Properties

Label 1008.4.bt.d.17.3
Level $1008$
Weight $4$
Character 1008.17
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.3
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.48442 - 14.6954i) q^{5} +(-3.52711 + 18.1813i) q^{7} +O(q^{10})\) \(q+(-8.48442 - 14.6954i) q^{5} +(-3.52711 + 18.1813i) q^{7} +(-60.3894 - 34.8658i) q^{11} +38.2009i q^{13} +(52.9872 - 91.7766i) q^{17} +(-50.3954 + 29.0958i) q^{19} +(-107.941 + 62.3199i) q^{23} +(-81.4706 + 141.111i) q^{25} -66.5957i q^{29} +(136.580 + 78.8547i) q^{31} +(297.108 - 102.425i) q^{35} +(-107.191 - 185.660i) q^{37} -448.509 q^{41} +320.784 q^{43} +(87.8142 + 152.099i) q^{47} +(-318.119 - 128.255i) q^{49} +(585.770 + 338.194i) q^{53} +1183.26i q^{55} +(-343.373 + 594.740i) q^{59} +(-91.1567 + 52.6294i) q^{61} +(561.379 - 324.112i) q^{65} +(426.641 - 738.964i) q^{67} -21.6022i q^{71} +(296.300 + 171.069i) q^{73} +(846.906 - 974.982i) q^{77} +(156.927 + 271.805i) q^{79} +627.751 q^{83} -1798.26 q^{85} +(207.480 + 359.367i) q^{89} +(-694.541 - 134.739i) q^{91} +(855.150 + 493.721i) q^{95} -223.956i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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
\(5\) −8.48442 14.6954i −0.758869 1.31440i −0.943428 0.331578i \(-0.892419\pi\)
0.184558 0.982822i \(-0.440914\pi\)
\(6\) 0 0
\(7\) −3.52711 + 18.1813i −0.190446 + 0.981698i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −60.3894 34.8658i −1.65528 0.955677i −0.974849 0.222865i \(-0.928459\pi\)
−0.680431 0.732812i \(-0.738208\pi\)
\(12\) 0 0
\(13\) 38.2009i 0.815001i 0.913205 + 0.407501i \(0.133600\pi\)
−0.913205 + 0.407501i \(0.866400\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 52.9872 91.7766i 0.755958 1.30936i −0.188938 0.981989i \(-0.560505\pi\)
0.944897 0.327369i \(-0.106162\pi\)
\(18\) 0 0
\(19\) −50.3954 + 29.0958i −0.608499 + 0.351317i −0.772378 0.635163i \(-0.780933\pi\)
0.163879 + 0.986481i \(0.447599\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −107.941 + 62.3199i −0.978578 + 0.564982i −0.901841 0.432069i \(-0.857784\pi\)
−0.0767375 + 0.997051i \(0.524450\pi\)
\(24\) 0 0
\(25\) −81.4706 + 141.111i −0.651765 + 1.12889i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 66.5957i 0.426431i −0.977005 0.213216i \(-0.931606\pi\)
0.977005 0.213216i \(-0.0683937\pi\)
\(30\) 0 0
\(31\) 136.580 + 78.8547i 0.791309 + 0.456862i 0.840423 0.541931i \(-0.182307\pi\)
−0.0491145 + 0.998793i \(0.515640\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 297.108 102.425i 1.43487 0.494658i
\(36\) 0 0
\(37\) −107.191 185.660i −0.476271 0.824926i 0.523359 0.852112i \(-0.324679\pi\)
−0.999630 + 0.0271864i \(0.991345\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −448.509 −1.70842 −0.854212 0.519925i \(-0.825960\pi\)
−0.854212 + 0.519925i \(0.825960\pi\)
\(42\) 0 0
\(43\) 320.784 1.13765 0.568827 0.822457i \(-0.307397\pi\)
0.568827 + 0.822457i \(0.307397\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 87.8142 + 152.099i 0.272532 + 0.472040i 0.969510 0.245054i \(-0.0788056\pi\)
−0.696977 + 0.717093i \(0.745472\pi\)
\(48\) 0 0
\(49\) −318.119 128.255i −0.927461 0.373921i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 585.770 + 338.194i 1.51815 + 0.876502i 0.999772 + 0.0213470i \(0.00679548\pi\)
0.518373 + 0.855155i \(0.326538\pi\)
\(54\) 0 0
\(55\) 1183.26i 2.90093i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −343.373 + 594.740i −0.757685 + 1.31235i 0.186344 + 0.982485i \(0.440336\pi\)
−0.944028 + 0.329864i \(0.892997\pi\)
\(60\) 0 0
\(61\) −91.1567 + 52.6294i −0.191335 + 0.110467i −0.592607 0.805492i \(-0.701901\pi\)
0.401272 + 0.915959i \(0.368568\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 561.379 324.112i 1.07124 0.618479i
