Properties

Label 24.8.f.b.11.3
Level 24
Weight 8
Character 24.11
Analytic conductor 7.497
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.49724061162\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{6}, \sqrt{-26})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.3
Root \(1.22474 - 2.54951i\)
Character \(\chi\) = 24.11
Dual form 24.8.f.b.11.4

$q$-expansion

\(f(q)\) \(=\) \(q+(4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 - 99.9200i) q^{4} -97.9796 q^{5} +(423.909 + 316.602i) q^{6} +1548.76i q^{7} +(-1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +O(q^{10})\) \(q+(4.89898 - 10.1980i) q^{2} +(-9.00000 + 45.8912i) q^{3} +(-80.0000 - 99.9200i) q^{4} -97.9796 q^{5} +(423.909 + 316.602i) q^{6} +1548.76i q^{7} +(-1410.91 + 326.337i) q^{8} +(-2025.00 - 826.041i) q^{9} +(-480.000 + 999.200i) q^{10} +1784.66i q^{11} +(5305.44 - 2772.01i) q^{12} +10141.9i q^{13} +(15794.3 + 7587.34i) q^{14} +(881.816 - 4496.40i) q^{15} +(-3584.00 + 15987.2i) q^{16} -27555.1i q^{17} +(-18344.4 + 16604.3i) q^{18} +11570.0 q^{19} +(7838.37 + 9790.12i) q^{20} +(-71074.4 - 13938.8i) q^{21} +(18200.0 + 8743.00i) q^{22} -55534.8 q^{23} +(-2277.85 - 67685.2i) q^{24} -68525.0 q^{25} +(103427. + 49684.8i) q^{26} +(56133.0 - 85495.3i) q^{27} +(154752. - 123901. i) q^{28} +54770.6 q^{29} +(-41534.4 - 31020.6i) q^{30} -71692.6i q^{31} +(145480. + 114871. i) q^{32} +(-81900.0 - 16061.9i) q^{33} +(-281008. - 134992. i) q^{34} -151747. i q^{35} +(79462.0 + 268421. i) q^{36} +282823. i q^{37} +(56681.2 - 117991. i) q^{38} +(-465423. - 91276.9i) q^{39} +(138240. - 31974.4i) q^{40} +403638. i q^{41} +(-490341. + 656533. i) q^{42} +495062. q^{43} +(178323. - 142773. i) q^{44} +(198409. + 80935.2i) q^{45} +(-272064. + 566346. i) q^{46} +1.13594e6 q^{47} +(-701415. - 308359. i) q^{48} -1.57511e6 q^{49} +(-335703. + 698821. i) q^{50} +(1.26454e6 + 247996. i) q^{51} +(1.01338e6 - 811350. i) q^{52} +572416. q^{53} +(-596890. - 991286. i) q^{54} -174860. i q^{55} +(-505418. - 2.18515e6i) q^{56} +(-104130. + 530961. i) q^{57} +(268320. - 558553. i) q^{58} +1.44050e6i q^{59} +(-519825. + 271601. i) q^{60} +1.78632e6i q^{61} +(-731124. - 351220. i) q^{62} +(1.27934e6 - 3.13624e6i) q^{63} +(1.88416e6 - 920862. i) q^{64} -993697. i q^{65} +(-565026. + 756532. i) q^{66} +1.40013e6 q^{67} +(-2.75330e6 + 2.20441e6i) q^{68} +(499813. - 2.54856e6i) q^{69} +(-1.54752e6 - 743405. i) q^{70} -3.56947e6 q^{71} +(3.12665e6 + 504634. i) q^{72} -2.22360e6 q^{73} +(2.88424e6 + 1.38555e6i) q^{74} +(616725. - 3.14469e6i) q^{75} +(-925600. - 1.15607e6i) q^{76} -2.76400e6 q^{77} +(-3.21094e6 + 4.29923e6i) q^{78} +5.59057e6i q^{79} +(351159. - 1.56642e6i) q^{80} +(3.41828e6 + 3.34547e6i) q^{81} +(4.11632e6 + 1.97742e6i) q^{82} -3.01333e6i q^{83} +(4.29318e6 + 8.21686e6i) q^{84} +2.69984e6i q^{85} +(2.42530e6 - 5.04866e6i) q^{86} +(-492935. + 2.51349e6i) q^{87} +(-582400. - 2.51798e6i) q^{88} -5.84533e6i q^{89} +(1.79738e6 - 1.62688e6i) q^{90} -1.57073e7 q^{91} +(4.44279e6 + 5.54904e6i) q^{92} +(3.29006e6 + 645233. i) q^{93} +(5.56493e6 - 1.15843e7i) q^{94} -1.13362e6 q^{95} +(-6.58087e6 + 5.64242e6i) q^{96} +6.86793e6 q^{97} +(-7.71645e6 + 1.60631e7i) q^{98} +(1.47420e6 - 3.61393e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 36q^{3} - 320q^{4} + 1872q^{6} - 8100q^{9} + O(q^{10}) \) \( 4q - 36q^{3} - 320q^{4} + 1872q^{6} - 8100q^{9} - 1920q^{10} + 2880q^{12} - 14336q^{16} - 33696q^{18} + 46280q^{19} + 72800q^{22} - 59904q^{24} - 274100q^{25} + 224532q^{27} + 619008q^{28} + 17280q^{30} - 327600q^{33} - 1124032q^{34} + 648000q^{36} + 552960q^{40} - 1392768q^{42} + 1980248q^{43} - 1088256q^{46} + 129024q^{48} - 6300452q^{49} + 5058144q^{51} + 4053504q^{52} - 3487536q^{54} - 416520q^{57} + 1073280q^{58} - 1797120q^{60} + 7536640q^{64} - 655200q^{66} + 5600504q^{67} - 6190080q^{70} + 1078272q^{72} - 8894392q^{73} + 2466900q^{75} - 3702400q^{76} - 9120384q^{78} + 13673124q^{81} + 16465280q^{82} - 5571072q^{84} - 2329600q^{88} + 3888000q^{90} - 62829312q^{91} + 22259712q^{94} - 21086208q^{96} + 27471704q^{97} + 5896800q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.89898 10.1980i 0.433013 0.901388i
\(3\) −9.00000 + 45.8912i −0.192450 + 0.981307i
\(4\) −80.0000 99.9200i −0.625000 0.780625i
\(5\) −97.9796 −0.350542 −0.175271 0.984520i \(-0.556080\pi\)
−0.175271 + 0.984520i \(0.556080\pi\)
\(6\) 423.909 + 316.602i 0.801205 + 0.598390i
\(7\) 1548.76i 1.70664i 0.521391 + 0.853318i \(0.325413\pi\)
−0.521391 + 0.853318i \(0.674587\pi\)
\(8\) −1410.91 + 326.337i −0.974279 + 0.225347i
\(9\) −2025.00 826.041i −0.925926 0.377705i
\(10\) −480.000 + 999.200i −0.151789 + 0.315975i
\(11\) 1784.66i 0.404278i 0.979357 + 0.202139i \(0.0647893\pi\)
−0.979357 + 0.202139i \(0.935211\pi\)
\(12\) 5305.44 2772.01i 0.886314 0.463085i
\(13\) 10141.9i 1.28031i 0.768244 + 0.640157i \(0.221131\pi\)
−0.768244 + 0.640157i \(0.778869\pi\)
\(14\) 15794.3 + 7587.34i 1.53834 + 0.738995i
\(15\) 881.816 4496.40i 0.0674619 0.343990i
\(16\) −3584.00 + 15987.2i −0.218750 + 0.975781i
\(17\) 27555.1i 1.36029i −0.733079 0.680144i \(-0.761917\pi\)
0.733079 0.680144i \(-0.238083\pi\)
\(18\) −18344.4 + 16604.3i −0.741397 + 0.671067i
\(19\) 11570.0 0.386986 0.193493 0.981102i \(-0.438018\pi\)
0.193493 + 0.981102i \(0.438018\pi\)
\(20\) 7838.37 + 9790.12i 0.219089 + 0.273642i
\(21\) −71074.4 13938.8i −1.67473 0.328442i
\(22\) 18200.0 + 8743.00i 0.364411 + 0.175058i
\(23\) −55534.8 −0.951739 −0.475870 0.879516i \(-0.657867\pi\)
−0.475870 + 0.879516i \(0.657867\pi\)
\(24\) −2277.85 67685.2i −0.0336345 0.999434i
\(25\) −68525.0 −0.877120
\(26\) 103427. + 49684.8i 1.15406 + 0.554392i
\(27\) 56133.0 85495.3i 0.548839 0.835928i
\(28\) 154752. 123901.i 1.33224 1.06665i
\(29\) 54770.6 0.417018 0.208509 0.978020i \(-0.433139\pi\)
0.208509 + 0.978020i \(0.433139\pi\)
\(30\) −41534.4 31020.6i −0.280856 0.209761i
\(31\) 71692.6i 0.432223i −0.976369 0.216112i \(-0.930662\pi\)
0.976369 0.216112i \(-0.0693375\pi\)
