Properties

Label 43.11.b.b.42.5
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 42.5
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.30

$q$-expansion

\(f(q)\) \(=\) \(q-46.2007i q^{2} +372.330i q^{3} -1110.50 q^{4} +2517.50i q^{5} +17201.9 q^{6} +25292.2i q^{7} +3996.58i q^{8} -79580.9 q^{9} +O(q^{10})\) \(q-46.2007i q^{2} +372.330i q^{3} -1110.50 q^{4} +2517.50i q^{5} +17201.9 q^{6} +25292.2i q^{7} +3996.58i q^{8} -79580.9 q^{9} +116310. q^{10} +71323.6 q^{11} -413475. i q^{12} +305041. q^{13} +1.16852e6 q^{14} -937343. q^{15} -952512. q^{16} -1.86577e6 q^{17} +3.67669e6i q^{18} -250385. i q^{19} -2.79570e6i q^{20} -9.41705e6 q^{21} -3.29520e6i q^{22} -7.17521e6 q^{23} -1.48805e6 q^{24} +3.42780e6 q^{25} -1.40931e7i q^{26} -7.64463e6i q^{27} -2.80871e7i q^{28} -7.03624e6i q^{29} +4.33059e7i q^{30} -2.56657e7 q^{31} +4.80992e7i q^{32} +2.65559e7i q^{33} +8.61999e7i q^{34} -6.36732e7 q^{35} +8.83749e7 q^{36} -4.75251e7i q^{37} -1.15680e7 q^{38} +1.13576e8i q^{39} -1.00614e7 q^{40} +9.96282e7 q^{41} +4.35074e8i q^{42} +(9.73908e7 + 1.10120e8i) q^{43} -7.92052e7 q^{44} -2.00345e8i q^{45} +3.31500e8i q^{46} +8.53994e7 q^{47} -3.54649e8i q^{48} -3.57220e8 q^{49} -1.58367e8i q^{50} -6.94683e8i q^{51} -3.38749e8 q^{52} -6.32854e8 q^{53} -3.53187e8 q^{54} +1.79557e8i q^{55} -1.01082e8 q^{56} +9.32259e7 q^{57} -3.25079e8 q^{58} -1.36284e9 q^{59} +1.04092e9 q^{60} -5.18564e8i q^{61} +1.18577e9i q^{62} -2.01278e9i q^{63} +1.24685e9 q^{64} +7.67942e8i q^{65} +1.22690e9 q^{66} +7.52892e8 q^{67} +2.07195e9 q^{68} -2.67155e9i q^{69} +2.94175e9i q^{70} +2.82572e9i q^{71} -3.18051e8i q^{72} -3.11851e9i q^{73} -2.19569e9 q^{74} +1.27627e9i q^{75} +2.78053e8i q^{76} +1.80393e9i q^{77} +5.24729e9 q^{78} +1.02175e9 q^{79} -2.39795e9i q^{80} -1.85284e9 q^{81} -4.60289e9i q^{82} -5.19494e9 q^{83} +1.04577e10 q^{84} -4.69709e9i q^{85} +(5.08764e9 - 4.49952e9i) q^{86} +2.61980e9 q^{87} +2.85050e8i q^{88} +4.43923e9i q^{89} -9.25609e9 q^{90} +7.71516e9i q^{91} +7.96810e9 q^{92} -9.55610e9i q^{93} -3.94551e9i q^{94} +6.30345e8 q^{95} -1.79088e10 q^{96} +6.65798e9 q^{97} +1.65038e10i q^{98} -5.67599e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 46.2007i 1.44377i −0.692012 0.721886i \(-0.743276\pi\)
0.692012 0.721886i \(-0.256724\pi\)
\(3\) 372.330i 1.53222i 0.642707 + 0.766112i \(0.277811\pi\)
−0.642707 + 0.766112i \(0.722189\pi\)
\(4\) −1110.50 −1.08448
\(5\) 2517.50i 0.805601i 0.915288 + 0.402801i \(0.131963\pi\)
−0.915288 + 0.402801i \(0.868037\pi\)
\(6\) 17201.9 2.21218
\(7\) 25292.2i 1.50486i 0.658671 + 0.752431i \(0.271119\pi\)
−0.658671 + 0.752431i \(0.728881\pi\)
\(8\) 3996.58i 0.121966i
\(9\) −79580.9 −1.34771
\(10\) 116310. 1.16310
\(11\) 71323.6 0.442863 0.221432 0.975176i \(-0.428927\pi\)
0.221432 + 0.975176i \(0.428927\pi\)
\(12\) 413475.i 1.66166i
\(13\) 305041. 0.821564 0.410782 0.911734i \(-0.365256\pi\)
0.410782 + 0.911734i \(0.365256\pi\)
\(14\) 1.16852e6 2.17268
\(15\) −937343. −1.23436
\(16\) −952512. −0.908386
\(17\) −1.86577e6 −1.31406 −0.657028 0.753866i \(-0.728187\pi\)
−0.657028 + 0.753866i \(0.728187\pi\)
\(18\) 3.67669e6i 1.94578i
\(19\) 250385.i 0.101121i −0.998721 0.0505603i \(-0.983899\pi\)
0.998721 0.0505603i \(-0.0161007\pi\)
\(20\) 2.79570e6i 0.873656i
\(21\) −9.41705e6 −2.30578
\(22\) 3.29520e6i 0.639394i
\(23\) −7.17521e6 −1.11480 −0.557398 0.830245i \(-0.688200\pi\)
−0.557398 + 0.830245i \(0.688200\pi\)
\(24\) −1.48805e6 −0.186879
\(25\) 3.42780e6 0.351006
\(26\) 1.40931e7i 1.18615i
\(27\) 7.64463e6i 0.532768i
\(28\) 2.80871e7i 1.63199i
\(29\) 7.03624e6i 0.343045i −0.985180 0.171522i \(-0.945131\pi\)
0.985180 0.171522i \(-0.0548685\pi\)
\(30\) 4.33059e7i 1.78214i
\(31\) −2.56657e7 −0.896487 −0.448244 0.893911i \(-0.647950\pi\)
−0.448244 + 0.893911i \(0.647950\pi\)
\(32\) 4.80992e7i 1.43347i
\(33\) 2.65559e7i 0.678566i
\(34\) 8.61999e7i 1.89720i
\(35\) −6.36732e7 −1.21232
\(36\) 8.83749e7 1.46156
\(37\) 4.75251e7i 0.685353i −0.939454 0.342676i \(-0.888667\pi\)
0.939454 0.342676i \(-0.111333\pi\)
\(38\) −1.15680e7 −0.145995
\(39\) 1.13576e8i 1.25882i
\(40\) −1.00614e7 −0.0982558
\(41\) 9.96282e7 0.859930 0.429965 0.902846i \(-0.358526\pi\)
0.429965 + 0.902846i \(0.358526\pi\)
\(42\) 4.35074e8i 3.32903i
\(43\) 9.73908e7 + 1.10120e8i 0.662484 + 0.749076i
\(44\) −7.92052e7 −0.480275
\(45\) 2.00345e8i 1.08572i
\(46\) 3.31500e8i 1.60951i
\(47\) 8.53994e7 0.372362 0.186181 0.982515i \(-0.440389\pi\)
