Properties

Label 43.9.b.b.42.2
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 42.2
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.27

$q$-expansion

\(f(q)\) \(=\) \(q-31.0929i q^{2} +76.9602i q^{3} -710.770 q^{4} -309.101i q^{5} +2392.92 q^{6} +1604.82i q^{7} +14140.1i q^{8} +638.125 q^{9} +O(q^{10})\) \(q-31.0929i q^{2} +76.9602i q^{3} -710.770 q^{4} -309.101i q^{5} +2392.92 q^{6} +1604.82i q^{7} +14140.1i q^{8} +638.125 q^{9} -9610.84 q^{10} -7356.08 q^{11} -54701.0i q^{12} +42183.4 q^{13} +49898.6 q^{14} +23788.4 q^{15} +257701. q^{16} -57088.6 q^{17} -19841.2i q^{18} -127050. i q^{19} +219700. i q^{20} -123507. q^{21} +228722. i q^{22} +287238. q^{23} -1.08823e6 q^{24} +295082. q^{25} -1.31161e6i q^{26} +554046. i q^{27} -1.14066e6i q^{28} +292238. i q^{29} -739653. i q^{30} -478095. q^{31} -4.39281e6i q^{32} -566125. i q^{33} +1.77505e6i q^{34} +496051. q^{35} -453560. q^{36} +1.22416e6i q^{37} -3.95036e6 q^{38} +3.24645e6i q^{39} +4.37073e6 q^{40} +5.52026e6 q^{41} +3.84021e6i q^{42} +(1.30315e6 + 3.16070e6i) q^{43} +5.22848e6 q^{44} -197245. i q^{45} -8.93108e6i q^{46} -1.51306e6 q^{47} +1.98328e7i q^{48} +3.18935e6 q^{49} -9.17496e6i q^{50} -4.39355e6i q^{51} -2.99827e7 q^{52} +7.83616e6 q^{53} +1.72269e7 q^{54} +2.27377e6i q^{55} -2.26924e7 q^{56} +9.77780e6 q^{57} +9.08655e6 q^{58} +1.53013e7 q^{59} -1.69081e7 q^{60} +3.41732e6i q^{61} +1.48654e7i q^{62} +1.02408e6i q^{63} -7.06139e7 q^{64} -1.30389e7i q^{65} -1.76025e7 q^{66} -3.26404e7 q^{67} +4.05769e7 q^{68} +2.21059e7i q^{69} -1.54237e7i q^{70} -4.27345e7i q^{71} +9.02318e6i q^{72} +5.32427e7i q^{73} +3.80629e7 q^{74} +2.27096e7i q^{75} +9.03034e7i q^{76} -1.18052e7i q^{77} +1.00942e8 q^{78} +4.22399e7 q^{79} -7.96556e7i q^{80} -3.84528e7 q^{81} -1.71641e8i q^{82} -4.72358e7 q^{83} +8.77854e7 q^{84} +1.76461e7i q^{85} +(9.82753e7 - 4.05188e7i) q^{86} -2.24907e7 q^{87} -1.04016e8i q^{88} +7.79613e7i q^{89} -6.13292e6 q^{90} +6.76969e7i q^{91} -2.04161e8 q^{92} -3.67943e7i q^{93} +4.70453e7i q^{94} -3.92712e7 q^{95} +3.38072e8 q^{96} +5.35770e7 q^{97} -9.91662e7i q^{98} -4.69410e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 31.0929i 1.94331i −0.236407 0.971654i \(-0.575970\pi\)
0.236407 0.971654i \(-0.424030\pi\)
\(3\) 76.9602i 0.950126i 0.879952 + 0.475063i \(0.157575\pi\)
−0.879952 + 0.475063i \(0.842425\pi\)
\(4\) −710.770 −2.77645
\(5\) 309.101i 0.494561i −0.968944 0.247280i \(-0.920463\pi\)
0.968944 0.247280i \(-0.0795369\pi\)
\(6\) 2392.92 1.84639
\(7\) 1604.82i 0.668397i 0.942503 + 0.334199i \(0.108466\pi\)
−0.942503 + 0.334199i \(0.891534\pi\)
\(8\) 14140.1i 3.45218i
\(9\) 638.125 0.0972603
\(10\) −9610.84 −0.961084
\(11\) −7356.08 −0.502430 −0.251215 0.967931i \(-0.580830\pi\)
−0.251215 + 0.967931i \(0.580830\pi\)
\(12\) 54701.0i 2.63797i
\(13\) 42183.4 1.47696 0.738480 0.674275i \(-0.235544\pi\)
0.738480 + 0.674275i \(0.235544\pi\)
\(14\) 49898.6 1.29890
\(15\) 23788.4 0.469895
\(16\) 257701. 3.93221
\(17\) −57088.6 −0.683524 −0.341762 0.939787i \(-0.611024\pi\)
−0.341762 + 0.939787i \(0.611024\pi\)
\(18\) 19841.2i 0.189007i
\(19\) 127050.i 0.974901i −0.873151 0.487450i \(-0.837927\pi\)
0.873151 0.487450i \(-0.162073\pi\)
\(20\) 219700.i 1.37312i
\(21\) −123507. −0.635062
\(22\) 228722.i 0.976377i
\(23\) 287238. 1.02643 0.513217 0.858259i \(-0.328454\pi\)
0.513217 + 0.858259i \(0.328454\pi\)
\(24\) −1.08823e6 −3.28001
\(25\) 295082. 0.755410
\(26\) 1.31161e6i 2.87019i
\(27\) 554046.i 1.04254i
\(28\) 1.14066e6i 1.85577i
\(29\) 292238.i 0.413186i 0.978427 + 0.206593i \(0.0662375\pi\)
−0.978427 + 0.206593i \(0.933762\pi\)
\(30\) 739653.i 0.913151i
\(31\) −478095. −0.517687 −0.258844 0.965919i \(-0.583341\pi\)
−0.258844 + 0.965919i \(0.583341\pi\)
\(32\) 4.39281e6i 4.18931i
\(33\) 566125.i 0.477372i
\(34\) 1.77505e6i 1.32830i
\(35\) 496051. 0.330563
\(36\) −453560. −0.270038
\(37\) 1.22416e6i 0.653180i 0.945166 + 0.326590i \(0.105900\pi\)
−0.945166 + 0.326590i \(0.894100\pi\)
\(38\) −3.95036e6 −1.89453
\(39\) 3.24645e6i 1.40330i
\(40\) 4.37073e6 1.70732
\(41\) 5.52026e6 1.95355 0.976775 0.214270i \(-0.0687371\pi\)
0.976775 + 0.214270i \(0.0687371\pi\)
\(42\) 3.84021e6i 1.23412i
\(43\) 1.30315e6 + 3.16070e6i 0.381172 + 0.924504i
\(44\) 5.22848e6 1.39497
\(45\) 197245.i 0.0481011i
\(46\) 8.93108e6i 1.99468i
\(47\) −1.51306e6 −0.310073 −0.155036 0.987909i \(-0.549549\pi\)
−0.155036 + 0.987909i \(0.549549\pi\)
