Properties

Label 43.7.b.b.42.15
Level 43
Weight 7
Character 43.42
Analytic conductor 9.892
Analytic rank 0
Dimension 20
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.15
Root \(8.33048i\) of \(x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + 80362197690736 x^{8} + 2545997652841536 x^{6} + 40210452531479040 x^{4} + 212033222410436608 x^{2} + 64236717122519040\)
Character \(\chi\) \(=\) 43.42
Dual form 43.7.b.b.42.6

$q$-expansion

\(f(q)\) \(=\) \(q+8.33048i q^{2} -16.8005i q^{3} -5.39690 q^{4} +47.9107i q^{5} +139.956 q^{6} -493.652i q^{7} +488.192i q^{8} +446.745 q^{9} +O(q^{10})\) \(q+8.33048i q^{2} -16.8005i q^{3} -5.39690 q^{4} +47.9107i q^{5} +139.956 q^{6} -493.652i q^{7} +488.192i q^{8} +446.745 q^{9} -399.119 q^{10} +2011.69 q^{11} +90.6704i q^{12} -124.091 q^{13} +4112.36 q^{14} +804.922 q^{15} -4412.28 q^{16} +3857.23 q^{17} +3721.60i q^{18} +11142.3i q^{19} -258.569i q^{20} -8293.58 q^{21} +16758.3i q^{22} -1130.75 q^{23} +8201.85 q^{24} +13329.6 q^{25} -1033.73i q^{26} -19753.0i q^{27} +2664.19i q^{28} -24367.1i q^{29} +6705.39i q^{30} -12408.9 q^{31} -5512.08i q^{32} -33797.2i q^{33} +32132.6i q^{34} +23651.2 q^{35} -2411.04 q^{36} -84686.2i q^{37} -92820.4 q^{38} +2084.78i q^{39} -23389.6 q^{40} +125398. q^{41} -69089.5i q^{42} +(-60660.4 + 51397.3i) q^{43} -10856.9 q^{44} +21403.9i q^{45} -9419.72i q^{46} -200638. q^{47} +74128.2i q^{48} -126043. q^{49} +111042. i q^{50} -64803.2i q^{51} +669.704 q^{52} -124888. q^{53} +164552. q^{54} +96381.3i q^{55} +240997. q^{56} +187195. q^{57} +202990. q^{58} -123831. q^{59} -4344.08 q^{60} +28789.1i q^{61} -103372. i q^{62} -220536. i q^{63} -236467. q^{64} -5945.26i q^{65} +281547. q^{66} +289876. q^{67} -20817.1 q^{68} +18997.2i q^{69} +197026. i q^{70} +420644. i q^{71} +218097. i q^{72} +330369. i q^{73} +705476. q^{74} -223943. i q^{75} -60133.7i q^{76} -993072. i q^{77} -17367.2 q^{78} -647349. q^{79} -211395. i q^{80} -6183.39 q^{81} +1.04462e6i q^{82} -76719.5 q^{83} +44759.6 q^{84} +184802. i q^{85} +(-428164. - 505330. i) q^{86} -409379. q^{87} +982088. i q^{88} +16908.5i q^{89} -178304. q^{90} +61257.5i q^{91} +6102.56 q^{92} +208476. i q^{93} -1.67141e6i q^{94} -533834. q^{95} -92605.5 q^{96} -1.10090e6 q^{97} -1.05000e6i q^{98} +898710. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.33048i 1.04131i 0.853767 + 0.520655i \(0.174312\pi\)
−0.853767 + 0.520655i \(0.825688\pi\)
\(3\) 16.8005i 0.622239i −0.950371 0.311120i \(-0.899296\pi\)
0.950371 0.311120i \(-0.100704\pi\)
\(4\) −5.39690 −0.0843265
\(5\) 47.9107i 0.383286i 0.981465 + 0.191643i \(0.0613815\pi\)
−0.981465 + 0.191643i \(0.938618\pi\)
\(6\) 139.956 0.647944
\(7\) 493.652i 1.43922i −0.694379 0.719609i \(-0.744321\pi\)
0.694379 0.719609i \(-0.255679\pi\)
\(8\) 488.192i 0.953500i
\(9\) 446.745 0.612818
\(10\) −399.119 −0.399119
\(11\) 2011.69 1.51141 0.755704 0.654913i \(-0.227295\pi\)
0.755704 + 0.654913i \(0.227295\pi\)
\(12\) 90.6704i 0.0524713i
\(13\) −124.091 −0.0564818 −0.0282409 0.999601i \(-0.508991\pi\)
−0.0282409 + 0.999601i \(0.508991\pi\)
\(14\) 4112.36 1.49867
\(15\) 804.922 0.238495
\(16\) −4412.28 −1.07722
\(17\) 3857.23 0.785106 0.392553 0.919729i \(-0.371592\pi\)
0.392553 + 0.919729i \(0.371592\pi\)
\(18\) 3721.60i 0.638134i
\(19\) 11142.3i 1.62447i 0.583328 + 0.812237i \(0.301750\pi\)
−0.583328 + 0.812237i \(0.698250\pi\)
\(20\) 258.569i 0.0323212i
\(21\) −8293.58 −0.895538
\(22\) 16758.3i 1.57385i
\(23\) −1130.75 −0.0929361 −0.0464681 0.998920i \(-0.514797\pi\)
−0.0464681 + 0.998920i \(0.514797\pi\)
\(24\) 8201.85 0.593305
\(25\) 13329.6 0.853092
\(26\) 1033.73i 0.0588151i
\(27\) 19753.0i 1.00356i
\(28\) 2664.19i 0.121364i
\(29\) 24367.1i 0.999102i −0.866284 0.499551i \(-0.833498\pi\)
0.866284 0.499551i \(-0.166502\pi\)
\(30\) 6705.39i 0.248348i
\(31\) −12408.9 −0.416533 −0.208266 0.978072i \(-0.566782\pi\)
−0.208266 + 0.978072i \(0.566782\pi\)
\(32\) 5512.08i 0.168215i
\(33\) 33797.2i 0.940458i
\(34\) 32132.6i 0.817539i
\(35\) 23651.2 0.551632
\(36\) −2411.04 −0.0516769
\(37\) 84686.2i 1.67189i −0.548814 0.835944i \(-0.684921\pi\)
0.548814 0.835944i \(-0.315079\pi\)
\(38\) −92820.4 −1.69158
\(39\) 2084.78i 0.0351452i
\(40\) −23389.6 −0.365463
\(41\) 125398. 1.81944 0.909721 0.415221i \(-0.136296\pi\)
0.909721 + 0.415221i \(0.136296\pi\)
\(42\) 69089.5i 0.932533i
\(43\) −60660.4 + 51397.3i −0.762957 + 0.646450i
