Properties

Label 43.9.b.b.42.10
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 42.10
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.19

$q$-expansion

\(f(q)\) \(=\) \(q-11.2266i q^{2} +77.9859i q^{3} +129.962 q^{4} +278.075i q^{5} +875.519 q^{6} +3160.13i q^{7} -4333.06i q^{8} +479.207 q^{9} +O(q^{10})\) \(q-11.2266i q^{2} +77.9859i q^{3} +129.962 q^{4} +278.075i q^{5} +875.519 q^{6} +3160.13i q^{7} -4333.06i q^{8} +479.207 q^{9} +3121.85 q^{10} -16312.7 q^{11} +10135.2i q^{12} -529.246 q^{13} +35477.7 q^{14} -21685.9 q^{15} -15375.4 q^{16} -122717. q^{17} -5379.88i q^{18} +126881. i q^{19} +36139.4i q^{20} -246446. q^{21} +183137. i q^{22} -33289.9 q^{23} +337918. q^{24} +313299. q^{25} +5941.65i q^{26} +549037. i q^{27} +410699. i q^{28} +1.14051e6i q^{29} +243460. i q^{30} +737944. q^{31} -936650. i q^{32} -1.27216e6i q^{33} +1.37770e6i q^{34} -878755. q^{35} +62278.9 q^{36} +1.37860e6i q^{37} +1.42445e6 q^{38} -41273.7i q^{39} +1.20492e6 q^{40} -5.06776e6 q^{41} +2.76676e6i q^{42} +(-586993. - 3.36803e6i) q^{43} -2.12004e6 q^{44} +133256. i q^{45} +373734. i q^{46} -3.40496e6 q^{47} -1.19906e6i q^{48} -4.22164e6 q^{49} -3.51730e6i q^{50} -9.57019e6i q^{51} -68782.1 q^{52} +8.04889e6 q^{53} +6.16384e6 q^{54} -4.53617e6i q^{55} +1.36931e7 q^{56} -9.89495e6 q^{57} +1.28041e7 q^{58} +1.77965e7 q^{59} -2.81836e6 q^{60} -8.79447e6i q^{61} -8.28463e6i q^{62} +1.51436e6i q^{63} -1.44515e7 q^{64} -147170. i q^{65} -1.42821e7 q^{66} +2.55566e6 q^{67} -1.59486e7 q^{68} -2.59614e6i q^{69} +9.86547e6i q^{70} +1.00216e7i q^{71} -2.07643e6i q^{72} -7.54723e6i q^{73} +1.54770e7 q^{74} +2.44329e7i q^{75} +1.64898e7i q^{76} -5.15505e7i q^{77} -463365. q^{78} +1.30718e7 q^{79} -4.27551e6i q^{80} -3.96730e7 q^{81} +5.68939e7i q^{82} +7.73406e7 q^{83} -3.20287e7 q^{84} -3.41246e7i q^{85} +(-3.78117e7 + 6.58996e6i) q^{86} -8.89439e7 q^{87} +7.06842e7i q^{88} +3.53743e7i q^{89} +1.49601e6 q^{90} -1.67249e6i q^{91} -4.32643e6 q^{92} +5.75492e7i q^{93} +3.82263e7i q^{94} -3.52826e7 q^{95} +7.30455e7 q^{96} +1.12025e8 q^{97} +4.73948e7i q^{98} -7.81718e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.2266i 0.701665i −0.936438 0.350833i \(-0.885899\pi\)
0.936438 0.350833i \(-0.114101\pi\)
\(3\) 77.9859i 0.962788i 0.876504 + 0.481394i \(0.159869\pi\)
−0.876504 + 0.481394i \(0.840131\pi\)
\(4\) 129.962 0.507666
\(5\) 278.075i 0.444921i 0.974942 + 0.222460i \(0.0714088\pi\)
−0.974942 + 0.222460i \(0.928591\pi\)
\(6\) 875.519 0.675555
\(7\) 3160.13i 1.31617i 0.752942 + 0.658087i \(0.228634\pi\)
−0.752942 + 0.658087i \(0.771366\pi\)
\(8\) 4333.06i 1.05788i
\(9\) 479.207 0.0730387
\(10\) 3121.85 0.312185
\(11\) −16312.7 −1.11418 −0.557091 0.830451i \(-0.688083\pi\)
−0.557091 + 0.830451i \(0.688083\pi\)
\(12\) 10135.2i 0.488775i
\(13\) −529.246 −0.0185304 −0.00926518 0.999957i \(-0.502949\pi\)
−0.00926518 + 0.999957i \(0.502949\pi\)
\(14\) 35477.7 0.923513
\(15\) −21685.9 −0.428364
\(16\) −15375.4 −0.234610
\(17\) −122717. −1.46930 −0.734648 0.678449i \(-0.762653\pi\)
−0.734648 + 0.678449i \(0.762653\pi\)
\(18\) 5379.88i 0.0512487i
\(19\) 126881.i 0.973606i 0.873512 + 0.486803i \(0.161837\pi\)
−0.873512 + 0.486803i \(0.838163\pi\)
\(20\) 36139.4i 0.225871i
\(21\) −246446. −1.26720
\(22\) 183137.i 0.781783i
\(23\) −33289.9 −0.118960 −0.0594800 0.998229i \(-0.518944\pi\)
−0.0594800 + 0.998229i \(0.518944\pi\)
\(24\) 337918. 1.01851
\(25\) 313299. 0.802046
\(26\) 5941.65i 0.0130021i
\(27\) 549037.i 1.03311i
\(28\) 410699.i 0.668176i
\(29\) 1.14051e6i 1.61253i 0.591553 + 0.806266i \(0.298515\pi\)
−0.591553 + 0.806266i \(0.701485\pi\)
\(30\) 243460.i 0.300568i
\(31\) 737944. 0.799055 0.399527 0.916721i \(-0.369174\pi\)
0.399527 + 0.916721i \(0.369174\pi\)
\(32\) 936650.i 0.893259i
\(33\) 1.27216e6i 1.07272i
\(34\) 1.37770e6i 1.03095i
\(35\) −878755. −0.585593
\(36\) 62278.9 0.0370792
\(37\) 1.37860e6i 0.735581i 0.929909 + 0.367790i \(0.119886\pi\)
−0.929909 + 0.367790i \(0.880114\pi\)
\(38\) 1.42445e6 0.683146
\(39\) 41273.7i 0.0178408i
\(40\) 1.20492e6 0.470671
\(41\) −5.06776e6 −1.79341 −0.896707 0.442625i \(-0.854047\pi\)
−0.896707 + 0.442625i \(0.854047\pi\)
\(42\) 2.76676e6i 0.889148i
\(43\) −586993. 3.36803e6i −0.171695 0.985150i
\(44\) −2.12004e6 −0.565632
\(45\) 133256.i 0.0324964i
\(46\) 373734.i 0.0834701i
\(47\) −3.40496e6 −0.697783 −0.348892 0.937163i \(-0.613442\pi\)
−0.348892 + 0.937163i \(0.613442\pi\)
