Properties

Label 43.9.b.b.42.12
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 42.12
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.17

$q$-expansion

\(f(q)\) \(=\) \(q-8.15532i q^{2} +11.7848i q^{3} +189.491 q^{4} -1153.14i q^{5} +96.1089 q^{6} +1566.67i q^{7} -3633.12i q^{8} +6422.12 q^{9} +O(q^{10})\) \(q-8.15532i q^{2} +11.7848i q^{3} +189.491 q^{4} -1153.14i q^{5} +96.1089 q^{6} +1566.67i q^{7} -3633.12i q^{8} +6422.12 q^{9} -9404.25 q^{10} -10047.4 q^{11} +2233.11i q^{12} -1635.86 q^{13} +12776.7 q^{14} +13589.6 q^{15} +18880.4 q^{16} +25926.9 q^{17} -52374.4i q^{18} -167816. i q^{19} -218510. i q^{20} -18462.9 q^{21} +81940.1i q^{22} -225426. q^{23} +42815.6 q^{24} -939115. q^{25} +13341.0i q^{26} +153004. i q^{27} +296869. i q^{28} -829628. i q^{29} -110827. i q^{30} -803727. q^{31} -1.08405e6i q^{32} -118407. i q^{33} -211442. i q^{34} +1.80659e6 q^{35} +1.21693e6 q^{36} -267963. i q^{37} -1.36859e6 q^{38} -19278.3i q^{39} -4.18951e6 q^{40} +2.02467e6 q^{41} +150571. i q^{42} +(-1.99883e6 + 2.77361e6i) q^{43} -1.90390e6 q^{44} -7.40562e6i q^{45} +1.83842e6i q^{46} +6.67489e6 q^{47} +222502. i q^{48} +3.31036e6 q^{49} +7.65878e6i q^{50} +305544. i q^{51} -309980. q^{52} +1.35151e7 q^{53} +1.24779e6 q^{54} +1.15861e7i q^{55} +5.69189e6 q^{56} +1.97768e6 q^{57} -6.76588e6 q^{58} -1.38645e7 q^{59} +2.57510e6 q^{60} +2.78916e6i q^{61} +6.55465e6i q^{62} +1.00613e7i q^{63} -4.00743e6 q^{64} +1.88638e6i q^{65} -965648. q^{66} -2.07321e6 q^{67} +4.91291e6 q^{68} -2.65660e6i q^{69} -1.47333e7i q^{70} +3.64571e7i q^{71} -2.33323e7i q^{72} +2.21335e7i q^{73} -2.18533e6 q^{74} -1.10673e7i q^{75} -3.17995e7i q^{76} -1.57410e7i q^{77} -157221. q^{78} -2.21707e7 q^{79} -2.17718e7i q^{80} +4.03324e7 q^{81} -1.65118e7i q^{82} +1.20032e7 q^{83} -3.49854e6 q^{84} -2.98974e7i q^{85} +(2.26196e7 + 1.63011e7i) q^{86} +9.77700e6 q^{87} +3.65035e7i q^{88} -4.53594e7i q^{89} -6.03952e7 q^{90} -2.56285e6i q^{91} -4.27162e7 q^{92} -9.47177e6i q^{93} -5.44359e7i q^{94} -1.93516e8 q^{95} +1.27754e7 q^{96} +1.49594e8 q^{97} -2.69970e7i q^{98} -6.45258e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.15532i 0.509708i −0.966980 0.254854i \(-0.917973\pi\)
0.966980 0.254854i \(-0.0820273\pi\)
\(3\) 11.7848i 0.145491i 0.997351 + 0.0727457i \(0.0231762\pi\)
−0.997351 + 0.0727457i \(0.976824\pi\)
\(4\) 189.491 0.740198
\(5\) 1153.14i 1.84503i −0.385962 0.922515i \(-0.626130\pi\)
0.385962 0.922515i \(-0.373870\pi\)
\(6\) 96.1089 0.0741581
\(7\) 1566.67i 0.652506i 0.945282 + 0.326253i \(0.105786\pi\)
−0.945282 + 0.326253i \(0.894214\pi\)
\(8\) 3633.12i 0.886992i
\(9\) 6422.12 0.978832
\(10\) −9404.25 −0.940425
\(11\) −10047.4 −0.686253 −0.343127 0.939289i \(-0.611486\pi\)
−0.343127 + 0.939289i \(0.611486\pi\)
\(12\) 2233.11i 0.107693i
\(13\) −1635.86 −0.0572760 −0.0286380 0.999590i \(-0.509117\pi\)
−0.0286380 + 0.999590i \(0.509117\pi\)
\(14\) 12776.7 0.332587
\(15\) 13589.6 0.268436
\(16\) 18880.4 0.288092
\(17\) 25926.9 0.310424 0.155212 0.987881i \(-0.450394\pi\)
0.155212 + 0.987881i \(0.450394\pi\)
\(18\) 52374.4i 0.498918i
\(19\) 167816.i 1.28771i −0.765147 0.643855i \(-0.777334\pi\)
0.765147 0.643855i \(-0.222666\pi\)
\(20\) 218510.i 1.36569i
\(21\) −18462.9 −0.0949341
\(22\) 81940.1i 0.349789i
\(23\) −225426. −0.805551 −0.402775 0.915299i \(-0.631954\pi\)
−0.402775 + 0.915299i \(0.631954\pi\)
\(24\) 42815.6 0.129050
\(25\) −939115. −2.40413
\(26\) 13341.0i 0.0291940i
\(27\) 153004.i 0.287903i
\(28\) 296869.i 0.482984i
\(29\) 829628.i 1.17298i −0.809956 0.586491i \(-0.800509\pi\)
0.809956 0.586491i \(-0.199491\pi\)
\(30\) 110827.i 0.136824i
\(31\) −803727. −0.870285 −0.435143 0.900362i \(-0.643302\pi\)
−0.435143 + 0.900362i \(0.643302\pi\)
\(32\) 1.08405e6i 1.03383i
\(33\) 118407.i 0.0998440i
\(34\) 211442.i 0.158225i
\(35\) 1.80659e6 1.20389
\(36\) 1.21693e6 0.724530
\(37\) 267963.i 0.142978i −0.997441 0.0714889i \(-0.977225\pi\)
0.997441 0.0714889i \(-0.0227751\pi\)
\(38\) −1.36859e6 −0.656356
\(39\) 19278.3i 0.00833317i
\(40\) −4.18951e6 −1.63653
\(41\) 2.02467e6 0.716503 0.358252 0.933625i \(-0.383373\pi\)
0.358252 + 0.933625i \(0.383373\pi\)
\(42\) 150571.i 0.0483886i
\(43\) −1.99883e6 + 2.77361e6i −0.584658 + 0.811280i
\(44\) −1.90390e6 −0.507964
\(45\) 7.40562e6i 1.80597i
\(46\) 1.83842e6i 0.410595i
\(47\) 6.67489e6 1.36789 0.683947 0.729531i \(-0.260262\pi\)
0.683947 + 0.729531i \(0.260262\pi\)
