Properties

Label 27.8.e.a.4.8
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 4.8
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-9.04432 - 3.29186i) q^{2} +(-20.3312 + 42.1146i) q^{3} +(-27.0904 - 22.7315i) q^{4} +(82.6399 - 468.674i) q^{5} +(322.518 - 313.970i) q^{6} +(-558.283 + 468.455i) q^{7} +(786.170 + 1361.69i) q^{8} +(-1360.28 - 1712.48i) q^{9} +O(q^{10})\) \(q+(-9.04432 - 3.29186i) q^{2} +(-20.3312 + 42.1146i) q^{3} +(-27.0904 - 22.7315i) q^{4} +(82.6399 - 468.674i) q^{5} +(322.518 - 313.970i) q^{6} +(-558.283 + 468.455i) q^{7} +(786.170 + 1361.69i) q^{8} +(-1360.28 - 1712.48i) q^{9} +(-2290.23 + 3966.80i) q^{10} +(1148.19 + 6511.69i) q^{11} +(1508.11 - 678.741i) q^{12} +(7649.25 - 2784.10i) q^{13} +(6591.37 - 2399.06i) q^{14} +(18057.9 + 13009.1i) q^{15} +(-1841.85 - 10445.7i) q^{16} +(-9782.26 + 16943.4i) q^{17} +(6665.56 + 19966.1i) q^{18} +(8437.34 + 14613.9i) q^{19} +(-12892.4 + 10818.0i) q^{20} +(-8378.22 - 33036.1i) q^{21} +(11051.0 - 62673.4i) q^{22} +(49888.7 + 41861.6i) q^{23} +(-73330.7 + 5424.48i) q^{24} +(-139412. - 50742.0i) q^{25} -78347.1 q^{26} +(99776.8 - 22470.8i) q^{27} +25772.8 q^{28} +(170386. + 62015.3i) q^{29} +(-120497. - 177102. i) q^{30} +(-55988.0 - 46979.5i) q^{31} +(17221.0 - 97664.9i) q^{32} +(-297581. - 84035.2i) q^{33} +(144249. - 121039. i) q^{34} +(173416. + 300366. i) q^{35} +(-2076.83 + 77313.2i) q^{36} +(51934.0 - 89952.3i) q^{37} +(-28203.0 - 159947. i) q^{38} +(-38267.4 + 378749. i) q^{39} +(703156. - 255928. i) q^{40} +(-427049. + 155433. i) q^{41} +(-32975.1 + 326369. i) q^{42} +(40840.2 + 231616. i) q^{43} +(116916. - 202504. i) q^{44} +(-915010. + 496009. i) q^{45} +(-313407. - 542836. i) q^{46} +(2850.34 - 2391.72i) q^{47} +(477362. + 134804. i) q^{48} +(-50777.1 + 287971. i) q^{49} +(1.09385e6 + 917853. i) q^{50} +(-514678. - 756456. i) q^{51} +(-270508. - 98456.9i) q^{52} +1.85134e6 q^{53} +(-976384. - 125218. i) q^{54} +3.14675e6 q^{55} +(-1.07679e6 - 391921. i) q^{56} +(-787000. + 58216.7i) q^{57} +(-1.33688e6 - 1.12177e6i) q^{58} +(-390206. + 2.21297e6i) q^{59} +(-193478. - 762904. i) q^{60} +(-659537. + 553418. i) q^{61} +(351723. + 609202. i) q^{62} +(1.56164e6 + 318820. i) q^{63} +(-1.15609e6 + 2.00240e6i) q^{64} +(-672702. - 3.81508e6i) q^{65} +(2.41479e6 + 1.73964e6i) q^{66} +(-1.12767e6 + 410437. i) q^{67} +(650154. - 236637. i) q^{68} +(-2.77728e6 + 1.24995e6i) q^{69} +(-579668. - 3.28746e6i) q^{70} +(-1.06466e6 + 1.84404e6i) q^{71} +(1.26245e6 - 3.19858e6i) q^{72} +(-1.06403e6 - 1.84295e6i) q^{73} +(-765818. + 642597. i) q^{74} +(4.97141e6 - 4.83966e6i) q^{75} +(103626. - 587690. i) q^{76} +(-3.69144e6 - 3.09749e6i) q^{77} +(1.59289e6 - 3.29956e6i) q^{78} +(-4.45698e6 - 1.62221e6i) q^{79} -5.04782e6 q^{80} +(-1.08224e6 + 4.65892e6i) q^{81} +4.37403e6 q^{82} +(1.09716e6 + 399334. i) q^{83} +(-523993. + 1.08541e6i) q^{84} +(7.13251e6 + 5.98489e6i) q^{85} +(393077. - 2.22925e6i) q^{86} +(-6.07590e6 + 5.91488e6i) q^{87} +(-7.96421e6 + 6.68276e6i) q^{88} +(1.66060e6 + 2.87625e6i) q^{89} +(9.90844e6 - 1.47398e6i) q^{90} +(-2.96622e6 + 5.13764e6i) q^{91} +(-399926. - 2.26809e6i) q^{92} +(3.11683e6 - 1.40276e6i) q^{93} +(-33652.6 + 12248.5i) q^{94} +(7.54642e6 - 2.74667e6i) q^{95} +(3.76300e6 + 2.71090e6i) q^{96} +(1.26967e6 + 7.20063e6i) q^{97} +(1.40721e6 - 2.43735e6i) q^{98} +(9.58931e6 - 1.08240e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.04432 3.29186i −0.799412 0.290962i −0.0901693 0.995926i \(-0.528741\pi\)
−0.709243 + 0.704964i \(0.750963\pi\)
\(3\) −20.3312 + 42.1146i −0.434750 + 0.900551i
\(4\) −27.0904 22.7315i −0.211644 0.177590i
\(5\) 82.6399 468.674i 0.295661 1.67678i −0.368841 0.929493i \(-0.620245\pi\)
0.664502 0.747286i \(-0.268644\pi\)
\(6\) 322.518 313.970i 0.609571 0.593416i