\(32\) 145480. + 114871.i 0.784836 + 0.619704i
\(33\) −81900.0 16061.9i −0.396721 0.0778034i
\(34\) −281008. 134992.i −1.22615 0.589022i
\(35\) 151747.i 0.598248i
\(36\) 79462.0 + 268421.i 0.283858 + 0.958866i
\(37\) 282823.i 0.917930i 0.888454 + 0.458965i \(0.151780\pi\)
−0.888454 + 0.458965i \(0.848220\pi\)
\(38\) 56681.2 117991.i 0.167570 0.348825i
\(39\) −465423. 91276.9i −1.25638 0.246397i
\(40\) 138240. 31974.4i 0.341526 0.0789937i
\(41\) 403638.i 0.914637i 0.889303 + 0.457319i \(0.151190\pi\)
−0.889303 + 0.457319i \(0.848810\pi\)
\(42\) −490341. + 656533.i −1.02123 + 1.36736i
\(43\) 495062. 0.949555 0.474777 0.880106i \(-0.342529\pi\)
0.474777 + 0.880106i \(0.342529\pi\)
\(44\) 178323. 142773.i 0.315590 0.252674i
\(45\) 198409. + 80935.2i 0.324576 + 0.132402i
\(46\) −272064. + 566346.i −0.412115 + 0.857886i
\(47\) 1.13594e6 1.59592 0.797961 0.602710i \(-0.205912\pi\)
0.797961 + 0.602710i \(0.205912\pi\)
\(48\) −701415. 308359.i −0.915442 0.402450i
\(49\) −1.57511e6 −1.91261
\(50\) −335703. + 698821.i −0.379804 + 0.790625i
\(51\) 1.26454e6 + 247996.i 1.33486 + 0.261788i
\(52\) 1.01338e6 811350.i 0.999445 0.800196i
\(53\) 572416. 0.528137 0.264068 0.964504i \(-0.414936\pi\)
0.264068 + 0.964504i \(0.414936\pi\)
\(54\) −596890. 991286.i −0.515841 0.856684i
\(55\) 174860.i 0.141717i
\(56\) −505418. 2.18515e6i −0.384585 1.66274i
\(57\) −104130. + 530961.i −0.0744756 + 0.379752i
\(58\) 268320. 558553.i 0.180574 0.375895i
\(59\) 1.44050e6i 0.913129i 0.889690 + 0.456565i \(0.150920\pi\)
−0.889690 + 0.456565i \(0.849080\pi\)
\(60\) −519825. + 271601.i −0.310691 + 0.162331i
\(61\) 1.78632e6i 1.00764i 0.863809 + 0.503819i \(0.168072\pi\)
−0.863809 + 0.503819i \(0.831928\pi\)
\(62\) −731124. 351220.i −0.389601 0.187158i
\(63\) 1.27934e6 3.13624e6i 0.644605 1.58022i
\(64\) 1.88416e6 920862.i 0.898438 0.439101i
\(65\) 993697.i 0.448804i
\(66\) −565026. + 756532.i −0.241916 + 0.323910i
\(67\) 1.40013e6 0.568729 0.284364 0.958716i \(-0.408217\pi\)
0.284364 + 0.958716i \(0.408217\pi\)
\(68\) −2.75330e6 + 2.20441e6i −1.06187 + 0.850180i
\(69\) 499813. 2.54856e6i 0.183162 0.933948i
\(70\) −1.54752e6 743405.i −0.539254 0.259049i
\(71\) −3.56947e6 −1.18359 −0.591793 0.806090i \(-0.701580\pi\)
−0.591793 + 0.806090i \(0.701580\pi\)
\(72\) 3.12665e6 + 504634.i 0.987225 + 0.159335i
\(73\) −2.22360e6 −0.669000 −0.334500 0.942396i \(-0.608567\pi\)
−0.334500 + 0.942396i \(0.608567\pi\)
\(74\) 2.88424e6 + 1.38555e6i 0.827411 + 0.397475i
\(75\) 616725. 3.14469e6i 0.168802 0.860724i
\(76\) −925600. 1.15607e6i −0.241867 0.302091i
\(77\) −2.76400e6 −0.689956
\(78\) −3.21094e6 + 4.29923e6i −0.766128 + 1.02579i
\(79\) 5.59057e6i 1.27574i 0.770145 + 0.637869i \(0.220184\pi\)
−0.770145 + 0.637869i \(0.779816\pi\)
\(80\) 351159. 1.56642e6i 0.0766812 0.342053i
\(81\) 3.41828e6 + 3.34547e6i 0.714678 + 0.699454i
\(82\) 4.11632e6 + 1.97742e6i 0.824443 + 0.396050i
\(83\) 3.01333e6i 0.578459i −0.957260 0.289230i \(-0.906601\pi\)
0.957260 0.289230i \(-0.0933991\pi\)
\(84\) 4.29318e6 + 8.21686e6i 0.790318 + 1.51261i
\(85\) 2.69984e6i 0.476839i
\(86\) 2.42530e6 5.04866e6i 0.411169 0.855917i
\(87\) −492935. + 2.51349e6i −0.0802551 + 0.409222i
\(88\) −582400. 2.51798e6i −0.0911029 0.393880i
\(89\) 5.84533e6i 0.878910i −0.898265 0.439455i \(-0.855172\pi\)
0.898265 0.439455i \(-0.144828\pi\)
\(90\) 1.79738e6 1.62688e6i 0.259891 0.235238i
\(91\) −1.57073e7 −2.18503
\(92\) 4.44279e6 + 5.54904e6i 0.594837 + 0.742951i
\(93\) 3.29006e6 + 645233.i 0.424144 + 0.0831814i
\(94\) 5.56493e6 1.15843e7i 0.691054 1.43854i
\(95\) −1.13362e6 −0.135655
\(96\) −6.58087e6 + 5.64242e6i −0.759162 + 0.650902i
\(97\) 6.86793e6 0.764055 0.382027 0.924151i \(-0.375226\pi\)
0.382027 + 0.924151i \(0.375226\pi\)
\(98\) −7.71645e6 + 1.60631e7i −0.828183 + 1.72400i
\(99\) 1.47420e6 3.61393e6i 0.152698 0.374332i
\(100\) 5.48200e6 + 6.84702e6i 0.548200 + 0.684702i
\(101\) −1.14364e7 −1.10449 −0.552246 0.833681i \(-0.686229\pi\)
−0.552246 + 0.833681i \(0.686229\pi\)
\(102\) 8.72401e6 1.16809e7i 0.813983 1.08987i
\(103\) 1.03302e6i 0.0931493i −0.998915 0.0465746i \(-0.985169\pi\)
0.998915 0.0465746i \(-0.0148305\pi\)
\(104\) −3.30967e6 1.43092e7i −0.288515 1.24738i
\(105\) 6.96384e6 + 1.36572e6i 0.587065 + 0.115133i
\(106\) 2.80426e6 5.83752e6i 0.228690 0.476056i
\(107\) 1.85726e7i 1.46565i 0.680419 + 0.732824i \(0.261798\pi\)
−0.680419 + 0.732824i \(0.738202\pi\)
\(108\) −1.30333e7 + 1.23081e6i −0.995571 + 0.0940176i
\(109\) 1.22187e7i 0.903714i −0.892090 0.451857i \(-0.850762\pi\)
0.892090 0.451857i \(-0.149238\pi\)
\(110\) −1.78323e6 856635.i −0.127742 0.0613651i
\(111\) −1.29791e7 2.54541e6i −0.900771 0.176656i
\(112\) −2.47603e7 5.55075e6i −1.66530 0.373327i
\(113\) 1.41210e7i 0.920641i −0.887753 0.460320i \(-0.847735\pi\)
0.887753 0.460320i \(-0.152265\pi\)
\(114\) 4.90463e6 + 3.66309e6i 0.310055 + 0.231569i
\(115\) 5.44128e6 0.333625
\(116\) −4.38165e6 5.47268e6i −0.260636 0.325534i
\(117\) 8.37761e6 2.05373e7i 0.483581 1.18548i
\(118\) 1.46903e7 + 7.05700e6i 0.823084 + 0.395397i
\(119\) 4.26762e7 2.32152
\(120\) 223182. + 6.63177e6i 0.0117903 + 0.350344i
\(121\) 1.63022e7 0.836559
\(122\) 1.82170e7 + 8.75114e6i 0.908273 + 0.436320i
\(123\) −1.85234e7 3.63275e6i −0.897540 0.176022i
\(124\) −7.16352e6 + 5.73541e6i −0.337404 + 0.270140i
\(125\) 1.43687e7 0.658010
\(126\) −2.57160e7 2.84111e7i −1.14527 1.26529i
\(127\) 1.07474e7i 0.465578i 0.972527 + 0.232789i \(0.0747851\pi\)
−0.972527 + 0.232789i \(0.925215\pi\)
\(128\) −160530. 2.37260e7i −0.00676582 0.999977i
\(129\) −4.45556e6 + 2.27190e7i −0.182742 + 0.931804i
\(130\) −1.01338e7 4.86810e6i −0.404547 0.194338i
\(131\) 3.13305e7i 1.21764i 0.793310 + 0.608818i \(0.208356\pi\)
−0.793310 + 0.608818i \(0.791644\pi\)
\(132\) 4.94709e6 + 9.46840e6i 0.187215 + 0.358317i
\(133\) 1.79191e7i 0.660445i
\(134\) 6.85919e6 1.42785e7i 0.246267 0.512645i
\(135\) −5.49989e6 + 8.37679e6i −0.192391 + 0.293028i
\(136\) 8.99226e6 + 3.88777e7i 0.306537 + 1.32530i
