Properties

Label 27.8.e.a.4.10
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 4.10
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.03404 - 0.740329i) q^{2} +(45.5454 - 10.6122i) q^{3} +(-94.4645 - 79.2651i) q^{4} +(-90.6912 + 514.336i) q^{5} +(-100.497 - 12.1330i) q^{6} +(-162.436 + 136.300i) q^{7} +(271.995 + 471.109i) q^{8} +(1961.76 - 966.672i) q^{9} +O(q^{10})\) \(q+(-2.03404 - 0.740329i) q^{2} +(45.5454 - 10.6122i) q^{3} +(-94.4645 - 79.2651i) q^{4} +(-90.6912 + 514.336i) q^{5} +(-100.497 - 12.1330i) q^{6} +(-162.436 + 136.300i) q^{7} +(271.995 + 471.109i) q^{8} +(1961.76 - 966.672i) q^{9} +(565.246 - 979.036i) q^{10} +(1142.76 + 6480.90i) q^{11} +(-5143.60 - 2607.68i) q^{12} +(-1678.15 + 610.796i) q^{13} +(431.308 - 156.983i) q^{14} +(1327.66 + 24388.0i) q^{15} +(2536.44 + 14384.9i) q^{16} +(-2532.23 + 4385.95i) q^{17} +(-4705.95 + 513.896i) q^{18} +(17955.1 + 31099.1i) q^{19} +(49336.0 - 41397.8i) q^{20} +(-5951.78 + 7931.65i) q^{21} +(2473.58 - 14028.4i) q^{22} +(-66994.5 - 56215.1i) q^{23} +(17387.6 + 18570.4i) q^{24} +(-182903. - 66571.1i) q^{25} +3865.60 q^{26} +(79090.7 - 64846.0i) q^{27} +26148.3 q^{28} +(184432. + 67127.8i) q^{29} +(15354.7 - 50589.0i) q^{30} +(-120098. - 100775. i) q^{31} +(17581.5 - 99709.9i) q^{32} +(120824. + 283048. i) q^{33} +(8397.70 - 7046.50i) q^{34} +(-55372.5 - 95908.0i) q^{35} +(-261940. - 64183.2i) q^{36} +(55637.4 - 96366.8i) q^{37} +(-13497.7 - 76549.3i) q^{38} +(-69950.0 + 45627.8i) q^{39} +(-266976. + 97171.1i) q^{40} +(54862.3 - 19968.3i) q^{41} +(17978.2 - 11727.0i) q^{42} +(-38334.2 - 217404. i) q^{43} +(405759. - 702795. i) q^{44} +(319279. + 1.09667e6i) q^{45} +(94651.6 + 163941. i) q^{46} +(86715.5 - 72763.0i) q^{47} +(268178. + 628246. i) q^{48} +(-135199. + 766751. i) q^{49} +(322746. + 270816. i) q^{50} +(-68786.9 + 226632. i) q^{51} +(206940. + 75320.1i) q^{52} +4493.84 q^{53} +(-208881. + 73346.0i) q^{54} -3.43699e6 q^{55} +(-108394. - 39452.2i) q^{56} +(1.14780e6 + 1.22588e6i) q^{57} +(-325445. - 273081. i) q^{58} +(-89420.8 + 507131. i) q^{59} +(1.80770e6 - 2.40904e6i) q^{60} +(1.27586e6 - 1.07058e6i) q^{61} +(169678. + 293891. i) q^{62} +(-186904. + 424412. i) q^{63} +(825253. - 1.42938e6i) q^{64} +(-161961. - 918525. i) q^{65} +(-36211.6 - 665179. i) q^{66} +(389352. - 141713. i) q^{67} +(586859. - 213599. i) q^{68} +(-3.64786e6 - 1.84938e6i) q^{69} +(41626.3 + 236074. i) q^{70} +(577126. - 999612. i) q^{71} +(988997. + 661274. i) q^{72} +(2.76794e6 + 4.79421e6i) q^{73} +(-184512. + 154824. i) q^{74} +(-9.03684e6 - 1.09101e6i) q^{75} +(768956. - 4.36097e6i) q^{76} +(-1.06897e6 - 896975. i) q^{77} +(176060. - 41022.5i) q^{78} +(5.63804e6 + 2.05208e6i) q^{79} -7.62867e6 q^{80} +(2.91406e6 - 3.79276e6i) q^{81} -126375. q^{82} +(4.99322e6 + 1.81738e6i) q^{83} +(1.19094e6 - 277491. i) q^{84} +(-2.02620e6 - 1.70018e6i) q^{85} +(-82977.2 + 470587. i) q^{86} +(9.11241e6 + 1.10013e6i) q^{87} +(-2.74238e6 + 2.30113e6i) q^{88} +(2.57485e6 + 4.45977e6i) q^{89} +(162473. - 2.46704e6i) q^{90} +(189341. - 327948. i) q^{91} +(1.87271e6 + 1.06207e7i) q^{92} +(-6.53937e6 - 3.31531e6i) q^{93} +(-230251. + 83804.5i) q^{94} +(-1.76237e7 + 6.41451e6i) q^{95} +(-257382. - 4.72790e6i) q^{96} +(-1.01705e6 - 5.76796e6i) q^{97} +(842647. - 1.45951e6i) q^{98} +(8.50672e6 + 1.16093e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.03404 0.740329i −0.179785 0.0654364i 0.250559 0.968101i \(-0.419386\pi\)
−0.430344 + 0.902665i \(0.641608\pi\)
\(3\) 45.5454 10.6122i 0.973912 0.226924i
\(4\) −94.4645 79.2651i −0.738004 0.619259i
\(5\) −90.6912 + 514.336i −0.324467 + 1.84014i 0.188929 + 0.981991i \(0.439498\pi\)
−0.513396 + 0.858152i \(0.671613\pi\)
\(6\) −100.497 12.1330i −0.189944 0.0229318i
\(7\) −162.436 + 136.300i −0.178995 + 0.150194i −0.727883 0.685701i \(-0.759496\pi\)
0.548888 + 0.835896i \(0.315051\pi\)
\(8\) 271.995 + 471.109i 0.187822 + 0.325317i
\(9\) 1961.76 966.672i 0.897011 0.442008i
\(10\) 565.246 979.036i 0.178747 0.309598i
\(11\) 1142.76 + 6480.90i 0.258869 + 1.46812i 0.785943 + 0.618298i \(0.212178\pi\)
−0.527075 + 0.849819i \(0.676711\pi\)
\(12\) −5143.60 2607.68i −0.859276 0.435633i
\(13\) −1678.15 + 610.796i −0.211850 + 0.0771071i −0.445765 0.895150i \(-0.647068\pi\)
0.233915 + 0.972257i \(0.424846\pi\)
\(14\) 431.308 156.983i 0.0420088 0.0152899i
\(15\) 1327.66 + 24388.0i 0.101570 + 1.86577i
\(16\) 2536.44 + 14384.9i 0.154812 + 0.877982i
\(17\) −2532.23 + 4385.95i −0.125006 + 0.216517i −0.921735 0.387819i \(-0.873228\pi\)
0.796729 + 0.604337i \(0.206562\pi\)
\(18\) −4705.95 + 513.896i −0.190193 + 0.0207693i
\(19\) 17955.1 + 31099.1i 0.600550 + 1.04018i 0.992738 + 0.120298i \(0.0383851\pi\)
−0.392188 + 0.919885i \(0.628282\pi\)
\(20\) 49336.0 41397.8i 1.37898 1.15710i
\(21\) −5951.78 + 7931.65i −0.140242 + 0.186894i
\(22\) 2473.58 14028.4i 0.0495276 0.280885i
\(23\) −66994.5 56215.1i −1.14813 0.963397i −0.148458 0.988919i \(-0.547431\pi\)
−0.999674 + 0.0255214i \(0.991875\pi\)
\(24\) 17387.6 + 18570.4i 0.256744 + 0.274209i
\(25\) −182903. 66571.1i −2.34115 0.852110i
\(26\) 3865.60 0.0431331
\(27\) 79090.7 64846.0i 0.773308 0.634031i
\(28\) 26148.3 0.225108
\(29\) 184432. + 67127.8i 1.40425 + 0.511104i 0.929436 0.368983i \(-0.120294\pi\)
0.474812 + 0.880087i \(0.342516\pi\)
\(30\) 15354.7 50589.0i 0.103828 0.342083i
\(31\) −120098. 100775.i −0.724055 0.607554i 0.204449 0.978877i \(-0.434460\pi\)
−0.928504 + 0.371323i \(0.878904\pi\)
\(32\) 17581.5 99709.9i 0.0948489 0.537915i
\(33\) 120824. + 283048.i 0.585267 + 1.37107i
\(34\) 8397.70 7046.50i 0.0366424 0.0307466i
\(35\) −55372.5 95908.0i −0.218301 0.378109i
\(36\) −261940. 64183.2i −0.935715 0.229278i
\(37\) 55637.4 96366.8i 0.180576 0.312767i −0.761501 0.648164i \(-0.775537\pi\)
0.942077 + 0.335397i \(0.108870\pi\)
\(38\) −13497.7 76549.3i −0.0399041 0.226307i
\(39\) −69950.0 + 45627.8i −0.188826 + 0.123169i
\(40\) −266976. + 97171.1i −0.659571 + 0.240064i
\(41\) 54862.3 19968.3i 0.124317 0.0452477i −0.279113 0.960258i \(-0.590040\pi\)
0.403430 + 0.915011i \(0.367818\pi\)
\(42\) 17978.2 11727.0i 0.0374432 0.0244239i
\(43\) −38334.2 217404.i −0.0735269 0.416992i −0.999248 0.0387841i \(-0.987652\pi\)
0.925721 0.378208i \(-0.123460\pi\)
\(44\) 405759. 702795.i 0.718098 1.24378i
\(45\) 319279. + 1.09667e6i 0.522308 + 1.79405i
