Properties

Label 43.11.b.b.42.6
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.6
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.29

$q$-expansion

\(f(q)\) \(=\) \(q-44.1717i q^{2} -389.187i q^{3} -927.142 q^{4} +5234.98i q^{5} -17191.1 q^{6} +21894.1i q^{7} -4278.39i q^{8} -92417.4 q^{9} +O(q^{10})\) \(q-44.1717i q^{2} -389.187i q^{3} -927.142 q^{4} +5234.98i q^{5} -17191.1 q^{6} +21894.1i q^{7} -4278.39i q^{8} -92417.4 q^{9} +231238. q^{10} +16244.7 q^{11} +360831. i q^{12} +326289. q^{13} +967102. q^{14} +2.03738e6 q^{15} -1.13838e6 q^{16} +287393. q^{17} +4.08224e6i q^{18} +139732. i q^{19} -4.85357e6i q^{20} +8.52091e6 q^{21} -717555. i q^{22} +1.90806e6 q^{23} -1.66509e6 q^{24} -1.76393e7 q^{25} -1.44127e7i q^{26} +1.29865e7i q^{27} -2.02990e7i q^{28} +3.83545e7i q^{29} -8.99948e7i q^{30} +5.40348e7 q^{31} +4.59030e7i q^{32} -6.32221e6i q^{33} -1.26946e7i q^{34} -1.14615e8 q^{35} +8.56840e7 q^{36} +8.73532e7i q^{37} +6.17221e6 q^{38} -1.26987e8i q^{39} +2.23973e7 q^{40} +8.87662e7 q^{41} -3.76384e8i q^{42} +(-6.67162e7 - 1.30998e8i) q^{43} -1.50611e7 q^{44} -4.83803e8i q^{45} -8.42821e7i q^{46} +1.99511e8 q^{47} +4.43041e8i q^{48} -1.96878e8 q^{49} +7.79160e8i q^{50} -1.11849e8i q^{51} -3.02516e8 q^{52} -3.58718e8 q^{53} +5.73638e8 q^{54} +8.50405e7i q^{55} +9.36717e7 q^{56} +5.43819e7 q^{57} +1.69419e9 q^{58} +9.43790e8 q^{59} -1.88894e9 q^{60} +1.50091e9i q^{61} -2.38681e9i q^{62} -2.02340e9i q^{63} +8.61918e8 q^{64} +1.70811e9i q^{65} -2.79263e8 q^{66} -1.23620e9 q^{67} -2.66454e8 q^{68} -7.42590e8i q^{69} +5.06276e9i q^{70} -1.85479e9i q^{71} +3.95398e8i q^{72} +1.84969e9i q^{73} +3.85854e9 q^{74} +6.86500e9i q^{75} -1.29552e8i q^{76} +3.55663e8i q^{77} -5.60925e9 q^{78} -8.05333e8 q^{79} -5.95938e9i q^{80} -4.02965e8 q^{81} -3.92096e9i q^{82} -6.35127e9 q^{83} -7.90010e9 q^{84} +1.50449e9i q^{85} +(-5.78640e9 + 2.94697e9i) q^{86} +1.49271e10 q^{87} -6.95010e7i q^{88} +3.36937e9i q^{89} -2.13704e10 q^{90} +7.14381e9i q^{91} -1.76904e9 q^{92} -2.10296e10i q^{93} -8.81277e9i q^{94} -7.31495e8 q^{95} +1.78649e10 q^{96} +1.34193e10 q^{97} +8.69646e9i q^{98} -1.50129e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 44.1717i 1.38037i −0.723635 0.690183i \(-0.757530\pi\)
0.723635 0.690183i \(-0.242470\pi\)
\(3\) 389.187i 1.60159i −0.598937 0.800796i \(-0.704410\pi\)
0.598937 0.800796i \(-0.295590\pi\)
\(4\) −927.142 −0.905412
\(5\) 5234.98i 1.67519i 0.546290 + 0.837596i \(0.316040\pi\)
−0.546290 + 0.837596i \(0.683960\pi\)
\(6\) −17191.1 −2.21078
\(7\) 21894.1i 1.30268i 0.758786 + 0.651340i \(0.225793\pi\)
−0.758786 + 0.651340i \(0.774207\pi\)
\(8\) 4278.39i 0.130566i
\(9\) −92417.4 −1.56510
\(10\) 231238. 2.31238
\(11\) 16244.7 0.100867 0.0504333 0.998727i \(-0.483940\pi\)
0.0504333 + 0.998727i \(0.483940\pi\)
\(12\) 360831.i 1.45010i
\(13\) 326289. 0.878790 0.439395 0.898294i \(-0.355193\pi\)
0.439395 + 0.898294i \(0.355193\pi\)
\(14\) 967102. 1.79818
\(15\) 2.03738e6 2.68297
\(16\) −1.13838e6 −1.08564
\(17\) 287393. 0.202410 0.101205 0.994866i \(-0.467730\pi\)
0.101205 + 0.994866i \(0.467730\pi\)
\(18\) 4.08224e6i 2.16041i
\(19\) 139732.i 0.0564324i 0.999602 + 0.0282162i \(0.00898269\pi\)
−0.999602 + 0.0282162i \(0.991017\pi\)
\(20\) 4.85357e6i 1.51674i
\(21\) 8.52091e6 2.08636
\(22\) 717555.i 0.139233i
\(23\) 1.90806e6 0.296450 0.148225 0.988954i \(-0.452644\pi\)
0.148225 + 0.988954i \(0.452644\pi\)
\(24\) −1.66509e6 −0.209114
\(25\) −1.76393e7 −1.80627
\(26\) 1.44127e7i 1.21305i
\(27\) 1.29865e7i 0.905054i
\(28\) 2.02990e7i 1.17946i
\(29\) 3.83545e7i 1.86994i 0.354733 + 0.934968i \(0.384572\pi\)
−0.354733 + 0.934968i \(0.615428\pi\)
\(30\) 8.99948e7i 3.70349i
\(31\) 5.40348e7 1.88741 0.943703 0.330794i \(-0.107317\pi\)
0.943703 + 0.330794i \(0.107317\pi\)
\(32\) 4.59030e7i 1.36802i
\(33\) 6.32221e6i 0.161547i
\(34\) 1.26946e7i 0.279399i
\(35\) −1.14615e8 −2.18224
\(36\) 8.56840e7 1.41706
\(37\) 8.73532e7i 1.25971i 0.776713 + 0.629855i \(0.216886\pi\)
−0.776713 + 0.629855i \(0.783114\pi\)
\(38\) 6.17221e6 0.0778974
\(39\) 1.26987e8i 1.40746i
\(40\) 2.23973e7 0.218723
\(41\) 8.87662e7 0.766176 0.383088 0.923712i \(-0.374861\pi\)
0.383088 + 0.923712i \(0.374861\pi\)
\(42\) 3.76384e8i 2.87994i
\(43\) −6.67162e7 1.30998e8i −0.453826 0.891091i
\(44\) −1.50611e7 −0.0913259
\(45\) 4.83803e8i 2.62184i
\(46\) 8.42821e7i 0.409210i
\(47\) 1.99511e8 0.869918 0.434959 0.900450i \(-0.356763\pi\)
