Properties

Label 177.11.c.a.58.17
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.17
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.84

$q$-expansion

\(f(q)\) \(=\) \(q-46.8090i q^{2} +140.296 q^{3} -1167.08 q^{4} -1767.61 q^{5} -6567.12i q^{6} +23434.9 q^{7} +6697.50i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-46.8090i q^{2} +140.296 q^{3} -1167.08 q^{4} -1767.61 q^{5} -6567.12i q^{6} +23434.9 q^{7} +6697.50i q^{8} +19683.0 q^{9} +82740.0i q^{10} +94929.5i q^{11} -163737. q^{12} +313428. i q^{13} -1.09697e6i q^{14} -247989. q^{15} -881588. q^{16} -1.98271e6 q^{17} -921341. i q^{18} +4.75901e6 q^{19} +2.06294e6 q^{20} +3.28783e6 q^{21} +4.44355e6 q^{22} -3.91113e6i q^{23} +939633. i q^{24} -6.64118e6 q^{25} +1.46712e7 q^{26} +2.76145e6 q^{27} -2.73505e7 q^{28} -311027. q^{29} +1.16081e7i q^{30} +2.23439e7i q^{31} +4.81245e7i q^{32} +1.33182e7i q^{33} +9.28087e7i q^{34} -4.14238e7 q^{35} -2.29717e7 q^{36} +7.51676e7i q^{37} -2.22764e8i q^{38} +4.39727e7i q^{39} -1.18386e7i q^{40} -3.58676e7 q^{41} -1.53900e8i q^{42} +9.01042e7i q^{43} -1.10790e8i q^{44} -3.47919e7 q^{45} -1.83076e8 q^{46} +3.59705e8i q^{47} -1.23683e8 q^{48} +2.66721e8 q^{49} +3.10867e8i q^{50} -2.78167e8 q^{51} -3.65796e8i q^{52} -5.69545e8 q^{53} -1.29261e8i q^{54} -1.67798e8i q^{55} +1.56955e8i q^{56} +6.67670e8 q^{57} +1.45589e7i q^{58} +(6.58825e8 + 2.77609e8i) q^{59} +2.89423e8 q^{60} +1.36499e9i q^{61} +1.04590e9 q^{62} +4.61270e8 q^{63} +1.34991e9 q^{64} -5.54018e8i q^{65} +6.23413e8 q^{66} -2.32778e8i q^{67} +2.31398e9 q^{68} -5.48716e8i q^{69} +1.93901e9i q^{70} +1.05078e9 q^{71} +1.31827e8i q^{72} -8.01361e8i q^{73} +3.51852e9 q^{74} -9.31732e8 q^{75} -5.55415e9 q^{76} +2.22467e9i q^{77} +2.05832e9 q^{78} +5.31912e8 q^{79} +1.55830e9 q^{80} +3.87420e8 q^{81} +1.67893e9i q^{82} +4.89302e9i q^{83} -3.83717e9 q^{84} +3.50466e9 q^{85} +4.21769e9 q^{86} -4.36359e7 q^{87} -6.35790e8 q^{88} +1.74792e9i q^{89} +1.62857e9i q^{90} +7.34516e9i q^{91} +4.56460e9i q^{92} +3.13477e9i q^{93} +1.68374e10 q^{94} -8.41206e9 q^{95} +6.75168e9i q^{96} -3.83740e9i q^{97} -1.24849e10i q^{98} +1.86850e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 46.8090i 1.46278i −0.681959 0.731390i \(-0.738872\pi\)
0.681959 0.731390i \(-0.261128\pi\)
\(3\) 140.296 0.577350
\(4\) −1167.08 −1.13973
\(5\) −1767.61 −0.565635 −0.282817 0.959174i \(-0.591269\pi\)
−0.282817 + 0.959174i \(0.591269\pi\)
\(6\) 6567.12i 0.844537i
\(7\) 23434.9 1.39436 0.697178 0.716898i \(-0.254439\pi\)
0.697178 + 0.716898i \(0.254439\pi\)
\(8\) 6697.50i 0.204391i
\(9\) 19683.0 0.333333
\(10\) 82740.0i 0.827400i
\(11\) 94929.5i 0.589437i 0.955584 + 0.294719i \(0.0952259\pi\)
−0.955584 + 0.294719i \(0.904774\pi\)
\(12\) −163737. −0.658022
\(13\) 313428.i 0.844152i 0.906561 + 0.422076i \(0.138698\pi\)
−0.906561 + 0.422076i \(0.861302\pi\)
\(14\) 1.09697e6i 2.03964i
\(15\) −247989. −0.326570
\(16\) −881588. −0.840748
\(17\) −1.98271e6 −1.39642 −0.698208 0.715895i \(-0.746019\pi\)
−0.698208 + 0.715895i \(0.746019\pi\)
\(18\) 921341.i 0.487594i
\(19\) 4.75901e6 1.92198 0.960989 0.276587i \(-0.0892035\pi\)
0.960989 + 0.276587i \(0.0892035\pi\)
\(20\) 2.06294e6 0.644670
\(21\) 3.28783e6 0.805032
\(22\) 4.44355e6 0.862218
\(23\) 3.91113e6i 0.607663i −0.952726 0.303831i \(-0.901734\pi\)
0.952726 0.303831i \(-0.0982659\pi\)
\(24\) 939633.i 0.118005i
\(25\) −6.64118e6 −0.680057
\(26\) 1.46712e7 1.23481
\(27\) 2.76145e6 0.192450
\(28\) −2.73505e7 −1.58919
\(29\) −311027. −0.0151638 −0.00758190 0.999971i \(-0.502413\pi\)
−0.00758190 + 0.999971i \(0.502413\pi\)
\(30\) 1.16081e7i 0.477700i
\(31\) 2.23439e7i 0.780460i 0.920717 + 0.390230i \(0.127605\pi\)
−0.920717 + 0.390230i \(0.872395\pi\)
\(32\) 4.81245e7i 1.43422i
\(33\) 1.33182e7i 0.340312i
\(34\) 9.28087e7i 2.04265i
\(35\) −4.14238e7 −0.788696
\(36\) −2.29717e7 −0.379909
\(37\) 7.51676e7i 1.08398i 0.840384 + 0.541991i \(0.182329\pi\)
−0.840384 + 0.541991i \(0.817671\pi\)
\(38\) 2.22764e8i 2.81143i
\(39\) 4.39727e7i 0.487371i
\(40\) 1.18386e7i 0.115611i
\(41\) −3.58676e7 −0.309587 −0.154794 0.987947i \(-0.549471\pi\)
−0.154794 + 0.987947i \(0.549471\pi\)
\(42\) 1.53900e8i 1.17758i
\(43\) 9.01042e7i 0.612919i 0.951884 + 0.306459i \(0.0991444\pi\)
−0.951884 + 0.306459i \(0.900856\pi\)
\(44\) 1.10790e8i 0.671798i
\(45\) −3.47919e7 −0.188545
\(46\) −1.83076e8 −0.888877
\(47\) 3.59705e8i 1.56840i 0.620508 + 0.784200i \(0.286926\pi\)
