Properties

Label 27.8.e.a.4.16
Level 27
Weight 8
Character 27.4
Analytic conductor 8.434
Analytic rank 0
Dimension 120
CM No

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 27.e (of order \(9\) and degree \(6\))

Newform invariants

Self dual: No
Analytic conductor: \(8.43439568807\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{9})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.16
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.16

$q$-expansion

\(f(q)\) \(=\) \(q+(11.7328 + 4.27037i) q^{2} +(-44.8117 + 13.3756i) q^{3} +(21.3678 + 17.9297i) q^{4} +(58.4278 - 331.360i) q^{5} +(-582.884 - 34.4297i) q^{6} +(-23.9260 + 20.0763i) q^{7} +(-624.951 - 1082.45i) q^{8} +(1829.18 - 1198.77i) q^{9} +O(q^{10})\) \(q+(11.7328 + 4.27037i) q^{2} +(-44.8117 + 13.3756i) q^{3} +(21.3678 + 17.9297i) q^{4} +(58.4278 - 331.360i) q^{5} +(-582.884 - 34.4297i) q^{6} +(-23.9260 + 20.0763i) q^{7} +(-624.951 - 1082.45i) q^{8} +(1829.18 - 1198.77i) q^{9} +(2100.55 - 3638.26i) q^{10} +(-823.923 - 4672.70i) q^{11} +(-1197.35 - 517.653i) q^{12} +(-1318.00 + 479.713i) q^{13} +(-366.451 + 133.377i) q^{14} +(1813.91 + 15630.3i) q^{15} +(-3329.94 - 18885.0i) q^{16} +(-8979.65 + 15553.2i) q^{17} +(26580.6 - 6253.60i) q^{18} +(-291.761 - 505.346i) q^{19} +(7189.67 - 6032.85i) q^{20} +(803.632 - 1219.68i) q^{21} +(10287.3 - 58342.1i) q^{22} +(-70143.6 - 58857.5i) q^{23} +(42483.5 + 40147.2i) q^{24} +(-32972.4 - 12001.0i) q^{25} -17512.3 q^{26} +(-65934.6 + 78185.6i) q^{27} -871.208 q^{28} +(165286. + 60159.4i) q^{29} +(-45465.3 + 191133. i) q^{30} +(26748.2 + 22444.4i) q^{31} +(13795.2 - 78236.4i) q^{32} +(99421.8 + 198371. i) q^{33} +(-171774. + 144136. i) q^{34} +(5254.55 + 9101.14i) q^{35} +(60579.3 + 7181.63i) q^{36} +(-147008. + 254625. i) q^{37} +(-1265.15 - 7175.03i) q^{38} +(52645.5 - 39125.9i) q^{39} +(-395194. + 143839. i) q^{40} +(765563. - 278642. i) q^{41} +(14637.3 - 10878.4i) q^{42} +(-117769. - 667900. i) q^{43} +(66174.7 - 114618. i) q^{44} +(-290350. - 676161. i) q^{45} +(-571635. - 990100. i) q^{46} +(717373. - 601947. i) q^{47} +(401819. + 801730. i) q^{48} +(-142837. + 810071. i) q^{49} +(-335608. - 281609. i) q^{50} +(194359. - 817075. i) q^{51} +(-36763.9 - 13381.0i) q^{52} +414902. q^{53} +(-1.10748e6 + 635767. i) q^{54} -1.59649e6 q^{55} +(36684.1 + 13351.9i) q^{56} +(19833.7 + 18742.9i) q^{57} +(1.68236e6 + 1.41167e6i) q^{58} +(282805. - 1.60386e6i) q^{59} +(-241488. + 366509. i) q^{60} +(1.50263e6 - 1.26086e6i) q^{61} +(217984. + 377559. i) q^{62} +(-19698.2 + 65405.1i) q^{63} +(-731331. + 1.26670e6i) q^{64} +(81950.1 + 464762. i) q^{65} +(319372. + 2.75201e6i) q^{66} +(728737. - 265239. i) q^{67} +(-470740. + 171335. i) q^{68} +(3.93052e6 + 1.69929e6i) q^{69} +(22785.0 + 129220. i) q^{70} +(-2.73783e6 + 4.74205e6i) q^{71} +(-2.44076e6 - 1.23082e6i) q^{72} +(-2.49605e6 - 4.32328e6i) q^{73} +(-2.81215e6 + 2.35967e6i) q^{74} +(1.63807e6 + 96757.4i) q^{75} +(2826.40 - 16029.3i) q^{76} +(113524. + 95257.7i) q^{77} +(784759. - 234239. i) q^{78} +(-1.31030e6 - 476909. i) q^{79} -6.45230e6 q^{80} +(1.90886e6 - 4.38555e6i) q^{81} +1.01721e7 q^{82} +(681748. + 248136. i) q^{83} +(39040.3 - 11653.0i) q^{84} +(4.62905e6 + 3.88424e6i) q^{85} +(1.47043e6 - 8.33922e6i) q^{86} +(-8.21145e6 - 485032. i) q^{87} +(-4.54304e6 + 3.81206e6i) q^{88} +(3.25203e6 + 5.63268e6i) q^{89} +(-519150. - 9.17313e6i) q^{90} +(21903.6 - 37938.2i) q^{91} +(-443517. - 2.51531e6i) q^{92} +(-1.49884e6 - 647998. i) q^{93} +(1.09873e7 - 3.99905e6i) q^{94} +(-184499. + 67152.0i) q^{95} +(428276. + 3.69043e6i) q^{96} +(-635518. - 3.60420e6i) q^{97} +(-5.13518e6 + 8.89440e6i) q^{98} +(-7.10861e6 - 7.55953e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} + O(q^{10}) \) \( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} - 3q^{10} + 9399q^{11} - 10545q^{12} - 6q^{13} + 16647q^{14} + 11709q^{15} + 378q^{16} - 58959q^{17} - 156051q^{18} - 3q^{19} + 240243q^{20} - 516q^{21} + 105762q^{22} - 144084q^{23} - 150894q^{24} - 107997q^{25} + 443202q^{26} + 114363q^{27} - 12q^{28} + 107886q^{29} - 179901q^{30} + 297975q^{31} - 639576q^{32} - 31338q^{33} - 265806q^{34} - 450672q^{35} + 51264q^{36} - 3q^{37} - 145596q^{38} + 1919661q^{39} + 283521q^{40} + 227085q^{41} + 3792042q^{42} - 1080969q^{43} - 1205115q^{44} - 4430925q^{45} - 3q^{46} - 5184339q^{47} - 2424039q^{48} + 976008q^{49} + 2324559q^{50} + 2918034q^{51} - 3366135q^{52} + 5631750q^{53} + 11971422q^{54} - 12q^{55} + 5254923q^{56} - 284637q^{57} + 3884295q^{58} - 12534492q^{59} - 29390886q^{60} + 3865440q^{61} - 9923646q^{62} + 3292389q^{63} - 10223619q^{64} + 17158395q^{65} + 39100653q^{66} + 5567061q^{67} + 19858455q^{68} - 12682935q^{69} - 1020993q^{70} - 18563877q^{71} - 33138540q^{72} + 3770934q^{73} - 36278085q^{74} - 26317941q^{75} - 1156998q^{76} + 8471751q^{77} + 36593658q^{78} + 16415526q^{79} + 101080590q^{80} + 45736524q^{81} - 12q^{82} + 3147699q^{83} - 27588054q^{84} - 7672131q^{85} - 70854834q^{86} - 55384731q^{87} - 34323078q^{88} - 54647613q^{89} - 25256970q^{90} + 3315066q^{91} + 73858515q^{92} + 69808065q^{93} + 22126539q^{94} + 32541447q^{95} + 33014034q^{96} + 41250117q^{97} - 88493274q^{98} - 111262167q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.7328 + 4.27037i 1.03704 + 0.377451i 0.803757 0.594958i \(-0.202831\pi\)
0.233282 + 0.972409i \(0.425053\pi\)
\(3\) −44.8117 + 13.3756i −0.958225 + 0.286016i
\(4\) 21.3678 + 17.9297i 0.166936 + 0.140076i
\(5\) 58.4278 331.360i 0.209038 1.18551i −0.681921 0.731426i \(-0.738855\pi\)
0.890958 0.454085i \(-0.150034\pi\)
\(6\) −582.884 34.4297i −1.10167 0.0650735i
\(7\) −23.9260 + 20.0763i −0.0263649 + 0.0221228i −0.655875 0.754870i \(-0.727700\pi\)
0.629510 + 0.776992i \(0.283256\pi\)
\(8\) −624.951 1082.45i −0.431550 0.747466i
\(9\) 1829.18 1198.77i 0.836390 0.548135i
\(10\) 2100.55 3638.26i 0.664253 1.15052i
\(11\) −823.923 4672.70i −0.186643 1.05851i −0.923826 0.382813i \(-0.874955\pi\)
0.737183 0.675693i \(-0.236156\pi\)
\(12\) −1197.35 517.653i −0.200026 0.0864778i
\(13\) −1318.00 + 479.713i −0.166385 + 0.0605592i −0.423870 0.905723i \(-0.639329\pi\)
0.257485 + 0.966282i \(0.417106\pi\)
\(14\) −366.451 + 133.377i −0.0356918 + 0.0129907i
\(15\) 1813.91 + 15630.3i 0.138770 + 1.19577i
\(16\) −3329.94 18885.0i −0.203243 1.15265i
\(17\) −8979.65 + 15553.2i −0.443290 + 0.767801i −0.997931 0.0642886i \(-0.979522\pi\)
0.554641 + 0.832090i \(0.312856\pi\)
\(18\) 26580.6 6253.60i 1.07426 0.252741i
\(19\) −291.761 505.346i −0.00975866 0.0169025i 0.861105 0.508427i \(-0.169773\pi\)