0.186181 + 0.982515i \(0.440389\pi\)
\(48\) 3.54649e8i 1.39185i
\(49\) −3.57220e8 −1.26461
\(50\) 1.58367e8i 0.506773i
\(51\) 6.94683e8i 2.01343i
\(52\) −3.38749e8 −0.890967
\(53\) −6.32854e8 −1.51330 −0.756649 0.653821i \(-0.773165\pi\)
−0.756649 + 0.653821i \(0.773165\pi\)
\(54\) −3.53187e8 −0.769195
\(55\) 1.79557e8i 0.356771i
\(56\) −1.01082e8 −0.183542
\(57\) 9.32259e7 0.154939
\(58\) −3.25079e8 −0.495278
\(59\) −1.36284e9 −1.90627 −0.953134 0.302550i \(-0.902162\pi\)
−0.953134 + 0.302550i \(0.902162\pi\)
\(60\) 1.04092e9 1.33864
\(61\) 5.18564e8i 0.613978i −0.951713 0.306989i \(-0.900678\pi\)
0.951713 0.306989i \(-0.0993216\pi\)
\(62\) 1.18577e9i 1.29432i
\(63\) 2.01278e9i 2.02811i
\(64\) 1.24685e9 1.16122
\(65\) 7.67942e8i 0.661853i
\(66\) 1.22690e9 0.979694
\(67\) 7.52892e8 0.557646 0.278823 0.960342i \(-0.410056\pi\)
0.278823 + 0.960342i \(0.410056\pi\)
\(68\) 2.07195e9 1.42506
\(69\) 2.67155e9i 1.70812i
\(70\) 2.94175e9i 1.75031i
\(71\) 2.82572e9i 1.56617i 0.621917 + 0.783083i \(0.286354\pi\)
−0.621917 + 0.783083i \(0.713646\pi\)
\(72\) 3.18051e8i 0.164374i
\(73\) 3.11851e9i 1.50430i −0.658994 0.752148i \(-0.729018\pi\)
0.658994 0.752148i \(-0.270982\pi\)
\(74\) −2.19569e9 −0.989493
\(75\) 1.27627e9i 0.537820i
\(76\) 2.78053e8i 0.109663i
\(77\) 1.80393e9i 0.666448i
\(78\) 5.24729e9 1.81745
\(79\) 1.02175e9 0.332056 0.166028 0.986121i \(-0.446906\pi\)
0.166028 + 0.986121i \(0.446906\pi\)
\(80\) 2.39795e9i 0.731797i
\(81\) −1.85284e9 −0.531390
\(82\) 4.60289e9i 1.24154i
\(83\) −5.19494e9 −1.31883 −0.659416 0.751778i \(-0.729197\pi\)
−0.659416 + 0.751778i \(0.729197\pi\)
\(84\) 1.04577e10 2.50057
\(85\) 4.69709e9i 1.05861i
\(86\) 5.08764e9 4.49952e9i 1.08149 0.956476i
\(87\) 2.61980e9 0.525621
\(88\) 2.85050e8i 0.0540142i
\(89\) 4.43923e9i 0.794983i 0.917606 + 0.397491i \(0.130119\pi\)
−0.917606 + 0.397491i \(0.869881\pi\)
\(90\) −9.25609e9 −1.56753
\(91\) 7.71516e9i 1.23634i
\(92\) 7.96810e9 1.20897
\(93\) 9.55610e9i 1.37362i
\(94\) 3.94551e9i 0.537606i
\(95\) 6.30345e8 0.0814630
\(96\) −1.79088e10 −2.19639
\(97\) 6.65798e9 0.775325 0.387662 0.921801i \(-0.373283\pi\)
0.387662 + 0.921801i \(0.373283\pi\)
\(98\) 1.65038e10i 1.82580i
\(99\) −5.67599e9 −0.596851
\(100\) −3.80658e9 −0.380658
\(101\) −7.20535e9 −0.685564 −0.342782 0.939415i \(-0.611369\pi\)
−0.342782 + 0.939415i \(0.611369\pi\)
\(102\) −3.20948e10 −2.90693
\(103\) −1.00832e10 −0.869785 −0.434892 0.900482i \(-0.643214\pi\)
−0.434892 + 0.900482i \(0.643214\pi\)
\(104\) 1.21912e9i 0.100203i
\(105\) 2.37075e10i 1.85754i
\(106\) 2.92383e10i 2.18486i
\(107\) 1.52468e10 1.08708 0.543540 0.839384i \(-0.317084\pi\)
0.543540 + 0.839384i \(0.317084\pi\)
\(108\) 8.48940e9i 0.577774i
\(109\) 2.99019e10 1.94342 0.971710 0.236177i \(-0.0758947\pi\)
0.971710 + 0.236177i \(0.0758947\pi\)
\(110\) 8.29568e9 0.515096
\(111\) 1.76950e10 1.05011
\(112\) 2.40911e10i 1.36700i
\(113\) 7.48999e9i 0.406527i 0.979124 + 0.203263i \(0.0651548\pi\)
−0.979124 + 0.203263i \(0.934845\pi\)
\(114\) 4.30710e9i 0.223697i
\(115\) 1.80636e10i 0.898081i
\(116\) 7.81377e9i 0.372024i
\(117\) −2.42754e10 −1.10723
\(118\) 6.29640e10i 2.75222i
\(119\) 4.71895e10i 1.97747i
\(120\) 3.74616e9i 0.150550i
\(121\) −2.08504e10 −0.803872
\(122\) −2.39580e10 −0.886445
\(123\) 3.70946e10i 1.31760i
\(124\) 2.85018e10 0.972220
\(125\) 3.32145e10i 1.08837i
\(126\) −9.29916e10 −2.92814
\(127\) 6.20334e10 1.87762 0.938809 0.344438i \(-0.111931\pi\)
0.938809 + 0.344438i \(0.111931\pi\)
\(128\) 8.35152e9i 0.243061i
\(129\) −4.10012e10 + 3.62615e10i −1.14775 + 1.01507i
\(130\) 3.54794e10 0.955565
\(131\) 2.92734e10i 0.758782i 0.925236 + 0.379391i \(0.123867\pi\)
−0.925236 + 0.379391i \(0.876133\pi\)
\(132\) 2.94905e10i 0.735889i
\(133\) 6.33278e9 0.152173
\(134\) 3.47841e10i 0.805114i
\(135\) 1.92454e10 0.429198
\(136\) 7.45669e9i 0.160270i
\(137\) 3.44989e10i 0.714830i 0.933946 + 0.357415i \(0.116342\pi\)
−0.933946 + 0.357415i \(0.883658\pi\)
\(138\) −1.23427e11 −2.46613
\(139\) −3.91308e9 −0.0754127 −0.0377063 0.999289i \(-0.512005\pi\)
−0.0377063 + 0.999289i \(0.512005\pi\)
\(140\) 7.07094e10 1.31473
\(141\) 3.17968e10i 0.570542i
\(142\) 1.30550e11 2.26119
\(143\) 2.17566e10 0.363840
\(144\) 7.58017e10 1.22424
\(145\) 1.77138e10 0.276357
\(146\) −1.44078e11 −2.17186
\(147\) 1.33004e11i 1.93766i
\(148\) 5.27768e10i 0.743249i
\(149\) 1.10802e11i 1.50875i −0.656446 0.754373i \(-0.727941\pi\)
