Properties

Label 3024.2.q.k.2881.7
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.7
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.k.2305.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.170100 - 0.294622i) q^{5} +(2.63360 - 0.253251i) q^{7} +O(q^{10})\) \(q+(0.170100 - 0.294622i) q^{5} +(2.63360 - 0.253251i) q^{7} +(0.335794 + 0.581612i) q^{11} +(1.62370 + 2.81233i) q^{13} +(1.10014 - 1.90550i) q^{17} +(-0.242085 - 0.419303i) q^{19} +(-2.09495 + 3.62856i) q^{23} +(2.44213 + 4.22990i) q^{25} +(-0.478868 + 0.829424i) q^{29} -2.08263 q^{31} +(0.373363 - 0.818995i) q^{35} +(4.81613 + 8.34178i) q^{37} +(3.90207 + 6.75858i) q^{41} +(3.66119 - 6.34136i) q^{43} -2.69901 q^{47} +(6.87173 - 1.33392i) q^{49} +(6.12335 - 10.6059i) q^{53} +0.228474 q^{55} -4.94297 q^{59} -3.52119 q^{61} +1.10477 q^{65} -12.3202 q^{67} -5.57304 q^{71} +(-3.71686 + 6.43779i) q^{73} +(1.03164 + 1.44669i) q^{77} +10.0127 q^{79} +(2.47376 - 4.28468i) q^{83} +(-0.374269 - 0.648252i) q^{85} +(8.52177 + 14.7601i) q^{89} +(4.98840 + 6.99536i) q^{91} -0.164714 q^{95} +(4.23657 - 7.33795i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{5} + 5q^{7} + O(q^{10}) \) \( 22q - 3q^{5} + 5q^{7} - 3q^{11} - 3q^{13} - 7q^{17} + q^{19} + 2q^{23} - 10q^{25} - 9q^{29} - 8q^{31} + 14q^{35} + 2q^{37} - 16q^{41} - 10q^{47} + 15q^{49} - 11q^{53} - 22q^{55} + 38q^{59} + 26q^{61} + 26q^{65} + 52q^{67} - 48q^{71} - 35q^{73} - 17q^{77} + 20q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} - 24q^{95} - 29q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0.170100 0.294622i 0.0760711 0.131759i −0.825480 0.564431i \(-0.809096\pi\)
0.901552 + 0.432672i \(0.142429\pi\)
\(6\) 0 0
\(7\) 2.63360 0.253251i 0.995408 0.0957197i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.335794 + 0.581612i 0.101246 + 0.175363i 0.912198 0.409749i \(-0.134384\pi\)
−0.810952 + 0.585112i \(0.801051\pi\)
\(12\) 0 0
\(13\) 1.62370 + 2.81233i 0.450333 + 0.780000i 0.998407 0.0564303i \(-0.0179719\pi\)
−0.548073 + 0.836430i \(0.684639\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.10014 1.90550i 0.266824 0.462152i −0.701216 0.712949i \(-0.747359\pi\)
0.968040 + 0.250796i \(0.0806925\pi\)
\(18\) 0 0
\(19\) −0.242085 0.419303i −0.0555380 0.0961946i 0.836920 0.547326i \(-0.184354\pi\)
−0.892458 + 0.451131i \(0.851021\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.09495 + 3.62856i −0.436827 + 0.756607i −0.997443 0.0714692i \(-0.977231\pi\)
0.560616 + 0.828076i \(0.310565\pi\)
\(24\) 0 0
\(25\) 2.44213 + 4.22990i 0.488426 + 0.845979i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.478868 + 0.829424i −0.0889235 + 0.154020i −0.907056 0.421009i \(-0.861676\pi\)
0.818133 + 0.575029i \(0.195009\pi\)
\(30\) 0 0
\(31\) −2.08263 −0.374052 −0.187026 0.982355i \(-0.559885\pi\)
−0.187026 + 0.982355i \(0.559885\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.373363 0.818995i 0.0631098 0.138435i
\(36\) 0 0
\(37\) 4.81613 + 8.34178i 0.791767 + 1.37138i 0.924872 + 0.380278i \(0.124172\pi\)
−0.133105 + 0.991102i \(0.542495\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.90207 + 6.75858i 0.609400 + 1.05551i 0.991339 + 0.131325i \(0.0419231\pi\)
−0.381939 + 0.924188i \(0.624744\pi\)
\(42\) 0 0
\(43\) 3.66119 6.34136i 0.558326 0.967048i −0.439311 0.898335i \(-0.644777\pi\)
0.997636 0.0687132i \(-0.0218893\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.69901 −0.393692 −0.196846 0.980434i \(-0.563070\pi\)
−0.196846 + 0.980434i \(0.563070\pi\)
\(48\) 0 0
\(49\) 6.87173 1.33392i 0.981675 0.190560i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.12335 10.6059i 0.841107 1.45684i −0.0478535 0.998854i \(-0.515238\pi\)
0.888960 0.457985i \(-0.151429\pi\)
\(54\) 0 0
\(55\) 0.228474 0.0308075
