Properties

Label 43.9.b.b.42.1
Level 43
Weight 9
Character 43.42
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.1
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.28

$q$-expansion

\(f(q)\) \(=\) \(q-31.2764i q^{2} -113.679i q^{3} -722.216 q^{4} +959.913i q^{5} -3555.47 q^{6} -3354.89i q^{7} +14581.6i q^{8} -6361.87 q^{9} +O(q^{10})\) \(q-31.2764i q^{2} -113.679i q^{3} -722.216 q^{4} +959.913i q^{5} -3555.47 q^{6} -3354.89i q^{7} +14581.6i q^{8} -6361.87 q^{9} +30022.7 q^{10} +5045.72 q^{11} +82100.6i q^{12} -13469.7 q^{13} -104929. q^{14} +109122. q^{15} +271172. q^{16} -93670.1 q^{17} +198977. i q^{18} +74948.1i q^{19} -693264. i q^{20} -381380. q^{21} -157812. i q^{22} -309529. q^{23} +1.65762e6 q^{24} -530808. q^{25} +421285. i q^{26} -22636.4i q^{27} +2.42295e6i q^{28} +568675. i q^{29} -3.41294e6i q^{30} +953857. q^{31} -4.74843e6i q^{32} -573591. i q^{33} +2.92967e6i q^{34} +3.22040e6 q^{35} +4.59465e6 q^{36} -3565.48i q^{37} +2.34411e6 q^{38} +1.53122e6i q^{39} -1.39970e7 q^{40} -264952. q^{41} +1.19282e7i q^{42} +(3.41591e6 + 140476. i) q^{43} -3.64410e6 q^{44} -6.10685e6i q^{45} +9.68097e6i q^{46} -8.56154e6 q^{47} -3.08266e7i q^{48} -5.49048e6 q^{49} +1.66018e7i q^{50} +1.06483e7i q^{51} +9.72805e6 q^{52} -381997. q^{53} -707985. q^{54} +4.84345e6i q^{55} +4.89195e7 q^{56} +8.52001e6 q^{57} +1.77861e7 q^{58} -9.85667e6 q^{59} -7.88095e7 q^{60} -1.09708e7i q^{61} -2.98332e7i q^{62} +2.13434e7i q^{63} -7.90937e7 q^{64} -1.29298e7i q^{65} -1.79399e7 q^{66} -1.57820e6 q^{67} +6.76500e7 q^{68} +3.51869e7i q^{69} -1.00723e8i q^{70} +4.72551e7i q^{71} -9.27661e7i q^{72} +1.85106e7i q^{73} -111516. q^{74} +6.03417e7i q^{75} -5.41287e7i q^{76} -1.69278e7i q^{77} +4.78912e7 q^{78} +2.99604e7 q^{79} +2.60302e8i q^{80} -4.43135e7 q^{81} +8.28675e6i q^{82} -5.39305e7 q^{83} +2.75438e8 q^{84} -8.99151e7i q^{85} +(4.39360e6 - 1.06838e8i) q^{86} +6.46463e7 q^{87} +7.35745e7i q^{88} +1.45976e7i q^{89} -1.91000e8 q^{90} +4.51894e7i q^{91} +2.23547e8 q^{92} -1.08433e8i q^{93} +2.67774e8i q^{94} -7.19437e7 q^{95} -5.39795e8 q^{96} +3.45903e7 q^{97} +1.71723e8i q^{98} -3.21002e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.2764i 1.95478i −0.211450 0.977389i \(-0.567819\pi\)
0.211450 0.977389i \(-0.432181\pi\)
\(3\) 113.679i 1.40344i −0.712452 0.701721i \(-0.752415\pi\)
0.712452 0.701721i \(-0.247585\pi\)
\(4\) −722.216 −2.82116
\(5\) 959.913i 1.53586i 0.640533 + 0.767931i \(0.278713\pi\)
−0.640533 + 0.767931i \(0.721287\pi\)
\(6\) −3555.47 −2.74342
\(7\) 3354.89i 1.39729i −0.715469 0.698644i \(-0.753787\pi\)
0.715469 0.698644i \(-0.246213\pi\)
\(8\) 14581.6i 3.55995i
\(9\) −6361.87 −0.969650
\(10\) 30022.7 3.00227
\(11\) 5045.72 0.344629 0.172315 0.985042i \(-0.444875\pi\)
0.172315 + 0.985042i \(0.444875\pi\)
\(12\) 82100.6i 3.95933i
\(13\) −13469.7 −0.471613 −0.235806 0.971800i \(-0.575773\pi\)
−0.235806 + 0.971800i \(0.575773\pi\)
\(14\) −104929. −2.73139
\(15\) 109122. 2.15549
\(16\) 271172. 4.13776
\(17\) −93670.1 −1.12152 −0.560758 0.827980i \(-0.689490\pi\)
−0.560758 + 0.827980i \(0.689490\pi\)
\(18\) 198977.i 1.89545i
\(19\) 74948.1i 0.575104i 0.957765 + 0.287552i \(0.0928414\pi\)
−0.957765 + 0.287552i \(0.907159\pi\)
\(20\) 693264.i 4.33290i
\(21\) −381380. −1.96101
\(22\) 157812.i 0.673673i
\(23\) −309529. −1.10609 −0.553045 0.833152i \(-0.686534\pi\)
−0.553045 + 0.833152i \(0.686534\pi\)
\(24\) 1.65762e6 4.99619
\(25\) −530808. −1.35887
\(26\) 421285.i 0.921898i
\(27\) 22636.4i 0.0425943i
\(28\) 2.42295e6i 3.94197i
\(29\) 568675.i 0.804029i 0.915633 + 0.402015i \(0.131690\pi\)
−0.915633 + 0.402015i \(0.868310\pi\)
\(30\) 3.41294e6i 4.21351i
\(31\) 953857. 1.03285 0.516424 0.856333i \(-0.327263\pi\)
0.516424 + 0.856333i \(0.327263\pi\)
\(32\) 4.74843e6i 4.52845i
\(33\) 573591.i 0.483667i
\(34\) 2.92967e6i 2.19231i
\(35\) 3.22040e6 2.14604
\(36\) 4.59465e6 2.73553
\(37\) 3565.48i 0.00190244i −1.00000 0.000951221i \(-0.999697\pi\)
1.00000 0.000951221i \(-0.000302783\pi\)
\(38\) 2.34411e6 1.12420
\(39\) 1.53122e6i 0.661881i
\(40\) −1.39970e7 −5.46759
\(41\) −264952. −0.0937630 −0.0468815 0.998900i \(-0.514928\pi\)
−0.0468815 + 0.998900i \(0.514928\pi\)
\(42\) 1.19282e7i 3.83334i
\(43\) 3.41591e6 + 140476.i 0.999155 + 0.0410893i
\(44\) −3.64410e6 −0.972252
\(45\) 6.10685e6i 1.48925i
\(46\) 9.68097e6i 2.16216i
\(47\) −8.56154e6 −1.75453 −0.877264 0.480008i \(-0.840634\pi\)