0.656446 0.754373i \(-0.272059\pi\)
\(150\) 5.89647e10 0.776489
\(151\) 7.24649e10i 0.923088i 0.887117 + 0.461544i \(0.152704\pi\)
−0.887117 + 0.461544i \(0.847296\pi\)
\(152\) 1.00068e9 0.0123333
\(153\) 1.48480e11 1.77096
\(154\) 8.33429e10 0.962199
\(155\) 6.46134e10i 0.722211i
\(156\) 1.26127e11i 1.36516i
\(157\) 1.17646e11i 1.23333i 0.787227 + 0.616664i \(0.211516\pi\)
−0.787227 + 0.616664i \(0.788484\pi\)
\(158\) 4.72058e10i 0.479413i
\(159\) 2.35631e11i 2.31871i
\(160\) −1.21090e11 −1.15480
\(161\) 1.81477e11i 1.67761i
\(162\) 8.56026e10i 0.767205i
\(163\) 1.40912e11i 1.22465i 0.790608 + 0.612323i \(0.209765\pi\)
−0.790608 + 0.612323i \(0.790235\pi\)
\(164\) −1.10638e11 −0.932574
\(165\) −6.68547e10 −0.546654
\(166\) 2.40010e11i 1.90409i
\(167\) 1.36599e10 0.105164 0.0525818 0.998617i \(-0.483255\pi\)
0.0525818 + 0.998617i \(0.483255\pi\)
\(168\) 3.76360e10i 0.281227i
\(169\) −4.48086e10 −0.325033
\(170\) −2.17009e11 −1.52838
\(171\) 1.99258e10i 0.136281i
\(172\) −1.08153e11 1.22289e11i −0.718449 0.812356i
\(173\) 1.77902e11 1.14802 0.574010 0.818848i \(-0.305387\pi\)
0.574010 + 0.818848i \(0.305387\pi\)
\(174\) 1.21037e11i 0.758877i
\(175\) 8.66965e10i 0.528216i
\(176\) −6.79366e10 −0.402291
\(177\) 5.07425e11i 2.92083i
\(178\) 2.05096e11 1.14777
\(179\) 1.67525e11i 0.911621i 0.890077 + 0.455811i \(0.150651\pi\)
−0.890077 + 0.455811i \(0.849349\pi\)
\(180\) 2.22484e11i 1.17743i
\(181\) −2.07998e11 −1.07070 −0.535348 0.844632i \(-0.679819\pi\)
−0.535348 + 0.844632i \(0.679819\pi\)
\(182\) 3.56446e11 1.78499
\(183\) 1.93077e11 0.940752
\(184\) 2.86763e10i 0.135967i
\(185\) 1.19645e11 0.552121
\(186\) −4.41499e11 −1.98319
\(187\) −1.33073e11 −0.581947
\(188\) −9.48364e10 −0.403818
\(189\) 1.93350e11 0.801741
\(190\) 2.91224e10i 0.117614i
\(191\) 5.41486e10i 0.213020i −0.994312 0.106510i \(-0.966032\pi\)
0.994312 0.106510i \(-0.0339676\pi\)
\(192\) 4.64238e11i 1.77924i
\(193\) 4.49258e11 1.67768 0.838841 0.544377i \(-0.183234\pi\)
0.838841 + 0.544377i \(0.183234\pi\)
\(194\) 3.07603e11i 1.11939i
\(195\) −2.85928e11 −1.01411
\(196\) 3.96695e11 1.37144
\(197\) −1.20058e10 −0.0404631 −0.0202316 0.999795i \(-0.506440\pi\)
−0.0202316 + 0.999795i \(0.506440\pi\)
\(198\) 2.62235e11i 0.861717i
\(199\) 1.99312e11i 0.638658i 0.947644 + 0.319329i \(0.103457\pi\)
−0.947644 + 0.319329i \(0.896543\pi\)
\(200\) 1.36994e10i 0.0428108i
\(201\) 2.80325e11i 0.854439i
\(202\) 3.32892e11i 0.989798i
\(203\) 1.77962e11 0.516234
\(204\) 7.71449e11i 2.18352i
\(205\) 2.50814e11i 0.692761i
\(206\) 4.65850e11i 1.25577i
\(207\) 5.71009e11 1.50242
\(208\) −2.90555e11 −0.746297
\(209\) 1.78583e10i 0.0447826i
\(210\) −1.09530e12 −2.68187
\(211\) 3.66095e11i 0.875349i 0.899134 + 0.437674i \(0.144198\pi\)
−0.899134 + 0.437674i \(0.855802\pi\)
\(212\) 7.02788e11 1.64114
\(213\) −1.05210e12 −2.39972
\(214\) 7.04415e11i 1.56949i
\(215\) −2.77229e11 + 2.45182e11i −0.603457 + 0.533698i
\(216\) 3.05524e10 0.0649794
\(217\) 6.49141e11i 1.34909i
\(218\) 1.38149e12i 2.80585i
\(219\) 1.16112e12 2.30492
\(220\) 1.99399e11i 0.386910i
\(221\) −5.69136e11 −1.07958
\(222\) 8.17522e11i 1.51612i
\(223\) 1.10099e11i 0.199645i 0.995005 + 0.0998227i \(0.0318276\pi\)
−0.995005 + 0.0998227i \(0.968172\pi\)
\(224\) −1.21654e12 −2.15717
\(225\) −2.72787e11 −0.473054
\(226\) 3.46043e11 0.586932
\(227\) 8.36307e10i 0.138751i 0.997591 + 0.0693756i \(0.0221007\pi\)
−0.997591 + 0.0693756i \(0.977899\pi\)
\(228\) −1.03528e11 −0.168028
\(229\) −6.58580e11 −1.04576 −0.522879 0.852407i \(-0.675142\pi\)
−0.522879 + 0.852407i \(0.675142\pi\)
\(230\) −8.34552e11 −1.29662
\(231\) −6.71658e11 −1.02115
\(232\) 2.81209e10 0.0418397
\(233\) 5.69687e11i 0.829577i −0.909918 0.414789i \(-0.863856\pi\)
0.909918 0.414789i \(-0.136144\pi\)
\(234\) 1.12154e12i 1.59859i
\(235\) 2.14993e11i 0.299976i
\(236\) 1.51344e12 2.06730
\(237\) 3.80430e11i 0.508784i
\(238\) −2.18019e12 −2.85502
\(239\) 6.54291e11 0.839038 0.419519 0.907747i \(-0.362199\pi\)
0.419519 + 0.907747i \(0.362199\pi\)
\(240\) 8.92831e11 1.12128
\(241\) 1.47198e11i 0.181058i −0.995894 0.0905288i \(-0.971144\pi\)
0.995894 0.0905288i \(-0.0288557\pi\)
\(242\) 9.63302e11i 1.16061i
\(243\) 1.14128e12i 1.34698i
\(244\) 5.75868e11i 0.665846i
\(245\) 8.99304e11i 1.01877i
\(246\) 1.71380e12 1.90232
\(247\) 7.63776e10i 0.0830771i
\(248\) 1.02575e11i 0.109341i
\(249\) 1.93423e12i 2.02075i
\(250\) 1.53453e12 1.57136