−0.870863 + 0.491525i \(0.836440\pi\)
\(20\) 7189.67 6032.85i 0.200957 0.168623i
\(21\) 803.632 1219.68i 0.0189361 0.0287394i
\(22\) 10287.3 58342.1i 0.205978 1.16816i
\(23\) −70143.6 58857.5i −1.20210 1.00868i −0.999568 0.0294069i \(-0.990638\pi\)
−0.202533 0.979275i \(-0.564917\pi\)
\(24\) 42483.5 + 40147.2i 0.627309 + 0.592810i
\(25\) −32972.4 12001.0i −0.422047 0.153612i
\(26\) −17512.3 −0.195406
\(27\) −65934.6 + 78185.6i −0.644674 + 0.764458i
\(28\) −871.208 −0.00750013
\(29\) 165286. + 60159.4i 1.25847 + 0.458047i 0.883257 0.468890i \(-0.155346\pi\)
0.375218 + 0.926937i \(0.377568\pi\)
\(30\) −45465.3 + 191133.i −0.307436 + 1.29244i
\(31\) 26748.2 + 22444.4i 0.161261 + 0.135314i 0.719847 0.694132i \(-0.244212\pi\)
−0.558587 + 0.829446i \(0.688656\pi\)
\(32\) 13795.2 78236.4i 0.0744222 0.422069i
\(33\) 99421.8 + 198371.i 0.481596 + 0.960904i
\(34\) −171774. + 144136.i −0.749517 + 0.628919i
\(35\) 5254.55 + 9101.14i 0.0207156 + 0.0358804i
\(36\) 60579.3 + 7181.63i 0.216404 + 0.0256545i
\(37\) −147008. + 254625.i −0.477127 + 0.826408i −0.999656 0.0262129i \(-0.991655\pi\)
0.522529 + 0.852621i \(0.324989\pi\)
\(38\) −1265.15 7175.03i −0.00374024 0.0212120i
\(39\) 52645.5 39125.9i 0.142113 0.105618i
\(40\) −395194. + 143839.i −0.976339 + 0.355358i
\(41\) 765563. 278642.i 1.73475 0.631398i 0.735801 0.677198i \(-0.236806\pi\)
0.998951 + 0.0458001i \(0.0145837\pi\)
\(42\) 14637.3 10878.4i 0.0304852 0.0226565i
\(43\) −117769. 667900.i −0.225887 1.28107i −0.860983 0.508633i \(-0.830151\pi\)
0.635097 0.772433i \(-0.280960\pi\)
\(44\) 66174.7 114618.i 0.117114 0.202847i
\(45\) −290350. 676161.i −0.474983 1.10613i
\(46\) −571635. 990100.i −0.865897 1.49978i
\(47\) 717373. 601947.i 1.00786 0.845699i 0.0198102 0.999804i \(-0.493694\pi\)
0.988055 + 0.154105i \(0.0492494\pi\)
\(48\) 401819. + 801730.i 0.524429 + 1.04637i
\(49\) −142837. + 810071.i −0.173442 + 0.983641i
\(50\) −335608. 281609.i −0.379698 0.318604i
\(51\) 194359. 817075.i 0.205168 0.862514i
\(52\) −36763.9 13381.0i −0.0362585 0.0131970i
\(53\) 414902. 0.382807 0.191403 0.981511i \(-0.438696\pi\)
0.191403 + 0.981511i \(0.438696\pi\)
\(54\) −1.10748e6 + 635767.i −0.957098 + 0.549439i
\(55\) −1.59649e6 −1.29389
\(56\) 36684.1 + 13351.9i 0.0279138 + 0.0101598i
\(57\) 19833.7 + 18742.9i 0.0141854 + 0.0134053i
\(58\) 1.68236e6 + 1.41167e6i 1.13220 + 0.950026i
\(59\) 282805. 1.60386e6i 0.179269 1.01668i −0.753832 0.657068i \(-0.771797\pi\)
0.933100 0.359616i \(-0.117092\pi\)
\(60\) −241488. + 366509.i −0.144333 + 0.219056i
\(61\) 1.50263e6 1.26086e6i 0.847613 0.711232i −0.111649 0.993748i \(-0.535613\pi\)
0.959263 + 0.282516i \(0.0911689\pi\)
\(62\) 217984. + 377559.i 0.116159 + 0.201194i
\(63\) −19698.2 + 65405.1i −0.00992507 + 0.0329549i
\(64\) −731331. + 1.26670e6i −0.348726 + 0.604011i
\(65\) 81950.1 + 464762.i 0.0370129 + 0.209910i
\(66\) 319372. + 2.75201e6i 0.136739 + 1.17827i
\(67\) 728737. 265239.i 0.296012 0.107739i −0.189745 0.981833i \(-0.560766\pi\)
0.485757 + 0.874094i \(0.338544\pi\)
\(68\) −470740. + 171335.i −0.181551 + 0.0660793i
\(69\) 3.93052e6 + 1.69929e6i 1.44038 + 0.622724i
\(70\) 22785.0 + 129220.i 0.00793974 + 0.0450285i
\(71\) −2.73783e6 + 4.74205e6i −0.907824 + 1.57240i −0.0907423 + 0.995874i \(0.528924\pi\)
−0.817081 + 0.576522i \(0.804409\pi\)
\(72\) −2.44076e6 1.23082e6i −0.770656 0.388625i
\(73\) −2.49605e6 4.32328e6i −0.750971 1.30072i −0.947353 0.320192i \(-0.896252\pi\)
0.196382 0.980528i \(-0.437081\pi\)
\(74\) −2.81215e6 + 2.35967e6i −0.806728 + 0.676925i
\(75\) 1.63807e6 + 96757.4i 0.448351 + 0.0264831i
\(76\) 2826.40 16029.3i 0.000738561 0.00418859i
\(77\) 113524. + 95257.7i 0.0283380 + 0.0237784i
\(78\) 784759. 234239.i 0.187243 0.0558892i
\(79\) −1.31030e6 476909.i −0.299003 0.108828i 0.188162 0.982138i \(-0.439747\pi\)
−0.487165 + 0.873310i \(0.661969\pi\)
\(80\) −6.45230e6 −1.40896
\(81\) 1.90886e6 4.38555e6i 0.399095 0.916909i
\(82\) 1.01721e7 2.03733
\(83\) 681748. + 248136.i 0.130873 + 0.0476339i 0.406626 0.913595i \(-0.366705\pi\)
−0.275753 + 0.961228i \(0.588927\pi\)
\(84\) 39040.3 11653.0i 0.00718681 0.00214516i
\(85\) 4.62905e6 + 3.88424e6i 0.817572 + 0.686024i
\(86\) 1.47043e6 8.33922e6i 0.249287 1.41378i
\(87\) −8.21145e6 485032.i −1.33691 0.0789684i
\(88\) −4.54304e6 + 3.81206e6i −0.710652 + 0.596307i
\(89\) 3.25203e6 + 5.63268e6i 0.488978 + 0.846935i 0.999920 0.0126807i \(-0.00403650\pi\)
−0.510942 + 0.859615i \(0.670703\pi\)
\(90\) −519150. 9.17313e6i −0.0750661 1.32638i
\(91\) 21903.6 37938.2i 0.00304699 0.00527754i
\(92\) −443517. 2.51531e6i −0.0593817 0.336771i
\(93\) −1.49884e6 647998.i −0.193226 0.0835378i
\(94\) 1.09873e7 3.99905e6i 1.36441 0.496603i
\(95\) −184499. + 67152.0i −0.0220780 + 0.00803574i
\(96\) 428276. + 3.69043e6i 0.0494054 + 0.425723i
\(97\) −635518. 3.60420e6i −0.0707012 0.400966i −0.999536 0.0304713i \(-0.990299\pi\)
0.928834 0.370495i \(-0.120812\pi\)
\(98\) −5.13518e6 + 8.89440e6i −0.551143 + 0.954608i
\(99\) −7.10861e6 7.55953e6i −0.736311 0.783018i
\(100\) −489373. 847620.i −0.0489373 0.0847620i
\(101\) 1.15220e6 966810.i 0.111276 0.0933719i −0.585452 0.810707i \(-0.699083\pi\)
0.696728 + 0.717335i \(0.254638\pi\)
\(102\) 5.76959e6 8.75655e6i 0.538324 0.817020i
\(103\) −2.33615e6 + 1.32489e7i −0.210654 + 1.19468i 0.677637 + 0.735397i \(0.263004\pi\)
−0.888291 + 0.459282i \(0.848107\pi\)
\(104\) 1.34295e6 + 1.12687e6i 0.117069 + 0.0982328i
\(105\) −357199. 337555.i −0.0301126 0.0284565i
\(106\) 4.86794e6 + 1.77179e6i 0.396986 + 0.144491i
\(107\) 1.85415e7 1.46320 0.731598 0.681736i \(-0.238775\pi\)
0.731598 + 0.681736i \(0.238775\pi\)
\(108\) −2.81072e6 + 488465.i −0.214701 + 0.0373122i
\(109\) −4.70819e6 −0.348226 −0.174113 0.984726i \(-0.555706\pi\)
−0.174113 + 0.984726i \(0.555706\pi\)
\(110\) −1.87312e7 6.81760e6i −1.34181 0.488379i
\(111\) 3.18190e6 1.33765e7i 0.220829 0.928351i
\(112\) 458813. + 384990.i 0.0308583 + 0.0258932i
\(113\) −1.29613e6 + 7.35074e6i −0.0845036 + 0.479244i 0.912959 + 0.408051i \(0.133792\pi\)
−0.997463 + 0.0711924i \(0.977320\pi\)
\(114\) 152664. + 304603.i 0.00965096 + 0.0192561i
\(115\) −2.36014e7 + 1.98039e7i −1.44709 + 1.21425i
\(116\) 2.45317e6 + 4.24901e6i 0.145923 + 0.252746i
\(117\) −1.83580e6 + 2.45747e6i −0.105968 + 0.141853i
\(118\) 1.01672e7 1.76101e7i 0.569657 0.986675i
\(119\) −97403.7 552404.i −0.00529860 0.0300499i
\(120\) 1.57854e7 1.17317e7i 0.833914 0.619762i
\(121\) −2.84332e6 + 1.03488e6i −0.145907 + 0.0531058i
\(122\) 2.30143e7 8.37653e6i 1.14746 0.417643i
\(123\) −3.05792e7 + 2.27263e7i −1.48169 + 1.10119i