\(44\) −10856.9 −0.127452
\(45\) 21403.9i 0.234885i
\(46\) 9419.72i 0.0967753i
\(47\) −200638. −1.93250 −0.966250 0.257606i \(-0.917066\pi\)
−0.966250 + 0.257606i \(0.917066\pi\)
\(48\) 74128.2i 0.670286i
\(49\) −126043. −1.07135
\(50\) 111042.i 0.888333i
\(51\) 64803.2i 0.488524i
\(52\) 669.704 0.00476291
\(53\) −124888. −0.838865 −0.419433 0.907786i \(-0.637771\pi\)
−0.419433 + 0.907786i \(0.637771\pi\)
\(54\) 164552. 1.04502
\(55\) 96381.3i 0.579301i
\(56\) 240997. 1.37229
\(57\) 187195. 1.01081
\(58\) 202990. 1.04038
\(59\) −123831. −0.602941 −0.301470 0.953476i \(-0.597477\pi\)
−0.301470 + 0.953476i \(0.597477\pi\)
\(60\) −4344.08 −0.0201115
\(61\) 28789.1i 0.126835i 0.997987 + 0.0634175i \(0.0202000\pi\)
−0.997987 + 0.0634175i \(0.979800\pi\)
\(62\) 103372.i 0.433740i
\(63\) 220536.i 0.881980i
\(64\) −236467. −0.902051
\(65\) 5945.26i 0.0216487i
\(66\) 281547. 0.979308
\(67\) 289876. 0.963801 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(68\) −20817.1 −0.0662053
\(69\) 18997.2i 0.0578285i
\(70\) 197026.i 0.574420i
\(71\) 420644.i 1.17528i 0.809124 + 0.587638i \(0.199942\pi\)
−0.809124 + 0.587638i \(0.800058\pi\)
\(72\) 218097.i 0.584322i
\(73\) 330369.i 0.849240i 0.905372 + 0.424620i \(0.139592\pi\)
−0.905372 + 0.424620i \(0.860408\pi\)
\(74\) 705476. 1.74095
\(75\) 223943.i 0.530827i
\(76\) 60133.7i 0.136986i
\(77\) 993072.i 2.17525i
\(78\) −17367.2 −0.0365970
\(79\) −647349. −1.31298 −0.656489 0.754336i \(-0.727959\pi\)
−0.656489 + 0.754336i \(0.727959\pi\)
\(80\) 211395.i 0.412881i
\(81\) −6183.39 −0.0116351
\(82\) 1.04462e6i 1.89460i
\(83\) −76719.5 −0.134175 −0.0670875 0.997747i \(-0.521371\pi\)
−0.0670875 + 0.997747i \(0.521371\pi\)
\(84\) 44759.6 0.0755176
\(85\) 184802.i 0.300920i
\(86\) −428164. 505330.i −0.673154 0.794474i
\(87\) −409379. −0.621681
\(88\) 982088.i 1.44113i
\(89\) 16908.5i 0.0239848i 0.999928 + 0.0119924i \(0.00381739\pi\)
−0.999928 + 0.0119924i \(0.996183\pi\)
\(90\) −178304. −0.244588
\(91\) 61257.5i 0.0812897i
\(92\) 6102.56 0.00783698
\(93\) 208476.i 0.259183i
\(94\) 1.67141e6i 2.01233i
\(95\) −533834. −0.622637
\(96\) −92605.5 −0.104670
\(97\) −1.10090e6 −1.20623 −0.603117 0.797653i \(-0.706075\pi\)
−0.603117 + 0.797653i \(0.706075\pi\)
\(98\) 1.05000e6i 1.11561i
\(99\) 898710. 0.926219
\(100\) −71938.3 −0.0719383
\(101\) −1.03617e6 −1.00569 −0.502846 0.864376i \(-0.667714\pi\)
−0.502846 + 0.864376i \(0.667714\pi\)
\(102\) 539842. 0.508705
\(103\) 1.09074e6 0.998178 0.499089 0.866551i \(-0.333668\pi\)
0.499089 + 0.866551i \(0.333668\pi\)
\(104\) 60580.0i 0.0538554i
\(105\) 397351.i 0.343247i
\(106\) 1.04037e6i 0.873519i
\(107\) 788177. 0.643387 0.321694 0.946844i \(-0.395748\pi\)
0.321694 + 0.946844i \(0.395748\pi\)
\(108\) 106605.i 0.0846266i
\(109\) −17946.9 −0.0138583 −0.00692913 0.999976i \(-0.502206\pi\)
−0.00692913 + 0.999976i \(0.502206\pi\)
\(110\) −802902. −0.603232
\(111\) −1.42277e6 −1.04031
\(112\) 2.17813e6i 1.55035i
\(113\) 457458.i 0.317041i −0.987356 0.158521i \(-0.949328\pi\)
0.987356 0.158521i \(-0.0506724\pi\)
\(114\) 1.55943e6i 1.05257i
\(115\) 54175.2i 0.0356211i
\(116\) 131507.i 0.0842509i
\(117\) −55436.8 −0.0346131
\(118\) 1.03157e6i 0.627848i
\(119\) 1.90413e6i 1.12994i
\(120\) 392956.i 0.227405i
\(121\) 2.27532e6 1.28436
\(122\) −239827. −0.132075
\(123\) 2.10674e6i 1.13213i
\(124\) 66969.7 0.0351248
\(125\) 1.38723e6i 0.710264i
\(126\) 1.83717e6 0.918414
\(127\) −1.91397e6 −0.934383 −0.467191 0.884156i \(-0.654734\pi\)
−0.467191 + 0.884156i \(0.654734\pi\)
\(128\) 2.32266e6i 1.10753i
\(129\) 863498. + 1.01912e6i 0.402246 + 0.474742i
\(130\) 49526.9 0.0225430
\(131\) 2.53980e6i 1.12976i 0.825174 + 0.564879i \(0.191077\pi\)
−0.825174 + 0.564879i \(0.808923\pi\)
\(132\) 182400.i 0.0793055i
\(133\) 5.50040e6 2.33797
\(134\) 2.41480e6i 1.00362i
\(135\) 946383. 0.384650
\(136\) 1.88307e6i 0.748599i
\(137\) 1.25787e6i 0.489186i 0.969626 + 0.244593i \(0.0786544\pi\)
−0.969626 + 0.244593i \(0.921346\pi\)
\(138\) −158256. −0.0602174
\(139\) −1.15999e6 −0.431927 −0.215963 0.976401i \(-0.569289\pi\)
−0.215963 + 0.976401i \(0.569289\pi\)
\(140\) −127643. −0.0465172
\(141\) 3.37081e6i 1.20248i
\(142\) −3.50417e6 −1.22383
\(143\) −249631. −0.0853671
\(144\) −1.97116e6 −0.660138
\(145\) 1.16745e6 0.382942
\(146\) −2.75213e6 −0.884322
\(147\) 2.11758e6i 0.666636i
\(148\) 457043.i 0.140985i