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.94297 −0.643520 −0.321760 0.946821i \(-0.604274\pi\)
−0.321760 + 0.946821i \(0.604274\pi\)
\(60\) 0 0
\(61\) −3.52119 −0.450842 −0.225421 0.974261i \(-0.572376\pi\)
−0.225421 + 0.974261i \(0.572376\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.10477 0.137029
\(66\) 0 0
\(67\) −12.3202 −1.50516 −0.752579 0.658502i \(-0.771190\pi\)
−0.752579 + 0.658502i \(0.771190\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.57304 −0.661398 −0.330699 0.943736i \(-0.607285\pi\)
−0.330699 + 0.943736i \(0.607285\pi\)
\(72\) 0 0
\(73\) −3.71686 + 6.43779i −0.435026 + 0.753487i −0.997298 0.0734657i \(-0.976594\pi\)
0.562272 + 0.826952i \(0.309927\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.03164 + 1.44669i 0.117566 + 0.164866i
\(78\) 0 0
\(79\) 10.0127 1.12652 0.563260 0.826279i \(-0.309547\pi\)
0.563260 + 0.826279i \(0.309547\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 2.47376 4.28468i 0.271530 0.470305i −0.697723 0.716367i \(-0.745804\pi\)
0.969254 + 0.246063i \(0.0791369\pi\)
\(84\) 0 0
\(85\) −0.374269 0.648252i −0.0405951 0.0703128i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8.52177 + 14.7601i 0.903306 + 1.56457i 0.823175 + 0.567788i \(0.192201\pi\)
0.0801310 + 0.996784i \(0.474466\pi\)
\(90\) 0 0
\(91\) 4.98840 + 6.99536i 0.522927 + 0.733313i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.164714 −0.0168993
\(96\) 0 0
\(97\) 4.23657 7.33795i 0.430159 0.745056i −0.566728 0.823905i \(-0.691791\pi\)
0.996887 + 0.0788485i \(0.0251243\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.28693 3.96107i −0.227558 0.394141i 0.729526 0.683953i \(-0.239741\pi\)
−0.957084 + 0.289812i \(0.906407\pi\)
\(102\) 0 0
\(103\) −0.903563 + 1.56502i −0.0890307 + 0.154206i −0.907102 0.420912i \(-0.861710\pi\)
0.818071 + 0.575117i \(0.195044\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.88188 + 6.72361i 0.375275 + 0.649996i 0.990368 0.138459i \(-0.0442149\pi\)
−0.615093 + 0.788454i \(0.710882\pi\)
\(108\) 0 0
\(109\) −1.07178 + 1.85638i −0.102658 + 0.177809i −0.912779 0.408454i \(-0.866068\pi\)
0.810121 + 0.586263i \(0.199401\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.91006 + 13.7006i 0.744116 + 1.28885i 0.950607 + 0.310398i \(0.100462\pi\)
−0.206491 + 0.978449i \(0.566204\pi\)
\(114\) 0 0
\(115\) 0.712702 + 1.23444i 0.0664598 + 0.115112i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.41477 5.29695i 0.221362 0.485571i
\(120\) 0 0
\(121\) 5.27449 9.13568i 0.479499 0.830516i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.36263 0.300763
\(126\) 0 0
\(127\) 13.8820 1.23183 0.615915 0.787812i \(-0.288786\pi\)
0.615915 + 0.787812i \(0.288786\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.08769 3.61599i 0.182402 0.315930i −0.760296 0.649577i \(-0.774946\pi\)
0.942698 + 0.333647i \(0.108279\pi\)
\(132\) 0 0
\(133\) −0.743743 1.04297i −0.0644907 0.0904369i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.38043 11.0512i −0.545117 0.944170i −0.998600 0.0529051i \(-0.983152\pi\)
0.453483 0.891265i \(-0.350181\pi\)
\(138\) 0 0
\(139\) −5.95986 10.3228i −0.505509 0.875567i −0.999980 0.00637264i \(-0.997972\pi\)
0.494471 0.869194i \(-0.335362\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.09046 + 1.88873i −0.0911885 + 0.157943i
\(144\) 0 0
\(145\) 0.162911 + 0.282170i 0.0135290 + 0.0234329i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.37548 + 9.31060i −0.440376 + 0.762754i −0.997717 0.0675295i \(-0.978488\pi\)
0.557341 + 0.830284i \(0.311822\pi\)
\(150\) 0 0
\(151\) −1.29050 2.23521i −0.105019 0.181899i 0.808727 0.588184i \(-0.200157\pi\)
−0.913746 + 0.406286i \(0.866824\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.354256 + 0.613589i −0.0284545 + 0.0492846i
