Properties

Label 405.2.r.a.152.5
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.5
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.865920 - 0.606324i) q^{2} +(-0.301851 - 0.829330i) q^{4} +(-2.13636 - 0.660292i) q^{5} +(-1.22161 - 2.61975i) q^{7} +(-0.788655 + 2.94330i) q^{8} +O(q^{10})\) \(q+(-0.865920 - 0.606324i) q^{2} +(-0.301851 - 0.829330i) q^{4} +(-2.13636 - 0.660292i) q^{5} +(-1.22161 - 2.61975i) q^{7} +(-0.788655 + 2.94330i) q^{8} +(1.44956 + 1.86708i) q^{10} +(-1.51740 - 1.80836i) q^{11} +(3.11956 + 4.45519i) q^{13} +(-0.530600 + 3.00918i) q^{14} +(1.11535 - 0.935892i) q^{16} +(0.716894 + 2.67549i) q^{17} +(-5.35751 + 3.09316i) q^{19} +(0.0972619 + 1.97105i) q^{20} +(0.217491 + 2.48593i) q^{22} +(-0.646627 - 0.301527i) q^{23} +(4.12803 + 2.82124i) q^{25} -5.74930i q^{26} +(-1.80389 + 1.80389i) q^{28} +(-0.623300 - 3.53491i) q^{29} +(-5.18043 + 1.88552i) q^{31} +(4.53781 - 0.397007i) q^{32} +(1.00144 - 2.75143i) q^{34} +(0.879991 + 6.40333i) q^{35} +(-4.26173 + 1.14193i) q^{37} +(6.51463 + 0.569956i) q^{38} +(3.62828 - 5.76719i) q^{40} +(-5.70140 - 1.00531i) q^{41} +(0.126221 - 1.44271i) q^{43} +(-1.04170 + 1.80428i) q^{44} +(0.377104 + 0.653164i) q^{46} +(-9.40770 + 4.38688i) q^{47} +(-0.871236 + 1.03830i) q^{49} +(-1.86396 - 4.94589i) q^{50} +(2.75318 - 3.93195i) q^{52} +(7.22940 + 7.22940i) q^{53} +(2.04765 + 4.86523i) q^{55} +(8.67413 - 1.52948i) q^{56} +(-1.60357 + 3.43887i) q^{58} +(-6.27320 - 5.26384i) q^{59} +(2.64019 + 0.960952i) q^{61} +(5.62907 + 1.50831i) q^{62} +(-6.69194 - 3.86359i) q^{64} +(-3.72276 - 11.5777i) q^{65} +(6.11610 - 4.28254i) q^{67} +(2.00246 - 1.40214i) q^{68} +(3.12049 - 6.07833i) q^{70} +(4.24004 + 2.44799i) q^{71} +(-6.73088 - 1.80353i) q^{73} +(4.38269 + 1.59517i) q^{74} +(4.18242 + 3.50947i) q^{76} +(-2.88379 + 6.18430i) q^{77} +(-12.8661 + 2.26863i) q^{79} +(-3.00075 + 1.26294i) q^{80} +(4.32741 + 4.32741i) q^{82} +(2.73492 - 3.90587i) q^{83} +(0.235061 - 6.18915i) q^{85} +(-0.984048 + 1.17274i) q^{86} +(6.51925 - 3.03998i) q^{88} +(-3.33276 - 5.77251i) q^{89} +(7.86060 - 13.6150i) q^{91} +(-0.0548802 + 0.627283i) q^{92} +(10.8062 + 1.90542i) q^{94} +(13.4879 - 3.07057i) q^{95} +(-18.2758 - 1.59893i) q^{97} +(1.38397 - 0.370833i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.865920 0.606324i −0.612298 0.428736i 0.225863 0.974159i \(-0.427480\pi\)
−0.838161 + 0.545424i \(0.816369\pi\)
\(3\) 0 0
\(4\) −0.301851 0.829330i −0.150926 0.414665i
\(5\) −2.13636 0.660292i −0.955407 0.295292i
\(6\) 0 0
\(7\) −1.22161 2.61975i −0.461725 0.990171i −0.989996 0.141096i \(-0.954937\pi\)
0.528271 0.849076i \(-0.322840\pi\)
\(8\) −0.788655 + 2.94330i −0.278832 + 1.04061i
\(9\) 0 0
\(10\) 1.44956 + 1.86708i 0.458392 + 0.590424i
\(11\) −1.51740 1.80836i −0.457512 0.545242i 0.487136 0.873326i \(-0.338041\pi\)
−0.944648 + 0.328084i \(0.893597\pi\)
\(12\) 0 0
\(13\) 3.11956 + 4.45519i 0.865210 + 1.23565i 0.970475 + 0.241203i \(0.0775421\pi\)
−0.105265 + 0.994444i \(0.533569\pi\)
\(14\) −0.530600 + 3.00918i −0.141809 + 0.804238i
\(15\) 0 0
\(16\) 1.11535 0.935892i 0.278838 0.233973i
\(17\) 0.716894 + 2.67549i 0.173872 + 0.648901i 0.996741 + 0.0806688i \(0.0257056\pi\)
−0.822869 + 0.568232i \(0.807628\pi\)
\(18\) 0 0
\(19\) −5.35751 + 3.09316i −1.22910 + 0.709619i −0.966841 0.255379i \(-0.917800\pi\)
−0.262256 + 0.964998i \(0.584466\pi\)
\(20\) 0.0972619 + 1.97105i 0.0217484 + 0.440741i
\(21\) 0 0
\(22\) 0.217491 + 2.48593i 0.0463692 + 0.530002i
\(23\) −0.646627 0.301527i −0.134831 0.0628728i 0.354032 0.935233i \(-0.384810\pi\)
−0.488863 + 0.872361i \(0.662588\pi\)
\(24\) 0 0
\(25\) 4.12803 + 2.82124i 0.825606 + 0.564247i
\(26\) 5.74930i 1.12753i
\(27\) 0 0
\(28\) −1.80389 + 1.80389i −0.340903 + 0.340903i
\(29\) −0.623300 3.53491i −0.115744 0.656416i −0.986379 0.164487i \(-0.947403\pi\)
0.870635 0.491929i \(-0.163708\pi\)
\(30\) 0 0
\(31\) −5.18043 + 1.88552i −0.930432 + 0.338650i −0.762381 0.647129i \(-0.775970\pi\)
−0.168051 + 0.985778i \(0.553747\pi\)
\(32\) 4.53781 0.397007i 0.802178 0.0701815i
\(33\) 0 0
\(34\) 1.00144 2.75143i 0.171745 0.471866i
\(35\) 0.879991 + 6.40333i 0.148746 + 1.08236i
\(36\) 0 0
\(37\) −4.26173 + 1.14193i −0.700624 + 0.187732i −0.591510 0.806298i \(-0.701468\pi\)
−0.109114 + 0.994029i \(0.534801\pi\)
\(38\) 6.51463 + 0.569956i 1.05681 + 0.0924591i
\(39\) 0 0
\(40\) 3.62828 5.76719i 0.573682 0.911873i
\(41\) −5.70140 1.00531i −0.890409 0.157003i −0.290314 0.956932i \(-0.593760\pi\)
−0.600095 + 0.799928i \(0.704871\pi\)
\(42\) 0 0
\(43\) 0.126221 1.44271i 0.0192485 0.220012i −0.980478 0.196629i \(-0.937001\pi\)
0.999727 0.0233831i \(-0.00744375\pi\)
\(44\) −1.04170 + 1.80428i −0.157042 + 0.272005i
\(45\) 0 0
\(46\) 0.377104 + 0.653164i 0.0556010 + 0.0963037i
\(47\) −9.40770 + 4.38688i −1.37225 + 0.639893i −0.962244 0.272188i \(-0.912253\pi\)
−0.410010 + 0.912081i \(0.634475\pi\)
\(48\) 0 0
\(49\) −0.871236 + 1.03830i −0.124462 + 0.148328i
\(50\) −1.86396 4.94589i −0.263604 0.699454i
\(51\) 0 0
