Properties

Label 27.8.e.a.7.3
Level 27
Weight 8
Character 27.7
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 7.3
Character \(\chi\) = 27.7
Dual form 27.8.e.a.4.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-16.4594 + 5.99073i) q^{2} +(7.02376 - 46.2349i) q^{3} +(136.969 - 114.931i) q^{4} +(-40.0449 - 227.106i) q^{5} +(161.374 + 803.077i) q^{6} +(882.649 + 740.631i) q^{7} +(-444.907 + 770.602i) q^{8} +(-2088.33 - 649.486i) q^{9} +O(q^{10})\) \(q+(-16.4594 + 5.99073i) q^{2} +(7.02376 - 46.2349i) q^{3} +(136.969 - 114.931i) q^{4} +(-40.0449 - 227.106i) q^{5} +(161.374 + 803.077i) q^{6} +(882.649 + 740.631i) q^{7} +(-444.907 + 770.602i) q^{8} +(-2088.33 - 649.486i) q^{9} +(2019.65 + 3498.13i) q^{10} +(647.465 - 3671.95i) q^{11} +(-4351.78 - 7140.02i) q^{12} +(-7567.07 - 2754.19i) q^{13} +(-18964.8 - 6902.62i) q^{14} +(-10781.5 + 256.335i) q^{15} +(-1267.76 + 7189.84i) q^{16} +(-10746.9 - 18614.2i) q^{17} +(38263.6 - 1820.50i) q^{18} +(-5562.25 + 9634.10i) q^{19} +(-31586.5 - 26504.2i) q^{20} +(40442.5 - 35607.2i) q^{21} +(11340.8 + 64317.0i) q^{22} +(-79672.0 + 66852.8i) q^{23} +(32503.8 + 25982.8i) q^{24} +(23439.9 - 8531.43i) q^{25} +141049. q^{26} +(-44696.9 + 91992.1i) q^{27} +206017. q^{28} +(-132448. + 48207.1i) q^{29} +(175921. - 68808.2i) q^{30} +(-10109.4 + 8482.81i) q^{31} +(-41983.7 - 238101. i) q^{32} +(-165225. - 55726.4i) q^{33} +(288400. + 241996. i) q^{34} +(132856. - 230114. i) q^{35} +(-360684. + 151055. i) q^{36} +(-203213. - 351975. i) q^{37} +(33836.0 - 191894. i) q^{38} +(-180489. + 330518. i) q^{39} +(192825. + 70182.5i) q^{40} +(-121630. - 44269.8i) q^{41} +(-452346. + 828354. i) q^{42} +(6197.05 - 35145.2i) q^{43} +(-333339. - 577359. i) q^{44} +(-63875.0 + 500282. i) q^{45} +(910857. - 1.57765e6i) q^{46} +(814928. + 683806. i) q^{47} +(323517. + 109115. i) q^{48} +(87529.3 + 496403. i) q^{49} +(-334697. + 280844. i) q^{50} +(-936108. + 366140. i) q^{51} +(-1.35300e6 + 492451. i) q^{52} +666315. q^{53} +(184584. - 1.78190e6i) q^{54} -859851. q^{55} +(-963429. + 350659. i) q^{56} +(406364. + 324838. i) q^{57} +(1.89122e6 - 1.58692e6i) q^{58} +(-293561. - 1.66487e6i) q^{59} +(-1.44727e6 + 1.27424e6i) q^{60} +(-1.87164e6 - 1.57049e6i) q^{61} +(115577. - 200185. i) q^{62} +(-1.36224e6 - 2.11995e6i) q^{63} +(1.65018e6 + 2.85819e6i) q^{64} +(-322470. + 1.82882e6i) q^{65} +(3.05334e6 - 72594.8i) q^{66} +(3.89129e6 + 1.41632e6i) q^{67} +(-3.61134e6 - 1.31442e6i) q^{68} +(2.53133e6 + 4.15319e6i) q^{69} +(-808184. + 4.58344e6i) q^{70} +(-2.19506e6 - 3.80195e6i) q^{71} +(1.42961e6 - 1.32031e6i) q^{72} +(1.13112e6 - 1.95915e6i) q^{73} +(5.45336e6 + 4.57591e6i) q^{74} +(-229813. - 1.14366e6i) q^{75} +(345399. + 1.95885e6i) q^{76} +(3.29105e6 - 2.76152e6i) q^{77} +(990694. - 6.52139e6i) q^{78} +(-7.23906e6 + 2.63480e6i) q^{79} +1.68362e6 q^{80} +(3.93931e6 + 2.71269e6i) q^{81} +2.26717e6 q^{82} +(-1.87778e6 + 683455. i) q^{83} +(1.44702e6 - 9.52520e6i) q^{84} +(-3.79703e6 + 3.18609e6i) q^{85} +(108546. + 615594. i) q^{86} +(1.29857e6 + 6.46231e6i) q^{87} +(2.54155e6 + 2.13262e6i) q^{88} +(-3.29415e6 + 5.70564e6i) q^{89} +(-1.94571e6 - 8.61700e6i) q^{90} +(-4.63923e6 - 8.03539e6i) q^{91} +(-3.22918e6 + 1.83136e7i) q^{92} +(321196. + 526989. i) q^{93} +(-1.75097e7 - 6.37302e6i) q^{94} +(2.41070e6 + 877424. i) q^{95} +(-1.13035e7 + 268746. i) q^{96} +(1.19613e6 - 6.78360e6i) q^{97} +(-4.41450e6 - 7.64614e6i) q^{98} +(-3.73700e6 + 7.24775e6i) 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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.4594 + 5.99073i −1.45482 + 0.529511i −0.943933 0.330137i \(-0.892905\pi\)
−0.510887 + 0.859648i \(0.670683\pi\)
\(3\) 7.02376 46.2349i 0.150191 0.988657i
\(4\) 136.969 114.931i 1.07007 0.897898i
\(5\) −40.0449 227.106i −0.143269 0.812520i −0.968741 0.248076i \(-0.920202\pi\)
0.825472 0.564444i \(-0.190909\pi\)
\(6\) 161.374 + 803.077i 0.305003 + 1.51785i
\(7\) 882.649 + 740.631i 0.972624 + 0.816129i 0.982960 0.183818i \(-0.0588457\pi\)
−0.0103360 + 0.999947i \(0.503290\pi\)
\(8\) −444.907 + 770.602i −0.307224 + 0.532127i
\(9\) −2088.33 649.486i −0.954885 0.296976i
\(10\) 2019.65 + 3498.13i 0.638669 + 1.10621i
\(11\) 647.465 3671.95i 0.146670 0.831808i −0.819341 0.573307i \(-0.805660\pi\)
0.966011 0.258501i \(-0.0832285\pi\)
\(12\) −4351.78 7140.02i −0.726998 1.19279i
\(13\) −7567.07 2754.19i −0.955270 0.347690i −0.183092 0.983096i \(-0.558610\pi\)
−0.772178 + 0.635406i \(0.780833\pi\)
\(14\) −18964.8 6902.62i −1.84714 0.672305i
\(15\) −10781.5 + 256.335i −0.824821 + 0.0196105i
\(16\) −1267.76 + 7189.84i −0.0773781 + 0.438833i
\(17\) −10746.9 18614.2i −0.530532 0.918909i −0.999365 0.0356221i \(-0.988659\pi\)
0.468833 0.883287i \(-0.344675\pi\)
\(18\) 38263.6 1820.50i 1.54644 0.0735762i
\(19\) −5562.25 + 9634.10i −0.186043 + 0.322236i −0.943927 0.330153i \(-0.892900\pi\)
0.757885 + 0.652389i \(0.226233\pi\)
\(20\) −31586.5 26504.2i −0.882868 0.740815i
\(21\) 40442.5 35607.2i 0.952951 0.839016i
\(22\) 11340.8 + 64317.0i 0.227073 + 1.28779i
\(23\) −79672.0 + 66852.8i −1.36540 + 1.14570i −0.391121 + 0.920339i \(0.627913\pi\)
−0.974275 + 0.225364i \(0.927643\pi\)
\(24\) 32503.8 + 25982.8i 0.479949 + 0.383660i
\(25\) 23439.9 8531.43i 0.300031 0.109202i
\(26\) 141049. 1.57385
\(27\) −44696.9 + 91992.1i −0.437023 + 0.899451i
\(28\) 206017. 1.77358
\(29\) −132448. + 48207.1i −1.00844 + 0.367044i −0.792835 0.609436i \(-0.791396\pi\)
−0.215609 + 0.976480i \(0.569174\pi\)
\(30\) 175921. 68808.2i 1.18958 0.465282i
\(31\) −10109.4 + 8482.81i −0.0609481 + 0.0511415i −0.672753 0.739867i \(-0.734888\pi\)
0.611805 + 0.791009i \(0.290444\pi\)
\(32\) −41983.7 238101.i −0.226493 1.28451i
\(33\) −165225. 55726.4i −0.800344 0.269937i
\(34\) 288400. + 241996.i 1.25840 + 1.05592i
\(35\) 132856. 230114.i 0.523773 0.907202i
\(36\) −360684. + 151055.i −1.28845 + 0.539604i
\(37\) −203213. 351975.i −0.659547 1.14237i −0.980733 0.195353i \(-0.937415\pi\)
0.321186 0.947016i \(-0.395919\pi\)
\(38\) 33836.0 191894.i 0.100031 0.567307i
\(39\) −180489. + 330518.i −0.487219 + 0.892214i
\(40\) 192825. + 70182.5i 0.476379 + 0.173388i
\(41\) −121630. 44269.8i −0.275612 0.100315i 0.200516 0.979690i \(-0.435738\pi\)
−0.476129 + 0.879376i \(0.657960\pi\)
\(42\) −452346. + 828354.i −0.942104 + 1.72522i
