Properties

Label 495.2.n.g.181.3
Level $495$
Weight $2$
Character 495.181
Analytic conductor $3.953$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 495.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.95259490005\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.3
Root \(-0.166559 + 0.121012i\) of defining polynomial
Character \(\chi\) \(=\) 495.181
Dual form 495.2.n.g.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.372637 + 1.14686i) q^{2} +(0.441609 - 0.320848i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-3.49122 + 2.53652i) q^{7} +(2.48368 + 1.80450i) q^{8} +O(q^{10})\) \(q+(0.372637 + 1.14686i) q^{2} +(0.441609 - 0.320848i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-3.49122 + 2.53652i) q^{7} +(2.48368 + 1.80450i) q^{8} +1.20588 q^{10} +(2.96210 - 1.49196i) q^{11} +(1.91048 + 5.87986i) q^{13} +(-4.20999 - 3.05873i) q^{14} +(-0.806633 + 2.48256i) q^{16} +(-0.248446 + 0.764638i) q^{17} +(1.51601 + 1.10144i) q^{19} +(-0.168680 - 0.519143i) q^{20} +(2.81486 + 2.84115i) q^{22} +8.08431 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-6.03145 + 4.38210i) q^{26} +(-0.727918 + 2.24030i) q^{28} +(0.857138 - 0.622747i) q^{29} +(-0.499089 - 1.53604i) q^{31} +2.99226 q^{32} -0.969511 q^{34} +(1.33353 + 4.10418i) q^{35} +(4.48304 - 3.25712i) q^{37} +(-0.698278 + 2.14908i) q^{38} +(2.48368 - 1.80450i) q^{40} +(-4.08714 - 2.96948i) q^{41} -9.87101 q^{43} +(0.829398 - 1.60925i) q^{44} +(3.01251 + 9.27156i) q^{46} +(-10.5056 - 7.63280i) q^{47} +(3.59157 - 11.0537i) q^{49} +(0.372637 - 1.14686i) q^{50} +(2.73023 + 1.98363i) q^{52} +(-0.823336 - 2.53397i) q^{53} +(-0.503601 - 3.27817i) q^{55} -13.2482 q^{56} +(1.03360 + 0.750957i) q^{58} +(-5.34734 + 3.88507i) q^{59} +(-1.65250 + 5.08587i) q^{61} +(1.57564 - 1.14477i) q^{62} +(2.72829 + 8.39682i) q^{64} +6.18245 q^{65} -7.49018 q^{67} +(0.135616 + 0.417384i) q^{68} +(-4.20999 + 3.05873i) q^{70} +(-1.80140 + 5.54415i) q^{71} +(-3.88448 + 2.82224i) q^{73} +(5.40600 + 3.92769i) q^{74} +1.02288 q^{76} +(-6.55696 + 12.7222i) q^{77} +(-4.31076 - 13.2672i) q^{79} +(2.11179 + 1.53431i) q^{80} +(1.88255 - 5.79391i) q^{82} +(3.72575 - 11.4667i) q^{83} +(0.650440 + 0.472572i) q^{85} +(-3.67830 - 11.3206i) q^{86} +(10.0491 + 1.63955i) q^{88} +12.7727 q^{89} +(-21.5843 - 15.6819i) q^{91} +(3.57011 - 2.59383i) q^{92} +(4.83894 - 14.8927i) q^{94} +(1.51601 - 1.10144i) q^{95} +(0.416434 + 1.28165i) q^{97} +14.0154 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/495\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(397\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.372637 + 1.14686i 0.263494 + 0.810951i 0.992037 + 0.125950i \(0.0401980\pi\)
−0.728543 + 0.685001i \(0.759802\pi\)
\(3\) 0 0
\(4\) 0.441609 0.320848i 0.220805 0.160424i
\(5\) 0.309017 0.951057i 0.138197 0.425325i
\(6\) 0 0
\(7\) −3.49122 + 2.53652i −1.31956 + 0.958715i −0.319620 + 0.947546i \(0.603555\pi\)
−0.999938 + 0.0111694i \(0.996445\pi\)
\(8\) 2.48368 + 1.80450i 0.878113 + 0.637986i
\(9\) 0 0
\(10\) 1.20588 0.381332
\(11\) 2.96210 1.49196i 0.893107 0.449844i
\(12\) 0 0
\(13\) 1.91048 + 5.87986i 0.529873 + 1.63078i 0.754474 + 0.656329i \(0.227892\pi\)
−0.224602 + 0.974451i \(0.572108\pi\)
\(14\) −4.20999 3.05873i −1.12517 0.817481i
\(15\) 0 0
\(16\) −0.806633 + 2.48256i −0.201658 + 0.620640i
\(17\) −0.248446 + 0.764638i −0.0602570 + 0.185452i −0.976654 0.214819i \(-0.931084\pi\)
0.916397 + 0.400271i \(0.131084\pi\)
\(18\) 0 0
\(19\) 1.51601 + 1.10144i 0.347795 + 0.252688i 0.747944 0.663762i \(-0.231041\pi\)
−0.400148 + 0.916450i \(0.631041\pi\)
\(20\) −0.168680 0.519143i −0.0377179 0.116084i
\(21\) 0 0
\(22\) 2.81486 + 2.84115i 0.600129 + 0.605735i
\(23\) 8.08431 1.68570 0.842848 0.538152i \(-0.180877\pi\)
0.842848 + 0.538152i \(0.180877\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.161803 0.117557i
\(26\) −6.03145 + 4.38210i −1.18286 + 0.859401i
\(27\) 0 0
\(28\) −0.727918 + 2.24030i −0.137564 + 0.423377i
\(29\) 0.857138 0.622747i 0.159166 0.115641i −0.505351 0.862914i \(-0.668637\pi\)
0.664518 + 0.747273i \(0.268637\pi\)
\(30\) 0 0
\(31\) −0.499089 1.53604i −0.0896391 0.275881i 0.896180 0.443690i \(-0.146331\pi\)
−0.985820 + 0.167809i \(0.946331\pi\)
\(32\) 2.99226 0.528962
\(33\) 0 0
\(34\) −0.969511 −0.166270
\(35\) 1.33353 + 4.10418i 0.225407 + 0.693733i
\(36\) 0 0
\(37\) 4.48304 3.25712i 0.737007 0.535467i −0.154765 0.987951i \(-0.549462\pi\)
0.891772 + 0.452484i \(0.149462\pi\)
\(38\) −0.698278 + 2.14908i −0.113276 + 0.348627i
\(39\) 0 0
\(40\) 2.48368 1.80450i 0.392704 0.285316i
\(41\) −4.08714 2.96948i −0.638304 0.463755i 0.220963 0.975282i \(-0.429080\pi\)
−0.859267 + 0.511527i \(0.829080\pi\)
\(42\) 0 0
\(43\) −9.87101 −1.50531 −0.752657 0.658412i \(-0.771228\pi\)
−0.752657 + 0.658412i \(0.771228\pi\)
\(44\) 0.829398 1.60925i 0.125037 0.242603i
