Properties

Label 3024.2.t.l.1873.6
Level $3024$
Weight $2$
Character 3024.1873
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.t (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 1873.6
Character \(\chi\) \(=\) 3024.1873
Dual form 3024.2.t.l.289.6

$q$-expansion

\(f(q)\) \(=\) \(q+0.481387 q^{5} +(-2.53326 + 0.763277i) q^{7} +O(q^{10})\) \(q+0.481387 q^{5} +(-2.53326 + 0.763277i) q^{7} +3.38159 q^{11} +(-2.86067 + 4.95482i) q^{13} +(-2.75605 + 4.77362i) q^{17} +(-2.18023 - 3.77626i) q^{19} +3.62585 q^{23} -4.76827 q^{25} +(-1.53131 - 2.65231i) q^{29} +(-4.67459 - 8.09663i) q^{31} +(-1.21948 + 0.367431i) q^{35} +(1.48552 + 2.57299i) q^{37} +(6.29558 - 10.9043i) q^{41} +(-1.90827 - 3.30522i) q^{43} +(1.88282 - 3.26114i) q^{47} +(5.83482 - 3.86716i) q^{49} +(-5.57860 + 9.66242i) q^{53} +1.62786 q^{55} +(-4.21141 - 7.29438i) q^{59} +(3.64312 - 6.31007i) q^{61} +(-1.37709 + 2.38519i) q^{65} +(1.28571 + 2.22692i) q^{67} -3.94304 q^{71} +(-0.862216 + 1.49340i) q^{73} +(-8.56646 + 2.58109i) q^{77} +(-2.79980 + 4.84940i) q^{79} +(-0.119494 - 0.206970i) q^{83} +(-1.32673 + 2.29796i) q^{85} +(-0.648116 - 1.12257i) q^{89} +(3.46492 - 14.7353i) q^{91} +(-1.04953 - 1.81784i) q^{95} +(-7.02669 - 12.1706i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 6q^{5} - 7q^{7} + O(q^{10}) \) \( 22q + 6q^{5} - 7q^{7} + 6q^{11} - 3q^{13} - 7q^{17} + q^{19} - 4q^{23} + 20q^{25} - 9q^{29} + 4q^{31} + 14q^{35} + 2q^{37} - 16q^{41} + 5q^{47} - 15q^{49} - 11q^{53} - 22q^{55} - 19q^{59} - 13q^{61} - 13q^{65} - 26q^{67} - 48q^{71} - 35q^{73} + 4q^{77} - 10q^{79} - 28q^{83} - 20q^{85} - 6q^{89} + 37q^{91} + 12q^{95} - 29q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) 0.481387 0.215283 0.107641 0.994190i \(-0.465670\pi\)
0.107641 + 0.994190i \(0.465670\pi\)
\(6\) 0 0
\(7\) −2.53326 + 0.763277i −0.957482 + 0.288491i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.38159 1.01959 0.509794 0.860296i \(-0.329721\pi\)
0.509794 + 0.860296i \(0.329721\pi\)
\(12\) 0 0
\(13\) −2.86067 + 4.95482i −0.793406 + 1.37422i 0.130440 + 0.991456i \(0.458361\pi\)
−0.923846 + 0.382764i \(0.874972\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.75605 + 4.77362i −0.668440 + 1.15777i 0.309900 + 0.950769i \(0.399704\pi\)
−0.978340 + 0.207003i \(0.933629\pi\)
\(18\) 0 0
\(19\) −2.18023 3.77626i −0.500178 0.866334i −1.00000 0.000205746i \(-0.999935\pi\)
0.499822 0.866128i \(-0.333399\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.62585 0.756042 0.378021 0.925797i \(-0.376605\pi\)
0.378021 + 0.925797i \(0.376605\pi\)
\(24\) 0 0
\(25\) −4.76827 −0.953653
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.53131 2.65231i −0.284358 0.492522i 0.688095 0.725620i \(-0.258447\pi\)
−0.972453 + 0.233098i \(0.925114\pi\)
\(30\) 0 0
\(31\) −4.67459 8.09663i −0.839581 1.45420i −0.890245 0.455481i \(-0.849467\pi\)
0.0506646 0.998716i \(-0.483866\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.21948 + 0.367431i −0.206130 + 0.0621072i
\(36\) 0 0
\(37\) 1.48552 + 2.57299i 0.244218 + 0.422997i 0.961911 0.273361i \(-0.0881355\pi\)
−0.717694 + 0.696359i \(0.754802\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.29558 10.9043i 0.983204 1.70296i 0.333545 0.942734i \(-0.391755\pi\)
0.649659 0.760226i \(-0.274912\pi\)
\(42\) 0 0
\(43\) −1.90827 3.30522i −0.291009 0.504042i 0.683040 0.730381i \(-0.260658\pi\)
−0.974049 + 0.226339i \(0.927324\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.88282 3.26114i 0.274638 0.475687i −0.695406 0.718617i \(-0.744775\pi\)
0.970044 + 0.242930i \(0.0781087\pi\)
\(48\) 0 0
\(49\) 5.83482 3.86716i 0.833545 0.552451i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.57860 + 9.66242i −0.766280 + 1.32724i 0.173287 + 0.984871i \(0.444561\pi\)
