Properties

Label 43.9.b.b.42.3
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 42.3
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.26

$q$-expansion

\(f(q)\) \(=\) \(q-25.4156i q^{2} -123.997i q^{3} -389.955 q^{4} -710.884i q^{5} -3151.46 q^{6} +4245.58i q^{7} +3404.55i q^{8} -8814.20 q^{9} +O(q^{10})\) \(q-25.4156i q^{2} -123.997i q^{3} -389.955 q^{4} -710.884i q^{5} -3151.46 q^{6} +4245.58i q^{7} +3404.55i q^{8} -8814.20 q^{9} -18067.6 q^{10} +19261.7 q^{11} +48353.1i q^{12} -24555.5 q^{13} +107904. q^{14} -88147.3 q^{15} -13299.6 q^{16} -142372. q^{17} +224018. i q^{18} -152283. i q^{19} +277213. i q^{20} +526438. q^{21} -489549. i q^{22} +169711. q^{23} +422153. q^{24} -114731. q^{25} +624094. i q^{26} +279389. i q^{27} -1.65558e6i q^{28} -350183. i q^{29} +2.24032e6i q^{30} -167211. q^{31} +1.20958e6i q^{32} -2.38839e6i q^{33} +3.61848e6i q^{34} +3.01811e6 q^{35} +3.43714e6 q^{36} +965271. i q^{37} -3.87037e6 q^{38} +3.04480e6i q^{39} +2.42024e6 q^{40} -4.61149e6 q^{41} -1.33798e7i q^{42} +(2.23132e6 - 2.59026e6i) q^{43} -7.51120e6 q^{44} +6.26587e6i q^{45} -4.31331e6i q^{46} +2.55322e6 q^{47} +1.64911e6i q^{48} -1.22601e7 q^{49} +2.91596e6i q^{50} +1.76537e7i q^{51} +9.57553e6 q^{52} -121198. q^{53} +7.10085e6 q^{54} -1.36929e7i q^{55} -1.44543e7 q^{56} -1.88826e7 q^{57} -8.90013e6 q^{58} +3.24451e6 q^{59} +3.43735e7 q^{60} -1.17814e7i q^{61} +4.24978e6i q^{62} -3.74214e7i q^{63} +2.73376e7 q^{64} +1.74561e7i q^{65} -6.07025e7 q^{66} -3.62950e7 q^{67} +5.55188e7 q^{68} -2.10436e7i q^{69} -7.67073e7i q^{70} +1.36356e7i q^{71} -3.00084e7i q^{72} -1.61861e7i q^{73} +2.45330e7 q^{74} +1.42262e7i q^{75} +5.93834e7i q^{76} +8.17772e7i q^{77} +7.73856e7 q^{78} +3.75891e7 q^{79} +9.45449e6i q^{80} -2.31866e7 q^{81} +1.17204e8i q^{82} +6.67652e7 q^{83} -2.05287e8 q^{84} +1.01210e8i q^{85} +(-6.58330e7 - 5.67103e7i) q^{86} -4.34216e7 q^{87} +6.55775e7i q^{88} -4.02096e7i q^{89} +1.59251e8 q^{90} -1.04252e8i q^{91} -6.61796e7 q^{92} +2.07336e7i q^{93} -6.48916e7i q^{94} -1.08255e8 q^{95} +1.49984e8 q^{96} +3.96028e6 q^{97} +3.11599e8i q^{98} -1.69777e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.4156i 1.58848i −0.607606 0.794239i \(-0.707870\pi\)
0.607606 0.794239i \(-0.292130\pi\)
\(3\) 123.997i 1.53082i −0.643540 0.765412i \(-0.722535\pi\)
0.643540 0.765412i \(-0.277465\pi\)
\(4\) −389.955 −1.52326
\(5\) 710.884i 1.13741i −0.822540 0.568707i \(-0.807444\pi\)
0.822540 0.568707i \(-0.192556\pi\)
\(6\) −3151.46 −2.43168
\(7\) 4245.58i 1.76825i 0.467247 + 0.884127i \(0.345246\pi\)
−0.467247 + 0.884127i \(0.654754\pi\)
\(8\) 3404.55i 0.831189i
\(9\) −8814.20 −1.34342
\(10\) −18067.6 −1.80676
\(11\) 19261.7 1.31560 0.657801 0.753192i \(-0.271487\pi\)
0.657801 + 0.753192i \(0.271487\pi\)
\(12\) 48353.1i 2.33185i
\(13\) −24555.5 −0.859756 −0.429878 0.902887i \(-0.641443\pi\)
−0.429878 + 0.902887i \(0.641443\pi\)
\(14\) 107904. 2.80883
\(15\) −88147.3 −1.74118
\(16\) −13299.6 −0.202936
\(17\) −142372. −1.70463 −0.852314 0.523030i \(-0.824802\pi\)
−0.852314 + 0.523030i \(0.824802\pi\)
\(18\) 224018.i 2.13400i
\(19\) 152283.i 1.16852i −0.811566 0.584261i \(-0.801385\pi\)
0.811566 0.584261i \(-0.198615\pi\)
\(20\) 277213.i 1.73258i
\(21\) 526438. 2.70689
\(22\) 489549.i 2.08980i
\(23\) 169711. 0.606454 0.303227 0.952918i \(-0.401936\pi\)
0.303227 + 0.952918i \(0.401936\pi\)
\(24\) 422153. 1.27240
\(25\) −114731. −0.293711
\(26\) 624094.i 1.36570i
\(27\) 279389.i 0.525720i
\(28\) 1.65558e6i 2.69351i
\(29\) 350183.i 0.495112i −0.968874 0.247556i \(-0.920373\pi\)
0.968874 0.247556i \(-0.0796274\pi\)
\(30\) 2.24032e6i 2.76583i
\(31\) −167211. −0.181058 −0.0905291 0.995894i \(-0.528856\pi\)
−0.0905291 + 0.995894i \(0.528856\pi\)
\(32\) 1.20958e6i 1.15355i
\(33\) 2.38839e6i 2.01396i
\(34\) 3.61848e6i 2.70776i
\(35\) 3.01811e6 2.01124
\(36\) 3.43714e6 2.04638
\(37\) 965271.i 0.515042i 0.966273 + 0.257521i \(0.0829056\pi\)
−0.966273 + 0.257521i \(0.917094\pi\)
\(38\) −3.87037e6 −1.85617
\(39\) 3.04480e6i 1.31614i
\(40\) 2.42024e6 0.945406
\(41\) −4.61149e6 −1.63195 −0.815974 0.578089i \(-0.803799\pi\)
−0.815974 + 0.578089i \(0.803799\pi\)
\(42\) 1.33798e7i 4.29983i
\(43\) 2.23132e6 2.59026e6i 0.652661 0.757650i
\(44\) −7.51120e6 −2.00401
\(45\) 6.26587e6i 1.52803i
\(46\) 4.31331e6i 0.963339i
\(47\) 2.55322e6 0.523234 0.261617 0.965172i \(-0.415744\pi\)
0.261617 + 0.965172i \(0.415744\pi\)