\(137\) 5.53966e6i 0.184061i 0.995756 + 0.0920303i \(0.0293357\pi\)
−0.995756 + 0.0920303i \(0.970664\pi\)
\(138\) −2.35417e7 1.75825e7i −0.762538 0.569512i
\(139\) −1.34182e7 −0.423783 −0.211891 0.977293i \(-0.567962\pi\)
−0.211891 + 0.977293i \(0.567962\pi\)
\(140\) −1.51625e7 + 1.21397e7i −0.467007 + 0.373905i
\(141\) −1.02234e7 + 5.21294e7i −0.307135 + 1.56609i
\(142\) −1.74868e7 + 3.64016e7i −0.512508 + 1.06687i
\(143\) −1.80998e7 −0.517603
\(144\) 2.04637e7 2.94135e7i 0.571104 0.820878i
\(145\) −5.36640e6 −0.146182
\(146\) −1.08934e7 + 2.26763e7i −0.289686 + 0.603029i
\(147\) 1.41760e7 7.22838e7i 0.368081 1.87685i
\(148\) 2.82597e7 2.26259e7i 0.716559 0.573706i
\(149\) 2.09354e7 0.518477 0.259238 0.965813i \(-0.416528\pi\)
0.259238 + 0.965813i \(0.416528\pi\)
\(150\) −2.90484e7 2.16952e7i −0.702753 0.524860i
\(151\) 3.02970e7i 0.716111i −0.933700 0.358055i \(-0.883440\pi\)
0.933700 0.358055i \(-0.116560\pi\)
\(152\) −1.63242e7 + 3.77572e6i −0.377033 + 0.0872062i
\(153\) −2.27616e7 + 5.57991e7i −0.513788 + 1.25953i
\(154\) −1.35408e7 + 2.81874e7i −0.298760 + 0.621918i
\(155\) 7.02441e6i 0.151513i
\(156\) 2.81134e7 + 5.38072e7i 0.592895 + 1.13476i
\(157\) 8.03861e7i 1.65780i −0.559397 0.828900i \(-0.688967\pi\)
0.559397 0.828900i \(-0.311033\pi\)
\(158\) 5.70129e7 + 2.73881e7i 1.14993 + 0.552411i
\(159\) −5.15175e6 + 2.62689e7i −0.101640 + 0.518264i
\(160\) −1.42541e7 1.12550e7i −0.275118 0.217233i
\(161\) 8.60101e7i 1.62427i
\(162\) 5.08633e7 1.84704e7i 0.939944 0.341329i
\(163\) 1.08125e8 1.95554 0.977772 0.209669i \(-0.0672388\pi\)
0.977772 + 0.209669i \(0.0672388\pi\)
\(164\) 4.03315e7 3.22911e7i 0.713989 0.571648i
\(165\) 8.02453e6 + 1.57374e6i 0.139068 + 0.0272734i
\(166\) −3.07300e7 1.47622e7i −0.521416 0.250480i
\(167\) −3.92926e7 −0.652834 −0.326417 0.945226i \(-0.605841\pi\)
−0.326417 + 0.945226i \(0.605841\pi\)
\(168\) 1.04828e8 3.52783e6i 1.70567 0.0574018i
\(169\) −4.01091e7 −0.639205
\(170\) 2.75330e7 + 1.32264e7i 0.429816 + 0.206477i
\(171\) −2.34292e7 9.55730e6i −0.358321 0.146167i
\(172\) −3.96050e7 4.94666e7i −0.593472 0.741246i
\(173\) −1.29099e8 −1.89566 −0.947831 0.318772i \(-0.896730\pi\)
−0.947831 + 0.318772i \(0.896730\pi\)
\(174\) 2.32178e7 + 1.73405e7i 0.334116 + 0.249539i
\(175\) 1.06129e8i 1.49692i
\(176\) −2.85317e7 6.39621e6i −0.394487 0.0884359i
\(177\) −6.61064e7 1.29645e7i −0.896060 0.175732i
\(178\) −5.96109e7 2.86362e7i −0.792238 0.380579i
\(179\) 2.75640e6i 0.0359216i −0.999839 0.0179608i \(-0.994283\pi\)
0.999839 0.0179608i \(-0.00571741\pi\)
\(180\) −7.78565e6 2.62998e7i −0.0995042 0.336123i
\(181\) 1.11231e8i 1.39428i 0.716933 + 0.697142i \(0.245545\pi\)
−0.716933 + 0.697142i \(0.754455\pi\)
\(182\) −7.69499e7 + 1.60184e8i −0.946146 + 1.96956i
\(183\) −8.19763e7 1.60769e7i −0.988802 0.193920i
\(184\) 7.83544e7 1.81231e7i 0.927259 0.214472i
\(185\) 2.77109e7i 0.321773i
\(186\) 2.26980e7 3.03911e7i 0.258638 0.346299i
\(187\) 4.91764e7 0.549935
\(188\) −9.08749e7 1.13503e8i −0.997451 1.24582i
\(189\) 1.32412e8 + 8.69365e7i 1.42662 + 0.936669i
\(190\) −5.55360e6 + 1.15607e7i −0.0587404 + 0.122278i
\(191\) 1.09860e8 1.14084 0.570418 0.821354i \(-0.306781\pi\)
0.570418 + 0.821354i \(0.306781\pi\)
\(192\) 2.53020e7 + 9.47541e7i 0.257989 + 0.966148i
\(193\) −5.60296e7 −0.561005 −0.280502 0.959853i \(-0.590501\pi\)
−0.280502 + 0.959853i \(0.590501\pi\)
\(194\) 3.36458e7 7.00394e7i 0.330845 0.688710i
\(195\) 4.56019e7 + 8.94327e6i 0.440415 + 0.0863725i
\(196\) 1.26009e8 + 1.57385e8i 1.19538 + 1.49303i
\(197\) −9.45130e7 −0.880765 −0.440382 0.897810i \(-0.645157\pi\)
−0.440382 + 0.897810i \(0.645157\pi\)
\(198\) −2.96329e7 3.27385e7i −0.271298 0.299730i
\(199\) 9.00414e7i 0.809947i 0.914328 + 0.404974i \(0.132719\pi\)
−0.914328 + 0.404974i \(0.867281\pi\)
\(200\) 9.66823e7 2.23623e7i 0.854559 0.197656i
\(201\) −1.26011e7 + 6.42534e7i −0.109452 + 0.558098i
\(202\) −5.60265e7 + 1.16628e8i −0.478259 + 0.995576i
\(203\) 8.48265e7i 0.711697i
\(204\) −7.63831e7 1.46192e8i −0.629929 1.20564i
\(205\) 3.95483e7i 0.320619i
\(206\) −1.05348e7 5.06076e6i −0.0839636 0.0403348i
\(207\) 1.12458e8 + 4.58741e7i 0.881240 + 0.359477i
\(208\) −1.62140e8 3.63485e7i −1.24931 0.280069i
\(209\) 2.06485e7i 0.156450i
\(210\) 4.80434e7 6.43269e7i 0.357986 0.479319i
\(211\) −9.47083e7 −0.694064 −0.347032 0.937853i \(-0.612810\pi\)
−0.347032 + 0.937853i \(0.612810\pi\)
\(212\) −4.57933e7 5.71958e7i −0.330086 0.412277i
\(213\) 3.21253e7 1.63807e8i 0.227781 1.16146i
\(214\) 1.89404e8 + 9.09868e7i 1.32112 + 0.634644i
\(215\) −4.85060e7 −0.332859
\(216\) −5.12981e7 + 1.38944e8i −0.346348 + 0.938106i
\(217\) 1.11035e8 0.737648
\(218\) −1.24606e8 5.98590e7i −0.814597 0.391320i
\(219\) 2.00124e7 1.02044e8i 0.128749 0.656494i
\(220\) −1.74720e7 + 1.39888e7i −0.110628 + 0.0885729i
\(221\) 2.79460e8 1.74160
\(222\) −8.95426e7 + 1.19891e8i −0.549280 + 0.735450i
\(223\) 1.44671e7i 0.0873601i 0.999046 + 0.0436801i \(0.0139082\pi\)
−0.999046 + 0.0436801i \(0.986092\pi\)
\(224\) −1.77907e8 + 2.25314e8i −1.05761 + 1.33943i
\(225\) 1.38763e8 + 5.66045e7i 0.812148 + 0.331293i
\(226\) −1.44006e8 6.91784e7i −0.829855 0.398649i
\(227\) 3.50766e7i 0.199034i 0.995036 + 0.0995169i \(0.0317297\pi\)
−0.995036 + 0.0995169i \(0.968270\pi\)
\(228\) 6.13840e7 3.20722e7i 0.342991 0.179208i
\(229\) 1.01759e7i 0.0559949i 0.999608 + 0.0279975i \(0.00891303\pi\)
−0.999608 + 0.0279975i \(0.991087\pi\)
\(230\) 2.66567e7 5.54904e7i 0.144464 0.300726i
\(231\) 2.48760e7 1.26843e8i 0.132782 0.677058i
\(232\) −7.72762e7 + 1.78737e7i −0.406291 + 0.0939737i
\(233\) 1.39333e8i 0.721621i 0.932639 + 0.360811i \(0.117500\pi\)
−0.932639 + 0.360811i \(0.882500\pi\)
\(234\) −1.68398e8 1.86047e8i −0.859177 0.949221i
\(235\) −1.11299e8 −0.559438
\(236\) 1.43935e8 1.15240e8i 0.712811 0.570706i
\(237\) −2.56558e8 5.03151e7i −1.25189 0.245516i
\(238\) 2.09070e8 4.35214e8i 1.00525 2.09259i
\(239\) −6.12372e7 −0.290150 −0.145075 0.989421i \(-0.546342\pi\)
