Properties

Label 1512.2.c.f.757.1
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.1
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.41290 - 0.0608900i) q^{2} +(1.99258 + 0.172063i) q^{4} -3.11390i q^{5} +1.00000 q^{7} +(-2.80485 - 0.364437i) q^{8} +O(q^{10})\) \(q+(-1.41290 - 0.0608900i) q^{2} +(1.99258 + 0.172063i) q^{4} -3.11390i q^{5} +1.00000 q^{7} +(-2.80485 - 0.364437i) q^{8} +(-0.189605 + 4.39964i) q^{10} -2.37402i q^{11} +1.09044i q^{13} +(-1.41290 - 0.0608900i) q^{14} +(3.94079 + 0.685701i) q^{16} +3.69300 q^{17} +1.08263i q^{19} +(0.535788 - 6.20472i) q^{20} +(-0.144554 + 3.35425i) q^{22} +4.87366 q^{23} -4.69640 q^{25} +(0.0663968 - 1.54068i) q^{26} +(1.99258 + 0.172063i) q^{28} -1.59607i q^{29} +7.45516 q^{31} +(-5.52620 - 1.20878i) q^{32} +(-5.21785 - 0.224867i) q^{34} -3.11390i q^{35} -4.61410i q^{37} +(0.0659213 - 1.52965i) q^{38} +(-1.13482 + 8.73404i) q^{40} -0.0380616 q^{41} -11.0608i q^{43} +(0.408481 - 4.73043i) q^{44} +(-6.88600 - 0.296757i) q^{46} +0.337175 q^{47} +1.00000 q^{49} +(6.63555 + 0.285964i) q^{50} +(-0.187624 + 2.17279i) q^{52} +8.14672i q^{53} -7.39246 q^{55} +(-2.80485 - 0.364437i) q^{56} +(-0.0971845 + 2.25509i) q^{58} -15.0761i q^{59} +5.53745i q^{61} +(-10.5334 - 0.453944i) q^{62} +(7.73437 + 2.04438i) q^{64} +3.39553 q^{65} +7.70421i q^{67} +(7.35861 + 0.635429i) q^{68} +(-0.189605 + 4.39964i) q^{70} -13.5472 q^{71} -14.6727 q^{73} +(-0.280953 + 6.51928i) q^{74} +(-0.186281 + 2.15723i) q^{76} -2.37402i q^{77} +5.18122 q^{79} +(2.13521 - 12.2712i) q^{80} +(0.0537773 + 0.00231757i) q^{82} +0.138321i q^{83} -11.4996i q^{85} +(-0.673490 + 15.6278i) q^{86} +(-0.865179 + 6.65876i) q^{88} -11.9531 q^{89} +1.09044i q^{91} +(9.71118 + 0.838577i) q^{92} +(-0.476396 - 0.0205306i) q^{94} +3.37121 q^{95} -5.30202 q^{97} +(-1.41290 - 0.0608900i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{7} + O(q^{10}) \) \( 24q + 24q^{7} + 20q^{10} - 4q^{16} + 4q^{22} - 24q^{25} - 16q^{31} + 4q^{34} + 12q^{40} - 52q^{46} + 24q^{49} + 12q^{52} - 8q^{55} - 28q^{58} + 24q^{64} + 20q^{70} - 24q^{76} + 32q^{79} + 44q^{82} - 60q^{88} + 12q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41290 0.0608900i −0.999073 0.0430557i
\(3\) 0 0
\(4\) 1.99258 + 0.172063i 0.996292 + 0.0860316i
\(5\) 3.11390i 1.39258i −0.717760 0.696290i \(-0.754833\pi\)
0.717760 0.696290i \(-0.245167\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.80485 0.364437i −0.991664 0.128848i
\(9\) 0 0
\(10\) −0.189605 + 4.39964i −0.0599585 + 1.39129i
\(11\) 2.37402i 0.715793i −0.933761 0.357897i \(-0.883494\pi\)
0.933761 0.357897i \(-0.116506\pi\)
\(12\) 0 0
\(13\) 1.09044i 0.302434i 0.988501 + 0.151217i \(0.0483192\pi\)
−0.988501 + 0.151217i \(0.951681\pi\)
\(14\) −1.41290 0.0608900i −0.377614 0.0162735i
\(15\) 0 0
\(16\) 3.94079 + 0.685701i 0.985197 + 0.171425i
\(17\) 3.69300 0.895684 0.447842 0.894113i \(-0.352193\pi\)
0.447842 + 0.894113i \(0.352193\pi\)
\(18\) 0 0
\(19\) 1.08263i 0.248372i 0.992259 + 0.124186i \(0.0396320\pi\)
−0.992259 + 0.124186i \(0.960368\pi\)
\(20\) 0.535788 6.20472i 0.119806 1.38742i
\(21\) 0 0
\(22\) −0.144554 + 3.35425i −0.0308190 + 0.715129i
\(23\) 4.87366 1.01623 0.508114 0.861290i \(-0.330343\pi\)
0.508114 + 0.861290i \(0.330343\pi\)
\(24\) 0 0
\(25\) −4.69640 −0.939280
\(26\) 0.0663968 1.54068i 0.0130215 0.302153i
\(27\) 0 0
\(28\) 1.99258 + 0.172063i 0.376563 + 0.0325169i
\(29\) 1.59607i 0.296382i −0.988959 0.148191i \(-0.952655\pi\)
0.988959 0.148191i \(-0.0473451\pi\)
\(30\) 0 0
\(31\) 7.45516 1.33899 0.669493 0.742818i \(-0.266511\pi\)
0.669493 + 0.742818i \(0.266511\pi\)
\(32\) −5.52620 1.20878i −0.976903 0.213685i
\(33\) 0 0
\(34\) −5.21785 0.224867i −0.894853 0.0385643i
\(35\) 3.11390i 0.526346i
\(36\) 0 0
\(37\) 4.61410i 0.758554i −0.925283 0.379277i \(-0.876173\pi\)
0.925283 0.379277i \(-0.123827\pi\)
\(38\) 0.0659213 1.52965i 0.0106938 0.248142i
\(39\) 0 0
\(40\) −1.13482 + 8.73404i −0.179431 + 1.38097i
\(41\) −0.0380616 −0.00594422 −0.00297211 0.999996i \(-0.500946\pi\)
−0.00297211 + 0.999996i \(0.500946\pi\)
\(42\) 0 0
\(43\) 11.0608i 1.68675i −0.537323 0.843377i \(-0.680564\pi\)
0.537323 0.843377i \(-0.319436\pi\)
\(44\) 0.408481 4.73043i 0.0615808 0.713139i
\(45\) 0 0
\(46\) −6.88600 0.296757i −1.01529 0.0437544i
\(47\) 0.337175 0.0491821 0.0245910 0.999698i \(-0.492172\pi\)