\(48\) 222502.i 0.0419149i
\(49\) 3.31036e6 0.574236
\(50\) 7.65878e6i 1.22540i
\(51\) 305544.i 0.0451640i
\(52\) −309980. −0.0423956
\(53\) 1.35151e7 1.71284 0.856420 0.516280i \(-0.172684\pi\)
0.856420 + 0.516280i \(0.172684\pi\)
\(54\) 1.24779e6 0.146746
\(55\) 1.15861e7i 1.26616i
\(56\) 5.69189e6 0.578768
\(57\) 1.97768e6 0.187351
\(58\) −6.76588e6 −0.597878
\(59\) −1.38645e7 −1.14419 −0.572093 0.820188i \(-0.693869\pi\)
−0.572093 + 0.820188i \(0.693869\pi\)
\(60\) 2.57510e6 0.198696
\(61\) 2.78916e6i 0.201444i 0.994915 + 0.100722i \(0.0321153\pi\)
−0.994915 + 0.100722i \(0.967885\pi\)
\(62\) 6.55465e6i 0.443591i
\(63\) 1.00613e7i 0.638694i
\(64\) −4.00743e6 −0.238862
\(65\) 1.88638e6i 0.105676i
\(66\) −965648. −0.0508912
\(67\) −2.07321e6 −0.102883 −0.0514416 0.998676i \(-0.516382\pi\)
−0.0514416 + 0.998676i \(0.516382\pi\)
\(68\) 4.91291e6 0.229775
\(69\) 2.65660e6i 0.117201i
\(70\) 1.47333e7i 0.613633i
\(71\) 3.64571e7i 1.43466i 0.696733 + 0.717330i \(0.254636\pi\)
−0.696733 + 0.717330i \(0.745364\pi\)
\(72\) 2.33323e7i 0.868217i
\(73\) 2.21335e7i 0.779396i 0.920943 + 0.389698i \(0.127421\pi\)
−0.920943 + 0.389698i \(0.872579\pi\)
\(74\) −2.18533e6 −0.0728769
\(75\) 1.10673e7i 0.349781i
\(76\) 3.17995e7i 0.953161i
\(77\) 1.57410e7i 0.447785i
\(78\) −157221. −0.00424748
\(79\) −2.21707e7 −0.569209 −0.284605 0.958645i \(-0.591862\pi\)
−0.284605 + 0.958645i \(0.591862\pi\)
\(80\) 2.17718e7i 0.531538i
\(81\) 4.03324e7 0.936945
\(82\) 1.65118e7i 0.365207i
\(83\) 1.20032e7 0.252922 0.126461 0.991972i \(-0.459638\pi\)
0.126461 + 0.991972i \(0.459638\pi\)
\(84\) −3.49854e6 −0.0702700
\(85\) 2.98974e7i 0.572741i
\(86\) 2.26196e7 + 1.63011e7i 0.413516 + 0.298004i
\(87\) 9.77700e6 0.170659
\(88\) 3.65035e7i 0.608701i
\(89\) 4.53594e7i 0.722949i −0.932382 0.361474i \(-0.882274\pi\)
0.932382 0.361474i \(-0.117726\pi\)
\(90\) −6.03952e7 −0.920519
\(91\) 2.56285e6i 0.0373729i
\(92\) −4.27162e7 −0.596267
\(93\) 9.47177e6i 0.126619i
\(94\) 5.44359e7i 0.697226i
\(95\) −1.93516e8 −2.37586
\(96\) 1.27754e7 0.150414
\(97\) 1.49594e8 1.68977 0.844884 0.534950i \(-0.179669\pi\)
0.844884 + 0.534950i \(0.179669\pi\)
\(98\) 2.69970e7i 0.292692i
\(99\) −6.45258e7 −0.671727
\(100\) −1.77954e8 −1.77954
\(101\) 5.23322e7 0.502902 0.251451 0.967870i \(-0.419092\pi\)
0.251451 + 0.967870i \(0.419092\pi\)
\(102\) 2.49181e6 0.0230204
\(103\) −3.20839e7 −0.285061 −0.142531 0.989790i \(-0.545524\pi\)
−0.142531 + 0.989790i \(0.545524\pi\)
\(104\) 5.94327e6i 0.0508034i
\(105\) 2.12903e7i 0.175156i
\(106\) 1.10220e8i 0.873047i
\(107\) 1.76389e8 1.34566 0.672830 0.739797i \(-0.265078\pi\)
0.672830 + 0.739797i \(0.265078\pi\)
\(108\) 2.89928e7i 0.213105i
\(109\) 1.39197e8 0.986104 0.493052 0.870000i \(-0.335881\pi\)
0.493052 + 0.870000i \(0.335881\pi\)
\(110\) 9.44886e7 0.645370
\(111\) 3.15790e6 0.0208021
\(112\) 2.95793e7i 0.187982i
\(113\) 8.95103e7i 0.548984i 0.961589 + 0.274492i \(0.0885096\pi\)
−0.961589 + 0.274492i \(0.911490\pi\)
\(114\) 1.61286e7i 0.0954941i
\(115\) 2.59949e8i 1.48627i
\(116\) 1.57207e8i 0.868239i
\(117\) −1.05057e7 −0.0560636
\(118\) 1.13070e8i 0.583201i
\(119\) 4.06188e7i 0.202553i
\(120\) 4.93725e7i 0.238101i
\(121\) −1.13408e8 −0.529056
\(122\) 2.27465e7 0.102678
\(123\) 2.38603e7i 0.104245i
\(124\) −1.52299e8 −0.644184
\(125\) 6.32487e8i 2.59067i
\(126\) 8.20533e7 0.325547
\(127\) −6.38872e7 −0.245583 −0.122792 0.992432i \(-0.539185\pi\)
−0.122792 + 0.992432i \(0.539185\pi\)
\(128\) 2.44836e8i 0.912085i
\(129\) −3.26864e7 2.35558e7i −0.118034 0.0850627i
\(130\) 1.53840e7 0.0538638
\(131\) 2.45176e8i 0.832517i 0.909246 + 0.416258i \(0.136659\pi\)
−0.909246 + 0.416258i \(0.863341\pi\)
\(132\) 2.24371e7i 0.0739044i
\(133\) 2.62911e8 0.840239
\(134\) 1.69077e7i 0.0524404i
\(135\) 1.76435e8 0.531190
\(136\) 9.41956e7i 0.275344i
\(137\) 4.58018e8i 1.30017i −0.759861 0.650085i \(-0.774733\pi\)
0.759861 0.650085i \(-0.225267\pi\)
\(138\) −2.16655e7 −0.0597381
\(139\) 5.84939e8 1.56694 0.783468 0.621433i \(-0.213449\pi\)
0.783468 + 0.621433i \(0.213449\pi\)
\(140\) 3.42332e8 0.891119
\(141\) 7.86623e7i 0.199017i
\(142\) 2.97320e8 0.731257
\(143\) 1.64362e7 0.0393058
\(144\) 1.21252e8 0.281993
\(145\) −9.56680e8 −2.16419
\(146\) 1.80506e8 0.397264
\(147\) 3.90119e7i 0.0835464i
\(148\) 5.07766e7i 0.105832i
\(149\) 7.73760e8i 1.56986i −0.619584 0.784930i \(-0.712699\pi\)
0.619584 0.784930i \(-0.287301\pi\)
\(150\) −9.02573e7 −0.178286