\(52\) 2.75318 3.93195i 0.381797 0.545263i
\(53\) 7.22940 + 7.22940i 0.993035 + 0.993035i 0.999976 0.00694140i \(-0.00220953\pi\)
−0.00694140 + 0.999976i \(0.502210\pi\)
\(54\) 0 0
\(55\) 2.04765 + 4.86523i 0.276105 + 0.656027i
\(56\) 8.67413 1.52948i 1.15913 0.204386i
\(57\) 0 0
\(58\) −1.60357 + 3.43887i −0.210559 + 0.451546i
\(59\) −6.27320 5.26384i −0.816701 0.685293i 0.135496 0.990778i \(-0.456737\pi\)
−0.952197 + 0.305484i \(0.901182\pi\)
\(60\) 0 0
\(61\) 2.64019 + 0.960952i 0.338042 + 0.123037i 0.505463 0.862848i \(-0.331322\pi\)
−0.167421 + 0.985885i \(0.553544\pi\)
\(62\) 5.62907 + 1.50831i 0.714893 + 0.191555i
\(63\) 0 0
\(64\) −6.69194 3.86359i −0.836493 0.482949i
\(65\) −3.72276 11.5777i −0.461751 1.43604i
\(66\) 0 0
\(67\) 6.11610 4.28254i 0.747201 0.523196i −0.136847 0.990592i \(-0.543697\pi\)
0.884048 + 0.467396i \(0.154808\pi\)
\(68\) 2.00246 1.40214i 0.242834 0.170034i
\(69\) 0 0
\(70\) 3.12049 6.07833i 0.372970 0.726499i
\(71\) 4.24004 + 2.44799i 0.503200 + 0.290523i 0.730034 0.683411i \(-0.239504\pi\)
−0.226834 + 0.973933i \(0.572838\pi\)
\(72\) 0 0
\(73\) −6.73088 1.80353i −0.787790 0.211088i −0.157574 0.987507i \(-0.550367\pi\)
−0.630216 + 0.776420i \(0.717034\pi\)
\(74\) 4.38269 + 1.59517i 0.509478 + 0.185435i
\(75\) 0 0
\(76\) 4.18242 + 3.50947i 0.479756 + 0.402563i
\(77\) −2.88379 + 6.18430i −0.328638 + 0.704767i
\(78\) 0 0
\(79\) −12.8661 + 2.26863i −1.44754 + 0.255241i −0.841529 0.540212i \(-0.818344\pi\)
−0.606015 + 0.795453i \(0.707233\pi\)
\(80\) −3.00075 + 1.26294i −0.335494 + 0.141201i
\(81\) 0 0
\(82\) 4.32741 + 4.32741i 0.477883 + 0.477883i
\(83\) 2.73492 3.90587i 0.300196 0.428724i −0.640509 0.767951i \(-0.721276\pi\)
0.940705 + 0.339227i \(0.110165\pi\)
\(84\) 0 0
\(85\) 0.235061 6.18915i 0.0254960 0.671307i
\(86\) −0.984048 + 1.17274i −0.106113 + 0.126460i
\(87\) 0 0
\(88\) 6.51925 3.03998i 0.694955 0.324063i
\(89\) −3.33276 5.77251i −0.353272 0.611885i 0.633549 0.773703i \(-0.281598\pi\)
−0.986821 + 0.161818i \(0.948264\pi\)
\(90\) 0 0
\(91\) 7.86060 13.6150i 0.824014 1.42723i
\(92\) −0.0548802 + 0.627283i −0.00572165 + 0.0653988i
\(93\) 0 0
\(94\) 10.8062 + 1.90542i 1.11457 + 0.196529i
\(95\) 13.4879 3.07057i 1.38383 0.315033i
\(96\) 0 0
\(97\) −18.2758 1.59893i −1.85563 0.162346i −0.896079 0.443894i \(-0.853597\pi\)
−0.959547 + 0.281548i \(0.909152\pi\)
\(98\) 1.38397 0.370833i 0.139802 0.0374597i
\(99\) 0 0
\(100\) 1.09368 4.27509i 0.109368 0.427509i
\(101\) 1.15191 3.16484i 0.114619 0.314913i −0.869097 0.494641i \(-0.835299\pi\)
0.983716 + 0.179728i \(0.0575217\pi\)
\(102\) 0 0
\(103\) −3.61346 + 0.316137i −0.356045 + 0.0311499i −0.263775 0.964584i \(-0.584968\pi\)
−0.0922694 + 0.995734i \(0.529412\pi\)
\(104\) −15.5732 + 5.66819i −1.52708 + 0.555812i
\(105\) 0 0
\(106\) −1.87673 10.6434i −0.182284 1.03378i
\(107\) 4.03460 4.03460i 0.390039 0.390039i −0.484662 0.874701i \(-0.661057\pi\)
0.874701 + 0.484662i \(0.161057\pi\)
\(108\) 0 0
\(109\) 15.8226i 1.51553i −0.652527 0.757765i \(-0.726291\pi\)
0.652527 0.757765i \(-0.273709\pi\)
\(110\) 1.17680 5.45444i 0.112204 0.520060i
\(111\) 0 0
\(112\) −3.81433 1.77865i −0.360420 0.168067i
\(113\) 0.232615 + 2.65880i 0.0218825 + 0.250119i 0.999255 + 0.0385931i \(0.0122876\pi\)
−0.977372 + 0.211526i \(0.932157\pi\)
\(114\) 0 0
\(115\) 1.18233 + 1.07113i 0.110253 + 0.0998836i
\(116\) −2.74346 + 1.58394i −0.254724 + 0.147065i
\(117\) 0 0
\(118\) 2.24050 + 8.36165i 0.206255 + 0.769753i
\(119\) 6.13333 5.14648i 0.562242 0.471777i
\(120\) 0 0
\(121\) 0.942447 5.34488i 0.0856770 0.485898i
\(122\) −1.70355 2.43292i −0.154232 0.220266i
\(123\) 0 0
\(124\) 3.12744 + 3.72713i 0.280852 + 0.334707i
\(125\) −6.95610 8.75287i −0.622172 0.782880i
\(126\) 0 0
\(127\) −0.846401 + 3.15881i −0.0751059 + 0.280299i −0.993257 0.115931i \(-0.963015\pi\)
0.918151 + 0.396230i \(0.129682\pi\)
\(128\) −0.398073 0.853671i −0.0351850 0.0754546i
\(129\) 0 0
\(130\) −3.79622 + 12.2826i −0.332950 + 1.07725i
\(131\) −0.497235 1.36614i −0.0434436 0.119360i 0.916074 0.401010i \(-0.131341\pi\)
−0.959517 + 0.281649i \(0.909118\pi\)
\(132\) 0 0
\(133\) 14.6481 + 10.2567i 1.27015 + 0.889368i
\(134\) −7.89266 −0.681822
\(135\) 0 0
\(136\) −8.44014 −0.723736
\(137\) 13.0703 + 9.15193i 1.11667 + 0.781902i 0.978035 0.208442i \(-0.0668391\pi\)
0.138637 + 0.990343i \(0.455728\pi\)
\(138\) 0 0
\(139\) −3.12149 8.57623i −0.264762 0.727426i −0.998830 0.0483514i \(-0.984603\pi\)
0.734069 0.679075i \(-0.237619\pi\)
\(140\) 5.04484 2.66266i 0.426367 0.225035i
\(141\) 0 0
\(142\) −2.18726 4.69060i −0.183551 0.393626i
\(143\) 3.32299 12.4016i 0.277883 1.03707i
\(144\) 0 0
\(145\) −1.00248 + 7.96338i −0.0832517 + 0.661323i
\(146\) 4.73488 + 5.64281i 0.391861 + 0.467002i
\(147\) 0 0
\(148\) 2.23344 + 3.18968i 0.183588 + 0.262190i
\(149\) −1.63395 + 9.26659i −0.133858 + 0.759149i 0.841789 + 0.539806i \(0.181502\pi\)
−0.975648 + 0.219343i \(0.929609\pi\)
\(150\) 0 0
\(151\) −0.808803 + 0.678666i −0.0658194 + 0.0552291i −0.675104 0.737723i \(-0.735901\pi\)
