Properties

Label 43.9.b.b.42.15
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 42.15
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.14

$q$-expansion

\(f(q)\) \(=\) \(q+5.87436i q^{2} +114.397i q^{3} +221.492 q^{4} +623.321i q^{5} -672.007 q^{6} +2434.57i q^{7} +2804.96i q^{8} -6525.57 q^{9} +O(q^{10})\) \(q+5.87436i q^{2} +114.397i q^{3} +221.492 q^{4} +623.321i q^{5} -672.007 q^{6} +2434.57i q^{7} +2804.96i q^{8} -6525.57 q^{9} -3661.61 q^{10} +24815.2 q^{11} +25337.9i q^{12} +8701.41 q^{13} -14301.5 q^{14} -71305.8 q^{15} +40224.6 q^{16} +10140.4 q^{17} -38333.6i q^{18} -186604. i q^{19} +138060. i q^{20} -278506. q^{21} +145774. i q^{22} -387538. q^{23} -320878. q^{24} +2096.22 q^{25} +51115.2i q^{26} +4052.57i q^{27} +539236. i q^{28} -1.03599e6i q^{29} -418876. i q^{30} +146035. q^{31} +954363. i q^{32} +2.83878e6i q^{33} +59568.6i q^{34} -1.51752e6 q^{35} -1.44536e6 q^{36} -2.77780e6i q^{37} +1.09618e6 q^{38} +995411. i q^{39} -1.74839e6 q^{40} +89036.0 q^{41} -1.63604e6i q^{42} +(-3.30170e6 - 887103. i) q^{43} +5.49637e6 q^{44} -4.06753e6i q^{45} -2.27654e6i q^{46} +867696. q^{47} +4.60155e6i q^{48} -162308. q^{49} +12314.0i q^{50} +1.16003e6i q^{51} +1.92729e6 q^{52} +1.05861e7 q^{53} -23806.3 q^{54} +1.54678e7i q^{55} -6.82886e6 q^{56} +2.13468e7 q^{57} +6.08576e6 q^{58} +1.99430e7 q^{59} -1.57936e7 q^{60} -9.32889e6i q^{61} +857860. i q^{62} -1.58869e7i q^{63} +4.69121e6 q^{64} +5.42377e6i q^{65} -1.66760e7 q^{66} -1.83542e7 q^{67} +2.24602e6 q^{68} -4.43330e7i q^{69} -8.91443e6i q^{70} +8.73139e6i q^{71} -1.83040e7i q^{72} +3.39275e7i q^{73} +1.63178e7 q^{74} +239800. i q^{75} -4.13312e7i q^{76} +6.04143e7i q^{77} -5.84741e6 q^{78} +2.74337e7 q^{79} +2.50728e7i q^{80} -4.32779e7 q^{81} +523029. i q^{82} -6.16851e7 q^{83} -6.16868e7 q^{84} +6.32074e6i q^{85} +(5.21116e6 - 1.93954e7i) q^{86} +1.18513e8 q^{87} +6.96057e7i q^{88} +9.46713e6i q^{89} +2.38941e7 q^{90} +2.11841e7i q^{91} -8.58366e7 q^{92} +1.67059e7i q^{93} +5.09716e6i q^{94} +1.16314e8 q^{95} -1.09176e8 q^{96} -1.54639e8 q^{97} -953454. i q^{98} -1.61934e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.87436i 0.367148i 0.983006 + 0.183574i \(0.0587666\pi\)
−0.983006 + 0.183574i \(0.941233\pi\)
\(3\) 114.397i 1.41230i 0.708061 + 0.706152i \(0.249570\pi\)
−0.708061 + 0.706152i \(0.750430\pi\)
\(4\) 221.492 0.865203
\(5\) 623.321i 0.997313i 0.866800 + 0.498657i \(0.166173\pi\)
−0.866800 + 0.498657i \(0.833827\pi\)
\(6\) −672.007 −0.518524
\(7\) 2434.57i 1.01398i 0.861952 + 0.506990i \(0.169242\pi\)
−0.861952 + 0.506990i \(0.830758\pi\)
\(8\) 2804.96i 0.684805i
\(9\) −6525.57 −0.994601
\(10\) −3661.61 −0.366161
\(11\) 24815.2 1.69491 0.847457 0.530864i \(-0.178133\pi\)
0.847457 + 0.530864i \(0.178133\pi\)
\(12\) 25337.9i 1.22193i
\(13\) 8701.41 0.304660 0.152330 0.988330i \(-0.451322\pi\)
0.152330 + 0.988330i \(0.451322\pi\)
\(14\) −14301.5 −0.372280
\(15\) −71305.8 −1.40851
\(16\) 40224.6 0.613778
\(17\) 10140.4 0.121412 0.0607059 0.998156i \(-0.480665\pi\)
0.0607059 + 0.998156i \(0.480665\pi\)
\(18\) 38333.6i 0.365165i
\(19\) 186604.i 1.43188i −0.698163 0.715938i \(-0.745999\pi\)
0.698163 0.715938i \(-0.254001\pi\)
\(20\) 138060.i 0.862878i
\(21\) −278506. −1.43205
\(22\) 145774.i 0.622284i
\(23\) −387538. −1.38485 −0.692426 0.721489i \(-0.743458\pi\)
−0.692426 + 0.721489i \(0.743458\pi\)
\(24\) −320878. −0.967152
\(25\) 2096.22 0.00536632
\(26\) 51115.2i 0.111855i
\(27\) 4052.57i 0.00762562i
\(28\) 539236.i 0.877298i
\(29\) 1.03599e6i 1.46474i −0.680905 0.732372i \(-0.738413\pi\)
0.680905 0.732372i \(-0.261587\pi\)
\(30\) 418876.i 0.517131i
\(31\) 146035. 0.158128 0.0790640 0.996870i \(-0.474807\pi\)
0.0790640 + 0.996870i \(0.474807\pi\)
\(32\) 954363.i 0.910152i
\(33\) 2.83878e6i 2.39373i
\(34\) 59568.6i 0.0445761i
\(35\) −1.51752e6 −1.01126
\(36\) −1.44536e6 −0.860531
\(37\) 2.77780e6i 1.48216i −0.671418 0.741079i \(-0.734314\pi\)
0.671418 0.741079i \(-0.265686\pi\)
\(38\) 1.09618e6 0.525710
\(39\) 995411.i 0.430273i
\(40\) −1.74839e6 −0.682965
\(41\) 89036.0 0.0315087 0.0157543 0.999876i \(-0.494985\pi\)
0.0157543 + 0.999876i \(0.494985\pi\)
\(42\) 1.63604e6i 0.525773i
\(43\) −3.30170e6 887103.i −0.965749 0.259478i
\(44\) 5.49637e6 1.46644
\(45\) 4.06753e6i 0.991928i
\(46\) 2.27654e6i 0.508445i
\(47\) 867696. 0.177818 0.0889090 0.996040i \(-0.471662\pi\)
0.0889090 + 0.996040i \(0.471662\pi\)