\(48\) 1.64911e6i 0.310660i
\(49\) −1.22601e7 −2.12672
\(50\) 2.91596e6i 0.466553i
\(51\) 1.76537e7i 2.60949i
\(52\) 9.57553e6 1.30963
\(53\) −121198. −0.0153600 −0.00768000 0.999971i \(-0.502445\pi\)
−0.00768000 + 0.999971i \(0.502445\pi\)
\(54\) 7.10085e6 0.835094
\(55\) 1.36929e7i 1.49638i
\(56\) −1.44543e7 −1.46975
\(57\) −1.88826e7 −1.78880
\(58\) −8.90013e6 −0.786474
\(59\) 3.24451e6 0.267757 0.133879 0.990998i \(-0.457257\pi\)
0.133879 + 0.990998i \(0.457257\pi\)
\(60\) 3.43735e7 2.65227
\(61\) 1.17814e7i 0.850900i −0.904982 0.425450i \(-0.860116\pi\)
0.904982 0.425450i \(-0.139884\pi\)
\(62\) 4.24978e6i 0.287607i
\(63\) 3.74214e7i 2.37551i
\(64\) 2.73376e7 1.62945
\(65\) 1.74561e7i 0.977899i
\(66\) −6.07025e7 −3.19912
\(67\) −3.62950e7 −1.80114 −0.900571 0.434708i \(-0.856852\pi\)
−0.900571 + 0.434708i \(0.856852\pi\)
\(68\) 5.55188e7 2.59659
\(69\) 2.10436e7i 0.928375i
\(70\) 7.67073e7i 3.19480i
\(71\) 1.36356e7i 0.536587i 0.963337 + 0.268294i \(0.0864598\pi\)
−0.963337 + 0.268294i \(0.913540\pi\)
\(72\) 3.00084e7i 1.11664i
\(73\) 1.61861e7i 0.569969i −0.958532 0.284985i \(-0.908011\pi\)
0.958532 0.284985i \(-0.0919885\pi\)
\(74\) 2.45330e7 0.818132
\(75\) 1.42262e7i 0.449620i
\(76\) 5.93834e7i 1.77996i
\(77\) 8.17772e7i 2.32632i
\(78\) 7.73856e7 2.09065
\(79\) 3.75891e7 0.965057 0.482529 0.875880i \(-0.339718\pi\)
0.482529 + 0.875880i \(0.339718\pi\)
\(80\) 9.45449e6i 0.230823i
\(81\) −2.31866e7 −0.538638
\(82\) 1.17204e8i 2.59231i
\(83\) 6.67652e7 1.40682 0.703409 0.710785i \(-0.251660\pi\)
0.703409 + 0.710785i \(0.251660\pi\)
\(84\) −2.05287e8 −4.12329
\(85\) 1.01210e8i 1.93887i
\(86\) −6.58330e7 5.67103e7i −1.20351 1.03674i
\(87\) −4.34216e7 −0.757929
\(88\) 6.55775e7i 1.09351i
\(89\) 4.02096e7i 0.640869i −0.947271 0.320435i \(-0.896171\pi\)
0.947271 0.320435i \(-0.103829\pi\)
\(90\) 1.59251e8 2.42724
\(91\) 1.04252e8i 1.52027i
\(92\) −6.61796e7 −0.923788
\(93\) 2.07336e7i 0.277168i
\(94\) 6.48916e7i 0.831146i
\(95\) −1.08255e8 −1.32909
\(96\) 1.49984e8 1.76588
\(97\) 3.96028e6 0.0447341 0.0223671 0.999750i \(-0.492880\pi\)
0.0223671 + 0.999750i \(0.492880\pi\)
\(98\) 3.11599e8i 3.37825i
\(99\) −1.69777e8 −1.76741
\(100\) 4.47398e7 0.447398
\(101\) −6.42933e7 −0.617846 −0.308923 0.951087i \(-0.599969\pi\)
−0.308923 + 0.951087i \(0.599969\pi\)
\(102\) 4.48680e8 4.14511
\(103\) −5.70467e7 −0.506852 −0.253426 0.967355i \(-0.581557\pi\)
−0.253426 + 0.967355i \(0.581557\pi\)
\(104\) 8.36004e7i 0.714620i
\(105\) 3.74236e8i 3.07885i
\(106\) 3.08032e6i 0.0243990i
\(107\) 1.77956e8 1.35762 0.678808 0.734316i \(-0.262497\pi\)
0.678808 + 0.734316i \(0.262497\pi\)
\(108\) 1.08949e8i 0.800809i
\(109\) 1.45829e8 1.03309 0.516546 0.856260i \(-0.327218\pi\)
0.516546 + 0.856260i \(0.327218\pi\)
\(110\) −3.48013e8 −2.37697
\(111\) 1.19690e8 0.788438
\(112\) 5.64646e7i 0.358843i
\(113\) 3.96357e6i 0.0243093i −0.999926 0.0121547i \(-0.996131\pi\)
0.999926 0.0121547i \(-0.00386905\pi\)
\(114\) 4.79913e8i 2.84147i
\(115\) 1.20645e8i 0.689790i
\(116\) 1.36556e8i 0.754185i
\(117\) 2.16437e8 1.15502
\(118\) 8.24614e7i 0.425327i
\(119\) 6.04453e8i 3.01422i
\(120\) 3.00102e8i 1.44725i
\(121\) 1.56655e8 0.730808
\(122\) −2.99432e8 −1.35164
\(123\) 5.71810e8i 2.49823i
\(124\) 6.52047e7 0.275799
\(125\) 1.96129e8i 0.803343i
\(126\) −9.51088e8 −3.77345
\(127\) −2.72143e8 −1.04612 −0.523061 0.852295i \(-0.675210\pi\)
−0.523061 + 0.852295i \(0.675210\pi\)
\(128\) 3.85150e8i 1.43480i
\(129\) −3.21183e8 2.76676e8i −1.15983 0.999109i
\(130\) 4.43658e8 1.55337
\(131\) 4.60295e7i 0.156297i 0.996942 + 0.0781486i \(0.0249009\pi\)
−0.996942 + 0.0781486i \(0.975099\pi\)
\(132\) 9.31365e8i 3.06778i
\(133\) 6.46529e8 2.06624
\(134\) 9.22462e8i 2.86108i
\(135\) 1.98613e8 0.597961
\(136\) 4.84713e8i 1.41687i
\(137\) 2.81241e8i 0.798357i −0.916873 0.399178i \(-0.869295\pi\)
0.916873 0.399178i \(-0.130705\pi\)
\(138\) −5.34836e8 −1.47470
\(139\) −6.05884e8 −1.62304 −0.811522 0.584322i \(-0.801360\pi\)
−0.811522 + 0.584322i \(0.801360\pi\)
\(140\) −1.17693e9 −3.06364
\(141\) 3.16591e8i 0.800980i
\(142\) 3.46557e8 0.852357
\(143\) −4.72981e8 −1.13110
\(144\) 1.17226e8 0.272629
\(145\) −2.48940e8 −0.563147
\(146\) −4.11381e8 −0.905384
\(147\) 1.52022e9i 3.25564i
\(148\) 3.76412e8i 0.784543i
\(149\) 6.51784e8i 1.32239i −0.750215 0.661194i \(-0.770050\pi\)
0.750215 0.661194i \(-0.229950\pi\)