\(46\) 94651.6 + 163941.i 0.143376 + 0.248334i
\(47\) 86715.5 72763.0i 0.121830 0.102228i −0.579837 0.814732i \(-0.696884\pi\)
0.701667 + 0.712505i \(0.252439\pi\)
\(48\) 268178. + 628246.i 0.350008 + 0.819947i
\(49\) −135199. + 766751.i −0.164167 + 0.931040i
\(50\) 322746. + 270816.i 0.365145 + 0.306393i
\(51\) −68786.9 + 226632.i −0.0726123 + 0.239236i
\(52\) 206940. + 75320.1i 0.204095 + 0.0742847i
\(53\) 4493.84 0.00414622 0.00207311 0.999998i \(-0.499340\pi\)
0.00207311 + 0.999998i \(0.499340\pi\)
\(54\) −208881. + 73346.0i −0.180518 + 0.0633867i
\(55\) −3.43699e6 −2.78554
\(56\) −108394. 39452.2i −0.0824798 0.0300202i
\(57\) 1.14780e6 + 1.22588e6i 0.820926 + 0.876768i
\(58\) −325445. 273081.i −0.219018 0.183778i
\(59\) −89420.8 + 507131.i −0.0566835 + 0.321468i −0.999944 0.0105857i \(-0.996630\pi\)
0.943260 + 0.332054i \(0.107742\pi\)
\(60\) 1.80770e6 2.40904e6i 1.08043 1.43984i
\(61\) 1.27586e6 1.07058e6i 0.719696 0.603897i −0.207605 0.978213i \(-0.566567\pi\)
0.927301 + 0.374316i \(0.122122\pi\)
\(62\) 169678. + 293891.i 0.0904181 + 0.156609i
\(63\) −186904. + 424412.i −0.0941731 + 0.213843i
\(64\) 825253. 1.42938e6i 0.393511 0.681582i
\(65\) −161961. 918525.i −0.0731498 0.414853i
\(66\) −36211.6 665179.i −0.0155040 0.284796i
\(67\) 389352. 141713.i 0.158154 0.0575635i −0.261730 0.965141i \(-0.584293\pi\)
0.419884 + 0.907578i \(0.362071\pi\)
\(68\) 586859. 213599.i 0.226335 0.0823794i
\(69\) −3.64786e6 1.84938e6i −1.33680 0.677726i
\(70\) 41626.3 + 236074.i 0.0145052 + 0.0822632i
\(71\) 577126. 999612.i 0.191367 0.331457i −0.754337 0.656488i \(-0.772041\pi\)
0.945703 + 0.325031i \(0.105375\pi\)
\(72\) 988997. + 661274.i 0.312271 + 0.208794i
\(73\) 2.76794e6 + 4.79421e6i 0.832772 + 1.44240i 0.895832 + 0.444393i \(0.146581\pi\)
−0.0630599 + 0.998010i \(0.520086\pi\)
\(74\) −184512. + 154824.i −0.0529313 + 0.0444146i
\(75\) −9.03684e6 1.09101e6i −2.47344 0.298617i
\(76\) 768956. 4.36097e6i 0.200934 1.13956i
\(77\) −1.06897e6 896975.i −0.266839 0.223905i
\(78\) 176060. 41022.5i 0.0420079 0.00978794i
\(79\) 5.63804e6 + 2.05208e6i 1.28657 + 0.468273i 0.892599 0.450851i \(-0.148879\pi\)
0.393970 + 0.919123i \(0.371101\pi\)
\(80\) −7.62867e6 −1.66584
\(81\) 2.91406e6 3.79276e6i 0.609257 0.792972i
\(82\) −126375. −0.0253112
\(83\) 4.99322e6 + 1.81738e6i 0.958534 + 0.348878i 0.773459 0.633847i \(-0.218525\pi\)
0.185075 + 0.982724i \(0.440747\pi\)
\(84\) 1.19094e6 277491.i 0.219235 0.0510824i
\(85\) −2.02620e6 1.70018e6i −0.357862 0.300282i
\(86\) −82977.2 + 470587.i −0.0140674 + 0.0797803i
\(87\) 9.11241e6 + 1.10013e6i 1.48360 + 0.179113i
\(88\) −2.74238e6 + 2.30113e6i −0.428982 + 0.359958i
\(89\) 2.57485e6 + 4.45977e6i 0.387157 + 0.670575i 0.992066 0.125719i \(-0.0401239\pi\)
−0.604909 + 0.796294i \(0.706791\pi\)
\(90\) 162473. 2.46704e6i 0.0234927 0.356721i
\(91\) 189341. 327948.i 0.0263390 0.0456205i
\(92\) 1.87271e6 + 1.06207e7i 0.250734 + 1.42198i
\(93\) −6.53937e6 3.31531e6i −0.843034 0.427399i
\(94\) −230251. + 83804.5i −0.0285926 + 0.0104069i
\(95\) −1.76237e7 + 6.41451e6i −2.10894 + 0.767593i
\(96\) −257382. 4.72790e6i −0.0296913 0.545405i
\(97\) −1.01705e6 5.76796e6i −0.113146 0.641684i −0.987651 0.156668i \(-0.949925\pi\)
0.874505 0.485016i \(-0.161186\pi\)
\(98\) 842647. 1.45951e6i 0.0904388 0.156645i
\(99\) 8.50672e6 + 1.16093e7i 0.881128 + 1.20250i
\(100\) 1.20010e7 + 2.07864e7i 1.20010 + 2.07864i
\(101\) 7.79318e6 6.53925e6i 0.752644 0.631543i −0.183557 0.983009i \(-0.558761\pi\)
0.936201 + 0.351466i \(0.114317\pi\)
\(102\) 307697. 410054.i 0.0287093 0.0382596i
\(103\) 102978. 584017.i 0.00928569 0.0526618i −0.979813 0.199917i \(-0.935933\pi\)
0.989099 + 0.147255i \(0.0470439\pi\)
\(104\) −744199. 624457.i −0.0648743 0.0544360i
\(105\) −3.53976e6 3.78054e6i −0.298408 0.318707i
\(106\) −9140.64 3326.92i −0.000745428 0.000271314i
\(107\) −5.29806e6 −0.418094 −0.209047 0.977906i \(-0.567036\pi\)
−0.209047 + 0.977906i \(0.567036\pi\)
\(108\) −1.26113e7 143489.i −0.963333 0.0109607i
\(109\) −2.37200e6 −0.175437 −0.0877185 0.996145i \(-0.527958\pi\)
−0.0877185 + 0.996145i \(0.527958\pi\)
\(110\) 6.99097e6 + 2.54450e6i 0.500799 + 0.182276i
\(111\) 1.51136e6 4.97950e6i 0.104891 0.345585i
\(112\) −2.37267e6 1.99091e6i −0.159578 0.133902i
\(113\) −3.57824e6 + 2.02932e7i −0.233289 + 1.32305i 0.612897 + 0.790163i \(0.290004\pi\)
−0.846187 + 0.532887i \(0.821107\pi\)
\(114\) −1.42711e6 3.34323e6i −0.0902176 0.211348i
\(115\) 3.49892e7 2.93595e7i 2.14532 1.80014i
\(116\) −1.21014e7 2.09602e7i −0.719834 1.24679i
\(117\) −2.70169e6 + 2.82046e6i −0.155950 + 0.162805i
\(118\) 557328. 965321.i 0.0312266 0.0540860i
\(119\) −186480. 1.05758e6i −0.0101442 0.0575307i
\(120\) −1.11283e7 + 7.25889e6i −0.587888 + 0.383474i
\(121\) −2.23842e7 + 8.14718e6i −1.14866 + 0.418079i
\(122\) −3.38773e6 + 1.23303e6i −0.168908 + 0.0614773i
\(123\) 2.28682e6 1.49167e6i 0.110806 0.0722778i
\(124\) 3.35713e6 + 1.90392e7i 0.158122 + 0.896754i
\(125\) 3.04264e7 5.27000e7i 1.39337 2.41338i
\(126\) 694373. 724898.i 0.0309240 0.0322835i
\(127\) −1.56983e7 2.71902e7i −0.680047 1.17788i −0.974966 0.222354i \(-0.928626\pi\)
0.294919 0.955522i \(-0.404707\pi\)
\(128\) −1.26646e7 + 1.06268e7i −0.533771 + 0.447887i
\(129\) −4.05307e6 9.49493e6i −0.166234 0.389429i
\(130\) −350576. + 1.98822e6i −0.0139953 + 0.0793711i
\(131\) 1.08086e7 + 9.06948e6i 0.420068 + 0.352479i 0.828189 0.560449i \(-0.189371\pi\)
−0.408121 + 0.912928i \(0.633816\pi\)
\(132\) 1.10223e7 3.63151e7i 0.417121 1.37429i
\(133\) −7.15537e6 2.60434e6i −0.263725 0.0959880i
\(134\) −896871. −0.0322005
\(135\) 2.61798e7 + 4.65601e7i 0.915794 + 1.62872i
\(136\) −2.75501e6 −0.0939156
\(137\) 2.23045e7 + 8.11817e6i 0.741089 + 0.269734i 0.684851 0.728683i \(-0.259867\pi\)
0.0562379 + 0.998417i \(0.482089\pi\)
\(138\) 6.05072e6 + 6.46232e6i 0.195988 + 0.209320i
\(139\) −4.00868e7 3.36368e7i −1.26605 1.06234i −0.995011 0.0997692i \(-0.968190\pi\)
−0.271035 0.962569i \(-0.587366\pi\)
\(140\) −2.37142e6 + 1.34490e7i −0.0730400 + 0.414231i
\(141\) 3.17732e6 4.23426e6i 0.0954539 0.127207i
\(142\) −1.91394e6 + 1.60598e6i −0.0560943 + 0.0470687i
\(143\) −5.87622e6 1.01779e7i −0.168044 0.291060i
\(144\) 1.88813e7 + 2.57678e7i 0.526943 + 0.719131i
\(145\) −5.12526e7 + 8.87721e7i −1.39614 + 2.41818i
\(146\) −2.08079e6 1.18008e7i −0.0553343 0.313816i