−0.939567 + 0.342364i \(0.888772\pi\)
\(54\) 0 0
\(55\) 1.62786 0.219500
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.21141 7.29438i −0.548279 0.949647i −0.998393 0.0566756i \(-0.981950\pi\)
0.450114 0.892971i \(-0.351383\pi\)
\(60\) 0 0
\(61\) 3.64312 6.31007i 0.466454 0.807922i −0.532812 0.846234i \(-0.678865\pi\)
0.999266 + 0.0383116i \(0.0121979\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.37709 + 2.38519i −0.170807 + 0.295846i
\(66\) 0 0
\(67\) 1.28571 + 2.22692i 0.157075 + 0.272062i 0.933813 0.357763i \(-0.116460\pi\)
−0.776738 + 0.629824i \(0.783127\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.94304 −0.467953 −0.233977 0.972242i \(-0.575174\pi\)
−0.233977 + 0.972242i \(0.575174\pi\)
\(72\) 0 0
\(73\) −0.862216 + 1.49340i −0.100915 + 0.174790i −0.912062 0.410053i \(-0.865510\pi\)
0.811147 + 0.584842i \(0.198844\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.56646 + 2.58109i −0.976238 + 0.294143i
\(78\) 0 0
\(79\) −2.79980 + 4.84940i −0.315002 + 0.545600i −0.979438 0.201746i \(-0.935339\pi\)
0.664436 + 0.747345i \(0.268672\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.119494 0.206970i −0.0131162 0.0227179i 0.859393 0.511316i \(-0.170842\pi\)
−0.872509 + 0.488598i \(0.837508\pi\)
\(84\) 0 0
\(85\) −1.32673 + 2.29796i −0.143904 + 0.249249i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.648116 1.12257i −0.0687002 0.118992i 0.829629 0.558315i \(-0.188552\pi\)
−0.898329 + 0.439323i \(0.855219\pi\)
\(90\) 0 0
\(91\) 3.46492 14.7353i 0.363222 1.54468i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.04953 1.81784i −0.107680 0.186507i
\(96\) 0 0
\(97\) −7.02669 12.1706i −0.713452 1.23574i −0.963553 0.267516i \(-0.913797\pi\)
0.250101 0.968220i \(-0.419536\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −10.6064 −1.05538 −0.527690 0.849437i \(-0.676942\pi\)
−0.527690 + 0.849437i \(0.676942\pi\)
\(102\) 0 0
\(103\) 0.159416 0.0157077 0.00785385 0.999969i \(-0.497500\pi\)
0.00785385 + 0.999969i \(0.497500\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.99030 6.91140i −0.385757 0.668150i 0.606117 0.795375i \(-0.292726\pi\)
−0.991874 + 0.127225i \(0.959393\pi\)
\(108\) 0 0
\(109\) −6.85612 + 11.8751i −0.656697 + 1.13743i 0.324769 + 0.945793i \(0.394714\pi\)
−0.981466 + 0.191639i \(0.938620\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.98656 + 15.5652i −0.845384 + 1.46425i 0.0399031 + 0.999204i \(0.487295\pi\)
−0.885287 + 0.465045i \(0.846038\pi\)
\(114\) 0 0
\(115\) 1.74544 0.162763
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.33820 14.1964i 0.306012 1.30139i
\(120\) 0 0
\(121\) 0.435176 0.0395615
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −4.70232 −0.420588
\(126\) 0 0
\(127\) −18.9684 −1.68317 −0.841587 0.540121i \(-0.818378\pi\)
−0.841587 + 0.540121i \(0.818378\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.88232 −0.426570 −0.213285 0.976990i \(-0.568416\pi\)
−0.213285 + 0.976990i \(0.568416\pi\)
\(132\) 0 0
\(133\) 8.40541 + 7.90214i 0.728842 + 0.685203i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.47482 0.553181 0.276591 0.960988i \(-0.410795\pi\)
0.276591 + 0.960988i \(0.410795\pi\)
\(138\) 0 0
\(139\) 11.3740 19.7003i 0.964727 1.67096i 0.254381 0.967104i \(-0.418128\pi\)
0.710346 0.703852i \(-0.248538\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.67362 + 16.7552i −0.808948 + 1.40114i
\(144\) 0 0
\(145\) −0.737155 1.27679i −0.0612174 0.106032i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.2046 1.16369 0.581843 0.813301i \(-0.302332\pi\)
0.581843 + 0.813301i \(0.302332\pi\)
\(150\) 0 0
\(151\) −2.52259 −0.205285 −0.102643 0.994718i \(-0.532730\pi\)
−0.102643 + 0.994718i \(0.532730\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.25029 3.89761i −0.180747 0.313064i
