Properties

Label 177.9.c.a.58.10
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.10
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.71

$q$-expansion

\(f(q)\) \(=\) \(q-25.6289i q^{2} +46.7654 q^{3} -400.842 q^{4} -239.734 q^{5} -1198.55i q^{6} -1755.35 q^{7} +3712.14i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-25.6289i q^{2} +46.7654 q^{3} -400.842 q^{4} -239.734 q^{5} -1198.55i q^{6} -1755.35 q^{7} +3712.14i q^{8} +2187.00 q^{9} +6144.13i q^{10} +3302.81i q^{11} -18745.5 q^{12} +13138.8i q^{13} +44987.8i q^{14} -11211.3 q^{15} -7477.27 q^{16} +119793. q^{17} -56050.5i q^{18} +148304. q^{19} +96095.5 q^{20} -82089.8 q^{21} +84647.5 q^{22} +144769. i q^{23} +173600. i q^{24} -333153. q^{25} +336735. q^{26} +102276. q^{27} +703620. q^{28} +397853. q^{29} +287332. i q^{30} +1.82954e6i q^{31} +1.14194e6i q^{32} +154457. i q^{33} -3.07016e6i q^{34} +420818. q^{35} -876641. q^{36} -278533. i q^{37} -3.80086e6i q^{38} +614443. i q^{39} -889927. i q^{40} +1.92610e6 q^{41} +2.10387e6i q^{42} -3.71138e6i q^{43} -1.32390e6i q^{44} -524298. q^{45} +3.71028e6 q^{46} -4.04454e6i q^{47} -349677. q^{48} -2.68353e6 q^{49} +8.53834e6i q^{50} +5.60215e6 q^{51} -5.26660e6i q^{52} -1.28463e6 q^{53} -2.62122e6i q^{54} -791796. i q^{55} -6.51613e6i q^{56} +6.93547e6 q^{57} -1.01966e7i q^{58} +(3.67157e6 - 1.15477e7i) q^{59} +4.49394e6 q^{60} -2.00520e7i q^{61} +4.68892e7 q^{62} -3.83896e6 q^{63} +2.73526e7 q^{64} -3.14983e6i q^{65} +3.95857e6 q^{66} -6.13210e6i q^{67} -4.80179e7 q^{68} +6.77018e6i q^{69} -1.07851e7i q^{70} +3.64592e7 q^{71} +8.11846e6i q^{72} -1.88627e7i q^{73} -7.13849e6 q^{74} -1.55800e7 q^{75} -5.94463e7 q^{76} -5.79760e6i q^{77} +1.57475e7 q^{78} +7.26205e7 q^{79} +1.79256e6 q^{80} +4.78297e6 q^{81} -4.93639e7i q^{82} +5.12745e7i q^{83} +3.29050e7 q^{84} -2.87184e7 q^{85} -9.51187e7 q^{86} +1.86058e7 q^{87} -1.22605e7 q^{88} +4.51465e7i q^{89} +1.34372e7i q^{90} -2.30633e7i q^{91} -5.80296e7i q^{92} +8.55591e7i q^{93} -1.03657e8 q^{94} -3.55534e7 q^{95} +5.34034e7i q^{96} +6.88077e7i q^{97} +6.87761e7i q^{98} +7.22324e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.6289i 1.60181i −0.598793 0.800904i \(-0.704353\pi\)
0.598793 0.800904i \(-0.295647\pi\)
\(3\) 46.7654 0.577350
\(4\) −400.842 −1.56579
\(5\) −239.734 −0.383574 −0.191787 0.981437i \(-0.561428\pi\)
−0.191787 + 0.981437i \(0.561428\pi\)
\(6\) 1198.55i 0.924804i
\(7\) −1755.35 −0.731093 −0.365546 0.930793i \(-0.619118\pi\)
−0.365546 + 0.930793i \(0.619118\pi\)
\(8\) 3712.14i 0.906285i
\(9\) 2187.00 0.333333
\(10\) 6144.13i 0.614413i
\(11\) 3302.81i 0.225586i 0.993618 + 0.112793i \(0.0359797\pi\)
−0.993618 + 0.112793i \(0.964020\pi\)
\(12\) −18745.5 −0.904009
\(13\) 13138.8i 0.460027i 0.973187 + 0.230014i \(0.0738771\pi\)
−0.973187 + 0.230014i \(0.926123\pi\)
\(14\) 44987.8i 1.17107i
\(15\) −11211.3 −0.221457
\(16\) −7477.27 −0.114094
\(17\) 119793. 1.43428 0.717141 0.696928i \(-0.245450\pi\)
0.717141 + 0.696928i \(0.245450\pi\)
\(18\) 56050.5i 0.533936i
\(19\) 148304. 1.13799 0.568994 0.822342i \(-0.307333\pi\)
0.568994 + 0.822342i \(0.307333\pi\)
\(20\) 96095.5 0.600597
\(21\) −82089.8 −0.422097
\(22\) 84647.5 0.361346
\(23\) 144769.i 0.517327i 0.965968 + 0.258663i \(0.0832820\pi\)
−0.965968 + 0.258663i \(0.916718\pi\)
\(24\) 173600.i 0.523244i
\(25\) −333153. −0.852871
\(26\) 336735. 0.736876
\(27\) 102276. 0.192450
\(28\) 703620. 1.14474
\(29\) 397853. 0.562511 0.281255 0.959633i \(-0.409249\pi\)
0.281255 + 0.959633i \(0.409249\pi\)
\(30\) 287332.i 0.354731i
\(31\) 1.82954e6i 1.98105i 0.137337 + 0.990524i \(0.456146\pi\)
−0.137337 + 0.990524i \(0.543854\pi\)
\(32\) 1.14194e6i 1.08904i
\(33\) 154457.i 0.130242i
\(34\) 3.07016e6i 2.29745i
\(35\) 420818. 0.280429
\(36\) −876641. −0.521930
\(37\) 278533.i 0.148617i −0.997235 0.0743086i \(-0.976325\pi\)
0.997235 0.0743086i \(-0.0236750\pi\)
\(38\) 3.80086e6i 1.82284i
\(39\) 614443.i 0.265597i
\(40\) 889927.i 0.347628i
\(41\) 1.92610e6 0.681622 0.340811 0.940132i \(-0.389298\pi\)
0.340811 + 0.940132i \(0.389298\pi\)
\(42\) 2.10387e6i 0.676118i
\(43\) 3.71138e6i 1.08558i −0.839869 0.542790i \(-0.817368\pi\)
0.839869 0.542790i \(-0.182632\pi\)
\(44\) 1.32390e6i 0.353221i
\(45\) −524298. −0.127858
\(46\) 3.71028e6 0.828658
\(47\) 4.04454e6i 0.828853i −0.910083 0.414427i \(-0.863982\pi\)
0.910083 0.414427i \(-0.136018\pi\)
\(48\) −349677. −0.0658723