0.434959 + 0.900450i \(0.356763\pi\)
\(48\) 4.43041e8i 1.73875i
\(49\) −1.96878e8 −0.696976
\(50\) 7.79160e8i 2.49331i
\(51\) 1.11849e8i 0.324177i
\(52\) −3.02516e8 −0.795667
\(53\) −3.58718e8 −0.857776 −0.428888 0.903358i \(-0.641094\pi\)
−0.428888 + 0.903358i \(0.641094\pi\)
\(54\) 5.73638e8 1.24931
\(55\) 8.50405e7i 0.168971i
\(56\) 9.36717e7 0.170086
\(57\) 5.43819e7 0.0903817
\(58\) 1.69419e9 2.58120
\(59\) 9.43790e8 1.32013 0.660063 0.751211i \(-0.270530\pi\)
0.660063 + 0.751211i \(0.270530\pi\)
\(60\) −1.88894e9 −2.42920
\(61\) 1.50091e9i 1.77708i 0.458803 + 0.888538i \(0.348278\pi\)
−0.458803 + 0.888538i \(0.651722\pi\)
\(62\) 2.38681e9i 2.60531i
\(63\) 2.02340e9i 2.03882i
\(64\) 8.61918e8 0.802723
\(65\) 1.70811e9i 1.47214i
\(66\) −2.79263e8 −0.222994
\(67\) −1.23620e9 −0.915616 −0.457808 0.889051i \(-0.651365\pi\)
−0.457808 + 0.889051i \(0.651365\pi\)
\(68\) −2.66454e8 −0.183264
\(69\) 7.42590e8i 0.474792i
\(70\) 5.06276e9i 3.01229i
\(71\) 1.85479e9i 1.02802i −0.857783 0.514012i \(-0.828159\pi\)
0.857783 0.514012i \(-0.171841\pi\)
\(72\) 3.95398e8i 0.204349i
\(73\) 1.84969e9i 0.892247i 0.894971 + 0.446124i \(0.147196\pi\)
−0.894971 + 0.446124i \(0.852804\pi\)
\(74\) 3.85854e9 1.73886
\(75\) 6.86500e9i 2.89291i
\(76\) 1.29552e8i 0.0510946i
\(77\) 3.55663e8i 0.131397i
\(78\) −5.60925e9 −1.94282
\(79\) −8.05333e8 −0.261722 −0.130861 0.991401i \(-0.541774\pi\)
−0.130861 + 0.991401i \(0.541774\pi\)
\(80\) 5.95938e9i 1.81866i
\(81\) −4.02965e8 −0.115569
\(82\) 3.92096e9i 1.05760i
\(83\) −6.35127e9 −1.61239 −0.806195 0.591649i \(-0.798477\pi\)
−0.806195 + 0.591649i \(0.798477\pi\)
\(84\) −7.90010e9 −1.88902
\(85\) 1.50449e9i 0.339075i
\(86\) −5.78640e9 + 2.94697e9i −1.23003 + 0.626446i
\(87\) 1.49271e10 2.99487
\(88\) 6.95010e7i 0.0131698i
\(89\) 3.36937e9i 0.603390i 0.953404 + 0.301695i \(0.0975525\pi\)
−0.953404 + 0.301695i \(0.902448\pi\)
\(90\) −2.13704e10 −3.61910
\(91\) 7.14381e9i 1.14478i
\(92\) −1.76904e9 −0.268410
\(93\) 2.10296e10i 3.02285i
\(94\) 8.81277e9i 1.20081i
\(95\) −7.31495e8 −0.0945351
\(96\) 1.78649e10 2.19100
\(97\) 1.34193e10 1.56269 0.781343 0.624102i \(-0.214535\pi\)
0.781343 + 0.624102i \(0.214535\pi\)
\(98\) 8.69646e9i 0.962082i
\(99\) −1.50129e9 −0.157866
\(100\) 1.63542e10 1.63542
\(101\) 1.38886e10 1.32145 0.660727 0.750626i \(-0.270248\pi\)
0.660727 + 0.750626i \(0.270248\pi\)
\(102\) −4.94058e9 −0.447484
\(103\) 1.78504e9 0.153979 0.0769894 0.997032i \(-0.475469\pi\)
0.0769894 + 0.997032i \(0.475469\pi\)
\(104\) 1.39599e9i 0.114740i
\(105\) 4.46068e10i 3.49506i
\(106\) 1.58452e10i 1.18404i
\(107\) 1.17048e10 0.834537 0.417268 0.908783i \(-0.362988\pi\)
0.417268 + 0.908783i \(0.362988\pi\)
\(108\) 1.20404e10i 0.819447i
\(109\) −7.22912e9 −0.469843 −0.234921 0.972014i \(-0.575483\pi\)
−0.234921 + 0.972014i \(0.575483\pi\)
\(110\) 3.75638e9 0.233242
\(111\) 3.39967e10 2.01754
\(112\) 2.49238e10i 1.41424i
\(113\) 5.13237e9i 0.278565i −0.990253 0.139282i \(-0.955520\pi\)
0.990253 0.139282i \(-0.0444795\pi\)
\(114\) 2.40214e9i 0.124760i
\(115\) 9.98863e9i 0.496611i
\(116\) 3.55601e10i 1.69306i
\(117\) −3.01548e10 −1.37539
\(118\) 4.16888e10i 1.82226i
\(119\) 6.29221e9i 0.263675i
\(120\) 8.71672e9i 0.350306i
\(121\) −2.56735e10 −0.989826
\(122\) 6.62979e10 2.45302
\(123\) 3.45467e10i 1.22710i
\(124\) −5.00979e10 −1.70888
\(125\) 4.12187e10i 1.35066i
\(126\) −8.93771e10 −2.81432
\(127\) −3.96185e9 −0.119917 −0.0599583 0.998201i \(-0.519097\pi\)
−0.0599583 + 0.998201i \(0.519097\pi\)
\(128\) 8.93230e9i 0.259964i
\(129\) −5.09826e10 + 2.59651e10i −1.42716 + 0.726843i
\(130\) 7.54503e10 2.03210
\(131\) 2.31997e10i 0.601349i 0.953727 + 0.300674i \(0.0972117\pi\)
−0.953727 + 0.300674i \(0.902788\pi\)
\(132\) 5.86159e9i 0.146267i
\(133\) −3.05932e9 −0.0735134
\(134\) 5.46049e10i 1.26389i
\(135\) −6.79842e10 −1.51614
\(136\) 1.22958e9i 0.0264278i
\(137\) 3.32676e10i 0.689317i −0.938728 0.344658i \(-0.887995\pi\)
0.938728 0.344658i \(-0.112005\pi\)
\(138\) −3.28015e10 −0.655388
\(139\) 3.77175e10 0.726890 0.363445 0.931616i \(-0.381600\pi\)
0.363445 + 0.931616i \(0.381600\pi\)
\(140\) 1.06265e11 1.97583
\(141\) 7.76472e10i 1.39325i
\(142\) −8.19293e10 −1.41905
\(143\) 5.30045e9 0.0886406
\(144\) 1.05206e11 1.69913
\(145\) −2.00785e11 −3.13250
\(146\) 8.17041e10 1.23163
\(147\) 7.66225e10i 1.11627i
\(148\) 8.09888e10i 1.14056i
\(149\) 4.43509e10i 0.603908i 0.953323 + 0.301954i \(0.0976389\pi\)
