Properties

Label 3024.2.q.b.2305.1
Level 3024
Weight 2
Character 3024.2305
Analytic conductor 24.147
Analytic rank 1
Dimension 2
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: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.b.2881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-2.50000 + 4.33013i) q^{11} +(2.50000 - 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +(-1.50000 - 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-0.500000 - 0.866025i) q^{29} +(-0.500000 + 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-2.50000 + 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(1.00000 + 6.92820i) q^{49} +(-4.50000 - 7.79423i) q^{53} +5.00000 q^{55} -14.0000 q^{61} -5.00000 q^{65} -4.00000 q^{67} -12.0000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(12.5000 - 4.33013i) q^{77} -8.00000 q^{79} +(4.50000 + 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-6.50000 + 11.2583i) q^{89} +(-12.5000 + 4.33013i) q^{91} -1.00000 q^{95} +(4.50000 + 7.79423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{5} - 4q^{7} + O(q^{10}) \) \( 2q - q^{5} - 4q^{7} - 5q^{11} + 5q^{13} + 3q^{17} + q^{19} - 3q^{23} + 4q^{25} - q^{29} - q^{35} - 3q^{37} - 5q^{41} - q^{43} + 2q^{49} - 9q^{53} + 10q^{55} - 28q^{61} - 10q^{65} - 8q^{67} - 24q^{71} - 3q^{73} + 25q^{77} - 16q^{79} + 9q^{83} + 3q^{85} - 13q^{89} - 25q^{91} - 2q^{95} + 9q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.500000 + 2.59808i −0.0845154 + 0.439155i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) 0 0
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −5.00000 −0.620174
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i \(-0.222841\pi\)
−0.940356 + 0.340193i \(0.889507\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 12.5000 4.33013i 1.42451 0.493464i
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 0 0
\(85\) 1.50000 2.59808i 0.162698 0.281801i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.50000 + 11.2583i −0.688999 + 1.19338i 0.283164 + 0.959072i \(0.408616\pi\)
−0.972162 + 0.234309i \(0.924717\pi\)
\(90\) 0 0
\(91\) −12.5000 + 4.33013i −1.31036 + 0.453921i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i \(-0.0156243\pi\)
−0.541890 + 0.840450i \(0.682291\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.50000 + 14.7224i −0.845782 + 1.46494i 0.0391591 + 0.999233i \(0.487532\pi\)
−0.884941 + 0.465704i \(0.845801\pi\)
\(102\) 0 0
\(103\) −0.500000 0.866025i −0.0492665 0.0853320i 0.840341 0.542059i \(-0.182355\pi\)
−0.889607 + 0.456727i \(0.849022\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.50000 + 14.7224i −0.821726 + 1.42327i 0.0826699 + 0.996577i \(0.473655\pi\)
−0.904396 + 0.426694i \(0.859678\pi\)
\(108\) 0 0
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.500000 + 0.866025i −0.0470360 + 0.0814688i −0.888585 0.458712i \(-0.848311\pi\)
0.841549 + 0.540181i \(0.181644\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.50000 7.79423i 0.137505 0.714496i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 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
\(141\) 0 0
\(142\) 0 0
\(143\) 12.5000 + 21.6506i 1.04530 + 1.81052i
\(144\) 0 0
\(145\) −0.500000 + 0.866025i −0.0415227 + 0.0719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 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
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.50000 + 7.79423i −0.118217 + 0.614271i
\(162\) 0 0
\(163\) −5.50000 + 9.52628i −0.430793 + 0.746156i −0.996942 0.0781474i \(-0.975100\pi\)
0.566149 + 0.824303i \(0.308433\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.50000 16.4545i 0.735132 1.27329i −0.219533 0.975605i \(-0.570453\pi\)
0.954665 0.297681i \(-0.0962132\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) −10.0000 + 3.46410i −0.755929 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) −15.0000 −1.09691
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 1.50000 + 2.59808i 0.106332 + 0.184173i 0.914282 0.405079i \(-0.132756\pi\)
−0.807950 + 0.589252i \(0.799423\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.500000 + 2.59808i −0.0350931 + 0.182349i
\(204\) 0 0
\(205\) 5.00000 0.349215
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.50000 + 4.33013i 0.172929 + 0.299521i
\(210\) 0 0