−0.877264 + 0.480008i \(0.840634\pi\)
\(48\) 3.08266e7i 5.80711i
\(49\) −5.49048e6 −0.952414
\(50\) 1.66018e7i 2.65629i
\(51\) 1.06483e7i 1.57398i
\(52\) 9.72805e6 1.33049
\(53\) −381997. −0.0484123 −0.0242062 0.999707i \(-0.507706\pi\)
−0.0242062 + 0.999707i \(0.507706\pi\)
\(54\) −707985. −0.0832624
\(55\) 4.84345e6i 0.529302i
\(56\) 4.89195e7 4.97428
\(57\) 8.52001e6 0.807125
\(58\) 1.77861e7 1.57170
\(59\) −9.85667e6 −0.813433 −0.406717 0.913554i \(-0.633326\pi\)
−0.406717 + 0.913554i \(0.633326\pi\)
\(60\) −7.88095e7 −6.08098
\(61\) 1.09708e7i 0.792354i −0.918174 0.396177i \(-0.870337\pi\)
0.918174 0.396177i \(-0.129663\pi\)
\(62\) 2.98332e7i 2.01899i
\(63\) 2.13434e7i 1.35488i
\(64\) −7.90937e7 −4.71435
\(65\) 1.29298e7i 0.724332i
\(66\) −1.79399e7 −0.945462
\(67\) −1.57820e6 −0.0783181 −0.0391590 0.999233i \(-0.512468\pi\)
−0.0391590 + 0.999233i \(0.512468\pi\)
\(68\) 6.76500e7 3.16397
\(69\) 3.51869e7i 1.55233i
\(70\) 1.00723e8i 4.19503i
\(71\) 4.72551e7i 1.85958i 0.368086 + 0.929792i \(0.380013\pi\)
−0.368086 + 0.929792i \(0.619987\pi\)
\(72\) 9.27661e7i 3.45191i
\(73\) 1.85106e7i 0.651823i 0.945400 + 0.325911i \(0.105671\pi\)
−0.945400 + 0.325911i \(0.894329\pi\)
\(74\) −111516. −0.00371885
\(75\) 6.03417e7i 1.90709i
\(76\) 5.41287e7i 1.62246i
\(77\) 1.69278e7i 0.481546i
\(78\) 4.78912e7 1.29383
\(79\) 2.99604e7 0.769200 0.384600 0.923083i \(-0.374339\pi\)
0.384600 + 0.923083i \(0.374339\pi\)
\(80\) 2.60302e8i 6.35503i
\(81\) −4.43135e7 −1.02943
\(82\) 8.28675e6i 0.183286i
\(83\) −5.39305e7 −1.13638 −0.568188 0.822899i \(-0.692355\pi\)
−0.568188 + 0.822899i \(0.692355\pi\)
\(84\) 2.75438e8 5.53232
\(85\) 8.99151e7i 1.72249i
\(86\) 4.39360e6 1.06838e8i 0.0803205 1.95313i
\(87\) 6.46463e7 1.12841
\(88\) 7.35745e7i 1.22686i
\(89\) 1.45976e7i 0.232659i 0.993211 + 0.116330i \(0.0371129\pi\)
−0.993211 + 0.116330i \(0.962887\pi\)
\(90\) −1.91000e8 −2.91115
\(91\) 4.51894e7i 0.658979i
\(92\) 2.23547e8 3.12045
\(93\) 1.08433e8i 1.44954i
\(94\) 2.67774e8i 3.42971i
\(95\) −7.19437e7 −0.883280
\(96\) −5.39795e8 −6.35542
\(97\) 3.45903e7 0.390721 0.195361 0.980731i \(-0.437412\pi\)
0.195361 + 0.980731i \(0.437412\pi\)
\(98\) 1.71723e8i 1.86176i
\(99\) −3.21002e7 −0.334170
\(100\) 3.83358e8 3.83358
\(101\) −1.49089e8 −1.43271 −0.716356 0.697735i \(-0.754192\pi\)
−0.716356 + 0.697735i \(0.754192\pi\)
\(102\) 3.33041e8 3.07678
\(103\) 2.09069e7 0.185755 0.0928776 0.995678i \(-0.470393\pi\)
0.0928776 + 0.995678i \(0.470393\pi\)
\(104\) 1.96410e8i 1.67892i
\(105\) 3.66091e8i 3.01184i
\(106\) 1.19475e7i 0.0946354i
\(107\) −2.05062e8 −1.56441 −0.782203 0.623024i \(-0.785904\pi\)
−0.782203 + 0.623024i \(0.785904\pi\)
\(108\) 1.63483e7i 0.120165i
\(109\) −1.27916e7 −0.0906193 −0.0453096 0.998973i \(-0.514427\pi\)
−0.0453096 + 0.998973i \(0.514427\pi\)
\(110\) 1.51486e8 1.03467
\(111\) −405320. −0.00266997
\(112\) 9.09753e8i 5.78165i
\(113\) 3.28021e7i 0.201182i 0.994928 + 0.100591i \(0.0320733\pi\)
−0.994928 + 0.100591i \(0.967927\pi\)
\(114\) 2.66476e8i 1.57775i
\(115\) 2.97121e8i 1.69880i
\(116\) 4.10706e8i 2.26829i
\(117\) 8.56927e7 0.457299
\(118\) 3.08281e8i 1.59008i
\(119\) 3.14253e8i 1.56708i
\(120\) 1.59117e9i 7.67345i
\(121\) −1.88900e8 −0.881231
\(122\) −3.43128e8 −1.54888
\(123\) 3.01194e7i 0.131591i
\(124\) −6.88890e8 −2.91382
\(125\) 1.34564e8i 0.551173i
\(126\) 6.67545e8 2.64849
\(127\) −3.31370e7 −0.127379 −0.0636895 0.997970i \(-0.520287\pi\)
−0.0636895 + 0.997970i \(0.520287\pi\)
\(128\) 1.25817e9i 4.68706i
\(129\) 1.59692e7 3.88317e8i 0.0576665 1.40226i
\(130\) −4.04397e8 −1.41591
\(131\) 2.70330e8i 0.917930i −0.888454 0.458965i \(-0.848220\pi\)
0.888454 0.458965i \(-0.151780\pi\)
\(132\) 4.14256e8i 1.36450i
\(133\) 2.51443e8 0.803586
\(134\) 4.93604e7i 0.153094i
\(135\) 2.17289e7 0.0654189
\(136\) 1.36586e9i 3.99254i
\(137\) 1.27305e8i 0.361378i 0.983540 + 0.180689i \(0.0578328\pi\)
−0.983540 + 0.180689i \(0.942167\pi\)
\(138\) 1.10052e9 3.03447
\(139\) −2.00149e8 −0.536159 −0.268080 0.963397i \(-0.586389\pi\)
−0.268080 + 0.963397i \(0.586389\pi\)
\(140\) −2.32582e9 −6.05431
\(141\) 9.73265e8i 2.46238i
\(142\) 1.47797e9 3.63507
\(143\) −6.79644e7 −0.162531
\(144\) −1.72516e9 −4.01218
\(145\) −5.45878e8 −1.23488
\(146\) 5.78947e8 1.27417
\(147\) 6.24151e8i 1.33666i
\(148\) 2.57505e6i 0.00536709i
\(149\) 7.17341e8i 1.45539i −0.685899 0.727697i \(-0.740591\pi\)