\(156\) 0 0
\(157\) 7.99693 0.638224 0.319112 0.947717i \(-0.396615\pi\)
0.319112 + 0.947717i \(0.396615\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.59833 + 10.0867i −0.362399 + 0.794946i
\(162\) 0 0
\(163\) −4.13306 7.15868i −0.323727 0.560711i 0.657527 0.753431i \(-0.271602\pi\)
−0.981254 + 0.192720i \(0.938269\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.99384 + 15.5778i 0.695964 + 1.20544i 0.969855 + 0.243684i \(0.0783560\pi\)
−0.273891 + 0.961761i \(0.588311\pi\)
\(168\) 0 0
\(169\) 1.22720 2.12557i 0.0944000 0.163506i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.9983 1.29236 0.646179 0.763186i \(-0.276366\pi\)
0.646179 + 0.763186i \(0.276366\pi\)
\(174\) 0 0
\(175\) 7.50283 + 10.5214i 0.567161 + 0.795343i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.65073 + 16.7156i −0.721329 + 1.24938i 0.239138 + 0.970986i \(0.423135\pi\)
−0.960467 + 0.278393i \(0.910198\pi\)
\(180\) 0 0
\(181\) 21.9640 1.63257 0.816287 0.577646i \(-0.196029\pi\)
0.816287 + 0.577646i \(0.196029\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.27690 0.240922
\(186\) 0 0
\(187\) 1.47768 0.108059
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.65744 0.481716 0.240858 0.970560i \(-0.422571\pi\)
0.240858 + 0.970560i \(0.422571\pi\)
\(192\) 0 0
\(193\) 6.34906 0.457015 0.228508 0.973542i \(-0.426615\pi\)
0.228508 + 0.973542i \(0.426615\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.8112 −1.69648 −0.848239 0.529614i \(-0.822337\pi\)
−0.848239 + 0.529614i \(0.822337\pi\)
\(198\) 0 0
\(199\) 10.4771 18.1468i 0.742701 1.28640i −0.208561 0.978009i \(-0.566878\pi\)
0.951261 0.308386i \(-0.0997887\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.05110 + 2.30565i −0.0737725 + 0.161825i
\(204\) 0 0
\(205\) 2.65497 0.185431
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.162581 0.281599i 0.0112460 0.0194786i
\(210\) 0 0
\(211\) 6.32431 + 10.9540i 0.435384 + 0.754106i 0.997327 0.0730693i \(-0.0232794\pi\)
−0.561943 + 0.827176i \(0.689946\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.24554 2.15733i −0.0849448 0.147129i
\(216\) 0 0
\(217\) −5.48482 + 0.527427i −0.372334 + 0.0358041i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.14520 0.480638
\(222\) 0 0
\(223\) 1.34432 2.32843i 0.0900225 0.155924i −0.817498 0.575932i \(-0.804639\pi\)
0.907520 + 0.420008i \(0.137973\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.9942 24.2387i −0.928829 1.60878i −0.785284 0.619136i \(-0.787483\pi\)
−0.143546 0.989644i \(-0.545850\pi\)
\(228\) 0 0
\(229\) −12.2695 + 21.2514i −0.810790 + 1.40433i 0.101521 + 0.994833i \(0.467629\pi\)
−0.912312 + 0.409497i \(0.865704\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.61844 + 7.99938i 0.302564 + 0.524057i 0.976716 0.214536i \(-0.0688240\pi\)
−0.674152 + 0.738593i \(0.735491\pi\)
\(234\) 0 0
\(235\) −0.459103 + 0.795189i −0.0299486 + 0.0518724i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 14.0126 + 24.2706i 0.906403 + 1.56994i 0.819023 + 0.573760i \(0.194516\pi\)
0.0873796 + 0.996175i \(0.472151\pi\)
\(240\) 0 0
\(241\) −9.91411 17.1717i −0.638624 1.10613i −0.985735 0.168305i \(-0.946171\pi\)
0.347111 0.937824i \(-0.387163\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.775879 2.25146i 0.0495691 0.143841i
\(246\) 0 0
\(247\) 0.786145 1.36164i 0.0500212 0.0866393i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.5759 1.04626 0.523132 0.852252i \(-0.324764\pi\)
0.523132 + 0.852252i \(0.324764\pi\)
\(252\) 0 0
\(253\) −2.81389 −0.176907
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.64750 6.31766i 0.227525 0.394085i −0.729549 0.683929i \(-0.760270\pi\)
0.957074 + 0.289844i \(0.0936033\pi\)
\(258\) 0 0
