Properties

Label 1200.3.bg.o.1057.1
Level $1200$
Weight $3$
Character 1200.1057
Analytic conductor $32.698$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.bg (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.6976317232\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1057.1
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1200.1057
Dual form 1200.3.bg.o.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 1.22474i) q^{3} +(7.44949 + 7.44949i) q^{7} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 + 1.22474i) q^{3} +(7.44949 + 7.44949i) q^{7} -3.00000i q^{9} +16.2474 q^{11} +(-12.2474 + 12.2474i) q^{13} +(7.55051 + 7.55051i) q^{17} +14.4949i q^{19} -18.2474 q^{21} +(-2.65153 + 2.65153i) q^{23} +(3.67423 + 3.67423i) q^{27} -34.2474i q^{29} +20.4949 q^{31} +(-19.8990 + 19.8990i) q^{33} +(-7.34847 - 7.34847i) q^{37} -30.0000i q^{39} +25.5051 q^{41} +(25.1010 - 25.1010i) q^{43} +(22.0454 + 22.0454i) q^{47} +61.9898i q^{49} -18.4949 q^{51} +(35.3031 - 35.3031i) q^{53} +(-17.7526 - 17.7526i) q^{57} +88.7423i q^{59} -102.495 q^{61} +(22.3485 - 22.3485i) q^{63} +(-24.6969 - 24.6969i) q^{67} -6.49490i q^{69} -77.9796 q^{71} +(44.1918 - 44.1918i) q^{73} +(121.035 + 121.035i) q^{77} +48.4949i q^{79} -9.00000 q^{81} +(-101.641 + 101.641i) q^{83} +(41.9444 + 41.9444i) q^{87} +156.969i q^{89} -182.474 q^{91} +(-25.1010 + 25.1010i) q^{93} +(-55.4041 - 55.4041i) q^{97} -48.7423i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 20q^{7} + O(q^{10}) \) \( 4q + 20q^{7} + 16q^{11} + 40q^{17} - 24q^{21} - 40q^{23} - 16q^{31} - 60q^{33} + 200q^{41} + 120q^{43} + 24q^{51} + 200q^{53} - 120q^{57} - 312q^{61} + 60q^{63} - 40q^{67} + 80q^{71} + 20q^{73} + 200q^{77} - 36q^{81} - 240q^{83} + 60q^{87} - 240q^{91} - 120q^{93} - 300q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 7.44949 + 7.44949i 1.06421 + 1.06421i 0.997792 + 0.0664211i \(0.0211581\pi\)
0.0664211 + 0.997792i \(0.478842\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) 16.2474 1.47704 0.738520 0.674231i \(-0.235525\pi\)
0.738520 + 0.674231i \(0.235525\pi\)
\(12\) 0 0
\(13\) −12.2474 + 12.2474i −0.942111 + 0.942111i −0.998414 0.0563023i \(-0.982069\pi\)
0.0563023 + 0.998414i \(0.482069\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.55051 + 7.55051i 0.444148 + 0.444148i 0.893403 0.449256i \(-0.148311\pi\)
−0.449256 + 0.893403i \(0.648311\pi\)
\(18\) 0 0
\(19\) 14.4949i 0.762889i 0.924392 + 0.381445i \(0.124573\pi\)
−0.924392 + 0.381445i \(0.875427\pi\)
\(20\) 0 0
\(21\) −18.2474 −0.868926
\(22\) 0 0
\(23\) −2.65153 + 2.65153i −0.115284 + 0.115284i −0.762395 0.647111i \(-0.775977\pi\)
0.647111 + 0.762395i \(0.275977\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) 34.2474i 1.18095i −0.807057 0.590473i \(-0.798941\pi\)
0.807057 0.590473i \(-0.201059\pi\)
\(30\) 0 0
\(31\) 20.4949 0.661126 0.330563 0.943784i \(-0.392761\pi\)
0.330563 + 0.943784i \(0.392761\pi\)
\(32\) 0 0
\(33\) −19.8990 + 19.8990i −0.602999 + 0.602999i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −7.34847 7.34847i −0.198607 0.198607i 0.600795 0.799403i \(-0.294851\pi\)
−0.799403 + 0.600795i \(0.794851\pi\)
\(38\) 0 0
\(39\) 30.0000i 0.769231i
\(40\) 0 0
\(41\) 25.5051 0.622076 0.311038 0.950398i \(-0.399323\pi\)
0.311038 + 0.950398i \(0.399323\pi\)
\(42\) 0 0
\(43\) 25.1010 25.1010i 0.583745 0.583745i −0.352186 0.935930i \(-0.614561\pi\)
0.935930 + 0.352186i \(0.114561\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 22.0454 + 22.0454i 0.469051 + 0.469051i 0.901607 0.432556i \(-0.142388\pi\)
−0.432556 + 0.901607i \(0.642388\pi\)
\(48\) 0 0
\(49\) 61.9898i 1.26510i
\(50\) 0 0
\(51\) −18.4949 −0.362645
\(52\) 0 0
\(53\) 35.3031 35.3031i 0.666096 0.666096i −0.290714 0.956810i \(-0.593893\pi\)