\(151\) 1.68887e7i 0.0324855i −0.999868 0.0162427i \(-0.994830\pi\)
0.999868 0.0162427i \(-0.00517045\pi\)
\(152\) −6.09694e8 −1.14219
\(153\) 1.66506e8 0.303853
\(154\) −1.28373e8 −0.228239
\(155\) 9.26812e8i 1.60570i
\(156\) 3.65306e6i 0.00616820i
\(157\) 1.03371e9i 1.70138i 0.525665 + 0.850692i \(0.323816\pi\)
−0.525665 + 0.850692i \(0.676184\pi\)
\(158\) 1.80810e8i 0.290130i
\(159\) 1.59273e8i 0.249203i
\(160\) −1.25007e9 −1.90746
\(161\) 3.53168e8i 0.525627i
\(162\) 3.28924e8i 0.477568i
\(163\) 9.59746e8i 1.35958i −0.733405 0.679792i \(-0.762070\pi\)
0.733405 0.679792i \(-0.237930\pi\)
\(164\) 3.83656e8 0.530354
\(165\) −1.36540e8 −0.184215
\(166\) 9.78902e7i 0.128916i
\(167\) 3.88487e8 0.499471 0.249736 0.968314i \(-0.419656\pi\)
0.249736 + 0.968314i \(0.419656\pi\)
\(168\) 6.70778e7i 0.0842058i
\(169\) −8.13055e8 −0.996719
\(170\) −2.43823e8 −0.291930
\(171\) 1.07773e9i 1.26045i
\(172\) −3.78759e8 + 5.25573e8i −0.432763 + 0.600508i
\(173\) 8.26563e8 0.922765 0.461383 0.887201i \(-0.347354\pi\)
0.461383 + 0.887201i \(0.347354\pi\)
\(174\) 7.97346e7i 0.0869861i
\(175\) 1.47128e9i 1.56871i
\(176\) −1.89699e8 −0.197704
\(177\) 1.63391e8i 0.166469i
\(178\) −3.69921e8 −0.368492
\(179\) 4.45921e8i 0.434356i −0.976132 0.217178i \(-0.930315\pi\)
0.976132 0.217178i \(-0.0696852\pi\)
\(180\) 1.40330e9i 1.33678i
\(181\) −9.84597e7 −0.0917369 −0.0458685 0.998947i \(-0.514606\pi\)
−0.0458685 + 0.998947i \(0.514606\pi\)
\(182\) −2.09008e7 −0.0190493
\(183\) −3.28698e7 −0.0293084
\(184\) 8.19000e8i 0.714517i
\(185\) −3.09000e8 −0.263798
\(186\) −7.72453e7 −0.0645387
\(187\) −2.60499e8 −0.213029
\(188\) 1.26483e9 1.01251
\(189\) −2.39706e8 −0.187859
\(190\) 1.57818e9i 1.21100i
\(191\) 1.95755e9i 1.47088i 0.677587 + 0.735442i \(0.263026\pi\)
−0.677587 + 0.735442i \(0.736974\pi\)
\(192\) 4.72268e7i 0.0347523i
\(193\) 8.96951e8 0.646457 0.323228 0.946321i \(-0.395232\pi\)
0.323228 + 0.946321i \(0.395232\pi\)
\(194\) 1.21999e9i 0.861287i
\(195\) −2.22306e7 −0.0153749
\(196\) 6.27282e8 0.425048
\(197\) −9.47778e8 −0.629277 −0.314638 0.949212i \(-0.601883\pi\)
−0.314638 + 0.949212i \(0.601883\pi\)
\(198\) 5.26229e8i 0.342384i
\(199\) 2.15162e9i 1.37200i −0.727602 0.686000i \(-0.759365\pi\)
0.727602 0.686000i \(-0.240635\pi\)
\(200\) 3.41192e9i 2.13245i
\(201\) 2.44324e7i 0.0149686i
\(202\) 4.26786e8i 0.256333i
\(203\) 1.29975e9 0.765378
\(204\) 5.78977e7i 0.0334303i
\(205\) 2.33473e9i 1.32197i
\(206\) 2.61654e8i 0.145298i
\(207\) −1.44771e9 −0.788499
\(208\) −3.08856e7 −0.0165007
\(209\) 1.68612e9i 0.883696i
\(210\) 1.73630e8 0.0892784
\(211\) 2.26160e9i 1.14100i 0.821298 + 0.570500i \(0.193250\pi\)
−0.821298 + 0.570500i \(0.806750\pi\)
\(212\) 2.56099e9 1.26784
\(213\) −4.29640e8 −0.208731
\(214\) 1.43851e9i 0.685894i
\(215\) 3.19836e9 + 2.30494e9i 1.49684 + 1.07871i
\(216\) 5.55880e8 0.255368
\(217\) 1.25917e9i 0.567866i
\(218\) 1.13519e9i 0.502624i
\(219\) −2.60839e8 −0.113395
\(220\) 2.19547e9i 0.937208i
\(221\) −4.24128e7 −0.0177798
\(222\) 2.57537e7i 0.0106030i
\(223\) 2.14578e9i 0.867692i −0.900987 0.433846i \(-0.857156\pi\)
0.900987 0.433846i \(-0.142844\pi\)
\(224\) 1.69835e9 0.674583
\(225\) −6.03111e9 −2.35324
\(226\) 7.29986e8 0.279821
\(227\) 4.15632e9i 1.56533i 0.622445 + 0.782664i \(0.286139\pi\)
−0.622445 + 0.782664i \(0.713861\pi\)
\(228\) 3.74751e8 0.138677
\(229\) 4.21103e9 1.53125 0.765625 0.643287i \(-0.222430\pi\)
0.765625 + 0.643287i \(0.222430\pi\)
\(230\) 2.11996e9 0.757561
\(231\) 1.85505e8 0.0651488
\(232\) −3.01414e9 −1.04043
\(233\) 4.28129e9i 1.45262i 0.687369 + 0.726309i \(0.258766\pi\)
−0.687369 + 0.726309i \(0.741234\pi\)
\(234\) 8.56772e7i 0.0285760i
\(235\) 7.69711e9i 2.52381i
\(236\) −2.62720e9 −0.846925
\(237\) 2.61278e8i 0.0828151i
\(238\) 3.31260e8 0.103243
\(239\) −5.77453e9 −1.76980 −0.884901 0.465778i \(-0.845774\pi\)
−0.884901 + 0.465778i \(0.845774\pi\)
\(240\) 2.56576e8 0.0773342
\(241\) 5.53206e9i 1.63991i 0.572431 + 0.819953i \(0.306001\pi\)
−0.572431 + 0.819953i \(0.693999\pi\)
\(242\) 9.24878e8i 0.269664i
\(243\) 1.47917e9i 0.424221i
\(244\) 5.28521e8i 0.149109i
\(245\) 3.81731e9i 1.05948i
\(246\) 1.94588e8 0.0531345
\(247\) 2.74523e8i 0.0737549i
\(248\) 2.92004e9i 0.771936i
\(249\) 1.41456e8i 0.0367979i
\(250\) 5.15814e9 1.32048
\(251\) −2.90089e9 −0.730865 −0.365432 0.930838i \(-0.619079\pi\)
−0.365432 + 0.930838i \(0.619079\pi\)
\(252\) 1.90653e9i 0.472760i