\(66\) 0 0
\(67\) 426.641 738.964i 0.777948 1.34745i −0.155174 0.987887i \(-0.549594\pi\)
0.933122 0.359559i \(-0.117073\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 21.6022i 0.0361086i −0.999837 0.0180543i \(-0.994253\pi\)
0.999837 0.0180543i \(-0.00574718\pi\)
\(72\) 0 0
\(73\) 296.300 + 171.069i 0.475059 + 0.274276i 0.718355 0.695676i \(-0.244895\pi\)
−0.243296 + 0.969952i \(0.578229\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 846.906 974.982i 1.25343 1.44298i
\(78\) 0 0
\(79\) 156.927 + 271.805i 0.223489 + 0.387095i 0.955865 0.293806i \(-0.0949219\pi\)
−0.732376 + 0.680901i \(0.761589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 627.751 0.830176 0.415088 0.909781i \(-0.363751\pi\)
0.415088 + 0.909781i \(0.363751\pi\)
\(84\) 0 0
\(85\) −1798.26 −2.29469
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 207.480 + 359.367i 0.247111 + 0.428009i 0.962723 0.270489i \(-0.0871854\pi\)
−0.715612 + 0.698498i \(0.753852\pi\)
\(90\) 0 0
\(91\) −694.541 134.739i −0.800085 0.155214i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 855.150 + 493.721i 0.923543 + 0.533208i
\(96\) 0 0
\(97\) 223.956i 0.234426i −0.993107 0.117213i \(-0.962604\pi\)
0.993107 0.117213i \(-0.0373960\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 974.570 1688.01i 0.960133 1.66300i 0.237973 0.971272i \(-0.423517\pi\)
0.722160 0.691727i \(-0.243150\pi\)
\(102\) 0 0
\(103\) 755.905 436.422i 0.723122 0.417495i −0.0927787 0.995687i \(-0.529575\pi\)
0.815901 + 0.578192i \(0.196242\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −490.143 + 282.984i −0.442840 + 0.255674i −0.704802 0.709404i \(-0.748964\pi\)
0.261961 + 0.965078i \(0.415631\pi\)
\(108\) 0 0
\(109\) 781.523 1353.64i 0.686755 1.18949i −0.286127 0.958192i \(-0.592368\pi\)
0.972882 0.231303i \(-0.0742988\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1609.24i 1.33969i 0.742502 + 0.669844i \(0.233639\pi\)
−0.742502 + 0.669844i \(0.766361\pi\)
\(114\) 0 0
\(115\) 1831.64 + 1057.50i 1.48523 + 0.857495i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1481.72 + 1287.08i 1.14142 + 0.991484i
\(120\) 0 0
\(121\) 1765.75 + 3058.37i 1.32664 + 2.29780i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 643.818 0.460679
\(126\) 0 0
\(127\) 741.194 0.517877 0.258938 0.965894i \(-0.416627\pi\)
0.258938 + 0.965894i \(0.416627\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −132.345 229.229i −0.0882676 0.152884i 0.818511 0.574490i \(-0.194800\pi\)
−0.906779 + 0.421606i \(0.861466\pi\)
\(132\) 0 0
\(133\) −351.249 1018.88i −0.229001 0.664269i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1028.68 + 593.907i 0.641502 + 0.370372i 0.785193 0.619251i \(-0.212564\pi\)
−0.143691 + 0.989623i \(0.545897\pi\)
\(138\) 0 0
\(139\) 1080.39i 0.659262i 0.944110 + 0.329631i \(0.106924\pi\)
−0.944110 + 0.329631i \(0.893076\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1331.91 2306.93i 0.778878 1.34906i
\(144\) 0 0
\(145\) −978.653 + 565.026i −0.560501 + 0.323606i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.97793 4.60606i 0.00438643 0.00253251i −0.497805 0.867289i \(-0.665861\pi\)
0.502192 + 0.864756i \(0.332527\pi\)
\(150\) 0 0
\(151\) −978.571 + 1694.94i −0.527384 + 0.913456i 0.472106 + 0.881542i \(0.343494\pi\)
−0.999491 + 0.0319147i \(0.989840\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2676.15i 1.38679i
\(156\) 0 0
\(157\) −188.970 109.102i −0.0960600 0.0554603i 0.451200 0.892423i \(-0.350996\pi\)
−0.547260 + 0.836962i \(0.684329\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −752.336 2182.32i −0.368276 1.06827i
\(162\) 0 0
\(163\) 1095.52 + 1897.50i 0.526430 + 0.911803i 0.999526 + 0.0307921i \(0.00980298\pi\)
