1.59103i 0.117017 0.993130i \(-0.462667\pi\)
0.801567 0.597905i \(-0.204000\pi\)
\(128\) −2.60368 2.18475i −0.230135 0.193106i
\(129\) 4.31701 + 2.28709i 0.380091 + 0.201367i
\(130\) −0.575055 3.26130i −0.0504357 0.286035i
\(131\) −1.84629 10.4708i −0.161311 0.914839i −0.952787 0.303639i \(-0.901798\pi\)
0.791476 0.611200i \(-0.209313\pi\)
\(132\) 1.87832 5.81053i 0.163487 0.505741i
\(133\) −5.41171 1.52020i −0.469255 0.131818i
\(134\) 9.63332 0.832192
\(135\) 16.3952 4.78119i 1.41107 0.411499i
\(136\) −1.00268 + 1.73668i −0.0859787 + 0.148919i
\(137\) 2.50596 + 2.10275i 0.214099 + 0.179650i 0.743530 0.668703i \(-0.233150\pi\)
−0.529431 + 0.848353i \(0.677595\pi\)
\(138\) −6.58563 7.29206i −0.560606 0.620741i
\(139\) −13.7217 4.99429i −1.16386 0.423610i −0.313385 0.949626i \(-0.601463\pi\)
−0.850475 + 0.526016i \(0.823685\pi\)
\(140\) 8.86906 0.668343i 0.749572 0.0564853i
\(141\) 0.757605 + 0.401369i 0.0638019 + 0.0338014i
\(142\) −7.15330 6.00233i −0.600291 0.503704i
\(143\) −1.75672 3.04272i −0.146904 0.254445i
\(144\) 0.667060 + 2.64165i 0.0555884 + 0.220137i
\(145\) −6.42112 + 11.1217i −0.533245 + 0.923608i
\(146\) 8.42635 + 7.07055i 0.697370 + 0.585163i
\(147\) −11.4433 4.00630i −0.943829 0.330434i
\(148\) 1.61900 + 9.18178i 0.133081 + 0.754738i
\(149\) 0.941784 0.790250i 0.0771539 0.0647398i −0.603395 0.797442i \(-0.706186\pi\)
0.680549 + 0.732703i \(0.261741\pi\)
\(150\) 9.83989 + 1.36786i 0.803424 + 0.111685i
\(151\) −4.50794 + 1.64076i −0.366851 + 0.133523i −0.518867 0.854855i \(-0.673646\pi\)
0.152015 + 0.988378i \(0.451424\pi\)
\(152\) −3.17430 + 5.49804i −0.257469 + 0.445950i
\(153\) −1.83679 + 0.824403i −0.148496 + 0.0666491i
\(154\) −8.21582 + 3.71122i −0.662050 + 0.299059i
\(155\) −31.8955 + 11.6090i −2.56191 + 0.932459i
\(156\) −1.59564 0.845352i −0.127754 0.0676823i
\(157\) 0.378984 + 2.14933i 0.0302462 + 0.171535i 0.996189 0.0872209i \(-0.0277986\pi\)
−0.965943 + 0.258756i \(0.916687\pi\)
\(158\) −0.156408 + 0.131242i −0.0124432 + 0.0104411i
\(159\) 4.31373 13.3444i 0.342101 1.05828i
\(160\) 2.89843 16.4378i 0.229141 1.29952i
\(161\) 1.50550 15.1085i 0.118650 1.19071i
\(162\) −3.28322 + 8.26873i −0.257954 + 0.649653i
\(163\) 9.88080 + 17.1140i 0.773924 + 1.34048i 0.935397 + 0.353599i \(0.115042\pi\)
−0.161473 + 0.986877i \(0.551625\pi\)
\(164\) −3.87128 3.24839i −0.302296 0.253657i
\(165\) 19.1876 4.10854i 1.49375 0.319850i
\(166\) 2.35263 + 13.3424i 0.182599 + 1.03557i
\(167\) −2.28071 + 1.91374i −0.176486 + 0.148090i −0.726752 0.686900i \(-0.758971\pi\)
0.550265 + 0.834990i \(0.314527\pi\)
\(168\) −7.57869 + 11.4049i −0.584708 + 0.879904i
\(169\) 11.2397 4.09092i 0.864594 0.314686i
\(170\) −2.18040 −0.167229
\(171\) −5.81497 + 2.60992i −0.444682 + 0.199585i
\(172\) 2.88497 0.219977
\(173\) −0.958517 + 5.43602i −0.0728747 + 0.413293i 0.926446 + 0.376429i \(0.122848\pi\)
−0.999320 + 0.0368643i \(0.988263\pi\)
\(174\) −2.51544 6.19916i −0.190695 0.469957i
\(175\) 8.65301 + 12.6803i 0.654106 + 0.958544i
\(176\) 0.543606 + 3.08294i 0.0409758 + 0.232385i
\(177\) 6.29395 + 15.5110i 0.473082 + 1.16588i
\(178\) −11.1391 + 4.05430i −0.834910 + 0.303882i
\(179\) −5.90252 −0.441175 −0.220587 0.975367i \(-0.570797\pi\)
−0.220587 + 0.975367i \(0.570797\pi\)
\(180\) 7.23355 7.02742i 0.539157 0.523793i
\(181\) −2.83075 + 4.90300i −0.210408 + 0.364437i −0.951842 0.306588i \(-0.900813\pi\)
0.741434 + 0.671025i \(0.234146\pi\)
\(182\) 0.658882 + 2.58311i 0.0488395 + 0.191473i
\(183\) −13.4075 7.10311i −0.991110 0.525077i
\(184\) −16.1139 5.86500i −1.18794 0.432373i
\(185\) −22.9502 + 19.2575i −1.68733 + 1.41584i
\(186\) 5.43883 16.8248i 0.398795 1.23366i
\(187\) −2.17377 + 0.791188i −0.158962 + 0.0578574i
\(188\) 0.506293 0.0369252
\(189\) −12.8715 + 4.82968i −0.936260 + 0.351307i
\(190\) −6.90276 −0.500779
\(191\) −4.04867 + 1.47360i −0.292952 + 0.106626i −0.484315 0.874894i \(-0.660931\pi\)
0.191364 + 0.981519i \(0.438709\pi\)
\(192\) 7.93658 + 8.78792i 0.572773 + 0.634213i
\(193\) −15.1185 + 12.6859i −1.08825 + 0.913154i −0.996580 0.0826352i \(-0.973666\pi\)
−0.0916745 + 0.995789i \(0.529222\pi\)
\(194\) −0.699794 0.254704i −0.0502423 0.0182867i
\(195\) −0.211201 5.79863i −0.0151244 0.415248i
\(196\) −7.07890 + 1.07298i −0.505636 + 0.0766413i
\(197\) −6.17755 + 10.6998i −0.440132 + 0.762332i −0.997699 0.0678007i \(-0.978402\pi\)
0.557567 + 0.830132i \(0.311735\pi\)
\(198\) −4.45355 + 9.20107i −0.316500 + 0.653892i
\(199\) 26.5953 1.88529 0.942644 0.333801i \(-0.108331\pi\)
0.942644 + 0.333801i \(0.108331\pi\)
\(200\) 16.2924 5.92994i 1.15204 0.419310i
\(201\) 16.7184 + 2.32405i 1.17922 + 0.163926i
\(202\) −1.00143 5.67942i −0.0704607 0.399602i
\(203\) 4.48158 9.31598i 0.314545 0.653854i
\(204\) −0.730565 + 0.937977i −0.0511498 + 0.0656715i
\(205\) 2.81987 15.9922i 0.196948 1.11695i
\(206\) 10.3074 0.718148
\(207\) −9.66996 14.2440i −0.672109 0.990023i
\(208\) 0.925702 0.0641859
\(209\) −6.88179 + 2.50477i −0.476023 + 0.173258i
\(210\) −14.8592 0.936053i −1.02538 0.0645938i
\(211\) −9.85354 + 8.26810i −0.678345 + 0.569199i −0.915522 0.402267i \(-0.868222\pi\)
0.237177 + 0.971466i \(0.423778\pi\)
\(212\) −1.43810 8.15589i −0.0987694 0.560149i
\(213\) −10.9663 12.1426i −0.751397 0.831998i
\(214\) −4.87248 4.08849i −0.333076 0.279484i
\(215\) 4.63521 + 8.02842i 0.316119 + 0.547534i
\(216\) 1.69246 + 15.4343i 0.115157 + 1.05017i
\(217\) 24.9008 11.2481i 1.69038 0.763570i
\(218\) −0.330780 + 1.87595i −0.0224033 + 0.127055i
\(219\) 12.9179 + 14.3036i 0.872912 + 0.966548i
\(220\) 8.87665 7.44840i 0.598464 0.502171i
\(221\) 0.118783 + 0.673654i 0.00799024 + 0.0453149i
\(222\) −0.568075 15.5968i −0.0381267 1.04679i
\(223\) −8.87626 + 3.23070i −0.594399 + 0.216343i −0.621663 0.783285i \(-0.713543\pi\)
0.0272643 + 0.999628i \(0.491320\pi\)
\(224\) −1.33229 + 13.3702i −0.0890175 + 0.893335i
\(225\) 16.7469 + 4.74776i 1.11646 + 0.316518i
\(226\) 7.89600 13.6763i 0.525234 0.909733i
\(227\) 19.7270 7.18003i 1.30933 0.476555i 0.409303 0.912399i \(-0.365772\pi\)
0.900023 + 0.435843i \(0.143550\pi\)
\(228\) −2.31284 + 2.96947i −0.153172 + 0.196658i
\(229\) 10.8428 9.09815i 0.716509 0.601223i −0.209908 0.977721i \(-0.567316\pi\)
0.926417 + 0.376498i \(0.122872\pi\)
\(230\) −3.23766 18.3617i −0.213485 1.21073i
\(231\) −15.1537 + 4.45865i −0.997038 + 0.293358i
\(232\) −8.94410 7.50499i −0.587209 0.492727i
\(233\) 5.14746 8.91566i 0.337221 0.584084i −0.646688 0.762755i \(-0.723846\pi\)
