Properties

Label 177.9.c.a.58.18
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.18
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.63

$q$-expansion

\(f(q)\) \(=\) \(q-20.4085i q^{2} -46.7654 q^{3} -160.507 q^{4} -745.364 q^{5} +954.411i q^{6} -9.58116 q^{7} -1948.88i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-20.4085i q^{2} -46.7654 q^{3} -160.507 q^{4} -745.364 q^{5} +954.411i q^{6} -9.58116 q^{7} -1948.88i q^{8} +2187.00 q^{9} +15211.8i q^{10} -18868.6i q^{11} +7506.15 q^{12} -7491.72i q^{13} +195.537i q^{14} +34857.2 q^{15} -80863.3 q^{16} -51296.7 q^{17} -44633.4i q^{18} -247403. q^{19} +119636. q^{20} +448.067 q^{21} -385080. q^{22} +518429. i q^{23} +91139.9i q^{24} +164942. q^{25} -152895. q^{26} -102276. q^{27} +1537.84 q^{28} -610858. q^{29} -711383. i q^{30} -514584. i q^{31} +1.15139e6i q^{32} +882397. i q^{33} +1.04689e6i q^{34} +7141.45 q^{35} -351028. q^{36} -3.23289e6i q^{37} +5.04913e6i q^{38} +350353. i q^{39} +1.45262e6i q^{40} -208023. q^{41} -9144.36i q^{42} -1.29880e6i q^{43} +3.02854e6i q^{44} -1.63011e6 q^{45} +1.05804e7 q^{46} -676594. i q^{47} +3.78160e6 q^{48} -5.76471e6 q^{49} -3.36622e6i q^{50} +2.39891e6 q^{51} +1.20247e6i q^{52} +9.26736e6 q^{53} +2.08730e6i q^{54} +1.40640e7i q^{55} +18672.5i q^{56} +1.15699e7 q^{57} +1.24667e7i q^{58} +(1.13610e7 + 4.21401e6i) q^{59} -5.59482e6 q^{60} -2.59096e6i q^{61} -1.05019e7 q^{62} -20954.0 q^{63} +2.79706e6 q^{64} +5.58406e6i q^{65} +1.80084e7 q^{66} -1.85490e7i q^{67} +8.23346e6 q^{68} -2.42445e7i q^{69} -145746. i q^{70} -1.90851e6 q^{71} -4.26219e6i q^{72} +3.02899e7i q^{73} -6.59784e7 q^{74} -7.71359e6 q^{75} +3.97099e7 q^{76} +180783. i q^{77} +7.15018e6 q^{78} +4.69983e7 q^{79} +6.02726e7 q^{80} +4.78297e6 q^{81} +4.24543e6i q^{82} +1.76048e7i q^{83} -71917.7 q^{84} +3.82347e7 q^{85} -2.65065e7 q^{86} +2.85670e7 q^{87} -3.67726e7 q^{88} +4.02754e7i q^{89} +3.32681e7i q^{90} +71779.4i q^{91} -8.32113e7i q^{92} +2.40647e7i q^{93} -1.38083e7 q^{94} +1.84405e8 q^{95} -5.38450e7i q^{96} -1.49120e7i q^{97} +1.17649e8i q^{98} -4.12656e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.4085i 1.27553i −0.770231 0.637765i \(-0.779859\pi\)
0.770231 0.637765i \(-0.220141\pi\)
\(3\) −46.7654 −0.577350
\(4\) −160.507 −0.626979
\(5\) −745.364 −1.19258 −0.596291 0.802768i \(-0.703360\pi\)
−0.596291 + 0.802768i \(0.703360\pi\)
\(6\) 954.411i 0.736428i
\(7\) −9.58116 −0.00399049 −0.00199524 0.999998i \(-0.500635\pi\)
−0.00199524 + 0.999998i \(0.500635\pi\)
\(8\) 1948.88i 0.475800i
\(9\) 2187.00 0.333333
\(10\) 15211.8i 1.52118i
\(11\) 18868.6i 1.28875i −0.764709 0.644375i \(-0.777117\pi\)
0.764709 0.644375i \(-0.222883\pi\)
\(12\) 7506.15 0.361987
\(13\) 7491.72i 0.262306i −0.991362 0.131153i \(-0.958132\pi\)
0.991362 0.131153i \(-0.0418679\pi\)
\(14\) 195.537i 0.00508999i
\(15\) 34857.2 0.688538
\(16\) −80863.3 −1.23388
\(17\) −51296.7 −0.614177 −0.307089 0.951681i \(-0.599355\pi\)
−0.307089 + 0.951681i \(0.599355\pi\)
\(18\) 44633.4i 0.425177i
\(19\) −247403. −1.89841 −0.949207 0.314652i \(-0.898112\pi\)
−0.949207 + 0.314652i \(0.898112\pi\)
\(20\) 119636. 0.747724
\(21\) 448.067 0.00230391
\(22\) −385080. −1.64384
\(23\) 518429.i 1.85258i 0.376807 + 0.926292i \(0.377022\pi\)
−0.376807 + 0.926292i \(0.622978\pi\)
\(24\) 91139.9i 0.274703i
\(25\) 164942. 0.422252
\(26\) −152895. −0.334579
\(27\) −102276. −0.192450
\(28\) 1537.84 0.00250195
\(29\) −610858. −0.863670 −0.431835 0.901953i \(-0.642134\pi\)
−0.431835 + 0.901953i \(0.642134\pi\)
\(30\) 711383.i 0.878251i
\(31\) 514584.i 0.557198i −0.960408 0.278599i \(-0.910130\pi\)
0.960408 0.278599i \(-0.0898700\pi\)
\(32\) 1.15139e6i 1.09805i
\(33\) 882397.i 0.744061i
\(34\) 1.04689e6i 0.783402i
\(35\) 7141.45 0.00475898
\(36\) −351028. −0.208993
\(37\) 3.23289e6i 1.72498i −0.506075 0.862489i \(-0.668904\pi\)
0.506075 0.862489i \(-0.331096\pi\)
\(38\) 5.04913e6i 2.42149i
\(39\) 350353.i 0.151442i
\(40\) 1.45262e6i 0.567430i
\(41\) −208023. −0.0736165 −0.0368083 0.999322i \(-0.511719\pi\)
−0.0368083 + 0.999322i \(0.511719\pi\)
\(42\) 9144.36i 0.00293871i
\(43\) 1.29880e6i 0.379898i −0.981794 0.189949i \(-0.939168\pi\)
0.981794 0.189949i \(-0.0608323\pi\)
\(44\) 3.02854e6i 0.808020i
\(45\) −1.63011e6 −0.397527
\(46\) 1.05804e7 2.36303
\(47\) 676594.i 0.138655i −0.997594 0.0693276i \(-0.977915\pi\)
0.997594 0.0693276i \(-0.0220854\pi\)
\(48\) 3.78160e6 0.712379
