Properties

Label 27.8.e.a.4.17
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 4.17
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.17

$q$-expansion

\(f(q)\) \(=\) \(q+(14.3397 + 5.21922i) q^{2} +(-40.6699 - 23.0860i) q^{3} +(80.3327 + 67.4072i) q^{4} +(-74.8052 + 424.241i) q^{5} +(-462.703 - 543.310i) q^{6} +(-616.615 + 517.401i) q^{7} +(-176.505 - 305.716i) q^{8} +(1121.08 + 1877.81i) q^{9} +O(q^{10})\) \(q+(14.3397 + 5.21922i) q^{2} +(-40.6699 - 23.0860i) q^{3} +(80.3327 + 67.4072i) q^{4} +(-74.8052 + 424.241i) q^{5} +(-462.703 - 543.310i) q^{6} +(-616.615 + 517.401i) q^{7} +(-176.505 - 305.716i) q^{8} +(1121.08 + 1877.81i) q^{9} +(-3286.89 + 5693.06i) q^{10} +(808.205 + 4583.56i) q^{11} +(-1710.96 - 4596.00i) q^{12} +(-2908.51 + 1058.61i) q^{13} +(-11542.5 + 4201.13i) q^{14} +(12836.3 - 15526.9i) q^{15} +(-3266.30 - 18524.1i) q^{16} +(2758.38 - 4777.66i) q^{17} +(6275.22 + 32778.3i) q^{18} +(-15604.9 - 27028.5i) q^{19} +(-34606.2 + 29038.1i) q^{20} +(37022.4 - 6807.50i) q^{21} +(-12333.2 + 69945.0i) q^{22} +(60272.5 + 50574.6i) q^{23} +(120.699 + 16508.2i) q^{24} +(-100971. - 36750.6i) q^{25} -47232.3 q^{26} +(-2243.13 - 102251. i) q^{27} -84410.9 q^{28} +(86153.5 + 31357.3i) q^{29} +(265107. - 155655. i) q^{30} +(210318. + 176478. i) q^{31} +(41997.4 - 238179. i) q^{32} +(72946.3 - 205071. i) q^{33} +(64490.0 - 54113.5i) q^{34} +(-173377. - 300298. i) q^{35} +(-36518.4 + 226418. i) q^{36} +(-114885. + 198986. i) q^{37} +(-82701.9 - 469026. i) q^{38} +(142728. + 24092.2i) q^{39} +(142901. - 52011.6i) q^{40} +(-803134. + 292317. i) q^{41} +(566419. + 95610.3i) q^{42} +(70970.3 + 402493. i) q^{43} +(-244039. + 422689. i) q^{44} +(-880505. + 335138. i) q^{45} +(600329. + 1.03980e6i) q^{46} +(603573. - 506458. i) q^{47} +(-294807. + 828780. i) q^{48} +(-30496.9 + 172957. i) q^{49} +(-1.25609e6 - 1.05398e6i) q^{50} +(-222480. + 130627. i) q^{51} +(-305007. - 111013. i) q^{52} +166829. q^{53} +(501506. - 1.47796e6i) q^{54} -2.00499e6 q^{55} +(267013. + 97184.9i) q^{56} +(10671.0 + 1.45950e6i) q^{57} +(1.07175e6 + 899308. i) q^{58} +(432993. - 2.45562e6i) q^{59} +(2.07780e6 - 382057. i) q^{60} +(-1.38983e6 + 1.16621e6i) q^{61} +(2.09482e6 + 3.62834e6i) q^{62} +(-1.66285e6 - 577836. i) q^{63} +(641505. - 1.11112e6i) q^{64} +(-231535. - 1.31310e6i) q^{65} +(2.11634e6 - 2.55993e6i) q^{66} +(2.49063e6 - 906517. i) q^{67} +(543637. - 197868. i) q^{68} +(-1.28371e6 - 3.44831e6i) q^{69} +(-918852. - 5.21107e6i) q^{70} +(-2.54538e6 + 4.40873e6i) q^{71} +(376199. - 674173. i) q^{72} +(760649. + 1.31748e6i) q^{73} +(-2.68596e6 + 2.25379e6i) q^{74} +(3.25807e6 + 3.82566e6i) q^{75} +(568330. - 3.22316e6i) q^{76} +(-2.86989e6 - 2.40813e6i) q^{77} +(1.92093e6 + 1.09040e6i) q^{78} +(1.61633e6 + 588296. i) q^{79} +8.10304e6 q^{80} +(-2.26934e6 + 4.21033e6i) q^{81} -1.30424e7 q^{82} +(4.95600e6 + 1.80384e6i) q^{83} +(3.43298e6 + 1.94871e6i) q^{84} +(1.82054e6 + 1.52761e6i) q^{85} +(-1.08301e6 + 6.14203e6i) q^{86} +(-2.77994e6 - 3.26423e6i) q^{87} +(1.25861e6 - 1.05610e6i) q^{88} +(-2.46514e6 - 4.26974e6i) q^{89} +(-1.43753e7 + 210220. i) q^{90} +(1.24570e6 - 2.15762e6i) q^{91} +(1.43276e6 + 8.12560e6i) q^{92} +(-4.47946e6 - 1.20327e7i) q^{93} +(1.12984e7 - 4.11227e6i) q^{94} +(1.26339e7 - 4.59838e6i) q^{95} +(-7.20662e6 + 8.71716e6i) q^{96} +(141016. + 799740. i) q^{97} +(-1.34002e6 + 2.32098e6i) q^{98} +(-7.70098e6 + 6.65618e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 14.3397 + 5.21922i 1.26746 + 0.461318i 0.886266 0.463176i \(-0.153290\pi\)
0.381195 + 0.924495i \(0.375513\pi\)
\(3\) −40.6699 23.0860i −0.869658 0.493655i
\(4\) 80.3327 + 67.4072i 0.627599 + 0.526618i
\(5\) −74.8052 + 424.241i −0.267631 + 1.51781i 0.493805 + 0.869572i \(0.335606\pi\)
−0.761437 + 0.648239i \(0.775506\pi\)
\(6\) −462.703 543.310i −0.874526 1.02688i
\(7\) −616.615 + 517.401i −0.679471 + 0.570144i −0.915852 0.401517i \(-0.868483\pi\)
0.236381 + 0.971661i \(0.424039\pi\)
\(8\) −176.505 305.716i −0.121883 0.211107i
\(9\) 1121.08 + 1877.81i 0.512610 + 0.858622i
\(10\) −3286.89 + 5693.06i −1.03941 + 1.80030i
\(11\) 808.205 + 4583.56i 0.183083 + 1.03831i 0.928394 + 0.371597i \(0.121190\pi\)
−0.745311 + 0.666717i \(0.767699\pi\)
\(12\) −1710.96 4596.00i −0.285829 0.767795i
\(13\) −2908.51 + 1058.61i −0.367171 + 0.133639i −0.519015 0.854765i \(-0.673701\pi\)
0.151844 + 0.988405i \(0.451479\pi\)
\(14\) −11542.5 + 4201.13i −1.12422 + 0.409183i
\(15\) 12836.3 15526.9i 0.982023 1.18786i
\(16\) −3266.30 18524.1i −0.199359 1.13062i
\(17\) 2758.38 4777.66i 0.136171 0.235854i −0.789873 0.613270i \(-0.789854\pi\)
0.926044 + 0.377416i \(0.123187\pi\)
\(18\) 6275.22 + 32778.3i 0.253615 + 1.32475i
\(19\) −15604.9 27028.5i −0.521944 0.904033i −0.999674 0.0255268i \(-0.991874\pi\)
0.477730 0.878507i \(-0.341460\pi\)
\(20\) −34606.2 + 29038.1i −0.967273 + 0.811638i
\(21\) 37022.4 6807.50i 0.872362 0.160406i
\(22\) −12333.2 + 69945.0i −0.246943 + 1.40048i
\(23\) 60272.5 + 50574.6i 1.03293 + 0.866733i 0.991197 0.132396i \(-0.0422669\pi\)
0.0417354 + 0.999129i \(0.486711\pi\)
\(24\) 120.699 + 16508.2i 0.00178223 + 0.243759i
\(25\) −100971. 36750.6i −1.29243 0.470407i
\(26\) −47232.3 −0.527026
\(27\) −2243.13 102251.i −0.0219322 0.999759i
\(28\) −84410.9 −0.726684
\(29\) 86153.5 + 31357.3i 0.655964 + 0.238751i 0.648493 0.761221i \(-0.275400\pi\)
0.00747109 + 0.999972i \(0.497622\pi\)
\(30\) 265107. 155655.i 1.79266 1.05254i
\(31\) 210318. + 176478.i 1.26798 + 1.06396i 0.994784 + 0.101999i \(0.0325239\pi\)
0.273192 + 0.961959i \(0.411921\pi\)
\(32\) 41997.4 238179.i 0.226567 1.28493i
\(33\) 72946.3 205071.i 0.353349 0.993357i
\(34\) 64490.0 54113.5i 0.281395 0.236118i
\(35\) −173377. 300298.i −0.683523 1.18390i
\(36\) −36518.4 + 226418.i −0.130453 + 0.808820i
\(37\) −114885. + 198986.i −0.372868 + 0.645827i −0.990006 0.141029i \(-0.954959\pi\)
0.617137 + 0.786856i \(0.288292\pi\)
\(38\) −82701.9 469026.i −0.244497 1.38661i
\(39\) 142728. + 24092.2i 0.385285 + 0.0650354i
\(40\) 142901. 52011.6i 0.353040 0.128496i
\(41\) −803134. + 292317.i −1.81989 + 0.662385i −0.824567 + 0.565765i \(0.808581\pi\)
−0.995321 + 0.0966205i \(0.969197\pi\)
\(42\) 566419. + 95610.3i 1.17968 + 0.199128i
\(43\) 70970.3 + 402493.i 0.136125 + 0.772002i 0.974070 + 0.226247i \(0.0726458\pi\)
−0.837945 + 0.545755i \(0.816243\pi\)
