Properties

Label 252.8.k.e.109.1
Level $252$
Weight $8$
Character 252.109
Analytic conductor $78.721$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(78.7210264220\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 89566 x^{14} - 207320 x^{13} + 5161603375 x^{12} - 17143558340 x^{11} + 178819626045814 x^{10} - 993183560713460 x^{9} + 4531523101103784409 x^{8} - 25038421018919762700 x^{7} + 77467785793463920028824 x^{6} - 352418565495722251364640 x^{5} + 967025470523891143640719680 x^{4} - 1651641278575894088053178880 x^{3} + 7200793191683961412674394484736 x^{2} + 21939035854717669821876654243840 x + 34494438285389383231614325978300416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{13}\cdot 7^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(-77.2060 - 133.725i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.8.k.e.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-173.134 - 299.876i) q^{5} +(334.186 + 843.720i) q^{7} +O(q^{10})\) \(q+(-173.134 - 299.876i) q^{5} +(334.186 + 843.720i) q^{7} +(-437.706 + 758.129i) q^{11} -507.478 q^{13} +(9804.06 - 16981.1i) q^{17} +(17766.7 + 30772.7i) q^{19} +(-48754.4 - 84445.0i) q^{23} +(-20888.0 + 36179.1i) q^{25} -56682.8 q^{29} +(26332.7 - 45609.6i) q^{31} +(195153. - 246291. i) q^{35} +(-171941. - 297810. i) q^{37} -279731. q^{41} +73777.2 q^{43} +(514934. + 891892. i) q^{47} +(-600182. + 563919. i) q^{49} +(-186831. + 323600. i) q^{53} +303127. q^{55} +(-520363. + 901296. i) q^{59} +(161336. + 279442. i) q^{61} +(87861.6 + 152181. i) q^{65} +(-1.50274e6 + 2.60282e6i) q^{67} +2.97728e6 q^{71} +(-1.26966e6 + 2.19911e6i) q^{73} +(-785924. - 115945. i) q^{77} +(936558. + 1.62217e6i) q^{79} -3.44787e6 q^{83} -6.78965e6 q^{85} +(-5.03292e6 - 8.71726e6i) q^{89} +(-169592. - 428169. i) q^{91} +(6.15201e6 - 1.06556e7i) q^{95} -1.52465e7 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 1680q^{7} + O(q^{10}) \) \( 16q + 1680q^{7} - 28280q^{13} + 42224q^{19} - 80460q^{25} + 164752q^{31} - 647980q^{37} + 1341440q^{43} + 230104q^{49} - 323120q^{55} - 4319336q^{61} - 3905760q^{67} + 6471780q^{73} - 6093104q^{79} + 456400q^{85} + 15969856q^{91} - 27141240q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −173.134 299.876i −0.619422 1.07287i −0.989591 0.143906i \(-0.954034\pi\)
0.370170 0.928964i \(-0.379300\pi\)
\(6\) 0 0
\(7\) 334.186 + 843.720i 0.368252 + 0.929726i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −437.706 + 758.129i −0.0991535 + 0.171739i −0.911335 0.411667i \(-0.864947\pi\)
0.812181 + 0.583406i \(0.198280\pi\)
\(12\) 0 0
\(13\) −507.478 −0.0640643 −0.0320321 0.999487i \(-0.510198\pi\)
−0.0320321 + 0.999487i \(0.510198\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 9804.06 16981.1i 0.483988 0.838292i −0.515843 0.856683i \(-0.672521\pi\)
0.999831 + 0.0183914i \(0.00585449\pi\)
\(18\) 0 0
\(19\) 17766.7 + 30772.7i 0.594248 + 1.02927i 0.993652 + 0.112493i \(0.0358837\pi\)
−0.399404 + 0.916775i \(0.630783\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −48754.4 84445.0i −0.835538 1.44719i −0.893592 0.448880i \(-0.851823\pi\)
0.0580543 0.998313i \(-0.481510\pi\)
\(24\) 0 0
\(25\) −20888.0 + 36179.1i −0.267367 + 0.463092i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −56682.8 −0.431577 −0.215789 0.976440i \(-0.569232\pi\)
−0.215789 + 0.976440i \(0.569232\pi\)
\(30\) 0 0
\(31\) 26332.7 45609.6i 0.158756 0.274973i −0.775664 0.631146i \(-0.782585\pi\)
0.934420 + 0.356172i \(0.115918\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 195153. 246291.i 0.769372 0.970979i
\(36\) 0 0
\(37\) −171941. 297810.i −0.558049 0.966569i −0.997659 0.0683807i \(-0.978217\pi\)
0.439610 0.898189i \(-0.355117\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −279731. −0.633865 −0.316933 0.948448i \(-0.602653\pi\)
−0.316933 + 0.948448i \(0.602653\pi\)
\(42\) 0 0
\(43\) 73777.2 0.141509 0.0707543 0.997494i \(-0.477459\pi\)