\(7\) −558.283 + 468.455i −0.615192 + 0.516208i −0.896288 0.443472i \(-0.853747\pi\)
0.281096 + 0.959680i \(0.409302\pi\)
\(8\) 786.170 + 1361.69i 0.542877 + 0.940290i
\(9\) −1360.28 1712.48i −0.621985 0.783029i
\(10\) −2290.23 + 3966.80i −0.724235 + 1.25441i
\(11\) 1148.19 + 6511.69i 0.260099 + 1.47509i 0.782638 + 0.622477i \(0.213874\pi\)
−0.522539 + 0.852615i \(0.675015\pi\)
\(12\) 1508.11 678.741i 0.251941 0.113389i
\(13\) 7649.25 2784.10i 0.965644 0.351466i 0.189401 0.981900i \(-0.439345\pi\)
0.776243 + 0.630434i \(0.217123\pi\)
\(14\) 6591.37 2399.06i 0.641989 0.233665i
\(15\) 18057.9 + 13009.1i 1.38149 + 0.995237i
\(16\) −1841.85 10445.7i −0.112418 0.637552i
\(17\) −9782.26 + 16943.4i −0.482912 + 0.836428i −0.999807 0.0196205i \(-0.993754\pi\)
0.516896 + 0.856048i \(0.327088\pi\)
\(18\) 6665.56 + 19966.1i 0.269391 + 0.806937i
\(19\) 8437.34 + 14613.9i 0.282207 + 0.488797i 0.971928 0.235278i \(-0.0756001\pi\)
−0.689721 + 0.724075i \(0.742267\pi\)
\(20\) −12892.4 + 10818.0i −0.360354 + 0.302373i
\(21\) −8378.22 33036.1i −0.197417 0.778433i
\(22\) 11051.0 62673.4i 0.221270 1.25489i
\(23\) 49888.7 + 41861.6i 0.854978 + 0.717411i 0.960880 0.276965i \(-0.0893287\pi\)
−0.105902 + 0.994377i \(0.533773\pi\)
\(24\) −73330.7 + 5424.48i −1.08280 + 0.0800975i
\(25\) −139412. 50742.0i −1.78448 0.649497i
\(26\) −78347.1 −0.874211
\(27\) 99776.8 22470.8i 0.975566 0.219708i
\(28\) 25772.8 0.221875
\(29\) 170386. + 62015.3i 1.29730 + 0.472178i 0.896116 0.443820i \(-0.146377\pi\)
0.401183 + 0.915998i \(0.368599\pi\)
\(30\) −120497. 177102.i −0.814801 1.19757i
\(31\) −55988.0 46979.5i −0.337543 0.283232i 0.458222 0.888838i \(-0.348486\pi\)
−0.795765 + 0.605606i \(0.792931\pi\)
\(32\) 17221.0 97664.9i 0.0929036 0.526882i
\(33\) −297581. 84035.2i −1.44147 0.407064i
\(34\) 144249. 121039.i 0.629415 0.528142i
\(35\) 173416. + 300366.i 0.683678 + 1.18416i
\(36\) −2076.83 + 77313.2i −0.00741894 + 0.276182i
\(37\) 51934.0 89952.3i 0.168556 0.291948i −0.769356 0.638820i \(-0.779423\pi\)
0.937913 + 0.346872i \(0.112756\pi\)
\(38\) −28203.0 159947.i −0.0833783 0.472862i
\(39\) −38267.4 + 378749.i −0.103301 + 1.02241i
\(40\) 703156. 255928.i 1.73717 0.632277i
\(41\) −427049. + 155433.i −0.967686 + 0.352209i −0.777041 0.629450i \(-0.783280\pi\)
−0.190645 + 0.981659i \(0.561058\pi\)
\(42\) −32975.1 + 326369.i −0.0686773 + 0.679730i
\(43\) 40840.2 + 231616.i 0.0783336 + 0.444252i 0.998597 + 0.0529524i \(0.0168632\pi\)
−0.920263 + 0.391299i \(0.872026\pi\)
\(44\) 116916. 202504.i 0.206914 0.358385i
\(45\) −915010. + 496009.i −1.49686 + 0.811421i
\(46\) −313407. 542836.i −0.474740 0.822274i
\(47\) 2850.34 2391.72i 0.00400455 0.00336022i −0.640783 0.767722i \(-0.721390\pi\)
0.644788 + 0.764362i \(0.276946\pi\)
\(48\) 477362. + 134804.i 0.623022 + 0.175938i
\(49\) −50777.1 + 287971.i −0.0616569 + 0.349674i
\(50\) 1.09385e6 + 917853.i 1.23756 + 1.03843i
\(51\) −514678. 756456.i −0.543300 0.798524i
\(52\) −270508. 98456.9i −0.266789 0.0971034i
\(53\) 1.85134e6 1.70813 0.854063 0.520169i \(-0.174131\pi\)
0.854063 + 0.520169i \(0.174131\pi\)
\(54\) −976384. 125218.i −0.843806 0.108215i
\(55\) 3.14675e6 2.55031
\(56\) −1.07679e6 391921.i −0.819359 0.298222i
\(57\) −787000. + 58216.7i −0.562876 + 0.0416376i
\(58\) −1.33688e6 1.12177e6i −0.899690 0.754930i
\(59\) −390206. + 2.21297e6i −0.247350 + 1.40279i 0.567621 + 0.823290i \(0.307864\pi\)
−0.814971 + 0.579502i \(0.803247\pi\)
\(60\) −193478. 762904.i −0.115639 0.455974i
\(61\) −659537. + 553418.i −0.372036 + 0.312175i −0.809566 0.587028i \(-0.800298\pi\)
0.437530 + 0.899204i \(0.355853\pi\)
\(62\) 351723. + 609202.i 0.187426 + 0.324631i
\(63\) 1.56164e6 + 318820.i 0.786846 + 0.160640i
\(64\) −1.15609e6 + 2.00240e6i −0.551265 + 0.954819i
\(65\) −672702. 3.81508e6i −0.303827 1.72309i
