Properties

Label 252.9.z.d.73.3
Level $252$
Weight $9$
Character 252.73
Analytic conductor $102.659$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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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 73.3
Root \(-122.377 + 211.963i\) of defining polynomial
Character \(\chi\) \(=\) 252.73
Dual form 252.9.z.d.145.3

$q$-expansion

\(f(q)\) \(=\) \(q+(133.903 - 77.3091i) q^{5} +(-2234.88 - 877.558i) q^{7} +O(q^{10})\) \(q+(133.903 - 77.3091i) q^{5} +(-2234.88 - 877.558i) q^{7} +(-3950.92 + 6843.20i) q^{11} -4177.64i q^{13} +(-110620. - 63866.3i) q^{17} +(139247. - 80394.4i) q^{19} +(16422.4 + 28444.4i) q^{23} +(-183359. + 317587. i) q^{25} -659560. q^{29} +(-5163.53 - 2981.17i) q^{31} +(-367101. + 55268.8i) q^{35} +(329534. + 570770. i) q^{37} -1.10208e6i q^{41} +4.57153e6 q^{43} +(1.35905e6 - 784649. i) q^{47} +(4.22459e6 + 3.92247e6i) q^{49} +(-4.31027e6 + 7.46560e6i) q^{53} +1.22177e6i q^{55} +(-1.85511e7 - 1.07105e7i) q^{59} +(2.16597e7 - 1.25052e7i) q^{61} +(-322970. - 559400. i) q^{65} +(-9.65705e6 + 1.67265e7i) q^{67} -9.50918e6 q^{71} +(6.91695e6 + 3.99350e6i) q^{73} +(1.48351e7 - 1.18266e7i) q^{77} +(-1.32777e6 - 2.29977e6i) q^{79} +5.37421e7i q^{83} -1.97498e7 q^{85} +(3.33121e7 - 1.92328e7i) q^{89} +(-3.66612e6 + 9.33654e6i) q^{91} +(1.24304e7 - 2.15302e7i) q^{95} -2.56754e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 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
\(5\) 133.903 77.3091i 0.214245 0.123695i −0.389037 0.921222i \(-0.627192\pi\)
0.603283 + 0.797527i \(0.293859\pi\)
\(6\) 0 0
\(7\) −2234.88 877.558i −0.930813 0.365497i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3950.92 + 6843.20i −0.269853 + 0.467400i −0.968824 0.247751i \(-0.920309\pi\)
0.698970 + 0.715151i \(0.253642\pi\)
\(12\) 0 0
\(13\) 4177.64i 0.146271i −0.997322 0.0731354i \(-0.976699\pi\)
0.997322 0.0731354i \(-0.0233005\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −110620. 63866.3i −1.32445 0.764674i −0.340019 0.940419i \(-0.610433\pi\)
−0.984436 + 0.175745i \(0.943767\pi\)
\(18\) 0 0
\(19\) 139247. 80394.4i 1.06849 0.616895i 0.140724 0.990049i \(-0.455057\pi\)
0.927769 + 0.373154i \(0.121724\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 16422.4 + 28444.4i 0.0586847 + 0.101645i 0.893875 0.448316i \(-0.147976\pi\)
−0.835191 + 0.549961i \(0.814643\pi\)
\(24\) 0 0
\(25\) −183359. + 317587.i −0.469399 + 0.813023i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −659560. −0.932528 −0.466264 0.884646i \(-0.654400\pi\)
−0.466264 + 0.884646i \(0.654400\pi\)
\(30\) 0 0
\(31\) −5163.53 2981.17i −0.00559114 0.00322804i 0.497202 0.867635i \(-0.334361\pi\)
−0.502793 + 0.864407i \(0.667694\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −367101. + 55268.8i −0.244632 + 0.0368305i
\(36\) 0 0
\(37\) 329534. + 570770.i 0.175830 + 0.304547i 0.940448 0.339937i \(-0.110406\pi\)
−0.764618 + 0.644484i \(0.777072\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.10208e6i 0.390013i −0.980802 0.195007i \(-0.937527\pi\)
0.980802 0.195007i \(-0.0624728\pi\)
\(42\) 0 0
\(43\) 4.57153e6 1.33717 0.668586 0.743635i \(-0.266900\pi\)
0.668586 + 0.743635i \(0.266900\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.35905e6 784649.i 0.278512 0.160799i −0.354237 0.935156i \(-0.615260\pi\)
0.632750 + 0.774356i \(0.281926\pi\)
\(48\) 0 0
\(49\) 4.22459e6 + 3.92247e6i 0.732824 + 0.680418i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.31027e6 + 7.46560e6i −0.546262 + 0.946153i 0.452265 + 0.891884i \(0.350616\pi\)
−0.998526 + 0.0542691i \(0.982717\pi\)
\(54\) 0 0
\(55\) 1.22177e6i 0.133518i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.85511e7 1.07105e7i −1.53095 0.883895i −0.999318 0.0369211i \(-0.988245\pi\)
−0.531634 0.846974i \(-0.678422\pi\)
