Properties

Label 27.8.e.a.4.1
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 4.1
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-20.1276 - 7.32584i) q^{2} +(46.7116 - 2.24141i) q^{3} +(253.398 + 212.626i) q^{4} +(26.6624 - 151.210i) q^{5} +(-956.612 - 297.088i) q^{6} +(-1123.74 + 942.932i) q^{7} +(-2171.79 - 3761.65i) q^{8} +(2176.95 - 209.400i) q^{9} +O(q^{10})\) \(q+(-20.1276 - 7.32584i) q^{2} +(46.7116 - 2.24141i) q^{3} +(253.398 + 212.626i) q^{4} +(26.6624 - 151.210i) q^{5} +(-956.612 - 297.088i) q^{6} +(-1123.74 + 942.932i) q^{7} +(-2171.79 - 3761.65i) q^{8} +(2176.95 - 209.400i) q^{9} +(-1644.39 + 2848.17i) q^{10} +(679.157 + 3851.69i) q^{11} +(12313.2 + 9364.14i) q^{12} +(-3148.81 + 1146.07i) q^{13} +(29526.0 - 10746.6i) q^{14} +(906.521 - 7123.04i) q^{15} +(8803.20 + 49925.5i) q^{16} +(-6063.94 + 10503.1i) q^{17} +(-45350.8 - 11733.3i) q^{18} +(16058.2 + 27813.5i) q^{19} +(38907.5 - 32647.2i) q^{20} +(-50378.4 + 46564.7i) q^{21} +(14547.1 - 82500.6i) q^{22} +(29951.3 + 25132.1i) q^{23} +(-109879. - 170845. i) q^{24} +(51259.8 + 18657.1i) q^{25} +71774.0 q^{26} +(101220. - 14660.9i) q^{27} -485246. q^{28} +(-144854. - 52722.5i) q^{29} +(-70428.3 + 136728. i) q^{30} +(192093. + 161185. i) q^{31} +(92014.2 - 521839. i) q^{32} +(40357.8 + 178396. i) q^{33} +(198996. - 166978. i) q^{34} +(112619. + 195062. i) q^{35} +(596159. + 409815. i) q^{36} +(-218330. + 378158. i) q^{37} +(-119454. - 677459. i) q^{38} +(-144517. + 60592.8i) q^{39} +(-626704. + 228102. i) q^{40} +(70665.2 - 25720.0i) q^{41} +(1.35512e6 - 568171. i) q^{42} +(-80607.5 - 457148. i) q^{43} +(-646873. + 1.12042e6i) q^{44} +(26379.4 - 334760. i) q^{45} +(-418733. - 725267. i) q^{46} +(-504663. + 423462. i) q^{47} +(523116. + 2.31237e6i) q^{48} +(230670. - 1.30820e6i) q^{49} +(-895058. - 751043. i) q^{50} +(-259715. + 504207. i) q^{51} +(-1.04159e6 - 379107. i) q^{52} -424944. q^{53} +(-2.14471e6 - 446431. i) q^{54} +600523. q^{55} +(5.98751e6 + 2.17927e6i) q^{56} +(812444. + 1.26322e6i) q^{57} +(2.52932e6 + 2.12235e6i) q^{58} +(181202. - 1.02765e6i) q^{59} +(1.74425e6 - 1.61221e6i) q^{60} +(1.35365e6 - 1.13585e6i) q^{61} +(-2.68556e6 - 4.65152e6i) q^{62} +(-2.24888e6 + 2.28803e6i) q^{63} +(-2.43041e6 + 4.20960e6i) q^{64} +(89343.1 + 506690. i) q^{65} +(494600. - 3.88634e6i) q^{66} +(-2.16437e6 + 787765. i) q^{67} +(-3.76981e6 + 1.37210e6i) q^{68} +(1.45540e6 + 1.10683e6i) q^{69} +(-837758. - 4.75116e6i) q^{70} +(-1.66456e6 + 2.88310e6i) q^{71} +(-5.51557e6 - 7.73415e6i) q^{72} +(-96767.0 - 167605. i) q^{73} +(7.16477e6 - 6.01196e6i) q^{74} +(2.43625e6 + 756607. i) q^{75} +(-1.84478e6 + 1.04623e7i) q^{76} +(-4.39508e6 - 3.68791e6i) q^{77} +(3.35268e6 - 160875. i) q^{78} +(561233. + 204272. i) q^{79} +7.78395e6 q^{80} +(4.69527e6 - 911709. i) q^{81} -1.61074e6 q^{82} +(341118. + 124157. i) q^{83} +(-2.26666e7 + 1.08764e6i) q^{84} +(1.42649e6 + 1.19697e6i) q^{85} +(-1.72656e6 + 9.79180e6i) q^{86} +(-6.88454e6 - 2.13808e6i) q^{87} +(1.30137e7 - 1.09198e7i) q^{88} +(-2.76656e6 - 4.79183e6i) q^{89} +(-2.98336e6 + 6.54467e6i) q^{90} +(2.45779e6 - 4.25701e6i) q^{91} +(2.24585e6 + 1.27369e7i) q^{92} +(9.33428e6 + 7.09867e6i) q^{93} +(1.32599e7 - 4.82620e6i) q^{94} +(4.63384e6 - 1.68658e6i) q^{95} +(3.12848e6 - 2.45822e7i) q^{96} +(289042. + 1.63924e6i) q^{97} +(-1.42265e7 + 2.46410e7i) q^{98} +(2.28504e6 + 8.24273e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −20.1276 7.32584i −1.77904 0.647519i −0.999783 0.0208191i \(-0.993373\pi\)
−0.779261 0.626700i \(-0.784405\pi\)
\(3\) 46.7116 2.24141i 0.998851 0.0479289i
\(4\) 253.398 + 212.626i 1.97967 + 1.66114i
\(5\) 26.6624 151.210i 0.0953904 0.540986i −0.899237 0.437463i \(-0.855877\pi\)
0.994627 0.103523i \(-0.0330117\pi\)
\(6\) −956.612 297.088i −1.80803 0.561507i
\(7\) −1123.74 + 942.932i −1.23829 + 1.03905i −0.240639 + 0.970615i \(0.577357\pi\)
−0.997655 + 0.0684374i \(0.978199\pi\)
\(8\) −2171.79 3761.65i −1.49969 2.59754i
\(9\) 2176.95 209.400i 0.995406 0.0957477i
\(10\) −1644.39 + 2848.17i −0.520003 + 0.900671i
\(11\) 679.157 + 3851.69i 0.153849 + 0.872523i 0.959830 + 0.280581i \(0.0905273\pi\)
−0.805981 + 0.591942i \(0.798362\pi\)
\(12\) 12313.2 + 9364.14i 2.05701 + 1.56435i
\(13\) −3148.81 + 1146.07i −0.397508 + 0.144681i −0.533036 0.846093i \(-0.678949\pi\)
0.135529 + 0.990773i \(0.456727\pi\)
\(14\) 29526.0 10746.6i 2.87579 1.04670i
\(15\) 906.521 7123.04i 0.0693519 0.544936i
\(16\) 8803.20 + 49925.5i 0.537305 + 3.04721i
\(17\) −6063.94 + 10503.1i −0.299353 + 0.518495i −0.975988 0.217824i \(-0.930104\pi\)
0.676635 + 0.736319i \(0.263438\pi\)
\(18\) −45350.8 11733.3i −1.83287 0.474205i
\(19\) 16058.2 + 27813.5i 0.537103 + 0.930290i 0.999058 + 0.0433871i \(0.0138149\pi\)
−0.461955 + 0.886903i \(0.652852\pi\)
\(20\) 38907.5 32647.2i 1.08750 0.912518i
\(21\) −50378.4 + 46564.7i −1.18707 + 1.09721i
\(22\) 14547.1 82500.6i 0.291271 1.65188i
\(23\) 29951.3 + 25132.1i 0.513296 + 0.430707i 0.862287 0.506419i \(-0.169031\pi\)
−0.348991 + 0.937126i \(0.613476\pi\)
\(24\) −109879. 170845.i −1.62247 2.52268i
\(25\) 51259.8 + 18657.1i 0.656126 + 0.238810i
\(26\) 71774.0 0.800867
\(27\) 101220. 14660.9i 0.989673 0.143346i
\(28\) −485246. −4.17743
\(29\) −144854. 52722.5i −1.10290 0.401424i −0.274517 0.961582i \(-0.588518\pi\)
−0.828386 + 0.560158i \(0.810740\pi\)
\(30\) −70428.3 + 136728.i −0.476237 + 0.924559i
\(31\) 192093. + 161185.i 1.15810 + 0.971762i 0.999878 0.0156414i \(-0.00497901\pi\)
0.158223 + 0.987403i \(0.449423\pi\)
\(32\) 92014.2 521839.i 0.496398 2.81521i
\(33\) 40357.8 + 178396.i 0.195492 + 0.864146i
\(34\) 198996. 166978.i 0.868298 0.728588i
\(35\) 112619. + 195062.i 0.443991 + 0.769015i
\(36\) 596159. + 409815.i 2.12963 + 1.46396i
\(37\) −218330. + 378158.i −0.708609 + 1.22735i 0.256764 + 0.966474i \(0.417344\pi\)
−0.965373 + 0.260873i \(0.915990\pi\)
\(38\) −119454. 677459.i −0.353150 2.00281i
\(39\) −144517. + 60592.8i −0.390116 + 0.163567i
\(40\) −626704. + 228102.i −1.54829 + 0.563532i
\(41\) 70665.2 25720.0i 0.160126 0.0582811i −0.260713 0.965416i \(-0.583958\pi\)
0.420840 + 0.907135i \(0.361736\pi\)
\(42\) 1.35512e6 568171.i 2.82231 1.18333i
\(43\) −80607.5 457148.i −0.154609 0.876833i −0.959142 0.282925i \(-0.908695\pi\)
0.804533 0.593908i \(-0.202416\pi\)