0.609284 + 0.792952i \(0.291457\pi\)
\(152\) −4.87887 18.2082i −0.395729 1.47688i
\(153\) 0 0
\(154\) 6.24682 3.60660i 0.503383 0.290628i
\(155\) 12.3122 0.607549i 0.988942 0.0487995i
\(156\) 0 0
\(157\) 1.94520 + 22.2338i 0.155244 + 1.77445i 0.530652 + 0.847590i \(0.321947\pi\)
−0.375408 + 0.926860i \(0.622497\pi\)
\(158\) 12.5165 + 5.83654i 0.995759 + 0.464330i
\(159\) 0 0
\(160\) −9.95651 2.14813i −0.787131 0.169825i
\(161\) 2.06235i 0.162536i
\(162\) 0 0
\(163\) −1.74889 + 1.74889i −0.136983 + 0.136983i −0.772274 0.635290i \(-0.780881\pi\)
0.635290 + 0.772274i \(0.280881\pi\)
\(164\) 0.887241 + 5.03179i 0.0692819 + 0.392917i
\(165\) 0 0
\(166\) −4.73644 + 1.72392i −0.367619 + 0.133802i
\(167\) −7.25686 + 0.634893i −0.561553 + 0.0491295i −0.364399 0.931243i \(-0.618725\pi\)
−0.197154 + 0.980373i \(0.563170\pi\)
\(168\) 0 0
\(169\) −5.67082 + 15.5805i −0.436217 + 1.19850i
\(170\) −3.95617 + 5.21678i −0.303424 + 0.400109i
\(171\) 0 0
\(172\) −1.23458 + 0.330806i −0.0941362 + 0.0252237i
\(173\) −20.4232 1.78680i −1.55275 0.135848i −0.721760 0.692143i \(-0.756667\pi\)
−0.830985 + 0.556295i \(0.812222\pi\)
\(174\) 0 0
\(175\) 2.34809 14.2608i 0.177499 1.07802i
\(176\) −3.38487 0.596843i −0.255144 0.0449887i
\(177\) 0 0
\(178\) −0.614106 + 7.01926i −0.0460292 + 0.526116i
\(179\) −7.17079 + 12.4202i −0.535970 + 0.928327i 0.463146 + 0.886282i \(0.346721\pi\)
−0.999116 + 0.0420450i \(0.986613\pi\)
\(180\) 0 0
\(181\) 1.03474 + 1.79221i 0.0769112 + 0.133214i 0.901916 0.431912i \(-0.142161\pi\)
−0.825005 + 0.565126i \(0.808828\pi\)
\(182\) −15.0617 + 7.02339i −1.11645 + 0.520609i
\(183\) 0 0
\(184\) 1.39745 1.66542i 0.103021 0.122776i
\(185\) 9.85857 + 0.374424i 0.724816 + 0.0275282i
\(186\) 0 0
\(187\) 3.75043 5.35618i 0.274259 0.391682i
\(188\) 6.47790 + 6.47790i 0.472449 + 0.472449i
\(189\) 0 0
\(190\) −13.5412 5.51919i −0.982384 0.400404i
\(191\) −22.9618 + 4.04878i −1.66145 + 0.292959i −0.923987 0.382424i \(-0.875089\pi\)
−0.737467 + 0.675383i \(0.763978\pi\)
\(192\) 0 0
\(193\) −0.131693 + 0.282417i −0.00947948 + 0.0203288i −0.910991 0.412427i \(-0.864681\pi\)
0.901511 + 0.432756i \(0.142459\pi\)
\(194\) 14.8559 + 12.4656i 1.06659 + 0.894977i
\(195\) 0 0
\(196\) 1.12408 + 0.409130i 0.0802911 + 0.0292236i
\(197\) 3.13774 + 0.840756i 0.223555 + 0.0599014i 0.368858 0.929486i \(-0.379749\pi\)
−0.145303 + 0.989387i \(0.546416\pi\)
\(198\) 0 0
\(199\) 5.52277 + 3.18857i 0.391499 + 0.226032i 0.682809 0.730596i \(-0.260758\pi\)
−0.291310 + 0.956629i \(0.594091\pi\)
\(200\) −11.5593 + 9.92504i −0.817369 + 0.701807i
\(201\) 0 0
\(202\) −2.91638 + 2.04207i −0.205196 + 0.143679i
\(203\) −8.49914 + 5.95116i −0.596523 + 0.417690i
\(204\) 0 0
\(205\) 11.5164 + 5.91229i 0.804342 + 0.412932i
\(206\) 3.32065 + 1.91718i 0.231360 + 0.133576i
\(207\) 0 0
\(208\) 7.64899 + 2.04954i 0.530362 + 0.142110i
\(209\) 13.7230 + 4.99477i 0.949241 + 0.345495i
\(210\) 0 0
\(211\) 4.91430 + 4.12359i 0.338314 + 0.283879i 0.796077 0.605195i \(-0.206905\pi\)
−0.457763 + 0.889074i \(0.651349\pi\)
\(212\) 3.81335 8.17776i 0.261902 0.561651i
\(213\) 0 0
\(214\) −5.93991 + 1.04737i −0.406044 + 0.0715965i
\(215\) −1.22226 + 2.99880i −0.0833578 + 0.204517i
\(216\) 0 0
\(217\) 11.2680 + 11.2680i 0.764925 + 0.764925i
\(218\) −9.59362 + 13.7011i −0.649762 + 0.927956i
\(219\) 0 0
\(220\) 3.41679 3.16675i 0.230360 0.213502i
\(221\) −9.68341 + 11.5402i −0.651376 + 0.776280i
\(222\) 0 0
\(223\) −9.41489 + 4.39023i −0.630467 + 0.293992i −0.711464 0.702723i \(-0.751968\pi\)
0.0809965 + 0.996714i \(0.474190\pi\)
\(224\) −6.58348 11.4029i −0.439877 0.761889i
\(225\) 0 0
\(226\) 1.41067 2.44335i 0.0938361 0.162529i
\(227\) −0.272304 + 3.11245i −0.0180734 + 0.206580i 0.981789 + 0.189976i \(0.0608411\pi\)
−0.999862 + 0.0166042i \(0.994714\pi\)
\(228\) 0 0
\(229\) 23.1368 + 4.07964i 1.52892 + 0.269590i 0.873933 0.486047i \(-0.161562\pi\)
0.654990 + 0.755638i \(0.272673\pi\)
\(230\) −0.374350 1.64439i −0.0246839 0.108428i
\(231\) 0 0
\(232\) 10.8959 + 0.953265i 0.715349 + 0.0625849i
\(233\) 3.20411 0.858538i 0.209908 0.0562447i −0.152333 0.988329i \(-0.548679\pi\)
0.362241 + 0.932085i \(0.382012\pi\)
\(234\) 0 0
\(235\) 22.9948 3.16011i 1.50002 0.206143i
\(236\) −2.47188 + 6.79145i −0.160906 + 0.442085i
\(237\) 0 0
\(238\) −8.43141 + 0.737653i −0.546527 + 0.0478149i
\(239\) 15.9837 5.81759i 1.03390 0.376309i 0.231335 0.972874i \(-0.425691\pi\)
0.802564 + 0.596566i \(0.203468\pi\)
\(240\) 0 0
\(241\) 3.22231 + 18.2746i 0.207567 + 1.17717i 0.893349 + 0.449364i \(0.148349\pi\)
−0.685782 + 0.727807i \(0.740540\pi\)
\(242\) −4.05681 + 4.05681i −0.260782 + 0.260782i
\(243\) 0 0
\(244\) 2.47965i 0.158744i
\(245\) 2.54685 1.64290i 0.162712 0.104961i
\(246\) 0 0
\(247\) −30.4937 14.2194i −1.94027 0.904761i
\(248\) −1.46409 16.7346i −0.0929695 1.06265i
\(249\) 0 0
\(250\) 0.716350 + 11.7969i 0.0453060 + 0.746103i
\(251\) 13.1493 7.59178i 0.829979 0.479189i −0.0238664 0.999715i \(-0.507598\pi\)
0.853846 + 0.520527i \(0.174264\pi\)
\(252\) 0 0