\(48\) 1.19906e6i 0.225879i
\(49\) −4.22164e6 −0.732313
\(50\) 3.51730e6i 0.562768i
\(51\) 9.57019e6i 1.41462i
\(52\) −68782.1 −0.00940723
\(53\) 8.04889e6 1.02008 0.510038 0.860152i \(-0.329631\pi\)
0.510038 + 0.860152i \(0.329631\pi\)
\(54\) 6.16384e6 0.724897
\(55\) 4.53617e6i 0.495723i
\(56\) 1.36931e7 1.39235
\(57\) −9.89495e6 −0.937377
\(58\) 1.28041e7 1.13146
\(59\) 1.77965e7 1.46868 0.734341 0.678781i \(-0.237491\pi\)
0.734341 + 0.678781i \(0.237491\pi\)
\(60\) −2.81836e6 −0.217466
\(61\) 8.79447e6i 0.635170i −0.948230 0.317585i \(-0.897128\pi\)
0.948230 0.317585i \(-0.102872\pi\)
\(62\) 8.28463e6i 0.560669i
\(63\) 1.51436e6i 0.0961316i
\(64\) −1.44515e7 −0.861379
\(65\) 147170.i 0.00824454i
\(66\) −1.42821e7 −0.752692
\(67\) 2.55566e6 0.126825 0.0634123 0.997987i \(-0.479802\pi\)
0.0634123 + 0.997987i \(0.479802\pi\)
\(68\) −1.59486e7 −0.745911
\(69\) 2.59614e6i 0.114533i
\(70\) 9.86547e6i 0.410890i
\(71\) 1.00216e7i 0.394372i 0.980366 + 0.197186i \(0.0631802\pi\)
−0.980366 + 0.197186i \(0.936820\pi\)
\(72\) 2.07643e6i 0.0772659i
\(73\) 7.54723e6i 0.265764i −0.991132 0.132882i \(-0.957577\pi\)
0.991132 0.132882i \(-0.0424231\pi\)
\(74\) 1.54770e7 0.516131
\(75\) 2.44329e7i 0.772200i
\(76\) 1.64898e7i 0.494267i
\(77\) 5.15505e7i 1.46646i
\(78\) −463365. −0.0125183
\(79\) 1.30718e7 0.335605 0.167802 0.985821i \(-0.446333\pi\)
0.167802 + 0.985821i \(0.446333\pi\)
\(80\) 4.27551e6i 0.104383i
\(81\) −3.96730e7 −0.921627
\(82\) 5.68939e7i 1.25838i
\(83\) 7.73406e7 1.62965 0.814826 0.579705i \(-0.196832\pi\)
0.814826 + 0.579705i \(0.196832\pi\)
\(84\) −3.20287e7 −0.643312
\(85\) 3.41246e7i 0.653720i
\(86\) −3.78117e7 + 6.58996e6i −0.691246 + 0.120473i
\(87\) −8.89439e7 −1.55253
\(88\) 7.06842e7i 1.17867i
\(89\) 3.53743e7i 0.563804i 0.959443 + 0.281902i \(0.0909653\pi\)
−0.959443 + 0.281902i \(0.909035\pi\)
\(90\) 1.49601e6 0.0228016
\(91\) 1.67249e6i 0.0243892i
\(92\) −4.32643e6 −0.0603919
\(93\) 5.75492e7i 0.769320i
\(94\) 3.82263e7i 0.489610i
\(95\) −3.52826e7 −0.433178
\(96\) 7.30455e7 0.860020
\(97\) 1.12025e8 1.26540 0.632702 0.774395i \(-0.281946\pi\)
0.632702 + 0.774395i \(0.281946\pi\)
\(98\) 4.73948e7i 0.513839i
\(99\) −7.81718e6 −0.0813784
\(100\) 4.07171e7 0.407171
\(101\) −6.20802e7 −0.596579 −0.298289 0.954475i \(-0.596416\pi\)
−0.298289 + 0.954475i \(0.596416\pi\)
\(102\) −1.07441e8 −0.992590
\(103\) 2.13424e8 1.89625 0.948124 0.317900i \(-0.102977\pi\)
0.948124 + 0.317900i \(0.102977\pi\)
\(104\) 2.29325e6i 0.0196028i
\(105\) 6.85305e7i 0.563802i
\(106\) 9.03620e7i 0.715752i
\(107\) −7.15021e7 −0.545486 −0.272743 0.962087i \(-0.587931\pi\)
−0.272743 + 0.962087i \(0.587931\pi\)
\(108\) 7.13541e7i 0.524474i
\(109\) 2.45917e7 0.174214 0.0871068 0.996199i \(-0.472238\pi\)
0.0871068 + 0.996199i \(0.472238\pi\)
\(110\) −5.09260e7 −0.347832
\(111\) −1.07511e8 −0.708208
\(112\) 4.85882e7i 0.308787i
\(113\) 4.74022e7i 0.290726i −0.989378 0.145363i \(-0.953565\pi\)
0.989378 0.145363i \(-0.0464351\pi\)
\(114\) 1.11087e8i 0.657725i
\(115\) 9.25709e6i 0.0529277i
\(116\) 1.48224e8i 0.818628i
\(117\) −253618. −0.00135343
\(118\) 1.99796e8i 1.03052i
\(119\) 3.87802e8i 1.93385i
\(120\) 9.39666e7i 0.453157i
\(121\) 5.17469e7 0.241403
\(122\) −9.87324e7 −0.445677
\(123\) 3.95213e8i 1.72668i
\(124\) 9.59050e7 0.405653
\(125\) 1.95744e8i 0.801767i
\(126\) 1.70011e7 0.0674522
\(127\) 4.11369e8 1.58131 0.790654 0.612263i \(-0.209741\pi\)
0.790654 + 0.612263i \(0.209741\pi\)
\(128\) 7.75402e7i 0.288860i
\(129\) 2.62659e8 4.57771e7i 0.948491 0.165306i
\(130\) −1.65223e6 −0.00578491
\(131\) 1.97954e8i 0.672171i 0.941831 + 0.336086i \(0.109103\pi\)
−0.941831 + 0.336086i \(0.890897\pi\)
\(132\) 1.65334e8i 0.544584i
\(133\) −4.00962e8 −1.28143
\(134\) 2.86914e7i 0.0889884i
\(135\) −1.52674e8 −0.459652
\(136\) 5.31741e8i 1.55433i
\(137\) 6.49306e8i 1.84318i −0.388169 0.921588i \(-0.626892\pi\)
0.388169 0.921588i \(-0.373108\pi\)
\(138\) −2.91459e7 −0.0803640
\(139\) −1.38946e8 −0.372208 −0.186104 0.982530i \(-0.559586\pi\)
−0.186104 + 0.982530i \(0.559586\pi\)
\(140\) −1.14205e8 −0.297285
\(141\) 2.65539e8i 0.671818i
\(142\) 1.12509e8 0.276717
\(143\) 8.63345e6 0.0206462
\(144\) −7.36798e6 −0.0171356
\(145\) −3.17149e8 −0.717449
\(146\) −8.47301e7 −0.186477
\(147\) 3.29228e8i 0.705063i
\(148\) 1.79166e8i 0.373429i
\(149\) 8.69163e7i 0.176342i −0.996105 0.0881710i \(-0.971898\pi\)
0.996105 0.0881710i \(-0.0281022\pi\)
