Properties

Label 2592.2.s.b.863.4
Level $2592$
Weight $2$
Character 2592.863
Analytic conductor $20.697$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(1\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.4
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2592.863
Dual form 2592.2.s.b.1727.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.67303 + 0.965926i) q^{5} +(-0.633975 + 0.366025i) q^{7} +O(q^{10})\) \(q+(1.67303 + 0.965926i) q^{5} +(-0.633975 + 0.366025i) q^{7} +(-2.63896 - 4.57081i) q^{11} +(-2.23205 + 3.86603i) q^{13} +0.896575i q^{17} -1.26795i q^{19} +(-0.707107 + 1.22474i) q^{23} +(-0.633975 - 1.09808i) q^{25} +(-4.69093 + 2.70831i) q^{29} +(-6.46410 - 3.73205i) q^{31} -1.41421 q^{35} -7.73205 q^{37} +(-0.328169 - 0.189469i) q^{41} +(7.56218 - 4.36603i) q^{43} +(2.31079 + 4.00240i) q^{47} +(-3.23205 + 5.59808i) q^{49} -2.44949i q^{53} -10.1962i q^{55} +(-5.41662 + 9.38186i) q^{59} +(0.598076 + 1.03590i) q^{61} +(-7.46859 + 4.31199i) q^{65} +(-11.3660 - 6.56218i) q^{67} +13.2827 q^{71} -13.7321 q^{73} +(3.34607 + 1.93185i) q^{77} +(-14.3660 + 8.29423i) q^{79} +(-5.27792 - 9.14162i) q^{83} +(-0.866025 + 1.50000i) q^{85} -14.9372i q^{89} -3.26795i q^{91} +(1.22474 - 2.12132i) q^{95} +(3.19615 + 5.53590i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{7} - 4 q^{13} - 12 q^{25} - 24 q^{31} - 48 q^{37} + 12 q^{43} - 12 q^{49} - 16 q^{61} - 84 q^{67} - 96 q^{73} - 108 q^{79} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 0
\(4\) 0 0
\(5\) 1.67303 + 0.965926i 0.748203 + 0.431975i 0.825044 0.565068i \(-0.191150\pi\)
−0.0768413 + 0.997043i \(0.524483\pi\)
\(6\) 0 0
\(7\) −0.633975 + 0.366025i −0.239620 + 0.138345i −0.615002 0.788526i \(-0.710845\pi\)
0.375382 + 0.926870i \(0.377511\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.63896 4.57081i −0.795676 1.37815i −0.922409 0.386214i \(-0.873783\pi\)
0.126733 0.991937i \(-0.459551\pi\)
\(12\) 0 0
\(13\) −2.23205 + 3.86603i −0.619060 + 1.07224i 0.370598 + 0.928793i \(0.379153\pi\)
−0.989658 + 0.143449i \(0.954181\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.896575i 0.217451i 0.994072 + 0.108726i \(0.0346770\pi\)
−0.994072 + 0.108726i \(0.965323\pi\)
\(18\) 0 0
\(19\) 1.26795i 0.290887i −0.989367 0.145444i \(-0.953539\pi\)
0.989367 0.145444i \(-0.0464610\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.707107 + 1.22474i −0.147442 + 0.255377i −0.930281 0.366847i \(-0.880437\pi\)
0.782839 + 0.622224i \(0.213771\pi\)
\(24\) 0 0
\(25\) −0.633975 1.09808i −0.126795 0.219615i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.69093 + 2.70831i −0.871084 + 0.502920i −0.867708 0.497074i \(-0.834408\pi\)
−0.00337538 + 0.999994i \(0.501074\pi\)
\(30\) 0 0
\(31\) −6.46410 3.73205i −1.16099 0.670296i −0.209447 0.977820i \(-0.567166\pi\)
−0.951540 + 0.307524i \(0.900500\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.41421 −0.239046
\(36\) 0 0
\(37\) −7.73205 −1.27114 −0.635571 0.772043i \(-0.719235\pi\)
−0.635571 + 0.772043i \(0.719235\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.328169 0.189469i −0.0512514 0.0295900i 0.474155 0.880441i \(-0.342754\pi\)
−0.525407 + 0.850851i \(0.676087\pi\)
\(42\) 0 0
\(43\) 7.56218 4.36603i 1.15322 0.665813i 0.203551 0.979064i \(-0.434752\pi\)
0.949670 + 0.313252i \(0.101418\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.31079 + 4.00240i 0.337063 + 0.583811i 0.983879 0.178836i \(-0.0572331\pi\)
−0.646816 + 0.762646i \(0.723900\pi\)
\(48\) 0 0
\(49\) −3.23205 + 5.59808i −0.461722 + 0.799725i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.44949i 0.336463i −0.985747 0.168232i \(-0.946194\pi\)
0.985747 0.168232i \(-0.0538057\pi\)
\(54\) 0 0