0.983909 + 0.178671i \(0.0571797\pi\)
\(234\) 2.45078 + 1.76939i 0.160212 + 0.115668i
\(235\) 0.813448 + 1.40893i 0.0530635 + 0.0919086i
\(236\) 7.57238 + 6.35398i 0.492920 + 0.413609i
\(237\) −0.303104 + 0.190033i −0.0196887 + 0.0123440i
\(238\) 1.75024 0.131892i 0.113451 0.00854930i
\(239\) 28.3320 + 10.3120i 1.83264 + 0.667028i 0.992126 + 0.125245i \(0.0399717\pi\)
0.840518 + 0.541783i \(0.182251\pi\)
\(240\) −1.59026 + 4.91940i −0.102651 + 0.317546i
\(241\) 3.05870 + 2.56656i 0.197028 + 0.165326i 0.735964 0.677020i \(-0.236729\pi\)
−0.538936 + 0.842347i \(0.681174\pi\)
\(242\) −0.435735 + 0.754715i −0.0280101 + 0.0485149i
\(243\) −7.69277 + 13.5581i −0.493491 + 0.869751i
\(244\) −8.95997 −0.573603
\(245\) −14.3594 17.9755i −0.917389 1.14841i
\(246\) 5.66997 + 6.27818i 0.361504 + 0.400282i
\(247\) 0.376048 + 2.13267i 0.0239273 + 0.135699i
\(248\) −5.35865 30.3904i −0.340275 1.92979i
\(249\) 0.864051 + 23.7229i 0.0547570 + 1.50338i
\(250\) 1.99677 + 1.67549i 0.126287 + 0.105967i
\(251\) 8.78270 15.2121i 0.554359 0.960178i −0.443594 0.896228i \(-0.646297\pi\)
0.997953 0.0639504i \(-0.0203700\pi\)
\(252\) −5.38139 + 6.07857i −0.338996 + 0.382914i
\(253\) −9.89063 17.1311i −0.621818 1.07702i
\(254\) −3.55392 + 20.1553i −0.222993 + 1.26466i
\(255\) −3.78402 0.526022i −0.236964 0.0329408i
\(256\) 16.0058 + 5.82564i 1.00036 + 0.364102i
\(257\) −0.906230 + 0.760418i −0.0565291 + 0.0474335i −0.670614 0.741806i \(-0.733969\pi\)
0.614085 + 0.789240i \(0.289525\pi\)
\(258\) −4.78336 0.664942i −0.297799 0.0413975i
\(259\) 17.2576 16.8466i 1.07234 1.04680i
\(260\) −1.71326 2.96745i −0.106252 0.184033i
\(261\) −2.86993 11.3653i −0.177644 0.703496i
\(262\) 5.25516 + 9.10220i 0.324665 + 0.562336i
\(263\) 1.75013 9.92549i 0.107918 0.612032i −0.882097 0.471068i \(-0.843869\pi\)
0.990015 0.140964i \(-0.0450202\pi\)
\(264\) 0.649352 + 17.8283i 0.0399648 + 1.09725i
\(265\) 20.3860 17.1059i 1.25230 1.05081i
\(266\) 5.54095 0.417548i 0.339737 0.0256015i
\(267\) −20.3097 + 4.34880i −1.24293 + 0.266142i
\(268\) 9.36646 3.40911i 0.572147 0.208245i
\(269\) −4.91936 + 8.52058i −0.299939 + 0.519509i −0.976122 0.217225i \(-0.930300\pi\)
0.676183 + 0.736734i \(0.263633\pi\)
\(270\) −13.6131 + 9.98441i −0.828468 + 0.607632i
\(271\) 5.99552 + 10.3846i 0.364202 + 0.630817i 0.988648 0.150252i \(-0.0480084\pi\)
−0.624446 + 0.781068i \(0.714675\pi\)
\(272\) 0.105837 0.600232i 0.00641731 0.0363944i
\(273\) 0.520293 + 4.64187i 0.0314896 + 0.280939i
\(274\) −3.03874 1.10601i −0.183577 0.0668166i
\(275\) 18.7941 + 6.84050i 1.13333 + 0.412498i
\(276\) −8.98376 4.75948i −0.540759 0.286487i
\(277\) 2.20992 12.5331i 0.132781 0.753040i −0.843598 0.536976i \(-0.819567\pi\)
0.976379 0.216065i \(-0.0693222\pi\)
\(278\) 14.4347 0.865738
\(279\) 13.4979 27.8869i 0.808101 1.66955i
\(280\) −23.6801 + 10.6967i −1.41516 + 0.639251i
\(281\) −18.1559 15.2346i −1.08309 0.908821i −0.0869166 0.996216i \(-0.527701\pi\)
−0.996174 + 0.0873949i \(0.972146\pi\)
\(282\) −0.839446 0.116693i −0.0499883 0.00694896i
\(283\) −2.41643 0.879507i −0.143642 0.0522813i 0.269199 0.963085i \(-0.413241\pi\)
−0.412841 + 0.910803i \(0.635463\pi\)
\(284\) −9.07928 3.30459i −0.538756 0.196091i
\(285\) −11.9795 1.66530i −0.709607 0.0986436i
\(286\) 2.66056 + 2.23247i 0.157322 + 0.132009i
\(287\) −1.29618 + 13.0078i −0.0765110 + 0.767826i
\(288\) 8.55742 + 12.6052i 0.504251 + 0.742767i
\(289\) −16.5496 −0.973507
\(290\) 2.20444 12.5020i 0.129449 0.734142i
\(291\) −1.15303 0.610858i −0.0675916 0.0358091i
\(292\) 10.6951 + 3.89270i 0.625883 + 0.227803i
\(293\) 6.68694 + 2.43385i 0.390655 + 0.142187i 0.529877 0.848074i \(-0.322238\pi\)
−0.139222 + 0.990261i \(0.544460\pi\)
\(294\) 11.9843 0.147446i 0.698938 0.00859922i
\(295\) −5.51577 + 31.2815i −0.321141 + 1.82128i
\(296\) −13.6190 23.5888i −0.791587 1.37107i
\(297\) −9.94877 + 14.8938i −0.577286 + 0.864225i
\(298\) −0.607651 + 1.05248i −0.0352003 + 0.0609686i
\(299\) −5.49664 + 2.00061i −0.317879 + 0.115698i
\(300\) 10.0514 2.15225i 0.580316 0.124260i
\(301\) −4.20639 6.16415i −0.242452 0.355296i
\(302\) 3.63273 3.04822i 0.209040 0.175406i
\(303\) −0.367798 10.0981i −0.0211294 0.580119i
\(304\) 0.335062 1.90023i 0.0192171 0.108986i
\(305\) −14.3957 24.9342i −0.824298 1.42773i
\(306\) 1.42748 1.38680i 0.0816038 0.0792783i
\(307\) 13.1124 + 22.7114i 0.748365 + 1.29621i 0.948606 + 0.316459i \(0.102494\pi\)
−0.200241 + 0.979747i \(0.564173\pi\)
\(308\) −6.67487 + 6.51589i −0.380336 + 0.371277i
\(309\) 17.8882 + 2.48666i 1.01762 + 0.141461i
\(310\) 25.7030 21.5674i 1.45983 1.22495i
\(311\) 8.88367 + 3.23339i 0.503747 + 0.183349i 0.581378 0.813633i \(-0.302514\pi\)
−0.0776317 + 0.996982i \(0.524736\pi\)
\(312\) 5.22515 + 0.726356i 0.295816 + 0.0411218i
\(313\) −3.62216 + 20.5423i −0.204737 + 1.16112i 0.693117 + 0.720825i \(0.256237\pi\)
−0.897854 + 0.440294i \(0.854874\pi\)
\(314\) −1.07872 1.86839i −0.0608756 0.105440i
\(315\) −25.5618 5.20928i −1.44025 0.293510i
\(316\) −0.105630 + 0.182957i −0.00594217 + 0.0102921i
\(317\) −6.32445 5.30684i −0.355216 0.298062i 0.447664 0.894202i \(-0.352256\pi\)
−0.802881 + 0.596140i \(0.796700\pi\)
\(318\) 0.504603 + 13.8541i 0.0282967 + 0.776901i
\(319\) −2.33879 13.2639i −0.130947 0.742637i
\(320\) 3.90182 + 22.1283i 0.218118 + 1.23701i
\(321\) −7.46970 8.27096i −0.416918 0.461640i
\(322\) 3.70962 + 14.5434i 0.206729 + 0.810470i
\(323\) 1.42583 0.0793355
\(324\) −0.266063 + 9.20156i −0.0147813 + 0.511198i
\(325\) 2.95708 5.12182i 0.164030 0.284108i
\(326\) −14.9645 12.5567i −0.828808 0.695453i
\(327\) −1.02663 + 3.17586i −0.0567730 + 0.175625i
\(328\) 13.8735 + 5.04953i 0.766035 + 0.278814i
\(329\) −0.738193 1.08177i −0.0406979 0.0596397i
\(330\) −16.4345 + 10.3037i −0.904687 + 0.567200i
\(331\) 0.524709 + 0.440283i 0.0288406 + 0.0242001i 0.657094 0.753809i \(-0.271785\pi\)
−0.628253 + 0.778009i \(0.716230\pi\)
\(332\) 7.00916 + 12.1402i 0.384678 + 0.666281i
\(333\) 2.77686 27.2048i 0.152171 1.49082i
\(334\) 1.47154 2.54878i 0.0805191 0.139463i
\(335\) 24.5358 + 20.5880i 1.34054 + 1.12484i
\(336\) 0.978950 4.04508i 0.0534061 0.220677i
\(337\) −1.52858 8.66903i −0.0832672 0.472232i −0.997717 0.0675326i \(-0.978487\pi\)
0.914450 0.404699i \(-0.132624\pi\)
\(338\) −9.05754 + 7.60018i −0.492665 + 0.413395i
\(339\) 17.0027 21.8299i 0.923460 1.18564i
\(340\) −2.11999 + 0.771615i −0.114973 + 0.0418467i
\(341\) 17.7989 30.8286i 0.963864 1.66946i
