Properties

Label 27.8.e.a.4.6
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 4.6
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.62864 - 3.50454i) q^{2} +(31.7200 - 34.3634i) q^{3} +(-17.6248 - 14.7890i) q^{4} +(40.7285 - 230.983i) q^{5} +(-425.848 + 219.708i) q^{6} +(500.665 - 420.108i) q^{7} +(773.656 + 1340.01i) q^{8} +(-174.680 - 2180.01i) q^{9} +O(q^{10})\) \(q+(-9.62864 - 3.50454i) q^{2} +(31.7200 - 34.3634i) q^{3} +(-17.6248 - 14.7890i) q^{4} +(40.7285 - 230.983i) q^{5} +(-425.848 + 219.708i) q^{6} +(500.665 - 420.108i) q^{7} +(773.656 + 1340.01i) q^{8} +(-174.680 - 2180.01i) q^{9} +(-1201.65 + 2081.32i) q^{10} +(-328.263 - 1861.67i) q^{11} +(-1067.26 + 136.541i) q^{12} +(-13604.6 + 4951.67i) q^{13} +(-6293.01 + 2290.47i) q^{14} +(-6645.44 - 8726.35i) q^{15} +(-2241.74 - 12713.6i) q^{16} +(-7312.15 + 12665.0i) q^{17} +(-5958.01 + 21602.7i) q^{18} +(-21696.6 - 37579.6i) q^{19} +(-4133.84 + 3468.70i) q^{20} +(1444.80 - 30530.4i) q^{21} +(-3363.57 + 19075.8i) q^{22} +(61924.7 + 51961.0i) q^{23} +(70587.6 + 15919.8i) q^{24} +(21719.2 + 7905.14i) q^{25} +148347. q^{26} +(-80453.4 - 63147.5i) q^{27} -15037.1 q^{28} +(85205.2 + 31012.1i) q^{29} +(33404.7 + 107312. i) q^{30} +(-114762. - 96296.5i) q^{31} +(11421.8 - 64776.5i) q^{32} +(-74385.8 - 47772.1i) q^{33} +(114791. - 96321.1i) q^{34} +(-76646.4 - 132756. i) q^{35} +(-29161.5 + 41005.7i) q^{36} +(40221.7 - 69666.1i) q^{37} +(77209.6 + 437877. i) q^{38} +(-261382. + 624567. i) q^{39} +(341029. - 124125. i) q^{40} +(181176. - 65942.8i) q^{41} +(-120906. + 288903. i) q^{42} +(-86932.1 - 493016. i) q^{43} +(-21746.7 + 37666.3i) q^{44} +(-510660. - 48440.7i) q^{45} +(-414151. - 717331. i) q^{46} +(615804. - 516721. i) q^{47} +(-507988. - 326240. i) q^{48} +(-68831.8 + 390364. i) q^{49} +(-181422. - 152232. i) q^{50} +(203271. + 653004. i) q^{51} +(313009. + 113926. i) q^{52} -1.14077e6 q^{53} +(553354. + 889976. i) q^{54} -443384. q^{55} +(950292. + 345878. i) q^{56} +(-1.97958e6 - 446459. i) q^{57} +(-711726. - 597209. i) q^{58} +(299570. - 1.69894e6i) q^{59} +(-11929.2 + 252080. i) q^{60} +(1.71084e6 - 1.43556e6i) q^{61} +(767524. + 1.32939e6i) q^{62} +(-1.00330e6 - 1.01807e6i) q^{63} +(-1.16321e6 + 2.01474e6i) q^{64} +(589656. + 3.34410e6i) q^{65} +(548815. + 720668. i) q^{66} +(-117367. + 42717.9i) q^{67} +(316178. - 115079. i) q^{68} +(3.74981e6 - 479736. i) q^{69} +(272754. + 1.54686e6i) q^{70} +(850034. - 1.47230e6i) q^{71} +(2.78610e6 - 1.92065e6i) q^{72} +(-868776. - 1.50476e6i) q^{73} +(-631428. + 529831. i) q^{74} +(960581. - 495593. i) q^{75} +(-173366. + 983206. i) q^{76} +(-946453. - 794169. i) q^{77} +(4.70557e6 - 5.09770e6i) q^{78} +(2.67970e6 + 975329. i) q^{79} -3.02792e6 q^{80} +(-4.72194e6 + 761608. i) q^{81} -1.97558e6 q^{82} +(2.05276e6 + 747144. i) q^{83} +(-476978. + 516726. i) q^{84} +(2.62759e6 + 2.20481e6i) q^{85} +(-890757. + 5.05173e6i) q^{86} +(3.76839e6 - 1.94423e6i) q^{87} +(2.24070e6 - 1.88017e6i) q^{88} +(-5.87690e6 - 1.01791e7i) q^{89} +(4.74720e6 + 2.25604e6i) q^{90} +(-4.73111e6 + 8.19453e6i) q^{91} +(-322962. - 1.83161e6i) q^{92} +(-6.94932e6 + 889069. i) q^{93} +(-7.74022e6 + 2.81721e6i) q^{94} +(-9.56393e6 + 3.48098e6i) q^{95} +(-1.86364e6 - 2.44720e6i) q^{96} +(1.94881e6 + 1.10522e7i) q^{97} +(2.03080e6 - 3.51745e6i) q^{98} +(-4.00113e6 + 1.04081e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.62864 3.50454i −0.851059 0.309760i −0.120587 0.992703i \(-0.538478\pi\)
−0.730472 + 0.682943i \(0.760700\pi\)
\(3\) 31.7200 34.3634i 0.678280 0.734803i
\(4\) −17.6248 14.7890i −0.137694 0.115539i
\(5\) 40.7285 230.983i 0.145715 0.826389i −0.821076 0.570819i \(-0.806626\pi\)
0.966790 0.255570i \(-0.0822632\pi\)
\(6\) −425.848 + 219.708i −0.804870 + 0.415257i
\(7\) 500.665 420.108i 0.551702 0.462933i −0.323815 0.946120i \(-0.604966\pi\)
0.875517 + 0.483188i \(0.160521\pi\)
\(8\) 773.656 + 1340.01i 0.534236 + 0.925323i
\(9\) −174.680 2180.01i −0.0798718 0.996805i
\(10\) −1201.65 + 2081.32i −0.379994 + 0.658170i
\(11\) −328.263 1861.67i −0.0743614 0.421724i −0.999149 0.0412412i \(-0.986869\pi\)
0.924788 0.380483i \(-0.124242\pi\)
\(12\) −1067.26 + 136.541i −0.178294 + 0.0228102i
\(13\) −13604.6 + 4951.67i −1.71745 + 0.625101i −0.997614 0.0690437i \(-0.978005\pi\)
−0.719836 + 0.694144i \(0.755783\pi\)
\(14\) −6293.01 + 2290.47i −0.612929 + 0.223088i
\(15\) −6645.44 8726.35i −0.508398 0.667595i
\(16\) −2241.74 12713.6i −0.136825 0.775974i
\(17\) −7312.15 + 12665.0i −0.360972 + 0.625222i −0.988121 0.153677i \(-0.950888\pi\)
0.627149 + 0.778899i \(0.284222\pi\)
\(18\) −5958.01 + 21602.7i −0.240795 + 0.873081i
\(19\) −21696.6 37579.6i −0.725696 1.25694i −0.958687 0.284463i \(-0.908185\pi\)
0.232992 0.972479i \(-0.425149\pi\)
\(20\) −4133.84 + 3468.70i −0.115544 + 0.0969531i
\(21\) 1444.80 30530.4i 0.0340439 0.719390i
\(22\) −3363.57 + 19075.8i −0.0673475 + 0.381947i
\(23\) 61924.7 + 51961.0i 1.06125 + 0.890492i 0.994231 0.107260i \(-0.0342077\pi\)
0.0670161 + 0.997752i \(0.478652\pi\)
\(24\) 70587.6 + 15919.8i 1.04229 + 0.235070i
\(25\) 21719.2 + 7905.14i 0.278006 + 0.101186i
\(26\) 148347. 1.65528
\(27\) −80453.4 63147.5i −0.786631 0.617423i
\(28\) −15037.1 −0.129453
\(29\) 85205.2 + 31012.1i 0.648743 + 0.236123i 0.645369 0.763871i \(-0.276704\pi\)
0.00337448 + 0.999994i \(0.498926\pi\)
\(30\) 33404.7 + 107312.i 0.225883 + 0.725645i
\(31\) −114762. 96296.5i −0.691881 0.580557i 0.227570 0.973762i \(-0.426922\pi\)
−0.919451 + 0.393205i \(0.871366\pi\)
\(32\) 11421.8 64776.5i 0.0616185 0.349456i
\(33\) −74385.8 47772.1i −0.360322 0.231406i
\(34\) 114791. 96321.1i 0.500878 0.420286i
\(35\) −76646.4 132756.i −0.302172 0.523377i
\(36\) −29161.5 + 41005.7i −0.104172 + 0.146482i
\(37\) 40221.7 69666.1i 0.130543 0.226108i −0.793343 0.608775i \(-0.791661\pi\)
0.923886 + 0.382667i \(0.124995\pi\)
\(38\) 77209.6 + 437877.i 0.228259 + 1.29452i
\(39\) −261382. + 624567.i −0.705586 + 1.68598i
\(40\) 341029. 124125.i 0.842523 0.306653i
\(41\) 181176. 65942.8i 0.410543 0.149425i −0.128489 0.991711i \(-0.541013\pi\)
0.539031 + 0.842286i \(0.318790\pi\)
\(42\) −120906. + 288903.i −0.251812 + 0.601698i
\(43\) −86932.1 493016.i −0.166740 0.945631i −0.947252 0.320490i \(-0.896152\pi\)
0.780512 0.625141i \(-0.214959\pi\)
\(44\) −21746.7 + 37666.3i −0.0384865 + 0.0666606i