\(60\) 0 0
\(61\) 2.16597e7 1.25052e7i 1.56435 0.903177i 0.567539 0.823346i \(-0.307896\pi\)
0.996808 0.0798301i \(-0.0254378\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −322970. 559400.i −0.0180929 0.0313379i
\(66\) 0 0
\(67\) −9.65705e6 + 1.67265e7i −0.479231 + 0.830053i −0.999716 0.0238177i \(-0.992418\pi\)
0.520485 + 0.853871i \(0.325751\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.50918e6 −0.374205 −0.187103 0.982340i \(-0.559910\pi\)
−0.187103 + 0.982340i \(0.559910\pi\)
\(72\) 0 0
\(73\) 6.91695e6 + 3.99350e6i 0.243570 + 0.140625i 0.616816 0.787107i \(-0.288422\pi\)
−0.373247 + 0.927732i \(0.621755\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.48351e7 1.18266e7i 0.422016 0.336431i
\(78\) 0 0
\(79\) −1.32777e6 2.29977e6i −0.0340891 0.0590441i 0.848478 0.529231i \(-0.177520\pi\)
−0.882567 + 0.470187i \(0.844186\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.37421e7i 1.13241i 0.824266 + 0.566203i \(0.191588\pi\)
−0.824266 + 0.566203i \(0.808412\pi\)
\(84\) 0 0
\(85\) −1.97498e7 −0.378344
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.33121e7 1.92328e7i 0.530936 0.306536i −0.210461 0.977602i \(-0.567497\pi\)
0.741398 + 0.671066i \(0.234163\pi\)
\(90\) 0 0
\(91\) −3.66612e6 + 9.33654e6i −0.0534615 + 0.136151i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.24304e7 2.15302e7i 0.152613 0.264334i
\(96\) 0 0
\(97\) 2.56754e7i 0.290021i −0.989430 0.145011i \(-0.953678\pi\)
0.989430 0.145011i \(-0.0463216\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.37265e8 + 7.92500e7i 1.31909 + 0.761577i 0.983582 0.180461i \(-0.0577589\pi\)
0.335507 + 0.942038i \(0.391092\pi\)
\(102\) 0 0
\(103\) −2.36862e7 + 1.36753e7i −0.210449 + 0.121503i −0.601520 0.798858i \(-0.705438\pi\)
0.391071 + 0.920361i \(0.372105\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.08597e7 + 1.40053e8i 0.616875 + 1.06846i 0.990053 + 0.140698i \(0.0449348\pi\)
−0.373178 + 0.927760i \(0.621732\pi\)
\(108\) 0 0
\(109\) −2.95165e7 + 5.11241e7i −0.209102 + 0.362176i −0.951432 0.307859i \(-0.900388\pi\)
0.742330 + 0.670035i \(0.233721\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.64113e8 1.00654 0.503268 0.864131i \(-0.332131\pi\)
0.503268 + 0.864131i \(0.332131\pi\)
\(114\) 0 0
\(115\) 4.39802e6 + 2.53920e6i 0.0251458 + 0.0145180i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.91176e8 + 2.39809e8i 0.953333 + 1.19585i
\(120\) 0 0
\(121\) 7.59599e7 + 1.31566e8i 0.354358 + 0.613767i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.17099e8i 0.479638i
\(126\) 0 0
\(127\) 1.21072e8 0.465403 0.232702 0.972548i \(-0.425243\pi\)
0.232702 + 0.972548i \(0.425243\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.54093e7 + 3.19906e7i −0.188147 + 0.108627i −0.591115 0.806587i \(-0.701312\pi\)
0.402968 + 0.915214i \(0.367979\pi\)
\(132\) 0 0
\(133\) −3.81751e8 + 5.74744e7i −1.22004 + 0.183683i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.56859e8 2.71688e8i 0.445274 0.771237i −0.552797 0.833316i \(-0.686440\pi\)
0.998071 + 0.0620787i \(0.0197730\pi\)
\(138\) 0 0
\(139\) 2.04519e8i 0.547867i −0.961749 0.273934i \(-0.911675\pi\)
0.961749 0.273934i \(-0.0883248\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.85884e7 + 1.65055e7i 0.0683670 + 0.0394717i
\(144\) 0 0
\(145\) −8.83172e7 + 5.09900e7i −0.199790 + 0.115349i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.34340e8 + 5.79093e8i 0.678333 + 1.17491i 0.975483 + 0.220076i \(0.0706306\pi\)
−0.297150 + 0.954831i \(0.596036\pi\)
\(150\) 0 0
\(151\) 1.10149e8 1.90784e8i 0.211872 0.366973i −0.740428 0.672135i \(-0.765377\pi\)
0.952300 + 0.305162i \(0.0987107\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −921886. −0.00159717
\(156\) 0 0
\(157\) 7.29270e8 + 4.21044e8i 1.20030 + 0.692994i 0.960622 0.277859i \(-0.0896247\pi\)
