Properties

Label 43.11.b.b.42.15
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 42.15
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.20

$q$-expansion

\(f(q)\) \(=\) \(q-10.4458i q^{2} -477.424i q^{3} +914.885 q^{4} -5026.78i q^{5} -4987.08 q^{6} +7308.14i q^{7} -20253.2i q^{8} -168885. q^{9} +O(q^{10})\) \(q-10.4458i q^{2} -477.424i q^{3} +914.885 q^{4} -5026.78i q^{5} -4987.08 q^{6} +7308.14i q^{7} -20253.2i q^{8} -168885. q^{9} -52508.8 q^{10} -141725. q^{11} -436788. i q^{12} +566244. q^{13} +76339.4 q^{14} -2.39990e6 q^{15} +725281. q^{16} -370530. q^{17} +1.76413e6i q^{18} -1.53235e6i q^{19} -4.59893e6i q^{20} +3.48908e6 q^{21} +1.48043e6i q^{22} +9.51431e6 q^{23} -9.66937e6 q^{24} -1.55029e7 q^{25} -5.91488e6i q^{26} +5.24381e7i q^{27} +6.68611e6i q^{28} -1.65562e7i q^{29} +2.50689e7i q^{30} +2.42402e7 q^{31} -2.83154e7i q^{32} +6.76627e7i q^{33} +3.87048e6i q^{34} +3.67364e7 q^{35} -1.54510e8 q^{36} +1.62761e7i q^{37} -1.60066e7 q^{38} -2.70339e8i q^{39} -1.01808e8 q^{40} -1.33025e8 q^{41} -3.64462e7i q^{42} +(1.01091e8 + 1.06734e8i) q^{43} -1.29662e8 q^{44} +8.48945e8i q^{45} -9.93846e7i q^{46} -2.40872e8 q^{47} -3.46267e8i q^{48} +2.29066e8 q^{49} +1.61940e8i q^{50} +1.76900e8i q^{51} +5.18049e8 q^{52} -2.67647e7 q^{53} +5.47758e8 q^{54} +7.12419e8i q^{55} +1.48013e8 q^{56} -7.31579e8 q^{57} -1.72943e8 q^{58} +6.95408e8 q^{59} -2.19564e9 q^{60} +9.17656e8i q^{61} -2.53208e8i q^{62} -1.23423e9i q^{63} +4.46911e8 q^{64} -2.84639e9i q^{65} +7.06792e8 q^{66} +1.19151e9 q^{67} -3.38993e8 q^{68} -4.54236e9i q^{69} -3.83741e8i q^{70} -4.68128e8i q^{71} +3.42045e9i q^{72} -2.00301e9i q^{73} +1.70017e8 q^{74} +7.40145e9i q^{75} -1.40192e9i q^{76} -1.03574e9i q^{77} -2.82390e9 q^{78} -1.34231e9 q^{79} -3.64583e9i q^{80} +1.50627e10 q^{81} +1.38956e9i q^{82} -1.99067e9 q^{83} +3.19211e9 q^{84} +1.86257e9i q^{85} +(1.11492e9 - 1.05598e9i) q^{86} -7.90431e9 q^{87} +2.87038e9i q^{88} -2.98276e8i q^{89} +8.86792e9 q^{90} +4.13819e9i q^{91} +8.70450e9 q^{92} -1.15728e10i q^{93} +2.51610e9i q^{94} -7.70278e9 q^{95} -1.35185e10 q^{96} -1.69052e9 q^{97} -2.39278e9i q^{98} +2.39351e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.4458i 0.326431i −0.986590 0.163216i \(-0.947813\pi\)
0.986590 0.163216i \(-0.0521866\pi\)
\(3\) 477.424i 1.96471i −0.187033 0.982354i \(-0.559887\pi\)
0.187033 0.982354i \(-0.440113\pi\)
\(4\) 914.885 0.893443
\(5\) 5026.78i 1.60857i −0.594244 0.804285i \(-0.702549\pi\)
0.594244 0.804285i \(-0.297451\pi\)
\(6\) −4987.08 −0.641342
\(7\) 7308.14i 0.434827i 0.976080 + 0.217414i \(0.0697620\pi\)
−0.976080 + 0.217414i \(0.930238\pi\)
\(8\) 20253.2i 0.618079i
\(9\) −168885. −2.86007
\(10\) −52508.8 −0.525088
\(11\) −141725. −0.879999 −0.439999 0.897998i \(-0.645021\pi\)
−0.439999 + 0.897998i \(0.645021\pi\)
\(12\) 436788.i 1.75535i
\(13\) 566244. 1.52506 0.762530 0.646952i \(-0.223957\pi\)
0.762530 + 0.646952i \(0.223957\pi\)
\(14\) 76339.4 0.141941
\(15\) −2.39990e6 −3.16037
\(16\) 725281. 0.691682
\(17\) −370530. −0.260963 −0.130481 0.991451i \(-0.541652\pi\)
−0.130481 + 0.991451i \(0.541652\pi\)
\(18\) 1.76413e6i 0.933618i
\(19\) 1.53235e6i 0.618856i −0.950923 0.309428i \(-0.899862\pi\)
0.950923 0.309428i \(-0.100138\pi\)
\(20\) 4.59893e6i 1.43716i
\(21\) 3.48908e6 0.854308
\(22\) 1.48043e6i 0.287259i
\(23\) 9.51431e6 1.47822 0.739108 0.673587i \(-0.235247\pi\)
0.739108 + 0.673587i \(0.235247\pi\)
\(24\) −9.66937e6 −1.21434
\(25\) −1.55029e7 −1.58750
\(26\) 5.91488e6i 0.497828i
\(27\) 5.24381e7i 3.65450i
\(28\) 6.68611e6i 0.388493i
\(29\) 1.65562e7i 0.807179i −0.914940 0.403590i \(-0.867762\pi\)
0.914940 0.403590i \(-0.132238\pi\)
\(30\) 2.50689e7i 1.03164i
\(31\) 2.42402e7 0.846696 0.423348 0.905967i \(-0.360855\pi\)
0.423348 + 0.905967i \(0.360855\pi\)
\(32\) 2.83154e7i 0.843866i
\(33\) 6.76627e7i 1.72894i
\(34\) 3.87048e6i 0.0851865i
\(35\) 3.67364e7 0.699450
\(36\) −1.54510e8 −2.55531
\(37\) 1.62761e7i 0.234715i 0.993090 + 0.117358i \(0.0374424\pi\)
−0.993090 + 0.117358i \(0.962558\pi\)
\(38\) −1.60066e7 −0.202014
\(39\) 2.70339e8i 2.99630i
\(40\) −1.01808e8 −0.994223
\(41\) −1.33025e8 −1.14819 −0.574097 0.818787i \(-0.694647\pi\)
−0.574097 + 0.818787i \(0.694647\pi\)
\(42\) 3.64462e7i 0.278873i
\(43\) 1.01091e8 + 1.06734e8i 0.687655 + 0.726038i
\(44\) −1.29662e8 −0.786228
\(45\) 8.48945e8i 4.60063i
\(46\) 9.93846e7i 0.482536i
\(47\) −2.40872e8 −1.05026 −0.525130 0.851022i \(-0.675983\pi\)