\(48\) 4.60155e6i 0.866841i
\(49\) −162308. −0.0281550
\(50\) 12314.0i 0.00197023i
\(51\) 1.16003e6i 0.171470i
\(52\) 1.92729e6 0.263593
\(53\) 1.05861e7 1.34164 0.670818 0.741622i \(-0.265943\pi\)
0.670818 + 0.741622i \(0.265943\pi\)
\(54\) −23806.3 −0.00279973
\(55\) 1.54678e7i 1.69036i
\(56\) −6.82886e6 −0.694378
\(57\) 2.13468e7 2.02224
\(58\) 6.08576e6 0.537777
\(59\) 1.99430e7 1.64582 0.822911 0.568171i \(-0.192349\pi\)
0.822911 + 0.568171i \(0.192349\pi\)
\(60\) −1.57936e7 −1.21865
\(61\) 9.32889e6i 0.673769i −0.941546 0.336884i \(-0.890627\pi\)
0.941546 0.336884i \(-0.109373\pi\)
\(62\) 857860.i 0.0580563i
\(63\) 1.58869e7i 1.00850i
\(64\) 4.69121e6 0.279618
\(65\) 5.42377e6i 0.303842i
\(66\) −1.66760e7 −0.878853
\(67\) −1.83542e7 −0.910830 −0.455415 0.890279i \(-0.650509\pi\)
−0.455415 + 0.890279i \(0.650509\pi\)
\(68\) 2.24602e6 0.105046
\(69\) 4.43330e7i 1.95583i
\(70\) 8.91443e6i 0.371280i
\(71\) 8.73139e6i 0.343598i 0.985132 + 0.171799i \(0.0549579\pi\)
−0.985132 + 0.171799i \(0.945042\pi\)
\(72\) 1.83040e7i 0.681107i
\(73\) 3.39275e7i 1.19470i 0.801980 + 0.597351i \(0.203780\pi\)
−0.801980 + 0.597351i \(0.796220\pi\)
\(74\) 1.63178e7 0.544171
\(75\) 239800.i 0.00757888i
\(76\) 4.13312e7i 1.23886i
\(77\) 6.04143e7i 1.71861i
\(78\) −5.84741e6 −0.157974
\(79\) 2.74337e7 0.704331 0.352165 0.935938i \(-0.385445\pi\)
0.352165 + 0.935938i \(0.385445\pi\)
\(80\) 2.50728e7i 0.612129i
\(81\) −4.32779e7 −1.00537
\(82\) 523029.i 0.0115683i
\(83\) −6.16851e7 −1.29977 −0.649887 0.760031i \(-0.725184\pi\)
−0.649887 + 0.760031i \(0.725184\pi\)
\(84\) −6.16868e7 −1.23901
\(85\) 6.32074e6i 0.121086i
\(86\) 5.21116e6 1.93954e7i 0.0952666 0.354572i
\(87\) 1.18513e8 2.06866
\(88\) 6.96057e7i 1.16068i
\(89\) 9.46713e6i 0.150889i 0.997150 + 0.0754446i \(0.0240376\pi\)
−0.997150 + 0.0754446i \(0.975962\pi\)
\(90\) 2.38941e7 0.364184
\(91\) 2.11841e7i 0.308920i
\(92\) −8.58366e7 −1.19818
\(93\) 1.67059e7i 0.223325i
\(94\) 5.09716e6i 0.0652855i
\(95\) 1.16314e8 1.42803
\(96\) −1.09176e8 −1.28541
\(97\) −1.54639e8 −1.74675 −0.873377 0.487044i \(-0.838075\pi\)
−0.873377 + 0.487044i \(0.838075\pi\)
\(98\) 953454.i 0.0103370i
\(99\) −1.61934e8 −1.68576
\(100\) 464296. 0.00464296
\(101\) 8.21423e7 0.789372 0.394686 0.918816i \(-0.370853\pi\)
0.394686 + 0.918816i \(0.370853\pi\)
\(102\) −6.81444e6 −0.0629549
\(103\) 1.77239e7 0.157475 0.0787373 0.996895i \(-0.474911\pi\)
0.0787373 + 0.996895i \(0.474911\pi\)
\(104\) 2.44071e7i 0.208633i
\(105\) 1.73599e8i 1.42820i
\(106\) 6.21869e7i 0.492578i
\(107\) 8.41719e7 0.642143 0.321072 0.947055i \(-0.395957\pi\)
0.321072 + 0.947055i \(0.395957\pi\)
\(108\) 897611.i 0.00659771i
\(109\) −7.25493e7 −0.513958 −0.256979 0.966417i \(-0.582727\pi\)
−0.256979 + 0.966417i \(0.582727\pi\)
\(110\) −9.08638e7 −0.620612
\(111\) 3.17771e8 2.09326
\(112\) 9.79293e7i 0.622359i
\(113\) 2.18133e8i 1.33785i −0.743331 0.668924i \(-0.766755\pi\)
0.743331 0.668924i \(-0.233245\pi\)
\(114\) 1.25399e8i 0.742462i
\(115\) 2.41561e8i 1.38113i
\(116\) 2.29462e8i 1.26730i
\(117\) −5.67817e7 −0.303015
\(118\) 1.17152e8i 0.604260i
\(119\) 2.46876e7i 0.123109i
\(120\) 2.00010e8i 0.964553i
\(121\) 4.01437e8 1.87273
\(122\) 5.48013e7 0.247373
\(123\) 1.01854e7i 0.0444998i
\(124\) 3.23455e7 0.136813
\(125\) 2.44791e8i 1.00267i
\(126\) 9.33256e7 0.370270
\(127\) −1.63395e8 −0.628093 −0.314047 0.949408i \(-0.601685\pi\)
−0.314047 + 0.949408i \(0.601685\pi\)
\(128\) 2.71875e8i 1.01281i
\(129\) 1.01482e8 3.77704e8i 0.366461 1.36393i
\(130\) −3.18612e7 −0.111555
\(131\) 1.37699e8i 0.467567i 0.972289 + 0.233784i \(0.0751108\pi\)
−0.972289 + 0.233784i \(0.924889\pi\)
\(132\) 6.28766e8i 2.07106i
\(133\) 4.54299e8 1.45189
\(134\) 1.07819e8i 0.334409i
\(135\) −2.52605e6 −0.00760513
\(136\) 2.84435e7i 0.0831434i
\(137\) 2.58691e8i 0.734345i 0.930153 + 0.367172i \(0.119674\pi\)
−0.930153 + 0.367172i \(0.880326\pi\)
\(138\) 2.60428e8 0.718078
\(139\) −4.65272e8 −1.24637 −0.623185 0.782074i \(-0.714162\pi\)
−0.623185 + 0.782074i \(0.714162\pi\)
\(140\) −3.36117e8 −0.874941
\(141\) 9.92614e7i 0.251133i
\(142\) −5.12914e7 −0.126151
\(143\) 2.15927e8 0.516373
\(144\) −2.62488e8 −0.610464
\(145\) 6.45751e8 1.46081
\(146\) −1.99302e8 −0.438632
\(147\) 1.85674e7i 0.0397633i
\(148\) 6.15261e8i 1.28237i
\(149\) 6.44932e8i 1.30849i −0.756285 0.654243i \(-0.772988\pi\)
0.756285 0.654243i \(-0.227012\pi\)
\(150\) −1.40867e6 −0.00278257
