Properties

Label 576.2.bd.a.37.5
Level $576$
Weight $2$
Character 576.37
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 37.5
Character \(\chi\) \(=\) 576.37
Dual form 576.2.bd.a.109.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809383 + 1.15970i) q^{2} +(-0.689800 + 1.87728i) q^{4} +(0.159018 - 0.799435i) q^{5} +(-0.742008 + 1.79137i) q^{7} +(-2.73539 + 0.719478i) q^{8} +O(q^{10})\) \(q+(0.809383 + 1.15970i) q^{2} +(-0.689800 + 1.87728i) q^{4} +(0.159018 - 0.799435i) q^{5} +(-0.742008 + 1.79137i) q^{7} +(-2.73539 + 0.719478i) q^{8} +(1.05581 - 0.462637i) q^{10} +(-1.29226 + 0.863458i) q^{11} +(1.07211 + 5.38985i) q^{13} +(-2.67801 + 0.589395i) q^{14} +(-3.04835 - 2.58989i) q^{16} +(-1.43298 + 1.43298i) q^{17} +(0.0883441 - 0.0175727i) q^{19} +(1.39107 + 0.849970i) q^{20} +(-2.04728 - 0.799759i) q^{22} +(-3.31519 + 1.37320i) q^{23} +(4.00559 + 1.65917i) q^{25} +(-5.38285 + 5.60577i) q^{26} +(-2.85106 - 2.62864i) q^{28} +(1.04042 + 0.695186i) q^{29} +2.58743i q^{31} +(0.536209 - 5.63138i) q^{32} +(-2.82165 - 0.501994i) q^{34} +(1.31409 + 0.878046i) q^{35} +(1.60572 + 0.319397i) q^{37} +(0.0918832 + 0.0882294i) q^{38} +(0.140201 + 2.30118i) q^{40} +(-0.605183 + 0.250675i) q^{41} +(-5.04263 - 7.54683i) q^{43} +(-0.729554 - 3.02154i) q^{44} +(-4.27576 - 2.73318i) q^{46} +(3.86580 - 3.86580i) q^{47} +(2.29133 + 2.29133i) q^{49} +(1.31792 + 5.98817i) q^{50} +(-10.8578 - 1.70527i) q^{52} +(8.70867 - 5.81895i) q^{53} +(0.484787 + 1.17038i) q^{55} +(0.740832 - 5.43394i) q^{56} +(0.0358915 + 1.76924i) q^{58} +(-1.17041 + 5.88407i) q^{59} +(3.52821 - 5.28034i) q^{61} +(-3.00064 + 2.09422i) q^{62} +(6.96470 - 3.93610i) q^{64} +4.47932 q^{65} +(3.15404 - 4.72036i) q^{67} +(-1.70163 - 3.67856i) q^{68} +(0.0453323 + 2.23462i) q^{70} +(-5.01419 + 12.1053i) q^{71} +(-1.75399 - 4.23450i) q^{73} +(0.929237 + 2.12066i) q^{74} +(-0.0279508 + 0.177968i) q^{76} +(-0.587905 - 2.95560i) q^{77} +(7.46021 + 7.46021i) q^{79} +(-2.55519 + 2.02512i) q^{80} +(-0.780532 - 0.498937i) q^{82} +(2.65306 - 0.527725i) q^{83} +(0.917704 + 1.37344i) q^{85} +(4.67063 - 11.9562i) q^{86} +(2.91358 - 3.29164i) q^{88} +(-7.09322 - 2.93811i) q^{89} +(-10.4507 - 2.07877i) q^{91} +(-0.291057 - 7.17078i) q^{92} +(7.61208 + 1.35425i) q^{94} -0.0734197i q^{95} -11.4524i q^{97} +(-0.802689 + 4.51182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809383 + 1.15970i 0.572320 + 0.820030i
\(3\) 0 0
\(4\) −0.689800 + 1.87728i −0.344900 + 0.938640i
\(5\) 0.159018 0.799435i 0.0711148 0.357518i −0.928800 0.370582i \(-0.879158\pi\)
0.999915 + 0.0130634i \(0.00415834\pi\)
\(6\) 0 0
\(7\) −0.742008 + 1.79137i −0.280453 + 0.677073i −0.999846 0.0175299i \(-0.994420\pi\)
0.719394 + 0.694603i \(0.244420\pi\)
\(8\) −2.73539 + 0.719478i −0.967106 + 0.254374i
\(9\) 0 0
\(10\) 1.05581 0.462637i 0.333876 0.146299i
\(11\) −1.29226 + 0.863458i −0.389630 + 0.260342i −0.734920 0.678154i \(-0.762780\pi\)
0.345290 + 0.938496i \(0.387780\pi\)
\(12\) 0 0
\(13\) 1.07211 + 5.38985i 0.297349 + 1.49487i 0.783716 + 0.621119i \(0.213322\pi\)
−0.486367 + 0.873755i \(0.661678\pi\)
\(14\) −2.67801 + 0.589395i −0.715729 + 0.157522i
\(15\) 0 0
\(16\) −3.04835 2.58989i −0.762088 0.647473i
\(17\) −1.43298 + 1.43298i −0.347548 + 0.347548i −0.859195 0.511648i \(-0.829035\pi\)
0.511648 + 0.859195i \(0.329035\pi\)
\(18\) 0 0
\(19\) 0.0883441 0.0175727i 0.0202675 0.00403146i −0.184946 0.982749i \(-0.559211\pi\)
0.205214 + 0.978717i \(0.434211\pi\)
\(20\) 1.39107 + 0.849970i 0.311053 + 0.190059i
\(21\) 0 0
\(22\) −2.04728 0.799759i −0.436481 0.170509i
\(23\) −3.31519 + 1.37320i −0.691266 + 0.286332i −0.700527 0.713625i \(-0.747052\pi\)
0.00926165 + 0.999957i \(0.497052\pi\)
\(24\) 0 0
\(25\) 4.00559 + 1.65917i 0.801118 + 0.331834i
\(26\) −5.38285 + 5.60577i −1.05566 + 1.09938i
\(27\) 0 0
\(28\) −2.85106 2.62864i −0.538799 0.496766i
\(29\) 1.04042 + 0.695186i 0.193201 + 0.129093i 0.648409 0.761293i \(-0.275435\pi\)
−0.455207 + 0.890385i \(0.650435\pi\)
\(30\) 0 0
\(31\) 2.58743i 0.464717i 0.972630 + 0.232358i \(0.0746442\pi\)
−0.972630 + 0.232358i \(0.925356\pi\)
\(32\) 0.536209 5.63138i 0.0947893 0.995497i
\(33\) 0 0
\(34\) −2.82165 0.501994i −0.483908 0.0860912i
\(35\) 1.31409 + 0.878046i 0.222122 + 0.148417i
\(36\) 0 0
\(37\) 1.60572 + 0.319397i 0.263979 + 0.0525086i 0.325305 0.945609i \(-0.394533\pi\)
−0.0613263 + 0.998118i \(0.519533\pi\)
\(38\) 0.0918832 + 0.0882294i 0.0149054 + 0.0143127i
\(39\) 0 0
\(40\) 0.140201 + 2.30118i 0.0221677 + 0.363848i
\(41\) −0.605183 + 0.250675i −0.0945137 + 0.0391488i −0.429439 0.903096i \(-0.641289\pi\)
0.334926 + 0.942245i \(0.391289\pi\)
\(42\) 0 0
\(43\) −5.04263 7.54683i −0.768994 1.15088i −0.984672 0.174416i \(-0.944196\pi\)
0.215678 0.976465i \(-0.430804\pi\)
\(44\) −0.729554 3.02154i −0.109984 0.455514i
\(45\) 0 0
\(46\) −4.27576 2.73318i −0.630426 0.402986i
\(47\) 3.86580 3.86580i 0.563885 0.563885i −0.366524 0.930409i \(-0.619452\pi\)
0.930409 + 0.366524i \(0.119452\pi\)
\(48\) 0 0
\(49\) 2.29133 + 2.29133i 0.327333 + 0.327333i
