Properties

Label 27.8.e.a.4.2
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 4.2
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-19.1819 - 6.98163i) q^{2} +(-45.3621 - 11.3703i) q^{3} +(221.148 + 185.565i) q^{4} +(73.2555 - 415.452i) q^{5} +(790.746 + 534.805i) q^{6} +(1090.38 - 914.934i) q^{7} +(-1640.05 - 2840.66i) q^{8} +(1928.43 + 1031.56i) q^{9} +O(q^{10})\) \(q+(-19.1819 - 6.98163i) q^{2} +(-45.3621 - 11.3703i) q^{3} +(221.148 + 185.565i) q^{4} +(73.2555 - 415.452i) q^{5} +(790.746 + 534.805i) q^{6} +(1090.38 - 914.934i) q^{7} +(-1640.05 - 2840.66i) q^{8} +(1928.43 + 1031.56i) q^{9} +(-4305.71 + 7457.72i) q^{10} +(-356.707 - 2022.99i) q^{11} +(-7921.78 - 10932.1i) q^{12} +(824.032 - 299.923i) q^{13} +(-27303.2 + 9937.54i) q^{14} +(-8046.84 + 18012.8i) q^{15} +(5210.24 + 29548.7i) q^{16} +(15072.9 - 26107.1i) q^{17} +(-29789.0 - 33250.9i) q^{18} +(-7133.23 - 12355.1i) q^{19} +(93293.7 - 78282.7i) q^{20} +(-59864.7 + 29105.4i) q^{21} +(-7281.44 + 41295.1i) q^{22} +(27506.4 + 23080.6i) q^{23} +(42097.1 + 147506. i) q^{24} +(-93820.9 - 34148.0i) q^{25} -17900.4 q^{26} +(-75748.5 - 68720.5i) q^{27} +410913. q^{28} +(-18256.8 - 6644.93i) q^{29} +(280113. - 289340. i) q^{30} +(96577.6 + 81038.2i) q^{31} +(33449.4 - 189701. i) q^{32} +(-6820.99 + 95822.7i) q^{33} +(-471397. + 395549. i) q^{34} +(-300235. - 520023. i) q^{35} +(235047. + 585976. i) q^{36} +(80433.0 - 139314. i) q^{37} +(50569.8 + 286796. i) q^{38} +(-40790.0 + 4235.64i) q^{39} +(-1.30030e6 + 473271. i) q^{40} +(-748958. + 272598. i) q^{41} +(1.35152e6 - 140342. i) q^{42} +(-2452.85 - 13910.8i) q^{43} +(296510. - 513571. i) q^{44} +(569832. - 725605. i) q^{45} +(-366484. - 634769. i) q^{46} +(-589117. + 494328. i) q^{47} +(99630.7 - 1.39963e6i) q^{48} +(208808. - 1.18421e6i) q^{49} +(1.56125e6 + 1.31005e6i) q^{50} +(-980583. + 1.01289e6i) q^{51} +(237888. + 86584.2i) q^{52} +1.68958e6 q^{53} +(973218. + 1.84704e6i) q^{54} -866586. q^{55} +(-4.38728e6 - 1.59684e6i) q^{56} +(183097. + 641560. i) q^{57} +(303807. + 254924. i) q^{58} +(-79286.9 + 449658. i) q^{59} +(-5.12209e6 + 2.49029e6i) q^{60} +(433924. - 364106. i) q^{61} +(-1.28676e6 - 2.22873e6i) q^{62} +(3.04652e6 - 639600. i) q^{63} +(-45752.7 + 79246.0i) q^{64} +(-64239.0 - 364317. i) q^{65} +(799839. - 1.79044e6i) q^{66} +(16844.7 - 6130.98i) q^{67} +(8.17789e6 - 2.97651e6i) q^{68} +(-985313. - 1.35974e6i) q^{69} +(2.12847e6 + 1.20712e7i) q^{70} +(-1.27574e6 + 2.20965e6i) q^{71} +(-232425. - 7.16983e6i) q^{72} +(-1.09490e6 - 1.89641e6i) q^{73} +(-2.51550e6 + 2.11075e6i) q^{74} +(3.86764e6 + 2.61580e6i) q^{75} +(715179. - 4.05598e6i) q^{76} +(-2.23984e6 - 1.87945e6i) q^{77} +(812001. + 203533. i) q^{78} +(2.98294e6 + 1.08570e6i) q^{79} +1.26578e7 q^{80} +(2.65474e6 + 3.97859e6i) q^{81} +1.62696e7 q^{82} +(-3.88072e6 - 1.41246e6i) q^{83} +(-1.86399e7 - 4.67221e6i) q^{84} +(-9.74207e6 - 8.17457e6i) q^{85} +(-50069.8 + 283960. i) q^{86} +(752611. + 509013. i) q^{87} +(-5.16159e6 + 4.33109e6i) q^{88} +(-986256. - 1.70825e6i) q^{89} +(-1.59964e7 + 9.94010e6i) q^{90} +(624095. - 1.08096e6i) q^{91} +(1.80002e6 + 1.02084e7i) q^{92} +(-3.45953e6 - 4.77418e6i) q^{93} +(1.47516e7 - 5.36914e6i) q^{94} +(-5.65551e6 + 2.05844e6i) q^{95} +(-3.67429e6 + 8.22490e6i) q^{96} +(-2.56578e6 - 1.45512e7i) q^{97} +(-1.22731e7 + 2.12576e7i) q^{98} +(1.39895e6 - 4.26916e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −19.1819 6.98163i −1.69545 0.617095i −0.700160 0.713986i \(-0.746888\pi\)
−0.995295 + 0.0968913i \(0.969110\pi\)
\(3\) −45.3621 11.3703i −0.969992 0.243135i
\(4\) 221.148 + 185.565i 1.72772 + 1.44973i
\(5\) 73.2555 415.452i 0.262087 1.48637i −0.515117 0.857120i \(-0.672252\pi\)
0.777204 0.629248i \(-0.216637\pi\)
\(6\) 790.746 + 534.805i 1.49454 + 1.01080i
\(7\) 1090.38 914.934i 1.20153 1.00820i 0.201940 0.979398i \(-0.435275\pi\)
0.999585 0.0288014i \(-0.00916904\pi\)
\(8\) −1640.05 2840.66i −1.13251 1.96157i
\(9\) 1928.43 + 1031.56i 0.881771 + 0.471678i
\(10\) −4305.71 + 7457.72i −1.36159 + 2.35834i
\(11\) −356.707 2022.99i −0.0808049 0.458267i −0.998183 0.0602510i \(-0.980810\pi\)
0.917378 0.398016i \(-0.130301\pi\)
\(12\) −7921.78 10932.1i −1.32339 1.82629i
\(13\) 824.032 299.923i 0.104026 0.0378624i −0.289483 0.957183i \(-0.593483\pi\)
0.393509 + 0.919321i \(0.371261\pi\)
\(14\) −27303.2 + 9937.54i −2.65929 + 0.967901i
\(15\) −8046.84 + 18012.8i −0.615610 + 1.37804i
\(16\) 5210.24 + 29548.7i 0.318008 + 1.80351i
\(17\) 15072.9 26107.1i 0.744091 1.28880i −0.206527 0.978441i \(-0.566216\pi\)
0.950618 0.310363i \(-0.100450\pi\)
\(18\) −29789.0 33250.9i −1.20393 1.34385i
\(19\) −7133.23 12355.1i −0.238588 0.413246i 0.721721 0.692184i \(-0.243351\pi\)
−0.960309 + 0.278937i \(0.910018\pi\)
\(20\) 93293.7 78282.7i 2.60764 2.18807i
\(21\) −59864.7 + 29105.4i −1.41060 + 0.685813i
\(22\) −7281.44 + 41295.1i −0.145793 + 0.826835i
\(23\) 27506.4 + 23080.6i 0.471396 + 0.395548i 0.847304 0.531109i \(-0.178224\pi\)
−0.375907 + 0.926657i \(0.622669\pi\)
\(24\) 42097.1 + 147506.i 0.621603 + 2.17806i
\(25\) −93820.9 34148.0i −1.20091 0.437095i
\(26\) −17900.4 −0.199736
\(27\) −75748.5 68720.5i −0.740630 0.671914i
\(28\) 410913. 3.53751
\(29\) −18256.8 6644.93i −0.139005 0.0505938i 0.271581 0.962416i \(-0.412454\pi\)
−0.410586 + 0.911822i \(0.634676\pi\)
\(30\) 280113. 289340.i 1.89412 1.95652i
\(31\) 96577.6 + 81038.2i 0.582251 + 0.488567i 0.885686 0.464286i \(-0.153689\pi\)
−0.303434 + 0.952852i \(0.598133\pi\)
\(32\) 33449.4 189701.i 0.180453 1.02340i
\(33\) −6820.99 + 95822.7i −0.0330407 + 0.464162i
\(34\) −471397. + 395549.i −2.05689 + 1.72593i
\(35\) −300235. 520023.i −1.18365 2.05014i
\(36\) 235047. + 585976.i 0.839645 + 2.09325i
\(37\) 80433.0 139314.i 0.261053 0.452157i −0.705469 0.708741i \(-0.749264\pi\)
0.966522 + 0.256584i \(0.0825970\pi\)
\(38\) 50569.8 + 286796.i 0.149503 + 0.847872i
\(39\) −40790.0 + 4235.64i −0.110110 + 0.0114339i
\(40\) −1.30030e6 + 473271.i −3.21243 + 1.16923i
\(41\) −748958. + 272598.i −1.69713 + 0.617703i −0.995493 0.0948362i \(-0.969767\pi\)
−0.701632 + 0.712539i \(0.747545\pi\)
\(42\) 1.35152e6 140342.i 2.81482 0.292291i
\(43\) −2452.85 13910.8i −0.00470469 0.0266816i 0.982365 0.186973i \(-0.0598677\pi\)
−0.987070 + 0.160291i \(0.948757\pi\)
\(44\) 296510. 513571.i 0.524754 0.908900i