\(124\) 169128. + 959174.i 0.00796600 + 0.0451774i
\(125\) 7.24029e6 1.25406e7i 0.331567 0.574291i
\(126\) −510418. + 683263.i −0.0227315 + 0.0304292i
\(127\) −8.47700e6 1.46826e7i −0.367222 0.636048i 0.621908 0.783090i \(-0.286358\pi\)
−0.989130 + 0.147043i \(0.953025\pi\)
\(128\) −2.17795e7 + 1.82752e7i −0.917939 + 0.770242i
\(129\) 1.42110e7 + 2.83545e7i 0.582856 + 1.16294i
\(130\) −1.02321e6 + 5.80290e6i −0.0408472 + 0.231656i
\(131\) 2.03854e7 + 1.71053e7i 0.792262 + 0.664787i 0.946304 0.323277i \(-0.104785\pi\)
−0.154042 + 0.988064i \(0.549229\pi\)
\(132\) −1.43232e6 + 6.02136e6i −0.0542038 + 0.227869i
\(133\) 17126.2 + 6233.41i 0.000631218 + 0.000229744i
\(134\) 9.68276e6 0.347642
\(135\) 2.20552e7 + 2.64163e7i 0.771512 + 0.924068i
\(136\) 2.24473e7 0.765207
\(137\) −5.05937e7 1.84146e7i −1.68103 0.611844i −0.687577 0.726111i \(-0.741326\pi\)
−0.993450 + 0.114268i \(0.963548\pi\)
\(138\) 3.88592e7 + 3.67221e7i 1.25868 + 1.18946i
\(139\) 4.83964e6 + 4.06094e6i 0.152848 + 0.128255i 0.716005 0.698095i \(-0.245969\pi\)
−0.563157 + 0.826350i \(0.690413\pi\)
\(140\) −50902.7 + 288684.i −0.00156781 + 0.00889148i
\(141\) −2.40953e7 + 3.65696e7i −0.723878 + 1.09864i
\(142\) −5.23726e7 + 4.39458e7i −1.53495 + 1.28798i
\(143\) 3.32749e6 + 5.76338e6i 0.0951569 + 0.164817i
\(144\) −2.87299e7 3.05523e7i −0.801798 0.852659i
\(145\) 2.95917e7 5.12544e7i 0.806088 1.39619i
\(146\) −1.08235e7 6.13831e7i −0.287828 1.63235i
\(147\) −4.43443e6 3.82112e7i −0.115140 0.992157i
\(148\) −7.70658e6 + 2.80497e6i −0.195409 + 0.0711232i
\(149\) 4.05805e7 1.47701e7i 1.00500 0.365790i 0.213489 0.976946i \(-0.431517\pi\)
0.791510 + 0.611156i \(0.209295\pi\)
\(150\) 1.88059e7 + 8.13041e6i 0.454962 + 0.196695i
\(151\) −1.05238e7 5.96837e7i −0.248745 1.41070i −0.811631 0.584170i \(-0.801420\pi\)
0.562886 0.826535i \(-0.309691\pi\)
\(152\) −364673. + 631632.i −0.00842270 + 0.0145885i
\(153\) 2.21931e6 + 3.92142e7i 0.0500955 + 0.885164i
\(154\) 925160. + 1.60242e6i 0.0204124 + 0.0353553i
\(155\) 9.00001e6 7.55191e6i 0.194125 0.162891i
\(156\) 1.82643e6 + 107884.i 0.0385184 + 0.00227520i
\(157\) 1.49750e7 8.49272e7i 0.308828 1.75145i −0.296087 0.955161i \(-0.595682\pi\)
0.604915 0.796290i \(-0.293207\pi\)
\(158\) −1.33368e7 1.11909e7i −0.269000 0.225718i
\(159\) −1.85925e7 + 5.54958e6i −0.366815 + 0.109489i
\(160\) −2.51184e7 9.14235e6i −0.484811 0.176457i
\(161\) 2.85990e6 0.0540082
\(162\) 4.11241e7 4.33030e7i 0.759966 0.800232i
\(163\) −6.66520e7 −1.20547 −0.602735 0.797941i \(-0.705922\pi\)
−0.602735 + 0.797941i \(0.705922\pi\)
\(164\) 2.13544e7 + 7.77235e6i 0.378036 + 0.137594i
\(165\) 7.15414e7 2.13540e7i 1.23983 0.370072i
\(166\) 6.93915e6 + 5.82264e6i 0.117741 + 0.0987965i
\(167\) 1.61244e7 9.14460e7i 0.267902 1.51935i −0.492740 0.870176i \(-0.664005\pi\)
0.760642 0.649171i \(-0.224884\pi\)
\(168\) −1.82247e6 107649.i −0.0296536 0.00175157i
\(169\) −4.65612e7 + 3.90694e7i −0.742028 + 0.622635i
\(170\) 3.77244e7 + 6.53406e7i 0.588913 + 1.02003i
\(171\) −1.13948e6 574615.i −0.0174269 0.00878801i
\(172\) 9.45879e6 1.63831e7i 0.141738 0.245497i
\(173\) 4.20370e6 + 2.38404e7i 0.0617263 + 0.350067i 0.999991 + 0.00415023i \(0.00132106\pi\)
−0.938265 + 0.345917i \(0.887568\pi\)
\(174\) −9.42716e7 4.07567e7i −1.35662 0.586512i
\(175\) 1.02983e6 374828.i 0.0145256 0.00528688i
\(176\) −8.55003e7 + 3.11196e7i −1.18215 + 0.430268i
\(177\) 8.77976e6 + 7.56547e7i 0.119008 + 1.02549i
\(178\) 1.41016e7 + 7.99742e7i 0.187413 + 1.06287i
\(179\) −7.53307e6 + 1.30477e7i −0.0981718 + 0.170039i −0.910928 0.412565i \(-0.864633\pi\)
0.812756 + 0.582604i \(0.197966\pi\)
\(180\) 5.91922e6 1.96540e7i 0.0756503 0.251186i
\(181\) 3.55840e7 + 6.16333e7i 0.446046 + 0.772575i 0.998124 0.0612174i \(-0.0194983\pi\)
−0.552078 + 0.833792i \(0.686165\pi\)
\(182\) 419000. 351583.i 0.00515186 0.00432293i
\(183\) −5.04707e7 + 7.65998e7i −0.608780 + 0.923951i
\(184\) −1.98738e7 + 1.12710e8i −0.235190 + 1.33383i
\(185\) 7.57832e7 + 6.35897e7i 0.879979 + 0.738390i
\(186\) −1.48183e7 1.40034e7i −0.168851 0.159565i
\(187\) 8.00740e7 + 2.91445e7i 0.895459 + 0.325920i
\(188\) 2.61214e7 0.286711
\(189\) 7874.16 3.19439e6i 8.48375e−5 0.0344169i
\(190\) −2.45144e6 −0.0259289
\(191\) 4.83766e7 + 1.76077e7i 0.502364 + 0.182846i 0.580757 0.814077i \(-0.302757\pi\)
−0.0783928 + 0.996923i \(0.524979\pi\)
\(192\) 1.58293e7 6.65452e7i 0.161401 0.678519i
\(193\) 7.42199e7 + 6.22779e7i 0.743139 + 0.623568i 0.933679 0.358112i \(-0.116579\pi\)
−0.190540 + 0.981679i \(0.561024\pi\)
\(194\) 7.93491e6 4.50011e7i 0.0780254 0.442504i
\(195\) −9.88882e6 1.97307e7i −0.0955044 0.190555i
\(196\) −1.75765e7 + 1.47484e7i −0.166738 + 0.139910i
\(197\) −3.12870e7 5.41907e7i −0.291563 0.505002i 0.682616 0.730777i \(-0.260842\pi\)
−0.974180 + 0.225775i \(0.927509\pi\)
\(198\) −5.11215e7 1.19051e8i −0.468032 1.08994i
\(199\) −8.57336e6 + 1.48495e7i −0.0771197 + 0.133575i −0.902006 0.431723i \(-0.857906\pi\)
0.824886 + 0.565299i \(0.191239\pi\)
\(200\) 7.61572e6 + 4.31909e7i 0.0673140 + 0.381757i
\(201\) −2.91082e7 + 2.16331e7i −0.252831 + 0.187903i
\(202\) 1.76471e7 6.42303e6i 0.150641 0.0548289i
\(203\) −5.16242e6 + 1.87897e6i −0.0433129 + 0.0157646i
\(204\) 1.88029e7 1.39743e7i 0.155067 0.115245i
\(205\) −4.76008e7 2.69958e8i −0.385901 2.18855i
\(206\) −8.39874e7 + 1.45470e8i −0.669389 + 1.15942i
\(207\) −1.98862e8 2.35750e7i −1.55832 0.184738i
\(208\) 1.34482e7 + 2.32930e7i 0.103620 + 0.179475i
\(209\) −2.12094e6 + 1.77968e6i −0.0160700 + 0.0134843i
\(210\) −2.74944e6 5.48582e6i −0.0204869 0.0408766i
\(211\) −1.02983e7 + 5.84048e7i −0.0754708 + 0.428016i 0.923538 + 0.383507i \(0.125284\pi\)
−0.999009 + 0.0445096i \(0.985827\pi\)
\(212\) 8.86553e6 + 7.43907e6i 0.0639042 + 0.0536220i
\(213\) 5.92587e7 2.49120e8i 0.420169 1.76636i
\(214\) 2.17543e8 + 7.91793e7i 1.51739 + 0.552285i
\(215\) −2.28196e8 −1.56594
\(216\) 1.25838e8 + 2.25085e7i 0.849615 + 0.151970i
\(217\) −1.09058e6 −0.00724515
\(218\) −5.52400e7 2.01057e7i −0.361124 0.131438i
\(219\) 1.69679e8 + 1.60348e8i 1.09163 + 1.03159i
\(220\) −3.41134e7 2.86246e7i −0.215996 0.181242i
\(221\) 4.37411e6 2.48068e7i 0.0272594 0.154596i
\(222\) 9.44551e7 1.43355e8i 0.579416 0.879384i
\(223\) 7.20065e7 6.04206e7i 0.434815 0.364853i −0.398950 0.916973i \(-0.630625\pi\)
0.833765 + 0.552119i \(0.186181\pi\)
\(224\) 1.24063e6 + 2.14884e6i 0.00737523 + 0.0127743i
\(225\) −7.46990e7 + 1.75744e7i −0.437196 + 0.102859i
\(226\) −4.65976e7 + 8.07094e7i −0.268525 + 0.465098i
\(227\) 3.75278e7 + 2.12831e8i 0.212942 + 1.20766i 0.884442 + 0.466651i \(0.154540\pi\)
−0.671499 + 0.741005i \(0.734349\pi\)
