Properties

Label 27.8.e.a.4.9
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 4.9
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.79327 - 1.01667i) q^{2} +(-34.1687 - 31.9296i) q^{3} +(-91.2849 - 76.5971i) q^{4} +(17.7337 - 100.573i) q^{5} +(62.9806 + 123.926i) q^{6} +(-71.4548 + 59.9577i) q^{7} +(367.352 + 636.273i) q^{8} +(147.997 + 2181.99i) q^{9} +O(q^{10})\) \(q+(-2.79327 - 1.01667i) q^{2} +(-34.1687 - 31.9296i) q^{3} +(-91.2849 - 76.5971i) q^{4} +(17.7337 - 100.573i) q^{5} +(62.9806 + 123.926i) q^{6} +(-71.4548 + 59.9577i) q^{7} +(367.352 + 636.273i) q^{8} +(147.997 + 2181.99i) q^{9} +(-151.785 + 262.899i) q^{10} +(148.107 + 839.955i) q^{11} +(673.366 + 5531.92i) q^{12} +(-2485.38 + 904.604i) q^{13} +(260.550 - 94.8324i) q^{14} +(-3817.20 + 2870.22i) q^{15} +(2269.42 + 12870.5i) q^{16} +(-3788.34 + 6561.60i) q^{17} +(1804.96 - 6245.35i) q^{18} +(10954.9 + 18974.4i) q^{19} +(-9322.43 + 7822.45i) q^{20} +(4355.95 + 232.851i) q^{21} +(440.253 - 2496.80i) q^{22} +(-44040.8 - 36954.6i) q^{23} +(7764.02 - 33470.0i) q^{24} +(63613.0 + 23153.3i) q^{25} +7862.02 q^{26} +(64613.2 - 79281.1i) q^{27} +11115.3 q^{28} +(-163583. - 59539.3i) q^{29} +(13580.5 - 4136.47i) q^{30} +(-44764.6 - 37562.0i) q^{31} +(23076.2 - 130872. i) q^{32} +(21758.9 - 33429.2i) q^{33} +(17252.9 - 14476.9i) q^{34} +(4762.97 + 8249.70i) q^{35} +(153624. - 210519. i) q^{36} +(-160525. + 278037. i) q^{37} +(-11309.3 - 64138.1i) q^{38} +(113806. + 48448.1i) q^{39} +(70506.4 - 25662.2i) q^{40} +(-178794. + 65075.5i) q^{41} +(-11930.6 - 5078.97i) q^{42} +(111455. + 632091. i) q^{43} +(50818.3 - 88019.8i) q^{44} +(222074. + 23810.3i) q^{45} +(85447.4 + 147999. i) q^{46} +(-705189. + 591724. i) q^{47} +(333408. - 512230. i) q^{48} +(-141496. + 802463. i) q^{49} +(-154149. - 129347. i) q^{50} +(338952. - 103241. i) q^{51} +(296168. + 107796. i) q^{52} -999005. q^{53} +(-261085. + 155764. i) q^{54} +87103.3 q^{55} +(-64398.6 - 23439.2i) q^{56} +(231532. - 998114. i) q^{57} +(396400. + 332619. i) q^{58} +(14506.4 - 82269.8i) q^{59} +(568303. + 30379.1i) q^{60} +(-1.04139e6 + 873833. i) q^{61} +(86851.7 + 150432. i) q^{62} +(-141402. - 147040. i) q^{63} +(638908. - 1.10662e6i) q^{64} +(46903.7 + 266004. i) q^{65} +(-94764.8 + 71255.2i) q^{66} +(1.23508e6 - 449533. i) q^{67} +(848419. - 308799. i) q^{68} +(324868. + 2.66890e6i) q^{69} +(-4917.06 - 27886.0i) q^{70} +(1.91696e6 - 3.32028e6i) q^{71} +(-1.33397e6 + 895724. i) q^{72} +(-2.51414e6 - 4.35461e6i) q^{73} +(731062. - 613434. i) q^{74} +(-1.43430e6 - 2.82226e6i) q^{75} +(453369. - 2.57118e6i) q^{76} +(-60944.7 - 51138.7i) q^{77} +(-268635. - 251032. i) q^{78} +(-1.36881e6 - 498206. i) q^{79} +1.33467e6 q^{80} +(-4.73916e6 + 645854. i) q^{81} +565579. q^{82} +(-863645. - 314341. i) q^{83} +(-379796. - 354909. i) q^{84} +(592739. + 497367. i) q^{85} +(331304. - 1.87892e6i) q^{86} +(3.68834e6 + 7.25752e6i) q^{87} +(-480033. + 402796. i) q^{88} +(6.12879e6 + 1.06154e7i) q^{89} +(-596105. - 292284. i) q^{90} +(123354. - 213656. i) q^{91} +(1.18964e6 + 6.74680e6i) q^{92} +(330207. + 2.71276e6i) q^{93} +(2.57137e6 - 935903. i) q^{94} +(2.10258e6 - 765277. i) q^{95} +(-4.96717e6 + 3.73489e6i) q^{96} +(1.53194e6 + 8.68808e6i) q^{97} +(1.21108e6 - 2.09764e6i) q^{98} +(-1.81085e6 + 447478. i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79327 1.01667i −0.246893 0.0898616i 0.215610 0.976480i \(-0.430826\pi\)
−0.462502 + 0.886618i \(0.653048\pi\)
\(3\) −34.1687 31.9296i −0.730641 0.682762i
\(4\) −91.2849 76.5971i −0.713163 0.598415i
\(5\) 17.7337 100.573i 0.0634461 0.359821i −0.936512 0.350636i \(-0.885965\pi\)
0.999958 0.00918458i \(-0.00292358\pi\)
\(6\) 62.9806 + 123.926i 0.119036 + 0.234226i
\(7\) −71.4548 + 59.9577i −0.0787387 + 0.0660696i −0.681308 0.731997i \(-0.738588\pi\)
0.602569 + 0.798067i \(0.294144\pi\)
\(8\) 367.352 + 636.273i 0.253669 + 0.439368i
\(9\) 147.997 + 2181.99i 0.0676711 + 0.997708i
\(10\) −151.785 + 262.899i −0.0479985 + 0.0831358i
\(11\) 148.107 + 839.955i 0.0335506 + 0.190275i 0.996977 0.0776985i \(-0.0247571\pi\)
−0.963426 + 0.267973i \(0.913646\pi\)
\(12\) 673.366 + 5531.92i 0.112491 + 0.924148i
\(13\) −2485.38 + 904.604i −0.313755 + 0.114198i −0.494098 0.869406i \(-0.664502\pi\)
0.180343 + 0.983604i \(0.442279\pi\)
\(14\) 260.550 94.8324i 0.0253772 0.00923653i
\(15\) −3817.20 + 2870.22i −0.292029 + 0.219581i
\(16\) 2269.42 + 12870.5i 0.138514 + 0.785553i
\(17\) −3788.34 + 6561.60i −0.187016 + 0.323921i −0.944254 0.329218i \(-0.893215\pi\)
0.757238 + 0.653139i \(0.226548\pi\)
\(18\) 1804.96 6245.35i 0.0729481 0.252408i
\(19\) 10954.9 + 18974.4i 0.366411 + 0.634643i 0.989002 0.147905i \(-0.0472529\pi\)
−0.622590 + 0.782548i \(0.713920\pi\)
\(20\) −9322.43 + 7822.45i −0.260570 + 0.218644i
\(21\) 4355.95 + 232.851i 0.102640 + 0.00548669i
\(22\) 440.253 2496.80i 0.00881502 0.0499924i
\(23\) −44040.8 36954.6i −0.754758 0.633317i 0.181998 0.983299i \(-0.441743\pi\)
−0.936757 + 0.349981i \(0.886188\pi\)
\(24\) 7764.02 33470.0i 0.114643 0.494216i
\(25\) 63613.0 + 23153.3i 0.814247 + 0.296362i
\(26\) 7862.02 0.0877259
\(27\) 64613.2 79281.1i 0.631754 0.775169i
\(28\) 11115.3 0.0956907
\(29\) −163583. 59539.3i −1.24550 0.453326i −0.366624 0.930369i \(-0.619486\pi\)
−0.878880 + 0.477043i \(0.841709\pi\)
\(30\) 13580.5 4136.47i 0.0918317 0.0279708i
\(31\) −44764.6 37562.0i −0.269879 0.226455i 0.497797 0.867294i \(-0.334142\pi\)
−0.767676 + 0.640838i \(0.778587\pi\)
\(32\) 23076.2 130872.i 0.124491 0.706026i
\(33\) 21758.9 33429.2i 0.105399 0.161930i
\(34\) 17252.9 14476.9i 0.0752809 0.0631682i
\(35\) 4762.97 + 8249.70i 0.0187776 + 0.0325237i
\(36\) 153624. 210519.i 0.548783 0.752024i
\(37\) −160525. + 278037.i −0.520999 + 0.902396i 0.478703 + 0.877977i \(0.341107\pi\)
−0.999702 + 0.0244192i \(0.992226\pi\)
\(38\) −11309.3 64138.1i −0.0334343 0.189615i
\(39\) 113806. + 48448.1i 0.307212 + 0.130783i
\(40\) 70506.4 25662.2i 0.174188 0.0633993i
\(41\) −178794. + 65075.5i −0.405143 + 0.147460i −0.536550 0.843869i \(-0.680273\pi\)
0.131407 + 0.991328i \(0.458051\pi\)
\(42\) −11930.6 5078.97i −0.0248479 0.0105780i
\(43\) 111455. + 632091.i 0.213776 + 1.21238i 0.883018 + 0.469339i \(0.155508\pi\)
−0.669242 + 0.743045i \(0.733381\pi\)
\(44\) 50818.3 88019.8i 0.0899364 0.155774i
\(45\) 222074. + 23810.3i 0.363290 + 0.0389512i
\(46\) 85447.4 + 147999.i 0.129433 + 0.224185i
