Properties

Label 43.11.b.b.42.13
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 42.13
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.22

$q$-expansion

\(f(q)\) \(=\) \(q-21.4666i q^{2} +198.865i q^{3} +563.184 q^{4} +4591.08i q^{5} +4268.96 q^{6} -9954.72i q^{7} -34071.5i q^{8} +19501.8 q^{9} +O(q^{10})\) \(q-21.4666i q^{2} +198.865i q^{3} +563.184 q^{4} +4591.08i q^{5} +4268.96 q^{6} -9954.72i q^{7} -34071.5i q^{8} +19501.8 q^{9} +98554.8 q^{10} +281457. q^{11} +111998. i q^{12} -387846. q^{13} -213694. q^{14} -913004. q^{15} -154698. q^{16} +790905. q^{17} -418637. i q^{18} +2.97737e6i q^{19} +2.58562e6i q^{20} +1.97965e6 q^{21} -6.04193e6i q^{22} -3.73725e6 q^{23} +6.77562e6 q^{24} -1.13123e7 q^{25} +8.32573e6i q^{26} +1.56210e7i q^{27} -5.60635e6i q^{28} +2.26181e7i q^{29} +1.95991e7i q^{30} +2.79032e7 q^{31} -3.15683e7i q^{32} +5.59719e7i q^{33} -1.69781e7i q^{34} +4.57029e7 q^{35} +1.09831e7 q^{36} +7.96095e6i q^{37} +6.39141e7 q^{38} -7.71289e7i q^{39} +1.56425e8 q^{40} +5.43511e7 q^{41} -4.24963e7i q^{42} +(-9.52801e7 + 1.11952e8i) q^{43} +1.58512e8 q^{44} +8.95340e7i q^{45} +8.02262e7i q^{46} -6.95452e7 q^{47} -3.07641e7i q^{48} +1.83379e8 q^{49} +2.42838e8i q^{50} +1.57283e8i q^{51} -2.18429e8 q^{52} -3.43114e8 q^{53} +3.35330e8 q^{54} +1.29219e9i q^{55} -3.39172e8 q^{56} -5.92095e8 q^{57} +4.85535e8 q^{58} +4.88010e8 q^{59} -5.14189e8 q^{60} -8.46701e8i q^{61} -5.98988e8i q^{62} -1.94135e8i q^{63} -8.36077e8 q^{64} -1.78063e9i q^{65} +1.20153e9 q^{66} -8.00338e8 q^{67} +4.45425e8 q^{68} -7.43208e8i q^{69} -9.81086e8i q^{70} +1.08276e9i q^{71} -6.64454e8i q^{72} +1.82954e9i q^{73} +1.70895e8 q^{74} -2.24963e9i q^{75} +1.67681e9i q^{76} -2.80183e9i q^{77} -1.65570e9 q^{78} -4.40059e9 q^{79} -7.10232e8i q^{80} -1.95491e9 q^{81} -1.16673e9i q^{82} +4.62097e9 q^{83} +1.11491e9 q^{84} +3.63111e9i q^{85} +(2.40322e9 + 2.04534e9i) q^{86} -4.49795e9 q^{87} -9.58965e9i q^{88} -7.45253e9i q^{89} +1.92199e9 q^{90} +3.86090e9i q^{91} -2.10476e9 q^{92} +5.54897e9i q^{93} +1.49290e9i q^{94} -1.36693e10 q^{95} +6.27783e9 q^{96} +1.42418e9 q^{97} -3.93652e9i q^{98} +5.48890e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 21.4666i 0.670832i −0.942070 0.335416i \(-0.891123\pi\)
0.942070 0.335416i \(-0.108877\pi\)
\(3\) 198.865i 0.818374i 0.912451 + 0.409187i \(0.134188\pi\)
−0.912451 + 0.409187i \(0.865812\pi\)
\(4\) 563.184 0.549985
\(5\) 4591.08i 1.46914i 0.678531 + 0.734572i \(0.262617\pi\)
−0.678531 + 0.734572i \(0.737383\pi\)
\(6\) 4268.96 0.548991
\(7\) 9954.72i 0.592296i −0.955142 0.296148i \(-0.904298\pi\)
0.955142 0.296148i \(-0.0957022\pi\)
\(8\) 34071.5i 1.03978i
\(9\) 19501.8 0.330264
\(10\) 98554.8 0.985548
\(11\) 281457. 1.74763 0.873813 0.486262i \(-0.161640\pi\)
0.873813 + 0.486262i \(0.161640\pi\)
\(12\) 111998.i 0.450093i
\(13\) −387846. −1.04458 −0.522291 0.852768i \(-0.674922\pi\)
−0.522291 + 0.852768i \(0.674922\pi\)
\(14\) −213694. −0.397331
\(15\) −913004. −1.20231
\(16\) −154698. −0.147532
\(17\) 790905. 0.557032 0.278516 0.960432i \(-0.410158\pi\)
0.278516 + 0.960432i \(0.410158\pi\)
\(18\) 418637.i 0.221552i
\(19\) 2.97737e6i 1.20244i 0.799082 + 0.601222i \(0.205319\pi\)
−0.799082 + 0.601222i \(0.794681\pi\)
\(20\) 2.58562e6i 0.808007i
\(21\) 1.97965e6 0.484720
\(22\) 6.04193e6i 1.17236i
\(23\) −3.73725e6 −0.580648 −0.290324 0.956928i \(-0.593763\pi\)
−0.290324 + 0.956928i \(0.593763\pi\)
\(24\) 6.77562e6 0.850928
\(25\) −1.13123e7 −1.15838
\(26\) 8.32573e6i 0.700738i
\(27\) 1.56210e7i 1.08865i
\(28\) 5.60635e6i 0.325754i
\(29\) 2.26181e7i 1.10272i 0.834266 + 0.551362i \(0.185892\pi\)
−0.834266 + 0.551362i \(0.814108\pi\)
\(30\) 1.95991e7i 0.806547i
\(31\) 2.79032e7 0.974644 0.487322 0.873222i \(-0.337974\pi\)
0.487322 + 0.873222i \(0.337974\pi\)
\(32\) 3.15683e7i 0.940810i
\(33\) 5.59719e7i 1.43021i
\(34\) 1.69781e7i 0.373674i
\(35\) 4.57029e7 0.870169
\(36\) 1.09831e7 0.181640
\(37\) 7.96095e6i 0.114804i 0.998351 + 0.0574019i \(0.0182816\pi\)
−0.998351 + 0.0574019i \(0.981718\pi\)
\(38\) 6.39141e7 0.806638
\(39\) 7.71289e7i 0.854858i
\(40\) 1.56425e8 1.52759
\(41\) 5.43511e7 0.469126 0.234563 0.972101i \(-0.424634\pi\)
0.234563 + 0.972101i \(0.424634\pi\)
\(42\) 4.24963e7i 0.325166i
\(43\) −9.52801e7 + 1.11952e8i −0.648126 + 0.761533i
\(44\) 1.58512e8 0.961168
\(45\) 8.95340e7i 0.485205i
\(46\) 8.02262e7i 0.389517i
\(47\) −6.95452e7 −0.303234 −0.151617 0.988439i \(-0.548448\pi\)
