Properties

Label 43.7.b.b.42.4
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 42.4
Root \(-11.9161i\) 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.42.17

$q$-expansion

\(f(q)\) \(=\) \(q-11.9161i q^{2} +41.5647i q^{3} -77.9927 q^{4} -111.502i q^{5} +495.288 q^{6} -49.3353i q^{7} +166.738i q^{8} -998.624 q^{9} +O(q^{10})\) \(q-11.9161i q^{2} +41.5647i q^{3} -77.9927 q^{4} -111.502i q^{5} +495.288 q^{6} -49.3353i q^{7} +166.738i q^{8} -998.624 q^{9} -1328.67 q^{10} -2545.27 q^{11} -3241.74i q^{12} -277.606 q^{13} -587.882 q^{14} +4634.57 q^{15} -3004.67 q^{16} -532.079 q^{17} +11899.7i q^{18} -6002.14i q^{19} +8696.37i q^{20} +2050.61 q^{21} +30329.6i q^{22} -18510.7 q^{23} -6930.40 q^{24} +3192.21 q^{25} +3307.97i q^{26} -11206.8i q^{27} +3847.79i q^{28} -27049.2i q^{29} -55225.8i q^{30} +26111.0 q^{31} +46475.1i q^{32} -105793. i q^{33} +6340.29i q^{34} -5501.00 q^{35} +77885.4 q^{36} +2171.52i q^{37} -71521.9 q^{38} -11538.6i q^{39} +18591.6 q^{40} -82696.8 q^{41} -24435.2i q^{42} +(74033.4 + 28990.0i) q^{43} +198512. q^{44} +111349. i q^{45} +220575. i q^{46} -16828.5 q^{47} -124888. i q^{48} +115215. q^{49} -38038.6i q^{50} -22115.7i q^{51} +21651.2 q^{52} -80461.4 q^{53} -133542. q^{54} +283804. i q^{55} +8226.04 q^{56} +249477. q^{57} -322320. q^{58} +151135. q^{59} -361462. q^{60} -348035. i q^{61} -311141. i q^{62} +49267.4i q^{63} +361501. q^{64} +30953.7i q^{65} -1.26064e6 q^{66} +261022. q^{67} +41498.3 q^{68} -769393. i q^{69} +65550.3i q^{70} +495540. i q^{71} -166508. i q^{72} +304044. i q^{73} +25876.0 q^{74} +132683. i q^{75} +468123. i q^{76} +125572. i q^{77} -137495. q^{78} -289935. q^{79} +335029. i q^{80} -262188. q^{81} +985421. i q^{82} +435765. q^{83} -159932. q^{84} +59328.1i q^{85} +(345446. - 882187. i) q^{86} +1.12429e6 q^{87} -424392. i q^{88} -1.28127e6i q^{89} +1.32684e6 q^{90} +13695.7i q^{91} +1.44370e6 q^{92} +1.08530e6i q^{93} +200530. i q^{94} -669253. q^{95} -1.93172e6 q^{96} -291513. q^{97} -1.37291e6i q^{98} +2.54177e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.9161i 1.48951i −0.667339 0.744754i \(-0.732567\pi\)
0.667339 0.744754i \(-0.267433\pi\)
\(3\) 41.5647i 1.53943i 0.638386 + 0.769717i \(0.279603\pi\)
−0.638386 + 0.769717i \(0.720397\pi\)
\(4\) −77.9927 −1.21864
\(5\) 111.502i 0.892019i −0.895028 0.446010i \(-0.852845\pi\)
0.895028 0.446010i \(-0.147155\pi\)
\(6\) 495.288 2.29300
\(7\) 49.3353i 0.143835i −0.997411 0.0719173i \(-0.977088\pi\)
0.997411 0.0719173i \(-0.0229118\pi\)
\(8\) 166.738i 0.325659i
\(9\) −998.624 −1.36985
\(10\) −1328.67 −1.32867
\(11\) −2545.27 −1.91230 −0.956149 0.292881i \(-0.905386\pi\)
−0.956149 + 0.292881i \(0.905386\pi\)
\(12\) 3241.74i 1.87601i
\(13\) −277.606 −0.126357 −0.0631783 0.998002i \(-0.520124\pi\)
−0.0631783 + 0.998002i \(0.520124\pi\)
\(14\) −587.882 −0.214243
\(15\) 4634.57 1.37320
\(16\) −3004.67 −0.733563
\(17\) −532.079 −0.108300 −0.0541501 0.998533i \(-0.517245\pi\)
−0.0541501 + 0.998533i \(0.517245\pi\)
\(18\) 11899.7i 2.04041i
\(19\) 6002.14i 0.875075i −0.899200 0.437537i \(-0.855851\pi\)
0.899200 0.437537i \(-0.144149\pi\)
\(20\) 8696.37i 1.08705i
\(21\) 2050.61 0.221424
\(22\) 30329.6i 2.84838i
\(23\) −18510.7 −1.52139 −0.760694 0.649110i \(-0.775141\pi\)
−0.760694 + 0.649110i \(0.775141\pi\)
\(24\) −6930.40 −0.501331
\(25\) 3192.21 0.204301
\(26\) 3307.97i 0.188209i
\(27\) 11206.8i 0.569367i
\(28\) 3847.79i 0.175282i
\(29\) 27049.2i 1.10907i −0.832159 0.554537i \(-0.812895\pi\)
0.832159 0.554537i \(-0.187105\pi\)
\(30\) 55225.8i 2.04540i
\(31\) 26111.0 0.876474 0.438237 0.898860i \(-0.355603\pi\)
0.438237 + 0.898860i \(0.355603\pi\)
\(32\) 46475.1i 1.41831i
\(33\) 105793.i 2.94386i
\(34\) 6340.29i 0.161314i
\(35\) −5501.00 −0.128303
\(36\) 77885.4 1.66935
\(37\) 2171.52i 0.0428705i 0.999770 + 0.0214352i \(0.00682357\pi\)
−0.999770 + 0.0214352i \(0.993176\pi\)
\(38\) −71521.9 −1.30343
\(39\) 11538.6i 0.194518i
\(40\) 18591.6 0.290494
\(41\) −82696.8 −1.19988 −0.599939 0.800046i \(-0.704809\pi\)
−0.599939 + 0.800046i \(0.704809\pi\)
\(42\) 24435.2i 0.329813i
\(43\) 74033.4 + 28990.0i 0.931156 + 0.364622i
\(44\) 198512. 2.33039
\(45\) 111349.i 1.22194i
\(46\) 220575.i 2.26612i
\(47\) −16828.5 −0.162088 −0.0810442 0.996711i \(-0.525826\pi\)
−0.0810442 + 0.996711i \(0.525826\pi\)
