Properties

Label 43.11.b.b.42.9
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 42.9
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.26

$q$-expansion

\(f(q)\) \(=\) \(q-41.1797i q^{2} -18.8325i q^{3} -671.767 q^{4} +4211.22i q^{5} -775.516 q^{6} -20378.0i q^{7} -14504.9i q^{8} +58694.3 q^{9} +O(q^{10})\) \(q-41.1797i q^{2} -18.8325i q^{3} -671.767 q^{4} +4211.22i q^{5} -775.516 q^{6} -20378.0i q^{7} -14504.9i q^{8} +58694.3 q^{9} +173417. q^{10} -306949. q^{11} +12651.0i q^{12} +198968. q^{13} -839160. q^{14} +79307.8 q^{15} -1.28519e6 q^{16} -2.08922e6 q^{17} -2.41701e6i q^{18} +2.97711e6i q^{19} -2.82896e6i q^{20} -383769. q^{21} +1.26401e7i q^{22} +1.17271e6 q^{23} -273163. q^{24} -7.96877e6 q^{25} -8.19343e6i q^{26} -2.21740e6i q^{27} +1.36893e7i q^{28} -2.43453e7i q^{29} -3.26587e6i q^{30} -3.70189e7 q^{31} +3.80709e7i q^{32} +5.78061e6i q^{33} +8.60332e7i q^{34} +8.58163e7 q^{35} -3.94289e7 q^{36} +7.72003e7i q^{37} +1.22597e8 q^{38} -3.74706e6i q^{39} +6.10832e7 q^{40} -6.69942e7 q^{41} +1.58035e7i q^{42} +(2.69450e7 + 1.44518e8i) q^{43} +2.06198e8 q^{44} +2.47175e8i q^{45} -4.82916e7i q^{46} -4.29292e8 q^{47} +2.42034e7i q^{48} -1.32788e8 q^{49} +3.28152e8i q^{50} +3.93451e7i q^{51} -1.33660e8 q^{52} +2.00012e8 q^{53} -9.13119e7 q^{54} -1.29263e9i q^{55} -2.95580e8 q^{56} +5.60664e7 q^{57} -1.00253e9 q^{58} +3.24891e8 q^{59} -5.32764e7 q^{60} +8.68845e8i q^{61} +1.52443e9i q^{62} -1.19607e9i q^{63} +2.51710e8 q^{64} +8.37897e8i q^{65} +2.38044e8 q^{66} -1.36258e9 q^{67} +1.40347e9 q^{68} -2.20850e7i q^{69} -3.53389e9i q^{70} -2.65191e9i q^{71} -8.51353e8i q^{72} +1.07991e7i q^{73} +3.17909e9 q^{74} +1.50072e8i q^{75} -1.99992e9i q^{76} +6.25501e9i q^{77} -1.54303e8 q^{78} +8.01396e8 q^{79} -5.41224e9i q^{80} +3.42408e9 q^{81} +2.75880e9i q^{82} -5.22410e9 q^{83} +2.57803e8 q^{84} -8.79815e9i q^{85} +(5.95121e9 - 1.10959e9i) q^{86} -4.58482e8 q^{87} +4.45225e9i q^{88} -6.11548e9i q^{89} +1.01786e10 q^{90} -4.05456e9i q^{91} -7.87784e8 q^{92} +6.97159e8i q^{93} +1.76781e10i q^{94} -1.25373e10 q^{95} +7.16971e8 q^{96} +3.80330e8 q^{97} +5.46816e9i q^{98} -1.80162e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 41.1797i 1.28687i −0.765503 0.643433i \(-0.777510\pi\)
0.765503 0.643433i \(-0.222490\pi\)
\(3\) 18.8325i 0.0775000i −0.999249 0.0387500i \(-0.987662\pi\)
0.999249 0.0387500i \(-0.0123376\pi\)
\(4\) −671.767 −0.656022
\(5\) 4211.22i 1.34759i 0.738918 + 0.673796i \(0.235337\pi\)
−0.738918 + 0.673796i \(0.764663\pi\)
\(6\) −775.516 −0.0997320
\(7\) 20378.0i 1.21247i −0.795285 0.606236i \(-0.792679\pi\)
0.795285 0.606236i \(-0.207321\pi\)
\(8\) 14504.9i 0.442653i
\(9\) 58694.3 0.993994
\(10\) 173417. 1.73417
\(11\) −306949. −1.90591 −0.952956 0.303110i \(-0.901975\pi\)
−0.952956 + 0.303110i \(0.901975\pi\)
\(12\) 12651.0i 0.0508417i
\(13\) 198968. 0.535878 0.267939 0.963436i \(-0.413657\pi\)
0.267939 + 0.963436i \(0.413657\pi\)
\(14\) −839160. −1.56029
\(15\) 79307.8 0.104438
\(16\) −1.28519e6 −1.22566
\(17\) −2.08922e6 −1.47143 −0.735713 0.677293i \(-0.763153\pi\)
−0.735713 + 0.677293i \(0.763153\pi\)
\(18\) 2.41701e6i 1.27914i
\(19\) 2.97711e6i 1.20234i 0.799121 + 0.601170i \(0.205298\pi\)
−0.799121 + 0.601170i \(0.794702\pi\)
\(20\) 2.82896e6i 0.884050i
\(21\) −383769. −0.0939665
\(22\) 1.26401e7i 2.45265i
\(23\) 1.17271e6 0.182201 0.0911003 0.995842i \(-0.470962\pi\)
0.0911003 + 0.995842i \(0.470962\pi\)
\(24\) −273163. −0.0343056
\(25\) −7.96877e6 −0.816002
\(26\) 8.19343e6i 0.689603i
\(27\) 2.21740e6i 0.154534i
\(28\) 1.36893e7i 0.795408i
\(29\) 2.43453e7i 1.18693i −0.804860 0.593464i \(-0.797760\pi\)
0.804860 0.593464i \(-0.202240\pi\)
\(30\) 3.26587e6i 0.134398i
\(31\) −3.70189e7 −1.29305 −0.646525 0.762893i \(-0.723778\pi\)
−0.646525 + 0.762893i \(0.723778\pi\)
\(32\) 3.80709e7i 1.13460i
\(33\) 5.78061e6i 0.147708i
\(34\) 8.60332e7i 1.89353i
\(35\) 8.58163e7 1.63392
\(36\) −3.94289e7 −0.652082
\(37\) 7.72003e7i 1.11330i 0.830749 + 0.556648i \(0.187913\pi\)
−0.830749 + 0.556648i \(0.812087\pi\)
\(38\) 1.22597e8 1.54725
\(39\) 3.74706e6i 0.0415305i
\(40\) 6.10832e7 0.596516
\(41\) −6.69942e7 −0.578253 −0.289127 0.957291i \(-0.593365\pi\)
−0.289127 + 0.957291i \(0.593365\pi\)
\(42\) 1.58035e7i 0.120922i
\(43\) 2.69450e7 + 1.44518e8i 0.183289 + 0.983059i
\(44\) 2.06198e8 1.25032
\(45\) 2.47175e8i 1.33950i
\(46\) 4.82916e7i 0.234468i
\(47\) −4.29292e8 −1.87182 −0.935909 0.352242i \(-0.885420\pi\)