\(45\) 0 0
\(46\) 3.01251 + 9.27156i 0.444171 + 1.36702i
\(47\) −10.5056 7.63280i −1.53241 1.11336i −0.954883 0.296983i \(-0.904020\pi\)
−0.577523 0.816375i \(-0.695980\pi\)
\(48\) 0 0
\(49\) 3.59157 11.0537i 0.513082 1.57910i
\(50\) 0.372637 1.14686i 0.0526988 0.162190i
\(51\) 0 0
\(52\) 2.73023 + 1.98363i 0.378614 + 0.275079i
\(53\) −0.823336 2.53397i −0.113094 0.348067i 0.878451 0.477833i \(-0.158578\pi\)
−0.991545 + 0.129766i \(0.958578\pi\)
\(54\) 0 0
\(55\) −0.503601 3.27817i −0.0679055 0.442028i
\(56\) −13.2482 −1.77037
\(57\) 0 0
\(58\) 1.03360 + 0.750957i 0.135719 + 0.0986054i
\(59\) −5.34734 + 3.88507i −0.696165 + 0.505793i −0.878681 0.477410i \(-0.841576\pi\)
0.182516 + 0.983203i \(0.441576\pi\)
\(60\) 0 0
\(61\) −1.65250 + 5.08587i −0.211581 + 0.651178i 0.787798 + 0.615934i \(0.211221\pi\)
−0.999379 + 0.0352447i \(0.988779\pi\)
\(62\) 1.57564 1.14477i 0.200106 0.145386i
\(63\) 0 0
\(64\) 2.72829 + 8.39682i 0.341037 + 1.04960i
\(65\) 6.18245 0.766839
\(66\) 0 0
\(67\) −7.49018 −0.915071 −0.457536 0.889191i \(-0.651268\pi\)
−0.457536 + 0.889191i \(0.651268\pi\)
\(68\) 0.135616 + 0.417384i 0.0164459 + 0.0506153i
\(69\) 0 0
\(70\) −4.20999 + 3.05873i −0.503190 + 0.365589i
\(71\) −1.80140 + 5.54415i −0.213787 + 0.657970i 0.785450 + 0.618925i \(0.212432\pi\)
−0.999237 + 0.0390448i \(0.987568\pi\)
\(72\) 0 0
\(73\) −3.88448 + 2.82224i −0.454643 + 0.330318i −0.791426 0.611265i \(-0.790661\pi\)
0.336783 + 0.941582i \(0.390661\pi\)
\(74\) 5.40600 + 3.92769i 0.628435 + 0.456584i
\(75\) 0 0
\(76\) 1.02288 0.117332
\(77\) −6.55696 + 12.7222i −0.747235 + 1.44983i
\(78\) 0 0
\(79\) −4.31076 13.2672i −0.484998 1.49267i −0.831983 0.554801i \(-0.812794\pi\)
0.346985 0.937871i \(-0.387206\pi\)
\(80\) 2.11179 + 1.53431i 0.236106 + 0.171541i
\(81\) 0 0
\(82\) 1.88255 5.79391i 0.207893 0.639830i
\(83\) 3.72575 11.4667i 0.408954 1.25863i −0.508595 0.861006i \(-0.669835\pi\)
0.917548 0.397624i \(-0.130165\pi\)
\(84\) 0 0
\(85\) 0.650440 + 0.472572i 0.0705501 + 0.0512576i
\(86\) −3.67830 11.3206i −0.396641 1.22074i
\(87\) 0 0
\(88\) 10.0491 + 1.63955i 1.07124 + 0.174777i
\(89\) 12.7727 1.35390 0.676951 0.736028i \(-0.263301\pi\)
0.676951 + 0.736028i \(0.263301\pi\)
\(90\) 0 0
\(91\) −21.5843 15.6819i −2.26265 1.64391i
\(92\) 3.57011 2.59383i 0.372209 0.270426i
\(93\) 0 0
\(94\) 4.83894 14.8927i 0.499099 1.53607i
\(95\) 1.51601 1.10144i 0.155539 0.113006i
\(96\) 0 0
\(97\) 0.416434 + 1.28165i 0.0422825 + 0.130132i 0.969969 0.243227i \(-0.0782060\pi\)
−0.927687 + 0.373359i \(0.878206\pi\)
\(98\) 14.0154 1.41577
\(99\) 0 0
\(100\) −0.545859 −0.0545859
\(101\) −2.60486 8.01692i −0.259193 0.797713i −0.992975 0.118328i \(-0.962247\pi\)
0.733782 0.679385i \(-0.237753\pi\)
\(102\) 0 0
\(103\) 8.00959 5.81931i 0.789208 0.573393i −0.118520 0.992952i \(-0.537815\pi\)
0.907728 + 0.419558i \(0.137815\pi\)
\(104\) −5.86517 + 18.0511i −0.575127 + 1.77006i
\(105\) 0 0
\(106\) 2.59930 1.88850i 0.252466 0.183427i
\(107\) −6.60758 4.80069i −0.638779 0.464100i 0.220652 0.975353i \(-0.429182\pi\)
−0.859430 + 0.511253i \(0.829182\pi\)
\(108\) 0 0
\(109\) 13.4997 1.29303 0.646517 0.762900i \(-0.276225\pi\)
0.646517 + 0.762900i \(0.276225\pi\)
\(110\) 3.57193 1.79912i 0.340570 0.171540i
\(111\) 0 0
\(112\) −3.48094 10.7132i −0.328917 1.01230i
\(113\) 10.9303 + 7.94132i 1.02824 + 0.747057i 0.967955 0.251125i \(-0.0808004\pi\)
0.0602808 + 0.998181i \(0.480800\pi\)
\(114\) 0 0
\(115\) 2.49819 7.68864i 0.232957 0.716969i
\(116\) 0.178713 0.550022i 0.0165931 0.0510682i
\(117\) 0 0
\(118\) −6.44824 4.68492i −0.593609 0.431282i
\(119\) −1.07214 3.29971i −0.0982830 0.302484i
\(120\) 0 0
\(121\) 6.54810 8.83869i 0.595281 0.803517i
\(122\) −6.44855 −0.583824
\(123\) 0 0
\(124\) −0.713237 0.518197i −0.0640506 0.0465355i
\(125\) −0.809017 + 0.587785i −0.0723607 + 0.0525731i
\(126\) 0 0
\(127\) −0.655154 + 2.01636i −0.0581355 + 0.178923i −0.975907 0.218186i \(-0.929986\pi\)
0.917772 + 0.397108i \(0.129986\pi\)
\(128\) −3.77172 + 2.74031i −0.333376 + 0.242212i
\(129\) 0 0
\(130\) 2.30381 + 7.09039i 0.202057 + 0.621869i
\(131\) 8.72324 0.762153 0.381076 0.924544i \(-0.375553\pi\)
0.381076 + 0.924544i \(0.375553\pi\)
\(132\) 0 0
\(133\) −8.08654 −0.701192
\(134\) −2.79112 8.59017i −0.241116 0.742078i
\(135\) 0 0
\(136\) −1.99685 + 1.45079i −0.171228 + 0.124405i
\(137\) −0.477068 + 1.46826i −0.0407587 + 0.125442i −0.969365 0.245623i \(-0.921007\pi\)
0.928607 + 0.371065i \(0.121007\pi\)
\(138\) 0 0
\(139\) −13.1046 + 9.52107i −1.11152 + 0.807566i −0.982902 0.184128i \(-0.941054\pi\)
−0.128617 + 0.991694i \(0.541054\pi\)
\(140\) 1.90572 + 1.38458i 0.161062 + 0.117019i
\(141\) 0 0
\(142\) −7.02962 −0.589913
\(143\) 14.4316 + 14.5664i 1.20683 + 1.21810i
\(144\) 0 0
\(145\) −0.327397 1.00763i −0.0271889 0.0836788i
\(146\) −4.68420 3.40327i −0.387667 0.281657i
\(147\) 0 0
