Properties

Label 378.2.bf.a.101.6
Level $378$
Weight $2$
Character 378.101
Analytic conductor $3.018$
Analytic rank $0$
Dimension $144$
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] = [378,2,Mod(5,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.bf (of order \(18\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 101.6
Character \(\chi\) \(=\) 378.101
Dual form 378.2.bf.a.131.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.642788 + 0.766044i) q^{2} +(-0.447826 + 1.67316i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.85498 - 1.55652i) q^{5} +(-0.993855 - 1.41854i) q^{6} +(-2.64190 - 0.142622i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.59890 - 1.49857i) q^{9} +O(q^{10})\) \(q+(-0.642788 + 0.766044i) q^{2} +(-0.447826 + 1.67316i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.85498 - 1.55652i) q^{5} +(-0.993855 - 1.41854i) q^{6} +(-2.64190 - 0.142622i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.59890 - 1.49857i) q^{9} +2.42151i q^{10} +(-3.21395 + 3.83024i) q^{11} +(1.72550 + 0.150482i) q^{12} +(-1.16088 + 3.18949i) q^{13} +(1.80744 - 1.93214i) q^{14} +(1.77358 + 3.80073i) q^{15} +(-0.939693 + 0.342020i) q^{16} -6.88980 q^{17} +(2.81851 - 1.02761i) q^{18} +7.33408i q^{19} +(-1.85498 - 1.55652i) q^{20} +(1.42174 - 4.35645i) q^{21} +(-0.868245 - 4.92406i) q^{22} +(0.798392 - 2.19357i) q^{23} +(-1.22441 + 1.22508i) q^{24} +(0.149981 - 0.850586i) q^{25} +(-1.69709 - 2.93945i) q^{26} +(3.67119 - 3.67727i) q^{27} +(0.318306 + 2.62653i) q^{28} +(-0.0659681 - 0.181246i) q^{29} +(-4.05156 - 1.08442i) q^{30} +(5.42663 - 0.956862i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-4.96929 - 7.09273i) q^{33} +(4.42868 - 5.27789i) q^{34} +(-5.12268 + 3.84761i) q^{35} +(-1.02451 + 2.81964i) q^{36} +(2.33166 - 4.03856i) q^{37} +(-5.61823 - 4.71426i) q^{38} +(-4.81664 - 3.37067i) q^{39} +(2.38472 - 0.420491i) q^{40} +(-7.91571 - 2.88108i) q^{41} +(2.42335 + 3.88939i) q^{42} +(-1.69656 + 9.62165i) q^{43} +(4.33015 + 2.50001i) q^{44} +(-7.15347 + 1.26542i) q^{45} +(1.16717 + 2.02160i) q^{46} +(1.34884 - 7.64966i) q^{47} +(-0.151434 - 1.72542i) q^{48} +(6.95932 + 0.753588i) q^{49} +(0.555181 + 0.661639i) q^{50} +(3.08543 - 11.5277i) q^{51} +(3.34262 + 0.589393i) q^{52} +(-2.26642 - 1.30852i) q^{53} +(0.457156 + 5.17600i) q^{54} +12.1076i q^{55} +(-2.21665 - 1.44447i) q^{56} +(-12.2711 - 3.28440i) q^{57} +(0.181246 + 0.0659681i) q^{58} +(11.4974 + 4.18471i) q^{59} +(3.43501 - 2.40663i) q^{60} +(7.33384 + 1.29315i) q^{61} +(-2.75517 + 4.77210i) q^{62} +(6.65232 + 4.32973i) q^{63} +(0.500000 + 0.866025i) q^{64} +(2.81108 + 7.72337i) q^{65} +(8.62754 + 0.752416i) q^{66} +(-8.07656 + 6.77704i) q^{67} +(1.19640 + 6.78513i) q^{68} +(3.31264 + 2.31817i) q^{69} +(0.345361 - 6.39740i) q^{70} +(-1.60661 + 0.927576i) q^{71} +(-1.50143 - 2.59725i) q^{72} +(5.38127 - 3.10688i) q^{73} +(1.59495 + 4.38209i) q^{74} +(1.35600 + 0.631857i) q^{75} +(7.22266 - 1.27355i) q^{76} +(9.03723 - 9.66074i) q^{77} +(5.67815 - 1.52313i) q^{78} +(-3.10226 - 2.60311i) q^{79} +(-1.21075 + 2.09709i) q^{80} +(4.50859 + 7.78926i) q^{81} +(7.29516 - 4.21186i) q^{82} +(-4.64525 + 1.69073i) q^{83} +(-4.53715 - 0.643655i) q^{84} +(-12.7805 + 10.7241i) q^{85} +(-6.28009 - 7.48431i) q^{86} +(0.332795 - 0.0292082i) q^{87} +(-4.69848 + 1.71011i) q^{88} +7.82284 q^{89} +(3.62879 - 6.29327i) q^{90} +(3.52182 - 8.26075i) q^{91} +(-2.29888 - 0.405354i) q^{92} +(-0.829211 + 9.50811i) q^{93} +(4.99296 + 5.95038i) q^{94} +(11.4156 + 13.6046i) q^{95} +(1.41909 + 0.993072i) q^{96} +(5.40634 + 0.953284i) q^{97} +(-5.05065 + 4.84675i) q^{98} +(14.0926 - 5.13810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.642788 + 0.766044i −0.454519 + 0.541675i
\(3\) −0.447826 + 1.67316i −0.258553 + 0.965997i
\(4\) −0.173648 0.984808i −0.0868241 0.492404i
\(5\) 1.85498 1.55652i 0.829574 0.696095i −0.125619 0.992079i \(-0.540092\pi\)
0.955193 + 0.295983i \(0.0956473\pi\)
\(6\) −0.993855 1.41854i −0.405739 0.579116i
\(7\) −2.64190 0.142622i −0.998546 0.0539061i
\(8\) 0.866025 + 0.500000i 0.306186 + 0.176777i
\(9\) −2.59890 1.49857i −0.866301 0.499522i
\(10\) 2.42151i 0.765749i
\(11\) −3.21395 + 3.83024i −0.969043 + 1.15486i 0.0188654 + 0.999822i \(0.493995\pi\)
−0.987908 + 0.155038i \(0.950450\pi\)
\(12\) 1.72550 + 0.150482i 0.498109 + 0.0434405i
\(13\) −1.16088 + 3.18949i −0.321970 + 0.884604i 0.668106 + 0.744066i \(0.267105\pi\)
−0.990075 + 0.140538i \(0.955117\pi\)
\(14\) 1.80744 1.93214i 0.483058 0.516386i
\(15\) 1.77358 + 3.80073i 0.457937 + 0.981343i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) −6.88980 −1.67102 −0.835511 0.549474i \(-0.814828\pi\)
−0.835511 + 0.549474i \(0.814828\pi\)
\(18\) 2.81851 1.02761i 0.664330 0.242211i
\(19\) 7.33408i 1.68255i 0.540605 + 0.841277i \(0.318195\pi\)
−0.540605 + 0.841277i \(0.681805\pi\)
\(20\) −1.85498 1.55652i −0.414787 0.348048i
\(21\) 1.42174 4.35645i 0.310250 0.950655i
\(22\) −0.868245 4.92406i −0.185110 1.04981i
\(23\) 0.798392 2.19357i 0.166476 0.457390i −0.828201 0.560432i \(-0.810635\pi\)
0.994677 + 0.103042i \(0.0328575\pi\)
\(24\) −1.22441 + 1.22508i −0.249931 + 0.250069i
\(25\) 0.149981 0.850586i 0.0299963 0.170117i
\(26\) −1.69709 2.93945i −0.332827 0.576473i
\(27\) 3.67119 3.67727i 0.706522 0.707691i
\(28\) 0.318306 + 2.62653i 0.0601543 + 0.496368i
\(29\) −0.0659681 0.181246i −0.0122500 0.0336565i 0.933417 0.358794i \(-0.116812\pi\)
−0.945667 + 0.325137i \(0.894590\pi\)
\(30\) −4.05156 1.08442i −0.739711 0.197986i
\(31\) 5.42663 0.956862i 0.974652 0.171857i 0.336429 0.941709i \(-0.390781\pi\)
0.638223 + 0.769851i \(0.279670\pi\)
\(32\) 0.342020 0.939693i 0.0604612 0.166116i
\(33\) −4.96929 7.09273i −0.865043 1.23469i
\(34\) 4.42868 5.27789i 0.759512 0.905151i
\(35\) −5.12268 + 3.84761i −0.865892 + 0.650364i
\(36\) −1.02451 + 2.81964i −0.170751 + 0.469941i
\(37\) 2.33166 4.03856i 0.383323 0.663935i −0.608212 0.793775i \(-0.708113\pi\)
0.991535 + 0.129840i \(0.0414463\pi\)
\(38\) −5.61823 4.71426i −0.911397 0.764753i
\(39\) −4.81664 3.37067i −0.771279 0.539739i
\(40\) 2.38472 0.420491i 0.377058 0.0664854i
\(41\) −7.91571 2.88108i −1.23623 0.449950i −0.360501 0.932759i \(-0.617394\pi\)
−0.875726 + 0.482809i \(0.839616\pi\)
\(42\) 2.42335 + 3.88939i 0.373932 + 0.600146i
\(43\) −1.69656 + 9.62165i −0.258722 + 1.46729i 0.527611 + 0.849486i \(0.323088\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(44\) 4.33015 + 2.50001i 0.652794 + 0.376891i
\(45\) −7.15347 + 1.26542i −1.06638 + 0.188637i
\(46\) 1.16717 + 2.02160i 0.172090 + 0.298069i
\(47\) 1.34884 7.64966i 0.196749 1.11582i −0.713158 0.701003i \(-0.752736\pi\)
0.909906 0.414813i \(-0.136153\pi\)
\(48\) −0.151434 1.72542i −0.0218576 0.249043i
\(49\) 6.95932 + 0.753588i 0.994188 + 0.107655i
\(50\) 0.555181 + 0.661639i 0.0785144 + 0.0935698i
\(51\) 3.08543 11.5277i 0.432047 1.61420i
\(52\) 3.34262 + 0.589393i 0.463537 + 0.0817341i
\(53\) −2.26642 1.30852i −0.311317 0.179739i 0.336199 0.941791i \(-0.390859\pi\)
−0.647516 + 0.762052i \(0.724192\pi\)
\(54\) 0.457156 + 5.17600i 0.0622110 + 0.704365i
\(55\) 12.1076i 1.63259i
\(56\) −2.21665 1.44447i −0.296212 0.193025i
\(57\) −12.2711 3.28440i −1.62534 0.435029i
\(58\) 0.181246 + 0.0659681i 0.0237988 + 0.00866204i
\(59\) 11.4974 + 4.18471i 1.49683 + 0.544802i 0.955238 0.295838i \(-0.0955989\pi\)
0.541594 + 0.840640i \(0.317821\pi\)
\(60\) 3.43501 2.40663i 0.443457 0.310694i
\(61\) 7.33384 + 1.29315i 0.939002 + 0.165571i 0.622145 0.782902i \(-0.286261\pi\)
0.316857 + 0.948473i \(0.397373\pi\)
\(62\) −2.75517 + 4.77210i −0.349907 + 0.606057i
\(63\) 6.65232 + 4.32973i 0.838114 + 0.545495i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) 2.81108 + 7.72337i 0.348671 + 0.957966i
\(66\) 8.62754 + 0.752416i 1.06198 + 0.0926160i
\(67\) −8.07656 + 6.77704i −0.986709 + 0.827947i −0.985088 0.172052i \(-0.944960\pi\)