\(259\) 14.7963 + 20.7493i 0.919399 + 1.28930i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 13.3899 + 23.1920i 0.825657 + 1.43008i 0.901416 + 0.432954i \(0.142529\pi\)
−0.0757586 + 0.997126i \(0.524138\pi\)
\(264\) 0 0
\(265\) −2.08316 3.60815i −0.127968 0.221647i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.1791 + 17.6307i −0.620630 + 1.07496i 0.368739 + 0.929533i \(0.379790\pi\)
−0.989369 + 0.145429i \(0.953544\pi\)
\(270\) 0 0
\(271\) −5.45842 9.45427i −0.331576 0.574306i 0.651245 0.758867i \(-0.274247\pi\)
−0.982821 + 0.184561i \(0.940914\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.64011 + 2.84075i −0.0989021 + 0.171303i
\(276\) 0 0
\(277\) −8.83689 15.3059i −0.530957 0.919645i −0.999347 0.0361231i \(-0.988499\pi\)
0.468390 0.883522i \(-0.344834\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.17614 + 12.4294i −0.428092 + 0.741478i −0.996704 0.0811286i \(-0.974148\pi\)
0.568611 + 0.822606i \(0.307481\pi\)
\(282\) 0 0
\(283\) −9.72841 −0.578294 −0.289147 0.957285i \(-0.593372\pi\)
−0.289147 + 0.957285i \(0.593372\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11.9881 + 16.8112i 0.707636 + 0.992334i
\(288\) 0 0
\(289\) 6.07937 + 10.5298i 0.357610 + 0.619399i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.26345 10.8486i −0.365915 0.633783i 0.623008 0.782216i \(-0.285911\pi\)
−0.988923 + 0.148433i \(0.952577\pi\)
\(294\) 0 0
\(295\) −0.840799 + 1.45631i −0.0489532 + 0.0847895i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −13.6063 −0.786871
\(300\) 0 0
\(301\) 8.03616 17.6278i 0.463196 1.01605i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.598954 + 1.03742i −0.0342960 + 0.0594025i
\(306\) 0 0
\(307\) −25.8747 −1.47675 −0.738375 0.674391i \(-0.764406\pi\)
−0.738375 + 0.674391i \(0.764406\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 28.4001 1.61042 0.805211 0.592988i \(-0.202052\pi\)
0.805211 + 0.592988i \(0.202052\pi\)
\(312\) 0 0
\(313\) −12.2015 −0.689668 −0.344834 0.938664i \(-0.612065\pi\)
−0.344834 + 0.938664i \(0.612065\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.95219 0.221977 0.110988 0.993822i \(-0.464598\pi\)
0.110988 + 0.993822i \(0.464598\pi\)
\(318\) 0 0
\(319\) −0.643204 −0.0360125
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.06531 −0.0592754
\(324\) 0 0
\(325\) −7.93058 + 13.7362i −0.439909 + 0.761945i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −7.10813 + 0.683527i −0.391884 + 0.0376841i
\(330\) 0 0
\(331\) 8.88286 0.488246 0.244123 0.969744i \(-0.421500\pi\)
0.244123 + 0.969744i \(0.421500\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.09567 + 3.62981i −0.114499 + 0.198318i
\(336\) 0 0
\(337\) −11.9741 20.7397i −0.652269 1.12976i −0.982571 0.185887i \(-0.940484\pi\)
0.330302 0.943875i \(-0.392849\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.699335 1.21128i −0.0378711 0.0655947i
\(342\) 0 0
\(343\) 17.7596 5.25329i 0.958928 0.283651i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.49059 0.509481 0.254741 0.967009i \(-0.418010\pi\)
0.254741 + 0.967009i \(0.418010\pi\)
\(348\) 0 0
\(349\) 4.26145 7.38104i 0.228110 0.395098i −0.729138 0.684367i \(-0.760079\pi\)
0.957248 + 0.289269i \(0.0934121\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −18.5872 32.1940i −0.989297 1.71351i −0.621018 0.783797i \(-0.713281\pi\)
−0.368279 0.929715i \(-0.620053\pi\)
\(354\) 0 0
\(355\) −0.947975 + 1.64194i −0.0503133 + 0.0871451i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.30964 9.19657i −0.280232 0.485376i 0.691210 0.722654i \(-0.257078\pi\)
−0.971442 + 0.237278i \(0.923745\pi\)
\(360\) 0 0
\(361\) 9.38279 16.2515i 0.493831 0.855340i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.26448 + 2.19014i 0.0661857 + 0.114637i
