Properties

Label 43.9.b.b.42.6
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 42.6
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.23

$q$-expansion

\(f(q)\) \(=\) \(q-23.5327i q^{2} +46.0777i q^{3} -297.789 q^{4} -373.886i q^{5} +1084.33 q^{6} -2487.41i q^{7} +983.414i q^{8} +4437.84 q^{9} +O(q^{10})\) \(q-23.5327i q^{2} +46.0777i q^{3} -297.789 q^{4} -373.886i q^{5} +1084.33 q^{6} -2487.41i q^{7} +983.414i q^{8} +4437.84 q^{9} -8798.55 q^{10} +7400.35 q^{11} -13721.4i q^{12} -36285.4 q^{13} -58535.4 q^{14} +17227.8 q^{15} -53091.6 q^{16} -88832.2 q^{17} -104435. i q^{18} +41818.3i q^{19} +111339. i q^{20} +114614. q^{21} -174150. i q^{22} -294498. q^{23} -45313.5 q^{24} +250835. q^{25} +853895. i q^{26} +506802. i q^{27} +740723. i q^{28} +43140.9i q^{29} -405417. i q^{30} -557310. q^{31} +1.50114e6i q^{32} +340991. i q^{33} +2.09046e6i q^{34} -930005. q^{35} -1.32154e6 q^{36} -3.70010e6i q^{37} +984099. q^{38} -1.67195e6i q^{39} +367684. q^{40} +1.14292e6 q^{41} -2.69718e6i q^{42} +(-2.60367e6 - 2.21565e6i) q^{43} -2.20374e6 q^{44} -1.65925e6i q^{45} +6.93034e6i q^{46} -721451. q^{47} -2.44634e6i q^{48} -422388. q^{49} -5.90282e6i q^{50} -4.09318e6i q^{51} +1.08054e7 q^{52} -8.22613e6 q^{53} +1.19264e7 q^{54} -2.76688e6i q^{55} +2.44615e6 q^{56} -1.92689e6 q^{57} +1.01522e6 q^{58} +5.76533e6 q^{59} -5.13025e6 q^{60} +1.24108e7i q^{61} +1.31150e7i q^{62} -1.10387e7i q^{63} +2.17346e7 q^{64} +1.35666e7i q^{65} +8.02445e6 q^{66} +2.60940e7 q^{67} +2.64533e7 q^{68} -1.35698e7i q^{69} +2.18856e7i q^{70} -3.21676e7i q^{71} +4.36424e6i q^{72} -1.56616e7i q^{73} -8.70735e7 q^{74} +1.15579e7i q^{75} -1.24530e7i q^{76} -1.84077e7i q^{77} -3.93455e7 q^{78} +2.11723e7 q^{79} +1.98502e7i q^{80} +5.76445e6 q^{81} -2.68960e7i q^{82} -5.69127e7 q^{83} -3.41308e7 q^{84} +3.32131e7i q^{85} +(-5.21402e7 + 6.12715e7i) q^{86} -1.98783e6 q^{87} +7.27761e6i q^{88} -6.26121e7i q^{89} -3.90466e7 q^{90} +9.02566e7i q^{91} +8.76983e7 q^{92} -2.56796e7i q^{93} +1.69777e7i q^{94} +1.56353e7 q^{95} -6.91693e7 q^{96} +1.82440e7 q^{97} +9.93994e6i q^{98} +3.28416e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.5327i 1.47080i −0.677636 0.735398i \(-0.736995\pi\)
0.677636 0.735398i \(-0.263005\pi\)
\(3\) 46.0777i 0.568861i 0.958697 + 0.284430i \(0.0918044\pi\)
−0.958697 + 0.284430i \(0.908196\pi\)
\(4\) −297.789 −1.16324
\(5\) 373.886i 0.598217i −0.954219 0.299108i \(-0.903311\pi\)
0.954219 0.299108i \(-0.0966892\pi\)
\(6\) 1084.33 0.836678
\(7\) 2487.41i 1.03599i −0.855384 0.517994i \(-0.826679\pi\)
0.855384 0.517994i \(-0.173321\pi\)
\(8\) 983.414i 0.240091i
\(9\) 4437.84 0.676398
\(10\) −8798.55 −0.879855
\(11\) 7400.35 0.505454 0.252727 0.967538i \(-0.418673\pi\)
0.252727 + 0.967538i \(0.418673\pi\)
\(12\) 13721.4i 0.661721i
\(13\) −36285.4 −1.27045 −0.635227 0.772325i \(-0.719094\pi\)
−0.635227 + 0.772325i \(0.719094\pi\)
\(14\) −58535.4 −1.52373
\(15\) 17227.8 0.340302
\(16\) −53091.6 −0.810114
\(17\) −88832.2 −1.06359 −0.531795 0.846873i \(-0.678482\pi\)
−0.531795 + 0.846873i \(0.678482\pi\)
\(18\) 104435.i 0.994843i
\(19\) 41818.3i 0.320887i 0.987045 + 0.160443i \(0.0512924\pi\)
−0.987045 + 0.160443i \(0.948708\pi\)
\(20\) 111339.i 0.695869i
\(21\) 114614. 0.589332
\(22\) 174150.i 0.743419i
\(23\) −294498. −1.05238 −0.526188 0.850368i \(-0.676379\pi\)
−0.526188 + 0.850368i \(0.676379\pi\)
\(24\) −45313.5 −0.136579
\(25\) 250835. 0.642137
\(26\) 853895.i 1.86858i
\(27\) 506802.i 0.953637i
\(28\) 740723.i 1.20510i
\(29\) 43140.9i 0.0609954i 0.999535 + 0.0304977i \(0.00970923\pi\)
−0.999535 + 0.0304977i \(0.990291\pi\)
\(30\) 405417.i 0.500515i
\(31\) −557310. −0.603463 −0.301731 0.953393i \(-0.597565\pi\)
−0.301731 + 0.953393i \(0.597565\pi\)
\(32\) 1.50114e6i 1.43160i
\(33\) 340991.i 0.287533i
\(34\) 2.09046e6i 1.56432i
\(35\) −930005. −0.619745
\(36\) −1.32154e6 −0.786812
\(37\) 3.70010e6i 1.97427i −0.159887 0.987135i \(-0.551113\pi\)
0.159887 0.987135i \(-0.448887\pi\)
\(38\) 984099. 0.471959
\(39\) 1.67195e6i 0.722711i
\(40\) 367684. 0.143627
\(41\) 1.14292e6 0.404463 0.202232 0.979338i \(-0.435181\pi\)
0.202232 + 0.979338i \(0.435181\pi\)
\(42\) 2.69718e6i 0.866787i
\(43\) −2.60367e6 2.21565e6i −0.761574 0.648078i
\(44\) −2.20374e6 −0.587963
\(45\) 1.65925e6i 0.404632i
\(46\) 6.93034e6i 1.54783i
\(47\) −721451. −0.147848 −0.0739240 0.997264i \(-0.523552\pi\)
−0.0739240 + 0.997264i \(0.523552\pi\)