\(150\) 3.61569e8 0.714211
\(151\) 1.34573e8i 0.258852i −0.991589 0.129426i \(-0.958687\pi\)
0.991589 0.129426i \(-0.0413135\pi\)
\(152\) 5.18455e8 0.971262
\(153\) 1.25490e9 2.29004
\(154\) 2.07842e9 3.69530
\(155\) 1.18868e8i 0.205938i
\(156\) 1.18734e9i 2.00482i
\(157\) 9.79370e7i 0.161194i −0.996747 0.0805969i \(-0.974317\pi\)
0.996747 0.0805969i \(-0.0256826\pi\)
\(158\) 9.55350e8i 1.53297i
\(159\) 1.50281e7i 0.0235135i
\(160\) 8.59873e8 1.31206
\(161\) 7.20520e8i 1.07237i
\(162\) 5.89303e8i 0.855615i
\(163\) 3.08528e8i 0.437063i 0.975830 + 0.218531i \(0.0701266\pi\)
−0.975830 + 0.218531i \(0.929873\pi\)
\(164\) 1.79827e9 2.48588
\(165\) −1.69787e9 −2.29070
\(166\) 1.69688e9i 2.23470i
\(167\) −6.12522e8 −0.787510 −0.393755 0.919215i \(-0.628824\pi\)
−0.393755 + 0.919215i \(0.628824\pi\)
\(168\) 1.79228e9i 2.24993i
\(169\) −2.12759e8 −0.260820
\(170\) 2.57232e9 3.07985
\(171\) 1.34225e9i 1.56982i
\(172\) −8.70113e8 + 1.01008e9i −0.994173 + 1.15410i
\(173\) −5.69720e7 −0.0636029 −0.0318015 0.999494i \(-0.510124\pi\)
−0.0318015 + 0.999494i \(0.510124\pi\)
\(174\) 1.10359e9i 1.20395i
\(175\) 4.87098e8i 0.519355i
\(176\) −2.56174e8 −0.266983
\(177\) 4.02309e8i 0.409890i
\(178\) −1.02195e9 −1.01801
\(179\) 3.49206e8i 0.340149i −0.985431 0.170074i \(-0.945599\pi\)
0.985431 0.170074i \(-0.0544008\pi\)
\(180\) 2.44341e9i 2.32759i
\(181\) 7.24881e8 0.675387 0.337693 0.941256i \(-0.390353\pi\)
0.337693 + 0.941256i \(0.390353\pi\)
\(182\) −2.64964e9 −2.41491
\(183\) −1.46086e9 −1.30258
\(184\) 5.77789e8i 0.504078i
\(185\) 6.86195e8 0.585816
\(186\) 5.26958e8 0.440275
\(187\) −2.74234e9 −2.24261
\(188\) −9.95639e8 −0.797023
\(189\) −1.18617e9 −0.929606
\(190\) 2.75138e9i 2.11123i
\(191\) 1.33591e9i 1.00379i 0.864929 + 0.501894i \(0.167363\pi\)
−0.864929 + 0.501894i \(0.832637\pi\)
\(192\) 3.38978e9i 2.49440i
\(193\) 1.61824e9 1.16631 0.583155 0.812361i \(-0.301818\pi\)
0.583155 + 0.812361i \(0.301818\pi\)
\(194\) 1.00653e8i 0.0710591i
\(195\) 2.16450e9 1.49699
\(196\) 4.78090e9 3.23955
\(197\) 9.06502e8 0.601872 0.300936 0.953644i \(-0.402701\pi\)
0.300936 + 0.953644i \(0.402701\pi\)
\(198\) 4.31498e9i 2.80749i
\(199\) 1.65380e9i 1.05456i −0.849692 0.527279i \(-0.823212\pi\)
0.849692 0.527279i \(-0.176788\pi\)
\(200\) 3.90607e8i 0.244129i
\(201\) 4.50047e9i 2.75723i
\(202\) 1.63406e9i 0.981434i
\(203\) 1.48673e9 0.875484
\(204\) 6.88415e9i 3.97493i
\(205\) 3.27824e9i 1.85620i
\(206\) 1.44988e9i 0.805124i
\(207\) −1.49586e9 −0.814725
\(208\) 3.26579e8 0.174476
\(209\) 2.93323e9i 1.53731i
\(210\) −9.51145e9 −4.89068
\(211\) 2.92300e9i 1.47468i −0.675520 0.737342i \(-0.736081\pi\)
0.675520 0.737342i \(-0.263919\pi\)
\(212\) 4.72617e7 0.0233973
\(213\) 1.69077e9 0.821421
\(214\) 4.52286e9i 2.15654i
\(215\) −1.84137e9 1.58621e9i −0.861762 0.742345i
\(216\) −9.51194e8 −0.436972
\(217\) 7.09907e8i 0.320157i
\(218\) 3.70634e9i 1.64104i
\(219\) −2.00703e9 −0.872523
\(220\) 5.33959e9i 2.27938i
\(221\) 3.49602e9 1.46556
\(222\) 3.04201e9i 1.25242i
\(223\) 2.27107e9i 0.918356i 0.888344 + 0.459178i \(0.151856\pi\)
−0.888344 + 0.459178i \(0.848144\pi\)
\(224\) −5.13538e9 −2.03977
\(225\) 1.01126e9 0.394578
\(226\) −1.00737e8 −0.0386148
\(227\) 5.65990e8i 0.213160i −0.994304 0.106580i \(-0.966010\pi\)
0.994304 0.106580i \(-0.0339900\pi\)
\(228\) 7.36335e9 2.72481
\(229\) −3.13606e9 −1.14036 −0.570181 0.821519i \(-0.693127\pi\)
−0.570181 + 0.821519i \(0.693127\pi\)
\(230\) −3.06626e9 −1.09572
\(231\) 1.01401e10 3.56118
\(232\) 1.19222e9 0.411532
\(233\) 2.14351e9i 0.727281i 0.931539 + 0.363641i \(0.118466\pi\)
−0.931539 + 0.363641i \(0.881534\pi\)
\(234\) 5.50088e9i 1.83472i
\(235\) 1.81504e9i 0.595134i
\(236\) −1.26521e9 −0.407865
\(237\) 4.66092e9i 1.47733i
\(238\) −1.53625e10 −4.78801
\(239\) 4.34656e9 1.33215 0.666077 0.745883i \(-0.267972\pi\)
0.666077 + 0.745883i \(0.267972\pi\)
\(240\) 1.17233e9 0.353349
\(241\) 8.68227e8i 0.257374i −0.991685 0.128687i \(-0.958924\pi\)
0.991685 0.128687i \(-0.0410763\pi\)
\(242\) 3.98149e9i 1.16087i
\(243\) 4.70814e9i 1.35028i
\(244\) 4.59422e9i 1.29614i
\(245\) 8.71552e9i 2.41896i
\(246\) 1.45329e10 3.96838
\(247\) 3.73938e9i 1.00464i
\(248\) 5.69278e8i 0.150494i
\(249\) 8.27867e9i 2.15359i
\(250\) −4.98474e9 −1.27609
\(251\) −4.77899e9 −1.20404 −0.602021 0.798481i \(-0.705638\pi\)
−0.602021 + 0.798481i \(0.705638\pi\)
\(252\) 1.45926e10i 3.61853i