\(66\) 2.41479e6 + 1.73964e6i 1.03389 + 0.744826i
\(67\) −1.12767e6 + 410437.i −0.458057 + 0.166719i −0.560735 0.827996i \(-0.689481\pi\)
0.102678 + 0.994715i \(0.467259\pi\)
\(68\) 650154. 236637.i 0.250747 0.0912643i
\(69\) −2.77728e6 + 1.24995e6i −1.01777 + 0.458057i
\(70\) −579668. 3.28746e6i −0.201993 1.14556i
\(71\) −1.06466e6 + 1.84404e6i −0.353025 + 0.611457i −0.986778 0.162079i \(-0.948180\pi\)
0.633753 + 0.773535i \(0.281513\pi\)
\(72\) 1.26245e6 3.19858e6i 0.398613 1.00993i
\(73\) −1.06403e6 1.84295e6i −0.320127 0.554476i 0.660387 0.750925i \(-0.270392\pi\)
−0.980514 + 0.196449i \(0.937059\pi\)
\(74\) −765818. + 642597.i −0.219692 + 0.184343i
\(75\) 4.97141e6 4.83966e6i 1.36071 1.32465i
\(76\) 103626. 587690.i 0.0270782 0.153568i
\(77\) −3.69144e6 3.09749e6i −0.921465 0.773201i
\(78\) 1.59289e6 3.29956e6i 0.380063 0.787272i
\(79\) −4.45698e6 1.62221e6i −1.01706 0.370179i −0.220919 0.975292i \(-0.570906\pi\)
−0.796139 + 0.605113i \(0.793128\pi\)
\(80\) −5.04782e6 −1.10227
\(81\) −1.08224e6 + 4.65892e6i −0.226268 + 0.974065i
\(82\) 4.37403e6 0.876059
\(83\) 1.09716e6 + 399334.i 0.210619 + 0.0766590i 0.445175 0.895444i \(-0.353141\pi\)
−0.234556 + 0.972103i \(0.575364\pi\)
\(84\) −523993. + 1.08541e6i −0.0964601 + 0.199810i
\(85\) 7.13251e6 + 5.98489e6i 1.25973 + 1.05704i
\(86\) 393077. 2.22925e6i 0.0666397 0.377932i
\(87\) −6.07590e6 + 5.91488e6i −0.989221 + 0.963005i
\(88\) −7.96421e6 + 6.68276e6i −1.24581 + 1.04536i
\(89\) 1.66060e6 + 2.87625e6i 0.249690 + 0.432476i 0.963440 0.267925i \(-0.0863380\pi\)
−0.713750 + 0.700401i \(0.753005\pi\)
\(90\) 9.90844e6 1.47398e6i 1.43270 0.213129i
\(91\) −2.96622e6 + 5.13764e6i −0.412628 + 0.714692i
\(92\) −399926. 2.26809e6i −0.0535454 0.303671i
\(93\) 3.11683e6 1.40276e6i 0.401812 0.180840i
\(94\) −33652.6 + 12248.5i −0.00417898 + 0.00152103i
\(95\) 7.54642e6 2.74667e6i 0.903042 0.328681i
\(96\) 3.76300e6 + 2.71090e6i 0.434095 + 0.312726i
\(97\) 1.26967e6 + 7.20063e6i 0.141250 + 0.801068i 0.970302 + 0.241897i \(0.0777696\pi\)
−0.829052 + 0.559172i \(0.811119\pi\)
\(98\) 1.40721e6 2.43735e6i 0.151031 0.261594i
\(99\) 9.58931e6 1.08240e7i 0.993263 1.12115i
\(100\) 2.62330e6 + 4.54368e6i 0.262330 + 0.454368i
\(101\) 7.42167e6 6.22752e6i 0.716766 0.601438i −0.209723 0.977761i \(-0.567256\pi\)
0.926488 + 0.376323i \(0.122812\pi\)
\(102\) 2.16476e6 + 8.53587e6i 0.201981 + 0.796430i
\(103\) −1.64642e6 + 9.33730e6i −0.148460 + 0.841959i 0.816063 + 0.577962i \(0.196152\pi\)
−0.964524 + 0.263997i \(0.914959\pi\)
\(104\) 9.80468e6 + 8.22710e6i 0.854706 + 0.717183i
\(105\) −1.61755e7 + 1.19655e6i −1.36363 + 0.100872i
\(106\) −1.67441e7 6.09435e6i −1.36550 0.497000i
\(107\) −1.78479e7 −1.40846 −0.704229 0.709973i \(-0.748707\pi\)
−0.704229 + 0.709973i \(0.748707\pi\)
\(108\) −3.21379e6 1.65934e6i −0.245490 0.126751i
\(109\) 1.87974e7 1.39029 0.695145 0.718870i \(-0.255340\pi\)
0.695145 + 0.718870i \(0.255340\pi\)
\(110\) −2.84602e7 1.03587e7i −2.03875 0.742043i
\(111\) 2.73242e6 + 4.01602e6i 0.189635 + 0.278718i
\(112\) 5.92159e6 + 4.96880e6i 0.398268 + 0.334186i
\(113\) 1.41145e6 8.00473e6i 0.0920219 0.521882i −0.903597 0.428383i \(-0.859084\pi\)
0.995619 0.0934995i \(-0.0298053\pi\)
\(114\) 7.30952e6 + 2.06417e6i 0.462085 + 0.130490i
\(115\) 2.37422e7 1.99221e7i 1.45572 1.22150i
\(116\) −3.20611e6 5.55315e6i −0.190711 0.330321i
\(117\) −1.51729e7 9.31206e6i −0.875824 0.537521i
\(118\) 1.08139e7 1.87303e7i 0.605894 1.04944i
\(119\) −2.47594e6 1.40417e7i −0.134687 0.763847i
\(120\) −3.51772e6 + 3.48165e7i −0.185835 + 1.83929i
\(121\) −2.27718e7 + 8.28826e6i −1.16855 + 0.425319i
\(122\) 7.78684e6 2.83418e6i 0.388241 0.141308i
\(123\) 2.13643e6 2.11452e7i 0.103519 1.02457i
\(124\) 448820. + 2.54539e6i 0.0211396 + 0.119889i
\(125\) −1.67125e7 + 2.89469e7i −0.765342 + 1.32561i