−0.145075 + 0.989421i \(0.546342\pi\)
\(240\) 6.87244e7 + 3.02129e7i 0.320901 + 0.141076i
\(241\) 1.39554e8 0.642218 0.321109 0.947042i \(-0.395944\pi\)
0.321109 + 0.947042i \(0.395944\pi\)
\(242\) 7.98640e7 1.66250e8i 0.362241 0.754064i
\(243\) −1.84292e8 + 1.26760e8i −0.823919 + 0.566708i
\(244\) 1.78489e8 1.42906e8i 0.786587 0.629774i
\(245\) 1.54329e8 0.670449
\(246\) −1.27793e8 + 1.71106e8i −0.547310 + 0.732812i
\(247\) 1.17342e8i 0.495464i
\(248\) 2.33960e7 + 1.01151e8i 0.0974002 + 0.421106i
\(249\) 1.38285e8 + 2.71199e7i 0.567646 + 0.111325i
\(250\) 7.03920e7 1.46533e8i 0.284927 0.593122i
\(251\) 3.29413e7i 0.131487i −0.997837 0.0657436i \(-0.979058\pi\)
0.997837 0.0657436i \(-0.0209419\pi\)
\(252\) −4.15720e8 + 1.23068e8i −1.63644 + 0.484442i
\(253\) 9.91106e7i 0.384767i
\(254\) 1.09603e8 + 5.26515e7i 0.419666 + 0.201601i
\(255\) −1.23899e8 2.42985e7i −0.467925 0.0917676i
\(256\) −2.42745e8 1.14596e8i −0.904297 0.426904i
\(257\) 3.21918e8i 1.18299i −0.806310 0.591493i \(-0.798539\pi\)
0.806310 0.591493i \(-0.201461\pi\)
\(258\) 2.09861e8 + 1.56738e8i 0.760788 + 0.568204i
\(259\) −4.38026e8 −1.56657
\(260\) −9.92902e7 + 7.94958e7i −0.350348 + 0.280503i
\(261\) −1.10910e8 4.52428e7i −0.386127 0.157510i
\(262\) 3.19509e8 + 1.53487e8i 1.09756 + 0.527252i
\(263\) 3.65537e8 1.23904 0.619521 0.784980i \(-0.287327\pi\)
0.619521 + 0.784980i \(0.287327\pi\)
\(264\) 1.20795e8 4.06517e6i 0.404049 0.0135977i
\(265\) −5.60851e7 −0.185134
\(266\) 1.82740e8 + 8.77855e7i 0.595317 + 0.285981i
\(267\) 2.68249e8 + 5.26080e7i 0.862480 + 0.169146i
\(268\) −1.12010e8 1.39901e8i −0.355456 0.443964i
\(269\) −3.85128e8 −1.20635 −0.603173 0.797611i \(-0.706097\pi\)
−0.603173 + 0.797611i \(0.706097\pi\)
\(270\) 5.84830e7 + 9.71258e7i 0.180824 + 0.300304i
\(271\) 3.67394e8i 1.12135i 0.828037 + 0.560673i \(0.189457\pi\)
−0.828037 + 0.560673i \(0.810543\pi\)
\(272\) 4.40529e8 + 9.87575e7i 1.32734 + 0.297563i
\(273\) 1.41366e8 7.20828e8i 0.420509 2.14418i
\(274\) 5.64936e7 + 2.71387e7i 0.165910 + 0.0797006i
\(275\) 1.22294e8i 0.354600i
\(276\) −2.94637e8 + 1.53943e8i −0.843540 + 0.440737i
\(277\) 8.69908e6i 0.0245920i 0.999924 + 0.0122960i \(0.00391404\pi\)
−0.999924 + 0.0122960i \(0.996086\pi\)
\(278\) −6.57356e7 + 1.36840e8i −0.183503 + 0.381993i
\(279\) −5.92210e7 + 1.45177e8i −0.163253 + 0.400207i
\(280\) 4.95206e7 + 2.14101e8i 0.134813 + 0.582860i
\(281\) 4.68539e8i 1.25972i 0.776710 + 0.629859i \(0.216887\pi\)
−0.776710 + 0.629859i \(0.783113\pi\)
\(282\) 4.81534e8 + 3.59640e8i 1.27866 + 0.954984i
\(283\) 1.79280e8 0.470197 0.235099 0.971972i \(-0.424459\pi\)
0.235099 + 0.971972i \(0.424459\pi\)
\(284\) 2.85558e8 + 3.56662e8i 0.739742 + 0.923937i
\(285\) 1.02026e7 5.20233e7i 0.0261069 0.133119i
\(286\) −8.86704e7 + 1.84582e8i −0.224129 + 0.466561i
\(287\) −6.25139e8 −1.56095
\(288\) −1.99709e8 3.52786e8i −0.492634 0.870237i
\(289\) −3.48945e8 −0.850383
\(290\) −2.62899e7 + 5.47268e7i −0.0632988 + 0.131767i
\(291\) −6.18113e7 + 3.15177e8i −0.147042 + 0.749772i
\(292\) 1.77888e8 + 2.22182e8i 0.418125 + 0.522238i
\(293\) −7.75663e7 −0.180151 −0.0900755 0.995935i \(-0.528711\pi\)
−0.0900755 + 0.995935i \(0.528711\pi\)
\(294\) −6.67705e8 4.98684e8i −1.53239 1.14448i
\(295\) 1.41140e8i 0.320091i
\(296\) −9.22958e7 3.99037e8i −0.206853 0.894319i
\(297\) 1.52580e8 + 1.00178e8i 0.337947 + 0.221884i
\(298\) 1.02562e8 2.13500e8i 0.224507 0.467349i
\(299\) 5.63227e8i 1.21853i
\(300\) −3.63556e8 + 1.89952e8i −0.777403 + 0.406181i
\(301\) 7.66732e8i 1.62054i
\(302\) −3.08970e8 1.48424e8i −0.645493 0.310085i
\(303\) 1.02927e8 5.24828e8i 0.212560 1.08385i
\(304\) −4.14669e7 + 1.84972e8i −0.0846533 + 0.377614i
\(305\) 1.75023e8i 0.353220i
\(306\) 4.57532e8 + 5.05483e8i 0.912845 + 1.00851i
\(307\) −1.34816e8 −0.265924 −0.132962 0.991121i \(-0.542449\pi\)
−0.132962 + 0.991121i \(0.542449\pi\)
\(308\) 2.21120e8 + 2.76179e8i 0.431222 + 0.538596i
\(309\) 4.74066e7 + 9.29720e6i 0.0914080 + 0.0179266i
\(310\) 7.16352e7 + 3.44124e7i 0.136572 + 0.0656069i
\(311\) 5.73695e7 0.108148 0.0540742 0.998537i \(-0.482779\pi\)
0.0540742 + 0.998537i \(0.482779\pi\)
\(312\) 6.86455e8 2.31016e7i 1.27959 0.0430627i
\(313\) 3.22598e8 0.594643 0.297321 0.954777i \(-0.403907\pi\)
0.297321 + 0.954777i \(0.403907\pi\)
\(314\) −8.19780e8 3.93810e8i −1.49432 0.717848i
\(315\) −1.25349e8 + 3.07287e8i −0.225961 + 0.553934i
\(316\) 5.58610e8 4.47246e8i 0.995873 0.797336i
\(317\) 6.42560e8 1.13294 0.566469 0.824083i \(-0.308309\pi\)
0.566469 + 0.824083i \(0.308309\pi\)
\(318\) 2.42653e8 + 1.81228e8i 0.423146 + 0.316032i
\(319\) 9.77467e7i 0.168591i
\(320\) −1.84609e8 + 9.02257e7i −0.314940 + 0.153924i
\(321\) −8.52318e8 1.67153e8i −1.43825 0.282064i
\(322\) −8.77134e8 4.21362e8i −1.46410 0.703331i
\(323\) 3.18813e8i 0.526413i
\(324\) 6.08164e7 6.09192e8i 0.0993376 0.995054i
\(325\) 6.94972e8i 1.12299i
\(326\) 5.29700e8 1.10266e9i 0.846776 1.76270i
\(327\) 5.60729e8 + 1.09968e8i 0.886821 + 0.173920i
\(328\) −1.31722e8 5.69496e8i −0.206111 0.891112i
\(329\) 1.75929e9i 2.72366i
\(330\) 5.53611e7 7.41247e7i 0.0848019 0.113544i
\(331\) 1.11052e9 1.68317 0.841583 0.540127i \(-0.181624\pi\)
0.841583 + 0.540127i \(0.181624\pi\)
\(332\) −3.01092e8 + 2.41066e8i −0.451560 + 0.361537i
\(333\) 2.33624e8 5.72718e8i 0.346707 0.849935i
\(334\) −1.92494e8 + 4.00707e8i −0.282686 + 0.588457i
\(335\) −1.37184e8 −0.199364
\(336\) 4.77574e8 1.08632e9i 0.686836 1.56233i
\(337\) −3.54194e8 −0.504123 −0.252062 0.967711i \(-0.581109\pi\)
−0.252062 + 0.967711i \(0.581109\pi\)
\(338\) −1.96494e8 + 4.09035e8i −0.276784 + 0.576171i
\(339\) 6.48028e8 + 1.27089e8i 0.903431 + 0.177177i
\(340\) 2.69768e8 2.15987e8i 0.372232 0.298024i
\(341\) 1.27947e8 0.174738
\(342\) −2.12245e8 + 1.92111e8i −0.286910 + 0.259694i
\(343\) 1.16400e9i 1.55749i
\(344\) −6.98486e8 + 1.61557e8i −0.925131 + 0.213979i
\(345\) −4.89715e7 + 2.49707e8i −0.0642062 + 0.327389i
\(346\) −6.32453e8 + 1.31656e9i −0.820846 + 1.70873i
