Properties

Label 27.8.e.a.4.20
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 4.20
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.20

$q$-expansion

\(f(q)\) \(=\) \(q+(20.7458 + 7.55086i) q^{2} +(-11.1469 - 45.4175i) q^{3} +(275.320 + 231.021i) q^{4} +(74.3769 - 421.812i) q^{5} +(111.689 - 1026.39i) q^{6} +(181.714 - 152.476i) q^{7} +(2554.39 + 4424.34i) q^{8} +(-1938.49 + 1012.53i) q^{9} +O(q^{10})\) \(q+(20.7458 + 7.55086i) q^{2} +(-11.1469 - 45.4175i) q^{3} +(275.320 + 231.021i) q^{4} +(74.3769 - 421.812i) q^{5} +(111.689 - 1026.39i) q^{6} +(181.714 - 152.476i) q^{7} +(2554.39 + 4424.34i) q^{8} +(-1938.49 + 1012.53i) q^{9} +(4728.06 - 8189.24i) q^{10} +(668.319 + 3790.22i) q^{11} +(7423.42 - 15079.5i) q^{12} +(-1107.04 + 402.929i) q^{13} +(4921.12 - 1791.14i) q^{14} +(-19986.7 + 1323.89i) q^{15} +(11596.9 + 65769.5i) q^{16} +(-7984.49 + 13829.5i) q^{17} +(-47861.1 + 6368.46i) q^{18} +(-10605.9 - 18369.9i) q^{19} +(117925. - 98950.8i) q^{20} +(-8950.61 - 6553.34i) q^{21} +(-14754.6 + 83677.7i) q^{22} +(283.404 + 237.804i) q^{23} +(172469. - 165332. i) q^{24} +(-98980.3 - 36025.9i) q^{25} -26008.9 q^{26} +(67594.7 + 76754.9i) q^{27} +85254.6 q^{28} +(-122889. - 44727.9i) q^{29} +(-424638. - 123452. i) q^{30} +(57631.3 + 48358.4i) q^{31} +(-142476. + 808020. i) q^{32} +(164693. - 72602.6i) q^{33} +(-270070. + 226615. i) q^{34} +(-50800.9 - 87989.7i) q^{35} +(-767622. - 169063. i) q^{36} +(51150.8 - 88595.9i) q^{37} +(-81319.1 - 461184. i) q^{38} +(30640.1 + 45787.5i) q^{39} +(2.05623e6 - 748406. i) q^{40} +(-140048. + 50973.3i) q^{41} +(-136204. - 203539. i) q^{42} +(-85790.5 - 486542. i) q^{43} +(-691620. + 1.19792e6i) q^{44} +(282918. + 892989. i) q^{45} +(4083.82 + 7073.38i) q^{46} +(-344242. + 288854. i) q^{47} +(2.85782e6 - 1.25983e6i) q^{48} +(-133236. + 755618. i) q^{49} +(-1.78140e6 - 1.49477e6i) q^{50} +(717105. + 208479. i) q^{51} +(-397875. - 144815. i) q^{52} +1.45598e6 q^{53} +(822743. + 2.10274e6i) q^{54} +1.64847e6 q^{55} +(1.13877e6 + 414479. i) q^{56} +(-716094. + 686461. i) q^{57} +(-2.21170e6 - 1.85584e6i) q^{58} +(235509. - 1.33564e6i) q^{59} +(-5.80860e6 - 4.25286e6i) q^{60} +(1.36590e6 - 1.14613e6i) q^{61} +(830462. + 1.43840e6i) q^{62} +(-197864. + 479564. i) q^{63} +(-4.78285e6 + 8.28413e6i) q^{64} +(87622.4 + 496931. i) q^{65} +(3.96490e6 - 262630. i) q^{66} +(2.45756e6 - 894479. i) q^{67} +(-5.39320e6 + 1.96297e6i) q^{68} +(7641.38 - 15522.3i) q^{69} +(-389508. - 2.20901e6i) q^{70} +(-685023. + 1.18649e6i) q^{71} +(-9.43144e6 - 5.99015e6i) q^{72} +(2.38594e6 + 4.13257e6i) q^{73} +(1.73014e6 - 1.45176e6i) q^{74} +(-532880. + 4.89701e6i) q^{75} +(1.32383e6 - 7.50780e6i) q^{76} +(699360. + 586833. i) q^{77} +(289919. + 1.18126e6i) q^{78} +(-1.49182e6 - 542976. i) q^{79} +2.86049e7 q^{80} +(2.73254e6 - 3.92556e6i) q^{81} -3.29030e6 q^{82} +(-9.69036e6 - 3.52700e6i) q^{83} +(-950325. - 3.87205e6i) q^{84} +(5.23961e6 + 4.39655e6i) q^{85} +(1.89402e6 - 1.07415e7i) q^{86} +(-661597. + 6.07988e6i) q^{87} +(-1.50621e7 + 1.26386e7i) q^{88} +(-5.34357e6 - 9.25534e6i) q^{89} +(-873468. + 2.06621e7i) q^{90} +(-139727. + 242014. i) q^{91} +(23089.0 + 130944. i) q^{92} +(1.55391e6 - 3.15652e6i) q^{93} +(-9.32269e6 + 3.39318e6i) q^{94} +(-8.53750e6 + 3.10740e6i) q^{95} +(3.82864e7 - 2.53604e6i) q^{96} +(-474057. - 2.68851e6i) q^{97} +(-8.46965e6 + 1.46699e7i) q^{98} +(-5.13324e6 - 6.67063e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.7458 + 7.55086i 1.83369 + 0.667408i 0.991807 + 0.127748i \(0.0407750\pi\)
0.841883 + 0.539660i \(0.181447\pi\)
\(3\) −11.1469 45.4175i −0.238358 0.971177i
\(4\) 275.320 + 231.021i 2.15094 + 1.80485i
\(5\) 74.3769 421.812i 0.266099 1.50912i −0.499789 0.866147i \(-0.666589\pi\)
0.765888 0.642974i \(-0.222300\pi\)
\(6\) 111.689 1026.39i 0.211097 1.93992i
\(7\) 181.714 152.476i 0.200237 0.168019i −0.537156 0.843483i \(-0.680501\pi\)
0.737393 + 0.675464i \(0.236057\pi\)
\(8\) 2554.39 + 4424.34i 1.76390 + 3.05516i
\(9\) −1938.49 + 1012.53i −0.886371 + 0.462976i
\(10\) 4728.06 8189.24i 1.49514 2.58966i
\(11\) 668.319 + 3790.22i 0.151394 + 0.858599i 0.962009 + 0.273019i \(0.0880222\pi\)
−0.810614 + 0.585580i \(0.800867\pi\)
\(12\) 7423.42 15079.5i 1.24014 2.51914i
\(13\) −1107.04 + 402.929i −0.139753 + 0.0508659i −0.410950 0.911658i \(-0.634803\pi\)
0.271197 + 0.962524i \(0.412581\pi\)
\(14\) 4921.12 1791.14i 0.479310 0.174454i
\(15\) −19986.7 + 1323.89i −1.52905 + 0.101282i
\(16\) 11596.9 + 65769.5i 0.707821 + 4.01425i
\(17\) −7984.49 + 13829.5i −0.394163 + 0.682710i −0.992994 0.118165i \(-0.962299\pi\)
0.598831 + 0.800875i \(0.295632\pi\)
\(18\) −47861.1 + 6368.46i −1.93432 + 0.257383i
\(19\) −10605.9 18369.9i −0.354740 0.614427i 0.632334 0.774696i \(-0.282097\pi\)
−0.987073 + 0.160269i \(0.948764\pi\)
\(20\) 117925. 98950.8i 3.29610 2.76576i
\(21\) −8950.61 6553.34i −0.210904 0.154417i
\(22\) −14754.6 + 83677.7i −0.295426 + 1.67545i
\(23\) 283.404 + 237.804i 0.00485689 + 0.00407541i 0.645213 0.764003i \(-0.276769\pi\)
−0.640356 + 0.768078i \(0.721213\pi\)
\(24\) 172469. 165332.i 2.54666 2.44128i
\(25\) −98980.3 36025.9i −1.26695 0.461131i
\(26\) −26008.9 −0.290212
\(27\) 67594.7 + 76754.9i 0.660906 + 0.750469i
\(28\) 85254.6 0.733947
\(29\) −122889. 44727.9i −0.935664 0.340554i −0.171212 0.985234i \(-0.554768\pi\)
−0.764452 + 0.644681i \(0.776990\pi\)
\(30\) −424638. 123452.i −2.87140 0.834782i
\(31\) 57631.3 + 48358.4i 0.347450 + 0.291545i 0.799765 0.600313i \(-0.204957\pi\)
−0.452315 + 0.891858i \(0.649402\pi\)
\(32\) −142476. + 808020.i −0.768628 + 4.35910i
\(33\) 164693. 72602.6i 0.797766 0.351685i
\(34\) −270070. + 226615.i −1.17842 + 0.988811i
\(35\) −50800.9 87989.7i −0.200278 0.346892i
\(36\) −767622. 169063.i −2.74213 0.603935i
\(37\) 51150.8 88595.9i 0.166015 0.287546i −0.771000 0.636835i \(-0.780243\pi\)
0.937015 + 0.349289i \(0.113577\pi\)
\(38\) −81319.1 461184.i −0.240409 1.36342i
\(39\) 30640.1 + 45787.5i 0.0827111 + 0.123601i
\(40\) 2.05623e6 748406.i 5.07997 1.84896i
\(41\) −140048. + 50973.3i −0.317346 + 0.115505i −0.495782 0.868447i \(-0.665119\pi\)
0.178436 + 0.983952i \(0.442896\pi\)
\(42\) −136204. 203539.i −0.283674 0.423912i
\(43\) −85790.5 486542.i −0.164551 0.933213i −0.949527 0.313687i \(-0.898436\pi\)
0.784976 0.619526i \(-0.212675\pi\)