\(55\) 10.1962i 1.37485i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.41662 + 9.38186i −0.705184 + 1.22141i 0.261442 + 0.965219i \(0.415802\pi\)
−0.966625 + 0.256194i \(0.917531\pi\)
\(60\) 0 0
\(61\) 0.598076 + 1.03590i 0.0765758 + 0.132633i 0.901770 0.432215i \(-0.142268\pi\)
−0.825195 + 0.564848i \(0.808935\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.46859 + 4.31199i −0.926364 + 0.534837i
\(66\) 0 0
\(67\) −11.3660 6.56218i −1.38858 0.801698i −0.395426 0.918498i \(-0.629403\pi\)
−0.993155 + 0.116800i \(0.962736\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.2827 1.57637 0.788185 0.615439i \(-0.211021\pi\)
0.788185 + 0.615439i \(0.211021\pi\)
\(72\) 0 0
\(73\) −13.7321 −1.60721 −0.803607 0.595160i \(-0.797089\pi\)
−0.803607 + 0.595160i \(0.797089\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.34607 + 1.93185i 0.381320 + 0.220155i
\(78\) 0 0
\(79\) −14.3660 + 8.29423i −1.61630 + 0.933174i −0.628439 + 0.777859i \(0.716306\pi\)
−0.987865 + 0.155315i \(0.950361\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.27792 9.14162i −0.579327 1.00342i −0.995557 0.0941638i \(-0.969982\pi\)
0.416230 0.909259i \(-0.363351\pi\)
\(84\) 0 0
\(85\) −0.866025 + 1.50000i −0.0939336 + 0.162698i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.9372i 1.58334i −0.610951 0.791669i \(-0.709213\pi\)
0.610951 0.791669i \(-0.290787\pi\)
\(90\) 0 0
\(91\) 3.26795i 0.342574i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.22474 2.12132i 0.125656 0.217643i
\(96\) 0 0
\(97\) 3.19615 + 5.53590i 0.324520 + 0.562085i 0.981415 0.191897i \(-0.0614639\pi\)
−0.656895 + 0.753982i \(0.728131\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.46739 3.15660i 0.544025 0.314093i −0.202683 0.979244i \(-0.564966\pi\)
0.746709 + 0.665151i \(0.231633\pi\)
\(102\) 0 0
\(103\) 3.46410 + 2.00000i 0.341328 + 0.197066i 0.660859 0.750510i \(-0.270192\pi\)
−0.319531 + 0.947576i \(0.603525\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.79315 0.173350 0.0866752 0.996237i \(-0.472376\pi\)
0.0866752 + 0.996237i \(0.472376\pi\)
\(108\) 0 0
\(109\) 3.92820 0.376254 0.188127 0.982145i \(-0.439758\pi\)
0.188127 + 0.982145i \(0.439758\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.5068 + 10.1075i 1.64690 + 0.950838i 0.978294 + 0.207221i \(0.0664418\pi\)
0.668605 + 0.743617i \(0.266892\pi\)
\(114\) 0 0
\(115\) −2.36603 + 1.36603i −0.220633 + 0.127383i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.328169 0.568406i −0.0300832 0.0521057i
\(120\) 0 0
\(121\) −8.42820 + 14.5981i −0.766200 + 1.32710i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.1087i 1.08304i
\(126\) 0 0
\(127\) 21.1244i 1.87448i −0.348680 0.937242i \(-0.613370\pi\)
0.348680 0.937242i \(-0.386630\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.0507680 0.0879327i 0.00443562 0.00768272i −0.863799 0.503836i \(-0.831921\pi\)
0.868235 + 0.496154i \(0.165255\pi\)
\(132\) 0 0
\(133\) 0.464102 + 0.803848i 0.0402427 + 0.0697024i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.21046 2.43091i 0.359723 0.207686i −0.309236 0.950985i \(-0.600073\pi\)
0.668959 + 0.743299i \(0.266740\pi\)
\(138\) 0 0
\(139\) −10.7321 6.19615i −0.910281 0.525551i −0.0297592 0.999557i \(-0.509474\pi\)
−0.880521 + 0.474006i \(0.842807\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 23.5612 1.97028
\(144\) 0 0
\(145\) −10.4641 −0.868996
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.58510 + 0.915158i 0.129856 + 0.0749727i 0.563521 0.826102i \(-0.309446\pi\)
−0.433665 + 0.901074i \(0.642780\pi\)
\(150\) 0 0
\(151\) 0.928203 0.535898i 0.0755361 0.0436108i −0.461756 0.887007i \(-0.652781\pi\)