\(151\) 1.88178e8i 0.361961i −0.983487 0.180980i \(-0.942073\pi\)
0.983487 0.180980i \(-0.0579271\pi\)
\(152\) 5.23416e8 0.980556
\(153\) −6.61722e7 −0.120756
\(154\) −3.54896e8 −0.630983
\(155\) 9.10264e7i 0.157703i
\(156\) 2.20475e8i 0.372273i
\(157\) 7.61809e8i 1.25386i −0.779077 0.626928i \(-0.784312\pi\)
0.779077 0.626928i \(-0.215688\pi\)
\(158\) 1.61156e8i 0.258593i
\(159\) 1.21102e9i 1.89480i
\(160\) −5.94875e8 −0.907707
\(161\) 9.43487e8i 1.40421i
\(162\) 2.54230e8i 0.369119i
\(163\) 3.05982e8i 0.433456i 0.976232 + 0.216728i \(0.0695385\pi\)
−0.976232 + 0.216728i \(0.930462\pi\)
\(164\) 1.97207e7 0.0272614
\(165\) −1.76947e9 −2.38730
\(166\) 3.62361e8i 0.477209i
\(167\) 4.61955e8 0.593928 0.296964 0.954889i \(-0.404026\pi\)
0.296964 + 0.954889i \(0.404026\pi\)
\(168\) 7.81198e8i 0.980673i
\(169\) −7.40016e8 −0.907182
\(170\) −3.71303e7 −0.0444563
\(171\) 1.21770e9i 1.42415i
\(172\) −7.31301e8 1.96486e8i −0.835569 0.224501i
\(173\) −4.46260e8 −0.498199 −0.249100 0.968478i \(-0.580135\pi\)
−0.249100 + 0.968478i \(0.580135\pi\)
\(174\) 6.96190e8i 0.759505i
\(175\) 5.10338e6i 0.00544134i
\(176\) 9.98182e8 1.04030
\(177\) 2.28141e9i 2.32440i
\(178\) −5.56133e7 −0.0553986
\(179\) 1.17123e9i 1.14085i 0.821350 + 0.570425i \(0.193221\pi\)
−0.821350 + 0.570425i \(0.806779\pi\)
\(180\) 9.00924e8i 0.858219i
\(181\) −1.36206e9 −1.26906 −0.634530 0.772898i \(-0.718806\pi\)
−0.634530 + 0.772898i \(0.718806\pi\)
\(182\) −1.24443e8 −0.113419
\(183\) 1.06719e9 0.951566
\(184\) 1.08703e9i 0.948353i
\(185\) 1.73146e9 1.47818
\(186\) −9.81362e7 −0.0819932
\(187\) 2.51637e8 0.205783
\(188\) 1.92188e8 0.153849
\(189\) −9.86624e6 −0.00773223
\(190\) 6.83270e8i 0.524298i
\(191\) 1.08502e9i 0.815274i 0.913144 + 0.407637i \(0.133647\pi\)
−0.913144 + 0.407637i \(0.866353\pi\)
\(192\) 5.36659e8i 0.394905i
\(193\) −1.56571e9 −1.12845 −0.564223 0.825622i \(-0.690824\pi\)
−0.564223 + 0.825622i \(0.690824\pi\)
\(194\) 9.08405e8i 0.641317i
\(195\) −6.20460e8 −0.429117
\(196\) −3.59498e7 −0.0243597
\(197\) −5.30678e8 −0.352343 −0.176172 0.984359i \(-0.556371\pi\)
−0.176172 + 0.984359i \(0.556371\pi\)
\(198\) 9.51257e8i 0.618924i
\(199\) 3.44705e8i 0.219804i −0.993942 0.109902i \(-0.964946\pi\)
0.993942 0.109902i \(-0.0350537\pi\)
\(200\) 5.87981e6i 0.00367488i
\(201\) 2.09966e9i 1.28637i
\(202\) 4.82534e8i 0.289816i
\(203\) 2.52218e9 1.48522
\(204\) 2.56937e8i 0.148357i
\(205\) 5.54980e7i 0.0314240i
\(206\) 1.04117e8i 0.0578164i
\(207\) 2.52891e9 1.37737
\(208\) 3.50010e8 0.186994
\(209\) 4.63061e9i 2.42691i
\(210\) 1.01978e9 0.524360
\(211\) 5.11802e8i 0.258209i −0.991631 0.129105i \(-0.958790\pi\)
0.991631 0.129105i \(-0.0412103\pi\)
\(212\) 2.34475e9 1.16079
\(213\) −9.98841e8 −0.485264
\(214\) 4.94456e8i 0.235761i
\(215\) 5.52950e8 2.05802e9i 0.258781 0.963154i
\(216\) −1.13673e7 −0.00522206
\(217\) 3.55531e8i 0.160339i
\(218\) 4.26181e8i 0.188698i
\(219\) −3.88118e9 −1.68728
\(220\) 3.42600e9i 1.46250i
\(221\) 8.82361e7 0.0369894
\(222\) 1.86670e9i 0.768534i
\(223\) 3.42233e9i 1.38389i 0.721949 + 0.691947i \(0.243247\pi\)
−0.721949 + 0.691947i \(0.756753\pi\)
\(224\) −2.32346e9 −0.922876
\(225\) −1.36790e7 −0.00533735
\(226\) 1.28139e9 0.491188
\(227\) 6.00502e8i 0.226158i −0.993586 0.113079i \(-0.963929\pi\)
0.993586 0.113079i \(-0.0360713\pi\)
\(228\) 4.72815e9 1.74965
\(229\) 2.23823e9 0.813883 0.406942 0.913454i \(-0.366595\pi\)
0.406942 + 0.913454i \(0.366595\pi\)
\(230\) 1.41901e9 0.507079
\(231\) −6.91119e9 −2.42720
\(232\) 2.90590e9 1.00306
\(233\) 2.27230e9i 0.770978i −0.922712 0.385489i \(-0.874033\pi\)
0.922712 0.385489i \(-0.125967\pi\)
\(234\) 3.33556e8i 0.111251i
\(235\) 5.40853e8i 0.177340i
\(236\) 4.41722e9 1.42397
\(237\) 3.13833e9i 0.994729i
\(238\) −1.45024e8 −0.0451992
\(239\) 3.04573e9 0.933468 0.466734 0.884398i \(-0.345431\pi\)
0.466734 + 0.884398i \(0.345431\pi\)
\(240\) −2.86824e9 −0.864512
\(241\) 3.05625e9i 0.905984i 0.891515 + 0.452992i \(0.149643\pi\)
−0.891515 + 0.452992i \(0.850357\pi\)
\(242\) 2.35819e9i 0.687569i
\(243\) 4.92425e9i 1.41226i
\(244\) 2.06627e9i 0.582946i
\(245\) 1.01170e8i 0.0280793i
\(246\) −5.98328e7 −0.0163380
\(247\) 1.62371e9i 0.436236i
\(248\) 4.09621e8i 0.108287i
\(249\) 7.05657e9i 1.83568i
\(250\) −1.43799e9 −0.368126
\(251\) −2.03301e9 −0.512206 −0.256103 0.966650i \(-0.582439\pi\)
−0.256103 + 0.966650i \(0.582439\pi\)
\(252\) 3.51883e9i 0.872561i