\(44\) −691620. + 1.19792e6i −1.22401 + 2.12004i
\(45\) 282918. + 892989.i 0.462825 + 1.46084i
\(46\) 4083.82 + 7073.38i 0.00618606 + 0.0107146i
\(47\) −344242. + 288854.i −0.483640 + 0.405822i −0.851740 0.523964i \(-0.824453\pi\)
0.368101 + 0.929786i \(0.380008\pi\)
\(48\) 2.85782e6 1.25983e6i 3.72984 1.64425i
\(49\) −133236. + 755618.i −0.161784 + 0.917521i
\(50\) −1.78140e6 1.49477e6i −2.01543 1.69114i
\(51\) 717105. + 208479.i 0.756985 + 0.220072i
\(52\) −397875. 144815.i −0.392406 0.142824i
\(53\) 1.45598e6 1.34335 0.671675 0.740846i \(-0.265575\pi\)
0.671675 + 0.740846i \(0.265575\pi\)
\(54\) 822743. + 2.10274e6i 0.711027 + 1.81722i
\(55\) 1.64847e6 1.33602
\(56\) 1.13877e6 + 414479.i 0.866521 + 0.315388i
\(57\) −716094. + 686461.i −0.512163 + 0.490969i
\(58\) −2.21170e6 1.85584e6i −1.48843 1.24894i
\(59\) 235509. 1.33564e6i 0.149288 0.846654i −0.814536 0.580113i \(-0.803008\pi\)
0.963824 0.266540i \(-0.0858806\pi\)
\(60\) −5.80860e6 4.25286e6i −3.47170 2.54186i
\(61\) 1.36590e6 1.14613e6i 0.770485 0.646514i −0.170348 0.985384i \(-0.554489\pi\)
0.940833 + 0.338870i \(0.110045\pi\)
\(62\) 830462. + 1.43840e6i 0.442536 + 0.766495i
\(63\) −197864. + 479564.i −0.0996955 + 0.241632i
\(64\) −4.78285e6 + 8.28413e6i −2.28064 + 3.95018i
\(65\) 87622.4 + 496931.i 0.0395748 + 0.224440i
\(66\) 3.96490e6 262630.i 1.69757 0.112445i
\(67\) 2.45756e6 894479.i 0.998257 0.363336i 0.209345 0.977842i \(-0.432867\pi\)
0.788912 + 0.614506i \(0.210645\pi\)
\(68\) −5.39320e6 + 1.96297e6i −2.08001 + 0.757062i
\(69\) 7641.38 15522.3i 0.00280027 0.00568831i
\(70\) −389508. 2.20901e6i −0.135729 0.769759i
\(71\) −685023. + 1.18649e6i −0.227144 + 0.393425i −0.956960 0.290218i \(-0.906272\pi\)
0.729817 + 0.683643i \(0.239605\pi\)
\(72\) −9.43144e6 5.99015e6i −2.97793 1.89136i
\(73\) 2.38594e6 + 4.13257e6i 0.717843 + 1.24334i 0.961853 + 0.273568i \(0.0882040\pi\)
−0.244009 + 0.969773i \(0.578463\pi\)
\(74\) 1.73014e6 1.45176e6i 0.496330 0.416471i
\(75\) −532880. + 4.89701e6i −0.145853 + 1.34034i
\(76\) 1.32383e6 7.50780e6i 0.345927 1.96185i
\(77\) 699360. + 586833.i 0.174576 + 0.146486i
\(78\) 289919. + 1.18126e6i 0.0691744 + 0.281847i
\(79\) −1.49182e6 542976.i −0.340424 0.123904i 0.166150 0.986100i \(-0.446866\pi\)
−0.506574 + 0.862196i \(0.669088\pi\)
\(80\) 2.86049e7 6.24635
\(81\) 2.73254e6 3.92556e6i 0.571306 0.820737i
\(82\) −3.29030e6 −0.659003
\(83\) −9.69036e6 3.52700e6i −1.86023 0.677068i −0.978822 0.204713i \(-0.934374\pi\)
−0.881408 0.472355i \(-0.843404\pi\)
\(84\) −950325. 3.87205e6i −0.174942 0.712792i
\(85\) 5.23961e6 + 4.39655e6i 0.925406 + 0.776508i
\(86\) 1.89402e6 1.07415e7i 0.321099 1.82105i
\(87\) −661597. + 6.07988e6i −0.107715 + 0.989869i
\(88\) −1.50621e7 + 1.26386e7i −2.35611 + 1.97701i
\(89\) −5.34357e6 9.25534e6i −0.803464 1.39164i −0.917323 0.398144i \(-0.869654\pi\)
0.113859 0.993497i \(-0.463679\pi\)
\(90\) −873468. + 2.06621e7i −0.126298 + 2.98762i
\(91\) −139727. + 242014.i −0.0194373 + 0.0336664i
\(92\) 23089.0 + 130944.i 0.00309135 + 0.0175319i
\(93\) 1.55391e6 3.15652e6i 0.200325 0.406928i
\(94\) −9.32269e6 + 3.39318e6i −1.15769 + 0.421366i
\(95\) −8.53750e6 + 3.10740e6i −1.02164 + 0.371847i
\(96\) 3.82864e7 2.53604e6i 4.41667 0.292555i
\(97\) −474057. 2.68851e6i −0.0527387 0.299096i 0.947017 0.321182i \(-0.104080\pi\)
−0.999756 + 0.0220863i \(0.992969\pi\)
\(98\) −8.46965e6 + 1.46699e7i −0.909022 + 1.57447i
\(99\) −5.13324e6 6.67063e6i −0.531702 0.690945i
\(100\) −1.89285e7 3.27852e7i −1.89285 3.27852i
\(101\) 8.46648e6 7.10422e6i 0.817670 0.686107i −0.134755 0.990879i \(-0.543025\pi\)
0.952425 + 0.304772i \(0.0985804\pi\)
\(102\) 1.33027e7 + 9.73982e6i 1.24120 + 0.908763i
\(103\) 3.56486e6 2.02173e7i 0.321449 1.82303i −0.212087 0.977251i \(-0.568026\pi\)
0.533536 0.845777i \(-0.320863\pi\)
\(104\) −4.61051e6 3.86868e6i −0.401913 0.337245i
\(105\) −3.43000e6 + 3.28806e6i −0.289155 + 0.277190i
\(106\) 3.02055e7 + 1.09939e7i 2.46329 + 0.896563i
\(107\) −2.04690e7 −1.61530 −0.807651 0.589661i \(-0.799261\pi\)
−0.807651 + 0.589661i \(0.799261\pi\)
\(108\) 878195. + 3.67480e7i 0.0670823 + 2.80705i
\(109\) 2.88042e6 0.213041 0.106521 0.994310i \(-0.466029\pi\)
0.106521 + 0.994310i \(0.466029\pi\)
\(110\) 3.41989e7 + 1.24474e7i 2.44984 + 0.891669i
\(111\) −4.59397e6 1.33557e6i −0.318829 0.0926908i
\(112\) 1.21356e7 + 1.01830e7i 0.816202 + 0.684875i
\(113\) −3.20478e6 + 1.81752e7i −0.208941 + 1.18496i 0.682176 + 0.731188i \(0.261034\pi\)
−0.891117 + 0.453774i \(0.850077\pi\)
\(114\) −2.00393e7 + 8.83408e6i −1.26682 + 0.558463i
\(115\) 121387. 101856.i 0.00744271 0.00624517i
\(116\) −2.35007e7 4.07044e7i −1.39791 2.42125i
\(117\) 1.73801e6 1.90198e6i 0.100323 0.109788i
\(118\) 1.49710e7 2.59306e7i 0.838811 1.45286i
\(119\) 657780. + 3.73046e6i 0.0357821 + 0.202931i
\(120\) −5.69113e7 8.50463e7i −3.00652 4.49284i
\(121\) 4.39280e6 1.59885e6i 0.225420 0.0820463i
\(122\) 3.69910e7 1.34636e7i 1.84432 0.671277i
\(123\) 3.87618e6 + 5.79243e6i 0.187817 + 0.280668i
\(124\) 4.69525e6 + 2.66281e7i 0.221148 + 1.25419i
\(125\) −5.82677e6 + 1.00923e7i −0.266835 + 0.462172i
\(126\) −7.72598e6 + 8.45490e6i −0.344078 + 0.376540i
\(127\) 3.27119e6 + 5.66587e6i 0.141708 + 0.245445i 0.928140 0.372232i \(-0.121407\pi\)
−0.786432 + 0.617677i \(0.788074\pi\)
\(128\) −8.13248e7 + 6.82397e7i −3.42759 + 2.87609i
\(129\) −2.11412e7 + 9.31983e6i −0.867093 + 0.382247i
\(130\) −1.93446e6 + 1.09709e7i −0.0772251 + 0.437965i
\(131\) −4.41726e6 3.70652e6i −0.171673 0.144051i 0.552903 0.833246i \(-0.313520\pi\)
−0.724576 + 0.689195i \(0.757965\pi\)
\(132\) 6.21160e7 + 1.80585e7i 2.35069 + 0.683397i
\(133\) −4.72821e6 1.72093e6i −0.174267 0.0634281i
\(134\) 5.77382e7 2.07299
\(135\) 3.74036e7 2.28035e7i 1.30842 0.797688i
\(136\) −8.15821e7 −2.78105
\(137\) −2.72622e7 9.92261e6i −0.905812 0.329689i −0.153233 0.988190i \(-0.548968\pi\)
−0.752579 + 0.658501i \(0.771191\pi\)
\(138\) 275733. 264323.i 0.00893125 0.00856167i
\(139\) 7.59299e6 + 6.37128e6i 0.239807 + 0.201222i 0.754768 0.655992i \(-0.227749\pi\)
−0.514961 + 0.857213i \(0.672194\pi\)
\(140\) 6.34097e6 3.59614e7i 0.195302 1.10761i
\(141\) 1.69562e7 + 1.24148e7i 0.509404 + 0.372969i
\(142\) −2.31704e7 + 1.94423e7i −0.679086 + 0.569821i
\(143\) −2.26705e6 3.92664e6i −0.0648312 0.112291i
