Properties

Label 882.3.s.f.557.1
Level $882$
Weight $3$
Character 882.557
Analytic conductor $24.033$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 557.1
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 882.557
Dual form 882.3.s.f.863.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-1.73205 + 1.00000i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-1.73205 + 1.00000i) q^{5} +2.82843i q^{8} +(1.41421 - 2.44949i) q^{10} +(-2.44949 - 1.41421i) q^{11} +12.7279 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-19.0526 - 11.0000i) q^{17} +(2.82843 + 4.89898i) q^{19} +4.00000i q^{20} +4.00000 q^{22} +(-2.44949 + 1.41421i) q^{23} +(-10.5000 + 18.1865i) q^{25} +(-15.5885 + 9.00000i) q^{26} +35.3553i q^{29} +(16.9706 - 29.3939i) q^{31} +(4.89898 + 2.82843i) q^{32} +31.1127 q^{34} +(-32.0000 - 55.4256i) q^{37} +(-6.92820 - 4.00000i) q^{38} +(-2.82843 - 4.89898i) q^{40} -20.0000i q^{41} +44.0000 q^{43} +(-4.89898 + 2.82843i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-58.8897 + 34.0000i) q^{47} -29.6985i q^{50} +(12.7279 - 22.0454i) q^{52} +(15.9217 + 9.19239i) q^{53} +5.65685 q^{55} +(-25.0000 - 43.3013i) q^{58} +(-86.6025 - 50.0000i) q^{59} +(-26.1630 - 45.3156i) q^{61} +48.0000i q^{62} -8.00000 q^{64} +(-22.0454 + 12.7279i) q^{65} +(-60.0000 + 103.923i) q^{67} +(-38.1051 + 22.0000i) q^{68} -8.48528i q^{71} +(37.4767 - 64.9115i) q^{73} +(78.3837 + 45.2548i) q^{74} +11.3137 q^{76} +(-46.0000 - 79.6743i) q^{79} +(6.92820 + 4.00000i) q^{80} +(14.1421 + 24.4949i) q^{82} -112.000i q^{83} +44.0000 q^{85} +(-53.8888 + 31.1127i) q^{86} +(4.00000 - 6.92820i) q^{88} +(17.3205 - 10.0000i) q^{89} +5.65685i q^{92} +(48.0833 - 83.2827i) q^{94} +(-9.79796 - 5.65685i) q^{95} -26.8701 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} - 84 q^{25} - 256 q^{37} + 352 q^{43} + 16 q^{46} - 200 q^{58} - 64 q^{64} - 480 q^{67} - 368 q^{79} + 352 q^{85} + 32 q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) −1.73205 + 1.00000i −0.346410 + 0.200000i −0.663103 0.748528i \(-0.730761\pi\)
0.316693 + 0.948528i \(0.397428\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 1.41421 2.44949i 0.141421 0.244949i
\(11\) −2.44949 1.41421i −0.222681 0.128565i 0.384510 0.923121i \(-0.374370\pi\)
−0.607191 + 0.794556i \(0.707704\pi\)
\(12\) 0 0
\(13\) 12.7279 0.979071 0.489535 0.871983i \(-0.337166\pi\)
0.489535 + 0.871983i \(0.337166\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −19.0526 11.0000i −1.12074 0.647059i −0.179149 0.983822i \(-0.557335\pi\)
−0.941589 + 0.336763i \(0.890668\pi\)
\(18\) 0 0
\(19\) 2.82843 + 4.89898i 0.148865 + 0.257841i 0.930808 0.365508i \(-0.119105\pi\)
−0.781944 + 0.623349i \(0.785771\pi\)
\(20\) 4.00000i 0.200000i
\(21\) 0 0
\(22\) 4.00000 0.181818
\(23\) −2.44949 + 1.41421i −0.106500 + 0.0614875i −0.552304 0.833643i \(-0.686251\pi\)
0.445804 + 0.895131i \(0.352918\pi\)
\(24\) 0 0
\(25\) −10.5000 + 18.1865i −0.420000 + 0.727461i
\(26\) −15.5885 + 9.00000i −0.599556 + 0.346154i
\(27\) 0 0
\(28\) 0 0
\(29\) 35.3553i 1.21915i 0.792729 + 0.609575i \(0.208660\pi\)
−0.792729 + 0.609575i \(0.791340\pi\)
\(30\) 0 0
\(31\) 16.9706 29.3939i 0.547438 0.948190i −0.451012 0.892518i \(-0.648937\pi\)
0.998449 0.0556715i \(-0.0177300\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 31.1127 0.915079
\(35\) 0 0
\(36\) 0 0
\(37\) −32.0000 55.4256i −0.864865 1.49799i −0.867181 0.497993i \(-0.834071\pi\)
0.00231643 0.999997i \(-0.499263\pi\)
\(38\) −6.92820 4.00000i −0.182321 0.105263i
\(39\) 0 0
\(40\) −2.82843 4.89898i −0.0707107 0.122474i
\(41\) 20.0000i 0.487805i −0.969800 0.243902i \(-0.921572\pi\)
0.969800 0.243902i \(-0.0784277\pi\)
\(42\) 0 0
\(43\) 44.0000 1.02326 0.511628 0.859207i \(-0.329043\pi\)
0.511628 + 0.859207i \(0.329043\pi\)
\(44\) −4.89898 + 2.82843i −0.111340 + 0.0642824i
\(45\) 0 0
\(46\) 2.00000 3.46410i 0.0434783 0.0753066i
\(47\) −58.8897 + 34.0000i −1.25297 + 0.723404i −0.971699 0.236223i \(-0.924090\pi\)
−0.281274 + 0.959627i \(0.590757\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 29.6985i 0.593970i
\(51\) 0 0
\(52\) 12.7279 22.0454i 0.244768 0.423950i
\(53\) 15.9217 + 9.19239i 0.300409 + 0.173441i 0.642627 0.766179i \(-0.277845\pi\)
−0.342218 + 0.939621i \(0.611178\pi\)
\(54\) 0 0
\(55\) 5.65685 0.102852
\(56\) 0 0
\(57\) 0 0
\(58\) −25.0000 43.3013i −0.431034 0.746574i