\(150\) 2.74299e8 0.541826
\(151\) 5.75666e8i 1.10729i 0.832752 + 0.553646i \(0.186764\pi\)
−0.832752 + 0.553646i \(0.813236\pi\)
\(152\) 5.49785e8 1.02996
\(153\) −5.88068e7 −0.107315
\(154\) −5.78739e8 −1.02896
\(155\) 2.05204e8i 0.355516i
\(156\) 5.36403e6i 0.00905717i
\(157\) 8.00910e8i 1.31821i 0.752050 + 0.659106i \(0.229065\pi\)
−0.752050 + 0.659106i \(0.770935\pi\)
\(158\) 1.46753e8i 0.235482i
\(159\) 6.27700e8i 0.982117i
\(160\) 2.60459e8 0.397430
\(161\) 1.05200e8i 0.156572i
\(162\) 4.45395e8i 0.646673i
\(163\) 1.22821e9i 1.73989i −0.493147 0.869946i \(-0.664153\pi\)
0.493147 0.869946i \(-0.335847\pi\)
\(164\) −6.58618e8 −0.910455
\(165\) 3.53757e8 0.477276
\(166\) 8.68275e8i 1.14347i
\(167\) 1.02872e9 1.32260 0.661302 0.750120i \(-0.270004\pi\)
0.661302 + 0.750120i \(0.270004\pi\)
\(168\) 1.06786e9i 1.34054i
\(169\) −8.15451e8 −0.999657
\(170\) −3.83105e8 −0.458693
\(171\) 6.08024e7i 0.0711109i
\(172\) −7.62870e7 4.37718e8i −0.0871639 0.500127i
\(173\) 1.79583e8 0.200485 0.100242 0.994963i \(-0.468038\pi\)
0.100242 + 0.994963i \(0.468038\pi\)
\(174\) 9.98542e8i 1.08935i
\(175\) 9.90067e8i 1.05563i
\(176\) 2.50815e8 0.261398
\(177\) 1.38788e9i 1.41403i
\(178\) 3.97135e8 0.395602
\(179\) 6.29234e8i 0.612915i 0.951884 + 0.306457i \(0.0991437\pi\)
−0.951884 + 0.306457i \(0.900856\pi\)
\(180\) 1.73182e7i 0.0164973i
\(181\) 6.87327e8 0.640396 0.320198 0.947351i \(-0.396251\pi\)
0.320198 + 0.947351i \(0.396251\pi\)
\(182\) −1.87764e7 −0.0171130
\(183\) 6.85844e8 0.611535
\(184\) 1.44247e8i 0.125845i
\(185\) −3.83354e8 −0.327275
\(186\) 6.46084e8 0.539805
\(187\) 2.00185e9 1.63706
\(188\) −4.42517e8 −0.354241
\(189\) −1.73503e9 −1.35975
\(190\) 3.96105e8i 0.303946i
\(191\) 1.44589e9i 1.08643i −0.839595 0.543214i \(-0.817207\pi\)
0.839595 0.543214i \(-0.182793\pi\)
\(192\) 1.12702e9i 0.829325i
\(193\) −2.20464e9 −1.58894 −0.794472 0.607301i \(-0.792252\pi\)
−0.794472 + 0.607301i \(0.792252\pi\)
\(194\) 1.25767e9i 0.887890i
\(195\) 1.14772e7 0.00793775
\(196\) −5.48655e8 −0.371770
\(197\) 4.52647e8 0.300535 0.150267 0.988645i \(-0.451987\pi\)
0.150267 + 0.988645i \(0.451987\pi\)
\(198\) 8.77607e7i 0.0571004i
\(199\) 1.89007e9i 1.20522i 0.798036 + 0.602610i \(0.205872\pi\)
−0.798036 + 0.602610i \(0.794128\pi\)
\(200\) 1.35754e9i 0.848465i
\(201\) 1.99305e8i 0.122105i
\(202\) 6.96953e8i 0.418599i
\(203\) −3.60418e9 −2.12237
\(204\) 1.24377e9i 0.718155i
\(205\) 1.40922e9i 0.797927i
\(206\) 2.39604e9i 1.33053i
\(207\) −1.59527e7 −0.00868867
\(208\) 8.13735e6 0.00434740
\(209\) 2.06978e9i 1.08478i
\(210\) −7.69367e8 −0.395600
\(211\) 2.76711e8i 0.139603i 0.997561 + 0.0698017i \(0.0222367\pi\)
−0.997561 + 0.0698017i \(0.977763\pi\)
\(212\) 1.04605e9 0.517858
\(213\) −7.81547e8 −0.379696
\(214\) 8.02729e8i 0.382749i
\(215\) 9.36567e8 1.63228e8i 0.438314 0.0763909i
\(216\) 2.37901e9 1.09290
\(217\) 2.33200e9i 1.05169i
\(218\) 2.76082e8i 0.122240i
\(219\) 5.88577e8 0.255875
\(220\) 5.89532e8i 0.251662i
\(221\) 6.49475e7 0.0272266
\(222\) 1.20699e9i 0.496925i
\(223\) 7.54321e8i 0.305026i −0.988301 0.152513i \(-0.951263\pi\)
0.988301 0.152513i \(-0.0487366\pi\)
\(224\) 2.95994e9 1.17568
\(225\) 1.50135e8 0.0585803
\(226\) −5.32167e8 −0.203993
\(227\) 2.68891e9i 1.01268i −0.862333 0.506342i \(-0.830998\pi\)
0.862333 0.506342i \(-0.169002\pi\)
\(228\) −1.28597e9 −0.475874
\(229\) −6.23178e8 −0.226605 −0.113303 0.993561i \(-0.536143\pi\)
−0.113303 + 0.993561i \(0.536143\pi\)
\(230\) −1.03926e8 −0.0371376
\(231\) 4.02021e9 1.41189
\(232\) 4.94192e9 1.70586
\(233\) 1.32982e9i 0.451199i −0.974220 0.225600i \(-0.927566\pi\)
0.974220 0.225600i \(-0.0724341\pi\)
\(234\) 2.84728e6i 0.000949657i
\(235\) 9.46836e8i 0.310458i
\(236\) 2.31288e9 0.745600
\(237\) 1.01942e9i 0.323116i
\(238\) −4.35372e9 −1.35691
\(239\) −1.85605e9 −0.568850 −0.284425 0.958698i \(-0.591803\pi\)
−0.284425 + 0.958698i \(0.591803\pi\)
\(240\) 3.33430e8 0.100498
\(241\) 2.51423e9i 0.745310i 0.927970 + 0.372655i \(0.121552\pi\)
−0.927970 + 0.372655i \(0.878448\pi\)
\(242\) 5.80944e8i 0.169384i
\(243\) 5.08295e8i 0.145778i
\(244\) 1.14295e9i 0.322454i
\(245\) 1.17393e9i 0.325821i
\(246\) −4.43692e9 −1.21155
\(247\) 6.71514e7i 0.0180413i
\(248\) 3.19756e9i 0.845301i
\(249\) 6.03147e9i 1.56901i
\(250\) 2.19755e9 0.562572
\(251\) 2.38831e9 0.601723 0.300862 0.953668i \(-0.402726\pi\)
0.300862 + 0.953668i \(0.402726\pi\)
\(252\) 1.96809e8i 0.0488027i