\(366\) 0 0
\(367\) 11.1799 + 19.3642i 0.583586 + 1.01080i 0.995050 + 0.0993751i \(0.0316844\pi\)
−0.411464 + 0.911426i \(0.634982\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 13.4405 29.4826i 0.697796 1.53066i
\(372\) 0 0
\(373\) 8.79264 15.2293i 0.455266 0.788544i −0.543438 0.839450i \(-0.682878\pi\)
0.998703 + 0.0509059i \(0.0162109\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.11015 −0.160181
\(378\) 0 0
\(379\) −10.0443 −0.515939 −0.257969 0.966153i \(-0.583053\pi\)
−0.257969 + 0.966153i \(0.583053\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.93619 6.81768i 0.201130 0.348367i −0.747763 0.663966i \(-0.768872\pi\)
0.948893 + 0.315599i \(0.102205\pi\)
\(384\) 0 0
\(385\) 0.601710 0.0578612i 0.0306660 0.00294888i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.82417 3.15956i −0.0924893 0.160196i 0.816069 0.577955i \(-0.196149\pi\)
−0.908558 + 0.417759i \(0.862816\pi\)
\(390\) 0 0
\(391\) 4.60949 + 7.98387i 0.233112 + 0.403762i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.70317 2.94997i 0.0856956 0.148429i
\(396\) 0 0
\(397\) 6.56071 + 11.3635i 0.329272 + 0.570317i 0.982368 0.186959i \(-0.0598632\pi\)
−0.653095 + 0.757276i \(0.726530\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.71872 9.90511i 0.285579 0.494638i −0.687170 0.726496i \(-0.741147\pi\)
0.972749 + 0.231859i \(0.0744807\pi\)
\(402\) 0 0
\(403\) −3.38157 5.85705i −0.168448 0.291760i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.23445 + 5.60224i −0.160326 + 0.277693i
\(408\) 0 0
\(409\) −18.4821 −0.913882 −0.456941 0.889497i \(-0.651055\pi\)
−0.456941 + 0.889497i \(0.651055\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −13.0178 + 1.25181i −0.640565 + 0.0615975i
\(414\) 0 0
\(415\) −0.841574 1.45765i −0.0413112 0.0715531i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.6290 18.4099i −0.519260 0.899385i −0.999749 0.0223843i \(-0.992874\pi\)
0.480489 0.877001i \(-0.340459\pi\)
\(420\) 0 0
\(421\) −8.60478 + 14.9039i −0.419371 + 0.726373i −0.995876 0.0907211i \(-0.971083\pi\)
0.576505 + 0.817094i \(0.304416\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 10.7468 0.521295
\(426\) 0 0
\(427\) −9.27341 + 0.891743i −0.448772 + 0.0431545i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.02962 5.24745i 0.145931 0.252761i −0.783789 0.621028i \(-0.786715\pi\)
0.929720 + 0.368267i \(0.120049\pi\)
\(432\) 0 0
\(433\) −17.6963 −0.850432 −0.425216 0.905092i \(-0.639802\pi\)
−0.425216 + 0.905092i \(0.639802\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.02862 0.0970421
\(438\) 0 0
\(439\) −27.3373 −1.30474 −0.652370 0.757901i \(-0.726225\pi\)
−0.652370 + 0.757901i \(0.726225\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.91771 0.0911132 0.0455566 0.998962i \(-0.485494\pi\)
0.0455566 + 0.998962i \(0.485494\pi\)
\(444\) 0 0
\(445\) 5.79822 0.274862
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −28.3249 −1.33674 −0.668368 0.743831i \(-0.733007\pi\)
−0.668368 + 0.743831i \(0.733007\pi\)
\(450\) 0 0
\(451\) −2.62058 + 4.53898i −0.123398 + 0.213732i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.90951 0.279782i 0.136400 0.0131164i
\(456\) 0 0
\(457\) 13.0085 0.608514 0.304257 0.952590i \(-0.401592\pi\)
0.304257 + 0.952590i \(0.401592\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.8278 20.4863i 0.550875 0.954144i −0.447336 0.894366i \(-0.647627\pi\)
0.998212 0.0597782i \(-0.0190393\pi\)
\(462\) 0 0
\(463\) 20.2403 + 35.0572i 0.940647 + 1.62925i 0.764241 + 0.644931i \(0.223114\pi\)
0.176406 + 0.984317i \(0.443553\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.6010 32.2179i −0.860753 1.49087i −0.871203 0.490923i \(-0.836659\pi\)
0.0104492 0.999945i \(-0.496674\pi\)
\(468\) 0 0