\(228\) 87746.5 + 756107.i 0.000490295 + 0.00422485i
\(229\) 1.18520e8 4.31377e7i 0.652179 0.237374i 0.00532318 0.999986i \(-0.498306\pi\)
0.646856 + 0.762612i \(0.276083\pi\)
\(230\) −3.61479e8 + 1.31568e8i −1.95901 + 0.713020i
\(231\) −6.36133e6 2.75021e6i −0.0339552 0.0146799i
\(232\) −3.81766e7 2.16510e8i −0.200720 1.13834i
\(233\) 1.40431e8 2.43233e8i 0.727305 1.25973i −0.230713 0.973022i \(-0.574106\pi\)
0.958018 0.286708i \(-0.0925609\pi\)
\(234\) −3.20333e7 + 2.09933e7i −0.163435 + 0.107109i
\(235\) −1.57547e8 2.72879e8i −0.791904 1.37162i
\(236\) 3.47997e7 2.92005e7i 0.172339 0.144610i
\(237\) 6.50957e7 + 3.84506e6i 0.317638 + 0.0187622i
\(238\) 1.21616e6 6.89717e6i 0.00584750 0.0331628i
\(239\) −5.50715e7 4.62105e7i −0.260936 0.218951i 0.502928 0.864328i \(-0.332256\pi\)
−0.763864 + 0.645377i \(0.776700\pi\)
\(240\) 2.89139e8 8.63037e7i 1.35010 0.402986i
\(241\) 2.99312e8 + 1.08940e8i 1.37741 + 0.501337i 0.921393 0.388633i \(-0.127053\pi\)
0.456019 + 0.889970i \(0.349275\pi\)
\(242\) −3.77793e7 −0.171356
\(243\) −2.68799e7 + 2.22056e8i −0.120172 + 0.992753i
\(244\) 5.47147e7 0.241123
\(245\) 2.60080e8 + 9.46613e7i 1.12986 + 0.411236i
\(246\) −4.55828e8 + 1.36058e8i −1.95222 + 0.582708i
\(247\) 626963. + 526084.i 0.00264730 + 0.00222135i
\(248\) 7.57855e6 4.29801e7i 0.0315504 0.178931i
\(249\) −3.38693e7 2.00059e6i −0.139030 0.00821220i
\(250\) 1.38501e8 1.16217e8i 0.560614 0.470411i
\(251\) −1.04814e8 1.81543e8i −0.418370 0.724639i 0.577405 0.816458i \(-0.304065\pi\)
−0.995776 + 0.0918189i \(0.970732\pi\)
\(252\) −1.59360e6 + 1.04438e6i −0.00627303 + 0.00411108i
\(253\) −2.17230e8 + 3.76254e8i −0.843333 + 1.46069i
\(254\) −3.67584e7 2.08467e8i −0.140747 0.798215i
\(255\) −2.59390e8 1.12143e8i −0.979632 0.423527i
\(256\) −1.57646e8 + 5.73784e7i −0.587277 + 0.213751i
\(257\) 2.84408e7 1.03516e7i 0.104514 0.0380401i −0.289234 0.957258i \(-0.593400\pi\)
0.393748 + 0.919218i \(0.371178\pi\)
\(258\) 4.56499e7 + 3.93363e8i 0.165490 + 1.42602i
\(259\) −1.59462e6 9.04352e6i −0.00570305 0.0323436i
\(260\) −6.58195e6 + 1.14003e7i −0.0232246 + 0.0402262i
\(261\) 3.74457e8 8.80982e7i 1.30365 0.306708i
\(262\) 1.66130e8 + 2.87746e8i 0.570682 + 0.988450i
\(263\) −2.08287e7 + 1.74774e7i −0.0706021 + 0.0592422i −0.677406 0.735610i \(-0.736896\pi\)
0.606804 + 0.794852i \(0.292451\pi\)
\(264\) 1.52593e8 2.31591e8i 0.510411 0.774654i
\(265\) 2.42418e7 1.37482e8i 0.0800210 0.453822i
\(266\) 174318. + 146270.i 0.000567880 + 0.000476508i
\(267\) −2.21070e8 2.08912e8i −0.710788 0.671698i
\(268\) 2.03272e7 + 7.39848e6i 0.0645067 + 0.0234785i
\(269\) 1.25633e8 0.393525 0.196762 0.980451i \(-0.436957\pi\)
0.196762 + 0.980451i \(0.436957\pi\)
\(270\) 1.45961e8 + 4.04120e8i 0.451297 + 1.24950i
\(271\) −1.57868e8 −0.481837 −0.240919 0.970545i \(-0.577449\pi\)
−0.240919 + 0.970545i \(0.577449\pi\)
\(272\) 3.23624e8 + 1.17789e8i 0.975101 + 0.354908i
\(273\) −474092. + 1.99305e6i −0.00141024 + 0.00592856i
\(274\) −5.14967e8 4.32108e8i −1.51235 1.26901i
\(275\) −2.89102e7 + 1.63958e8i −0.0838276 + 0.475410i
\(276\) 5.35187e7 + 1.06783e8i 0.153223 + 0.305718i
\(277\) −3.17808e8 + 2.66672e8i −0.898432 + 0.753874i −0.969883 0.243570i \(-0.921682\pi\)
0.0714509 + 0.997444i \(0.477237\pi\)
\(278\) 3.94406e7 + 6.83131e7i 0.110100 + 0.190698i
\(279\) 7.58330e7 + 8.98996e6i 0.209047 + 0.0247824i
\(280\) 6.56766e6 1.13755e7i 0.0178796 0.0309684i
\(281\) 2.21478e7 + 1.25606e8i 0.0595467 + 0.337706i 0.999998 0.00222368i \(-0.000707819\pi\)
−0.940451 + 0.339930i \(0.889597\pi\)
\(282\) −4.38870e8 + 3.26167e8i −1.16537 + 0.866099i
\(283\) −3.42675e8 + 1.24724e8i −0.898733 + 0.327112i −0.749745 0.661727i \(-0.769824\pi\)
−0.148988 + 0.988839i \(0.547602\pi\)
\(284\) −1.43525e8 + 5.22388e7i −0.371803 + 0.135325i
\(285\) 7.36950e6 5.47698e6i 0.0188574 0.0140147i
\(286\) 1.44288e7 + 8.18299e7i 0.0364712 + 0.206838i
\(287\) −1.27228e7 + 2.20364e7i −0.0317683 + 0.0550244i
\(288\) −6.85536e7 1.59646e8i −0.169105 0.393808i
\(289\) 4.39012e7 + 7.60392e7i 0.106988 + 0.185308i
\(290\) 5.66068e8 4.74988e8i 1.36294 1.14364i
\(291\) 7.66872e7 + 1.53010e8i 0.182430 + 0.363994i
\(292\) 2.41802e7 1.37132e8i 0.0568354 0.322330i
\(293\) 5.57487e8 + 4.67787e8i 1.29479 + 1.08646i 0.991021 + 0.133708i \(0.0426886\pi\)
0.303766 + 0.952747i \(0.401756\pi\)
\(294\) 1.11148e8 4.67260e8i 0.255086 1.07237i
\(295\) −5.14934e8 1.87421e8i −1.16782 0.425050i
\(296\) 3.67490e8 0.823616
\(297\) 4.19663e8 + 2.43674e8i 0.929507 + 0.539711i
\(298\) 5.39195e8 1.18029
\(299\) 1.20684e8 + 4.39254e7i 0.261096 + 0.0950313i
\(300\) 3.32671e7 + 3.14376e7i 0.0711363 + 0.0672242i
\(301\) 1.62267e7 + 1.36158e7i 0.0342963 + 0.0287780i
\(302\) 1.31398e8 7.45194e8i 0.274514 1.55684i
\(303\) −3.87004e7 + 5.87359e7i −0.0799219 + 0.121298i
\(304\) −8.57191e6 + 7.19268e6i −0.0174993 + 0.0146836i
\(305\) −3.30003e8 5.71581e8i −0.665990 1.15353i
\(306\) −1.41421e8 + 4.69568e8i −0.282155 + 0.936858i
\(307\) −4.13469e8 + 7.16149e8i −0.815565 + 1.41260i 0.0933562 + 0.995633i \(0.470240\pi\)
−0.908921 + 0.416968i \(0.863093\pi\)
\(308\) 717808. + 4.07089e6i 0.00139985 + 0.00793893i
\(309\) −7.25264e7 6.24956e8i −0.139843 1.20502i
\(310\) 1.37844e8 5.01713e7i 0.262799 0.0956509i
\(311\) −8.28125e8 + 3.01413e8i −1.56111 + 0.568199i −0.970991 0.239115i \(-0.923143\pi\)
−0.590122 + 0.807314i \(0.700921\pi\)
\(312\) −7.52525e7 3.25341e7i −0.140275 0.0606454i
\(313\) 9.82087e7 + 5.56969e8i 0.181028 + 1.02666i 0.930954 + 0.365137i \(0.118978\pi\)
−0.749926 + 0.661521i \(0.769911\pi\)
\(314\) 5.38368e8 9.32481e8i 0.981354 1.69976i
\(315\) 2.05217e7 + 1.03487e7i 0.0369936 + 0.0186551i
\(316\) −1.94473e7 3.36838e7i −0.0346701 0.0600504i
\(317\) −2.63284e8 + 2.20922e8i −0.464213 + 0.389521i −0.844678 0.535274i \(-0.820208\pi\)
0.380465 + 0.924795i \(0.375764\pi\)
\(318\) −2.41840e8 1.42850e7i −0.421728 0.0249106i
\(319\) 1.44923e8 8.21901e8i 0.249960 1.41759i
\(320\) 3.77005e8 + 3.16345e8i 0.643165 + 0.539679i
\(321\) −8.30879e8 + 2.48005e8i −1.40207 + 0.418498i
\(322\) 3.35545e7 + 1.22128e7i 0.0560086 + 0.0203855i
\(323\) 1.04797e7 0.0173037
\(324\) 1.19420e8 5.94842e7i 0.195060 0.0971614i
\(325\) 4.92147e7 0.0795249
\(326\) −7.82012e8 2.84629e8i −1.25012 0.455006i
\(327\) 2.10982e8 6.29750e7i 0.333679 0.0995981i
\(328\) −7.80054e8 6.54543e8i −1.22058 1.02419i
\(329\) −5.07899e6 + 2.88044e7i −0.00786306 + 0.0445936i
\(330\) 9.30567e8 + 5.49666e7i 1.42544 + 0.0841977i
\(331\) 9.42875e8 7.91166e8i 1.42908 1.19914i 0.482825 0.875717i \(-0.339611\pi\)
0.946255 0.323423i \(-0.104834\pi\)