0.956810 + 0.290714i \(0.0938929\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −17.7526 17.7526i −0.311448 0.311448i
\(58\) 0 0
\(59\) 88.7423i 1.50411i 0.659102 + 0.752054i \(0.270937\pi\)
−0.659102 + 0.752054i \(0.729063\pi\)
\(60\) 0 0
\(61\) −102.495 −1.68024 −0.840122 0.542397i \(-0.817517\pi\)
−0.840122 + 0.542397i \(0.817517\pi\)
\(62\) 0 0
\(63\) 22.3485 22.3485i 0.354738 0.354738i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −24.6969 24.6969i −0.368611 0.368611i 0.498359 0.866970i \(-0.333936\pi\)
−0.866970 + 0.498359i \(0.833936\pi\)
\(68\) 0 0
\(69\) 6.49490i 0.0941289i
\(70\) 0 0
\(71\) −77.9796 −1.09830 −0.549152 0.835722i \(-0.685049\pi\)
−0.549152 + 0.835722i \(0.685049\pi\)
\(72\) 0 0
\(73\) 44.1918 44.1918i 0.605368 0.605368i −0.336364 0.941732i \(-0.609197\pi\)
0.941732 + 0.336364i \(0.109197\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 121.035 + 121.035i 1.57189 + 1.57189i
\(78\) 0 0
\(79\) 48.4949i 0.613859i 0.951732 + 0.306930i \(0.0993017\pi\)
−0.951732 + 0.306930i \(0.900698\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) −101.641 + 101.641i −1.22459 + 1.22459i −0.258613 + 0.965981i \(0.583266\pi\)
−0.965981 + 0.258613i \(0.916734\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 41.9444 + 41.9444i 0.482119 + 0.482119i
\(88\) 0 0
\(89\) 156.969i 1.76370i 0.471529 + 0.881850i \(0.343702\pi\)
−0.471529 + 0.881850i \(0.656298\pi\)
\(90\) 0 0
\(91\) −182.474 −2.00521
\(92\) 0 0
\(93\) −25.1010 + 25.1010i −0.269903 + 0.269903i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −55.4041 55.4041i −0.571176 0.571176i 0.361281 0.932457i \(-0.382340\pi\)
−0.932457 + 0.361281i \(0.882340\pi\)
\(98\) 0 0
\(99\) 48.7423i 0.492347i
\(100\) 0 0
\(101\) 45.7526 0.452996 0.226498 0.974012i \(-0.427272\pi\)
0.226498 + 0.974012i \(0.427272\pi\)
\(102\) 0 0
\(103\) 23.1566 23.1566i 0.224822 0.224822i −0.585704 0.810525i \(-0.699182\pi\)
0.810525 + 0.585704i \(0.199182\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.3383 + 16.3383i 0.152694 + 0.152694i 0.779320 0.626626i \(-0.215565\pi\)
−0.626626 + 0.779320i \(0.715565\pi\)
\(108\) 0 0
\(109\) 159.485i 1.46316i 0.681754 + 0.731581i \(0.261217\pi\)
−0.681754 + 0.731581i \(0.738783\pi\)
\(110\) 0 0
\(111\) 18.0000 0.162162
\(112\) 0 0
\(113\) −13.0556 + 13.0556i −0.115536 + 0.115536i −0.762511 0.646975i \(-0.776034\pi\)
0.646975 + 0.762511i \(0.276034\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 36.7423 + 36.7423i 0.314037 + 0.314037i
\(118\) 0 0
\(119\) 112.495i 0.945335i
\(120\) 0 0
\(121\) 142.980 1.18165
\(122\) 0 0
\(123\) −31.2372 + 31.2372i −0.253961 + 0.253961i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 7.44949 + 7.44949i 0.0586574 + 0.0586574i 0.735827 0.677170i \(-0.236794\pi\)
−0.677170 + 0.735827i \(0.736794\pi\)
\(128\) 0 0
\(129\) 61.4847i 0.476626i
\(130\) 0 0
\(131\) −19.7526 −0.150783 −0.0753914 0.997154i \(-0.524021\pi\)
−0.0753914 + 0.997154i \(0.524021\pi\)
\(132\) 0 0
\(133\) −107.980 + 107.980i −0.811877 + 0.811877i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 101.641 + 101.641i 0.741907 + 0.741907i 0.972945 0.231037i \(-0.0742120\pi\)
−0.231037 + 0.972945i \(0.574212\pi\)
\(138\) 0 0
\(139\) 24.0204i 0.172809i −0.996260 0.0864044i \(-0.972462\pi\)
0.996260 0.0864044i \(-0.0275377\pi\)
\(140\) 0 0
\(141\) −54.0000 −0.382979
\(142\) 0 0
\(143\) −198.990 + 198.990i −1.39154 + 1.39154i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −75.9217 75.9217i −0.516474 0.516474i
\(148\) 0 0
\(149\) 199.732i 1.34048i −0.742143 0.670242i \(-0.766190\pi\)
0.742143 0.670242i \(-0.233810\pi\)
\(150\) 0 0
\(151\) 158.990 1.05291 0.526456 0.850202i \(-0.323520\pi\)
0.526456 + 0.850202i \(0.323520\pi\)