−0.953323 + 0.301954i \(0.902361\pi\)
\(150\) 3.03239e11 3.99327
\(151\) 4.70013e10i 0.598722i 0.954140 + 0.299361i \(0.0967735\pi\)
−0.954140 + 0.299361i \(0.903226\pi\)
\(152\) 5.97829e8 0.00736816
\(153\) −2.65601e10 −0.316790
\(154\) 1.57103e10 0.181376
\(155\) 2.82871e11i 3.16177i
\(156\) 1.17735e11i 1.27433i
\(157\) 1.29297e11i 1.35547i −0.735308 0.677733i \(-0.762963\pi\)
0.735308 0.677733i \(-0.237037\pi\)
\(158\) 3.55729e10i 0.361272i
\(159\) 1.39608e11i 1.37381i
\(160\) −2.40301e11 −2.29169
\(161\) 4.17753e10i 0.386180i
\(162\) 1.77997e10i 0.159528i
\(163\) 4.46002e10i 0.387613i −0.981040 0.193807i \(-0.937917\pi\)
0.981040 0.193807i \(-0.0620834\pi\)
\(164\) −8.22989e10 −0.693705
\(165\) 3.30966e10 0.270623
\(166\) 2.80547e11i 2.22569i
\(167\) −9.28129e9 −0.0714539 −0.0357270 0.999362i \(-0.511375\pi\)
−0.0357270 + 0.999362i \(0.511375\pi\)
\(168\) 3.64558e10i 0.272408i
\(169\) −3.13942e10 −0.227727
\(170\) 6.64561e10 0.468048
\(171\) 1.29137e10i 0.0883222i
\(172\) 6.18554e10 + 1.21454e11i 0.410899 + 0.806804i
\(173\) −8.77693e10 −0.566386 −0.283193 0.959063i \(-0.591394\pi\)
−0.283193 + 0.959063i \(0.591394\pi\)
\(174\) 6.59355e11i 4.13402i
\(175\) 3.86198e11i 2.35299i
\(176\) −1.84926e10 −0.109505
\(177\) 3.67311e11i 2.11430i
\(178\) 1.48831e11 0.832900
\(179\) 3.05725e11i 1.66367i 0.555026 + 0.831833i \(0.312708\pi\)
−0.555026 + 0.831833i \(0.687292\pi\)
\(180\) 4.48554e11i 2.37384i
\(181\) −5.19389e10 −0.267362 −0.133681 0.991024i \(-0.542680\pi\)
−0.133681 + 0.991024i \(0.542680\pi\)
\(182\) 3.15555e11 1.58022
\(183\) 5.84135e11 2.84615
\(184\) 8.16341e9i 0.0387064i
\(185\) −4.57292e11 −2.11026
\(186\) −9.28916e11 −4.17265
\(187\) 4.66860e9 0.0204164
\(188\) −1.84975e11 −0.787635
\(189\) −2.84329e11 −1.17900
\(190\) 3.23114e10i 0.130493i
\(191\) 4.65718e11i 1.83213i 0.401031 + 0.916064i \(0.368652\pi\)
−0.401031 + 0.916064i \(0.631348\pi\)
\(192\) 3.35447e11i 1.28564i
\(193\) −1.21544e11 −0.453888 −0.226944 0.973908i \(-0.572873\pi\)
−0.226944 + 0.973908i \(0.572873\pi\)
\(194\) 5.92754e11i 2.15708i
\(195\) 6.64775e11 2.35777
\(196\) 1.82534e11 0.631050
\(197\) 2.78554e11 0.938813 0.469406 0.882982i \(-0.344468\pi\)
0.469406 + 0.882982i \(0.344468\pi\)
\(198\) 6.63146e10i 0.217913i
\(199\) 4.27701e11i 1.37049i −0.728314 0.685244i \(-0.759696\pi\)
0.728314 0.685244i \(-0.240304\pi\)
\(200\) 7.54680e10i 0.235838i
\(201\) 4.81111e11i 1.46644i
\(202\) 6.13484e11i 1.82409i
\(203\) −8.39740e11 −2.43593
\(204\) 1.03700e11i 0.293514i
\(205\) 4.64689e11i 1.28349i
\(206\) 7.88481e10i 0.212547i
\(207\) −1.76338e11 −0.463973
\(208\) −3.71440e11 −0.954051
\(209\) 2.26990e9i 0.00569215i
\(210\) 1.97036e12 4.82446
\(211\) 1.70602e11i 0.407917i −0.978980 0.203959i \(-0.934619\pi\)
0.978980 0.203959i \(-0.0653808\pi\)
\(212\) 3.32582e11 0.776640
\(213\) −7.21860e11 −1.64647
\(214\) 5.17022e11i 1.15197i
\(215\) 6.85770e11 3.49258e11i 1.49275 0.760245i
\(216\) 5.55615e10 0.118169
\(217\) 1.18305e12i 2.45869i
\(218\) 3.19323e11i 0.648555i
\(219\) 7.19876e11 1.42902
\(220\) 7.88446e10i 0.152988i
\(221\) 9.37730e10 0.177876
\(222\) 1.50169e12i 2.78495i
\(223\) 5.36910e11i 0.973593i −0.873515 0.486796i \(-0.838165\pi\)
0.873515 0.486796i \(-0.161835\pi\)
\(224\) −1.00501e12 −1.78209
\(225\) 1.63018e12 2.82699
\(226\) −2.26706e11 −0.384521
\(227\) 1.51475e11i 0.251311i 0.992074 + 0.125656i \(0.0401034\pi\)
−0.992074 + 0.125656i \(0.959897\pi\)
\(228\) −5.04198e10 −0.0818327
\(229\) −4.10757e11 −0.652240 −0.326120 0.945328i \(-0.605741\pi\)
−0.326120 + 0.945328i \(0.605741\pi\)
\(230\) 4.41215e11 0.685506
\(231\) 1.38419e11 0.210444
\(232\) 1.64096e11 0.244150
\(233\) 1.03337e12i 1.50479i −0.658712 0.752395i \(-0.728899\pi\)
0.658712 0.752395i \(-0.271101\pi\)
\(234\) 1.33199e12i 1.89855i
\(235\) 1.04444e12i 1.45728i
\(236\) −8.75027e11 −1.19526
\(237\) 3.13425e11i 0.419171i
\(238\) 2.77938e11 0.363968
\(239\) −6.49764e11 −0.833232 −0.416616 0.909082i \(-0.636784\pi\)
−0.416616 + 0.909082i \(0.636784\pi\)
\(240\) −2.31931e12 −2.91275
\(241\) 9.03941e11i 1.11187i −0.831225 0.555936i \(-0.812360\pi\)
0.831225 0.555936i \(-0.187640\pi\)
\(242\) 1.13404e12i 1.36632i
\(243\) 9.23671e11i 1.09015i
\(244\) 1.39156e12i 1.60899i
\(245\) 1.03065e12i 1.16757i
\(246\) −1.52599e12 −1.69385
\(247\) 4.55930e10i 0.0495923i
\(248\) 2.31182e11i 0.246431i
\(249\) 2.47183e12i 2.58239i
\(250\) −1.82070e12 −1.86440