−0.525130 + 0.851022i \(0.675983\pi\)
\(48\) 3.46267e8i 1.35895i
\(49\) 2.29066e8 0.810925
\(50\) 1.61940e8i 0.518209i
\(51\) 1.76900e8i 0.512716i
\(52\) 5.18049e8 1.36255
\(53\) −2.67647e7 −0.0640004 −0.0320002 0.999488i \(-0.510188\pi\)
−0.0320002 + 0.999488i \(0.510188\pi\)
\(54\) 5.47758e8 1.19294
\(55\) 7.12419e8i 1.41554i
\(56\) 1.48013e8 0.268758
\(57\) −7.31579e8 −1.21587
\(58\) −1.72943e8 −0.263489
\(59\) 6.95408e8 0.972701 0.486351 0.873764i \(-0.338328\pi\)
0.486351 + 0.873764i \(0.338328\pi\)
\(60\) −2.19564e9 −2.82361
\(61\) 9.17656e8i 1.08650i 0.839570 + 0.543251i \(0.182807\pi\)
−0.839570 + 0.543251i \(0.817193\pi\)
\(62\) 2.53208e8i 0.276388i
\(63\) 1.23423e9i 1.24364i
\(64\) 4.46911e8 0.416218
\(65\) 2.84639e9i 2.45317i
\(66\) 7.06792e8 0.564380
\(67\) 1.19151e9 0.882522 0.441261 0.897379i \(-0.354531\pi\)
0.441261 + 0.897379i \(0.354531\pi\)
\(68\) −3.38993e8 −0.233155
\(69\) 4.54236e9i 2.90426i
\(70\) 3.83741e8i 0.228322i
\(71\) 4.68128e8i 0.259462i −0.991549 0.129731i \(-0.958589\pi\)
0.991549 0.129731i \(-0.0414113\pi\)
\(72\) 3.42045e9i 1.76775i
\(73\) 2.00301e9i 0.966206i −0.875564 0.483103i \(-0.839510\pi\)
0.875564 0.483103i \(-0.160490\pi\)
\(74\) 1.70017e8 0.0766184
\(75\) 7.40145e9i 3.11897i
\(76\) 1.40192e9i 0.552912i
\(77\) 1.03574e9i 0.382647i
\(78\) −2.82390e9 −0.978085
\(79\) −1.34231e9 −0.436233 −0.218116 0.975923i \(-0.569991\pi\)
−0.218116 + 0.975923i \(0.569991\pi\)
\(80\) 3.64583e9i 1.11262i
\(81\) 1.50627e10 4.31995
\(82\) 1.38956e9i 0.374807i
\(83\) −1.99067e9 −0.505369 −0.252684 0.967549i \(-0.581313\pi\)
−0.252684 + 0.967549i \(0.581313\pi\)
\(84\) 3.19211e9 0.763275
\(85\) 1.86257e9i 0.419777i
\(86\) 1.11492e9 1.05598e9i 0.237002 0.224472i
\(87\) −7.90431e9 −1.58587
\(88\) 2.87038e9i 0.543909i
\(89\) 2.98276e8i 0.0534157i −0.999643 0.0267079i \(-0.991498\pi\)
0.999643 0.0267079i \(-0.00850238\pi\)
\(90\) 8.86792e9 1.50179
\(91\) 4.13819e9i 0.663138i
\(92\) 8.70450e9 1.32070
\(93\) 1.15728e10i 1.66351i
\(94\) 2.51610e9i 0.342838i
\(95\) −7.70278e9 −0.995473
\(96\) −1.35185e10 −1.65795
\(97\) −1.69052e9 −0.196861 −0.0984307 0.995144i \(-0.531382\pi\)
−0.0984307 + 0.995144i \(0.531382\pi\)
\(98\) 2.39278e9i 0.264711i
\(99\) 2.39351e10 2.51686
\(100\) −1.41834e10 −1.41834
\(101\) −1.31880e10 −1.25479 −0.627397 0.778700i \(-0.715880\pi\)
−0.627397 + 0.778700i \(0.715880\pi\)
\(102\) 1.84786e9 0.167367
\(103\) −1.56077e10 −1.34633 −0.673165 0.739492i \(-0.735066\pi\)
−0.673165 + 0.739492i \(0.735066\pi\)
\(104\) 1.14683e10i 0.942608i
\(105\) 1.75388e10i 1.37421i
\(106\) 2.79578e8i 0.0208917i
\(107\) −6.63611e9 −0.473145 −0.236573 0.971614i \(-0.576024\pi\)
−0.236573 + 0.971614i \(0.576024\pi\)
\(108\) 4.79748e10i 3.26509i
\(109\) 8.75386e9 0.568941 0.284470 0.958685i \(-0.408182\pi\)
0.284470 + 0.958685i \(0.408182\pi\)
\(110\) 7.44179e9 0.462076
\(111\) 7.77059e9 0.461147
\(112\) 5.30046e9i 0.300762i
\(113\) 2.39279e10i 1.29871i 0.760485 + 0.649355i \(0.224961\pi\)
−0.760485 + 0.649355i \(0.775039\pi\)
\(114\) 7.64194e9i 0.396898i
\(115\) 4.78263e10i 2.37781i
\(116\) 1.51470e10i 0.721168i
\(117\) −9.56299e10 −4.36179
\(118\) 7.26409e9i 0.317520i
\(119\) 2.70789e9i 0.113474i
\(120\) 4.86058e10i 1.95336i
\(121\) −5.85155e9 −0.225602
\(122\) 9.58566e9 0.354669
\(123\) 6.35095e10i 2.25587i
\(124\) 2.21770e10 0.756474
\(125\) 2.88400e10i 0.945030i
\(126\) −1.28925e10 −0.405962
\(127\) 1.15940e10 0.350924 0.175462 0.984486i \(-0.443858\pi\)
0.175462 + 0.984486i \(0.443858\pi\)
\(128\) 3.36633e10i 0.979732i
\(129\) 5.09572e10 4.82633e10i 1.42645 1.35104i
\(130\) −2.97328e10 −0.800790
\(131\) 1.40406e10i 0.363941i −0.983304 0.181970i \(-0.941753\pi\)
0.983304 0.181970i \(-0.0582475\pi\)
\(132\) 6.19036e10i 1.54471i
\(133\) 1.11986e10 0.269095
\(134\) 1.24463e10i 0.288083i
\(135\) 2.63595e11 5.87852
\(136\) 7.50443e9i 0.161296i
\(137\) 6.16181e10i 1.27675i −0.769726 0.638374i \(-0.779607\pi\)
0.769726 0.638374i \(-0.220393\pi\)
\(138\) −4.74486e10 −0.948042
\(139\) −3.92886e10 −0.757169 −0.378584 0.925567i \(-0.623589\pi\)
−0.378584 + 0.925567i \(0.623589\pi\)
\(140\) 3.36096e10 0.624918
\(141\) 1.14998e11i 2.06345i
\(142\) −4.88998e9 −0.0846964
\(143\) −8.02508e10 −1.34205
\(144\) −1.22489e11 −1.97826
\(145\) −8.32243e10 −1.29840
\(146\) −2.09231e10 −0.315400
\(147\) 1.09362e11i 1.59323i
\(148\) 1.48907e10i 0.209705i
\(149\) 7.35802e10i 1.00191i 0.865473 + 0.500956i \(0.167018\pi\)