\(152\) 0 0
\(153\) 22.6515 22.6515i 0.148049 0.148049i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 37.3485 + 37.3485i 0.237888 + 0.237888i 0.815975 0.578087i \(-0.196201\pi\)
−0.578087 + 0.815975i \(0.696201\pi\)
\(158\) 0 0
\(159\) 86.4745i 0.543865i
\(160\) 0 0
\(161\) −39.5051 −0.245373
\(162\) 0 0
\(163\) 8.98979 8.98979i 0.0551521 0.0551521i −0.678993 0.734145i \(-0.737583\pi\)
0.734145 + 0.678993i \(0.237583\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 88.3587 + 88.3587i 0.529094 + 0.529094i 0.920302 0.391208i \(-0.127943\pi\)
−0.391208 + 0.920302i \(0.627943\pi\)
\(168\) 0 0
\(169\) 131.000i 0.775148i
\(170\) 0 0
\(171\) 43.4847 0.254296
\(172\) 0 0
\(173\) −170.631 + 170.631i −0.986307 + 0.986307i −0.999908 0.0136005i \(-0.995671\pi\)
0.0136005 + 0.999908i \(0.495671\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −108.687 108.687i −0.614049 0.614049i
\(178\) 0 0
\(179\) 75.7526i 0.423199i −0.977357 0.211599i \(-0.932133\pi\)
0.977357 0.211599i \(-0.0678672\pi\)
\(180\) 0 0
\(181\) −279.444 −1.54389 −0.771944 0.635690i \(-0.780716\pi\)
−0.771944 + 0.635690i \(0.780716\pi\)
\(182\) 0 0
\(183\) 125.530 125.530i 0.685957 0.685957i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 122.677 + 122.677i 0.656024 + 0.656024i
\(188\) 0 0
\(189\) 54.7423i 0.289642i
\(190\) 0 0
\(191\) 69.4847 0.363794 0.181897 0.983318i \(-0.441776\pi\)
0.181897 + 0.983318i \(0.441776\pi\)
\(192\) 0 0
\(193\) 53.5857 53.5857i 0.277646 0.277646i −0.554523 0.832169i \(-0.687099\pi\)
0.832169 + 0.554523i \(0.187099\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −260.252 260.252i −1.32108 1.32108i −0.912906 0.408171i \(-0.866167\pi\)
−0.408171 0.912906i \(-0.633833\pi\)
\(198\) 0 0
\(199\) 65.0102i 0.326684i 0.986569 + 0.163342i \(0.0522275\pi\)
−0.986569 + 0.163342i \(0.947773\pi\)
\(200\) 0 0
\(201\) 60.4949 0.300970
\(202\) 0 0
\(203\) 255.126 255.126i 1.25678 1.25678i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 7.95459 + 7.95459i 0.0384280 + 0.0384280i
\(208\) 0 0
\(209\) 235.505i 1.12682i
\(210\) 0 0
\(211\) −12.0204 −0.0569688 −0.0284844 0.999594i \(-0.509068\pi\)
−0.0284844 + 0.999594i \(0.509068\pi\)
\(212\) 0 0
\(213\) 95.5051 95.5051i 0.448381 0.448381i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 152.677 + 152.677i 0.703578 + 0.703578i
\(218\) 0 0
\(219\) 108.247i 0.494281i
\(220\) 0 0
\(221\) −184.949 −0.836873
\(222\) 0 0
\(223\) −239.722 + 239.722i −1.07499 + 1.07499i −0.0780357 + 0.996951i \(0.524865\pi\)
−0.996951 + 0.0780357i \(0.975135\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.02041 + 2.02041i 0.00890049 + 0.00890049i 0.711543 0.702643i \(-0.247997\pi\)
−0.702643 + 0.711543i \(0.747997\pi\)
\(228\) 0 0
\(229\) 284.969i 1.24441i −0.782855 0.622204i \(-0.786237\pi\)
0.782855 0.622204i \(-0.213763\pi\)
\(230\) 0 0
\(231\) −296.474 −1.28344
\(232\) 0 0
\(233\) −151.237 + 151.237i −0.649087 + 0.649087i −0.952772 0.303685i \(-0.901783\pi\)
0.303685 + 0.952772i \(0.401783\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −59.3939 59.3939i −0.250607 0.250607i
\(238\) 0 0
\(239\) 50.9694i 0.213261i 0.994299 + 0.106631i \(0.0340062\pi\)
−0.994299 + 0.106631i \(0.965994\pi\)
\(240\) 0 0
\(241\) −32.0000 −0.132780 −0.0663900 0.997794i \(-0.521148\pi\)
−0.0663900 + 0.997794i \(0.521148\pi\)
\(242\) 0 0
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −177.526 177.526i −0.718727 0.718727i
\(248\) 0 0
\(249\) 248.969i 0.999877i
\(250\) 0 0
\(251\) 373.237 1.48700 0.743500 0.668735i \(-0.233164\pi\)
0.743500 + 0.668735i \(0.233164\pi\)
\(252\) 0 0
\(253\) −43.0806 + 43.0806i −0.170279 + 0.170279i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 206.136 + 206.136i 0.802086 + 0.802086i 0.983421 0.181335i \(-0.0580418\pi\)
