Properties

Label 252.9.z.d.73.4
Level $252$
Weight $9$
Character 252.73
Analytic conductor $102.659$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.z (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(102.659409735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{10}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.4
Root \(-28.8366 + 49.9465i\) of defining polynomial
Character \(\chi\) \(=\) 252.73
Dual form 252.9.z.d.145.4

$q$-expansion

\(f(q)\) \(=\) \(q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +O(q^{10})\) \(q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +(7474.44 - 12946.1i) q^{11} -39673.5i q^{13} +(-84679.4 - 48889.7i) q^{17} +(-177843. + 102678. i) q^{19} +(185312. + 320970. i) q^{23} +(-167741. + 290535. i) q^{25} -117048. q^{29} +(437915. + 252830. i) q^{31} +(478588. + 298070. i) q^{35} +(-986447. - 1.70858e6i) q^{37} -3.25966e6i q^{41} -4.13332e6 q^{43} +(4.79532e6 - 2.76858e6i) q^{47} +(-3.20947e6 + 4.78876e6i) q^{49} +(3.39093e6 - 5.87326e6i) q^{53} -3.51040e6i q^{55} +(1.91904e7 + 1.10796e7i) q^{59} +(-3.97144e6 + 2.29291e6i) q^{61} +(-4.65820e6 - 8.06823e6i) q^{65} +(-1.86385e7 + 3.22828e7i) q^{67} -4.19870e7 q^{71} +(1.08607e7 + 6.27044e6i) q^{73} +(3.58722e7 + 1.19951e6i) q^{77} +(-2.01064e7 - 3.48253e7i) q^{79} -5.31441e6i q^{83} -2.29612e7 q^{85} +(-6.45415e7 + 3.72630e7i) q^{89} +(8.40397e7 - 4.48445e7i) q^{91} +(-2.41115e7 + 4.17623e7i) q^{95} -3.76415e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(5\) 203.366 117.413i 0.325386 0.187862i −0.328405 0.944537i \(-0.606511\pi\)
0.653791 + 0.756676i \(0.273178\pi\)
\(6\) 0 0
\(7\) 1130.34 + 2118.29i 0.470778 + 0.882251i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 7474.44 12946.1i 0.510514 0.884237i −0.489411 0.872053i \(-0.662788\pi\)
0.999926 0.0121839i \(-0.00387834\pi\)
\(12\) 0 0
\(13\) 39673.5i 1.38908i −0.719455 0.694539i \(-0.755608\pi\)
0.719455 0.694539i \(-0.244392\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −84679.4 48889.7i −1.01387 0.585358i −0.101547 0.994831i \(-0.532379\pi\)
−0.912322 + 0.409473i \(0.865713\pi\)
\(18\) 0 0
\(19\) −177843. + 102678.i −1.36465 + 0.787882i −0.990239 0.139380i \(-0.955489\pi\)
−0.374413 + 0.927262i \(0.622156\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 185312. + 320970.i 0.662205 + 1.14697i 0.980035 + 0.198825i \(0.0637124\pi\)
−0.317830 + 0.948148i \(0.602954\pi\)
\(24\) 0 0
\(25\) −167741. + 290535.i −0.429416 + 0.743771i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −117048. −0.165490 −0.0827448 0.996571i \(-0.526369\pi\)
−0.0827448 + 0.996571i \(0.526369\pi\)
\(30\) 0 0
\(31\) 437915. + 252830.i 0.474180 + 0.273768i 0.717988 0.696056i \(-0.245063\pi\)
−0.243808 + 0.969823i \(0.578397\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 478588. + 298070.i 0.318926 + 0.198631i
\(36\) 0 0
\(37\) −986447. 1.70858e6i −0.526341 0.911649i −0.999529 0.0306877i \(-0.990230\pi\)
0.473188 0.880961i \(-0.343103\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.25966e6i 1.15355i −0.816903 0.576776i \(-0.804311\pi\)
0.816903 0.576776i \(-0.195689\pi\)
\(42\) 0 0
\(43\) −4.13332e6 −1.20900 −0.604498 0.796607i \(-0.706626\pi\)
−0.604498 + 0.796607i \(0.706626\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.79532e6 2.76858e6i 0.982711 0.567369i 0.0796238 0.996825i \(-0.474628\pi\)
0.903088 + 0.429456i \(0.141295\pi\)
\(48\) 0 0
\(49\) −3.20947e6 + 4.78876e6i −0.556735 + 0.830690i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.39093e6 5.87326e6i 0.429749 0.744347i −0.567102 0.823648i \(-0.691935\pi\)
0.996851 + 0.0793006i \(0.0252687\pi\)
\(54\) 0 0
\(55\) 3.51040e6i 0.383624i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.91904e7 + 1.10796e7i 1.58371 + 0.914355i 0.994312 + 0.106511i \(0.0339680\pi\)