\(126\) −1.30745e7 8.02422e6i −0.582274 0.357360i
\(127\) −2.00632e7 3.47505e7i −0.869135 1.50539i −0.862882 0.505406i \(-0.831343\pi\)
−0.00625349 0.999980i \(-0.501991\pi\)
\(128\) 7.32349e6 6.14514e6i 0.308662 0.258998i
\(129\) −1.05848e7 2.98907e6i −0.434127 0.122595i
\(130\) −6.47459e6 + 3.67192e7i −0.258470 + 1.46586i
\(131\) 3.00639e7 + 2.52266e7i 1.16841 + 0.980414i 0.999986 0.00530038i \(-0.00168717\pi\)
0.168426 + 0.985714i \(0.446132\pi\)
\(132\) 6.15135e6 + 9.04103e6i 0.232788 + 0.342144i
\(133\) −1.15564e7 4.20617e6i −0.425932 0.155027i
\(134\) 1.15501e7 0.414685
\(135\) −2.28595e6 4.86198e7i −0.0799648 1.70077i
\(136\) −3.07621e7 −1.04865
\(137\) 2.14430e7 + 7.80461e6i 0.712465 + 0.259316i 0.672723 0.739894i \(-0.265124\pi\)
0.0397412 + 0.999210i \(0.487347\pi\)
\(138\) 2.92333e7 2.16247e6i 0.946893 0.0700444i
\(139\) 9.54259e6 + 8.00718e6i 0.301380 + 0.252888i 0.780918 0.624633i \(-0.214751\pi\)
−0.479538 + 0.877521i \(0.659196\pi\)
\(140\) 2.12986e6 1.20790e7i 0.0655999 0.372035i
\(141\) 42775.4 + 168667.i 0.00128507 + 0.00506716i
\(142\) 1.56994e7 1.31734e7i 0.460123 0.386089i
\(143\) 2.69120e7 + 4.66129e7i 0.769607 + 1.33300i
\(144\) −1.53826e7 + 1.73632e7i −0.429300 + 0.484574i
\(145\) 4.31456e7 7.47304e7i 1.17530 2.03568i
\(146\) 3.55666e6 + 2.01708e7i 0.0945817 + 0.536400i
\(147\) −1.10954e7 7.99327e6i −0.288094 0.207546i
\(148\) −3.45166e6 + 1.25630e6i −0.0875211 + 0.0318551i
\(149\) 4.71967e6 1.71782e6i 0.116885 0.0425427i −0.282915 0.959145i \(-0.591302\pi\)
0.399801 + 0.916602i \(0.369079\pi\)
\(150\) −6.08944e7 + 2.74062e7i −1.47319 + 0.663024i
\(151\) −2.05410e6 1.16494e7i −0.0485515 0.275349i 0.950861 0.309618i \(-0.100201\pi\)
−0.999413 + 0.0342683i \(0.989090\pi\)
\(152\) −1.32664e7 + 2.29780e7i −0.306407 + 0.530713i
\(153\) 4.23219e7 6.29580e6i 0.955311 0.142112i
\(154\) 2.31901e7 + 4.01664e7i 0.511658 + 0.886217i
\(155\) −2.66449e7 + 2.23577e7i −0.574716 + 0.482244i
\(156\) 9.64624e6 9.39059e6i 0.203433 0.198042i
\(157\) 1.60206e6 9.08572e6i 0.0330392 0.187374i −0.963822 0.266548i \(-0.914117\pi\)
0.996861 + 0.0791734i \(0.0252281\pi\)
\(158\) 3.49702e7 + 2.93435e7i 0.705340 + 0.591851i
\(159\) −3.76400e7 + 7.79684e7i −0.742608 + 1.53826i
\(160\) −4.43499e7 1.61420e7i −0.855997 0.311558i
\(161\) −4.74622e7 −0.896309
\(162\) 2.51246e7 3.85742e7i 0.464298 0.712844i
\(163\) 1.89734e7 0.343154 0.171577 0.985171i \(-0.445114\pi\)
0.171577 + 0.985171i \(0.445114\pi\)
\(164\) 1.51022e7 + 5.49674e6i 0.267353 + 0.0973087i
\(165\) −6.39772e7 + 1.32524e8i −1.10874 + 2.29668i
\(166\) −8.60853e6 7.22341e6i −0.146066 0.122564i
\(167\) 2.50178e6 1.41883e7i 0.0415663 0.235734i −0.956946 0.290267i \(-0.906256\pi\)
0.998512 + 0.0545330i \(0.0173670\pi\)
\(168\) 3.83981e7 3.73805e7i 0.624780 0.608223i
\(169\) 2.69165e6 2.25857e6i 0.0428959 0.0359939i
\(170\) −4.48073e7 7.76085e7i −0.699483 1.21154i
\(171\) 1.35489e7 3.43278e7i 0.207214 0.525001i
\(172\) 4.15861e6 7.20293e6i 0.0623159 0.107934i
\(173\) 1.33308e6 + 7.56029e6i 0.0195747 + 0.111014i 0.993030 0.117865i \(-0.0376051\pi\)
−0.973455 + 0.228879i \(0.926494\pi\)
\(174\) 7.44233e7 3.34950e7i 1.07099 0.482012i
\(175\) 1.01602e8 3.69801e7i 1.43307 0.521596i
\(176\) 6.59041e7 2.39871e7i 0.911209 0.331653i
\(177\) −8.52650e7 6.14258e7i −1.15575 0.832615i
\(178\) −5.55081e6 3.14802e7i −0.0737711 0.418377i
\(179\) −1.75405e7 + 3.03810e7i −0.228589 + 0.395929i −0.957390 0.288797i \(-0.906745\pi\)
0.728801 + 0.684726i \(0.240078\pi\)
\(180\) 3.60630e7 + 7.36251e6i 0.460902 + 0.0940962i
\(181\) 6.91653e7 + 1.19798e8i 0.866989 + 1.50167i 0.865059 + 0.501670i \(0.167281\pi\)
0.00192972 + 0.999998i \(0.499386\pi\)
\(182\) 4.37398e7 3.67021e7i 0.537808 0.451274i
\(183\) −9.89776e6 3.90278e7i −0.119387 0.470756i
