Properties

Label 43.9.b.b.42.5
Level 43
Weight 9
Character 43.42
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.5
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.24

$q$-expansion

\(f(q)\) \(=\) \(q-23.8212i q^{2} +128.615i q^{3} -311.450 q^{4} +1187.44i q^{5} +3063.75 q^{6} -1045.51i q^{7} +1320.89i q^{8} -9980.70 q^{9} +O(q^{10})\) \(q-23.8212i q^{2} +128.615i q^{3} -311.450 q^{4} +1187.44i q^{5} +3063.75 q^{6} -1045.51i q^{7} +1320.89i q^{8} -9980.70 q^{9} +28286.2 q^{10} -7720.54 q^{11} -40057.0i q^{12} -32771.9 q^{13} -24905.4 q^{14} -152722. q^{15} -48266.1 q^{16} +74818.8 q^{17} +237752. i q^{18} -221516. i q^{19} -369827. i q^{20} +134468. q^{21} +183913. i q^{22} +272622. q^{23} -169885. q^{24} -1.01938e6 q^{25} +780665. i q^{26} -439823. i q^{27} +325625. i q^{28} +11057.0i q^{29} +3.63801e6i q^{30} -669910. q^{31} +1.48790e6i q^{32} -992974. i q^{33} -1.78227e6i q^{34} +1.24148e6 q^{35} +3.10849e6 q^{36} +3.02251e6i q^{37} -5.27678e6 q^{38} -4.21494e6i q^{39} -1.56847e6 q^{40} -874510. q^{41} -3.20319e6i q^{42} +(-3.02666e6 - 1.58983e6i) q^{43} +2.40456e6 q^{44} -1.18514e7i q^{45} -6.49420e6i q^{46} -2.23823e6 q^{47} -6.20772e6i q^{48} +4.67171e6 q^{49} +2.42828e7i q^{50} +9.62278e6i q^{51} +1.02068e7 q^{52} -1.95235e6 q^{53} -1.04771e7 q^{54} -9.16765e6i q^{55} +1.38100e6 q^{56} +2.84902e7 q^{57} +263392. q^{58} -2.07104e7 q^{59} +4.75651e7 q^{60} +1.01183e7i q^{61} +1.59581e7i q^{62} +1.04349e7i q^{63} +2.30875e7 q^{64} -3.89145e7i q^{65} -2.36538e7 q^{66} -2.69928e7 q^{67} -2.33023e7 q^{68} +3.50632e7i q^{69} -2.95735e7i q^{70} +1.28888e7i q^{71} -1.31834e7i q^{72} +1.98955e7i q^{73} +7.19998e7 q^{74} -1.31107e8i q^{75} +6.89912e7i q^{76} +8.07192e6i q^{77} -1.00405e8 q^{78} +4.68555e7 q^{79} -5.73129e7i q^{80} -8.91576e6 q^{81} +2.08319e7i q^{82} +2.60253e7 q^{83} -4.18801e7 q^{84} +8.88425e7i q^{85} +(-3.78716e7 + 7.20986e7i) q^{86} -1.42210e6 q^{87} -1.01979e7i q^{88} -2.43427e7i q^{89} -2.82316e8 q^{90} +3.42634e7i q^{91} -8.49083e7 q^{92} -8.61602e7i q^{93} +5.33175e7i q^{94} +2.63036e8 q^{95} -1.91366e8 q^{96} +3.57432e6 q^{97} -1.11286e8i q^{98} +7.70564e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.8212i 1.48883i −0.667720 0.744413i \(-0.732730\pi\)
0.667720 0.744413i \(-0.267270\pi\)
\(3\) 128.615i 1.58783i 0.608026 + 0.793917i \(0.291961\pi\)
−0.608026 + 0.793917i \(0.708039\pi\)
\(4\) −311.450 −1.21660
\(5\) 1187.44i 1.89990i 0.312406 + 0.949949i \(0.398865\pi\)
−0.312406 + 0.949949i \(0.601135\pi\)
\(6\) 3063.75 2.36401
\(7\) 1045.51i 0.435448i −0.976010 0.217724i \(-0.930137\pi\)
0.976010 0.217724i \(-0.0698633\pi\)
\(8\) 1320.89i 0.322482i
\(9\) −9980.70 −1.52122
\(10\) 28286.2 2.82862
\(11\) −7720.54 −0.527323 −0.263662 0.964615i \(-0.584930\pi\)
−0.263662 + 0.964615i \(0.584930\pi\)
\(12\) 40057.0i 1.93176i
\(13\) −32771.9 −1.14743 −0.573717 0.819054i \(-0.694499\pi\)
−0.573717 + 0.819054i \(0.694499\pi\)
\(14\) −24905.4 −0.648307
\(15\) −152722. −3.01672
\(16\) −48266.1 −0.736482
\(17\) 74818.8 0.895808 0.447904 0.894082i \(-0.352171\pi\)
0.447904 + 0.894082i \(0.352171\pi\)
\(18\) 237752.i 2.26482i
\(19\) 221516.i 1.69977i −0.526966 0.849886i \(-0.676671\pi\)
0.526966 0.849886i \(-0.323329\pi\)
\(20\) 369827.i 2.31142i
\(21\) 134468. 0.691420
\(22\) 183913.i 0.785092i
\(23\) 272622. 0.974205 0.487102 0.873345i \(-0.338054\pi\)
0.487102 + 0.873345i \(0.338054\pi\)
\(24\) −169885. −0.512047
\(25\) −1.01938e6 −2.60961
\(26\) 780665.i 1.70833i
\(27\) 439823.i 0.827604i
\(28\) 325625.i 0.529767i
\(29\) 11057.0i 0.0156332i 0.999969 + 0.00781658i \(0.00248812\pi\)
−0.999969 + 0.00781658i \(0.997512\pi\)
\(30\) 3.63801e6i 4.49137i
\(31\) −669910. −0.725387 −0.362694 0.931908i \(-0.618143\pi\)
−0.362694 + 0.931908i \(0.618143\pi\)
\(32\) 1.48790e6i 1.41898i
\(33\) 992974.i 0.837302i
\(34\) 1.78227e6i 1.33370i
\(35\) 1.24148e6 0.827307
\(36\) 3.10849e6 1.85071
\(37\) 3.02251e6i 1.61273i 0.591421 + 0.806363i \(0.298567\pi\)
−0.591421 + 0.806363i \(0.701433\pi\)
\(38\) −5.27678e6 −2.53066
\(39\) 4.21494e6i 1.82193i
\(40\) −1.56847e6 −0.612682
\(41\) −874510. −0.309478 −0.154739 0.987955i \(-0.549454\pi\)
−0.154739 + 0.987955i \(0.549454\pi\)
\(42\) 3.20319e6i 1.02940i
\(43\) −3.02666e6 1.58983e6i −0.885298 0.465025i
\(44\) 2.40456e6 0.641542
\(45\) 1.18514e7i 2.89015i
\(46\) 6.49420e6i 1.45042i
\(47\) −2.23823e6 −0.458685 −0.229342 0.973346i \(-0.573658\pi\)