−0.935909 + 0.352242i \(0.885420\pi\)
\(48\) 2.42034e7i 0.0949884i
\(49\) −1.32788e8 −0.470086
\(50\) 3.28152e8i 1.05009i
\(51\) 3.93451e7i 0.114036i
\(52\) −1.33660e8 −0.351548
\(53\) 2.00012e8 0.478275 0.239137 0.970986i \(-0.423135\pi\)
0.239137 + 0.970986i \(0.423135\pi\)
\(54\) −9.13119e7 −0.198865
\(55\) 1.29263e9i 2.56839i
\(56\) −2.95580e8 −0.536704
\(57\) 5.60664e7 0.0931813
\(58\) −1.00253e9 −1.52742
\(59\) 3.24891e8 0.454441 0.227221 0.973843i \(-0.427036\pi\)
0.227221 + 0.973843i \(0.427036\pi\)
\(60\) −5.32764e7 −0.0685138
\(61\) 8.68845e8i 1.02871i 0.857577 + 0.514355i \(0.171969\pi\)
−0.857577 + 0.514355i \(0.828031\pi\)
\(62\) 1.52443e9i 1.66398i
\(63\) 1.19607e9i 1.20519i
\(64\) 2.51710e8 0.234423
\(65\) 8.37897e8i 0.722144i
\(66\) 2.38044e8 0.190080
\(67\) −1.36258e9 −1.00923 −0.504614 0.863345i \(-0.668365\pi\)
−0.504614 + 0.863345i \(0.668365\pi\)
\(68\) 1.40347e9 0.965288
\(69\) 2.20850e7i 0.0141205i
\(70\) 3.53389e9i 2.10263i
\(71\) 2.65191e9i 1.46983i −0.678159 0.734916i \(-0.737222\pi\)
0.678159 0.734916i \(-0.262778\pi\)
\(72\) 8.51353e8i 0.439995i
\(73\) 1.07991e7i 0.00520922i 0.999997 + 0.00260461i \(0.000829074\pi\)
−0.999997 + 0.00260461i \(0.999171\pi\)
\(74\) 3.17909e9 1.43266
\(75\) 1.50072e8i 0.0632402i
\(76\) 1.99992e9i 0.788761i
\(77\) 6.25501e9i 2.31086i
\(78\) −1.54303e8 −0.0534442
\(79\) 8.01396e8 0.260442 0.130221 0.991485i \(-0.458431\pi\)
0.130221 + 0.991485i \(0.458431\pi\)
\(80\) 5.41224e9i 1.65168i
\(81\) 3.42408e9 0.982017
\(82\) 2.75880e9i 0.744134i
\(83\) −5.22410e9 −1.32624 −0.663118 0.748515i \(-0.730767\pi\)
−0.663118 + 0.748515i \(0.730767\pi\)
\(84\) 2.57803e8 0.0616441
\(85\) 8.79815e9i 1.98288i
\(86\) 5.95121e9 1.10959e9i 1.26506 0.235868i
\(87\) −4.58482e8 −0.0919869
\(88\) 4.45225e9i 0.843658i
\(89\) 6.11548e9i 1.09517i −0.836751 0.547584i \(-0.815548\pi\)
0.836751 0.547584i \(-0.184452\pi\)
\(90\) 1.01786e10 1.72375
\(91\) 4.05456e9i 0.649737i
\(92\) −7.87784e8 −0.119528
\(93\) 6.97159e8i 0.100211i
\(94\) 1.76781e10i 2.40878i
\(95\) −1.25373e10 −1.62026
\(96\) 7.16971e8 0.0879316
\(97\) 3.80330e8 0.0442897 0.0221448 0.999755i \(-0.492951\pi\)
0.0221448 + 0.999755i \(0.492951\pi\)
\(98\) 5.46816e9i 0.604938i
\(99\) −1.80162e10 −1.89446
\(100\) 5.35316e9 0.535316
\(101\) −1.00808e9 −0.0959149 −0.0479575 0.998849i \(-0.515271\pi\)
−0.0479575 + 0.998849i \(0.515271\pi\)
\(102\) 1.62022e9 0.146748
\(103\) −7.72985e9 −0.666784 −0.333392 0.942788i \(-0.608193\pi\)
−0.333392 + 0.942788i \(0.608193\pi\)
\(104\) 2.88600e9i 0.237208i
\(105\) 1.61614e9i 0.126628i
\(106\) 8.23644e9i 0.615475i
\(107\) 1.71519e10 1.22291 0.611453 0.791281i \(-0.290585\pi\)
0.611453 + 0.791281i \(0.290585\pi\)
\(108\) 1.48958e9i 0.101378i
\(109\) −1.06240e10 −0.690490 −0.345245 0.938513i \(-0.612204\pi\)
−0.345245 + 0.938513i \(0.612204\pi\)
\(110\) −5.32301e10 −3.30517
\(111\) 1.45387e9 0.0862804
\(112\) 2.61897e10i 1.48607i
\(113\) 1.02518e10i 0.556426i −0.960519 0.278213i \(-0.910258\pi\)
0.960519 0.278213i \(-0.0897420\pi\)
\(114\) 2.30880e9i 0.119912i
\(115\) 4.93852e9i 0.245532i
\(116\) 1.63543e10i 0.778651i
\(117\) 1.16783e10 0.532659
\(118\) 1.33789e10i 0.584804i
\(119\) 4.25740e10i 1.78406i
\(120\) 1.15035e9i 0.0462299i
\(121\) 6.82802e10 2.63250
\(122\) 3.57788e10 1.32381
\(123\) 1.26167e9i 0.0448146i
\(124\) 2.48681e10 0.848269
\(125\) 7.56694e9i 0.247953i
\(126\) −4.92539e10 −1.55092
\(127\) −4.52404e10 −1.36933 −0.684664 0.728858i \(-0.740051\pi\)
−0.684664 + 0.728858i \(0.740051\pi\)
\(128\) 2.86193e10i 0.832931i
\(129\) 2.72163e9 5.07441e8i 0.0761871 0.0142049i
\(130\) 3.45044e10 0.929303
\(131\) 2.50465e10i 0.649218i −0.945848 0.324609i \(-0.894767\pi\)
0.945848 0.324609i \(-0.105233\pi\)
\(132\) 3.88322e9i 0.0968998i
\(133\) 6.06676e10 1.45780
\(134\) 5.61108e10i 1.29874i
\(135\) 9.33797e9 0.208249
\(136\) 3.03038e10i 0.651332i
\(137\) 9.00858e10i 1.86661i −0.359086 0.933304i \(-0.616912\pi\)
0.359086 0.933304i \(-0.383088\pi\)
\(138\) −9.09452e8 −0.0181712
\(139\) 5.76790e10 1.11159 0.555794 0.831320i \(-0.312414\pi\)
0.555794 + 0.831320i \(0.312414\pi\)
\(140\) −5.76485e10 −1.07188
\(141\) 8.08464e9i 0.145066i
\(142\) −1.09205e11 −1.89147
\(143\) −6.10729e10 −1.02134
\(144\) −7.54336e10 −1.21830
\(145\) 1.02523e11 1.59949
\(146\) 4.44703e8 0.00670356
\(147\) 2.50072e9i 0.0364317i
\(148\) 5.18606e10i 0.730347i
\(149\) 2.29987e10i 0.313164i −0.987665 0.156582i \(-0.949952\pi\)
0.987665 0.156582i \(-0.0500476\pi\)