−0.620508 + 0.784200i \(0.713074\pi\)
\(48\) −1.23683e8 −0.485406
\(49\) 2.66721e8 0.944227
\(50\) 3.10867e8i 0.994775i
\(51\) −2.78167e8 −0.806221
\(52\) 3.65796e8i 0.962103i
\(53\) −5.69545e8 −1.36191 −0.680956 0.732324i \(-0.738435\pi\)
−0.680956 + 0.732324i \(0.738435\pi\)
\(54\) 1.29261e8i 0.281512i
\(55\) 1.67798e8i 0.333406i
\(56\) 1.56955e8i 0.284994i
\(57\) 6.67670e8 1.10965
\(58\) 1.45589e7i 0.0221813i
\(59\) 6.58825e8 + 2.77609e8i 0.921531 + 0.388306i
\(60\) 2.89423e8 0.372200
\(61\) 1.36499e9i 1.61614i 0.589086 + 0.808070i \(0.299488\pi\)
−0.589086 + 0.808070i \(0.700512\pi\)
\(62\) 1.04590e9 1.14164
\(63\) 4.61270e8 0.464785
\(64\) 1.34991e9 1.25720
\(65\) 5.54018e8i 0.477482i
\(66\) 6.23413e8 0.497802
\(67\) 2.32778e8i 0.172413i −0.996277 0.0862063i \(-0.972526\pi\)
0.996277 0.0862063i \(-0.0274744\pi\)
\(68\) 2.31398e9 1.59153
\(69\) 5.48716e8i 0.350834i
\(70\) 1.93901e9i 1.15369i
\(71\) 1.05078e9 0.582397 0.291198 0.956663i \(-0.405946\pi\)
0.291198 + 0.956663i \(0.405946\pi\)
\(72\) 1.31827e8i 0.0681305i
\(73\) 8.01361e8i 0.386557i −0.981144 0.193279i \(-0.938088\pi\)
0.981144 0.193279i \(-0.0619121\pi\)
\(74\) 3.51852e9 1.58563
\(75\) −9.31732e8 −0.392631
\(76\) −5.55415e9 −2.19053
\(77\) 2.22467e9i 0.821885i
\(78\) 2.05832e9 0.712917
\(79\) 5.31912e8 0.172864 0.0864319 0.996258i \(-0.472454\pi\)
0.0864319 + 0.996258i \(0.472454\pi\)
\(80\) 1.55830e9 0.475557
\(81\) 3.87420e8 0.111111
\(82\) 1.67893e9i 0.452858i
\(83\) 4.89302e9i 1.24218i 0.783737 + 0.621092i \(0.213311\pi\)
−0.783737 + 0.621092i \(0.786689\pi\)
\(84\) −3.83717e9 −0.917517
\(85\) 3.50466e9 0.789862
\(86\) 4.21769e9 0.896566
\(87\) −4.36359e7 −0.00875483
\(88\) −6.35790e8 −0.120476
\(89\) 1.74792e9i 0.313020i 0.987676 + 0.156510i \(0.0500243\pi\)
−0.987676 + 0.156510i \(0.949976\pi\)
\(90\) 1.62857e9i 0.275800i
\(91\) 7.34516e9i 1.17705i
\(92\) 4.56460e9i 0.692570i
\(93\) 3.13477e9i 0.450599i
\(94\) 1.68374e10 2.29423
\(95\) −8.41206e9 −1.08714
\(96\) 6.75168e9i 0.828048i
\(97\) 3.83740e9i 0.446867i −0.974719 0.223433i \(-0.928273\pi\)
0.974719 0.223433i \(-0.0717265\pi\)
\(98\) 1.24849e10i 1.38120i
\(99\) 1.86850e9i 0.196479i
\(100\) 7.75080e9 0.775080
\(101\) 3.98484e9i 0.379144i −0.981867 0.189572i \(-0.939290\pi\)
0.981867 0.189572i \(-0.0607100\pi\)
\(102\) 1.30207e10i 1.17932i
\(103\) 2.06401e10i 1.78043i −0.455538 0.890216i \(-0.650553\pi\)
0.455538 0.890216i \(-0.349447\pi\)
\(104\) −2.09918e9 −0.172537
\(105\) −5.81160e9 −0.455354
\(106\) 2.66598e10i 1.99218i
\(107\) −1.07525e10 −0.766638 −0.383319 0.923616i \(-0.625219\pi\)
−0.383319 + 0.923616i \(0.625219\pi\)
\(108\) −3.22284e9 −0.219341
\(109\) 2.23699e10i 1.45389i 0.686696 + 0.726944i \(0.259060\pi\)
−0.686696 + 0.726944i \(0.740940\pi\)
\(110\) −7.85446e9 −0.487700
\(111\) 1.05457e10i 0.625837i
\(112\) −2.06600e10 −1.17230
\(113\) 6.77175e9i 0.367544i −0.982969 0.183772i \(-0.941169\pi\)
0.982969 0.183772i \(-0.0588308\pi\)
\(114\) 3.12530e10i 1.62318i
\(115\) 6.91334e9i 0.343715i
\(116\) 3.62994e8 0.0172826
\(117\) 6.16920e9i 0.281384i
\(118\) 1.29946e10 3.08389e10i 0.568006 1.34800i
\(119\) −4.64647e10 −1.94710
\(120\) 1.66090e9i 0.0667480i
\(121\) 1.69258e10 0.652564
\(122\) 6.38936e10 2.36406
\(123\) −5.03209e9 −0.178740
\(124\) 2.60772e10i 0.889513i
\(125\) 2.90008e10 0.950299
\(126\) 2.15916e10i 0.679879i
\(127\) 3.98283e10 1.20552 0.602758 0.797924i \(-0.294068\pi\)
0.602758 + 0.797924i \(0.294068\pi\)
\(128\) 1.39086e10i 0.404792i
\(129\) 1.26413e10i 0.353869i
\(130\) −2.59330e10 −0.698451
\(131\) 3.06971e10i 0.795684i 0.917454 + 0.397842i \(0.130241\pi\)
−0.917454 + 0.397842i \(0.869759\pi\)
\(132\) 1.55435e10i 0.387863i
\(133\) 1.11527e11 2.67992
\(134\) −1.08961e10 −0.252202
\(135\) −4.88116e9 −0.108857
\(136\) 1.32792e10i 0.285415i
\(137\) 1.42474e10 0.295211 0.147606 0.989046i \(-0.452843\pi\)
0.147606 + 0.989046i \(0.452843\pi\)
\(138\) −2.56848e10 −0.513194
\(139\) 5.30355e9 0.102210 0.0511049 0.998693i \(-0.483726\pi\)
0.0511049 + 0.998693i \(0.483726\pi\)
\(140\) 4.83450e10 0.898899
\(141\) 5.04652e10i 0.905516i
\(142\) 4.91858e10i 0.851919i
\(143\) −2.97535e10 −0.497575
\(144\) −1.73523e10 −0.280249
\(145\) 5.49774e8 0.00857718
\(146\) −3.75109e10 −0.565449
\(147\) 3.74199e10 0.545150
\(148\) 8.77267e10i 1.23544i
\(149\) 1.39088e11i 1.89391i −0.321367 0.946955i \(-0.604142\pi\)
0.321367 0.946955i \(-0.395858\pi\)
\(150\) 4.36134e10i 0.574333i