−0.473096 + 0.881011i \(0.656864\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1567.81 0.726471 0.363235 0.931697i \(-0.381672\pi\)
0.363235 + 0.931697i \(0.381672\pi\)
\(168\) 0 0
\(169\) 737.693 0.335773
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 388.338 + 672.621i 0.170664 + 0.295598i 0.938652 0.344866i \(-0.112076\pi\)
−0.767989 + 0.640464i \(0.778742\pi\)
\(174\) 0 0
\(175\) −2278.23 1978.96i −0.984103 0.854829i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1513.06 + 873.568i 0.631797 + 0.364768i 0.781448 0.623971i \(-0.214482\pi\)
−0.149650 + 0.988739i \(0.547815\pi\)
\(180\) 0 0
\(181\) 1787.57i 0.734085i 0.930204 + 0.367042i \(0.119630\pi\)
−0.930204 + 0.367042i \(0.880370\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1818.90 + 3150.43i −0.722855 + 1.25202i
\(186\) 0 0
\(187\) −6399.73 + 3694.89i −2.50265 + 1.44490i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −588.184 + 339.588i −0.222825 + 0.128648i −0.607258 0.794505i \(-0.707730\pi\)
0.384433 + 0.923153i \(0.374397\pi\)
\(192\) 0 0
\(193\) −1698.73 + 2942.29i −0.633562 + 1.09736i 0.353255 + 0.935527i \(0.385075\pi\)
−0.986818 + 0.161835i \(0.948259\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3407.09i 1.23221i −0.787665 0.616104i \(-0.788710\pi\)
0.787665 0.616104i \(-0.211290\pi\)
\(198\) 0 0
\(199\) −181.152 104.588i −0.0645302 0.0372565i 0.467388 0.884052i \(-0.345195\pi\)
−0.531918 + 0.846796i \(0.678529\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1210.80 + 234.890i 0.418627 + 0.0812122i
\(204\) 0 0
\(205\) 3805.34 + 6591.04i 1.29647 + 2.24555i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4057.79 1.34298
\(210\) 0 0
\(211\) −2275.52 −0.742434 −0.371217 0.928546i \(-0.621059\pi\)
−0.371217 + 0.928546i \(0.621059\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2721.67 4714.06i −0.863331 1.49533i
\(216\) 0 0
\(217\) −1915.42 + 2205.08i −0.599202 + 0.689818i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3505.94 + 2024.16i 1.06713 + 0.616107i
\(222\) 0 0
\(223\) 3401.49i 1.02144i −0.859747 0.510719i \(-0.829379\pi\)
0.859747 0.510719i \(-0.170621\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1502.78 + 2602.90i −0.439397 + 0.761058i −0.997643 0.0686172i \(-0.978141\pi\)
0.558246 + 0.829676i \(0.311475\pi\)
\(228\) 0 0
\(229\) −397.955 + 229.759i −0.114837 + 0.0663009i −0.556318 0.830969i \(-0.687786\pi\)
0.441482 + 0.897270i \(0.354453\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5044.86 + 2912.65i −1.41845 + 0.818944i −0.996163 0.0875166i \(-0.972107\pi\)
−0.422290 + 0.906461i \(0.638774\pi\)
\(234\) 0 0
\(235\) 1490.10 2580.94i 0.413633 0.716433i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4219.42i 1.14197i 0.820959 + 0.570987i \(0.193439\pi\)
−0.820959 + 0.570987i \(0.806561\pi\)
\(240\) 0 0
\(241\) 2837.81 + 1638.41i 0.758503 + 0.437922i 0.828758 0.559607i \(-0.189048\pi\)
−0.0702548 + 0.997529i \(0.522381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 814.292 + 5763.07i 0.212340 + 1.50281i
\(246\) 0 0
\(247\) −1111.48 1925.15i −0.286324 0.495928i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3221.43 0.810100 0.405050 0.914294i \(-0.367254\pi\)
0.405050 + 0.914294i \(0.367254\pi\)
\(252\) 0 0
\(253\) 8691.34 2.15976
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −411.892 713.418i −0.0999732 0.173159i 0.811700 0.584074i \(-0.198542\pi\)
−0.911673 + 0.410916i \(0.865209\pi\)
\(258\) 0 0
\(259\) 3753.61 1294.02i 0.900532 0.310450i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2955.61 + 1706.42i 0.692969 + 0.400086i 0.804723 0.593650i \(-0.202314\pi\)
−0.111754 + 0.993736i \(0.535647\pi\)
\(264\) 0 0