\(184\) −1.77813e7 + 1.00843e8i −0.210427 + 1.19339i
\(185\) −3.78665e7 3.17737e7i −0.439697 0.368950i
\(186\) −3.28073e7 + 2.42685e6i −0.373831 + 0.0276533i
\(187\) −1.21562e8 4.42449e7i −1.35941 0.494786i
\(188\) −131584. −0.00144428
\(189\) −4.51771e7 + 5.92860e7i −0.486745 + 0.638757i
\(190\) −7.72938e7 −0.817537
\(191\) 2.71297e6 + 987439.i 0.0281726 + 0.0102540i 0.356068 0.934460i \(-0.384117\pi\)
−0.327895 + 0.944714i \(0.606339\pi\)
\(192\) −6.08257e7 8.93994e7i −0.620201 0.911549i
\(193\) 1.68294e7 + 1.41215e7i 0.168507 + 0.141394i 0.723141 0.690700i \(-0.242697\pi\)
−0.554634 + 0.832094i \(0.687142\pi\)
\(194\) 1.22202e7 6.93044e7i 0.120164 0.681482i
\(195\) 1.74348e8 + 4.92347e7i 1.68382 + 0.475500i
\(196\) 7.92161e6 6.64702e6i 0.0751479 0.0630566i
\(197\) 2.35158e7 + 4.07306e7i 0.219144 + 0.379568i 0.954546 0.298062i \(-0.0963403\pi\)
−0.735403 + 0.677630i \(0.763007\pi\)
\(198\) −1.22360e8 + 6.63289e7i −1.12024 + 0.607260i
\(199\) −1.64698e7 + 2.85265e7i −0.148150 + 0.256604i −0.930544 0.366180i \(-0.880665\pi\)
0.782393 + 0.622784i \(0.213999\pi\)
\(200\) −4.05072e7 2.29728e8i −0.358036 2.03053i
\(201\) 5.64146e6 5.58360e7i 0.0490010 0.484985i
\(202\) −8.76241e7 + 3.18926e7i −0.747987 + 0.272245i
\(203\) −1.24175e8 + 4.51959e7i −1.04183 + 0.379195i
\(204\) −3.25257e6 + 3.21921e7i −0.0268238 + 0.265487i
\(205\) 3.75562e7 + 2.12992e8i 0.304469 + 1.72673i
\(206\) 4.56278e7 7.90297e7i 0.363659 0.629876i
\(207\) 3.82461e6 1.42377e8i 0.0299703 1.11569i
\(208\) −4.31705e7 7.47735e7i −0.332633 0.576138i
\(209\) −8.54735e7 + 7.17208e7i −0.647619 + 0.543417i
\(210\) 1.50236e8 + 4.24257e7i 1.11945 + 0.316127i
\(211\) 3.80369e7 2.15718e8i 0.278751 1.58087i −0.448039 0.894014i \(-0.647877\pi\)
0.726790 0.686860i \(-0.241012\pi\)
\(212\) −5.01535e7 4.20838e7i −0.361514 0.303347i
\(213\) −5.60152e7 8.23291e7i −0.397171 0.583747i
\(214\) 1.61422e8 + 5.87528e7i 1.12594 + 0.409808i
\(215\) 1.11927e8 0.768072
\(216\) 1.09040e8 + 1.18199e8i 0.736201 + 0.798040i
\(217\) 5.32649e7 0.353860
\(218\) −1.70010e8 6.18785e7i −1.11141 0.404522i
\(219\) 9.92480e7 7.34166e6i 0.638509 0.0472324i
\(220\) −8.52466e7 7.15304e7i −0.539756 0.452909i
\(221\) −2.76549e7 + 1.56839e8i −0.172345 + 0.977419i
\(222\) −1.14927e7 4.53169e7i −0.0704997 0.277987i
\(223\) 1.30737e7 1.09701e7i 0.0789460 0.0662435i −0.602461 0.798149i \(-0.705813\pi\)
0.681407 + 0.731905i \(0.261369\pi\)
\(224\) 3.61374e7 + 6.25919e7i 0.214827 + 0.372092i
\(225\) 1.02745e8 + 3.07765e8i 0.601345 + 1.80128i
\(226\) −3.91161e7 + 6.77510e7i −0.225411 + 0.390424i
\(227\) 9.81035e6 + 5.56373e7i 0.0556665 + 0.315700i 0.999908 0.0135528i \(-0.00431412\pi\)
−0.944242 + 0.329253i \(0.893203\pi\)
\(228\) 2.26435e7 + 1.63126e7i 0.126524 + 0.0911489i
\(229\) −1.35844e8 + 4.94433e7i −0.747511 + 0.272072i −0.687558 0.726129i \(-0.741317\pi\)
−0.0599531 + 0.998201i \(0.519095\pi\)
\(230\) −2.80313e8 + 1.02026e8i −1.51913 + 0.552919i
\(231\) 2.05501e8 9.24880e7i 1.09691 0.493677i
\(232\) 4.95067e7 + 2.80766e8i 0.260289 + 1.47617i
\(233\) 9.53905e7 1.65221e8i 0.494037 0.855697i −0.505940 0.862569i \(-0.668854\pi\)
0.999976 + 0.00687208i \(0.00218747\pi\)
\(234\) 1.06574e8 + 1.34168e8i 0.543746 + 0.684532i
\(235\) −885384. 1.53353e6i −0.00445035 0.00770824i
\(236\) 6.08750e7 5.10802e7i 0.301472 0.252965i
\(237\) 1.58934e8 1.54722e8i 0.775531 0.754978i
\(238\) −2.38303e7 + 1.35148e8i −0.114580 + 0.649817i
\(239\) 2.14523e8 + 1.80006e8i 1.01644 + 0.852893i 0.989176 0.146735i \(-0.0468766\pi\)
0.0272625 + 0.999628i \(0.491321\pi\)
\(240\) 1.02628e8 2.12587e8i 0.479212 0.992652i
\(241\) −3.51690e8 1.28005e8i −1.61845 0.589069i −0.635368 0.772209i \(-0.719152\pi\)
−0.983087 + 0.183140i \(0.941374\pi\)
\(242\) 2.33239e8 1.05791
\(243\) −1.74206e8 1.40300e8i −0.778825 0.627241i