\(48\) 2.44634e6i 0.460842i
\(49\) −422388. −0.0732702
\(50\) 5.90282e6i 0.944452i
\(51\) 4.09318e6i 0.605035i
\(52\) 1.08054e7 1.47784
\(53\) −8.22613e6 −1.04254 −0.521269 0.853392i \(-0.674541\pi\)
−0.521269 + 0.853392i \(0.674541\pi\)
\(54\) 1.19264e7 1.40260
\(55\) 2.76688e6i 0.302371i
\(56\) 2.44615e6 0.248732
\(57\) −1.92689e6 −0.182540
\(58\) 1.01522e6 0.0897118
\(59\) 5.76533e6 0.475791 0.237895 0.971291i \(-0.423542\pi\)
0.237895 + 0.971291i \(0.423542\pi\)
\(60\) −5.13025e6 −0.395853
\(61\) 1.24108e7i 0.896355i 0.893945 + 0.448178i \(0.147927\pi\)
−0.893945 + 0.448178i \(0.852073\pi\)
\(62\) 1.31150e7i 0.887570i
\(63\) 1.10387e7i 0.700740i
\(64\) 2.17346e7 1.29548
\(65\) 1.35666e7i 0.760007i
\(66\) 8.02445e6 0.422902
\(67\) 2.60940e7 1.29492 0.647458 0.762101i \(-0.275832\pi\)
0.647458 + 0.762101i \(0.275832\pi\)
\(68\) 2.64533e7 1.23721
\(69\) 1.35698e7i 0.598655i
\(70\) 2.18856e7i 0.911518i
\(71\) 3.21676e7i 1.26586i −0.774209 0.632930i \(-0.781852\pi\)
0.774209 0.632930i \(-0.218148\pi\)
\(72\) 4.36424e6i 0.162397i
\(73\) 1.56616e7i 0.551498i −0.961230 0.275749i \(-0.911074\pi\)
0.961230 0.275749i \(-0.0889258\pi\)
\(74\) −8.70735e7 −2.90375
\(75\) 1.15579e7i 0.365286i
\(76\) 1.24530e7i 0.373268i
\(77\) 1.84077e7i 0.523644i
\(78\) −3.93455e7 −1.06296
\(79\) 2.11723e7 0.543576 0.271788 0.962357i \(-0.412385\pi\)
0.271788 + 0.962357i \(0.412385\pi\)
\(80\) 1.98502e7i 0.484624i
\(81\) 5.76445e6 0.133911
\(82\) 2.68960e7i 0.594883i
\(83\) −5.69127e7 −1.19921 −0.599607 0.800294i \(-0.704676\pi\)
−0.599607 + 0.800294i \(0.704676\pi\)
\(84\) −3.41308e7 −0.685535
\(85\) 3.32131e7i 0.636258i
\(86\) −5.21402e7 + 6.12715e7i −0.953189 + 1.12012i
\(87\) −1.98783e6 −0.0346979
\(88\) 7.27761e6i 0.121355i
\(89\) 6.26121e7i 0.997926i −0.866623 0.498963i \(-0.833714\pi\)
0.866623 0.498963i \(-0.166286\pi\)
\(90\) −3.90466e7 −0.595132
\(91\) 9.02566e7i 1.31617i
\(92\) 8.76983e7 1.22417
\(93\) 2.56796e7i 0.343286i
\(94\) 1.69777e7i 0.217454i
\(95\) 1.56353e7 0.191960
\(96\) −6.91693e7 −0.814383
\(97\) 1.82440e7 0.206079 0.103039 0.994677i \(-0.467143\pi\)
0.103039 + 0.994677i \(0.467143\pi\)
\(98\) 9.93994e6i 0.107765i
\(99\) 3.28416e7 0.341888
\(100\) −7.46958e7 −0.746958
\(101\) 1.12667e8 1.08271 0.541354 0.840795i \(-0.317912\pi\)
0.541354 + 0.840795i \(0.317912\pi\)
\(102\) −9.63237e7 −0.889882
\(103\) 5.41519e6 0.0481132 0.0240566 0.999711i \(-0.492342\pi\)
0.0240566 + 0.999711i \(0.492342\pi\)
\(104\) 3.56836e7i 0.305025i
\(105\) 4.28525e7i 0.352549i
\(106\) 1.93583e8i 1.53336i
\(107\) 1.01525e8 0.774527 0.387264 0.921969i \(-0.373420\pi\)
0.387264 + 0.921969i \(0.373420\pi\)
\(108\) 1.50920e8i 1.10931i
\(109\) 1.10356e8 0.781791 0.390896 0.920435i \(-0.372165\pi\)
0.390896 + 0.920435i \(0.372165\pi\)
\(110\) −6.51123e7 −0.444726
\(111\) 1.70492e8 1.12308
\(112\) 1.32060e8i 0.839268i
\(113\) 5.64521e7i 0.346231i −0.984901 0.173116i \(-0.944617\pi\)
0.984901 0.173116i \(-0.0553835\pi\)
\(114\) 4.53450e7i 0.268479i
\(115\) 1.10109e8i 0.629549i
\(116\) 1.28469e7i 0.0709523i
\(117\) −1.61029e8 −0.859332
\(118\) 1.35674e8i 0.699791i
\(119\) 2.20962e8i 1.10187i
\(120\) 1.69421e7i 0.0817036i
\(121\) −1.59594e8 −0.744517
\(122\) 2.92060e8 1.31836
\(123\) 5.26630e7i 0.230083i
\(124\) 1.65961e8 0.701971
\(125\) 2.39832e8i 0.982354i
\(126\) −2.59771e8 −1.03064
\(127\) −3.89323e6 −0.0149656 −0.00748281 0.999972i \(-0.502382\pi\)
−0.00748281 + 0.999972i \(0.502382\pi\)
\(128\) 1.27181e8i 0.473785i
\(129\) 1.02092e8 1.19971e8i 0.368666 0.433230i
\(130\) 3.19259e8 1.11782
\(131\) 5.05331e8i 1.71590i −0.513736 0.857948i \(-0.671739\pi\)
0.513736 0.857948i \(-0.328261\pi\)
\(132\) 1.01543e8i 0.334469i
\(133\) 1.04019e8 0.332435
\(134\) 6.14063e8i 1.90456i
\(135\) 1.89486e8 0.570481
\(136\) 8.73588e7i 0.255359i
\(137\) 2.61606e8i 0.742618i 0.928509 + 0.371309i \(0.121091\pi\)
−0.928509 + 0.371309i \(0.878909\pi\)
\(138\) −3.19334e8 −0.880500
\(139\) 6.91310e8 1.85188 0.925942 0.377666i \(-0.123273\pi\)
0.925942 + 0.377666i \(0.123273\pi\)
\(140\) 2.76946e8 0.720912
\(141\) 3.32428e7i 0.0841048i
\(142\) −7.56992e8 −1.86182
\(143\) −2.68525e8 −0.642156
\(144\) −2.35612e8 −0.547959
\(145\) 1.61298e7 0.0364885
\(146\) −3.68559e8 −0.811141
\(147\) 1.94627e7i 0.0416805i
\(148\) 1.10185e9i 2.29655i
\(149\) 5.93902e8i 1.20495i −0.798137 0.602476i \(-0.794181\pi\)
0.798137 0.602476i \(-0.205819\pi\)