\(48\) 124888.i 1.12927i
\(49\) 115215. 0.979312
\(50\) 38038.6i 0.304308i
\(51\) 22115.7i 0.166721i
\(52\) 21651.2 0.153983
\(53\) −80461.4 −0.540456 −0.270228 0.962796i \(-0.587099\pi\)
−0.270228 + 0.962796i \(0.587099\pi\)
\(54\) −133542. −0.848077
\(55\) 283804.i 1.70581i
\(56\) 8226.04 0.0468411
\(57\) 249477. 1.34712
\(58\) −322320. −1.65197
\(59\) 151135. 0.735881 0.367941 0.929849i \(-0.380063\pi\)
0.367941 + 0.929849i \(0.380063\pi\)
\(60\) −361462. −1.67344
\(61\) 348035.i 1.53332i −0.642053 0.766660i \(-0.721917\pi\)
0.642053 0.766660i \(-0.278083\pi\)
\(62\) 311141.i 1.30551i
\(63\) 49267.4i 0.197033i
\(64\) 361501. 1.37902
\(65\) 30953.7i 0.112713i
\(66\) −1.26064e6 −4.38490
\(67\) 261022. 0.867867 0.433934 0.900945i \(-0.357125\pi\)
0.433934 + 0.900945i \(0.357125\pi\)
\(68\) 41498.3 0.131979
\(69\) 769393.i 2.34208i
\(70\) 65550.3i 0.191109i
\(71\) 495540.i 1.38453i 0.721642 + 0.692267i \(0.243388\pi\)
−0.721642 + 0.692267i \(0.756612\pi\)
\(72\) 166508.i 0.446106i
\(73\) 304044.i 0.781570i 0.920482 + 0.390785i \(0.127796\pi\)
−0.920482 + 0.390785i \(0.872204\pi\)
\(74\) 25876.0 0.0638559
\(75\) 132683.i 0.314508i
\(76\) 468123.i 1.06640i
\(77\) 125572.i 0.275055i
\(78\) −137495. −0.289736
\(79\) −289935. −0.588056 −0.294028 0.955797i \(-0.594996\pi\)
−0.294028 + 0.955797i \(0.594996\pi\)
\(80\) 335029.i 0.654353i
\(81\) −262188. −0.493352
\(82\) 985421.i 1.78723i
\(83\) 435765. 0.762110 0.381055 0.924552i \(-0.375561\pi\)
0.381055 + 0.924552i \(0.375561\pi\)
\(84\) −159932. −0.269835
\(85\) 59328.1i 0.0966059i
\(86\) 345446. 882187.i 0.543107 1.38696i
\(87\) 1.12429e6 1.70734
\(88\) 424392.i 0.622758i
\(89\) 1.28127e6i 1.81748i −0.417365 0.908739i \(-0.637046\pi\)
0.417365 0.908739i \(-0.362954\pi\)
\(90\) 1.32684e6 1.82009
\(91\) 13695.7i 0.0181745i
\(92\) 1.44370e6 1.85402
\(93\) 1.08530e6i 1.34927i
\(94\) 200530.i 0.241432i
\(95\) −669253. −0.780584
\(96\) −1.93172e6 −2.18339
\(97\) −291513. −0.319406 −0.159703 0.987165i \(-0.551054\pi\)
−0.159703 + 0.987165i \(0.551054\pi\)
\(98\) 1.37291e6i 1.45869i
\(99\) 2.54177e6 2.61957
\(100\) −248969. −0.248969
\(101\) −1.83351e6 −1.77959 −0.889793 0.456365i \(-0.849151\pi\)
−0.889793 + 0.456365i \(0.849151\pi\)
\(102\) −263532. −0.248332
\(103\) −1.58097e6 −1.44682 −0.723408 0.690421i \(-0.757425\pi\)
−0.723408 + 0.690421i \(0.757425\pi\)
\(104\) 46287.3i 0.0411492i
\(105\) 228648.i 0.197514i
\(106\) 958784.i 0.805014i
\(107\) 1.41201e6 1.15262 0.576312 0.817230i \(-0.304491\pi\)
0.576312 + 0.817230i \(0.304491\pi\)
\(108\) 874052.i 0.693851i
\(109\) −738817. −0.570502 −0.285251 0.958453i \(-0.592077\pi\)
−0.285251 + 0.958453i \(0.592077\pi\)
\(110\) 3.38182e6 2.54081
\(111\) −90258.5 −0.0659962
\(112\) 148236.i 0.105512i
\(113\) 1.67172e6i 1.15859i −0.815119 0.579293i \(-0.803329\pi\)
0.815119 0.579293i \(-0.196671\pi\)
\(114\) 2.97279e6i 2.00655i
\(115\) 2.06399e6i 1.35711i
\(116\) 2.10964e6i 1.35156i
\(117\) 277224. 0.173090
\(118\) 1.80093e6i 1.09610i
\(119\) 26250.3i 0.0155773i
\(120\) 772756.i 0.447197i
\(121\) 4.70683e6 2.65688
\(122\) −4.14720e6 −2.28389
\(123\) 3.43727e6i 1.84713i
\(124\) −2.03647e6 −1.06810
\(125\) 2.09816e6i 1.07426i
\(126\) 587074. 0.293482
\(127\) −2.87492e6 −1.40351 −0.701753 0.712420i \(-0.747599\pi\)
−0.701753 + 0.712420i \(0.747599\pi\)
\(128\) 1.33327e6i 0.635752i
\(129\) −1.20496e6 + 3.07718e6i −0.561311 + 1.43345i
\(130\) 368846. 0.167886
\(131\) 1.71744e6i 0.763956i 0.924171 + 0.381978i \(0.124757\pi\)
−0.924171 + 0.381978i \(0.875243\pi\)
\(132\) 8.25110e6i 3.58749i
\(133\) −296117. −0.125866
\(134\) 3.11036e6i 1.29270i
\(135\) −1.24959e6 −0.507886
\(136\) 88717.6i 0.0352690i
\(137\) 120280.i 0.0467771i −0.999726 0.0233886i \(-0.992555\pi\)
0.999726 0.0233886i \(-0.00744549\pi\)
\(138\) −9.16814e6 −3.48854
\(139\) −2.80418e6 −1.04415 −0.522073 0.852901i \(-0.674841\pi\)
−0.522073 + 0.852901i \(0.674841\pi\)
\(140\) 429038. 0.156355
\(141\) 699472.i 0.249524i
\(142\) 5.90489e6 2.06227
\(143\) 706581. 0.241632
\(144\) 3.00054e6 1.00488
\(145\) −3.01605e6 −0.989315
\(146\) 3.62301e6 1.16415
\(147\) 4.78888e6i 1.50758i
\(148\) 169362.i 0.0522435i
\(149\) 5.36200e6i 1.62094i 0.585778 + 0.810471i \(0.300789\pi\)
−0.585778 + 0.810471i \(0.699211\pi\)
\(150\) 1.58106e6 0.468463
\(151\) 382921.i 0.111219i −0.998453 0.0556095i \(-0.982290\pi\)