\(49\) −2.68353e6 −0.465503
\(50\) 8.53834e6i 1.36614i
\(51\) 5.60215e6 0.828083
\(52\) 5.26660e6i 0.720306i
\(53\) −1.28463e6 −0.162808 −0.0814038 0.996681i \(-0.525940\pi\)
−0.0814038 + 0.996681i \(0.525940\pi\)
\(54\) 2.62122e6i 0.308268i
\(55\) 791796.i 0.0865292i
\(56\) 6.51613e6i 0.662579i
\(57\) 6.93547e6 0.657017
\(58\) 1.01966e7i 0.901035i
\(59\) 3.67157e6 1.15477e7i 0.303000 0.952990i
\(60\) 4.49394e6 0.346755
\(61\) 2.00520e7i 1.44823i −0.689679 0.724115i \(-0.742248\pi\)
0.689679 0.724115i \(-0.257752\pi\)
\(62\) 4.68892e7 3.17326
\(63\) −3.83896e6 −0.243698
\(64\) 2.73526e7 1.63034
\(65\) 3.14983e6i 0.176455i
\(66\) 3.95857e6 0.208623
\(67\) 6.13210e6i 0.304306i −0.988357 0.152153i \(-0.951379\pi\)
0.988357 0.152153i \(-0.0486206\pi\)
\(68\) −4.80179e7 −2.24578
\(69\) 6.77018e6i 0.298679i
\(70\) 1.07851e7i 0.449193i
\(71\) 3.64592e7 1.43474 0.717372 0.696691i \(-0.245345\pi\)
0.717372 + 0.696691i \(0.245345\pi\)
\(72\) 8.11846e6i 0.302095i
\(73\) 1.88627e7i 0.664221i −0.943240 0.332111i \(-0.892239\pi\)
0.943240 0.332111i \(-0.107761\pi\)
\(74\) −7.13849e6 −0.238056
\(75\) −1.55800e7 −0.492405
\(76\) −5.94463e7 −1.78185
\(77\) 5.79760e6i 0.164925i
\(78\) 1.57475e7 0.425435
\(79\) 7.26205e7 1.86445 0.932225 0.361879i \(-0.117865\pi\)
0.932225 + 0.361879i \(0.117865\pi\)
\(80\) 1.79256e6 0.0437636
\(81\) 4.78297e6 0.111111
\(82\) 4.93639e7i 1.09183i
\(83\) 5.12745e7i 1.08041i 0.841533 + 0.540205i \(0.181653\pi\)
−0.841533 + 0.540205i \(0.818347\pi\)
\(84\) 3.29050e7 0.660914
\(85\) −2.87184e7 −0.550154
\(86\) −9.51187e7 −1.73889
\(87\) 1.86058e7 0.324766
\(88\) −1.22605e7 −0.204446
\(89\) 4.51465e7i 0.719555i 0.933038 + 0.359778i \(0.117147\pi\)
−0.933038 + 0.359778i \(0.882853\pi\)
\(90\) 1.34372e7i 0.204804i
\(91\) 2.30633e7i 0.336323i
\(92\) 5.80296e7i 0.810024i
\(93\) 8.55591e7i 1.14376i
\(94\) −1.03657e8 −1.32766
\(95\) −3.55534e7 −0.436503
\(96\) 5.34034e7i 0.628759i
\(97\) 6.88077e7i 0.777230i 0.921400 + 0.388615i \(0.127046\pi\)
−0.921400 + 0.388615i \(0.872954\pi\)
\(98\) 6.87761e7i 0.745647i
\(99\) 7.22324e6i 0.0751954i
\(100\) 1.33542e8 1.33542
\(101\) 1.23394e8i 1.18579i −0.805280 0.592895i \(-0.797985\pi\)
0.805280 0.592895i \(-0.202015\pi\)
\(102\) 1.43577e8i 1.32643i
\(103\) 4.13868e7i 0.367716i −0.982953 0.183858i \(-0.941141\pi\)
0.982953 0.183858i \(-0.0588587\pi\)
\(104\) −4.87733e7 −0.416916
\(105\) 1.96797e7 0.161906
\(106\) 3.29237e7i 0.260787i
\(107\) −1.55501e8 −1.18631 −0.593156 0.805088i \(-0.702118\pi\)
−0.593156 + 0.805088i \(0.702118\pi\)
\(108\) −4.09965e7 −0.301336
\(109\) 1.54559e8i 1.09493i −0.836827 0.547467i \(-0.815592\pi\)
0.836827 0.547467i \(-0.184408\pi\)
\(110\) −2.02929e7 −0.138603
\(111\) 1.30257e7i 0.0858042i
\(112\) 1.31253e7 0.0834134
\(113\) 6.02902e7i 0.369771i 0.982760 + 0.184885i \(0.0591914\pi\)
−0.982760 + 0.184885i \(0.940809\pi\)
\(114\) 1.77749e8i 1.05242i
\(115\) 3.47061e7i 0.198433i
\(116\) −1.59476e8 −0.880773
\(117\) 2.87347e7i 0.153342i
\(118\) −2.95956e8 9.40983e7i −1.52651 0.485349i
\(119\) −2.10279e8 −1.04859
\(120\) 4.16178e7i 0.200703i
\(121\) 2.03450e8 0.949111
\(122\) −5.13911e8 −2.31979
\(123\) 9.00749e7 0.393535
\(124\) 7.33356e8i 3.10190i
\(125\) 1.73514e8 0.710714
\(126\) 9.83884e7i 0.390357i
\(127\) −5.45221e7 −0.209584 −0.104792 0.994494i \(-0.533418\pi\)
−0.104792 + 0.994494i \(0.533418\pi\)
\(128\) 4.08680e8i 1.52245i
\(129\) 1.73564e8i 0.626760i
\(130\) −8.07267e7 −0.282647
\(131\) 1.30574e8i 0.443375i −0.975118 0.221687i \(-0.928844\pi\)
0.975118 0.221687i \(-0.0711565\pi\)
\(132\) 6.19129e7i 0.203932i
\(133\) −2.60325e8 −0.831974
\(134\) −1.57159e8 −0.487440
\(135\) −2.45190e7 −0.0738189
\(136\) 4.44688e8i 1.29987i
\(137\) 2.49809e8 0.709131 0.354566 0.935031i \(-0.384629\pi\)
0.354566 + 0.935031i \(0.384629\pi\)
\(138\) 1.73513e8 0.478426
\(139\) −1.91233e8 −0.512277 −0.256138 0.966640i \(-0.582450\pi\)
−0.256138 + 0.966640i \(0.582450\pi\)
\(140\) −1.68682e8 −0.439092
\(141\) 1.89144e8i 0.478539i
\(142\) 9.34411e8i 2.29818i
\(143\) −4.33951e7 −0.103776
\(144\) −1.63528e7 −0.0380314
\(145\) −9.53790e7 −0.215765
\(146\) −4.83431e8 −1.06395
\(147\) −1.25496e8 −0.268758
\(148\) 1.11648e8i 0.232703i
\(149\) 8.24265e8i 1.67233i 0.548478 + 0.836165i \(0.315207\pi\)
−0.548478 + 0.836165i \(0.684793\pi\)
\(150\) 3.99299e8i 0.788738i
\(151\) 5.40833e8i 1.04029i 0.854077 + 0.520147i \(0.174123\pi\)