\(45\) −510660. 48440.7i −0.835388 0.0792440i
\(46\) −414151. 717331.i −0.627345 1.08659i
\(47\) 615804. 516721.i 0.865167 0.725962i −0.0979075 0.995196i \(-0.531215\pi\)
0.963075 + 0.269234i \(0.0867705\pi\)
\(48\) −507988. 326240.i −0.662994 0.425788i
\(49\) −68831.8 + 390364.i −0.0835801 + 0.474006i
\(50\) −181422. 152232.i −0.205256 0.172230i
\(51\) 203271. + 653004.i 0.214575 + 0.689319i
\(52\) 313009. + 113926.i 0.308706 + 0.112360i
\(53\) −1.14077e6 −1.05253 −0.526264 0.850321i \(-0.676408\pi\)
−0.526264 + 0.850321i \(0.676408\pi\)
\(54\) 553354. + 889976.i 0.478217 + 0.769131i
\(55\) −443384. −0.359344
\(56\) 950292. + 345878.i 0.723101 + 0.263187i
\(57\) −1.97958e6 446459.i −1.41583 0.319315i
\(58\) −711726. 597209.i −0.478977 0.401910i
\(59\) 299570. 1.69894e6i 0.189896 1.07695i −0.729606 0.683868i \(-0.760296\pi\)
0.919502 0.393086i \(-0.128592\pi\)
\(60\) −11929.2 + 252080.i −0.00712990 + 0.150664i
\(61\) 1.71084e6 1.43556e6i 0.965061 0.809782i −0.0167084 0.999860i \(-0.505319\pi\)
0.981769 + 0.190078i \(0.0608742\pi\)
\(62\) 767524. + 1.32939e6i 0.408998 + 0.708405i
\(63\) −1.00330e6 1.01807e6i −0.505519 0.512964i
\(64\) −1.16321e6 + 2.01474e6i −0.554661 + 0.960701i
\(65\) 589656. + 3.34410e6i 0.266319 + 1.51037i
\(66\) 548815. + 720668.i 0.234975 + 0.308554i
\(67\) −117367. + 42717.9i −0.0476741 + 0.0173520i −0.365747 0.930714i \(-0.619186\pi\)
0.318073 + 0.948066i \(0.396964\pi\)
\(68\) 316178. 115079.i 0.121941 0.0443830i
\(69\) 3.74981e6 479736.i 1.37416 0.175805i
\(70\) 272754. + 1.54686e6i 0.0950447 + 0.539025i
\(71\) 850034. 1.47230e6i 0.281859 0.488194i −0.689984 0.723825i \(-0.742382\pi\)
0.971843 + 0.235631i \(0.0757156\pi\)
\(72\) 2.78610e6 1.92065e6i 0.879696 0.606436i
\(73\) −868776. 1.50476e6i −0.261383 0.452729i 0.705226 0.708982i \(-0.250845\pi\)
−0.966610 + 0.256253i \(0.917512\pi\)
\(74\) −631428. + 529831.i −0.181139 + 0.151994i
\(75\) 960581. 495593.i 0.262918 0.135647i
\(76\) −173366. + 983206.i −0.0453018 + 0.256919i
\(77\) −946453. 794169.i −0.236255 0.198242i
\(78\) 4.70557e6 5.09770e6i 1.12275 1.21631i
\(79\) 2.67970e6 + 975329.i 0.611492 + 0.222565i 0.629156 0.777279i \(-0.283401\pi\)
−0.0176641 + 0.999844i \(0.505623\pi\)
\(80\) −3.02792e6 −0.661194
\(81\) −4.72194e6 + 761608.i −0.987241 + 0.159233i
\(82\) −1.97558e6 −0.395682
\(83\) 2.05276e6 + 747144.i 0.394062 + 0.143427i 0.531449 0.847091i \(-0.321648\pi\)
−0.137386 + 0.990518i \(0.543870\pi\)
\(84\) −476978. + 516726.i −0.0878053 + 0.0951223i
\(85\) 2.62759e6 + 2.20481e6i 0.464078 + 0.389408i
\(86\) −890757. + 5.05173e6i −0.151013 + 0.856438i
\(87\) 3.76839e6 1.94423e6i 0.613534 0.316541i
\(88\) 2.24070e6 1.88017e6i 0.350505 0.294108i
\(89\) −5.87690e6 1.01791e7i −0.883656 1.53054i −0.847246 0.531201i \(-0.821741\pi\)
−0.0364102 0.999337i \(-0.511592\pi\)
\(90\) 4.74720e6 + 2.25604e6i 0.686418 + 0.326211i
\(91\) −4.73111e6 + 8.19453e6i −0.658140 + 1.13993i
\(92\) −322962. 1.83161e6i −0.0432408 0.245231i
\(93\) −6.94932e6 + 889069.i −0.895884 + 0.114616i
\(94\) −7.74022e6 + 2.81721e6i −0.961183 + 0.349842i
\(95\) −9.56393e6 + 3.48098e6i −1.14447 + 0.416552i
\(96\) −1.86364e6 2.44720e6i −0.214987 0.282307i
\(97\) 1.94881e6 + 1.10522e7i 0.216804 + 1.22956i 0.877748 + 0.479123i \(0.159045\pi\)
−0.660943 + 0.750436i \(0.729844\pi\)
\(98\) 2.03080e6 3.51745e6i 0.217960 0.377517i
\(99\) −4.00113e6 + 1.04081e6i −0.414438 + 0.107808i
\(100\) −265888. 460532.i −0.0265888 0.0460532i
\(101\) −5.41482e6 + 4.54357e6i −0.522949 + 0.438806i −0.865658 0.500635i \(-0.833100\pi\)
0.342709 + 0.939441i \(0.388655\pi\)
\(102\) 331259. 6.99991e6i 0.0309077 0.653118i
\(103\) 2.04951e6 1.16234e7i 0.184808 1.04810i −0.741394 0.671070i \(-0.765835\pi\)
0.926202 0.377028i \(-0.123054\pi\)
\(104\) −1.71606e7 1.43994e7i −1.49594 1.25524i
\(105\) −6.99315e6 1.57718e6i −0.589536 0.132959i
\(106\) 1.09841e7 + 3.99788e6i 0.895764 + 0.326032i
\(107\) 1.36780e7 1.07940 0.539698 0.841859i \(-0.318539\pi\)
0.539698 + 0.841859i \(0.318539\pi\)
\(108\) 484090. + 2.30279e6i 0.0369779 + 0.175902i
\(109\) 6.11021e6 0.451922 0.225961 0.974136i \(-0.427448\pi\)
0.225961 + 0.974136i \(0.427448\pi\)
\(110\) 4.26918e6 + 1.55386e6i 0.305823 + 0.111311i
\(111\) −1.11813e6 3.59196e6i −0.0775997 0.249288i
\(112\) −6.46343e6 5.42346e6i −0.434710 0.364765i
\(113\) 316170. 1.79309e6i 0.0206132 0.116904i −0.972765 0.231794i \(-0.925541\pi\)
0.993378 + 0.114890i \(0.0366516\pi\)
\(114\) 1.74960e7 + 1.12363e7i 1.10604 + 0.710324i
\(115\) 1.45242e7 1.21873e7i 0.890533 0.747246i
\(116\) −1.04309e6 1.80668e6i −0.0620466 0.107468i
\(117\) 1.31711e7 + 2.87932e7i 0.760279 + 1.66203i
\(118\) −8.83846e6 + 1.53087e7i −0.495210 + 0.857729i
\(119\) 1.65974e6 + 9.41283e6i 0.0902868 + 0.512042i
\(120\) 6.55213e6 1.56561e7i 0.346137 0.827086i
\(121\) 1.49539e7 5.44277e6i 0.767371 0.279300i
\(122\) −2.15040e7 + 7.82683e6i −1.07216 + 0.390235i
\(123\) 3.48091e6 8.31754e6i 0.168665 0.403020i
\(124\) 598528. + 3.39442e6i 0.0281909 + 0.159878i
\(125\) 1.18725e7 2.05638e7i 0.543697 0.941712i
\(126\) 6.09251e6 + 1.33187e7i 0.271331 + 0.593152i
\(127\) 1.66734e7 + 2.88791e7i 0.722288 + 1.25104i 0.960080 + 0.279724i \(0.0902430\pi\)
−0.237792 + 0.971316i \(0.576424\pi\)
\(128\) 1.18113e7 9.91083e6i 0.497808 0.417710i
\(129\) −1.96992e7 1.26512e7i −0.807950 0.518882i
\(130\) 6.04195e6 3.42656e7i 0.241199 1.36791i
\(131\) 3.80495e7 + 3.19273e7i 1.47877 + 1.24083i 0.907491 + 0.420072i \(0.137995\pi\)
0.571275 + 0.820759i \(0.306449\pi\)
\(132\) 604536. + 1.94207e6i 0.0228778 + 0.0734945i
\(133\) −2.66503e7 9.69990e6i −0.982247 0.357509i
\(134\) 1.27979e6 0.0459484
\(135\) −1.78627e7 + 1.60115e7i −0.624856 + 0.560096i
\(136\) −2.26283e7 −0.771377
\(137\) 3.63910e7 + 1.32452e7i 1.20913 + 0.440086i 0.866401 0.499349i \(-0.166428\pi\)
0.342726 + 0.939435i \(0.388650\pi\)
\(138\) −3.77868e7 8.52214e6i −1.22395 0.276040i
\(139\) −4.58471e7 3.84703e7i −1.44797 1.21499i −0.934043 0.357162i \(-0.883744\pi\)
−0.513930 0.857832i \(-0.671811\pi\)
\(140\) −612439. + 3.47332e6i −0.0188632 + 0.106978i
\(141\) 1.77706e6 3.75515e7i 0.0533869 1.12813i
\(142\) −1.33444e7 + 1.11973e7i −0.391102 + 0.328173i
\(143\) 1.36843e7 + 2.37018e7i 0.391332 + 0.677807i
\(144\) −2.73241e7 + 7.10783e6i −0.762566 + 0.198366i
\(145\) 1.06336e7 1.84179e7i 0.289661 0.501708i