\(156\) 0 0
\(157\) −8.74064 15.1392i −0.697579 1.20824i −0.969303 0.245867i \(-0.920927\pi\)
0.271724 0.962375i \(-0.412406\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −9.18523 + 2.76753i −0.723897 + 0.218112i
\(162\) 0 0
\(163\) −0.881184 1.52625i −0.0690196 0.119546i 0.829450 0.558580i \(-0.188654\pi\)
−0.898470 + 0.439035i \(0.855320\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.57220 + 6.18723i −0.276425 + 0.478782i −0.970494 0.241127i \(-0.922483\pi\)
0.694069 + 0.719909i \(0.255816\pi\)
\(168\) 0 0
\(169\) −9.86684 17.0899i −0.758988 1.31461i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.94691 8.56830i 0.376107 0.651436i −0.614385 0.789006i \(-0.710596\pi\)
0.990492 + 0.137570i \(0.0439293\pi\)
\(174\) 0 0
\(175\) 12.0793 3.63951i 0.913106 0.275121i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.02967 3.51550i 0.151705 0.262761i −0.780149 0.625593i \(-0.784857\pi\)
0.931854 + 0.362833i \(0.118190\pi\)
\(180\) 0 0
\(181\) 4.58084 0.340491 0.170246 0.985402i \(-0.445544\pi\)
0.170246 + 0.985402i \(0.445544\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.715109 + 1.23861i 0.0525759 + 0.0910641i
\(186\) 0 0
\(187\) −9.31984 + 16.1424i −0.681534 + 1.18045i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.59624 + 9.69298i −0.404930 + 0.701359i −0.994313 0.106494i \(-0.966037\pi\)
0.589383 + 0.807853i \(0.299371\pi\)
\(192\) 0 0
\(193\) −8.14679 14.1106i −0.586419 1.01571i −0.994697 0.102849i \(-0.967204\pi\)
0.408278 0.912857i \(-0.366129\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.17438 0.226165 0.113082 0.993586i \(-0.463928\pi\)
0.113082 + 0.993586i \(0.463928\pi\)
\(198\) 0 0
\(199\) −1.44140 + 2.49658i −0.102178 + 0.176978i −0.912582 0.408894i \(-0.865915\pi\)
0.810404 + 0.585872i \(0.199248\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.90367 + 5.55019i 0.414356 + 0.389547i
\(204\) 0 0
\(205\) 3.03061 5.24917i 0.211667 0.366618i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.37264 12.7698i −0.509976 0.883305i
\(210\) 0 0
\(211\) 0.242718 0.420400i 0.0167094 0.0289415i −0.857550 0.514401i \(-0.828014\pi\)
0.874259 + 0.485459i \(0.161348\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.918617 1.59109i −0.0626492 0.108512i
\(216\) 0 0
\(217\) 18.0219 + 16.9429i 1.22341 + 1.15016i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −15.7683 27.3115i −1.06069 1.83717i
\(222\) 0 0
\(223\) −2.14795 3.72037i −0.143838 0.249134i 0.785101 0.619368i \(-0.212611\pi\)
−0.928939 + 0.370234i \(0.879278\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.3827 −1.15373 −0.576866 0.816839i \(-0.695725\pi\)
−0.576866 + 0.816839i \(0.695725\pi\)
\(228\) 0 0
\(229\) 7.33125 0.484463 0.242231 0.970218i \(-0.422121\pi\)
0.242231 + 0.970218i \(0.422121\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.16624 + 3.75205i 0.141915 + 0.245805i 0.928218 0.372037i \(-0.121341\pi\)
−0.786302 + 0.617842i \(0.788007\pi\)
\(234\) 0 0
\(235\) 0.906366 1.56987i 0.0591248 0.102407i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.77960 3.08236i 0.115113 0.199381i −0.802712 0.596367i \(-0.796610\pi\)
0.917825 + 0.396986i \(0.129944\pi\)
\(240\) 0 0
\(241\) 16.0185 1.03184 0.515921 0.856636i \(-0.327450\pi\)
0.515921 + 0.856636i \(0.327450\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.80881 1.86160i 0.179448 0.118933i
\(246\) 0 0
\(247\) 24.9476 1.58738
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.8007 −0.807972 −0.403986 0.914765i \(-0.632375\pi\)
−0.403986 + 0.914765i \(0.632375\pi\)
\(252\) 0 0
\(253\) 12.2612 0.770852
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −16.4154 −1.02396 −0.511981 0.858997i \(-0.671088\pi\)
−0.511981 + 0.858997i \(0.671088\pi\)
\(258\) 0 0