0.685899 0.727697i \(-0.259409\pi\)
\(150\) 1.88727e9 3.72795
\(151\) 3.89398e8i 0.749007i −0.927226 0.374503i \(-0.877813\pi\)
0.927226 0.374503i \(-0.122187\pi\)
\(152\) −1.09286e9 −2.04734
\(153\) 5.95917e8 1.08748
\(154\) −5.29442e8 −0.941316
\(155\) 9.15620e8i 1.58631i
\(156\) 1.10587e9i 1.86727i
\(157\) 8.94542e8i 1.47232i −0.676808 0.736160i \(-0.736637\pi\)
0.676808 0.736160i \(-0.263363\pi\)
\(158\) 9.37055e8i 1.50362i
\(159\) 4.34249e7i 0.0679439i
\(160\) 4.55808e9 6.95507
\(161\) 1.03844e9i 1.54553i
\(162\) 1.38597e9i 2.01230i
\(163\) 8.43950e8i 1.19555i −0.801665 0.597773i \(-0.796052\pi\)
0.801665 0.597773i \(-0.203948\pi\)
\(164\) 1.91352e8 0.264520
\(165\) 5.50598e8 0.742845
\(166\) 1.68675e9i 2.22136i
\(167\) 1.21430e9 1.56120 0.780602 0.625028i \(-0.214913\pi\)
0.780602 + 0.625028i \(0.214913\pi\)
\(168\) 5.56112e9i 6.98112i
\(169\) −6.34297e8 −0.777581
\(170\) −2.81223e9 −3.36709
\(171\) 4.76810e8i 0.557650i
\(172\) −2.46703e9 1.01454e8i −2.81877 0.115919i
\(173\) −6.89077e8 −0.769278 −0.384639 0.923067i \(-0.625674\pi\)
−0.384639 + 0.923067i \(0.625674\pi\)
\(174\) 2.02190e9i 2.20579i
\(175\) 1.78080e9i 1.89873i
\(176\) 1.36826e9 1.42599
\(177\) 1.12049e9i 1.14161i
\(178\) 4.56560e8 0.454797
\(179\) 1.17356e9i 1.14312i 0.820560 + 0.571560i \(0.193662\pi\)
−0.820560 + 0.571560i \(0.806338\pi\)
\(180\) 4.41046e9i 4.20140i
\(181\) −1.12673e9 −1.04980 −0.524901 0.851164i \(-0.675898\pi\)
−0.524901 + 0.851164i \(0.675898\pi\)
\(182\) 1.41336e9 1.28816
\(183\) −1.24715e9 −1.11202
\(184\) 4.51342e9i 3.93763i
\(185\) 3.42255e6 0.00292189
\(186\) −3.39141e9 −2.83353
\(187\) −4.72633e8 −0.386507
\(188\) 6.18328e9 4.94980
\(189\) −7.59425e7 −0.0595165
\(190\) 2.25014e9i 1.72662i
\(191\) 5.17933e8i 0.389171i −0.980886 0.194585i \(-0.937664\pi\)
0.980886 0.194585i \(-0.0623362\pi\)
\(192\) 8.99128e9i 6.61632i
\(193\) −8.56057e8 −0.616983 −0.308492 0.951227i \(-0.599824\pi\)
−0.308492 + 0.951227i \(0.599824\pi\)
\(194\) 1.08186e9i 0.763773i
\(195\) −1.46984e9 −1.01656
\(196\) 3.96531e9 2.68691
\(197\) 1.73863e9 1.15437 0.577183 0.816615i \(-0.304152\pi\)
0.577183 + 0.816615i \(0.304152\pi\)
\(198\) 1.00398e9i 0.653227i
\(199\) 6.62621e8i 0.422526i 0.977429 + 0.211263i \(0.0677576\pi\)
−0.977429 + 0.211263i \(0.932242\pi\)
\(200\) 7.74002e9i 4.83751i
\(201\) 1.79408e8i 0.109915i
\(202\) 4.66296e9i 2.80063i
\(203\) 1.90784e9 1.12346
\(204\) 7.69037e9i 4.44045i
\(205\) 2.54331e8i 0.144007i
\(206\) 6.53894e8i 0.363110i
\(207\) 1.96919e9 1.07252
\(208\) −3.65262e9 −1.95142
\(209\) 3.78167e8i 0.198198i
\(210\) −1.14500e10 −5.88748
\(211\) 5.32912e8i 0.268859i 0.990923 + 0.134430i \(0.0429203\pi\)
−0.990923 + 0.134430i \(0.957080\pi\)
\(212\) 2.75884e8 0.136579
\(213\) 5.37191e9 2.60982
\(214\) 6.41360e9i 3.05806i
\(215\) −1.34845e8 + 3.27898e9i −0.0631075 + 1.53456i
\(216\) 3.30074e8 0.151634
\(217\) 3.20008e9i 1.44319i
\(218\) 4.00077e8i 0.177140i
\(219\) 2.10427e9 0.914796
\(220\) 3.49801e9i 1.49324i
\(221\) 1.26171e9 0.528921
\(222\) 1.26770e7i 0.00521919i
\(223\) 3.32528e8i 0.134465i −0.997737 0.0672325i \(-0.978583\pi\)
0.997737 0.0672325i \(-0.0214169\pi\)
\(224\) −1.59304e10 −6.32755
\(225\) 3.37694e9 1.31763
\(226\) 1.02593e9 0.393265
\(227\) 4.20770e9i 1.58468i −0.610079 0.792340i \(-0.708862\pi\)
0.610079 0.792340i \(-0.291138\pi\)
\(228\) −6.15329e9 −2.27703
\(229\) 7.65732e8 0.278442 0.139221 0.990261i \(-0.455540\pi\)
0.139221 + 0.990261i \(0.455540\pi\)
\(230\) −9.29289e9 −3.32078
\(231\) −1.92433e9 −0.675822
\(232\) −8.29217e9 −2.86231
\(233\) 1.30824e9i 0.443878i 0.975061 + 0.221939i \(0.0712386\pi\)
−0.975061 + 0.221939i \(0.928761\pi\)
\(234\) 2.68016e9i 0.893918i
\(235\) 8.21833e9i 2.69471i
\(236\) 7.11864e9 2.29482
\(237\) 3.40586e9i 1.07953i
\(238\) 9.82870e9 3.06329
\(239\) −4.43573e9 −1.35948 −0.679741 0.733452i \(-0.737908\pi\)
−0.679741 + 0.733452i \(0.737908\pi\)
\(240\) 2.95908e10 8.91891
\(241\) 9.19495e8i 0.272572i −0.990670 0.136286i \(-0.956483\pi\)
0.990670 0.136286i \(-0.0435166\pi\)
\(242\) 5.90811e9i 1.72261i
\(243\) 4.88899e9i 1.40215i
\(244\) 7.92329e9i 2.23535i
\(245\) 5.27038e9i 1.46278i
\(246\) 9.42028e8 0.257231
\(247\) 1.00953e9i 0.271226i
\(248\) 1.39087e10i 3.67689i
\(249\) 6.13076e9i 1.59484i
\(250\) −4.20868e9 −1.07742
\(251\) 4.86683e9 1.22617 0.613086 0.790016i \(-0.289928\pi\)
0.613086 + 0.790016i \(0.289928\pi\)