0.0707543 + 0.997494i \(0.477459\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 514934. + 891892.i 0.723451 + 1.25305i 0.959608 + 0.281339i \(0.0907786\pi\)
−0.236157 + 0.971715i \(0.575888\pi\)
\(48\) 0 0
\(49\) −600182. + 563919.i −0.728781 + 0.684747i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −186831. + 323600.i −0.172378 + 0.298568i −0.939251 0.343231i \(-0.888478\pi\)
0.766873 + 0.641799i \(0.221812\pi\)
\(54\) 0 0
\(55\) 303127. 0.245671
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −520363. + 901296.i −0.329856 + 0.571328i −0.982483 0.186352i \(-0.940334\pi\)
0.652627 + 0.757679i \(0.273667\pi\)
\(60\) 0 0
\(61\) 161336. + 279442.i 0.0910073 + 0.157629i 0.907935 0.419110i \(-0.137658\pi\)
−0.816928 + 0.576740i \(0.804325\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 87861.6 + 152181.i 0.0396828 + 0.0687326i
\(66\) 0 0
\(67\) −1.50274e6 + 2.60282e6i −0.610410 + 1.05726i 0.380762 + 0.924673i \(0.375662\pi\)
−0.991171 + 0.132587i \(0.957672\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.97728e6 0.987224 0.493612 0.869682i \(-0.335676\pi\)
0.493612 + 0.869682i \(0.335676\pi\)
\(72\) 0 0
\(73\) −1.26966e6 + 2.19911e6i −0.381994 + 0.661633i −0.991347 0.131266i \(-0.958096\pi\)
0.609353 + 0.792899i \(0.291429\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −785924. 115945.i −0.196184 0.0289424i
\(78\) 0 0
\(79\) 936558. + 1.62217e6i 0.213717 + 0.370169i 0.952875 0.303363i \(-0.0981095\pi\)
−0.739158 + 0.673532i \(0.764776\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.44787e6 −0.661878 −0.330939 0.943652i \(-0.607365\pi\)
−0.330939 + 0.943652i \(0.607365\pi\)
\(84\) 0 0
\(85\) −6.78965e6 −1.19917
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.03292e6 8.71726e6i −0.756754 1.31074i −0.944498 0.328518i \(-0.893451\pi\)
0.187744 0.982218i \(-0.439882\pi\)
\(90\) 0 0
\(91\) −169592. 428169.i −0.0235918 0.0595622i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 6.15201e6 1.06556e7i 0.736181 1.27510i
\(96\) 0 0
\(97\) −1.52465e7 −1.69617 −0.848085 0.529860i \(-0.822244\pi\)
−0.848085 + 0.529860i \(0.822244\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.13213e6 + 1.96091e6i −0.109338 + 0.189379i −0.915502 0.402313i \(-0.868206\pi\)
0.806164 + 0.591692i \(0.201540\pi\)
\(102\) 0 0
\(103\) 281141. + 486950.i 0.0253509 + 0.0439091i 0.878423 0.477885i \(-0.158596\pi\)
−0.853072 + 0.521794i \(0.825263\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.95243e6 + 1.37740e7i 0.627562 + 1.08697i 0.988039 + 0.154201i \(0.0492804\pi\)
−0.360477 + 0.932768i \(0.617386\pi\)
\(108\) 0 0
\(109\) −6.02223e6 + 1.04308e7i −0.445415 + 0.771481i −0.998081 0.0619216i \(-0.980277\pi\)
0.552666 + 0.833403i \(0.313610\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.75416e7 −1.14366 −0.571828 0.820374i \(-0.693765\pi\)
−0.571828 + 0.820374i \(0.693765\pi\)
\(114\) 0 0
\(115\) −1.68820e7 + 2.92405e7i −1.03510 + 1.79285i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.76037e7 + 2.59702e6i 0.957611 + 0.141273i
\(120\) 0 0
\(121\) 9.36041e6 + 1.62127e7i 0.480337 + 0.831968i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.25865e7 −0.576393
\(126\) 0 0
\(127\) −1.98177e7 −0.858499 −0.429250 0.903186i \(-0.641222\pi\)
−0.429250 + 0.903186i \(0.641222\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.15059e7 + 1.99289e7i 0.447170 + 0.774521i 0.998201 0.0599637i \(-0.0190985\pi\)
−0.551030 + 0.834485i \(0.685765\pi\)
\(132\) 0 0
\(133\) −2.00262e7 + 2.52739e7i −0.738104 + 0.931519i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.94076e6 + 6.82560e6i −0.130936 + 0.226787i −0.924038 0.382302i \(-0.875131\pi\)
0.793102 + 0.609089i \(0.208465\pi\)
\(138\) 0 0
\(139\) −3.33107e7 −1.05204 −0.526020 0.850472i \(-0.676316\pi\)
−0.526020 + 0.850472i \(0.676316\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 222126. 384734.i 0.00635220 0.0110023i