−0.229342 + 0.973346i \(0.573658\pi\)
\(48\) 6.20772e6i 1.16941i
\(49\) 4.67171e6 0.810385
\(50\) 2.42828e7i 3.88525i
\(51\) 9.62278e6i 1.42239i
\(52\) 1.02068e7 1.39597
\(53\) −1.95235e6 −0.247431 −0.123715 0.992318i \(-0.539481\pi\)
−0.123715 + 0.992318i \(0.539481\pi\)
\(54\) −1.04771e7 −1.23216
\(55\) 9.16765e6i 1.00186i
\(56\) 1.38100e6 0.140424
\(57\) 2.84902e7 2.69896
\(58\) 263392. 0.0232750
\(59\) −2.07104e7 −1.70915 −0.854574 0.519330i \(-0.826182\pi\)
−0.854574 + 0.519330i \(0.826182\pi\)
\(60\) 4.75651e7 3.67015
\(61\) 1.01183e7i 0.730783i 0.930854 + 0.365392i \(0.119065\pi\)
−0.930854 + 0.365392i \(0.880935\pi\)
\(62\) 1.59581e7i 1.07997i
\(63\) 1.04349e7i 0.662411i
\(64\) 2.30875e7 1.37612
\(65\) 3.89145e7i 2.18001i
\(66\) −2.36538e7 −1.24660
\(67\) −2.69928e7 −1.33952 −0.669760 0.742577i \(-0.733603\pi\)
−0.669760 + 0.742577i \(0.733603\pi\)
\(68\) −2.33023e7 −1.08984
\(69\) 3.50632e7i 1.54688i
\(70\) 2.95735e7i 1.23172i
\(71\) 1.28888e7i 0.507200i 0.967309 + 0.253600i \(0.0816148\pi\)
−0.967309 + 0.253600i \(0.918385\pi\)
\(72\) 1.31834e7i 0.490564i
\(73\) 1.98955e7i 0.700589i 0.936640 + 0.350294i \(0.113918\pi\)
−0.936640 + 0.350294i \(0.886082\pi\)
\(74\) 7.19998e7 2.40107
\(75\) 1.31107e8i 4.14363i
\(76\) 6.89912e7i 2.06795i
\(77\) 8.07192e6i 0.229622i
\(78\) −1.00405e8 −2.71254
\(79\) 4.68555e7 1.20296 0.601482 0.798886i \(-0.294577\pi\)
0.601482 + 0.798886i \(0.294577\pi\)
\(80\) 5.73129e7i 1.39924i
\(81\) −8.91576e6 −0.207118
\(82\) 2.08319e7i 0.460759i
\(83\) 2.60253e7 0.548382 0.274191 0.961675i \(-0.411590\pi\)
0.274191 + 0.961675i \(0.411590\pi\)
\(84\) −4.18801e7 −0.841182
\(85\) 8.88425e7i 1.70194i
\(86\) −3.78716e7 + 7.20986e7i −0.692340 + 1.31805i
\(87\) −1.42210e6 −0.0248229
\(88\) 1.01979e7i 0.170052i
\(89\) 2.43427e7i 0.387980i −0.981004 0.193990i \(-0.937857\pi\)
0.981004 0.193990i \(-0.0621429\pi\)
\(90\) −2.82316e8 −4.30294
\(91\) 3.42634e7i 0.499648i
\(92\) −8.49083e7 −1.18522
\(93\) 8.61602e7i 1.15179i
\(94\) 5.33175e7i 0.682901i
\(95\) 2.63036e8 3.22939
\(96\) −1.91366e8 −2.25310
\(97\) 3.57432e6 0.0403744 0.0201872 0.999796i \(-0.493574\pi\)
0.0201872 + 0.999796i \(0.493574\pi\)
\(98\) 1.11286e8i 1.20652i
\(99\) 7.70564e7 0.802173
\(100\) 3.17486e8 3.17486
\(101\) −4.79756e7 −0.461036 −0.230518 0.973068i \(-0.574042\pi\)
−0.230518 + 0.973068i \(0.574042\pi\)
\(102\) 2.29226e8 2.11770
\(103\) 2.85028e7 0.253243 0.126622 0.991951i \(-0.459587\pi\)
0.126622 + 0.991951i \(0.459587\pi\)
\(104\) 4.32879e7i 0.370027i
\(105\) 1.59672e8i 1.31363i
\(106\) 4.65073e7i 0.368381i
\(107\) −1.05259e8 −0.803016 −0.401508 0.915855i \(-0.631514\pi\)
−0.401508 + 0.915855i \(0.631514\pi\)
\(108\) 1.36983e8i 1.00686i
\(109\) 4.41249e7 0.312592 0.156296 0.987710i \(-0.450045\pi\)
0.156296 + 0.987710i \(0.450045\pi\)
\(110\) −2.18384e8 −1.49160
\(111\) −3.88739e8 −2.56074
\(112\) 5.04628e7i 0.320700i
\(113\) 2.43450e8i 1.49313i 0.665314 + 0.746563i \(0.268298\pi\)
−0.665314 + 0.746563i \(0.731702\pi\)
\(114\) 6.78671e8i 4.01827i
\(115\) 3.23722e8i 1.85089i
\(116\) 3.44371e6i 0.0190193i
\(117\) 3.27086e8 1.74549
\(118\) 4.93346e8i 2.54462i
\(119\) 7.82239e7i 0.390078i
\(120\) 2.01728e8i 0.972838i
\(121\) −1.54752e8 −0.721930
\(122\) 2.41030e8 1.08801
\(123\) 1.12475e8i 0.491399i
\(124\) 2.08644e8 0.882507
\(125\) 7.46605e8i 3.05809i
\(126\) 2.48573e8 0.986215
\(127\) 4.14402e8 1.59297 0.796483 0.604661i \(-0.206691\pi\)
0.796483 + 0.604661i \(0.206691\pi\)
\(128\) 1.69070e8i 0.629834i
\(129\) 2.04475e8 3.89272e8i 0.738382 1.40571i
\(130\) −9.26990e8 −3.24565
\(131\) 7.37862e7i 0.250548i 0.992122 + 0.125274i \(0.0399809\pi\)
−0.992122 + 0.125274i \(0.960019\pi\)
\(132\) 3.09262e8i 1.01866i
\(133\) −2.31598e8 −0.740163
\(134\) 6.43002e8i 1.99431i
\(135\) 5.22261e8 1.57236
\(136\) 9.88270e7i 0.288882i
\(137\) 3.82975e8i 1.08715i −0.839362 0.543573i \(-0.817071\pi\)
0.839362 0.543573i \(-0.182929\pi\)
\(138\) 8.35248e8 2.30303
\(139\) −1.29166e8 −0.346011 −0.173005 0.984921i \(-0.555348\pi\)
−0.173005 + 0.984921i \(0.555348\pi\)
\(140\) −3.86658e8 −1.00650
\(141\) 2.87869e8i 0.728315i
\(142\) 3.07027e8 0.755133
\(143\) 2.53017e8 0.605069
\(144\) 4.81729e8 1.12035
\(145\) −1.31295e7 −0.0297014
\(146\) 4.73935e8 1.04305
\(147\) 6.00849e8i 1.28676i
\(148\) 9.41360e8i 1.96205i
\(149\) 1.46858e8i 0.297957i 0.988840 + 0.148979i \(0.0475985\pi\)