\(150\) 2.71989e8 0.537261
\(151\) 1.81225e8i 0.348587i 0.984694 + 0.174293i \(0.0557641\pi\)
−0.984694 + 0.174293i \(0.944236\pi\)
\(152\) −4.11247e7 −0.0770422
\(153\) −3.94223e8 −0.719410
\(154\) −4.33183e8 −0.770173
\(155\) 2.08370e8i 0.361002i
\(156\) 4.97889e8i 0.840686i
\(157\) 2.30311e8i 0.379067i −0.981874 0.189533i \(-0.939302\pi\)
0.981874 0.189533i \(-0.0606975\pi\)
\(158\) 4.98243e8i 0.799489i
\(159\) 3.79041e8i 0.593059i
\(160\) 5.61256e8 0.856409
\(161\) 7.32536e8i 1.09025i
\(162\) 1.35653e8i 0.196956i
\(163\) 8.19691e8i 1.16118i 0.814196 + 0.580590i \(0.197178\pi\)
−0.814196 + 0.580590i \(0.802822\pi\)
\(164\) −3.40348e8 −0.470488
\(165\) 1.27492e8 0.172007
\(166\) 1.33931e9i 1.76380i
\(167\) 2.35824e8 0.303195 0.151597 0.988442i \(-0.451558\pi\)
0.151597 + 0.988442i \(0.451558\pi\)
\(168\) 1.12713e8i 0.141494i
\(169\) 5.00903e8 0.614054
\(170\) 7.81594e8 0.935805
\(171\) 1.85583e8i 0.217047i
\(172\) 7.75345e8 + 6.59796e8i 0.885893 + 0.753869i
\(173\) −1.31006e9 −1.46254 −0.731270 0.682088i \(-0.761072\pi\)
−0.731270 + 0.682088i \(0.761072\pi\)
\(174\) 4.67792e7i 0.0510335i
\(175\) 6.23927e8i 0.665245i
\(176\) −3.92896e8 −0.409475
\(177\) 2.65653e8i 0.270659i
\(178\) −1.47343e9 −1.46774
\(179\) 5.68976e8i 0.554219i −0.960838 0.277110i \(-0.910623\pi\)
0.960838 0.277110i \(-0.0893765\pi\)
\(180\) 4.94106e8i 0.470684i
\(181\) 3.63916e8 0.339068 0.169534 0.985524i \(-0.445774\pi\)
0.169534 + 0.985524i \(0.445774\pi\)
\(182\) 2.12398e9 1.93582
\(183\) −5.71861e8 −0.509901
\(184\) 2.89614e8i 0.252667i
\(185\) −1.38341e9 −1.18104
\(186\) −6.04311e8 −0.504904
\(187\) −6.57389e8 −0.537596
\(188\) 2.14840e8 0.171982
\(189\) 1.26062e9 0.987956
\(190\) 3.67940e8i 0.282334i
\(191\) 1.85510e9i 1.39390i −0.717118 0.696952i \(-0.754539\pi\)
0.717118 0.696952i \(-0.245461\pi\)
\(192\) 1.00148e9i 0.736948i
\(193\) −2.33960e9 −1.68621 −0.843105 0.537749i \(-0.819275\pi\)
−0.843105 + 0.537749i \(0.819275\pi\)
\(194\) 4.29331e8i 0.303099i
\(195\) −6.25118e8 −0.432338
\(196\) 1.25783e8 0.0852307
\(197\) 2.19809e8 0.145942 0.0729710 0.997334i \(-0.476752\pi\)
0.0729710 + 0.997334i \(0.476752\pi\)
\(198\) 7.72852e8i 0.502847i
\(199\) 4.33133e8i 0.276190i −0.990419 0.138095i \(-0.955902\pi\)
0.990419 0.138095i \(-0.0440980\pi\)
\(200\) 2.46674e8i 0.154171i
\(201\) 1.20235e9i 0.736627i
\(202\) 2.65136e9i 1.59244i
\(203\) 1.07309e8 0.0631905
\(204\) 1.21891e9i 0.703800i
\(205\) 4.27320e8i 0.241957i
\(206\) 1.27434e8i 0.0707647i
\(207\) −1.30694e9 −0.711825
\(208\) 1.92645e9 1.02921
\(209\) 3.09470e8i 0.162193i
\(210\) −1.00844e9 −0.518527
\(211\) 1.78019e9i 0.898127i −0.893500 0.449063i \(-0.851758\pi\)
0.893500 0.449063i \(-0.148242\pi\)
\(212\) 2.44965e9 1.21272
\(213\) 1.48221e9 0.720097
\(214\) 2.38915e9i 1.13917i
\(215\) −8.28399e8 + 9.73475e8i −0.387691 + 0.455587i
\(216\) −4.98396e8 −0.228960
\(217\) 1.38626e9i 0.625180i
\(218\) 2.59698e9i 1.14986i
\(219\) 7.21649e8 0.313725
\(220\) 8.23948e8i 0.351730i
\(221\) 3.22331e9 1.35124
\(222\) 4.01215e9i 1.65183i
\(223\) 1.99684e8i 0.0807465i 0.999185 + 0.0403732i \(0.0128547\pi\)
−0.999185 + 0.0403732i \(0.987145\pi\)
\(224\) 3.73396e9 1.48312
\(225\) 1.11317e9 0.434340
\(226\) −1.32847e9 −0.509236
\(227\) 5.20422e9i 1.95998i 0.199036 + 0.979992i \(0.436219\pi\)
−0.199036 + 0.979992i \(0.563781\pi\)
\(228\) 5.73808e8 0.212338
\(229\) −3.23276e9 −1.17552 −0.587762 0.809034i \(-0.699991\pi\)
−0.587762 + 0.809034i \(0.699991\pi\)
\(230\) 2.59115e9 0.925938
\(231\) 8.48183e8 0.297880
\(232\) −4.24254e7 −0.0146445
\(233\) 2.31185e9i 0.784397i −0.919881 0.392199i \(-0.871715\pi\)
0.919881 0.392199i \(-0.128285\pi\)
\(234\) 3.78946e9i 1.26390i
\(235\) 2.69740e8i 0.0884451i
\(236\) −1.71685e9 −0.553458
\(237\) 9.75573e8i 0.309219i
\(238\) 5.19983e9 1.62062
\(239\) 1.60464e9 0.491798 0.245899 0.969295i \(-0.420917\pi\)
0.245899 + 0.969295i \(0.420917\pi\)
\(240\) −9.14651e8 −0.275683
\(241\) 2.76525e9i 0.819723i 0.912148 + 0.409861i \(0.134423\pi\)
−0.912148 + 0.409861i \(0.865577\pi\)
\(242\) 3.75568e9i 1.09503i
\(243\) 3.59074e9i 1.02981i
\(244\) 3.69580e9i 1.04268i
\(245\) 1.57925e8i 0.0438314i
\(246\) 1.23930e9 0.338406
\(247\) 1.51740e9i 0.407672i
\(248\) 5.48067e8i 0.144886i
\(249\) 2.62241e9i 0.682186i
\(250\) −5.64391e9 −1.44484
\(251\) 4.50337e9 1.13460 0.567299 0.823512i \(-0.307988\pi\)
0.567299 + 0.823512i \(0.307988\pi\)
\(252\) 3.28721e9i 0.815128i