\(149\) 6.01941e6i 1.81968i −0.414959 0.909840i \(-0.636204\pi\)
0.414959 0.909840i \(-0.363796\pi\)
\(150\) 1.86555e6 0.552756
\(151\) 2.07076e6i 0.601449i 0.953711 + 0.300725i \(0.0972285\pi\)
−0.953711 + 0.300725i \(0.902771\pi\)
\(152\) −5.43956e6 −1.54894
\(153\) 1.72320e6 0.481128
\(154\) 8.27277e6 2.26511
\(155\) 594520.i 0.159651i
\(156\) 11251.3i 0.00296367i
\(157\) 1.17682e6i 0.304096i 0.988373 + 0.152048i \(0.0485869\pi\)
−0.988373 + 0.152048i \(0.951413\pi\)
\(158\) 5.39273e6i 1.36722i
\(159\) 2.09817e6i 0.521975i
\(160\) 264088. 0.0644746
\(161\) 558199.i 0.133755i
\(162\) 51510.6i 0.0121158i
\(163\) 2.85797e6i 0.659925i −0.943994 0.329962i \(-0.892964\pi\)
0.943994 0.329962i \(-0.107036\pi\)
\(164\) −676759. −0.153427
\(165\) 1.61925e6 0.360464
\(166\) 639110.i 0.139718i
\(167\) −1.92344e6 −0.412980 −0.206490 0.978449i \(-0.566204\pi\)
−0.206490 + 0.978449i \(0.566204\pi\)
\(168\) 4.04886e6i 0.853896i
\(169\) −4.81141e6 −0.996810
\(170\) −1.53949e6 −0.313351
\(171\) 4.97775e6i 0.995507i
\(172\) 327378. 277386.i 0.0643375 0.0545129i
\(173\) 4.93838e6 0.953775 0.476887 0.878964i \(-0.341765\pi\)
0.476887 + 0.878964i \(0.341765\pi\)
\(174\) 3.41032e6i 0.647362i
\(175\) 6.58017e6i 1.22779i
\(176\) −8.87611e6 −1.62811
\(177\) 2.08042e6i 0.375173i
\(178\) −140856. −0.0249756
\(179\) 6.45397e6i 1.12530i −0.826695 0.562650i \(-0.809782\pi\)
0.826695 0.562650i \(-0.190218\pi\)
\(180\) 115514.i 0.0198070i
\(181\) −807853. −0.136238 −0.0681188 0.997677i \(-0.521700\pi\)
−0.0681188 + 0.997677i \(0.521700\pi\)
\(182\) −510305. −0.0846477
\(183\) 483671. 0.0789217
\(184\) 552025.i 0.0886146i
\(185\) 4.05737e6 0.640811
\(186\) −1.73670e6 −0.269890
\(187\) 7.75953e6 1.18662
\(188\) 1.08282e6 0.162961
\(189\) −9.75113e6 −1.44434
\(190\) 4.44709e6i 0.648359i
\(191\) 1.42360e6i 0.204310i 0.994768 + 0.102155i \(0.0325738\pi\)
−0.994768 + 0.102155i \(0.967426\pi\)
\(192\) 3.97276e6i 0.561292i
\(193\) 457518. 0.0636409 0.0318204 0.999494i \(-0.489870\pi\)
0.0318204 + 0.999494i \(0.489870\pi\)
\(194\) 9.17100e6i 1.25606i
\(195\) −99883.2 −0.0134706
\(196\) 680243. 0.0903432
\(197\) −6.24148e6 −0.816373 −0.408187 0.912898i \(-0.633839\pi\)
−0.408187 + 0.912898i \(0.633839\pi\)
\(198\) 7.48668e6i 0.964481i
\(199\) 9.27567e6i 1.17703i 0.808488 + 0.588513i \(0.200286\pi\)
−0.808488 + 0.588513i \(0.799714\pi\)
\(200\) 6.50739e6i 0.813423i
\(201\) 4.87004e6i 0.599715i
\(202\) 8.63176e6i 1.04724i
\(203\) −1.20289e7 −1.43793
\(204\) 349736.i 0.0411955i
\(205\) 6.00789e6i 0.697366i
\(206\) 9.08635e6i 1.03941i
\(207\) −505158. −0.0569530
\(208\) 547521. 0.0608431
\(209\) 2.24147e7i 2.45524i
\(210\) 3.31013e6 0.357426
\(211\) 1.36638e7i 1.45453i −0.686354 0.727267i \(-0.740790\pi\)
0.686354 0.727267i \(-0.259210\pi\)
\(212\) 674007. 0.0707386
\(213\) 7.06701e6 0.731303
\(214\) 6.56589e6i 0.669965i
\(215\) −2.46248e6 2.90628e6i −0.247775 0.292430i
\(216\) 9.64328e6 0.956893
\(217\) 6.12569e6i 0.599482i
\(218\) 149506.i 0.0144307i
\(219\) 5.55034e6 0.528430
\(220\) 520160.i 0.0488505i
\(221\) −478645. −0.0443442
\(222\) 1.18523e7i 1.08329i
\(223\) 1.05558e7i 0.951865i 0.879482 + 0.475933i \(0.157889\pi\)
−0.879482 + 0.475933i \(0.842111\pi\)
\(224\) −2.72105e6 −0.242099
\(225\) 5.95491e6 0.522791
\(226\) 3.81084e6 0.330138
\(227\) 1.22631e7i 1.04839i −0.851599 0.524194i \(-0.824367\pi\)
0.851599 0.524194i \(-0.175633\pi\)
\(228\) −1.01027e6 −0.0852382
\(229\) 1.47550e7 1.22866 0.614332 0.789048i \(-0.289426\pi\)
0.614332 + 0.789048i \(0.289426\pi\)
\(230\) 451305. 0.0370926
\(231\) −1.66841e7 −1.35352
\(232\) 1.18958e7 0.952644
\(233\) 1.30644e7i 1.03282i −0.856343 0.516408i \(-0.827269\pi\)
0.856343 0.516408i \(-0.172731\pi\)
\(234\) 461815.i 0.0360430i
\(235\) 9.61271e6i 0.740700i
\(236\) 668305. 0.0508439
\(237\) 1.08758e7i 0.816986i
\(238\) 1.58623e7 1.17662
\(239\) 1.34499e7 0.985199 0.492600 0.870256i \(-0.336047\pi\)
0.492600 + 0.870256i \(0.336047\pi\)
\(240\) −3.55154e6 −0.256911
\(241\) 1.99696e7i 1.42665i 0.700832 + 0.713326i \(0.252812\pi\)
−0.700832 + 0.713326i \(0.747188\pi\)
\(242\) 1.89545e7i 1.33741i
\(243\) 1.42961e7i 0.996319i
\(244\) 155372.i 0.0106956i
\(245\) 6.03882e6i 0.410633i
\(246\) 1.75501e7 1.17890
\(247\) 1.38265e6i 0.0917532i
\(248\) 6.05794e6i 0.397164i
\(249\) 1.28892e6i 0.0834889i
\(250\) −1.15563e7 −0.739605
\(251\) −3.10748e6 −0.196511 −0.0982554 0.995161i \(-0.531326\pi\)