\(469\) −32.4466 + 3.12011i −1.49825 + 0.144073i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.91761 0.226112
\(474\) 0 0
\(475\) 1.18240 2.04799i 0.0542525 0.0939680i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −20.2918 35.1463i −0.927154 1.60588i −0.788060 0.615598i \(-0.788914\pi\)
−0.139094 0.990279i \(-0.544419\pi\)
\(480\) 0 0
\(481\) −15.6399 + 27.0891i −0.713118 + 1.23516i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.44128 2.49637i −0.0654452 0.113354i
\(486\) 0 0
\(487\) −10.5255 + 18.2307i −0.476956 + 0.826113i −0.999651 0.0264072i \(-0.991593\pi\)
0.522695 + 0.852520i \(0.324927\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.97925 8.62432i −0.224711 0.389210i 0.731522 0.681818i \(-0.238810\pi\)
−0.956233 + 0.292608i \(0.905477\pi\)
\(492\) 0 0
\(493\) 1.05365 + 1.82497i 0.0474538 + 0.0821924i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.6772 + 1.41138i −0.658361 + 0.0633088i
\(498\) 0 0
\(499\) 11.3150 19.5982i 0.506531 0.877337i −0.493440 0.869780i \(-0.664261\pi\)
0.999971 0.00755788i \(-0.00240577\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −43.4520 −1.93743 −0.968714 0.248179i \(-0.920168\pi\)
−0.968714 + 0.248179i \(0.920168\pi\)
\(504\) 0 0
\(505\) −1.55602 −0.0692422
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.77739 + 8.27468i −0.211754 + 0.366769i −0.952264 0.305277i \(-0.901251\pi\)
0.740510 + 0.672046i \(0.234584\pi\)
\(510\) 0 0
\(511\) −8.15836 + 17.8959i −0.360905 + 0.791667i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.307392 + 0.532419i 0.0135453 + 0.0234612i
\(516\) 0 0
\(517\) −0.906312 1.56978i −0.0398596 0.0690388i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.581462 + 1.00712i −0.0254743 + 0.0441228i −0.878482 0.477776i \(-0.841443\pi\)
0.853007 + 0.521899i \(0.174776\pi\)
\(522\) 0 0
\(523\) 3.20567 + 5.55239i 0.140174 + 0.242789i 0.927562 0.373669i \(-0.121900\pi\)
−0.787388 + 0.616458i \(0.788567\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.29119 + 3.96846i −0.0998059 + 0.172869i
\(528\) 0 0
\(529\) 2.72237 + 4.71528i 0.118364 + 0.205012i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12.6716 + 21.9478i −0.548866 + 0.950665i
\(534\) 0 0
\(535\) 2.64123 0.114190
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.08331 + 3.54876i 0.132808 + 0.152856i
\(540\) 0 0
\(541\) −7.37443 12.7729i −0.317052 0.549150i 0.662820 0.748779i \(-0.269360\pi\)
−0.979871 + 0.199629i \(0.936026\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.364621 + 0.631542i 0.0156187 + 0.0270523i
\(546\) 0 0
\(547\) −6.57905 + 11.3952i −0.281300 + 0.487226i −0.971705 0.236197i \(-0.924099\pi\)
0.690405 + 0.723423i \(0.257432\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.463706 0.0197545
\(552\) 0 0
\(553\) 26.3696 2.53573i 1.12135 0.107830i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.1869 21.1083i 0.516374 0.894385i −0.483446 0.875374i \(-0.660615\pi\)
0.999819 0.0190111i \(-0.00605177\pi\)
\(558\) 0 0
\(559\) 23.7787 1.00573
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.11965 −0.131478 −0.0657388 0.997837i \(-0.520940\pi\)
−0.0657388 + 0.997837i \(0.520940\pi\)
\(564\) 0 0
\(565\) 5.38201 0.226423
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.4769 0.900358 0.450179 0.892938i \(-0.351360\pi\)
0.450179 + 0.892938i \(0.351360\pi\)
\(570\) 0 0
\(571\) −33.0460 −1.38293 −0.691466 0.722409i \(-0.743035\pi\)
−0.691466 + 0.722409i \(0.743035\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −20.4646 −0.853432
\(576\) 0 0
\(577\) 0.904826 1.56720i 0.0376684 0.0652436i −0.846577 0.532267i \(-0.821340\pi\)
0.884245 + 0.467023i \(0.154674\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.42980 11.9106i 0.225266 0.494136i
\(582\) 0 0