\(252\) 1.54145e10i 3.82233i
\(253\) −1.56180e9 −0.381191
\(254\) 1.03641e9i 0.248998i
\(255\) −1.02214e10 −2.41742
\(256\) 1.91032e10 4.44781
\(257\) 9.95226e8i 0.228134i −0.993473 0.114067i \(-0.963612\pi\)
0.993473 0.114067i \(-0.0363878\pi\)
\(258\) −1.21452e10 4.99459e8i −2.74110 0.112725i
\(259\) −1.19618e7 −0.00265826
\(260\) 9.33808e9i 2.04345i
\(261\) 3.61784e9i 0.779627i
\(262\) −8.45497e9 −1.79435
\(263\) 4.32574e9i 0.904145i −0.891981 0.452072i \(-0.850685\pi\)
0.891981 0.452072i \(-0.149315\pi\)
\(264\) 8.36386e9 1.72183
\(265\) 3.66684e8i 0.0743546i
\(266\) 7.86423e9i 1.57083i
\(267\) 1.65943e9 0.326524
\(268\) 1.13980e9 0.220947
\(269\) −4.97219e9 −0.949595 −0.474797 0.880095i \(-0.657479\pi\)
−0.474797 + 0.880095i \(0.657479\pi\)
\(270\) 6.79604e8i 0.127879i
\(271\) 6.79997e9 1.26075 0.630377 0.776290i \(-0.282901\pi\)
0.630377 + 0.776290i \(0.282901\pi\)
\(272\) −2.54007e10 −4.64056
\(273\) 5.13708e9 0.924839
\(274\) 3.98164e9 0.706414
\(275\) −2.67831e9 −0.468306
\(276\) 2.54125e10i 4.37937i
\(277\) 8.34803e9i 1.41796i 0.705227 + 0.708982i \(0.250845\pi\)
−0.705227 + 0.708982i \(0.749155\pi\)
\(278\) 6.25994e9i 1.04807i
\(279\) −6.06832e9 −1.00150
\(280\) 4.69585e10i 7.63980i
\(281\) −6.24432e9 −1.00152 −0.500760 0.865586i \(-0.666946\pi\)
−0.500760 + 0.865586i \(0.666946\pi\)
\(282\) 3.04403e10 4.81340
\(283\) 4.82638e9 0.752447 0.376224 0.926529i \(-0.377222\pi\)
0.376224 + 0.926529i \(0.377222\pi\)
\(284\) 3.41284e10i 5.24617i
\(285\) 8.17847e9i 1.23963i
\(286\) 2.12569e9i 0.317713i
\(287\) 8.88883e8i 0.131014i
\(288\) 3.02089e10i 4.39101i
\(289\) 1.79832e9 0.257796
\(290\) 1.70731e10i 2.41391i
\(291\) 3.93218e9i 0.548355i
\(292\) 1.33687e10i 1.83889i
\(293\) 8.17623e9 1.10939 0.554693 0.832055i \(-0.312836\pi\)
0.554693 + 0.832055i \(0.312836\pi\)
\(294\) 1.95212e10 2.61287
\(295\) 9.46154e9i 1.24932i
\(296\) 5.19903e7 0.00677261
\(297\) 1.14217e8i 0.0146792i
\(298\) −2.24359e10 −2.84497
\(299\) 4.16928e9 0.521646
\(300\) 4.35797e10i 5.38021i
\(301\) 4.71282e8 1.14600e10i 0.0574137 1.39611i
\(302\) −1.21790e10 −1.46414
\(303\) 1.69482e10i 2.01073i
\(304\) 2.03239e10i 2.37964i
\(305\) 1.05310e10 1.21695
\(306\) 1.86382e10i 2.12578i
\(307\) −5.25589e9 −0.591688 −0.295844 0.955236i \(-0.595601\pi\)
−0.295844 + 0.955236i \(0.595601\pi\)
\(308\) 1.22255e10i 1.35852i
\(309\) 2.37667e9i 0.260697i
\(310\) 2.86373e10 3.10088
\(311\) 1.34118e10 1.43366 0.716831 0.697247i \(-0.245592\pi\)
0.716831 + 0.697247i \(0.245592\pi\)
\(312\) −2.23276e10 −2.35627
\(313\) 2.87909e9i 0.299970i 0.988688 + 0.149985i \(0.0479225\pi\)
−0.988688 + 0.149985i \(0.952078\pi\)
\(314\) −2.79781e10 −2.87806
\(315\) −2.04878e10 −2.08091
\(316\) −2.16379e10 −2.17003
\(317\) −1.72017e10 −1.70347 −0.851736 0.523972i \(-0.824450\pi\)
−0.851736 + 0.523972i \(0.824450\pi\)
\(318\) 1.35818e9 0.132815
\(319\) 2.86937e9i 0.277092i
\(320\) 7.59231e10i 7.24059i
\(321\) 2.33112e10i 2.19555i
\(322\) 3.24786e10 3.02116
\(323\) 7.02040e9i 0.644988i
\(324\) 3.20039e10 2.90418
\(325\) 7.14984e9 0.640860
\(326\) −2.63958e10 −2.33703
\(327\) 1.45414e9i 0.127179i
\(328\) 3.86341e9i 0.333792i
\(329\) 2.87230e10i 2.45158i
\(330\) 1.72207e10i 1.45210i
\(331\) 6.13133e9i 0.510790i 0.966837 + 0.255395i \(0.0822056\pi\)
−0.966837 + 0.255395i \(0.917794\pi\)
\(332\) 3.89495e10 3.20589
\(333\) 2.26832e7i 0.00184470i
\(334\) 3.79790e10i 3.05181i
\(335\) 1.51493e9i 0.120286i
\(336\) −1.03420e11 −8.11421
\(337\) 8.98842e9 0.696890 0.348445 0.937329i \(-0.386710\pi\)
0.348445 + 0.937329i \(0.386710\pi\)
\(338\) 1.98386e10i 1.52000i
\(339\) 3.72891e9 0.282347
\(340\) 6.49381e10i 4.85942i
\(341\) 4.81289e9 0.355949
\(342\) −1.49129e10 −1.09008
\(343\) 9.20331e8i 0.0664918i
\(344\) −2.04837e9 + 4.98094e10i −0.146276 + 3.55695i
\(345\) −3.37764e10 −2.38417
\(346\) 2.15519e10i 1.50377i
\(347\) 2.09994e10i 1.44840i −0.689589 0.724201i \(-0.742209\pi\)
0.689589 0.724201i \(-0.257791\pi\)
\(348\) −4.66885e10 −3.18342
\(349\) 1.43451e10i 0.966944i −0.875360 0.483472i \(-0.839375\pi\)
0.875360 0.483472i \(-0.160625\pi\)
\(350\) 5.56972e10 3.71160
\(351\) 3.04906e8i 0.0200880i
\(352\) 2.39592e10i 1.56064i
\(353\) 2.42506e10 1.56179 0.780895 0.624662i \(-0.214763\pi\)
0.780895 + 0.624662i \(0.214763\pi\)
\(354\) 3.50451e10 2.23159
\(355\) −4.53608e10 −2.85606
\(356\) 1.05426e10i 0.656368i
\(357\) 3.57239e10 2.19931
\(358\) 3.67047e10 2.23455