0.0245910 + 0.999698i \(0.492172\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 6.63555 + 0.285964i 0.938409 + 0.0404413i
\(51\) 0 0
\(52\) −0.187624 + 2.17279i −0.0260188 + 0.301312i
\(53\) 8.14672i 1.11904i 0.828818 + 0.559519i \(0.189014\pi\)
−0.828818 + 0.559519i \(0.810986\pi\)
\(54\) 0 0
\(55\) −7.39246 −0.996799
\(56\) −2.80485 0.364437i −0.374814 0.0486999i
\(57\) 0 0
\(58\) −0.0971845 + 2.25509i −0.0127610 + 0.296108i
\(59\) 15.0761i 1.96274i −0.192129 0.981370i \(-0.561539\pi\)
0.192129 0.981370i \(-0.438461\pi\)
\(60\) 0 0
\(61\) 5.53745i 0.708998i 0.935056 + 0.354499i \(0.115349\pi\)
−0.935056 + 0.354499i \(0.884651\pi\)
\(62\) −10.5334 0.453944i −1.33774 0.0576510i
\(63\) 0 0
\(64\) 7.73437 + 2.04438i 0.966796 + 0.255548i
\(65\) 3.39553 0.421163
\(66\) 0 0
\(67\) 7.70421i 0.941219i 0.882342 + 0.470609i \(0.155966\pi\)
−0.882342 + 0.470609i \(0.844034\pi\)
\(68\) 7.35861 + 0.635429i 0.892363 + 0.0770571i
\(69\) 0 0
\(70\) −0.189605 + 4.39964i −0.0226622 + 0.525858i
\(71\) −13.5472 −1.60776 −0.803878 0.594794i \(-0.797234\pi\)
−0.803878 + 0.594794i \(0.797234\pi\)
\(72\) 0 0
\(73\) −14.6727 −1.71731 −0.858656 0.512553i \(-0.828700\pi\)
−0.858656 + 0.512553i \(0.828700\pi\)
\(74\) −0.280953 + 6.51928i −0.0326601 + 0.757851i
\(75\) 0 0
\(76\) −0.186281 + 2.15723i −0.0213679 + 0.247452i
\(77\) 2.37402i 0.270544i
\(78\) 0 0
\(79\) 5.18122 0.582932 0.291466 0.956581i \(-0.405857\pi\)
0.291466 + 0.956581i \(0.405857\pi\)
\(80\) 2.13521 12.2712i 0.238723 1.37197i
\(81\) 0 0
\(82\) 0.0537773 + 0.00231757i 0.00593870 + 0.000255932i
\(83\) 0.138321i 0.0151827i 0.999971 + 0.00759136i \(0.00241643\pi\)
−0.999971 + 0.00759136i \(0.997584\pi\)
\(84\) 0 0
\(85\) 11.4996i 1.24731i
\(86\) −0.673490 + 15.6278i −0.0726243 + 1.68519i
\(87\) 0 0
\(88\) −0.865179 + 6.65876i −0.0922284 + 0.709826i
\(89\) −11.9531 −1.26703 −0.633514 0.773731i \(-0.718388\pi\)
−0.633514 + 0.773731i \(0.718388\pi\)
\(90\) 0 0
\(91\) 1.09044i 0.114309i
\(92\) 9.71118 + 0.838577i 1.01246 + 0.0874277i
\(93\) 0 0
\(94\) −0.476396 0.0205306i −0.0491364 0.00211757i
\(95\) 3.37121 0.345879
\(96\) 0 0
\(97\) −5.30202 −0.538339 −0.269169 0.963093i \(-0.586749\pi\)
−0.269169 + 0.963093i \(0.586749\pi\)
\(98\) −1.41290 0.0608900i −0.142725 0.00615081i
\(99\) 0 0
\(100\) −9.35797 0.808077i −0.935797 0.0808077i
\(101\) 0.0753369i 0.00749630i −0.999993 0.00374815i \(-0.998807\pi\)
0.999993 0.00374815i \(-0.00119308\pi\)
\(102\) 0 0
\(103\) 15.3347 1.51097 0.755487 0.655163i \(-0.227400\pi\)
0.755487 + 0.655163i \(0.227400\pi\)
\(104\) 0.397396 3.05852i 0.0389679 0.299913i
\(105\) 0 0
\(106\) 0.496053 11.5105i 0.0481809 1.11800i
\(107\) 4.03726i 0.390297i 0.980774 + 0.195148i \(0.0625189\pi\)
−0.980774 + 0.195148i \(0.937481\pi\)
\(108\) 0 0
\(109\) 12.2335i 1.17176i −0.810399 0.585879i \(-0.800749\pi\)
0.810399 0.585879i \(-0.199251\pi\)
\(110\) 10.4448 + 0.450127i 0.995875 + 0.0429179i
\(111\) 0 0
\(112\) 3.94079 + 0.685701i 0.372370 + 0.0647926i
\(113\) −11.1934 −1.05299 −0.526495 0.850178i \(-0.676494\pi\)
−0.526495 + 0.850178i \(0.676494\pi\)
\(114\) 0 0
\(115\) 15.1761i 1.41518i
\(116\) 0.274624 3.18030i 0.0254982 0.295284i
\(117\) 0 0
\(118\) −0.917982 + 21.3010i −0.0845071 + 1.96092i
\(119\) 3.69300 0.338537
\(120\) 0 0
\(121\) 5.36404 0.487640
\(122\) 0.337175 7.82388i 0.0305264 0.708340i
\(123\) 0 0
\(124\) 14.8550 + 1.28276i 1.33402 + 0.115195i
\(125\) 0.945386i 0.0845579i
\(126\) 0 0
\(127\) −2.43139 −0.215751 −0.107876 0.994164i \(-0.534405\pi\)
−0.107876 + 0.994164i \(0.534405\pi\)
\(128\) −10.8034 3.35946i −0.954897 0.296937i
\(129\) 0 0
\(130\) −4.79755 0.206753i −0.420773 0.0181335i
\(131\) 8.83723i 0.772112i −0.922475 0.386056i \(-0.873837\pi\)
0.922475 0.386056i \(-0.126163\pi\)
\(132\) 0 0
\(133\) 1.08263i 0.0938760i
\(134\) 0.469109 10.8853i 0.0405248 0.940346i
\(135\) 0 0
\(136\) −10.3583 1.34586i −0.888218 0.115407i
\(137\) 11.1478 0.952422 0.476211 0.879331i \(-0.342010\pi\)
0.476211 + 0.879331i \(0.342010\pi\)
\(138\) 0 0
\(139\) 17.2724i 1.46502i −0.680755 0.732511i \(-0.738348\pi\)
0.680755 0.732511i \(-0.261652\pi\)
\(140\) 0.535788 6.20472i 0.0452824 0.524394i
\(141\) 0 0
\(142\) 19.1409 + 0.824888i 1.60627 + 0.0692231i
\(143\) 2.58872 0.216480
\(144\) 0 0
\(145\) −4.97000 −0.412736
\(146\) 20.7311 + 0.893421i 1.71572 + 0.0739400i
\(147\) 0 0
\(148\) 0.793917 9.19400i 0.0652596 0.755742i
\(149\) 13.7236i 1.12428i 0.827042 + 0.562140i \(0.190022\pi\)