\(265\) 11477.5i 2.66060i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3209.91 5559.73i 0.727553 1.26016i −0.230361 0.973105i \(-0.573991\pi\)
0.957914 0.287054i \(-0.0926758\pi\)
\(270\) 0 0
\(271\) −7375.18 + 4258.06i −1.65317 + 0.954461i −0.677419 + 0.735597i \(0.736902\pi\)
−0.975756 + 0.218863i \(0.929765\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9839.92 5681.08i 2.15771 1.24575i
\(276\) 0 0
\(277\) 3028.50 5245.52i 0.656914 1.13781i −0.324497 0.945887i \(-0.605195\pi\)
0.981410 0.191921i \(-0.0614717\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4217.81i 0.895421i 0.894179 + 0.447710i \(0.147760\pi\)
−0.894179 + 0.447710i \(0.852240\pi\)
\(282\) 0 0
\(283\) 708.451 + 409.024i 0.148809 + 0.0859151i 0.572556 0.819866i \(-0.305952\pi\)
−0.423747 + 0.905781i \(0.639285\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1581.94 8154.48i 0.325363 1.67716i
\(288\) 0 0
\(289\) −3158.79 5471.19i −0.642945 1.11361i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −699.920 −0.139556 −0.0697778 0.997563i \(-0.522229\pi\)
−0.0697778 + 0.997563i \(0.522229\pi\)
\(294\) 0 0
\(295\) 11653.3 2.29993
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2380.67 4123.45i −0.460461 0.797542i
\(300\) 0 0
\(301\) −1131.44 + 5832.27i −0.216662 + 1.11683i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1546.82 + 893.059i 0.290396 + 0.167660i
\(306\) 0 0
\(307\) 8523.88i 1.58464i −0.610108 0.792319i \(-0.708874\pi\)
0.610108 0.792319i \(-0.291126\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1170.89 + 2028.04i −0.213489 + 0.369774i −0.952804 0.303586i \(-0.901816\pi\)
0.739315 + 0.673360i \(0.235149\pi\)
\(312\) 0 0
\(313\) 3462.94 1999.33i 0.625357 0.361050i −0.153595 0.988134i \(-0.549085\pi\)
0.778952 + 0.627084i \(0.215752\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6056.74 + 3496.86i −1.07312 + 0.619569i −0.929034 0.369996i \(-0.879359\pi\)
−0.144091 + 0.989564i \(0.546026\pi\)
\(318\) 0 0
\(319\) −2321.91 + 4021.67i −0.407531 + 0.705864i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6166.82i 1.06232i
\(324\) 0 0
\(325\) −5390.57 3112.25i −0.920047 0.531189i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3075.08 + 1060.11i −0.515303 + 0.177646i
\(330\) 0 0
\(331\) −2095.81 3630.05i −0.348025 0.602797i 0.637874 0.770141i \(-0.279814\pi\)
−0.985899 + 0.167344i \(0.946481\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −14479.2 −2.36144
\(336\) 0 0
\(337\) 2226.74 0.359936 0.179968 0.983672i \(-0.442401\pi\)
0.179968 + 0.983672i \(0.442401\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5498.67 9523.98i −0.873225 1.51247i
\(342\) 0 0
\(343\) 3453.88 5331.45i 0.543708 0.839274i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1073.31 + 619.673i 0.166046 + 0.0958668i 0.580720 0.814103i \(-0.302771\pi\)
−0.414674 + 0.909970i \(0.636104\pi\)
\(348\) 0 0
\(349\) 8806.73i 1.35075i 0.737473 + 0.675377i \(0.236019\pi\)
−0.737473 + 0.675377i \(0.763981\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2424.56 4199.45i 0.365570 0.633185i −0.623298 0.781985i \(-0.714208\pi\)
0.988867 + 0.148799i \(0.0475409\pi\)
\(354\) 0 0
\(355\) −317.454 + 183.282i −0.0474612 + 0.0274017i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1691.26 + 976.450i −0.248639 + 0.143552i −0.619141 0.785280i \(-0.712519\pi\)
0.370502 + 0.928832i \(0.379186\pi\)
\(360\) 0 0
\(361\) −1736.37 + 3007.49i −0.253152 + 0.438473i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5805.69i 0.832557i
\(366\) 0 0
\(367\) 1159.84 + 669.633i 0.164968 + 0.0952440i 0.580211 0.814466i \(-0.302970\pi\)
−0.415243 + 0.909710i \(0.636304\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8214.89 + 9457.21i −1.14958 + 1.32343i