\(144\) −8.90741e7 1.15752e8i −2.48590 3.23041i
\(145\) −2.80069e7 + 4.85094e7i −0.762916 + 1.32141i
\(146\) 1.82938e7 + 1.03750e8i 0.486486 + 2.75900i
\(147\) 3.58034e7 2.37157e6i 0.929638 0.0615780i
\(148\) 3.45504e7 1.25753e7i 0.876066 0.318862i
\(149\) 4.43187e7 1.61307e7i 1.09758 0.399485i 0.271154 0.962536i \(-0.412595\pi\)
0.826422 + 0.563051i \(0.190372\pi\)
\(150\) −4.80317e7 + 9.75688e7i −1.16201 + 2.36043i
\(151\) −3.38591e6 1.92024e7i −0.0800306 0.453876i −0.998319 0.0579632i \(-0.981539\pi\)
0.918288 0.395913i \(-0.129572\pi\)
\(152\) 5.41833e7 9.38482e7i 1.25145 2.16757i
\(153\) 1.47506e6 3.48930e7i 0.0332959 0.787622i
\(154\) 1.00777e7 + 1.74551e7i 0.222351 + 0.385123i
\(155\) 2.46846e7 2.07129e7i 0.532434 0.446765i
\(156\) −2.14204e6 + 1.96847e7i −0.0451743 + 0.415139i
\(157\) −1.01274e7 + 5.74354e7i −0.208857 + 1.18449i 0.682396 + 0.730983i \(0.260938\pi\)
−0.891253 + 0.453506i \(0.850173\pi\)
\(158\) −2.68490e7 2.25290e7i −0.541537 0.454404i
\(159\) −1.62297e7 6.61268e7i −0.320199 1.30463i
\(160\) 3.30236e8 + 1.20196e8i 6.37389 + 2.31991i
\(161\) 87757.7 0.00165727
\(162\) 8.63302e7 6.08060e7i 1.59537 1.12368i
\(163\) 7.69394e7 1.39153 0.695764 0.718270i \(-0.255066\pi\)
0.695764 + 0.718270i \(0.255066\pi\)
\(164\) −5.03339e7 1.83201e7i −0.891061 0.324320i
\(165\) −1.83754e7 7.48694e7i −0.318451 1.29751i
\(166\) −1.74403e8 1.46341e8i −2.95920 2.48307i
\(167\) 1.14304e7 6.48250e7i 0.189913 1.07705i −0.729567 0.683909i \(-0.760278\pi\)
0.919479 0.393138i \(-0.128611\pi\)
\(168\) 6.13081e6 5.63403e7i 0.0997551 0.916721i
\(169\) −4.70050e7 + 3.94419e7i −0.749101 + 0.628570i
\(170\) 7.55022e7 + 1.30774e8i 1.17866 + 2.04150i
\(171\) 3.91596e7 + 2.48712e7i 0.598896 + 0.380374i
\(172\) 8.87816e7 1.53774e8i 1.33037 2.30427i
\(173\) 2.26446e7 + 1.28424e8i 0.332509 + 1.88575i 0.450559 + 0.892746i \(0.351225\pi\)
−0.118050 + 0.993008i \(0.537664\pi\)
\(174\) −5.96337e7 + 1.21137e8i −0.858163 + 1.74322i
\(175\) −2.34791e7 + 8.54571e6i −0.331168 + 0.120535i
\(176\) −2.41531e8 + 8.79100e7i −3.33947 + 1.21547i
\(177\) −6.32864e7 + 4.19200e6i −0.857835 + 0.0568218i
\(178\) −4.09710e7 2.32358e8i −0.544511 3.08808i
\(179\) −4.24865e7 + 7.35888e7i −0.553689 + 0.959017i 0.444316 + 0.895870i \(0.353447\pi\)
−0.998004 + 0.0631466i \(0.979886\pi\)
\(180\) −1.28406e8 + 3.11218e8i −1.64109 + 3.97751i
\(181\) 3.36936e7 + 5.83590e7i 0.422350 + 0.731532i 0.996169 0.0874505i \(-0.0278720\pi\)
−0.573819 + 0.818982i \(0.694539\pi\)
\(182\) −4.72617e6 + 3.96573e6i −0.0581112 + 0.0487611i
\(183\) −6.72797e7 4.92599e7i −0.811531 0.594176i
\(184\) −328201. + 1.86132e6i −0.00388398 + 0.0220272i
\(185\) −3.35664e7 2.81655e7i −0.389766 0.327052i
\(186\) 5.60715e7 5.37512e7i 0.638920 0.612481i
\(187\) −5.77532e7 2.10205e7i −0.645848 0.235070i
\(188\) −1.61508e8 −1.77273
\(189\) 2.39861e7 + 3.64085e6i 0.258431 + 0.0392271i
\(190\) −2.00581e8 −2.12155
\(191\) 5.02800e7 + 1.83004e7i 0.522130 + 0.190040i 0.589621 0.807680i \(-0.299277\pi\)
−0.0674908 + 0.997720i \(0.521499\pi\)
\(192\) 4.29558e8 + 1.24882e8i 4.37994 + 1.27335i
\(193\) 3.78659e7 + 3.17733e7i 0.379139 + 0.318135i 0.812364 0.583150i \(-0.198180\pi\)
−0.433226 + 0.901286i \(0.642625\pi\)
\(194\) 1.04659e7 5.93549e7i 0.102913 0.583648i
\(195\) 2.15926e7 9.51884e6i 0.208538 0.0919311i
\(196\) −2.11246e8 + 1.77257e8i −2.00398 + 1.68154i
\(197\) 5.55820e7 + 9.62708e7i 0.517967 + 0.897145i 0.999782 + 0.0208722i \(0.00664431\pi\)
−0.481815 + 0.876273i \(0.660022\pi\)
\(198\) −5.61243e7 1.77148e8i −0.513834 1.62184i
\(199\) −3.10526e7 + 5.37848e7i −0.279327 + 0.483808i −0.971218 0.238194i \(-0.923445\pi\)
0.691891 + 0.722002i \(0.256778\pi\)
\(200\) −9.34439e7 5.29946e8i −0.825935 4.68411i
\(201\) −6.80192e7 1.01646e8i −0.590806 0.882881i
\(202\) 2.29287e8 8.34537e7i 1.95727 0.712387i
\(203\) −2.91505e7 + 1.06099e7i −0.244574 + 0.0890176i
\(204\) 1.49271e8 + 2.23065e8i 1.23103 + 1.83961i
\(205\) 1.10848e7 + 6.28652e7i 0.0898650 + 0.509650i
\(206\) 2.26614e8 3.92507e8i 1.80614 3.12833i
\(207\) −790160. 174027.i −0.00619182 0.00136370i
\(208\) −3.93387e7 6.81367e7i −0.303109 0.525000i
\(209\) 6.25381e7 5.24757e7i 0.473841 0.397600i
\(210\) −9.59859e7 + 4.23141e7i −0.715220 + 0.315295i
\(211\) 3.64318e7 2.06615e8i 0.266988 1.51417i −0.496325 0.868137i \(-0.665317\pi\)
0.763313 0.646029i \(-0.223571\pi\)
\(212\) 4.00860e8 + 3.36362e8i 2.88946 + 2.42455i
\(213\) 6.15235e7 + 1.78863e7i 0.436227 + 0.126821i
\(214\) −4.24647e8 1.54559e8i −2.96196 1.07807i
\(215\) −2.11610e8 −1.45212
\(216\) −1.66926e8 + 4.95124e8i −1.12703 + 3.34292i
\(217\) 1.78459e7 0.118557
\(218\) 5.97568e7 + 2.17497e7i 0.390651 + 0.142185i
\(219\) 1.61095e8 1.54429e8i 1.03640 0.993514i
\(220\) 4.53857e8 + 3.80832e8i 2.87369 + 2.41131i
\(221\) 3.26681e6 1.85270e7i 0.0203588 0.115460i
\(222\) −8.52211e7 6.23960e7i −0.522771 0.382756i
\(223\) −1.22115e8 + 1.02466e8i −0.737395 + 0.618748i −0.932137 0.362106i \(-0.882058\pi\)
0.194741 + 0.980855i \(0.437613\pi\)
\(224\) 9.73138e7 + 1.68552e8i 0.578504 + 1.00200i
\(225\) 2.28350e8 3.03845e7i 1.33648 0.177833i
\(226\) −2.03724e8 + 3.52861e8i −1.17399 + 2.03340i
\(227\) 1.90090e6 + 1.07805e7i 0.0107862 + 0.0611717i 0.989726 0.142979i \(-0.0456680\pi\)
−0.978940 + 0.204150i \(0.934557\pi\)
\(228\) −3.55742e8 + 2.35639e7i −1.98776 + 0.131666i
\(229\) −2.37020e7 + 8.62684e6i −0.130425 + 0.0474709i −0.406408 0.913692i \(-0.633219\pi\)
0.275983 + 0.961163i \(0.410997\pi\)
\(230\) 3.28738e6 1.19651e6i 0.0178157 0.00648438i
\(231\) 1.88568e7 3.83045e7i 0.100653 0.204460i
\(232\) −1.16015e8 6.57955e8i −0.609968 3.45930i
\(233\) −1.33852e8 + 2.31839e8i −0.693233 + 1.20071i 0.277540 + 0.960714i \(0.410481\pi\)
−0.970773 + 0.240001i \(0.922852\pi\)
\(234\) 5.04181e7 2.63348e7i 0.257235 0.134361i
\(235\) 9.62384e7 + 1.66690e8i 0.483739 + 0.837860i
\(236\) 3.73400e8 3.13320e8i 1.84919 1.55166i
\(237\) −8.03148e6 + 7.38070e7i −0.0391901 + 0.360146i
\(238\) −1.45220e7 + 8.23582e7i −0.0698243 + 0.395993i
\(239\) −1.77578e8 1.49005e8i −0.841387 0.706008i 0.116488 0.993192i \(-0.462836\pi\)
−0.957875 + 0.287184i \(0.907281\pi\)
\(240\) −3.18857e8 1.29916e9i −1.48887 6.06631i
\(241\) 2.09362e8 + 7.62016e7i 0.963471 + 0.350675i 0.775393 0.631479i \(-0.217552\pi\)
0.188078 + 0.982154i \(0.439774\pi\)
\(242\) 1.03205e8 0.468109