\(146\) 3.09163e6 + 1.75335e7i 0.0822152 + 0.466266i
\(147\) 1.12309e7 + 1.47477e7i 0.291611 + 0.382924i
\(148\) −1.73919e6 + 633014.i −0.0440993 + 0.0160508i
\(149\) −3.49514e7 + 1.27213e7i −0.865591 + 0.315049i −0.736380 0.676568i \(-0.763467\pi\)
−0.129210 + 0.991617i \(0.541244\pi\)
\(150\) −1.09859e7 + 1.40550e6i −0.265777 + 0.0340024i
\(151\) 4.67429e6 + 2.65092e7i 0.110483 + 0.626582i 0.988888 + 0.148664i \(0.0474973\pi\)
−0.878404 + 0.477918i \(0.841392\pi\)
\(152\) 3.35714e7 5.81474e7i 0.775385 1.34301i
\(153\) 2.88872e7 + 1.37283e7i 0.652056 + 0.309881i
\(154\) 6.32986e6 + 1.09636e7i 0.139660 + 0.241898i
\(155\) −2.69169e7 + 2.25860e7i −0.580583 + 0.487167i
\(156\) 1.38435e7 7.14230e6i 0.291951 0.150627i
\(157\) 9.19247e6 5.21331e7i 0.189576 1.07514i −0.730358 0.683065i \(-0.760647\pi\)
0.919934 0.392074i \(-0.128242\pi\)
\(158\) −2.23837e7 1.87822e7i −0.451474 0.378832i
\(159\) −3.61854e7 + 3.92008e7i −0.713909 + 0.773402i
\(160\) −1.44971e7 5.27650e6i −0.279808 0.101842i
\(161\) 5.28328e7 0.997730
\(162\) 4.81350e7 + 9.21498e6i 0.889525 + 0.170291i
\(163\) −7.24867e7 −1.31100 −0.655499 0.755196i \(-0.727541\pi\)
−0.655499 + 0.755196i \(0.727541\pi\)
\(164\) −4.16843e6 1.51719e6i −0.0737937 0.0268587i
\(165\) −1.40642e7 + 1.52362e7i −0.243736 + 0.264047i
\(166\) −1.71469e7 1.43880e7i −0.290943 0.244130i
\(167\) −9.57358e6 + 5.42945e7i −0.159062 + 0.902086i 0.795916 + 0.605408i \(0.206990\pi\)
−0.954978 + 0.296678i \(0.904121\pi\)
\(168\) 4.20288e7 2.16840e7i 0.683856 0.352822i
\(169\) 1.12498e8 9.43970e7i 1.79284 1.50437i
\(170\) −1.75733e7 3.04378e7i −0.274335 0.475162i
\(171\) −7.81342e7 + 5.38633e7i −1.19496 + 0.823771i
\(172\) −5.75905e6 + 9.97497e6i −0.0862981 + 0.149473i
\(173\) −45494.7 258013.i −0.000668036 0.00378862i 0.984472 0.175542i \(-0.0561678\pi\)
−0.985140 + 0.171754i \(0.945057\pi\)
\(174\) −4.30981e7 + 5.51381e6i −0.620206 + 0.0793467i
\(175\) 1.41951e7 5.16658e6i 0.200219 0.0728736i
\(176\) −2.29326e7 + 8.34678e6i −0.317073 + 0.115405i
\(177\) −4.88791e7 6.41848e7i −0.662547 0.870013i
\(178\) 2.09135e7 + 1.18607e8i 0.277944 + 1.57630i
\(179\) −1.97153e7 + 3.41478e7i −0.256931 + 0.445018i −0.965418 0.260706i \(-0.916045\pi\)
0.708487 + 0.705724i \(0.249378\pi\)
\(180\) 8.28391e6 + 8.40590e6i 0.105872 + 0.107431i
\(181\) −3.34406e7 5.79208e7i −0.419178 0.726038i 0.576679 0.816971i \(-0.304348\pi\)
−0.995857 + 0.0909330i \(0.971015\pi\)
\(182\) 7.42722e7 6.23218e7i 0.913222 0.766285i
\(183\) 4.93706e6 1.04326e8i 0.0595510 1.25839i
\(184\) −2.17199e7 + 1.23180e8i −0.257037 + 1.45773i
\(185\) −1.44535e7 1.21279e7i −0.167831 0.140827i
\(186\) 7.00282e7 + 1.57936e7i 0.797954 + 0.179964i
\(187\) 2.59784e7 + 9.45537e6i 0.290514 + 0.105738i
\(188\) −1.84952e7 −0.203005
\(189\) −6.68090e7 + 2.18336e6i −0.719811 + 0.0235239i
\(190\) 1.04287e8 1.10304
\(191\) −4.44089e7 1.61635e7i −0.461161 0.167849i 0.100983 0.994888i \(-0.467801\pi\)
−0.562144 + 0.827039i \(0.690023\pi\)
\(192\) 3.23361e7 + 1.03879e8i 0.329711 + 1.05919i
\(193\) 4.78792e7 + 4.01754e7i 0.479398 + 0.402263i 0.850209 0.526446i \(-0.176476\pi\)
−0.370811 + 0.928709i \(0.620920\pi\)
\(194\) 1.99686e7 1.13248e8i 0.196355 1.11359i
\(195\) 1.33618e8 + 8.58125e7i 1.29046 + 0.828761i
\(196\) 6.98624e6 5.86215e6i 0.0662746 0.0556110i
\(197\) −4.50661e7 7.80567e7i −0.419970 0.727409i 0.575966 0.817473i \(-0.304626\pi\)
−0.995936 + 0.0900647i \(0.971293\pi\)
\(198\) 4.21730e7 + 4.00048e6i 0.386106 + 0.0366256i
\(199\) −4.99770e6 + 8.65627e6i −0.0449557 + 0.0778655i −0.887628 0.460562i \(-0.847648\pi\)
0.842672 + 0.538427i \(0.180981\pi\)
\(200\) 6.21021e6 + 3.52198e7i 0.0548910 + 0.311302i
\(201\) −2.25494e6 + 5.38812e6i −0.0195861 + 0.0468006i
\(202\) 6.80605e7 2.47720e7i 0.580985 0.211461i
\(203\) 5.56877e7 2.02687e7i 0.467222 0.170055i
\(204\) 6.07466e6 1.45153e7i 0.0500976 0.119707i
\(205\) −7.85262e6 4.45344e7i −0.0636614 0.361042i
\(206\) −6.04685e7 + 1.04735e8i −0.481941 + 0.834747i
\(207\) 1.02459e8 1.44073e8i 0.802883 1.12898i
\(208\) 9.34513e7 + 1.61862e8i 0.720052 + 1.24717i
\(209\) −6.28388e7 + 5.27280e7i −0.476119 + 0.399511i
\(210\) 6.18072e7 + 3.96939e7i 0.460545 + 0.295771i
\(211\) −1.34821e7 + 7.64607e7i −0.0988026 + 0.560337i 0.894713 + 0.446641i \(0.147380\pi\)
−0.993516 + 0.113696i \(0.963731\pi\)
\(212\) 2.01059e7 + 1.68709e7i 0.144927 + 0.121608i
\(213\) −2.36301e7 7.59115e7i −0.167547 0.538243i
\(214\) −1.31701e8 4.79352e7i −0.918629 0.334354i
\(215\) −1.17419e8 −0.805756
\(216\) 2.23751e7 1.56663e8i 0.151070 1.05774i
\(217\) −9.79122e7 −0.650471
\(218\) −5.88330e7 2.14135e7i −0.384612 0.139987i
\(219\) −7.92664e7 1.78771e7i −0.509958 0.115012i
\(220\) 7.81457e6 + 6.55720e6i 0.0494795 + 0.0415183i
\(221\) 3.67659e7 2.08510e8i 0.229125 1.29943i
\(222\) −1.82214e6 + 3.85042e7i −0.0111776 + 0.236196i
\(223\) 7.52079e7 6.31069e7i 0.454147 0.381075i −0.386825 0.922153i \(-0.626428\pi\)
0.840972 + 0.541078i \(0.181984\pi\)
\(224\) −2.14946e7 3.72298e7i −0.127780 0.221321i
\(225\) 1.34394e7 4.87290e7i 0.0786577 0.285200i
\(226\) −9.32824e6 + 1.61570e7i −0.0537552 + 0.0931067i
\(227\) 2.17289e7 + 1.23231e8i 0.123296 + 0.699245i 0.982305 + 0.187286i \(0.0599690\pi\)
−0.859010 + 0.511959i \(0.828920\pi\)
\(228\) 2.82871e7 + 3.71447e7i 0.158058 + 0.207551i
\(229\) −3.17049e8 + 1.15396e8i −1.74462 + 0.634991i −0.999490 0.0319238i \(-0.989837\pi\)
−0.745134 + 0.666915i \(0.767614\pi\)
\(230\) −1.82559e8 + 6.64460e7i −0.989363 + 0.360099i
\(231\) −5.73118e7 + 7.33226e6i −0.305916 + 0.0391377i
\(232\) 2.43629e7 + 1.38169e8i 0.128091 + 0.726443i
\(233\) −9.13771e7 + 1.58270e8i −0.473251 + 0.819695i −0.999531 0.0306162i \(-0.990253\pi\)
0.526280 + 0.850311i \(0.323586\pi\)
\(234\) −2.59132e7 3.23398e8i −0.132210 1.64999i
\(235\) −9.42729e7 1.63285e8i −0.473859 0.820748i
\(236\) −3.04055e7 + 2.55133e7i −0.150578 + 0.126350i
\(237\) 1.18516e8 6.11458e7i 0.578304 0.298365i
\(238\) 1.70066e7 9.64493e7i 0.0817708 0.463745i
\(239\) 1.94053e8 + 1.62830e8i 0.919449 + 0.771510i 0.973893 0.227007i \(-0.0728941\pi\)
−0.0544437 + 0.998517i \(0.517339\pi\)
\(240\) −9.60456e7 + 1.04049e8i −0.448475 + 0.485848i
\(241\) −2.05548e8 7.48132e7i −0.945916 0.344285i −0.177417 0.984136i \(-0.556774\pi\)
−0.768499 + 0.639851i \(0.778996\pi\)
\(242\) −1.63060e8 −0.739594
\(243\) −1.23609e8 + 1.86420e8i −0.552621 + 0.833433i