\(44\) −244039. + 422689.i −0.431893 + 0.748060i
\(45\) −880505. + 335138.i −1.44042 + 0.548251i
\(46\) 600329. + 1.03980e6i 0.909362 + 1.57506i
\(47\) 603573. 506458.i 0.847983 0.711542i −0.111362 0.993780i \(-0.535521\pi\)
0.959344 + 0.282238i \(0.0910767\pi\)
\(48\) −294807. + 828780.i −0.384763 + 1.08167i
\(49\) −30496.9 + 172957.i −0.0370314 + 0.210015i
\(50\) −1.25609e6 1.05398e6i −1.42110 1.19245i
\(51\) −222480. + 130627.i −0.234852 + 0.137891i
\(52\) −305007. 111013.i −0.300814 0.109487i
\(53\) 166829. 0.153924 0.0769618 0.997034i \(-0.475478\pi\)
0.0769618 + 0.997034i \(0.475478\pi\)
\(54\) 501506. 1.47796e6i 0.433409 1.27727i
\(55\) −2.00499e6 −1.62496
\(56\) 267013. + 97184.9i 0.203177 + 0.0739505i
\(57\) 10671.0 + 1.45950e6i 0.00763212 + 1.04386i
\(58\) 1.07175e6 + 899308.i 0.721269 + 0.605216i
\(59\) 432993. 2.45562e6i 0.274472 1.55661i −0.466160 0.884700i \(-0.654363\pi\)
0.740633 0.671910i \(-0.234526\pi\)
\(60\) 2.07780e6 382057.i 1.24187 0.228349i
\(61\) −1.38983e6 + 1.16621e6i −0.783984 + 0.657841i −0.944249 0.329233i \(-0.893210\pi\)
0.160264 + 0.987074i \(0.448765\pi\)
\(62\) 2.09482e6 + 3.62834e6i 1.11629 + 1.93347i
\(63\) −1.66285e6 577836.i −0.837841 0.291147i
\(64\) 641505. 1.11112e6i 0.305893 0.529823i
\(65\) −231535. 1.31310e6i −0.104573 0.593063i
\(66\) 2.11634e6 2.55993e6i 0.906110 1.09604i
\(67\) 2.49063e6 906517.i 1.01169 0.368226i 0.217609 0.976036i \(-0.430174\pi\)
0.794082 + 0.607810i \(0.207952\pi\)
\(68\) 543637. 197868.i 0.209666 0.0763121i
\(69\) −1.28371e6 3.44831e6i −0.470431 1.26367i
\(70\) −918852. 5.21107e6i −0.320186 1.81587i
\(71\) −2.54538e6 + 4.40873e6i −0.844012 + 1.46187i 0.0424645 + 0.999098i \(0.486479\pi\)
−0.886476 + 0.462774i \(0.846854\pi\)
\(72\) 376199. 674173.i 0.118783 0.212867i
\(73\) 760649. + 1.31748e6i 0.228852 + 0.396383i 0.957468 0.288539i \(-0.0931695\pi\)
−0.728616 + 0.684922i \(0.759836\pi\)
\(74\) −2.68596e6 + 2.25379e6i −0.770528 + 0.646550i
\(75\) 3.25807e6 + 3.82566e6i 0.891756 + 1.04711i
\(76\) 568330. 3.22316e6i 0.148509 0.842236i
\(77\) −2.86989e6 2.40813e6i −0.716387 0.601120i
\(78\) 1.92093e6 + 1.09040e6i 0.458332 + 0.260169i
\(79\) 1.61633e6 + 588296.i 0.368838 + 0.134246i 0.519788 0.854295i \(-0.326011\pi\)
−0.150950 + 0.988541i \(0.548233\pi\)
\(80\) 8.10304e6 1.76943
\(81\) −2.26934e6 + 4.21033e6i −0.474463 + 0.880276i
\(82\) −1.30424e7 −2.61221
\(83\) 4.95600e6 + 1.80384e6i 0.951389 + 0.346277i 0.770654 0.637254i \(-0.219930\pi\)
0.180736 + 0.983532i \(0.442152\pi\)
\(84\) 3.43298e6 + 1.94871e6i 0.631966 + 0.358731i
\(85\) 1.82054e6 + 1.52761e6i 0.321539 + 0.269803i
\(86\) −1.08301e6 + 6.14203e6i −0.183606 + 1.04128i
\(87\) −2.77994e6 3.26423e6i −0.452603 0.531452i
\(88\) 1.25861e6 1.05610e6i 0.196881 0.165203i
\(89\) −2.46514e6 4.26974e6i −0.370660 0.642002i 0.619007 0.785385i \(-0.287535\pi\)
−0.989667 + 0.143383i \(0.954202\pi\)
\(90\) −1.43753e7 + 210220.i −2.07859 + 0.0303966i
\(91\) 1.24570e6 2.15762e6i 0.173289 0.300145i
\(92\) 1.43276e6 + 8.12560e6i 0.191830 + 1.08792i
\(93\) −4.47946e6 1.20327e7i −0.577477 1.55122i
\(94\) 1.12984e7 4.11227e6i 1.40303 0.510662i
\(95\) 1.26339e7 4.59838e6i 1.51184 0.550265i
\(96\) −7.20662e6 + 8.71716e6i −0.831347 + 1.00560i
\(97\) 141016. + 799740.i 0.0156880 + 0.0889708i 0.991646 0.128986i \(-0.0411721\pi\)
−0.975959 + 0.217956i \(0.930061\pi\)
\(98\) −1.34002e6 + 2.32098e6i −0.143820 + 0.249103i
\(99\) −7.70098e6 + 6.65618e6i −0.797669 + 0.689448i
\(100\) −5.63405e6 9.75847e6i −0.563405 0.975847i
\(101\) −491797. + 412666.i −0.0474964 + 0.0398542i −0.666227 0.745749i \(-0.732092\pi\)
0.618730 + 0.785603i \(0.287647\pi\)
\(102\) −3.87206e6 + 711977.i −0.361278 + 0.0664302i
\(103\) −841127. + 4.77027e6i −0.0758457 + 0.430143i 0.923113 + 0.384528i \(0.125636\pi\)
−0.998959 + 0.0456147i \(0.985475\pi\)
\(104\) 837001. + 702327.i 0.0729641 + 0.0612242i
\(105\) 118560. + 1.62156e7i 0.00999481 + 1.36701i
\(106\) 2.39227e6 + 870715.i 0.195092 + 0.0710077i
\(107\) 7.46049e6 0.588741 0.294371 0.955691i \(-0.404890\pi\)
0.294371 + 0.955691i \(0.404890\pi\)
\(108\) 6.71227e6 8.36533e6i 0.512727 0.638998i
\(109\) 1.64202e7 1.21446 0.607232 0.794525i \(-0.292280\pi\)
0.607232 + 0.794525i \(0.292280\pi\)
\(110\) −2.87510e7 1.04645e7i −2.05958 0.749625i
\(111\) 9.26612e6 5.44051e6i 0.643084 0.377580i
\(112\) 1.15985e7 + 9.73226e6i 0.780077 + 0.654562i
\(113\) 4.78123e6 2.71157e7i 0.311721 1.76786i −0.278326 0.960487i \(-0.589780\pi\)
0.590047 0.807369i \(-0.299109\pi\)
\(114\) −7.46443e6 + 2.09845e7i −0.471878 + 1.32657i
\(115\) −2.59645e7 + 2.17868e7i −1.59198 + 1.33583i
\(116\) 4.80724e6 + 8.32638e6i 0.285952 + 0.495283i
\(117\) −5.24853e6 4.27483e6i −0.302961 0.246757i
\(118\) 1.90254e7 3.29530e7i 1.06598 1.84632i
\(119\) 771107. + 4.37317e6i 0.0419470 + 0.237893i
\(120\) −7.01249e6 1.18369e6i −0.370457 0.0625324i
\(121\) −2.04388e6 + 743911.i −0.104883 + 0.0381744i
\(122\) −2.60164e7 + 9.46920e6i −1.29714 + 0.472122i
\(123\) 3.94118e7 + 6.65263e6i 1.90967 + 0.322348i
\(124\) 4.99956e6 + 2.83539e7i 0.235481 + 1.33548i
\(125\) 6.31672e6 1.09409e7i 0.289272 0.501034i
\(126\) −2.08289e7 1.69648e7i −0.927620 0.755529i
\(127\) −5.72533e6 9.91657e6i −0.248021 0.429584i 0.714956 0.699170i \(-0.246447\pi\)
−0.962977 + 0.269585i \(0.913113\pi\)
\(128\) −8.71646e6 + 7.31398e6i −0.367371 + 0.308261i
\(129\) 6.40557e6 1.80077e7i 0.262721 0.738576i
\(130\) 3.53322e6 2.00379e7i 0.141049 0.799926i
\(131\) 1.19378e7 + 1.00170e7i 0.463953 + 0.389303i 0.844583 0.535425i \(-0.179848\pi\)
−0.380630 + 0.924727i \(0.624293\pi\)
\(132\) 1.96832e7 1.15568e7i 0.744882 0.437350i
\(133\) 2.36068e7 + 8.59218e6i 0.870075 + 0.316681i
\(134\) 4.04462e7 1.45215
\(135\) 4.35470e7 + 6.69730e6i 1.52332 + 0.234278i
\(136\) −1.94747e6 −0.0663874
\(137\) −7.92221e6 2.88345e6i −0.263223 0.0958055i 0.207037 0.978333i \(-0.433618\pi\)
−0.470261 + 0.882528i \(0.655840\pi\)
\(138\) −410520. 5.61477e7i −0.0132971 1.81868i
\(139\) −3.96011e7 3.32293e7i −1.25071 1.04947i −0.996608 0.0822901i \(-0.973777\pi\)
−0.254099 0.967178i \(-0.581779\pi\)
\(140\) 6.31437e6 3.58106e7i 0.194483 1.10297i
\(141\) −3.62393e7 + 6.66352e6i −1.08871 + 0.200187i
\(142\) −5.95101e7 + 4.99349e7i −1.74414 + 1.46351i
\(143\) −7.20288e6 1.24758e7i −0.205982 0.356772i
