Properties

Label 27.8.e.a.4.5
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 4.5
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.9790 - 5.08793i) q^{2} +(-44.6310 + 13.9670i) q^{3} +(71.4707 + 59.9711i) q^{4} +(-48.7897 + 276.700i) q^{5} +(694.958 + 31.8356i) q^{6} +(-1113.53 + 934.359i) q^{7} +(258.112 + 447.063i) q^{8} +(1796.85 - 1246.72i) q^{9} +O(q^{10})\) \(q+(-13.9790 - 5.08793i) q^{2} +(-44.6310 + 13.9670i) q^{3} +(71.4707 + 59.9711i) q^{4} +(-48.7897 + 276.700i) q^{5} +(694.958 + 31.8356i) q^{6} +(-1113.53 + 934.359i) q^{7} +(258.112 + 447.063i) q^{8} +(1796.85 - 1246.72i) q^{9} +(2089.86 - 3619.74i) q^{10} +(-907.590 - 5147.20i) q^{11} +(-4027.42 - 1678.34i) q^{12} +(-12245.3 + 4456.91i) q^{13} +(20319.9 - 7395.83i) q^{14} +(-1687.13 - 13030.8i) q^{15} +(-3407.26 - 19323.5i) q^{16} +(9922.78 - 17186.8i) q^{17} +(-31461.3 + 8285.59i) q^{18} +(16321.4 + 28269.5i) q^{19} +(-20081.0 + 16850.0i) q^{20} +(36647.6 - 57253.9i) q^{21} +(-13501.4 + 76570.3i) q^{22} +(-892.868 - 749.205i) q^{23} +(-17763.9 - 16347.8i) q^{24} +(-769.027 - 279.903i) q^{25} +193853. q^{26} +(-62782.3 + 80738.7i) q^{27} -135619. q^{28} +(114798. + 41783.0i) q^{29} +(-42715.7 + 190742. i) q^{30} +(-135317. - 113544. i) q^{31} +(-39212.6 + 222386. i) q^{32} +(112397. + 217048. i) q^{33} +(-226155. + 189767. i) q^{34} +(-204209. - 353700. i) q^{35} +(203189. + 18655.1i) q^{36} +(209464. - 362802. i) q^{37} +(-84323.2 - 478221. i) q^{38} +(484269. - 369946. i) q^{39} +(-136296. + 49607.6i) q^{40} +(215118. - 78296.4i) q^{41} +(-803599. + 613890. i) q^{42} +(-21996.2 - 124747. i) q^{43} +(243817. - 422303. i) q^{44} +(257299. + 558015. i) q^{45} +(8669.47 + 15016.0i) q^{46} +(-325194. + 272870. i) q^{47} +(421960. + 814838. i) q^{48} +(223906. - 1.26983e6i) q^{49} +(9326.08 + 7825.51i) q^{50} +(-202817. + 905653. i) q^{51} +(-1.14246e6 - 415823. i) q^{52} +651094. q^{53} +(1.28842e6 - 809212. i) q^{54} +1.46851e6 q^{55} +(-705132. - 256647. i) q^{56} +(-1.12328e6 - 1.03374e6i) q^{57} +(-1.39217e6 - 1.16817e6i) q^{58} +(31334.1 - 177705. i) q^{59} +(660893. - 1.03250e6i) q^{60} +(-1.87457e6 + 1.57295e6i) q^{61} +(1.31388e6 + 2.27571e6i) q^{62} +(-835955. + 3.06715e6i) q^{63} +(423850. - 734130. i) q^{64} +(-635786. - 3.60572e6i) q^{65} +(-466872. - 3.60598e6i) q^{66} +(634629. - 230986. i) q^{67} +(1.73990e6 - 633271. i) q^{68} +(50313.7 + 20967.1i) q^{69} +(1.05503e6 + 5.98335e6i) q^{70} +(99174.4 - 171775. i) q^{71} +(1.02115e6 + 481512. i) q^{72} +(1.58654e6 + 2.74797e6i) q^{73} +(-4.77400e6 + 4.00586e6i) q^{74} +(38231.8 + 1751.38i) q^{75} +(-528850. + 2.99926e6i) q^{76} +(5.81996e6 + 4.88352e6i) q^{77} +(-8.65183e6 + 2.70753e6i) q^{78} +(-1.88547e6 - 686256. i) q^{79} +5.51306e6 q^{80} +(1.67436e6 - 4.48032e6i) q^{81} -3.40549e6 q^{82} +(-5.41964e6 - 1.97259e6i) q^{83} +(6.05281e6 - 1.89418e6i) q^{84} +(4.27145e6 + 3.58417e6i) q^{85} +(-327218. + 1.85575e6i) q^{86} +(-5.70713e6 - 261440. i) q^{87} +(2.06686e6 - 1.73431e6i) q^{88} +(-3.84449e6 - 6.65885e6i) q^{89} +(-757636. - 9.10959e6i) q^{90} +(9.47106e6 - 1.64044e7i) q^{91} +(-18883.3 - 107093. i) q^{92} +(7.62519e6 + 3.17763e6i) q^{93} +(5.93421e6 - 2.15988e6i) q^{94} +(-8.61850e6 + 3.13688e6i) q^{95} +(-1.35595e6 - 1.04730e7i) q^{96} +(644396. + 3.65455e6i) q^{97} +(-9.59079e6 + 1.66117e7i) q^{98} +(-8.04791e6 - 8.11723e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −13.9790 5.08793i −1.23558 0.449713i −0.360073 0.932924i \(-0.617248\pi\)
−0.875504 + 0.483211i \(0.839471\pi\)
\(3\) −44.6310 + 13.9670i −0.954360 + 0.298660i
\(4\) 71.4707 + 59.9711i 0.558365 + 0.468524i
\(5\) −48.7897 + 276.700i −0.174555 + 0.989952i 0.764101 + 0.645097i \(0.223183\pi\)
−0.938656 + 0.344855i \(0.887928\pi\)
\(6\) 694.958 + 31.8356i 1.31350 + 0.0601705i
\(7\) −1113.53 + 934.359i −1.22704 + 1.02960i −0.228609 + 0.973518i \(0.573418\pi\)
−0.998426 + 0.0560867i \(0.982138\pi\)
\(8\) 258.112 + 447.063i 0.178235 + 0.308713i
\(9\) 1796.85 1246.72i 0.821604 0.570058i
\(10\) 2089.86 3619.74i 0.660871 1.14466i
\(11\) −907.590 5147.20i −0.205596 1.16599i −0.896499 0.443047i \(-0.853898\pi\)
0.690902 0.722948i \(-0.257213\pi\)
\(12\) −4027.42 1678.34i −0.672810 0.280379i
\(13\) −12245.3 + 4456.91i −1.54585 + 0.562642i −0.967439 0.253105i \(-0.918548\pi\)
−0.578409 + 0.815747i \(0.696326\pi\)
\(14\) 20319.9 7395.83i 1.97912 0.720342i
\(15\) −1687.13 13030.8i −0.129071 0.996903i
\(16\) −3407.26 19323.5i −0.207962 1.17941i
\(17\) 9922.78 17186.8i 0.489849 0.848443i −0.510083 0.860125i \(-0.670385\pi\)
0.999932 + 0.0116820i \(0.00371858\pi\)
\(18\) −31461.3 + 8285.59i −1.27152 + 0.334865i
\(19\) 16321.4 + 28269.5i 0.545909 + 0.945542i 0.998549 + 0.0538488i \(0.0171489\pi\)
−0.452640 + 0.891693i \(0.649518\pi\)
\(20\) −20081.0 + 16850.0i −0.561282 + 0.470971i
\(21\) 36647.6 57253.9i 0.863531 1.34908i
\(22\) −13501.4 + 76570.3i −0.270333 + 1.53314i
\(23\) −892.868 749.205i −0.0153017 0.0128397i 0.635105 0.772426i \(-0.280957\pi\)
−0.650406 + 0.759586i \(0.725401\pi\)
\(24\) −17763.9 16347.8i −0.262301 0.241391i
\(25\) −769.027 279.903i −0.00984355 0.00358276i
\(26\) 193853. 2.16304
\(27\) −62782.3 + 80738.7i −0.613852 + 0.789421i
\(28\) −135619. −1.16753
\(29\) 114798. + 41783.0i 0.874060 + 0.318132i 0.739810 0.672816i \(-0.234915\pi\)
0.134250 + 0.990948i \(0.457138\pi\)
\(30\) −42715.7 + 190742.i −0.288844 + 1.28980i
\(31\) −135317. 113544.i −0.815804 0.684541i 0.136182 0.990684i \(-0.456517\pi\)
−0.951985 + 0.306143i \(0.900961\pi\)
\(32\) −39212.6 + 222386.i −0.211544 + 1.19973i
\(33\) 112397. + 217048.i 0.544449 + 1.05137i
\(34\) −226155. + 189767.i −0.986803 + 0.828026i
\(35\) −204209. 353700.i −0.805074 1.39443i
\(36\) 203189. + 18655.1i 0.725841 + 0.0666406i
\(37\) 209464. 362802.i 0.679834 1.17751i −0.295196 0.955437i \(-0.595385\pi\)
0.975031 0.222071i \(-0.0712817\pi\)
\(38\) −84323.2 478221.i −0.249290 1.41379i
\(39\) 484269. 369946.i 1.30726 0.998646i
\(40\) −136296. + 49607.6i −0.336723 + 0.122557i
\(41\) 215118. 78296.4i 0.487453 0.177418i −0.0865894 0.996244i \(-0.527597\pi\)
0.574042 + 0.818826i \(0.305375\pi\)
\(42\) −803599. + 613890.i −1.67366 + 1.27855i
\(43\) −21996.2 124747.i −0.0421899 0.239271i 0.956419 0.291998i \(-0.0943199\pi\)
−0.998609 + 0.0527265i \(0.983209\pi\)
\(44\) 243817. 422303.i 0.431499 0.747378i