\(47\) −705189. + 591724.i −0.990747 + 0.831336i −0.985676 0.168651i \(-0.946059\pi\)
−0.00507165 + 0.999987i \(0.501614\pi\)
\(48\) 333408. 512230.i 0.435142 0.668529i
\(49\) −141496. + 802463.i −0.171814 + 0.974403i
\(50\) −154149. 129347.i −0.174400 0.146339i
\(51\) 338952. 103241.i 0.357802 0.108982i
\(52\) 296168. + 107796.i 0.292096 + 0.106314i
\(53\) −999005. −0.921727 −0.460863 0.887471i \(-0.652460\pi\)
−0.460863 + 0.887471i \(0.652460\pi\)
\(54\) −261085. + 155764.i −0.225633 + 0.134613i
\(55\) 87103.3 0.0705936
\(56\) −64398.6 23439.2i −0.0490025 0.0178355i
\(57\) 231532. 998114.i 0.165595 0.713868i
\(58\) 396400. + 332619.i 0.266769 + 0.223846i
\(59\) 14506.4 82269.8i 0.00919554 0.0521505i −0.979865 0.199663i \(-0.936015\pi\)
0.989060 + 0.147512i \(0.0471265\pi\)
\(60\) 568303. + 30379.1i 0.339665 + 0.0181571i
\(61\) −1.04139e6 + 873833.i −0.587436 + 0.492917i −0.887380 0.461040i \(-0.847477\pi\)
0.299944 + 0.953957i \(0.403032\pi\)
\(62\) 86851.7 + 150432.i 0.0462815 + 0.0801619i
\(63\) −141402. 147040.i −0.0712465 0.0740872i
\(64\) 638908. 1.10662e6i 0.304655 0.527678i
\(65\) 46903.7 + 266004.i 0.0211841 + 0.120141i
\(66\) −94764.8 + 71255.2i −0.0405736 + 0.0305079i
\(67\) 1.23508e6 449533.i 0.501688 0.182599i −0.0787651 0.996893i \(-0.525098\pi\)
0.580453 + 0.814294i \(0.302875\pi\)
\(68\) 848419. 308799.i 0.327212 0.119095i
\(69\) 324868. + 2.66890e6i 0.119052 + 0.978048i
\(70\) −4917.06 27886.0i −0.00171341 0.00971726i
\(71\) 1.91696e6 3.32028e6i 0.635637 1.10096i −0.350743 0.936472i \(-0.614071\pi\)
0.986380 0.164484i \(-0.0525958\pi\)
\(72\) −1.33397e6 + 895724.i −0.421195 + 0.282820i
\(73\) −2.51414e6 4.35461e6i −0.756413 1.31015i −0.944669 0.328025i \(-0.893617\pi\)
0.188256 0.982120i \(-0.439716\pi\)
\(74\) 731062. 613434.i 0.209722 0.175977i
\(75\) −1.43430e6 2.82226e6i −0.392577 0.772471i
\(76\) 453369. 2.57118e6i 0.118469 0.671871i
\(77\) −60944.7 51138.7i −0.0152131 0.0127653i
\(78\) −268635. 251032.i −0.0640961 0.0598959i
\(79\) −1.36881e6 498206.i −0.312355 0.113688i 0.181086 0.983467i \(-0.442039\pi\)
−0.493441 + 0.869779i \(0.664261\pi\)
\(80\) 1.33467e6 0.291447
\(81\) −4.73916e6 + 645854.i −0.990841 + 0.135032i
\(82\) 565579. 0.113278
\(83\) −863645. 314341.i −0.165791 0.0603431i 0.257791 0.966201i \(-0.417005\pi\)
−0.423582 + 0.905858i \(0.639228\pi\)
\(84\) −379796. 354909.i −0.0699155 0.0653340i
\(85\) 592739. + 497367.i 0.104688 + 0.0878437i
\(86\) 331304. 1.87892e6i 0.0561670 0.318539i
\(87\) 3.68834e6 + 7.25752e6i 0.600501 + 1.18160i
\(88\) −480033. + 402796.i −0.0750900 + 0.0630080i
\(89\) 6.12879e6 + 1.06154e7i 0.921531 + 1.59614i 0.797048 + 0.603916i \(0.206394\pi\)
0.124483 + 0.992222i \(0.460273\pi\)
\(90\) −596105. 292284.i −0.0861934 0.0422626i
\(91\) 123354. 213656.i 0.0171597 0.0297215i
\(92\) 1.18964e6 + 6.74680e6i 0.159279 + 0.903318i
\(93\) 330207. + 2.71276e6i 0.0425693 + 0.349720i
\(94\) 2.57137e6 935903.i 0.319314 0.116221i
\(95\) 2.10258e6 765277.i 0.251605 0.0915769i
\(96\) −4.96717e6 + 3.73489e6i −0.573006 + 0.430853i
\(97\) 1.53194e6 + 8.68808e6i 0.170428 + 0.966547i 0.943289 + 0.331972i \(0.107714\pi\)
−0.772861 + 0.634575i \(0.781175\pi\)
\(98\) 1.21108e6 2.09764e6i 0.129981 0.225134i
\(99\) −1.81085e6 + 447478.i −0.187568 + 0.0463498i
\(100\) −4.03344e6 6.98612e6i −0.403344 0.698612i
\(101\) −9.12143e6 + 7.65379e6i −0.880923 + 0.739182i −0.966369 0.257160i \(-0.917213\pi\)
0.0854454 + 0.996343i \(0.472769\pi\)
\(102\) −1.05175e6 56222.1i −0.0981321 0.00524574i
\(103\) 2.16462e6 1.22762e7i 0.195187 1.10696i −0.716964 0.697110i \(-0.754469\pi\)
0.912152 0.409853i \(-0.134420\pi\)
\(104\) −1.48858e6 1.24907e6i −0.129765 0.108886i
\(105\) 100666. 433961.i 0.00848631 0.0365838i
\(106\) 2.79050e6 + 1.01566e6i 0.227568 + 0.0828279i
\(107\) 1.15589e7 0.912169 0.456084 0.889937i \(-0.349252\pi\)
0.456084 + 0.889937i \(0.349252\pi\)
\(108\) −1.19709e7 + 2.28798e6i −0.914417 + 0.174771i
\(109\) −1.80853e7 −1.33762 −0.668811 0.743432i \(-0.733197\pi\)
−0.668811 + 0.743432i \(0.733197\pi\)
\(110\) −243303. 88555.2i −0.0174291 0.00634366i
\(111\) 1.43626e7 4.37467e6i 0.996785 0.303609i
\(112\) −933847. 783591.i −0.0628077 0.0527019i
\(113\) 4.76173e6 2.70051e7i 0.310449 1.76064i −0.286228 0.958161i \(-0.592402\pi\)
0.596677 0.802481i \(-0.296487\pi\)
\(114\) −1.66148e6 + 2.55261e6i −0.105034 + 0.161368i
\(115\) −4.49765e6 + 3.77397e6i −0.275767 + 0.231396i
\(116\) 1.03721e7 + 1.79650e7i 0.616970 + 1.06862i
\(117\) −2.34166e6 5.28918e6i −0.135168 0.305308i
\(118\) −124161. + 215054.i −0.00695664 + 0.0120493i
\(119\) −122723. 695999.i −0.00667595 0.0378612i
\(120\) −3.22850e6 1.37440e6i −0.170556 0.0726070i
\(121\) 1.76284e7 6.41620e6i 0.904614 0.329252i
\(122\) 3.79730e6 1.38210e6i 0.189328 0.0689098i
\(123\) 8.18698e6 + 3.48527e6i 0.396694 + 0.168876i
\(124\) 1.20919e6 + 6.85768e6i 0.0569535 + 0.322999i
\(125\) 7.44593e6 1.28967e7i 0.340984 0.590601i
\(126\) 245484. + 554482.i 0.0109327 + 0.0246939i
\(127\) −4.34281e6 7.52196e6i −0.188130 0.325850i 0.756497 0.653997i \(-0.226909\pi\)
−0.944627 + 0.328147i \(0.893576\pi\)
\(128\) −1.59401e7 + 1.33753e7i −0.671826 + 0.563729i
\(129\) 1.63742e7 2.51564e7i 0.671577 1.03177i
\(130\) 139423. 790707.i 0.00556587 0.0315656i
\(131\) −2.62177e7 2.19993e7i −1.01893 0.854986i −0.0294400 0.999567i \(-0.509372\pi\)
−0.989493 + 0.144580i \(0.953817\pi\)
\(132\) −4.54683e6 + 1.38491e6i −0.172068 + 0.0524099i
\(133\) −1.92044e6 698982.i −0.0707814 0.0257623i
\(134\) −3.90694e6 −0.140272
\(135\) −6.82770e6 7.90429e6i −0.238840 0.276500i
\(136\) −5.56663e6 −0.189761
\(137\) −3.66398e7 1.33358e7i −1.21739 0.443095i −0.348131 0.937446i \(-0.613184\pi\)
−0.869263 + 0.494351i \(0.835406\pi\)
\(138\) 1.80594e6 7.78524e6i 0.0584960 0.252171i
\(139\) 3.61361e7 + 3.03218e7i 1.14127 + 0.957642i 0.999480 0.0322544i \(-0.0102687\pi\)
0.141793 + 0.989896i \(0.454713\pi\)
\(140\) 197117. 1.11790e6i 0.00607120 0.0344315i
\(141\) 4.29889e7 + 2.29801e6i 1.29148 + 0.0690374i
\(142\) −8.73022e6 + 7.32552e6i −0.255868 + 0.214699i
\(143\) −1.12793e6 1.95363e6i −0.0322556 0.0558684i
\(144\) −2.77474e7 + 6.85663e6i −0.774379 + 0.191356i
\(145\) −8.88898e6 + 1.53962e7i −0.242139 + 0.419396i
\(146\) 2.59547e6 + 1.47197e7i 0.0690211 + 0.391438i
\(147\) 3.04571e7 2.29012e7i 0.790820 0.594631i
\(148\) 3.59504e7 1.30849e7i 0.911565 0.331782i