\(583\) 8.22473 0.340633
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.65901 2.87349i 0.0684746 0.118601i −0.829755 0.558127i \(-0.811520\pi\)
0.898230 + 0.439526i \(0.144853\pi\)
\(588\) 0 0
\(589\) 0.504173 + 0.873253i 0.0207741 + 0.0359818i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −15.3784 26.6362i −0.631516 1.09382i −0.987242 0.159228i \(-0.949100\pi\)
0.355726 0.934590i \(-0.384234\pi\)
\(594\) 0 0
\(595\) −1.14985 1.61246i −0.0471391 0.0661042i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13.9705 0.570817 0.285409 0.958406i \(-0.407871\pi\)
0.285409 + 0.958406i \(0.407871\pi\)
\(600\) 0 0
\(601\) −7.50432 + 12.9979i −0.306108 + 0.530194i −0.977507 0.210901i \(-0.932360\pi\)
0.671400 + 0.741096i \(0.265693\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.79438 3.10796i −0.0729519 0.126356i
\(606\) 0 0
\(607\) 11.6644 20.2034i 0.473444 0.820030i −0.526093 0.850427i \(-0.676344\pi\)
0.999538 + 0.0303969i \(0.00967712\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.38239 7.59052i −0.177292 0.307080i
\(612\) 0 0
\(613\) 22.3374 38.6895i 0.902198 1.56265i 0.0775635 0.996987i \(-0.475286\pi\)
0.824635 0.565666i \(-0.191381\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.18488 + 2.05227i 0.0477013 + 0.0826212i 0.888890 0.458120i \(-0.151477\pi\)
−0.841189 + 0.540741i \(0.818144\pi\)
\(618\) 0 0
\(619\) −11.3863 19.7217i −0.457655 0.792682i 0.541181 0.840906i \(-0.317977\pi\)
−0.998837 + 0.0482236i \(0.984644\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 26.1810 + 36.7142i 1.04892 + 1.47092i
\(624\) 0 0
\(625\) −11.6387 + 20.1588i −0.465547 + 0.806351i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 21.1937 0.845049
\(630\) 0 0
\(631\) −17.8652 −0.711201 −0.355600 0.934638i \(-0.615724\pi\)
−0.355600 + 0.934638i \(0.615724\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.36133 4.08995i 0.0937067 0.162305i
\(636\) 0 0
\(637\) 14.9091 + 17.1597i 0.590718 + 0.679891i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12.7900 22.1529i −0.505175 0.874988i −0.999982 0.00598543i \(-0.998095\pi\)
0.494808 0.869003i \(-0.335239\pi\)
\(642\) 0 0
\(643\) −7.99334 13.8449i −0.315227 0.545989i 0.664259 0.747503i \(-0.268747\pi\)
−0.979486 + 0.201514i \(0.935414\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 7.47306 12.9437i 0.293796 0.508870i −0.680908 0.732369i \(-0.738415\pi\)
0.974704 + 0.223499i \(0.0717479\pi\)
\(648\) 0 0
\(649\) −1.65982 2.87489i −0.0651536 0.112849i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.82885 + 8.36381i −0.188967 + 0.327301i −0.944906 0.327341i \(-0.893847\pi\)
0.755939 + 0.654642i \(0.227181\pi\)
\(654\) 0 0
\(655\) −0.710233 1.23016i −0.0277511 0.0480663i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.80353 16.9802i 0.381891 0.661455i −0.609441 0.792831i \(-0.708606\pi\)
0.991333 + 0.131376i \(0.0419396\pi\)
\(660\) 0 0
\(661\) −10.2655 −0.399281 −0.199641 0.979869i \(-0.563977\pi\)
−0.199641 + 0.979869i \(0.563977\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.433792 + 0.0417140i −0.0168217 + 0.00161760i
\(666\) 0 0
\(667\) −2.00641 3.47520i −0.0776885 0.134560i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.18239 2.04797i −0.0456458 0.0790608i
\(672\) 0 0
\(673\) −17.1584 + 29.7191i −0.661406 + 1.14559i 0.318840 + 0.947808i \(0.396707\pi\)
−0.980246 + 0.197780i \(0.936627\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.47419 −0.287256 −0.143628 0.989632i \(-0.545877\pi\)
−0.143628 + 0.989632i \(0.545877\pi\)
\(678\) 0 0
\(679\) 9.29910 20.3982i 0.356867 0.782810i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −18.1577 + 31.4501i −0.694786 + 1.20340i 0.275467 + 0.961310i \(0.411167\pi\)
−0.970253 + 0.242094i \(0.922166\pi\)