−0.988840 + 0.148979i \(0.952401\pi\)
\(150\) −3.12313e9 −6.16914
\(151\) 4.27850e7i 0.0822970i 0.999153 + 0.0411485i \(0.0131017\pi\)
−0.999153 + 0.0411485i \(0.986898\pi\)
\(152\) 2.92597e8 0.548146
\(153\) −7.46744e8 −1.36272
\(154\) 1.92283e8 0.341867
\(155\) 7.95475e8i 1.37816i
\(156\) 1.31274e9i 2.21657i
\(157\) 7.84735e8i 1.29159i 0.763511 + 0.645795i \(0.223474\pi\)
−0.763511 + 0.645795i \(0.776526\pi\)
\(158\) 1.11616e9i 1.79100i
\(159\) 2.51100e8i 0.392879i
\(160\) −1.76679e9 −2.69591
\(161\) 2.85030e8i 0.424216i
\(162\) 2.12384e8i 0.308363i
\(163\) 8.52878e8i 1.20819i 0.796911 + 0.604097i \(0.206466\pi\)
−0.796911 + 0.604097i \(0.793534\pi\)
\(164\) 2.72366e8 0.376511
\(165\) 1.17909e9 1.59079
\(166\) 6.19954e8i 0.816446i
\(167\) 6.08443e8 0.782266 0.391133 0.920334i \(-0.372083\pi\)
0.391133 + 0.920334i \(0.372083\pi\)
\(168\) 1.77617e8i 0.222970i
\(169\) 2.58264e8 0.316605
\(170\) 2.11634e9 2.53390
\(171\) 2.21088e9i 2.58572i
\(172\) 9.42652e8 + 4.95151e8i 1.07705 + 0.565750i
\(173\) −1.45079e9 −1.61965 −0.809824 0.586673i \(-0.800437\pi\)
−0.809824 + 0.586673i \(0.800437\pi\)
\(174\) 3.38760e7i 0.0369569i
\(175\) 1.06577e9i 1.13635i
\(176\) 3.72640e8 0.388364
\(177\) 2.66365e9i 2.71384i
\(178\) −5.79873e8 −0.577634
\(179\) 4.36516e8i 0.425194i 0.977140 + 0.212597i \(0.0681922\pi\)
−0.977140 + 0.212597i \(0.931808\pi\)
\(180\) 3.69113e9i 3.51617i
\(181\) 1.12797e9 1.05095 0.525474 0.850810i \(-0.323888\pi\)
0.525474 + 0.850810i \(0.323888\pi\)
\(182\) 8.16195e8 0.743889
\(183\) −1.30136e9 −1.16036
\(184\) 3.60103e8i 0.314163i
\(185\) −3.58904e9 −3.06401
\(186\) −2.05244e9 −1.71482
\(187\) −5.77642e8 −0.472381
\(188\) 6.97098e8 0.558036
\(189\) −4.59840e8 −0.360379
\(190\) 6.26584e9i 4.80800i
\(191\) 1.96549e9i 1.47685i 0.674335 + 0.738425i \(0.264430\pi\)
−0.674335 + 0.738425i \(0.735570\pi\)
\(192\) 2.96939e9i 2.18506i
\(193\) 4.37331e8 0.315197 0.157598 0.987503i \(-0.449625\pi\)
0.157598 + 0.987503i \(0.449625\pi\)
\(194\) 8.51445e7i 0.0601104i
\(195\) 5.00497e9 3.46149
\(196\) −1.45500e9 −0.985915
\(197\) −1.98231e9 −1.31615 −0.658077 0.752950i \(-0.728630\pi\)
−0.658077 + 0.752950i \(0.728630\pi\)
\(198\) 1.83558e9i 1.19430i
\(199\) 3.04777e9i 1.94344i −0.236143 0.971718i \(-0.575883\pi\)
0.236143 0.971718i \(-0.424117\pi\)
\(200\) 1.34648e9i 0.841552i
\(201\) 3.47167e9i 2.12694i
\(202\) 1.14284e9i 0.686402i
\(203\) 1.15603e7 0.00680744
\(204\) 2.99702e9i 1.73049i
\(205\) 1.03843e9i 0.587976i
\(206\) 6.78970e8i 0.377035i
\(207\) −2.72096e9 −1.48198
\(208\) 1.58177e9 0.845065
\(209\) 1.71022e9i 0.896330i
\(210\) 3.80358e9 1.95576
\(211\) 2.99574e8i 0.151138i 0.997141 + 0.0755690i \(0.0240773\pi\)
−0.997141 + 0.0755690i \(0.975923\pi\)
\(212\) 6.08059e8 0.301025
\(213\) −1.65769e9 −0.805350
\(214\) 2.50740e9i 1.19555i
\(215\) 1.88782e9 3.59396e9i 0.883499 1.68197i
\(216\) 5.80955e8 0.266887
\(217\) 7.00399e8i 0.315869i
\(218\) 1.05111e9i 0.465395i
\(219\) −2.55885e9 −1.11242
\(220\) 2.85526e9i 1.21886i
\(221\) −2.45195e9 −1.02788
\(222\) 9.26022e9i 3.81250i
\(223\) 2.78431e9i 1.12589i 0.826493 + 0.562947i \(0.190333\pi\)
−0.826493 + 0.562947i \(0.809667\pi\)
\(224\) 1.55562e9 0.617891
\(225\) 1.01741e10 3.96978
\(226\) 5.79928e9 2.22301
\(227\) 9.25556e8i 0.348578i −0.984695 0.174289i \(-0.944237\pi\)
0.984695 0.174289i \(-0.0557626\pi\)
\(228\) −8.87327e9 −3.28355
\(229\) −4.49307e9 −1.63381 −0.816905 0.576772i \(-0.804312\pi\)
−0.816905 + 0.576772i \(0.804312\pi\)
\(230\) 7.71144e9 2.75565
\(231\) −1.03817e9 −0.364602
\(232\) −1.46051e7 −0.00504141
\(233\) 1.03025e9i 0.349559i −0.984608 0.174779i \(-0.944079\pi\)
0.984608 0.174779i \(-0.0559212\pi\)
\(234\) 7.79158e9i 2.59874i
\(235\) 2.65776e9i 0.871454i
\(236\) 6.45024e9 2.07935
\(237\) 6.02630e9i 1.91011i
\(238\) −1.86339e9 −0.580758
\(239\) −4.62921e8 −0.141878 −0.0709390 0.997481i \(-0.522600\pi\)
−0.0709390 + 0.997481i \(0.522600\pi\)
\(240\) 7.37127e9 2.22176
\(241\) 2.39828e9i 0.710938i 0.934688 + 0.355469i \(0.115679\pi\)
−0.934688 + 0.355469i \(0.884321\pi\)
\(242\) 3.68638e9i 1.07483i
\(243\) 4.03237e9i 1.15647i
\(244\) 3.15135e9i 0.889072i
\(245\) 5.54735e9i 1.53965i
\(246\) −2.67928e9 −0.731608
\(247\) 7.25949e9i 1.95038i
\(248\) 8.84875e8i 0.233924i
\(249\) 3.34723e9i 0.870740i
\(250\) −1.77850e10 −4.55297
\(251\) 6.66643e9 1.67957 0.839786 0.542918i \(-0.182681\pi\)
0.839786 + 0.542918i \(0.182681\pi\)
\(252\) 3.24996e9i 0.805890i