−0.865473 + 0.500956i \(0.832982\pi\)
\(150\) 7.73141e10 1.01813
\(151\) 1.34133e11i 1.70864i −0.519745 0.854321i \(-0.673973\pi\)
0.519745 0.854321i \(-0.326027\pi\)
\(152\) −3.10350e10 −0.382502
\(153\) 6.25768e10 0.746374
\(154\) −1.08192e10 −0.124908
\(155\) 1.21850e11i 1.36197i
\(156\) 2.47329e11i 2.67702i
\(157\) 4.35018e10i 0.456046i 0.973656 + 0.228023i \(0.0732262\pi\)
−0.973656 + 0.228023i \(0.926774\pi\)
\(158\) 1.40215e10i 0.142400i
\(159\) 1.27781e10i 0.125742i
\(160\) −1.42335e11 −1.35742
\(161\) 6.95319e10i 0.642769i
\(162\) 1.57342e11i 1.41017i
\(163\) 1.49268e10i 0.129726i −0.997894 0.0648632i \(-0.979339\pi\)
0.997894 0.0648632i \(-0.0206611\pi\)
\(164\) −1.21703e11 −1.02585
\(165\) 3.40126e11 2.78112
\(166\) 2.07941e10i 0.164968i
\(167\) 3.58201e10 0.275769 0.137884 0.990448i \(-0.455970\pi\)
0.137884 + 0.990448i \(0.455970\pi\)
\(168\) 7.06651e10i 0.528030i
\(169\) 1.82774e11 1.32581
\(170\) 1.94561e10 0.137028
\(171\) 2.58790e11i 1.76997i
\(172\) 9.24867e10 + 9.76491e10i 0.614380 + 0.648673i
\(173\) 1.78323e11 1.15074 0.575369 0.817894i \(-0.304858\pi\)
0.575369 + 0.817894i \(0.304858\pi\)
\(174\) 8.25669e10i 0.517678i
\(175\) 1.13297e11i 0.690287i
\(176\) −1.02790e11 −0.608679
\(177\) 3.32004e11i 1.91107i
\(178\) −3.11574e9 −0.0174366
\(179\) 2.02752e11i 1.10332i 0.834070 + 0.551658i \(0.186005\pi\)
−0.834070 + 0.551658i \(0.813995\pi\)
\(180\) 7.76688e11i 4.11040i
\(181\) −1.13688e11 −0.585223 −0.292612 0.956231i \(-0.594524\pi\)
−0.292612 + 0.956231i \(0.594524\pi\)
\(182\) 4.32267e10 0.216469
\(183\) 4.38111e11 2.13466
\(184\) 1.92695e11i 0.913655i
\(185\) 8.18163e10 0.377556
\(186\) −1.20888e11 −0.543022
\(187\) 5.25133e10 0.229647
\(188\) −2.20370e11 −0.938348
\(189\) −3.83225e11 −1.58908
\(190\) 8.04617e10i 0.324953i
\(191\) 4.88802e11i 1.92294i −0.274909 0.961470i \(-0.588648\pi\)
0.274909 0.961470i \(-0.411352\pi\)
\(192\) 2.13366e11i 0.817746i
\(193\) 4.82406e11 1.80147 0.900734 0.434372i \(-0.143030\pi\)
0.900734 + 0.434372i \(0.143030\pi\)
\(194\) 1.76588e10i 0.0642618i
\(195\) −1.35893e12 −4.81975
\(196\) 2.09569e11 0.724515
\(197\) 2.18452e10 0.0736248 0.0368124 0.999322i \(-0.488280\pi\)
0.0368124 + 0.999322i \(0.488280\pi\)
\(198\) 2.50021e11i 0.821582i
\(199\) 4.07116e11i 1.30453i 0.757993 + 0.652263i \(0.226180\pi\)
−0.757993 + 0.652263i \(0.773820\pi\)
\(200\) 3.13984e11i 0.981199i
\(201\) 5.68858e11i 1.73390i
\(202\) 1.37759e11i 0.409604i
\(203\) 1.20995e11 0.350983
\(204\) 1.61843e11i 0.458082i
\(205\) 6.68690e11i 1.84695i
\(206\) 1.63035e11i 0.439484i
\(207\) −1.60682e12 −4.22781
\(208\) 4.10686e11 1.05486
\(209\) 2.17171e11i 0.544592i
\(210\) −1.83207e11 −0.448587
\(211\) 4.28555e11i 1.02469i −0.858779 0.512347i \(-0.828776\pi\)
0.858779 0.512347i \(-0.171224\pi\)
\(212\) −2.44866e10 −0.0571807
\(213\) −2.23496e11 −0.509766
\(214\) 6.93195e10i 0.154449i
\(215\) 5.36527e11 5.08162e11i 1.16788 1.10614i
\(216\) 1.06204e12 2.25877
\(217\) 1.77151e11i 0.368167i
\(218\) 9.14411e10i 0.185720i
\(219\) −9.56286e11 −1.89831
\(220\) 6.51781e11i 1.26470i
\(221\) −2.09811e11 −0.397984
\(222\) 8.11701e10i 0.150533i
\(223\) 5.05478e11i 0.916596i −0.888799 0.458298i \(-0.848459\pi\)
0.888799 0.458298i \(-0.151541\pi\)
\(224\) 2.06933e11 0.366936
\(225\) 2.61820e12 4.54036
\(226\) 2.49946e11 0.423940
\(227\) 9.87423e10i 0.163823i 0.996640 + 0.0819113i \(0.0261024\pi\)
−0.996640 + 0.0819113i \(0.973898\pi\)
\(228\) −6.69311e11 −1.08631
\(229\) −1.17644e10 −0.0186807 −0.00934034 0.999956i \(-0.502973\pi\)
−0.00934034 + 0.999956i \(0.502973\pi\)
\(230\) −4.99585e11 −0.776193
\(231\) −4.94489e11 −0.751790
\(232\) −3.35316e11 −0.498901
\(233\) 1.08585e11i 0.158121i 0.996870 + 0.0790603i \(0.0251920\pi\)
−0.996870 + 0.0790603i \(0.974808\pi\)
\(234\) 9.98931e11i 1.42382i
\(235\) 1.21081e12i 1.68942i
\(236\) 6.36218e11 0.869053
\(237\) 6.40852e11i 0.857069i
\(238\) −2.82860e10 −0.0370414
\(239\) 7.24762e11 0.929406 0.464703 0.885467i \(-0.346161\pi\)
0.464703 + 0.885467i \(0.346161\pi\)
\(240\) −1.74061e12 −2.18597
\(241\) 7.31179e11i 0.899371i 0.893187 + 0.449685i \(0.148464\pi\)
−0.893187 + 0.449685i \(0.851536\pi\)
\(242\) 6.11241e10i 0.0736437i
\(243\) 4.09489e12i 4.83294i
\(244\) 8.39550e11i 0.970728i
\(245\) 1.15147e12i 1.30443i
\(246\) 6.63408e11 0.736386
\(247\) 8.67683e11i 0.943792i
\(248\) 4.90942e11i 0.523325i
\(249\) 9.50393e11i 0.992902i
\(250\) 3.01257e11 0.308487