\(253\) 5.43049e8 0.132543
\(254\) 4.61829e9i 1.10955i
\(255\) 2.66124e9 0.629394
\(256\) −4.57011e9 −1.06406
\(257\) 5.77650e9i 1.32414i 0.749444 + 0.662068i \(0.230321\pi\)
−0.749444 + 0.662068i \(0.769679\pi\)
\(258\) −5.13923e8 2.94878e9i −0.115990 0.665523i
\(259\) −4.35655e9 −0.968152
\(260\) 1.91266e7i 0.00418547i
\(261\) 5.46542e8i 0.117777i
\(262\) 2.22236e9 0.471639
\(263\) 5.48436e9i 1.14631i 0.819446 + 0.573156i \(0.194281\pi\)
−0.819446 + 0.573156i \(0.805719\pi\)
\(264\) −5.51237e9 −1.13481
\(265\) 2.23820e9i 0.453853i
\(266\) 4.50146e9i 0.899138i
\(267\) −2.75870e9 −0.542824
\(268\) 3.32139e8 0.0643845
\(269\) 5.81055e9 1.10971 0.554853 0.831948i \(-0.312774\pi\)
0.554853 + 0.831948i \(0.312774\pi\)
\(270\) 1.71401e9i 0.322522i
\(271\) −4.93446e9 −0.914877 −0.457439 0.889241i \(-0.651233\pi\)
−0.457439 + 0.889241i \(0.651233\pi\)
\(272\) 1.88682e9 0.344711
\(273\) 1.30430e8 0.0234816
\(274\) −7.28952e9 −1.29329
\(275\) −5.11077e9 −0.893625
\(276\) 3.37401e8i 0.0581446i
\(277\) 6.54007e9i 1.11087i 0.831560 + 0.555435i \(0.187448\pi\)
−0.831560 + 0.555435i \(0.812552\pi\)
\(278\) 1.55989e9i 0.261166i
\(279\) 3.53628e8 0.0583619
\(280\) 3.80770e9i 0.619485i
\(281\) 5.69943e9 0.914126 0.457063 0.889434i \(-0.348901\pi\)
0.457063 + 0.889434i \(0.348901\pi\)
\(282\) −2.98111e9 −0.471391
\(283\) −2.71819e9 −0.423774 −0.211887 0.977294i \(-0.567961\pi\)
−0.211887 + 0.977294i \(0.567961\pi\)
\(284\) 1.30244e9i 0.200209i
\(285\) 2.75154e9i 0.417058i
\(286\) 9.69247e7i 0.0144867i
\(287\) 1.60148e10i 2.36044i
\(288\) 4.48849e8i 0.0652425i
\(289\) 8.08372e9 1.15883
\(290\) 3.56052e9i 0.503409i
\(291\) 8.73639e9i 1.21832i
\(292\) 9.80857e8i 0.134919i
\(293\) 1.69386e9 0.229830 0.114915 0.993375i \(-0.463340\pi\)
0.114915 + 0.993375i \(0.463340\pi\)
\(294\) −3.69613e9 −0.494718
\(295\) 4.94878e9i 0.653447i
\(296\) 5.97355e9 0.778154
\(297\) 8.95629e9i 1.15107i
\(298\) −9.75778e8 −0.123733
\(299\) 1.76185e7 0.00220437
\(300\) 3.17536e9i 0.392020i
\(301\) 1.06434e10 1.85497e9i 1.29663 0.225981i
\(302\) 6.46279e9 0.776949
\(303\) 4.84138e9i 0.574379i
\(304\) 1.95085e9i 0.228417i
\(305\) 2.44553e9 0.282600
\(306\) 6.60203e8i 0.0752995i
\(307\) −1.07653e9 −0.121192 −0.0605961 0.998162i \(-0.519300\pi\)
−0.0605961 + 0.998162i \(0.519300\pi\)
\(308\) 6.69962e9i 0.744471i
\(309\) 1.66441e10i 1.82569i
\(310\) 2.30375e9 0.249453
\(311\) −6.92038e9 −0.739756 −0.369878 0.929080i \(-0.620601\pi\)
−0.369878 + 0.929080i \(0.620601\pi\)
\(312\) −1.78841e8 −0.0188734
\(313\) 4.87540e9i 0.507964i 0.967209 + 0.253982i \(0.0817403\pi\)
−0.967209 + 0.253982i \(0.918260\pi\)
\(314\) 8.99154e9 0.924944
\(315\) −4.21105e8 −0.0427709
\(316\) 1.69885e9 0.170375
\(317\) −4.22998e9 −0.418892 −0.209446 0.977820i \(-0.567166\pi\)
−0.209446 + 0.977820i \(0.567166\pi\)
\(318\) 7.04696e9 0.689118
\(319\) 1.86049e10i 1.79666i
\(320\) 4.01862e9i 0.383245i
\(321\) 5.57615e9i 0.525188i
\(322\) −1.18105e9 −0.109861
\(323\) 1.55705e10i 1.43052i
\(324\) −5.15600e9 −0.467878
\(325\) −1.65812e8 −0.0148622
\(326\) −1.37887e10 −1.22082
\(327\) 1.91780e9i 0.167731i
\(328\) 2.19589e10i 1.89721i
\(329\) 1.07601e10i 0.918404i
\(330\) 3.97151e9i 0.334888i
\(331\) 1.00613e10i 0.838186i −0.907943 0.419093i \(-0.862348\pi\)
0.907943 0.419093i \(-0.137652\pi\)
\(332\) 1.00514e10 0.827319
\(333\) 6.60632e8i 0.0537258i
\(334\) 1.15490e10i 0.928025i
\(335\) 7.10665e8i 0.0564268i
\(336\) 3.78919e9 0.297296
\(337\) −1.58839e10 −1.23151 −0.615753 0.787939i \(-0.711148\pi\)
−0.615753 + 0.787939i \(0.711148\pi\)
\(338\) 9.15477e9i 0.701424i
\(339\) 3.69670e9 0.279908
\(340\) 4.43492e9i 0.331871i
\(341\) −1.20379e10 −0.890293
\(342\) 6.82607e8 0.0498960
\(343\) 4.87660e9i 0.352322i
\(344\) −1.45939e10 + 2.54348e9i −1.04217 + 0.181633i
\(345\) 7.21922e8 0.0509582
\(346\) 2.01612e9i 0.140673i
\(347\) 2.05288e10i 1.41595i −0.706240 0.707973i \(-0.749610\pi\)
0.706240 0.707973i \(-0.250390\pi\)
\(348\) −1.15594e10 −0.788165
\(349\) 4.83149e9i 0.325671i −0.986653 0.162835i \(-0.947936\pi\)
0.986653 0.162835i \(-0.0520640\pi\)
\(350\) 1.11151e10 0.740700
\(351\) 2.90575e8i 0.0191439i
\(352\) 1.52793e10i 0.995254i
\(353\) −2.45055e10 −1.57821 −0.789105 0.614258i \(-0.789455\pi\)
−0.789105 + 0.614258i \(0.789455\pi\)
\(354\) 1.55812e10 0.992176
\(355\) −2.78677e9 −0.175464
\(356\) 4.59733e9i 0.286224i
\(357\) 3.02431e10 1.86189
\(358\) 7.06419e9 0.430061