\(147\) 1.97922e6 + 3.63567e7i 0.0513906 + 0.944005i
\(148\) −1.28943e7 + 4.69314e6i −0.326950 + 0.119000i
\(149\) 6.20665e6 2.25903e6i 0.153711 0.0559462i −0.264019 0.964518i \(-0.585048\pi\)
0.417730 + 0.908571i \(0.362826\pi\)
\(150\) 1.75735e7 + 8.90938e6i 0.425148 + 0.215540i
\(151\) −3.83912e6 2.17728e7i −0.0907430 0.514629i −0.995969 0.0896984i \(-0.971410\pi\)
0.905226 0.424930i \(-0.139701\pi\)
\(152\) −9.76737e6 + 1.69176e7i −0.225593 + 0.390738i
\(153\) −727860. + 1.10520e7i −0.0164296 + 0.249472i
\(154\) 1.51027e6 + 2.61587e6i 0.0333222 + 0.0577157i
\(155\) 6.27238e7 5.26315e7i 1.35292 1.13523i
\(156\) 1.02245e7 + 1.23439e6i 0.215628 + 0.0260326i
\(157\) 6.53239e6 3.70470e7i 0.134717 0.764020i −0.840339 0.542061i \(-0.817644\pi\)
0.975056 0.221958i \(-0.0712449\pi\)
\(158\) −9.94876e6 8.34800e6i −0.200664 0.168377i
\(159\) 204674. 47689.5i 0.00403806 0.000940877i
\(160\) 4.96899e7 + 1.80856e7i 0.959065 + 0.349071i
\(161\) 1.85445e7 0.350206
\(162\) −8.73519e6 + 5.55725e6i −0.161425 + 0.102697i
\(163\) 5.68920e7 1.02895 0.514475 0.857505i \(-0.327987\pi\)
0.514475 + 0.857505i \(0.327987\pi\)
\(164\) −6.76533e6 2.46238e6i −0.119767 0.0435914i
\(165\) −1.56539e8 + 3.64740e7i −2.71287 + 0.632106i
\(166\) −8.81093e6 7.39325e6i −0.149501 0.125446i
\(167\) 1.28799e7 7.30455e7i 0.213996 1.21363i −0.668645 0.743581i \(-0.733126\pi\)
0.882641 0.470048i \(-0.155763\pi\)
\(168\) −5.35553e6 646568.i −0.0871404 0.0105204i
\(169\) −4.56250e7 + 3.82840e7i −0.727109 + 0.610117i
\(170\) 2.86267e6 + 4.95829e6i 0.0446889 + 0.0774035i
\(171\) 6.52862e7 + 4.36524e7i 0.998470 + 0.667608i
\(172\) −1.36113e7 + 2.35755e7i −0.203963 + 0.353274i
\(173\) 1.01641e7 + 5.76433e7i 0.149247 + 0.846423i 0.963858 + 0.266415i \(0.0858392\pi\)
−0.814611 + 0.580007i \(0.803050\pi\)
\(174\) −1.77205e7 8.98389e6i −0.255008 0.129283i
\(175\) 3.87837e7 1.41161e7i 0.547036 0.199105i
\(176\) −9.03282e7 + 3.28768e7i −1.24890 + 0.454564i
\(177\) 1.30906e6 + 2.40464e7i 0.0177441 + 0.325945i
\(178\) −1.93564e6 1.09776e7i −0.0257250 0.145894i
\(179\) −3.94374e7 + 6.83076e7i −0.513952 + 0.890191i 0.485917 + 0.874005i \(0.338486\pi\)
−0.999869 + 0.0161860i \(0.994848\pi\)
\(180\) 5.67674e7 1.28904e8i 0.725513 1.64746i
\(181\) −1.06871e7 1.85106e7i −0.133963 0.232031i 0.791238 0.611508i \(-0.209437\pi\)
−0.925201 + 0.379478i \(0.876104\pi\)
\(182\) −627915. + 526883.i −0.00772060 + 0.00647835i
\(183\) 4.67485e7 6.22994e7i 0.563883 0.751459i
\(184\) 8.26126e6 4.68519e7i 0.0977651 0.554453i
\(185\) 4.45191e7 + 3.73559e7i 0.516946 + 0.433769i
\(186\) 1.08469e7 + 1.15847e7i 0.123598 + 0.132005i
\(187\) −3.13186e7 1.13991e7i −0.350233 0.127474i
\(188\) −1.39591e7 −0.153216
\(189\) −4.00868e6 + 2.13134e7i −0.0431902 + 0.229635i
\(190\) 4.05961e7 0.429385
\(191\) 6.19285e7 + 2.25401e7i 0.643093 + 0.234067i 0.642920 0.765933i \(-0.277723\pi\)
0.000173062 1.00000i \(0.499945\pi\)
\(192\) 2.24176e7 7.38594e7i 0.228578 0.753098i
\(193\) −5.91285e7 4.96147e7i −0.592034 0.496775i 0.296840 0.954927i \(-0.404067\pi\)
−0.888874 + 0.458152i \(0.848512\pi\)
\(194\) −2.20148e6 + 1.24852e7i −0.0216475 + 0.122769i
\(195\) −1.71241e7 4.01158e7i −0.165382 0.387431i
\(196\) 7.35481e7 6.17142e7i 0.697711 0.585449i
\(197\) −6.54850e7 1.13423e8i −0.610253 1.05699i −0.991198 0.132391i \(-0.957734\pi\)
0.380945 0.924598i \(-0.375599\pi\)
\(198\) −8.70827e6 2.99115e7i −0.0797267 0.273849i
\(199\) 2.10078e7 3.63866e7i 0.188971 0.327307i −0.755936 0.654645i \(-0.772818\pi\)
0.944907 + 0.327338i \(0.106151\pi\)
\(200\) −1.83863e7 1.04274e8i −0.162514 0.921661i
\(201\) 1.62293e7 1.05862e7i 0.140966 0.0919508i
\(202\) −2.06928e7 + 7.53156e6i −0.176640 + 0.0642917i
\(203\) −3.91080e7 + 1.42342e7i −0.328118 + 0.119425i
\(204\) 2.44620e7 1.59563e7i 0.201737 0.131591i
\(205\) 5.29485e6 + 3.00286e7i 0.0429255 + 0.243443i
\(206\) −641826. + 1.11167e6i −0.00511542 + 0.00886018i
\(207\) −1.85769e8 4.55189e7i −1.45572 0.356694i
\(208\) −1.30427e7 2.25907e7i −0.100496 0.174063i
\(209\) −1.81032e8 + 1.51904e8i −1.37165 + 1.15095i
\(210\) 4.40115e6 + 1.03103e7i 0.0327943 + 0.0768256i
\(211\) −3.54729e7 + 2.01177e8i −0.259961 + 1.47431i 0.523049 + 0.852303i \(0.324794\pi\)
−0.783010 + 0.622009i \(0.786317\pi\)
\(212\) −424508. 356205.i −0.00305993 0.00256758i
\(213\) 1.56774e7 5.16523e7i 0.111159 0.366236i
\(214\) 1.07765e7 + 3.92231e6i 0.0751671 + 0.0273586i
\(215\) 1.15295e8 0.791182
\(216\) 5.20618e7 + 1.96226e7i 0.351505 + 0.132485i
\(217\) 3.32439e7 0.220853
\(218\) 4.82473e6 + 1.75606e6i 0.0315410 + 0.0114800i
\(219\) 1.76944e8 + 1.88980e8i 1.13836 + 1.21580i
\(220\) 3.24674e8 + 2.72434e8i 2.05574 + 1.72497i
\(221\) 1.57054e6 8.90696e6i 0.00978758 0.0555081i
\(222\) −6.76063e6 + 9.00957e6i −0.0414717 + 0.0552674i
\(223\) 1.19480e8 1.00255e8i 0.721484 0.605397i −0.206311 0.978486i \(-0.566146\pi\)
0.927795 + 0.373089i \(0.121702\pi\)
\(224\) 1.07346e7 + 1.85929e7i 0.0638143 + 0.110530i
\(225\) −4.23164e8 + 4.62101e7i −2.47668 + 0.270457i
\(226\) 2.23019e7 3.86280e7i 0.128518 0.222599i
\(227\) 2.16305e7 + 1.22673e8i 0.122737 + 0.696078i 0.982626 + 0.185596i \(0.0594217\pi\)
−0.859889 + 0.510482i \(0.829467\pi\)
\(228\) −1.12570e7 2.06782e8i −0.0629000 1.15542i
\(229\) 7.79188e7 2.83601e7i 0.428764 0.156057i −0.118619 0.992940i \(-0.537847\pi\)
0.547382 + 0.836883i \(0.315624\pi\)
\(230\) −9.29050e7 + 3.38147e7i −0.503491 + 0.183256i
\(231\) −5.82057e7 2.95089e7i −0.310687 0.157511i
\(232\) 1.85401e7 + 1.05146e8i 0.0974774 + 0.552822i
\(233\) −7.30589e7 + 1.26542e8i −0.378379 + 0.655372i −0.990827 0.135139i \(-0.956852\pi\)
0.612447 + 0.790511i \(0.290185\pi\)
\(234\) 7.58340e6 3.73677e6i 0.0386909 0.0190652i
\(235\) 2.95602e7 + 5.11998e7i 0.148583 + 0.257354i
\(236\) 4.86449e7 4.08179e7i 0.240904 0.202143i
\(237\) 2.78564e8 + 3.36308e7i 1.35927 + 0.164103i
\(238\) −403651. + 2.28922e6i −0.00194082 + 0.0110070i
\(239\) 2.13495e8 + 1.79143e8i 1.01157 + 0.848804i 0.988544 0.150931i \(-0.0482270\pi\)
0.0230212 + 0.999735i \(0.492671\pi\)
\(240\) −3.47451e8 + 8.09569e7i −1.62239 + 0.378020i
\(241\) −2.18034e8 7.93580e7i −1.00338 0.365200i −0.212493 0.977163i \(-0.568158\pi\)
−0.790887 + 0.611962i \(0.790380\pi\)
\(242\) 5.15618e7 0.233870
\(243\) 9.24724e7 2.03667e8i 0.413419 0.910541i
\(244\) −2.05383e8 −0.905107
\(245\) −3.82106e8 1.39075e8i −1.65998 0.604183i