\(253\) −9.61685e9 −2.34720
\(254\) 9.59842e8i 0.230603i
\(255\) −7.23071e8 −0.171010
\(256\) −3.96142e8 −0.0922339
\(257\) 7.06887e9i 1.62038i 0.586166 + 0.810191i \(0.300637\pi\)
−0.586166 + 0.810191i \(0.699363\pi\)
\(258\) 2.21877e9 + 5.96139e8i 0.500764 + 0.134545i
\(259\) 6.76274e9 1.50288
\(260\) 1.20132e9i 0.262885i
\(261\) 6.76040e9i 1.45684i
\(262\) −8.08891e8 −0.171666
\(263\) 5.55283e9i 1.16062i −0.814394 0.580312i \(-0.802931\pi\)
0.814394 0.580312i \(-0.197069\pi\)
\(264\) −7.96266e9 −1.63924
\(265\) 6.59856e9i 1.33803i
\(266\) 2.66872e9i 0.533060i
\(267\) −1.08301e9 −0.213101
\(268\) −4.06532e9 −0.788052
\(269\) 9.84458e9 1.88013 0.940066 0.340993i \(-0.110763\pi\)
0.940066 + 0.340993i \(0.110763\pi\)
\(270\) 1.48389e7i 0.00279221i
\(271\) −3.61617e9 −0.670457 −0.335229 0.942137i \(-0.608814\pi\)
−0.335229 + 0.942137i \(0.608814\pi\)
\(272\) 4.07895e8 0.0745199
\(273\) −2.42339e9 −0.436288
\(274\) −1.51965e9 −0.269613
\(275\) 5.20182e7 0.00909545
\(276\) 9.81941e9i 1.69219i
\(277\) 3.11399e9i 0.528931i 0.964395 + 0.264465i \(0.0851955\pi\)
−0.964395 + 0.264465i \(0.914805\pi\)
\(278\) 2.73317e9i 0.457602i
\(279\) −9.52959e8 −0.157274
\(280\) 4.25657e9i 0.692513i
\(281\) −9.27076e9 −1.48693 −0.743464 0.668776i \(-0.766819\pi\)
−0.743464 + 0.668776i \(0.766819\pi\)
\(282\) −5.83097e8 −0.0922029
\(283\) −4.58820e9 −0.715314 −0.357657 0.933853i \(-0.616424\pi\)
−0.357657 + 0.933853i \(0.616424\pi\)
\(284\) 1.93393e9i 0.297282i
\(285\) 1.33059e10i 2.01681i
\(286\) 1.26844e9i 0.189585i
\(287\) 2.16764e8i 0.0319491i
\(288\) 6.22777e9i 0.905238i
\(289\) −6.87293e9 −0.985259
\(290\) 3.79338e9i 0.536333i
\(291\) 1.76902e10i 2.46695i
\(292\) 7.51465e9i 1.03366i
\(293\) 4.17635e9 0.566665 0.283332 0.959022i \(-0.408560\pi\)
0.283332 + 0.959022i \(0.408560\pi\)
\(294\) 1.09072e8 0.0145990
\(295\) 1.24309e10i 1.64140i
\(296\) 7.79163e9 1.01499
\(297\) 1.00565e8i 0.0129248i
\(298\) 3.78856e9 0.480407
\(299\) −3.37213e9 −0.421909
\(300\) 5.31138e7i 0.00655726i
\(301\) 2.15971e9 8.03821e9i 0.263105 0.979250i
\(302\) 1.10543e9 0.132893
\(303\) 9.39680e9i 1.11483i
\(304\) 7.50605e9i 0.878855i
\(305\) 5.81489e9 0.671958
\(306\) 3.88719e8i 0.0443354i
\(307\) 1.21829e10 1.37151 0.685755 0.727833i \(-0.259472\pi\)
0.685755 + 0.727833i \(0.259472\pi\)
\(308\) 1.33813e10i 1.48694i
\(309\) 2.02755e9i 0.222402i
\(310\) −5.34722e8 −0.0579004
\(311\) 4.50189e9 0.481230 0.240615 0.970621i \(-0.422651\pi\)
0.240615 + 0.970621i \(0.422651\pi\)
\(312\) −2.79209e9 −0.294653
\(313\) 4.06436e9i 0.423462i −0.977328 0.211731i \(-0.932090\pi\)
0.977328 0.211731i \(-0.0679101\pi\)
\(314\) 4.47514e9 0.460350
\(315\) 9.90266e9 1.00580
\(316\) 6.07635e9 0.609389
\(317\) 1.19109e9 0.117953 0.0589763 0.998259i \(-0.481216\pi\)
0.0589763 + 0.998259i \(0.481216\pi\)
\(318\) −7.11396e9 −0.695670
\(319\) 2.57082e10i 2.48262i
\(320\) 2.92413e9i 0.278867i
\(321\) 9.62897e9i 0.906901i
\(322\) 5.54239e9 0.515553
\(323\) 1.89224e9i 0.173847i
\(324\) −9.58570e9 −0.869849
\(325\) 1.82401e7 0.00163491
\(326\) −1.79745e9 −0.159142
\(327\) 8.29939e9i 0.725864i
\(328\) 2.49742e8i 0.0215773i
\(329\) 2.11246e9i 0.180304i
\(330\) 1.03945e10i 0.876492i
\(331\) 2.05943e10i 1.71567i −0.513923 0.857836i \(-0.671808\pi\)
0.513923 0.857836i \(-0.328192\pi\)
\(332\) −1.36628e10 −1.12457
\(333\) 1.81268e10i 1.47416i
\(334\) 2.71369e9i 0.218059i
\(335\) 1.14406e10i 0.908383i
\(336\) −1.12028e10 −0.878959
\(337\) −1.99136e10 −1.54394 −0.771969 0.635660i \(-0.780728\pi\)
−0.771969 + 0.635660i \(0.780728\pi\)
\(338\) 4.34712e9i 0.333070i
\(339\) 2.49536e10 1.88945
\(340\) 1.39999e9i 0.104764i
\(341\) 3.62388e9 0.268013
\(342\) −7.15319e9 −0.522872
\(343\) 1.36396e10i 0.985431i
\(344\) 2.48829e9 9.26115e9i 0.177692 0.661350i
\(345\) 2.76337e10 1.95058
\(346\) 2.62149e9i 0.182913i
\(347\) 2.86452e10i 1.97576i −0.155233 0.987878i \(-0.549613\pi\)
0.155233 0.987878i \(-0.450387\pi\)
\(348\) 2.62497e10 1.78981
\(349\) 1.74936e10i 1.17917i 0.807706 + 0.589585i \(0.200709\pi\)
−0.807706 + 0.589585i \(0.799291\pi\)
\(350\) −2.99791e7 −0.00199778
\(351\) 3.52630e7i 0.00232323i
\(352\) 2.36828e10i 1.54263i
\(353\) 2.64209e10 1.70156 0.850782 0.525519i \(-0.176129\pi\)
0.850782 + 0.525519i \(0.176129\pi\)
\(354\) −1.34018e10 −0.853398
\(355\) −5.44246e9 −0.342674
\(356\) 2.09689e9i 0.130550i
\(357\) −2.82417e9 −0.173867
\(358\) −6.88020e9 −0.418860