\(251\) 8.33837e11 0.836975 0.418488 0.908222i \(-0.362560\pi\)
0.418488 + 0.908222i \(0.362560\pi\)
\(252\) 1.12918e12i 1.11112i
\(253\) −1.34841e12 −1.30083
\(254\) 1.21108e11i 0.114553i
\(255\) 8.89237e11 0.824739
\(256\) 1.05996e11 0.0964026
\(257\) 5.20426e11i 0.464187i 0.972693 + 0.232094i \(0.0745576\pi\)
−0.972693 + 0.232094i \(0.925442\pi\)
\(258\) −5.04149e11 5.32289e11i −0.441022 0.465639i
\(259\) −1.18948e11 −0.102061
\(260\) 2.60412e12i 2.19176i
\(261\) 2.79608e12i 2.30859i
\(262\) −1.46666e11 −0.118802
\(263\) 1.65088e12i 1.31201i 0.754759 + 0.656003i \(0.227754\pi\)
−0.754759 + 0.656003i \(0.772246\pi\)
\(264\) 1.37039e12 1.06862
\(265\) 1.34540e11i 0.102949i
\(266\) 1.16979e11i 0.0878411i
\(267\) −1.42404e11 −0.104946
\(268\) 1.09010e12 0.788482
\(269\) 2.76077e11 0.196006 0.0980029 0.995186i \(-0.468755\pi\)
0.0980029 + 0.995186i \(0.468755\pi\)
\(270\) 2.75346e12i 1.91893i
\(271\) −1.40676e12 −0.962443 −0.481221 0.876599i \(-0.659807\pi\)
−0.481221 + 0.876599i \(0.659807\pi\)
\(272\) −2.68739e11 −0.180503
\(273\) 1.97567e12 1.30287
\(274\) −6.43650e11 −0.416771
\(275\) 2.19714e12 1.39700
\(276\) 4.15574e12i 2.59479i
\(277\) 7.73200e11i 0.474125i 0.971494 + 0.237063i \(0.0761847\pi\)
−0.971494 + 0.237063i \(0.923815\pi\)
\(278\) 4.10401e11i 0.247164i
\(279\) −4.09379e12 −2.42161
\(280\) 7.44030e11i 0.432315i
\(281\) 1.32834e12 0.758191 0.379095 0.925358i \(-0.376235\pi\)
0.379095 + 0.925358i \(0.376235\pi\)
\(282\) 1.20125e12 0.673576
\(283\) 1.24791e12 0.687465 0.343733 0.939068i \(-0.388309\pi\)
0.343733 + 0.939068i \(0.388309\pi\)
\(284\) 4.28284e11i 0.231814i
\(285\) 3.67749e12i 1.95581i
\(286\) 8.38284e11i 0.438088i
\(287\) 9.72169e11i 0.499266i
\(288\) 4.78204e12i 2.41352i
\(289\) −1.87870e12 −0.931898
\(290\) 8.69344e11i 0.423840i
\(291\) 8.07093e11i 0.386775i
\(292\) 1.83253e12i 0.863249i
\(293\) −8.68763e11 −0.402312 −0.201156 0.979559i \(-0.564470\pi\)
−0.201156 + 0.979559i \(0.564470\pi\)
\(294\) −1.14237e12 −0.520081
\(295\) 3.49566e12i 1.56466i
\(296\) 3.29643e11 0.145073
\(297\) 7.43177e12i 3.21596i
\(298\) 7.68605e11 0.327056
\(299\) 5.38742e12 2.25437
\(300\) 6.77148e12i 2.78662i
\(301\) −7.80025e11 + 7.38787e11i −0.315701 + 0.299011i
\(302\) −1.40113e12 −0.557755
\(303\) 6.29627e12i 2.46530i
\(304\) 1.11138e12i 0.428051i
\(305\) 4.61286e12 1.74772
\(306\) 6.53665e11i 0.243640i
\(307\) −2.17669e12 −0.798187 −0.399094 0.916910i \(-0.630675\pi\)
−0.399094 + 0.916910i \(0.630675\pi\)
\(308\) 9.47586e11i 0.341873i
\(309\) 7.45147e12i 2.64514i
\(310\) −1.27282e12 −0.444590
\(311\) −4.62636e12 −1.59015 −0.795074 0.606512i \(-0.792568\pi\)
−0.795074 + 0.606512i \(0.792568\pi\)
\(312\) −5.47522e12 −1.85195
\(313\) 9.03142e11i 0.300631i −0.988638 0.150316i \(-0.951971\pi\)
0.988638 0.150316i \(-0.0480290\pi\)
\(314\) 4.54411e11 0.148868
\(315\) −6.20421e12 −2.00048
\(316\) −1.22806e12 −0.389749
\(317\) −8.37166e11 −0.261526 −0.130763 0.991414i \(-0.541743\pi\)
−0.130763 + 0.991414i \(0.541743\pi\)
\(318\) 1.33477e11 0.0410461
\(319\) 2.34642e12i 0.710317i
\(320\) 2.24652e12i 0.669516i
\(321\) 3.16824e12i 0.929592i
\(322\) 7.26317e11 0.209820
\(323\) 5.67781e11i 0.161498i
\(324\) 1.37807e13 3.85963
\(325\) −8.77843e12 −2.42103
\(326\) −1.55922e11 −0.0423468
\(327\) 4.17930e12i 1.11780i
\(328\) 2.69419e12i 0.709675i
\(329\) 1.76033e12i 0.456682i
\(330\) 3.55289e12i 0.907845i
\(331\) 5.95726e12i 1.49936i −0.661800 0.749681i \(-0.730207\pi\)
0.661800 0.749681i \(-0.269793\pi\)
\(332\) −1.82123e12 −0.451518
\(333\) 2.74878e12i 0.671303i
\(334\) 3.74170e11i 0.0900196i
\(335\) 5.98948e12i 1.41960i
\(336\) 2.53056e12 0.590910
\(337\) −5.64572e11 −0.129888 −0.0649441 0.997889i \(-0.520687\pi\)
−0.0649441 + 0.997889i \(0.520687\pi\)
\(338\) 1.90922e12i 0.432786i
\(339\) 1.14238e13 2.55159
\(340\) 1.70404e12i 0.375047i
\(341\) −3.43543e12 −0.745092
\(342\) 2.70327e12 0.577775
\(343\) 3.73842e12i 0.787440i
\(344\) 2.16170e12 2.04742e12i 0.448749 0.425025i
\(345\) −2.28334e13 −4.67171
\(346\) 1.86273e12i 0.375637i
\(347\) 3.49319e12i 0.694344i −0.937801 0.347172i \(-0.887142\pi\)
0.937801 0.347172i \(-0.112858\pi\)
\(348\) −7.23154e12 −1.41688
\(349\) 2.19585e11i 0.0424107i −0.999775 0.0212054i \(-0.993250\pi\)
0.999775 0.0212054i \(-0.00675038\pi\)
\(350\) −1.18348e12 −0.225331
\(351\) 2.96928e13i 5.57334i
\(352\) 4.01300e12i 0.742601i
\(353\) 7.26715e12 1.32584 0.662919 0.748691i \(-0.269317\pi\)
0.662919 + 0.748691i \(0.269317\pi\)