\(332\) 1.01184e7 + 1.75257e7i 0.0151751 + 0.0262840i
\(333\) 3.63329e7 + 6.41984e8i 0.0539194 + 0.952730i
\(334\) 5.79692e8 1.00406e9i 0.851304 1.47450i
\(335\) −4.53111e7 2.56972e8i −0.0658487 0.373447i
\(336\) −2.57097e7 1.11151e7i −0.0369751 0.0159855i
\(337\) −4.73735e8 + 1.72425e8i −0.674265 + 0.245412i −0.656383 0.754428i \(-0.727914\pi\)
−0.0178817 + 0.999840i \(0.505692\pi\)
\(338\) −7.13132e8 + 2.59559e8i −1.00453 + 0.365618i
\(339\) −4.02389e7 3.46736e8i −0.0560979 0.483393i
\(340\) 2.92694e7 + 1.65995e8i 0.0403867 + 0.229044i
\(341\) 8.28374e7 1.43479e8i 0.113132 0.195951i
\(342\) −1.09154e7 1.16078e7i −0.0147553 0.0156913i
\(343\) −2.57066e7 4.45252e7i −0.0343966 0.0595767i
\(344\) −6.49366e8 + 5.44883e8i −0.860072 + 0.721686i
\(345\) 7.92729e8 1.20313e9i 1.03934 1.57742i
\(346\) −5.24863e7 + 2.97665e8i −0.0681208 + 0.386332i
\(347\) 7.83156e8 + 6.57146e8i 1.00623 + 0.844323i 0.987835 0.155507i \(-0.0497013\pi\)
0.0183907 + 0.999831i \(0.494146\pi\)
\(348\) −1.66764e8 1.57593e8i −0.212117 0.200451i
\(349\) 4.87337e8 + 1.77376e8i 0.613677 + 0.223360i 0.630112 0.776505i \(-0.283009\pi\)
−0.0164341 + 0.999865i \(0.505231\pi\)
\(350\) 1.36834e7 0.0170591
\(351\) 4.93952e7 1.34678e8i 0.0609691 0.166235i
\(352\) −3.76941e8 −0.460653
\(353\) −3.76022e8 1.36861e8i −0.454989 0.165603i 0.104351 0.994541i \(-0.466723\pi\)
−0.559341 + 0.828938i \(0.688946\pi\)
\(354\) −2.20063e8 + 9.25131e8i −0.263655 + 1.10839i
\(355\) 1.41136e9 + 1.18427e9i 1.67432 + 1.40492i
\(356\) −3.15036e7 + 1.78666e8i −0.0370071 + 0.209878i
\(357\) 1.17536e7 + 2.34513e7i 0.0136720 + 0.0272790i
\(358\) −1.44102e8 + 1.20916e8i −0.165989 + 0.139281i
\(359\) −4.30683e7 7.45965e7i −0.0491278 0.0850918i 0.840416 0.541942i \(-0.182311\pi\)
−0.889544 + 0.456850i \(0.848977\pi\)
\(360\) −5.50453e8 + 7.36856e8i −0.621816 + 0.832384i
\(361\) 4.46766e8 7.73821e8i 0.499810 0.865696i
\(362\) 1.54301e8 + 8.75086e8i 0.170958 + 0.969551i
\(363\) 1.13572e8 8.44061e7i 0.124623 0.0926191i
\(364\) 1.14825e6 417930.i 0.00124791 0.000454202i
\(365\) −1.57840e9 + 5.74492e8i −1.69900 + 0.618385i
\(366\) −9.19271e8 + 6.83198e8i −0.980076 + 0.728388i
\(367\) 1.07820e8 + 6.11477e8i 0.113859 + 0.645727i 0.987309 + 0.158812i \(0.0507665\pi\)
−0.873450 + 0.486914i \(0.838122\pi\)
\(368\) −8.77950e8 + 1.52065e9i −0.918338 + 1.59061i
\(369\) 1.06633e9 1.42742e9i 1.10484 1.47897i
\(370\) 6.17595e8 + 1.06971e9i 0.633866 + 1.09789i
\(371\) −9.92694e6 + 8.32969e6i −0.0100927 + 0.00846876i
\(372\) −2.04085e7 4.07201e7i −0.0205547 0.0410117i
\(373\) −1.06983e8 + 6.06732e8i −0.106742 + 0.605363i 0.883768 + 0.467925i \(0.154998\pi\)
−0.990510 + 0.137439i \(0.956113\pi\)
\(374\) 8.15030e8 + 6.83892e8i 0.805607 + 0.675984i
\(375\) −1.56712e8 + 6.58808e8i −0.153459 + 0.645133i
\(376\) −1.09990e9 4.00330e8i −1.06707 0.388384i
\(377\) −2.46707e8 −0.237130
\(378\) 1.37336e7 3.74454e7i 0.0130787 0.0356596i
\(379\) −2.91803e8 −0.275330 −0.137665 0.990479i \(-0.543960\pi\)
−0.137665 + 0.990479i \(0.543960\pi\)
\(380\) −5.14634e6 1.87312e6i −0.00481123 0.00175114i
\(381\) 5.76258e8 + 5.44567e8i 0.533801 + 0.504445i
\(382\) 4.92400e8 + 4.13173e8i 0.451956 + 0.379236i
\(383\) 2.22449e8 1.26157e9i 0.202318 1.14740i −0.699286 0.714842i \(-0.746499\pi\)
0.901604 0.432562i \(-0.142390\pi\)
\(384\) 7.31536e8 1.11026e9i 0.659290 1.00061i
\(385\) 3.81975e7 3.20515e7i 0.0341132 0.0286244i
\(386\) 6.04855e8 + 1.04764e9i 0.535298 + 0.927163i
\(387\) −1.01608e9 1.08053e9i −0.891127 0.947654i
\(388\) 5.10427e7 8.84085e7i 0.0443631 0.0768392i
\(389\) −2.67610e8 1.51769e9i −0.230504 1.30725i −0.851878 0.523740i \(-0.824537\pi\)
0.621374 0.783514i \(-0.286575\pi\)
\(390\) −3.17658e7 2.73724e8i −0.0271165 0.233661i
\(391\) 1.54529e9 5.62439e8i 1.30735 0.475835i
\(392\) 9.66125e8 3.51641e8i 0.810087 0.294848i
\(393\) −1.14230e9 4.93853e8i −0.949305 0.410416i
\(394\) −1.35668e8 7.69414e8i −0.111749 0.633758i
\(395\) −2.34587e8 + 4.06316e8i −0.191520 + 0.331722i
\(396\) −1.63550e7 2.88986e8i −0.0132348 0.233853i
\(397\) 2.71109e7 + 4.69574e7i 0.0217459 + 0.0376649i 0.876694 0.481049i \(-0.159744\pi\)
−0.854948 + 0.518714i \(0.826411\pi\)
\(398\) −1.64002e8 + 1.37614e8i −0.130394 + 0.109414i
\(399\) −850829. 50256.6i −0.000670559 3.96085e-5i
\(400\) −1.16842e8 + 6.62646e8i −0.0912831 + 0.517692i
\(401\) −8.19063e8 6.87275e8i −0.634325 0.532262i 0.267944 0.963434i \(-0.413656\pi\)
−0.902270 + 0.431172i \(0.858100\pi\)
\(402\) −4.33901e8 + 1.29513e8i −0.333119 + 0.0994312i
\(403\) −4.60210e7 1.67503e7i −0.0350258 0.0127484i
\(404\) 4.19546e7 0.0316552
\(405\) −1.34167e9 8.88759e8i −1.00358 0.664801i
\(406\) −6.85933e7 −0.0508675
\(407\) 1.31091e9 + 4.77132e8i 0.963811 + 0.350799i
\(408\) −1.00590e9 + 3.00248e8i −0.733240 + 0.218861i
\(409\) −2.45796e8 2.06247e8i −0.177641 0.149058i 0.549632 0.835407i \(-0.314768\pi\)
−0.727273 + 0.686349i \(0.759212\pi\)
\(410\) 5.94331e8 3.37062e9i 0.425878 2.41527i
\(411\) 2.51350e9 + 1.48467e8i 1.78580 + 0.105483i
\(412\) −2.87468e8 + 2.41214e8i −0.202511 + 0.169927i
\(413\) 2.54333e7 + 4.40517e7i 0.0177655 + 0.0307707i
\(414\) −2.23253e9 1.12582e9i −1.54631 0.779770i
\(415\) 1.22055e8 2.11406e8i 0.0838280 0.145194i
\(416\) 1.93490e7 + 1.09733e8i 0.0131774 + 0.0747330i
\(417\) −2.71190e8 1.17244e8i −0.183146 0.0791801i
\(418\) −3.24844e7 + 1.18233e7i −0.0217549 + 0.00791814i
\(419\) 8.51254e8 3.09831e8i 0.565340 0.205767i −0.0435089 0.999053i \(-0.513854\pi\)
0.608849 + 0.793286i \(0.291631\pi\)
\(420\) −1.58029e6 1.36173e7i −0.00104079 0.00896846i
\(421\) 4.59221e8 + 2.60437e9i 0.299940 + 1.70104i 0.646417 + 0.762984i \(0.276267\pi\)
−0.346477 + 0.938058i \(0.612622\pi\)
\(422\) −3.70238e8 + 6.41272e8i −0.239821 + 0.415383i
\(423\) 5.90609e8 1.96104e9i 0.379410 1.25978i
\(424\) −2.59293e8 4.49109e8i −0.165200 0.286135i
\(425\) 4.82734e8 4.05062e8i 0.305033 0.255953i
\(426\) 1.75910e9 2.66981e9i 1.10245 1.67319i
\(427\) −1.06386e7 + 6.03345e7i −0.00661282 + 0.0375032i
\(428\) 3.96192e8 + 3.32444e8i 0.244260 + 0.204958i
\(429\) −2.26199e8 2.13760e8i −0.138322 0.130715i
\(430\) −2.67737e9 9.74484e8i −1.62394 0.591065i
\(431\) −1.52696e9 −0.918666 −0.459333 0.888264i \(-0.651912\pi\)
−0.459333 + 0.888264i \(0.651912\pi\)
\(432\) 1.69609e9 + 9.84822e8i 1.01218 + 0.587712i
\(433\) −1.11387e9 −0.659365 −0.329682 0.944092i \(-0.606942\pi\)
−0.329682 + 0.944092i \(0.606942\pi\)
\(434\) −1.27955e7 4.65717e6i −0.00751350 0.00273469i
\(435\) −6.40497e8 + 2.69261e9i −0.373082 + 1.56841i
\(436\) −1.00604e8 8.44164e7i −0.0581314 0.0487780i