\(48\) 1.98328e7i 3.73610i
\(49\) 3.18935e6 0.553245
\(50\) 9.17496e6i 1.46799i
\(51\) 4.39355e6i 0.649434i
\(52\) −2.99827e7 −4.10070
\(53\) 7.83616e6 0.993116 0.496558 0.868004i \(-0.334597\pi\)
0.496558 + 0.868004i \(0.334597\pi\)
\(54\) 1.72269e7 2.02597
\(55\) 2.27377e6i 0.248482i
\(56\) −2.26924e7 −2.30743
\(57\) 9.77780e6 0.926279
\(58\) 9.08655e6 0.802947
\(59\) 1.53013e7 1.26276 0.631378 0.775475i \(-0.282489\pi\)
0.631378 + 0.775475i \(0.282489\pi\)
\(60\) −1.69081e7 −1.30464
\(61\) 3.41732e6i 0.246812i 0.992356 + 0.123406i \(0.0393817\pi\)
−0.992356 + 0.123406i \(0.960618\pi\)
\(62\) 1.48654e7i 1.00603i
\(63\) 1.02408e6i 0.0650085i
\(64\) −7.06139e7 −4.20892
\(65\) 1.30389e7i 0.730447i
\(66\) −1.76025e7 −0.927681
\(67\) −3.26404e7 −1.61978 −0.809892 0.586580i \(-0.800474\pi\)
−0.809892 + 0.586580i \(0.800474\pi\)
\(68\) 4.05769e7 1.89777
\(69\) 2.21059e7i 0.975242i
\(70\) 1.54237e7i 0.642386i
\(71\) 4.27345e7i 1.68169i −0.541279 0.840843i \(-0.682060\pi\)
0.541279 0.840843i \(-0.317940\pi\)
\(72\) 9.02318e6i 0.335761i
\(73\) 5.32427e7i 1.87486i 0.348175 + 0.937430i \(0.386802\pi\)
−0.348175 + 0.937430i \(0.613198\pi\)
\(74\) 3.80629e7 1.26933
\(75\) 2.27096e7i 0.717734i
\(76\) 9.03034e7i 2.70676i
\(77\) 1.18052e7i 0.335823i
\(78\) 1.00942e8 2.72704
\(79\) 4.22399e7 1.08446 0.542231 0.840230i \(-0.317580\pi\)
0.542231 + 0.840230i \(0.317580\pi\)
\(80\) 7.96556e7i 1.94472i
\(81\) −3.84528e7 −0.893280
\(82\) 1.71641e8i 3.79635i
\(83\) −4.72358e7 −0.995311 −0.497656 0.867375i \(-0.665806\pi\)
−0.497656 + 0.867375i \(0.665806\pi\)
\(84\) 8.77854e7 1.76322
\(85\) 1.76461e7i 0.338044i
\(86\) 9.82753e7 4.05188e7i 1.79660 0.740735i
\(87\) −2.24907e7 −0.392578
\(88\) 1.04016e8i 1.73448i
\(89\) 7.79613e7i 1.24256i 0.783587 + 0.621282i \(0.213388\pi\)
−0.783587 + 0.621282i \(0.786612\pi\)
\(90\) −6.13292e6 −0.0934754
\(91\) 6.76969e7i 0.987196i
\(92\) −2.04161e8 −2.84984
\(93\) 3.67943e7i 0.491868i
\(94\) 4.70453e7i 0.602567i
\(95\) −3.92712e7 −0.482148
\(96\) 3.38072e8 3.98038
\(97\) 5.35770e7 0.605190 0.302595 0.953119i \(-0.402147\pi\)
0.302595 + 0.953119i \(0.402147\pi\)
\(98\) 9.91662e7i 1.07513i
\(99\) −4.69410e6 −0.0488665
\(100\) −2.09735e8 −2.09735
\(101\) 4.84542e7 0.465635 0.232818 0.972520i \(-0.425205\pi\)
0.232818 + 0.972520i \(0.425205\pi\)
\(102\) −1.36608e8 −1.26205
\(103\) −1.76149e8 −1.56506 −0.782531 0.622612i \(-0.786072\pi\)
−0.782531 + 0.622612i \(0.786072\pi\)
\(104\) 5.96480e8i 5.09874i
\(105\) 3.81762e7i 0.314077i
\(106\) 2.43649e8i 1.92993i
\(107\) −4.01578e7 −0.306362 −0.153181 0.988198i \(-0.548952\pi\)
−0.153181 + 0.988198i \(0.548952\pi\)
\(108\) 3.93800e8i 2.89455i
\(109\) 4.85598e7 0.344010 0.172005 0.985096i \(-0.444976\pi\)
0.172005 + 0.985096i \(0.444976\pi\)
\(110\) 7.06981e7 0.482878
\(111\) −9.42120e7 −0.620603
\(112\) 4.13565e8i 2.62828i
\(113\) 7.49574e7i 0.459728i −0.973223 0.229864i \(-0.926172\pi\)
0.973223 0.229864i \(-0.0738281\pi\)
\(114\) 3.04020e8i 1.80005i
\(115\) 8.87855e7i 0.507634i
\(116\) 2.07714e8i 1.14719i
\(117\) 2.69183e7 0.143650
\(118\) 4.75762e8i 2.45393i
\(119\) 9.16170e7i 0.456865i
\(120\) 3.36372e8i 1.62216i
\(121\) −1.60247e8 −0.747564
\(122\) 1.06254e8 0.479632
\(123\) 4.24841e8i 1.85612i
\(124\) 3.39816e8 1.43733
\(125\) 2.11952e8i 0.868157i
\(126\) 3.18416e7 0.126332
\(127\) −7.98391e7 −0.306903 −0.153451 0.988156i \(-0.549039\pi\)
−0.153451 + 0.988156i \(0.549039\pi\)
\(128\) 1.07103e9i 3.98991i
\(129\) −2.43248e8 + 1.00291e8i −0.878395 + 0.362162i
\(130\) −4.05418e8 −1.41948
\(131\) 1.37065e8i 0.465415i −0.972547 0.232707i \(-0.925242\pi\)
0.972547 0.232707i \(-0.0747584\pi\)
\(132\) 4.02385e8i 1.32540i
\(133\) 2.03893e8 0.651621
\(134\) 1.01489e9i 3.14774i
\(135\) 1.71256e8 0.515597
\(136\) 8.07241e8i 2.35965i
\(137\) 3.72743e8i 1.05810i 0.848590 + 0.529051i \(0.177452\pi\)
−0.848590 + 0.529051i \(0.822548\pi\)
\(138\) 6.87338e8 1.89520
\(139\) −1.21246e8 −0.324794 −0.162397 0.986726i \(-0.551922\pi\)
−0.162397 + 0.986726i \(0.551922\pi\)
\(140\) −3.52579e8 −0.917791
\(141\) 1.16445e8i 0.294608i
\(142\) −1.32874e9 −3.26803
\(143\) −3.10305e8 −0.742069
\(144\) 1.64446e8 0.382448
\(145\) 9.03310e7 0.204345
\(146\) 1.65547e9 3.64343
\(147\) 2.45453e8i 0.525653i
\(148\) 8.70100e8i 1.81352i
\(149\) 5.70992e8i 1.15847i 0.815160 + 0.579235i \(0.196649\pi\)
−0.815160 + 0.579235i \(0.803351\pi\)