\(59\) −86.6025 50.0000i −1.46784 0.847458i −0.468488 0.883470i \(-0.655201\pi\)
−0.999351 + 0.0360121i \(0.988535\pi\)
\(60\) 0 0
\(61\) −26.1630 45.3156i −0.428901 0.742878i 0.567875 0.823115i \(-0.307766\pi\)
−0.996776 + 0.0802368i \(0.974432\pi\)
\(62\) 48.0000i 0.774194i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) −22.0454 + 12.7279i −0.339160 + 0.195814i
\(66\) 0 0
\(67\) −60.0000 + 103.923i −0.895522 + 1.55109i −0.0623656 + 0.998053i \(0.519864\pi\)
−0.833157 + 0.553037i \(0.813469\pi\)
\(68\) −38.1051 + 22.0000i −0.560369 + 0.323529i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.48528i 0.119511i −0.998213 0.0597555i \(-0.980968\pi\)
0.998213 0.0597555i \(-0.0190321\pi\)
\(72\) 0 0
\(73\) 37.4767 64.9115i 0.513379 0.889198i −0.486501 0.873680i \(-0.661727\pi\)
0.999880 0.0155181i \(-0.00493978\pi\)
\(74\) 78.3837 + 45.2548i 1.05924 + 0.611552i
\(75\) 0 0
\(76\) 11.3137 0.148865
\(77\) 0 0
\(78\) 0 0
\(79\) −46.0000 79.6743i −0.582278 1.00854i −0.995209 0.0977733i \(-0.968828\pi\)
0.412930 0.910763i \(-0.364505\pi\)
\(80\) 6.92820 + 4.00000i 0.0866025 + 0.0500000i
\(81\) 0 0
\(82\) 14.1421 + 24.4949i 0.172465 + 0.298718i
\(83\) 112.000i 1.34940i −0.738093 0.674699i \(-0.764274\pi\)
0.738093 0.674699i \(-0.235726\pi\)
\(84\) 0 0
\(85\) 44.0000 0.517647
\(86\) −53.8888 + 31.1127i −0.626614 + 0.361776i
\(87\) 0 0
\(88\) 4.00000 6.92820i 0.0454545 0.0787296i
\(89\) 17.3205 10.0000i 0.194612 0.112360i −0.399528 0.916721i \(-0.630826\pi\)
0.594140 + 0.804362i \(0.297492\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.65685i 0.0614875i
\(93\) 0 0
\(94\) 48.0833 83.2827i 0.511524 0.885986i
\(95\) −9.79796 5.65685i −0.103136 0.0595458i
\(96\) 0 0
\(97\) −26.8701 −0.277011 −0.138505 0.990362i \(-0.544230\pi\)
−0.138505 + 0.990362i \(0.544230\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 21.0000 + 36.3731i 0.210000 + 0.363731i
\(101\) −72.7461 42.0000i −0.720259 0.415842i 0.0945892 0.995516i \(-0.469846\pi\)
−0.814848 + 0.579675i \(0.803180\pi\)
\(102\) 0 0
\(103\) −79.1960 137.171i −0.768893 1.33176i −0.938164 0.346192i \(-0.887475\pi\)
0.169271 0.985570i \(-0.445859\pi\)
\(104\) 36.0000i 0.346154i
\(105\) 0 0
\(106\) −26.0000 −0.245283
\(107\) −120.025 + 69.2965i −1.12173 + 0.647631i −0.941842 0.336057i \(-0.890907\pi\)
−0.179887 + 0.983687i \(0.557573\pi\)
\(108\) 0 0
\(109\) −35.0000 + 60.6218i −0.321101 + 0.556163i −0.980715 0.195441i \(-0.937386\pi\)
0.659615 + 0.751604i \(0.270720\pi\)
\(110\) −6.92820 + 4.00000i −0.0629837 + 0.0363636i
\(111\) 0 0
\(112\) 0 0
\(113\) 21.2132i 0.187727i −0.995585 0.0938637i \(-0.970078\pi\)
0.995585 0.0938637i \(-0.0299218\pi\)
\(114\) 0 0
\(115\) 2.82843 4.89898i 0.0245950 0.0425998i
\(116\) 61.2372 + 35.3553i 0.527907 + 0.304787i
\(117\) 0 0
\(118\) 141.421 1.19849
\(119\) 0 0
\(120\) 0 0
\(121\) −56.5000 97.8609i −0.466942 0.808768i
\(122\) 64.0859 + 37.0000i 0.525294 + 0.303279i
\(123\) 0 0
\(124\) −33.9411 58.7878i −0.273719 0.474095i
\(125\) 92.0000i 0.736000i
\(126\) 0 0
\(127\) −20.0000 −0.157480 −0.0787402 0.996895i \(-0.525090\pi\)
−0.0787402 + 0.996895i \(0.525090\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 18.0000 31.1769i 0.138462 0.239822i
\(131\) 124.708 72.0000i 0.951967 0.549618i 0.0582755 0.998301i \(-0.481440\pi\)
0.893691 + 0.448682i \(0.148106\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 169.706i 1.26646i
\(135\) 0 0
\(136\) 31.1127 53.8888i 0.228770 0.396241i
\(137\) −172.689 99.7021i −1.26050 0.727752i −0.287332 0.957831i \(-0.592768\pi\)
−0.973172 + 0.230079i \(0.926102\pi\)
\(138\) 0 0
\(139\) −5.65685 −0.0406968 −0.0203484 0.999793i \(-0.506478\pi\)
−0.0203484 + 0.999793i \(0.506478\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.0422535 + 0.0731852i
\(143\) −31.1769 18.0000i −0.218020 0.125874i
\(144\) 0 0
\(145\) −35.3553 61.2372i −0.243830 0.422326i
\(146\) 106.000i 0.726027i
\(147\) 0 0
\(148\) −128.000 −0.864865
\(149\) −15.9217 + 9.19239i −0.106857 + 0.0616939i −0.552476 0.833529i \(-0.686317\pi\)
0.445619 + 0.895223i \(0.352984\pi\)
\(150\) 0 0
\(151\) 32.0000 55.4256i 0.211921 0.367057i −0.740395 0.672172i \(-0.765362\pi\)
0.952316 + 0.305115i \(0.0986949\pi\)
\(152\) −13.8564 + 8.00000i −0.0911606 + 0.0526316i
\(153\) 0 0
\(154\) 0 0
\(155\) 67.8823i 0.437950i
\(156\) 0 0