0.239678 + 0.970852i \(0.422958\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.17405e7 7.79814e7i −0.0174736 0.116061i
\(162\) 0 0
\(163\) 5.08666e8 + 8.81036e8i 0.720581 + 1.24808i 0.960767 + 0.277355i \(0.0894580\pi\)
−0.240187 + 0.970727i \(0.577209\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.85051e8i 1.00933i 0.863316 + 0.504664i \(0.168383\pi\)
−0.863316 + 0.504664i \(0.831617\pi\)
\(168\) 0 0
\(169\) 7.98278e8 0.978605
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.30544e8 2.48575e8i 0.480655 0.277506i −0.240035 0.970764i \(-0.577159\pi\)
0.720689 + 0.693258i \(0.243825\pi\)
\(174\) 0 0
\(175\) 6.88487e8 5.48862e8i 0.734080 0.585208i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.80361e8 + 1.52483e9i −0.857529 + 1.48528i 0.0167496 + 0.999860i \(0.494668\pi\)
−0.874279 + 0.485424i \(0.838665\pi\)
\(180\) 0 0
\(181\) 1.40594e9i 1.30994i 0.755653 + 0.654972i \(0.227320\pi\)
−0.755653 + 0.654972i \(0.772680\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.82515e7 + 5.09520e7i 0.0753417 + 0.0434985i
\(186\) 0 0
\(187\) 8.74100e8 5.04662e8i 0.714817 0.412700i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.46452e8 6.00072e8i −0.260321 0.450889i 0.706006 0.708206i \(-0.250495\pi\)
−0.966327 + 0.257317i \(0.917162\pi\)
\(192\) 0 0
\(193\) −5.17803e8 + 8.96861e8i −0.373195 + 0.646392i −0.990055 0.140680i \(-0.955071\pi\)
0.616860 + 0.787073i \(0.288404\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.58650e9 1.05335 0.526676 0.850066i \(-0.323438\pi\)
0.526676 + 0.850066i \(0.323438\pi\)
\(198\) 0 0
\(199\) 4.38090e8 + 2.52932e8i 0.279352 + 0.161284i 0.633130 0.774046i \(-0.281770\pi\)
−0.353778 + 0.935329i \(0.615103\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.47404e9 + 5.78802e8i 0.868009 + 0.340836i
\(204\) 0 0
\(205\) −8.52012e7 1.47573e8i −0.0482425 0.0835585i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.27053e9i 0.665885i
\(210\) 0 0
\(211\) 8.53493e8 0.430596 0.215298 0.976548i \(-0.430928\pi\)
0.215298 + 0.976548i \(0.430928\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.12143e8 3.53421e8i 0.286483 0.165401i
\(216\) 0 0
\(217\) 8.92373e6 + 1.11939e7i 0.00402446 + 0.00504825i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.66811e8 + 4.62130e8i −0.111850 + 0.193729i
\(222\) 0 0
\(223\) 1.19055e9i 0.481426i −0.970596 0.240713i \(-0.922619\pi\)
0.970596 0.240713i \(-0.0773812\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.55248e9 + 8.96322e8i 0.584684 + 0.337567i 0.762993 0.646407i \(-0.223729\pi\)
−0.178309 + 0.983975i \(0.557063\pi\)
\(228\) 0 0
\(229\) −3.51985e9 + 2.03219e9i −1.27992 + 0.738961i −0.976833 0.214003i \(-0.931350\pi\)
−0.303085 + 0.952964i \(0.598016\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.96945e8 8.60734e8i −0.168610 0.292042i 0.769321 0.638862i \(-0.220595\pi\)
−0.937932 + 0.346820i \(0.887261\pi\)
\(234\) 0 0
\(235\) 1.21321e8 2.10134e8i 0.0397800 0.0689010i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.71719e9 −0.526291 −0.263145 0.964756i \(-0.584760\pi\)
−0.263145 + 0.964756i \(0.584760\pi\)
\(240\) 0 0
\(241\) −3.95118e9 2.28121e9i −1.17127 0.676235i −0.217293 0.976106i \(-0.569723\pi\)
−0.953980 + 0.299872i \(0.903056\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 8.68929e8 + 1.98633e8i 0.241168 + 0.0551300i
\(246\) 0 0
\(247\) −3.35859e8 5.81725e8i −0.0902338 0.156289i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.49784e8i 0.0377373i 0.999822 + 0.0188687i \(0.00600644\pi\)
−0.999822 + 0.0188687i \(0.993994\pi\)
\(252\) 0 0
\(253\) −2.59534e8 −0.0633450
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.35751e9 3.67051e9i 1.45732 0.841384i 0.458440 0.888725i \(-0.348408\pi\)
0.998879 + 0.0473414i \(0.0150749\pi\)
\(258\) 0 0