\(150\) 6.17991e9 0.0813816
\(151\) 9.49837e10i 1.20994i −0.796248 0.604971i \(-0.793185\pi\)
0.796248 0.604971i \(-0.206815\pi\)
\(152\) 4.31826e10 0.532219
\(153\) −1.22625e11 −1.46259
\(154\) 2.57579e11 2.97377
\(155\) 1.55895e11i 1.74250i
\(156\) 2.51715e9i 0.0272449i
\(157\) 1.21491e11i 1.27364i 0.771012 + 0.636820i \(0.219751\pi\)
−0.771012 + 0.636820i \(0.780249\pi\)
\(158\) 3.30012e10i 0.335154i
\(159\) 3.76673e9i 0.0370663i
\(160\) −1.60325e11 −1.52898
\(161\) 2.38974e10i 0.220913i
\(162\) 1.41003e11i 1.26372i
\(163\) 1.84974e11i 1.60758i −0.594912 0.803791i \(-0.702813\pi\)
0.594912 0.803791i \(-0.297187\pi\)
\(164\) 4.50045e10 0.379347
\(165\) −2.43435e10 −0.199050
\(166\) 2.15127e11i 1.70669i
\(167\) 8.11760e10 0.624950 0.312475 0.949926i \(-0.398842\pi\)
0.312475 + 0.949926i \(0.398842\pi\)
\(168\) 5.56651e9i 0.0415946i
\(169\) −9.82703e10 −0.712835
\(170\) −3.62305e11 −2.55170
\(171\) 1.74740e11i 1.19512i
\(172\) −1.81007e10 9.70824e10i −0.120241 0.644908i
\(173\) 1.35005e10 0.0871203 0.0435602 0.999051i \(-0.486130\pi\)
0.0435602 + 0.999051i \(0.486130\pi\)
\(174\) 1.88802e10i 0.118375i
\(175\) 1.62388e11i 0.989380i
\(176\) 3.94489e11 2.33599
\(177\) 6.11851e9i 0.0352192i
\(178\) −2.51834e11 −1.40933
\(179\) 2.77340e11i 1.50920i −0.656185 0.754600i \(-0.727831\pi\)
0.656185 0.754600i \(-0.272169\pi\)
\(180\) 1.66044e11i 0.878740i
\(181\) 1.47844e11 0.761044 0.380522 0.924772i \(-0.375744\pi\)
0.380522 + 0.924772i \(0.375744\pi\)
\(182\) −1.66966e11 −0.836123
\(183\) 1.63625e10 0.0797251
\(184\) 1.70099e10i 0.0806517i
\(185\) −3.25108e11 −1.50027
\(186\) 2.87088e10 0.128958
\(187\) 6.41283e11 2.80441
\(188\) 2.88384e11 1.22795
\(189\) −4.51862e10 −0.187369
\(190\) 5.16281e11i 2.08506i
\(191\) 2.41346e10i 0.0949452i −0.998873 0.0474726i \(-0.984883\pi\)
0.998873 0.0474726i \(-0.0151167\pi\)
\(192\) 4.74032e9i 0.0181678i
\(193\) 3.27870e11 1.22438 0.612188 0.790712i \(-0.290290\pi\)
0.612188 + 0.790712i \(0.290290\pi\)
\(194\) 1.56619e10i 0.0569948i
\(195\) 1.57797e10 0.0559662
\(196\) 8.92024e10 0.308387
\(197\) 2.22343e11 0.749362 0.374681 0.927154i \(-0.377752\pi\)
0.374681 + 0.927154i \(0.377752\pi\)
\(198\) 7.41900e11i 2.43792i
\(199\) 8.68831e10i 0.278401i 0.990264 + 0.139200i \(0.0444532\pi\)
−0.990264 + 0.139200i \(0.955547\pi\)
\(200\) 1.15586e11i 0.361206i
\(201\) 2.56609e10i 0.0782152i
\(202\) 4.15122e10i 0.123430i
\(203\) −4.96108e11 −1.43912
\(204\) 2.64308e10i 0.0748098i
\(205\) 2.82128e11i 0.779249i
\(206\) 3.18313e11i 0.858060i
\(207\) 6.88312e10 0.181106
\(208\) −2.55712e11 −0.656803
\(209\) 9.13821e11i 2.29155i
\(210\) −6.65519e10 −0.162954
\(211\) 6.37697e10i 0.152476i 0.997090 + 0.0762381i \(0.0242909\pi\)
−0.997090 + 0.0762381i \(0.975709\pi\)
\(212\) −1.34362e11 −0.313759
\(213\) −4.99421e10 −0.113912
\(214\) 7.06309e11i 1.57372i
\(215\) −6.08598e11 + 1.13471e11i −1.32476 + 0.246998i
\(216\) −3.21631e10 −0.0684052
\(217\) 7.54372e11i 1.56779i
\(218\) 4.37495e11i 0.888568i
\(219\) 2.03374e8 0.000403714
\(220\) 8.68346e11i 1.68492i
\(221\) −4.15686e11 −0.788505
\(222\) 5.98701e10i 0.111031i
\(223\) 2.01118e11i 0.364692i 0.983234 + 0.182346i \(0.0583691\pi\)
−0.983234 + 0.182346i \(0.941631\pi\)
\(224\) 7.75810e11 1.37567
\(225\) −4.67722e11 −0.811101
\(226\) −4.22165e11 −0.716045
\(227\) 7.86063e11i 1.30415i 0.758154 + 0.652076i \(0.226102\pi\)
−0.758154 + 0.652076i \(0.773898\pi\)
\(228\) −3.76636e10 −0.0611290
\(229\) −6.66086e11 −1.05768 −0.528839 0.848722i \(-0.677372\pi\)
−0.528839 + 0.848722i \(0.677372\pi\)
\(230\) 2.03367e11 0.315966
\(231\) 1.17797e11 0.179092
\(232\) −3.53125e11 −0.525398
\(233\) 6.74973e11i 0.982895i 0.870907 + 0.491447i \(0.163532\pi\)
−0.870907 + 0.491447i \(0.836468\pi\)
\(234\) 4.80908e11i 0.685461i
\(235\) 1.80784e12i 2.52245i
\(236\) −2.18251e11 −0.298123
\(237\) 1.50923e10i 0.0201843i
\(238\) 1.75319e12 2.29585
\(239\) 2.80487e11 0.359686 0.179843 0.983695i \(-0.442441\pi\)
0.179843 + 0.983695i \(0.442441\pi\)
\(240\) −1.01926e11 −0.128006
\(241\) 8.56037e9i 0.0105295i 0.999986 + 0.00526474i \(0.00167583\pi\)
−0.999986 + 0.00526474i \(0.998324\pi\)
\(242\) 2.81176e12i 3.38767i
\(243\) 1.95419e11i 0.230641i
\(244\) 5.83661e11i 0.674857i
\(245\) 5.59199e11i 0.633484i
\(246\) 5.19551e10 0.0576704
\(247\) 5.92349e11i 0.644307i
\(248\) 5.36954e11i 0.572373i
\(249\) 9.83828e10i 0.102783i
\(250\) 3.11604e11 0.319083
\(251\) −1.08237e12 −1.08645 −0.543224 0.839588i \(-0.682797\pi\)