\(251\) −5.57229e11 −0.559326 −0.279663 0.960098i \(-0.590223\pi\)
−0.279663 + 0.960098i \(0.590223\pi\)
\(252\) 2.23520e12i 2.19944i
\(253\) −5.11762e11 −0.493702
\(254\) 2.86599e12i 2.71085i
\(255\) 1.74887e12 1.62202
\(256\) 8.90923e11 0.810290
\(257\) 1.63650e11i 0.145966i 0.997333 + 0.0729828i \(0.0232518\pi\)
−0.997333 + 0.0729828i \(0.976748\pi\)
\(258\) 1.67531e12 + 1.89428e12i 1.46554 + 1.65709i
\(259\) 1.20201e12 1.03136
\(260\) 8.52803e11i 0.717764i
\(261\) 5.59950e11i 0.462324i
\(262\) 1.35245e12 1.09551
\(263\) 2.20675e12i 1.75377i 0.480696 + 0.876887i \(0.340384\pi\)
−0.480696 + 0.876887i \(0.659616\pi\)
\(264\) −1.06133e11 −0.0827618
\(265\) 1.59321e12i 1.21912i
\(266\) 2.92579e11i 0.219703i
\(267\) −1.65286e12 −1.21809
\(268\) −8.36090e11 −0.604755
\(269\) −2.28588e12 −1.62290 −0.811451 0.584421i \(-0.801322\pi\)
−0.811451 + 0.584421i \(0.801322\pi\)
\(270\) 8.89151e11i 0.619665i
\(271\) 2.10457e12 1.43985 0.719924 0.694053i \(-0.244177\pi\)
0.719924 + 0.694053i \(0.244177\pi\)
\(272\) 1.77717e12 1.19367
\(273\) −2.87259e12 −1.89435
\(274\) 1.59387e12 1.03205
\(275\) 2.44483e11 0.155448
\(276\) 2.96677e12i 1.85241i
\(277\) 1.69302e12i 1.03816i 0.854726 + 0.519080i \(0.173725\pi\)
−0.854726 + 0.519080i \(0.826275\pi\)
\(278\) 1.80787e11i 0.108879i
\(279\) 2.04250e12 1.20820
\(280\) 2.54475e11i 0.147861i
\(281\) −1.67292e12 −0.954867 −0.477433 0.878668i \(-0.658433\pi\)
−0.477433 + 0.878668i \(0.658433\pi\)
\(282\) 1.46903e12 0.823733
\(283\) −2.59661e12 −1.43046 −0.715229 0.698890i \(-0.753678\pi\)
−0.715229 + 0.698890i \(0.753678\pi\)
\(284\) 3.13798e12i 1.69847i
\(285\) 2.34697e11i 0.124819i
\(286\) 1.00517e12i 0.525303i
\(287\) 2.51982e12i 1.29408i
\(288\) 3.82778e12i 1.93190i
\(289\) 1.46511e12 0.726742
\(290\) 8.18388e11i 0.398997i
\(291\) 2.47897e12i 1.18797i
\(292\) 3.46313e12i 1.63138i
\(293\) 2.22776e12 1.03165 0.515823 0.856695i \(-0.327486\pi\)
0.515823 + 0.856695i \(0.327486\pi\)
\(294\) −6.14488e12 −2.79754
\(295\) 3.43095e12i 1.53569i
\(296\) 1.89937e11 0.0835896
\(297\) 5.45243e11i 0.235943i
\(298\) −5.11913e12 −2.17829
\(299\) −2.18873e12 −0.915876
\(300\) 1.41731e12i 0.583254i
\(301\) −2.78519e12 + 2.46323e12i −1.12726 + 0.996947i
\(302\) 3.34793e12 1.33273
\(303\) 2.68277e12i 1.05044i
\(304\) 2.38495e11i 0.0918566i
\(305\) 1.30549e12 0.494622
\(306\) 6.85986e12i 2.55687i
\(307\) 1.96871e12 0.721922 0.360961 0.932581i \(-0.382449\pi\)
0.360961 + 0.932581i \(0.382449\pi\)
\(308\) 2.00327e12i 0.722748i
\(309\) 3.75428e12i 1.33270i
\(310\) −2.98519e12 −1.04271
\(311\) −4.26791e12 −1.46694 −0.733472 0.679720i \(-0.762101\pi\)
−0.733472 + 0.679720i \(0.762101\pi\)
\(312\) −4.53915e11 −0.153533
\(313\) 4.54518e12i 1.51297i 0.654012 + 0.756484i \(0.273085\pi\)
−0.654012 + 0.756484i \(0.726915\pi\)
\(314\) 5.43532e12 1.78064
\(315\) 5.06717e12 1.63385
\(316\) −1.13466e12 −0.360107
\(317\) 1.59917e12 0.499571 0.249786 0.968301i \(-0.419640\pi\)
0.249786 + 0.968301i \(0.419640\pi\)
\(318\) −1.08863e13 −3.34769
\(319\) 5.01850e11i 0.151922i
\(320\) 3.13894e12i 0.935477i
\(321\) 5.67686e12i 1.66565i
\(322\) −8.38436e12 −2.42209
\(323\) 4.67161e11i 0.132878i
\(324\) 2.05759e12 0.576280
\(325\) 1.04562e12 0.288374
\(326\) 6.51024e12 1.76811
\(327\) 1.11334e13i 2.97775i
\(328\) 3.98172e11i 0.104882i
\(329\) 2.15994e12i 0.560353i
\(330\) 3.08873e12i 0.789243i
\(331\) 2.83663e12i 0.713942i 0.934115 + 0.356971i \(0.116191\pi\)
−0.934115 + 0.356971i \(0.883809\pi\)
\(332\) 5.76900e12 1.43024
\(333\) 3.78209e12i 0.923656i
\(334\) 6.31098e11i 0.151832i
\(335\) 1.89541e12i 0.449241i
\(336\) 8.96986e12 2.09454
\(337\) −6.48421e12 −1.49179 −0.745895 0.666064i \(-0.767978\pi\)
−0.745895 + 0.666064i \(0.767978\pi\)
\(338\) 2.07019e12i 0.469274i
\(339\) −2.78875e12 −0.622890
\(340\) 5.21614e12i 1.14803i
\(341\) −1.83057e12 −0.397021
\(342\) 9.20588e11 0.196759
\(343\) 1.89047e12i 0.398197i
\(344\) −4.40105e11 + 3.89230e11i −0.0913616 + 0.0808004i
\(345\) 6.72563e12 1.37606
\(346\) 8.21918e12i 1.65748i
\(347\) 7.21366e12i 1.43387i −0.697142 0.716933i \(-0.745545\pi\)
0.697142 0.716933i \(-0.254455\pi\)
\(348\) −2.90931e12 −0.570024
\(349\) 2.31109e12i 0.446364i −0.974777 0.223182i \(-0.928356\pi\)
0.974777 0.223182i \(-0.0716445\pi\)
\(350\) 4.00544e12 0.762623
\(351\) 2.33193e12i 0.437703i
\(352\) 3.43061e12i 0.634831i
\(353\) 2.26403e12 0.413056 0.206528 0.978441i \(-0.433784\pi\)
0.206528 + 0.978441i \(0.433784\pi\)
\(354\) −2.34434e13 −4.21701