0.589397 + 0.807843i \(0.299365\pi\)
\(60\) 0 0
\(61\) −3.97144e6 + 2.29291e6i −0.286833 + 0.165603i −0.636513 0.771266i \(-0.719624\pi\)
0.349680 + 0.936869i \(0.386290\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.65820e6 8.06823e6i −0.260954 0.451986i
\(66\) 0 0
\(67\) −1.86385e7 + 3.22828e7i −0.924934 + 1.60203i −0.133267 + 0.991080i \(0.542547\pi\)
−0.791667 + 0.610952i \(0.790787\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.19870e7 −1.65227 −0.826135 0.563472i \(-0.809465\pi\)
−0.826135 + 0.563472i \(0.809465\pi\)
\(72\) 0 0
\(73\) 1.08607e7 + 6.27044e6i 0.382443 + 0.220804i 0.678881 0.734249i \(-0.262465\pi\)
−0.296438 + 0.955052i \(0.595799\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.58722e7 + 1.19951e6i 1.02046 + 0.0341224i
\(78\) 0 0
\(79\) −2.01064e7 3.48253e7i −0.516209 0.894100i −0.999823 0.0188184i \(-0.994010\pi\)
0.483614 0.875281i \(-0.339324\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.31441e6i 0.111981i −0.998431 0.0559903i \(-0.982168\pi\)
0.998431 0.0559903i \(-0.0178316\pi\)
\(84\) 0 0
\(85\) −2.29612e7 −0.439865
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.45415e7 + 3.72630e7i −1.02868 + 0.593907i −0.916605 0.399793i \(-0.869082\pi\)
−0.112072 + 0.993700i \(0.535749\pi\)
\(90\) 0 0
\(91\) 8.40397e7 4.48445e7i 1.22552 0.653948i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.41115e7 + 4.17623e7i −0.296026 + 0.512731i
\(96\) 0 0
\(97\) 3.76415e7i 0.425187i −0.977141 0.212593i \(-0.931809\pi\)
0.977141 0.212593i \(-0.0681909\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.57943e8 9.11884e7i −1.51780 0.876303i −0.999781 0.0209346i \(-0.993336\pi\)
−0.518020 0.855368i \(-0.673331\pi\)
\(102\) 0 0
\(103\) −9.37340e7 + 5.41173e7i −0.832814 + 0.480826i −0.854815 0.518932i \(-0.826330\pi\)
0.0220010 + 0.999758i \(0.492996\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.48762e6 + 1.64330e7i 0.0723806 + 0.125367i 0.899944 0.436005i \(-0.143607\pi\)
−0.827564 + 0.561372i \(0.810274\pi\)
\(108\) 0 0
\(109\) 3.98197e7 6.89697e7i 0.282093 0.488599i −0.689807 0.723993i \(-0.742305\pi\)
0.971900 + 0.235394i \(0.0756381\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.14140e8 −1.31336 −0.656680 0.754169i \(-0.728040\pi\)
−0.656680 + 0.754169i \(0.728040\pi\)
\(114\) 0 0
\(115\) 7.53723e7 + 4.35162e7i 0.430944 + 0.248806i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.84586e6 2.34637e8i 0.0391249 1.17006i
\(120\) 0 0
\(121\) −4.55511e6 7.88969e6i −0.0212499 0.0368060i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.70509e8i 0.698406i
\(126\) 0 0
\(127\) 2.22002e8 0.853381 0.426690 0.904398i \(-0.359679\pi\)
0.426690 + 0.904398i \(0.359679\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.38205e8 + 2.52998e8i −1.48796 + 0.859075i −0.999906 0.0137373i \(-0.995627\pi\)
−0.488056 + 0.872812i \(0.662294\pi\)
\(132\) 0 0
\(133\) −4.18523e8 2.60661e8i −1.33756 0.833048i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.73086e8 + 2.99795e8i −0.491339 + 0.851023i −0.999950 0.00997260i \(-0.996826\pi\)
0.508612 + 0.860996i \(0.330159\pi\)
\(138\) 0 0
\(139\) 1.04014e8i 0.278632i −0.990248 0.139316i \(-0.955510\pi\)
0.990248 0.139316i \(-0.0444904\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5.13617e8 2.96537e8i −1.22827 0.709144i
\(144\) 0 0
\(145\) −2.38035e7 + 1.37430e7i −0.0538480 + 0.0310891i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.71762e8 2.97501e8i −0.348483 0.603591i 0.637497 0.770453i \(-0.279970\pi\)
−0.985980 + 0.166862i \(0.946637\pi\)
\(150\) 0 0
\(151\) −4.21266e8 + 7.29654e8i −0.810305 + 1.40349i 0.102346 + 0.994749i \(0.467365\pi\)
−0.912651 + 0.408740i \(0.865968\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.18743e8 0.205722
\(156\) 0 0
\(157\) −3.00370e8 1.73419e8i −0.494377 0.285429i 0.232011 0.972713i \(-0.425469\pi\)