−0.543224 + 0.839588i \(0.682797\pi\)
\(252\) 8.03482e11i 0.790630i
\(253\) −3.59961e11 −0.347258
\(254\) 1.86299e12i 1.76214i
\(255\) −1.65691e11 −0.153673
\(256\) 1.43628e12 1.30629
\(257\) 1.25145e11i 0.111621i 0.998441 + 0.0558106i \(0.0177743\pi\)
−0.998441 + 0.0558106i \(0.982226\pi\)
\(258\) −2.08963e10 1.12076e11i −0.0182797 0.0980425i
\(259\) 1.57319e12 1.34984
\(260\) 5.62872e11i 0.473743i
\(261\) 1.42893e12i 1.17980i
\(262\) −1.03141e12 −0.835456
\(263\) 8.17179e10i 0.0649439i −0.999473 0.0324720i \(-0.989662\pi\)
0.999473 0.0324720i \(-0.0103380\pi\)
\(264\) 8.38470e10 0.0653835
\(265\) 8.42296e11i 0.644519i
\(266\) 2.49827e12i 1.87599i
\(267\) −1.15170e11 −0.0848755
\(268\) 9.15339e11 0.662076
\(269\) 1.08953e12 0.773534 0.386767 0.922177i \(-0.373592\pi\)
0.386767 + 0.922177i \(0.373592\pi\)
\(270\) 3.84535e11i 0.267989i
\(271\) 1.20425e12 0.823892 0.411946 0.911208i \(-0.364849\pi\)
0.411946 + 0.911208i \(0.364849\pi\)
\(272\) 2.68505e12 1.80346
\(273\) −7.63576e10 −0.0503546
\(274\) −3.70970e12 −2.40207
\(275\) 2.44601e12 1.55523
\(276\) 1.48359e10i 0.00926339i
\(277\) 9.20016e11i 0.564153i 0.959392 + 0.282076i \(0.0910231\pi\)
−0.959392 + 0.282076i \(0.908977\pi\)
\(278\) 2.37520e12i 1.43046i
\(279\) −2.17280e12 −1.28528
\(280\) 1.24475e12i 0.723258i
\(281\) −1.19875e12 −0.684224 −0.342112 0.939659i \(-0.611142\pi\)
−0.342112 + 0.939659i \(0.611142\pi\)
\(282\) 3.32923e11 0.186680
\(283\) −2.28969e12 −1.26137 −0.630687 0.776037i \(-0.717227\pi\)
−0.630687 + 0.776037i \(0.717227\pi\)
\(284\) 1.78147e12i 0.964242i
\(285\) 2.36108e11i 0.125570i
\(286\) 2.51496e12i 1.31432i
\(287\) 1.36521e12i 0.701116i
\(288\) 2.23455e12i 1.12779i
\(289\) 2.34883e12 1.16510
\(290\) 4.22188e12i 2.05833i
\(291\) 7.16257e9i 0.00343245i
\(292\) 7.25446e9i 0.00341736i
\(293\) −2.04015e11 −0.0944767 −0.0472384 0.998884i \(-0.515042\pi\)
−0.0472384 + 0.998884i \(0.515042\pi\)
\(294\) 1.02979e11 0.0468827
\(295\) 1.36819e12i 0.612401i
\(296\) 1.11978e12 0.492804
\(297\) 6.80629e11i 0.294529i
\(298\) −9.47080e11 −0.403000
\(299\) 2.33331e11 0.0976373
\(300\) 1.00813e11i 0.0414869i
\(301\) 2.94499e12 5.49085e11i 1.19193 0.222232i
\(302\) −3.91140e12 −1.55703
\(303\) 1.89846e10i 0.00743340i
\(304\) 3.82617e12i 1.47366i
\(305\) −3.65890e12 −1.38628
\(306\) 5.04966e12i 1.88215i
\(307\) −1.58303e12 −0.580492 −0.290246 0.956952i \(-0.593737\pi\)
−0.290246 + 0.956952i \(0.593737\pi\)
\(308\) 4.20190e12i 1.51598i
\(309\) 1.45572e11i 0.0516757i
\(310\) −6.41970e12 −2.24237
\(311\) −1.19646e12 −0.411242 −0.205621 0.978632i \(-0.565921\pi\)
−0.205621 + 0.978632i \(0.565921\pi\)
\(312\) −5.43506e10 −0.0183836
\(313\) 3.25449e12i 1.08333i 0.840594 + 0.541665i \(0.182206\pi\)
−0.840594 + 0.541665i \(0.817794\pi\)
\(314\) 5.00297e12 1.63900
\(315\) 5.03693e12 1.62410
\(316\) −5.38351e11 −0.170856
\(317\) −5.13842e11 −0.160521 −0.0802607 0.996774i \(-0.525575\pi\)
−0.0802607 + 0.996774i \(0.525575\pi\)
\(318\) −1.55113e11 −0.0476993
\(319\) 7.47275e12i 2.26218i
\(320\) 1.06001e12i 0.315907i
\(321\) 3.23013e11i 0.0947752i
\(322\) −9.84087e11 −0.284285
\(323\) 6.21983e12i 1.76915i
\(324\) −2.30018e12 −0.644225
\(325\) −1.58553e12 −0.437278
\(326\) −7.61718e12 −2.06874
\(327\) 2.00077e11i 0.0535130i
\(328\) 9.71742e11i 0.255966i
\(329\) 8.74812e12i 2.26953i
\(330\) 1.00246e12i 0.256151i
\(331\) 2.16998e12i 0.546154i 0.961992 + 0.273077i \(0.0880413\pi\)
−0.961992 + 0.273077i \(0.911959\pi\)
\(332\) 3.50937e12 0.870040
\(333\) 4.53122e12i 1.10661i
\(334\) 3.34280e12i 0.804226i
\(335\) 5.73815e12i 1.36003i
\(336\) 4.93217e11 0.115171
\(337\) 4.97435e11 0.114442 0.0572211 0.998362i \(-0.481776\pi\)
0.0572211 + 0.998362i \(0.481776\pi\)
\(338\) 4.04674e12i 0.917322i
\(339\) −1.93067e11 −0.0431230
\(340\) 5.91031e12i 1.30081i
\(341\) 1.13629e13 2.46444
\(342\) 7.19572e12 1.53796
\(343\) 3.05033e12i 0.642505i
\(344\) 2.09621e12 3.90833e11i 0.435154 0.0811333i
\(345\) 9.30047e10 0.0190287
\(346\) 5.55947e11i 0.112112i
\(347\) 5.03418e12i 1.00065i 0.865838 + 0.500324i \(0.166786\pi\)
−0.865838 + 0.500324i \(0.833214\pi\)
\(348\) 3.07993e11 0.0603455
\(349\) 7.27438e12i 1.40498i −0.711695 0.702488i \(-0.752072\pi\)
0.711695 0.702488i \(-0.247928\pi\)
\(350\) 6.68708e12 1.27320
\(351\) 4.41191e11i 0.0828116i
\(352\) 1.16858e13i 2.16245i
\(353\) 7.54518e11 0.137656 0.0688282 0.997629i \(-0.478074\pi\)
0.0688282 + 0.997629i \(0.478074\pi\)
\(354\) −2.51958e11 −0.0453223