\(151\) 2.16390e10i 0.275646i −0.990457 0.137823i \(-0.955989\pi\)
0.990457 0.137823i \(-0.0440106\pi\)
\(152\) 3.18734e10i 0.392836i
\(153\) −3.90257e10 −0.465472
\(154\) 1.04134e11 1.20224
\(155\) 3.94953e10i 0.441456i
\(156\) 5.13197e10i 0.555471i
\(157\) 1.78422e10i 0.187047i 0.995617 + 0.0935233i \(0.0298130\pi\)
−0.995617 + 0.0935233i \(0.970187\pi\)
\(158\) 2.48982e10i 0.252862i
\(159\) −7.99050e10 −0.786300
\(160\) 8.50653e10i 0.811246i
\(161\) 9.16570e10i 0.847298i
\(162\) 1.81348e10i 0.162531i
\(163\) 1.59769e11 1.38853 0.694265 0.719720i \(-0.255730\pi\)
0.694265 + 0.719720i \(0.255730\pi\)
\(164\) 4.18604e10 0.352845
\(165\) 2.35414e10i 0.192492i
\(166\) 2.29037e11 1.81704
\(167\) −9.17186e10 −0.706115 −0.353057 0.935602i \(-0.614858\pi\)
−0.353057 + 0.935602i \(0.614858\pi\)
\(168\) 2.20202e10i 0.164542i
\(169\) 3.96216e10 0.287408
\(170\) 1.64049e11i 1.15539i
\(171\) 9.36715e10 0.640659
\(172\) 1.05159e11i 0.698561i
\(173\) 1.28145e11i 0.826934i −0.910519 0.413467i \(-0.864318\pi\)
0.910519 0.413467i \(-0.135682\pi\)
\(174\) 2.04255e9i 0.0128064i
\(175\) −1.55636e11 −0.948241
\(176\) 8.36887e10i 0.495568i
\(177\) 9.24305e10 + 3.89475e10i 0.532046 + 0.224188i
\(178\) 8.18184e10 0.457879
\(179\) 6.15213e10i 0.334781i 0.985891 + 0.167390i \(0.0535340\pi\)
−0.985891 + 0.167390i \(0.946466\pi\)
\(180\) 4.06049e10 0.214890
\(181\) −1.23559e11 −0.636037 −0.318018 0.948085i \(-0.603017\pi\)
−0.318018 + 0.948085i \(0.603017\pi\)
\(182\) 3.43819e11 1.72176
\(183\) 1.91502e11i 0.933079i
\(184\) 2.61948e10 0.124201
\(185\) 1.32867e11i 0.613138i
\(186\) 1.46735e11 0.659128
\(187\) 1.88218e11i 0.823099i
\(188\) 4.19805e11i 1.78755i
\(189\) 6.47144e10 0.268344
\(190\) 3.93760e11i 1.59024i
\(191\) 2.99961e11i 1.18004i −0.807387 0.590022i \(-0.799119\pi\)
0.807387 0.590022i \(-0.200881\pi\)
\(192\) 1.89387e11 0.725847
\(193\) 3.30759e11 1.23517 0.617583 0.786506i \(-0.288112\pi\)
0.617583 + 0.786506i \(0.288112\pi\)
\(194\) −1.79625e11 −0.653668
\(195\) 7.77265e10i 0.275674i
\(196\) −3.11285e11 −1.07616
\(197\) −7.32865e10 −0.246998 −0.123499 0.992345i \(-0.539411\pi\)
−0.123499 + 0.992345i \(0.539411\pi\)
\(198\) 8.74624e10 0.287406
\(199\) −1.66376e11 −0.533119 −0.266559 0.963818i \(-0.585887\pi\)
−0.266559 + 0.963818i \(0.585887\pi\)
\(200\) 4.44793e10i 0.138998i
\(201\) 3.26579e10i 0.0995424i
\(202\) −1.86526e11 −0.554604
\(203\) −7.28890e9 −0.0211437
\(204\) 3.24643e11 0.918873
\(205\) 6.33999e10 0.175113
\(206\) −9.66142e11 −2.60438
\(207\) 7.69827e10i 0.202554i
\(208\) 2.76314e11i 0.709719i
\(209\) 4.51770e11i 1.13289i
\(210\) 2.72035e11i 0.666083i
\(211\) 7.07742e11i 1.69224i 0.532990 + 0.846121i \(0.321068\pi\)
−0.532990 + 0.846121i \(0.678932\pi\)
\(212\) 6.64706e11 1.55221
\(213\) 1.47420e11 0.336247
\(214\) 5.03313e11i 1.12142i
\(215\) 1.59269e11i 0.346688i
\(216\) 1.84948e10i 0.0393351i
\(217\) 5.23628e11i 1.08824i
\(218\) 1.04711e12 2.12672
\(219\) 1.12428e11i 0.223179i
\(220\) 1.95834e11i 0.379993i
\(221\) 6.21436e11i 1.17879i
\(222\) 4.93634e11 0.915463
\(223\) −4.68814e11 −0.850112 −0.425056 0.905167i \(-0.639746\pi\)
−0.425056 + 0.905167i \(0.639746\pi\)
\(224\) 1.12779e12i 1.99981i
\(225\) −1.30718e11 −0.226686
\(226\) −3.16979e11 −0.537636
\(227\) 5.84135e10i 0.0969134i 0.998825 + 0.0484567i \(0.0154303\pi\)
−0.998825 + 0.0484567i \(0.984570\pi\)
\(228\) −7.79225e11 −1.26470
\(229\) 3.60838e11i 0.572975i 0.958084 + 0.286487i \(0.0924876\pi\)
−0.958084 + 0.286487i \(0.907512\pi\)
\(230\) 3.23607e11 0.502780
\(231\) 3.12112e11i 0.474516i
\(232\) 2.08310e9i 0.00309935i
\(233\) 7.99418e11i 1.16411i 0.813149 + 0.582056i \(0.197751\pi\)
−0.813149 + 0.582056i \(0.802249\pi\)
\(234\) 2.88774e11 0.411603
\(235\) 6.35817e11i 0.887142i
\(236\) −7.68902e11 3.23993e11i −1.05029 0.442563i
\(237\) 7.46251e10 0.0998029
\(238\) 2.17497e12i 2.84818i
\(239\) 1.02266e12 1.31142 0.655711 0.755012i \(-0.272369\pi\)
0.655711 + 0.755012i \(0.272369\pi\)
\(240\) 2.18624e11 0.274563
\(241\) −1.27239e12 −1.56508 −0.782538 0.622603i \(-0.786075\pi\)
−0.782538 + 0.622603i \(0.786075\pi\)
\(242\) 7.92281e11i 0.954558i
\(243\) 5.43536e10 0.0641500
\(244\) 1.59305e12i 1.84196i
\(245\) −4.71458e11 −0.534088
\(246\) 2.35547e11i 0.261458i
\(247\) 1.49160e12i 1.62244i
\(248\) −1.49648e11 −0.159519
\(249\) 6.86471e11i 0.717176i
\(250\) 1.35750e12i 1.39008i
\(251\) −9.11290e10 −0.0914720 −0.0457360 0.998954i \(-0.514563\pi\)
