Properties

Label 2268.2.i.b.2053.1
Level $2268$
Weight $2$
Character 2268.2053
Analytic conductor $18.110$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2053.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2053
Dual form 2268.2.i.b.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{5} +(2.00000 - 1.73205i) q^{7} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 - 1.73205i) q^{11} +(1.50000 - 2.59808i) q^{13} +(4.00000 + 6.92820i) q^{17} +(0.500000 - 0.866025i) q^{19} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{29} +3.00000 q^{31} +(-5.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.00000 - 5.19615i) q^{41} +(-5.50000 - 9.52628i) q^{43} -6.00000 q^{47} +(1.00000 - 6.92820i) q^{49} +(-6.00000 - 10.3923i) q^{53} -4.00000 q^{55} -4.00000 q^{59} -6.00000 q^{61} -6.00000 q^{65} +13.0000 q^{67} +10.0000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-1.00000 - 5.19615i) q^{77} -3.00000 q^{79} +(1.00000 + 1.73205i) q^{83} +(8.00000 - 13.8564i) q^{85} +(-1.50000 - 7.79423i) q^{91} -2.00000 q^{95} +(-5.00000 - 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{5} + 4q^{7} + O(q^{10}) \) \( 2q - 2q^{5} + 4q^{7} + 2q^{11} + 3q^{13} + 8q^{17} + q^{19} + 8q^{23} + q^{25} + 4q^{29} + 6q^{31} - 10q^{35} + q^{37} + 6q^{41} - 11q^{43} - 12q^{47} + 2q^{49} - 12q^{53} - 8q^{55} - 8q^{59} - 12q^{61} - 12q^{65} + 26q^{67} + 20q^{71} + 11q^{73} - 2q^{77} - 6q^{79} + 2q^{83} + 16q^{85} - 3q^{91} - 4q^{95} - 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0 0
\(13\) 1.50000 2.59808i 0.416025 0.720577i −0.579510 0.814965i \(-0.696756\pi\)
0.995535 + 0.0943882i \(0.0300895\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.00000 + 6.92820i 0.970143 + 1.68034i 0.695113 + 0.718900i \(0.255354\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 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
\(23\) 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i \(0.147321\pi\)
−0.0607377 + 0.998154i \(0.519345\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 + 3.46410i 0.371391 + 0.643268i 0.989780 0.142605i \(-0.0455477\pi\)
−0.618389 + 0.785872i \(0.712214\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −5.00000 1.73205i −0.845154 0.292770i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 0 0
\(43\) −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i \(-0.849958\pi\)
0.0522047 0.998636i \(-0.483375\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.00000 10.3923i −0.824163 1.42749i −0.902557 0.430570i \(-0.858312\pi\)
0.0783936 0.996922i \(-0.475021\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) 13.0000 1.58820 0.794101 0.607785i \(-0.207942\pi\)
0.794101 + 0.607785i \(0.207942\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.00000 5.19615i −0.113961 0.592157i
\(78\) 0 0
\(79\) −3.00000 −0.337526 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) 8.00000 13.8564i 0.867722 1.50294i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) −1.50000 7.79423i −0.157243 0.817057i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.00000 −0.205196
\(96\) 0 0
\(97\) −5.00000 8.66025i −0.507673 0.879316i −0.999961 0.00888289i \(-0.997172\pi\)
0.492287 0.870433i \(-0.336161\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) 0 0
\(103\) −5.50000 9.52628i −0.541931 0.938652i −0.998793 0.0491146i \(-0.984360\pi\)
0.456862 0.889538i \(-0.348973\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0 0
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i \(0.395477\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(114\) 0 0
\(115\) 8.00000 13.8564i 0.746004 1.29212i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 20.0000 + 6.92820i 1.83340 + 0.635107i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 3.00000 0.266207 0.133103 0.991102i \(-0.457506\pi\)
0.133103 + 0.991102i \(0.457506\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 1.73205i −0.0873704 0.151330i 0.819028 0.573753i \(-0.194513\pi\)
−0.906399 + 0.422423i \(0.861180\pi\)
\(132\) 0 0
\(133\) −0.500000 2.59808i −0.0433555 0.225282i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 0 0