\(148\) 0.934712 2.87675i 0.0768329 0.236467i
\(149\) 4.33189 13.3322i 0.354883 1.09222i −0.601195 0.799102i \(-0.705308\pi\)
0.956078 0.293114i \(-0.0946915\pi\)
\(150\) 0 0
\(151\) 10.9906 + 7.98516i 0.894404 + 0.649823i 0.937023 0.349269i \(-0.113570\pi\)
−0.0426183 + 0.999091i \(0.513570\pi\)
\(152\) 1.77772 + 5.47126i 0.144192 + 0.443777i
\(153\) 0 0
\(154\) −17.0339 2.77914i −1.37263 0.223950i
\(155\) −1.61509 −0.129727
\(156\) 0 0
\(157\) 3.54409 + 2.57493i 0.282849 + 0.205502i 0.720159 0.693809i \(-0.244069\pi\)
−0.437310 + 0.899311i \(0.644069\pi\)
\(158\) 13.6092 9.88766i 1.08269 0.786620i
\(159\) 0 0
\(160\) 0.924660 2.84581i 0.0731008 0.224981i
\(161\) −28.2241 + 20.5060i −2.22437 + 1.61610i
\(162\) 0 0
\(163\) −1.44826 4.45729i −0.113437 0.349122i 0.878181 0.478328i \(-0.158757\pi\)
−0.991618 + 0.129206i \(0.958757\pi\)
\(164\) −2.75767 −0.215338
\(165\) 0 0
\(166\) 14.5390 1.12844
\(167\) 0.509622 + 1.56846i 0.0394358 + 0.121371i 0.968836 0.247702i \(-0.0796753\pi\)
−0.929401 + 0.369073i \(0.879675\pi\)
\(168\) 0 0
\(169\) −20.4056 + 14.8255i −1.56966 + 1.14043i
\(170\) −0.299595 + 0.922060i −0.0229779 + 0.0707188i
\(171\) 0 0
\(172\) −4.35913 + 3.16709i −0.332380 + 0.241489i
\(173\) 13.4072 + 9.74090i 1.01933 + 0.740587i 0.966146 0.257998i \(-0.0830626\pi\)
0.0531852 + 0.998585i \(0.483063\pi\)
\(174\) 0 0
\(175\) 4.31539 0.326213
\(176\) 1.31456 + 8.55707i 0.0990886 + 0.645013i
\(177\) 0 0
\(178\) 4.75957 + 14.6485i 0.356745 + 1.09795i
\(179\) −14.2383 10.3447i −1.06422 0.773201i −0.0893553 0.996000i \(-0.528481\pi\)
−0.974864 + 0.222799i \(0.928481\pi\)
\(180\) 0 0
\(181\) 2.59782 7.99527i 0.193094 0.594284i −0.806899 0.590689i \(-0.798856\pi\)
0.999994 0.00359434i \(-0.00114412\pi\)
\(182\) 9.94183 30.5978i 0.736937 2.26806i
\(183\) 0 0
\(184\) 20.0788 + 14.5881i 1.48023 + 1.07545i
\(185\) −1.71237 5.27013i −0.125896 0.387468i
\(186\) 0 0
\(187\) 0.404889 + 2.63561i 0.0296084 + 0.192735i
\(188\) −7.08835 −0.516971
\(189\) 0 0
\(190\) 1.82812 + 1.32820i 0.132626 + 0.0963581i
\(191\) 4.30212 3.12567i 0.311290 0.226166i −0.421160 0.906987i \(-0.638377\pi\)
0.732450 + 0.680821i \(0.238377\pi\)
\(192\) 0 0
\(193\) 4.72401 14.5390i 0.340042 1.04654i −0.624143 0.781310i \(-0.714552\pi\)
0.964185 0.265231i \(-0.0854483\pi\)
\(194\) −1.31469 + 0.955181i −0.0943895 + 0.0685780i
\(195\) 0 0
\(196\) −1.96049 6.03378i −0.140035 0.430984i
\(197\) −1.69118 −0.120492 −0.0602458 0.998184i \(-0.519188\pi\)
−0.0602458 + 0.998184i \(0.519188\pi\)
\(198\) 0 0
\(199\) 3.44855 0.244461 0.122230 0.992502i \(-0.460995\pi\)
0.122230 + 0.992502i \(0.460995\pi\)
\(200\) −0.948680 2.91974i −0.0670818 0.206457i
\(201\) 0 0
\(202\) 8.22360 5.97480i 0.578611 0.420385i
\(203\) −1.41285 + 4.34830i −0.0991624 + 0.305191i
\(204\) 0 0
\(205\) −4.08714 + 2.96948i −0.285458 + 0.207398i
\(206\) 9.65858 + 7.01737i 0.672945 + 0.488923i
\(207\) 0 0
\(208\) −16.1382 −1.11898
\(209\) 6.13387 + 1.00076i 0.424289 + 0.0692241i
\(210\) 0 0
\(211\) −0.121891 0.375140i −0.00839129 0.0258257i 0.946773 0.321901i \(-0.104322\pi\)
−0.955164 + 0.296076i \(0.904322\pi\)
\(212\) −1.17661 0.854858i −0.0808100 0.0587119i
\(213\) 0 0
\(214\) 3.04348 9.36687i 0.208048 0.640306i
\(215\) −3.05031 + 9.38789i −0.208029 + 0.640249i
\(216\) 0 0
\(217\) 5.63863 + 4.09670i 0.382775 + 0.278102i
\(218\) 5.03047 + 15.4822i 0.340707 + 1.04859i
\(219\) 0 0
\(220\) −1.27419 1.28609i −0.0859057 0.0867082i
\(221\) −4.97062 −0.334360
\(222\) 0 0
\(223\) 6.28724 + 4.56795i 0.421025 + 0.305893i 0.778050 0.628202i \(-0.216209\pi\)
−0.357025 + 0.934095i \(0.616209\pi\)
\(224\) −10.4467 + 7.58994i −0.697996 + 0.507124i
\(225\) 0 0
\(226\) −5.03454 + 15.4947i −0.334893 + 1.03069i
\(227\) −22.0993 + 16.0560i −1.46678 + 1.06568i −0.485248 + 0.874377i \(0.661271\pi\)
−0.981531 + 0.191301i \(0.938729\pi\)
\(228\) 0 0
\(229\) 4.81517 + 14.8196i 0.318195 + 0.979304i 0.974419 + 0.224738i \(0.0721526\pi\)
−0.656224 + 0.754566i \(0.727847\pi\)
\(230\) 9.74869 0.642810
\(231\) 0 0
\(232\) 3.25260 0.213544
\(233\) −8.61681 26.5198i −0.564506 1.73737i −0.669414 0.742889i \(-0.733455\pi\)
0.104908 0.994482i \(-0.466545\pi\)
\(234\) 0 0
\(235\) −10.5056 + 7.63280i −0.685313 + 0.497909i
\(236\) −1.11492 + 3.43137i −0.0725750 + 0.223363i
\(237\) 0 0
\(238\) 3.38478 2.45919i 0.219403 0.159405i
\(239\) −15.1657 11.0185i −0.980988 0.712729i −0.0230587 0.999734i \(-0.507340\pi\)
−0.957929 + 0.287005i \(0.907340\pi\)
\(240\) 0 0
\(241\) −11.0049 −0.708886 −0.354443 0.935078i \(-0.615329\pi\)
−0.354443 + 0.935078i \(0.615329\pi\)
\(242\) 12.5768 + 4.21611i 0.808466 + 0.271022i
\(243\) 0 0
\(244\) 0.902031 + 2.77617i 0.0577466 + 0.177726i
\(245\) −9.40286 6.83158i −0.600727 0.436454i
\(246\) 0 0
\(247\) −3.58003 + 11.0182i −0.227792 + 0.701070i
\(248\) 1.53220 4.71563i 0.0972949 0.299443i
\(249\) 0 0