\(144\) 3.11229e7 2.69005e7i 0.868584 0.750743i
\(145\) −1.97478e7 + 3.42042e7i −0.537936 + 0.931733i
\(146\) 4.03124e6 + 2.28623e7i 0.107202 + 0.607974i
\(147\) 5.23318e6 6.33008e6i 0.135880 0.164361i
\(148\) −2.26421e7 + 8.24104e6i −0.574117 + 0.208961i
\(149\) 1.00010e7 3.64007e6i 0.247681 0.0901484i −0.215197 0.976571i \(-0.569039\pi\)
0.462877 + 0.886422i \(0.346817\pi\)
\(150\) 2.67528e7 + 7.18634e7i 0.647216 + 1.73855i
\(151\) 165178. + 936769.i 0.00390420 + 0.0221418i 0.986698 0.162566i \(-0.0519771\pi\)
−0.982793 + 0.184708i \(0.940866\pi\)
\(152\) −5.50869e6 + 9.54134e6i −0.127232 + 0.220372i
\(153\) 1.20639e7 176418.i 0.272312 0.00398220i
\(154\) −2.85848e7 4.95104e7i −0.630686 1.09238i
\(155\) −9.06022e7 + 7.60243e7i −1.95424 + 1.63980i
\(156\) 9.84173e6 + 1.15563e7i 0.207556 + 0.243715i
\(157\) −4.54094e6 + 2.57530e7i −0.0936477 + 0.531103i 0.901506 + 0.432767i \(0.142463\pi\)
−0.995153 + 0.0983352i \(0.968648\pi\)
\(158\) 2.01072e7 + 1.68720e7i 0.405557 + 0.340303i
\(159\) −6.78490e6 3.85140e6i −0.133861 0.0759851i
\(160\) 9.79037e7 + 3.56340e7i 1.88964 + 0.687773i
\(161\) −6.33323e7 −1.19601
\(162\) −5.45163e7 + 4.85306e7i −1.00745 + 0.896837i
\(163\) −3.45524e7 −0.624915 −0.312458 0.949932i \(-0.601152\pi\)
−0.312458 + 0.949932i \(0.601152\pi\)
\(164\) −8.42222e7 3.06544e7i −1.49099 0.542674i
\(165\) 8.15428e7 + 4.62872e7i 1.41316 + 0.802171i
\(166\) 6.16529e7 + 5.17329e7i 1.04611 + 0.877786i
\(167\) 3.54630e6 2.01120e7i 0.0589206 0.334155i −0.941071 0.338209i \(-0.890179\pi\)
0.999992 + 0.00405317i \(0.00129017\pi\)
\(168\) −8.61579e6 1.01168e7i −0.140189 0.164611i
\(169\) −4.07294e7 + 3.41760e7i −0.649089 + 0.544650i
\(170\) 1.81330e7 + 3.14073e7i 0.283073 + 0.490297i
\(171\) 3.32600e7 5.96040e7i 0.508669 0.911569i
\(172\) −2.14297e7 + 3.71172e7i −0.321119 + 0.556194i
\(173\) −1.27659e7 7.23990e7i −0.187452 1.06309i −0.922765 0.385364i \(-0.874076\pi\)
0.735313 0.677728i \(-0.237035\pi\)
\(174\) −2.28267e7 6.13172e7i −0.328489 0.882389i
\(175\) 8.12753e7 2.95818e7i 1.14637 0.417245i
\(176\) 8.22666e7 2.99426e7i 1.13744 0.413995i
\(177\) −7.43002e7 + 8.98739e7i −1.00713 + 1.21822i
\(178\) −1.30646e7 7.40928e7i −0.173630 0.984705i
\(179\) 5.01716e7 8.68997e7i 0.653841 1.13249i −0.328342 0.944559i \(-0.606490\pi\)
0.982183 0.187927i \(-0.0601769\pi\)
\(180\) −9.33241e7 3.24298e7i −1.19272 0.414468i
\(181\) −4.57125e7 7.91764e7i −0.573007 0.992477i −0.996255 0.0864635i \(-0.972443\pi\)
0.423248 0.906014i \(-0.360890\pi\)
\(182\) 2.91241e7 2.44380e7i 0.358099 0.300481i
\(183\) 8.34472e7 1.53439e7i 1.00654 0.185079i
\(184\) 4.82306e6 2.73529e7i 0.0570769 0.323699i
\(185\) −7.58241e7 6.36240e7i −0.880453 0.738788i
\(186\) −1.43249e6 1.95925e8i −0.0163229 2.23252i
\(187\) 2.41280e7 + 8.78188e6i 0.269821 + 0.0982069i
\(188\) 8.26255e7 0.906905
\(189\) 5.42881e7 + 6.18891e7i 0.584909 + 0.666803i
\(190\) 2.05167e8 2.17005
\(191\) 1.35830e8 + 4.94382e7i 1.41052 + 0.513388i 0.931283 0.364296i \(-0.118690\pi\)
0.479239 + 0.877684i \(0.340913\pi\)
\(192\) −5.17411e7 + 3.03793e7i −0.527572 + 0.309759i
\(193\) 6.88600e7 + 5.77804e7i 0.689471 + 0.578535i 0.918757 0.394824i \(-0.129194\pi\)
−0.229285 + 0.973359i \(0.573639\pi\)
\(194\) −2.15190e6 + 1.22040e7i −0.0211600 + 0.120004i
\(195\) −2.08977e7 + 5.87488e7i −0.201826 + 0.567385i
\(196\) −1.41084e7 + 1.18384e7i −0.133839 + 0.112304i
\(197\) 3.12747e7 + 5.41694e7i 0.291448 + 0.504803i 0.974152 0.225892i \(-0.0725296\pi\)
−0.682704 + 0.730695i \(0.739196\pi\)
\(198\) −1.45170e8 + 5.52544e7i −1.32907 + 0.505870i
\(199\) −6.87593e7 + 1.19095e8i −0.618509 + 1.07129i 0.371249 + 0.928533i \(0.378929\pi\)
−0.989758 + 0.142755i \(0.954404\pi\)
\(200\) 6.58673e6 + 3.73552e7i 0.0582190 + 0.330176i
\(201\) −1.22222e8 2.06307e7i −1.06160 0.179196i
\(202\) −9.20601e6 + 3.35071e6i −0.0785853 + 0.0286027i
\(203\) −6.93479e7 + 2.52406e7i −0.581831 + 0.211769i
\(204\) −2.66776e7 4.50312e6i −0.220009 0.0371371i
\(205\) −6.39343e7 3.62590e8i −0.518317 2.93952i
\(206\) −3.69586e7 + 6.40141e7i −0.294564 + 0.510200i
\(207\) −2.73992e7 + 1.69878e8i −0.214705 + 1.33119i
\(208\) 2.91099e7 + 5.04199e7i 0.224295 + 0.388490i
\(209\) 1.11275e8 9.33707e7i 0.843111 0.707454i
\(210\) −8.29329e7 + 2.33146e8i −0.617959 + 1.73724i
\(211\) 6.16170e6 3.49447e7i 0.0451556 0.256090i −0.953870 0.300219i \(-0.902940\pi\)
0.999026 + 0.0441289i \(0.0140512\pi\)
\(212\) 1.34018e7 + 1.12454e7i 0.0966023 + 0.0810590i
\(213\) 2.05300e8 1.20540e8i 1.45566 0.854678i
\(214\) 1.06981e8 + 3.89380e7i 0.746207 + 0.271597i
\(215\) −1.76063e8 −1.20818
\(216\) −3.08639e7 + 1.87336e7i −0.208383 + 0.126483i
\(217\) −2.20995e8 −1.46816
\(218\) 2.35460e8 + 8.57004e7i 1.53929 + 0.560254i
\(219\) −520152. 7.11422e7i −0.00334638 0.457691i
\(220\) −1.61067e8 1.35151e8i −1.01983 0.855736i
\(221\) −2.96510e6 + 1.68159e7i −0.0184785 + 0.104797i
\(222\) 1.61269e8 2.96533e7i 0.989269 0.181902i
\(223\) −1.18564e8 + 9.94873e7i −0.715957 + 0.600760i −0.926264 0.376876i \(-0.876998\pi\)
0.210306 + 0.977636i \(0.432554\pi\)
\(224\) 9.73379e7 + 1.68594e8i 0.578647 + 1.00225i
\(225\) −4.41863e7 2.30805e8i −0.258612 1.35085i
\(226\) 2.10084e8 3.63877e8i 1.21064 2.09689i
\(227\) 6.40427e6 + 3.63204e7i 0.0363395 + 0.206092i 0.997572 0.0696491i \(-0.0221880\pi\)
−0.961232 + 0.275741i \(0.911077\pi\)
\(228\) −9.75235e7 + 1.17965e8i −0.544926 + 0.659145i
\(229\) 6.48055e7 2.35873e7i 0.356605 0.129794i −0.157504 0.987518i \(-0.550345\pi\)
0.514109 + 0.857725i \(0.328123\pi\)
\(230\) −4.86034e8 + 1.76902e8i −2.63402 + 0.958705i
\(231\) 6.11243e7 + 1.64192e8i 0.326266 + 0.876417i
\(232\) −5.62011e6 3.18732e7i −0.0295486 0.167578i
\(233\) −1.15066e8 + 1.99300e8i −0.595937 + 1.03219i 0.397477 + 0.917612i \(0.369886\pi\)
−0.993414 + 0.114581i \(0.963447\pi\)
\(234\) −5.29510e7 8.86930e7i −0.270159 0.452516i
\(235\) 1.69710e8 + 2.93946e8i 0.853040 + 1.47751i
\(236\) 2.00310e8 1.68080e8i 0.991998 0.832386i
\(237\) −5.21546e7 6.12404e7i −0.254491 0.298826i
\(238\) −1.17671e7 + 6.67344e7i −0.0565782 + 0.320871i
\(239\) 2.54819e8 + 2.13819e8i 1.20737 + 1.01310i 0.999388 + 0.0349688i \(0.0111332\pi\)
0.207980 + 0.978133i \(0.433311\pi\)
\(240\) −3.29550e8 1.87066e8i −1.53880 0.873487i
\(241\) −2.52156e8 9.17773e7i −1.16041 0.422353i −0.311164 0.950356i \(-0.600719\pi\)
−0.849242 + 0.528003i \(0.822941\pi\)