\(253\) 3.26892e9 0.797853
\(254\) 6.91669e9i 1.66174i
\(255\) 1.25497e10 2.96807
\(256\) −2.79041e9 −0.649692
\(257\) 4.13081e9i 0.946898i −0.880821 0.473449i \(-0.843009\pi\)
0.880821 0.473449i \(-0.156991\pi\)
\(258\) −7.03190e9 + 8.16308e9i −1.58706 + 1.84236i
\(259\) −4.09813e9 −0.910724
\(260\) 6.80709e9i 1.48960i
\(261\) 3.08658e9i 0.665145i
\(262\) 1.16987e9 0.248275
\(263\) 8.67393e9i 1.81298i −0.422229 0.906489i \(-0.638752\pi\)
0.422229 0.906489i \(-0.361248\pi\)
\(264\) 8.13140e9 1.67398
\(265\) 8.61576e7i 0.0174707i
\(266\) 1.64319e10i 3.28218i
\(267\) −4.98586e9 −0.981058
\(268\) 1.41534e10 2.74361
\(269\) −5.79853e9 −1.10741 −0.553705 0.832713i \(-0.686786\pi\)
−0.553705 + 0.832713i \(0.686786\pi\)
\(270\) 5.04788e9i 0.949848i
\(271\) −7.28151e8 −0.135003 −0.0675016 0.997719i \(-0.521503\pi\)
−0.0675016 + 0.997719i \(0.521503\pi\)
\(272\) 1.89350e9 0.345931
\(273\) −1.29269e10 −2.32726
\(274\) −7.14793e9 −1.26817
\(275\) −2.20991e9 −0.386407
\(276\) 8.20605e9i 1.41416i
\(277\) 4.67054e9i 0.793319i 0.917966 + 0.396659i \(0.129831\pi\)
−0.917966 + 0.396659i \(0.870169\pi\)
\(278\) 1.53989e10i 2.57817i
\(279\) 1.47383e9 0.243238
\(280\) 1.02753e10i 1.67172i
\(281\) 4.09921e9 0.657468 0.328734 0.944422i \(-0.393378\pi\)
0.328734 + 0.944422i \(0.393378\pi\)
\(282\) −8.04635e9 −1.27234
\(283\) −3.83506e8 −0.0597898 −0.0298949 0.999553i \(-0.509517\pi\)
−0.0298949 + 0.999553i \(0.509517\pi\)
\(284\) 5.31726e9i 0.817363i
\(285\) 1.34233e10i 2.03461i
\(286\) 1.20211e10i 1.79672i
\(287\) 1.95785e10i 2.88570i
\(288\) 1.06615e10i 1.54970i
\(289\) 1.32941e10 1.90576
\(290\) 6.32696e9i 0.894547i
\(291\) 4.91062e8i 0.0684800i
\(292\) 6.31186e9i 0.868212i
\(293\) −7.92297e9 −1.07502 −0.537511 0.843257i \(-0.680635\pi\)
−0.537511 + 0.843257i \(0.680635\pi\)
\(294\) 3.86373e10 5.17151
\(295\) 2.30647e9i 0.304551i
\(296\) −3.28631e9 −0.428097
\(297\) 5.38152e9i 0.691638i
\(298\) −1.65655e10 −2.10058
\(299\) −4.16733e9 −0.521403
\(300\) 5.54759e9i 0.684888i
\(301\) 1.09971e10 + 9.47323e9i 1.33972 + 1.15407i
\(302\) −3.42027e9 −0.411181
\(303\) 7.97216e9i 0.945813i
\(304\) 2.02531e9i 0.237135i
\(305\) −8.37522e9 −0.967825
\(306\) 3.18940e10i 3.63767i
\(307\) 1.17322e10 1.32077 0.660386 0.750926i \(-0.270393\pi\)
0.660386 + 0.750926i \(0.270393\pi\)
\(308\) 3.18894e10i 3.54359i
\(309\) 7.07360e9i 0.775902i
\(310\) 3.02110e9 0.327128
\(311\) 2.02378e9 0.216333 0.108166 0.994133i \(-0.465502\pi\)
0.108166 + 0.994133i \(0.465502\pi\)
\(312\) −1.03662e10 −1.09396
\(313\) 1.45585e10i 1.51683i 0.651769 + 0.758417i \(0.274027\pi\)
−0.651769 + 0.758417i \(0.725973\pi\)
\(314\) −2.48913e9 −0.256053
\(315\) −2.66022e10 −2.70194
\(316\) −1.46580e10 −1.47003
\(317\) 1.69110e10 1.67468 0.837342 0.546680i \(-0.184109\pi\)
0.837342 + 0.546680i \(0.184109\pi\)
\(318\) 3.81950e8 0.0373506
\(319\) 6.74514e9i 0.651370i
\(320\) 1.94339e10i 1.85336i
\(321\) 2.20659e10i 2.07827i
\(322\) 1.83125e10 1.70343
\(323\) 2.16809e10i 1.99189i
\(324\) 9.04173e9 0.820487
\(325\) 2.81727e9 0.252520
\(326\) 7.84143e9 0.694265
\(327\) 1.80824e10i 1.58148i
\(328\) 1.57001e10i 1.35646i
\(329\) 1.08399e10i 0.925211i
\(330\) 4.31524e10i 3.63873i
\(331\) 2.26514e10i 1.88705i −0.331304 0.943524i \(-0.607488\pi\)
0.331304 0.943524i \(-0.392512\pi\)
\(332\) −2.60354e10 −2.14295
\(333\) 8.50809e9i 0.691919i
\(334\) 1.55676e10i 1.25094i
\(335\) 2.58016e10i 2.04865i
\(336\) −7.00143e9 −0.549325
\(337\) −2.09936e10 −1.62767 −0.813837 0.581093i \(-0.802625\pi\)
−0.813837 + 0.581093i \(0.802625\pi\)
\(338\) 5.40740e9i 0.414306i
\(339\) −4.91470e8 −0.0372133
\(340\) 3.94674e10i 2.95340i
\(341\) −3.22077e9 −0.238200
\(342\) 3.41142e10 2.49362
\(343\) 2.75764e10i 1.99233i
\(344\) 8.81866e9 + 7.59663e9i 0.629751 + 0.542484i
\(345\) −1.49595e10 −1.05595
\(346\) 1.44798e9i 0.101032i
\(347\) 4.17920e9i 0.288254i 0.989559 + 0.144127i \(0.0460373\pi\)
−0.989559 + 0.144127i \(0.953963\pi\)
\(348\) 1.69325e10 1.15452
\(349\) 1.39214e10i 0.938387i −0.883096 0.469193i \(-0.844545\pi\)
0.883096 0.469193i \(-0.155455\pi\)
\(350\) −1.23799e10 −0.824984
\(351\) 6.86053e9i 0.451991i
\(352\) 2.32987e10i 1.51761i
\(353\) 1.37614e10 0.886267 0.443134 0.896456i \(-0.353867\pi\)
0.443134 + 0.896456i \(0.353867\pi\)
\(354\) −1.02249e10 −0.651101
\(355\) 9.69332e9 0.610322
\(356\) 1.56799e10i 0.976211i
\(357\) −7.49502e10 −4.61423
\(358\) −8.87529e9 −0.540319