\(354\) −3.46805e12 −0.623834
\(355\) −2.35318e12 −0.417362
\(356\) 2.72889e11i 0.0477239i
\(357\) −1.29281e12 −0.222943
\(358\) 2.11791e12 0.360157
\(359\) 1.90200e12 0.318961 0.159480 0.987201i \(-0.449018\pi\)
0.159480 + 0.987201i \(0.449018\pi\)
\(360\) 1.71939e13 2.84355
\(361\) 3.78298e12 0.617018
\(362\) 1.18756e12i 0.191035i
\(363\) 2.79367e12i 0.443243i
\(364\) 3.78597e12i 0.592476i
\(365\) −1.00687e13 −1.55421
\(366\) 4.57642e12i 0.696820i
\(367\) 7.89705e12 1.18614 0.593068 0.805153i \(-0.297917\pi\)
0.593068 + 0.805153i \(0.297917\pi\)
\(368\) 6.90055e12 1.02246
\(369\) 2.24659e13 3.28392
\(370\) 8.54637e11i 0.123246i
\(371\) 1.95600e11i 0.0278291i
\(372\) 1.05878e13i 1.48625i
\(373\) 9.69913e12i 1.34335i −0.740847 0.671674i \(-0.765575\pi\)
0.740847 0.671674i \(-0.234425\pi\)
\(374\) 5.48543e11i 0.0749640i
\(375\) 1.37689e13 1.85671
\(376\) 4.87843e12i 0.649144i
\(377\) 9.37484e12i 1.23100i
\(378\) 4.00309e12i 0.518724i
\(379\) 9.41452e12 1.20393 0.601966 0.798522i \(-0.294384\pi\)
0.601966 + 0.798522i \(0.294384\pi\)
\(380\) −7.04716e12 −0.889398
\(381\) 5.53524e12i 0.689464i
\(382\) −5.10593e12 −0.627708
\(383\) 6.22024e12i 0.754767i 0.926057 + 0.377384i \(0.123176\pi\)
−0.926057 + 0.377384i \(0.876824\pi\)
\(384\) −1.60717e13 −1.92489
\(385\) −5.20646e12 −0.615515
\(386\) 5.03912e12i 0.588055i
\(387\) −1.70727e13 1.80257e13i −1.96674 2.07652i
\(388\) −1.54663e12 −0.175884
\(389\) 1.64883e12i 0.185109i −0.995708 0.0925547i \(-0.970497\pi\)
0.995708 0.0925547i \(-0.0295033\pi\)
\(390\) 1.41951e13i 1.57332i
\(391\) −3.52534e12 −0.385760
\(392\) 4.63933e12i 0.501216i
\(393\) −6.70334e12 −0.715037
\(394\) 2.28190e11i 0.0240334i
\(395\) 6.74751e12i 0.701711i
\(396\) 2.18979e13 2.24867
\(397\) −2.98785e12 −0.302974 −0.151487 0.988459i \(-0.548406\pi\)
−0.151487 + 0.988459i \(0.548406\pi\)
\(398\) 4.25265e12 0.425838
\(399\) 5.34649e12i 0.528693i
\(400\) −1.12440e13 −1.09804
\(401\) 1.38543e13 1.33617 0.668085 0.744085i \(-0.267114\pi\)
0.668085 + 0.744085i \(0.267114\pi\)
\(402\) −5.94217e12 −0.565998
\(403\) 1.37259e13 1.29126
\(404\) −1.20655e13 −1.12109
\(405\) 7.57171e13i 6.94894i
\(406\) 1.26389e12i 0.114572i
\(407\) 2.30672e12i 0.206549i
\(408\) 3.58279e12 0.316899
\(409\) 2.08622e13i 1.82282i 0.411502 + 0.911409i \(0.365004\pi\)
−0.411502 + 0.911409i \(0.634996\pi\)
\(410\) 6.98500e12 0.602903
\(411\) −2.94179e13 −2.50844
\(412\) −1.42792e13 −1.20287
\(413\) 5.08214e12i 0.422957i
\(414\) 1.67845e13i 1.38009i
\(415\) 1.00067e13i 0.812921i
\(416\) 1.60335e13i 1.28695i
\(417\) 1.87573e13i 1.48761i
\(418\) 2.26853e12 0.177772
\(419\) 3.56689e11i 0.0276198i −0.999905 0.0138099i \(-0.995604\pi\)
0.999905 0.0138099i \(-0.00439596\pi\)
\(420\) 1.60460e13i 1.22778i
\(421\) 1.13802e13i 0.860480i 0.902714 + 0.430240i \(0.141571\pi\)
−0.902714 + 0.430240i \(0.858429\pi\)
\(422\) −4.47660e12 −0.334492
\(423\) 4.06796e13 3.00382
\(424\) 5.42071e11i 0.0395573i
\(425\) 5.74429e12 0.414278
\(426\) 2.33459e12i 0.166404i
\(427\) −6.70636e12 −0.472441
\(428\) −6.07128e12 −0.422728
\(429\) 3.83136e13i 2.63674i
\(430\) −5.30816e12 5.60446e12i −0.361079 0.381234i
\(431\) 1.90208e13 1.27892 0.639458 0.768826i \(-0.279159\pi\)
0.639458 + 0.768826i \(0.279159\pi\)
\(432\) 3.80324e13i 2.52775i
\(433\) 5.41588e12i 0.355820i −0.984047 0.177910i \(-0.943066\pi\)
0.984047 0.177910i \(-0.0569335\pi\)
\(434\) 1.85048e12 0.120181
\(435\) 3.97332e13i 2.55098i
\(436\) 8.00878e12 0.508316
\(437\) 1.45792e13i 0.914803i
\(438\) 9.98918e12i 0.619668i
\(439\) −1.61738e13 −0.991951 −0.495976 0.868336i \(-0.665189\pi\)
−0.495976 + 0.868336i \(0.665189\pi\)
\(440\) 1.44288e13 0.874915
\(441\) −3.86858e13 −2.31931
\(442\) 2.19164e12i 0.129915i
\(443\) 2.44931e12 0.143557 0.0717786 0.997421i \(-0.477133\pi\)
0.0717786 + 0.997421i \(0.477133\pi\)
\(444\) 7.10920e12 0.412008
\(445\) −1.49937e12 −0.0859229
\(446\) −5.28012e12 −0.299206
\(447\) 3.51290e13 1.96847
\(448\) 3.26609e12i 0.180983i
\(449\) 5.17378e12i 0.283515i 0.989901 + 0.141758i \(0.0452753\pi\)
−0.989901 + 0.141758i \(0.954725\pi\)
\(450\) 2.73492e13i 1.48212i
\(451\) 1.88530e13 1.01041
\(452\) 2.18913e13i 1.16032i
\(453\) −6.40384e13 −3.35698
\(454\) 1.03144e12 0.0534768
\(455\) 2.08018e13 1.06670
\(456\) 1.48168e13i 0.751504i
\(457\) 2.19511e13i 1.10122i 0.834761 + 0.550612i \(0.185606\pi\)
−0.834761 + 0.550612i \(0.814394\pi\)
\(458\) 1.22889e11i 0.00609796i
\(459\) 1.94299e13i 0.953690i