\(45\) 569832. 725605.i 0.932188 1.18702i
\(46\) −366484. 634769.i −0.555140 0.961531i
\(47\) −589117. + 494328.i −0.827673 + 0.694501i −0.954756 0.297392i \(-0.903883\pi\)
0.127082 + 0.991892i \(0.459439\pi\)
\(48\) 99630.7 1.39963e6i 0.130032 1.82671i
\(49\) 208808. 1.18421e6i 0.253549 1.43795i
\(50\) 1.56125e6 + 1.31005e6i 1.76636 + 1.48215i
\(51\) −980583. + 1.01289e6i −1.03512 + 1.06922i
\(52\) 237888. + 86584.2i 0.234618 + 0.0853939i
\(53\) 1.68958e6 1.55888 0.779442 0.626475i \(-0.215503\pi\)
0.779442 + 0.626475i \(0.215503\pi\)
\(54\) 973218. + 1.84704e6i 0.841069 + 1.59624i
\(55\) −866586. −0.702331
\(56\) −4.38728e6 1.59684e6i −3.33840 1.21508i
\(57\) 183097. + 641560.i 0.130954 + 0.458855i
\(58\) 303807. + 254924.i 0.204456 + 0.171559i
\(59\) −79286.9 + 449658.i −0.0502597 + 0.285037i −0.999571 0.0293019i \(-0.990672\pi\)
0.949311 + 0.314339i \(0.101783\pi\)
\(60\) −5.12209e6 + 2.49029e6i −3.06138 + 1.48840i
\(61\) 433924. 364106.i 0.244771 0.205387i −0.512146 0.858898i \(-0.671149\pi\)
0.756917 + 0.653511i \(0.226705\pi\)
\(62\) −1.28676e6 2.22873e6i −0.685688 1.18765i
\(63\) 3.04652e6 639600.i 1.53502 0.322268i
\(64\) −45752.7 + 79246.0i −0.0218166 + 0.0377874i
\(65\) −64239.0 364317.i −0.0290136 0.164544i
\(66\) 799839. 1.79044e6i 0.342451 0.766577i
\(67\) 16844.7 6130.98i 0.00684230 0.00249039i −0.338597 0.940932i \(-0.609952\pi\)
0.345439 + 0.938441i \(0.387730\pi\)
\(68\) 8.17789e6 2.97651e6i 3.15399 1.14796i
\(69\) −985313. 1.35974e6i −0.361079 0.498292i
\(70\) 2.12847e6 + 1.20712e7i 0.741693 + 4.20635i
\(71\) −1.27574e6 + 2.20965e6i −0.423017 + 0.732687i −0.996233 0.0867174i \(-0.972362\pi\)
0.573216 + 0.819404i \(0.305696\pi\)
\(72\) −232425. 7.16983e6i −0.0733871 2.26384i
\(73\) −1.09490e6 1.89641e6i −0.329414 0.570563i 0.652981 0.757374i \(-0.273518\pi\)
−0.982396 + 0.186811i \(0.940185\pi\)
\(74\) −2.51550e6 + 2.11075e6i −0.721627 + 0.605517i
\(75\) 3.86764e6 + 2.61580e6i 1.05860 + 0.715961i
\(76\) 715179. 4.05598e6i 0.186882 1.05986i
\(77\) −2.23984e6 1.87945e6i −0.559114 0.469152i
\(78\) 812001. + 203533.i 0.193743 + 0.0485629i
\(79\) 2.98294e6 + 1.08570e6i 0.680691 + 0.247751i 0.659144 0.752017i \(-0.270919\pi\)
0.0215468 + 0.999768i \(0.493141\pi\)
\(80\) 1.26578e7 2.76403
\(81\) 2.65474e6 + 3.97859e6i 0.555039 + 0.831824i
\(82\) 1.62696e7 3.25858
\(83\) −3.88072e6 1.41246e6i −0.744969 0.271147i −0.0584821 0.998288i \(-0.518626\pi\)
−0.686487 + 0.727142i \(0.740848\pi\)
\(84\) −1.86399e7 4.67221e6i −3.43135 0.860091i
\(85\) −9.74207e6 8.17457e6i −1.72062 1.44377i
\(86\) −50069.8 + 283960.i −0.00848851 + 0.0481407i
\(87\) 752611. + 509013.i 0.122533 + 0.0828726i
\(88\) −5.16159e6 + 4.33109e6i −0.807410 + 0.677498i
\(89\) −986256. 1.70825e6i −0.148294 0.256853i 0.782303 0.622898i \(-0.214045\pi\)
−0.930597 + 0.366045i \(0.880712\pi\)
\(90\) −1.59964e7 + 9.94010e6i −2.31298 + 1.43728i
\(91\) 624095. 1.08096e6i 0.0868172 0.150372i
\(92\) 1.80002e6 + 1.02084e7i 0.241002 + 1.36679i
\(93\) −3.45953e6 4.77418e6i −0.445992 0.615472i
\(94\) 1.47516e7 5.36914e6i 1.83186 0.666741i
\(95\) −5.65551e6 + 2.05844e6i −0.676767 + 0.246323i
\(96\) −3.67429e6 + 8.22490e6i −0.423862 + 0.948814i
\(97\) −2.56578e6 1.45512e7i −0.285442 1.61882i −0.703703 0.710494i \(-0.748471\pi\)
0.418261 0.908327i \(-0.362640\pi\)
\(98\) −1.22731e7 + 2.12576e7i −1.31723 + 2.28151i
\(99\) 1.39895e6 4.26916e6i 0.144903 0.442200i
\(100\) −1.44116e7 2.49616e7i −1.44116 2.49616i
\(101\) −6.19985e6 + 5.20230e6i −0.598765 + 0.502424i −0.891049 0.453908i \(-0.850029\pi\)
0.292283 + 0.956332i \(0.405585\pi\)
\(102\) 2.58810e7 1.25830e7i 2.41480 1.17404i
\(103\) −3.55317e6 + 2.01511e7i −0.320395 + 1.81705i 0.219837 + 0.975537i \(0.429447\pi\)
−0.540233 + 0.841516i \(0.681664\pi\)
\(104\) −2.20344e6 1.84890e6i −0.192081 0.161175i
\(105\) 7.70648e6 + 2.70031e7i 0.649671 + 2.27641i
\(106\) −3.24093e7 1.17960e7i −2.64302 0.961979i
\(107\) 1.52697e7 1.20500 0.602498 0.798120i \(-0.294172\pi\)
0.602498 + 0.798120i \(0.294172\pi\)
\(108\) −3.99949e6 2.92537e7i −0.305507 2.23459i
\(109\) −5.36888e6 −0.397092 −0.198546 0.980092i \(-0.563622\pi\)
−0.198546 + 0.980092i \(0.563622\pi\)
\(110\) 1.66227e7 + 6.05018e6i 1.19077 + 0.433405i
\(111\) −5.23265e6 + 5.40503e6i −0.363154 + 0.375118i
\(112\) 3.27162e7 + 2.74522e7i 2.20039 + 1.84635i
\(113\) −1.56632e6 + 8.88306e6i −0.102119 + 0.579146i 0.890213 + 0.455545i \(0.150555\pi\)
−0.992332 + 0.123601i \(0.960556\pi\)
\(114\) 967001. 1.35846e7i 0.0611308 0.858779i
\(115\) 1.16039e7 9.73682e6i 0.711477 0.597000i
\(116\) −2.80438e6 4.85733e6i −0.166814 0.288931i
\(117\) 1.89848e6 + 271657.i 0.109586 + 0.0156809i
\(118\) 4.66022e6 8.07174e6i 0.261108 0.452252i
\(119\) −7.45109e6 4.22572e7i −0.405327 2.29872i
\(120\) 6.43655e7 6.68373e6i 3.40031 0.353089i
\(121\) 1.43467e7 5.22178e6i 0.736213 0.267960i
\(122\) −1.08655e7 + 3.95473e6i −0.541741 + 0.197178i
\(123\) 3.70738e7 3.84975e6i 1.79638 0.186537i
\(124\) 6.32006e6 + 3.58428e7i 0.297677 + 1.68821i
\(125\) −4.58081e6 + 7.93420e6i −0.209777 + 0.363344i
\(126\) −6.29035e7 9.00098e6i −2.80142 0.400860i
\(127\) 7.62266e6 + 1.32028e7i 0.330213 + 0.571945i 0.982553 0.185981i \(-0.0595462\pi\)
−0.652341 + 0.757926i \(0.726213\pi\)
\(128\) −1.74569e7 + 1.46481e7i −0.735755 + 0.617372i
\(129\) −46903.6 + 658912.i −0.00192372 + 0.0270249i
\(130\) −1.31131e6 + 7.43678e6i −0.0523483 + 0.296882i
\(131\) 5.63340e6 + 4.72698e6i 0.218938 + 0.183711i 0.745660 0.666327i \(-0.232135\pi\)
−0.526722 + 0.850038i \(0.676579\pi\)
\(132\) −1.92898e7 + 1.99252e7i −0.729993 + 0.754040i
\(133\) −1.90820e7 6.94528e6i −0.703304 0.255982i
\(134\) −365918. −0.0131376
\(135\) −3.40991e7 + 2.64358e7i −1.19282 + 0.924748i
\(136\) −9.88815e7 −3.37077
\(137\) 3.38816e7 + 1.23319e7i 1.12575 + 0.409740i 0.836748 0.547588i \(-0.184454\pi\)
0.289003 + 0.957328i \(0.406676\pi\)
\(138\) 9.40696e6 + 3.29615e7i 0.304700 + 1.06765i
\(139\) 1.46861e7 + 1.23231e7i 0.463825 + 0.389195i 0.844536 0.535499i \(-0.179876\pi\)
−0.380711 + 0.924694i \(0.624321\pi\)
\(140\) 3.01017e7 1.70715e8i 0.927134 5.25804i
\(141\) 3.23442e7 1.57253e7i 0.971694 0.472424i
\(142\) 3.98980e7 3.34784e7i 1.16934 0.981196i
\(143\) −900679. 1.56002e6i −0.0257569 0.0446123i
\(144\) −2.04337e7 + 6.23574e7i −0.570267 + 1.74028i