\(43\) 6197.05 35145.2i 0.0118863 0.0674104i −0.978288 0.207252i \(-0.933548\pi\)
0.990174 + 0.139841i \(0.0446592\pi\)
\(44\) −333339. 577359.i −0.589931 1.02179i
\(45\) −63875.0 + 500282.i −0.104493 + 0.818410i
\(46\) 910857. 1.57765e6i 1.37974 2.38978i
\(47\) 814928. + 683806.i 1.14492 + 0.960705i 0.999589 0.0286771i \(-0.00912944\pi\)
0.145335 + 0.989382i \(0.453574\pi\)
\(48\) 323517. + 109115.i 0.422234 + 0.142409i
\(49\) 87529.3 + 496403.i 0.106284 + 0.602765i
\(50\) −334697. + 280844.i −0.378667 + 0.317739i
\(51\) −936108. + 366140.i −0.988167 + 0.386502i
\(52\) −1.35300e6 + 492451.i −1.33440 + 0.485681i
\(53\) 666315. 0.614772 0.307386 0.951585i \(-0.400546\pi\)
0.307386 + 0.951585i \(0.400546\pi\)
\(54\) 184584. 1.78190e6i 0.159520 1.53995i
\(55\) −859851. −0.696873
\(56\) −963429. + 350659.i −0.733097 + 0.266826i
\(57\) 406364. + 324838.i 0.290639 + 0.232330i
\(58\) 1.89122e6 1.58692e6i 1.27275 1.06797i
\(59\) −293561. 1.66487e6i −0.186087 1.05535i −0.924550 0.381060i \(-0.875559\pi\)
0.738463 0.674294i \(-0.235552\pi\)
\(60\) −1.44727e6 + 1.27424e6i −0.865011 + 0.761590i
\(61\) −1.87164e6 1.57049e6i −1.05577 0.885893i −0.0620779 0.998071i \(-0.519773\pi\)
−0.993688 + 0.112178i \(0.964217\pi\)
\(62\) 115577. 200185.i 0.0615885 0.106674i
\(63\) −1.36224e6 2.11995e6i −0.686374 1.06815i
\(64\) 1.65018e6 + 2.85819e6i 0.786867 + 1.36289i
\(65\) −322470. + 1.82882e6i −0.145644 + 0.825988i
\(66\) 3.05334e6 72594.8i 1.30729 0.0310815i
\(67\) 3.89129e6 + 1.41632e6i 1.58064 + 0.575305i 0.975343 0.220696i \(-0.0708329\pi\)
0.605295 + 0.796001i \(0.293055\pi\)
\(68\) −3.61134e6 1.31442e6i −1.39280 0.506936i
\(69\) 2.53133e6 + 4.15319e6i 0.927636 + 1.52198i
\(70\) −808184. + 4.58344e6i −0.281622 + 1.59716i
\(71\) −2.19506e6 3.80195e6i −0.727850 1.26067i −0.957790 0.287468i \(-0.907186\pi\)
0.229940 0.973205i \(-0.426147\pi\)
\(72\) 1.42961e6 1.32031e6i 0.451392 0.416882i
\(73\) 1.13112e6 1.95915e6i 0.340313 0.589439i −0.644178 0.764876i \(-0.722800\pi\)
0.984491 + 0.175437i \(0.0561337\pi\)
\(74\) 5.45336e6 + 4.57591e6i 1.56442 + 1.31270i
\(75\) −229813. 1.14366e6i −0.0629015 0.313029i
\(76\) 345399. + 1.95885e6i 0.0902554 + 0.511864i
\(77\) 3.29105e6 2.76152e6i 0.821517 0.689335i
\(78\) 990694. 6.52139e6i 0.236379 1.55600i
\(79\) −7.23906e6 + 2.63480e6i −1.65191 + 0.601247i −0.989062 0.147504i \(-0.952876\pi\)
−0.662852 + 0.748751i \(0.730654\pi\)
\(80\) 1.68362e6 0.367646
\(81\) 3.93931e6 + 2.71269e6i 0.823611 + 0.567155i
\(82\) 2.26717e6 0.454084
\(83\) −1.87778e6 + 683455.i −0.360471 + 0.131201i −0.515906 0.856645i \(-0.672544\pi\)
0.155434 + 0.987846i \(0.450322\pi\)
\(84\) 1.44702e6 9.52520e6i 0.266377 1.75346i
\(85\) −3.79703e6 + 3.18609e6i −0.670623 + 0.562719i
\(86\) 108546. + 615594.i 0.0184022 + 0.104364i
\(87\) 1.29857e6 + 6.46231e6i 0.211421 + 1.05213i
\(88\) 2.54155e6 + 2.13262e6i 0.397567 + 0.333598i
\(89\) −3.29415e6 + 5.70564e6i −0.495312 + 0.857906i −0.999985 0.00540466i \(-0.998280\pi\)
0.504673 + 0.863310i \(0.331613\pi\)
\(90\) −1.94571e6 8.61700e6i −0.281339 1.24597i
\(91\) −4.63923e6 8.03539e6i −0.645359 1.11779i
\(92\) −3.22918e6 + 1.83136e7i −0.432349 + 2.45197i
\(93\) 321196. + 526989.i 0.0414076 + 0.0679378i
\(94\) −1.75097e7 6.37302e6i −2.17436 0.791403i
\(95\) 2.41070e6 + 877424.i 0.288477 + 0.104997i
\(96\) −1.13035e7 + 268746.i −1.30396 + 0.0310022i
\(97\) 1.19613e6 6.78360e6i 0.133069 0.754674i −0.843115 0.537733i \(-0.819281\pi\)
0.976185 0.216941i \(-0.0696080\pi\)
\(98\) −4.41450e6 7.64614e6i −0.473795 0.820636i
\(99\) −3.73700e6 + 7.24775e6i −0.387080 + 0.750723i
\(100\) 2.23002e6 3.86252e6i 0.223002 0.386252i
\(101\) −132538. 111213.i −0.0128002 0.0107406i 0.636365 0.771388i \(-0.280437\pi\)
−0.649165 + 0.760647i \(0.724882\pi\)
\(102\) 1.32143e7 1.16344e7i 1.23295 1.08554i
\(103\) −3.57406e6 2.02695e7i −0.322279 1.82773i −0.528147 0.849153i \(-0.677113\pi\)
0.205869 0.978580i \(-0.433998\pi\)
\(104\) 5.48903e6 4.60584e6i 0.478496 0.401506i
\(105\) −9.70613e6 7.75885e6i −0.818246 0.654086i
\(106\) −1.09671e7 + 3.99171e6i −0.894382 + 0.325528i
\(107\) 2.02493e7 1.59797 0.798983 0.601353i \(-0.205371\pi\)
0.798983 + 0.601353i \(0.205371\pi\)
\(108\) 4.45064e6 + 1.77372e7i 0.339969 + 1.35488i
\(109\) 6.50872e6 0.481396 0.240698 0.970600i \(-0.422624\pi\)
0.240698 + 0.970600i \(0.422624\pi\)
\(110\) 1.41526e7 5.15114e6i 1.01382 0.369002i
\(111\) −1.77009e7 + 6.92335e6i −1.22847 + 0.480492i
\(112\) −6.44401e6 + 5.40717e6i −0.433404 + 0.363669i
\(113\) 1.93666e6 + 1.09834e7i 0.126264 + 0.716078i 0.980549 + 0.196274i \(0.0628841\pi\)
−0.854285 + 0.519804i \(0.826005\pi\)
\(114\) −8.63453e6 2.91222e6i −0.545848 0.184101i
\(115\) 1.83731e7 + 1.54169e7i 1.12653 + 0.945267i
\(116\) −1.26008e7 + 2.18253e7i −0.749542 + 1.29825i
\(117\) 1.40138e7 + 1.06664e7i 0.808917 + 0.615695i
\(118\) 1.48056e7 + 2.56441e7i 0.829545 + 1.43681i
\(119\) 4.30049e6 2.43893e7i 0.233939 1.32674i
\(120\) 4.59923e6 8.42229e6i 0.242969 0.444934i
\(121\) 5.24791e6 + 1.91008e6i 0.269301 + 0.0980175i
\(122\) 4.02145e7 + 1.46369e7i 2.00504 + 0.729775i
\(123\) −2.90111e6 + 5.31263e6i −0.140571 + 0.257420i
\(124\) −409744. + 2.32377e6i −0.0192991 + 0.109450i
\(125\) −1.18844e7 2.05843e7i −0.544241 0.942653i
\(126\) 3.51217e7 + 2.67324e7i 1.56415 + 1.19053i
\(127\) 5.90579e6 1.02291e7i 0.255838 0.443124i −0.709285 0.704922i \(-0.750982\pi\)
0.965123 + 0.261798i \(0.0843154\pi\)
\(128\) −2.05768e7 1.72660e7i −0.867246 0.727706i
\(129\) −1.58141e6 533372.i −0.0648605 0.0218759i
\(130\) −5.64830e6 3.20331e7i −0.225484 1.27878i
\(131\) 7.08938e6 5.94870e6i 0.275524 0.231192i −0.494546 0.869151i \(-0.664666\pi\)
0.770070 + 0.637960i \(0.220221\pi\)
\(132\) −2.90354e7 + 1.13566e7i −1.09880 + 0.429775i
\(133\) −1.20448e7 + 4.38396e6i −0.443936 + 0.161579i
\(134\) −7.25332e7 −2.60417
\(135\) 2.26818e7 + 6.46711e6i 0.793433 + 0.226226i
\(136\) 1.91255e7 0.651968
\(137\) −7.83598e6 + 2.85206e6i −0.260358 + 0.0947627i −0.468901 0.883250i \(-0.655350\pi\)
0.208543 + 0.978013i \(0.433128\pi\)
\(138\) −6.65449e7 5.31944e7i −2.15545 1.72302i
\(139\) 2.03804e7 1.71012e7i 0.643667 0.540101i −0.261475 0.965210i \(-0.584209\pi\)
0.905142 + 0.425109i \(0.139764\pi\)
\(140\) −8.24995e6 4.67878e7i −0.254099 1.44107i
\(141\) 3.73396e7 3.28752e7i 1.12177 0.987647i
\(142\) 5.89058e7 + 4.94279e7i 1.72643 + 1.44865i
