Properties

Label 1900.2.s.a.349.1
Level $1900$
Weight $2$
Character 1900.349
Analytic conductor $15.172$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1900.349
Dual form 1900.2.s.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{3} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{3} +(-1.00000 + 1.73205i) q^{9} -4.00000 q^{11} +(0.866025 + 0.500000i) q^{13} +(-2.59808 + 1.50000i) q^{17} +(4.00000 + 1.73205i) q^{19} +(-4.33013 - 2.50000i) q^{23} -5.00000i q^{27} +(3.50000 - 6.06218i) q^{29} +4.00000 q^{31} +(3.46410 - 2.00000i) q^{33} -10.0000i q^{37} -1.00000 q^{39} +(2.50000 + 4.33013i) q^{41} +(-4.33013 + 2.50000i) q^{43} +(-6.06218 - 3.50000i) q^{47} +7.00000 q^{49} +(1.50000 - 2.59808i) q^{51} +(-9.52628 - 5.50000i) q^{53} +(-4.33013 + 0.500000i) q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(-2.59808 - 1.50000i) q^{67} +5.00000 q^{69} +(-5.50000 - 9.52628i) q^{71} +(12.9904 - 7.50000i) q^{73} +(-6.50000 - 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +7.00000i q^{87} +(1.50000 - 2.59808i) q^{89} +(-3.46410 + 2.00000i) q^{93} +(4.33013 - 2.50000i) q^{97} +(4.00000 - 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{9} - 16 q^{11} + 16 q^{19} + 14 q^{29} + 16 q^{31} - 4 q^{39} + 10 q^{41} + 28 q^{49} + 6 q^{51} + 6 q^{59} - 22 q^{61} + 20 q^{69} - 22 q^{71} - 26 q^{79} - 2 q^{81} + 6 q^{89} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i \(-0.759881\pi\)
0.228714 + 0.973494i \(0.426548\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0 0
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) 0.866025 + 0.500000i 0.240192 + 0.138675i 0.615265 0.788320i \(-0.289049\pi\)
−0.375073 + 0.926995i \(0.622382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.59808 + 1.50000i −0.630126 + 0.363803i −0.780801 0.624780i \(-0.785189\pi\)
0.150675 + 0.988583i \(0.451855\pi\)
\(18\) 0 0
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.33013 2.50000i −0.902894 0.521286i −0.0247559 0.999694i \(-0.507881\pi\)
−0.878138 + 0.478407i \(0.841214\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000i 0.962250i
\(28\) 0 0
\(29\) 3.50000 6.06218i 0.649934 1.12572i −0.333205 0.942855i \(-0.608130\pi\)
0.983138 0.182864i \(-0.0585367\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 3.46410 2.00000i 0.603023 0.348155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000i 1.64399i −0.569495 0.821995i \(-0.692861\pi\)
0.569495 0.821995i \(-0.307139\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) 0 0
\(43\) −4.33013 + 2.50000i −0.660338 + 0.381246i −0.792406 0.609994i \(-0.791172\pi\)
0.132068 + 0.991241i \(0.457838\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.06218 3.50000i −0.884260 0.510527i −0.0121990 0.999926i \(-0.503883\pi\)
−0.872060 + 0.489398i \(0.837217\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 0 0
\(51\) 1.50000 2.59808i 0.210042 0.363803i
\(52\) 0 0
\(53\) −9.52628 5.50000i −1.30854 0.755483i −0.326683 0.945134i \(-0.605931\pi\)
−0.981852 + 0.189651i \(0.939264\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.33013 + 0.500000i −0.573539 + 0.0662266i
\(58\) 0 0
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i \(-0.391996\pi\)
−0.650236 + 0.759733i \(0.725330\pi\)
\(68\) 0 0
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) −5.50000 9.52628i −0.652730 1.13056i −0.982458 0.186485i \(-0.940290\pi\)
0.329728 0.944076i \(-0.393043\pi\)
\(72\) 0 0
\(73\) 12.9904 7.50000i 1.52041 0.877809i 0.520699 0.853740i \(-0.325671\pi\)
0.999710 0.0240681i \(-0.00766187\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.50000 11.2583i −0.731307 1.26666i −0.956325 0.292306i \(-0.905577\pi\)