\(45\) 257299. + 558015.i 0.420915 + 0.912856i
\(46\) 8669.47 + 15016.0i 0.0131323 + 0.0227458i
\(47\) −325194. + 272870.i −0.456877 + 0.383366i −0.841981 0.539508i \(-0.818610\pi\)
0.385103 + 0.922874i \(0.374166\pi\)
\(48\) 421960. + 814838.i 0.550715 + 1.06347i
\(49\) 223906. 1.26983e6i 0.271881 1.54192i
\(50\) 9326.08 + 7825.51i 0.0105512 + 0.00885355i
\(51\) −202817. + 905653.i −0.214096 + 0.956018i
\(52\) −1.14246e6 415823.i −1.12676 0.410107i
\(53\) 651094. 0.600728 0.300364 0.953825i \(-0.402892\pi\)
0.300364 + 0.953825i \(0.402892\pi\)
\(54\) 1.28842e6 809212.i 1.11348 0.699333i
\(55\) 1.46851e6 1.19017
\(56\) −705132. 256647.i −0.536553 0.195289i
\(57\) −1.12328e6 1.03374e6i −0.803389 0.739346i
\(58\) −1.39217e6 1.16817e6i −0.936901 0.786153i
\(59\) 31334.1 177705.i 0.0198626 0.112646i −0.973265 0.229687i \(-0.926230\pi\)
0.993127 + 0.117041i \(0.0373408\pi\)
\(60\) 660893. 1.03250e6i 0.395004 0.617109i
\(61\) −1.87457e6 + 1.57295e6i −1.05742 + 0.887281i −0.993854 0.110697i \(-0.964692\pi\)
−0.0635661 + 0.997978i \(0.520247\pi\)
\(62\) 1.31388e6 + 2.27571e6i 0.700142 + 1.21268i
\(63\) −835955. + 3.06715e6i −0.421203 + 1.54541i
\(64\) 423850. 734130.i 0.202107 0.350060i
\(65\) −635786. 3.60572e6i −0.287153 1.62853i
\(66\) −466872. 3.60598e6i −0.199892 1.54390i
\(67\) 634629. 230986.i 0.257785 0.0938262i −0.209895 0.977724i \(-0.567312\pi\)
0.467680 + 0.883898i \(0.345090\pi\)
\(68\) 1.73990e6 633271.i 0.671031 0.244235i
\(69\) 50313.7 + 20967.1i 0.0184380 + 0.00768364i
\(70\) 1.05503e6 + 5.98335e6i 0.367638 + 2.08498i
\(71\) 99174.4 171775.i 0.0328848 0.0569582i −0.849115 0.528209i \(-0.822864\pi\)
0.881999 + 0.471250i \(0.156197\pi\)
\(72\) 1.02115e6 + 481512.i 0.322423 + 0.152035i
\(73\) 1.58654e6 + 2.74797e6i 0.477333 + 0.826765i 0.999662 0.0259789i \(-0.00827028\pi\)
−0.522330 + 0.852744i \(0.674937\pi\)
\(74\) −4.77400e6 + 4.00586e6i −1.36953 + 1.14917i
\(75\) 38231.8 + 1751.38i 0.0104643 + 0.000479364i
\(76\) −528850. + 2.99926e6i −0.138193 + 0.783729i
\(77\) 5.81996e6 + 4.88352e6i 1.45279 + 1.21903i
\(78\) −8.65183e6 + 2.70753e6i −2.06432 + 0.646014i
\(79\) −1.88547e6 686256.i −0.430254 0.156600i 0.117810 0.993036i \(-0.462413\pi\)
−0.548064 + 0.836436i \(0.684635\pi\)
\(80\) 5.51306e6 1.20386
\(81\) 1.67436e6 4.48032e6i 0.350067 0.936725i
\(82\) −3.40549e6 −0.682073
\(83\) −5.41964e6 1.97259e6i −1.04039 0.378672i −0.235363 0.971907i \(-0.575628\pi\)
−0.805029 + 0.593236i \(0.797850\pi\)
\(84\) 6.05281e6 1.89418e6i 1.11424 0.348694i
\(85\) 4.27145e6 + 3.58417e6i 0.754413 + 0.633027i
\(86\) −327218. + 1.85575e6i −0.0554745 + 0.314611i
\(87\) −5.70713e6 261440.i −0.929181 0.0425652i
\(88\) 2.06686e6 1.73431e6i 0.323313 0.271292i
\(89\) −3.84449e6 6.65885e6i −0.578061 1.00123i −0.995702 0.0926189i \(-0.970476\pi\)
0.417641 0.908612i \(-0.362857\pi\)
\(90\) −757636. 9.10959e6i −0.109550 1.31720i
\(91\) 9.47106e6 1.64044e7i 1.31751 2.28199i
\(92\) −18883.3 107093.i −0.00252825 0.0143384i
\(93\) 7.62519e6 + 3.17763e6i 0.983015 + 0.409650i
\(94\) 5.93421e6 2.15988e6i 0.736912 0.268214i
\(95\) −8.61850e6 + 3.13688e6i −1.03133 + 0.375374i
\(96\) −1.35595e6 1.04730e7i −0.156421 1.20815i
\(97\) 644396. + 3.65455e6i 0.0716889 + 0.406568i 0.999443 + 0.0333755i \(0.0106257\pi\)
−0.927754 + 0.373192i \(0.878263\pi\)
\(98\) −9.59079e6 + 1.66117e7i −1.02935 + 1.78289i
\(99\) −8.04791e6 8.11723e6i −0.833604 0.840784i
\(100\) −38176.8 66124.2i −0.00381768 0.00661242i
\(101\) 2.32678e6 1.95240e6i 0.224714 0.188557i −0.523479 0.852039i \(-0.675366\pi\)
0.748193 + 0.663481i \(0.230922\pi\)
\(102\) 7.44306e6 1.16282e7i 0.694466 1.08495i
\(103\) 1.18989e6 6.74820e6i 0.107294 0.608496i −0.882985 0.469401i \(-0.844470\pi\)
0.990279 0.139094i \(-0.0444191\pi\)
\(104\) −5.15318e6 4.32403e6i −0.449219 0.376940i
\(105\) 1.40541e7 + 1.29338e7i 1.18479 + 1.09034i
\(106\) −9.10162e6 3.31272e6i −0.742246 0.270156i
\(107\) 1.45630e6 0.114923 0.0574615 0.998348i \(-0.481699\pi\)
0.0574615 + 0.998348i \(0.481699\pi\)
\(108\) −9.32908e6 + 2.00534e6i −0.712616 + 0.153181i
\(109\) 2.55020e6 0.188617 0.0943086 0.995543i \(-0.469936\pi\)
0.0943086 + 0.995543i \(0.469936\pi\)
\(110\) −2.05283e7 7.47168e6i −1.47054 0.535234i
\(111\) −4.28134e6 + 1.91178e7i −0.297132 + 1.32680i
\(112\) 2.18492e7 + 1.83336e7i 1.46951 + 1.23306i
\(113\) 3.75329e6 2.12860e7i 0.244702 1.38777i −0.576481 0.817110i \(-0.695575\pi\)
0.821183 0.570664i \(-0.193314\pi\)
\(114\) 1.04427e7 + 2.01657e7i 0.660156 + 1.27481i
\(115\) 250868. 210503.i 0.0153816 0.0129067i
\(116\) 5.69892e6 + 9.87082e6i 0.338992 + 0.587152i
\(117\) −1.64464e7 + 2.32748e7i −0.949336 + 1.34349i
\(118\) −1.34217e6 + 2.32470e6i −0.0752003 + 0.130251i
\(119\) 5.00933e6 + 2.84093e7i 0.272499 + 1.54542i
\(120\) 5.39014e6 4.11767e6i 0.284752 0.217529i
\(121\) −7.35799e6 + 2.67809e6i −0.377581 + 0.137428i
\(122\) 3.42076e7 1.24506e7i 1.70555 0.620768i
\(123\) −8.50735e6 + 6.49898e6i −0.412217 + 0.314903i
\(124\) −2.86182e6 1.62302e7i −0.134793 0.764447i
\(125\) −1.08604e7 + 1.88107e7i −0.497347 + 0.861430i
\(126\) 2.72912e7 3.86223e7i 1.21542 1.72005i
\(127\) −1.26383e7 2.18901e7i −0.547488 0.948276i −0.998446 0.0557312i \(-0.982251\pi\)
0.450958 0.892545i \(-0.351082\pi\)
\(128\) 1.24819e7 1.04736e7i 0.526074 0.441429i
\(129\) 2.72405e6 + 5.26036e6i 0.111725 + 0.215750i
\(130\) −9.45801e6 + 5.36390e7i −0.377570 + 2.14131i
\(131\) −1.79294e7 1.50446e7i −0.696815 0.584697i 0.224051 0.974577i \(-0.428072\pi\)
−0.920865 + 0.389881i \(0.872516\pi\)
\(132\) −4.98350e6 + 2.22532e7i −0.188593 + 0.842138i
\(133\) −4.45882e7 1.62288e7i −1.64338 0.598143i
\(134\) −1.00467e7 −0.360709
\(135\) −1.92773e7 2.13111e7i −0.674338 0.745482i
\(136\) 1.02448e7 0.349233
\(137\) 1.17515e7 + 4.27721e6i 0.390456 + 0.142115i 0.529786 0.848132i \(-0.322272\pi\)
−0.139329 + 0.990246i \(0.544495\pi\)
\(138\) −596654. 549091.i −0.0193262 0.0177856i
\(139\) −3.67752e6 3.08581e6i −0.116146 0.0974579i 0.582865 0.812569i \(-0.301932\pi\)
−0.699011 + 0.715111i \(0.746376\pi\)
\(140\) 6.61681e6 3.75258e7i 0.203798 1.15580i
\(141\) 1.07026e7 1.67204e7i 0.321529 0.502320i
\(142\) −2.26033e6 + 1.89665e6i −0.0662466 + 0.0555875i
\(143\) 3.40543e7 + 5.89838e7i 0.973859 + 1.68677i
\(144\) −3.02133e7 3.04735e7i −0.843197 0.850460i