\(150\) 7.06107e8 1.39478
\(151\) 5.19180e8i 0.998644i −0.866417 0.499322i \(-0.833583\pi\)
0.866417 0.499322i \(-0.166417\pi\)
\(152\) 1.79651e9 3.36554
\(153\) −3.64297e7 −0.0664797
\(154\) −3.67058e8 −0.652607
\(155\) 1.47779e8i 0.256028i
\(156\) 2.30748e9i 3.89618i
\(157\) 7.05045e8i 1.16043i −0.814464 0.580214i \(-0.802969\pi\)
0.814464 0.580214i \(-0.197031\pi\)
\(158\) 1.31336e9i 2.10744i
\(159\) 6.03073e8i 0.943585i
\(160\) −1.35782e9 −2.07187
\(161\) 4.60966e8i 0.686066i
\(162\) 1.19561e9i 1.73592i
\(163\) 2.10320e8i 0.297940i 0.988842 + 0.148970i \(0.0475958\pi\)
−0.988842 + 0.148970i \(0.952404\pi\)
\(164\) −3.92364e9 −5.42393
\(165\) −1.74990e8 −0.236090
\(166\) 1.46870e9i 1.93420i
\(167\) 1.19295e8 0.153375 0.0766877 0.997055i \(-0.475566\pi\)
0.0766877 + 0.997055i \(0.475566\pi\)
\(168\) 1.74641e9i 2.19235i
\(169\) 9.63713e8 1.18141
\(170\) 5.48670e8 0.656924
\(171\) 8.10738e7i 0.0948192i
\(172\) −9.26242e8 2.24653e9i −1.05830 2.56684i
\(173\) 1.83412e8 0.204759 0.102380 0.994745i \(-0.467354\pi\)
0.102380 + 0.994745i \(0.467354\pi\)
\(174\) 6.99303e8i 0.762901i
\(175\) 4.73554e8i 0.504914i
\(176\) −1.89567e9 −1.97566
\(177\) 1.17759e9i 1.19978i
\(178\) 2.42404e9 2.41469
\(179\) 1.83639e9i 1.78876i −0.447304 0.894382i \(-0.647616\pi\)
0.447304 0.894382i \(-0.352384\pi\)
\(180\) 1.40196e8i 0.133550i
\(181\) 7.96225e8 0.741859 0.370930 0.928661i \(-0.379039\pi\)
0.370930 + 0.928661i \(0.379039\pi\)
\(182\) 2.10490e9 1.91843
\(183\) −2.62998e8 −0.234502
\(184\) 4.06159e9i 3.54344i
\(185\) 3.78390e8 0.323037
\(186\) −1.14404e9 −0.955852
\(187\) 4.19948e8 0.343423
\(188\) 1.07544e9 0.860900
\(189\) −8.89145e8 −0.696828
\(190\) 1.22106e9i 0.936962i
\(191\) 1.27800e9i 0.960279i −0.877192 0.480140i \(-0.840586\pi\)
0.877192 0.480140i \(-0.159414\pi\)
\(192\) 5.43446e9i 3.99900i
\(193\) −2.03388e8 −0.146587 −0.0732937 0.997310i \(-0.523351\pi\)
−0.0732937 + 0.997310i \(0.523351\pi\)
\(194\) 1.66587e9i 1.17607i
\(195\) 1.00348e9 0.694016
\(196\) −2.26689e9 −1.53606
\(197\) 1.84082e9 1.22221 0.611107 0.791548i \(-0.290725\pi\)
0.611107 + 0.791548i \(0.290725\pi\)
\(198\) 1.45953e8i 0.0949627i
\(199\) 3.93508e8i 0.250923i 0.992098 + 0.125462i \(0.0400412\pi\)
−0.992098 + 0.125462i \(0.959959\pi\)
\(200\) 4.17250e9i 2.60781i
\(201\) 2.51202e9i 1.53900i
\(202\) 1.50658e9i 0.904873i
\(203\) −4.68990e8 −0.276172
\(204\) 3.12281e9i 1.80312i
\(205\) 1.70632e9i 0.966149i
\(206\) 5.47699e9i 3.04140i
\(207\) 1.83294e8 0.0998313
\(208\) 1.08707e10 5.80772
\(209\) 9.34590e8i 0.489820i
\(210\) 1.18701e9 0.610348
\(211\) 3.33053e9i 1.68029i 0.542362 + 0.840145i \(0.317530\pi\)
−0.542362 + 0.840145i \(0.682470\pi\)
\(212\) −5.56971e9 −2.75733
\(213\) 3.28885e9 1.59781
\(214\) 1.24862e9i 0.595355i
\(215\) 9.76973e8 4.02805e8i 0.457224 0.188513i
\(216\) −7.83429e9 −3.59903
\(217\) 7.67258e8i 0.346021i
\(218\) 1.50987e9i 0.668517i
\(219\) −4.09757e9 −1.78135
\(220\) 1.61613e9i 0.689898i
\(221\) −2.40819e9 −1.00954
\(222\) 2.92933e9i 1.20602i
\(223\) 2.90423e9i 1.17439i 0.809446 + 0.587195i \(0.199768\pi\)
−0.809446 + 0.587195i \(0.800232\pi\)
\(224\) 7.04968e9 2.80013
\(225\) 1.88299e8 0.0734714
\(226\) −2.33065e9 −0.893393
\(227\) 2.65538e9i 1.00005i −0.866010 0.500027i \(-0.833323\pi\)
0.866010 0.500027i \(-0.166677\pi\)
\(228\) −6.94977e9 −2.57176
\(229\) −6.07345e8 −0.220848 −0.110424 0.993885i \(-0.535221\pi\)
−0.110424 + 0.993885i \(0.535221\pi\)
\(230\) −2.76060e9 −0.986490
\(231\) 9.08531e8 0.319074
\(232\) −4.13229e9 −1.42639
\(233\) 9.56751e8i 0.324620i −0.986740 0.162310i \(-0.948106\pi\)
0.986740 0.162310i \(-0.0518944\pi\)
\(234\) 8.36969e8i 0.279155i
\(235\) 4.67686e8i 0.153350i
\(236\) −1.08757e10 −3.50598
\(237\) 3.25079e9i 1.03037i
\(238\) −2.84864e9 −0.887830
\(239\) 1.06815e8 0.0327373 0.0163686 0.999866i \(-0.494789\pi\)
0.0163686 + 0.999866i \(0.494789\pi\)
\(240\) 6.13032e9 1.84773
\(241\) 5.00348e9i 1.48321i −0.670835 0.741607i \(-0.734064\pi\)
0.670835 0.741607i \(-0.265936\pi\)
\(242\) 4.98255e9i 1.45275i
\(243\) 6.75763e8i 0.193807i
\(244\) 2.42893e9i 0.685260i
\(245\) 9.85829e8i 0.273613i
\(246\) 1.32095e10 3.60701
\(247\) 5.35941e9i 1.43989i
\(248\) 6.76034e9i 1.78715i
\(249\) 3.63528e9i 0.945671i
\(250\) −6.59022e9 −1.68710
\(251\) 6.27266e9 1.58036 0.790182 0.612872i \(-0.209986\pi\)
0.790182 + 0.612872i \(0.209986\pi\)
\(252\) 7.27884e8i 0.180493i
\(253\) −2.11295e9 −0.515712