−0.827042 + 0.562140i \(0.809978\pi\)
\(150\) 0 0
\(151\) −12.8195 −1.04324 −0.521620 0.853178i \(-0.674672\pi\)
−0.521620 + 0.853178i \(0.674672\pi\)
\(152\) 0.394550 3.03662i 0.0320023 0.246302i
\(153\) 0 0
\(154\) −0.144554 + 3.35425i −0.0116485 + 0.270293i
\(155\) 23.2146i 1.86465i
\(156\) 0 0
\(157\) 21.1418i 1.68730i −0.536892 0.843651i \(-0.680402\pi\)
0.536892 0.843651i \(-0.319598\pi\)
\(158\) −7.32055 0.315484i −0.582392 0.0250986i
\(159\) 0 0
\(160\) −3.76403 + 17.2080i −0.297573 + 1.36042i
\(161\) 4.87366 0.384098
\(162\) 0 0
\(163\) 0.386568i 0.0302784i 0.999885 + 0.0151392i \(0.00481914\pi\)
−0.999885 + 0.0151392i \(0.995181\pi\)
\(164\) −0.0758409 0.00654899i −0.00592218 0.000511390i
\(165\) 0 0
\(166\) 0.00842236 0.195434i 0.000653702 0.0151686i
\(167\) −14.4336 −1.11690 −0.558451 0.829537i \(-0.688604\pi\)
−0.558451 + 0.829537i \(0.688604\pi\)
\(168\) 0 0
\(169\) 11.8109 0.908534
\(170\) −0.700213 + 16.2479i −0.0537039 + 1.24615i
\(171\) 0 0
\(172\) 1.90315 22.0395i 0.145114 1.68050i
\(173\) 13.9493i 1.06055i 0.847826 + 0.530274i \(0.177911\pi\)
−0.847826 + 0.530274i \(0.822089\pi\)
\(174\) 0 0
\(175\) −4.69640 −0.355014
\(176\) 1.62786 9.35550i 0.122705 0.705197i
\(177\) 0 0
\(178\) 16.8886 + 0.727825i 1.26585 + 0.0545528i
\(179\) 10.6569i 0.796537i −0.917269 0.398269i \(-0.869611\pi\)
0.917269 0.398269i \(-0.130389\pi\)
\(180\) 0 0
\(181\) 6.63866i 0.493448i −0.969086 0.246724i \(-0.920646\pi\)
0.969086 0.246724i \(-0.0793540\pi\)
\(182\) 0.0663968 1.54068i 0.00492166 0.114203i
\(183\) 0 0
\(184\) −13.6699 1.77614i −1.00776 0.130939i
\(185\) −14.3679 −1.05635
\(186\) 0 0
\(187\) 8.76724i 0.641124i
\(188\) 0.671850 + 0.0580154i 0.0489997 + 0.00423121i
\(189\) 0 0
\(190\) −4.76319 0.205273i −0.345558 0.0148920i
\(191\) 9.81148 0.709934 0.354967 0.934879i \(-0.384492\pi\)
0.354967 + 0.934879i \(0.384492\pi\)
\(192\) 0 0
\(193\) 17.4539 1.25636 0.628180 0.778068i \(-0.283800\pi\)
0.628180 + 0.778068i \(0.283800\pi\)
\(194\) 7.49124 + 0.322840i 0.537839 + 0.0231785i
\(195\) 0 0
\(196\) 1.99258 + 0.172063i 0.142327 + 0.0122902i
\(197\) 27.6871i 1.97262i 0.164888 + 0.986312i \(0.447274\pi\)
−0.164888 + 0.986312i \(0.552726\pi\)
\(198\) 0 0
\(199\) 9.29804 0.659121 0.329560 0.944134i \(-0.393099\pi\)
0.329560 + 0.944134i \(0.393099\pi\)
\(200\) 13.1727 + 1.71154i 0.931450 + 0.121024i
\(201\) 0 0
\(202\) −0.00458726 + 0.106444i −0.000322759 + 0.00748935i
\(203\) 1.59607i 0.112022i
\(204\) 0 0
\(205\) 0.118520i 0.00827780i
\(206\) −21.6665 0.933730i −1.50957 0.0650561i
\(207\) 0 0
\(208\) −0.747715 + 4.29719i −0.0518447 + 0.297957i
\(209\) 2.57018 0.177783
\(210\) 0 0
\(211\) 16.3068i 1.12260i −0.827611 0.561302i \(-0.810301\pi\)
0.827611 0.561302i \(-0.189699\pi\)
\(212\) −1.40175 + 16.2330i −0.0962725 + 1.11489i
\(213\) 0 0
\(214\) 0.245829 5.70426i 0.0168045 0.389935i
\(215\) −34.4422 −2.34894
\(216\) 0 0
\(217\) 7.45516 0.506089
\(218\) −0.744898 + 17.2848i −0.0504509 + 1.17067i
\(219\) 0 0
\(220\) −14.7301 1.27197i −0.993103 0.0857562i
\(221\) 4.02699i 0.270885i
\(222\) 0 0
\(223\) −18.8846 −1.26461 −0.632304 0.774720i \(-0.717891\pi\)
−0.632304 + 0.774720i \(0.717891\pi\)
\(224\) −5.52620 1.20878i −0.369235 0.0807652i
\(225\) 0 0
\(226\) 15.8152 + 0.681568i 1.05201 + 0.0453372i
\(227\) 12.9709i 0.860907i −0.902613 0.430454i \(-0.858354\pi\)
0.902613 0.430454i \(-0.141646\pi\)
\(228\) 0 0
\(229\) 5.92552i 0.391569i 0.980647 + 0.195785i \(0.0627253\pi\)
−0.980647 + 0.195785i \(0.937275\pi\)
\(230\) −0.924073 + 21.4424i −0.0609315 + 1.41387i
\(231\) 0 0
\(232\) −0.581666 + 4.47673i −0.0381882 + 0.293912i
\(233\) 12.2093 0.799861 0.399930 0.916546i \(-0.369034\pi\)
0.399930 + 0.916546i \(0.369034\pi\)
\(234\) 0 0
\(235\) 1.04993i 0.0684900i
\(236\) 2.59404 30.0404i 0.168858 1.95546i
\(237\) 0 0
\(238\) −5.21785 0.224867i −0.338223 0.0145759i
\(239\) 22.5273 1.45717 0.728585 0.684956i \(-0.240178\pi\)
0.728585 + 0.684956i \(0.240178\pi\)
\(240\) 0 0
\(241\) −16.1826 −1.04241 −0.521206 0.853431i \(-0.674518\pi\)
−0.521206 + 0.853431i \(0.674518\pi\)
\(242\) −7.57887 0.326616i −0.487188 0.0209957i
\(243\) 0 0
\(244\) −0.952791 + 11.0338i −0.0609962 + 0.706369i
\(245\) 3.11390i 0.198940i
\(246\) 0 0
\(247\) −1.18054 −0.0751162
\(248\) −20.9106 2.71693i −1.32782 0.172525i
\(249\) 0 0
\(250\) −0.0575645 + 1.33574i −0.00364070 + 0.0844794i