0.537292 + 0.843396i \(0.319447\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.20977 12.4877i −0.579103 1.00304i
\(156\) 0 0
\(157\) −5.33013 + 9.23205i −0.425390 + 0.736798i −0.996457 0.0841060i \(-0.973197\pi\)
0.571066 + 0.820904i \(0.306530\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.03528i 0.0815912i
\(162\) 0 0
\(163\) 1.60770i 0.125924i −0.998016 0.0629622i \(-0.979945\pi\)
0.998016 0.0629622i \(-0.0200548\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.32868 + 9.22955i −0.412346 + 0.714204i −0.995146 0.0984115i \(-0.968624\pi\)
0.582800 + 0.812616i \(0.301957\pi\)
\(168\) 0 0
\(169\) −3.46410 6.00000i −0.266469 0.461538i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.58991 + 5.53674i −0.729107 + 0.420950i −0.818095 0.575082i \(-0.804970\pi\)
0.0889883 + 0.996033i \(0.471637\pi\)
\(174\) 0 0
\(175\) 0.803848 + 0.464102i 0.0607652 + 0.0350828i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −21.8695 −1.63461 −0.817303 0.576208i \(-0.804532\pi\)
−0.817303 + 0.576208i \(0.804532\pi\)
\(180\) 0 0
\(181\) −23.3205 −1.73340 −0.866700 0.498830i \(-0.833763\pi\)
−0.866700 + 0.498830i \(0.833763\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −12.9360 7.46859i −0.951072 0.549101i
\(186\) 0 0
\(187\) 4.09808 2.36603i 0.299681 0.173021i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.2277 + 17.7148i 0.740048 + 1.28180i 0.952473 + 0.304623i \(0.0985305\pi\)
−0.212425 + 0.977177i \(0.568136\pi\)
\(192\) 0 0
\(193\) 4.23205 7.33013i 0.304630 0.527634i −0.672549 0.740052i \(-0.734801\pi\)
0.977179 + 0.212418i \(0.0681340\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.76079i 0.695428i 0.937601 + 0.347714i \(0.113042\pi\)
−0.937601 + 0.347714i \(0.886958\pi\)
\(198\) 0 0
\(199\) 8.00000i 0.567105i −0.958957 0.283552i \(-0.908487\pi\)
0.958957 0.283552i \(-0.0915130\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.98262 3.43400i 0.139153 0.241019i
\(204\) 0 0
\(205\) −0.366025 0.633975i −0.0255643 0.0442787i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.79555 + 3.34607i −0.400887 + 0.231452i
\(210\) 0 0
\(211\) −16.5622 9.56218i −1.14019 0.658287i −0.193710 0.981059i \(-0.562052\pi\)
−0.946477 + 0.322771i \(0.895386\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 16.8690 1.15046
\(216\) 0 0
\(217\) 5.46410 0.370927
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.46618 2.00120i −0.233161 0.134615i
\(222\) 0 0
\(223\) 14.9545 8.63397i 1.00143 0.578174i 0.0927563 0.995689i \(-0.470432\pi\)
0.908670 + 0.417515i \(0.137099\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.67475 15.0251i −0.575763 0.997251i −0.995958 0.0898175i \(-0.971372\pi\)
0.420195 0.907434i \(-0.361962\pi\)
\(228\) 0 0
\(229\) −5.50000 + 9.52628i −0.363450 + 0.629514i −0.988526 0.151050i \(-0.951735\pi\)
0.625076 + 0.780564i \(0.285068\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 18.8009i 1.23169i 0.787869 + 0.615843i \(0.211185\pi\)
−0.787869 + 0.615843i \(0.788815\pi\)
\(234\) 0 0
\(235\) 8.92820i 0.582412i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.52056 + 16.4901i −0.615834 + 1.06666i 0.374404 + 0.927266i \(0.377847\pi\)
−0.990238 + 0.139390i \(0.955486\pi\)
\(240\) 0 0
\(241\) 8.06218 + 13.9641i 0.519331 + 0.899507i 0.999748 + 0.0224667i \(0.00715197\pi\)
−0.480417 + 0.877040i \(0.659515\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −10.8147 + 6.24384i −0.690923 + 0.398904i
\(246\) 0 0
\(247\) 4.90192 + 2.83013i 0.311902 + 0.180077i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −23.8386 −1.50468 −0.752338 0.658777i \(-0.771074\pi\)
−0.752338 + 0.658777i \(0.771074\pi\)
\(252\) 0 0
\(253\) 7.46410 0.469264