\(253\) −2.10479e9 −0.513721
\(254\) 9.87155e9i 2.37165i
\(255\) −1.14264e10 −2.70240
\(256\) 1.88296e9 0.438412
\(257\) 5.34258e9i 1.22467i −0.790599 0.612334i \(-0.790231\pi\)
0.790599 0.612334i \(-0.209769\pi\)
\(258\) −9.27293e9 4.87084e9i −2.09285 1.09932i
\(259\) 3.16007e9 0.702259
\(260\) 1.21199e10i 2.65220i
\(261\) 1.10357e8i 0.0237814i
\(262\) 1.75768e9 0.373022
\(263\) 1.45518e9i 0.304155i −0.988369 0.152078i \(-0.951404\pi\)
0.988369 0.152078i \(-0.0485964\pi\)
\(264\) 1.31160e9 0.270015
\(265\) 2.31829e9i 0.470093i
\(266\) 5.51694e9i 1.10197i
\(267\) 3.13083e9 0.616047
\(268\) 8.40692e9 1.62966
\(269\) −3.65582e9 −0.698194 −0.349097 0.937087i \(-0.613512\pi\)
−0.349097 + 0.937087i \(0.613512\pi\)
\(270\) 1.24409e10i 2.34097i
\(271\) −7.70139e9 −1.42788 −0.713940 0.700207i \(-0.753091\pi\)
−0.713940 + 0.700207i \(0.753091\pi\)
\(272\) −3.61121e9 −0.659747
\(273\) −4.40677e9 −0.793359
\(274\) −9.12293e9 −1.61857
\(275\) 7.87016e9 1.37611
\(276\) 1.09204e10i 1.88193i
\(277\) 2.17850e9i 0.370032i 0.982736 + 0.185016i \(0.0592336\pi\)
−0.982736 + 0.185016i \(0.940766\pi\)
\(278\) 3.07690e9i 0.515150i
\(279\) 6.68617e9 1.10347
\(280\) 1.63985e9i 0.266792i
\(281\) 2.46057e9 0.394649 0.197324 0.980338i \(-0.436775\pi\)
0.197324 + 0.980338i \(0.436775\pi\)
\(282\) −6.85740e9 −1.08433
\(283\) −2.55764e9 −0.398744 −0.199372 0.979924i \(-0.563890\pi\)
−0.199372 + 0.979924i \(0.563890\pi\)
\(284\) 4.01422e9i 0.617061i
\(285\) 3.38303e10i 5.12774i
\(286\) 6.02716e9i 0.900842i
\(287\) 9.14311e8i 0.134762i
\(288\) 1.48503e10i 2.15857i
\(289\) −1.37791e9 −0.197528
\(290\) 3.12761e8i 0.0442202i
\(291\) 4.59709e8i 0.0641078i
\(292\) 6.19645e9i 0.852338i
\(293\) 8.21345e9 1.11444 0.557218 0.830366i \(-0.311869\pi\)
0.557218 + 0.830366i \(0.311869\pi\)
\(294\) 1.43130e10 1.91576
\(295\) 2.45922e10i 3.24721i
\(296\) −3.99239e9 −0.520075
\(297\) 3.39567e9i 0.436415i
\(298\) 3.49834e9 0.443606
\(299\) −8.93435e9 −1.11784
\(300\) 4.08333e10i 5.04114i
\(301\) −1.66218e9 + 3.16441e9i −0.202494 + 0.385502i
\(302\) 1.01919e9 0.122526
\(303\) 6.17036e9i 0.732048i
\(304\) 1.06917e10i 1.25185i
\(305\) −1.20148e10 −1.38841
\(306\) 1.77883e10i 2.02885i
\(307\) 1.23393e10 1.38911 0.694554 0.719441i \(-0.255602\pi\)
0.694554 + 0.719441i \(0.255602\pi\)
\(308\) 2.51400e9i 0.279359i
\(309\) 3.66587e9i 0.402108i
\(310\) −1.89492e10 −2.05184
\(311\) 1.48263e10 1.58486 0.792430 0.609963i \(-0.208816\pi\)
0.792430 + 0.609963i \(0.208816\pi\)
\(312\) 5.56745e9 0.587541
\(313\) 4.43851e8i 0.0462445i −0.999733 0.0231223i \(-0.992639\pi\)
0.999733 0.0231223i \(-0.00736070\pi\)
\(314\) 1.86933e10 1.92295
\(315\) −1.23908e10 −1.25851
\(316\) −1.45932e10 −1.46353
\(317\) 1.69495e10 1.67850 0.839249 0.543748i \(-0.182995\pi\)
0.839249 + 0.543748i \(0.182995\pi\)
\(318\) −5.98151e9 −0.584928
\(319\) 8.53663e7i 0.00824373i
\(320\) 2.74150e10i 2.61450i
\(321\) 1.35378e10i 1.27506i
\(322\) −6.78976e9 −0.631584
\(323\) 1.65736e10i 1.52267i
\(324\) 2.77681e9 0.251980
\(325\) 3.34069e10 2.99436
\(326\) 2.03166e10 1.79879
\(327\) 5.67510e9i 0.496344i
\(328\) 1.15513e9i 0.0998010i
\(329\) 2.34010e9i 0.199734i
\(330\) 2.80874e10i 2.36841i
\(331\) 1.21801e10i 1.01470i 0.861740 + 0.507351i \(0.169375\pi\)
−0.861740 + 0.507351i \(0.830625\pi\)
\(332\) −8.10558e9 −0.667163
\(333\) 3.01667e10i 2.45330i
\(334\) 1.44939e10i 1.16466i
\(335\) 3.20523e10i 2.54495i
\(336\) −6.49025e9 −0.509218
\(337\) 1.06848e10 0.828411 0.414205 0.910183i \(-0.364059\pi\)
0.414205 + 0.910183i \(0.364059\pi\)
\(338\) 6.15217e9i 0.471369i
\(339\) −3.13113e10 −2.37084
\(340\) 2.76700e10i 2.07059i
\(341\) 5.17207e9 0.382514
\(342\) 5.26659e10 3.84969
\(343\) 1.09115e10i 0.788329i
\(344\) 2.09998e9 3.99787e9i 0.149962 0.285492i
\(345\) −4.16353e10 −2.93890
\(346\) 3.45596e10i 2.41137i
\(347\) 4.88319e9i 0.336810i 0.985718 + 0.168405i \(0.0538617\pi\)
−0.985718 + 0.168405i \(0.946138\pi\)
\(348\) 4.42912e8 0.0301995
\(349\) 1.60675e10i 1.08304i 0.840687 + 0.541521i \(0.182152\pi\)
−0.840687 + 0.541521i \(0.817848\pi\)
\(350\) 2.53880e10 1.69183
\(351\) 1.44138e10i 0.949621i
\(352\) 1.14874e10i 0.748259i
\(353\) 1.51491e10 0.975634 0.487817 0.872946i \(-0.337793\pi\)
0.487817 + 0.872946i \(0.337793\pi\)
\(354\) −6.34514e10 −4.04044
\(355\) −1.53046e10 −0.963629
\(356\) 7.58154e9i 0.472017i
\(357\) 1.00607e10 0.619379
\(358\) 1.03983e10 0.633040