\(144\) 0 0
\(145\) 9.81371e6 + 1.69978e7i 0.267328 + 0.463026i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.85252e7 + 4.94071e7i 0.706443 + 1.22360i 0.966168 + 0.257913i \(0.0830347\pi\)
−0.259725 + 0.965683i \(0.583632\pi\)
\(150\) 0 0
\(151\) −3.16251e7 + 5.47762e7i −0.747502 + 1.29471i 0.201515 + 0.979485i \(0.435414\pi\)
−0.949017 + 0.315226i \(0.897920\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.82363e7 −0.393347
\(156\) 0 0
\(157\) −5.92448e6 + 1.02615e7i −0.122180 + 0.211623i −0.920627 0.390443i \(-0.872322\pi\)
0.798447 + 0.602065i \(0.205655\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.49549e7 6.93554e7i 1.03780 1.30975i
\(162\) 0 0
\(163\) −2.57630e7 4.46228e7i −0.465950 0.807049i 0.533294 0.845930i \(-0.320954\pi\)
−0.999244 + 0.0388808i \(0.987621\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.95166e7 −1.65344 −0.826719 0.562615i \(-0.809795\pi\)
−0.826719 + 0.562615i \(0.809795\pi\)
\(168\) 0 0
\(169\) −6.24910e7 −0.995896
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −5.24458e7 9.08388e7i −0.770104 1.33386i −0.937505 0.347971i \(-0.886871\pi\)
0.167401 0.985889i \(-0.446462\pi\)
\(174\) 0 0
\(175\) −3.75055e7 5.53307e6i −0.529007 0.0780428i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.92027e7 1.19863e8i 0.901856 1.56206i 0.0767740 0.997049i \(-0.475538\pi\)
0.825082 0.565012i \(-0.191129\pi\)
\(180\) 0 0
\(181\) 3.73519e7 0.468206 0.234103 0.972212i \(-0.424785\pi\)
0.234103 + 0.972212i \(0.424785\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.95374e7 + 1.03122e8i −0.691335 + 1.19743i
\(186\) 0 0
\(187\) 8.58259e6 + 1.48655e7i 0.0959782 + 0.166239i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.95067e7 + 6.84276e7i 0.410255 + 0.710582i 0.994917 0.100694i \(-0.0321064\pi\)
−0.584663 + 0.811277i \(0.698773\pi\)
\(192\) 0 0
\(193\) −2.99903e7 + 5.19448e7i −0.300283 + 0.520105i −0.976200 0.216873i \(-0.930414\pi\)
0.675917 + 0.736978i \(0.263748\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.03085e8 0.960650 0.480325 0.877091i \(-0.340519\pi\)
0.480325 + 0.877091i \(0.340519\pi\)
\(198\) 0 0
\(199\) −1.91440e7 + 3.31584e7i −0.172205 + 0.298268i −0.939191 0.343396i \(-0.888423\pi\)
0.766985 + 0.641665i \(0.221756\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.89426e7 4.78244e7i −0.158929 0.401249i
\(204\) 0 0
\(205\) 4.84308e7 + 8.38847e7i 0.392630 + 0.680055i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.11063e7 −0.235687
\(210\) 0 0
\(211\) 1.27808e8 0.936635 0.468318 0.883560i \(-0.344860\pi\)
0.468318 + 0.883560i \(0.344860\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.27733e7 2.21240e7i −0.0876535 0.151820i
\(216\) 0 0
\(217\) 4.72817e7 + 6.97533e6i 0.314112 + 0.0463399i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −4.97535e6 + 8.61755e6i −0.0310063 + 0.0537045i
\(222\) 0 0
\(223\) −6.36267e7 −0.384213 −0.192107 0.981374i \(-0.561532\pi\)
−0.192107 + 0.981374i \(0.561532\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.87102e7 + 1.53651e8i −0.503365 + 0.871854i 0.496627 + 0.867964i \(0.334572\pi\)
−0.999992 + 0.00388995i \(0.998762\pi\)
\(228\) 0 0
\(229\) −4.96856e7 8.60580e7i −0.273405 0.473551i 0.696326 0.717725i \(-0.254817\pi\)
−0.969731 + 0.244174i \(0.921483\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.33649e8 + 2.31486e8i 0.692180 + 1.19889i 0.971122 + 0.238582i \(0.0766827\pi\)
−0.278943 + 0.960308i \(0.589984\pi\)
\(234\) 0 0
\(235\) 1.78305e8 3.08833e8i 0.896243 1.55234i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.52202e8 −0.721152 −0.360576 0.932730i \(-0.617420\pi\)
−0.360576 + 0.932730i \(0.617420\pi\)
\(240\) 0 0
\(241\) 1.05229e8 1.82262e8i 0.484256 0.838757i −0.515580 0.856841i \(-0.672424\pi\)
0.999836 + 0.0180846i \(0.00575684\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.73018e8 + 8.23471e7i 1.18607 + 0.357740i