−0.854077 + 0.520147i \(0.825877\pi\)
\(152\) 5.50524e8i 1.03134i
\(153\) 2.61987e8 0.478094
\(154\) −1.48586e8 −0.264177
\(155\) 4.38603e8i 0.759880i
\(156\) 2.46295e8i 0.415869i
\(157\) 1.06979e9i 1.76076i 0.474272 + 0.880379i \(0.342711\pi\)
−0.474272 + 0.880379i \(0.657289\pi\)
\(158\) 1.86119e9i 2.98649i
\(159\) −6.00762e7 −0.0939970
\(160\) 2.73763e8i 0.417729i
\(161\) 2.54121e8i 0.378214i
\(162\) 1.22582e8i 0.177979i
\(163\) 1.06110e9 1.50316 0.751579 0.659643i \(-0.229293\pi\)
0.751579 + 0.659643i \(0.229293\pi\)
\(164\) −7.72062e8 −1.06728
\(165\) 3.70286e7i 0.0499576i
\(166\) 1.31411e9 1.73061
\(167\) 6.71744e6 0.00863650 0.00431825 0.999991i \(-0.498625\pi\)
0.00431825 + 0.999991i \(0.498625\pi\)
\(168\) 3.04729e8i 0.382540i
\(169\) 6.43101e8 0.788375
\(170\) 7.36022e8i 0.881241i
\(171\) 3.24340e8 0.379329
\(172\) 1.48768e9i 1.69979i
\(173\) 1.61132e9i 1.79887i 0.437060 + 0.899433i \(0.356020\pi\)
−0.437060 + 0.899433i \(0.643980\pi\)
\(174\) 4.76846e8i 0.520213i
\(175\) 5.84801e8 0.623528
\(176\) 2.46960e7i 0.0257381i
\(177\) 1.71702e8 5.40034e8i 0.174937 0.550209i
\(178\) 1.15706e9 1.15259
\(179\) 4.00114e7i 0.0389737i −0.999810 0.0194869i \(-0.993797\pi\)
0.999810 0.0194869i \(-0.00620325\pi\)
\(180\) 2.10161e8 0.200199
\(181\) 7.36437e8 0.686153 0.343077 0.939307i \(-0.388531\pi\)
0.343077 + 0.939307i \(0.388531\pi\)
\(182\) −5.91088e8 −0.538725
\(183\) 9.37738e8i 0.836136i
\(184\) −5.37404e8 −0.468845
\(185\) 6.67737e7i 0.0570058i
\(186\) 2.19279e9 1.83208
\(187\) 3.95652e8i 0.323555i
\(188\) 1.62122e9i 1.29781i
\(189\) −1.79530e8 −0.140699
\(190\) 9.11196e8i 0.699194i
\(191\) 1.70160e9i 1.27857i −0.768971 0.639283i \(-0.779231\pi\)
0.768971 0.639283i \(-0.220769\pi\)
\(192\) 1.27915e9 0.941278
\(193\) 2.42920e9 1.75079 0.875394 0.483410i \(-0.160602\pi\)
0.875394 + 0.483410i \(0.160602\pi\)
\(194\) 1.76347e9 1.24497
\(195\) 1.47303e8i 0.101876i
\(196\) 1.07567e9 0.728880
\(197\) −2.28650e9 −1.51812 −0.759059 0.651022i \(-0.774341\pi\)
−0.759059 + 0.651022i \(0.774341\pi\)
\(198\) 1.85124e8 0.120449
\(199\) 2.26762e9 1.44597 0.722983 0.690865i \(-0.242770\pi\)
0.722983 + 0.690865i \(0.242770\pi\)
\(200\) 1.23671e9i 0.772944i
\(201\) 2.86770e8i 0.175691i
\(202\) −3.16245e9 −1.89941
\(203\) −6.98373e8 −0.411248
\(204\) −2.24558e9 −1.29660
\(205\) −4.61752e8 −0.261453
\(206\) −1.06070e9 −0.589011
\(207\) 3.16610e8i 0.172442i
\(208\) 9.82427e7i 0.0524864i
\(209\) 4.89819e8i 0.256714i
\(210\) 5.04370e8i 0.259342i
\(211\) 1.01729e9i 0.513234i 0.966513 + 0.256617i \(0.0826080\pi\)
−0.966513 + 0.256617i \(0.917392\pi\)
\(212\) 5.14934e8 0.254922
\(213\) 1.70503e9 0.828349
\(214\) 3.98533e9i 1.90024i
\(215\) 8.89744e8i 0.416401i
\(216\) 3.79663e8i 0.174415i
\(217\) 3.21149e9i 1.44833i
\(218\) −3.96118e9 −1.75387
\(219\) 8.82122e8i 0.383488i
\(220\) 3.17385e8i 0.135486i
\(221\) 1.57394e9i 0.659809i
\(222\) −3.33834e8 −0.137442
\(223\) 3.43376e9 1.38852 0.694258 0.719727i \(-0.255733\pi\)
0.694258 + 0.719727i \(0.255733\pi\)
\(224\) 2.00451e9i 0.796191i
\(225\) −7.28605e8 −0.284290
\(226\) 1.54517e9 0.592302
\(227\) 8.60197e8i 0.323962i −0.986794 0.161981i \(-0.948212\pi\)
0.986794 0.161981i \(-0.0517884\pi\)
\(228\) −2.78003e9 −1.02875
\(229\) 1.87481e9i 0.681734i −0.940112 0.340867i \(-0.889279\pi\)
0.940112 0.340867i \(-0.110721\pi\)
\(230\) −8.89480e8 −0.317852
\(231\) 2.71127e8i 0.0952192i
\(232\) 1.47689e9i 0.509795i
\(233\) 2.13434e9i 0.724167i −0.932146 0.362084i \(-0.882065\pi\)
0.932146 0.362084i \(-0.117935\pi\)
\(234\) 7.36438e8 0.245625
\(235\) 9.69614e8i 0.317927i
\(236\) −1.47172e9 + 4.62881e9i −0.474435 + 1.49218i
\(237\) 3.39612e9 1.07644
\(238\) 5.38922e9i 1.67965i
\(239\) −1.40442e9 −0.430434 −0.215217 0.976566i \(-0.569046\pi\)
−0.215217 + 0.976566i \(0.569046\pi\)
\(240\) 8.38296e7 0.0252669
\(241\) −2.58892e9 −0.767452 −0.383726 0.923447i \(-0.625359\pi\)
−0.383726 + 0.923447i \(0.625359\pi\)
\(242\) 5.21421e9i 1.52029i
\(243\) 2.23677e8 0.0641500
\(244\) 8.03767e9i 2.26762i
\(245\) 6.43334e8 0.178555
\(246\) 2.30852e9i 0.630367i
\(247\) 1.94854e9i 0.523505i
\(248\) −6.79152e9 −1.79540
\(249\) 2.39787e9i 0.623775i
\(250\) 4.44698e9i 1.13843i
\(251\) 3.85692e9 0.971731 0.485866 0.874033i \(-0.338504\pi\)
0.485866 + 0.874033i \(0.338504\pi\)
\(252\) 1.53882e9 0.381579
\(253\) −4.78145e8 −0.116702
\(254\) 1.39734e9i 0.335713i