\(347\) 4.20183e8i 0.539865i −0.962879 0.269932i \(-0.912999\pi\)
0.962879 0.269932i \(-0.0870014\pi\)
\(348\) 2.90582e8 1.51825e8i 0.369608 0.193115i
\(349\) 2.71958e7i 0.0342462i 0.999853 + 0.0171231i \(0.00545072\pi\)
−0.999853 + 0.0171231i \(0.994549\pi\)
\(350\) −1.08231e9 5.19923e8i −1.34931 0.648187i
\(351\) 8.67082e8 + 5.69294e8i 1.07025 + 0.702687i
\(352\) −2.05005e8 + 2.59632e8i −0.250533 + 0.317292i
\(353\) 8.90412e8i 1.07741i −0.842496 0.538703i \(-0.818914\pi\)
0.842496 0.538703i \(-0.181086\pi\)
\(354\) −4.56067e8 + 6.10643e8i −0.546408 + 0.731603i
\(355\) 3.49736e8 0.414897
\(356\) −5.84065e8 + 4.67627e8i −0.686099 + 0.549318i
\(357\) −3.84086e8 + 1.95846e9i −0.446776 + 2.27812i
\(358\) −2.81098e7 1.35035e7i −0.0323793 0.0155545i
\(359\) −1.13487e9 −1.29454 −0.647269 0.762261i \(-0.724089\pi\)
−0.647269 + 0.762261i \(0.724089\pi\)
\(360\) −3.06348e8 4.94438e7i −0.346064 0.0558538i
\(361\) −7.60007e8 −0.850241
\(362\) 1.13434e9 + 5.44919e8i 1.25679 + 0.603743i
\(363\) −1.46720e8 + 7.48126e8i −0.160996 + 0.820921i
\(364\) 1.25659e9 + 1.56948e9i 1.36564 + 1.70569i
\(365\) 2.17867e8 0.234513
\(366\) −5.65553e8 + 7.57237e8i −0.602961 + 0.807324i
\(367\) 1.04021e9i 1.09847i −0.835668 0.549235i \(-0.814919\pi\)
0.835668 0.549235i \(-0.185081\pi\)
\(368\) 1.99037e8 8.87846e8i 0.208193 0.928689i
\(369\) 3.33422e8 8.17368e8i 0.345463 0.846886i
\(370\) −2.82597e8 1.35755e8i −0.290043 0.139332i
\(371\) 8.86535e8i 0.901337i
\(372\) −1.98733e8 3.80361e8i −0.200156 0.383085i
\(373\) 3.18791e7i 0.0318072i 0.999874 + 0.0159036i \(0.00506249\pi\)
−0.999874 + 0.0159036i \(0.994938\pi\)
\(374\) 2.40914e8 5.01503e8i 0.238129 0.495704i
\(375\) −1.29318e8 + 6.59397e8i −0.126634 + 0.645710i
\(376\) −1.60270e9 + 3.70698e8i −1.55487 + 0.359636i
\(377\) 5.55477e8i 0.533914i
\(378\) 1.53526e9 9.24438e8i 1.46205 0.880353i
\(379\) 5.34127e7 0.0503973 0.0251987 0.999682i \(-0.491978\pi\)
0.0251987 + 0.999682i \(0.491978\pi\)
\(380\) 9.06899e7 + 1.13272e8i 0.0847845 + 0.105896i
\(381\) −4.93213e8 9.67270e7i −0.456874 0.0896005i
\(382\) 5.38202e8 1.12036e9i 0.493997 1.02834i
\(383\) 1.30505e9 1.18695 0.593473 0.804854i \(-0.297756\pi\)
0.593473 + 0.804854i \(0.297756\pi\)
\(384\) 1.09026e9 + 2.06167e8i 0.982586 + 0.185806i
\(385\) 2.70816e8 0.241859
\(386\) −2.74488e8 + 5.71392e8i −0.242922 + 0.505683i
\(387\) −1.00250e9 4.08942e8i −0.879217 0.358652i
\(388\) −5.49434e8 6.86243e8i −0.477534 0.596440i
\(389\) 7.16057e8 0.616771 0.308385 0.951262i \(-0.400211\pi\)
0.308385 + 0.951262i \(0.400211\pi\)
\(390\) 3.14607e8 4.21237e8i 0.268560 0.359584i
\(391\) 1.53027e9i 1.29464i
\(392\) 2.22234e9 5.14018e8i 1.86341 0.431000i
\(393\) −1.43779e9 2.81974e8i −1.19487 0.234334i
\(394\) −4.63017e8 + 9.63847e8i −0.381382 + 0.793910i
\(395\) 5.47762e8i 0.447200i
\(396\) −4.79040e8 + 1.41812e8i −0.387649 + 0.114757i
\(397\) 4.15822e7i 0.0333535i 0.999861 + 0.0166767i \(0.00530862\pi\)
−0.999861 + 0.0166767i \(0.994691\pi\)
\(398\) 9.18246e8 + 4.41111e8i 0.730076 + 0.350717i
\(399\) −8.22331e8 1.61272e8i −0.648099 0.127103i
\(400\) 2.45594e8 1.09552e9i 0.191870 0.855877i
\(401\) 1.22525e9i 0.948895i −0.880284 0.474447i \(-0.842648\pi\)
0.880284 0.474447i \(-0.157352\pi\)
\(402\) 5.93526e8 + 4.43283e8i 0.455668 + 0.340322i
\(403\) 7.27097e8 0.553382
\(404\) 9.14908e8 + 1.14272e9i 0.690308 + 0.862194i
\(405\) −3.34922e8 3.27787e8i −0.250525 0.245188i
\(406\) 8.65064e8 + 4.15563e8i 0.641515 + 0.308174i
\(407\) −5.04743e8 −0.371099
\(408\) −1.86507e9 + 6.27663e7i −1.35952 + 0.0457526i
\(409\) 1.98246e9 1.43276 0.716381 0.697710i \(-0.245797\pi\)
0.716381 + 0.697710i \(0.245797\pi\)
\(410\) −4.03315e8 1.93746e8i −0.289002 0.138832i
\(411\) −2.54221e8 4.98569e7i −0.180620 0.0354225i
\(412\) −1.03220e8 + 8.26418e7i −0.0727146 + 0.0582183i
\(413\) −2.23099e9 −1.55838
\(414\) 1.01876e9 9.22115e8i 0.705616 0.638681i
\(415\) 2.95245e8i 0.202775i
\(416\) −1.16500e9 + 1.47544e9i −0.793416 + 1.00484i
\(417\) 1.20764e8 6.15778e8i 0.0815571 0.415861i
\(418\) 2.10574e8 + 1.01156e8i 0.141022 + 0.0677449i
\(419\) 2.00028e9i 1.32844i −0.747538 0.664219i \(-0.768764\pi\)
0.747538 0.664219i \(-0.231236\pi\)
\(420\) −4.20644e8 8.05084e8i −0.277040 0.530236i
\(421\) 2.32447e9i 1.51823i −0.650959 0.759113i \(-0.725633\pi\)
0.650959 0.759113i \(-0.274367\pi\)
\(422\) −4.63974e8 + 9.65839e8i −0.300538 + 0.625620i
\(423\) −2.30027e9 9.38330e8i −1.47770 0.602788i
\(424\) −8.07626e8 + 1.86801e8i −0.514552 + 0.119014i
\(425\) 1.88821e9i 1.19314i
\(426\) −1.51313e9 1.13010e9i −0.948295 0.708247i
\(427\) −2.76658e9 −1.71967
\(428\) 1.85577e9 1.48581e9i 1.14412 0.916029i
\(429\) 1.62898e8 8.30620e8i 0.0996128 0.507927i
\(430\) −2.37630e8 + 4.94666e8i −0.144132 + 0.300035i
\(431\) 7.11491e8 0.428055 0.214027 0.976828i \(-0.431342\pi\)
0.214027 + 0.976828i \(0.431342\pi\)
\(432\) 1.16565e9 + 1.20382e9i 0.695624 + 0.718406i
\(433\) 9.95747e8 0.589442 0.294721 0.955583i \(-0.404773\pi\)
0.294721 + 0.955583i \(0.404773\pi\)
\(434\) 5.43956e8 1.13233e9i 0.319411 0.664907i
\(435\) 4.82976e7 2.46270e8i 0.0281328 0.143450i
\(436\) −1.22089e9 + 9.77493e8i −0.705461 + 0.564821i
\(437\) −6.42538e8 −0.368310
\(438\) −9.42604e8 7.03996e8i −0.536006 0.400323i
\(439\) 5.41401e8i 0.305417i −0.988271 0.152708i \(-0.951200\pi\)
0.988271 0.152708i \(-0.0487995\pi\)
\(440\) 5.70633e7 + 2.46711e8i 0.0319354 + 0.138072i
\(441\) 3.18960e9 + 1.30111e9i 1.77093 + 0.722401i
\(442\) 1.36907e9 2.84995e9i 0.754133 1.56985i
\(443\) 2.02764e9i 1.10810i 0.832484 + 0.554050i \(0.186918\pi\)
−0.832484 + 0.554050i \(0.813082\pi\)
\(444\) 7.83991e8 + 1.50050e9i 0.425080 + 0.813574i
\(445\) 5.72723e8i 0.308095i
\(446\) 1.47536e8 + 7.08738e7i 0.0787454 + 0.0378281i
\(447\) −1.88419e8 + 9.60750e8i −0.0997809 + 0.508785i
\(448\) 1.42619e9 + 2.91811e9i 0.749386 + 1.53331i
\(449\) 2.36412e9i 1.23256i −0.787528 0.616279i \(-0.788639\pi\)
0.787528 0.616279i \(-0.211361\pi\)
\(450\) 1.25705e9 1.13781e9i 0.650294 0.588606i
\(451\) −7.20356e8 −0.369768