\(259\) −2.35586e8 1.56479e9i −0.0523541 0.347742i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.40019e9 + 4.15725e9i −0.501675 + 0.868926i 0.498323 + 0.866991i \(0.333949\pi\)
−0.999998 + 0.00193513i \(0.999384\pi\)
\(264\) 0 0
\(265\) 1.33289e9i 0.270278i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.69474e9 + 1.55581e9i 0.514645 + 0.297131i 0.734741 0.678348i \(-0.237304\pi\)
−0.220096 + 0.975478i \(0.570637\pi\)
\(270\) 0 0
\(271\) −3.16838e9 + 1.82927e9i −0.587436 + 0.339156i −0.764083 0.645118i \(-0.776808\pi\)
0.176647 + 0.984274i \(0.443475\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.44888e9 2.50953e9i −0.253338 0.438794i
\(276\) 0 0
\(277\) 5.24448e9 9.08370e9i 0.890806 1.54292i 0.0518958 0.998653i \(-0.483474\pi\)
0.838911 0.544269i \(-0.183193\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.88553e9 −0.302419 −0.151210 0.988502i \(-0.548317\pi\)
−0.151210 + 0.988502i \(0.548317\pi\)
\(282\) 0 0
\(283\) 1.50968e9 + 8.71616e8i 0.235364 + 0.135887i 0.613044 0.790049i \(-0.289945\pi\)
−0.377680 + 0.925936i \(0.623278\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.67143e8 + 2.46303e9i −0.142549 + 0.363029i
\(288\) 0 0
\(289\) 4.66994e9 + 8.08857e9i 0.669453 + 1.15953i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.68210e9i 1.04234i −0.853453 0.521170i \(-0.825496\pi\)
0.853453 0.521170i \(-0.174504\pi\)
\(294\) 0 0
\(295\) −3.31207e9 −0.437333
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.18831e8 6.86068e7i 0.0148677 0.00858386i
\(300\) 0 0
\(301\) −1.02168e10 4.01178e9i −1.24466 0.488732i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.93354e9 3.34899e9i 0.223436 0.387003i
\(306\) 0 0
\(307\) 8.93846e9i 1.00626i −0.864211 0.503129i \(-0.832182\pi\)
0.864211 0.503129i \(-0.167818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.36754e10 7.89550e9i −1.46184 0.843992i −0.462740 0.886494i \(-0.653134\pi\)
−0.999096 + 0.0425024i \(0.986467\pi\)
\(312\) 0 0
\(313\) −8.18174e9 + 4.72373e9i −0.852449 + 0.492162i −0.861476 0.507798i \(-0.830460\pi\)
0.00902752 + 0.999959i \(0.497126\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.46257e9 1.46576e10i −0.838041 1.45153i −0.891530 0.452961i \(-0.850368\pi\)
0.0534897 0.998568i \(-0.482966\pi\)
\(318\) 0 0
\(319\) 2.60587e9 4.51350e9i 0.251646 0.435863i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.05380e10 −1.88689
\(324\) 0 0
\(325\) 1.32677e9 + 7.66009e8i 0.118922 + 0.0686595i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.72589e9 + 5.60950e8i −0.318014 + 0.0478785i
\(330\) 0 0
\(331\) 1.02406e10 + 1.77372e10i 0.853123 + 1.47765i 0.878375 + 0.477972i \(0.158628\pi\)
−0.0252519 + 0.999681i \(0.508039\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.98631e9i 0.237113i
\(336\) 0 0
\(337\) 2.14997e10 1.66691 0.833456 0.552586i \(-0.186359\pi\)
0.833456 + 0.552586i \(0.186359\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.08014e7 2.35567e7i 0.00301757 0.00174220i
\(342\) 0 0
\(343\) −5.99925e9 1.24736e10i −0.433431 0.901187i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.58609e9 + 1.31395e10i −0.523239 + 0.906277i 0.476395 + 0.879231i \(0.341943\pi\)
−0.999634 + 0.0270456i \(0.991390\pi\)
\(348\) 0 0
\(349\) 1.30313e9i 0.0878387i −0.999035 0.0439194i \(-0.986016\pi\)
0.999035 0.0439194i \(-0.0139845\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.83413e10 1.05893e10i −1.18122 0.681978i −0.224924 0.974376i \(-0.572213\pi\)
−0.956297 + 0.292399i \(0.905547\pi\)
\(354\) 0 0
\(355\) −1.27331e9 + 7.35147e8i −0.0801717 + 0.0462872i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.50520e10 2.60708e10i −0.906184 1.56956i −0.819320 0.573337i \(-0.805649\pi\)
−0.0868642 0.996220i \(-0.527685\pi\)
\(360\) 0 0
\(361\) 4.43472e9 7.68117e9i 0.261119 0.452271i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.23494e9 0.0695783
\(366\) 0 0