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.688524 + 0.397520i 0.0429490 + 0.0247966i 0.521321 0.853361i \(-0.325440\pi\)
−0.478372 + 0.878157i \(0.658773\pi\)
\(258\) 0 0
\(259\) 4.90192 2.83013i 0.304591 0.175856i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.72500 + 6.45189i 0.229694 + 0.397841i 0.957717 0.287711i \(-0.0928943\pi\)
−0.728024 + 0.685552i \(0.759561\pi\)
\(264\) 0 0
\(265\) 2.36603 4.09808i 0.145344 0.251743i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 22.7661i 1.38807i −0.719939 0.694037i \(-0.755830\pi\)
0.719939 0.694037i \(-0.244170\pi\)
\(270\) 0 0
\(271\) 13.2679i 0.805971i 0.915206 + 0.402985i \(0.132027\pi\)
−0.915206 + 0.402985i \(0.867973\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.34607 + 5.79555i −0.201775 + 0.349485i
\(276\) 0 0
\(277\) −0.535898 0.928203i −0.0321990 0.0557703i 0.849477 0.527626i \(-0.176918\pi\)
−0.881676 + 0.471856i \(0.843584\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.91808 + 5.72620i −0.591663 + 0.341597i −0.765755 0.643133i \(-0.777634\pi\)
0.174092 + 0.984729i \(0.444301\pi\)
\(282\) 0 0
\(283\) −16.7321 9.66025i −0.994617 0.574242i −0.0879660 0.996123i \(-0.528037\pi\)
−0.906651 + 0.421881i \(0.861370\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.277401 0.0163745
\(288\) 0 0
\(289\) 16.1962 0.952715
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 20.6126 + 11.9007i 1.20420 + 0.695246i 0.961487 0.274852i \(-0.0886287\pi\)
0.242715 + 0.970098i \(0.421962\pi\)
\(294\) 0 0
\(295\) −18.1244 + 10.4641i −1.05524 + 0.609244i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.15660 5.46739i −0.182551 0.316187i
\(300\) 0 0
\(301\) −3.19615 + 5.53590i −0.184223 + 0.319084i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.31079i 0.132315i
\(306\) 0 0
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.1087 20.9730i 0.686624 1.18927i −0.286299 0.958140i \(-0.592425\pi\)
0.972923 0.231128i \(-0.0742415\pi\)
\(312\) 0 0
\(313\) −14.1603 24.5263i −0.800385 1.38631i −0.919363 0.393410i \(-0.871295\pi\)
0.118978 0.992897i \(-0.462038\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.33178 3.65565i 0.355628 0.205322i −0.311533 0.950235i \(-0.600843\pi\)
0.667161 + 0.744913i \(0.267509\pi\)
\(318\) 0 0
\(319\) 24.7583 + 14.2942i 1.38620 + 0.800323i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.13681 0.0632539
\(324\) 0 0
\(325\) 5.66025 0.313974
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.92996 1.69161i −0.161534 0.0932618i
\(330\) 0 0
\(331\) −6.75833 + 3.90192i −0.371471 + 0.214469i −0.674101 0.738639i \(-0.735469\pi\)
0.302630 + 0.953108i \(0.402135\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.6772 21.9575i −0.692627 1.19967i
\(336\) 0 0
\(337\) 2.46410 4.26795i 0.134228 0.232490i −0.791074 0.611720i \(-0.790478\pi\)
0.925302 + 0.379230i \(0.123811\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 39.3949i 2.13335i
\(342\) 0 0
\(343\) 9.85641i 0.532196i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.88160 11.9193i 0.369424 0.639860i −0.620052 0.784561i \(-0.712888\pi\)
0.989476 + 0.144700i \(0.0462218\pi\)
\(348\) 0 0
\(349\) 1.07180 + 1.85641i 0.0573720 + 0.0993712i 0.893285 0.449491i \(-0.148395\pi\)
−0.835913 + 0.548862i \(0.815061\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 24.2311 13.9898i 1.28969 0.744604i 0.311092 0.950380i \(-0.399305\pi\)
0.978599 + 0.205776i \(0.0659719\pi\)
\(354\) 0 0
\(355\) 22.2224 + 12.8301i 1.17944 + 0.680952i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2.44949 0.129279 0.0646396 0.997909i \(-0.479410\pi\)
0.0646396 + 0.997909i \(0.479410\pi\)
\(360\) 0 0
\(361\) 17.3923 0.915384
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −22.9742 13.2641i −1.20252 0.694277i