−0.00162103 + 0.999999i \(0.500516\pi\)
\(68\) 1.19640 + 6.78513i 0.145085 + 0.822818i
\(69\) 3.31264 + 2.31817i 0.398795 + 0.279075i
\(70\) 0.345361 6.39740i 0.0412785 0.764635i
\(71\) −1.60661 + 0.927576i −0.190669 + 0.110083i −0.592296 0.805721i \(-0.701778\pi\)
0.401627 + 0.915804i \(0.368445\pi\)
\(72\) −1.50143 2.59725i −0.176945 0.306089i
\(73\) 5.38127 3.10688i 0.629830 0.363633i −0.150856 0.988556i \(-0.548203\pi\)
0.780686 + 0.624923i \(0.214870\pi\)
\(74\) 1.59495 + 4.38209i 0.185409 + 0.509408i
\(75\) 1.35600 + 0.631857i 0.156577 + 0.0729606i
\(76\) 7.22266 1.27355i 0.828496 0.146086i
\(77\) 9.03723 9.66074i 1.02989 1.10094i
\(78\) 5.67815 1.52313i 0.642924 0.172461i
\(79\) −3.10226 2.60311i −0.349032 0.292872i 0.451369 0.892337i \(-0.350936\pi\)
−0.800401 + 0.599465i \(0.795380\pi\)
\(80\) −1.21075 + 2.09709i −0.135366 + 0.234462i
\(81\) 4.50859 + 7.78926i 0.500955 + 0.865473i
\(82\) 7.29516 4.21186i 0.805616 0.465122i
\(83\) −4.64525 + 1.69073i −0.509882 + 0.185582i −0.584133 0.811658i \(-0.698566\pi\)
0.0742514 + 0.997240i \(0.476343\pi\)
\(84\) −4.53715 0.643655i −0.495043 0.0702285i
\(85\) −12.7805 + 10.7241i −1.38624 + 1.16319i
\(86\) −6.28009 7.48431i −0.677199 0.807054i
\(87\) 0.332795 0.0292082i 0.0356794 0.00313145i
\(88\) −4.69848 + 1.71011i −0.500860 + 0.182298i
\(89\) 7.82284 0.829219 0.414609 0.909999i \(-0.363918\pi\)
0.414609 + 0.909999i \(0.363918\pi\)
\(90\) 3.62879 6.29327i 0.382509 0.663369i
\(91\) 3.52182 8.26075i 0.369187 0.865962i
\(92\) −2.29888 0.405354i −0.239675 0.0422611i
\(93\) −0.829211 + 9.50811i −0.0859851 + 0.985945i
\(94\) 4.99296 + 5.95038i 0.514984 + 0.613734i
\(95\) 11.4156 + 13.6046i 1.17122 + 1.39580i
\(96\) 1.41909 + 0.993072i 0.144835 + 0.101355i
\(97\) 5.40634 + 0.953284i 0.548931 + 0.0967913i 0.441233 0.897392i \(-0.354541\pi\)
0.107697 + 0.994184i \(0.465652\pi\)
\(98\) −5.05065 + 4.84675i −0.510192 + 0.489596i
\(99\) 14.0926 5.13810i 1.41636 0.516398i
\(100\) −0.863708 −0.0863708
\(101\) 3.60013 1.31034i 0.358227 0.130384i −0.156636 0.987656i \(-0.550065\pi\)
0.514863 + 0.857273i \(0.327843\pi\)
\(102\) 6.84746 + 9.77345i 0.677999 + 0.967716i
\(103\) −9.63304 11.4802i −0.949171 1.13118i −0.991241 0.132064i \(-0.957840\pi\)
0.0420700 0.999115i \(-0.486605\pi\)
\(104\) −2.60009 + 2.18174i −0.254960 + 0.213937i
\(105\) −4.14357 10.2941i −0.404371 1.00460i
\(106\) 2.45921 0.895081i 0.238860 0.0869379i
\(107\) −12.2712 + 7.08479i −1.18630 + 0.684912i −0.957464 0.288552i \(-0.906826\pi\)
−0.228839 + 0.973464i \(0.573493\pi\)
\(108\) −4.25890 2.97687i −0.409813 0.286449i
\(109\) −1.77473 + 3.07392i −0.169988 + 0.294428i −0.938415 0.345509i \(-0.887706\pi\)
0.768427 + 0.639937i \(0.221040\pi\)
\(110\) −9.27496 7.78262i −0.884333 0.742043i
\(111\) 5.71296 + 5.70981i 0.542250 + 0.541951i
\(112\) 2.53136 0.769564i 0.239191 0.0727169i
\(113\) 2.13816 0.377016i 0.201142 0.0354667i −0.0721695 0.997392i \(-0.522992\pi\)
0.273311 + 0.961926i \(0.411881\pi\)
\(114\) 10.4037 7.28901i 0.974394 0.682678i
\(115\) −1.93331 5.31174i −0.180283 0.495322i
\(116\) −0.167037 + 0.0964389i −0.0155090 + 0.00895413i
\(117\) 7.79667 6.54951i 0.720802 0.605503i
\(118\) −10.5960 + 6.11763i −0.975445 + 0.563173i
\(119\) 18.2022 + 0.982638i 1.66859 + 0.0900783i
\(120\) −0.364395 + 4.17832i −0.0332645 + 0.381426i
\(121\) −2.43111 13.7875i −0.221010 1.25341i
\(122\) −5.70471 + 4.78682i −0.516481 + 0.433379i
\(123\) 8.36537 11.9540i 0.754280 1.07786i
\(124\) −1.88465 5.17803i −0.169247 0.465001i
\(125\) 5.00804 + 8.67417i 0.447932 + 0.775841i
\(126\) −7.59280 + 2.31288i −0.676420 + 0.206048i
\(127\) −7.34238 + 12.7174i −0.651531 + 1.12848i 0.331221 + 0.943553i \(0.392540\pi\)
−0.982751 + 0.184931i \(0.940794\pi\)
\(128\) −0.984808 0.173648i −0.0870455 0.0153485i
\(129\) −15.3388 7.14743i −1.35050 0.629296i
\(130\) −7.72337 2.81108i −0.677384 0.246548i
\(131\) 1.19666 + 0.435548i 0.104552 + 0.0380540i 0.393767 0.919210i \(-0.371172\pi\)
−0.289214 + 0.957264i \(0.593394\pi\)
\(132\) −6.12206 + 6.12544i −0.532857 + 0.533151i
\(133\) 1.04600 19.3759i 0.0906999 1.68011i
\(134\) 10.5432i 0.910794i
\(135\) 1.08627 12.5356i 0.0934914 1.07889i
\(136\) −5.96674 3.44490i −0.511644 0.295398i
\(137\) −8.13627 1.43464i −0.695129 0.122570i −0.185090 0.982722i \(-0.559258\pi\)
−0.510038 + 0.860152i \(0.670369\pi\)
\(138\) −3.90514 + 1.04753i −0.332428 + 0.0891720i
\(139\) −1.33413 1.58995i −0.113159 0.134858i 0.706491 0.707722i \(-0.250277\pi\)
−0.819651 + 0.572864i \(0.805832\pi\)
\(140\) 4.67870 + 4.37673i 0.395422 + 0.369901i
\(141\) 12.1950 + 5.68254i 1.02701 + 0.478556i
\(142\) 0.322144 1.82697i 0.0270337 0.153316i
\(143\) −8.48549 14.6973i −0.709592 1.22905i
\(144\) 2.95471 + 0.519315i 0.246226 + 0.0432763i
\(145\) −0.404482 0.233528i −0.0335904 0.0193934i
\(146\) −1.07901 + 6.11935i −0.0892993 + 0.506441i
\(147\) −4.37744 + 11.3065i −0.361045 + 0.932548i
\(148\) −4.38209 1.59495i −0.360206 0.131104i
\(149\) −8.08444 + 1.42550i −0.662303 + 0.116782i −0.494688 0.869071i \(-0.664718\pi\)
−0.167615 + 0.985853i \(0.553607\pi\)
\(150\) −1.35565 + 0.632605i −0.110688 + 0.0516520i
\(151\) 7.75915 + 6.51070i 0.631430 + 0.529833i 0.901373 0.433043i \(-0.142560\pi\)
−0.269943 + 0.962876i \(0.587005\pi\)
\(152\) −3.66704 + 6.35150i −0.297436 + 0.515175i
\(153\) 17.9059 + 10.3248i 1.44761 + 0.834713i
\(154\) 1.59154 + 13.1327i 0.128250 + 1.05827i
\(155\) 8.57694 10.2216i 0.688917 0.821019i
\(156\) −2.48306 + 5.32877i −0.198804 + 0.426643i
\(157\) −5.33273 + 14.6515i −0.425598 + 1.16932i 0.522860 + 0.852418i \(0.324865\pi\)
−0.948458 + 0.316902i \(0.897357\pi\)
\(158\) 3.98819 0.703225i 0.317283 0.0559456i
\(159\) 3.20432 3.20609i 0.254119 0.254260i
\(160\) −0.828205 2.27547i −0.0654754 0.179892i
\(161\) −2.42213 + 5.68132i −0.190890 + 0.447751i
\(162\) −8.86499 1.55306i −0.696499 0.122020i
\(163\) 2.69868 + 4.67426i 0.211377 + 0.366116i 0.952146 0.305644i \(-0.0988718\pi\)
−0.740769 + 0.671760i \(0.765538\pi\)
\(164\) −1.46276 + 8.29575i −0.114223 + 0.647789i
\(165\) −20.2579 5.42210i −1.57708 0.422110i
\(166\) 1.69073 4.64525i 0.131226 0.360541i
\(167\) −1.74196 9.87912i −0.134797 0.764469i −0.975001 0.222200i \(-0.928676\pi\)
0.840205 0.542269i \(-0.182435\pi\)
\(168\) 3.40949 3.06192i 0.263048 0.236233i
\(169\) 1.13339 + 0.951030i 0.0871841 + 0.0731561i
\(170\) 16.6837i 1.27958i
\(171\) 10.9906 19.0606i 0.840473 1.45760i
\(172\) 9.77008 0.744962
\(173\) 13.8080 5.02572i 1.04981 0.382098i 0.241217 0.970471i \(-0.422454\pi\)
0.808590 + 0.588373i \(0.200231\pi\)
\(174\) −0.191542 + 0.273710i −0.0145207 + 0.0207499i
\(175\) −0.517549 + 2.22578i −0.0391230 + 0.168253i
\(176\) 1.71011 4.69848i 0.128904 0.354162i
\(177\) −12.1505 + 17.3629i −0.913287 + 1.30508i
\(178\) −5.02842 + 5.99264i −0.376896 + 0.449167i
\(179\) 22.9601i 1.71612i 0.513551 + 0.858059i \(0.328330\pi\)
−0.513551 + 0.858059i \(0.671670\pi\)
\(180\) 2.48838 + 6.82505i 0.185473 + 0.508709i
\(181\) −1.45591 0.840572i −0.108217 0.0624792i 0.444915 0.895573i \(-0.353234\pi\)
−0.553132 + 0.833094i \(0.686567\pi\)
\(182\) 4.06432 + 8.00778i 0.301267 + 0.593576i
\(183\) −5.44793 + 11.6915i −0.402723 + 0.864264i
\(184\) 1.78821 1.50049i 0.131829 0.110617i
\(185\) −1.96088 11.1207i −0.144167 0.817612i
\(186\) −6.75063 6.74691i −0.494980 0.494707i
\(187\) 22.1435 26.3896i 1.61929 1.92980i
\(188\) −7.76766 −0.566515
\(189\) −10.2234 + 9.19141i −0.743643 + 0.668577i
\(190\) −17.7595 −1.28841
\(191\) −0.129125 + 0.153885i −0.00934316 + 0.0111347i −0.770696 0.637203i \(-0.780091\pi\)
0.761353 + 0.648338i \(0.224536\pi\)
\(192\) −1.67291 + 0.448749i −0.120732 + 0.0323857i
\(193\) 0.933322 + 5.29313i 0.0671820 + 0.381008i 0.999797 + 0.0201358i \(0.00640987\pi\)
−0.932615 + 0.360872i \(0.882479\pi\)
\(194\) −4.20539 + 3.52874i −0.301929 + 0.253349i
\(195\) −14.1813 + 1.24464i −1.01554 + 0.0891306i