−0.726388 + 0.687284i \(0.758803\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.70440e8 + 7.55349e8i −0.700166 + 1.12420i
\(162\) 0 0
\(163\) 6.38287e7 + 1.10555e8i 0.0904203 + 0.156612i 0.907688 0.419646i \(-0.137846\pi\)
−0.817268 + 0.576258i \(0.804512\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.84232e8i 0.622569i −0.950317 0.311284i \(-0.899241\pi\)
0.950317 0.311284i \(-0.100759\pi\)
\(168\) 0 0
\(169\) −7.58252e8 −0.929537
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.57674e8 4.37444e8i 0.845860 0.488357i −0.0133921 0.999910i \(-0.504263\pi\)
0.859252 + 0.511553i \(0.170930\pi\)
\(174\) 0 0
\(175\) −8.05041e8 2.69192e7i −0.858352 0.0287019i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.06371e8 1.05027e9i 0.590645 1.02303i −0.403501 0.914979i \(-0.632207\pi\)
0.994146 0.108048i \(-0.0344599\pi\)
\(180\) 0 0
\(181\) 2.75613e8i 0.256794i 0.991723 + 0.128397i \(0.0409832\pi\)
−0.991723 + 0.128397i \(0.959017\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.01220e8 2.31644e8i −0.342528 0.197758i
\(186\) 0 0
\(187\) −1.26586e9 + 7.30846e8i −1.03519 + 0.597667i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.56485e8 1.65668e9i −0.718695 1.24482i −0.961517 0.274746i \(-0.911406\pi\)
0.242821 0.970071i \(-0.421927\pi\)
\(192\) 0 0
\(193\) 4.90016e8 8.48733e8i 0.353168 0.611705i −0.633635 0.773632i \(-0.718438\pi\)
0.986803 + 0.161928i \(0.0517711\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.49081e9 −0.989824 −0.494912 0.868943i \(-0.664800\pi\)
−0.494912 + 0.868943i \(0.664800\pi\)
\(198\) 0 0
\(199\) −8.60781e8 4.96972e8i −0.548884 0.316898i 0.199788 0.979839i \(-0.435975\pi\)
−0.748672 + 0.662941i \(0.769308\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.32304e8 2.47940e8i −0.0779090 0.146004i
\(204\) 0 0
\(205\) −3.82728e8 6.62904e8i −0.216708 0.375349i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.06983e9i 1.60890i
\(210\) 0 0
\(211\) −4.64537e8 −0.234364 −0.117182 0.993110i \(-0.537386\pi\)
−0.117182 + 0.993110i \(0.537386\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.40576e8 + 4.85307e8i −0.393390 + 0.227124i
\(216\) 0 0
\(217\) −4.05745e7 + 1.21341e9i −0.0182984 + 0.547229i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.93962e9 + 3.35952e9i −0.813107 + 1.40834i
\(222\) 0 0
\(223\) 6.58116e7i 0.0266123i −0.999911 0.0133062i \(-0.995764\pi\)
0.999911 0.0133062i \(-0.00423561\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.98442e9 1.14570e9i −0.747360 0.431489i 0.0773791 0.997002i \(-0.475345\pi\)
−0.824739 + 0.565513i \(0.808678\pi\)
\(228\) 0 0
\(229\) 2.77398e9 1.60156e9i 1.00870 0.582373i 0.0978887 0.995197i \(-0.468791\pi\)
0.910811 + 0.412825i \(0.135458\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.43830e8 1.28835e9i −0.252377 0.437130i 0.711803 0.702380i \(-0.247879\pi\)
−0.964180 + 0.265249i \(0.914546\pi\)
\(234\) 0 0
\(235\) 6.50137e8 1.12607e9i 0.213173 0.369227i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.50233e8 −0.291232 −0.145616 0.989341i \(-0.546516\pi\)
−0.145616 + 0.989341i \(0.546516\pi\)
\(240\) 0 0
\(241\) −3.55088e9 2.05010e9i −1.05261 0.607725i −0.129232 0.991614i \(-0.541251\pi\)
−0.923379 + 0.383889i \(0.874584\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9.04318e7 + 1.35071e9i −0.0250990 + 0.374884i
\(246\) 0 0
\(247\) 4.07358e9 + 7.05564e9i 1.09443 + 1.89561i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.77515e9i 1.20307i −0.798845 0.601537i \(-0.794555\pi\)
0.798845 0.601537i \(-0.205445\pi\)
\(252\) 0 0
\(253\) 5.54042e9 1.35226
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.28158e9 2.47197e9i 0.981457 0.566645i 0.0787473 0.996895i \(-0.474908\pi\)
0.902710 + 0.430250i \(0.141575\pi\)
\(258\) 0 0