\(145\) −1.71623e7 + 2.97260e7i −0.467507 + 0.809746i
\(146\) −8.19673e6 4.64860e7i −0.217975 1.23619i
\(147\) 7.74257e6 + 5.98012e7i 0.201036 + 1.55274i
\(148\) 3.67282e7 1.33680e7i 0.931286 0.338960i
\(149\) 6.23558e7 2.26956e7i 1.54428 0.562070i 0.577209 0.816596i \(-0.304142\pi\)
0.967066 + 0.254526i \(0.0819195\pi\)
\(150\) −525530. 219003.i −0.0127139 0.00529823i
\(151\) 1.12358e7 + 6.37212e7i 0.265573 + 1.50614i 0.767399 + 0.641170i \(0.221551\pi\)
−0.501826 + 0.864969i \(0.667338\pi\)
\(152\) −8.42551e6 + 1.45934e7i −0.194600 + 0.337058i
\(153\) −3.59730e6 4.32529e7i −0.0812002 0.976327i
\(154\) −5.65100e7 9.78781e7i −1.24682 2.15955i
\(155\) 3.80198e7 3.19024e7i 0.820066 0.688117i
\(156\) 5.67971e7 + 2.60184e6i 1.19782 + 0.0548712i
\(157\) 3.29216e6 1.86708e7i 0.0678941 0.385047i −0.931859 0.362821i \(-0.881814\pi\)
0.999753 0.0222258i \(-0.00707527\pi\)
\(158\) 2.28653e7 + 1.91863e7i 0.461188 + 0.386982i
\(159\) −2.90590e7 + 9.09380e6i −0.573311 + 0.179414i
\(160\) −5.96209e7 2.17002e7i −1.15074 0.418837i
\(161\) 1.69426e6 0.0319955
\(162\) −4.62014e7 + 5.41113e7i −0.853793 + 0.999966i
\(163\) −8.36502e7 −1.51290 −0.756450 0.654051i \(-0.773068\pi\)
−0.756450 + 0.654051i \(0.773068\pi\)
\(164\) 2.00701e7 + 7.30493e6i 0.355301 + 0.129319i
\(165\) −6.55411e7 + 2.05106e7i −1.13585 + 0.355456i
\(166\) 6.57245e7 + 5.51494e7i 1.11519 + 0.935756i
\(167\) 7.92334e6 4.49355e7i 0.131644 0.746590i −0.845494 0.533984i \(-0.820694\pi\)
0.977138 0.212605i \(-0.0681948\pi\)
\(168\) 3.50553e7 + 1.60586e6i 0.570389 + 0.0261292i
\(169\) 8.20144e7 6.88183e7i 1.30703 1.09673i
\(170\) −4.14744e7 7.18358e7i −0.647454 1.12142i
\(171\) 6.45712e7 + 3.04479e7i 0.987535 + 0.465661i
\(172\) 5.90912e6 1.02349e7i 0.0885468 0.153368i
\(173\) −8.80285e6 4.99234e7i −0.129259 0.733066i −0.978686 0.205360i \(-0.934163\pi\)
0.849427 0.527706i \(-0.176948\pi\)
\(174\) 7.84495e7 + 3.26921e7i 1.12893 + 0.470458i
\(175\) 1.11786e6 406868.i 0.0157672 0.00573879i
\(176\) −9.63696e7 + 3.50757e7i −1.33243 + 0.484966i
\(177\) 1.08352e6 + 8.36877e6i 0.0146869 + 0.113437i
\(178\) 1.98622e7 + 1.12644e8i 0.263972 + 1.49706i
\(179\) 3.53574e7 6.12409e7i 0.460782 0.798098i −0.538218 0.842805i \(-0.680902\pi\)
0.999000 + 0.0447080i \(0.0142357\pi\)
\(180\) −1.50754e7 + 5.53123e7i −0.192670 + 0.706916i
\(181\) 1.97529e7 + 3.42129e7i 0.247602 + 0.428860i 0.962860 0.270001i \(-0.0870240\pi\)
−0.715258 + 0.698861i \(0.753691\pi\)
\(182\) −2.15860e8 + 1.81128e8i −2.65413 + 2.22708i
\(183\) 6.16946e7 9.63845e7i 0.744164 1.16259i
\(184\) 104482. 592548.i 0.00123646 0.00701231i
\(185\) 9.01677e7 + 7.56597e7i 1.04701 + 0.878544i
\(186\) −9.04247e7 8.32164e7i −1.03037 0.948229i
\(187\) −9.74695e7 3.54760e7i −1.08999 0.396725i
\(188\) −3.96061e7 −0.434720
\(189\) −5.52929e6 1.48566e8i −0.0595735 1.60067i
\(190\) 1.36438e8 1.44310
\(191\) −6.48347e7 2.35979e7i −0.673272 0.245051i −0.0173159 0.999850i \(-0.505512\pi\)
−0.655956 + 0.754799i \(0.727734\pi\)
\(192\) −8.66329e6 + 3.86848e7i −0.0883341 + 0.394445i
\(193\) −1.22446e8 1.02745e8i −1.22601 1.02875i −0.998488 0.0549746i \(-0.982492\pi\)
−0.227525 0.973772i \(-0.573063\pi\)
\(194\) 9.58610e6 5.43655e7i 0.0942618 0.534585i
\(195\) 7.87366e7 + 1.52047e8i 0.760424 + 1.46844i
\(196\) 9.21560e7 7.73281e7i 0.874233 0.733569i
\(197\) 1.06329e8 + 1.84167e8i 0.990878 + 1.71625i 0.612144 + 0.790746i \(0.290307\pi\)
0.378735 + 0.925505i \(0.376359\pi\)
\(198\) 7.12015e7 + 1.54418e8i 0.651870 + 1.41374i
\(199\) 9.66545e7 1.67411e8i 0.869434 1.50590i 0.00685748 0.999976i \(-0.497817\pi\)
0.862576 0.505927i \(-0.168849\pi\)
\(200\) −73360.9 416050.i −0.000648425 0.00367740i
\(201\) −2.50979e7 + 1.91730e7i −0.217998 + 0.166534i
\(202\) −4.24596e7 + 1.54540e7i −0.362448 + 0.131920i
\(203\) −1.66871e8 + 6.07360e7i −1.40005 + 0.509577i
\(204\) −6.88084e7 + 5.25645e7i −0.567461 + 0.433498i
\(205\) 1.11691e7 + 6.33431e7i 0.0905482 + 0.513524i
\(206\) −5.09678e7 + 8.82787e7i −0.406219 + 0.703592i
\(207\) −2.53840e6 233054.i −0.0198913 0.00182625i
\(208\) 1.27846e8 + 2.21436e8i 0.985066 + 1.70618i
\(209\) 1.30696e8 1.09667e8i 0.990260 0.830927i
\(210\) −1.30656e8 2.52307e8i −0.973559 1.88002i
\(211\) −5.41896e6 + 3.07324e7i −0.0397125 + 0.225221i −0.998204 0.0598988i \(-0.980922\pi\)
0.958492 + 0.285120i \(0.0920333\pi\)
\(212\) 4.65342e7 + 3.90468e7i 0.335426 + 0.281456i
\(213\) −2.02708e6 + 9.05166e6i −0.0143728 + 0.0641800i
\(214\) −2.03575e7 7.40954e6i −0.141996 0.0516824i
\(215\) 3.55907e7 0.244231
\(216\) −5.23002e7 7.22800e6i −0.353114 0.0488012i
\(217\) 2.56770e8 1.70583
\(218\) −3.56491e7 1.29752e7i −0.233051 0.0848237i
\(219\) −1.09190e8 1.00485e8i −0.702469 0.646471i
\(220\) 1.04956e8 + 8.80682e7i 0.664548 + 0.557622i
\(221\) −4.49072e7 + 2.54682e8i −0.279862 + 1.58717i
\(222\) 1.57119e8 2.45464e8i 0.963811 1.50575i
\(223\) −1.41637e8 + 1.18848e8i −0.855285 + 0.717670i −0.960947 0.276732i \(-0.910748\pi\)
0.105662 + 0.994402i \(0.466304\pi\)
\(224\) −1.64124e8 2.84271e8i −0.975671 1.68991i
\(225\) −1.73079e6 + 455816.i −0.0101299 + 0.00266779i
\(226\) −1.60769e8 + 2.78459e8i −0.926449 + 1.60466i
\(227\) −1.48267e6 8.40864e6i −0.00841306 0.0477128i 0.980312 0.197454i \(-0.0632672\pi\)
−0.988725 + 0.149741i \(0.952156\pi\)
\(228\) −1.82874e7 1.41246e8i −0.102183 0.789232i
\(229\) 4.96069e7 1.80554e7i 0.272972 0.0993536i −0.201907 0.979405i \(-0.564714\pi\)
0.474879 + 0.880051i \(0.342492\pi\)
\(230\) −4.57790e6 + 1.66622e6i −0.0248095 + 0.00902994i
\(231\) −3.27958e8 1.36669e8i −1.75056 0.729507i
\(232\) 1.09511e7 + 6.21067e7i 0.0575770 + 0.326536i
\(233\) 1.86820e8 3.23582e8i 0.967559 1.67586i 0.264983 0.964253i \(-0.414634\pi\)
0.702576 0.711609i \(-0.252033\pi\)
\(234\) 3.48324e8 2.41679e8i 1.77716 1.23306i
\(235\) −5.96370e7 1.03294e8i −0.299763 0.519205i
\(236\) 1.28966e7 1.08215e7i 0.0638680 0.0535916i
\(237\) 9.37354e7 + 4.29396e6i 0.457388 + 0.0209527i
\(238\) 7.45194e7 4.22620e8i 0.358302 2.03203i
\(239\) −9.83600e7 8.25339e7i −0.466043 0.391057i 0.379306 0.925271i \(-0.376163\pi\)
−0.845349 + 0.534215i \(0.820607\pi\)
\(240\) −2.46053e8 + 7.70006e7i −1.14892 + 0.359546i
\(241\) 1.54190e7 + 5.61206e6i 0.0709572 + 0.0258263i 0.377255 0.926109i \(-0.376868\pi\)
−0.306298 + 0.951936i \(0.599090\pi\)
\(242\) 1.16483e8 0.528335
\(243\) −1.21518e7 + 2.23347e8i −0.0543275 + 0.998523i