0.998453 0.0556095i \(-0.0177102\pi\)
\(152\) 1.00078e6 0.284976
\(153\) 531347. 0.148356
\(154\) 1.49632e6 0.409696
\(155\) 2.91144e6i 0.781831i
\(156\) 899926.i 0.237046i
\(157\) 4.70730e6i 1.21639i −0.793787 0.608195i \(-0.791894\pi\)
0.793787 0.608195i \(-0.208106\pi\)
\(158\) 3.45488e6i 0.875915i
\(159\) 3.34436e6i 0.831996i
\(160\) 5.18209e6 1.26516
\(161\) 913232.i 0.218828i
\(162\) 3.12425e6i 0.734853i
\(163\) 6.94062e6i 1.60264i −0.598237 0.801319i \(-0.704132\pi\)
0.598237 0.801319i \(-0.295868\pi\)
\(164\) 6.44974e6 1.46221
\(165\) −1.17962e7 −2.62598
\(166\) 5.19260e6i 1.13517i
\(167\) 544241. 0.116854 0.0584268 0.998292i \(-0.481392\pi\)
0.0584268 + 0.998292i \(0.481392\pi\)
\(168\) 341913.i 0.0721087i
\(169\) −4.74974e6 −0.984034
\(170\) 706958. 0.143895
\(171\) 5.99388e6i 1.19873i
\(172\) −5.77406e6 2.26100e6i −1.13474 0.444341i
\(173\) 3.91149e6 0.755447 0.377724 0.925918i \(-0.376707\pi\)
0.377724 + 0.925918i \(0.376707\pi\)
\(174\) 1.33971e7i 2.54310i
\(175\) 157488.i 0.0293856i
\(176\) 7.64770e6 1.40279
\(177\) 6.28186e6i 1.13284i
\(178\) −1.52676e7 −2.70715
\(179\) 574368.i 0.100145i 0.998746 + 0.0500727i \(0.0159453\pi\)
−0.998746 + 0.0500727i \(0.984055\pi\)
\(180\) 8.68441e6i 1.48910i
\(181\) 2.94218e6 0.496173 0.248086 0.968738i \(-0.420198\pi\)
0.248086 + 0.968738i \(0.420198\pi\)
\(182\) 163199. 0.0270710
\(183\) 1.44660e7 2.36044
\(184\) 3.08644e6i 0.495454i
\(185\) 242130. 0.0382413
\(186\) 1.29325e7 2.00975
\(187\) 1.35428e6 0.207102
\(188\) 1.31250e6 0.197527
\(189\) −552893. −0.0818947
\(190\) 7.97486e6i 1.16269i
\(191\) 1.07146e7i 1.53772i −0.639418 0.768859i \(-0.720825\pi\)
0.639418 0.768859i \(-0.279175\pi\)
\(192\) 1.50257e7i 2.12291i
\(193\) 4.03291e6 0.560978 0.280489 0.959857i \(-0.409503\pi\)
0.280489 + 0.959857i \(0.409503\pi\)
\(194\) 3.47369e6i 0.475757i
\(195\) −1.28658e6 −0.173514
\(196\) −8.98593e6 −1.19342
\(197\) −5.70839e6 −0.746646 −0.373323 0.927701i \(-0.621782\pi\)
−0.373323 + 0.927701i \(0.621782\pi\)
\(198\) 3.02879e7i 3.90187i
\(199\) 8.41961e6i 1.06840i −0.845359 0.534198i \(-0.820614\pi\)
0.845359 0.534198i \(-0.179386\pi\)
\(200\) 532261.i 0.0665326i
\(201\) 1.08493e7i 1.33602i
\(202\) 2.18482e7i 2.65071i
\(203\) −1.33448e6 −0.159523
\(204\) 1.72486e6i 0.203172i
\(205\) 9.22089e6i 1.07031i
\(206\) 1.88390e7i 2.15504i
\(207\) 1.84853e7 2.08408
\(208\) 834114. 0.0926906
\(209\) 1.52771e7i 1.67340i
\(210\) −2.72458e6 −0.294199
\(211\) 1.18232e7i 1.25860i 0.777164 + 0.629298i \(0.216658\pi\)
−0.777164 + 0.629298i \(0.783342\pi\)
\(212\) 6.27540e6 0.658619
\(213\) −2.05970e7 −2.13140
\(214\) 1.68256e7i 1.71684i
\(215\) 3.23245e6 8.25490e6i 0.325250 0.830609i
\(216\) 1.86860e6 0.185420
\(217\) 1.28819e6i 0.126067i
\(218\) 8.80379e6i 0.849767i
\(219\) −1.26375e7 −1.20317
\(220\) 2.21346e7i 2.07876i
\(221\) 147708. 0.0136845
\(222\) 1.07553e6i 0.0983019i
\(223\) 1.59450e6i 0.143784i 0.997412 + 0.0718918i \(0.0229036\pi\)
−0.997412 + 0.0718918i \(0.977096\pi\)
\(224\) 2.29286e6 0.204002
\(225\) −3.18782e6 −0.279863
\(226\) −1.99203e7 −1.72572
\(227\) 1.36878e7i 1.17019i 0.810966 + 0.585093i \(0.198942\pi\)
−0.810966 + 0.585093i \(0.801058\pi\)
\(228\) −1.94574e7 −1.64165
\(229\) 3.27069e6 0.272354 0.136177 0.990685i \(-0.456518\pi\)
0.136177 + 0.990685i \(0.456518\pi\)
\(230\) 2.45947e7 2.02142
\(231\) −5.21934e6 −0.423428
\(232\) 4.51012e6 0.361180
\(233\) 1.71626e7i 1.35680i −0.734695 0.678398i \(-0.762675\pi\)
0.734695 0.678398i \(-0.237325\pi\)
\(234\) 3.30342e6i 0.257819i
\(235\) 1.87642e6i 0.144586i
\(236\) −1.17874e7 −0.896771
\(237\) 1.20511e7i 0.905274i
\(238\) 312800. 0.0232026
\(239\) −1.03077e7 −0.755040 −0.377520 0.926001i \(-0.623223\pi\)
−0.377520 + 0.926001i \(0.623223\pi\)
\(240\) −1.39254e7 −1.00733
\(241\) 1.27257e6i 0.0909143i 0.998966 + 0.0454571i \(0.0144744\pi\)
−0.998966 + 0.0454571i \(0.985526\pi\)
\(242\) 5.60869e7i 3.95745i
\(243\) 1.90675e7i 1.32885i
\(244\) 2.71441e7i 1.86856i
\(245\) 1.28468e7i 0.873565i
\(246\) −4.09587e7 −2.75132
\(247\) 1.66623e6i 0.110572i
\(248\) 4.35369e6i 0.285432i
\(249\) 1.81124e7i 1.17322i
\(250\) −2.50019e7 −1.60012
\(251\) 1.41003e7 0.891677 0.445839 0.895113i \(-0.352906\pi\)
0.445839 + 0.895113i \(0.352906\pi\)
\(252\) 3.84250e6i 0.240111i
\(253\) 4.71148e7 2.90935