−0.0457360 + 0.998954i \(0.514563\pi\)
\(252\) −5.38339e11 −0.529729
\(253\) 3.71281e11 0.358179
\(254\) 1.86432e12i 1.76341i
\(255\) 4.91690e11 0.456027
\(256\) 7.31265e11 0.665082
\(257\) −2.55145e11 −0.227573 −0.113787 0.993505i \(-0.536298\pi\)
−0.113787 + 0.993505i \(0.536298\pi\)
\(258\) 5.91725e11 0.517633
\(259\) 1.76155e12i 1.51146i
\(260\) 6.46584e11i 0.544199i
\(261\) −6.12195e9 −0.00505460
\(262\) 1.43690e12 1.16391
\(263\) −7.33648e11 −0.583055 −0.291527 0.956563i \(-0.594163\pi\)
−0.291527 + 0.956563i \(0.594163\pi\)
\(264\) −8.91989e10 −0.0695568
\(265\) 1.00673e12 0.770345
\(266\) 5.22047e12i 3.92014i
\(267\) 2.45226e11i 0.180722i
\(268\) 2.71671e11i 0.196503i
\(269\) 1.39603e12i 0.991138i 0.868569 + 0.495569i \(0.165040\pi\)
−0.868569 + 0.495569i \(0.834960\pi\)
\(270\) 2.28482e11i 0.159233i
\(271\) −9.96160e10 −0.0681527 −0.0340763 0.999419i \(-0.510849\pi\)
−0.0340763 + 0.999419i \(0.510849\pi\)
\(272\) 1.74793e12 1.17403
\(273\) 1.03050e12i 0.679569i
\(274\) 6.66907e11i 0.431830i
\(275\) 6.30444e11i 0.400851i
\(276\) 6.40396e11i 0.399856i
\(277\) 3.71966e11 0.228089 0.114045 0.993476i \(-0.463619\pi\)
0.114045 + 0.993476i \(0.463619\pi\)
\(278\) 2.48254e11i 0.149510i
\(279\) 4.39795e11i 0.260153i
\(280\) 2.77436e11i 0.161203i
\(281\) −6.97032e11 −0.397852 −0.198926 0.980015i \(-0.563745\pi\)
−0.198926 + 0.980015i \(0.563745\pi\)
\(282\) 2.36222e12 1.32457
\(283\) 3.25531e12i 1.79333i 0.442709 + 0.896665i \(0.354017\pi\)
−0.442709 + 0.896665i \(0.645983\pi\)
\(284\) −1.22634e12 −0.663774
\(285\) −1.18018e12 −0.627659
\(286\) 1.39273e12i 0.727843i
\(287\) −8.40555e11 −0.431675
\(288\) 9.47234e11i 0.478074i
\(289\) 1.91515e12 0.949977
\(290\) 2.57344e10i 0.0125465i
\(291\) 5.38372e11i 0.257999i
\(292\) 9.35254e11i 0.440570i
\(293\) −3.61416e12 −1.67367 −0.836834 0.547457i \(-0.815596\pi\)
−0.836834 + 0.547457i \(0.815596\pi\)
\(294\) 1.75159e12i 0.797435i
\(295\) −1.16454e12 4.90705e11i −0.521250 0.219639i
\(296\) −5.03435e11 −0.221557
\(297\) 2.62143e11i 0.113437i
\(298\) −6.51058e12 −2.77037
\(299\) 1.22585e12 0.512960
\(300\) 1.08741e12 0.447493
\(301\) 2.11159e12i 0.854627i
\(302\) −1.01290e12 −0.403210
\(303\) 5.59057e11i 0.218899i
\(304\) −4.19548e12 −1.61590
\(305\) 2.41276e12i 0.914145i
\(306\) 1.82675e12i 0.680883i
\(307\) 5.03330e12 1.84570 0.922849 0.385162i \(-0.125855\pi\)
0.922849 + 0.385162i \(0.125855\pi\)
\(308\) 2.59637e12i 0.936725i
\(309\) 2.89573e12i 1.02793i
\(310\) −1.84874e12 −0.645753
\(311\) 1.10745e12 0.380648 0.190324 0.981721i \(-0.439046\pi\)
0.190324 + 0.981721i \(0.439046\pi\)
\(312\) −2.94507e11 −0.0996145
\(313\) 5.97747e12i 1.98974i −0.101170 0.994869i \(-0.532259\pi\)
0.101170 0.994869i \(-0.467741\pi\)
\(314\) 8.35175e11 0.273608
\(315\) −8.15345e11 −0.262899
\(316\) −6.20784e11 −0.197018
\(317\) 4.52422e12 1.41334 0.706671 0.707542i \(-0.250196\pi\)
0.706671 + 0.707542i \(0.250196\pi\)
\(318\) 3.74027e12i 1.15018i
\(319\) 2.95256e10i 0.00893811i
\(320\) −2.38612e12 −0.711119
\(321\) −1.50853e12 −0.442619
\(322\) −4.29037e12 −1.23941
\(323\) −9.43573e12 −2.68388
\(324\) −4.52151e11 −0.126636
\(325\) 2.08153e12i 0.574071i
\(326\) 7.47864e12i 2.03111i
\(327\) 3.13841e12i 0.839403i
\(328\) 2.40223e11i 0.0632770i
\(329\) 8.42965e12i 2.18691i
\(330\) −1.10195e12 −0.281574
\(331\) −3.81915e12 −0.961228 −0.480614 0.876932i \(-0.659586\pi\)
−0.480614 + 0.876932i \(0.659586\pi\)
\(332\) 5.71055e12i 1.41575i
\(333\) 1.47952e12i 0.361327i
\(334\) 4.29326e12i 1.03289i
\(335\) 4.11461e11i 0.0975226i
\(336\) −2.89851e12 −0.676829
\(337\) 1.65690e11i 0.0381196i 0.999818 + 0.0190598i \(0.00606728\pi\)
−0.999818 + 0.0190598i \(0.993933\pi\)
\(338\) 1.85465e12i 0.420415i
\(339\) 9.50051e11i 0.212201i
\(340\) −4.09022e12 −0.900227
\(341\) −2.12110e12 −0.460033
\(342\) 4.38467e12i 0.937144i
\(343\) −3.69204e11 −0.0777670
\(344\) −6.03473e11 −0.125275
\(345\) 9.69915e11i 0.198444i
\(346\) −5.99833e12 −1.20962
\(347\) 5.16211e12i 1.02608i 0.858366 + 0.513038i \(0.171480\pi\)
−0.858366 + 0.513038i \(0.828520\pi\)
\(348\) 5.09267e10 0.00997812
\(349\) 1.91896e12i 0.370628i 0.982679 + 0.185314i \(0.0593302\pi\)
−0.982679 + 0.185314i \(0.940670\pi\)
\(350\) 7.28515e12i 1.38707i
\(351\) 8.65514e11i 0.162457i
\(352\) −4.56843e12 −0.845384
\(353\) 1.14718e12i 0.209295i −0.994509 0.104647i \(-0.966629\pi\)
0.994509 0.104647i \(-0.0333714\pi\)
\(354\) 1.82309e12 4.32658e12i 0.327939 0.778267i