\(251\) 6.88454i 0.434548i −0.976111 0.217274i \(-0.930283\pi\)
0.976111 0.217274i \(-0.0697166\pi\)
\(252\) 0 0
\(253\) 11.5702i 0.727409i
\(254\) 3.43532 + 0.148047i 0.215551 + 0.00928932i
\(255\) 0 0
\(256\) 15.0596 + 5.40440i 0.941227 + 0.337775i
\(257\) −2.70139 −0.168508 −0.0842541 0.996444i \(-0.526851\pi\)
−0.0842541 + 0.996444i \(0.526851\pi\)
\(258\) 0 0
\(259\) 4.61410i 0.286707i
\(260\) 6.76587 + 0.584245i 0.419602 + 0.0362333i
\(261\) 0 0
\(262\) −0.538098 + 12.4861i −0.0332438 + 0.771396i
\(263\) 13.5500 0.835527 0.417763 0.908556i \(-0.362814\pi\)
0.417763 + 0.908556i \(0.362814\pi\)
\(264\) 0 0
\(265\) 25.3681 1.55835
\(266\) 0.0659213 1.52965i 0.00404190 0.0937889i
\(267\) 0 0
\(268\) −1.32561 + 15.3513i −0.0809745 + 0.937729i
\(269\) 6.41522i 0.391143i 0.980689 + 0.195571i \(0.0626562\pi\)
−0.980689 + 0.195571i \(0.937344\pi\)
\(270\) 0 0
\(271\) −14.5096 −0.881397 −0.440698 0.897655i \(-0.645269\pi\)
−0.440698 + 0.897655i \(0.645269\pi\)
\(272\) 14.5533 + 2.53229i 0.882425 + 0.153543i
\(273\) 0 0
\(274\) −15.7508 0.678790i −0.951539 0.0410072i
\(275\) 11.1493i 0.672330i
\(276\) 0 0
\(277\) 25.3175i 1.52118i 0.649231 + 0.760591i \(0.275091\pi\)
−0.649231 + 0.760591i \(0.724909\pi\)
\(278\) −1.05171 + 24.4042i −0.0630776 + 1.46366i
\(279\) 0 0
\(280\) −1.13482 + 8.73404i −0.0678185 + 0.521958i
\(281\) −0.719979 −0.0429504 −0.0214752 0.999769i \(-0.506836\pi\)
−0.0214752 + 0.999769i \(0.506836\pi\)
\(282\) 0 0
\(283\) 11.3262i 0.673275i −0.941634 0.336637i \(-0.890710\pi\)
0.941634 0.336637i \(-0.109290\pi\)
\(284\) −26.9939 2.33097i −1.60180 0.138318i
\(285\) 0 0
\(286\) −3.65761 0.157627i −0.216279 0.00932069i
\(287\) −0.0380616 −0.00224670
\(288\) 0 0
\(289\) −3.36176 −0.197751
\(290\) 7.02213 + 0.302623i 0.412354 + 0.0177707i
\(291\) 0 0
\(292\) −29.2366 2.52463i −1.71094 0.147743i
\(293\) 15.2567i 0.891304i 0.895206 + 0.445652i \(0.147028\pi\)
−0.895206 + 0.445652i \(0.852972\pi\)
\(294\) 0 0
\(295\) −46.9455 −2.73327
\(296\) −1.68155 + 12.9419i −0.0977381 + 0.752231i
\(297\) 0 0
\(298\) 0.835628 19.3901i 0.0484066 1.12324i
\(299\) 5.31443i 0.307342i
\(300\) 0 0
\(301\) 11.0608i 0.637533i
\(302\) 18.1128 + 0.780581i 1.04227 + 0.0449174i
\(303\) 0 0
\(304\) −0.742360 + 4.26642i −0.0425773 + 0.244696i
\(305\) 17.2431 0.987337
\(306\) 0 0
\(307\) 25.5497i 1.45820i 0.684409 + 0.729098i \(0.260060\pi\)
−0.684409 + 0.729098i \(0.739940\pi\)
\(308\) 0.408481 4.73043i 0.0232753 0.269541i
\(309\) 0 0
\(310\) −1.41354 + 32.8000i −0.0802836 + 1.86292i
\(311\) 3.00328 0.170300 0.0851501 0.996368i \(-0.472863\pi\)
0.0851501 + 0.996368i \(0.472863\pi\)
\(312\) 0 0
\(313\) −5.53962 −0.313118 −0.156559 0.987669i \(-0.550040\pi\)
−0.156559 + 0.987669i \(0.550040\pi\)
\(314\) −1.28733 + 29.8713i −0.0726480 + 1.68574i
\(315\) 0 0
\(316\) 10.3240 + 0.891496i 0.580771 + 0.0501506i
\(317\) 32.1705i 1.80688i 0.428718 + 0.903439i \(0.358966\pi\)
−0.428718 + 0.903439i \(0.641034\pi\)
\(318\) 0 0
\(319\) −3.78909 −0.212148
\(320\) 6.36601 24.0841i 0.355871 1.34634i
\(321\) 0 0
\(322\) −6.88600 0.296757i −0.383742 0.0165376i
\(323\) 3.99815i 0.222463i
\(324\) 0 0
\(325\) 5.12114i 0.284070i
\(326\) 0.0235381 0.546183i 0.00130366 0.0302503i
\(327\) 0 0
\(328\) 0.106757 + 0.0138710i 0.00589467 + 0.000765900i
\(329\) 0.337175 0.0185891
\(330\) 0 0
\(331\) 24.9617i 1.37202i 0.727592 + 0.686010i \(0.240639\pi\)
−0.727592 + 0.686010i \(0.759361\pi\)
\(332\) −0.0238000 + 0.275616i −0.00130619 + 0.0151264i
\(333\) 0 0
\(334\) 20.3932 + 0.878859i 1.11587 + 0.0480890i
\(335\) 23.9902 1.31072
\(336\) 0 0
\(337\) 17.7899 0.969076 0.484538 0.874770i \(-0.338988\pi\)
0.484538 + 0.874770i \(0.338988\pi\)
\(338\) −16.6877 0.719168i −0.907691 0.0391176i
\(339\) 0 0
\(340\) 1.97866 22.9140i 0.107308 1.24269i
\(341\) 17.6987i 0.958437i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.03095 + 31.0238i −0.217334 + 1.67269i
\(345\) 0 0
\(346\) 0.849375 19.7091i 0.0456627 1.05957i
\(347\) 2.08108i 0.111718i −0.998439 0.0558591i \(-0.982210\pi\)
0.998439 0.0558591i \(-0.0177898\pi\)
\(348\) 0 0
\(349\) 7.11683i 0.380955i −0.981692 0.190477i \(-0.938996\pi\)
0.981692 0.190477i \(-0.0610036\pi\)
\(350\) 6.63555 + 0.285964i 0.354685 + 0.0152854i
\(351\) 0 0
\(352\) −2.86967 + 13.1193i −0.152954 + 0.699260i
\(353\) 28.9449 1.54058 0.770290 0.637694i \(-0.220111\pi\)
0.770290 + 0.637694i \(0.220111\pi\)