−0.151617 + 0.988439i \(0.548448\pi\)
\(48\) 3.07641e7i 0.120736i
\(49\) 1.83379e8 0.649185
\(50\) 2.42838e8i 0.777081i
\(51\) 1.57283e8i 0.455860i
\(52\) −2.18429e8 −0.574504
\(53\) −3.43114e8 −0.820463 −0.410232 0.911981i \(-0.634552\pi\)
−0.410232 + 0.911981i \(0.634552\pi\)
\(54\) 3.35330e8 0.730303
\(55\) 1.29219e9i 2.56751i
\(56\) −3.39172e8 −0.615857
\(57\) −5.92095e8 −0.984049
\(58\) 4.85535e8 0.739743
\(59\) 4.88010e8 0.682604 0.341302 0.939954i \(-0.389132\pi\)
0.341302 + 0.939954i \(0.389132\pi\)
\(60\) −5.14189e8 −0.661252
\(61\) 8.46701e8i 1.00249i −0.865305 0.501246i \(-0.832875\pi\)
0.865305 0.501246i \(-0.167125\pi\)
\(62\) 5.98988e8i 0.653822i
\(63\) 1.94135e8i 0.195614i
\(64\) −8.36077e8 −0.778657
\(65\) 1.78063e9i 1.53464i
\(66\) 1.20153e9 0.959431
\(67\) −8.00338e8 −0.592788 −0.296394 0.955066i \(-0.595784\pi\)
−0.296394 + 0.955066i \(0.595784\pi\)
\(68\) 4.45425e8 0.306359
\(69\) 7.43208e8i 0.475188i
\(70\) 9.81086e8i 0.583737i
\(71\) 1.08276e9i 0.600125i 0.953920 + 0.300063i \(0.0970076\pi\)
−0.953920 + 0.300063i \(0.902992\pi\)
\(72\) 6.64454e8i 0.343402i
\(73\) 1.82954e9i 0.882525i 0.897378 + 0.441263i \(0.145469\pi\)
−0.897378 + 0.441263i \(0.854531\pi\)
\(74\) 1.70895e8 0.0770140
\(75\) 2.24963e9i 0.947992i
\(76\) 1.67681e9i 0.661326i
\(77\) 2.80183e9i 1.03511i
\(78\) −1.65570e9 −0.573466
\(79\) −4.40059e9 −1.43013 −0.715065 0.699058i \(-0.753603\pi\)
−0.715065 + 0.699058i \(0.753603\pi\)
\(80\) 7.10232e8i 0.216746i
\(81\) −1.95491e9 −0.560662
\(82\) 1.16673e9i 0.314704i
\(83\) 4.62097e9 1.17312 0.586561 0.809905i \(-0.300482\pi\)
0.586561 + 0.809905i \(0.300482\pi\)
\(84\) 1.11491e9 0.266589
\(85\) 3.63111e9i 0.818360i
\(86\) 2.40322e9 + 2.04534e9i 0.510860 + 0.434784i
\(87\) −4.49795e9 −0.902441
\(88\) 9.58965e9i 1.81714i
\(89\) 7.45253e9i 1.33461i −0.744786 0.667304i \(-0.767448\pi\)
0.744786 0.667304i \(-0.232552\pi\)
\(90\) 1.92199e9 0.325491
\(91\) 3.86090e9i 0.618702i
\(92\) −2.10476e9 −0.319348
\(93\) 5.54897e9i 0.797623i
\(94\) 1.49290e9i 0.203419i
\(95\) −1.36693e10 −1.76656
\(96\) 6.27783e9 0.769934
\(97\) 1.42418e9 0.165846 0.0829232 0.996556i \(-0.473574\pi\)
0.0829232 + 0.996556i \(0.473574\pi\)
\(98\) 3.93652e9i 0.435494i
\(99\) 5.48890e9 0.577178
\(100\) −6.37094e9 −0.637094
\(101\) 6.64206e9 0.631969 0.315985 0.948764i \(-0.397665\pi\)
0.315985 + 0.948764i \(0.397665\pi\)
\(102\) 3.37634e9 0.305805
\(103\) 4.24087e8 0.0365822 0.0182911 0.999833i \(-0.494177\pi\)
0.0182911 + 0.999833i \(0.494177\pi\)
\(104\) 1.32145e10i 1.08613i
\(105\) 9.08870e9i 0.712123i
\(106\) 7.36550e9i 0.550393i
\(107\) −2.47617e10 −1.76547 −0.882736 0.469868i \(-0.844301\pi\)
−0.882736 + 0.469868i \(0.844301\pi\)
\(108\) 8.79750e9i 0.598743i
\(109\) 1.78573e10 1.16060 0.580300 0.814403i \(-0.302935\pi\)
0.580300 + 0.814403i \(0.302935\pi\)
\(110\) 2.77389e10 1.72237
\(111\) −1.58315e9 −0.0939524
\(112\) 1.53998e9i 0.0873827i
\(113\) 7.64076e9i 0.414710i −0.978266 0.207355i \(-0.933515\pi\)
0.978266 0.207355i \(-0.0664855\pi\)
\(114\) 1.27103e10i 0.660131i
\(115\) 1.71580e10i 0.853056i
\(116\) 1.27382e10i 0.606482i
\(117\) −7.56367e9 −0.344988
\(118\) 1.04759e10i 0.457913i
\(119\) 7.87324e9i 0.329928i
\(120\) 3.11074e10i 1.25014i
\(121\) 5.32806e10 2.05420
\(122\) −1.81758e10 −0.672503
\(123\) 1.08085e10i 0.383920i
\(124\) 1.57147e10 0.536039
\(125\) 7.10112e9i 0.232689i
\(126\) −4.16741e9 −0.131224
\(127\) 4.24675e10 1.28540 0.642700 0.766118i \(-0.277814\pi\)
0.642700 + 0.766118i \(0.277814\pi\)
\(128\) 1.43782e10i 0.418462i
\(129\) −2.22633e10 1.89479e10i −0.623219 0.530410i
\(130\) −3.82241e10 −1.02949
\(131\) 1.39356e10i 0.361217i 0.983555 + 0.180609i \(0.0578067\pi\)
−0.983555 + 0.180609i \(0.942193\pi\)
\(132\) 3.15225e10i 0.786595i
\(133\) 2.96389e10 0.712203
\(134\) 1.71806e10i 0.397661i
\(135\) −7.17171e10 −1.59939
\(136\) 2.69473e10i 0.579190i
\(137\) 1.51743e10i 0.314417i −0.987565 0.157208i \(-0.949751\pi\)
0.987565 0.157208i \(-0.0502494\pi\)
\(138\) −1.59542e10 −0.318771
\(139\) 9.42053e10 1.81552 0.907760 0.419490i \(-0.137791\pi\)
0.907760 + 0.419490i \(0.137791\pi\)
\(140\) 2.57392e10 0.478580
\(141\) 1.38301e10i 0.248159i
\(142\) 2.32433e10 0.402583
\(143\) −1.09162e11 −1.82554
\(144\) −3.01689e9 −0.0487245
\(145\) −1.03842e11 −1.62006
\(146\) 3.92740e10 0.592026
\(147\) 3.64676e10i 0.531276i
\(148\) 4.48348e9i 0.0631403i
\(149\) 8.46017e10i 1.15199i −0.817454 0.575994i \(-0.804615\pi\)