0.225018 0.974355i \(-0.427756\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 7.00000i 0.750479i
\(88\) 0 0
\(89\) 1.50000 2.59808i 0.159000 0.275396i −0.775509 0.631337i \(-0.782506\pi\)
0.934508 + 0.355942i \(0.115840\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.46410 + 2.00000i −0.359211 + 0.207390i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 4.33013 2.50000i 0.439658 0.253837i −0.263795 0.964579i \(-0.584974\pi\)
0.703452 + 0.710742i \(0.251641\pi\)
\(98\) 0 0
\(99\) 4.00000 6.92820i 0.402015 0.696311i
\(100\) 0 0
\(101\) 0.500000 0.866025i 0.0497519 0.0861727i −0.840077 0.542467i \(-0.817490\pi\)
0.889829 + 0.456294i \(0.150824\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20.0000i 1.93347i −0.255774 0.966736i \(-0.582330\pi\)
0.255774 0.966736i \(-0.417670\pi\)
\(108\) 0 0
\(109\) 1.50000 + 2.59808i 0.143674 + 0.248851i 0.928877 0.370387i \(-0.120775\pi\)
−0.785203 + 0.619238i \(0.787442\pi\)
\(110\) 0 0
\(111\) 5.00000 + 8.66025i 0.474579 + 0.821995i
\(112\) 0 0
\(113\) 14.0000i 1.31701i 0.752577 + 0.658505i \(0.228811\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.73205 + 1.00000i −0.160128 + 0.0924500i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −4.33013 2.50000i −0.390434 0.225417i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2.59808 1.50000i −0.230542 0.133103i 0.380280 0.924871i \(-0.375828\pi\)
−0.610822 + 0.791768i \(0.709161\pi\)
\(128\) 0 0
\(129\) 2.50000 4.33013i 0.220113 0.381246i
\(130\) 0 0
\(131\) −7.50000 12.9904i −0.655278 1.13497i −0.981824 0.189794i \(-0.939218\pi\)
0.326546 0.945181i \(-0.394115\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.33013 2.50000i −0.369948 0.213589i 0.303488 0.952835i \(-0.401849\pi\)
−0.673436 + 0.739246i \(0.735182\pi\)
\(138\) 0 0
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 0 0
\(141\) 7.00000 0.589506
\(142\) 0 0
\(143\) −3.46410 2.00000i −0.289683 0.167248i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.06218 + 3.50000i −0.500000 + 0.288675i
\(148\) 0 0
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −6.06218 + 3.50000i −0.483814 + 0.279330i −0.722005 0.691888i \(-0.756779\pi\)
0.238190 + 0.971219i \(0.423446\pi\)
\(158\) 0 0
\(159\) 11.0000 0.872357
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.9904 7.50000i −1.00523 0.580367i −0.0954356 0.995436i \(-0.530424\pi\)
−0.909790 + 0.415068i \(0.863758\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −7.00000 + 5.19615i −0.535303 + 0.397360i
\(172\) 0 0
\(173\) 12.9904 7.50000i 0.987640 0.570214i 0.0830722 0.996544i \(-0.473527\pi\)
0.904568 + 0.426329i \(0.140193\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.59808 1.50000i −0.195283 0.112747i
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 2.50000 4.33013i 0.185824 0.321856i −0.758030 0.652219i \(-0.773838\pi\)
0.943854 + 0.330364i \(0.107171\pi\)
\(182\) 0 0
\(183\) 11.0000i 0.813143i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 10.3923 6.00000i 0.759961 0.438763i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 0 0
\(193\) 12.9904 7.50000i 0.935068 0.539862i 0.0466572 0.998911i \(-0.485143\pi\)
0.888411 + 0.459049i \(0.151810\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 0 0
\(199\) −3.50000 + 6.06218i −0.248108 + 0.429736i −0.963001 0.269498i \(-0.913142\pi\)
0.714893 + 0.699234i \(0.246476\pi\)
\(200\) 0 0
\(201\) 3.00000 0.211604
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 8.66025 5.00000i 0.601929 0.347524i
\(208\) 0 0
\(209\) −16.0000 6.92820i −1.10674 0.479234i
\(210\) 0 0
\(211\) 4.50000 + 7.79423i 0.309793 + 0.536577i 0.978317 0.207114i \(-0.0664070\pi\)