\(355\) 1.11678e13 1.98073
\(356\) 4.10818e12i 0.718454i
\(357\) 8.01775e11 0.138265
\(358\) −1.14208e13 −1.94214
\(359\) −6.02737e12 −1.01078 −0.505389 0.862892i \(-0.668651\pi\)
−0.505389 + 0.862892i \(0.668651\pi\)
\(360\) 3.58524e12 0.592933
\(361\) −2.73212e12 −0.445620
\(362\) 6.08815e12i 0.979361i
\(363\) 1.28589e12i 0.204019i
\(364\) 2.72372e12i 0.426242i
\(365\) −4.54774e10 −0.00701990
\(366\) 6.73804e11i 0.102595i
\(367\) −9.28837e12 −1.39511 −0.697556 0.716530i \(-0.745729\pi\)
−0.697556 + 0.716530i \(0.745729\pi\)
\(368\) −1.50715e12 −0.223315
\(369\) −3.93218e12 −0.574780
\(370\) 1.33878e13i 1.93064i
\(371\) 4.07585e12i 0.579894i
\(372\) 4.68328e11i 0.0657408i
\(373\) 3.36263e12i 0.465731i 0.972509 + 0.232866i \(0.0748102\pi\)
−0.972509 + 0.232866i \(0.925190\pi\)
\(374\) 2.64078e13i 3.60890i
\(375\) 1.42504e11 0.0192164
\(376\) 6.22682e12i 0.828566i
\(377\) 4.84392e12i 0.636049i
\(378\) 1.86075e12i 0.241118i
\(379\) 5.76499e11 0.0737229 0.0368615 0.999320i \(-0.488264\pi\)
0.0368615 + 0.999320i \(0.488264\pi\)
\(380\) 8.42213e12 1.06293
\(381\) 8.51989e11i 0.106123i
\(382\) −9.93854e11 −0.122182
\(383\) 4.64396e12i 0.563501i −0.959488 0.281751i \(-0.909085\pi\)
0.959488 0.281751i \(-0.0909151\pi\)
\(384\) 5.38973e11 0.0645522
\(385\) −2.63412e13 −3.11410
\(386\) 1.35016e13i 1.57561i
\(387\) 1.58152e12 + 8.48239e12i 0.182188 + 0.977155i
\(388\) −2.55493e11 −0.0290550
\(389\) 6.56720e12i 0.737279i −0.929572 0.368640i \(-0.879824\pi\)
0.929572 0.368640i \(-0.120176\pi\)
\(390\) 6.49803e11i 0.0720209i
\(391\) −2.45003e12 −0.268095
\(392\) 1.92607e12i 0.208085i
\(393\) −4.71688e11 −0.0503143
\(394\) 9.15600e12i 0.964328i
\(395\) 3.37486e12i 0.350970i
\(396\) 1.21027e13 1.24281
\(397\) 3.69878e11 0.0375064 0.0187532 0.999824i \(-0.494030\pi\)
0.0187532 + 0.999824i \(0.494030\pi\)
\(398\) 3.57782e12 0.358264
\(399\) 1.14252e12i 0.112980i
\(400\) 1.02414e13 1.00014
\(401\) 1.28581e13 1.24009 0.620047 0.784564i \(-0.287113\pi\)
0.620047 + 0.784564i \(0.287113\pi\)
\(402\) 1.05671e12 0.100652
\(403\) −7.36557e12 −0.692917
\(404\) 6.77191e11 0.0629223
\(405\) 1.44196e13i 1.32336i
\(406\) 2.04296e13i 1.85195i
\(407\) 2.36966e13i 2.12184i
\(408\) 5.70696e11 0.0504782
\(409\) 1.08776e13i 0.950424i 0.879871 + 0.475212i \(0.157629\pi\)
−0.879871 + 0.475212i \(0.842371\pi\)
\(410\) −1.16179e13 −1.00279
\(411\) −1.69654e12 −0.144662
\(412\) 5.19265e12 0.437425
\(413\) 6.62063e12i 0.550997i
\(414\) 2.83445e12i 0.233059i
\(415\) 2.19998e13i 1.78722i
\(416\) 7.57489e12i 0.608008i
\(417\) 1.08624e12i 0.0861481i
\(418\) −3.76309e13 −2.94892
\(419\) 1.20480e13i 0.932919i 0.884543 + 0.466459i \(0.154471\pi\)
−0.884543 + 0.466459i \(0.845529\pi\)
\(420\) 1.08567e12i 0.0830710i
\(421\) 2.17260e12i 0.164274i −0.996621 0.0821372i \(-0.973825\pi\)
0.996621 0.0821372i \(-0.0261746\pi\)
\(422\) 2.62602e12 0.196216
\(423\) −2.51970e13 −1.86058
\(424\) 2.90115e12i 0.211710i
\(425\) 1.66485e13 1.20069
\(426\) 2.05660e12i 0.146589i
\(427\) 1.77053e13 1.24728
\(428\) −1.15221e13 −0.802253
\(429\) 1.15016e12i 0.0791535i
\(430\) 4.67271e12 + 2.50619e13i 0.317853 + 1.70479i
\(431\) 2.01490e13 1.35477 0.677386 0.735628i \(-0.263113\pi\)
0.677386 + 0.735628i \(0.263113\pi\)
\(432\) 2.84979e12i 0.189406i
\(433\) 2.69988e13i 1.77380i −0.461961 0.886900i \(-0.652854\pi\)
0.461961 0.886900i \(-0.347146\pi\)
\(434\) 3.10648e13 2.01753
\(435\) 1.93077e12i 0.123961i
\(436\) 7.13688e12 0.452977
\(437\) 3.49127e12i 0.219067i
\(438\) 8.37486e9i 0.000519526i
\(439\) −2.46701e12 −0.151303 −0.0756516 0.997134i \(-0.524104\pi\)
−0.0756516 + 0.997134i \(0.524104\pi\)
\(440\) −1.87494e13 −1.13691
\(441\) −7.79389e12 −0.467263
\(442\) 1.71178e13i 1.01470i
\(443\) −2.40592e13 −1.41014 −0.705070 0.709138i \(-0.749084\pi\)
−0.705070 + 0.709138i \(0.749084\pi\)
\(444\) −9.76665e11 −0.0566018
\(445\) 2.57537e13 1.47584
\(446\) 8.28197e12 0.469309
\(447\) −4.33123e11 −0.0242702
\(448\) 5.12934e12i 0.284231i
\(449\) 2.08597e13i 1.14308i 0.820575 + 0.571539i \(0.193654\pi\)
−0.820575 + 0.571539i \(0.806346\pi\)
\(450\) 1.92606e13i 1.04378i
\(451\) 2.05638e13 1.10210
\(452\) 6.88680e12i 0.365027i
\(453\) −1.78878e12 −0.0937704
\(454\) 3.23698e13 1.67827
\(455\) 1.70747e13 0.875579
\(456\) 8.13236e11i 0.0412470i
\(457\) 5.28568e12i 0.265167i 0.991172 + 0.132583i \(0.0423273\pi\)
−0.991172 + 0.132583i \(0.957673\pi\)
\(458\) 2.74292e13i 1.36109i
\(459\) 4.63263e12i 0.227386i
\(460\) 3.31754e12i 0.161074i