−0.0982554 + 0.995161i \(0.531326\pi\)
\(252\) 1.19021e6i 0.0743743i
\(253\) −2.27472e6 −0.140464
\(254\) 1.59443e7i 0.972982i
\(255\) 3.10477e6 0.187244
\(256\) 4.21496e6 0.251231
\(257\) 795874.i 0.0468862i 0.999725 + 0.0234431i \(0.00746285\pi\)
−0.999725 + 0.0234431i \(0.992537\pi\)
\(258\) −8.48978e6 + 7.19335e6i −0.494353 + 0.418863i
\(259\) −4.18055e7 −2.40621
\(260\) 32086.0i 0.00182556i
\(261\) 1.08859e7i 0.612268i
\(262\) −2.11577e7 −1.17643
\(263\) 2.05517e7i 1.12974i −0.825179 0.564871i \(-0.808926\pi\)
0.825179 0.564871i \(-0.191074\pi\)
\(264\) 1.64995e7 0.896726
\(265\) 5.98346e6i 0.321525i
\(266\) 4.58210e7i 2.43455i
\(267\) 284071. 0.0149243
\(268\) −1.56443e6 −0.0812740
\(269\) −5.28734e6 −0.271632 −0.135816 0.990734i \(-0.543366\pi\)
−0.135816 + 0.990734i \(0.543366\pi\)
\(270\) 7.88382e6i 0.400540i
\(271\) −5.39678e6 −0.271161 −0.135580 0.990766i \(-0.543290\pi\)
−0.135580 + 0.990766i \(0.543290\pi\)
\(272\) −1.70191e7 −0.845729
\(273\) 1.02915e6 0.0505816
\(274\) −1.04787e7 −0.509395
\(275\) 2.68149e7 1.28937
\(276\) 102526.i 0.00487648i
\(277\) 7.82259e6i 0.368054i 0.982921 + 0.184027i \(0.0589134\pi\)
−0.982921 + 0.184027i \(0.941087\pi\)
\(278\) 9.66328e6i 0.449770i
\(279\) −5.54362e6 −0.255259
\(280\) 1.15463e7i 0.525981i
\(281\) −5.00396e6 −0.225525 −0.112763 0.993622i \(-0.535970\pi\)
−0.112763 + 0.993622i \(0.535970\pi\)
\(282\) −2.80805e7 −1.25215
\(283\) −3.71907e7 −1.64088 −0.820438 0.571736i \(-0.806270\pi\)
−0.820438 + 0.571736i \(0.806270\pi\)
\(284\) 2.27017e6i 0.0991069i
\(285\) 8.96865e6i 0.387429i
\(286\) 2.07955e6i 0.0888936i
\(287\) 6.19028e7i 2.61857i
\(288\) 2.46249e6i 0.103086i
\(289\) −9.25937e6 −0.383608
\(290\) 9.72538e6i 0.398761i
\(291\) 1.84956e7i 0.750566i
\(292\) 1.78297e6i 0.0716134i
\(293\) 2.43355e7 0.967468 0.483734 0.875215i \(-0.339280\pi\)
0.483734 + 0.875215i \(0.339280\pi\)
\(294\) −1.76405e7 −0.694175
\(295\) 5.93285e6i 0.231098i
\(296\) 4.13431e7 1.59415
\(297\) 3.97369e7i 1.51679i
\(298\) 5.01446e7 1.89485
\(299\) 140316. 0.00524920
\(300\) 1.20860e6i 0.0447628i
\(301\) 2.53724e7 + 2.99451e7i 0.930382 + 1.09806i
\(302\) −1.72504e7 −0.626295
\(303\) 1.74081e7i 0.625781i
\(304\) 4.91627e7i 1.74991i
\(305\) −1.37931e6 −0.0486140
\(306\) 1.43550e7i 0.501003i
\(307\) −5.56753e7 −1.92419 −0.962094 0.272718i \(-0.912077\pi\)
−0.962094 + 0.272718i \(0.912077\pi\)
\(308\) 5.35951e6i 0.183431i
\(309\) 1.83249e7i 0.621105i
\(310\) 4.95264e6 0.166246
\(311\) 2.20696e7 0.733692 0.366846 0.930282i \(-0.380438\pi\)
0.366846 + 0.930282i \(0.380438\pi\)
\(312\) −1.01777e6 −0.0335109
\(313\) 2.38515e7i 0.777826i −0.921275 0.388913i \(-0.872851\pi\)
0.921275 0.388913i \(-0.127149\pi\)
\(314\) −9.80348e6 −0.316659
\(315\) 1.05661e7 0.338050
\(316\) 3.49368e6 0.110719
\(317\) 4.51895e7 1.41860 0.709300 0.704906i \(-0.249011\pi\)
0.709300 + 0.704906i \(0.249011\pi\)
\(318\) −1.74788e7 −0.543538
\(319\) 4.90190e7i 1.51005i
\(320\) 1.13293e7i 0.345743i
\(321\) 1.32417e7i 0.400341i
\(322\) −4.65006e6 −0.139281
\(323\) 4.29782e7i 1.27538i
\(324\) 33371.2 0.000981152
\(325\) −1.65407e6 −0.0481842
\(326\) 2.38082e7 0.687186
\(327\) 301515.i 0.00862315i
\(328\) 6.12182e7i 1.73484i
\(329\) 9.90453e7i 2.78129i
\(330\) 1.34891e7i 0.375355i
\(331\) 4.81328e7i 1.32726i 0.748059 + 0.663632i \(0.230986\pi\)
−0.748059 + 0.663632i \(0.769014\pi\)
\(332\) 414047. 0.0113145
\(333\) 3.78331e7i 1.02456i
\(334\) 1.60232e7i 0.430040i
\(335\) 1.38881e7i 0.369411i
\(336\) 3.65935e7 0.964688
\(337\) 7.06937e7 1.84710 0.923551 0.383476i \(-0.125273\pi\)
0.923551 + 0.383476i \(0.125273\pi\)
\(338\) 4.00814e7i 1.03799i
\(339\) −7.68550e6 −0.197275
\(340\) 997360.i 0.0253755i
\(341\) −2.49629e7 −0.629551
\(342\) −4.14670e7 −1.03663
\(343\) 4.14384e6i 0.102688i
\(344\) −2.50917e7 2.96139e7i −0.616390 0.727479i
\(345\) −910168. −0.0221648
\(346\) 4.11390e7i 0.993175i
\(347\) 3.36102e7i 0.804420i 0.915547 + 0.402210i \(0.131758\pi\)
−0.915547 + 0.402210i \(0.868242\pi\)
\(348\) 2.20937e6 0.0524242
\(349\) 3.01730e7i 0.709811i 0.934902 + 0.354905i \(0.115487\pi\)
−0.934902 + 0.354905i \(0.884513\pi\)
\(350\) 5.48159e7 1.27851
\(351\) 2.45117e6i 0.0566828i
\(352\) 1.10886e7i 0.254242i
\(353\) −1.35366e6 −0.0307740 −0.0153870 0.999882i \(-0.504898\pi\)
−0.0153870 + 0.999882i \(0.504898\pi\)
\(354\) −1.73309e7 −0.390672