\(372\) 0 0
\(373\) 3493.37 + 6050.69i 0.484933 + 0.839928i 0.999850 0.0173119i \(-0.00551082\pi\)
−0.514918 + 0.857240i \(0.672177\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2544.01 0.347542
\(378\) 0 0
\(379\) −5328.03 −0.722117 −0.361059 0.932543i \(-0.617585\pi\)
−0.361059 + 0.932543i \(0.617585\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2600.62 4504.40i −0.346959 0.600951i 0.638749 0.769416i \(-0.279452\pi\)
−0.985708 + 0.168465i \(0.946119\pi\)
\(384\) 0 0
\(385\) −21513.3 4173.51i −2.84784 0.552472i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2739.35 + 1581.56i 0.357045 + 0.206140i 0.667784 0.744355i \(-0.267243\pi\)
−0.310739 + 0.950495i \(0.600576\pi\)
\(390\) 0 0
\(391\) 13208.6i 1.70841i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2662.87 4612.22i 0.339198 0.587509i
\(396\) 0 0
\(397\) 6689.56 3862.22i 0.845692 0.488260i −0.0135032 0.999909i \(-0.504298\pi\)
0.859195 + 0.511649i \(0.170965\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8214.37 + 4742.57i −1.02296 + 0.590605i −0.914959 0.403546i \(-0.867778\pi\)
−0.107999 + 0.994151i \(0.534444\pi\)
\(402\) 0 0
\(403\) −3012.32 + 5217.49i −0.372343 + 0.644917i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14949.2i 1.82064i
\(408\) 0 0
\(409\) −13564.1 7831.22i −1.63985 0.946770i −0.980882 0.194602i \(-0.937659\pi\)
−0.658971 0.752168i \(-0.729008\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −9602.03 8340.69i −1.14403 0.993749i
\(414\) 0 0
\(415\) −5326.10 9225.07i −0.629995 1.09118i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13214.3 −1.54071 −0.770357 0.637613i \(-0.779922\pi\)
−0.770357 + 0.637613i \(0.779922\pi\)
\(420\) 0 0
\(421\) −3985.81 −0.461417 −0.230709 0.973023i \(-0.574104\pi\)
−0.230709 + 0.973023i \(0.574104\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8633.80 + 14954.2i 0.985414 + 1.70679i
\(426\) 0 0
\(427\) −635.350 1842.98i −0.0720064 0.208871i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −875.377 505.399i −0.0978316 0.0564831i 0.450286 0.892884i \(-0.351322\pi\)
−0.548118 + 0.836401i \(0.684655\pi\)
\(432\) 0 0
\(433\) 10704.5i 1.18805i −0.804446 0.594026i \(-0.797538\pi\)
0.804446 0.594026i \(-0.202462\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3626.49 6281.26i 0.396976 0.687583i
\(438\) 0 0
\(439\) 5935.42 3426.82i 0.645289 0.372558i −0.141360 0.989958i \(-0.545147\pi\)
0.786649 + 0.617400i \(0.211814\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13821.3 + 7979.76i −1.48233 + 0.855823i −0.999799 0.0200558i \(-0.993616\pi\)
−0.482531 + 0.875879i \(0.660282\pi\)
\(444\) 0 0
\(445\) 3520.70 6098.03i 0.375050 0.649605i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2486.47i 0.261345i −0.991426 0.130673i \(-0.958286\pi\)
0.991426 0.130673i \(-0.0417137\pi\)
\(450\) 0 0
\(451\) 27085.2 + 15637.6i 2.82792 + 1.63270i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3912.73 + 11349.8i 0.403147 + 1.16942i
\(456\) 0 0
\(457\) −2649.67 4589.36i −0.271217 0.469762i 0.697957 0.716140i \(-0.254093\pi\)
−0.969174 + 0.246378i \(0.920759\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −633.711 −0.0640236 −0.0320118 0.999487i \(-0.510191\pi\)
−0.0320118 + 0.999487i \(0.510191\pi\)
\(462\) 0 0
\(463\) −1208.19 −0.121273 −0.0606366 0.998160i \(-0.519313\pi\)
−0.0606366 + 0.998160i \(0.519313\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2211.57 3830.55i −0.219142 0.379564i 0.735404 0.677629i \(-0.236992\pi\)
−0.954546 + 0.298064i \(0.903659\pi\)
\(468\) 0 0
\(469\) 11930.5 + 10363.3i 1.17463 + 1.02033i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −19372.0 11184.4i −1.88314 1.08723i
\(474\) 0 0