\(145\) −4.09806e6 + 7.09805e6i −0.111632 + 0.193353i
\(146\) 7.76208e6 + 4.40210e7i 0.206416 + 1.17064i
\(147\) −2.29368e7 + 5.13440e7i −0.595555 + 1.33315i
\(148\) 4.36394e7 1.58834e7i 1.10653 0.402743i
\(149\) 3.33730e6 1.21468e6i 0.0826502 0.0300822i −0.300364 0.953825i \(-0.597108\pi\)
0.383014 + 0.923742i \(0.374886\pi\)
\(150\) −5.59260e7 7.71783e7i −1.35299 1.86714i
\(151\) 1.26566e7 + 7.17790e7i 0.299155 + 1.69659i 0.649816 + 0.760092i \(0.274846\pi\)
−0.350660 + 0.936503i \(0.614043\pi\)
\(152\) −2.33977e7 + 4.05261e7i −0.540408 + 0.936013i
\(153\) 5.59981e7 3.47971e7i 1.26402 0.785458i
\(154\) 2.98428e7 + 5.16892e7i 0.658440 + 1.14045i
\(155\) 4.07424e7 3.41869e7i 0.878790 0.737393i
\(156\) −9.80660e6 6.63249e6i −0.206815 0.139875i
\(157\) 5.05629e6 2.86757e7i 0.104276 0.591377i −0.887231 0.461325i \(-0.847374\pi\)
0.991507 0.130053i \(-0.0415146\pi\)
\(158\) −4.96385e7 4.16516e7i −1.00119 0.840102i
\(159\) −7.66429e7 1.92110e7i −1.51210 0.379019i
\(160\) −7.63614e7 2.77933e7i −1.47385 0.536438i
\(161\) 5.11095e7 0.965186
\(162\) −2.31458e7 9.48512e7i −0.427730 1.75283i
\(163\) −4.34125e7 −0.785160 −0.392580 0.919718i \(-0.628417\pi\)
−0.392580 + 0.919718i \(0.628417\pi\)
\(164\) −2.16215e8 7.86958e7i −3.82765 1.39315i
\(165\) 3.93101e7 + 9.85334e6i 0.681256 + 0.170761i
\(166\) 6.45781e7 + 5.41875e7i 1.09574 + 0.919434i
\(167\) −1.36287e6 + 7.72920e6i −0.0226436 + 0.128418i −0.994034 0.109070i \(-0.965213\pi\)
0.971391 + 0.237488i \(0.0763240\pi\)
\(168\) 1.80860e8 + 1.22321e8i 2.94279 + 1.99030i
\(169\) −4.74791e7 + 3.98397e7i −0.756657 + 0.634910i
\(170\) 1.29799e8 + 2.24819e8i 2.02629 + 3.50963i
\(171\) −1.01091e6 3.11844e7i −0.0154606 0.476925i
\(172\) 2.03891e6 3.53150e6i 0.0305527 0.0529188i
\(173\) −1.55348e7 8.81021e7i −0.228110 1.29367i −0.856651 0.515897i \(-0.827459\pi\)
0.628541 0.777776i \(-0.283652\pi\)
\(174\) −1.08827e7 1.50183e7i −0.156609 0.216121i
\(175\) −1.33543e8 + 4.86057e7i −1.88360 + 0.685574i
\(176\) 5.79182e7 2.10805e7i 0.800793 0.291465i
\(177\) 8.70937e6 1.94959e7i 0.118054 0.264264i
\(178\) 6.99190e6 + 3.96531e7i 0.0929235 + 0.526995i
\(179\) 1.22778e7 2.12657e7i 0.160005 0.277137i −0.774865 0.632127i \(-0.782182\pi\)
0.934870 + 0.354989i \(0.115516\pi\)
\(180\) 2.60664e8 5.47249e7i 3.33140 0.699408i
\(181\) −6.47329e7 1.12121e8i −0.811428 1.40543i −0.911865 0.410491i \(-0.865357\pi\)
0.100437 0.994943i \(-0.467976\pi\)
\(182\) −1.95182e7 + 1.63777e7i −0.239988 + 0.201374i
\(183\) −2.38237e7 + 1.15827e7i −0.287362 + 0.139712i
\(184\) 2.04521e7 1.15990e8i 0.242034 1.37264i
\(185\) −5.19862e7 4.36216e7i −0.603653 0.506525i
\(186\) 3.30287e7 + 1.15731e8i 0.376354 + 1.31872i
\(187\) −5.81909e7 2.11797e7i −0.650742 0.236851i
\(188\) −2.22012e8 −2.43682
\(189\) −1.45469e8 5.62631e6i −1.56731 0.0606188i
\(190\) 1.22855e8 1.29943
\(191\) 1.55434e8 + 5.65734e7i 1.61410 + 0.587483i 0.982244 0.187605i \(-0.0600726\pi\)
0.631852 + 0.775089i \(0.282295\pi\)
\(192\) 2.97649e6 3.07454e6i 0.0303494 0.0313492i
\(193\) −6.16406e7 5.17226e7i −0.617186 0.517881i 0.279732 0.960078i \(-0.409755\pi\)
−0.896918 + 0.442198i \(0.854199\pi\)
\(194\) −5.23750e7 + 2.97033e8i −0.515013 + 2.92078i
\(195\) −1.22838e6 + 1.72566e7i −0.0118635 + 0.166661i
\(196\) 2.65925e8 2.23138e8i 2.52269 2.11679i
\(197\) −5.19210e7 8.99298e7i −0.483850 0.838053i 0.515978 0.856602i \(-0.327429\pi\)
−0.999828 + 0.0185487i \(0.994095\pi\)
\(198\) −5.66401e7 + 7.21236e7i −0.518557 + 0.660312i
\(199\) 6.51006e7 1.12758e8i 0.585598 1.01428i −0.409203 0.912443i \(-0.634193\pi\)
0.994801 0.101841i \(-0.0324734\pi\)
\(200\) 5.68685e7 + 3.22518e8i 0.502652 + 2.85068i
\(201\) −833823. + 86584.3i −0.00724248 + 0.000752061i
\(202\) 1.55245e8 5.65047e7i 1.32522 0.482342i
\(203\) −2.59864e7 + 9.45828e6i −0.218027 + 0.0793553i
\(204\) −4.04810e8 + 4.20355e7i −3.33845 + 0.346666i
\(205\) 5.83864e7 + 3.31126e8i 0.473340 + 2.68444i
\(206\) 2.08844e8 3.61728e8i 1.66451 2.88302i
\(207\) 2.92352e7 + 7.28839e7i 0.229092 + 0.571130i
\(208\) 1.31558e7 + 2.27864e7i 0.101366 + 0.175572i
\(209\) −2.24498e7 + 1.88376e7i −0.170098 + 0.142729i
\(210\) 4.07008e7 5.71774e8i 0.303274 4.26046i
\(211\) 1.12387e7 6.37381e7i 0.0823624 0.467100i −0.915532 0.402245i \(-0.868230\pi\)
0.997895 0.0648558i \(-0.0206588\pi\)
\(212\) 3.73647e8 + 3.13527e8i 2.69331 + 2.25995i
\(213\) 8.29945e7 8.57285e7i 0.588465 0.607851i
\(214\) −2.92901e8 1.06607e8i −2.04302 0.743598i
\(215\) −5.95896e6 −0.0408918
\(216\) −7.09798e7 + 3.27881e8i −0.479233 + 2.21375i
\(217\) 1.79450e8 1.19216
\(218\) 1.02985e8 + 3.74836e7i 0.673252 + 0.245044i
\(219\) 2.81039e7 + 9.84746e7i 0.180806 + 0.633534i
\(220\) −1.91643e8 1.60808e8i −1.21343 1.01819i
\(221\) 4.59046e6 2.60338e7i 0.0286077 0.162242i
\(222\) 1.38108e8 6.71461e7i 0.847195 0.411894i
\(223\) −1.00153e7 + 8.40386e6i −0.0604781 + 0.0507471i −0.672526 0.740074i \(-0.734791\pi\)
0.612048 + 0.790821i \(0.290346\pi\)
\(224\) −1.37091e8 2.37449e8i −0.814971 1.41157i
\(225\) −1.45702e8 1.62634e8i −0.852757 0.951859i
\(226\) 9.20633e7 1.59458e8i 0.530526 0.918898i
\(227\) −3.05092e7 1.73026e8i −0.173117 0.981797i −0.940295 0.340362i \(-0.889450\pi\)
0.767177 0.641435i \(-0.221661\pi\)
\(228\) −7.85597e7 + 1.75856e8i −0.438963 + 0.982618i
\(229\) −3.22812e8 + 1.17494e8i −1.77634 + 0.646534i −0.776472 + 0.630152i \(0.782993\pi\)
−0.999866 + 0.0163824i \(0.994785\pi\)
\(230\) −2.90563e8 + 1.05756e8i −1.57468 + 0.573138i
\(231\) 8.02340e7 + 1.10723e8i 0.428269 + 0.591014i
\(232\) 1.10662e7 + 6.27593e7i 0.0581820 + 0.329967i
\(233\) 9.95569e7 1.72438e8i 0.515615 0.893072i −0.484220 0.874946i \(-0.660897\pi\)
0.999836 0.0181258i \(-0.00576993\pi\)
\(234\) −3.45198e7 1.84654e7i −0.176122 0.0942113i
\(235\) 1.62214e8 + 2.80962e8i 0.815361 + 1.41225i
\(236\) −1.00975e8 + 8.47280e7i −0.500059 + 0.419600i
\(237\) −1.22968e8 8.31666e7i −0.600028 0.405817i
\(238\) −1.52098e8 + 8.62593e8i −0.731317 + 4.14750i
\(239\) 1.07480e8 + 9.01861e7i 0.509253 + 0.427314i 0.860866 0.508832i \(-0.169922\pi\)
−0.351613 + 0.936145i \(0.614367\pi\)
\(240\) −5.74183e8 1.43923e8i −2.68109 0.672032i
\(241\) 2.01677e8 + 7.34045e7i 0.928106 + 0.337803i 0.761458 0.648214i \(-0.224484\pi\)
0.166647 + 0.986017i \(0.446706\pi\)
\(242\) −3.11653e8 −1.41357
\(243\) −7.51866e7 2.10662e8i −0.336139 0.941813i