\(253\) 0.435919 + 1.62687i 0.0274060 + 0.102281i
\(254\) 2.64818 2.22208i 0.166161 0.139426i
\(255\) 0 0
\(256\) −2.85653 + 16.2002i −0.178533 + 1.01251i
\(257\) −4.98418 7.11815i −0.310905 0.444018i 0.633041 0.774118i \(-0.281806\pi\)
−0.943946 + 0.330100i \(0.892917\pi\)
\(258\) 0 0
\(259\) 8.19772 + 9.76966i 0.509382 + 0.607057i
\(260\) −8.47800 + 6.58213i −0.525783 + 0.408207i
\(261\) 0 0
\(262\) −0.397759 + 1.48446i −0.0245736 + 0.0917099i
\(263\) −9.97382 21.3889i −0.615012 1.31890i −0.929214 0.369541i \(-0.879515\pi\)
0.314203 0.949356i \(-0.398263\pi\)
\(264\) 0 0
\(265\) −10.6711 20.2181i −0.655518 1.24199i
\(266\) −6.46518 17.7629i −0.396406 1.08912i
\(267\) 0 0
\(268\) −5.39779 3.77957i −0.329723 0.230874i
\(269\) −10.2124 −0.622659 −0.311330 0.950302i \(-0.600774\pi\)
−0.311330 + 0.950302i \(0.600774\pi\)
\(270\) 0 0
\(271\) 4.84409 0.294258 0.147129 0.989117i \(-0.452997\pi\)
0.147129 + 0.989117i \(0.452997\pi\)
\(272\) 3.30356 + 2.31318i 0.200308 + 0.140257i
\(273\) 0 0
\(274\) −5.76881 15.8497i −0.348506 0.957514i
\(275\) −1.16204 11.7459i −0.0700734 0.708305i
\(276\) 0 0
\(277\) −5.71185 12.2491i −0.343192 0.735978i 0.656642 0.754203i \(-0.271976\pi\)
−0.999834 + 0.0182248i \(0.994199\pi\)
\(278\) −2.49701 + 9.31897i −0.149761 + 0.558914i
\(279\) 0 0
\(280\) −19.5409 2.45994i −1.16779 0.147010i
\(281\) 10.1156 + 12.0553i 0.603445 + 0.719158i 0.978130 0.207994i \(-0.0666936\pi\)
−0.374685 + 0.927152i \(0.622249\pi\)
\(282\) 0 0
\(283\) −17.2952 24.7001i −1.02809 1.46827i −0.877443 0.479680i \(-0.840753\pi\)
−0.150648 0.988587i \(-0.548136\pi\)
\(284\) 0.750327 4.25532i 0.0445237 0.252507i
\(285\) 0 0
\(286\) −10.3968 + 8.72397i −0.614777 + 0.515859i
\(287\) 4.33122 + 16.1643i 0.255664 + 0.954150i
\(288\) 0 0
\(289\) 8.07815 4.66392i 0.475185 0.274348i
\(290\) 5.69646 6.28782i 0.334508 0.369234i
\(291\) 0 0
\(292\) 0.536001 + 6.12652i 0.0313671 + 0.358527i
\(293\) 6.65512 + 3.10333i 0.388796 + 0.181299i 0.607180 0.794564i \(-0.292301\pi\)
−0.218384 + 0.975863i \(0.570078\pi\)
\(294\) 0 0
\(295\) 9.92611 + 15.3876i 0.577921 + 0.895899i
\(296\) 13.4441i 0.781424i
\(297\) 0 0
\(298\) 7.03343 7.03343i 0.407435 0.407435i
\(299\) −0.673830 3.82148i −0.0389686 0.221002i
\(300\) 0 0
\(301\) −3.93374 + 1.43176i −0.226737 + 0.0825254i
\(302\) 1.11185 0.0972742i 0.0639798 0.00559750i
\(303\) 0 0
\(304\) −3.08065 + 8.46402i −0.176687 + 0.485445i
\(305\) −5.00588 3.79623i −0.286636 0.217372i
\(306\) 0 0
\(307\) 13.2129 3.54038i 0.754099 0.202060i 0.138764 0.990326i \(-0.455687\pi\)
0.615336 + 0.788265i \(0.289020\pi\)
\(308\) 5.99930 + 0.524871i 0.341842 + 0.0299073i
\(309\) 0 0
\(310\) −11.0298 6.93911i −0.626449 0.394115i
\(311\) −3.80231 0.670449i −0.215609 0.0380177i 0.0648001 0.997898i \(-0.479359\pi\)
−0.280409 + 0.959881i \(0.590470\pi\)
\(312\) 0 0
\(313\) 2.14418 24.5081i 0.121196 1.38528i −0.655401 0.755281i \(-0.727500\pi\)
0.776597 0.629997i \(-0.216944\pi\)
\(314\) 11.7965 20.4321i 0.665714 1.15305i
\(315\) 0 0
\(316\) 5.76508 + 9.98541i 0.324311 + 0.561723i
\(317\) −14.9555 + 6.97386i −0.839984 + 0.391691i −0.794493 0.607274i \(-0.792263\pi\)
−0.0454916 + 0.998965i \(0.514485\pi\)
\(318\) 0 0
\(319\) −5.44660 + 6.49101i −0.304951 + 0.363427i
\(320\) 11.7453 + 12.6726i 0.656580 + 0.708422i
\(321\) 0 0
\(322\) 1.25045 1.78583i 0.0696849 0.0995203i
\(323\) −12.1165 12.1165i −0.674178 0.674178i
\(324\) 0 0
\(325\) 0.308476 + 27.1922i 0.0171112 + 1.50835i
\(326\) 2.57479 0.454005i 0.142604 0.0251450i
\(327\) 0 0
\(328\) 7.45537 15.9881i 0.411654 0.882794i
\(329\) 22.9851 + 19.2867i 1.26721 + 1.06331i
\(330\) 0 0
\(331\) −19.3973 7.06005i −1.06617 0.388056i −0.251429 0.967876i \(-0.580901\pi\)
−0.814744 + 0.579820i \(0.803123\pi\)
\(332\) −4.06479 1.08916i −0.223084 0.0597752i
\(333\) 0 0
\(334\) 6.66881 + 3.85024i 0.364901 + 0.210676i
\(335\) −15.8939 + 5.11062i −0.868377 + 0.279223i
\(336\) 0 0
\(337\) −8.57053 + 6.00115i −0.466867 + 0.326904i −0.783227 0.621735i \(-0.786428\pi\)
0.316361 + 0.948639i \(0.397539\pi\)
\(338\) 14.3573 10.0531i 0.780933 0.546815i
\(339\) 0 0
\(340\) −5.20380 + 1.67326i −0.282215 + 0.0907452i
\(341\) 11.2705 + 6.50701i 0.610330 + 0.352374i
\(342\) 0 0
\(343\) −15.7602 4.22292i −0.850968 0.228016i
\(344\) 4.14679 + 1.50931i 0.223580 + 0.0813765i
\(345\) 0 0
\(346\) 16.6015 + 13.9303i 0.892500 + 0.748896i
\(347\) 4.85639 10.4146i 0.260705 0.559083i −0.731767 0.681554i \(-0.761304\pi\)
0.992472 + 0.122472i \(0.0390821\pi\)
\(348\) 0 0
\(349\) 15.6377 2.75735i 0.837067 0.147597i 0.261347 0.965245i \(-0.415833\pi\)
0.575719 + 0.817647i \(0.304722\pi\)
\(350\) −10.6799 + 10.9250i −0.570867 + 0.583968i
\(351\) 0 0
\(352\) −7.60358 7.60358i −0.405272 0.405272i
\(353\) −4.97772 + 7.10893i −0.264938 + 0.378370i −0.929475 0.368885i \(-0.879740\pi\)
0.664538 + 0.747255i \(0.268629\pi\)
\(354\) 0 0
\(355\) −7.44184 8.02943i −0.394972 0.426158i
\(356\) −3.78131 + 4.50640i −0.200409 + 0.238838i
\(357\) 0 0
\(358\) 13.7400 6.40706i 0.726180 0.338623i