\(254\) 3.42577e7i 2.09053i
\(255\) −2.46595e6 −0.148718
\(256\) 7.24878e6 0.432061
\(257\) 1.82508e7i 1.07518i −0.843206 0.537591i \(-0.819334\pi\)
0.843206 0.537591i \(-0.180666\pi\)
\(258\) 3.66678e7 + 1.43584e7i 2.13514 + 0.836077i
\(259\) 107132. 0.00616626
\(260\) 2.41416e6i 0.137356i
\(261\) 2.70120e7i 1.51927i
\(262\) 2.04652e7 1.13792
\(263\) 2.34584e7i 1.28953i −0.764381 0.644765i \(-0.776955\pi\)
0.764381 0.644765i \(-0.223045\pi\)
\(264\) 1.76397e7 0.958694
\(265\) 8.97165e6i 0.482097i
\(266\) 3.52855e6i 0.187479i
\(267\) 5.32554e7 2.79789
\(268\) −2.03578e7 −1.05761
\(269\) 8.18861e6 0.420682 0.210341 0.977628i \(-0.432543\pi\)
0.210341 + 0.977628i \(0.432543\pi\)
\(270\) 1.48902e7i 0.756501i
\(271\) 7.82358e6 0.393095 0.196548 0.980494i \(-0.437027\pi\)
0.196548 + 0.980494i \(0.437027\pi\)
\(272\) 1.59872e6 0.0794451
\(273\) −569260. −0.0279784
\(274\) −1.43327e6 −0.0696749
\(275\) −8.12503e6 −0.390685
\(276\) 6.00070e7i 2.85414i
\(277\) 1.33278e7i 0.627074i 0.949576 + 0.313537i \(0.101514\pi\)
−0.949576 + 0.313537i \(0.898486\pi\)
\(278\) 3.34147e7i 1.55526i
\(279\) −2.60751e7 −1.20064
\(280\) 917224.i 0.0417832i
\(281\) −1.46200e7 −0.658914 −0.329457 0.944170i \(-0.606866\pi\)
−0.329457 + 0.944170i \(0.606866\pi\)
\(282\) −8.33496e6 −0.371669
\(283\) −2.77184e6 −0.122295 −0.0611475 0.998129i \(-0.519476\pi\)
−0.0611475 + 0.998129i \(0.519476\pi\)
\(284\) 3.86485e7i 1.68724i
\(285\) 2.78173e7i 1.20166i
\(286\) 8.41966e6i 0.359912i
\(287\) 4.07987e6i 0.172584i
\(288\) 4.64112e7i 1.94288i
\(289\) −2.38545e7 −0.988271
\(290\) 3.59395e7i 1.47359i
\(291\) 1.21166e7i 0.491704i
\(292\) 2.37132e7i 0.952449i
\(293\) −2.86988e7 −1.14093 −0.570467 0.821320i \(-0.693238\pi\)
−0.570467 + 0.821320i \(0.693238\pi\)
\(294\) 5.70646e7 2.24556
\(295\) 1.68519e7i 0.656420i
\(296\) −362074. −0.0139612
\(297\) 2.85244e7i 1.08880i
\(298\) 6.38939e7 2.41441
\(299\) 5.13868e6 0.192238
\(300\) 1.03483e7i 0.383271i
\(301\) 1.43023e6 3.65246e6i 0.0524452 0.133932i
\(302\) −4.56292e6 −0.165662
\(303\) 7.62092e7i 2.73955i
\(304\) 1.80345e7i 0.641923i
\(305\) −3.88067e7 −1.36775
\(306\) 6.33157e6i 0.220977i
\(307\) 3.96953e7 1.37190 0.685952 0.727646i \(-0.259386\pi\)
0.685952 + 0.727646i \(0.259386\pi\)
\(308\) 9.79366e6i 0.335191i
\(309\) 6.57127e7i 2.22728i
\(310\) −3.46929e7 −1.16454
\(311\) 4.44492e7 1.47769 0.738845 0.673876i \(-0.235372\pi\)
0.738845 + 0.673876i \(0.235372\pi\)
\(312\) 1.92392e6 0.0633465
\(313\) 1.99405e7i 0.650284i −0.945665 0.325142i \(-0.894588\pi\)
0.945665 0.325142i \(-0.105412\pi\)
\(314\) −5.60925e7 −1.81182
\(315\) 5.49343e6 0.175757
\(316\) 2.26128e7 0.716626
\(317\) −2.35773e7 −0.740145 −0.370073 0.929003i \(-0.620667\pi\)
−0.370073 + 0.929003i \(0.620667\pi\)
\(318\) −3.98516e7 −1.23926
\(319\) 6.88475e7i 2.12088i
\(320\) 4.03083e7i 1.23011i
\(321\) 5.86899e7i 1.77439i
\(322\) 1.08821e7 0.325947
\(323\) 3.19361e6i 0.0947708i
\(324\) 2.04487e7 0.601217
\(325\) −886175. −0.0258148
\(326\) −8.27049e7 −2.38714
\(327\) 3.07087e7i 0.878250i
\(328\) 1.37887e7i 0.390752i
\(329\) 830239.i 0.0233139i
\(330\) 1.40564e8i 3.91141i
\(331\) 4.55500e7i 1.25604i 0.778196 + 0.628021i \(0.216135\pi\)
−0.778196 + 0.628021i \(0.783865\pi\)
\(332\) −3.39865e7 −0.928735
\(333\) 2.16853e6i 0.0587263i
\(334\) 6.48522e6i 0.174054i
\(335\) 2.91046e7i 0.774155i
\(336\) −6.16140e6 −0.162428
\(337\) −2.55279e7 −0.666998 −0.333499 0.942750i \(-0.608229\pi\)
−0.333499 + 0.942750i \(0.608229\pi\)
\(338\) 5.65983e7i 1.46573i
\(339\) 6.94846e7 1.78357
\(340\) 4.62716e6i 0.117727i
\(341\) −6.64596e7 −1.67608
\(342\) 7.14235e7 1.78551
\(343\) 1.14884e7i 0.284693i
\(344\) −4.83372e6 + 1.23442e7i −0.118742 + 0.303240i
\(345\) −8.57892e7 −2.08918
\(346\) 4.66096e7i 1.12524i
\(347\) 5.97749e6i 0.143064i −0.997438 0.0715320i \(-0.977211\pi\)
0.997438 0.0715320i \(-0.0227888\pi\)
\(348\) −8.76865e7 −2.08063
\(349\) 8.42603e7i 1.98220i 0.133134 + 0.991098i \(0.457496\pi\)
−0.133134 + 0.991098i \(0.542504\pi\)
\(350\) −1.87664e6 −0.0437701
\(351\) 3.11108e6i 0.0719433i
\(352\) 1.18292e8i 2.71223i
\(353\) 4.96924e7 1.12971 0.564854 0.825191i \(-0.308933\pi\)
0.564854 + 0.825191i \(0.308933\pi\)
\(354\) 7.48551e7 1.68737
\(355\) 5.52539e7 1.23503
\(356\) 9.99293e7i 2.21484i
\(357\) −1.09108e6 −0.0239802
\(358\) 6.84420e6 0.149167
