Properties

Label 882.3.s.f.863.4
Level $882$
Weight $3$
Character 882.863
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 863.4
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.f.557.4

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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 \(-0.269239\pi\)
−0.316693 + 0.948528i \(0.602572\pi\)
\(6\) 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 \(-0.625630\pi\)
0.607191 + 0.794556i \(0.292296\pi\)
\(12\) 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 \(-0.442665\pi\)
0.941589 + 0.336763i \(0.109332\pi\)
\(18\) 0 0
\(19\) 2.82843 4.89898i 0.148865 0.257841i −0.781944 0.623349i \(-0.785771\pi\)
0.930808 + 0.365508i \(0.119105\pi\)
\(20\) 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 \(-0.313749\pi\)
−0.445804 + 0.895131i \(0.647082\pi\)
\(24\) 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 0.998449 + 0.0556715i \(0.0177300\pi\)
−0.451012 + 0.892518i \(0.648937\pi\)
\(32\) −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 0.00231643 + 0.999997i \(0.499263\pi\)
−0.867181 + 0.497993i \(0.834071\pi\)
\(38\) 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 \(-0.0759097\pi\)
0.281274 + 0.959627i \(0.409243\pi\)
\(48\) 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 \(-0.722155\pi\)
0.342218 + 0.939621i \(0.388822\pi\)
\(54\) 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 \(-0.344799\pi\)
0.999351 + 0.0360121i \(0.0114655\pi\)
\(60\) 0 0
\(61\) −26.1630 + 45.3156i −0.428901 + 0.742878i −0.996776 0.0802368i \(-0.974432\pi\)
0.567875 + 0.823115i \(0.307766\pi\)
\(62\) 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 −0.833157 0.553037i \(-0.813469\pi\)
−0.0623656 0.998053i \(-0.519864\pi\)
\(68\) 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 0.999880 + 0.0155181i \(0.00493978\pi\)
−0.486501 + 0.873680i \(0.661727\pi\)
\(74\) −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 0.412930 + 0.910763i \(0.364505\pi\)
−0.995209 + 0.0977733i \(0.968828\pi\)
\(80\) −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 \(-0.369174\pi\)
−0.594140 + 0.804362i \(0.702508\pi\)
\(90\) 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 \(-0.530154\pi\)
0.814848 + 0.579675i \(0.196820\pi\)
\(102\) 0 0
\(103\) −79.1960 + 137.171i −0.768893 + 1.33176i 0.169271 + 0.985570i \(0.445859\pi\)
−0.938164 + 0.346192i \(0.887475\pi\)
\(104\) 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 \(-0.109093\pi\)
0.179887 + 0.983687i \(0.442427\pi\)
\(108\) 0 0
\(109\) −35.0000 60.6218i −0.321101 0.556163i 0.659615 0.751604i \(-0.270720\pi\)
−0.980715 + 0.195441i \(0.937386\pi\)
\(110\) 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 \(-0.518560\pi\)
−0.893691 + 0.448682i \(0.851894\pi\)
\(132\) 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 \(-0.407232\pi\)
0.973172 + 0.230079i \(0.0738984\pi\)
\(138\) 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 \(-0.313683\pi\)
−0.445619 + 0.895223i \(0.647016\pi\)
\(150\) 0 0
\(151\) 32.0000 + 55.4256i 0.211921 + 0.367057i 0.952316 0.305115i \(-0.0986949\pi\)
−0.740395 + 0.672172i \(0.765362\pi\)
\(152\) 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 0.999783 + 0.0208459i \(0.00663595\pi\)
−0.481838 + 0.876260i \(0.660031\pi\)
\(158\) −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 −0.285650 0.958334i \(-0.592209\pi\)
0.972767 0.231787i \(-0.0744572\pi\)
\(164\) 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 \(-0.482218\pi\)
−0.836758 + 0.547573i \(0.815552\pi\)
\(174\) 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 \(-0.750627\pi\)
0.256916 + 0.966434i \(0.417294\pi\)
\(180\) 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 \(-0.446472\pi\)
−0.770124 + 0.637894i \(0.779806\pi\)
\(192\) 0 0
\(193\) −61.0000 105.655i −0.316062 0.547436i 0.663601 0.748087i \(-0.269027\pi\)
−0.979663 + 0.200651i \(0.935694\pi\)
\(194\) −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 −0.769063 0.639172i \(-0.779277\pi\)