\(359\) −10.2032 17.6725i −0.538505 0.932718i −0.998985 0.0450476i \(-0.985656\pi\)
0.460480 0.887670i \(-0.347677\pi\)
\(360\) 0 0
\(361\) 9.63526 16.6888i 0.507119 0.878356i
\(362\) 0.190664 2.17930i 0.0100211 0.114541i
\(363\) 0 0
\(364\) −13.6640 2.40933i −0.716189 0.126283i
\(365\) 13.1887 + 8.29733i 0.690328 + 0.434302i
\(366\) 0 0
\(367\) 25.8506 + 2.26163i 1.34939 + 0.118056i 0.738818 0.673906i \(-0.235385\pi\)
0.610571 + 0.791962i \(0.290940\pi\)
\(368\) −1.00341 + 0.268864i −0.0523066 + 0.0140155i
\(369\) 0 0
\(370\) −8.30971 6.30171i −0.432001 0.327610i
\(371\) 10.1077 27.7707i 0.524766 1.44178i
\(372\) 0 0
\(373\) 4.75950 0.416402i 0.246438 0.0215605i 0.0367323 0.999325i \(-0.488305\pi\)
0.209705 + 0.977765i \(0.432750\pi\)
\(374\) −6.49515 + 2.36404i −0.335856 + 0.122242i
\(375\) 0 0
\(376\) −5.49248 31.1494i −0.283253 1.60641i
\(377\) 13.8043 13.8043i 0.710956 0.710956i
\(378\) 0 0
\(379\) 25.3002i 1.29958i −0.760112 0.649792i \(-0.774856\pi\)
0.760112 0.649792i \(-0.225144\pi\)
\(380\) −6.61786 10.2591i −0.339489 0.526280i
\(381\) 0 0
\(382\) 22.3379 + 10.4163i 1.14291 + 0.532946i
\(383\) 1.07406 + 12.2766i 0.0548819 + 0.627303i 0.972971 + 0.230929i \(0.0741764\pi\)
−0.918089 + 0.396375i \(0.870268\pi\)
\(384\) 0 0
\(385\) 10.2442 11.3077i 0.522095 0.576295i
\(386\) 0.285272 0.164702i 0.0145200 0.00838310i
\(387\) 0 0
\(388\) 4.19054 + 15.6393i 0.212742 + 0.793965i
\(389\) −6.83430 + 5.73466i −0.346513 + 0.290759i −0.799388 0.600815i \(-0.794843\pi\)
0.452875 + 0.891574i \(0.350398\pi\)
\(390\) 0 0
\(391\) 0.343168 1.94620i 0.0173548 0.0984238i
\(392\) −2.36892 3.38317i −0.119649 0.170876i
\(393\) 0 0
\(394\) −2.20727 2.63052i −0.111200 0.132524i
\(395\) 28.9844 + 3.64875i 1.45836 + 0.183588i
\(396\) 0 0
\(397\) 3.52782 13.1660i 0.177056 0.660782i −0.819136 0.573599i \(-0.805547\pi\)
0.996192 0.0871833i \(-0.0277866\pi\)
\(398\) −2.84897 6.10964i −0.142806 0.306249i
\(399\) 0 0
\(400\) 7.24458 0.716715i 0.362229 0.0358358i
\(401\) 1.00354 + 2.75721i 0.0501146 + 0.137689i 0.962225 0.272257i \(-0.0877700\pi\)
−0.912110 + 0.409945i \(0.865548\pi\)
\(402\) 0 0
\(403\) −24.5610 17.1978i −1.22347 0.856683i
\(404\) −2.97240 −0.147882
\(405\) 0 0
\(406\) 10.9679 0.544328
\(407\) 8.53175 + 5.97399i 0.422903 + 0.296120i
\(408\) 0 0
\(409\) 9.80467 + 26.9381i 0.484810 + 1.33200i 0.905325 + 0.424719i \(0.139627\pi\)
−0.420515 + 0.907285i \(0.638151\pi\)
\(410\) −6.38754 12.1022i −0.315458 0.597687i
\(411\) 0 0
\(412\) 1.35291 + 2.90132i 0.0666530 + 0.142938i
\(413\) −6.12654 + 22.8645i −0.301467 + 1.12509i
\(414\) 0 0
\(415\) −8.42177 + 6.53847i −0.413408 + 0.320961i
\(416\) 15.9247 + 18.9783i 0.780772 + 0.930488i
\(417\) 0 0
\(418\) −8.85459 12.6457i −0.433092 0.618519i
\(419\) 2.30839 13.0915i 0.112772 0.639563i −0.875057 0.484020i \(-0.839176\pi\)
0.987829 0.155543i \(-0.0497127\pi\)
\(420\) 0 0
\(421\) 6.93437 5.81863i 0.337960 0.283582i −0.457974 0.888966i \(-0.651425\pi\)
0.795934 + 0.605383i \(0.206980\pi\)
\(422\) −1.75516 6.55035i −0.0854399 0.318866i
\(423\) 0 0
\(424\) −26.9798 + 15.5768i −1.31025 + 0.756476i
\(425\) −4.58882 + 13.0670i −0.222590 + 0.633843i
\(426\) 0 0
\(427\) −0.707831 8.09054i −0.0342543 0.391529i
\(428\) −4.56386 2.12816i −0.220602 0.102869i
\(429\) 0 0
\(430\) 2.87663 1.85564i 0.138723 0.0894868i
\(431\) 0.295969i 0.0142563i −0.999975 0.00712817i \(-0.997731\pi\)
0.999975 0.00712817i \(-0.00226899\pi\)
\(432\) 0 0
\(433\) 12.8171 12.8171i 0.615949 0.615949i −0.328541 0.944490i \(-0.606557\pi\)
0.944490 + 0.328541i \(0.106557\pi\)
\(434\) −2.92514 16.5893i −0.140411 0.796312i
\(435\) 0 0
\(436\) −13.1221 + 4.77607i −0.628437 + 0.228732i
\(437\) 4.39698 0.384686i 0.210336 0.0184020i
\(438\) 0 0
\(439\) −9.75841 + 26.8110i −0.465743 + 1.27962i 0.455362 + 0.890306i \(0.349510\pi\)
−0.921105 + 0.389313i \(0.872712\pi\)
\(440\) −15.9347 + 2.18986i −0.759658 + 0.104398i
\(441\) 0 0
\(442\) 15.3822 4.12164i 0.731655 0.196046i
\(443\) 40.1651 + 3.51399i 1.90830 + 0.166955i 0.979204 0.202878i \(-0.0650296\pi\)
0.929098 + 0.369833i \(0.120585\pi\)
\(444\) 0 0
\(445\) 3.30842 + 14.5327i 0.156834 + 0.688917i
\(446\) 10.8144 + 1.90688i 0.512079 + 0.0902933i
\(447\) 0 0
\(448\) −1.94671 + 22.2510i −0.0919734 + 1.05126i
\(449\) 3.91232 6.77634i 0.184634 0.319795i −0.758819 0.651301i \(-0.774223\pi\)
0.943453 + 0.331506i \(0.107557\pi\)
\(450\) 0 0
\(451\) 6.83332 + 11.8357i 0.321768 + 0.557319i
\(452\) 2.13480 0.995476i 0.100413 0.0468232i
\(453\) 0 0
\(454\) 2.12294 2.53003i 0.0996347 0.118740i
\(455\) −25.7829 + 23.8961i −1.20872 + 1.12027i
\(456\) 0 0
\(457\) −3.14363 + 4.48957i −0.147053 + 0.210013i −0.885920 0.463838i \(-0.846472\pi\)
0.738867 + 0.673851i \(0.235361\pi\)
\(458\) −17.5610 17.5610i −0.820573 0.820573i
\(459\) 0 0
\(460\) 0.531434 1.30386i 0.0247782 0.0607929i
\(461\) −29.6880 + 5.23480i −1.38271 + 0.243809i −0.815019 0.579434i \(-0.803274\pi\)
−0.567689 + 0.823243i \(0.692163\pi\)
\(462\) 0 0