\(149\) −3.92839e7 + 1.42982e7i −0.972888 + 0.354102i −0.779071 0.626936i \(-0.784309\pi\)
−0.193817 + 0.981038i \(0.562087\pi\)
\(150\) 1.13709e6 + 9.34154e6i 0.0275090 + 0.225995i
\(151\) 1.32141e7 + 7.49408e7i 0.312333 + 1.77133i 0.586800 + 0.809732i \(0.300388\pi\)
−0.274467 + 0.961597i \(0.588501\pi\)
\(152\) −8.04859e6 + 1.39406e7i −0.185895 + 0.321979i
\(153\) −1.48780e7 7.29502e6i −0.335834 0.164667i
\(154\) 118244. + 204805.i 0.00260890 + 0.00451875i
\(155\) −4.57156e6 + 3.83600e6i −0.0986061 + 0.0827403i
\(156\) −6.67776e6 1.31398e7i −0.140830 0.277110i
\(157\) −5.59139e6 + 3.17104e7i −0.115311 + 0.653962i 0.871285 + 0.490778i \(0.163287\pi\)
−0.986596 + 0.163184i \(0.947824\pi\)
\(158\) 3.31695e6 + 2.78325e6i 0.0669020 + 0.0561374i
\(159\) 3.41347e7 + 3.18979e7i 0.673451 + 0.629320i
\(160\) −1.27529e7 4.64168e6i −0.246144 0.0895892i
\(161\) 5.36264e6 0.101272
\(162\) 1.38944e7 + 3.01411e6i 0.256766 + 0.0557002i
\(163\) −2.69668e7 −0.487723 −0.243862 0.969810i \(-0.578414\pi\)
−0.243862 + 0.969810i \(0.578414\pi\)
\(164\) 2.13058e7 + 7.75466e6i 0.377175 + 0.137281i
\(165\) −2.97621e6 2.78118e6i −0.0515785 0.0481987i
\(166\) 2.09282e6 + 1.75608e6i 0.0355102 + 0.0297966i
\(167\) 9.18251e6 5.20766e7i 0.152565 0.865237i −0.808414 0.588614i \(-0.799674\pi\)
0.960979 0.276622i \(-0.0892151\pi\)
\(168\) 1.45201e6 + 2.85711e6i 0.0236258 + 0.0464884i
\(169\) −4.27094e7 + 3.58374e7i −0.680643 + 0.571128i
\(170\) −1.15002e6 1.99190e6i −0.0179529 0.0310954i
\(171\) −3.97805e7 + 2.67115e7i −0.608393 + 0.408519i
\(172\) 3.82422e7 6.62375e7i 0.573052 0.992555i
\(173\) −2.82336e6 1.60121e7i −0.0414576 0.235118i 0.957037 0.289966i \(-0.0936438\pi\)
−0.998495 + 0.0548475i \(0.982533\pi\)
\(174\) −2.92406e6 2.40221e7i −0.0420788 0.345691i
\(175\) −5.93368e6 + 2.15968e6i −0.0836933 + 0.0304619i
\(176\) −1.04745e7 + 3.81242e6i −0.144824 + 0.0527116i
\(177\) −3.12251e6 + 2.34787e6i −0.0423250 + 0.0318249i
\(178\) −6.32707e6 3.58826e7i −0.0840877 0.476885i
\(179\) −1.34135e7 + 2.32328e7i −0.174806 + 0.302773i −0.940094 0.340915i \(-0.889263\pi\)
0.765288 + 0.643688i \(0.222596\pi\)
\(180\) −1.84482e7 1.91837e7i −0.235776 0.245177i
\(181\) −6.80934e6 1.17941e7i −0.0853553 0.147840i 0.820187 0.572095i \(-0.193869\pi\)
−0.905543 + 0.424255i \(0.860536\pi\)
\(182\) −561780. + 471389.i −0.00690742 + 0.00579602i
\(183\) 6.34842e7 + 3.39360e6i 0.765750 + 0.0409338i
\(184\) 7.33474e6 4.15974e7i 0.0868005 0.492270i
\(185\) 2.51164e7 + 2.10751e7i 0.291646 + 0.244720i
\(186\) 1.83562e6 7.91319e6i 0.0209164 0.0901688i
\(187\) −6.07253e6 2.21022e6i −0.0679085 0.0247167i
\(188\) 1.09697e8 1.20405
\(189\) 136588. + 9.53908e6i 0.00147163 + 0.102776i
\(190\) −6.65111e6 −0.0703488
\(191\) −4.39943e6 1.60126e6i −0.0456856 0.0166282i 0.319076 0.947729i \(-0.396627\pi\)
−0.364762 + 0.931101i \(0.618850\pi\)
\(192\) −5.71647e7 + 1.74117e7i −0.582872 + 0.177536i
\(193\) −7.01961e7 5.89015e7i −0.702850 0.589761i 0.219733 0.975560i \(-0.429481\pi\)
−0.922583 + 0.385799i \(0.873926\pi\)
\(194\) 4.55376e6 2.58257e7i 0.0447780 0.253948i
\(195\) 6.89077e6 1.05866e7i 0.0665498 0.102244i
\(196\) 7.43828e7 6.24146e7i 0.705629 0.592093i
\(197\) −3.12458e7 5.41194e7i −0.291179 0.504337i 0.682910 0.730503i \(-0.260714\pi\)
−0.974089 + 0.226166i \(0.927381\pi\)
\(198\) 5.51314e6 + 591108.i 0.0504744 + 0.00541177i
\(199\) −1.06641e7 + 1.84707e7i −0.0959261 + 0.166149i −0.909995 0.414620i \(-0.863915\pi\)
0.814069 + 0.580769i \(0.197248\pi\)
\(200\) 8.63661e6 + 4.89807e7i 0.0763376 + 0.432932i
\(201\) −5.65545e7 2.40757e7i −0.491226 0.209119i
\(202\) 3.32600e7 1.21057e7i 0.283918 0.103338i
\(203\) 1.52586e7 5.55369e6i 0.128020 0.0465956i
\(204\) −3.88492e7 1.65384e7i −0.320388 0.136392i
\(205\) 3.37416e6 + 1.91358e7i 0.0273544 + 0.155135i
\(206\) −1.85272e7 + 3.20900e7i −0.147664 + 0.255761i
\(207\) 7.41166e7 1.01566e8i 0.580790 0.795885i
\(208\) −1.72831e7 2.99352e7i −0.133168 0.230653i
\(209\) −1.43151e7 + 1.20118e7i −0.108463 + 0.0910116i
\(210\) −722381. + 1.10983e6i −0.00538269 + 0.00826968i
\(211\) 7.31062e6 4.14606e7i 0.0535755 0.303842i −0.946231 0.323490i \(-0.895144\pi\)
0.999807 + 0.0196488i \(0.00625481\pi\)
\(212\) 9.11941e7 + 7.65210e7i 0.657342 + 0.551575i
\(213\) −1.71515e8 + 5.22415e7i −1.21611 + 0.370414i
\(214\) −3.22873e7 1.17516e7i −0.225208 0.0819690i
\(215\) 6.55478e7 0.449804
\(216\) 7.41802e7 + 1.19875e7i 0.500841 + 0.0809360i
\(217\) 5.45078e6 0.0362117
\(218\) 5.05173e7 + 1.83868e7i 0.330249 + 0.120201i
\(219\) −5.31365e7 + 2.29067e8i −0.341852 + 1.47370i
\(220\) −7.95122e6 6.67187e6i −0.0503448 0.0422443i
\(221\) 3.47982e6 1.97350e7i 0.0216862 0.122989i
\(222\) −4.45661e7 2.38232e6i −0.273382 0.0146139i
\(223\) 1.32683e8 1.11334e8i 0.801211 0.672296i −0.147282 0.989095i \(-0.547052\pi\)
0.948493 + 0.316799i \(0.102608\pi\)
\(224\) 6.19786e6 + 1.07350e7i 0.0368446 + 0.0638167i
\(225\) −4.11056e7 + 1.42229e8i −0.240581 + 0.832436i
\(226\) −4.07560e7 + 7.05915e7i −0.234862 + 0.406793i
\(227\) −1.15748e7 6.56437e7i −0.0656782 0.372480i −0.999876 0.0157250i \(-0.994994\pi\)
0.934198 0.356755i \(-0.116117\pi\)
\(228\) −9.75880e7 + 7.33781e7i −0.545286 + 0.410010i
\(229\) −2.24942e8 + 8.18721e7i −1.23779 + 0.450517i −0.876257 0.481843i \(-0.839967\pi\)
−0.361529 + 0.932361i \(0.617745\pi\)
\(230\) 1.64000e7 5.96913e6i 0.0888786 0.0323492i
\(231\) 449561. + 3.69329e6i 0.00239964 + 0.0197138i
\(232\) −2.22093e7 1.25955e8i −0.116769 0.662229i
\(233\) −2.86871e7 + 4.96876e7i −0.148573 + 0.257337i −0.930700 0.365782i \(-0.880801\pi\)
0.782127 + 0.623119i \(0.214135\pi\)
\(234\) 1.16355e6 + 1.71548e7i 0.00593651 + 0.0875248i
\(235\) 4.70058e7 + 8.14164e7i 0.236273 + 0.409237i
\(236\) −7.62585e6 + 6.39885e6i −0.0377656 + 0.0316891i
\(237\) 3.08629e7 + 6.07286e7i 0.150597 + 0.296329i
\(238\) −364800. + 2.06888e6i −0.00175402 + 0.00994756i
\(239\) 2.51123e8 + 2.10717e8i 1.18985 + 0.998405i 0.999862 + 0.0166192i \(0.00529028\pi\)
0.189991 + 0.981786i \(0.439154\pi\)
\(240\) −4.56039e7 4.26156e7i −0.212943 0.198989i
\(241\) 2.44981e7 + 8.91659e6i 0.112739 + 0.0410336i 0.397774 0.917484i \(-0.369783\pi\)
−0.285035 + 0.958517i \(0.592005\pi\)
\(242\) −5.57640e7 −0.252930
\(243\) 1.82553e8 + 1.29252e8i 0.816144 + 0.577849i
\(244\) 1.61997e8 0.713907
\(245\) 7.81969e7 + 2.84613e7i 0.339710 + 0.123644i
