Properties

Label 2592.2.s.b.863.1
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 863.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2592.863
Dual form 2592.2.s.b.1727.1

$q$-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 0.0768413 0.997043i \(-0.475517\pi\)
−0.825044 + 0.565068i \(0.808850\pi\)
\(6\) 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 \(0.126217\pi\)
−0.126733 + 0.991937i \(0.540449\pi\)
\(12\) 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 \(-0.965323\pi\)
0.994072 0.108726i \(-0.0346770\pi\)
\(18\) 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 −0.782839 0.622224i \(-0.786229\pi\)
0.930281 + 0.366847i \(0.119563\pi\)
\(24\) 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 0.00337538 0.999994i \(-0.498926\pi\)
0.867708 + 0.497074i \(0.165592\pi\)
\(30\) 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 0.525407 0.850851i \(-0.323913\pi\)
−0.474155 + 0.880441i \(0.657246\pi\)
\(42\) 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 0.646816 0.762646i \(-0.276100\pi\)
−0.983879 + 0.178836i \(0.942767\pi\)
\(48\) 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 \(0.0538057\pi\)
−0.985747 + 0.168232i \(0.946194\pi\)
\(54\) 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 \(-0.584198\pi\)
0.966625 0.256194i \(-0.0824687\pi\)
\(60\) 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 \(-0.788979\pi\)
−0.788185 + 0.615439i \(0.788979\pi\)
\(72\) 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 \(0.0300178\pi\)
−0.416230 + 0.909259i \(0.636649\pi\)
\(84\) 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 \(0.290787\pi\)
−0.610951 + 0.791669i \(0.709213\pi\)
\(90\) 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 −0.746709 0.665151i \(-0.768367\pi\)
0.202683 + 0.979244i \(0.435034\pi\)
\(102\) 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 \(-0.527624\pi\)
−0.0866752 + 0.996237i \(0.527624\pi\)
\(108\) 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 \(-0.933558\pi\)
−0.668605 0.743617i \(-0.733108\pi\)
\(114\) 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 −0.868235 0.496154i \(-0.834745\pi\)
0.863799 + 0.503836i \(0.168079\pi\)
\(132\) 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 −0.668959 0.743299i \(-0.733260\pi\)
0.309236 + 0.950985i \(0.399927\pi\)
\(138\) 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 0.433665 0.901074i \(-0.357220\pi\)
−0.563521 + 0.826102i \(0.690554\pi\)
\(150\) 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 −0.582800 0.812616i \(-0.698043\pi\)
0.995146 + 0.0984115i \(0.0313761\pi\)
\(168\) 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 −0.0889883 0.996033i \(-0.528363\pi\)
0.818095 + 0.575082i \(0.195030\pi\)
\(174\) 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 \(-0.195468\pi\)
0.817303 + 0.576208i \(0.195468\pi\)
\(180\) 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 \(-0.901470\pi\)
0.212425 0.977177i \(-0.431864\pi\)
\(192\) 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 \(-0.886958\pi\)
0.937601 0.347714i \(-0.113042\pi\)
\(198\) 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 \(0.0286284\pi\)
−0.420195 + 0.907434i \(0.638038\pi\)
\(228\) 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 \(-0.788815\pi\)
0.787869 0.615843i \(-0.211185\pi\)
\(234\) 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 \(-0.622153\pi\)
0.990238 0.139390i \(-0.0445140\pi\)
\(240\) 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 \(-0.228926\pi\)
0.752338 + 0.658777i \(0.228926\pi\)
\(252\) 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 0.478372 0.878157i \(-0.341227\pi\)
−0.521321 + 0.853361i \(0.674560\pi\)
\(258\) 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 0.728024 0.685552i \(-0.240439\pi\)
−0.957717 + 0.287711i \(0.907106\pi\)
\(264\) 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 \(0.244170\pi\)
−0.719939 + 0.694037i \(0.755830\pi\)
\(270\) 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 −0.174092 0.984729i \(-0.555699\pi\)
0.765755 + 0.643133i \(0.222366\pi\)
\(282\) 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 −0.242715 0.970098i \(-0.578038\pi\)
−0.961487 + 0.274852i \(0.911371\pi\)
\(294\) 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 \(0.407575\pi\)
−0.972923 + 0.231128i \(0.925759\pi\)
\(312\) 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 −0.667161 0.744913i \(-0.732491\pi\)
0.311533 + 0.950235i \(0.399157\pi\)
\(318\) 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 −0.989476 0.144700i \(-0.953778\pi\)
0.620052 + 0.784561i \(0.287112\pi\)