\(463\) 0.0761934 0.163397i 0.00354101 0.00759371i −0.904529 0.426411i \(-0.859778\pi\)
0.908070 + 0.418818i \(0.137555\pi\)
\(464\) −4.00350 3.35933i −0.185858 0.155953i
\(465\) 0 0
\(466\) −3.29505 1.19930i −0.152640 0.0555566i
\(467\) 12.1916 + 3.26672i 0.564158 + 0.151166i 0.529616 0.848238i \(-0.322336\pi\)
0.0345422 + 0.999403i \(0.489003\pi\)
\(468\) 0 0
\(469\) −18.6907 10.7911i −0.863055 0.498285i
\(470\) −21.8277 11.2059i −1.00684 0.516890i
\(471\) 0 0
\(472\) 20.4404 14.3126i 0.940848 0.658789i
\(473\) −2.80048 + 1.96091i −0.128766 + 0.0901629i
\(474\) 0 0
\(475\) −30.8425 2.34615i −1.41515 0.107649i
\(476\) −6.11948 3.53308i −0.280486 0.161939i
\(477\) 0 0
\(478\) −17.3679 4.65373i −0.794391 0.212857i
\(479\) 33.4923 + 12.1902i 1.53030 + 0.556985i 0.963696 0.267003i \(-0.0860335\pi\)
0.566607 + 0.823988i \(0.308256\pi\)
\(480\) 0 0
\(481\) −18.3822 15.4245i −0.838157 0.703297i
\(482\) 8.29007 17.7781i 0.377602 0.809771i
\(483\) 0 0
\(484\) −4.71715 + 0.831760i −0.214416 + 0.0378073i
\(485\) 37.9878 + 15.4832i 1.72494 + 0.703058i
\(486\) 0 0
\(487\) 4.88907 + 4.88907i 0.221545 + 0.221545i 0.809149 0.587604i \(-0.199929\pi\)
−0.587604 + 0.809149i \(0.699929\pi\)
\(488\) −4.91057 + 7.01302i −0.222291 + 0.317464i
\(489\) 0 0
\(490\) −3.20150 0.121592i −0.144629 0.00549295i
\(491\) 16.6934 19.8944i 0.753361 0.897821i −0.244048 0.969763i \(-0.578475\pi\)
0.997409 + 0.0719426i \(0.0229198\pi\)
\(492\) 0 0
\(493\) 9.01076 4.20179i 0.405824 0.189239i
\(494\) 17.7835 + 30.8019i 0.800117 + 1.38584i
\(495\) 0 0
\(496\) −4.01336 + 6.95135i −0.180205 + 0.312125i
\(497\) 1.23344 14.0983i 0.0553275 0.632396i
\(498\) 0 0
\(499\) 11.0477 + 1.94801i 0.494564 + 0.0872050i 0.415367 0.909654i \(-0.363653\pi\)
0.0791972 + 0.996859i \(0.474764\pi\)
\(500\) −5.15931 + 8.41096i −0.230731 + 0.376150i
\(501\) 0 0
\(502\) −15.9894 1.39889i −0.713640 0.0624354i
\(503\) −29.1890 + 7.82118i −1.30147 + 0.348729i −0.842008 0.539466i \(-0.818626\pi\)
−0.459467 + 0.888195i \(0.651960\pi\)
\(504\) 0 0
\(505\) −4.55060 + 6.00063i −0.202499 + 0.267024i
\(506\) 0.608940 1.67305i 0.0270707 0.0743761i
\(507\) 0 0
\(508\) 2.87518 0.251546i 0.127566 0.0111605i
\(509\) −22.0511 + 8.02596i −0.977399 + 0.355744i −0.780829 0.624745i \(-0.785203\pi\)
−0.196571 + 0.980490i \(0.562981\pi\)
\(510\) 0 0
\(511\) 3.49769 + 19.8364i 0.154729 + 0.877511i
\(512\) 10.9640 10.9640i 0.484544 0.484544i
\(513\) 0 0
\(514\) 9.18578i 0.405167i
\(515\) 7.92837 + 1.71056i 0.349366 + 0.0753762i
\(516\) 0 0
\(517\) 22.2083 + 10.3559i 0.976719 + 0.455452i
\(518\) −1.17499 13.4302i −0.0516262 0.590090i
\(519\) 0 0
\(520\) 37.0126 1.82639i 1.62311 0.0800925i
\(521\) 14.2319 8.21681i 0.623512 0.359985i −0.154723 0.987958i \(-0.549449\pi\)
0.778235 + 0.627973i \(0.216115\pi\)
\(522\) 0 0
\(523\) 3.78176 + 14.1137i 0.165365 + 0.617150i 0.997993 + 0.0633182i \(0.0201683\pi\)
−0.832629 + 0.553832i \(0.813165\pi\)
\(524\) −0.982891 + 0.824743i −0.0429378 + 0.0360291i
\(525\) 0 0
\(526\) −4.33208 + 24.5685i −0.188888 + 1.07124i
\(527\) −8.75850 12.5084i −0.381526 0.544876i
\(528\) 0 0
\(529\) −14.4569 17.2291i −0.628561 0.749090i
\(530\) −3.01843 + 23.9774i −0.131112 + 1.04151i
\(531\) 0 0
\(532\) 4.08464 15.2441i 0.177091 0.660914i
\(533\) −13.3070 28.5370i −0.576390 1.23607i
\(534\) 0 0
\(535\) −11.2833 + 5.95532i −0.487822 + 0.257471i
\(536\) 7.78131 + 21.3790i 0.336101 + 0.923431i
\(537\) 0 0
\(538\) 8.84309 + 6.19200i 0.381253 + 0.266956i
\(539\) 3.19963 0.137818
\(540\) 0 0
\(541\) −28.4337 −1.22246 −0.611230 0.791453i \(-0.709325\pi\)
−0.611230 + 0.791453i \(0.709325\pi\)
\(542\) −4.19460 2.93709i −0.180173 0.126159i
\(543\) 0 0
\(544\) 4.31531 + 11.8562i 0.185017 + 0.508331i
\(545\) −10.4475 + 33.8027i −0.447523 + 1.44795i
\(546\) 0 0
\(547\) 4.44356 + 9.52924i 0.189993 + 0.407441i 0.978111 0.208083i \(-0.0667224\pi\)
−0.788118 + 0.615524i \(0.788945\pi\)
\(548\) 3.64467 13.6021i 0.155693 0.581053i
\(549\) 0 0
\(550\) −6.11559 + 10.8756i −0.260770 + 0.463737i
\(551\) 14.2734 + 17.0103i 0.608066 + 0.724665i
\(552\) 0 0
\(553\) 21.6605 + 30.9344i 0.921099 + 1.31547i
\(554\) −2.48092 + 14.0700i −0.105404 + 0.597776i
\(555\) 0 0
\(556\) −6.17030 + 5.17749i −0.261679 + 0.219575i
\(557\) 4.48926 + 16.7541i 0.190216 + 0.709896i 0.993454 + 0.114237i \(0.0364423\pi\)
−0.803238 + 0.595659i \(0.796891\pi\)
\(558\) 0 0
\(559\) 6.82132 3.93829i 0.288511 0.166572i
\(560\) 6.97433 + 6.31840i 0.294719 + 0.267001i
\(561\) 0 0
\(562\) −1.44988 16.5722i −0.0611596 0.699057i
\(563\) −21.2542 9.91099i −0.895758 0.417699i −0.0804714 0.996757i \(-0.525643\pi\)
−0.815286 + 0.579058i \(0.803420\pi\)
\(564\) 0 0
\(565\) 1.25864 5.83373i 0.0529512 0.245427i
\(566\) 31.8748i 1.33980i
\(567\) 0 0
\(568\) −10.5491 + 10.5491i −0.442630 + 0.442630i
\(569\) −6.84027 38.7931i −0.286759 1.62629i −0.698934 0.715186i \(-0.746342\pi\)
0.412175 0.911105i \(-0.364769\pi\)
\(570\) 0 0
\(571\) 31.4980 11.4643i 1.31815 0.479767i 0.415285 0.909691i \(-0.363682\pi\)
0.902865 + 0.429924i \(0.141460\pi\)