\(355\) −2.01534e7 −0.450466
\(356\) 91253.6i 0.00202255i
\(357\) −3.19902e7 −0.703093
\(358\) 5.37647e7 1.17179
\(359\) 4.50676e7 0.974050 0.487025 0.873388i \(-0.338082\pi\)
0.487025 + 0.873388i \(0.338082\pi\)
\(360\) −1.04492e7 −0.223962
\(361\) −7.71042e7 −1.63891
\(362\) 6.72981e6i 0.141865i
\(363\) 3.82263e7i 0.799177i
\(364\) 330601.i 0.00685488i
\(365\) −1.58282e7 −0.325501
\(366\) 4.02921e6i 0.0821820i
\(367\) −3.86047e7 −0.780983 −0.390492 0.920606i \(-0.627695\pi\)
−0.390492 + 0.920606i \(0.627695\pi\)
\(368\) 4.98920e6 0.100112
\(369\) 5.60208e7 1.11499
\(370\) 3.37999e7i 0.667283i
\(371\) 6.16511e7i 1.20731i
\(372\) 1.12512e6i 0.0218560i
\(373\) 5.22223e7i 1.00631i −0.864198 0.503153i \(-0.832173\pi\)
0.864198 0.503153i \(-0.167827\pi\)
\(374\) 6.46406e7i 1.23564i
\(375\) 2.33062e7 0.441954
\(376\) 9.79498e7i 1.84264i
\(377\) 3.02373e6i 0.0564311i
\(378\) 8.12316e7i 1.50401i
\(379\) −4.96049e7 −0.911186 −0.455593 0.890188i \(-0.650573\pi\)
−0.455593 + 0.890188i \(0.650573\pi\)
\(380\) 2.88105e6 0.0525049
\(381\) 3.21556e7i 0.581410i
\(382\) −1.18593e7 −0.212750
\(383\) 7.72156e6i 0.137439i 0.997636 + 0.0687193i \(0.0218913\pi\)
−0.997636 + 0.0687193i \(0.978109\pi\)
\(384\) −3.90217e7 −0.689149
\(385\) 4.75788e7 0.833741
\(386\) 3.81134e6i 0.0662699i
\(387\) −2.70997e7 + 2.29615e7i −0.467554 + 0.396156i
\(388\) 5.94143e6 0.101717
\(389\) 7.60790e7i 1.29246i 0.763144 + 0.646228i \(0.223655\pi\)
−0.763144 + 0.646228i \(0.776345\pi\)
\(390\) 832075.i 0.0140271i
\(391\) −4.36157e6 −0.0729647
\(392\) 6.15333e7i 1.02153i
\(393\) 4.26698e7 0.702979
\(394\) 5.19945e7i 0.850098i
\(395\) 3.10150e7i 0.503246i
\(396\) −4.85024e6 −0.0781049
\(397\) 1.53245e7 0.244914 0.122457 0.992474i \(-0.460923\pi\)
0.122457 + 0.992474i \(0.460923\pi\)
\(398\) −7.72708e7 −1.22565
\(399\) 9.24092e7i 1.45478i
\(400\) −5.88137e7 −0.918964
\(401\) 2.42146e7 0.375530 0.187765 0.982214i \(-0.439876\pi\)
0.187765 + 0.982214i \(0.439876\pi\)
\(402\) 4.05698e7 0.624489
\(403\) 1.53983e6 0.0235265
\(404\) 5.59208e6 0.0848066
\(405\) 296251.i 0.00445959i
\(406\) 1.00206e8i 1.49733i
\(407\) 1.70362e8i 2.52691i
\(408\) 3.16364e7 0.465807
\(409\) 9.87818e7i 1.44380i 0.691997 + 0.721900i \(0.256731\pi\)
−0.691997 + 0.721900i \(0.743269\pi\)
\(410\) −5.00486e7 −0.726174
\(411\) 2.11328e7 0.304391
\(412\) −5.88659e6 −0.0841729
\(413\) 6.11296e7i 0.867763i
\(414\) 4.20821e6i 0.0593057i
\(415\) 3.67569e6i 0.0514273i
\(416\) 683997.i 0.00950111i
\(417\) 1.94884e7i 0.268762i
\(418\) −1.86725e8 −2.55667
\(419\) 8.18950e7i 1.11331i 0.830745 + 0.556654i \(0.187915\pi\)
−0.830745 + 0.556654i \(0.812085\pi\)
\(420\) 2.14446e6i 0.0289448i
\(421\) 3.91015e7i 0.524019i −0.965065 0.262010i \(-0.915615\pi\)
0.965065 0.262010i \(-0.0843852\pi\)
\(422\) 1.13826e8 1.51462
\(423\) −8.96339e7 −1.18427
\(424\) 6.09692e7i 0.799858i
\(425\) 5.14152e7 0.669768
\(426\) 5.88716e7i 0.761513i
\(427\) 1.42118e7 0.182543
\(428\) −4.25371e6 −0.0542546
\(429\) 4.19392e6i 0.0531187i
\(430\) 2.42107e7 2.05136e7i 0.304511 0.258010i
\(431\) 1.04216e8 1.30167 0.650836 0.759218i \(-0.274418\pi\)
0.650836 + 0.759218i \(0.274418\pi\)
\(432\) 8.71559e7i 1.08105i
\(433\) 1.75892e7i 0.216662i 0.994115 + 0.108331i \(0.0345507\pi\)
−0.994115 + 0.108331i \(0.965449\pi\)
\(434\) −5.10299e7 −0.624246
\(435\) 1.96136e7i 0.238281i
\(436\) 96857.3 0.00116862
\(437\) 1.25992e7i 0.150972i
\(438\) 4.62370e7i 0.550260i
\(439\) −4.59377e6 −0.0542970 −0.0271485 0.999631i \(-0.508643\pi\)
−0.0271485 + 0.999631i \(0.508643\pi\)
\(440\) −4.70526e7 −0.552364
\(441\) −5.63091e7 −0.656543
\(442\) 3.98734e6i 0.0461761i
\(443\) −5.13129e7 −0.590221 −0.295111 0.955463i \(-0.595357\pi\)
−0.295111 + 0.955463i \(0.595357\pi\)
\(444\) 7.67853e6 0.0877261
\(445\) −810100. −0.00919302
\(446\) −8.79346e7 −0.991187
\(447\) −1.01129e8 −1.13228
\(448\) 1.16733e8i 1.29825i
\(449\) 1.08274e8i 1.19615i −0.801440 0.598076i \(-0.795932\pi\)
0.801440 0.598076i \(-0.204068\pi\)
\(450\) 4.96073e7i 0.544387i
\(451\) 2.52261e8 2.74992
\(452\) 2.46885e6i 0.0267350i
\(453\) 3.47897e7 0.374245
\(454\) 1.02157e8 1.09170
\(455\) −2.93489e6 −0.0311572
\(456\) 9.13872e7i 0.963808i
\(457\) 7.81647e7i 0.818958i −0.912319 0.409479i \(-0.865710\pi\)
0.912319 0.409479i \(-0.134290\pi\)
\(458\) 1.22916e8i 1.27942i
\(459\) 7.61920e7i 0.787900i
\(460\) 292378.i 0.00300380i