\(354\) 0 0
\(355\) 42.1847i 2.23893i
\(356\) −23.8176 2.05669i −1.26233 0.109004i
\(357\) 0 0
\(358\) −0.648901 + 15.0572i −0.0342955 + 0.795799i
\(359\) −10.0190 −0.528780 −0.264390 0.964416i \(-0.585171\pi\)
−0.264390 + 0.964416i \(0.585171\pi\)
\(360\) 0 0
\(361\) 17.8279 0.938311
\(362\) −0.404228 + 9.37977i −0.0212457 + 0.492990i
\(363\) 0 0
\(364\) −0.187624 + 2.17279i −0.00983420 + 0.113885i
\(365\) 45.6894i 2.39149i
\(366\) 0 0
\(367\) 31.4662 1.64252 0.821261 0.570552i \(-0.193271\pi\)
0.821261 + 0.570552i \(0.193271\pi\)
\(368\) 19.2061 + 3.34187i 1.00119 + 0.174207i
\(369\) 0 0
\(370\) 20.3004 + 0.874860i 1.05537 + 0.0454818i
\(371\) 8.14672i 0.422956i
\(372\) 0 0
\(373\) 31.8121i 1.64717i 0.567193 + 0.823585i \(0.308030\pi\)
−0.567193 + 0.823585i \(0.691970\pi\)
\(374\) −0.533837 + 12.3873i −0.0276041 + 0.640530i
\(375\) 0 0
\(376\) −0.945726 0.122879i −0.0487721 0.00633700i
\(377\) 1.74042 0.0896360
\(378\) 0 0
\(379\) 15.2806i 0.784911i −0.919771 0.392456i \(-0.871626\pi\)
0.919771 0.392456i \(-0.128374\pi\)
\(380\) 6.71742 + 0.580060i 0.344596 + 0.0297565i
\(381\) 0 0
\(382\) −13.8627 0.597420i −0.709275 0.0305667i
\(383\) 19.0555 0.973691 0.486845 0.873488i \(-0.338147\pi\)
0.486845 + 0.873488i \(0.338147\pi\)
\(384\) 0 0
\(385\) −7.39246 −0.376755
\(386\) −24.6607 1.06277i −1.25520 0.0540935i
\(387\) 0 0
\(388\) −10.5647 0.912282i −0.536343 0.0463141i
\(389\) 3.69055i 0.187118i −0.995614 0.0935591i \(-0.970176\pi\)
0.995614 0.0935591i \(-0.0298244\pi\)
\(390\) 0 0
\(391\) 17.9984 0.910219
\(392\) −2.80485 0.364437i −0.141666 0.0184068i
\(393\) 0 0
\(394\) 1.68587 39.1192i 0.0849327 1.97080i
\(395\) 16.1338i 0.811780i
\(396\) 0 0
\(397\) 14.8184i 0.743715i 0.928290 + 0.371857i \(0.121279\pi\)
−0.928290 + 0.371857i \(0.878721\pi\)
\(398\) −13.1372 0.566157i −0.658510 0.0283789i
\(399\) 0 0
\(400\) −18.5075 3.22032i −0.925376 0.161016i
\(401\) −1.80006 −0.0898908 −0.0449454 0.998989i \(-0.514311\pi\)
−0.0449454 + 0.998989i \(0.514311\pi\)
\(402\) 0 0
\(403\) 8.12940i 0.404954i
\(404\) 0.0129627 0.150115i 0.000644919 0.00746851i
\(405\) 0 0
\(406\) −0.0971845 + 2.25509i −0.00482319 + 0.111918i
\(407\) −10.9540 −0.542968
\(408\) 0 0
\(409\) −25.6731 −1.26945 −0.634727 0.772736i \(-0.718888\pi\)
−0.634727 + 0.772736i \(0.718888\pi\)
\(410\) 0.00721668 0.167457i 0.000356406 0.00827012i
\(411\) 0 0
\(412\) 30.5557 + 2.63854i 1.50537 + 0.129992i
\(413\) 15.0761i 0.741846i
\(414\) 0 0
\(415\) 0.430719 0.0211431
\(416\) 1.31810 6.02599i 0.0646254 0.295448i
\(417\) 0 0
\(418\) −3.63142 0.156498i −0.177618 0.00765458i
\(419\) 17.3661i 0.848392i 0.905571 + 0.424196i \(0.139443\pi\)
−0.905571 + 0.424196i \(0.860557\pi\)
\(420\) 0 0
\(421\) 30.4837i 1.48568i −0.669468 0.742841i \(-0.733478\pi\)
0.669468 0.742841i \(-0.266522\pi\)
\(422\) −0.992918 + 23.0398i −0.0483345 + 1.12156i
\(423\) 0 0
\(424\) 2.96896 22.8503i 0.144186 1.10971i
\(425\) −17.3438 −0.841298
\(426\) 0 0
\(427\) 5.53745i 0.267976i
\(428\) −0.694664 + 8.04459i −0.0335778 + 0.388850i
\(429\) 0 0
\(430\) 48.6635 + 2.09718i 2.34676 + 0.101135i
\(431\) −9.49698 −0.457453 −0.228727 0.973491i \(-0.573456\pi\)
−0.228727 + 0.973491i \(0.573456\pi\)
\(432\) 0 0
\(433\) 25.6935 1.23475 0.617376 0.786668i \(-0.288196\pi\)
0.617376 + 0.786668i \(0.288196\pi\)
\(434\) −10.5334 0.453944i −0.505620 0.0217900i
\(435\) 0 0
\(436\) 2.10494 24.3763i 0.100808 1.16741i
\(437\) 5.27637i 0.252403i
\(438\) 0 0
\(439\) 11.0047 0.525227 0.262614 0.964901i \(-0.415416\pi\)
0.262614 + 0.964901i \(0.415416\pi\)
\(440\) 20.7347 + 2.69408i 0.988490 + 0.128435i
\(441\) 0 0
\(442\) 0.245203 5.68975i 0.0116631 0.270634i
\(443\) 32.0650i 1.52346i 0.647897 + 0.761728i \(0.275649\pi\)
−0.647897 + 0.761728i \(0.724351\pi\)
\(444\) 0 0
\(445\) 37.2208i 1.76444i
\(446\) 26.6821 + 1.14988i 1.26344 + 0.0544486i
\(447\) 0 0
\(448\) 7.73437 + 2.04438i 0.365415 + 0.0965879i
\(449\) 16.5474 0.780922 0.390461 0.920619i \(-0.372316\pi\)
0.390461 + 0.920619i \(0.372316\pi\)
\(450\) 0 0
\(451\) 0.0903588i 0.00425483i
\(452\) −22.3039 1.92598i −1.04909 0.0905904i
\(453\) 0 0
\(454\) −0.789796 + 18.3266i −0.0370670 + 0.860109i
\(455\) 3.39553 0.159185
\(456\) 0 0
\(457\) −26.9067 −1.25864 −0.629321 0.777145i \(-0.716667\pi\)
−0.629321 + 0.777145i \(0.716667\pi\)
\(458\) 0.360804 8.37217i 0.0168593 0.391206i
\(459\) 0 0
\(460\) 2.61125 30.2397i 0.121750 1.40993i