\(572\) −11.2880 + 0.987576i −0.471977 + 0.0412926i
\(573\) 0 0
\(574\) 6.05032 16.6231i 0.252536 0.693836i
\(575\) −1.81862 3.06900i −0.0758415 0.127986i
\(576\) 0 0
\(577\) −21.0819 + 5.64888i −0.877651 + 0.235166i −0.669393 0.742908i \(-0.733446\pi\)
−0.208257 + 0.978074i \(0.566779\pi\)
\(578\) −9.82287 0.859390i −0.408578 0.0357459i
\(579\) 0 0
\(580\) 6.90687 1.57237i 0.286792 0.0652891i
\(581\) −13.5734 2.39335i −0.563119 0.0992930i
\(582\) 0 0
\(583\) 2.10351 24.0432i 0.0871185 0.995769i
\(584\) 10.6167 18.3886i 0.439321 0.760927i
\(585\) 0 0
\(586\) −3.88117 6.72239i −0.160330 0.277699i
\(587\) 22.1244 10.3168i 0.913173 0.425819i 0.0915170 0.995804i \(-0.470828\pi\)
0.821656 + 0.569984i \(0.193051\pi\)
\(588\) 0 0
\(589\) 21.9220 26.1256i 0.903279 1.07649i
\(590\) 0.734633 19.3428i 0.0302444 0.796332i
\(591\) 0 0
\(592\) −3.68461 + 5.26217i −0.151437 + 0.216274i
\(593\) 4.09490 + 4.09490i 0.168157 + 0.168157i 0.786169 0.618012i \(-0.212062\pi\)
−0.618012 + 0.786169i \(0.712062\pi\)
\(594\) 0 0
\(595\) −16.5012 + 6.94491i −0.676481 + 0.284714i
\(596\) 8.17827 1.44205i 0.334995 0.0590687i
\(597\) 0 0
\(598\) −1.73357 + 3.71765i −0.0708910 + 0.152026i
\(599\) −30.3866 25.4974i −1.24156 1.04180i −0.997400 0.0720615i \(-0.977042\pi\)
−0.244163 0.969734i \(-0.578513\pi\)
\(600\) 0 0
\(601\) −22.4811 8.18244i −0.917022 0.333769i −0.159969 0.987122i \(-0.551139\pi\)
−0.757053 + 0.653353i \(0.773362\pi\)
\(602\) 4.27441 + 1.14533i 0.174212 + 0.0466800i
\(603\) 0 0
\(604\) 0.806976 + 0.465908i 0.0328354 + 0.0189575i
\(605\) −5.54258 + 10.7963i −0.225338 + 0.438931i
\(606\) 0 0
\(607\) −26.5308 + 18.5771i −1.07685 + 0.754020i −0.970691 0.240329i \(-0.922745\pi\)
−0.106160 + 0.994349i \(0.533856\pi\)
\(608\) −23.0833 + 16.1631i −0.936152 + 0.655501i
\(609\) 0 0
\(610\) 2.03295 + 6.32242i 0.0823116 + 0.255987i
\(611\) −48.8923 28.2280i −1.97797 1.14198i
\(612\) 0 0
\(613\) 14.7737 + 3.95860i 0.596704 + 0.159886i 0.544515 0.838751i \(-0.316714\pi\)
0.0521885 + 0.998637i \(0.483380\pi\)
\(614\) −13.5879 4.94560i −0.548364 0.199588i
\(615\) 0 0
\(616\) −15.9279 13.3651i −0.641755 0.538497i
\(617\) −11.3221 + 24.2804i −0.455812 + 0.977492i 0.535325 + 0.844646i \(0.320189\pi\)
−0.991137 + 0.132845i \(0.957589\pi\)
\(618\) 0 0
\(619\) 18.6300 3.28497i 0.748802 0.132034i 0.213792 0.976879i \(-0.431419\pi\)
0.535011 + 0.844845i \(0.320308\pi\)
\(620\) −4.22032 10.0275i −0.169492 0.402714i
\(621\) 0 0
\(622\) 2.88598 + 2.88598i 0.115717 + 0.115717i
\(623\) −11.0512 + 15.7827i −0.442757 + 0.632322i
\(624\) 0 0
\(625\) 9.08124 + 23.2923i 0.363250 + 0.931692i
\(626\) −16.7165 + 19.9220i −0.668126 + 0.796242i
\(627\) 0 0
\(628\) 17.8520 8.32451i 0.712371 0.332184i
\(629\) −6.11042 10.5836i −0.243638 0.421994i
\(630\) 0 0
\(631\) 0.0126965 0.0219910i 0.000505440 0.000875448i −0.865773 0.500438i \(-0.833172\pi\)
0.866278 + 0.499562i \(0.166506\pi\)
\(632\) 3.46961 39.6578i 0.138014 1.57750i
\(633\) 0 0
\(634\) 17.1787 + 3.02907i 0.682253 + 0.120300i
\(635\) 3.89395 6.18947i 0.154527 0.245622i
\(636\) 0 0
\(637\) −7.34369 0.642490i −0.290968 0.0254564i
\(638\) 8.65198 2.31829i 0.342535 0.0917820i
\(639\) 0 0
\(640\) 0.286754 + 2.08659i 0.0113349 + 0.0824797i
\(641\) −9.97230 + 27.3987i −0.393882 + 1.08218i 0.571331 + 0.820720i \(0.306427\pi\)
−0.965214 + 0.261463i \(0.915795\pi\)
\(642\) 0 0
\(643\) −1.74781 + 0.152914i −0.0689270 + 0.00603033i −0.121567 0.992583i \(-0.538792\pi\)
0.0526401 + 0.998614i \(0.483236\pi\)
\(644\) 1.71037 0.622522i 0.0673979 0.0245308i
\(645\) 0 0
\(646\) 3.14539 + 17.8384i 0.123754 + 0.701842i
\(647\) −14.7341 + 14.7341i −0.579259 + 0.579259i −0.934699 0.355440i \(-0.884331\pi\)
0.355440 + 0.934699i \(0.384331\pi\)
\(648\) 0 0
\(649\) 19.3315i 0.758830i
\(650\) 16.2201 23.7333i 0.636206 0.930896i
\(651\) 0 0
\(652\) 1.97831 + 0.922501i 0.0774766 + 0.0361279i
\(653\) −0.812604 9.28810i −0.0317996 0.363471i −0.995377 0.0960426i \(-0.969382\pi\)
0.963578 0.267429i \(-0.0861741\pi\)
\(654\) 0 0
\(655\) 0.160218 + 3.24688i 0.00626023 + 0.126866i
\(656\) −7.29994 + 4.21462i −0.285015 + 0.164553i
\(657\) 0 0
\(658\) −8.20920 30.6372i −0.320028 1.19436i
\(659\) 14.0775 11.8125i 0.548383 0.460148i −0.326010 0.945366i \(-0.605704\pi\)
0.874393 + 0.485218i \(0.161260\pi\)
\(660\) 0 0
\(661\) 4.43306 25.1412i 0.172426 0.977878i −0.768647 0.639674i \(-0.779070\pi\)
0.941073 0.338204i \(-0.109819\pi\)
\(662\) 12.5159 + 17.8745i 0.486443 + 0.694712i
\(663\) 0 0
\(664\) 9.33923 + 11.1301i 0.362432 + 0.431930i
\(665\) −24.5211 31.5839i −0.950886 1.22477i
\(666\) 0 0
\(667\) −0.662829 + 2.47371i −0.0256648 + 0.0957825i
\(668\) 2.71703 + 5.82669i 0.105125 + 0.225441i
\(669\) 0 0
\(670\) 16.8615 + 5.21146i 0.651418 + 0.201336i
\(671\) −2.26847 6.23257i −0.0875733 0.240606i
\(672\) 0 0
\(673\) 3.83098 + 2.68248i 0.147673 + 0.103402i 0.645078 0.764117i \(-0.276825\pi\)
−0.497405 + 0.867518i \(0.665714\pi\)
\(674\) 11.0600 0.426017
\(675\) 0 0
\(676\) 14.6331 0.562810