\(196\) −0.466333 6.98445i −0.0333095 0.498889i
\(197\) 5.06568 + 2.92467i 0.360915 + 0.208374i 0.669482 0.742828i \(-0.266516\pi\)
−0.308567 + 0.951203i \(0.599849\pi\)
\(198\) −5.12255 + 14.0983i −0.364044 + 1.00192i
\(199\) 8.97040i 0.635895i 0.948108 + 0.317947i \(0.102994\pi\)
−0.948108 + 0.317947i \(0.897006\pi\)
\(200\) 0.555181 0.661639i 0.0392572 0.0467849i
\(201\) −7.72215 16.5483i −0.544678 1.16723i
\(202\) −1.31034 + 3.60013i −0.0921953 + 0.253304i
\(203\) 0.148432 + 0.488243i 0.0104179 + 0.0342679i
\(204\) −11.8884 1.03679i −0.832352 0.0725901i
\(205\) −19.1680 + 6.97657i −1.33875 + 0.487265i
\(206\) 14.9863 1.04415
\(207\) −5.36215 + 4.50442i −0.372695 + 0.313079i
\(208\) 3.39418i 0.235344i
\(209\) −28.0913 23.5714i −1.94311 1.63047i
\(210\) 10.5492 + 3.44277i 0.727963 + 0.237573i
\(211\) −4.38305 24.8575i −0.301742 1.71126i −0.638458 0.769657i \(-0.720427\pi\)
0.336716 0.941606i \(-0.390684\pi\)
\(212\) −0.895081 + 2.45921i −0.0614744 + 0.168899i
\(213\) −0.832497 3.10350i −0.0570418 0.212648i
\(214\) 2.46052 13.9543i 0.168198 0.953897i
\(215\) 11.8292 + 20.4887i 0.806743 + 1.39732i
\(216\) 5.01798 1.34901i 0.341431 0.0917888i
\(217\) −14.4731 + 1.75398i −0.982499 + 0.119068i
\(218\) −1.21399 3.33540i −0.0822215 0.225902i
\(219\) 2.78842 + 10.3950i 0.188424 + 0.702432i
\(220\) 11.9237 2.10246i 0.803893 0.141748i
\(221\) 7.99822 21.9749i 0.538018 1.47819i
\(222\) −8.04618 + 0.706185i −0.540024 + 0.0473960i
\(223\) −6.40857 + 7.63744i −0.429150 + 0.511441i −0.936677 0.350195i \(-0.886115\pi\)
0.507527 + 0.861636i \(0.330560\pi\)
\(224\) −1.03761 + 2.43380i −0.0693279 + 0.162615i
\(225\) −1.66445 + 1.98583i −0.110963 + 0.132389i
\(226\) −1.08557 + 1.88027i −0.0722113 + 0.125074i
\(227\) −10.0514 8.43416i −0.667138 0.559795i 0.245079 0.969503i \(-0.421186\pi\)
−0.912217 + 0.409708i \(0.865631\pi\)
\(228\) −1.10365 + 12.6550i −0.0730910 + 0.838096i
\(229\) −7.65616 + 1.34999i −0.505934 + 0.0892097i −0.420788 0.907159i \(-0.638247\pi\)
−0.0851452 + 0.996369i \(0.527135\pi\)
\(230\) 5.31174 + 1.93331i 0.350246 + 0.127479i
\(231\) 12.1168 + 19.4470i 0.797228 + 1.27952i
\(232\) 0.0334929 0.189948i 0.00219892 0.0124707i
\(233\) −3.83908 2.21649i −0.251506 0.145207i 0.368947 0.929450i \(-0.379718\pi\)
−0.620454 + 0.784243i \(0.713052\pi\)
\(234\) 0.00561452 + 10.1825i 0.000367032 + 0.665653i
\(235\) −9.40474 16.2895i −0.613497 1.06261i
\(236\) 2.12463 12.0494i 0.138302 0.784348i
\(237\) 5.74468 4.02483i 0.373157 0.261441i
\(238\) −12.4529 + 13.3121i −0.807201 + 0.862893i
\(239\) 0.0442139 + 0.0526920i 0.00285996 + 0.00340836i 0.767473 0.641082i \(-0.221514\pi\)
−0.764613 + 0.644490i \(0.777070\pi\)
\(240\) −2.96655 2.96491i −0.191490 0.191384i
\(241\) 12.0443 + 2.12373i 0.775840 + 0.136801i 0.547529 0.836787i \(-0.315569\pi\)
0.228311 + 0.973588i \(0.426680\pi\)
\(242\) 12.1245 + 7.00011i 0.779395 + 0.449984i
\(243\) −15.0517 + 4.05534i −0.965568 + 0.260150i
\(244\) 7.44697i 0.476744i
\(245\) 14.0824 9.43440i 0.899691 0.602742i
\(246\) 3.78014 + 14.0921i 0.241013 + 0.898481i
\(247\) −23.3919 8.51397i −1.48839 0.541731i
\(248\) 5.17803 + 1.88465i 0.328805 + 0.119675i
\(249\) −0.748593 8.52938i −0.0474402 0.540527i
\(250\) −9.86390 1.73927i −0.623848 0.110001i
\(251\) 3.13252 5.42569i 0.197723 0.342466i −0.750067 0.661362i \(-0.769979\pi\)
0.947790 + 0.318896i \(0.103312\pi\)
\(252\) 3.10879 7.30311i 0.195835 0.460053i
\(253\) 5.83588 + 10.1080i 0.366899 + 0.635488i
\(254\) −5.02248 13.7992i −0.315139 0.865836i
\(255\) −12.2196 26.1862i −0.765223 1.63985i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) 0.930208 + 5.27547i 0.0580248 + 0.329075i 0.999978 0.00666986i \(-0.00212310\pi\)
−0.941953 + 0.335745i \(0.891012\pi\)
\(258\) 15.3348 7.15589i 0.954704 0.445506i
\(259\) −6.73601 + 10.3369i −0.418556 + 0.642306i
\(260\) 7.11790 4.10952i 0.441433 0.254862i
\(261\) −0.100164 + 0.569898i −0.00620002 + 0.0352758i
\(262\) −1.10285 + 0.636728i −0.0681340 + 0.0393372i
\(263\) 9.33788 + 25.6556i 0.575798 + 1.58199i 0.795193 + 0.606357i \(0.207370\pi\)
−0.219394 + 0.975636i \(0.570408\pi\)
\(264\) −0.757173 8.62713i −0.0466008 0.530963i
\(265\) −6.24091 + 1.10044i −0.383376 + 0.0675996i
\(266\) 14.1705 + 13.2559i 0.868847 + 0.812771i
\(267\) −3.50327 + 13.0888i −0.214397 + 0.801023i
\(268\) 8.07656 + 6.77704i 0.493354 + 0.413974i
\(269\) −4.92476 + 8.52993i −0.300268 + 0.520079i −0.976196 0.216888i \(-0.930409\pi\)
0.675929 + 0.736967i \(0.263743\pi\)
\(270\) 8.90455 + 8.88983i 0.541914 + 0.541018i
\(271\) 16.5456 9.55259i 1.00507 0.580279i 0.0953270 0.995446i \(-0.469610\pi\)
0.909745 + 0.415167i \(0.136277\pi\)
\(272\) 6.47429 2.35645i 0.392562 0.142881i
\(273\) 12.2444 + 9.59194i 0.741062 + 0.580530i
\(274\) 6.32890 5.31057i 0.382343 0.320824i
\(275\) 2.77592 + 3.30821i 0.167394 + 0.199492i
\(276\) 1.70772 3.66486i 0.102793 0.220598i
\(277\) −6.45570 + 2.34968i −0.387885 + 0.141179i −0.528599 0.848872i \(-0.677283\pi\)
0.140714 + 0.990050i \(0.455060\pi\)
\(278\) 2.07554 0.124482
\(279\) −15.5372 5.64538i −0.930189 0.337980i
\(280\) −6.36018 + 0.770782i −0.380093 + 0.0460630i
\(281\) −16.2044 2.85728i −0.966675 0.170451i −0.332042 0.943265i \(-0.607738\pi\)
−0.634633 + 0.772814i \(0.718849\pi\)
\(282\) −12.1919 + 5.68926i −0.726016 + 0.338791i
\(283\) −2.84602 3.39175i −0.169178 0.201619i 0.674793 0.738007i \(-0.264233\pi\)
−0.843971 + 0.536388i \(0.819788\pi\)
\(284\) 1.19247 + 1.42113i 0.0707600 + 0.0843285i
\(285\) −27.8748 + 13.0076i −1.65116 + 0.770504i
\(286\) 16.7131 + 2.94698i 0.988269 + 0.174259i
\(287\) 20.5016 + 8.74050i 1.21017 + 0.515936i
\(288\) −2.29707 + 1.92963i −0.135356 + 0.113705i
\(289\) 30.4693 1.79231
\(290\) 0.438889 0.159742i 0.0257724 0.00938040i
\(291\) −4.01609 + 8.61874i −0.235428 + 0.505240i
\(292\) −3.99413 4.76001i −0.233738 0.278559i
\(293\) 10.9748 9.20896i 0.641155 0.537993i −0.263217 0.964737i \(-0.584784\pi\)
0.904373 + 0.426743i \(0.140339\pi\)
\(294\) −5.84756 10.6210i −0.341036 0.619431i
\(295\) 27.8410 10.1333i 1.62097 0.589984i
\(296\) 4.03856 2.33166i 0.234736 0.135525i
\(297\) 2.28579 + 25.8801i 0.132635 + 1.50172i
\(298\) 4.10458 7.10934i 0.237772 0.411833i
\(299\) 6.06951 + 5.09292i 0.351009 + 0.294531i
\(300\) 0.386791 1.44512i 0.0223314 0.0834339i
\(301\) 5.85440 25.1775i 0.337442 1.45121i
\(302\) −9.97497 + 1.75886i −0.573995 + 0.101211i
\(303\) 0.580171 + 6.61039i 0.0333299 + 0.379757i
\(304\) −2.50840 6.89178i −0.143867 0.395271i
\(305\) 15.6170 9.01646i 0.894225 0.516281i
\(306\) −19.4190 + 7.08006i −1.11011 + 0.404740i
\(307\) 26.2998 15.1842i 1.50101 0.866608i 0.501009 0.865442i \(-0.332962\pi\)
0.999999 0.00116606i \(-0.000371168\pi\)
\(308\) −11.0833 7.22236i −0.631528 0.411532i
\(309\) 23.5221 10.9764i 1.33813 0.624427i
\(310\) 2.31705 + 13.1406i 0.131600 + 0.746338i
\(311\) 13.8700 11.6383i 0.786493 0.659946i −0.158382 0.987378i \(-0.550628\pi\)
0.944875 + 0.327432i \(0.106183\pi\)
\(312\) −2.48600 5.32740i −0.140742 0.301605i
\(313\) 9.29912 + 25.5491i 0.525617 + 1.44412i 0.864182 + 0.503179i \(0.167836\pi\)
−0.338565 + 0.940943i \(0.609942\pi\)
\(314\) −7.79593 13.5029i −0.439950 0.762015i
\(315\) 19.0793 2.32287i 1.07499 0.130879i
\(316\) −2.02486 + 3.50716i −0.113907 + 0.197293i
\(317\) 0.539221 + 0.0950793i 0.0302857 + 0.00534018i 0.188770 0.982021i \(-0.439550\pi\)
−0.158485 + 0.987361i \(0.550661\pi\)
\(318\) 0.396309 + 4.51549i 0.0222239 + 0.253216i
\(319\) 0.906234 + 0.329842i 0.0507393 + 0.0184676i
\(320\) 2.27547 + 0.828205i 0.127203 + 0.0462981i
\(321\) −6.35858 23.7044i −0.354902 1.32305i
\(322\) −2.79523 5.50734i −0.155772 0.306912i
\(323\) 50.5303i 2.81158i
\(324\) 6.88802 5.79269i 0.382668 0.321816i
\(325\) 2.53882 + 1.46579i 0.140829 + 0.0813074i
\(326\) −5.31537 0.937243i −0.294391 0.0519091i
\(327\) −4.34838 4.34598i −0.240466 0.240333i