\(157\) 81.3173 140.846i 0.517944 0.897106i −0.481838 0.876260i \(-0.660031\pi\)
0.999783 0.0208459i \(-0.00663595\pi\)
\(158\) 112.677 + 65.0538i 0.713143 + 0.411733i
\(159\) 0 0
\(160\) −11.3137 −0.0707107
\(161\) 0 0
\(162\) 0 0
\(163\) 112.000 + 193.990i 0.687117 + 1.19012i 0.972767 + 0.231787i \(0.0744572\pi\)
−0.285650 + 0.958334i \(0.592209\pi\)
\(164\) −34.6410 20.0000i −0.211226 0.121951i
\(165\) 0 0
\(166\) 79.1960 + 137.171i 0.477084 + 0.826334i
\(167\) 292.000i 1.74850i −0.485473 0.874251i \(-0.661353\pi\)
0.485473 0.874251i \(-0.338647\pi\)
\(168\) 0 0
\(169\) −7.00000 −0.0414201
\(170\) −53.8888 + 31.1127i −0.316993 + 0.183016i
\(171\) 0 0
\(172\) 44.0000 76.2102i 0.255814 0.443083i
\(173\) 135.100 78.0000i 0.780925 0.450867i −0.0558332 0.998440i \(-0.517782\pi\)
0.836758 + 0.547573i \(0.184448\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 11.3137i 0.0642824i
\(177\) 0 0
\(178\) −14.1421 + 24.4949i −0.0794502 + 0.137612i
\(179\) 80.8332 + 46.6690i 0.451582 + 0.260721i 0.708498 0.705713i \(-0.249373\pi\)
−0.256916 + 0.966434i \(0.582706\pi\)
\(180\) 0 0
\(181\) −190.919 −1.05480 −0.527400 0.849617i \(-0.676833\pi\)
−0.527400 + 0.849617i \(0.676833\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.00000 6.92820i −0.0217391 0.0376533i
\(185\) 110.851 + 64.0000i 0.599196 + 0.345946i
\(186\) 0 0
\(187\) 31.1127 + 53.8888i 0.166378 + 0.288175i
\(188\) 136.000i 0.723404i
\(189\) 0 0
\(190\) 16.0000 0.0842105
\(191\) 115.126 66.4680i 0.602754 0.348000i −0.167370 0.985894i \(-0.553528\pi\)
0.770124 + 0.637894i \(0.220194\pi\)
\(192\) 0 0
\(193\) −61.0000 + 105.655i −0.316062 + 0.547436i −0.979663 0.200651i \(-0.935694\pi\)
0.663601 + 0.748087i \(0.269027\pi\)
\(194\) 32.9090 19.0000i 0.169634 0.0979381i
\(195\) 0 0
\(196\) 0 0
\(197\) 7.07107i 0.0358937i −0.999839 0.0179469i \(-0.994287\pi\)
0.999839 0.0179469i \(-0.00571297\pi\)
\(198\) 0 0
\(199\) −186.676 + 323.333i −0.938071 + 1.62479i −0.169008 + 0.985615i \(0.554056\pi\)
−0.769063 + 0.639172i \(0.779277\pi\)
\(200\) −51.4393 29.6985i −0.257196 0.148492i
\(201\) 0 0
\(202\) 118.794 0.588089
\(203\) 0 0
\(204\) 0 0
\(205\) 20.0000 + 34.6410i 0.0975610 + 0.168981i
\(206\) 193.990 + 112.000i 0.941698 + 0.543689i
\(207\) 0 0
\(208\) −25.4558 44.0908i −0.122384 0.211975i
\(209\) 16.0000i 0.0765550i
\(210\) 0 0
\(211\) −12.0000 −0.0568720 −0.0284360 0.999596i \(-0.509053\pi\)
−0.0284360 + 0.999596i \(0.509053\pi\)
\(212\) 31.8434 18.3848i 0.150205 0.0867206i
\(213\) 0 0
\(214\) 98.0000 169.741i 0.457944 0.793182i
\(215\) −76.2102 + 44.0000i −0.354466 + 0.204651i
\(216\) 0 0
\(217\) 0 0
\(218\) 98.9949i 0.454105i
\(219\) 0 0
\(220\) 5.65685 9.79796i 0.0257130 0.0445362i
\(221\) −242.499 140.007i −1.09728 0.633516i
\(222\) 0 0
\(223\) −203.647 −0.913214 −0.456607 0.889668i \(-0.650935\pi\)
−0.456607 + 0.889668i \(0.650935\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 15.0000 + 25.9808i 0.0663717 + 0.114959i
\(227\) −176.669 102.000i −0.778278 0.449339i 0.0575414 0.998343i \(-0.481674\pi\)
−0.835820 + 0.549004i \(0.815007\pi\)
\(228\) 0 0
\(229\) 23.3345 + 40.4166i 0.101897 + 0.176492i 0.912466 0.409152i \(-0.134175\pi\)
−0.810569 + 0.585643i \(0.800842\pi\)
\(230\) 8.00000i 0.0347826i
\(231\) 0 0
\(232\) −100.000 −0.431034
\(233\) 268.219 154.856i 1.15116 0.664620i 0.201987 0.979388i \(-0.435260\pi\)
0.949168 + 0.314769i \(0.101927\pi\)
\(234\) 0 0
\(235\) 68.0000 117.779i 0.289362 0.501189i
\(236\) −173.205 + 100.000i −0.733920 + 0.423729i
\(237\) 0 0
\(238\) 0 0
\(239\) 42.4264i 0.177516i 0.996053 + 0.0887582i \(0.0282898\pi\)
−0.996053 + 0.0887582i \(0.971710\pi\)
\(240\) 0 0
\(241\) −188.798 + 327.007i −0.783392 + 1.35688i 0.146563 + 0.989201i \(0.453179\pi\)
−0.929955 + 0.367674i \(0.880154\pi\)
\(242\) 138.396 + 79.9031i 0.571885 + 0.330178i
\(243\) 0 0
\(244\) −104.652 −0.428901
\(245\) 0 0
\(246\) 0 0
\(247\) 36.0000 + 62.3538i 0.145749 + 0.252445i
\(248\) 83.1384 + 48.0000i 0.335236 + 0.193548i
\(249\) 0 0
\(250\) 65.0538 + 112.677i 0.260215 + 0.450706i
\(251\) 332.000i 1.32271i 0.750073 + 0.661355i \(0.230018\pi\)
−0.750073 + 0.661355i \(0.769982\pi\)
\(252\) 0 0
\(253\) 8.00000 0.0316206
\(254\) 24.4949 14.1421i 0.0964366 0.0556777i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 155.885 90.0000i 0.606555 0.350195i −0.165061 0.986283i \(-0.552782\pi\)