\(242\) −3.31912e7 −0.150546
\(243\) 1.89493e8 1.18844e8i 0.847173 0.531318i
\(244\) −1.90260e8 −0.838459
\(245\) −7.10941e7 2.58761e7i −0.308853 0.112413i
\(246\) 5.30431e8 + 3.01095e8i 2.27173 + 1.28953i
\(247\) 7.39997e7 + 6.20932e7i 0.312457 + 0.262183i
\(248\) 1.68299e7 9.54469e7i 0.0700648 0.397357i
\(249\) −1.59917e8 1.87776e8i −0.656442 0.770801i
\(250\) 1.47683e8 1.23920e8i 0.597778 0.501595i
\(251\) −8.47540e6 1.46798e7i −0.0338300 0.0585953i 0.848615 0.529011i \(-0.177437\pi\)
−0.882445 + 0.470416i \(0.844104\pi\)
\(252\) −9.46312e7 1.58507e8i −0.372505 0.623947i
\(253\) −1.83099e8 + 3.17137e8i −0.710829 + 1.23119i
\(254\) −3.03428e7 1.72082e8i −0.116181 0.658898i
\(255\) −3.87747e7 1.04157e8i −0.146439 0.393366i
\(256\) −3.17486e8 + 1.15555e8i −1.18273 + 0.430477i
\(257\) 4.75131e7 1.72933e7i 0.174601 0.0635496i −0.253240 0.967403i \(-0.581496\pi\)
0.427842 + 0.903854i \(0.359274\pi\)
\(258\) 1.85840e8 2.24793e8i 0.673707 0.814919i
\(259\) −3.21160e7 1.82139e8i −0.114861 0.651409i
\(260\) 6.99125e7 1.21092e8i 0.246688 0.427276i
\(261\) 3.77018e7 + 1.96934e8i 0.131256 + 0.685611i
\(262\) 1.18903e8 + 2.05946e8i 0.408450 + 0.707456i
\(263\) 1.64740e8 1.38233e8i 0.558410 0.468562i −0.319367 0.947631i \(-0.603470\pi\)
0.877777 + 0.479069i \(0.159026\pi\)
\(264\) −7.55688e7 + 1.38953e7i −0.252772 + 0.0464786i
\(265\) −1.24796e7 + 7.07756e7i −0.0411947 + 0.233627i
\(266\) 2.93670e8 + 2.46418e8i 0.956695 + 0.802763i
\(267\) 1.68572e6 + 2.30560e8i 0.00541997 + 0.741300i
\(268\) 2.61185e8 + 9.50636e7i 0.828851 + 0.301677i
\(269\) −2.96638e8 −0.929169 −0.464584 0.885529i \(-0.653796\pi\)
−0.464584 + 0.885529i \(0.653796\pi\)
\(270\) 5.89496e8 + 3.23319e8i 1.82267 + 0.999672i
\(271\) 6.35912e7 0.194091 0.0970453 0.995280i \(-0.469061\pi\)
0.0970453 + 0.995280i \(0.469061\pi\)
\(272\) −9.75117e7 3.54914e7i −0.293809 0.106938i
\(273\) −1.00473e8 + 5.89920e7i −0.298870 + 0.175478i
\(274\) −9.85527e7 8.26955e7i −0.289429 0.242859i
\(275\) 8.68429e7 4.92510e8i 0.251808 1.42807i
\(276\) 1.29317e8 3.63544e8i 0.370232 1.04082i
\(277\) 3.33156e8 2.79551e8i 0.941820 0.790281i −0.0360810 0.999349i \(-0.511487\pi\)
0.977901 + 0.209068i \(0.0670430\pi\)
\(278\) −3.94437e8 6.83185e8i −1.10108 1.90713i
\(279\) −9.56084e7 + 5.92783e8i −0.263561 + 1.63411i
\(280\) −6.12038e7 + 1.06008e8i −0.166619 + 0.288593i
\(281\) 2.66123e7 + 1.50926e8i 0.0715500 + 0.405780i 0.999456 + 0.0329672i \(0.0104957\pi\)
−0.927906 + 0.372813i \(0.878393\pi\)
\(282\) −5.54438e8 9.35881e7i −1.47225 0.248513i
\(283\) 3.10072e8 1.12857e8i 0.813224 0.295989i 0.0982690 0.995160i \(-0.468669\pi\)
0.714955 + 0.699171i \(0.246447\pi\)
\(284\) −5.01657e8 + 1.82588e8i −1.29955 + 0.472998i
\(285\) −6.19979e8 1.04651e8i −1.58643 0.267785i
\(286\) −3.81734e7 2.16492e8i −0.0964893 0.547218i
\(287\) 3.43979e8 5.95790e8i 0.858906 1.48767i
\(288\) 4.94336e8 1.88154e8i 1.21941 0.464130i
\(289\) 1.89952e8 + 3.29006e8i 0.462915 + 0.801793i
\(290\) −4.61696e8 + 3.87409e8i −1.11164 + 0.932775i
\(291\) 1.27277e7 3.57808e7i 0.0302777 0.0851186i
\(292\) −2.77028e7 + 1.57110e8i −0.0651153 + 0.369287i
\(293\) 1.81153e8 + 1.52006e8i 0.420736 + 0.353040i 0.828443 0.560073i \(-0.189227\pi\)
−0.407707 + 0.913113i \(0.633671\pi\)
\(294\) 1.08080e8 6.34583e7i 0.248045 0.145637i
\(295\) 1.00939e9 + 3.67387e8i 2.28918 + 0.833195i
\(296\) 8.11108e7 0.181785
\(297\) 4.66862e8 9.29215e7i 1.03405 0.205811i
\(298\) 1.62410e8 0.355513
\(299\) −2.28842e8 8.32917e7i −0.495093 0.180199i
\(300\) 3.85271e6 + 5.26943e8i 0.00823839 + 1.12678i
\(301\) −2.52012e8 2.11463e8i −0.532645 0.446942i
\(302\) −2.52061e6 + 1.42951e7i −0.00526600 + 0.0298650i
\(303\) 2.95281e7 5.42949e6i 0.0609798 0.0112127i
\(304\) −4.49709e8 + 3.77351e8i −0.918067 + 0.770349i
\(305\) −3.90786e8 6.76862e8i −0.788660 1.36600i
\(306\) 1.73913e8 + 6.04342e7i 0.346982 + 0.120575i
\(307\) 2.20322e8 3.81609e8i 0.434584 0.752722i −0.562678 0.826676i \(-0.690229\pi\)
0.997262 + 0.0739549i \(0.0235621\pi\)
\(308\) −6.82214e7 3.86903e8i −0.133043 0.754526i
\(309\) 1.44335e8 1.74588e8i 0.278302 0.336635i
\(310\) −1.69599e9 + 6.17291e8i −3.23339 + 1.17686i
\(311\) 3.80506e8 1.38493e8i 0.717299 0.261075i 0.0425203 0.999096i \(-0.486461\pi\)
0.674779 + 0.738020i \(0.264239\pi\)
\(312\) −1.78268e7 4.78865e7i −0.0332302 0.0892632i
\(313\) 1.13977e8 + 6.46397e8i 0.210094 + 1.19150i 0.889220 + 0.457479i \(0.151247\pi\)
−0.679127 + 0.734021i \(0.737641\pi\)
\(314\) −1.99526e8 + 3.45589e8i −0.363702 + 0.629951i
\(315\) 3.69532e8 6.62225e8i 0.666139 1.19377i
\(316\) 9.01888e7 + 1.56212e8i 0.160786 + 0.278489i
\(317\) 3.11371e8 2.61271e8i 0.548998 0.460664i −0.325603 0.945506i \(-0.605567\pi\)
0.874602 + 0.484842i \(0.161123\pi\)
\(318\) −7.71921e7 9.06397e7i −0.134610 0.158061i
\(319\) −7.40984e7 + 4.20233e8i −0.127803 + 0.724808i
\(320\) 4.23395e8 + 3.55270e8i 0.722304 + 0.606085i
\(321\) −3.03417e8 1.72233e8i −0.512003 0.290635i
\(322\) −9.08166e8 3.30545e8i −1.51590 0.551741i
\(323\) −1.72177e8 −0.284294
\(324\) −4.66109e8 + 1.85258e8i −0.761342 + 0.302600i
\(325\) 3.32581e8 0.537410
\(326\) −4.95470e8 1.80336e8i −0.792056 0.288285i
\(327\) −6.67806e8 3.79075e8i −1.05617 0.599526i
\(328\) 2.31123e8 + 1.93935e8i 0.361647 + 0.303458i
\(329\) −1.10130e8 + 6.24579e8i −0.170498 + 0.966944i
\(330\) 9.27716e8 + 1.08933e9i 1.42107 + 1.66864i
\(331\) −2.77253e8 + 2.32643e8i −0.420221 + 0.352607i −0.828247 0.560363i \(-0.810662\pi\)
0.408026 + 0.912970i \(0.366217\pi\)
\(332\) 2.76538e8 + 4.78977e8i 0.414735 + 0.718343i
\(333\) −5.02451e8 + 7.34768e6i −0.745657 + 0.0109042i
\(334\) 1.55822e8 2.69892e8i 0.228832 0.396348i
\(335\) 1.98269e8 + 1.12444e9i 0.288137 + 1.63411i
\(336\) −2.47029e8 6.63572e8i −0.355272 0.954334i
\(337\) 8.38522e8 3.05197e8i 1.19347 0.434386i 0.332526 0.943094i \(-0.392099\pi\)
0.860939 + 0.508708i \(0.169877\pi\)
\(338\) −7.62419e8 + 2.77498e8i −1.07395 + 0.390887i
\(339\) −8.20445e8 + 9.92414e8i −1.14380 + 1.38355i
\(340\) 4.32768e7 + 2.45435e8i 0.0597143 + 0.338657i
\(341\) −6.38917e8 + 1.10664e9i −0.872578 + 1.51135i
\(342\) 7.88024e8 6.81112e8i 1.06524 0.920720i
\(343\) −4.02132e8 6.96513e8i −0.538070 0.931965i
\(344\) 1.10522e8 9.27388e7i 0.146384 0.122831i
\(345\) 1.55895e9 2.86652e8i 2.04392 0.375827i
\(346\) 1.94807e8 1.10481e9i 0.252836 1.43390i