\(250\) −0.975576 0.708797i −0.0617008 0.0448283i
\(251\) −7.20429 22.1725i −0.454731 1.39952i −0.871451 0.490482i \(-0.836821\pi\)
0.416721 0.909035i \(-0.363179\pi\)
\(252\) 0 0
\(253\) 23.9466 12.0615i 1.50551 0.758299i
\(254\) −2.55661 −0.160416
\(255\) 0 0
\(256\) 9.73730 + 7.07456i 0.608581 + 0.442160i
\(257\) −14.1360 + 10.2704i −0.881779 + 0.640650i −0.933721 0.358000i \(-0.883459\pi\)
0.0519427 + 0.998650i \(0.483459\pi\)
\(258\) 0 0
\(259\) −7.38954 + 22.7427i −0.459164 + 1.41316i
\(260\) 2.73023 1.98363i 0.169322 0.123019i
\(261\) 0 0
\(262\) 3.25060 + 10.0043i 0.200823 + 0.618069i
\(263\) 1.61187 0.0993921 0.0496961 0.998764i \(-0.484175\pi\)
0.0496961 + 0.998764i \(0.484175\pi\)
\(264\) 0 0
\(265\) −2.66437 −0.163671
\(266\) −3.01334 9.27412i −0.184760 0.568633i
\(267\) 0 0
\(268\) −3.30773 + 2.40321i −0.202052 + 0.146799i
\(269\) 2.52549 7.77266i 0.153982 0.473908i −0.844074 0.536226i \(-0.819849\pi\)
0.998056 + 0.0623184i \(0.0198494\pi\)
\(270\) 0 0
\(271\) −8.49430 + 6.17147i −0.515992 + 0.374890i −0.815092 0.579332i \(-0.803314\pi\)
0.299100 + 0.954222i \(0.403314\pi\)
\(272\) −1.69786 1.23356i −0.102948 0.0747958i
\(273\) 0 0
\(274\) −1.86166 −0.112467
\(275\) −3.27334 0.534057i −0.197390 0.0322048i
\(276\) 0 0
\(277\) 2.75712 + 8.48554i 0.165659 + 0.509846i 0.999084 0.0427860i \(-0.0136234\pi\)
−0.833425 + 0.552632i \(0.813623\pi\)
\(278\) −15.8026 11.4812i −0.947775 0.688599i
\(279\) 0 0
\(280\) −4.09392 + 12.5998i −0.244659 + 0.752982i
\(281\) 1.35769 4.17854i 0.0809930 0.249271i −0.902358 0.430987i \(-0.858165\pi\)
0.983351 + 0.181717i \(0.0581654\pi\)
\(282\) 0 0
\(283\) −10.5211 7.64404i −0.625416 0.454391i 0.229393 0.973334i \(-0.426326\pi\)
−0.854809 + 0.518943i \(0.826326\pi\)
\(284\) 0.983313 + 3.02633i 0.0583489 + 0.179579i
\(285\) 0 0
\(286\) −11.3278 + 21.9789i −0.669829 + 1.29964i
\(287\) 21.8013 1.28689
\(288\) 0 0
\(289\) 13.2303 + 9.61241i 0.778255 + 0.565436i
\(290\) 1.03360 0.750957i 0.0606953 0.0440977i
\(291\) 0 0
\(292\) −0.809912 + 2.49265i −0.0473965 + 0.145871i
\(293\) −12.5757 + 9.13679i −0.734681 + 0.533777i −0.891041 0.453923i \(-0.850024\pi\)
0.156360 + 0.987700i \(0.450024\pi\)
\(294\) 0 0
\(295\) 2.04250 + 6.28618i 0.118919 + 0.365996i
\(296\) 17.0119 0.988796
\(297\) 0 0
\(298\) 16.9044 0.979243
\(299\) 15.4449 + 47.5346i 0.893204 + 2.74900i
\(300\) 0 0
\(301\) 34.4619 25.0380i 1.98635 1.44317i
\(302\) −5.06233 + 15.5802i −0.291304 + 0.896542i
\(303\) 0 0
\(304\) −3.95726 + 2.87512i −0.226964 + 0.164899i
\(305\) 4.32630 + 3.14324i 0.247723 + 0.179981i
\(306\) 0 0
\(307\) 8.76859 0.500450 0.250225 0.968188i \(-0.419495\pi\)
0.250225 + 0.968188i \(0.419495\pi\)
\(308\) 1.18628 + 7.72203i 0.0675945 + 0.440004i
\(309\) 0 0
\(310\) −0.601841 1.85228i −0.0341823 0.105202i
\(311\) 1.41676 + 1.02934i 0.0803370 + 0.0583682i 0.627229 0.778835i \(-0.284189\pi\)
−0.546892 + 0.837203i \(0.684189\pi\)
\(312\) 0 0
\(313\) −5.41621 + 16.6694i −0.306142 + 0.942209i 0.673106 + 0.739546i \(0.264960\pi\)
−0.979249 + 0.202663i \(0.935040\pi\)
\(314\) −1.63242 + 5.02408i −0.0921230 + 0.283525i
\(315\) 0 0
\(316\) −6.16041 4.47580i −0.346550 0.251783i
\(317\) −0.615520 1.89438i −0.0345711 0.106399i 0.932282 0.361733i \(-0.117815\pi\)
−0.966853 + 0.255334i \(0.917815\pi\)
\(318\) 0 0
\(319\) 1.60981 3.12346i 0.0901323 0.174880i
\(320\) 8.82894 0.493553
\(321\) 0 0
\(322\) −34.0348 24.7278i −1.89669 1.37802i
\(323\) −1.21885 + 0.885546i −0.0678186 + 0.0492731i
\(324\) 0 0
\(325\) 1.91048 5.87986i 0.105975 0.326156i
\(326\) 4.57220 3.32190i 0.253231 0.183983i
\(327\) 0 0
\(328\) −4.79272 14.7505i −0.264634 0.814458i
\(329\) 56.0383 3.08949
\(330\) 0 0
\(331\) −10.3437 −0.568541 −0.284271 0.958744i \(-0.591751\pi\)
−0.284271 + 0.958744i \(0.591751\pi\)
\(332\) −2.03373 6.25918i −0.111616 0.343517i
\(333\) 0 0
\(334\) −1.60889 + 1.16893i −0.0880347 + 0.0639609i
\(335\) −2.31459 + 7.12359i −0.126460 + 0.389203i
\(336\) 0 0
\(337\) 16.6809 12.1194i 0.908667 0.660185i −0.0320107 0.999488i \(-0.510191\pi\)
0.940677 + 0.339303i \(0.110191\pi\)
\(338\) −24.6067 17.8778i −1.33843 0.972423i
\(339\) 0 0
\(340\) 0.438864 0.0238007
\(341\) −3.77007 3.80528i −0.204161 0.206068i
\(342\) 0 0
\(343\) 6.16434 + 18.9719i 0.332843 + 1.02438i
\(344\) −24.5164 17.8122i −1.32184 0.960370i
\(345\) 0 0
\(346\) −6.17542 + 19.0060i −0.331992 + 1.02177i
\(347\) 0.922028 2.83771i 0.0494971 0.152336i −0.923253 0.384193i \(-0.874480\pi\)
0.972750 + 0.231856i \(0.0744799\pi\)
\(348\) 0 0
\(349\) −9.13355 6.63591i −0.488908 0.355212i 0.315857 0.948807i \(-0.397708\pi\)
−0.804764 + 0.593595i \(0.797708\pi\)
\(350\) 1.60807 + 4.94914i 0.0859551 + 0.264542i
\(351\) 0 0
\(352\) 8.86339 4.46434i 0.472420 0.237950i
\(353\) −13.4952 −0.718275 −0.359137 0.933285i \(-0.616929\pi\)
−0.359137 + 0.933285i \(0.616929\pi\)