\(359\) −1.52025e10 −0.915242 −0.457621 0.889147i \(-0.651298\pi\)
−0.457621 + 0.889147i \(0.651298\pi\)
\(360\) 1.56544e10 0.932022
\(361\) −3.20858e10 −1.88923
\(362\) 2.68695e10i 1.56468i
\(363\) 1.99034e10i 1.14630i
\(364\) 1.06713e10i 0.607873i
\(365\) −2.36246e10 −1.33105
\(366\) 3.10000e10i 1.72758i
\(367\) −9.87809e9 −0.544514 −0.272257 0.962225i \(-0.587770\pi\)
−0.272257 + 0.962225i \(0.587770\pi\)
\(368\) −1.31584e10 −0.717485
\(369\) 8.72822e9 0.470783
\(370\) 8.54952e10i 4.56178i
\(371\) 2.04120e9i 0.107743i
\(372\) 2.68346e10i 1.40127i
\(373\) 2.67857e10i 1.38378i −0.722002 0.691891i \(-0.756778\pi\)
0.722002 0.691891i \(-0.243222\pi\)
\(374\) 1.37601e10i 0.703292i
\(375\) 9.60243e10 4.85575
\(376\) 2.95645e9i 0.147917i
\(377\) 3.62360e8i 0.0179380i
\(378\) 1.09539e10i 0.536541i
\(379\) 1.56805e10 0.759983 0.379991 0.924990i \(-0.375927\pi\)
0.379991 + 0.924990i \(0.375927\pi\)
\(380\) −8.19226e10 −3.92888
\(381\) 5.32981e10i 2.52937i
\(382\) 4.68203e10 2.19877
\(383\) 2.95831e10i 1.37483i −0.726266 0.687414i \(-0.758746\pi\)
0.726266 0.687414i \(-0.241254\pi\)
\(384\) 2.17448e10 1.00007
\(385\) −9.58488e9 −0.436259
\(386\) 1.04178e10i 0.469273i
\(387\) 3.02081e10 + 1.58676e10i 1.34673 + 0.707403i
\(388\) −1.11322e9 −0.0491195
\(389\) 1.92230e10i 0.839502i −0.907639 0.419751i \(-0.862117\pi\)
0.907639 0.419751i \(-0.137883\pi\)
\(390\) 1.19224e11i 5.15355i
\(391\) 2.03973e10 0.872701
\(392\) 6.17079e9i 0.261334i
\(393\) −9.48998e9 −0.397828
\(394\) 4.72210e10i 1.95952i
\(395\) 5.56380e10i 2.28551i
\(396\) −2.39992e10 −0.975924
\(397\) −2.76966e10 −1.11497 −0.557486 0.830186i \(-0.688234\pi\)
−0.557486 + 0.830186i \(0.688234\pi\)
\(398\) −7.26016e10 −2.89344
\(399\) 2.97868e10i 1.17526i
\(400\) 4.92015e10 1.92193
\(401\) −3.55121e10 −1.37340 −0.686702 0.726939i \(-0.740942\pi\)
−0.686702 + 0.726939i \(0.740942\pi\)
\(402\) −8.26994e10 −3.16664
\(403\) 2.19542e10 0.832334
\(404\) 1.49420e10 0.560897
\(405\) 1.05869e10i 0.393503i
\(406\) 2.75379e8i 0.0101351i
\(407\) 2.33354e10i 0.850428i
\(408\) −1.27106e10 −0.458696
\(409\) 5.61655e9i 0.200713i −0.994952 0.100357i \(-0.968002\pi\)
0.994952 0.100357i \(-0.0319984\pi\)
\(410\) −2.47365e10 −0.875394
\(411\) 4.92561e10 1.72621
\(412\) −8.87718e9 −0.308096
\(413\) 2.16529e10i 0.744246i
\(414\) 6.48166e10i 2.20640i
\(415\) 3.09034e10i 1.04187i
\(416\) 4.87614e10i 1.62818i
\(417\) 1.66127e10i 0.549408i
\(418\) 4.07396e10 1.33448
\(419\) 3.04720e10i 0.988655i 0.869276 + 0.494328i \(0.164586\pi\)
−0.869276 + 0.494328i \(0.835414\pi\)
\(420\) 4.97299e10i 1.59816i
\(421\) 2.98892e10i 0.951449i 0.879594 + 0.475724i \(0.157814\pi\)
−0.879594 + 0.475724i \(0.842186\pi\)
\(422\) 7.13620e9 0.225018
\(423\) 2.23391e10 0.697758
\(424\) 2.57883e9i 0.0797919i
\(425\) −7.62687e10 −2.33771
\(426\) 3.94882e10i 1.19903i
\(427\) 1.05788e10 0.318219
\(428\) 3.27829e10 0.976951
\(429\) 3.25416e10i 0.960749i
\(430\) −8.56125e10 4.49701e10i −2.50417 1.31538i
\(431\) 1.21255e10 0.351390 0.175695 0.984445i \(-0.443783\pi\)
0.175695 + 0.984445i \(0.443783\pi\)
\(432\) 2.12285e10i 0.609516i
\(433\) 6.14766e9i 0.174887i −0.996169 0.0874436i \(-0.972130\pi\)
0.996169 0.0874436i \(-0.0278698\pi\)
\(434\) 1.66844e10 0.470273
\(435\) 1.68865e9i 0.0471609i
\(436\) −1.37427e10 −0.380300
\(437\) 6.03903e10i 1.65593i
\(438\) 6.09549e10i 1.65620i
\(439\) 2.09828e10 0.564945 0.282472 0.959275i \(-0.408845\pi\)
0.282472 + 0.959275i \(0.408845\pi\)
\(440\) 1.21094e10 0.323082
\(441\) −4.66269e10 −1.23277
\(442\) 5.84084e10i 1.53033i
\(443\) 4.56919e10 1.18638 0.593191 0.805062i \(-0.297868\pi\)
0.593191 + 0.805062i \(0.297868\pi\)
\(444\) 1.21073e11 3.11540
\(445\) 2.89054e10 0.737122
\(446\) 6.63256e10 1.67626
\(447\) −1.88881e10 −0.473106
\(448\) 2.41383e10i 0.599231i
\(449\) 4.66900e10i 1.14878i 0.818580 + 0.574392i \(0.194762\pi\)
−0.818580 + 0.574392i \(0.805238\pi\)
\(450\) 2.42360e11i 5.91031i
\(451\) 6.75169e9 0.163195
\(452\) 7.58226e10i 1.81654i
\(453\) −5.50278e9 −0.130674
\(454\) −2.20479e10 −0.518971
\(455\) −4.06856e10 −0.949281
\(456\) 3.76323e10i 0.870364i
\(457\) 5.13987e10i 1.17839i −0.807992 0.589193i \(-0.799446\pi\)
0.807992 0.589193i \(-0.200554\pi\)
\(458\) 1.07030e11i 2.43246i
\(459\) 3.29070e10i 0.741374i
\(460\) 1.00823e11i 2.25179i
\(461\) −5.31807e9 −0.117747 −0.0588736 0.998265i \(-0.518751\pi\)
−0.0588736 + 0.998265i \(0.518751\pi\)