\(347\) 6.98288e8 + 5.85933e8i 0.897184 + 0.752827i 0.969638 0.244545i \(-0.0786386\pi\)
−0.0724541 + 0.997372i \(0.523083\pi\)
\(348\) −3.28731e6 4.49613e8i −0.00418132 0.571888i
\(349\) −1.01596e9 3.69778e8i −1.27934 0.465642i −0.389126 0.921184i \(-0.627223\pi\)
−0.890214 + 0.455542i \(0.849445\pi\)
\(350\) 1.31986e9 1.64546
\(351\) 1.14769e8 + 2.95024e8i 0.141660 + 0.364152i
\(352\) 1.12565e9 1.37564
\(353\) 1.13624e9 + 4.13558e8i 1.37486 + 0.500409i 0.920617 0.390468i \(-0.127687\pi\)
0.454245 + 0.890877i \(0.349909\pi\)
\(354\) −1.53451e9 + 9.00974e8i −1.83848 + 1.07945i
\(355\) −1.67996e9 1.40965e9i −1.99296 1.67229i
\(356\) 8.97800e7 5.09168e8i 0.105464 0.598117i
\(357\) 6.95979e7 1.95658e8i 0.0809575 0.227593i
\(358\) 1.17299e9 9.84259e8i 1.35115 1.13375i
\(359\) −4.31741e8 7.47797e8i −0.492484 0.853008i 0.507478 0.861665i \(-0.330578\pi\)
−0.999963 + 0.00865689i \(0.997244\pi\)
\(360\) 2.57870e8 + 2.10031e8i 0.291302 + 0.237260i
\(361\) −4.00909e7 + 6.94395e7i −0.0448509 + 0.0776840i
\(362\) −2.42264e8 1.37395e9i −0.268416 1.52227i
\(363\) 1.00298e8 + 1.69301e7i 0.110058 + 0.0185775i
\(364\) 2.45510e8 8.93583e7i 0.266818 0.0971136i
\(365\) −6.15831e8 + 2.24144e8i −0.662883 + 0.241270i
\(366\) 1.27669e9 + 2.15503e8i 1.36114 + 0.229757i
\(367\) 1.83299e8 + 1.03954e9i 0.193566 + 1.09777i 0.914446 + 0.404708i \(0.132627\pi\)
−0.720880 + 0.693060i \(0.756262\pi\)
\(368\) 7.39983e8 1.28169e9i 0.774024 1.34065i
\(369\) −1.44929e9 1.18042e9i −1.50163 1.22305i
\(370\) −7.55226e8 1.30809e9i −0.775124 1.34255i
\(371\) −1.02869e8 + 8.63174e7i −0.104587 + 0.0877586i
\(372\) 4.51246e8 1.26857e9i 0.454478 1.27766i
\(373\) 1.06064e8 6.01517e8i 0.105824 0.600160i −0.885063 0.465470i \(-0.845885\pi\)
0.990888 0.134690i \(-0.0430037\pi\)
\(374\) 3.00154e8 + 2.51859e8i 0.296683 + 0.248947i
\(375\) −5.09481e8 + 2.99137e8i −0.498906 + 0.292928i
\(376\) −2.61366e8 9.51293e7i −0.253566 0.0922905i
\(377\) −2.83774e8 −0.272758
\(378\) 4.55462e8 + 1.17081e9i 0.433741 + 1.11498i
\(379\) −3.10082e8 −0.292577 −0.146288 0.989242i \(-0.546733\pi\)
−0.146288 + 0.989242i \(0.546733\pi\)
\(380\) 1.32488e9 + 4.82218e8i 1.23861 + 0.450817i
\(381\) 3.91513e6 + 5.35480e8i 0.00362668 + 0.496028i
\(382\) 1.68974e9 + 1.41786e9i 1.55095 + 1.30140i
\(383\) 1.77373e7 1.00593e8i 0.0161321 0.0914899i −0.975679 0.219206i \(-0.929653\pi\)
0.991811 + 0.127716i \(0.0407645\pi\)
\(384\) 5.23347e8 9.62307e7i 0.471662 0.0867270i
\(385\) 1.23631e9 1.03739e9i 1.10412 0.926463i
\(386\) 6.85862e8 + 1.18795e9i 0.606990 + 1.05134i
\(387\) −6.76240e8 + 5.84494e8i −0.593079 + 0.512615i
\(388\) −4.25800e7 + 7.37507e7i −0.0370079 + 0.0640996i
\(389\) 6.11266e7 + 3.46666e8i 0.0526510 + 0.298599i 0.999750 0.0223418i \(-0.00711219\pi\)
−0.947099 + 0.320940i \(0.896001\pi\)
\(390\) −6.06289e8 + 7.33370e8i −0.517552 + 0.626033i
\(391\) 4.07883e8 1.48457e8i 0.345078 0.125598i
\(392\) 5.82585e7 2.12044e7i 0.0488492 0.0177797i
\(393\) −2.54256e8 6.82984e8i −0.211299 0.567593i
\(394\) 1.65748e8 + 9.40002e8i 0.136524 + 0.774269i
\(395\) −3.70489e8 + 6.41706e8i −0.302472 + 0.523898i
\(396\) −1.06731e9 + 1.56080e7i −0.863693 + 0.0126303i
\(397\) 1.13732e8 + 1.96989e8i 0.0912250 + 0.158006i 0.908027 0.418912i \(-0.137588\pi\)
−0.816802 + 0.576918i \(0.804255\pi\)
\(398\) −1.60757e9 + 1.34891e9i −1.27814 + 1.07249i
\(399\) −7.61727e8 8.94428e8i −0.600336 0.704921i
\(400\) −3.50969e8 + 1.99045e9i −0.274195 + 1.55504i
\(401\) 7.11748e7 + 5.97227e7i 0.0551215 + 0.0462524i 0.669932 0.742422i \(-0.266323\pi\)
−0.614811 + 0.788675i \(0.710768\pi\)
\(402\) −1.64494e9 9.33740e8i −1.26287 0.716861i
\(403\) −7.98535e8 2.90643e8i −0.607752 0.221204i
\(404\) −6.73240e7 −0.0507967
\(405\) −1.61644e9 1.27770e9i −1.20911 0.955734i
\(406\) −1.12616e9 −0.835141
\(407\) −1.00491e9 3.65759e8i −0.738837 0.268915i
\(408\) 7.92035e7 + 4.49593e7i 0.0577343 + 0.0327725i
\(409\) 1.42242e9 + 1.19355e9i 1.02801 + 0.862600i 0.990612 0.136700i \(-0.0436497\pi\)
0.0373946 + 0.999301i \(0.488094\pi\)
\(410\) 9.75636e8 5.53311e9i 0.699108 3.96484i
\(411\) 2.55628e8 + 3.00161e8i 0.181619 + 0.213259i
\(412\) −3.89120e8 + 3.26511e8i −0.274122 + 0.230015i
\(413\) 1.00355e9 + 1.73821e9i 0.700996 + 1.21416i
\(414\) −1.27953e9 + 2.29300e9i −0.886234 + 1.58819i
\(415\) −1.13600e9 + 1.96760e9i −0.780205 + 1.35136i
\(416\) 1.29989e8 + 7.37205e8i 0.0885279 + 0.502067i
\(417\) 8.43443e8 + 2.26566e9i 0.569613 + 1.53010i
\(418\) 2.08297e9 7.58138e8i 1.39497 0.507728i
\(419\) −1.52224e9 + 5.54049e8i −1.01096 + 0.367958i −0.793801 0.608178i \(-0.791901\pi\)
−0.217157 + 0.976137i \(0.569678\pi\)
\(420\) −1.08353e9 + 1.31064e9i −0.713620 + 0.863198i
\(421\) −7.47418e7 4.23882e8i −0.0488176 0.276858i 0.950621 0.310353i \(-0.100447\pi\)
−0.999439 + 0.0334949i \(0.989336\pi\)
\(422\) 2.70741e8 4.68937e8i 0.175372 0.303754i
\(423\) 1.62768e9 + 5.65614e8i 1.04563 + 0.363353i
\(424\) −2.94461e7 5.10021e7i −0.0187606 0.0324944i
\(425\) −4.54099e8 + 3.81035e8i −0.286939 + 0.240770i
\(426\) 3.57306e9 6.56999e8i 2.23927 0.411747i
\(427\) 2.53594e8 1.43820e9i 0.157631 0.893968i
\(428\) 5.99322e8 + 5.02891e8i 0.369494 + 0.310042i
\(429\) 4.92552e6 + 6.73673e8i 0.00301197 + 0.411954i
\(430\) −2.52469e9 9.18911e8i −1.53133 0.557358i
\(431\) 3.48354e8 0.209580 0.104790 0.994494i \(-0.466583\pi\)
0.104790 + 0.994494i \(0.466583\pi\)
\(432\) −1.88679e9 + 3.75536e8i −1.12598 + 0.224108i
\(433\) 3.68080e8 0.217889 0.108944 0.994048i \(-0.465253\pi\)
0.108944 + 0.994048i \(0.465253\pi\)
\(434\) −3.16901e9 1.15342e9i −1.86084 0.677290i
\(435\) 1.59278e9 9.35183e8i 0.927775 0.544734i
\(436\) 1.31908e9 + 1.10684e9i 0.762197 + 0.639559i
\(437\) 4.26410e8 2.41829e9i 0.244423 1.38619i
\(438\) 3.63848e8 1.02287e9i 0.206900 0.581650i
\(439\) 1.27051e9 1.06609e9i 0.716726 0.601404i −0.209752 0.977755i \(-0.567266\pi\)
0.926477 + 0.376350i \(0.122821\pi\)
\(440\) 3.53892e8 + 6.12958e8i 0.198055 + 0.343041i
\(441\) −3.58969e8 + 1.36631e8i −0.199307 + 0.0758600i
\(442\) −1.30285e8 + 2.25660e8i −0.0717654 + 0.124301i
\(443\) −3.69958e8 2.09814e9i −0.202181 1.14662i −0.901815 0.432122i \(-0.857765\pi\)
0.699634 0.714501i \(-0.253346\pi\)
\(444\) 1.11110e9 + 1.87552e8i 0.602440 + 0.101691i
\(445\) 1.99581e9 7.26414e8i 1.07364 0.390773i
\(446\) −2.21942e9 + 8.07804e8i −1.18459 + 0.431155i