\(328\) −5.41467 6.45295i −0.298975 0.356304i
\(329\) −4.65452 + 20.0173i −0.256612 + 1.10359i
\(330\) 17.1751 12.0332i 0.945458 0.662406i
\(331\) −2.28385 + 12.9524i −0.125532 + 0.711927i 0.855459 + 0.517871i \(0.173275\pi\)
−0.980991 + 0.194056i \(0.937836\pi\)
\(332\) 2.47168 + 4.28108i 0.135651 + 0.234955i
\(333\) −12.1118 + 7.00166i −0.663723 + 0.383689i
\(334\) 8.68755 + 5.01576i 0.475362 + 0.274450i
\(335\) −4.43332 + 25.1426i −0.242218 + 1.37369i
\(336\) 0.153991 + 4.57999i 0.00840089 + 0.249859i
\(337\) −6.44993 2.34758i −0.351350 0.127881i 0.160315 0.987066i \(-0.448749\pi\)
−0.511665 + 0.859185i \(0.670971\pi\)
\(338\) −1.45706 + 0.256919i −0.0792537 + 0.0139746i
\(339\) −0.326720 + 3.74632i −0.0177450 + 0.203472i
\(340\) 12.7805 + 10.7241i 0.693118 + 0.581595i
\(341\) −13.7759 + 23.8606i −0.746008 + 1.29212i
\(342\) 7.53661 + 20.6712i 0.407533 + 1.11777i
\(343\) −18.2784 2.98346i −0.986939 0.161092i
\(344\) −6.28009 + 7.48431i −0.338600 + 0.403527i
\(345\) 9.75316 0.856000i 0.525092 0.0460855i
\(346\) −5.02572 + 13.8080i −0.270184 + 0.742325i
\(347\) 6.68724 1.17914i 0.358990 0.0632996i 0.00875547 0.999962i \(-0.497213\pi\)
0.350234 + 0.936662i \(0.386102\pi\)
\(348\) −0.0865537 0.322667i −0.00463977 0.0172968i
\(349\) 10.7820 + 29.6233i 0.577147 + 1.58570i 0.792966 + 0.609265i \(0.208536\pi\)
−0.215819 + 0.976433i \(0.569242\pi\)
\(350\) −1.37237 1.82717i −0.0733563 0.0976662i
\(351\) 7.46680 + 15.9781i 0.398548 + 0.852847i
\(352\) 2.50001 + 4.33015i 0.133251 + 0.230798i
\(353\) 0.857051 4.86058i 0.0456162 0.258702i −0.953468 0.301495i \(-0.902514\pi\)
0.999084 + 0.0427926i \(0.0136255\pi\)
\(354\) −5.49056 20.4685i −0.291820 1.08789i
\(355\) −1.53645 + 4.22135i −0.0815461 + 0.224046i
\(356\) −1.35842 7.70399i −0.0719962 0.408311i
\(357\) −9.79553 + 30.0151i −0.518434 + 1.58857i
\(358\) −17.5884 14.7585i −0.929578 0.780009i
\(359\) 2.36896i 0.125029i 0.998044 + 0.0625145i \(0.0199120\pi\)
−0.998044 + 0.0625145i \(0.980088\pi\)
\(360\) −6.82779 2.48085i −0.359856 0.130752i
\(361\) −34.7887 −1.83099
\(362\) 1.57976 0.574985i 0.0830303 0.0302206i
\(363\) 24.1574 + 2.10679i 1.26793 + 0.110578i
\(364\) −8.74681 2.03385i −0.458457 0.106603i
\(365\) 5.14626 14.1392i 0.269368 0.740082i
\(366\) −5.45438 11.6885i −0.285105 0.610970i
\(367\) −7.86783 + 9.37652i −0.410697 + 0.489450i −0.931251 0.364379i \(-0.881281\pi\)
0.520553 + 0.853829i \(0.325726\pi\)
\(368\) 2.33434i 0.121686i
\(369\) 16.2547 + 19.3499i 0.846184 + 1.00731i
\(370\) 9.77940 + 5.64614i 0.508407 + 0.293529i
\(371\) 5.80105 + 3.78023i 0.301176 + 0.196260i
\(372\) 9.50765 0.834453i 0.492949 0.0432644i
\(373\) 14.2079 11.9218i 0.735655 0.617288i −0.196012 0.980602i \(-0.562799\pi\)
0.931667 + 0.363313i \(0.118355\pi\)
\(374\) 5.98203 + 33.9258i 0.309323 + 1.75426i
\(375\) −16.7560 + 4.49470i −0.865275 + 0.232105i
\(376\) 4.99296 5.95038i 0.257492 0.306867i
\(377\) 0.654662 0.0337168
\(378\) −0.469549 13.7397i −0.0241510 0.706694i
\(379\) −15.4787 −0.795089 −0.397544 0.917583i \(-0.630137\pi\)
−0.397544 + 0.917583i \(0.630137\pi\)
\(380\) 11.4156 13.6046i 0.585609 0.697901i
\(381\) −17.9900 17.9801i −0.921658 0.921150i
\(382\) −0.0348829 0.197831i −0.00178477 0.0101219i
\(383\) −25.6604 + 21.5316i −1.31118 + 1.10021i −0.323089 + 0.946368i \(0.604721\pi\)
−0.988095 + 0.153846i \(0.950834\pi\)
\(384\) 0.731563 1.56997i 0.0373324 0.0801173i
\(385\) 1.72681 31.9871i 0.0880065 1.63021i
\(386\) −4.65470 2.68739i −0.236918 0.136785i
\(387\) 18.8279 22.4633i 0.957075 1.14188i
\(388\) 5.48974i 0.278699i
\(389\) 15.1378 18.0406i 0.767518 0.914693i −0.230780 0.973006i \(-0.574128\pi\)
0.998298 + 0.0583133i \(0.0185723\pi\)
\(390\) 8.16210 11.6635i 0.413304 0.590606i
\(391\) −5.50076 + 15.1132i −0.278186 + 0.764309i
\(392\) 5.65015 + 4.13229i 0.285376 + 0.208712i
\(393\) −1.26463 + 1.80715i −0.0637924 + 0.0911584i
\(394\) −5.49658 + 2.00059i −0.276914 + 0.100788i
\(395\) −9.80642 −0.493415
\(396\) −7.50719 12.9863i −0.377251 0.652586i
\(397\) 2.57168i 0.129069i 0.997915 + 0.0645344i \(0.0205562\pi\)
−0.997915 + 0.0645344i \(0.979444\pi\)
\(398\) −6.87172 5.76606i −0.344448 0.289027i
\(399\) 31.9505 + 10.4272i 1.59953 + 0.522012i
\(400\) 0.149981 + 0.850586i 0.00749906 + 0.0425293i
\(401\) −7.84541 + 21.5551i −0.391781 + 1.07641i 0.574407 + 0.818570i \(0.305233\pi\)
−0.966188 + 0.257840i \(0.916989\pi\)
\(402\) 17.6404 + 4.72152i 0.879824 + 0.235488i
\(403\) −3.24776 + 18.4190i −0.161783 + 0.917514i
\(404\) −1.91559 3.31790i −0.0953042 0.165072i
\(405\) 20.4875 + 7.43126i 1.01803 + 0.369262i
\(406\) −0.469426 0.200131i −0.0232972 0.00993234i
\(407\) 7.97479 + 21.9105i 0.395296 + 1.08607i
\(408\) 8.43592 8.44057i 0.417640 0.417871i
\(409\) 9.74312 1.71797i 0.481766 0.0849484i 0.0725096 0.997368i \(-0.476899\pi\)
0.409257 + 0.912419i \(0.365788\pi\)
\(410\) 6.97657 19.1680i 0.344548 0.946639i
\(411\) 6.04402 12.9708i 0.298130 0.639802i
\(412\) −9.63304 + 11.4802i −0.474586 + 0.565589i
\(413\) −29.7782 12.6954i −1.46529 0.624698i
\(414\) −0.00386138 7.00303i −0.000189776 0.344180i
\(415\) −5.98521 + 10.3667i −0.293802 + 0.508880i
\(416\) 2.60009 + 2.18174i 0.127480 + 0.106968i
\(417\) 3.25770 1.52018i 0.159530 0.0744437i
\(418\) 36.1135 6.36778i 1.76637 0.311458i
\(419\) 5.78462 + 2.10543i 0.282597 + 0.102857i 0.479430 0.877580i \(-0.340843\pi\)
−0.196833 + 0.980437i \(0.563066\pi\)
\(420\) −9.41819 + 5.86817i −0.459561 + 0.286338i
\(421\) 3.55173 20.1429i 0.173101 0.981704i −0.767212 0.641393i \(-0.778357\pi\)
0.940313 0.340310i \(-0.110532\pi\)
\(422\) 21.8593 + 12.6205i 1.06410 + 0.614356i
\(423\) −14.9690 + 17.8594i −0.727819 + 0.868353i
\(424\) −1.30852 2.26642i −0.0635474 0.110067i
\(425\) −1.03334 + 5.86037i −0.0501244 + 0.284270i
\(426\) 2.91254 + 1.35716i 0.141113 + 0.0657547i
\(427\) −19.1909 4.46236i −0.928711 0.215949i
\(428\) 9.10803 + 10.8545i 0.440253 + 0.524673i
\(429\) 28.3909 7.61571i 1.37073 0.367690i
\(430\) −23.2989 4.10823i −1.12357 0.198116i
\(431\) −5.50792 3.18000i −0.265307 0.153175i 0.361446 0.932393i \(-0.382283\pi\)
−0.626753 + 0.779218i \(0.715617\pi\)
\(432\) −2.19209 + 4.71113i −0.105467 + 0.226664i
\(433\) 10.0805i 0.484439i −0.970221 0.242220i \(-0.922125\pi\)
0.970221 0.242220i \(-0.0778755\pi\)
\(434\) 7.95951 12.2145i 0.382069 0.586314i
\(435\) 0.571866 0.572182i 0.0274189 0.0274340i
\(436\) 3.33540 + 1.21399i 0.159737 + 0.0581394i
\(437\) 16.0878 + 5.85547i 0.769583 + 0.280105i
\(438\) −9.75543 4.54576i −0.466132 0.217205i
\(439\) −30.6887 5.41125i −1.46469 0.258265i −0.616250 0.787551i \(-0.711349\pi\)
−0.848444 + 0.529286i \(0.822460\pi\)
\(440\) −6.05380 + 10.4855i −0.288604 + 0.499876i
\(441\) −16.9573 12.3875i −0.807490 0.589881i
\(442\) 11.6926 + 20.2522i 0.556161 + 0.963299i
\(443\) 1.23830 + 3.40220i 0.0588334 + 0.161643i 0.965627 0.259931i \(-0.0836998\pi\)
−0.906794 + 0.421574i \(0.861478\pi\)
\(444\) 4.63102 6.61766i 0.219778 0.314060i
\(445\) 14.5112 12.1764i 0.687899 0.577215i
\(446\) −1.73127 9.81850i −0.0819779 0.464920i
\(447\) 1.23533 14.1649i 0.0584293 0.669977i
\(448\) −1.19744 2.35927i −0.0565736 0.111465i
\(449\) −13.3495 + 7.70733i −0.630001 + 0.363731i −0.780753 0.624840i \(-0.785164\pi\)
0.150751 + 0.988572i \(0.451831\pi\)
\(450\) −0.451351 2.55151i −0.0212769 0.120279i
\(451\) 36.4760 21.0594i 1.71759 0.991649i
\(452\) −0.742577 2.04021i −0.0349279 0.0959635i
\(453\) −14.3682 + 10.0666i −0.675075 + 0.472970i
\(454\) 12.9219 2.27848i 0.606454 0.106934i
\(455\) −6.32507 20.8053i −0.296524 0.975369i
\(456\) −8.98485 8.97990i −0.420754 0.420522i
\(457\) −6.15453 5.16426i −0.287897 0.241574i 0.487389 0.873185i \(-0.337949\pi\)
−0.775285 + 0.631611i \(0.782394\pi\)
\(458\) 3.88714 6.73272i 0.181634 0.314599i
\(459\) −25.2938 + 25.3357i −1.18061 + 1.18257i
\(460\) −4.89533 + 2.82632i −0.228246 + 0.131778i
\(461\) −4.79686 + 1.74591i −0.223412 + 0.0813153i −0.451301 0.892372i \(-0.649040\pi\)