\(139\) 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i \(-0.765320\pi\)
0.952355 + 0.304991i \(0.0986536\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i \(-0.330232\pi\)
−0.999953 + 0.00974235i \(0.996899\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.00000 5.19615i −0.240966 0.417365i
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 20.0000 + 6.92820i 1.57622 + 0.546019i
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 + 1.73205i −0.0773823 + 0.134030i −0.902120 0.431486i \(-0.857990\pi\)
0.824737 + 0.565516i \(0.191323\pi\)
\(168\) 0 0
\(169\) 2.00000 + 3.46410i 0.153846 + 0.266469i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −16.0000 −1.21646 −0.608229 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 0 0
\(175\) −0.500000 2.59808i −0.0377964 0.196396i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) −15.0000 −1.11494 −0.557471 0.830197i \(-0.688228\pi\)
−0.557471 + 0.830197i \(0.688228\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) 0 0
\(187\) 16.0000 1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 −0.434145 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(192\) 0 0
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.00000 −0.569976 −0.284988 0.958531i \(-0.591990\pi\)
−0.284988 + 0.958531i \(0.591990\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.0000 + 3.46410i 0.701862 + 0.243132i
\(204\) 0 0
\(205\) −12.0000 −0.838116
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.00000 1.73205i −0.0691714 0.119808i
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.0000 + 19.0526i −0.750194 + 1.29937i
\(216\) 0 0
\(217\) 6.00000 5.19615i 0.407307 0.352738i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i \(0.370447\pi\)
−0.993210 + 0.116331i \(0.962887\pi\)
\(228\) 0 0
\(229\) −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i \(-0.177186\pi\)
−0.882073 + 0.471113i \(0.843853\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.00000 12.1244i 0.458585 0.794293i −0.540301 0.841472i \(-0.681690\pi\)
0.998886 + 0.0471787i \(0.0150230\pi\)
\(234\) 0 0
\(235\) 6.00000 + 10.3923i 0.391397 + 0.677919i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.00000 15.5885i 0.582162 1.00833i −0.413061 0.910703i \(-0.635540\pi\)
0.995223 0.0976302i \(-0.0311262\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −13.0000 + 5.19615i −0.830540 + 0.331970i
\(246\) 0 0
\(247\) −1.50000 2.59808i −0.0954427 0.165312i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 0 0
\(259\) −0.500000 2.59808i −0.0310685 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 0 0
\(265\) −12.0000 + 20.7846i −0.737154 + 1.27679i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.00000 1.73205i −0.0609711 0.105605i 0.833929 0.551872i \(-0.186086\pi\)
−0.894900 + 0.446267i \(0.852753\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 + 17.3205i 0.596550 + 1.03325i 0.993326 + 0.115339i \(0.0367956\pi\)
−0.396776 + 0.917915i \(0.629871\pi\)
\(282\) 0 0
\(283\) 19.0000 1.12943 0.564716 0.825285i \(-0.308986\pi\)
0.564716 + 0.825285i \(0.308986\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.00000 15.5885i −0.177084 0.920158i
\(288\) 0 0
\(289\) −23.5000 + 40.7032i −1.38235 + 2.39431i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −12.0000 + 20.7846i −0.701047 + 1.21425i 0.267052 + 0.963682i \(0.413951\pi\)
−0.968099 + 0.250568i \(0.919383\pi\)
\(294\) 0 0
\(295\) 4.00000 + 6.92820i 0.232889 + 0.403376i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 24.0000 1.38796
\(300\) 0 0
\(301\) −27.5000 9.52628i −1.58507 0.549086i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.00000 + 10.3923i 0.343559 + 0.595062i
\(306\) 0 0
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.00000 0.113410 0.0567048 0.998391i \(-0.481941\pi\)
0.0567048 + 0.998391i \(0.481941\pi\)
\(312\) 0 0
\(313\) −17.0000 −0.960897 −0.480448 0.877023i \(-0.659526\pi\)
−0.480448 + 0.877023i \(0.659526\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.0000 1.34797 0.673987 0.738743i \(-0.264580\pi\)
0.673987 + 0.738743i \(0.264580\pi\)
\(318\) 0 0