\(461\) 28.9351i 1.34764i 0.738895 + 0.673821i \(0.235348\pi\)
−0.738895 + 0.673821i \(0.764652\pi\)
\(462\) 0 0
\(463\) 10.3287 0.480017 0.240009 0.970771i \(-0.422850\pi\)
0.240009 + 0.970771i \(0.422850\pi\)
\(464\) 1.09442 6.28977i 0.0508074 0.291995i
\(465\) 0 0
\(466\) −17.2506 0.743426i −0.799119 0.0344386i
\(467\) 22.1113i 1.02319i −0.859227 0.511595i \(-0.829055\pi\)
0.859227 0.511595i \(-0.170945\pi\)
\(468\) 0 0
\(469\) 7.70421i 0.355747i
\(470\) −0.0639303 + 1.48345i −0.00294888 + 0.0684264i
\(471\) 0 0
\(472\) −5.49428 + 42.2862i −0.252895 + 1.94638i
\(473\) −26.2585 −1.20737
\(474\) 0 0
\(475\) 5.08446i 0.233291i
\(476\) 7.35861 + 0.635429i 0.337281 + 0.0291248i
\(477\) 0 0
\(478\) −31.8289 1.37169i −1.45582 0.0627395i
\(479\) −5.77499 −0.263866 −0.131933 0.991259i \(-0.542118\pi\)
−0.131933 + 0.991259i \(0.542118\pi\)
\(480\) 0 0
\(481\) 5.03140 0.229412
\(482\) 22.8644 + 0.985357i 1.04145 + 0.0448818i
\(483\) 0 0
\(484\) 10.6883 + 0.922954i 0.485832 + 0.0419525i
\(485\) 16.5100i 0.749680i
\(486\) 0 0
\(487\) 12.5566 0.568993 0.284497 0.958677i \(-0.408174\pi\)
0.284497 + 0.958677i \(0.408174\pi\)
\(488\) 2.01805 15.5317i 0.0913529 0.703088i
\(489\) 0 0
\(490\) −0.189605 + 4.39964i −0.00856550 + 0.198756i
\(491\) 20.9548i 0.945677i −0.881149 0.472839i \(-0.843229\pi\)
0.881149 0.472839i \(-0.156771\pi\)
\(492\) 0 0
\(493\) 5.89428i 0.265465i
\(494\) 1.66799 + 0.0718832i 0.0750465 + 0.00323418i
\(495\) 0 0
\(496\) 29.3792 + 5.11201i 1.31916 + 0.229536i
\(497\) −13.5472 −0.607675
\(498\) 0 0
\(499\) 13.0152i 0.582641i −0.956626 0.291320i \(-0.905905\pi\)
0.956626 0.291320i \(-0.0940946\pi\)
\(500\) 0.162666 1.88376i 0.00727464 0.0842443i
\(501\) 0 0
\(502\) −0.419200 + 9.72718i −0.0187098 + 0.434146i
\(503\) −22.9100 −1.02150 −0.510752 0.859728i \(-0.670633\pi\)
−0.510752 + 0.859728i \(0.670633\pi\)
\(504\) 0 0
\(505\) −0.234592 −0.0104392
\(506\) −0.704506 + 16.3475i −0.0313191 + 0.726735i
\(507\) 0 0
\(508\) −4.84475 0.418353i −0.214951 0.0185614i
\(509\) 24.5703i 1.08906i −0.838741 0.544530i \(-0.816708\pi\)
0.838741 0.544530i \(-0.183292\pi\)
\(510\) 0 0
\(511\) −14.6727 −0.649083
\(512\) −20.9487 8.55287i −0.925811 0.377987i
\(513\) 0 0
\(514\) 3.81680 + 0.164488i 0.168352 + 0.00725524i
\(515\) 47.7508i 2.10415i
\(516\) 0 0
\(517\) 0.800460i 0.0352042i
\(518\) −0.280953 + 6.51928i −0.0123444 + 0.286441i
\(519\) 0 0
\(520\) −9.52394 1.23745i −0.417652 0.0542660i
\(521\) 1.51316 0.0662929 0.0331465 0.999451i \(-0.489447\pi\)
0.0331465 + 0.999451i \(0.489447\pi\)
\(522\) 0 0
\(523\) 0.202190i 0.00884117i 0.999990 + 0.00442059i \(0.00140712\pi\)
−0.999990 + 0.00442059i \(0.998593\pi\)
\(524\) 1.52056 17.6089i 0.0664260 0.769249i
\(525\) 0 0
\(526\) −19.1448 0.825057i −0.834752 0.0359742i
\(527\) 27.5319 1.19931
\(528\) 0 0
\(529\) 0.752559 0.0327199
\(530\) −35.8426 1.54466i −1.55690 0.0670958i
\(531\) 0 0
\(532\) −0.186281 + 2.15723i −0.00807629 + 0.0935279i
\(533\) 0.0415038i 0.00179773i
\(534\) 0 0
\(535\) 12.5716 0.543520
\(536\) 2.80770 21.6092i 0.121274 0.933373i
\(537\) 0 0
\(538\) 0.390623 9.06408i 0.0168409 0.390780i
\(539\) 2.37402i 0.102256i
\(540\) 0 0
\(541\) 28.5045i 1.22550i 0.790275 + 0.612752i \(0.209938\pi\)
−0.790275 + 0.612752i \(0.790062\pi\)
\(542\) 20.5007 + 0.883490i 0.880580 + 0.0379492i
\(543\) 0 0
\(544\) −20.4082 4.46403i −0.874996 0.191394i
\(545\) −38.0940 −1.63177
\(546\) 0 0
\(547\) 37.9150i 1.62113i 0.585648 + 0.810565i \(0.300840\pi\)
−0.585648 + 0.810565i \(0.699160\pi\)
\(548\) 22.2130 + 1.91813i 0.948891 + 0.0819383i
\(549\) 0 0
\(550\) 0.678882 15.7529i 0.0289476 0.671706i
\(551\) 1.72795 0.0736132
\(552\) 0 0
\(553\) 5.18122 0.220328
\(554\) 1.54158 35.7712i 0.0654956 1.51977i
\(555\) 0 0
\(556\) 2.97194 34.4166i 0.126038 1.45959i
\(557\) 16.6109i 0.703828i −0.936032 0.351914i \(-0.885531\pi\)
0.936032 0.351914i \(-0.114469\pi\)
\(558\) 0 0
\(559\) 12.0611 0.510131
\(560\) 2.13521 12.2712i 0.0902289 0.518554i
\(561\) 0 0
\(562\) 1.01726 + 0.0438395i 0.0429105 + 0.00184926i
\(563\) 6.84219i 0.288364i −0.989551 0.144182i \(-0.953945\pi\)
0.989551 0.144182i \(-0.0460551\pi\)
\(564\) 0 0
\(565\) 34.8553i 1.46637i
\(566\) −0.689654 + 16.0029i −0.0289883 + 0.672651i
\(567\) 0 0
\(568\) 37.9979 + 4.93710i 1.59435 + 0.207156i
\(569\) −15.3184 −0.642180 −0.321090 0.947049i \(-0.604049\pi\)