\(253\) 2.26496e9 0.552812
\(254\) 5.21020e8i 0.125176i
\(255\) 3.52336e8 0.0833289
\(256\) −3.02262e9 −0.703758
\(257\) 4.03352e9i 0.924596i −0.886725 0.462298i \(-0.847025\pi\)
0.886725 0.462298i \(-0.152975\pi\)
\(258\) −1.92105e8 + 2.66568e8i −0.0433571 + 0.0601630i
\(259\) 4.19810e8 0.0932939
\(260\) 3.57452e8i 0.0782211i
\(261\) 5.32797e9i 1.14815i
\(262\) 1.99949e9 0.424340
\(263\) 5.82399e8i 0.121730i 0.998146 + 0.0608650i \(0.0193859\pi\)
−0.998146 + 0.0608650i \(0.980614\pi\)
\(264\) −4.30187e8 −0.0885609
\(265\) 1.55849e10i 3.16024i
\(266\) 2.14413e9i 0.428276i
\(267\) 5.34552e8 0.105183
\(268\) −3.92855e8 −0.0761540
\(269\) −3.25850e9 −0.622313 −0.311156 0.950359i \(-0.600716\pi\)
−0.311156 + 0.950359i \(0.600716\pi\)
\(270\) 1.43888e9i 0.270751i
\(271\) 2.65797e9 0.492802 0.246401 0.969168i \(-0.420752\pi\)
0.246401 + 0.969168i \(0.420752\pi\)
\(272\) 4.89510e8 0.0894305
\(273\) 3.02027e7 0.00543744
\(274\) −3.73528e9 −0.662706
\(275\) 9.43569e9 1.64984
\(276\) 5.03402e8i 0.0867518i
\(277\) 2.12193e9i 0.360422i 0.983628 + 0.180211i \(0.0576780\pi\)
−0.983628 + 0.180211i \(0.942322\pi\)
\(278\) 4.77036e9i 0.798679i
\(279\) −5.16163e9 −0.851863
\(280\) 6.56356e9i 1.06784i
\(281\) −5.91486e9 −0.948679 −0.474339 0.880342i \(-0.657313\pi\)
−0.474339 + 0.880342i \(0.657313\pi\)
\(282\) 6.41516e8 0.101440
\(283\) −6.44035e9 −1.00407 −0.502035 0.864847i \(-0.667415\pi\)
−0.502035 + 0.864847i \(0.667415\pi\)
\(284\) 6.90829e9i 1.06193i
\(285\) 2.28054e9i 0.345668i
\(286\) 1.34042e8i 0.0200345i
\(287\) 3.17198e9i 0.467523i
\(288\) 6.96192e9i 1.01195i
\(289\) −6.30355e9 −0.903637
\(290\) 7.80203e9i 1.10310i
\(291\) 1.76294e9i 0.245847i
\(292\) 4.19409e9i 0.576908i
\(293\) 9.16798e9 1.24395 0.621976 0.783037i \(-0.286330\pi\)
0.621976 + 0.783037i \(0.286330\pi\)
\(294\) 3.18155e8 0.0425842
\(295\) 1.59878e10i 2.11106i
\(296\) −9.73543e8 −0.126820
\(297\) 1.53729e9i 0.197575i
\(298\) −6.31026e9 −0.800170
\(299\) 3.68766e8 0.0461387
\(300\) 2.09715e9i 0.258907i
\(301\) −4.34532e9 3.13150e9i −0.529365 0.381493i
\(302\) −1.37733e8 −0.0165581
\(303\) 6.16725e8i 0.0731680i
\(304\) 3.16842e9i 0.370979i
\(305\) 3.21630e9 0.371670
\(306\) 1.35791e9i 0.154876i
\(307\) −6.19557e9 −0.697474 −0.348737 0.937221i \(-0.613389\pi\)
−0.348737 + 0.937221i \(0.613389\pi\)
\(308\) 2.98277e9i 0.331449i
\(309\) 3.78102e8i 0.0414740i
\(310\) 7.55845e9 0.818438
\(311\) 4.05221e8 0.0433162 0.0216581 0.999765i \(-0.493105\pi\)
0.0216581 + 0.999765i \(0.493105\pi\)
\(312\) −7.00403e7 −0.00739145
\(313\) 7.98641e9i 0.832098i 0.909342 + 0.416049i \(0.136586\pi\)
−0.909342 + 0.416049i \(0.863414\pi\)
\(314\) 8.43028e9 0.867208
\(315\) 1.16021e10 1.17841
\(316\) −4.20115e9 −0.421328
\(317\) 1.01939e10 1.00949 0.504745 0.863268i \(-0.331586\pi\)
0.504745 + 0.863268i \(0.331586\pi\)
\(318\) 1.29892e9 0.127021
\(319\) 8.33563e9i 0.804963i
\(320\) 4.62115e9i 0.440707i
\(321\) 2.07871e9i 0.195782i
\(322\) −2.88020e9 −0.267916
\(323\) 4.35094e9i 0.399736i
\(324\) 7.64262e9 0.693525
\(325\) 1.53626e9 0.137699
\(326\) −7.82703e9 −0.692990
\(327\) 1.64040e9i 0.143470i
\(328\) 7.35586e9i 0.635533i
\(329\) 1.04573e10i 0.892560i
\(330\) 1.11353e9i 0.0938958i
\(331\) 1.22332e9i 0.101913i 0.998701 + 0.0509565i \(0.0162270\pi\)
−0.998701 + 0.0509565i \(0.983773\pi\)
\(332\) 2.27450e9 0.187212
\(333\) 1.72089e9i 0.139951i
\(334\) 3.16823e9i 0.254584i
\(335\) 2.39071e9i 0.189823i
\(336\) −3.48586e8 −0.0273497
\(337\) −7.58634e9 −0.588183 −0.294092 0.955777i \(-0.595017\pi\)
−0.294092 + 0.955777i \(0.595017\pi\)
\(338\) 6.63072e9i 0.508035i
\(339\) −1.05486e9 −0.0798724
\(340\) 5.66529e9i 0.423942i
\(341\) 8.07539e9 0.597236
\(342\) −8.78925e9 −0.642462
\(343\) 1.42177e10i 1.02720i
\(344\) 1.00768e10 + 7.26198e9i 0.719599 + 0.518587i
\(345\) −3.06345e9 −0.216239
\(346\) 6.74088e9i 0.470341i
\(347\) 7.28005e9i 0.502130i −0.967970 0.251065i \(-0.919219\pi\)
0.967970 0.251065i \(-0.0807809\pi\)
\(348\) 1.85265e9 0.126321
\(349\) 2.15740e9i 0.145422i 0.997353 + 0.0727108i \(0.0231650\pi\)
−0.997353 + 0.0727108i \(0.976835\pi\)
\(350\) −1.19988e10 −0.799584
\(351\) 2.50292e8i 0.0164899i
\(352\) 1.08920e10i 0.709473i
\(353\) −1.82199e10 −1.17340 −0.586701 0.809804i \(-0.699574\pi\)
−0.586701 + 0.809804i \(0.699574\pi\)
\(354\) −1.33250e9 −0.0848507
\(355\) 4.20403e10 2.64699
\(356\) 8.59519e9i 0.535125i
\(357\) −4.78685e8 −0.0294698
\(358\) −3.63663e9 −0.221394