\(259\) −5.72711 5.38420i −0.355865 0.334558i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 25.6528 1.58182 0.790910 0.611933i \(-0.209608\pi\)
0.790910 + 0.611933i \(0.209608\pi\)
\(264\) 0 0
\(265\) −2.68547 + 4.65136i −0.164967 + 0.285731i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −5.35397 + 9.27335i −0.326437 + 0.565406i −0.981802 0.189906i \(-0.939182\pi\)
0.655365 + 0.755313i \(0.272515\pi\)
\(270\) 0 0
\(271\) 12.7513 + 22.0859i 0.774587 + 1.34162i 0.935026 + 0.354578i \(0.115376\pi\)
−0.160439 + 0.987046i \(0.551291\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.1243 −0.972334
\(276\) 0 0
\(277\) −12.7825 −0.768023 −0.384012 0.923328i \(-0.625458\pi\)
−0.384012 + 0.923328i \(0.625458\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.4763 + 18.1454i 0.624961 + 1.08246i 0.988548 + 0.150904i \(0.0482185\pi\)
−0.363587 + 0.931560i \(0.618448\pi\)
\(282\) 0 0
\(283\) 7.53085 + 13.0438i 0.447663 + 0.775374i 0.998233 0.0594141i \(-0.0189232\pi\)
−0.550571 + 0.834788i \(0.685590\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.62537 + 32.4286i −0.450112 + 1.91420i
\(288\) 0 0
\(289\) −6.69162 11.5902i −0.393625 0.681778i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.134459 + 0.232890i −0.00785519 + 0.0136056i −0.869926 0.493182i \(-0.835834\pi\)
0.862071 + 0.506787i \(0.169167\pi\)
\(294\) 0 0
\(295\) −2.02732 3.51142i −0.118035 0.204443i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.3724 + 17.9654i −0.599849 + 1.03897i
\(300\) 0 0
\(301\) 7.35695 + 6.91645i 0.424048 + 0.398658i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.75375 3.03759i 0.100420 0.173932i
\(306\) 0 0
\(307\) 5.03514 0.287371 0.143685 0.989623i \(-0.454105\pi\)
0.143685 + 0.989623i \(0.454105\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.23815 3.87659i −0.126914 0.219821i 0.795566 0.605868i \(-0.207174\pi\)
−0.922479 + 0.386046i \(0.873841\pi\)
\(312\) 0 0
\(313\) −5.48895 + 9.50715i −0.310254 + 0.537376i −0.978417 0.206639i \(-0.933747\pi\)
0.668163 + 0.744015i \(0.267081\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.4826 21.6205i 0.701092 1.21433i −0.266992 0.963699i \(-0.586030\pi\)
0.968084 0.250628i \(-0.0806371\pi\)
\(318\) 0 0
\(319\) −5.17828 8.96905i −0.289928 0.502170i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0352 1.33736
\(324\) 0 0
\(325\) 13.6404 23.6259i 0.756635 1.31053i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.28052 + 9.69844i −0.125729 + 0.534692i
\(330\) 0 0
\(331\) 6.01206 10.4132i 0.330453 0.572361i −0.652148 0.758092i \(-0.726132\pi\)
0.982601 + 0.185731i \(0.0594653\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.618925 + 1.07201i 0.0338155 + 0.0585702i
\(336\) 0 0
\(337\) −14.1286 + 24.4715i −0.769636 + 1.33305i 0.168125 + 0.985766i \(0.446229\pi\)
−0.937761 + 0.347282i \(0.887105\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −15.8076 27.3795i −0.856027 1.48268i
\(342\) 0 0
\(343\) −11.8294 + 14.2501i −0.638728 + 0.769433i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −9.80293 16.9792i −0.526249 0.911490i −0.999532 0.0305797i \(-0.990265\pi\)
0.473283 0.880910i \(-0.343069\pi\)
\(348\) 0 0
\(349\) −8.22904 14.2531i −0.440490 0.762952i 0.557236 0.830354i \(-0.311862\pi\)
−0.997726 + 0.0674029i \(0.978529\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 27.3709 1.45680 0.728402 0.685150i \(-0.240263\pi\)
0.728402 + 0.685150i \(0.240263\pi\)
\(354\) 0 0
\(355\) −1.89813 −0.100742
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.88714 + 13.6609i 0.416267 + 0.720996i 0.995561 0.0941231i \(-0.0300047\pi\)
−0.579293 + 0.815119i \(0.696671\pi\)
\(360\) 0 0
\(361\) −0.00677168 + 0.0117289i −0.000356404 + 0.000617310i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.415060 + 0.718905i −0.0217252 + 0.0376292i