\(461\) 1.36693e8 1.39522 0.697609 0.716479i \(-0.254247\pi\)
0.697609 + 0.716479i \(0.254247\pi\)
\(462\) 1.38986e8i 1.40944i
\(463\) 1.22553e8i 1.23476i 0.786667 + 0.617378i \(0.211805\pi\)
−0.786667 + 0.617378i \(0.788195\pi\)
\(464\) 1.07514e8i 1.07625i
\(465\) −9.98822e6 −0.0993411
\(466\) 1.08833e8 1.07548
\(467\) 6.94572e6i 0.0681972i −0.999418 0.0340986i \(-0.989144\pi\)
0.999418 0.0340986i \(-0.0108560\pi\)
\(468\) 299187. 0.00291880
\(469\) 1.43098e8i 1.38712i
\(470\) 8.00785e7 0.771298
\(471\) 1.97711e7 0.189221
\(472\) 6.04535e7i 0.574904i
\(473\) −1.22030e8 + 1.03395e8i −1.15314 + 0.977050i
\(474\) −9.06003e7 −0.850736
\(475\) 1.48522e8i 1.38583i
\(476\) 1.02764e7i 0.0952839i
\(477\) −5.57929e7 −0.514072
\(478\) 1.12044e8i 1.02590i
\(479\) 5.80479e6 0.0528178 0.0264089 0.999651i \(-0.491593\pi\)
0.0264089 + 0.999651i \(0.491593\pi\)
\(480\) 4.43680e6i 0.0401186i
\(481\) 1.05088e7i 0.0944313i
\(482\) −1.66356e8 −1.48559
\(483\) 9.37799e6 0.0832278
\(484\) −1.22796e7 −0.108305
\(485\) 5.27447e7i 0.462332i
\(486\) 1.19093e8 1.03748
\(487\) 2.69087e7 0.232973 0.116487 0.993192i \(-0.462837\pi\)
0.116487 + 0.993192i \(0.462837\pi\)
\(488\) −1.40546e7 −0.120937
\(489\) −4.80152e7 −0.410631
\(490\) 5.03063e7 0.427596
\(491\) 2.15902e7i 0.182395i 0.995833 + 0.0911974i \(0.0290694\pi\)
−0.995833 + 0.0911974i \(0.970931\pi\)
\(492\) 1.13699e7i 0.0954684i
\(493\) 9.39895e7i 0.784402i
\(494\) 1.15181e7 0.0955435
\(495\) 4.30578e7i 0.355007i
\(496\) 5.47516e7 0.448696
\(497\) 2.07652e8 1.69148
\(498\) −1.07373e7 −0.0869379
\(499\) 1.53896e8i 1.23859i −0.785160 0.619293i \(-0.787419\pi\)
0.785160 0.619293i \(-0.212581\pi\)
\(500\) 7.48676e6i 0.0598941i
\(501\) 3.23147e7i 0.256972i
\(502\) 2.58868e7i 0.204629i
\(503\) 2.00534e8i 1.57574i 0.615842 + 0.787870i \(0.288816\pi\)
−0.615842 + 0.787870i \(0.711184\pi\)
\(504\) 1.07664e8 0.840968
\(505\) 4.96435e7i 0.385468i
\(506\) 1.89495e7i 0.146267i
\(507\) 8.08339e7i 0.620254i
\(508\) 1.03295e7 0.0787933
\(509\) −1.49488e8 −1.13359 −0.566793 0.823860i \(-0.691816\pi\)
−0.566793 + 0.823860i \(0.691816\pi\)
\(510\) 2.58642e7i 0.194979i
\(511\) 1.63087e8 1.22224
\(512\) 1.13538e8i 0.845921i
\(513\) 2.20094e8 1.63025
\(514\) −6.63001e6 −0.0488230
\(515\) 5.22579e7i 0.382587i
\(516\) −4.66021e6 5.50010e6i −0.0339200 0.0400333i
\(517\) −4.03620e8 −2.92080
\(518\) 3.48260e8i 2.50561i
\(519\) 8.29670e7i 0.593476i
\(520\) 2.90243e6 0.0206420
\(521\) 9.54093e7i 0.674649i −0.941388 0.337324i \(-0.890478\pi\)
0.941388 0.337324i \(-0.109522\pi\)
\(522\) 9.06846e7 0.637561
\(523\) 2.34864e8i 1.64176i −0.571097 0.820882i \(-0.693482\pi\)
0.571097 0.820882i \(-0.306518\pi\)
\(524\) 1.37070e7i 0.0952686i
\(525\) −1.10550e8 −0.763976
\(526\) 1.71205e8 1.17641
\(527\) −4.78640e7 −0.327022
\(528\) 1.49123e8i 1.01308i
\(529\) −1.46757e8 −0.991363
\(530\) 4.98451e7 0.334807
\(531\) −5.53210e7 −0.369493
\(532\) −2.96851e7 −0.197153
\(533\) −1.55607e7 −0.102765
\(534\) 2.36645e6i 0.0155408i
\(535\) 3.77621e7i 0.246601i
\(536\) 1.41515e8i 0.918984i
\(537\) −1.08430e8 −0.700205
\(538\) 4.40461e7i 0.282853i
\(539\) −2.53559e8 −1.61925
\(540\) −5.10753e6 −0.0324362
\(541\) −1.30081e8 −0.821529 −0.410764 0.911742i \(-0.634738\pi\)
−0.410764 + 0.911742i \(0.634738\pi\)
\(542\) 4.49577e7i 0.282362i
\(543\) 1.35723e7i 0.0847723i
\(544\) 2.12614e7i 0.132067i
\(545\) 859846.i 0.00531167i
\(546\) 8.57335e6i 0.0526711i
\(547\) −3.76027e7 −0.229751 −0.114875 0.993380i \(-0.536647\pi\)
−0.114875 + 0.993380i \(0.536647\pi\)
\(548\) 6.78860e6i 0.0412514i
\(549\) 1.28614e7i 0.0777268i
\(550\) 2.23381e8i 1.34263i
\(551\) 2.71505e8 1.62302
\(552\) −9.27427e6 −0.0551395
\(553\) 3.19565e8i 1.88966i
\(554\) −6.51660e7 −0.383258
\(555\) 6.81657e7i 0.398738i
\(556\) 6.26035e6 0.0364229
\(557\) −1.07813e8 −0.623884 −0.311942 0.950101i \(-0.600979\pi\)
−0.311942 + 0.950101i \(0.600979\pi\)
\(558\) 4.61810e7i 0.265804i
\(559\) 7.52738e6 6.37791e6i 0.0430932 0.0365126i
\(560\) −1.04356e8 −0.594226
\(561\) 1.30364e8i 0.738359i
\(562\) 4.16854e7i 0.234842i
\(563\) −1.93573e8 −1.08472 −0.542362 0.840145i \(-0.682470\pi\)
−0.542362 + 0.840145i \(0.682470\pi\)
\(564\) 1.81919e7i 0.101401i
\(565\) 2.19171e7 0.121517
\(566\) 3.09817e8i 1.70866i
\(567\) 3.05244e6i 0.0167455i
\(568\) −2.05355e8 −1.12063
\(569\) 1.27767e8 0.693556 0.346778 0.937947i \(-0.387276\pi\)
0.346778 + 0.937947i \(0.387276\pi\)