\(49\) −5.76471e6 −0.999984
\(50\) 3.36622e6i 0.538596i
\(51\) 2.39891e6 0.354595
\(52\) 1.20247e6i 0.164460i
\(53\) 9.26736e6 1.17450 0.587249 0.809406i \(-0.300211\pi\)
0.587249 + 0.809406i \(0.300211\pi\)
\(54\) 2.08730e6i 0.245476i
\(55\) 1.40640e7i 1.53694i
\(56\) 18672.5i 0.00189867i
\(57\) 1.15699e7 1.09605
\(58\) 1.24667e7i 1.10164i
\(59\) 1.13610e7 + 4.21401e6i 0.937581 + 0.347766i
\(60\) −5.59482e6 −0.431699
\(61\) 2.59096e6i 0.187129i −0.995613 0.0935647i \(-0.970174\pi\)
0.995613 0.0935647i \(-0.0298262\pi\)
\(62\) −1.05019e7 −0.710723
\(63\) −20954.0 −0.00133016
\(64\) 2.79706e6 0.166718
\(65\) 5.58406e6i 0.312821i
\(66\) 1.80084e7 0.949072
\(67\) 1.85490e7i 0.920493i −0.887791 0.460247i \(-0.847761\pi\)
0.887791 0.460247i \(-0.152239\pi\)
\(68\) 8.23346e6 0.385076
\(69\) 2.42445e7i 1.06959i
\(70\) 145746.i 0.00607023i
\(71\) −1.90851e6 −0.0751038 −0.0375519 0.999295i \(-0.511956\pi\)
−0.0375519 + 0.999295i \(0.511956\pi\)
\(72\) 4.26219e6i 0.158600i
\(73\) 3.02899e7i 1.06661i 0.845922 + 0.533306i \(0.179051\pi\)
−0.845922 + 0.533306i \(0.820949\pi\)
\(74\) −6.59784e7 −2.20026
\(75\) −7.71359e6 −0.243787
\(76\) 3.97099e7 1.19027
\(77\) 180783.i 0.00514274i
\(78\) 7.15018e6 0.193169
\(79\) 4.69983e7 1.20663 0.603315 0.797503i \(-0.293846\pi\)
0.603315 + 0.797503i \(0.293846\pi\)
\(80\) 6.02726e7 1.47150
\(81\) 4.78297e6 0.111111
\(82\) 4.24543e6i 0.0939001i
\(83\) 1.76048e7i 0.370953i 0.982649 + 0.185477i \(0.0593829\pi\)
−0.982649 + 0.185477i \(0.940617\pi\)
\(84\) −71917.7 −0.00144450
\(85\) 3.82347e7 0.732457
\(86\) −2.65065e7 −0.484572
\(87\) 2.85670e7 0.498640
\(88\) −3.67726e7 −0.613187
\(89\) 4.02754e7i 0.641919i 0.947093 + 0.320959i \(0.104005\pi\)
−0.947093 + 0.320959i \(0.895995\pi\)
\(90\) 3.32681e7i 0.507058i
\(91\) 71779.4i 0.00104673i
\(92\) 8.32113e7i 1.16153i
\(93\) 2.40647e7i 0.321698i
\(94\) −1.38083e7 −0.176859
\(95\) 1.84405e8 2.26402
\(96\) 5.38450e7i 0.633958i
\(97\) 1.49120e7i 0.168441i −0.996447 0.0842205i \(-0.973160\pi\)
0.996447 0.0842205i \(-0.0268400\pi\)
\(98\) 1.17649e8i 1.27551i
\(99\) 4.12656e7i 0.429584i
\(100\) −2.64743e7 −0.264743
\(101\) 6.64302e7i 0.638381i −0.947691 0.319190i \(-0.896589\pi\)
0.947691 0.319190i \(-0.103411\pi\)
\(102\) 4.89581e7i 0.452297i
\(103\) 4.90921e7i 0.436177i 0.975929 + 0.218089i \(0.0699821\pi\)
−0.975929 + 0.218089i \(0.930018\pi\)
\(104\) −1.46004e7 −0.124805
\(105\) −333973. −0.00274760
\(106\) 1.89133e8i 1.49811i
\(107\) −6.05131e7 −0.461652 −0.230826 0.972995i \(-0.574143\pi\)
−0.230826 + 0.972995i \(0.574143\pi\)
\(108\) 1.64160e7 0.120662
\(109\) 1.84365e8i 1.30609i −0.757319 0.653045i \(-0.773491\pi\)
0.757319 0.653045i \(-0.226509\pi\)
\(110\) 2.87025e8 1.96042
\(111\) 1.51187e8i 0.995917i
\(112\) 774764. 0.00492377
\(113\) 6.09578e7i 0.373866i −0.982373 0.186933i \(-0.940145\pi\)
0.982373 0.186933i \(-0.0598547\pi\)
\(114\) 2.36124e8i 1.39805i
\(115\) 3.86418e8i 2.20936i
\(116\) 9.80467e7 0.541503
\(117\) 1.63844e7i 0.0874353i
\(118\) 8.60015e7 2.31861e8i 0.443586 1.19591i
\(119\) 491482. 0.00245087
\(120\) 6.79324e7i 0.327606i
\(121\) −1.41665e8 −0.660879
\(122\) −5.28777e7 −0.238689
\(123\) 9.72826e6 0.0425025
\(124\) 8.25942e7i 0.349351i
\(125\) 1.68216e8 0.689012
\(126\) 427640.i 0.00169666i
\(127\) −2.19348e8 −0.843178 −0.421589 0.906787i \(-0.638528\pi\)
−0.421589 + 0.906787i \(0.638528\pi\)
\(128\) 2.37671e8i 0.885394i
\(129\) 6.07387e7i 0.219334i
\(130\) 1.13962e8 0.399013
\(131\) 2.41637e8i 0.820498i −0.911973 0.410249i \(-0.865442\pi\)
0.911973 0.410249i \(-0.134558\pi\)
\(132\) 1.41631e8i 0.466511i
\(133\) 2.37041e6 0.00757560
\(134\) −3.78557e8 −1.17412
\(135\) 7.62327e7 0.229513
\(136\) 9.99709e7i 0.292225i
\(137\) 5.38039e8 1.52733 0.763663 0.645615i \(-0.223399\pi\)
0.763663 + 0.645615i \(0.223399\pi\)
\(138\) −4.94794e8 −1.36429
\(139\) 4.35719e8 1.16720 0.583602 0.812040i \(-0.301643\pi\)
0.583602 + 0.812040i \(0.301643\pi\)
\(140\) −1.14625e6 −0.00298378
\(141\) 3.16411e7i 0.0800527i
\(142\) 3.89499e7i 0.0957973i
\(143\) −1.41358e8 −0.338047
\(144\) −1.76848e8 −0.411292
\(145\) 4.55311e8 1.03000
\(146\) 6.18172e8 1.36050
\(147\) 2.69589e8 0.577341
\(148\) 5.18900e8i 1.08153i
\(149\) 3.83709e8i 0.778496i 0.921133 + 0.389248i \(0.127265\pi\)
−0.921133 + 0.389248i \(0.872735\pi\)
\(150\) 1.57423e8i 0.310958i
\(151\) 4.20489e8i 0.808811i −0.914580 0.404405i \(-0.867479\pi\)