\(342\) 4.51917 4.39038i 0.244369 0.237405i
\(343\) 12.6139 + 13.5606i 0.681084 + 0.732205i
\(344\) −7.92003 + 2.88265i −0.427019 + 0.155422i
\(345\) −1.18910 32.6473i −0.0640189 1.75767i
\(346\) −0.947516 5.37363i −0.0509388 0.288888i
\(347\) 2.53038 2.12324i 0.135838 0.113982i −0.572337 0.820018i \(-0.693963\pi\)
0.708175 + 0.706037i \(0.249519\pi\)
\(348\) −4.63957 5.13724i −0.248707 0.275385i
\(349\) −3.90078 + 22.1224i −0.208804 + 1.18419i 0.682537 + 0.730851i \(0.260877\pi\)
−0.891341 + 0.453334i \(0.850234\pi\)
\(350\) −12.3250 8.85333i −0.658799 0.473230i
\(351\) 3.82639 + 3.66197i 0.204238 + 0.195462i
\(352\) 8.75270 + 15.1601i 0.466520 + 0.808037i
\(353\) −3.45775 2.90140i −0.184037 0.154426i 0.546115 0.837710i \(-0.316106\pi\)
−0.730152 + 0.683285i \(0.760551\pi\)
\(354\) −11.0907 12.2804i −0.589464 0.652695i
\(355\) −5.39130 30.5756i −0.286141 1.62278i
\(356\) −9.39574 + 7.88396i −0.497973 + 0.417849i
\(357\) 3.06931 + 0.193351i 0.162445 + 0.0102332i
\(358\) 5.48289 1.99561i 0.289780 0.105471i
\(359\) −19.1054 −1.00835 −0.504173 0.863603i \(-0.668203\pi\)
−0.504173 + 0.863603i \(0.668203\pi\)
\(360\) −12.8363 + 26.5199i −0.676531 + 1.39772i
\(361\) −14.4861 −0.762424
\(362\) 0.971825 5.51150i 0.0510780 0.289678i
\(363\) −0.938282 + 1.20467i −0.0492470 + 0.0632286i
\(364\) 1.55476 + 2.27838i 0.0814915 + 0.119420i
\(365\) 6.35078 + 36.0170i 0.332415 + 1.88522i
\(366\) 14.8558 + 2.06514i 0.776527 + 0.107946i
\(367\) 5.04865 1.83756i 0.263537 0.0959197i −0.206872 0.978368i \(-0.566328\pi\)
0.470409 + 0.882448i \(0.344106\pi\)
\(368\) 5.21187 0.271687
\(369\) 8.32546 + 12.2635i 0.433406 + 0.638412i
\(370\) 14.8078 25.6478i 0.769820 1.33337i
\(371\) −15.3294 + 14.9643i −0.795863 + 0.776907i
\(372\) −0.665931 18.2835i −0.0345269 0.947954i
\(373\) 35.0210 + 12.7466i 1.81332 + 0.659994i 0.996547 + 0.0830314i \(0.0264602\pi\)
0.816771 + 0.576962i \(0.195762\pi\)
\(374\) 1.75174 1.46988i 0.0905801 0.0760058i
\(375\) 3.06113 + 3.38949i 0.158076 + 0.175032i
\(376\) −1.38991 + 0.505886i −0.0716792 + 0.0260891i
\(377\) −3.98270 −0.205120
\(378\) 10.3235 8.83809i 0.530984 0.454582i
\(379\) −35.8364 −1.84079 −0.920397 0.390985i \(-0.872134\pi\)
−0.920397 + 0.390985i \(0.872134\pi\)
\(380\) −6.71154 + 2.44280i −0.344295 + 0.125313i
\(381\) −11.0302 + 34.1216i −0.565095 + 1.74810i
\(382\) 3.26263 2.73767i 0.166931 0.140071i
\(383\) 4.95949 + 1.80511i 0.253418 + 0.0922366i 0.465606 0.884992i \(-0.345837\pi\)
−0.212188 + 0.977229i \(0.568059\pi\)
\(384\) 5.20205 + 2.75598i 0.265466 + 0.140641i
\(385\) −28.8570 8.10619i −1.47069 0.413130i
\(386\) 9.75465 16.8956i 0.496499 0.859961i
\(387\) −8.14096 2.30798i −0.413828 0.117321i
\(388\) −0.770545 −0.0391185
\(389\) 0.0879882 0.0320251i 0.00446118 0.00162374i −0.339789 0.940502i \(-0.610356\pi\)
0.344250 + 0.938878i \(0.388133\pi\)
\(390\) 2.15667 + 5.31498i 0.109207 + 0.269135i
\(391\) 0.668771 + 3.79279i 0.0338212 + 0.191810i
\(392\) 18.3614 10.0188i 0.927389 0.506027i
\(393\) 6.92427 + 17.0644i 0.349283 + 0.860786i
\(394\) 2.12082 12.0278i 0.106845 0.605950i
\(395\) −0.678854 −0.0341569
\(396\) −1.07403 + 10.5222i −0.0539719 + 0.528762i
\(397\) 2.18794 0.109809 0.0549047 0.998492i \(-0.482514\pi\)
0.0549047 + 0.998492i \(0.482514\pi\)
\(398\) −24.7045 + 8.99172i −1.23833 + 0.450714i
\(399\) 9.71690 + 0.612116i 0.486453 + 0.0306442i
\(400\) −4.03673 + 3.38722i −0.201837 + 0.169361i
\(401\) −0.0591179 0.335274i −0.00295221 0.0167428i 0.983296 0.182013i \(-0.0582614\pi\)
−0.986248 + 0.165271i \(0.947150\pi\)
\(402\) −16.3156 + 3.49357i −0.813746 + 0.174243i
\(403\) −8.06370 6.76625i −0.401682 0.337051i
\(404\) −2.98357 5.16769i −0.148438 0.257102i
\(405\) −26.0339 + 14.0435i −1.29364 + 0.697826i
\(406\) −1.01329 + 10.1689i −0.0502888 + 0.504673i
\(407\) 5.45611 30.9431i 0.270449 1.53379i
\(408\) 1.06837 3.30498i 0.0528924 0.163621i
\(409\) −4.72780 + 3.96710i −0.233775 + 0.196160i −0.752148 0.658994i \(-0.770982\pi\)
0.518373 + 0.855154i \(0.326538\pi\)
\(410\) 2.78750 + 15.8087i 0.137665 + 0.780736i
\(411\) −5.00682 2.65255i −0.246968 0.130841i
\(412\) 10.0218 3.64765i 0.493740 0.179707i
\(413\) 2.53538 25.4438i 0.124758 1.25201i
\(414\) 13.7983 + 9.96195i 0.678150 + 0.489603i
\(415\) −22.5229 + 39.0107i −1.10560 + 1.91496i
\(416\) 4.86424 1.77044i 0.238489 0.0868029i
\(417\) 25.0511 + 3.48239i 1.22676 + 0.170533i
\(418\) 5.54570 4.65339i 0.271249 0.227605i
\(419\) −0.733174 4.15804i −0.0358179 0.203133i 0.961647 0.274289i \(-0.0884424\pi\)
−0.997465 + 0.0711555i \(0.977331\pi\)
\(420\) −14.7788 + 4.34835i −0.721131 + 0.212178i
\(421\) 9.95815 + 8.35588i 0.485330 + 0.407241i 0.852349 0.522973i \(-0.175177\pi\)
−0.367019 + 0.930213i \(0.619622\pi\)
\(422\) 6.35762 11.0117i 0.309484 0.536043i
\(423\) −1.42868 0.405034i −0.0694650 0.0196934i
\(424\) 12.0973 + 20.9532i 0.587498 + 1.01758i
\(425\) −2.98294 2.50298i −0.144694 0.121412i
\(426\) 14.2920 + 7.57173i 0.692451 + 0.366851i
\(427\) 13.0639 + 19.1442i 0.632209 + 0.926454i
\(428\) −6.18437 2.25093i −0.298933 0.108803i
\(429\) 4.07874 + 4.51626i 0.196923 + 0.218047i
\(430\) −7.02005 5.89052i −0.338537 0.284066i
\(431\) −6.67486 + 11.5612i −0.321517 + 0.556883i −0.980801 0.195011i \(-0.937526\pi\)
0.659285 + 0.751893i \(0.270859\pi\)
\(432\) −2.08778 4.23214i −0.100448 0.203619i
\(433\) 20.5362 0.986905 0.493452 0.869773i \(-0.335735\pi\)
0.493452 + 0.869773i \(0.335735\pi\)
\(434\) −19.3276 + 18.8673i −0.927755 + 0.905658i
\(435\) 6.84186 21.1650i 0.328042 1.01479i
\(436\) 0.342258 + 1.94104i 0.0163912 + 0.0929589i
\(437\) 2.11721 + 12.0073i 0.101280 + 0.574388i
\(438\) −16.8355 8.91925i −0.804433 0.426178i
\(439\) −20.3215 17.0518i −0.969892 0.813836i 0.0126418 0.999920i \(-0.495976\pi\)
−0.982534 + 0.186084i \(0.940420\pi\)
\(440\) −16.9264 + 29.3174i −0.806934 + 1.39765i
\(441\) 20.8340 + 2.63533i 0.992095 + 0.125492i
\(442\) −0.338098 0.585602i −0.0160817 0.0278543i
\(443\) −1.64293 + 9.31754i −0.0780582 + 0.442690i 0.920582 + 0.390550i \(0.127715\pi\)
−0.998640 + 0.0521396i \(0.983396\pi\)
\(444\) −6.07184 14.9637i −0.288157 0.710145i
\(445\) −37.0357 13.4799i −1.75566 0.639008i
\(446\) 7.15295 6.00204i 0.338702 0.284205i
\(447\) −1.30847 + 1.67996i −0.0618886 + 0.0794592i
\(448\) −4.47059 17.5267i −0.211216 0.828060i
\(449\) −3.24013 5.61207i −0.152911 0.264850i 0.779385 0.626545i \(-0.215532\pi\)
−0.932297 + 0.361695i \(0.882198\pi\)
\(450\) −17.1615 + 1.25179i −0.809000 + 0.0590100i