0.817454 0.575994i \(-0.195385\pi\)
\(150\) −4.82919e10 −0.635943
\(151\) 9.79693e10i 1.24797i −0.781435 0.623986i \(-0.785512\pi\)
0.781435 0.623986i \(-0.214488\pi\)
\(152\) 1.01443e11 1.25028
\(153\) 1.54240e10 0.183967
\(154\) −6.01457e10 −0.694386
\(155\) 1.28106e11i 1.43189i
\(156\) 4.34378e10i 0.470159i
\(157\) 1.82495e11i 1.91317i −0.291455 0.956584i \(-0.594139\pi\)
0.291455 0.956584i \(-0.405861\pi\)
\(158\) 9.44658e10i 0.959377i
\(159\) 6.82333e10i 0.671446i
\(160\) 1.44933e11 1.38219
\(161\) 3.72033e10i 0.343916i
\(162\) 4.19652e10i 0.376110i
\(163\) 3.99764e10i 0.347429i −0.984796 0.173714i \(-0.944423\pi\)
0.984796 0.173714i \(-0.0555770\pi\)
\(164\) 3.06097e10 0.258012
\(165\) −2.56971e11 −2.10119
\(166\) 9.91967e10i 0.786967i
\(167\) −1.57900e11 −1.21563 −0.607813 0.794080i \(-0.707953\pi\)
−0.607813 + 0.794080i \(0.707953\pi\)
\(168\) 6.74494e10i 0.504002i
\(169\) 1.25658e10 0.0911497
\(170\) 7.79475e10 0.548982
\(171\) 5.80640e10i 0.397124i
\(172\) −5.36602e10 + 6.30495e10i −0.356460 + 0.418831i
\(173\) −1.39091e11 −0.897569 −0.448784 0.893640i \(-0.648143\pi\)
−0.448784 + 0.893640i \(0.648143\pi\)
\(174\) 9.65559e10i 0.605386i
\(175\) 1.12611e11i 0.686107i
\(176\) −4.35410e10 −0.257831
\(177\) 9.70481e10i 0.558626i
\(178\) −1.59981e11 −0.895297
\(179\) 3.01180e11i 1.63893i −0.573130 0.819465i \(-0.694271\pi\)
0.573130 0.819465i \(-0.305729\pi\)
\(180\) 5.04242e10i 0.266856i
\(181\) −3.06485e11 −1.57767 −0.788836 0.614603i \(-0.789316\pi\)
−0.788836 + 0.614603i \(0.789316\pi\)
\(182\) 8.28804e10 0.415045
\(183\) 1.68379e11 0.820413
\(184\) 1.27334e11i 0.603746i
\(185\) −3.65493e10 −0.168663
\(186\) 1.19118e11 0.535071
\(187\) 2.22606e11 0.973483
\(188\) −3.91668e10 −0.166774
\(189\) 1.55503e11 0.644805
\(190\) 2.93434e11i 1.18507i
\(191\) 3.13253e11i 1.23234i −0.787615 0.616168i \(-0.788684\pi\)
0.787615 0.616168i \(-0.211316\pi\)
\(192\) 1.66266e11i 0.637233i
\(193\) 3.96142e11 1.47933 0.739664 0.672976i \(-0.234984\pi\)
0.739664 + 0.672976i \(0.234984\pi\)
\(194\) 3.05723e10i 0.111255i
\(195\) 3.54105e11 1.25591
\(196\) 1.03276e11 0.357042
\(197\) 2.34601e11 0.790677 0.395339 0.918535i \(-0.370627\pi\)
0.395339 + 0.918535i \(0.370627\pi\)
\(198\) 1.17828e11i 0.387189i
\(199\) 1.92218e11i 0.615925i −0.951399 0.307962i \(-0.900353\pi\)
0.951399 0.307962i \(-0.0996471\pi\)
\(200\) 3.85428e11i 1.20446i
\(201\) 1.59159e11i 0.485122i
\(202\) 1.42583e11i 0.423945i
\(203\) 2.25157e11 0.653140
\(204\) 8.85795e10i 0.250716i
\(205\) 2.49530e11i 0.689213i
\(206\) 9.10372e9i 0.0245405i
\(207\) −7.28830e10 −0.191767
\(208\) 5.99991e10 0.154109
\(209\) 8.38002e11i 2.10142i
\(210\) 1.95104e11 0.477715
\(211\) 2.97067e11i 0.710301i 0.934809 + 0.355150i \(0.115570\pi\)
−0.934809 + 0.355150i \(0.884430\pi\)
\(212\) −1.93236e11 −0.451242
\(213\) −2.15324e11 −0.491127
\(214\) 5.31549e11i 1.18434i
\(215\) −5.13979e11 4.37438e11i −1.11880 0.952191i
\(216\) 5.32230e11 1.13196
\(217\) 2.77769e11i 0.577278i
\(218\) 3.83335e11i 0.778568i
\(219\) −3.63831e11 −0.722236
\(220\) 7.27741e11i 1.41209i
\(221\) −3.06749e11 −0.581865
\(222\) 3.39849e10i 0.0630263i
\(223\) 5.72221e11i 1.03762i −0.854889 0.518811i \(-0.826375\pi\)
0.854889 0.518811i \(-0.173625\pi\)
\(224\) −3.14254e11 −0.557238
\(225\) −2.20611e11 −0.382573
\(226\) −1.64021e11 −0.278200
\(227\) 2.30229e11i 0.381972i 0.981593 + 0.190986i \(0.0611685\pi\)
−0.981593 + 0.190986i \(0.938831\pi\)
\(228\) −3.33458e11 −0.541212
\(229\) 1.23658e11 0.196357 0.0981785 0.995169i \(-0.468698\pi\)
0.0981785 + 0.995169i \(0.468698\pi\)
\(230\) −3.68324e11 −0.572257
\(231\) 5.57185e11 0.847109
\(232\) 7.70634e11 1.14659
\(233\) 1.29810e12i 1.89029i 0.326654 + 0.945144i \(0.394079\pi\)
−0.326654 + 0.945144i \(0.605921\pi\)
\(234\) 1.62366e11i 0.231429i
\(235\) 3.19287e11i 0.445495i
\(236\) 2.74840e11 0.375422
\(237\) 8.75123e11i 1.17038i
\(238\) −1.69012e11 −0.221326
\(239\) −3.98118e11 −0.510531 −0.255266 0.966871i \(-0.582163\pi\)
−0.255266 + 0.966871i \(0.582163\pi\)
\(240\) 1.41240e11 0.177379
\(241\) 8.56905e11i 1.05402i 0.849860 + 0.527008i \(0.176686\pi\)
−0.849860 + 0.527008i \(0.823314\pi\)
\(242\) 1.14375e12i 1.37802i
\(243\) 5.33641e11i 0.629822i
\(244\) 4.76849e11i 0.551355i
\(245\) 8.41905e11i 0.953746i
\(246\) 2.32023e11 0.257546
\(247\) 1.15476e12i 1.25605i
\(248\) 9.50704e11i 1.01341i
\(249\) 9.18949e11i 0.960052i
\(250\) −1.52437e11 −0.156095
\(251\) 6.33616e11 0.636000 0.318000 0.948091i \(-0.396989\pi\)