\(366\) 0 0
\(367\) −10.8564 + 6.26795i −0.566700 + 0.327184i −0.755830 0.654768i \(-0.772766\pi\)
0.189130 + 0.981952i \(0.439433\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.896575 + 1.55291i 0.0465479 + 0.0806233i
\(372\) 0 0
\(373\) 16.1244 27.9282i 0.834887 1.44607i −0.0592345 0.998244i \(-0.518866\pi\)
0.894122 0.447823i \(-0.147801\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 24.1803i 1.24535i
\(378\) 0 0
\(379\) 14.3923i 0.739283i 0.929174 + 0.369642i \(0.120520\pi\)
−0.929174 + 0.369642i \(0.879480\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.60849 16.6424i 0.490971 0.850387i −0.508975 0.860781i \(-0.669975\pi\)
0.999946 + 0.0103947i \(0.00330879\pi\)
\(384\) 0 0
\(385\) 3.73205 + 6.46410i 0.190203 + 0.329441i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.29392 5.36585i 0.471221 0.272059i −0.245530 0.969389i \(-0.578962\pi\)
0.716751 + 0.697330i \(0.245629\pi\)
\(390\) 0 0
\(391\) −1.09808 0.633975i −0.0555321 0.0320615i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −32.0464 −1.61243
\(396\) 0 0
\(397\) 21.5885 1.08349 0.541747 0.840542i \(-0.317763\pi\)
0.541747 + 0.840542i \(0.317763\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.2820 + 9.40044i 0.813086 + 0.469436i 0.848026 0.529954i \(-0.177791\pi\)
−0.0349403 + 0.999389i \(0.511124\pi\)
\(402\) 0 0
\(403\) 28.8564 16.6603i 1.43744 0.829906i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 20.4046 + 35.3417i 1.01142 + 1.75182i
\(408\) 0 0
\(409\) −7.40192 + 12.8205i −0.366002 + 0.633933i −0.988936 0.148340i \(-0.952607\pi\)
0.622935 + 0.782274i \(0.285940\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.93048i 0.390233i
\(414\) 0 0
\(415\) 20.3923i 1.00102i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.795040 + 1.37705i −0.0388402 + 0.0672732i −0.884792 0.465986i \(-0.845700\pi\)
0.845952 + 0.533259i \(0.179033\pi\)
\(420\) 0 0
\(421\) −4.42820 7.66987i −0.215817 0.373807i 0.737708 0.675120i \(-0.235908\pi\)
−0.953525 + 0.301313i \(0.902575\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.984508 0.568406i 0.0477557 0.0275717i
\(426\) 0 0
\(427\) −0.758330 0.437822i −0.0366982 0.0211877i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.48528 0.408722 0.204361 0.978896i \(-0.434488\pi\)
0.204361 + 0.978896i \(0.434488\pi\)
\(432\) 0 0
\(433\) −34.1769 −1.64244 −0.821219 0.570613i \(-0.806706\pi\)
−0.821219 + 0.570613i \(0.806706\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.55291 + 0.896575i 0.0742860 + 0.0428890i
\(438\) 0 0
\(439\) −6.46410 + 3.73205i −0.308515 + 0.178121i −0.646262 0.763116i \(-0.723669\pi\)
0.337747 + 0.941237i \(0.390335\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.52245 + 14.7613i 0.404914 + 0.701331i 0.994311 0.106512i \(-0.0339682\pi\)
−0.589398 + 0.807843i \(0.700635\pi\)
\(444\) 0 0
\(445\) 14.4282 24.9904i 0.683962 1.18466i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 23.0064i 1.08574i 0.839818 + 0.542868i \(0.182662\pi\)
−0.839818 + 0.542868i \(0.817338\pi\)
\(450\) 0 0
\(451\) 2.00000i 0.0941763i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.15660 5.46739i 0.147984 0.256315i
\(456\) 0 0
\(457\) 1.40192 + 2.42820i 0.0655792 + 0.113587i 0.896951 0.442130i \(-0.145777\pi\)
−0.831372 + 0.555717i \(0.812444\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.8589 17.8164i 1.43724 0.829791i 0.439583 0.898202i \(-0.355126\pi\)
0.997657 + 0.0684108i \(0.0217929\pi\)
\(462\) 0 0
\(463\) 15.9282 + 9.19615i 0.740246 + 0.427381i 0.822159 0.569258i \(-0.192769\pi\)
−0.0819125 + 0.996640i \(0.526103\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.0716 0.558606 0.279303 0.960203i \(-0.409897\pi\)