\(259\) 2.50423e9 4.02085e9i 0.556514 0.893550i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.41497e9 + 5.91490e9i −0.713779 + 1.23630i 0.249650 + 0.968336i \(0.419685\pi\)
−0.963429 + 0.267965i \(0.913649\pi\)
\(264\) 0 0
\(265\) 1.59256e9i 0.322933i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.01169e9 + 1.73880e9i 0.575176 + 0.332078i 0.759214 0.650841i \(-0.225584\pi\)
−0.184038 + 0.982919i \(0.558917\pi\)
\(270\) 0 0
\(271\) −5.59984e9 + 3.23307e9i −1.03824 + 0.599429i −0.919335 0.393477i \(-0.871272\pi\)
−0.118907 + 0.992905i \(0.537939\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.50754e9 + 4.34318e9i 0.438446 + 0.759411i
\(276\) 0 0
\(277\) 2.15914e9 3.73973e9i 0.366742 0.635216i −0.622312 0.782769i \(-0.713806\pi\)
0.989054 + 0.147553i \(0.0471397\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.64214e9 −0.904938 −0.452469 0.891780i \(-0.649457\pi\)
−0.452469 + 0.891780i \(0.649457\pi\)
\(282\) 0 0
\(283\) 3.51708e9 + 2.03059e9i 0.548323 + 0.316574i 0.748445 0.663197i \(-0.230801\pi\)
−0.200122 + 0.979771i \(0.564134\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.90489e9 3.68452e9i 1.01772 0.543067i
\(288\) 0 0
\(289\) 1.29252e9 + 2.23871e9i 0.185287 + 0.320927i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.43223e7i 0.0114412i −0.999984 0.00572061i \(-0.998179\pi\)
0.999984 0.00572061i \(-0.00182094\pi\)
\(294\) 0 0
\(295\) 5.20356e9 0.687088
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.27340e10 7.35197e9i 1.59323 0.919854i
\(300\) 0 0
\(301\) −4.67205e9 8.75554e9i −0.569169 1.06664i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.38438e8 + 9.32601e8i −0.0622209 + 0.107770i
\(306\) 0 0
\(307\) 6.10423e9i 0.687191i −0.939118 0.343596i \(-0.888355\pi\)
0.939118 0.343596i \(-0.111645\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.74096e9 + 1.00514e9i 0.186100 + 0.107445i 0.590156 0.807289i \(-0.299066\pi\)
−0.404055 + 0.914735i \(0.632400\pi\)
\(312\) 0 0
\(313\) −1.10102e10 + 6.35672e9i −1.14714 + 0.662302i −0.948189 0.317708i \(-0.897087\pi\)
−0.198951 + 0.980009i \(0.563754\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.98773e9 5.17489e9i −0.295872 0.512465i 0.679315 0.733846i \(-0.262277\pi\)
−0.975187 + 0.221381i \(0.928943\pi\)
\(318\) 0 0
\(319\) −8.74866e8 + 1.51531e9i −0.0844849 + 0.146332i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.00795e10 1.84477
\(324\) 0 0
\(325\) 1.15265e10 + 6.65485e9i 1.03316 + 0.596492i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.12850e10 + 7.02842e9i 0.963201 + 0.599894i
\(330\) 0 0
\(331\) 6.42439e9 + 1.11274e10i 0.535205 + 0.927002i 0.999153 + 0.0411400i \(0.0130990\pi\)
−0.463948 + 0.885862i \(0.653568\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.75362e9i 0.695038i
\(336\) 0 0
\(337\) −9.70137e9 −0.752166 −0.376083 0.926586i \(-0.622729\pi\)
−0.376083 + 0.926586i \(0.622729\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.54634e9 3.77953e9i 0.484151 0.279525i
\(342\) 0 0
\(343\) −1.37718e10 1.38565e9i −0.994976 0.100110i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.48892e8 1.12391e9i 0.0447563 0.0775203i −0.842779 0.538259i \(-0.819082\pi\)
0.887536 + 0.460739i \(0.152416\pi\)
\(348\) 0 0
\(349\) 2.01643e10i 1.35919i 0.733587 + 0.679596i \(0.237845\pi\)
−0.733587 + 0.679596i \(0.762155\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.27487e10 + 1.31340e10i 1.46507 + 0.845857i 0.999238 0.0390186i \(-0.0124232\pi\)
0.465828 + 0.884875i \(0.345756\pi\)
\(354\) 0 0
\(355\) −8.53872e9 + 4.92983e9i −0.537625 + 0.310398i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.13441e10 1.96486e10i −0.682958 1.18292i −0.974074 0.226230i \(-0.927360\pi\)
0.291116 0.956688i \(-0.405973\pi\)
\(360\) 0 0
\(361\) 1.25936e10 2.18128e10i 0.741517 1.28435i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.94493e9 0.165922