\(143\) −1.50127e7 + 2.60027e7i −0.429320 + 0.743605i
\(144\) 7.31721e6 1.41914e7i 0.204210 0.396056i
\(145\) 1.62520e7 + 2.81493e7i 0.442709 + 0.766795i
\(146\) −6.88076e6 + 3.90228e7i −0.182979 + 1.03773i
\(147\) 2.35659e7 560292.i 0.611891 0.0145480i
\(148\) −6.82869e7 2.48544e7i −1.73150 0.630213i
\(149\) −2.76199e7 1.00528e7i −0.684022 0.248964i −0.0234486 0.999725i \(-0.507465\pi\)
−0.660574 + 0.750761i \(0.729687\pi\)
\(150\) 1.06340e7 + 1.74473e7i 0.257262 + 0.422093i
\(151\) 7.34521e6 4.16568e7i 0.173614 0.984615i −0.766117 0.642701i \(-0.777814\pi\)
0.939731 0.341914i \(-0.111075\pi\)
\(152\) −4.94937e6 8.57257e6i −0.114314 0.197997i
\(153\) 1.03535e7 + 4.58526e7i 0.233704 + 1.03501i
\(154\) −3.76252e7 + 6.51687e7i −0.830149 + 1.43786i
\(155\) 2.33133e6 + 1.95622e6i 0.0502855 + 0.0421945i
\(156\) 1.32653e7 + 6.60146e7i 0.279757 + 1.39221i
\(157\) 4.90430e6 + 2.78137e7i 0.101141 + 0.573600i 0.992692 + 0.120679i \(0.0385071\pi\)
−0.891550 + 0.452921i \(0.850382\pi\)
\(158\) 1.03366e8 8.67345e7i 2.08487 1.74941i
\(159\) 4.68003e6 3.08070e7i 0.0923335 0.607798i
\(160\) −5.23930e7 + 1.90695e7i −1.01124 + 0.368061i
\(161\) −1.19836e8 −2.26306
\(162\) −8.10896e7 2.10499e7i −1.49852 0.388997i
\(163\) 9.63217e7 1.74208 0.871039 0.491214i \(-0.163447\pi\)
0.871039 + 0.491214i \(0.163447\pi\)
\(164\) −2.17476e7 + 7.91549e6i −0.384998 + 0.140128i
\(165\) −6.03939e6 + 3.97551e7i −0.104664 + 0.688969i
\(166\) 2.68127e7 2.24985e7i 0.454948 0.381747i
\(167\) 1.67672e6 + 9.50917e6i 0.0278583 + 0.157992i 0.995563 0.0940926i \(-0.0299950\pi\)
−0.967705 + 0.252085i \(0.918884\pi\)
\(168\) 9.44582e6 + 4.70070e7i 0.153694 + 0.764857i
\(169\) 1.60683e6 + 1.34829e6i 0.0256074 + 0.0214872i
\(170\) 4.34099e7 7.51881e7i 0.677669 1.17376i
\(171\) 1.78730e7 1.65066e7i 0.273346 0.252448i
\(172\) −3.19047e6 5.52605e6i −0.0478085 0.0828067i
\(173\) 3.17168e6 1.79875e7i 0.0465723 0.264125i −0.952627 0.304142i \(-0.901630\pi\)
0.999199 + 0.0400174i \(0.0127413\pi\)
\(174\) −6.00877e7 9.85864e7i −0.864695 1.41871i
\(175\) 2.70078e7 + 9.83005e6i 0.380940 + 0.138651i
\(176\) 2.55799e7 + 9.31034e6i 0.353676 + 0.128727i
\(177\) −7.90370e7 + 1.87914e6i −1.07133 + 0.0254715i
\(178\) 2.00388e7 1.13646e8i 0.266319 1.51037i
\(179\) −1.56516e7 2.71094e7i −0.203973 0.353292i 0.745832 0.666134i \(-0.232052\pi\)
−0.949805 + 0.312842i \(0.898719\pi\)
\(180\) 4.87490e7 + 7.58645e7i 0.623034 + 0.969583i
\(181\) 1.38544e7 2.39965e7i 0.173665 0.300796i −0.766034 0.642801i \(-0.777772\pi\)
0.939698 + 0.342004i \(0.111106\pi\)
\(182\) 1.24497e8 + 1.04465e8i 1.53077 + 1.28446i
\(183\) −8.57575e7 + 7.55043e7i −1.03441 + 0.910737i
\(184\) −1.60702e7 9.11387e7i −0.190178 1.07855i
\(185\) −7.17981e7 + 6.02458e7i −0.833704 + 0.699561i
\(186\) −8.44374e6 6.74973e6i −0.0962143 0.0769115i
\(187\) −7.53086e7 + 2.74101e7i −0.842169 + 0.306524i
\(188\) 1.90211e8 2.08777
\(189\) −1.07584e8 + 4.80929e7i −1.15913 + 0.518161i
\(190\) −4.49352e7 −0.475279
\(191\) 3.13583e6 1.14135e6i 0.0325639 0.0118523i −0.325687 0.945478i \(-0.605596\pi\)
0.358251 + 0.933625i \(0.383373\pi\)
\(192\) 1.43739e8 5.62206e7i 1.46561 0.573246i
\(193\) −2.79276e7 + 2.34341e7i −0.279630 + 0.234637i −0.771806 0.635859i \(-0.780646\pi\)
0.492176 + 0.870496i \(0.336202\pi\)
\(194\) 2.09511e7 + 1.18820e8i 0.206016 + 1.16838i
\(195\) 8.22903e7 + 2.77546e7i 0.794745 + 0.268048i
\(196\) 6.90410e7 + 5.79322e7i 0.654954 + 0.549571i
\(197\) −938749. + 1.62596e6i −0.00874818 + 0.0151523i −0.870366 0.492405i \(-0.836118\pi\)
0.861618 + 0.507557i \(0.169451\pi\)
\(198\) 1.80895e7 1.41681e8i 0.165615 1.29713i
\(199\) −8.42423e7 1.45912e8i −0.757783 1.31252i −0.943979 0.330006i \(-0.892949\pi\)
0.186196 0.982513i \(-0.440384\pi\)
\(200\) −3.85425e6 + 2.18585e7i −0.0340671 + 0.193204i
\(201\) 9.28147e7 1.69966e8i 0.806178 1.47630i
\(202\) 2.84775e6 + 1.03650e6i 0.0243093 + 0.00884785i
\(203\) −1.52609e8 5.55450e7i −1.28039 0.466025i
\(204\) −8.61373e7 + 1.57738e8i −0.710372 + 1.30086i
\(205\) −5.18327e6 + 2.93958e7i −0.0420209 + 0.238312i
\(206\) 1.80256e8 + 3.12213e8i 1.43666 + 2.48837i
\(207\) 2.09802e8 8.78651e7i 1.64404 0.688525i
\(208\) 2.93954e7 5.09144e7i 0.226495 0.392300i
\(209\) 3.17746e7 + 2.66621e7i 0.240751 + 0.202014i
\(210\) 2.06238e8 + 6.95593e7i 1.53675 + 0.518307i
\(211\) 1.85769e7 + 1.05355e8i 0.136139 + 0.772085i 0.974059 + 0.226292i \(0.0726604\pi\)
−0.837920 + 0.545793i \(0.816228\pi\)
\(212\) 9.12648e7 7.65802e7i 0.657851 0.552003i
\(213\) −1.91200e8 + 7.47843e7i −1.35569 + 0.530252i
\(214\) −3.33292e8 + 1.21308e8i −2.32475 + 0.846141i
\(215\) −8.22985e6 −0.0564752
\(216\) −5.10033e7 7.53714e7i −0.344358 0.508884i
\(217\) −1.52057e7 −0.101018
\(218\) −1.07130e8 + 3.89920e7i −0.700344 + 0.254905i
\(219\) −8.26366e7 6.60578e7i −0.531641 0.424981i
\(220\) −1.17773e8 + 9.88235e7i −0.745706 + 0.625721i
\(221\) 3.00556e7 + 1.70454e8i 0.187306 + 1.06227i
\(222\) 2.49870e8 2.19995e8i 1.53278 1.34952i
\(223\) 4.75147e7 + 3.98696e7i 0.286920 + 0.240755i 0.774875 0.632114i \(-0.217813\pi\)
−0.487955 + 0.872869i \(0.662257\pi\)
\(224\) 1.39288e8 2.41254e8i 0.828031 1.43419i
\(225\) −5.44914e7 + 2.59258e6i −0.318925 + 0.0151738i
\(226\) −9.76746e7 1.69177e8i −0.562862 0.974906i
\(227\) 1.33534e7 7.57308e7i 0.0757706 0.429717i −0.923199 0.384323i \(-0.874435\pi\)
0.998969 0.0453933i \(-0.0144541\pi\)
\(228\) 9.29934e7 2.21096e6i 0.519613 0.0123541i
\(229\) 2.44709e8 + 8.90666e7i 1.34656 + 0.490107i 0.911872 0.410475i \(-0.134637\pi\)
0.434686 + 0.900582i \(0.356859\pi\)
\(230\) −3.94769e8 1.43684e8i −2.13942 0.778685i
\(231\) −1.04563e8 1.71557e8i −0.558131 0.915731i
\(232\) 2.17786e7 1.23512e8i 0.114504 0.649385i
\(233\) −1.04965e8 1.81804e8i −0.543622 0.941581i −0.998692 0.0511252i \(-0.983719\pi\)
0.455070 0.890455i \(-0.349614\pi\)
\(234\) −2.94557e8 9.16093e7i −1.50285 0.467395i
\(235\) 1.22663e8 2.12458e8i 0.616560 1.06791i
\(236\) −2.31554e8 1.94297e8i −1.14673 0.962219i
\(237\) 7.09744e7 + 3.53203e8i 0.346324 + 1.72348i
\(238\) 7.53262e7 + 4.27196e8i 0.362182 + 2.05403i
\(239\) −2.89505e8 + 2.42923e8i −1.37171 + 1.15100i −0.399544 + 0.916714i \(0.630832\pi\)
−0.972167 + 0.234289i \(0.924724\pi\)
\(240\) 1.18254e7 7.78422e7i 0.0552173 0.363476i
\(241\) −2.21320e8 + 8.05539e7i −1.01850 + 0.370704i −0.796691 0.604387i \(-0.793418\pi\)