0.279303 + 0.960203i \(0.409897\pi\)
\(468\) 0 0
\(469\) 9.60770 0.443642
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −39.9125 23.0435i −1.83518 1.05954i
\(474\) 0 0
\(475\) −1.39230 + 0.803848i −0.0638833 + 0.0368831i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.6443 + 27.0967i 0.714805 + 1.23808i 0.963035 + 0.269378i \(0.0868181\pi\)
−0.248229 + 0.968701i \(0.579849\pi\)
\(480\) 0 0
\(481\) 17.2583 29.8923i 0.786912 1.36297i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.3490i 0.560739i
\(486\) 0 0
\(487\) 36.9282i 1.67338i 0.547679 + 0.836688i \(0.315511\pi\)
−0.547679 + 0.836688i \(0.684489\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.12184 + 12.3354i −0.321404 + 0.556688i −0.980778 0.195127i \(-0.937488\pi\)
0.659374 + 0.751815i \(0.270821\pi\)
\(492\) 0 0
\(493\) −2.42820 4.20577i −0.109361 0.189418i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.42091 + 4.86181i −0.377729 + 0.218082i
\(498\) 0 0
\(499\) 31.5622 + 18.2224i 1.41292 + 0.815748i 0.995662 0.0930414i \(-0.0296589\pi\)
0.417255 + 0.908790i \(0.362992\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −29.1165 −1.29824 −0.649120 0.760686i \(-0.724863\pi\)
−0.649120 + 0.760686i \(0.724863\pi\)
\(504\) 0 0
\(505\) 12.1962 0.542722
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −31.9957 18.4727i −1.41818 0.818788i −0.422044 0.906575i \(-0.638687\pi\)
−0.996139 + 0.0877870i \(0.972021\pi\)
\(510\) 0 0
\(511\) 8.70577 5.02628i 0.385121 0.222350i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.86370 + 6.69213i 0.170255 + 0.294891i
\(516\) 0 0
\(517\) 12.1962 21.1244i 0.536386 0.929048i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.2789i 0.669383i −0.942328 0.334691i \(-0.891368\pi\)
0.942328 0.334691i \(-0.108632\pi\)
\(522\) 0 0
\(523\) 16.1962i 0.708208i 0.935206 + 0.354104i \(0.115214\pi\)
−0.935206 + 0.354104i \(0.884786\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.34607 5.79555i 0.145757 0.252458i
\(528\) 0 0
\(529\) 10.5000 + 18.1865i 0.456522 + 0.790719i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.46498 0.845807i 0.0634554 0.0366360i
\(534\) 0 0
\(535\) 3.00000 + 1.73205i 0.129701 + 0.0748831i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 34.1170 1.46952
\(540\) 0 0
\(541\) 7.00000 0.300954 0.150477 0.988614i \(-0.451919\pi\)
0.150477 + 0.988614i \(0.451919\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 6.57201 + 3.79435i 0.281514 + 0.162532i
\(546\) 0 0
\(547\) 1.14359 0.660254i 0.0488965 0.0282304i −0.475352 0.879795i \(-0.657679\pi\)
0.524249 + 0.851565i \(0.324346\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.43400 + 5.94786i 0.146293 + 0.253387i
\(552\) 0 0
\(553\) 6.07180 10.5167i 0.258199 0.447214i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.03339i 0.0861574i 0.999072 + 0.0430787i \(0.0137166\pi\)
−0.999072 + 0.0430787i \(0.986283\pi\)
\(558\) 0 0
\(559\) 38.9808i 1.64871i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.27981 7.41284i 0.180372 0.312414i −0.761635 0.648006i \(-0.775603\pi\)
0.942007 + 0.335592i \(0.108936\pi\)
\(564\) 0 0
\(565\) 19.5263 + 33.8205i 0.821477 + 1.42284i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.09154 3.51695i 0.255371 0.147438i −0.366850 0.930280i \(-0.619564\pi\)
0.622221 + 0.782842i \(0.286231\pi\)
\(570\) 0 0
\(571\) 34.5167 + 19.9282i 1.44448 + 0.833969i 0.998144 0.0608975i \(-0.0193963\pi\)
0.446333 + 0.894867i \(0.352730\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.79315 0.0747796
\(576\) 0 0
\(577\) 18.4641 0.768671 0.384335 0.923194i \(-0.374431\pi\)
0.384335 + 0.923194i \(0.374431\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.69213 + 3.86370i 0.277636 + 0.160293i