\(359\) −4.90249e7 −1.05958 −0.529789 0.848129i \(-0.677729\pi\)
−0.529789 + 0.848129i \(0.677729\pi\)
\(360\) −1.85661e7 −0.397935
\(361\) 1.10202e7 0.234244
\(362\) 3.50592e7i 0.739053i
\(363\) 1.95638e8i 4.09009i
\(364\) 1.06817e6i 0.0221480i
\(365\) 3.39016e7 0.697175
\(366\) 1.72377e8i 3.51590i
\(367\) −5.67938e7 −1.14895 −0.574477 0.818520i \(-0.694795\pi\)
−0.574477 + 0.818520i \(0.694795\pi\)
\(368\) 5.56187e7 1.11603
\(369\) 8.25830e7 1.64366
\(370\) 2.88523e6i 0.0569607i
\(371\) 3.96959e6i 0.0777363i
\(372\) 8.46452e7i 1.64427i
\(373\) 5.89791e7i 1.13651i 0.822854 + 0.568253i \(0.192381\pi\)
−0.822854 + 0.568253i \(0.807619\pi\)
\(374\) 1.61377e7i 0.308481i
\(375\) 8.72096e7 1.65375
\(376\) 2.80595e6i 0.0527856i
\(377\) 7.50901e6i 0.140139i
\(378\) 6.58831e6i 0.121983i
\(379\) −3.87859e7 −0.712453 −0.356227 0.934400i \(-0.615937\pi\)
−0.356227 + 0.934400i \(0.615937\pi\)
\(380\) 5.21968e7 0.951247
\(381\) 1.19495e8i 2.16060i
\(382\) −1.27676e8 −2.29044
\(383\) 5.47849e7i 0.975135i 0.873085 + 0.487568i \(0.162116\pi\)
−0.873085 + 0.487568i \(0.837884\pi\)
\(384\) 5.54169e7 0.978697
\(385\) 1.40015e7 0.245354
\(386\) 4.80564e7i 0.835582i
\(387\) −7.39315e7 2.89501e7i −1.27555 0.499479i
\(388\) 2.27359e7 0.389239
\(389\) 5.34997e7i 0.908872i −0.890779 0.454436i \(-0.849841\pi\)
0.890779 0.454436i \(-0.150159\pi\)
\(390\) 1.53310e7i 0.258450i
\(391\) 9.84918e6 0.164767
\(392\) 1.92107e7i 0.318922i
\(393\) −7.13850e7 −1.17606
\(394\) 6.80216e7i 1.11214i
\(395\) 3.23284e7i 0.524558i
\(396\) −1.98239e8 −3.19230
\(397\) 5.42699e7 0.867337 0.433668 0.901073i \(-0.357219\pi\)
0.433668 + 0.901073i \(0.357219\pi\)
\(398\) −1.00329e8 −1.59139
\(399\) 1.23080e7i 0.193762i
\(400\) −9.59154e6 −0.149868
\(401\) −4.38375e7 −0.679849 −0.339925 0.940453i \(-0.610402\pi\)
−0.339925 + 0.940453i \(0.610402\pi\)
\(402\) 1.29281e8 1.99002
\(403\) −7.24857e6 −0.110748
\(404\) 1.43000e8 2.16867
\(405\) 2.92346e7i 0.440080i
\(406\) 1.59017e7i 0.237611i
\(407\) 5.52710e6i 0.0819811i
\(408\) 3.68752e6 0.0542942
\(409\) 2.63760e7i 0.385513i −0.981247 0.192756i \(-0.938257\pi\)
0.981247 0.192756i \(-0.0617427\pi\)
\(410\) 1.09877e8 1.59424
\(411\) 4.99942e6 0.0720103
\(412\) 1.23304e8 1.76314
\(413\) 7.45626e6i 0.105845i
\(414\) 2.20272e8i 3.10426i
\(415\) 4.85888e7i 0.679817i
\(416\) 1.29018e7i 0.179213i
\(417\) 1.16555e8i 1.60739i
\(418\) 1.82042e8 2.49255
\(419\) 7.54058e7i 1.02509i 0.858660 + 0.512546i \(0.171297\pi\)
−0.858660 + 0.512546i \(0.828703\pi\)
\(420\) 1.78328e7i 0.240698i
\(421\) 8.94310e6i 0.119851i 0.998203 + 0.0599255i \(0.0190863\pi\)
−0.998203 + 0.0599255i \(0.980914\pi\)
\(422\) 1.40886e8 1.87469
\(423\) 1.68054e7 0.222038
\(424\) 1.34159e7i 0.176005i
\(425\) −1.69851e6 −0.0221259
\(426\) 2.45435e8i 3.17473i
\(427\) −1.71704e7 −0.220545
\(428\) −1.10127e8 −1.40463
\(429\) 2.93688e7i 0.371976i
\(430\) −9.83660e7 3.85181e7i −1.23720 0.484462i
\(431\) −8.33129e7 −1.04059 −0.520296 0.853986i \(-0.674178\pi\)
−0.520296 + 0.853986i \(0.674178\pi\)
\(432\) 3.36729e7i 0.417667i
\(433\) 2.94658e7i 0.362956i −0.983395 0.181478i \(-0.941912\pi\)
0.983395 0.181478i \(-0.0580881\pi\)
\(434\) −1.53502e7 −0.187778
\(435\) 1.25361e8i 1.52298i
\(436\) 5.76223e7 0.695234
\(437\) 1.11104e8i 1.33133i
\(438\) 1.50589e8i 1.79214i
\(439\) −4.77584e7 −0.564490 −0.282245 0.959342i \(-0.591079\pi\)
−0.282245 + 0.959342i \(0.591079\pi\)
\(440\) −4.73207e7 −0.555512
\(441\) −1.15057e8 −1.34151
\(442\) 1.76010e6i 0.0203831i
\(443\) 1.09518e7 0.125972 0.0629861 0.998014i \(-0.479938\pi\)
0.0629861 + 0.998014i \(0.479938\pi\)
\(444\) 7.03950e6 0.0804253
\(445\) −1.42864e8 −1.62123
\(446\) 1.90001e7 0.214167
\(447\) −2.22870e8 −2.49533
\(448\) 1.78348e7i 0.198351i
\(449\) 7.02943e7i 0.776571i −0.921539 0.388286i \(-0.873067\pi\)
0.921539 0.388286i \(-0.126933\pi\)
\(450\) 3.79862e7i 0.416858i
\(451\) 2.10486e8 2.29452
\(452\) 1.30382e8i 1.41189i
\(453\) 1.59160e7 0.171214
\(454\) 1.63104e8 1.74300
\(455\) 1.52711e6 0.0162120
\(456\) 4.15972e7i 0.438702i
\(457\) 7.12167e7i 0.746162i −0.927799 0.373081i \(-0.878301\pi\)
0.927799 0.373081i \(-0.121699\pi\)
\(458\) 3.89738e7i 0.405673i
\(459\) 5.96293e6i 0.0616626i
\(460\) 1.60976e8i 1.65382i
\(461\) −2.56236e7 −0.261540 −0.130770 0.991413i \(-0.541745\pi\)
−0.130770 + 0.991413i \(0.541745\pi\)