\(677\) 32.1483 + 22.5105i 1.23556 + 0.865147i 0.994436 0.105347i \(-0.0335953\pi\)
0.241123 + 0.970495i \(0.422484\pi\)
\(678\) 0 0
\(679\) 18.1371 + 49.8312i 0.696038 + 1.91235i
\(680\) 18.0311 + 5.57296i 0.691462 + 0.213713i
\(681\) 0 0
\(682\) −5.81397 12.4681i −0.222628 0.477428i
\(683\) −9.77386 + 36.4765i −0.373986 + 1.39574i 0.480834 + 0.876812i \(0.340334\pi\)
−0.854820 + 0.518924i \(0.826333\pi\)
\(684\) 0 0
\(685\) −21.8799 28.1820i −0.835987 1.07678i
\(686\) 11.0866 + 13.2125i 0.423287 + 0.504454i
\(687\) 0 0
\(688\) −1.20944 1.72726i −0.0461096 0.0658513i
\(689\) −9.65582 + 54.7609i −0.367858 + 2.08622i
\(690\) 0 0
\(691\) 10.1478 8.51501i 0.386040 0.323926i −0.429028 0.903291i \(-0.641144\pi\)
0.815068 + 0.579365i \(0.196699\pi\)
\(692\) 4.68292 + 17.4769i 0.178018 + 0.664372i
\(693\) 0 0
\(694\) −10.5198 + 6.07363i −0.399327 + 0.230552i
\(695\) 1.00580 + 20.3830i 0.0381522 + 0.773170i
\(696\) 0 0
\(697\) −1.39761 15.9747i −0.0529381 0.605086i
\(698\) −15.2128 7.09386i −0.575814 0.268507i
\(699\) 0 0
\(700\) −12.5357 + 2.35731i −0.473805 + 0.0890979i
\(701\) 1.42181i 0.0537011i −0.999639 0.0268505i \(-0.991452\pi\)
0.999639 0.0268505i \(-0.00854782\pi\)
\(702\) 0 0
\(703\) 19.3001 19.3001i 0.727916 0.727916i
\(704\) 3.16755 + 17.9641i 0.119381 + 0.677046i
\(705\) 0 0
\(706\) 8.62062 3.13765i 0.324441 0.118087i
\(707\) −9.69826 + 0.848488i −0.364741 + 0.0319107i
\(708\) 0 0
\(709\) 12.4901 34.3163i 0.469077 1.28878i −0.449410 0.893325i \(-0.648366\pi\)
0.918487 0.395452i \(-0.129412\pi\)
\(710\) 1.57560 + 11.4650i 0.0591313 + 0.430274i
\(711\) 0 0
\(712\) 19.6186 5.25679i 0.735239 0.197007i
\(713\) 3.91834 + 0.342810i 0.146743 + 0.0128384i
\(714\) 0 0
\(715\) −15.2878 + 24.3000i −0.571730 + 0.908770i
\(716\) 12.4649 + 2.19790i 0.465836 + 0.0821395i
\(717\) 0 0
\(718\) −1.88008 + 21.4894i −0.0701639 + 0.801977i
\(719\) −12.9014 + 22.3459i −0.481142 + 0.833363i −0.999766 0.0216398i \(-0.993111\pi\)
0.518624 + 0.855003i \(0.326445\pi\)
\(720\) 0 0
\(721\) 5.24243 + 9.08015i 0.195238 + 0.338162i
\(722\) −18.4622 + 8.60904i −0.687090 + 0.320395i
\(723\) 0 0
\(724\) 1.17400 1.39912i 0.0436314 0.0519978i
\(725\) 7.39982 16.3507i 0.274822 0.607249i
\(726\) 0 0
\(727\) −0.926059 + 1.32255i −0.0343456 + 0.0490507i −0.835958 0.548794i \(-0.815087\pi\)
0.801612 + 0.597845i \(0.203976\pi\)
\(728\) 33.8736 + 33.8736i 1.25544 + 1.25544i
\(729\) 0 0
\(730\) −6.38948 15.1814i −0.236485 0.561890i
\(731\) 3.95045 0.696570i 0.146112 0.0257636i
\(732\) 0 0
\(733\) −5.62244 + 12.0574i −0.207669 + 0.445349i −0.982362 0.186990i \(-0.940127\pi\)
0.774692 + 0.632338i \(0.217905\pi\)
\(734\) −21.0132 17.6322i −0.775613 0.650816i
\(735\) 0 0
\(736\) −3.05398 1.11156i −0.112571 0.0409725i
\(737\) −17.0249 4.56182i −0.627122 0.168037i
\(738\) 0 0
\(739\) 30.9063 + 17.8437i 1.13691 + 0.656393i 0.945663 0.325150i \(-0.105415\pi\)
0.191243 + 0.981543i \(0.438748\pi\)
\(740\) −2.66530 8.28902i −0.0979784 0.304711i
\(741\) 0 0
\(742\) −25.5905 + 17.9187i −0.939457 + 0.657815i
\(743\) 28.8465 20.1985i 1.05828 0.741012i 0.0912848 0.995825i \(-0.470903\pi\)
0.966990 + 0.254813i \(0.0820138\pi\)
\(744\) 0 0
\(745\) 9.60936 18.7179i 0.352060 0.685769i
\(746\) −4.37382 2.52523i −0.160137 0.0924551i
\(747\) 0 0
\(748\) −5.57411 1.49358i −0.203810 0.0546106i
\(749\) −15.4983 5.64093i −0.566296 0.206115i
\(750\) 0 0
\(751\) 19.0262 + 15.9649i 0.694275 + 0.582566i 0.920138 0.391593i \(-0.128076\pi\)
−0.225864 + 0.974159i \(0.572520\pi\)
\(752\) −6.38726 + 13.6975i −0.232919 + 0.499497i
\(753\) 0 0
\(754\) −20.3233 + 3.58354i −0.740130 + 0.130505i
\(755\) 2.17601 0.915826i 0.0791930 0.0333303i
\(756\) 0 0
\(757\) 17.8009 + 17.8009i 0.646986 + 0.646986i 0.952263 0.305278i \(-0.0987493\pi\)
−0.305278 + 0.952263i \(0.598749\pi\)
\(758\) −15.3401 + 21.9080i −0.557178 + 0.795733i
\(759\) 0 0
\(760\) −1.59972 + 42.1206i −0.0580281 + 1.52788i
\(761\) 31.3105 37.3144i 1.13500 1.35265i 0.207765 0.978179i \(-0.433381\pi\)
0.927240 0.374467i \(-0.122174\pi\)
\(762\) 0 0
\(763\) −41.4512 + 19.3290i −1.50063 + 0.699757i
\(764\) 10.2888 + 17.8207i 0.372236 + 0.644731i
\(765\) 0 0
\(766\) 6.51352 11.2818i 0.235343 0.407626i
\(767\) 3.88180 44.3691i 0.140164 1.60208i
\(768\) 0 0
\(769\) −43.1365 7.60612i −1.55554 0.274284i −0.671254 0.741227i \(-0.734244\pi\)
−0.884287 + 0.466944i \(0.845355\pi\)
\(770\) −15.7268 + 3.58026i −0.566756 + 0.129024i
\(771\) 0 0
\(772\) 0.273968 + 0.0239691i 0.00986034 + 0.000862668i
\(773\) 22.0592 5.91076i 0.793416 0.212595i 0.160725 0.986999i \(-0.448617\pi\)
0.632691 + 0.774404i \(0.281950\pi\)
\(774\) 0 0
\(775\) −26.7045 6.83173i −0.959252 0.245403i
\(776\) 19.1194 52.5302i 0.686347 1.88572i
\(777\) 0 0
\(778\) 9.39502 0.821958i 0.336828 0.0294686i
\(779\) 33.6549 12.2494i 1.20581 0.438879i
\(780\) 0 0
\(781\) −2.00697 11.3821i −0.0718150 0.407283i
\(782\) −1.47719 + 1.47719i −0.0528241 + 0.0528241i
\(783\) 0 0
\(784\) 1.97345i 0.0704805i
\(785\) 10.5251 48.7837i 0.375659 1.74116i
\(786\) 0 0
\(787\) −15.6093 7.