\(460\) 4.37556e13i 2.12444i
\(461\) 4.11135e13 1.97460 0.987300 0.158864i \(-0.0507833\pi\)
0.987300 + 0.158864i \(0.0507833\pi\)
\(462\) 5.16533e12i 0.245408i
\(463\) 2.72180e13i 1.27924i −0.768693 0.639618i \(-0.779092\pi\)
0.768693 0.639618i \(-0.220908\pi\)
\(464\) 1.20079e13i 0.558311i
\(465\) −5.81742e13 −2.67587
\(466\) 1.13425e12 0.0516155
\(467\) 2.92917e13i 1.31874i −0.751818 0.659371i \(-0.770823\pi\)
0.751818 0.659371i \(-0.229177\pi\)
\(468\) −8.74904e13 −3.89701
\(469\) 8.70776e12i 0.383744i
\(470\) 1.26479e13 0.551479
\(471\) 2.07688e13 0.895998
\(472\) 1.40842e13i 0.601206i
\(473\) −1.43271e13 1.51268e13i −0.605135 0.638912i
\(474\) 6.69421e12 0.279774
\(475\) 2.37558e13i 0.982432i
\(476\) 2.47740e12i 0.101382i
\(477\) 4.52014e12 0.183046
\(478\) 7.57072e12i 0.303387i
\(479\) 5.43350e12 0.215477 0.107739 0.994179i \(-0.465639\pi\)
0.107739 + 0.994179i \(0.465639\pi\)
\(480\) 6.79544e13i 2.66693i
\(481\) 9.21624e12i 0.357955i
\(482\) 7.63776e12 0.293583
\(483\) 3.31962e13 1.26285
\(484\) −5.35349e12 −0.201563
\(485\) 8.49785e12i 0.316665i
\(486\) −4.27744e13 −1.57762
\(487\) −2.85945e13 −1.04385 −0.521925 0.852992i \(-0.674786\pi\)
−0.521925 + 0.852992i \(0.674786\pi\)
\(488\) 1.85855e13 0.671544
\(489\) −7.12641e12 −0.254874
\(490\) −1.20280e13 −0.425807
\(491\) 2.23033e13i 0.781560i 0.920484 + 0.390780i \(0.127795\pi\)
−0.920484 + 0.390780i \(0.872205\pi\)
\(492\) 5.81039e13i 2.01549i
\(493\) 6.13456e12i 0.210644i
\(494\) −9.06365e12 −0.308083
\(495\) 1.20317e14i 4.04855i
\(496\) 1.75810e13 0.585645
\(497\) 3.42115e12 0.112821
\(498\) 9.92762e12 0.324114
\(499\) 8.65964e12i 0.279896i −0.990159 0.139948i \(-0.955306\pi\)
0.990159 0.139948i \(-0.0446936\pi\)
\(500\) 2.63853e13i 0.844330i
\(501\) 1.71014e13i 0.541805i
\(502\) 8.71010e12i 0.273215i
\(503\) 5.57072e13i 1.73010i −0.501685 0.865050i \(-0.667286\pi\)
0.501685 0.865050i \(-0.332714\pi\)
\(504\) −2.49972e13 −0.768667
\(505\) 6.62932e13i 2.01842i
\(506\) 1.40852e13i 0.424631i
\(507\) 8.72607e13i 2.60483i
\(508\) 1.06072e13 0.313531
\(509\) 4.10921e13 1.20273 0.601367 0.798973i \(-0.294623\pi\)
0.601367 + 0.798973i \(0.294623\pi\)
\(510\) 9.28880e12i 0.269221i
\(511\) 1.46383e13 0.420132
\(512\) 3.55785e13i 1.01120i
\(513\) 8.03534e13 2.26161
\(514\) 5.43627e12 0.151525
\(515\) 7.84563e13i 2.16567i
\(516\) 4.66200e13 4.41553e13i 1.27445 1.20708i
\(517\) 3.41375e13 0.924228
\(518\) 1.24251e12i 0.0333158i
\(519\) 8.51356e13i 2.26086i
\(520\) −5.76485e13 −1.51625
\(521\) 6.96468e13i 1.81431i 0.420792 + 0.907157i \(0.361752\pi\)
−0.420792 + 0.907157i \(0.638248\pi\)
\(522\) 2.92073e13 0.753597
\(523\) 5.84635e13i 1.49409i 0.664775 + 0.747044i \(0.268528\pi\)
−0.664775 + 0.747044i \(0.731472\pi\)
\(524\) 1.28456e13i 0.325160i
\(525\) −5.40909e13 −1.35621
\(526\) 1.72447e13 0.428280
\(527\) −8.98172e12 −0.220956
\(528\) 4.90745e13i 1.19588i
\(529\) 4.90956e13 1.18512
\(530\) 1.40538e12 0.0336058
\(531\) −1.17444e14 −2.78200
\(532\) 1.02454e13 0.240421
\(533\) −7.53249e13 −1.75107
\(534\) 1.48753e12i 0.0342577i
\(535\) 3.33582e13i 0.761087i
\(536\) 2.41320e13i 0.545468i
\(537\) 9.67986e13 2.16769
\(538\) 2.88385e12i 0.0639824i
\(539\) −3.24643e13 −0.713613
\(540\) 2.41159e14 5.25212
\(541\) −2.63024e13 −0.567556 −0.283778 0.958890i \(-0.591588\pi\)
−0.283778 + 0.958890i \(0.591588\pi\)
\(542\) 1.46948e13i 0.314172i
\(543\) 5.42774e13i 1.14979i
\(544\) 1.04917e13i 0.220218i
\(545\) 4.40037e13i 0.915181i
\(546\) 2.06375e13i 0.425298i
\(547\) 2.10805e13 0.430471 0.215235 0.976562i \(-0.430948\pi\)
0.215235 + 0.976562i \(0.430948\pi\)
\(548\) 5.63735e13i 1.14070i
\(549\) 1.54978e14i 3.10748i
\(550\) 2.29509e13i 0.456023i
\(551\) −2.53698e13 −0.499527
\(552\) −9.19973e13 −1.79506
\(553\) 9.80981e12i 0.189686i
\(554\) 8.07670e12 0.154769
\(555\) 3.90611e13i 0.741787i
\(556\) −3.59446e13 −0.676487
\(557\) 1.96259e13 0.366062 0.183031 0.983107i \(-0.441409\pi\)
0.183031 + 0.983107i \(0.441409\pi\)
\(558\) 4.27630e13i 0.790491i
\(559\) 5.72422e13 + 6.04374e13i 1.04871 + 1.10725i
\(560\) 2.66442e13 0.483797
\(561\) 2.50711e13i 0.451189i
\(562\) 1.38756e13i 0.247497i
\(563\) 6.45640e13 1.14143 0.570714 0.821149i \(-0.306667\pi\)
0.570714 + 0.821149i \(0.306667\pi\)
\(564\) 1.05210e14i 1.84358i
\(565\) 1.20280e14 2.08907
\(566\) 1.30354e13i 0.224410i
\(567\) 1.10081e14i 1.87843i
\(568\) −9.48110e12 −0.160368
\(569\) −4.65334e11 −0.00780195 −0.00390097 0.999992i \(-0.501242\pi\)