\(244\) −2.28309e8 −1.00614
\(245\) 3.40439e8 + 1.23910e8i 1.47896 + 0.538299i
\(246\) 1.51990e8 4.75643e7i 0.650943 0.203708i
\(247\) −3.25855e8 2.73425e8i −1.37589 1.15451i
\(248\) 1.58346e7 8.98024e7i 0.0659213 0.373858i
\(249\) 2.69435e8 + 1.23427e7i 1.10600 + 0.0506653i
\(250\) 2.47524e8 2.07697e8i 1.00191 0.840700i
\(251\) 3.82624e7 + 6.62724e7i 0.152726 + 0.264530i 0.932229 0.361869i \(-0.117861\pi\)
−0.779502 + 0.626399i \(0.784528\pi\)
\(252\) −2.43687e8 + 1.69079e8i −0.959246 + 0.665559i
\(253\) −3.04595e6 + 5.27574e6i −0.0118250 + 0.0204815i
\(254\) 6.52945e7 + 3.70304e8i 0.250011 + 1.41788i
\(255\) −2.40699e8 1.00306e8i −0.909041 0.378823i
\(256\) −3.29735e8 + 1.20014e8i −1.22836 + 0.447086i
\(257\) −4.35244e8 + 1.58416e8i −1.59944 + 0.582147i −0.979312 0.202357i \(-0.935140\pi\)
−0.620124 + 0.784504i \(0.712918\pi\)
\(258\) −1.13151e7 8.73941e7i −0.0410193 0.316820i
\(259\) 1.05744e8 + 5.99704e8i 0.378187 + 2.14480i
\(260\) 1.70799e8 2.95832e8i 0.602668 1.04385i
\(261\) 2.58366e8 6.80428e7i 0.899485 0.236887i
\(262\) 1.74089e8 + 3.01531e8i 0.598022 + 1.03581i
\(263\) 8.43471e7 7.07756e7i 0.285907 0.239905i −0.488543 0.872540i \(-0.662471\pi\)
0.774450 + 0.632636i \(0.218027\pi\)
\(264\) −6.80232e7 + 1.06272e8i −0.227533 + 0.355470i
\(265\) −3.17667e7 + 1.80158e8i −0.104860 + 0.594692i
\(266\) 5.40726e8 + 4.53723e8i 1.76154 + 1.47810i
\(267\) 2.64587e8 + 2.43495e8i 0.850706 + 0.782891i
\(268\) 5.92099e7 + 2.15506e7i 0.187898 + 0.0683893i
\(269\) −4.69317e8 −1.47005 −0.735027 0.678038i \(-0.762830\pi\)
−0.735027 + 0.678038i \(0.762830\pi\)
\(270\) 1.61047e8 + 3.95988e8i 0.497944 + 1.22436i
\(271\) −2.09491e8 −0.639401 −0.319700 0.947519i \(-0.603582\pi\)
−0.319700 + 0.947519i \(0.603582\pi\)
\(272\) −3.65918e8 1.33183e8i −1.10254 0.401290i
\(273\) −1.93584e8 + 8.64425e8i −0.575838 + 2.57133i
\(274\) −1.42512e8 1.19582e8i −0.418528 0.351187i
\(275\) −742755. + 4.21237e6i −0.00215368 + 0.0122141i
\(276\) 2.33854e6 + 4.51590e6i 0.00669518 + 0.0129289i
\(277\) 2.62394e8 2.20175e8i 0.741779 0.622426i −0.191536 0.981486i \(-0.561347\pi\)
0.933315 + 0.359059i \(0.116902\pi\)
\(278\) 3.57076e7 + 6.18474e7i 0.0996790 + 0.172649i
\(279\) −3.84701e8 3.53200e7i −1.06050 0.0973658i
\(280\) 1.05417e8 1.82588e8i 0.286985 0.497073i
\(281\) −5.75090e7 3.26150e8i −0.154619 0.876889i −0.959133 0.282955i \(-0.908685\pi\)
0.804514 0.593934i \(-0.202426\pi\)
\(282\) −2.34683e8 + 1.79280e8i −0.623174 + 0.476059i
\(283\) 3.85415e8 1.40279e8i 1.01082 0.367910i 0.217075 0.976155i \(-0.430348\pi\)
0.793749 + 0.608245i \(0.208126\pi\)
\(284\) 1.73896e7 6.32930e6i 0.0450480 0.0163961i
\(285\) 3.40839e8 2.60376e8i 0.872153 0.666260i
\(286\) −1.75939e8 9.97798e8i −0.444714 2.52210i
\(287\) −1.66382e8 + 2.88182e8i −0.415451 + 0.719582i
\(288\) 2.06793e8 + 4.48480e8i 0.510108 + 1.10629i
\(289\) 8.24614e6 + 1.42827e7i 0.0200959 + 0.0348072i
\(290\) 3.91155e8 3.28218e8i 0.941795 0.790260i
\(291\) −7.98030e7 1.54106e8i −0.189843 0.366601i
\(292\) −5.14074e7 + 2.91546e8i −0.120833 + 0.685278i
\(293\) −3.29074e8 2.76126e8i −0.764288 0.641313i 0.174951 0.984577i \(-0.444023\pi\)
−0.939239 + 0.343264i \(0.888468\pi\)
\(294\) 1.96031e8 8.75352e8i 0.449893 2.00894i
\(295\) 4.76421e7 + 1.73403e7i 0.108047 + 0.0393260i
\(296\) 2.16261e8 0.484682
\(297\) 4.72559e8 + 2.49875e8i 1.04667 + 0.553446i
\(298\) −9.87143e8 −2.16084
\(299\) 1.42726e7 + 5.19479e6i 0.0308782 + 0.0112388i
\(300\) 2.62742e6 + 2.41798e6i 0.00561831 + 0.00517044i
\(301\) 1.41052e8 + 1.18357e8i 0.298123 + 0.250155i
\(302\) 1.67145e8 9.47924e8i 0.349195 1.98038i
\(303\) −7.65773e7 + 1.19635e8i −0.158143 + 0.247065i
\(304\) 4.90655e8 4.11708e8i 1.00166 0.840489i
\(305\) −3.43776e8 5.95438e8i −0.693788 1.20168i
\(306\) −1.69781e8 + 6.22934e8i −0.338738 + 1.24284i
\(307\) −1.18005e8 + 2.04391e8i −0.232764 + 0.403159i −0.958621 0.284687i \(-0.908110\pi\)
0.725856 + 0.687846i \(0.241444\pi\)
\(308\) 1.23086e8 + 6.98058e8i 0.240040 + 1.36133i
\(309\) 4.11458e7 + 3.17798e8i 0.0793362 + 0.612768i
\(310\) −6.93794e8 + 2.52520e8i −1.32271 + 0.481427i
\(311\) −2.11061e8 + 7.68201e7i −0.397876 + 0.144815i −0.533206 0.845986i \(-0.679013\pi\)
0.135330 + 0.990801i \(0.456791\pi\)
\(312\) 2.90385e8 + 1.21011e8i 0.541294 + 0.225572i
\(313\) −5.05690e7 2.86791e8i −0.0932136 0.528641i −0.995280 0.0970436i \(-0.969061\pi\)
0.902067 0.431597i \(-0.142050\pi\)
\(314\) −1.41017e8 + 2.44248e8i −0.257049 + 0.445222i
\(315\) −8.07896e8 3.80954e8i −1.45636 0.686730i
\(316\) −9.36006e7 1.62121e8i −0.166868 0.289024i
\(317\) 1.81766e8 1.52519e8i 0.320483 0.268917i −0.468326 0.883556i \(-0.655143\pi\)
0.788809 + 0.614639i \(0.210698\pi\)
\(318\) 4.52483e8 + 2.07280e7i 0.789055 + 0.0361462i
\(319\) 1.10876e8 6.28810e8i 0.191237 1.08456i
\(320\) 1.82454e8 + 1.53097e8i 0.311264 + 0.261182i
\(321\) −6.49960e7 + 2.03401e7i −0.109678 + 0.0343229i
\(322\) −2.36840e7 8.62026e6i −0.0395329 0.0143888i
\(323\) 6.47815e8 1.06965
\(324\) 3.88358e8 2.19799e8i 0.634343 0.359020i
\(325\) 1.06644e7 0.0172324
\(326\) 1.16934e9 + 4.25606e8i 1.86931 + 0.680372i
\(327\) −1.13818e8 + 3.56185e7i −0.180009 + 0.0563324i
\(328\) 9.05279e7 + 7.59620e7i 0.141652 + 0.118861i
\(329\) 1.07153e8 6.07695e8i 0.165890 0.940806i
\(330\) 1.02055e9 + 4.67510e7i 1.56328 + 0.0716130i
\(331\) −2.05567e8 + 1.72491e8i −0.311570 + 0.261438i −0.785141 0.619318i \(-0.787409\pi\)
0.473571 + 0.880756i \(0.342965\pi\)
\(332\) −2.69047e8 4.66004e8i −0.403502 0.698886i
\(333\) −7.59369e7 9.13043e8i −0.112693 1.35499i
\(334\) −3.39389e8 + 5.87838e8i −0.498408 + 0.863267i
\(335\) 3.29505e7 + 1.86872e8i 0.0478856 + 0.271573i
\(336\) −1.23121e9 5.13081e8i −1.77070 0.737902i
\(337\) −4.05987e7 + 1.47767e7i −0.0577840 + 0.0210317i −0.370750 0.928733i \(-0.620899\pi\)
0.312966 + 0.949764i \(0.398677\pi\)
\(338\) −1.49662e9 + 5.44725e8i −2.10816 + 0.767306i
\(339\) 1.29787e8 + 1.00244e9i 0.180939 + 1.39752i
\(340\) 9.03370e7 + 5.12327e8i 0.124649 + 0.706921i
\(341\) −4.61623e8 + 7.99554e8i −0.630445 + 1.09196i
\(342\) −7.47722e8 7.54163e8i −1.01076 1.01947i
\(343\) 3.38603e8 + 5.86477e8i 0.453065 + 0.784732i
\(344\) 5.00923e7 4.20324e7i 0.0663462 0.0556711i
\(345\) −8.25640e6 + 1.28988e7i −0.0108249 + 0.0169115i
\(346\) −1.30952e8 + 7.42666e8i −0.169960 + 0.963890i