\(582\) 0 0
\(583\) −11.1962 + 6.46410i −0.463697 + 0.267716i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.845807 + 1.46498i 0.0349102 + 0.0604663i 0.882953 0.469462i \(-0.155552\pi\)
−0.848042 + 0.529928i \(0.822219\pi\)
\(588\) 0 0
\(589\) −4.73205 + 8.19615i −0.194981 + 0.337717i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21.1488i 0.868478i 0.900798 + 0.434239i \(0.142983\pi\)
−0.900798 + 0.434239i \(0.857017\pi\)
\(594\) 0 0
\(595\) 1.26795i 0.0519808i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.20977 + 12.4877i −0.294583 + 0.510233i −0.974888 0.222696i \(-0.928514\pi\)
0.680305 + 0.732929i \(0.261847\pi\)
\(600\) 0 0
\(601\) −1.89230 3.27757i −0.0771887 0.133695i 0.824847 0.565356i \(-0.191261\pi\)
−0.902036 + 0.431661i \(0.857928\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −28.2013 + 16.2820i −1.14655 + 0.661959i
\(606\) 0 0
\(607\) −5.83013 3.36603i −0.236638 0.136623i 0.376993 0.926216i \(-0.376958\pi\)
−0.613630 + 0.789593i \(0.710291\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −20.6312 −0.834649
\(612\) 0 0
\(613\) 13.6077 0.549610 0.274805 0.961500i \(-0.411387\pi\)
0.274805 + 0.961500i \(0.411387\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.03699 4.64016i −0.323557 0.186806i 0.329420 0.944184i \(-0.393147\pi\)
−0.652977 + 0.757378i \(0.726480\pi\)
\(618\) 0 0
\(619\) −4.26795 + 2.46410i −0.171543 + 0.0990406i −0.583313 0.812247i \(-0.698244\pi\)
0.411770 + 0.911288i \(0.364911\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.46739 + 9.46979i 0.219046 + 0.379399i
\(624\) 0 0
\(625\) 8.52628 14.7679i 0.341051 0.590718i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.93237i 0.276412i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 20.4046 35.3417i 0.809730 1.40249i
\(636\) 0 0
\(637\) −14.4282 24.9904i −0.571666 0.990155i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 32.1158 18.5421i 1.26850 0.732367i 0.293794 0.955869i \(-0.405082\pi\)
0.974704 + 0.223502i \(0.0717488\pi\)
\(642\) 0 0
\(643\) −3.46410 2.00000i −0.136611 0.0788723i 0.430137 0.902764i \(-0.358465\pi\)
−0.566748 + 0.823891i \(0.691799\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.6660 −0.655206 −0.327603 0.944815i \(-0.606241\pi\)
−0.327603 + 0.944815i \(0.606241\pi\)
\(648\) 0 0
\(649\) 57.1769 2.24439
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.64566 + 5.56892i 0.377464 + 0.217929i 0.676714 0.736246i \(-0.263403\pi\)
−0.299251 + 0.954175i \(0.596737\pi\)
\(654\) 0 0
\(655\) 0.169873 0.0980762i 0.00663749 0.00383215i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10.8840 18.8516i −0.423981 0.734356i 0.572344 0.820014i \(-0.306034\pi\)
−0.996325 + 0.0856577i \(0.972701\pi\)
\(660\) 0 0
\(661\) 4.25833 7.37564i 0.165630 0.286879i −0.771249 0.636534i \(-0.780368\pi\)
0.936879 + 0.349654i \(0.113701\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.79315i 0.0695354i
\(666\) 0 0
\(667\) 7.66025i 0.296606i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.15660 5.46739i 0.121859 0.211066i
\(672\) 0 0
\(673\) −15.1603 26.2583i −0.584385 1.01218i −0.994952 0.100354i \(-0.968003\pi\)
0.410567 0.911830i \(-0.365331\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.6130 19.4064i 1.29185 0.745850i 0.312869 0.949796i \(-0.398710\pi\)
0.978982 + 0.203946i \(0.0653767\pi\)
\(678\) 0 0
\(679\) −4.05256 2.33975i −0.155523 0.0897912i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.37945 −0.205839 −0.102920 0.994690i \(-0.532818\pi\)
−0.102920 + 0.994690i \(0.532818\pi\)
\(684\) 0 0
\(685\) 9.39230 0.358862
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.46979 + 5.46739i 0.360770 + 0.208291i