\(451\) 8.51545 + 14.7492i 0.400977 + 0.694512i
\(452\) 2.83740 16.0917i 0.133460 0.756890i
\(453\) 7.03989 4.41371i 0.330763 0.207374i
\(454\) −15.8970 + 13.3392i −0.746083 + 0.626038i
\(455\) −3.84238 + 7.98726i −0.180134 + 0.374449i
\(456\) 3.38229 10.4630i 0.158390 0.489974i
\(457\) −26.1336 + 9.51184i −1.22248 + 0.444945i −0.871015 0.491257i \(-0.836538\pi\)
−0.351462 + 0.936202i \(0.614315\pi\)
\(458\) −6.99588 + 12.1172i −0.326896 + 0.566200i
\(459\) 2.81193 2.06238i 0.131249 0.0962636i
\(460\) −9.64594 16.7073i −0.449744 0.778980i
\(461\) −3.90326 + 22.1365i −0.181793 + 1.03100i 0.748214 + 0.663457i \(0.230911\pi\)
−0.930007 + 0.367541i \(0.880200\pi\)
\(462\) 12.5689 9.26505i 0.584759 0.431049i
\(463\) 0.905268 + 0.329491i 0.0420714 + 0.0153127i 0.362970 0.931801i \(-0.381763\pi\)
−0.320899 + 0.947114i \(0.603985\pi\)
\(464\) 3.33461 + 1.21370i 0.154806 + 0.0563446i
\(465\) 49.8101 31.2288i 2.30989 1.44820i
\(466\) −1.76718 + 10.0222i −0.0818628 + 0.464267i
\(467\) 16.4557 0.761479 0.380740 0.924682i \(-0.375669\pi\)
0.380740 + 0.924682i \(0.375669\pi\)
\(468\) 3.00905 + 0.853070i 0.139093 + 0.0394332i
\(469\) −20.9407 15.0421i −0.966950 0.694582i
\(470\) −1.23197 1.03375i −0.0568266 0.0476831i
\(471\) −1.42133 3.50279i −0.0654916 0.161400i
\(472\) −27.1371 9.87710i −1.24909 0.454630i
\(473\) −9.13618 3.32530i −0.420082 0.152897i
\(474\) 0.217307 0.279001i 0.00998122 0.0128150i
\(475\) −9.44346 7.92401i −0.433296 0.363578i
\(476\) 1.65508 0.747626i 0.0758603 0.0342674i
\(477\) −2.46660 + 24.1652i −0.112938 + 1.10645i
\(478\) −29.8042 −1.36321
\(479\) 1.51826 8.61050i 0.0693713 0.393424i −0.930276 0.366861i \(-0.880433\pi\)
0.999647 0.0265632i \(-0.00845633\pi\)
\(480\) 1.05229 + 28.8912i 0.0480303 + 1.31870i
\(481\) −8.73084 3.17776i −0.398092 0.144894i
\(482\) −3.70899 1.34996i −0.168940 0.0614891i
\(483\) 2.92934 + 26.1346i 0.133290 + 1.18916i
\(484\) −0.156580 + 0.888009i −0.00711727 + 0.0403640i
\(485\) −1.23801 2.14430i −0.0562153 0.0973678i
\(486\) 2.56196 15.1951i 0.116213 0.689263i
\(487\) 14.5826 25.2578i 0.660800 1.14454i −0.319605 0.947551i \(-0.603550\pi\)
0.980406 0.196989i \(-0.0631163\pi\)
\(488\) 24.5975 8.95277i 1.11348 0.405273i
\(489\) −22.9412 25.4020i −1.03744 1.14872i
\(490\) 19.4160 + 11.8428i 0.877125 + 0.535001i
\(491\) 15.5226 13.0250i 0.700526 0.587811i −0.221398 0.975184i \(-0.571062\pi\)
0.921923 + 0.387373i \(0.126617\pi\)
\(492\) 7.73467 + 4.09773i 0.348706 + 0.184740i
\(493\) −0.455349 + 2.58241i −0.0205079 + 0.116306i
\(494\) −1.07036 1.85392i −0.0481577 0.0834116i
\(495\) −31.0073 + 13.9169i −1.39368 + 0.625520i
\(496\) 4.68956 + 8.12256i 0.210568 + 0.364714i
\(497\) 6.17720 + 24.2174i 0.277085 + 1.08630i
\(498\) −8.82322 21.7443i −0.395378 0.974385i
\(499\) −1.74812 + 1.46684i −0.0782565 + 0.0656650i −0.681077 0.732212i \(-0.738488\pi\)
0.602820 + 0.797877i \(0.294044\pi\)
\(500\) 2.53439 + 0.922442i 0.113341 + 0.0412529i
\(501\) 3.16871 4.06833i 0.141568 0.181760i
\(502\) −3.01519 + 17.1000i −0.134575 + 0.763211i
\(503\) −13.6032 23.5614i −0.606535 1.05055i −0.991807 0.127747i \(-0.959226\pi\)
0.385272 0.922803i \(-0.374108\pi\)
\(504\) 8.69969 22.0644i 0.387515 0.982826i
\(505\) 9.58723 16.6056i 0.426626 0.738939i
\(506\) 14.9794 + 12.5692i 0.665916 + 0.558770i
\(507\) −17.5527 + 11.0048i −0.779541 + 0.488739i
\(508\) 3.67723 + 20.8546i 0.163151 + 0.925275i
\(509\) 1.12521 + 6.38139i 0.0498741 + 0.282850i 0.999537 0.0304233i \(-0.00968554\pi\)
−0.949663 + 0.313273i \(0.898574\pi\)
\(510\) 3.69285 0.790730i 0.163522 0.0350141i
\(511\) −7.27654 28.5273i −0.321895 1.26197i
\(512\) −10.0398 −0.443701
\(513\) 8.90207 6.52914i 0.393036 0.288268i
\(514\) 0.584711 1.01275i 0.0257905 0.0446705i
\(515\) 26.2526 + 22.0286i 1.15683 + 0.970695i
\(516\) −4.88616 + 1.04625i −0.215101 + 0.0460585i
\(517\) −1.60334 0.583567i −0.0705147 0.0256652i
\(518\) −10.3350 + 21.4836i −0.454094 + 0.943936i
\(519\) −0.347995 9.55438i −0.0152753 0.419391i
\(520\) 7.66842 + 6.43457i 0.336282 + 0.282174i
\(521\) 12.3264 + 21.3500i 0.540030 + 0.935359i 0.998902 + 0.0468563i \(0.0149203\pi\)
−0.458872 + 0.888502i \(0.651746\pi\)
\(522\) 6.50846 + 9.58702i 0.284867 + 0.419613i
\(523\) −2.97729 + 5.15682i −0.130188 + 0.225492i −0.923749 0.382999i \(-0.874891\pi\)
0.793561 + 0.608491i \(0.208225\pi\)
\(524\) 8.33073 + 6.99031i 0.363930 + 0.305373i
\(525\) −19.2538 18.3381i −0.840306 0.800341i
\(526\) 1.73005 + 9.81158i 0.0754336 + 0.427805i
\(527\) −5.30922 + 4.45496i −0.231273 + 0.194061i
\(528\) −2.03873 5.02431i −0.0887241 0.218655i
\(529\) −9.33410 + 3.39734i −0.405831 + 0.147710i
\(530\) −13.1533 + 22.7822i −0.571342 + 0.989594i
\(531\) −16.2850 23.9879i −0.706707 1.04099i
\(532\) 5.23969 2.36685i 0.227169 0.102616i
\(533\) 4.73239 1.72245i 0.204983 0.0746076i
\(534\) 17.3955 10.9062i 0.752777 0.471959i
\(535\) −3.67229 20.8266i −0.158767 0.900413i
\(536\) −22.3071 + 18.7179i −0.963519 + 0.808488i
\(537\) 9.99685 2.14057i 0.431396 0.0923725i
\(538\) 1.68887 9.57804i 0.0728123 0.412939i
\(539\) 23.6543 + 4.76141i 1.01886 + 0.205088i
\(540\) −9.70265 + 14.5253i −0.417535 + 0.625071i
\(541\) 2.08931 + 3.61879i 0.0898264 + 0.155584i 0.907438 0.420187i \(-0.138035\pi\)
−0.817611 + 0.575771i \(0.804702\pi\)
\(542\) −9.08025 7.61924i −0.390030 0.327274i
\(543\) 3.01623 9.33059i 0.129439 0.400414i
\(544\) −0.591828 3.35643i −0.0253744 0.143906i
\(545\) −4.85171 + 4.07107i −0.207824 + 0.174385i
\(546\) −2.05270 4.13596i −0.0878473 0.177003i
\(547\) 18.7934 6.84024i 0.803548 0.292468i 0.0925921 0.995704i \(-0.470485\pi\)
0.710956 + 0.703237i \(0.248263\pi\)
\(548\) −3.34596 −0.142932
\(549\) 25.2837 + 7.16797i 1.07908 + 0.305921i
\(550\) −19.7708 −0.843028
\(551\) −1.44156 + 8.17547i −0.0614124 + 0.348287i
\(552\) 29.4185 + 4.08951i 1.25213 + 0.174061i
\(553\) 0.544927 0.0410639i 0.0231726 0.00174621i
\(554\) 2.18456 + 12.3892i 0.0928130 + 0.526369i
\(555\) 31.8861 40.9387i 1.35349 1.73775i
\(556\) 14.0349 5.10827i 0.595211 0.216639i
\(557\) 25.3785 1.07532 0.537661 0.843161i \(-0.319308\pi\)
0.537661 + 0.843161i \(0.319308\pi\)
\(558\) −3.10993 + 30.4679i −0.131654 + 1.28981i
\(559\) −1.43749 + 2.48981i −0.0607995 + 0.105308i
\(560\) 5.65119 5.51659i 0.238806 0.233119i
\(561\) 3.39470 2.12833i 0.143324 0.0898582i
\(562\) 22.0159 + 8.01313i 0.928685 + 0.338014i
\(563\) 8.75110 7.34304i 0.368815 0.309472i −0.439478 0.898254i \(-0.644836\pi\)