\(570\) −7.47132e7 −0.403434
\(571\) 1.71269e8i 0.919965i 0.887928 + 0.459982i \(0.152144\pi\)
−0.887928 + 0.459982i \(0.847856\pi\)
\(572\) 1.34723e6 0.00719871
\(573\) 2.39172e7 0.127130
\(574\) 5.15680e8 2.72675
\(575\) −1.50725e7 −0.0792831
\(576\) −1.05640e8 −0.552794
\(577\) 5.40566e7i 0.281398i 0.990052 + 0.140699i \(0.0449350\pi\)
−0.990052 + 0.140699i \(0.955065\pi\)
\(578\) 7.71350e7i 0.399455i
\(579\) 7.68651e6i 0.0395998i
\(580\) −6.30059e6 −0.0322921
\(581\) 3.78727e7i 0.193107i
\(582\) −1.54077e8 −0.781571
\(583\) −2.51235e8 −1.26787
\(584\) −1.61283e8 −0.809750
\(585\) 2.65601e6i 0.0132667i
\(586\) 2.02726e8i 1.00743i
\(587\) 1.30895e8i 0.647155i −0.946202 0.323578i \(-0.895114\pi\)
0.946202 0.323578i \(-0.104886\pi\)
\(588\) 1.14284e7i 0.0562151i
\(589\) 1.38264e8i 0.676646i
\(590\) 4.94235e7 0.240645
\(591\) 1.04860e8i 0.507980i
\(592\) 3.73659e8i 1.80098i
\(593\) 2.81686e8i 1.35083i −0.737437 0.675416i \(-0.763964\pi\)
0.737437 0.675416i \(-0.236036\pi\)
\(594\) 3.31028e8 1.57945
\(595\) 9.12281e7 0.433090
\(596\) 3.24861e7i 0.153447i
\(597\) 1.55836e8 0.732392
\(598\) 1.16890e6i 0.00546604i
\(599\) 1.77903e8 0.827758 0.413879 0.910332i \(-0.364174\pi\)
0.413879 + 0.910332i \(0.364174\pi\)
\(600\) 1.09327e8 0.506144
\(601\) 1.04686e8i 0.482240i −0.970495 0.241120i \(-0.922485\pi\)
0.970495 0.241120i \(-0.0775147\pi\)
\(602\) −2.49457e8 + 2.11364e8i −1.14342 + 0.968816i
\(603\) 1.29500e8 0.590635
\(604\) 1.11757e7i 0.0507181i
\(605\) 1.09012e8i 0.492275i
\(606\) −1.45018e8 −0.651632
\(607\) 3.06425e8i 1.37012i −0.728488 0.685058i \(-0.759777\pi\)
0.728488 0.685058i \(-0.240223\pi\)
\(608\) 6.14171e7 0.273262
\(609\) 2.02091e8i 0.894734i
\(610\) 1.14903e7i 0.0506223i
\(611\) 2.48973e7 0.109151
\(612\) −9.29991e6 −0.0405718
\(613\) −2.57269e7 −0.111688 −0.0558440 0.998440i \(-0.517785\pi\)
−0.0558440 + 0.998440i \(0.517785\pi\)
\(614\) 4.63802e8i 2.00368i
\(615\) 1.00935e8 0.433928
\(616\) 4.84810e8 2.07410
\(617\) −1.22820e8 −0.522894 −0.261447 0.965218i \(-0.584200\pi\)
−0.261447 + 0.965218i \(0.584200\pi\)
\(618\) 1.52655e8 0.646763
\(619\) −7.80094e7 −0.328908 −0.164454 0.986385i \(-0.552586\pi\)
−0.164454 + 0.986385i \(0.552586\pi\)
\(620\) 3.20857e6i 0.0134628i
\(621\) 2.23358e7i 0.0932668i
\(622\) 1.83851e8i 0.764001i
\(623\) 8.34693e6 0.0345193
\(624\) 9.19861e6i 0.0378589i
\(625\) 1.41811e8 0.580858
\(626\) 1.98694e8 0.809958
\(627\) 3.76578e8 1.52775
\(628\) 6.35118e6i 0.0256434i
\(629\) 3.26654e8i 1.31261i
\(630\) 8.80203e7i 0.352015i
\(631\) 2.93500e8i 1.16821i 0.811678 + 0.584105i \(0.198554\pi\)
−0.811678 + 0.584105i \(0.801446\pi\)
\(632\) 3.16031e8i 1.25192i
\(633\) −2.29558e8 −0.905069
\(634\) 3.76451e8i 1.47720i
\(635\) 9.16998e7i 0.358136i
\(636\) 1.13236e7i 0.0440163i
\(637\) 1.56408e7 0.0605118
\(638\) 4.08351e8 1.57243
\(639\) 1.87920e8i 0.720231i
\(640\) 1.11280e8 0.424501
\(641\) 6.47635e7i 0.245899i 0.992413 + 0.122949i \(0.0392353\pi\)
−0.992413 + 0.122949i \(0.960765\pi\)
\(642\) 1.10310e8 0.416879
\(643\) 1.49102e8 0.560855 0.280427 0.959875i \(-0.409524\pi\)
0.280427 + 0.959875i \(0.409524\pi\)
\(644\) 3.01254e6i 0.0112791i
\(645\) −4.88269e7 + 4.13708e7i −0.181962 + 0.154175i
\(646\) −3.58029e8 −1.32807
\(647\) 9.73636e7i 0.359488i 0.983713 + 0.179744i \(0.0575269\pi\)
−0.983713 + 0.179744i \(0.942473\pi\)
\(648\) 3.01868e6i 0.0110941i
\(649\) −2.49110e8 −0.911290
\(650\) 1.37792e7i 0.0501747i
\(651\) 1.02914e8 0.373021
\(652\) 1.54242e7i 0.0556492i
\(653\) 2.89942e8i 1.04129i 0.853773 + 0.520645i \(0.174308\pi\)
−0.853773 + 0.520645i \(0.825692\pi\)
\(654\) −2.51177e6 −0.00897938
\(655\) −1.21684e8 −0.433020
\(656\) −5.53289e8 −1.95993
\(657\) 1.47590e8i 0.520430i
\(658\) −8.25095e8 −2.89619
\(659\) 3.85283e8 1.34624 0.673122 0.739532i \(-0.264953\pi\)
0.673122 + 0.739532i \(0.264953\pi\)
\(660\) −8.73892e6 −0.0303967
\(661\) −1.05838e8 −0.366470 −0.183235 0.983069i \(-0.558657\pi\)
−0.183235 + 0.983069i \(0.558657\pi\)
\(662\) −4.00970e8 −1.38209
\(663\) 8.04146e6i 0.0275927i
\(664\) 3.74538e7i 0.127936i
\(665\) 2.63528e8i 0.896111i
\(666\) 3.15168e8 1.06689
\(667\) 2.75532e7i 0.0928527i
\(668\) 1.03806e7 0.0348252
\(669\) 1.77342e8 0.592288
\(670\) −1.15695e8 −0.384671
\(671\) 5.79147e7i 0.191700i
\(672\) 4.57149e7i 0.150643i
\(673\) 3.67800e8i 1.20661i −0.797511 0.603304i \(-0.793851\pi\)