\(355\) −7.11377e12 −1.26171
\(356\) 4.92979e12i 0.862140i
\(357\) 1.75701e13 3.02993
\(358\) 7.73977e12 1.31617
\(359\) 6.50793e12 1.09137 0.545683 0.837992i \(-0.316270\pi\)
0.545683 + 0.837992i \(0.316270\pi\)
\(360\) 8.00695e11 0.132420
\(361\) 6.06837e12 0.989775
\(362\) 9.60965e12i 1.54584i
\(363\) 7.76322e12i 1.23171i
\(364\) 8.56772e12i 1.34078i
\(365\) 7.85088e12 1.21186
\(366\) 8.92030e12i 1.35823i
\(367\) −6.62772e12 −0.995483 −0.497741 0.867326i \(-0.665837\pi\)
−0.497741 + 0.867326i \(0.665837\pi\)
\(368\) 6.83447e12 1.01267
\(369\) −7.92850e12 −1.15893
\(370\) 5.52766e12i 0.797137i
\(371\) 1.60063e13i 2.27730i
\(372\) 1.06121e13i 1.48966i
\(373\) 1.15355e12i 0.159769i −0.996804 0.0798844i \(-0.974545\pi\)
0.996804 0.0798844i \(-0.0254551\pi\)
\(374\) 6.14809e12i 0.840199i
\(375\) −1.23668e13 −1.66763
\(376\) 3.41305e11i 0.0454154i
\(377\) 2.14634e12i 0.281833i
\(378\) 8.93289e12i 1.15753i
\(379\) 1.20748e12 0.154413 0.0772067 0.997015i \(-0.475400\pi\)
0.0772067 + 0.997015i \(0.475400\pi\)
\(380\) −7.00001e11 −0.0883447
\(381\) 2.30969e13i 2.87693i
\(382\) −2.50170e12 −0.307552
\(383\) 3.74979e9i 0.000455002i 1.00000 0.000227501i \(7.24158e-5\pi\)
−1.00000 0.000227501i \(0.999928\pi\)
\(384\) 3.10952e12 0.372424
\(385\) −4.54140e12 −0.536891
\(386\) 2.07560e13i 2.42219i
\(387\) −7.75044e12 8.76348e12i −0.892836 1.00954i
\(388\) −7.39371e12 −0.840822
\(389\) 9.33224e12i 1.04770i 0.851810 + 0.523851i \(0.175505\pi\)
−0.851810 + 0.523851i \(0.824495\pi\)
\(390\) 1.32101e13i 1.46414i
\(391\) 1.33873e13 1.46490
\(392\) 1.42766e12i 0.154239i
\(393\) −1.08994e13 −1.16262
\(394\) 5.54676e11i 0.0584195i
\(395\) 2.57227e12i 0.267505i
\(396\) 6.30322e12 0.647271
\(397\) −7.85222e12 −0.796233 −0.398116 0.917335i \(-0.630336\pi\)
−0.398116 + 0.917335i \(0.630336\pi\)
\(398\) 9.20836e12 0.922076
\(399\) 2.35789e12i 0.233162i
\(400\) −3.26502e12 −0.318849
\(401\) 1.05265e13 1.01522 0.507612 0.861586i \(-0.330528\pi\)
0.507612 + 0.861586i \(0.330528\pi\)
\(402\) 1.29512e13 1.23361
\(403\) −7.82908e12 −0.736521
\(404\) 8.00157e12 0.743479
\(405\) 4.66454e12i 0.428088i
\(406\) 8.22197e12i 0.745325i
\(407\) 3.38966e12i 0.303518i
\(408\) 2.77635e12 0.245569
\(409\) 1.33735e13i 1.16850i 0.811573 + 0.584250i \(0.198611\pi\)
−0.811573 + 0.584250i \(0.801389\pi\)
\(410\) 1.15878e13 1.00019
\(411\) −1.28450e13 −1.09528
\(412\) 1.11974e13 0.943262
\(413\) 3.44691e13i 2.86867i
\(414\) 2.63810e13i 2.16915i
\(415\) 1.30783e13i 1.06245i
\(416\) 1.46722e13i 1.17769i
\(417\) 1.45696e12i 0.115549i
\(418\) −8.25068e11 −0.0646559
\(419\) 1.85553e13i 1.43680i −0.695629 0.718401i \(-0.744874\pi\)
0.695629 0.718401i \(-0.255126\pi\)
\(420\) 2.63273e13i 2.01446i
\(421\) 2.02826e13i 1.53360i 0.641884 + 0.766802i \(0.278153\pi\)
−0.641884 + 0.766802i \(0.721847\pi\)
\(422\) 1.69138e13 1.26380
\(423\) −6.79616e12 −0.501836
\(424\) 2.52925e12i 0.184571i
\(425\) −6.39548e12 −0.461242
\(426\) 4.86078e13i 3.46464i
\(427\) 1.31156e13 0.923952
\(428\) −1.69317e13 −1.17891
\(429\) 8.10064e12i 0.557485i
\(430\) 1.13276e13 + 1.28082e13i 0.770539 + 0.871254i
\(431\) −4.60294e12 −0.309492 −0.154746 0.987954i \(-0.549456\pi\)
−0.154746 + 0.987954i \(0.549456\pi\)
\(432\) 7.28161e12i 0.483959i
\(433\) 1.00692e13i 0.661540i −0.943711 0.330770i \(-0.892692\pi\)
0.943711 0.330770i \(-0.107308\pi\)
\(434\) −2.99908e13 −1.94778
\(435\) 6.59537e12i 0.423441i
\(436\) −3.32062e13 −2.10759
\(437\) 1.79656e12i 0.112729i
\(438\) 5.36444e13i 3.32778i
\(439\) 2.63240e12 0.161447 0.0807234 0.996737i \(-0.474277\pi\)
0.0807234 + 0.996737i \(0.474277\pi\)
\(440\) −7.17615e11 −0.0435139
\(441\) 2.84279e13 1.70432
\(442\) 2.62945e13i 1.55867i
\(443\) −8.76270e12 −0.513593 −0.256797 0.966465i \(-0.582667\pi\)
−0.256797 + 0.966465i \(0.582667\pi\)
\(444\) −1.96504e13 −1.13882
\(445\) −1.11758e13 −0.640439
\(446\) 5.08666e12 0.288242
\(447\) 4.12550e13 2.31174
\(448\) 3.15355e13i 1.74747i
\(449\) 2.25448e13i 1.23542i −0.786406 0.617710i \(-0.788060\pi\)
0.786406 0.617710i \(-0.211940\pi\)
\(450\) 1.26029e13i 0.682982i
\(451\) 7.10584e12 0.380831
\(452\) 8.31767e12i 0.440869i
\(453\) −2.69809e13 −1.41438
\(454\) 3.86380e12 0.200325
\(455\) −1.94229e13 −0.995997
\(456\) 3.72584e11i 0.0188973i
\(457\) 6.81262e12i 0.341769i −0.985291 0.170885i \(-0.945337\pi\)
0.985291 0.170885i \(-0.0546626\pi\)
\(458\) 3.04268e13i 1.50984i
\(459\) 1.42631e13i 0.700086i
\(460\) 2.00597e13i 0.973949i