\(355\) −1.85736e12 −0.329424
\(356\) 2.03997e12i 0.356757i
\(357\) −6.51882e12 −1.12416
\(358\) 2.87975e12 0.489711
\(359\) 9.15431e12 1.53516 0.767579 0.640954i \(-0.221461\pi\)
0.767579 + 0.640954i \(0.221461\pi\)
\(360\) 2.33018e11i 0.0385370i
\(361\) 1.65171e13 2.69400
\(362\) 5.78368e12i 0.930383i
\(363\) 2.37463e12 0.376758
\(364\) 8.57240e12i 1.34151i
\(365\) 1.41649e12i 0.218650i
\(366\) 8.96403e12 1.36489
\(367\) 7.00729e12i 1.05249i −0.850331 0.526247i \(-0.823599\pi\)
0.850331 0.526247i \(-0.176401\pi\)
\(368\) 3.44800e12i 0.510891i
\(369\) −7.05982e11 −0.103196
\(370\) −6.21937e12 −0.896887
\(371\) −1.33473e13 −1.89899
\(372\) 3.65853e12i 0.513560i
\(373\) 1.19357e13 1.65312 0.826558 0.562851i \(-0.190296\pi\)
0.826558 + 0.562851i \(0.190296\pi\)
\(374\) −8.81028e12 −1.20401
\(375\) 4.06870e12 0.548655
\(376\) −2.40912e12 −0.320567
\(377\) 9.74845e10i 0.0128006i
\(378\) 3.02921e12i 0.392528i
\(379\) −1.25306e13 −1.60242 −0.801211 0.598382i \(-0.795810\pi\)
−0.801211 + 0.598382i \(0.795810\pi\)
\(380\) 9.81756e12 1.23904
\(381\) 5.58776e12 0.696005
\(382\) −1.40409e13 −1.72615
\(383\) 2.41110e12 0.292564 0.146282 0.989243i \(-0.453269\pi\)
0.146282 + 0.989243i \(0.453269\pi\)
\(384\) 1.95132e12i 0.233707i
\(385\) 3.93234e12i 0.464887i
\(386\) 1.54825e13i 1.80678i
\(387\) 1.77352e12i 0.204306i
\(388\) 4.47856e12i 0.509307i
\(389\) 1.42297e12 0.159753 0.0798764 0.996805i \(-0.474547\pi\)
0.0798764 + 0.996805i \(0.474547\pi\)
\(390\) −3.63830e12 −0.403251
\(391\) 7.75463e12i 0.848550i
\(392\) 1.78636e12i 0.192992i
\(393\) 4.30668e12i 0.459388i
\(394\) 3.43047e12i 0.361303i
\(395\) −9.40212e11 −0.0977778
\(396\) 2.18069e12i 0.223933i
\(397\) 1.22123e13i 1.23835i 0.785252 + 0.619176i \(0.212533\pi\)
−0.785252 + 0.619176i \(0.787467\pi\)
\(398\) 7.78787e12i 0.779836i
\(399\) 1.56468e13 1.54725
\(400\) 5.85479e12 0.571757
\(401\) 1.38555e13i 1.33629i −0.744031 0.668145i \(-0.767089\pi\)
0.744031 0.668145i \(-0.232911\pi\)
\(402\) −1.52868e12 −0.145609
\(403\) −7.00320e12 −0.658827
\(404\) 4.65063e12i 0.432121i
\(405\) −6.84808e11 −0.0628483
\(406\) 3.41186e11i 0.0309287i
\(407\) −7.13562e12 −0.638939
\(408\) 1.86302e12i 0.164785i
\(409\) 1.09414e13i 0.956000i 0.878360 + 0.478000i \(0.158638\pi\)
−0.878360 + 0.478000i \(0.841362\pi\)
\(410\) 2.96769e12i 0.256152i
\(411\) 1.99886e12 0.170440
\(412\) 2.40887e13i 2.02921i
\(413\) 1.54395e13 + 6.50575e12i 1.28494 + 0.541436i
\(414\) −3.60348e12 −0.296292
\(415\) 8.64894e12i 0.702623i
\(416\) −1.50835e13 −1.21070
\(417\) 7.44067e11 0.0590108
\(418\) 2.11469e13 1.65716
\(419\) 8.31526e12i 0.643881i 0.946760 + 0.321941i \(0.104335\pi\)
−0.946760 + 0.321941i \(0.895665\pi\)
\(420\) 6.78261e12 0.518980
\(421\) 6.87852e11i 0.0520097i −0.999662 0.0260049i \(-0.991721\pi\)
0.999662 0.0260049i \(-0.00827853\pi\)
\(422\) 3.31287e13 2.47538
\(423\) 7.08007e12i 0.522800i
\(424\) 3.81453e12i 0.278363i
\(425\) 1.31675e13 0.949642
\(426\) 6.90058e12i 0.491855i
\(427\) 3.19884e13i 2.25347i
\(428\) 1.25490e13 0.873759
\(429\) −4.17430e12 −0.287275
\(430\) −7.45523e12 −0.507129
\(431\) 1.96055e13i 1.31823i 0.752042 + 0.659115i \(0.229069\pi\)
−0.752042 + 0.659115i \(0.770931\pi\)
\(432\) −2.43446e12 −0.161802
\(433\) −2.62642e12 −0.172554 −0.0862770 0.996271i \(-0.527497\pi\)
−0.0862770 + 0.996271i \(0.527497\pi\)
\(434\) 2.45105e13 1.59186
\(435\) 7.71312e10 0.00495204
\(436\) 2.61075e13i 1.65704i
\(437\) 1.86131e13i 1.16791i
\(438\) −5.26263e12 −0.326462
\(439\) 3.30354e12 0.202608 0.101304 0.994855i \(-0.467698\pi\)
0.101304 + 0.994855i \(0.467698\pi\)
\(440\) 1.12383e12 0.0681454
\(441\) 5.24987e12 0.314742
\(442\) −2.90888e13 −1.72431
\(443\) 2.95988e13i 1.73482i 0.497592 + 0.867411i \(0.334218\pi\)
−0.497592 + 0.867411i \(0.665782\pi\)
\(444\) 1.23077e13i 0.713284i
\(445\) 3.08964e12i 0.177055i
\(446\) 2.19447e13i 1.24353i
\(447\) 1.95135e13i 1.09345i
\(448\) 3.16351e13 1.75299
\(449\) 2.67342e13 1.46499 0.732497 0.680770i \(-0.238355\pi\)
0.732497 + 0.680770i \(0.238355\pi\)
\(450\) 6.11880e12i 0.331592i
\(451\) 3.40489e12i 0.182482i
\(452\) 7.90319e12i 0.418900i
\(453\) 3.03587e12i 0.159145i
\(454\) 2.73428e12 0.141763
\(455\) 1.29834e13i 0.665779i
\(456\) 4.47172e12i 0.226804i
\(457\) 3.62683e13i 1.81947i −0.415186 0.909737i \(-0.636283\pi\)
0.415186 0.909737i \(-0.363717\pi\)
\(458\) 1.68905e13 0.838136
\(459\) −5.47515e12 −0.268740
\(460\) 8.06843e12i 0.391742i