\(354\) 0 0
\(355\) 4.71614 + 3.42647i 0.250307 + 0.181858i
\(356\) 5.64054 4.09809i 0.298948 0.217198i
\(357\) 0 0
\(358\) 6.55822 20.1841i 0.346613 1.06676i
\(359\) 19.9818 14.5176i 1.05460 0.766211i 0.0815173 0.996672i \(-0.474023\pi\)
0.973082 + 0.230461i \(0.0740234\pi\)
\(360\) 0 0
\(361\) −4.78623 14.7305i −0.251907 0.775289i
\(362\) 10.1375 0.532814
\(363\) 0 0
\(364\) −14.5633 −0.763327
\(365\) 1.48374 + 4.56647i 0.0776624 + 0.239020i
\(366\) 0 0
\(367\) −5.13314 + 3.72944i −0.267948 + 0.194675i −0.713643 0.700509i \(-0.752956\pi\)
0.445696 + 0.895184i \(0.352956\pi\)
\(368\) −6.52107 + 20.0698i −0.339934 + 1.04621i
\(369\) 0 0
\(370\) 5.40600 3.92769i 0.281044 0.204191i
\(371\) 9.30191 + 6.75823i 0.482931 + 0.350870i
\(372\) 0 0
\(373\) 13.1832 0.682601 0.341301 0.939954i \(-0.389133\pi\)
0.341301 + 0.939954i \(0.389133\pi\)
\(374\) −2.87179 + 1.44647i −0.148497 + 0.0747954i
\(375\) 0 0
\(376\) −12.3193 37.9148i −0.635318 1.95531i
\(377\) 5.29921 + 3.85010i 0.272923 + 0.198290i
\(378\) 0 0
\(379\) −5.72802 + 17.6290i −0.294229 + 0.905543i 0.689251 + 0.724523i \(0.257940\pi\)
−0.983479 + 0.181020i \(0.942060\pi\)
\(380\) 0.316086 0.972814i 0.0162149 0.0499043i
\(381\) 0 0
\(382\) 5.18783 + 3.76918i 0.265432 + 0.192848i
\(383\) −8.77123 26.9951i −0.448189 1.37938i −0.878949 0.476917i \(-0.841754\pi\)
0.430760 0.902467i \(-0.358246\pi\)
\(384\) 0 0
\(385\) 10.0733 + 10.1674i 0.513384 + 0.518180i
\(386\) 18.4345 0.938293
\(387\) 0 0
\(388\) 0.595116 + 0.432377i 0.0302125 + 0.0219506i
\(389\) −15.5100 + 11.2687i −0.786388 + 0.571344i −0.906889 0.421369i \(-0.861550\pi\)
0.120502 + 0.992713i \(0.461550\pi\)
\(390\) 0 0
\(391\) −2.00851 + 6.18157i −0.101575 + 0.312615i
\(392\) 28.8667 20.9729i 1.45799 1.05929i
\(393\) 0 0
\(394\) −0.630196 1.93954i −0.0317488 0.0977127i
\(395\) −13.9499 −0.701896
\(396\) 0 0
\(397\) 16.2455 0.815339 0.407670 0.913130i \(-0.366342\pi\)
0.407670 + 0.913130i \(0.366342\pi\)
\(398\) 1.28505 + 3.95499i 0.0644140 + 0.198246i
\(399\) 0 0
\(400\) 2.11179 1.53431i 0.105590 0.0767154i
\(401\) −3.80853 + 11.7215i −0.190189 + 0.585342i −0.999999 0.00135034i \(-0.999570\pi\)
0.809810 + 0.586692i \(0.199570\pi\)
\(402\) 0 0
\(403\) 8.07820 5.86915i 0.402404 0.292363i
\(404\) −3.72254 2.70458i −0.185203 0.134558i
\(405\) 0 0
\(406\) −5.51336 −0.273623
\(407\) 8.41972 16.3364i 0.417350 0.809768i
\(408\) 0 0
\(409\) −0.604903 1.86170i −0.0299106 0.0920552i 0.934987 0.354682i \(-0.115411\pi\)
−0.964897 + 0.262627i \(0.915411\pi\)
\(410\) −4.92859 3.58083i −0.243406 0.176845i
\(411\) 0 0
\(412\) 1.67000 5.13972i 0.0822748 0.253216i
\(413\) 8.81420 27.1273i 0.433718 1.33485i
\(414\) 0 0
\(415\) −9.75413 7.08679i −0.478811 0.347877i
\(416\) 5.71667 + 17.5941i 0.280283 + 0.862621i
\(417\) 0 0
\(418\) 1.13797 + 7.40760i 0.0556602 + 0.362318i
\(419\) 20.5776 1.00528 0.502640 0.864496i \(-0.332362\pi\)
0.502640 + 0.864496i \(0.332362\pi\)
\(420\) 0 0
\(421\) 13.8507 + 10.0632i 0.675044 + 0.490448i 0.871710 0.490022i \(-0.163011\pi\)
−0.196666 + 0.980471i \(0.563011\pi\)
\(422\) 0.384812 0.279582i 0.0187324 0.0136098i
\(423\) 0 0
\(424\) 2.52764 7.77927i 0.122753 0.377795i
\(425\) 0.650440 0.472572i 0.0315510 0.0229231i
\(426\) 0 0
\(427\) −7.13117 21.9475i −0.345101 1.06211i
\(428\) −4.45826 −0.215498
\(429\) 0 0
\(430\) −11.9032 −0.574025
\(431\) 3.27801 + 10.0887i 0.157896 + 0.485955i 0.998443 0.0557847i \(-0.0177660\pi\)
−0.840547 + 0.541739i \(0.817766\pi\)
\(432\) 0 0
\(433\) −20.0848 + 14.5925i −0.965215 + 0.701270i −0.954356 0.298671i \(-0.903457\pi\)
−0.0108592 + 0.999941i \(0.503457\pi\)
\(434\) −2.59718 + 7.99329i −0.124668 + 0.383690i
\(435\) 0 0
\(436\) 5.96158 4.33134i 0.285508 0.207434i
\(437\) 12.2559 + 8.90440i 0.586277 + 0.425955i
\(438\) 0 0
\(439\) 6.78781 0.323965 0.161982 0.986794i \(-0.448211\pi\)
0.161982 + 0.986794i \(0.448211\pi\)
\(440\) 4.66466 9.05066i 0.222379 0.431473i
\(441\) 0 0
\(442\) −1.85223 5.70059i −0.0881018 0.271149i
\(443\) 12.2566 + 8.90495i 0.582329 + 0.423087i 0.839563 0.543262i \(-0.182811\pi\)
−0.257234 + 0.966349i \(0.582811\pi\)
\(444\) 0 0
\(445\) 3.94698 12.1476i 0.187105 0.575849i
\(446\) −2.89593 + 8.91276i −0.137126 + 0.422031i
\(447\) 0 0
\(448\) −30.8238 22.3948i −1.45629 1.05805i
\(449\) −5.54099 17.0534i −0.261495 0.804800i −0.992480 0.122406i \(-0.960939\pi\)
0.730985 0.682394i \(-0.239061\pi\)
\(450\) 0 0
\(451\) −16.5369 2.69805i −0.778691 0.127046i
\(452\) 7.37488 0.346885
\(453\) 0 0
\(454\) −26.6490 19.3616i −1.25070 0.908686i
\(455\) −21.5843 + 15.6819i −1.01189 + 0.735180i
\(456\) 0 0
\(457\) −12.7310 + 39.1820i −0.595531 + 1.83286i −0.0434679 + 0.999055i \(0.513841\pi\)
−0.552063 + 0.833802i \(0.686159\pi\)
\(458\) −15.2016 + 11.0446i −0.710325 + 0.516081i
\(459\) 0 0
\(460\) −1.36366 4.19691i −0.0635809 0.195682i