\(244\) 3.04472e7 0.134178
\(245\) 1.30768e8 + 4.75958e7i 0.568096 + 0.206770i
\(246\) −8.89294e7 + 1.84211e8i −0.380866 + 0.788936i
\(247\) 1.05226e8 + 8.82950e7i 0.444307 + 0.372818i
\(248\) 1.99553e7 1.13172e8i 0.0830762 0.471149i
\(249\) −3.91245e7 + 3.80876e7i −0.160602 + 0.156346i
\(250\) 2.46442e8 2.06789e8i 0.997527 0.837024i
\(251\) −1.27098e8 2.20141e8i −0.507320 0.878703i −0.999964 0.00847263i \(-0.997303\pi\)
0.492645 0.870231i \(-0.336030\pi\)
\(252\) −3.50583e7 4.41355e7i −0.138003 0.173735i
\(253\) −2.15308e8 + 3.72925e8i −0.835870 + 1.44777i
\(254\) 6.70642e7 + 3.80340e8i 0.256787 + 1.45631i
\(255\) −3.97064e8 + 1.78703e8i −1.49958 + 0.674902i
\(256\) 1.91645e8 6.97529e7i 0.713932 0.259850i
\(257\) −4.80108e8 + 1.74745e8i −1.76430 + 0.642154i −0.999996 0.00269854i \(-0.999141\pi\)
−0.764307 + 0.644852i \(0.776919\pi\)
\(258\) 8.58922e7 + 6.18777e7i 0.311376 + 0.224318i
\(259\) 1.31447e7 + 7.45475e7i 0.0470113 + 0.266615i
\(260\) −6.84989e7 + 1.18644e8i −0.241700 + 0.418637i
\(261\) −1.25572e8 3.76141e8i −0.437172 1.30951i
\(262\) −1.88865e8 3.27124e8i −0.648779 1.12372i
\(263\) 1.68693e8 1.41550e8i 0.571810 0.479805i −0.310436 0.950594i \(-0.600475\pi\)
0.882246 + 0.470789i \(0.156031\pi\)
\(264\) −1.19520e8 4.71278e8i −0.399785 1.57639i
\(265\) 1.52994e8 8.67674e8i 0.505027 2.86415i
\(266\) 9.06733e7 + 7.60839e7i 0.295389 + 0.247860i
\(267\) −1.54894e8 + 1.14580e7i −0.498019 + 0.0368399i
\(268\) 3.98788e7 + 1.45147e7i 0.126552 + 0.0460613i
\(269\) −8.65406e7 −0.271073 −0.135537 0.990772i \(-0.543276\pi\)
−0.135537 + 0.990772i \(0.543276\pi\)
\(270\) −1.39375e8 + 4.47258e8i −0.430934 + 1.38288i
\(271\) 2.18253e8 0.666144 0.333072 0.942901i \(-0.391915\pi\)
0.333072 + 0.942901i \(0.391915\pi\)
\(272\) 1.95002e8 + 7.09749e7i 0.587554 + 0.213852i
\(273\) −1.56063e8 2.29376e8i −0.464227 0.682304i
\(274\) −1.68245e8 1.41175e8i −0.494102 0.414601i
\(275\) 1.70345e8 9.66072e8i 0.493928 2.80121i
\(276\) 1.03651e8 + 2.92704e7i 0.296750 + 0.0838006i
\(277\) 1.09435e6 918271.i 0.00309370 0.00259592i −0.641239 0.767341i \(-0.721579\pi\)
0.644333 + 0.764745i \(0.277135\pi\)
\(278\) −5.99477e7 1.03832e8i −0.167346 0.289852i
\(279\) −4.29220e6 + 1.59784e8i −0.0118322 + 0.440472i
\(280\) −2.72669e8 + 4.72277e8i −0.742305 + 1.28571i
\(281\) 7.49485e7 + 4.25054e8i 0.201507 + 1.14280i 0.902842 + 0.429973i \(0.141477\pi\)
−0.701335 + 0.712832i \(0.747412\pi\)
\(282\) 168356. 1.66629e6i 0.000447050 0.00442466i
\(283\) 1.79575e8 6.53601e7i 0.470971 0.171419i −0.0956211 0.995418i \(-0.530484\pi\)
0.566592 + 0.823998i \(0.308261\pi\)
\(284\) 7.07598e7 2.57544e7i 0.183304 0.0667172i
\(285\) −3.77530e7 + 3.73658e8i −0.0966037 + 0.956130i
\(286\) −8.99571e7 5.10172e8i −0.227381 1.28954i
\(287\) 1.65601e8 2.86829e8i 0.413500 0.716203i
\(288\) −1.90675e8 + 1.03361e8i −0.470349 + 0.254967i
\(289\) 1.37842e7 + 2.38749e7i 0.0335922 + 0.0581833i
\(290\) −6.36225e8 + 5.33856e8i −1.53185 + 1.28538i
\(291\) −3.29066e8 9.29263e7i −0.782812 0.221061i
\(292\) −1.30681e7 + 7.41131e7i −0.0307166 + 0.174203i
\(293\) −1.89468e8 1.58983e8i −0.440048 0.369244i 0.395679 0.918389i \(-0.370509\pi\)
−0.835727 + 0.549145i \(0.814954\pi\)
\(294\) 7.40379e7 + 1.08818e8i 0.169918 + 0.249739i
\(295\) 1.00491e9 + 3.65759e8i 2.27904 + 0.829503i
\(296\) 1.63316e8 0.366022
\(297\) 2.60886e8 + 6.23915e8i 0.577833 + 1.38190i
\(298\) −4.83410e7 −0.105818
\(299\) 4.98158e8 + 1.81315e8i 1.07775 + 0.392269i
\(300\) −2.44690e8 + 1.81004e7i −0.523229 + 0.0387048i
\(301\) −1.31302e8 1.10175e8i −0.277516 0.232864i
\(302\) −1.97702e7 + 1.12123e8i −0.0413036 + 0.234244i
\(303\) 1.11378e8 + 4.39174e8i 0.230012 + 0.906959i
\(304\) 1.37111e8 1.15050e8i 0.279909 0.234871i
\(305\) 2.04868e8 + 3.54842e8i 0.413452 + 0.716120i
\(306\) −4.03497e8 8.23766e7i −0.805037 0.164354i