0.227889 + 0.973687i \(0.426818\pi\)
\(462\) −22.6858 3.21829i −1.05544 0.149728i
\(463\) −25.3683 + 21.2865i −1.17897 + 0.989270i −0.178980 + 0.983853i \(0.557280\pi\)
−0.999985 + 0.00541710i \(0.998276\pi\)
\(464\) 0.123980 + 0.147753i 0.00575560 + 0.00685926i
\(465\) 13.2614 + 18.9281i 0.614981 + 0.877768i
\(466\) 4.16565 1.51617i 0.192970 0.0702353i
\(467\) 7.56317 0.349982 0.174991 0.984570i \(-0.444010\pi\)
0.174991 + 0.984570i \(0.444010\pi\)
\(468\) −7.80389 6.54091i −0.360735 0.302354i
\(469\) 22.3041 16.7524i 1.02991 0.773554i
\(470\) 18.5237 + 3.26623i 0.854435 + 0.150660i
\(471\) −22.1262 15.4838i −1.01952 0.713458i
\(472\) 7.86467 + 9.37275i 0.362001 + 0.431416i
\(473\) −31.4006 37.4217i −1.44380 1.72065i
\(474\) −0.609411 + 6.98779i −0.0279912 + 0.320960i
\(475\) 6.23827 + 1.09997i 0.286231 + 0.0504703i
\(476\) −2.19307 18.0963i −0.100519 0.829442i
\(477\) 3.92931 + 6.79710i 0.179911 + 0.311218i
\(478\) −0.0687846 −0.00314613
\(479\) −21.4742 + 7.81596i −0.981180 + 0.357120i −0.782299 0.622903i \(-0.785953\pi\)
−0.198881 + 0.980024i \(0.563731\pi\)
\(480\) 4.17812 0.366699i 0.190704 0.0167374i
\(481\) 10.1741 + 12.1251i 0.463901 + 0.552856i
\(482\) −9.36878 + 7.86134i −0.426736 + 0.358074i
\(483\) −8.42104 6.59684i −0.383171 0.300167i
\(484\) −13.1559 + 4.78836i −0.597996 + 0.217653i
\(485\) 11.5125 6.64673i 0.522755 0.301812i
\(486\) 6.56849 14.1370i 0.297953 0.641268i
\(487\) 10.6212 18.3965i 0.481293 0.833624i −0.518477 0.855092i \(-0.673501\pi\)
0.999770 + 0.0214680i \(0.00683399\pi\)
\(488\) 5.70471 + 4.78682i 0.258240 + 0.216689i
\(489\) −9.02931 + 2.42206i −0.408319 + 0.109530i
\(490\) −1.82482 + 16.8521i −0.0824370 + 0.761298i
\(491\) −1.95216 + 0.344218i −0.0880997 + 0.0155344i −0.217524 0.976055i \(-0.569798\pi\)
0.129425 + 0.991589i \(0.458687\pi\)
\(492\) −13.2250 6.16249i −0.596230 0.277826i
\(493\) 0.454507 + 1.24875i 0.0204700 + 0.0562408i
\(494\) 21.5581 12.4466i 0.969946 0.559999i
\(495\) 18.1441 31.4665i 0.815515 1.41431i
\(496\) −4.77210 + 2.75517i −0.214274 + 0.123711i
\(497\) 4.37680 2.22143i 0.196326 0.0996447i
\(498\) 7.01507 + 4.90912i 0.314353 + 0.219983i
\(499\) −0.746568 4.23400i −0.0334210 0.189540i 0.963527 0.267612i \(-0.0862346\pi\)
−0.996948 + 0.0780724i \(0.975123\pi\)
\(500\) 7.67276 6.43821i 0.343136 0.287925i
\(501\) 17.3094 + 1.50957i 0.773327 + 0.0674425i
\(502\) 2.14277 + 5.88722i 0.0956366 + 0.262759i
\(503\) −19.4696 33.7223i −0.868106 1.50360i −0.863930 0.503613i \(-0.832004\pi\)
−0.00417666 0.999991i \(-0.501329\pi\)
\(504\) 3.59622 + 7.07582i 0.160188 + 0.315182i
\(505\) 4.63862 8.03433i 0.206416 0.357523i
\(506\) −11.4944 2.02678i −0.510991 0.0901014i
\(507\) −2.09879 + 1.47045i −0.0932103 + 0.0653049i
\(508\) 13.7992 + 5.02248i 0.612239 + 0.222837i
\(509\) −26.4855 9.63994i −1.17395 0.427283i −0.319889 0.947455i \(-0.603646\pi\)
−0.854061 + 0.520172i \(0.825868\pi\)
\(510\) 27.9145 + 7.47141i 1.23607 + 0.330840i
\(511\) −14.6599 + 7.44059i −0.648516 + 0.329152i
\(512\) 1.00000i 0.0441942i
\(513\) 26.9694 + 26.9248i 1.19073 + 1.18876i
\(514\) −4.63917 2.67843i −0.204625 0.118140i
\(515\) −35.7383 6.30162i −1.57482 0.277682i
\(516\) −4.37530 + 16.3469i −0.192612 + 0.719631i
\(517\) 24.9649 + 29.7520i 1.09795 + 1.30849i
\(518\) −3.58872 11.8045i −0.157679 0.518662i
\(519\) 2.22520 + 25.3537i 0.0976755 + 1.11290i
\(520\) −1.42722 + 8.09417i −0.0625878 + 0.354953i
\(521\) 19.7992 + 34.2932i 0.867418 + 1.50241i 0.864626 + 0.502416i \(0.167555\pi\)
0.00279144 + 0.999996i \(0.499111\pi\)
\(522\) −0.372183 0.443054i −0.0162900 0.0193919i
\(523\) 3.31222 + 1.91231i 0.144833 + 0.0836196i 0.570666 0.821183i \(-0.306685\pi\)
−0.425832 + 0.904802i \(0.640019\pi\)
\(524\) 0.221133 1.25411i 0.00966026 0.0547860i
\(525\) −3.49230 1.86270i −0.152416 0.0812950i
\(526\) −25.6556 9.33788i −1.11864 0.407151i
\(527\) −37.3884 + 6.59258i −1.62866 + 0.287178i
\(528\) 7.09546 + 4.96538i 0.308790 + 0.216091i
\(529\) 13.4447 + 11.2815i 0.584553 + 0.490498i
\(530\) 3.16859 5.48817i 0.137635 0.238391i
\(531\) −23.6095 28.1052i −1.02457 1.21966i
\(532\) −19.2632 + 2.33449i −0.835166 + 0.101213i
\(533\) 18.3784 21.9025i 0.796055 0.948701i
\(534\) −7.77476 11.0970i −0.336447 0.480214i
\(535\) −11.7353 + 32.2425i −0.507362 + 1.39397i
\(536\) −10.3830 + 1.83081i −0.448478 + 0.0790789i
\(537\) −38.4158 10.2821i −1.65776 0.443707i
\(538\) −3.36873 9.25551i −0.145236 0.399034i
\(539\) −25.2533 + 24.2339i −1.08774 + 1.04383i
\(540\) −12.5337 + 1.10701i −0.539366 + 0.0476380i
\(541\) 3.72015 + 6.44349i 0.159942 + 0.277027i 0.934847 0.355050i \(-0.115536\pi\)
−0.774906 + 0.632077i \(0.782203\pi\)
\(542\) −3.31758 + 18.8149i −0.142502 + 0.808171i
\(543\) 2.05841 2.05954i 0.0883346 0.0883833i
\(544\) −2.35645 + 6.47429i −0.101032 + 0.277583i
\(545\) 1.49251 + 8.46447i 0.0639323 + 0.362578i
\(546\) −15.2184 + 3.21415i −0.651286 + 0.137553i
\(547\) −0.528178 0.443194i −0.0225832 0.0189496i 0.631426 0.775436i \(-0.282470\pi\)
−0.654009 + 0.756486i \(0.726914\pi\)
\(548\) 8.26179i 0.352926i
\(549\) −17.1221 14.3510i −0.730752 0.612487i
\(550\) −4.31856 −0.184144
\(551\) 1.32927 0.483815i 0.0566289 0.0206112i
\(552\) 1.70974 + 3.66391i 0.0727714 + 0.155947i
\(553\) 7.82462 + 7.31961i 0.332737 + 0.311261i
\(554\) 2.34968 6.45570i 0.0998285 0.274276i
\(555\) 19.4848 + 1.69929i 0.827086 + 0.0721309i
\(556\) −1.33413 + 1.58995i −0.0565797 + 0.0674291i
\(557\) 6.32554i 0.268022i −0.990980 0.134011i \(-0.957214\pi\)
0.990980 0.134011i \(-0.0427857\pi\)
\(558\) 14.3117 8.27341i 0.605864 0.350242i
\(559\) −28.7186 16.5807i −1.21467 0.701289i
\(560\) 3.49779 5.36763i 0.147809 0.226824i
\(561\) 34.2374 + 48.8675i 1.44551 + 2.06319i
\(562\) 12.6048 10.5767i 0.531702 0.446151i
\(563\) −0.615555 3.49098i −0.0259425 0.147127i 0.969085 0.246727i \(-0.0793550\pi\)
−0.995028 + 0.0995993i \(0.968244\pi\)
\(564\) 3.47857 12.9965i 0.146474 0.547252i
\(565\) 3.37943 4.02745i 0.142174 0.169436i
\(566\) 4.42762 0.186107
\(567\) −10.8003 21.2215i −0.453572 0.891220i
\(568\) −1.85515 −0.0778404
\(569\) −13.9480 + 16.6225i −0.584729 + 0.696853i −0.974584 0.224024i \(-0.928081\pi\)
0.389855 + 0.920876i \(0.372525\pi\)
\(570\) 7.95319 29.7145i 0.333123 1.24460i
\(571\) −5.61673 31.8541i −0.235053 1.33305i −0.842502 0.538693i \(-0.818918\pi\)
0.607449 0.794359i \(-0.292193\pi\)
\(572\) −13.0005 + 10.9087i −0.543579 + 0.456117i
\(573\) −0.199648 0.284960i −0.00834043 0.0119044i
\(574\) −19.8738 + 10.0869i −0.829517 + 0.421019i
\(575\) −1.74607 1.00810i −0.0728163 0.0420405i
\(576\) −0.00165416 3.00000i −6.89233e−5 0.125000i
\(577\) 22.6710i 0.943805i −0.881651 0.471903i \(-0.843567\pi\)
0.881651 0.471903i \(-0.156433\pi\)
\(578\) −19.5853 + 23.3409i −0.814641 + 0.970852i
\(579\) −9.27421 0.808812i −0.385423 0.0336131i
\(580\) −0.159742 + 0.438889i −0.00663294 + 0.0182239i
\(581\) 12.5134 3.80424i 0.519145 0.157826i
\(582\) −4.02085 8.61653i −0.166669 0.357167i
\(583\) 12.2961 4.47542i 0.509253 0.185353i
\(584\) 6.21376 0.257127
\(585\) 4.26827 24.2849i 0.176471 1.00406i
\(586\) 14.3266i 0.591826i
\(587\) 7.53131 + 6.31952i 0.310850 + 0.260834i 0.784843 0.619694i \(-0.212743\pi\)
−0.473993 + 0.880529i \(0.657188\pi\)
\(588\) 11.8949 + 2.34757i 0.490538 + 0.0968123i
\(589\) 7.01770 + 39.7994i 0.289159 + 1.63990i
\(590\) −10.1333 + 27.8410i −0.417181 + 1.14620i
\(591\) −7.16198 + 7.16593i −0.294604 + 0.294767i
\(592\) −0.809778 + 4.59248i −0.0332817 + 0.188750i
\(593\) 4.00013 + 6.92843i 0.164266 + 0.284517i 0.936394 0.350950i \(-0.114141\pi\)
−0.772129 + 0.635466i \(0.780808\pi\)
\(594\) −21.2946 14.8844i −0.873728 0.610715i
\(595\) 35.2943 26.5092i 1.44692 1.08677i
\(596\) 2.80770 + 7.71408i 0.115008 + 0.315981i
\(597\) −15.0089 4.01718i −0.614273 0.164412i
\(598\) −7.80281 + 1.37585i −0.319081 + 0.0562625i