\(253\) −2.17939e9 −0.531927
\(254\) 9.16182e7i 0.0220114i
\(255\) −1.53038e9 −0.361942
\(256\) 2.57114e9 0.598640
\(257\) 4.59914e9i 1.05425i 0.849787 + 0.527126i \(0.176730\pi\)
−0.849787 + 0.527126i \(0.823270\pi\)
\(258\) −2.82325e9 2.40250e9i −0.637192 0.542232i
\(259\) −9.20365e9 −2.04532
\(260\) 4.03999e9i 0.884070i
\(261\) 1.91453e8i 0.0412572i
\(262\) −1.18918e10 −2.52373
\(263\) 4.72634e9i 0.987875i −0.869498 0.493937i \(-0.835557\pi\)
0.869498 0.493937i \(-0.164443\pi\)
\(264\) −3.35335e8 −0.0690341
\(265\) 3.07563e9i 0.623664i
\(266\) 2.44785e9i 0.488944i
\(267\) 2.88502e9 0.567681
\(268\) −7.77052e9 −1.50630
\(269\) −6.99220e9 −1.33538 −0.667690 0.744440i \(-0.732717\pi\)
−0.667690 + 0.744440i \(0.732717\pi\)
\(270\) 4.45912e9i 0.839062i
\(271\) 4.98868e8 0.0924929 0.0462464 0.998930i \(-0.485274\pi\)
0.0462464 + 0.998930i \(0.485274\pi\)
\(272\) 4.71624e9 0.861630
\(273\) −4.15882e9 −0.748720
\(274\) 6.15631e9 1.09224
\(275\) 1.85626e9 0.324570
\(276\) 4.04094e9i 0.696379i
\(277\) 2.44613e9i 0.415489i 0.978183 + 0.207745i \(0.0666123\pi\)
−0.978183 + 0.207745i \(0.933388\pi\)
\(278\) 1.62684e10i 2.72374i
\(279\) −2.47326e9 −0.408181
\(280\) 9.14581e8i 0.148796i
\(281\) 5.33032e9 0.854925 0.427462 0.904033i \(-0.359408\pi\)
0.427462 + 0.904033i \(0.359408\pi\)
\(282\) −7.82293e8 −0.123701
\(283\) 6.55249e9 1.02155 0.510776 0.859714i \(-0.329358\pi\)
0.510776 + 0.859714i \(0.329358\pi\)
\(284\) 9.57917e9i 1.47250i
\(285\) 7.20437e8i 0.109198i
\(286\) 6.31912e9i 0.944480i
\(287\) 2.84290e9i 0.419019i
\(288\) 6.66185e9i 0.968333i
\(289\) 9.15395e8 0.131225
\(290\) 3.79577e8i 0.0536671i
\(291\) 8.40641e8i 0.117230i
\(292\) 4.66385e9i 0.641524i
\(293\) −6.99212e9 −0.948720 −0.474360 0.880331i \(-0.657321\pi\)
−0.474360 + 0.880331i \(0.657321\pi\)
\(294\) −4.58010e8 −0.0613035
\(295\) 2.15557e9i 0.284626i
\(296\) 3.63873e9 0.474005
\(297\) 3.75051e9i 0.482019i
\(298\) −1.39761e10 −1.77224
\(299\) 1.06860e10 1.33700
\(300\) 3.44181e9i 0.424915i
\(301\) −5.51122e9 + 6.47639e9i −0.671400 + 0.788982i
\(302\) 4.26472e9 0.512700
\(303\) 5.19144e9i 0.615910i
\(304\) 2.22020e9i 0.259955i
\(305\) 4.64022e9 0.536215
\(306\) 9.27715e9i 1.05811i
\(307\) 1.24677e10 1.40357 0.701783 0.712391i \(-0.252387\pi\)
0.701783 + 0.712391i \(0.252387\pi\)
\(308\) 5.48161e9i 0.609123i
\(309\) 2.49519e8i 0.0273697i
\(310\) 4.90352e9 0.530959
\(311\) 7.46273e9 0.797731 0.398865 0.917010i \(-0.369404\pi\)
0.398865 + 0.917010i \(0.369404\pi\)
\(312\) 1.64422e9 0.173517
\(313\) 1.52569e10i 1.58960i −0.606869 0.794802i \(-0.707575\pi\)
0.606869 0.794802i \(-0.292425\pi\)
\(314\) −5.41984e9 −0.557530
\(315\) −4.12722e9 −0.419194
\(316\) −6.30489e9 −0.632309
\(317\) 2.80977e9 0.278250 0.139125 0.990275i \(-0.455571\pi\)
0.139125 + 0.990275i \(0.455571\pi\)
\(318\) −8.91988e9 −0.872269
\(319\) 3.19258e8i 0.0308304i
\(320\) 8.12624e9i 0.774979i
\(321\) 4.67803e9i 0.440598i
\(322\) 1.72386e10 1.60353
\(323\) 3.71481e9i 0.341292i
\(324\) −1.71659e9 −0.155771
\(325\) −9.10164e9 −0.815805
\(326\) 1.92896e10 1.70786
\(327\) 5.08496e9i 0.444730i
\(328\) 1.12396e9i 0.0971082i
\(329\) 1.79454e9i 0.153169i
\(330\) 3.00023e9i 0.252987i
\(331\) 6.18867e9i 0.515567i −0.966203 0.257784i \(-0.917008\pi\)
0.966203 0.257784i \(-0.0829922\pi\)
\(332\) 1.69480e10 1.39497
\(333\) 1.64205e10i 1.33539i
\(334\) 5.54957e9i 0.445937i
\(335\) 9.75617e9i 0.774641i
\(336\) −6.08504e9 −0.477426
\(337\) 1.61697e10 1.25367 0.626835 0.779152i \(-0.284350\pi\)
0.626835 + 0.779152i \(0.284350\pi\)
\(338\) 1.17876e10i 0.903148i
\(339\) 2.60118e9 0.196957
\(340\) 9.89049e9i 0.740120i
\(341\) −4.12429e9 −0.305022
\(342\) 4.36728e9 0.319232
\(343\) 1.32888e10i 0.960081i
\(344\) 2.17890e9 2.56049e9i 0.155598 0.182847i
\(345\) −5.07355e9 −0.358126
\(346\) 3.08294e10i 2.15110i
\(347\) 2.32144e10i 1.60118i −0.599214 0.800589i \(-0.704520\pi\)
0.599214 0.800589i \(-0.295480\pi\)
\(348\) 5.91956e8 0.0403620
\(349\) 1.73500e10i 1.16949i 0.811216 + 0.584747i \(0.198806\pi\)
−0.811216 + 0.584747i \(0.801194\pi\)
\(350\) −1.46827e10 −0.978440
\(351\) 1.83895e10i 1.21155i
\(352\) 1.11090e10i 0.723609i
\(353\) −1.64013e10 −1.05628 −0.528139 0.849158i \(-0.677110\pi\)
−0.528139 + 0.849158i \(0.677110\pi\)
\(354\) 6.25154e9 0.398083
\(355\) −1.20270e10 −0.757258
\(356\) 1.86452e10i 1.16083i
\(357\) −1.01814e10 −0.626809
\(358\) −1.33896e10 −0.815143