\(366\) 0 0
\(367\) 9.38693e8 + 5.41955e8i 0.0517439 + 0.0298744i 0.525649 0.850702i \(-0.323823\pi\)
−0.473905 + 0.880576i \(0.657156\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.62741e10 + 5.44179e8i 0.859018 + 0.0287241i
\(372\) 0 0
\(373\) 1.91674e9 + 3.31989e9i 0.0990211 + 0.171510i 0.911280 0.411788i \(-0.135096\pi\)
−0.812259 + 0.583297i \(0.801762\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.64369e9i 0.229878i
\(378\) 0 0
\(379\) 3.26734e10 1.58357 0.791785 0.610800i \(-0.209152\pi\)
0.791785 + 0.610800i \(0.209152\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.54251e10 8.90569e9i 0.716858 0.413878i −0.0967371 0.995310i \(-0.530841\pi\)
0.813595 + 0.581432i \(0.197507\pi\)
\(384\) 0 0
\(385\) 7.43603e9 3.96794e9i 0.338453 0.180602i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.92749e9 1.19988e10i 0.302536 0.524008i −0.674173 0.738573i \(-0.735500\pi\)
0.976710 + 0.214565i \(0.0688333\pi\)
\(390\) 0 0
\(391\) 3.62394e10i 1.55051i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.17791e9 4.72152e9i −0.335934 0.193951i
\(396\) 0 0
\(397\) −1.66863e10 + 9.63385e9i −0.671735 + 0.387827i −0.796734 0.604330i \(-0.793441\pi\)
0.124998 + 0.992157i \(0.460107\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.58138e9 1.65954e10i −0.370553 0.641817i 0.619097 0.785314i \(-0.287499\pi\)
−0.989651 + 0.143497i \(0.954165\pi\)
\(402\) 0 0
\(403\) 1.00306e10 1.73736e10i 0.380285 0.658672i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.94926e10 −1.07482
\(408\) 0 0
\(409\) 3.45544e10 + 1.99500e10i 1.23484 + 0.712935i 0.968035 0.250815i \(-0.0806987\pi\)
0.266805 + 0.963751i \(0.414032\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.77806e9 + 5.31744e10i −0.0611148 + 1.82769i
\(414\) 0 0
\(415\) −6.23984e8 1.08077e9i −0.0210369 0.0364369i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.17883e10i 1.68026i 0.542387 + 0.840129i \(0.317521\pi\)
−0.542387 + 0.840129i \(0.682479\pi\)
\(420\) 0 0
\(421\) 5.78196e9 0.184055 0.0920273 0.995756i \(-0.470665\pi\)
0.0920273 + 0.995756i \(0.470665\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.84083e10 1.64016e10i 0.870743 0.502724i
\(426\) 0 0
\(427\) −9.34612e9 5.82088e9i −0.281138 0.175096i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.29999e10 + 2.25165e10i −0.376730 + 0.652516i −0.990584 0.136903i \(-0.956285\pi\)
0.613854 + 0.789420i \(0.289618\pi\)
\(432\) 0 0
\(433\) 3.85244e10i 1.09593i 0.836500 + 0.547967i \(0.184598\pi\)
−0.836500 + 0.547967i \(0.815402\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.59128e10 3.80548e10i −1.80736 1.04348i
\(438\) 0 0
\(439\) 5.36255e10 3.09607e10i 1.44382 0.833591i 0.445720 0.895172i \(-0.352948\pi\)
0.998102 + 0.0615814i \(0.0196144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.82777e9 1.18260e10i −0.177282 0.307061i 0.763667 0.645611i \(-0.223397\pi\)
−0.940949 + 0.338550i \(0.890064\pi\)
\(444\) 0 0
\(445\) −8.75037e9 + 1.51561e10i −0.223144 + 0.386498i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.45335e10 −1.58782 −0.793908 0.608038i \(-0.791957\pi\)
−0.793908 + 0.608038i \(0.791957\pi\)
\(450\) 0 0
\(451\) −4.21999e10 2.43641e10i −1.02001 0.588904i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.18255e10 1.89872e10i 0.275914 0.443013i
\(456\) 0 0
\(457\) 2.13781e10 + 3.70279e10i 0.490122 + 0.848916i 0.999935 0.0113692i \(-0.00361901\pi\)
−0.509814 + 0.860285i \(0.670286\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.19885e10i 0.708256i 0.935197 + 0.354128i \(0.115222\pi\)
−0.935197 + 0.354128i \(0.884778\pi\)
\(462\) 0 0
\(463\) −6.84419e9 −0.148935 −0.0744677 0.997223i \(-0.523726\pi\)
−0.0744677 + 0.997223i \(0.523726\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.83350e10 1.05857e10i 0.385490 0.222563i −0.294714 0.955585i \(-0.595224\pi\)