\(599\) −10.6127 + 29.1583i −0.433625 + 1.19137i 0.509947 + 0.860206i \(0.329665\pi\)
−0.943572 + 0.331168i \(0.892557\pi\)
\(600\) 0.858400 + 1.22520i 0.0350440 + 0.0500187i
\(601\) 0.959416 1.14339i 0.0391354 0.0466398i −0.746122 0.665810i \(-0.768086\pi\)
0.785257 + 0.619170i \(0.212531\pi\)
\(602\) 15.5240 + 20.6685i 0.632709 + 0.842386i
\(603\) 31.1460 5.50960i 1.26837 0.224368i
\(604\) 5.06442 8.77184i 0.206068 0.356921i
\(605\) −25.9702 21.7916i −1.05584 0.885953i
\(606\) −5.43678 3.80464i −0.220854 0.154553i
\(607\) 21.8941 3.86051i 0.888652 0.156693i 0.289357 0.957221i \(-0.406559\pi\)
0.599295 + 0.800528i \(0.295447\pi\)
\(608\) 6.89178 + 2.50840i 0.279499 + 0.101729i
\(609\) −0.883378 + 0.0297014i −0.0357963 + 0.00120356i
\(610\) −3.13138 + 17.7590i −0.126786 + 0.719039i
\(611\) 22.8326 + 13.1824i 0.923709 + 0.533304i
\(612\) 7.05864 19.4268i 0.285329 0.785281i
\(613\) −6.67374 11.5593i −0.269550 0.466874i 0.699196 0.714930i \(-0.253542\pi\)
−0.968746 + 0.248056i \(0.920208\pi\)
\(614\) −5.27342 + 29.9070i −0.212818 + 1.20695i
\(615\) −3.08897 35.1953i −0.124559 1.41921i
\(616\) 12.6568 3.84783i 0.509959 0.155034i
\(617\) −13.5612 16.1616i −0.545952 0.650640i 0.420559 0.907265i \(-0.361834\pi\)
−0.966511 + 0.256625i \(0.917389\pi\)
\(618\) −6.71128 + 25.0745i −0.269967 + 1.00864i
\(619\) 4.76309 + 0.839862i 0.191445 + 0.0337569i 0.268548 0.963266i \(-0.413456\pi\)
−0.0771035 + 0.997023i \(0.524567\pi\)
\(620\) −11.5557 6.67168i −0.464088 0.267941i
\(621\) −5.13528 10.9889i −0.206072 0.440970i
\(622\) 18.1059i 0.725982i
\(623\) −20.6672 1.11571i −0.828013 0.0447000i
\(624\) 5.67899 + 1.52000i 0.227342 + 0.0608489i
\(625\) 26.8494 + 9.77239i 1.07398 + 0.390895i
\(626\) −25.5491 9.29912i −1.02115 0.371668i
\(627\) 52.0186 36.4452i 2.07742 1.45548i
\(628\) 15.3550 + 2.70750i 0.612730 + 0.108041i
\(629\) −16.0647 + 27.8248i −0.640541 + 1.10945i
\(630\) −10.4845 + 16.1087i −0.417712 + 0.641785i
\(631\) −19.0055 32.9186i −0.756599 1.31047i −0.944575 0.328294i \(-0.893526\pi\)
0.187977 0.982174i \(-0.439807\pi\)
\(632\) −1.38508 3.80549i −0.0550957 0.151374i
\(633\) 43.5534 + 3.79833i 1.73109 + 0.150970i
\(634\) −0.419440 + 0.351952i −0.0166581 + 0.0139778i
\(635\) 6.17480 + 35.0191i 0.245040 + 1.38969i
\(636\) −3.71381 2.59891i −0.147262 0.103054i
\(637\) −10.4825 + 21.3218i −0.415331 + 0.844801i
\(638\) −0.835189 + 0.482197i −0.0330655 + 0.0190904i
\(639\) 5.56545 0.00306872i 0.220166 0.000121397i
\(640\) −2.09709 + 1.21075i −0.0828947 + 0.0478593i
\(641\) 11.8230 + 32.4833i 0.466979 + 1.28301i 0.920141 + 0.391586i \(0.128074\pi\)
−0.453162 + 0.891428i \(0.649704\pi\)
\(642\) 22.2459 + 10.3659i 0.877974 + 0.409111i
\(643\) −31.4889 + 5.55235i −1.24180 + 0.218963i −0.755688 0.654932i \(-0.772697\pi\)
−0.486114 + 0.873895i \(0.661586\pi\)
\(644\) 6.01561 + 1.39878i 0.237048 + 0.0551196i
\(645\) −39.5782 + 10.6167i −1.55839 + 0.418030i
\(646\) 38.7085 + 32.4803i 1.52296 + 1.27792i
\(647\) −21.5308 + 37.2925i −0.846464 + 1.46612i 0.0378791 + 0.999282i \(0.487940\pi\)
−0.884343 + 0.466837i \(0.845394\pi\)
\(648\) 0.00992496 + 8.99999i 0.000389889 + 0.353553i
\(649\) −52.9805 + 30.5883i −2.07966 + 1.20070i
\(650\) −2.75478 + 1.00266i −0.108052 + 0.0393275i
\(651\) 3.54676 25.0013i 0.139009 0.979877i
\(652\) 4.13462 3.46936i 0.161924 0.135871i
\(653\) 3.37859 + 4.02645i 0.132215 + 0.157567i 0.828090 0.560596i \(-0.189428\pi\)
−0.695875 + 0.718163i \(0.744983\pi\)
\(654\) 6.12430 0.537508i 0.239479 0.0210182i
\(655\) 2.89772 1.05468i 0.113223 0.0412099i
\(656\) 8.42372 0.328891
\(657\) −18.6413 + 0.0102785i −0.727265 + 0.000401004i
\(658\) −12.3423 16.4324i −0.481151 0.640603i
\(659\) 24.3847 + 4.29967i 0.949892 + 0.167492i 0.627065 0.778967i \(-0.284256\pi\)
0.322826 + 0.946458i \(0.395367\pi\)
\(660\) −1.82198 + 20.8917i −0.0709205 + 0.813208i
\(661\) −11.7380 13.9888i −0.456554 0.544100i 0.487833 0.872937i \(-0.337788\pi\)
−0.944387 + 0.328837i \(0.893343\pi\)
\(662\) −8.45406 10.0752i −0.328576 0.391582i
\(663\) 33.1857 + 23.2232i 1.28882 + 0.901915i
\(664\) −4.86827 0.858407i −0.188925 0.0333126i
\(665\) −28.2186 37.5702i −1.09427 1.45691i
\(666\) 2.42174 13.7788i 0.0938404 0.533916i
\(667\) −0.450243 −0.0174335
\(668\) −9.42654 + 3.43098i −0.364724 + 0.132749i
\(669\) −9.90870 14.1428i −0.383092 0.546792i
\(670\) −16.4107 19.5575i −0.633999 0.755571i
\(671\) −28.5237 + 23.9342i −1.10114 + 0.923970i
\(672\) −3.60746 2.82600i −0.139161 0.109015i
\(673\) 40.1228 14.6035i 1.54662 0.562924i 0.578998 0.815329i \(-0.303444\pi\)
0.967622 + 0.252405i \(0.0812216\pi\)
\(674\) 5.94429 3.43194i 0.228965 0.132193i
\(675\) −2.57723 3.67419i −0.0991975 0.141420i
\(676\) 0.739770 1.28132i 0.0284527 0.0492815i
\(677\) 28.5915 + 23.9911i 1.09886 + 0.922053i 0.997348 0.0727810i \(-0.0231874\pi\)
0.101512 + 0.994834i \(0.467632\pi\)
\(678\) −2.65984 2.65837i −0.102150 0.102094i
\(679\) −14.1471 3.28955i −0.542915 0.126241i
\(680\) −16.4302 + 2.89710i −0.630071 + 0.111099i
\(681\) 18.6130 13.0406i 0.713250 0.499716i
\(682\) −9.42329 25.8903i −0.360836 0.991390i
\(683\) 9.60985 5.54825i 0.367711 0.212298i −0.304747 0.952433i \(-0.598572\pi\)
0.672458 + 0.740135i \(0.265239\pi\)
\(684\) −20.6795 7.51381i −0.790700 0.287298i
\(685\) −17.3257 + 10.0030i −0.661981 + 0.382195i
\(686\) 14.0346 12.0843i 0.535843 0.461381i
\(687\) 1.16989 13.4145i 0.0446342 0.511796i
\(688\) −1.69656 9.62165i −0.0646806 0.366822i
\(689\) 6.80455 5.70969i 0.259233 0.217522i
\(690\) −5.61348 + 8.02158i −0.213701 + 0.305376i
\(691\) −5.17181 14.2094i −0.196745 0.540553i 0.801612 0.597844i \(-0.203976\pi\)
−0.998357 + 0.0572914i \(0.981754\pi\)
\(692\) −7.34711 12.7256i −0.279295 0.483753i
\(693\) −37.9642 + 11.5644i −1.44214 + 0.439297i
\(694\) −3.39520 + 5.88066i −0.128880 + 0.223227i
\(695\) −4.94958 0.872744i −0.187748 0.0331051i
\(696\) 0.302813 + 0.141102i 0.0114781 + 0.00534847i
\(697\) 54.5377 + 19.8501i 2.06576 + 0.751876i
\(698\) −29.6233 10.7820i −1.12126 0.408105i
\(699\) 5.42778 5.43077i 0.205298 0.205411i
\(700\) 2.28183 + 0.123184i 0.0862452 + 0.00465591i
\(701\) 32.4598i 1.22599i −0.790087 0.612994i \(-0.789965\pi\)
0.790087 0.612994i \(-0.210035\pi\)
\(702\) −17.0395 4.55062i −0.643114 0.171752i
\(703\) 29.6191 + 17.1006i 1.11711 + 0.644961i
\(704\) −4.92406 0.868245i −0.185583 0.0327232i
\(705\) 31.4665 8.44073i 1.18510 0.317896i
\(706\) 3.17252 + 3.78086i 0.119399 + 0.142294i
\(707\) −9.69809 + 2.94834i −0.364734 + 0.110884i
\(708\) 19.2090 + 8.95087i 0.721919 + 0.336394i
\(709\) −5.13784 + 29.1382i −0.192956 + 1.09431i 0.722344 + 0.691534i \(0.243065\pi\)
−0.915300 + 0.402773i \(0.868046\pi\)
\(710\) −2.24613 3.89042i −0.0842959 0.146005i
\(711\) 4.16155 + 11.4142i 0.156070 + 0.428065i
\(712\) 6.77478 + 3.91142i 0.253895 + 0.146587i
\(713\) 2.23364 12.6676i 0.0836506 0.474406i
\(714\) −16.6964 26.7971i −0.624848 1.00286i
\(715\) −38.6170 14.0554i −1.44419 0.525644i
\(716\) 22.6113 3.98698i 0.845023 0.149000i
\(717\) −0.107962 + 0.0503798i −0.00403192 + 0.00188147i
\(718\) −1.81473 1.52274i −0.0677251 0.0568281i
\(719\) 18.0895 31.3319i 0.674624 1.16848i −0.301954 0.953322i \(-0.597639\pi\)
0.976579 0.215161i \(-0.0690276\pi\)
\(720\) 6.28926 3.63573i 0.234387 0.135496i
\(721\) 23.8122 + 31.7035i 0.886814 + 1.18070i
\(722\) 22.3618 26.6497i 0.832219 0.991800i
\(723\) −8.94707 + 19.2009i −0.332745 + 0.714088i
\(724\) −0.574985 + 1.57976i −0.0213692 + 0.0587113i
\(725\) −0.164059 + 0.0289281i −0.00609301 + 0.00107436i
\(726\) −17.1420 + 17.1514i −0.636198 + 0.636549i
\(727\) 4.64416 + 12.7597i 0.172242 + 0.473232i 0.995536 0.0943840i \(-0.0300881\pi\)
−0.823294 + 0.567616i \(0.807866\pi\)
\(728\) 7.18036 5.39311i 0.266122 0.199882i
\(729\) −0.0446623 27.0000i −0.00165416 0.999999i
\(730\) 7.52333 + 13.0308i 0.278451 + 0.482291i
\(731\) 11.6889 66.2912i 0.432331 2.45187i