\(319\) 8.00000 0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) −1.50000 2.59808i −0.0832050 0.144115i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.0000 + 10.3923i −0.661581 + 0.572946i
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.0000 22.5167i −0.710266 1.23022i
\(336\) 0 0
\(337\) −10.5000 + 18.1865i −0.571971 + 0.990684i 0.424392 + 0.905479i \(0.360488\pi\)
−0.996363 + 0.0852050i \(0.972845\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −24.0000 −1.28839 −0.644194 0.764862i \(-0.722807\pi\)
−0.644194 + 0.764862i \(0.722807\pi\)
\(348\) 0 0
\(349\) 7.00000 + 12.1244i 0.374701 + 0.649002i 0.990282 0.139072i \(-0.0444119\pi\)
−0.615581 + 0.788074i \(0.711079\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 0 0
\(355\) −10.0000 17.3205i −0.530745 0.919277i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.0000 19.0526i 0.575766 0.997257i
\(366\) 0 0
\(367\) −2.50000 + 4.33013i −0.130499 + 0.226031i −0.923869 0.382709i \(-0.874991\pi\)
0.793370 + 0.608740i \(0.208325\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −30.0000 10.3923i −1.55752 0.539542i
\(372\) 0 0
\(373\) 2.50000 + 4.33013i 0.129445 + 0.224205i 0.923462 0.383691i \(-0.125347\pi\)
−0.794017 + 0.607896i \(0.792014\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 13.0000 0.667765 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.0000 24.2487i −0.715367 1.23905i −0.962818 0.270151i \(-0.912926\pi\)
0.247451 0.968900i \(-0.420407\pi\)
\(384\) 0 0
\(385\) −8.00000 + 6.92820i −0.407718 + 0.353094i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i \(-0.751748\pi\)
0.964490 + 0.264120i \(0.0850816\pi\)
\(390\) 0 0
\(391\) −32.0000 + 55.4256i −1.61831 + 2.80299i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.00000 + 5.19615i 0.150946 + 0.261447i
\(396\) 0 0
\(397\) −1.50000 + 2.59808i −0.0752828 + 0.130394i −0.901209 0.433384i \(-0.857319\pi\)
0.825926 + 0.563778i \(0.190653\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 0 0
\(403\) 4.50000 7.79423i 0.224161 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.00000 1.73205i −0.0495682 0.0858546i
\(408\) 0 0
\(409\) −19.0000 −0.939490 −0.469745 0.882802i \(-0.655654\pi\)
−0.469745 + 0.882802i \(0.655654\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.00000 + 6.92820i −0.393654 + 0.340915i
\(414\) 0 0
\(415\) 2.00000 3.46410i 0.0981761 0.170046i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9.00000 15.5885i 0.439679 0.761546i −0.557986 0.829851i \(-0.688426\pi\)
0.997665 + 0.0683046i \(0.0217590\pi\)
\(420\) 0 0
\(421\) 13.5000 + 23.3827i 0.657950 + 1.13960i 0.981146 + 0.193270i \(0.0619094\pi\)
−0.323196 + 0.946332i \(0.604757\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.00000 0.388057
\(426\) 0 0
\(427\) −12.0000 + 10.3923i −0.580721 + 0.502919i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) 24.0000 1.14546 0.572729 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −22.0000 −1.03824 −0.519122 0.854700i \(-0.673741\pi\)
−0.519122 + 0.854700i \(0.673741\pi\)
\(450\) 0 0
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −12.0000 + 10.3923i −0.562569 + 0.487199i
\(456\) 0 0
\(457\) 13.0000 0.608114 0.304057 0.952654i \(-0.401659\pi\)
0.304057 + 0.952654i \(0.401659\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.00000 + 3.46410i 0.0931493 + 0.161339i 0.908835 0.417156i \(-0.136973\pi\)
−0.815685 + 0.578496i \(0.803640\pi\)
\(462\) 0 0
\(463\) 5.50000 9.52628i 0.255607 0.442724i −0.709453 0.704752i \(-0.751058\pi\)
0.965060 + 0.262029i \(0.0843915\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.0000 29.4449i 0.786666 1.36255i −0.141332 0.989962i \(-0.545139\pi\)
0.927999 0.372584i \(-0.121528\pi\)
\(468\) 0 0
\(469\) 26.0000 22.5167i 1.20057 1.03972i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −22.0000 −1.01156
\(474\) 0 0
\(475\) −0.500000 0.866025i −0.0229416 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) 0 0
\(481\) −1.50000 2.59808i −0.0683941 0.118462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.0000 + 17.3205i −0.454077 + 0.786484i
\(486\) 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