0.680204 + 0.733023i \(0.261891\pi\)
\(468\) 0 0
\(469\) −8.94519e10 2.99112e9i −1.84883 0.0618219i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.08942e10 + 5.35104e10i −0.617210 + 1.06904i
\(474\) 0 0
\(475\) 6.88928e10i 1.35332i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.99972e9 5.77334e9i −0.189953 0.109669i 0.402008 0.915636i \(-0.368313\pi\)
−0.591960 + 0.805967i \(0.701646\pi\)
\(480\) 0 0
\(481\) −6.77852e10 + 3.91358e10i −1.26635 + 0.731128i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.41961e9 7.65500e9i −0.0798762 0.138350i
\(486\) 0 0
\(487\) 3.40949e10 5.90541e10i 0.606141 1.04987i −0.385729 0.922612i \(-0.626050\pi\)
0.991870 0.127255i \(-0.0406165\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.71885e10 0.639857 0.319929 0.947442i \(-0.396341\pi\)
0.319929 + 0.947442i \(0.396341\pi\)
\(492\) 0 0
\(493\) 9.91152e9 + 5.72242e9i 0.167785 + 0.0968706i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.74595e10 8.89404e10i −0.777853 1.45772i
\(498\) 0 0
\(499\) 2.66255e10 + 4.61166e10i 0.429432 + 0.743799i 0.996823 0.0796501i \(-0.0253803\pi\)
−0.567390 + 0.823449i \(0.692047\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.10881e10i 1.42295i −0.702711 0.711475i \(-0.748027\pi\)
0.702711 0.711475i \(-0.251973\pi\)
\(504\) 0 0
\(505\) −4.28270e10 −0.658494
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.02031e9 + 2.89848e9i −0.0747927 + 0.0431816i −0.536930 0.843627i \(-0.680416\pi\)
0.462137 + 0.886808i \(0.347083\pi\)
\(510\) 0 0
\(511\) −1.00629e9 + 3.00938e10i −0.0147584 + 0.441361i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.27082e10 + 2.20113e10i −0.180657 + 0.312907i
\(516\) 0 0
\(517\) 8.27743e10i 1.15860i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.38767e10 + 3.68792e10i 0.866945 + 0.500531i 0.866332 0.499469i \(-0.166471\pi\)
0.000613137 1.00000i \(0.499805\pi\)
\(522\) 0 0
\(523\) −8.49467e10 + 4.90440e10i −1.13538 + 0.655510i −0.945281 0.326256i \(-0.894213\pi\)
−0.190095 + 0.981766i \(0.560880\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.47216e10 4.28190e10i −0.320504 0.555129i
\(528\) 0 0
\(529\) −2.95256e10 + 5.11398e10i −0.377030 + 0.653035i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.29322e11 −1.60237
\(534\) 0 0
\(535\) 3.85892e9 + 2.22795e9i 0.0471032 + 0.0271950i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.80069e10 + 7.73435e10i 0.450305 + 0.916365i
\(540\) 0 0
\(541\) 1.61177e10 + 2.79168e10i 0.188155 + 0.325894i 0.944635 0.328123i \(-0.106416\pi\)
−0.756480 + 0.654017i \(0.773083\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.87015e10i 0.211978i
\(546\) 0 0
\(547\) −9.97958e10 −1.11471 −0.557356 0.830273i \(-0.688184\pi\)
−0.557356 + 0.830273i \(0.688184\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.08161e10 1.20182e10i 0.225836 0.130386i
\(552\) 0 0
\(553\) 5.10428e10 8.19554e10i 0.545801 0.876349i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.01561e10 5.22319e10i 0.313295 0.542644i −0.665778 0.746150i \(-0.731900\pi\)
0.979074 + 0.203506i \(0.0652337\pi\)
\(558\) 0 0
\(559\) 1.63983e11i 1.67939i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.10263e8 + 6.36604e7i 0.00109748 + 0.000633630i 0.500549 0.865708i \(-0.333132\pi\)
−0.499451 + 0.866342i \(0.666465\pi\)
\(564\) 0 0
\(565\) −4.35488e10 + 2.51429e10i −0.427349 + 0.246730i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.12713e10 + 8.88046e10i 0.489132 + 0.847201i 0.999922 0.0125047i \(-0.00398046\pi\)
−0.510790 + 0.859705i \(0.670647\pi\)
\(570\) 0 0
\(571\) 3.04428e10 5.27285e10i 0.286378 0.496022i −0.686564 0.727069i \(-0.740882\pi\)
0.972943 + 0.231047i \(0.0742152\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.24337e11 −1.13745
\(576\) 0 0
