Properties

Label 882.3.s.f.557.3
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 557.3
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 882.557
Dual form 882.3.s.f.863.3

$q$-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 0.607191 0.794556i \(-0.292296\pi\)
−0.384510 + 0.923121i \(0.625630\pi\)
\(12\) 0 0
\(13\) −12.7279 −0.979071 −0.489535 0.871983i \(-0.662834\pi\)
−0.489535 + 0.871983i \(0.662834\pi\)
\(14\) 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 0.781944 0.623349i \(-0.214229\pi\)
−0.930808 + 0.365508i \(0.880895\pi\)
\(20\) 4.00000i 0.200000i
\(21\) 0 0
\(22\) 4.00000 0.181818
\(23\) 2.44949 1.41421i 0.106500 0.0614875i −0.445804 0.895131i \(-0.647082\pi\)
0.552304 + 0.833643i \(0.313749\pi\)
\(24\) 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 \(-0.791340\pi\)
0.792729 0.609575i \(-0.208660\pi\)
\(30\) 0 0
\(31\) −16.9706 + 29.3939i −0.547438 + 0.948190i 0.451012 + 0.892518i \(0.351063\pi\)
−0.998449 + 0.0556715i \(0.982270\pi\)
\(32\) −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 0.342218 0.939621i \(-0.388822\pi\)
−0.642627 + 0.766179i \(0.722155\pi\)
\(54\) 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 0.996776 0.0802368i \(-0.0255676\pi\)
−0.567875 + 0.823115i \(0.692234\pi\)
\(62\) 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 \(0.0190321\pi\)
−0.998213 + 0.0597555i \(0.980968\pi\)
\(72\) 0 0
\(73\) −37.4767 + 64.9115i −0.513379 + 0.889198i 0.486501 + 0.873680i \(0.338273\pi\)
−0.999880 + 0.0155181i \(0.995060\pi\)
\(74\) −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 \(-0.455770\pi\)
0.138505 + 0.990362i \(0.455770\pi\)
\(98\) 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 \(0.112525\pi\)
−0.169271 + 0.985570i \(0.554141\pi\)
\(104\) 36.0000i 0.346154i
\(105\) 0 0
\(106\) −26.0000 −0.245283
\(107\) 120.025 69.2965i 1.12173 0.647631i 0.179887 0.983687i \(-0.442427\pi\)
0.941842 + 0.336057i \(0.109093\pi\)
\(108\) 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 \(0.0299218\pi\)
−0.995585 + 0.0938637i \(0.970078\pi\)
\(114\) 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 0.973172 0.230079i \(-0.0738984\pi\)
0.287332 + 0.957831i \(0.407232\pi\)
\(138\) 0 0
\(139\) 5.65685 0.0406968 0.0203484 0.999793i \(-0.493522\pi\)
0.0203484 + 0.999793i \(0.493522\pi\)
\(140\) 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 −0.445619 0.895223i \(-0.647016\pi\)
0.552476 + 0.833529i \(0.313683\pi\)
\(150\) 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 \(0.339969\pi\)
−0.999783 + 0.0208459i \(0.993364\pi\)
\(158\) −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 0.256916 0.966434i \(-0.417294\pi\)
−0.708498 + 0.705713i \(0.750627\pi\)
\(180\) 0 0
\(181\) 190.919 1.05480 0.527400 0.849617i \(-0.323167\pi\)
0.527400 + 0.849617i \(0.323167\pi\)
\(182\) 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 −0.770124 0.637894i \(-0.779806\pi\)
0.167370 + 0.985894i \(0.446472\pi\)
\(192\) 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 \(0.00571297\pi\)
−0.999839 + 0.0179469i \(0.994287\pi\)
\(198\) 0 0
\(199\) 186.676 323.333i 0.938071 1.62479i 0.169008 0.985615i \(-0.445944\pi\)
0.769063 0.639172i \(-0.220723\pi\)
\(200\) 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 \(-0.349065\pi\)
0.456607 + 0.889668i \(0.349065\pi\)
\(224\) 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 0.810569 0.585643i \(-0.199158\pi\)
−0.912466 + 0.409152i \(0.865825\pi\)
\(230\) 8.00000i 0.0347826i
\(231\) 0 0
\(232\) −100.000 −0.431034
\(233\) −268.219 + 154.856i −1.15116 + 0.664620i −0.949168 0.314769i \(-0.898073\pi\)
−0.201987 + 0.979388i \(0.564740\pi\)
\(234\) 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 \(-0.971710\pi\)
0.996053 0.0887582i \(-0.0282898\pi\)
\(240\) 0 0
\(241\) 188.798 327.007i 0.783392 1.35688i −0.146563 0.989201i \(-0.546821\pi\)
0.929955 0.367674i \(-0.119846\pi\)
\(242\) −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 0.741374 0.671092i \(-0.234175\pi\)
−0.210496 + 0.977595i \(0.567508\pi\)
\(264\) 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 \(-0.875074\pi\)
0.130756 0.991415i \(-0.458259\pi\)
\(272\) 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 \(-0.706051\pi\)
0.603058 0.797697i \(-0.293949\pi\)
\(282\) 0 0
\(283\) 62.2254 107.778i 0.219878 0.380839i −0.734893 0.678183i \(-0.762767\pi\)
0.954770 + 0.297344i \(0.0961008\pi\)
\(284\) 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 \(-0.347614\pi\)
0.460656 + 0.887579i \(0.347614\pi\)
\(308\) 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 0.639825 0.768521i \(-0.279007\pi\)
−0.985471 + 0.169844i \(0.945674\pi\)
\(314\) 230.000i 0.732484i
\(315\) 0 0
\(316\) −184.000 −0.582278
\(317\) −395.593 + 228.395i −1.24793 + 0.720491i −0.970695 0.240313i \(-0.922750\pi\)