0.318000 + 0.948091i \(0.396989\pi\)
\(252\) 1.09334e11i 0.107585i
\(253\) −1.05188e12 −1.01476
\(254\) 9.11634e11i 0.862287i
\(255\) −7.22099e11 −0.669724
\(256\) −1.16479e12 −1.05937
\(257\) 1.61085e12i 1.43678i −0.695641 0.718390i \(-0.744879\pi\)
0.695641 0.718390i \(-0.255121\pi\)
\(258\) −4.06746e11 + 4.77917e11i −0.355816 + 0.418075i
\(259\) 7.92490e10 0.0679978
\(260\) 1.00282e12i 0.844029i
\(261\) 4.41094e11i 0.364190i
\(262\) 2.99150e11 0.242316
\(263\) 7.22918e10i 0.0574527i −0.999587 0.0287263i \(-0.990855\pi\)
0.999587 0.0287263i \(-0.00914513\pi\)
\(264\) 1.90705e12 1.48710
\(265\) 1.57526e12i 1.20538i
\(266\) 6.36247e11i 0.477769i
\(267\) 1.48205e12 1.09221
\(268\) −4.50738e11 −0.326024
\(269\) −1.04098e12 −0.739063 −0.369531 0.929218i \(-0.620482\pi\)
−0.369531 + 0.929218i \(0.620482\pi\)
\(270\) 1.53952e12i 1.07292i
\(271\) 2.43860e12 1.66838 0.834190 0.551477i \(-0.185936\pi\)
0.834190 + 0.551477i \(0.185936\pi\)
\(272\) −1.22352e11 −0.0821800
\(273\) −7.67797e11 −0.506329
\(274\) −3.25741e11 −0.210921
\(275\) −3.18394e12 −2.02442
\(276\) 4.18563e11i 0.261346i
\(277\) 1.02076e12i 0.625931i 0.949764 + 0.312966i \(0.101322\pi\)
−0.949764 + 0.312966i \(0.898678\pi\)
\(278\) 2.02227e12i 1.21791i
\(279\) 5.44162e11 0.321890
\(280\) 1.55717e12i 0.904783i
\(281\) −3.03748e12 −1.73373 −0.866867 0.498539i \(-0.833870\pi\)
−0.866867 + 0.498539i \(0.833870\pi\)
\(282\) −2.96886e11 −0.166473
\(283\) 2.97432e12 1.63853 0.819267 0.573413i \(-0.194381\pi\)
0.819267 + 0.573413i \(0.194381\pi\)
\(284\) 6.09795e11i 0.330060i
\(285\) 2.71835e12i 1.44571i
\(286\) 2.34334e12i 1.22463i
\(287\) 5.41050e11i 0.277861i
\(288\) 6.15638e11i 0.310716i
\(289\) −1.39046e12 −0.689716
\(290\) 2.22913e12i 1.08679i
\(291\) 2.83219e11i 0.135724i
\(292\) 1.03037e12i 0.485375i
\(293\) 1.21603e12 0.563128 0.281564 0.959542i \(-0.409147\pi\)
0.281564 + 0.959542i \(0.409147\pi\)
\(294\) 7.82836e11 0.356397
\(295\) 2.24049e12i 1.00284i
\(296\) 2.71241e11 0.119371
\(297\) 4.39663e12i 1.90256i
\(298\) −1.81611e12 −0.772790
\(299\) 1.44948e12 0.606534
\(300\) 1.26696e12i 0.521381i
\(301\) 1.11445e12 + 9.48487e11i 0.451053 + 0.383883i
\(302\) −2.10307e12 −0.837180
\(303\) 1.32087e12i 0.517187i
\(304\) 4.60595e11i 0.177399i
\(305\) 3.88727e12 1.47280
\(306\) 3.31102e11i 0.123411i
\(307\) 1.99500e12 0.731561 0.365781 0.930701i \(-0.380802\pi\)
0.365781 + 0.930701i \(0.380802\pi\)
\(308\) 1.57794e12i 0.569296i
\(309\) 8.43361e10i 0.0299379i
\(310\) 2.75000e12 0.960559
\(311\) −4.26280e12 −1.46519 −0.732593 0.680667i \(-0.761690\pi\)
−0.732593 + 0.680667i \(0.761690\pi\)
\(312\) −2.62790e12 −0.888863
\(313\) 3.58899e12i 1.19468i 0.801989 + 0.597339i \(0.203775\pi\)
−0.801989 + 0.597339i \(0.796225\pi\)
\(314\) −3.91756e12 −1.28341
\(315\) 8.91287e11 0.287385
\(316\) −2.47834e12 −0.786550
\(317\) 5.45005e12 1.70257 0.851283 0.524706i \(-0.175825\pi\)
0.851283 + 0.524706i \(0.175825\pi\)
\(318\) −1.46474e12 −0.450427
\(319\) 6.36603e12i 1.92715i
\(320\) 3.83849e12i 1.14396i
\(321\) 4.92423e12i 1.44482i
\(322\) 7.98629e11 0.230710
\(323\) 2.35482e12i 0.669799i
\(324\) −1.10097e12 −0.308355
\(325\) 4.38744e12 1.21003
\(326\) −8.58158e11 −0.233066
\(327\) 3.55119e12i 0.949805i
\(328\) 1.85182e12i 0.487787i
\(329\) 6.92304e11i 0.179604i
\(330\) 5.51630e12i 1.40954i
\(331\) 5.62247e12i 1.41510i −0.706663 0.707550i \(-0.749800\pi\)
0.706663 0.707550i \(-0.250200\pi\)
\(332\) 2.60246e12 0.645199
\(333\) 1.55252e11i 0.0379155i
\(334\) 3.38958e12i 0.815481i
\(335\) 3.67441e12i 0.870891i
\(336\) −3.06248e11 −0.0715117
\(337\) 2.77529e12 0.638496 0.319248 0.947671i \(-0.396570\pi\)
0.319248 + 0.947671i \(0.396570\pi\)
\(338\) 2.69744e11i 0.0611461i
\(339\) 1.51948e12 0.339388
\(340\) 2.04498e12i 0.450085i
\(341\) 7.85355e12 1.70331
\(342\) 1.24644e12 0.266403
\(343\) 4.63745e12i 0.976806i
\(344\) 3.81436e12 + 3.24633e12i 0.791826 + 0.673908i
\(345\) 3.41213e12 0.698119
\(346\) 2.98581e12i 0.602118i
\(347\) 6.90565e12i 1.37264i −0.727299 0.686321i \(-0.759225\pi\)
0.727299 0.686321i \(-0.240775\pi\)
\(348\) −2.53318e12 −0.496329
\(349\) 1.08800e12i 0.210137i 0.994465 + 0.105069i \(0.0335063\pi\)
−0.994465 + 0.105069i \(0.966494\pi\)
\(350\) 2.41738e12 0.460262
\(351\) 6.05853e12i 1.13719i
\(352\) 8.88513e12i 1.64418i
\(353\) −7.47744e12 −1.36420 −0.682102 0.731257i \(-0.738934\pi\)
−0.682102 + 0.731257i \(0.738934\pi\)
\(354\) 2.08329e12 0.374744