\(251\) 1.76657e12 1.77322 0.886611 0.462516i \(-0.153053\pi\)
0.886611 + 0.462516i \(0.153053\pi\)
\(252\) 1.87598e12i 1.84597i
\(253\) 3.09957e10 0.0299019
\(254\) 1.75002e11i 0.165529i
\(255\) 5.85529e11 0.543060
\(256\) 1.27716e12 1.16157
\(257\) 8.68522e11i 0.774667i 0.921940 + 0.387333i \(0.126604\pi\)
−0.921940 + 0.387333i \(0.873396\pi\)
\(258\) 1.14692e12 + 2.25199e12i 1.00331 + 1.97001i
\(259\) −1.91252e12 −1.64100
\(260\) 1.58366e12i 1.33290i
\(261\) 3.54462e12i 2.92663i
\(262\) 1.02477e12 0.830082
\(263\) 2.81196e11i 0.223476i 0.993738 + 0.111738i \(0.0356417\pi\)
−0.993738 + 0.111738i \(0.964358\pi\)
\(264\) −2.70489e10 −0.0210926
\(265\) 1.87788e12i 1.43694i
\(266\) 1.35135e11i 0.101475i
\(267\) 1.31131e12 0.966385
\(268\) 1.14613e12 0.829010
\(269\) 1.95784e12 1.39000 0.695002 0.719008i \(-0.255403\pi\)
0.695002 + 0.719008i \(0.255403\pi\)
\(270\) 3.00298e12i 2.09283i
\(271\) −9.57099e11 −0.654803 −0.327401 0.944885i \(-0.606173\pi\)
−0.327401 + 0.944885i \(0.606173\pi\)
\(272\) −3.27161e11 −0.219744
\(273\) 2.78028e12 1.83348
\(274\) −1.46949e12 −0.951510
\(275\) −2.86545e11 −0.182192
\(276\) 6.88487e11i 0.429883i
\(277\) 1.00767e12i 0.617900i −0.951078 0.308950i \(-0.900022\pi\)
0.951078 0.308950i \(-0.0999775\pi\)
\(278\) 1.66605e12i 1.00337i
\(279\) −4.99376e12 −2.95397
\(280\) 4.90369e11i 0.284927i
\(281\) −1.64012e12 −0.936147 −0.468073 0.883690i \(-0.655052\pi\)
−0.468073 + 0.883690i \(0.655052\pi\)
\(282\) −3.42981e12 −1.92320
\(283\) −3.07182e12 −1.69225 −0.846124 0.532986i \(-0.821070\pi\)
−0.846124 + 0.532986i \(0.821070\pi\)
\(284\) 1.71965e12i 0.930785i
\(285\) 2.84688e11i 0.151407i
\(286\) 2.34130e11i 0.122357i
\(287\) 1.94346e12i 0.998082i
\(288\) 4.24224e12i 2.14108i
\(289\) −1.93340e12 −0.959030
\(290\) 8.86902e12i 4.32400i
\(291\) 5.22262e12i 2.50278i
\(292\) 1.71493e12i 0.807852i
\(293\) 2.79147e12 1.29269 0.646346 0.763045i \(-0.276296\pi\)
0.646346 + 0.763045i \(0.276296\pi\)
\(294\) 3.38455e12 1.54086
\(295\) 4.94072e12i 2.21146i
\(296\) 3.73731e11 0.164475
\(297\) 2.10962e11i 0.0912898i
\(298\) 1.95905e12 0.833614
\(299\) 6.22577e11 0.260518
\(300\) 6.36483e12i 2.61927i
\(301\) 2.86809e12 1.46069e12i 1.16081 0.591190i
\(302\) 2.07613e12 0.826456
\(303\) 5.40526e12i 2.11643i
\(304\) 1.59068e11i 0.0612653i
\(305\) −7.85724e12 −2.97694
\(306\) 1.17320e12i 0.437287i
\(307\) 4.91023e11 0.180057 0.0900284 0.995939i \(-0.471304\pi\)
0.0900284 + 0.995939i \(0.471304\pi\)
\(308\) 3.29750e11i 0.118968i
\(309\) 6.94713e11i 0.246611i
\(310\) 1.24949e13 4.36440
\(311\) −1.24650e12 −0.428439 −0.214220 0.976785i \(-0.568721\pi\)
−0.214220 + 0.976785i \(0.568721\pi\)
\(312\) −5.43301e11 −0.183767
\(313\) 5.02951e12i 1.67419i 0.547060 + 0.837093i \(0.315747\pi\)
−0.547060 + 0.837093i \(0.684253\pi\)
\(314\) −5.71125e12 −1.87104
\(315\) 1.05924e13 3.41542
\(316\) 7.46658e11 0.236966
\(317\) −2.31349e12 −0.722723 −0.361362 0.932426i \(-0.617688\pi\)
−0.361362 + 0.932426i \(0.617688\pi\)
\(318\) 6.16674e12 1.89636
\(319\) 6.23057e11i 0.188614i
\(320\) 4.51212e12i 1.34472i
\(321\) 4.55536e12i 1.33659i
\(322\) 1.84529e12 0.533070
\(323\) 4.01580e10i 0.0114225i
\(324\) 3.73606e11 0.104638
\(325\) −5.75552e12 −1.58733
\(326\) −1.97007e12 −0.535048
\(327\) 2.81348e12i 0.752497i
\(328\) 3.79777e11i 0.100037i
\(329\) 4.36813e12i 1.13323i
\(330\) 1.46194e12i 0.373558i
\(331\) 5.06669e12i 1.27522i −0.770361 0.637608i \(-0.779924\pi\)
0.770361 0.637608i \(-0.220076\pi\)
\(332\) 5.88853e12 1.45988
\(333\) 8.07296e12i 1.97157i
\(334\) 4.09971e11i 0.0986326i
\(335\) 6.47146e12i 1.53383i
\(336\) −9.70001e12 −2.26504
\(337\) 2.41861e12 0.556437 0.278218 0.960518i \(-0.410256\pi\)
0.278218 + 0.960518i \(0.410256\pi\)
\(338\) 1.38673e12i 0.314347i
\(339\) −1.99745e12 −0.446147
\(340\) 1.39488e12i 0.307002i
\(341\) 8.77778e11 0.190376
\(342\) −5.70420e11 −0.121917
\(343\) 1.87407e12i 0.394743i
\(344\) −5.60460e11 + 2.85438e11i −0.116346 + 0.0592542i
\(345\) 3.88744e12 0.795369
\(346\) 3.87692e12i 0.781820i
\(347\) 1.55356e12i 0.308803i −0.988008 0.154402i \(-0.950655\pi\)
0.988008 0.154402i \(-0.0493449\pi\)
\(348\) −1.38395e13 −2.71159
\(349\) 5.81530e12i 1.12317i −0.827419 0.561585i \(-0.810192\pi\)
0.827419 0.561585i \(-0.189808\pi\)
\(350\) −1.70591e13 −3.24799
\(351\) 4.23736e12i 0.795353i
\(352\) 7.45679e11i 0.137987i
\(353\) 8.34462e12 1.52241 0.761207 0.648509i \(-0.224607\pi\)
0.761207 + 0.648509i \(0.224607\pi\)