\(684\) 0 0
\(685\) −4.34125 −0.165871
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 39.7699 1.51511
\(690\) 0 0
\(691\) −50.9624 −1.93870 −0.969350 0.245684i \(-0.920987\pi\)
−0.969350 + 0.245684i \(0.920987\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.05509 −0.153818
\(696\) 0 0
\(697\) 17.1713 0.650410
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −36.6075 −1.38265 −0.691324 0.722545i \(-0.742972\pi\)
−0.691324 + 0.722545i \(0.742972\pi\)
\(702\) 0 0
\(703\) 2.33182 4.03883i 0.0879463 0.152327i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.02600 9.85272i −0.264240 0.370550i
\(708\) 0 0
\(709\) −5.87578 −0.220670 −0.110335 0.993894i \(-0.535192\pi\)
−0.110335 + 0.993894i \(0.535192\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.36301 7.55695i 0.163396 0.283010i
\(714\) 0 0
\(715\) 0.370973 + 0.642545i 0.0138736 + 0.0240298i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8.09642 14.0234i −0.301945 0.522985i 0.674631 0.738155i \(-0.264303\pi\)
−0.976577 + 0.215170i \(0.930969\pi\)
\(720\) 0 0
\(721\) −1.98328 + 4.35046i −0.0738614 + 0.162020i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.67783 −0.173730
\(726\) 0 0
\(727\) 22.8771 39.6243i 0.848464 1.46958i −0.0341138 0.999418i \(-0.510861\pi\)
0.882578 0.470166i \(-0.155806\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.05565 13.9528i −0.297949 0.516063i
\(732\) 0 0
\(733\) −13.5916 + 23.5414i −0.502019 + 0.869522i 0.497978 + 0.867189i \(0.334076\pi\)
−0.999997 + 0.00233276i \(0.999257\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.13706 7.16560i −0.152391 0.263948i
\(738\) 0 0
\(739\) −12.1738 + 21.0856i −0.447821 + 0.775648i −0.998244 0.0592377i \(-0.981133\pi\)
0.550423 + 0.834886i \(0.314466\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.0683178 0.118330i −0.00250634 0.00434110i 0.864770 0.502169i \(-0.167464\pi\)
−0.867276 + 0.497828i \(0.834131\pi\)
\(744\) 0 0
\(745\) 1.82874 + 3.16747i 0.0669998 + 0.116047i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 11.9261 + 16.7242i 0.435769 + 0.611090i
\(750\) 0 0
\(751\) 3.71446 6.43364i 0.135543 0.234767i −0.790262 0.612769i \(-0.790056\pi\)
0.925805 + 0.378002i \(0.123389\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.878055 −0.0319557
\(756\) 0 0
\(757\) −14.0794 −0.511723 −0.255861 0.966713i \(-0.582359\pi\)
−0.255861 + 0.966713i \(0.582359\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 19.3616 33.5353i 0.701858 1.21565i −0.265955 0.963985i \(-0.585687\pi\)
0.967813 0.251669i \(-0.0809793\pi\)
\(762\) 0 0
\(763\) −2.35252 + 5.16041i −0.0851671 + 0.186819i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.02589 13.9013i −0.289798 0.501945i
\(768\) 0 0
\(769\) 5.14295 + 8.90786i 0.185460 + 0.321226i 0.943731 0.330713i \(-0.107289\pi\)
−0.758272 + 0.651939i \(0.773956\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.6768 39.2773i 0.815627 1.41271i −0.0932501 0.995643i \(-0.529726\pi\)
0.908877 0.417064i \(-0.136941\pi\)
\(774\) 0 0
\(775\) −5.08606 8.80931i −0.182697 0.316440i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.88926 3.27229i 0.0676898 0.117242i
\(780\) 0 0
\(781\) −1.87139 3.24135i −0.0669637 0.115985i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.36028 2.35607i 0.0485504 0.0840917i
\(786\) 0 0
\(787\) −26.1087 −0.930675 −0.465337 0.885133i \(-0.654067\pi\)
−0.465337 + 0.885133i \(0.654067\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24.3017 + 34.0788i 0.864067 + 1.21170i
\(792\) 0 0
\(793\) −5.71735 9.90274i −0.203029 0.351657i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.1618 + 27.9931i 0.572481 + 0.991567i 0.996310 + 0.0858244i \(0.0273524\pi\)
−0.423829 + 0.905742i \(0.639314\pi\)