\(359\) 5.08982e9 0.306425 0.153213 0.988193i \(-0.451038\pi\)
0.153213 + 0.988193i \(0.451038\pi\)
\(360\) 1.14092e10 0.679277
\(361\) −1.78373e10 −1.05027
\(362\) 8.00124e9i 0.465933i
\(363\) 4.59230e10i 2.64487i
\(364\) 4.69212e9i 0.267278i
\(365\) −2.11477e10 −1.19149
\(366\) 6.26908e9i 0.349365i
\(367\) 2.73675e10 1.50859 0.754294 0.656537i \(-0.227979\pi\)
0.754294 + 0.656537i \(0.227979\pi\)
\(368\) −1.55886e10 −0.849992
\(369\) −5.81011e8 −0.0313385
\(370\) 1.01712e10i 0.542709i
\(371\) 2.57727e10i 1.36039i
\(372\) 3.70021e9i 0.193221i
\(373\) 2.95512e10i 1.52665i −0.646013 0.763326i \(-0.723565\pi\)
0.646013 0.763326i \(-0.276435\pi\)
\(374\) 1.47821e9i 0.0755526i
\(375\) −2.80033e10 −1.41607
\(376\) 2.43385e9i 0.121771i
\(377\) 9.01453e9i 0.446250i
\(378\) 5.79579e7i 0.00283887i
\(379\) 3.25095e10 1.57563 0.787815 0.615912i \(-0.211212\pi\)
0.787815 + 0.615912i \(0.211212\pi\)
\(380\) 2.57626e10 1.23554
\(381\) 1.86918e10i 0.887058i
\(382\) −6.37379e9 −0.299326
\(383\) 9.61425e9i 0.446807i −0.974726 0.223404i \(-0.928283\pi\)
0.974726 0.223404i \(-0.0717168\pi\)
\(384\) −3.11016e10 −1.43040
\(385\) −3.76575e10 −1.71399
\(386\) 9.19753e9i 0.414307i
\(387\) 2.15455e10 + 5.78886e9i 0.960535 + 0.258077i
\(388\) −3.42513e10 −1.51130
\(389\) 1.61948e10i 0.707259i −0.935386 0.353629i \(-0.884947\pi\)
0.935386 0.353629i \(-0.115053\pi\)
\(390\) 3.64481e9i 0.157549i
\(391\) −3.92981e9 −0.168137
\(392\) 4.55267e8i 0.0192806i
\(393\) −1.57522e10 −0.660347
\(394\) 3.11739e9i 0.129362i
\(395\) 1.71000e10i 0.702439i
\(396\) −3.58670e10 −1.45853
\(397\) −8.23528e9 −0.331525 −0.165762 0.986166i \(-0.553009\pi\)
−0.165762 + 0.986166i \(0.553009\pi\)
\(398\) 2.02492e9 0.0807005
\(399\) 5.19702e10i 2.05051i
\(400\) 8.43195e7 0.00329373
\(401\) −2.90216e10 −1.12239 −0.561194 0.827684i \(-0.689658\pi\)
−0.561194 + 0.827684i \(0.689658\pi\)
\(402\) 1.23342e10 0.472287
\(403\) 1.27071e9 0.0481754
\(404\) 1.81939e10 0.682967
\(405\) 2.69760e10i 1.00267i
\(406\) 1.48162e10i 0.545295i
\(407\) 6.89318e10i 2.51213i
\(408\) −3.25384e9 −0.117424
\(409\) 3.99243e10i 1.42674i −0.700788 0.713369i \(-0.747168\pi\)
0.700788 0.713369i \(-0.252832\pi\)
\(410\) −3.26015e8 −0.0115373
\(411\) −2.95934e10 −1.03712
\(412\) 3.92570e9 0.136247
\(413\) 4.85526e10i 1.66883i
\(414\) 1.48557e10i 0.505700i
\(415\) 3.84496e10i 1.29628i
\(416\) 8.30431e9i 0.277287i
\(417\) 5.32255e10i 1.76025i
\(418\) 2.72019e10 0.891033
\(419\) 2.61104e10i 0.847144i 0.905863 + 0.423572i \(0.139224\pi\)
−0.905863 + 0.423572i \(0.860776\pi\)
\(420\) 3.84507e10i 1.23568i
\(421\) 1.77984e10i 0.566569i 0.959036 + 0.283284i \(0.0914240\pi\)
−0.959036 + 0.283284i \(0.908576\pi\)
\(422\) 3.00651e9 0.0948009
\(423\) −5.66221e9 −0.176858
\(424\) 2.96937e10i 0.918758i
\(425\) 2.12566e7 0.000651535
\(426\) 5.86756e9i 0.178164i
\(427\) 2.27118e10 0.683188
\(428\) 1.86434e10 0.555584
\(429\) 2.47014e10i 0.729276i
\(430\) 1.20896e10 + 3.24823e9i 0.353620 + 0.0950107i
\(431\) 7.12863e9 0.206584 0.103292 0.994651i \(-0.467062\pi\)
0.103292 + 0.994651i \(0.467062\pi\)
\(432\) 1.63013e8i 0.00468044i
\(433\) 2.26003e10i 0.642928i −0.946922 0.321464i \(-0.895825\pi\)
0.946922 0.321464i \(-0.104175\pi\)
\(434\) −2.08852e9 −0.0588680
\(435\) 7.38718e10i 2.06311i
\(436\) −1.60691e10 −0.444678
\(437\) 7.23160e10i 1.98294i
\(438\) 2.27995e10i 0.619482i
\(439\) 5.85076e10 1.57527 0.787633 0.616144i \(-0.211306\pi\)
0.787633 + 0.616144i \(0.211306\pi\)
\(440\) −4.33867e10 −1.15757
\(441\) 1.05915e9 0.0280029
\(442\) 5.18331e8i 0.0135806i
\(443\) −3.14896e10 −0.817621 −0.408810 0.912619i \(-0.634056\pi\)
−0.408810 + 0.912619i \(0.634056\pi\)
\(444\) 7.03837e10 1.81109
\(445\) −5.90106e9 −0.150484
\(446\) −2.01040e10 −0.508093
\(447\) 7.37780e10 1.84798
\(448\) 1.14211e10i 0.283527i
\(449\) 7.24862e10i 1.78349i 0.452540 + 0.891744i \(0.350518\pi\)
−0.452540 + 0.891744i \(0.649482\pi\)
\(450\) 8.03556e7i 0.00195959i
\(451\) 2.20945e9 0.0534045
\(452\) 4.83146e10i 1.15751i
\(453\) 2.15269e10 0.511199
\(454\) 3.52757e9 0.0830332
\(455\) −1.32045e10 −0.308090
\(456\) 5.98770e10i 1.38484i
\(457\) 3.18344e10i 0.729846i −0.931038 0.364923i \(-0.881095\pi\)
0.931038 0.364923i \(-0.118905\pi\)
\(458\) 1.31482e10i 0.298815i
\(459\) 4.10948e7i 0.000925841i
\(460\) 5.35037e10i 1.19496i
\(461\) 2.31271e10 0.512055 0.256028 0.966669i \(-0.417586\pi\)
0.256028 + 0.966669i \(0.417586\pi\)
\(462\) 4.05988e10i 0.891139i