\(243\) −2.08748e8 8.03472e7i −0.933257 0.359210i
\(244\) 6.40839e8 2.82413
\(245\) 3.08819e8 + 1.12401e8i 1.34160 + 0.488302i
\(246\) 3.66767e7 + 1.49437e8i 0.157079 + 0.640009i
\(247\) 1.91429e7 + 1.60628e7i 0.0808293 + 0.0678239i
\(248\) −6.67410e7 + 3.78507e8i −0.277851 + 1.57577i
\(249\) −5.21700e7 + 4.79427e8i −0.214152 + 1.96800i
\(250\) −1.97087e8 + 1.65375e8i −0.797750 + 0.669392i
\(251\) −2.04853e7 3.54815e7i −0.0817680 0.141626i 0.822241 0.569139i \(-0.192723\pi\)
−0.904009 + 0.427512i \(0.859390\pi\)
\(252\) −1.65265e8 + 8.63227e7i −0.650549 + 0.339800i
\(253\) −711926. + 1.23309e6i −0.00276384 + 0.00478711i
\(254\) 2.50814e7 + 1.42244e8i 0.0960359 + 0.544646i
\(255\) 1.41275e8 2.86978e8i 0.533549 1.08382i
\(256\) −1.05185e9 + 3.82843e8i −3.91846 + 1.42620i
\(257\) 7.66129e7 2.78848e7i 0.281537 0.102471i −0.197392 0.980325i \(-0.563247\pi\)
0.478929 + 0.877853i \(0.341025\pi\)
\(258\) −5.08965e8 + 3.37131e7i −1.84509 + 0.122217i
\(259\) −4.21392e6 2.38983e7i −0.0150708 0.0854710i
\(260\) −9.06774e7 + 1.57058e8i −0.319958 + 0.554183i
\(261\) 2.83508e8 3.77239e7i 0.987013 0.131333i
\(262\) −6.36523e7 1.10249e8i −0.218655 0.378721i
\(263\) 1.81878e8 1.52613e8i 0.616502 0.517306i −0.280200 0.959942i \(-0.590401\pi\)
0.896702 + 0.442635i \(0.145956\pi\)
\(264\) 7.41909e8 + 5.43201e8i 2.48163 + 1.81696i
\(265\) 1.08291e8 6.14149e8i 0.357464 2.02728i
\(266\) −8.50961e7 7.14041e7i −0.277220 0.232615i
\(267\) −3.60790e8 + 3.45860e8i −1.16002 + 1.11202i
\(268\) 8.83260e8 + 3.21480e8i 2.80296 + 1.02019i
\(269\) −3.56724e8 −1.11738 −0.558688 0.829378i \(-0.688695\pi\)
−0.558688 + 0.829378i \(0.688695\pi\)
\(270\) 9.48156e8 1.90648e8i 2.93161 0.589465i
\(271\) −1.37040e8 −0.418268 −0.209134 0.977887i \(-0.567065\pi\)
−0.209134 + 0.977887i \(0.567065\pi\)
\(272\) −1.00216e9 3.64756e8i −3.01957 1.09903i
\(273\) 1.25492e7 + 3.64834e6i 0.0373290 + 0.0108524i
\(274\) −4.90652e8 4.11706e8i −1.44094 1.20909i
\(275\) 7.03957e7 3.99234e8i 0.204118 1.15761i
\(276\) 5.68980e6 2.50827e6i 0.0162898 0.00718113i
\(277\) 1.92441e8 1.61477e8i 0.544025 0.456491i −0.328887 0.944369i \(-0.606673\pi\)
0.872912 + 0.487878i \(0.162229\pi\)
\(278\) 1.09414e8 + 1.89511e8i 0.305434 + 0.529027i
\(279\) −1.60682e8 3.53891e7i −0.442948 0.0975561i
\(280\) 2.59531e8 4.49521e8i 0.706539 1.22376i
\(281\) −733413. 4.15939e6i −0.00197186 0.0111830i 0.983806 0.179237i \(-0.0573628\pi\)
−0.985778 + 0.168054i \(0.946252\pi\)
\(282\) 2.58029e8 + 3.85589e8i 0.685167 + 1.02389i
\(283\) 3.45992e8 1.25931e8i 0.907430 0.330277i 0.154204 0.988039i \(-0.450719\pi\)
0.753226 + 0.657762i \(0.228497\pi\)
\(284\) −4.62706e8 + 1.68411e8i −1.19865 + 0.436272i
\(285\) 2.36297e8 + 3.53114e8i 0.604646 + 0.903562i
\(286\) −1.73822e7 9.85796e7i −0.0439364 0.249176i
\(287\) −1.76764e7 + 3.06165e7i −0.0441375 + 0.0764484i
\(288\) −5.41956e8 1.71060e9i −1.33687 4.21964i
\(289\) 7.76653e7 + 1.34520e8i 0.189271 + 0.327827i
\(290\) −9.47314e8 + 7.94891e8i −2.28087 + 1.91388i
\(291\) −1.16821e8 + 5.14991e7i −0.277905 + 0.122511i
\(292\) −2.97813e8 + 1.68898e9i −0.700010 + 3.96995i
\(293\) −2.21696e8 1.86025e8i −0.514897 0.432050i 0.347951 0.937513i \(-0.386877\pi\)
−0.862849 + 0.505462i \(0.831322\pi\)
\(294\) 7.60679e8 + 2.21146e8i 1.74576 + 0.507533i
\(295\) −5.45871e8 1.98681e8i −1.23798 0.450587i
\(296\) 5.22638e8 1.17133
\(297\) −2.45743e8 + 3.07496e8i −0.544295 + 0.681070i
\(298\) 1.04123e9 2.27924
\(299\) −409557. 149067.i −0.000886064 0.000322501i
\(300\) −1.27803e9 + 1.22514e9i −2.73284 + 2.61976i
\(301\) −8.97752e7 7.53303e7i −0.189746 0.159216i
\(302\) 7.47516e7 4.23937e8i 0.156169 0.885681i
\(303\) −4.17031e8 3.05336e8i −0.861229 0.630563i
\(304\) 1.08519e9 9.10580e8i 2.21537 1.85892i
\(305\) −3.81859e8 6.61399e8i −0.770643 1.33479i
\(306\) 2.94074e8 7.12746e8i 0.586720 1.42203i
\(307\) −3.20051e8 + 5.54344e8i −0.631299 + 1.09344i 0.355988 + 0.934491i \(0.384144\pi\)
−0.987287 + 0.158951i \(0.949189\pi\)
\(308\) 5.69772e7 + 3.23134e8i 0.111115 + 0.630166i
\(309\) −9.57957e8 + 6.34538e7i −1.84710 + 0.122350i
\(310\) 6.68503e8 2.43315e8i 1.27449 0.463877i
\(311\) 2.51876e8 9.16754e7i 0.474816 0.172819i −0.0935165 0.995618i \(-0.529811\pi\)
0.568333 + 0.822799i \(0.307589\pi\)
\(312\) −1.24313e8 + 2.52521e8i −0.231725 + 0.470714i
\(313\) −3.50530e7 1.98795e8i −0.0646129 0.366438i −0.999921 0.0126026i \(-0.995988\pi\)
0.935308 0.353836i \(-0.115123\pi\)
\(314\) −6.43789e8 + 1.11507e9i −1.17352 + 2.03259i
\(315\) 1.87569e8 + 1.19130e8i 0.338123 + 0.214751i
\(316\) −2.85288e8 4.94133e8i −0.508603 0.880925i
\(317\) −7.41838e8 + 6.22476e8i −1.30798 + 1.09753i −0.319275 + 0.947662i \(0.603439\pi\)
−0.988707 + 0.149865i \(0.952116\pi\)
\(318\) 1.62617e8 1.49440e9i 0.283577 2.60599i
\(319\) 8.73998e7 4.95669e8i 0.150745 0.854918i
\(320\) 3.13862e9 + 2.63361e9i 5.35443 + 4.49290i
\(321\) 2.28166e8 + 9.29651e8i 0.385020 + 1.56874i
\(322\) 1.82061e6 + 662646.i 0.00303893 + 0.00110608i
\(323\) 3.38730e8 0.559301
\(324\) 1.65921e9 4.49512e8i 2.71015 0.734232i
\(325\) 1.24091e8 0.200516
\(326\) 1.59617e9 + 5.80959e8i 2.55163 + 0.928718i
\(327\) −3.21078e7 1.30822e8i −0.0507801 0.206901i
\(328\) −5.83261e8 4.89414e8i −0.912650 0.765804i
\(329\) −1.85103e7 + 1.04977e8i −0.0286569 + 0.162521i
\(330\) 1.84116e8 1.69198e9i 0.282029 2.59177i
\(331\) −3.68507e7 + 3.09214e7i −0.0558532 + 0.0468664i −0.670287 0.742102i \(-0.733829\pi\)
0.614434 + 0.788968i \(0.289385\pi\)
\(332\) −1.85314e9 3.20973e9i −2.77923 4.81377i
\(333\) −9.44968e6 + 2.23534e8i −0.0140237 + 0.331733i
\(334\) 7.26618e8 1.25854e9i 1.06707 1.84822i
\(335\) −1.94517e8 1.10316e9i −0.282683 1.60318i
\(336\) 3.27210e8 6.64676e8i 0.470586 0.955922i
\(337\) −4.40613e8 + 1.60370e8i −0.627122 + 0.228254i −0.635978 0.771707i \(-0.719403\pi\)
0.00885603 + 0.999961i \(0.497181\pi\)
\(338\) −1.27298e9 + 4.63326e8i −1.79313 + 0.652647i
\(339\) 8.61195e8 5.70444e7i 1.20061 0.0795269i
\(340\) 4.26873e8 + 2.42092e9i 0.589010 + 3.34044i
\(341\) −1.44773e8 + 2.50754e8i −0.197719 + 0.342459i
\(342\) 6.24598e8 + 8.11663e8i 0.844324 + 1.09720i
\(343\) 1.88679e8 + 3.26802e8i 0.252461 + 0.437275i
\(344\) 1.93348e9 1.62239e9i 2.56086 2.14882i
\(345\) −5.97914e6 4.37773e6i −0.00783920 0.00573960i
\(346\) −4.99931e8 + 2.83525e9i −0.648849 + 3.67981i