−0.668524 + 0.743690i \(0.733074\pi\)
\(212\) 0 0
\(213\) 9.52628 + 5.50000i 0.652730 + 0.376854i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −7.50000 + 12.9904i −0.506803 + 0.877809i
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) −21.6506 + 12.5000i −1.44983 + 0.837062i −0.998471 0.0552786i \(-0.982395\pi\)
−0.451363 + 0.892341i \(0.649062\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.0000i 1.32745i 0.747978 + 0.663723i \(0.231025\pi\)
−0.747978 + 0.663723i \(0.768975\pi\)
\(228\) 0 0
\(229\) −2.00000 −0.132164 −0.0660819 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.1865 + 10.5000i −1.19144 + 0.687878i −0.958633 0.284645i \(-0.908124\pi\)
−0.232806 + 0.972523i \(0.574791\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 11.2583 + 6.50000i 0.731307 + 0.422220i
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) 0 0
\(243\) 13.8564 + 8.00000i 0.888889 + 0.513200i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.59808 + 3.50000i 0.165312 + 0.222700i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.5000 26.8468i 0.978351 1.69455i 0.309951 0.950753i \(-0.399687\pi\)
0.668400 0.743802i \(-0.266979\pi\)
\(252\) 0 0
\(253\) 17.3205 + 10.0000i 1.08893 + 0.628695i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.9186 + 11.5000i 1.24249 + 0.717350i 0.969600 0.244696i \(-0.0786881\pi\)
0.272887 + 0.962046i \(0.412021\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 7.00000 + 12.1244i 0.433289 + 0.750479i
\(262\) 0 0
\(263\) −7.79423 + 4.50000i −0.480613 + 0.277482i −0.720672 0.693276i \(-0.756167\pi\)
0.240059 + 0.970758i \(0.422833\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.00000i 0.183597i
\(268\) 0 0
\(269\) 13.5000 + 23.3827i 0.823110 + 1.42567i 0.903356 + 0.428892i \(0.141096\pi\)
−0.0802460 + 0.996775i \(0.525571\pi\)
\(270\) 0 0
\(271\) −15.5000 26.8468i −0.941558 1.63083i −0.762501 0.646988i \(-0.776029\pi\)
−0.179057 0.983839i \(-0.557305\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.0000i 0.600842i −0.953807 0.300421i \(-0.902873\pi\)
0.953807 0.300421i \(-0.0971271\pi\)
\(278\) 0 0
\(279\) −4.00000 + 6.92820i −0.239474 + 0.414781i
\(280\) 0 0
\(281\) −3.50000 + 6.06218i −0.208792 + 0.361639i −0.951334 0.308160i \(-0.900287\pi\)
0.742542 + 0.669800i \(0.233620\pi\)
\(282\) 0 0
\(283\) −7.79423 + 4.50000i −0.463319 + 0.267497i −0.713439 0.700718i \(-0.752863\pi\)
0.250120 + 0.968215i \(0.419530\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 0 0
\(291\) −2.50000 + 4.33013i −0.146553 + 0.253837i
\(292\) 0 0
\(293\) 30.0000i 1.75262i −0.481749 0.876309i \(-0.659998\pi\)
0.481749 0.876309i \(-0.340002\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 20.0000i 1.16052i
\(298\) 0 0
\(299\) −2.50000 4.33013i −0.144579 0.250418i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.00000i 0.0574485i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −23.3827 + 13.5000i −1.33452 + 0.770486i −0.985989 0.166811i \(-0.946653\pi\)
−0.348532 + 0.937297i \(0.613320\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −20.0000 −1.13410 −0.567048 0.823685i \(-0.691915\pi\)
−0.567048 + 0.823685i \(0.691915\pi\)
\(312\) 0 0
\(313\) −9.52628 5.50000i −0.538457 0.310878i 0.205996 0.978553i \(-0.433957\pi\)
−0.744453 + 0.667674i \(0.767290\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.9904 + 7.50000i 0.729612 + 0.421242i 0.818280 0.574819i \(-0.194928\pi\)
−0.0886679 + 0.996061i \(0.528261\pi\)
\(318\) 0 0
\(319\) −14.0000 + 24.2487i −0.783850 + 1.35767i
\(320\) 0 0
\(321\) 10.0000 + 17.3205i 0.558146 + 0.966736i
\(322\) 0 0