0.808293 + 0.588781i \(0.200392\pi\)
\(564\) −0.857488 + 0.183609i −0.0361068 + 0.00773135i
\(565\) 49.3394 17.9581i 2.07573 0.755502i
\(566\) 2.54199 0.106848
\(567\) 20.0483 12.8477i 0.841952 0.539553i
\(568\) 28.2270 1.18438
\(569\) 6.17207 2.24645i 0.258747 0.0941760i −0.209390 0.977832i \(-0.567148\pi\)
0.468136 + 0.883656i \(0.344926\pi\)
\(570\) 11.6909 2.50332i 0.489679 0.104852i
\(571\) 11.5513 9.69268i 0.483406 0.405626i −0.368250 0.929727i \(-0.620043\pi\)
0.851656 + 0.524101i \(0.175598\pi\)
\(572\) 3.37690 + 1.22909i 0.141195 + 0.0513908i
\(573\) 6.32267 3.96404i 0.264133 0.165600i
\(574\) −3.19384 12.5213i −0.133308 0.522628i
\(575\) 16.6489 28.8368i 0.694307 1.20258i
\(576\) −16.6288 12.0055i −0.692868 0.500229i
\(577\) 5.26403 0.219144 0.109572 0.993979i \(-0.465052\pi\)
0.109572 + 0.993979i \(0.465052\pi\)
\(578\) 15.3731 5.59534i 0.639435 0.232735i
\(579\) 21.0050 26.9685i 0.872938 1.12077i
\(580\) −2.28093 12.9358i −0.0947104 0.537129i
\(581\) 15.7197 32.6769i 0.652163 1.35567i
\(582\) 1.27758 + 0.177599i 0.0529575 + 0.00736171i
\(583\) −4.84649 + 27.4858i −0.200721 + 1.13835i
\(584\) −33.2505 −1.37592
\(585\) 2.46060 + 9.74431i 0.101733 + 0.402878i
\(586\) −7.03442 −0.290589
\(587\) 24.2835 8.83848i 1.00229 0.364803i 0.211822 0.977308i \(-0.432060\pi\)
0.790467 + 0.612505i \(0.209838\pi\)
\(588\) 11.6001 4.38445i 0.478381 0.180812i
\(589\) −16.8081 + 14.1036i −0.692565 + 0.581131i
\(590\) −5.45247 30.9225i −0.224475 1.27306i
\(591\) 6.58233 20.3622i 0.270761 0.837589i
\(592\) 6.34170 + 5.32132i 0.260642 + 0.218705i
\(593\) −2.90388 5.02967i −0.119248 0.206544i 0.800222 0.599704i \(-0.204715\pi\)
−0.919470 + 0.393160i \(0.871382\pi\)
\(594\) 4.20598 17.1986i 0.172573 0.705666i
\(595\) 4.73969 + 3.40462i 0.194308 + 0.139576i
\(596\) −0.218357 + 1.23837i −0.00894426 + 0.0507254i
\(597\) −45.0433 + 9.64488i −1.84350 + 0.394739i
\(598\) 4.42947 3.71677i 0.181135 0.151990i
\(599\) −0.120606 0.683991i −0.00492783 0.0279471i 0.982245 0.187604i \(-0.0600722\pi\)
−0.987173 + 0.159657i \(0.948961\pi\)
\(600\) −25.4432 + 15.9518i −1.03871 + 0.651229i
\(601\) −11.0211 + 4.01136i −0.449560 + 0.163627i −0.556871 0.830599i \(-0.687998\pi\)
0.107311 + 0.994226i \(0.465776\pi\)
\(602\) 5.99142 + 4.30377i 0.244192 + 0.175408i
\(603\) −29.1580 + 2.12684i −1.18741 + 0.0866117i
\(604\) 2.45337 4.24936i 0.0998262 0.172904i
\(605\) −2.72276 + 0.991004i −0.110696 + 0.0402900i
\(606\) 3.75575 + 9.25582i 0.152567 + 0.375992i
\(607\) −11.7889 + 9.89206i −0.478497 + 0.401506i −0.849882 0.526972i \(-0.823327\pi\)
0.371386 + 0.928479i \(0.378883\pi\)
\(608\) −1.87363 10.6259i −0.0759856 0.430936i
\(609\) −4.21179 + 17.4034i −0.170670 + 0.705220i
\(610\) 21.8024 + 18.2944i 0.882754 + 0.740719i
\(611\) −0.252270 + 0.436945i −0.0102058 + 0.0176769i
\(612\) 0.897166 1.85356i 0.0362658 0.0749255i
\(613\) 13.8987 + 24.0732i 0.561362 + 0.972307i 0.997378 + 0.0723685i \(0.0230558\pi\)
−0.436016 + 0.899939i \(0.643611\pi\)
\(614\) −19.8588 16.6635i −0.801436 0.672485i
\(615\) 1.02377 + 28.1081i 0.0412823 + 1.13343i
\(616\) 11.8137 24.5574i 0.475986 0.989445i
\(617\) −24.7888 9.02237i −0.997958 0.363227i −0.209161 0.977881i \(-0.567073\pi\)
−0.788797 + 0.614654i \(0.789295\pi\)
\(618\) −17.4572 + 3.73801i −0.702230 + 0.150365i
\(619\) −25.2673 21.2017i −1.01558 0.852170i −0.0265117 0.999649i \(-0.508440\pi\)
−0.989065 + 0.147478i \(0.952884\pi\)
\(620\) 17.3586 30.0659i 0.697137 1.20748i
\(621\) 21.5433 + 20.6175i 0.864501 + 0.827354i
\(622\) −9.34530 −0.374712
\(623\) 30.5445 + 8.58023i 1.22374 + 0.343760i
\(624\) −1.56782 + 0.335710i −0.0627632 + 0.0134392i
\(625\) −3.53286 20.0358i −0.141314 0.801433i
\(626\) −3.58059 20.3065i −0.143109 0.811612i
\(627\) 10.7470 6.73793i 0.429195 0.269087i
\(628\) −1.71004 1.43489i −0.0682379 0.0572584i
\(629\) −3.05870 + 5.29782i −0.121958 + 0.211238i
\(630\) 25.5058 3.80338i 1.01618 0.151530i
\(631\) −7.91347 13.7065i −0.315030 0.545648i 0.664414 0.747365i \(-0.268681\pi\)
−0.979444 + 0.201717i \(0.935348\pi\)
\(632\) 0.107174 0.607812i 0.00426314 0.0241775i
\(633\) 13.6901 17.5768i 0.544131 0.698614i
\(634\) 7.66904 + 2.79130i 0.304577 + 0.110857i
\(635\) −52.1270 + 43.7397i −2.06860 + 1.73576i
\(636\) 5.39343 + 13.2918i 0.213863 + 0.527053i
\(637\) 2.60119 6.64392i 0.103063 0.263242i
\(638\) 6.65698 + 11.5302i 0.263552 + 0.456486i
\(639\) 22.9767 + 16.5885i 0.908945 + 0.656230i
\(640\) 5.58549 + 9.67436i 0.220786 + 0.382413i
\(641\) −5.36237 + 30.4115i −0.211801 + 1.20118i 0.674571 + 0.738210i \(0.264329\pi\)
−0.886372 + 0.462974i \(0.846782\pi\)
\(642\) 9.73503 + 5.15749i 0.384211 + 0.203550i
\(643\) 0.978642 0.821178i 0.0385939 0.0323841i −0.623287 0.781993i \(-0.714203\pi\)
0.661881 + 0.749609i \(0.269759\pi\)
\(644\) 8.75357 + 12.8277i 0.344939 + 0.505482i
\(645\) −10.7620 11.9164i −0.423754 0.469209i
\(646\) −1.32447 + 0.482067i −0.0521105 + 0.0189667i
\(647\) −17.0297 + 29.4963i −0.669507 + 1.15962i 0.308535 + 0.951213i \(0.400161\pi\)
−0.978042 + 0.208408i \(0.933172\pi\)
\(648\) −8.46375 25.5266i −0.332487 1.00278i
\(649\) −16.6566 28.8500i −0.653828 1.13246i
\(650\) −1.01520 + 5.75747i −0.0398193 + 0.225827i
\(651\) −38.0943 + 28.0808i −1.49303 + 1.10057i
\(652\) −18.9936 6.91312i −0.743848 0.270739i
\(653\) 32.9788 + 12.0033i 1.29056 + 0.469725i 0.893911 0.448245i \(-0.147951\pi\)
0.396649 + 0.917971i \(0.370173\pi\)
\(654\) −0.120092 3.29718i −0.00469596 0.128930i
\(655\) −6.06816 + 34.4142i −0.237103 + 1.34468i
\(656\) −4.48721 −0.175196
\(657\) −27.0658 19.5407i −1.05594 0.762355i
\(658\) 1.05145 + 0.755282i 0.0409899 + 0.0294440i
\(659\) −21.1607 17.7559i −0.824304 0.691673i 0.129672 0.991557i \(-0.458608\pi\)
−0.953976 + 0.299884i \(0.903052\pi\)
\(660\) −12.3328 + 15.8342i −0.480055 + 0.616346i
\(661\) −14.1428 5.14758i −0.550093 0.200217i 0.0519948 0.998647i \(-0.483442\pi\)
−0.602088 + 0.798430i \(0.705664\pi\)
\(662\) −0.636263 0.231581i −0.0247291 0.00900065i
\(663\) −0.445482 1.09786i −0.0173011 0.0426375i
\(664\) −31.3725 26.3247i −1.21749 1.02159i
\(665\) 15.0050 + 10.7785i 0.581871 + 0.417971i
\(666\) 6.61836 + 26.2096i 0.256456 + 1.01560i
\(667\) −22.4233 −0.868234
\(668\) 0.528793 2.99894i 0.0204596 0.116032i
\(669\) 13.8617 8.69071i 0.535926 0.336002i
\(670\) −29.7522 10.8289i −1.14943 0.418358i
\(671\) 28.3746 + 10.3275i 1.09539 + 0.398689i
\(672\) −2.59232 23.1277i −0.100001 0.892172i