\(50\) 1.31792 + 5.98817i 0.186382 + 0.846856i
\(51\) 0 0
\(52\) −10.8578 1.70527i −1.50570 0.236478i
\(53\) 8.70867 5.81895i 1.19623 0.799294i 0.212186 0.977229i \(-0.431942\pi\)
0.984042 + 0.177935i \(0.0569417\pi\)
\(54\) 0 0
\(55\) 0.484787 + 1.17038i 0.0653687 + 0.157814i
\(56\) 0.740832 5.43394i 0.0989979 0.726141i
\(57\) 0 0
\(58\) 0.0358915 + 1.76924i 0.00471278 + 0.232313i
\(59\) −1.17041 + 5.88407i −0.152375 + 0.766040i 0.826716 + 0.562619i \(0.190206\pi\)
−0.979091 + 0.203421i \(0.934794\pi\)
\(60\) 0 0
\(61\) 3.52821 5.28034i 0.451741 0.676078i −0.533782 0.845622i \(-0.679230\pi\)
0.985523 + 0.169544i \(0.0542296\pi\)
\(62\) −3.00064 + 2.09422i −0.381082 + 0.265967i
\(63\) 0 0
\(64\) 6.96470 3.93610i 0.870588 0.492013i
\(65\) 4.47932 0.555591
\(66\) 0 0
\(67\) 3.15404 4.72036i 0.385328 0.576684i −0.587208 0.809436i \(-0.699773\pi\)
0.972536 + 0.232752i \(0.0747731\pi\)
\(68\) −1.70163 3.67856i −0.206353 0.446091i
\(69\) 0 0
\(70\) 0.0453323 + 2.23462i 0.00541824 + 0.267088i
\(71\) −5.01419 + 12.1053i −0.595075 + 1.43664i 0.283471 + 0.958981i \(0.408514\pi\)
−0.878546 + 0.477657i \(0.841486\pi\)
\(72\) 0 0
\(73\) −1.75399 4.23450i −0.205289 0.495611i 0.787381 0.616466i \(-0.211436\pi\)
−0.992670 + 0.120855i \(0.961436\pi\)
\(74\) 0.929237 + 2.12066i 0.108022 + 0.246522i
\(75\) 0 0
\(76\) −0.0279508 + 0.177968i −0.00320617 + 0.0204143i
\(77\) −0.587905 2.95560i −0.0669979 0.336821i
\(78\) 0 0
\(79\) 7.46021 + 7.46021i 0.839340 + 0.839340i 0.988772 0.149432i \(-0.0477446\pi\)
−0.149432 + 0.988772i \(0.547745\pi\)
\(80\) −2.55519 + 2.02512i −0.285679 + 0.226416i
\(81\) 0 0
\(82\) −0.780532 0.498937i −0.0861953 0.0550984i
\(83\) 2.65306 0.527725i 0.291211 0.0579254i −0.0473232 0.998880i \(-0.515069\pi\)
0.338534 + 0.940954i \(0.390069\pi\)
\(84\) 0 0
\(85\) 0.917704 + 1.37344i 0.0995389 + 0.148971i
\(86\) 4.67063 11.9562i 0.503647 1.28927i
\(87\) 0 0
\(88\) 2.91358 3.29164i 0.310589 0.350890i
\(89\) −7.09322 2.93811i −0.751880 0.311439i −0.0263716 0.999652i \(-0.508395\pi\)
−0.725508 + 0.688213i \(0.758395\pi\)
\(90\) 0 0
\(91\) −10.4507 2.07877i −1.09553 0.217915i
\(92\) −0.291057 7.17078i −0.0303448 0.747605i
\(93\) 0 0
\(94\) 7.61208 + 1.35425i 0.785126 + 0.139680i
\(95\) 0.0734197i 0.00753271i
\(96\) 0 0
\(97\) 11.4524i 1.16281i −0.813614 0.581406i \(-0.802503\pi\)
0.813614 0.581406i \(-0.197497\pi\)
\(98\) −0.802689 + 4.51182i −0.0810838 + 0.455762i
\(99\) 0 0
\(100\) −5.87778 + 6.37511i −0.587778 + 0.637511i
\(101\) 11.4055 + 2.26869i 1.13489 + 0.225743i 0.726566 0.687097i \(-0.241115\pi\)
0.408319 + 0.912839i \(0.366115\pi\)
\(102\) 0 0
\(103\) 12.3890 + 5.13170i 1.22073 + 0.505641i 0.897640 0.440729i \(-0.145280\pi\)
0.323086 + 0.946370i \(0.395280\pi\)
\(104\) −6.81050 13.9720i −0.667825 1.37006i
\(105\) 0 0
\(106\) 13.7969 + 5.38968i 1.34007 + 0.523492i
\(107\) −5.26269 7.87617i −0.508764 0.761419i 0.484808 0.874620i \(-0.338889\pi\)
−0.993572 + 0.113202i \(0.963889\pi\)
\(108\) 0 0
\(109\) 16.8083 3.34339i 1.60995 0.320238i 0.693519 0.720438i \(-0.256059\pi\)
0.916428 + 0.400200i \(0.131059\pi\)
\(110\) −0.964909 + 1.50949i −0.0920004 + 0.143924i
\(111\) 0 0
\(112\) 6.90135 3.53900i 0.652116 0.334404i
\(113\) 9.98074 + 9.98074i 0.938909 + 0.938909i 0.998238 0.0593295i \(-0.0188963\pi\)
−0.0593295 + 0.998238i \(0.518896\pi\)
\(114\) 0 0
\(115\) 0.570609 + 2.86865i 0.0532096 + 0.267503i
\(116\) −2.02274 + 1.47362i −0.187807 + 0.136822i
\(117\) 0 0
\(118\) −7.77105 + 3.40513i −0.715383 + 0.313468i
\(119\) −1.50371 3.63027i −0.137844 0.332786i
\(120\) 0 0
\(121\) −3.28515 + 7.93106i −0.298650 + 0.721005i
\(122\) 8.97927 0.182156i 0.812945 0.0164917i
\(123\) 0 0
\(124\) −4.85733 1.78481i −0.436201 0.160281i
\(125\) 4.22757 6.32701i 0.378126 0.565905i
\(126\) 0 0
\(127\) −9.01235 −0.799717 −0.399858 0.916577i \(-0.630941\pi\)
−0.399858 + 0.916577i \(0.630941\pi\)
\(128\) 10.2018 + 4.89114i 0.901720 + 0.432320i
\(129\) 0 0
\(130\) 3.62548 + 5.19465i 0.317976 + 0.455601i
\(131\) −4.77693 + 7.14918i −0.417362 + 0.624627i −0.979267 0.202575i \(-0.935069\pi\)
0.561904 + 0.827202i \(0.310069\pi\)
\(132\) 0 0
\(133\) −0.0340728 + 0.171296i −0.00295449 + 0.0148532i
\(134\) 8.02702 0.162839i 0.693429 0.0140671i
\(135\) 0 0
\(136\) 2.88875 4.95074i 0.247709 0.424523i
\(137\) −1.16308 2.80792i −0.0993685 0.239897i 0.866376 0.499393i \(-0.166444\pi\)
−0.965744 + 0.259496i \(0.916444\pi\)
\(138\) 0 0
\(139\) 6.85100 4.57769i 0.581094 0.388275i −0.230000 0.973191i \(-0.573873\pi\)
0.811094 + 0.584916i \(0.198873\pi\)
\(140\) −2.55480 + 1.86124i −0.215920 + 0.157303i
\(141\) 0 0
\(142\) −18.0969 + 3.98289i −1.51866 + 0.334237i
\(143\) −6.03934 6.03934i −0.505035 0.505035i
\(144\) 0 0
\(145\) 0.721201 0.721201i 0.0598925 0.0598925i
\(146\) 3.49109 5.46142i 0.288925 0.451991i
\(147\) 0 0
\(148\) −1.70722 + 2.79406i −0.140333 + 0.229671i
\(149\) 8.41009 + 12.5866i 0.688982 + 1.03113i 0.996819 + 0.0796950i \(0.0253946\pi\)
−0.307838 + 0.951439i \(0.599605\pi\)
\(150\) 0 0