\(359\) −1.62715e10 −0.979601 −0.489801 0.871835i \(-0.662930\pi\)
−0.489801 + 0.871835i \(0.662930\pi\)
\(360\) 8.90474e10 5.30165
\(361\) 1.13663e10 0.669256
\(362\) 3.52402e10i 2.05213i
\(363\) 2.14739e10i 1.23676i
\(364\) 3.26365e10i 1.85908i
\(365\) −1.77686e10 −1.00111
\(366\) 3.90064e10i 2.17376i
\(367\) −1.48349e10 −0.817750 −0.408875 0.912590i \(-0.634079\pi\)
−0.408875 + 0.912590i \(0.634079\pi\)
\(368\) −8.39358e10 −4.57674
\(369\) 1.68559e9 0.0909173
\(370\) 1.07045e8i 0.00571164i
\(371\) 1.28156e9i 0.0676460i
\(372\) 7.83122e10i 4.08938i
\(373\) 8.79867e9i 0.454550i −0.973831 0.227275i \(-0.927018\pi\)
0.973831 0.227275i \(-0.0729816\pi\)
\(374\) 1.47823e10i 0.755535i
\(375\) −1.52970e10 −0.773540
\(376\) 1.24841e11i 6.24604i
\(377\) 7.65989e9i 0.379190i
\(378\) 2.37521e9i 0.116342i
\(379\) −2.14636e10 −1.04027 −0.520136 0.854084i \(-0.674119\pi\)
−0.520136 + 0.854084i \(0.674119\pi\)
\(380\) 5.19589e10 2.49187
\(381\) 3.76697e9i 0.178769i
\(382\) −1.61991e10 −0.760743
\(383\) 2.03358e10i 0.945075i −0.881310 0.472538i \(-0.843338\pi\)
0.881310 0.472538i \(-0.156662\pi\)
\(384\) 1.43028e11 6.57802
\(385\) 1.62492e10 0.739588
\(386\) 2.67744e10i 1.20606i
\(387\) −2.17316e10 8.93693e8i −0.968831 0.0398423i
\(388\) −2.49816e10 −1.10229
\(389\) 1.22806e10i 0.536318i −0.963375 0.268159i \(-0.913585\pi\)
0.963375 0.268159i \(-0.0864153\pi\)
\(390\) 4.59714e10i 1.98714i
\(391\) 2.89936e10 1.24050
\(392\) 8.00598e10i 3.39055i
\(393\) −3.07308e10 −1.28826
\(394\) 5.43783e10i 2.25653i
\(395\) 2.87594e10i 1.18138i
\(396\) 2.31833e10 0.942745
\(397\) 2.41690e10 0.972964 0.486482 0.873691i \(-0.338280\pi\)
0.486482 + 0.873691i \(0.338280\pi\)
\(398\) 2.07244e10 0.825944
\(399\) 2.85837e10i 1.12779i
\(400\) −1.43941e11 −5.62268
\(401\) −2.06970e10 −0.800441 −0.400220 0.916419i \(-0.631066\pi\)
−0.400220 + 0.916419i \(0.631066\pi\)
\(402\) 5.61123e9 0.214859
\(403\) −1.28482e10 −0.487104
\(404\) 1.07674e11 4.04191
\(405\) 4.25371e10i 1.58106i
\(406\) 5.96704e10i 2.19612i
\(407\) 1.79904e7i 0.000655637i
\(408\) −1.55269e11 −5.60330
\(409\) 1.95719e9i 0.0699422i 0.999388 + 0.0349711i \(0.0111339\pi\)
−0.999388 + 0.0349711i \(0.988866\pi\)
\(410\) −7.95456e9 −0.281501
\(411\) 1.44718e10 0.507174
\(412\) −1.50993e10 −0.524044
\(413\) 3.30680e10i 1.13660i
\(414\) 6.15891e10i 2.09654i
\(415\) 5.17686e10i 1.74532i
\(416\) 6.39600e10i 2.13568i
\(417\) 2.27527e10i 0.752469i
\(418\) 1.18277e10 0.387432
\(419\) 2.78733e10i 0.904341i 0.891931 + 0.452171i \(0.149350\pi\)
−0.891931 + 0.452171i \(0.850650\pi\)
\(420\) 2.64397e11i 8.49688i
\(421\) 2.18730e10i 0.696274i −0.937444 0.348137i \(-0.886814\pi\)
0.937444 0.348137i \(-0.113186\pi\)
\(422\) 1.66676e10 0.525560
\(423\) 5.44674e10 1.70128
\(424\) 5.57011e9i 0.172346i
\(425\) 4.97208e10 1.52399
\(426\) 1.68014e11i 5.10161i
\(427\) −3.68058e10 −1.10715
\(428\) 1.48099e11 4.41343
\(429\) 7.72612e9i 0.228104i
\(430\) 1.02555e11 + 4.21747e9i 2.99973 + 0.123361i
\(431\) 1.78281e10 0.516649 0.258324 0.966058i \(-0.416830\pi\)
0.258324 + 0.966058i \(0.416830\pi\)
\(432\) 6.13836e9i 0.176245i
\(433\) 9.84525e9i 0.280076i 0.990146 + 0.140038i \(0.0447224\pi\)
−0.990146 + 0.140038i \(0.955278\pi\)
\(434\) −1.00087e11 −2.82111
\(435\) 6.20548e10i 1.73308i
\(436\) 9.23833e9 0.255651
\(437\) 2.31986e10i 0.636116i
\(438\) 6.58140e10i 1.78822i
\(439\) 4.30569e10 1.15927 0.579635 0.814877i \(-0.303195\pi\)
0.579635 + 0.814877i \(0.303195\pi\)
\(440\) −7.06251e10 −1.88429
\(441\) 3.49297e10 0.923508
\(442\) 3.94618e10i 1.03392i
\(443\) 9.46657e9 0.245798 0.122899 0.992419i \(-0.460781\pi\)
0.122899 + 0.992419i \(0.460781\pi\)
\(444\) 2.92728e8 0.00753240
\(445\) −1.40124e10 −0.357332
\(446\) −1.04003e10 −0.262849
\(447\) −8.15465e10 −2.04256
\(448\) 2.65351e11i 6.58731i
\(449\) 2.05489e10i 0.505596i −0.967519 0.252798i \(-0.918649\pi\)
0.967519 0.252798i \(-0.0813508\pi\)
\(450\) 1.05619e11i 2.57567i
\(451\) −1.33687e9 −0.0323135
\(452\) 2.36902e10i 0.567564i
\(453\) −4.42663e10 −1.05119
\(454\) −1.31602e11 −3.09770
\(455\) −4.33779e10 −1.01210
\(456\) 1.24235e11i 2.87333i
\(457\) 2.06983e10i 0.474538i 0.971444 + 0.237269i \(0.0762522\pi\)
−0.971444 + 0.237269i \(0.923748\pi\)
\(458\) 2.39494e10i 0.544293i
\(459\) 2.12035e9i 0.0477702i
\(460\) 2.14586e11i 4.79258i
\(461\) 3.94084e10 0.872541 0.436270 0.899816i \(-0.356299\pi\)
0.436270 + 0.899816i \(0.356299\pi\)