\(359\) −3.19339e10 −1.92254 −0.961269 0.275613i \(-0.911119\pi\)
−0.961269 + 0.275613i \(0.911119\pi\)
\(360\) 1.63173e9 0.0971488
\(361\) 1.52348e10 0.897032
\(362\) 8.56394e9i 0.498700i
\(363\) 7.35371e9i 0.423526i
\(364\) 2.68775e10i 1.53103i
\(365\) −5.85563e9 −0.329915
\(366\) 1.34574e10i 0.749960i
\(367\) −4.75693e9 −0.262218 −0.131109 0.991368i \(-0.541854\pi\)
−0.131109 + 0.991368i \(0.541854\pi\)
\(368\) 1.56354e10 0.852545
\(369\) 5.07209e9 0.273578
\(370\) 3.25555e10i 1.73707i
\(371\) 2.04617e10i 1.08006i
\(372\) 7.64711e9i 0.399324i
\(373\) 1.66167e10i 0.858439i −0.903200 0.429220i \(-0.858789\pi\)
0.903200 0.429220i \(-0.141211\pi\)
\(374\) 1.54702e10i 0.790693i
\(375\) 1.10509e10 0.558822
\(376\) 7.09485e8i 0.0354970i
\(377\) 1.56539e9i 0.0774919i
\(378\) 2.96659e10i 1.45308i
\(379\) 3.60255e10 1.74603 0.873017 0.487689i \(-0.162160\pi\)
0.873017 + 0.487689i \(0.162160\pi\)
\(380\) −4.65601e9 −0.223295
\(381\) 1.79391e8i 0.00851335i
\(382\) −4.36555e10 −2.05015
\(383\) 5.37123e9i 0.249619i −0.992181 0.124810i \(-0.960168\pi\)
0.992181 0.124810i \(-0.0398320\pi\)
\(384\) 5.86020e9 0.269518
\(385\) −6.88236e9 −0.313252
\(386\) 5.50571e10i 2.48007i
\(387\) −1.15547e10 9.83270e9i −0.515127 0.438358i
\(388\) −5.43286e9 −0.239719
\(389\) 3.33530e10i 1.45659i 0.685266 + 0.728293i \(0.259686\pi\)
−0.685266 + 0.728293i \(0.740314\pi\)
\(390\) 1.47107e10i 0.635881i
\(391\) 2.61609e10 1.11930
\(392\) 4.15382e8i 0.0175915i
\(393\) 2.32845e10 0.976106
\(394\) 5.17270e9i 0.214651i
\(395\) 7.91603e9i 0.325176i
\(396\) −9.77987e9 −0.397697
\(397\) 3.58311e10 1.44244 0.721220 0.692706i \(-0.243582\pi\)
0.721220 + 0.692706i \(0.243582\pi\)
\(398\) −1.01928e10 −0.406220
\(399\) 4.79296e9i 0.189109i
\(400\) −1.33172e10 −0.520204
\(401\) −3.38981e10 −1.31098 −0.655492 0.755202i \(-0.727539\pi\)
−0.655492 + 0.755202i \(0.727539\pi\)
\(402\) 2.82946e10 1.08343
\(403\) 2.02223e10 0.766672
\(404\) −3.35511e10 −1.25945
\(405\) 2.15524e9i 0.0801081i
\(406\) 2.52527e9i 0.0929403i
\(407\) 2.73820e10i 0.997902i
\(408\) 4.02529e9 0.145264
\(409\) 3.60185e10i 1.28716i 0.765380 + 0.643579i \(0.222551\pi\)
−0.765380 + 0.643579i \(0.777449\pi\)
\(410\) −1.00560e10 −0.355869
\(411\) −1.20542e10 −0.422446
\(412\) −1.61258e9 −0.0559672
\(413\) 1.43407e10i 0.492913i
\(414\) 3.07558e10i 1.04695i
\(415\) 2.12788e10i 0.717390i
\(416\) 5.44697e10i 1.81879i
\(417\) 3.18540e10i 1.05346i
\(418\) 7.28267e9 0.238553
\(419\) 5.29067e9i 0.171654i −0.996310 0.0858271i \(-0.972647\pi\)
0.996310 0.0858271i \(-0.0273533\pi\)
\(420\) 1.27610e10i 0.410098i
\(421\) 4.80310e10i 1.52895i 0.644654 + 0.764474i \(0.277001\pi\)
−0.644654 + 0.764474i \(0.722999\pi\)
\(422\) −4.18928e10 −1.32096
\(423\) −3.20169e9 −0.100004
\(424\) 8.08970e9i 0.250305i
\(425\) −2.22822e10 −0.682970
\(426\) 3.48804e10i 1.05912i
\(427\) 3.08707e10 0.928613
\(428\) −3.02330e10 −0.900960
\(429\) 1.23730e10i 0.365297i
\(430\) 2.29085e10 + 1.94945e10i 0.670075 + 0.570214i
\(431\) 2.78280e10 0.806442 0.403221 0.915103i \(-0.367891\pi\)
0.403221 + 0.915103i \(0.367891\pi\)
\(432\) 2.69069e10i 0.772554i
\(433\) 2.80139e10i 0.796932i 0.917183 + 0.398466i \(0.130457\pi\)
−0.917183 + 0.398466i \(0.869543\pi\)
\(434\) 3.26224e10 0.919512
\(435\) 7.43223e8i 0.0207569i
\(436\) −3.28629e10 −0.909410
\(437\) 1.23154e10i 0.337694i
\(438\) 1.69824e10i 0.461426i
\(439\) −4.49882e10 −1.21127 −0.605634 0.795743i \(-0.707081\pi\)
−0.605634 + 0.795743i \(0.707081\pi\)
\(440\) 2.72099e9 0.0725967
\(441\) −1.87449e9 −0.0495598
\(442\) 7.58534e10i 1.98740i
\(443\) 2.77199e10 0.719742 0.359871 0.933002i \(-0.382821\pi\)
0.359871 + 0.933002i \(0.382821\pi\)
\(444\) −5.07707e10 −1.30642
\(445\) −2.34098e10 −0.596976
\(446\) 4.69911e9 0.118762
\(447\) 2.73657e10 0.685450
\(448\) 5.40627e10i 1.34210i
\(449\) 5.79249e10i 1.42521i −0.701564 0.712607i \(-0.747514\pi\)
0.701564 0.712607i \(-0.252486\pi\)
\(450\) 2.61958e10i 0.638825i
\(451\) 8.45798e9 0.204438
\(452\) 1.68108e10i 0.402750i
\(453\) −8.35045e9 −0.198297
\(454\) 1.22470e11 2.88274
\(455\) 3.37456e10 0.787358
\(456\) 1.89493e9i 0.0438263i
\(457\) 6.50756e10i 1.49195i 0.665975 + 0.745974i \(0.268016\pi\)
−0.665975 + 0.745974i \(0.731984\pi\)
\(458\) 7.60756e10i 1.72895i
\(459\) 4.50203e10i 1.01428i
\(460\) 3.27891e10i 0.732316i
\(461\) −1.47188e10 −0.325888 −0.162944 0.986635i \(-0.552099\pi\)
−0.162944 + 0.986635i \(0.552099\pi\)
\(462\) 1.99601e10i 0.438121i