\(475\) 9481.80i 0.915905i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1210.61 2096.84i 0.115479 0.200015i −0.802492 0.596662i \(-0.796493\pi\)
0.917971 + 0.396648i \(0.129827\pi\)
\(480\) 0 0
\(481\) 7092.36 4094.78i 0.672315 0.388162i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3291.14 + 1900.14i −0.308130 + 0.177899i
\(486\) 0 0
\(487\) 5304.79 9188.16i 0.493599 0.854939i −0.506373 0.862314i \(-0.669014\pi\)
0.999973 + 0.00737514i \(0.00234760\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16314.2i 1.49949i −0.661728 0.749744i \(-0.730176\pi\)
0.661728 0.749744i \(-0.269824\pi\)
\(492\) 0 0
\(493\) −6111.92 3528.72i −0.558351 0.322364i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 392.756 + 76.1934i 0.0354478 + 0.00687675i
\(498\) 0 0
\(499\) −1876.73 3250.60i −0.168365 0.291617i 0.769480 0.638671i \(-0.220515\pi\)
−0.937845 + 0.347054i \(0.887182\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −9135.50 −0.809805 −0.404903 0.914360i \(-0.632695\pi\)
−0.404903 + 0.914360i \(0.632695\pi\)
\(504\) 0 0
\(505\) −33074.6 −2.91446
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.73217 3.00021i −0.000150839 0.000261261i 0.865950 0.500131i \(-0.166715\pi\)
−0.866101 + 0.499869i \(0.833381\pi\)
\(510\) 0 0
\(511\) −4155.34 + 4783.75i −0.359729 + 0.414130i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12826.8 7405.57i −1.09751 0.633648i
\(516\) 0 0
\(517\) 12246.9i 1.04181i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5027.11 + 8707.20i −0.422728 + 0.732187i −0.996205 0.0870347i \(-0.972261\pi\)
0.573477 + 0.819222i \(0.305594\pi\)
\(522\) 0 0
\(523\) 1142.12 659.405i 0.0954905 0.0551314i −0.451494 0.892274i \(-0.649109\pi\)
0.546985 + 0.837143i \(0.315776\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14474.0 8356.59i 1.19639 0.690737i
\(528\) 0 0
\(529\) 1684.04 2916.83i 0.138410 0.239733i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 17133.4i 1.39237i
\(534\) 0 0
\(535\) 8317.16 + 4801.91i 0.672116 + 0.388046i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14739.3 + 18836.7i 1.17786 + 1.50530i
\(540\) 0 0
\(541\) 2144.41 + 3714.23i 0.170417 + 0.295170i 0.938566 0.345101i \(-0.112155\pi\)
−0.768149 + 0.640271i \(0.778822\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −26523.1 −2.08463
\(546\) 0 0
\(547\) 8456.92 0.661045 0.330523 0.943798i \(-0.392775\pi\)
0.330523 + 0.943798i \(0.392775\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1937.65 + 3356.11i 0.149813 + 0.259483i
\(552\) 0 0
\(553\) −5495.27 + 1894.45i −0.422573 + 0.145678i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12043.6 + 6953.36i 0.916163 + 0.528947i 0.882409 0.470483i \(-0.155920\pi\)
0.0337539 + 0.999430i \(0.489254\pi\)
\(558\) 0 0
\(559\) 12254.2i 0.927190i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9052.19 + 15678.8i −0.677627 + 1.17369i 0.298066 + 0.954545i \(0.403658\pi\)
−0.975693 + 0.219140i \(0.929675\pi\)
\(564\) 0 0
\(565\) 23648.5 13653.5i 1.76089 1.01665i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 664.706 383.768i 0.0489735 0.0282749i −0.475313 0.879817i \(-0.657665\pi\)
0.524287 + 0.851542i \(0.324332\pi\)
\(570\) 0 0
\(571\) −10674.7 + 18489.2i −0.782354 + 1.35508i 0.148213 + 0.988955i \(0.452648\pi\)
−0.930567 + 0.366121i \(0.880686\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 20309.0i 1.47294i
\(576\) 0 0
\(577\) 14315.8 + 8265.21i 1.03288 + 0.596335i 0.917809 0.397022i \(-0.129956\pi\)
0.115073 + 0.993357i \(0.463290\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2214.15 + 11413.3i −0.158104 + 0.814982i
\(582\) 0 0
\(583\) −23582.9 40846.7i −1.67530 2.90171i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10940.7 −0.769286 −0.384643 0.923065i \(-0.625675\pi\)