\(254\) 2.48243e9i 0.596407i
\(255\) −1.35805e9 −0.321185
\(256\) 1.52244e10 3.54471
\(257\) 3.46689e9i 0.794708i −0.917665 0.397354i \(-0.869928\pi\)
0.917665 0.397354i \(-0.130072\pi\)
\(258\) 3.11834e9 + 7.56329e9i 0.703792 + 1.70699i
\(259\) −1.96457e9 −0.436584
\(260\) 9.26768e9i 2.02805i
\(261\) 1.86485e8i 0.0401866i
\(262\) −4.26174e9 −0.904444
\(263\) 1.63128e9i 0.340961i −0.985361 0.170480i \(-0.945468\pi\)
0.985361 0.170480i \(-0.0545319\pi\)
\(264\) 8.00510e9 1.64798
\(265\) 2.42216e9i 0.491156i
\(266\) 6.33962e9i 1.26630i
\(267\) −5.99992e9 −1.18059
\(268\) 2.31999e10 4.49724
\(269\) 3.80777e8 0.0727212 0.0363606 0.999339i \(-0.488424\pi\)
0.0363606 + 0.999339i \(0.488424\pi\)
\(270\) 5.32485e9i 1.00196i
\(271\) −4.98415e9 −0.924089 −0.462045 0.886857i \(-0.652884\pi\)
−0.462045 + 0.886857i \(0.652884\pi\)
\(272\) −1.47118e10 −2.68776
\(273\) −5.20997e9 −0.937961
\(274\) 1.15897e10 2.05622
\(275\) −2.17065e9 −0.379541
\(276\) 1.57122e10i 2.70771i
\(277\) 1.03473e10i 1.75755i 0.477233 + 0.878777i \(0.341640\pi\)
−0.477233 + 0.878777i \(0.658360\pi\)
\(278\) 3.76989e9i 0.631174i
\(279\) −3.05084e8 −0.0503504
\(280\) 7.01424e9i 1.14116i
\(281\) 5.27555e9 0.846140 0.423070 0.906097i \(-0.360952\pi\)
0.423070 + 0.906097i \(0.360952\pi\)
\(282\) −3.62062e9 −0.572515
\(283\) 6.87347e9 1.07159 0.535797 0.844347i \(-0.320011\pi\)
0.535797 + 0.844347i \(0.320011\pi\)
\(284\) 3.03744e10i 4.66911i
\(285\) 3.02232e9i 0.458101i
\(286\) 9.64829e9i 1.44207i
\(287\) 8.85904e9i 1.30575i
\(288\) 2.80316e9i 0.407454i
\(289\) −3.71665e9 −0.532795
\(290\) 2.80866e9i 0.397106i
\(291\) 4.12330e9i 0.575007i
\(292\) 3.78433e10i 5.20545i
\(293\) −1.19152e10 −1.61671 −0.808355 0.588696i \(-0.799642\pi\)
−0.808355 + 0.588696i \(0.799642\pi\)
\(294\) 7.63185e9 1.02151
\(295\) 4.72963e9i 0.624510i
\(296\) −1.73099e10 −2.25490
\(297\) 4.07561e9i 0.523801i
\(298\) 1.77538e10 2.25127
\(299\) 1.21167e10 1.51600
\(300\) 1.61413e10i 1.99275i
\(301\) −5.07235e9 + 2.09133e9i −0.617936 + 0.254775i
\(302\) −1.61428e10 −1.94067
\(303\) 3.72904e9i 0.442412i
\(304\) 3.27410e10i 3.83352i
\(305\) 1.05629e9 0.122064
\(306\) 1.13270e9i 0.129191i
\(307\) 6.03350e9 0.679229 0.339614 0.940565i \(-0.389703\pi\)
0.339614 + 0.940565i \(0.389703\pi\)
\(308\) 8.39079e9i 0.932395i
\(309\) 1.35565e10i 1.48701i
\(310\) 4.59490e9 0.497541
\(311\) −1.24617e10 −1.33209 −0.666046 0.745911i \(-0.732015\pi\)
−0.666046 + 0.745911i \(0.732015\pi\)
\(312\) −4.59052e10 −4.84444
\(313\) 6.35655e9i 0.662283i 0.943581 + 0.331142i \(0.107434\pi\)
−0.943581 + 0.331142i \(0.892566\pi\)
\(314\) −2.19219e10 −2.25507
\(315\) 3.16543e8 0.0321507
\(316\) −3.00228e10 −3.01095
\(317\) 1.40297e10 1.38935 0.694676 0.719323i \(-0.255548\pi\)
0.694676 + 0.719323i \(0.255548\pi\)
\(318\) 1.87513e10 1.83368
\(319\) 2.14973e9i 0.207597i
\(320\) 2.18268e10i 2.08157i
\(321\) 3.09055e9i 0.291082i
\(322\) 1.43328e10 1.33324
\(323\) 7.25311e9i 0.666368i
\(324\) 2.73311e10 2.48014
\(325\) 1.24476e10 1.11571
\(326\) 6.53945e9 0.578990
\(327\) 3.73717e9i 0.326853i
\(328\) 7.80573e10i 6.74401i
\(329\) 2.42819e9i 0.207252i
\(330\) 5.44094e9i 0.458795i
\(331\) 1.45095e10i 1.20876i 0.796696 + 0.604380i \(0.206579\pi\)
−0.796696 + 0.604380i \(0.793421\pi\)
\(332\) 3.35738e10 2.76343
\(333\) 7.81170e8i 0.0635285i
\(334\) 3.70923e9i 0.298056i
\(335\) 1.00892e10i 0.801081i
\(336\) −3.18280e10 −2.49720
\(337\) −1.52910e10 −1.18554 −0.592772 0.805370i \(-0.701966\pi\)
−0.592772 + 0.805370i \(0.701966\pi\)
\(338\) 2.99647e10i 2.29584i
\(339\) 5.76874e9 0.436800
\(340\) 1.25423e10i 0.938562i
\(341\) 3.51691e9 0.260102
\(342\) −2.52082e9 −0.184263
\(343\) 1.43698e10i 1.03818i
\(344\) −4.46927e10 + 1.84268e10i −3.19156 + 1.31588i
\(345\) 6.83295e9 0.482317
\(346\) 5.70282e9i 0.397910i
\(347\) 3.46237e8i 0.0238812i −0.999929 0.0119406i \(-0.996199\pi\)
0.999929 0.0119406i \(-0.00380090\pi\)
\(348\) 1.59857e10 1.08997
\(349\) 2.52716e10i 1.70346i −0.523983 0.851729i \(-0.675554\pi\)
0.523983 0.851729i \(-0.324446\pi\)
\(350\) 1.47242e10 0.981203
\(351\) 2.33716e10i 1.53978i
\(352\) 3.23139e10i 2.10484i
\(353\) 2.62821e9 0.169263 0.0846315 0.996412i \(-0.473029\pi\)
0.0846315 + 0.996412i \(0.473029\pi\)
\(354\) 3.66147e10 2.33154
\(355\) −1.32092e10 −0.831696
\(356\) 5.54126e10i 3.44991i
\(357\) 7.05087e9 0.434080
\(358\) −5.70988e10 −3.47612
\(359\) 2.51278e10 1.51278 0.756392 0.654119i \(-0.226960\pi\)