\(366\) 0 0
\(367\) −18.8137 −0.982066 −0.491033 0.871141i \(-0.663381\pi\)
−0.491033 + 0.871141i \(0.663381\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.75695 28.7355i 0.350803 1.49187i
\(372\) 0 0
\(373\) −17.5737 −0.909934 −0.454967 0.890508i \(-0.650349\pi\)
−0.454967 + 0.890508i \(0.650349\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 17.5223 0.902446
\(378\) 0 0
\(379\) −34.4618 −1.77018 −0.885091 0.465419i \(-0.845904\pi\)
−0.885091 + 0.465419i \(0.845904\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −22.7410 −1.16201 −0.581005 0.813900i \(-0.697340\pi\)
−0.581005 + 0.813900i \(0.697340\pi\)
\(384\) 0 0
\(385\) −4.12378 + 1.24250i −0.210167 + 0.0633239i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −15.7638 −0.799255 −0.399628 0.916678i \(-0.630861\pi\)
−0.399628 + 0.916678i \(0.630861\pi\)
\(390\) 0 0
\(391\) −9.99303 + 17.3084i −0.505369 + 0.875325i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.34779 + 2.33444i −0.0678145 + 0.117458i
\(396\) 0 0
\(397\) −5.39875 9.35091i −0.270955 0.469308i 0.698151 0.715950i \(-0.254006\pi\)
−0.969107 + 0.246642i \(0.920673\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.3295 −0.615704 −0.307852 0.951434i \(-0.599610\pi\)
−0.307852 + 0.951434i \(0.599610\pi\)
\(402\) 0 0
\(403\) 53.4898 2.66452
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.02342 + 8.70082i 0.249002 + 0.431284i
\(408\) 0 0
\(409\) −9.31771 16.1387i −0.460731 0.798010i 0.538266 0.842775i \(-0.319079\pi\)
−0.998998 + 0.0447650i \(0.985746\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.2362 + 15.2641i 0.798932 + 0.751096i
\(414\) 0 0
\(415\) −0.0575230 0.0996328i −0.00282369 0.00489078i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.90976 + 10.2360i −0.288711 + 0.500062i −0.973502 0.228677i \(-0.926560\pi\)
0.684791 + 0.728739i \(0.259893\pi\)
\(420\) 0 0
\(421\) 4.81800 + 8.34503i 0.234815 + 0.406712i 0.959219 0.282664i \(-0.0912182\pi\)
−0.724404 + 0.689376i \(0.757885\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.1416 22.7619i 0.637460 1.10411i
\(426\) 0 0
\(427\) −4.41265 + 18.7658i −0.213543 + 0.908139i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −18.2913 + 31.6815i −0.881062 + 1.52604i −0.0309004 + 0.999522i \(0.509837\pi\)
−0.850162 + 0.526522i \(0.823496\pi\)
\(432\) 0 0
\(433\) −7.69388 −0.369744 −0.184872 0.982763i \(-0.559187\pi\)
−0.184872 + 0.982763i \(0.559187\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.90518 13.6922i −0.378156 0.654985i
\(438\) 0 0
\(439\) −10.2717 + 17.7911i −0.490241 + 0.849122i −0.999937 0.0112324i \(-0.996425\pi\)
0.509696 + 0.860355i \(0.329758\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 16.8401 29.1679i 0.800098 1.38581i −0.119454 0.992840i \(-0.538114\pi\)
0.919551 0.392970i \(-0.128552\pi\)
\(444\) 0 0
\(445\) −0.311995 0.540391i −0.0147900 0.0256170i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.5141 1.06250 0.531252 0.847214i \(-0.321722\pi\)
0.531252 + 0.847214i \(0.321722\pi\)
\(450\) 0 0
\(451\) 21.2891 36.8738i 1.00246 1.73632i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.66797 7.09340i 0.0781955 0.332544i
\(456\) 0 0
\(457\) 11.8559 20.5349i 0.554594 0.960584i −0.443342 0.896353i \(-0.646207\pi\)
0.997935 0.0642314i \(-0.0204596\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.57340 + 9.65342i 0.259579 + 0.449605i 0.966129 0.258059i \(-0.0830828\pi\)
−0.706550 + 0.707663i \(0.749749\pi\)
\(462\) 0 0
\(463\) −10.3208 + 17.8761i −0.479647 + 0.830773i −0.999727 0.0233441i \(-0.992569\pi\)
0.520080 + 0.854117i \(0.325902\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.68477 15.0425i −0.401883 0.696082i 0.592070 0.805887i \(-0.298311\pi\)
−0.993953 + 0.109804i \(0.964978\pi\)
\(468\) 0 0