−0.221809 + 0.975090i \(0.571196\pi\)
\(242\) −9.78203e7 −0.443685
\(243\) 1.53089e8 1.63080e8i 0.684421 0.729087i
\(244\) −4.36855e8 −1.92519
\(245\) 1.09231e8 3.97569e7i 0.474531 0.172715i
\(246\) 1.59241e7 1.04823e8i 0.0681995 0.448933i
\(247\) 6.86241e7 5.75824e7i 0.289759 0.243137i
\(248\) −2.03912e6 1.15644e7i −0.00848909 0.0481440i
\(249\) 1.84104e7 + 9.16192e7i 0.0755729 + 0.376088i
\(250\) 3.18925e8 + 2.67610e8i 1.29092 + 1.08321i
\(251\) 1.28760e8 2.23019e8i 0.513954 0.890194i −0.485915 0.874006i \(-0.661514\pi\)
0.999869 0.0161879i \(-0.00515300\pi\)
\(252\) −4.30233e8 1.33805e8i −1.69357 0.526710i
\(253\) 1.93896e8 + 3.35837e8i 0.752742 + 1.30379i
\(254\) −3.59258e7 + 2.03745e8i −0.137559 + 0.780134i
\(255\) 1.20639e8 + 1.97934e8i 0.455614 + 0.747531i
\(256\) 4.51480e7 + 1.64325e7i 0.168189 + 0.0612160i
\(257\) 3.87015e8 + 1.40862e8i 1.42220 + 0.517640i 0.934687 0.355473i \(-0.115680\pi\)
0.487518 + 0.873113i \(0.337902\pi\)
\(258\) 2.92243e7 694823.i 0.105944 0.00251887i
\(259\) 8.13179e7 4.61177e8i 0.290829 1.64937i
\(260\) 1.66019e8 + 2.87554e8i 0.585804 + 1.01464i
\(261\) 3.07905e8 1.46495e7i 1.07195 0.0510012i
\(262\) −8.10499e7 + 1.40383e8i −0.278418 + 0.482235i
\(263\) 1.05346e8 + 8.83958e7i 0.357086 + 0.299631i 0.803628 0.595132i \(-0.202900\pi\)
−0.446542 + 0.894763i \(0.647345\pi\)
\(264\) 1.16453e8 1.02530e8i 0.389525 0.342954i
\(265\) −2.66825e7 1.51324e8i −0.0880778 0.499514i
\(266\) 1.71988e8 1.44315e8i 0.560288 0.470138i
\(267\) 2.40663e8 + 1.92380e8i 0.773783 + 0.618544i
\(268\) 6.95767e8 2.53238e8i 2.20796 0.803633i
\(269\) 2.29185e8 0.717883 0.358941 0.933360i \(-0.383138\pi\)
0.358941 + 0.933360i \(0.383138\pi\)
\(270\) −4.12072e8 + 2.94361e7i −1.27409 + 0.0910137i
\(271\) −2.08163e8 −0.635348 −0.317674 0.948200i \(-0.602902\pi\)
−0.317674 + 0.948200i \(0.602902\pi\)
\(272\) 1.47457e8 5.36701e7i 0.444299 0.161712i
\(273\) −4.04100e8 + 1.58056e8i −1.20204 + 0.470155i
\(274\) 1.11890e8 9.38866e7i 0.328597 0.275725i
\(275\) −1.61505e7 9.15940e7i −0.0468297 0.265585i
\(276\) 8.24045e8 + 2.77931e8i 2.35922 + 0.795710i
\(277\) −3.90805e8 3.27924e8i −1.10479 0.927032i −0.107055 0.994253i \(-0.534142\pi\)
−0.997738 + 0.0672212i \(0.978587\pi\)
\(278\) −2.33001e8 + 4.03569e8i −0.650430 + 1.12658i
\(279\) 2.66213e7 1.11490e7i 0.0733862 0.0307342i
\(280\) 1.18217e8 + 2.04758e8i 0.321831 + 0.557428i
\(281\) 1.96864e7 1.11647e8i 0.0529291 0.300176i −0.946839 0.321708i \(-0.895743\pi\)
0.999768 + 0.0215318i \(0.00685430\pi\)
\(282\) −4.17640e8 + 7.64798e8i −1.10900 + 2.03084i
\(283\) 2.48118e8 + 9.03076e7i 0.650737 + 0.236849i 0.646232 0.763141i \(-0.276344\pi\)
0.00450515 + 0.999990i \(0.498566\pi\)
\(284\) −7.37618e8 2.68471e8i −1.91081 0.695478i
\(285\) 5.74998e7 1.05296e8i 0.147133 0.269435i
\(286\) 9.13243e7 5.17926e8i 0.230837 1.30914i
\(287\) −7.45694e7 1.29158e8i −0.186198 0.322504i
\(288\) −6.69674e7 + 5.24503e8i −0.165192 + 1.29382i
\(289\) −2.58223e7 + 4.47255e7i −0.0629291 + 0.108996i
\(290\) −4.36133e8 3.65959e8i −1.05009 0.881129i
\(291\) −3.05238e8 1.02949e8i −0.726128 0.244906i
\(292\) −7.02390e7 3.98345e8i −0.165097 0.936309i
\(293\) 3.16343e8 2.65443e8i 0.734720 0.616503i −0.196694 0.980465i \(-0.563021\pi\)
0.931414 + 0.363962i \(0.118576\pi\)
\(294\) −3.84525e8 + 1.50399e8i −0.882488 + 0.345168i
\(295\) −3.66346e8 + 1.33339e8i −0.830835 + 0.302399i
\(296\) 3.61644e8 0.810514
\(297\) 3.08851e8 + 2.23686e8i 0.684072 + 0.495441i
\(298\) 5.14831e8 1.12696
\(299\) 7.87009e8 2.86448e8i 1.70267 0.619721i
\(300\) −1.62920e8 1.30234e8i −0.348377 0.278485i
\(301\) 3.14995e7 2.64312e7i 0.0665764 0.0558642i
\(302\) 1.28657e8 + 7.29649e8i 0.268787 + 1.52437i
\(303\) −6.07283e6 + 5.34676e6i −0.0125413 + 0.0110418i
\(304\) −6.22161e7 5.22055e7i −0.127012 0.106576i
\(305\) −2.81719e8 + 4.87951e8i −0.568547 + 0.984752i
\(306\) −4.45102e8 6.92681e8i −0.888045 1.38200i
\(307\) −1.67717e8 2.90494e8i −0.330821 0.572998i 0.651852 0.758346i \(-0.273992\pi\)
−0.982673 + 0.185348i \(0.940659\pi\)
\(308\) 1.33389e8 7.56487e8i 0.260131 1.47528i
\(309\) −9.62261e8 + 2.28783e7i −1.85540 + 0.0441132i
\(310\) −5.00915e7 1.82318e7i −0.0954988 0.0347587i
\(311\) −2.37574e8 8.64698e7i −0.447855 0.163006i 0.108240 0.994125i \(-0.465479\pi\)
−0.556095 + 0.831119i \(0.687701\pi\)
\(312\) −1.74397e8 2.86135e8i −0.325086 0.533372i
\(313\) −4.63659e7 + 2.62954e8i −0.0854660 + 0.484702i 0.911789 + 0.410659i \(0.134701\pi\)
−0.997255 + 0.0740429i \(0.976410\pi\)
\(314\) −2.47346e8 4.28416e8i −0.450870 0.780929i
\(315\) −4.26903e8 + 3.94266e8i −0.769560 + 0.710726i
\(316\) −6.88709e8 + 1.19288e9i −1.22781 + 2.12663i
\(317\) −5.13358e8 4.30758e8i −0.905133 0.759497i 0.0660535 0.997816i \(-0.478959\pi\)
−0.971187 + 0.238319i \(0.923404\pi\)
\(318\) 1.07526e8 + 5.35102e8i 0.187507 + 0.933129i
\(319\) 9.12589e7 + 5.17555e8i 0.157401 + 0.892667i
\(320\) 5.83032e8 4.89222e8i 0.994644 0.834605i
\(321\) 1.42227e8 9.36227e8i 0.240001 1.57984i
\(322\) 1.97242e9 7.17904e8i 3.29234 1.19831i
\(323\) 2.39108e8 0.394807
\(324\) 8.51336e8 8.11934e7i 1.39057 0.132621i
\(325\) −2.00868e8 −0.324579
\(326\) −1.58540e9 + 5.77038e8i −2.53441 + 0.922449i
\(327\) 4.57156e7 3.00930e8i 0.0723016 0.475936i
\(328\) 8.82287e7 7.40327e7i 0.138055 0.115842i
\(329\) 2.12848e8 + 1.20712e9i 0.329522 + 1.86881i
\(330\) −1.38758e8 6.90526e8i −0.212549 1.05775i
\(331\) −2.33055e7 1.95556e7i −0.0353232 0.0296397i 0.624955 0.780661i \(-0.285117\pi\)
−0.660278 + 0.751021i \(0.729562\pi\)
\(332\) −1.78648e8 + 3.09427e8i −0.267926 + 0.464061i
\(333\) 1.95774e8 + 8.67026e8i 0.290536 + 1.28670i
\(334\) −8.45648e7 1.46471e8i −0.124187 0.215099i
\(335\) 1.65827e8 9.40453e8i 0.240990 1.36672i
\(336\) 2.04739e8 + 3.35917e8i 0.294451 + 0.483108i
\(337\) −6.64502e8 2.41859e8i −0.945784 0.344237i −0.177337 0.984150i \(-0.556748\pi\)
−0.768447 + 0.639913i \(0.778970\pi\)
\(338\) −3.45247e7 1.25660e7i −0.0486319 0.0177006i
\(339\) 5.21417e8 1.23970e7i 0.726919 0.0172829i
\(340\) −1.53897e8 + 8.72794e8i −0.212351 + 1.20430i
\(341\) 2.46030e7 + 4.26136e7i 0.0336007 + 0.0581980i
\(342\) −1.95293e8 + 3.78762e8i −0.263995 + 0.512006i
\(343\) 1.84056e8 3.18795e8i 0.246275 0.426562i
\(344\) 2.43259e7 + 2.04118e7i 0.0322191 + 0.0270351i
\(345\) 8.41847e8 7.41196e8i 1.10374 0.971776i