\(347\) −1.18634e8 9.95456e7i −0.152425 0.127900i 0.563386 0.826194i \(-0.309498\pi\)
−0.715811 + 0.698294i \(0.753943\pi\)
\(348\) −1.58673e9 + 1.52107e9i −2.01826 + 1.93474i
\(349\) −3.38949e8 1.23367e8i −0.426820 0.155350i 0.119673 0.992813i \(-0.461815\pi\)
−0.546493 + 0.837464i \(0.684038\pi\)
\(350\) −5.51622e8 −0.687706
\(351\) −1.05757e8 5.77347e7i −0.130537 0.0712627i
\(352\) −3.15780e9 −3.85909
\(353\) 6.09526e8 + 2.21849e8i 0.737532 + 0.268440i 0.683349 0.730091i \(-0.260523\pi\)
0.0541823 + 0.998531i \(0.482745\pi\)
\(354\) −1.34458e9 3.90900e8i −1.61093 0.468333i
\(355\) 4.49528e8 + 3.77199e8i 0.533283 + 0.447478i
\(356\) 6.66985e8 3.78266e9i 0.783504 4.44347i
\(357\) 1.62096e8 7.14578e7i 0.188553 0.0831210i
\(358\) −1.43708e9 + 1.20585e9i −1.65535 + 1.38900i
\(359\) 7.00922e8 + 1.21403e9i 0.799538 + 1.38484i 0.919917 + 0.392112i \(0.128255\pi\)
−0.120380 + 0.992728i \(0.538411\pi\)
\(360\) −3.22820e9 + 3.53277e9i −3.64672 + 3.99077i
\(361\) 2.21966e8 3.84456e8i 0.248320 0.430102i
\(362\) 2.58341e8 + 1.46512e9i 0.286228 + 1.62328i
\(363\) −1.21582e8 1.81688e8i −0.133412 0.199367i
\(364\) −9.43801e7 + 3.43515e7i −0.102571 + 0.0373329i
\(365\) 1.92063e9 6.99052e8i 2.06737 0.752461i
\(366\) −1.02382e9 1.52996e9i −1.09154 1.63116i
\(367\) −1.52720e8 8.66116e8i −0.161274 0.914628i −0.952824 0.303524i \(-0.901837\pi\)
0.791550 0.611104i \(-0.209274\pi\)
\(368\) −1.23536e7 + 2.13971e7i −0.0129219 + 0.0223814i
\(369\) 2.19870e8 2.40614e8i 0.227811 0.249304i
\(370\) −4.83688e8 8.37773e8i −0.496432 0.859845i
\(371\) 2.64571e8 2.22001e8i 0.268988 0.225708i
\(372\) 1.15704e9 5.10068e8i 1.16533 0.513721i
\(373\) 1.26781e8 7.19010e8i 0.126495 0.717388i −0.853914 0.520414i \(-0.825778\pi\)
0.980409 0.196974i \(-0.0631113\pi\)
\(374\) −1.03942e9 8.72173e8i −1.02740 0.862089i
\(375\) 5.23316e8 + 1.52140e8i 0.512453 + 0.148982i
\(376\) −2.15732e9 7.85199e8i −2.09294 0.761768i
\(377\) 1.54065e8 0.148084
\(378\) 4.70121e8 + 2.56648e8i 0.447701 + 0.244409i
\(379\) 1.16704e9 1.10116 0.550578 0.834783i \(-0.314407\pi\)
0.550578 + 0.834783i \(0.314407\pi\)
\(380\) −3.06842e9 1.11681e9i −2.86862 1.04409i
\(381\) 2.20866e8 2.11726e8i 0.204593 0.196127i
\(382\) 9.04917e8 + 7.59315e8i 0.830590 + 0.696948i
\(383\) −2.53271e8 + 1.43637e9i −0.230350 + 1.30638i 0.621838 + 0.783146i \(0.286386\pi\)
−0.852188 + 0.523236i \(0.824725\pi\)
\(384\) 4.00579e9 + 2.93291e9i 3.61018 + 2.64326i
\(385\) 2.99550e8 2.51352e8i 0.267520 0.224476i
\(386\) 5.45644e8 + 9.45084e8i 0.482897 + 0.836401i
\(387\) 6.58942e8 + 8.56293e8i 0.577908 + 0.750990i
\(388\) 4.90585e8 8.49719e8i 0.426386 0.738523i
\(389\) 9.25459e7 + 5.24854e8i 0.0797138 + 0.452079i 0.998373 + 0.0570275i \(0.0181623\pi\)
−0.918659 + 0.395052i \(0.870727\pi\)
\(390\) 5.19833e8 3.44330e7i 0.443749 0.0293934i
\(391\) −5.55155e6 + 2.02060e6i −0.00469673 + 0.00170947i
\(392\) −3.68345e9 + 1.34066e9i −3.08854 + 1.12414i
\(393\) −1.19102e8 + 2.41937e8i −0.0989794 + 0.201061i
\(394\) 4.26166e8 + 2.41691e9i 0.351028 + 1.99078i
\(395\) −3.39991e8 + 5.88881e8i −0.277573 + 0.480770i
\(396\) 1.27771e8 3.02245e9i 0.103395 2.44583i
\(397\) −5.23216e8 9.06236e8i −0.419676 0.726900i 0.576231 0.817287i \(-0.304523\pi\)
−0.995907 + 0.0903871i \(0.971190\pi\)
\(398\) −1.05033e9 + 8.81335e8i −0.835097 + 0.700729i
\(399\) −2.54552e7 + 2.33926e8i −0.0200619 + 0.184363i
\(400\) 1.22154e9 6.92767e9i 0.954325 5.41225i
\(401\) 1.82182e9 + 1.52869e9i 1.41092 + 1.18390i 0.956001 + 0.293364i \(0.0947749\pi\)
0.454915 + 0.890535i \(0.349670\pi\)
\(402\) −6.43603e8 2.62232e9i −0.494114 2.01324i
\(403\) −8.32851e7 3.03133e7i −0.0633869 0.0230710i
\(404\) 3.97222e9 2.99708
\(405\) −1.45261e9 1.44459e9i −1.08657 1.08057i
\(406\) −6.84866e8 −0.507884
\(407\) 3.69983e8 + 1.34663e8i 0.272020 + 0.0990074i
\(408\) 9.09388e8 + 3.70525e9i 0.662886 + 2.70089i
\(409\) −3.75933e8 3.15445e8i −0.271693 0.227978i 0.496753 0.867892i \(-0.334525\pi\)
−0.768446 + 0.639914i \(0.778970\pi\)
\(410\) −2.44723e8 + 1.38789e9i −0.175360 + 0.994516i
\(411\) −1.46771e8 + 1.34878e9i −0.104278 + 0.958288i
\(412\) 5.65210e9 4.74268e9i 3.98171 3.34105i
\(413\) −1.60857e8 2.78612e8i −0.112361 0.194615i
\(414\) −1.50785e7 9.57672e6i −0.0104437 0.00663308i
\(415\) −2.20847e9 + 3.82519e9i −1.51678 + 2.62715i
\(416\) −1.67849e8 9.51917e8i −0.114312 0.648295i
\(417\) 2.04729e8 4.15875e8i 0.138262 0.280858i
\(418\) 1.69364e9 6.16435e8i 1.13424 0.412829i
\(419\) −8.40641e8 + 3.05968e8i −0.558292 + 0.203202i −0.605727 0.795673i \(-0.707118\pi\)
0.0474347 + 0.998874i \(0.484895\pi\)
\(420\) −1.70396e9 + 1.12868e8i −1.12224 + 0.0743359i
\(421\) 9.14928e7 + 5.18881e8i 0.0597585 + 0.338907i 0.999999 0.00160462i \(-0.000510767\pi\)
−0.940240 + 0.340512i \(0.889400\pi\)
\(422\) 2.31593e9 4.01131e9i 1.50014 2.59832i
\(423\) 3.74839e8 9.08496e8i 0.240798 0.583622i
\(424\) 3.71914e9 + 6.44174e9i 2.36953 + 4.10414i
\(425\) 1.28853e9 1.08120e9i 0.814203 0.683197i
\(426\) 1.14130e9 + 8.35621e8i 0.715263 + 0.523692i
\(427\) 7.34461e7 4.16533e8i 0.0456532 0.258912i
\(428\) −5.63553e9 4.72877e9i −3.47442 2.91538i
\(429\) −1.53067e8 + 1.46733e8i −0.0936014 + 0.0897281i
\(430\) −4.39003e9 1.59784e9i −2.66274 0.969156i
\(431\) −6.26640e8 −0.377006 −0.188503 0.982073i \(-0.560363\pi\)
−0.188503 + 0.982073i \(0.560363\pi\)
\(432\) −4.26424e9 + 5.33579e9i −2.54477 + 3.18424i
\(433\) −1.47405e9 −0.872581 −0.436290 0.899806i \(-0.643708\pi\)
−0.436290 + 0.899806i \(0.643708\pi\)
\(434\) 3.70228e8 + 1.34752e8i 0.217398 + 0.0791263i
\(435\) 2.51536e9 + 7.31273e8i 1.46517 + 0.425958i
\(436\) 7.93039e8 + 6.65438e8i 0.458239 + 0.384508i
\(437\) 1.36270e6 7.72824e6i 0.000781113 0.00442991i
\(438\) 4.50812e9 1.98735e9i 2.56352 1.13009i
\(439\) 2.79357e8 2.34408e8i 0.157592 0.132235i −0.560582 0.828099i \(-0.689423\pi\)
0.718174 + 0.695864i \(0.244978\pi\)
\(440\) 4.21084e9 + 7.29339e9i 2.35659 + 4.08174i
\(441\) −5.06808e8 1.59966e9i −0.281390 0.888165i
\(442\) 2.07668e8 3.59691e8i 0.114391 0.198131i
\(443\) −4.13559e8 2.34541e9i −0.226009 1.28176i −0.860748 0.509032i \(-0.830004\pi\)
0.634739 0.772727i \(-0.281108\pi\)
\(444\) −9.56269e8 1.42901e9i −0.518489 0.774812i
\(445\) −4.30145e9 + 1.56560e9i −2.31396 + 0.842211i
\(446\) −3.30708e9 + 1.20368e9i −1.76511 + 0.642448i
\(447\) −1.22663e9 1.83304e9i −0.649588 0.970721i