−0.169008 0.985615i \(-0.554056\pi\)
\(200\) 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 \(-0.518326\pi\)
0.835820 + 0.549004i \(0.184993\pi\)
\(228\) 0 0
\(229\) 23.3345 40.4166i 0.101897 0.176492i −0.810569 0.585643i \(-0.800842\pi\)
0.912466 + 0.409152i \(0.134175\pi\)
\(230\) 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 \(-0.564740\pi\)
−0.949168 + 0.314769i \(0.898073\pi\)
\(234\) 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 −0.929955 0.367674i \(-0.880154\pi\)
0.146563 0.989201i \(-0.453179\pi\)
\(242\) −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 \(-0.447218\pi\)
−0.771616 + 0.636089i \(0.780551\pi\)
\(258\) 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 \(-0.567508\pi\)
0.741374 + 0.671092i \(0.234175\pi\)
\(264\) 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 −0.741694 + 0.670738i \(0.765978\pi\)
−0.951723 + 0.306957i \(0.900689\pi\)
\(270\) 0 0
\(271\) 214.960 372.322i 0.793212 1.37388i −0.130756 0.991415i \(-0.541741\pi\)
0.923968 0.382469i \(-0.124926\pi\)
\(272\) 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 0.802465 0.596699i \(-0.203521\pi\)
−0.917989 + 0.396606i \(0.870188\pi\)
\(278\) −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 0.734893 0.678183i \(-0.237233\pi\)
−0.954770 + 0.297344i \(0.903899\pi\)
\(284\) 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 \(-0.568929\pi\)
0.738371 + 0.674395i \(0.235595\pi\)
\(312\) 0 0
\(313\) 108.187 187.386i 0.345646 0.598677i −0.639825 0.768521i \(-0.720993\pi\)
0.985471 + 0.169844i \(0.0543263\pi\)
\(314\) 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 \(-0.589417\pi\)
−0.970695 + 0.240313i \(0.922750\pi\)
\(318\) 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 −0.189945 0.981795i \(-0.560831\pi\)
0.945232 0.326401i \(-0.105836\pi\)
\(332\) 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 \(-0.551293\pi\)
0.774583 + 0.632472i \(0.217960\pi\)
\(348\) 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 \(-0.766588\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(354\) 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 \(-0.160735\pi\)
0.0186333 + 0.999826i \(0.494069\pi\)
\(360\) 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 −0.991431 0.130629i \(-0.958300\pi\)
0.382587 0.923919i \(-0.375033\pi\)
\(368\) −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 −0.991543 0.129781i \(-0.958573\pi\)
0.608165 + 0.793811i \(0.291906\pi\)
\(374\) 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 \(-0.181351\pi\)
−0.0461164 + 0.998936i \(0.514685\pi\)
\(384\) 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 \(-0.581765\pi\)
0.710582 + 0.703615i \(0.248432\pi\)
\(390\) 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 \(-0.933038\pi\)
0.669820 + 0.742524i \(0.266371\pi\)
\(398\) 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 \(-0.520790\pi\)
−0.896813 + 0.442410i \(0.854124\pi\)
\(402\) 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 0.802406 + 0.596779i \(0.203553\pi\)
0.115623 + 0.993293i \(0.463114\pi\)
\(410\) 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 −0.807312 + 0.590125i \(0.799078\pi\)
−0.914719 + 0.404090i \(0.867588\pi\)
\(432\) 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 −0.220458 0.975396i \(-0.570755\pi\)
0.954947 0.296776i \(-0.0959114\pi\)
\(440\) 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 \(-0.106241\pi\)
0.188695 + 0.982036i \(0.439574\pi\)
\(444\) 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 −0.995952 0.0898873i \(-0.971349\pi\)
0.575821 + 0.817576i \(0.304683\pi\)
\(458\) 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 \(-0.226364\pi\)
−0.186447 + 0.982465i \(0.559697\pi\)
\(468\) 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 \(-0.533935\pi\)
0.807905 + 0.589312i \(0.200601\pi\)
\(480\) 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 0.797826 0.602888i \(-0.205983\pi\)