\(461\) −2.33485e13 −1.12138 −0.560692 0.828025i \(-0.689465\pi\)
−0.560692 + 0.828025i \(0.689465\pi\)
\(462\) 3.10311e13i 1.47430i
\(463\) 3.70670e13i 1.74214i −0.491160 0.871070i \(-0.663427\pi\)
0.491160 0.871070i \(-0.336573\pi\)
\(464\) 6.70210e12i 0.311617i
\(465\) 2.40575e13 1.10659
\(466\) −2.63199e13 −1.19772
\(467\) 2.89598e13i 1.30380i −0.758305 0.651900i \(-0.773972\pi\)
0.758305 0.651900i \(-0.226028\pi\)
\(468\) 2.69580e13 1.20076
\(469\) 1.90423e13i 0.839180i
\(470\) 9.93284e12 0.433096
\(471\) −4.38031e13 −1.88973
\(472\) 5.44668e12i 0.232499i
\(473\) 6.94626e12 + 7.85419e12i 0.293390 + 0.331738i
\(474\) 1.75761e13 0.734568
\(475\) 8.58268e11i 0.0354940i
\(476\) 5.24041e13i 2.14452i
\(477\) 5.03631e13 2.03949
\(478\) 3.02287e13i 1.21138i
\(479\) −5.00231e12 −0.198378 −0.0991888 0.995069i \(-0.531625\pi\)
−0.0991888 + 0.995069i \(0.531625\pi\)
\(480\) 4.50855e13i 1.76942i
\(481\) 1.44971e13i 0.563061i
\(482\) −6.80065e12 −0.261406
\(483\) 6.75693e13 2.57048
\(484\) 2.31544e13 0.871781
\(485\) 1.67615e13i 0.624603i
\(486\) −5.27278e13 −1.94473
\(487\) 4.68407e13 1.70993 0.854965 0.518685i \(-0.173578\pi\)
0.854965 + 0.518685i \(0.173578\pi\)
\(488\) 2.07248e12 0.0748844
\(489\) −5.24659e13 −1.87643
\(490\) −4.15485e13 −1.47087
\(491\) 4.76896e13i 1.67115i 0.549373 + 0.835577i \(0.314867\pi\)
−0.549373 + 0.835577i \(0.685133\pi\)
\(492\) 4.11937e13i 1.42891i
\(493\) 1.31280e13i 0.450780i
\(494\) −3.52870e12 −0.119944
\(495\) 1.42893e13i 0.480824i
\(496\) 2.44469e13 0.814357
\(497\) −7.14687e13 −2.35686
\(498\) −8.93629e13 −2.91750
\(499\) 5.25062e12i 0.169710i 0.996393 + 0.0848551i \(0.0270427\pi\)
−0.996393 + 0.0848551i \(0.972957\pi\)
\(500\) 3.68849e13i 1.18032i
\(501\) 5.08600e12i 0.161134i
\(502\) 2.57444e13i 0.807539i
\(503\) 1.87015e13i 0.580814i −0.956903 0.290407i \(-0.906209\pi\)
0.956903 0.290407i \(-0.0937907\pi\)
\(504\) 8.04421e12 0.247361
\(505\) 1.81395e13i 0.552291i
\(506\) 2.36437e13i 0.712793i
\(507\) 1.66836e13i 0.498023i
\(508\) −6.88884e13 −2.03623
\(509\) 4.81590e13 1.40958 0.704788 0.709418i \(-0.251042\pi\)
0.704788 + 0.709418i \(0.251042\pi\)
\(510\) 8.07989e13i 2.34183i
\(511\) 7.88741e13 2.26376
\(512\) 4.97132e13i 1.41294i
\(513\) −1.91410e12 −0.0538738
\(514\) 7.56075e12 0.210741
\(515\) 2.53845e13i 0.700700i
\(516\) 4.55320e13 4.02686e13i 1.24471 1.10082i
\(517\) 6.09099e12 0.164906
\(518\) 5.55339e13i 1.48905i
\(519\) 6.62382e13i 1.75902i
\(520\) −3.06914e12 −0.0807234
\(521\) 4.77518e13i 1.24395i 0.783039 + 0.621973i \(0.213669\pi\)
−0.783039 + 0.621973i \(0.786331\pi\)
\(522\) 2.58701e13 0.667491
\(523\) 3.62939e12i 0.0927524i −0.998924 0.0463762i \(-0.985233\pi\)
0.998924 0.0463762i \(-0.0147673\pi\)
\(524\) 3.25083e13i 0.822882i
\(525\) −3.22797e13 −0.809345
\(526\) 1.01953e14 2.53205
\(527\) 4.78862e13 1.17803
\(528\) 2.52949e13i 0.616400i
\(529\) 1.00571e13 0.242770
\(530\) −7.36076e13 −1.76012
\(531\) 1.08456e14 2.56909
\(532\) −7.03259e12 −0.165028
\(533\) 3.03907e13 0.706487
\(534\) 7.63633e13i 1.75865i
\(535\) 3.83840e13i 0.875753i
\(536\) 3.00899e12i 0.0680138i
\(537\) −6.23746e13 −1.39681
\(538\) 1.05609e14i 2.34310i
\(539\) −2.54782e13 −0.560048
\(540\) −2.13721e13 −0.465456
\(541\) −3.40244e13 −0.734183 −0.367092 0.930185i \(-0.619646\pi\)
−0.367092 + 0.930185i \(0.619646\pi\)
\(542\) 9.72326e13i 2.07881i
\(543\) 7.74439e13i 1.64055i
\(544\) 8.97421e13i 1.88366i
\(545\) 7.52782e13i 1.56562i
\(546\) 1.32715e14i 2.73501i
\(547\) −7.53319e13 −1.53831 −0.769153 0.639065i \(-0.779321\pi\)
−0.769153 + 0.639065i \(0.779321\pi\)
\(548\) 3.83112e13i 0.775217i
\(549\) 4.12678e13i 0.827464i
\(550\) 1.12953e13i 0.224431i
\(551\) −1.76177e12 −0.0346889
\(552\) 1.06770e13 0.208332
\(553\) 2.58424e13i 0.499698i
\(554\) 7.82189e13 1.49887
\(555\) 4.45473e13i 0.845973i
\(556\) 4.34549e12 0.0817833
\(557\) 5.40321e13 1.00780 0.503901 0.863761i \(-0.331897\pi\)
0.503901 + 0.863761i \(0.331897\pi\)
\(558\) 9.43647e13i 1.74437i
\(559\) 2.97082e13 + 3.35912e13i 0.544273 + 0.615413i
\(560\) 6.06495e13 1.10125
\(561\) 4.95473e13i 0.891673i
\(562\) 7.72899e13i 1.37861i
\(563\) −1.21882e12 −0.0215476 −0.0107738 0.999942i \(-0.503429\pi\)
−0.0107738 + 0.999942i \(0.503429\pi\)
\(564\) 3.53105e13i 0.618740i
\(565\) −1.88561e13 −0.327498
\(566\) 1.19965e14i 2.06526i
\(567\) 4.68624e13i 0.799668i
\(568\) −1.12932e13 −0.191019
\(569\) −1.25274e12 −0.0210039 −0.0105020 0.999945i \(-0.503343\pi\)