\(452\) −1.41097e9 + 1.12968e9i −0.718675 + 0.575401i
\(453\) 1.39036e9 + 2.72673e8i 0.702724 + 0.137816i
\(454\) 3.57712e8 + 1.71840e8i 0.179407 + 0.0861842i
\(455\) 1.53900e9 0.765946
\(456\) −2.63547e7 7.83117e8i −0.0130161 0.386767i
\(457\) 5.36394e8 0.262892 0.131446 0.991323i \(-0.458038\pi\)
0.131446 + 0.991323i \(0.458038\pi\)
\(458\) 1.03774e8 + 4.98515e7i 0.0504731 + 0.0242465i
\(459\) −2.35583e9 1.54675e9i −1.13710 0.746579i
\(460\) −4.35302e8 5.43693e8i −0.208516 0.260436i
\(461\) 3.68025e9 1.74954 0.874770 0.484539i \(-0.161013\pi\)
0.874770 + 0.484539i \(0.161013\pi\)
\(462\) −1.17169e9 8.75090e8i −0.552796 0.412863i
\(463\) 1.19699e9i 0.560478i 0.959930 + 0.280239i \(0.0904138\pi\)
−0.959930 + 0.280239i \(0.909586\pi\)
\(464\) −1.96298e8 + 8.75628e8i −0.0912226 + 0.406918i
\(465\) −3.22358e8 6.32197e7i −0.148680 0.0291586i
\(466\) 1.42093e9 + 6.82591e8i 0.650460 + 0.312471i
\(467\) 1.60918e9i 0.731130i 0.930786 + 0.365565i \(0.119124\pi\)
−0.930786 + 0.365565i \(0.880876\pi\)
\(468\) −2.72230e9 + 8.05894e8i −1.22765 + 0.363427i
\(469\) 2.16846e9i 0.970613i
\(470\) −5.45249e8 + 1.13503e9i −0.242244 + 0.504271i
\(471\) 3.68901e9 + 7.23475e8i 1.62681 + 0.319044i
\(472\) −4.70090e8 2.03242e9i −0.205771 0.889642i
\(473\) 8.83516e8i 0.383884i
\(474\) −1.76999e9 + 2.36989e9i −0.763389 + 1.02213i
\(475\) −7.92834e8 −0.339434
\(476\) −3.41410e9 4.26421e9i −1.45095 1.81223i
\(477\) −1.15914e9 4.72839e8i −0.489016 0.199480i
\(478\) −3.00000e8 + 6.24500e8i −0.125639 + 0.261538i
\(479\) −1.54958e9 −0.644227 −0.322114 0.946701i \(-0.604393\pi\)
−0.322114 + 0.946701i \(0.604393\pi\)
\(480\) 6.44791e8 5.52842e8i 0.266118 0.228169i
\(481\) −2.86836e9 −1.17524
\(482\) 6.83672e8 1.42318e9i 0.278088 0.578887i
\(483\) 3.94710e9 + 7.74091e8i 1.59391 + 0.312591i
\(484\) −1.30417e9 1.62891e9i −0.522849 0.653039i
\(485\) −6.72917e8 −0.267834
\(486\) 3.89858e8 + 2.50041e9i 0.154056 + 0.988062i
\(487\) 2.60156e9i 1.02066i 0.859978 + 0.510331i \(0.170477\pi\)
−0.859978 + 0.510331i \(0.829523\pi\)
\(488\) −5.82943e8 2.52033e9i −0.227068 0.981720i
\(489\) −9.73121e8 + 4.96196e9i −0.376345 + 1.91899i
\(490\) 7.56054e8 1.57385e9i 0.290313 0.604335i
\(491\) 4.79977e9i 1.82993i 0.403531 + 0.914966i \(0.367783\pi\)
−0.403531 + 0.914966i \(0.632217\pi\)
\(492\) 1.11889e9 + 2.14148e9i 0.423555 + 0.810656i
\(493\) 1.50921e9i 0.567264i
\(494\) 1.19665e9 + 5.74854e8i 0.446605 + 0.214542i
\(495\) −1.44442e8 + 3.54091e8i −0.0535271 + 0.131219i
\(496\) 1.14616e9 + 2.56946e8i 0.421755 + 0.0945489i
\(497\) 5.52826e9i 2.01995i
\(498\) 9.54026e8 1.27738e9i 0.346145 0.463464i
\(499\) 2.27878e8 0.0821015 0.0410508 0.999157i \(-0.486929\pi\)
0.0410508 + 0.999157i \(0.486929\pi\)
\(500\) −1.14950e9 1.43572e9i −0.411256 0.513659i
\(501\) 3.53633e8 1.80318e9i 0.125638 0.640631i
\(502\) −3.35937e8 1.61379e8i −0.118521 0.0569356i
\(503\) 1.71998e9 0.602609 0.301304 0.953528i \(-0.402578\pi\)
0.301304 + 0.953528i \(0.402578\pi\)
\(504\) −7.81556e8 + 4.84243e9i −0.271928 + 1.68483i
\(505\) 1.12053e9 0.387172
\(506\) −1.01073e9 4.85541e8i −0.346825 0.166609i
\(507\) 3.60982e8 1.84066e9i 0.123015 0.627256i
\(508\) 1.07388e9 8.59795e8i 0.363441 0.290986i
\(509\) −2.37984e9 −0.799900 −0.399950 0.916537i \(-0.630973\pi\)
−0.399950 + 0.916537i \(0.630973\pi\)
\(510\) −8.54775e8 + 1.14449e9i −0.285336 + 0.382045i
\(511\) 3.44382e9i 1.14174i
\(512\) −2.35786e9 + 1.91412e9i −0.776378 + 0.630267i
\(513\) 6.49459e8 9.89180e8i 0.212393 0.323493i
\(514\) −3.28294e9 1.57707e9i −1.06633 0.512248i
\(515\) 1.01215e8i 0.0326528i
\(516\) 2.62652e9 1.37232e9i 0.841603 0.439725i
\(517\) 2.02726e9i 0.645196i
\(518\) −2.14588e9 + 4.46700e9i −0.678345 + 1.41209i
\(519\) 1.16189e9 5.92450e9i 0.364820 1.86023i
\(520\) 3.24280e8 + 1.40201e9i 0.101137 + 0.437261i
\(521\) 1.09986e9i 0.340725i 0.985381 + 0.170362i \(0.0544938\pi\)
−0.985381 + 0.170362i \(0.945506\pi\)
\(522\) −1.00474e9 + 9.09426e8i −0.309175 + 0.279847i
\(523\) 1.33421e9 0.407821 0.203910 0.978990i \(-0.434635\pi\)
0.203910 + 0.978990i \(0.434635\pi\)
\(524\) 3.13054e9 2.50644e9i 0.950516 0.761022i
\(525\) 4.87037e9 + 9.55159e8i 1.46894 + 0.288083i
\(526\) 1.79076e9 3.72776e9i 0.536521 1.11686i
\(527\) −1.97550e9 −0.587948
\(528\) 5.50315e8 1.25179e9i 0.162702 0.370093i
\(529\) −3.20708e8 −0.0941922
\(530\) −2.74760e8 + 5.71958e8i −0.0801655 + 0.166878i
\(531\) 1.18992e9 2.91702e9i 0.344894 0.845490i
\(532\) 1.79048e9 1.43353e9i 0.515560 0.412778i
\(533\) −4.09365e9 −1.17102
\(534\) 1.85065e9 2.47789e9i 0.525931 0.704186i
\(535\) 1.81974e9i 0.513772i
\(536\) −1.97545e9 + 4.56913e8i −0.554100 + 0.128161i
\(537\) 1.26494e8 + 2.48076e7i 0.0352502 + 0.00691312i
\(538\) −1.88673e9 + 3.92755e9i −0.522363 + 1.08739i
\(539\) 2.81104e9i 0.773225i
\(540\) 1.27700e9 1.20595e8i 0.348990 0.0329571i
\(541\) 2.75610e9i 0.748351i 0.927358 + 0.374175i \(0.122074\pi\)
−0.927358 + 0.374175i \(0.877926\pi\)
\(542\) 3.74670e9 + 1.79986e9i 1.01077 + 0.485557i
\(543\) −5.10453e9 1.00108e9i −1.36822 0.268330i
\(544\) 3.16527e9 4.00872e9i 0.842976 1.06760i
\(545\) 1.19718e9i 0.316790i
\(546\) −6.65848e9 4.97298e9i −1.75066 1.30750i
\(547\) 1.81654e9 0.474559 0.237280 0.971441i \(-0.423744\pi\)
0.237280 + 0.971441i \(0.423744\pi\)
\(548\) 5.53522e8 4.43173e8i 0.143682 0.115038i
\(549\) 1.47557e9 3.61730e9i 0.380590 0.932998i
\(550\) −1.24715e9 5.99114e8i −0.319633 0.153547i
\(551\) 6.33696e8 0.161380
\(552\) 1.26500e8 + 3.75888e9i 0.0320113 + 0.951201i
\(553\) −8.65845e9 −2.17722
\(554\) 8.87136e7 + 4.26166e7i 0.0221669 + 0.0106487i
\(555\) 1.27169e9 + 2.49398e8i 0.315758 + 0.0619253i
\(556\) 1.07346e9 + 1.34075e9i 0.264864 + 0.330815i
\(557\) −2.69747e9 −0.661400 −0.330700 0.943736i \(-0.607285\pi\)
−0.330700 + 0.943736i \(0.607285\pi\)
\(558\) 1.19040e9 + 1.31516e9i 0.290051 + 0.320449i
\(559\) 5.02086e9i 1.21573i
\(560\) 2.42601e9 + 5.43861e8i 0.583759 + 0.130867i
\(561\) −4.42588e8 + 2.25676e9i −0.105835 + 0.539655i
\(562\) 4.77817e9 + 2.29536e9i 1.13549 + 0.545474i