0.914580 0.404405i \(-0.132521\pi\)
\(152\) 4.82158e8i 0.903265i
\(153\) −1.12186e8 −0.204726
\(154\) 3.68951e6 0.00655973
\(155\) 3.83552e8i 0.664504i
\(156\) 5.62340e7i 0.0949512i
\(157\) 6.63546e8i 1.09213i 0.837744 + 0.546063i \(0.183874\pi\)
−0.837744 + 0.546063i \(0.816126\pi\)
\(158\) 9.59165e8i 1.53909i
\(159\) −4.33391e8 −0.678097
\(160\) 8.58202e8i 1.30951i
\(161\) 4.96715e6i 0.00739271i
\(162\) 9.76132e7i 0.141726i
\(163\) −1.11230e9 −1.57569 −0.787844 0.615875i \(-0.788803\pi\)
−0.787844 + 0.615875i \(0.788803\pi\)
\(164\) 3.33890e7 0.0461560
\(165\) 6.57707e8i 0.887354i
\(166\) 3.59288e8 0.473162
\(167\) 1.07732e9 1.38509 0.692545 0.721375i \(-0.256490\pi\)
0.692545 + 0.721375i \(0.256490\pi\)
\(168\) 873226.i 0.00109620i
\(169\) 7.59605e8 0.931196
\(170\) 7.80313e8i 0.934271i
\(171\) −5.41071e8 −0.632805
\(172\) 2.08466e8i 0.238188i
\(173\) 1.16285e9i 1.29819i 0.760708 + 0.649094i \(0.224852\pi\)
−0.760708 + 0.649094i \(0.775148\pi\)
\(174\) 5.83009e8i 0.636031i
\(175\) −1.58034e6 −0.00168499
\(176\) 1.52578e9i 1.59016i
\(177\) −5.31302e8 1.97070e8i −0.541313 0.200783i
\(178\) 8.21961e8 0.818787
\(179\) 2.40794e8i 0.234549i −0.993100 0.117275i \(-0.962584\pi\)
0.993100 0.117275i \(-0.0374158\pi\)
\(180\) 2.61644e8 0.249241
\(181\) 2.27371e8 0.211846 0.105923 0.994374i \(-0.466220\pi\)
0.105923 + 0.994374i \(0.466220\pi\)
\(182\) 1.46491e6 0.00133513
\(183\) 1.21167e8i 0.108039i
\(184\) 1.01035e9 0.881458
\(185\) 2.40968e9i 2.05718i
\(186\) 4.91125e8 0.410336
\(187\) 9.67897e8i 0.791521i
\(188\) 1.08598e8i 0.0869340i
\(189\) 979921. 0.000767970
\(190\) 3.76344e9i 2.88782i
\(191\) 2.24021e9i 1.68328i 0.540041 + 0.841639i \(0.318409\pi\)
−0.540041 + 0.841639i \(0.681591\pi\)
\(192\) −1.30805e8 −0.0962545
\(193\) 1.85555e9 1.33735 0.668673 0.743557i \(-0.266863\pi\)
0.668673 + 0.743557i \(0.266863\pi\)
\(194\) −3.04331e8 −0.214852
\(195\) 2.61141e8i 0.180608i
\(196\) 9.25274e8 0.626969
\(197\) −1.47257e9 −0.977711 −0.488856 0.872365i \(-0.662586\pi\)
−0.488856 + 0.872365i \(0.662586\pi\)
\(198\) −8.42169e8 −0.547947
\(199\) −2.12427e9 −1.35456 −0.677280 0.735725i \(-0.736841\pi\)
−0.677280 + 0.735725i \(0.736841\pi\)
\(200\) 3.21452e8i 0.200907i
\(201\) 8.67450e8i 0.531447i
\(202\) −1.35574e9 −0.814275
\(203\) 5.85272e6 0.00344647
\(204\) −3.85041e8 −0.222324
\(205\) 1.55053e8 0.0877937
\(206\) 1.00190e9 0.556357
\(207\) 1.13380e9i 0.617528i
\(208\) 6.05805e8i 0.323653i
\(209\) 4.66815e9i 2.44658i
\(210\) 6.81588e6i 0.00350465i
\(211\) 9.65517e8i 0.487113i 0.969887 + 0.243557i \(0.0783142\pi\)
−0.969887 + 0.243557i \(0.921686\pi\)
\(212\) −1.48747e9 −0.736386
\(213\) 8.92524e7 0.0433612
\(214\) 1.23498e9i 0.588851i
\(215\) 9.68076e8i 0.453060i
\(216\) 1.99323e8i 0.0915677i
\(217\) 4.93031e6i 0.00222349i
\(218\) −3.76262e9 −1.66596
\(219\) 1.41652e9i 0.615809i
\(220\) 2.25736e9i 0.963630i
\(221\) 3.84301e8i 0.161102i
\(222\) 3.08550e9 1.27032
\(223\) −7.11385e8 −0.287664 −0.143832 0.989602i \(-0.545942\pi\)
−0.143832 + 0.989602i \(0.545942\pi\)
\(224\) 1.10316e7i 0.00438175i
\(225\) 3.60729e8 0.140751
\(226\) −1.24406e9 −0.476877
\(227\) 3.41826e9i 1.28736i −0.765293 0.643682i \(-0.777406\pi\)
0.765293 0.643682i \(-0.222594\pi\)
\(228\) −1.85705e9 −0.687201
\(229\) 3.98469e9i 1.44895i −0.689302 0.724474i \(-0.742083\pi\)
0.689302 0.724474i \(-0.257917\pi\)
\(230\) −7.88621e9 −2.81810
\(231\) 8.45439e6i 0.00296916i
\(232\) 1.19049e9i 0.410934i
\(233\) 1.78068e9i 0.604173i −0.953281 0.302086i \(-0.902317\pi\)
0.953281 0.302086i \(-0.0976831\pi\)
\(234\) −3.34381e8 −0.111526
\(235\) 5.04308e8i 0.165358i
\(236\) −1.82352e9 6.76376e8i −0.587844 0.218042i
\(237\) −2.19789e9 −0.696648
\(238\) 1.00304e7i 0.00312616i
\(239\) 2.78608e9 0.853889 0.426944 0.904278i \(-0.359590\pi\)
0.426944 + 0.904278i \(0.359590\pi\)
\(240\) −2.81867e9 −0.849570
\(241\) −5.34206e9 −1.58358 −0.791791 0.610792i \(-0.790851\pi\)
−0.791791 + 0.610792i \(0.790851\pi\)
\(242\) 2.89118e9i 0.842972i
\(243\) −2.23677e8 −0.0641500
\(244\) 4.15867e8i 0.117326i
\(245\) 4.29681e9 1.19256
\(246\) 1.98539e8i 0.0542133i
\(247\) 1.85348e9i 0.497965i
\(248\) −1.00286e9 −0.265115
\(249\) 8.23296e8i 0.214170i
\(250\) 3.43303e9i 0.878856i
\(251\) −1.54496e9 −0.389245 −0.194623 0.980878i \(-0.562348\pi\)
−0.194623 + 0.980878i \(0.562348\pi\)
\(252\) 3.36326e6 0.000833984
\(253\) 9.78203e9 2.38752
\(254\) 4.47657e9i 1.07550i