\(359\) 2.80903e10 1.69114 0.845569 0.533867i \(-0.179262\pi\)
0.845569 + 0.533867i \(0.179262\pi\)
\(360\) −2.69055e10 −1.60188
\(361\) −1.11785e10 −0.658197
\(362\) 8.02971e8i 0.0467590i
\(363\) 1.33649e9i 0.0769732i
\(364\) 4.85636e8i 0.0276634i
\(365\) 2.55231e10 1.43801
\(366\) 2.68063e8i 0.0149387i
\(367\) 1.01135e10 0.557491 0.278746 0.960365i \(-0.410081\pi\)
0.278746 + 0.960365i \(0.410081\pi\)
\(368\) −4.25613e9 −0.232072
\(369\) 1.30027e10 0.701336
\(370\) 2.52000e9i 0.134460i
\(371\) 2.11737e10i 1.11764i
\(372\) 1.79481e9i 0.0937232i
\(373\) 3.73566e10i 1.92989i −0.262452 0.964945i \(-0.584531\pi\)
0.262452 0.964945i \(-0.415469\pi\)
\(374\) 2.12445e9i 0.108583i
\(375\) −7.45374e9 −0.376920
\(376\) 2.42507e10i 1.21331i
\(377\) 1.35715e9i 0.0671837i
\(378\) 1.95488e9i 0.0957529i
\(379\) −1.85816e10 −0.900590 −0.450295 0.892880i \(-0.648681\pi\)
−0.450295 + 0.892880i \(0.648681\pi\)
\(380\) −3.66694e10 −1.75861
\(381\) 7.52898e8i 0.0357303i
\(382\) 1.59644e10 0.749721
\(383\) 3.19636e10i 1.48546i −0.669591 0.742730i \(-0.733531\pi\)
0.669591 0.742730i \(-0.266469\pi\)
\(384\) 2.88534e9 0.132701
\(385\) −1.81516e10 −0.826176
\(386\) 7.31493e9i 0.329504i
\(387\) −1.28367e10 + 1.78124e10i −0.572282 + 0.794107i
\(388\) 2.83467e10 1.25076
\(389\) 1.02069e10i 0.445753i −0.974847 0.222877i \(-0.928455\pi\)
0.974847 0.222877i \(-0.0715447\pi\)
\(390\) 1.81298e8i 0.00783672i
\(391\) −5.84460e9 −0.250062
\(392\) 1.20269e10i 0.509343i
\(393\) −2.88935e9 −0.121124
\(394\) 7.72944e9i 0.320747i
\(395\) 2.55660e10i 1.05021i
\(396\) −1.22270e10 −0.497211
\(397\) −1.37116e10 −0.551982 −0.275991 0.961160i \(-0.589006\pi\)
−0.275991 + 0.961160i \(0.589006\pi\)
\(398\) −1.75472e10 −0.699319
\(399\) 3.09836e9i 0.122248i
\(400\) −1.77308e10 −0.692611
\(401\) −4.03228e10 −1.55946 −0.779729 0.626118i \(-0.784643\pi\)
−0.779729 + 0.626118i \(0.784643\pi\)
\(402\) −1.99254e8 −0.00762963
\(403\) 1.31478e9 0.0498465
\(404\) 9.91647e9 0.372247
\(405\) 4.65090e10i 1.72869i
\(406\) 1.05999e10i 0.390119i
\(407\) 2.69235e9i 0.0981190i
\(408\) 1.11008e9 0.0400601
\(409\) 4.14921e10i 1.48276i 0.671083 + 0.741382i \(0.265829\pi\)
−0.671083 + 0.741382i \(0.734171\pi\)
\(410\) −1.90405e10 −0.673818
\(411\) 5.39765e9 0.189164
\(412\) −6.07960e9 −0.211002
\(413\) 2.17211e10i 0.746589i
\(414\) 1.18066e10i 0.401904i
\(415\) 1.38415e10i 0.466648i
\(416\) 1.77336e9i 0.0592139i
\(417\) 6.89339e9i 0.227976i
\(418\) 1.37508e10 0.450426
\(419\) 2.11727e10i 0.686941i 0.939164 + 0.343470i \(0.111602\pi\)
−0.939164 + 0.343470i \(0.888398\pi\)
\(420\) 4.03432e9i 0.129650i
\(421\) 9.68981e8i 0.0308451i −0.999881 0.0154226i \(-0.995091\pi\)
0.999881 0.0154226i \(-0.00490935\pi\)
\(422\) 1.84440e10 0.581576
\(423\) 4.28669e10 1.33894
\(424\) 4.91021e10i 1.51928i
\(425\) −2.43483e10 −0.746300
\(426\) 3.50385e9i 0.106392i
\(427\) −4.36969e9 −0.131443
\(428\) 3.34240e10 0.996056
\(429\) 1.93697e8i 0.00571866i
\(430\) 1.87975e10 2.60837e10i 0.549827 0.762948i
\(431\) 2.61536e10 0.757917 0.378959 0.925414i \(-0.376282\pi\)
0.378959 + 0.925414i \(0.376282\pi\)
\(432\) 2.88876e9i 0.0829425i
\(433\) 3.22035e10i 0.916118i 0.888922 + 0.458059i \(0.151455\pi\)
−0.888922 + 0.458059i \(0.848545\pi\)
\(434\) −1.02690e10 −0.289446
\(435\) 1.12743e10i 0.314871i
\(436\) 2.63765e10 0.729912
\(437\) 3.78300e10i 1.03732i
\(438\) 2.12722e9i 0.0577985i
\(439\) −1.53021e10 −0.411997 −0.205998 0.978552i \(-0.566044\pi\)
−0.205998 + 0.978552i \(0.566044\pi\)
\(440\) 4.20938e10 1.12307
\(441\) 2.12595e10 0.562081
\(442\) 3.45890e8i 0.00906251i
\(443\) 3.37252e10 0.875669 0.437834 0.899056i \(-0.355746\pi\)
0.437834 + 0.899056i \(0.355746\pi\)
\(444\) 5.98392e8 0.0153976
\(445\) −5.23059e10 −1.33386
\(446\) −1.74995e10 −0.442269
\(447\) 9.11861e9 0.228401
\(448\) 6.27831e9i 0.155859i
\(449\) 2.28762e10i 0.562859i −0.959582 0.281429i \(-0.909192\pi\)
0.959582 0.281429i \(-0.0908085\pi\)
\(450\) 4.91856e10i 1.19947i
\(451\) −2.03427e10 −0.491703
\(452\) 1.69614e10i 0.406357i
\(453\) 1.99030e8 0.00472636
\(454\) 3.38961e10 0.797859
\(455\) −2.95533e9 −0.0689541
\(456\) 7.18513e9i 0.166179i
\(457\) 3.74308e10i 0.858152i 0.903268 + 0.429076i \(0.141161\pi\)
−0.903268 + 0.429076i \(0.858839\pi\)
\(458\) 3.43423e10i 0.780490i
\(459\) 3.96691e9i 0.0893720i
\(460\) 4.92579e10i 1.10013i
\(461\) −8.15419e10 −1.80542 −0.902708 0.430254i \(-0.858424\pi\)
−0.902708 + 0.430254i \(0.858424\pi\)