\(255\) −1.34303e9 −0.317632
\(256\) −3.47177e9 −0.808335
\(257\) 7.36020e9 1.68716 0.843582 0.537000i \(-0.180443\pi\)
0.843582 + 0.537000i \(0.180443\pi\)
\(258\) −4.44826e9 −1.00395
\(259\) 4.88923e8i 0.108653i
\(260\) 1.26258e9i 0.276291i
\(261\) 8.70105e8 0.187504
\(262\) −3.34647e9 −0.710201
\(263\) 5.56299e9 1.16275 0.581373 0.813637i \(-0.302516\pi\)
0.581373 + 0.813637i \(0.302516\pi\)
\(264\) −5.73367e8 −0.118037
\(265\) 3.07970e8 0.0624489
\(266\) 6.67186e9i 1.33266i
\(267\) 2.11129e9i 0.415436i
\(268\) 2.45800e9i 0.476479i
\(269\) 1.88061e9i 0.359162i 0.983743 + 0.179581i \(0.0574741\pi\)
−0.983743 + 0.179581i \(0.942526\pi\)
\(270\) 6.28396e8i 0.118244i
\(271\) −5.55098e9 −1.02918 −0.514592 0.857435i \(-0.672056\pi\)
−0.514592 + 0.857435i \(0.672056\pi\)
\(272\) −8.95722e8 −0.163643
\(273\) 1.07856e9i 0.194176i
\(274\) 6.40235e9i 1.13589i
\(275\) 1.10034e9i 0.192396i
\(276\) 2.71377e9i 0.467668i
\(277\) −7.43367e9 −1.26265 −0.631327 0.775517i \(-0.717489\pi\)
−0.631327 + 0.775517i \(0.717489\pi\)
\(278\) 4.90111e9i 0.820569i
\(279\) 4.00120e9i 0.660350i
\(280\) 1.56214e9i 0.254148i
\(281\) 2.25008e9 0.360888 0.180444 0.983585i \(-0.442247\pi\)
0.180444 + 0.983585i \(0.442247\pi\)
\(282\) −4.84757e9 −0.766527
\(283\) 1.89174e9i 0.294928i −0.989067 0.147464i \(-0.952889\pi\)
0.989067 0.147464i \(-0.0471111\pi\)
\(284\) −1.46144e10 −2.24650
\(285\) −1.66267e9 −0.252015
\(286\) 1.11217e9i 0.166229i
\(287\) −3.38099e9 −0.498329
\(288\) 2.49743e9i 0.363014i
\(289\) 7.37453e9 1.05717
\(290\) 2.44446e9i 0.345614i
\(291\) 3.21782e9i 0.448734i
\(292\) 7.56097e9i 1.04003i
\(293\) 2.55240e9 0.346320 0.173160 0.984894i \(-0.444602\pi\)
0.173160 + 0.984894i \(0.444602\pi\)
\(294\) 3.21634e9i 0.430499i
\(295\) −8.80199e8 + 2.76838e9i −0.116223 + 0.365543i
\(296\) 1.03395e9 0.134690
\(297\) 3.37798e8i 0.0434141i
\(298\) 2.11250e10 2.67875
\(299\) −1.90210e9 −0.237984
\(300\) 6.24512e9 0.771002
\(301\) 6.51479e9i 0.793660i
\(302\) 1.38610e10 1.66635
\(303\) 5.77056e9i 0.684616i
\(304\) −1.10891e9 −0.129838
\(305\) 4.80714e9i 0.555504i
\(306\) 6.71444e9i 0.765815i
\(307\) 8.22450e9 0.925883 0.462942 0.886389i \(-0.346794\pi\)
0.462942 + 0.886389i \(0.346794\pi\)
\(308\) 2.32392e9i 0.258237i
\(309\) 1.93547e9i 0.212301i
\(310\) −1.12409e10 −1.21718
\(311\) −4.06228e9 −0.434239 −0.217119 0.976145i \(-0.569666\pi\)
−0.217119 + 0.976145i \(0.569666\pi\)
\(312\) −2.28090e9 −0.240707
\(313\) 1.18792e9i 0.123768i −0.998083 0.0618840i \(-0.980289\pi\)
0.998083 0.0618840i \(-0.0197109\pi\)
\(314\) 2.74175e10 2.82039
\(315\) 9.20329e8 0.0934762
\(316\) −2.91093e10 −2.91934
\(317\) −4.81904e9 −0.477225 −0.238613 0.971115i \(-0.576693\pi\)
−0.238613 + 0.971115i \(0.576693\pi\)
\(318\) 1.53969e9i 0.150565i
\(319\) 1.31403e9i 0.126895i
\(320\) −6.55735e9 −0.625358
\(321\) −7.27207e9 −0.684917
\(322\) −6.51285e9 −0.605826
\(323\) 1.77657e10 1.63220
\(324\) −1.91721e9 −0.173977
\(325\) 4.37724e9i 0.392344i
\(326\) 2.71948e10i 2.40777i
\(327\) 7.22801e9i 0.632161i
\(328\) 7.14997e9i 0.617744i
\(329\) 7.09960e9i 0.605969i
\(330\) −9.49004e8 −0.0800225
\(331\) −7.42414e9 −0.618492 −0.309246 0.950982i \(-0.600077\pi\)
−0.309246 + 0.950982i \(0.600077\pi\)
\(332\) 2.05530e10i 1.69170i
\(333\) 6.09151e8i 0.0495391i
\(334\) 1.72161e8i 0.0138340i
\(335\) 1.47007e9i 0.116724i
\(336\) 6.13807e8 0.0481587
\(337\) 1.50440e10i 1.16639i −0.812332 0.583196i \(-0.801802\pi\)
0.812332 0.583196i \(-0.198198\pi\)
\(338\) 1.64820e10i 1.26282i
\(339\) 2.81949e9i 0.213487i
\(340\) 1.15115e10 0.861425
\(341\) −6.04262e9 −0.446898
\(342\) 8.31249e9i 0.607612i
\(343\) 1.48298e10 1.07142
\(344\) 1.37772e10 0.983845
\(345\) 1.62304e9i 0.114565i
\(346\) 4.12965e10 2.88144
\(347\) 1.82555e10i 1.25915i −0.776941 0.629573i \(-0.783230\pi\)
0.776941 0.629573i \(-0.216770\pi\)
\(348\) −7.45797e9 −0.508515
\(349\) 3.56777e9i 0.240489i −0.992744 0.120245i \(-0.961632\pi\)
0.992744 0.120245i \(-0.0383679\pi\)
\(350\) 1.49878e10i 0.998772i
\(351\) 1.34379e9i 0.0885323i
\(352\) −3.77162e9 −0.245673
\(353\) 4.28882e9i 0.276210i 0.990418 + 0.138105i \(0.0441011\pi\)
−0.990418 + 0.138105i \(0.955899\pi\)
\(354\) −1.38405e10 4.40054e9i −0.881330 0.280216i
\(355\) −8.74052e9 −0.550331
\(356\) 1.80966e10i 1.12667i
\(357\) −9.83376e9 −0.605406
\(358\) −1.02545e9 −0.0624284
\(359\) −6.19358e9 −0.372876 −0.186438 0.982467i \(-0.559694\pi\)