\(463\) 2.13619e10i 0.464854i −0.972614 0.232427i \(-0.925333\pi\)
0.972614 0.232427i \(-0.0746667\pi\)
\(464\) 2.29042e9i 0.0494132i
\(465\) −9.60123e9 −0.205360
\(466\) −5.44042e10 −1.15369
\(467\) 4.57818e10i 0.962554i 0.876569 + 0.481277i \(0.159827\pi\)
−0.876569 + 0.481277i \(0.840173\pi\)
\(468\) 4.79528e10 0.999609
\(469\) 6.49064e10i 1.34152i
\(470\) 6.34772e9 0.130085
\(471\) 1.06122e10 0.215636
\(472\) 5.66971e9i 0.114233i
\(473\) −1.92681e10 1.63966e10i −0.384941 0.327573i
\(474\) 2.29579e10 0.454798
\(475\) 1.04895e10i 0.206053i
\(476\) 6.58000e10i 1.28173i
\(477\) −3.65063e10 −0.705171
\(478\) 3.77616e10i 0.723334i
\(479\) 1.62487e10 0.308658 0.154329 0.988020i \(-0.450678\pi\)
0.154329 + 0.988020i \(0.450678\pi\)
\(480\) 2.58614e10i 0.487177i
\(481\) 1.34260e11i 2.50822i
\(482\) 6.50740e10 1.20564
\(483\) −3.37536e10 −0.620200
\(484\) 4.75253e10 0.866051
\(485\) 6.82116e9i 0.123280i
\(486\) 8.44998e10 1.51464
\(487\) 7.51248e10 1.33557 0.667786 0.744353i \(-0.267242\pi\)
0.667786 + 0.744353i \(0.267242\pi\)
\(488\) −1.22050e10 −0.215207
\(489\) −3.77695e10 −0.660549
\(490\) 3.71640e9 0.0644671
\(491\) 1.57898e10i 0.271676i −0.990731 0.135838i \(-0.956627\pi\)
0.990731 0.135838i \(-0.0433726\pi\)
\(492\) 1.56825e10i 0.267642i
\(493\) 3.83230e9i 0.0648742i
\(494\) −3.57085e10 −0.599602
\(495\) 1.22790e10i 0.204523i
\(496\) 2.95885e10 0.488873
\(497\) −8.00139e10 −1.31141
\(498\) −6.17124e10 −1.00336
\(499\) 1.13287e11i 1.82716i 0.406657 + 0.913581i \(0.366694\pi\)
−0.406657 + 0.913581i \(0.633306\pi\)
\(500\) 7.14195e10i 1.14271i
\(501\) 1.08662e10i 0.172475i
\(502\) 1.05976e11i 1.66876i
\(503\) 6.13184e10i 0.957897i 0.877843 + 0.478949i \(0.158982\pi\)
−0.877843 + 0.478949i \(0.841018\pi\)
\(504\) 1.08556e10 0.168242
\(505\) 4.21246e10i 0.647695i
\(506\) 5.12869e10i 0.782356i
\(507\) 2.30804e10i 0.349311i
\(508\) 1.15936e9 0.0174086
\(509\) −3.60434e10 −0.536976 −0.268488 0.963283i \(-0.586524\pi\)
−0.268488 + 0.963283i \(0.586524\pi\)
\(510\) 3.60141e10i 0.532343i
\(511\) −3.89567e10 −0.571345
\(512\) 9.30642e10i 1.35426i
\(513\) −2.11936e10 −0.306010
\(514\) 1.08230e11 1.55059
\(515\) 2.02466e9i 0.0287822i
\(516\) −3.04019e10 + 3.57261e10i −0.428846 + 0.503950i
\(517\) −5.33898e9 −0.0747303
\(518\) 2.16587e11i 3.00825i
\(519\) 6.03647e10i 0.831982i
\(520\) −1.33416e10 −0.182471
\(521\) 3.97439e10i 0.539411i −0.962943 0.269705i \(-0.913074\pi\)
0.962943 0.269705i \(-0.0869263\pi\)
\(522\) 4.50540e9 0.0606809
\(523\) 1.18662e11i 1.58601i −0.609218 0.793003i \(-0.708517\pi\)
0.609218 0.793003i \(-0.291483\pi\)
\(524\) 1.50482e11i 1.99600i
\(525\) 2.87491e10 0.378432
\(526\) −1.11224e11 −1.45296
\(527\) 4.95071e10 0.641837
\(528\) 1.81038e10i 0.232934i
\(529\) 8.41811e9 0.107496
\(530\) 7.23780e10 0.917283
\(531\) 2.55856e10 0.321824
\(532\) −3.09758e10 −0.386701
\(533\) −4.14713e10 −0.513852
\(534\) 6.78924e10i 0.834942i
\(535\) 3.79586e10i 0.463335i
\(536\) 2.56612e10i 0.310898i
\(537\) 2.62171e10 0.315274
\(538\) 1.64546e11i 1.96407i
\(539\) −3.12582e9 −0.0370347
\(540\) −5.64268e10 −0.663606
\(541\) −1.01448e11 −1.18428 −0.592141 0.805834i \(-0.701717\pi\)
−0.592141 + 0.805834i \(0.701717\pi\)
\(542\) 1.17397e10i 0.136038i
\(543\) 1.67684e10i 0.192883i
\(544\) 1.33350e11i 1.52264i
\(545\) 4.12606e10i 0.467681i
\(546\) 9.78683e10i 1.10121i
\(547\) −8.17603e10 −0.913257 −0.456629 0.889657i \(-0.650943\pi\)
−0.456629 + 0.889657i \(0.650943\pi\)
\(548\) 7.79035e10i 0.863843i
\(549\) 5.50772e10i 0.606293i
\(550\) 4.36829e10i 0.477376i
\(551\) −1.80408e9 −0.0195726
\(552\) 1.33447e10 0.143732
\(553\) 5.26642e10i 0.563138i
\(554\) 5.75640e10 0.611100
\(555\) 6.37446e10i 0.671848i
\(556\) −2.05865e11 −2.15418
\(557\) −1.33090e11 −1.38269 −0.691343 0.722526i \(-0.742981\pi\)
−0.691343 + 0.722526i \(0.742981\pi\)
\(558\) 5.82025e10i 0.600350i
\(559\) 9.44754e10 + 8.03958e10i 0.967545 + 0.823353i
\(560\) 4.93755e10 0.502064
\(561\) 3.02910e10i 0.305817i
\(562\) 1.25437e11i 1.25742i
\(563\) −7.48660e10 −0.745162 −0.372581 0.928000i \(-0.621527\pi\)
−0.372581 + 0.928000i \(0.621527\pi\)
\(564\) 9.89934e9i 0.0978340i
\(565\) −2.11066e10 −0.207122
\(566\) 1.54198e11i 1.50250i
\(567\) 1.43385e10i 0.138731i
\(568\) 3.16341e10 0.303922
\(569\) −1.64918e11 −1.57333 −0.786663 0.617383i \(-0.788193\pi\)
−0.786663 + 0.617383i \(0.788193\pi\)
\(570\) 1.69538e10 0.160609