−0.0105020 + 0.999945i \(0.503343\pi\)
\(570\) 1.08431e13 0.180211
\(571\) 7.69973e13i 1.26851i −0.773122 0.634257i \(-0.781306\pi\)
0.773122 0.634257i \(-0.218694\pi\)
\(572\) −2.41608e13 −0.394577
\(573\) 2.01612e13 0.326394
\(574\) 1.16417e14 1.86835
\(575\) −2.45951e13 −0.391300
\(576\) −9.92250e13 −1.56498
\(577\) 6.44502e13i 1.00773i 0.863782 + 0.503866i \(0.168090\pi\)
−0.863782 + 0.503866i \(0.831910\pi\)
\(578\) 6.76890e13i 1.04925i
\(579\) 1.67272e14i 2.57058i
\(580\) −1.96712e13 −0.299703
\(581\) 1.31391e14i 1.98466i
\(582\) 1.14530e14 1.71516
\(583\) −4.51374e13 −0.670184
\(584\) 1.24634e13 0.183473
\(585\) 6.11135e13i 0.891985i
\(586\) 1.02924e14i 1.48946i
\(587\) 5.33136e13i 0.764976i −0.923960 0.382488i \(-0.875067\pi\)
0.923960 0.382488i \(-0.124933\pi\)
\(588\) 1.47702e14i 2.10135i
\(589\) 6.42629e12i 0.0906534i
\(590\) −1.58512e14 −2.21719
\(591\) 4.47012e12i 0.0619986i
\(592\) 4.52682e13i 0.622565i
\(593\) 1.02559e14i 1.39862i −0.714817 0.699312i \(-0.753490\pi\)
0.714817 0.699312i \(-0.246510\pi\)
\(594\) −2.51906e13 −0.340648
\(595\) 1.18800e14 1.59305
\(596\) 1.23046e14i 1.63620i
\(597\) −7.42099e13 −0.978567
\(598\) 1.01121e14i 1.32232i
\(599\) −1.12585e14 −1.45998 −0.729992 0.683456i \(-0.760476\pi\)
−0.729992 + 0.683456i \(0.760476\pi\)
\(600\) −5.10072e12 −0.0655957
\(601\) 5.45771e12i 0.0696046i 0.999394 + 0.0348023i \(0.0110802\pi\)
−0.999394 + 0.0348023i \(0.988920\pi\)
\(602\) 1.13803e14 + 1.28678e14i 1.43936 + 1.62750i
\(603\) −5.99158e13 −0.751545
\(604\) 8.04726e13i 1.00107i
\(605\) 5.24909e13i 0.647601i
\(606\) −1.23946e14 −1.51659
\(607\) 1.42238e14i 1.72612i −0.505101 0.863060i \(-0.668545\pi\)
0.505101 0.863060i \(-0.331455\pi\)
\(608\) 1.20433e13 0.144953
\(609\) 6.62606e13i 0.790987i
\(610\) 6.03144e13i 0.714121i
\(611\) 2.60503e13 0.305919
\(612\) −1.64887e14 −1.92057
\(613\) 4.10317e13 0.474042 0.237021 0.971505i \(-0.423829\pi\)
0.237021 + 0.971505i \(0.423829\pi\)
\(614\) 9.09559e13i 1.04229i
\(615\) −9.33858e13 −1.06146
\(616\) −7.20955e12 −0.0812839
\(617\) −1.66102e14 −1.85759 −0.928793 0.370598i \(-0.879153\pi\)
−0.928793 + 0.370598i \(0.879153\pi\)
\(618\) −1.73450e14 −1.92412
\(619\) 1.21414e13 0.133603 0.0668015 0.997766i \(-0.478721\pi\)
0.0668015 + 0.997766i \(0.478721\pi\)
\(620\) 7.17535e13i 0.783222i
\(621\) 5.48518e13i 0.593927i
\(622\) 1.97181e14i 2.11793i
\(623\) −1.12278e14 −1.19634
\(624\) 1.08182e14i 1.14349i
\(625\) −5.01431e13 −0.525788
\(626\) 2.09991e14 2.18438
\(627\) 6.64920e12 0.0686170
\(628\) 1.30646e14i 1.33752i
\(629\) 8.86709e13i 0.900591i
\(630\) 2.34107e14i 2.35891i
\(631\) 5.98910e13i 0.598708i 0.954142 + 0.299354i \(0.0967711\pi\)
−0.954142 + 0.299354i \(0.903229\pi\)
\(632\) 4.08352e12i 0.0404995i
\(633\) −1.36308e14 −1.34123
\(634\) 7.38826e13i 0.721267i
\(635\) 1.56169e14i 1.51261i
\(636\) 2.61669e14i 2.51459i
\(637\) −1.08967e14 −1.03896
\(638\) −2.31858e13 −0.219340
\(639\) 2.24873e14i 2.11074i
\(640\) 2.10250e13 0.195810
\(641\) 1.27984e14i 1.18267i 0.806425 + 0.591336i \(0.201399\pi\)
−0.806425 + 0.591336i \(0.798601\pi\)
\(642\) 2.62275e14 2.40482
\(643\) 1.20161e14 1.09323 0.546613 0.837386i \(-0.315917\pi\)
0.546613 + 0.837386i \(0.315917\pi\)
\(644\) 2.01531e14i 1.81933i
\(645\) −9.12886e13 1.03221e14i −0.817745 0.924630i
\(646\) 2.15832e13 0.191846
\(647\) 2.11239e13i 0.186317i −0.995651 0.0931586i \(-0.970304\pi\)
0.995651 0.0931586i \(-0.0296964\pi\)
\(648\) 7.40502e12i 0.0648114i
\(649\) −9.72024e13 −0.844216
\(650\) 4.83083e13i 0.416346i
\(651\) 2.41695e14 2.06711
\(652\) 1.56484e14i 1.32810i
\(653\) 1.49697e14i 1.26080i 0.776270 + 0.630401i \(0.217109\pi\)
−0.776270 + 0.630401i \(0.782891\pi\)
\(654\) 5.14371e14 4.29920
\(655\) −7.36960e13 −0.611276
\(656\) −9.48971e13 −0.781149
\(657\) 2.48174e14i 2.02735i
\(658\) 9.97907e13 0.809022
\(659\) 1.56549e14 1.25957 0.629786 0.776769i \(-0.283143\pi\)
0.629786 + 0.776769i \(0.283143\pi\)
\(660\) 7.42424e13 0.592833
\(661\) 1.48883e14 1.17988 0.589940 0.807447i \(-0.299151\pi\)
0.589940 + 0.807447i \(0.299151\pi\)
\(662\) 1.31054e14 1.03077
\(663\) 2.11907e14i 1.65416i
\(664\) 2.07620e13i 0.160853i
\(665\) 1.59428e13i 0.122590i
\(666\) 1.74735e14 1.33355
\(667\) 5.04865e13i 0.382425i
\(668\) −1.51694e13 −0.114048
\(669\) −4.09932e13 −0.305901
\(670\) 8.75692e13 0.648601
\(671\) 3.69858e13i 0.271909i
\(672\) 4.52953e14i 3.30527i
\(673\) 2.94088e13i 0.213011i 0.994312 + 0.106506i \(0.0339662\pi\)