\(461\) 16.8145 0.783128 0.391564 0.920151i \(-0.371934\pi\)
0.391564 + 0.920151i \(0.371934\pi\)
\(462\) 0 0
\(463\) −35.7050 −1.65935 −0.829676 0.558245i \(-0.811475\pi\)
−0.829676 + 0.558245i \(0.811475\pi\)
\(464\) 0.854612 + 2.63023i 0.0396744 + 0.122105i
\(465\) 0 0
\(466\) 27.2035 19.7645i 1.26018 0.915573i
\(467\) −11.1095 + 34.1916i −0.514087 + 1.58220i 0.270849 + 0.962622i \(0.412696\pi\)
−0.784936 + 0.619576i \(0.787304\pi\)
\(468\) 0 0
\(469\) 26.1499 18.9990i 1.20749 0.877293i
\(470\) −12.6685 9.20422i −0.584355 0.424559i
\(471\) 0 0
\(472\) −20.2917 −0.934000
\(473\) −29.2389 + 14.7272i −1.34441 + 0.677156i
\(474\) 0 0
\(475\) −0.579062 1.78217i −0.0265692 0.0817716i
\(476\) −1.53217 1.11319i −0.0702270 0.0510229i
\(477\) 0 0
\(478\) 6.98539 21.4988i 0.319504 0.983333i
\(479\) −4.29272 + 13.2116i −0.196139 + 0.603655i 0.803822 + 0.594870i \(0.202796\pi\)
−0.999961 + 0.00878522i \(0.997204\pi\)
\(480\) 0 0
\(481\) 27.7162 + 20.1370i 1.26375 + 0.918167i
\(482\) −4.10082 12.6210i −0.186787 0.574872i
\(483\) 0 0
\(484\) 0.0558246 6.00419i 0.00253748 0.272918i
\(485\) 1.34761 0.0611918
\(486\) 0 0
\(487\) 11.3265 + 8.22916i 0.513251 + 0.372899i 0.814055 0.580787i \(-0.197255\pi\)
−0.300804 + 0.953686i \(0.597255\pi\)
\(488\) −13.2817 + 9.64972i −0.601234 + 0.436822i
\(489\) 0 0
\(490\) 4.33100 13.3294i 0.195655 0.602163i
\(491\) 20.4259 14.8403i 0.921806 0.669731i −0.0221670 0.999754i \(-0.507057\pi\)
0.943973 + 0.330023i \(0.107057\pi\)
\(492\) 0 0
\(493\) 0.263224 + 0.810119i 0.0118550 + 0.0364859i
\(494\) −13.9703 −0.628555
\(495\) 0 0
\(496\) 4.21590 0.189299
\(497\) −7.77376 23.9252i −0.348701 1.07319i
\(498\) 0 0
\(499\) 7.16997 5.20929i 0.320972 0.233200i −0.415618 0.909539i \(-0.636435\pi\)
0.736590 + 0.676340i \(0.236435\pi\)
\(500\) −0.168680 + 0.519143i −0.00754359 + 0.0232168i
\(501\) 0 0
\(502\) 22.7441 16.5246i 1.01512 0.737528i
\(503\) −0.534909 0.388634i −0.0238504 0.0173283i 0.575796 0.817593i \(-0.304692\pi\)
−0.599647 + 0.800265i \(0.704692\pi\)
\(504\) 0 0
\(505\) −8.42949 −0.375107
\(506\) 22.7562 + 22.9687i 1.01164 + 1.02108i
\(507\) 0 0
\(508\) 0.357621 + 1.10065i 0.0158669 + 0.0488333i
\(509\) −31.3224 22.7570i −1.38834 1.00869i −0.996045 0.0888492i \(-0.971681\pi\)
−0.392295 0.919839i \(-0.628319\pi\)
\(510\) 0 0
\(511\) 6.40290 19.7061i 0.283248 0.871747i
\(512\) −7.36638 + 22.6714i −0.325551 + 1.00194i
\(513\) 0 0
\(514\) −17.0463 12.3848i −0.751879 0.546272i
\(515\) −3.05939 9.41583i −0.134813 0.414911i
\(516\) 0 0
\(517\) −42.5066 6.93510i −1.86944 0.305005i
\(518\) −28.8362 −1.26699
\(519\) 0 0
\(520\) 15.3552 + 11.1562i 0.673371 + 0.489233i
\(521\) 19.8803 14.4439i 0.870971 0.632797i −0.0598763 0.998206i \(-0.519071\pi\)
0.930847 + 0.365408i \(0.119071\pi\)
\(522\) 0 0
\(523\) 10.4121 32.0453i 0.455291 1.40124i −0.415501 0.909593i \(-0.636394\pi\)
0.870793 0.491650i \(-0.163606\pi\)
\(524\) 3.85226 2.79883i 0.168287 0.122268i
\(525\) 0 0
\(526\) 0.600642 + 1.84859i 0.0261892 + 0.0806021i
\(527\) 1.29851 0.0565640
\(528\) 0 0
\(529\) 42.3561 1.84157
\(530\) −0.992842 3.05565i −0.0431263 0.132729i
\(531\) 0 0
\(532\) −3.57109 + 2.59455i −0.154826 + 0.112488i
\(533\) 9.65172 29.7050i 0.418063 1.28666i
\(534\) 0 0
\(535\) −6.60758 + 4.80069i −0.285671 + 0.207552i
\(536\) −18.6032 13.5160i −0.803536 0.583803i
\(537\) 0 0
\(538\) 9.85523 0.424889
\(539\) −5.85314 38.1008i −0.252113 1.64112i
\(540\) 0 0
\(541\) −2.53653 7.80665i −0.109054 0.335634i 0.881606 0.471985i \(-0.156462\pi\)
−0.990661 + 0.136351i \(0.956462\pi\)
\(542\) −10.2431 7.44204i −0.439978 0.319663i
\(543\) 0 0
\(544\) −0.743415 + 2.28800i −0.0318737 + 0.0980971i
\(545\) 4.17163 12.8390i 0.178693 0.549960i
\(546\) 0 0
\(547\) −28.3770 20.6171i −1.21331 0.881523i −0.217785 0.975997i \(-0.569883\pi\)
−0.995527 + 0.0944734i \(0.969883\pi\)
\(548\) 0.260412 + 0.801465i 0.0111242 + 0.0342369i
\(549\) 0 0
\(550\) −0.607281 3.95307i −0.0258945 0.168559i
\(551\) 1.98534 0.0845785
\(552\) 0 0
\(553\) 48.7022 + 35.3843i 2.07103 + 1.50469i
\(554\) −8.70430 + 6.32404i −0.369810 + 0.268683i
\(555\) 0 0
\(556\) −2.73231 + 8.40918i −0.115876 + 0.356629i
\(557\) −32.0476 + 23.2839i −1.35790 + 0.986572i −0.359325 + 0.933212i \(0.616993\pi\)
−0.998575 + 0.0533600i \(0.983007\pi\)
\(558\) 0 0
\(559\) −18.8584 58.0402i −0.797625 2.45484i
\(560\) −11.2645 −0.476014
\(561\) 0 0
\(562\) 5.29812 0.223488
\(563\) 6.69959 + 20.6192i 0.282354 + 0.868996i 0.987179 + 0.159615i \(0.0510254\pi\)
−0.704825 + 0.709381i \(0.748975\pi\)
\(564\) 0 0
\(565\) 10.9303 7.94132i 0.459841 0.334094i
\(566\) 4.84607 14.9147i 0.203696 0.626911i
\(567\) 0 0
\(568\) −14.4785 + 10.5193i −0.607505 + 0.441378i
\(569\) 22.2187 + 16.1428i 0.931457 + 0.676743i 0.946349 0.323146i \(-0.104741\pi\)
−0.0148922 + 0.999889i \(0.504741\pi\)
\(570\) 0 0
\(571\) 23.8306 0.997281 0.498641 0.866809i \(-0.333833\pi\)