\(359\) −2.54268e9 −0.153079 −0.0765393 0.997067i \(-0.524387\pi\)
−0.0765393 + 0.997067i \(0.524387\pi\)
\(360\) 5.77405e8 0.0343772
\(361\) 8.84687e8 0.0520908
\(362\) 7.71637e9i 0.449344i
\(363\) 4.03553e9i 0.232420i
\(364\) 2.17360e8i 0.0123815i
\(365\) 2.09870e9 0.118244
\(366\) 7.69973e9i 0.429093i
\(367\) 1.75953e10 0.969914 0.484957 0.874538i \(-0.338835\pi\)
0.484957 + 0.874538i \(0.338835\pi\)
\(368\) 5.11844e8 0.0279091
\(369\) −2.42850e9 −0.130989
\(370\) 4.30378e9i 0.229637i
\(371\) 2.54356e10i 1.34260i
\(372\) 7.47923e9i 0.390558i
\(373\) 1.05811e10i 0.546635i −0.961924 0.273318i \(-0.911879\pi\)
0.961924 0.273318i \(-0.0881210\pi\)
\(374\) 2.24741e10i 1.14867i
\(375\) −1.52653e10 −0.771932
\(376\) 1.47539e10i 0.738169i
\(377\) 6.03612e8i 0.0298808i
\(378\) 1.94785e10i 0.954090i
\(379\) 2.81900e9 0.136628 0.0683138 0.997664i \(-0.478238\pi\)
0.0683138 + 0.997664i \(0.478238\pi\)
\(380\) −4.58541e9 −0.219909
\(381\) 3.20810e10i 1.52247i
\(382\) −1.62325e10 −0.762308
\(383\) 3.93346e10i 1.82801i −0.405699 0.914007i \(-0.632972\pi\)
0.405699 0.914007i \(-0.367028\pi\)
\(384\) 6.04704e9 0.278111
\(385\) 1.43349e10 0.652457
\(386\) 2.47507e10i 1.11491i
\(387\) −2.81291e8 1.61398e9i −0.0125404 0.0719540i
\(388\) 1.45591e10 0.642403
\(389\) 2.95328e10i 1.28975i 0.764288 + 0.644875i \(0.223091\pi\)
−0.764288 + 0.644875i \(0.776909\pi\)
\(390\) 1.28850e8i 0.00556964i
\(391\) 4.08523e9 0.174787
\(392\) 1.82926e10i 0.774697i
\(393\) −1.54376e10 −0.647159
\(394\) 5.08171e9i 0.210875i
\(395\) 3.63495e9i 0.149317i
\(396\) −1.01594e9 −0.0413130
\(397\) −4.05863e10 −1.63387 −0.816935 0.576730i \(-0.804329\pi\)
−0.816935 + 0.576730i \(0.804329\pi\)
\(398\) 2.12192e10 0.845661
\(399\) 3.12694e10i 1.23375i
\(400\) −4.81709e9 −0.188168
\(401\) 1.60282e10 0.619881 0.309940 0.950756i \(-0.399691\pi\)
0.309940 + 0.950756i \(0.399691\pi\)
\(402\) 2.23753e9 0.0856770
\(403\) −3.90553e8 −0.0148068
\(404\) −8.06810e9 −0.302863
\(405\) 1.10321e10i 0.410051i
\(406\) 4.04628e10i 1.48920i
\(407\) 2.24887e10i 0.819571i
\(408\) −4.14683e10 −1.49649
\(409\) 4.50915e10i 1.61139i 0.592328 + 0.805697i \(0.298209\pi\)
−0.592328 + 0.805697i \(0.701791\pi\)
\(410\) −1.58208e10 −0.559877
\(411\) 5.06367e10 1.77459
\(412\) 2.77372e10 0.962661
\(413\) 5.62395e10i 1.93304i
\(414\) 1.79096e8i 0.00609654i
\(415\) 2.15065e10i 0.725066i
\(416\) 4.95718e8i 0.0165524i
\(417\) 1.08358e10i 0.358358i
\(418\) −2.32367e10 −0.761149
\(419\) 5.81410e9i 0.188637i 0.995542 + 0.0943184i \(0.0300672\pi\)
−0.995542 + 0.0943184i \(0.969933\pi\)
\(420\) 8.90639e9i 0.286223i
\(421\) 4.04666e10i 1.28815i −0.764960 0.644077i \(-0.777241\pi\)
0.764960 0.644077i \(-0.222759\pi\)
\(422\) 3.10653e9 0.0979549
\(423\) −1.63168e9 −0.0509652
\(424\) 3.48763e10i 1.07911i
\(425\) −3.84471e10 −1.17844
\(426\) 8.77415e9i 0.266420i
\(427\) 2.77917e10 0.835994
\(428\) −9.29259e9 −0.276925
\(429\) 6.73287e8i 0.0198779i
\(430\) −1.83251e9 1.05145e10i −0.0536008 0.307549i
\(431\) −1.24158e10 −0.359803 −0.179901 0.983685i \(-0.557578\pi\)
−0.179901 + 0.983685i \(0.557578\pi\)
\(432\) 8.44164e9i 0.242377i
\(433\) 4.05793e10i 1.15439i −0.816606 0.577195i \(-0.804147\pi\)
0.816606 0.577195i \(-0.195853\pi\)
\(434\) 2.61805e10 0.737938
\(435\) 2.47331e10i 0.690752i
\(436\) 3.19600e9 0.0884423
\(437\) 4.22386e9i 0.115820i
\(438\) 6.60775e9i 0.179538i
\(439\) 4.33049e10 1.16595 0.582973 0.812491i \(-0.301889\pi\)
0.582973 + 0.812491i \(0.301889\pi\)
\(440\) −1.96555e10 −0.524414
\(441\) −2.02304e9 −0.0534872
\(442\) 7.29142e8i 0.0191039i
\(443\) 5.62607e9 0.146080 0.0730400 0.997329i \(-0.476730\pi\)
0.0730400 + 0.997329i \(0.476730\pi\)
\(444\) −1.39724e10 −0.359533
\(445\) −9.83673e9 −0.250848
\(446\) −8.46850e9 −0.214026
\(447\) 6.77824e9 0.169780
\(448\) 4.56688e10i 1.13372i
\(449\) 3.19821e10i 0.786903i 0.919345 + 0.393451i \(0.128719\pi\)
−0.919345 + 0.393451i \(0.871281\pi\)
\(450\) 1.68551e9i 0.0411038i
\(451\) 8.26691e10 1.99819
\(452\) 6.16050e9i 0.147592i
\(453\) −4.48938e10 −1.06609
\(454\) −3.01875e10 −0.710565
\(455\) 4.65077e8 0.0108512
\(456\) 4.28754e10i 0.991629i
\(457\) 7.26146e10i 1.66479i 0.554184 + 0.832394i \(0.313030\pi\)
−0.554184 + 0.832394i \(0.686970\pi\)
\(458\) 6.99620e9i 0.159001i
\(459\) 6.73761e10i 1.51794i
\(460\) 1.20307e9i 0.0268696i
\(461\) 5.17863e10 1.14660 0.573299 0.819346i \(-0.305663\pi\)
0.573299 + 0.819346i \(0.305663\pi\)
\(462\) 4.51334e10i 0.990673i