\(367\) −5.68403e9 3.28168e9i −0.313323 0.180897i 0.335090 0.942186i \(-0.391233\pi\)
−0.648412 + 0.761289i \(0.724567\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.61844e10 1.29022e10i 0.854283 0.681034i
\(372\) 0 0
\(373\) −6.45827e9 1.11861e10i −0.333642 0.577885i 0.649581 0.760293i \(-0.274944\pi\)
−0.983223 + 0.182407i \(0.941611\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.75540e9i 0.136402i
\(378\) 0 0
\(379\) −2.24358e10 −1.08739 −0.543694 0.839283i \(-0.682975\pi\)
−0.543694 + 0.839283i \(0.682975\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.40505e10 1.38855e10i 1.11771 0.645309i 0.176894 0.984230i \(-0.443395\pi\)
0.940815 + 0.338921i \(0.110062\pi\)
\(384\) 0 0
\(385\) 1.07217e9 2.73051e9i 0.0488003 0.124280i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.31848e9 + 1.44080e10i −0.363284 + 0.629226i −0.988499 0.151226i \(-0.951678\pi\)
0.625216 + 0.780452i \(0.285011\pi\)
\(390\) 0 0
\(391\) 4.19535e9i 0.179499i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.55587e8 2.05298e8i −0.0146069 0.00843329i
\(396\) 0 0
\(397\) −1.08327e10 + 6.25426e9i −0.436088 + 0.251776i −0.701937 0.712239i \(-0.747681\pi\)
0.265849 + 0.964015i \(0.414348\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.27309e8 + 1.43294e9i 0.0319956 + 0.0554180i 0.881580 0.472035i \(-0.156480\pi\)
−0.849584 + 0.527453i \(0.823147\pi\)
\(402\) 0 0
\(403\) −1.24543e7 + 2.15714e7i −0.000472169 + 0.000817821i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.20786e9 −0.189794
\(408\) 0 0
\(409\) 1.00393e10 + 5.79619e9i 0.358765 + 0.207133i 0.668539 0.743677i \(-0.266920\pi\)
−0.309774 + 0.950810i \(0.600253\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.20604e10 + 4.02163e10i 1.10197 + 1.38230i
\(414\) 0 0
\(415\) 4.15476e9 + 7.19625e9i 0.140073 + 0.242613i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.35810e10i 0.765079i 0.923939 + 0.382540i \(0.124950\pi\)
−0.923939 + 0.382540i \(0.875050\pi\)
\(420\) 0 0
\(421\) 8.62676e9 0.274612 0.137306 0.990529i \(-0.456156\pi\)
0.137306 + 0.990529i \(0.456156\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.05663e10 2.34209e10i 1.24340 0.717875i
\(426\) 0 0
\(427\) −5.93809e10 + 8.94007e9i −1.78622 + 0.268924i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.28994e10 2.23424e10i 0.373818 0.647472i −0.616331 0.787487i \(-0.711382\pi\)
0.990149 + 0.140015i \(0.0447152\pi\)
\(432\) 0 0
\(433\) 4.11174e10i 1.16970i −0.811142 0.584849i \(-0.801154\pi\)
0.811142 0.584849i \(-0.198846\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.57354e9 + 2.64053e9i 0.125408 + 0.0724046i
\(438\) 0 0
\(439\) −3.33223e10 + 1.92386e10i −0.897174 + 0.517983i −0.876282 0.481798i \(-0.839984\pi\)
−0.0208914 + 0.999782i \(0.506650\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.20399e9 1.07456e10i −0.161085 0.279008i 0.774173 0.632974i \(-0.218166\pi\)
−0.935258 + 0.353966i \(0.884833\pi\)
\(444\) 0 0
\(445\) 2.97374e9 5.15067e9i 0.0758338 0.131348i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.45902e10 −0.851076 −0.425538 0.904941i \(-0.639915\pi\)
−0.425538 + 0.904941i \(0.639915\pi\)
\(450\) 0 0
\(451\) 7.54178e9 + 4.35425e9i 0.182292 + 0.105246i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.30893e8 + 1.53362e9i 0.00538723 + 0.0357826i
\(456\) 0 0
\(457\) −2.64356e9 4.57878e9i −0.0606072 0.104975i 0.834130 0.551568i \(-0.185970\pi\)
−0.894737 + 0.446593i \(0.852637\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.55209e10i 0.786466i 0.919439 + 0.393233i \(0.128643\pi\)
−0.919439 + 0.393233i \(0.871357\pi\)
\(462\) 0 0
\(463\) 5.68452e8 0.0123700 0.00618500 0.999981i \(-0.498031\pi\)
0.00618500 + 0.999981i \(0.498031\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.20351e9 + 6.94848e8i −0.0253036 + 0.0146091i −0.512598 0.858628i \(-0.671317\pi\)