\(255\) −1.78806e9 −0.422884
\(256\) 5.56656e9 1.29607
\(257\) −4.83589e9 −1.10852 −0.554260 0.832343i \(-0.686999\pi\)
−0.554260 + 0.832343i \(0.686999\pi\)
\(258\) 1.23959e9 0.279768
\(259\) 3.09748e7i 0.00688351i
\(260\) 8.96279e8i 0.196133i
\(261\) −1.33595e9 −0.287890
\(262\) −4.93144e9 −1.04657
\(263\) −2.71747e9 −0.567991 −0.283996 0.958826i \(-0.591660\pi\)
−0.283996 + 0.958826i \(0.591660\pi\)
\(264\) 1.71968e9 0.354024
\(265\) −6.90755e9 −1.40069
\(266\) 4.83765e7i 0.00966291i
\(267\) 1.88349e9i 0.370612i
\(268\) 2.97723e9i 0.577130i
\(269\) 2.89769e9i 0.553405i −0.960956 0.276703i \(-0.910758\pi\)
0.960956 0.276703i \(-0.0892417\pi\)
\(270\) 1.55580e9i 0.292750i
\(271\) 9.35608e8 0.173467 0.0867335 0.996232i \(-0.472357\pi\)
0.0867335 + 0.996232i \(0.472357\pi\)
\(272\) 4.14802e9 0.757819
\(273\) 3.35679e6i 0.000604329i
\(274\) 1.09806e10i 1.94815i
\(275\) 3.11223e9i 0.544178i
\(276\) 3.89141e9i 0.670610i
\(277\) 7.02822e9 1.19379 0.596893 0.802321i \(-0.296402\pi\)
0.596893 + 0.802321i \(0.296402\pi\)
\(278\) 8.89236e9i 1.48881i
\(279\) 1.12540e9i 0.185733i
\(280\) 1.39178e7i 0.00226432i
\(281\) −6.80104e9 −1.09081 −0.545406 0.838172i \(-0.683625\pi\)
−0.545406 + 0.838172i \(0.683625\pi\)
\(282\) 6.45748e8 0.102110
\(283\) 1.19844e10i 1.86840i 0.356748 + 0.934201i \(0.383886\pi\)
−0.356748 + 0.934201i \(0.616114\pi\)
\(284\) 3.06329e8 0.0470885
\(285\) −8.62379e9 −1.30713
\(286\) 2.88491e9i 0.431189i
\(287\) 1.99310e6 0.000293766
\(288\) 2.51808e9i 0.366016i
\(289\) −4.34441e9 −0.622786
\(290\) 9.29221e9i 1.31379i
\(291\) 6.97364e8i 0.0972495i
\(292\) 4.86173e9i 0.668744i
\(293\) −4.51579e9 −0.612722 −0.306361 0.951915i \(-0.599111\pi\)
−0.306361 + 0.951915i \(0.599111\pi\)
\(294\) 5.50190e9i 0.736416i
\(295\) −8.46809e9 3.14097e9i −1.11814 0.414740i
\(296\) −6.30050e9 −0.820744
\(297\) 1.92980e9i 0.248020i
\(298\) 7.83091e9 0.992996
\(299\) 3.88392e9 0.485944
\(300\) 1.23808e9 0.152850
\(301\) 1.24440e7i 0.00151598i
\(302\) −8.58155e9 −1.03166
\(303\) 3.10663e9i 0.368569i
\(304\) 2.00058e10 2.34241
\(305\) 1.93121e9i 0.223167i
\(306\) 2.28954e9i 0.261134i
\(307\) −1.32798e9 −0.149499 −0.0747493 0.997202i \(-0.523816\pi\)
−0.0747493 + 0.997202i \(0.523816\pi\)
\(308\) 2.90169e7i 0.00322439i
\(309\) 2.29581e9i 0.251827i
\(310\) 7.82773e9 0.847596
\(311\) 8.76178e9 0.936592 0.468296 0.883572i \(-0.344868\pi\)
0.468296 + 0.883572i \(0.344868\pi\)
\(312\) 6.82794e8 0.0720562
\(313\) 9.86985e9i 1.02833i −0.857691 0.514166i \(-0.828102\pi\)
0.857691 0.514166i \(-0.171898\pi\)
\(314\) 1.35420e10 1.39304
\(315\) 1.56184e7 0.00158633
\(316\) −7.54354e9 −0.756532
\(317\) 1.42367e10 1.40985 0.704923 0.709283i \(-0.250981\pi\)
0.704923 + 0.709283i \(0.250981\pi\)
\(318\) 8.84486e9i 0.864934i
\(319\) 1.15260e10i 1.11306i
\(320\) −2.08483e9 −0.198824
\(321\) 2.82992e9 0.266535
\(322\) −1.01372e8 −0.00942963
\(323\) 1.26910e10 1.16596
\(324\) −7.67698e8 −0.0696644
\(325\) 1.23570e9i 0.110759i
\(326\) 2.27003e10i 2.00984i
\(327\) 8.62191e9i 0.754071i
\(328\) 4.05410e8i 0.0350267i
\(329\) 6.48255e6i 0.000553302i
\(330\) −1.34228e10 −1.13185
\(331\) 4.64201e8 0.0386718 0.0193359 0.999813i \(-0.493845\pi\)
0.0193359 + 0.999813i \(0.493845\pi\)
\(332\) 2.82569e9i 0.232580i
\(333\) 7.07033e9i 0.574993i
\(334\) 2.19864e10i 1.76672i
\(335\) 1.38257e10i 1.09776i
\(336\) −3.62321e7 −0.00284274
\(337\) 2.28503e10i 1.77162i 0.464044 + 0.885812i \(0.346398\pi\)
−0.464044 + 0.885812i \(0.653602\pi\)
\(338\) 1.55024e10i 1.18777i
\(339\) 2.85071e9i 0.215851i
\(340\) −6.13692e9 −0.459235
\(341\) −9.70948e9 −0.718089
\(342\) 1.10424e10i 0.807162i
\(343\) 1.10466e8 0.00798091
\(344\) −2.53119e9 −0.180755
\(345\) 1.80710e10i 1.27557i
\(346\) 2.37319e10 1.65588
\(347\) 3.93570e9i 0.271459i −0.990746 0.135729i \(-0.956662\pi\)
0.990746 0.135729i \(-0.0433377\pi\)
\(348\) −4.58519e9 −0.312637
\(349\) 1.21596e10i 0.819627i 0.912169 + 0.409814i \(0.134406\pi\)
−0.912169 + 0.409814i \(0.865594\pi\)
\(350\) 3.22523e7i 0.00214926i
\(351\) 7.66222e8i 0.0504808i
\(352\) 2.17251e10 1.41511
\(353\) 2.82640e8i 0.0182027i −0.999959 0.00910133i \(-0.997103\pi\)
0.999959 0.00910133i \(-0.00289708\pi\)
\(354\) −4.02189e9 + 1.08431e10i −0.256105 + 0.690461i
\(355\) 1.42254e9 0.0895675
\(356\) 6.46447e9i 0.402470i
\(357\) −2.29843e7 −0.00141501
\(358\) −4.91425e9 −0.299175
\(359\) −2.95778e10 −1.78069 −0.890345 0.455286i \(-0.849537\pi\)