\(463\) 3.23815e10i 0.704650i −0.935878 0.352325i \(-0.885391\pi\)
0.935878 0.352325i \(-0.114609\pi\)
\(464\) 1.75358e10i 0.378316i
\(465\) −1.60030e10 −0.342287
\(466\) −1.49294e10 −0.316591
\(467\) 3.11892e10i 0.655747i −0.944722 0.327873i \(-0.893668\pi\)
0.944722 0.327873i \(-0.106332\pi\)
\(468\) −3.29608e7 −0.000687091
\(469\) 8.07621e9i 0.166923i
\(470\) −1.06298e10 −0.217838
\(471\) −6.24597e10 −1.26916
\(472\) 7.71136e10i 1.55368i
\(473\) 9.57546e9 + 5.49419e10i 0.191300 + 1.09764i
\(474\) 1.14446e10 0.226719
\(475\) 3.97518e10i 0.780877i
\(476\) 5.03997e10i 0.981749i
\(477\) 3.85708e9 0.0745050
\(478\) 2.08372e10i 0.399143i
\(479\) −9.30639e9 −0.176782 −0.0883912 0.996086i \(-0.528173\pi\)
−0.0883912 + 0.996086i \(0.528173\pi\)
\(480\) 2.03122e10i 0.382641i
\(481\) 7.29616e8i 0.0136306i
\(482\) 2.82264e10 0.522958
\(483\) 8.20414e9 0.150746
\(484\) 6.72515e9 0.122552
\(485\) 3.11515e10i 0.563004i
\(486\) 5.70645e9 0.102287
\(487\) −9.25780e10 −1.64586 −0.822928 0.568146i \(-0.807661\pi\)
−0.822928 + 0.568146i \(0.807661\pi\)
\(488\) −3.81070e10 −0.671932
\(489\) 9.57830e10 1.67515
\(490\) −1.31793e10 −0.228617
\(491\) 5.31182e9i 0.0913939i −0.998955 0.0456970i \(-0.985449\pi\)
0.998955 0.0456970i \(-0.0145509\pi\)
\(492\) 5.13629e10i 0.876575i
\(493\) 1.39960e11i 2.36929i
\(494\) −7.53885e8 −0.0126589
\(495\) 2.17376e9i 0.0362069i
\(496\) −1.13462e10 −0.187466
\(497\) −3.16697e10 −0.519062
\(498\) 6.77132e10 1.10092
\(499\) 1.79703e10i 0.289837i 0.989444 + 0.144918i \(0.0462920\pi\)
−0.989444 + 0.144918i \(0.953708\pi\)
\(500\) 2.54394e10i 0.407030i
\(501\) 8.02253e10i 1.27339i
\(502\) 2.68128e10i 0.422208i
\(503\) 8.02520e10i 1.25367i 0.779151 + 0.626836i \(0.215650\pi\)
−0.779151 + 0.626836i \(0.784350\pi\)
\(504\) 6.56180e9 0.101695
\(505\) 1.72630e10i 0.265430i
\(506\) 6.09662e9i 0.0930009i
\(507\) 6.35936e10i 0.962458i
\(508\) 5.34625e10 0.802776
\(509\) 6.47170e10 0.964156 0.482078 0.876128i \(-0.339882\pi\)
0.482078 + 0.876128i \(0.339882\pi\)
\(510\) 2.98767e10i 0.441624i
\(511\) 2.38503e10 0.349792
\(512\) 3.14567e10i 0.457755i
\(513\) −6.96625e10 −1.00584
\(514\) 6.48507e10 0.929100
\(515\) 5.93481e10i 0.843680i
\(516\) 3.41358e10 5.94931e9i 0.481516 0.0839204i
\(517\) 5.55443e10 0.777458
\(518\) 4.89094e10i 0.679318i
\(519\) 1.40050e10i 0.193025i
\(520\) −6.37698e8 −0.00872171
\(521\) 1.28872e11i 1.74908i 0.484955 + 0.874539i \(0.338836\pi\)
−0.484955 + 0.874539i \(0.661164\pi\)
\(522\) 6.13583e9 0.0826402
\(523\) 2.50640e10i 0.334999i 0.985872 + 0.167500i \(0.0535693\pi\)
−0.985872 + 0.167500i \(0.946431\pi\)
\(524\) 2.57266e10i 0.341238i
\(525\) −7.72112e10 −1.01635
\(526\) 6.15710e10 0.804327
\(527\) −9.05583e10 −1.17405
\(528\) 1.95600e10i 0.251671i
\(529\) −7.72028e10 −0.985849
\(530\) 2.51275e10 0.318453
\(531\) 8.52822e9 0.107271
\(532\) −5.21100e10 −0.650541
\(533\) 2.68209e9 0.0332326
\(534\) 3.09709e10i 0.380881i
\(535\) 1.98830e10i 0.242698i
\(536\) 1.10738e10i 0.134165i
\(537\) −4.90714e10 −0.590107
\(538\) 6.52330e10i 0.778643i
\(539\) 6.88665e10 0.815931
\(540\) −1.98418e10 −0.233349
\(541\) −8.94644e10 −1.04439 −0.522193 0.852827i \(-0.674886\pi\)
−0.522193 + 0.852827i \(0.674886\pi\)
\(542\) 5.53975e10i 0.641938i
\(543\) 5.36017e10i 0.616566i
\(544\) 1.14943e11i 1.31246i
\(545\) 6.83834e9i 0.0775113i
\(546\) 1.46429e9i 0.0164762i
\(547\) −2.63222e9 −0.0294018 −0.0147009 0.999892i \(-0.504680\pi\)
−0.0147009 + 0.999892i \(0.504680\pi\)
\(548\) 8.43854e10i 0.935718i
\(549\) 4.21437e9i 0.0463920i
\(550\) 5.73768e10i 0.627026i
\(551\) −1.44710e11 −1.56997
\(552\) −1.12492e10 −0.121162
\(553\) 4.13087e10i 0.441714i
\(554\) 7.34230e10 0.779459
\(555\) 2.98962e10i 0.315097i
\(556\) −1.80577e10 −0.188957
\(557\) −9.49214e10 −0.986151 −0.493075 0.869987i \(-0.664127\pi\)
−0.493075 + 0.869987i \(0.664127\pi\)
\(558\) 3.97005e9i 0.0409505i
\(559\) 3.10663e8 + 1.78252e9i 0.00318158 + 0.0182552i
\(560\) 1.35112e10 0.137386
\(561\) 1.56116e11i 1.57615i
\(562\) 6.39855e10i 0.641411i
\(563\) 1.59291e11 1.58547 0.792734 0.609568i \(-0.208657\pi\)
0.792734 + 0.609568i \(0.208657\pi\)
\(564\) 3.45101e10i 0.341059i
\(565\) 1.31814e10 0.129350
\(566\) 3.05161e10i 0.297347i
\(567\) 1.25372e11i 1.21302i
\(568\) 4.34244e10 0.417197
\(569\) 6.53976e10 0.623897 0.311949 0.950099i \(-0.399018\pi\)
0.311949 + 0.950099i \(0.399018\pi\)
\(570\) −3.08906e10 −0.292635