\(151\) −15.1739 + 6.28523i −1.23483 + 0.511485i −0.902096 0.431534i \(-0.857972\pi\)
−0.332738 + 0.943019i \(0.607972\pi\)
\(152\) −0.229012 + 0.111630i −0.0185753 + 0.00905438i
\(153\) 0 0
\(154\) 2.95176 3.07400i 0.237860 0.247710i
\(155\) 2.06848 + 0.411447i 0.166145 + 0.0330482i
\(156\) 0 0
\(157\) −3.65930 2.44507i −0.292044 0.195138i 0.400914 0.916116i \(-0.368693\pi\)
−0.692958 + 0.720978i \(0.743693\pi\)
\(158\) −2.61343 + 14.6898i −0.207913 + 1.16865i
\(159\) 0 0
\(160\) −4.41666 1.32415i −0.349168 0.104684i
\(161\) 6.95765i 0.548340i
\(162\) 0 0
\(163\) 3.89914 + 2.60532i 0.305404 + 0.204065i 0.698823 0.715295i \(-0.253708\pi\)
−0.393418 + 0.919360i \(0.628708\pi\)
\(164\) −0.0531320 1.30901i −0.00414891 0.102217i
\(165\) 0 0
\(166\) 2.75934 + 2.64961i 0.214166 + 0.205650i
\(167\) −9.51475 3.94114i −0.736274 0.304975i −0.0171464 0.999853i \(-0.505458\pi\)
−0.719127 + 0.694878i \(0.755458\pi\)
\(168\) 0 0
\(169\) −15.8906 + 6.58210i −1.22235 + 0.506315i
\(170\) −0.850003 + 2.17590i −0.0651923 + 0.166884i
\(171\) 0 0
\(172\) 17.6459 4.26063i 1.34549 0.324870i
\(173\) 10.2124 2.03137i 0.776434 0.154442i 0.209060 0.977903i \(-0.432960\pi\)
0.567374 + 0.823460i \(0.307960\pi\)
\(174\) 0 0
\(175\) −5.94436 + 5.94436i −0.449351 + 0.449351i
\(176\) 6.17551 + 0.714679i 0.465497 + 0.0538710i
\(177\) 0 0
\(178\) −2.33381 10.6040i −0.174927 0.794807i
\(179\) −4.62243 23.2385i −0.345497 1.73693i −0.628500 0.777810i \(-0.716331\pi\)
0.283003 0.959119i \(-0.408669\pi\)
\(180\) 0 0
\(181\) −6.85149 + 4.57802i −0.509267 + 0.340282i −0.783510 0.621379i \(-0.786573\pi\)
0.274243 + 0.961660i \(0.411573\pi\)
\(182\) −6.04786 13.8022i −0.448298 1.02309i
\(183\) 0 0
\(184\) 8.08036 6.14144i 0.595692 0.452753i
\(185\) 0.510675 1.23288i 0.0375456 0.0906431i
\(186\) 0 0
\(187\) 0.614458 3.08909i 0.0449336 0.225896i
\(188\) 4.59056 + 9.92382i 0.334801 + 0.723769i
\(189\) 0 0
\(190\) 0.0851447 0.0594247i 0.00617705 0.00431112i
\(191\) 2.15250 0.155750 0.0778748 0.996963i \(-0.475187\pi\)
0.0778748 + 0.996963i \(0.475187\pi\)
\(192\) 0 0
\(193\) −5.53246 −0.398236 −0.199118 0.979976i \(-0.563808\pi\)
−0.199118 + 0.979976i \(0.563808\pi\)
\(194\) 13.2813 9.26935i 0.953541 0.665500i
\(195\) 0 0
\(196\) −5.88203 + 2.72091i −0.420145 + 0.194351i
\(197\) −2.86767 + 14.4167i −0.204313 + 1.02715i 0.733415 + 0.679781i \(0.237925\pi\)
−0.937728 + 0.347370i \(0.887075\pi\)
\(198\) 0 0
\(199\) 0.633559 1.52955i 0.0449118 0.108427i −0.899832 0.436237i \(-0.856311\pi\)
0.944743 + 0.327811i \(0.106311\pi\)
\(200\) −12.1506 1.65654i −0.859175 0.117135i
\(201\) 0 0
\(202\) 6.60039 + 15.0631i 0.464402 + 1.05984i
\(203\) −2.01733 + 1.34794i −0.141589 + 0.0946068i
\(204\) 0 0
\(205\) 0.104164 + 0.523666i 0.00727511 + 0.0365744i
\(206\) 4.07623 + 18.5210i 0.284005 + 1.29042i
\(207\) 0 0
\(208\) 10.6910 19.2068i 0.741285 1.33175i
\(209\) −0.0989898 + 0.0989898i −0.00684727 + 0.00684727i
\(210\) 0 0
\(211\) 8.05837 1.60291i 0.554761 0.110349i 0.0902547 0.995919i \(-0.471232\pi\)
0.464506 + 0.885570i \(0.346232\pi\)
\(212\) 4.91655 + 20.3625i 0.337670 + 1.39850i
\(213\) 0 0
\(214\) 4.87445 12.4780i 0.333211 0.852977i
\(215\) −6.83507 + 2.83118i −0.466148 + 0.193085i
\(216\) 0 0
\(217\) −4.63504 1.91990i −0.314647 0.130331i
\(218\) 17.4817 + 16.7865i 1.18401 + 1.13693i
\(219\) 0 0
\(220\) −2.53153 + 0.102753i −0.170676 + 0.00692763i
\(221\) −9.25983 6.18722i −0.622883 0.416197i
\(222\) 0 0
\(223\) 1.76595i 0.118256i 0.998250 + 0.0591282i \(0.0188321\pi\)
−0.998250 + 0.0591282i \(0.981168\pi\)
\(224\) 9.69000 + 5.13908i 0.647440 + 0.343369i
\(225\) 0 0
\(226\) −3.49641 + 19.6529i −0.232578 + 1.30729i
\(227\) 6.55957 + 4.38296i 0.435374 + 0.290908i 0.753879 0.657014i \(-0.228181\pi\)
−0.318505 + 0.947921i \(0.603181\pi\)
\(228\) 0 0
\(229\) 22.3445 + 4.44460i 1.47657 + 0.293707i 0.866713 0.498807i \(-0.166228\pi\)
0.609853 + 0.792515i \(0.291228\pi\)
\(230\) −2.86492 + 2.98357i −0.188907 + 0.196731i
\(231\) 0 0
\(232\) −3.34612 1.15305i −0.219684 0.0757011i
\(233\) −3.96025 + 1.64039i −0.259445 + 0.107466i −0.508615 0.860994i \(-0.669842\pi\)
0.249170 + 0.968460i \(0.419842\pi\)
\(234\) 0 0
\(235\) −2.47573 3.70519i −0.161499 0.241700i
\(236\) −10.2387 6.25602i −0.666482 0.407232i
\(237\) 0 0
\(238\) 2.99294 4.68212i 0.194003 0.303497i
\(239\) 2.96983 2.96983i 0.192103 0.192103i −0.604501 0.796604i \(-0.706628\pi\)
0.796604 + 0.604501i \(0.206628\pi\)
\(240\) 0 0
\(241\) −16.9923 16.9923i −1.09457 1.09457i −0.995034 0.0995381i \(-0.968263\pi\)
−0.0995381 0.995034i \(-0.531737\pi\)
\(242\) −11.8566 + 2.60948i −0.762170 + 0.167744i
\(243\) 0 0
\(244\) 7.47891 + 10.2658i 0.478788 + 0.657201i
\(245\) 2.19613 1.46741i 0.140306 0.0937493i
\(246\) 0 0
\(247\) 0.189429 + 0.457321i 0.0120531 + 0.0290986i
\(248\) −1.86160 7.07763i −0.118212 0.449430i
\(249\) 0 0
\(250\) 10.7592 0.218264i 0.680468 0.0138042i
\(251\) 1.88276 9.46528i 0.118839 0.597443i −0.874767 0.484543i \(-0.838986\pi\)
0.993606 0.112900i \(-0.0360141\pi\)
\(252\) 0 0
\(253\) 3.09838 4.63705i 0.194793 0.291529i