−0.181335 + 0.983421i \(0.558042\pi\)
\(258\) 0 0
\(259\) 109.485i 0.422721i
\(260\) 0 0
\(261\) −102.742 −0.393649
\(262\) 0 0
\(263\) 210.833 210.833i 0.801647 0.801647i −0.181706 0.983353i \(-0.558162\pi\)
0.983353 + 0.181706i \(0.0581619\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −192.247 192.247i −0.720028 0.720028i
\(268\) 0 0
\(269\) 205.258i 0.763040i 0.924361 + 0.381520i \(0.124599\pi\)
−0.924361 + 0.381520i \(0.875401\pi\)
\(270\) 0 0
\(271\) 66.0000 0.243542 0.121771 0.992558i \(-0.461143\pi\)
0.121771 + 0.992558i \(0.461143\pi\)
\(272\) 0 0
\(273\) 223.485 223.485i 0.818625 0.818625i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −148.157 148.157i −0.534861 0.534861i 0.387154 0.922015i \(-0.373458\pi\)
−0.922015 + 0.387154i \(0.873458\pi\)
\(278\) 0 0
\(279\) 61.4847i 0.220375i
\(280\) 0 0
\(281\) 324.434 1.15457 0.577284 0.816543i \(-0.304113\pi\)
0.577284 + 0.816543i \(0.304113\pi\)
\(282\) 0 0
\(283\) 304.747 304.747i 1.07684 1.07684i 0.0800537 0.996791i \(-0.474491\pi\)
0.996791 0.0800537i \(-0.0255092\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 190.000 + 190.000i 0.662021 + 0.662021i
\(288\) 0 0
\(289\) 174.980i 0.605466i
\(290\) 0 0
\(291\) 135.712 0.466363
\(292\) 0 0
\(293\) 145.151 145.151i 0.495396 0.495396i −0.414605 0.910001i \(-0.636080\pi\)
0.910001 + 0.414605i \(0.136080\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 59.6969 + 59.6969i 0.201000 + 0.201000i
\(298\) 0 0
\(299\) 64.9490i 0.217221i
\(300\) 0 0
\(301\) 373.980 1.24246
\(302\) 0 0
\(303\) −56.0352 + 56.0352i −0.184935 + 0.184935i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 120.606 + 120.606i 0.392854 + 0.392854i 0.875703 0.482850i \(-0.160398\pi\)
−0.482850 + 0.875703i \(0.660398\pi\)
\(308\) 0 0
\(309\) 56.7219i 0.183566i
\(310\) 0 0
\(311\) 18.0204 0.0579434 0.0289717 0.999580i \(-0.490777\pi\)
0.0289717 + 0.999580i \(0.490777\pi\)
\(312\) 0 0
\(313\) 323.586 323.586i 1.03382 1.03382i 0.0344125 0.999408i \(-0.489044\pi\)
0.999408 0.0344125i \(-0.0109560\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −62.4495 62.4495i −0.197002 0.197002i 0.601712 0.798713i \(-0.294486\pi\)
−0.798713 + 0.601712i \(0.794486\pi\)
\(318\) 0 0
\(319\) 556.434i 1.74431i
\(320\) 0 0
\(321\) −40.0204 −0.124674
\(322\) 0 0
\(323\) −109.444 + 109.444i −0.338836 + 0.338836i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −195.328 195.328i −0.597334 0.597334i
\(328\) 0 0
\(329\) 328.454i 0.998341i
\(330\) 0 0
\(331\) −618.413 −1.86832 −0.934159 0.356857i \(-0.883848\pi\)
−0.934159 + 0.356857i \(0.883848\pi\)
\(332\) 0 0
\(333\) −22.0454 + 22.0454i −0.0662024 + 0.0662024i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 55.4041 + 55.4041i 0.164404 + 0.164404i 0.784514 0.620111i \(-0.212912\pi\)
−0.620111 + 0.784514i \(0.712912\pi\)
\(338\) 0 0
\(339\) 31.9796i 0.0943351i
\(340\) 0 0
\(341\) 332.990 0.976510
\(342\) 0 0
\(343\) −96.7673 + 96.7673i −0.282121 + 0.282121i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 413.081 + 413.081i 1.19043 + 1.19043i 0.976946 + 0.213488i \(0.0684826\pi\)
0.213488 + 0.976946i \(0.431517\pi\)
\(348\) 0 0
\(349\) 258.454i 0.740556i −0.928921 0.370278i \(-0.879262\pi\)
0.928921 0.370278i \(-0.120738\pi\)
\(350\) 0 0
\(351\) −90.0000 −0.256410
\(352\) 0 0
\(353\) 83.9138 83.9138i 0.237716 0.237716i −0.578188 0.815904i \(-0.696240\pi\)
0.815904 + 0.578188i \(0.196240\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −137.778 137.778i −0.385932 0.385932i
\(358\) 0 0
\(359\) 138.515i 0.385837i 0.981215 + 0.192918i \(0.0617952\pi\)
−0.981215 + 0.192918i \(0.938205\pi\)
\(360\) 0 0
\(361\) 150.898 0.418000
\(362\) 0 0