\(462\) 1.51285e9i 0.0332068i
\(463\) 2.57195e10i 0.559679i 0.960047 + 0.279840i \(0.0902813\pi\)
−0.960047 + 0.279840i \(0.909719\pi\)
\(464\) 1.56637e10i 0.337926i
\(465\) −1.09223e10 −0.233616
\(466\) 3.49153e10 0.740410
\(467\) 5.31933e10i 1.11838i −0.829040 0.559190i \(-0.811112\pi\)
0.829040 0.559190i \(-0.188888\pi\)
\(468\) −1.99073e9 −0.0414982
\(469\) 3.24803e9i 0.0671320i
\(470\) −6.27724e10 −1.28640
\(471\) −1.21821e10 −0.247537
\(472\) 5.03715e10i 1.01488i
\(473\) 2.00831e10 2.78676e10i 0.401223 0.556744i
\(474\) −2.13081e9 −0.0422115
\(475\) 1.57598e11i 3.09583i
\(476\) 7.69689e9i 0.149930i
\(477\) 8.67957e10 1.67658
\(478\) 4.70931e10i 0.902082i
\(479\) 2.65359e10 0.504071 0.252036 0.967718i \(-0.418900\pi\)
0.252036 + 0.967718i \(0.418900\pi\)
\(480\) 1.47318e10i 0.277518i
\(481\) 4.38351e8i 0.00818920i
\(482\) 4.51158e10 0.835873
\(483\) 4.16201e9 0.0764742
\(484\) −2.14897e10 −0.391606
\(485\) 1.72503e11i 3.11767i
\(486\) 1.20631e10 0.216228
\(487\) 7.74386e10 1.37671 0.688354 0.725375i \(-0.258334\pi\)
0.688354 + 0.725375i \(0.258334\pi\)
\(488\) 1.01334e10 0.178679
\(489\) 1.13104e10 0.197808
\(490\) −3.11314e10 −0.540026
\(491\) 8.99438e10i 1.54755i −0.633459 0.773776i \(-0.718366\pi\)
0.633459 0.773776i \(-0.281634\pi\)
\(492\) 4.52131e9i 0.0771620i
\(493\) 2.15097e10i 0.364122i
\(494\) 2.23882e9 0.0375934
\(495\) 7.44075e10i 1.23936i
\(496\) −1.51747e10 −0.250722
\(497\) −5.71162e10 −0.936125
\(498\) 1.15362e9 0.0187562
\(499\) 4.06147e10i 0.655059i −0.944841 0.327530i \(-0.893784\pi\)
0.944841 0.327530i \(-0.106216\pi\)
\(500\) 1.19850e11i 1.91761i
\(501\) 4.57824e9i 0.0726688i
\(502\) 2.36577e10i 0.372527i
\(503\) 6.63800e10i 1.03697i 0.855087 + 0.518484i \(0.173503\pi\)
−0.855087 + 0.518484i \(0.826497\pi\)
\(504\) 3.65540e10 0.566517
\(505\) 6.03465e10i 0.927869i
\(506\) 1.84714e10i 0.281772i
\(507\) 9.58169e9i 0.145014i
\(508\) −1.21060e10 −0.181780
\(509\) −2.27423e10 −0.338815 −0.169408 0.985546i \(-0.554185\pi\)
−0.169408 + 0.985546i \(0.554185\pi\)
\(510\) 2.87341e9i 0.0424734i
\(511\) −3.46758e10 −0.508561
\(512\) 3.80276e10i 0.553374i
\(513\) 2.56764e10 0.370736
\(514\) −3.28947e10 −0.471274
\(515\) 3.69973e10i 0.525946i
\(516\) −6.19377e9 4.46361e9i −0.0873688 0.0629633i
\(517\) −6.70655e10 −0.938723
\(518\) 3.42368e9i 0.0475526i
\(519\) 9.74088e9i 0.134254i
\(520\) 6.85345e9 0.0937337
\(521\) 1.10812e11i 1.50396i −0.659189 0.751978i \(-0.729100\pi\)
0.659189 0.751978i \(-0.270900\pi\)
\(522\) −4.34513e10 −0.585222
\(523\) 8.07121e10i 1.07878i 0.842057 + 0.539389i \(0.181345\pi\)
−0.842057 + 0.539389i \(0.818655\pi\)
\(524\) 4.64586e10i 0.616227i
\(525\) 1.73388e10 0.228234
\(526\) 4.74965e9 0.0620467
\(527\) −2.08382e10 −0.270157
\(528\) 2.23557e9i 0.0287642i
\(529\) −2.74940e10 −0.351088
\(530\) −1.27100e11 −1.61080
\(531\) −8.90396e10 −1.11997
\(532\) 4.98193e10 0.621943
\(533\) −3.31207e9 −0.0410384
\(534\) 4.35944e9i 0.0536125i
\(535\) 2.03401e11i 2.48278i
\(536\) 7.53223e9i 0.0912567i
\(537\) 5.25509e9 0.0631950
\(538\) 2.65741e10i 0.317198i
\(539\) −3.32606e10 −0.394071
\(540\) 3.34328e10 0.393186
\(541\) 2.03972e10 0.238112 0.119056 0.992888i \(-0.462013\pi\)
0.119056 + 0.992888i \(0.462013\pi\)
\(542\) 2.16766e10i 0.251185i
\(543\) 1.16033e9i 0.0133469i
\(544\) 2.81062e10i 0.320927i
\(545\) 1.60514e11i 1.81939i
\(546\) 2.46312e8i 0.00277150i
\(547\) 1.36264e11 1.52206 0.761029 0.648718i \(-0.224695\pi\)
0.761029 + 0.648718i \(0.224695\pi\)
\(548\) 8.67902e10i 0.962384i
\(549\) 1.79123e10i 0.197180i
\(550\) 7.69511e10i 0.840938i
\(551\) −1.39225e11 −1.51046
\(552\) −9.65176e9 −0.103956
\(553\) 3.47342e10i 0.371412i
\(554\) 1.73050e10 0.183710
\(555\) 3.64151e9i 0.0383804i
\(556\) 1.10840e11 1.15984
\(557\) 1.43090e11 1.48658 0.743290 0.668970i \(-0.233264\pi\)
0.743290 + 0.668970i \(0.233264\pi\)
\(558\) 4.20947e10i 0.434201i
\(559\) 3.26980e9 4.53723e9i 0.0334868 0.0464669i
\(560\) 3.41091e10 0.346831
\(561\) 3.06993e9i 0.0309940i
\(562\) 4.82376e10i 0.483549i
\(563\) −1.55272e11 −1.54546 −0.772731 0.634734i \(-0.781110\pi\)
−0.772731 + 0.634734i \(0.781110\pi\)
\(564\) 1.49058e10i 0.147312i
\(565\) 1.03218e11 1.01289
\(566\) 5.25231e10i 0.511782i
\(567\) 6.31874e10i 0.611362i
\(568\) 1.32453e11 1.27253
\(569\) −1.98849e11 −1.89703 −0.948515 0.316732i \(-0.897414\pi\)
−0.948515 + 0.316732i \(0.897414\pi\)
\(570\) −1.85986e10 −0.176189
\(571\) 1.76753e10i 0.166273i 0.996538 + 0.0831367i \(0.0264938\pi\)