\(463\) 3.12379e10i 0.679764i −0.940468 0.339882i \(-0.889613\pi\)
0.940468 0.339882i \(-0.110387\pi\)
\(464\) 4.16721e10i 0.899028i
\(465\) −1.04131e10 −0.222725
\(466\) 1.33483e10 0.283063
\(467\) 8.61020e9i 0.181028i 0.995895 + 0.0905140i \(0.0288510\pi\)
−0.995895 + 0.0905140i \(0.971149\pi\)
\(468\) −1.25767e10 −0.262170
\(469\) 4.46846e10i 0.923563i
\(470\) −3.17716e9 −0.0651101
\(471\) 8.71484e10 1.77083
\(472\) 5.59394e10i 1.12707i
\(473\) −8.19325e10 2.20137e10i −1.63686 0.439792i
\(474\) −1.84357e10 −0.365212
\(475\) 3.91162e8i 0.00768391i
\(476\) 5.46809e9i 0.106514i
\(477\) −6.90807e10 −1.33439
\(478\) 1.78917e10i 0.342721i
\(479\) −4.39993e10 −0.835803 −0.417902 0.908492i \(-0.637234\pi\)
−0.417902 + 0.908492i \(0.637234\pi\)
\(480\) 6.80516e10i 1.28196i
\(481\) 2.41708e10i 0.451555i
\(482\) −1.79535e10 −0.332630
\(483\) 1.07932e11 1.98317
\(484\) 8.89150e10 1.62029
\(485\) 9.63897e10i 1.74206i
\(486\) 2.89268e10 0.518509
\(487\) −8.06027e9 −0.143296 −0.0716479 0.997430i \(-0.522826\pi\)
−0.0716479 + 0.997430i \(0.522826\pi\)
\(488\) 2.61672e10 0.461400
\(489\) −3.50033e10 −0.612171
\(490\) 5.94308e8 0.0103093
\(491\) 9.23725e10i 1.58934i 0.607042 + 0.794670i \(0.292356\pi\)
−0.607042 + 0.794670i \(0.707644\pi\)
\(492\) 2.25599e9i 0.0385013i
\(493\) 1.05053e10i 0.177837i
\(494\) 9.53828e9 0.160163
\(495\) 1.00937e11i 1.68123i
\(496\) 5.87418e9 0.0970555
\(497\) −2.12571e10 −0.348401
\(498\) 4.14528e10 0.673964
\(499\) 9.81123e10i 1.58242i 0.611546 + 0.791209i \(0.290548\pi\)
−0.611546 + 0.791209i \(0.709452\pi\)
\(500\) 5.42193e10i 0.867508i
\(501\) 5.28461e10i 0.838807i
\(502\) 1.19426e10i 0.188055i
\(503\) 9.29511e9i 0.145205i −0.997361 0.0726027i \(-0.976869\pi\)
0.997361 0.0726027i \(-0.0231305\pi\)
\(504\) 4.45622e10 0.690629
\(505\) 5.12010e10i 0.787251i
\(506\) 5.64929e10i 0.861770i
\(507\) 8.46553e10i 1.28122i
\(508\) −3.61907e10 −0.543428
\(509\) −9.44904e10 −1.40772 −0.703860 0.710339i \(-0.748542\pi\)
−0.703860 + 0.710339i \(0.748542\pi\)
\(510\) 4.24758e9i 0.0627858i
\(511\) −8.25986e10 −1.21140
\(512\) 6.72729e10i 0.978950i
\(513\) 7.56224e8 0.0109190
\(514\) −4.15251e10 −0.594919
\(515\) 1.10477e10i 0.157051i
\(516\) 2.24773e10 8.36583e10i 0.317063 1.18008i
\(517\) 2.15321e10 0.301386
\(518\) 3.97268e10i 0.551778i
\(519\) 5.10506e10i 0.703609i
\(520\) −1.52135e10 −0.208072
\(521\) 9.40814e10i 1.27689i 0.769668 + 0.638444i \(0.220422\pi\)
−0.769668 + 0.638444i \(0.779578\pi\)
\(522\) −3.97131e10 −0.534874
\(523\) 4.56576e7i 0.000610248i 1.00000 0.000305124i \(9.71239e-5\pi\)
−1.00000 0.000305124i \(0.999903\pi\)
\(524\) 3.04991e10i 0.404541i
\(525\) −5.83810e8 −0.00768483
\(526\) 3.26193e10 0.426120
\(527\) 1.48085e9 0.0191986
\(528\) 1.14189e11i 1.46922i
\(529\) 7.18749e10 0.917813
\(530\) −3.87624e10 −0.491255
\(531\) −1.30140e11 −1.63694
\(532\) 1.00623e11 1.25618
\(533\) 7.74738e8 0.00959944
\(534\) 6.36198e9i 0.0782397i
\(535\) 5.24661e10i 0.640418i
\(536\) 5.14829e10i 0.623741i
\(537\) −1.33984e11 −1.61123
\(538\) 5.78306e10i 0.690286i
\(539\) −4.02770e9 −0.0477202
\(540\) −5.59500e8 −0.00657998
\(541\) −9.37761e10 −1.09472 −0.547360 0.836897i \(-0.684367\pi\)
−0.547360 + 0.836897i \(0.684367\pi\)
\(542\) 2.12427e10i 0.246157i
\(543\) 1.55815e11i 1.79230i
\(544\) 9.67766e9i 0.110503i
\(545\) 4.52215e10i 0.512577i
\(546\) 1.42359e10i 0.160182i
\(547\) 8.48538e10 0.947811 0.473906 0.880576i \(-0.342844\pi\)
0.473906 + 0.880576i \(0.342844\pi\)
\(548\) 5.72981e10i 0.635357i
\(549\) 6.08764e10i 0.670131i
\(550\) 3.05574e8i 0.00333937i
\(551\) −1.93319e11 −2.09733
\(552\) 1.24352e11 1.33936
\(553\) 6.67893e10i 0.714177i
\(554\) −1.82927e10 −0.194196
\(555\) 1.98073e11i 2.08763i
\(556\) −1.03054e11 −1.07836
\(557\) 4.81386e10 0.500118 0.250059 0.968231i \(-0.419550\pi\)
0.250059 + 0.968231i \(0.419550\pi\)
\(558\) 5.59803e9i 0.0577429i
\(559\) −2.87295e10 7.71904e9i −0.294226 0.0790526i
\(560\) −6.10414e10 −0.620687
\(561\) 2.87864e10i 0.290627i
\(562\) 5.44598e10i 0.545922i
\(563\) 5.17901e10 0.515482 0.257741 0.966214i \(-0.417022\pi\)
0.257741 + 0.966214i \(0.417022\pi\)
\(564\) 2.19856e10i 0.217281i
\(565\) 1.35967e11 1.33425
\(566\) 2.69528e10i 0.262626i
\(567\) 1.05363e11i 1.01943i
\(568\) −2.44912e10 −0.235297
\(569\) −2.44189e10 −0.232958 −0.116479 0.993193i \(-0.537161\pi\)
−0.116479 + 0.993193i \(0.537161\pi\)
\(570\) −7.81637e10 −0.740467