\(491\) −18.0000 + 31.1769i −0.812329 + 1.40699i 0.0989017 + 0.995097i \(0.468467\pi\)
−0.911230 + 0.411897i \(0.864866\pi\)
\(492\) 0 0
\(493\) −16.0000 + 27.7128i −0.720604 + 1.24812i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.0000 17.3205i 0.897123 0.776931i
\(498\) 0 0
\(499\) 14.5000 + 25.1147i 0.649109 + 1.12429i 0.983336 + 0.181797i \(0.0581915\pi\)
−0.334227 + 0.942493i \(0.608475\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 27.5000 + 9.52628i 1.21653 + 0.421418i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −11.0000 + 19.0526i −0.484718 + 0.839556i
\(516\) 0 0
\(517\) −6.00000 + 10.3923i −0.263880 + 0.457053i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −18.0000 31.1769i −0.788594 1.36589i −0.926828 0.375486i \(-0.877476\pi\)
0.138234 0.990400i \(-0.455857\pi\)
\(522\) 0 0
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.0000 + 20.7846i 0.522728 + 0.905392i
\(528\) 0 0
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.00000 15.5885i −0.389833 0.675211i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.0000 8.66025i −0.473804 0.373024i
\(540\) 0 0
\(541\) 7.50000 12.9904i 0.322450 0.558500i −0.658543 0.752543i \(-0.728827\pi\)
0.980993 + 0.194043i \(0.0621602\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 11.0000 19.0526i 0.471188 0.816122i
\(546\) 0 0
\(547\) 6.00000 + 10.3923i 0.256541 + 0.444343i 0.965313 0.261095i \(-0.0840836\pi\)
−0.708772 + 0.705438i \(0.750750\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) −6.00000 + 5.19615i −0.255146 + 0.220963i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.0000 + 19.0526i 0.466085 + 0.807283i 0.999250 0.0387286i \(-0.0123308\pi\)
−0.533165 + 0.846011i \(0.678997\pi\)
\(558\) 0 0
\(559\) −33.0000 −1.39575
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 46.0000 1.93867 0.969334 0.245745i \(-0.0790327\pi\)
0.969334 + 0.245745i \(0.0790327\pi\)
\(564\) 0 0
\(565\) 28.0000 1.17797
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −21.0000 −0.878823 −0.439411 0.898286i \(-0.644813\pi\)
−0.439411 + 0.898286i \(0.644813\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) 20.5000 + 35.5070i 0.853426 + 1.47818i 0.878097 + 0.478482i \(0.158813\pi\)
−0.0246713 + 0.999696i \(0.507854\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.00000 + 1.73205i 0.207435 + 0.0718576i
\(582\) 0 0
\(583\) −24.0000 −0.993978
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.0000 + 27.7128i 0.660391 + 1.14383i 0.980513 + 0.196454i \(0.0629426\pi\)
−0.320122 + 0.947376i \(0.603724\pi\)
\(588\) 0 0
\(589\) 1.50000 2.59808i 0.0618064 0.107052i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) −8.00000 41.5692i −0.327968 1.70417i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) 0.500000 + 0.866025i 0.0203954 + 0.0353259i 0.876043 0.482233i \(-0.160174\pi\)
−0.855648 + 0.517559i \(0.826841\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) 0 0
\(607\) 1.50000 + 2.59808i 0.0608831 + 0.105453i 0.894860 0.446346i \(-0.147275\pi\)
−0.833977 + 0.551799i \(0.813942\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9.00000 + 15.5885i −0.364101 + 0.630641i
\(612\) 0 0
\(613\) 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i \(0.0404979\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 13.0000 22.5167i 0.523360 0.906487i −0.476270 0.879299i \(-0.658012\pi\)
0.999630 0.0271876i \(-0.00865514\pi\)
\(618\) 0 0
\(619\) 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957138\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.00000 5.19615i −0.119051 0.206203i
\(636\) 0 0
\(637\) −16.5000 12.9904i −0.653754 0.514698i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −20.0000 + 34.6410i −0.789953 + 1.36824i 0.136043 + 0.990703i \(0.456562\pi\)
−0.925995 + 0.377535i \(0.876772\pi\)
\(642\) 0 0
\(643\) −17.5000 + 30.3109i −0.690133 + 1.19534i 0.281661 + 0.959514i \(0.409114\pi\)
−0.971794 + 0.235831i \(0.924219\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) 0 0
\(649\) −4.00000 + 6.92820i −0.157014 + 0.271956i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 0 0