\(44\) −646873. + 1.12042e6i −1.14481 + 1.98287i
\(45\) 26379.4 334760.i 0.0431540 0.547634i
\(46\) −418733. 725267.i −0.634286 1.09861i
\(47\) −504663. + 423462.i −0.709021 + 0.594939i −0.924324 0.381608i \(-0.875370\pi\)
0.215304 + 0.976547i \(0.430926\pi\)
\(48\) 523116. + 2.31237e6i 0.682737 + 3.01795i
\(49\) 230670. 1.30820e6i 0.280095 1.58850i
\(50\) −895058. 751043.i −1.01264 0.849708i
\(51\) −259715. + 504207.i −0.274158 + 0.532247i
\(52\) −1.04159e6 379107.i −1.02727 0.373896i
\(53\) −424944. −0.392072 −0.196036 0.980597i \(-0.562807\pi\)
−0.196036 + 0.980597i \(0.562807\pi\)
\(54\) −2.14471e6 446431.i −1.85349 0.385812i
\(55\) 600523. 0.486699
\(56\) 5.98751e6 + 2.17927e6i 4.55604 + 1.65826i
\(57\) 812444. + 1.26322e6i 0.581074 + 0.903479i
\(58\) 2.52932e6 + 2.12235e6i 1.70218 + 1.42830i
\(59\) 181202. 1.02765e6i 0.114863 0.651422i −0.871955 0.489587i \(-0.837148\pi\)
0.986818 0.161835i \(-0.0517412\pi\)
\(60\) 1.74425e6 1.61221e6i 1.04251 0.963592i
\(61\) 1.35365e6 1.13585e6i 0.763575 0.640715i −0.175480 0.984483i \(-0.556148\pi\)
0.939055 + 0.343768i \(0.111703\pi\)
\(62\) −2.68556e6 4.65152e6i −1.43108 2.47870i
\(63\) −2.24888e6 + 2.28803e6i −1.13312 + 1.15284i
\(64\) −2.43041e6 + 4.20960e6i −1.15891 + 2.00729i
\(65\) 89343.1 + 506690.i 0.0403519 + 0.228847i
\(66\) 494600. 3.88634e6i 0.211763 1.66394i
\(67\) −2.16437e6 + 787765.i −0.879163 + 0.319989i −0.741872 0.670542i \(-0.766062\pi\)
−0.137291 + 0.990531i \(0.543839\pi\)
\(68\) −3.76981e6 + 1.37210e6i −1.45391 + 0.529182i
\(69\) 1.45540e6 + 1.10683e6i 0.533349 + 0.405610i
\(70\) −837758. 4.75116e6i −0.291928 1.65561i
\(71\) −1.66456e6 + 2.88310e6i −0.551943 + 0.955994i 0.446191 + 0.894938i \(0.352780\pi\)
−0.998134 + 0.0610561i \(0.980553\pi\)
\(72\) −5.51557e6 7.73415e6i −1.74151 2.44202i
\(73\) −96767.0 167605.i −0.0291137 0.0504264i 0.851101 0.525001i \(-0.175935\pi\)
−0.880215 + 0.474575i \(0.842602\pi\)
\(74\) 7.16477e6 6.01196e6i 2.05538 1.72467i
\(75\) 2.43625e6 + 756607.i 0.666818 + 0.207088i
\(76\) −1.84478e6 + 1.04623e7i −0.482056 + 2.73388i
\(77\) −4.39508e6 3.68791e6i −1.09711 0.920583i
\(78\) 3.35268e6 160875.i 0.799947 0.0383847i
\(79\) 561233. + 204272.i 0.128070 + 0.0466137i 0.405260 0.914201i \(-0.367181\pi\)
−0.277190 + 0.960815i \(0.589403\pi\)
\(80\) 7.78395e6 1.69975
\(81\) 4.69527e6 911709.i 0.981665 0.190616i
\(82\) −1.61074e6 −0.322609
\(83\) 341118. + 124157.i 0.0654835 + 0.0238340i 0.374554 0.927205i \(-0.377796\pi\)
−0.309071 + 0.951039i \(0.600018\pi\)
\(84\) −2.26666e7 + 1.08764e6i −4.17263 + 0.200220i
\(85\) 1.42649e6 + 1.19697e6i 0.251943 + 0.211405i
\(86\) −1.72656e6 + 9.79180e6i −0.292709 + 1.66004i
\(87\) −6.88454e6 2.13808e6i −1.12088 0.348102i
\(88\) 1.30137e7 1.09198e7i 2.03569 1.70815i
\(89\) −2.76656e6 4.79183e6i −0.415983 0.720503i 0.579548 0.814938i \(-0.303229\pi\)
−0.995531 + 0.0944345i \(0.969896\pi\)
\(90\) −2.98336e6 + 6.54467e6i −0.431376 + 0.946322i
\(91\) 2.45779e6 4.25701e6i 0.341900 0.592189i
\(92\) 2.24585e6 + 1.27369e7i 0.300693 + 1.70532i
\(93\) 9.33428e6 + 7.09867e6i 1.20335 + 0.915139i
\(94\) 1.32599e7 4.82620e6i 1.64661 0.599318i
\(95\) 4.63384e6 1.68658e6i 0.554509 0.201825i
\(96\) 3.12848e6 2.45822e7i 0.360897 2.83577i
\(97\) 289042. + 1.63924e6i 0.0321558 + 0.182365i 0.996655 0.0817199i \(-0.0260413\pi\)
−0.964500 + 0.264085i \(0.914930\pi\)
\(98\) −1.42265e7 + 2.46410e7i −1.52688 + 2.64464i
\(99\) 2.28504e6 + 8.24273e6i 0.236685 + 0.853784i
\(100\) 9.02216e6 + 1.56268e7i 0.902216 + 1.56268i
\(101\) −1.22247e7 + 1.02577e7i −1.18063 + 0.990663i −0.180651 + 0.983547i \(0.557820\pi\)
−0.999975 + 0.00711522i \(0.997735\pi\)
\(102\) 8.92117e6 8.24583e6i 0.832379 0.769367i
\(103\) 2.83434e6 1.60743e7i 0.255576 1.44945i −0.539012 0.842298i \(-0.681202\pi\)
0.794589 0.607148i \(-0.207687\pi\)
\(104\) 1.11497e7 + 9.35569e6i 0.971954 + 0.815566i
\(105\) 5.69784e6 + 8.85925e6i 0.480339 + 0.746852i
\(106\) 8.55309e6 + 3.11307e6i 0.697514 + 0.253874i
\(107\) 6.40133e6 0.505158 0.252579 0.967576i \(-0.418721\pi\)
0.252579 + 0.967576i \(0.418721\pi\)
\(108\) 2.87661e7 + 1.78069e7i 2.19735 + 1.36021i
\(109\) −4.45494e6 −0.329495 −0.164748 0.986336i \(-0.552681\pi\)
−0.164748 + 0.986336i \(0.552681\pi\)
\(110\) −1.20871e7 4.39933e6i −0.865858 0.315147i
\(111\) −9.35092e6 + 1.81537e7i −0.648969 + 1.25990i
\(112\) −5.69689e7 4.78025e7i −3.83155 3.21505i
\(113\) 1.72967e6 9.80942e6i 0.112768 0.639542i −0.875062 0.484010i \(-0.839180\pi\)
0.987831 0.155532i \(-0.0497091\pi\)
\(114\) −7.09837e6 3.13775e7i −0.448737 1.98358i
\(115\) 4.59880e6 3.85886e6i 0.281970 0.236601i
\(116\) −2.54955e7 4.41595e7i −1.51656 2.62677i
\(117\) −6.61483e6 + 3.15431e6i −0.381828 + 0.182077i
\(118\) −1.11755e7 + 1.93566e7i −0.626155 + 1.08453i
\(119\) −3.08936e6 1.75206e7i −0.168056 0.953092i
\(120\) −2.87631e7 + 1.20597e7i −1.51950 + 0.637092i
\(121\) 3.93769e6 1.43320e6i 0.202066 0.0735460i
\(122\) −3.55667e7 + 1.29452e7i −1.77331 + 0.645431i
\(123\) 3.24324e6 1.35981e6i 0.157149 0.0658888i
\(124\) 1.44038e7 + 8.16881e7i 0.678425 + 3.84754i
\(125\) 1.01856e7 1.76420e7i 0.466447 0.807910i
\(126\) 6.20264e7 2.95776e7i 2.76235 1.31724i
\(127\) −1.28874e7 2.23216e7i −0.558280 0.966970i −0.997640 0.0686587i \(-0.978128\pi\)
0.439360 0.898311i \(-0.355205\pi\)
\(128\) 2.77996e7 2.33266e7i 1.17166 0.983144i
\(129\) −4.78996e6 2.11734e7i −0.196457 0.868415i
\(130\) 1.91367e6 1.08530e7i 0.0763951 0.433258i
\(131\) 2.59630e7 + 2.17855e7i 1.00903 + 0.846679i 0.988210 0.153104i \(-0.0489271\pi\)
0.0208225 + 0.999783i \(0.493372\pi\)
\(132\) −2.77052e7 + 5.37864e7i −1.04846 + 2.03547i
\(133\) −4.42715e7 1.61135e7i −1.63171 0.593895i
\(134\) 4.93345e7 1.77127
\(135\) 481888. 1.56963e7i 0.0168569 0.549073i
\(136\) 5.26784e7 1.79575
\(137\) 4.79985e6 + 1.74700e6i 0.159480 + 0.0580459i 0.420526 0.907280i \(-0.361845\pi\)
−0.261047 + 0.965326i \(0.584068\pi\)
\(138\) −2.11853e7 3.29398e7i −0.686212 1.06695i
\(139\) 2.79272e7 + 2.34337e7i 0.882015 + 0.740099i 0.966592 0.256318i \(-0.0825096\pi\)
−0.0845773 + 0.996417i \(0.526954\pi\)
\(140\) −1.29378e7 + 7.33742e7i −0.398487 + 2.25993i
\(141\) −2.26245e7 + 2.09118e7i −0.679691 + 0.628238i
\(142\) 5.46246e7 4.58355e7i 1.60096 1.34336i
\(143\) −6.55286e6 1.13499e7i −0.187394 0.324575i