\(462\) 6.01863e10i 1.32108i
\(463\) 3.51471e10i 0.764832i −0.923990 0.382416i \(-0.875092\pi\)
0.923990 0.382416i \(-0.124908\pi\)
\(464\) 1.54209e11i 3.32688i
\(465\) 1.04087e11 2.22630
\(466\) 4.09171e10 0.867683
\(467\) 4.16099e9i 0.0874840i 0.999043 + 0.0437420i \(0.0139280\pi\)
−0.999043 + 0.0437420i \(0.986072\pi\)
\(468\) −6.18886e10 −1.29011
\(469\) 5.29468e9i 0.109433i
\(470\) −2.57040e11 −5.26756
\(471\) −1.01690e11 −2.06632
\(472\) 1.43726e11i 2.89579i
\(473\) 1.72357e10 + 7.08803e8i 0.344338 + 0.0141606i
\(474\) −1.06523e11 −2.11024
\(475\) 3.97831e10i 0.781491i
\(476\) 2.26958e11i 4.42098i
\(477\) 2.43021e9 0.0469430
\(478\) 1.38734e11i 2.65748i
\(479\) −9.43016e10 −1.79134 −0.895668 0.444723i \(-0.853302\pi\)
−0.895668 + 0.444723i \(0.853302\pi\)
\(480\) 5.18157e11i 9.76104i
\(481\) 4.80261e7i 0.000897216i
\(482\) −2.87585e10 −0.532818
\(483\) 1.18048e11 2.16906
\(484\) 1.36426e11 2.48609
\(485\) 3.32037e10i 0.600093i
\(486\) 1.52910e11 2.74089
\(487\) 1.36814e10 0.243228 0.121614 0.992577i \(-0.461193\pi\)
0.121614 + 0.992577i \(0.461193\pi\)
\(488\) 1.59972e11 2.82074
\(489\) −9.59393e10 −1.67788
\(490\) −1.64839e11 −2.85940
\(491\) 9.15932e10i 1.57593i 0.615720 + 0.787965i \(0.288865\pi\)
−0.615720 + 0.787965i \(0.711135\pi\)
\(492\) 2.17527e10i 0.371238i
\(493\) 5.32678e10i 0.901731i
\(494\) −3.15745e10 −0.530187
\(495\) 3.08134e10i 0.513238i
\(496\) 2.58660e11 4.27368
\(497\) 1.58536e11 2.59837
\(498\) 1.91748e11 3.11755
\(499\) 5.23882e10i 0.844951i 0.906374 + 0.422475i \(0.138839\pi\)
−0.906374 + 0.422475i \(0.861161\pi\)
\(500\) 9.71841e10i 1.55495i
\(501\) 1.38040e11i 2.19106i
\(502\) 1.52217e11i 2.39689i
\(503\) 1.09470e11i 1.71010i −0.518543 0.855052i \(-0.673525\pi\)
0.518543 0.855052i \(-0.326475\pi\)
\(504\) −3.11220e11 −4.82331
\(505\) 1.43112e11i 2.20045i
\(506\) 4.88474e10i 0.745143i
\(507\) 7.21061e10i 1.09129i
\(508\) 2.39321e10 0.359356
\(509\) −2.73186e10 −0.406993 −0.203496 0.979076i \(-0.565231\pi\)
−0.203496 + 0.979076i \(0.565231\pi\)
\(510\) 3.19690e11i 4.72551i
\(511\) 6.21011e10 0.910784
\(512\) 2.75387e11i 4.00741i
\(513\) 1.69655e9 0.0244961
\(514\) −3.11271e10 −0.445950
\(515\) 2.00688e10i 0.285294i
\(516\) −1.15332e10 + 2.80449e11i −0.162686 + 3.95598i
\(517\) −4.31991e10 −0.604662
\(518\) 3.74123e8i 0.00519631i
\(519\) 7.83334e10i 1.07964i
\(520\) 1.88536e11 2.57859
\(521\) 1.39505e11i 1.89339i 0.322132 + 0.946695i \(0.395601\pi\)
−0.322132 + 0.946695i \(0.604399\pi\)
\(522\) −1.13153e11 −1.52400
\(523\) 8.40035e10i 1.12277i 0.827555 + 0.561385i \(0.189731\pi\)
−0.827555 + 0.561385i \(0.810269\pi\)
\(524\) 1.95237e11i 2.58962i
\(525\) 2.02440e11 2.66476
\(526\) −1.35294e11 −1.76740
\(527\) −8.93478e10 −1.15835
\(528\) 1.55542e11i 2.00130i
\(529\) 1.74974e10 0.223434
\(530\) −1.14686e10 −0.145347
\(531\) 6.27069e10 0.788746
\(532\) −1.81596e11 −2.26704
\(533\) 3.56883e9 0.0442198
\(534\) 5.19012e10i 0.638282i
\(535\) 1.96841e11i 2.40271i
\(536\) 2.30126e10i 0.278809i
\(537\) 1.33409e11 1.60430
\(538\) 1.55512e11i 1.85625i
\(539\) −2.77034e10 −0.328230
\(540\) −1.56930e10 −0.184557
\(541\) −1.49875e11 −1.74960 −0.874801 0.484483i \(-0.839008\pi\)
−0.874801 + 0.484483i \(0.839008\pi\)
\(542\) 2.12679e11i 2.46449i
\(543\) 1.28086e11i 1.47334i
\(544\) 4.44785e11i 5.07873i
\(545\) 1.22789e10i 0.139179i
\(546\) 1.60670e11i 1.80785i
\(547\) 1.07146e11 1.19681 0.598406 0.801193i \(-0.295801\pi\)
0.598406 + 0.801193i \(0.295801\pi\)
\(548\) 9.19414e10i 1.01950i
\(549\) 6.97949e10i 0.768306i
\(550\) 8.37679e10i 0.915434i
\(551\) −4.26211e10 −0.462400
\(552\) −5.13081e11 −5.52623
\(553\) 1.00514e11i 1.07479i
\(554\) 2.61097e11 2.77180
\(555\) 3.89072e8i 0.00410070i
\(556\) 1.44551e11 1.51259
\(557\) 3.95668e10 0.411065 0.205532 0.978650i \(-0.434107\pi\)
0.205532 + 0.978650i \(0.434107\pi\)
\(558\) 1.89795e11i 1.95771i
\(559\) −4.60114e10 1.89218e9i −0.471214 0.0193783i
\(560\) 8.73284e11 8.87980
\(561\) 5.37283e10i 0.542440i
\(562\) 1.95300e11i 1.95775i
\(563\) −3.42250e10 −0.340652 −0.170326 0.985388i \(-0.554482\pi\)
−0.170326 + 0.985388i \(0.554482\pi\)
\(564\) 7.02908e11i 6.94675i
\(565\) −3.14872e10 −0.308987
\(566\) 1.50952e11i 1.47087i
\(567\) 1.48667e11i 1.43841i
\(568\) −6.89054e11 −6.62003
\(569\) −8.05501e10 −0.768453 −0.384226 0.923239i \(-0.625532\pi\)
−0.384226 + 0.923239i \(0.625532\pi\)
\(570\) 2.55794e11 2.42320