\(246\) −1.93251e7 1.80587e7i −0.0827654 0.0773419i
\(247\) −4.43912e7 3.72487e7i −0.187438 0.157279i
\(248\) 7.45528e6 4.22810e7i 0.0310372 0.176021i
\(249\) 1.94728e7 + 3.83165e7i 0.0799339 + 0.157285i
\(250\) −3.39102e7 + 2.84540e7i −0.137259 + 0.115174i
\(251\) −1.43854e8 2.49162e8i −0.574200 0.994543i −0.996128 0.0879138i \(-0.971980\pi\)
0.421928 0.906629i \(-0.361353\pi\)
\(252\) 1.64503e6 + 2.42535e7i 0.00647550 + 0.0954713i
\(253\) 2.45175e7 4.24655e7i 0.0951819 0.164860i
\(254\) 4.48330e6 + 2.54261e7i 0.0171664 + 0.0973557i
\(255\) −4.37236e6 3.59203e7i −0.0165130 0.135659i
\(256\) −9.55732e7 + 3.47858e7i −0.356038 + 0.129587i
\(257\) −3.75434e8 + 1.36647e8i −1.37964 + 0.502150i −0.922070 0.387022i \(-0.873504\pi\)
−0.457574 + 0.889172i \(0.651282\pi\)
\(258\) −7.13133e7 + 5.36217e7i −0.258524 + 0.194389i
\(259\) −5.20020e6 2.94918e7i −0.0185982 0.105476i
\(260\) 1.60935e7 2.78748e7i 0.0567865 0.0983571i
\(261\) 1.05704e8 3.65747e8i 0.368002 1.27333i
\(262\) 5.08673e7 + 8.81048e7i 0.174737 + 0.302653i
\(263\) 3.92062e8 3.28979e8i 1.32895 1.11512i 0.344630 0.938738i \(-0.388004\pi\)
0.984321 0.176385i \(-0.0564402\pi\)
\(264\) 2.92632e7 + 1.56429e6i 0.0978833 + 0.00523244i
\(265\) −1.77161e7 + 1.00473e8i −0.0584800 + 0.331657i
\(266\) 4.65367e6 + 3.90490e6i 0.0151604 + 0.0127211i
\(267\) 1.29532e8 5.58403e8i 0.416475 1.79539i
\(268\) −1.47177e8 5.35681e7i −0.467056 0.169994i
\(269\) −5.94184e8 −1.86118 −0.930588 0.366067i \(-0.880704\pi\)
−0.930588 + 0.366067i \(0.880704\pi\)
\(270\) 1.10356e7 + 2.90204e7i 0.0341211 + 0.0897283i
\(271\) 2.99559e8 0.914302 0.457151 0.889389i \(-0.348870\pi\)
0.457151 + 0.889389i \(0.348870\pi\)
\(272\) −9.30485e7 3.38669e7i −0.280361 0.102043i
\(273\) −1.10368e7 + 3.36168e6i −0.0328303 + 0.00999971i
\(274\) 8.87869e7 + 7.45010e7i 0.260749 + 0.218794i
\(275\) −1.00262e7 + 5.68613e7i −0.0290717 + 0.164874i
\(276\) 1.74774e8 2.68514e8i 0.500375 0.768750i
\(277\) 1.61256e8 1.35310e8i 0.455865 0.382516i −0.385742 0.922607i \(-0.626054\pi\)
0.841607 + 0.540091i \(0.181610\pi\)
\(278\) −7.01108e7 1.21436e8i −0.195717 0.338992i
\(279\) 7.53347e7 1.03235e8i 0.207673 0.284585i
\(280\) −3.49938e6 + 6.06110e6i −0.00952659 + 0.0165005i
\(281\) −5.67400e7 3.21788e8i −0.152552 0.865164i −0.960990 0.276583i \(-0.910798\pi\)
0.808438 0.588581i \(-0.200313\pi\)
\(282\) −1.17743e8 5.01244e7i −0.312655 0.133100i
\(283\) −1.93609e8 + 7.04680e7i −0.507777 + 0.184816i −0.583189 0.812337i \(-0.698195\pi\)
0.0754114 + 0.997153i \(0.475973\pi\)
\(284\) −4.29313e8 + 1.56257e8i −1.11214 + 0.404787i
\(285\) −9.62774e7 4.09861e7i −0.246358 0.104877i
\(286\) 1.16442e6 + 6.60375e6i 0.00294326 + 0.0166920i
\(287\) 8.87388e6 1.53700e7i 0.0221578 0.0383785i
\(288\) 2.88975e8 + 3.09834e7i 0.712832 + 0.0764284i
\(289\) 1.76466e8 + 3.05649e8i 0.430050 + 0.744869i
\(290\) 4.04822e7 3.39686e7i 0.0974700 0.0817870i
\(291\) 2.25063e8 3.45775e8i 0.535400 0.822560i
\(292\) −1.04048e8 + 5.90086e8i −0.244565 + 1.38700i
\(293\) 5.62511e8 + 4.72003e8i 1.30646 + 1.09625i 0.988991 + 0.147976i \(0.0472759\pi\)
0.317465 + 0.948270i \(0.397169\pi\)
\(294\) −1.08358e8 + 3.30045e7i −0.248682 + 0.0757457i
\(295\) −8.01687e6 2.91790e6i −0.0181814 0.00661750i
\(296\) −2.35877e8 −0.528645
\(297\) 7.61622e7 + 4.25301e7i 0.168691 + 0.0941996i
\(298\) 1.24267e8 0.272019
\(299\) 1.42887e8 + 5.20068e7i 0.309133 + 0.112515i
\(300\) −8.52470e7 + 3.67493e8i −0.182287 + 0.785822i
\(301\) −4.58627e7 3.84834e7i −0.0969342 0.0813375i
\(302\) 3.92794e7 2.22765e8i 0.0820617 0.465395i
\(303\) 5.56050e8 + 2.97241e7i 1.14832 + 0.0613847i
\(304\) −2.19349e8 + 1.84055e8i −0.447793 + 0.375743i
\(305\) 6.94162e7 + 1.20232e8i 0.140091 + 0.242645i
\(306\) 3.41417e7 + 3.55030e7i 0.0681177 + 0.0708337i
\(307\) −1.94488e8 + 3.36864e8i −0.383627 + 0.664461i −0.991578 0.129513i \(-0.958658\pi\)
0.607951 + 0.793975i \(0.291992\pi\)
\(308\) 1.64626e6 + 9.33639e6i 0.00321048 + 0.0182075i
\(309\) −4.65936e8 + 3.50345e8i −0.898405 + 0.675526i
\(310\) 1.66696e7 6.06722e6i 0.0317803 0.0115671i
\(311\) −5.43007e8 + 1.97638e8i −1.02363 + 0.372572i −0.798653 0.601792i \(-0.794454\pi\)
−0.224980 + 0.974363i \(0.572232\pi\)
\(312\) 1.09806e7 + 9.02091e7i 0.0204684 + 0.168155i
\(313\) −7.46811e7 4.23538e8i −0.137659 0.780705i −0.972971 0.230928i \(-0.925824\pi\)
0.835312 0.549777i \(-0.185287\pi\)
\(314\) 4.78572e7 8.28911e7i 0.0872355 0.151096i
\(315\) −1.72958e7 + 1.16137e7i −0.0311785 + 0.0209354i
\(316\) 8.67905e7 + 1.50326e8i 0.154728 + 0.267996i
\(317\) 7.96155e7 6.68053e7i 0.140375 0.117789i −0.569896 0.821717i \(-0.693017\pi\)
0.710271 + 0.703928i \(0.248572\pi\)
\(318\) −6.29180e7 1.23803e8i −0.109718 0.215892i
\(319\) 2.57826e7 1.46220e8i 0.0444692 0.252198i
\(320\) −9.99661e7 8.38815e7i −0.170541 0.143101i
\(321\) −3.94954e8 3.69073e8i −0.666467 0.622794i
\(322\) −1.49793e7 5.45203e6i −0.0250033 0.00910045i
\(323\) −1.66003e8 −0.274099
\(324\) 4.82085e8 + 3.04050e8i 0.787437 + 0.496635i
\(325\) −1.79047e8 −0.289318
\(326\) 7.53258e7 + 2.74163e7i 0.120415 + 0.0438276i
\(327\) 6.17952e8 + 5.77458e8i 0.977321 + 0.913278i
\(328\) −1.07086e8 8.98558e7i −0.167562 0.140601i
\(329\) 1.49107e7 8.45630e7i 0.0230841 0.130917i
\(330\) 5.48582e6 + 1.07944e7i 0.00840316 + 0.0165348i
\(331\) 3.10609e8 2.60632e8i 0.470777 0.395029i −0.376301 0.926498i \(-0.622804\pi\)
0.847078 + 0.531469i \(0.178360\pi\)
\(332\) 5.47601e7 + 9.48473e7i 0.0821261 + 0.142247i
\(333\) −6.30431e8 3.09115e8i −0.935584 0.458738i
\(334\) −7.85939e7 + 1.36129e8i −0.115419 + 0.199911i
\(335\) −2.33083e7 1.32188e8i −0.0338730 0.192103i
\(336\) 6.88855e6 + 5.65917e7i 0.00990696 + 0.0813888i
\(337\) 2.42930e8 8.84192e7i 0.345761 0.125847i −0.163302 0.986576i \(-0.552214\pi\)
0.509063 + 0.860729i \(0.329992\pi\)
\(338\) 1.55734e8 5.66824e7i 0.219368 0.0798436i
\(339\) −1.02496e9 + 7.70688e8i −1.42893 + 1.07443i
\(340\) −1.60112e7 9.08042e7i −0.0220927 0.125294i
\(341\) 2.49204e7 4.31634e7i 0.0340342 0.0589489i
\(342\) 1.38275e8 3.41689e7i 0.186918 0.0461891i
\(343\) −7.64124e7 1.32350e8i −0.102243 0.177090i
\(344\) −3.61239e8 + 3.03116e8i −0.478454 + 0.401471i
\(345\) 2.74180e8 + 1.46565e7i 0.359476 + 0.0192161i
\(346\) −8.39254e6 + 4.75965e7i −0.0108925 + 0.0617744i
\(347\) 7.50596e8 + 6.29825e8i 0.964390 + 0.809220i 0.981662 0.190631i \(-0.0610535\pi\)
−0.0172713 + 0.999851i \(0.505498\pi\)