\(577\) −2.41312e10 1.39322e10i −0.217709 0.125694i 0.387180 0.922004i \(-0.373449\pi\)
−0.604889 + 0.796310i \(0.706783\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.12574e10 6.00709e9i 0.0987951 0.0527181i
\(582\) 0 0
\(583\) −5.06906e10 8.77986e10i −0.438786 0.760000i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.01355e9i 0.0338047i −0.999857 0.0169023i \(-0.994620\pi\)
0.999857 0.0169023i \(-0.00538043\pi\)
\(588\) 0 0
\(589\) −1.03840e11 −0.862787
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.32222e11 + 7.63384e10i −1.06926 + 0.617340i −0.927980 0.372630i \(-0.878456\pi\)
−0.141283 + 0.989969i \(0.545123\pi\)
\(594\) 0 0
\(595\) −2.59540e10 4.86384e10i −0.207079 0.388071i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.45784e10 9.45325e10i 0.423949 0.734301i −0.572373 0.819993i \(-0.693977\pi\)
0.996322 + 0.0856928i \(0.0273104\pi\)
\(600\) 0 0
\(601\) 1.79228e11i 1.37375i 0.726776 + 0.686875i \(0.241018\pi\)
−0.726776 + 0.686875i \(0.758982\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.85271e9 1.06966e9i −0.0138289 0.00798409i
\(606\) 0 0
\(607\) 3.96127e10 2.28704e10i 0.291796 0.168469i −0.346955 0.937882i \(-0.612784\pi\)
0.638752 + 0.769413i \(0.279451\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.09839e11 1.90247e11i −0.788119 1.36506i
\(612\) 0 0
\(613\) 6.70156e10 1.16074e11i 0.474607 0.822044i −0.524970 0.851121i \(-0.675924\pi\)
0.999577 + 0.0290771i \(0.00925685\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.21594e11 −0.839015 −0.419508 0.907752i \(-0.637797\pi\)
−0.419508 + 0.907752i \(0.637797\pi\)
\(618\) 0 0
\(619\) −3.51231e10 2.02783e10i −0.239238 0.138124i 0.375589 0.926787i \(-0.377441\pi\)
−0.614826 + 0.788662i \(0.710774\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.51888e11 9.45974e10i −1.00825 0.627953i
\(624\) 0 0
\(625\) −4.55036e10 7.88146e10i −0.298212 0.516519i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.92908e11i 1.23239i
\(630\) 0 0
\(631\) 2.35096e11 1.48296 0.741478 0.670978i \(-0.234125\pi\)
0.741478 + 0.670978i \(0.234125\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.51478e10 2.60661e10i 0.277678 0.160317i
\(636\) 0 0
\(637\) 1.89987e11 + 1.27331e11i 1.15389 + 0.773349i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.51414e11 + 2.62257e11i −0.896881 + 1.55344i −0.0654207 + 0.997858i \(0.520839\pi\)
−0.831460 + 0.555585i \(0.812494\pi\)
\(642\) 0 0
\(643\) 1.17949e11i 0.690001i −0.938603 0.345000i \(-0.887879\pi\)
0.938603 0.345000i \(-0.112121\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.55386e11 + 8.97120e10i 0.886735 + 0.511957i 0.872873 0.487947i \(-0.162254\pi\)
0.0138619 + 0.999904i \(0.495587\pi\)
\(648\) 0 0
\(649\) 2.86875e11 1.65627e11i 1.61701 0.933582i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.14200e11 + 1.97801e11i 0.628079 + 1.08786i 0.987937 + 0.154858i \(0.0494918\pi\)
−0.359858 + 0.933007i \(0.617175\pi\)
\(654\) 0 0
\(655\) −5.94106e10 + 1.02902e11i −0.322774 + 0.559061i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.80179e11 1.48557 0.742785 0.669530i \(-0.233504\pi\)
0.742785 + 0.669530i \(0.233504\pi\)
\(660\) 0 0
\(661\) −8.31508e9 4.80071e9i −0.0435573 0.0251478i 0.478063 0.878325i \(-0.341339\pi\)
−0.521621 + 0.853178i \(0.674672\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.15719e11 3.86943e9i −0.591720 0.0197861i
\(666\) 0 0
\(667\) −2.16903e10 3.75688e10i −0.109588 0.189812i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.85530e10i 0.338171i
\(672\) 0 0
\(673\) −1.19348e11 −0.581776 −0.290888 0.956757i \(-0.593951\pi\)
−0.290888 + 0.956757i \(0.593951\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.44704e10 4.87690e10i 0.402115 0.232161i −0.285281 0.958444i \(-0.592087\pi\)
0.687396 + 0.726283i \(0.258754\pi\)
\(678\) 0 0