\(363\) −175.114 + 175.114i −0.482406 + 0.482406i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −408.964 408.964i −1.11434 1.11434i −0.992556 0.121786i \(-0.961138\pi\)
−0.121786 0.992556i \(-0.538862\pi\)
\(368\) 0 0
\(369\) 76.5153i 0.207359i
\(370\) 0 0
\(371\) 525.980 1.41773
\(372\) 0 0
\(373\) 143.106 143.106i 0.383661 0.383661i −0.488758 0.872419i \(-0.662550\pi\)
0.872419 + 0.488758i \(0.162550\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 419.444 + 419.444i 1.11258 + 1.11258i
\(378\) 0 0
\(379\) 194.000i 0.511873i 0.966694 + 0.255937i \(0.0823839\pi\)
−0.966694 + 0.255937i \(0.917616\pi\)
\(380\) 0 0
\(381\) −18.2474 −0.0478936
\(382\) 0 0
\(383\) 51.4893 51.4893i 0.134437 0.134437i −0.636686 0.771123i \(-0.719695\pi\)
0.771123 + 0.636686i \(0.219695\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −75.3031 75.3031i −0.194582 0.194582i
\(388\) 0 0
\(389\) 35.1964i 0.0904792i −0.998976 0.0452396i \(-0.985595\pi\)
0.998976 0.0452396i \(-0.0144051\pi\)
\(390\) 0 0
\(391\) −40.0408 −0.102406
\(392\) 0 0
\(393\) 24.1918 24.1918i 0.0615568 0.0615568i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −409.267 409.267i −1.03090 1.03090i −0.999507 0.0313917i \(-0.990006\pi\)
−0.0313917 0.999507i \(-0.509994\pi\)
\(398\) 0 0
\(399\) 264.495i 0.662894i
\(400\) 0 0
\(401\) 375.898 0.937401 0.468701 0.883357i \(-0.344722\pi\)
0.468701 + 0.883357i \(0.344722\pi\)
\(402\) 0 0
\(403\) −251.010 + 251.010i −0.622854 + 0.622854i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −119.394 119.394i −0.293351 0.293351i
\(408\) 0 0
\(409\) 207.959i 0.508458i 0.967144 + 0.254229i \(0.0818216\pi\)
−0.967144 + 0.254229i \(0.918178\pi\)
\(410\) 0 0
\(411\) −248.969 −0.605765
\(412\) 0 0
\(413\) −661.085 + 661.085i −1.60069 + 1.60069i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 29.4189 + 29.4189i 0.0705489 + 0.0705489i
\(418\) 0 0
\(419\) 810.186i 1.93362i −0.255499 0.966809i \(-0.582240\pi\)
0.255499 0.966809i \(-0.417760\pi\)
\(420\) 0 0
\(421\) −505.959 −1.20180 −0.600902 0.799323i \(-0.705192\pi\)
−0.600902 + 0.799323i \(0.705192\pi\)
\(422\) 0 0
\(423\) 66.1362 66.1362i 0.156350 0.156350i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −763.535 763.535i −1.78814 1.78814i
\(428\) 0 0
\(429\) 487.423i 1.13619i
\(430\) 0 0
\(431\) 92.4541 0.214511 0.107255 0.994232i \(-0.465794\pi\)
0.107255 + 0.994232i \(0.465794\pi\)
\(432\) 0 0
\(433\) −69.8990 + 69.8990i −0.161430 + 0.161430i −0.783200 0.621770i \(-0.786414\pi\)
0.621770 + 0.783200i \(0.286414\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −38.4337 38.4337i −0.0879489 0.0879489i
\(438\) 0 0
\(439\) 128.929i 0.293687i −0.989160 0.146843i \(-0.953089\pi\)
0.989160 0.146843i \(-0.0469114\pi\)
\(440\) 0 0
\(441\) 185.969 0.421699
\(442\) 0 0
\(443\) −335.555 + 335.555i −0.757461 + 0.757461i −0.975860 0.218399i \(-0.929917\pi\)
0.218399 + 0.975860i \(0.429917\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 244.621 + 244.621i 0.547250 + 0.547250i
\(448\) 0 0
\(449\) 521.423i 1.16130i −0.814153 0.580650i \(-0.802799\pi\)
0.814153 0.580650i \(-0.197201\pi\)
\(450\) 0 0
\(451\) 414.393 0.918831
\(452\) 0 0
\(453\) −194.722 + 194.722i −0.429850 + 0.429850i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −548.939 548.939i −1.20118 1.20118i −0.973808 0.227371i \(-0.926987\pi\)
−0.227371 0.973808i \(-0.573013\pi\)
\(458\) 0 0
\(459\) 55.4847i 0.120882i
\(460\) 0 0
\(461\) 142.288 0.308651 0.154326 0.988020i \(-0.450680\pi\)
0.154326 + 0.988020i \(0.450680\pi\)
\(462\) 0 0
\(463\) 537.045 537.045i 1.15993 1.15993i 0.175434 0.984491i \(-0.443867\pi\)
0.984491 0.175434i \(-0.0561329\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −367.044 367.044i −0.785962 0.785962i 0.194867 0.980830i \(-0.437572\pi\)