0.487295 + 0.873238i \(0.337984\pi\)
\(468\) 0 0
\(469\) 3.62608e10 2.89071e10i 0.749456 0.597466i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.80617e10 + 3.12839e10i −0.360840 + 0.624994i
\(474\) 0 0
\(475\) 5.89641e10i 1.15828i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.91139e10 + 2.83559e10i 0.932958 + 0.538644i 0.887746 0.460334i \(-0.152270\pi\)
0.0452122 + 0.998977i \(0.485604\pi\)
\(480\) 0 0
\(481\) 2.38447e9 1.37668e9i 0.0445464 0.0257189i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.98494e9 3.43802e9i −0.0358741 0.0621357i
\(486\) 0 0
\(487\) 2.00673e10 3.47576e10i 0.356758 0.617923i −0.630659 0.776060i \(-0.717215\pi\)
0.987417 + 0.158137i \(0.0505487\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.70262e8 0.0115324 0.00576619 0.999983i \(-0.498165\pi\)
0.00576619 + 0.999983i \(0.498165\pi\)
\(492\) 0 0
\(493\) 7.29603e10 + 4.21237e10i 1.23509 + 0.713080i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.12519e10 + 8.34486e9i 0.348315 + 0.136771i
\(498\) 0 0
\(499\) 4.56562e10 + 7.90788e10i 0.736372 + 1.27543i 0.954119 + 0.299428i \(0.0967959\pi\)
−0.217747 + 0.976005i \(0.569871\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.38153e10i 0.684468i 0.939615 + 0.342234i \(0.111184\pi\)
−0.939615 + 0.342234i \(0.888816\pi\)
\(504\) 0 0
\(505\) 2.45070e10 0.376812
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.28346e10 3.05041e10i 0.787132 0.454451i −0.0518199 0.998656i \(-0.516502\pi\)
0.838952 + 0.544206i \(0.183169\pi\)
\(510\) 0 0
\(511\) −1.19540e10 1.49950e10i −0.175320 0.219920i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.11444e9 + 3.66232e9i −0.0300585 + 0.0520628i
\(516\) 0 0
\(517\) 1.24004e10i 0.173569i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.04455e10 + 5.22187e10i 1.22754 + 0.708721i 0.966515 0.256611i \(-0.0826058\pi\)
0.261026 + 0.965332i \(0.415939\pi\)
\(522\) 0 0
\(523\) −6.17123e10 + 3.56296e10i −0.824831 + 0.476216i −0.852079 0.523413i \(-0.824659\pi\)
0.0272488 + 0.999629i \(0.491325\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.80792e8 + 6.59552e8i 0.00493680 + 0.00855079i
\(528\) 0 0
\(529\) 3.86161e10 6.68851e10i 0.493112 0.854095i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.60411e9 −0.0570476
\(534\) 0 0
\(535\) 2.16548e10 + 1.25024e10i 0.264325 + 0.152608i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.35333e10 + 1.34123e10i −0.515782 + 0.158909i
\(540\) 0 0
\(541\) 5.99851e10 + 1.03897e11i 0.700251 + 1.21287i 0.968378 + 0.249487i \(0.0802621\pi\)
−0.268127 + 0.963384i \(0.586405\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.12759e9i 0.103459i
\(546\) 0 0
\(547\) 7.67882e10 0.857720 0.428860 0.903371i \(-0.358915\pi\)
0.428860 + 0.903371i \(0.358915\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9.18418e10 + 5.30249e10i −0.996400 + 0.575272i
\(552\) 0 0
\(553\) 9.49234e8 + 6.30492e9i 0.0101502 + 0.0674185i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.00412e9 1.03994e10i 0.0623775 0.108041i −0.833150 0.553047i \(-0.813465\pi\)
0.895528 + 0.445006i \(0.146798\pi\)
\(558\) 0 0
\(559\) 1.90982e10i 0.195589i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.79826e10 4.50233e10i −0.776183 0.448129i 0.0588931 0.998264i \(-0.481243\pi\)
−0.835076 + 0.550135i \(0.814576\pi\)
\(564\) 0 0
\(565\) 2.19753e10 1.26874e10i 0.215645 0.124503i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.50444e10 + 9.53398e10i 0.525127 + 0.909547i 0.999572 + 0.0292615i \(0.00931555\pi\)
−0.474445 + 0.880285i \(0.657351\pi\)
\(570\) 0 0
\(571\) 2.27688e9 3.94367e9i 0.0214188 0.0370985i −0.855117 0.518435i \(-0.826515\pi\)
0.876536 + 0.481336i \(0.159848\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.20448e10 −0.110186
\(576\) 0 0