\(246\) −5.75580e6 + 1.34112e6i −0.0246509 + 0.00574372i
\(247\) −4.91265e7 4.12220e7i −0.207432 0.174056i
\(248\) 1.48096e7 8.39896e7i 0.0616543 0.349659i
\(249\) 2.46705e8 + 2.97844e7i 1.01270 + 0.122262i
\(250\) −1.00904e8 + 8.46683e7i −0.408430 + 0.342713i
\(251\) 1.24993e8 + 2.16494e8i 0.498916 + 0.864149i 0.999999 0.00125082i \(-0.000398147\pi\)
−0.501083 + 0.865399i \(0.667065\pi\)
\(252\) 5.12968e7 2.52769e7i 0.201924 0.0994995i
\(253\) 2.87766e8 4.98425e8i 1.11716 1.93499i
\(254\) 1.18012e7 + 6.69278e7i 0.0451863 + 0.256265i
\(255\) −1.10327e8 5.59331e7i −0.416668 0.211241i
\(256\) −1.64897e8 + 6.00174e7i −0.614287 + 0.223582i
\(257\) 2.40909e8 8.76839e7i 0.885295 0.322221i 0.140950 0.990017i \(-0.454984\pi\)
0.744345 + 0.667796i \(0.232762\pi\)
\(258\) 1.21473e6 + 2.23136e7i 0.00440363 + 0.0808912i
\(259\) 4.09729e6 + 2.32369e7i 0.0146537 + 0.0831053i
\(260\) −5.75075e7 + 9.96059e7i −0.202917 + 0.351462i
\(261\) 4.26703e8 4.65965e7i 1.48554 0.162223i
\(262\) −1.52707e7 2.64495e7i −0.0524570 0.0908581i
\(263\) 7.47307e7 6.27065e7i 0.253311 0.212553i −0.507286 0.861778i \(-0.669351\pi\)
0.760596 + 0.649225i \(0.224907\pi\)
\(264\) −1.00483e8 + 1.33909e8i −0.336108 + 0.447914i
\(265\) −407552. + 2.31134e6i −0.00134531 + 0.00762964i
\(266\) 1.26262e7 + 1.05946e7i 0.0411327 + 0.0345144i
\(267\) 1.64600e8 + 1.75797e8i 0.529226 + 0.565226i
\(268\) −4.80129e7 1.74752e7i −0.152365 0.0554564i
\(269\) −1.04761e8 −0.328146 −0.164073 0.986448i \(-0.552463\pi\)
−0.164073 + 0.986448i \(0.552463\pi\)
\(270\) −1.87808e7 1.14087e8i −0.0580686 0.352746i
\(271\) −4.39506e8 −1.34144 −0.670722 0.741709i \(-0.734016\pi\)
−0.670722 + 0.741709i \(0.734016\pi\)
\(272\) −6.95141e7 2.53011e7i −0.209451 0.0762339i
\(273\) 5.14335e6 1.69458e7i 0.0152995 0.0504073i
\(274\) −3.93580e7 3.30253e7i −0.115586 0.0969884i
\(275\) 2.22427e8 1.26145e9i 0.644947 3.65767i
\(276\) 1.98002e8 + 4.63848e8i 0.566874 + 1.32799i
\(277\) −5.16881e8 + 4.33715e8i −1.46121 + 1.22610i −0.537349 + 0.843360i \(0.680574\pi\)
−0.923857 + 0.382738i \(0.874981\pi\)
\(278\) 5.66357e7 + 9.80959e7i 0.158101 + 0.273838i
\(279\) −3.33021e8 8.16000e7i −0.918029 0.224944i
\(280\) 3.01221e7 5.21730e7i 0.0820034 0.142034i
\(281\) −1.17443e8 6.66052e8i −0.315759 1.79076i −0.567934 0.823074i \(-0.692257\pi\)
0.252176 0.967681i \(-0.418854\pi\)
\(282\) −9.59752e6 + 6.26037e6i −0.0254851 + 0.0166237i
\(283\) 5.51597e8 2.00765e8i 1.44667 0.526545i 0.505010 0.863113i \(-0.331489\pi\)
0.941659 + 0.336569i \(0.109266\pi\)
\(284\) −1.33752e8 + 4.86819e7i −0.346487 + 0.126111i
\(285\) −7.34607e8 + 4.79178e8i −1.87974 + 1.22614i
\(286\) 4.41745e6 + 2.50526e7i 0.0111658 + 0.0633245i
\(287\) −6.18996e6 + 1.07213e7i −0.0154561 + 0.0267708i
\(288\) −6.18960e7 2.12603e8i −0.152682 0.524439i
\(289\) 1.92345e8 + 3.33151e8i 0.468747 + 0.811893i
\(290\) 1.69970e8 1.42622e8i 0.409242 0.343394i
\(291\) −1.07532e8 2.51911e8i −0.255808 0.599268i
\(292\) 1.18542e8 6.72283e8i 0.278632 1.58020i
\(293\) 1.13149e8 + 9.49435e7i 0.262794 + 0.220510i 0.764658 0.644436i \(-0.222908\pi\)
−0.501864 + 0.864946i \(0.667352\pi\)
\(294\) 2.28901e7 7.54162e7i 0.0525330 0.173081i
\(295\) −2.52726e8 9.19846e7i −0.573155 0.208611i
\(296\) 6.05323e7 0.135665
\(297\) 5.10642e8 + 4.38476e8i 1.13102 + 0.971176i
\(298\) −1.42970e7 −0.0312959
\(299\) 1.46763e8 + 5.34173e7i 0.317517 + 0.115567i
\(300\) 7.67181e8 + 8.19367e8i 1.64049 + 1.75208i
\(301\) 3.58591e7 + 3.00893e7i 0.0757908 + 0.0635960i
\(302\) −8.31008e6 + 4.71288e7i −0.0173612 + 0.0984605i
\(303\) 2.85547e8 3.80535e8i 0.589697 0.785861i
\(304\) −4.01814e8 + 3.37162e8i −0.820290 + 0.688305i
\(305\) 4.34925e8 + 7.53313e8i 0.877739 + 1.52029i
\(306\) 9.66263e6 2.19414e7i 0.0192784 0.0437763i
\(307\) 8.86953e7 1.53625e8i 0.174951 0.303024i −0.765193 0.643801i \(-0.777357\pi\)
0.940144 + 0.340777i \(0.110690\pi\)
\(308\) 2.98812e7 + 1.69465e8i 0.0582734 + 0.330485i
\(309\) −1.50753e6 2.76921e7i −0.00290677 0.0533951i
\(310\) −1.66547e8 + 6.06182e7i −0.317520 + 0.115568i
\(311\) −2.41108e8 + 8.77560e7i −0.454517 + 0.165431i −0.559126 0.829083i \(-0.688863\pi\)
0.104609 + 0.994513i \(0.466641\pi\)
\(312\) −4.05217e7 2.05436e7i −0.0755347 0.0382943i
\(313\) −3.13647e7 1.77878e8i −0.0578143 0.327881i 0.942159 0.335166i \(-0.108792\pi\)
−0.999973 + 0.00728452i \(0.997681\pi\)
\(314\) −4.07141e7 + 7.05189e7i −0.0742149 + 0.128544i
\(315\) −2.01339e8 1.34622e8i −0.362946 0.242677i
\(316\) −3.69936e8 6.40748e8i −0.659511 1.14231i
\(317\) −5.92264e8 + 4.96969e8i −1.04426 + 0.876237i −0.992478 0.122421i \(-0.960934\pi\)
−0.0517808 + 0.998658i \(0.516490\pi\)
\(318\) −451620. 54523.7i −0.000787550 9.50803e-5i
\(319\) −2.24287e8 + 1.27200e9i −0.386845 + 2.19391i
\(320\) 6.60338e8 + 5.54089e8i 1.12653 + 0.945268i
\(321\) −2.41302e8 + 5.62240e7i −0.407187 + 0.0948756i
\(322\) −3.77201e7 1.37290e7i −0.0629619 0.0229163i
\(323\) −1.81865e8 −0.300290
\(324\) −5.75909e8 + 1.27298e8i −0.940689 + 0.207929i
\(325\) 3.47599e8 0.561678
\(326\) −1.15720e8 4.21188e7i −0.184990 0.0673309i
\(327\) −1.08034e8 + 2.51721e7i −0.170860 + 0.0398109i
\(328\) 2.43295e7 + 2.04149e7i 0.0380693 + 0.0319439i
\(329\) −4.16814e6 + 2.36387e7i −0.00645293 + 0.0365964i
\(330\) 3.45409e8 + 4.17010e7i 0.529097 + 0.0638774i
\(331\) 5.89810e8 4.94909e8i 0.893952 0.750115i −0.0750468 0.997180i \(-0.523911\pi\)
0.968999 + 0.247065i \(0.0794662\pi\)
\(332\) −3.27627e8 5.67466e8i −0.491356 0.851053i
\(333\) 1.59923e7 2.42832e8i 0.0237332 0.360372i
\(334\) −8.02759e7 + 1.39042e8i −0.117889 + 0.204189i
\(335\) 3.75770e7 + 2.13110e8i 0.0546092 + 0.309704i
\(336\) −1.29192e8 6.54974e7i −0.185801 0.0941969i
\(337\) −2.90825e8 + 1.05851e8i −0.413930 + 0.150658i −0.540586 0.841289i \(-0.681798\pi\)
0.126657 + 0.991947i \(0.459575\pi\)
\(338\) 1.21146e8 4.40934e7i 0.170647 0.0621105i
\(339\) 5.23830e7 + 9.62234e8i 0.0730283 + 1.34147i
\(340\) 5.66387e7 + 3.21214e8i 0.0781514 + 0.443219i
\(341\) 5.15866e8 8.93506e8i 0.704525 1.22027i
\(342\) −1.00477e8 1.37124e8i −0.135824 0.185362i
\(343\) −1.69862e8 2.94209e8i −0.227282 0.393665i
\(344\) 9.19942e7 7.71923e7i 0.121844 0.102240i
\(345\) 1.28203e9 1.70850e9i 1.68086 2.24000i
\(346\) 2.20009e7 1.24773e8i 0.0285545 0.161940i
\(347\) 6.56018e8 + 5.50464e8i 0.842873 + 0.707255i 0.958208 0.286072i \(-0.0923496\pi\)
−0.115335 + 0.993327i \(0.536794\pi\)