\(355\) −4.97105e12 −0.881670
\(356\) 4.19715e12i 0.734014i
\(357\) 1.56571e12 0.270004
\(358\) −6.46531e12 −1.09945
\(359\) −7.05719e12 −1.18348 −0.591738 0.806130i \(-0.701558\pi\)
−0.591738 + 0.806130i \(0.701558\pi\)
\(360\) 3.05056e12 0.504506
\(361\) −2.73367e12 −0.445872
\(362\) 6.57920e12i 1.05835i
\(363\) 1.05956e13i 1.68110i
\(364\) 2.17440e12i 0.340276i
\(365\) −8.39955e12 −1.29656
\(366\) 3.61453e12i 0.550359i
\(367\) −2.86369e11 −0.0430127 −0.0215063 0.999769i \(-0.506846\pi\)
−0.0215063 + 0.999769i \(0.506846\pi\)
\(368\) 5.78147e11 0.0856642
\(369\) 1.05994e12 0.154935
\(370\) 7.84590e11i 0.113145i
\(371\) 3.41560e12i 0.485957i
\(372\) 3.12509e12i 0.438681i
\(373\) 9.31022e12i 1.28948i 0.764400 + 0.644742i \(0.223035\pi\)
−0.764400 + 0.644742i \(0.776965\pi\)
\(374\) 4.77859e12i 0.653043i
\(375\) 1.41216e12 0.190427
\(376\) 2.36951e12i 0.315296i
\(377\) 8.77235e12i 1.15189i
\(378\) 3.33812e12i 0.432556i
\(379\) −9.20492e12 −1.17713 −0.588564 0.808450i \(-0.700307\pi\)
−0.588564 + 0.808450i \(0.700307\pi\)
\(380\) −7.69836e12 −0.971583
\(381\) 8.44530e12i 1.05194i
\(382\) −6.72449e12 −0.826690
\(383\) 5.91711e12i 0.717985i 0.933340 + 0.358993i \(0.116880\pi\)
−0.933340 + 0.358993i \(0.883120\pi\)
\(384\) 2.85933e12 0.342458
\(385\) 1.28634e13 1.52073
\(386\) 8.50383e12i 0.992380i
\(387\) −1.85813e12 + 2.18326e12i −0.214053 + 0.251507i
\(388\) 8.02076e11 0.0912130
\(389\) 1.45448e13i 1.63290i −0.577417 0.816449i \(-0.695939\pi\)
0.577417 0.816449i \(-0.304061\pi\)
\(390\) 7.60143e12i 0.842504i
\(391\) −2.95581e12 −0.323440
\(392\) 6.24798e12i 0.675009i
\(393\) −2.77130e12 −0.295611
\(394\) 5.03610e12i 0.530411i
\(395\) 2.02035e13i 2.10107i
\(396\) 3.09127e12 0.317439
\(397\) 1.45663e12 0.147705 0.0738526 0.997269i \(-0.476471\pi\)
0.0738526 + 0.997269i \(0.476471\pi\)
\(398\) −4.12626e12 −0.413182
\(399\) 5.89414e12i 0.582849i
\(400\) 1.75000e12 0.170899
\(401\) 8.65402e11 0.0834634 0.0417317 0.999129i \(-0.486713\pi\)
0.0417317 + 0.999129i \(0.486713\pi\)
\(402\) −3.41661e12 −0.325436
\(403\) −1.08221e13 −1.01809
\(404\) 3.74071e12 0.347574
\(405\) 8.97512e12i 0.823693i
\(406\) 4.83337e12i 0.438147i
\(407\) 2.24066e12i 0.200634i
\(408\) 5.35887e12 0.473994
\(409\) 2.00482e12i 0.175170i −0.996157 0.0875849i \(-0.972085\pi\)
0.996157 0.0875849i \(-0.0279149\pi\)
\(410\) 5.35657e12 0.462346
\(411\) 3.01763e12 0.257311
\(412\) 2.38839e11 0.0201196
\(413\) 4.85801e12i 0.404304i
\(414\) 1.56455e12i 0.128644i
\(415\) 2.12152e13i 1.72348i
\(416\) 1.22436e13i 0.982752i
\(417\) 1.87341e13i 1.48577i
\(418\) 1.79891e13 1.40970
\(419\) 1.47181e12i 0.113968i −0.998375 0.0569839i \(-0.981852\pi\)
0.998375 0.0569839i \(-0.0181484\pi\)
\(420\) 5.11861e12i 0.391657i
\(421\) 2.78330e12i 0.210450i 0.994448 + 0.105225i \(0.0335563\pi\)
−0.994448 + 0.105225i \(0.966444\pi\)
\(422\) 6.37703e12 0.476492
\(423\) −1.35625e12 −0.100147
\(424\) 1.16904e13i 0.853100i
\(425\) −8.94699e12 −0.645257
\(426\) 4.62227e12i 0.329463i
\(427\) −8.42867e12 −0.593772
\(428\) −1.39454e13 −0.970983
\(429\) 2.17085e13i 1.49397i
\(430\) −9.39031e12 + 1.10334e13i −0.638760 + 0.750527i
\(431\) −1.09047e13 −0.733210 −0.366605 0.930377i \(-0.619480\pi\)
−0.366605 + 0.930377i \(0.619480\pi\)
\(432\) 2.41654e12i 0.160611i
\(433\) 7.48067e12i 0.491474i 0.969336 + 0.245737i \(0.0790300\pi\)
−0.969336 + 0.245737i \(0.920970\pi\)
\(434\) −5.96276e12 −0.387256
\(435\) 2.06504e13i 1.32582i
\(436\) 1.00569e13 0.638313
\(437\) 1.11272e13i 0.698197i
\(438\) 7.81022e12i 0.484499i
\(439\) −1.29772e13 −0.795902 −0.397951 0.917407i \(-0.630279\pi\)
−0.397951 + 0.917407i \(0.630279\pi\)
\(440\) 4.40268e13 2.66965
\(441\) 3.57621e12 0.214402
\(442\) 6.58487e12i 0.390333i
\(443\) −7.54555e12 −0.442254 −0.221127 0.975245i \(-0.570974\pi\)
−0.221127 + 0.975245i \(0.570974\pi\)
\(444\) −8.91607e11 −0.0516724
\(445\) 3.42151e13 1.96073
\(446\) −1.22836e13 −0.696070
\(447\) 1.68243e13 0.942757
\(448\) 8.32291e12i 0.461196i
\(449\) 2.77542e13i 1.52089i 0.649405 + 0.760443i \(0.275018\pi\)
−0.649405 + 0.760443i \(0.724982\pi\)
\(450\) 4.73576e12i 0.256642i
\(451\) 1.52975e13 0.819856
\(452\) 4.30316e12i 0.228084i
\(453\) 1.94826e13 1.02131
\(454\) 4.94225e12 0.256239
\(455\) −1.77257e13 −0.908962
\(456\) 2.01735e13i 1.02319i
\(457\) 2.13666e13i 1.07190i −0.844249 0.535951i \(-0.819953\pi\)
0.844249 0.535951i \(-0.180047\pi\)
\(458\) 2.65453e12i 0.131723i
\(459\) 1.23547e13i 0.606414i