0.771616 + 0.636089i \(0.219449\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 50.9117i 0.195814i
\(261\) 0 0
\(262\) −101.823 + 176.363i −0.388639 + 0.673142i
\(263\) −139.621 80.6102i −0.530878 0.306503i 0.210496 0.977595i \(-0.432492\pi\)
−0.741374 + 0.671092i \(0.765825\pi\)
\(264\) 0 0
\(265\) −36.7696 −0.138753
\(266\) 0 0
\(267\) 0 0
\(268\) 120.000 + 207.846i 0.447761 + 0.775545i
\(269\) 455.529 + 263.000i 1.69342 + 0.977695i 0.951723 + 0.306957i \(0.0993108\pi\)
0.741694 + 0.670738i \(0.234022\pi\)
\(270\) 0 0
\(271\) 214.960 + 372.322i 0.793212 + 1.37388i 0.923968 + 0.382469i \(0.124926\pi\)
−0.130756 + 0.991415i \(0.541741\pi\)
\(272\) 88.0000i 0.323529i
\(273\) 0 0
\(274\) 282.000 1.02920
\(275\) 51.4393 29.6985i 0.187052 0.107994i
\(276\) 0 0
\(277\) −32.0000 + 55.4256i −0.115523 + 0.200093i −0.917989 0.396606i \(-0.870188\pi\)
0.802465 + 0.596699i \(0.203521\pi\)
\(278\) 6.92820 4.00000i 0.0249216 0.0143885i
\(279\) 0 0
\(280\) 0 0
\(281\) 448.306i 1.59539i 0.603058 + 0.797697i \(0.293949\pi\)
−0.603058 + 0.797697i \(0.706051\pi\)
\(282\) 0 0
\(283\) −62.2254 + 107.778i −0.219878 + 0.380839i −0.954770 0.297344i \(-0.903899\pi\)
0.734893 + 0.678183i \(0.237233\pi\)
\(284\) −14.6969 8.48528i −0.0517498 0.0298778i
\(285\) 0 0
\(286\) 50.9117 0.178013
\(287\) 0 0
\(288\) 0 0
\(289\) 97.5000 + 168.875i 0.337370 + 0.584342i
\(290\) 86.6025 + 50.0000i 0.298629 + 0.172414i
\(291\) 0 0
\(292\) −74.9533 129.823i −0.256689 0.444599i
\(293\) 284.000i 0.969283i 0.874713 + 0.484642i \(0.161050\pi\)
−0.874713 + 0.484642i \(0.838950\pi\)
\(294\) 0 0
\(295\) 200.000 0.677966
\(296\) 156.767 90.5097i 0.529619 0.305776i
\(297\) 0 0
\(298\) 13.0000 22.5167i 0.0436242 0.0755593i
\(299\) −31.1769 + 18.0000i −0.104271 + 0.0602007i
\(300\) 0 0
\(301\) 0 0
\(302\) 90.5097i 0.299701i
\(303\) 0 0
\(304\) 11.3137 19.5959i 0.0372161 0.0644603i
\(305\) 90.6311 + 52.3259i 0.297151 + 0.171560i
\(306\) 0 0
\(307\) −282.843 −0.921312 −0.460656 0.887579i \(-0.652386\pi\)
−0.460656 + 0.887579i \(0.652386\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −48.0000 83.1384i −0.154839 0.268189i
\(311\) −162.813 94.0000i −0.523514 0.302251i 0.214857 0.976645i \(-0.431071\pi\)
−0.738371 + 0.674395i \(0.764405\pi\)
\(312\) 0 0
\(313\) 108.187 + 187.386i 0.345646 + 0.598677i 0.985471 0.169844i \(-0.0543263\pi\)
−0.639825 + 0.768521i \(0.720993\pi\)
\(314\) 230.000i 0.732484i
\(315\) 0 0
\(316\) −184.000 −0.582278
\(317\) 395.593 228.395i 1.24793 0.720491i 0.277231 0.960803i \(-0.410583\pi\)
0.970695 + 0.240313i \(0.0772500\pi\)
\(318\) 0 0
\(319\) 50.0000 86.6025i 0.156740 0.271481i
\(320\) 13.8564 8.00000i 0.0433013 0.0250000i
\(321\) 0 0
\(322\) 0 0
\(323\) 124.451i 0.385297i
\(324\) 0 0
\(325\) −133.643 + 231.477i −0.411210 + 0.712236i
\(326\) −274.343 158.392i −0.841542 0.485865i
\(327\) 0 0
\(328\) 56.5685 0.172465
\(329\) 0 0
\(330\) 0 0
\(331\) 250.000 + 433.013i 0.755287 + 1.30820i 0.945232 + 0.326401i \(0.105836\pi\)
−0.189945 + 0.981795i \(0.560831\pi\)
\(332\) −193.990 112.000i −0.584306 0.337349i
\(333\) 0 0
\(334\) 206.475 + 357.626i 0.618189 + 1.07074i
\(335\) 240.000i 0.716418i
\(336\) 0 0
\(337\) 86.0000 0.255193 0.127596 0.991826i \(-0.459274\pi\)
0.127596 + 0.991826i \(0.459274\pi\)
\(338\) 8.57321 4.94975i 0.0253645 0.0146442i
\(339\) 0 0
\(340\) 44.0000 76.2102i 0.129412 0.224148i
\(341\) −83.1384 + 48.0000i −0.243808 + 0.140762i
\(342\) 0 0
\(343\) 0 0
\(344\) 124.451i 0.361776i
\(345\) 0 0
\(346\) −110.309 + 191.060i −0.318811 + 0.552197i
\(347\) −213.106 123.037i −0.614137 0.354572i 0.160446 0.987045i \(-0.448707\pi\)
−0.774583 + 0.632472i \(0.782040\pi\)
\(348\) 0 0
\(349\) 445.477 1.27644 0.638220 0.769854i \(-0.279671\pi\)
0.638220 + 0.769854i \(0.279671\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −8.00000 13.8564i −0.0227273 0.0393648i
\(353\) 188.794 + 109.000i 0.534826 + 0.308782i 0.742979 0.669314i \(-0.233412\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(354\) 0 0
\(355\) 8.48528 + 14.6969i 0.0239022 + 0.0413998i
\(356\) 40.0000i 0.112360i
\(357\) 0 0
\(358\) −132.000 −0.368715
\(359\) −320.883 + 185.262i −0.893825 + 0.516050i −0.875192 0.483776i \(-0.839265\pi\)
−0.0186333 + 0.999826i \(0.505931\pi\)
\(360\) 0 0
\(361\) 164.500 284.922i 0.455679 0.789259i