−0.186438 + 0.982467i \(0.559694\pi\)
\(360\) 1.94627e9i 0.115876i
\(361\) 5.01040e9 0.295015
\(362\) 1.88741e10i 1.09909i
\(363\) 9.51443e9 0.547969
\(364\) 9.24475e9i 0.526611i
\(365\) 4.52203e9i 0.254778i
\(366\) −2.40332e10 −1.33933
\(367\) 2.89548e10i 1.59609i 0.602599 + 0.798044i \(0.294132\pi\)
−0.602599 + 0.798044i \(0.705868\pi\)
\(368\) 1.08248e9i 0.0590239i
\(369\) 4.21238e9 0.227207
\(370\) 1.71134e9 0.0913123
\(371\) 2.25498e9 0.119028
\(372\) 3.42957e10i 1.79089i
\(373\) 2.97339e10 1.53609 0.768045 0.640395i \(-0.221230\pi\)
0.768045 + 0.640395i \(0.221230\pi\)
\(374\) 1.01401e10 0.518272
\(375\) 8.11445e9 0.410331
\(376\) 1.50139e10 0.751177
\(377\) 5.22733e9i 0.258770i
\(378\) 4.60117e9i 0.225373i
\(379\) −2.01521e10 −0.976707 −0.488353 0.872646i \(-0.662402\pi\)
−0.488353 + 0.872646i \(0.662402\pi\)
\(380\) 1.42513e10 0.683471
\(381\) −2.54975e9 −0.121003
\(382\) −4.36101e10 −2.04802
\(383\) 1.58914e10 0.738529 0.369265 0.929324i \(-0.379610\pi\)
0.369265 + 0.929324i \(0.379610\pi\)
\(384\) 1.91121e10i 0.878989i
\(385\) 1.38988e9i 0.0632608i
\(386\) 6.22577e10i 2.80443i
\(387\) 8.11679e9i 0.361860i
\(388\) 2.75810e10i 1.21698i
\(389\) 2.81843e10 1.23086 0.615431 0.788191i \(-0.288982\pi\)
0.615431 + 0.788191i \(0.288982\pi\)
\(390\) −3.77522e9 −0.163186
\(391\) 1.73423e10i 0.741992i
\(392\) 9.96166e9i 0.421879i
\(393\) 6.10634e9i 0.255983i
\(394\) 5.86004e10i 2.43173i
\(395\) −1.74096e10 −0.715155
\(396\) 2.89538e9i 0.117740i
\(397\) 3.92674e10i 1.58078i 0.612607 + 0.790388i \(0.290121\pi\)
−0.612607 + 0.790388i \(0.709879\pi\)
\(398\) 5.81167e10i 2.31616i
\(399\) −1.21742e10 −0.480341
\(400\) 2.49107e9 0.0973075
\(401\) 1.00645e10i 0.389239i −0.980879 0.194619i \(-0.937653\pi\)
0.980879 0.194619i \(-0.0623471\pi\)
\(402\) −7.34961e9 −0.281423
\(403\) −2.40380e10 −0.911337
\(404\) 4.94614e10i 1.85670i
\(405\) −1.14664e9 −0.0426194
\(406\) 1.78986e10i 0.658740i
\(407\) 9.19940e8 0.0335260
\(408\) 2.07960e10i 0.750480i
\(409\) 1.66826e10i 0.596171i −0.954539 0.298085i \(-0.903652\pi\)
0.954539 0.298085i \(-0.0963480\pi\)
\(410\) 1.18342e10i 0.418797i
\(411\) 1.16824e10 0.409417
\(412\) 1.65896e10i 0.575766i
\(413\) −6.44490e9 + 2.02704e10i −0.221521 + 0.696725i
\(414\) 8.11438e9 0.276219
\(415\) 1.22922e10i 0.414418i
\(416\) −1.50038e10 −0.500989
\(417\) −8.94310e9 −0.295763
\(418\) 1.25535e10 0.411207
\(419\) 1.14293e9i 0.0370820i 0.999828 + 0.0185410i \(0.00590212\pi\)
−0.999828 + 0.0185410i \(0.994098\pi\)
\(420\) −7.88846e9 −0.253510
\(421\) 2.00529e10i 0.638334i 0.947698 + 0.319167i \(0.103403\pi\)
−0.947698 + 0.319167i \(0.896597\pi\)
\(422\) 2.60721e10 0.822103
\(423\) 8.84541e9i 0.276284i
\(424\) 4.76873e9i 0.147550i
\(425\) −3.99093e10 −1.22326
\(426\) 4.36981e10i 1.32686i
\(427\) 3.51983e10i 1.05879i
\(428\) 6.23314e10 1.85751
\(429\) −2.02939e9 −0.0599150
\(430\) 2.28032e10 0.666994
\(431\) 3.68452e10i 1.06776i 0.845562 + 0.533878i \(0.179266\pi\)
−0.845562 + 0.533878i \(0.820734\pi\)
\(432\) −7.64744e8 −0.0219574
\(433\) −1.93863e10 −0.551498 −0.275749 0.961230i \(-0.588926\pi\)
−0.275749 + 0.961230i \(0.588926\pi\)
\(434\) −8.23071e10 −2.31995
\(435\) −4.46043e9 −0.124572
\(436\) 6.19537e10i 1.71444i
\(437\) 2.14698e10i 0.588711i
\(438\) −2.26078e10 −0.614275
\(439\) −3.11626e10 −0.839025 −0.419513 0.907750i \(-0.637799\pi\)
−0.419513 + 0.907750i \(0.637799\pi\)
\(440\) 2.93926e9 0.0784201
\(441\) −5.86889e9 −0.155168
\(442\) 4.03383e10 1.05689
\(443\) 6.59173e9i 0.171153i 0.996332 + 0.0855766i \(0.0272732\pi\)
−0.996332 + 0.0855766i \(0.972727\pi\)
\(444\) 5.22124e9i 0.134351i
\(445\) 1.08232e10i 0.276003i
\(446\) 8.80036e10i 2.22413i
\(447\) 3.85471e10i 0.965520i
\(448\) −4.80135e10 −1.19193
\(449\) −4.41656e10 −1.08667 −0.543336 0.839515i \(-0.682839\pi\)
−0.543336 + 0.839515i \(0.682839\pi\)
\(450\) 1.86734e10i 0.455378i
\(451\) 6.36155e9i 0.153765i
\(452\) 2.41668e10i 0.578983i
\(453\) 2.52923e10i 0.600614i
\(454\) −2.20459e10 −0.518925
\(455\) 5.52906e9i 0.129005i
\(456\) 2.57455e10i 0.595445i
\(457\) 4.56812e10i 1.04730i −0.851933 0.523651i \(-0.824569\pi\)
0.851933 0.523651i \(-0.175431\pi\)
\(458\) −4.80493e10 −1.09201
\(459\) 1.22519e10 0.276028
\(460\) 1.39117e10i 0.310705i
\(461\) −1.89312e10 −0.419156 −0.209578 0.977792i \(-0.567209\pi\)
−0.209578 + 0.977792i \(0.567209\pi\)
\(462\) −6.94869e9 −0.152523