\(359\) 3.97968e9 0.239591 0.119795 0.992799i \(-0.461776\pi\)
0.119795 + 0.992799i \(0.461776\pi\)
\(360\) −2.13325e10 −1.27008
\(361\) −6.20650e9 −0.365442
\(362\) 1.84233e10i 1.07284i
\(363\) 1.94247e10i 1.11874i
\(364\) 4.06537e10i 2.31576i
\(365\) −1.15065e10 −0.648291
\(366\) 3.71286e10i 2.06912i
\(367\) 3.22905e10 1.77996 0.889981 0.455998i \(-0.150718\pi\)
0.889981 + 0.455998i \(0.150718\pi\)
\(368\) −2.25709e9 −0.123072
\(369\) 4.06466e10 2.19240
\(370\) 1.74401e10i 0.930555i
\(371\) 5.14555e8i 0.0271604i
\(372\) 8.08518e9i 0.422200i
\(373\) 2.21792e8i 0.0114580i −0.999984 0.00572902i \(-0.998176\pi\)
0.999984 0.00572902i \(-0.00182361\pi\)
\(374\) 6.96982e10i 3.56234i
\(375\) −2.43193e10 −1.22978
\(376\) 8.69255e9i 0.434907i
\(377\) 8.59892e9i 0.425676i
\(378\) 3.01472e10i 1.47666i
\(379\) −1.63002e10 −0.790019 −0.395009 0.918677i \(-0.629259\pi\)
−0.395009 + 0.918677i \(0.629259\pi\)
\(380\) 4.22147e10 2.02456
\(381\) 3.37449e10i 1.60143i
\(382\) 3.39529e10 1.59450
\(383\) 3.14817e10i 1.46306i 0.681809 + 0.731531i \(0.261194\pi\)
−0.681809 + 0.731531i \(0.738806\pi\)
\(384\) −4.77574e10 −2.19642
\(385\) 5.81341e10 2.64599
\(386\) 4.11286e10i 1.85266i
\(387\) −1.96673e10 + 2.28310e10i −0.876799 + 1.01784i
\(388\) −1.54433e9 −0.0681417
\(389\) 2.51872e10i 1.09997i −0.835174 0.549986i \(-0.814633\pi\)
0.835174 0.549986i \(-0.185367\pi\)
\(390\) 5.50122e10i 2.37794i
\(391\) −2.41621e10 −1.03378
\(392\) 4.17402e10i 1.76771i
\(393\) 5.70751e9 0.239264
\(394\) 2.30393e10i 0.956060i
\(395\) 2.67215e10i 1.09767i
\(396\) 6.62052e10 2.69223
\(397\) 2.97336e10 1.19698 0.598488 0.801132i \(-0.295768\pi\)
0.598488 + 0.801132i \(0.295768\pi\)
\(398\) −4.20324e10 −1.67514
\(399\) 8.01675e10i 3.16305i
\(400\) 1.52588e9 0.0596046
\(401\) 1.21677e10 0.470576 0.235288 0.971926i \(-0.424397\pi\)
0.235288 + 0.971926i \(0.424397\pi\)
\(402\) 1.14382e11 4.37980
\(403\) 4.10595e9 0.155666
\(404\) 2.50715e10 0.941141
\(405\) 1.64830e10i 0.612655i
\(406\) 3.77862e10i 1.39069i
\(407\) 1.85928e10i 0.677590i
\(408\) −6.01029e10 −2.16898
\(409\) 2.93025e9i 0.104716i −0.998628 0.0523578i \(-0.983326\pi\)
0.998628 0.0523578i \(-0.0166736\pi\)
\(410\) 8.33185e10 2.94853
\(411\) −3.48730e10 −1.22214
\(412\) 2.22456e10 0.772069
\(413\) 1.37748e10i 0.473463i
\(414\) 3.80184e10i 1.29417i
\(415\) 4.74623e10i 1.60013i
\(416\) 2.97019e10i 0.991770i
\(417\) 7.51276e10i 2.48459i
\(418\) −7.45499e10 −2.44198
\(419\) 9.01121e9i 0.292366i −0.989258 0.146183i \(-0.953301\pi\)
0.989258 0.146183i \(-0.0466989\pi\)
\(420\) 1.45935e11i 4.68989i
\(421\) 3.93187e10i 1.25161i −0.779978 0.625807i \(-0.784770\pi\)
0.779978 0.625807i \(-0.215230\pi\)
\(422\) −7.42899e10 −2.34250
\(423\) −2.25046e10 −0.702925
\(424\) 4.12624e8i 0.0127671i
\(425\) 1.63345e10 0.500668
\(426\) 4.29720e10i 1.30481i
\(427\) 5.00189e10 1.50461
\(428\) −6.93947e10 −2.06800
\(429\) 5.86481e10i 1.73151i
\(430\) −4.03145e10 + 4.67996e10i −1.17920 + 1.36889i
\(431\) 4.46793e10 1.29478 0.647392 0.762157i \(-0.275860\pi\)
0.647392 + 0.762157i \(0.275860\pi\)
\(432\) 3.71577e9i 0.106688i
\(433\) 3.91721e7i 0.00111436i −1.00000 0.000557180i \(-0.999823\pi\)
1.00000 0.000557180i \(-0.000177356\pi\)
\(434\) −1.80427e10 −0.508562
\(435\) 3.08677e10i 0.862080i
\(436\) −5.68668e10 −1.57367
\(437\) 2.58440e10i 0.708655i
\(438\) 5.10099e10i 1.38598i
\(439\) 3.54045e10 0.953235 0.476618 0.879111i \(-0.341863\pi\)
0.476618 + 0.879111i \(0.341863\pi\)
\(440\) 4.66180e10 1.24378
\(441\) 1.08063e11 2.85709
\(442\) 8.88536e10i 2.32802i
\(443\) −3.92702e10 −1.01964 −0.509821 0.860280i \(-0.670288\pi\)
−0.509821 + 0.860280i \(0.670288\pi\)
\(444\) −4.66739e10 −1.20100
\(445\) −2.85843e10 −0.728934
\(446\) 5.77207e10 1.45879
\(447\) −8.08191e10 −2.02434
\(448\) 1.16064e11i 2.88128i
\(449\) 3.13621e9i 0.0771650i 0.999255 + 0.0385825i \(0.0122842\pi\)
−0.999255 + 0.0385825i \(0.987716\pi\)
\(450\) 2.57018e10i 0.626778i
\(451\) −8.88254e10 −2.14699
\(452\) 1.54561e9i 0.0370295i
\(453\) −1.66867e10 −0.396257
\(454\) −1.43850e10 −0.338600
\(455\) −7.41112e10 −1.72917
\(456\) 6.42867e10i 1.48683i
\(457\) 1.45128e10i 0.332726i −0.986065 0.166363i \(-0.946798\pi\)
0.986065 0.166363i \(-0.0532024\pi\)
\(458\) 7.97050e10i 1.81144i
\(459\) 3.97773e10i 0.896157i
\(460\) 4.70460e10i 1.05073i
\(461\) 6.92222e10 1.53265 0.766323 0.642456i \(-0.222084\pi\)
0.766323 + 0.642456i \(0.222084\pi\)