\(362\) 233.827 135.000i 0.645931 0.372928i
\(363\) 0 0
\(364\) 0 0
\(365\) 149.907i 0.410703i
\(366\) 0 0
\(367\) −223.446 + 387.019i −0.608844 + 1.05455i 0.382587 + 0.923919i \(0.375033\pi\)
−0.991431 + 0.130629i \(0.958300\pi\)
\(368\) 9.79796 + 5.65685i 0.0266249 + 0.0153719i
\(369\) 0 0
\(370\) −181.019 −0.489241
\(371\) 0 0
\(372\) 0 0
\(373\) −143.000 247.683i −0.383378 0.664030i 0.608165 0.793811i \(-0.291906\pi\)
−0.991543 + 0.129781i \(0.958573\pi\)
\(374\) −76.2102 44.0000i −0.203771 0.117647i
\(375\) 0 0
\(376\) −96.1665 166.565i −0.255762 0.442993i
\(377\) 450.000i 1.19363i
\(378\) 0 0
\(379\) −188.000 −0.496042 −0.248021 0.968755i \(-0.579780\pi\)
−0.248021 + 0.968755i \(0.579780\pi\)
\(380\) −19.5959 + 11.3137i −0.0515682 + 0.0297729i
\(381\) 0 0
\(382\) −94.0000 + 162.813i −0.246073 + 0.426211i
\(383\) −304.841 + 176.000i −0.795929 + 0.459530i −0.842046 0.539406i \(-0.818649\pi\)
0.0461164 + 0.998936i \(0.485315\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 172.534i 0.446979i
\(387\) 0 0
\(388\) −26.8701 + 46.5403i −0.0692527 + 0.119949i
\(389\) −177.588 102.530i −0.456524 0.263575i 0.254057 0.967189i \(-0.418235\pi\)
−0.710582 + 0.703615i \(0.751568\pi\)
\(390\) 0 0
\(391\) 62.2254 0.159144
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 + 8.66025i 0.0126904 + 0.0219803i
\(395\) 159.349 + 92.0000i 0.403414 + 0.232911i
\(396\) 0 0
\(397\) −122.329 211.881i −0.308135 0.533705i 0.669820 0.742524i \(-0.266371\pi\)
−0.977954 + 0.208819i \(0.933038\pi\)
\(398\) 528.000i 1.32663i
\(399\) 0 0
\(400\) 84.0000 0.210000
\(401\) 385.795 222.739i 0.962081 0.555458i 0.0652684 0.997868i \(-0.479210\pi\)
0.896813 + 0.442410i \(0.145876\pi\)
\(402\) 0 0
\(403\) 216.000 374.123i 0.535980 0.928345i
\(404\) −145.492 + 84.0000i −0.360129 + 0.207921i
\(405\) 0 0
\(406\) 0 0
\(407\) 181.019i 0.444765i
\(408\) 0 0
\(409\) 375.474 650.340i 0.918029 1.59007i 0.115623 0.993293i \(-0.463114\pi\)
0.802406 0.596779i \(-0.203553\pi\)
\(410\) −48.9898 28.2843i −0.119487 0.0689860i
\(411\) 0 0
\(412\) −316.784 −0.768893
\(413\) 0 0
\(414\) 0 0
\(415\) 112.000 + 193.990i 0.269880 + 0.467445i
\(416\) 62.3538 + 36.0000i 0.149889 + 0.0865385i
\(417\) 0 0
\(418\) 11.3137 + 19.5959i 0.0270663 + 0.0468802i
\(419\) 236.000i 0.563246i −0.959525 0.281623i \(-0.909127\pi\)
0.959525 0.281623i \(-0.0908727\pi\)
\(420\) 0 0
\(421\) −96.0000 −0.228029 −0.114014 0.993479i \(-0.536371\pi\)
−0.114014 + 0.993479i \(0.536371\pi\)
\(422\) 14.6969 8.48528i 0.0348269 0.0201073i
\(423\) 0 0
\(424\) −26.0000 + 45.0333i −0.0613208 + 0.106211i
\(425\) 400.104 231.000i 0.941421 0.543529i
\(426\) 0 0
\(427\) 0 0
\(428\) 277.186i 0.647631i
\(429\) 0 0
\(430\) 62.2254 107.778i 0.144710 0.250645i
\(431\) 742.195 + 428.507i 1.72203 + 0.994215i 0.914719 + 0.404090i \(0.132412\pi\)
0.807312 + 0.590125i \(0.200922\pi\)
\(432\) 0 0
\(433\) 156.978 0.362535 0.181268 0.983434i \(-0.441980\pi\)
0.181268 + 0.983434i \(0.441980\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 70.0000 + 121.244i 0.160550 + 0.278082i
\(437\) −13.8564 8.00000i −0.0317080 0.0183066i
\(438\) 0 0
\(439\) 322.441 + 558.484i 0.734489 + 1.27217i 0.954947 + 0.296776i \(0.0959114\pi\)
−0.220458 + 0.975396i \(0.570755\pi\)
\(440\) 16.0000i 0.0363636i
\(441\) 0 0
\(442\) 396.000 0.895928
\(443\) −502.145 + 289.914i −1.13351 + 0.654433i −0.944816 0.327603i \(-0.893759\pi\)
−0.188695 + 0.982036i \(0.560426\pi\)
\(444\) 0 0
\(445\) −20.0000 + 34.6410i −0.0449438 + 0.0778450i
\(446\) 249.415 144.000i 0.559227 0.322870i
\(447\) 0 0
\(448\) 0 0
\(449\) 869.741i 1.93706i −0.248891 0.968532i \(-0.580066\pi\)
0.248891 0.968532i \(-0.419934\pi\)
\(450\) 0 0
\(451\) −28.2843 + 48.9898i −0.0627146 + 0.108625i
\(452\) −36.7423 21.2132i −0.0812884 0.0469319i
\(453\) 0 0
\(454\) 288.500 0.635462
\(455\) 0 0
\(456\) 0 0
\(457\) −192.000 332.554i −0.420131 0.727689i 0.575821 0.817576i \(-0.304683\pi\)
−0.995952 + 0.0898873i \(0.971349\pi\)
\(458\) −57.1577 33.0000i −0.124798 0.0720524i
\(459\) 0 0
\(460\) −5.65685 9.79796i −0.0122975 0.0212999i
\(461\) 268.000i 0.581345i −0.956823 0.290672i \(-0.906121\pi\)
0.956823 0.290672i \(-0.0938790\pi\)
\(462\) 0 0
\(463\) −716.000 −1.54644 −0.773218 0.634140i \(-0.781354\pi\)
−0.773218 + 0.634140i \(0.781354\pi\)
\(464\) 122.474 70.7107i 0.263954 0.152394i
\(465\) 0 0