\(346\) 5.55543e7 + 3.15064e8i 0.0721026 + 0.408914i
\(347\) −1.57729e7 + 1.32350e7i −0.0202655 + 0.0170048i −0.652864 0.757475i \(-0.726433\pi\)
0.632599 + 0.774480i \(0.281988\pi\)
\(348\) 9.20584e8 + 7.35893e8i 1.17094 + 0.936025i
\(349\) −1.24307e8 + 4.52439e7i −0.156533 + 0.0569733i −0.419098 0.907941i \(-0.637654\pi\)
0.262565 + 0.964914i \(0.415431\pi\)
\(350\) −5.03422e8 −0.627616
\(351\) 5.91588e8 5.73007e8i 0.730204 0.707270i
\(352\) −9.01480e8 −1.10168
\(353\) 5.68285e8 2.06839e8i 0.687630 0.250277i 0.0255098 0.999675i \(-0.491879\pi\)
0.662120 + 0.749398i \(0.269657\pi\)
\(354\) 1.28964e9 5.04419e8i 1.54511 0.604338i
\(355\) −7.75546e8 + 6.50760e8i −0.920043 + 0.772008i
\(356\) 2.04557e8 + 1.16010e9i 0.240292 + 1.36276i
\(357\) −1.09743e9 3.70137e8i −1.27655 0.430550i
\(358\) 4.20021e8 + 3.52439e8i 0.483816 + 0.405970i
\(359\) −5.23792e8 + 9.07235e8i −0.597487 + 1.03488i 0.395704 + 0.918378i \(0.370501\pi\)
−0.993191 + 0.116500i \(0.962833\pi\)
\(360\) −3.57100e8 2.71801e8i −0.403395 0.307038i
\(361\) 3.85059e8 + 6.66941e8i 0.430776 + 0.746126i
\(362\) −8.42782e7 + 4.77966e8i −0.0933760 + 0.529562i
\(363\) 1.25173e8 2.29221e8i 0.137352 0.251525i
\(364\) −1.55895e9 5.67411e8i −1.69425 0.616656i
\(365\) −4.90232e8 1.78430e8i −0.527687 0.192062i
\(366\) 9.59191e8 1.75651e9i 1.02264 1.87269i
\(367\) −1.79776e8 + 1.01956e9i −0.189846 + 1.07667i 0.729723 + 0.683743i \(0.239649\pi\)
−0.919569 + 0.392928i \(0.871462\pi\)
\(368\) −3.79656e8 6.57583e8i −0.397121 0.687833i
\(369\) 2.25252e8 + 1.71447e8i 0.233387 + 0.177639i
\(370\) 8.20838e8 1.42173e9i 0.842464 1.45919i
\(371\) 5.88122e8 + 4.93493e8i 0.597942 + 0.501733i
\(372\) 1.04561e8 + 3.52661e7i 0.105310 + 0.0355187i
\(373\) −1.43167e8 8.11942e8i −0.142844 0.810110i −0.969073 0.246775i \(-0.920629\pi\)
0.826228 0.563335i \(-0.190482\pi\)
\(374\) 1.07533e9 9.02308e8i 1.06290 0.891875i
\(375\) −1.03519e9 + 4.04894e8i −1.01370 + 0.396489i
\(376\) −8.89510e8 + 3.23755e8i −0.862965 + 0.314094i
\(377\) 1.13501e9 1.09095
\(378\) 1.48265e9 1.43609e9i 1.41195 1.36760i
\(379\) 2.48784e8 0.234739 0.117369 0.993088i \(-0.462554\pi\)
0.117369 + 0.993088i \(0.462554\pi\)
\(380\) 4.31036e8 1.56884e8i 0.402968 0.146668i
\(381\) −4.31462e8 3.44900e8i −0.399673 0.319489i
\(382\) −4.47764e7 + 3.75718e7i −0.0410986 + 0.0344858i
\(383\) 8.95175e6 + 5.07679e7i 0.00814165 + 0.0461736i 0.988608 0.150514i \(-0.0480928\pi\)
−0.980466 + 0.196687i \(0.936982\pi\)
\(384\) −9.42817e8 + 8.30093e8i −0.849705 + 0.748114i
\(385\) −7.58947e8 6.36832e8i −0.677796 0.568738i
\(386\) 3.19285e8 5.53018e8i 0.282568 0.489422i
\(387\) −3.57678e7 + 6.93700e7i −0.0313692 + 0.0608392i
\(388\) −6.15813e8 1.06662e9i −0.535227 0.927040i
\(389\) −1.45469e8 + 8.24998e8i −0.125299 + 0.710607i 0.855831 + 0.517256i \(0.173047\pi\)
−0.981130 + 0.193351i \(0.938065\pi\)
\(390\) −1.52072e9 + 3.61559e7i −1.29814 + 0.0308640i
\(391\) 2.10064e9 + 7.64569e8i 1.77718 + 0.646842i
\(392\) −4.21472e8 1.53403e8i −0.353401 0.128627i
\(393\) −2.25243e8 3.69559e8i −0.187188 0.307121i
\(394\) 5.71055e6 3.23861e7i 0.00470372 0.0266761i
\(395\) 8.88267e8 + 1.53852e9i 0.725193 + 1.25607i
\(396\) 3.21135e8 + 1.42222e9i 0.259869 + 1.15089i
\(397\) −3.58350e8 + 6.20681e8i −0.287436 + 0.497853i −0.973197 0.229973i \(-0.926136\pi\)
0.685761 + 0.727827i \(0.259469\pi\)
\(398\) 2.26070e9 + 1.89695e9i 1.79743 + 1.50822i
\(399\) 1.18092e8 + 5.87684e8i 0.0930712 + 0.463168i
\(400\) 3.16234e7 + 1.79345e8i 0.0247058 + 0.140113i
\(401\) −4.22468e7 + 3.54493e7i −0.0327181 + 0.0274538i −0.659000 0.752143i \(-0.729020\pi\)
0.626282 + 0.779597i \(0.284576\pi\)
\(402\) −5.09455e8 + 3.35356e9i −0.391124 + 2.57463i
\(403\) 9.98619e7 3.63468e7i 0.0760033 0.0276629i
\(404\) −3.09355e7 −0.0233412
\(405\) 4.58318e8 1.00327e9i 0.342827 0.750456i
\(406\) 2.84460e9 2.10951
\(407\) −1.42401e9 + 5.18298e8i −1.04697 + 0.381065i
\(408\) 1.34333e8 8.84265e8i 0.0979201 0.644573i
\(409\) 7.02207e8 5.89222e8i 0.507497 0.425841i −0.352750 0.935718i \(-0.614753\pi\)
0.860247 + 0.509877i \(0.170309\pi\)
\(410\) −9.07888e7 5.14889e8i −0.0650562 0.368952i
\(411\) 7.68269e7 + 3.82328e8i 0.0545842 + 0.271638i
\(412\) −2.81913e9 2.36553e9i −1.98598 1.66643i
\(413\) 9.73942e8 1.68692e9i 0.680312 1.17833i
\(414\) −2.92684e9 + 2.70307e9i −2.02720 + 1.87222i
\(415\) 2.30412e8 + 3.99086e8i 0.158248 + 0.274093i
\(416\) −3.38082e8 + 1.91736e9i −0.230248 + 1.30580i
\(417\) −6.47525e8 1.06240e9i −0.437301 0.717485i
\(418\) −6.82717e8 2.48489e8i −0.457218 0.166414i
\(419\) −1.71682e9 6.24871e8i −1.14019 0.414994i −0.298205 0.954502i \(-0.596388\pi\)
−0.841980 + 0.539508i \(0.818610\pi\)
\(420\) −2.22118e9 + 5.28096e7i −1.46289 + 0.0347808i
\(421\) −4.30655e8 + 2.44236e9i −0.281282 + 1.59523i 0.436990 + 0.899466i \(0.356045\pi\)
−0.718272 + 0.695763i \(0.755067\pi\)
\(422\) −9.36916e8 1.62279e9i −0.606886 1.05116i
\(423\) −1.25772e9 1.95730e9i −0.807965 1.25738i
\(424\) −2.96448e8 + 5.13464e8i −0.188872 + 0.327137i
\(425\) −4.10712e8 3.44628e8i −0.259523 0.217766i
\(426\) 2.69903e9 2.37634e9i 1.69151 1.48927i
\(427\) −4.88847e8 2.77239e9i −0.303861 1.72328i
\(428\) 2.77354e9 2.32728e9i 1.70994 1.43481i
\(429\) 1.09679e9 + 8.76746e8i 0.670690 + 0.536134i
\(430\) 1.35458e8 4.93029e7i 0.0821612 0.0299042i
\(431\) −1.25952e9 −0.757765 −0.378883 0.925445i \(-0.623692\pi\)
−0.378883 + 0.925445i \(0.623692\pi\)
\(432\) −6.04744e8 4.37988e8i −0.360893 0.261378i
\(433\) −8.82502e8 −0.522406 −0.261203 0.965284i \(-0.584119\pi\)
−0.261203 + 0.965284i \(0.584119\pi\)
\(434\) 2.50277e8 9.10933e7i 0.146963 0.0534900i
\(435\) 1.41563e9 5.53696e8i 0.824588 0.322522i
\(436\) 8.91495e8 7.48053e8i 0.515129 0.432245i
\(437\) −2.00911e8 1.13942e9i −0.115164 0.653129i
\(438\) 1.75588e9 + 5.92218e8i 0.998474 + 0.336761i
\(439\) −2.45599e9 2.06082e9i −1.38548 1.16256i −0.967133 0.254273i \(-0.918164\pi\)
−0.418351 0.908286i \(-0.637392\pi\)
\(440\) 3.82554e8 6.62603e8i 0.214096 0.370825i
\(441\) 1.39616e8 1.09350e9i 0.0775178 0.607135i
\(442\) −1.51584e9 2.62551e9i −0.834979 1.44623i
\(443\) −2.35212e8 + 1.33395e9i −0.128543 + 0.729001i 0.850598 + 0.525817i \(0.176240\pi\)
−0.979141 + 0.203184i \(0.934871\pi\)
\(444\) −1.62877e9 + 2.98267e9i −0.883120 + 1.61720i
\(445\) 1.42770e9 + 5.19641e8i 0.768028 + 0.279539i