−0.384643 + 0.923065i \(0.625675\pi\)
\(588\) 0 0
\(589\) −9177.36 −0.642014
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11096.9 + 19220.4i 0.768459 + 1.33101i 0.938398 + 0.345555i \(0.112309\pi\)
−0.169940 + 0.985454i \(0.554357\pi\)
\(594\) 0 0
\(595\) 6342.67 32694.7i 0.437015 2.25270i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11509.9 + 6645.23i 0.785110 + 0.453283i 0.838238 0.545304i \(-0.183586\pi\)
−0.0531284 + 0.998588i \(0.516919\pi\)
\(600\) 0 0
\(601\) 9590.78i 0.650942i −0.945552 0.325471i \(-0.894477\pi\)
0.945552 0.325471i \(-0.105523\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 29962.8 51897.0i 2.01349 3.48746i
\(606\) 0 0
\(607\) 3936.82 2272.93i 0.263247 0.151985i −0.362568 0.931957i \(-0.618100\pi\)
0.625815 + 0.779972i \(0.284767\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5810.30 + 3354.58i −0.384713 + 0.222114i
\(612\) 0 0
\(613\) −10676.4 + 18492.1i −0.703451 + 1.21841i 0.263796 + 0.964578i \(0.415025\pi\)
−0.967248 + 0.253835i \(0.918308\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9496.27i 0.619620i 0.950798 + 0.309810i \(0.100265\pi\)
−0.950798 + 0.309810i \(0.899735\pi\)
\(618\) 0 0
\(619\) −15773.7 9106.96i −1.02423 0.591340i −0.108905 0.994052i \(-0.534734\pi\)
−0.915327 + 0.402712i \(0.868068\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7265.56 + 2504.74i −0.467237 + 0.161076i
\(624\) 0 0
\(625\) 4721.41 + 8177.71i 0.302170 + 0.523374i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −22718.9 −1.44016
\(630\) 0 0
\(631\) 6711.25 0.423409 0.211704 0.977334i \(-0.432099\pi\)
0.211704 + 0.977334i \(0.432099\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6288.60 10892.2i −0.393001 0.680697i
\(636\) 0 0
\(637\) 4899.45 12152.4i 0.304746 0.755882i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 25619.6 + 14791.5i 1.57865 + 0.911434i 0.995048 + 0.0993938i \(0.0316904\pi\)
0.583602 + 0.812040i \(0.301643\pi\)
\(642\) 0 0
\(643\) 3793.02i 0.232631i −0.993212 0.116316i \(-0.962892\pi\)
0.993212 0.116316i \(-0.0371084\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5797.58 + 10041.7i −0.352282 + 0.610170i −0.986649 0.162862i \(-0.947927\pi\)
0.634367 + 0.773032i \(0.281261\pi\)
\(648\) 0 0
\(649\) 41472.2 23944.0i 2.50836 1.44820i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18076.2 10436.3i 1.08327 0.625427i 0.151494 0.988458i \(-0.451591\pi\)
0.931777 + 0.363031i \(0.118258\pi\)
\(654\) 0 0
\(655\) −2245.74 + 3889.74i −0.133967 + 0.232038i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 26007.1i 1.53732i −0.639659 0.768658i \(-0.720925\pi\)
0.639659 0.768658i \(-0.279075\pi\)
\(660\) 0 0
\(661\) 14619.8 + 8440.73i 0.860277 + 0.496681i 0.864105 0.503312i \(-0.167885\pi\)
−0.00382819 + 0.999993i \(0.501219\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11992.7 + 13806.3i −0.699334 + 0.805092i
\(666\) 0 0
\(667\) 4150.24 + 7188.42i 0.240926 + 0.417296i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7339.87 0.422284
\(672\) 0 0
\(673\) 2688.00 0.153960 0.0769799 0.997033i \(-0.475472\pi\)
0.0769799 + 0.997033i \(0.475472\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10001.4 + 17323.0i 0.567779 + 0.983422i 0.996785 + 0.0801203i \(0.0255305\pi\)
−0.429006 + 0.903301i \(0.641136\pi\)
\(678\) 0 0
\(679\) 4071.82 + 789.919i 0.230135 + 0.0446455i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 9088.08 + 5247.00i 0.509144 + 0.293955i 0.732482 0.680787i \(-0.238362\pi\)
−0.223337 + 0.974741i \(0.571695\pi\)
\(684\) 0 0
\(685\) 20155.8i 1.12425i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −12919.3 + 22376.9i −0.714350 + 1.23729i
\(690\) 0 0