\(571\) 1.38007e11i 1.29825i −0.760683 0.649124i \(-0.775136\pi\)
0.760683 0.649124i \(-0.224864\pi\)
\(572\) 1.12202e9 0.0104814
\(573\) 1.12759e11 1.04600
\(574\) −1.79792e11 −1.65624
\(575\) −1.04297e10 −0.0954113
\(576\) −6.92527e9 −0.0629139
\(577\) 6.28157e9i 0.0566716i 0.999598 + 0.0283358i \(0.00902077\pi\)
−0.999598 + 0.0283358i \(0.990979\pi\)
\(578\) 9.07530e10i 0.813111i
\(579\) 1.71931e11i 1.52982i
\(580\) −4.12174e10 −0.364224
\(581\) 2.44407e11i 2.14491i
\(582\) 9.80804e10 0.854850
\(583\) −1.31300e11 −1.13655
\(584\) −3.27026e10 −0.281146
\(585\) 7.05249e7i 0.000602170i
\(586\) 1.90164e10i 0.161264i
\(587\) 7.97093e10i 0.671362i 0.941976 + 0.335681i \(0.108966\pi\)
−0.941976 + 0.335681i \(0.891034\pi\)
\(588\) 4.27873e10i 0.357936i
\(589\) 9.36313e10i 0.777965i
\(590\) 5.55582e10 0.458501
\(591\) 3.53001e10i 0.289351i
\(592\) 2.11964e10i 0.172574i
\(593\) 1.09184e11i 0.882960i −0.897271 0.441480i \(-0.854454\pi\)
0.897271 0.441480i \(-0.145546\pi\)
\(594\) −1.00549e11 −0.807667
\(595\) 1.07838e11 0.860409
\(596\) 1.12958e10i 0.0895228i
\(597\) −1.47399e11 −1.16037
\(598\) 1.97797e8i 0.00154673i
\(599\) −6.17501e10 −0.479656 −0.239828 0.970815i \(-0.577091\pi\)
−0.239828 + 0.970815i \(0.577091\pi\)
\(600\) 1.05869e11 0.816893
\(601\) 6.83095e10i 0.523580i 0.965125 + 0.261790i \(0.0843128\pi\)
−0.965125 + 0.261790i \(0.915687\pi\)
\(602\) −2.08251e10 1.19490e11i −0.158563 0.909799i
\(603\) 1.22469e9 0.00926309
\(604\) 7.48149e10i 0.562135i
\(605\) 1.43895e10i 0.107405i
\(606\) −5.43525e10 −0.403022
\(607\) 9.53091e10i 0.702068i −0.936363 0.351034i \(-0.885830\pi\)
0.936363 0.351034i \(-0.114170\pi\)
\(608\) 1.18843e11 0.869683
\(609\) 2.81075e11i 2.04340i
\(610\) 2.74550e10i 0.198291i
\(611\) 1.80206e9 0.0129302
\(612\) −7.64268e9 −0.0544804
\(613\) 2.29649e11 1.62638 0.813190 0.581998i \(-0.197729\pi\)
0.813190 + 0.581998i \(0.197729\pi\)
\(614\) 1.20859e10i 0.0850363i
\(615\) 1.09899e11 0.768235
\(616\) −2.23371e11 −1.55133
\(617\) 1.63025e11 1.12490 0.562451 0.826831i \(-0.309859\pi\)
0.562451 + 0.826831i \(0.309859\pi\)
\(618\) 1.86857e11 1.28102
\(619\) 2.44766e11 1.66720 0.833600 0.552368i \(-0.186276\pi\)
0.833600 + 0.552368i \(0.186276\pi\)
\(620\) 2.66688e10i 0.180483i
\(621\) 1.82774e10i 0.122899i
\(622\) 7.76927e10i 0.519061i
\(623\) −1.11788e11 −0.742064
\(624\) 6.34598e8i 0.00418563i
\(625\) 6.79509e10 0.445323
\(626\) 5.47343e10 0.356420
\(627\) 1.61414e11 1.04441
\(628\) 1.04088e11i 0.669211i
\(629\) 1.69177e11i 1.08079i
\(630\) 4.72760e9i 0.0300109i
\(631\) 2.93871e11i 1.85370i −0.375432 0.926850i \(-0.622506\pi\)
0.375432 0.926850i \(-0.377494\pi\)
\(632\) 5.66410e10i 0.355028i
\(633\) −2.15795e10 −0.134409
\(634\) 4.74885e10i 0.293922i
\(635\) 1.14392e11i 0.703557i
\(636\) 8.15774e10i 0.498587i
\(637\) 2.23428e9 0.0135700
\(638\) −2.08871e11 −1.26065
\(639\) 4.80244e9i 0.0288044i
\(640\) 2.15620e10 0.128520
\(641\) 1.49515e11i 0.885629i −0.896613 0.442815i \(-0.853980\pi\)
0.896613 0.442815i \(-0.146020\pi\)
\(642\) −6.26015e10 −0.368506
\(643\) 3.12896e11 1.83045 0.915223 0.402948i \(-0.132015\pi\)
0.915223 + 0.402948i \(0.132015\pi\)
\(644\) 1.36721e10i 0.0794862i
\(645\) 1.27295e10 + 7.30390e10i 0.0735482 + 0.422003i
\(646\) −1.74805e11 −1.00374
\(647\) 4.68994e10i 0.267639i −0.991006 0.133820i \(-0.957276\pi\)
0.991006 0.133820i \(-0.0427243\pi\)
\(648\) 1.71906e11i 0.974967i
\(649\) −2.90311e11 −1.63638
\(650\) 1.86151e9i 0.0104283i
\(651\) −1.81863e11 −1.01256
\(652\) 1.59621e11i 0.883284i
\(653\) 1.20001e11i 0.659982i 0.943984 + 0.329991i \(0.107046\pi\)
−0.943984 + 0.329991i \(0.892954\pi\)
\(654\) 2.15305e10 0.117691
\(655\) −5.50462e10 −0.299063
\(656\) 7.79187e10 0.420752
\(657\) 3.61668e9i 0.0194110i
\(658\) −1.20800e11 −0.644412
\(659\) −2.66563e11 −1.41338 −0.706688 0.707526i \(-0.749811\pi\)
−0.706688 + 0.707526i \(0.749811\pi\)
\(660\) 4.59752e10 0.242297
\(661\) −3.28604e11 −1.72134 −0.860671 0.509162i \(-0.829955\pi\)
−0.860671 + 0.509162i \(0.829955\pi\)
\(662\) −1.12954e11 −0.588126
\(663\) 5.06498e9i 0.0262134i
\(664\) 3.35122e11i 1.72397i
\(665\) 1.11498e11i 0.570137i
\(666\) 7.41669e9 0.0376975
\(667\) 3.79676e10i 0.191827i
\(668\) 1.33694e11 0.671440
\(669\) 5.88264e10 0.293676
\(670\) 7.97838e9 0.0395928
\(671\) 1.43462e11i 0.707696i
\(672\) 2.30833e11i 1.13194i
\(673\) 2.06329e11i 1.00577i −0.864352 0.502887i \(-0.832271\pi\)
0.864352 0.502887i \(-0.167729\pi\)