−0.890345 + 0.455286i \(0.849537\pi\)
\(360\) 3.17688e9i 0.189143i
\(361\) 4.42248e10 2.60398
\(362\) 4.64029e9i 0.270216i
\(363\) 6.62503e9 0.381559
\(364\) 1.15211e7i 0.000656277i
\(365\) 2.25770e10i 1.27202i
\(366\) 2.47284e9 0.137807
\(367\) 2.17893e9i 0.120110i −0.998195 0.0600549i \(-0.980872\pi\)
0.998195 0.0600549i \(-0.0191276\pi\)
\(368\) 4.19219e10i 2.28586i
\(369\) −4.54946e8 −0.0245388
\(370\) 4.91779e10 2.62400
\(371\) −8.87920e7 −0.00468682
\(372\) 3.86255e9i 0.201698i
\(373\) 1.38820e10 0.717162 0.358581 0.933499i \(-0.383261\pi\)
0.358581 + 0.933499i \(0.383261\pi\)
\(374\) 1.97533e10 1.00961
\(375\) −7.86667e9 −0.397801
\(376\) −1.31860e9 −0.0659721
\(377\) 4.57637e9i 0.226546i
\(378\) 1.99987e7i 0.000979569i
\(379\) −3.68929e10 −1.78808 −0.894038 0.447992i \(-0.852139\pi\)
−0.894038 + 0.447992i \(0.852139\pi\)
\(380\) −2.95983e10 −1.41949
\(381\) 1.02579e10 0.486809
\(382\) 4.57194e10 2.14707
\(383\) 2.01201e10 0.935051 0.467525 0.883980i \(-0.345146\pi\)
0.467525 + 0.883980i \(0.345146\pi\)
\(384\) 1.11148e10i 0.511183i
\(385\) 1.34749e8i 0.00613314i
\(386\) 3.78690e10i 1.70583i
\(387\) 2.84047e9i 0.126633i
\(388\) 2.39347e9i 0.105609i
\(389\) 3.43685e9 0.150094 0.0750468 0.997180i \(-0.476089\pi\)
0.0750468 + 0.997180i \(0.476089\pi\)
\(390\) −5.32949e9 −0.230370
\(391\) 2.65937e10i 1.13781i
\(392\) 1.12347e10i 0.475792i
\(393\) 1.13002e10i 0.473715i
\(394\) 3.00529e10i 1.24710i
\(395\) −3.50308e10 −1.43900
\(396\) 6.62341e9i 0.269340i
\(397\) 1.45748e10i 0.586735i −0.956000 0.293367i \(-0.905224\pi\)
0.956000 0.293367i \(-0.0947759\pi\)
\(398\) 4.33532e10i 1.72778i
\(399\) −1.10853e8 −0.00437377
\(400\) −1.33378e10 −0.521007
\(401\) 1.18427e10i 0.458007i 0.973426 + 0.229004i \(0.0735468\pi\)
−0.973426 + 0.229004i \(0.926453\pi\)
\(402\) 1.77033e10 0.677877
\(403\) −3.85512e9 −0.146156
\(404\) 1.06625e10i 0.400252i
\(405\) −3.56505e9 −0.132509
\(406\) 1.19445e8i 0.00439607i
\(407\) −6.10001e10 −2.22307
\(408\) 4.67517e9i 0.168716i
\(409\) 4.23668e10i 1.51402i 0.653402 + 0.757011i \(0.273341\pi\)
−0.653402 + 0.757011i \(0.726659\pi\)
\(410\) 3.16439e9i 0.111984i
\(411\) −2.51616e10 −0.881802
\(412\) 7.87961e9i 0.273474i
\(413\) −1.08852e8 4.03751e7i −0.00374141 0.00138776i
\(414\) 2.31392e10 0.787676
\(415\) 1.31220e10i 0.442392i
\(416\) 8.62587e9 0.288024
\(417\) −2.03765e10 −0.673886
\(418\) 9.52700e10 3.12069
\(419\) 4.74282e10i 1.53880i 0.638770 + 0.769398i \(0.279444\pi\)
−0.638770 + 0.769398i \(0.720556\pi\)
\(420\) 5.36048e7 0.00172269
\(421\) 3.98015e10i 1.26698i −0.773750 0.633492i \(-0.781621\pi\)
0.773750 0.633492i \(-0.218379\pi\)
\(422\) 1.97047e10 0.621328
\(423\) 1.47971e9i 0.0462184i
\(424\) 1.80609e10i 0.558826i
\(425\) −8.46099e9 −0.259338
\(426\) 1.82151e9i 0.0553086i
\(427\) 2.48244e7i 0.000746737i
\(428\) 9.71276e9 0.289446
\(429\) 6.61067e9 0.195172
\(430\) 1.97570e10 0.577892
\(431\) 8.98991e9i 0.260523i 0.991480 + 0.130262i \(0.0415817\pi\)
−0.991480 + 0.130262i \(0.958418\pi\)
\(432\) 8.27037e9 0.237460
\(433\) −3.14066e10 −0.893447 −0.446724 0.894672i \(-0.647409\pi\)
−0.446724 + 0.894672i \(0.647409\pi\)
\(434\) 1.00620e8 0.00283613
\(435\) −2.12928e10 −0.594669
\(436\) 2.95918e10i 0.818891i
\(437\) 1.28261e11i 3.51697i
\(438\) −2.89090e10 −0.785483
\(439\) 2.85002e10 0.767342 0.383671 0.923470i \(-0.374660\pi\)
0.383671 + 0.923470i \(0.374660\pi\)
\(440\) 2.74089e10 0.731276
\(441\) −1.26074e10 −0.333328
\(442\) 7.84300e9 0.205491
\(443\) 9.12836e9i 0.237016i −0.992953 0.118508i \(-0.962189\pi\)
0.992953 0.118508i \(-0.0378112\pi\)
\(444\) 2.42666e10i 0.624419i
\(445\) 3.00198e10i 0.765541i
\(446\) 1.45183e10i 0.366924i
\(447\) 1.79443e10i 0.449465i
\(448\) −2.67991e7 −0.000665284
\(449\) −5.59798e10 −1.37736 −0.688678 0.725068i \(-0.741808\pi\)
−0.688678 + 0.725068i \(0.741808\pi\)
\(450\) 7.36193e9i 0.179532i
\(451\) 3.92510e9i 0.0948733i
\(452\) 9.78413e9i 0.234406i
\(453\) 1.96643e10i 0.466967i
\(454\) −6.97615e10 −1.64207
\(455\) 5.35018e7i 0.00124831i
\(456\) 2.25483e10i 0.521500i
\(457\) 8.40061e10i 1.92596i −0.269581 0.962978i \(-0.586885\pi\)
0.269581 0.962978i \(-0.413115\pi\)
\(458\) −8.13216e10 −1.84818
\(459\) 5.24641e9 0.118198
\(460\) 6.20227e10i 1.38522i
\(461\) −1.23474e10 −0.273383 −0.136691 0.990614i \(-0.543647\pi\)
−0.136691 + 0.990614i \(0.543647\pi\)
\(462\) −1.72541e8 −0.00378726