\(563\) 2.68748e9i 0.634695i −0.948309 0.317348i \(-0.897208\pi\)
0.948309 0.317348i \(-0.102792\pi\)
\(564\) 6.02665e9 3.14883e9i 1.41449 0.739048i
\(565\) 1.38357e9i 0.322724i
\(566\) 8.78291e8 1.82831e9i 0.203601 0.423830i
\(567\) −5.18132e9 + 5.29410e9i −1.19371 + 1.21969i
\(568\) 5.03619e9 1.16485e9i 1.15314 0.266718i
\(569\) 1.62319e9i 0.369383i −0.982797 0.184692i \(-0.940871\pi\)
0.982797 0.184692i \(-0.0591286\pi\)
\(570\) −4.80554e8 3.58908e8i −0.108688 0.0811748i
\(571\) 2.25862e9 0.507712 0.253856 0.967242i \(-0.418301\pi\)
0.253856 + 0.967242i \(0.418301\pi\)
\(572\) 1.44798e9 + 1.80853e9i 0.323502 + 0.404054i
\(573\) −9.88741e8 + 5.04161e9i −0.219554 + 1.11951i
\(574\) −3.06254e9 + 6.37519e9i −0.675912 + 1.40702i
\(575\) 3.80552e9 0.834790
\(576\) −4.57609e9 + 3.08353e8i −0.997737 + 0.0672309i
\(577\) −2.78955e9 −0.604530 −0.302265 0.953224i \(-0.597743\pi\)
−0.302265 + 0.953224i \(0.597743\pi\)
\(578\) −1.70947e9 + 3.55855e9i −0.368227 + 0.766525i
\(579\) 5.04266e8 2.57126e9i 0.107965 0.550518i
\(580\) 4.29312e8 + 5.36211e8i 0.0913640 + 0.114114i
\(581\) 4.66692e9 0.987220
\(582\) 2.91138e9 + 2.17440e9i 0.612164 + 0.457203i
\(583\) 1.02157e9i 0.213514i
\(584\) 3.13729e9 7.25643e8i 0.651793 0.150757i
\(585\) −8.20835e8 + 2.01224e9i −0.169516 + 0.415560i
\(586\) −3.79996e8 + 7.91024e8i −0.0780076 + 0.162386i
\(587\) 1.54318e9i 0.314907i −0.987526 0.157453i \(-0.949672\pi\)
0.987526 0.157453i \(-0.0503284\pi\)
\(588\) −8.35668e9 + 4.36624e9i −1.69517 + 0.885700i
\(589\) 8.29483e8i 0.167265i
\(590\) −1.43935e9 6.91442e8i −0.288526 0.138603i
\(591\) 8.50617e8 4.33731e9i 0.169503 0.864300i
\(592\) −4.52155e9 1.01364e9i −0.895698 0.200797i
\(593\) 2.51226e9i 0.494735i −0.968922 0.247368i \(-0.920434\pi\)
0.968922 0.247368i \(-0.0795655\pi\)
\(594\) 1.76911e9 1.06524e9i 0.346339 0.208543i
\(595\) −4.18140e9 −0.813790
\(596\) −1.67483e9 2.09186e9i −0.324048 0.404736i
\(597\) −4.13211e9 8.10373e8i −0.794806 0.155874i
\(598\) −5.74382e9 2.75924e9i −1.09836 0.527637i
\(599\) −6.19749e9 −1.17821 −0.589104 0.808058i \(-0.700519\pi\)
−0.589104 + 0.808058i \(0.700519\pi\)
\(600\) 1.56089e8 + 4.63813e9i 0.0295015 + 0.876624i
\(601\) 7.79137e9 1.46404 0.732020 0.681283i \(-0.238578\pi\)
0.732020 + 0.681283i \(0.238578\pi\)
\(602\) 7.81916e9 + 3.75620e9i 1.46074 + 0.701716i
\(603\) −2.83526e9 1.15656e9i −0.526601 0.214812i
\(604\) −3.02727e9 + 2.42376e9i −0.559014 + 0.447569i
\(605\) −1.59728e9 −0.293249
\(606\) −4.84798e9 3.62078e9i −0.884925 0.660918i
\(607\) 1.08410e9i 0.196748i −0.995150 0.0983740i \(-0.968636\pi\)
0.995150 0.0983740i \(-0.0313641\pi\)
\(608\) 1.68320e9 + 1.32905e9i 0.303721 + 0.239817i
\(609\) −3.89279e9 7.63438e8i −0.698393 0.136966i
\(610\) −1.78489e9 8.57433e8i −0.318388 0.152949i
\(611\) 1.15205e10i 2.04328i
\(612\) 7.39637e9 2.18958e9i 1.30433 0.386128i
\(613\) 3.88620e9i 0.681418i 0.940169 + 0.340709i \(0.110667\pi\)
−0.940169 + 0.340709i \(0.889333\pi\)
\(614\) −6.60461e8 + 1.37486e9i −0.115148 + 0.239700i
\(615\) 1.81492e9 + 3.55935e8i 0.314626 + 0.0617032i
\(616\) 3.89975e9 9.01998e8i 0.672209 0.155479i
\(617\) 2.18111e9i 0.373834i −0.982376 0.186917i \(-0.940150\pi\)
0.982376 0.186917i \(-0.0598496\pi\)
\(618\) 3.27057e8 4.37908e8i 0.0557396 0.0746316i
\(619\) 1.16433e10 1.97315 0.986574 0.163316i \(-0.0522191\pi\)
0.986574 + 0.163316i \(0.0522191\pi\)
\(620\) 7.01879e8 5.61953e8i 0.118275 0.0946954i
\(621\) −3.11734e9 + 4.74796e9i −0.522352 + 0.795586i
\(622\) 2.81052e8 5.85057e8i 0.0468296 0.0974836i
\(623\) 9.05301e9 1.49998
\(624\) 3.12734e9 7.11367e9i 0.515262 1.17205i
\(625\) 3.94568e9 0.646459
\(626\) 1.58040e9 3.28987e9i 0.257488 0.536004i
\(627\) −9.47583e8 1.85836e8i −0.153526 0.0301089i
\(628\) −8.03217e9 + 6.43089e9i −1.29412 + 1.03612i
\(629\) 7.79323e9 1.24865
\(630\) 2.51965e9 + 2.78371e9i 0.401465 + 0.443539i
\(631\) 1.06242e10i 1.68342i −0.539927 0.841712i \(-0.681548\pi\)
0.539927 0.841712i \(-0.318452\pi\)
\(632\) −1.82441e9 7.88777e9i −0.287484 1.24292i
\(633\) 8.52374e8 4.34627e9i 0.133573 0.681089i
\(634\) 3.14789e9 6.55285e9i 0.490577 1.02122i
\(635\) 1.05303e9i 0.163205i
\(636\) 3.03692e9 1.58675e9i 0.468095 0.244572i
\(637\) 1.59746e10i 2.44874i
\(638\) 9.96825e8 + 4.78859e8i 0.151966 + 0.0730021i
\(639\) 7.22819e9 + 2.94853e9i 1.09591 + 0.447047i
\(640\) 1.57286e7 + 2.32467e9i 0.00237171 + 0.350534i
\(641\) 6.89527e9i 1.03407i 0.855965 + 0.517033i \(0.172964\pi\)
−0.855965 + 0.517033i \(0.827036\pi\)
\(642\) −5.88013e9 + 7.87309e9i −0.877029 + 1.17428i
\(643\) −9.21146e9 −1.36644 −0.683219 0.730213i \(-0.739421\pi\)
−0.683219 + 0.730213i \(0.739421\pi\)
\(644\) −8.59413e9 + 6.88081e9i −1.26795 + 1.01517i
\(645\) 4.36554e8 2.22600e9i 0.0640588 0.326637i
\(646\) −3.25126e9 1.56186e9i −0.474502 0.227943i
\(647\) −1.53229e8 −0.0222421 −0.0111210 0.999938i \(-0.503540\pi\)
−0.0111210 + 0.999938i \(0.503540\pi\)
\(648\) −5.91462e9 3.60463e9i −0.853915 0.520413i
\(649\) −2.57080e9 −0.369158
\(650\) −7.08735e9 3.40465e9i −1.01225 0.486269i
\(651\) −9.99311e8 + 5.09551e9i −0.141960 + 0.723859i
\(652\) −8.64996e9 1.08038e10i −1.22222 1.52655i
\(653\) 5.61194e9 0.788710 0.394355 0.918958i \(-0.370968\pi\)
0.394355 + 0.918958i \(0.370968\pi\)
\(654\) 3.86846e9 5.17960e9i 0.540774 0.724060i
\(655\) 3.06975e9i 0.426833i
\(656\) −6.45305e9 1.44664e9i −0.892486 0.200077i
\(657\) 4.50279e9 + 1.83678e9i 0.619445 + 0.252685i
\(658\) 1.79413e10 + 8.61874e9i 2.45507 + 1.17938i
\(659\) 1.89758e9i 0.258287i 0.991626 + 0.129143i \(0.0412228\pi\)
−0.991626 + 0.129143i \(0.958777\pi\)
\(660\) −4.84714e8 9.27710e8i −0.0656269 0.125605i
\(661\) 2.56052e9i 0.344844i −0.985023 0.172422i \(-0.944841\pi\)
0.985023 0.172422i \(-0.0551592\pi\)
\(662\) 5.44040e9 1.13251e10i 0.728832 1.51719i
\(663\) −2.51514e9 + 1.28248e10i −0.335170 + 1.70904i
\(664\) 9.83361e8 + 4.25152e9i 0.130354 + 0.563581i
\(665\) 1.75571e9i 0.231514i
\(666\) −4.69608e9 5.18824e9i −0.615993 0.680550i