−0.321090 + 0.947049i \(0.604049\pi\)
\(570\) 0 0
\(571\) 36.6853i 1.53523i 0.640911 + 0.767616i \(0.278557\pi\)
−0.640911 + 0.767616i \(0.721443\pi\)
\(572\) 5.15825 + 0.445424i 0.215677 + 0.0186241i
\(573\) 0 0
\(574\) 0.0537773 + 0.00231757i 0.00224462 + 9.67334e-5i
\(575\) −22.8886 −0.954523
\(576\) 0 0
\(577\) −23.9150 −0.995596 −0.497798 0.867293i \(-0.665858\pi\)
−0.497798 + 0.867293i \(0.665858\pi\)
\(578\) 4.74984 + 0.204697i 0.197567 + 0.00851429i
\(579\) 0 0
\(580\) −9.90315 0.855154i −0.411206 0.0355083i
\(581\) 0.138321i 0.00573852i
\(582\) 0 0
\(583\) 19.3404 0.800999
\(584\) 41.1548 + 5.34728i 1.70300 + 0.221272i
\(585\) 0 0
\(586\) 0.928978 21.5562i 0.0383757 0.890477i
\(587\) 45.0433i 1.85914i 0.368651 + 0.929568i \(0.379820\pi\)
−0.368651 + 0.929568i \(0.620180\pi\)
\(588\) 0 0
\(589\) 8.07118i 0.332567i
\(590\) 66.3294 + 2.85851i 2.73074 + 0.117683i
\(591\) 0 0
\(592\) 3.16389 18.1832i 0.130035 0.747325i
\(593\) 13.4524 0.552425 0.276212 0.961097i \(-0.410921\pi\)
0.276212 + 0.961097i \(0.410921\pi\)
\(594\) 0 0
\(595\) 11.4996i 0.471439i
\(596\) −2.36132 + 27.3454i −0.0967235 + 1.12011i
\(597\) 0 0
\(598\) 0.323596 7.50877i 0.0132328 0.307057i
\(599\) −21.8377 −0.892263 −0.446132 0.894967i \(-0.647199\pi\)
−0.446132 + 0.894967i \(0.647199\pi\)
\(600\) 0 0
\(601\) −16.3704 −0.667764 −0.333882 0.942615i \(-0.608359\pi\)
−0.333882 + 0.942615i \(0.608359\pi\)
\(602\) −0.673490 + 15.6278i −0.0274494 + 0.636942i
\(603\) 0 0
\(604\) −25.5440 2.20577i −1.03937 0.0897515i
\(605\) 16.7031i 0.679078i
\(606\) 0 0
\(607\) 28.8256 1.17000 0.584998 0.811034i \(-0.301095\pi\)
0.584998 + 0.811034i \(0.301095\pi\)
\(608\) 1.30866 5.98283i 0.0530734 0.242636i
\(609\) 0 0
\(610\) −24.3628 1.04993i −0.986421 0.0425105i
\(611\) 0.367669i 0.0148743i
\(612\) 0 0
\(613\) 34.6397i 1.39908i 0.714592 + 0.699541i \(0.246612\pi\)
−0.714592 + 0.699541i \(0.753388\pi\)
\(614\) 1.55572 36.0992i 0.0627837 1.45684i
\(615\) 0 0
\(616\) −0.865179 + 6.65876i −0.0348591 + 0.268289i
\(617\) 38.6359 1.55542 0.777711 0.628622i \(-0.216381\pi\)
0.777711 + 0.628622i \(0.216381\pi\)
\(618\) 0 0
\(619\) 25.9642i 1.04359i −0.853071 0.521794i \(-0.825263\pi\)
0.853071 0.521794i \(-0.174737\pi\)
\(620\) 3.99438 46.2571i 0.160418 1.85773i
\(621\) 0 0
\(622\) −4.24333 0.182869i −0.170142 0.00733239i
\(623\) −11.9531 −0.478891
\(624\) 0 0
\(625\) −26.4258 −1.05703
\(626\) 7.82694 + 0.337307i 0.312828 + 0.0134815i
\(627\) 0 0
\(628\) 3.63773 42.1269i 0.145161 1.68105i
\(629\) 17.0399i 0.679425i
\(630\) 0 0
\(631\) 5.94731 0.236759 0.118379 0.992968i \(-0.462230\pi\)
0.118379 + 0.992968i \(0.462230\pi\)
\(632\) −14.5325 1.88823i −0.578073 0.0751096i
\(633\) 0 0
\(634\) 1.95886 45.4538i 0.0777964 1.80520i
\(635\) 7.57112i 0.300451i
\(636\) 0 0
\(637\) 1.09044i 0.0432048i
\(638\) 5.35362 + 0.230718i 0.211952 + 0.00913420i
\(639\) 0 0
\(640\) −10.4610 + 33.6408i −0.413508 + 1.32977i
\(641\) −41.7290 −1.64820 −0.824098 0.566447i \(-0.808318\pi\)
−0.824098 + 0.566447i \(0.808318\pi\)
\(642\) 0 0
\(643\) 36.9825i 1.45845i −0.684275 0.729224i \(-0.739881\pi\)
0.684275 0.729224i \(-0.260119\pi\)
\(644\) 9.71118 + 0.838577i 0.382674 + 0.0330446i
\(645\) 0 0
\(646\) 0.243447 5.64900i 0.00957831 0.222257i
\(647\) −2.39044 −0.0939778 −0.0469889 0.998895i \(-0.514963\pi\)
−0.0469889 + 0.998895i \(0.514963\pi\)
\(648\) 0 0
\(649\) −35.7909 −1.40492
\(650\) −0.311826 + 7.23567i −0.0122308 + 0.283806i
\(651\) 0 0
\(652\) −0.0665141 + 0.770270i −0.00260489 + 0.0301661i
\(653\) 27.1588i 1.06280i −0.847120 0.531402i \(-0.821665\pi\)
0.847120 0.531402i \(-0.178335\pi\)
\(654\) 0 0
\(655\) −27.5183 −1.07523
\(656\) −0.149993 0.0260988i −0.00585623 0.00101899i
\(657\) 0 0
\(658\) −0.476396 0.0205306i −0.0185718 0.000800365i
\(659\) 41.3343i 1.61016i −0.593169 0.805078i \(-0.702123\pi\)
0.593169 0.805078i \(-0.297877\pi\)
\(660\) 0 0
\(661\) 6.44768i 0.250786i −0.992107 0.125393i \(-0.959981\pi\)
0.992107 0.125393i \(-0.0400192\pi\)
\(662\) 1.51992 35.2684i 0.0590733 1.37075i
\(663\) 0 0
\(664\) 0.0504093 0.387970i 0.00195626 0.0150562i
\(665\) 3.37121 0.130730
\(666\) 0 0
\(667\) 7.77869i 0.301192i
\(668\) −28.7601 2.48348i −1.11276 0.0960889i
\(669\) 0 0
\(670\) −33.8958 1.46076i −1.30951 0.0564341i
\(671\) 13.1460 0.507496
\(672\) 0 0
\(673\) −36.1564 −1.39373 −0.696863 0.717204i \(-0.745421\pi\)
−0.696863 + 0.717204i \(0.745421\pi\)