\(461\) −2.05871e13 −0.988760 −0.494380 0.869246i \(-0.664605\pi\)
−0.494380 + 0.869246i \(0.664605\pi\)
\(462\) 4.85086e12i 0.230467i
\(463\) 5.27910e12i 0.248116i −0.992275 0.124058i \(-0.960409\pi\)
0.992275 0.124058i \(-0.0395909\pi\)
\(464\) 3.12884e13i 1.45477i
\(465\) −2.93589e12 −0.135044
\(466\) 2.77952e13 1.26485
\(467\) 2.92808e13i 1.31825i 0.752032 + 0.659127i \(0.229074\pi\)
−0.752032 + 0.659127i \(0.770926\pi\)
\(468\) −7.84508e12 −0.349436
\(469\) 2.77668e13i 1.22366i
\(470\) −7.44465e13 −3.24605
\(471\) 2.28798e12 0.0987071
\(472\) 4.71250e12i 0.201160i
\(473\) −8.27073e12 4.43596e13i −0.349332 1.87362i
\(474\) −6.21495e11 −0.0259744
\(475\) 2.37239e13i 0.981112i
\(476\) 2.85998e13i 1.17038i
\(477\) 1.17396e13 0.475402
\(478\) 1.15504e13i 0.462868i
\(479\) −2.31846e13 −0.919435 −0.459718 0.888065i \(-0.652049\pi\)
−0.459718 + 0.888065i \(0.652049\pi\)
\(480\) 3.01932e12i 0.118496i
\(481\) 1.53604e13i 0.596591i
\(482\) 3.52513e11 0.0135500
\(483\) −4.50047e11 −0.0171207
\(484\) −4.58684e13 −1.72698
\(485\) 1.60166e12i 0.0596844i
\(486\) −8.04731e12 −0.296804
\(487\) −6.90238e12 −0.251973 −0.125986 0.992032i \(-0.540210\pi\)
−0.125986 + 0.992032i \(0.540210\pi\)
\(488\) 1.26025e13 0.455362
\(489\) −3.48352e12 −0.124588
\(490\) −2.30276e13 −0.815209
\(491\) 4.35665e13i 1.52667i −0.646002 0.763336i \(-0.723560\pi\)
0.646002 0.763336i \(-0.276440\pi\)
\(492\) 8.47547e11i 0.0293994i
\(493\) 5.08625e13i 1.74648i
\(494\) 2.43927e13 0.829136
\(495\) 7.58701e13i 2.55296i
\(496\) 4.75765e13 1.58484
\(497\) −5.40407e13 −1.78213
\(498\) 4.05137e12 0.132268
\(499\) 1.71296e13i 0.553660i −0.960919 0.276830i \(-0.910716\pi\)
0.960919 0.276830i \(-0.0892839\pi\)
\(500\) 5.08322e12i 0.162663i
\(501\) 1.52875e12i 0.0484336i
\(502\) 4.45718e13i 1.39811i
\(503\) 8.11768e11i 0.0252111i 0.999921 + 0.0126056i \(0.00401258\pi\)
−0.999921 + 0.0126056i \(0.995987\pi\)
\(504\) −1.73489e13 −0.533481
\(505\) 4.24523e12i 0.129254i
\(506\) 1.48231e13i 0.446874i
\(507\) 1.85068e12i 0.0552447i
\(508\) 3.03910e13 0.898310
\(509\) −5.59364e13 −1.63721 −0.818607 0.574355i \(-0.805253\pi\)
−0.818607 + 0.574355i \(0.805253\pi\)
\(510\) 6.82311e12i 0.197757i
\(511\) 2.20064e11 0.00631603
\(512\) 2.98396e13i 0.848092i
\(513\) 6.60145e12 0.185803
\(514\) 5.15342e12 0.143641
\(515\) 3.25521e13i 0.898552i
\(516\) −1.82830e12 + 3.40882e11i −0.0499804 + 0.00931870i
\(517\) 1.31771e14 3.56752
\(518\) 6.47834e13i 1.73706i
\(519\) 2.54248e11i 0.00675182i
\(520\) 1.21536e13 0.319660
\(521\) 1.30236e12i 0.0339267i 0.999856 + 0.0169633i \(0.00539985\pi\)
−0.999856 + 0.0169633i \(0.994600\pi\)
\(522\) −5.88429e13 −1.51824
\(523\) 1.21766e13i 0.311185i 0.987821 + 0.155592i \(0.0497287\pi\)
−0.987821 + 0.155592i \(0.950271\pi\)
\(524\) 1.68254e13i 0.425901i
\(525\) 3.05817e12 0.0766769
\(526\) −3.36512e12 −0.0835741
\(527\) 7.73405e13 1.90263
\(528\) 7.42921e12i 0.181039i
\(529\) −4.00513e13 −0.966803
\(530\) 3.46855e13 0.829409
\(531\) 1.90693e13 0.451712
\(532\) −4.07545e13 −0.956350
\(533\) −1.33297e13 −0.309873
\(534\) 4.74266e12i 0.109223i
\(535\) 7.22304e13i 1.64798i
\(536\) 1.97641e13i 0.446738i
\(537\) −5.22299e12 −0.116963
\(538\) 4.48667e13i 0.995434i
\(539\) 4.07591e13 0.895943
\(540\) −6.27294e12 −0.136616
\(541\) −1.10489e13 −0.238414 −0.119207 0.992869i \(-0.538035\pi\)
−0.119207 + 0.992869i \(0.538035\pi\)
\(542\) 4.95906e13i 1.06024i
\(543\) 2.78426e12i 0.0589809i
\(544\) 7.95384e13i 1.66948i
\(545\) 4.47402e13i 0.930499i
\(546\) 3.14438e12i 0.0647995i
\(547\) 8.07039e13 1.64800 0.824002 0.566588i \(-0.191737\pi\)
0.824002 + 0.566588i \(0.191737\pi\)
\(548\) 6.05166e13i 1.22454i
\(549\) 5.09963e13i 1.02253i
\(550\) 1.00726e14i 2.00137i
\(551\) 7.24786e13 1.42709
\(552\) −3.20339e11 −0.00625050
\(553\) 1.63308e13i 0.315779i
\(554\) 3.78860e13 0.725988
\(555\) 6.12259e12i 0.116271i
\(556\) −3.87468e13 −0.729226
\(557\) 3.13382e12 0.0584518 0.0292259 0.999573i \(-0.490696\pi\)
0.0292259 + 0.999573i \(0.490696\pi\)
\(558\) 8.94753e13i 1.65399i
\(559\) 5.36118e12 + 2.87544e13i 0.0982203 + 0.526800i
\(560\) −1.10291e14 −2.00262
\(561\) 1.20769e13i 0.217342i
\(562\) 4.93643e13i 0.880504i
\(563\) −5.11185e13 −0.903725 −0.451863 0.892088i \(-0.649240\pi\)
−0.451863 + 0.892088i \(0.649240\pi\)
\(564\) 5.43099e12i 0.0951664i
\(565\) 4.31725e13 0.749834
\(566\) 9.42885e13i 1.62322i
\(567\) 6.97760e13i 1.19067i
\(568\) −3.84656e13 −0.650625