\(348\) 2.19215e8 9.45019e8i 0.278833 1.20202i
\(349\) 6.60998e8 + 2.40583e8i 0.832359 + 0.302954i 0.722827 0.691029i \(-0.242842\pi\)
0.109533 + 0.993983i \(0.465065\pi\)
\(350\) 1.87701e7 0.0234006
\(351\) −8.88703e7 + 2.55493e8i −0.109694 + 0.315358i
\(352\) 1.13344e8 0.138516
\(353\) 1.65891e8 + 6.03794e7i 0.200730 + 0.0730596i 0.440429 0.897788i \(-0.354827\pi\)
−0.239699 + 0.970847i \(0.577049\pi\)
\(354\) 1.11090e7 3.38368e6i 0.0133096 0.00405394i
\(355\) −2.99935e8 2.51676e8i −0.355818 0.298567i
\(356\) 2.53641e8 1.43847e9i 0.297951 1.68977i
\(357\) −1.80297e7 + 2.76999e7i −0.0209725 + 0.0322210i
\(358\) 6.10876e7 5.12586e7i 0.0703659 0.0590440i
\(359\) 5.25329e8 + 9.09896e8i 0.599240 + 1.03791i 0.992934 + 0.118672i \(0.0378636\pi\)
−0.393694 + 0.919242i \(0.628803\pi\)
\(360\) 6.64294e7 + 1.50046e8i 0.0750415 + 0.169499i
\(361\) 2.06918e8 3.58393e8i 0.231485 0.400944i
\(362\) 7.02964e6 + 3.98671e7i 0.00778849 + 0.0441707i
\(363\) −8.07205e8 3.43634e8i −0.885749 0.377071i
\(364\) −2.76258e7 + 1.00550e7i −0.0300234 + 0.0109276i
\(365\) −4.82542e8 + 1.75631e8i −0.519409 + 0.189050i
\(366\) −1.73879e8 7.40216e7i −0.185380 0.0789178i
\(367\) −3.45224e7 1.95786e8i −0.0364561 0.206753i 0.961139 0.276065i \(-0.0890306\pi\)
−0.997595 + 0.0693125i \(0.977919\pi\)
\(368\) 3.75678e8 6.50693e8i 0.392960 0.680626i
\(369\) −1.68455e8 3.80494e8i −0.174538 0.394235i
\(370\) −4.87304e7 8.44036e7i −0.0500143 0.0866273i
\(371\) 7.13838e7 5.98981e7i 0.0725756 0.0608982i
\(372\) 1.77647e8 2.72927e8i 0.178919 0.274882i
\(373\) 3.07993e8 1.74672e9i 0.307298 1.74277i −0.305187 0.952293i \(-0.598719\pi\)
0.612485 0.790482i \(-0.290170\pi\)
\(374\) 1.47152e7 + 1.23475e7i 0.0145450 + 0.0122047i
\(375\) −6.66205e8 + 2.02918e8i −0.652377 + 0.198706i
\(376\) −6.35551e8 2.31322e8i −0.616585 0.224418i
\(377\) 4.60425e8 0.442552
\(378\) 9.31655e6 2.67841e7i 0.00887225 0.0255068i
\(379\) −1.34274e9 −1.26694 −0.633470 0.773767i \(-0.718370\pi\)
−0.633470 + 0.773767i \(0.718370\pi\)
\(380\) −2.50552e8 9.11934e7i −0.234237 0.0852552i
\(381\) −9.17855e7 + 3.95680e8i −0.0850231 + 0.366527i
\(382\) 1.06609e7 + 8.94552e6i 0.00978522 + 0.00821077i
\(383\) 2.62664e8 1.48964e9i 0.238894 1.35483i −0.595363 0.803457i \(-0.702992\pi\)
0.834257 0.551376i \(-0.185897\pi\)
\(384\) 9.71723e8 + 5.19443e7i 0.875756 + 0.0468143i
\(385\) −6.22395e6 + 5.22252e6i −0.00555845 + 0.00466409i
\(386\) 1.36194e8 + 2.35894e8i 0.120532 + 0.208767i
\(387\) −1.36272e9 + 3.36740e8i −1.19514 + 0.295329i
\(388\) 5.25639e8 9.10434e8i 0.456853 0.791293i
\(389\) 1.96843e8 + 1.11635e9i 0.169549 + 0.961562i 0.944249 + 0.329233i \(0.106790\pi\)
−0.774699 + 0.632330i \(0.782099\pi\)
\(390\) −3.00109e7 + 2.25657e7i −0.0256185 + 0.0192629i
\(391\) 4.09323e8 1.48982e8i 0.346296 0.126042i
\(392\) −5.62564e8 + 2.04757e8i −0.471706 + 0.171687i
\(393\) 1.93396e8 + 1.58881e9i 0.160721 + 1.32038i
\(394\) 3.22567e7 + 1.82937e8i 0.0265695 + 0.150683i
\(395\) −7.43802e7 + 1.28830e8i −0.0607250 + 0.105179i
\(396\) 1.99579e8 + 9.78581e7i 0.161503 + 0.0791888i
\(397\) −4.92408e8 8.52876e8i −0.394965 0.684099i 0.598132 0.801398i \(-0.295910\pi\)
−0.993097 + 0.117298i \(0.962577\pi\)
\(398\) 4.85662e7 4.07519e7i 0.0386139 0.0324009i
\(399\) 4.33006e7 + 8.52021e7i 0.0341262 + 0.0671499i
\(400\) −1.53630e8 + 8.71276e8i −0.120023 + 0.680685i
\(401\) 1.91879e9 + 1.61006e9i 1.48601 + 1.24691i 0.899461 + 0.437001i \(0.143959\pi\)
0.586552 + 0.809912i \(0.300485\pi\)
\(402\) 1.33495e8 + 1.24747e8i 0.102488 + 0.0957723i
\(403\) 1.45236e8 + 5.28614e7i 0.110536 + 0.0402320i
\(404\) 1.41891e9 1.07058
\(405\) −1.90876e7 + 4.88085e8i −0.0142777 + 0.365093i
\(406\) −4.82678e7 −0.0357945
\(407\) −2.57314e8 9.36546e7i −0.189183 0.0688571i
\(408\) 1.90204e8 + 1.77740e8i 0.138647 + 0.129561i
\(409\) 2.93961e8 + 2.46663e8i 0.212451 + 0.178267i 0.742803 0.669510i \(-0.233496\pi\)
−0.530352 + 0.847777i \(0.677940\pi\)
\(410\) 1.00298e7 5.68820e7i 0.00718704 0.0407598i
\(411\) 8.26126e8 + 1.62556e9i 0.586949 + 1.15493i
\(412\) −1.13792e9 + 9.54827e8i −0.801624 + 0.672643i
\(413\) 3.89616e6 + 6.74835e6i 0.00272152 + 0.00471381i
\(414\) −3.10287e8 + 2.08349e8i −0.214913 + 0.144308i
\(415\) −4.69299e7 + 8.12849e7i −0.0322315 + 0.0558267i
\(416\) 6.10339e7 + 3.46140e8i 0.0415666 + 0.235736i
\(417\) −2.66559e8 2.18987e9i −0.180019 1.47891i
\(418\) 5.21981e7 1.89986e7i 0.0349573 0.0127234i
\(419\) −1.55490e9 + 5.65937e8i −1.03265 + 0.375854i −0.802090 0.597204i \(-0.796278\pi\)
−0.230561 + 0.973058i \(0.574056\pi\)
\(420\) −4.24295e7 + 3.19034e7i −0.0279444 + 0.0210119i
\(421\) 2.66057e8 + 1.50888e9i 0.173775 + 0.985527i 0.939548 + 0.342416i \(0.111245\pi\)
−0.765773 + 0.643110i \(0.777644\pi\)
\(422\) −6.25723e7 + 1.08378e8i −0.0405311 + 0.0702019i
\(423\) −1.39550e9 1.45114e9i −0.896475 0.932219i
\(424\) −3.66987e8 6.35640e8i −0.233814 0.404977i
\(425\) −3.92910e8 + 3.29691e8i −0.248275 + 0.208327i
\(426\) 5.32201e8 + 2.84493e7i 0.333536 + 0.0178294i
\(427\) 2.20196e7 1.24879e8i 0.0136871 0.0776234i
\(428\) −1.05516e9 8.85382e8i −0.650525 0.545856i
\(429\) −2.38388e7 + 1.02767e8i −0.0145776 + 0.0628426i
\(430\) −1.83093e8 6.66404e7i −0.111053 0.0404202i
\(431\) −2.07109e8 −0.124603 −0.0623014 0.998057i \(-0.519844\pi\)
−0.0623014 + 0.998057i \(0.519844\pi\)
\(432\) 1.16702e9 + 6.51683e8i 0.696443 + 0.388905i
\(433\) 2.64895e8 0.156807 0.0784036 0.996922i \(-0.475018\pi\)
0.0784036 + 0.996922i \(0.475018\pi\)
\(434\) −1.52255e7 5.54163e6i −0.00894042 0.00325405i
\(435\) 7.95319e8 2.42245e8i 0.463264 0.141105i
\(436\) 1.65092e9 + 1.38528e9i 0.953944 + 0.800454i
\(437\) 2.18730e8 1.24048e9i 0.125379 0.711057i
\(438\) 3.81310e8 5.85824e8i 0.216830 0.333125i
\(439\) −1.95598e9 + 1.64126e9i −1.10342 + 0.925875i −0.997650 0.0685159i \(-0.978174\pi\)
−0.105765 + 0.994391i \(0.533729\pi\)
\(440\) 3.19976e7 + 5.54215e7i 0.0179074 + 0.0310166i
\(441\) −1.77190e9 1.89980e8i −0.983796 0.105481i
\(442\) −2.97840e7 + 5.15875e7i −0.0164061 + 0.0284162i
\(443\) −1.36850e8 7.76118e8i −0.0747882 0.424145i −0.999097 0.0424985i \(-0.986468\pi\)
0.924308 0.381647i \(-0.124643\pi\)
\(444\) −1.64617e9 7.00790e8i −0.892555 0.379968i
\(445\) 1.17631e9 4.28141e8i 0.632791 0.230317i
\(446\) −4.83808e8 + 1.76092e8i −0.258227 + 0.0939869i
\(447\) 1.79881e9 + 7.65771e8i 0.952599 + 0.405530i