\(466\) −219.000 + 379.319i −0.469957 + 0.813990i
\(467\) −266.736 + 154.000i −0.571169 + 0.329764i −0.757616 0.652701i \(-0.773636\pi\)
0.186447 + 0.982465i \(0.440303\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 192.333i 0.409219i
\(471\) 0 0
\(472\) 141.421 244.949i 0.299622 0.518960i
\(473\) −107.778 62.2254i −0.227860 0.131555i
\(474\) 0 0
\(475\) −118.794 −0.250093
\(476\) 0 0
\(477\) 0 0
\(478\) −30.0000 51.9615i −0.0627615 0.108706i
\(479\) −336.018 194.000i −0.701499 0.405010i 0.106407 0.994323i \(-0.466065\pi\)
−0.807905 + 0.589312i \(0.799399\pi\)
\(480\) 0 0
\(481\) −407.294 705.453i −0.846764 1.46664i
\(482\) 534.000i 1.10788i
\(483\) 0 0
\(484\) −226.000 −0.466942
\(485\) 46.5403 26.8701i 0.0959594 0.0554022i
\(486\) 0 0
\(487\) −60.0000 + 103.923i −0.123203 + 0.213394i −0.921029 0.389494i \(-0.872650\pi\)
0.797826 + 0.602888i \(0.205983\pi\)
\(488\) 128.172 74.0000i 0.262647 0.151639i
\(489\) 0 0
\(490\) 0 0
\(491\) 619.426i 1.26156i −0.775962 0.630780i \(-0.782735\pi\)
0.775962 0.630780i \(-0.217265\pi\)
\(492\) 0 0
\(493\) 388.909 673.610i 0.788862 1.36635i
\(494\) −88.1816 50.9117i −0.178505 0.103060i
\(495\) 0 0
\(496\) −135.765 −0.273719
\(497\) 0 0
\(498\) 0 0
\(499\) −238.000 412.228i −0.476954 0.826108i 0.522697 0.852518i \(-0.324926\pi\)
−0.999651 + 0.0264100i \(0.991592\pi\)
\(500\) −159.349 92.0000i −0.318697 0.184000i
\(501\) 0 0
\(502\) −234.759 406.615i −0.467648 0.809991i
\(503\) 968.000i 1.92445i 0.272250 + 0.962227i \(0.412232\pi\)
−0.272250 + 0.962227i \(0.587768\pi\)
\(504\) 0 0
\(505\) 168.000 0.332673
\(506\) −9.79796 + 5.65685i −0.0193636 + 0.0111796i
\(507\) 0 0
\(508\) −20.0000 + 34.6410i −0.0393701 + 0.0681910i
\(509\) 219.970 127.000i 0.432162 0.249509i −0.268105 0.963390i \(-0.586398\pi\)
0.700267 + 0.713881i \(0.253064\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −127.279 + 220.454i −0.247625 + 0.428899i
\(515\) 274.343 + 158.392i 0.532705 + 0.307557i
\(516\) 0 0
\(517\) 192.333 0.372017
\(518\) 0 0
\(519\) 0 0
\(520\) −36.0000 62.3538i −0.0692308 0.119911i
\(521\) 698.016 + 403.000i 1.33976 + 0.773512i 0.986772 0.162114i \(-0.0518313\pi\)
0.352991 + 0.935627i \(0.385165\pi\)
\(522\) 0 0
\(523\) −305.470 529.090i −0.584073 1.01164i −0.994990 0.0999714i \(-0.968125\pi\)
0.410917 0.911673i \(-0.365208\pi\)
\(524\) 288.000i 0.549618i
\(525\) 0 0
\(526\) 228.000 0.433460
\(527\) −646.665 + 373.352i −1.22707 + 0.708449i
\(528\) 0 0
\(529\) −260.500 + 451.199i −0.492439 + 0.852929i
\(530\) 45.0333 26.0000i 0.0849685 0.0490566i
\(531\) 0 0
\(532\) 0 0
\(533\) 254.558i 0.477596i
\(534\) 0 0
\(535\) 138.593 240.050i 0.259052 0.448692i
\(536\) −293.939 169.706i −0.548393 0.316615i
\(537\) 0 0
\(538\) −743.876 −1.38267
\(539\) 0 0
\(540\) 0 0
\(541\) 40.0000 + 69.2820i 0.0739372 + 0.128063i 0.900624 0.434600i \(-0.143110\pi\)
−0.826686 + 0.562663i \(0.809777\pi\)
\(542\) −526.543 304.000i −0.971482 0.560886i
\(543\) 0 0
\(544\) −62.2254 107.778i −0.114385 0.198120i
\(545\) 140.000i 0.256881i
\(546\) 0 0
\(547\) 256.000 0.468007 0.234004 0.972236i \(-0.424817\pi\)
0.234004 + 0.972236i \(0.424817\pi\)
\(548\) −345.378 + 199.404i −0.630252 + 0.363876i
\(549\) 0 0
\(550\) −42.0000 + 72.7461i −0.0763636 + 0.132266i
\(551\) −173.205 + 100.000i −0.314347 + 0.181488i
\(552\) 0 0
\(553\) 0 0
\(554\) 90.5097i 0.163375i
\(555\) 0 0
\(556\) −5.65685 + 9.79796i −0.0101742 + 0.0176222i
\(557\) 679.733 + 392.444i 1.22035 + 0.704568i 0.964992 0.262279i \(-0.0844742\pi\)
0.255355 + 0.966847i \(0.417808\pi\)
\(558\) 0 0
\(559\) 560.029 1.00184
\(560\) 0 0
\(561\) 0 0
\(562\) −317.000 549.060i −0.564057 0.976975i
\(563\) −523.079 302.000i −0.929093 0.536412i −0.0425684 0.999094i \(-0.513554\pi\)
−0.886525 + 0.462681i \(0.846887\pi\)
\(564\) 0 0
\(565\) 21.2132 + 36.7423i 0.0375455 + 0.0650307i
\(566\) 176.000i 0.310954i
\(567\) 0 0
\(568\) 24.0000 0.0422535
\(569\) −375.997 + 217.082i −0.660803 + 0.381515i −0.792583 0.609764i \(-0.791264\pi\)
0.131780 + 0.991279i \(0.457931\pi\)
\(570\) 0 0
\(571\) 124.000 214.774i 0.217163 0.376137i −0.736777 0.676136i \(-0.763653\pi\)
0.953939 + 0.299999i \(0.0969864\pi\)
\(572\) −62.3538 + 36.0000i −0.109010 + 0.0629371i
\(573\) 0 0
\(574\) 0 0
\(575\) 59.3970i 0.103299i
\(576\) 0 0
\(577\) 383.959 665.036i 0.665440 1.15258i −0.313726 0.949514i \(-0.601577\pi\)