\(447\) −4.90774e8 8.28417e7i −0.259900 0.0438705i
\(448\) 1.79333e8 + 1.01705e9i 0.0942295 + 0.534402i
\(449\) −1.11177e9 + 1.92564e9i −0.579633 + 1.00395i 0.415888 + 0.909416i \(0.363471\pi\)
−0.995521 + 0.0945383i \(0.969863\pi\)
\(450\) 5.71004e8 3.54029e9i 0.295390 1.83145i
\(451\) −1.98895e9 3.44496e9i −1.02095 1.76834i
\(452\) 2.21188e9 1.85599e9i 1.12662 0.945347i
\(453\) 1.49084e7 4.19115e7i 0.00753510 0.0211831i
\(454\) −9.77291e7 + 5.54249e8i −0.0490149 + 0.277977i
\(455\) 8.22168e8 + 6.89880e8i 0.409186 + 0.343348i
\(456\) 4.44309e8 2.60872e8i 0.219436 0.128840i
\(457\) 1.34765e9 + 4.90503e8i 0.660495 + 0.240400i 0.650450 0.759549i \(-0.274580\pi\)
0.0100449 + 0.999950i \(0.496803\pi\)
\(458\) 1.05240e9 0.511860
\(459\) −4.94709e8 2.71331e8i −0.238784 0.130965i
\(460\) −3.55439e9 −1.70260
\(461\) 7.36767e8 + 2.68161e8i 0.350249 + 0.127480i 0.511153 0.859490i \(-0.329219\pi\)
−0.160904 + 0.986970i \(0.551441\pi\)
\(462\) 1.95470e7 + 2.67349e9i 0.00922219 + 1.26134i
\(463\) −1.51481e9 1.27108e9i −0.709291 0.595166i 0.215109 0.976590i \(-0.430989\pi\)
−0.924400 + 0.381424i \(0.875434\pi\)
\(464\) 2.99463e8 1.69834e9i 0.139165 0.789245i
\(465\) 5.43987e9 1.00026e9i 2.50902 0.461346i
\(466\) −2.69020e9 + 2.25734e9i −1.23150 + 1.03335i
\(467\) 4.05180e8 + 7.01792e8i 0.184093 + 0.318859i 0.943271 0.332025i \(-0.107732\pi\)
−0.759177 + 0.650884i \(0.774398\pi\)
\(468\) −1.33474e8 6.97198e8i −0.0601919 0.314409i
\(469\) −1.06673e9 + 1.84763e9i −0.477473 + 0.827008i
\(470\) 8.99417e8 + 5.10085e9i 0.399594 + 2.26621i
\(471\) 7.79211e8 9.42538e8i 0.343623 0.415648i
\(472\) −8.27148e8 + 3.01057e8i −0.362065 + 0.131781i
\(473\) −1.78749e9 + 6.50594e8i −0.776658 + 0.282680i
\(474\) −4.28253e8 1.15037e9i −0.184704 0.496152i
\(475\) 5.82337e8 + 3.30260e9i 0.249314 + 1.41393i
\(476\) −2.32838e8 + 4.03287e8i −0.0989530 + 0.171392i
\(477\) 1.87028e8 + 3.13272e8i 0.0789027 + 0.132162i
\(478\) 2.53806e9 + 4.39605e9i 1.06293 + 1.84105i
\(479\) 1.79266e9 1.50422e9i 0.745286 0.625369i −0.188966 0.981984i \(-0.560513\pi\)
0.934252 + 0.356614i \(0.116069\pi\)
\(480\) −3.15909e9 3.70943e9i −1.30382 1.53096i
\(481\) 1.23494e8 7.00371e8i 0.0505987 0.286959i
\(482\) −3.13683e9 2.63212e9i −1.27593 1.07063i
\(483\) 2.57572e9 + 1.46209e9i 1.04012 + 0.590416i
\(484\) −2.14335e8 7.80116e7i −0.0859280 0.0312752i
\(485\) −3.49831e8 −0.139240
\(486\) 3.33755e9 7.15175e8i 1.31887 0.282609i
\(487\) −3.06883e8 −0.120399 −0.0601993 0.998186i \(-0.519174\pi\)
−0.0601993 + 0.998186i \(0.519174\pi\)
\(488\) 6.01840e8 + 2.19052e8i 0.234429 + 0.0853252i
\(489\) 1.40524e9 + 7.97674e8i 0.543463 + 0.308493i
\(490\) −8.84414e8 7.42111e8i −0.339601 0.284959i
\(491\) −6.28869e8 + 3.56649e9i −0.239759 + 1.35974i 0.592596 + 0.805499i \(0.298103\pi\)
−0.832356 + 0.554242i \(0.813008\pi\)
\(492\) 2.71762e9 + 3.19106e9i 1.02875 + 1.20797i
\(493\) 3.87459e8 3.25117e8i 0.145634 0.122201i
\(494\) 7.37055e8 + 1.27662e9i 0.275078 + 0.476449i
\(495\) −2.24775e9 3.76499e9i −0.832972 1.39523i
\(496\) 2.58214e9 4.47240e9i 0.950153 1.64571i
\(497\) −7.11563e8 4.03547e9i −0.259995 1.47451i
\(498\) −1.31311e9 3.52729e9i −0.476430 1.27979i
\(499\) −3.57448e9 + 1.30100e9i −1.28784 + 0.468734i −0.893017 0.450024i \(-0.851416\pi\)
−0.394821 + 0.918758i \(0.629193\pi\)
\(500\) 1.24493e9 4.53119e8i 0.445401 0.162113i
\(501\) −6.08533e8 + 7.36085e8i −0.216198 + 0.261514i
\(502\) −4.49174e7 2.54739e8i −0.0158471 0.0898736i
\(503\) 2.51099e9 4.34917e9i 0.879747 1.52377i 0.0281288 0.999604i \(-0.491045\pi\)
0.851618 0.524162i \(-0.175622\pi\)
\(504\) 1.16848e8 + 6.10351e8i 0.0406551 + 0.212360i
\(505\) −1.38281e8 2.39510e8i −0.0477797 0.0827568i
\(506\) −4.28080e9 + 3.59202e9i −1.46892 + 1.23257i
\(507\) 2.44544e9 4.49657e8i 0.833355 0.153234i
\(508\) 2.08516e8 1.18255e9i 0.0705694 0.400219i
\(509\) 1.34130e9 + 1.12548e9i 0.450831 + 0.378292i 0.839744 0.542982i \(-0.182705\pi\)
−0.388913 + 0.921274i \(0.627149\pi\)
\(510\) −1.23998e7 1.69595e9i −0.00413923 0.566131i
\(511\) −1.15070e9 4.18819e8i −0.381493 0.138852i
\(512\) −3.69930e9 −1.21808
\(513\) −2.72870e9 + 1.65625e9i −0.892369 + 0.541646i
\(514\) 7.71581e8 0.250617
\(515\) −1.96082e9 7.13682e8i −0.632577 0.230239i
\(516\) 1.72843e9 1.01483e9i 0.553831 0.325177i
\(517\) 2.80919e9 + 2.35719e9i 0.894055 + 0.750201i
\(518\) 4.90090e8 2.77944e9i 0.154925 0.878624i
\(519\) −1.15221e9 + 3.23917e9i −0.361782 + 1.01706i
\(520\) −3.60568e8 + 3.02553e8i −0.112454 + 0.0943603i
\(521\) −1.44563e8 2.50390e8i −0.0447842 0.0775685i 0.842764 0.538283i \(-0.180927\pi\)
−0.887549 + 0.460714i \(0.847593\pi\)
\(522\) −4.87207e8 + 3.02074e9i −0.149923 + 0.929537i
\(523\) 2.37240e9 4.10912e9i 0.725158 1.25601i −0.233751 0.972296i \(-0.575100\pi\)
0.958909 0.283714i \(-0.0915665\pi\)
\(524\) 2.83778e8 + 1.60938e9i 0.0861626 + 0.488652i
\(525\) −3.98838e9 6.73230e8i −1.20293 0.203051i
\(526\) 3.08379e9 1.12241e9i 0.923919 0.336279i
\(527\) 1.42329e9 5.18035e8i 0.423600 0.154178i
\(528\) −4.03703e9 6.81442e8i −1.19356 0.201470i
\(529\) 4.83739e8 + 2.74342e9i 0.142075 + 0.805746i
\(530\) −5.48348e8 + 9.49766e8i −0.159989 + 0.277109i
\(531\) 5.09660e9 1.93987e9i 1.47724 0.562265i
\(532\) 1.31723e9 + 2.28150e9i 0.379288 + 0.656946i
\(533\) 2.02647e9 1.70041e9i 0.579690 0.486418i
\(534\) −1.17917e9 + 3.31495e9i −0.335106 + 0.942070i
\(535\) −5.58084e8 + 3.16505e9i −0.157565 + 0.893598i
\(536\) −7.16746e8 6.01421e8i −0.201043 0.168695i
\(537\) −4.04664e9 + 2.37594e9i −1.12768 + 0.662104i
\(538\) −4.25370e9 1.54822e9i −1.17769 0.428642i
\(539\) −8.17406e8 −0.224842
\(540\) 3.04680e9 + 3.47339e9i 0.832657 + 0.949239i
\(541\) −2.40558e8 −0.0653173 −0.0326587 0.999467i \(-0.510397\pi\)
−0.0326587 + 0.999467i \(0.510397\pi\)
\(542\) 9.11878e8 + 3.31897e8i 0.246002 + 0.0895376i
\(543\) 3.12594e7 + 4.27541e9i 0.00837879 + 1.14598i
\(544\) −1.02209e9 8.57638e8i −0.272204 0.228406i
\(545\) −1.22831e9 + 6.96611e9i −0.325028 + 1.84333i
\(546\) −1.74865e9 + 3.21534e8i −0.459757 + 0.0845381i
\(547\) −3.21786e9 + 2.70010e9i −0.840642 + 0.705382i −0.957708 0.287742i \(-0.907096\pi\)
0.117066 + 0.993124i \(0.462651\pi\)
\(548\) −4.42048e8 7.65649e8i −0.114746 0.198746i
\(549\) −3.74802e9 1.30242e9i −0.966715 0.335930i
\(550\) 3.81582e9 6.60919e9i 0.977954 1.69387i
\(551\) −4.96877e8 2.81793e9i −0.126537 0.717628i