−0.980830 + 0.194867i \(0.937572\pi\)
\(468\) 0 0
\(469\) 367.959i 0.784561i
\(470\) 0 0
\(471\) −91.4847 −0.194235
\(472\) 0 0
\(473\) 407.828 407.828i 0.862215 0.862215i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −105.909 105.909i −0.222032 0.222032i
\(478\) 0 0
\(479\) 94.9694i 0.198266i −0.995074 0.0991330i \(-0.968393\pi\)
0.995074 0.0991330i \(-0.0316069\pi\)
\(480\) 0 0
\(481\) 180.000 0.374220
\(482\) 0 0
\(483\) 48.3837 48.3837i 0.100173 0.100173i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 244.621 + 244.621i 0.502302 + 0.502302i 0.912153 0.409851i \(-0.134419\pi\)
−0.409851 + 0.912153i \(0.634419\pi\)
\(488\) 0 0
\(489\) 22.0204i 0.0450315i
\(490\) 0 0
\(491\) −163.217 −0.332417 −0.166209 0.986091i \(-0.553153\pi\)
−0.166209 + 0.986091i \(0.553153\pi\)
\(492\) 0 0
\(493\) 258.586 258.586i 0.524515 0.524515i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −580.908 580.908i −1.16883 1.16883i
\(498\) 0 0
\(499\) 8.55613i 0.0171465i −0.999963 0.00857327i \(-0.997271\pi\)
0.999963 0.00857327i \(-0.00272899\pi\)
\(500\) 0 0
\(501\) −216.434 −0.432003
\(502\) 0 0
\(503\) 46.5903 46.5903i 0.0926249 0.0926249i −0.659276 0.751901i \(-0.729137\pi\)
0.751901 + 0.659276i \(0.229137\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 160.442 + 160.442i 0.316453 + 0.316453i
\(508\) 0 0
\(509\) 336.227i 0.660564i −0.943882 0.330282i \(-0.892856\pi\)
0.943882 0.330282i \(-0.107144\pi\)
\(510\) 0 0
\(511\) 658.413 1.28848
\(512\) 0 0
\(513\) −53.2577 + 53.2577i −0.103816 + 0.103816i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 358.182 + 358.182i 0.692808 + 0.692808i
\(518\) 0 0
\(519\) 417.959i 0.805316i
\(520\) 0 0
\(521\) 252.556 0.484753 0.242376 0.970182i \(-0.422073\pi\)
0.242376 + 0.970182i \(0.422073\pi\)
\(522\) 0 0
\(523\) −33.6867 + 33.6867i −0.0644106 + 0.0644106i −0.738578 0.674168i \(-0.764502\pi\)
0.674168 + 0.738578i \(0.264502\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 154.747 + 154.747i 0.293637 + 0.293637i
\(528\) 0 0
\(529\) 514.939i 0.973419i
\(530\) 0 0
\(531\) 266.227 0.501369
\(532\) 0 0
\(533\) −312.372 + 312.372i −0.586065 + 0.586065i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 92.7775 + 92.7775i 0.172770 + 0.172770i
\(538\) 0 0
\(539\) 1007.18i 1.86860i
\(540\) 0 0
\(541\) −604.474 −1.11733 −0.558664 0.829394i \(-0.688686\pi\)
−0.558664 + 0.829394i \(0.688686\pi\)
\(542\) 0 0
\(543\) 342.247 342.247i 0.630290 0.630290i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 615.353 + 615.353i 1.12496 + 1.12496i 0.990985 + 0.133975i \(0.0427742\pi\)
0.133975 + 0.990985i \(0.457226\pi\)
\(548\) 0 0
\(549\) 307.485i 0.560081i
\(550\) 0 0
\(551\) 496.413 0.900931
\(552\) 0 0
\(553\) −361.262 + 361.262i −0.653277 + 0.653277i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 439.040 + 439.040i 0.788222 + 0.788222i 0.981203 0.192980i \(-0.0618154\pi\)
−0.192980 + 0.981203i \(0.561815\pi\)
\(558\) 0 0
\(559\) 614.847i 1.09991i
\(560\) 0 0
\(561\) −300.495 −0.535642
\(562\) 0 0
\(563\) −52.5765 + 52.5765i −0.0933864 + 0.0933864i −0.752257 0.658870i \(-0.771035\pi\)
0.658870 + 0.752257i \(0.271035\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −67.0454 67.0454i −0.118246 0.118246i
\(568\) 0 0
\(569\) 680.929i 1.19671i −0.801231 0.598356i \(-0.795821\pi\)
0.801231 0.598356i \(-0.204179\pi\)
\(570\) 0 0
\(571\) −254.495 −0.445700 −0.222850 0.974853i \(-0.571536\pi\)
−0.222850 + 0.974853i \(0.571536\pi\)
\(572\) 0 0
\(573\) −85.1010 + 85.1010i −0.148518 + 0.148518i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 279.999 + 279.999i 0.485267 + 0.485267i 0.906809 0.421542i \(-0.138511\pi\)
−0.421542 + 0.906809i \(0.638511\pi\)
\(578\) 0 0
