Properties

Label 27.8.e.a.4.3
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 4.3
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.3

$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −16.4594 5.99073i −1.45482 0.529511i −0.510887 0.859648i \(-0.670683\pi\)
−0.943933 + 0.330137i \(0.892905\pi\)
\(3\) 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 0.825472 + 0.564444i \(0.190909\pi\)
−0.968741 + 0.248076i \(0.920202\pi\)
\(6\) 161.374 803.077i 0.305003 1.51785i
\(7\) 882.649 740.631i 0.972624 0.816129i −0.0103360 0.999947i \(-0.503290\pi\)
0.982960 + 0.183818i \(0.0588457\pi\)
\(8\) −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 0.966011 + 0.258501i \(0.0832285\pi\)
−0.819341 + 0.573307i \(0.805660\pi\)
\(12\) −4351.78 + 7140.02i −0.726998 + 1.19279i
\(13\) −7567.07 + 2754.19i −0.955270 + 0.347690i −0.772178 0.635406i \(-0.780833\pi\)
−0.183092 + 0.983096i \(0.558610\pi\)
\(14\) −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 0.468833 + 0.883287i \(0.344675\pi\)
−0.999365 + 0.0356221i \(0.988659\pi\)
\(18\) 38263.6 + 1820.50i 1.54644 + 0.0735762i
\(19\) −5562.25 9634.10i −0.186043 0.322236i 0.757885 0.652389i \(-0.226233\pi\)
−0.943927 + 0.330153i \(0.892900\pi\)
\(20\) −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 −0.974275 0.225364i \(-0.927643\pi\)
−0.391121 0.920339i \(-0.627913\pi\)
\(24\) 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 −0.215609 0.976480i \(-0.569174\pi\)
−0.792835 + 0.609436i \(0.791396\pi\)
\(30\) 175921. + 68808.2i 1.18958 + 0.465282i
\(31\) −10109.4 8482.81i −0.0609481 0.0511415i 0.611805 0.791009i \(-0.290444\pi\)
−0.672753 + 0.739867i \(0.734888\pi\)
\(32\) −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 0.321186 + 0.947016i \(0.395919\pi\)
−0.980733 + 0.195353i \(0.937415\pi\)
\(38\) 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 −0.476129 0.879376i \(-0.657960\pi\)
0.200516 + 0.979690i \(0.435738\pi\)
\(42\) −452346. 828354.i −0.942104 1.72522i
\(43\) 6197.05 + 35145.2i 0.0118863 + 0.0674104i 0.990174 0.139841i \(-0.0446592\pi\)
−0.978288 + 0.207252i \(0.933548\pi\)
\(44\) −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 0.145335 0.989382i \(-0.453574\pi\)
0.999589 + 0.0286771i \(0.00912944\pi\)
\(48\) 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 0.738463 + 0.674294i \(0.235552\pi\)
−0.924550 + 0.381060i \(0.875559\pi\)
\(60\) −1.44727e6 1.27424e6i −0.865011 0.761590i
\(61\) −1.87164e6 + 1.57049e6i −1.05577 + 0.885893i −0.993688 0.112178i \(-0.964217\pi\)
−0.0620779 + 0.998071i \(0.519773\pi\)
\(62\) 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 0.605295 0.796001i \(-0.293055\pi\)
0.975343 + 0.220696i \(0.0708329\pi\)
\(68\) −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 0.229940 + 0.973205i \(0.426147\pi\)
−0.957790 + 0.287468i \(0.907186\pi\)
\(72\) 1.42961e6 + 1.32031e6i 0.451392 + 0.416882i
\(73\) 1.13112e6 + 1.95915e6i 0.340313 + 0.589439i 0.984491 0.175437i \(-0.0561337\pi\)
−0.644178 + 0.764876i \(0.722800\pi\)
\(74\) 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 −0.662852 0.748751i \(-0.730654\pi\)
−0.989062 + 0.147504i \(0.952876\pi\)
\(80\) 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 0.155434 0.987846i \(-0.450322\pi\)
−0.515906 + 0.856645i \(0.672544\pi\)
\(84\) 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 0.504673 0.863310i \(-0.331613\pi\)
−0.999985 + 0.00540466i \(0.998280\pi\)
\(90\) −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 0.976185 + 0.216941i \(0.0696080\pi\)