\(571\) 2.56402e10i 0.241200i −0.992701 0.120600i \(-0.961518\pi\)
0.992701 0.120600i \(-0.0384818\pi\)
\(572\) 7.99638e10 0.746981
\(573\) 8.54785e10 0.792937
\(574\) −6.69012e10 −0.616291
\(575\) −7.38703e10 −0.675769
\(576\) 9.64547e10 0.876261
\(577\) 7.01456e10i 0.632844i −0.948618 0.316422i \(-0.897518\pi\)
0.948618 0.316422i \(-0.102482\pi\)
\(578\) 2.15417e10i 0.193005i
\(579\) 1.07803e11i 0.959218i
\(580\) −4.80327e9 −0.0424449
\(581\) 1.41565e11i 1.24237i
\(582\) 1.97826e10 0.172421
\(583\) −6.08762e10 −0.526955
\(584\) 1.54018e10 0.132410
\(585\) 6.02065e10i 0.514067i
\(586\) 1.64544e11i 1.39537i
\(587\) 1.89363e11i 1.59493i 0.603363 + 0.797467i \(0.293827\pi\)
−0.603363 + 0.797467i \(0.706173\pi\)
\(588\) 5.79577e9i 0.0484844i
\(589\) 2.33058e10i 0.193643i
\(590\) −5.07265e10 −0.418627
\(591\) 1.01283e10i 0.0830207i
\(592\) 1.96444e11i 1.59938i
\(593\) 6.58027e10i 0.532139i 0.963954 + 0.266069i \(0.0857250\pi\)
−0.963954 + 0.266069i \(0.914275\pi\)
\(594\) 8.82597e10 0.708951
\(595\) 8.26144e10 0.659155
\(596\) 1.76858e11i 1.40165i
\(597\) 1.99578e10 0.157114
\(598\) 2.51471e11i 1.96645i
\(599\) 9.67186e10 0.751282 0.375641 0.926765i \(-0.377423\pi\)
0.375641 + 0.926765i \(0.377423\pi\)
\(600\) −1.13662e10 −0.0877021
\(601\) 8.07367e10i 0.618833i 0.950927 + 0.309416i \(0.100134\pi\)
−0.950927 + 0.309416i \(0.899866\pi\)
\(602\) 1.52407e11 + 1.29694e11i 1.16043 + 0.987492i
\(603\) 1.15801e11 0.875878
\(604\) 5.39669e10i 0.405490i
\(605\) 5.96698e10i 0.445382i
\(606\) 1.22169e11 0.905878
\(607\) 2.18215e11i 1.60742i −0.595019 0.803712i \(-0.702855\pi\)
0.595019 0.803712i \(-0.297145\pi\)
\(608\) −6.27753e10 −0.459383
\(609\) 4.94455e9i 0.0359466i
\(610\) 1.09197e11i 0.788662i
\(611\) 2.61782e10 0.187834
\(612\) 1.17395e11 0.836846
\(613\) 2.66467e11 1.88713 0.943564 0.331189i \(-0.107450\pi\)
0.943564 + 0.331189i \(0.107450\pi\)
\(614\) 2.93399e11i 2.06436i
\(615\) 1.96899e10 0.137640
\(616\) 1.81024e10 0.125722
\(617\) 1.98336e11 1.36855 0.684277 0.729222i \(-0.260118\pi\)
0.684277 + 0.729222i \(0.260118\pi\)
\(618\) 5.87187e9 0.0402553
\(619\) 2.63949e11 1.79786 0.898932 0.438088i \(-0.144344\pi\)
0.898932 + 0.438088i \(0.144344\pi\)
\(620\) 6.20504e10i 0.419931i
\(621\) 1.49252e11i 1.00358i
\(622\) 1.75618e11i 1.17330i
\(623\) −1.55742e11 −1.03384
\(624\) 8.87665e10i 0.585478i
\(625\) 8.31237e9 0.0544759
\(626\) −3.59036e11 −2.33798
\(627\) −1.42597e10 −0.0922655
\(628\) 6.85841e10i 0.440945i
\(629\) 3.28688e11i 2.09982i
\(630\) 9.71247e10i 0.616549i
\(631\) 7.50901e10i 0.473658i −0.971551 0.236829i \(-0.923892\pi\)
0.971551 0.236829i \(-0.0761082\pi\)
\(632\) 2.08212e10i 0.130508i
\(633\) 8.20273e10 0.510909
\(634\) 6.61217e10i 0.409248i
\(635\) 1.45562e9i 0.00895269i
\(636\) 1.12874e11i 0.689870i
\(637\) 1.53265e10 0.0930864
\(638\) 7.51300e9 0.0453452
\(639\) 1.42755e11i 0.856224i
\(640\) −4.75510e10 −0.283426
\(641\) 1.48724e11i 0.880948i −0.897765 0.440474i \(-0.854810\pi\)
0.897765 0.440474i \(-0.145190\pi\)
\(642\) 1.10087e11 0.648029
\(643\) −1.86069e11 −1.08851 −0.544253 0.838921i \(-0.683187\pi\)
−0.544253 + 0.838921i \(0.683187\pi\)
\(644\) 2.18141e11i 1.26822i
\(645\) −4.48555e10 3.81707e10i −0.259165 0.220542i
\(646\) −8.74196e10 −0.501971
\(647\) 8.09539e10i 0.461977i 0.972956 + 0.230989i \(0.0741960\pi\)
−0.972956 + 0.230989i \(0.925804\pi\)
\(648\) 5.66884e9i 0.0321510i
\(649\) 4.26654e10 0.240490
\(650\) 2.14187e11i 1.19988i
\(651\) −6.38756e10 −0.355640
\(652\) 2.44095e11i 1.35073i
\(653\) 4.75870e10i 0.261719i 0.991401 + 0.130860i \(0.0417737\pi\)
−0.991401 + 0.130860i \(0.958226\pi\)
\(654\) 1.19663e11 0.654107
\(655\) −1.88936e11 −1.02648
\(656\) −6.06793e10 −0.327661
\(657\) 6.95036e10i 0.373032i
\(658\) 4.22304e10 0.225280
\(659\) 1.65374e10 0.0876850 0.0438425 0.999038i \(-0.486040\pi\)
0.0438425 + 0.999038i \(0.486040\pi\)
\(660\) −3.79656e10 −0.200085
\(661\) 1.78227e11 0.933615 0.466808 0.884359i \(-0.345404\pi\)
0.466808 + 0.884359i \(0.345404\pi\)
\(662\) −1.45636e11 −0.758294
\(663\) 1.48523e11i 0.768669i
\(664\) 5.59688e10i 0.287921i
\(665\) 3.88912e10i 0.198868i
\(666\) −3.86419e11 −1.96409
\(667\) 1.27049e10i 0.0641902i
\(668\) −7.02258e10 −0.352688
\(669\) −9.20098e9 −0.0459335
\(670\) −2.29589e11 −1.13934
\(671\) 9.18442e10i 0.453066i
\(672\) 1.72052e11i 0.843690i
\(673\) 4.02539e11i 1.96222i 0.193456 + 0.981109i \(0.438030\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(674\) 3.80518e11i 1.84389i