\(579\) 131.258i 0.226697i
\(580\) 0 0
\(581\) −1514.35 −2.60646
\(582\) 0 0
\(583\) 573.585 573.585i 0.983850 0.983850i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 312.347 + 312.347i 0.532108 + 0.532108i 0.921199 0.389091i \(-0.127211\pi\)
−0.389091 + 0.921199i \(0.627211\pi\)
\(588\) 0 0
\(589\) 297.071i 0.504366i
\(590\) 0 0
\(591\) 637.485 1.07865
\(592\) 0 0
\(593\) 424.570 424.570i 0.715969 0.715969i −0.251808 0.967777i \(-0.581025\pi\)
0.967777 + 0.251808i \(0.0810251\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −79.6209 79.6209i −0.133368 0.133368i
\(598\) 0 0
\(599\) 396.536i 0.661996i 0.943631 + 0.330998i \(0.107385\pi\)
−0.943631 + 0.330998i \(0.892615\pi\)
\(600\) 0 0
\(601\) 238.908 0.397518 0.198759 0.980048i \(-0.436309\pi\)
0.198759 + 0.980048i \(0.436309\pi\)
\(602\) 0 0
\(603\) −74.0908 + 74.0908i −0.122870 + 0.122870i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 92.8025 + 92.8025i 0.152887 + 0.152887i 0.779406 0.626519i \(-0.215521\pi\)
−0.626519 + 0.779406i \(0.715521\pi\)
\(608\) 0 0
\(609\) 624.929i 1.02616i
\(610\) 0 0
\(611\) −540.000 −0.883797
\(612\) 0 0
\(613\) −301.943 + 301.943i −0.492567 + 0.492567i −0.909114 0.416547i \(-0.863240\pi\)
0.416547 + 0.909114i \(0.363240\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 372.904 + 372.904i 0.604382 + 0.604382i 0.941472 0.337090i \(-0.109443\pi\)
−0.337090 + 0.941472i \(0.609443\pi\)
\(618\) 0 0
\(619\) 815.939i 1.31816i 0.752074 + 0.659078i \(0.229053\pi\)
−0.752074 + 0.659078i \(0.770947\pi\)
\(620\) 0 0
\(621\) −19.4847 −0.0313763
\(622\) 0 0
\(623\) −1169.34 + 1169.34i −1.87695 + 1.87695i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −288.434 288.434i −0.460022 0.460022i
\(628\) 0 0
\(629\) 110.969i 0.176422i
\(630\) 0 0
\(631\) −550.434 −0.872320 −0.436160 0.899869i \(-0.643662\pi\)
−0.436160 + 0.899869i \(0.643662\pi\)
\(632\) 0 0
\(633\) 14.7219 14.7219i 0.0232574 0.0232574i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −759.217 759.217i −1.19186 1.19186i
\(638\) 0 0
\(639\) 233.939i 0.366101i
\(640\) 0 0
\(641\) 927.939 1.44764 0.723821 0.689988i \(-0.242384\pi\)
0.723821 + 0.689988i \(0.242384\pi\)
\(642\) 0 0
\(643\) 190.960 190.960i 0.296983 0.296983i −0.542848 0.839831i \(-0.682654\pi\)
0.839831 + 0.542848i \(0.182654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −637.146 637.146i −0.984770 0.984770i 0.0151154 0.999886i \(-0.495188\pi\)
−0.999886 + 0.0151154i \(0.995188\pi\)
\(648\) 0 0
\(649\) 1441.84i 2.22163i
\(650\) 0 0
\(651\) −373.980 −0.574469
\(652\) 0 0
\(653\) 404.116 404.116i 0.618860 0.618860i −0.326379 0.945239i \(-0.605828\pi\)
0.945239 + 0.326379i \(0.105828\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −132.576 132.576i −0.201789 0.201789i
\(658\) 0 0
\(659\) 453.196i 0.687703i −0.939024 0.343852i \(-0.888268\pi\)
0.939024 0.343852i \(-0.111732\pi\)
\(660\) 0 0
\(661\) 717.546 1.08555 0.542773 0.839879i \(-0.317374\pi\)
0.542773 + 0.839879i \(0.317374\pi\)
\(662\) 0 0
\(663\) 226.515 226.515i 0.341652 0.341652i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 90.8082 + 90.8082i 0.136144 + 0.136144i
\(668\) 0 0
\(669\) 587.196i 0.877723i
\(670\) 0 0
\(671\) −1665.28 −2.48179
\(672\) 0 0
\(673\) 121.413 121.413i 0.180406 0.180406i −0.611127 0.791533i \(-0.709283\pi\)
0.791533 + 0.611127i \(0.209283\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 671.943 + 671.943i 0.992531 + 0.992531i 0.999972 0.00744150i \(-0.00236873\pi\)
−0.00744150 + 0.999972i \(0.502369\pi\)
\(678\) 0 0
\(679\) 825.464i 1.21571i
\(680\) 0 0
\(681\) −4.94897 −0.00726722
\(682\) 0 0
\(683\) 802.095 802.095i 1.17437 1.17437i 0.193214 0.981157i \(-0.438109\pi\)