\(348\) −7.73597e8 8.26220e8i −0.983982 1.05092i
\(349\) 6.84067e8 + 2.48980e8i 0.861410 + 0.313527i 0.734683 0.678410i \(-0.237331\pi\)
0.126726 + 0.991938i \(0.459553\pi\)
\(350\) −8.93380e7 −0.111378
\(351\) −9.31183e7 + 1.57130e8i −0.114937 + 0.193947i
\(352\) 6.66301e8 0.814275
\(353\) −1.25707e9 4.57538e8i −1.52107 0.553625i −0.559656 0.828725i \(-0.689067\pi\)
−0.961416 + 0.275100i \(0.911289\pi\)
\(354\) 1.51396e7 4.98804e7i 0.0181385 0.0597611i
\(355\) 4.61796e8 + 3.87493e8i 0.547836 + 0.459689i
\(356\) 1.10272e8 6.25385e8i 0.129536 0.734637i
\(357\) −1.97166e7 4.61890e7i −0.0229347 0.0537279i
\(358\) 1.30787e8 1.09743e8i 0.150652 0.126412i
\(359\) 4.06140e7 + 7.03455e7i 0.0463282 + 0.0802427i 0.888260 0.459342i \(-0.151915\pi\)
−0.841931 + 0.539585i \(0.818581\pi\)
\(360\) −4.29810e8 + 4.48704e8i −0.485532 + 0.506876i
\(361\) −1.97833e8 + 3.42656e8i −0.221321 + 0.383339i
\(362\) 8.03402e6 + 4.55632e7i 0.00890129 + 0.0504817i
\(363\) −9.33037e8 + 6.08612e8i −1.02383 + 0.667832i
\(364\) −4.38808e7 + 1.59713e7i −0.0476891 + 0.0173574i
\(365\) −2.71686e9 + 9.88855e8i −2.92443 + 1.06441i
\(366\) −1.41210e8 + 9.21101e7i −0.150550 + 0.0982027i
\(367\) −1.70000e8 9.64118e8i −0.179522 1.01812i −0.932794 0.360411i \(-0.882637\pi\)
0.753272 0.657710i \(-0.228475\pi\)
\(368\) 6.38718e8 1.10629e9i 0.668101 1.15718i
\(369\) 8.83241e7 9.22069e7i 0.0915139 0.0955369i
\(370\) −6.28977e7 1.08942e8i −0.0645548 0.111812i
\(371\) −729964. + 612512.i −0.000742151 + 0.000622739i
\(372\) 3.54950e8 + 8.31522e8i 0.357492 + 0.837478i
\(373\) −1.03160e8 + 5.85051e8i −0.102928 + 0.583732i 0.889100 + 0.457713i \(0.151331\pi\)
−0.992028 + 0.126019i \(0.959780\pi\)
\(374\) 5.52642e7 + 4.63722e7i 0.0546252 + 0.0458360i
\(375\) 8.26519e8 2.72313e9i 0.809363 2.66661i
\(376\) 5.78654e7 + 2.10613e7i 0.0561386 + 0.0204328i
\(377\) −3.50506e8 −0.336900
\(378\) 2.39327e7 4.03846e7i 0.0227914 0.0384587i
\(379\) 9.36183e8 0.883331 0.441666 0.897180i \(-0.354388\pi\)
0.441666 + 0.897180i \(0.354388\pi\)
\(380\) 2.17326e9 + 7.91003e8i 2.03175 + 0.739496i
\(381\) −1.00353e9 1.07180e9i −0.929595 0.992830i
\(382\) −1.09278e8 9.16949e7i −0.100302 0.0841634i
\(383\) 4.59875e7 2.60808e8i 0.0418258 0.237206i −0.956727 0.290987i \(-0.906016\pi\)
0.998553 + 0.0537815i \(0.0171274\pi\)
\(384\) −4.64038e8 + 6.18401e8i −0.418210 + 0.557328i
\(385\) 5.58293e8 4.68463e8i 0.498597 0.418372i
\(386\) 8.35383e7 + 1.44693e8i 0.0739316 + 0.128053i
\(387\) −2.85361e8 3.89438e8i −0.250268 0.341547i
\(388\) −3.61123e8 + 6.25484e8i −0.313866 + 0.543632i
\(389\) 9.40863e7 + 5.33590e8i 0.0810407 + 0.459604i 0.998141 + 0.0609478i \(0.0194123\pi\)
−0.917100 + 0.398657i \(0.869477\pi\)
\(390\) 5.13220e6 + 9.42745e7i 0.00438104 + 0.0804763i
\(391\) 4.16202e8 1.51485e8i 0.352116 0.128160i
\(392\) −3.97997e8 + 1.44859e8i −0.333717 + 0.121463i
\(393\) 5.88528e8 + 2.98370e8i 0.489095 + 0.247960i
\(394\) 4.92283e7 + 2.79187e8i 0.0405488 + 0.229964i
\(395\) −1.56678e9 + 2.71374e9i −1.27914 + 2.21553i
\(396\) 1.16631e8 1.77095e9i 0.0943799 1.43309i
\(397\) 2.97752e8 + 5.15722e8i 0.238830 + 0.413665i 0.960379 0.278698i \(-0.0899029\pi\)
−0.721549 + 0.692363i \(0.756570\pi\)
\(398\) −6.96687e7 + 5.84590e7i −0.0553920 + 0.0464794i
\(399\) −3.53532e8 4.26816e7i −0.278627 0.0336384i
\(400\) 4.93695e8 2.79988e9i 0.385699 2.18741i
\(401\) 5.36750e8 + 4.50386e8i 0.415687 + 0.348803i 0.826520 0.562908i \(-0.190317\pi\)
−0.410833 + 0.911711i \(0.634762\pi\)
\(402\) −4.08483e7 + 9.51776e6i −0.0313605 + 0.00730708i
\(403\) 2.63096e8 + 9.57590e7i 0.200238 + 0.0728806i
\(404\) −1.25451e9 −0.946543
\(405\) 1.68647e9 + 1.84277e9i 1.26150 + 1.37841i
\(406\) 9.00851e7 0.0668055
\(407\) 6.88124e8 + 2.50456e8i 0.505925 + 0.184142i
\(408\) −1.25478e8 + 2.92367e7i −0.0914656 + 0.0213117i
\(409\) −1.30592e9 1.09580e9i −0.943811 0.791952i 0.0344331 0.999407i \(-0.489037\pi\)
−0.978245 + 0.207455i \(0.933482\pi\)
\(410\) 1.14611e7 6.49992e7i 0.00821265 0.0465762i
\(411\) 1.10202e9 + 1.33046e8i 0.782965 + 0.0945267i
\(412\) −5.60199e7 + 4.70063e7i −0.0394641 + 0.0331143i
\(413\) −5.45969e7 9.45645e7i −0.0381366 0.0660546i
\(414\) 3.44162e8 + 2.30117e8i 0.238375 + 0.159385i
\(415\) −1.38759e9 + 2.40337e9i −0.952997 + 1.65064i
\(416\) 3.13980e7 + 1.78067e8i 0.0213833 + 0.121271i
\(417\) −2.18273e9 1.10659e9i −1.47409 0.747329i
\(418\) 4.80684e8 1.74954e8i 0.321916 0.117168i
\(419\) −1.33918e9 + 4.87420e8i −0.889382 + 0.323709i −0.745990 0.665957i \(-0.768023\pi\)
−0.143392 + 0.989666i \(0.545801\pi\)
\(420\) 3.47160e7 + 6.37706e8i 0.0228643 + 0.419999i
\(421\) 2.90630e8 + 1.64824e9i 0.189825 + 1.07655i 0.919598 + 0.392861i \(0.128515\pi\)
−0.729773 + 0.683689i \(0.760374\pi\)
\(422\) 2.21090e8 3.82939e8i 0.143211 0.248048i
\(423\) 9.97774e7 2.26569e8i 0.0640975 0.145549i
\(424\) 1.22230e6 + 2.11709e6i 0.000778750 + 0.00134883i
\(425\) 7.55130e8 6.33629e8i 0.477156 0.400381i
\(426\) −7.01280e7 + 9.34562e7i −0.0439499 + 0.0585699i
\(427\) −6.13267e7 + 3.47801e8i −0.0381199 + 0.216189i
\(428\) 5.00479e8 + 4.19952e8i 0.308555 + 0.258908i
\(429\) −3.75645e8 4.01198e8i −0.229708 0.245334i
\(430\) −2.34514e8 8.53563e7i −0.142243 0.0517721i
\(431\) 1.45659e9 0.876330 0.438165 0.898895i \(-0.355629\pi\)
0.438165 + 0.898895i \(0.355629\pi\)
\(432\) 1.13341e9 + 9.73231e8i 0.676385 + 0.580795i
\(433\) 2.09919e9 1.24264 0.621318 0.783559i \(-0.286598\pi\)
0.621318 + 0.783559i \(0.286598\pi\)
\(434\) −6.76194e7 2.46114e7i −0.0397061 0.0144518i
\(435\) −1.39225e9 + 4.58706e9i −0.810972 + 2.67191i
\(436\) 2.24069e8 + 1.88017e8i 0.129473 + 0.108641i
\(437\) 5.45346e8 3.09281e9i 0.312599 1.77284i
\(438\) −2.20002e8 5.15389e8i −0.125103 0.293073i
\(439\) 4.17846e8 3.50615e8i 0.235717 0.197790i −0.517276 0.855819i \(-0.673054\pi\)
0.752993 + 0.658029i \(0.228609\pi\)
\(440\) −9.34844e8 1.61920e9i −0.523185 0.906182i
\(441\) 4.75969e8 + 1.63488e9i 0.264267 + 0.907716i
\(442\) −9.78860e6 + 1.69544e7i −0.00539191 + 0.00933907i
\(443\) −2.14897e7 1.21874e8i −0.0117440 0.0666037i 0.978373 0.206851i \(-0.0663214\pi\)
−0.990117 + 0.140247i \(0.955210\pi\)
\(444\) −5.37471e8 + 3.50587e8i −0.291417 + 0.190088i
\(445\) −2.52733e9 + 9.19874e8i −1.35957 + 0.494844i
\(446\) −3.17248e8 + 1.15469e8i −0.169327 + 0.0616300i
\(447\) 2.58711e8 1.68755e8i 0.137006 0.0893675i