\(732\) 12.4600 + 3.33495i 0.460533 + 0.123263i
\(733\) −2.39661 + 6.58463i −0.0885208 + 0.243209i −0.976051 0.217540i \(-0.930197\pi\)
0.887531 + 0.460749i \(0.152419\pi\)
\(734\) −2.12548 12.0542i −0.0784530 0.444929i
\(735\) 9.47875 + 27.7870i 0.349629 + 1.02494i
\(736\) −1.78821 1.50049i −0.0659143 0.0553087i
\(737\) 52.7162i 1.94183i
\(738\) −25.2712 + 0.0139342i −0.930245 + 0.000512924i
\(739\) −29.5115 −1.08560 −0.542799 0.839863i \(-0.682635\pi\)
−0.542799 + 0.839863i \(0.682635\pi\)
\(740\) −10.6113 + 3.86219i −0.390078 + 0.141977i
\(741\) 24.7207 35.3256i 0.908139 1.29772i
\(742\) −6.62467 + 2.01398i −0.243199 + 0.0739355i
\(743\) −8.86180 + 24.3476i −0.325108 + 0.893226i 0.664222 + 0.747535i \(0.268763\pi\)
−0.989330 + 0.145691i \(0.953459\pi\)
\(744\) −5.47217 + 7.81966i −0.200620 + 0.286683i
\(745\) −12.7777 + 15.2278i −0.468138 + 0.557905i
\(746\) 18.5471i 0.679056i
\(747\) 14.6062 + 2.56717i 0.534414 + 0.0939277i
\(748\) −29.8338 17.2246i −1.09083 0.629793i
\(749\) 33.4298 16.9672i 1.22150 0.619968i
\(750\) 7.32739 15.7250i 0.267559 0.574194i
\(751\) 40.8561 34.2824i 1.49086 1.25098i 0.597319 0.802004i \(-0.296233\pi\)
0.893543 0.448977i \(-0.148212\pi\)
\(752\) 1.34884 + 7.64966i 0.0491872 + 0.278954i
\(753\) 7.67520 + 7.67096i 0.279700 + 0.279545i
\(754\) −0.420809 + 0.501500i −0.0153250 + 0.0182636i
\(755\) 24.5271 0.892632
\(756\) 10.8270 + 8.47202i 0.393776 + 0.308124i
\(757\) 25.1071 0.912532 0.456266 0.889843i \(-0.349187\pi\)
0.456266 + 0.889843i \(0.349187\pi\)
\(758\) 9.94953 11.8574i 0.361383 0.430680i
\(759\) −19.5258 + 5.23769i −0.708742 + 0.190116i
\(760\) 3.08391 + 17.4897i 0.111865 + 0.634419i
\(761\) 15.5918 13.0831i 0.565202 0.474261i −0.314848 0.949142i \(-0.601954\pi\)
0.880050 + 0.474882i \(0.157509\pi\)
\(762\) 25.3373 2.22377i 0.917875 0.0805587i
\(763\) 5.12708 7.86789i 0.185613 0.284837i
\(764\) 0.173970 + 0.100441i 0.00629400 + 0.00363384i
\(765\) 49.2859 8.71847i 1.78194 0.315217i
\(766\) 33.4972i 1.21030i
\(767\) −26.6941 + 31.8128i −0.963869 + 1.14869i
\(768\) 0.732429 + 1.56957i 0.0264293 + 0.0566370i
\(769\) 15.8222 43.4711i 0.570563 1.56761i −0.233056 0.972463i \(-0.574873\pi\)
0.803619 0.595145i \(-0.202905\pi\)
\(770\) 23.3936 + 21.8837i 0.843046 + 0.788635i
\(771\) −9.24326 0.806113i −0.332888 0.0290315i
\(772\) 5.05065 1.83829i 0.181777 0.0661614i
\(773\) −12.5168 −0.450196 −0.225098 0.974336i \(-0.572270\pi\)
−0.225098 + 0.974336i \(0.572270\pi\)
\(774\) 5.10558 + 28.8621i 0.183516 + 1.03743i
\(775\) 4.75933i 0.170960i
\(776\) 4.20539 + 3.52874i 0.150965 + 0.126674i
\(777\) −14.2787 15.8996i −0.512247 0.570393i
\(778\) 4.08946 + 23.1925i 0.146614 + 0.831491i
\(779\) 21.1301 58.0545i 0.757064 2.08002i
\(780\) 3.68829 + 13.7497i 0.132062 + 0.492318i
\(781\) 1.61073 9.13488i 0.0576363 0.326872i
\(782\) −8.04158 13.9284i −0.287566 0.498079i
\(783\) −0.908672 0.422806i −0.0324733 0.0151099i
\(784\) −6.79736 + 1.67209i −0.242763 + 0.0597173i
\(785\) 12.9132 + 35.4789i 0.460894 + 1.26629i
\(786\) −0.571462 2.13038i −0.0203834 0.0759880i
\(787\) 43.0811 7.59636i 1.53568 0.270781i 0.659104 0.752052i \(-0.270936\pi\)
0.876572 + 0.481271i \(0.159825\pi\)
\(788\) 2.00059 5.49658i 0.0712682 0.195808i
\(789\) −47.1076 + 4.13447i −1.67707 + 0.147191i
\(790\) 6.30345 7.51215i 0.224267 0.267270i
\(791\) −5.70260 + 0.691091i −0.202761 + 0.0245724i
\(792\) 14.7736 + 2.59659i 0.524958 + 0.0922658i
\(793\) −12.6382 + 21.8900i −0.448795 + 0.777336i
\(794\) −1.97002 1.65304i −0.0699133 0.0586643i
\(795\) 0.953636 10.9348i 0.0338220 0.387818i
\(796\) 8.83412 1.55769i 0.313117 0.0552110i
\(797\) −42.0638 15.3100i −1.48997 0.542307i −0.536532 0.843880i \(-0.680266\pi\)
−0.953443 + 0.301573i \(0.902488\pi\)
\(798\) −28.5251 + 17.7731i −1.00978 + 0.629160i
\(799\) −9.29324 + 52.7046i −0.328771 + 1.86455i
\(800\) −0.747993 0.431854i −0.0264455 0.0152683i
\(801\) −20.3308 11.7230i −0.718353 0.414213i
\(802\) −11.4692 19.8653i −0.404992 0.701467i
\(803\) −5.39506 + 30.5969i −0.190388 + 1.07974i
\(804\) −14.9559 + 10.4784i −0.527455 + 0.369545i
\(805\) 4.35006 + 14.3088i 0.153320 + 0.504320i
\(806\) −12.0221 14.3274i −0.423461 0.504662i
\(807\) −12.0665 12.0598i −0.424760 0.424526i
\(808\) 3.77298 + 0.665278i 0.132733 + 0.0234044i
\(809\) 5.43121 + 3.13571i 0.190951 + 0.110246i 0.592428 0.805624i \(-0.298170\pi\)
−0.401477 + 0.915869i \(0.631503\pi\)
\(810\) −18.8618 + 10.9176i −0.662735 + 0.383605i
\(811\) 19.9066i 0.699014i 0.936934 + 0.349507i \(0.113651\pi\)
−0.936934 + 0.349507i \(0.886349\pi\)
\(812\) 0.455050 0.230959i 0.0159691 0.00810508i
\(813\) 8.57343 + 31.9612i 0.300683 + 1.12093i
\(814\) −21.9105 7.97479i −0.767964 0.279516i
\(815\) 12.2816 + 4.47013i 0.430205 + 0.156582i
\(816\) 1.04335 + 11.8878i 0.0365245 + 0.416156i
\(817\) −70.5659 12.4427i −2.46879 0.435314i
\(818\) −4.94671 + 8.56795i −0.172958 + 0.299572i
\(819\) −21.5322 + 16.1912i −0.752395 + 0.565766i
\(820\) 10.1991 + 17.6653i 0.356167 + 0.616899i
\(821\) 16.1481 + 44.3664i 0.563571 + 1.54840i 0.814362 + 0.580357i \(0.197087\pi\)
−0.250791 + 0.968041i \(0.580691\pi\)
\(822\) 6.05117 + 12.9674i 0.211059 + 0.452292i
\(823\) 31.4232 26.3672i 1.09534 0.919103i 0.0982415 0.995163i \(-0.468678\pi\)
0.997103 + 0.0760592i \(0.0242338\pi\)
\(824\) −2.60235 14.7587i −0.0906572 0.514143i
\(825\) −6.77828 + 3.16304i −0.235989 + 0.110123i
\(826\) 28.8662 14.6510i 1.00439 0.509772i
\(827\) 31.4445 18.1545i 1.09343 0.631294i 0.158945 0.987287i \(-0.449191\pi\)
0.934488 + 0.355993i \(0.115857\pi\)
\(828\) 5.36711 + 4.49850i 0.186520 + 0.156334i
\(829\) 16.8935 9.75348i 0.586736 0.338752i −0.177070 0.984198i \(-0.556662\pi\)
0.763806 + 0.645446i \(0.223328\pi\)
\(830\) −4.09412 11.2485i −0.142109 0.390441i
\(831\) −1.04035 11.8536i −0.0360894 0.411198i
\(832\) −3.34262 + 0.589393i −0.115884 + 0.0204335i
\(833\) −47.9483 5.19207i −1.66131 0.179895i
\(834\) −0.929480 + 3.47270i −0.0321853 + 0.120250i
\(835\) −18.6083 15.6142i −0.643967 0.540352i
\(836\) −18.3353 + 31.7576i −0.634139 + 1.09836i
\(837\) 16.4036 23.4680i 0.566991 0.811174i
\(838\) −5.33113 + 3.07793i −0.184161 + 0.106325i
\(839\) 34.8662 12.6902i 1.20371 0.438116i 0.339195 0.940716i \(-0.389845\pi\)
0.864519 + 0.502600i \(0.167623\pi\)
\(840\) 1.55862 10.9867i 0.0537774 0.379079i
\(841\) 22.1868 18.6169i 0.765062 0.641963i
\(842\) 13.1473 + 15.6684i 0.453087 + 0.539968i
\(843\) 12.0374 25.8330i 0.414592 0.889735i
\(844\) −23.7188 + 8.63293i −0.816434 + 0.297158i
\(845\) 3.58272 0.123249
\(846\) −4.05918 22.9467i −0.139557 0.788925i
\(847\) 4.45636 + 36.7720i 0.153122 + 1.26350i
\(848\) 2.57728 + 0.454444i 0.0885042 + 0.0156057i
\(849\) 6.94945 3.24291i 0.238505 0.111297i
\(850\) −3.82508 4.55856i −0.131199 0.156357i
\(851\) −6.99726 8.33901i −0.239863 0.285857i
\(852\) −2.91179 + 1.35877i −0.0997562 + 0.0465506i
\(853\) 13.9159 + 2.45375i 0.476472 + 0.0840149i 0.406727 0.913550i \(-0.366670\pi\)
0.0697457 + 0.997565i \(0.477781\pi\)
\(854\) 15.7540 11.8327i 0.539091 0.404907i
\(855\) −9.28067 52.4641i −0.317392 1.79423i
\(856\) −14.1696 −0.484306
\(857\) 12.8209 4.66641i 0.437952 0.159402i −0.113628 0.993523i \(-0.536247\pi\)
0.551580 + 0.834122i \(0.314025\pi\)
\(858\) −12.4153 + 26.6440i −0.423853 + 0.909610i
\(859\) 1.52611 + 1.81875i 0.0520702 + 0.0620549i 0.791451 0.611233i \(-0.209326\pi\)
−0.739381 + 0.673288i \(0.764882\pi\)
\(860\) 18.1233 15.2073i 0.618001 0.518564i
\(861\) −23.8054 + 30.3882i −0.811286 + 1.03563i
\(862\) 5.97644 2.17525i 0.203559 0.0740892i
\(863\) 9.85889 5.69203i 0.335601 0.193759i −0.322724 0.946493i \(-0.604599\pi\)
0.658325 + 0.752734i \(0.271265\pi\)
\(864\) −2.19988 4.70750i −0.0748415 0.160152i
\(865\) 17.7911 30.8151i 0.604915 1.04774i
\(866\) 7.72214 + 6.47964i 0.262409 + 0.220187i
\(867\) −13.6450 + 50.9799i −0.463408 + 1.73137i
\(868\) 4.24056 + 13.9487i 0.143934 + 0.473448i