\(437\) −9.27817e6 + 5.26191e7i −0.00531836 + 0.0301619i
\(438\) 1.30606e9 + 2.60591e9i 0.742683 + 1.48184i
\(439\) 6.04561e8 5.07287e8i 0.341047 0.286173i −0.456136 0.889910i \(-0.650767\pi\)
0.797183 + 0.603737i \(0.206322\pi\)
\(440\) 9.97726e8 + 1.72811e9i 0.558376 + 0.967136i
\(441\) 7.09814e8 + 1.65300e9i 0.394103 + 0.917777i
\(442\) 1.57255e8 2.72373e8i 0.0866215 0.150033i
\(443\) 4.52625e8 + 2.56697e9i 0.247358 + 1.40284i 0.814952 + 0.579528i \(0.196763\pi\)
−0.567594 + 0.823308i \(0.692126\pi\)
\(444\) 3.07827e8 2.28776e8i 0.166904 0.124042i
\(445\) 2.05646e9 7.48488e8i 1.10627 0.402648i
\(446\) 1.10285e9 4.01406e8i 0.588635 0.214246i
\(447\) −1.62092e9 + 1.20466e9i −0.858393 + 0.637955i
\(448\) −7.93287e6 4.49895e7i −0.00416828 0.0236395i
\(449\) −3.11792e8 + 5.40039e8i −0.162556 + 0.281555i −0.935785 0.352572i \(-0.885307\pi\)
0.773229 + 0.634127i \(0.218640\pi\)
\(450\) −9.51475e8 1.12797e8i −0.492213 0.0583516i
\(451\) −1.93277e9 3.34766e9i −0.992118 1.71840i
\(452\) −1.59492e8 + 1.33830e8i −0.0812371 + 0.0681661i
\(453\) 1.26990e9 + 2.53377e9i 0.641838 + 1.28063i
\(454\) −4.68562e8 + 2.65735e9i −0.235002 + 1.33276i
\(455\) −1.12914e7 9.47464e6i −0.00561965 0.00471545i
\(456\) 7.89315e6 3.31823e7i 0.00389828 0.0163881i
\(457\) −2.38568e9 8.68315e8i −1.16924 0.425570i −0.316852 0.948475i \(-0.602626\pi\)
−0.852391 + 0.522905i \(0.824848\pi\)
\(458\) 1.57478e9 0.765933
\(459\) −6.23967e8 1.72757e9i −0.301174 0.833858i
\(460\) −8.59388e8 −0.411658
\(461\) −2.76455e9 1.00621e9i −1.31423 0.478340i −0.412623 0.910902i \(-0.635387\pi\)
−0.901604 + 0.432562i \(0.857610\pi\)
\(462\) −6.28915e7 5.94328e7i −0.0296719 0.0280401i
\(463\) 1.42767e9 + 1.19796e9i 0.668489 + 0.560929i 0.912618 0.408814i \(-0.134058\pi\)
−0.244129 + 0.969743i \(0.578502\pi\)
\(464\) 5.85716e8 3.32176e9i 0.272191 1.54367i
\(465\) −3.02295e8 + 4.58795e8i −0.139426 + 0.211609i
\(466\) 2.68634e9 2.25411e9i 1.22973 1.03187i
\(467\) 2.40313e8 + 4.16234e8i 0.109186 + 0.189116i 0.915441 0.402453i \(-0.131842\pi\)
−0.806255 + 0.591569i \(0.798509\pi\)
\(468\) −8.32887e7 + 1.95953e7i −0.0375600 + 0.00883672i
\(469\) −1.21107e7 + 2.09764e7i −0.00542083 + 0.00938916i
\(470\) −6.83163e8 3.87441e9i −0.303516 1.72133i
\(471\) 4.64902e8 + 4.00604e9i 0.205016 + 1.76661i
\(472\) −1.91284e9 + 6.96216e8i −0.837300 + 0.304752i
\(473\) −3.02386e9 + 1.10060e9i −1.31386 + 0.478205i
\(474\) 7.47332e8 + 3.23096e8i 0.322322 + 0.139350i
\(475\) 3.55544e6 + 2.01639e7i 0.00152218 + 0.00863270i
\(476\) 7.82314e6 1.35501e7i 0.00332473 0.00575861i
\(477\) 7.58932e8 4.97372e8i 0.320176 0.209830i
\(478\) −4.48804e8 7.77352e8i −0.187957 0.325552i
\(479\) 2.45775e9 2.06230e9i 1.02179 0.857387i 0.0319420 0.999490i \(-0.489831\pi\)
0.989852 + 0.142103i \(0.0453864\pi\)
\(480\) 1.24788e9 + 7.37099e7i 0.515027 + 0.0304216i
\(481\) 7.16095e7 4.06117e8i 0.0293402 0.166396i
\(482\) 3.04653e9 + 2.55634e9i 1.23920 + 1.03981i
\(483\) −1.28157e8 + 3.82530e7i −0.0517520 + 0.0154472i
\(484\) −7.93106e7 2.88667e7i −0.0317960 0.0115728i
\(485\) −1.23142e9 −0.490129
\(486\) −1.26364e9 + 2.49055e9i −0.499339 + 0.984164i
\(487\) 1.04461e9 0.409828 0.204914 0.978780i \(-0.434308\pi\)
0.204914 + 0.978780i \(0.434308\pi\)
\(488\) −2.30388e9 8.38544e8i −0.897409 0.326630i
\(489\) 2.98679e9 8.91513e8i 1.15511 0.344784i
\(490\) 2.64721e9 + 2.22128e9i 1.01649 + 0.852935i
\(491\) 2.27722e8 1.29148e9i 0.0868200 0.492381i −0.910129 0.414325i \(-0.864018\pi\)
0.996949 0.0780556i \(-0.0248712\pi\)
\(492\) −1.06089e9 6.26643e7i −0.401597 0.0237215i
\(493\) −2.41988e9 + 2.03052e9i −0.909558 + 0.763210i
\(494\) 5.10943e6 + 8.84979e6i 0.00190690 + 0.00330285i
\(495\) −2.92027e9 + 1.91382e9i −1.08219 + 0.709225i
\(496\) 3.34793e8 5.79878e8i 0.123194 0.213378i
\(497\) −2.96976e7 1.68424e8i −0.0108511 0.0615398i
\(498\) −3.88837e8 1.68107e8i −0.141080 0.0609934i
\(499\) −1.63693e9 + 5.95793e8i −0.589763 + 0.214656i −0.619625 0.784898i \(-0.712715\pi\)
0.0298620 + 0.999554i \(0.490493\pi\)
\(500\) 3.79558e8 1.38148e8i 0.135795 0.0494252i
\(501\) 5.00587e8 + 4.31353e9i 0.177847 + 1.53250i
\(502\) −4.54500e8 2.57760e9i −0.160351 0.909393i
\(503\) 3.53472e8 6.12232e8i 0.123842 0.214500i −0.797438 0.603401i \(-0.793812\pi\)
0.921280 + 0.388901i \(0.127145\pi\)
\(504\) 8.31078e7 1.95527e7i 0.0289158 0.00680300i
\(505\) −2.53042e8 4.38282e8i −0.0874325 0.151438i
\(506\) −4.15546e9 + 3.48684e9i −1.42591 + 1.19648i
\(507\) 1.56391e9 2.37356e9i 0.532946 0.808856i
\(508\) 8.21198e7 4.65725e8i 0.0277923 0.157618i
\(509\) 1.64438e9 + 1.37980e9i 0.552702 + 0.463772i 0.875855 0.482575i \(-0.160298\pi\)
−0.323153 + 0.946347i \(0.604743\pi\)
\(510\) −2.56447e9 2.42344e9i −0.856056 0.808977i
\(511\) 1.46516e8 + 5.33275e7i 0.0485749 + 0.0176798i
\(512\) 1.54454e9 0.508574
\(513\) 5.87479e7 + 1.05082e7i 0.0192124 + 0.00343652i
\(514\) 3.77894e8 0.122744
\(515\) 4.25368e9 + 1.54821e9i 1.37227 + 0.499465i
\(516\) −2.04730e8 + 8.60673e8i −0.0656006 + 0.275781i
\(517\) −3.40378e9 2.85611e9i −1.08329 0.908987i
\(518\) 1.99100e7 1.12915e8i 0.00629385 0.0356942i
\(519\) −5.07255e8 1.01210e9i −0.159273 0.317789i
\(520\) 4.51865e8 3.79160e8i 0.140928 0.118253i
\(521\) −9.45411e8 1.63750e9i −0.292879 0.507282i 0.681610 0.731716i \(-0.261280\pi\)
−0.974489 + 0.224434i \(0.927947\pi\)
\(522\) 4.76962e9 + 5.65436e8i 1.46770 + 0.173995i
\(523\) −3.16738e8 + 5.48606e8i −0.0968154 + 0.167689i −0.910365 0.413807i \(-0.864199\pi\)
0.813549 + 0.581496i \(0.197532\pi\)
\(524\) 1.28896e8 + 7.31007e8i 0.0391364 + 0.221954i
\(525\) −4.11350e7 + 3.05714e7i −0.0124066 + 0.00922056i
\(526\) −3.19013e8 + 1.16111e8i −0.0955782 + 0.0347876i
\(527\) −5.89271e8 + 2.14477e8i −0.175379 + 0.0638328i
\(528\) 3.41517e9 2.53814e9i 1.00970 0.750408i
\(529\) 8.64683e8 + 4.90386e9i 0.253958 + 1.44027i
\(530\) 8.71522e8 1.50952e9i 0.254280 0.440427i
\(531\) −1.40537e9 3.27278e9i −0.407342 0.948607i
\(532\) 254185. + 440261.i 7.31912e−5 + 0.000126771i
\(533\) −8.75344e8 + 7.34501e8i −0.250400 + 0.210110i
\(534\) −1.70162e9 3.39517e9i −0.483581 0.964865i
\(535\) 1.08334e9 6.14393e9i 0.305863 1.73464i
\(536\) −7.42531e8 6.23058e8i −0.208275 0.174764i
\(537\) 1.63049e8 6.85448e8i 0.0454369 0.191014i
\(538\) 1.47403e9 + 5.36501e8i 0.408100 + 0.148536i
\(539\) 3.90290e9 1.07356
\(540\) −2.36615e6 + 9.59902e8i −0.000646643 + 0.262330i
\(541\) 5.15908e9 1.40082 0.700409 0.713742i \(-0.253001\pi\)
0.700409 + 0.713742i \(0.253001\pi\)
\(542\) −1.85222e9 6.74154e8i −0.499684 0.181870i
\(543\) −2.41897e9 2.28594e9i −0.648382 0.612724i
\(544\) 1.09295e9 + 9.17094e8i 0.291075 + 0.244241i