0.756392 + 0.654119i \(0.226960\pi\)
\(360\) 2.78907e9 0.166054
\(361\) 8.41845e8 0.0495682
\(362\) 2.47570e10i 1.44166i
\(363\) 1.23326e10i 0.710280i
\(364\) 4.81170e10i 2.74090i
\(365\) 1.64574e10 0.927232
\(366\) 8.17736e9i 0.455710i
\(367\) 9.39858e9 0.518081 0.259041 0.965866i \(-0.416594\pi\)
0.259041 + 0.965866i \(0.416594\pi\)
\(368\) 7.40217e10 4.03616
\(369\) 3.52262e9 0.190003
\(370\) 1.17653e10i 0.627761i
\(371\) 1.25756e10i 0.663796i
\(372\) 2.61523e10i 1.36565i
\(373\) 5.81508e9i 0.300414i 0.988655 + 0.150207i \(0.0479940\pi\)
−0.988655 + 0.150207i \(0.952006\pi\)
\(374\) 1.30574e10i 0.667377i
\(375\) 1.63119e10 0.824859
\(376\) 2.13948e10i 1.07043i
\(377\) 1.23276e10i 0.610258i
\(378\) 2.76461e10i 1.35415i
\(379\) −2.73939e10 −1.32769 −0.663845 0.747871i \(-0.731076\pi\)
−0.663845 + 0.747871i \(0.731076\pi\)
\(380\) 2.79128e10 1.33866
\(381\) 6.14444e9i 0.291596i
\(382\) −3.97368e10 −1.86612
\(383\) 1.63024e9i 0.0757627i 0.999282 + 0.0378813i \(0.0120609\pi\)
−0.999282 + 0.0378813i \(0.987939\pi\)
\(384\) −8.24270e10 −3.79092
\(385\) −3.64899e9 −0.166085
\(386\) 6.32393e9i 0.284864i
\(387\) 8.31574e8 + 2.01692e9i 0.0370729 + 0.0899176i
\(388\) −3.80810e10 −1.68028
\(389\) 5.91193e9i 0.258185i 0.991633 + 0.129092i \(0.0412064\pi\)
−0.991633 + 0.129092i \(0.958794\pi\)
\(390\) 3.12011e10i 1.34869i
\(391\) −1.63980e10 −0.701592
\(392\) 4.50978e10i 1.90990i
\(393\) 1.05485e10 0.442202
\(394\) 5.72366e10i 2.37514i
\(395\) 1.30564e10i 0.536332i
\(396\) 3.33643e9 0.135675
\(397\) −2.24349e10 −0.903154 −0.451577 0.892232i \(-0.649138\pi\)
−0.451577 + 0.892232i \(0.649138\pi\)
\(398\) 1.22353e10 0.487622
\(399\) 1.56916e10i 0.619122i
\(400\) 7.60430e10 2.97043
\(401\) −1.52627e10 −0.590272 −0.295136 0.955455i \(-0.595365\pi\)
−0.295136 + 0.955455i \(0.595365\pi\)
\(402\) −7.81059e10 −2.99075
\(403\) −2.01677e10 −0.764603
\(404\) −3.44398e10 −1.29281
\(405\) 1.18858e10i 0.441781i
\(406\) 1.45823e10i 0.536688i
\(407\) 9.00505e9i 0.328177i
\(408\) 6.21255e10 2.24197
\(409\) 7.64531e9i 0.273213i 0.990625 + 0.136607i \(0.0436196\pi\)
−0.990625 + 0.136607i \(0.956380\pi\)
\(410\) −5.30544e10 −1.87753
\(411\) −2.86864e10 −1.00533
\(412\) 1.25202e11 4.34531
\(413\) 2.45558e10i 0.844023i
\(414\) 5.69915e9i 0.194003i
\(415\) 1.46006e10i 0.492242i
\(416\) 1.85304e11i 6.18745i
\(417\) 9.33111e9i 0.308595i
\(418\) 2.90592e10 0.951870
\(419\) 2.18738e10i 0.709689i 0.934925 + 0.354844i \(0.115466\pi\)
−0.934925 + 0.354844i \(0.884534\pi\)
\(420\) 2.71345e10i 0.872017i
\(421\) 1.91405e10i 0.609291i −0.952466 0.304645i \(-0.901462\pi\)
0.952466 0.304645i \(-0.0985380\pi\)
\(422\) 1.03556e11 3.26532
\(423\) −9.65519e8 −0.0301578
\(424\) 1.10804e11i 3.42842i
\(425\) −1.68458e10 −0.516340
\(426\) 1.02260e11i 3.10504i
\(427\) −5.48419e9 −0.164968
\(428\) 2.85430e10 0.850597
\(429\) 2.38811e10i 0.705059i
\(430\) −1.25244e10 3.03769e10i −0.366339 0.888526i
\(431\) 1.65854e10 0.480636 0.240318 0.970694i \(-0.422748\pi\)
0.240318 + 0.970694i \(0.422748\pi\)
\(432\) 1.42778e11i 4.09947i
\(433\) 2.27110e8i 0.00646078i −0.999995 0.00323039i \(-0.998972\pi\)
0.999995 0.00323039i \(-0.00102827\pi\)
\(434\) −2.38563e10 −0.672425
\(435\) 6.95190e9i 0.194154i
\(436\) −3.45148e10 −0.955125
\(437\) 3.64937e10i 1.00067i
\(438\) 1.27405e11i 3.46172i
\(439\) −3.63557e10 −0.978846 −0.489423 0.872046i \(-0.662793\pi\)
−0.489423 + 0.872046i \(0.662793\pi\)
\(440\) −3.21514e10 −0.857807
\(441\) 2.03520e9 0.0538088
\(442\) 7.48778e10i 1.96184i
\(443\) −5.00268e10 −1.29894 −0.649468 0.760389i \(-0.725008\pi\)
−0.649468 + 0.760389i \(0.725008\pi\)
\(444\) 6.69631e10 1.72307
\(445\) 2.40979e10 0.614524
\(446\) 9.03012e10 2.28220
\(447\) −4.39437e10 −1.10069
\(448\) 1.13323e11i 2.81323i
\(449\) 6.46660e10i 1.59108i −0.605904 0.795538i \(-0.707188\pi\)
0.605904 0.795538i \(-0.292812\pi\)
\(450\) 5.85477e9i 0.142778i
\(451\) −4.06075e10 −0.981522
\(452\) 5.32775e10i 1.27641i
\(453\) 3.99562e10 0.948837
\(454\) −8.25636e10 −1.94341
\(455\) 2.09252e10 0.488228
\(456\) 1.38260e11i 3.19769i
\(457\) 7.15621e10i 1.64066i −0.571891 0.820330i \(-0.693790\pi\)
0.571891 0.820330i \(-0.306210\pi\)
\(458\) 1.88841e10i 0.429176i
\(459\) 3.16297e10i 0.712598i
\(460\) 6.31061e10i 1.40942i
\(461\) −9.56302e9 −0.211734 −0.105867 0.994380i \(-0.533762\pi\)
−0.105867 + 0.994380i \(0.533762\pi\)
\(462\) 2.82489e10i 0.620059i