\(244\) −5.13838e7 −0.226444
\(245\) 8.73641e7 + 3.17979e7i 0.379535 + 0.138139i
\(246\) −6.26655e7 + 6.78876e7i −0.268383 + 0.290749i
\(247\) 4.81256e8 + 4.03822e8i 2.03206 + 1.70510i
\(248\) 4.02523e7 2.28282e8i 0.167575 0.950367i
\(249\) 9.07880e7 4.68403e7i 0.372675 0.192275i
\(250\) −1.86383e8 + 1.56394e8i −0.754424 + 0.633036i
\(251\) 1.19420e8 + 2.06842e8i 0.476673 + 0.825622i 0.999643 0.0267291i \(-0.00850915\pi\)
−0.522969 + 0.852351i \(0.675176\pi\)
\(252\) 2.62668e6 + 3.27811e7i 0.0103396 + 0.129039i
\(253\) 7.64067e7 1.32340e8i 0.296626 0.513772i
\(254\) −5.93339e7 3.36499e8i −0.227188 1.28845i
\(255\) 1.59112e8 2.03562e7i 0.600913 0.0768785i
\(256\) 1.31364e8 4.78124e7i 0.489368 0.178115i
\(257\) 1.34696e8 4.90255e7i 0.494983 0.180159i −0.0824534 0.996595i \(-0.526276\pi\)
0.577436 + 0.816436i \(0.304053\pi\)
\(258\) 1.45340e8 + 1.90851e8i 0.526884 + 0.691870i
\(259\) −9.12966e6 5.17769e7i −0.0326517 0.185177i
\(260\) 3.90633e7 6.76597e7i 0.137836 0.238739i
\(261\) 5.27233e7 1.91166e8i 0.183553 0.665530i
\(262\) −2.54474e8 4.40762e8i −0.874157 1.51408i
\(263\) 7.33625e7 6.15585e7i 0.248673 0.208662i −0.509927 0.860217i \(-0.670328\pi\)
0.758601 + 0.651556i \(0.225883\pi\)
\(264\) 6.46610e6 1.36637e8i 0.0216286 0.457040i
\(265\) −4.64620e7 + 2.63499e8i −0.153369 + 0.869799i
\(266\) 2.22612e8 + 1.86794e8i 0.725208 + 0.608522i
\(267\) −5.36203e8 1.20931e8i −1.72401 0.388820i
\(268\) 2.70032e6 + 982836.i 0.00856926 + 0.00311896i
\(269\) 6.32296e7 0.198056 0.0990279 0.995085i \(-0.468427\pi\)
0.0990279 + 0.995085i \(0.468427\pi\)
\(270\) 2.28107e8 9.15678e7i 0.705285 0.283119i
\(271\) 5.76999e8 1.76109 0.880547 0.473959i \(-0.157176\pi\)
0.880547 + 0.473959i \(0.157176\pi\)
\(272\) 1.77409e8 + 6.45717e7i 0.534546 + 0.194559i
\(273\) 1.31520e8 + 4.22508e8i 0.391223 + 1.25680i
\(274\) −3.03977e8 2.55067e8i −0.892717 0.749079i
\(275\) 7.58717e6 4.30290e7i 0.0219996 0.124766i
\(276\) −7.31845e7 4.70006e7i −0.209526 0.134562i
\(277\) 3.72124e8 3.12249e8i 1.05198 0.882719i 0.0586828 0.998277i \(-0.481310\pi\)
0.993301 + 0.115558i \(0.0368655\pi\)
\(278\) 3.06625e8 + 5.31090e8i 0.855954 + 1.48256i
\(279\) −1.89881e8 + 2.67003e8i −0.523440 + 0.736040i
\(280\) 1.18596e8 2.05414e8i 0.322862 0.559213i
\(281\) −8.79465e7 4.98770e8i −0.236454 1.34100i −0.839530 0.543313i \(-0.817170\pi\)
0.603076 0.797684i \(-0.293942\pi\)
\(282\) −1.48711e8 + 3.55342e8i −0.394886 + 0.943571i
\(283\) 7.72926e7 2.81322e7i 0.202715 0.0737821i −0.238667 0.971101i \(-0.576711\pi\)
0.441382 + 0.897319i \(0.354488\pi\)
\(284\) −3.67556e7 + 1.33779e7i −0.0952158 + 0.0346557i
\(285\) −1.83750e8 + 4.39065e8i −0.470186 + 1.12350i
\(286\) −4.86968e7 2.76173e8i −0.123089 0.698073i
\(287\) 6.30057e7 1.09129e8i 0.157323 0.272492i
\(288\) −1.43209e8 1.35846e7i −0.353261 0.0335100i
\(289\) 9.82343e7 + 1.70147e8i 0.239398 + 0.414650i
\(290\) −1.66933e8 + 1.40073e8i −0.401928 + 0.337258i
\(291\) 4.41608e8 + 2.83610e8i 1.05054 + 0.674677i
\(292\) −6.94191e6 + 3.93696e7i −0.0163170 + 0.0925381i
\(293\) 5.79154e8 + 4.85968e8i 1.34511 + 1.12868i 0.980282 + 0.197606i \(0.0633167\pi\)
0.364828 + 0.931075i \(0.381128\pi\)
\(294\) −5.64544e7 1.81359e8i −0.129563 0.416220i
\(295\) −3.80226e8 1.38391e8i −0.862313 0.313856i
\(296\) 1.24471e8 0.278963
\(297\) −9.11500e7 + 1.70507e8i −0.201887 + 0.377654i
\(298\) 3.81116e8 0.834259
\(299\) −1.09975e9 4.00278e8i −2.37929 0.865989i
\(300\) −2.42594e7 5.47128e6i −0.0518747 0.0116994i
\(301\) −2.50644e8 2.10315e8i −0.529755 0.444517i
\(302\) 4.78955e7 2.71629e8i 0.100062 0.567482i
\(303\) −1.56258e7 + 3.30194e8i −0.0322696 + 0.681898i
\(304\) −4.29133e8 + 3.60085e8i −0.876060 + 0.735102i
\(305\) −2.61911e8 4.53643e8i −0.528572 0.915513i
\(306\) −2.30033e8 2.33421e8i −0.458950 0.465708i
\(307\) −2.39067e7 + 4.14077e7i −0.0471559 + 0.0816764i −0.888640 0.458606i \(-0.848349\pi\)
0.841484 + 0.540282i \(0.181682\pi\)
\(308\) 4.93613e6 + 2.79942e7i 0.00962629 + 0.0545934i
\(309\) −3.34407e8 4.39122e8i −0.644794 0.846701i
\(310\) 3.38327e8 1.23141e8i 0.645016 0.234767i
\(311\) 2.06722e7 7.52407e6i 0.0389696 0.0141838i −0.322462 0.946582i \(-0.604510\pi\)
0.361431 + 0.932399i \(0.382288\pi\)
\(312\) −1.03915e9 + 1.32944e8i −1.93703 + 0.247816i
\(313\) 1.36196e7 + 7.72409e7i 0.0251050 + 0.142378i 0.994784 0.102005i \(-0.0325258\pi\)
−0.969679 + 0.244383i \(0.921415\pi\)
\(314\) −2.71213e8 + 4.69755e8i −0.494376 + 0.856284i
\(315\) −2.76020e8 + 1.90280e8i −0.497570 + 0.343009i
\(316\) −3.28050e7 5.68200e7i −0.0584838 0.101297i
\(317\) 2.03372e7 1.70650e7i 0.0358579 0.0300883i −0.624683 0.780879i \(-0.714772\pi\)
0.660540 + 0.750790i \(0.270327\pi\)
\(318\) 4.85796e8 2.50637e8i 0.847148 0.437070i
\(319\) 2.97647e7 1.68804e8i 0.0513375 0.291149i
\(320\) 4.17994e8 + 3.50738e8i 0.713091 + 0.598354i
\(321\) 4.33868e8 4.70023e8i 0.732132 0.793143i
\(322\) −5.08708e8 1.85154e8i −0.849127 0.309057i
\(323\) 6.34596e8 1.04782
\(324\) 9.44869e7 + 5.64096e7i 0.154335 + 0.0921393i
\(325\) −3.34625e8 −0.540712
\(326\) 6.97948e8 + 2.54032e8i 1.11574 + 0.406095i
\(327\) 1.93816e8 2.09967e8i 0.306530 0.332074i
\(328\) 2.28532e8 + 1.91761e8i 0.357593 + 0.300056i
\(329\) 9.12331e7 5.17409e8i 0.141243 0.801029i
\(330\) 1.88814e8 9.74151e7i 0.289225 0.149220i
\(331\) −8.64870e8 + 7.25712e8i −1.31085 + 1.09993i −0.322689 + 0.946505i \(0.604587\pi\)
−0.988160 + 0.153428i \(0.950969\pi\)
\(332\) −2.51301e7 4.35265e7i −0.0376886 0.0652786i
\(333\) −1.58899e8 7.55146e7i −0.235812 0.112067i
\(334\) 2.82457e8 4.89231e8i 0.414802 0.718457i
\(335\) 5.08695e6 + 2.88495e7i 0.00739265 + 0.0419258i
\(336\) −3.91388e8 + 5.00727e7i −0.562886 + 0.0720135i
\(337\) −2.80186e7 + 1.01980e7i −0.0398788 + 0.0145147i −0.361883 0.932224i \(-0.617866\pi\)
0.322004 + 0.946738i \(0.395644\pi\)
\(338\) −1.41402e9 + 5.14661e8i −1.99181 + 0.724958i
\(339\) −5.15877e7 6.77415e7i −0.0719195 0.0944400i
\(340\) −1.37039e7 7.77187e7i −0.0189090 0.107238i
\(341\) −1.41601e8 + 2.45259e8i −0.193386 + 0.334954i
\(342\) 9.41091e8 2.44806e8i 1.27216 0.330926i
\(343\) 3.98656e8 + 6.90492e8i 0.533419 + 0.923910i
\(344\) 5.93392e8 4.97915e8i 0.785936 0.659478i
\(345\) 4.19133e7 8.85680e8i 0.0549522 1.16121i
\(346\) −466165. + 2.64375e6i −0.000605025 + 0.00343127i
\(347\) −2.55480e7 2.14373e7i −0.0328249 0.0275434i 0.626228 0.779640i \(-0.284598\pi\)