\(462\) 2.47304e10i 0.542828i
\(463\) 1.73963e10i 0.378558i 0.981923 + 0.189279i \(0.0606151\pi\)
−0.981923 + 0.189279i \(0.939385\pi\)
\(464\) 5.33680e8i 0.0115135i
\(465\) 1.02310e11 2.18829
\(466\) −2.45419e10 −0.520432
\(467\) 1.29922e10i 0.273158i −0.990629 0.136579i \(-0.956389\pi\)
0.990629 0.136579i \(-0.0436108\pi\)
\(468\) −1.01871e11 −2.12357
\(469\) 2.82213e10i 0.583292i
\(470\) −6.33111e10 −1.29744
\(471\) −1.00928e11 −2.05083
\(472\) 2.73560e10i 0.551169i
\(473\) 2.33674e10 + 1.22743e10i 0.466838 + 0.245218i
\(474\) 1.43554e11 2.84382
\(475\) 2.25809e11i 4.43574i
\(476\) 2.43628e10i 0.474570i
\(477\) 1.94858e10 0.376396
\(478\) 1.10273e10i 0.211231i
\(479\) −4.10168e10 −0.779148 −0.389574 0.920995i \(-0.627378\pi\)
−0.389574 + 0.920995i \(0.627378\pi\)
\(480\) 2.27235e11i 4.28065i
\(481\) 9.90532e10i 1.85050i
\(482\) 5.71299e10 1.05846
\(483\) 3.66590e10 0.673584
\(484\) 4.81975e10 0.878301
\(485\) 4.24427e9i 0.0767072i
\(486\) −9.60560e10 −1.72179
\(487\) −1.49123e10 −0.265112 −0.132556 0.991176i \(-0.542318\pi\)
−0.132556 + 0.991176i \(0.542318\pi\)
\(488\) −1.33651e10 −0.235664
\(489\) −1.09692e11 −1.91841
\(490\) 1.32145e11 2.29227
\(491\) 2.57099e10i 0.442359i −0.975233 0.221180i \(-0.929009\pi\)
0.975233 0.221180i \(-0.0709907\pi\)
\(492\) 3.50303e10i 0.597837i
\(493\) 8.27274e8i 0.0140043i
\(494\) 1.72930e11 2.90377
\(495\) 9.14995e10i 1.52405i
\(496\) 3.23340e10 0.534235
\(497\) 1.34754e10 0.220860
\(498\) 7.97351e10 1.29638
\(499\) 4.88036e10i 0.787136i 0.919296 + 0.393568i \(0.128759\pi\)
−0.919296 + 0.393568i \(0.871241\pi\)
\(500\) 2.32530e11i 3.72048i
\(501\) 7.82546e10i 1.24211i
\(502\) 1.58802e11i 2.50059i
\(503\) 6.69023e10i 1.04513i −0.852601 0.522563i \(-0.824976\pi\)
0.852601 0.522563i \(-0.175024\pi\)
\(504\) −1.37834e10 −0.213616
\(505\) 5.69679e10i 0.875921i
\(506\) 5.01387e10i 0.764841i
\(507\) 3.32165e10i 0.502716i
\(508\) −1.29065e11 −1.93800
\(509\) −3.93507e9 −0.0586248 −0.0293124 0.999570i \(-0.509332\pi\)
−0.0293124 + 0.999570i \(0.509332\pi\)
\(510\) 2.72192e11i 4.02341i
\(511\) 2.08010e10 0.305070
\(512\) 8.81363e10i 1.28255i
\(513\) −9.74278e10 −1.40674
\(514\) −1.27267e11 −1.82332
\(515\) 3.38452e10i 0.481136i
\(516\) −6.36837e10 + 1.21239e11i −0.898316 + 1.71018i
\(517\) 1.72804e10 0.241875
\(518\) 7.52767e10i 1.04554i
\(519\) 1.86593e11i 2.57173i
\(520\) 5.14016e10 0.703012
\(521\) 2.38175e10i 0.323256i 0.986852 + 0.161628i \(0.0516744\pi\)
−0.986852 + 0.161628i \(0.948326\pi\)
\(522\) −2.62884e9 −0.0354064
\(523\) 8.63612e10i 1.15428i −0.816645 0.577141i \(-0.804168\pi\)
0.816645 0.577141i \(-0.195832\pi\)
\(524\) 2.29807e10i 0.304817i
\(525\) −1.37074e11 −1.80434
\(526\) −3.46643e10 −0.452834
\(527\) −5.01219e10 −0.649808
\(528\) 4.79270e10i 0.616658i
\(529\) −3.98798e9 −0.0509250
\(530\) −5.52244e10 −0.699887
\(531\) 2.06704e11 2.59998
\(532\) 7.21311e10 0.900484
\(533\) 2.86593e10 0.355105
\(534\) 7.45801e10i 0.917187i
\(535\) 1.24988e11i 1.52565i
\(536\) 3.56544e10i 0.431971i
\(537\) −5.61422e10 −0.675138
\(538\) 8.70861e10i 1.03949i
\(539\) −3.60681e10 −0.427335
\(540\) −1.62658e11 −1.91294
\(541\) 1.11202e11 1.29815 0.649074 0.760725i \(-0.275157\pi\)
0.649074 + 0.760725i \(0.275157\pi\)
\(542\) 1.83456e11i 2.12586i
\(543\) 1.45073e11i 1.66873i
\(544\) 1.11323e11i 1.27113i
\(545\) 5.23955e10i 0.593892i
\(546\) 1.04975e11i 1.18117i
\(547\) −4.80348e10 −0.536546 −0.268273 0.963343i \(-0.586453\pi\)
−0.268273 + 0.963343i \(0.586453\pi\)
\(548\) 1.19278e11i 1.32262i
\(549\) 1.00988e11i 1.11168i
\(550\) 1.87477e11i 2.04879i
\(551\) 2.44931e9 0.0265728
\(552\) −4.63145e10 −0.498839
\(553\) 4.89880e10i 0.523829i
\(554\) 5.18945e10 0.550912
\(555\) 4.61602e11i 4.86515i
\(556\) 4.02288e10 0.420957
\(557\) −4.60143e10 −0.478049 −0.239024 0.971014i \(-0.576828\pi\)
−0.239024 + 0.971014i \(0.576828\pi\)
\(558\) 1.59273e11i 1.64287i
\(559\) 9.91892e10 + 5.21016e10i 1.01582 + 0.533585i
\(560\) −5.99213e10 −0.609297
\(561\) 7.42931e10i 0.750062i
\(562\) 5.86138e10i 0.587563i
\(563\) 3.36946e10 0.335372 0.167686 0.985840i \(-0.446371\pi\)
0.167686 + 0.985840i \(0.446371\pi\)
\(564\) 8.96569e10i 0.886069i
\(565\) −2.89082e11 −2.83679
\(566\) 6.09261e10i 0.593660i
\(567\) 9.32153e9i 0.0901893i
\(568\) −1.70246e10 −0.163563
\(569\) −4.56726e10 −0.435719 −0.217860 0.975980i \(-0.569907\pi\)
−0.217860 + 0.975980i \(0.569907\pi\)
\(570\) 8.05878e11 7.63431