\(446\) −1.02091e9 3.71582e8i −0.544899 0.198327i
\(447\) −6.58787e8 + 1.20639e9i −0.348874 + 0.638871i
\(448\) −6.60337e8 + 3.74496e9i −0.346971 + 1.96777i
\(449\) 4.55200e8 + 7.88429e8i 0.237323 + 0.411056i 0.959945 0.280188i \(-0.0903967\pi\)
−0.722622 + 0.691243i \(0.757063\pi\)
\(450\) 8.81364e8 3.69116e8i 0.455944 0.190950i
\(451\) −2.41308e8 + 4.17958e8i −0.123867 + 0.214543i
\(452\) 1.52759e9 + 1.28180e9i 0.778077 + 0.652884i
\(453\) −1.87441e9 6.32192e8i −0.947371 0.319526i
\(454\) 2.33894e8 + 1.32648e9i 0.117307 + 0.665282i
\(455\) −1.63911e9 + 1.37537e9i −0.815770 + 0.684512i
\(456\) −4.31115e8 + 1.68622e8i −0.212920 + 0.0832794i
\(457\) 3.65382e8 1.32988e8i 0.179077 0.0651788i −0.250925 0.968006i \(-0.580735\pi\)
0.430003 + 0.902828i \(0.358513\pi\)
\(458\) −4.56133e9 −2.21852
\(459\) 2.19271e9 1.56634e8i 1.05837 0.0756037i
\(460\) 4.28844e9 2.05422
\(461\) 9.51312e8 3.46249e8i 0.452241 0.164602i −0.105850 0.994382i \(-0.533756\pi\)
0.558091 + 0.829780i \(0.311534\pi\)
\(462\) 2.74880e9 + 2.19733e9i 1.29687 + 1.03669i
\(463\) −4.67271e7 + 3.92087e7i −0.0218794 + 0.0183590i −0.653662 0.756787i \(-0.726768\pi\)
0.631782 + 0.775146i \(0.282324\pi\)
\(464\) −1.78689e8 1.01339e9i −0.0830395 0.470940i
\(465\) 1.06820e8 9.40488e7i 0.0492684 0.0433778i
\(466\) 2.81679e9 + 2.36357e9i 1.28945 + 1.08198i
\(467\) 9.95176e8 1.72370e9i 0.452159 0.783162i −0.546361 0.837550i \(-0.683987\pi\)
0.998520 + 0.0543880i \(0.0173208\pi\)
\(468\) 3.14535e9 1.49649e8i 1.41843 0.0674861i
\(469\) 2.38568e9 + 4.13212e9i 1.06784 + 1.84956i
\(470\) −7.46176e8 + 4.23177e9i −0.331512 + 1.88010i
\(471\) 1.32041e9 3.13934e7i 0.582284 0.0138441i
\(472\) 1.41356e9 + 5.14494e8i 0.618753 + 0.225208i
\(473\) −1.25039e8 4.55106e7i −0.0543291 0.0197742i
\(474\) −3.28414e9 5.38833e9i −1.41644 2.32397i
\(475\) −4.81860e7 + 2.73276e8i −0.0206297 + 0.116997i
\(476\) −2.21405e9 3.83484e9i −0.940942 1.62976i
\(477\) −1.39149e9 4.32762e8i −0.587036 0.182572i
\(478\) 3.30978e9 5.73271e9i 1.38612 2.40084i
\(479\) −8.28100e8 6.94859e8i −0.344278 0.288883i 0.454210 0.890895i \(-0.349922\pi\)
−0.798487 + 0.602012i \(0.794366\pi\)
\(480\) 5.13681e8 + 2.55633e9i 0.212006 + 1.05505i
\(481\) 5.68321e8 + 3.22311e9i 0.232855 + 1.32059i
\(482\) 3.16022e9 2.65174e9i 1.28544 1.07861i
\(483\) −8.41697e8 + 5.54059e9i −0.339892 + 2.23739i
\(484\) 9.38331e8 3.41525e8i 0.376181 0.136919i
\(485\) −1.58850e9 −0.632252
\(486\) −1.54279e9 + 3.60132e9i −0.609650 + 1.42310i
\(487\) 6.04240e8 0.237060 0.118530 0.992950i \(-0.462182\pi\)
0.118530 + 0.992950i \(0.462182\pi\)
\(488\) 2.04293e9 7.43566e8i 0.795764 0.289634i
\(489\) 6.76540e8 4.45342e9i 0.261645 1.72232i
\(490\) −1.55971e9 + 1.30875e9i −0.598903 + 0.502539i
\(491\) 2.57128e8 + 1.45825e9i 0.0980312 + 0.555962i 0.993776 + 0.111394i \(0.0355317\pi\)
−0.895745 + 0.444568i \(0.853357\pi\)
\(492\) 2.13222e8 + 1.06110e9i 0.0807149 + 0.401677i
\(493\) 2.32074e9 + 1.94733e9i 0.872293 + 0.731940i
\(494\) −7.84550e8 + 1.35888e9i −0.292804 + 0.507151i
\(495\) 1.79566e9 + 5.58461e8i 0.665434 + 0.206954i
\(496\) −4.81737e7 8.34393e7i −0.0177266 0.0307033i
\(497\) 8.78376e8 4.98152e9i 0.320947 1.82018i
\(498\) −8.51891e8 1.39771e9i −0.309087 0.507123i
\(499\) −2.58862e9 9.42180e8i −0.932644 0.339455i −0.169387 0.985550i \(-0.554179\pi\)
−0.763257 + 0.646095i \(0.776401\pi\)
\(500\) −3.99357e9 1.45354e9i −1.42878 0.520035i
\(501\) 4.51433e8 1.07330e7i 0.160384 0.00381321i
\(502\) −7.83268e8 + 4.44213e9i −0.276342 + 1.56722i
\(503\) 1.60198e9 + 2.77472e9i 0.561268 + 0.972145i 0.997386 + 0.0722554i \(0.0230197\pi\)
−0.436118 + 0.899889i \(0.643647\pi\)
\(504\) 2.23971e9 1.06561e8i 0.779264 0.0370758i
\(505\) −1.99496e7 + 3.45538e7i −0.00689311 + 0.0119392i
\(506\) −5.20331e9 4.36610e9i −1.78547 1.49819i
\(507\) 7.36240e7 6.48215e7i 0.0250895 0.0220898i
\(508\) −3.66731e8 2.07983e9i −0.124115 0.703892i
\(509\) 3.51368e9 2.94833e9i 1.18100 0.990976i 0.181028 0.983478i \(-0.442058\pi\)
0.999972 0.00749826i \(-0.00238679\pi\)
\(510\) −3.17142e9 2.53516e9i −1.05866 0.846270i
\(511\) 2.44939e9 8.91506e8i 0.812054 0.295564i
\(512\) 2.59667e9 0.855010
\(513\) −6.37646e8 9.42297e8i −0.208530 0.308161i
\(514\) −7.21391e9 −2.34315
\(515\) −4.46020e9 + 1.62338e9i −1.43890 + 0.523715i
\(516\) −2.77906e8 + 1.08697e8i −0.0890478 + 0.0348293i
\(517\) 3.03854e9 2.54964e9i 0.967048 0.811450i
\(518\) 1.42434e9 + 8.07785e9i 0.450257 + 2.55353i
\(519\) −8.09372e8 2.72982e8i −0.254134 0.0857133i
\(520\) −1.26582e9 1.06215e9i −0.394785 0.331264i
\(521\) 4.84337e8 8.38897e8i 0.150043 0.259882i −0.781200 0.624281i \(-0.785392\pi\)
0.931243 + 0.364399i \(0.118725\pi\)
\(522\) −4.98018e9 + 2.08570e9i −1.53249 + 0.641808i
\(523\) 5.98358e8 + 1.03639e9i 0.182896 + 0.316786i 0.942866 0.333173i \(-0.108119\pi\)
−0.759969 + 0.649959i \(0.774786\pi\)
\(524\) 2.87339e8 1.62958e9i 0.0872438 0.494784i
\(525\) 6.44188e8 1.17966e9i 0.194292 0.355795i
\(526\) −2.26349e9 8.23842e8i −0.678154 0.246828i
\(527\) 2.66545e8 + 9.70146e7i 0.0793294 + 0.0288735i
\(528\) 6.10130e8 1.11729e9i 0.180386 0.330330i
\(529\) 1.28710e9 7.29950e9i 0.378022 2.14387i
\(530\) 1.34572e9 + 2.33086e9i 0.392636 + 0.680065i
\(531\) −4.68255e8 + 3.66747e9i −0.135722 + 1.06301i
\(532\) −1.14592e9 + 1.98479e9i −0.329962 + 0.571511i
\(533\) 7.98458e8 + 6.69986e8i 0.228406 + 0.191655i
\(534\) −5.11366e9 1.72472e9i −1.45324 0.490143i
\(535\) −8.10884e8 4.59875e9i −0.228939 1.29838i
\(536\) −2.82268e9 + 2.36851e9i −0.791745 + 0.664353i
\(537\) −1.36333e9 + 5.33241e8i −0.379919 + 0.148598i
\(538\) −3.77225e9 + 1.37299e9i −1.04439 + 0.380127i
\(539\) 1.87944e9 0.516974
\(540\) 3.84999e9 1.72105e9i 1.05216 0.470344i
\(541\) −2.76050e9 −0.749544 −0.374772 0.927117i \(-0.622279\pi\)
−0.374772 + 0.927117i \(0.622279\pi\)
\(542\) 3.42624e9 1.24705e9i 0.924316 0.336424i
\(543\) −1.01217e9 8.09101e8i −0.271301 0.216872i
\(544\) −3.98086e9 + 3.34034e9i −1.06018 + 0.889600i
\(545\) −2.60641e8 1.47817e9i −0.0689692 0.391144i
\(546\) 5.70438e9 5.02236e9i 1.49980 1.32049i
\(547\) −1.62513e9 1.36365e9i −0.424553 0.356243i 0.405339 0.914167i \(-0.367154\pi\)
−0.829892 + 0.557924i \(0.811598\pi\)
\(548\) −7.45500e8 + 1.29124e9i −0.193515 + 0.335178i
\(549\) 2.88859e9 + 4.49531e9i 0.745047 + 1.15946i
\(550\) 8.14543e8 + 1.41083e9i 0.208759 + 0.361581i