\(545\) −2.75089e8 + 1.56011e9i −0.0727922 + 0.412825i
\(546\) −1.40735e7 + 2.13594e7i −0.00370022 + 0.00561585i
\(547\) −4.14033e9 + 3.47415e9i −1.08163 + 0.907596i −0.996055 0.0887352i \(-0.971717\pi\)
−0.0855760 + 0.996332i \(0.527273\pi\)
\(548\) −7.50908e8 1.30061e9i −0.194919 0.337610i
\(549\) 1.23711e9 4.10765e9i 0.319084 1.05947i
\(550\) −1.03936e9 + 1.80022e9i −0.266376 + 0.461378i
\(551\) −1.78230e7 1.01079e8i −0.00453888 0.0257413i
\(552\) −6.16987e8 5.31655e9i −0.156131 1.34537i
\(553\) 4.09248e7 1.48954e7i 0.0102908 0.00374554i
\(554\) −4.86755e9 + 1.77164e9i −1.21626 + 0.442683i
\(555\) −4.24653e9 1.83592e9i −1.05441 0.455855i
\(556\) 3.06009e7 + 1.73547e8i 0.00755045 + 0.0428208i
\(557\) 2.34474e9 4.06121e9i 0.574912 0.995777i −0.421139 0.906996i \(-0.638370\pi\)
0.996051 0.0887809i \(-0.0282971\pi\)
\(558\) 8.51340e8 + 4.29312e8i 0.207436 + 0.104605i
\(559\) 4.75620e8 + 8.23797e8i 0.115164 + 0.199471i
\(560\) 1.54378e8 1.29538e8i 0.0371472 0.0311702i
\(561\) −3.97808e9 2.34977e8i −0.951270 0.0561895i
\(562\) −2.76531e8 + 1.56829e9i −0.0657154 + 0.372690i
\(563\) 4.38437e9 + 3.67893e9i 1.03545 + 0.868844i 0.991489 0.130189i \(-0.0415585\pi\)
0.0439587 + 0.999033i \(0.486003\pi\)
\(564\) −1.17055e9 + 3.49391e8i −0.274733 + 0.0820039i
\(565\) 2.36001e9 + 8.58974e8i 0.550484 + 0.200360i
\(566\) −4.55314e9 −1.05549
\(567\) 4.23742e7 + 1.43251e8i 0.00976249 + 0.0330034i
\(568\) 6.84402e9 1.56708
\(569\) −3.24330e8 1.18046e8i −0.0738064 0.0268633i 0.304853 0.952399i \(-0.401393\pi\)
−0.378660 + 0.925536i \(0.623615\pi\)
\(570\) 1.09853e8 3.27896e7i 0.0248457 0.00741607i
\(571\) −3.78617e9 3.17698e9i −0.851087 0.714147i 0.108942 0.994048i \(-0.465254\pi\)
−0.960029 + 0.279901i \(0.909698\pi\)
\(572\) −3.22346e7 + 1.82812e8i −0.00720172 + 0.0408430i
\(573\) −2.40335e9 1.41961e8i −0.533675 0.0315230i
\(574\) −2.43377e8 + 2.04217e8i −0.0537140 + 0.0450714i
\(575\) 1.60646e9 + 2.78246e9i 0.352396 + 0.610369i
\(576\) 1.80748e8 + 3.19373e9i 0.0394090 + 0.696337i
\(577\) −2.42521e9 + 4.20058e9i −0.525574 + 0.910321i 0.473982 + 0.880534i \(0.342816\pi\)
−0.999556 + 0.0297863i \(0.990517\pi\)
\(578\) 1.90367e8 + 1.07962e9i 0.0410057 + 0.232555i
\(579\) −4.15893e9 1.79804e9i −0.890445 0.384968i
\(580\) 1.55129e9 5.64622e8i 0.330137 0.120160i
\(581\) −2.12932e7 + 7.75007e6i −0.00450426 + 0.00163942i
\(582\) 2.46342e8 + 2.12271e9i 0.0517973 + 0.446335i
\(583\) −3.41847e8 1.93871e9i −0.0714483 0.405203i
\(584\) −3.11982e9 + 5.40368e9i −0.648163 + 1.12265i
\(585\) 7.07045e8 + 7.51896e8i 0.146016 + 0.155279i
\(586\) 4.54323e9 + 7.86911e9i 0.932660 + 1.61542i
\(587\) 6.17249e9 5.17933e9i 1.25958 1.05692i 0.263857 0.964562i \(-0.415005\pi\)
0.995726 0.0923536i \(-0.0294390\pi\)
\(588\) 5.90362e8 8.95998e8i 0.119756 0.181755i
\(589\) 3.53809e6 2.00655e7i 0.000713452 0.00404619i
\(590\) −5.24123e9 4.39792e9i −1.05063 0.881587i
\(591\) 2.12686e9 + 2.00990e9i 0.423822 + 0.400514i
\(592\) 5.29812e9 + 1.92836e9i 1.04953 + 0.381998i
\(593\) −2.20455e9 −0.434138 −0.217069 0.976156i \(-0.569650\pi\)
−0.217069 + 0.976156i \(0.569650\pi\)
\(594\) 3.88322e9 + 4.65108e9i 0.760221 + 0.910545i
\(595\) −1.88736e8 −0.0367320
\(596\) 1.13194e9 + 4.11992e8i 0.219009 + 0.0797127i
\(597\) 1.85566e8 7.80106e8i 0.0356934 0.150053i
\(598\) 1.22838e9 + 1.03073e9i 0.234898 + 0.197102i
\(599\) −1.71789e9 + 9.74263e9i −0.326589 + 1.85218i 0.171678 + 0.985153i \(0.445081\pi\)
−0.498267 + 0.867024i \(0.666030\pi\)
\(600\) −9.18979e8 1.83359e9i −0.173691 0.346556i
\(601\) −1.64725e9 + 1.38221e9i −0.309528 + 0.259725i −0.784297 0.620386i \(-0.786976\pi\)
0.474769 + 0.880110i \(0.342532\pi\)
\(602\) 1.32239e8 + 2.29045e8i 0.0247043 + 0.0427891i
\(603\) 1.01503e9 1.35876e9i 0.188525 0.252367i
\(604\) 8.45239e8 1.46400e9i 0.156081 0.270340i
\(605\) 1.76790e8 + 1.00263e9i 0.0324575 + 0.184076i
\(606\) −7.04886e8 + 5.23869e8i −0.128666 + 0.0956243i
\(607\) 1.80031e9 6.55260e8i 0.326729 0.118920i −0.173448 0.984843i \(-0.555491\pi\)
0.500176 + 0.865924i \(0.333269\pi\)
\(608\) −4.35613e7 + 1.58550e7i −0.00786029 + 0.00286091i
\(609\) 2.06205e8 1.53251e8i 0.0369946 0.0274942i
\(610\) −1.43097e9 8.11546e9i −0.255257 1.44763i
\(611\) −6.56736e8 + 1.13750e9i −0.116479 + 0.201747i
\(612\) −6.55678e8 + 8.77713e8i −0.115627 + 0.154783i
\(613\) −9.39670e8 1.62756e9i −0.164765 0.285381i 0.771807 0.635857i \(-0.219353\pi\)
−0.936572 + 0.350476i \(0.886020\pi\)
\(614\) −7.90936e9 + 6.63674e9i −1.37896 + 1.15709i
\(615\) 5.74393e9 + 1.14606e10i 0.995741 + 1.98675i
\(616\) 3.21646e7 1.82415e8i 0.00554429 0.0314432i
\(617\) −3.49587e9 2.93338e9i −0.599180 0.502772i 0.292002 0.956418i \(-0.405679\pi\)
−0.891182 + 0.453646i \(0.850123\pi\)
\(618\) 1.81786e9 7.64217e9i 0.309814 1.30244i
\(619\) 7.50602e9 + 2.73197e9i 1.27202 + 0.462976i 0.887784 0.460261i \(-0.152244\pi\)
0.384232 + 0.923237i \(0.374466\pi\)
\(620\) 3.27714e8 0.0552235
\(621\) 9.22670e9 1.60348e9i 1.54606 0.268684i
\(622\) −1.10033e10 −1.83340
\(623\) −1.90891e8 6.94788e7i −0.0316285 0.0115118i
\(624\) −9.14199e8 8.63923e8i −0.150624 0.142341i
\(625\) −5.83236e9 4.89393e9i −0.955573 0.801821i
\(626\) −1.22621e9 + 6.95417e9i −0.199781 + 1.13301i
\(627\) 7.12386e7 1.08119e8i 0.0115419 0.0175173i
\(628\) 1.84270e9 1.54621e9i 0.296890 0.249121i
\(629\) −2.64015e9 4.57288e9i −0.423011 0.732677i
\(630\) 1.96584e8 + 2.09054e8i 0.0313224 + 0.0333093i
\(631\) 3.85189e9 6.67168e9i 0.610340 1.05714i −0.380843 0.924640i \(-0.624366\pi\)
0.991183 0.132500i \(-0.0423004\pi\)
\(632\) 3.02643e8 + 1.71637e9i 0.0476892 + 0.270459i
\(633\) −3.19715e8 2.75497e9i −0.0501015 0.431722i
\(634\) −4.03247e9 + 1.46770e9i −0.628432 + 0.228731i
\(635\) −5.36052e9 + 1.95107e9i −0.830805 + 0.302388i
\(636\) −4.96782e8 2.14775e8i −0.0765713 0.0331043i
\(637\) −2.00342e8 1.13620e9i −0.0307103 0.174167i
\(638\) 5.21017e9 9.02428e9i 0.794291 1.37575i
\(639\) 6.76652e8 + 1.19561e10i 0.102592 + 1.81275i
\(640\) 4.78315e9 + 8.28465e9i 0.721247 + 1.24924i
\(641\) 5.12736e9 4.30237e9i 0.768937 0.645215i −0.171499 0.985184i \(-0.554861\pi\)
0.940437 + 0.339969i \(0.110417\pi\)
\(642\) −1.08076e10 6.38380e8i −1.61196 0.0952153i
\(643\) 4.08258e8 2.31535e9i 0.0605615 0.343461i −0.939438 0.342718i \(-0.888652\pi\)
1.00000 0.000743046i \(-0.000236519\pi\)
\(644\) 6.11097e7 + 5.12771e7i 0.00901591 + 0.00756525i
\(645\) 1.02259e10 3.05227e9i 1.50052 0.447883i
\(646\) 1.22955e8 + 4.47521e7i 0.0179446 + 0.00653129i
\(647\) 6.95949e9 1.01021 0.505106 0.863057i \(-0.331453\pi\)
0.505106 + 0.863057i \(0.331453\pi\)