\(448\) 3.94022e8 + 2.23461e9i 0.207037 + 1.17416i
\(449\) 6.03881e8 1.04595e9i 0.314840 0.545318i −0.664564 0.747232i \(-0.731383\pi\)
0.979403 + 0.201913i \(0.0647159\pi\)
\(450\) 4.96673e9 + 1.09389e9i 2.56937 + 0.565885i
\(451\) −2.86797e8 4.96747e8i −0.147217 0.254986i
\(452\) −5.08119e9 + 4.26363e9i −2.58810 + 2.17167i
\(453\) −8.34384e8 + 3.67827e8i −0.421718 + 0.185909i
\(454\) −4.19667e7 + 2.38005e8i −0.0210479 + 0.119369i
\(455\) 9.16922e7 + 7.69389e7i 0.0456344 + 0.0382918i
\(456\) −4.86632e9 1.41475e9i −2.40339 0.698719i
\(457\) 2.73143e9 + 9.94160e8i 1.33870 + 0.487247i 0.909403 0.415915i \(-0.136539\pi\)
0.429298 + 0.903163i \(0.358761\pi\)
\(458\) −5.56859e8 −0.270842
\(459\) −1.60119e9 + 3.21955e8i −0.772857 + 0.155400i
\(460\) 5.69513e7 0.0272804
\(461\) −2.22181e8 8.08674e7i −0.105622 0.0384433i 0.288669 0.957429i \(-0.406787\pi\)
−0.394291 + 0.918986i \(0.629010\pi\)
\(462\) 6.80431e8 6.52275e8i 0.321024 0.307740i
\(463\) −1.87014e9 1.56923e9i −0.875669 0.734774i 0.0896145 0.995977i \(-0.471436\pi\)
−0.965284 + 0.261203i \(0.915881\pi\)
\(464\) 1.51660e9 8.60105e9i 0.704786 3.99704i
\(465\) −1.21588e9 8.90229e8i −0.560798 0.410597i
\(466\) −4.52745e9 + 3.79898e9i −2.07254 + 1.73907i
\(467\) −2.56212e7 4.43772e7i −0.0116410 0.0201628i 0.860146 0.510048i \(-0.170372\pi\)
−0.871787 + 0.489885i \(0.837039\pi\)
\(468\) 9.17908e8 1.22138e8i 0.413941 0.0550795i
\(469\) 3.10186e8 5.37258e8i 0.138841 0.240479i
\(470\) 7.37893e8 + 4.18480e9i 0.327832 + 1.85923i
\(471\) 2.72146e9 1.80266e8i 1.20013 0.0794951i
\(472\) 6.51088e9 2.36977e9i 2.84999 1.03731i
\(473\) 1.78677e9 6.50330e8i 0.776344 0.282566i
\(474\) −7.23926e8 + 1.47054e9i −0.312227 + 0.634240i
\(475\) 3.87981e8 + 2.20035e9i 0.166105 + 0.942028i
\(476\) −6.80714e8 + 1.17903e9i −0.289295 + 0.501073i
\(477\) −2.82240e9 + 1.47422e9i −1.19071 + 0.621939i
\(478\) −2.55888e9 4.43211e9i −1.07165 1.85615i
\(479\) 2.33941e9 1.96300e9i 0.972596 0.816105i −0.0103595 0.999946i \(-0.503298\pi\)
0.982956 + 0.183841i \(0.0588531\pi\)
\(480\) 1.77789e9 1.63383e10i 0.733771 6.74315i
\(481\) −2.09281e7 + 1.18689e8i −0.00857477 + 0.0486299i
\(482\) 3.76800e9 + 3.16173e9i 1.53266 + 1.28606i
\(483\) −978227. 3.98573e6i −0.000395025 0.00160951i
\(484\) 1.57880e9 + 5.74634e8i 0.632947 + 0.230374i
\(485\) −1.16931e9 −0.465406
\(486\) −3.72397e9 3.24310e9i −1.47156 1.28154i
\(487\) 7.31295e8 0.286907 0.143453 0.989657i \(-0.454179\pi\)
0.143453 + 0.989657i \(0.454179\pi\)
\(488\) 8.55989e9 + 3.11555e9i 3.33426 + 1.21357i
\(489\) −8.57637e8 3.49439e9i −0.331682 1.35142i
\(490\) 5.55799e9 + 4.66370e9i 2.13418 + 1.79079i
\(491\) −5.89689e8 + 3.34429e9i −0.224822 + 1.27503i 0.638204 + 0.769867i \(0.279677\pi\)
−0.863026 + 0.505160i \(0.831434\pi\)
\(492\) −2.70983e8 + 2.49025e9i −0.102580 + 0.942683i
\(493\) 1.59977e9 1.34237e9i 0.601303 0.504554i
\(494\) 2.75848e8 + 4.77782e8i 0.102950 + 0.178314i
\(495\) −3.19555e9 + 1.66912e9i −1.18421 + 0.618544i
\(496\) −2.51216e9 + 4.35119e9i −0.924404 + 1.60112i
\(497\) 5.64338e7 + 3.20052e8i 0.0206201 + 0.116943i
\(498\) −4.70240e9 + 9.55218e9i −1.70615 + 3.46577i
\(499\) 1.31647e9 4.79155e8i 0.474305 0.172633i −0.0937964 0.995591i \(-0.529900\pi\)
0.568102 + 0.822958i \(0.307678\pi\)
\(500\) −3.93575e9 + 1.43250e9i −1.40810 + 0.512506i
\(501\) −3.07160e9 + 2.03459e8i −1.09127 + 0.0722844i
\(502\) −1.57068e8 8.90775e8i −0.0554146 0.314272i
\(503\) −5.45560e8 + 9.44937e8i −0.191141 + 0.331066i −0.945629 0.325248i \(-0.894552\pi\)
0.754487 + 0.656314i \(0.227886\pi\)
\(504\) −2.62718e9 + 3.49575e8i −0.914076 + 0.121628i
\(505\) −2.36694e9 4.09966e9i −0.817837 1.41654i
\(506\) −2.40804e7 + 2.02059e7i −0.00826299 + 0.00693347i
\(507\) 2.31531e9 + 1.69519e9i 0.789008 + 0.577685i
\(508\) −4.08311e8 + 2.31564e9i −0.138187 + 0.783698i
\(509\) 2.44336e9 + 2.05022e9i 0.821249 + 0.689110i 0.953264 0.302138i \(-0.0977004\pi\)
−0.132015 + 0.991248i \(0.542145\pi\)
\(510\) 5.09779e9 4.88684e9i 1.70171 1.63130i
\(511\) 1.06368e9 + 3.87146e8i 0.352644 + 0.128352i
\(512\) −1.11236e10 −3.66269
\(513\) 6.93081e8 2.05577e9i 0.226659 0.672299i
\(514\) 1.79995e9 0.584643
\(515\) −8.26277e9 3.00740e9i −2.66563 0.970211i
\(516\) −7.97368e9 2.31813e9i −2.55496 0.742786i
\(517\) −1.32488e9 1.11171e9i −0.421659 0.353814i
\(518\) 9.30318e7 5.27610e8i 0.0294088 0.166786i
\(519\) 5.58028e9 2.45999e9i 1.75215 0.772410i
\(520\) −1.97477e9 + 1.65703e9i −0.615893 + 0.516795i
\(521\) 3.03146e8 + 5.25065e8i 0.0939119 + 0.162660i 0.909154 0.416460i \(-0.136729\pi\)
−0.815242 + 0.579120i \(0.803396\pi\)
\(522\) 6.16645e9 + 1.35812e9i 1.89753 + 0.417917i
\(523\) 4.59749e8 7.96308e8i 0.140529 0.243403i −0.787167 0.616740i \(-0.788453\pi\)
0.927696 + 0.373337i \(0.121786\pi\)
\(524\) −3.59876e8 2.04096e9i −0.109268 0.619691i
\(525\) 6.49844e8 + 9.71105e8i 0.195998 + 0.292893i
\(526\) 4.92557e9 1.79276e9i 1.47573 0.537121i
\(527\) −1.12893e9 + 4.10897e8i −0.335993 + 0.122291i
\(528\) 6.68497e9 + 9.98979e9i 1.97643 + 2.95351i
\(529\) −5.91218e8 3.35296e9i −0.173641 0.984768i
\(530\) 6.88395e9 1.19233e10i 2.00850 3.47883i
\(531\) 8.95838e8 + 2.82758e9i 0.259656 + 0.819566i
\(532\) −9.04201e8 1.56612e9i −0.260360 0.450957i
\(533\) 1.34500e8 1.12859e8i 0.0384748 0.0322842i
\(534\) −1.00964e10 + 4.45088e9i −2.86928 + 1.26489i
\(535\) −1.52242e9 + 8.63408e9i −0.429830 + 2.43769i
\(536\) 1.02351e10 + 8.58823e9i 2.87087 + 2.40895i
\(537\) 3.81581e9 + 1.10934e9i 1.06335 + 0.309140i
\(538\) −7.40053e9 2.69357e9i −2.04892 0.745746i
\(539\) −2.95300e9 −0.812276
\(540\) 1.55661e10 + 2.36277e9i 4.25403 + 0.645718i
\(541\) 5.66883e9 1.53923 0.769614 0.638510i \(-0.220449\pi\)
0.769614 + 0.638510i \(0.220449\pi\)
\(542\) −2.84301e9 1.03477e9i −0.766974 0.279156i
\(543\) 2.27494e9 2.18080e9i 0.609776 0.584543i
\(544\) −1.00369e10 8.42200e9i −2.67304 2.24295i
\(545\) 2.14237e8 1.21500e9i 0.0566900 0.321505i
\(546\) 2.32796e8 + 1.70445e8i 0.0612069 + 0.0448136i
\(547\) 2.96934e9 2.49157e9i 0.775719 0.650906i −0.166447 0.986050i \(-0.553230\pi\)
0.942167 + 0.335144i \(0.108785\pi\)
\(548\) −5.21349e9 9.03003e9i −1.35331 2.34400i
\(549\) −1.48730e9 + 3.60477e9i −0.383615 + 0.929767i
\(550\) 4.47498e9 7.75089e9i 1.14689 1.98647i
\(551\) 4.81698e8 + 2.73184e9i 0.122672 + 0.695705i