\(462\) 2.57717e11i 5.65686i
\(463\) 3.30451e10i 0.719090i 0.933128 + 0.359545i \(0.117068\pi\)
−0.933128 + 0.359545i \(0.882932\pi\)
\(464\) 4.65731e9i 0.100476i
\(465\) 1.47392e10 0.315255
\(466\) 5.44788e10 1.15527
\(467\) 2.97268e10i 0.625001i 0.949918 + 0.312501i \(0.101167\pi\)
−0.949918 + 0.312501i \(0.898833\pi\)
\(468\) −8.44006e10 −1.75939
\(469\) 1.54093e11i 3.18488i
\(470\) −4.61304e10 −0.945357
\(471\) −1.21439e10 −0.246759
\(472\) 1.10461e10i 0.222557i
\(473\) 4.29790e10 4.98928e10i 0.858641 0.996766i
\(474\) −1.18460e11 −2.34671
\(475\) 1.74715e10i 0.343207i
\(476\) 2.35709e11i 4.59144i
\(477\) 1.06826e9 0.0206350
\(478\) 1.10471e11i 2.11610i
\(479\) −7.52787e10 −1.42998 −0.714990 0.699135i \(-0.753569\pi\)
−0.714990 + 0.699135i \(0.753569\pi\)
\(480\) 1.06622e11i 2.00854i
\(481\) 2.37027e10i 0.442810i
\(482\) −2.20666e10 −0.408833
\(483\) 8.93422e10 1.64160
\(484\) −6.10885e10 −1.11321
\(485\) 2.81530e9i 0.0508812i
\(486\) 1.19660e11 2.14489
\(487\) 8.28852e10 1.47354 0.736769 0.676145i \(-0.236351\pi\)
0.736769 + 0.676145i \(0.236351\pi\)
\(488\) 4.01104e10 0.707258
\(489\) 3.82564e10 0.669066
\(490\) 2.21511e11 3.84247
\(491\) 3.32135e10i 0.571464i −0.958310 0.285732i \(-0.907763\pi\)
0.958310 0.285732i \(-0.0922367\pi\)
\(492\) 2.22980e11i 3.80545i
\(493\) 4.98564e10i 0.843982i
\(494\) 9.50387e10 1.59585
\(495\) 1.20691e11i 2.01028i
\(496\) 2.22385e9 0.0367433
\(497\) −5.78909e10 −0.948823
\(498\) −2.10408e11 −3.42093
\(499\) 1.20030e11i 1.93592i 0.251103 + 0.967960i \(0.419207\pi\)
−0.251103 + 0.967960i \(0.580793\pi\)
\(500\) 7.64814e10i 1.22370i
\(501\) 7.59508e10i 1.20554i
\(502\) 1.21461e11i 1.91259i
\(503\) 4.36030e9i 0.0681152i −0.999420 0.0340576i \(-0.989157\pi\)
0.999420 0.0340576i \(-0.0108430\pi\)
\(504\) 1.27403e11 1.97450
\(505\) 4.57051e10i 0.702747i
\(506\) 8.30818e10i 1.26737i
\(507\) 2.63814e10i 0.399269i
\(508\) 1.06124e11 1.59352
\(509\) −4.13833e10 −0.616530 −0.308265 0.951301i \(-0.599748\pi\)
−0.308265 + 0.951301i \(0.599748\pi\)
\(510\) 3.18959e11i 4.71471i
\(511\) 6.87194e10 1.00785
\(512\) 2.76785e10i 0.402775i
\(513\) 4.25462e10 0.614315
\(514\) −1.04987e11 −1.50413
\(515\) 4.05536e10i 0.576501i
\(516\) 1.25247e11 + 1.07891e11i 1.76672 + 1.52190i
\(517\) 4.91794e10 0.688368
\(518\) 1.04157e11i 1.44667i
\(519\) 7.06435e9i 0.0973649i
\(520\) −5.94302e10 −0.812818
\(521\) 2.54747e10i 0.345747i 0.984944 + 0.172874i \(0.0553053\pi\)
−0.984944 + 0.172874i \(0.944695\pi\)
\(522\) 7.84475e10 1.05657
\(523\) 4.78528e10i 0.639588i −0.947487 0.319794i \(-0.896386\pi\)
0.947487 0.319794i \(-0.103614\pi\)
\(524\) 1.79494e10i 0.238082i
\(525\) −6.03986e10 −0.795042
\(526\) −2.20453e11 −2.87988
\(527\) 2.38062e10 0.308637
\(528\) 3.17647e10i 0.408705i
\(529\) −4.95092e10 −0.632213
\(530\) 2.18975e9 0.0277518
\(531\) −2.85978e10 −0.359711
\(532\) −2.52117e11 −3.14743
\(533\) 1.13238e11 1.40308
\(534\) 1.26719e11i 1.55839i
\(535\) 1.26506e11i 1.54417i
\(536\) 1.23568e11i 1.49709i
\(537\) −4.33004e10 −0.520708
\(538\) 1.47373e11i 1.75910i
\(539\) −2.36151e11 −2.79792
\(540\) −7.74502e10 −0.910851
\(541\) 9.62804e10 1.12396 0.561978 0.827152i \(-0.310041\pi\)
0.561978 + 0.827152i \(0.310041\pi\)
\(542\) 1.85064e10i 0.214450i
\(543\) 8.98829e10i 1.03390i
\(544\) 1.72211e11i 1.96637i
\(545\) 1.03668e11i 1.17505i
\(546\) 3.28546e11i 3.69680i
\(547\) 2.42196e10 0.270531 0.135265 0.990809i \(-0.456811\pi\)
0.135265 + 0.990809i \(0.456811\pi\)
\(548\) 1.09671e11i 1.21611i
\(549\) 1.03844e11i 1.14312i
\(550\) 5.61664e10i 0.613798i
\(551\) −5.33269e10 −0.578549
\(552\) 7.16439e10 0.771655
\(553\) 1.59587e11i 1.70647i
\(554\) 1.18705e11 1.26017
\(555\) 8.50860e10i 0.896781i
\(556\) 2.36267e11 2.47232
\(557\) 9.97285e10 1.03609 0.518046 0.855353i \(-0.326660\pi\)
0.518046 + 0.855353i \(0.326660\pi\)
\(558\) 3.74584e10i 0.386378i
\(559\) −5.47911e10 + 6.36050e10i −0.561129 + 0.651395i
\(560\) −4.01398e10 −0.408153
\(561\) 3.40041e11i 3.43305i
\(562\) 1.04184e11i 1.04437i
\(563\) 1.38700e11 1.38052 0.690261 0.723561i \(-0.257496\pi\)
0.690261 + 0.723561i \(0.257496\pi\)
\(564\) 1.23456e11i 1.22010i
\(565\) −2.81764e9 −0.0276498
\(566\) 9.74706e9i 0.0949747i
\(567\) 9.84405e10i 0.952449i
\(568\) −4.64230e10 −0.446005
\(569\) 8.10953e9 0.0773654 0.0386827 0.999252i \(-0.487684\pi\)
0.0386827 + 0.999252i \(0.487684\pi\)
\(570\) 3.41162e11 3.23193