\(673\) 0.00646443 0.0366616i 0.000249185 0.00141320i −0.984683 0.174355i \(-0.944216\pi\)
0.984932 + 0.172942i \(0.0553272\pi\)
\(674\) 4.35086 + 7.53592i 0.167589 + 0.290273i
\(675\) −30.0853 1.96777i −1.15798 0.0757396i
\(676\) −6.11702 + 10.5950i −0.235270 + 0.407500i
\(677\) −41.0269 + 14.9326i −1.57679 + 0.573906i −0.974504 0.224372i \(-0.927967\pi\)
−0.602289 + 0.798278i \(0.705745\pi\)
\(678\) −8.41338 + 26.0265i −0.323114 + 0.999541i
\(679\) 1.12348 + 1.64638i 0.0431153 + 0.0631822i
\(680\) 5.04896 4.23658i 0.193619 0.162465i
\(681\) −30.8069 + 19.3146i −1.18052 + 0.740137i
\(682\) −6.11055 + 34.6546i −0.233985 + 1.32699i
\(683\) 18.1682 + 31.4683i 0.695188 + 1.20410i 0.970117 + 0.242636i \(0.0780121\pi\)
−0.274930 + 0.961464i \(0.588655\pi\)
\(684\) 2.84027 5.86804i 0.108601 0.224370i
\(685\) −5.37587 9.31128i −0.205401 0.355766i
\(686\) −16.3019 8.33189i −0.622409 0.318113i
\(687\) −15.0644 + 19.3413i −0.574744 + 0.737918i
\(688\) 1.96233 1.64659i 0.0748131 0.0627757i
\(689\) 7.75533 + 2.82271i 0.295455 + 0.107537i
\(690\) 12.1424 + 29.9243i 0.462255 + 1.13920i
\(691\) −2.27489 + 12.9016i −0.0865411 + 0.490799i 0.910472 + 0.413570i \(0.135718\pi\)
−0.997013 + 0.0772288i \(0.975393\pi\)
\(692\) −2.82293 4.88946i −0.107312 0.185869i
\(693\) 24.0482 13.0470i 0.913516 0.495614i
\(694\) −1.63263 + 2.82781i −0.0619740 + 0.107342i
\(695\) 36.7649 + 30.8494i 1.39457 + 1.17019i
\(696\) 17.8700 + 9.46728i 0.677360 + 0.358856i
\(697\) −0.575786 3.26545i −0.0218095 0.123688i
\(698\) −3.85601 21.8685i −0.145952 0.827735i
\(699\) −5.48474 + 16.9668i −0.207452 + 0.641745i
\(700\) −15.1167 4.24640i −0.571356 0.160499i
\(701\) 28.0556 1.05965 0.529823 0.848108i \(-0.322258\pi\)
0.529823 + 0.848108i \(0.322258\pi\)
\(702\) −4.79246 2.10795i −0.180880 0.0795595i
\(703\) −9.68330 + 16.7720i −0.365213 + 0.632567i
\(704\) −18.0522 15.1476i −0.680368 0.570897i
\(705\) −1.88866 2.09125i −0.0711310 0.0787611i
\(706\) 4.19288 + 1.52608i 0.157801 + 0.0574349i
\(707\) −6.69135 + 13.9095i −0.251654 + 0.523120i
\(708\) −15.1293 8.01533i −0.568595 0.301234i
\(709\) −6.10789 5.12513i −0.229387 0.192478i 0.520849 0.853649i \(-0.325615\pi\)
−0.750236 + 0.661171i \(0.770060\pi\)
\(710\) 15.3455 + 26.5791i 0.575905 + 0.997497i
\(711\) 0.444439 0.431774i 0.0166678 0.0161928i
\(712\) 17.9162 31.0318i 0.671439 1.16297i
\(713\) −45.4001 38.0952i −1.70025 1.42668i
\(714\) −2.91647 + 0.858112i −0.109146 + 0.0321140i
\(715\) 2.00521 + 11.3721i 0.0749906 + 0.425293i
\(716\) 4.62478 3.88065i 0.172836 0.145027i
\(717\) −51.7244 7.19030i −1.93168 0.268527i
\(718\) 17.7472 6.45944i 0.662319 0.241064i
\(719\) −2.30942 + 4.00003i −0.0861269 + 0.149176i −0.905871 0.423554i \(-0.860782\pi\)
0.819744 + 0.572730i \(0.194116\pi\)
\(720\) 0.909311 8.90851i 0.0338880 0.332001i
\(721\) −22.4059 16.0947i −0.834439 0.599396i
\(722\) 13.4562 4.89766i 0.500788 0.182272i
\(723\) −6.11117 3.23762i −0.227277 0.120408i
\(724\) −1.00555 5.70273i −0.0373708 0.211940i
\(725\) 17.3675 14.5730i 0.645011 0.541229i
\(726\) 0.464286 1.43625i 0.0172313 0.0533043i
\(727\) −6.05182 + 34.3216i −0.224450 + 1.27292i 0.639285 + 0.768970i \(0.279230\pi\)
−0.863735 + 0.503947i \(0.831881\pi\)
\(728\) −6.54478 4.70126i −0.242566 0.174240i
\(729\) 8.11203 25.7526i 0.300446 0.953799i
\(730\) −18.0765 31.3093i −0.669040 1.15881i
\(731\) 1.45006 + 1.21675i 0.0536325 + 0.0450030i
\(732\) 15.1751 3.24937i 0.560889 0.120100i
\(733\) 1.50548 + 8.53800i 0.0556062 + 0.315358i 0.999906 0.0137288i \(-0.00437014\pi\)
−0.944300 + 0.329087i \(0.893259\pi\)
\(734\) −4.06846 + 3.41384i −0.150170 + 0.126007i
\(735\) 30.8388 + 25.2369i 1.13751 + 0.930877i
\(736\) 27.3865 9.96789i 1.00948 0.367421i
\(737\) −33.5913 −1.23735
\(738\) −11.8798 8.57686i −0.437302 0.315718i
\(739\) 24.9119 0.916399 0.458200 0.888849i \(-0.348495\pi\)
0.458200 + 0.888849i \(0.348495\pi\)
\(740\) 5.32113 30.1776i 0.195609 1.10935i
\(741\) −1.41032 3.47565i −0.0518094 0.127681i
\(742\) 9.18026 19.0832i 0.337018 0.700568i
\(743\) 4.31621 + 24.4785i 0.158347 + 0.898028i 0.955662 + 0.294465i \(0.0951415\pi\)
−0.797316 + 0.603562i \(0.793747\pi\)
\(744\) 20.0969 + 49.5277i 0.736790 + 1.81577i
\(745\) −3.79700 + 1.38200i −0.139111 + 0.0506324i
\(746\) −36.8408 −1.34884
\(747\) −10.0666 39.8652i −0.368319 1.45859i
\(748\) 1.18304 2.04908i 0.0432561 0.0749218i
\(749\) 4.20761 + 16.4957i 0.153743 + 0.602740i
\(750\) −3.98947 2.11357i −0.145675 0.0771767i
\(751\) 1.20024 + 0.436851i 0.0437974 + 0.0159409i 0.363826 0.931467i \(-0.381470\pi\)
−0.320029 + 0.947408i \(0.603693\pi\)
\(752\) 0.344376 0.288965i 0.0125581 0.0105375i
\(753\) −9.35818 + 28.9492i −0.341031 + 1.05497i
\(754\) 3.69956 1.34653i 0.134730 0.0490378i
\(755\) 15.7670 0.573822
\(756\) 6.90983 12.2466i 0.251308 0.445405i
\(757\) 27.7454 1.00843 0.504213 0.863580i \(-0.331783\pi\)
0.504213 + 0.863580i \(0.331783\pi\)
\(758\) 33.2887 12.1161i 1.20910 0.440077i
\(759\) 22.9640 + 25.4273i 0.833541 + 0.922953i
\(760\) 15.9841 13.4123i 0.579806 0.486515i
\(761\) −34.4957 12.5554i −1.25047 0.455133i −0.369908 0.929069i \(-0.620611\pi\)
−0.880559 + 0.473936i \(0.842833\pi\)
\(762\) −1.29027 35.4250i −0.0467416 1.28331i
\(763\) 3.64828 3.56139i 0.132077 0.128931i
\(764\) 2.20342 3.81643i 0.0797169 0.138074i
\(765\) 6.59960 0.481388i 0.238609 0.0174046i
\(766\) −5.21720 −0.188505
\(767\) −9.25676 + 3.36918i −0.334242 + 0.121654i
\(768\) −29.2211 4.06207i −1.05442 0.146577i
\(769\) 5.19872 + 29.4834i 0.187471 + 1.06320i 0.922740 + 0.385423i \(0.125945\pi\)
−0.735269 + 0.677775i \(0.762944\pi\)
\(770\) 29.5462 2.22650i 1.06477 0.0802376i
\(771\) 1.25908 1.61654i 0.0453445 0.0582181i
\(772\) 3.50530 19.8796i 0.126159 0.715481i
\(773\) 25.2716 0.908956 0.454478 0.890758i \(-0.349826\pi\)
0.454478 + 0.890758i \(0.349826\pi\)
\(774\) 8.34252 0.608519i 0.299866 0.0218728i
\(775\) 59.9218 2.15246
\(776\) 2.11535 0.769926i 0.0759368 0.0276387i
\(777\) −23.1190 + 34.7909i −0.829391 + 1.24812i
\(778\) −0.0709054 + 0.0594967i −0.00254208 + 0.00213306i
\(779\) −1.82284 10.3378i −0.0653100 0.370392i
\(780\) 3.97783 + 4.40453i 0.142429 + 0.157707i
\(781\) 24.9435 + 20.9300i 0.892547 + 0.748936i
\(782\) −1.90355 3.29704i −0.0680708 0.117902i
\(783\) 8.98237 + 18.2082i 0.321004 + 0.650708i
\(784\) −4.20260 + 4.77009i −0.150093 + 0.170360i
\(785\) 1.24560 7.06416i 0.0444574 0.252131i
\(786\) −12.2014 13.5102i −0.435209 0.481894i