\(254\) −7.29444 10.4516i −0.457694 0.655792i
\(255\) 0 0
\(256\) 2.58492 + 15.7898i 0.161557 + 0.986863i
\(257\) 4.05808 0.253136 0.126568 0.991958i \(-0.459604\pi\)
0.126568 + 0.991958i \(0.459604\pi\)
\(258\) 0 0
\(259\) −1.76361 + 2.63944i −0.109586 + 0.164007i
\(260\) −3.08983 + 8.40893i −0.191623 + 0.521499i
\(261\) 0 0
\(262\) −12.1573 + 0.246626i −0.751078 + 0.0152366i
\(263\) −8.26702 + 19.9584i −0.509766 + 1.23068i 0.434252 + 0.900791i \(0.357013\pi\)
−0.944018 + 0.329893i \(0.892987\pi\)
\(264\) 0 0
\(265\) −3.26704 7.88734i −0.200693 0.484515i
\(266\) −0.226229 + 0.0991296i −0.0138710 + 0.00607802i
\(267\) 0 0
\(268\) 6.68577 + 9.17712i 0.408399 + 0.560582i
\(269\) −4.65173 23.3858i −0.283621 1.42586i −0.815362 0.578952i \(-0.803462\pi\)
0.531741 0.846907i \(-0.321538\pi\)
\(270\) 0 0
\(271\) −5.40955 5.40955i −0.328607 0.328607i 0.523450 0.852057i \(-0.324645\pi\)
−0.852057 + 0.523450i \(0.824645\pi\)
\(272\) 8.07947 0.656964i 0.489890 0.0398343i
\(273\) 0 0
\(274\) 2.31496 3.62150i 0.139852 0.218783i
\(275\) −6.60887 + 1.31458i −0.398530 + 0.0792725i
\(276\) 0 0
\(277\) −10.2748 15.3773i −0.617351 0.923931i −1.00000 3.72366e-5i \(-0.999988\pi\)
0.382649 0.923894i \(-0.375012\pi\)
\(278\) 10.8538 + 4.23999i 0.650969 + 0.254297i
\(279\) 0 0
\(280\) −4.22628 1.45634i −0.252568 0.0870329i
\(281\) −22.5624 9.34566i −1.34596 0.557515i −0.410796 0.911727i \(-0.634749\pi\)
−0.935165 + 0.354212i \(0.884749\pi\)
\(282\) 0 0
\(283\) −30.7342 6.11341i −1.82696 0.363405i −0.842455 0.538767i \(-0.818890\pi\)
−0.984504 + 0.175362i \(0.943890\pi\)
\(284\) −19.2663 17.7633i −1.14324 1.05406i
\(285\) 0 0
\(286\) 2.11567 11.8919i 0.125102 0.703186i
\(287\) 1.27011i 0.0749720i
\(288\) 0 0
\(289\) 12.8932i 0.758421i
\(290\) 1.42010 + 0.252648i 0.0833914 + 0.0148360i
\(291\) 0 0
\(292\) 9.15924 0.371768i 0.536004 0.0217561i
\(293\) −11.5609 2.29960i −0.675394 0.134344i −0.154535 0.987987i \(-0.549388\pi\)
−0.520858 + 0.853643i \(0.674388\pi\)
\(294\) 0 0
\(295\) 4.51781 + 1.87134i 0.263037 + 0.108954i
\(296\) −4.62207 + 0.281603i −0.268652 + 0.0163679i
\(297\) 0 0
\(298\) −7.78967 + 19.9405i −0.451243 + 1.15512i
\(299\) −10.9556 16.3962i −0.633577 0.948215i
\(300\) 0 0
\(301\) 17.2608 3.43339i 0.994897 0.197897i
\(302\) −19.5705 12.5100i −1.12615 0.719868i
\(303\) 0 0
\(304\) −0.314815 0.175234i −0.0180559 0.0100503i
\(305\) −3.66024 3.66024i −0.209585 0.209585i
\(306\) 0 0
\(307\) −3.01807 15.1728i −0.172250 0.865960i −0.966164 0.257929i \(-0.916960\pi\)
0.793914 0.608031i \(-0.208040\pi\)
\(308\) 5.95401 + 0.935108i 0.339261 + 0.0532827i
\(309\) 0 0
\(310\) 1.19704 + 2.73184i 0.0679874 + 0.155158i
\(311\) 11.7272 + 28.3120i 0.664989 + 1.60543i 0.789884 + 0.613256i \(0.210141\pi\)
−0.124895 + 0.992170i \(0.539859\pi\)
\(312\) 0 0
\(313\) −6.18242 + 14.9257i −0.349451 + 0.843649i 0.647234 + 0.762291i \(0.275926\pi\)
−0.996685 + 0.0813577i \(0.974074\pi\)
\(314\) −0.126235 6.22268i −0.00712387 0.351166i
\(315\) 0 0
\(316\) −19.1510 + 8.85885i −1.07733 + 0.498349i
\(317\) −15.9809 + 23.9172i −0.897579 + 1.34332i 0.0413265 + 0.999146i \(0.486842\pi\)
−0.938905 + 0.344176i \(0.888158\pi\)
\(318\) 0 0
\(319\) −1.94475 −0.108885
\(320\) −2.03915 6.19374i −0.113992 0.346241i
\(321\) 0 0
\(322\) 8.06878 5.63140i 0.449655 0.313826i
\(323\) −0.101414 + 0.151776i −0.00564281 + 0.00844506i
\(324\) 0 0
\(325\) −4.64824 + 23.3683i −0.257838 + 1.29624i
\(326\) 0.134509 + 6.63053i 0.00744977 + 0.367231i
\(327\) 0 0
\(328\) 1.47506 1.12111i 0.0814463 0.0619029i
\(329\) 4.05661 + 9.79352i 0.223648 + 0.539934i
\(330\) 0 0
\(331\) 17.2884 11.5517i 0.950256 0.634941i 0.0191998 0.999816i \(-0.493888\pi\)
0.931057 + 0.364875i \(0.118888\pi\)
\(332\) −0.839388 + 5.34455i −0.0460674 + 0.293320i
\(333\) 0 0
\(334\) −3.13054 14.2241i −0.171296 0.778310i
\(335\) −3.27207 3.27207i −0.178772 0.178772i
\(336\) 0 0
\(337\) −0.552793 + 0.552793i −0.0301125 + 0.0301125i −0.722003 0.691890i \(-0.756778\pi\)
0.691890 + 0.722003i \(0.256778\pi\)
\(338\) −20.4948 13.1008i −1.11477 0.712592i
\(339\) 0 0
\(340\) −3.21136 + 0.775387i −0.174161 + 0.0420513i
\(341\) −2.23414 3.34362i −0.120985 0.181067i
\(342\) 0 0
\(343\) −18.3444 + 7.59848i −0.990502 + 0.410280i
\(344\) 19.2233 + 17.0155i 1.03645 + 0.917412i
\(345\) 0 0
\(346\) 10.6215 + 10.1991i 0.571016 + 0.548309i
\(347\) −20.3020 4.03831i −1.08987 0.216788i −0.382726 0.923862i \(-0.625015\pi\)
−0.707140 + 0.707074i \(0.750015\pi\)
\(348\) 0 0
\(349\) −24.9728 16.6863i −1.33676 0.893195i −0.337913 0.941177i \(-0.609721\pi\)
−0.998848 + 0.0479825i \(0.984721\pi\)
\(350\) −11.7049 2.08240i −0.625654 0.111309i
\(351\) 0 0
\(352\) 4.16954 + 7.74018i 0.222237 + 0.412553i
\(353\) 14.1087i 0.750928i −0.926837 0.375464i \(-0.877483\pi\)
0.926837 0.375464i \(-0.122517\pi\)
\(354\) 0 0
\(355\) 8.88008 + 5.93348i 0.471306 + 0.314916i
\(356\) 10.4085 11.2892i 0.551652 0.598329i
\(357\) 0 0
\(358\) 23.2084 24.1695i 1.22660 1.27740i
\(359\) 21.9299 + 9.08367i 1.15742 + 0.479418i 0.877014 0.480465i \(-0.159532\pi\)