\(462\) 6.21940e7i 0.630700i
\(463\) 1.17056e8i 1.17937i −0.807632 0.589687i \(-0.799251\pi\)
0.807632 0.589687i \(-0.200749\pi\)
\(464\) 8.12740e7i 0.813575i
\(465\) 1.21013e8 1.20358
\(466\) −2.04510e8 −2.02096
\(467\) 1.05647e8i 1.03730i 0.854987 + 0.518650i \(0.173565\pi\)
−0.854987 + 0.518650i \(0.826435\pi\)
\(468\) −2.16214e7 −0.210934
\(469\) 1.28776e7i 0.124829i
\(470\) 2.23595e7 0.215362
\(471\) 1.95658e8 1.87255
\(472\) 2.51998e7i 0.239647i
\(473\) −1.88435e8 7.37873e7i −1.78065 0.697265i
\(474\) −1.43601e8 −1.34841
\(475\) 1.91601e7i 0.178779i
\(476\) 2.04733e6i 0.0189831i
\(477\) 8.03508e7 0.740346
\(478\) 1.22828e8i 1.12464i
\(479\) 2.53782e7 0.230916 0.115458 0.993312i \(-0.463166\pi\)
0.115458 + 0.993312i \(0.463166\pi\)
\(480\) 2.15392e8i 1.94763i
\(481\) 602826.i 0.00541697i
\(482\) 1.51641e7 0.135418
\(483\) −3.79582e7 −0.336872
\(484\) −3.67098e8 −3.23777
\(485\) 3.25044e7i 0.284916i
\(486\) −2.27210e8 −1.97933
\(487\) 2.41863e7 0.209403 0.104701 0.994504i \(-0.466611\pi\)
0.104701 + 0.994504i \(0.466611\pi\)
\(488\) 5.80304e7 0.499340
\(489\) 2.88485e8 2.46715
\(490\) −1.53083e8 −1.30118
\(491\) 4.10861e7i 0.347097i 0.984825 + 0.173548i \(0.0555233\pi\)
−0.984825 + 0.173548i \(0.944477\pi\)
\(492\) 2.68082e8i 2.25098i
\(493\) 1.43923e7i 0.120113i
\(494\) 1.98549e7 0.164697
\(495\) 2.83413e8i 2.33671i
\(496\) −7.84551e7 −0.642949
\(497\) 2.44476e7 0.199144
\(498\) 2.15829e8 1.74752
\(499\) 6.96419e7i 0.560491i −0.959928 0.280246i \(-0.909584\pi\)
0.959928 0.280246i \(-0.0904159\pi\)
\(500\) 1.63641e8i 1.30913i
\(501\) 2.26212e7i 0.179888i
\(502\) 1.68020e8i 1.32816i
\(503\) 3.35079e7i 0.263296i −0.991297 0.131648i \(-0.957973\pi\)
0.991297 0.131648i \(-0.0420268\pi\)
\(504\) −8.21473e6 −0.0641655
\(505\) 2.04441e8i 1.58742i
\(506\) 5.61423e8i 4.33350i
\(507\) 1.97422e8i 1.51485i
\(508\) 2.24223e8 1.71036
\(509\) −3.31260e7 −0.251198 −0.125599 0.992081i \(-0.540085\pi\)
−0.125599 + 0.992081i \(0.540085\pi\)
\(510\) 2.93845e7i 0.221517i
\(511\) 1.50001e7 0.112417
\(512\) 1.71706e8i 1.27931i
\(513\) −6.72651e7 −0.498239
\(514\) −2.17478e8 −1.60149
\(515\) 1.76283e8i 1.29059i
\(516\) 9.39780e7 2.39997e8i 0.684033 1.74686i
\(517\) 4.28331e7 0.309961
\(518\) 1.27660e6i 0.00918469i
\(519\) 1.62580e8i 1.16296i
\(520\) −5.16114e6 −0.0367059
\(521\) 2.11591e8i 1.49618i 0.663598 + 0.748090i \(0.269029\pi\)
−0.663598 + 0.748090i \(0.730971\pi\)
\(522\) 3.21877e8 2.26297
\(523\) 1.63093e7i 0.114007i 0.998374 + 0.0570034i \(0.0181546\pi\)
−0.998374 + 0.0570034i \(0.981845\pi\)
\(524\) 1.33948e8i 0.930984i
\(525\) 6.54596e6 0.0452372
\(526\) −2.79532e8 −1.92077
\(527\) −1.38931e7 −0.0949223
\(528\) 3.17874e8i 2.15950i
\(529\) 1.94612e8 1.31462
\(530\) 1.06907e8 0.718088
\(531\) −1.50927e8 −1.00805
\(532\) 2.30950e7 0.153385
\(533\) 2.29571e7 0.151613
\(534\) 6.34595e8i 4.16747i
\(535\) 1.57443e8i 1.02816i
\(536\) 4.35222e7i 0.282629i
\(537\) −2.38734e7 −0.154167
\(538\) 9.75760e7i 0.626609i
\(539\) −2.93253e8 −1.87274
\(540\) 9.74589e7 0.618928
\(541\) 5.73217e7 0.362016 0.181008 0.983482i \(-0.442064\pi\)
0.181008 + 0.983482i \(0.442064\pi\)
\(542\) 9.32264e7i 0.585519i
\(543\) 1.22291e8i 0.763825i
\(544\) 2.47284e7i 0.153603i
\(545\) 8.23798e7i 0.508899i
\(546\) 6.78334e6i 0.0416740i
\(547\) 1.30026e8 0.794455 0.397228 0.917720i \(-0.369972\pi\)
0.397228 + 0.917720i \(0.369972\pi\)
\(548\) 9.38100e6i 0.0570043i
\(549\) 3.47556e8i 2.10043i
\(550\) 9.68184e7i 0.581929i
\(551\) −1.62353e8 −0.970522
\(552\) 1.28287e8 0.762719
\(553\) 1.43040e7i 0.0845829i
\(554\) 1.58815e8 0.934031
\(555\) 1.00640e7i 0.0588699i
\(556\) 2.18705e8 1.27243
\(557\) 2.40668e8 1.39268 0.696341 0.717711i \(-0.254810\pi\)
0.696341 + 0.717711i \(0.254810\pi\)
\(558\) 3.10713e8i 1.78837i
\(559\) −2.05521e7 8.04778e6i −0.117658 0.0460724i
\(560\) 1.65287e7 0.0941185
\(561\) 5.62904e7i 0.318820i
\(562\) 1.74213e8i 0.981459i
\(563\) 2.85376e8 1.59916 0.799580 0.600559i \(-0.205055\pi\)
0.799580 + 0.600559i \(0.205055\pi\)
\(564\) 5.45537e7i 0.304079i
\(565\) −1.86401e8 −1.03348
\(566\) 3.30294e7i 0.182159i
\(567\) 1.29351e7i 0.0709611i
\(568\) −8.26251e7 −0.450886
\(569\) 1.77690e8 0.964552 0.482276 0.876019i \(-0.339810\pi\)
0.482276 + 0.876019i \(0.339810\pi\)
\(570\) −3.31473e8 −1.78988