\(244\) 1.63527e8 0.720649
\(245\) −4.76687e8 1.73500e8i −2.07086 0.753733i
\(246\) −7.38023e8 1.84990e8i −3.16080 0.792275i
\(247\) −9.58359e6 8.04159e6i −0.0404659 0.0339549i
\(248\) 7.18093e7 4.07251e8i 0.298951 1.69543i
\(249\) 1.59977e8 + 1.08197e8i 0.656690 + 0.444138i
\(250\) 1.43262e8 1.20211e8i 0.579885 0.486581i
\(251\) 1.73699e8 + 3.00855e8i 0.693329 + 1.20088i 0.970741 + 0.240129i \(0.0771899\pi\)
−0.277412 + 0.960751i \(0.589477\pi\)
\(252\) 7.92419e8 + 4.23882e8i 3.11927 + 1.66856i
\(253\) 3.68800e7 6.38781e7i 0.143176 0.247988i
\(254\) −5.40396e7 3.06474e8i −0.206916 1.17348i
\(255\) 3.48973e8 + 4.81585e8i 1.31796 + 1.81879i
\(256\) 4.48131e8 1.63106e8i 1.66942 0.607618i
\(257\) −5.96993e7 + 2.17288e7i −0.219383 + 0.0798490i −0.449374 0.893344i \(-0.648353\pi\)
0.229990 + 0.973193i \(0.426131\pi\)
\(258\) 5.49998e6 1.23117e7i 0.0199385 0.0446323i
\(259\) −3.97609e7 2.25496e8i −0.142203 0.806471i
\(260\) 5.33982e7 9.24884e7i 0.188417 0.326348i
\(261\) −2.83523e7 3.16473e7i −0.0987068 0.110178i
\(262\) −7.50571e7 1.30003e8i −0.257832 0.446579i
\(263\) 1.72849e8 1.45037e8i 0.585897 0.491626i −0.300981 0.953630i \(-0.597314\pi\)
0.886878 + 0.462004i \(0.152870\pi\)
\(264\) 2.83386e8 1.37778e8i 0.947905 0.460858i
\(265\) 1.23771e8 7.01941e8i 0.408563 2.31707i
\(266\) 3.17539e8 + 2.66447e8i 1.03446 + 0.868011i
\(267\) 2.53154e7 + 8.87036e7i 0.0813944 + 0.285202i
\(268\) 4.86287e6 + 1.76994e6i 0.0154319 + 0.00561677i
\(269\) 5.92755e8 1.85670 0.928351 0.371705i \(-0.121227\pi\)
0.928351 + 0.371705i \(0.121227\pi\)
\(270\) 8.38650e8 2.69020e8i 2.59303 0.831786i
\(271\) −6.87155e7 −0.209731 −0.104865 0.994486i \(-0.533441\pi\)
−0.104865 + 0.994486i \(0.533441\pi\)
\(272\) 8.49964e8 + 3.09362e8i 2.56100 + 0.932127i
\(273\) −4.06011e7 + 4.19386e7i −0.120773 + 0.124751i
\(274\) −5.63817e8 4.73098e8i −1.65581 1.38939i
\(275\) −3.56144e7 + 2.01979e8i −0.103267 + 0.585656i
\(276\) 3.44202e7 4.83543e8i 0.0985444 1.38437i
\(277\) 1.76840e8 1.48386e8i 0.499920 0.419483i −0.357645 0.933858i \(-0.616420\pi\)
0.857566 + 0.514374i \(0.171976\pi\)
\(278\) −1.95671e8 3.38913e8i −0.546224 0.946087i
\(279\) 1.02648e8 + 2.55902e8i 0.282966 + 0.705439i
\(280\) −9.84804e8 + 1.70573e9i −2.68100 + 4.64363i
\(281\) 4.79284e7 + 2.71815e8i 0.128861 + 0.730806i 0.978940 + 0.204150i \(0.0654431\pi\)
−0.850079 + 0.526655i \(0.823446\pi\)
\(282\) −7.30211e8 + 7.58253e7i −1.93899 + 0.201346i
\(283\) −3.85024e8 + 1.40137e8i −1.00980 + 0.367537i −0.793356 0.608758i \(-0.791668\pi\)
−0.216444 + 0.976295i \(0.569446\pi\)
\(284\) −6.92159e8 + 2.51925e8i −1.79305 + 0.652616i
\(285\) 2.79951e8 2.90701e7i 0.716348 0.0743858i
\(286\) 6.38522e6 + 3.62124e7i 0.0161397 + 0.0915326i
\(287\) −5.67236e8 + 9.82481e8i −1.41637 + 2.45323i
\(288\) 2.60193e8 3.31320e8i 0.641832 0.817287i
\(289\) −2.49216e8 4.31655e8i −0.607343 1.05195i
\(290\) 1.28164e8 1.07543e8i 0.308585 0.258933i
\(291\) −4.90630e7 + 6.89248e8i −0.116716 + 1.63965i
\(292\) 1.09774e8 6.22562e8i 0.258025 1.46333i
\(293\) −2.86380e8 2.40301e8i −0.665129 0.558110i 0.246490 0.969145i \(-0.420723\pi\)
−0.911619 + 0.411036i \(0.865167\pi\)
\(294\) 7.98436e8 8.24738e8i 1.83242 1.89278i
\(295\) 1.81004e8 + 6.58799e7i 0.410497 + 0.149409i
\(296\) −5.27658e8 −1.18258
\(297\) −1.12001e8 + 1.77751e8i −0.248069 + 0.393700i
\(298\) −7.24962e7 −0.158693
\(299\) 2.95886e7 + 1.07694e7i 0.0640140 + 0.0232992i
\(300\) 3.69919e8 + 1.29617e9i 0.791010 + 2.77165i
\(301\) −1.54020e7 1.29238e7i −0.0325532 0.0273154i
\(302\) 2.58358e8 1.46522e9i 0.539756 3.06111i
\(303\) 3.40390e8 1.65493e8i 0.702955 0.341766i
\(304\) 3.27912e8 2.75151e8i 0.669422 0.561711i
\(305\) −1.19481e8 2.06948e8i −0.241129 0.417649i
\(306\) −1.31709e9 + 2.76515e8i −2.62779 + 0.551689i
\(307\) 1.80261e8 3.12222e8i 0.355565 0.615856i −0.631650 0.775254i \(-0.717622\pi\)
0.987214 + 0.159398i \(0.0509553\pi\)
\(308\) −1.46576e8 8.31273e8i −0.285848 1.62112i
\(309\) 3.90303e8 8.73692e8i 0.752570 1.68463i
\(310\) −1.02020e9 + 3.71321e8i −1.94499 + 0.707919i
\(311\) −7.55450e8 + 2.74961e8i −1.42411 + 0.518335i −0.935238 0.354020i \(-0.884815\pi\)
−0.488874 + 0.872354i \(0.662592\pi\)
\(312\) 7.89298e7 + 1.08924e8i 0.147130 + 0.203040i
\(313\) 1.46510e8 + 8.30898e8i 0.270061 + 1.53159i 0.754227 + 0.656614i \(0.228012\pi\)
−0.484166 + 0.874976i \(0.660877\pi\)
\(314\) −2.97192e8 + 5.14752e8i −0.541731 + 0.938305i
\(315\) −4.25488e7 1.31254e9i −0.0767009 2.36606i
\(316\) 4.58202e8 + 7.93630e8i 0.816869 + 1.41486i
\(317\) 2.99587e8 2.51383e8i 0.528221 0.443230i −0.339266 0.940691i \(-0.610179\pi\)
0.867487 + 0.497461i \(0.165734\pi\)
\(318\) 1.33603e9 + 9.03596e8i 2.32981 + 1.57572i
\(319\) −6.93027e6 + 3.93035e7i −0.0119532 + 0.0677898i
\(320\) 2.95713e7 + 2.48133e7i 0.0504482 + 0.0423311i
\(321\) −6.92663e8 1.73620e8i −1.16884 0.292977i
\(322\) −9.80376e8 3.56828e8i −1.63643 0.595612i
\(323\) −4.30074e8 −0.710124
\(324\) −1.51198e8 + 1.37248e9i −0.246966 + 2.24181i
\(325\) −8.75533e7 −0.141475
\(326\) 8.32733e8 + 3.03090e8i 1.33120 + 0.484518i
\(327\) 2.43544e8 + 6.10458e7i 0.385176 + 0.0965470i
\(328\) 2.00269e9 + 1.68046e9i 3.13368 + 2.62947i
\(329\) −1.90081e8 + 1.07801e9i −0.294276 + 1.66892i
\(330\) −6.85249e8 4.63454e8i −1.04966 0.709918i
\(331\) −1.64447e8 + 1.37988e8i −0.249246 + 0.209142i −0.758848 0.651268i \(-0.774237\pi\)
0.509602 + 0.860411i \(0.329793\pi\)
\(332\) −5.96107e8 1.03249e9i −0.894007 1.54847i
\(333\) 2.98821e8 1.85686e8i 0.443461 0.275566i
\(334\) 8.01048e7 1.38746e8i 0.117637 0.203754i
\(335\) −1.31316e6 7.44731e6i −0.00190837 0.0108229i
\(336\) −1.17194e9 1.61728e9i −1.68545 2.32594i
\(337\) 7.80153e8 2.83953e8i 1.11039 0.404149i 0.279253 0.960218i \(-0.409913\pi\)
0.831136 + 0.556069i \(0.187691\pi\)
\(338\) 1.18888e9 4.32718e8i 1.67468 0.609533i
\(339\) 1.72055e8 3.85144e8i 0.239865 0.536938i
\(340\) −6.37523e8 3.61557e9i −0.879669 4.98885i
\(341\) 1.29489e8 2.24282e8i 0.176845 0.306305i
\(342\) −1.98327e8 + 6.05232e8i −0.268096 + 0.818146i
\(343\) −2.69685e8 4.67109e8i −0.360851 0.625012i
\(344\) −3.54930e7 + 2.97821e7i −0.0470097 + 0.0394459i
\(345\) −6.37087e8 + 3.09742e8i −0.835279 + 0.406101i
\(346\) −3.17110e8 + 1.79842e9i −0.411570 + 2.33413i
\(347\) −1.55054e8 1.30106e8i −0.199219 0.167164i 0.537721 0.843123i \(-0.319285\pi\)