−0.843115 + 0.537733i \(0.819281\pi\)
\(98\) −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 −0.649165 0.760647i \(-0.724882\pi\)
0.636365 + 0.771388i \(0.280437\pi\)
\(102\) 1.32143e7 + 1.16344e7i 1.23295 + 1.08554i
\(103\) −3.57406e6 + 2.02695e7i −0.322279 + 1.82773i 0.205869 + 0.978580i \(0.433998\pi\)
−0.528147 + 0.849153i \(0.677113\pi\)
\(104\) 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 −0.854285 0.519804i \(-0.826005\pi\)
0.980549 0.196274i \(-0.0628841\pi\)
\(114\) −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 0.965123 0.261798i \(-0.0843154\pi\)
−0.709285 + 0.704922i \(0.750982\pi\)
\(128\) −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 0.770070 0.637960i \(-0.220221\pi\)
−0.494546 + 0.869151i \(0.664666\pi\)
\(132\) −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 0.208543 0.978013i \(-0.433128\pi\)
−0.468901 + 0.883250i \(0.655350\pi\)
\(138\) −6.65449e7 + 5.31944e7i −2.15545 + 1.72302i
\(139\) 2.03804e7 + 1.71012e7i 0.643667 + 0.540101i 0.905142 0.425109i \(-0.139764\pi\)
−0.261475 + 0.965210i \(0.584209\pi\)
\(140\) −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 −0.660574 0.750761i \(-0.729687\pi\)
−0.0234486 + 0.999725i \(0.507465\pi\)
\(150\) 1.06340e7 1.74473e7i 0.257262 0.422093i
\(151\) 7.34521e6 + 4.16568e7i 0.173614 + 0.984615i 0.939731 + 0.341914i \(0.111075\pi\)
−0.766117 + 0.642701i \(0.777814\pi\)
\(152\) −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 −0.891550 0.452921i \(-0.850382\pi\)
0.992692 0.120679i \(-0.0385071\pi\)
\(158\) 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 −0.967705 0.252085i \(-0.918884\pi\)
0.995563 + 0.0940926i \(0.0299950\pi\)
\(168\) 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 0.999199 0.0400174i \(-0.0127413\pi\)
−0.952627 + 0.304142i \(0.901630\pi\)
\(174\) −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 −0.949805 0.312842i \(-0.898719\pi\)
0.745832 + 0.666134i \(0.232052\pi\)
\(180\) 4.87490e7 7.58645e7i 0.623034 0.969583i
\(181\) 1.38544e7 + 2.39965e7i 0.173665 + 0.300796i 0.939698 0.342004i \(-0.111106\pi\)
−0.766034 + 0.642801i \(0.777772\pi\)
\(182\) 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 0.358251 0.933625i \(-0.383373\pi\)
−0.325687 + 0.945478i \(0.605596\pi\)
\(192\) 1.43739e8 + 5.62206e7i 1.46561 + 0.573246i
\(193\) −2.79276e7 2.34341e7i −0.279630 0.234637i 0.492176 0.870496i \(-0.336202\pi\)
−0.771806 + 0.635859i \(0.780646\pi\)
\(194\) 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 0.861618 0.507557i \(-0.169451\pi\)
−0.870366 + 0.492405i \(0.836118\pi\)
\(198\) 1.80895e7 + 1.41681e8i 0.165615 + 1.29713i
\(199\) −8.42423e7 + 1.45912e8i −0.757783 + 1.31252i 0.186196 + 0.982513i \(0.440384\pi\)
−0.943979 + 0.330006i \(0.892949\pi\)
\(200\) −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 −0.837920 0.545793i \(-0.816228\pi\)
0.974059 0.226292i \(-0.0726604\pi\)
\(212\) 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 −0.487955 0.872869i \(-0.662257\pi\)
0.774875 + 0.632114i \(0.217813\pi\)
\(224\) 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 0.998969 + 0.0453933i \(0.0144541\pi\)
−0.923199 + 0.384323i \(0.874435\pi\)
\(228\) 9.29934e7 + 2.21096e6i 0.519613 + 0.0123541i
\(229\) 2.44709e8 8.90666e7i 1.34656 0.490107i 0.434686 0.900582i \(-0.356859\pi\)
0.911872 + 0.410475i \(0.134637\pi\)
\(230\) −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 0.455070 + 0.890455i \(0.349614\pi\)