\(448\) 2.06974e7 + 1.17381e8i 0.0108754 + 0.0616772i
\(449\) −4.22203e8 + 7.31277e8i −0.220120 + 0.381259i −0.954844 0.297107i \(-0.903978\pi\)
0.734724 + 0.678366i \(0.237311\pi\)
\(450\) 2.59419e8 3.55495e8i 0.134202 0.183903i
\(451\) −8.11411e7 1.40540e8i −0.0416507 0.0721412i
\(452\) −2.50319e9 + 2.10042e9i −1.27500 + 1.06985i
\(453\) 1.94133e9 2.98255e9i 0.981193 1.50745i
\(454\) −3.44064e7 + 1.95128e8i −0.0172561 + 0.0978645i
\(455\) −1.93005e7 1.61950e7i −0.00960569 0.00806013i
\(456\) 7.20126e8 2.19342e8i 0.355657 0.108329i
\(457\) 3.20839e9 + 1.16776e9i 1.57246 + 0.572330i 0.973548 0.228481i \(-0.0733759\pi\)
0.598916 + 0.800812i \(0.295598\pi\)
\(458\) 7.11560e8 0.346085
\(459\) 2.75434e8 + 7.24310e8i 0.132945 + 0.349607i
\(460\) 6.99643e8 0.335138
\(461\) −1.01927e9 3.70985e8i −0.484549 0.176361i 0.0881826 0.996104i \(-0.471894\pi\)
−0.572732 + 0.819743i \(0.694116\pi\)
\(462\) 2.49910e6 1.07734e7i 0.00117906 0.00508284i
\(463\) −7.77235e6 6.52178e6i −0.00363931 0.00305374i 0.640966 0.767569i \(-0.278534\pi\)
−0.644605 + 0.764515i \(0.722978\pi\)
\(464\) 3.95063e8 2.24051e9i 0.183592 1.04120i
\(465\) 2.78686e8 + 1.48974e7i 0.128538 + 0.00687109i
\(466\) 1.30647e8 1.09626e8i 0.0598064 0.0501836i
\(467\) −1.49651e9 2.59203e9i −0.679941 1.17769i −0.974998 0.222212i \(-0.928672\pi\)
0.295058 0.955479i \(-0.404661\pi\)
\(468\) −1.91378e8 + 6.62187e8i −0.0863041 + 0.298621i
\(469\) −6.12995e7 + 1.06174e8i −0.0274380 + 0.0475240i
\(470\) −4.85265e7 2.75208e8i −0.0215594 0.122269i
\(471\) 1.20355e9 9.04970e8i 0.530751 0.399081i
\(472\) 5.76750e7 2.09920e7i 0.0252459 0.00918875i
\(473\) −5.14421e8 + 1.87234e8i −0.223514 + 0.0813524i
\(474\) −2.44676e7 2.01009e8i −0.0105528 0.0866945i
\(475\) 2.57553e8 + 1.46066e9i 0.110265 + 0.625347i
\(476\) −4.21087e7 + 7.29344e7i −0.0178957 + 0.0309962i
\(477\) −1.47850e8 2.17982e9i −0.0623743 0.919614i
\(478\) −4.87225e8 8.43898e8i −0.204048 0.353421i
\(479\) 2.74769e8 2.30559e8i 0.114234 0.0958534i −0.583882 0.811839i \(-0.698467\pi\)
0.698115 + 0.715985i \(0.254022\pi\)
\(480\) 2.87543e8 + 5.65796e8i 0.118675 + 0.233516i
\(481\) 1.47452e8 8.36240e8i 0.0604146 0.342628i
\(482\) −5.93648e7 4.98130e7i −0.0241471 0.0202618i
\(483\) −1.83234e8 1.71227e8i −0.0739933 0.0691446i
\(484\) −2.10067e9 7.64580e8i −0.842167 0.306524i
\(485\) 9.00954e8 0.358597
\(486\) −3.78514e8 5.46631e8i −0.149573 0.216007i
\(487\) −3.28482e9 −1.28872 −0.644362 0.764720i \(-0.722877\pi\)
−0.644362 + 0.764720i \(0.722877\pi\)
\(488\) −9.38555e8 3.41606e8i −0.365587 0.133063i
\(489\) 9.21422e8 + 8.61042e8i 0.356350 + 0.332999i
\(490\) −1.89490e8 1.59001e8i −0.0727610 0.0610538i
\(491\) 6.11570e8 3.46838e9i 0.233164 1.32234i −0.613283 0.789863i \(-0.710152\pi\)
0.846447 0.532473i \(-0.178737\pi\)
\(492\) −4.80386e8 9.45251e8i −0.181850 0.357824i
\(493\) 1.01038e9 8.47811e8i 0.379770 0.318665i
\(494\) 8.61273e7 + 1.49177e8i 0.0321438 + 0.0556746i
\(495\) 1.28910e7 + 1.90058e8i 0.00477715 + 0.0704318i
\(496\) 3.81852e8 6.61387e8i 0.140511 0.243371i
\(497\) 6.21000e7 + 3.52186e8i 0.0226905 + 0.128684i
\(498\) −1.54377e7 1.26826e8i −0.00560119 0.0460156i
\(499\) 1.73356e9 6.30963e8i 0.624578 0.227328i −0.0102919 0.999947i \(-0.503276\pi\)
0.634870 + 0.772619i \(0.281054\pi\)
\(500\) −1.66755e9 + 6.06940e8i −0.596602 + 0.217145i
\(501\) −1.97654e9 + 1.48619e9i −0.702221 + 0.528012i
\(502\) 1.48508e8 + 8.42229e8i 0.0523945 + 0.297144i
\(503\) −8.38833e8 + 1.45290e9i −0.293892 + 0.509036i −0.974727 0.223401i \(-0.928284\pi\)
0.680835 + 0.732437i \(0.261617\pi\)
\(504\) 4.16132e7 1.43986e8i 0.0144785 0.0500971i
\(505\) 6.08008e8 + 1.05310e9i 0.210082 + 0.363873i
\(506\) −1.11657e8 + 9.36917e7i −0.0383143 + 0.0321495i
\(507\) 2.60360e9 + 1.39178e8i 0.887250 + 0.0474287i
\(508\) −1.79728e8 + 1.01929e9i −0.0608265 + 0.344964i
\(509\) 6.77475e8 + 5.68469e8i 0.227710 + 0.191071i 0.749503 0.662001i \(-0.230292\pi\)
−0.521794 + 0.853072i \(0.674737\pi\)
\(510\) −2.43059e7 + 1.04780e8i −0.00811363 + 0.0349772i
\(511\) 4.40740e8 + 1.60416e8i 0.146120 + 0.0531833i
\(512\) 2.96580e9 0.976554
\(513\) 2.21214e9 + 3.57482e8i 0.723438 + 0.116908i
\(514\) 1.18761e9 0.385748
\(515\) −1.19627e9 4.35405e8i −0.385925 0.140465i
\(516\) −3.42163e9 + 1.04219e9i −1.09637 + 0.333943i
\(517\) −6.01465e8 5.04689e8i −0.191423 0.160623i
\(518\) −1.54578e7 + 8.76656e7i −0.00488645 + 0.0277125i
\(519\) −4.14789e8 + 6.37260e8i −0.130239 + 0.200092i
\(520\) −1.52021e8 + 1.27561e8i −0.0474124 + 0.0397837i
\(521\) 6.28110e8 + 1.08792e9i 0.194582 + 0.337027i 0.946764 0.321930i \(-0.104332\pi\)
−0.752181 + 0.658956i \(0.770998\pi\)
\(522\) −6.67105e8 + 9.14166e8i −0.205280 + 0.281306i
\(523\) −2.41460e9 + 4.18220e9i −0.738055 + 1.27835i 0.215315 + 0.976545i \(0.430922\pi\)
−0.953370 + 0.301804i \(0.902411\pi\)
\(524\) 7.08201e8 + 4.01641e9i 0.215029 + 1.21949i
\(525\) 2.71704e8 + 1.15667e8i 0.0819479 + 0.0348860i
\(526\) −1.42960e9 + 5.20331e8i −0.428315 + 0.155894i
\(527\) 4.16050e8 1.51430e8i 0.123825 0.0450686i
\(528\) 4.79630e8 + 2.04183e8i 0.141804 + 0.0603671i
\(529\) −1.72932e7 9.80749e7i −0.00507904 0.0288047i
\(530\) 1.51634e8 2.62637e8i 0.0442415 0.0766285i
\(531\) 1.81659e8 + 1.94771e7i 0.0526532 + 0.00564538i
\(532\) 1.21767e8 + 2.10907e8i 0.0350622 + 0.0607294i
\(533\) 3.85502e8 3.23475e8i 0.110276 0.0925326i
\(534\) −9.29531e8 + 1.42808e9i −0.264161 + 0.405844i
\(535\) 2.04983e8 1.16252e9i 0.0578736 0.328217i
\(536\) 7.39735e8 + 6.20712e8i 0.207491 + 0.174106i
\(537\) 1.20014e9 3.65548e8i 0.334442 0.101867i
\(538\) 1.65972e9 + 6.04088e8i 0.459511 + 0.167248i
\(539\) −6.94989e8 −0.191169
\(540\) 1.78202e7 + 1.24453e9i 0.00487005 + 0.340115i
\(541\) 6.02766e8 0.163666 0.0818330 0.996646i \(-0.473923\pi\)
0.0818330 + 0.996646i \(0.473923\pi\)
\(542\) −8.36749e8 3.04552e8i −0.225735 0.0821606i
\(543\) −1.43916e8 + 6.20410e8i −0.0385753 + 0.166295i
\(544\) 7.71307e8 + 6.47203e8i 0.205414 + 0.172363i
\(545\) −3.20720e8 + 1.81890e9i −0.0848670 + 0.481305i
\(546\) 3.42465e7 + 1.83068e6i 0.00900415 + 0.000481324i
\(547\) 5.84294e8 4.90281e8i 0.152643 0.128082i −0.563268 0.826274i \(-0.690456\pi\)
0.715911 + 0.698192i \(0.246012\pi\)
\(548\) 2.32318e9 + 4.02386e9i 0.603046 + 1.04451i
\(549\) −2.06081e9 2.14298e9i −0.531540 0.552733i
\(550\) 8.58149e7 1.48636e8i 0.0219934 0.0380938i
\(551\) −6.62306e8 3.75613e9i −0.168666 0.956554i