\(571\) 1.77572e10i 0.167043i −0.996506 0.0835217i \(-0.973383\pi\)
0.996506 0.0835217i \(-0.0266168\pi\)
\(572\) −7.88020e10 −0.736128
\(573\) −2.52790e11 −2.34499
\(574\) 2.17800e10 0.200637
\(575\) −2.77906e11 −2.54229
\(576\) −2.30430e11 −2.09338
\(577\) 1.55926e11i 1.40675i 0.710821 + 0.703373i \(0.248323\pi\)
−0.710821 + 0.703373i \(0.751677\pi\)
\(578\) 3.28234e10i 0.294085i
\(579\) 5.62472e10i 0.500480i
\(580\) 4.08919e9 0.0361348
\(581\) 2.72098e10i 0.238792i
\(582\) 1.09508e10 0.0954454
\(583\) 1.50732e10 0.130476
\(584\) −2.62797e10 −0.225927
\(585\) 3.88394e11i 3.31626i
\(586\) 1.95654e11i 1.65920i
\(587\) 2.42355e10i 0.204127i −0.994778 0.102063i \(-0.967456\pi\)
0.994778 0.102063i \(-0.0325445\pi\)
\(588\) 1.87134e11i 1.56547i
\(589\) 1.48396e11i 1.23299i
\(590\) −5.85817e11 −4.83452
\(591\) 2.54954e11i 2.08983i
\(592\) 1.45885e11i 1.18774i
\(593\) 6.73194e10i 0.544404i 0.962240 + 0.272202i \(0.0877519\pi\)
−0.962240 + 0.272202i \(0.912248\pi\)
\(594\) 8.08889e10 0.649746
\(595\) 9.28859e10 0.741109
\(596\) 4.57390e10i 0.362495i
\(597\) 3.91988e11 3.08585
\(598\) 2.12827e11i 1.66426i
\(599\) 6.22767e10 0.483747 0.241874 0.970308i \(-0.422238\pi\)
0.241874 + 0.970308i \(0.422238\pi\)
\(600\) 1.73177e11 1.33624
\(601\) 1.57836e11i 1.20979i 0.796307 + 0.604893i \(0.206784\pi\)
−0.796307 + 0.604893i \(0.793216\pi\)
\(602\) 7.53800e10 + 3.95952e10i 0.573945 + 0.301479i
\(603\) 2.69407e11 2.03770
\(604\) 1.33254e10i 0.100123i
\(605\) 1.83758e11i 1.37159i
\(606\) −1.46985e11 −1.08989
\(607\) 1.00707e11i 0.741833i 0.928666 + 0.370917i \(0.120956\pi\)
−0.928666 + 0.370917i \(0.879044\pi\)
\(608\) 3.29595e11 2.41194
\(609\) 1.48682e9i 0.0108091i
\(610\) 2.86208e11i 2.06711i
\(611\) 7.33511e10 0.526310
\(612\) 2.32573e11 1.65788
\(613\) −1.80424e11 −1.27777 −0.638884 0.769303i \(-0.720604\pi\)
−0.638884 + 0.769303i \(0.720604\pi\)
\(614\) 2.93936e11i 2.06814i
\(615\) 1.33557e11 0.933608
\(616\) −1.06621e10 −0.0740490
\(617\) 3.85259e10 0.265835 0.132918 0.991127i \(-0.457565\pi\)
0.132918 + 0.991127i \(0.457565\pi\)
\(618\) 8.73254e10 0.598669
\(619\) −5.48744e9 −0.0373773 −0.0186886 0.999825i \(-0.505949\pi\)
−0.0186886 + 0.999825i \(0.505949\pi\)
\(620\) 2.47751e11i 1.67667i
\(621\) 1.19906e11i 0.806256i
\(622\) 3.53180e11i 2.35958i
\(623\) −2.54506e10 −0.168945
\(624\) 2.03439e11i 1.34182i
\(625\) 4.88351e11 3.20046
\(626\) −1.05731e10 −0.0688500
\(627\) −2.19960e11 −1.42322
\(628\) 2.44406e11i 1.57135i
\(629\) 2.26140e11i 1.44469i
\(630\) 2.95164e11i 1.87371i
\(631\) 1.07158e11i 0.675936i 0.941158 + 0.337968i \(0.109740\pi\)
−0.941158 + 0.337968i \(0.890260\pi\)
\(632\) 6.18908e10i 0.387934i
\(633\) −3.85295e10 −0.239982
\(634\) 4.03758e11i 2.49899i
\(635\) 4.92075e11i 3.02647i
\(636\) 7.82052e10i 0.477977i
\(637\) −1.53101e11 −0.929863
\(638\) −2.03353e9 −0.0122735
\(639\) 1.28639e11i 0.771561i
\(640\) 2.00759e11 1.19662
\(641\) 3.02938e10i 0.179441i 0.995967 + 0.0897203i \(0.0285973\pi\)
−0.995967 + 0.0897203i \(0.971403\pi\)
\(642\) −3.22488e11 −1.89834
\(643\) 5.55577e10 0.325013 0.162506 0.986707i \(-0.448042\pi\)
0.162506 + 0.986707i \(0.448042\pi\)
\(644\) 8.87726e10i 0.516102i
\(645\) 4.62236e11 + 2.42801e11i 2.67070 + 1.40285i
\(646\) −3.94802e11 −2.26699
\(647\) 2.27072e10i 0.129583i −0.997899 0.0647913i \(-0.979362\pi\)
0.997899 0.0647913i \(-0.0206382\pi\)
\(648\) 1.17767e10i 0.0667919i
\(649\) 1.59895e11 0.901274
\(650\) 7.95794e11i 4.45807i
\(651\) −9.00815e10 −0.501547
\(652\) 2.65629e11i 1.46989i
\(653\) 6.93373e10i 0.381341i 0.981654 + 0.190671i \(0.0610663\pi\)
−0.981654 + 0.190671i \(0.938934\pi\)
\(654\) 1.35188e11 0.738969
\(655\) −8.76164e10 −0.476015
\(656\) 4.22092e10 0.227925
\(657\) 1.98571e11i 1.06575i
\(658\) 5.57440e10 0.297368
\(659\) 7.72055e10 0.409361 0.204680 0.978829i \(-0.434384\pi\)
0.204680 + 0.978829i \(0.434384\pi\)
\(660\) −3.67228e11 −1.93535
\(661\) −1.37353e11 −0.719501 −0.359750 0.933049i \(-0.617138\pi\)
−0.359750 + 0.933049i \(0.617138\pi\)
\(662\) 2.90144e11 1.51071
\(663\) 3.15357e11i 1.63210i
\(664\) 3.43764e10i 0.176843i
\(665\) 2.75007e11i 1.40623i
\(666\) −7.18608e11 −3.65254
\(667\) 3.01440e9i 0.0152299i
\(668\) −1.89500e11 −0.951705
\(669\) −3.58102e11 −1.78773
\(670\) −7.63524e11 −3.78899
\(671\) 7.81188e10i 0.385359i
\(672\) 2.00075e11i 0.981108i
\(673\) 1.37895e11i 0.672184i −0.941829 0.336092i \(-0.890895\pi\)