\(211\) 6.50000 11.2583i 0.447478 0.775055i −0.550743 0.834675i \(-0.685655\pi\)
0.998221 + 0.0596196i \(0.0189888\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.500000 + 0.866025i −0.0340997 + 0.0590624i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 15.0000 1.00901
\(222\) 0 0
\(223\) 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i \(0.0528144\pi\)
−0.350100 + 0.936713i \(0.613852\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.50000 12.9904i 0.485135 0.840278i −0.514719 0.857359i \(-0.672104\pi\)
0.999854 + 0.0170808i \(0.00543724\pi\)
\(240\) 0 0
\(241\) −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i \(-0.948609\pi\)
0.632709 + 0.774389i \(0.281943\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.50000 4.33013i 0.351382 0.276642i
\(246\) 0 0
\(247\) −2.50000 4.33013i −0.159071 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.5000 25.1147i −0.904485 1.56661i −0.821607 0.570055i \(-0.806922\pi\)
−0.0828783 0.996560i \(-0.526411\pi\)
\(258\) 0 0
\(259\) 7.50000 2.59808i 0.466027 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.50000 + 4.33013i −0.154157 + 0.267007i −0.932752 0.360520i \(-0.882599\pi\)
0.778595 + 0.627527i \(0.215933\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.0000 + 17.3205i 0.603023 + 1.04447i
\(276\) 0 0
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −14.5000 25.1147i −0.864997 1.49822i −0.867050 0.498222i \(-0.833987\pi\)
0.00205220 0.999998i \(-0.499347\pi\)
\(282\) 0 0
\(283\) −28.0000 −1.66443 −0.832214 0.554455i \(-0.812927\pi\)
−0.832214 + 0.554455i \(0.812927\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 12.5000 4.33013i 0.737852 0.255599i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.50000 + 4.33013i −0.146052 + 0.252969i −0.929765 0.368154i \(-0.879990\pi\)
0.783713 + 0.621123i \(0.213323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −15.0000 −0.867472
\(300\) 0 0
\(301\) −0.500000 + 2.59808i −0.0288195 + 0.149751i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.00000 + 12.1244i 0.400819 + 0.694239i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 5.00000 0.279946
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) 0 0
\(337\) 14.5000 25.1147i 0.789865 1.36809i −0.136184 0.990684i \(-0.543484\pi\)
0.926049 0.377403i \(-0.123183\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 0 0
\(349\) −9.50000 16.4545i −0.508523 0.880788i −0.999951 0.00987003i \(-0.996858\pi\)
0.491428 0.870918i \(-0.336475\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.50000 9.52628i 0.292735 0.507033i −0.681720 0.731613i \(-0.738768\pi\)
0.974456 + 0.224580i \(0.0721011\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 5.50000 9.52628i 0.290279 0.502778i −0.683597 0.729860i \(-0.739585\pi\)
0.973876 + 0.227082i \(0.0729186\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.50000 + 2.59808i −0.0785136 + 0.135990i
\(366\) 0 0
\(367\) −1.50000 + 2.59808i −0.0782994 + 0.135618i −0.902516 0.430656i \(-0.858282\pi\)
0.824217 + 0.566274i \(0.191616\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.50000 + 23.3827i −0.233628 + 1.21397i
\(372\) 0 0
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.00000 −0.257513
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −13.5000 23.3827i −0.689818 1.19480i −0.971897 0.235408i \(-0.924357\pi\)
0.282079 0.959391i \(-0.408976\pi\)
\(384\) 0 0
\(385\) −10.0000 8.66025i −0.509647 0.441367i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.50000 + 7.79423i −0.228159 + 0.395183i −0.957263 0.289220i \(-0.906604\pi\)
0.729103 + 0.684403i \(0.239937\pi\)
\(390\) 0 0
\(391\) 4.50000 7.79423i 0.227575 0.394171i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 0 0
\(397\) −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i \(-0.956176\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.50000 12.9904i −0.371761 0.643909i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 4.50000 7.79423i 0.220896 0.382604i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 0 0
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) 28.0000 + 24.2487i 1.35501 + 1.17348i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 4.50000 + 7.79423i 0.216757 + 0.375435i 0.953815 0.300395i \(-0.0971186\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.00000 −0.143509