\(246\) 0 0
\(247\) −9.01619e6 1.56165e7i −0.0380701 0.0659393i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.72017e8 −0.686615 −0.343307 0.939223i \(-0.611547\pi\)
−0.343307 + 0.939223i \(0.611547\pi\)
\(252\) 0 0
\(253\) 8.53603e7 0.331386
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.04935e7 + 5.28163e7i 0.112058 + 0.194089i 0.916600 0.399806i \(-0.130923\pi\)
−0.804542 + 0.593896i \(0.797589\pi\)
\(258\) 0 0
\(259\) 1.93808e8 2.44594e8i 0.693142 0.874774i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.37264e7 7.57363e7i 0.148217 0.256720i −0.782351 0.622837i \(-0.785980\pi\)
0.930569 + 0.366118i \(0.119313\pi\)
\(264\) 0 0
\(265\) 1.29387e8 0.427100
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.71329e8 4.69955e8i 0.849890 1.47205i −0.0314155 0.999506i \(-0.510001\pi\)
0.881306 0.472547i \(-0.156665\pi\)
\(270\) 0 0
\(271\) −2.54907e7 4.41512e7i −0.0778018 0.134757i 0.824499 0.565863i \(-0.191457\pi\)
−0.902301 + 0.431106i \(0.858123\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.82856e7 3.16716e7i −0.0530207 0.0918345i
\(276\) 0 0
\(277\) 1.11619e8 1.93330e8i 0.315543 0.546536i −0.664010 0.747724i \(-0.731147\pi\)
0.979553 + 0.201187i \(0.0644800\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.34774e8 −1.16894 −0.584469 0.811416i \(-0.698697\pi\)
−0.584469 + 0.811416i \(0.698697\pi\)
\(282\) 0 0
\(283\) 3.24748e8 5.62480e8i 0.851714 1.47521i −0.0279467 0.999609i \(-0.508897\pi\)
0.879660 0.475602i \(-0.157770\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.34822e7 2.36014e8i −0.233422 0.589321i
\(288\) 0 0
\(289\) 1.29303e7 + 2.23959e7i 0.0315112 + 0.0545790i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.61039e7 −0.153529 −0.0767645 0.997049i \(-0.524459\pi\)
−0.0767645 + 0.997049i \(0.524459\pi\)
\(294\) 0 0
\(295\) 3.60370e8 0.817280
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.47418e7 + 4.28540e7i 0.0535281 + 0.0927134i
\(300\) 0 0
\(301\) 2.46553e7 + 6.22473e7i 0.0521108 + 0.131564i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 5.58653e7 9.67615e7i 0.112744 0.195278i
\(306\) 0 0
\(307\) 5.80890e8 1.14580 0.572901 0.819625i \(-0.305818\pi\)
0.572901 + 0.819625i \(0.305818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.05179e7 3.55381e7i 0.0386787 0.0669935i −0.846038 0.533123i \(-0.821018\pi\)
0.884717 + 0.466129i \(0.154352\pi\)
\(312\) 0 0
\(313\) 1.58978e8 + 2.75359e8i 0.293044 + 0.507567i 0.974528 0.224266i \(-0.0719985\pi\)
−0.681484 + 0.731833i \(0.738665\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.78346e8 6.55314e8i −0.667085 1.15543i −0.978715 0.205222i \(-0.934208\pi\)
0.311630 0.950203i \(-0.399125\pi\)
\(318\) 0 0
\(319\) 2.48104e7 4.29729e7i 0.0427924 0.0741186i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.96741e8 1.15044
\(324\) 0 0
\(325\) 1.06002e7 1.83601e7i 0.0171286 0.0296677i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.80423e8 + 7.32518e8i −0.898584 + 1.13405i
\(330\) 0 0
\(331\) −2.07896e8 3.60086e8i −0.315100 0.545769i 0.664359 0.747414i \(-0.268705\pi\)
−0.979459 + 0.201645i \(0.935371\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.04070e9 1.51240
\(336\) 0 0
\(337\) 7.71149e8 1.09757 0.548787 0.835962i \(-0.315090\pi\)
0.548787 + 0.835962i \(0.315090\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.30520e7 + 3.99272e7i 0.0314824 + 0.0545291i
\(342\) 0 0
\(343\) −6.76362e8 3.17932e8i −0.905002 0.425407i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.96630e8 + 8.60189e8i −0.638087 + 1.10520i 0.347765 + 0.937582i \(0.386941\pi\)
−0.985852 + 0.167618i \(0.946393\pi\)
\(348\) 0 0
\(349\) 2.57730e8 0.324546 0.162273 0.986746i \(-0.448118\pi\)
0.162273 + 0.986746i \(0.448118\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.84532e8 + 8.39235e8i −0.586288 + 1.01548i 0.408425 + 0.912792i \(0.366078\pi\)