\(463\) 7.27727e10i 1.58360i −0.610782 0.791799i \(-0.709145\pi\)
0.610782 0.791799i \(-0.290855\pi\)
\(464\) 4.93960e10 1.06566
\(465\) 1.79370e10i 0.383652i
\(466\) −3.63409e10 −0.770641
\(467\) 4.37284e10i 0.919382i 0.888079 + 0.459691i \(0.152040\pi\)
−0.888079 + 0.459691i \(0.847960\pi\)
\(468\) 2.62980e9i 0.0548201i
\(469\) 1.77721e8i 0.00367322i
\(470\) 1.02922e10 0.210919
\(471\) 3.10310e10i 0.630539i
\(472\) 8.21257e9 2.21412e10i 0.165467 0.446101i
\(473\) −2.45065e10 −0.489594
\(474\) 4.48557e10i 0.888596i
\(475\) −4.08073e10 −0.801610
\(476\) −7.88861e7 −0.00153664
\(477\) 2.02677e10 0.391499
\(478\) 5.68596e10i 1.08916i
\(479\) 1.70958e9 0.0324748 0.0162374 0.999868i \(-0.494831\pi\)
0.0162374 + 0.999868i \(0.494831\pi\)
\(480\) 4.01341e10i 0.756047i
\(481\) −2.42199e10 −0.452472
\(482\) 1.09023e11i 2.01991i
\(483\) 2.32291e8i 0.00426818i
\(484\) 2.27382e10 0.414357
\(485\) 1.11148e10i 0.200880i
\(486\) 4.56492e9i 0.0818253i
\(487\) −5.61408e10 −0.998074 −0.499037 0.866581i \(-0.666313\pi\)
−0.499037 + 0.866581i \(0.666313\pi\)
\(488\) −5.04946e9 −0.0890361
\(489\) 5.20169e10 0.909724
\(490\) 8.76913e10i 1.52115i
\(491\) 7.10838e10 1.22305 0.611526 0.791224i \(-0.290556\pi\)
0.611526 + 0.791224i \(0.290556\pi\)
\(492\) −1.56145e9 −0.0266482
\(493\) 3.13350e10 0.530447
\(494\) 3.78267e10 0.635170
\(495\) 3.07579e10i 0.512314i
\(496\) 4.16110e10i 0.687513i
\(497\) 1.82858e7 0.000299701
\(498\) −1.68022e10 −0.273180
\(499\) 1.00041e11 1.61353 0.806764 0.590873i \(-0.201217\pi\)
0.806764 + 0.590873i \(0.201217\pi\)
\(500\) −2.69998e10 −0.431996
\(501\) −5.03811e10 −0.799682
\(502\) 3.15304e10i 0.496495i
\(503\) 4.91625e10i 0.768001i 0.923333 + 0.384000i \(0.125454\pi\)
−0.923333 + 0.384000i \(0.874546\pi\)
\(504\) 4.08367e7i 0.000632891i
\(505\) 4.95147e10i 0.761322i
\(506\) 1.99636e11i 3.04535i
\(507\) −3.55232e10 −0.537626
\(508\) 3.52069e10 0.528655
\(509\) 3.67029e10i 0.546801i 0.961900 + 0.273401i \(0.0881485\pi\)
−0.961900 + 0.273401i \(0.911851\pi\)
\(510\) 3.64916e10i 0.539402i
\(511\) 2.90212e8i 0.00425630i
\(512\) 5.27613e10i 0.767777i
\(513\) 2.53034e10 0.365350
\(514\) 9.86932e10i 1.41395i
\(515\) 3.65915e10i 0.520177i
\(516\) 9.74897e9i 0.137518i
\(517\) −1.27664e10 −0.178692
\(518\) 6.32149e8 0.00878013
\(519\) 5.43809e10i 0.749509i
\(520\) 1.08826e10 0.148840
\(521\) 1.06289e10 0.144257 0.0721284 0.997395i \(-0.477021\pi\)
0.0721284 + 0.997395i \(0.477021\pi\)
\(522\) 2.72646e10i 0.367213i
\(523\) −8.08156e10 −1.08016 −0.540081 0.841613i \(-0.681606\pi\)
−0.540081 + 0.841613i \(0.681606\pi\)
\(524\) 3.87843e10i 0.514435i
\(525\) 7.39051e7 0.000972830
\(526\) 5.54595e10i 0.724491i
\(527\) 2.63965e10i 0.342218i
\(528\) 7.13536e10i 0.918079i
\(529\) −1.90457e11 −2.43206
\(530\) 1.40973e11i 1.78662i
\(531\) 2.48465e10 + 9.21603e9i 0.312527 + 0.115922i
\(532\) −3.80467e8 −0.00474974
\(533\) 1.55845e9i 0.0193100i
\(534\) −3.84393e10 −0.472727
\(535\) 4.51043e10 0.550558
\(536\) −3.61496e10 −0.437970
\(537\) 1.12608e10i 0.135417i
\(538\) −5.91375e10 −0.705885
\(539\) 1.08772e11i 1.28873i
\(540\) −1.22359e10 −0.143900
\(541\) 1.39091e11i 1.62372i 0.583852 + 0.811860i \(0.301545\pi\)
−0.583852 + 0.811860i \(0.698455\pi\)
\(542\) 1.90943e10i 0.221262i
\(543\) −1.06331e10 −0.122309
\(544\) 5.90623e10i 0.674396i
\(545\) 1.37419e11i 1.55762i
\(546\) −6.85070e7 −0.000770840
\(547\) −1.46170e11 −1.63271 −0.816356 0.577549i \(-0.804009\pi\)
−0.816356 + 0.577549i \(0.804009\pi\)
\(548\) −8.63589e10 −0.957601
\(549\) 5.66644e9i 0.0623765i
\(550\) −6.35159e10 −0.694116
\(551\) 1.51128e11 1.63960
\(552\) −4.72495e10 −0.508910
\(553\) −4.50298e8 −0.00481504
\(554\) 1.43435e11i 1.52271i
\(555\) 1.12689e11i 1.18771i
\(556\) −6.99357e10 −0.731813
\(557\) −1.35038e11 −1.40292 −0.701461 0.712707i \(-0.747469\pi\)
−0.701461 + 0.712707i \(0.747469\pi\)
\(558\) −2.29676e10 −0.236908
\(559\) −9.73022e9 −0.0996496
\(560\) −5.77481e8 −0.00587200
\(561\) 4.52641e10i 0.456985i
\(562\) 1.38799e11i 1.39137i
\(563\) 6.90974e10i 0.687746i 0.939016 + 0.343873i \(0.111739\pi\)
−0.939016 + 0.343873i \(0.888261\pi\)
\(564\) 5.07862e9i 0.0501914i
\(565\) 4.54357e10i 0.445865i
\(566\) 2.44583e11 2.38320
\(567\) −4.58264e7 −0.000443387
\(568\) 3.71946e9i 0.0357344i
\(569\) 1.44373e11i 1.37733i 0.725082 + 0.688663i \(0.241802\pi\)
−0.725082 + 0.688663i \(0.758198\pi\)
\(570\) 1.75999e11i 1.66728i
\(571\) 1.99214e11i 1.87402i −0.349301 0.937010i \(-0.613581\pi\)