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 0 0
\(445\) 13.0000 0.616259
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −12.5000 21.6506i −0.588602 1.01949i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.0000 + 8.66025i 0.468807 + 0.405999i
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.50000 + 16.4545i 0.442459 + 0.766362i 0.997871 0.0652135i \(-0.0207728\pi\)
−0.555412 + 0.831575i \(0.687440\pi\)
\(462\) 0 0
\(463\) 6.50000 11.2583i 0.302081 0.523219i −0.674526 0.738251i \(-0.735652\pi\)
0.976607 + 0.215032i \(0.0689855\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.5000 23.3827i 0.624705 1.08202i −0.363892 0.931441i \(-0.618552\pi\)
0.988598 0.150581i \(-0.0481143\pi\)
\(468\) 0 0
\(469\) 8.00000 + 6.92820i 0.369406 + 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.00000 0.229900
\(474\) 0 0
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.5000 + 21.6506i −0.571140 + 0.989243i 0.425310 + 0.905048i \(0.360165\pi\)
−0.996449 + 0.0841949i \(0.973168\pi\)
\(480\) 0 0
\(481\) 7.50000 + 12.9904i 0.341971 + 0.592310i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.50000 7.79423i 0.204334 0.353918i
\(486\) 0 0
\(487\) 9.50000 + 16.4545i 0.430486 + 0.745624i 0.996915 0.0784867i \(-0.0250088\pi\)
−0.566429 + 0.824110i \(0.691675\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.50000 + 11.2583i −0.293341 + 0.508081i −0.974598 0.223963i \(-0.928100\pi\)
0.681257 + 0.732045i \(0.261434\pi\)
\(492\) 0 0
\(493\) 1.50000 2.59808i 0.0675566 0.117011i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 + 20.7846i 1.07655 + 0.932317i
\(498\) 0 0
\(499\) 15.5000 + 26.8468i 0.693875 + 1.20183i 0.970558 + 0.240866i \(0.0774314\pi\)
−0.276683 + 0.960961i \(0.589235\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 17.0000 0.756490
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i \(-0.944480\pi\)
0.342126 0.939654i \(-0.388853\pi\)
\(510\) 0 0
\(511\) −1.50000 + 7.79423i −0.0663561 + 0.344796i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.500000 + 0.866025i −0.0220326 + 0.0381616i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50000 + 2.59808i 0.0657162 + 0.113824i 0.897011 0.442007i \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) 0 0
\(523\) 0.500000 0.866025i 0.0218635 0.0378686i −0.854887 0.518815i \(-0.826373\pi\)
0.876750 + 0.480946i \(0.159707\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12.5000 + 21.6506i 0.541435 + 0.937793i
\(534\) 0 0
\(535\) 17.0000 0.734974
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −32.5000 12.9904i −1.39987 0.559535i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.50000 7.79423i 0.192759 0.333868i
\(546\) 0 0
\(547\) −14.5000 25.1147i −0.619975 1.07383i −0.989490 0.144604i \(-0.953809\pi\)
0.369514 0.929225i \(-0.379524\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.00000 −0.0426014
\(552\) 0 0
\(553\) 16.0000 + 13.8564i 0.680389 + 0.589234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i \(-0.879909\pi\)
0.145802 0.989314i \(-0.453424\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) 1.00000 0.0420703
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 0 0
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.50000 23.3827i 0.186691 0.970077i
\(582\) 0 0
\(583\) 45.0000 1.86371
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.5000 + 32.0429i 0.763577 + 1.32255i 0.940996 + 0.338418i \(0.109892\pi\)
−0.177419 + 0.984135i \(0.556775\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.50000 12.9904i 0.307988 0.533451i −0.669934 0.742421i \(-0.733678\pi\)
0.977922 + 0.208970i \(0.0670110\pi\)
\(594\) 0 0
\(595\) −7.50000 + 2.59808i −0.307470 + 0.106511i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −9.50000 16.4545i −0.383701 0.664590i 0.607887 0.794024i \(-0.292017\pi\)
−0.991588 + 0.129433i \(0.958684\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 0 0
\(619\) 12.5000 21.6506i 0.502417 0.870212i −0.497579 0.867419i \(-0.665777\pi\)
0.999996 0.00279365i \(-0.000889247\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 32.5000 11.2583i 1.30209 0.451055i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.00000 −0.358854
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.00000 10.3923i −0.238103 0.412406i
\(636\) 0 0