\(571\) 4.34370e10i 0.408616i −0.978907 0.204308i \(-0.934506\pi\)
0.978907 0.204308i \(-0.0654944\pi\)
\(572\) 1.84441e11 1.72296
\(573\) 1.65648e11 1.53662
\(574\) −4.97599e11 −4.58387
\(575\) −1.94711e10 −0.178122
\(576\) −2.40959e11 −2.18904
\(577\) 1.29380e11i 1.16725i −0.812024 0.583624i \(-0.801634\pi\)
0.812024 0.583624i \(-0.198366\pi\)
\(578\) 3.37878e11i 3.02725i
\(579\) 2.00657e11i 1.78542i
\(580\) 9.70752e10 0.857821
\(581\) 2.83457e11i 2.48761i
\(582\) −1.24806e10 −0.108779
\(583\) −2.33448e9 −0.0202076
\(584\) 5.51065e10 0.473752
\(585\) 1.53861e11i 1.31373i
\(586\) 2.01367e11i 1.70765i
\(587\) 2.11829e11i 1.78415i 0.451883 + 0.892077i \(0.350752\pi\)
−0.451883 + 0.892077i \(0.649248\pi\)
\(588\) 5.92816e11i 4.95919i
\(589\) 2.54634e10i 0.211570i
\(590\) −5.86205e10 −0.483773
\(591\) 1.12403e11i 0.921360i
\(592\) 1.28377e10i 0.104521i
\(593\) 9.55395e9i 0.0772617i −0.999254 0.0386308i \(-0.987700\pi\)
0.999254 0.0386308i \(-0.0122996\pi\)
\(594\) 1.36775e11 1.09865
\(595\) −4.29696e11 −3.42841
\(596\) 2.54166e11i 2.01434i
\(597\) −2.05066e11 −1.61434
\(598\) 1.05915e11i 0.828237i
\(599\) 8.88356e8 0.00690048 0.00345024 0.999994i \(-0.498902\pi\)
0.00345024 + 0.999994i \(0.498902\pi\)
\(600\) −4.84340e10 −0.373719
\(601\) 5.66506e10i 0.434217i −0.976148 0.217108i \(-0.930337\pi\)
0.976148 0.217108i \(-0.0696625\pi\)
\(602\) 2.40768e11 2.79499e11i 1.83321 2.12811i
\(603\) 3.19912e11 2.41970
\(604\) 5.24776e10i 0.394299i
\(605\) 1.11364e11i 0.831232i
\(606\) 2.02618e11 1.50240
\(607\) 1.71828e10i 0.126573i −0.997995 0.0632863i \(-0.979842\pi\)
0.997995 0.0632863i \(-0.0201581\pi\)
\(608\) 1.84199e11 1.34795
\(609\) 1.84350e11i 1.34021i
\(610\) 2.12862e11i 1.53737i
\(611\) −6.26955e10 −0.449854
\(612\) −4.89353e11 −3.48832
\(613\) −2.11244e11 −1.49603 −0.748017 0.663679i \(-0.768994\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(614\) 2.98183e11i 2.09802i
\(615\) 4.06491e11 2.84152
\(616\) −2.78414e11 −1.93361
\(617\) −8.35394e10 −0.576435 −0.288218 0.957565i \(-0.593063\pi\)
−0.288218 + 0.957565i \(0.593063\pi\)
\(618\) 1.79780e11 1.23250
\(619\) 6.90104e10 0.470059 0.235029 0.971988i \(-0.424481\pi\)
0.235029 + 0.971988i \(0.424481\pi\)
\(620\) 4.63530e10i 0.313698i
\(621\) 4.74153e10i 0.318825i
\(622\) 5.14357e10i 0.343640i
\(623\) 1.70713e11 1.13322
\(624\) 4.04947e10i 0.267092i
\(625\) −1.84241e11 −1.20744
\(626\) 3.70013e11 2.40946
\(627\) −3.63711e11 −2.35335
\(628\) 3.81910e10i 0.245540i
\(629\) 1.37428e11i 0.877955i
\(630\) 6.76113e11i 4.29197i
\(631\) 1.16433e11i 0.734446i −0.930133 0.367223i \(-0.880309\pi\)
0.930133 0.367223i \(-0.119691\pi\)
\(632\) 1.27974e11i 0.802145i
\(633\) −3.62442e11 −2.25748
\(634\) 4.29804e11i 2.66020i
\(635\) 1.93462e11i 1.18987i
\(636\) 5.86029e9i 0.0358171i
\(637\) 3.01053e11 1.82846
\(638\) −1.71432e11 −1.03469
\(639\) 1.20187e11i 0.720864i
\(640\) −2.73797e11 −1.63196
\(641\) 2.88483e11i 1.70879i 0.519625 + 0.854395i \(0.326072\pi\)
−0.519625 + 0.854395i \(0.673928\pi\)
\(642\) −5.60820e11 −3.30129
\(643\) −2.45488e10 −0.143610 −0.0718052 0.997419i \(-0.522876\pi\)
−0.0718052 + 0.997419i \(0.522876\pi\)
\(644\) 2.80970e11i 1.63349i
\(645\) −1.96684e11 + 2.28324e11i −1.13640 + 1.31921i
\(646\) 5.51033e11 3.16408
\(647\) 9.34246e9i 0.0533144i 0.999645 + 0.0266572i \(0.00848625\pi\)
−0.999645 + 0.0266572i \(0.991514\pi\)
\(648\) 7.89400e10i 0.447710i
\(649\) 6.24949e10 0.352262
\(650\) 7.16028e10i 0.401122i
\(651\) −8.80262e10 −0.490104
\(652\) 1.20312e11i 0.665761i
\(653\) 2.90231e11i 1.59622i 0.602515 + 0.798108i \(0.294165\pi\)
−0.602515 + 0.798108i \(0.705835\pi\)
\(654\) −4.59575e11 −2.51215
\(655\) 3.27217e10 0.177775
\(656\) 6.13312e10 0.331181
\(657\) 1.42668e11i 0.765710i
\(658\) 2.75502e11 1.46968
\(659\) 3.20513e11 1.69943 0.849717 0.527239i \(-0.176773\pi\)
0.849717 + 0.527239i \(0.176773\pi\)
\(660\) 6.62092e11 3.48934
\(661\) −1.23308e11 −0.645930 −0.322965 0.946411i \(-0.604680\pi\)
−0.322965 + 0.946411i \(0.604680\pi\)
\(662\) −5.75700e11 −2.99753
\(663\) 4.33495e11i 2.24352i
\(664\) 2.27305e11i 1.16933i
\(665\) 4.59607e11i 2.35017i
\(666\) −2.16239e11 −1.09910
\(667\) 5.94299e10i 0.300263i
\(668\) 2.38856e11 1.19958
\(669\) 2.81605e11 1.40584
\(670\) 6.55763e11 3.25423
\(671\) 2.26931e11i 1.11945i
\(672\) 6.36770e11i 3.12252i
\(673\) 1.36670e11i 0.666214i 0.942889 + 0.333107i \(0.108097\pi\)