−0.996538 + 0.0831367i \(0.973506\pi\)
\(572\) 3.11451e9 0.0290941
\(573\) −2.30693e10 −0.214001
\(574\) 2.58685e10 0.238300
\(575\) 2.11701e11 1.93665
\(576\) −2.57362e10 −0.233805
\(577\) 6.20468e10i 0.559779i −0.960032 0.279889i \(-0.909702\pi\)
0.960032 0.279889i \(-0.0902978\pi\)
\(578\) 5.14075e10i 0.460591i
\(579\) 1.05704e10i 0.0940540i
\(580\) −1.81282e11 −1.60193
\(581\) 1.88051e10i 0.165033i
\(582\) 1.43773e10 0.125310
\(583\) −1.35792e11 −1.17544
\(584\) 8.04136e10 0.691318
\(585\) 1.21146e10i 0.103439i
\(586\) 7.47679e10i 0.634051i
\(587\) 1.47391e11i 1.24142i 0.784039 + 0.620712i \(0.213156\pi\)
−0.784039 + 0.620712i \(0.786844\pi\)
\(588\) 7.39239e9i 0.0618409i
\(589\) 1.34878e11i 1.12068i
\(590\) 1.30386e11 1.07602
\(591\) 1.11694e10i 0.0915544i
\(592\) 5.05925e9i 0.0411907i
\(593\) 5.54340e10i 0.448289i 0.974556 + 0.224144i \(0.0719587\pi\)
−0.974556 + 0.224144i \(0.928041\pi\)
\(594\) −1.25371e10 −0.100705
\(595\) 4.68393e10 0.373717
\(596\) 1.46620e11i 1.16201i
\(597\) 2.53565e10 0.199614
\(598\) 3.00740e9i 0.0235173i
\(599\) −1.08881e11 −0.845759 −0.422880 0.906186i \(-0.638981\pi\)
−0.422880 + 0.906186i \(0.638981\pi\)
\(600\) −4.02088e10 −0.310253
\(601\) 1.15997e10i 0.0889098i −0.999011 0.0444549i \(-0.985845\pi\)
0.999011 0.0444549i \(-0.0141551\pi\)
\(602\) −2.55384e10 + 3.54374e10i −0.194450 + 0.269821i
\(603\) −1.33144e10 −0.100705
\(604\) 3.20026e9i 0.0240457i
\(605\) 1.30776e11i 0.976124i
\(606\) 5.02959e9 0.0372943
\(607\) 1.26228e11i 0.929825i 0.885357 + 0.464912i \(0.153914\pi\)
−0.885357 + 0.464912i \(0.846086\pi\)
\(608\) −1.81921e11 −1.33128
\(609\) 1.53173e10i 0.111356i
\(610\) 2.62300e10i 0.189443i
\(611\) −1.09192e10 −0.0783475
\(612\) 3.15513e10 0.224911
\(613\) −3.92822e10 −0.278198 −0.139099 0.990278i \(-0.544421\pi\)
−0.139099 + 0.990278i \(0.544421\pi\)
\(614\) 5.05269e10i 0.355508i
\(615\) 2.75144e10 0.192335
\(616\) −5.71889e10 −0.397181
\(617\) −8.85815e10 −0.611227 −0.305613 0.952156i \(-0.598862\pi\)
−0.305613 + 0.952156i \(0.598862\pi\)
\(618\) −3.08355e9 −0.0211396
\(619\) 2.85485e11 1.94456 0.972278 0.233827i \(-0.0751249\pi\)
0.972278 + 0.233827i \(0.0751249\pi\)
\(620\) 1.75622e11i 1.18854i
\(621\) 3.44910e10i 0.231921i
\(622\) 3.30471e9i 0.0220786i
\(623\) 7.10631e10 0.471728
\(624\) 3.63981e8i 0.00240072i
\(625\) 3.62507e11 2.37572
\(626\) 6.51318e10 0.424127
\(627\) −1.98706e10 −0.128570
\(628\) 1.95879e11i 1.25936i
\(629\) 6.94746e9i 0.0443837i
\(630\) 9.46192e10i 0.600644i
\(631\) 2.01760e11i 1.27268i −0.771409 0.636339i \(-0.780448\pi\)
0.771409 0.636339i \(-0.219552\pi\)
\(632\) 8.05490e10i 0.504884i
\(633\) −2.66525e10 −0.166006
\(634\) 8.31343e10i 0.514545i
\(635\) 7.36711e10i 0.453108i
\(636\) 3.01808e10i 0.184460i
\(637\) −5.41528e9 −0.0328899
\(638\) 6.79798e10 0.410296
\(639\) 2.34132e11i 1.40429i
\(640\) −2.82331e11 −1.68282
\(641\) 2.00339e11i 1.18668i −0.804952 0.593340i \(-0.797809\pi\)
0.804952 0.593340i \(-0.202191\pi\)
\(642\) 1.69525e10 0.0997917
\(643\) −2.88308e10 −0.168660 −0.0843302 0.996438i \(-0.526875\pi\)
−0.0843302 + 0.996438i \(0.526875\pi\)
\(644\) 6.69220e10i 0.389068i
\(645\) −2.71632e10 + 3.76921e10i −0.156943 + 0.217777i
\(646\) −3.54833e10 −0.203748
\(647\) 2.38176e10i 0.135919i 0.997688 + 0.0679596i \(0.0216489\pi\)
−0.997688 + 0.0679596i \(0.978351\pi\)
\(648\) 1.46532e11i 0.831063i
\(649\) 1.39303e11 0.785202
\(650\) 1.25287e10i 0.0701863i
\(651\) 1.48391e10 0.0826197
\(652\) 1.81863e11i 1.00636i
\(653\) 4.13167e10i 0.227234i 0.993525 + 0.113617i \(0.0362437\pi\)
−0.993525 + 0.113617i \(0.963756\pi\)
\(654\) 1.33780e10 0.0731276
\(655\) 2.82723e11 1.53602
\(656\) 3.82265e10 0.206419
\(657\) 1.42144e11i 0.762898i
\(658\) 8.52829e10 0.454944
\(659\) 7.00111e10 0.371215 0.185607 0.982624i \(-0.440575\pi\)
0.185607 + 0.982624i \(0.440575\pi\)
\(660\) −2.58731e10 −0.136356
\(661\) −1.97163e11 −1.03281 −0.516403 0.856346i \(-0.672729\pi\)
−0.516403 + 0.856346i \(0.672729\pi\)
\(662\) 9.97659e9 0.0519458
\(663\) 4.99826e8i 0.00258681i
\(664\) 4.36092e10i 0.224339i
\(665\) 3.03174e11i 1.55027i
\(666\) −1.40344e10 −0.0713342
\(667\) 1.87020e11i 0.944897i
\(668\) 7.36146e10 0.369708
\(669\) 2.52876e10 0.126242
\(670\) 1.94970e10 0.0967540
\(671\) 2.80239e10i 0.138242i
\(672\) 2.00148e10i 0.0981461i
\(673\) 3.14113e11i 1.53118i 0.643331 + 0.765588i \(0.277552\pi\)
−0.643331 + 0.765588i \(0.722448\pi\)