\(460\) 9.66312e12i 0.469168i
\(461\) 1.20763e13 0.580004 0.290002 0.957026i \(-0.406344\pi\)
0.290002 + 0.957026i \(0.406344\pi\)
\(462\) 1.19609e13i 0.568268i
\(463\) 1.51558e13i 0.712320i 0.934425 + 0.356160i \(0.115914\pi\)
−0.934425 + 0.356160i \(0.884086\pi\)
\(464\) 3.49899e12i 0.162687i
\(465\) −2.54757e13 −1.17182
\(466\) 2.78658e13 1.26807
\(467\) 3.12334e13i 1.40616i −0.711111 0.703080i \(-0.751808\pi\)
0.711111 0.703080i \(-0.248192\pi\)
\(468\) −4.25974e12 −0.189738
\(469\) 7.96715e12i 0.351106i
\(470\) −6.85402e12 −0.298852
\(471\) 3.62919e13 1.56569
\(472\) 1.66272e13i 0.709757i
\(473\) −2.68172e13 + 3.15096e13i −1.13268 + 1.33087i
\(474\) −1.87859e13 −0.785129
\(475\) 3.36811e13i 1.39289i
\(476\) 4.43409e12i 0.181455i
\(477\) −6.69132e12 −0.270969
\(478\) 8.54625e12i 0.342481i
\(479\) −4.43874e13 −1.76028 −0.880141 0.474713i \(-0.842552\pi\)
−0.880141 + 0.474713i \(0.842552\pi\)
\(480\) 2.88220e13i 1.13114i
\(481\) 3.08762e12i 0.119922i
\(482\) 1.83948e13 0.707067
\(483\) −7.39843e12 −0.281452
\(484\) 3.00068e13 1.12978
\(485\) 6.53852e12i 0.243652i
\(486\) 1.14555e13 0.422505
\(487\) −1.37180e13 −0.500779 −0.250389 0.968145i \(-0.580559\pi\)
−0.250389 + 0.968145i \(0.580559\pi\)
\(488\) −2.88483e13 −1.04237
\(489\) 7.94991e12 0.284327
\(490\) 1.80729e13 0.639803
\(491\) 4.55887e13i 1.59753i 0.601641 + 0.798766i \(0.294514\pi\)
−0.601641 + 0.798766i \(0.705486\pi\)
\(492\) 6.08719e12i 0.211150i
\(493\) 1.78888e13i 0.614252i
\(494\) −2.47888e13 −0.842599
\(495\) 2.52000e13i 0.847957i
\(496\) −4.31659e12 −0.143791
\(497\) 1.07786e13 0.355452
\(498\) 1.97267e13 0.644034
\(499\) 5.81864e13i 1.88070i −0.340214 0.940348i \(-0.610499\pi\)
0.340214 0.940348i \(-0.389501\pi\)
\(500\) 3.99924e12i 0.127976i
\(501\) 3.14008e13i 0.994837i
\(502\) 1.36016e13i 0.426649i
\(503\) 2.77763e13i 0.862650i −0.902197 0.431325i \(-0.858046\pi\)
0.902197 0.431325i \(-0.141954\pi\)
\(504\) −6.61445e12 −0.203395
\(505\) 3.04942e13i 0.928454i
\(506\) 2.25802e13i 0.680731i
\(507\) 2.49889e12i 0.0745946i
\(508\) 2.39171e13 0.706951
\(509\) 1.00508e13 0.294180 0.147090 0.989123i \(-0.453009\pi\)
0.147090 + 0.989123i \(0.453009\pi\)
\(510\) 1.55010e13i 0.449272i
\(511\) 1.82125e13 0.522717
\(512\) 1.02809e13i 0.292200i
\(513\) −4.65095e13 −1.30905
\(514\) −3.45796e13 −0.963838
\(515\) 1.94702e12i 0.0537445i
\(516\) −1.25383e13 1.06711e13i −0.342761 0.291717i
\(517\) −1.95740e13 −0.529940
\(518\) 1.70121e12i 0.0456151i
\(519\) 2.76603e13i 0.734547i
\(520\) −6.06686e13 −1.59569
\(521\) 5.84779e13i 1.52336i −0.647953 0.761681i \(-0.724375\pi\)
0.647953 0.761681i \(-0.275625\pi\)
\(522\) 9.46879e12 0.244310
\(523\) 9.90764e12i 0.253199i −0.991954 0.126599i \(-0.959594\pi\)
0.991954 0.126599i \(-0.0404063\pi\)
\(524\) 7.84830e12i 0.198664i
\(525\) −2.23944e13 −0.561492
\(526\) −1.55186e12 −0.0385411
\(527\) 2.20688e13 0.542907
\(528\) 8.65877e12i 0.211002i
\(529\) −2.74595e13 −0.662847
\(530\) −3.38155e13 −0.808606
\(531\) 9.51706e12 0.225440
\(532\) 1.66922e13 0.391701
\(533\) −2.10798e13 −0.490040
\(534\) 3.18145e13i 0.732688i
\(535\) 1.13683e14i 2.59373i
\(536\) 2.72687e13i 0.616369i
\(537\) 5.98940e13 1.34126
\(538\) 2.23463e13i 0.495787i
\(539\) 5.16132e13 1.13453
\(540\) −4.03900e13 −0.879639
\(541\) 7.39783e13 1.59631 0.798157 0.602450i \(-0.205809\pi\)
0.798157 + 0.602450i \(0.205809\pi\)
\(542\) 5.23486e13i 1.11920i
\(543\) 6.09492e13i 1.29113i
\(544\) 2.49676e13i 0.524061i
\(545\) 8.19841e13i 1.70509i
\(546\) 1.64820e13i 0.339662i
\(547\) −9.16879e13 −1.87230 −0.936150 0.351601i \(-0.885637\pi\)
−0.936150 + 0.351601i \(0.885637\pi\)
\(548\) 8.54593e12i 0.172924i
\(549\) 1.65122e13i 0.331087i
\(550\) 6.83484e13i 1.35805i
\(551\) −6.73426e13 −1.32596
\(552\) −2.53222e13 −0.494090
\(553\) 4.38067e13i 0.847061i
\(554\) 2.19124e13 0.419894
\(555\) 7.26837e12i 0.138030i
\(556\) 5.30549e13 0.998509
\(557\) 3.64850e13 0.680515 0.340258 0.940332i \(-0.389486\pi\)
0.340258 + 0.940332i \(0.389486\pi\)
\(558\) 1.16813e13i 0.215934i
\(559\) 3.69540e13 4.34200e13i 0.677021 0.795483i
\(560\) −7.07017e12 −0.128378
\(561\) 4.42685e13i 0.796673i
\(562\) 6.52045e13i 1.16304i
\(563\) 6.24849e13 1.10467 0.552336 0.833622i \(-0.313737\pi\)
0.552336 + 0.833622i \(0.313737\pi\)
\(564\) 7.78890e12i 0.136484i
\(565\) 3.50793e13 0.609268
\(566\) 6.38485e13i 1.09918i
\(567\) 1.94606e13i 0.332078i
\(568\) 3.68913e13 0.623997
\(569\) −3.57357e13 −0.599158 −0.299579 0.954072i \(-0.596846\pi\)