\(354\) −1.62247e13 −2.91851
\(355\) 9.70978e12 1.72214
\(356\) 3.12388e12i 0.546317i
\(357\) 2.44885e12 0.422300
\(358\) 1.35044e13 2.29647
\(359\) 5.63916e12 0.945675 0.472838 0.881150i \(-0.343230\pi\)
0.472838 + 0.881150i \(0.343230\pi\)
\(360\) −2.06990e12 −0.342323
\(361\) 6.11154e12 0.996815
\(362\) 2.29423e12i 0.369058i
\(363\) 9.99180e12i 1.58530i
\(364\) 6.62333e12i 1.03650i
\(365\) −9.68310e12 −1.49469
\(366\) 2.58023e13i 3.92873i
\(367\) −3.17914e12 −0.477506 −0.238753 0.971080i \(-0.576739\pi\)
−0.238753 + 0.971080i \(0.576739\pi\)
\(368\) −2.17209e12 −0.321839
\(369\) −8.20354e12 −1.19914
\(370\) 2.01994e13i 2.91293i
\(371\) 7.85382e12i 1.11741i
\(372\) 1.94975e13i 2.73693i
\(373\) 3.17793e12i 0.440149i −0.975483 0.220075i \(-0.929370\pi\)
0.975483 0.220075i \(-0.0706301\pi\)
\(374\) 2.06220e11i 0.0281821i
\(375\) −1.60418e13 −2.16320
\(376\) 8.53588e11i 0.113582i
\(377\) 1.25146e13i 1.64328i
\(378\) 1.25593e13i 1.62745i
\(379\) 4.13270e12 0.528491 0.264246 0.964455i \(-0.414877\pi\)
0.264246 + 0.964455i \(0.414877\pi\)
\(380\) 6.78199e11 0.0855932
\(381\) 1.54190e12i 0.192057i
\(382\) 2.05716e13 2.52901
\(383\) 8.82149e12i 1.07040i 0.844724 + 0.535202i \(0.179765\pi\)
−0.844724 + 0.535202i \(0.820235\pi\)
\(384\) 3.47633e12 0.416356
\(385\) −1.86189e12 −0.220115
\(386\) 5.36883e12i 0.626532i
\(387\) 6.16574e12 + 1.21065e13i 0.710281 + 1.39464i
\(388\) −1.24416e13 −1.41487
\(389\) 9.50961e12i 1.06762i 0.845606 + 0.533808i \(0.179239\pi\)
−0.845606 + 0.533808i \(0.820761\pi\)
\(390\) 2.93643e13i 3.25459i
\(391\) 5.48361e11 0.0600044
\(392\) 8.42323e11i 0.0910014i
\(393\) 9.02903e12 0.963115
\(394\) 1.23042e13i 1.29591i
\(395\) 4.21590e12i 0.438434i
\(396\) 1.39191e12 0.142934
\(397\) −1.98113e12 −0.200891 −0.100446 0.994943i \(-0.532027\pi\)
−0.100446 + 0.994943i \(0.532027\pi\)
\(398\) −1.88923e13 −1.89177
\(399\) 1.19065e12i 0.117738i
\(400\) 2.00802e13 1.96096
\(401\) 6.65423e12 0.641765 0.320883 0.947119i \(-0.396021\pi\)
0.320883 + 0.947119i \(0.396021\pi\)
\(402\) 2.12515e13 2.02423
\(403\) 1.76310e13 1.65863
\(404\) −1.28767e13 −1.19646
\(405\) 2.10951e12i 0.193601i
\(406\) 3.70928e13i 3.36247i
\(407\) 1.41902e12i 0.127063i
\(408\) −4.78535e11 −0.0423266
\(409\) 2.33376e12i 0.203911i −0.994789 0.101955i \(-0.967490\pi\)
0.994789 0.101955i \(-0.0325099\pi\)
\(410\) 2.05261e13 1.77169
\(411\) −1.29473e13 −1.10400
\(412\) −1.65498e12 −0.139414
\(413\) 2.06635e13i 1.71970i
\(414\) 7.78914e12i 0.640453i
\(415\) 3.32488e13i 2.70106i
\(416\) 1.49776e13i 1.20220i
\(417\) 1.46791e13i 1.16418i
\(418\) 1.00266e11 0.00785725
\(419\) 5.16084e12i 0.399623i 0.979834 + 0.199811i \(0.0640329\pi\)
−0.979834 + 0.199811i \(0.935967\pi\)
\(420\) 4.13568e13i 3.16447i
\(421\) 1.86467e13i 1.40991i −0.709251 0.704956i \(-0.750967\pi\)
0.709251 0.704956i \(-0.249033\pi\)
\(422\) −7.53579e12 −0.563075
\(423\) −1.84383e13 −1.36151
\(424\) 1.53474e12i 0.111996i
\(425\) −5.06942e12 −0.365606
\(426\) 3.18858e13i 2.27274i
\(427\) −3.28612e13 −2.31496
\(428\) −1.08520e13 −0.755600
\(429\) 2.06287e12i 0.141966i
\(430\) −1.54273e13 3.02917e13i −1.04942 2.06054i
\(431\) 6.14696e12 0.413308 0.206654 0.978414i \(-0.433743\pi\)
0.206654 + 0.978414i \(0.433743\pi\)
\(432\) 1.47836e13i 0.982564i
\(433\) 3.26476e12i 0.214492i 0.994233 + 0.107246i \(0.0342033\pi\)
−0.994233 + 0.107246i \(0.965797\pi\)
\(434\) 5.22572e13 3.39389
\(435\) 7.81429e13i 5.01699i
\(436\) 6.70242e12 0.425401
\(437\) 2.66617e11i 0.0167294i
\(438\) 3.17982e13i 1.97257i
\(439\) −1.89155e13 −1.16010 −0.580049 0.814581i \(-0.696967\pi\)
−0.580049 + 0.814581i \(0.696967\pi\)
\(440\) 3.63836e11 0.0220619
\(441\) 1.81950e13 1.09083
\(442\) 4.14211e12i 0.245533i
\(443\) −1.44922e13 −0.849405 −0.424703 0.905333i \(-0.639621\pi\)
−0.424703 + 0.905333i \(0.639621\pi\)
\(444\) −3.15198e13 −1.82671
\(445\) −1.76386e13 −1.01079
\(446\) −2.37163e13 −1.34391
\(447\) 1.72608e13 0.967214
\(448\) 1.88710e13i 1.04569i
\(449\) 3.15308e13i 1.72784i −0.503629 0.863920i \(-0.668002\pi\)
0.503629 0.863920i \(-0.331998\pi\)
\(450\) 7.20080e13i 3.90228i
\(451\) 1.44198e12 0.0772816
\(452\) 4.75844e12i 0.252216i
\(453\) 1.82923e13 0.958909
\(454\) 6.69092e12 0.346902
\(455\) −3.73977e13 −1.91773
\(456\) 2.32667e11i 0.0118008i
\(457\) 3.13837e12i 0.157443i −0.996897 0.0787214i \(-0.974916\pi\)
0.996897 0.0787214i \(-0.0250838\pi\)
\(458\) 1.81438e13i 0.900331i
\(459\) 3.73223e12i 0.183192i