\(323\) −12.9904 + 1.50000i −0.722804 + 0.0834622i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.59808 1.50000i −0.143674 0.0829502i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 0 0
\(333\) 17.3205 + 10.0000i 0.949158 + 0.547997i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 4.33013 2.50000i 0.235877 0.136184i −0.377403 0.926049i \(-0.623183\pi\)
0.613280 + 0.789865i \(0.289850\pi\)
\(338\) 0 0
\(339\) −7.00000 12.1244i −0.380188 0.658505i
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.33013 2.50000i 0.232453 0.134207i −0.379250 0.925294i \(-0.623818\pi\)
0.611703 + 0.791087i \(0.290485\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 2.50000 4.33013i 0.133440 0.231125i
\(352\) 0 0
\(353\) 30.0000i 1.59674i 0.602168 + 0.798369i \(0.294304\pi\)
−0.602168 + 0.798369i \(0.705696\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 7.50000 + 12.9904i 0.395835 + 0.685606i 0.993207 0.116358i \(-0.0371219\pi\)
−0.597372 + 0.801964i \(0.703789\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 0 0
\(363\) −4.33013 + 2.50000i −0.227273 + 0.131216i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 21.6506 + 12.5000i 1.13015 + 0.652495i 0.943974 0.330021i \(-0.107056\pi\)
0.186180 + 0.982516i \(0.440389\pi\)
\(368\) 0 0
\(369\) −10.0000 −0.520579
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0000i 0.517780i −0.965907 0.258890i \(-0.916643\pi\)
0.965907 0.258890i \(-0.0833568\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.06218 3.50000i 0.312218 0.180259i
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 3.00000 0.153695
\(382\) 0 0
\(383\) −25.1147 + 14.5000i −1.28330 + 0.740915i −0.977451 0.211164i \(-0.932275\pi\)
−0.305852 + 0.952079i \(0.598941\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.0000i 0.508329i
\(388\) 0 0
\(389\) 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i \(-0.809102\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(390\) 0 0
\(391\) 15.0000 0.758583
\(392\) 0 0
\(393\) 12.9904 + 7.50000i 0.655278 + 0.378325i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 21.6506 12.5000i 1.08661 0.627357i 0.153941 0.988080i \(-0.450803\pi\)
0.932673 + 0.360723i \(0.117470\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.50000 16.4545i −0.474407 0.821698i 0.525163 0.851002i \(-0.324004\pi\)
−0.999571 + 0.0293039i \(0.990671\pi\)
\(402\) 0 0
\(403\) 3.46410 + 2.00000i 0.172559 + 0.0996271i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 40.0000i 1.98273i
\(408\) 0 0
\(409\) −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 0 0
\(411\) 5.00000 0.246632
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 9.00000i 0.440732i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) 0 0
\(423\) 12.1244 7.00000i 0.589506 0.340352i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.00000 0.193122
\(430\) 0 0
\(431\) −10.5000 + 18.1865i −0.505767 + 0.876014i 0.494211 + 0.869342i \(0.335457\pi\)
−0.999978 + 0.00667224i \(0.997876\pi\)
\(432\) 0 0
\(433\) 21.6506 + 12.5000i 1.04046 + 0.600712i 0.919964 0.392002i \(-0.128217\pi\)
0.120499 + 0.992713i \(0.461551\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.9904 17.5000i −0.621414 0.837139i
\(438\) 0 0
\(439\) −6.50000 11.2583i −0.310228 0.537331i 0.668184 0.743996i \(-0.267072\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) −7.00000 + 12.1244i −0.333333 + 0.577350i
\(442\) 0 0
\(443\) −21.6506 12.5000i −1.02865 0.593893i −0.112054 0.993702i \(-0.535743\pi\)
−0.916598 + 0.399809i \(0.869076\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.59808 1.50000i −0.122885 0.0709476i
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) −10.0000 17.3205i −0.470882 0.815591i