\(869\) 19.9410 3.51614i 0.676453 0.119277i
\(870\) 0.0707280 + 0.805866i 0.00239791 + 0.0273214i
\(871\) −12.2394 33.6274i −0.414715 1.13942i
\(872\) −3.07392 + 1.77473i −0.104096 + 0.0600999i
\(873\) −12.6220 10.5793i −0.427190 0.358054i
\(874\) −14.8266 + 8.56013i −0.501517 + 0.289551i
\(875\) −11.9936 23.6306i −0.405458 0.798860i
\(876\) 9.75292 4.55114i 0.329521 0.153769i
\(877\) 5.87513 + 33.3195i 0.198389 + 1.12512i 0.907509 + 0.420032i \(0.137981\pi\)
−0.709120 + 0.705088i \(0.750908\pi\)
\(878\) 23.8716 20.0306i 0.805627 0.676002i
\(879\) 10.4932 + 22.4866i 0.353927 + 0.758454i
\(880\) −4.14104 11.3774i −0.139595 0.383533i
\(881\) 7.95465 + 13.7779i 0.267999 + 0.464188i 0.968345 0.249616i \(-0.0803043\pi\)
−0.700346 + 0.713804i \(0.746971\pi\)
\(882\) 20.3893 5.02750i 0.686544 0.169285i
\(883\) −10.3954 + 18.0053i −0.349832 + 0.605926i −0.986219 0.165443i \(-0.947095\pi\)
0.636388 + 0.771369i \(0.280428\pi\)
\(884\) −23.0299 4.06080i −0.774581 0.136580i
\(885\) 4.48665 + 51.1203i 0.150817 + 1.71839i
\(886\) −3.40220 1.23830i −0.114299 0.0416015i
\(887\) 21.0676 + 7.66796i 0.707379 + 0.257465i 0.670558 0.741857i \(-0.266055\pi\)
0.0368210 + 0.999322i \(0.488277\pi\)
\(888\) 2.09266 + 7.80132i 0.0702251 + 0.261795i
\(889\) 21.2116 32.5509i 0.711416 1.09172i
\(890\) 18.9431i 0.634973i
\(891\) −44.3251 7.76533i −1.48495 0.260148i
\(892\) 8.63425 + 4.98498i 0.289096 + 0.166910i
\(893\) 56.1032 + 9.89251i 1.87742 + 0.331040i
\(894\) 10.0569 + 10.0513i 0.336353 + 0.336167i
\(895\) 35.7378 + 42.5906i 1.19458 + 1.42365i
\(896\) 2.57700 + 0.599217i 0.0860916 + 0.0200184i
\(897\) −11.2393 + 7.87449i −0.375271 + 0.262922i
\(898\) 2.67673 15.1805i 0.0893235 0.506579i
\(899\) −0.531412 0.920433i −0.0177236 0.0306981i
\(900\) 2.24469 + 1.29432i 0.0748231 + 0.0431441i
\(901\) 15.6152 + 9.01544i 0.520218 + 0.300348i
\(902\) −7.31385 + 41.4789i −0.243525 + 1.38110i
\(903\) 39.5042 + 21.0705i 1.31462 + 0.701182i
\(904\) 2.04021 + 0.742577i 0.0678565 + 0.0246977i
\(905\) −4.00906 + 0.706906i −0.133266 + 0.0234983i
\(906\) 1.52421 17.4773i 0.0506386 0.580646i
\(907\) 12.0780 + 10.1346i 0.401043 + 0.336515i 0.820897 0.571077i \(-0.193474\pi\)
−0.419854 + 0.907592i \(0.637919\pi\)
\(908\) −6.56061 + 11.3633i −0.217722 + 0.377105i
\(909\) −11.3200 1.98959i −0.375462 0.0659906i
\(910\) 20.0035 + 8.52812i 0.663109 + 0.282704i
\(911\) −17.4198 + 20.7601i −0.577145 + 0.687814i −0.973081 0.230464i \(-0.925976\pi\)
0.395936 + 0.918278i \(0.370420\pi\)
\(912\) 12.6544 1.11063i 0.419028 0.0367766i
\(913\) 8.45369 23.2263i 0.279776 0.768679i
\(914\) 7.91211 1.39512i 0.261709 0.0461464i
\(915\) 8.09225 + 30.1674i 0.267522 + 0.997305i
\(916\) 2.65896 + 7.30543i 0.0878544 + 0.241378i
\(917\) −3.09934 1.32135i −0.102349 0.0436347i
\(918\) −3.14971 35.6616i −0.103956 1.17701i
\(919\) −22.2295 38.5026i −0.733283 1.27008i −0.955473 0.295080i \(-0.904654\pi\)
0.222190 0.975003i \(-0.428680\pi\)
\(920\) 0.981570 5.56676i 0.0323614 0.183531i
\(921\) 13.6278 + 50.8036i 0.449051 + 1.67403i
\(922\) 1.74591 4.79686i 0.0574986 0.157976i
\(923\) −1.09341 6.20106i −0.0359902 0.204110i
\(924\) 17.0475 15.3097i 0.560822 0.503652i
\(925\) −3.08543 2.58899i −0.101448 0.0851254i
\(926\) 33.1160i 1.08826i
\(927\) 7.83147 + 44.2717i 0.257219 + 1.45407i
\(928\) −0.192878 −0.00633153
\(929\) 31.2490 11.3737i 1.02525 0.373159i 0.225977 0.974133i \(-0.427442\pi\)
0.799269 + 0.600973i \(0.205220\pi\)
\(930\) −23.0240 2.00794i −0.754986 0.0658430i
\(931\) −5.52688 + 51.0402i −0.181136 + 1.67277i
\(932\) −1.51617 + 4.16565i −0.0496638 + 0.136450i
\(933\) 13.2613 + 28.4185i 0.434156 + 0.930381i
\(934\) −4.86151 + 5.79373i −0.159074 + 0.189577i
\(935\) 83.4189i 2.72809i
\(936\) 10.0269 1.77371i 0.327738 0.0579755i
\(937\) 5.02418 + 2.90071i 0.164133 + 0.0947621i 0.579816 0.814747i \(-0.303124\pi\)
−0.415684 + 0.909509i \(0.636458\pi\)
\(938\) −1.50369 + 27.8541i −0.0490974 + 0.909470i
\(939\) −46.9121 + 4.11731i −1.53092 + 0.134363i
\(940\) −14.4089 + 12.0905i −0.469966 + 0.394348i
\(941\) −4.72645 26.8050i −0.154078 0.873818i −0.959624 0.281285i \(-0.909239\pi\)
0.805546 0.592533i \(-0.201872\pi\)
\(942\) 26.0837 6.99683i 0.849854 0.227969i
\(943\) −12.6397 + 15.0634i −0.411605 + 0.490532i
\(944\) −12.2353 −0.398224
\(945\) −4.65768 + 32.9628i −0.151514 + 1.07228i
\(946\) 48.8506 1.58827
\(947\) −20.8785 + 24.8820i −0.678460 + 0.808557i −0.989909 0.141706i \(-0.954741\pi\)
0.311449 + 0.950263i \(0.399186\pi\)
\(948\) −4.96123 4.95850i −0.161133 0.161045i
\(949\) 3.66235 + 20.7702i 0.118885 + 0.674229i
\(950\) −4.85251 + 4.07174i −0.157436 + 0.132105i
\(951\) −0.400560 + 0.859622i −0.0129890 + 0.0278752i
\(952\) 15.2722 + 9.95208i 0.494976 + 0.322549i
\(953\) −5.71083 3.29715i −0.184992 0.106805i 0.404644 0.914474i \(-0.367395\pi\)
−0.589636 + 0.807669i \(0.700729\pi\)
\(954\) −7.73260 1.35907i −0.250352 0.0440015i
\(955\) 0.486440i 0.0157408i
\(956\) 0.0442139 0.0526920i 0.00142998 0.00170418i
\(957\) −0.957713 + 1.36856i −0.0309585 + 0.0442392i
\(958\) 7.81596 21.4742i 0.252522 0.693799i
\(959\) 21.2906 + 4.95061i 0.687511 + 0.159863i
\(960\) −2.40473 + 3.43633i −0.0776125 + 0.110907i
\(961\) −0.597715 + 0.217550i −0.0192811 + 0.00701776i
\(962\) −15.8282 −0.510320
\(963\) 42.5087 0.0234387i 1.36982 0.000755303i
\(964\) 12.2301i 0.393904i
\(965\) 9.97015 + 8.36595i 0.320950 + 0.269309i
\(966\) 10.4664 2.21053i 0.336752 0.0711225i
\(967\) −9.31089 52.8047i −0.299418 1.69808i −0.648681 0.761060i \(-0.724679\pi\)
0.349263 0.937025i \(-0.386432\pi\)
\(968\) 4.78836 13.1559i 0.153904 0.422847i
\(969\) 84.5451 + 22.6288i 2.71598 + 0.726942i
\(970\) −2.30839 + 13.0915i −0.0741178 + 0.420343i
\(971\) −12.0307 20.8377i −0.386083 0.668715i 0.605836 0.795589i \(-0.292839\pi\)
−0.991919 + 0.126875i \(0.959505\pi\)
\(972\) 6.60744 + 14.1188i 0.211934 + 0.452862i
\(973\) 3.29788 + 4.39078i 0.105725 + 0.140762i
\(974\) 7.26534 + 19.9613i 0.232796 + 0.639603i
\(975\) −3.58945 + 3.59143i −0.114954 + 0.115018i
\(976\) −7.33384 + 1.29315i −0.234750 + 0.0413928i
\(977\) 7.78932 21.4010i 0.249202 0.684678i −0.750514 0.660855i \(-0.770194\pi\)
0.999716 0.0238233i \(-0.00758391\pi\)
\(978\) 3.94852 8.47372i 0.126260 0.270960i
\(979\) −25.1422 + 29.9633i −0.803549 + 0.957632i
\(980\) −11.7364 12.2302i −0.374907 0.390679i
\(981\) 9.21883 5.32927i 0.294335 0.170151i
\(982\) 0.991137 1.71670i 0.0316285 0.0547821i
\(983\) 6.33239 + 5.31350i 0.201972 + 0.169474i 0.738164 0.674622i \(-0.235693\pi\)
−0.536192 + 0.844096i \(0.680138\pi\)
\(984\) 13.2216 6.16978i 0.421490 0.196685i
\(985\) 13.9491 2.45959i 0.444454 0.0783692i
\(986\) −1.24875 0.454507i −0.0397682 0.0144745i
\(987\) −31.4076 16.7520i −0.999716 0.533222i
\(988\) −4.32266 + 24.5150i −0.137522 + 0.779926i
\(989\) 19.7512 + 11.4034i 0.628052 + 0.362606i
\(990\) 12.4419 + 34.1254i 0.395431 + 1.08458i
\(991\) −8.83684 15.3059i −0.280711 0.486206i 0.690849 0.722999i \(-0.257237\pi\)
−0.971560 + 0.236793i \(0.923904\pi\)
\(992\) 0.956862 5.42663i 0.0303804 0.172296i
\(993\) −20.6486 9.62166i −0.655263 0.305334i
\(994\) −1.11164 + 4.78073i −0.0352590 + 0.151636i
\(995\) 13.9626 + 16.6399i 0.442643 + 0.527522i
\(996\) −8.26980 + 2.21833i −0.262039 + 0.0702905i
\(997\) −40.7715 7.18912i −1.29125 0.227682i −0.514498 0.857492i \(-0.672022\pi\)
−0.776749 + 0.629810i \(0.783133\pi\)
\(998\) 3.72331 + 2.14966i 0.117859 + 0.0680462i
\(999\) −6.29089 23.4005i −0.199035 0.740358i
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 378.2.bf.a.101.6 yes 144
7.5 odd 6 378.2.ba.a.47.22 144
27.23 odd 18 378.2.ba.a.185.22 yes 144
189.131 even 18 inner 378.2.bf.a.131.6 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.ba.a.47.22 144 7.5 odd 6
378.2.ba.a.185.22 yes 144 27.23 odd 18
378.2.bf.a.101.6 yes 144 1.1 even 1 trivial
378.2.bf.a.131.6 yes 144 189.131 even 18 inner