0.280403 + 0.959882i \(0.409532\pi\)
\(360\) 0 0
\(361\) −17.5462 + 7.26788i −0.923485 + 0.382520i
\(362\) −10.8546 4.24029i −0.570505 0.222865i
\(363\) 0 0
\(364\) 11.1113 18.1849i 0.582392 0.953150i
\(365\) −3.66412 + 0.728839i −0.191789 + 0.0381492i
\(366\) 0 0
\(367\) 11.6037 11.6037i 0.605711 0.605711i −0.336111 0.941822i \(-0.609112\pi\)
0.941822 + 0.336111i \(0.109112\pi\)
\(368\) 13.6623 + 4.40000i 0.712198 + 0.229366i
\(369\) 0 0
\(370\) 1.84310 0.405642i 0.0958181 0.0210883i
\(371\) 3.96196 + 19.9181i 0.205695 + 1.03410i
\(372\) 0 0
\(373\) 12.5475 8.38398i 0.649685 0.434106i −0.186573 0.982441i \(-0.559738\pi\)
0.836259 + 0.548335i \(0.184738\pi\)
\(374\) 4.07974 1.78767i 0.210958 0.0924381i
\(375\) 0 0
\(376\) −7.79311 + 13.3558i −0.401899 + 0.688774i
\(377\) −2.63150 + 6.35301i −0.135529 + 0.327197i
\(378\) 0 0
\(379\) −0.563697 + 2.83390i −0.0289552 + 0.145567i −0.992559 0.121769i \(-0.961143\pi\)
0.963603 + 0.267336i \(0.0861434\pi\)
\(380\) 0.137829 + 0.0506449i 0.00707050 + 0.00259803i
\(381\) 0 0
\(382\) 1.74220 + 2.49625i 0.0891386 + 0.127719i
\(383\) 34.7104 1.77362 0.886808 0.462137i \(-0.152917\pi\)
0.886808 + 0.462137i \(0.152917\pi\)
\(384\) 0 0
\(385\) −2.45629 −0.125184
\(386\) −4.47788 6.41599i −0.227918 0.326565i
\(387\) 0 0
\(388\) 21.4993 + 7.89984i 1.09146 + 0.401053i
\(389\) −6.28614 + 31.6026i −0.318720 + 1.60231i 0.406403 + 0.913694i \(0.366783\pi\)
−0.725123 + 0.688619i \(0.758217\pi\)
\(390\) 0 0
\(391\) 2.78283 6.71836i 0.140734 0.339762i
\(392\) −7.91624 4.61912i −0.399831 0.233301i
\(393\) 0 0
\(394\) −19.0401 + 8.34303i −0.959227 + 0.420316i
\(395\) 7.15026 4.77765i 0.359769 0.240390i
\(396\) 0 0
\(397\) −0.587551 2.95382i −0.0294883 0.148248i 0.963236 0.268656i \(-0.0865796\pi\)
−0.992724 + 0.120408i \(0.961580\pi\)
\(398\) 2.28661 0.503252i 0.114617 0.0252257i
\(399\) 0 0
\(400\) −7.91338 15.4318i −0.395669 0.771589i
\(401\) −14.8685 + 14.8685i −0.742498 + 0.742498i −0.973058 0.230560i \(-0.925944\pi\)
0.230560 + 0.973058i \(0.425944\pi\)
\(402\) 0 0
\(403\) −13.9459 + 2.77400i −0.694693 + 0.138183i
\(404\) −12.1264 + 19.8463i −0.603313 + 0.987390i
\(405\) 0 0
\(406\) −3.19600 1.24850i −0.158615 0.0619620i
\(407\) −2.35079 + 0.973727i −0.116524 + 0.0482659i
\(408\) 0 0
\(409\) 14.6721 + 6.07739i 0.725490 + 0.300508i 0.714697 0.699434i \(-0.246565\pi\)
0.0107925 + 0.999942i \(0.496565\pi\)
\(410\) −0.522986 + 0.544645i −0.0258285 + 0.0268981i
\(411\) 0 0
\(412\) −18.1796 + 19.7178i −0.895643 + 0.971426i
\(413\) −9.67206 6.46266i −0.475931 0.318007i
\(414\) 0 0
\(415\) 2.20486i 0.108232i
\(416\) 30.9272 3.14736i 1.51633 0.154312i
\(417\) 0 0
\(418\) −0.194919 0.0346777i −0.00953380 0.00169614i
\(419\) 21.4066 + 14.3034i 1.04578 + 0.698768i 0.954850 0.297090i \(-0.0960160\pi\)
0.0909301 + 0.995857i \(0.471016\pi\)
\(420\) 0 0
\(421\) 11.3448 + 2.25662i 0.552911 + 0.109981i 0.463635 0.886026i \(-0.346545\pi\)
0.0892757 + 0.996007i \(0.471545\pi\)
\(422\) 8.38119 + 8.04790i 0.407990 + 0.391766i
\(423\) 0 0
\(424\) −19.6350 + 22.1828i −0.953560 + 1.07729i
\(425\) −8.11746 + 3.36236i −0.393755 + 0.163099i
\(426\) 0 0
\(427\) 6.84106 + 10.2384i 0.331062 + 0.495469i
\(428\) 18.4160 4.44656i 0.890170 0.214933i
\(429\) 0 0
\(430\) −8.81550 5.63511i −0.425121 0.271749i
\(431\) 16.7738 16.7738i 0.807965 0.807965i −0.176361 0.984326i \(-0.556433\pi\)
0.984326 + 0.176361i \(0.0564326\pi\)
\(432\) 0 0
\(433\) 14.5447 + 14.5447i 0.698975 + 0.698975i 0.964189 0.265215i \(-0.0854428\pi\)
−0.265215 + 0.964189i \(0.585443\pi\)
\(434\) −1.52502 6.92918i −0.0732033 0.332611i
\(435\) 0 0
\(436\) −5.31791 + 33.8602i −0.254682 + 1.62161i
\(437\) −0.268747 + 0.179571i −0.0128559 + 0.00859004i
\(438\) 0 0
\(439\) 5.28898 + 12.7687i 0.252429 + 0.609418i 0.998399 0.0565614i \(-0.0180137\pi\)
−0.745970 + 0.665980i \(0.768014\pi\)
\(440\) −2.16814 2.85265i −0.103362 0.135995i
\(441\) 0 0
\(442\) −0.319437 15.7464i −0.0151941 0.748981i
\(443\) 2.91450 14.6522i 0.138472 0.696147i −0.847707 0.530465i \(-0.822017\pi\)
0.986179 0.165682i \(-0.0529826\pi\)
\(444\) 0 0
\(445\) −3.47677 + 5.20336i −0.164815 + 0.246663i
\(446\) −2.04796 + 1.42933i −0.0969739 + 0.0676805i
\(447\) 0 0
\(448\) 1.88314 + 15.3970i 0.0889698 + 0.727438i
\(449\) 32.7646 1.54626 0.773130 0.634248i \(-0.218690\pi\)
0.773130 + 0.634248i \(0.218690\pi\)
\(450\) 0 0
\(451\) 0.565604 0.846486i 0.0266332 0.0398595i
\(452\) −25.6213 + 11.8519i −1.20513 + 0.557468i
\(453\) 0 0
\(454\) 0.226286 + 11.1546i 0.0106201 + 0.523512i
\(455\) −3.32369 + 8.02409i −0.155817 + 0.376175i
\(456\) 0 0
\(457\) −10.4684 25.2729i −0.489691 1.18222i −0.954876 0.297005i \(-0.904012\pi\)
0.465185 0.885213i \(-0.345988\pi\)
\(458\) 12.9309 + 29.5103i 0.604219 + 1.37892i
\(459\) 0 0
\(460\) −5.77885 0.907598i −0.269440 0.0423170i
\(461\) −1.87909 9.44683i −0.0875181 0.439983i −0.999554 0.0298721i \(-0.990490\pi\)
0.912036 0.410111i \(-0.134510\pi\)
\(462\) 0 0
\(463\) −2.57440 2.57440i −0.119643 0.119643i 0.644751 0.764393i \(-0.276961\pi\)