\(674\) 6.18690e10i 0.299801i
\(675\) 1.43688e11i 0.692158i
\(676\) −1.54066e11 −0.737770
\(677\) 2.15963e11i 1.02808i 0.857767 + 0.514038i \(0.171851\pi\)
−0.857767 + 0.514038i \(0.828149\pi\)
\(678\) 8.60274e9i 0.0407116i
\(679\) 2.34364e11i 1.10258i
\(680\) −1.08621e11 −0.508017
\(681\) −4.89814e10 −0.227742
\(682\) 6.58574e10i 0.304416i
\(683\) −1.59874e11 −0.734674 −0.367337 0.930088i \(-0.619730\pi\)
−0.367337 + 0.930088i \(0.619730\pi\)
\(684\) 2.04220e11i 0.932984i
\(685\) −5.28160e11 −2.39885
\(686\) 1.15950e11 0.523571
\(687\) 4.96261e10i 0.222784i
\(688\) −3.77386e10 + 5.23667e10i −0.168435 + 0.233723i
\(689\) −2.21088e10 −0.0981046
\(690\) 2.49834e10i 0.110219i
\(691\) 3.44476e11i 1.51094i −0.655183 0.755470i \(-0.727409\pi\)
0.655183 0.755470i \(-0.272591\pi\)
\(692\) 1.56626e11 0.683029
\(693\) 1.01090e11i 0.438306i
\(694\) −5.93711e10 −0.255940
\(695\) 6.74518e11i 2.89104i
\(696\) 3.55210e10i 0.151373i
\(697\) 5.24934e10 0.222420
\(698\) 1.75943e10 0.0741225
\(699\) −5.04542e10 −0.211343
\(700\) 2.78794e11i 1.16116i
\(701\) 3.62423e10 0.150087 0.0750437 0.997180i \(-0.476090\pi\)
0.0750437 + 0.997180i \(0.476090\pi\)
\(702\) −2.04121e9 −0.00840505
\(703\) −4.49685e10 −0.184114
\(704\) 4.02644e10 0.163920
\(705\) 9.07089e10 0.367192
\(706\) 1.48589e11i 0.598092i
\(707\) 8.19871e10i 0.328147i
\(708\) 3.09610e10i 0.123220i
\(709\) −2.60959e11 −1.03273 −0.516365 0.856368i \(-0.672715\pi\)
−0.516365 + 0.856368i \(0.672715\pi\)
\(710\) 3.42852e11i 1.34919i
\(711\) −1.42383e11 −0.557160
\(712\) −1.64796e11 −0.641250
\(713\) 1.81181e11 0.701059
\(714\) 3.90383e9i 0.0150210i
\(715\) 1.89533e10i 0.0725204i
\(716\) 8.44978e10i 0.321509i
\(717\) 6.80517e10i 0.257491i
\(718\) 2.29086e11i 0.861985i
\(719\) 2.99391e11 1.12027 0.560135 0.828402i \(-0.310749\pi\)
0.560135 + 0.828402i \(0.310749\pi\)
\(720\) 1.39821e11i 0.520286i
\(721\) 5.02648e10i 0.186004i
\(722\) 9.11646e10i 0.335488i
\(723\) −6.51943e10 −0.238592
\(724\) −1.86572e10 −0.0679035
\(725\) 7.79116e11i 2.82000i
\(726\) −1.08995e10 −0.0392338
\(727\) 2.92370e11i 1.04664i 0.852138 + 0.523318i \(0.175306\pi\)
−0.852138 + 0.523318i \(0.824694\pi\)
\(728\) −9.31113e9 −0.0331495
\(729\) 2.47189e11 0.875224
\(730\) 2.08149e11i 0.732964i
\(731\) −5.18234e10 + 7.19110e10i −0.181492 + 0.251841i
\(732\) −6.22851e9 −0.0216940
\(733\) 1.93990e11i 0.671992i 0.941863 + 0.335996i \(0.109073\pi\)
−0.941863 + 0.335996i \(0.890927\pi\)
\(734\) 8.24790e10i 0.284157i
\(735\) 4.49863e10 0.154146
\(736\) 2.44374e11i 0.832806i
\(737\) 2.08305e10 0.0706040
\(738\) 1.06041e11i 0.357476i
\(739\) 3.15121e11i 1.05657i −0.849066 0.528287i \(-0.822834\pi\)
0.849066 0.528287i \(-0.177166\pi\)
\(740\) −5.85527e10 −0.195263
\(741\) −3.23520e9 −0.0107307
\(742\) 1.72678e11 0.569669
\(743\) 2.35524e11i 0.772821i 0.922327 + 0.386411i \(0.126285\pi\)
−0.922327 + 0.386411i \(0.873715\pi\)
\(744\) −3.44121e10 −0.112310
\(745\) −8.92256e11 −2.89644
\(746\) −3.04655e11 −0.983679
\(747\) 7.70862e10 0.247568
\(748\) −4.93621e10 −0.157684
\(749\) 2.76342e11i 0.878052i
\(750\) 6.07876e10i 0.192119i
\(751\) 4.32289e11i 1.35898i −0.733683 0.679492i \(-0.762200\pi\)
0.733683 0.679492i \(-0.237800\pi\)
\(752\) 1.26024e11 0.394079
\(753\) 3.41865e10i 0.106335i
\(754\) 1.10680e10 0.0342440
\(755\) −1.94751e10 −0.0599366
\(756\) −4.54220e10 −0.139053
\(757\) 1.51060e11i 0.460007i 0.973190 + 0.230004i \(0.0738738\pi\)
−0.973190 + 0.230004i \(0.926126\pi\)
\(758\) 1.51539e11i 0.459037i
\(759\) 2.66921e10i 0.0804294i
\(760\) 7.03065e11i 2.10737i
\(761\) 1.99597e11i 0.595135i −0.954701 0.297568i \(-0.903825\pi\)
0.954701 0.297568i \(-0.0961754\pi\)
\(762\) −6.14012e9 −0.0182120
\(763\) 2.18075e11i 0.643439i
\(764\) 3.70937e11i 1.08875i
\(765\) 1.92005e11i 0.560617i
\(766\) −2.60674e11 −0.757150
\(767\) 2.26804e10 0.0655344
\(768\) 3.56210e10i 0.102391i
\(769\) 2.01782e11 0.577002 0.288501 0.957480i \(-0.406843\pi\)
0.288501 + 0.957480i \(0.406843\pi\)
\(770\) 1.48032e11i 0.421108i
\(771\) 4.75343e10 0.134521
\(772\) 1.69964e11 0.478506
\(773\) 2.36295e11i 0.661816i −0.943663 0.330908i \(-0.892645\pi\)
0.943663 0.330908i \(-0.107355\pi\)
\(774\) 1.45266e11 + 1.04687e11i 0.404762 + 0.291696i
\(775\) 7.54792e11 2.09228
\(776\) 5.43493e11i 1.49881i
\(777\) 4.94737e9i 0.0135735i
\(778\) −8.32403e10 −0.227204
\(779\) 3.39771e11i 0.922648i
\(780\) −4.21250e9 −0.0113805
\(781\) 3.66301e11i 0.984541i
\(782\)