\(569\) −2.55807e13 −0.428895 −0.214447 0.976736i \(-0.568795\pi\)
−0.214447 + 0.976736i \(0.568795\pi\)
\(570\) 9.72286e12 0.161592
\(571\) 2.03558e13i 0.335357i −0.985842 0.167678i \(-0.946373\pi\)
0.985842 0.167678i \(-0.0536270\pi\)
\(572\) 4.10268e13 0.670019
\(573\) −4.54514e11 −0.00735825
\(574\) 5.62189e13 0.902241
\(575\) −9.34502e12 −0.148676
\(576\) 1.47739e13 0.233015
\(577\) 3.08235e13i 0.481951i −0.970531 0.240976i \(-0.922533\pi\)
0.970531 0.240976i \(-0.0774674\pi\)
\(578\) 9.67240e13i 1.49932i
\(579\) 6.17460e12i 0.0948891i
\(580\) −6.88718e13 −1.04930
\(581\) 1.06457e14i 1.60802i
\(582\) −2.94952e11 −0.00441710
\(583\) −6.13935e13 −0.911549
\(584\) 1.56639e11 0.00230588
\(585\) 4.91798e13i 0.717807i
\(586\) 8.40129e12i 0.121579i
\(587\) 1.42551e13i 0.204541i −0.994757 0.102270i \(-0.967389\pi\)
0.994757 0.102270i \(-0.0326107\pi\)
\(588\) 1.67990e12i 0.0239000i
\(589\) 1.10209e14i 1.55468i
\(590\) 5.63416e13 0.788077
\(591\) 4.18727e12i 0.0580755i
\(592\) 9.92175e13i 1.36452i
\(593\) 8.86135e13i 1.20844i 0.796816 + 0.604222i \(0.206516\pi\)
−0.796816 + 0.604222i \(0.793484\pi\)
\(594\) 2.80281e13 0.379019
\(595\) −1.79289e14 −2.40419
\(596\) 1.54498e13i 0.205443i
\(597\) 1.63623e12 0.0215760
\(598\) 9.60848e12i 0.125646i
\(599\) 1.17392e14 1.52232 0.761159 0.648566i \(-0.224631\pi\)
0.761159 + 0.648566i \(0.224631\pi\)
\(600\) 2.17677e12 0.0279935
\(601\) 8.60541e13i 1.09749i 0.835991 + 0.548743i \(0.184894\pi\)
−0.835991 + 0.548743i \(0.815106\pi\)
\(602\) −2.26111e13 1.21274e14i −0.285983 1.53385i
\(603\) −7.99760e13 −1.00317
\(604\) 6.38069e13i 0.793748i
\(605\) 2.87543e14i 3.54753i
\(606\) 7.81779e11 0.00956579
\(607\) 2.31920e12i 0.0281446i 0.999901 + 0.0140723i \(0.00447950\pi\)
−0.999901 + 0.0140723i \(0.995521\pi\)
\(608\) −1.13341e14 −1.36418
\(609\) 9.34295e12i 0.111532i
\(610\) 1.50672e14i 1.78396i
\(611\) −8.54153e13 −1.00307
\(612\) 8.23755e13 0.959491
\(613\) −4.60706e13 −0.532257 −0.266129 0.963938i \(-0.585745\pi\)
−0.266129 + 0.963938i \(0.585745\pi\)
\(614\) 6.51885e13i 0.747014i
\(615\) −5.31317e12 −0.0603918
\(616\) 9.07280e13 1.02291
\(617\) −1.11511e14 −1.24707 −0.623535 0.781796i \(-0.714304\pi\)
−0.623535 + 0.781796i \(0.714304\pi\)
\(618\) 5.99462e12 0.0664997
\(619\) 1.41742e14 1.55972 0.779859 0.625955i \(-0.215291\pi\)
0.779859 + 0.625955i \(0.215291\pi\)
\(620\) 1.04725e14i 1.14312i
\(621\) 2.60036e12i 0.0281563i
\(622\) 4.92700e13i 0.529213i
\(623\) −1.24621e14 −1.32786
\(624\) 4.81570e12i 0.0509022i
\(625\) −1.09686e14 −1.15014
\(626\) 1.34019e14 1.39410
\(627\) −1.72095e13 −0.177595
\(628\) 8.16138e13i 0.835536i
\(629\) 1.61288e14i 1.63813i
\(630\) 2.07419e14i 2.09000i
\(631\) 1.17813e14i 1.17774i 0.808230 + 0.588868i \(0.200426\pi\)
−0.808230 + 0.588868i \(0.799574\pi\)
\(632\) 1.16241e13i 0.115286i
\(633\) 1.20094e12 0.0118169
\(634\) 2.11598e13i 0.206569i
\(635\) 1.90517e14i 1.84530i
\(636\) 2.53036e12i 0.0243163i
\(637\) −2.64205e13 −0.251909
\(638\) 3.07726e14 2.91112
\(639\) 1.55652e14i 1.46100i
\(640\) −1.20522e14 −1.12245
\(641\) 1.89395e14i 1.75017i 0.483973 + 0.875083i \(0.339193\pi\)
−0.483973 + 0.875083i \(0.660807\pi\)
\(642\) −1.33016e13 −0.121963
\(643\) 4.33309e13 0.394224 0.197112 0.980381i \(-0.436844\pi\)
0.197112 + 0.980381i \(0.436844\pi\)
\(644\) 1.60535e13i 0.144924i
\(645\) 2.13695e12 + 1.14614e13i 0.0191424 + 0.102669i
\(646\) −2.56131e14 −2.27666
\(647\) 5.57765e13i 0.491960i 0.969275 + 0.245980i \(0.0791098\pi\)
−0.969275 + 0.245980i \(0.920890\pi\)
\(648\) 4.96658e13i 0.434693i
\(649\) −9.97249e13 −0.866124
\(650\) 6.52916e13i 0.562717i
\(651\) 1.42067e13 0.121503
\(652\) 1.24259e14i 1.05461i
\(653\) 8.97054e13i 0.755531i −0.925901 0.377766i \(-0.876692\pi\)
0.925901 0.377766i \(-0.123308\pi\)
\(654\) 8.23912e12 0.0688640
\(655\) 1.05476e14 0.874880
\(656\) 8.61006e13 0.708740
\(657\) 6.33845e11i 0.00517793i
\(658\) 3.60245e14 2.92057
\(659\) −1.01949e14 −0.820264 −0.410132 0.912026i \(-0.634517\pi\)
−0.410132 + 0.912026i \(0.634517\pi\)
\(660\) 1.63531e13 0.130581
\(661\) 1.91888e14 1.52069 0.760346 0.649518i \(-0.225029\pi\)
0.760346 + 0.649518i \(0.225029\pi\)
\(662\) 8.93589e13 0.702826
\(663\) 7.82841e12i 0.0611091i
\(664\) 7.57748e13i 0.587063i
\(665\) 2.55485e14i 1.96452i
\(666\) 1.86594e14 1.42406
\(667\) 2.85498e13i 0.216259i
\(668\) −5.45313e13 −0.409981
\(669\) 3.78755e12 0.0282636
\(670\) −2.36295e14 −1.75017
\(671\) 2.66691e14i 1.96063i
\(672\) 1.46104e13i 0.106615i