\(679\) 7.97354e10 4.25476e10i 0.375121 0.200169i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.69347e11 2.93317e11i 0.778204 1.34789i −0.154772 0.987950i \(-0.549464\pi\)
0.932976 0.359939i \(-0.117203\pi\)
\(684\) 0 0
\(685\) 8.12907e10i 0.369214i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.33012e11 1.34530e11i −1.03396 0.596955i
\(690\) 0 0
\(691\) 2.57158e11 1.48470e11i 1.12794 0.651219i 0.184527 0.982827i \(-0.440925\pi\)
0.943417 + 0.331608i \(0.107591\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.22126e10 2.11529e10i −0.0523443 0.0906630i
\(696\) 0 0
\(697\) −1.59364e11 + 2.76026e11i −0.675240 + 1.16955i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.94718e11 0.806370 0.403185 0.915118i \(-0.367903\pi\)
0.403185 + 0.915118i \(0.367903\pi\)
\(702\) 0 0
\(703\) 3.50865e11 + 2.02572e11i 1.43654 + 0.829389i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.46340e10 4.37642e11i 0.0585714 1.75163i
\(708\) 0 0
\(709\) −2.00882e11 3.47938e11i −0.794979 1.37694i −0.922852 0.385154i \(-0.874148\pi\)
0.127873 0.991791i \(-0.459185\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.87410e11i 0.725161i
\(714\) 0 0
\(715\) −1.39270e11 −0.532884
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.54791e11 8.93684e10i 0.579201 0.334402i −0.181615 0.983370i \(-0.558132\pi\)
0.760816 + 0.648968i \(0.224799\pi\)
\(720\) 0 0
\(721\) −2.20587e11 1.37384e11i −0.816280 0.508389i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.96337e10 3.40065e10i 0.0710639 0.123086i
\(726\) 0 0
\(727\) 1.97437e11i 0.706790i 0.935474 + 0.353395i \(0.114973\pi\)
−0.935474 + 0.353395i \(0.885027\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.50006e11 + 2.02076e11i 1.22576 + 0.707695i
\(732\) 0 0
\(733\) 1.01144e11 5.83958e10i 0.350370 0.202286i −0.314478 0.949265i \(-0.601830\pi\)
0.664848 + 0.746979i \(0.268496\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.78624e11 + 4.82591e11i 0.944384 + 1.63572i
\(738\) 0 0
\(739\) −8.45542e10 + 1.46452e11i −0.283503 + 0.491042i −0.972245 0.233965i \(-0.924830\pi\)
0.688742 + 0.725006i \(0.258163\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.84466e11 0.605287 0.302644 0.953104i \(-0.402131\pi\)
0.302644 + 0.953104i \(0.402131\pi\)
\(744\) 0 0
\(745\) −6.98611e10 4.03343e10i −0.226783 0.130933i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.40856e10 + 3.86724e10i −0.0765298 + 0.122878i
\(750\) 0 0
\(751\) 1.50650e11 + 2.60933e11i 0.473596 + 0.820293i 0.999543 0.0302244i \(-0.00962218\pi\)
−0.525947 + 0.850518i \(0.676289\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.97849e11i 0.608900i
\(756\) 0 0
\(757\) 4.94329e11 1.50533 0.752666 0.658403i \(-0.228768\pi\)
0.752666 + 0.658403i \(0.228768\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.78956e10 3.34260e10i 0.172626 0.0996658i −0.411197 0.911546i \(-0.634889\pi\)
0.583824 + 0.811881i \(0.301556\pi\)
\(762\) 0 0
\(763\) 1.91107e11 + 6.39031e9i 0.563870 + 0.0188549i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.39565e11 7.61348e11i 1.27011 2.19989i
\(768\) 0 0
\(769\) 1.20153e11i 0.343581i 0.985134 + 0.171790i \(0.0549552\pi\)
−0.985134 + 0.171790i \(0.945045\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.05856e11 + 1.76586e11i 0.856640 + 0.494582i 0.862886 0.505399i \(-0.168655\pi\)
−0.00624545 + 0.999980i \(0.501988\pi\)
\(774\) 0 0
\(775\) −1.46912e11 + 8.48198e10i −0.407241 + 0.235120i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.34694e11 + 5.79707e11i 0.908862 + 1.57420i
\(780\) 0 0
\(781\) −3.13829e11 + 5.43568e11i −0.843508 + 1.46100i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −8.14468e10 −0.214484
\(786\) 0 0
\(787\) −4.79863e11 2.77049e11i −1.25089 0.722201i −0.279602 0.960116i \(-0.590203\pi\)
−0.971286 + 0.237915i \(0.923536\pi\)
\(788\) 0 0