−0.764393 + 0.644751i \(0.776961\pi\)
\(464\) −1.37111 4.81375i −0.0636521 0.223473i
\(465\) 0 0
\(466\) −5.10772 3.26499i −0.236610 0.151248i
\(467\) 29.4251 5.85303i 1.36163 0.270846i 0.540386 0.841417i \(-0.318278\pi\)
0.821248 + 0.570572i \(0.193278\pi\)
\(468\) 0 0
\(469\) 6.11557 + 9.15259i 0.282391 + 0.422627i
\(470\) 2.29309 5.87001i 0.105772 0.270763i
\(471\) 0 0
\(472\) −1.03192 16.9373i −0.0474979 0.779602i
\(473\) 13.0327 + 5.39834i 0.599246 + 0.248216i
\(474\) 0 0
\(475\) 0.383026 + 0.0761886i 0.0175744 + 0.00349577i
\(476\) 7.85228 0.318719i 0.359909 0.0146085i
\(477\) 0 0
\(478\) 5.84784 + 1.04038i 0.267474 + 0.0475858i
\(479\) 13.1017i 0.598630i 0.954154 + 0.299315i \(0.0967582\pi\)
−0.954154 + 0.299315i \(0.903242\pi\)
\(480\) 0 0
\(481\) 8.99701i 0.410228i
\(482\) 5.95267 33.4593i 0.271137 1.52403i
\(483\) 0 0
\(484\) −12.6227 11.6380i −0.573760 0.528999i
\(485\) −9.15542 1.82113i −0.415726 0.0826931i
\(486\) 0 0
\(487\) 8.42271 + 3.48880i 0.381670 + 0.158093i 0.565265 0.824909i \(-0.308774\pi\)
−0.183596 + 0.983002i \(0.558774\pi\)
\(488\) −5.85194 + 16.9822i −0.264905 + 0.768750i
\(489\) 0 0
\(490\) 3.47926 + 1.35916i 0.157177 + 0.0614004i
\(491\) 6.91581 + 10.3502i 0.312106 + 0.467100i 0.954048 0.299654i \(-0.0968711\pi\)
−0.641942 + 0.766753i \(0.721871\pi\)
\(492\) 0 0
\(493\) −2.48708 + 0.494711i −0.112013 + 0.0222807i
\(494\) −0.377034 + 0.589828i −0.0169636 + 0.0265376i
\(495\) 0 0
\(496\) 6.70117 7.88741i 0.300892 0.354155i
\(497\) −17.9645 17.9645i −0.805818 0.805818i
\(498\) 0 0
\(499\) −0.940281 4.72711i −0.0420927 0.211615i 0.954015 0.299759i \(-0.0969063\pi\)
−0.996108 + 0.0881445i \(0.971906\pi\)
\(500\) 8.96139 + 12.3007i 0.400766 + 0.550104i
\(501\) 0 0
\(502\) 12.5007 5.47760i 0.557936 0.244477i
\(503\) −10.6536 25.7202i −0.475022 1.14680i −0.961916 0.273344i \(-0.911870\pi\)
0.486894 0.873461i \(-0.338130\pi\)
\(504\) 0 0
\(505\) 3.62734 8.75716i 0.161414 0.389689i
\(506\) 7.88536 0.159965i 0.350547 0.00711131i
\(507\) 0 0
\(508\) 6.21671 16.9187i 0.275822 0.750646i
\(509\) 13.0686 19.5585i 0.579256 0.866917i −0.419918 0.907562i \(-0.637941\pi\)
0.999174 + 0.0406446i \(0.0129411\pi\)
\(510\) 0 0
\(511\) 8.88701 0.393138
\(512\) −16.2192 + 15.7777i −0.716796 + 0.697283i
\(513\) 0 0
\(514\) 3.28454 + 4.70615i 0.144875 + 0.207579i
\(515\) 6.07253 9.08818i 0.267588 0.400473i
\(516\) 0 0
\(517\) −1.65765 + 8.33356i −0.0729033 + 0.366510i
\(518\) −4.48839 + 0.0910529i −0.197208 + 0.00400064i
\(519\) 0 0
\(520\) −12.2527 + 3.22277i −0.537315 + 0.141328i
\(521\) −7.67162 18.5209i −0.336100 0.811417i −0.998083 0.0618976i \(-0.980285\pi\)
0.661983 0.749519i \(-0.269715\pi\)
\(522\) 0 0
\(523\) 23.7322 15.8574i 1.03774 0.693394i 0.0847500 0.996402i \(-0.472991\pi\)
0.952988 + 0.303008i \(0.0979908\pi\)
\(524\) −10.1259 13.8991i −0.442351 0.607187i
\(525\) 0 0
\(526\) −29.8368 + 6.56670i −1.30095 + 0.286322i
\(527\) −3.70773 3.70773i −0.161511 0.161511i
\(528\) 0 0
\(529\) −7.15862 + 7.15862i −0.311244 + 0.311244i
\(530\) 6.50264 10.1727i 0.282457 0.441872i
\(531\) 0 0
\(532\) −0.298066 0.182124i −0.0129228 0.00789607i
\(533\) −1.99992 2.99309i −0.0866261 0.129645i
\(534\) 0 0
\(535\) −7.13335 + 2.95473i −0.308402 + 0.127744i
\(536\) −5.23134 + 15.1813i −0.225960 + 0.655732i
\(537\) 0 0
\(538\) 23.3555 24.3227i 1.00693 1.04863i
\(539\) −4.93945 0.982518i −0.212757 0.0423201i
\(540\) 0 0
\(541\) 9.15217 + 6.11529i 0.393483 + 0.262917i 0.736535 0.676400i \(-0.236461\pi\)
−0.343052 + 0.939316i \(0.611461\pi\)
\(542\) 1.89505 10.6518i 0.0813994 0.457536i
\(543\) 0 0
\(544\) 7.30127 + 8.83802i 0.313039 + 0.378927i
\(545\) 13.9688i 0.598359i
\(546\) 0 0
\(547\) 22.1909 + 14.8275i 0.948813 + 0.633976i 0.930670 0.365859i \(-0.119225\pi\)
0.0181423 + 0.999835i \(0.494225\pi\)
\(548\) 6.07354 0.246521i 0.259449 0.0105309i
\(549\) 0 0
\(550\) −6.87362 6.60029i −0.293092 0.281437i
\(551\) 0.104131 + 0.0431326i 0.00443614 + 0.00183751i
\(552\) 0 0
\(553\) −18.8995 + 7.82843i −0.803689 + 0.332899i
\(554\) 9.51678 24.3617i 0.404329 1.03503i
\(555\) 0 0
\(556\) 3.86779 + 16.0189i 0.164031 + 0.679354i
\(557\) 3.07874 0.612399i 0.130450 0.0259482i −0.129433 0.991588i \(-0.541316\pi\)
0.259884 + 0.965640i \(0.416316\pi\)
\(558\) 0 0
\(559\) 35.2700 35.2700i 1.49176 1.49176i
\(560\) −1.73176 6.07994i −0.0731803 0.256924i
\(561\) 0 0
\(562\) −7.42349 33.7298i −0.313141 1.42281i
\(563\) −3.12631 15.7170i −0.131758 0.662394i −0.989052 0.147566i \(-0.952856\pi\)
0.857294 0.514827i \(-0.172144\pi\)
\(564\) 0 0
\(565\) 9.56607 6.39184i 0.402447 0.268907i
\(566\) −17.7860 40.5905i −0.747602 1.70615i
\(567\) 0 0
\(568\) 5.00625 36.7204i 0.210057 1.54075i
\(569\) −9.52243 + 22.9892i −0.399201 + 0.963756i 0.588655 + 0.808384i \(0.299658\pi\)
−0.987856 + 0.155372i \(0.950342\pi\)
\(570\) 0 0
\(571\) −1.30200 + 6.54559i −0.0544870 + 0.273924i −0.998419 0.0562165i \(-0.982096\pi\)
0.943932 + 0.330141i \(0.107096\pi\)
\(572\) 15.5035 7.17159i 0.648232 0.299859i
\(573\) 0 0