\(571\) 1.70378e11i 1.60277i 0.598152 + 0.801383i \(0.295902\pi\)
−0.598152 + 0.801383i \(0.704098\pi\)
\(572\) 4.78262e10 0.446767
\(573\) −1.24122e11 −1.15141
\(574\) −1.27335e9 −0.0117301
\(575\) −8.12365e8 −0.00743156
\(576\) −3.06129e10 −0.278108
\(577\) 1.12467e11i 1.01466i −0.861751 0.507332i \(-0.830632\pi\)
0.861751 0.507332i \(-0.169368\pi\)
\(578\) 4.03741e10i 0.361736i
\(579\) 1.79111e11i 1.59371i
\(580\) 1.43029e11 1.26390
\(581\) 1.50176e11i 1.31795i
\(582\) 1.03918e11 0.905734
\(583\) 2.62698e11 2.27396
\(584\) −9.51652e10 −0.818138
\(585\) 3.53932e10i 0.302201i
\(586\) 2.45334e10i 0.208050i
\(587\) 2.80170e10i 0.235977i −0.993015 0.117988i \(-0.962355\pi\)
0.993015 0.117988i \(-0.0376446\pi\)
\(588\) 4.11254e9i 0.0344033i
\(589\) 2.72506e10i 0.226420i
\(590\) −7.30236e10 −0.602636
\(591\) 6.07077e10i 0.497616i
\(592\) 1.11736e11i 0.909716i
\(593\) 9.56213e10i 0.773278i 0.922231 + 0.386639i \(0.126364\pi\)
−0.922231 + 0.386639i \(0.873636\pi\)
\(594\) −5.90758e8 −0.00474530
\(595\) −1.53883e10 −0.122778
\(596\) 1.42847e11i 1.13210i
\(597\) 3.94331e10 0.310430
\(598\) 1.98091e10i 0.154903i
\(599\) 1.13123e11 0.878707 0.439353 0.898314i \(-0.355208\pi\)
0.439353 + 0.898314i \(0.355208\pi\)
\(600\) −6.72630e8 −0.00519005
\(601\) 8.52889e10i 0.653724i −0.945072 0.326862i \(-0.894009\pi\)
0.945072 0.326862i \(-0.105991\pi\)
\(602\) 4.72194e10 + 1.26869e10i 0.359529 + 0.0965985i
\(603\) 1.19772e11 0.905912
\(604\) 4.16799e10i 0.313169i
\(605\) 2.50224e11i 1.86770i
\(606\) −5.52002e10 −0.409308
\(607\) 7.30935e9i 0.0538423i 0.999638 + 0.0269212i \(0.00857031\pi\)
−0.999638 + 0.0269212i \(0.991430\pi\)
\(608\) 1.78088e11 1.30323
\(609\) 2.88528e11i 2.09758i
\(610\) 3.41588e10i 0.246708i
\(611\) 7.55017e9 0.0541741
\(612\) −1.46566e10 −0.104479
\(613\) −1.49080e11 −1.05579 −0.527895 0.849310i \(-0.677019\pi\)
−0.527895 + 0.849310i \(0.677019\pi\)
\(614\) 7.15670e10i 0.503547i
\(615\) −6.34878e9 −0.0443802
\(616\) −1.69460e11 −1.17691
\(617\) 3.12248e10 0.215456 0.107728 0.994180i \(-0.465642\pi\)
0.107728 + 0.994180i \(0.465642\pi\)
\(618\) −1.19106e10 −0.0816543
\(619\) −1.39975e11 −0.953429 −0.476715 0.879058i \(-0.658173\pi\)
−0.476715 + 0.879058i \(0.658173\pi\)
\(620\) 2.01616e10i 0.136445i
\(621\) 1.57053e9i 0.0105604i
\(622\) 2.64457e10i 0.176683i
\(623\) −2.30483e10 −0.152999
\(624\) 4.00400e10i 0.264092i
\(625\) −1.51765e11 −0.994605
\(626\) 2.38755e10 0.155473
\(627\) 5.29726e11 3.42753
\(628\) 1.68735e11i 1.08484i
\(629\) 2.81681e10i 0.179951i
\(630\) 5.81718e10i 0.369275i
\(631\) 1.57640e11i 0.994375i 0.867643 + 0.497188i \(0.165634\pi\)
−0.867643 + 0.497188i \(0.834366\pi\)
\(632\) 7.69506e10i 0.482329i
\(633\) 5.85483e10 0.364670
\(634\) 6.99689e9i 0.0433060i
\(635\) 1.01848e11i 0.626406i
\(636\) 2.68231e11i 1.63938i
\(637\) −1.41231e9 −0.00857770
\(638\) 1.51019e11 0.911486
\(639\) 5.69774e10i 0.341742i
\(640\) −1.69465e11 −1.01009
\(641\) 6.49048e10i 0.384454i −0.981350 0.192227i \(-0.938429\pi\)
0.981350 0.192227i \(-0.0615711\pi\)
\(642\) −5.65641e10 −0.332967
\(643\) 7.92194e10 0.463434 0.231717 0.972783i \(-0.425566\pi\)
0.231717 + 0.972783i \(0.425566\pi\)
\(644\) 2.08975e11i 1.21493i
\(645\) 2.35430e11 + 6.32555e10i 1.36027 + 0.365477i
\(646\) 1.11157e10 0.0638274
\(647\) 9.19245e10i 0.524583i −0.964989 0.262291i \(-0.915522\pi\)
0.964989 0.262291i \(-0.0844782\pi\)
\(648\) 1.21393e11i 0.688482i
\(649\) 4.94891e11 2.78953
\(650\) 1.07149e8i 0.000600252i
\(651\) −4.06715e10 −0.226447
\(652\) 6.77725e10i 0.375027i
\(653\) 2.05884e11i 1.13232i −0.824295 0.566161i \(-0.808428\pi\)
0.824295 0.566161i \(-0.191572\pi\)
\(654\) 4.87536e10 0.266499
\(655\) −8.58304e10 −0.466311
\(656\) 3.58143e9 0.0193393
\(657\) 2.21396e11i 1.18825i
\(658\) −1.24094e10 −0.0661982
\(659\) −3.07836e11 −1.63222 −0.816108 0.577899i \(-0.803873\pi\)
−0.816108 + 0.577899i \(0.803873\pi\)
\(660\) −3.91923e11 −2.06550
\(661\) 1.12652e11 0.590108 0.295054 0.955481i \(-0.404662\pi\)
0.295054 + 0.955481i \(0.404662\pi\)
\(662\) 1.20978e11 0.629905
\(663\) 1.00939e10i 0.0522402i
\(664\) 1.73024e11i 0.890092i
\(665\) 2.83174e11i 1.44799i
\(666\) −1.06483e11 −0.541233
\(667\) 4.01484e11i 2.02845i
\(668\) 1.02319e11 0.513868
\(669\) −3.91503e11 −1.95448
\(670\) 6.72061e10 0.333511
\(671\) 2.31499e11i 1.14198i
\(672\) 2.65796e11i 1.30338i
\(673\) 8.41903e10i 0.410395i −0.978721 0.205197i \(-0.934216\pi\)
0.978721 0.205197i \(-0.0657836\pi\)