\(577\) 2.58023e10 + 1.48969e10i 0.232785 + 0.134398i 0.611856 0.790969i \(-0.290423\pi\)
−0.379071 + 0.925367i \(0.623757\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.71618e10 1.20107e11i 0.413891 1.05406i
\(582\) 0 0
\(583\) −3.40591e10 5.89920e10i −0.294821 0.510645i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.87063e10i 0.410235i 0.978737 + 0.205118i \(0.0657577\pi\)
−0.978737 + 0.205118i \(0.934242\pi\)
\(588\) 0 0
\(589\) −9.58676e8 −0.00796546
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.48606e11 8.57978e10i 1.20176 0.693837i 0.240815 0.970571i \(-0.422585\pi\)
0.960947 + 0.276734i \(0.0892520\pi\)
\(594\) 0 0
\(595\) 4.41385e10 + 1.73316e10i 0.352168 + 0.138284i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.22733e11 + 2.12580e11i −0.953355 + 1.65126i −0.215268 + 0.976555i \(0.569063\pi\)
−0.738087 + 0.674705i \(0.764271\pi\)
\(600\) 0 0
\(601\) 6.97408e10i 0.534551i 0.963620 + 0.267275i \(0.0861233\pi\)
−0.963620 + 0.267275i \(0.913877\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.03426e10 + 1.17448e10i 0.151839 + 0.0876644i
\(606\) 0 0
\(607\) 8.32636e10 4.80723e10i 0.613339 0.354111i −0.160932 0.986965i \(-0.551450\pi\)
0.774271 + 0.632854i \(0.218117\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.27798e9 5.67763e9i −0.0235202 0.0407383i
\(612\) 0 0
\(613\) −5.64299e10 + 9.77394e10i −0.399638 + 0.692194i −0.993681 0.112239i \(-0.964198\pi\)
0.594043 + 0.804433i \(0.297531\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.66934e11 1.15187 0.575936 0.817495i \(-0.304638\pi\)
0.575936 + 0.817495i \(0.304638\pi\)
\(618\) 0 0
\(619\) −2.13512e11 1.23271e11i −1.45432 0.839650i −0.455595 0.890187i \(-0.650573\pi\)
−0.998722 + 0.0505371i \(0.983907\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9.13266e10 + 1.37496e10i −0.606240 + 0.0912723i
\(624\) 0 0
\(625\) −6.25718e10 1.08378e11i −0.410071 0.710263i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.41846e10i 0.537811i
\(630\) 0 0
\(631\) −2.85012e11 −1.79782 −0.898910 0.438133i \(-0.855640\pi\)
−0.898910 + 0.438133i \(0.855640\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.62120e10 9.35998e9i 0.0997104 0.0575679i
\(636\) 0 0
\(637\) 1.63867e10 1.76488e10i 0.0995254 0.107191i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.12062e11 1.94098e11i 0.663785 1.14971i −0.315828 0.948816i \(-0.602282\pi\)
0.979613 0.200893i \(-0.0643844\pi\)
\(642\) 0 0
\(643\) 2.37170e11i 1.38745i 0.720241 + 0.693724i \(0.244031\pi\)
−0.720241 + 0.693724i \(0.755969\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.95163e11 + 1.12678e11i 1.11373 + 0.643014i 0.939794 0.341742i \(-0.111017\pi\)
0.173940 + 0.984756i \(0.444350\pi\)
\(648\) 0 0
\(649\) 1.46588e11 8.46326e10i 0.826265 0.477044i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.06390e10 + 1.56991e11i 0.498497 + 0.863422i 0.999998 0.00173469i \(-0.000552168\pi\)
−0.501502 + 0.865157i \(0.667219\pi\)
\(654\) 0 0
\(655\) −4.94632e9 + 8.56729e9i −0.0268731 + 0.0465455i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.00364e11 −1.06238 −0.531189 0.847253i \(-0.678255\pi\)
−0.531189 + 0.847253i \(0.678255\pi\)
\(660\) 0 0
\(661\) −8.46518e10 4.88737e10i −0.443435 0.256017i 0.261618 0.965171i \(-0.415744\pi\)
−0.705054 + 0.709154i \(0.749077\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.66745e10 + 3.72089e10i −0.238667 + 0.190266i
\(666\) 0 0
\(667\) −1.08315e10 1.87608e10i −0.0547251 0.0947867i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.97629e11i 0.974901i
\(672\) 0 0
\(673\) −2.14833e11 −1.04723 −0.523614 0.851956i \(-0.675416\pi\)
−0.523614 + 0.851956i \(0.675416\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.10418e11 1.21485e11i 1.00168 0.578320i 0.0929348 0.995672i \(-0.470375\pi\)
0.908745 + 0.417352i \(0.137042\pi\)
\(678\) 0 0