\(460\) 9.26087e12i 0.449638i
\(461\) −1.70711e13 −0.819895 −0.409947 0.912109i \(-0.634453\pi\)
−0.409947 + 0.912109i \(0.634453\pi\)
\(462\) 6.11423e12i 0.290490i
\(463\) 1.76507e13i 0.829576i −0.909918 0.414788i \(-0.863856\pi\)
0.909918 0.414788i \(-0.136144\pi\)
\(464\) 4.36619e13i 2.03008i
\(465\) 1.10090e14 5.06386
\(466\) −4.56457e13 −2.07716
\(467\) 3.03925e13i 1.36830i −0.729340 0.684152i \(-0.760173\pi\)
0.729340 0.684152i \(-0.239827\pi\)
\(468\) 2.79577e13 1.24530
\(469\) 2.70655e13i 1.19276i
\(470\) 4.61346e13 2.01158
\(471\) −5.03205e13 −2.17090
\(472\) 4.03790e12i 0.172364i
\(473\) −1.08378e12 2.12802e12i −0.0457759 0.0898813i
\(474\) 1.38445e13 0.578610
\(475\) 2.46479e12i 0.101932i
\(476\) 5.83378e12i 0.238734i
\(477\) 3.31518e13 1.34250
\(478\) 2.87012e13i 1.15017i
\(479\) 4.42392e13 1.75440 0.877201 0.480123i \(-0.159408\pi\)
0.877201 + 0.480123i \(0.159408\pi\)
\(480\) 9.35221e13i 3.67035i
\(481\) 2.85024e13i 1.10702i
\(482\) −3.99286e13 −1.53479
\(483\) 1.62584e13 0.618503
\(484\) 2.38030e13 0.896200
\(485\) 7.02498e13i 2.61780i
\(486\) 4.08001e13 1.50481
\(487\) −1.57076e13 −0.573411 −0.286705 0.958019i \(-0.592560\pi\)
−0.286705 + 0.958019i \(0.592560\pi\)
\(488\) 6.42149e12 0.232026
\(489\) −1.73578e13 −0.620798
\(490\) −4.55258e13 −1.61167
\(491\) 1.54818e13i 0.542519i −0.962506 0.271260i \(-0.912560\pi\)
0.962506 0.271260i \(-0.0874402\pi\)
\(492\) 3.20296e13i 1.11103i
\(493\) 1.10228e13i 0.378493i
\(494\) 2.01392e12 0.0684555
\(495\) 7.85922e12i 0.264456i
\(496\) −6.15120e13 −2.04905
\(497\) 4.06091e13 1.33919
\(498\) 1.09185e14 3.56465
\(499\) 2.61506e13i 0.845237i 0.906308 + 0.422618i \(0.138889\pi\)
−0.906308 + 0.422618i \(0.861111\pi\)
\(500\) 3.82156e13i 1.22290i
\(501\) 3.61216e12i 0.114440i
\(502\) 7.80326e13i 2.44770i
\(503\) 9.51220e12i 0.295421i −0.989031 0.147710i \(-0.952810\pi\)
0.989031 0.147710i \(-0.0471904\pi\)
\(504\) −8.65690e12 −0.266201
\(505\) 7.27065e13i 2.21369i
\(506\) 1.36914e12i 0.0412756i
\(507\) 1.22182e13i 0.364726i
\(508\) 3.67320e12 0.108574
\(509\) −3.68569e13 −1.07877 −0.539387 0.842058i \(-0.681344\pi\)
−0.539387 + 0.842058i \(0.681344\pi\)
\(510\) 2.58638e13i 0.749621i
\(511\) −4.04974e13 −1.16231
\(512\) 4.72676e13i 1.34343i
\(513\) −1.81464e12 −0.0510744
\(514\) 3.83641e13 1.06932
\(515\) 9.34462e12i 0.257944i
\(516\) 4.72681e13 2.40733e13i 1.29217 0.658093i
\(517\) 3.24100e12 0.0877457
\(518\) 8.44795e13i 2.26518i
\(519\) 3.41587e13i 0.907119i
\(520\) 7.30798e12 0.192212
\(521\) 3.11431e13i 0.811285i −0.914032 0.405643i \(-0.867048\pi\)
0.914032 0.405643i \(-0.132952\pi\)
\(522\) −1.56572e14 −4.03982
\(523\) 6.70568e13i 1.71370i −0.515568 0.856849i \(-0.672419\pi\)
0.515568 0.856849i \(-0.327581\pi\)
\(524\) 2.15094e13i 0.544468i
\(525\) −1.50303e14 −3.76853
\(526\) 1.24209e13 0.308479
\(527\) 1.55292e13 0.382029
\(528\) 7.19706e12i 0.175382i
\(529\) −3.77858e13 −0.912117
\(530\) −8.29492e13 −1.98350
\(531\) −8.72226e13 −2.06612
\(532\) 2.83642e12 0.0665599
\(533\) 2.89634e13 0.673308
\(534\) 5.79230e13i 1.33397i
\(535\) 6.12744e13i 1.39801i
\(536\) 5.28893e12i 0.119548i
\(537\) 1.18984e14 2.66451
\(538\) 8.64812e13i 1.91872i
\(539\) −3.19823e12 −0.0703016
\(540\) 6.30310e13 1.37273
\(541\) −7.26190e12 −0.156698 −0.0783491 0.996926i \(-0.524965\pi\)
−0.0783491 + 0.996926i \(0.524965\pi\)
\(542\) 4.22767e13i 0.903868i
\(543\) 2.02139e13i 0.428205i
\(544\) 1.31922e13i 0.276900i
\(545\) 3.78442e13i 0.787077i
\(546\) 1.22810e14i 2.53087i
\(547\) −2.42391e12 −0.0494971 −0.0247485 0.999694i \(-0.507879\pi\)
−0.0247485 + 0.999694i \(0.507879\pi\)
\(548\) 3.08438e13i 0.624116i
\(549\) 1.38710e14i 2.78130i
\(550\) 1.26572e13i 0.251492i
\(551\) −5.35936e12 −0.105525
\(552\) −3.17709e12 −0.0619918
\(553\) 1.76321e13i 0.340940i
\(554\) −4.45104e13 −0.852928
\(555\) 1.77972e14i 3.37977i
\(556\) −3.49695e13 −0.658135
\(557\) −7.15510e13 −1.33457 −0.667283 0.744805i \(-0.732543\pi\)
−0.667283 + 0.744805i \(0.732543\pi\)
\(558\) 2.20583e14i 4.07756i
\(559\) −2.17687e13 4.27431e13i −0.398818 0.783082i
\(560\) 1.30475e14 2.36913
\(561\) 1.81696e12i 0.0326987i
\(562\) 7.24469e13i 1.29223i
\(563\) 7.78919e13 1.37705 0.688526 0.725212i \(-0.258258\pi\)
0.688526 + 0.725212i \(0.258258\pi\)
\(564\) 7.19900e13i 1.26147i
\(565\) 2.68678e13 0.466649
\(566\) 1.35688e14i 2.33592i
\(567\) 8.82257e12i 0.150550i
\(568\) −7.93552e12 −0.134225