\(675\) 1.27123e11i 0.612365i
\(676\) −1.49163e11 −0.714292
\(677\) 3.11966e11i 1.48509i −0.669796 0.742545i \(-0.733618\pi\)
0.669796 0.742545i \(-0.266382\pi\)
\(678\) 6.12130e10i 0.289684i
\(679\) 4.53802e10i 0.213495i
\(680\) −3.26622e10 −0.152760
\(681\) −2.39799e11 −1.11496
\(682\) 9.70558e10i 0.448626i
\(683\) 2.47854e11 1.13897 0.569487 0.822000i \(-0.307142\pi\)
0.569487 + 0.822000i \(0.307142\pi\)
\(684\) 5.52647e10i 0.252478i
\(685\) 9.78108e10 0.444247
\(686\) −3.12721e11 −1.41208
\(687\) 1.48958e11i 0.668709i
\(688\) 1.38233e11 + 1.17632e11i 0.616962 + 0.525017i
\(689\) 2.98489e11 1.32450
\(690\) 1.19394e11i 0.526730i
\(691\) 1.76475e11i 0.774052i −0.922069 0.387026i \(-0.873502\pi\)
0.922069 0.387026i \(-0.126498\pi\)
\(692\) 3.90123e11 1.70128
\(693\) 8.16904e10i 0.354191i
\(694\) −5.46298e11 −2.35501
\(695\) 2.58471e11i 1.10783i
\(696\) 1.95487e9i 0.00833067i
\(697\) −1.01528e11 −0.430184
\(698\) 4.08293e11 1.72009
\(699\) 1.06525e11 0.446213
\(700\) 1.85799e11i 0.773840i
\(701\) −2.51419e11 −1.04118 −0.520589 0.853807i \(-0.674288\pi\)
−0.520589 + 0.853807i \(0.674288\pi\)
\(702\) −4.32756e11 −1.78194
\(703\) 1.54732e11 0.633518
\(704\) 1.60843e11 0.654806
\(705\) −1.24290e10 −0.0503129
\(706\) 3.85966e11i 1.55357i
\(707\) 2.80249e11i 1.12167i
\(708\) 7.91086e10i 0.314841i
\(709\) 2.53180e11 1.00195 0.500973 0.865463i \(-0.332976\pi\)
0.500973 + 0.865463i \(0.332976\pi\)
\(710\) 2.83028e11i 1.11377i
\(711\) 9.39595e10 0.367674
\(712\) 6.15736e10 0.239593
\(713\) 1.64127e11 0.635070
\(714\) 2.39596e11i 0.921907i
\(715\) 1.00398e11i 0.384148i
\(716\) 1.69435e11i 0.644690i
\(717\) 7.39382e10i 0.279764i
\(718\) 7.51493e11i 2.82766i
\(719\) −2.91790e11 −1.09183 −0.545914 0.837841i \(-0.683818\pi\)
−0.545914 + 0.837841i \(0.683818\pi\)
\(720\) 8.80921e10i 0.327798i
\(721\) 1.34698e10i 0.0498447i
\(722\) 3.58516e11i 1.31935i
\(723\) −1.27417e11 −0.466308
\(724\) −1.08370e11 −0.394418
\(725\) 1.08212e10i 0.0391674i
\(726\) −1.73053e11 −0.622920
\(727\) 7.09422e10i 0.253961i 0.991905 + 0.126980i \(0.0405285\pi\)
−0.991905 + 0.126980i \(0.959471\pi\)
\(728\) −8.87597e10 −0.316002
\(729\) −1.27632e11 −0.451909
\(730\) 1.37799e11i 0.485238i
\(731\) 2.31290e11 + 1.96821e11i 0.810003 + 0.689289i
\(732\) 1.70294e11 0.593137
\(733\) 5.49791e11i 1.90450i 0.305316 + 0.952251i \(0.401238\pi\)
−0.305316 + 0.952251i \(0.598762\pi\)
\(734\) 1.11944e11i 0.385669i
\(735\) −7.27681e9 −0.0249340
\(736\) 4.42084e11i 1.50659i
\(737\) 1.93105e11 0.654520
\(738\) 1.19360e11i 0.402377i
\(739\) 2.61314e11i 0.876162i 0.898936 + 0.438081i \(0.144342\pi\)
−0.898936 + 0.438081i \(0.855658\pi\)
\(740\) 4.11966e11 1.37383
\(741\) 6.99181e10 0.231909
\(742\) 4.81520e11 1.58854
\(743\) 1.87745e11i 0.616045i 0.951379 + 0.308023i \(0.0996673\pi\)
−0.951379 + 0.308023i \(0.900333\pi\)
\(744\) 2.52537e10 0.0824201
\(745\) −2.22052e11 −0.720823
\(746\) −3.91036e11 −1.26259
\(747\) −2.52570e11 −0.811146
\(748\) 1.95763e11 0.625352
\(749\) 2.52533e11i 0.802400i
\(750\) 2.60059e11i 0.821913i
\(751\) 1.34471e10i 0.0422736i −0.999777 0.0211368i \(-0.993271\pi\)
0.999777 0.0211368i \(-0.00672855\pi\)
\(752\) 3.83030e10 0.119774
\(753\) 2.07505e11i 0.645429i
\(754\) −3.68378e10 −0.113975
\(755\) 6.77575e10 0.208531
\(756\) −3.75399e11 −1.14923
\(757\) 2.39956e11i 0.730716i −0.930867 0.365358i \(-0.880947\pi\)
0.930867 0.365358i \(-0.119053\pi\)
\(758\) 8.47778e11i 2.56806i
\(759\) 1.00421e11i 0.302593i
\(760\) 1.53759e10i 0.0460879i
\(761\) 1.35338e11i 0.403535i −0.979433 0.201768i \(-0.935331\pi\)
0.979433 0.201768i \(-0.0646686\pi\)
\(762\) −4.22156e9 −0.0125214
\(763\) 2.74501e11i 0.809926i
\(764\) 5.52427e11i 1.62144i
\(765\) 1.47394e11i 0.430363i
\(766\) −1.26400e11 −0.367139
\(767\) −2.09197e11 −0.604470
\(768\) 1.18472e11i 0.340543i
\(769\) −5.25701e11 −1.50326 −0.751629 0.659586i \(-0.770732\pi\)
−0.751629 + 0.659586i \(0.770732\pi\)
\(770\) 1.61961e11i 0.460730i
\(771\) −2.11918e11 −0.599722
\(772\) 6.96707e11 1.96147
\(773\) 3.97129e11i 1.11228i −0.831089 0.556140i \(-0.812282\pi\)
0.831089 0.556140i \(-0.187718\pi\)
\(774\) −2.31390e11 + 2.71913e11i −0.644735 + 0.757647i
\(775\) −1.39793e11 −0.387505
\(776\) 1.79414e10i 0.0494777i
\(777\) 4.24083e11i 1.16350i
\(778\) 7.84886e11 2.14234
\(779\) 4.77949e10i 0.129787i
\(780\) 1.86153e11 0.502913
\(781\) 2.38051e11i 0.639833i
\(782\)