\(673\) 2.47373e14i 1.79174i −0.444311 0.895872i \(-0.646552\pi\)
0.444311 0.895872i \(-0.353448\pi\)
\(674\) 2.04842e13i 0.147272i
\(675\) 1.76700e13i 0.126101i
\(676\) 6.60147e13 0.467635
\(677\) 1.53590e14i 1.07999i 0.841667 + 0.539996i \(0.181574\pi\)
−0.841667 + 0.539996i \(0.818426\pi\)
\(678\) 7.95042e12i 0.0554935i
\(679\) 7.75037e12i 0.0536999i
\(680\) −1.27616e14 −0.877729
\(681\) 1.48035e13 0.101072
\(682\) 4.67921e14i 3.17140i
\(683\) 5.59491e13 0.376434 0.188217 0.982127i \(-0.439729\pi\)
0.188217 + 0.982127i \(0.439729\pi\)
\(684\) 1.17384e14i 0.784024i
\(685\) 3.79371e14 2.51543
\(686\) −1.25612e14 −0.826817
\(687\) 1.25441e13i 0.0819699i
\(688\) −3.46295e13 1.85734e14i −0.224649 1.20489i
\(689\) 3.97960e13 0.256297
\(690\) 3.82990e12i 0.0244874i
\(691\) 5.03376e13i 0.319523i −0.987156 0.159762i \(-0.948927\pi\)
0.987156 0.159762i \(-0.0510726\pi\)
\(692\) −9.06919e12 −0.0571529
\(693\) 3.67133e14i 2.29698i
\(694\) 2.07306e14 1.28770
\(695\) 2.42899e14i 1.49797i
\(696\) 6.65022e12i 0.0407183i
\(697\) 1.39965e14 0.850858
\(698\) −2.99557e14 −1.80802
\(699\) 1.27114e13 0.0761743
\(700\) 1.09087e14i 0.649055i
\(701\) −1.59980e14 −0.945095 −0.472548 0.881305i \(-0.656666\pi\)
−0.472548 + 0.881305i \(0.656666\pi\)
\(702\) −1.81681e13 −0.106567
\(703\) −2.29834e14 −1.33856
\(704\) −7.72621e13 −0.446790
\(705\) −3.40462e13 −0.195489
\(706\) 3.10708e13i 0.177145i
\(707\) 2.05426e13i 0.116294i
\(708\) 4.11021e12i 0.0231046i
\(709\) −3.37818e14 −1.88561 −0.942803 0.333350i \(-0.891821\pi\)
−0.942803 + 0.333350i \(0.891821\pi\)
\(710\) 4.59886e14i 2.54893i
\(711\) 4.70374e13 0.258878
\(712\) −8.87042e13 −0.484780
\(713\) −4.34123e13 −0.235594
\(714\) 3.30169e13i 0.177928i
\(715\) 2.57192e14i 1.37634i
\(716\) 1.86307e14i 0.990068i
\(717\) 5.28228e12i 0.0278757i
\(718\) 2.48205e14i 1.30074i
\(719\) −1.71498e14 −0.892512 −0.446256 0.894905i \(-0.647243\pi\)
−0.446256 + 0.894905i \(0.647243\pi\)
\(720\) 3.17668e14i 1.64176i
\(721\) 1.57519e14i 0.808456i
\(722\) 1.12508e14i 0.573453i
\(723\) 1.61213e11 0.000816035
\(724\) −9.93164e13 −0.499262
\(725\) 1.94002e14i 0.968537i
\(726\) −5.29524e13 −0.262544
\(727\) 3.28609e13i 0.161811i 0.996722 + 0.0809053i \(0.0257811\pi\)
−0.996722 + 0.0809053i \(0.974219\pi\)
\(728\) −5.88109e13 −0.287608
\(729\) 1.98508e14 0.964143
\(730\) 1.87274e12i 0.00903366i
\(731\) −5.62939e13 3.01929e14i −0.269696 1.44650i
\(732\) −1.09918e13 −0.0523014
\(733\) 3.08912e14i 1.45987i −0.683515 0.729937i \(-0.739549\pi\)
0.683515 0.729937i \(-0.260451\pi\)
\(734\) 3.82492e14i 1.79532i
\(735\) −1.05311e13 −0.0490950
\(736\) 4.46460e13i 0.206725i
\(737\) 4.18244e14 1.92350
\(738\) 1.61926e14i 0.739665i
\(739\) 2.73153e14i 1.23932i −0.784869 0.619661i \(-0.787270\pi\)
0.784869 0.619661i \(-0.212730\pi\)
\(740\) 2.18397e14 0.984209
\(741\) 1.11554e13 0.0499338
\(742\) −1.67842e14 −0.746246
\(743\) 2.07176e14i 0.914946i 0.889224 + 0.457473i \(0.151245\pi\)
−0.889224 + 0.457473i \(0.848755\pi\)
\(744\) 1.01122e13 0.0443589
\(745\) 9.68527e13 0.422017
\(746\) 1.38472e14 0.599333
\(747\) −3.06625e14 −1.31827
\(748\) −4.30792e14 −1.83975
\(749\) 3.49521e14i 1.48274i
\(750\) 5.86828e12i 0.0247289i
\(751\) 2.30080e13i 0.0963115i 0.998840 + 0.0481558i \(0.0153344\pi\)
−0.998840 + 0.0481558i \(0.984666\pi\)
\(752\) 5.51724e14 2.29421
\(753\) 2.03838e13i 0.0841997i
\(754\) −1.99471e14 −0.818509
\(755\) 3.99998e14 1.63051
\(756\) 3.03546e13 0.122918
\(757\) 1.51453e14i 0.609256i −0.952471 0.304628i \(-0.901468\pi\)
0.952471 0.304628i \(-0.0985321\pi\)
\(758\) 2.37401e13i 0.0948715i
\(759\) 6.77896e12i 0.0269125i
\(760\) 1.81851e14i 0.717214i
\(761\) 1.71220e14i 0.670858i 0.942065 + 0.335429i \(0.108881\pi\)
−0.942065 + 0.335429i \(0.891119\pi\)
\(762\) 3.50847e13 0.136566
\(763\) 2.16497e14i 0.837200i
\(764\) 1.62128e13i 0.0622861i
\(765\) 5.16402e14i 1.97097i
\(766\) −1.91237e14 −0.725150
\(767\) 6.46428e13 0.243525
\(768\) 2.70488e13i 0.101238i
\(769\) 1.83718e14 0.683155 0.341577 0.939854i \(-0.389039\pi\)
0.341577 + 0.939854i \(0.389039\pi\)
\(770\) 1.08472e15i 4.00743i
\(771\) 2.35679e12 0.00865064
\(772\) −2.20252e14 −0.803218
\(773\) 3.49327e14i 1.26571i 0.774270 + 0.632855i \(0.218117\pi\)
−0.774270 + 0.632855i \(0.781883\pi\)
\(774\) 3.49302e14 6.51264e13i 1.25747 0.234451i
\(775\) 2.94995e14 1.05513
\(776\) 5.51664e12i 0.0196050i
\(777\) 2.96271e13i 0.104612i
\(778\) −2.70435e14 −0.948779
\(779\) 1.99449e14i 0.695257i
\(780\) −1.06003e13