\(469\) −4.95680 4.66001i −0.228884 0.215179i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.45300 11.1769i −0.296709 0.513916i
\(474\) 0 0
\(475\) 10.3959 + 18.0062i 0.476997 + 0.826182i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.09033 −0.186892 −0.0934461 0.995624i \(-0.529788\pi\)
−0.0934461 + 0.995624i \(0.529788\pi\)
\(480\) 0 0
\(481\) −16.9983 −0.775056
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.38256 5.85876i −0.153594 0.266033i
\(486\) 0 0
\(487\) 0.843065 1.46023i 0.0382029 0.0661694i −0.846292 0.532720i \(-0.821170\pi\)
0.884495 + 0.466550i \(0.154503\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.85070 11.8658i 0.309168 0.535494i −0.669013 0.743251i \(-0.733283\pi\)
0.978181 + 0.207757i \(0.0666162\pi\)
\(492\) 0 0
\(493\) 16.8815 0.760305
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.98875 3.00963i 0.448057 0.135000i
\(498\) 0 0
\(499\) 6.55655 0.293511 0.146756 0.989173i \(-0.453117\pi\)
0.146756 + 0.989173i \(0.453117\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 26.8584 1.19756 0.598779 0.800914i \(-0.295653\pi\)
0.598779 + 0.800914i \(0.295653\pi\)
\(504\) 0 0
\(505\) −5.10580 −0.227205
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 39.7337 1.76117 0.880584 0.473891i \(-0.157151\pi\)
0.880584 + 0.473891i \(0.157151\pi\)
\(510\) 0 0
\(511\) 1.04434 4.44129i 0.0461989 0.196471i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.0767406 0.00338160
\(516\) 0 0
\(517\) 6.36694 11.0279i 0.280018 0.485005i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −11.7585 + 20.3663i −0.515148 + 0.892262i 0.484698 + 0.874682i \(0.338930\pi\)
−0.999845 + 0.0175802i \(0.994404\pi\)
\(522\) 0 0
\(523\) 10.9289 + 18.9294i 0.477887 + 0.827725i 0.999679 0.0253481i \(-0.00806942\pi\)
−0.521791 + 0.853073i \(0.674736\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 51.5336 2.24484
\(528\) 0 0
\(529\) −9.85320 −0.428400
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 36.0191 + 62.3869i 1.56016 + 2.70228i
\(534\) 0 0
\(535\) −1.92088 3.32706i −0.0830468 0.143841i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 19.7310 13.0772i 0.849874 0.563273i
\(540\) 0 0
\(541\) 14.0063 + 24.2596i 0.602178 + 1.04300i 0.992491 + 0.122320i \(0.0390334\pi\)
−0.390313 + 0.920682i \(0.627633\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.30045 + 5.71654i −0.141376 + 0.244870i
\(546\) 0 0
\(547\) 2.02714 + 3.51112i 0.0866744 + 0.150124i 0.906103 0.423056i \(-0.139043\pi\)
−0.819429 + 0.573181i \(0.805709\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.67722 + 11.5653i −0.284459 + 0.492698i
\(552\) 0 0
\(553\) 3.39119 14.4218i 0.144208 0.613278i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.926620 1.60495i 0.0392621 0.0680040i −0.845727 0.533616i \(-0.820833\pi\)
0.884989 + 0.465612i \(0.154166\pi\)
\(558\) 0 0
\(559\) 21.8357 0.923553
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.2331 38.5088i −0.937013 1.62295i −0.771005 0.636830i \(-0.780245\pi\)
−0.166008 0.986124i \(-0.553088\pi\)
\(564\) 0 0
\(565\) −4.32601 + 7.49287i −0.181997 + 0.315227i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.63116 13.2176i 0.319915 0.554109i −0.660555 0.750778i \(-0.729679\pi\)
0.980470 + 0.196669i \(0.0630124\pi\)
\(570\) 0 0
\(571\) −12.7634 22.1068i −0.534130 0.925140i −0.999205 0.0398690i \(-0.987306\pi\)
0.465075 0.885271i \(-0.346027\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −17.2890 −0.721002
\(576\) 0 0
\(577\) −3.26981 + 5.66348i −0.136124 + 0.235774i −0.926026 0.377459i \(-0.876798\pi\)
0.789902 + 0.613233i \(0.210131\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.460686 + 0.433102i 0.0191125 + 0.0179681i
\(582\) 0 0