\(452\) 0 0
\(453\) 13.8564 8.00000i 0.651031 0.375873i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.0000i 1.02912i 0.857455 + 0.514558i \(0.172044\pi\)
−0.857455 + 0.514558i \(0.827956\pi\)
\(458\) 0 0
\(459\) 7.50000 + 12.9904i 0.350070 + 0.606339i
\(460\) 0 0
\(461\) −5.50000 9.52628i −0.256161 0.443683i 0.709050 0.705159i \(-0.249124\pi\)
−0.965210 + 0.261476i \(0.915791\pi\)
\(462\) 0 0
\(463\) 20.0000i 0.929479i −0.885448 0.464739i \(-0.846148\pi\)
0.885448 0.464739i \(-0.153852\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.0000i 0.925490i 0.886492 + 0.462745i \(0.153135\pi\)
−0.886492 + 0.462745i \(0.846865\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 3.50000 6.06218i 0.161271 0.279330i
\(472\) 0 0
\(473\) 17.3205 10.0000i 0.796398 0.459800i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 19.0526 11.0000i 0.872357 0.503655i
\(478\) 0 0
\(479\) −11.5000 + 19.9186i −0.525448 + 0.910103i 0.474112 + 0.880464i \(0.342769\pi\)
−0.999561 + 0.0296389i \(0.990564\pi\)
\(480\) 0 0
\(481\) 5.00000 8.66025i 0.227980 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.00000i 0.362515i 0.983436 + 0.181257i \(0.0580167\pi\)
−0.983436 + 0.181257i \(0.941983\pi\)
\(488\) 0 0
\(489\) 2.00000 + 3.46410i 0.0904431 + 0.156652i
\(490\) 0 0
\(491\) 0.500000 + 0.866025i 0.0225647 + 0.0390832i 0.877087 0.480331i \(-0.159483\pi\)
−0.854523 + 0.519414i \(0.826150\pi\)
\(492\) 0 0
\(493\) 21.0000i 0.945792i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.50000 4.33013i −0.111915 0.193843i 0.804627 0.593780i \(-0.202365\pi\)
−0.916542 + 0.399937i \(0.869032\pi\)
\(500\) 0 0
\(501\) 15.0000 0.670151
\(502\) 0 0
\(503\) −18.1865 10.5000i −0.810897 0.468172i 0.0363700 0.999338i \(-0.488421\pi\)
−0.847267 + 0.531167i \(0.821754\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) 0 0
\(509\) 7.50000 12.9904i 0.332432 0.575789i −0.650556 0.759458i \(-0.725464\pi\)
0.982988 + 0.183669i \(0.0587976\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 8.66025 20.0000i 0.382360 0.883022i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 24.2487 + 14.0000i 1.06646 + 0.615719i
\(518\) 0 0
\(519\) −7.50000 + 12.9904i −0.329213 + 0.570214i
\(520\) 0 0
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 0 0
\(523\) 16.4545 + 9.50000i 0.719504 + 0.415406i 0.814570 0.580065i \(-0.196973\pi\)
−0.0950659 + 0.995471i \(0.530306\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.3923 + 6.00000i −0.452696 + 0.261364i
\(528\) 0 0
\(529\) 1.00000 + 1.73205i 0.0434783 + 0.0753066i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 5.00000i 0.216574i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −10.3923 + 6.00000i −0.448461 + 0.258919i
\(538\) 0 0
\(539\) −28.0000 −1.20605
\(540\) 0 0
\(541\) 0.500000 0.866025i 0.0214967 0.0372333i −0.855077 0.518501i \(-0.826490\pi\)
0.876574 + 0.481268i \(0.159824\pi\)
\(542\) 0 0
\(543\) 5.00000i 0.214571i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 21.6506 + 12.5000i 0.925714 + 0.534461i 0.885454 0.464728i \(-0.153848\pi\)
0.0402607 + 0.999189i \(0.487181\pi\)
\(548\) 0 0
\(549\) −11.0000 19.0526i −0.469469 0.813143i
\(550\) 0 0
\(551\) 24.5000 18.1865i 1.04374 0.774772i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.33013 2.50000i −0.183473 0.105928i 0.405450 0.914117i \(-0.367115\pi\)
−0.588924 + 0.808189i \(0.700448\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) −6.00000 + 10.3923i −0.253320 + 0.438763i
\(562\) 0 0
\(563\) 36.0000i 1.51722i 0.651546 + 0.758610i \(0.274121\pi\)
−0.651546 + 0.758610i \(0.725879\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.0000 −0.922288 −0.461144 0.887325i \(-0.652561\pi\)