−0.299579 + 0.954072i \(0.596846\pi\)
\(570\) −5.83538e13 −0.969828
\(571\) 2.48707e13i 0.409740i −0.978789 0.204870i \(-0.934323\pi\)
0.978789 0.204870i \(-0.0656771\pi\)
\(572\) −6.14782e13 −1.00402
\(573\) 6.22951e13 1.00851
\(574\) −1.16145e13 −0.186398
\(575\) 4.22771e13 0.672614
\(576\) −1.63050e13 −0.257162
\(577\) 1.12449e13i 0.175824i 0.996128 + 0.0879120i \(0.0280194\pi\)
−0.996128 + 0.0879120i \(0.971981\pi\)
\(578\) 2.98485e13i 0.462683i
\(579\) 7.87788e13i 1.21064i
\(580\) −5.84820e13 −0.891009
\(581\) 4.60005e13i 0.694836i
\(582\) 6.07976e12 0.0910483
\(583\) −9.65718e13 −1.43386
\(584\) 6.23351e13 0.917631
\(585\) 3.47254e13i 0.506836i
\(586\) 2.61041e13i 0.377764i
\(587\) 8.96698e13i 1.28664i −0.765599 0.643318i \(-0.777557\pi\)
0.765599 0.643318i \(-0.222443\pi\)
\(588\) 2.05380e13i 0.292194i
\(589\) 8.30782e13i 1.17195i
\(590\) 4.80958e13 0.672740
\(591\) 4.66540e13i 0.647070i
\(592\) 1.23155e12i 0.0169372i
\(593\) 3.41621e13i 0.465877i 0.972491 + 0.232939i \(0.0748341\pi\)
−0.972491 + 0.232939i \(0.925166\pi\)
\(594\) 9.43809e13 1.27630
\(595\) 3.61467e13 0.484711
\(596\) 4.76464e13i 0.633576i
\(597\) 3.82253e13 0.504057
\(598\) 3.11154e13i 0.406883i
\(599\) 3.96588e13 0.514288 0.257144 0.966373i \(-0.417219\pi\)
0.257144 + 0.966373i \(0.417219\pi\)
\(600\) −7.66482e13 −0.985702
\(601\) 1.06834e14i 1.36250i 0.732052 + 0.681249i \(0.238563\pi\)
−0.732052 + 0.681249i \(0.761437\pi\)
\(602\) 2.03608e13 2.39234e13i 0.257521 0.302581i
\(603\) −1.56080e13 −0.195777
\(604\) 5.51748e13i 0.686366i
\(605\) 2.44615e14i 3.01791i
\(606\) 2.83547e13 0.346946
\(607\) 9.01507e13i 1.09402i 0.837126 + 0.547011i \(0.184234\pi\)
−0.837126 + 0.547011i \(0.815766\pi\)
\(608\) 9.39907e13 1.13127
\(609\) 4.47759e13i 0.534512i
\(610\) 8.34465e13i 0.988004i
\(611\) 2.69728e13 0.316753
\(612\) 8.68658e12 0.101179
\(613\) −8.92183e13 −1.03075 −0.515373 0.856966i \(-0.672346\pi\)
−0.515373 + 0.856966i \(0.672346\pi\)
\(614\) 4.28259e13i 0.490755i
\(615\) −4.96228e13 −0.564034
\(616\) −9.54624e13 −1.07629
\(617\) 9.22488e13 1.03166 0.515828 0.856692i \(-0.327484\pi\)
0.515828 + 0.856692i \(0.327484\pi\)
\(618\) 1.81041e12 0.0200833
\(619\) −3.98980e13 −0.439034 −0.219517 0.975609i \(-0.570448\pi\)
−0.219517 + 0.975609i \(0.570448\pi\)
\(620\) 7.21472e13i 0.787519i
\(621\) 5.83796e13i 0.632125i
\(622\) 9.15079e13i 0.982894i
\(623\) −7.41879e13 −0.790483
\(624\) 1.19317e13i 0.126119i
\(625\) −7.78704e13 −0.816530
\(626\) 7.70436e13 0.801428
\(627\) −1.66649e14 −1.71975
\(628\) 1.02778e14i 1.05221i
\(629\) 6.29635e12i 0.0639493i
\(630\) 1.91329e13i 0.192787i
\(631\) 1.53005e12i 0.0152954i 0.999971 + 0.00764769i \(0.00243436\pi\)
−0.999971 + 0.00764769i \(0.997566\pi\)
\(632\) 1.49935e14i 1.48702i
\(633\) −5.90762e13 −0.581292
\(634\) 1.16994e14i 1.14214i
\(635\) 1.94972e14i 1.88844i
\(636\) 3.84279e13i 0.369285i
\(637\) −7.11226e13 −0.678126
\(638\) 1.36657e14 1.29279
\(639\) 2.11158e13i 0.198200i
\(640\) 6.60116e13 0.614781
\(641\) 2.31328e13i 0.213766i 0.994272 + 0.106883i \(0.0340870\pi\)
−0.994272 + 0.106883i \(0.965913\pi\)
\(642\) −1.05706e14 −0.969229
\(643\) 1.53455e14 1.39613 0.698063 0.716036i \(-0.254045\pi\)
0.698063 + 0.716036i \(0.254045\pi\)
\(644\) 2.09523e13i 0.189149i
\(645\) 8.69910e13 1.02212e14i 0.779249 0.915598i
\(646\) 5.05500e13 0.449323
\(647\) 1.02218e14i 0.901587i −0.892628 0.450793i \(-0.851141\pi\)
0.892628 0.450793i \(-0.148859\pi\)
\(648\) 6.66066e13i 0.582964i
\(649\) 1.37354e14 1.19294
\(650\) 9.41836e13i 0.811724i
\(651\) 5.52385e13 0.472429
\(652\) 2.25141e13i 0.191081i
\(653\) 4.90839e13i 0.413403i 0.978404 + 0.206701i \(0.0662729\pi\)
−0.978404 + 0.206701i \(0.933727\pi\)
\(654\) 7.62319e13 0.637160
\(655\) −6.39793e13 −0.530680
\(656\) −8.40804e12 −0.0692110
\(657\) 3.56792e13i 0.291466i
\(658\) 1.48614e13 0.120484
\(659\) 1.76149e14 1.41727 0.708635 0.705575i \(-0.249311\pi\)
0.708635 + 0.705575i \(0.249311\pi\)
\(660\) −1.44722e14 −1.15562
\(661\) 9.18643e13 0.728014 0.364007 0.931396i \(-0.381408\pi\)
0.364007 + 0.931396i \(0.381408\pi\)
\(662\) −1.20695e14 −0.949295
\(663\) 6.10016e13i 0.476183i
\(664\) 1.57443e14i 1.21979i
\(665\) 1.36074e14i 1.04633i
\(666\) 3.33274e12 0.0254350
\(667\) 8.45297e13i 0.640295i
\(668\) −8.89269e13 −0.668576
\(669\) 1.13795e14 0.849163
\(670\) −7.88772e13 −0.584222
\(671\) 2.38310e14i 1.75198i
\(672\) 6.24941e13i 0.456029i