\(583\) −18.8646 + 32.6744i −0.781291 + 1.35323i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.2055 + 26.3366i 0.627597 + 1.08703i 0.988033 + 0.154245i \(0.0492947\pi\)
−0.360436 + 0.932784i \(0.617372\pi\)
\(588\) 0 0
\(589\) −20.3833 + 35.3049i −0.839880 + 1.45471i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21.3291 + 36.9432i 0.875883 + 1.51707i 0.855819 + 0.517275i \(0.173053\pi\)
0.0200633 + 0.999799i \(0.493613\pi\)
\(594\) 0 0
\(595\) 1.60697 6.83399i 0.0658792 0.280166i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 22.2787 + 38.5879i 0.910284 + 1.57666i 0.813663 + 0.581337i \(0.197470\pi\)
0.0966209 + 0.995321i \(0.469197\pi\)
\(600\) 0 0
\(601\) 14.1961 + 24.5884i 0.579071 + 1.00298i 0.995586 + 0.0938518i \(0.0299180\pi\)
−0.416515 + 0.909129i \(0.636749\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.209488 0.00851691
\(606\) 0 0
\(607\) −14.0278 −0.569372 −0.284686 0.958621i \(-0.591889\pi\)
−0.284686 + 0.958621i \(0.591889\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.7723 + 18.6581i 0.435799 + 0.754826i
\(612\) 0 0
\(613\) −9.97062 + 17.2696i −0.402709 + 0.697513i −0.994052 0.108907i \(-0.965265\pi\)
0.591342 + 0.806421i \(0.298598\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.51584 2.62551i 0.0610254 0.105699i −0.833899 0.551918i \(-0.813896\pi\)
0.894924 + 0.446219i \(0.147230\pi\)
\(618\) 0 0
\(619\) −2.55431 −0.102666 −0.0513331 0.998682i \(-0.516347\pi\)
−0.0513331 + 0.998682i \(0.516347\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.49868 + 2.34907i 0.100107 + 0.0941136i
\(624\) 0 0
\(625\) 21.5777 0.863108
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −16.3766 −0.652980
\(630\) 0 0
\(631\) −37.1162 −1.47757 −0.738786 0.673941i \(-0.764600\pi\)
−0.738786 + 0.673941i \(0.764600\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.13115 −0.362358
\(636\) 0 0
\(637\) 2.46960 + 39.9731i 0.0978491 + 1.58379i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21.0968 −0.833275 −0.416638 0.909073i \(-0.636792\pi\)
−0.416638 + 0.909073i \(0.636792\pi\)
\(642\) 0 0
\(643\) −9.31948 + 16.1418i −0.367524 + 0.636571i −0.989178 0.146722i \(-0.953128\pi\)
0.621654 + 0.783292i \(0.286461\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.78509 8.28801i 0.188121 0.325835i −0.756503 0.653991i \(-0.773094\pi\)
0.944624 + 0.328155i \(0.106427\pi\)
\(648\) 0 0
\(649\) −14.2413 24.6666i −0.559019 0.968249i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 32.8560 1.28575 0.642877 0.765970i \(-0.277741\pi\)
0.642877 + 0.765970i \(0.277741\pi\)
\(654\) 0 0
\(655\) −2.35028 −0.0918332
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.8011 + 42.9568i 0.966114 + 1.67336i 0.706593 + 0.707620i \(0.250231\pi\)
0.259521 + 0.965738i \(0.416435\pi\)
\(660\) 0 0
\(661\) 1.65895 + 2.87338i 0.0645255 + 0.111761i 0.896483 0.443077i \(-0.146113\pi\)
−0.831958 + 0.554839i \(0.812780\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4.04626 + 3.80399i 0.156907 + 0.147512i
\(666\) 0 0
\(667\) −5.55232 9.61690i −0.214987 0.372368i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.3196 21.3381i 0.475591 0.823748i
\(672\) 0 0
\(673\) 21.8005 + 37.7597i 0.840349 + 1.45553i 0.889600 + 0.456741i \(0.150983\pi\)
−0.0492503 + 0.998786i \(0.515683\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.14039 + 15.8316i −0.351294 + 0.608459i −0.986476 0.163903i \(-0.947591\pi\)
0.635183 + 0.772362i \(0.280925\pi\)
\(678\) 0 0
\(679\) 27.0900 + 25.4680i 1.03962 + 0.977371i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 22.5380 39.0369i 0.862391 1.49371i −0.00722317 0.999974i \(-0.502299\pi\)
0.869614 0.493732i \(-0.164367\pi\)
\(684\) 0 0
\(685\) 3.11689 0.119090
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −31.9171 55.2820i −1.21594 2.10608i
\(690\) 0 0