\(569\) −5.62609e13 −0.943289 −0.471645 0.881789i \(-0.656340\pi\)
−0.471645 + 0.881789i \(0.656340\pi\)
\(570\) 1.25752e13 0.208997
\(571\) 9.80201e12i 0.161486i −0.996735 0.0807430i \(-0.974271\pi\)
0.996735 0.0807430i \(-0.0257293\pi\)
\(572\) −4.91427e12 −0.0802563
\(573\) 1.81251e14 2.93432
\(574\) 8.58460e13 1.37772
\(575\) −3.36569e13 −0.535469
\(576\) −7.96562e13 −1.25634
\(577\) 8.14357e13i 1.27331i −0.771147 0.636657i \(-0.780317\pi\)
0.771147 0.636657i \(-0.219683\pi\)
\(578\) 8.54016e13i 1.32381i
\(579\) 4.73035e13i 0.726943i
\(580\) 1.86156e14 2.83620
\(581\) 1.39056e14i 2.10043i
\(582\) −2.30692e14 −3.45476
\(583\) −5.82725e12 −0.0865209
\(584\) 7.91371e12 0.116497
\(585\) 1.57859e14i 2.30405i
\(586\) 1.23304e14i 1.78439i
\(587\) 7.99336e13i 1.14693i 0.819228 + 0.573467i \(0.194402\pi\)
−0.819228 + 0.573467i \(0.805598\pi\)
\(588\) 7.10399e13i 1.01069i
\(589\) 7.55041e12i 0.106511i
\(590\) 2.18240e14 3.05263
\(591\) 1.08410e14i 1.50360i
\(592\) 9.94409e13i 1.36759i
\(593\) 3.00724e13i 0.410105i −0.978751 0.205052i \(-0.934264\pi\)
0.978751 0.205052i \(-0.0657365\pi\)
\(594\) 9.31856e12 0.126013
\(595\) −3.29396e13 −0.441706
\(596\) 4.11195e13i 0.546785i
\(597\) −1.66456e14 −2.19496
\(598\) 2.75003e13i 0.359610i
\(599\) 8.26667e13 1.07200 0.536002 0.844217i \(-0.319934\pi\)
0.536002 + 0.844217i \(0.319934\pi\)
\(600\) 2.93712e13 0.377715
\(601\) 1.17845e13i 0.150293i 0.997172 + 0.0751466i \(0.0239425\pi\)
−0.997172 + 0.0751466i \(0.976058\pi\)
\(602\) −6.45214e13 1.26688e14i −0.816058 1.60234i
\(603\) 1.14246e14 1.43303
\(604\) 4.35769e13i 0.542090i
\(605\) 1.34400e14i 1.65815i
\(606\) −2.38760e14 −2.92145
\(607\) 1.83173e13i 0.222289i −0.993804 0.111145i \(-0.964548\pi\)
0.993804 0.111145i \(-0.0354517\pi\)
\(608\) −6.41413e12 −0.0772005
\(609\) 3.26816e14i 3.90136i
\(610\) 3.47068e14i 4.10927i
\(611\) 6.50983e13 0.764476
\(612\) 2.46250e13 0.286826
\(613\) 3.12591e13 0.361138 0.180569 0.983562i \(-0.442206\pi\)
0.180569 + 0.983562i \(0.442206\pi\)
\(614\) 2.16893e13i 0.248545i
\(615\) 1.80851e14 2.05563
\(616\) 1.52167e12 0.0171560
\(617\) −5.75834e13 −0.643979 −0.321990 0.946743i \(-0.604352\pi\)
−0.321990 + 0.946743i \(0.604352\pi\)
\(618\) −3.06867e13 −0.340414
\(619\) 2.57630e13 0.283494 0.141747 0.989903i \(-0.454728\pi\)
0.141747 + 0.989903i \(0.454728\pi\)
\(620\) 2.62262e14i 2.86270i
\(621\) 2.47790e13i 0.268304i
\(622\) 5.50600e13i 0.591404i
\(623\) −7.37694e13 −0.786025
\(624\) 1.44559e14i 1.52800i
\(625\) 4.35199e13 0.456339
\(626\) 2.22162e14 2.31099
\(627\) 8.83417e11 0.00911650
\(628\) 1.19876e14i 1.22726i
\(629\) 2.51047e13i 0.254977i
\(630\) 4.67887e14i 4.71453i
\(631\) 7.65352e13i 0.765094i 0.923936 + 0.382547i \(0.124953\pi\)
−0.923936 + 0.382547i \(0.875047\pi\)
\(632\) 3.44553e12i 0.0341720i
\(633\) −6.63961e13 −0.653317
\(634\) 1.02191e14i 0.997623i
\(635\) 2.07402e13i 0.200883i
\(636\) 1.29437e14i 1.24386i
\(637\) −6.42392e13 −0.612496
\(638\) 2.75215e13 0.260357
\(639\) 1.71415e14i 1.60896i
\(640\) −4.67604e13 −0.435490
\(641\) 7.91033e13i 0.730978i −0.930816 0.365489i \(-0.880902\pi\)
0.930816 0.365489i \(-0.119098\pi\)
\(642\) −2.01218e14 −1.84498
\(643\) −7.07860e13 −0.644010 −0.322005 0.946738i \(-0.604357\pi\)
−0.322005 + 0.946738i \(0.604357\pi\)
\(644\) 3.87316e13i 0.349652i
\(645\) −1.35926e14 2.66893e14i −1.21760 2.39077i
\(646\) 1.77385e12 0.0157672
\(647\) 5.00521e12i 0.0441470i −0.999756 0.0220735i \(-0.992973\pi\)
0.999756 0.0220735i \(-0.00702678\pi\)
\(648\) 1.72404e12i 0.0150894i
\(649\) 1.53316e13 0.133157
\(650\) 2.54231e14i 2.19110i
\(651\) 4.60426e14 3.93781
\(652\) 4.13507e13i 0.350950i
\(653\) 4.06276e13i 0.342181i 0.985255 + 0.171090i \(0.0547290\pi\)
−0.985255 + 0.171090i \(0.945271\pi\)
\(654\) 1.24276e14 1.03872
\(655\) −1.21450e14 −1.00737
\(656\) −1.01049e14 −0.831792
\(657\) 1.70944e14i 1.39645i
\(658\) 1.92948e14 1.56427
\(659\) 1.05908e14 0.852123 0.426062 0.904694i \(-0.359901\pi\)
0.426062 + 0.904694i \(0.359901\pi\)
\(660\) −3.06853e13 −0.245025
\(661\) 4.93221e13 0.390872 0.195436 0.980716i \(-0.437388\pi\)
0.195436 + 0.980716i \(0.437388\pi\)
\(662\) −2.23804e14 −1.76027
\(663\) 3.64952e13i 0.284884i
\(664\) 2.71732e13i 0.210524i
\(665\) 1.60155e13i 0.123149i
\(666\) −3.56597e14 −2.72149
\(667\) 7.31826e13i 0.554343i
\(668\) 8.60508e12 0.0646952
\(669\) −2.08958e14 −1.55930
\(670\) −2.85856e14 −2.11725
\(671\) 2.43818e13i 0.179248i
\(672\) 3.91136e14i 2.85418i