\(461\) 6.27032e12 0.301152 0.150576 0.988598i \(-0.451887\pi\)
0.150576 + 0.988598i \(0.451887\pi\)
\(462\) 1.46096e13 0.694112
\(463\) 8.72483e12i 0.410064i 0.978755 + 0.205032i \(0.0657299\pi\)
−0.978755 + 0.205032i \(0.934270\pi\)
\(464\) 2.74198e11 0.0127489
\(465\) 5.54104e12i 0.254875i
\(466\) 3.74200e13 1.70284
\(467\) 1.01511e13i 0.457012i −0.973543 0.228506i \(-0.926616\pi\)
0.973543 0.228506i \(-0.0733840\pi\)
\(468\) 7.19995e12i 0.320701i
\(469\) 5.45515e12i 0.240404i
\(470\) −2.97620e13 −1.29769
\(471\) 2.50319e12i 0.107991i
\(472\) −1.85929e12 + 4.41248e12i −0.0793664 + 0.188353i
\(473\) −8.55355e12 −0.361277
\(474\) 3.49313e12i 0.145990i
\(475\) −3.16054e13 −1.30705
\(476\) 5.42281e13 2.21916
\(477\) −1.12104e13 −0.453971
\(478\) 4.78698e13i 1.91832i
\(479\) −3.02354e13 −1.19905 −0.599525 0.800356i \(-0.704644\pi\)
−0.599525 + 0.800356i \(0.704644\pi\)
\(480\) 1.19343e13i 0.468373i
\(481\) −2.35596e13 −0.915045
\(482\) 5.95593e13i 2.28936i
\(483\) 1.28591e13i 0.489188i
\(484\) −1.97538e13 −0.743745
\(485\) 6.78302e12i 0.252764i
\(486\) 2.54424e12i 0.0938374i
\(487\) −3.69676e13 −1.34951 −0.674755 0.738042i \(-0.735751\pi\)
−0.674755 + 0.738042i \(0.735751\pi\)
\(488\) −9.14199e12 −0.330325
\(489\) 2.24150e13 0.801668
\(490\) 2.20685e13i 0.781254i
\(491\) −8.28368e12 −0.290279 −0.145140 0.989411i \(-0.546363\pi\)
−0.145140 + 0.989411i \(0.546363\pi\)
\(492\) 5.87285e12 0.203715
\(493\) 6.16677e11 0.0211750
\(494\) 6.98205e13 2.37328
\(495\) 3.30277e12i 0.111135i
\(496\) 1.96981e13i 0.656171i
\(497\) 2.46249e13 0.812068
\(498\) 3.21330e13 1.04907
\(499\) −4.89323e13 −1.58159 −0.790793 0.612083i \(-0.790332\pi\)
−0.790793 + 0.612083i \(0.790332\pi\)
\(500\) −3.38463e13 −1.08308
\(501\) −1.28678e13 −0.407675
\(502\) 4.26566e12i 0.133803i
\(503\) 2.94499e13i 0.914626i 0.889306 + 0.457313i \(0.151188\pi\)
−0.889306 + 0.457313i \(0.848812\pi\)
\(504\) 3.08935e12i 0.0949981i
\(505\) 7.04364e12i 0.214457i
\(506\) 1.73793e13i 0.523937i
\(507\) 5.55876e12 0.165935
\(508\) −4.64829e13 −1.37396
\(509\) 1.45727e13i 0.426532i 0.976994 + 0.213266i \(0.0684100\pi\)
−0.976994 + 0.213266i \(0.931590\pi\)
\(510\) 2.30155e13i 0.667067i
\(511\) 1.87798e13i 0.538998i
\(512\) 4.84721e13i 1.37766i
\(513\) 1.31418e13 0.369885
\(514\) 1.19431e13i 0.332890i
\(515\) 3.64836e13i 1.00708i
\(516\) 1.47534e13i 0.403314i
\(517\) −3.41466e13 −0.924473
\(518\) 8.24562e13 2.21093
\(519\) 1.79782e13i 0.477430i
\(520\) 3.71053e12 0.0975932
\(521\) 3.17829e13 0.827952 0.413976 0.910288i \(-0.364140\pi\)
0.413976 + 0.910288i \(0.364140\pi\)
\(522\) 2.86562e11i 0.00739378i
\(523\) −2.72361e13 −0.696044 −0.348022 0.937486i \(-0.613147\pi\)
−0.348022 + 0.937486i \(0.613147\pi\)
\(524\) 3.58260e13i 0.906863i
\(525\) −2.18351e13 −0.547467
\(526\) 3.43413e13i 0.852881i
\(527\) 4.43015e13i 1.08985i
\(528\) 1.17412e13i 0.286116i
\(529\) 2.61296e13 0.630746
\(530\) 4.71242e13i 1.12685i
\(531\) 1.29676e13 + 5.46418e12i 0.307177 + 0.129435i
\(532\) −1.30161e14 −3.05438
\(533\) 1.12419e13i 0.261339i
\(534\) 1.14788e13 0.264357
\(535\) 1.90062e13 0.433637
\(536\) 1.55903e12 0.0352396
\(537\) 8.63120e12i 0.193286i
\(538\) 6.53469e13 1.44982
\(539\) 2.53197e13i 0.556563i
\(540\) 5.69671e12 0.124067
\(541\) 6.37938e13i 1.37655i 0.725450 + 0.688275i \(0.241632\pi\)
−0.725450 + 0.688275i \(0.758368\pi\)
\(542\) 4.66293e12i 0.0996924i
\(543\) −1.73349e13 −0.367216
\(544\) 9.54169e13i 2.00277i
\(545\) 3.95412e13i 0.822370i
\(546\) 4.82365e13 0.994060
\(547\) −3.69130e13 −0.753776 −0.376888 0.926259i \(-0.623006\pi\)
−0.376888 + 0.926259i \(0.623006\pi\)
\(548\) −1.66279e13 −0.336461
\(549\) 2.68670e13i 0.538713i
\(550\) −2.95104e13 −0.586357
\(551\) −1.48018e12 −0.0291445
\(552\) 3.67502e12 0.0717075
\(553\) 1.24653e13 0.241034
\(554\) 1.74114e13i 0.333644i
\(555\) 1.86407e13i 0.353995i
\(556\) −6.18967e12 −0.116491
\(557\) −6.25309e13 −1.16632 −0.583161 0.812356i \(-0.698184\pi\)
−0.583161 + 0.812356i \(0.698184\pi\)
\(558\) 2.05864e13 0.380548
\(559\) −2.82412e13 −0.517396
\(560\) 3.65187e13 0.663095
\(561\) 2.64062e13i 0.475217i
\(562\) 3.26274e13i 0.581970i
\(563\) 7.84435e13i 1.38680i −0.720551 0.693402i \(-0.756111\pi\)
0.720551 0.693402i \(-0.243889\pi\)
\(564\) 5.88970e13i 1.03204i
\(565\) 1.19698e13i 0.207896i
\(566\) 1.52378e14 2.62325
\(567\) 9.07917e12 0.154928
\(568\) 7.03758e12i 0.119037i
\(569\) 7.06371e13i 1.18433i −0.805818 0.592163i \(-0.798274\pi\)