0.498641 + 0.866809i \(0.333833\pi\)
\(572\) 11.0467 + 1.80231i 0.461886 + 0.0753582i
\(573\) 0 0
\(574\) 8.12395 + 25.0029i 0.339087 + 1.04360i
\(575\) −6.54034 4.75184i −0.272751 0.198165i
\(576\) 0 0
\(577\) −4.96685 + 15.2864i −0.206773 + 0.636381i 0.792863 + 0.609400i \(0.208589\pi\)
−0.999636 + 0.0269812i \(0.991411\pi\)
\(578\) −6.09395 + 18.7553i −0.253475 + 0.780116i
\(579\) 0 0
\(580\) −0.467876 0.339932i −0.0194275 0.0141149i
\(581\) 16.0780 + 49.4831i 0.667030 + 2.05291i
\(582\) 0 0
\(583\) −6.21939 6.27748i −0.257581 0.259987i
\(584\) −14.7405 −0.609966
\(585\) 0 0
\(586\) −15.1648 11.0178i −0.626451 0.455143i
\(587\) 14.3837 10.4504i 0.593680 0.431334i −0.249950 0.968259i \(-0.580414\pi\)
0.843630 + 0.536925i \(0.180414\pi\)
\(588\) 0 0
\(589\) 0.935237 2.87836i 0.0385358 0.118601i
\(590\) −6.44824 + 4.68492i −0.265470 + 0.192875i
\(591\) 0 0
\(592\) 4.46983 + 13.7567i 0.183709 + 0.565398i
\(593\) −20.2944 −0.833389 −0.416695 0.909046i \(-0.636812\pi\)
−0.416695 + 0.909046i \(0.636812\pi\)
\(594\) 0 0
\(595\) −3.46952 −0.142236
\(596\) −2.36460 7.27750i −0.0968579 0.298098i
\(597\) 0 0
\(598\) −48.7601 + 35.4263i −1.99395 + 1.44869i
\(599\) 2.78334 8.56623i 0.113724 0.350007i −0.877955 0.478744i \(-0.841092\pi\)
0.991679 + 0.128737i \(0.0410923\pi\)
\(600\) 0 0
\(601\) −33.2571 + 24.1627i −1.35659 + 0.985618i −0.357933 + 0.933747i \(0.616519\pi\)
−0.998654 + 0.0518711i \(0.983481\pi\)
\(602\) 41.5568 + 30.1928i 1.69373 + 1.23057i
\(603\) 0 0
\(604\) 7.41558 0.301736
\(605\) −6.38262 8.95891i −0.259490 0.364232i
\(606\) 0 0
\(607\) 0.367905 + 1.13230i 0.0149328 + 0.0459585i 0.958245 0.285948i \(-0.0923083\pi\)
−0.943312 + 0.331906i \(0.892308\pi\)
\(608\) 4.53629 + 3.29580i 0.183971 + 0.133663i
\(609\) 0 0
\(610\) −1.99271 + 6.13293i −0.0806825 + 0.248315i
\(611\) 24.8089 76.3540i 1.00366 3.08895i
\(612\) 0 0
\(613\) −0.110508 0.0802891i −0.00446339 0.00324284i 0.585551 0.810635i \(-0.300878\pi\)
−0.590015 + 0.807392i \(0.700878\pi\)
\(614\) 3.26750 + 10.0563i 0.131866 + 0.405840i
\(615\) 0 0
\(616\) −39.2426 + 19.7658i −1.58113 + 0.796389i
\(617\) −17.7011 −0.712620 −0.356310 0.934368i \(-0.615965\pi\)
−0.356310 + 0.934368i \(0.615965\pi\)
\(618\) 0 0
\(619\) 5.73528 + 4.16693i 0.230521 + 0.167483i 0.697050 0.717023i \(-0.254496\pi\)
−0.466529 + 0.884506i \(0.654496\pi\)
\(620\) −0.713237 + 0.518197i −0.0286443 + 0.0208113i
\(621\) 0 0
\(622\) −0.652565 + 2.00839i −0.0261655 + 0.0805290i
\(623\) −44.5923 + 32.3982i −1.78655 + 1.29801i
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.0123607 + 0.0380423i
\(626\) −21.1357 −0.844752
\(627\) 0 0
\(628\) 2.39127 0.0954219
\(629\) 1.37672 + 4.23712i 0.0548936 + 0.168945i
\(630\) 0 0
\(631\) −19.5299 + 14.1893i −0.777473 + 0.564867i −0.904220 0.427068i \(-0.859547\pi\)
0.126746 + 0.991935i \(0.459547\pi\)
\(632\) 13.2340 40.7301i 0.526421 1.62016i
\(633\) 0 0
\(634\) 1.94322 1.41183i 0.0771750 0.0560709i
\(635\) 1.71521 + 1.24618i 0.0680662 + 0.0494530i
\(636\) 0 0
\(637\) 71.8560 2.84704
\(638\) 4.18204 + 0.682313i 0.165568 + 0.0270130i
\(639\) 0 0
\(640\) 1.44067 + 4.43392i 0.0569474 + 0.175266i
\(641\) 34.6422 + 25.1690i 1.36828 + 0.994116i 0.997869 + 0.0652496i \(0.0207844\pi\)
0.370415 + 0.928867i \(0.379216\pi\)
\(642\) 0 0
\(643\) −10.5810 + 32.5651i −0.417275 + 1.28424i 0.492925 + 0.870072i \(0.335928\pi\)
−0.910200 + 0.414169i \(0.864072\pi\)
\(644\) −5.88472 + 18.1113i −0.231890 + 0.713685i
\(645\) 0 0
\(646\) −1.46978 1.06786i −0.0578279 0.0420144i
\(647\) −3.36612 10.3598i −0.132336 0.407287i 0.862830 0.505494i \(-0.168690\pi\)
−0.995166 + 0.0982061i \(0.968690\pi\)
\(648\) 0 0
\(649\) −10.0430 + 19.4860i −0.394222 + 0.764893i
\(650\) 7.45528 0.292420
\(651\) 0 0
\(652\) −2.06968 1.50371i −0.0810549 0.0588898i
\(653\) 34.0195 24.7166i 1.33129 0.967237i 0.331571 0.943430i \(-0.392421\pi\)
0.999717 0.0238064i \(-0.00757854\pi\)
\(654\) 0 0
\(655\) 2.69563 8.29629i 0.105327 0.324163i
\(656\) 10.6687 7.75129i 0.416544 0.302637i
\(657\) 0 0
\(658\) 20.8819 + 64.2679i 0.814062 + 2.50543i
\(659\) 0.425249 0.0165654 0.00828268 0.999966i \(-0.497364\pi\)
0.00828268 + 0.999966i \(0.497364\pi\)
\(660\) 0 0
\(661\) −7.08477 −0.275565 −0.137783 0.990462i \(-0.543998\pi\)
−0.137783 + 0.990462i \(0.543998\pi\)
\(662\) −3.85444 11.8628i −0.149807 0.461059i
\(663\) 0 0
\(664\) 29.9451 21.7564i 1.16210 0.844312i
\(665\) −2.49888 + 7.69076i −0.0969024 + 0.298235i
\(666\) 0 0
\(667\) 6.92937 5.03448i 0.268306 0.194936i
\(668\) 0.728290 + 0.529134i 0.0281784 + 0.0204728i
\(669\) 0 0
\(670\) −9.03224 −0.348946
\(671\) 2.69305 + 17.5303i 0.103964 + 0.676750i
\(672\) 0 0
\(673\) −3.79575 11.6821i −0.146315 0.450313i 0.850862 0.525389i \(-0.176080\pi\)
−0.997178 + 0.0750760i \(0.976080\pi\)
\(674\) 20.1151 + 14.6145i 0.774806 + 0.562929i