\(463\) 1.69947e10i 0.369819i 0.982756 + 0.184909i \(0.0591991\pi\)
−0.982756 + 0.184909i \(0.940801\pi\)
\(464\) 7.53102e10i 1.62473i
\(465\) −1.13731e10 −0.243259
\(466\) −2.97482e10 −0.630837
\(467\) 4.90505e10i 1.03128i 0.856806 + 0.515640i \(0.172446\pi\)
−0.856806 + 0.515640i \(0.827554\pi\)
\(468\) −1.91327e10 −0.398835
\(469\) 5.23821e10i 1.08266i
\(470\) 1.45417e10 0.298006
\(471\) 5.42604e10 1.10255
\(472\) 2.16362e11i 4.35927i
\(473\) −9.58609e9 2.32503e10i −0.191512 0.464499i
\(474\) 1.01077e11 2.00234
\(475\) 3.74902e10i 0.736449i
\(476\) 6.51187e10i 1.26846i
\(477\) 5.00045e9 0.0965908
\(478\) 3.32121e9i 0.0636186i
\(479\) 3.24807e10 0.616997 0.308499 0.951225i \(-0.400174\pi\)
0.308499 + 0.951225i \(0.400174\pi\)
\(480\) 1.04498e11i 1.96854i
\(481\) 5.16395e10i 0.964721i
\(482\) −1.55573e11 −2.88234
\(483\) −3.54761e10 −0.651849
\(484\) 1.13899e11 2.07557
\(485\) 1.65607e10i 0.299303i
\(486\) 2.10115e10 0.376627
\(487\) 6.76777e10 1.20318 0.601589 0.798806i \(-0.294535\pi\)
0.601589 + 0.798806i \(0.294535\pi\)
\(488\) −4.83214e10 −0.852040
\(489\) −1.61862e10 −0.283081
\(490\) −3.06523e10 −0.531715
\(491\) 5.31270e10i 0.914091i 0.889443 + 0.457046i \(0.151092\pi\)
−0.889443 + 0.457046i \(0.848908\pi\)
\(492\) 3.01964e11i 5.15341i
\(493\) 1.66835e10i 0.282422i
\(494\) −1.66640e11 −2.79815
\(495\) 1.45095e9i 0.0241675i
\(496\) −1.23206e11 −2.03566
\(497\) 6.85812e10 1.12403
\(498\) −1.13031e11 −1.83773
\(499\) 8.54031e10i 1.37744i −0.725029 0.688718i \(-0.758174\pi\)
0.725029 0.688718i \(-0.241826\pi\)
\(500\) 1.50649e11i 2.41039i
\(501\) 9.18096e9i 0.145726i
\(502\) 1.95036e11i 3.07113i
\(503\) 3.93175e10i 0.614206i −0.951676 0.307103i \(-0.900640\pi\)
0.951676 0.307103i \(-0.0993596\pi\)
\(504\) −1.44806e10 −0.224421
\(505\) 1.49772e10i 0.230285i
\(506\) 6.56978e10i 1.00219i
\(507\) 7.41675e10i 1.12249i
\(508\) 5.67473e10 0.852100
\(509\) 4.01712e10 0.598471 0.299236 0.954179i \(-0.403268\pi\)
0.299236 + 0.954179i \(0.403268\pi\)
\(510\) 4.22257e10i 0.624161i
\(511\) −8.54451e10 −1.25315
\(512\) 1.99187e11i 2.89855i
\(513\) 7.03916e10 1.01637
\(514\) −1.07796e11 −1.54436
\(515\) 5.44478e10i 0.774018i
\(516\) 1.72893e11 7.12838e10i 2.43882 1.00552i
\(517\) 1.11302e10 0.155790
\(518\) 6.10841e10i 0.848417i
\(519\) 1.41154e10i 0.194547i
\(520\) 1.84372e11 2.52164
\(521\) 2.34037e10i 0.317639i 0.987308 + 0.158819i \(0.0507687\pi\)
−0.987308 + 0.158819i \(0.949231\pi\)
\(522\) 5.79835e9 0.0780949
\(523\) 1.53893e9i 0.0205689i −0.999947 0.0102844i \(-0.996726\pi\)
0.999947 0.0102844i \(-0.00327370\pi\)
\(524\) 9.74214e10i 1.29220i
\(525\) −3.64448e10 −0.479732
\(526\) −5.07211e10 −0.662592
\(527\) 2.72938e10 0.353852
\(528\) 1.45891e11i 1.87713i
\(529\) 4.19490e9 0.0535673
\(530\) −7.53121e10 −0.954468
\(531\) 9.76413e9 0.122816
\(532\) −1.44921e11 −1.80919
\(533\) 2.32864e11 2.88531
\(534\) 1.86555e11i 2.29426i
\(535\) 1.24128e10i 0.151515i
\(536\) 4.61541e11i 5.59179i
\(537\) 1.41329e11 1.69955
\(538\) 1.18395e10i 0.141320i
\(539\) −2.34611e10 −0.277967
\(540\) −1.21724e11 −1.43153
\(541\) −2.14855e10 −0.250816 −0.125408 0.992105i \(-0.540024\pi\)
−0.125408 + 0.992105i \(0.540024\pi\)
\(542\) 1.54972e11i 1.79579i
\(543\) 6.12776e10i 0.704860i
\(544\) 2.50780e11i 2.86350i
\(545\) 1.50099e10i 0.170134i
\(546\) 1.61993e11i 1.82275i
\(547\) −7.55950e10 −0.844391 −0.422196 0.906505i \(-0.638741\pi\)
−0.422196 + 0.906505i \(0.638741\pi\)
\(548\) 2.64935e11i 2.93777i
\(549\) 2.18068e9i 0.0240050i
\(550\) 6.74917e10i 0.737564i
\(551\) 3.71289e10 0.402815
\(552\) −3.12581e11 −3.36671
\(553\) 6.77874e10i 0.724851i
\(554\) 3.21728e11 3.41547
\(555\) 2.91210e10i 0.306926i
\(556\) 8.61780e10 0.901773
\(557\) −1.76314e11 −1.83175 −0.915877 0.401459i \(-0.868503\pi\)
−0.915877 + 0.401459i \(0.868503\pi\)
\(558\) 9.48597e9i 0.0978464i
\(559\) 5.49715e10 + 1.33329e11i 0.562976 + 1.36546i
\(560\) 1.27833e11 1.29984
\(561\) 3.23193e10i 0.326295i
\(562\) 1.64032e11i 1.64431i
\(563\) 4.11955e9 0.0410031 0.0205015 0.999790i \(-0.493474\pi\)
0.0205015 + 0.999790i \(0.493474\pi\)
\(564\) 8.27657e10i 0.817964i
\(565\) −2.31694e10 −0.227364
\(566\) 2.13716e11i 2.08244i
\(567\) 6.17099e10i 0.597066i
\(568\) 6.04271e11 5.80549
\(569\) −5.45267e10 −0.520188 −0.260094 0.965583i \(-0.583754\pi\)
−0.260094 + 0.965583i \(0.583754\pi\)
\(570\) −9.39729e10 −0.890232