\(144\) 2.96186e7 + 1.06842e8i 0.826600 + 2.98176i
\(145\) −1.18343e7 + 2.04977e7i −0.322371 + 0.558363i
\(146\) 719835. + 4.08239e6i 0.0191425 + 0.108562i
\(147\) 7.84277e6 6.16250e7i 0.203638 1.60010i
\(148\) −1.35731e8 + 4.94019e7i −3.44161 + 1.25264i
\(149\) 2.78631e7 1.01413e7i 0.690044 0.251155i 0.0268899 0.999638i \(-0.491440\pi\)
0.663154 + 0.748483i \(0.269217\pi\)
\(150\) −4.34930e7 3.30762e7i −1.05220 0.800197i
\(151\) −5.72769e6 3.24834e7i −0.135382 0.767788i −0.974593 0.223983i \(-0.928094\pi\)
0.839211 0.543806i \(-0.183017\pi\)
\(152\) 6.97498e7 1.20810e8i 1.61098 2.79030i
\(153\) −1.10016e7 + 2.41344e7i −0.248333 + 0.544775i
\(154\) 6.14453e7 + 1.06426e8i 1.35571 + 2.34815i
\(155\) 2.94946e7 2.47489e7i 0.636181 0.533820i
\(156\) −4.95040e7 1.53741e7i −1.04401 0.324230i
\(157\) −2.07199e6 + 1.17508e7i −0.0427305 + 0.242337i −0.998690 0.0511604i \(-0.983708\pi\)
0.955960 + 0.293497i \(0.0948192\pi\)
\(158\) −9.79979e6 8.22300e6i −0.197659 0.165856i
\(159\) −1.98498e7 + 952475.i −0.391622 + 0.0187916i
\(160\) −7.64540e7 2.78270e7i −1.47564 0.537089i
\(161\) −5.73554e7 −1.08314
\(162\) −1.01184e8 1.60463e7i −1.86985 0.296533i
\(163\) 9.91609e6 0.179343 0.0896714 0.995971i \(-0.471418\pi\)
0.0896714 + 0.995971i \(0.471418\pi\)
\(164\) 2.33752e7 + 8.50787e6i 0.413810 + 0.150615i
\(165\) 2.80514e7 1.34602e6i 0.486139 0.0233269i
\(166\) −5.95633e6 4.99796e6i −0.101065 0.0848036i
\(167\) 6.90342e6 3.91512e7i 0.114698 0.650486i −0.872201 0.489148i \(-0.837308\pi\)
0.986899 0.161338i \(-0.0515810\pi\)
\(168\) 2.84571e8 + 8.83770e7i 4.63029 + 1.43799i
\(169\) −3.94666e7 + 3.31164e7i −0.628965 + 0.527764i
\(170\) −1.99430e7 3.45423e7i −0.311329 0.539237i
\(171\) 4.07820e7 + 5.71862e7i 0.623709 + 0.874590i
\(172\) 7.67758e7 1.32980e8i 1.15047 1.99267i
\(173\) 1.59915e7 + 9.06921e7i 0.234815 + 1.33170i 0.843002 + 0.537911i \(0.180786\pi\)
−0.608186 + 0.793794i \(0.708103\pi\)
\(174\) 1.22906e8 + 9.34694e7i 1.76868 + 1.34508i
\(175\) −7.51952e7 + 2.73688e7i −1.06061 + 0.386032i
\(176\) −1.86319e8 + 6.78144e7i −2.57609 + 0.937622i
\(177\) 6.16086e6 4.84093e7i 0.0835093 0.656178i
\(178\) 2.05801e7 + 1.16715e8i 0.273512 + 1.55116i
\(179\) 3.39791e7 5.88535e7i 0.442819 0.766984i −0.555079 0.831798i \(-0.687312\pi\)
0.997897 + 0.0648136i \(0.0206453\pi\)
\(180\) 7.78633e7 7.92187e7i 0.995129 1.01245i
\(181\) −4.72439e6 8.18288e6i −0.0592203 0.102573i 0.834895 0.550409i \(-0.185528\pi\)
−0.894116 + 0.447836i \(0.852195\pi\)
\(182\) −8.06555e7 + 6.76780e7i −0.991709 + 0.832143i
\(183\) 6.06852e7 5.60913e7i 0.731988 0.676576i
\(184\) 2.94903e7 1.67248e8i 0.348993 1.97924i
\(185\) 5.13601e7 + 4.30963e7i 0.596383 + 0.500425i
\(186\) −1.35873e8 2.11261e8i −1.54823 2.40726i
\(187\) −4.45729e7 1.62232e7i −0.498454 0.181422i
\(188\) −2.17920e8 −2.39191
\(189\) −9.99206e7 + 1.11918e8i −1.07656 + 1.20583i
\(190\) −1.05624e8 −1.11718
\(191\) 1.08683e8 + 3.95575e7i 1.12861 + 0.410782i 0.837789 0.545994i \(-0.183848\pi\)
0.290826 + 0.956776i \(0.406070\pi\)
\(192\) −1.04093e8 + 2.02085e8i −1.06137 + 2.06053i
\(193\) 2.68063e7 + 2.24931e7i 0.268402 + 0.225216i 0.767048 0.641590i \(-0.221725\pi\)
−0.498646 + 0.866806i \(0.666169\pi\)
\(194\) 6.19108e6 3.51114e7i 0.0608780 0.345256i
\(195\) 5.30906e6 + 2.34681e7i 0.0512740 + 0.226650i
\(196\) 3.36608e8 2.82448e8i 3.19321 2.67942i
\(197\) 8.88067e7 + 1.53818e8i 0.827588 + 1.43342i 0.899926 + 0.436044i \(0.143621\pi\)
−0.0723379 + 0.997380i \(0.523046\pi\)
\(198\) 1.43927e7 1.82646e8i 0.131769 1.67218i
\(199\) −6.44461e7 + 1.11624e8i −0.579710 + 1.00409i 0.415802 + 0.909455i \(0.363501\pi\)
−0.995512 + 0.0946326i \(0.969832\pi\)
\(200\) −4.11442e7 2.33341e8i −0.363667 2.06246i
\(201\) −9.93354e7 + 4.16490e7i −0.862815 + 0.361759i
\(202\) 3.21199e8 1.16907e8i 2.74186 0.997955i
\(203\) 2.12492e8 7.73409e7i 1.78282 0.648893i
\(204\) −1.73019e8 + 7.25428e7i −1.42688 + 0.598258i
\(205\) −2.00502e6 1.13711e7i −0.0162548 0.0921854i
\(206\) −1.74806e8 + 3.02773e8i −1.39323 + 2.41314i
\(207\) 7.04652e7 + 4.84396e7i 0.552177 + 0.379581i
\(208\) −8.49380e7 1.47117e8i −0.654456 1.13355i
\(209\) −9.62231e7 + 8.07408e7i −0.729067 + 0.611760i
\(210\) −4.97824e7 2.20057e8i −0.370944 1.63971i
\(211\) −3.12660e7 + 1.77318e8i −0.229131 + 1.29947i 0.625497 + 0.780227i \(0.284896\pi\)
−0.854628 + 0.519241i \(0.826215\pi\)
\(212\) −1.07680e8 9.03542e7i −0.776174 0.651287i
\(213\) −7.12920e7 + 1.38405e8i −0.505489 + 0.981349i
\(214\) −1.28843e8 4.68951e7i −0.898697 0.327099i
\(215\) −7.12746e7 −0.489103
\(216\) −2.74977e8 3.48912e8i −1.85655 2.35574i
\(217\) −3.67850e8 −2.44378
\(218\) 8.96672e7 + 3.26362e7i 0.586187 + 0.213354i
\(219\) −4.89582e6 7.61222e6i −0.0314971 0.0489730i
\(220\) 1.52171e8 + 1.27687e8i 0.963503 + 0.808475i
\(221\) 7.05694e6 4.00219e7i 0.0439788 0.249416i
\(222\) 3.21203e8 2.96888e8i 1.97035 1.82120i
\(223\) 1.88784e8 1.58409e8i 1.13998 0.956559i 0.140544 0.990074i \(-0.455115\pi\)
0.999438 + 0.0335159i \(0.0106704\pi\)
\(224\) 3.88658e8 + 6.73176e8i 2.31047 + 4.00185i
\(225\) 1.15497e8 + 2.98817e7i 0.675977 + 0.174891i
\(226\) −1.06676e8 + 1.84769e8i −0.614736 + 1.06475i
\(227\) −1.29989e7 7.37204e7i −0.0737591 0.418309i −0.999221 0.0394677i \(-0.987434\pi\)
0.925462 0.378841i \(-0.123677\pi\)
\(228\) −6.27225e7 + 4.92845e8i −0.350470 + 2.75384i
\(229\) 2.82300e8 1.02749e8i 1.55341 0.565395i 0.584195 0.811613i \(-0.301410\pi\)
0.969214 + 0.246218i \(0.0791880\pi\)
\(230\) −1.20832e8 + 4.39793e7i −0.654840 + 0.238342i
\(231\) −2.13567e8 1.62417e8i −1.13997 0.866941i
\(232\) 1.16268e8 + 6.59391e8i 0.611300 + 3.46685i
\(233\) 1.65588e8 2.86807e8i 0.857599 1.48540i −0.0166147 0.999862i \(-0.505289\pi\)
0.874213 0.485542i \(-0.161378\pi\)
\(234\) 1.56249e8 1.50295e7i 0.797187 0.0766812i
\(235\) 5.05763e7 + 8.76007e7i 0.254220 + 0.440322i
\(236\) 2.64421e8 2.21876e8i 1.30950 1.09880i
\(237\) 2.66739e7 + 8.28392e6i 0.130157 + 0.0404219i
\(238\) −6.61720e7 + 3.75280e8i −0.318167 + 1.80441i
\(239\) −7.68469e7 6.44822e7i −0.364111 0.305525i 0.442316 0.896859i \(-0.354157\pi\)
−0.806427 + 0.591334i \(0.798601\pi\)
\(240\) 3.63601e8 1.74471e7i 1.69780 0.0814672i
\(241\) −8.42094e7 3.06497e7i −0.387526 0.141048i 0.140907 0.990023i \(-0.454998\pi\)
−0.528433 + 0.848975i \(0.677220\pi\)
\(242\) −8.97557e7 −0.407106