0.805818 0.592163i \(-0.201726\pi\)
\(570\) 5.52430e13i 0.918128i
\(571\) 2.77152e13i 0.456601i −0.973591 0.228300i \(-0.926683\pi\)
0.973591 0.228300i \(-0.0733169\pi\)
\(572\) 3.47248e13 0.567100
\(573\) 4.20834e13i 0.681299i
\(574\) 3.93455e13i 0.631445i
\(575\) 2.59745e13i 0.413245i
\(576\) 2.65703e13 0.419068
\(577\) 1.24044e13 0.193952 0.0969762 0.995287i \(-0.469083\pi\)
0.0969762 + 0.995287i \(0.469083\pi\)
\(578\) 8.96461e13i 1.38961i
\(579\) 4.64042e13 0.713123
\(580\) −6.41632e11 −0.00977565
\(581\) 1.14667e14i 1.73205i
\(582\) −2.52007e13 −0.377396
\(583\) 5.40666e13i 0.802762i
\(584\) 5.36711e12 0.0790090
\(585\) 1.09047e13i 0.159161i
\(586\) 1.69175e14i 2.44821i
\(587\) 7.69311e13i 1.10385i −0.833893 0.551926i \(-0.813893\pi\)
0.833893 0.551926i \(-0.186107\pi\)
\(588\) −4.36721e13 −0.621323
\(589\) 1.06335e14i 1.50003i
\(590\) −2.29694e13 + 5.45111e13i −0.321284 + 0.762474i
\(591\) −1.02818e13 −0.142604
\(592\) 6.62669e13i 0.911356i
\(593\) −1.05383e14 −1.43713 −0.718567 0.695458i \(-0.755202\pi\)
−0.718567 + 0.695458i \(0.755202\pi\)
\(594\) 1.22706e13 0.165934
\(595\) 8.21314e13 1.10135
\(596\) 1.62327e14i 2.15854i
\(597\) −2.33418e13 −0.307796
\(598\) 5.73810e13i 0.750347i
\(599\) 3.76129e13 0.487756 0.243878 0.969806i \(-0.421580\pi\)
0.243878 + 0.969806i \(0.421580\pi\)
\(600\) 6.24027e12i 0.0802504i
\(601\) 8.72793e13i 1.11311i −0.830810 0.556556i \(-0.812123\pi\)
0.830810 0.556556i \(-0.187877\pi\)
\(602\) 9.88412e13 1.25013
\(603\) 4.58178e12i 0.0574708i
\(604\) 2.52545e13i 0.314162i
\(605\) −2.99182e13 −0.369113
\(606\) −2.61689e13 −0.320201
\(607\) −7.53303e13 −0.914169 −0.457084 0.889423i \(-0.651106\pi\)
−0.457084 + 0.889423i \(0.651106\pi\)
\(608\) 2.29025e14i 2.75654i
\(609\) −1.02260e12 −0.0122073
\(610\) −1.12939e14 −1.33719
\(611\) −1.12741e14 −1.32397
\(612\) 4.55462e13 0.530511
\(613\) 1.41627e13i 0.163622i 0.996648 + 0.0818112i \(0.0260705\pi\)
−0.996648 + 0.0818112i \(0.973930\pi\)
\(614\) 2.35603e14i 2.69985i
\(615\) 8.89476e12 0.101102
\(616\) −1.48997e13 −0.167986
\(617\) −1.12007e14 −1.25262 −0.626310 0.779574i \(-0.715435\pi\)
−0.626310 + 0.779574i \(0.715435\pi\)
\(618\) −1.35546e14 −1.50364
\(619\) −4.68024e13 −0.515009 −0.257504 0.966277i \(-0.582900\pi\)
−0.257504 + 0.966277i \(0.582900\pi\)
\(620\) 4.60943e13i 0.503139i
\(621\) 1.08004e13i 0.116945i
\(622\) 5.18388e13i 0.556805i
\(623\) 4.09624e13i 0.436461i
\(624\) 3.87658e13i 0.409756i
\(625\) 1.35932e13 0.142535
\(626\) −2.79799e14 −2.91055
\(627\) 6.33816e13i 0.654072i
\(628\) 2.08233e13i 0.213182i
\(629\) 1.49036e14i 1.51369i
\(630\) 3.81655e13i 0.384563i
\(631\) 1.21461e14 1.21420 0.607099 0.794626i \(-0.292333\pi\)
0.607099 + 0.794626i \(0.292333\pi\)
\(632\) 3.56248e12i 0.0353319i
\(633\) 9.92934e13i 0.977017i
\(634\) 2.11774e14i 2.06741i
\(635\) −7.04009e13 −0.681882
\(636\) 9.32556e13 0.896168
\(637\) 8.35977e13i 0.797071i
\(638\) −1.38207e12 −0.0130745
\(639\) 2.06824e13 0.194132
\(640\) 2.45849e13i 0.228965i
\(641\) 1.69559e14 1.56686 0.783431 0.621478i \(-0.213468\pi\)
0.783431 + 0.621478i \(0.213468\pi\)
\(642\) 7.06129e13i 0.647454i
\(643\) −1.18664e14 −1.07960 −0.539801 0.841792i \(-0.681501\pi\)
−0.539801 + 0.841792i \(0.681501\pi\)
\(644\) 1.06971e14i 0.965689i
\(645\) 2.23448e13i 0.200161i
\(646\) 4.41677e14i 3.92593i
\(647\) 9.89076e13 0.872385 0.436192 0.899853i \(-0.356327\pi\)
0.436192 + 0.899853i \(0.356327\pi\)
\(648\) 2.59475e12i 0.0227102i
\(649\) −2.63533e13 + 6.25419e13i −0.228882 + 0.543184i
\(650\) −9.74343e13 −0.839741
\(651\) 7.34630e13i 0.628295i
\(652\) −1.86464e14 −1.58255
\(653\) −1.28969e14 −1.08622 −0.543110 0.839661i \(-0.682753\pi\)
−0.543110 + 0.839661i \(0.682753\pi\)
\(654\) 1.46906e14 1.22786
\(655\) 5.42604e13i 0.450067i
\(656\) 3.16205e13 0.260285
\(657\) 1.57732e13i 0.128852i
\(658\) 3.94584e14 3.19897
\(659\) 7.29197e13i 0.586702i 0.956005 + 0.293351i \(0.0947705\pi\)
−0.956005 + 0.293351i \(0.905229\pi\)
\(660\) 2.74748e13i 0.219389i
\(661\) −1.40088e14 −1.11018 −0.555092 0.831789i \(-0.687317\pi\)
−0.555092 + 0.831789i \(0.687317\pi\)
\(662\) 1.78770e14i 1.40607i
\(663\) 8.71851e13i 0.680573i
\(664\) −3.27710e13 −0.253892
\(665\) −1.97136e14 −1.51586
\(666\) 6.92550e13 0.528543
\(667\) 1.21647e12i 0.00921448i
\(668\) 1.07043e14 0.804779
\(669\) −6.57727e13 −0.490812
\(670\) 1.92601e13 0.142654
\(671\) −1.29577e14 −0.952613
\(672\) 1.58225e14i 1.15459i