0.349301 0.937010i \(-0.386419\pi\)
\(572\) 2.26890e10 0.211948
\(573\) 1.04764e11i 0.971841i
\(574\) 4.06761e7i 0.000374707i
\(575\) 8.55108e10i 0.782257i
\(576\) 6.11716e9 0.0555725
\(577\) 3.59503e9 0.0324339 0.0162170 0.999868i \(-0.494838\pi\)
0.0162170 + 0.999868i \(0.494838\pi\)
\(578\) 8.86628e10i 0.794383i
\(579\) −8.67755e10 −0.772117
\(580\) −7.30805e10 −0.645787
\(581\) 1.68675e8i 0.00148028i
\(582\) 1.42321e10 0.124045
\(583\) 1.74862e11i 1.51364i
\(584\) 5.90313e10 0.507494
\(585\) 1.22123e10i 0.104274i
\(586\) 9.21605e10i 0.781546i
\(587\) 2.44880e10i 0.206253i 0.994668 + 0.103127i \(0.0328847\pi\)
−0.994668 + 0.103127i \(0.967115\pi\)
\(588\) −4.32708e10 −0.361981
\(589\) 1.27310e11i 1.05779i
\(590\) −6.41024e10 + 1.72821e11i −0.529013 + 1.42623i
\(591\) 6.88652e10 0.564482
\(592\) 2.61422e11i 2.12841i
\(593\) −2.20863e10 −0.178609 −0.0893047 0.996004i \(-0.528464\pi\)
−0.0893047 + 0.996004i \(0.528464\pi\)
\(594\) 3.93844e10 0.316357
\(595\) −3.66333e8 −0.00292286
\(596\) 6.15878e10i 0.488101i
\(597\) 9.93425e10 0.782056
\(598\) 7.92650e10i 0.619836i
\(599\) 9.41366e9 0.0731225 0.0365612 0.999331i \(-0.488360\pi\)
0.0365612 + 0.999331i \(0.488360\pi\)
\(600\) 1.50328e10i 0.115994i
\(601\) 2.30456e11i 1.76640i 0.468996 + 0.883200i \(0.344616\pi\)
−0.468996 + 0.883200i \(0.655384\pi\)
\(602\) 2.53963e8 0.00193368
\(603\) 4.05666e10i 0.306831i
\(604\) 6.74913e10i 0.507107i
\(605\) 1.05592e11 0.788153
\(606\) 6.34017e10 0.470122
\(607\) −1.33548e11 −0.983747 −0.491873 0.870667i \(-0.663688\pi\)
−0.491873 + 0.870667i \(0.663688\pi\)
\(608\) 2.84857e11i 2.08455i
\(609\) −2.73705e8 −0.00198982
\(610\) 3.94131e10 0.284657
\(611\) −5.06885e9 −0.0363701
\(612\) 1.80066e10 0.128359
\(613\) 1.23977e11i 0.878011i −0.898484 0.439005i \(-0.855331\pi\)
0.898484 0.439005i \(-0.144669\pi\)
\(614\) 2.71020e10i 0.190690i
\(615\) −7.25109e9 −0.0506877
\(616\) 3.52324e8 0.00244692
\(617\) 3.54912e10 0.244895 0.122448 0.992475i \(-0.460926\pi\)
0.122448 + 0.992475i \(0.460926\pi\)
\(618\) −4.68540e10 −0.321213
\(619\) 5.21829e10 0.355439 0.177720 0.984081i \(-0.443128\pi\)
0.177720 + 0.984081i \(0.443128\pi\)
\(620\) 6.15627e10i 0.416630i
\(621\) 5.30228e10i 0.356530i
\(622\) 1.78815e11i 1.19465i
\(623\) 3.85885e8i 0.00256157i
\(624\) 2.83307e10i 0.186861i
\(625\) −1.89813e11 −1.24396
\(626\) −2.01429e11 −1.31167
\(627\) 2.18308e11i 1.41254i
\(628\) 1.06504e11i 0.684740i
\(629\) 1.65836e11i 1.05944i
\(630\) 3.18747e8i 0.00202341i
\(631\) 2.09062e11 1.31873 0.659367 0.751821i \(-0.270824\pi\)
0.659367 + 0.751821i \(0.270824\pi\)
\(632\) 9.15939e10i 0.574114i
\(633\) 4.51527e10i 0.281235i
\(634\) 2.90549e11i 1.79830i
\(635\) 1.63494e11 1.00556
\(636\) 6.95622e10 0.425153
\(637\) 4.31876e10i 0.262302i
\(638\) 2.35229e11 1.41974
\(639\) −4.17392e9 −0.0250346
\(640\) 1.77152e11i 1.05591i
\(641\) −1.35735e11 −0.804009 −0.402004 0.915638i \(-0.631686\pi\)
−0.402004 + 0.915638i \(0.631686\pi\)
\(642\) 5.77544e10i 0.339973i
\(643\) 2.93118e11 1.71474 0.857372 0.514697i \(-0.172096\pi\)
0.857372 + 0.514697i \(0.172096\pi\)
\(644\) 7.97261e8i 0.00463508i
\(645\) 4.52724e10i 0.261574i
\(646\) 2.59004e11i 1.48722i
\(647\) 1.79140e11 1.02229 0.511147 0.859493i \(-0.329221\pi\)
0.511147 + 0.859493i \(0.329221\pi\)
\(648\) 9.32141e9i 0.0528666i
\(649\) 7.95124e10 2.14366e11i 0.448184 1.20831i
\(650\) −2.52188e10 −0.141277
\(651\) 2.30568e8i 0.00128373i
\(652\) 1.78531e11 0.987923
\(653\) 4.74277e10 0.260843 0.130422 0.991459i \(-0.458367\pi\)
0.130422 + 0.991459i \(0.458367\pi\)
\(654\) 1.75960e11 0.961841
\(655\) 1.80107e11i 0.978512i
\(656\) 1.68214e10 0.0908337
\(657\) 6.62440e10i 0.355537i
\(658\) 1.32299e8 0.000705754
\(659\) 1.18263e11i 0.627057i 0.949579 + 0.313529i \(0.101511\pi\)
−0.949579 + 0.313529i \(0.898489\pi\)
\(660\) 1.05566e11i 0.556352i
\(661\) −1.08992e11 −0.570935 −0.285468 0.958388i \(-0.592149\pi\)
−0.285468 + 0.958388i \(0.592149\pi\)
\(662\) 9.47364e9i 0.0493270i
\(663\) 1.79720e10i 0.0930125i
\(664\) 3.43096e10 0.176499
\(665\) −1.76682e9 −0.00903452
\(666\) −1.44295e11 −0.733421
\(667\) 3.16686e11i 1.60002i
\(668\) −1.72917e11 −0.868422
\(669\) 3.32682e10 0.166083
\(670\) 2.82162e11 1.40023
\(671\) −4.88879e10 −0.241163
\(672\) 5.15898e8i 0.00252980i
\(673\) 1.57368e11i 0.767110i −0.923518 0.383555i \(-0.874700\pi\)
0.923518 0.383555i \(-0.125300\pi\)