\(571\) 1.76714e11i 1.66237i 0.555999 + 0.831183i \(0.312336\pi\)
−0.555999 + 0.831183i \(0.687664\pi\)
\(572\) 4.90850e10 0.458527
\(573\) −5.88781e10 −0.546179
\(574\) 2.78011e10 0.256103
\(575\) 1.64301e11 1.50303
\(576\) 5.03184e11 4.57127
\(577\) 1.37822e10i 0.124342i −0.998066 0.0621708i \(-0.980198\pi\)
0.998066 0.0621708i \(-0.0198023\pi\)
\(578\) 5.62452e10i 0.503935i
\(579\) 9.73155e10i 0.865900i
\(580\) 3.94242e11 3.48378
\(581\) 1.80931e11i 1.58784i
\(582\) −1.22985e11 −1.07191
\(583\) −1.92745e9 −0.0166843
\(584\) −2.69914e11 −2.32046
\(585\) 8.22576e10i 0.702348i
\(586\) 2.55723e11i 2.16860i
\(587\) 1.82554e11i 1.53759i 0.639498 + 0.768793i \(0.279142\pi\)
−0.639498 + 0.768793i \(0.720858\pi\)
\(588\) 4.50772e11i 3.77092i
\(589\) 7.14898e10i 0.593995i
\(590\) −2.95923e11 −2.44214
\(591\) 1.97646e11i 1.62009i
\(592\) 9.66861e8i 0.00787185i
\(593\) 1.43538e11i 1.16078i −0.814340 0.580388i \(-0.802901\pi\)
0.814340 0.580388i \(-0.197099\pi\)
\(594\) −3.57229e9 −0.0286946
\(595\) −3.01655e11 −2.40682
\(596\) 5.18075e11i 4.10589i
\(597\) 7.53260e10 0.592990
\(598\) 1.30400e11i 1.01970i
\(599\) −2.27622e11 −1.76810 −0.884050 0.467392i \(-0.845194\pi\)
−0.884050 + 0.467392i \(0.845194\pi\)
\(600\) −8.79876e11 −6.78917
\(601\) 3.77861e10i 0.289624i 0.989459 + 0.144812i \(0.0462578\pi\)
−0.989459 + 0.144812i \(0.953742\pi\)
\(602\) −3.58428e11 1.47400e10i −2.72908 0.112231i
\(603\) 1.00403e10 0.0759411
\(604\) 2.81229e11i 2.11306i
\(605\) 1.81327e11i 1.35345i
\(606\) 5.30080e11 3.93053
\(607\) 2.22698e11i 1.64044i −0.572047 0.820221i \(-0.693850\pi\)
0.572047 0.820221i \(-0.306150\pi\)
\(608\) 3.55886e11 2.60433
\(609\) 2.16881e11i 1.57671i
\(610\) 3.29373e11i 2.37886i
\(611\) 1.15322e11 0.827458
\(612\) −4.30381e11 −3.06794
\(613\) 2.51319e11 1.77985 0.889926 0.456105i \(-0.150756\pi\)
0.889926 + 0.456105i \(0.150756\pi\)
\(614\) 1.64386e11i 1.15662i
\(615\) −2.89120e10 −0.202105
\(616\) 2.46834e11 1.71428
\(617\) −9.10397e10 −0.628189 −0.314094 0.949392i \(-0.601701\pi\)
−0.314094 + 0.949392i \(0.601701\pi\)
\(618\) −7.43339e10 −0.509604
\(619\) −1.28665e11 −0.876391 −0.438195 0.898880i \(-0.644382\pi\)
−0.438195 + 0.898880i \(0.644382\pi\)
\(620\) 6.61275e11i 4.47523i
\(621\) 7.00661e9i 0.0471131i
\(622\) 4.19474e11i 2.80249i
\(623\) 4.89732e10 0.325092
\(624\) 4.15225e11i 2.73871i
\(625\) −7.81775e10 −0.512344
\(626\) 9.00476e10 0.586374
\(627\) 4.29896e10 0.278159
\(628\) 6.46052e11i 4.15364i
\(629\) 3.33979e8i 0.00213362i
\(630\) 6.40785e11i 4.06771i
\(631\) 1.01164e11i 0.638131i 0.947733 + 0.319066i \(0.103369\pi\)
−0.947733 + 0.319066i \(0.896631\pi\)
\(632\) 4.36870e11i 2.73832i
\(633\) 6.05808e10 0.377329
\(634\) 5.38009e11i 3.32991i
\(635\) 3.18086e10i 0.195637i
\(636\) 3.13622e10i 0.191680i
\(637\) 7.39552e10 0.449170
\(638\) 8.97437e10 0.541653
\(639\) 3.00631e11i 1.80315i
\(640\) −1.20774e12 −7.19867
\(641\) 6.04868e10i 0.358285i 0.983823 + 0.179142i \(0.0573323\pi\)
−0.983823 + 0.179142i \(0.942668\pi\)
\(642\) 7.29090e11 4.29182
\(643\) −9.88166e10 −0.578077 −0.289039 0.957317i \(-0.593336\pi\)
−0.289039 + 0.957317i \(0.593336\pi\)
\(644\) 7.49975e11i 4.36017i
\(645\) 3.72751e11 + 1.53290e10i 2.15367 + 0.0885678i
\(646\) −2.19573e11 −1.26081
\(647\) 6.03495e10i 0.344395i −0.985062 0.172197i \(-0.944913\pi\)
0.985062 0.172197i \(-0.0550867\pi\)
\(648\) 6.46161e11i 3.66472i
\(649\) −4.97339e10 −0.280333
\(650\) 2.23622e11i 1.25274i
\(651\) −3.63782e11 −2.02543
\(652\) 6.09514e11i 3.37282i
\(653\) 7.86810e10i 0.432730i 0.976313 + 0.216365i \(0.0694202\pi\)
−0.976313 + 0.216365i \(0.930580\pi\)
\(654\) 4.54803e10 0.248606
\(655\) 2.59494e11 1.40981
\(656\) −7.18476e10 −0.387969
\(657\) 1.17762e11i 0.632040i
\(658\) 8.98353e11 4.79230
\(659\) 8.07210e10 0.428001 0.214001 0.976834i \(-0.431351\pi\)
0.214001 + 0.976834i \(0.431351\pi\)
\(660\) −3.97650e11 −2.09568
\(661\) −2.27444e10 −0.119143 −0.0595716 0.998224i \(-0.518973\pi\)
−0.0595716 + 0.998224i \(0.518973\pi\)
\(662\) 1.91766e11 0.998481
\(663\) 1.43430e11i 0.742310i
\(664\) 7.86391e11i 4.04545i
\(665\) 2.41363e11i 1.23420i
\(666\) 7.09448e8 0.00360599
\(667\) 1.76021e11i 0.889328i
\(668\) −8.76986e11 −4.40440
\(669\) −3.78014e10 −0.188714
\(670\) −4.73817e10 −0.235132
\(671\) 5.53556e10i 0.273068i
\(672\) 1.81095e12i 8.88035i
\(673\) 9.31399e10i 0.454020i 0.973892 + 0.227010i \(0.0728951\pi\)