−0.736940 + 0.675959i \(0.763730\pi\)
\(348\) 7.19832e7 + 2.52225e8i 0.0915595 + 0.320820i
\(349\) 1.04791e9 + 3.81407e8i 1.31957 + 0.480286i 0.903322 0.428963i \(-0.141121\pi\)
0.416252 + 0.909249i \(0.363343\pi\)
\(350\) 2.90096e9 3.61662
\(351\) −8.30301e7 3.39092e7i −0.102485 0.0418546i
\(352\) −3.95694e8 −0.483571
\(353\) −1.19574e8 4.35213e7i −0.144685 0.0526612i 0.268662 0.963234i \(-0.413418\pi\)
−0.413348 + 0.910573i \(0.635641\pi\)
\(354\) −3.03175e8 + 3.13163e8i −0.363231 + 0.375196i
\(355\) 8.24548e8 + 6.91878e8i 0.978175 + 0.820786i
\(356\) 9.88823e7 5.60789e8i 0.116156 0.658756i
\(357\) −1.42480e8 + 2.00159e9i −0.165736 + 2.32829i
\(358\) −3.83980e8 + 3.22198e8i −0.442302 + 0.371135i
\(359\) −3.11954e8 5.40320e8i −0.355844 0.616340i 0.631418 0.775443i \(-0.282473\pi\)
−0.987262 + 0.159102i \(0.949140\pi\)
\(360\) −2.99575e9 4.28667e8i −3.38413 0.484241i
\(361\) 3.45170e8 5.97852e8i 0.386152 0.668834i
\(362\) 4.58913e8 + 2.60263e9i 0.508453 + 2.88358i
\(363\) −7.10170e8 + 7.37442e7i −0.779272 + 0.0809197i
\(364\) 3.38606e8 1.23242e8i 0.367993 0.133939i
\(365\) −8.68077e8 + 3.15954e8i −0.934401 + 0.340094i
\(366\) 5.37849e8 5.58504e7i 0.573425 0.0595446i
\(367\) −2.24001e8 1.27037e9i −0.236547 1.34153i −0.839331 0.543621i \(-0.817053\pi\)
0.602783 0.797905i \(-0.294058\pi\)
\(368\) −5.38688e8 + 9.33034e8i −0.563469 + 0.975956i
\(369\) −1.72552e9 2.46907e8i −1.78783 0.255824i
\(370\) 6.92643e8 + 1.19969e9i 0.710892 + 1.23130i
\(371\) 1.84228e9 1.54585e9i 1.87304 1.57166i
\(372\) 1.20853e8 1.69776e9i 0.121718 1.70993i
\(373\) −3.19177e7 + 1.81014e8i −0.0318457 + 0.180606i −0.996582 0.0826138i \(-0.973673\pi\)
0.964736 + 0.263219i \(0.0847843\pi\)
\(374\) 9.68341e8 + 8.12534e8i 0.957145 + 0.803140i
\(375\) 2.98009e8 3.07826e8i 0.291823 0.301437i
\(376\) 2.37040e9 + 8.62755e8i 2.29966 + 0.837008i
\(377\) −1.70371e7 −0.0163758
\(378\) 2.75109e9 + 1.12353e9i 2.61989 + 1.06995i
\(379\) −1.19349e9 −1.12611 −0.563055 0.826420i \(-0.690374\pi\)
−0.563055 + 0.826420i \(0.690374\pi\)
\(380\) −1.63268e9 5.94245e8i −1.52636 0.555550i
\(381\) −1.95659e8 6.85580e8i −0.181244 0.635069i
\(382\) −2.58654e9 2.17037e9i −2.37410 1.99210i
\(383\) −2.31806e8 + 1.31463e9i −0.210828 + 1.19566i 0.677173 + 0.735824i \(0.263205\pi\)
−0.888001 + 0.459841i \(0.847906\pi\)
\(384\) 9.58436e8 4.65978e8i 0.863781 0.419958i
\(385\) −9.44904e8 + 7.92868e8i −0.843869 + 0.708090i
\(386\) 8.21274e8 + 1.42249e9i 0.726829 + 1.25891i
\(387\) 9.61967e6 2.93563e7i 0.00843668 0.0257462i
\(388\) 2.13278e9 3.69409e9i 1.85368 3.21068i
\(389\) −6.79064e7 3.85116e8i −0.0584907 0.331717i 0.941495 0.337026i \(-0.109421\pi\)
−0.999986 + 0.00530900i \(0.998310\pi\)
\(390\) 1.44042e8 3.22438e8i 0.122960 0.275245i
\(391\) 1.01717e9 3.70219e8i 0.860546 0.313213i
\(392\) −3.70639e9 + 1.34902e9i −3.10778 + 1.13114i
\(393\) −2.01795e8 2.78479e8i −0.167702 0.231429i
\(394\) 3.68085e8 + 2.08752e9i 0.303188 + 1.71946i
\(395\) 6.69574e8 1.15974e9i 0.546650 0.946825i
\(396\) 1.10158e9 6.84519e8i 0.891421 0.553927i
\(397\) 7.23870e8 + 1.25378e9i 0.580623 + 1.00567i 0.995406 + 0.0957476i \(0.0305242\pi\)
−0.414783 + 0.909920i \(0.636142\pi\)
\(398\) −2.03598e9 + 1.70839e9i −1.61876 + 1.35830i
\(399\) 7.86629e8 + 5.32020e8i 0.619961 + 0.419298i
\(400\) 5.20201e8 2.95021e9i 0.406407 2.30485i
\(401\) 1.51681e9 + 1.27276e9i 1.17470 + 0.985689i 0.999999 + 0.00106694i \(0.000339619\pi\)
0.174699 + 0.984622i \(0.444105\pi\)
\(402\) 1.65988e7 + 4.16059e6i 0.0127434 + 0.00319422i
\(403\) 1.03888e8 + 3.78122e7i 0.0790677 + 0.0287783i
\(404\) −2.33645e9 −1.76287
\(405\) 1.84739e9 8.11463e8i 1.38187 0.606983i
\(406\) 5.64502e8 0.418625
\(407\) −3.10522e8 1.13021e8i −0.228303 0.0830955i
\(408\) 4.48547e9 + 1.12431e9i 3.26962 + 0.819552i
\(409\) −7.01868e8 5.88937e8i −0.507252 0.425635i 0.352909 0.935658i \(-0.385193\pi\)
−0.860161 + 0.510023i \(0.829637\pi\)
\(410\) 1.19184e9 6.75925e9i 0.854031 4.84345i
\(411\) −1.39672e9 9.44645e8i −0.992348 0.671154i
\(412\) −4.52510e9 + 3.79701e9i −3.18778 + 2.67486i
\(413\) 3.24955e8 + 5.62839e8i 0.226986 + 0.393150i
\(414\) −5.19375e7 1.60216e9i −0.0359732 1.10970i
\(415\) −8.71096e8 + 1.50878e9i −0.598270 + 1.03623i
\(416\) −2.93323e7 1.66352e8i −0.0199765 0.113293i
\(417\) −5.26074e8 7.25986e8i −0.355280 0.490289i
\(418\) 5.62146e8 2.04604e8i 0.376471 0.137024i
\(419\) 2.37980e9 8.66177e8i 1.58049 0.575251i 0.605180 0.796089i \(-0.293101\pi\)
0.975311 + 0.220837i \(0.0708790\pi\)
\(420\) −3.30655e9 + 7.40172e9i −2.17772 + 4.87484i
\(421\) 2.39087e8 + 1.35593e9i 0.156159 + 0.885623i 0.957718 + 0.287708i \(0.0928932\pi\)
−0.801559 + 0.597916i \(0.795996\pi\)
\(422\) −6.60576e8 + 1.14415e9i −0.427887 + 0.741122i
\(423\) −1.64600e9 + 3.45568e8i −1.05740 + 0.221995i
\(424\) −2.77100e9 4.79952e9i −1.76545 3.05786i
\(425\) −2.30566e9 + 1.93468e9i −1.45691 + 1.22250i
\(426\) −2.19052e9 + 1.06500e9i −1.37282 + 0.667444i
\(427\) 1.40008e8 7.94023e8i 0.0870271 0.493555i
\(428\) 3.37685e9 + 2.83351e9i 2.08189 + 1.74691i
\(429\) 2.31187e7 + 8.10068e7i 0.0141372 + 0.0495360i
\(430\) 1.14304e8 + 4.16033e7i 0.0693301 + 0.0252341i
\(431\) −8.73043e8 −0.525249 −0.262625 0.964898i \(-0.584588\pi\)
−0.262625 + 0.964898i \(0.584588\pi\)
\(432\) 1.63594e9 2.59632e9i 0.976278 1.54941i
\(433\) −2.12507e8 −0.125796 −0.0628979 0.998020i \(-0.520034\pi\)
−0.0628979 + 0.998020i \(0.520034\pi\)
\(434\) −3.44220e9 1.25286e9i −2.02126 0.735677i
\(435\) 2.66603e8 2.75386e8i 0.155293 0.160409i
\(436\) −1.18732e9 9.96276e8i −0.686062 0.575674i
\(437\) 8.89541e7 5.04484e8i 0.0509895 0.289176i
\(438\) 1.48427e8 2.08514e9i 0.0844023 1.18570i
\(439\) 1.67587e9 1.40623e9i 0.945400 0.793285i −0.0331169 0.999451i \(-0.510543\pi\)
0.978517 + 0.206167i \(0.0660989\pi\)
\(440\) 1.42125e9 + 2.46167e9i 0.795399 + 1.37767i
\(441\) 1.62426e9 2.06827e9i 0.901819 1.14835i
\(442\) −2.69812e8 + 4.67328e8i −0.148622 + 0.257421i
\(443\) −1.24614e8 7.06719e8i −0.0681009 0.386219i −0.999739 0.0228326i \(-0.992732\pi\)
0.931638 0.363387i \(-0.118380\pi\)
\(444\) −2.16017e9 + 2.24313e8i −1.17125 + 0.121622i
\(445\) −7.81944e8 + 2.84604e8i −0.420645 + 0.153102i
\(446\) 2.50785e8 9.12784e7i 0.133854 0.0487188i
\(447\) −1.65198e8 + 1.71542e7i −0.0874841 + 0.00908437i