\(574\) 1.47294 1.02800i 0.0614794 0.0429080i
\(575\) −15.5577 −0.648800
\(576\) 0 0
\(577\) 41.6755 1.73497 0.867487 0.497460i \(-0.165734\pi\)
0.867487 + 0.497460i \(0.165734\pi\)
\(578\) −14.9522 + 10.4355i −0.621928 + 0.434059i
\(579\) 0 0
\(580\) 0.856412 + 1.85138i 0.0355606 + 0.0768744i
\(581\) −1.02324 + 5.14417i −0.0424511 + 0.213416i
\(582\) 0 0
\(583\) −6.22942 + 15.0391i −0.257996 + 0.622858i
\(584\) 7.84446 + 10.3210i 0.324606 + 0.427088i
\(585\) 0 0
\(586\) −6.69033 15.2684i −0.276375 0.630731i
\(587\) −8.51613 + 5.69029i −0.351498 + 0.234864i −0.718767 0.695251i \(-0.755293\pi\)
0.367268 + 0.930115i \(0.380293\pi\)
\(588\) 0 0
\(589\) 0.0454683 + 0.228584i 0.00187349 + 0.00941865i
\(590\) 1.48645 + 6.75393i 0.0611962 + 0.278055i
\(591\) 0 0
\(592\) −4.06759 5.13228i −0.167177 0.210935i
\(593\) 17.7593 17.7593i 0.729285 0.729285i −0.241192 0.970477i \(-0.577538\pi\)
0.970477 + 0.241192i \(0.0775384\pi\)
\(594\) 0 0
\(595\) −3.14128 + 0.624839i −0.128780 + 0.0256159i
\(596\) −29.4298 + 7.10587i −1.20549 + 0.291068i
\(597\) 0 0
\(598\) 10.1474 25.9759i 0.414956 1.06223i
\(599\) 23.1403 9.58504i 0.945488 0.391634i 0.143955 0.989584i \(-0.454018\pi\)
0.801533 + 0.597950i \(0.204018\pi\)
\(600\) 0 0
\(601\) 10.7219 + 4.44117i 0.437356 + 0.181159i 0.590487 0.807047i \(-0.298936\pi\)
−0.153131 + 0.988206i \(0.548936\pi\)
\(602\) 17.9523 + 17.2384i 0.731681 + 0.702585i
\(603\) 0 0
\(604\) −1.33219 32.8212i −0.0542061 1.33548i
\(605\) 5.81797 + 3.88744i 0.236534 + 0.158047i
\(606\) 0 0
\(607\) 23.5570i 0.956147i 0.878320 + 0.478074i \(0.158665\pi\)
−0.878320 + 0.478074i \(0.841335\pi\)
\(608\) −0.0515879 0.506922i −0.00209216 0.0205584i
\(609\) 0 0
\(610\) 1.28224 7.20731i 0.0519163 0.291815i
\(611\) 24.9806 + 16.6915i 1.01061 + 0.675267i
\(612\) 0 0
\(613\) −7.55995 1.50377i −0.305343 0.0607366i 0.0400405 0.999198i \(-0.487251\pi\)
−0.345384 + 0.938461i \(0.612251\pi\)
\(614\) 15.1532 15.7807i 0.611531 0.636857i
\(615\) 0 0
\(616\) 3.73463 + 7.66172i 0.150473 + 0.308699i
\(617\) −41.1541 + 17.0466i −1.65680 + 0.686270i −0.997827 0.0658956i \(-0.979010\pi\)
−0.658975 + 0.752165i \(0.729010\pi\)
\(618\) 0 0
\(619\) 25.0137 + 37.4356i 1.00538 + 1.50466i 0.856723 + 0.515777i \(0.172497\pi\)
0.148662 + 0.988888i \(0.452503\pi\)
\(620\) −2.19924 + 3.59931i −0.0883236 + 0.144552i
\(621\) 0 0
\(622\) −23.3416 + 36.5153i −0.935912 + 1.46413i
\(623\) 10.5265 10.5265i 0.421734 0.421734i
\(624\) 0 0
\(625\) 10.9429 + 10.9429i 0.437718 + 0.437718i
\(626\) −22.3132 + 4.91084i −0.891815 + 0.196277i
\(627\) 0 0
\(628\) 7.11425 5.18292i 0.283890 0.206821i
\(629\) −2.75865 + 1.84327i −0.109994 + 0.0734960i
\(630\) 0 0
\(631\) −14.4914 34.9853i −0.576893 1.39274i −0.895587 0.444886i \(-0.853244\pi\)
0.318694 0.947858i \(-0.396756\pi\)
\(632\) −25.7740 15.0391i −1.02524 0.598224i
\(633\) 0 0
\(634\) −40.6714 + 0.825073i −1.61527 + 0.0327678i
\(635\) −1.43312 + 7.20479i −0.0568717 + 0.285913i
\(636\) 0 0
\(637\) −9.89337 + 14.8065i −0.391989 + 0.586654i
\(638\) −1.57405 2.25533i −0.0623172 0.0892892i
\(639\) 0 0
\(640\) 5.53241 7.37790i 0.218688 0.291637i
\(641\) 7.36049 0.290722 0.145361 0.989379i \(-0.453566\pi\)
0.145361 + 0.989379i \(0.453566\pi\)
\(642\) 0 0
\(643\) 5.65643 8.46545i 0.223068 0.333845i −0.703008 0.711182i \(-0.748160\pi\)
0.926076 + 0.377337i \(0.123160\pi\)
\(644\) 13.0615 + 4.79938i 0.514693 + 0.189122i
\(645\) 0 0
\(646\) −0.258097 + 0.00523585i −0.0101547 + 0.000206002i
\(647\) 15.0418 36.3142i 0.591356 1.42766i −0.290838 0.956772i \(-0.593934\pi\)
0.882194 0.470886i \(-0.156066\pi\)
\(648\) 0 0
\(649\) −3.56817 8.61432i −0.140063 0.338142i
\(650\) −30.8624 + 13.5233i −1.21052 + 0.530429i
\(651\) 0 0
\(652\) −7.58054 + 5.52262i −0.296877 + 0.216283i
\(653\) −0.411603 2.06927i −0.0161073 0.0809767i 0.971896 0.235412i \(-0.0756441\pi\)
−0.988003 + 0.154436i \(0.950644\pi\)
\(654\) 0 0
\(655\) 4.95569 + 4.95569i 0.193635 + 0.193635i
\(656\) 2.49403 + 0.803213i 0.0973756 + 0.0313602i
\(657\) 0 0
\(658\) −8.07418 + 12.6312i −0.314764 + 0.492414i
\(659\) 13.9933 2.78344i 0.545101 0.108427i 0.0851445 0.996369i \(-0.472865\pi\)
0.459957 + 0.887941i \(0.347865\pi\)
\(660\) 0 0
\(661\) −2.17698 3.25808i −0.0846746 0.126724i 0.786715 0.617317i \(-0.211780\pi\)
−0.871389 + 0.490593i \(0.836780\pi\)
\(662\) 27.3895 + 10.6995i 1.06452 + 0.415850i
\(663\) 0 0
\(664\) −6.87745 + 3.35235i −0.266897 + 0.130096i
\(665\) 0.131522 + 0.0544780i 0.00510019 + 0.00211257i
\(666\) 0 0
\(667\) −4.40382 0.875975i −0.170517 0.0339179i
\(668\) 13.9619 15.1432i 0.540202 0.585910i
\(669\) 0 0
\(670\) 1.14626 6.44298i 0.0442838 0.248914i
\(671\) 9.87001i 0.381027i
\(672\) 0 0
\(673\) 36.5991i 1.41079i −0.708813 0.705397i \(-0.750769\pi\)
0.708813 0.705397i \(-0.249231\pi\)
\(674\) −1.08849 0.193652i −0.0419272 0.00745919i
\(675\) 0 0
\(676\) −1.39511 34.3714i −0.0536582 1.32198i
\(677\) 16.1895 + 3.22028i 0.622211 + 0.123766i 0.496121 0.868253i \(-0.334757\pi\)
0.126090 + 0.992019i \(0.459757\pi\)
\(678\) 0 0