−0.00390097 + 0.999992i \(0.501242\pi\)
\(570\) 3.84143e13 0.638438
\(571\) 6.79642e13i 1.11970i −0.828596 0.559848i \(-0.810860\pi\)
0.828596 0.559848i \(-0.189140\pi\)
\(572\) −7.34203e13 −1.19905
\(573\) −2.33366e14 −3.77801
\(574\) −1.01551e13 −0.162976
\(575\) −1.47499e14 −2.34666
\(576\) −7.54763e13 −1.19041
\(577\) 8.47586e13i 1.32527i −0.748942 0.662636i \(-0.769438\pi\)
0.748942 0.662636i \(-0.230562\pi\)
\(578\) 1.96245e13i 0.304201i
\(579\) 2.30312e14i 3.53936i
\(580\) −7.61406e13 −1.16005
\(581\) 1.45481e13i 0.219748i
\(582\) 8.43073e12 0.126256
\(583\) 3.79321e12 0.0563202
\(584\) −4.05675e13 −0.597191
\(585\) 4.80711e14i 7.01624i
\(586\) 9.07493e12i 0.131327i
\(587\) 1.42421e13i 0.204354i 0.994766 + 0.102177i \(0.0325808\pi\)
−0.994766 + 0.102177i \(0.967419\pi\)
\(588\) 1.00053e14i 1.42346i
\(589\) 3.71444e13i 0.523983i
\(590\) −3.65150e13 −0.510754
\(591\) 1.04294e13i 0.144651i
\(592\) 1.18047e13i 0.162348i
\(593\) 4.45083e13i 0.606971i 0.952836 + 0.303485i \(0.0981503\pi\)
−0.952836 + 0.303485i \(0.901850\pi\)
\(594\) −7.76308e13 −1.04979
\(595\) −1.36119e13 −0.182531
\(596\) 6.73175e13i 0.895152i
\(597\) 1.94367e14 2.56301
\(598\) 5.62760e13i 0.735897i
\(599\) 1.13656e13 0.147387 0.0736936 0.997281i \(-0.476521\pi\)
0.0736936 + 0.997281i \(0.476521\pi\)
\(600\) 1.49903e14 1.92777
\(601\) 2.65428e13i 0.338513i −0.985572 0.169256i \(-0.945863\pi\)
0.985572 0.169256i \(-0.0541366\pi\)
\(602\) 7.71723e12 + 8.14799e12i 0.0976065 + 0.103055i
\(603\) −2.01228e14 −2.52408
\(604\) 1.22716e14i 1.52657i
\(605\) 2.94144e13i 0.362897i
\(606\) 6.57696e13 0.804752
\(607\) 1.05162e14i 1.27619i 0.769959 + 0.638094i \(0.220277\pi\)
−0.769959 + 0.638094i \(0.779723\pi\)
\(608\) −4.33891e13 −0.522231
\(609\) 5.77658e13i 0.689580i
\(610\) 4.81850e13i 0.570509i
\(611\) −1.36392e14 −1.60171
\(612\) 5.72506e13 0.666842
\(613\) 1.04062e14 1.20223 0.601116 0.799162i \(-0.294723\pi\)
0.601116 + 0.799162i \(0.294723\pi\)
\(614\) 2.27373e13i 0.260553i
\(615\) 3.19249e14 3.62872
\(616\) −2.09771e13 −0.236506
\(617\) −1.03295e14 −1.15519 −0.577596 0.816323i \(-0.696009\pi\)
−0.577596 + 0.816323i \(0.696009\pi\)
\(618\) 7.78366e13 0.863458
\(619\) −1.62504e13 −0.178817 −0.0894087 0.995995i \(-0.528498\pi\)
−0.0894087 + 0.995995i \(0.528498\pi\)
\(620\) 1.11479e14i 1.21684i
\(621\) 4.98912e14i 5.40214i
\(622\) 4.83261e13i 0.519074i
\(623\) 2.17985e12 0.0232266
\(624\) 1.96072e14i 2.07249i
\(625\) −6.42304e12 −0.0673504
\(626\) −9.43405e12 −0.0981355
\(627\) 1.03683e14 1.06996
\(628\) 3.97992e13i 0.407451i
\(629\) 6.03078e12i 0.0612520i
\(630\) 6.48080e13i 0.653019i
\(631\) 1.21127e13i 0.121086i 0.998166 + 0.0605432i \(0.0192833\pi\)
−0.998166 + 0.0605432i \(0.980717\pi\)
\(632\) 2.71861e13i 0.269626i
\(633\) −2.04602e14 −2.01322
\(634\) 8.74488e12i 0.0853704i
\(635\) 5.82804e13i 0.564486i
\(636\) 1.16905e13i 0.112343i
\(637\) 1.29708e14 1.23671
\(638\) 2.45102e13 0.231870
\(639\) 7.90596e13i 0.742080i
\(640\) −1.69218e14 −1.57597
\(641\) 1.35807e14i 1.25496i 0.778631 + 0.627482i \(0.215914\pi\)
−0.778631 + 0.627482i \(0.784086\pi\)
\(642\) 3.30948e13 0.303448
\(643\) −1.89535e13 −0.172438 −0.0862191 0.996276i \(-0.527479\pi\)
−0.0862191 + 0.996276i \(0.527479\pi\)
\(644\) 6.36137e13i 0.574277i
\(645\) −2.42609e14 2.56151e14i −2.17324 2.29455i
\(646\) 5.93093e12 0.0527182
\(647\) 8.06429e13i 0.711287i 0.934622 + 0.355643i \(0.115738\pi\)
−0.934622 + 0.355643i \(0.884262\pi\)
\(648\) 3.05069e14i 2.67007i
\(649\) −9.85564e13 −0.855976
\(650\) 9.16977e13i 0.790300i
\(651\) 8.45760e13 0.723339
\(652\) 1.36563e13i 0.115903i
\(653\) 1.21280e14i 1.02147i −0.859739 0.510733i \(-0.829374\pi\)
0.859739 0.510733i \(-0.170626\pi\)
\(654\) −4.36562e13 −0.364886
\(655\) −7.05792e13 −0.585424
\(656\) −9.64809e13 −0.794186
\(657\) 3.38278e14i 2.76342i
\(658\) −1.83880e13 −0.149075
\(659\) 2.00699e14 1.61480 0.807398 0.590008i \(-0.200875\pi\)
0.807398 + 0.590008i \(0.200875\pi\)
\(660\) 3.11176e14 2.48477
\(661\) 2.33784e13 0.185271 0.0926353 0.995700i \(-0.470471\pi\)
0.0926353 + 0.995700i \(0.470471\pi\)
\(662\) −6.22283e13 −0.489438
\(663\) 1.00169e14i 0.781923i
\(664\) 4.03174e13i 0.312358i
\(665\) 5.62930e13i 0.432859i
\(666\) −2.87132e13 −0.219134
\(667\) 1.57521e14i 1.19319i
\(668\) 3.27713e13 0.246384
\(669\) −2.41327e14 −1.80084
\(670\) −6.25650e13 −0.463401
\(671\) 1.30054e14i 0.956121i
\(672\) 9.87948e13i 0.720921i