\(347\) 5.77414e8 + 4.84508e8i 0.741880 + 0.622512i 0.933342 0.358988i \(-0.116878\pi\)
−0.191462 + 0.981500i \(0.561323\pi\)
\(348\) −3.92214e8 3.60948e8i −0.498879 0.459110i
\(349\) 1.09453e9 + 3.98378e8i 1.37829 + 0.501656i 0.921659 0.388001i \(-0.126834\pi\)
0.456630 + 0.889657i \(0.349056\pi\)
\(350\) −1.76967e7 −0.0220624
\(351\) 4.08940e8 1.26848e9i 0.504760 1.56570i
\(352\) 1.18025e9 1.44237
\(353\) 9.91085e8 + 3.60726e8i 1.19922 + 0.436481i 0.862953 0.505285i \(-0.168613\pi\)
0.336269 + 0.941766i \(0.390835\pi\)
\(354\) 2.74332e7 1.22500e8i 0.0328674 0.146765i
\(355\) 4.26915e7 + 3.58224e7i 0.0506457 + 0.0424968i
\(356\) 1.24570e8 7.06471e8i 0.146332 0.829888i
\(357\) −6.20363e8 1.19797e9i −0.721618 1.39350i
\(358\) −8.05850e8 + 6.76188e8i −0.928247 + 0.778892i
\(359\) −1.38517e8 2.39918e8i −0.158005 0.273673i 0.776144 0.630556i \(-0.217173\pi\)
−0.934149 + 0.356882i \(0.883840\pi\)
\(360\) −1.83056e8 + 2.59060e8i −0.206788 + 0.292645i
\(361\) −8.58414e7 + 1.48682e8i −0.0960332 + 0.166334i
\(362\) −1.02051e8 5.78763e8i −0.113068 0.641240i
\(363\) 2.90990e8 2.22295e8i 0.319304 0.243925i
\(364\) 1.66069e9 6.04442e8i 1.80482 0.656901i
\(365\) −8.37770e8 + 3.04923e8i −0.901779 + 0.328221i
\(366\) −1.35282e9 + 1.03346e9i −1.44231 + 1.10182i
\(367\) −8.94979e7 5.07568e8i −0.0945108 0.535998i −0.994896 0.100904i \(-0.967826\pi\)
0.900385 0.435093i \(-0.143285\pi\)
\(368\) −1.14350e7 + 1.98061e7i −0.0119611 + 0.0207172i
\(369\) 2.88920e8 4.08878e8i 0.299354 0.423644i
\(370\) −8.75500e8 1.51641e9i −0.898566 1.55636i
\(371\) −7.25010e8 + 6.08355e8i −0.737115 + 0.618513i
\(372\) 3.54412e8 + 6.84398e8i 0.356951 + 0.689300i
\(373\) −1.53209e8 + 8.68892e8i −0.152863 + 0.866931i 0.807850 + 0.589388i \(0.200631\pi\)
−0.960713 + 0.277543i \(0.910480\pi\)
\(374\) 1.18202e9 + 9.91835e8i 1.16836 + 0.980368i
\(375\) 2.21981e8 9.91227e8i 0.217373 0.970652i
\(376\) −2.05927e8 7.49512e7i −0.199781 0.0727145i
\(377\) −1.59196e9 −1.53016
\(378\) −6.78598e8 + 2.10493e9i −0.646236 + 2.00455i
\(379\) 7.76438e8 0.732605 0.366302 0.930496i \(-0.380624\pi\)
0.366302 + 0.930496i \(0.380624\pi\)
\(380\) −8.04092e8 2.92666e8i −0.751732 0.273608i
\(381\) 8.69796e8 + 8.00459e8i 0.805712 + 0.741484i
\(382\) 7.86257e8 + 6.59748e8i 0.721677 + 0.605559i
\(383\) 8.65351e6 4.90765e7i 0.00787040 0.0446352i −0.980620 0.195921i \(-0.937230\pi\)
0.988490 + 0.151286i \(0.0483414\pi\)
\(384\) −4.10797e8 + 6.41781e8i −0.370227 + 0.578399i
\(385\) −1.63523e9 + 1.37212e9i −1.46038 + 1.22540i
\(386\) 1.18891e9 + 2.05926e9i 1.05219 + 1.82245i
\(387\) −1.95048e8 1.96728e8i −0.171062 0.172535i
\(388\) −1.73112e8 + 2.99839e8i −0.150458 + 0.260601i
\(389\) −9.37950e7 5.31938e8i −0.0807897 0.458181i −0.998186 0.0602061i \(-0.980824\pi\)
0.917396 0.397975i \(-0.130287\pi\)
\(390\) −3.27054e8 2.52606e9i −0.279186 2.15634i
\(391\) −2.17362e7 + 7.91131e6i −0.0183893 + 0.00669314i
\(392\) 6.25489e8 2.27659e8i 0.524467 0.190891i
\(393\) 1.01034e9 + 4.21035e8i 0.839637 + 0.349900i
\(394\) −5.49340e8 3.11546e9i −0.452486 2.56617i
\(395\) 2.81879e8 4.88228e8i 0.230130 0.398596i
\(396\) −8.83909e7 1.06279e9i −0.0715277 0.860028i
\(397\) −1.47182e8 2.54926e8i −0.118056 0.204478i 0.800941 0.598743i \(-0.204333\pi\)
−0.918997 + 0.394264i \(0.870999\pi\)
\(398\) −2.20290e9 + 1.84846e9i −1.75148 + 1.46966i
\(399\) 2.21668e9 + 1.01545e8i 1.74702 + 0.0800301i
\(400\) −2.78844e6 + 1.58140e7i −0.00217846 + 0.0123547i
\(401\) 1.87746e7 + 1.57538e7i 0.0145400 + 0.0122005i 0.650029 0.759910i \(-0.274757\pi\)
−0.635489 + 0.772110i \(0.719201\pi\)
\(402\) 4.48394e8 1.40322e8i 0.344246 0.107729i
\(403\) 2.16305e9 + 7.87285e8i 1.64626 + 0.599190i
\(404\) 2.83384e8 0.213816
\(405\) 1.15801e9 + 6.81889e8i 0.866207 + 0.510060i
\(406\) 2.64170e9 1.95904
\(407\) −2.05752e9 7.48877e8i −1.51274 0.550592i
\(408\) −4.57234e8 + 1.43088e8i −0.333294 + 0.104302i
\(409\) −4.46240e8 3.74440e8i −0.322506 0.270614i 0.467132 0.884187i \(-0.345287\pi\)
−0.789638 + 0.613573i \(0.789732\pi\)
\(410\) 1.66153e8 9.42299e8i 0.119059 0.675220i
\(411\) −5.84222e8 2.67629e7i −0.415080 0.0190146i
\(412\) 4.89739e8 4.10940e8i 0.345004 0.289493i
\(413\) 1.31149e8 + 2.27156e8i 0.0916091 + 0.158672i
\(414\) 3.42984e7 + 1.61730e7i 0.0237560 + 0.0112019i
\(415\) 8.10237e8 1.40337e9i 0.556473 0.963839i
\(416\) −5.10985e8 2.89794e9i −0.348002 1.97362i
\(417\) 2.07231e8 + 8.63588e7i 0.139952 + 0.0583218i
\(418\) −2.38497e9 + 8.68057e8i −1.59722 + 0.581341i
\(419\) −9.34163e8 + 3.40008e8i −0.620403 + 0.225808i −0.633049 0.774112i \(-0.718197\pi\)
0.0126460 + 0.999920i \(0.495975\pi\)
\(420\) 2.28806e8 + 1.76723e9i 0.150694 + 1.16391i
\(421\) 2.85153e8 + 1.61718e9i 0.186248 + 1.05626i 0.924342 + 0.381566i \(0.124615\pi\)
−0.738094 + 0.674698i \(0.764274\pi\)
\(422\) 2.32116e8 4.02036e8i 0.150353 0.260418i
\(423\) −2.44132e8 + 8.95730e8i −0.156832 + 0.575421i
\(424\) 1.68055e8 + 2.91080e8i 0.107071 + 0.185452i
\(425\) −1.24415e7 + 1.04397e7i −0.00786162 + 0.00659668i
\(426\) 7.43906e7 1.16219e8i 0.0466213 0.0728357i
\(427\) 6.17682e8 3.50305e9i 0.383943 2.17745i
\(428\) 1.04083e8 + 8.73358e7i 0.0641690 + 0.0538442i
\(429\) −2.34370e9 2.15687e9i −1.43318 1.31893i
\(430\) −4.97521e8 1.81083e8i −0.301767 0.109834i
\(431\) 3.04996e9 1.83495 0.917473 0.397799i \(-0.130226\pi\)
0.917473 + 0.397799i \(0.130226\pi\)
\(432\) 1.77407e9 + 9.38076e8i 1.05871 + 0.559815i
\(433\) −3.22545e9 −1.90934 −0.954669 0.297668i \(-0.903791\pi\)
−0.954669 + 0.297668i \(0.903791\pi\)
\(434\) −3.58938e9 1.30643e9i −2.10768 0.767133i
\(435\) 3.50790e8 1.56641e9i 0.204331 0.912415i
\(436\) 1.82264e8 + 1.52938e8i 0.105317 + 0.0883716i
\(437\) 6.60681e6 3.74691e7i 0.00378710 0.0214777i
\(438\) 1.01510e9 + 1.96023e9i 0.577228 + 1.11467i
\(439\) −2.57187e9 + 2.15805e9i −1.45085 + 1.21741i −0.518896 + 0.854837i \(0.673657\pi\)
−0.931956 + 0.362572i \(0.881899\pi\)
\(440\) 3.79041e8 + 6.56518e8i 0.212130 + 0.367420i
\(441\) −1.18080e9 2.56085e9i −0.655603 1.42183i
\(442\) 1.92356e9 3.33170e9i 1.05956 1.83522i
\(443\) 2.87944e8 + 1.63301e9i 0.157360 + 0.892433i 0.956596 + 0.291416i \(0.0941265\pi\)
−0.799236 + 0.601017i \(0.794762\pi\)
\(444\) −1.45250e9 + 1.10961e9i −0.787548 + 0.601628i
\(445\) 2.03008e9 7.38887e8i 1.09207 0.397483i
\(446\) 2.58463e9 9.40730e8i 1.37952 0.502103i