−0.994713 + 0.102689i \(0.967255\pi\)
\(354\) 0 0
\(355\) −5.15468e8 8.92816e8i −0.611508 1.05916i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.83984e7 + 3.18669e7i 0.0209869 + 0.0363504i 0.876328 0.481715i \(-0.159986\pi\)
−0.855341 + 0.518065i \(0.826652\pi\)
\(360\) 0 0
\(361\) −1.84372e8 + 3.19342e8i −0.206262 + 0.357257i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8.79282e8 0.946462
\(366\) 0 0
\(367\) 5.21654e8 9.03531e8i 0.550872 0.954139i −0.447339 0.894364i \(-0.647628\pi\)
0.998212 0.0597748i \(-0.0190382\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.35464e8 4.94900e7i −0.341065 0.0503163i
\(372\) 0 0
\(373\) 3.17534e8 + 5.49986e8i 0.316818 + 0.548745i 0.979822 0.199871i \(-0.0640523\pi\)
−0.663004 + 0.748616i \(0.730719\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.87653e7 0.0276487
\(378\) 0 0
\(379\) −1.23849e9 −1.16857 −0.584284 0.811550i \(-0.698624\pi\)
−0.584284 + 0.811550i \(0.698624\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.63548e8 + 2.83273e8i 0.148747 + 0.257638i 0.930765 0.365619i \(-0.119143\pi\)
−0.782017 + 0.623257i \(0.785809\pi\)
\(384\) 0 0
\(385\) 1.01301e8 + 2.55754e8i 0.0904690 + 0.228407i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.96563e7 + 1.03328e8i −0.0513846 + 0.0890008i −0.890574 0.454839i \(-0.849697\pi\)
0.839189 + 0.543840i \(0.183030\pi\)
\(390\) 0 0
\(391\) −1.91196e9 −1.61756
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.24299e8 5.61703e8i 0.264762 0.458582i
\(396\) 0 0
\(397\) 1.15614e9 + 2.00250e9i 0.927353 + 1.60622i 0.787733 + 0.616017i \(0.211255\pi\)
0.139620 + 0.990205i \(0.455412\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.43632e8 1.63442e9i −0.730798 1.26578i −0.956543 0.291593i \(-0.905815\pi\)
0.225745 0.974187i \(-0.427519\pi\)
\(402\) 0 0
\(403\) −1.33633e7 + 2.31459e7i −0.0101706 + 0.0176159i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.01038e8 0.221330
\(408\) 0 0
\(409\) −9.34476e8 + 1.61856e9i −0.675362 + 1.16976i 0.301001 + 0.953624i \(0.402679\pi\)
−0.976363 + 0.216138i \(0.930654\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −9.34339e8 1.37840e8i −0.652649 0.0962832i
\(414\) 0 0
\(415\) 5.96943e8 + 1.03394e9i 0.409982 + 0.710109i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.19342e9 0.792584 0.396292 0.918125i \(-0.370297\pi\)
0.396292 + 0.918125i \(0.370297\pi\)
\(420\) 0 0
\(421\) −4.94195e7 −0.0322783 −0.0161392 0.999870i \(-0.505137\pi\)
−0.0161392 + 0.999870i \(0.505137\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.09575e8 + 7.09404e8i 0.258804 + 0.448262i
\(426\) 0 0
\(427\) −1.81854e8 + 2.29508e8i −0.113038 + 0.142659i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.26012e8 + 1.43069e9i −0.496954 + 0.860749i −0.999994 0.00351400i \(-0.998881\pi\)
0.503040 + 0.864263i \(0.332215\pi\)
\(432\) 0 0
\(433\) −2.35353e9 −1.39320 −0.696598 0.717462i \(-0.745304\pi\)
−0.696598 + 0.717462i \(0.745304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.73240e9 3.00061e9i 0.993034 1.71999i
\(438\) 0 0
\(439\) −6.32030e8 1.09471e9i −0.356543 0.617551i 0.630838 0.775915i \(-0.282711\pi\)
−0.987381 + 0.158364i \(0.949378\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.58299e9 2.74182e9i −0.865099 1.49840i −0.866949 0.498398i \(-0.833922\pi\)
0.00184942 0.999998i \(-0.499411\pi\)
\(444\) 0 0
\(445\) −1.74273e9 + 3.01850e9i −0.937499 + 1.62380i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.54070e9 −1.84598 −0.922989 0.384827i \(-0.874261\pi\)
−0.922989 + 0.384827i \(0.874261\pi\)
\(450\) 0 0
\(451\) 1.22440e8 2.12072e8i 0.0628500 0.108859i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9.90357e7 + 1.24987e8i −0.0492892 + 0.0622051i
\(456\) 0 0
\(457\) 1.67457e9 + 2.90044e9i 0.820724 + 1.42154i 0.905144 + 0.425105i \(0.139763\pi\)
−0.0844204 + 0.996430i \(0.526904\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.58651e9 1.22959 0.614795 0.788687i \(-0.289239\pi\)