\(637\) 32.5000 + 12.9904i 1.28770 + 0.514698i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) 0 0
\(643\) −9.50000 + 16.4545i −0.374643 + 0.648901i −0.990274 0.139134i \(-0.955568\pi\)
0.615630 + 0.788035i \(0.288902\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.5000 26.8468i −0.609368 1.05546i −0.991345 0.131284i \(-0.958090\pi\)
0.381977 0.924172i \(-0.375243\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i \(-0.147971\pi\)
−0.835182 + 0.549973i \(0.814638\pi\)
\(654\) 0 0
\(655\) 0.500000 0.866025i 0.0195366 0.0338384i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −13.5000 23.3827i −0.525885 0.910860i −0.999545 0.0301523i \(-0.990401\pi\)
0.473660 0.880708i \(-0.342933\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.00000 + 1.73205i 0.0775567 + 0.0671660i
\(666\) 0 0
\(667\) −1.50000 + 2.59808i −0.0580802 + 0.100598i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 35.0000 60.6218i 1.35116 2.34028i
\(672\) 0 0
\(673\) 14.5000 + 25.1147i 0.558934 + 0.968102i 0.997586 + 0.0694449i \(0.0221228\pi\)
−0.438652 + 0.898657i \(0.644544\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) 4.50000 23.3827i 0.172694 0.897345i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.50000 + 7.79423i 0.172188 + 0.298238i 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −45.0000 −1.71436
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.00000 −0.341389
\(696\) 0 0
\(697\) −15.0000 −0.568166
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 1.50000 + 2.59808i 0.0565736 + 0.0979883i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 42.5000 14.7224i 1.59838 0.553694i
\(708\) 0 0
\(709\) −6.00000 −0.225335 −0.112667 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 12.5000 21.6506i 0.467473 0.809688i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.5000 23.3827i 0.503465 0.872027i −0.496527 0.868021i \(-0.665392\pi\)
0.999992 0.00400572i \(-0.00127506\pi\)
\(720\) 0 0
\(721\) −0.500000 + 2.59808i −0.0186210 + 0.0967574i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.00000 −0.148556
\(726\) 0 0
\(727\) 23.5000 + 40.7032i 0.871567 + 1.50960i 0.860376 + 0.509661i \(0.170229\pi\)
0.0111912 + 0.999937i \(0.496438\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) −13.5000 23.3827i −0.498634 0.863659i 0.501365 0.865236i \(-0.332831\pi\)
−0.999999 + 0.00157675i \(0.999498\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.0000 17.3205i 0.368355 0.638009i
\(738\) 0 0
\(739\) −4.50000 7.79423i −0.165535 0.286715i 0.771310 0.636460i \(-0.219602\pi\)
−0.936845 + 0.349744i \(0.886268\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7.50000 12.9904i 0.275148 0.476571i −0.695024 0.718986i \(-0.744606\pi\)
0.970173 + 0.242415i \(0.0779397\pi\)
\(744\) 0 0
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 42.5000 14.7224i 1.55292 0.537946i
\(750\) 0 0
\(751\) 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i \(0.0246899\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.00000 −0.181969
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) 0 0
\(763\) 4.50000 23.3827i 0.162911 0.846510i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 15.5000 + 26.8468i 0.557496 + 0.965612i 0.997705 + 0.0677162i \(0.0215712\pi\)
−0.440208 + 0.897896i \(0.645095\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.50000 + 4.33013i 0.0895718 + 0.155143i
\(780\) 0 0
\(781\) 30.0000 51.9615i 1.07348 1.85933i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.00000 + 12.1244i 0.249841 + 0.432737i
\(786\) 0 0
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.50000 0.866025i 0.0888898 0.0307923i
\(792\) 0 0
\(793\) −35.0000 + 60.6218i −1.24289 + 2.15274i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.5000 19.9186i 0.407351 0.705552i −0.587241 0.809412i \(-0.699786\pi\)
0.994592 + 0.103860i \(0.0331193\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 15.0000 0.529339
\(804\) 0 0
\(805\) 7.50000 2.59808i 0.264340 0.0915702i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −4.50000 7.79423i −0.158212 0.274030i 0.776012 0.630718i \(-0.217239\pi\)
−0.934224 + 0.356687i \(0.883906\pi\)
\(810\) 0 0
\(811\) 28.0000 0.983213 0.491606 0.870817i \(-0.336410\pi\)
0.491606 + 0.870817i \(0.336410\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 11.0000 0.385313
\(816\) 0 0
\(817\) −1.00000 −0.0349856