\(679\) 20.5154 + 8.49775i 0.787308 + 0.326114i
\(680\) −3.49844 3.09663i −0.134159 0.118750i
\(681\) 0 0
\(682\) 2.06932 5.29720i 0.0792384 0.202840i
\(683\) −13.9637 20.8982i −0.534307 0.799647i 0.461875 0.886945i \(-0.347177\pi\)
−0.996182 + 0.0872981i \(0.972177\pi\)
\(684\) 0 0
\(685\) −2.42970 + 0.483297i −0.0928341 + 0.0184658i
\(686\) −23.6596 15.1238i −0.903326 0.577431i
\(687\) 0 0
\(688\) −4.17376 + 36.0653i −0.159123 + 1.37498i
\(689\) 40.6999 + 40.6999i 1.55054 + 1.55054i
\(690\) 0 0
\(691\) −0.174353 0.876532i −0.00663270 0.0333449i 0.977327 0.211735i \(-0.0679112\pi\)
−0.983960 + 0.178390i \(0.942911\pi\)
\(692\) −3.23105 + 20.5727i −0.122826 + 0.782059i
\(693\) 0 0
\(694\) −11.7488 26.8127i −0.445979 1.01780i
\(695\) −2.57014 6.20486i −0.0974909 0.235364i
\(696\) 0 0
\(697\) 0.508002 1.22642i 0.0192419 0.0464541i
\(698\) −0.861488 42.4664i −0.0326078 1.60738i
\(699\) 0 0
\(700\) −7.05880 15.2596i −0.266798 0.576760i
\(701\) 2.15514 3.22540i 0.0813986 0.121822i −0.788536 0.614988i \(-0.789161\pi\)
0.869935 + 0.493167i \(0.164161\pi\)
\(702\) 0 0
\(703\) 0.147468 0.00556188
\(704\) −5.60152 + 11.1002i −0.211115 + 0.418354i
\(705\) 0 0
\(706\) 16.3618 11.4193i 0.615784 0.429771i
\(707\) −12.5270 + 18.7480i −0.471126 + 0.705090i
\(708\) 0 0
\(709\) −2.60789 + 13.1108i −0.0979414 + 0.492385i 0.900413 + 0.435036i \(0.143265\pi\)
−0.998354 + 0.0573482i \(0.981735\pi\)
\(710\) 0.306337 + 15.1007i 0.0114966 + 0.566718i
\(711\) 0 0
\(712\) 21.5166 + 2.93345i 0.806369 + 0.109936i
\(713\) −3.55306 8.57784i −0.133063 0.321243i
\(714\) 0 0
\(715\) −5.78842 + 3.86770i −0.216475 + 0.144644i
\(716\) 46.8137 + 7.35233i 1.74951 + 0.274770i
\(717\) 0 0
\(718\) 7.21538 + 32.7842i 0.269276 + 1.22350i
\(719\) −5.54087 5.54087i −0.206640 0.206640i 0.596198 0.802838i \(-0.296677\pi\)
−0.802838 + 0.596198i \(0.796677\pi\)
\(720\) 0 0
\(721\) −18.3855 + 18.3855i −0.684712 + 0.684712i
\(722\) −22.6301 14.4658i −0.842207 0.538362i
\(723\) 0 0
\(724\) −3.86807 16.0201i −0.143756 0.595381i
\(725\) 3.01406 + 4.51086i 0.111939 + 0.167529i
\(726\) 0 0
\(727\) −1.51607 + 0.627975i −0.0562278 + 0.0232903i −0.410620 0.911807i \(-0.634688\pi\)
0.354392 + 0.935097i \(0.384688\pi\)
\(728\) 30.0824 1.83279i 1.11493 0.0679278i
\(729\) 0 0
\(730\) −3.81091 3.65937i −0.141048 0.135439i
\(731\) 18.0404 + 3.58846i 0.667248 + 0.132724i
\(732\) 0 0
\(733\) −35.6822 23.8421i −1.31795 0.880628i −0.320182 0.947356i \(-0.603744\pi\)
−0.997771 + 0.0667277i \(0.978744\pi\)
\(734\) 22.8487 + 4.06497i 0.843362 + 0.150041i
\(735\) 0 0
\(736\) 5.95537 + 19.4055i 0.219518 + 0.715294i
\(737\) 8.82329i 0.325010i
\(738\) 0 0
\(739\) 2.79111 + 1.86496i 0.102673 + 0.0686036i 0.605847 0.795581i \(-0.292835\pi\)
−0.503174 + 0.864185i \(0.667835\pi\)
\(740\) 1.96219 + 1.80912i 0.0721317 + 0.0665045i
\(741\) 0 0
\(742\) −19.8923 + 20.7161i −0.730268 + 0.760511i
\(743\) 5.81769 + 2.40977i 0.213430 + 0.0884058i 0.486837 0.873493i \(-0.338151\pi\)
−0.273407 + 0.961899i \(0.588151\pi\)
\(744\) 0 0
\(745\) 11.3995 4.72184i 0.417646 0.172995i
\(746\) 19.8786 + 7.76548i 0.727808 + 0.284314i
\(747\) 0 0
\(748\) 5.37523 + 3.28436i 0.196538 + 0.120088i
\(749\) 18.0141 3.58322i 0.658220 0.130928i
\(750\) 0 0
\(751\) 24.4261 24.4261i 0.891321 0.891321i −0.103326 0.994648i \(-0.532949\pi\)
0.994648 + 0.103326i \(0.0329486\pi\)
\(752\) −21.7963 + 1.77232i −0.794831 + 0.0646298i
\(753\) 0 0
\(754\) −9.49747 + 2.09027i −0.345878 + 0.0761231i
\(755\) 2.61172 + 13.1300i 0.0950503 + 0.477850i
\(756\) 0 0
\(757\) −14.3344 + 9.57795i −0.520993 + 0.348116i −0.788097 0.615551i \(-0.788933\pi\)
0.267104 + 0.963668i \(0.413933\pi\)
\(758\) −3.74271 + 1.63999i −0.135941 + 0.0595670i
\(759\) 0 0
\(760\) 0.0528239 + 0.200832i 0.00191612 + 0.00728493i
\(761\) −14.8711 + 35.9019i −0.539076 + 1.30144i 0.386293 + 0.922376i \(0.373755\pi\)
−0.925369 + 0.379068i \(0.876245\pi\)
\(762\) 0 0
\(763\) −6.48269 + 32.5907i −0.234689 + 1.17986i
\(764\) −1.48480 + 4.04085i −0.0537180 + 0.146193i
\(765\) 0 0
\(766\) 28.0940 + 40.2535i 1.01508 + 1.45442i
\(767\) −32.9690 −1.19044
\(768\) 0 0
\(769\) 13.8807 0.500550 0.250275 0.968175i \(-0.419479\pi\)
0.250275 + 0.968175i \(0.419479\pi\)
\(770\) −1.98808 2.84856i −0.0716455 0.102655i
\(771\) 0 0
\(772\) 3.81629 10.3860i 0.137351 0.373800i
\(773\) −0.0884866 + 0.444852i −0.00318264 + 0.0160002i −0.982344 0.187084i \(-0.940096\pi\)
0.979161 + 0.203084i \(0.0650964\pi\)
\(774\) 0 0
\(775\) −4.29299 + 10.3642i −0.154209 + 0.372293i
\(776\) 8.23972 + 31.3267i 0.295789 + 1.12456i
\(777\) 0 0
\(778\) −41.7373 + 18.2885i −1.49636 + 0.655676i
\(779\) −0.0490593 + 0.0327804i −0.00175773 + 0.00117448i
\(780\) 0 0
\(781\) −3.97282 19.9727i −0.142159 0.714680i
\(782\) 10.0436 2.21047i 0.359160 0.0790464i
\(783\) 0 0
\(784\) −1.05049 12.9191i −0.0375173 0.461396i
\(785\) −2.53656 + 2.53656i −0.0905339 + 0.0905339i
\(786\) 0 0
\(787\) −9.18877 + 1.82776i −0.327544 + 0.0651526i −0.356123 0.934439i \(-0.615902\pi\)
0.0285792 + 0.999592i \(0.490902\pi\)
\(788\) −25.0861