−0.998692 + 0.0511252i \(0.983719\pi\)
\(234\) −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 −0.972167 0.234289i \(-0.924724\pi\)
−0.399544 0.916714i \(-0.630832\pi\)
\(240\) 1.18254e7 + 7.78422e7i 0.0552173 + 0.363476i
\(241\) −2.21320e8 8.05539e7i −1.01850 0.370704i −0.221809 0.975090i \(-0.571196\pi\)
−0.796691 + 0.604387i \(0.793418\pi\)
\(242\) −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 0.999869 + 0.0161879i \(0.00515300\pi\)
−0.485915 + 0.874006i \(0.661514\pi\)
\(252\) −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 0.487518 0.873113i \(-0.337902\pi\)
0.934687 + 0.355473i \(0.115680\pi\)
\(258\) 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 −0.446542 0.894763i \(-0.647345\pi\)
0.803628 + 0.595132i \(0.202900\pi\)
\(264\) 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 −0.997738 0.0672212i \(-0.978587\pi\)
−0.107055 + 0.994253i \(0.534142\pi\)
\(278\) −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 0.999768 0.0215318i \(-0.00685430\pi\)
−0.946839 + 0.321708i \(0.895743\pi\)
\(282\) −4.17640e8 7.64798e8i −1.10900 2.03084i
\(283\) 2.48118e8 9.03076e7i 0.650737 0.236849i 0.00450515 0.999990i \(-0.498566\pi\)
0.646232 + 0.763141i \(0.276344\pi\)
\(284\) −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 0.931414 0.363962i \(-0.118576\pi\)
−0.196694 + 0.980465i \(0.563021\pi\)
\(294\) −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 −0.982673 0.185348i \(-0.940659\pi\)
0.651852 + 0.758346i \(0.273992\pi\)
\(308\) 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 −0.556095 0.831119i \(-0.687701\pi\)
0.108240 + 0.994125i \(0.465479\pi\)
\(312\) −1.74397e8 + 2.86135e8i −0.325086 + 0.533372i
\(313\) −4.63659e7 2.62954e8i −0.0854660 0.484702i −0.997255 0.0740429i \(-0.976410\pi\)
0.911789 0.410659i \(-0.134701\pi\)
\(314\) −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 −0.971187 0.238319i \(-0.923404\pi\)
0.0660535 + 0.997816i \(0.478959\pi\)
\(318\) 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 −0.660278 0.751021i \(-0.729562\pi\)
0.624955 + 0.780661i \(0.285117\pi\)
\(332\) −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 −0.768447 0.639913i \(-0.778970\pi\)
−0.177337 + 0.984150i \(0.556748\pi\)
\(338\) −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 0.632599 0.774480i \(-0.281988\pi\)
−0.652864 + 0.757475i \(0.726433\pi\)
\(348\) 9.20584e8 7.35893e8i 1.17094 0.936025i
\(349\) −1.24307e8 4.52439e7i −0.156533 0.0569733i 0.262565 0.964914i \(-0.415431\pi\)
−0.419098 + 0.907941i \(0.637654\pi\)
\(350\) −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 0.662120 0.749398i \(-0.269657\pi\)
0.0255098 + 0.999675i \(0.491879\pi\)
\(354\) 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 −0.993191 0.116500i \(-0.962833\pi\)
0.395704 0.918378i \(-0.370501\pi\)
\(360\) −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 −0.919569 0.392928i \(-0.871462\pi\)
0.729723 0.683743i \(-0.239649\pi\)
\(368\) −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 0.826228 + 0.563335i \(0.190482\pi\)
−0.969073 + 0.246775i \(0.920629\pi\)
\(374\) 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 −0.980466 0.196687i \(-0.936982\pi\)
0.988608 + 0.150514i \(0.0480928\pi\)
\(384\) −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 −0.981130 0.193351i \(-0.938065\pi\)
0.855831 0.517256i \(-0.173047\pi\)
\(390\) −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 0.685761 0.727827i \(-0.259469\pi\)
−0.973197 + 0.229973i \(0.926136\pi\)