0.979166 0.203063i \(-0.0650895\pi\)
\(578\) −238.825 137.886i −0.413192 0.238557i
\(579\) 0 0
\(580\) −141.421 −0.243830
\(581\) 0 0
\(582\) 0 0
\(583\) −26.0000 45.0333i −0.0445969 0.0772441i
\(584\) 183.597 + 106.000i 0.314379 + 0.181507i
\(585\) 0 0
\(586\) −200.818 347.828i −0.342693 0.593562i
\(587\) 1140.00i 1.94208i −0.238920 0.971039i \(-0.576793\pi\)
0.238920 0.971039i \(-0.423207\pi\)
\(588\) 0 0
\(589\) 192.000 0.325976
\(590\) −244.949 + 141.421i −0.415168 + 0.239697i
\(591\) 0 0
\(592\) −128.000 + 221.703i −0.216216 + 0.374497i
\(593\) −590.629 + 341.000i −0.996002 + 0.575042i −0.907063 0.420995i \(-0.861681\pi\)
−0.0889392 + 0.996037i \(0.528348\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 36.7696i 0.0616939i
\(597\) 0 0
\(598\) 25.4558 44.0908i 0.0425683 0.0737305i
\(599\) 913.660 + 527.502i 1.52531 + 0.880637i 0.999550 + 0.0300033i \(0.00955177\pi\)
0.525759 + 0.850634i \(0.323782\pi\)
\(600\) 0 0
\(601\) 555.786 0.924769 0.462384 0.886680i \(-0.346994\pi\)
0.462384 + 0.886680i \(0.346994\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −64.0000 110.851i −0.105960 0.183529i
\(605\) 195.722 + 113.000i 0.323507 + 0.186777i
\(606\) 0 0
\(607\) −212.132 367.423i −0.349476 0.605310i 0.636680 0.771128i \(-0.280307\pi\)
−0.986156 + 0.165817i \(0.946974\pi\)
\(608\) 32.0000i 0.0526316i
\(609\) 0 0
\(610\) −148.000 −0.242623
\(611\) −749.544 + 432.749i −1.22675 + 0.708264i
\(612\) 0 0
\(613\) −156.000 + 270.200i −0.254486 + 0.440783i −0.964756 0.263147i \(-0.915240\pi\)
0.710270 + 0.703930i \(0.248573\pi\)
\(614\) 346.410 200.000i 0.564186 0.325733i
\(615\) 0 0
\(616\) 0 0
\(617\) 490.732i 0.795352i 0.917526 + 0.397676i \(0.130183\pi\)
−0.917526 + 0.397676i \(0.869817\pi\)
\(618\) 0 0
\(619\) 138.593 240.050i 0.223898 0.387803i −0.732090 0.681208i \(-0.761455\pi\)
0.955988 + 0.293405i \(0.0947884\pi\)
\(620\) 117.576 + 67.8823i 0.189638 + 0.109488i
\(621\) 0 0
\(622\) 265.872 0.427447
\(623\) 0 0
\(624\) 0 0
\(625\) −170.500 295.315i −0.272800 0.472503i
\(626\) −265.004 153.000i −0.423329 0.244409i
\(627\) 0 0
\(628\) −162.635 281.691i −0.258972 0.448553i
\(629\) 1408.00i 2.23847i
\(630\) 0 0
\(631\) −316.000 −0.500792 −0.250396 0.968143i \(-0.580561\pi\)
−0.250396 + 0.968143i \(0.580561\pi\)
\(632\) 225.353 130.108i 0.356571 0.205867i
\(633\) 0 0
\(634\) −323.000 + 559.452i −0.509464 + 0.882417i
\(635\) 34.6410 20.0000i 0.0545528 0.0314961i
\(636\) 0 0
\(637\) 0 0
\(638\) 141.421i 0.221664i
\(639\) 0 0
\(640\) −11.3137 + 19.5959i −0.0176777 + 0.0306186i
\(641\) −375.997 217.082i −0.586578 0.338661i 0.177165 0.984181i \(-0.443307\pi\)
−0.763743 + 0.645520i \(0.776641\pi\)
\(642\) 0 0
\(643\) −158.392 −0.246333 −0.123166 0.992386i \(-0.539305\pi\)
−0.123166 + 0.992386i \(0.539305\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 88.0000 + 152.420i 0.136223 + 0.235945i
\(647\) −758.638 438.000i −1.17255 0.676971i −0.218269 0.975889i \(-0.570041\pi\)
−0.954279 + 0.298918i \(0.903374\pi\)
\(648\) 0 0
\(649\) 141.421 + 244.949i 0.217907 + 0.377425i
\(650\) 378.000i 0.581538i
\(651\) 0 0
\(652\) 448.000 0.687117
\(653\) 253.522 146.371i 0.388242 0.224152i −0.293156 0.956065i \(-0.594706\pi\)
0.681398 + 0.731913i \(0.261372\pi\)
\(654\) 0 0
\(655\) −144.000 + 249.415i −0.219847 + 0.380787i
\(656\) −69.2820 + 40.0000i −0.105613 + 0.0609756i
\(657\) 0 0
\(658\) 0 0
\(659\) 907.925i 1.37773i −0.724889 0.688866i \(-0.758109\pi\)
0.724889 0.688866i \(-0.241891\pi\)
\(660\) 0 0
\(661\) 392.444 679.733i 0.593713 1.02834i −0.400014 0.916509i \(-0.630995\pi\)
0.993727 0.111832i \(-0.0356719\pi\)
\(662\) −612.372 353.553i −0.925034 0.534069i
\(663\) 0 0
\(664\) 316.784 0.477084
\(665\) 0 0
\(666\) 0 0
\(667\) −50.0000 86.6025i −0.0749625 0.129839i
\(668\) −505.759 292.000i −0.757124 0.437126i
\(669\) 0 0
\(670\) 169.706 + 293.939i 0.253292 + 0.438715i
\(671\) 148.000i 0.220566i
\(672\) 0 0
\(673\) −264.000 −0.392273 −0.196137 0.980577i \(-0.562840\pi\)
−0.196137 + 0.980577i \(0.562840\pi\)
\(674\) −105.328 + 60.8112i −0.156273 + 0.0902243i
\(675\) 0 0
\(676\) −7.00000 + 12.1244i −0.0103550 + 0.0179354i
\(677\) 259.808 150.000i 0.383763 0.221566i −0.295691 0.955284i \(-0.595550\pi\)
0.679454 + 0.733718i \(0.262217\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 124.451i 0.183016i