0.614795 + 0.788687i \(0.289239\pi\)
\(462\) 0 0
\(463\) −1.17364e9 −0.549544 −0.274772 0.961509i \(-0.588602\pi\)
−0.274772 + 0.961509i \(0.588602\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.66720e8 + 8.08383e8i 0.212054 + 0.367289i 0.952357 0.304984i \(-0.0986513\pi\)
−0.740303 + 0.672273i \(0.765318\pi\)
\(468\) 0 0
\(469\) −2.69824e9 3.98063e8i −1.20775 0.178175i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.22927e7 + 5.59327e7i −0.0140311 + 0.0243025i
\(474\) 0 0
\(475\) −1.48444e9 −0.635529
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.06626e8 + 5.31091e8i −0.127478 + 0.220798i −0.922699 0.385522i \(-0.874021\pi\)
0.795221 + 0.606320i \(0.207355\pi\)
\(480\) 0 0
\(481\) 8.72561e7 + 1.51132e8i 0.0357510 + 0.0619225i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.63968e9 + 4.57207e9i 1.05064 + 1.81977i
\(486\) 0 0
\(487\) 1.79545e8 3.10981e8i 0.0704403 0.122006i −0.828654 0.559761i \(-0.810893\pi\)
0.899094 + 0.437755i \(0.144226\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.24919e9 0.857514 0.428757 0.903420i \(-0.358952\pi\)
0.428757 + 0.903420i \(0.358952\pi\)
\(492\) 0 0
\(493\) −5.55722e8 + 9.62539e8i −0.208878 + 0.361788i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.94967e8 + 2.51199e9i 0.363547 + 0.917848i
\(498\) 0 0
\(499\) −1.31886e9 2.28433e9i −0.475168 0.823015i 0.524428 0.851455i \(-0.324279\pi\)
−0.999595 + 0.0284401i \(0.990946\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.36665e9 −1.52989 −0.764946 0.644094i \(-0.777234\pi\)
−0.764946 + 0.644094i \(0.777234\pi\)
\(504\) 0 0
\(505\) 7.84040e8 0.270906
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.37515e8 1.45062e9i −0.281501 0.487575i 0.690253 0.723568i \(-0.257499\pi\)
−0.971755 + 0.235993i \(0.924166\pi\)
\(510\) 0 0
\(511\) −2.27974e9 3.36322e8i −0.755808 0.111502i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9.73498e7 1.68615e8i 0.0314058 0.0543965i
\(516\) 0 0
\(517\) −9.01559e8 −0.286931
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.53370e9 + 2.65645e9i −0.475125 + 0.822941i −0.999594 0.0284883i \(-0.990931\pi\)
0.524469 + 0.851430i \(0.324264\pi\)
\(522\) 0 0
\(523\) 3.71080e8 + 6.42729e8i 0.113426 + 0.196459i 0.917149 0.398544i \(-0.130484\pi\)
−0.803724 + 0.595003i \(0.797151\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.16335e8 8.94318e8i −0.153672 0.266167i
\(528\) 0 0
\(529\) −3.05156e9 + 5.28546e9i −0.896246 + 1.55234i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.41957e8 0.0406081
\(534\) 0 0
\(535\) 2.75367e9 4.76949e9i 0.777451 1.34658i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.64820e8 7.01846e8i −0.0453366 0.193055i
\(540\) 0 0
\(541\) 2.27287e9 + 3.93672e9i 0.617139 + 1.06892i 0.990005 + 0.141031i \(0.0450419\pi\)
−0.372866 + 0.927885i \(0.621625\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.17060e9 1.10360
\(546\) 0 0
\(547\) 1.93020e9 0.504252 0.252126 0.967694i \(-0.418870\pi\)
0.252126 + 0.967694i \(0.418870\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.00706e9 1.74429e9i −0.256464 0.444209i
\(552\) 0 0
\(553\) −1.05567e9 + 1.33230e9i −0.265454 + 0.335014i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.03481e9 3.52440e9i 0.498920 0.864155i −0.501079 0.865402i \(-0.667063\pi\)
0.999999 + 0.00124625i \(0.000396694\pi\)
\(558\) 0 0
\(559\) −3.74403e7 −0.00906564
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.00511e9 + 3.47296e9i −0.473543 + 0.820201i −0.999541 0.0302848i \(-0.990359\pi\)
0.525998 + 0.850486i \(0.323692\pi\)
\(564\) 0 0
\(565\) 3.03704e9 + 5.26032e9i 0.708405 + 1.22699i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.19263e9 + 2.06570e9i 0.271402 + 0.470083i 0.969221 0.246192i \(-0.0791793\pi\)
−0.697819 + 0.716274i \(0.745846\pi\)
\(570\) 0 0
\(571\) 6.06291e8 1.05013e9i 0.136287 0.236056i −0.789801 0.613363i \(-0.789816\pi\)