−0.973892 + 0.227010i \(0.927105\pi\)
\(674\) 2.81126e11i 1.36226i
\(675\) 1.20156e10i 0.0578801i
\(676\) 4.58099e11 2.19368
\(677\) 1.19826e11i 0.570420i 0.958465 + 0.285210i \(0.0920634\pi\)
−0.958465 + 0.285210i \(0.907937\pi\)
\(678\) 1.16627e11i 0.551925i
\(679\) 1.16046e11i 0.545950i
\(680\) 1.31110e12 6.13199
\(681\) −4.78327e11 −2.22401
\(682\) 1.50530e11i 0.695802i
\(683\) 2.38715e11 1.09697 0.548487 0.836159i \(-0.315204\pi\)
0.548487 + 0.836159i \(0.315204\pi\)
\(684\) 3.44360e11i 1.57322i
\(685\) −1.22201e11 −0.555027
\(686\) −2.87847e10 −0.129977
\(687\) 8.70476e10i 0.390778i
\(688\) 9.26301e11 + 3.80933e10i 4.13427 + 0.170018i
\(689\) 5.14539e9 0.0228319
\(690\) 1.05641e12i 4.66052i
\(691\) 3.43316e11i 1.50585i −0.658107 0.752924i \(-0.728643\pi\)
0.658107 0.752924i \(-0.271357\pi\)
\(692\) 4.97662e11 2.17025
\(693\) 1.07693e11i 0.466931i
\(694\) −6.56787e11 −2.83130
\(695\) 1.92126e11i 0.823466i
\(696\) 9.42644e11i 4.01708i
\(697\) 2.48180e10 0.105157
\(698\) −4.48663e11 −1.89016
\(699\) 1.48719e11 0.622957
\(700\) 1.28612e12i 5.35662i
\(701\) −1.30956e11 −0.542319 −0.271159 0.962534i \(-0.587407\pi\)
−0.271159 + 0.962534i \(0.587407\pi\)
\(702\) 9.53636e9 0.0392676
\(703\) 2.67226e8 0.00109410
\(704\) −3.99084e11 −1.62470
\(705\) −9.34250e11 −3.78187
\(706\) 7.58471e11i 3.05295i
\(707\) 5.00176e11i 2.00191i
\(708\) 8.09239e11i 3.22065i
\(709\) 1.43918e11 0.569549 0.284775 0.958594i \(-0.408081\pi\)
0.284775 + 0.958594i \(0.408081\pi\)
\(710\) 1.41873e12i 5.58297i
\(711\) −1.90604e11 −0.745855
\(712\) −2.12855e11 −0.828256
\(713\) −2.95247e11 −1.14242
\(714\) 1.11732e12i 4.29915i
\(715\) 6.52399e10i 0.249626i
\(716\) 8.47562e11i 3.22492i
\(717\) 5.04248e11i 1.90795i
\(718\) 5.08914e11i 1.91490i
\(719\) 5.08125e11 1.90132 0.950660 0.310234i \(-0.100407\pi\)
0.950660 + 0.310234i \(0.100407\pi\)
\(720\) 1.65601e12i 6.16215i
\(721\) 7.01404e10i 0.259554i
\(722\) 3.55499e11i 1.30825i
\(723\) −1.04527e11 −0.382539
\(724\) 8.13745e11 2.96165
\(725\) 3.01857e11i 1.09257i
\(726\) 6.71627e11 2.41758
\(727\) 1.86214e11i 0.666613i −0.942819 0.333306i \(-0.891836\pi\)
0.942819 0.333306i \(-0.108164\pi\)
\(728\) −6.58933e11 −2.34593
\(729\) 2.65034e11 0.938407
\(730\) 5.55738e11i 1.95695i
\(731\) −3.19969e11 1.31584e10i −1.12057 0.0460823i
\(732\) 9.00711e11 3.13719
\(733\) 2.14404e11i 0.742705i 0.928492 + 0.371352i \(0.121106\pi\)
−0.928492 + 0.371352i \(0.878894\pi\)
\(734\) 4.63983e11i 1.59852i
\(735\) −5.99131e11 −2.05292
\(736\) 1.46978e12i 5.00887i
\(737\) −7.96313e9 −0.0269907
\(738\) 5.27192e10i 0.177723i
\(739\) 5.48486e11i 1.83902i −0.393061 0.919512i \(-0.628584\pi\)
0.393061 0.919512i \(-0.371416\pi\)
\(740\) −2.47182e9 −0.00824310
\(741\) −1.14762e11 −0.380650
\(742\) 4.00825e10 0.132233
\(743\) 5.34775e11i 1.75475i −0.479805 0.877375i \(-0.659292\pi\)
0.479805 0.877375i \(-0.340708\pi\)
\(744\) 1.58113e12 5.16030
\(745\) 6.88585e11 2.23528
\(746\) −2.75191e11 −0.888544
\(747\) 3.43099e11 1.10189
\(748\) 3.41343e11 1.09040
\(749\) 6.87959e11i 2.18592i
\(750\) 4.78437e11i 1.51210i
\(751\) 3.06199e11i 0.962596i 0.876557 + 0.481298i \(0.159835\pi\)
−0.876557 + 0.481298i \(0.840165\pi\)
\(752\) −2.32165e12 −7.25982
\(753\) 5.53256e11i 1.72086i
\(754\) −2.39574e11 −0.741233
\(755\) 3.73788e11 1.15037
\(756\) 5.48468e10 0.167905
\(757\) 3.81892e11i 1.16294i 0.813568 + 0.581470i \(0.197522\pi\)
−0.813568 + 0.581470i \(0.802478\pi\)
\(758\) 6.71306e11i 2.03350i
\(759\) 1.77543e11i 0.534979i
\(760\) 1.04905e12i 3.14443i
\(761\) 4.86988e10i 0.145204i −0.997361 0.0726022i \(-0.976870\pi\)
0.997361 0.0726022i \(-0.0231304\pi\)
\(762\) 1.17818e11 0.349454
\(763\) 4.29146e10i 0.126621i
\(764\) 3.74060e11i 1.09791i
\(765\) 5.72029e11i 1.67021i
\(766\) −6.36032e11 −1.84741
\(767\) 1.32767e11 0.383626
\(768\) 2.17163e12i 6.24224i
\(769\) 1.78411e11 0.510172 0.255086 0.966918i \(-0.417896\pi\)
0.255086 + 0.966918i \(0.417896\pi\)
\(770\) 5.08218e11i 1.44573i
\(771\) −1.13136e11 −0.320172
\(772\) 6.18258e11 1.74061
\(773\) 2.72750e11i 0.763917i −0.924180 0.381958i \(-0.875250\pi\)
0.924180 0.381958i \(-0.124750\pi\)
\(774\) −2.79515e10 + 6.79688e11i −0.0778828 + 1.89385i
\(775\) −5.06315e11 −1.40350
\(776\) 5.04380e11i 1.39095i
\(777\) 1.35980e9i 0.00373071i
\(778\) −3.84095e11 −1.04838
\(779\) 1.98576e10i 0.0539234i
\(780\) 1.06154e12 2.86787
\(781\) 2.38436e11i 0.640867i
\(782\) 9.06817e11i &min