\(552\) 8.81948e7 5.84191e6i 0.0223181 0.00147832i
\(553\) −3.53874e8 + 1.28800e8i −0.0889837 + 0.0323874i
\(554\) 5.21164e9 1.89688e9i 1.30224 0.473976i
\(555\) −9.05046e8 + 1.83846e9i −0.224722 + 0.456487i
\(556\) 6.18605e8 + 3.50828e9i 0.152634 + 0.865631i
\(557\) 1.80572e8 3.12760e8i 0.0442749 0.0766864i −0.843039 0.537853i \(-0.819236\pi\)
0.887314 + 0.461167i \(0.152569\pi\)
\(558\) −3.06627e9 1.94747e9i −0.747120 0.474515i
\(559\) 2.91015e8 + 5.04053e8i 0.0704652 + 0.122049i
\(560\) 5.19791e9 4.36156e9i 1.25075 1.04950i
\(561\) −3.10926e8 + 2.85732e9i −0.0743510 + 0.683264i
\(562\) 1.61917e7 9.18280e7i 0.00384784 0.0218222i
\(563\) −3.74323e9 3.14095e9i −0.884031 0.741790i 0.0829727 0.996552i \(-0.473559\pi\)
−0.967004 + 0.254762i \(0.918003\pi\)
\(564\) 1.80032e9 + 7.33529e9i 0.422544 + 1.72163i
\(565\) 7.42816e9 + 2.70363e9i 1.73265 + 0.630634i
\(566\) 8.12877e9 1.88437
\(567\) −1.02013e8 1.12997e9i −0.0235026 0.260332i
\(568\) −6.99927e9 −1.60263
\(569\) −5.70298e9 2.07572e9i −1.29780 0.472362i −0.401523 0.915849i \(-0.631519\pi\)
−0.896281 + 0.443487i \(0.853741\pi\)
\(570\) 2.23586e9 + 9.10989e9i 0.505688 + 2.06040i
\(571\) 4.38826e7 + 3.68219e7i 0.00986430 + 0.00827713i 0.647706 0.761890i \(-0.275728\pi\)
−0.637842 + 0.770167i \(0.720173\pi\)
\(572\) 2.82973e8 1.60482e9i 0.0632206 0.358542i
\(573\) 2.70692e8 2.48759e9i 0.0601084 0.552379i
\(574\) −5.97893e8 + 5.01692e8i −0.131957 + 0.110725i
\(575\) −1.94843e7 3.37478e7i −0.00427412 0.00740300i
\(576\) 8.83589e8 2.09015e10i 0.192651 4.55721i
\(577\) −7.03962e8 + 1.21930e9i −0.152558 + 0.264238i −0.932167 0.362029i \(-0.882084\pi\)
0.779609 + 0.626266i \(0.215418\pi\)
\(578\) 5.95487e8 + 3.37717e9i 0.128270 + 0.727455i
\(579\) 1.02097e9 2.07395e9i 0.218595 0.444041i
\(580\) −1.89175e10 + 6.88542e9i −4.02594 + 1.46532i
\(581\) −2.29865e9 + 8.36641e8i −0.486247 + 0.176979i
\(582\) −2.81241e9 + 1.86290e8i −0.591355 + 0.0391706i
\(583\) 9.73057e8 + 5.51848e9i 0.203375 + 1.15340i
\(584\) −1.21893e10 + 2.11124e10i −2.53240 + 4.38625i
\(585\) −6.73013e8 8.74577e8i −0.138988 0.180615i
\(586\) −3.19461e9 5.53323e9i −0.655808 1.13589i
\(587\) −2.47488e9 + 2.07667e9i −0.505035 + 0.423775i −0.859378 0.511341i \(-0.829149\pi\)
0.354343 + 0.935115i \(0.384705\pi\)
\(588\) 1.04053e10 + 7.61840e9i 2.11073 + 1.54541i
\(589\) 2.77110e8 1.57157e9i 0.0558790 0.316906i
\(590\) −9.82434e9 8.24360e9i −1.96934 1.65247i
\(591\) 3.75281e9 3.59751e9i 0.747825 0.716880i
\(592\) 6.42010e9 + 2.33673e9i 1.27179 + 0.462894i
\(593\) 1.51977e9 0.299286 0.149643 0.988740i \(-0.452188\pi\)
0.149643 + 0.988740i \(0.452188\pi\)
\(594\) −7.42001e9 + 4.52368e9i −1.45262 + 0.885604i
\(595\) 1.62248e9 0.315769
\(596\) 1.59284e10 + 5.79745e9i 3.08183 + 1.12170i
\(597\) 2.78891e9 + 8.10799e8i 0.536444 + 0.155956i
\(598\) −7.37102e6 6.18502e6i −0.00140953 0.00118273i
\(599\) −2.15478e8 + 1.22203e9i −0.0409646 + 0.232322i −0.998415 0.0562752i \(-0.982078\pi\)
0.957451 + 0.288597i \(0.0931887\pi\)
\(600\) −2.30272e10 + 1.01512e10i −4.35223 + 1.91863i
\(601\) 4.80746e9 4.03394e9i 0.903348 0.757999i −0.0674941 0.997720i \(-0.521500\pi\)
0.970842 + 0.239721i \(0.0770559\pi\)
\(602\) −1.29365e9 2.24067e9i −0.241674 0.418591i
\(603\) −3.85828e9 + 4.22229e9i −0.716610 + 0.784220i
\(604\) 3.50396e9 6.06904e9i 0.647038 1.12070i
\(605\) −3.47691e8 1.97186e9i −0.0638337 0.362019i
\(606\) −6.34610e9 9.48339e9i −1.15838 1.73105i
\(607\) 1.45781e9 5.30601e8i 0.264571 0.0962958i −0.206329 0.978483i \(-0.566152\pi\)
0.470899 + 0.882187i \(0.343929\pi\)
\(608\) 1.63544e10 5.95251e9i 2.95101 1.07408i
\(609\) 8.06814e8 + 1.20567e9i 0.144748 + 0.216307i
\(610\) −2.92784e9 1.66046e10i −0.522268 2.96193i
\(611\) 2.64702e8 4.58478e8i 0.0469476 0.0813156i
\(612\) 8.46713e9 9.26597e9i 1.49316 1.63403i
\(613\) −3.57889e9 6.19882e9i −0.627534 1.08692i −0.988045 0.154165i \(-0.950731\pi\)
0.360511 0.932755i \(-0.382602\pi\)
\(614\) −1.08255e10 + 9.08367e9i −1.88738 + 1.58370i
\(615\) 2.73162e9 1.20420e9i 0.473540 0.208754i
\(616\) −8.09907e8 + 4.59321e9i −0.139605 + 0.791742i
\(617\) 8.65380e8 + 7.26140e8i 0.148323 + 0.124458i 0.713930 0.700217i \(-0.246914\pi\)
−0.565607 + 0.824675i \(0.691358\pi\)
\(618\) −2.03527e10 5.91700e9i −3.46867 1.00842i
\(619\) 6.34463e9 + 2.30926e9i 1.07520 + 0.391341i 0.818119 0.575049i \(-0.195017\pi\)
0.257081 + 0.966390i \(0.417239\pi\)
\(620\) 1.15813e10 1.95158
\(621\) 903979. + 3.78269e7i 0.000151474 + 0.00633841i
\(622\) 5.91761e9 0.986007
\(623\) −2.38221e9 8.67055e8i −0.394705 0.143661i
\(624\) −2.65609e9 + 2.54618e9i −0.437620 + 0.419510i
\(625\) −2.48020e9 2.08113e9i −0.406356 0.340973i
\(626\) 7.73873e8 4.38885e9i 0.126084 0.715057i
\(627\) −3.08042e9 2.25538e9i −0.499084 0.365413i
\(628\) −1.60571e10 + 1.34735e10i −2.58707 + 2.17081i
\(629\) 8.16826e8 + 1.41478e9i 0.130874 + 0.226680i
\(630\) 2.99175e9 + 3.88776e9i 0.476686 + 0.619452i
\(631\) −5.57349e9 + 9.65357e9i −0.883130 + 1.52963i −0.0352884 + 0.999377i \(0.511235\pi\)
−0.847842 + 0.530249i \(0.822098\pi\)
\(632\) −1.40837e9 7.98727e9i −0.221926 1.25860i
\(633\) −9.79004e9 + 6.48479e8i −1.53416 + 0.101621i
\(634\) −2.00903e10 + 7.31226e9i −3.13093 + 1.13957i
\(635\) 2.63324e9 9.58420e8i 0.408114 0.148541i
\(636\) 1.08083e10 2.19554e10i 1.66594 3.38409i
\(637\) −1.56963e8 8.90183e8i −0.0240608 0.136456i
\(638\) 5.55591e9 9.62312e9i 0.846999 1.46705i
\(639\) 1.26552e8 2.99362e9i 0.0191874 0.453882i
\(640\) 2.27356e10 + 3.93793e10i 3.42829 + 5.93797i
\(641\) 5.08974e8 4.27080e8i 0.0763296 0.0640481i −0.603825 0.797117i \(-0.706357\pi\)
0.680154 + 0.733069i \(0.261913\pi\)
\(642\) −2.28617e9 + 2.10092e10i −0.340985 + 3.13356i
\(643\) 3.34835e8 1.89894e9i 0.0496698 0.281691i −0.949849 0.312709i \(-0.898764\pi\)
0.999519 + 0.0310174i \(0.00987472\pi\)
\(644\) 2.41615e7 + 2.02739e7i 0.00356470 + 0.00299114i
\(645\) 2.35880e9 + 9.61080e9i 0.346124 + 1.41026i
\(646\) 7.02724e9 + 2.55771e9i 1.02558 + 0.373282i
\(647\) 3.77725e9 0.548291 0.274145 0.961688i \(-0.411605\pi\)
0.274145 + 0.961688i \(0.411605\pi\)
\(648\) 2.43480e10 + 2.06226e9i 3.51520 + 0.297735i
\(649\) 5.21975e9 0.749538
\(650\) 2.57437e9 + 9.36993e8i 0.367683 + 0.133826i
\(651\) −1.98926e8 8.10515e8i −0.0282592 0.115140i
\(652\) 2.11830e10 + 1.77746e10i 2.99309 + 2.51150i