0.941829 0.336092i \(-0.109105\pi\)
\(674\) 2.54524e11i 1.23336i
\(675\) 4.48346e11i 2.15972i
\(676\) −8.04364e10 −0.385182
\(677\) 2.93763e11i 1.39844i −0.714908 0.699218i \(-0.753532\pi\)
0.714908 0.699218i \(-0.246468\pi\)
\(678\) 7.45872e11i 3.52976i
\(679\) 3.73699e9i 0.0175810i
\(680\) −1.17351e11 −0.548846
\(681\) 1.19040e11 0.553483
\(682\) 1.23205e11i 0.569496i
\(683\) −1.66608e11 −0.765619 −0.382810 0.923827i \(-0.625044\pi\)
−0.382810 + 0.923827i \(0.625044\pi\)
\(684\) 6.88580e11i 3.14579i
\(685\) 4.54758e11 2.06547
\(686\) −2.59925e11 −1.17368
\(687\) 5.77875e11i 2.59422i
\(688\) 1.46085e11 + 7.67347e10i 0.652006 + 0.342482i
\(689\) 6.39821e10 0.283911
\(690\) 9.91803e11i 4.37552i
\(691\) 3.05698e11i 1.34085i 0.741977 + 0.670425i \(0.233888\pi\)
−0.741977 + 0.670425i \(0.766112\pi\)
\(692\) 4.51849e11 1.97047
\(693\) 8.05634e10i 0.349305i
\(694\) 1.16323e11 0.501452
\(695\) 1.53377e11i 0.657385i
\(696\) 1.87843e9i 0.00800492i
\(697\) −6.54298e10 −0.277233
\(698\) 3.82746e11 1.61246
\(699\) 1.32505e11 0.555041
\(700\) 3.31935e11i 1.38249i
\(701\) 2.10620e11 0.872221 0.436111 0.899893i \(-0.356356\pi\)
0.436111 + 0.899893i \(0.356356\pi\)
\(702\) 3.43354e11 1.41382
\(703\) 6.69534e11 2.74127
\(704\) −1.78248e11 −0.725663
\(705\) 3.41827e11 1.38372
\(706\) 3.60869e11i 1.45255i
\(707\) 5.01590e10i 0.200757i
\(708\) 8.29595e11i 3.30166i
\(709\) −3.74546e11 −1.48225 −0.741123 0.671369i \(-0.765707\pi\)
−0.741123 + 0.671369i \(0.765707\pi\)
\(710\) 3.64575e11i 1.43468i
\(711\) −4.67651e11 −1.82997
\(712\) 3.21539e10 0.125116
\(713\) −1.82633e11 −0.706676
\(714\) 2.39659e11i 0.922148i
\(715\) 3.00441e11i 1.14957i
\(716\) 1.35953e11i 0.517292i
\(717\) 5.95383e10i 0.225279i
\(718\) 3.62141e11i 1.36264i
\(719\) −7.82761e10 −0.292896 −0.146448 0.989218i \(-0.546784\pi\)
−0.146448 + 0.989218i \(0.546784\pi\)
\(720\) 5.72023e11i 2.12855i
\(721\) 2.98000e10i 0.110274i
\(722\) 7.64323e11i 2.81273i
\(723\) −3.08454e11 −1.12885
\(724\) −3.51305e11 −1.27859
\(725\) 1.12713e10i 0.0407965i
\(726\) −4.74122e11 −1.70665
\(727\) 3.82480e11i 1.36921i 0.728913 + 0.684606i \(0.240026\pi\)
−0.728913 + 0.684606i \(0.759974\pi\)
\(728\) −4.52580e10 −0.161127
\(729\) 4.60125e11 1.62917
\(730\) 5.62767e11i 1.98170i
\(731\) −2.26451e11 1.18949e11i −0.793057 0.416573i
\(732\) 4.05309e11 1.41170
\(733\) 1.33780e11i 0.463421i −0.972785 0.231711i \(-0.925568\pi\)
0.972785 0.231711i \(-0.0744322\pi\)
\(734\) 2.35308e11i 0.810686i
\(735\) −7.13470e11 −2.44470
\(736\) 4.05636e11i 1.38237i
\(737\) 2.08399e11 0.706360
\(738\) 2.07917e11i 0.700913i
\(739\) 1.57627e11i 0.528509i −0.964453 0.264254i \(-0.914874\pi\)
0.964453 0.264254i \(-0.0851259\pi\)
\(740\) 1.11780e12 3.72768
\(741\) −9.33676e11 −3.09687
\(742\) 4.86239e10 0.160411
\(743\) 1.29006e11i 0.423307i −0.977345 0.211654i \(-0.932115\pi\)
0.977345 0.211654i \(-0.0678848\pi\)
\(744\) 1.13808e11 0.371433
\(745\) −1.74385e11 −0.566088
\(746\) −6.38068e11 −2.06021
\(747\) −2.59751e11 −0.834208
\(748\) 1.79906e11 0.574699
\(749\) 1.10050e11i 0.349672i
\(750\) 2.28741e12i 7.22936i
\(751\) 2.48684e11i 0.781788i −0.920436 0.390894i \(-0.872166\pi\)
0.920436 0.390894i \(-0.127834\pi\)
\(752\) 1.08031e11 0.337813
\(753\) 8.57400e11i 2.66688i
\(754\) −8.63185e9 −0.0267066
\(755\) −5.08045e10 −0.156356
\(756\) 1.43217e11 0.438438
\(757\) 1.23839e11i 0.377117i −0.982062 0.188558i \(-0.939619\pi\)
0.982062 0.188558i \(-0.0603814\pi\)
\(758\) 3.73529e11i 1.13148i
\(759\) 2.70707e11i 0.815703i
\(760\) 3.47441e11i 1.04142i
\(761\) 2.24574e9i 0.00669608i −0.999994 0.00334804i \(-0.998934\pi\)
0.999994 0.00334804i \(-0.00106572\pi\)
\(762\) 1.26962e12 3.76578
\(763\) 4.61331e10i 0.136118i
\(764\) 6.12151e11i 1.79674i
\(765\) 8.86710e11i 2.58902i
\(766\) −7.04705e11 −2.04688
\(767\) 6.78717e11 1.96113
\(768\) 2.42177e11i 0.696125i
\(769\) −2.16341e10 −0.0618635 −0.0309317 0.999521i \(-0.509847\pi\)
−0.0309317 + 0.999521i \(0.509847\pi\)
\(770\) 2.28324e11i 0.649513i
\(771\) 6.87133e11 1.94457
\(772\) −1.36207e11 −0.383469
\(773\) 1.23331e11i 0.345425i −0.984972 0.172712i \(-0.944747\pi\)
0.984972 0.172712i \(-0.0552531\pi\)
\(774\) 3.77985e11 7.19595e11i 1.05320 2.00504i
\(775\) 6.82892e11 1.89298
\(776\) 4.72126e9i 0.0130200i
\(777\) 4.06431e11i 1.11507i
\(778\) −4.57914e11 −1.24987
\(779\) 1.93718e11i 0.526042i
\(780\) −1.55880e12 −4.21125
\(781\) 9.95086e10i 0.267459i
\(782\) 4.85888e11i