\(552\) −8.27622e8 + 1.00110e9i −0.209433 + 0.253331i
\(553\) −1.30104e9 + 4.73539e8i −0.327154 + 0.119074i
\(554\) 6.23638e9 2.26986e9i 1.55829 0.567172i
\(555\) 1.61494e9 + 4.33805e9i 0.400987 + 1.07713i
\(556\) −9.41374e8 5.33880e9i −0.232274 1.31729i
\(557\) 2.08587e9 3.61283e9i 0.511439 0.885838i −0.488473 0.872579i \(-0.662446\pi\)
0.999912 0.0132592i \(-0.00422065\pi\)
\(558\) −4.46486e9 + 8.00132e9i −1.08790 + 1.94958i
\(559\) −6.32501e8 1.09552e9i −0.153151 0.265265i
\(560\) −4.99645e9 + 4.19252e9i −1.20227 + 1.00883i
\(561\) −7.78546e8 9.14177e8i −0.186172 0.218605i
\(562\) −4.06103e8 + 2.30312e9i −0.0965070 + 0.547318i
\(563\) 4.03054e9 + 3.38202e9i 0.951884 + 0.798725i 0.979614 0.200890i \(-0.0643835\pi\)
−0.0277301 + 0.999615i \(0.508828\pi\)
\(564\) −3.36037e9 1.90749e9i −0.788697 0.447698i
\(565\) 1.11460e10 + 4.05679e9i 2.59985 + 0.946266i
\(566\) 5.03536e9 1.16728
\(567\) −7.79122e8 3.77031e9i −0.179500 0.868634i
\(568\) 1.79709e9 0.411482
\(569\) 6.95553e8 + 2.53160e8i 0.158284 + 0.0576107i 0.419947 0.907549i \(-0.362049\pi\)
−0.261663 + 0.965159i \(0.584271\pi\)
\(570\) −8.34410e9 4.73647e9i −1.88720 1.07125i
\(571\) −3.32909e9 2.79344e9i −0.748340 0.627932i 0.186724 0.982413i \(-0.440213\pi\)
−0.935063 + 0.354481i \(0.884658\pi\)
\(572\) 2.62328e8 1.48774e9i 0.0586083 0.332384i
\(573\) −4.38287e9 5.14642e9i −0.973235 1.14278i
\(574\) 8.04212e9 6.74814e9i 1.77492 1.48933i
\(575\) −4.22715e9 7.32164e9i −0.927279 1.60609i
\(576\) 2.80564e9 4.10287e7i 0.611721 0.00894560i
\(577\) −3.82504e9 + 6.62517e9i −0.828936 + 1.43576i 0.0699372 + 0.997551i \(0.477720\pi\)
−0.898873 + 0.438208i \(0.855613\pi\)
\(578\) 1.00670e9 + 5.70925e9i 0.216846 + 1.22979i
\(579\) −1.46661e9 3.93962e9i −0.314007 0.843489i
\(580\) −3.89200e9 + 1.41657e9i −0.828276 + 0.301468i
\(581\) −3.98925e9 + 1.45197e9i −0.843869 + 0.307143i
\(582\) 3.69259e8 4.46657e8i 0.0776426 0.0939169i
\(583\) 1.34832e8 + 7.64669e8i 0.0281807 + 0.159821i
\(584\) 2.68517e8 4.65085e8i 0.0557862 0.0966245i
\(585\) 2.20618e9 1.90686e9i 0.455612 0.393799i
\(586\) 1.80433e9 + 3.12519e9i 0.370403 + 0.641557i
\(587\) 4.30578e8 3.61298e8i 0.0878656 0.0737280i −0.597797 0.801648i \(-0.703957\pi\)
0.685662 + 0.727920i \(0.259513\pi\)
\(588\) 8.47088e8 1.55759e8i 0.171834 0.0315960i
\(589\) 1.48794e9 8.43852e9i 0.300042 1.70162i
\(590\) 1.25568e10 + 1.05364e10i 2.51708 + 2.11208i
\(591\) −2.13865e7 2.92507e9i −0.00426170 0.582881i
\(592\) 4.06129e9 + 1.47819e9i 0.804522 + 0.292822i
\(593\) 4.15541e9 0.818319 0.409160 0.912463i \(-0.365822\pi\)
0.409160 + 0.912463i \(0.365822\pi\)
\(594\) 7.17963e9 + 1.10419e9i 1.40556 + 0.216168i
\(595\) −1.91296e9 −0.372303
\(596\) 1.04878e9 + 3.81723e8i 0.202918 + 0.0738561i
\(597\) 5.54585e9 3.25619e9i 1.06674 0.626325i
\(598\) −2.84681e9 2.38875e9i −0.544382 0.456791i
\(599\) 9.79683e8 5.55606e9i 0.186248 1.05627i −0.738093 0.674699i \(-0.764274\pi\)
0.924341 0.381567i \(-0.124615\pi\)
\(600\) 5.94499e8 1.67129e9i 0.112363 0.315881i
\(601\) −1.35622e9 + 1.13800e9i −0.254840 + 0.213836i −0.761253 0.648455i \(-0.775416\pi\)
0.506413 + 0.862291i \(0.330971\pi\)
\(602\) −2.51010e9 4.34762e9i −0.468924 0.812201i
\(603\) 4.49446e9 + 3.66065e9i 0.834769 + 0.679904i
\(604\) −4.98758e7 + 8.63873e7i −0.00921001 + 0.0159522i
\(605\) −1.62705e8 9.22746e8i −0.0298715 0.169410i
\(606\) 4.51761e8 + 7.62564e7i 0.0824622 + 0.0139195i
\(607\) −4.78376e9 + 1.74114e9i −0.868178 + 0.315991i −0.737429 0.675425i \(-0.763960\pi\)
−0.130749 + 0.991416i \(0.541738\pi\)
\(608\) −7.09299e9 + 2.58164e9i −1.27987 + 0.465835i
\(609\) 3.40307e9 + 5.74431e8i 0.610535 + 0.103057i
\(610\) −2.07106e9 1.17456e10i −0.369436 2.09518i
\(611\) −1.21936e9 + 2.11199e9i −0.216265 + 0.374582i
\(612\) 9.81016e8 + 7.99020e8i 0.173000 + 0.140905i
\(613\) −2.61033e9 4.52123e9i −0.457704 0.792766i 0.541135 0.840936i \(-0.317995\pi\)
−0.998839 + 0.0481692i \(0.984661\pi\)
\(614\) 5.15105e9 4.32225e9i 0.898063 0.753564i
\(615\) −5.77053e9 + 1.62225e10i −1.00035 + 2.81225i
\(616\) −2.29651e8 + 1.30242e9i −0.0395855 + 0.224501i
\(617\) −3.09360e9 2.59584e9i −0.530233 0.444918i 0.337949 0.941164i \(-0.390267\pi\)
−0.868182 + 0.496246i \(0.834711\pi\)
\(618\) 2.98093e9 1.75022e9i 0.508033 0.298286i
\(619\) 1.22011e9 + 4.44085e8i 0.206768 + 0.0752573i 0.443328 0.896360i \(-0.353798\pi\)
−0.236560 + 0.971617i \(0.576020\pi\)
\(620\) −1.24029e10 −2.09003
\(621\) 5.03612e9 6.27639e9i 0.843870 1.05169i
\(622\) 6.17916e9 1.02959
\(623\) 3.72921e9 + 1.35732e9i 0.617886 + 0.224892i
\(624\) −1.99061e7 2.72260e9i −0.00327975 0.448578i
\(625\) −2.26162e9 1.89773e9i −0.370544 0.310924i
\(626\) −1.73929e9 + 9.86400e9i −0.283375 + 1.60710i
\(627\) −6.68108e9 + 1.22849e9i −1.08246 + 0.199037i
\(628\) −2.10072e9 + 1.76271e9i −0.338462 + 0.284003i
\(629\) 6.33791e8 + 1.09776e9i 0.101547 + 0.175885i
\(630\) 8.75527e9 7.56744e9i 1.39501 1.20575i
\(631\) −4.79052e9 + 8.29742e9i −0.759067 + 1.31474i 0.184260 + 0.982877i \(0.441011\pi\)
−0.943327 + 0.331865i \(0.892322\pi\)
\(632\) −1.05439e8 5.97975e8i −0.0166147 0.0942265i
\(633\) −1.05733e9 + 1.27895e9i −0.165690 + 0.200420i
\(634\) 5.82860e9 2.12144e9i 0.908347 0.330611i
\(635\) 4.63530e9 1.68711e9i 0.718406 0.261478i
\(636\) −2.85438e8 7.66744e8i −0.0439958 0.118182i
\(637\) −9.43933e7 5.35331e8i −0.0144695 0.0820605i
\(638\) −3.25584e9 + 5.63927e9i −0.496352 + 0.859708i
\(639\) −1.11323e10 + 1.62795e8i −1.68784 + 0.0246824i
\(640\) −2.45085e9 4.24500e9i −0.369562 0.640101i
\(641\) −8.13283e8 + 6.82425e8i −0.121966 + 0.102342i −0.701731 0.712442i \(-0.747589\pi\)
0.579765 + 0.814784i \(0.303145\pi\)
\(642\) −3.45199e9 4.05336e9i −0.514869 0.604565i
\(643\) 7.03282e8 3.98851e9i 0.104326 0.591660i −0.887162 0.461458i \(-0.847326\pi\)
0.991488 0.130202i \(-0.0415625\pi\)
\(644\) −5.08766e9 4.26905e9i −0.750615 0.629841i
\(645\) 7.16046e9 + 4.06458e9i 1.05071 + 0.596426i
\(646\) −2.46897e9 8.98631e8i −0.360331 0.131150i
\(647\) 6.53105e8 0.0948022 0.0474011 0.998876i \(-0.484906\pi\)
0.0474011 + 0.998876i \(0.484906\pi\)
\(648\) 1.68771e9 4.93717e7i 0.243661 0.00712796i
\(649\) 1.16054e10 1.66650
\(650\) 4.76911e9 + 1.73581e9i 0.681146 + 0.247917i
\(651\) 8.98786e9 + 5.10189e9i 1.27680 + 0.724766i
\(652\) −2.77569e9 2.32908e9i −0.392197 0.329092i