\(653\) −1.79644e9 + 1.01881e10i −0.252473 + 1.43185i 0.550003 + 0.835163i \(0.314627\pi\)
−0.802476 + 0.596684i \(0.796484\pi\)
\(654\) 3.21712e8 2.95644e9i 0.0449723 0.413283i
\(655\) −1.89200e9 + 1.58757e9i −0.263073 + 0.220744i
\(656\) −4.97662e9 8.61975e9i −0.688289 1.19215i
\(657\) −8.80948e9 5.59513e9i −1.21191 0.769717i
\(658\) −1.17668e9 + 2.03807e9i −0.161016 + 0.278887i
\(659\) −1.59689e9 9.05639e9i −0.217358 1.23270i −0.876768 0.480914i \(-0.840305\pi\)
0.659410 0.751783i \(-0.270806\pi\)
\(660\) 1.22373e10 2.48581e10i 1.65684 3.36562i
\(661\) 5.51751e9 2.00821e9i 0.743084 0.270461i 0.0573915 0.998352i \(-0.481722\pi\)
0.685693 + 0.727891i \(0.259499\pi\)
\(662\) −9.97982e8 + 3.63236e8i −0.133696 + 0.0486615i
\(663\) −8.77865e8 + 5.81486e7i −0.116985 + 0.00774893i
\(664\) −9.14834e9 5.18828e10i −1.21270 6.87757i
\(665\) −1.07758e9 + 1.86642e9i −0.142093 + 0.246112i
\(666\) −1.88392e9 + 4.56605e9i −0.247117 + 0.598936i
\(667\) −2.41907e7 4.18995e7i −0.00315652 0.00546725i
\(668\) 1.81230e10 1.52070e10i 2.35240 1.97390i
\(669\) 6.01496e9 + 4.40395e9i 0.776678 + 0.568658i
\(670\) 4.29439e9 2.43547e10i 0.551620 3.12839i
\(671\) 5.25693e9 + 4.41109e9i 0.671743 + 0.563660i
\(672\) 6.57047e9 6.29858e9i 0.835227 0.800664i
\(673\) −6.86582e9 2.49895e9i −0.868239 0.316013i −0.130785 0.991411i \(-0.541750\pi\)
−0.737454 + 0.675397i \(0.763972\pi\)
\(674\) −1.03518e10 −1.30229
\(675\) −3.92538e9 1.00324e10i −0.491268 1.25557i
\(676\) −2.20533e10 −2.74575
\(677\) 1.07487e9 + 3.91219e8i 0.133136 + 0.0484574i 0.407729 0.913103i \(-0.366321\pi\)
−0.274593 + 0.961561i \(0.588543\pi\)
\(678\) 1.82969e10 + 5.31933e9i 2.25463 + 0.655471i
\(679\) −4.96075e8 4.16257e8i −0.0608140 0.0510290i
\(680\) −6.06782e9 + 3.44123e10i −0.740034 + 4.19694i
\(681\) 4.68436e8 2.06504e8i 0.0568375 0.0250561i
\(682\) −4.89685e9 + 4.10895e9i −0.591115 + 0.496004i
\(683\) −8.09160e9 1.40151e10i −0.971767 1.68315i −0.690216 0.723604i \(-0.742484\pi\)
−0.281551 0.959546i \(-0.590849\pi\)
\(684\) 5.03564e9 + 1.58942e10i 0.601669 + 1.89908i
\(685\) −6.21315e9 + 1.07615e10i −0.738576 + 1.27925i
\(686\) 1.44667e9 + 8.20446e9i 0.171094 + 0.970322i
\(687\) 6.56014e8 + 9.80324e8i 0.0771906 + 0.115351i
\(688\) 3.10047e10 1.12848e10i 3.62968 1.32110i
\(689\) −1.61182e9 + 5.86656e8i −0.187737 + 0.0683307i
\(690\) −9.09866e7 1.35967e8i −0.0105440 0.0157566i
\(691\) 1.81260e9 + 1.02798e10i 0.208991 + 1.18525i 0.891034 + 0.453937i \(0.149981\pi\)
−0.682043 + 0.731312i \(0.738908\pi\)
\(692\) −2.34341e10 + 4.05891e10i −2.68830 + 4.65627i
\(693\) −1.94989e9 4.29449e8i −0.222558 0.0490168i
\(694\) −1.70950e9 2.96094e9i −0.194138 0.336258i
\(695\) 3.25223e9 2.72894e9i 0.367480 0.308353i
\(696\) −2.85894e10 + 1.26033e10i −3.21420 + 1.41694i
\(697\) 4.13274e8 2.34379e9i 0.0462300 0.262183i
\(698\) −6.10024e9 5.11871e9i −0.678974 0.569727i
\(699\) 1.20216e10 + 3.49494e9i 1.33134 + 0.387052i
\(700\) −8.43852e9 3.07137e9i −0.929872 0.338446i
\(701\) 6.13549e9 0.672723 0.336361 0.941733i \(-0.390804\pi\)
0.336361 + 0.941733i \(0.390804\pi\)
\(702\) −1.75806e9 1.99631e9i −0.191803 0.217795i
\(703\) −2.17000e9 −0.235568
\(704\) −3.45952e10 1.25916e10i −3.73690 1.36012i
\(705\) 6.49787e9 6.22898e9i 0.698407 0.669507i
\(706\) 1.09700e10 + 9.20489e9i 1.17325 + 0.984470i
\(707\) 4.55253e8 2.58187e9i 0.0484490 0.274768i
\(708\) −1.83925e10 1.34663e10i −1.94771 1.42604i
\(709\) −5.89315e9 + 4.94494e9i −0.620992 + 0.521074i −0.898115 0.439760i \(-0.855063\pi\)
0.277123 + 0.960834i \(0.410619\pi\)
\(710\) 6.47766e9 + 1.12196e10i 0.679225 + 1.17645i
\(711\) 3.44165e9 4.57950e8i 0.359107 0.0477831i
\(712\) 2.72992e10 4.72835e10i 2.83445 4.90942i
\(713\) 4.83311e6 + 2.74099e7i 0.000499359 + 0.00283201i
\(714\) 3.90238e9 2.58488e8i 0.401223 0.0265765i
\(715\) −1.82492e9 + 6.64217e8i −0.186712 + 0.0679577i
\(716\) −2.86980e10 + 1.04452e10i −2.92183 + 1.06346i
\(717\) −4.78801e9 + 9.72609e9i −0.485107 + 0.985419i
\(718\) 5.37421e9 + 3.04787e10i 0.541850 + 3.07298i
\(719\) −1.72080e9 + 2.98051e9i −0.172655 + 0.299047i −0.939347 0.342968i \(-0.888568\pi\)
0.766692 + 0.642015i \(0.221901\pi\)
\(720\) −5.54505e10 + 2.89633e10i −5.53658 + 2.89191i
\(721\) −2.43487e9 4.21732e9i −0.241937 0.419047i
\(722\) 7.50784e9 6.29983e9i 0.742395 0.622943i
\(723\) 1.12714e9 1.03581e10i 0.110916 1.01929i
\(724\) −4.20564e9 + 2.38514e10i −0.411857 + 2.33576i
\(725\) 1.05522e10 + 8.85436e9i 1.02840 + 0.862927i
\(726\) −1.15042e9 4.68731e9i −0.111578 0.454617i
\(727\) −2.89938e8 1.05529e8i −0.0279857 0.0101859i 0.327989 0.944681i \(-0.393629\pi\)
−0.355975 + 0.934495i \(0.615851\pi\)
\(728\) −1.42767e9 −0.137141
\(729\) −1.32227e9 + 1.03764e10i −0.126407 + 0.991978i
\(730\) 4.51235e10 4.29312
\(731\) 7.41364e9 + 2.69835e9i 0.701974 + 0.255498i
\(732\) −7.14337e9 2.91053e10i −0.673154 2.74273i
\(733\) 2.73921e8 + 2.29847e8i 0.0256899 + 0.0215564i 0.655542 0.755159i \(-0.272440\pi\)
−0.629852 + 0.776715i \(0.716885\pi\)
\(734\) 3.37163e9 1.91215e10i 0.314705 1.78478i
\(735\) 1.66259e9 1.52787e10i 0.154447 1.41932i
\(736\) −2.32529e8 + 1.95115e8i −0.0214983 + 0.0180392i
\(737\) 5.03271e9 + 8.71691e9i 0.463090 + 0.802096i
\(738\) 6.37823e9 3.33153e9i 0.584121 0.305103i
\(739\) −5.27775e9 + 9.14134e9i −0.481054 + 0.833209i −0.999764 0.0217409i \(-0.993079\pi\)
0.518710 + 0.854950i \(0.326412\pi\)
\(740\) −2.73467e9 1.55091e10i −0.248081 1.40694i
\(741\) 5.16148e8 1.04847e9i 0.0466027 0.0946660i
\(742\) 7.16505e9 2.60786e9i 0.643881 0.234353i
\(743\) 3.48170e9 1.26723e9i 0.311408 0.113343i −0.181588 0.983375i \(-0.558124\pi\)
0.492996 + 0.870031i \(0.335902\pi\)
\(744\) 1.79348e10 1.18798e9i 1.59658 0.105755i
\(745\) −3.50783e9 1.98939e10i −0.310808 1.76268i
\(746\) 8.05932e9 1.39592e10i 0.710743 1.23104i
\(747\) 2.23559e10 2.97470e9i 1.96232 0.261109i
\(748\) −1.10445e10 1.91296e10i −0.964915 1.67128i
\(749\) −3.71950e9 + 3.12103e9i −0.323443 + 0.271401i
\(750\) 9.70783e9 + 7.10775e9i 0.840248 + 0.615202i
\(751\) −7.25305e8 + 4.11341e9i −0.0624857 + 0.354374i 0.937494 + 0.348002i \(0.113140\pi\)
−0.999980 + 0.00637264i \(0.997972\pi\)
\(752\) −2.29899e10 1.92908e10i −1.97140 1.65420i
\(753\) −1.38313e9 + 1.32590e9i −0.118054 + 0.113169i
\(754\) 3.19621e9 + 1.16332e9i 0.271541 + 0.0988328i
\(755\) −8.35166e9 −0.706250
\(756\) 5.76276e9 +