\(447\) −2.46601e9 + 1.88385e9i −1.30593 + 0.997631i
\(448\) 2.13973e8 + 1.21350e9i 0.112431 + 0.637627i
\(449\) 5.98167e8 1.03606e9i 0.311861 0.540158i −0.666905 0.745143i \(-0.732381\pi\)
0.978765 + 0.204985i \(0.0657145\pi\)
\(450\) 2.65137e7 + 2.43427e6i 0.0137160 + 0.00125929i
\(451\) −5.98246e8 1.03619e9i −0.307087 0.531891i
\(452\) 1.54479e9 1.29623e9i 0.786839 0.660236i
\(453\) −1.39146e9 2.68701e9i −0.703275 1.35808i
\(454\) −2.20563e7 + 1.25088e8i −0.0110621 + 0.0627364i
\(455\) 4.07700e9 + 3.42101e9i 2.02909 + 1.70261i
\(456\) 1.72213e8 7.68997e8i 0.0850530 0.379794i
\(457\) −1.60911e9 5.85668e8i −0.788641 0.287042i −0.0838698 0.996477i \(-0.526728\pi\)
−0.704771 + 0.709435i \(0.748950\pi\)
\(458\) −7.85317e8 −0.381958
\(459\) 7.64663e8 + 1.88018e9i 0.369084 + 0.907516i
\(460\) 3.05538e7 0.0146357
\(461\) 1.07096e9 + 3.89799e8i 0.509122 + 0.185305i 0.583792 0.811903i \(-0.301568\pi\)
−0.0746704 + 0.997208i \(0.523790\pi\)
\(462\) 3.88915e9 + 3.57912e9i 1.83488 + 1.68861i
\(463\) 1.89525e9 + 1.59031e9i 0.887429 + 0.744642i 0.967693 0.252132i \(-0.0811318\pi\)
−0.0802636 + 0.996774i \(0.525576\pi\)
\(464\) 4.16249e8 2.36067e9i 0.193437 1.09704i
\(465\) −1.25128e9 + 1.95485e9i −0.577124 + 0.901632i
\(466\) −4.25791e9 + 3.57281e9i −1.94915 + 1.63553i
\(467\) −1.17152e9 2.02914e9i −0.532282 0.921940i −0.999290 0.0376863i \(-0.988001\pi\)
0.467008 0.884253i \(-0.345332\pi\)
\(468\) −2.57125e9 + 6.77159e8i −1.15953 + 0.305373i
\(469\) −4.90852e8 + 8.50180e8i −0.219708 + 0.380545i
\(470\) 3.08110e8 + 1.74738e9i 0.136887 + 0.776326i
\(471\) 1.13841e8 + 8.79276e8i 0.0502027 + 0.387750i
\(472\) 8.75330e7 3.18594e7i 0.0383155 0.0139457i
\(473\) −6.22134e8 + 2.26438e8i −0.270315 + 0.0983865i
\(474\) −1.28848e9 5.36944e8i −0.555715 0.231582i
\(475\) −4.63889e6 2.63084e7i −0.00198603 0.0112633i
\(476\) −1.34572e9 + 2.33085e9i −0.571913 + 0.990582i
\(477\) 1.16992e9 8.11730e8i 0.493561 0.342450i
\(478\) 9.55045e8 + 1.65419e9i 0.399969 + 0.692766i
\(479\) 3.30790e9 2.77566e9i 1.37524 1.15396i 0.404303 0.914625i \(-0.367514\pi\)
0.970936 0.239338i \(-0.0769303\pi\)
\(480\) 2.96403e9 + 1.35780e8i 1.22331 + 0.0560393i
\(481\) −9.47964e8 + 5.37617e9i −0.388404 + 2.20275i
\(482\) −1.86988e8 1.56902e8i −0.0760587 0.0638209i
\(483\) −7.56164e7 + 2.36636e7i −0.0305352 + 0.00955579i
\(484\) −6.86489e8 2.49862e8i −0.275217 0.100171i
\(485\) −1.04265e9 −0.414996
\(486\) 1.30624e9 3.06033e9i 0.516175 1.20932i
\(487\) −2.79409e9 −1.09620 −0.548099 0.836414i \(-0.684648\pi\)
−0.548099 + 0.836414i \(0.684648\pi\)
\(488\) −1.18706e9 4.32054e8i −0.462384 0.168294i
\(489\) 3.73339e9 1.16834e9i 1.44385 0.451843i
\(490\) −4.12854e9 3.46426e9i −1.58530 1.33022i
\(491\) −2.52664e7 + 1.43293e8i −0.00963293 + 0.0546311i −0.989245 0.146266i \(-0.953275\pi\)
0.979612 + 0.200897i \(0.0643856\pi\)
\(492\) −9.97777e8 4.57076e7i −0.377708 0.0173026i
\(493\) 1.85723e9 1.55840e9i 0.698074 0.585754i
\(494\) 3.16395e9 + 5.48012e9i 1.18082 + 2.04525i
\(495\) 2.63869e9 1.83082e9i 0.977846 0.678465i
\(496\) −1.73301e9 + 3.00167e9i −0.637700 + 1.10453i
\(497\) 5.00664e7 + 2.83941e8i 0.0182936 + 0.103748i
\(498\) −3.70362e9 1.54340e9i −1.34377 0.559985i
\(499\) 6.29801e8 2.29229e8i 0.226909 0.0825881i −0.226064 0.974113i \(-0.572586\pi\)
0.452973 + 0.891524i \(0.350364\pi\)
\(500\) −1.90430e9 + 6.93107e8i −0.681302 + 0.247974i
\(501\) 2.73986e8 + 2.11618e9i 0.0973410 + 0.751832i
\(502\) −1.97679e8 1.12110e9i −0.0697426 0.395530i
\(503\) 7.62736e8 1.32110e9i 0.267231 0.462857i −0.700915 0.713245i \(-0.747225\pi\)
0.968146 + 0.250388i \(0.0805581\pi\)
\(504\) −1.58698e9 + 4.17945e8i −0.552160 + 0.145416i
\(505\) 4.26706e8 + 7.39077e8i 0.147438 + 0.255370i
\(506\) 6.94218e7 5.82518e7i 0.0238215 0.0199886i
\(507\) −2.69920e9 + 4.21692e9i −0.919830 + 1.43703i
\(508\) 4.09507e8 2.32243e9i 0.138592 0.785995i
\(509\) −1.09385e9 9.17852e8i −0.367660 0.308504i 0.440175 0.897912i \(-0.354916\pi\)
−0.807835 + 0.589408i \(0.799361\pi\)
\(510\) 2.85437e9 + 2.62683e9i 0.952829 + 0.876873i
\(511\) −4.33424e9 1.57754e9i −1.43695 0.523005i
\(512\) 3.13435e9 1.03205
\(513\) −3.30714e9 4.57054e8i −1.08154 0.149471i
\(514\) 6.89027e9 2.23803
\(515\) 1.80917e9 + 6.58485e8i 0.583653 + 0.212432i
\(516\) −1.20779e8 + 5.39326e8i −0.0387007 + 0.172813i
\(517\) 1.69966e9 + 1.42618e9i 0.540935 + 0.453898i
\(518\) 1.57306e9 8.92126e9i 0.497268 2.82015i
\(519\) 1.09016e9 + 2.10518e9i 0.342298 + 0.661004i
\(520\) 1.44788e9 1.21492e9i 0.451566 0.378909i
\(521\) −1.78017e9 3.08334e9i −0.551478 0.955188i −0.998168 0.0604993i \(-0.980731\pi\)
0.446690 0.894689i \(-0.352603\pi\)
\(522\) −3.95789e9 3.63380e8i −1.21791 0.111819i
\(523\) 2.56113e9 4.43601e9i 0.782845 1.35593i −0.147432 0.989072i \(-0.547101\pi\)
0.930278 0.366856i \(-0.119566\pi\)
\(524\) −3.79190e8 2.15050e9i −0.115132 0.652949i
\(525\) −4.42085e7 + 3.37720e7i −0.0133336 + 0.0101859i
\(526\) −1.53919e9 + 5.60218e8i −0.461149 + 0.167844i
\(527\) −3.29418e9 + 1.19898e9i −0.980415 + 0.356842i
\(528\) 3.81117e9 2.91145e9i 1.12678 0.860777i
\(529\) −5.91006e8 3.35176e9i −0.173579 0.984415i
\(530\) 1.36069e9 2.35679e9i 0.397004 0.687632i
\(531\) −1.65245e8 3.58373e8i −0.0478958 0.103873i
\(532\) −2.21349e9 3.83388e9i −0.637364 1.10395i
\(533\) −2.28521e9 + 1.91752e9i −0.653704 + 0.548523i
\(534\) −2.45977e9 4.75001e9i −0.699037 1.34990i
\(535\) −7.10524e7 + 4.02958e8i −0.0200604 + 0.113768i
\(536\) 2.67071e8 + 2.24099e8i 0.0749117 + 0.0628584i
\(537\) −7.22689e8 + 3.22708e9i −0.201392 + 0.899289i
\(538\) 6.56056e9 + 2.38785e9i 1.81637 + 0.661103i
\(539\) −6.73930e9 −1.85376
\(540\) −9.97138e7 2.67920e9i −0.0272507 0.732195i
\(541\) −6.07172e9 −1.64862 −0.824312 0.566136i \(-0.808438\pi\)
−0.824312 + 0.566136i \(0.808438\pi\)
\(542\) 2.92847e9 + 1.06588e9i 0.790029 + 0.287547i
\(543\) −1.35944e9 1.25107e9i −0.364385 0.335338i
\(544\) 3.43299e9 + 2.88062e9i 0.914274 + 0.767167i
\(545\) −1.24423e8 + 7.05640e8i −0.0329241 + 0.186722i
\(546\) 7.10423e9 1.10988e10i 1.86785 2.91812i
\(547\) 4.45844e9 3.74108e9i 1.16474 0.977330i 0.164777 0.986331i \(-0.447310\pi\)
0.999959 + 0.00900117i \(0.00286520\pi\)
\(548\) 5.83382e8 + 1.01045e9i 0.151433 + 0.262290i
\(549\) −1.40729e9 + 5.16342e9i −0.362979 + 1.33179i
\(550\) 3.18152e7 5.51055e7i 0.00815389 0.0141230i