\(653\) −7.53604e8 + 4.27390e9i −0.105912 + 0.600659i 0.884940 + 0.465706i \(0.154200\pi\)
−0.990852 + 0.134953i \(0.956912\pi\)
\(654\) −7.59765e9 8.92124e9i −1.06208 1.24711i
\(655\) −5.14262e9 + 4.31517e9i −0.715056 + 0.600003i
\(656\) 8.03820e9 + 1.39226e10i 1.11172 + 1.92555i
\(657\) −1.62123e9 + 2.90535e9i −0.223031 + 0.399687i
\(658\) −4.83904e9 + 8.38147e9i −0.662169 + 1.14691i
\(659\) −1.65038e9 9.35976e9i −0.224639 1.27399i −0.863375 0.504563i \(-0.831653\pi\)
0.638736 0.769426i \(-0.279458\pi\)
\(660\) 3.43047e9 + 9.21495e9i 0.464462 + 1.24764i
\(661\) −1.20521e10 + 4.38661e9i −1.62315 + 0.590777i −0.983978 0.178289i \(-0.942944\pi\)
−0.639169 + 0.769066i \(0.720722\pi\)
\(662\) −5.18993e9 + 1.88898e9i −0.695278 + 0.253060i
\(663\) 5.08802e8 6.15449e8i 0.0678034 0.0820153i
\(664\) −3.23298e8 1.83351e9i −0.0428563 0.243050i
\(665\) −5.41107e9 + 9.37224e9i −0.713522 + 1.23586i
\(666\) −7.24335e9 2.51704e9i −0.950122 0.330165i
\(667\) 3.60680e9 + 6.24717e9i 0.470633 + 0.815160i
\(668\) 1.64058e9 1.37661e9i 0.212951 0.178687i
\(669\) 7.11876e9 1.30896e9i 0.919206 0.169019i
\(670\) −3.02559e9 + 1.71590e10i −0.388640 + 2.20409i
\(671\) −6.46865e9 5.42784e9i −0.826579 0.693582i
\(672\) −6.65622e7 9.10384e9i −0.00846126 1.15726i
\(673\) 1.91680e9 + 6.97657e8i 0.242395 + 0.0882245i 0.460361 0.887732i \(-0.347720\pi\)
−0.217966 + 0.975956i \(0.569942\pi\)
\(674\) 1.36170e10 1.71306
\(675\) −3.53130e9 + 1.04069e10i −0.441948 + 1.30244i
\(676\) −5.57561e9 −0.694191
\(677\) −4.41213e9 1.60589e9i −0.546498 0.198909i 0.0539920 0.998541i \(-0.482805\pi\)
−0.600490 + 0.799632i \(0.705028\pi\)
\(678\) −1.69445e10 + 9.94883e9i −2.08798 + 1.22594i
\(679\) −5.00739e8 4.20170e8i −0.0613857 0.0515087i
\(680\) 1.45681e8 8.26199e8i 0.0177673 0.100764i
\(681\) 5.78031e8 1.62500e9i 0.0701352 0.197168i
\(682\) −1.49377e10 + 1.25342e10i −1.80317 + 1.51304i
\(683\) −4.60439e9 7.97504e9i −0.552968 0.957768i −0.998059 0.0622828i \(-0.980162\pi\)
0.445091 0.895485i \(-0.353171\pi\)
\(684\) 6.68960e9 2.54620e9i 0.799289 0.304225i
\(685\) 1.81590e9 3.14523e9i 0.215861 0.373883i
\(686\) −2.13119e9 1.20866e10i −0.252051 1.42945i
\(687\) −3.18017e9 5.36806e8i −0.374198 0.0631639i
\(688\) 7.22402e9 2.62933e9i 0.845706 0.307812i
\(689\) −4.85223e8 + 1.76607e8i −0.0565163 + 0.0205703i
\(690\) 2.38509e10 + 4.02598e9i 2.76397 + 0.466552i
\(691\) −2.94934e9 1.67265e10i −0.340057 1.92856i −0.370061 0.929008i \(-0.620663\pi\)
0.0300040 0.999550i \(-0.490448\pi\)
\(692\) 3.85469e9 6.67652e9i 0.442199 0.765912i
\(693\) 1.30462e9 8.08879e9i 0.148908 0.923246i
\(694\) 6.95512e9 + 1.20466e10i 0.789853 + 1.36807i
\(695\) 1.70596e10 1.43147e10i 1.92762 1.61747i
\(696\) −5.07254e8 + 1.42602e9i −0.0570287 + 0.160323i
\(697\) −8.18761e8 + 4.64342e9i −0.0915888 + 0.519426i
\(698\) −1.26385e10 1.06050e10i −1.40671 1.18037i
\(699\) 9.28073e9 5.44909e9i 1.02781 0.603468i
\(700\) 8.52309e9 + 3.10215e9i 0.939191 + 0.341837i
\(701\) −1.61361e10 −1.76924 −0.884619 0.466314i \(-0.845582\pi\)
−0.884619 + 0.466314i \(0.845582\pi\)
\(702\) 1.05948e8 + 4.82956e9i 0.0115588 + 0.526899i
\(703\) 7.17106e9 0.778466
\(704\) 5.61135e9 + 2.04236e9i 0.606126 + 0.220612i
\(705\) −1.16052e8 1.58727e10i −0.0124736 1.70604i
\(706\) 1.41349e10 + 1.18606e10i 1.51174 + 1.26850i
\(707\) 8.97350e7 5.08912e8i 0.00954979 0.0541596i
\(708\) −1.20269e10 + 2.21145e9i −1.27361 + 0.234186i
\(709\) 7.70381e9 6.46426e9i 0.811790 0.681173i −0.139244 0.990258i \(-0.544467\pi\)
0.951034 + 0.309085i \(0.100023\pi\)
\(710\) −1.67328e10 2.89820e10i −1.75454 3.03896i
\(711\) 7.07325e8 + 3.69468e9i 0.0738032 + 0.385508i
\(712\) −8.70218e8 + 1.50726e9i −0.0903542 + 0.156498i
\(713\) 3.75110e9 + 2.12736e10i 0.387566 + 2.19799i
\(714\) 2.01919e9 2.44243e9i 0.207603 0.251118i
\(715\) 5.83154e9 2.12251e9i 0.596640 0.217159i
\(716\) 9.88809e9 3.59897e9i 1.00674 0.366423i
\(717\) −5.42726e9 1.45787e10i −0.549874 1.47708i
\(718\) −2.28811e9 1.29765e10i −0.230697 1.30835i
\(719\) −3.56690e9 + 6.17806e9i −0.357882 + 0.619871i −0.987607 0.156948i \(-0.949834\pi\)
0.629724 + 0.776819i \(0.283168\pi\)
\(720\) 9.08413e9 + 1.52159e10i 0.907026 + 1.51927i
\(721\) −1.94949e9 3.37662e9i −0.193708 0.335512i
\(722\) −9.37311e8 + 7.86498e8i −0.0926838 + 0.0777709i
\(723\) 8.13639e9 + 9.55384e9i 0.800659 + 0.940143i
\(724\) 1.66484e9 9.44180e9i 0.163038 0.924634i
\(725\) −7.54664e9 6.33238e9i −0.735480 0.617141i
\(726\) 1.34988e9 + 7.66251e8i 0.130924 + 0.0743178i
\(727\) 9.01138e9 + 3.27987e9i 0.869803 + 0.316582i 0.738087 0.674705i \(-0.235729\pi\)
0.131716 + 0.991288i \(0.457951\pi\)
\(728\) −8.79492e8 −0.0844836
\(729\) −1.04503e10 + 4.58726e8i −0.999038 + 0.0438538i
\(730\) −1.00007e10 −0.951480
\(731\) 2.11874e9 + 7.71157e8i 0.200616 + 0.0730183i
\(732\) 7.73783e9 + 4.39232e9i 0.729173 + 0.413910i
\(733\) 7.22881e9 + 6.06569e9i 0.677958 + 0.568874i 0.915409 0.402525i \(-0.131867\pi\)
−0.237451 + 0.971400i \(0.576312\pi\)
\(734\) −2.79714e9 + 1.58634e10i −0.261083 + 1.48067i
\(735\) 2.29401e9 + 2.69365e9i 0.213103 + 0.250228i
\(736\) 1.45771e10 1.22316e10i 1.34772 1.13087i
\(737\) 6.16802e9 + 1.06833e10i 0.567557 + 0.983037i
\(738\) −1.46215e10 2.44910e10i −1.33904 2.24290i
\(739\) −6.56259e9 + 1.13667e10i −0.598163 + 1.03605i 0.394929 + 0.918712i \(0.370769\pi\)
−0.993092 + 0.117337i \(0.962564\pi\)
\(740\) −1.80244e9 1.02222e10i −0.163513 0.927326i
\(741\) −1.57608e9 4.23368e9i −0.142303 0.382256i
\(742\) −1.92562e9 + 7.00868e8i −0.173044 + 0.0629829i
\(743\) 2.34378e9 8.53067e8i 0.209632 0.0762996i −0.235070 0.971978i \(-0.575532\pi\)
0.444702 + 0.895679i \(0.353310\pi\)
\(744\) −2.88795e9 + 3.49328e9i −0.257090 + 0.310977i
\(745\) 7.96141e8 + 4.51514e9i 0.0705412 + 0.400059i
\(746\) 4.66037e9 8.07200e9i 0.410993 0.711861i
\(747\) 2.16881e9 + 1.13287e10i 0.190370 + 0.994389i
\(748\) 1.34631e9 + 2.33187e9i 0.117622 + 0.203727i
\(749\) −4.60025e9 + 3.86007e9i −0.400033 + 0.335667i
\(750\) −8.86706e9 + 1.63043e9i −0.767477 + 0.141120i
\(751\) −1.53845e8 + 8.72498e8i −0.0132539 + 0.0751666i −0.990717 0.135938i \(-0.956595\pi\)
0.977463 + 0.211105i \(0.0677062\pi\)
\(752\) −1.13531e10 9.52642e9i −0.973539 0.816897i
\(753\) 5.79569e6 + 7.92689e8i 0.000494679 + 0.0676582i
\(754\) −4.06922e9 1.48108e9i −0.345710 0.125828i
\(755\) −4.09772e8 −0.0346520
\(756\) 1.89345e8