\(571\) 5.26888e6i 0.0283015i 0.999900 + 0.0141508i \(0.00450448\pi\)
−0.999900 + 0.0141508i \(0.995496\pi\)
\(572\) −5.51081e7 −0.294461
\(573\) 4.45350e8 2.36722
\(574\) 4.86160e7 0.257065
\(575\) −5.90901e7 −0.310822
\(576\) −3.61004e8 −1.88906
\(577\) 5.49076e7i 0.285828i 0.989735 + 0.142914i \(0.0456472\pi\)
−0.989735 + 0.142914i \(0.954353\pi\)
\(578\) 2.84251e8i 1.47204i
\(579\) 1.67627e8i 0.863589i
\(580\) 2.35230e8 1.20561
\(581\) 2.14986e7i 0.109618i
\(582\) −1.44383e8 −0.732397
\(583\) 2.04796e8 1.03351
\(584\) −5.06955e7 −0.254525
\(585\) 3.09111e7i 0.154400i
\(586\) 3.41977e8i 1.69943i
\(587\) 1.92743e8i 0.952936i −0.879192 0.476468i \(-0.841917\pi\)
0.879192 0.476468i \(-0.158083\pi\)
\(588\) 3.73497e8i 1.83720i
\(589\) 1.56722e8i 0.766980i
\(590\) −2.00808e8 −0.977743
\(591\) 2.37267e8i 1.14941i
\(592\) 6.52470e6i 0.0314482i
\(593\) 3.30813e8i 1.58642i −0.608948 0.793210i \(-0.708408\pi\)
0.608948 0.793210i \(-0.291592\pi\)
\(594\) 3.39899e8 1.62178
\(595\) 2.92697e6 0.0138953
\(596\) 4.18196e8i 1.97534i
\(597\) 3.49958e8 1.64473
\(598\) 6.12329e7i 0.286340i
\(599\) 3.28927e7 0.153045 0.0765226 0.997068i \(-0.475618\pi\)
0.0765226 + 0.997068i \(0.475618\pi\)
\(600\) −2.21233e7 −0.102423
\(601\) 7.51027e7i 0.345965i 0.984925 + 0.172983i \(0.0553404\pi\)
−0.984925 + 0.172983i \(0.944660\pi\)
\(602\) −4.35229e7 1.70427e7i −0.199493 0.0781176i
\(603\) −2.60663e8 −1.18885
\(604\) 2.98651e7i 0.135535i
\(605\) 5.24823e8i 2.36999i
\(606\) −9.08114e8 −4.08059
\(607\) 3.49954e8i 1.56475i 0.622809 + 0.782374i \(0.285991\pi\)
−0.622809 + 0.782374i \(0.714009\pi\)
\(608\) 2.78950e8 1.24113
\(609\) 5.54672e7i 0.245575i
\(610\) 4.62423e8i 2.03728i
\(611\) 4.67169e6 0.0204810
\(612\) −4.14412e7 −0.180791
\(613\) 1.29934e8 0.564081 0.282041 0.959402i \(-0.408989\pi\)
0.282041 + 0.959402i \(0.408989\pi\)
\(614\) 4.73012e8i 2.04346i
\(615\) −3.83264e8 −1.64768
\(616\) −2.09375e7 −0.0895741
\(617\) 3.41618e8 1.45441 0.727203 0.686423i \(-0.240820\pi\)
0.727203 + 0.686423i \(0.240820\pi\)
\(618\) −7.83037e8 −3.31755
\(619\) −1.53447e8 −0.646972 −0.323486 0.946233i \(-0.604855\pi\)
−0.323486 + 0.946233i \(0.604855\pi\)
\(620\) 2.27071e8i 0.952768i
\(621\) 2.07447e8i 0.866229i
\(622\) 5.29660e8i 2.20103i
\(623\) −6.32116e7 −0.261416
\(624\) 3.46697e7i 0.142691i
\(625\) −1.84072e8 −0.753960
\(626\) −2.37612e8 −0.968604
\(627\) −6.34986e8 −2.57609
\(628\) 3.67135e8i 1.48234i
\(629\) 1.15542e6i 0.00464288i
\(630\) 6.54601e7i 0.261791i
\(631\) 1.27596e8i 0.507866i −0.967222 0.253933i \(-0.918276\pi\)
0.967222 0.253933i \(-0.0817243\pi\)
\(632\) 4.83430e7i 0.191506i
\(633\) −4.91426e8 −1.93753
\(634\) 2.80949e8i 1.10245i
\(635\) 3.20560e8i 1.25195i
\(636\) 2.60835e8i 1.01390i
\(637\) −3.19843e7 −0.123743
\(638\) 8.20391e8 3.15907
\(639\) 4.94858e8i 1.89661i
\(640\) −1.48663e8 −0.567103
\(641\) 8.34287e7i 0.316768i −0.987378 0.158384i \(-0.949372\pi\)
0.987378 0.158384i \(-0.0506284\pi\)
\(642\) 6.99353e8 2.64296
\(643\) −3.32211e8 −1.24963 −0.624815 0.780773i \(-0.714826\pi\)
−0.624815 + 0.780773i \(0.714826\pi\)
\(644\) 7.12254e7i 0.266672i
\(645\) 3.43113e8 + 1.34356e8i 1.27867 + 0.500700i
\(646\) 3.80553e7 0.141162
\(647\) 2.30541e8i 0.851206i −0.904910 0.425603i \(-0.860062\pi\)
0.904910 0.425603i \(-0.139938\pi\)
\(648\) 4.37165e7i 0.160665i
\(649\) −3.84678e8 −1.40722
\(650\) 1.05597e7i 0.0384514i
\(651\) 5.35434e7 0.194072
\(652\) 5.41317e8i 1.95303i
\(653\) 2.83522e8i 1.01823i 0.860697 + 0.509117i \(0.170028\pi\)
−0.860697 + 0.509117i \(0.829972\pi\)
\(654\) −3.65927e8 −1.30816
\(655\) 1.91499e8 0.681464
\(656\) 2.48477e8 0.880186
\(657\) 3.03626e8i 1.07064i
\(658\) 9.89319e6 0.0347263
\(659\) 3.17640e8 1.10989 0.554943 0.831888i \(-0.312740\pi\)
0.554943 + 0.831888i \(0.312740\pi\)
\(660\) 9.20018e8 3.20011
\(661\) 2.93585e8 1.01655 0.508277 0.861194i \(-0.330283\pi\)
0.508277 + 0.861194i \(0.330283\pi\)
\(662\) 5.42776e8 1.87088
\(663\) 6.13944e6i 0.0210663i
\(664\) 7.26584e7i 0.248188i
\(665\) 3.30178e7i 0.112275i
\(666\) −2.58404e7 −0.0874734
\(667\) 5.00701e8i 1.68733i
\(668\) −4.24468e7 −0.142402
\(669\) −6.62748e7 −0.221345
\(670\) −3.46813e8 −1.15311
\(671\) 8.85841e8i 2.93217i
\(672\) 9.53021e7i 0.314047i
\(673\) 3.04183e8i 0.997906i −0.866629 0.498953i \(-0.833718\pi\)
0.866629 0.498953i \(-0.166282\pi\)
\(674\) 3.04192e8i 0.993499i