\(674\) 1.16980e11i 0.566853i
\(675\) 8.49507e6i 4.09216e-5i
\(676\) −1.63908e11 −0.784896
\(677\) 2.00105e11i 0.952583i 0.879287 + 0.476292i \(0.158019\pi\)
−0.879287 + 0.476292i \(0.841981\pi\)
\(678\) 1.46587e11i 0.693706i
\(679\) 3.76479e11i 1.77117i
\(680\) −1.77294e10 −0.0829200
\(681\) 6.86954e10 0.319403
\(682\) 2.12880e10i 0.0984005i
\(683\) 1.23376e10 0.0566955 0.0283478 0.999598i \(-0.490975\pi\)
0.0283478 + 0.999598i \(0.490975\pi\)
\(684\) 2.69710e11i 1.23217i
\(685\) −1.61248e11 −0.732372
\(686\) −8.01242e10 −0.361799
\(687\) 2.56046e11i 1.14945i
\(688\) −1.32810e11 3.56833e10i −0.592756 0.159262i
\(689\) 9.21144e10 0.408743
\(690\) 1.62330e11i 0.716149i
\(691\) 7.88294e9i 0.0345761i 0.999851 + 0.0172880i \(0.00550323\pi\)
−0.999851 + 0.0172880i \(0.994497\pi\)
\(692\) −9.88429e10 −0.431043
\(693\) 3.94238e11i 1.70933i
\(694\) 1.68272e11 0.725394
\(695\) 2.90013e11i 1.24302i
\(696\) 3.32425e11i 1.41663i
\(697\) 9.02863e8 0.00382552
\(698\) −1.02764e11 −0.432930
\(699\) 2.59943e11 1.08885
\(700\) 1.13036e9i 0.00470786i
\(701\) −2.09607e11 −0.868026 −0.434013 0.900907i \(-0.642903\pi\)
−0.434013 + 0.900907i \(0.642903\pi\)
\(702\) −2.07148e8 −0.000852967
\(703\) −5.18348e11 −2.12227
\(704\) 1.16414e11 0.473928
\(705\) −6.18717e10 −0.250458
\(706\) 1.55206e11i 0.624725i
\(707\) 1.99981e11i 0.800407i
\(708\) 5.05314e11i 2.01108i
\(709\) 2.55986e11 1.01305 0.506525 0.862225i \(-0.330930\pi\)
0.506525 + 0.862225i \(0.330930\pi\)
\(710\) 3.19710e10i 0.125812i
\(711\) −1.79021e11 −0.700528
\(712\) −2.65549e10 −0.103330
\(713\) −5.65940e10 −0.218984
\(714\) 1.65902e10i 0.0638350i
\(715\) 1.34592e11i 0.514986i
\(716\) 2.59417e11i 0.987066i
\(717\) 3.48421e11i 1.31834i
\(718\) 2.98994e10i 0.112503i
\(719\) 1.70885e11 0.639425 0.319712 0.947515i \(-0.396414\pi\)
0.319712 + 0.947515i \(0.396414\pi\)
\(720\) 1.63614e11i 0.608824i
\(721\) 4.31500e10i 0.159676i
\(722\) 1.04783e11i 0.385605i
\(723\) −3.49624e11 −1.27952
\(724\) −3.01685e11 −1.09799
\(725\) 2.17165e9i 0.00786029i
\(726\) −2.69768e11 −0.971056
\(727\) 6.84993e10i 0.245216i −0.992455 0.122608i \(-0.960874\pi\)
0.992455 0.122608i \(-0.0391257\pi\)
\(728\) −5.94207e10 −0.211550
\(729\) 2.79371e11 0.989172
\(730\) 1.24229e11i 0.437454i
\(731\) −3.34807e10 8.99561e9i −0.117253 0.0315037i
\(732\) 2.36375e11 0.823297
\(733\) 3.03637e11i 1.05181i −0.850542 0.525907i \(-0.823726\pi\)
0.850542 0.525907i \(-0.176274\pi\)
\(734\) 1.60767e11i 0.553874i
\(735\) 1.15735e10 0.0396565
\(736\) 3.69852e11i 1.26043i
\(737\) −4.55465e11 −1.54378
\(738\) 3.41307e9i 0.0115059i
\(739\) 2.59994e11i 0.871738i −0.900010 0.435869i \(-0.856441\pi\)
0.900010 0.435869i \(-0.143559\pi\)
\(740\) 3.83505e11 1.27892
\(741\) 1.85747e11 0.616098
\(742\) −1.51398e11 −0.499464
\(743\) 3.83121e11i 1.25713i −0.777757 0.628565i \(-0.783643\pi\)
0.777757 0.628565i \(-0.216357\pi\)
\(744\) −4.68593e10 −0.152934
\(745\) 4.01999e11 1.30497
\(746\) 1.73595e11 0.560507
\(747\) 4.02531e11 1.29276
\(748\) 5.57356e10 0.178044
\(749\) 2.04922e11i 0.651120i
\(750\) 1.64501e11i 0.519906i
\(751\) 5.66675e11i 1.78145i 0.454541 + 0.890726i \(0.349803\pi\)
−0.454541 + 0.890726i \(0.650197\pi\)
\(752\) 3.49027e10 0.109141
\(753\) 2.32569e11i 0.723390i
\(754\) 5.29546e10 0.163840
\(755\) 1.17295e11 0.360988
\(756\) −2.18529e9 −0.00668994
\(757\) 3.67371e11i 1.11872i −0.828925 0.559360i \(-0.811047\pi\)
0.828925 0.559360i \(-0.188953\pi\)
\(758\) 1.90973e11i 0.578489i
\(759\) 1.10013e12i 3.31496i
\(760\) 3.26256e11i 0.977922i
\(761\) 4.84998e11i 1.44611i 0.690790 + 0.723055i \(0.257263\pi\)
−0.690790 + 0.723055i \(0.742737\pi\)
\(762\) 1.09803e11 0.325681
\(763\) 1.76626e11i 0.521143i
\(764\) 2.40323e11i 0.705377i
\(765\) 4.12465e10i 0.120432i
\(766\) 5.64776e10 0.164044
\(767\) 1.73532e11 0.501417
\(768\) 4.53172e10i 0.130262i
\(769\) −3.76649e11 −1.07704 −0.538519 0.842613i \(-0.681016\pi\)
−0.538519 + 0.842613i \(0.681016\pi\)
\(770\) 2.21214e11i 0.629288i
\(771\) −8.08654e11 −2.28847
\(772\) −3.46791e11 −0.976335
\(773\) 1.40564e11i 0.393693i −0.980434 0.196846i \(-0.936930\pi\)
0.980434 0.196846i \(-0.0630700\pi\)
\(774\) −3.40058e10 + 1.26566e11i −0.0947523 + 0.352658i
\(775\) 3.06121e8 0.000848566
\(776\) 4.33756e11i 1.19619i
\(777\) 7.73634e11i 2.12252i
\(778\) 9.51343e10 0.259668
\(779\) 1.66144e10i 0.0451165i
\(780\) −1.37427e11 −0.371273
\(781\) 2.16672e11i 0.582368i
\(782\)