\(307\) 3.70781e8 6.42211e8i 0.731362 1.26676i −0.224939 0.974373i \(-0.572218\pi\)
0.956301 0.292384i \(-0.0944485\pi\)
\(308\) 2.95920e7 + 1.67824e8i 0.0577094 + 0.327286i
\(309\) −3.59763e8 2.59177e8i −0.693684 0.499737i
\(310\) 3.14584e8 1.14499e8i 0.599750 0.218291i
\(311\) −4.12998e8 + 1.50319e8i −0.778551 + 0.283369i −0.700568 0.713585i \(-0.747070\pi\)
−0.0779827 + 0.996955i \(0.524848\pi\)
\(312\) −5.45822e8 + 2.45653e8i −1.01744 + 0.457911i
\(313\) 3.61761e7 + 2.05165e8i 0.0666832 + 0.378179i 0.999826 + 0.0186725i \(0.00594399\pi\)
−0.933142 + 0.359507i \(0.882945\pi\)
\(314\) −4.43984e7 + 7.69003e7i −0.0809308 + 0.140176i
\(315\) 2.78476e8 7.05554e8i 0.501997 1.27187i
\(316\) 8.38660e7 + 1.45260e8i 0.149514 + 0.258965i
\(317\) 7.80686e8 6.55073e8i 1.37648 1.15500i 0.405982 0.913881i \(-0.366930\pi\)
0.970495 0.241121i \(-0.0775149\pi\)
\(318\) 5.97089e8 5.81265e8i 1.04122 1.01363i
\(319\) −2.08190e8 + 1.18070e9i −0.359081 + 2.03645i
\(320\) 8.42934e8 + 7.07306e8i 1.43803 + 1.20665i
\(321\) 3.62870e8 7.51658e8i 0.612327 1.26839i
\(322\) 4.29264e8 + 1.56239e8i 0.716520 + 0.260792i
\(323\) −3.30145e8 −0.545125
\(324\) 1.35223e8 1.01611e8i 0.220873 0.165972i
\(325\) −1.20767e9 −1.95145
\(326\) −1.71601e8 6.24578e7i −0.274321 0.0998448i
\(327\) −3.82175e8 + 7.91646e8i −0.604428 + 1.25203i
\(328\) −5.47384e8 4.59310e8i −0.856512 0.718699i
\(329\) −470883. + 2.67051e6i −0.000728999 + 0.00413436i
\(330\) 1.01488e9 9.87985e8i 1.55459 1.51339i
\(331\) −2.49086e8 + 2.09008e8i −0.377530 + 0.316785i −0.811732 0.584030i \(-0.801475\pi\)
0.434202 + 0.900816i \(0.357030\pi\)
\(332\) −2.06451e7 3.57583e7i −0.0309623 0.0536283i
\(333\) −2.24687e8 + 3.34243e7i −0.333444 + 0.0496030i
\(334\) −6.93327e7 + 1.20088e8i −0.101818 + 0.176354i
\(335\) 9.91710e7 + 5.62427e8i 0.144121 + 0.817352i
\(336\) −3.29652e8 + 1.48364e8i −0.474099 + 0.213373i
\(337\) −6.64011e8 + 2.41680e8i −0.945085 + 0.343983i −0.768172 0.640244i \(-0.778833\pi\)
−0.176913 + 0.984227i \(0.556611\pi\)
\(338\) −3.17791e7 + 1.15666e7i −0.0447644 + 0.0162929i
\(339\) 3.08420e8 + 2.22189e8i 0.429975 + 0.309759i
\(340\) −5.71768e7 3.24266e8i −0.0788940 0.447430i
\(341\) 2.41631e8 4.18518e8i 0.329999 0.571575i
\(342\) −2.35543e8 + 2.65871e8i −0.318404 + 0.359401i
\(343\) −4.06647e8 7.04333e8i −0.544112 0.942429i
\(344\) −2.83281e8 + 2.37701e8i −0.375200 + 0.314830i
\(345\) 3.56303e8 + 1.40494e9i 0.467146 + 1.84200i
\(346\) 1.28306e7 7.27660e7i 0.0166525 0.0944413i
\(347\) −6.25865e8 5.25163e8i −0.804133 0.674747i 0.145067 0.989422i \(-0.453660\pi\)
−0.949200 + 0.314674i \(0.898105\pi\)
\(348\) 2.99053e8 2.21218e7i 0.380383 0.0281380i
\(349\) −3.60098e8 1.31065e8i −0.453452 0.165043i 0.105190 0.994452i \(-0.466455\pi\)
−0.558642 + 0.829409i \(0.688677\pi\)
\(350\) −1.04065e9 −1.29738
\(351\) 7.00657e8 4.49674e8i 0.864829 0.555038i
\(352\) 6.55737e8 0.801364
\(353\) −4.10360e8 1.49359e8i −0.496539 0.180725i 0.0815977 0.996665i \(-0.473998\pi\)
−0.578137 + 0.815940i \(0.696220\pi\)
\(354\) 5.68958e8 + 8.36235e8i 0.681662 + 1.00188i
\(355\) 7.76270e8 + 6.51367e8i 0.920902 + 0.772728i
\(356\) 2.03952e7 1.15667e8i 0.0239581 0.135873i
\(357\) 6.41701e8 + 1.81213e8i 0.746438 + 0.210790i
\(358\) 2.58652e8 2.17035e8i 0.297937 0.249999i
\(359\) −1.12794e8 1.95365e8i −0.128664 0.222852i 0.794495 0.607270i \(-0.207735\pi\)
−0.923159 + 0.384418i \(0.874402\pi\)
\(360\) −1.39476e9 8.56009e8i −1.57558 0.966985i
\(361\) 3.04558e8 5.27511e8i 0.340718 0.590141i
\(362\) −2.31195e8 1.31117e9i −0.256152 1.45271i
\(363\) 1.13922e8 1.12754e9i 0.125007 1.23725i
\(364\) 1.97143e8 7.17540e7i 0.214252 0.0779814i
\(365\) −9.51672e8 + 3.46380e8i −1.02438 + 0.372845i
\(366\) −3.89557e7 + 3.85562e8i −0.0415325 + 0.411065i