−0.994312 + 0.106506i \(0.966034\pi\)
\(674\) 2.99575e14i 2.15380i
\(675\) 2.62042e13i 0.187005i
\(676\) 4.97601e13 0.352491
\(677\) 1.54013e14i 1.08297i 0.840711 + 0.541484i \(0.182137\pi\)
−0.840711 + 0.541484i \(0.817863\pi\)
\(678\) 1.28842e14i 0.899311i
\(679\) 1.68395e14i 1.16676i
\(680\) 1.87723e13 0.129114
\(681\) −3.11383e13 −0.212598
\(682\) 8.45735e13i 0.573208i
\(683\) 8.90638e13 0.599235 0.299618 0.954059i \(-0.403141\pi\)
0.299618 + 0.954059i \(0.403141\pi\)
\(684\) 2.21277e13i 0.147794i
\(685\) −8.68512e13 −0.575868
\(686\) −8.73409e13 −0.574906
\(687\) 2.45209e14i 1.60233i
\(688\) −9.27659e13 1.04891e14i −0.601792 0.680450i
\(689\) −1.93046e14 −1.24327
\(690\) 3.10729e14i 1.98672i
\(691\) 2.05726e14i 1.30587i 0.757415 + 0.652934i \(0.226462\pi\)
−0.757415 + 0.652934i \(0.773538\pi\)
\(692\) −1.97561e14 −1.24500
\(693\) 1.43558e14i 0.898178i
\(694\) −3.33276e14 −2.07017
\(695\) 9.85119e12i 0.0607526i
\(696\) 1.04702e13i 0.0641078i
\(697\) −1.85883e14 −1.13000
\(698\) −1.06774e14 −0.644448
\(699\) 2.12112e14 1.27110
\(700\) 9.62769e13i 0.572838i
\(701\) −2.83348e13 −0.167390 −0.0836950 0.996491i \(-0.526672\pi\)
−0.0836950 + 0.996491i \(0.526672\pi\)
\(702\) −1.07737e14 −0.631943
\(703\) −1.18996e13 −0.0693033
\(704\) 8.89295e13 0.514260
\(705\) −8.00486e13 −0.459630
\(706\) 1.04600e14i 0.596359i
\(707\) 1.82239e14i 1.03168i
\(708\) 5.63498e14i 3.16757i
\(709\) 5.65638e13 0.315724 0.157862 0.987461i \(-0.449540\pi\)
0.157862 + 0.987461i \(0.449540\pi\)
\(710\) 3.28661e14i 1.82161i
\(711\) −8.13121e13 −0.447515
\(712\) −1.77417e13 −0.0969607
\(713\) 1.84156e14 0.999400
\(714\) 8.11749e14i 4.37452i
\(715\) 5.47724e13i 0.293110i
\(716\) 1.86037e14i 0.988632i
\(717\) 2.43612e14i 1.28559i
\(718\) 3.00671e14i 1.57568i
\(719\) 1.57454e14 0.819424 0.409712 0.912215i \(-0.365629\pi\)
0.409712 + 0.912215i \(0.365629\pi\)
\(720\) 1.90831e14i 0.986250i
\(721\) 2.55026e14i 1.30891i
\(722\) 2.80363e14i 1.42901i
\(723\) 5.48063e13 0.277421
\(724\) 2.30983e14 1.16115
\(725\) 2.41188e13i 0.120411i
\(726\) −3.58666e14 −1.77831
\(727\) 8.96966e13i 0.441676i −0.975310 0.220838i \(-0.929121\pi\)
0.975310 0.220838i \(-0.0708793\pi\)
\(728\) −3.08342e13 −0.150791
\(729\) 3.15524e14 1.53248
\(730\) 3.62716e14i 1.74965i
\(731\) −1.81709e14 2.05460e14i −0.870541 0.984327i
\(732\) −2.14413e14 −1.02022
\(733\) 2.97971e14i 1.40817i −0.710116 0.704084i \(-0.751358\pi\)
0.710116 0.704084i \(-0.248642\pi\)
\(734\) 3.06205e14i 1.43725i
\(735\) 3.34838e14 1.56098
\(736\) 3.45122e14i 1.59802i
\(737\) 5.36990e13 0.246961
\(738\) 3.66302e14i 1.67324i
\(739\) 1.09759e13i 0.0497987i −0.999690 0.0248994i \(-0.992073\pi\)
0.999690 0.0248994i \(-0.00792653\pi\)
\(740\) −1.32866e14 −0.598763
\(741\) 2.84377e13 0.127293
\(742\) −7.39501e14 −3.28791
\(743\) 1.78778e14i 0.789533i 0.918781 + 0.394766i \(0.129175\pi\)
−0.918781 + 0.394766i \(0.870825\pi\)
\(744\) 3.81917e13 0.167534
\(745\) 2.78945e14 1.21545
\(746\) −5.32948e13 −0.230670
\(747\) 4.13417e14 1.77740
\(748\) 1.47779e14 0.631108
\(749\) 3.85626e14i 1.63590i
\(750\) 5.71353e14i 2.40768i
\(751\) 1.49336e14i 0.625121i 0.949898 + 0.312561i \(0.101187\pi\)
−0.949898 + 0.312561i \(0.898813\pi\)
\(752\) −8.13440e13 −0.338249
\(753\) 2.07473e14i 0.857012i
\(754\) −9.91624e13 −0.406902
\(755\) −1.82431e14 −0.743641
\(756\) −2.14716e14 −0.869470
\(757\) 2.40950e14i 0.969278i −0.874714 0.484639i \(-0.838951\pi\)
0.874714 0.484639i \(-0.161049\pi\)
\(758\) 5.57865e13i 0.222938i
\(759\) 1.90544e14i 0.756462i
\(760\) 2.51922e12i 0.00993570i
\(761\) 1.15549e13i 0.0452735i 0.999744 + 0.0226367i \(0.00720611\pi\)
−0.999744 + 0.0226367i \(0.992794\pi\)
\(762\) 1.06709e15 4.15363
\(763\) 7.56286e14i 2.92458i
\(764\) 6.01323e13i 0.231015i
\(765\) 3.73798e14i 1.42669i
\(766\) 1.73243e11 0.000656919
\(767\) −4.15721e14 −1.56612
\(768\) 3.31718e14i 1.24155i
\(769\) 2.51778e13 0.0936237 0.0468118 0.998904i \(-0.485094\pi\)
0.0468118 + 0.998904i \(0.485094\pi\)
\(770\) 2.09816e14i 0.775149i
\(771\) −6.09319e13 −0.223652
\(772\) −4.98903e14 −1.81941
\(773\) 4.49217e13i 0.162764i −0.996683 0.0813821i \(-0.974067\pi\)
0.996683 0.0813821i \(-0.0259334\pi\)
\(774\) −4.04879e14 + 3.58076e14i −1.45754 + 1.28905i
\(775\) −8.79766e13 −0.314673
\(776\) 2.66091e13i 0.0945631i
\(777\) 4.47546e14i 1.58027i
\(778\) 4.31156e14 1.51264
\(779\) 2.49454e13i 0.0869567i
\(780\) 3.17524e14 1.09978