0.926088 + 0.377307i \(0.123150\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.07353e9 0.893579
\(576\) 0 0
\(577\) 3.05691e9 5.29472e9i 0.662471 1.14743i −0.317493 0.948261i \(-0.602841\pi\)
0.979964 0.199173i \(-0.0638256\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.15223e9 2.90904e9i −0.243738 0.615365i
\(582\) 0 0
\(583\) −1.63554e8 2.83284e8i −0.0341838 0.0592081i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8.73746e9 −1.78300 −0.891502 0.453018i \(-0.850347\pi\)
−0.891502 + 0.453018i \(0.850347\pi\)
\(588\) 0 0
\(589\) 1.87138e9 0.377362
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.48503e9 2.57215e9i −0.292445 0.506529i 0.681943 0.731406i \(-0.261135\pi\)
−0.974387 + 0.224877i \(0.927802\pi\)
\(594\) 0 0
\(595\) −2.26901e9 5.72856e9i −0.441597 1.11490i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.58591e9 4.47892e9i 0.491608 0.851491i −0.508345 0.861154i \(-0.669743\pi\)
0.999953 + 0.00966288i \(0.00307584\pi\)
\(600\) 0 0
\(601\) −2.35291e8 −0.0442125 −0.0221062 0.999756i \(-0.507037\pi\)
−0.0221062 + 0.999756i \(0.507037\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.24120e9 5.61393e9i 0.595063 1.03068i
\(606\) 0 0
\(607\) −3.12330e9 5.40971e9i −0.566830 0.981778i −0.996877 0.0789718i \(-0.974836\pi\)
0.430047 0.902807i \(-0.358497\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.61318e8 4.52616e8i −0.0463474 0.0802760i
\(612\) 0 0
\(613\) 3.50079e9 6.06355e9i 0.613840 1.06320i −0.376747 0.926316i \(-0.622957\pi\)
0.990587 0.136885i \(-0.0437092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.98807e9 −1.02633 −0.513167 0.858289i \(-0.671528\pi\)
−0.513167 + 0.858289i \(0.671528\pi\)
\(618\) 0 0
\(619\) 5.02918e9 8.71079e9i 0.852275 1.47618i −0.0268758 0.999639i \(-0.508556\pi\)
0.879150 0.476544i \(-0.158111\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.67300e9 7.15956e9i 0.939949 1.18626i
\(624\) 0 0
\(625\) 3.81102e9 + 6.60087e9i 0.624397 + 1.08149i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.74286e9 −1.08036
\(630\) 0 0
\(631\) 9.39565e9 1.48876 0.744379 0.667757i \(-0.232746\pi\)
0.744379 + 0.667757i \(0.232746\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.43111e9 + 5.94285e9i 0.531773 + 0.921058i
\(636\) 0 0
\(637\) 3.04579e8 2.86177e8i 0.0466888 0.0438678i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.20822e9 + 3.82475e9i −0.331161 + 0.573588i −0.982740 0.184993i \(-0.940774\pi\)
0.651579 + 0.758581i \(0.274107\pi\)
\(642\) 0 0
\(643\) −8.74949e9 −1.29791 −0.648954 0.760827i \(-0.724793\pi\)
−0.648954 + 0.760827i \(0.724793\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.90059e9 + 8.48807e9i −0.711350 + 1.23209i 0.253001 + 0.967466i \(0.418583\pi\)
−0.964351 + 0.264628i \(0.914751\pi\)
\(648\) 0 0
\(649\) −4.55532e8 7.89005e8i −0.0654128 0.113298i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.61621e9 + 7.99551e9i 0.648768 + 1.12370i 0.983417 + 0.181357i \(0.0580489\pi\)
−0.334649 + 0.942343i \(0.608618\pi\)
\(654\) 0 0
\(655\) 3.98413e9 6.90072e9i 0.553974 0.959511i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.45582e9 0.334270 0.167135 0.985934i \(-0.446548\pi\)
0.167135 + 0.985934i \(0.446548\pi\)
\(660\) 0 0
\(661\) 4.69707e9 8.13557e9i 0.632590 1.09568i −0.354431 0.935082i \(-0.615325\pi\)
0.987020 0.160595i \(-0.0513414\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.10463e10 + 1.62962e9i 1.45660 + 0.214887i
\(666\) 0 0
\(667\) 2.76354e9 + 4.78658e9i 0.360599 + 0.624576i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.82471e8 −0.0360948
\(672\) 0 0
\(673\) 1.12505e10 1.42272 0.711362 0.702825i \(-0.248079\pi\)
0.711362 + 0.702825i \(0.248079\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.57926e8 1.31277e9i −0.0938785 0.162602i 0.815261 0.579093i \(-0.196593\pi\)
−0.909140 + 0.416491i \(0.863260\pi\)