\(448\) 6.07739e7 + 3.44666e8i 0.0319333 + 0.181103i
\(449\) 9.74253e8 1.68746e9i 0.507937 0.879773i −0.492021 0.870583i \(-0.663742\pi\)
0.999958 0.00918913i \(-0.00292503\pi\)
\(450\) 8.94942e8 + 2.19287e8i 0.462968 + 0.113441i
\(451\) 1.92107e8 + 3.32738e8i 0.0986108 + 0.170799i
\(452\) 1.94656e9 1.63336e9i 0.991478 0.831949i
\(453\) −4.05911e8 9.50907e8i −0.205157 0.480612i
\(454\) 4.68209e7 2.65535e8i 0.0234825 0.133176i
\(455\) 1.51504e8 + 1.27127e8i 0.0754020 + 0.0632698i
\(456\) −2.65326e8 + 8.74170e8i −0.131040 + 0.431737i
\(457\) 1.35018e9 + 4.91425e8i 0.661736 + 0.240852i 0.650986 0.759090i \(-0.274356\pi\)
0.0107502 + 0.999942i \(0.496578\pi\)
\(458\) −1.79485e8 −0.0872972
\(459\) 8.41356e7 + 5.11093e8i 0.0406102 + 0.246692i
\(460\) −5.63242e9 −2.69800
\(461\) 3.63269e8 + 1.32219e8i 0.172693 + 0.0628551i 0.426920 0.904290i \(-0.359599\pi\)
−0.254227 + 0.967145i \(0.581821\pi\)
\(462\) 9.65461e7 + 1.03114e8i 0.0455500 + 0.0486484i
\(463\) −2.20494e9 1.85017e9i −1.03244 0.866318i −0.0412988 0.999147i \(-0.513150\pi\)
−0.991139 + 0.132829i \(0.957594\pi\)
\(464\) −4.97823e8 + 2.82330e9i −0.231346 + 1.31203i
\(465\) 2.29824e9 3.06276e9i 1.06001 1.41263i
\(466\) 2.42287e8 2.03303e8i 0.110912 0.0930663i
\(467\) −1.38027e9 2.39070e9i −0.627126 1.08621i −0.988126 0.153648i \(-0.950898\pi\)
0.360999 0.932566i \(-0.382436\pi\)
\(468\) 4.78778e8 5.22832e7i 0.215910 0.0235777i
\(469\) −4.39295e7 + 7.60882e7i −0.0196631 + 0.0340575i
\(470\) −2.22219e7 1.26027e8i −0.00987276 0.0559912i
\(471\) −9.56297e7 1.75664e9i −0.0421716 0.774659i
\(472\) −2.63236e8 + 9.58099e7i −0.115225 + 0.0419386i
\(473\) 1.36517e9 4.96880e8i 0.593159 0.215892i
\(474\) −5.41710e8 2.74635e8i −0.233638 0.118449i
\(475\) −1.21373e9 6.88339e9i −0.519629 2.94696i
\(476\) −6.62136e7 + 1.14685e8i −0.0281399 + 0.0487398i
\(477\) 8.81585e6 4.34407e6i 0.00371920 0.00183266i
\(478\) −3.01631e8 5.22440e8i −0.126322 0.218796i
\(479\) −7.18403e8 + 6.02811e8i −0.298671 + 0.250615i −0.779791 0.626040i \(-0.784675\pi\)
0.481120 + 0.876655i \(0.340230\pi\)
\(480\) 2.45507e9 + 2.96399e8i 1.01326 + 0.122330i
\(481\) −3.45074e7 + 1.95701e8i −0.0141385 + 0.0801835i
\(482\) 3.84739e8 + 3.22834e8i 0.156495 + 0.131315i
\(483\) 8.44615e8 1.96797e8i 0.341070 0.0794702i
\(484\) 2.76030e9 + 1.00467e9i 1.10662 + 0.402776i
\(485\) 3.05890e9 1.21750
\(486\) −3.38873e8 + 3.45807e8i −0.133909 + 0.136649i
\(487\) −2.59206e9 −1.01694 −0.508468 0.861081i \(-0.669788\pi\)
−0.508468 + 0.861081i \(0.669788\pi\)
\(488\) 8.51385e8 + 3.09879e8i 0.331632 + 0.120704i
\(489\) 2.59117e9 6.03749e8i 1.00211 0.233494i
\(490\) 6.74256e8 + 5.65768e8i 0.258904 + 0.217246i
\(491\) 4.11572e8 2.33414e9i 0.156914 0.889901i −0.800102 0.599864i \(-0.795221\pi\)
0.957016 0.290037i \(-0.0936675\pi\)
\(492\) −3.34261e8 4.03550e7i −0.126534 0.0152764i
\(493\) −7.61445e8 + 6.38928e8i −0.286203 + 0.240153i
\(494\) 6.94072e7 + 1.20217e8i 0.0259036 + 0.0448663i
\(495\) −6.74257e9 + 3.32245e9i −2.49866 + 1.23123i
\(496\) 1.14500e9 1.98321e9i 0.421329 0.729763i
\(497\) 4.25011e7 + 2.41036e8i 0.0155293 + 0.0880713i
\(498\) −4.79756e8 2.43225e8i −0.174067 0.0882481i
\(499\) −4.26453e8 + 1.55216e8i −0.153645 + 0.0559224i −0.417698 0.908586i \(-0.637163\pi\)
0.264053 + 0.964508i \(0.414941\pi\)
\(500\) −7.05149e9 + 2.56653e9i −2.52282 + 0.918230i
\(501\) −1.88553e8 3.46357e9i −0.0669886 1.23053i
\(502\) −9.39634e7 5.32893e8i −0.0331509 0.188008i
\(503\) 7.34150e8 1.27159e9i 0.257215 0.445510i −0.708280 0.705932i \(-0.750528\pi\)
0.965495 + 0.260422i \(0.0838617\pi\)
\(504\) −2.50781e8 + 2.73856e7i −0.0872545 + 0.00952831i
\(505\) 2.65660e9 + 4.60136e9i 0.917922 + 1.58989i
\(506\) −9.54324e8 + 8.00773e8i −0.327468 + 0.274778i
\(507\) −1.67173e9 + 2.22784e9i −0.569691 + 0.759199i
\(508\) −6.72306e8 + 3.81284e9i −0.227533 + 1.29040i
\(509\) 4.24591e9 + 3.56274e9i 1.42711 + 1.19749i 0.947395 + 0.320066i \(0.103705\pi\)
0.479717 + 0.877423i \(0.340739\pi\)
\(510\) 1.83000e8 + 1.95448e8i 0.0610878 + 0.0652432i
\(511\) −1.10307e9 4.01483e8i −0.365703 0.133105i
\(512\) 2.49599e9 0.821859
\(513\) 3.43673e9 + 1.29533e9i 1.12392 + 0.423615i
\(514\) −5.54933e8 −0.180248
\(515\) 2.91042e8 + 1.05930e8i 0.0938922 + 0.0341740i
\(516\) −3.69745e8 + 1.21820e9i −0.118476 + 0.390342i
\(517\) 5.70664e8 + 4.78844e8i 0.181620 + 0.152397i
\(518\) 8.86889e6 5.02980e7i 0.00280359 0.0159000i
\(519\) 1.07465e9 + 2.51752e9i 0.337427 + 0.790474i
\(520\) 3.88673e8 3.26135e8i 0.121220 0.101715i
\(521\) −1.56199e9 2.70545e9i −0.483891 0.838124i 0.515938 0.856626i \(-0.327444\pi\)
−0.999829 + 0.0185022i \(0.994110\pi\)
\(522\) −9.02426e8 2.21121e8i −0.277693 0.0680431i
\(523\) 2.42528e9 4.20071e9i 0.741321 1.28401i −0.210573 0.977578i \(-0.567533\pi\)
0.951894 0.306428i \(-0.0991338\pi\)
\(524\) −3.02134e8 1.71349e9i −0.0917361 0.520261i
\(525\) 1.61662e9 1.05450e9i 0.487584 0.318046i
\(526\) −1.98428e8 + 7.22220e7i −0.0594502 + 0.0216381i
\(527\) 7.46109e8 2.71562e8i 0.222057 0.0808223i
\(528\) −3.76514e9 + 2.45597e9i −1.11317 + 0.726112i
\(529\) 7.36889e8 + 4.17911e9i 0.216425 + 1.22741i
\(530\) 2.54013e6 4.39963e6i 0.000741123 0.00128366i
\(531\) 3.14807e8 + 1.08131e9i 0.0912458 + 0.313415i
\(532\) 4.69495e8 + 8.13189e8i 0.135189 + 0.234154i
\(533\) −7.98706e7 + 6.70194e7i −0.0228477 + 0.0191715i
\(534\) −2.04655e8 4.79436e8i −0.0581606 0.136250i
\(535\) 4.80488e8 2.72498e9i 0.135658 0.769353i
\(536\) 1.72664e8 + 1.44882e8i 0.0484312 + 0.0406386i
\(537\) −1.07130e9 + 3.52961e9i −0.298539 + 0.983596i
\(538\) 2.13088e8 + 7.75576e7i 0.0589957 + 0.0214727i
\(539\) −5.12374e9 −1.40937
\(540\) 1.21754e9 6.47342e9i 0.332739 1.76911i
\(541\) 4.43727e9 1.20483 0.602415 0.798183i \(-0.294205\pi\)
0.602415 + 0.798183i \(0.294205\pi\)
\(542\) 8.93972e8 + 3.25379e8i 0.241172 + 0.0877793i
\(543\) −6.83186e8 7.29658e8i −0.183121 0.195578i
\(544\) 3.92802e8 + 3.29600e8i 0.104611 + 0.0877792i
\(545\) 2.15119e8 1.22000e9i 0.0569235 0.322829i
\(546\) −2.30072e7 + 3.06606e7i −0.00604909 + 0.00806133i
\(547\) 1.32077e9 1.10825e9i 0.345041 0.289524i −0.453754 0.891127i \(-0.649916\pi\)
0.798795 + 0.601603i \(0.205471\pi\)
\(548\) −1.46349e9 2.53485e9i −0.379891 0.657991i
\(549\) 1.46804e9 3.33356e9i 0.378648 0.859814i
\(550\) −1.38631e9 + 2.40116e9i −0.355297 + 0.615392i
\(551\) 1.22388e9 + 6.94096e9i 0.311679 + 1.76762i