\(681\) 0 0
\(682\) 67.8823 117.576i 0.0995341 0.172398i
\(683\) 1006.74 + 581.242i 1.47400 + 0.851013i 0.999571 0.0292824i \(-0.00932220\pi\)
0.474426 + 0.880295i \(0.342656\pi\)
\(684\) 0 0
\(685\) 398.808 0.582202
\(686\) 0 0
\(687\) 0 0
\(688\) −88.0000 152.420i −0.127907 0.221541i
\(689\) 202.650 + 117.000i 0.294122 + 0.169811i
\(690\) 0 0
\(691\) 254.558 + 440.908i 0.368391 + 0.638073i 0.989314 0.145799i \(-0.0465753\pi\)
−0.620923 + 0.783872i \(0.713242\pi\)
\(692\) 312.000i 0.450867i
\(693\) 0 0
\(694\) 348.000 0.501441
\(695\) 9.79796 5.65685i 0.0140978 0.00813936i
\(696\) 0 0
\(697\) −220.000 + 381.051i −0.315638 + 0.546702i
\(698\) −545.596 + 315.000i −0.781656 + 0.451289i
\(699\) 0 0
\(700\) 0 0
\(701\) 182.434i 0.260248i −0.991498 0.130124i \(-0.958463\pi\)
0.991498 0.130124i \(-0.0415375\pi\)
\(702\) 0 0
\(703\) 181.019 313.535i 0.257495 0.445995i
\(704\) 19.5959 + 11.3137i 0.0278351 + 0.0160706i
\(705\) 0 0
\(706\) −308.299 −0.436684
\(707\) 0 0
\(708\) 0 0
\(709\) −659.000 1141.42i −0.929478 1.60990i −0.784196 0.620513i \(-0.786924\pi\)
−0.145282 0.989390i \(-0.546409\pi\)
\(710\) −20.7846 12.0000i −0.0292741 0.0169014i
\(711\) 0 0
\(712\) 28.2843 + 48.9898i 0.0397251 + 0.0688059i
\(713\) 96.0000i 0.134642i
\(714\) 0 0
\(715\) 72.0000 0.100699
\(716\) 161.666 93.3381i 0.225791 0.130360i
\(717\) 0 0
\(718\) 262.000 453.797i 0.364903 0.632030i
\(719\) −879.882 + 508.000i −1.22376 + 0.706537i −0.965717 0.259597i \(-0.916410\pi\)
−0.258041 + 0.966134i \(0.583077\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 465.276i 0.644427i
\(723\) 0 0
\(724\) −190.919 + 330.681i −0.263700 + 0.456742i
\(725\) −642.991 371.231i −0.886884 0.512043i
\(726\) 0 0
\(727\) 384.666 0.529114 0.264557 0.964370i \(-0.414774\pi\)
0.264557 + 0.964370i \(0.414774\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −106.000 183.597i −0.145205 0.251503i
\(731\) −838.313 484.000i −1.14680 0.662107i
\(732\) 0 0
\(733\) −277.893 481.325i −0.379117 0.656650i 0.611817 0.791000i \(-0.290439\pi\)
−0.990934 + 0.134349i \(0.957106\pi\)
\(734\) 632.000i 0.861035i
\(735\) 0 0
\(736\) −16.0000 −0.0217391
\(737\) 293.939 169.706i 0.398831 0.230265i
\(738\) 0 0
\(739\) 600.000 1039.23i 0.811908 1.40627i −0.0996190 0.995026i \(-0.531762\pi\)
0.911527 0.411240i \(-0.134904\pi\)
\(740\) 221.703 128.000i 0.299598 0.172973i
\(741\) 0 0
\(742\) 0 0
\(743\) 1309.56i 1.76253i 0.472620 + 0.881266i \(0.343308\pi\)
−0.472620 + 0.881266i \(0.656692\pi\)
\(744\) 0 0
\(745\) 18.3848 31.8434i 0.0246776 0.0427428i
\(746\) 350.277 + 202.233i 0.469540 + 0.271089i
\(747\) 0 0
\(748\) 124.451 0.166378
\(749\) 0 0
\(750\) 0 0
\(751\) 284.000 + 491.902i 0.378162 + 0.654997i 0.990795 0.135371i \(-0.0432227\pi\)
−0.612632 + 0.790368i \(0.709889\pi\)
\(752\) 235.559 + 136.000i 0.313243 + 0.180851i
\(753\) 0 0
\(754\) −318.198 551.135i −0.422013 0.730949i
\(755\) 128.000i 0.169536i
\(756\) 0 0
\(757\) −358.000 −0.472919 −0.236460 0.971641i \(-0.575987\pi\)
−0.236460 + 0.971641i \(0.575987\pi\)
\(758\) 230.252 132.936i 0.303763 0.175377i
\(759\) 0 0
\(760\) 16.0000 27.7128i 0.0210526 0.0364642i
\(761\) −439.941 + 254.000i −0.578109 + 0.333771i −0.760382 0.649477i \(-0.774988\pi\)
0.182273 + 0.983248i \(0.441655\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 265.872i 0.348000i
\(765\) 0 0
\(766\) 248.902 431.110i 0.324937 0.562807i
\(767\) −1102.27 636.396i −1.43712 0.829721i
\(768\) 0 0
\(769\) 861.256 1.11997 0.559984 0.828503i \(-0.310807\pi\)
0.559984 + 0.828503i \(0.310807\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 122.000 + 211.310i 0.158031 + 0.273718i
\(773\) 772.495 + 446.000i 0.999346 + 0.576973i 0.908055 0.418851i \(-0.137567\pi\)
0.0912915 + 0.995824i \(0.470901\pi\)
\(774\) 0 0
\(775\) 356.382 + 617.271i 0.459848 + 0.796479i
\(776\) 76.0000i 0.0979381i
\(777\) 0 0
\(778\) 290.000 0.372751
\(779\) 97.9796 56.5685i 0.125776 0.0726169i
\(780\) 0 0
\(781\) −12.0000 + 20.7846i −0.0153649 + 0.0266128i
\(782\) −76.2102 + 44.0000i −0.0974555 + 0.0562660i
\(783\) 0 0
\(784\) 0 0
\(785\) 325.269i 0.414356i
\(786\) 0 0
\(787\) −214.960 + 372.322i −0.273139 + 0.473091i −0.969664 0.244442i \(-0.921395\pi\)
0.696525 + 0.717533i \(0.254729\pi\)
\(788\) −12.2474 7.07107i −0.0155424 0.00897344i
\(789\) 0 0
\(790\) −260.215 −0.329386
\(791\) 0 0
\(792\) 0 0