\(673\) 1.28168e14i 0.928336i −0.885747 0.464168i \(-0.846353\pi\)
0.885747 0.464168i \(-0.153647\pi\)
\(674\) 5.95760e13i 0.428324i
\(675\) 1.76710e14i 1.26108i
\(676\) 7.07684e12 0.0501310
\(677\) 2.96060e13i 0.208179i 0.994568 + 0.104089i \(0.0331928\pi\)
−0.994568 + 0.104089i \(0.966807\pi\)
\(678\) 3.26181e13i 0.227672i
\(679\) 1.41773e13i 0.0982303i
\(680\) 1.23717e14 0.850913
\(681\) −4.57846e13 −0.312596
\(682\) 1.68589e14i 1.14264i
\(683\) −1.89445e14 −1.27462 −0.637309 0.770608i \(-0.719953\pi\)
−0.637309 + 0.770608i \(0.719953\pi\)
\(684\) 3.27007e13i 0.218412i
\(685\) 6.96663e13 0.461924
\(686\) −9.95503e13 −0.655273
\(687\) 2.45913e13i 0.160694i
\(688\) 1.47397e13 1.73188e13i 0.0956194 0.112350i
\(689\) 1.33075e14 0.857040
\(690\) 7.32468e13i 0.468320i
\(691\) 1.36965e14i 0.869399i 0.900575 + 0.434700i \(0.143145\pi\)
−0.900575 + 0.434700i \(0.856855\pi\)
\(692\) −7.83337e13 −0.493649
\(693\) 5.46405e13i 0.341860i
\(694\) −1.48241e14 −0.920812
\(695\) 4.32503e14i 2.66726i
\(696\) 1.53252e14i 0.938339i
\(697\) 4.29866e13 0.261318
\(698\) 2.33558e13 0.140967
\(699\) −2.58146e14 −1.54696
\(700\) 6.34209e13i 0.377348i
\(701\) 5.00960e13 0.295946 0.147973 0.988991i \(-0.452725\pi\)
0.147973 + 0.988991i \(0.452725\pi\)
\(702\) −1.30056e14 −0.762861
\(703\) −2.37027e13 −0.138045
\(704\) −2.35320e14 −1.36080
\(705\) 6.34950e13 0.364581
\(706\) 1.60515e14i 0.915151i
\(707\) 6.61199e13i 0.374313i
\(708\) 5.46560e13i 0.307236i
\(709\) 5.61827e13 0.313596 0.156798 0.987631i \(-0.449883\pi\)
0.156798 + 0.987631i \(0.449883\pi\)
\(710\) 1.06712e14i 0.591452i
\(711\) −8.58193e13 −0.472321
\(712\) −2.53919e14 −1.38770
\(713\) −1.04281e14 −0.565925
\(714\) 3.36105e13i 0.181127i
\(715\) 5.01170e14i 2.68198i
\(716\) 1.69620e14i 0.901386i
\(717\) 7.91717e13i 0.417806i
\(718\) 1.51494e14i 0.793914i
\(719\) 1.13106e14 0.588628 0.294314 0.955709i \(-0.404909\pi\)
0.294314 + 0.955709i \(0.404909\pi\)
\(720\) 1.38508e13i 0.0715833i
\(721\) 4.22167e12i 0.0216675i
\(722\) 5.86827e13i 0.299105i
\(723\) −1.70408e14 −0.862579
\(724\) −1.72608e14 −0.867696
\(725\) 2.55864e14i 1.27738i
\(726\) 2.27452e14 1.12774
\(727\) 1.64326e14i 0.809161i 0.914502 + 0.404581i \(0.132582\pi\)
−0.914502 + 0.404581i \(0.867418\pi\)
\(728\) 1.31546e14 0.643313
\(729\) −2.21558e14 −1.07609
\(730\) 1.80310e14i 0.869772i
\(731\) −7.53575e13 + 8.85432e13i −0.361027 + 0.424198i
\(732\) 9.48284e13 0.451215
\(733\) 7.12596e13i 0.336762i 0.985722 + 0.168381i \(0.0538539\pi\)
−0.985722 + 0.168381i \(0.946146\pi\)
\(734\) 6.14738e12i 0.0288543i
\(735\) −1.67425e14 −0.780521
\(736\) 1.17979e14i 0.546280i
\(737\) −2.25261e14 −1.03597
\(738\) 2.27534e13i 0.103936i
\(739\) 1.25433e14i 0.569100i −0.958661 0.284550i \(-0.908156\pi\)
0.958661 0.284550i \(-0.0918442\pi\)
\(740\) −2.05840e13 −0.0927622
\(741\) 2.29641e14 1.02792
\(742\) 7.33215e13 0.325996
\(743\) 2.75150e14i 1.21514i −0.794267 0.607569i \(-0.792145\pi\)
0.794267 0.607569i \(-0.207855\pi\)
\(744\) 1.89062e14 0.829352
\(745\) 3.88413e14 1.69244
\(746\) 1.99859e14 0.865026
\(747\) 9.01171e13 0.387440
\(748\) 1.25368e14 0.535401
\(749\) 2.46496e14i 1.04568i
\(750\) 3.03144e13i 0.127744i
\(751\) 1.89466e14i 0.793106i 0.918012 + 0.396553i \(0.129794\pi\)
−0.918012 + 0.396553i \(0.870206\pi\)
\(752\) 1.07585e13 0.0447367
\(753\) 1.26004e14i 0.520486i
\(754\) −1.88313e14 −0.772721
\(755\) 4.49784e14 1.83345
\(756\) 8.75767e13 0.354633
\(757\) 2.42227e14i 0.974415i −0.873286 0.487207i \(-0.838016\pi\)
0.873286 0.487207i \(-0.161984\pi\)
\(758\) 1.97598e14i 0.789655i
\(759\) 2.09181e14i 0.830450i
\(760\) 4.65734e14i 1.83684i
\(761\) 3.33654e14i 1.30729i 0.756800 + 0.653646i \(0.226762\pi\)
−0.756800 + 0.653646i \(0.773238\pi\)
\(762\) 1.81292e14 0.705674
\(763\) 1.77764e14i 0.687419i
\(764\) 1.76419e14i 0.677766i
\(765\) 7.08129e13i 0.270275i
\(766\) 1.27020e14 0.481647
\(767\) −1.89273e14 −0.713035
\(768\) 2.31637e14i 0.866965i
\(769\) −3.02892e14 −1.12631 −0.563153 0.826353i \(-0.690412\pi\)
−0.563153 + 0.826353i \(0.690412\pi\)
\(770\) 2.76134e14i 1.02015i
\(771\) 3.20342e14 1.17582
\(772\) 2.23101e14 0.813608
\(773\) 3.06858e14i 1.11183i −0.831238 0.555917i \(-0.812367\pi\)
0.831238 0.555917i \(-0.187633\pi\)
\(774\) 4.68671e13 + 3.98877e13i 0.168719 + 0.143593i
\(775\) −3.15651e14 −1.12901
\(776\) 4.85239e13i 0.172444i
\(777\) 1.57599e13i 0.0556477i
\(778\) −3.12227e14 −1.09540
\(779\) 1.61823e14i 0.564097i
\(780\) 1.99426e14 0.690731