0.981157 0.193214i \(-0.0618913\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 349.015 + 349.015i 0.508027 + 0.508027i
\(688\) 0 0
\(689\) 864.745i 1.25507i
\(690\) 0 0
\(691\) 1146.49 1.65918 0.829591 0.558371i \(-0.188574\pi\)
0.829591 + 0.558371i \(0.188574\pi\)
\(692\) 0 0
\(693\) 363.106 363.106i 0.523962 0.523962i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 192.577 + 192.577i 0.276293 + 0.276293i
\(698\) 0 0
\(699\) 370.454i 0.529977i
\(700\) 0 0
\(701\) −673.217 −0.960366 −0.480183 0.877168i \(-0.659430\pi\)
−0.480183 + 0.877168i \(0.659430\pi\)
\(702\) 0 0
\(703\) 106.515 106.515i 0.151515 0.151515i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 340.833 + 340.833i 0.482084 + 0.482084i
\(708\) 0 0
\(709\) 955.939i 1.34829i −0.738598 0.674146i \(-0.764512\pi\)
0.738598 0.674146i \(-0.235488\pi\)
\(710\) 0 0
\(711\) 145.485 0.204620
\(712\) 0 0
\(713\) −54.3429 + 54.3429i −0.0762172 + 0.0762172i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −62.4245 62.4245i −0.0870634 0.0870634i
\(718\) 0 0
\(719\) 89.0306i 0.123826i −0.998082 0.0619128i \(-0.980280\pi\)
0.998082 0.0619128i \(-0.0197201\pi\)
\(720\) 0 0
\(721\) 345.010 0.478516
\(722\) 0 0
\(723\) 39.1918 39.1918i 0.0542072 0.0542072i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 332.703 + 332.703i 0.457638 + 0.457638i 0.897879 0.440242i \(-0.145107\pi\)
−0.440242 + 0.897879i \(0.645107\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 379.051 0.518538
\(732\) 0 0
\(733\) −229.823 + 229.823i −0.313537 + 0.313537i −0.846278 0.532741i \(-0.821162\pi\)
0.532741 + 0.846278i \(0.321162\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −401.262 401.262i −0.544454 0.544454i
\(738\) 0 0
\(739\) 923.281i 1.24936i −0.780879 0.624682i \(-0.785228\pi\)
0.780879 0.624682i \(-0.214772\pi\)
\(740\) 0 0
\(741\) 434.847 0.586838
\(742\) 0 0
\(743\) −585.782 + 585.782i −0.788401 + 0.788401i −0.981232 0.192831i \(-0.938233\pi\)
0.192831 + 0.981232i \(0.438233\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 304.924 + 304.924i 0.408198 + 0.408198i
\(748\) 0 0
\(749\) 243.423i 0.324998i
\(750\) 0 0
\(751\) −1354.27 −1.80329 −0.901645 0.432477i \(-0.857639\pi\)
−0.901645 + 0.432477i \(0.857639\pi\)
\(752\) 0 0
\(753\) −457.120 + 457.120i −0.607066 + 0.607066i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 985.832 + 985.832i 1.30229 + 1.30229i 0.926846 + 0.375442i \(0.122509\pi\)
0.375442 + 0.926846i \(0.377491\pi\)
\(758\) 0 0
\(759\) 105.526i 0.139032i
\(760\) 0 0
\(761\) 206.495 0.271347 0.135673 0.990754i \(-0.456680\pi\)
0.135673 + 0.990754i \(0.456680\pi\)
\(762\) 0 0
\(763\) −1188.08 + 1188.08i −1.55712 + 1.55712i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1086.87 1086.87i −1.41704 1.41704i
\(768\) 0 0
\(769\) 852.969i 1.10919i −0.832119 0.554596i \(-0.812873\pi\)
0.832119 0.554596i \(-0.187127\pi\)
\(770\) 0 0
\(771\) −504.929 −0.654901
\(772\) 0 0
\(773\) 491.035 491.035i 0.635233 0.635233i −0.314143 0.949376i \(-0.601717\pi\)
0.949376 + 0.314143i \(0.101717\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 134.091 + 134.091i 0.172575 + 0.172575i
\(778\) 0 0
\(779\) 369.694i 0.474575i
\(780\) 0 0
\(781\) −1266.97 −1.62224
\(782\) 0 0
\(783\) 125.833 125.833i 0.160706 0.160706i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −958.586 958.586i −1.21803 1.21803i −0.968323 0.249702i \(-0.919667\pi\)
−0.249702 0.968323i \(-0.580333\pi\)
\(788\) 0 0
\(789\) 516.434i 0.654542i
\(790\) 0 0
\(791\) −194.515 −0.245911
\(792\) 0 0
\(793\) 1255.30 1255.30i 1.58298 1.58298i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −169.065 169.065i −0.212126 0.212126i 0.593044 0.805170i \(-0.297926\pi\)
−0.805170 + 0.593044i \(0.797926\pi\)
\(798\) 0 0
\(799\) 332.908i 0.416656i