\(674\) 1.78323e11i 0.864106i
\(675\) 1.72013e11i 0.828601i
\(676\) −1.05978e11 −0.507492
\(677\) 3.04887e11i 1.45139i −0.688016 0.725695i \(-0.741518\pi\)
0.688016 0.725695i \(-0.258482\pi\)
\(678\) 4.15015e10i 0.196402i
\(679\) 3.54015e11i 1.66549i
\(680\) −1.47864e11 −0.691555
\(681\) 2.09697e11 0.974999
\(682\) 1.35145e11i 0.624688i
\(683\) −2.76020e11 −1.26840 −0.634202 0.773168i \(-0.718671\pi\)
−0.634202 + 0.773168i \(0.718671\pi\)
\(684\) 7.90203e9i 0.0361006i
\(685\) 1.80556e11 0.820067
\(686\) 5.47478e10 0.247212
\(687\) 4.85991e10i 0.218173i
\(688\) 9.02523e9 + 5.17848e10i 0.0402814 + 0.231126i
\(689\) −4.25984e9 −0.0189024
\(690\) 8.10477e9i 0.0357556i
\(691\) 1.83321e11i 0.804080i 0.915622 + 0.402040i \(0.131699\pi\)
−0.915622 + 0.402040i \(0.868301\pi\)
\(692\) 2.33391e10 0.101779
\(693\) 2.47033e10i 0.107108i
\(694\) −2.30470e11 −0.993520
\(695\) 3.86374e10i 0.165603i
\(696\) 3.85400e11i 1.64238i
\(697\) 6.21900e11 2.63505
\(698\) −5.42414e10 −0.228512
\(699\) 1.03707e11 0.434409
\(700\) 1.28671e11i 0.535908i
\(701\) 2.61721e11 1.08384 0.541922 0.840429i \(-0.317697\pi\)
0.541922 + 0.840429i \(0.317697\pi\)
\(702\) −3.26218e9 −0.0134326
\(703\) −1.74918e11 −0.716166
\(704\) 2.35744e11 0.959733
\(705\) 7.38398e10 0.298906
\(706\) 2.75115e11i 1.10738i
\(707\) 1.96182e11i 0.785201i
\(708\) 1.80372e11i 0.717855i
\(709\) −2.88387e11 −1.14127 −0.570637 0.821202i \(-0.693304\pi\)
−0.570637 + 0.821202i \(0.693304\pi\)
\(710\) 3.12861e10i 0.123117i
\(711\) 6.26410e9 0.0245121
\(712\) 1.53279e11 0.596435
\(713\) −2.45661e10 −0.0950555
\(714\) 3.39528e11i 1.30642i
\(715\) 2.40075e9i 0.00918592i
\(716\) 8.17768e10i 0.311156i
\(717\) 1.44746e11i 0.547683i
\(718\) 2.85458e10i 0.107410i
\(719\) −1.09961e10 −0.0411456 −0.0205728 0.999788i \(-0.506549\pi\)
−0.0205728 + 0.999788i \(0.506549\pi\)
\(720\) 2.04885e9i 0.00762397i
\(721\) 6.74450e11i 2.49579i
\(722\) 9.93207e9i 0.0365503i
\(723\) −1.96074e11 −0.717575
\(724\) 8.93266e10 0.325107
\(725\) 3.57322e11i 1.29332i
\(726\) 4.53054e10 0.163081
\(727\) 5.25195e11i 1.88011i −0.341024 0.940054i \(-0.610774\pi\)
0.341024 0.940054i \(-0.389226\pi\)
\(728\) −7.24699e9 −0.0258007
\(729\) −2.99934e11 −1.06198
\(730\) 2.35614e10i 0.0829677i
\(731\) 7.20340e10 + 4.13315e11i 0.252271 + 1.44748i
\(732\) 8.91340e10 0.310455
\(733\) 8.73247e10i 0.302497i −0.988496 0.151249i \(-0.951671\pi\)
0.988496 0.151249i \(-0.0483294\pi\)
\(734\) 1.97537e11i 0.680555i
\(735\) 9.15503e10 0.313697
\(736\) 3.11810e10i 0.106262i
\(737\) −4.16898e10 −0.141306
\(738\) 2.72639e10i 0.0919101i
\(739\) 2.90510e10i 0.0974054i 0.998813 + 0.0487027i \(0.0155087\pi\)
−0.998813 + 0.0487027i \(0.984491\pi\)
\(740\) −4.98216e10 −0.166146
\(741\) 5.23686e9 0.0173699
\(742\) 2.85556e11 0.942054
\(743\) 4.72649e11i 1.55090i −0.631409 0.775450i \(-0.717523\pi\)
0.631409 0.775450i \(-0.282477\pi\)
\(744\) 2.49364e11 0.813846
\(745\) 2.41693e10 0.0784582
\(746\) −1.18791e11 −0.383555
\(747\) 3.70621e10 0.119028
\(748\) 2.60166e11 0.831081
\(749\) 2.25956e11i 0.717955i
\(750\) 1.71378e11i 0.541638i
\(751\) 1.12217e11i 0.352777i 0.984321 + 0.176389i \(0.0564416\pi\)
−0.984321 + 0.176389i \(0.943558\pi\)
\(752\) 5.23525e10 0.163707
\(753\) 1.86255e11i 0.579332i
\(754\) −6.77654e9 −0.0209663
\(755\) −1.60078e11 −0.492657
\(756\) −2.25489e11 −0.690299
\(757\) 4.09584e11i 1.24727i −0.781717 0.623634i \(-0.785656\pi\)
0.781717 0.623634i \(-0.214344\pi\)
\(758\) 3.16479e10i 0.0958669i
\(759\) 4.23502e10i 0.127611i
\(760\) 1.52882e11i 0.458248i
\(761\) 3.43697e11i 1.02480i 0.858748 + 0.512398i \(0.171243\pi\)
−0.858748 + 0.512398i \(0.828757\pi\)
\(762\) 3.60162e11 1.06826
\(763\) 7.77130e10i 0.229295i
\(764\) 1.87911e11i 0.551542i
\(765\) 1.63527e10i 0.0477468i
\(766\) −4.41595e11 −1.28265
\(767\) −9.41874e9 −0.0272152
\(768\) 3.56404e11i 1.02447i
\(769\) −2.31427e10 −0.0661774 −0.0330887 0.999452i \(-0.510534\pi\)
−0.0330887 + 0.999452i \(0.510534\pi\)
\(770\) 1.60933e11i 0.457807i
\(771\) −4.50485e11 −1.27486
\(772\) −2.86520e11 −0.806653
\(773\) 4.68931e10i 0.131338i −0.997841 0.0656690i \(-0.979082\pi\)
0.997841 0.0656690i \(-0.0209182\pi\)
\(774\) −1.81196e10 + 3.15795e9i −0.0504876 + 0.00879917i
\(775\) 2.31197e11 0.640878
\(776\) 4.85413e11i 1.33864i
\(777\) 3.39749e11i 0.932125i
\(778\) 3.31554e11 0.904974
\(779\) 6.43004e11i 1.74608i
\(780\) 1.49160e9 0.00402972
\(781\) 1.63481e11i 0.439402i
\(782\)