\(787\) −27.3199 + 22.9241i −0.973848 + 0.817155i −0.983150 0.182802i \(-0.941483\pi\)
0.00930231 + 0.999957i \(0.497039\pi\)
\(788\) −2.19441 12.4451i −0.0781725 0.443338i
\(789\) 0.635395 + 17.4451i 0.0226207 + 0.621062i
\(790\) 0.630593 0.229517i 0.0224355 0.00816585i
\(791\) −38.5192 + 17.3998i −1.36959 + 0.618665i
\(792\) −7.56528 29.9595i −0.268821 1.06457i
\(793\) 4.46448 7.73270i 0.158538 0.274596i
\(794\) −2.03239 + 0.739730i −0.0721269 + 0.0262520i
\(795\) −28.3234 + 36.3646i −1.00453 + 1.28972i
\(796\) −20.8381 + 17.4852i −0.738587 + 0.619748i
\(797\) −9.36603 53.1174i −0.331762 1.88152i −0.457122 0.889404i \(-0.651120\pi\)
0.125360 0.992111i \(-0.459991\pi\)
\(798\) −9.23306 + 2.71663i −0.326847 + 0.0961678i
\(799\) 0.254476 + 0.213531i 0.00900271 + 0.00755417i
\(800\) −14.7334 + 25.5191i −0.520906 + 0.902235i
\(801\) 32.8206 14.7308i 1.15966 0.520487i
\(802\) 0.168269 + 0.291451i 0.00594180 + 0.0102915i
\(803\) −29.3826 24.6549i −1.03689 0.870053i
\(804\) −14.6273 + 9.17066i −0.515864 + 0.323424i
\(805\) −21.6333 + 44.9697i −0.762473 + 1.58497i
\(806\) 9.77807 + 3.55893i 0.344418 + 0.125358i
\(807\) 5.24169 16.2150i 0.184516 0.570795i
\(808\) 13.3542 + 11.2055i 0.469800 + 0.394209i
\(809\) −11.1820 + 19.3678i −0.393138 + 0.680935i −0.992862 0.119272i \(-0.961944\pi\)
0.599723 + 0.800207i \(0.295277\pi\)
\(810\) 19.4351 21.8470i 0.682880 0.767627i
\(811\) 1.68477 0.0591603 0.0295801 0.999562i \(-0.490583\pi\)
0.0295801 + 0.999562i \(0.490583\pi\)
\(812\) 2.61342 + 10.2458i 0.0917131 + 0.359556i
\(813\) −13.9204 15.4136i −0.488209 0.540578i
\(814\) 5.39349 + 30.5880i 0.189042 + 1.07211i
\(815\) −11.2785 63.9634i −0.395068 2.24054i
\(816\) 0.0384247 + 1.05497i 0.00134513 + 0.0369313i
\(817\) 4.59064 + 3.85201i 0.160606 + 0.134765i
\(818\) 3.05044 5.28351i 0.106656 0.184734i
\(819\) −2.56459 7.67306i −0.0896142 0.268119i
\(820\) 8.30478 + 14.3843i 0.290016 + 0.502322i
\(821\) 5.58672 31.6838i 0.194978 1.10577i −0.717473 0.696587i \(-0.754701\pi\)
0.912450 0.409187i \(-0.134188\pi\)
\(822\) 5.54769 + 0.771194i 0.193498 + 0.0268985i
\(823\) 33.2243 + 12.0927i 1.15813 + 0.421523i 0.848428 0.529311i \(-0.177550\pi\)
0.309699 + 0.950835i \(0.399772\pi\)
\(824\) −23.8679 + 20.0276i −0.831478 + 0.697693i
\(825\) −34.3116 4.76971i −1.19458 0.166060i
\(826\) 6.24728 + 24.4921i 0.217371 + 0.852190i
\(827\) 13.4267 + 23.2557i 0.466891 + 0.808680i 0.999285 0.0378175i \(-0.0120406\pi\)
−0.532393 + 0.846497i \(0.678707\pi\)
\(828\) 16.9415 + 4.80294i 0.588757 + 0.166914i
\(829\) −5.28060 9.14627i −0.183403 0.317663i 0.759634 0.650350i \(-0.225378\pi\)
−0.943037 + 0.332687i \(0.892045\pi\)
\(830\) 7.73233 43.8522i 0.268393 1.52213i
\(831\) 0.802325 + 22.0282i 0.0278323 + 0.764151i
\(832\) −5.33811 + 4.47921i −0.185066 + 0.155289i
\(833\) −4.01057 2.44624i −0.138958 0.0847572i
\(834\) −24.4475 + 5.23482i −0.846548 + 0.181267i
\(835\) 9.19516 3.34676i 0.318212 0.115820i
\(836\) 3.74529 6.48703i 0.129534 0.224359i
\(837\) −12.7476 + 52.1260i −0.440622 + 1.80174i
\(838\) 2.08686 + 3.61455i 0.0720894 + 0.124863i
\(839\) −2.05067 + 11.6299i −0.0707970 + 0.401510i 0.928730 + 0.370757i \(0.120902\pi\)
−0.999527 + 0.0307530i \(0.990209\pi\)
\(840\) 36.2269 26.7043i 1.24995 0.921386i
\(841\) 12.9044 + 4.69681i 0.444979 + 0.161959i
\(842\) −12.0753 4.39504i −0.416142 0.151463i
\(843\) 36.2748 + 19.2179i 1.24937 + 0.661900i
\(844\) 2.28459 12.9566i 0.0786389 0.445983i
\(845\) −39.3122 −1.35238
\(846\) 1.46406 0.106791i 0.0503353 0.00367155i
\(847\) 2.12566 0.960193i 0.0730384 0.0329926i
\(848\) −5.63314 4.72676i −0.193443 0.162318i
\(849\) 4.41156 + 0.613258i 0.151404 + 0.0210470i
\(850\) 3.61712 + 1.31652i 0.124066 + 0.0451564i
\(851\) −49.1561 17.8914i −1.68505 0.613308i
\(852\) 16.5756 + 2.30421i 0.567872 + 0.0789408i
\(853\) 20.3608 + 17.0848i 0.697142 + 0.584971i 0.920959 0.389660i \(-0.127407\pi\)
−0.223817 + 0.974631i \(0.571852\pi\)
\(854\) −18.6078 13.3664i −0.636745 0.457388i
\(855\) 20.8932 1.52399i 0.714532 0.0521194i
\(856\) 19.2269 0.657161
\(857\) 0.0666804 0.378164i 0.00227776 0.0129178i −0.983648 0.180103i \(-0.942357\pi\)
0.985925 + 0.167186i \(0.0534679\pi\)
\(858\) −5.31569 2.81619i −0.181475 0.0961430i
\(859\) 21.6189 + 7.86864i 0.737628 + 0.268475i 0.683390 0.730054i \(-0.260505\pi\)
0.0542377 + 0.998528i \(0.482727\pi\)
\(860\) −8.91016 3.24303i −0.303834 0.110586i
\(861\) −2.52205 22.5008i −0.0859512 0.766827i
\(862\) 2.29155 12.9960i 0.0780504 0.442646i
\(863\) −4.64080 8.03809i −0.157975 0.273620i 0.776164 0.630532i \(-0.217163\pi\)
−0.934138 + 0.356912i \(0.883830\pi\)
\(864\) −19.0647 18.2455i −0.648593 0.620724i
\(865\) 9.07105 15.7115i 0.308425 0.534208i
\(866\) −19.0762 + 6.94317i −0.648235 + 0.235938i
\(867\) 28.0294 6.00179i 0.951929 0.203831i
\(868\) −12.1153 + 25.1844i −0.411220 + 0.854814i
\(869\) 0.545393 0.457639i 0.0185012 0.0155244i
\(870\) 0.800334 + 21.9736i 0.0271339 + 0.744974i
\(871\) −1.72486 + 9.78217i −0.0584447 + 0.331456i
\(872\) −2.87907 4.98669i −0.0974976 0.168871i
\(873\) 2.17436 + 0.616436i 0.0735910 + 0.0208632i
\(874\) −6.02631 10.4379i −0.203843 0.353066i
\(875\) −1.72430 6.76003i −0.0582920 0.228531i
\(876\) −19.5256 2.71428i −0.659707 0.0917070i
\(877\) −26.0131 + 21.8276i −0.878401 + 0.737066i −0.965850 0.259103i \(-0.916573\pi\)
0.0874490 + 0.996169i \(0.472129\pi\)
\(878\) 24.6419 + 8.96892i 0.831624 + 0.302686i
\(879\) −12.2080 1.69706i −0.411767 0.0572404i
\(880\) 1.78666 10.1327i 0.0602283 0.341572i
\(881\) 21.0963 + 36.5398i 0.710752 + 1.23106i 0.964575 + 0.263807i \(0.0849783\pi\)
−0.253824 + 0.967250i \(0.581688\pi\)
\(882\) −20.2438 + 4.59588i −0.681646 + 0.154751i
\(883\) −13.5520 + 23.4728i −0.456062 + 0.789923i −0.998749 0.0500123i \(-0.984074\pi\)
0.542686 + 0.839936i \(0.317407\pi\)
\(884\) −0.535969 0.449731i −0.0180266 0.0151261i
\(885\) −2.00253 54.9805i −0.0673144 1.84815i
\(886\) −1.62408 9.21061i −0.0545620 0.309436i
\(887\) −8.08948 45.8777i −0.271618 1.54042i −0.749503 0.662001i \(-0.769707\pi\)
0.477885 0.878423i \(-0.341404\pi\)
\(888\) 31.6205 + 35.0124i 1.06111 + 1.17494i
\(889\) 39.1973 38.2637i 1.31464 1.28332i
\(890\) 38.9602 1.30595
\(891\) 11.4485 28.8330i 0.383540 0.965941i
\(892\) 4.83075 8.36711i 0.161746 0.280151i
\(893\) 0.805627 + 0.676001i 0.0269593 + 0.0226215i
\(894\) 0.647466 2.00291i 0.0216545 0.0669874i
\(895\) 18.2298 + 6.63509i 0.609354 + 0.221787i
\(896\) −5.06876 7.42789i −0.169335 0.248148i