\(673\) 1.68095e14i 1.21753i −0.793351 0.608765i \(-0.791665\pi\)
0.793351 0.608765i \(-0.208335\pi\)
\(674\) 5.89741e12i 0.0423996i
\(675\) 8.12943e14i 5.80151i
\(676\) 1.67217e14 1.18453
\(677\) 1.26890e14i 0.892242i 0.894973 + 0.446121i \(0.147195\pi\)
−0.894973 + 0.446121i \(0.852805\pi\)
\(678\) 1.19330e14i 0.832918i
\(679\) 1.23545e13i 0.0856007i
\(680\) 3.77231e13 0.259455
\(681\) 4.71419e13 0.321863
\(682\) 3.58859e13i 0.243221i
\(683\) −7.77449e12 −0.0523080 −0.0261540 0.999658i \(-0.508326\pi\)
−0.0261540 + 0.999658i \(0.508326\pi\)
\(684\) 2.36763e14i 1.58137i
\(685\) −3.09741e14 −2.05374
\(686\) 3.90508e13 0.257045
\(687\) 5.61661e12i 0.0367021i
\(688\) 7.33194e13 + 7.74120e13i 0.475638 + 0.502188i
\(689\) −1.51553e13 −0.0976044
\(690\) 2.38514e14i 1.52499i
\(691\) 2.72610e14i 1.73042i −0.501410 0.865210i \(-0.667185\pi\)
0.501410 0.865210i \(-0.332815\pi\)
\(692\) 1.63145e14 1.02812
\(693\) 1.74921e14i 1.09440i
\(694\) −3.64892e13 −0.226656
\(695\) 1.97495e14i 1.21796i
\(696\) 1.60088e14i 0.980193i
\(697\) 4.92900e13 0.299636
\(698\) −2.29374e12 −0.0138442
\(699\) 5.18409e13 0.310661
\(700\) 1.03654e14i 0.616732i
\(701\) −2.61157e14 −1.54281 −0.771404 0.636346i \(-0.780445\pi\)
−0.771404 + 0.636346i \(0.780445\pi\)
\(702\) 3.10165e14 1.81931
\(703\) 2.49406e13 0.145255
\(704\) −6.33383e13 −0.366271
\(705\) 5.78070e14 3.31921
\(706\) 7.59112e13i 0.432795i
\(707\) 9.63798e13i 0.545619i
\(708\) 3.03746e14i 1.70743i
\(709\) 1.73483e14 0.968335 0.484167 0.874975i \(-0.339123\pi\)
0.484167 + 0.874975i \(0.339123\pi\)
\(710\) 2.45808e13i 0.136240i
\(711\) 2.26696e14 1.24766
\(712\) −6.04106e12 −0.0330151
\(713\) 2.30629e14 1.25160
\(714\) 1.35044e13i 0.0727755i
\(715\) 4.03403e14i 2.15878i
\(716\) 1.85495e14i 0.985749i
\(717\) 3.46018e14i 1.82601i
\(718\) 1.98679e13i 0.104119i
\(719\) 1.87163e14 0.974037 0.487019 0.873392i \(-0.338084\pi\)
0.487019 + 0.873392i \(0.338084\pi\)
\(720\) 6.15724e14i 3.18217i
\(721\) 1.14063e14i 0.585421i
\(722\) 3.95162e13i 0.201414i
\(723\) 3.49083e14 1.76700
\(724\) −1.04011e14 −0.522864
\(725\) 2.56669e14i 1.28139i
\(726\) 2.91821e13 0.144688
\(727\) 3.95170e14i 1.94586i −0.231094 0.972931i \(-0.574231\pi\)
0.231094 0.972931i \(-0.425769\pi\)
\(728\) 8.38117e13 0.409872
\(729\) −1.06556e15 −5.17536
\(730\) 1.05176e14i 0.507343i
\(731\) −3.74573e13 3.95481e13i −0.179452 0.189469i
\(732\) 4.00821e14 1.90720
\(733\) 9.69391e12i 0.0458120i −0.999738 0.0229060i \(-0.992708\pi\)
0.999738 0.0229060i \(-0.00729184\pi\)
\(734\) 8.24910e13i 0.387192i
\(735\) −5.49737e14 −2.56282
\(736\) 2.69402e14i 1.24742i
\(737\) −1.68867e14 −0.776618
\(738\) 2.34675e14i 1.07198i
\(739\) 2.97871e14i 1.35147i 0.737145 + 0.675734i \(0.236173\pi\)
−0.737145 + 0.675734i \(0.763827\pi\)
\(740\) 7.48525e13 0.337324
\(741\) −4.14253e14 −1.85428
\(742\) −2.04320e12 −0.00908429
\(743\) 2.86394e14i 1.26480i 0.774644 + 0.632398i \(0.217929\pi\)
−0.774644 + 0.632398i \(0.782071\pi\)
\(744\) −2.34387e14 −1.02818
\(745\) 3.69872e14 1.61165
\(746\) −1.01315e14 −0.438511
\(747\) 3.36193e14 1.44539
\(748\) 4.80436e13 0.205176
\(749\) 4.84976e13i 0.205736i
\(750\) 1.43827e14i 0.606087i
\(751\) 3.73464e14i 1.56333i −0.623701 0.781663i \(-0.714372\pi\)
0.623701 0.781663i \(-0.285628\pi\)
\(752\) −1.74700e14 −0.726447
\(753\) 3.98094e14i 1.64441i
\(754\) −9.79277e13 −0.401836
\(755\) −6.74258e14 −2.74847
\(756\) −3.50607e14 −1.41975
\(757\) 1.06247e14i 0.427401i 0.976899 + 0.213701i \(0.0685517\pi\)
−0.976899 + 0.213701i \(0.931448\pi\)
\(758\) 9.83422e13i 0.393001i
\(759\) 6.43764e14i 2.55575i
\(760\) 1.56006e14i 0.615281i
\(761\) 4.08008e14i 1.59862i 0.600919 + 0.799310i \(0.294801\pi\)
−0.600919 + 0.799310i \(0.705199\pi\)
\(762\) −5.78200e13 −0.225063
\(763\) 6.39745e13i 0.247391i
\(764\) 4.47197e14i 1.71804i
\(765\) 3.14560e14i 1.20059i
\(766\) 6.49754e13 0.246380
\(767\) 3.93771e14 1.48343
\(768\) 5.06049e13i 0.189403i
\(769\) −9.49805e13 −0.353185 −0.176593 0.984284i \(-0.556508\pi\)
−0.176593 + 0.984284i \(0.556508\pi\)
\(770\) 5.43856e13i 0.200923i
\(771\) 2.48464e14 0.911992
\(772\) 4.41346e14 1.60951
\(773\) 1.72137e14i 0.623700i −0.950131 0.311850i \(-0.899051\pi\)
0.950131 0.311850i \(-0.100949\pi\)
\(774\) −1.88293e14 + 1.78338e14i −0.677842 + 0.642007i
\(775\) −3.75793e14 −1.34413
\(776\) 3.42384e13i 0.121676i
\(777\) 5.67886e13i 0.200519i
\(778\) −1.72234e13 −0.0604255
\(779\) 2.03841e14i 0.710567i
\(780\) −1.24327e15