\(675\) 0 0
\(676\) −4.25456 + 13.0942i −0.163637 + 0.503623i
\(677\) −5.33859 + 16.4305i −0.205179 + 0.631475i 0.794527 + 0.607228i \(0.207719\pi\)
−0.999706 + 0.0242467i \(0.992281\pi\)
\(678\) 0 0
\(679\) −4.70480 3.41824i −0.180554 0.131180i
\(680\) 0.762728 + 2.34743i 0.0292493 + 0.0900200i
\(681\) 0 0
\(682\) 2.95925 5.74172i 0.113316 0.219862i
\(683\) −26.8858 −1.02876 −0.514379 0.857563i \(-0.671978\pi\)
−0.514379 + 0.857563i \(0.671978\pi\)
\(684\) 0 0
\(685\) 1.24898 + 0.907437i 0.0477211 + 0.0346714i
\(686\) −19.4610 + 14.1392i −0.743024 + 0.539838i
\(687\) 0 0
\(688\) 7.96228 24.5054i 0.303559 0.934259i
\(689\) 13.3264 9.68220i 0.507696 0.368862i
\(690\) 0 0
\(691\) 7.70472 + 23.7127i 0.293102 + 0.902074i 0.983853 + 0.178981i \(0.0572801\pi\)
−0.690751 + 0.723093i \(0.742720\pi\)
\(692\) 9.04609 0.343881
\(693\) 0 0
\(694\) 3.59803 0.136579
\(695\) 5.00552 + 15.4054i 0.189870 + 0.584361i
\(696\) 0 0
\(697\) 3.28601 2.38743i 0.124467 0.0904302i
\(698\) 4.20695 12.9477i 0.159235 0.490076i
\(699\) 0 0
\(700\) 1.90572 1.38458i 0.0720293 0.0523323i
\(701\) 16.2387 + 11.7981i 0.613325 + 0.445607i 0.850584 0.525840i \(-0.176249\pi\)
−0.237258 + 0.971447i \(0.576249\pi\)
\(702\) 0 0
\(703\) 10.3838 0.391634
\(704\) 20.6092 + 20.8017i 0.776740 + 0.783995i
\(705\) 0 0
\(706\) −5.02879 15.4770i −0.189261 0.582485i
\(707\) 29.4292 + 21.3816i 1.10680 + 0.804137i
\(708\) 0 0
\(709\) −3.50289 + 10.7808i −0.131554 + 0.404881i −0.995038 0.0994949i \(-0.968277\pi\)
0.863484 + 0.504376i \(0.168277\pi\)
\(710\) −2.17227 + 6.68557i −0.0815240 + 0.250905i
\(711\) 0 0
\(712\) 31.7232 + 23.0483i 1.18888 + 0.863771i
\(713\) −4.03479 12.4178i −0.151104 0.465051i
\(714\) 0 0
\(715\) 18.3131 9.22399i 0.684869 0.344958i
\(716\) −9.60684 −0.359025
\(717\) 0 0
\(718\) 24.0956 + 17.5065i 0.899240 + 0.653336i
\(719\) 3.75010 2.72460i 0.139855 0.101611i −0.515658 0.856795i \(-0.672452\pi\)
0.655513 + 0.755184i \(0.272452\pi\)
\(720\) 0 0
\(721\) −13.2025 + 40.6330i −0.491685 + 1.51325i
\(722\) 15.1103 10.9782i 0.562345 0.408568i
\(723\) 0 0
\(724\) −1.41804 4.36429i −0.0527012 0.162198i
\(725\) −1.05948 −0.0393481
\(726\) 0 0
\(727\) −2.22651 −0.0825766 −0.0412883 0.999147i \(-0.513146\pi\)
−0.0412883 + 0.999147i \(0.513146\pi\)
\(728\) −25.3105 77.8977i −0.938069 2.88708i
\(729\) 0 0
\(730\) −4.68420 + 3.40327i −0.173370 + 0.125961i
\(731\) 2.45241 7.54775i 0.0907057 0.279164i
\(732\) 0 0
\(733\) 24.6573 17.9145i 0.910737 0.661689i −0.0304645 0.999536i \(-0.509699\pi\)
0.941201 + 0.337847i \(0.109699\pi\)
\(734\) −6.18994 4.49725i −0.228475 0.165997i
\(735\) 0 0
\(736\) 24.1904 0.891669
\(737\) −22.1867 + 11.1751i −0.817257 + 0.411639i
\(738\) 0 0
\(739\) −2.84351 8.75141i −0.104600 0.321926i 0.885036 0.465522i \(-0.154133\pi\)
−0.989636 + 0.143596i \(0.954133\pi\)
\(740\) −2.44711 1.77793i −0.0899575 0.0653579i
\(741\) 0 0
\(742\) −4.28450 + 13.1863i −0.157289 + 0.484086i
\(743\) −0.534297 + 1.64440i −0.0196014 + 0.0603270i −0.960379 0.278698i \(-0.910097\pi\)
0.940777 + 0.339025i \(0.110097\pi\)
\(744\) 0 0
\(745\) −11.3410 8.23975i −0.415504 0.301881i
\(746\) 4.91255 + 15.1193i 0.179861 + 0.553556i
\(747\) 0 0
\(748\) 1.02443 + 1.03400i 0.0374569 + 0.0378068i
\(749\) 35.2456 1.28785
\(750\) 0 0
\(751\) −27.4077 19.9129i −1.00012 0.726631i −0.0380072 0.999277i \(-0.512101\pi\)
−0.962114 + 0.272647i \(0.912101\pi\)
\(752\) 27.4231 19.9240i 1.00002 0.726555i
\(753\) 0 0
\(754\) −2.44084 + 7.51213i −0.0888901 + 0.273576i
\(755\) 10.9906 7.98516i 0.399990 0.290610i
\(756\) 0 0
\(757\) −8.30257 25.5527i −0.301762 0.928728i −0.980866 0.194685i \(-0.937631\pi\)
0.679104 0.734042i \(-0.262369\pi\)
\(758\) −22.3525 −0.811879
\(759\) 0 0
\(760\) 5.75282 0.208677
\(761\) 5.38966 + 16.5877i 0.195375 + 0.601303i 0.999972 + 0.00748151i \(0.00238146\pi\)
−0.804597 + 0.593821i \(0.797619\pi\)
\(762\) 0 0
\(763\) −47.1304 + 34.2422i −1.70623 + 1.23965i
\(764\) 0.896990 2.76065i 0.0324520 0.0998769i
\(765\) 0 0
\(766\) 27.6910 20.1187i 1.00052 0.726918i
\(767\) −33.0597 24.0193i −1.19372 0.867286i
\(768\) 0 0
\(769\) −41.6485 −1.50188 −0.750942 0.660368i \(-0.770400\pi\)
−0.750942 + 0.660368i \(0.770400\pi\)
\(770\) −7.90689 + 15.3414i −0.284945 + 0.552867i
\(771\) 0 0
\(772\) −2.57865 7.93626i −0.0928075 0.285632i
\(773\) 17.9209 + 13.0203i 0.644570 + 0.468308i 0.861417 0.507898i \(-0.169577\pi\)
−0.216847 + 0.976206i \(0.569577\pi\)
\(774\) 0 0
\(775\) −0.499089 + 1.53604i −0.0179278 + 0.0551762i
\(776\) −1.27845 + 3.93466i −0.0458937 + 0.141246i
\(777\) 0 0
\(778\) −18.7032 13.5886i −0.670540 0.487176i
\(779\) −2.92541 9.00350i −0.104814 0.322584i
\(780\) 0 0
\(781\) 2.93572 + 19.1100i 0.105048 + 0.683809i
\(782\) −7.83783 −0.280280
\(783\) 0 0
\(784\) 24.5445 + 17.8326i 0.876588 + 0.636879i
\(785\) 3.54409 2.57493i 0.126494 0.0919033i
\(786\)