\(551\) 6.92479e8 + 3.92724e9i 0.176350 + 1.00013i
\(552\) 3.61295e6 + 2.79053e7i 0.000914271 + 0.00706155i
\(553\) 2.74073e9 9.97545e8i 0.689173 0.250839i
\(554\) −4.78823e9 + 1.74277e9i −1.19644 + 0.435468i
\(555\) −5.08101e9 2.11740e9i −1.26161 0.525747i
\(556\) −7.77760e7 4.41090e8i −0.0191904 0.108834i
\(557\) −2.93533e9 + 5.08415e9i −0.719721 + 1.24659i 0.241389 + 0.970428i \(0.422397\pi\)
−0.961110 + 0.276165i \(0.910936\pi\)
\(558\) 5.19802e9 + 2.45107e9i 1.26654 + 0.597222i
\(559\) 8.25336e8 + 1.42952e9i 0.199843 + 0.346139i
\(560\) −6.13893e9 + 5.15117e9i −1.47718 + 1.23950i
\(561\) 4.84565e9 + 2.21977e8i 1.15873 + 0.0530808i
\(562\) −8.55509e8 + 4.85184e9i −0.203305 + 1.15300i
\(563\) 2.65677e8 + 2.22929e8i 0.0627442 + 0.0526487i 0.673620 0.739077i \(-0.264738\pi\)
−0.610876 + 0.791726i \(0.709183\pi\)
\(564\) 1.76766e9 5.53177e8i 0.414879 0.129834i
\(565\) 5.70671e9 + 2.07707e9i 1.33112 + 0.484487i
\(566\) −6.10143e9 −1.41441
\(567\) 2.32179e9 + 6.55341e9i 0.534912 + 1.50983i
\(568\) 1.02393e8 0.0234449
\(569\) −1.80928e9 6.58523e8i −0.411730 0.149857i 0.127847 0.991794i \(-0.459193\pi\)
−0.539576 + 0.841937i \(0.681416\pi\)
\(570\) −6.08935e9 + 1.90562e9i −1.37724 + 0.430997i
\(571\) 1.63198e9 + 1.36939e9i 0.366850 + 0.307823i 0.807514 0.589849i \(-0.200813\pi\)
−0.440664 + 0.897672i \(0.645257\pi\)
\(572\) −1.10343e9 + 6.25789e9i −0.246525 + 1.39811i
\(573\) 3.22323e9 + 1.47654e8i 0.715730 + 0.0327872i
\(574\) 3.79210e9 3.18195e9i 0.836928 0.702266i
\(575\) 476935. + 826076.i 0.000104622 + 0.000181210i
\(576\) −1.53658e8 1.84754e9i −0.0335025 0.402824i
\(577\) −1.90566e9 + 3.30070e9i −0.412980 + 0.715303i −0.995214 0.0977184i \(-0.968846\pi\)
0.582234 + 0.813022i \(0.302179\pi\)
\(578\) −4.26030e7 2.41614e8i −0.00917683 0.0520444i
\(579\) 6.89993e9 + 2.87539e9i 1.47730 + 0.615633i
\(580\) −3.00931e9 + 1.09530e9i −0.640425 + 0.233096i
\(581\) 7.87801e9 2.86736e9i 1.66648 0.606549i
\(582\) 3.31483e8 + 2.56027e9i 0.0696997 + 0.538339i
\(583\) −5.90926e8 3.35131e9i −0.123508 0.700446i
\(584\) −8.19011e8 + 1.41857e9i −0.170155 + 0.294717i
\(585\) −5.63772e9 5.68629e9i −1.16428 1.17431i
\(586\) 3.19520e9 + 5.53426e9i 0.655929 + 1.13610i
\(587\) 5.21898e9 4.37924e9i 1.06501 0.893646i 0.0704150 0.997518i \(-0.477568\pi\)
0.994591 + 0.103872i \(0.0331232\pi\)
\(588\) −3.03297e9 + 4.73837e9i −0.615245 + 0.961187i
\(589\) 1.00128e9 5.67854e9i 0.201907 1.14507i
\(590\) −5.77761e8 4.84799e8i −0.115815 0.0971806i
\(591\) −7.31783e9 6.73448e9i −1.45823 1.34199i
\(592\) −7.72431e9 2.81142e9i −1.53015 0.556928i
\(593\) 2.62252e9 0.516450 0.258225 0.966085i \(-0.416862\pi\)
0.258225 + 0.966085i \(0.416862\pi\)
\(594\) −5.33454e9 5.89734e9i −1.04435 1.15453i
\(595\) −8.10527e9 −1.57746
\(596\) 5.81769e9 + 2.11747e9i 1.12561 + 0.409689i
\(597\) −1.97557e9 + 8.82167e9i −0.379999 + 1.69684i
\(598\) −1.73085e8 1.45235e8i −0.0330982 0.0277727i
\(599\) −7.73130e8 + 4.38464e9i −0.146980 + 0.833566i 0.818776 + 0.574113i \(0.194653\pi\)
−0.965756 + 0.259452i \(0.916458\pi\)
\(600\) 9.08512e6 + 1.75441e7i 0.00171712 + 0.00331590i
\(601\) 1.73505e9 1.45588e9i 0.326025 0.273567i −0.465053 0.885283i \(-0.653965\pi\)
0.791078 + 0.611716i \(0.209520\pi\)
\(602\) −1.36957e9 2.37216e9i −0.255856 0.443156i
\(603\) 8.52358e8 1.20625e9i 0.158311 0.224041i
\(604\) −3.01840e9 + 5.22802e9i −0.557375 + 0.965402i
\(605\) −3.82034e8 2.16662e9i −0.0701387 0.397776i
\(606\) 1.67917e9 1.28276e9i 0.306507 0.234148i
\(607\) 2.96993e9 1.08097e9i 0.538996 0.196179i −0.0581547 0.998308i \(-0.518522\pi\)
0.597151 + 0.802129i \(0.296299\pi\)
\(608\) −6.92674e9 + 2.52113e9i −1.24987 + 0.454917i
\(609\) 6.59931e9 5.04139e9i 1.18396 0.904460i
\(610\) 1.77609e9 + 1.00727e10i 0.316819 + 1.79677i
\(611\) 2.76593e9 4.79073e9i 0.490565 0.849683i
\(612\) 2.33682e9 3.30705e9i 0.412093 0.583191i
\(613\) −1.00478e9 1.74033e9i −0.176181 0.305155i 0.764388 0.644756i \(-0.223041\pi\)
−0.940570 + 0.339601i \(0.889708\pi\)
\(614\) 2.68951e9 2.25677e9i 0.468904 0.393457i
\(615\) −1.38320e9 2.67107e9i −0.239785 0.463044i
\(616\) −6.81043e8 + 3.86239e9i −0.117393 + 0.665769i
\(617\) −8.20634e9 6.88594e9i −1.40654 1.18023i −0.958108 0.286408i \(-0.907539\pi\)
−0.448430 0.893818i \(-0.648017\pi\)
\(618\) 1.04176e9 4.65183e9i 0.177544 0.792801i
\(619\) 7.40586e9 + 2.69551e9i 1.25504 + 0.456798i 0.882102 0.471058i \(-0.156128\pi\)
0.372939 + 0.927856i \(0.378350\pi\)
\(620\) 4.63052e9 0.780295
\(621\) 1.16546e8 2.50522e7i 0.0195289 0.00419784i
\(622\) 3.34128e9 0.556732
\(623\) 1.05027e10 + 3.82267e9i 1.74017 + 0.633372i
\(624\) −8.79867e9 8.09727e9i −1.44968 1.33411i
\(625\) −4.72403e9 3.96393e9i −0.773985 0.649450i
\(626\) −7.52270e8 + 4.26633e9i −0.122564 + 0.695096i
\(627\) −4.30137e9 + 6.71995e9i −0.696900 + 1.08875i
\(628\) 1.35500e9 1.13698e9i 0.218313 0.183187i
\(629\) −4.15693e9 7.20001e9i −0.666032 1.15360i
\(630\) 9.35528e9 + 9.43586e9i 1.49061 + 1.50345i
\(631\) 1.33633e9 2.31459e9i 0.211744 0.366752i −0.740516 0.672038i \(-0.765419\pi\)
0.952260 + 0.305287i \(0.0987523\pi\)
\(632\) −1.79864e8 1.02006e9i −0.0283422 0.160737i
\(633\) −1.87385e8 1.44731e9i −0.0293645 0.226802i
\(634\) −3.31690e9 + 1.20725e9i −0.516916 + 0.188142i
\(635\) 6.67361e9 2.42900e9i 1.03432 0.376460i
\(636\) −2.62223e9 1.09276e9i −0.404176 0.168432i
\(637\) 2.91775e9 + 1.65474e10i 0.447260 + 2.53654i
\(638\) −4.74927e9 + 8.22598e9i −0.724027 + 1.25405i
\(639\) −3.59537e7 4.32296e8i −0.00545118 0.0655433i
\(640\) 2.28905e9 + 3.96475e9i 0.345164 + 0.597842i
\(641\) −3.13227e9 + 2.62829e9i −0.469739 + 0.394158i −0.846699 0.532072i \(-0.821414\pi\)
0.376960 + 0.926229i \(0.376969\pi\)
\(642\) 1.01207e9 + 4.63622e7i 0.150951 + 0.00691498i
\(643\) 1.66790e9 9.45913e9i 0.247418 1.40318i −0.567391 0.823448i \(-0.692047\pi\)
0.814809 0.579729i \(-0.196842\pi\)
\(644\) 1.21090e8 + 1.01606e8i 0.0178652 + 0.0149907i
\(645\) −1.58845e9 + 4.97093e8i −0.233085 + 0.0729422i
\(646\) −9.05579e9 3.29604e9i −1.32164 0.481037i
\(647\) 6.66441e9 0.967378 0.483689 0.875240i \(-0.339296\pi\)
0.483689 + 0.875240i \(0.339296\pi\)
\(648\) 2.43516e9 4.07882e8i 0.351573 0.0588873i
\(649\) −9.43120e8 −0.135429
\(650\) −1.49078e8 5.42599e7i −0.0212920 0.00774966i
\(651\) −1.14599e10 + 3.58629e9i −1.62797 + 0.509462i
\(652\) −5.97854e9 5.01659e9i −0.844751 0.708830i