\(678\) 0 0
\(679\) −5.09517e9 1.28638e10i −0.624618 1.57697i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.96753e9 3.40787e9i 0.236293 0.409271i −0.723355 0.690476i \(-0.757401\pi\)
0.959648 + 0.281206i \(0.0907343\pi\)
\(684\) 0 0
\(685\) 2.72911e9 0.324418
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.48125e7 1.64220e8i 0.0110433 0.0191275i
\(690\) 0 0
\(691\) 5.25151e8 + 9.09587e8i 0.0605495 + 0.104875i 0.894711 0.446645i \(-0.147381\pi\)
−0.834162 + 0.551520i \(0.814048\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.76720e9 + 9.98909e9i 0.651656 + 1.12870i
\(696\) 0 0
\(697\) −2.74250e9 + 4.75015e9i −0.306783 + 0.531364i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.15758e10 −1.26922 −0.634609 0.772834i \(-0.718839\pi\)
−0.634609 + 0.772834i \(0.718839\pi\)
\(702\) 0 0
\(703\) 6.10962e9 1.05822e10i 0.663240 1.14876i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.03280e9 2.99892e8i −0.216335 0.0319152i
\(708\) 0 0
\(709\) 8.50354e9 + 1.47286e10i 0.896061 + 1.55202i 0.832486 + 0.554047i \(0.186917\pi\)
0.0635758 + 0.997977i \(0.479750\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −5.13534e9 −0.530586
\(714\) 0 0
\(715\) −1.53830e8 −0.0157388
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.12756e8 3.68504e8i −0.0213467 0.0369735i 0.855155 0.518373i \(-0.173462\pi\)
−0.876501 + 0.481399i \(0.840129\pi\)
\(720\) 0 0
\(721\) −3.16896e8 + 3.99936e8i −0.0314879 + 0.0397390i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.18399e9 2.05073e9i 0.115389 0.199860i
\(726\) 0 0
\(727\) 3.28106e9 0.316697 0.158348 0.987383i \(-0.449383\pi\)
0.158348 + 0.987383i \(0.449383\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 7.23316e8 1.25282e9i 0.0684884 0.118625i
\(732\) 0 0
\(733\) 3.71639e9 + 6.43698e9i 0.348544 + 0.603696i 0.985991 0.166798i \(-0.0533429\pi\)
−0.637447 + 0.770494i \(0.720010\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.31551e9 2.27854e9i −0.121049 0.209662i
\(738\) 0 0
\(739\) −5.35283e9 + 9.27138e9i −0.487897 + 0.845062i −0.999903 0.0139196i \(-0.995569\pi\)
0.512006 + 0.858982i \(0.328902\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.15663e9 0.282333 0.141167 0.989986i \(-0.454915\pi\)
0.141167 + 0.989986i \(0.454915\pi\)
\(744\) 0 0
\(745\) 9.87735e9 1.71081e10i 0.875172 1.51584i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.96381e9 + 1.13127e10i −0.779482 + 0.983739i
\(750\) 0 0
\(751\) −1.38864e9 2.40519e9i −0.119632 0.207209i 0.799990 0.600014i \(-0.204838\pi\)
−0.919622 + 0.392805i \(0.871505\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.19015e10 1.85208
\(756\) 0 0
\(757\) 1.22142e9 0.102336 0.0511682 0.998690i \(-0.483706\pi\)
0.0511682 + 0.998690i \(0.483706\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.08867e10 1.88563e10i −0.895466 1.55099i −0.833226 0.552932i \(-0.813509\pi\)
−0.0622399 0.998061i \(-0.519824\pi\)
\(762\) 0 0
\(763\) −1.08132e10 1.59524e9i −0.881291 0.130014i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.64073e8 4.57388e8i 0.0211320 0.0366017i
\(768\) 0 0
\(769\) −1.87936e10 −1.49028 −0.745138 0.666910i \(-0.767617\pi\)
−0.745138 + 0.666910i \(0.767617\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.59566e9 7.95992e9i 0.357866 0.619841i −0.629738 0.776807i \(-0.716838\pi\)
0.987604 + 0.156966i \(0.0501713\pi\)
\(774\) 0 0
\(775\) 1.10008e9 + 1.90539e9i 0.0848920 + 0.147037i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.96988e9 8.60809e9i −0.376674 0.652418i
\(780\) 0 0
\(781\) −1.30317e9 + 2.25716e9i −0.0978868 + 0.169545i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 4.10291e9 0.302725
\(786\) 0 0
\(787\) 8.75830e9 1.51698e10i 0.640484 1.10935i −0.344841 0.938661i \(-0.612067\pi\)
0.985325 0.170690i \(-0.0545995\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.86217e9 1.48002e10i −0.421154 1.06329i
\(792\) 0 0
\(793\)