\(552\) −1.57881e9 + 1.18713e9i −0.399523 + 0.300408i
\(553\) 1.27679e8 4.64715e7i 0.0321057 0.0116855i
\(554\) −5.87997e8 + 2.14013e8i −0.146923 + 0.0534757i
\(555\) −1.85272e8 1.52206e9i −0.0460027 0.377927i
\(556\) −9.76119e8 5.53585e9i −0.240847 1.36591i
\(557\) −8.90216e8 + 1.54190e9i −0.218274 + 0.378062i −0.954280 0.298913i \(-0.903376\pi\)
0.736006 + 0.676975i \(0.236709\pi\)
\(558\) −3.15386e8 + 2.11773e8i −0.0768462 + 0.0516001i
\(559\) −8.48799e8 1.47016e9i −0.205525 0.355979i
\(560\) −9.53687e7 + 8.00238e7i −0.0229482 + 0.0192558i
\(561\) 1.36919e8 + 2.69414e8i 0.0327411 + 0.0644244i
\(562\) −1.68662e8 + 9.56529e8i −0.0400811 + 0.227311i
\(563\) 2.03607e9 + 1.70846e9i 0.480853 + 0.403484i 0.850735 0.525595i \(-0.176157\pi\)
−0.369882 + 0.929079i \(0.620602\pi\)
\(564\) −3.74822e9 3.50260e9i −0.879727 0.822079i
\(565\) −2.63154e9 9.57803e8i −0.613819 0.223412i
\(566\) 6.12446e8 0.141974
\(567\) 2.99912e8 3.30299e8i 0.0690961 0.0760968i
\(568\) 2.81680e9 0.644966
\(569\) 6.27572e9 + 2.28418e9i 1.42814 + 0.519801i 0.936398 0.350940i \(-0.114138\pi\)
0.491742 + 0.870741i \(0.336360\pi\)
\(570\) 2.27260e8 + 2.12368e8i 0.0513997 + 0.0480315i
\(571\) −4.63584e9 3.88993e9i −1.04208 0.874411i −0.0498434 0.998757i \(-0.515872\pi\)
−0.992239 + 0.124346i \(0.960317\pi\)
\(572\) −4.66796e7 + 2.64733e8i −0.0104290 + 0.0591455i
\(573\) 9.91950e7 + 1.95185e8i 0.0220267 + 0.0433417i
\(574\) −4.04134e7 + 3.39109e7i −0.00891936 + 0.00748423i
\(575\) −1.94595e9 3.37048e9i −0.426869 0.739358i
\(576\) 2.50919e9 + 1.23031e9i 0.547085 + 0.268248i
\(577\) 7.03594e8 1.21866e9i 0.152478 0.264099i −0.779660 0.626203i \(-0.784608\pi\)
0.932138 + 0.362104i \(0.117941\pi\)
\(578\) −1.82175e8 1.03317e9i −0.0392412 0.222548i
\(579\) 5.17804e8 + 4.25392e9i 0.110864 + 0.910782i
\(580\) 1.99073e9 7.24568e8i 0.423658 0.154199i
\(581\) 8.05588e7 2.93210e7i 0.0170410 0.00620243i
\(582\) −9.80200e8 + 7.37029e8i −0.206103 + 0.154972i
\(583\) −1.47959e8 8.39120e8i −0.0309245 0.175382i
\(584\) 1.84715e9 3.19935e9i 0.383757 0.664687i
\(585\) −5.73476e8 + 1.41711e8i −0.118432 + 0.0292656i
\(586\) −1.09138e9 1.89032e9i −0.224044 0.388056i
\(587\) 6.95585e9 5.83665e9i 1.41944 1.19105i 0.467801 0.883834i \(-0.345046\pi\)
0.951639 0.307218i \(-0.0993980\pi\)
\(588\) −4.53444e9 2.42392e8i −0.919820 0.0491698i
\(589\) 2.22325e8 1.26087e9i 0.0448316 0.254253i
\(590\) 1.94268e7 + 1.63010e7i 0.00389420 + 0.00326762i
\(591\) −6.60383e8 + 2.84686e9i −0.131595 + 0.567296i
\(592\) −3.94278e9 1.43505e9i −0.781046 0.284277i
\(593\) −7.94531e9 −1.56466 −0.782329 0.622865i \(-0.785968\pi\)
−0.782329 + 0.622865i \(0.785968\pi\)
\(594\) −1.69503e8 1.96230e8i −0.0331837 0.0384161i
\(595\) −7.21750e7 −0.0140468
\(596\) 4.68123e9 + 1.70383e9i 0.905728 + 0.329658i
\(597\) 9.54139e8 2.90620e8i 0.183528 0.0559004i
\(598\) −3.46250e8 2.90538e8i −0.0662118 0.0555583i
\(599\) −9.38560e8 + 5.32284e9i −0.178430 + 1.01193i 0.755680 + 0.654941i \(0.227307\pi\)
−0.934110 + 0.356986i \(0.883804\pi\)
\(600\) 1.26883e9 1.94937e9i 0.239814 0.368438i
\(601\) 4.31442e9 3.62023e9i 0.810703 0.680261i −0.140072 0.990141i \(-0.544733\pi\)
0.950776 + 0.309880i \(0.100289\pi\)
\(602\) 8.89823e7 + 1.54122e8i 0.0166232 + 0.0287923i
\(603\) 1.16366e9 + 2.62840e9i 0.216131 + 0.488181i
\(604\) 4.53401e9 7.85313e9i 0.837246 1.45015i
\(605\) −3.32680e8 1.88672e9i −0.0610777 0.346389i
\(606\) −1.52298e9 6.48346e8i −0.277997 0.118346i
\(607\) −8.29875e9 + 3.02050e9i −1.50609 + 0.548173i −0.957630 0.288001i \(-0.907009\pi\)
−0.548464 + 0.836174i \(0.684787\pi\)
\(608\) 2.73600e9 9.95823e8i 0.493689 0.179688i
\(609\) −6.98694e8 2.97440e8i −0.125351 0.0533629i
\(610\) −7.16620e7 4.06415e8i −0.0127830 0.0724963i
\(611\) 1.21739e9 2.10857e9i 0.215916 0.373977i
\(612\) 7.99359e8 + 1.80554e9i 0.140965 + 0.318402i
\(613\) 3.58349e9 + 6.20679e9i 0.628340 + 1.08832i 0.987885 + 0.155189i \(0.0495987\pi\)
−0.359545 + 0.933128i \(0.617068\pi\)
\(614\) 8.85737e8 7.43222e8i 0.154424 0.129577i
\(615\) 4.95710e8 7.61582e8i 0.0859339 0.132024i
\(616\) 1.01500e7 5.75634e7i 0.00174958 0.00992234i
\(617\) 1.91802e9 + 1.60941e9i 0.328741 + 0.275847i 0.792187 0.610279i \(-0.208943\pi\)
−0.463446 + 0.886125i \(0.653387\pi\)
\(618\) 1.65767e9 5.04908e8i 0.282514 0.0860503i
\(619\) −2.62559e9 9.55636e8i −0.444948 0.161948i 0.109822 0.993951i \(-0.464972\pi\)
−0.554771 + 0.832003i \(0.687194\pi\)
\(620\) 7.11141e8 0.119835
\(621\) −5.77542e9 + 1.10385e9i −0.967750 + 0.184964i
\(622\) 1.71770e9 0.286208
\(623\) −1.07441e9 3.91052e8i −0.178016 0.0647927i
\(624\) −3.65279e8 + 1.57469e9i −0.0601837 + 0.259447i
\(625\) 2.88637e9 + 2.42196e9i 0.472904 + 0.396813i
\(626\) −2.21993e8 + 1.25898e9i −0.0361683 + 0.205121i
\(627\) 8.72662e8 + 4.66489e7i 0.141387 + 0.00755797i
\(628\) 2.93933e9 2.46639e9i 0.473576 0.397378i
\(629\) −1.21625e9 2.10660e9i −0.194870 0.337524i
\(630\) 6.01192e7 1.48560e7i 0.00957903 0.00236706i
\(631\) −3.18279e9 + 5.51275e9i −0.504318 + 0.873505i 0.495669 + 0.868511i \(0.334923\pi\)
−0.999988 + 0.00499356i \(0.998410\pi\)
\(632\) −1.85840e8 1.05395e9i −0.0292840 0.166078i
\(633\) −1.57362e9 + 1.18323e9i −0.246596 + 0.185420i
\(634\) −2.90307e8 + 1.05663e8i −0.0452423 + 0.0164669i
\(635\) −8.33520e8 + 3.03377e8i −0.129184 + 0.0470191i
\(636\) −6.72696e8 5.52642e9i −0.103686 0.851812i
\(637\) −3.74240e8 2.12242e9i −0.0573670 0.325345i
\(638\) −2.20676e8 + 3.82221e8i −0.0336420 + 0.0582697i
\(639\) 7.52850e9 + 3.69140e9i 1.14145 + 0.559677i
\(640\) 1.06252e9 + 1.84034e9i 0.160217 + 0.277503i
\(641\) 1.03004e9 8.64306e8i 0.154472 0.129618i −0.562276 0.826950i \(-0.690074\pi\)
0.716748 + 0.697332i \(0.245630\pi\)
\(642\) 7.27990e8 + 1.43246e9i 0.108581 + 0.213653i
\(643\) −1.23020e9 + 6.97681e9i −0.182489 + 1.03495i 0.746650 + 0.665217i \(0.231661\pi\)
−0.929139 + 0.369730i \(0.879450\pi\)
\(644\) −4.89529e8 4.10763e8i −0.0722233 0.0606026i
\(645\) −2.23968e9 2.09292e9i −0.328645 0.307109i
\(646\) 4.63692e8 + 1.68770e8i 0.0676730 + 0.0246310i
\(647\) −1.23163e10 −1.78778 −0.893889 0.448287i \(-0.852034\pi\)
−0.893889 + 0.448287i \(0.852034\pi\)
\(648\) −2.15188e9 2.77815e9i −0.310675 0.401091i
\(649\) 7.12515e7 0.0102315
\(650\) 5.00127e8 + 1.82031e8i 0.0714305 + 0.0259986i
\(651\) −1.86246e8 1.74041e8i −0.0264578 0.0247240i
\(652\) 2.46167e9 + 2.06558e9i 0.347827 + 0.291861i