\(673\) 2.59237e14i 1.87768i 0.344351 + 0.938841i \(0.388099\pi\)
−0.344351 + 0.938841i \(0.611901\pi\)
\(674\) 7.75580e12 0.0557606
\(675\) −1.83393e13 −0.130877
\(676\) −4.62416e13 −0.327567
\(677\) 4.40432e13 0.309696 0.154848 0.987938i \(-0.450511\pi\)
0.154848 + 0.987938i \(0.450511\pi\)
\(678\) −4.44709e13 −0.310404
\(679\) 8.99292e13i 0.623091i
\(680\) 2.34724e13i 0.161441i
\(681\) 8.19518e12i 0.0559530i
\(682\) 9.92864e13i 0.672927i
\(683\) 1.45348e14i 0.977923i 0.872305 + 0.488962i \(0.162624\pi\)
−0.872305 + 0.488962i \(0.837376\pi\)
\(684\) −1.09322e14 −0.730177
\(685\) −2.51839e13 −0.166982
\(686\) 1.72821e13i 0.113756i
\(687\) 5.06242e13i 0.330807i
\(688\) 7.94348e13i 0.515310i
\(689\) 1.78511e14i 1.14966i
\(690\) 4.54007e13 0.290280
\(691\) 2.12932e13i 0.135161i 0.997714 + 0.0675803i \(0.0215279\pi\)
−0.997714 + 0.0675803i \(0.978472\pi\)
\(692\) 1.49556e14i 0.942480i
\(693\) 4.37881e13i 0.273962i
\(694\) 2.41633e14 1.50093
\(695\) −9.37460e12 −0.0578134
\(696\) 2.92251e11i 0.00178941i
\(697\) 7.11151e13 0.432312
\(698\) 8.98245e13 0.542148
\(699\) 1.12155e14i 0.672100i
\(700\) 1.81639e14 1.08074
\(701\) 2.46761e14i 1.45776i −0.684642 0.728880i \(-0.740041\pi\)
0.684642 0.728880i \(-0.259959\pi\)
\(702\) 4.05138e13 0.237639
\(703\) 3.57723e14i 2.08339i
\(704\) 1.28146e14i 0.741043i
\(705\) 8.92027e13i 0.512192i
\(706\) −5.36984e13 −0.306153
\(707\) 9.33844e13i 0.528661i
\(708\) −1.07874e14 4.54549e13i −0.606388 0.255514i
\(709\) −5.55549e13 −0.310092 −0.155046 0.987907i \(-0.549553\pi\)
−0.155046 + 0.987907i \(0.549553\pi\)
\(710\) 8.69413e13i 0.481875i
\(711\) 1.04696e13 0.0576213
\(712\) −1.17067e13 −0.0639785
\(713\) 8.73899e13 0.474257
\(714\) 3.05139e14i 1.64440i
\(715\) 5.25926e13 0.281446
\(716\) 7.18004e13i 0.381559i
\(717\) 1.43475e14 0.757150
\(718\) 4.28504e14i 2.24560i
\(719\) 2.35164e14i 1.22385i −0.790917 0.611923i \(-0.790396\pi\)
0.790917 0.611923i \(-0.209604\pi\)
\(720\) 3.06721e13 0.158519
\(721\) 4.83699e14i 2.48256i
\(722\) 7.73148e14i 3.94073i
\(723\) −1.78511e14 −0.903597
\(724\) 1.44204e14 0.724909
\(725\) 2.06559e12 0.0103123
\(726\) 1.11154e14i 0.551114i
\(727\) −2.62595e14 −1.29305 −0.646524 0.762894i \(-0.723778\pi\)
−0.646524 + 0.762894i \(0.723778\pi\)
\(728\) −4.91942e13 −0.240578
\(729\) 7.62560e12 0.0370370
\(730\) 6.63046e13 0.319838
\(731\) 1.78651e14i 0.855889i
\(732\) 2.23499e14i 1.06346i
\(733\) 1.07122e14 0.506242 0.253121 0.967435i \(-0.418543\pi\)
0.253121 + 0.967435i \(0.418543\pi\)
\(734\) −3.28004e14 −1.53957
\(735\) −6.61438e13 −0.308356
\(736\) 1.88221e14 0.871523
\(737\) 2.20975e13 0.101626
\(738\) 3.30463e13i 0.150953i
\(739\) 1.38816e14i 0.629821i −0.949121 0.314911i \(-0.898025\pi\)
0.949121 0.314911i \(-0.101975\pi\)
\(740\) 1.55067e14i 0.698811i
\(741\) 2.09266e14i 0.936717i
\(742\) 6.24772e14i 2.77780i
\(743\) 4.74890e13 0.209725 0.104862 0.994487i \(-0.466560\pi\)
0.104862 + 0.994487i \(0.466560\pi\)
\(744\) −2.09951e13 −0.0920986
\(745\) 2.45854e14i 1.07126i
\(746\) 5.58698e14i 2.41815i
\(747\) 9.63092e13i 0.414062i
\(748\) 2.19665e14i 0.938110i
\(749\) −2.51984e14 −1.06897
\(750\) 1.90452e14i 0.802563i
\(751\) 2.08342e13i 0.0872120i 0.999049 + 0.0436060i \(0.0138846\pi\)
−0.999049 + 0.0436060i \(0.986115\pi\)
\(752\) 3.17111e14i 1.31863i
\(753\) −1.27850e13 −0.0528114
\(754\) −4.56315e12 −0.0187244
\(755\) 3.82493e13i 0.155915i
\(756\) −7.55269e13 −0.305839
\(757\) −2.46077e13 −0.0989902 −0.0494951 0.998774i \(-0.515761\pi\)
−0.0494951 + 0.998774i \(0.515761\pi\)
\(758\) 5.86546e14i 2.34399i
\(759\) 5.20893e13 0.206795
\(760\) 5.63398e13i 0.222202i
\(761\) 1.25845e14 0.493074 0.246537 0.969133i \(-0.420707\pi\)
0.246537 + 0.969133i \(0.420707\pi\)
\(762\) 2.61557e14i 1.01810i
\(763\) 5.24237e14i 2.02724i
\(764\) 3.50079e14i 1.34493i
\(765\) 6.89822e13 0.263287
\(766\) 1.12861e14i 0.427957i
\(767\) −8.70104e13 + 2.06494e14i −0.327789 + 0.777912i
\(768\) 1.02594e14 0.383985
\(769\) 4.86302e14i 1.80832i −0.427198 0.904158i \(-0.640499\pi\)
0.427198 0.904158i \(-0.359501\pi\)
\(770\) −1.84069e14 −0.680028
\(771\) −3.57958e13 −0.131389
\(772\) −3.86023e14 −1.40775
\(773\) 5.16389e14i 1.87102i −0.353294 0.935512i \(-0.614938\pi\)
0.353294 0.935512i \(-0.385062\pi\)
\(774\) 8.30168e13 0.298855
\(775\) 1.48390e14i 0.530758i
\(776\) 2.57010e13 0.0913358
\(777\) 2.47138e14i 0.872639i
\(778\) 6.66079e13i 0.233683i
\(779\) −1.70694e14 −0.