\(897\) 8.58390 5.38173i 0.286608 0.179691i
\(898\) 4.90720 + 4.11763i 0.163755 + 0.137407i
\(899\) −20.1762 34.9462i −0.672914 1.16552i
\(900\) −16.2431 + 7.29035i −0.541436 + 0.243012i
\(901\) 2.71694 4.70588i 0.0905145 0.156776i
\(902\) −12.8967 10.8216i −0.429413 0.360320i
\(903\) 9.35965 + 8.91451i 0.311470 + 0.296656i
\(904\) 8.28934 + 47.0112i 0.275699 + 1.56357i
\(905\) 14.2542 11.9607i 0.473826 0.397587i
\(906\) −5.04716 + 6.48008i −0.167681 + 0.215286i
\(907\) −35.5630 + 12.9439i −1.18085 + 0.429795i −0.856503 0.516143i \(-0.827367\pi\)
−0.324349 + 0.945938i \(0.605145\pi\)
\(908\) −10.7361 + 18.5954i −0.356289 + 0.617110i
\(909\) 4.28503 + 16.9693i 0.142126 + 0.562836i
\(910\) 0.868768 8.71852i 0.0287994 0.289016i
\(911\) 23.3109 8.48446i 0.772323 0.281103i 0.0743555 0.997232i \(-0.476310\pi\)
0.697968 + 0.716129i \(0.254088\pi\)
\(912\) 0.121646 + 3.33985i 0.00402810 + 0.110594i
\(913\) −8.20358 46.5248i −0.271499 1.53975i
\(914\) 21.0598 17.6712i 0.696595 0.584513i
\(915\) 33.4240 + 37.0093i 1.10496 + 1.22349i
\(916\) −2.51395 + 14.2573i −0.0830631 + 0.471074i
\(917\) 2.78929 27.9919i 0.0921104 0.924374i
\(918\) −1.91474 + 2.86646i −0.0631958 + 0.0946072i
\(919\) −3.64579 6.31469i −0.120263 0.208302i 0.799608 0.600522i \(-0.205041\pi\)
−0.919871 + 0.392220i \(0.871707\pi\)
\(920\) 43.1745 + 36.2277i 1.42342 + 1.19439i
\(921\) −30.4443 33.7100i −1.00317 1.11078i
\(922\) −3.85846 21.8824i −0.127072 0.720659i
\(923\) 7.37588 6.18910i 0.242780 0.203717i
\(924\) 8.94194 13.4564i 0.294168 0.442682i
\(925\) 49.7004 18.0895i 1.63414 0.594779i
\(926\) −0.952309 −0.0312948
\(927\) −31.1982 + 2.27566i −1.02468 + 0.0747425i
\(928\) 19.8435 0.651394
\(929\) −0.718866 + 4.07689i −0.0235852 + 0.133759i −0.994327 0.106368i \(-0.966078\pi\)
0.970742 + 0.240127i \(0.0771889\pi\)
\(930\) −35.7107 + 45.8492i −1.17100 + 1.50345i
\(931\) −12.6968 7.74438i −0.416120 0.253812i
\(932\) 1.82849 + 10.3699i 0.0598943 + 0.339677i
\(933\) −16.2185 2.25456i −0.530970 0.0738110i
\(934\) −15.2858 + 5.56359i −0.500168 + 0.182046i
\(935\) 7.60302 0.248645
\(936\) −9.11303 + 0.664722i −0.297869 + 0.0217271i
\(937\) −14.3792 + 24.9055i −0.469748 + 0.813627i −0.999402 0.0345870i \(-0.988988\pi\)
0.529654 + 0.848214i \(0.322322\pi\)
\(938\) 24.5376 + 6.89284i 0.801182 + 0.225059i
\(939\) −1.31505 36.1052i −0.0429149 1.17825i
\(940\) −1.56367 0.569130i −0.0510014 0.0185630i
\(941\) −40.2253 + 33.7530i −1.31131 + 1.10032i −0.323235 + 0.946319i \(0.604770\pi\)
−0.988071 + 0.153997i \(0.950785\pi\)
\(942\) 2.50456 + 2.77322i 0.0816030 + 0.0903564i
\(943\) 26.6442 9.69770i 0.867654 0.315800i
\(944\) 8.77718 0.285673
\(945\) 45.1822 0.447367i 1.46978 0.0145528i
\(946\) 9.61093 0.312478
\(947\) −11.5642 + 4.20902i −0.375786 + 0.136775i −0.523006 0.852329i \(-0.675190\pi\)
0.147220 + 0.989104i \(0.452967\pi\)
\(948\) 0.112552 0.348174i 0.00365551 0.0113082i
\(949\) −8.68855 + 7.29056i −0.282042 + 0.236662i
\(950\) 11.4512 + 4.16788i 0.371525 + 0.135224i
\(951\) 12.6360 + 6.69439i 0.409751 + 0.217081i
\(952\) −3.79661 + 3.70618i −0.123049 + 0.120118i
\(953\) 24.1041 41.7496i 0.780810 1.35240i −0.150661 0.988586i \(-0.548140\pi\)
0.931471 0.363817i \(-0.118527\pi\)
\(954\) −5.87889 23.2812i −0.190336 0.753756i
\(955\) 14.1607 0.458229
\(956\) −28.9786 + 10.5473i −0.937235 + 0.341126i
\(957\) 8.77133 + 21.6164i 0.283537 + 0.698759i
\(958\) 1.50084 + 8.51168i 0.0484899 + 0.275000i
\(959\) 4.87853 + 7.14912i 0.157536 + 0.230857i
\(960\) −14.6333 36.0628i −0.472287 1.16392i
\(961\) 13.1369 74.5033i 0.423773 2.40333i
\(962\) 9.18453 0.296121
\(963\) 15.6506 + 11.2993i 0.504334 + 0.364114i
\(964\) −4.08398 −0.131536
\(965\) 60.9535 22.1853i 1.96216 0.714169i
\(966\) −11.5570 23.2862i −0.371842 0.749221i
\(967\) −20.0152 + 16.7948i −0.643646 + 0.540083i −0.905136 0.425123i \(-0.860231\pi\)
0.261489 + 0.965206i \(0.415786\pi\)
\(968\) −0.457441 2.59428i −0.0147027 0.0833833i
\(969\) −2.41488 + 0.517085i −0.0775770 + 0.0166112i
\(970\) 1.87498 + 1.57329i 0.0602019 + 0.0505154i
\(971\) 3.07654 + 5.32872i 0.0987307 + 0.171007i 0.911160 0.412054i \(-0.135188\pi\)
−0.812429 + 0.583060i \(0.801855\pi\)
\(972\) −2.88636 15.6808i −0.0925801 0.502962i
\(973\) −31.3779 22.5394i −1.00593 0.722580i
\(974\) −5.00636 + 28.3925i −0.160414 + 0.909753i
\(975\) −3.15084 + 9.74702i −0.100908 + 0.312154i
\(976\) −6.09448 + 5.11388i −0.195080 + 0.163691i
\(977\) 5.54814 + 31.4651i 0.177501 + 1.00666i 0.935218 + 0.354073i \(0.115204\pi\)
−0.757717 + 0.652583i \(0.773685\pi\)
\(978\) 29.8985 + 15.8399i 0.956050 + 0.506503i
\(979\) 38.8419 14.1373i 1.24139 0.451829i
\(980\) 23.0691 + 4.64361i 0.736916 + 0.148335i
\(981\) 0.587031 5.75113i 0.0187425 0.183619i
\(982\) −10.0154 + 17.3472i −0.319604 + 0.553570i
\(983\) 15.0250 5.46866i 0.479224 0.174423i −0.0911023 0.995842i \(-0.529039\pi\)
0.570326 + 0.821418i \(0.306817\pi\)
\(984\) −25.3282 3.52091i −0.807433 0.112243i
\(985\) 31.1070 26.1019i 0.991152 0.831675i
\(986\) −0.450123 2.55277i −0.0143348 0.0812969i
\(987\) 1.64256 + 1.56443i 0.0522831 + 0.0497965i
\(988\) −1.69679 1.42377i −0.0539819 0.0452962i
\(989\) −8.09335 + 14.0181i −0.257353 + 0.445749i
\(990\) 24.0977 23.4110i 0.765875 0.744049i
\(991\) −24.1001 41.7427i −0.765566 1.32600i −0.939947 0.341321i \(-0.889126\pi\)
0.174381 0.984678i \(-0.444208\pi\)
\(992\) 40.1767 + 33.7123i 1.27561 + 1.07037i
\(993\) −1.04835 0.555401i −0.0332683 0.0176251i
\(994\) −13.9258 20.4072i −0.441700 0.647278i
\(995\) −82.1387 29.8960i −2.60397 0.947768i
\(996\) −16.2738 18.0195i −0.515656 0.570970i
\(997\) −16.3867 13.7501i −0.518973 0.435470i 0.345301 0.938492i \(-0.387777\pi\)
−0.864274 + 0.503022i \(0.832221\pi\)
\(998\) 1.12791 1.95359i 0.0357033 0.0618399i
\(999\) 5.16290 + 47.0827i 0.163347 + 1.48963i
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 189.2.w.a.25.8 yes 132
3.2 odd 2 567.2.w.a.235.15 132
7.2 even 3 189.2.u.a.79.15 yes 132
21.2 odd 6 567.2.u.a.478.8 132
27.13 even 9 189.2.u.a.67.15 132
27.14 odd 18 567.2.u.a.172.8 132
189.121 even 9 inner 189.2.w.a.121.8 yes 132
189.149 odd 18 567.2.w.a.415.15 132
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.u.a.67.15 132 27.13 even 9
189.2.u.a.79.15 yes 132 7.2 even 3
189.2.w.a.25.8 yes 132 1.1 even 1 trivial
189.2.w.a.121.8 yes 132 189.121 even 9 inner
567.2.u.a.172.8 132 27.14 odd 18
567.2.u.a.478.8 132 21.2 odd 6
567.2.w.a.235.15 132 3.2 odd 2
567.2.w.a.415.15 132 189.149 odd 18