−0.921029 + 0.389494i \(0.872650\pi\)
\(488\) −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 −0.999651 0.0264100i \(-0.991592\pi\)
0.522697 + 0.852518i \(0.324926\pi\)
\(500\) 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 \(-0.413602\pi\)
−0.700267 + 0.713881i \(0.746936\pi\)
\(510\) 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 \(-0.948169\pi\)
−0.352991 + 0.935627i \(0.614835\pi\)
\(522\) 0 0
\(523\) −305.470 + 529.090i −0.584073 + 1.01164i 0.410917 + 0.911673i \(0.365208\pi\)
−0.994990 + 0.0999714i \(0.968125\pi\)
\(524\) 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 −0.826686 0.562663i \(-0.809777\pi\)
0.900624 + 0.434600i \(0.143110\pi\)
\(542\) 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 \(-0.915526\pi\)
−0.255355 + 0.966847i \(0.582192\pi\)
\(558\) 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 \(-0.486446\pi\)
0.886525 + 0.462681i \(0.153113\pi\)
\(564\) 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 \(-0.208736\pi\)
−0.131780 + 0.991279i \(0.542069\pi\)
\(570\) 0 0
\(571\) 124.000 + 214.774i 0.217163 + 0.376137i 0.953939 0.299999i \(-0.0969864\pi\)
−0.736777 + 0.676136i \(0.763653\pi\)
\(572\) 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 0.979166 + 0.203063i \(0.0650895\pi\)
−0.313726 + 0.949514i \(0.601577\pi\)
\(578\) 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 \(-0.138319\pi\)
0.0889392 + 0.996037i \(0.471652\pi\)
\(594\) 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 −0.525759 + 0.850634i \(0.676218\pi\)
−0.999550 + 0.0300033i \(0.990448\pi\)
\(600\) 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 −0.986156 0.165817i \(-0.946974\pi\)
0.636680 + 0.771128i \(0.280307\pi\)
\(608\) 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 0.710270 0.703930i \(-0.248573\pi\)
−0.964756 + 0.263147i \(0.915240\pi\)
\(614\) −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 0.955988 0.293405i \(-0.0947884\pi\)
−0.732090 + 0.681208i \(0.761455\pi\)
\(620\) −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 \(-0.556693\pi\)
0.763743 + 0.645520i \(0.223359\pi\)
\(642\) 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 \(-0.429959\pi\)
0.954279 + 0.298918i \(0.0966257\pi\)
\(648\) 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 \(-0.405294\pi\)
−0.681398 + 0.731913i \(0.738628\pi\)
\(654\) 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 0.993727 + 0.111832i \(0.0356719\pi\)
−0.400014 + 0.916509i \(0.630995\pi\)
\(662\) 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 \(-0.404450\pi\)
−0.679454 + 0.733718i \(0.737783\pi\)
\(678\) 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 \(-0.990678\pi\)
−0.474426 + 0.880295i \(0.657344\pi\)
\(684\) 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 \(-0.713242\pi\)
0.989314 + 0.145799i \(0.0465753\pi\)
\(692\) 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 −0.145282 + 0.989390i \(0.546409\pi\)
−0.784196 + 0.620513i \(0.786924\pi\)
\(710\) 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 \(-0.0835898\pi\)
0.258041 + 0.966134i \(0.416923\pi\)
\(720\) 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 −0.990934 0.134349i \(-0.957106\pi\)
0.611817 + 0.791000i \(0.290439\pi\)
\(734\) 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 0.911527 + 0.411240i \(0.134904\pi\)
−0.0996190 + 0.995026i \(0.531762\pi\)
\(740\) −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 −0.612632 0.790368i \(-0.709889\pi\)
0.990795 + 0.135371i \(0.0432227\pi\)
\(752\) −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 \(-0.225012\pi\)
−0.182273 + 0.983248i \(0.558345\pi\)
\(762\) 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 \(-0.862433\pi\)
−0.0912915 + 0.995824i \(0.529099\pi\)
\(774\) 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 \(-0.254729\pi\)
−0.969664 + 0.244442i \(0.921395\pi\)
\(788\) 12.2474 7.07107i 0.0155424 0.00897344i
\(789\) 0 0
\(790\) −260.215 −0.329386
\(791\) 0 0
\(792\) 0 0
\(793\) −333.000 +