\(648\) −5.94007e9 + 6.74512e8i −0.857588 + 0.0973817i
\(649\) −7.72739e9 −1.10963
\(650\) 5.77424e8 + 2.10165e8i 0.0824704 + 0.0300168i
\(651\) 4.88706e7 1.45872e7i 0.00694248 0.00207223i
\(652\) −1.42421e9 1.19505e9i −0.201236 0.168857i
\(653\) 5.09434e6 2.88914e7i 0.000715965 0.00406044i −0.984448 0.175678i \(-0.943788\pi\)
0.985164 + 0.171618i \(0.0548993\pi\)
\(654\) 2.74433e9 + 1.62102e8i 0.383631 + 0.0226603i
\(655\) 6.85911e9 5.75547e9i 0.953724 0.800270i
\(656\) −7.81143e9 1.35298e10i −1.08036 1.87123i
\(657\) −9.74837e9 4.91589e9i −1.34107 0.676275i
\(658\) −1.82596e8 + 3.16265e8i −0.0249862 + 0.0432774i
\(659\) 5.64439e8 + 3.20109e9i 0.0768277 + 0.435712i 0.998823 + 0.0485098i \(0.0154472\pi\)
−0.921995 + 0.387202i \(0.873442\pi\)
\(660\) 1.91155e9 + 8.26427e8i 0.258811 + 0.111892i
\(661\) 3.76126e9 1.36899e9i 0.506557 0.184372i −0.0760840 0.997101i \(-0.524242\pi\)
0.582641 + 0.812730i \(0.302019\pi\)
\(662\) 1.44411e10 5.25613e9i 1.93463 0.704147i
\(663\) 1.35796e8 + 1.17014e9i 0.0180962 + 0.155934i
\(664\) −1.57465e8 8.93029e8i −0.0208735 0.118380i
\(665\) 3.06615e6 5.31072e6i 0.000404313 0.000700290i
\(666\) −2.31523e9 + 7.68740e9i −0.303693 + 1.00837i
\(667\) −8.05297e9 1.39481e10i −1.05079 1.82002i
\(668\) 1.98414e9 1.66489e9i 0.257546 0.216107i
\(669\) −2.41857e9 + 3.67069e9i −0.312297 + 0.473976i
\(670\) 5.65742e8 3.20848e9i 0.0726703 0.412134i
\(671\) −7.12966e9 5.98249e9i −0.911045 0.764457i
\(672\) −8.43370e7 7.96990e7i −0.0107208 0.0101312i
\(673\) 4.20093e9 + 1.52901e9i 0.531242 + 0.193356i 0.593693 0.804692i \(-0.297669\pi\)
−0.0624509 + 0.998048i \(0.519892\pi\)
\(674\) −6.29453e9 −0.791870
\(675\) 3.11232e9 1.78669e9i 0.389513 0.223607i
\(676\) −1.69541e9 −0.211087
\(677\) 1.07349e10 + 3.90718e9i 1.32965 + 0.483953i 0.906538 0.422124i \(-0.138715\pi\)
0.423112 + 0.906077i \(0.360938\pi\)
\(678\) 1.00858e9 4.24000e9i 0.124281 0.522471i
\(679\) 8.75644e7 + 7.34753e7i 0.0107345 + 0.00900735i
\(680\) 1.31155e9 7.43816e9i 0.159957 0.907161i
\(681\) −4.52843e9 9.03535e9i −0.549456 1.09630i
\(682\) 1.58462e9 1.32965e9i 0.191284 0.160507i
\(683\) −2.13520e9 3.69827e9i −0.256428 0.444146i 0.708855 0.705355i \(-0.249212\pi\)
−0.965282 + 0.261209i \(0.915879\pi\)
\(684\) −1.40455e7 3.27088e7i −0.00167819 0.00390812i
\(685\) −9.05795e9 + 1.56888e10i −1.07675 + 1.86498i
\(686\) −1.11470e8 6.32180e8i −0.0131833 0.0747664i
\(687\) −4.73409e9 + 3.51836e9i −0.557042 + 0.413991i
\(688\) −1.22211e10 + 4.44812e9i −1.43071 + 0.520736i
\(689\) −5.46841e8 + 1.99034e8i −0.0636933 + 0.0231825i
\(690\) 1.44387e10 1.07308e10i 1.67323 1.24354i
\(691\) −1.56858e9 8.89586e9i −0.180856 1.02569i −0.931165 0.364599i \(-0.881206\pi\)
0.750308 0.661088i \(-0.229905\pi\)
\(692\) −3.37627e8 + 5.84787e8i −0.0387316 + 0.0670852i
\(693\) 3.21848e8 + 3.81549e7i 0.0367354 + 0.00435495i
\(694\) 6.38232e9 + 1.10545e10i 0.724804 + 1.25540i
\(695\) 1.62840e9 1.36639e9i 0.183999 0.154393i
\(696\) 4.60673e9 + 9.19157e9i 0.517917 + 1.03337i
\(697\) −2.54071e9 + 1.44091e10i −0.284210 + 1.61184i
\(698\) 4.96034e9 + 4.16222e9i 0.552100 + 0.463267i
\(699\) −3.03955e9 + 1.27781e10i −0.336619 + 1.41513i
\(700\) 2.87258e7 + 1.04553e7i 0.00316540 + 0.00115211i
\(701\) 3.79544e9 0.416149 0.208074 0.978113i \(-0.433280\pi\)
0.208074 + 0.978113i \(0.433280\pi\)
\(702\) 1.15467e9 1.36921e9i 0.125973 0.149379i
\(703\) 1.71565e8 0.0186245
\(704\) 6.52148e9 + 2.37362e9i 0.704437 + 0.256394i
\(705\) 1.07099e10 + 1.01209e10i 1.15113 + 1.08782i
\(706\) −3.82732e9 3.21151e9i −0.409335 0.343473i
\(707\) −8.15756e6 + 4.62638e7i −0.000868145 + 0.00492349i
\(708\) −1.16886e9 + 1.77399e9i −0.123779 + 0.187860i
\(709\) −7.26389e9 + 6.09512e9i −0.765433 + 0.642275i −0.939535 0.342453i \(-0.888742\pi\)
0.174102 + 0.984728i \(0.444298\pi\)
\(710\) 1.15019e10 + 1.99219e10i 1.20605 + 2.08894i
\(711\) −2.96848e9 + 6.98393e8i −0.309735 + 0.0728713i
\(712\) 4.06471e9 7.04029e9i 0.422037 0.730989i
\(713\) −5.55194e8 3.14866e9i −0.0573629 0.325321i
\(714\) 3.77560e7 + 3.25341e8i 0.00388188 + 0.0334499i
\(715\) 2.10417e9 7.65856e8i 0.215283 0.0783567i
\(716\) −3.94906e8 + 1.43734e8i −0.0402067 + 0.0146340i
\(717\) 3.08594e9 + 1.33415e9i 0.312659 + 0.135173i
\(718\) −1.86755e8 1.05914e9i −0.0188294 0.106787i
\(719\) −1.50998e8 + 2.61535e8i −0.0151502 + 0.0262409i −0.873501 0.486822i \(-0.838156\pi\)
0.858351 + 0.513063i \(0.171489\pi\)
\(720\) −1.18024e10 + 7.73484e9i −1.17844 + 0.772303i
\(721\) −2.10095e8 3.63895e8i −0.0208758 0.0361579i
\(722\) 8.54630e9 7.17119e9i 0.845080 0.709106i
\(723\) −1.48698e10 8.78328e8i −1.46326 0.0864317i
\(724\) −3.44716e8 + 1.95498e9i −0.0337579 + 0.191451i
\(725\) −4.72792e9 3.96720e9i −0.460773 0.386635i
\(726\) 1.69296e9 5.05322e8i 0.164198 0.0490106i
\(727\) −3.70623e9 1.34896e9i −0.357735 0.130205i 0.156899 0.987615i \(-0.449850\pi\)
−0.514635 + 0.857410i \(0.672072\pi\)
\(728\) −5.47548e7 −0.00525971
\(729\) −1.76561e9 1.03103e10i −0.168791 0.985652i
\(730\) −2.09723e10 −1.99534
\(731\) 1.14455e10 + 4.16582e9i 1.08374 + 0.394448i
\(732\) −2.45186e9 + 7.31844e8i −0.231051 + 0.0689652i
\(733\) 1.34767e10 + 1.13083e10i 1.26392 + 1.06056i 0.995253 + 0.0973245i \(0.0310285\pi\)
0.268670 + 0.963232i \(0.413416\pi\)
\(734\) −1.34621e9 + 7.63474e9i −0.125654 + 0.712620i
\(735\) −1.29208e10 7.63203e8i −1.20028 0.0708980i
\(736\) −5.57244e9 + 4.67583e9i −0.515197 + 0.432302i
\(737\) −1.83980e9 3.18663e9i −0.169291 0.293221i
\(738\) 1.86066e10 1.21940e10i 1.70400 1.11673i
\(739\) −3.56882e9 + 6.18137e9i −0.325288 + 0.563416i −0.981571 0.191099i \(-0.938795\pi\)
0.656282 + 0.754516i \(0.272128\pi\)
\(740\) 4.79176e8 + 2.71754e9i 0.0434695 + 0.246528i
\(741\) −3.51320e7 1.51887e7i −0.00317205 0.00137138i
\(742\) −1.52041e8 + 5.53385e7i −0.0136631 + 0.00497294i
\(743\) 5.30495e9 1.93084e9i 0.474483 0.172698i −0.0936991 0.995601i \(-0.529869\pi\)
0.568182 + 0.822903i \(0.307647\pi\)
\(744\) 2.35278e8 + 2.02738e9i 0.0209448 + 0.180480i
\(745\) −2.52320e9 1.43098e10i −0.223565 1.26790i
\(746\) −3.84618e9 + 6.66178e9i −0.339191 + 0.587495i
\(747\) 1.54450e9 3.63374e8i 0.135571 0.0318957i
\(748\) 1.18845e9 + 2.05846e9i 0.103831 + 0.179840i
\(749\) −4.43625e8 + 3.72245e8i −0.0385771 + 0.0323700i
\(750\) −4.65202e9 + 7.06041e9i −0.402650 + 0.611105i
\(751\) 5.99285e7 3.39871e8i 0.00516290 0.0292802i −0.982117 0.188269i \(-0.939712\pi\)
0.987280 + 0.158989i \(0.0508234\pi\)
\(752\) −1.37566e10 1.15431e10i −1.17964 0.989832i
\(753\) 7.12515e9 + 6.73331e9i 0.608151 + 0.574706i
\(754\) −2.89455e9 1.05353e9i −0.245913 0.0895051i
\(755\) −2.03917e10 −1.72440