\(653\) −2.02195e8 + 1.14670e9i −0.0284167 + 0.161159i −0.995714 0.0924862i \(-0.970519\pi\)
0.967297 + 0.253646i \(0.0816297\pi\)
\(654\) 1.77228e9 + 8.11871e7i 0.247748 + 0.0113492i
\(655\) 5.03761e9 4.22706e9i 0.700455 0.587751i
\(656\) −2.24592e9 3.89005e9i −0.310621 0.538012i
\(657\) 6.27672e9 + 2.95972e9i 0.863483 + 0.407166i
\(658\) −4.58980e9 + 7.94976e9i −0.628063 + 1.08784i
\(659\) 1.23203e9 + 6.98717e9i 0.167695 + 0.951047i 0.946242 + 0.323460i \(0.104846\pi\)
−0.778546 + 0.627587i \(0.784043\pi\)
\(660\) −5.91432e9 2.46466e9i −0.800757 0.333698i
\(661\) −1.01580e9 + 3.69720e8i −0.136805 + 0.0497930i −0.409515 0.912303i \(-0.634302\pi\)
0.272710 + 0.962096i \(0.412080\pi\)
\(662\) 3.75124e9 1.36534e9i 0.502541 0.182910i
\(663\) −1.55287e9 1.19939e10i −0.206937 1.59832i
\(664\) −5.17003e8 2.93207e9i −0.0685338 0.388675i
\(665\) 6.66595e9 1.15458e10i 0.878995 1.52246i
\(666\) −3.58398e9 + 1.31497e10i −0.470116 + 1.72488i
\(667\) −7.11954e7 1.23314e8i −0.00928991 0.0160906i
\(668\) 3.26112e9 2.73640e9i 0.423300 0.355191i
\(669\) 4.66147e9 7.28254e9i 0.601910 0.940355i
\(670\) 4.90175e8 2.77992e9i 0.0629636 0.357084i
\(671\) 9.79764e9 + 8.22120e9i 1.25197 + 1.05052i
\(672\) 1.12954e10 + 1.03950e10i 1.43585 + 1.32139i
\(673\) −1.44400e10 5.25574e9i −1.82606 0.664631i −0.993925 0.110058i \(-0.964896\pi\)
−0.832135 0.554573i \(-0.812881\pi\)
\(674\) 6.42711e8 0.0808548
\(675\) 7.08803e7 4.45173e7i 0.00887079 0.00557142i
\(676\) 9.98873e9 1.24365
\(677\) −7.79088e9 2.83565e9i −0.964998 0.351230i −0.189008 0.981976i \(-0.560527\pi\)
−0.775990 + 0.630745i \(0.782749\pi\)
\(678\) 3.28603e9 1.46734e10i 0.404919 1.80811i
\(679\) −4.13221e9 3.46734e9i −0.506569 0.425062i
\(680\) −4.99839e8 + 2.83473e9i −0.0609606 + 0.345724i
\(681\) 1.83616e8 + 3.54577e8i 0.0222790 + 0.0430225i
\(682\) 1.05211e10 8.82824e9i 1.27003 1.06568i
\(683\) −7.72507e8 1.33802e9i −0.0927748 0.160691i 0.815903 0.578189i \(-0.196240\pi\)
−0.908678 + 0.417498i \(0.862907\pi\)
\(684\) 2.78896e9 + 6.04853e9i 0.333232 + 0.722693i
\(685\) −1.75686e9 + 3.04297e9i −0.208843 + 0.361726i
\(686\) −1.74936e9 9.92113e9i −0.206893 1.17335i
\(687\) −1.96182e9 + 1.49869e9i −0.230840 + 0.176345i
\(688\) −2.33560e9 + 8.50089e8i −0.273426 + 0.0995188i
\(689\) −7.97282e9 + 2.90187e9i −0.928634 + 0.337995i
\(690\) 1.81044e8 1.38304e8i 0.0209803 0.0160274i
\(691\) −1.26315e9 7.16370e9i −0.145641 0.825970i −0.966850 0.255343i \(-0.917811\pi\)
0.821210 0.570627i \(-0.193300\pi\)
\(692\) 2.36482e9 4.09598e9i 0.271285 0.469880i
\(693\) 1.65460e10 + 1.51911e9i 1.88854 + 0.173390i
\(694\) −5.60651e9 9.71075e9i −0.636699 1.10279i
\(695\) 1.03327e9 8.67015e8i 0.116753 0.0979670i
\(696\) −1.35620e9 2.61893e9i −0.152472 0.294436i
\(697\) 7.88903e8 4.47409e9i 0.0882488 0.500484i
\(698\) −1.32735e10 1.11378e10i −1.47738 1.23967i
\(699\) −3.81851e9 + 1.70511e10i −0.422886 + 1.88835i
\(700\) 1.04295e8 + 3.79602e7i 0.0114926 + 0.00418297i
\(701\) 5.92973e9 0.650162 0.325081 0.945686i \(-0.394608\pi\)
0.325081 + 0.945686i \(0.394608\pi\)
\(702\) −1.21705e10 + 1.56514e10i −1.32779 + 1.70755i
\(703\) 1.36750e10 1.48451
\(704\) −4.16340e9 1.51535e9i −0.449721 0.163685i
\(705\) 4.10437e9 + 3.77718e9i 0.441148 + 0.405981i
\(706\) −1.20190e10 1.00851e10i −1.28544 1.07861i
\(707\) −7.66686e8 + 4.34809e9i −0.0815924 + 0.462733i
\(708\) −4.24444e8 + 6.63102e8i −0.0449474 + 0.0702205i
\(709\) −8.26288e9 + 6.93338e9i −0.870702 + 0.730606i −0.964246 0.265009i \(-0.914625\pi\)
0.0935436 + 0.995615i \(0.470181\pi\)
\(710\) −4.14521e8 7.17972e8i −0.0434653 0.0752841i
\(711\) −4.24348e9 + 1.11755e9i −0.442770 + 0.116607i
\(712\) 1.98462e9 3.43746e9i 0.206062 0.356909i
\(713\) 3.57521e7 + 2.02760e8i 0.00369392 + 0.0209493i
\(714\) 2.57685e9 + 1.99028e10i 0.264938 + 2.04630i
\(715\) −1.79823e10 + 6.54503e9i −1.83982 + 0.669639i
\(716\) 6.19970e9 2.25651e9i 0.631212 0.229742i
\(717\) 5.54265e9 + 2.30978e9i 0.561566 + 0.234020i
\(718\) 7.15636e8 + 4.05857e9i 0.0721533 + 0.409202i
\(719\) −2.49223e9 + 4.31667e9i −0.250056 + 0.433109i −0.963541 0.267561i \(-0.913782\pi\)
0.713485 + 0.700670i \(0.247116\pi\)
\(720\) 9.90613e9 6.87322e9i 0.989100 0.686273i
\(721\) 4.98027e9 + 8.62607e9i 0.494856 + 0.857116i
\(722\) 1.95645e9 1.64166e9i 0.193459 0.162332i
\(723\) −7.66549e8 3.51152e7i −0.0754320 0.00345550i
\(724\) −6.40036e8 + 3.62982e9i −0.0626786 + 0.355468i
\(725\) −7.65876e7 6.42646e7i −0.00746406 0.00626309i
\(726\) −5.19875e9 + 1.62691e9i −0.504221 + 0.157792i
\(727\) −1.26797e10 4.61504e9i −1.22388 0.445456i −0.352383 0.935856i \(-0.614629\pi\)
−0.871498 + 0.490399i \(0.836851\pi\)
\(728\) 9.77839e9 0.939307
\(729\) −2.57713e9 1.01379e10i −0.246371 0.969176i
\(730\) 1.32626e10 1.26182
\(731\) −2.36226e9 8.59792e8i −0.223675 0.0814109i
\(732\) 1.01896e10 3.18878e9i 0.960218 0.300494i
\(733\) 1.45312e10 + 1.21931e10i 1.36281 + 1.14354i 0.975102 + 0.221756i \(0.0711788\pi\)
0.387712 + 0.921781i \(0.373266\pi\)
\(734\) −1.33138e9 + 7.55063e9i −0.124270 + 0.704769i
\(735\) −1.69248e10 7.75314e8i −1.57223 0.0720231i
\(736\) 2.01624e8 1.69183e8i 0.0186410 0.0156417i
\(737\) −1.76491e9 3.05692e9i −0.162401 0.281286i
\(738\) −6.11914e9 + 4.24568e9i −0.560394 + 0.388821i
\(739\) −1.46342e9 + 2.53471e9i −0.133387 + 0.231033i −0.924980 0.380016i \(-0.875919\pi\)
0.791593 + 0.611048i \(0.209252\pi\)
\(740\) 1.90696e9 + 1.08149e10i 0.172994 + 0.981096i
\(741\) 1.83621e10 + 7.65201e9i 1.65790 + 0.690895i
\(742\) 1.32302e10 4.81538e9i 1.18892 0.432730i
\(743\) −1.63542e10 + 5.95245e9i −1.46275 + 0.532396i −0.946121 0.323815i \(-0.895035\pi\)
−0.516626 + 0.856211i \(0.672812\pi\)
\(744\) 5.47553e8 + 4.22913e9i 0.0487439 + 0.376483i
\(745\) 3.23757e9 + 1.83612e10i 0.286861 + 1.62687i
\(746\) 6.56256e9 1.13667e10i 0.578745 1.00242i
\(747\) −1.21975e10 + 3.21232e9i −1.07066 + 0.281966i
\(748\) −4.83868e9 8.38085e9i −0.422738 0.732204i
\(749\) −1.62163e9 + 1.36071e9i −0.141015 + 0.118325i
\(750\) −8.14635e9 + 1.27269e10i −0.705096 + 1.10156i
\(751\) 2.03661e8 1.15502e9i 0.0175456 0.0995060i −0.974777 0.223179i \(-0.928356\pi\)
0.992323 + 0.123673i \(0.0394675\pi\)
\(752\) 6.38082e9 + 5.35414e9i 0.547160 + 0.459122i
\(753\) −2.63331e9 2.42339e9i −0.224760 0.206843i
\(754\) 2.22539e10 + 8.09975e9i 1.89063 + 0.688133i
\(755\) −1.81799e10 −1.53736