\(551\) 2.72277e8 1.54416e9i 0.0693393 0.393243i
\(552\) −4.32666e9 + 1.02869e8i −1.09488 + 0.0260313i
\(553\) −8.34097e9 3.03586e9i −2.09739 0.763386i
\(554\) 8.39693e9 + 3.05623e9i 2.09815 + 0.763664i
\(555\) 2.28117e9 + 3.74273e9i 0.566411 + 0.929316i
\(556\) 8.26036e8 4.68468e9i 0.203816 1.15590i
\(557\) 3.23479e9 + 5.60281e9i 0.793145 + 1.37377i 0.924011 + 0.382367i \(0.124891\pi\)
−0.130866 + 0.991400i \(0.541776\pi\)
\(558\) −3.71380e8 + 3.42987e8i −0.0904896 + 0.0835715i
\(559\) −1.43690e8 + 2.48878e8i −0.0347925 + 0.0602623i
\(560\) 1.48605e9 + 1.24694e9i 0.357582 + 0.300047i
\(561\) 7.38354e8 + 3.67441e9i 0.176561 + 0.878653i
\(562\) 3.44822e8 + 1.95558e9i 0.0819441 + 0.464728i
\(563\) −3.43877e9 + 2.88547e9i −0.812128 + 0.681456i −0.951115 0.308838i \(-0.900060\pi\)
0.138987 + 0.990294i \(0.455615\pi\)
\(564\) 1.33599e9 8.79437e9i 0.313565 2.06409i
\(565\) 2.41683e9 8.79655e8i 0.563738 0.205184i
\(566\) −4.62488e9 −1.07212
\(567\) 1.46793e9 + 5.31192e9i 0.338192 + 1.22380i
\(568\) 3.90639e9 0.894451
\(569\) 3.71235e9 1.35119e9i 0.844805 0.307484i 0.116885 0.993145i \(-0.462709\pi\)
0.727920 + 0.685662i \(0.240487\pi\)
\(570\) −3.15614e8 + 2.07757e9i −0.0713828 + 0.469888i
\(571\) 6.17683e9 5.18298e9i 1.38848 1.16507i 0.422527 0.906350i \(-0.361143\pi\)
0.965952 0.258722i \(-0.0833013\pi\)
\(572\) 9.32240e8 + 5.28699e9i 0.208277 + 1.18120i
\(573\) −3.07448e7 1.53001e8i −0.00682702 0.0339746i
\(574\) 2.00112e9 + 1.67914e9i 0.441653 + 0.370591i
\(575\) −1.29715e9 + 2.24674e9i −0.284547 + 0.492850i
\(576\) −1.58977e9 7.04063e9i −0.346621 1.53509i
\(577\) 7.53097e8 + 1.30440e9i 0.163206 + 0.282681i 0.936017 0.351956i \(-0.114483\pi\)
−0.772811 + 0.634636i \(0.781150\pi\)
\(578\) 1.57081e8 8.90849e8i 0.0338357 0.191892i
\(579\) 8.87315e8 + 1.45583e9i 0.189978 + 0.311698i
\(580\) 5.46125e9 + 1.98773e9i 1.16224 + 0.423019i
\(581\) −2.16361e9 7.87488e8i −0.457680 0.166582i
\(582\) 5.64078e9 1.34112e8i 1.18607 0.0281993i
\(583\) 4.31415e8 2.44668e9i 0.0901687 0.511372i
\(584\) 1.00649e9 + 1.74328e9i 0.209104 + 0.362179i
\(585\) 1.86122e9 3.60974e9i 0.384372 0.745471i
\(586\) −3.61662e9 + 6.26417e9i −0.742439 + 1.28594i
\(587\) 1.05438e9 + 8.84728e8i 0.215161 + 0.180541i 0.743998 0.668182i \(-0.232927\pi\)
−0.528837 + 0.848723i \(0.677372\pi\)
\(588\) 3.16342e9 2.78520e9i 0.641706 0.564983i
\(589\) −2.54931e7 1.44579e8i −0.00514067 0.0291542i
\(590\) 5.23104e9 4.38937e9i 1.04859 0.879873i
\(591\) 6.85826e7 + 5.48233e7i 0.0136665 + 0.0109247i
\(592\) 2.78827e9 1.01485e9i 0.552344 0.201037i
\(593\) 4.57156e9 0.900271 0.450136 0.892960i \(-0.351376\pi\)
0.450136 + 0.892960i \(0.351376\pi\)
\(594\) −6.42355e9 1.83150e9i −1.25754 0.358554i
\(595\) −5.71117e9 −1.11152
\(596\) −4.93846e9 + 1.79745e9i −0.955498 + 0.347773i
\(597\) −7.33793e9 + 2.87009e9i −1.41144 + 0.552058i
\(598\) −1.12377e10 + 9.42952e9i −2.14893 + 1.80317i
\(599\) −1.12694e9 6.39119e9i −0.214243 1.21503i −0.882215 0.470846i \(-0.843949\pi\)
0.667972 0.744186i \(-0.267162\pi\)
\(600\) 9.83556e8 + 3.31730e8i 0.185896 + 0.0626982i
\(601\) 5.32078e9 + 4.46466e9i 0.999803 + 0.838934i 0.986957 0.160983i \(-0.0514665\pi\)
0.0128458 + 0.999917i \(0.495911\pi\)
\(602\) −3.60120e8 + 6.23746e8i −0.0672759 + 0.116525i
\(603\) −7.20645e9 5.48508e9i −1.33848 1.01876i
\(604\) −3.78158e9 6.54990e9i −0.698304 1.20950i
\(605\) 2.23639e8 1.26832e9i 0.0410586 0.232855i
\(606\) 6.79242e7 1.24385e8i 0.0123985 0.0227046i
\(607\) 1.18260e9 + 4.30431e8i 0.214624 + 0.0781166i 0.447094 0.894487i \(-0.352459\pi\)
−0.232471 + 0.972603i \(0.574681\pi\)
\(608\) 2.52742e9 + 9.19904e8i 0.456052 + 0.165989i
\(609\) −3.64001e9 + 6.66572e9i −0.653043 + 1.19588i
\(610\) 1.71374e9 9.71908e9i 0.305696 1.73369i
\(611\) −4.28329e9 7.41887e9i −0.759684 1.31581i
\(612\) 6.68799e9 + 5.09046e9i 1.17941 + 0.897692i
\(613\) −3.71922e9 + 6.44188e9i −0.652140 + 1.12954i 0.330463 + 0.943819i \(0.392795\pi\)
−0.982603 + 0.185720i \(0.940538\pi\)
\(614\) 4.50079e9 + 3.77661e9i 0.784693 + 0.658436i
\(615\) 1.32271e9 + 4.46117e8i 0.229298 + 0.0773367i
\(616\) 6.63819e8 + 3.76471e9i 0.114424 + 0.648931i
\(617\) 1.32701e9 1.11349e9i 0.227444 0.190848i −0.521943 0.852980i \(-0.674793\pi\)
0.749387 + 0.662132i \(0.230348\pi\)
\(618\) 1.57012e10 6.14121e9i 2.67592 1.04663i
\(619\) −7.25643e9 + 2.64112e9i −1.22972 + 0.447581i −0.873501 0.486822i \(-0.838156\pi\)
−0.356217 + 0.934403i \(0.615934\pi\)
\(620\) 5.44151e8 0.0916956
\(621\) −2.58884e9 1.03173e10i −0.433794 1.72880i
\(622\) 4.42834e9 0.737861
\(623\) −7.13336e9 + 2.59633e9i −1.18191 + 0.430182i
\(624\) −2.14756e9 1.71671e9i −0.353833 0.282846i
\(625\) −2.70608e9 + 2.27067e9i −0.443364 + 0.372026i
\(626\) −8.12133e8 4.60583e9i −0.132317 0.750409i
\(627\) 1.45590e9 1.28183e9i 0.235882 0.207680i
\(628\) 3.86839e9 + 3.24596e9i 0.623263 + 0.522980i
\(629\) −4.36782e9 + 7.56529e9i −0.699822 + 1.21213i
\(630\) 4.66464e9 9.04684e9i 0.743234 1.44147i
\(631\) 5.50653e9 + 9.53759e9i 0.872520 + 1.51125i 0.859381 + 0.511335i \(0.170849\pi\)
0.0131385 + 0.999914i \(0.495818\pi\)
\(632\) 1.19033e9 6.75068e9i 0.187567 1.06374i
\(633\) 5.00154e9 1.18914e8i 0.783774 0.0186346i
\(634\) 1.10301e10 + 4.01463e9i 1.71897 + 0.625653i
\(635\) −2.55959e9 9.31616e8i −0.396701 0.144387i
\(636\) −2.89966e9 4.75750e9i −0.446938 0.733295i
\(637\) 7.04848e8 3.99739e9i 0.108046 0.612757i
\(638\) −4.60260e9 7.97194e9i −0.701667 1.21532i
\(639\) 2.11470e9 + 9.36540e9i 0.320624 + 1.41995i
\(640\) −3.09721e9 + 5.36453e9i −0.467026 + 0.808912i
\(641\) −8.26242e9 6.93300e9i −1.23909 1.03972i −0.997594 0.0693229i \(-0.977916\pi\)
−0.241500 0.970401i \(-0.577639\pi\)
\(642\) 3.26772e9 + 1.62618e10i 0.487385 + 2.42547i
\(643\) −5.08411e8 2.88334e9i −0.0754183 0.427718i −0.999016 0.0443549i \(-0.985877\pi\)
0.923598 0.383364i \(-0.125234\pi\)
\(644\) −1.64138e10 + 1.37728e10i −2.42164 + 2.03200i
\(645\) −5.78045e7 + 3.80507e8i −0.00848209 + 0.0558346i
\(646\) −3.93557e9 + 1.43243e9i −0.574373 + 0.209055i
\(647\) 6.62258e9 0.961307 0.480654 0.876911i \(-0.340399\pi\)
0.480654 + 0.876911i \(0.340399\pi\)
\(648\) −3.84303e9 + 1.82874e9i −0.554831 + 0.264022i
\(649\) −6.30340e9 −0.905145
\(650\) 3.30618e9 1.20335e9i 0.472203 0.171868i
\(651\) −1.06801e8 + 7.03034e8i −0.0151720 + 0.0998718i
\(652\) 1.31931e10 1.10703e10i 1.86415 1.56421i