−0.659053 + 0.752097i \(0.729043\pi\)
\(348\) −9.51704e7 2.14640e7i −0.121053 0.0273013i
\(349\) 6.26000e8 + 2.27845e8i 0.788289 + 0.286914i 0.704625 0.709580i \(-0.251115\pi\)
0.0836642 + 0.996494i \(0.473338\pi\)
\(350\) −1.54786e8 −0.192971
\(351\) 1.40722e9 + 4.60718e8i 1.73695 + 0.568670i
\(352\) −1.24342e8 −0.151956
\(353\) −5.04698e8 1.83695e8i −0.610688 0.222272i 0.0181160 0.999836i \(-0.494233\pi\)
−0.628804 + 0.777563i \(0.716455\pi\)
\(354\) 2.45701e8 + 7.89310e8i 0.294371 + 0.945663i
\(355\) −3.05456e8 2.56308e8i −0.362368 0.304062i
\(356\) −4.69591e7 + 2.66318e8i −0.0551626 + 0.312843i
\(357\) 3.76103e8 + 2.41541e8i 0.437490 + 0.280965i
\(358\) 3.09504e8 2.59704e8i 0.356513 0.299150i
\(359\) 3.26243e8 + 5.65069e8i 0.372143 + 0.644571i 0.989895 0.141802i \(-0.0452897\pi\)
−0.617752 + 0.786373i \(0.711956\pi\)
\(360\) −3.30164e8 7.21767e8i −0.372968 0.815339i
\(361\) −4.94551e8 + 8.56587e8i −0.553268 + 0.958288i
\(362\) 1.19002e8 + 6.74892e8i 0.131848 + 0.747746i
\(363\) 2.87306e8 6.86510e8i 0.315262 0.753310i
\(364\) 2.04574e8 7.44588e7i 0.222329 0.0809210i
\(365\) −3.82959e8 + 1.39386e8i −0.412218 + 0.150035i
\(366\) −4.13152e8 + 9.87218e8i −0.440480 + 1.05252i
\(367\) −1.03104e8 5.84735e8i −0.108880 0.617487i −0.989600 0.143849i \(-0.954052\pi\)
0.880720 0.473637i \(-0.157059\pi\)
\(368\) 5.21790e8 9.03766e8i 0.545793 0.945342i
\(369\) −1.75404e8 3.83448e8i −0.181739 0.397296i
\(370\) 9.66647e7 + 1.67428e8i 0.0992115 + 0.171839i
\(371\) −5.71146e8 + 4.79248e8i −0.580682 + 0.487250i
\(372\) 1.35629e8 + 8.71037e7i 0.136600 + 0.0877276i
\(373\) −8.30356e7 + 4.70918e8i −0.0828483 + 0.469856i 0.914952 + 0.403563i \(0.132228\pi\)
−0.997800 + 0.0662931i \(0.978883\pi\)
\(374\) −2.17000e8 1.82085e8i −0.214491 0.179979i
\(375\) −3.30044e8 1.06026e9i −0.323194 1.03825i
\(376\) 1.16883e9 + 4.25420e8i 1.13395 + 0.412725i
\(377\) −1.31274e9 −1.26178
\(378\) 6.50931e8 + 2.13112e8i 0.619889 + 0.202949i
\(379\) −3.37822e8 −0.318750 −0.159375 0.987218i \(-0.550948\pi\)
−0.159375 + 0.987218i \(0.550948\pi\)
\(380\) 2.20043e8 + 8.00890e7i 0.205714 + 0.0748739i
\(381\) 1.52126e9 + 3.43094e8i 1.40918 + 0.317816i
\(382\) 3.70951e8 + 3.11265e8i 0.340483 + 0.285699i
\(383\) 3.36446e8 1.90808e9i 0.305999 1.73540i −0.312768 0.949830i \(-0.601256\pi\)
0.618766 0.785575i \(-0.287633\pi\)
\(384\) 3.40844e7 7.20246e8i 0.0307182 0.649115i
\(385\) −2.21987e8 + 1.86269e8i −0.198251 + 0.166352i
\(386\) −3.20215e8 5.54629e8i −0.283391 0.490848i
\(387\) −1.05960e9 + 2.75633e8i −0.929292 + 0.241737i
\(388\) 1.29104e8 2.23615e8i 0.112209 0.194352i
\(389\) −7.67737e7 4.35405e8i −0.0661285 0.375033i −0.999855 0.0170454i \(-0.994574\pi\)
0.933726 0.357988i \(-0.116537\pi\)
\(390\) −9.85831e8 1.29453e9i −0.841543 1.10506i
\(391\) −1.11089e9 + 4.04331e8i −0.939836 + 0.342072i
\(392\) −5.76345e8 + 2.09772e8i −0.483260 + 0.175892i
\(393\) 2.30406e9 2.94773e8i 1.91478 0.244970i
\(394\) 1.60372e8 + 9.09515e8i 0.132097 + 0.749158i
\(395\) 3.34424e8 5.79240e8i 0.273029 0.472899i
\(396\) 8.59118e7 + 4.08285e7i 0.0695216 + 0.0330392i
\(397\) 6.96996e8 + 1.20723e9i 0.559066 + 0.968331i 0.997575 + 0.0696042i \(0.0221736\pi\)
−0.438508 + 0.898727i \(0.644493\pi\)
\(398\) 7.84572e7 6.58334e7i 0.0623795 0.0523427i
\(399\) −1.17867e9 + 6.08111e8i −0.928937 + 0.479267i
\(400\) 5.18136e7 2.93850e8i 0.0404794 0.229570i
\(401\) 1.08073e9 + 9.06841e8i 0.836975 + 0.702305i 0.956881 0.290480i \(-0.0938149\pi\)
−0.119906 + 0.992785i \(0.538259\pi\)
\(402\) 4.05949e7 4.39777e7i 0.0311659 0.0337631i
\(403\) 2.03812e9 + 7.41814e8i 1.55118 + 0.564582i
\(404\) 1.62630e8 0.122706
\(405\) −1.63994e7 + 1.12171e9i −0.0122669 + 0.839048i
\(406\) −6.07229e8 −0.450310
\(407\) −1.42899e8 5.20108e7i −0.105062 0.0382396i
\(408\) −7.17772e8 + 7.77586e8i −0.523210 + 0.566810i
\(409\) 1.37147e8 + 1.15080e8i 0.0991186 + 0.0831704i 0.691000 0.722854i \(-0.257170\pi\)
−0.591882 + 0.806025i \(0.701615\pi\)
\(410\) −8.04625e7 + 4.56325e8i −0.0576567 + 0.326988i
\(411\) 1.60947e9 8.30377e8i 1.14350 0.589969i
\(412\) −2.08020e8 + 1.74550e8i −0.146543 + 0.122964i
\(413\) −5.63756e8 9.76454e8i −0.393791 0.682066i
\(414\) −1.49145e9 + 1.02816e9i −1.03302 + 0.712129i
\(415\) 2.56183e8 4.43723e8i 0.175947 0.304750i
\(416\) 1.65362e8 + 9.37815e8i 0.112618 + 0.638691i
\(417\) −2.77624e9 + 3.55182e8i −1.87491 + 0.239869i
\(418\) 7.89839e8 2.87478e8i 0.528958 0.192525i
\(419\) −2.58729e9 + 9.41698e8i −1.71829 + 0.625407i −0.997689 0.0679431i \(-0.978356\pi\)
−0.720601 + 0.693350i \(0.756134\pi\)
\(420\) 9.99282e7 + 1.31219e8i 0.0658136 + 0.0864221i
\(421\) −5.01180e8 2.84233e9i −0.327345 1.85647i −0.492653 0.870226i \(-0.663973\pi\)
0.165307 0.986242i \(-0.447138\pi\)
\(422\) 3.97773e8 6.88963e8i 0.257657 0.446275i
\(423\) −1.23403e9 1.25220e9i −0.792745 0.804419i
\(424\) −8.82566e8 1.52865e9i −0.562298 0.973929i
\(425\) −2.58933e8 + 2.17270e8i −0.163616 + 0.137290i
\(426\) −3.85087e7 + 8.13737e8i −0.0241337 + 0.509977i
\(427\) 2.53465e8 1.43747e9i 0.157551 0.893516i
\(428\) −2.41073e8 2.02284e8i −0.148626 0.124712i
\(429\) 1.24854e9 + 2.81586e8i 0.763488 + 0.172191i
\(430\) 1.13058e9 + 4.11499e8i 0.685746 + 0.249591i
\(431\) −1.23472e9 −0.742844 −0.371422 0.928464i \(-0.621130\pi\)
−0.371422 + 0.928464i \(0.621130\pi\)
\(432\) −6.22473e8 + 1.16441e9i −0.371473 + 0.694884i
\(433\) −2.51517e9 −1.48888 −0.744440 0.667690i \(-0.767283\pi\)
−0.744440 + 0.667690i \(0.767283\pi\)
\(434\) 9.42761e8 + 3.43137e8i 0.553589 + 0.201490i
\(435\) −2.95603e8 9.49620e8i −0.172185 0.553143i
\(436\) −1.07691e8 9.03638e7i −0.0622269 0.0522146i
\(437\) 6.09119e8 3.45449e9i 0.349154 1.98015i
\(438\) 7.00576e8 + 4.49924e8i 0.398379 + 0.255847i
\(439\) 9.80830e8 8.23014e8i 0.553309 0.464281i −0.322751 0.946484i \(-0.604608\pi\)
0.876060 + 0.482203i \(0.160163\pi\)
\(440\) −3.43027e8 5.94139e8i −0.191974 0.332509i
\(441\) 8.63023e8 + 8.18654e7i 0.479167 + 0.0454533i
\(442\) −1.08474e9 + 1.87882e9i −0.597511 + 1.03492i
\(443\) 2.96016e8 + 1.67879e9i 0.161772 + 0.917453i 0.952331 + 0.305067i \(0.0986790\pi\)
−0.790559 + 0.612386i \(0.790210\pi\)
\(444\) −3.34147e7 + 7.98437e7i −0.0181175 + 0.0432912i
\(445\) −2.59055e9 + 9.42884e8i −1.39358 + 0.507222i
\(446\) −9.45310e8 + 3.44065e8i −0.504548 + 0.183640i