\(463\) 1.11150e10i 0.241872i −0.992660 0.120936i \(-0.961410\pi\)
0.992660 0.120936i \(-0.0385897\pi\)
\(464\) −2.97486e9 −0.0641792
\(465\) 2.05114e10i 0.438717i
\(466\) −5.47007e10 −1.15998
\(467\) 2.77925e10i 0.584332i 0.956368 + 0.292166i \(0.0943760\pi\)
−0.956368 + 0.292166i \(0.905624\pi\)
\(468\) 1.15181e10i 0.240102i
\(469\) 1.07640e10i 0.222476i
\(470\) 2.48502e10 0.509258
\(471\) 5.00291e10i 1.01657i
\(472\) 4.28668e10 + 1.36294e10i 0.863681 + 0.274605i
\(473\) 1.22580e10 0.244892
\(474\) 8.70390e10i 1.72425i
\(475\) −4.94077e10 −0.970556
\(476\) 8.42885e10 1.64188
\(477\) −2.80949e9 −0.0542692
\(478\) 3.59939e10i 0.689473i
\(479\) −8.70053e10 −1.65274 −0.826368 0.563130i \(-0.809597\pi\)
−0.826368 + 0.563130i \(0.809597\pi\)
\(480\) 1.28026e10i 0.241176i
\(481\) 3.65960e9 0.0683680
\(482\) 6.63514e10i 1.22931i
\(483\) 1.18841e10i 0.218362i
\(484\) −8.15514e10 −1.48611
\(485\) 1.64955e10i 0.298126i
\(486\) 5.73261e9i 0.102756i
\(487\) 1.01454e11 1.80365 0.901825 0.432101i \(-0.142228\pi\)
0.901825 + 0.432101i \(0.142228\pi\)
\(488\) 7.44358e10 1.31251
\(489\) 4.96226e10 0.867848
\(490\) 1.64880e10i 0.286011i
\(491\) −3.52846e10 −0.607099 −0.303549 0.952816i \(-0.598172\pi\)
−0.303549 + 0.952816i \(0.598172\pi\)
\(492\) −3.61058e10 −0.616192
\(493\) 4.76599e10 0.806800
\(494\) 4.99389e10 0.838555
\(495\) 1.73166e9i 0.0288431i
\(496\) 1.36800e10i 0.226026i
\(497\) −6.39989e10 −1.04893
\(498\) 6.14548e10 0.999169
\(499\) 8.78804e10 1.41739 0.708696 0.705514i \(-0.249284\pi\)
0.708696 + 0.705514i \(0.249284\pi\)
\(500\) −6.95517e10 −1.11283
\(501\) 3.14144e8 0.00498629
\(502\) 9.88488e10i 1.55653i
\(503\) 1.18462e11i 1.85057i 0.379269 + 0.925287i \(0.376176\pi\)
−0.379269 + 0.925287i \(0.623824\pi\)
\(504\) 1.42508e10i 0.220860i
\(505\) 2.95817e10i 0.454839i
\(506\) 1.22543e10i 0.186934i
\(507\) 3.00749e10 0.455168
\(508\) 2.18548e10 0.328164
\(509\) 8.56499e10i 1.27601i −0.770030 0.638007i \(-0.779759\pi\)
0.770030 0.638007i \(-0.220241\pi\)
\(510\) 3.44203e10i 0.508785i
\(511\) 3.31107e10i 0.485607i
\(512\) 1.56443e10i 0.227655i
\(513\) 1.51679e10 0.219006
\(514\) 1.88634e11i 2.70251i
\(515\) 9.92183e9i 0.141047i
\(516\) 6.95718e10i 0.981373i
\(517\) 1.33583e10 0.186978
\(518\) 1.25306e10 0.174041
\(519\) 7.53542e10i 1.03858i
\(520\) 1.16926e10 0.159918
\(521\) −1.11648e11 −1.51530 −0.757652 0.652658i \(-0.773654\pi\)
−0.757652 + 0.652658i \(0.773654\pi\)
\(522\) 2.22999e10i 0.300345i
\(523\) −7.64824e9 −0.102224 −0.0511122 0.998693i \(-0.516277\pi\)
−0.0511122 + 0.998693i \(0.516277\pi\)
\(524\) 5.23395e10i 0.694231i
\(525\) 2.73484e10 0.359994
\(526\) 1.42573e11i 1.86250i
\(527\) 2.19166e11i 2.84138i
\(528\) 1.15492e9i 0.0148599i
\(529\) 5.73529e10 0.732373
\(530\) 7.89293e9i 0.100031i
\(531\) 8.02972e9 2.52549e10i 0.101000 0.317663i
\(532\) 1.04349e11 1.30270
\(533\) 2.53068e10i 0.313565i
\(534\) 5.41102e10 0.665448
\(535\) 3.72789e10 0.455039
\(536\) 2.27633e10 0.275788
\(537\) 1.87115e9i 0.0225015i
\(538\) 4.81980e10 0.575308
\(539\) 8.86320e9i 0.105011i
\(540\) 9.82825e9 0.115585
\(541\) 2.00200e10i 0.233709i 0.993149 + 0.116855i \(0.0372811\pi\)
−0.993149 + 0.116855i \(0.962719\pi\)
\(542\) 1.42266e11i 1.64855i
\(543\) 3.44397e10 0.396151
\(544\) 1.36796e11i 1.56199i
\(545\) 3.70530e10i 0.419989i
\(546\) −2.76425e10 −0.311033
\(547\) −4.77890e9 −0.0533800 −0.0266900 0.999644i \(-0.508497\pi\)
−0.0266900 + 0.999644i \(0.508497\pi\)
\(548\) −1.00134e11 −1.11035
\(549\) 4.38537e10i 0.482744i
\(550\) −2.82005e10 −0.308181
\(551\) 5.90031e10 0.640130
\(552\) −2.51319e10 −0.270688
\(553\) −1.27475e11 −1.36309
\(554\) 1.90517e11i 2.02253i
\(555\) 3.12270e9i 0.0329123i
\(556\) 7.66544e10 0.802117
\(557\) 2.70838e10 0.281378 0.140689 0.990054i \(-0.455068\pi\)
0.140689 + 0.990054i \(0.455068\pi\)
\(558\) 1.02547e11 1.05775
\(559\) 4.87633e10 0.499396
\(560\) −3.14657e9 −0.0319952
\(561\) 1.85028e10i 0.186804i
\(562\) 5.76671e10i 0.578073i
\(563\) 9.90305e10i 0.985678i 0.870120 + 0.492839i \(0.164041\pi\)
−0.870120 + 0.492839i \(0.835959\pi\)
\(564\) 7.58170e10i 0.749291i
\(565\) 1.44536e10i 0.141835i
\(566\) −4.84834e10 −0.472419
\(567\) −8.39580e9 −0.0812325
\(568\) 1.35342e11i 1.30029i
\(569\) 2.36985e10i 0.226085i −0.993590 0.113042i \(-0.963940\pi\)
0.993590 0.113042i \(-0.0360596\pi\)
\(570\) 4.26124e10i 0.403680i
\(571\) 1.46131e11i 1.37467i −0.726341 0.687334i \(-0.758781\pi\)