−0.942889 + 0.333107i \(0.891903\pi\)
\(674\) 5.33566e11i 2.58552i
\(675\) 3.20545e10i 0.154410i
\(676\) 8.29663e10 0.397297
\(677\) 7.59379e10i 0.361496i 0.983529 + 0.180748i \(0.0578519\pi\)
−0.983529 + 0.180748i \(0.942148\pi\)
\(678\) 1.24910e10i 0.0591125i
\(679\) 1.68137e10i 0.0791012i
\(680\) −3.44575e11 −1.61157
\(681\) −7.01809e10 −0.326310
\(682\) 8.18580e10i 0.378376i
\(683\) 2.26713e11 1.04182 0.520911 0.853611i \(-0.325592\pi\)
0.520911 + 0.853611i \(0.325592\pi\)
\(684\) 5.23417e11i 2.39124i
\(685\) −1.99930e11 −0.908062
\(686\) −7.00872e11 −3.16477
\(687\) 3.88861e11i 1.74569i
\(688\) −2.96757e10 + 3.44495e10i −0.132449 + 0.153755i
\(689\) 2.97607e9 0.0132059
\(690\) 3.80206e11i 1.67735i
\(691\) 2.53902e11i 1.11366i −0.830625 0.556832i \(-0.812017\pi\)
0.830625 0.556832i \(-0.187983\pi\)
\(692\) 2.22165e10 0.0968839
\(693\) 7.20800e11i 3.12523i
\(694\) 1.06217e11 0.457885
\(695\) 4.30713e11i 1.84607i
\(696\) 1.47831e11i 0.629983i
\(697\) 6.56549e11 2.78186
\(698\) −3.53822e11 −1.49061
\(699\) 2.65789e11 1.11334
\(700\) 1.89946e11i 0.791114i
\(701\) 1.87896e10 0.0778116 0.0389058 0.999243i \(-0.487613\pi\)
0.0389058 + 0.999243i \(0.487613\pi\)
\(702\) −1.74365e11 −0.717977
\(703\) 1.46994e11 0.601837
\(704\) 5.26570e11 2.14371
\(705\) −2.25059e11 −0.911046
\(706\) 3.49755e11i 1.40782i
\(707\) 2.72962e11i 1.09251i
\(708\) 1.56882e11i 0.624369i
\(709\) 1.66008e11 0.656969 0.328484 0.944509i \(-0.393462\pi\)
0.328484 + 0.944509i \(0.393462\pi\)
\(710\) 2.46362e11i 0.969483i
\(711\) −3.31317e11 −1.29648
\(712\) 1.36896e11 0.532683
\(713\) −2.83775e10 −0.109804
\(714\) 1.90491e12i 7.32961i
\(715\) 3.36235e11i 1.28653i
\(716\) 1.36174e11i 0.518136i
\(717\) 5.38959e11i 2.03929i
\(718\) 1.01146e11i 0.380585i
\(719\) −3.71527e11 −1.39019 −0.695097 0.718916i \(-0.744638\pi\)
−0.695097 + 0.718916i \(0.744638\pi\)
\(720\) 8.33338e10i 0.310092i
\(721\) 2.42196e11i 0.896244i
\(722\) 1.57742e11i 0.580496i
\(723\) −1.07657e11 −0.393995
\(724\) −2.82671e11 −1.02879
\(725\) 4.01768e10i 0.145420i
\(726\) −4.93692e11 −1.77709
\(727\) 2.49562e11i 0.893390i −0.894686 0.446695i \(-0.852601\pi\)
0.894686 0.446695i \(-0.147399\pi\)
\(728\) 3.54932e11 1.26363
\(729\) 4.31666e11 1.52840
\(730\) 2.92444e11i 1.02980i
\(731\) −3.17678e11 + 3.68781e11i −1.11254 + 1.29151i
\(732\) 5.69669e11 1.98417
\(733\) 3.98663e11i 1.38099i −0.723337 0.690495i \(-0.757393\pi\)
0.723337 0.690495i \(-0.242607\pi\)
\(734\) 8.20684e11i 2.82743i
\(735\) 1.08070e12 3.70301
\(736\) 2.05279e11i 0.699575i
\(737\) −6.99105e11 −2.36959
\(738\) 1.03306e12i 3.48257i
\(739\) 2.31276e11i 0.775449i −0.921775 0.387724i \(-0.873261\pi\)
0.921775 0.387724i \(-0.126739\pi\)
\(740\) −2.67585e11 −0.892350
\(741\) 4.63671e11 1.53793
\(742\) −1.30777e10 −0.0431437
\(743\) 2.82004e11i 0.925336i −0.886532 0.462668i \(-0.846892\pi\)
0.886532 0.462668i \(-0.153108\pi\)
\(744\) −7.05886e10 −0.230379
\(745\) −4.63343e11 −1.50410
\(746\) −5.63698e9 −0.0182008
\(747\) −5.88482e11 −1.88995
\(748\) 1.06939e12 3.41608
\(749\) 7.55524e11i 2.40061i
\(750\) 6.18091e11i 1.95347i
\(751\) 1.06170e11i 0.333766i −0.985977 0.166883i \(-0.946630\pi\)
0.985977 0.166883i \(-0.0533702\pi\)
\(752\) −3.39568e10 −0.106183
\(753\) 5.92579e11i 1.84318i
\(754\) 2.18547e11 0.676176
\(755\) −9.56661e10 −0.294422
\(756\) 4.62552e11 1.41603
\(757\) 1.79106e11i 0.545415i 0.962097 + 0.272707i \(0.0879191\pi\)
−0.962097 + 0.272707i \(0.912081\pi\)
\(758\) 4.14281e11i 1.25493i
\(759\) 4.05336e11i 1.22137i
\(760\) 3.68561e11i 1.10473i
\(761\) 2.33012e11i 0.694767i −0.937723 0.347383i \(-0.887070\pi\)
0.937723 0.347383i \(-0.112930\pi\)
\(762\) 8.57647e11 2.54383
\(763\) 6.19129e11i 1.82677i
\(764\) 5.20943e11i 1.52903i
\(765\) 8.92086e11i 2.60472i
\(766\) 8.00127e11 2.32404
\(767\) −7.96706e10 −0.230206
\(768\) 3.46001e11i 0.994564i
\(769\) −8.40202e10 −0.240258 −0.120129 0.992758i \(-0.538331\pi\)
−0.120129 + 0.992758i \(0.538331\pi\)
\(770\) 1.47751e12i 4.20309i
\(771\) −5.12208e11 −1.44953
\(772\) −6.31041e11 −1.77660
\(773\) 3.81824e11i 1.06941i −0.845038 0.534706i \(-0.820422\pi\)
0.845038 0.534706i \(-0.179578\pi\)
\(774\) 5.80265e11 + 4.99856e11i 1.61682 + 1.39278i
\(775\) 1.91843e10 0.0531787
\(776\) 1.34830e10i 0.0371825i
\(777\) 5.08155e11i 1.39416i
\(778\) −6.40149e11 −1.74728
\(779\) 7.02252e11i 1.90697i
\(780\) −8.44057e11 −2.28031
\(781\) 2.62645e11i 0.705935i
\(782\)