\(243\) 2.17280e8 5.31114e7i 0.971401 0.237447i
\(244\) 5.84523e8 2.57595
\(245\) −1.91662e8 6.97593e7i −0.832636 0.303055i
\(246\) −7.52403e7 + 3.61034e6i −0.322239 + 0.0154623i
\(247\) −8.24405e7 6.91758e7i −0.348098 0.292089i
\(248\) 1.89137e8 1.07265e9i 0.787399 4.46556i
\(249\) 1.62125e7 + 5.03498e6i 0.0665506 + 0.0206681i
\(250\) −3.34254e8 + 2.80473e8i −1.35297 + 1.13527i
\(251\) −1.10349e8 1.91130e8i −0.440464 0.762905i 0.557260 0.830338i \(-0.311853\pi\)
−0.997724 + 0.0674327i \(0.978519\pi\)
\(252\) −1.05636e9 + 1.01611e8i −4.15824 + 0.399979i
\(253\) −7.64595e7 + 1.32432e8i −0.296831 + 0.514126i
\(254\) 9.58675e7 + 5.43692e8i 0.367074 + 2.08178i
\(255\) 6.93165e7 + 5.27149e7i 0.261786 + 0.199087i
\(256\) −1.45763e8 + 5.30533e7i −0.543008 + 0.197639i
\(257\) 1.25635e8 4.57274e7i 0.461684 0.168039i −0.100698 0.994917i \(-0.532107\pi\)
0.562382 + 0.826878i \(0.309885\pi\)
\(258\) −5.87028e7 + 4.61261e8i −0.212809 + 1.67216i
\(259\) −1.11231e8 6.30822e8i −0.397811 2.25610i
\(260\) −8.50962e7 + 1.47391e8i −0.300264 + 0.520073i
\(261\) −3.26380e8 8.44420e7i −1.13627 0.293979i
\(262\) −3.62975e8 6.28691e8i −1.24687 2.15965i
\(263\) −1.59114e8 + 1.33512e8i −0.539340 + 0.452560i −0.871312 0.490729i \(-0.836731\pi\)
0.331972 + 0.943289i \(0.392286\pi\)
\(264\) 5.83416e8 5.39251e8i 1.95148 1.80375i
\(265\) −1.13300e7 + 6.42558e7i −0.0373999 + 0.212106i
\(266\) 7.73034e8 + 6.48652e8i 2.51833 + 2.11313i
\(267\) −1.39971e8 2.17633e8i −0.450038 0.699738i
\(268\) −7.15946e8 2.60583e8i −2.27200 0.826941i
\(269\) −2.54854e8 −0.798286 −0.399143 0.916889i \(-0.630692\pi\)
−0.399143 + 0.916889i \(0.630692\pi\)
\(270\) −1.24688e8 + 3.12399e8i −0.385524 + 0.965910i
\(271\) 2.08428e8 0.636157 0.318078 0.948064i \(-0.396963\pi\)
0.318078 + 0.948064i \(0.396963\pi\)
\(272\) −5.77752e8 2.10284e8i −1.74081 0.633601i
\(273\) 1.05265e8 2.04361e8i 0.313124 0.607895i
\(274\) −8.38112e7 7.03259e7i −0.246136 0.206533i
\(275\) −3.70477e7 + 2.10108e8i −0.107423 + 0.609226i
\(276\) 1.33456e8 + 5.89925e8i 0.382081 + 1.68894i
\(277\) 3.01004e8 2.52572e8i 0.850927 0.714013i −0.109066 0.994034i \(-0.534786\pi\)
0.959994 + 0.280022i \(0.0903417\pi\)
\(278\) −3.90436e8 6.76255e8i −1.08992 1.88779i
\(279\) 4.51930e8 + 3.10669e8i 1.24582 + 0.856412i
\(280\) 4.89170e8 8.47267e8i 1.33170 2.30657i
\(281\) 9.31249e7 + 5.28137e8i 0.250376 + 1.41996i 0.807668 + 0.589638i \(0.200730\pi\)
−0.557291 + 0.830317i \(0.688159\pi\)
\(282\) 6.08572e8 2.55160e8i 1.61600 0.677550i
\(283\) 1.08331e8 3.94293e7i 0.284119 0.103411i −0.196030 0.980598i \(-0.562805\pi\)
0.480149 + 0.877187i \(0.340583\pi\)
\(284\) −1.03482e9 + 3.76643e8i −2.68071 + 0.975698i
\(285\) 2.12674e8 8.91692e7i 0.544198 0.228170i
\(286\) 4.87458e7 + 2.76451e8i 0.123213 + 0.698775i
\(287\) −5.51573e7 + 9.55352e7i −0.137726 + 0.238548i
\(288\) 9.10375e7 1.15529e9i 0.224567 2.84981i
\(289\) 1.31627e8 + 2.27984e8i 0.320775 + 0.555599i
\(290\) 3.88360e8 3.25872e8i 0.935063 0.784611i
\(291\) 1.71758e7 + 7.59236e7i 0.0408594 + 0.180614i
\(292\) 1.11167e7 6.30460e7i 0.0261298 0.148190i
\(293\) −3.85288e8 3.23295e8i −0.894846 0.750865i 0.0743298 0.997234i \(-0.476318\pi\)
−0.969176 + 0.246368i \(0.920763\pi\)
\(294\) −6.09311e8 + 1.18291e9i −1.39837 + 2.71478i
\(295\) −1.50560e8 5.47992e7i −0.341453 0.124279i
\(296\) 1.89666e9 4.25078
\(297\) 1.25213e8 + 3.79910e8i 0.277334 + 0.841458i
\(298\) −6.35110e8 −1.39025
\(299\) −1.23114e8 4.48099e7i −0.266354 0.0969449i
\(300\) 4.56466e8 + 7.09733e8i 0.976077 + 1.51765i
\(301\) 5.21641e8 + 4.37709e8i 1.10253 + 0.925130i
\(302\) −1.22683e8 + 6.95772e8i −0.256307 + 1.45359i
\(303\) −5.48042e8 + 5.06555e8i −1.13179 + 1.04611i
\(304\) −1.24724e9 + 1.04656e9i −2.54620 + 2.13652i
\(305\) −1.35660e8 2.34970e8i −0.273780 0.474201i
\(306\) 3.98240e8 4.05172e8i 0.794548 0.808378i
\(307\) 3.27748e8 5.67676e8i 0.646481 1.11974i −0.337477 0.941334i \(-0.609573\pi\)
0.983957 0.178404i \(-0.0570933\pi\)
\(308\) −3.29558e8 1.86902e9i −0.642695 3.64490i
\(309\) 9.63672e7 7.57210e8i 0.185812 1.46003i
\(310\) −7.74961e8 + 2.82063e8i −1.47745 + 0.537749i
\(311\) 2.59909e8 9.45992e7i 0.489960 0.178331i −0.0852131 0.996363i \(-0.527157\pi\)
0.575173 + 0.818032i \(0.304935\pi\)
\(312\) 5.41790e8 + 4.12029e8i 1.00993 + 0.768044i
\(313\) 4.49129e7 + 2.54714e8i 0.0827877 + 0.469513i 0.997812 + 0.0661139i \(0.0210601\pi\)
−0.915024 + 0.403399i \(0.867829\pi\)
\(314\) 1.27789e8 2.21337e8i 0.232937 0.403459i
\(315\) 2.86013e8 + 4.01059e8i 0.515583 + 0.722971i
\(316\) 9.87817e7 + 1.71095e8i 0.176105 + 0.305023i
\(317\) −5.93746e8 + 4.98212e8i −1.04687 + 0.878429i −0.992761 0.120106i \(-0.961677\pi\)
−0.0541103 + 0.998535i \(0.517232\pi\)
\(318\) 4.06507e8 + 1.26246e8i 0.708880 + 0.220151i
\(319\) 1.04692e8 5.93739e8i 0.180571 1.02407i
\(320\) 5.71733e8 + 4.79741e8i 0.975368 + 0.818431i
\(321\) 2.99016e8 1.43480e7i 0.504577 0.0242117i
\(322\) 1.15443e9 + 4.20177e8i 1.92695 + 0.701352i
\(323\) −3.89503e8 −0.643134
\(324\) 1.38363e9 + 7.67313e8i 2.26001 + 1.25333i
\(325\) −1.82790e8 −0.295366
\(326\) −1.99587e8 7.26437e7i −0.319059 0.116128i
\(327\) −2.08098e8 + 9.98537e6i −0.329117 + 0.0157924i
\(328\) −2.50219e8 2.09959e8i −0.391528 0.328531i
\(329\) 1.67815e8 9.51726e8i 0.259803 1.47342i
\(330\) −5.74468e8 1.78408e8i −0.879968 0.273285i
\(331\) 1.26526e8 1.06168e8i 0.191771 0.160915i −0.541847 0.840477i \(-0.682275\pi\)
0.733618 + 0.679562i \(0.237830\pi\)
\(332\) 6.00397e7 + 1.03992e8i 0.0900441 + 0.155961i
\(333\) −3.96107e8 + 8.68950e8i −0.587838 + 1.28956i
\(334\) −4.25765e8 + 7.37446e8i −0.625255 + 1.08297i
\(335\) 6.14108e7 + 3.48278e8i 0.0892459 + 0.506139i
\(336\) −2.76825e9 2.10524e9i −3.98124 3.02771i
\(337\) −7.41785e8 + 2.69988e8i −1.05578 + 0.384272i −0.810841 0.585266i \(-0.800990\pi\)
−0.244938 + 0.969539i \(0.578768\pi\)
\(338\) 1.03697e9 3.77427e8i 1.46069 0.531649i
\(339\) 5.88085e7 4.62091e8i 0.0819863 0.644212i
\(340\) 1.06963e8 + 6.06618e8i 0.147590 + 0.837026i
\(341\) −4.90375e8 + 8.49354e8i −0.669712 + 1.15997i
\(342\) −4.01906e8 1.44978e9i −0.543292 1.95980i
\(343\) 3.70281e8 + 6.41345e8i 0.495452 + 0.858148i
\(344\) −1.54457e9 + 1.29604e9i −2.04575 + 1.71658i
\(345\) 2.06168e8 1.90561e8i 0.270306 0.249843i
\(346\) 3.42526e8 1.94256e9i 0.444557 2.52121i