\(691\) 20.8977 36.1960i 0.794988 1.37696i −0.127859 0.991792i \(-0.540811\pi\)
0.922847 0.385167i \(-0.125856\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.47528 9.48346i 0.207689 0.359728i
\(696\) 0 0
\(697\) 34.7019 + 60.1054i 1.31443 + 2.27665i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19.3967 −0.732604 −0.366302 0.930496i \(-0.619376\pi\)
−0.366302 + 0.930496i \(0.619376\pi\)
\(702\) 0 0
\(703\) 6.47753 11.2194i 0.244305 0.423148i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 26.8689 8.09565i 1.01051 0.304468i
\(708\) 0 0
\(709\) 8.61542 14.9223i 0.323559 0.560420i −0.657661 0.753314i \(-0.728454\pi\)
0.981220 + 0.192894i \(0.0617873\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −16.9494 29.3572i −0.634759 1.09943i
\(714\) 0 0
\(715\) −4.65675 + 8.06573i −0.174153 + 0.301641i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.08444 + 8.80650i 0.189617 + 0.328427i 0.945123 0.326715i \(-0.105942\pi\)
−0.755505 + 0.655143i \(0.772609\pi\)
\(720\) 0 0
\(721\) −0.403841 + 0.121678i −0.0150398 + 0.00453153i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 7.30172 + 12.6469i 0.271179 + 0.469696i
\(726\) 0 0
\(727\) 0.0914356 + 0.158371i 0.00339116 + 0.00587366i 0.867716 0.497060i \(-0.165587\pi\)
−0.864325 + 0.502934i \(0.832254\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 21.0372 0.778088
\(732\) 0 0
\(733\) 41.9343 1.54888 0.774440 0.632647i \(-0.218032\pi\)
0.774440 + 0.632647i \(0.218032\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.34776 + 7.53054i 0.160152 + 0.277391i
\(738\) 0 0
\(739\) 11.8013 20.4404i 0.434116 0.751911i −0.563107 0.826384i \(-0.690394\pi\)
0.997223 + 0.0744729i \(0.0237274\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −11.1821 + 19.3680i −0.410233 + 0.710544i −0.994915 0.100718i \(-0.967886\pi\)
0.584682 + 0.811263i \(0.301219\pi\)
\(744\) 0 0
\(745\) 6.83791 0.250522
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.3838 + 14.4627i 0.562111 + 0.528454i
\(750\) 0 0
\(751\) −31.0462 −1.13289 −0.566445 0.824099i \(-0.691682\pi\)
−0.566445 + 0.824099i \(0.691682\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.21434 −0.0441943
\(756\) 0 0
\(757\) −44.0639 −1.60153 −0.800764 0.598980i \(-0.795573\pi\)
−0.800764 + 0.598980i \(0.795573\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5.74941 −0.208416 −0.104208 0.994556i \(-0.533231\pi\)
−0.104208 + 0.994556i \(0.533231\pi\)
\(762\) 0 0
\(763\) 8.30431 35.3159i 0.300636 1.27852i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 48.1898 1.74003
\(768\) 0 0
\(769\) −7.48401 + 12.9627i −0.269880 + 0.467446i −0.968831 0.247724i \(-0.920317\pi\)
0.698950 + 0.715170i \(0.253651\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10.0605 17.4253i 0.361850 0.626743i −0.626415 0.779490i \(-0.715479\pi\)
0.988265 + 0.152747i \(0.0488119\pi\)
\(774\) 0 0
\(775\) 22.2897 + 38.6069i 0.800669 + 1.38680i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −54.9031 −1.96711
\(780\) 0 0
\(781\) −13.3338 −0.477120
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.20763 7.28783i −0.150177 0.260114i
\(786\) 0 0
\(787\) −12.0572 20.8837i −0.429794 0.744425i 0.567061 0.823676i \(-0.308081\pi\)
−0.996855 + 0.0792508i \(0.974747\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10.8848 46.2899i 0.387017 1.64588i
\(792\) 0 0
\(793\) 20.8435 + 36.1021i 0.740175 + 1.28202i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.54611 2.67794i 0.0547661 0.0948576i −0.837343 0.546678i \(-0.815892\pi\)
0.892109 + 0.451821i \(0.149225\pi\)
\(798\) 0 0
\(799\) 10.3783 + 17.9758i 0.367158 + 0.635936i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.91567 + 5.05008i −0.102892 + 0.178213i
\(804\) 0 0
\(805\) −4.42165 + 1.33225i −0.155843 + 0.0469557i
\(806\) 0 0