\(673\) 2.16473e14i 1.56794i −0.620801 0.783968i \(-0.713193\pi\)
0.620801 0.783968i \(-0.286807\pi\)
\(674\) 1.06834e14i 0.768087i
\(675\) 2.29074e14i 1.63477i
\(676\) 2.91068e13 0.206187
\(677\) 1.92061e14i 1.35050i 0.737588 + 0.675251i \(0.235964\pi\)
−0.737588 + 0.675251i \(0.764036\pi\)
\(678\) 8.82309e13i 0.615846i
\(679\) 2.93804e14i 2.03568i
\(680\) 6.43681e12 0.0442717
\(681\) 5.89521e13 0.402498
\(682\) 3.87730e13i 0.262789i
\(683\) 1.63569e14 1.10052 0.550260 0.834994i \(-0.314529\pi\)
0.550260 + 0.834994i \(0.314529\pi\)
\(684\) 1.19728e13i 0.0799679i
\(685\) 1.74155e14 1.15474
\(686\) 8.27809e13 0.544891
\(687\) 1.59861e14i 1.04462i
\(688\) 7.59482e13 + 1.49125e14i 0.492692 + 0.967405i
\(689\) −1.17046e14 −0.753805
\(690\) 1.71715e14i 1.09790i
\(691\) 5.58274e13i 0.354370i −0.984178 0.177185i \(-0.943301\pi\)
0.984178 0.177185i \(-0.0566991\pi\)
\(692\) 8.13746e13 0.512812
\(693\) 3.28695e13i 0.205649i
\(694\) −6.86236e13 −0.426262
\(695\) 1.97450e14i 1.21768i
\(696\) 6.38639e13i 0.391029i
\(697\) 2.55108e13 0.155081
\(698\) −2.56872e14 −1.55039
\(699\) −4.02174e14 −2.41006
\(700\) 3.58061e14i 2.13043i
\(701\) −8.36705e13 −0.494290 −0.247145 0.968978i \(-0.579492\pi\)
−0.247145 + 0.968978i \(0.579492\pi\)
\(702\) 1.87172e14 1.09788
\(703\) −1.22061e13 −0.0710884
\(704\) 1.40016e13 0.0809680
\(705\) 4.06481e14 2.33397
\(706\) 3.68596e14i 2.10149i
\(707\) 3.04079e14i 1.72143i
\(708\) 3.40549e14i 1.91431i
\(709\) 1.75974e14 0.982241 0.491120 0.871092i \(-0.336587\pi\)
0.491120 + 0.871092i \(0.336587\pi\)
\(710\) 4.28898e14i 2.37718i
\(711\) 7.44267e13 0.409620
\(712\) 1.44155e13 0.0787823
\(713\) 1.03101e14 0.559522
\(714\) 1.08170e14i 0.582928i
\(715\) 2.77477e13i 0.148490i
\(716\) 2.83451e14i 1.50630i
\(717\) 2.52880e14i 1.33450i
\(718\) 2.49091e14i 1.30538i
\(719\) −1.71319e14 −0.891583 −0.445792 0.895137i \(-0.647078\pi\)
−0.445792 + 0.895137i \(0.647078\pi\)
\(720\) 5.50750e14i 2.84637i
\(721\) 3.90818e13i 0.200585i
\(722\) 2.69957e14i 1.37597i
\(723\) −3.51802e14 −1.78077
\(724\) 4.81547e13 0.242073
\(725\) 6.76549e14i 3.37761i
\(726\) 4.41355e14 2.18829
\(727\) 2.33883e14i 1.15167i −0.817567 0.575833i \(-0.804678\pi\)
0.817567 0.575833i \(-0.195322\pi\)
\(728\) 3.05640e13 0.149470
\(729\) 3.35686e14 1.63040
\(730\) 4.27719e14i 2.06321i
\(731\) −1.91737e13 3.76478e13i −0.0918586 0.180365i
\(732\) −5.41576e14 −2.57694
\(733\) 1.03433e14i 0.488809i −0.969673 0.244405i \(-0.921407\pi\)
0.969673 0.244405i \(-0.0785925\pi\)
\(734\) 1.40428e14i 0.659133i
\(735\) −4.01117e14 −1.86997
\(736\) 8.75855e13i 0.405549i
\(737\) −2.00816e13 −0.0923551
\(738\) 3.62365e14i 1.65525i
\(739\) 1.10575e14i 0.501690i 0.968027 + 0.250845i \(0.0807084\pi\)
−0.968027 + 0.250845i \(0.919292\pi\)
\(740\) 4.23975e14 1.91065
\(741\) 1.77442e13 0.0794266
\(742\) −3.46917e14 −1.54243
\(743\) 6.99827e13i 0.309063i 0.987988 + 0.154531i \(0.0493867\pi\)
−0.987988 + 0.154531i \(0.950613\pi\)
\(744\) −8.99730e13 −0.394682
\(745\) −2.32176e14 −1.01166
\(746\) −1.40375e14 −0.607567
\(747\) 5.86968e14 2.52355
\(748\) −4.32845e12 −0.0184852
\(749\) 2.56267e14i 1.08713i
\(750\) 7.08594e14i 2.98601i
\(751\) 2.78846e14i 1.16725i 0.812023 + 0.583626i \(0.198367\pi\)
−0.812023 + 0.583626i \(0.801633\pi\)
\(752\) −2.27119e14 −0.944419
\(753\) 6.87527e14i 2.83998i
\(754\) 5.52794e14 2.26833
\(755\) −2.46051e14 −1.00297
\(756\) 2.63613e14 1.06748
\(757\) 2.25706e14i 0.907955i −0.891013 0.453977i \(-0.850005\pi\)
0.891013 0.453977i \(-0.149995\pi\)
\(758\) 1.82548e14i 0.729511i
\(759\) 1.20631e13i 0.0478907i
\(760\) 3.12962e12i 0.0123431i
\(761\) 9.98414e13i 0.391190i −0.980685 0.195595i \(-0.937336\pi\)
0.980685 0.195595i \(-0.0626638\pi\)
\(762\) 6.81084e13 0.265110
\(763\) 1.58275e14i 0.612055i
\(764\) 4.31786e14i 1.65883i
\(765\) 1.39041e14i 0.530685i
\(766\) 3.89660e14 1.47755
\(767\) 3.07948e14 1.16011
\(768\) 4.97053e14i 1.86036i
\(769\) −2.32066e14 −0.862940 −0.431470 0.902127i \(-0.642005\pi\)
−0.431470 + 0.902127i \(0.642005\pi\)
\(770\) 8.22428e13i 0.303840i
\(771\) 3.38017e14 1.24070
\(772\) 1.12689e14 0.410956
\(773\) 8.76719e13i 0.317660i 0.987306 + 0.158830i \(0.0507722\pi\)
−0.987306 + 0.158830i \(0.949228\pi\)
\(774\) 5.34764e14 2.72351e14i 1.92512 0.980448i
\(775\) −9.53139e14 −3.40916
\(776\) 5.74131e13i 0.204034i
\(777\) 7.44329e14i 2.62821i
\(778\) 4.20056e14 1.47370
\(779\) 1.24035e13i 0.0432372i
\(780\) −6.16341e14 −2.13476