\(448\) 2.26172e7 + 1.28269e8i 0.0118841 + 0.0673980i
\(449\) −1.09974e8 + 1.90481e8i −0.0573361 + 0.0993090i −0.893269 0.449523i \(-0.851594\pi\)
0.835933 + 0.548832i \(0.184927\pi\)
\(450\) 1.65938e9 + 4.13686e9i 0.858424 + 2.14007i
\(451\) 8.18622e8 + 1.41789e9i 0.420209 + 0.727823i
\(452\) −1.99477e9 + 1.67381e9i −1.01604 + 0.852555i
\(453\) 2.42020e8 3.39995e9i 0.122323 1.71842i
\(454\) −6.22782e8 + 3.53197e9i −0.312350 + 1.77142i
\(455\) −4.03371e8 3.38468e8i −0.200754 0.168453i
\(456\) 1.52216e9 1.57231e9i 0.751769 0.776534i
\(457\) 1.72870e9 + 6.29196e8i 0.847253 + 0.308375i 0.728920 0.684599i \(-0.240023\pi\)
0.118333 + 0.992974i \(0.462245\pi\)
\(458\) 7.01244e9 3.41067
\(459\) −2.93584e9 + 9.41752e8i −1.41706 + 0.454561i
\(460\) 4.37298e9 2.09472
\(461\) 8.28667e8 + 3.01610e8i 0.393937 + 0.143381i 0.531391 0.847127i \(-0.321670\pi\)
−0.137454 + 0.990508i \(0.543892\pi\)
\(462\) −7.66008e8 2.68405e9i −0.361398 1.26632i
\(463\) −9.79961e8 8.22285e8i −0.458855 0.385025i 0.383855 0.923394i \(-0.374596\pi\)
−0.842709 + 0.538369i \(0.819041\pi\)
\(464\) 1.01227e8 5.74086e8i 0.0470417 0.266787i
\(465\) −2.23687e9 + 1.08754e9i −1.03171 + 0.501601i
\(466\) −3.11359e9 + 2.61261e9i −1.42531 + 1.19598i
\(467\) 6.10000e8 + 1.05655e9i 0.277154 + 0.480044i 0.970676 0.240391i \(-0.0772755\pi\)
−0.693523 + 0.720435i \(0.743942\pi\)
\(468\) 3.69434e8 + 4.12368e8i 0.166601 + 0.185962i
\(469\) 1.27576e7 2.20969e7i 0.00571038 0.00989068i
\(470\) −1.14999e9 6.52190e9i −0.510917 2.89756i
\(471\) −5.55415e8 + 1.24330e9i −0.244931 + 0.548279i
\(472\) 1.40736e9 5.12237e8i 0.616039 0.224220i
\(473\) −2.72664e7 + 9.92416e6i −0.0118472 + 0.00431201i
\(474\) 1.77811e9 + 2.45381e9i 0.766893 + 1.05832i
\(475\) 2.47343e8 + 1.40275e9i 0.105894 + 0.600556i
\(476\) 6.19366e9 1.07277e10i 2.63223 4.55915i
\(477\) 3.25824e9 + 1.74290e9i 1.37458 + 0.735291i
\(478\) −1.43201e9 2.48032e9i −0.599722 1.03875i
\(479\) 9.25925e8 7.76943e8i 0.384947 0.323009i −0.429694 0.902975i \(-0.641378\pi\)
0.814641 + 0.579966i \(0.196934\pi\)
\(480\) 3.14789e9 + 2.12901e9i 1.29920 + 0.878686i
\(481\) 2.44959e7 1.38923e8i 0.0100366 0.0569202i
\(482\) −3.35607e9 2.81607e9i −1.36510 1.14546i
\(483\) −2.31843e9 5.81130e8i −0.936223 0.234671i
\(484\) 4.14172e9 + 1.50746e9i 1.66044 + 0.604349i
\(485\) −6.23331e9 −2.48097
\(486\) −2.85456e7 + 4.56582e9i −0.0112801 + 1.80423i
\(487\) −4.27898e9 −1.67876 −0.839381 0.543543i \(-0.817082\pi\)
−0.839381 + 0.543543i \(0.817082\pi\)
\(488\) −1.74596e9 6.35477e8i −0.680087 0.247531i
\(489\) 1.96928e9 + 4.93613e8i 0.761599 + 0.190900i
\(490\) 7.93244e9 + 6.65610e9i 3.04593 + 2.55584i
\(491\) 4.96082e8 2.81342e9i 0.189133 1.07263i −0.731395 0.681954i \(-0.761131\pi\)
0.920529 0.390675i \(-0.127758\pi\)
\(492\) 8.91316e9 + 6.02823e9i 3.37407 + 2.28198i
\(493\) −4.48662e8 + 3.76472e8i −0.168638 + 0.141504i
\(494\) 1.27688e8 + 2.21162e8i 0.0476547 + 0.0825403i
\(495\) −1.67115e9 8.93935e8i −0.619295 0.331274i
\(496\) −1.89138e9 + 3.27597e9i −0.695975 + 1.20546i
\(497\) 6.30644e8 + 3.57656e9i 0.230429 + 1.30683i
\(498\) −2.31327e9 3.19233e9i −0.839312 1.15826i
\(499\) −9.87318e8 + 3.59354e8i −0.355717 + 0.129471i −0.513697 0.857972i \(-0.671724\pi\)
0.157979 + 0.987442i \(0.449502\pi\)
\(500\) −2.48534e9 + 9.04591e8i −0.889184 + 0.323636i
\(501\) 1.49706e8 3.35116e8i 0.0531871 0.119059i
\(502\) −1.23141e9 6.98367e9i −0.434450 2.46389i
\(503\) 1.23083e9 2.13186e9i 0.431232 0.746916i −0.565748 0.824578i \(-0.691412\pi\)
0.996980 + 0.0776627i \(0.0247457\pi\)
\(504\) −6.81335e9 7.60515e9i −2.37057 2.64607i
\(505\) 1.70713e9 + 2.95684e9i 0.589858 + 1.02166i
\(506\) −1.15340e9 + 9.67819e8i −0.395780 + 0.332099i
\(507\) 2.60674e9 1.26736e9i 0.888320 0.431889i
\(508\) −7.64250e8 + 4.33427e9i −0.258650 + 1.46688i
\(509\) 2.16258e9 + 1.81462e9i 0.726875 + 0.609921i 0.929278 0.369382i \(-0.120430\pi\)
−0.202403 + 0.979302i \(0.564875\pi\)
\(510\) −3.33171e9 1.16741e10i −1.11217 3.89698i
\(511\) −2.92894e9 1.06605e9i −0.971041 0.353430i
\(512\) −6.81783e9 −2.24492
\(513\) −3.08718e8 + 1.42608e9i −0.100961 + 0.466373i
\(514\) 1.29685e9 0.421229
\(515\) 8.11151e9 + 2.95235e9i 2.61684 + 0.952451i
\(516\) −1.32644e8 + 1.37013e8i −0.0425023 + 0.0439024i
\(517\) 1.21016e9 + 1.01545e9i 0.385147 + 0.323177i
\(518\) −8.11637e8 + 4.60302e9i −0.256571 + 1.45509i
\(519\) −2.97057e8 + 4.17313e9i −0.0932727 + 1.31032i
\(520\) −9.29545e8 + 7.79981e8i −0.289907 + 0.243261i
\(521\) −2.13068e9 3.69044e9i −0.660063 1.14326i −0.980599 0.196027i \(-0.937196\pi\)
0.320535 0.947237i \(-0.396137\pi\)
\(522\) 3.22902e8 + 8.05000e8i 0.0993627 + 0.247713i
\(523\) 1.58485e9 2.74504e9i 0.484431 0.839060i −0.515409 0.856944i \(-0.672360\pi\)
0.999840 + 0.0178849i \(0.00569324\pi\)
\(524\) 3.68651e8 + 2.09072e9i 0.111932 + 0.634800i
\(525\) 6.61045e9 6.86431e8i 1.99376 0.207033i
\(526\) −4.32816e9 + 1.57532e9i −1.29674 + 0.471975i
\(527\) 3.57137e9 1.29987e9i 1.06291 0.386869i
\(528\) −2.86698e9 + 2.97708e8i −0.847629 + 0.0880180i
\(529\) −3.67354e8 2.08337e9i −0.107892 0.611888i
\(530\) −7.27486e9 + 1.26004e10i −2.12255 + 3.67637i
\(531\) −6.16749e8 + 7.85347e8i −0.178763 + 0.227631i
\(532\) −2.93114e9 5.07688e9i −0.844006 1.46186i
\(533\) −5.35407e8 + 4.49260e8i −0.153158 + 0.128515i
\(534\) 1.33700e8 1.87824e9i 0.0379959 0.533774i
\(535\) 1.11859e9 6.34381e9i 0.315814 1.79107i
\(536\) −4.50423e7 3.77949e7i −0.0126341 0.0106012i
\(537\) −7.98743e8 + 8.25056e8i −0.222586 + 0.229918i
\(538\) −1.13702e10 4.13840e9i −3.14795 1.14576i
\(539\) −2.47013e9 −0.679451
\(540\) −1.24465e10 4.81393e8i −3.40149 0.131559i
\(541\) −1.00998e9 −0.274234 −0.137117 0.990555i \(-0.543784\pi\)
−0.137117 + 0.990555i \(0.543784\pi\)
\(542\) 1.31809e9 + 4.79746e8i 0.355589 + 0.129424i
\(543\) 1.66157e9 + 5.82206e9i 0.445369 + 1.56055i
\(544\) −4.44835e9 3.73261e9i −1.18469 0.994069i
\(545\) −3.93300e8 + 2.23052e9i −0.104073 + 0.590225i
\(546\) 1.07161e9 5.20999e8i 0.281748 0.136982i
\(547\) 1.79764e7 1.50840e7i 0.00469622 0.00394059i −0.640436 0.768011i \(-0.721247\pi\)
0.645133 + 0.764071i \(0.276802\pi\)
\(548\) 5.20448e9 + 9.01442e9i 1.35097 + 2.33995i
\(549\) 1.21239e9 2.54534e8i 0.312708 0.0656513i
\(550\) 2.09330e9 3.62570e9i 0.536490 0.929227i
\(551\) 4.81310e7 + 2.72964e8i 0.0122573 + 0.0695145i