\(667\) −3.04168e9 −0.396892
\(668\) 3.14341e9 + 3.92612e9i 0.408022 + 0.509619i
\(669\) −6.63911e8 1.30204e8i −0.0857271 0.0168125i
\(670\) −6.72060e8 + 1.39901e9i −0.0863270 + 0.179704i
\(671\) −3.18797e9 −0.407366
\(672\) −8.73875e9 1.01922e10i −1.11085 1.29561i
\(673\) 9.40490e9 1.18933 0.594664 0.803974i \(-0.297285\pi\)
0.594664 + 0.803974i \(0.297285\pi\)
\(674\) −1.73519e9 + 3.61209e9i −0.218292 + 0.454411i
\(675\) −3.84651e9 + 5.85856e9i −0.481398 + 0.733209i
\(676\) 3.20873e9 + 4.00770e9i 0.399503 + 0.498979i
\(677\) −1.31467e10 −1.62838 −0.814188 0.580601i \(-0.802818\pi\)
−0.814188 + 0.580601i \(0.802818\pi\)
\(678\) 4.47073e9 5.98601e9i 0.550903 0.737622i
\(679\) 1.06368e10i 1.30396i
\(680\) −8.81058e8 3.80922e9i −0.107454 0.464574i
\(681\) −1.60971e9 3.15689e8i −0.195313 0.0383041i
\(682\) 6.26808e8 1.30480e9i 0.0756640 0.157507i
\(683\) 1.03400e9i 0.124179i −0.998071 0.0620894i \(-0.980224\pi\)
0.998071 0.0620894i \(-0.0197764\pi\)
\(684\) 9.19375e8 + 3.10563e9i 0.109849 + 0.371068i
\(685\) 5.42773e8i 0.0645211i
\(686\) −1.18705e10 5.70242e9i −1.40390 0.674411i
\(687\) −4.66984e8 9.15831e7i −0.0549482 0.0107762i
\(688\) −1.77430e9 + 7.91465e9i −0.207715 + 0.926557i
\(689\) 5.80538e9i 0.676181i
\(690\) 2.30661e9 + 1.72272e9i 0.267302 + 0.199638i
\(691\) −5.74897e9 −0.662853 −0.331426 0.943481i \(-0.607530\pi\)
−0.331426 + 0.943481i \(0.607530\pi\)
\(692\) 1.03279e10 + 1.28996e10i 1.18479 + 1.47980i
\(693\) 5.59711e9 + 2.28318e9i 0.638848 + 0.260600i
\(694\) −4.28504e9 2.05847e9i −0.486628 0.233768i
\(695\) 1.31471e9 0.148554
\(696\) −1.24759e8 3.70716e9i −0.0140262 0.416782i
\(697\) 1.11223e10 1.24417
\(698\) 2.77343e8 + 1.33232e8i 0.0308691 + 0.0148290i
\(699\) −6.39417e9 1.25400e9i −0.708132 0.138876i
\(700\) −1.06044e10 + 8.49030e9i −1.16854 + 0.935578i
\(701\) 1.30713e10 1.43319 0.716596 0.697488i \(-0.245699\pi\)
0.716596 + 0.697488i \(0.245699\pi\)
\(702\) 1.00535e10 6.05358e9i 1.09683 0.660439i
\(703\) 3.27227e9i 0.355226i
\(704\) 1.64342e9 + 3.36258e9i 0.177519 + 0.363219i
\(705\) 1.00169e9 5.10762e9i 0.107664 0.548980i
\(706\) −9.08045e9 4.36211e9i −0.971161 0.466531i
\(707\) 1.77122e10i 1.88497i
\(708\) 3.99310e9 + 7.64251e9i 0.422857 + 0.809319i
\(709\) 2.53582e9i 0.267213i 0.991034 + 0.133606i \(0.0426558\pi\)
−0.991034 + 0.133606i \(0.957344\pi\)
\(710\) 1.71335e9 3.56662e9i 0.179656 0.373983i
\(711\) 4.61804e9 1.13209e10i 0.481853 1.18124i
\(712\) 1.90755e9 + 8.24722e9i 0.198060 + 0.856303i
\(713\) 3.98144e9i 0.411364i
\(714\) 1.80908e10 + 1.35114e10i 1.86001 + 1.38917i
\(715\) 1.77341e9 0.181442
\(716\) −2.75419e8 + 2.20512e8i −0.0280413 + 0.0224510i
\(717\) 5.51135e8 2.81025e9i 0.0558394 0.284726i
\(718\) −5.55970e9 + 1.15734e10i −0.560552 + 1.16688i
\(719\) −9.86480e9 −0.989777 −0.494889 0.868956i \(-0.664791\pi\)
−0.494889 + 0.868956i \(0.664791\pi\)
\(720\) −2.00502e9 + 2.88193e9i −0.200196 + 0.287753i
\(721\) 1.59990e9 0.158972
\(722\) −3.72326e9 + 7.75058e9i −0.368165 + 0.766397i
\(723\) −1.25598e9 + 6.40429e9i −0.123595 + 0.630213i
\(724\) 1.11142e10 8.89849e9i 1.08841 0.871428i
\(725\) −3.75315e9 −0.365775
\(726\) 6.91064e9 + 5.16130e9i 0.670255 + 0.500589i
\(727\) 6.26064e9i 0.604294i −0.953261 0.302147i \(-0.902297\pi\)
0.953261 0.302147i \(-0.0977033\pi\)
\(728\) 2.21616e10 5.12589e9i 2.12883 0.492390i
\(729\) −4.15853e9 9.59821e9i −0.397551 0.917580i
\(730\) 1.06733e9 2.22182e9i 0.101547 0.211387i
\(731\) 1.36415e10i 1.29167i
\(732\) 4.95170e9 + 9.47722e9i 0.466623 + 0.893084i
\(733\) 1.23202e10i 1.15546i 0.816228 + 0.577730i \(0.196061\pi\)
−0.816228 + 0.577730i \(0.803939\pi\)
\(734\) −1.06081e10 5.09595e9i −0.990147 0.475651i
\(735\) −1.38896e9 + 7.08234e9i −0.129028 + 0.657917i
\(736\) −8.07921e9 6.37933e9i −0.746959 0.589797i
\(737\) 2.49874e9i 0.229925i
\(738\) −6.70212e9 7.40452e9i −0.613783 0.678109i
\(739\) −4.48620e9 −0.408906 −0.204453 0.978876i \(-0.565542\pi\)
−0.204453 + 0.978876i \(0.565542\pi\)
\(740\) −2.76887e9 + 2.21687e9i −0.251184 + 0.201108i
\(741\) −5.38494e9 1.05607e9i −0.486202 0.0953521i
\(742\) 9.04092e9 + 4.34312e9i 0.812454 + 0.390290i
\(743\) −5.92519e9 −0.529958 −0.264979 0.964254i \(-0.585365\pi\)
−0.264979 + 0.964254i \(0.585365\pi\)
\(744\) −4.85252e9 + 1.63305e8i −0.431979 + 0.0145376i
\(745\) −2.05124e9 −0.181748
\(746\) 3.25104e8 + 1.56175e8i 0.0286706 + 0.0137729i
\(747\) −2.48913e9 + 6.10199e9i −0.218487 + 0.535611i
\(748\) −3.93411e9 4.91370e9i −0.343709 0.429293i
\(749\) −2.87645e10 −2.50133
\(750\) 6.09103e9 + 4.54917e9i 0.527201 + 0.393747i
\(751\) 8.98243e9i 0.773845i 0.922112 + 0.386923i \(0.126462\pi\)
−0.922112 + 0.386923i \(0.873538\pi\)
\(752\) −4.07120e9 + 1.81604e10i −0.349108 + 1.55727i
\(753\) 1.51172e9 + 2.96472e8i 0.129029 + 0.0253047i
\(754\) 5.66477e9 + 2.72127e9i 0.481263 + 0.231191i
\(755\) 2.96849e9i 0.251027i
\(756\) −1.90623e9 2.01855e10i −0.160454 1.69908i
\(757\) 9.92682e9i 0.831715i −0.909430 0.415857i \(-0.863482\pi\)
0.909430 0.415857i \(-0.136518\pi\)
\(758\) 2.61668e8 5.44705e8i 0.0218227 0.0454275i
\(759\) 4.54830e9 + 8.91996e8i 0.377575 + 0.0740485i
\(760\) 1.59944e9 3.69944e8i 0.132166 0.0305695i
\(761\) 1.63216e9i 0.134250i −0.997745 0.0671252i \(-0.978617\pi\)
0.997745 0.0671252i \(-0.0213827\pi\)
\(762\) −3.40266e9 + 4.55594e9i −0.278597 + 0.373023i
\(763\) 1.89238e10 1.54231
\(764\) −8.78881e9 1.09772e10i −0.713023 0.890565i
\(765\) 2.23018e9 5.46717e9i 0.180104 0.441517i
\(766\) 6.39341e9 1.33089e10i 0.513963 1.06990i
\(767\) −1.46094e10 −1.16909
\(768\) 7.44366e9 1.01085e10i 0.592956 0.805235i
\(769\) −2.07502e10 −1.64543 −0.822717 0.568451i \(-0.807543\pi\)
−0.822717 + 0.568451i \(0.807543\pi\)
\(770\) 1.32672e9 2.76179e9i 0.104728 0.218009i
\(771\) 1.47732e10 + 2.89727e9i 1.16087 + 0.227666i
\(772\) 4.48236e9 + 5.59847e9i 0.350628 + 0.437934i
\(773\) 8.12995e9 0.633082 0.316541 0.948579i \(-0.397479\pi\)
0.316541 + 0.948579i \(0.397479\pi\)
\(774\) −9.08163e9 + 8.22014e9i −0.703997 + 0.637215i
\(775\)