\(571\) 1.57005e11i 1.47697i −0.674272 0.738483i \(-0.735543\pi\)
0.674272 0.738483i \(-0.264457\pi\)
\(572\) 2.20555e11 2.06032
\(573\) 9.83552e10 0.912387
\(574\) 2.75453e11 2.53747
\(575\) 8.47588e10 0.775378
\(576\) −4.50605e10 −0.409361
\(577\) 1.19552e11i 1.07858i −0.842120 0.539291i \(-0.818692\pi\)
0.842120 0.539291i \(-0.181308\pi\)
\(578\) 1.15562e11i 1.03539i
\(579\) 1.56528e10i 0.139276i
\(580\) −6.42046e10 −0.567354
\(581\) 7.58050e10i 0.665263i
\(582\) 1.28205e11 1.11742
\(583\) −5.76434e10 −0.498971
\(584\) −7.52860e11 −6.47236
\(585\) 8.32046e9i 0.0710435i
\(586\) 3.70480e11i 3.14177i
\(587\) 9.65927e10i 0.813564i −0.913525 0.406782i \(-0.866651\pi\)
0.913525 0.406782i \(-0.133349\pi\)
\(588\) 1.74461e11i 1.45945i
\(589\) 6.07420e10i 0.504694i
\(590\) −1.47058e11 −1.21362
\(591\) 1.41670e11i 1.16126i
\(592\) 3.15469e11i 2.56844i
\(593\) 1.38229e11i 1.11784i −0.829222 0.558920i \(-0.811216\pi\)
0.829222 0.558920i \(-0.188784\pi\)
\(594\) −1.26723e11 −1.01791
\(595\) −2.83189e10 −0.225948
\(596\) 4.05844e11i 3.21643i
\(597\) −3.02845e10 −0.238409
\(598\) 3.76744e11i 2.94606i
\(599\) 7.61743e10 0.591700 0.295850 0.955234i \(-0.404397\pi\)
0.295850 + 0.955234i \(0.404397\pi\)
\(600\) −3.21117e11 −2.47775
\(601\) 1.66678e11i 1.27756i −0.769391 0.638778i \(-0.779440\pi\)
0.769391 0.638778i \(-0.220560\pi\)
\(602\) 6.50255e10 + 1.57714e11i 0.495106 + 1.20084i
\(603\) −2.08287e10 −0.157541
\(604\) 3.69018e11i 2.77268i
\(605\) 4.95324e10i 0.369716i
\(606\) 1.15947e11 0.859743
\(607\) 7.27298e10i 0.535745i 0.963454 + 0.267872i \(0.0863205\pi\)
−0.963454 + 0.267872i \(0.913679\pi\)
\(608\) −5.58107e11 −4.08417
\(609\) 3.60936e10i 0.262398i
\(610\) 3.28433e10i 0.237207i
\(611\) −6.38259e10 −0.457965
\(612\) 2.58931e10 0.184577
\(613\) −1.54770e11 −1.09608 −0.548042 0.836451i \(-0.684627\pi\)
−0.548042 + 0.836451i \(0.684627\pi\)
\(614\) 1.87599e11i 1.31995i
\(615\) 1.31318e11 0.917963
\(616\) 1.66927e11 1.15932
\(617\) 9.53827e10 0.658156 0.329078 0.944303i \(-0.393262\pi\)
0.329078 + 0.944303i \(0.393262\pi\)
\(618\) −4.21510e11 −2.88971
\(619\) −6.89842e9 −0.0469880 −0.0234940 0.999724i \(-0.507479\pi\)
−0.0234940 + 0.999724i \(0.507479\pi\)
\(620\) 1.05037e11i 0.710848i
\(621\) 1.59143e11i 1.07009i
\(622\) 3.87469e11i 2.58867i
\(623\) −1.25114e11 −0.830527
\(624\) 8.36614e11i 5.51806i
\(625\) 4.97518e10 0.326053
\(626\) 1.97644e11 1.28702
\(627\) −7.19263e10 −0.465390
\(628\) 5.01125e11i 3.22187i
\(629\) 6.98858e10i 0.446464i
\(630\) 9.84224e9i 0.0624787i
\(631\) 7.55488e10i 0.476552i −0.971198 0.238276i \(-0.923418\pi\)
0.971198 0.238276i \(-0.0765823\pi\)
\(632\) 5.97278e11i 3.74376i
\(633\) −2.56319e11 −1.59649
\(634\) 4.36225e11i 2.69994i
\(635\) 2.46783e10i 0.151782i
\(636\) 4.28646e11i 2.61981i
\(637\) 1.34538e11 0.817121
\(638\) −6.68414e10 −0.403425
\(639\) 2.72699e10i 0.163561i
\(640\) 3.31057e11 1.97325
\(641\) 6.44169e10i 0.381564i 0.981632 + 0.190782i \(0.0611024\pi\)
−0.981632 + 0.190782i \(0.938898\pi\)
\(642\) −9.60943e10 −0.565663
\(643\) −8.74404e10 −0.511527 −0.255763 0.966739i \(-0.582327\pi\)
−0.255763 + 0.966739i \(0.582327\pi\)
\(644\) 3.27641e11i 1.90483i
\(645\) 3.10000e10 + 7.51880e10i 0.179111 + 0.434420i
\(646\) 2.25520e11 1.29496
\(647\) 2.45475e11i 1.40085i 0.713728 + 0.700423i \(0.247005\pi\)
−0.713728 + 0.700423i \(0.752995\pi\)
\(648\) 5.43728e11i 3.08377i
\(649\) −1.12557e11 −0.634447
\(650\) 3.87031e11i 2.16817i
\(651\) 5.90483e10 0.328763
\(652\) 1.49489e11i 0.827215i
\(653\) 2.93482e10i 0.161410i 0.996738 + 0.0807048i \(0.0257171\pi\)
−0.996738 + 0.0807048i \(0.974283\pi\)
\(654\) 1.16200e11 0.635175
\(655\) −4.23667e10 −0.230176
\(656\) 1.42258e12 7.68177
\(657\) 3.39755e10i 0.182349i
\(658\) −7.54994e10 −0.402754
\(659\) −2.33390e11 −1.23749 −0.618744 0.785593i \(-0.712358\pi\)
−0.618744 + 0.785593i \(0.712358\pi\)
\(660\) 1.24378e11 0.655490
\(661\) −2.66026e11 −1.39353 −0.696767 0.717297i \(-0.745379\pi\)
−0.696767 + 0.717297i \(0.745379\pi\)
\(662\) 4.51143e11 2.34900
\(663\) 1.85335e11i 0.959188i
\(664\) 6.67921e11i 3.43600i
\(665\) 6.30233e10i 0.322266i
\(666\) 2.42889e10 0.123455
\(667\) 8.39421e10i 0.424108i
\(668\) −8.47913e10 −0.425839
\(669\) −2.23511e11 −1.11582
\(670\) 3.13702e11 1.55675
\(671\) 2.51381e10i 0.124006i
\(672\) 5.42545e11i 2.66047i
\(673\) 2.88073e11i 1.40424i 0.712058 + 0.702121i \(0.247763\pi\)
−0.712058 + 0.702121i \(0.752237\pi\)