−0.277231 + 0.960803i \(0.589417\pi\)
\(318\) 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 0.774583 0.632472i \(-0.217960\pi\)
−0.160446 + 0.987045i \(0.551293\pi\)
\(348\) 0 0
\(349\) −445.477 −1.27644 −0.638220 0.769854i \(-0.720329\pi\)
−0.638220 + 0.769854i \(0.720329\pi\)
\(350\) 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 0.0186333 0.999826i \(-0.494069\pi\)
0.875192 + 0.483776i \(0.160735\pi\)
\(360\) 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 \(-0.624967\pi\)
0.991431 0.130629i \(-0.0416998\pi\)
\(368\) −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 0.710582 0.703615i \(-0.248432\pi\)
−0.254057 + 0.967189i \(0.581765\pi\)
\(390\) 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 0.977954 0.208819i \(-0.0669619\pi\)
−0.669820 + 0.742524i \(0.733629\pi\)
\(398\) 528.000i 1.32663i
\(399\) 0 0
\(400\) 84.0000 0.210000
\(401\) −385.795 + 222.739i −0.962081 + 0.555458i −0.896813 0.442410i \(-0.854124\pi\)
−0.0652684 + 0.997868i \(0.520790\pi\)
\(402\) 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 \(0.536886\pi\)
−0.802406 + 0.596779i \(0.796447\pi\)
\(410\) 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 \(-0.867588\pi\)
−0.807312 0.590125i \(-0.799078\pi\)
\(432\) 0 0
\(433\) −156.978 −0.362535 −0.181268 0.983434i \(-0.558020\pi\)
−0.181268 + 0.983434i \(0.558020\pi\)
\(434\) 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 \(-0.904089\pi\)
0.220458 0.975396i \(-0.429245\pi\)
\(440\) 16.0000i 0.0363636i
\(441\) 0 0
\(442\) 396.000 0.895928
\(443\) 502.145 289.914i 1.13351 0.654433i 0.188695 0.982036i \(-0.439574\pi\)
0.944816 + 0.327603i \(0.106241\pi\)
\(444\) 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 \(0.419934\pi\)
−0.248891 + 0.968532i \(0.580066\pi\)
\(450\) 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 \(0.217265\pi\)
−0.775962 + 0.630780i \(0.782735\pi\)
\(492\) 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 \(0.0318751\pi\)
−0.410917 + 0.911673i \(0.634792\pi\)
\(524\) 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 −0.255355 0.966847i \(-0.582192\pi\)
−0.964992 + 0.262279i \(0.915526\pi\)
\(558\) 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 −0.131780 0.991279i \(-0.542069\pi\)
0.792583 + 0.609764i \(0.208736\pi\)
\(570\) 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 \(0.398423\pi\)
−0.979166 + 0.203063i \(0.934911\pi\)
\(578\) 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 \(-0.990448\pi\)
−0.525759 0.850634i \(-0.676218\pi\)
\(600\) 0 0
\(601\) −555.786 −0.924769 −0.462384 0.886680i \(-0.653006\pi\)
−0.462384 + 0.886680i \(0.653006\pi\)
\(602\) 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 0.986156 0.165817i \(-0.0530262\pi\)
−0.636680 + 0.771128i \(0.719693\pi\)
\(608\) 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 \(-0.869817\pi\)
0.917526 0.397676i \(-0.130183\pi\)
\(618\) 0 0
\(619\) −138.593 + 240.050i −0.223898 + 0.387803i −0.955988 0.293405i \(-0.905212\pi\)
0.732090 + 0.681208i \(0.238545\pi\)
\(620\) −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 0.763743 0.645520i \(-0.223359\pi\)
−0.177165 + 0.984181i \(0.556693\pi\)
\(642\) 0 0
\(643\) 158.392 0.246333 0.123166 0.992386i \(-0.460695\pi\)
0.123166 + 0.992386i \(0.460695\pi\)
\(644\) 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 −0.681398 0.731913i \(-0.738628\pi\)
0.293156 + 0.956065i \(0.405294\pi\)
\(654\) 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 \(0.241891\pi\)
−0.724889 + 0.688866i \(0.758109\pi\)
\(660\) 0 0
\(661\) −392.444 + 679.733i −0.593713 + 1.02834i 0.400014 + 0.916509i \(0.369005\pi\)
−0.993727 + 0.111832i \(0.964328\pi\)
\(662\) 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 −0.474426 0.880295i \(-0.657344\pi\)
−0.999571 + 0.0292824i \(0.990678\pi\)
\(684\) 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 0.620923 0.783872i \(-0.286758\pi\)
−0.989314 + 0.145799i \(0.953425\pi\)
\(692\) 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 \(0.0415375\pi\)
−0.991498 + 0.130124i \(0.958463\pi\)
\(702\) 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 \(-0.585226\pi\)
−0.264557 + 0.964370i \(0.585226\pi\)
\(728\) 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 0.990934 0.134349i \(-0.0428944\pi\)
−0.611817 + 0.791000i \(0.709561\pi\)
\(734\) 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 \(-0.656692\pi\)
0.472620 0.881266i \(-0.343308\pi\)
\(744\) 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 \(-0.689193\pi\)
−0.559984 + 0.828503i \(0.689193\pi\)
\(770\) 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 −0.696525 0.717533i \(-0.745271\pi\)
0.969664 + 0.244442i \(0.0786047\pi\)
\(788\) 12.2474 + 7.07107i 0.0155424 + 0.00897344i
\(789\) 0 0
\(790\) 260.215 0.329386
\(791\) 0 0
\(792\) 0 0