0.726341 0.687334i \(-0.241219\pi\)
\(572\) 1.73946e10 0.162491
\(573\) 7.95758e10i 0.738181i
\(574\) 8.66512e10i 0.798228i
\(575\) 4.82302e10i 0.441213i
\(576\) 5.98201e10 0.543447
\(577\) −5.60882e10 −0.506021 −0.253011 0.967464i \(-0.581421\pi\)
−0.253011 + 0.967464i \(0.581421\pi\)
\(578\) 1.89001e11i 1.69338i
\(579\) 1.13602e11 1.01082
\(580\) 3.82319e10 0.337842
\(581\) 9.00049e10i 0.789881i
\(582\) 8.24692e10 0.718786
\(583\) 4.24289e9i 0.0367272i
\(584\) 7.00211e10 0.601974
\(585\) 6.88867e9i 0.0588183i
\(586\) 6.54153e10i 0.554739i
\(587\) 2.14359e10i 0.180546i −0.995917 0.0902732i \(-0.971226\pi\)
0.995917 0.0902732i \(-0.0287740\pi\)
\(588\) 5.03042e10 0.420819
\(589\) 2.71327e11i 2.25441i
\(590\) 7.09507e10 + 2.25586e10i 0.585529 + 0.186167i
\(591\) −1.06929e11 −0.876486
\(592\) 2.08266e9i 0.0169563i
\(593\) 1.87169e10 0.151361 0.0756805 0.997132i \(-0.475887\pi\)
0.0756805 + 0.997132i \(0.475887\pi\)
\(594\) 8.65739e9 0.0695411
\(595\) 5.04109e10 0.402214
\(596\) 3.30400e11i 2.61852i
\(597\) 1.06046e11 0.834829
\(598\) 4.87488e10i 0.381205i
\(599\) −8.71690e10 −0.677103 −0.338552 0.940948i \(-0.609937\pi\)
−0.338552 + 0.940948i \(0.609937\pi\)
\(600\) 5.78352e10i 0.446259i
\(601\) 4.72599e10i 0.362238i 0.983461 + 0.181119i \(0.0579720\pi\)
−0.983461 + 0.181119i \(0.942028\pi\)
\(602\) 1.66967e11 1.27129
\(603\) 1.34109e10i 0.101435i
\(604\) 2.16789e11i 1.62888i
\(605\) −4.87740e10 −0.364055
\(606\) −1.47893e11 −1.09662
\(607\) −4.28839e10 −0.315893 −0.157946 0.987448i \(-0.550487\pi\)
−0.157946 + 0.987448i \(0.550487\pi\)
\(608\) 1.69354e11i 1.23932i
\(609\) −3.26597e10 −0.237434
\(610\) 1.23202e11 0.889811
\(611\) 5.31406e10 0.381295
\(612\) −1.05015e11 −0.748595
\(613\) 1.02665e11i 0.727077i −0.931579 0.363538i \(-0.881569\pi\)
0.931579 0.363538i \(-0.118431\pi\)
\(614\) 2.10785e11i 1.48309i
\(615\) −2.15940e10 −0.150950
\(616\) 2.15215e10 0.149469
\(617\) −1.21352e11 −0.837345 −0.418673 0.908137i \(-0.637505\pi\)
−0.418673 + 0.908137i \(0.637505\pi\)
\(618\) −4.96040e10 −0.340066
\(619\) −8.51181e10 −0.579775 −0.289887 0.957061i \(-0.593618\pi\)
−0.289887 + 0.957061i \(0.593618\pi\)
\(620\) 1.75811e11i 1.18981i
\(621\) 1.48064e10i 0.0995595i
\(622\) 1.04112e11i 0.695567i
\(623\) 7.92481e10i 0.526062i
\(624\) 4.59436e9i 0.0303030i
\(625\) 8.85405e10 0.580259
\(626\) −3.04450e10 −0.198252
\(627\) 2.29066e10i 0.148214i
\(628\) 4.28816e11i 2.75697i
\(629\) 3.33662e10i 0.213159i
\(630\) 2.35871e10i 0.149731i
\(631\) 1.10368e11 0.696186 0.348093 0.937460i \(-0.386829\pi\)
0.348093 + 0.937460i \(0.386829\pi\)
\(632\) 2.69578e11i 1.68972i
\(633\) 4.75740e10i 0.296316i
\(634\) 1.23507e11i 0.764423i
\(635\) 1.30708e10 0.0803910
\(636\) 2.40811e10 0.147180
\(637\) 3.52585e10i 0.214144i
\(638\) 3.36773e10 0.203261
\(639\) 7.97363e10 0.478248
\(640\) 9.79746e10i 0.583974i
\(641\) 2.92806e11 1.73440 0.867198 0.497964i \(-0.165919\pi\)
0.867198 + 0.497964i \(0.165919\pi\)
\(642\) 1.86375e11i 1.09711i
\(643\) −8.22453e10 −0.481135 −0.240568 0.970632i \(-0.577334\pi\)
−0.240568 + 0.970632i \(0.577334\pi\)
\(644\) 1.01862e11i 0.592203i
\(645\) 4.16092e10i 0.240409i
\(646\) 4.55316e11i 2.61446i
\(647\) −3.20501e11 −1.82899 −0.914497 0.404592i \(-0.867413\pi\)
−0.914497 + 0.404592i \(0.867413\pi\)
\(648\) 1.77551e10i 0.100698i
\(649\) 3.81399e10 + 1.21265e10i 0.214982 + 0.0683528i
\(650\) −1.12184e11 −0.628460
\(651\) 1.50187e11i 0.836194i
\(652\) −4.25332e11 −2.35363
\(653\) −1.66879e11 −0.917804 −0.458902 0.888487i \(-0.651757\pi\)
−0.458902 + 0.888487i \(0.651757\pi\)
\(654\) −1.85246e11 −1.01260
\(655\) 3.13030e10i 0.170067i
\(656\) −1.44020e10 −0.0777691
\(657\) 4.12528e10i 0.221407i
\(658\) 1.81955e11 0.970646
\(659\) 1.80669e11i 0.957947i −0.877829 0.478974i \(-0.841009\pi\)
0.877829 0.478974i \(-0.158991\pi\)
\(660\) 1.48426e10i 0.0782231i
\(661\) −1.56896e11 −0.821874 −0.410937 0.911664i \(-0.634798\pi\)
−0.410937 + 0.911664i \(0.634798\pi\)
\(662\) 1.90273e11i 0.990705i
\(663\) 7.36058e10i 0.380941i
\(664\) −1.90338e11 −0.979160
\(665\) 6.24089e10 0.319124
\(666\) −1.56119e10 −0.0793521
\(667\) 5.75969e10i 0.291002i
\(668\) −2.69263e9 −0.0135229
\(669\) 1.60581e11 0.801660
\(670\) 3.76764e10 0.186969
\(671\) 6.62278e10 0.326701
\(672\) 9.37419e10i 0.459681i
\(673\) 2.73935e9i 0.0133532i −0.999978 0.00667662i \(-0.997875\pi\)
0.999978 0.00667662i \(-0.00212525\pi\)