\(552\) −1.20939e8 2.22156e9i −0.0306041 0.562174i
\(553\) −1.19552e9 + 4.35134e8i −0.300621 + 0.109417i
\(554\) 1.37245e9 4.99530e8i 0.342935 0.124818i
\(555\) 2.42406e9 + 1.22895e9i 0.601892 + 0.305146i
\(556\) 1.12055e9 + 6.35497e9i 0.276484 + 1.56802i
\(557\) −2.42582e9 + 4.20165e9i −0.594793 + 1.03021i 0.398783 + 0.917045i \(0.369433\pi\)
−0.993576 + 0.113167i \(0.963901\pi\)
\(558\) 6.16965e8 + 4.12522e8i 0.150328 + 0.100514i
\(559\) 1.97120e8 + 3.41422e8i 0.0477297 + 0.0826703i
\(560\) 1.23917e9 1.03979e9i 0.298177 0.250200i
\(561\) −1.54739e9 1.86815e8i −0.370023 0.0446726i
\(562\) −2.54214e8 + 1.44172e9i −0.0604120 + 0.342613i
\(563\) −4.95851e9 4.16068e9i −1.17104 0.982620i −0.171044 0.985263i \(-0.554714\pi\)
−0.999997 + 0.00264387i \(0.999158\pi\)
\(564\) −6.35772e8 + 1.48137e8i −0.149219 + 0.0347685i
\(565\) −1.01130e10 3.68083e9i −2.35890 0.858571i
\(566\) −1.27060e9 −0.294545
\(567\) 4.36054e7 + 1.01327e9i 0.0100462 + 0.233445i
\(568\) 6.27901e8 0.143771
\(569\) −5.27390e9 1.91954e9i −1.20016 0.436822i −0.336879 0.941548i \(-0.609371\pi\)
−0.863280 + 0.504726i \(0.831594\pi\)
\(570\) 1.84897e9 4.30814e8i 0.418184 0.0974378i
\(571\) −7.88028e8 6.61234e8i −0.177139 0.148638i 0.549907 0.835226i \(-0.314663\pi\)
−0.727047 + 0.686588i \(0.759108\pi\)
\(572\) −2.51659e8 + 1.42723e9i −0.0562247 + 0.318866i
\(573\) 3.05976e9 + 3.69402e8i 0.679432 + 0.0820273i
\(574\) 2.05279e7 1.72250e7i 0.00453057 0.00380160i
\(575\) 8.51118e9 + 1.47418e10i 1.86703 + 3.23380i
\(576\) 2.37209e8 3.60186e9i 0.0517193 0.785322i
\(577\) 2.69489e9 4.66769e9i 0.584018 1.01155i −0.410979 0.911645i \(-0.634813\pi\)
0.994997 0.0999040i \(-0.0318536\pi\)
\(578\) −1.44595e8 8.20040e8i −0.0311463 0.176639i
\(579\) −3.21955e9 1.63224e9i −0.689319 0.349469i
\(580\) 1.18781e10 4.32327e9i 2.52783 0.920056i
\(581\) −1.05879e9 + 3.85368e8i −0.223972 + 0.0815191i
\(582\) 3.22281e7 + 5.92005e8i 0.00677648 + 0.124479i
\(583\) 5.13537e6 + 2.91241e7i 0.00107333 + 0.00608714i
\(584\) −1.50573e9 + 2.60800e9i −0.312825 + 0.541829i
\(585\) −1.20564e9 1.64537e9i −0.248985 0.339795i
\(586\) −1.59860e8 2.76886e8i −0.0328170 0.0568407i
\(587\) −2.16440e9 + 1.81615e9i −0.441677 + 0.370611i −0.836337 0.548216i \(-0.815307\pi\)
0.394659 + 0.918828i \(0.370863\pi\)
\(588\) 2.69485e9 3.59130e9i 0.546657 0.728503i
\(589\) 9.77621e8 5.54436e9i 0.197136 1.11802i
\(590\) 4.45954e8 + 3.74200e8i 0.0893940 + 0.0750104i
\(591\) −4.18621e9 4.47097e9i −0.834189 0.890934i
\(592\) 1.52734e9 + 5.55908e8i 0.302559 + 0.110123i
\(593\) 2.83505e9 0.558303 0.279151 0.960247i \(-0.409947\pi\)
0.279151 + 0.960247i \(0.409947\pi\)
\(594\) −7.14048e8 1.26992e9i −0.139790 0.248613i
\(595\) 5.60864e8 0.109156
\(596\) −7.65370e8 2.78572e8i −0.148084 0.0538983i
\(597\) 5.70668e8 1.88018e9i 0.109767 0.361651i
\(598\) −2.58974e8 2.17305e8i −0.0495225 0.0415543i
\(599\) 5.39501e8 3.05966e9i 0.102565 0.581674i −0.889600 0.456740i \(-0.849017\pi\)
0.992165 0.124934i \(-0.0398718\pi\)
\(600\) −1.94399e9 4.55408e9i −0.367421 0.860739i
\(601\) −1.26340e9 + 1.06012e9i −0.237400 + 0.199202i −0.753724 0.657191i \(-0.771744\pi\)
0.516324 + 0.856393i \(0.327300\pi\)
\(602\) −5.06627e7 8.77503e7i −0.00946456 0.0163931i
\(603\) 6.26828e8 6.54383e8i 0.116423 0.121541i
\(604\) −1.36316e9 + 2.36106e9i −0.251720 + 0.435991i
\(605\) −2.16033e9 1.22519e10i −0.396622 2.24936i
\(606\) −8.62535e8 + 5.62624e8i −0.157443 + 0.102698i
\(607\) −3.26204e9 + 1.18729e9i −0.592010 + 0.215474i −0.620613 0.784117i \(-0.713116\pi\)
0.0286030 + 0.999591i \(0.490894\pi\)
\(608\) 3.41656e9 1.24353e9i 0.616491 0.224385i
\(609\) −1.63014e9 + 1.06332e9i −0.292458 + 0.190767i
\(610\) −3.26955e8 1.85425e9i −0.0583221 0.330761i
\(611\) −1.01078e8 + 1.75073e8i −0.0179272 + 0.0310509i
\(612\) 9.44798e8 9.86331e8i 0.166613 0.173937i
\(613\) −1.23668e9 2.14199e9i −0.216842 0.375582i 0.736999 0.675894i \(-0.236242\pi\)
−0.953841 + 0.300312i \(0.902909\pi\)
\(614\) −2.94142e8 + 2.46815e8i −0.0512824 + 0.0430310i
\(615\) 5.59825e8 + 1.31147e9i 0.0970486 + 0.227351i
\(616\) 1.31818e8 7.47576e8i 0.0227217 0.128861i
\(617\) 2.69618e8 + 2.26236e8i 0.0462116 + 0.0387761i 0.665601 0.746308i \(-0.268175\pi\)
−0.619389 + 0.785084i \(0.712620\pi\)
\(618\) −1.74349e7 + 5.74428e7i −0.00297139 + 0.00978985i
\(619\) 7.55408e9 + 2.74946e9i 1.28016 + 0.465940i 0.890485 0.455013i \(-0.150365\pi\)
0.389675 + 0.920953i \(0.372587\pi\)
\(620\) −1.00970e10 −1.70146
\(621\) −8.94397e9 1.01763e8i −1.49868 0.0170518i
\(622\) 5.55390e8 0.0925405
\(623\) −1.02612e9 3.73476e8i −0.170016 0.0618806i
\(624\) −8.33773e8 8.90489e8i −0.137373 0.146718i
\(625\) 1.26974e10 + 1.06544e10i 2.08034 + 1.74561i
\(626\) −6.78912e7 + 3.85030e8i −0.0110612 + 0.0627313i
\(627\) −6.63313e9 + 8.83965e9i −1.07469 + 1.43218i
\(628\) −3.55362e9 + 2.98184e9i −0.572548 + 0.480425i
\(629\) 2.81774e8 + 4.88046e8i 0.0451464 + 0.0781958i
\(630\) 3.09867e8 + 4.22883e8i 0.0493723 + 0.0673796i
\(631\) 8.86696e8 1.53580e9i 0.140499 0.243351i −0.787186 0.616716i \(-0.788463\pi\)
0.927685 + 0.373365i \(0.121796\pi\)
\(632\) 5.66765e8 + 3.21428e9i 0.0893086 + 0.506494i
\(633\) 5.19299e8 + 9.53912e9i 0.0813775 + 1.49484i
\(634\) 1.57261e9 5.72382e8i 0.245080 0.0892018i
\(635\) 1.54086e10 5.60827e9i 2.38811 0.869202i
\(636\) −2.31145e7 1.17185e7i −0.00356275 0.00180623i
\(637\) −2.41445e8 1.36930e9i −0.0370109 0.209899i
\(638\) 1.39790e9 2.42124e9i 0.213111 0.369118i
\(639\) 1.65888e8 2.51889e9i 0.0251514 0.381906i
\(640\) −4.31719e9 7.47759e9i −0.650985 1.12754i
\(641\) −7.85616e9 + 6.59210e9i −1.17817 + 0.988600i −0.178178 + 0.983998i \(0.557020\pi\)
−0.999989 + 0.00460150i \(0.998535\pi\)
\(642\) 5.32442e8 + 6.42813e7i 0.0794144 + 0.00958764i
\(643\) −2.07032e9 + 1.17414e10i −0.307114 + 1.74173i 0.306270 + 0.951945i \(0.400919\pi\)
−0.613384 + 0.789785i \(0.710192\pi\)
\(644\) −1.75179e9 1.46993e9i −0.258454 0.216868i
\(645\) 5.25116e9 1.22353e9i 0.770542 0.179538i
\(646\) 3.69921e8 + 1.34640e8i 0.0539877 + 0.0196499i
\(647\) 1.19279e10 1.73140 0.865700 0.500564i \(-0.166874\pi\)
0.865700 + 0.500564i \(0.166874\pi\)
\(648\) 2.57941e9 + 3.41227e8i 0.372399 + 0.0492642i
\(649\) −3.38885e9 −0.486626
\(650\) −7.07029e8 2.57338e8i −0.100981 0.0367542i
\(651\) 1.51411e9 3.52791e8i 0.215092 0.0501169i
\(652\) −5.37427e9 4.50955e9i −0.759370 0.637187i