\(653\) −1.91191e9 + 1.08430e10i −0.268703 + 1.52389i 0.489577 + 0.871960i \(0.337151\pi\)
−0.758280 + 0.651929i \(0.773960\pi\)
\(654\) −1.13902e9 2.24125e9i −0.159225 0.313306i
\(655\) −2.67747e9 + 2.24667e9i −0.372289 + 0.312388i
\(656\) −1.24331e9 2.15348e9i −0.171956 0.297836i
\(657\) 9.12962e9 6.13028e9i 1.25595 0.843338i
\(658\) −1.27622e8 + 2.21048e8i −0.0174637 + 0.0302480i
\(659\) −2.98677e8 1.69388e9i −0.0406539 0.230560i 0.957710 0.287734i \(-0.0929020\pi\)
−0.998364 + 0.0571744i \(0.981791\pi\)
\(660\) 5.86524e7 + 4.81848e8i 0.00794113 + 0.0652389i
\(661\) −1.11089e9 + 4.04331e8i −0.149612 + 0.0544543i −0.415741 0.909483i \(-0.636478\pi\)
0.266129 + 0.963938i \(0.414255\pi\)
\(662\) −1.13259e9 + 4.12229e8i −0.151729 + 0.0552250i
\(663\) −7.49033e8 + 5.63210e8i −0.0998167 + 0.0750539i
\(664\) −1.17255e8 6.64988e8i −0.0155433 0.0881506i
\(665\) −1.04355e8 + 1.80749e8i −0.0137606 + 0.0238341i
\(666\) 1.44670e9 + 1.50438e9i 0.189766 + 0.197332i
\(667\) 5.00407e9 + 8.66731e9i 0.652955 + 1.13095i
\(668\) −4.82714e9 + 4.05045e9i −0.626574 + 0.525758i
\(669\) −8.08844e9 4.32374e8i −1.04442 0.0558301i
\(670\) −6.92847e7 + 3.92933e8i −0.00889971 + 0.0504727i
\(671\) −8.88218e8 7.45303e8i −0.113499 0.0952367i
\(672\) 1.30992e8 5.64696e8i 0.0166515 0.0717831i
\(673\) 6.11709e9 + 2.22644e9i 0.773556 + 0.281551i 0.698483 0.715627i \(-0.253859\pi\)
0.0750732 + 0.997178i \(0.476081\pi\)
\(674\) −7.68462e8 −0.0966747
\(675\) 5.94586e9 3.54730e9i 0.744134 0.443951i
\(676\) 6.64376e9 0.827181
\(677\) −7.62549e9 2.77545e9i −0.944512 0.343774i −0.176566 0.984289i \(-0.556499\pi\)
−0.767946 + 0.640515i \(0.778721\pi\)
\(678\) 3.64654e9 1.11069e9i 0.449342 0.136864i
\(679\) −6.30382e8 5.28954e8i −0.0772787 0.0648445i
\(680\) −9.87171e7 + 5.59853e8i −0.0120396 + 0.0682798i
\(681\) −1.70048e9 + 2.61253e9i −0.206328 + 0.316991i
\(682\) −1.13492e8 + 9.52315e7i −0.0137000 + 0.0114957i
\(683\) −1.15474e8 2.00007e8i −0.0138679 0.0240199i 0.859008 0.511962i \(-0.171081\pi\)
−0.872876 + 0.487942i \(0.837748\pi\)
\(684\) 5.67739e9 + 6.08719e8i 0.678347 + 0.0727311i
\(685\) −1.99098e9 + 3.44848e9i −0.236674 + 0.409931i
\(686\) 7.88845e7 + 4.47376e8i 0.00932947 + 0.0529101i
\(687\) 1.03001e10 + 4.38485e9i 1.21197 + 0.515948i
\(688\) −7.88240e9 + 2.86896e9i −0.922781 + 0.335865i
\(689\) 2.48291e9 9.03704e8i 0.289197 0.105259i
\(690\) −7.50960e8 3.19690e8i −0.0870251 0.0370474i
\(691\) 9.83487e8 + 5.57763e9i 0.113395 + 0.643097i 0.987532 + 0.157417i \(0.0503168\pi\)
−0.874137 + 0.485680i \(0.838572\pi\)
\(692\) −9.68748e8 + 1.67792e9i −0.111132 + 0.192486i
\(693\) 1.02564e8 1.40549e8i 0.0117066 0.0160421i
\(694\) −1.45630e9 2.52238e9i −0.165383 0.286452i
\(695\) 3.69038e9 3.09660e9i 0.416989 0.349895i
\(696\) −3.26284e9 + 5.01286e9i −0.366829 + 0.563577i
\(697\) 2.50332e8 1.41970e9i 0.0280028 0.158812i
\(698\) −1.60175e9 1.34403e9i −0.178280 0.149594i
\(699\) 2.56671e9 7.81789e8i 0.284254 0.0865803i
\(700\) 7.07081e8 + 2.57356e8i 0.0779158 + 0.0283590i
\(701\) −2.15700e9 −0.236503 −0.118252 0.992984i \(-0.537729\pi\)
−0.118252 + 0.992984i \(0.537729\pi\)
\(702\) 5.07990e8 6.23310e8i 0.0554212 0.0680024i
\(703\) −7.03411e9 −0.763599
\(704\) 1.02414e9 + 3.72756e8i 0.110625 + 0.0402643i
\(705\) 9.93471e8 4.28277e9i 0.106781 0.460323i
\(706\) −4.01993e8 3.37312e8i −0.0429934 0.0360758i
\(707\) 1.92867e8 1.09380e9i 0.0205253 0.116405i
\(708\) 4.64878e8 + 2.48504e7i 0.0492292 + 0.00263159i
\(709\) 8.53023e9 7.15771e9i 0.898874 0.754245i −0.0710958 0.997469i \(-0.522650\pi\)
0.969970 + 0.243224i \(0.0782052\pi\)
\(710\) 5.81931e8 + 1.00793e9i 0.0610193 + 0.105688i
\(711\) 8.84499e8 3.06046e9i 0.0922899 0.319332i
\(712\) −4.50285e9 + 7.79917e9i −0.467528 + 0.809782i
\(713\) 5.83381e8 + 3.30852e9i 0.0602752 + 0.341838i
\(714\) 7.85234e7 5.90431e7i 0.00807338 0.00607051i
\(715\) −2.16485e8 + 7.87940e7i −0.0221491 + 0.00806161i
\(716\) 3.00402e9 1.09337e9i 0.305849 0.111320i
\(717\) −1.85241e9 1.52182e10i −0.187681 1.54186i
\(718\) −5.42324e8 3.07567e9i −0.0546793 0.310102i
\(719\) 5.85530e9 1.01417e10i 0.587487 1.01756i −0.407074 0.913395i \(-0.633451\pi\)
0.994560 0.104161i \(-0.0332158\pi\)
\(720\) 1.97527e8 + 2.91223e9i 0.0197225 + 0.290779i
\(721\) 5.81379e8 + 1.00698e9i 0.0577679 + 0.100057i
\(722\) −9.42345e8 + 7.90722e8i −0.0931816 + 0.0781886i
\(723\) −5.52365e8 1.08688e9i −0.0543554 0.106955i
\(724\) −2.81806e8 + 1.59820e9i −0.0275972 + 0.156512i
\(725\) −9.02748e9 7.57495e9i −0.879799 0.738239i
\(726\) 1.90538e9 + 1.78052e9i 0.184801 + 0.172691i
\(727\) −1.50149e9 5.46499e8i −0.144928 0.0527495i 0.268538 0.963269i \(-0.413460\pi\)
−0.413466 + 0.910520i \(0.635682\pi\)
\(728\) 1.81258e8 0.0174115
\(729\) −2.11063e9 1.02452e10i −0.201774 0.979432i
\(730\) 1.52643e9 0.145227
\(731\) −4.56976e9 1.66326e9i −0.432696 0.157488i
\(732\) −5.53521e9 5.17249e9i −0.521609 0.487429i
\(733\) −1.19038e10 9.98845e9i −1.11640 0.936772i −0.117985 0.993015i \(-0.537643\pi\)
−0.998417 + 0.0562431i \(0.982088\pi\)
\(734\) −1.02619e8 + 5.81982e8i −0.00957839 + 0.0543217i
\(735\) −1.76312e9 3.46928e9i −0.163786 0.322281i
\(736\) −5.85261e9 + 4.91092e9i −0.541099 + 0.454036i
\(737\) 5.60511e8 + 9.70834e8i 0.0515760 + 0.0893323i
\(738\) 8.37039e7 + 1.23409e9i 0.00766564 + 0.113018i
\(739\) 8.72867e9 1.51185e10i 0.795596 1.37801i −0.126864 0.991920i \(-0.540491\pi\)
0.922460 0.386093i \(-0.126176\pi\)
\(740\) −6.78450e8 3.84768e9i −0.0615470 0.349050i
\(741\) 3.27453e8 + 2.69013e9i 0.0295655 + 0.242890i
\(742\) −2.60291e8 + 9.47381e7i −0.0233908 + 0.00851356i
\(743\) 1.95892e10 7.12987e9i 1.75208 0.637706i 0.752306 0.658814i \(-0.228941\pi\)
0.999777 + 0.0211076i \(0.00671925\pi\)
\(744\) −1.60475e9 + 1.20664e9i −0.142857 + 0.107417i
\(745\) 7.41360e8 + 4.20446e9i 0.0656874 + 0.372532i
\(746\) −2.63614e9 + 4.56593e9i −0.232478 + 0.402664i
\(747\) 5.58071e8 1.93098e9i 0.0489855 0.169495i
\(748\) 3.85034e8 + 6.66899e8i 0.0336390 + 0.0582645i
\(749\) −8.25943e8 + 6.93048e8i −0.0718230 + 0.0602667i
\(750\) 2.06719e9 + 1.10504e8i 0.178923 + 0.00956450i
\(751\) 1.58622e8 8.99592e8i 0.0136655 0.0775007i −0.977212 0.212264i \(-0.931916\pi\)
0.990878 + 0.134763i \(0.0430274\pi\)
\(752\) −9.21615e9 7.73327e9i −0.790291 0.663133i
\(753\) −3.04036e9 + 1.31067e10i −0.259503 + 1.11870i
\(754\) −1.28609e9 4.68099e8i −0.109263 0.0397684i
\(755\) 7.77136e9 0.657178