−0.461144 + 0.887325i \(0.652561\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −13.8564 + 8.00000i −0.578860 + 0.334205i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 10.0000i 0.416305i 0.978096 + 0.208153i \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) 0 0
\(579\) −7.50000 + 12.9904i −0.311689 + 0.539862i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 38.1051 + 22.0000i 1.57815 + 0.911147i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.9904 + 7.50000i −0.536170 + 0.309558i −0.743525 0.668708i \(-0.766848\pi\)
0.207355 + 0.978266i \(0.433514\pi\)
\(588\) 0 0
\(589\) 16.0000 + 6.92820i 0.659269 + 0.285472i
\(590\) 0 0
\(591\) 1.00000 + 1.73205i 0.0411345 + 0.0712470i
\(592\) 0 0
\(593\) 4.33013 + 2.50000i 0.177817 + 0.102663i 0.586267 0.810118i \(-0.300597\pi\)
−0.408450 + 0.912781i \(0.633930\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.00000i 0.286491i
\(598\) 0 0
\(599\) 22.5000 38.9711i 0.919325 1.59232i 0.118882 0.992908i \(-0.462069\pi\)
0.800443 0.599409i \(-0.204598\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 5.19615 3.00000i 0.211604 0.122169i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 32.0000i 1.29884i −0.760430 0.649420i \(-0.775012\pi\)
0.760430 0.649420i \(-0.224988\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.50000 6.06218i −0.141595 0.245249i
\(612\) 0 0
\(613\) −25.1147 + 14.5000i −1.01437 + 0.585649i −0.912470 0.409145i \(-0.865827\pi\)
−0.101905 + 0.994794i \(0.532494\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −38.9711 22.5000i −1.56892 0.905816i −0.996295 0.0859976i \(-0.972592\pi\)
−0.572624 0.819818i \(-0.694074\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) −12.5000 + 21.6506i −0.501608 + 0.868810i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 17.3205 2.00000i 0.691714 0.0798723i
\(628\) 0 0
\(629\) 15.0000 + 25.9808i 0.598089 + 1.03592i
\(630\) 0 0
\(631\) −20.5000 + 35.5070i −0.816092 + 1.41351i 0.0924489 + 0.995717i \(0.470531\pi\)
−0.908541 + 0.417796i \(0.862803\pi\)
\(632\) 0 0
\(633\) −7.79423 4.50000i −0.309793 0.178859i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.06218 + 3.50000i 0.240192 + 0.138675i
\(638\) 0 0
\(639\) 22.0000 0.870307
\(640\) 0 0
\(641\) −19.5000 33.7750i −0.770204 1.33403i −0.937451 0.348117i \(-0.886821\pi\)
0.167247 0.985915i \(-0.446512\pi\)
\(642\) 0 0
\(643\) 16.4545 9.50000i 0.648901 0.374643i −0.139134 0.990274i \(-0.544432\pi\)
0.788035 + 0.615630i \(0.211098\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 32.0000i 1.25805i −0.777385 0.629025i \(-0.783454\pi\)
0.777385 0.629025i \(-0.216546\pi\)
\(648\) 0 0
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 30.0000i 1.17399i −0.809590 0.586995i \(-0.800311\pi\)
0.809590 0.586995i \(-0.199689\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 30.0000i 1.17041i
\(658\) 0 0
\(659\) 2.50000 4.33013i 0.0973862 0.168678i −0.813216 0.581962i \(-0.802285\pi\)
0.910602 + 0.413284i \(0.135618\pi\)
\(660\) 0 0
\(661\) −15.5000 + 26.8468i −0.602880 + 1.04422i 0.389503 + 0.921025i \(0.372647\pi\)
−0.992383 + 0.123194i \(0.960686\pi\)
\(662\) 0 0
\(663\) 2.59808 1.50000i 0.100901 0.0582552i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −30.3109 + 17.5000i −1.17364 + 0.677603i
\(668\) 0 0
\(669\) 12.5000 21.6506i 0.483278 0.837062i
\(670\) 0 0
\(671\) 22.0000 38.1051i 0.849301 1.47103i
\(672\) 0 0
\(673\) 10.0000i 0.385472i −0.981251 0.192736i \(-0.938264\pi\)
0.981251 0.192736i \(-0.0617360\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.0000i 0.384331i −0.981363 0.192166i \(-0.938449\pi\)