\(447\) −6.71514e8 + 1.60457e9i −0.355614 + 0.849731i
\(448\) 2.64029e8 + 1.49738e9i 0.138732 + 0.786791i
\(449\) −3.77958e8 + 6.54642e8i −0.197052 + 0.341304i −0.947571 0.319544i \(-0.896470\pi\)
0.750519 + 0.660849i \(0.229803\pi\)
\(450\) −3.00176e8 + 4.22095e8i −0.155286 + 0.218357i
\(451\) −1.82237e8 3.15645e8i −0.0935448 0.162024i
\(452\) −3.20904e7 + 2.69271e7i −0.0163452 + 0.0137153i
\(453\) 1.05921e9 + 6.80249e8i 0.535353 + 0.343815i
\(454\) 2.22647e8 1.26270e9i 0.111666 0.633291i
\(455\) 1.70011e9 + 1.42656e9i 0.846128 + 0.709985i
\(456\) −9.33253e8 2.99806e9i −0.460917 1.48069i
\(457\) 1.03487e9 + 3.76661e8i 0.507198 + 0.184605i 0.582929 0.812523i \(-0.301907\pi\)
−0.0757307 + 0.997128i \(0.524129\pi\)
\(458\) 3.45716e9 1.68147
\(459\) 1.38805e9 5.57199e8i 0.669979 0.268947i
\(460\) −4.36224e8 −0.208957
\(461\) 3.67619e9 + 1.33802e9i 1.74761 + 0.636078i 0.999618 0.0276295i \(-0.00879587\pi\)
0.747992 + 0.663708i \(0.231018\pi\)
\(462\) 5.77531e8 + 1.30252e8i 0.272476 + 0.0614521i
\(463\) −1.44193e9 1.20992e9i −0.675165 0.566531i 0.239424 0.970915i \(-0.423041\pi\)
−0.914589 + 0.404384i \(0.867486\pi\)
\(464\) 2.03267e8 1.15278e9i 0.0944611 0.535715i
\(465\) −7.76756e7 + 1.64138e9i −0.0358261 + 0.757051i
\(466\) 1.43450e9 1.20369e9i 0.656674 0.551015i
\(467\) 1.18916e9 + 2.05968e9i 0.540294 + 0.935817i 0.998887 + 0.0471703i \(0.0150204\pi\)
−0.458593 + 0.888647i \(0.651646\pi\)
\(468\) 1.93684e8 7.02264e8i 0.0873439 0.316694i
\(469\) −4.08152e7 + 7.06940e7i −0.0182691 + 0.0316430i
\(470\) 3.35480e8 + 1.90260e9i 0.149047 + 0.845288i
\(471\) −1.49988e9 1.96955e9i −0.661430 0.868547i
\(472\) 2.50837e9 9.12971e8i 1.09798 0.399632i
\(473\) −8.89298e8 + 3.23678e8i −0.386397 + 0.140637i
\(474\) −1.35543e9 + 1.73409e8i −0.584593 + 0.0747906i
\(475\) −1.74161e8 9.87715e8i −0.0745629 0.422867i
\(476\) 1.09954e8 1.90445e8i 0.0467289 0.0809368i
\(477\) 1.99270e8 + 2.48690e9i 0.0840674 + 1.04917i
\(478\) −1.29782e9 2.24790e9i −0.543523 0.941409i
\(479\) 1.72599e9 1.44828e9i 0.717571 0.602114i −0.209141 0.977886i \(-0.567067\pi\)
0.926712 + 0.375772i \(0.122622\pi\)
\(480\) −6.41166e8 + 3.30797e8i −0.264622 + 0.136527i
\(481\) −2.02237e8 + 1.14694e9i −0.0828615 + 0.469931i
\(482\) 1.71696e9 + 1.44070e9i 0.698385 + 0.586014i
\(483\) 1.67586e9 1.81551e9i 0.676741 0.733135i
\(484\) −3.44053e8 1.25225e8i −0.137932 0.0502033i
\(485\) 2.63225e9 1.04769
\(486\) 1.84350e9 1.36178e9i 0.728477 0.538121i
\(487\) 3.01715e9 1.18371 0.591856 0.806044i \(-0.298395\pi\)
0.591856 + 0.806044i \(0.298395\pi\)
\(488\) 3.24727e9 + 1.18191e9i 1.26488 + 0.460379i
\(489\) −2.29928e9 + 2.49089e9i −0.889224 + 0.963325i
\(490\) −7.29760e8 6.12341e8i −0.280217 0.235130i
\(491\) −4.34057e8 + 2.46166e9i −0.165486 + 0.938518i 0.783076 + 0.621926i \(0.213650\pi\)
−0.948562 + 0.316592i \(0.897461\pi\)
\(492\) −1.84358e8 + 9.51161e7i −0.0697887 + 0.0360061i
\(493\) −1.01580e9 + 8.52359e8i −0.381808 + 0.320375i
\(494\) −3.21863e9 5.57483e9i −1.20123 2.08059i
\(495\) 7.74502e7 + 9.66583e8i 0.0287015 + 0.358196i
\(496\) −9.67005e8 + 1.67490e9i −0.355830 + 0.616316i
\(497\) −1.92943e8 1.09424e9i −0.0704989 0.399819i
\(498\) −1.03832e9 + 1.32838e8i −0.376728 + 0.0481971i
\(499\) 1.07293e9 3.90513e8i 0.386561 0.140697i −0.141427 0.989949i \(-0.545169\pi\)
0.527987 + 0.849252i \(0.322947\pi\)
\(500\) −5.13368e8 + 1.86851e8i −0.183668 + 0.0668498i
\(501\) 1.56207e9 + 2.05120e9i 0.554967 + 0.728746i
\(502\) −4.24970e8 2.41012e9i −0.149932 0.850308i
\(503\) −9.44778e8 + 1.63640e9i −0.331010 + 0.573327i −0.982710 0.185150i \(-0.940723\pi\)
0.651700 + 0.758477i \(0.274056\pi\)
\(504\) 5.88022e8 2.13207e9i 0.204591 0.741812i
\(505\) 8.28950e8 + 1.43578e9i 0.286423 + 0.496100i
\(506\) −1.19948e9 + 1.00649e9i −0.411593 + 0.345367i
\(507\) 3.24641e8 6.86008e9i 0.110631 2.33777i
\(508\) 1.33228e8 7.55573e8i 0.0450891 0.255713i
\(509\) −2.96163e9 2.48510e9i −0.995448 0.835280i −0.00910105 0.999959i \(-0.502897\pi\)
−0.986347 + 0.164678i \(0.947341\pi\)
\(510\) −1.60337e9 3.61611e8i −0.535227 0.120711i
\(511\) −1.06713e9 3.88404e8i −0.353789 0.128769i
\(512\) −3.40598e9 −1.12150
\(513\) −6.27494e8 + 4.39350e9i −0.205210 + 1.43681i
\(514\) −1.46875e9 −0.477066
\(515\) −2.60133e9 9.46805e8i −0.839207 0.305447i
\(516\) 1.60096e8 + 5.14307e8i 0.0512988 + 0.164797i
\(517\) −1.16411e9 9.76805e8i −0.370491 0.310879i
\(518\) −9.35478e7 + 5.30536e8i −0.0295719 + 0.167711i
\(519\) −1.03093e7 6.62084e6i −0.00323700 0.00207887i
\(520\) −4.02494e9 + 3.37733e9i −1.25530 + 1.05332i
\(521\) 2.61938e9 + 4.53690e9i 0.811458 + 1.40549i 0.911843 + 0.410538i \(0.134659\pi\)
−0.100385 + 0.994949i \(0.532008\pi\)
\(522\) −1.17760e9 + 1.65589e9i −0.362369 + 0.509549i
\(523\) 4.73456e7 8.20049e7i 0.0144718 0.0250659i −0.858699 0.512481i \(-0.828727\pi\)
0.873171 + 0.487415i \(0.162060\pi\)
\(524\) −1.98443e8 1.12543e9i −0.0602527 0.341710i
\(525\) 2.72727e8 6.51674e8i 0.0822565 0.196550i
\(526\) −9.22115e8 + 3.35623e8i −0.276271 + 0.100554i
\(527\) 2.05875e9 7.49324e8i 0.612727 0.223014i
\(528\) −4.40599e8 + 1.05280e9i −0.130264 + 0.311263i
\(529\) 5.43482e8 + 3.08224e9i 0.159621 + 0.905257i
\(530\) 1.37081e9 2.37431e9i 0.399955 0.692743i
\(531\) −3.75605e9 3.56295e8i −1.08868 0.103271i
\(532\) 3.26255e8 + 5.65090e8i 0.0939433 + 0.162715i
\(533\) −2.13831e9 + 1.79425e9i −0.611680 + 0.513261i
\(534\) 4.73910e9 + 3.04354e9i 1.34679 + 0.864939i
\(535\) 5.57086e8 3.15939e9i 0.157284 0.892001i
\(536\) −1.48044e8 1.24223e8i −0.0415254 0.0348439i
\(537\) 5.48066e8 + 1.76065e9i 0.152729 + 0.490641i
\(538\) −6.08815e8 2.21591e8i −0.168557 0.0613498i
\(539\) 7.49325e8 0.206115
\(540\) 5.51621e8 1.80273e7i 0.150752 0.00492667i
\(541\) 3.36457e9 0.913566 0.456783 0.889578i \(-0.349002\pi\)
0.456783 + 0.889578i \(0.349002\pi\)
\(542\) −5.55571e9 2.02211e9i −1.49879 0.545517i
\(543\) −3.05109e9 6.88118e8i −0.817815 0.184444i
\(544\) 7.36877e8 + 6.18313e8i 0.196245 + 0.164669i
\(545\) 2.48860e8 1.41135e9i 0.0658517 0.373463i
\(546\) 2.14331e8 4.52909e9i 0.0563523 1.19079i
\(547\) 4.42019e9 3.70898e9i 1.15474 0.968944i 0.154923 0.987927i \(-0.450487\pi\)
0.999820 + 0.0189821i \(0.00604254\pi\)
\(548\) −4.45501e8 7.71631e8i −0.115642 0.200298i
\(549\) −3.42840e9 3.47889e9i −0.884276 0.897299i
\(550\) −2.23851e8 + 3.87721e8i −0.0573706 + 0.0993688i