\(398\) 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 0.626282 0.779597i \(-0.284576\pi\)
−0.659000 + 0.752143i \(0.729020\pi\)
\(402\) −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 0.860247 0.509877i \(-0.170309\pi\)
−0.352750 + 0.935718i \(0.614753\pi\)
\(410\) −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 −0.841980 0.539508i \(-0.818610\pi\)
−0.298205 + 0.954502i \(0.596388\pi\)
\(420\) −2.22118e9 5.28096e7i −1.46289 0.0347808i
\(421\) −4.30655e8 2.44236e9i −0.281282 1.59523i −0.718272 0.695763i \(-0.755067\pi\)
0.436990 0.899466i \(-0.356045\pi\)
\(422\) −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 −0.418351 + 0.908286i \(0.637392\pi\)
−0.967133 + 0.254273i \(0.918164\pi\)
\(440\) 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 −0.979141 0.203184i \(-0.934871\pi\)
0.850598 0.525817i \(-0.176240\pi\)
\(444\) −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 −0.722622 0.691243i \(-0.757063\pi\)
0.959945 + 0.280188i \(0.0903967\pi\)
\(450\) 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 0.430003 0.902828i \(-0.358513\pi\)
−0.250925 + 0.968006i \(0.580735\pi\)
\(458\) −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 0.558091 0.829780i \(-0.311534\pi\)
−0.105850 + 0.994382i \(0.533756\pi\)
\(462\) 2.74880e9 2.19733e9i 1.29687 1.03669i
\(463\) −4.67271e7 3.92087e7i −0.0218794 0.0183590i 0.631782 0.775146i \(-0.282324\pi\)
−0.653662 + 0.756787i \(0.726768\pi\)
\(464\) −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 0.998520 0.0543880i \(-0.0173208\pi\)
−0.546361 + 0.837550i \(0.683987\pi\)
\(468\) 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 −0.798487 0.602012i \(-0.794366\pi\)
0.454210 + 0.890895i \(0.349922\pi\)
\(480\) 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 −0.895745 0.444568i \(-0.853357\pi\)
0.993776 0.111394i \(-0.0355317\pi\)
\(492\) 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 −0.763257 0.646095i \(-0.776401\pi\)
−0.169387 + 0.985550i \(0.554179\pi\)
\(500\) −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 −0.436118 0.899889i \(-0.643647\pi\)
0.997386 0.0722554i \(-0.0230197\pi\)
\(504\) 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 0.999972 + 0.00749826i \(0.00238679\pi\)
0.181028 + 0.983478i \(0.442058\pi\)
\(510\) −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 0.931243 0.364399i \(-0.118725\pi\)
−0.781200 + 0.624281i \(0.785392\pi\)
\(522\) −4.98018e9 2.08570e9i −1.53249 0.641808i
\(523\) 5.98358e8 1.03639e9i 0.182896 0.316786i −0.759969 0.649959i \(-0.774786\pi\)
0.942866 + 0.333173i \(0.108119\pi\)
\(524\) 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 −0.829892 0.557924i \(-0.811598\pi\)
0.405339 + 0.914167i \(0.367154\pi\)
\(548\) −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 −0.130866 0.991400i \(-0.541776\pi\)
0.924011 0.382367i \(-0.124891\pi\)
\(558\) −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 0.138987 0.990294i \(-0.455615\pi\)
−0.951115 + 0.308838i \(0.900060\pi\)
\(564\) 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 0.727920 0.685662i \(-0.240487\pi\)
0.116885 + 0.993145i \(0.462709\pi\)
\(570\) −3.15614e8 2.07757e9i −0.0713828 0.469888i
\(571\) 6.17683e9 + 5.18298e9i 1.38848 + 1.16507i 0.965952 + 0.258722i \(0.0833013\pi\)
0.422527 + 0.906350i \(0.361143\pi\)
\(572\) 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 −0.772811 0.634636i \(-0.781150\pi\)
0.936017 + 0.351956i \(0.114483\pi\)
\(578\) 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 −0.528837 0.848723i \(-0.677372\pi\)