\(552\) −2.24659e9 + 5.02898e9i −0.568508 + 1.27260i
\(553\) 4.24587e9 1.54537e9i 1.06765 0.388593i
\(554\) −4.42810e9 + 1.61170e9i −1.10645 + 0.402716i
\(555\) 1.86221e9 + 2.56987e9i 0.462385 + 0.638094i
\(556\) 9.61060e8 + 5.45044e9i 0.237131 + 1.34484i
\(557\) 5.16392e8 8.94417e8i 0.126615 0.219304i −0.795748 0.605628i \(-0.792922\pi\)
0.922363 + 0.386324i \(0.126255\pi\)
\(558\) −1.82357e8 5.62534e9i −0.0444328 1.37066i
\(559\) −6.19340e6 1.07273e7i −0.00149964 0.00259746i
\(560\) 1.38017e10 1.15810e10i 3.32105 2.78669i
\(561\) 2.39884e9 + 1.62240e9i 0.573629 + 0.387962i
\(562\) 9.78359e8 5.54855e9i 0.232499 1.31857i
\(563\) −4.78029e9 4.01114e9i −1.12895 0.947301i −0.129928 0.991523i \(-0.541475\pi\)
−0.999022 + 0.0442223i \(0.985919\pi\)
\(564\) 1.00709e10 + 2.52434e9i 2.36370 + 0.592476i
\(565\) 3.57575e9 + 1.30147e9i 0.834060 + 0.303573i
\(566\) 8.36387e9 1.93887
\(567\) 6.53480e9 + 1.90925e9i 1.50554 + 0.439867i
\(568\) 8.36912e9 1.91629
\(569\) −1.73115e9 6.30087e8i −0.393950 0.143386i 0.137447 0.990509i \(-0.456110\pi\)
−0.531397 + 0.847123i \(0.678333\pi\)
\(570\) −5.57294e9 1.39689e9i −1.26044 0.315937i
\(571\) 4.20704e9 + 3.53013e9i 0.945694 + 0.793532i 0.978567 0.205928i \(-0.0660212\pi\)
−0.0328729 + 0.999460i \(0.510466\pi\)
\(572\) 9.03023e7 5.12130e8i 0.0201750 0.114418i
\(573\) −6.40756e9 4.33362e9i −1.42282 0.962298i
\(574\) 1.77400e10 1.48856e10i 3.91527 3.28530i
\(575\) −1.79252e9 3.10473e9i −0.393211 0.681062i
\(576\) −1.69978e8 + 1.05624e8i −0.0370607 + 0.0230294i
\(577\) −2.68343e9 + 4.64783e9i −0.581533 + 1.00724i 0.413765 + 0.910384i \(0.364214\pi\)
−0.995298 + 0.0968611i \(0.969120\pi\)
\(578\) 1.76678e9 + 1.00199e10i 0.380570 + 2.15832i
\(579\) 2.20804e9 + 3.04711e9i 0.472751 + 0.652400i
\(580\) −2.22342e9 + 8.09260e8i −0.473178 + 0.172223i
\(581\) −5.52375e9 + 2.01048e9i −1.16847 + 0.425288i
\(582\) 5.75320e9 1.28785e10i 1.20970 2.70792i
\(583\) −6.02686e8 3.41800e9i −0.125965 0.714385i
\(584\) −3.59137e9 + 6.22044e9i −0.746132 + 1.29234i
\(585\) 2.51935e8 7.68828e8i 0.0520286 0.158776i
\(586\) 3.81561e9 + 6.60883e9i 0.783290 + 1.35670i
\(587\) −9.01725e8 + 7.56637e8i −0.184010 + 0.154402i −0.730140 0.683298i \(-0.760545\pi\)
0.546130 + 0.837701i \(0.316101\pi\)
\(588\) −1.46001e10 + 7.09834e9i −2.96165 + 1.43991i
\(589\) 3.12326e8 1.77129e9i 0.0629803 0.357179i
\(590\) −3.01204e9 2.52740e9i −0.603780 0.506631i
\(591\) 1.33271e9 + 4.66976e9i 0.265571 + 0.930546i
\(592\) 4.53563e9 + 1.65083e9i 0.898487 + 0.327022i
\(593\) −3.67640e9 −0.723989 −0.361994 0.932180i \(-0.617904\pi\)
−0.361994 + 0.932180i \(0.617904\pi\)
\(594\) 3.38938e9 2.62766e9i 0.663541 0.514418i
\(595\) −1.81017e10 −3.52298
\(596\) 9.63439e8 + 3.50663e8i 0.186407 + 0.0678466i
\(597\) −4.23518e9 + 4.37470e9i −0.814633 + 0.841469i
\(598\) −4.92377e8 4.13153e8i −0.0941550 0.0790054i
\(599\) −7.35614e7 + 4.17187e8i −0.0139848 + 0.0793117i −0.991001 0.133851i \(-0.957265\pi\)
0.977017 + 0.213163i \(0.0683766\pi\)
\(600\) 1.08745e9 1.52767e10i 0.205531 2.88735i
\(601\) −2.58126e9 + 2.16593e9i −0.485032 + 0.406990i −0.852242 0.523148i \(-0.824758\pi\)
0.367210 + 0.930138i \(0.380313\pi\)
\(602\) 2.05210e8 + 3.55434e8i 0.0383363 + 0.0664004i
\(603\) 3.88084e7 + 5.55317e6i 0.00720801 + 0.00103141i
\(604\) −1.05207e10 + 1.82224e10i −1.94274 + 3.36493i
\(605\) −1.11842e9 6.34290e9i −0.205335 1.16451i
\(606\) −7.68472e9 + 7.97983e8i −1.40273 + 0.145660i
\(607\) 8.88217e9 3.23284e9i 1.61198 0.586711i 0.630146 0.776476i \(-0.282995\pi\)
0.981830 + 0.189765i \(0.0607726\pi\)
\(608\) −2.58238e9 + 9.39909e8i −0.465969 + 0.169599i
\(609\) 1.28634e9 1.33574e8i 0.230779 0.0239641i
\(610\) 8.47043e8 + 4.80382e9i 0.151095 + 0.856904i
\(611\) −3.37191e8 + 5.84032e8i −0.0598042 + 0.103584i
\(612\) 1.88410e10 + 2.69599e9i 3.32256 + 0.475432i
\(613\) −1.32845e9 2.30095e9i −0.232935 0.403455i 0.725736 0.687974i \(-0.241500\pi\)
−0.958670 + 0.284519i \(0.908166\pi\)
\(614\) −5.63757e9 + 4.73048e9i −0.982885 + 0.824739i
\(615\) 1.11647e9 1.56844e10i 0.193546 2.71898i
\(616\) −1.66541e9 + 9.44503e9i −0.287071 + 1.62806i
\(617\) 7.45544e9 + 6.25586e9i 1.27784 + 1.07223i 0.993538 + 0.113496i \(0.0362050\pi\)
0.284298 + 0.958736i \(0.408239\pi\)
\(618\) −1.35865e10 + 1.40341e10i −2.31552 + 2.39180i
\(619\) −8.35258e9 3.04009e9i −1.41548 0.515192i −0.482746 0.875760i \(-0.660361\pi\)
−0.932733 + 0.360568i \(0.882583\pi\)
\(620\) 1.53540e10 2.58732
\(621\) −4.97457e8 3.63858e9i −0.0833557 0.609693i
\(622\) 1.64106e10 2.73438
\(623\) −2.63832e9 9.60271e8i −0.437139 0.159106i
\(624\) −3.37684e8 1.18322e9i −0.0556370 0.194949i
\(625\) −3.01456e9 2.52952e9i −0.493906 0.414436i
\(626\) 2.99069e9 1.69611e10i 0.487261 2.76339i
\(627\) 1.23256e9 5.99251e8i 0.199696 0.0970895i
\(628\) 6.43938e9 5.40328e9i 1.03749 0.870561i
\(629\) −2.42472e9 4.19974e9i −0.388494 0.672892i
\(630\) −8.34751e9 + 2.54740e10i −1.33004 + 4.05888i
\(631\) 1.62452e8 2.81375e8i 0.0257408 0.0445844i −0.852868 0.522127i \(-0.825139\pi\)
0.878609 + 0.477542i \(0.158472\pi\)
\(632\) −1.80808e9 1.02541e10i −0.284910 1.61580i
\(633\) −1.23453e9 + 2.76350e9i −0.193459 + 0.433059i
\(634\) −7.50171e9 + 2.73040e9i −1.16909 + 0.425514i
\(635\) 6.04355e9 2.19967e9i 0.936665 0.340918i
\(636\) −1.33845e10 1.84707e10i −2.06301 2.84697i
\(637\) −1.83107e8 1.03845e9i −0.0280684 0.159184i
\(638\) 4.07338e8 7.05531e8i 0.0620988 0.107558i
\(639\) −4.73956e9 + 2.94515e9i −0.718596 + 0.446534i
\(640\) 4.80678e9 + 8.32558e9i 0.724810 + 1.25541i
\(641\) 1.86001e9 1.56073e9i 0.278940 0.234059i −0.492574 0.870270i \(-0.663944\pi\)
0.771514 + 0.636212i \(0.219500\pi\)
\(642\) 1.20744e10 + 8.16628e9i 1.80092 + 1.21801i
\(643\) −6.75910e8 + 3.83328e9i −0.100265 + 0.568633i 0.892741 + 0.450570i \(0.148779\pi\)
−0.993006 + 0.118062i \(0.962332\pi\)
\(644\) 1.13027e10 + 9.48413e9i 1.66757 + 1.39926i
\(645\) 2.70311e8 + 6.77551e7i 0.0396647 + 0.00994221i
\(646\) 8.24963e9 + 3.00262e9i 1.20398 + 0.438214i
\(647\) 1.67552e9 0.243212 0.121606 0.992578i \(-0.461196\pi\)
0.121606 + 0.992578i \(0.461196\pi\)
\(648\) 6.94789e9 1.40663e10i 1.00309 2.03080i
\(649\) 9.37935e8 0.134684
\(650\) 1.67944e9 + 6.11265e8i 0.239865 + 0.0873037i
\(651\) −8.14024e9 2.04040e9i −1.15639 0.289856i
\(652\) −9.60057e9 8.05584e9i −1.35653 1.13827i