\(675\) 3.57746e7i 0.116322i
\(676\) 3.70445e8 1.19918
\(677\) 4.01476e8i 1.29388i −0.762541 0.646940i \(-0.776048\pi\)
0.762541 0.646940i \(-0.223952\pi\)
\(678\) 8.27983e8i 2.65664i
\(679\) 1.43819e7i 0.0459416i
\(680\) −9.89223e6 −0.0314606
\(681\) −5.68928e8 −1.80142
\(682\) 7.91937e8i 2.49653i
\(683\) −1.64796e8 −0.517232 −0.258616 0.965980i \(-0.583266\pi\)
−0.258616 + 0.965980i \(0.583266\pi\)
\(684\) 4.67479e8i 1.46081i
\(685\) −1.34116e7 −0.0417261
\(686\) −1.36897e8 −0.424053
\(687\) 1.35945e8i 0.419270i
\(688\) −2.22446e8 8.71054e7i −0.683062 0.267473i
\(689\) 2.23365e7 0.0682902
\(690\) 1.02227e9i 3.11185i
\(691\) 5.47737e8i 1.66011i −0.557679 0.830057i \(-0.688308\pi\)
0.557679 0.830057i \(-0.311692\pi\)
\(692\) −3.05068e8 −0.920615
\(693\) 1.25399e8i 0.376785i
\(694\) −7.12282e7 −0.213095
\(695\) 3.12672e8i 0.931398i
\(696\) 1.87462e8i 0.556013i
\(697\) 4.40012e7 0.129947
\(698\) 1.00405e9 2.95250
\(699\) 7.13357e8 2.08870
\(700\) 1.22829e7i 0.0358103i
\(701\) −3.75496e8 −1.09006 −0.545030 0.838416i \(-0.683482\pi\)
−0.545030 + 0.838416i \(0.683482\pi\)
\(702\) 3.70719e7 0.107160
\(703\) 1.30338e7 0.0375149
\(704\) −9.20118e8 −2.63709
\(705\) −7.79928e7 −0.222581
\(706\) 5.92138e8i 1.68271i
\(707\) 9.04566e7i 0.255966i
\(708\) 4.89939e8i 1.38052i
\(709\) 1.86689e8 0.523818 0.261909 0.965093i \(-0.415648\pi\)
0.261909 + 0.965093i \(0.415648\pi\)
\(710\) 6.58409e8i 1.83959i
\(711\) 2.89536e8 0.805552
\(712\) 2.13635e8 0.591879
\(713\) −4.83334e8 −1.33346
\(714\) 1.30014e7i 0.0357188i
\(715\) 7.87855e7i 0.215540i
\(716\) 4.47965e7i 0.122041i
\(717\) 4.28438e8i 1.16233i
\(718\) 5.84184e8i 1.57825i
\(719\) −6.32011e8 −1.70035 −0.850174 0.526501i \(-0.823504\pi\)
−0.850174 + 0.526501i \(0.823504\pi\)
\(720\) 3.34568e8i 0.896368i
\(721\) 7.79978e7i 0.208102i
\(722\) 1.31318e8i 0.348909i
\(723\) −5.28942e7 −0.139956
\(724\) −2.29468e8 −0.604654
\(725\) 8.63466e7i 0.226585i
\(726\) 2.33124e9 6.09223
\(727\) 6.56629e7i 0.170890i −0.996343 0.0854451i \(-0.972769\pi\)
0.996343 0.0854451i \(-0.0272312\pi\)
\(728\) −2.28360e6 −0.00591868
\(729\) 6.01402e8 1.55232
\(730\) 4.03974e8i 1.03845i
\(731\) −3.93916e7 1.54250e7i −0.100844 0.0394886i
\(732\) −1.12824e9 −2.87652
\(733\) 2.03328e8i 0.516281i −0.966107 0.258141i \(-0.916890\pi\)
0.966107 0.258141i \(-0.0831098\pi\)
\(734\) 6.76759e8i 1.71138i
\(735\) 5.33972e8 1.34480
\(736\) 8.60289e8i 2.15780i
\(737\) −6.64372e8 −1.65962
\(738\) 9.84065e8i 2.44824i
\(739\) 6.14810e8i 1.52338i −0.647943 0.761688i \(-0.724371\pi\)
0.647943 0.761688i \(-0.275629\pi\)
\(740\) −1.88843e7 −0.0466022
\(741\) −6.92562e7 −0.170217
\(742\) 4.73019e7 0.115789
\(743\) 2.10819e8i 0.513977i −0.966414 0.256989i \(-0.917270\pi\)
0.966414 0.256989i \(-0.0827303\pi\)
\(744\) −1.80960e8 −0.439403
\(745\) 5.97876e8 1.44591
\(746\) 7.02799e8 1.69284
\(747\) −4.35165e8 −1.04398
\(748\) −1.05624e8 −0.252382
\(749\) 6.96620e7i 0.165787i
\(750\) 1.03920e9i 2.46328i
\(751\) 5.50957e8i 1.30076i 0.759608 + 0.650381i \(0.225391\pi\)
−0.759608 + 0.650381i \(0.774609\pi\)
\(752\) 5.05642e7 0.118902
\(753\) 5.86075e8i 1.37268i
\(754\) 8.94778e7 0.208738
\(755\) −4.26967e7 −0.0992094
\(756\) 4.31216e7 0.0997997
\(757\) 5.62713e8i 1.29718i −0.761139 0.648589i \(-0.775360\pi\)
0.761139 0.648589i \(-0.224640\pi\)
\(758\) 4.62175e8i 1.06120i
\(759\) 1.95831e9i 4.47875i
\(760\) 1.11590e8i 0.254204i
\(761\) 5.58509e8i 1.26729i 0.773624 + 0.633645i \(0.218442\pi\)
−0.773624 + 0.633645i \(0.781558\pi\)
\(762\) −1.42391e9 −3.21824
\(763\) 3.64497e7i 0.0820579i
\(764\) 8.35662e8i 1.87392i
\(765\) 5.92465e7i 0.132336i
\(766\) 6.52821e8 1.45247
\(767\) −4.19558e7 −0.0929835
\(768\) 3.01293e8i 0.665129i
\(769\) −2.08570e8 −0.458640 −0.229320 0.973351i \(-0.573650\pi\)
−0.229320 + 0.973351i \(0.573650\pi\)
\(770\) 1.66843e8i 0.365457i
\(771\) 7.58588e8 1.65517
\(772\) −3.14537e8 −0.683628
\(773\) 1.37228e8i 0.297101i 0.988905 + 0.148550i \(0.0474607\pi\)
−0.988905 + 0.148550i \(0.952539\pi\)
\(774\) −3.44971e8 + 8.80973e8i −0.743978 + 1.89994i
\(775\) 8.33518e7 0.179065
\(776\) 4.86062e7i 0.104017i
\(777\) 4.45293e6i 0.00949254i
\(778\) −6.37506e8 −1.35377
\(779\) 4.96358e8i 1.04998i
\(780\) 1.00344e8 0.211450
\(781\) 1.26128e9i 2.64764i
\(782\) 1.17363e8i 0.245421i
\(783\) −3.03136e8 −0.631470