\(348\) 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 −0.978599 0.205776i \(-0.934028\pi\)
−0.311092 + 0.950380i \(0.600695\pi\)
\(354\) 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 \(-0.520590\pi\)
−0.0646396 + 0.997909i \(0.520590\pi\)
\(360\) 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 −0.999946 0.0103947i \(-0.996691\pi\)
0.508975 + 0.860781i \(0.330025\pi\)
\(384\) 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 −0.716751 0.697330i \(-0.754371\pi\)
0.245530 + 0.969389i \(0.421038\pi\)
\(390\) 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 0.0349403 0.999389i \(-0.488876\pi\)
−0.848026 + 0.529954i \(0.822209\pi\)
\(402\) 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 −0.845952 0.533259i \(-0.820967\pi\)
0.884792 + 0.465986i \(0.154300\pi\)
\(420\) 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 \(-0.565512\pi\)
−0.204361 + 0.978896i \(0.565512\pi\)
\(432\) 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 0.589398 0.807843i \(-0.299365\pi\)
−0.994311 + 0.106512i \(0.966032\pi\)
\(444\) 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 \(-0.817338\pi\)
0.839818 0.542868i \(-0.182662\pi\)
\(450\) 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 −0.997657 0.0684108i \(-0.978207\pi\)
−0.439583 + 0.898202i \(0.644874\pi\)
\(462\) 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 \(-0.590103\pi\)
−0.279303 + 0.960203i \(0.590103\pi\)
\(468\) 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 \(-0.913182\pi\)
0.248229 0.968701i \(-0.420151\pi\)
\(480\) 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 −0.659374 0.751815i \(-0.729179\pi\)
0.980778 + 0.195127i \(0.0625119\pi\)
\(492\) 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 \(-0.275137\pi\)
0.649120 + 0.760686i \(0.275137\pi\)
\(504\) 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 0.996139 0.0877870i \(-0.0279795\pi\)
0.422044 + 0.906575i \(0.361313\pi\)
\(510\) 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 \(0.108632\pi\)
−0.942328 + 0.334691i \(0.891368\pi\)
\(522\) 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 \(-0.986283\pi\)
0.999072 0.0430787i \(-0.0137166\pi\)
\(558\) 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 −0.942007 0.335592i \(-0.891064\pi\)
0.761635 + 0.648006i \(0.224397\pi\)
\(564\) 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 −0.622221 0.782842i \(-0.713769\pi\)
0.366850 + 0.930280i \(0.380436\pi\)
\(570\) 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 0.848042 0.529928i \(-0.177781\pi\)
−0.882953 + 0.469462i \(0.844448\pi\)
\(588\) 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 \(-0.857017\pi\)
0.900798 0.434239i \(-0.142983\pi\)
\(594\) 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 −0.680305 0.732929i \(-0.738153\pi\)
0.974888 + 0.222696i \(0.0714859\pi\)
\(600\) 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 0.652977 0.757378i \(-0.273520\pi\)
−0.329420 + 0.944184i \(0.606853\pi\)
\(618\) 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 −0.974704 0.223502i \(-0.928251\pi\)
−0.293794 + 0.955869i \(0.594918\pi\)
\(642\) 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 \(-0.393759\pi\)
0.327603 + 0.944815i \(0.393759\pi\)
\(648\) 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 0.299251 0.954175i \(-0.403263\pi\)
−0.676714 + 0.736246i \(0.736597\pi\)
\(654\) 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 0.996325 0.0856577i \(-0.0272991\pi\)
−0.572344 + 0.820014i \(0.693966\pi\)
\(660\) 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 −0.978982 0.203946i \(-0.934623\pi\)
−0.312869 + 0.949796i \(0.601290\pi\)
\(678\) 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 \(-0.467182\pi\)
0.102920 + 0.994690i \(0.467182\pi\)
\(684\) 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 \(0.0486952\pi\)
−0.988321 + 0.152384i \(0.951305\pi\)
\(702\) 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 \(-0.262600\pi\)
0.678570 + 0.734535i \(0.262600\pi\)
\(720\) 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 \(0.350756\pi\)
−0.998502 + 0.0547064i \(0.982578\pi\)
\(744\) 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 0.532719 0.846292i \(-0.321170\pi\)
−0.466551 + 0.884494i \(0.654504\pi\)
\(762\) 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 \(-0.776041\pi\)
0.762527 0.646957i \(-0.223959\pi\)
\(774\) 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 \(0.0284994\pi\)
0.575432 + 0.817850i \(0.304834\pi\)
\(798\) 0 0
\(799\) −3.58846 + 2.07180i −0.126950 + 0.0732949i
\(800\) 0 0
\(801\) 0 0