\(653\) 3.30249e8 + 1.87294e9i 0.0464136 + 0.263225i 0.999180 0.0404781i \(-0.0128881\pi\)
−0.952767 + 0.303703i \(0.901777\pi\)
\(654\) 1.05034e9 + 5.22700e9i 0.146827 + 0.730685i
\(655\) −1.63488e9 1.37183e9i −0.227322 0.190746i
\(656\) 4.72492e8 8.18380e8i 0.0653478 0.113186i
\(657\) −3.63460e9 + 3.35672e9i −0.500008 + 0.461782i
\(658\) −1.07349e10 1.85934e10i −1.46895 2.54430i
\(659\) 8.20340e8 4.65238e9i 0.111659 0.633252i −0.876691 0.481054i \(-0.840254\pi\)
0.988350 0.152197i \(-0.0486349\pi\)
\(660\) 3.74189e9 + 6.13935e9i 0.506625 + 0.831225i
\(661\) 5.17660e9 + 1.88413e9i 0.697171 + 0.253750i 0.666203 0.745771i \(-0.267919\pi\)
0.0309686 + 0.999520i \(0.490141\pi\)
\(662\) 5.00747e8 + 1.82257e8i 0.0670834 + 0.0244164i
\(663\) 8.09201e9 1.92392e8i 1.07835 0.0256383i
\(664\) 3.08765e8 1.75109e9i 0.0409298 0.232124i
\(665\) 1.47796e9 + 2.55990e9i 0.194889 + 0.337557i
\(666\) −8.41644e9 1.30979e10i −1.10400 1.71807i
\(667\) 7.32962e9 1.26953e10i 0.956403 1.65654i
\(668\) 1.32256e9 + 1.10976e9i 0.171671 + 0.144049i
\(669\) 2.17710e9 1.91680e9i 0.281117 0.247506i
\(670\) 2.90459e9 + 1.64727e10i 0.373098 + 2.11594i
\(671\) −6.97859e9 + 5.85574e9i −0.891742 + 0.748260i
\(672\) −1.01760e10 8.13449e9i −1.29356 1.03404i
\(673\) −1.19084e10 + 4.33429e9i −1.50591 + 0.548107i −0.957583 0.288157i \(-0.906958\pi\)
−0.548328 + 0.836263i \(0.684735\pi\)
\(674\) 1.23862e10 1.55822
\(675\) −2.62866e8 + 2.53761e9i −0.0328982 + 0.317587i
\(676\) 3.75047e8 0.0466952
\(677\) 6.06415e8 2.20717e8i 0.0751120 0.0273385i −0.304191 0.952611i \(-0.598386\pi\)
0.379303 + 0.925273i \(0.376164\pi\)
\(678\) −8.50795e9 + 3.32772e9i −1.04838 + 0.410055i
\(679\) 6.07991e9 5.10165e9i 0.745338 0.625413i
\(680\) −7.65879e8 4.34352e9i −0.0934069 0.529737i
\(681\) −3.40762e9 1.14931e9i −0.413462 0.139451i
\(682\) −6.60238e8 5.54005e8i −0.0796994 0.0668757i
\(683\) −1.59602e9 + 2.76439e9i −0.191675 + 0.331992i −0.945806 0.324733i \(-0.894725\pi\)
0.754130 + 0.656725i \(0.228059\pi\)
\(684\) 5.50939e8 4.31507e9i 0.0658275 0.515574i
\(685\) 9.61513e8 + 1.66539e9i 0.114298 + 0.197970i
\(686\) −1.11964e9 + 6.34980e9i −0.132417 + 0.750976i
\(687\) 5.83676e9 1.06885e10i 0.686789 1.25767i
\(688\) 2.44832e8 + 8.91116e7i 0.0286622 + 0.0104322i
\(689\) −5.04205e9 1.83516e9i −0.587273 0.213750i
\(690\) −9.41599e9 + 1.72429e10i −1.09117 + 1.99820i
\(691\) −9.59221e8 + 5.44001e9i −0.110598 + 0.627230i 0.878239 + 0.478223i \(0.158719\pi\)
−0.988836 + 0.149007i \(0.952392\pi\)
\(692\) −1.63290e9 2.82826e9i −0.187321 0.324450i
\(693\) −8.66637e9 + 3.62948e9i −0.989170 + 0.414265i
\(694\) 1.80325e8 3.12331e8i 0.0204784 0.0354697i
\(695\) −4.69992e9 3.94370e9i −0.531060 0.445612i
\(696\) −5.55761e9 1.87445e9i −0.624822 0.210737i
\(697\) 4.83103e8 + 2.73981e9i 0.0540412 + 0.306483i
\(698\) 1.77497e9 1.48938e9i 0.197559 0.165772i
\(699\) −9.14293e9 + 3.57608e9i −1.01255 + 0.396038i
\(700\) 4.82903e9 1.75762e9i 0.532129 0.193679i
\(701\) 1.18768e10 1.30222 0.651112 0.758982i \(-0.274303\pi\)
0.651112 + 0.758982i \(0.274303\pi\)
\(702\) −6.30445e9 + 1.29754e10i −0.687808 + 1.41560i
\(703\) 4.52129e9 0.490816
\(704\) 1.15636e10 4.20880e9i 1.24907 0.454626i
\(705\) −8.96143e9 7.16355e9i −0.963197 0.769957i
\(706\) −8.11452e9 + 6.80889e9i −0.867853 + 0.728215i
\(707\) −3.46172e7 1.96324e8i −0.00368404 0.0208932i
\(708\) −1.06097e10 + 9.34119e9i −1.12353 + 0.989204i
\(709\) −1.20839e9 1.01396e9i −0.127335 0.106846i 0.576896 0.816817i \(-0.304264\pi\)
−0.704231 + 0.709971i \(0.748708\pi\)
\(710\) 8.86649e9 1.53572e10i 0.929710 1.61031i
\(711\) 1.68288e10 8.00681e8i 1.75594 0.0835441i
\(712\) −2.93119e9 5.07696e9i −0.304343 0.527138i
\(713\) 2.38339e8 1.35169e9i 0.0246253 0.139657i
\(714\) 2.02804e10 4.82178e8i 2.08513 0.0495751i
\(715\) 6.50655e9 + 2.36819e9i 0.665702 + 0.242296i
\(716\) −5.25950e9 1.91430e9i −0.535486 0.194901i
\(717\) 9.19812e9 + 1.50914e10i 0.931927 + 1.52902i
\(718\) 3.18631e9 1.80704e10i 0.321257 1.82194i
\(719\) 2.09939e9 + 3.63626e9i 0.210641 + 0.364841i 0.951915 0.306361i \(-0.0991116\pi\)
−0.741274 + 0.671202i \(0.765778\pi\)
\(720\) −3.51597e9 1.09349e9i −0.351060 0.109182i
\(721\) 1.18576e10 2.05379e10i 1.17821 2.04072i
\(722\) −1.03333e10 8.67067e9i −1.02178 0.857378i
\(723\) 2.16990e9 + 1.07985e10i 0.213529 + 1.06262i
\(724\) −8.60313e8 4.87908e9i −0.0842504 0.477807i
\(725\) −2.69329e9 + 2.25994e9i −0.262482 + 0.220249i
\(726\) −6.87066e8 + 4.52271e9i −0.0666378 + 0.438653i
\(727\) 1.16901e10 4.25486e9i 1.12836 0.410690i 0.290665 0.956825i \(-0.406124\pi\)
0.837697 + 0.546135i \(0.183901\pi\)
\(728\) 8.25611e9 0.793078
\(729\) −6.46473e9 8.22351e9i −0.618023 0.786160i
\(730\) 9.13785e9 0.869388
\(731\) −7.20798e8 + 2.62349e8i −0.0682500 + 0.0248410i
\(732\) −3.06837e9 + 2.01980e10i −0.289147 + 1.90335i
\(733\) −6.19618e9 + 5.19921e9i −0.581112 + 0.487611i −0.885312 0.464997i \(-0.846055\pi\)
0.304200 + 0.952608i \(0.401611\pi\)
\(734\) −3.14892e9 1.78584e10i −0.293917 1.66689i
\(735\) −1.07094e9 5.32953e9i −0.0994856 0.495089i
\(736\) 1.92627e10 + 1.61633e10i 1.78092 + 1.49437i
\(737\) 7.72012e9 1.33716e10i 0.710375 1.23041i
\(738\) −4.73461e9 1.47250e9i −0.433598 0.134852i
\(739\) −1.58506e8 2.74541e8i −0.0144474 0.0250237i 0.858711 0.512460i \(-0.171266\pi\)
−0.873159 + 0.487436i \(0.837932\pi\)
\(740\) −2.91004e9 + 1.65037e10i −0.263990 + 1.49716i
\(741\) −2.18032e9 3.57727e9i −0.196860 0.322989i
\(742\) −1.26365e10 4.59932e9i −1.13557 0.413314i
\(743\) 6.68477e8 + 2.43306e8i 0.0597896 + 0.0217616i 0.371742 0.928336i \(-0.378761\pi\)
−0.311952 + 0.950098i \(0.600983\pi\)
\(744\) −5.49001e8 + 1.30528e7i −0.0488729 + 0.00116198i
\(745\) −1.17702e9 + 6.67521e9i −0.104289 + 0.591450i
\(746\) 7.22058e9 + 1.25064e10i 0.636775 + 1.10293i
\(747\) 4.36532e9 2.07693e8i 0.383172 0.0182305i
\(748\) −7.16471e9 + 1.24096e10i −0.625955 + 1.08419i
\(749\) 1.78731e10 + 1.49973e10i 1.55422 + 1.30415i
\(750\) 1.46130e10 1.28658e10i 1.26481 1.11359i
\(751\) −4.04775e7 2.29559e8i −0.00348717 0.0197767i 0.983015 0.183528i \(-0.0587517\pi\)
−0.986502 + 0.163751i \(0.947641\pi\)
\(752\) −5.94959e9 + 4.99230e9i −0.510181 + 0.428093i
\(753\) −9.40690e9 7.51965e9i −0.802905 0.641823i
\(754\) −1.86817e10 + 6.79957e9i −1.58714 + 0.577672i
\(755\) −9.75465e9 −0.824892
\(756\) &mi