\(674\) −25.1354 1.08322i −0.968178 0.0417243i
\(675\) 0 0
\(676\) 23.5343 + 2.03223i 0.905165 + 0.0781626i
\(677\) 47.4088i 1.82207i −0.412330 0.911035i \(-0.635285\pi\)
0.412330 0.911035i \(-0.364715\pi\)
\(678\) 0 0
\(679\) −5.30202 −0.203473
\(680\) −4.19089 + 32.2548i −0.160713 + 1.23691i
\(681\) 0 0
\(682\) −1.07767 + 25.0065i −0.0412662 + 0.957548i
\(683\) 3.55646i 0.136084i −0.997682 0.0680420i \(-0.978325\pi\)
0.997682 0.0680420i \(-0.0216752\pi\)
\(684\) 0 0
\(685\) 34.7132i 1.32632i
\(686\) −1.41290 0.0608900i −0.0539449 0.00232479i
\(687\) 0 0
\(688\) 7.58438 43.5882i 0.289152 1.66178i
\(689\) −8.88350 −0.338435
\(690\) 0 0
\(691\) 41.6181i 1.58323i 0.611023 + 0.791613i \(0.290758\pi\)
−0.611023 + 0.791613i \(0.709242\pi\)
\(692\) −2.40017 + 27.7952i −0.0912407 + 1.05662i
\(693\) 0 0
\(694\) −0.126717 + 2.94036i −0.00481010 + 0.111615i
\(695\) −53.7845 −2.04016
\(696\) 0 0
\(697\) −0.140561 −0.00532414
\(698\) −0.433343 + 10.0554i −0.0164023 + 0.380602i
\(699\) 0 0
\(700\) −9.35797 0.808077i −0.353698 0.0305424i
\(701\) 34.8945i 1.31795i 0.752166 + 0.658973i \(0.229009\pi\)
−0.752166 + 0.658973i \(0.770991\pi\)
\(702\) 0 0
\(703\) 4.99537 0.188404
\(704\) 4.85340 18.3615i 0.182919 0.692026i
\(705\) 0 0
\(706\) −40.8963 1.76245i −1.53915 0.0663308i
\(707\) 0.0753369i 0.00283334i
\(708\) 0 0
\(709\) 49.2296i 1.84886i −0.381357 0.924428i \(-0.624543\pi\)
0.381357 0.924428i \(-0.375457\pi\)
\(710\) 2.56862 59.6028i 0.0963987 2.23685i
\(711\) 0 0
\(712\) 33.5267 + 4.35615i 1.25647 + 0.163254i
\(713\) 36.3339 1.36072
\(714\) 0 0
\(715\) 8.06103i 0.301466i
\(716\) 1.83367 21.2349i 0.0685274 0.793584i
\(717\) 0 0
\(718\) 14.1558 + 0.610054i 0.528290 + 0.0227670i
\(719\) 10.9969 0.410117 0.205058 0.978750i \(-0.434262\pi\)
0.205058 + 0.978750i \(0.434262\pi\)
\(720\) 0 0
\(721\) 15.3347 0.571095
\(722\) −25.1891 1.08554i −0.937441 0.0403996i
\(723\) 0 0
\(724\) 1.14227 13.2281i 0.0424521 0.491618i
\(725\) 7.49577i 0.278386i
\(726\) 0 0
\(727\) 9.03008 0.334907 0.167454 0.985880i \(-0.446446\pi\)
0.167454 + 0.985880i \(0.446446\pi\)
\(728\) 0.397396 3.05852i 0.0147285 0.113356i
\(729\) 0 0
\(730\) 2.78203 64.5547i 0.102967 2.38928i
\(731\) 40.8474i 1.51080i
\(732\) 0 0
\(733\) 41.6840i 1.53963i −0.638265 0.769817i \(-0.720347\pi\)
0.638265 0.769817i \(-0.279653\pi\)
\(734\) −44.4587 1.91598i −1.64100 0.0707200i
\(735\) 0 0
\(736\) −26.9328 5.89119i −0.992756 0.217152i
\(737\) 18.2899 0.673718
\(738\) 0 0
\(739\) 34.7320i 1.27764i 0.769358 + 0.638818i \(0.220576\pi\)
−0.769358 + 0.638818i \(0.779424\pi\)
\(740\) −28.6292 2.47218i −1.05243 0.0908792i
\(741\) 0 0
\(742\) 0.496053 11.5105i 0.0182107 0.422564i
\(743\) 15.9173 0.583951 0.291975 0.956426i \(-0.405687\pi\)
0.291975 + 0.956426i \(0.405687\pi\)
\(744\) 0 0
\(745\) 42.7339 1.56565
\(746\) 1.93704 44.9474i 0.0709201 1.64564i
\(747\) 0 0
\(748\) 1.50852 17.4695i 0.0551569 0.638747i
\(749\) 4.03726i 0.147518i
\(750\) 0 0
\(751\) 13.7001 0.499925 0.249963 0.968255i \(-0.419582\pi\)
0.249963 + 0.968255i \(0.419582\pi\)
\(752\) 1.32874 + 0.231201i 0.0484540 + 0.00843104i
\(753\) 0 0
\(754\) −2.45904 0.105974i −0.0895529 0.00385934i
\(755\) 39.9188i 1.45279i
\(756\) 0 0
\(757\) 27.3072i 0.992496i 0.868181 + 0.496248i \(0.165289\pi\)
−0.868181 + 0.496248i \(0.834711\pi\)
\(758\) −0.930435 + 21.5900i −0.0337949 + 0.784183i
\(759\) 0 0
\(760\) −9.45573 1.22859i −0.342995 0.0445657i
\(761\) 18.3078 0.663657 0.331829 0.943340i \(-0.392334\pi\)
0.331829 + 0.943340i \(0.392334\pi\)
\(762\) 0 0
\(763\) 12.2335i 0.442883i
\(764\) 19.5502 + 1.68819i 0.707301 + 0.0610767i
\(765\) 0 0
\(766\) −26.9236 1.16029i −0.972788 0.0419229i
\(767\) 16.4396 0.593598
\(768\) 0 0
\(769\) −13.3631 −0.481884 −0.240942 0.970540i \(-0.577456\pi\)
−0.240942 + 0.970540i \(0.577456\pi\)
\(770\) 10.4448 + 0.450127i 0.376405 + 0.0162214i
\(771\) 0 0
\(772\) 34.7784 + 3.00317i 1.25170 + 0.108087i
\(773\) 39.3918i 1.41682i 0.705799 + 0.708412i \(0.250588\pi\)
−0.705799 + 0.708412i \(0.749412\pi\)
\(774\) 0 0
\(775\) −35.0124 −1.25768
\(776\) 14.8714 + 1.93225i 0.533851 + 0.0693638i
\(777\) 0 0
\(778\) −0.224717 + 5.21438i −0.00805651 + 0.186945i
\(779\) 0.0412066i 0.00147638i
\(780\) 0 0
\(781\) 32.1613i 1.15082i
\(782\) −25.4300 1.09592i −0.909375 0.0391901i
\(783\) 0 0
\(784\) 3.94079 + 0.685701i 0.140742 + 0.0244893i
\(785\) −65.8336 −2.34970
\(786\)