\(679\) −2.25316e10 + 5.73814e10i −0.106002 + 0.269955i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.78386e11 3.08973e11i 0.819742 1.41984i −0.0861296 0.996284i \(-0.527450\pi\)
0.905872 0.423552i \(-0.139217\pi\)
\(684\) 0 0
\(685\) 4.85065e10i 0.220312i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.11886e10 + 1.80068e10i 0.138395 + 0.0799022i
\(690\) 0 0
\(691\) 3.06169e11 1.76767e11i 1.34291 0.775332i 0.355680 0.934608i \(-0.384249\pi\)
0.987234 + 0.159275i \(0.0509158\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.58112e10 2.73858e10i −0.0677682 0.117378i
\(696\) 0 0
\(697\) −7.03861e10 + 1.21912e11i −0.298233 + 0.516555i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.14132e11 −1.30089 −0.650445 0.759553i \(-0.725418\pi\)
−0.650445 + 0.759553i \(0.725418\pi\)
\(702\) 0 0
\(703\) 9.17734e10 + 5.29854e10i 0.375747 + 0.216938i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.37224e11 2.97572e11i −0.949471 1.19101i
\(708\) 0 0
\(709\) −1.40578e11 2.43487e11i −0.556328 0.963589i −0.997799 0.0663130i \(-0.978876\pi\)
0.441471 0.897276i \(-0.354457\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.95831e8i 0.000757747i
\(714\) 0 0
\(715\) 5.10412e9 0.0195297
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4.14076e11 + 2.39067e11i −1.54940 + 0.894548i −0.551215 + 0.834363i \(0.685836\pi\)
−0.998187 + 0.0601845i \(0.980831\pi\)
\(720\) 0 0
\(721\) 6.49367e10 9.77652e9i 0.240298 0.0361779i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.20936e11 2.09468e11i 0.437728 0.758167i
\(726\) 0 0
\(727\) 5.00817e11i 1.79284i −0.443206 0.896420i \(-0.646159\pi\)
0.443206 0.896420i \(-0.353841\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.05701e11 2.91967e11i −1.77102 1.02250i
\(732\) 0 0
\(733\) −8.44252e10 + 4.87429e10i −0.292453 + 0.168848i −0.639048 0.769167i \(-0.720671\pi\)
0.346594 + 0.938015i \(0.387338\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.63085e10 1.32170e11i −0.258644 0.447985i
\(738\) 0 0
\(739\) −1.10837e11 + 1.91976e11i −0.371628 + 0.643678i −0.989816 0.142352i \(-0.954534\pi\)
0.618188 + 0.786030i \(0.287867\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.62831e11 −0.862426 −0.431213 0.902250i \(-0.641914\pi\)
−0.431213 + 0.902250i \(0.641914\pi\)
\(744\) 0 0
\(745\) 8.95384e10 + 5.16950e10i 0.290659 + 0.167812i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.78071e10 3.83961e11i −0.183677 1.22000i
\(750\) 0 0
\(751\) −1.37391e11 2.37969e11i −0.431917 0.748102i 0.565122 0.825008i \(-0.308829\pi\)
−0.997038 + 0.0769059i \(0.975496\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.40622e10i 0.104830i
\(756\) 0 0
\(757\) 1.73327e11 0.527817 0.263909 0.964548i \(-0.414988\pi\)
0.263909 + 0.964548i \(0.414988\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.50804e11 + 2.02537e11i −1.04599 + 0.603901i −0.921523 0.388323i \(-0.873054\pi\)
−0.124464 + 0.992224i \(0.539721\pi\)
\(762\) 0 0
\(763\) 1.10830e11 8.83538e10i 0.327009 0.260692i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.47446e10 + 7.74999e10i −0.129288 + 0.223934i
\(768\) 0 0
\(769\) 6.69043e11i 1.91315i 0.291488 + 0.956574i \(0.405850\pi\)
−0.291488 + 0.956574i \(0.594150\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7.11009e10 + 4.10502e10i 0.199140 + 0.114973i 0.596254 0.802796i \(-0.296655\pi\)
−0.397115 + 0.917769i \(0.629988\pi\)
\(774\) 0 0
\(775\) 1.89356e9 1.09325e9i 0.00524895 0.00303048i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −8.86014e10 1.53462e11i −0.240597 0.416727i
\(780\) 0 0
\(781\) 3.75701e10 6.50732e10i 0.100981 0.174903i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.30202e11 0.342878
\(786\) 0 0
\(787\) 1.30594e11 + 7.53983e10i 0.340427 + 0.196545i 0.660461 0.750861i \(-0.270361\pi\)
−0.320034 + 0.947406i \(0.603694\pi\)
\(788\) 0 0
\(789\) 0