0.981363 0.192166i \(-0.0615511\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −10.0000 17.3205i −0.383201 0.663723i
\(682\) 0 0
\(683\) 16.0000i 0.612223i 0.951996 + 0.306111i \(0.0990280\pi\)
−0.951996 + 0.306111i \(0.900972\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.73205 1.00000i 0.0660819 0.0381524i
\(688\) 0 0
\(689\) −5.50000 9.52628i −0.209533 0.362922i
\(690\) 0 0
\(691\) 36.0000 1.36950 0.684752 0.728776i \(-0.259910\pi\)
0.684752 + 0.728776i \(0.259910\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −12.9904 7.50000i −0.492046 0.284083i
\(698\) 0 0
\(699\) 10.5000 18.1865i 0.397146 0.687878i
\(700\) 0 0
\(701\) −17.5000 30.3109i −0.660966 1.14483i −0.980362 0.197205i \(-0.936813\pi\)
0.319396 0.947621i \(-0.396520\pi\)
\(702\) 0 0
\(703\) 17.3205 40.0000i 0.653255 1.50863i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.50000 2.59808i 0.0563337 0.0975728i −0.836483 0.547992i \(-0.815392\pi\)
0.892817 + 0.450420i \(0.148726\pi\)
\(710\) 0 0
\(711\) 26.0000 0.975076
\(712\) 0 0
\(713\) −17.3205 10.0000i −0.648658 0.374503i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 10.3923 6.00000i 0.388108 0.224074i
\(718\) 0 0
\(719\) 3.50000 + 6.06218i 0.130528 + 0.226081i 0.923880 0.382682i \(-0.124999\pi\)
−0.793352 + 0.608763i \(0.791666\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 19.0000i 0.706618i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −6.06218 + 3.50000i −0.224834 + 0.129808i −0.608186 0.793794i \(-0.708103\pi\)
0.383353 + 0.923602i \(0.374769\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 7.50000 12.9904i 0.277398 0.480467i
\(732\) 0 0
\(733\) 30.0000i 1.10808i −0.832492 0.554038i \(-0.813086\pi\)
0.832492 0.554038i \(-0.186914\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.3923 + 6.00000i 0.382805 + 0.221013i
\(738\) 0 0
\(739\) −6.50000 11.2583i −0.239106 0.414144i 0.721352 0.692569i \(-0.243521\pi\)
−0.960458 + 0.278425i \(0.910188\pi\)
\(740\) 0 0
\(741\) −4.00000 1.73205i −0.146944 0.0636285i
\(742\) 0 0
\(743\) −21.6506 + 12.5000i −0.794285 + 0.458581i −0.841469 0.540306i \(-0.818309\pi\)
0.0471840 + 0.998886i \(0.484975\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −14.5000 + 25.1147i −0.529113 + 0.916450i 0.470311 + 0.882501i \(0.344142\pi\)
−0.999424 + 0.0339490i \(0.989192\pi\)
\(752\) 0 0
\(753\) 31.0000i 1.12970i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 14.7224 8.50000i 0.535096 0.308938i −0.207993 0.978130i \(-0.566693\pi\)
0.743089 + 0.669193i \(0.233360\pi\)
\(758\) 0 0
\(759\) −20.0000 −0.725954
\(760\) 0 0
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.00000i 0.108324i
\(768\) 0 0
\(769\) 3.50000 6.06218i 0.126213 0.218608i −0.795993 0.605305i \(-0.793051\pi\)
0.922207 + 0.386698i \(0.126384\pi\)
\(770\) 0 0
\(771\) −23.0000 −0.828325
\(772\) 0 0
\(773\) 18.1865 + 10.5000i 0.654124 + 0.377659i 0.790034 0.613062i \(-0.210063\pi\)
−0.135910 + 0.990721i \(0.543396\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.50000 + 21.6506i 0.0895718 + 0.775715i
\(780\) 0 0
\(781\) 22.0000 + 38.1051i 0.787222 + 1.36351i
\(782\) 0 0
\(783\) −30.3109 17.5000i −1.08322 0.625399i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 52.0000i 1.85360i −0.375555 0.926800i \(-0.622548\pi\)
0.375555 0.926800i \(-0.377452\pi\)
\(788\) 0 0
\(789\) 4.50000 7.79423i 0.160204 0.277482i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −9.52628 + 5.50000i −0.338288 + 0.195311i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.0000i 0.637593i −0.947823 0.318796i \(-0.896721\pi\)
0.947823 0.318796i \(-0.103279\pi\)
\(798\) 0 0
\(799\) 21.0000 0.742927
\(800\) 0