0.797511 0.603304i \(-0.206149\pi\)
\(674\) 5.88912e8i 1.92341i
\(675\) 2.63300e8i 0.856128i
\(676\) 2.59667e7 0.0840575
\(677\) 1.77988e8i 0.573621i −0.957987 0.286810i \(-0.907405\pi\)
0.957987 0.286810i \(-0.0925950\pi\)
\(678\) 6.40239e7i 0.205425i
\(679\) 5.43460e8i 1.73603i
\(680\) −9.02191e7 −0.286927
\(681\) −2.06025e8 −0.652348
\(682\) 2.07953e8i 0.655558i
\(683\) 4.22123e8 1.32488 0.662440 0.749115i \(-0.269521\pi\)
0.662440 + 0.749115i \(0.269521\pi\)
\(684\) 2.68644e7i 0.0839477i
\(685\) −6.02655e7 −0.187498
\(686\) −3.45201e7 −0.106930
\(687\) 2.47891e8i 0.764523i
\(688\) 2.67650e8 2.26779e8i 0.821869 0.696366i
\(689\) 1.54974e7 0.0473806
\(690\) 7.58214e6i 0.0230805i
\(691\) 3.29787e7i 0.0999538i −0.998750 0.0499769i \(-0.984085\pi\)
0.998750 0.0499769i \(-0.0159148\pi\)
\(692\) −2.66519e7 −0.0804285
\(693\) 4.43650e8i 1.33303i
\(694\) −2.79989e8 −0.837651
\(695\) 5.55760e7i 0.165551i
\(696\) 1.99855e8i 0.592773i
\(697\) 4.83687e8 1.42845
\(698\) −2.51356e8 −0.739133
\(699\) −2.19489e8 −0.642659
\(700\) 3.55125e7i 0.103535i
\(701\) −5.33584e8 −1.54899 −0.774496 0.632579i \(-0.781996\pi\)
−0.774496 + 0.632579i \(0.781996\pi\)
\(702\) −2.04194e7 −0.0590244
\(703\) 9.43596e8 2.71594
\(704\) −4.75698e8 −1.36337
\(705\) −1.61498e8 −0.460892
\(706\) 1.12766e7i 0.0320453i
\(707\) 5.11505e8i 1.44741i
\(708\) 1.12278e7i 0.0316371i
\(709\) 9.62028e7 0.269929 0.134964 0.990850i \(-0.456908\pi\)
0.134964 + 0.990850i \(0.456908\pi\)
\(710\) 1.67887e8i 0.469075i
\(711\) −2.89200e8 −0.804617
\(712\) −8.25461e6 −0.0228695
\(713\) 1.40314e7 0.0387109
\(714\) 2.66494e8i 0.732137i
\(715\) 1.19600e7i 0.0327200i
\(716\) 3.48314e7i 0.0948926i
\(717\) 2.25964e8i 0.613030i
\(718\) 3.75435e8i 1.01429i
\(719\) −5.90610e8 −1.58896 −0.794482 0.607288i \(-0.792258\pi\)
−0.794482 + 0.607288i \(0.792258\pi\)
\(720\) 9.44397e7i 0.253021i
\(721\) 5.38444e8i 1.43660i
\(722\) 6.42315e8i 1.70662i
\(723\) 3.35498e8 0.887719
\(724\) 4.35990e6 0.0114884
\(725\) 3.24803e8i 0.852326i
\(726\) 3.18444e8 0.832191
\(727\) 6.66392e8i 1.73431i 0.498040 + 0.867154i \(0.334053\pi\)
−0.498040 + 0.867154i \(0.665947\pi\)
\(728\) −2.99054e7 −0.0775097
\(729\) −2.44689e8 −0.631584
\(730\) 1.31856e8i 0.338948i
\(731\) −2.33981e8 + 1.98251e8i −0.599002 + 0.507532i
\(732\) −2.61032e6 −0.00665520
\(733\) 1.91149e8i 0.485357i −0.970107 0.242678i \(-0.921974\pi\)
0.970107 0.242678i \(-0.0780260\pi\)
\(734\) 3.21595e8i 0.813246i
\(735\) −1.01455e8 −0.255512
\(736\) 6.23281e6i 0.0156333i
\(737\) 5.83139e8 1.45670
\(738\) 4.66680e8i 1.16105i
\(739\) 5.39175e8i 1.33597i −0.744175 0.667985i \(-0.767157\pi\)
0.744175 0.667985i \(-0.232843\pi\)
\(740\) −2.18972e7 −0.0540374
\(741\) −2.32291e7 −0.0570924
\(742\) −5.13583e8 −1.25718
\(743\) 2.06678e8i 0.503881i 0.967743 + 0.251940i \(0.0810687\pi\)
−0.967743 + 0.251940i \(0.918931\pi\)
\(744\) −1.01776e8 −0.247131
\(745\) 2.88394e8 0.697457
\(746\) 4.35037e8 1.04788
\(747\) −3.42740e7 −0.0822249
\(748\) −4.18774e7 −0.100063
\(749\) 3.89085e8i 0.925975i
\(750\) 1.94152e8i 0.460211i
\(751\) 1.65838e7i 0.0391529i −0.999808 0.0195765i \(-0.993768\pi\)
0.999808 0.0195765i \(-0.00623178\pi\)
\(752\) 8.85270e8 2.08172
\(753\) 5.22070e7i 0.122277i
\(754\) −2.51891e7 −0.0587623
\(755\) −9.92116e7 −0.230527
\(756\) 5.26259e7 0.121796
\(757\) 4.14585e8i 0.955710i −0.878439 0.477855i \(-0.841415\pi\)
0.878439 0.477855i \(-0.158585\pi\)
\(758\) 4.13233e8i 0.948827i
\(759\) 3.82163e7i 0.0874025i
\(760\) 2.60613e8i 0.593685i
\(761\) 4.74981e8i 1.07776i 0.842383 + 0.538880i \(0.181152\pi\)
−0.842383 + 0.538880i \(0.818848\pi\)
\(762\) −2.67872e8 −0.605428
\(763\) 8.85950e6i 0.0199451i
\(764\) 7.68305e6i 0.0172287i
\(765\) 8.25595e7i 0.184409i
\(766\) −6.43243e7 −0.143116
\(767\) 1.53663e7 0.0340552
\(768\) 7.08133e7i 0.156326i
\(769\) 5.57822e8 1.22664 0.613319 0.789835i \(-0.289834\pi\)
0.613319 + 0.789835i \(0.289834\pi\)
\(770\) 3.96354e8i 0.868183i
\(771\) 1.33710e7 0.0291744
\(772\) −2.46918e6 −0.00536661
\(773\) 2.66540e8i 0.577063i 0.957470 + 0.288532i \(0.0931670\pi\)
−0.957470 + 0.288532i \(0.906833\pi\)
\(774\) −1.91280e8 2.25754e8i −0.412521 0.486869i
\(775\) −1.65406e8 −0.355341
\(776\) 5.37449e8i 1.15014i
\(777\) 7.02351e8i 1.49724i
\(778\) −6.33775e8 −1.34585
\(779\) 1.39721e9i 2.95563i
\(780\) 539059. 0.00113593
\(781\) 8.46203e8i 1.77632i
\(782\) 3.63340e7i 0.0759789i