\(674\) 4.75443e11i 2.30388i
\(675\) 1.63489e11i 0.787541i
\(676\) −6.84978e11 −3.28012
\(677\) 2.49369e11i 1.18710i −0.804796 0.593551i \(-0.797725\pi\)
0.804796 0.593551i \(-0.202275\pi\)
\(678\) 1.79367e11i 0.848836i
\(679\) 8.59816e10i 0.404507i
\(680\) −2.49519e11 −1.16699
\(681\) 2.04359e11 0.950178
\(682\) 1.09351e11i 0.505458i
\(683\) −7.43209e10 −0.341530 −0.170765 0.985312i \(-0.554624\pi\)
−0.170765 + 0.985312i \(0.554624\pi\)
\(684\) 5.76249e10i 0.263260i
\(685\) 1.15215e11 0.523296
\(686\) 4.46800e11 2.01751
\(687\) 4.67414e10i 0.209834i
\(688\) 3.35824e11 + 8.14515e11i 1.49885 + 3.63534i
\(689\) 3.30556e11 1.46679
\(690\) 2.12457e11i 0.937290i
\(691\) 1.05148e11i 0.461200i 0.973049 + 0.230600i \(0.0740689\pi\)
−0.973049 + 0.230600i \(0.925931\pi\)
\(692\) −1.30364e11 −0.568503
\(693\) 7.53319e9i 0.0326622i
\(694\) −1.07655e10 −0.0464085
\(695\) 3.74772e10i 0.160630i
\(696\) 3.18022e11i 1.35525i
\(697\) −3.15144e11 −1.33530
\(698\) −7.85769e11 −3.31034
\(699\) 7.36318e10 0.308430
\(700\) 3.36588e11i 1.40187i
\(701\) −3.01602e11 −1.24900 −0.624501 0.781024i \(-0.714697\pi\)
−0.624501 + 0.781024i \(0.714697\pi\)
\(702\) 7.26691e11 2.99227
\(703\) 1.55530e11 0.636786
\(704\) 5.19442e11 2.11469
\(705\) −3.59932e10 −0.145702
\(706\) 8.17189e10i 0.328930i
\(707\) 7.77603e10i 0.311229i
\(708\) 8.36996e11i 3.33112i
\(709\) −3.95499e11 −1.56516 −0.782582 0.622547i \(-0.786098\pi\)
−0.782582 + 0.622547i \(0.786098\pi\)
\(710\) 4.10714e11i 1.61624i
\(711\) 2.69543e10 0.105475
\(712\) −1.10238e12 −4.28956
\(713\) −1.37327e11 −0.531372
\(714\) 2.19232e11i 0.843551i
\(715\) 9.59154e10i 0.366998i
\(716\) 1.30525e12i 4.96641i
\(717\) 8.22054e9i 0.0311045i
\(718\) 7.81297e11i 2.93981i
\(719\) 3.76466e11 1.40867 0.704337 0.709866i \(-0.251244\pi\)
0.704337 + 0.709866i \(0.251244\pi\)
\(720\) 5.08302e10i 0.189144i
\(721\) 2.82688e11i 1.04608i
\(722\) 2.61754e10i 0.0963263i
\(723\) 3.85069e11 1.40924
\(724\) −5.65933e11 −2.05973
\(725\) 8.62342e10i 0.312124i
\(726\) −3.83458e11 −1.38029
\(727\) 1.34308e11i 0.480800i 0.970674 + 0.240400i \(0.0772785\pi\)
−0.970674 + 0.240400i \(0.922721\pi\)
\(728\) −9.57244e11 −3.40798
\(729\) −3.04296e11 −1.07742
\(730\) 5.11707e11i 1.80190i
\(731\) −7.43951e10 1.80440e11i −0.260540 0.631921i
\(732\) 1.86931e11 0.651084
\(733\) 1.41612e10i 0.0490550i −0.999699 0.0245275i \(-0.992192\pi\)
0.999699 0.0245275i \(-0.00780813\pi\)
\(734\) 2.92229e11i 1.00679i
\(735\) 7.58696e10 0.259967
\(736\) 1.26178e12i 4.30006i
\(737\) 2.40106e11 0.813828
\(738\) 1.09529e11i 0.369234i
\(739\) 1.01671e11i 0.340893i −0.985367 0.170447i \(-0.945479\pi\)
0.985367 0.170447i \(-0.0545210\pi\)
\(740\) −2.68948e11 −0.896896
\(741\) 4.12461e11 1.36808
\(742\) 3.91014e11 1.28996
\(743\) 7.42954e10i 0.243785i 0.992543 + 0.121892i \(0.0388963\pi\)
−0.992543 + 0.121892i \(0.961104\pi\)
\(744\) 5.20277e11 1.69802
\(745\) 1.76494e11 0.572934
\(746\) 1.80808e11 0.583797
\(747\) −3.01423e10 −0.0968043
\(748\) −2.98487e11 −0.953496
\(749\) 6.44461e10i 0.204771i
\(750\) 5.07185e11i 1.60295i
\(751\) 3.61993e10i 0.113799i 0.998380 + 0.0568997i \(0.0181215\pi\)
−0.998380 + 0.0568997i \(0.981878\pi\)
\(752\) −3.89917e11 −1.21927
\(753\) 4.82746e11i 1.50155i
\(754\) 3.83302e11 1.18592
\(755\) −1.60479e11 −0.493890
\(756\) 6.31978e11 1.93471
\(757\) 1.37097e11i 0.417489i 0.977970 + 0.208744i \(0.0669377\pi\)
−0.977970 + 0.208744i \(0.933062\pi\)
\(758\) 8.51755e11i 2.58011i
\(759\) 1.62613e11i 0.489991i
\(760\) 5.55301e11i 1.66446i
\(761\) 3.33327e10i 0.0993876i 0.998764 + 0.0496938i \(0.0158245\pi\)
−0.998764 + 0.0496938i \(0.984175\pi\)
\(762\) −1.91049e11 −0.566662
\(763\) 7.79298e10i 0.229935i
\(764\) 9.08365e11i 2.66617i
\(765\) 1.12604e10i 0.0328783i
\(766\) 5.06888e10 0.147230
\(767\) 6.45461e11 1.86504
\(768\) 1.17167e12i 3.36792i
\(769\) −2.60316e11 −0.744381 −0.372190 0.928156i \(-0.621393\pi\)
−0.372190 + 0.928156i \(0.621393\pi\)
\(770\) 1.13458e11i 0.322754i
\(771\) 2.66813e11 0.755073
\(772\) 1.44562e11 0.406992
\(773\) 4.75435e11i 1.33160i 0.746131 + 0.665799i \(0.231909\pi\)
−0.746131 + 0.665799i \(0.768091\pi\)
\(774\) 6.27119e10 2.58561e10i 0.174738 0.0720442i
\(775\) −1.41077e11 −0.391066
\(776\) 7.57587e11i 2.08923i
\(777\) 1.51193e11i 0.414810i
\(778\) 1.83819e11 0.501733
\(779\) 7.01350e11i 1.90452i
\(780\) −7.13243e11 −1.92690
\(781\) 3.14358e11i 0.844929i
\(782\) 5.09863e11i