\(691\) −2514.74 + 1451.88i −0.138444 + 0.0799310i −0.567622 0.823289i \(-0.692137\pi\)
0.429178 + 0.903220i \(0.358803\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 15876.8 9166.47i 0.866534 0.500294i
\(696\) 0 0
\(697\) −23765.3 + 41162.6i −1.29150 + 2.23694i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5829.71i 0.314102i 0.987591 + 0.157051i \(0.0501986\pi\)
−0.987591 + 0.157051i \(0.949801\pi\)
\(702\) 0 0
\(703\) 10803.8 + 6237.59i 0.579621 + 0.334644i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27252.7 + 23672.7i 1.44971 + 1.25927i
\(708\) 0 0
\(709\) 7940.28 + 13753.0i 0.420597 + 0.728495i 0.995998 0.0893760i \(-0.0284873\pi\)
−0.575401 + 0.817872i \(0.695154\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −19656.9 −1.03248
\(714\) 0 0
\(715\) −45201.7 −2.36427
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2601.36 + 4505.68i 0.134929 + 0.233705i 0.925570 0.378575i \(-0.123586\pi\)
−0.790641 + 0.612280i \(0.790253\pi\)
\(720\) 0 0
\(721\) 5268.56 + 15282.6i 0.272138 + 0.789397i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9397.40 + 5425.59i 0.481394 + 0.277933i
\(726\) 0 0
\(727\) 37948.0i 1.93592i 0.251107 + 0.967959i \(0.419206\pi\)
−0.251107 + 0.967959i \(0.580794\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16997.5 29440.5i 0.860019 1.48960i
\(732\) 0 0
\(733\) −15869.6 + 9162.32i −0.799669 + 0.461689i −0.843355 0.537356i \(-0.819423\pi\)
0.0436864 + 0.999045i \(0.486090\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −51529.2 + 29750.4i −2.57545 + 1.48693i
\(738\) 0 0
\(739\) −9963.10 + 17256.6i −0.495939 + 0.858991i −0.999989 0.00468324i \(-0.998509\pi\)
0.504050 + 0.863674i \(0.331843\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7621.89i 0.376339i 0.982137 + 0.188170i \(0.0602555\pi\)
−0.982137 + 0.188170i \(0.939745\pi\)
\(744\) 0 0
\(745\) −135.376 78.1595i −0.00665745 0.00384368i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3416.23 9909.55i −0.166657 0.483428i
\(750\) 0 0
\(751\) −17180.8 29758.1i −0.834803 1.44592i −0.894191 0.447687i \(-0.852248\pi\)
0.0593874 0.998235i \(-0.481085\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 33210.4 1.60086
\(756\) 0 0
\(757\) 13327.2 0.639874 0.319937 0.947439i \(-0.396338\pi\)
0.319937 + 0.947439i \(0.396338\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −11743.9 20341.0i −0.559414 0.968934i −0.997545 0.0700230i \(-0.977693\pi\)
0.438131 0.898911i \(-0.355641\pi\)
\(762\) 0 0
\(763\) 21854.4 + 18983.5i 1.03693 + 0.900720i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22719.6 13117.2i −1.06957 0.617514i
\(768\) 0 0
\(769\) 27145.7i 1.27295i 0.771297 + 0.636476i \(0.219609\pi\)
−0.771297 + 0.636476i \(0.780391\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10441.9 18085.9i 0.485859 0.841532i −0.514009 0.857785i \(-0.671840\pi\)
0.999868 + 0.0162524i \(0.00517352\pi\)
\(774\) 0 0
\(775\) −22254.6 + 12848.7i −1.03149 + 0.595533i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22602.8 13049.7i 1.03957 0.600199i
\(780\) 0 0
\(781\) −753.180 + 1304.55i −0.0345082 + 0.0597699i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3702.66i 0.168348i
\(786\) 0 0
\(787\) 690.527 + 398.676i 0.0312766 + 0.0180575i 0.515557 0.856855i \(-0.327585\pi\)
−0.484280 + 0.874913i \(0.660918\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −29258.1 5675.97i −1.31517 0.255138i
\(792\) 0 0
\(793\) −2010.49 3482.27i −0.0900309 0.155938i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 14974.0 0.665504 0.332752 0.943014i \(-0.392023\pi\)
0.332752 + 0.943014i \(0.392023\pi\)
\(798\) 0 0
\(799\) 18612.1 0.824092
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −11928.9 20661.5i −0.524238 0.908006