\(551\) −6.83239e8 3.87484e9i −0.173997 0.986786i
\(552\) 3.54391e9 + 4.65363e9i 0.896801 + 1.17762i
\(553\) 1.75137e9 6.37448e8i 0.440394 0.160290i
\(554\) −4.67734e9 + 1.70241e9i −1.16873 + 0.425384i
\(555\) −8.75221e8 + 1.11972e8i −0.217316 + 0.0278026i
\(556\) 2.39111e8 + 1.35607e9i 0.0589981 + 0.334595i
\(557\) 1.34591e9 2.33119e9i 0.330007 0.571590i −0.652505 0.757784i \(-0.726282\pi\)
0.982513 + 0.186194i \(0.0596154\pi\)
\(558\) 2.76402e9 1.90543e9i 0.673475 0.464273i
\(559\) 3.62393e9 + 6.27683e9i 0.877483 + 1.51984i
\(560\) −1.51597e9 + 1.27205e9i −0.364782 + 0.306088i
\(561\) 1.14895e9 5.92780e8i 0.274747 0.141750i
\(562\) −9.01151e8 + 5.11068e9i −0.214151 + 1.21451i
\(563\) 1.55263e9 + 1.30282e9i 0.366682 + 0.307683i 0.807447 0.589940i \(-0.200848\pi\)
−0.440765 + 0.897622i \(0.645293\pi\)
\(564\) −5.86669e8 + 6.35558e8i −0.137694 + 0.149169i
\(565\) −4.01296e8 1.46060e8i −0.0936042 0.0340691i
\(566\) −8.42812e8 −0.195377
\(567\) −2.04416e9 + 2.36504e9i −0.470948 + 0.544875i
\(568\) 2.63053e9 0.602316
\(569\) −4.17244e9 1.51865e9i −0.949506 0.345592i −0.179593 0.983741i \(-0.557478\pi\)
−0.769913 + 0.638149i \(0.779700\pi\)
\(570\) 3.30798e9 3.58364e9i 0.748171 0.810518i
\(571\) −1.76542e9 1.48136e9i −0.396846 0.332993i 0.422427 0.906397i \(-0.361178\pi\)
−0.819273 + 0.573404i \(0.805623\pi\)
\(572\) 1.09343e8 6.20118e8i 0.0244291 0.138544i
\(573\) −1.96408e9 + 1.01333e9i −0.436133 + 0.225014i
\(574\) −9.89105e8 + 8.29958e8i −0.218299 + 0.183174i
\(575\) 9.34196e8 + 1.61808e9i 0.204928 + 0.354945i
\(576\) 4.59534e9 + 2.18387e9i 1.00193 + 0.476156i
\(577\) 1.43171e9 2.47980e9i 0.310271 0.537404i −0.668150 0.744026i \(-0.732914\pi\)
0.978421 + 0.206622i \(0.0662470\pi\)
\(578\) −3.49577e8 1.98255e9i −0.0753000 0.427048i
\(579\) 2.89929e9 3.70924e8i 0.620750 0.0794164i
\(580\) −4.59796e8 + 1.67352e8i −0.0978515 + 0.0356150i
\(581\) 1.34163e9 4.88312e8i 0.283802 0.103295i
\(582\) −3.25817e9 4.27841e9i −0.685082 0.899605i
\(583\) 3.74474e8 + 2.12375e9i 0.0782675 + 0.443877i
\(584\) 1.34427e9 2.32834e9i 0.279281 0.483728i
\(585\) 7.18719e9 1.86960e9i 1.48427 0.386104i
\(586\) −3.87337e9 6.70888e9i −0.795148 1.37724i
\(587\) 5.34892e9 4.48828e9i 1.09152 0.915896i 0.0946967 0.995506i \(-0.469812\pi\)
0.996826 + 0.0796098i \(0.0253674\pi\)
\(588\) 2.01606e7 4.26018e8i 0.00408961 0.0864187i
\(589\) −1.12885e9 + 6.40202e9i −0.227631 + 1.29096i
\(590\) 3.17606e9 + 2.66503e9i 0.636659 + 0.534220i
\(591\) −4.11179e9 9.27340e8i −0.819359 0.184792i
\(592\) −9.75870e8 3.55188e8i −0.193315 0.0703610i
\(593\) −2.38323e9 −0.469325 −0.234663 0.972077i \(-0.575399\pi\)
−0.234663 + 0.972077i \(0.575399\pi\)
\(594\) 1.47520e9 1.32231e9i 0.288800 0.258869i
\(595\) 2.24180e9 0.436302
\(596\) 8.04147e8 + 2.92686e8i 0.155587 + 0.0566291i
\(597\) 1.38931e8 + 4.46315e8i 0.0267233 + 0.0858482i
\(598\) 9.18635e9 + 7.70826e9i 1.75666 + 1.47402i
\(599\) −6.27748e8 + 3.56014e9i −0.119342 + 0.676820i 0.865167 + 0.501484i \(0.167212\pi\)
−0.984509 + 0.175336i \(0.943899\pi\)
\(600\) 1.40726e9 + 9.03771e8i 0.265977 + 0.170816i
\(601\) −4.57245e9 + 3.83674e9i −0.859188 + 0.720944i −0.961793 0.273778i \(-0.911727\pi\)
0.102605 + 0.994722i \(0.467282\pi\)
\(602\) 1.67630e9 + 2.90344e9i 0.313159 + 0.542407i
\(603\) 1.13627e8 + 2.48399e8i 0.0211043 + 0.0461359i
\(604\) 3.09661e8 5.36349e8i 0.0571818 0.0990417i
\(605\) −6.48137e8 3.67577e9i −0.118993 0.674845i
\(606\) 1.30763e9 3.12455e9i 0.238688 0.570340i
\(607\) −3.55983e8 + 1.29567e8i −0.0646054 + 0.0235145i −0.374121 0.927380i \(-0.622055\pi\)
0.309515 + 0.950894i \(0.399833\pi\)
\(608\) −2.68209e9 + 9.76202e8i −0.483962 + 0.176148i
\(609\) 1.06992e9 2.55654e9i 0.191951 0.458661i
\(610\) 9.32036e8 + 5.28584e9i 0.166256 + 0.942886i
\(611\) −5.81914e9 + 1.00790e10i −1.03208 + 1.78762i
\(612\) −3.06104e8 6.69170e8i −0.0539808 0.118007i
\(613\) −3.04856e7 5.28025e7i −0.00534543 0.00925855i 0.863340 0.504622i \(-0.168368\pi\)
−0.868686 + 0.495364i \(0.835035\pi\)
\(614\) 3.75304e8 3.14917e8i 0.0654325 0.0549044i
\(615\) −1.77944e9 1.14279e9i −0.308475 0.198109i
\(616\) 3.31966e8 1.88267e9i 0.0572217 0.324520i
\(617\) 1.66391e9 + 1.39619e9i 0.285189 + 0.239302i 0.774148 0.633005i \(-0.218179\pi\)
−0.488959 + 0.872307i \(0.662623\pi\)
\(618\) 1.68097e9 + 5.40009e9i 0.286483 + 0.920324i
\(619\) −8.01647e9 2.91776e9i −1.35852 0.494461i −0.442924 0.896559i \(-0.646059\pi\)
−0.915596 + 0.402099i \(0.868281\pi\)
\(620\) 8.08430e8 0.136230
\(621\) −1.70085e9 8.09083e9i −0.285000 1.35573i
\(622\) −2.25414e8 −0.0375590
\(623\) −7.21868e9 2.62738e9i −1.19605 0.435327i
\(624\) 8.52641e9 + 1.92298e9i 1.40482 + 0.316832i
\(625\) −2.88308e9 2.41919e9i −0.472363 0.396360i
\(626\) 1.39555e8 7.91455e8i 0.0227371 0.128948i
\(627\) −1.81337e8 + 3.83188e9i −0.0293799 + 0.620835i
\(628\) −9.33011e8 + 7.82889e8i −0.150324 + 0.126137i
\(629\) 5.88214e8 + 1.01882e9i 0.0942450 + 0.163237i
\(630\) 3.32454e9 8.64813e8i 0.529712 0.137794i
\(631\) 3.47776e9 6.02365e9i 0.551057 0.954458i −0.447142 0.894463i \(-0.647558\pi\)
0.998199 0.0599954i \(-0.0191086\pi\)
\(632\) 7.66210e8 + 4.34539e9i 0.120736 + 0.684730i
\(633\) 2.19979e9 + 2.88862e9i 0.344722 + 0.452666i
\(634\) −2.55625e8 + 9.30397e7i −0.0398373 + 0.0144996i
\(635\) 7.34967e9 2.67506e9i 1.13909 0.414597i
\(636\) 1.21750e9 1.55762e8i 0.187659 0.0240084i
\(637\) −9.96527e8 5.65158e9i −0.152757 0.866327i
\(638\) −8.78174e8 + 1.52104e9i −0.133878 + 0.231883i
\(639\) −3.35812e9 1.59590e9i −0.509147 0.241966i
\(640\) −1.80818e9 3.13185e9i −0.272653 0.472249i
\(641\) 4.27059e8 3.58345e8i 0.0640449 0.0537401i −0.610203 0.792245i \(-0.708912\pi\)
0.674248 + 0.738505i \(0.264468\pi\)
\(642\) −5.82477e9 + 3.00518e9i −0.868772 + 0.448226i
\(643\) 8.51622e8 4.82979e9i 0.126331 0.716457i −0.854178 0.519981i \(-0.825939\pi\)
0.980509 0.196476i \(-0.0629497\pi\)
\(644\) −9.31169e8 7.81344e8i −0.137381 0.115277i
\(645\) −3.72453e9 + 4.03491e9i −0.546529 + 0.592072i
\(646\) −6.11029e9 2.22396e9i −0.891760 0.324574i
\(647\) −4.81759e8 −0.0699302 −0.0349651 0.999389i \(-0.511132\pi\)
−0.0349651 + 0.999389i \(0.511132\pi\)
\(648\) −4.67372e9 5.73823e9i −0.674761 0.828449i
\(649\) −3.26121e9 −0.468299
\(650\) 3.22198e9 + 1.17270e9i 0.460178 + 0.167491i
\(651\) −3.10578e9 + 3.36459e9i −0.441201 + 0.477968i
\(652\) 1.27757e9 + 1.07201e9i 0.180516 + 0.151471i