0.743998 + 0.668182i \(0.232927\pi\)
\(588\) 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 0.667972 + 0.744186i \(0.267162\pi\)
−0.882215 + 0.470846i \(0.843949\pi\)
\(600\) 9.83556e8 3.31730e8i 0.185896 0.0626982i
\(601\) 5.32078e9 4.46466e9i 0.999803 0.838934i 0.0128458 0.999917i \(-0.495911\pi\)
0.986957 + 0.160983i \(0.0514665\pi\)
\(602\) −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 −0.232471 0.972603i \(-0.574681\pi\)
0.447094 + 0.894487i \(0.352459\pi\)
\(608\) 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 −0.982603 0.185720i \(-0.940538\pi\)
0.330463 0.943819i \(-0.392795\pi\)
\(614\) 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 0.749387 0.662132i \(-0.230348\pi\)
−0.521943 + 0.852980i \(0.674793\pi\)
\(618\) 1.57012e10 + 6.14121e9i 2.67592 + 1.04663i
\(619\) −7.25643e9 2.64112e9i −1.22972 0.447581i −0.356217 0.934403i \(-0.615934\pi\)
−0.873501 + 0.486822i \(0.838156\pi\)
\(620\) 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 0.0131385 0.999914i \(-0.495818\pi\)
0.859381 0.511335i \(-0.170849\pi\)
\(632\) 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 −0.241500 + 0.970401i \(0.577639\pi\)
−0.997594 + 0.0693229i \(0.977916\pi\)
\(642\) 3.26772e9 1.62618e10i 0.487385 2.42547i
\(643\) −5.08411e8 + 2.88334e9i −0.0754183 + 0.427718i 0.923598 + 0.383364i \(0.125234\pi\)
−0.999016 + 0.0443549i \(0.985877\pi\)
\(644\) −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 −0.952767 0.303703i \(-0.901777\pi\)
0.999180 + 0.0404781i \(0.0128881\pi\)
\(654\) 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 0.988350 + 0.152197i \(0.0486349\pi\)
−0.876691 + 0.481054i \(0.840254\pi\)
\(660\) 3.74189e9 6.13935e9i 0.506625 0.831225i
\(661\) 5.17660e9 1.88413e9i 0.697171 0.253750i 0.0309686 0.999520i \(-0.490141\pi\)
0.666203 + 0.745771i \(0.267919\pi\)
\(662\) 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 −0.548328 0.836263i \(-0.684735\pi\)
−0.957583 + 0.288157i \(0.906958\pi\)
\(674\) 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 0.379303 0.925273i \(-0.376164\pi\)
−0.304191 + 0.952611i \(0.598386\pi\)
\(678\) −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 0.754130 0.656725i \(-0.228059\pi\)
−0.945806 + 0.324733i \(0.894725\pi\)
\(684\) 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 −0.988836 0.149007i \(-0.952392\pi\)
0.878239 0.478223i \(-0.158719\pi\)
\(692\) −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 −0.704231 0.709971i \(-0.748708\pi\)
0.576896 + 0.816817i \(0.304264\pi\)
\(710\) 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 −0.741274 0.671202i \(-0.765778\pi\)
0.951915 + 0.306361i \(0.0991116\pi\)
\(720\) −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 0.837697 0.546135i \(-0.183901\pi\)
0.290665 + 0.956825i \(0.406124\pi\)
\(728\) 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 0.304200 0.952608i \(-0.401611\pi\)
−0.885312 + 0.464997i \(0.846055\pi\)
\(734\) −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 −0.873159 0.487436i \(-0.837932\pi\)
0.858711 + 0.512460i \(0.171266\pi\)
\(740\) −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 −0.311952 0.950098i \(-0.600983\pi\)
0.371742 + 0.928336i \(0.378761\pi\)
\(744\) −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 −0.986502 0.163751i \(-0.947641\pi\)
0.983015 + 0.183528i \(0.0587517\pi\)
\(752\) −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
\(756\) −9.20833e9 1.89520e10i