\(347\) 1.17238e9 + 9.83747e8i 1.50632 + 1.26395i 0.870559 + 0.492064i \(0.163757\pi\)
0.635760 + 0.771887i \(0.280687\pi\)
\(348\) −1.28992e9 2.00562e9i −1.64072 2.55106i
\(349\) 2.69213e8 + 9.79855e7i 0.339006 + 0.123388i 0.505913 0.862585i \(-0.331156\pi\)
−0.166907 + 0.985973i \(0.553378\pi\)
\(350\) 1.71400e9 2.13684
\(351\) −3.01919e8 + 1.62170e8i −0.372663 + 0.200168i
\(352\) 2.07245e9 2.53271
\(353\) −4.00689e8 1.45839e8i −0.484837 0.176466i 0.0880249 0.996118i \(-0.471945\pi\)
−0.572862 + 0.819652i \(0.694167\pi\)
\(354\) −4.78642e8 + 9.29228e8i −0.573455 + 1.11330i
\(355\) 3.91573e8 + 3.28568e8i 0.464529 + 0.389786i
\(356\) 3.17826e8 1.80248e9i 0.373349 2.11737i
\(357\) −1.83580e8 8.11492e8i −0.213543 0.943942i
\(358\) −1.11507e9 + 9.35653e8i −1.28443 + 1.07777i
\(359\) −3.07774e8 5.33080e8i −0.351076 0.608081i 0.635362 0.772214i \(-0.280851\pi\)
−0.986438 + 0.164133i \(0.947517\pi\)
\(360\) −1.31654e9 + 6.27799e8i −1.48722 + 0.709188i
\(361\) −6.87926e7 + 1.19152e8i −0.0769603 + 0.133299i
\(362\) 3.51441e7 + 1.99312e8i 0.0389378 + 0.220827i
\(363\) 1.80724e8 7.57732e7i 0.198309 0.0831462i
\(364\) 1.52795e9 5.56129e8i 1.66056 0.604394i
\(365\) −2.79237e7 + 1.01634e7i −0.0300571 + 0.0109399i
\(366\) −1.63236e9 + 6.84412e8i −1.74034 + 0.729682i
\(367\) −1.02479e8 5.81190e8i −0.108219 0.613743i −0.989885 0.141869i \(-0.954689\pi\)
0.881666 0.471874i \(-0.156422\pi\)
\(368\) −9.91065e8 + 1.71657e9i −1.03666 + 1.79554i
\(369\) 1.48449e8 7.07886e7i 0.153810 0.0733451i
\(370\) −7.18039e8 1.24368e9i −0.736957 1.27645i
\(371\) 4.77528e8 4.00693e8i 0.485501 0.407383i
\(372\) 8.55923e8 + 3.78350e9i 0.862054 + 3.81060i
\(373\) −4.47420e7 + 2.53744e8i −0.0446410 + 0.253172i −0.998959 0.0456218i \(-0.985473\pi\)
0.954318 + 0.298794i \(0.0965842\pi\)
\(374\) 7.78296e8 + 6.53068e8i 0.769297 + 0.645517i
\(375\) 4.36244e8 8.46917e8i 0.427189 0.829338i
\(376\) 2.68894e9 + 9.78693e8i 2.60869 + 0.949487i
\(377\) 5.16542e8 0.496491
\(378\) 2.83106e9 1.52064e9i 2.69605 1.44812i
\(379\) 4.63730e8 0.437550 0.218775 0.975775i \(-0.429794\pi\)
0.218775 + 0.975775i \(0.429794\pi\)
\(380\) 1.53282e9 + 5.57900e8i 1.43300 + 0.521571i
\(381\) −6.52023e8 1.01379e9i −0.603985 0.939101i
\(382\) −1.89774e9 1.59239e9i −1.74187 1.46160i
\(383\) −1.22375e8 + 6.94021e8i −0.111300 + 0.631215i 0.877216 + 0.480097i \(0.159398\pi\)
−0.988516 + 0.151118i \(0.951713\pi\)
\(384\) 1.24628e9 1.15193e9i 1.12320 1.03817i
\(385\) −6.74833e8 + 5.66252e8i −0.602676 + 0.505705i
\(386\) −3.74764e8 6.49111e8i −0.331667 0.574465i
\(387\) −2.71205e8 9.78309e8i −0.237854 0.858001i
\(388\) −2.75302e8 + 4.76837e8i −0.239276 + 0.414438i
\(389\) −6.68602e7 3.79183e8i −0.0575896 0.326607i 0.942379 0.334548i \(-0.108584\pi\)
−0.999968 + 0.00794063i \(0.997472\pi\)
\(390\) 6.50646e7 5.11249e8i 0.0555417 0.436421i
\(391\) −4.45587e8 + 1.62180e8i −0.376976 + 0.137208i
\(392\) −5.42193e9 + 1.97342e9i −4.54625 + 1.65470i
\(393\) 1.26160e9 + 9.59444e8i 1.04845 + 0.797344i
\(394\) −6.60620e8 3.74656e9i −0.544146 3.08600i
\(395\) 4.58518e7 7.94177e7i 0.0374341 0.0648377i
\(396\) −1.17360e9 + 2.57455e9i −0.949698 + 2.08338i
\(397\) 3.45992e8 + 5.99276e8i 0.277523 + 0.480684i 0.970769 0.240017i \(-0.0771531\pi\)
−0.693245 + 0.720702i \(0.743820\pi\)
\(398\) 2.11488e9 1.77460e9i 1.68150 1.41094i
\(399\) −2.10411e9 6.53458e8i −1.65830 0.515006i
\(400\) −4.80211e8 + 2.72341e9i −0.375165 + 2.12767i
\(401\) −1.41296e9 1.18561e9i −1.09427 0.918199i −0.0972402 0.995261i \(-0.531002\pi\)
−0.997026 + 0.0770623i \(0.975446\pi\)
\(402\) 2.30450e9 1.10579e8i 1.76923 0.0848950i
\(403\) −7.89597e8 2.87390e8i −0.600949 0.218728i
\(404\) −5.27876e9 −3.98288
\(405\) −1.26722e7 7.34281e8i −0.00947896 0.549250i
\(406\) −4.84355e9 −3.59188
\(407\) −1.60483e9 5.84109e8i −1.17991 0.429451i
\(408\) 2.46069e9 1.18074e8i 1.79369 0.0860684i
\(409\) 1.87886e9 + 1.57655e9i 1.35789 + 1.13940i 0.976629 + 0.214932i \(0.0689530\pi\)
0.381256 + 0.924469i \(0.375491\pi\)
\(410\) −4.29463e7 + 2.43560e8i −0.0307739 + 0.174527i
\(411\) 2.28125e8 + 7.08469e7i 0.162079 + 0.0503355i
\(412\) 4.13603e9 3.47055e9i 2.91369 2.44488i
\(413\) 7.65378e8 + 1.32567e9i 0.534627 + 0.926001i
\(414\) −1.06343e9 1.49119e9i −0.736561 1.03284i
\(415\) 2.78688e7 4.82702e7i 0.0191404 0.0331521i
\(416\) 3.08330e8 + 1.74863e9i 0.209986 + 1.19089i
\(417\) 1.35705e9 + 1.03203e9i 0.916474 + 0.696974i
\(418\) 2.52823e9 9.20201e8i 1.69317 0.616263i
\(419\) 6.22164e8 2.26449e8i 0.413196 0.150391i −0.127054 0.991896i \(-0.540552\pi\)
0.540249 + 0.841505i \(0.318330\pi\)
\(420\) −4.39886e8 + 3.45643e9i −0.289713 + 2.27643i
\(421\) −1.57618e8 8.93894e8i −0.102948 0.583846i −0.992020 0.126080i \(-0.959761\pi\)
0.889072 0.457767i \(-0.151351\pi\)
\(422\) 1.92832e9 3.33994e9i 1.24906 2.16344i
\(423\) −1.00995e9 + 1.02753e9i −0.648799 + 0.660093i
\(424\) 9.22888e8 + 1.59849e9i 0.587988 + 1.01842i
\(425\) −5.06793e8 + 4.25250e8i −0.320235 + 0.268709i
\(426\) 2.44887e9 2.26349e9i 1.53473 1.41855i
\(427\) −4.50127e8 + 2.55280e9i −0.279794 + 1.58679i
\(428\) 1.62208e9 + 1.36109e9i 1.00005 + 0.839138i
\(429\) −3.31535e8 5.15484e8i −0.202735 0.315221i
\(430\) 1.43459e9 + 5.22146e8i 0.870135 + 0.316703i
\(431\) 2.66454e9 1.60307 0.801533 0.597950i \(-0.204018\pi\)
0.801533 + 0.597950i \(0.204018\pi\)
\(432\) 1.62301e9 + 4.92437e9i 0.968562 + 2.93872i
\(433\) 1.22014e8 0.0722271 0.0361136 0.999348i \(-0.488502\pi\)
0.0361136 + 0.999348i \(0.488502\pi\)
\(434\) 7.40394e9 + 2.69481e9i 4.34759 + 1.58239i
\(435\) −5.06858e8 + 9.84006e8i −0.295239 + 0.573172i
\(436\) −1.12887e9 9.47237e8i −0.652293 0.547338i
\(437\) −2.18051e8 + 1.23663e9i −0.124989 + 0.708848i
\(438\) 4.27750e7 + 1.89082e8i 0.0243238 + 0.107520i
\(439\) −1.33776e9 + 1.12251e9i −0.754660 + 0.633235i −0.936731 0.350050i \(-0.886164\pi\)
0.182071 + 0.983285i \(0.441720\pi\)
\(440\) −1.30421e9 2.25895e9i −0.729898 1.26422i
\(441\) 2.28221e8 2.89618e9i 0.126713 1.60802i
\(442\) −4.35233e8 + 7.53846e8i −0.239742 + 0.415245i
\(443\) 3.76151e8 + 2.13326e9i 0.205565 + 1.16582i 0.896548 + 0.442947i \(0.146067\pi\)
−0.690983 + 0.722871i \(0.742822\pi\)
\(444\) −6.22947e9 + 2.61187e9i −3.37762 + 1.41616i
\(445\) −7.98336e8 + 2.90571e8i −0.429463 + 0.156312i
\(446\) −4.96024e9 + 1.80538e9i −2.64747 + 0.963600i