\(653\) 1.35275e9 7.67184e9i 0.190118 1.07821i −0.729085 0.684424i \(-0.760054\pi\)
0.919202 0.393786i \(-0.128835\pi\)
\(654\) −2.60202e9 + 1.34246e9i −0.363738 + 0.187664i
\(655\) 8.92436e9 7.48843e9i 1.24089 1.04123i
\(656\) −1.24452e9 2.15557e9i −0.172123 0.298125i
\(657\) −3.12865e9 + 2.15680e9i −0.430406 + 0.296709i
\(658\) −2.69173e9 + 4.66221e9i −0.368333 + 0.637971i
\(659\) 1.55001e9 + 8.79056e9i 0.210978 + 1.19651i 0.887752 + 0.460323i \(0.152266\pi\)
−0.676774 + 0.736191i \(0.736623\pi\)
\(660\) 4.73206e8 6.05401e7i 0.0640687 0.00819671i
\(661\) −4.12137e9 + 1.50005e9i −0.555055 + 0.202024i −0.604291 0.796764i \(-0.706544\pi\)
0.0492360 + 0.998787i \(0.484321\pi\)
\(662\) 1.08708e10 3.95665e9i 1.45633 0.530059i
\(663\) −5.99888e9 7.87733e9i −0.799416 1.04974i
\(664\) 5.86949e8 + 3.32875e9i 0.0778058 + 0.441259i
\(665\) −3.32594e9 + 5.76069e9i −0.438569 + 0.759624i
\(666\) 1.26534e9 + 1.28397e9i 0.165976 + 0.168420i
\(667\) 3.66488e9 + 6.34776e9i 0.478211 + 0.828286i
\(668\) 9.71693e8 8.15347e8i 0.126128 0.105834i
\(669\) 2.17032e8 4.58615e9i 0.0280241 0.592184i
\(670\) 5.21238e7 2.95609e8i 0.00669536 0.0379713i
\(671\) −3.23415e9 2.71378e9i −0.413268 0.346773i
\(672\) −1.96115e9 4.42302e8i −0.249298 0.0562246i
\(673\) −1.12582e10 4.09766e9i −1.42370 0.518183i −0.488578 0.872520i \(-0.662484\pi\)
−0.935118 + 0.354338i \(0.884706\pi\)
\(674\) 3.05520e8 0.0384353
\(675\) −1.24819e9 2.00751e9i −0.156214 0.251243i
\(676\) −3.37879e9 −0.420676
\(677\) 3.99817e9 + 1.45522e9i 0.495224 + 0.180247i 0.577544 0.816359i \(-0.304011\pi\)
−0.0823209 + 0.996606i \(0.526233\pi\)
\(678\) 2.59316e8 + 8.33050e8i 0.0319540 + 0.102652i
\(679\) 5.61884e9 + 4.71477e9i 0.688815 + 0.577984i
\(680\) −9.21619e8 + 5.22676e9i −0.112401 + 0.637458i
\(681\) 4.92387e9 + 3.16221e9i 0.597437 + 0.383686i
\(682\) 2.22294e9 1.86527e9i 0.268338 0.225162i
\(683\) 1.45095e8 + 2.51312e8i 0.0174253 + 0.0301815i 0.874607 0.484833i \(-0.161120\pi\)
−0.857181 + 0.515015i \(0.827786\pi\)
\(684\) 2.17369e9 + 2.06193e8i 0.259717 + 0.0246365i
\(685\) 4.54157e9 7.86623e9i 0.539870 0.935082i
\(686\) −1.41866e9 8.04560e9i −0.167781 0.951534i
\(687\) −6.09139e9 + 1.45552e10i −0.716750 + 1.71266i
\(688\) −6.07311e9 + 2.21043e9i −0.710971 + 0.258772i
\(689\) 1.55198e10 5.64873e9i 1.80767 0.657936i
\(690\) −3.50747e9 + 8.38101e9i −0.406464 + 0.971235i
\(691\) −7.48833e7 4.24684e8i −0.00863399 0.0489658i 0.980186 0.198077i \(-0.0634697\pi\)
−0.988820 + 0.149112i \(0.952359\pi\)
\(692\) −3.01392e6 + 5.22026e6i −0.000345749 + 0.000598854i
\(693\) −1.56597e9 + 2.20201e9i −0.178738 + 0.251334i
\(694\) 1.70864e8 + 2.95946e8i 0.0194041 + 0.0336089i
\(695\) −1.07533e10 + 9.02307e9i −1.21505 + 1.01955i
\(696\) 5.52073e9 + 3.54552e9i 0.620674 + 0.398610i
\(697\) −4.89622e8 + 2.77679e9i −0.0547705 + 0.310619i
\(698\) −5.22903e9 4.38768e9i −0.582006 0.488361i
\(699\) 2.54020e9 + 8.16035e9i 0.281318 + 0.903730i
\(700\) −3.26594e8 1.18871e8i −0.0359886 0.0130988i
\(701\) 1.10118e9 0.120738 0.0603691 0.998176i \(-0.480772\pi\)
0.0603691 + 0.998176i \(0.480772\pi\)
\(702\) −1.19350e10 9.36774e9i −1.30210 1.02201i
\(703\) −3.49070e9 −0.378939
\(704\) 4.13261e9 + 1.50415e9i 0.446396 + 0.162475i
\(705\) −8.60138e9 1.93989e9i −0.924498 0.208504i
\(706\) 4.21578e9 + 3.53746e9i 0.450881 + 0.378334i
\(707\) −8.02221e8 + 4.54962e9i −0.0853741 + 0.484180i
\(708\) −8.77429e7 + 1.85412e9i −0.00929171 + 0.196345i
\(709\) 4.73358e9 3.97195e9i 0.498802 0.418544i −0.358366 0.933581i \(-0.616666\pi\)
0.857168 + 0.515037i \(0.172222\pi\)
\(710\) 2.04288e9 + 3.53838e9i 0.214210 + 0.371022i
\(711\) 1.65814e9 6.01214e9i 0.173013 0.627315i
\(712\) 9.09340e9 1.57502e10i 0.944161 1.63534i
\(713\) −2.10292e9 1.19263e10i −0.217275 1.23223i
\(714\) −2.77487e9 3.64378e9i −0.285298 0.374635i
\(715\) 6.03206e9 2.19549e9i 0.617155 0.224626i
\(716\) 8.52490e8 3.10281e8i 0.0867948 0.0315907i
\(717\) 1.17507e10 1.50335e9i 1.19055 0.152315i
\(718\) −1.16097e9 6.58417e9i −0.117053 0.663843i
\(719\) −7.56941e8 + 1.31106e9i −0.0759470 + 0.131544i −0.901498 0.432784i \(-0.857531\pi\)
0.825551 + 0.564328i \(0.190865\pi\)
\(720\) 5.28915e8 + 6.60090e9i 0.0528108 + 0.659082i
\(721\) −3.85695e9 6.68043e9i −0.383240 0.663791i
\(722\) 7.76379e9 6.51459e9i 0.767704 0.644180i
\(723\) −9.09080e9 + 4.69023e9i −0.894578 + 0.461540i
\(724\) −2.67205e8 + 1.51540e9i −0.0261674 + 0.148403i
\(725\) 1.60543e9 + 1.34712e9i 0.156462 + 0.131287i
\(726\) −5.17226e9 + 5.60328e9i −0.501652 + 0.543456i
\(727\) 8.60802e9 + 3.13306e9i 0.830870 + 0.302412i 0.722216 0.691668i \(-0.243124\pi\)
0.108654 + 0.994080i \(0.465346\pi\)
\(728\) −1.46410e10 −1.40641
\(729\) 2.48514e9 + 1.01609e10i 0.237577 + 0.971369i
\(730\) 4.17585e9 0.397297
\(731\) 6.87972e9 + 2.50401e9i 0.651418 + 0.237097i
\(732\) −1.62989e9 + 1.76572e9i −0.153593 + 0.166392i
\(733\) −3.13125e9 2.62743e9i −0.293666 0.246415i 0.484036 0.875048i \(-0.339170\pi\)
−0.777702 + 0.628633i \(0.783615\pi\)
\(734\) −1.05647e9 + 5.99153e9i −0.0986099 + 0.559244i
\(735\) 3.86387e9 1.99349e9i 0.358936 0.185186i
\(736\) 4.07315e9 3.41777e9i 0.376580 0.315988i
\(737\) 1.18054e8 + 2.04475e8i 0.0108629 + 0.0188150i
\(738\) 3.45094e8 + 4.30679e9i 0.0316038 + 0.394418i
\(739\) 1.38299e9 2.39541e9i 0.126056 0.218336i −0.796089 0.605179i \(-0.793101\pi\)
0.922145 + 0.386844i \(0.126435\pi\)
\(740\) 7.53807e7 + 4.27505e8i 0.00683832 + 0.0387820i
\(741\) 2.91421e10 3.72833e9i 2.63122 0.336628i
\(742\) 7.17890e9 2.61291e9i 0.645125 0.234806i
\(743\) 9.85051e8 3.58529e8i 0.0881045 0.0320674i −0.297592 0.954693i \(-0.596183\pi\)
0.385696 + 0.922626i \(0.373961\pi\)
\(744\) −6.56774e9 8.62433e9i −0.584670 0.767750i
\(745\) 1.51488e9 + 8.59129e9i 0.134224 + 0.761222i
\(746\) 2.44987e9 4.24330e9i 0.216052 0.374212i
\(747\) 1.27021e9 4.60556e9i 0.111494 0.404259i
\(748\) −3.18030e8 5.50844e8i −0.0277851 0.0481252i
\(749\) 6.84812e9 5.74625e9i 0.595504 0.499687i
\(750\) −5.37854e8 + 1.13655e10i −0.0465533 + 0.983729i
\(751\) −3.33526e9 + 1.89152e10i −0.287336 + 1.62956i 0.409484 + 0.912317i \(0.365709\pi\)
−0.696820 + 0.717246i \(0.745402\pi\)
\(752\) −7.94983e9 6.67070e9i −0.681704 0.572017i
\(753\) 1.08958e10 + 2.45736e9i 0.929988 + 0.209742i
\(754\) 1.26399e10 + 4.60056e9i 1.07385 + 0.390851i
\(755\) 6.31356e9 0.533900