\(690\) 0 0
\(691\) −2.24167 + 1.29423i −0.0852771 + 0.0492348i −0.542032 0.840358i \(-0.682345\pi\)
0.456755 + 0.889593i \(0.349012\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.9700 20.7327i −0.454050 0.786437i
\(696\) 0 0
\(697\) 0.169873 0.294229i 0.00643440 0.0111447i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.06918i 0.304769i −0.988321 0.152384i \(-0.951305\pi\)
0.988321 0.152384i \(-0.0486952\pi\)
\(702\) 0 0
\(703\) 9.80385i 0.369759i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.31079 + 4.00240i −0.0869062 + 0.150526i
\(708\) 0 0
\(709\) 6.50000 + 11.2583i 0.244113 + 0.422815i 0.961882 0.273466i \(-0.0881700\pi\)
−0.717769 + 0.696281i \(0.754837\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.14162 5.27792i 0.342356 0.197660i
\(714\) 0 0
\(715\) 39.4186 + 22.7583i 1.47417 + 0.851113i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −36.3906 −1.35714 −0.678570 0.734535i \(-0.737400\pi\)
−0.678570 + 0.734535i \(0.737400\pi\)
\(720\) 0 0
\(721\) −2.92820 −0.109052
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.94786 + 3.43400i 0.220898 + 0.127535i
\(726\) 0 0
\(727\) 22.4378 12.9545i 0.832173 0.480455i −0.0224233 0.999749i \(-0.507138\pi\)
0.854596 + 0.519293i \(0.173805\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.91447 + 6.78006i 0.144782 + 0.250770i
\(732\) 0 0
\(733\) −19.6603 + 34.0526i −0.726168 + 1.25776i 0.232323 + 0.972639i \(0.425367\pi\)
−0.958491 + 0.285121i \(0.907966\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 69.2693i 2.55157i
\(738\) 0 0
\(739\) 32.0000i 1.17714i 0.808447 + 0.588570i \(0.200309\pi\)
−0.808447 + 0.588570i \(0.799691\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.9000 25.8076i 0.546628 0.946788i −0.451874 0.892082i \(-0.649244\pi\)
0.998502 0.0547064i \(-0.0174223\pi\)
\(744\) 0 0
\(745\) 1.76795 + 3.06218i 0.0647726 + 0.112190i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.13681 + 0.656339i −0.0415382 + 0.0239821i
\(750\) 0 0
\(751\) 8.15064 + 4.70577i 0.297421 + 0.171716i 0.641284 0.767304i \(-0.278402\pi\)
−0.343863 + 0.939020i \(0.611736\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.07055 0.0753551
\(756\) 0 0
\(757\) −24.7846 −0.900812 −0.450406 0.892824i \(-0.648721\pi\)
−0.450406 + 0.892824i \(0.648721\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.82534 1.05386i −0.0661684 0.0382023i 0.466551 0.884494i \(-0.345496\pi\)
−0.532719 + 0.846292i \(0.678830\pi\)
\(762\) 0 0
\(763\) −2.49038 + 1.43782i −0.0901578 + 0.0520527i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −24.1803 41.8816i −0.873101 1.51226i
\(768\) 0 0
\(769\) 20.0167 34.6699i 0.721819 1.25023i −0.238451 0.971155i \(-0.576640\pi\)
0.960270 0.279073i \(-0.0900271\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 35.9745i 1.29391i 0.762527 + 0.646957i \(0.223959\pi\)
−0.762527 + 0.646957i \(0.776041\pi\)
\(774\) 0 0
\(775\) 9.46410i 0.339961i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.240237 + 0.416102i −0.00860737 + 0.0149084i
\(780\) 0 0
\(781\) −35.0526 60.7128i −1.25428 2.17248i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −17.8350 + 10.2970i −0.636557 + 0.367516i
\(786\) 0 0
\(787\) −21.4186 12.3660i −0.763490 0.440801i 0.0670573 0.997749i \(-0.478639\pi\)
−0.830547 + 0.556948i \(0.811972\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14.7985 −0.526173
\(792\) 0 0
\(793\) −5.33975 −0.189620
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −44.3632 25.6131i −1.57143 0.907264i −0.995995 0.0894138i \(-0.971501\pi\)
−0.575432 0.817850i \(-0.695166\pi\)
\(798\) 0 0
\(799\) −3.58846 + 2.07180i −0.126950 + 0.0732949i
\(800\) 0 0
\(801\) 0 0