\(447\) 1.27880e9 5.36170e8i 0.677213 0.283940i
\(448\) −1.23821e9 7.02222e9i −0.650609 3.68979i
\(449\) −2.64481e8 + 4.58094e8i −0.137890 + 0.238832i −0.926698 0.375808i \(-0.877365\pi\)
0.788808 + 0.614640i \(0.210699\pi\)
\(450\) −2.10577e9 1.44756e9i −1.08935 0.748846i
\(451\) 1.47058e8 + 2.54712e8i 0.0754869 + 0.130747i
\(452\) 2.52403e9 2.11792e9i 1.28561 1.07876i
\(453\) −3.40358e8 1.50451e9i −0.172026 0.760417i
\(454\) −2.78428e8 + 1.57904e9i −0.139642 + 0.791950i
\(455\) −5.78173e8 4.85145e8i −0.287752 0.241452i
\(456\) 2.98734e9 5.79958e9i 1.47539 2.86431i
\(457\) 9.65658e8 + 3.51471e8i 0.473278 + 0.172259i 0.567637 0.823279i \(-0.307858\pi\)
−0.0943584 + 0.995538i \(0.530080\pi\)
\(458\) −6.43473e9 −3.12969
\(459\) −4.59806e8 + 1.15202e9i −0.221937 + 0.556051i
\(460\) 1.98582e9 0.951235
\(461\) 2.20000e9 + 8.00735e8i 1.04585 + 0.380658i 0.807095 0.590421i \(-0.201038\pi\)
0.238755 + 0.971080i \(0.423261\pi\)
\(462\) 3.10876e9 + 4.83362e9i 1.46669 + 2.28048i
\(463\) −2.79237e9 2.34307e9i −1.30749 1.09712i −0.988798 0.149258i \(-0.952311\pi\)
−0.318694 0.947858i \(-0.603244\pi\)
\(464\) 1.35702e9 7.69603e9i 0.630627 3.57646i
\(465\) 1.32227e9 1.22217e9i 0.609865 0.563698i
\(466\) −5.43400e9 + 4.55967e9i −2.48753 + 2.08729i
\(467\) 1.67559e9 + 2.90221e9i 0.761305 + 1.31862i 0.942178 + 0.335113i \(0.108774\pi\)
−0.180873 + 0.983507i \(0.557892\pi\)
\(468\) −2.34687e9 6.07190e8i −1.05835 0.273819i
\(469\) 1.68938e9 2.92610e9i 0.756177 1.30974i
\(470\) −3.76230e8 2.13370e9i −0.167152 0.947964i
\(471\) −7.04474e7 + 5.53544e8i −0.0310665 + 0.244106i
\(472\) −4.25918e9 + 1.55021e9i −1.86436 + 0.678570i
\(473\) 1.70605e9 6.20950e8i 0.741270 0.269800i
\(474\) −4.76195e8 3.62144e8i −0.205381 0.156192i
\(475\) 3.04220e8 + 1.72532e9i 0.130245 + 0.738654i
\(476\) 2.94250e9 5.09657e9i 1.25053 2.16598i
\(477\) −9.25082e8 + 8.89833e7i −0.390271 + 0.0375400i
\(478\) 1.07436e9 + 1.86084e9i 0.449936 + 0.779312i
\(479\) −1.61103e8 + 1.35181e8i −0.0669774 + 0.0562007i −0.675662 0.737212i \(-0.736142\pi\)
0.608684 + 0.793412i \(0.291698\pi\)
\(480\) −3.63366e9 1.12848e9i −1.49969 0.465746i
\(481\) 2.54082e8 1.44097e9i 0.104104 0.590402i
\(482\) 1.47040e9 + 1.23381e9i 0.598095 + 0.501861i
\(483\) −2.67916e9 + 1.28557e8i −1.08189 + 0.0519136i
\(484\) 1.30254e9 + 4.74086e8i 0.522194 + 0.190063i
\(485\) 2.55576e8 0.101724
\(486\) −4.76241e9 5.22756e8i −1.88192 0.206572i
\(487\) 1.69417e8 0.0664671 0.0332335 0.999448i \(-0.489419\pi\)
0.0332335 + 0.999448i \(0.489419\pi\)
\(488\) −7.21249e9 2.62513e9i −2.80941 1.02254i
\(489\) 4.63197e8 2.22261e7i 0.179137 0.00859571i
\(490\) 3.34665e9 + 2.80817e9i 1.28506 + 1.07830i
\(491\) 8.42914e8 4.78041e9i 0.321365 1.82255i −0.212713 0.977115i \(-0.568230\pi\)
0.534078 0.845436i \(-0.320659\pi\)
\(492\) 1.11096e9 + 3.45023e8i 0.420554 + 0.130608i
\(493\) 1.43213e9 1.20170e9i 0.538294 0.451682i
\(494\) 1.15256e9 + 1.99629e9i 0.430148 + 0.745039i
\(495\) 1.30731e9 1.25750e8i 0.484462 0.0466003i
\(496\) −6.35622e9 + 1.10093e10i −2.33891 + 4.05111i
\(497\) −8.48031e8 4.80942e9i −0.309859 1.75730i
\(498\) −2.89433e8 2.20112e8i −0.105013 0.0798622i
\(499\) −2.44046e9 + 8.88253e8i −0.879264 + 0.320026i −0.741913 0.670497i \(-0.766081\pi\)
−0.137351 + 0.990522i \(0.543859\pi\)
\(500\) 6.33217e9 2.30472e9i 2.26547 0.824562i
\(501\) 2.34716e8 1.84429e9i 0.0833893 0.655235i
\(502\) 8.20869e8 + 4.65538e9i 0.289608 + 1.64245i
\(503\) −9.78179e8 + 1.69425e9i −0.342713 + 0.593596i −0.984935 0.172922i \(-0.944679\pi\)
0.642223 + 0.766518i \(0.278012\pi\)
\(504\) 1.34909e10 + 3.49039e9i 4.69389 + 1.21442i
\(505\) 1.22513e9 + 2.12199e9i 0.423314 + 0.733202i
\(506\) 2.50912e9 2.10540e9i 0.860982 0.722450i
\(507\) −1.76932e9 + 1.63538e9i −0.602947 + 0.557303i
\(508\) 1.48052e9 8.39646e9i 0.501062 2.84167i
\(509\) −2.96935e9 2.49158e9i −0.998043 0.837458i −0.0113310 0.999936i \(-0.503607\pi\)
−0.986712 + 0.162478i \(0.948051\pi\)
\(510\) −1.00899e9 1.56883e9i −0.336816 0.523696i
\(511\) 2.66782e8 + 9.71006e7i 0.0884469 + 0.0321920i
\(512\) −1.32258e9 −0.435489
\(513\) 2.03317e9 + 2.57985e9i 0.664910 + 0.843691i
\(514\) −2.86372e9 −0.930165
\(515\) −2.35503e9 8.57161e8i −0.759751 0.276527i
\(516\) 3.28826e9 6.38378e9i 1.05364 2.04552i
\(517\) −1.97379e9 1.65621e9i −0.628180 0.527106i
\(518\) −2.38249e9 + 1.35118e10i −0.753143 + 4.27129i
\(519\) 9.50266e8 + 4.20053e9i 0.298373 + 1.31892i
\(520\) 1.71195e9 1.43650e9i 0.533925 0.448016i
\(521\) 5.30177e8 + 9.18293e8i 0.164244 + 0.284478i 0.936386 0.350971i \(-0.114148\pi\)
−0.772143 + 0.635449i \(0.780815\pi\)
\(522\) 5.95064e9 + 4.09062e9i 1.83112 + 1.25876i
\(523\) 1.53786e9 2.66366e9i 0.470069 0.814183i −0.529345 0.848406i \(-0.677562\pi\)
0.999414 + 0.0342234i \(0.0108958\pi\)
\(524\) 1.94679e9 + 1.10408e10i 0.591100 + 3.35229i
\(525\) −3.45115e9 + 1.44699e9i −1.04089 + 0.436422i
\(526\) 4.18067e9 1.52164e9i 1.25255 0.455891i
\(527\) −2.85778e9 + 1.04015e9i −0.850535 + 0.309569i
\(528\) −8.55124e9 + 3.58534e9i −2.52820 + 1.06001i
\(529\) −3.25785e8 1.84762e9i −0.0956835 0.542648i
\(530\) 6.98774e8 1.21031e9i 0.203879 0.353128i
\(531\) 1.79278e8 2.27508e9i 0.0519634 0.659427i
\(532\) −7.79216e9 1.34964e10i −2.24371 3.88622i
\(533\) −1.93034e8 + 1.61975e8i −0.0552191 + 0.0463344i
\(534\) 1.22294e9 + 5.40583e9i 0.347543 + 1.53627i
\(535\) 1.70675e8 9.67946e8i 0.0481872 0.273283i
\(536\) 7.66384e9 + 6.43073e9i 2.14966 + 1.80378i
\(537\) 1.45530e9 2.82530e9i 0.405549 0.787327i
\(538\) 5.12960e9 + 1.86702e9i 1.42019 + 0.516906i
\(539\) 5.19542e9 1.42909
\(540\) 3.45956e9 3.87496e9i 0.945459 1.05898i
\(541\) 1.67953e9 0.456033 0.228017 0.973657i \(-0.426776\pi\)
0.228017 + 0.973657i \(0.426776\pi\)
\(542\) −4.19516e9 1.52691e9i −1.13175 0.411924i
\(543\) −2.39025e8 3.71646e8i −0.0640685 0.0996164i
\(544\) 4.92293e9 + 4.13083e9i 1.31108 + 1.10012i
\(545\) −1.18780e8 + 6.73633e8i −0.0314307 + 0.178252i
\(546\) −3.61586e9 + 3.34213e9i −0.950685 + 0.878718i
\(547\) 7.99746e8 6.71067e8i 0.208928 0.175311i −0.532319 0.846544i \(-0.678679\pi\)
0.741247 + 0.671233i \(0.234235\pi\)
\(548\) 8.44815e8 + 1.46326e9i 0.219295 + 0.379831i
\(549\) 2.70898e9 2.75614e9i 0.698720 0.710882i
\(550\) 2.28490e9 3.95756e9i 0.585596 1.01428i
\(551\) −8.59687e8 4.87553e9i −0.218932 1.24163i