\(655\) −2.00000 + 3.46410i −0.0781465 + 0.135354i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −14.0000 24.2487i −0.545363 0.944596i −0.998584 0.0531977i \(-0.983059\pi\)
0.453221 0.891398i \(-0.350275\pi\)
\(660\) 0 0
\(661\) −29.0000 −1.12797 −0.563985 0.825785i \(-0.690732\pi\)
−0.563985 + 0.825785i \(0.690732\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.00000 + 3.46410i −0.155113 + 0.134332i
\(666\) 0 0
\(667\) −16.0000 + 27.7128i −0.619522 + 1.07304i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −6.00000 + 10.3923i −0.231627 + 0.401190i
\(672\) 0 0
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 0 0
\(679\) −25.0000 8.66025i −0.959412 0.332350i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.0000 + 31.1769i 0.688751 + 1.19295i 0.972242 + 0.233977i \(0.0751739\pi\)
−0.283491 + 0.958975i \(0.591493\pi\)
\(684\) 0 0
\(685\) −8.00000 −0.305664
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −36.0000 −1.37149
\(690\) 0 0
\(691\) −43.0000 −1.63580 −0.817899 0.575362i \(-0.804861\pi\)
−0.817899 + 0.575362i \(0.804861\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −10.0000 −0.379322
\(696\) 0 0
\(697\) 48.0000 1.81813
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.00000 0.302156 0.151078 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(702\) 0 0
\(703\) −0.500000 0.866025i −0.0188579 0.0326628i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.00000 25.9808i −0.188044 0.977107i
\(708\) 0 0
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 12.0000 + 20.7846i 0.449404 + 0.778390i
\(714\) 0 0
\(715\) −6.00000 + 10.3923i −0.224387 + 0.388650i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) −27.5000 9.52628i −1.02415 0.354777i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.00000 0.148556
\(726\) 0 0
\(727\) 11.5000 + 19.9186i 0.426511 + 0.738739i 0.996560 0.0828714i \(-0.0264091\pi\)
−0.570049 + 0.821611i \(0.693076\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 44.0000 76.2102i 1.62740 2.81874i
\(732\) 0 0
\(733\) −22.5000 38.9711i −0.831056 1.43943i −0.897201 0.441622i \(-0.854403\pi\)
0.0661448 0.997810i \(-0.478930\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.0000 22.5167i 0.478861 0.829412i
\(738\) 0 0
\(739\) 4.50000 + 7.79423i 0.165535 + 0.286715i 0.936845 0.349744i \(-0.113732\pi\)
−0.771310 + 0.636460i \(0.780398\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i \(-0.940442\pi\)
0.652369 + 0.757902i \(0.273775\pi\)
\(744\) 0 0
\(745\) −12.0000 + 20.7846i −0.439646 + 0.761489i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −7.50000 12.9904i −0.273679 0.474026i 0.696122 0.717923i \(-0.254907\pi\)
−0.969801 + 0.243898i \(0.921574\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.00000 + 6.92820i 0.145000 + 0.251147i 0.929373 0.369142i \(-0.120348\pi\)
−0.784373 + 0.620289i \(0.787015\pi\)
\(762\) 0 0
\(763\) 27.5000 + 9.52628i 0.995567 + 0.344874i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.00000 + 10.3923i −0.216647 + 0.375244i
\(768\) 0 0
\(769\) −15.5000 + 26.8468i −0.558944 + 0.968120i 0.438641 + 0.898663i \(0.355460\pi\)
−0.997585 + 0.0694574i \(0.977873\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 11.0000 + 19.0526i 0.395643 + 0.685273i 0.993183 0.116566i \(-0.0371886\pi\)
−0.597540 + 0.801839i \(0.703855\pi\)
\(774\) 0 0
\(775\) 1.50000 2.59808i 0.0538816 0.0933257i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3.00000 5.19615i −0.107486 0.186171i
\(780\) 0 0
\(781\) 10.0000 17.3205i 0.357828 0.619777i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.00000 3.46410i −0.0713831 0.123639i
\(786\) 0 0
\(787\) 24.0000 0.855508 0.427754 0.903895i \(-0.359305\pi\)
0.427754 + 0.903895i \(0.359305\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.00000 + 36.3731i 0.248891 + 1.29328i
\(792\) 0 0
\(793\) −9.00000 + 15.5885i −0.319599 + 0.553562i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −24.0000 + 41.5692i −0.850124 + 1.47246i 0.0309726 + 0.999520i \(0.490140\pi\)
−0.881096 + 0.472937i \(0.843194\pi\)
\(798\) 0 0
\(799\) −24.0000 41.5692i −0.849059 1.47061i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 22.0000