\(674\) 4.66339e11 2.25976
\(675\) −1.68696e10 −0.0812625
\(676\) −1.21922e11 −0.583840
\(677\) −3.19743e11 −1.52211 −0.761056 0.648686i \(-0.775319\pi\)
−0.761056 + 0.648686i \(0.775319\pi\)
\(678\) 5.81788e10 0.275325
\(679\) 1.42874e8i 0.000672162i
\(680\) 7.45147e10i 0.348503i
\(681\) 1.59856e11i 0.743260i
\(682\) 1.98156e11i 0.915945i
\(683\) 2.81760e11i 1.29478i −0.762157 0.647392i \(-0.775860\pi\)
0.762157 0.647392i \(-0.224140\pi\)
\(684\) 8.68455e10 0.396755
\(685\) −4.01035e11 −1.82146
\(686\) 2.25445e9i 0.0101799i
\(687\) 1.86346e11i 0.836551i
\(688\) 1.05025e11i 0.468748i
\(689\) 6.94284e10i 0.308078i
\(690\) 3.68802e11 1.62703
\(691\) 1.05880e11i 0.464409i −0.972667 0.232204i \(-0.925406\pi\)
0.972667 0.232204i \(-0.0745938\pi\)
\(692\) 1.86644e11i 0.813937i
\(693\) 3.95373e8i 0.00171425i
\(694\) −8.03216e10 −0.346254
\(695\) −3.24769e11 −1.39199
\(696\) 5.56735e10i 0.237253i
\(697\) 1.06709e10 0.0452136
\(698\) 2.48159e11 1.04546
\(699\) 8.32740e10i 0.348819i
\(700\) 2.53655e8 0.00105645
\(701\) 2.03854e10i 0.0844203i −0.999109 0.0422102i \(-0.986560\pi\)
0.999109 0.0422102i \(-0.0134399\pi\)
\(702\) 1.56374e10 0.0643898
\(703\) 7.99827e11i 3.27473i
\(704\) 5.27766e10i 0.214857i
\(705\) 2.35842e10i 0.0954694i
\(706\) −5.76826e9 −0.0232181
\(707\) 6.36478e8i 0.00254745i
\(708\) 8.52775e10 + 3.16310e10i 0.339392 + 0.125887i
\(709\) −7.84044e10 −0.310281 −0.155141 0.987892i \(-0.549583\pi\)
−0.155141 + 0.987892i \(0.549583\pi\)
\(710\) 2.90319e10i 0.114246i
\(711\) 1.02785e11 0.402210
\(712\) 7.84918e10 0.305425
\(713\) 2.66775e11 1.03226
\(714\) 4.69076e8i 0.00180489i
\(715\) 1.05363e11 0.403149
\(716\) 3.86491e10i 0.147057i
\(717\) −1.30292e11 −0.492993
\(718\) 6.03639e11i 2.27133i
\(719\) 2.56436e11i 0.959542i −0.877394 0.479771i \(-0.840720\pi\)
0.877394 0.479771i \(-0.159280\pi\)
\(720\) 1.31816e11 0.490500
\(721\) 4.70359e8i 0.00174056i
\(722\) 9.02562e11i 3.32145i
\(723\) 2.49823e11 0.914281
\(724\) −3.64945e10 −0.132823
\(725\) −1.00756e11 −0.364687
\(726\) 1.35207e11i 0.486690i
\(727\) 1.68647e11 0.603729 0.301864 0.953351i \(-0.402391\pi\)
0.301864 + 0.953351i \(0.402391\pi\)
\(728\) 1.39889e8 0.000498033
\(729\) 1.04604e10 0.0370370
\(730\) −4.60763e11 −1.62250
\(731\) 6.66240e10i 0.233325i
\(732\) 1.94482e10i 0.0677383i
\(733\) −1.48717e11 −0.515162 −0.257581 0.966257i \(-0.582925\pi\)
−0.257581 + 0.966257i \(0.582925\pi\)
\(734\) −4.44686e10 −0.153204
\(735\) −2.00942e11 −0.688527
\(736\) −5.96912e11 −2.03422
\(737\) −3.49993e11 −1.18629
\(738\) 9.28475e9i 0.0313000i
\(739\) 2.57928e11i 0.864809i 0.901680 + 0.432405i \(0.142335\pi\)
−0.901680 + 0.432405i \(0.857665\pi\)
\(740\) 3.86769e11i 1.28981i
\(741\) 8.66785e10i 0.287500i
\(742\) 1.81211e9i 0.00597818i
\(743\) −3.83734e10 −0.125914 −0.0629571 0.998016i \(-0.520053\pi\)
−0.0629571 + 0.998016i \(0.520053\pi\)
\(744\) 4.68991e10 0.153064
\(745\) 2.86002e11i 0.928420i
\(746\) 2.83311e11i 0.914762i
\(747\) 3.85017e10i 0.123651i
\(748\) 1.55354e11i 0.496267i
\(749\) 5.79786e8 0.00184222
\(750\) 1.60547e11i 0.507408i
\(751\) 5.65819e10i 0.177876i 0.996037 + 0.0889380i \(0.0283473\pi\)
−0.996037 + 0.0889380i \(0.971653\pi\)
\(752\) 5.47116e10i 0.171083i
\(753\) 7.22508e10 0.224731
\(754\) 9.33969e10 0.288966
\(755\) 3.13417e11i 0.964573i
\(756\) −1.57284e8 −0.000481501
\(757\) 2.69700e11 0.821292 0.410646 0.911795i \(-0.365303\pi\)
0.410646 + 0.911795i \(0.365303\pi\)
\(758\) 7.52928e11i 2.28075i
\(759\) −4.57460e11 −1.37843
\(760\) 3.59383e11i 1.07722i
\(761\) 5.23769e11 1.56171 0.780856 0.624711i \(-0.214783\pi\)
0.780856 + 0.624711i \(0.214783\pi\)
\(762\) 2.09348e11i 0.620940i
\(763\) 1.76643e9i 0.00521193i
\(764\) 3.59569e11i 1.05538i
\(765\) 8.36193e10 0.244152
\(766\) 4.10621e11i 1.19269i
\(767\) 3.15702e10 8.51135e10i 0.0912211 0.245933i
\(768\) −2.60322e11 −0.748284
\(769\) 3.65241e11i 1.04442i 0.852818 + 0.522208i \(0.174892\pi\)
−0.852818 + 0.522208i \(0.825108\pi\)
\(770\) −2.75003e9 −0.00782302
\(771\) 2.26152e11 0.640005
\(772\) −2.97828e11 −0.838488
\(773\) 5.96411e11i 1.67043i 0.549924 + 0.835214i \(0.314657\pi\)
−0.549924 + 0.835214i \(0.685343\pi\)
\(774\) −5.79697e10 −0.161524
\(775\) 8.48766e10i 0.235278i
\(776\) −2.90616e10 −0.0801442
\(777\) 1.44855e9i 0.00397419i
\(778\) 7.01409e10i 0.191449i
\(779\) 5.14655e10 0.139755
\(780\) 4.19148e10i 0.113237i
\(781\) 3.60110e10i 0.0967901i
\(782\) −5.42737e11