\(552\) 1.00267e9 7.87851e9i 0.253729 1.99369i
\(553\) −8.23296e8 + 2.99655e8i −0.207023 + 0.0753501i
\(554\) −7.90878e9 + 2.87856e9i −1.97617 + 0.719268i
\(555\) 2.49571e9 + 1.89798e9i 0.619682 + 0.471266i
\(556\) 2.09408e9 + 1.18761e10i 0.516692 + 2.93030i
\(557\) −2.83704e7 + 4.91391e7i −0.00695621 + 0.0120485i −0.869483 0.493964i \(-0.835548\pi\)
0.862526 + 0.506012i \(0.168881\pi\)
\(558\) −6.82036e9 9.56378e9i −1.66183 2.33029i
\(559\) 7.77743e8 + 1.34709e9i 0.188319 + 0.326179i
\(560\) −8.74716e9 + 7.33974e9i −2.10479 + 1.76613i
\(561\) −2.11843e9 6.57906e8i −0.506576 0.157324i
\(562\) 1.99467e9 1.13123e10i 0.474017 2.68829i
\(563\) 1.90973e8 + 1.60245e8i 0.0451016 + 0.0378447i 0.665060 0.746790i \(-0.268406\pi\)
−0.619958 + 0.784635i \(0.712850\pi\)
\(564\) −1.01794e10 + 4.88449e8i −2.38916 + 0.114642i
\(565\) −1.43717e9 5.23086e8i −0.335226 0.122012i
\(566\) −2.46929e9 −0.572421
\(567\) −4.41660e9 + 5.45185e9i −1.01753 + 1.25604i
\(568\) 1.44603e10 3.31098
\(569\) −5.22920e9 1.90327e9i −1.18999 0.433120i −0.330268 0.943887i \(-0.607139\pi\)
−0.859719 + 0.510767i \(0.829361\pi\)
\(570\) −4.93385e9 + 2.36746e8i −1.11590 + 0.0535453i
\(571\) −6.28388e9 5.27280e9i −1.41254 1.18526i −0.955196 0.295975i \(-0.904356\pi\)
−0.457346 0.889289i \(-0.651200\pi\)
\(572\) 7.52802e8 4.26935e9i 0.168188 0.953840i
\(573\) 5.16543e9 + 1.60419e9i 1.14701 + 0.356217i
\(574\) 1.81006e9 1.51882e9i 0.399485 0.335208i
\(575\) 1.06641e9 + 1.84707e9i 0.233930 + 0.405178i
\(576\) −4.40940e9 + 9.67302e9i −0.961392 + 2.10903i
\(577\) 2.54978e9 4.41636e9i 0.552571 0.957081i −0.445517 0.895273i \(-0.646980\pi\)
0.998088 0.0618076i \(-0.0196865\pi\)
\(578\) −9.79151e8 5.55304e9i −0.210912 1.19614i
\(579\) 1.30258e9 + 9.90607e8i 0.278888 + 0.212093i
\(580\) −7.35714e9 + 2.67778e9i −1.56571 + 0.569872i
\(581\) −5.00401e8 + 1.82131e8i −0.105853 + 0.0385272i
\(582\) 2.10496e8 1.65399e9i 0.0442603 0.347777i
\(583\) −2.88603e8 1.63675e9i −0.0603200 0.342092i
\(584\) −4.20315e8 + 7.28006e8i −0.0873232 + 0.151248i
\(585\) 3.00597e8 + 1.08433e9i 0.0620781 + 0.223932i
\(586\) 5.38651e9 + 9.32970e9i 1.10577 + 1.91525i
\(587\) −2.09533e9 + 1.75819e9i −0.427581 + 0.358783i −0.831038 0.556216i \(-0.812253\pi\)
0.403457 + 0.914999i \(0.367808\pi\)
\(588\) 1.50904e10 1.39481e10i 3.06112 2.82939i
\(589\) −1.39847e9 + 7.93114e9i −0.282001 + 1.59931i
\(590\) 2.62895e9 + 2.20595e9i 0.526987 + 0.442195i
\(591\) 4.49308e9 + 6.98602e9i 0.895339 + 1.39211i
\(592\) −2.08017e10 7.57120e9i −4.12072 1.49982i
\(593\) 7.40184e8 0.145763 0.0728816 0.997341i \(-0.476780\pi\)
0.0728816 + 0.997341i \(0.476780\pi\)
\(594\) 2.62919e8 8.56395e9i 0.0514718 1.67657i
\(595\) −2.73167e9 −0.531641
\(596\) 9.21675e9 + 3.35462e9i 1.78327 + 0.649056i
\(597\) −2.76019e9 + 5.35859e9i −0.530919 + 1.03072i
\(598\) 2.14972e9 + 1.80383e9i 0.411082 + 0.344939i
\(599\) −1.55540e8 + 8.82113e8i −0.0295698 + 0.167699i −0.996017 0.0891682i \(-0.971579\pi\)
0.966447 + 0.256867i \(0.0826903\pi\)
\(600\) −2.44493e9 1.08075e10i −0.462101 2.04266i
\(601\) −1.76738e9 + 1.48301e9i −0.332100 + 0.278665i −0.793555 0.608499i \(-0.791772\pi\)
0.461455 + 0.887164i \(0.347328\pi\)
\(602\) −7.29279e9 1.26315e10i −1.36240 2.35975i
\(603\) −4.54677e9 + 2.16815e9i −0.844485 + 0.402697i
\(604\) 5.45543e9 9.44908e9i 1.00739 1.74486i
\(605\) −1.11726e8 6.33632e8i −0.0205122 0.116330i
\(606\) 1.47417e10 6.18086e9i 2.69088 1.12822i
\(607\) 6.86069e9 2.49709e9i 1.24511 0.453182i 0.366362 0.930472i \(-0.380603\pi\)
0.878746 + 0.477290i \(0.158381\pi\)
\(608\) 1.59918e10 5.82052e9i 2.88558 1.05027i
\(609\) 9.75251e9 4.08900e9i 1.74967 0.733596i
\(610\) 1.00915e9 + 5.72320e9i 0.180013 + 1.02090i
\(611\) 1.10377e9 1.91179e9i 0.195765 0.339074i
\(612\) −7.91939e9 + 3.77640e9i −1.39657 + 0.665959i
\(613\) 3.89545e9 + 6.74712e9i 0.683040 + 1.18306i 0.974049 + 0.226339i \(0.0726758\pi\)
−0.291009 + 0.956720i \(0.593991\pi\)
\(614\) −1.07555e10 + 9.02492e9i −1.87517 + 1.57345i
\(615\) −1.19145e8 5.26666e8i −0.0206544 0.0913004i
\(616\) −4.32743e9 + 2.45421e10i −0.745930 + 4.23038i
\(617\) −6.68078e8 5.60584e8i −0.114506 0.0960822i 0.583737 0.811943i \(-0.301590\pi\)
−0.698243 + 0.715861i \(0.746034\pi\)
\(618\) −7.48684e9 + 1.45348e10i −1.27597 + 2.47714i
\(619\) −7.96465e9 2.89890e9i −1.34974 0.491265i −0.436872 0.899524i \(-0.643914\pi\)
−0.912866 + 0.408259i \(0.866136\pi\)
\(620\) 1.27361e10 2.14618
\(621\) 3.40012e9 + 2.10475e9i 0.569735 + 0.352679i
\(622\) −5.92436e9 −0.987132
\(623\) 7.62727e9 + 2.77610e9i 1.26375 + 0.459967i
\(624\) −4.29734e9 6.68169e9i −0.708033 1.10088i
\(625\) 8.68563e8 + 7.28811e8i 0.142305 + 0.119408i
\(626\) 9.62004e8 5.45580e9i 0.156735 0.888890i
\(627\) −4.31376e9 + 3.98721e9i −0.698908 + 0.646000i
\(628\) −3.02357e9 + 2.53708e9i −0.487148 + 0.408766i
\(629\) −2.64788e9 4.58626e9i −0.424249 0.734820i
\(630\) −2.81865e9 1.01676e10i −0.449107 1.62005i
\(631\) 5.60535e9 9.70875e9i 0.888178 1.53837i 0.0461503 0.998935i \(-0.485305\pi\)
0.842027 0.539435i \(-0.181362\pi\)
\(632\) −4.50479e8 2.55479e9i −0.0709847 0.402574i
\(633\) −1.06304e9 + 8.35291e9i −0.166586 + 1.30896i
\(634\) 1.56005e10 5.67812e9i 2.43123 0.884895i
\(635\) −3.71887e9 + 1.35356e9i −0.576372 + 0.209782i
\(636\) −5.23243e9 3.97924e9i −0.806498 0.613338i
\(637\) 7.72952e8 + 4.38363e9i 0.118485 + 0.671964i
\(638\) −6.45684e9 + 1.11836e10i −0.984346 + 1.70494i
\(639\) −3.01994e9 + 6.62492e9i −0.457873 + 1.00445i
\(640\) −2.78602e9 4.82553e9i −0.420101 0.727637i
\(641\) 8.04090e9 6.74712e9i 1.20587 1.01185i 0.206430 0.978461i \(-0.433815\pi\)
0.999443 0.0333862i \(-0.0106291\pi\)
\(642\) −6.12359e9 1.90176e9i −0.913342 0.283650i
\(643\) −2.67605e8 + 1.51766e9i −0.0396968 + 0.225132i −0.998202 0.0599442i \(-0.980908\pi\)
0.958505 + 0.285076i \(0.0920188\pi\)
\(644\) −1.45337e10 1.21953e10i −2.14426 1.79925i
\(645\) −3.32935e9 + 1.59756e8i −0.488541 + 0.0234422i
\(646\) 7.83975e9 + 2.85344e9i 1.14416 + 0.416442i
\(647\) 8.22546e9 1.19398 0.596988 0.802251i \(-0.296364\pi\)
0.596988 + 0.802251i \(0.296364\pi\)
\(648\) −1.36267e10 1.56819e10i −1.96733 2.26405i
\(649\) 4.08125e9 0.586052
\(650\) 3.67912e9 + 1.33909e9i 0.525470 + 0.191255i
\(651\) −1.71829e10 + 8.24505e8i −2.44097 + 0.117128i
\(652\) 2.51272e9 + 2.10842e9i 0.355040 + 0.297914i