\(674\) −3.85562e11 −1.86834
\(675\) −3.40735e10 −0.164135
\(676\) −2.57782e11 −1.23443
\(677\) −2.83127e11 −1.34781 −0.673903 0.738820i \(-0.735383\pi\)
−0.673903 + 0.738820i \(0.735383\pi\)
\(678\) 7.22606e10 0.341966
\(679\) 1.20782e11i 0.568228i
\(680\) 1.06607e11i 0.498597i
\(681\) 4.02274e10i 0.187040i
\(682\) 1.54866e11i 0.715844i
\(683\) 3.34373e11i 1.53655i 0.640117 + 0.768277i \(0.278886\pi\)
−0.640117 + 0.768277i \(0.721114\pi\)
\(684\) −1.30009e11 −0.593949
\(685\) −5.98878e10 −0.272005
\(686\) 3.80072e11i 1.71621i
\(687\) 8.76761e10i 0.393599i
\(688\) 2.77510e10i 0.123858i
\(689\) 1.68786e10i 0.0748960i
\(690\) −4.15969e10 −0.183512
\(691\) 3.07698e11i 1.34962i −0.737990 0.674812i \(-0.764225\pi\)
0.737990 0.674812i \(-0.235775\pi\)
\(692\) 6.45886e11i 2.81664i
\(693\) 1.26794e10i 0.0549749i
\(694\) −4.67869e11 −2.01691
\(695\) 4.58451e10 0.196496
\(696\) 6.90673e10i 0.294330i
\(697\) 2.30733e11 0.977639
\(698\) −9.14381e10 −0.385217
\(699\) 9.98130e10i 0.418098i
\(700\) −2.34413e11 −0.976313
\(701\) 7.07046e10i 0.292803i 0.989225 + 0.146401i \(0.0467691\pi\)
−0.989225 + 0.146401i \(0.953231\pi\)
\(702\) 3.44398e10 0.141812
\(703\) 4.13074e10i 0.169124i
\(704\) 9.03404e10i 0.367783i
\(705\) 4.53444e10i 0.183555i
\(706\) 1.09918e11 0.442435
\(707\) 2.16600e11i 0.866923i
\(708\) −6.88254e10 + 2.16468e11i −0.273915 + 0.861512i
\(709\) 3.94533e11 1.56134 0.780671 0.624942i \(-0.214877\pi\)
0.780671 + 0.624942i \(0.214877\pi\)
\(710\) 2.24010e11i 0.881524i
\(711\) 1.58821e11 0.621483
\(712\) −1.67590e11 −0.652122
\(713\) −2.64861e11 −1.02485
\(714\) 2.52029e11i 0.969744i
\(715\) 1.04033e10 0.0398058
\(716\) 1.60383e10i 0.0610246i
\(717\) −6.56784e10 −0.248511
\(718\) 1.58735e11i 0.597275i
\(719\) 2.33339e11i 0.873114i 0.899676 + 0.436557i \(0.143802\pi\)
−0.899676 + 0.436557i \(0.856198\pi\)
\(720\) 3.92032e9 0.0145879
\(721\) 7.26485e10i 0.268835i
\(722\) 1.28411e11i 0.472557i
\(723\) −1.21072e11 −0.443089
\(724\) −2.95195e11 −1.07437
\(725\) −1.32546e11 −0.479749
\(726\) 2.43845e11i 0.877742i
\(727\) 3.33581e11 1.19416 0.597081 0.802181i \(-0.296327\pi\)
0.597081 + 0.802181i \(0.296327\pi\)
\(728\) 8.56144e10 0.304804
\(729\) 1.04604e10 0.0370370
\(730\) 1.15895e11 0.408106
\(731\) 4.44596e11i 1.55703i
\(732\) 3.75885e11i 1.30921i
\(733\) 1.35099e10 0.0467989 0.0233995 0.999726i \(-0.492551\pi\)
0.0233995 + 0.999726i \(0.492551\pi\)
\(734\) 7.42081e11 2.55663
\(735\) 3.00858e10 0.103089
\(736\) −1.65318e11 −0.563390
\(737\) 2.02532e10 0.0686472
\(738\) 1.07959e11i 0.363943i
\(739\) 2.13081e11i 0.714441i 0.934020 + 0.357221i \(0.116276\pi\)
−0.934020 + 0.357221i \(0.883724\pi\)
\(740\) 2.67657e10i 0.0892590i
\(741\) 9.11241e10i 0.302246i
\(742\) 5.77928e10i 0.190659i
\(743\) 1.07130e11 0.351524 0.175762 0.984433i \(-0.443761\pi\)
0.175762 + 0.984433i \(0.443761\pi\)
\(744\) −3.17608e11 −1.03657
\(745\) 1.97604e11i 0.641463i
\(746\) 7.62049e11i 2.46052i
\(747\) 1.12137e11i 0.360137i
\(748\) 1.58594e11i 0.506618i
\(749\) 2.72960e11 0.867304
\(750\) 2.07965e11i 0.657271i
\(751\) 1.88581e11i 0.592841i −0.955058 0.296421i \(-0.904207\pi\)
0.955058 0.296421i \(-0.0957930\pi\)
\(752\) 3.02421e10i 0.0945673i
\(753\) 1.80370e11 0.561029
\(754\) 1.33971e11 0.414501
\(755\) 1.29656e11i 0.399030i
\(756\) 7.19633e10 0.220305
\(757\) 3.24459e11 0.988044 0.494022 0.869449i \(-0.335526\pi\)
0.494022 + 0.869449i \(0.335526\pi\)
\(758\) 5.16478e11i 1.56450i
\(759\) −2.23606e10 −0.0673778
\(760\) 1.31979e11i 0.395596i
\(761\) 3.60109e11 1.07373 0.536866 0.843668i \(-0.319608\pi\)
0.536866 + 0.843668i \(0.319608\pi\)
\(762\) 6.53473e10i 0.193824i
\(763\) 2.71306e11i 0.800499i
\(764\) 6.82071e11i 2.00196i
\(765\) −6.28071e10 −0.183385
\(766\) 4.07280e11i 1.18298i
\(767\) 1.51724e11 + 4.82401e10i 0.438402 + 0.139389i
\(768\) −1.62359e11 −0.466693
\(769\) 1.48428e10i 0.0424434i −0.999775 0.0212217i \(-0.993244\pi\)
0.999775 0.0212217i \(-0.00675559\pi\)
\(770\) 3.56212e10 0.101332
\(771\) 3.44203e11 0.974085
\(772\) −9.73724e11 −2.74136
\(773\) 1.95676e11i 0.548049i −0.961723 0.274024i \(-0.911645\pi\)
0.961723 0.274024i \(-0.0883549\pi\)
\(774\) −2.08025e11 −0.579630
\(775\) 6.09516e11i 1.68958i
\(776\) −2.55424e11 −0.704392
\(777\) 2.28647e10i 0.0627308i
\(778\) 7.22334e11i 1.97160i
\(779\) 2.85648e11 0.775678
\(780\) 5.90452e10i 0.159517i
\(781\) 1.20418e11i 0.323658i
\(782\) 4.44464e11 1.18853