\(653\) 2.93308e8 1.66343e9i 0.0412218 0.233781i −0.957235 0.289311i \(-0.906574\pi\)
0.998457 + 0.0555303i \(0.0176849\pi\)
\(654\) −4.24542e9 2.87130e9i −0.593470 0.401381i
\(655\) 2.37651e9 1.99413e9i 0.330442 0.277274i
\(656\) −1.19572e10 2.07104e10i −1.65373 2.86435i
\(657\) −1.55167e8 4.78656e9i −0.0213461 0.658483i
\(658\) 1.11724e10 1.93511e10i 1.52881 2.64798i
\(659\) 5.05095e8 + 2.86453e9i 0.0687502 + 0.389902i 0.999694 + 0.0247391i \(0.00787549\pi\)
−0.930944 + 0.365163i \(0.881013\pi\)
\(660\) 6.86490e9 + 9.47362e9i 0.929460 + 1.28266i
\(661\) −1.25534e9 + 4.56908e8i −0.169067 + 0.0615352i −0.425167 0.905115i \(-0.639785\pi\)
0.256100 + 0.966650i \(0.417562\pi\)
\(662\) 4.11778e9 1.49875e9i 0.551646 0.200783i
\(663\) −5.04244e8 + 1.12875e9i −0.0671960 + 0.150418i
\(664\) 2.35225e9 + 1.33403e10i 0.311814 + 1.76839i
\(665\) −4.28329e9 + 7.41888e9i −0.564810 + 0.978279i
\(666\) −7.02833e9 + 1.47556e9i −0.921919 + 0.193551i
\(667\) −3.48809e8 6.04156e8i −0.0455143 0.0788331i
\(668\) −1.73566e9 + 1.45639e9i −0.225293 + 0.189043i
\(669\) 5.49870e8 2.67339e8i 0.0710017 0.0345200i
\(670\) −2.68055e7 + 1.52021e8i −0.00344320 + 0.0195273i
\(671\) −8.91365e8 7.47944e8i −0.113901 0.0955741i
\(672\) 3.51888e9 + 1.23300e10i 0.447313 + 1.56736i
\(673\) −2.84482e8 1.03543e8i −0.0359751 0.0130939i 0.323970 0.946067i \(-0.394982\pi\)
−0.359945 + 0.932974i \(0.617205\pi\)
\(674\) −1.69473e10 −2.13201
\(675\) 4.76013e9 + 9.03409e9i 0.595738 + 1.13063i
\(676\) −1.78927e10 −2.22773
\(677\) −3.86470e9 1.40664e9i −0.478691 0.174229i 0.0913941 0.995815i \(-0.470868\pi\)
−0.570086 + 0.821585i \(0.693090\pi\)
\(678\) −5.98927e9 + 6.18657e9i −0.738023 + 0.762335i
\(679\) −1.61111e10 1.35188e10i −1.97506 1.65727i
\(680\) −7.24362e9 + 4.10806e10i −0.883434 + 5.01020i
\(681\) −5.83400e8 + 8.19573e9i −0.0707867 + 0.994427i
\(682\) −4.04970e9 + 3.39811e9i −0.488853 + 0.410196i
\(683\) −3.84016e9 6.65135e9i −0.461187 0.798798i 0.537834 0.843051i \(-0.319243\pi\)
−0.999020 + 0.0442524i \(0.985909\pi\)
\(684\) 5.56316e9 7.08393e9i 0.664699 0.846405i
\(685\) 7.60534e9 1.31728e10i 0.904069 1.56589i
\(686\) 1.91189e9 + 1.08429e10i 0.226115 + 1.28236i
\(687\) 1.59794e10 1.65930e9i 1.88023 0.195243i
\(688\) 3.98266e8 1.44957e8i 0.0466245 0.0169699i
\(689\) 1.39227e9 5.06745e8i 0.162165 0.0590231i
\(690\) 1.43830e10 1.49354e9i 1.66678 0.173079i
\(691\) 2.15612e9 + 1.22280e10i 0.248600 + 1.40988i 0.811982 + 0.583682i \(0.198389\pi\)
−0.563383 + 0.826196i \(0.690500\pi\)
\(692\) 1.29132e10 2.23663e10i 1.48136 2.56580i
\(693\) −2.38062e9 5.93493e9i −0.271721 0.677406i
\(694\) 2.06588e9 + 3.57820e9i 0.234610 + 0.406356i
\(695\) 6.19549e9 5.19863e9i 0.700050 0.587412i
\(696\) 2.11608e8 2.97272e9i 0.0237903 0.334211i
\(697\) −4.17224e9 + 2.36619e10i −0.466718 + 2.64689i
\(698\) −1.74380e10 1.46322e10i −1.94090 1.62861i
\(699\) −6.47677e9 + 6.69013e9i −0.717280 + 0.740909i
\(700\) −3.85523e10 1.40319e10i −4.24822 1.54623i
\(701\) 9.40931e9 1.03168 0.515840 0.856685i \(-0.327480\pi\)
0.515840 + 0.856685i \(0.327480\pi\)
\(702\) 1.35593e9 + 1.23013e9i 0.147931 + 0.134206i
\(703\) −2.29499e9 −0.249136
\(704\) 1.76634e8 + 6.42895e7i 0.0190796 + 0.00694442i
\(705\) −4.16372e9 1.45894e10i −0.447528 1.56811i
\(706\) 1.98980e9 + 1.66964e9i 0.212811 + 0.178569i
\(707\) −2.00041e9 + 1.13449e10i −0.212888 + 1.20735i
\(708\) 5.54381e9 2.69532e9i 0.587073 0.285427i
\(709\) 9.34783e9 7.84376e9i 0.985029 0.826537i 0.000188147 1.00000i \(-0.499940\pi\)
0.984840 + 0.173463i \(0.0554957\pi\)
\(710\) −1.09859e10 1.90282e10i −1.15195 1.99523i
\(711\) 4.63244e9 + 5.17079e9i 0.483355 + 0.539527i
\(712\) −3.23503e9 + 5.60323e9i −0.335891 + 0.581780i
\(713\) 7.86090e8 + 4.45814e9i 0.0812192 + 0.460617i
\(714\) 1.67074e10 3.73996e10i 1.71777 3.84524i
\(715\) −7.14095e8 + 2.59909e8i −0.0730608 + 0.0265920i
\(716\) 6.66137e9 2.42454e9i 0.678216 0.246851i
\(717\) −3.85005e9 5.31310e9i −0.390076 0.538308i
\(718\) 2.21155e9 + 1.25423e10i 0.222977 + 1.26457i
\(719\) −3.17644e9 + 5.50175e9i −0.318705 + 0.552014i −0.980218 0.197920i \(-0.936581\pi\)
0.661513 + 0.749934i \(0.269915\pi\)
\(720\) 2.44097e10 + 1.30573e10i 2.43724 + 1.30373i
\(721\) 1.45626e10 + 2.52231e10i 1.44699 + 2.50626i
\(722\) −1.07950e10 + 9.05808e9i −1.06744 + 0.895686i
\(723\) −8.31387e9 5.62291e9i −0.818124 0.553321i
\(724\) 6.49013e9 3.68074e10i 0.635578 3.60454i
\(725\) 1.48596e9 + 1.24687e9i 0.144818 + 0.121517i
\(726\) 1.41372e10 + 3.54359e9i 1.37116 + 0.343689i
\(727\) 5.50383e9 + 2.00323e9i 0.531244 + 0.193357i 0.593694 0.804691i \(-0.297669\pi\)
−0.0624496 + 0.998048i \(0.519891\pi\)
\(728\) −4.09419e9 −0.393286
\(729\) 1.01533e9 + 1.04110e10i 0.0970644 + 0.995278i
\(730\) 1.88572e10 1.79411
\(731\) −4.00141e8 1.45640e8i −0.0378881 0.0137901i
\(732\) −7.41790e9 1.85934e9i −0.699024 0.175215i
\(733\) 9.77686e9 + 8.20376e9i 0.916928 + 0.769394i 0.973424 0.229009i \(-0.0735484\pi\)
−0.0564962 + 0.998403i \(0.517993\pi\)
\(734\) −4.57251e9 + 2.59320e10i −0.426794 + 2.42047i
\(735\) 1.96507e10 + 1.32904e10i 1.82546 + 1.23462i
\(736\) 5.29849e9 4.44596e9i 0.489868 0.411048i
\(737\) −1.84115e7 3.18897e7i −0.00169416 0.00293437i
\(738\) 3.13748e10 + 1.67831e10i 2.87332 + 1.53700i
\(739\) −6.62488e8 + 1.14746e9i −0.0603841 + 0.104588i −0.894637 0.446793i \(-0.852566\pi\)
0.834253 + 0.551382i \(0.185899\pi\)
\(740\) −3.40199e9 1.92936e10i −0.308618 1.75026i
\(741\) 3.43296e8 + 4.73751e8i 0.0309960 + 0.0427747i
\(742\) −4.61309e10 + 1.67903e10i −4.14552 + 1.50884i
\(743\) −1.93765e9 + 7.05249e8i −0.173307 + 0.0630785i −0.427216 0.904149i \(-0.640506\pi\)
0.253909 + 0.967228i \(0.418283\pi\)
\(744\) −7.88798e9 + 1.76572e10i −0.702199 + 1.57187i
\(745\) −2.60166e8 1.47547e9i −0.0230517 0.130733i
\(746\) 1.87601e9 3.24935e9i 0.165444 0.286557i
\(747\) −6.02666e9 6.72703e9i −0.528998 0.590475i
\(748\) −8.93855e9 1.54820e10i −0.780929 1.35261i
\(749\) 1.66497e10 1.39707e10i 1.44783 1.21488i
\(750\) −7.86551e9 + 3.82410e9i −0.680789 + 0.330990i
\(751\) 3.69089e8 2.09321e9i 0.0317974 0.180332i −0.964773 0.263085i \(-0.915260\pi\)
0.996570 + 0.0827528i \(0.0263712\pi\)
\(752\) −1.76762e10 1.48321e10i −1.51575 1.27186i
\(753\) −4.45853e9 1.56224e10i −0.380548 1.33342i
\(754\) 3.26805e8 + 1.18947e8i 0.0277644 + 0.0101054i
\(755\) 3.07479e10 2.60017
\(756\)