\(653\) −1.41692e9 + 8.03573e9i −0.199135 + 1.12935i 0.707270 + 0.706943i \(0.249926\pi\)
−0.906406 + 0.422409i \(0.861185\pi\)
\(654\) 4.26165e9 + 1.32351e9i 0.595739 + 0.185014i
\(655\) 3.98643e9 3.34501e9i 0.554293 0.465107i
\(656\) 1.90616e9 + 3.30157e9i 0.263631 + 0.456623i
\(657\) −2.45754e8 3.44606e8i −0.0338081 0.0474071i
\(658\) −1.03499e10 + 1.79266e10i −1.41627 + 2.45305i
\(659\) 1.20175e9 + 6.81545e9i 0.163574 + 0.927675i 0.950522 + 0.310656i \(0.100549\pi\)
−0.786948 + 0.617019i \(0.788340\pi\)
\(660\) 7.39437e9 + 5.62338e9i 1.00115 + 0.761367i
\(661\) −1.32327e10 + 4.81632e9i −1.78215 + 0.648650i −0.782488 + 0.622666i \(0.786050\pi\)
−0.999662 + 0.0259835i \(0.991728\pi\)
\(662\) −3.32444e9 + 1.21000e9i −0.445364 + 0.162099i
\(663\) 2.39935e8 1.88531e9i 0.0319740 0.251237i
\(664\) −2.73802e8 1.55281e9i −0.0362951 0.205840i
\(665\) −3.61691e9 + 6.26468e9i −0.476939 + 0.826082i
\(666\) 1.43385e10 1.45881e10i 1.88080 1.91354i
\(667\) −3.01353e9 5.21959e9i −0.393220 0.681077i
\(668\) 1.00739e10 8.45300e9i 1.30761 1.09722i
\(669\) 8.46335e9 7.82266e9i 1.09283 1.01010i
\(670\) 1.31538e9 7.45988e9i 0.168962 0.958231i
\(671\) 5.29427e9 + 4.44242e9i 0.676514 + 0.567663i
\(672\) 1.96637e10 + 3.05740e10i 2.49962 + 3.88651i
\(673\) 2.79426e9 + 1.01703e9i 0.353358 + 0.128612i 0.512599 0.858628i \(-0.328683\pi\)
−0.159242 + 0.987240i \(0.550905\pi\)
\(674\) 1.69082e10 2.12710
\(675\) 5.46203e9 + 1.13695e9i 0.683583 + 0.142291i
\(676\) −1.70422e10 −2.12184
\(677\) −1.01110e10 3.68009e9i −1.25237 0.455824i −0.371166 0.928566i \(-0.621042\pi\)
−0.881201 + 0.472742i \(0.843264\pi\)
\(678\) −4.56888e9 + 8.86996e9i −0.562997 + 1.09299i
\(679\) −1.87050e9 1.56953e9i −0.229305 0.192410i
\(680\) 1.40453e9 7.96551e9i 0.171297 0.971476i
\(681\) −7.72437e8 3.41446e9i −0.0937235 0.414293i
\(682\) 1.60923e10 1.35030e10i 1.94255 1.62999i
\(683\) 6.49743e9 + 1.12539e10i 0.780313 + 1.35154i 0.931759 + 0.363077i \(0.118274\pi\)
−0.151446 + 0.988466i \(0.548393\pi\)
\(684\) −1.82520e9 + 2.31622e10i −0.218079 + 2.76747i
\(685\) 3.92141e8 6.79207e8i 0.0466149 0.0807394i
\(686\) −2.75446e9 1.56213e10i −0.325764 1.84750i
\(687\) 1.29564e10 5.43231e9i 1.52453 0.639198i
\(688\) 2.21137e10 8.04873e9i 2.58882 0.942253i
\(689\) 1.33807e9 4.87017e8i 0.155852 0.0567253i
\(690\) −5.54569e9 + 2.32518e9i −0.642664 + 0.269454i
\(691\) 3.01289e8 + 1.70869e9i 0.0347384 + 0.197011i 0.997238 0.0742717i \(-0.0236632\pi\)
−0.962500 + 0.271283i \(0.912552\pi\)
\(692\) −1.52313e10 + 2.63814e10i −1.74729 + 3.02640i
\(693\) −1.03401e10 7.10807e9i −1.18021 0.811308i
\(694\) −1.63905e10 2.83892e10i −1.86137 3.22399i
\(695\) 4.28803e9 3.59808e9i 0.484519 0.406560i
\(696\) 6.90906e9 + 3.05406e10i 0.776760 + 3.43357i
\(697\) −1.58371e8 + 8.98165e8i −0.0177158 + 0.100471i
\(698\) −4.70078e9 3.94442e9i −0.523210 0.439025i
\(699\) 7.09205e9 1.37684e10i 0.785419 1.52480i
\(700\) −2.48737e10 9.05327e9i −2.74092 0.997613i
\(701\) −1.72534e10 −1.89174 −0.945872 0.324541i \(-0.894790\pi\)
−0.945872 + 0.324541i \(0.894790\pi\)
\(702\) 7.26494e9 1.05227e9i 0.792596 0.114801i
\(703\) −1.40239e10 −1.52239
\(704\) −1.78647e10 6.50221e9i −1.92971 0.702355i
\(705\) 2.55885e9 + 3.97861e9i 0.275032 + 0.427631i
\(706\) 6.99650e9 + 5.87076e9i 0.748281 + 0.627882i
\(707\) 4.06505e9 2.30541e10i 0.432612 2.45346i
\(708\) 1.18542e10 1.09568e10i 1.25533 1.16030i
\(709\) −8.80926e9 + 7.39184e9i −0.928277 + 0.778917i −0.975507 0.219967i \(-0.929405\pi\)
0.0472305 + 0.998884i \(0.484960\pi\)
\(710\) −5.47437e9 9.48189e9i −0.574024 0.994239i
\(711\) 1.26455e9 + 3.27168e8i 0.131945 + 0.0341372i
\(712\) −1.20168e10 + 2.08137e10i −1.24769 + 2.16107i
\(713\) 1.70251e9 + 9.65542e9i 0.175904 + 0.997603i
\(714\) −2.24984e9 + 1.76783e10i −0.231317 + 1.81759i
\(715\) −1.89093e9 + 6.88244e8i −0.193466 + 0.0704160i
\(716\) 2.11240e10 7.68851e9i 2.15071 0.782793i
\(717\) −3.73418e9 2.83982e9i −0.378336 0.287723i
\(718\) 2.28948e9 + 1.29843e10i 0.230835 + 1.30913i
\(719\) 3.01431e9 5.22093e9i 0.302438 0.523838i −0.674250 0.738504i \(-0.735533\pi\)
0.976688 + 0.214666i \(0.0688661\pi\)
\(720\) 1.69453e10 1.62996e9i 1.69194 0.162747i
\(721\) 1.19719e10 + 2.07360e10i 1.18957 + 2.06040i
\(722\) 2.25752e9 1.89428e9i 0.223229 0.187312i
\(723\) −4.00226e9 1.24295e9i −0.393841 0.122312i
\(724\) 5.42744e8 3.07806e9i 0.0531509 0.301433i
\(725\) −6.44154e9 5.40510e9i −0.627779 0.526769i
\(726\) −4.19263e9 + 2.01180e8i −0.406639 + 0.0195122i
\(727\) 6.43880e9 + 2.34353e9i 0.621490 + 0.226204i 0.633523 0.773724i \(-0.281608\pi\)
−0.0120331 + 0.999928i \(0.503830\pi\)
\(728\) −2.13512e10 −2.05098
\(729\) 1.00305e10 2.96794e9i 0.958904 0.283732i
\(730\) 6.36491e8 0.0605568
\(731\) 5.29025e9 + 1.92549e9i 0.500916 + 0.182319i
\(732\) 2.73040e10 1.31016e9i 2.57299 0.123462i
\(733\) 7.81407e9 + 6.55678e9i 0.732847 + 0.614932i 0.930906 0.365258i \(-0.119019\pi\)
−0.198059 + 0.980190i \(0.563464\pi\)
\(734\) −2.19504e9 + 1.24487e10i −0.204883 + 1.16195i
\(735\) −9.10921e9 2.82898e9i −0.846204 0.262799i
\(736\) 1.58708e10 1.33172e10i 1.46733 1.23124i
\(737\) −4.50417e9 7.80146e9i −0.414456 0.717859i
\(738\) −3.50650e9 + 3.37289e8i −0.321127 + 0.0308891i
\(739\) 5.22487e9 9.04974e9i 0.476233 0.824860i −0.523396 0.852090i \(-0.675335\pi\)
0.999629 + 0.0272293i \(0.00866842\pi\)
\(740\) 3.85116e9 + 2.18410e10i 0.349366 + 1.98135i
\(741\) −4.00598e9 3.04653e9i −0.361697 0.275069i
\(742\) −1.25469e10 + 4.56670e9i −1.12752 + 0.410382i
\(743\) 1.30385e10 4.74562e9i 1.16618 0.424456i 0.314880 0.949131i \(-0.398036\pi\)
0.851302 + 0.524676i \(0.175813\pi\)
\(744\) 6.43064e9 5.05290e10i 0.572465 4.49817i
\(745\) −7.90574e8 4.48357e9i −0.0700480 0.397262i
\(746\) 2.75944e9 4.77949e9i 0.243352 0.421498i
\(747\) 7.68597e8 + 1.98853e8i 0.0674647 + 0.0174546i
\(748\) −7.84520e9 1.35883e10i −0.685407 1.18716i
\(749\) −7.19345e9 + 6.03602e9i −0.625534 + 0.524885i
\(750\) −1.49849e10 + 1.38505e10i −1.29700 + 1.19882i
\(751\) 3.68014e9 2.08711e10i 0.317048 1.79807i −0.243451 0.969913i \(-0.578280\pi\)
0.560499 0.828155i \(-0.310609\pi\)
\(752\) −2.55842e10 2.14677e10i −2.19386 1.84087i
\(753\) −5.58298e9 8.68065e9i −0.476523 0.740917i
\(754\) −1.03967e10 3.78411e9i −0.883279 0.321487i
\(755\) −5.06453e9 −0.428277
\(756\) −4.91164e10 + 7.11414e9i