\(653\) −2.45112e8 + 1.39010e9i −0.0344484 + 0.195367i −0.997175 0.0751085i \(-0.976070\pi\)
0.962727 + 0.270475i \(0.0871808\pi\)
\(654\) 2.38380e8 + 2.87794e7i 0.0333232 + 0.00402309i
\(655\) −5.64500e9 + 4.73672e9i −0.784909 + 0.658617i
\(656\) 4.26395e8 + 7.38538e8i 0.0589724 + 0.102143i
\(657\) 1.00645e10 + 6.72941e9i 1.38456 + 0.925759i
\(658\) 2.59786e7 4.49962e7i 0.00355488 0.00615722i
\(659\) −7.46756e8 4.23506e9i −0.101644 0.576449i −0.992508 0.122180i \(-0.961012\pi\)
0.890864 0.454269i \(-0.150100\pi\)
\(660\) 1.76785e10 + 8.96260e9i 2.39355 + 1.21347i
\(661\) −1.11612e10 + 4.06234e9i −1.50316 + 0.547105i −0.956876 0.290495i \(-0.906180\pi\)
−0.546283 + 0.837601i \(0.683958\pi\)
\(662\) −1.56609e9 + 5.70010e8i −0.209804 + 0.0763624i
\(663\) −2.29916e7 4.22338e8i −0.00306388 0.0562811i
\(664\) 5.01944e8 + 2.84667e9i 0.0665376 + 0.377354i
\(665\) 1.98843e9 3.44407e9i 0.262202 0.454147i
\(666\) −2.12304e8 + 4.82089e8i −0.0278483 + 0.0632365i
\(667\) −8.58235e9 1.48651e10i −1.11987 1.93966i
\(668\) −7.00665e9 + 5.87928e9i −0.909480 + 0.763144i
\(669\) 4.37782e9 5.83410e9i 0.565283 0.753326i
\(670\) 8.13383e7 4.61293e8i 0.0104480 0.0592536i
\(671\) 8.39629e9 + 7.04532e9i 1.07290 + 0.900269i
\(672\) 6.86223e8 + 7.32902e8i 0.0872314 + 0.0931652i
\(673\) −6.24055e9 2.27137e9i −0.789169 0.287234i −0.0841785 0.996451i \(-0.526827\pi\)
−0.704991 + 0.709217i \(0.749049\pi\)
\(674\) 6.69912e8 0.0842769
\(675\) −1.87828e10 + 6.59535e9i −2.35070 + 0.825420i
\(676\) 7.34453e9 0.914430
\(677\) −1.24292e10 4.52386e9i −1.53951 0.560336i −0.573583 0.819147i \(-0.694447\pi\)
−0.965928 + 0.258811i \(0.916669\pi\)
\(678\) 6.05821e8 1.99600e9i 0.0746518 0.245956i
\(679\) 9.51380e8 + 7.98303e8i 0.116630 + 0.0978641i
\(680\) 2.49856e8 1.41700e9i 0.0304725 0.172818i
\(681\) 2.28700e9 + 5.35763e9i 0.277492 + 0.650067i
\(682\) −1.71078e9 + 1.43551e9i −0.206514 + 0.173285i
\(683\) 2.37902e9 + 4.12059e9i 0.285710 + 0.494865i 0.972781 0.231726i \(-0.0744371\pi\)
−0.687071 + 0.726590i \(0.741104\pi\)
\(684\) −2.70712e9 9.29851e9i −0.323452 1.11101i
\(685\) −6.19828e9 + 1.07357e10i −0.736808 + 1.27619i
\(686\) 1.27693e8 + 7.24185e8i 0.0151020 + 0.0856475i
\(687\) 3.24788e9 2.11856e9i 0.382165 0.249283i
\(688\) 3.03009e9 1.10286e9i 0.354729 0.129111i
\(689\) −7.54134e6 + 2.74482e6i −0.000878377 + 0.000319703i
\(690\) −3.87255e9 + 2.52603e9i −0.448771 + 0.292729i
\(691\) −1.42200e9 8.06458e9i −0.163956 0.929841i −0.950134 0.311841i \(-0.899054\pi\)
0.786178 0.618000i \(-0.212057\pi\)
\(692\) 3.60896e9 6.25090e9i 0.414010 0.717086i
\(693\) −2.96415e9 7.26306e8i −0.338325 0.0828998i
\(694\) −9.26839e8 1.60533e9i −0.105256 0.182308i
\(695\) 2.09361e10 1.75675e10i 2.36564 1.98501i
\(696\) 1.96024e9 + 4.59217e9i 0.220383 + 0.516280i
\(697\) −5.13443e7 + 2.91188e8i −0.00574351 + 0.0325731i
\(698\) −1.20709e9 1.01287e9i −0.134352 0.112735i
\(699\) −1.98461e9 + 6.53870e9i −0.219789 + 0.724138i
\(700\) −4.78260e9 1.74072e9i −0.527012 0.191817i
\(701\) −1.14813e10 −1.25886 −0.629432 0.777055i \(-0.716712\pi\)
−0.629432 + 0.777055i \(0.716712\pi\)
\(702\) 3.05734e8 2.50669e8i 0.0333552 0.0273477i
\(703\) 3.99589e9 0.433781
\(704\) 1.02067e10 + 3.71495e9i 1.10251 + 0.401281i
\(705\) 1.88967e9 + 2.01822e9i 0.203107 + 0.216923i
\(706\) 2.21821e9 + 1.86130e9i 0.237239 + 0.199067i
\(707\) −3.74593e8 + 2.12442e9i −0.0398650 + 0.226086i
\(708\) 1.78238e9 2.37529e9i 0.188749 0.251536i
\(709\) 1.08138e10 9.07382e9i 1.13950 0.956155i 0.140079 0.990140i \(-0.455264\pi\)
0.999422 + 0.0339851i \(0.0108199\pi\)
\(710\) −6.52437e8 1.13005e9i −0.0684124 0.118494i
\(711\) 1.30442e10 1.42444e9i 1.36105 0.148628i
\(712\) −1.40069e9 + 2.42607e9i −0.145433 + 0.251897i
\(713\) 2.38089e9 + 1.35027e10i 0.245995 + 1.39510i
\(714\) 5.90917e6 + 1.08547e8i 0.000607551 + 0.0111602i
\(715\) 5.76779e9 2.09930e9i 0.590117 0.214785i
\(716\) 9.13984e9 3.32663e9i 0.930557 0.338695i
\(717\) 1.16248e10 + 5.89350e9i 1.17779 + 0.597113i
\(718\) −3.05315e7 1.73153e8i −0.00307832 0.0174580i
\(719\) −1.83808e9 + 3.18365e9i −0.184422 + 0.319429i −0.943382 0.331709i \(-0.892375\pi\)
0.758959 + 0.651138i \(0.225708\pi\)
\(720\) −1.49657e10 + 7.37443e9i −1.49428 + 0.736316i
\(721\) 6.28743e7 + 1.08902e8i 0.00624741 + 0.0108208i
\(722\) 6.56077e8 5.50514e8i 0.0648746 0.0544362i
\(723\) −1.07726e10 1.30057e9i −1.06008 0.127982i
\(724\) −4.57693e8 + 2.59571e9i −0.0448218 + 0.254197i
\(725\) −2.92644e10 2.45557e10i −2.85204 2.39315i
\(726\) 2.34840e9 5.47184e8i 0.227769 0.0530707i
\(727\) −1.18793e10 4.32370e9i −1.14662 0.417335i −0.302319 0.953207i \(-0.597761\pi\)
−0.844299 + 0.535872i \(0.819983\pi\)
\(728\) 2.05999e8 0.0197881
\(729\) 2.05034e9 1.02574e10i 0.196010 0.980602i
\(730\) 6.25826e9 0.595421
\(731\) 1.05059e9 + 3.82385e8i 0.0994773 + 0.0362068i
\(732\) −9.35424e9 + 2.17956e9i −0.881495 + 0.205390i
\(733\) 7.60362e8 + 6.38019e8i 0.0713110 + 0.0598370i 0.677746 0.735296i \(-0.262957\pi\)
−0.606435 + 0.795133i \(0.707401\pi\)
\(734\) −3.67978e8 + 2.08691e9i −0.0343468 + 0.194790i
\(735\) −1.88791e10 2.27925e9i −1.75378 0.211732i
\(736\) −6.78307e9 + 5.69167e9i −0.627125 + 0.526220i
\(737\) 1.36336e9 + 2.36141e9i 0.125451 + 0.217288i
\(738\) −2.47918e8 + 1.22163e8i −0.0227044 + 0.0111878i
\(739\) 6.20181e9 1.07419e10i 0.565279 0.979092i −0.431745 0.901996i \(-0.642102\pi\)
0.997024 0.0770962i \(-0.0245649\pi\)
\(740\) −1.24445e9 7.05761e9i −0.112893 0.640246i
\(741\) −2.67494e9 1.35613e9i −0.241518 0.122444i
\(742\) 1.93823e6 705459.i 0.000174178 6.33954e-5i
\(743\) −6.92470e8 + 2.52038e8i −0.0619356 + 0.0225427i −0.372802 0.927911i \(-0.621603\pi\)
0.310867 + 0.950454i \(0.399381\pi\)
\(744\) −2.16803e8 3.98250e9i −0.0193001 0.354528i
\(745\) 5.99013e8 + 3.39717e9i 0.0530749 + 0.301003i
\(746\) 6.42962e8 1.11364e9i 0.0567021 0.0982110i
\(747\) 1.15523e10 1.26153e9i 1.01402 0.110733i
\(748\) 2.05495e9 + 3.55928e9i 0.179534 + 0.310962i
\(749\) 8.60598e8 7.22128e8i 0.0748366 0.0627954i
\(750\) −3.69718e9 + 4.92706e9i −0.320005 + 0.426455i
\(751\) 1.96234e9 1.11290e10i 0.169058 0.958773i −0.775724 0.631072i \(-0.782615\pi\)
0.944782 0.327701i \(-0.106274\pi\)
\(752\) 1.26663e9 + 1.06283e9i 0.108615 + 0.0911385i
\(753\) 7.99033e9 + 8.53386e9i 0.681997 + 0.728389i
\(754\) 7.12942e8 + 2.59490e8i 0.0605696 + 0.0220455i
\(755\) 1.15467e10 0.976434
\(756\)