\(367\) 1.28246e8 + 7.27318e8i 0.135429 + 0.768057i 0.974560 + 0.224127i \(0.0719530\pi\)
−0.839131 + 0.543930i \(0.816936\pi\)
\(368\) 3.45384e8 5.98223e8i 0.361273 0.625743i
\(369\) 8.47084e8 + 5.19882e8i 0.877676 + 0.538657i
\(370\) 2.37882e8 + 4.12023e8i 0.244149 + 0.422878i
\(371\) −1.03357e9 + 8.67268e8i −1.05083 + 0.881748i
\(372\) −1.16323e8 3.28490e7i −0.117156 0.0330843i
\(373\) 1.54415e8 8.75729e8i 0.154066 0.873753i −0.805568 0.592503i \(-0.798140\pi\)
0.959634 0.281250i \(-0.0907491\pi\)
\(374\) 9.53795e8 + 8.00329e8i 0.942768 + 0.791076i
\(375\) −8.79300e8 1.29236e9i −0.861049 1.26554i
\(376\) 5.49762e6 + 2.00097e6i 0.00533356 + 0.00194126i
\(377\) 1.47598e9 1.41868
\(378\) 6.03757e8 3.87485e8i 0.574964 0.369006i
\(379\) −1.45027e9 −1.36839 −0.684195 0.729299i \(-0.739846\pi\)
−0.684195 + 0.729299i \(0.739846\pi\)
\(380\) −2.66871e8 9.71333e7i −0.249494 0.0908083i
\(381\) 1.87141e9 1.38434e8i 1.73353 0.128235i
\(382\) −2.12864e7 1.78614e7i −0.0195380 0.0163943i
\(383\) 3.77450e8 2.14063e9i 0.343292 1.94691i 0.0225295 0.999746i \(-0.492828\pi\)
0.320763 0.947160i \(-0.396061\pi\)
\(384\) 1.09905e8 + 4.33364e8i 0.0990505 + 0.390566i
\(385\) −1.75677e9 + 1.47411e9i −1.56893 + 1.31649i
\(386\) −1.05724e8 1.83120e8i −0.0935662 0.162061i
\(387\) 3.41085e8 3.85001e8i 0.299140 0.337655i
\(388\) 1.29286e8 2.23929e8i 0.112367 0.194626i
\(389\) −2.97047e8 1.68463e9i −0.255859 1.45105i −0.793858 0.608104i \(-0.791931\pi\)
0.537998 0.842946i \(-0.319181\pi\)
\(390\) −1.41478e9 1.01922e9i −1.20771 0.870047i
\(391\) −1.19730e9 + 4.35782e8i −1.01294 + 0.368681i
\(392\) −4.32046e8 + 1.57252e8i −0.362267 + 0.131854i
\(393\) −1.67365e9 + 7.53242e8i −1.39088 + 0.625980i
\(394\) −7.86051e7 4.45792e8i −0.0647461 0.367194i
\(395\) −1.12861e9 + 1.95481e9i −0.921413 + 1.59593i
\(396\) −5.05824e8 + 7.52463e7i −0.409323 + 0.0608908i
\(397\) 1.15338e9 + 1.99771e9i 0.925137 + 1.60238i 0.791341 + 0.611375i \(0.209383\pi\)
0.133796 + 0.991009i \(0.457283\pi\)
\(398\) 2.42864e8 2.03787e8i 0.193095 0.162026i
\(399\) 4.12097e8 4.01175e8i 0.324784 0.316176i
\(400\) −2.73256e8 + 1.54971e9i −0.213481 + 1.21071i
\(401\) 1.77414e9 + 1.48868e9i 1.37399 + 1.15291i 0.971377 + 0.237542i \(0.0763418\pi\)
0.402611 + 0.915371i \(0.368103\pi\)
\(402\) −2.34827e8 + 4.86427e8i −0.180284 + 0.373445i
\(403\) −5.59062e8 2.03482e8i −0.425493 0.154867i
\(404\) −3.42617e8 −0.258508
\(405\) 2.09408e9 + 8.92228e8i 1.56639 + 0.667396i
\(406\) 1.27185e9 0.943183
\(407\) 6.45371e8 + 2.34896e8i 0.474492 + 0.172701i
\(408\) 6.25431e8 1.29553e9i 0.455899 0.944360i
\(409\) 1.25352e9 + 1.05183e9i 0.905940 + 0.760174i 0.971342 0.237685i \(-0.0763887\pi\)
−0.0654025 + 0.997859i \(0.520833\pi\)
\(410\) 3.61469e8 2.04999e9i 0.259017 1.46896i
\(411\) −7.64650e8 + 7.44386e8i −0.543271 + 0.528873i
\(412\) 2.56853e8 2.15526e8i 0.180944 0.151830i
\(413\) −8.18831e8 1.41826e9i −0.571964 0.990671i
\(414\) −5.03277e8 + 1.27511e9i −0.348583 + 0.883177i
\(415\) 2.77827e8 4.81210e8i 0.190812 0.330496i
\(416\) −1.40181e8 7.95008e8i −0.0954693 0.541433i
\(417\) −5.31232e8 + 2.39087e8i −0.358763 + 0.161465i
\(418\) 1.00914e9 3.67299e8i 0.675828 0.245981i
\(419\) −1.01760e9 + 3.70375e8i −0.675814 + 0.245976i −0.657049 0.753848i \(-0.728196\pi\)
−0.0187648 + 0.999824i \(0.505973\pi\)
\(420\) 4.65401e8 + 3.35280e8i 0.306517 + 0.220818i
\(421\) −4.49541e8 2.54948e9i −0.293618 1.66519i −0.672768 0.739854i \(-0.734895\pi\)
0.379150 0.925335i \(-0.376216\pi\)
\(422\) −1.05413e9 + 1.82581e9i −0.682811 + 1.18266i
\(423\) −7.97304e6 1.62775e6i −0.00512192 0.00104567i
\(424\) 1.45547e9 + 2.52094e9i 0.927303 + 1.60614i
\(425\) 2.22351e9 1.86575e9i 1.40500 1.17894i
\(426\) 2.35603e8 + 9.29005e8i 0.147655 + 0.582216i
\(427\) 1.08957e8 6.17927e8i 0.0677264 0.384096i
\(428\) 4.83507e8 + 4.05710e8i 0.298091 + 0.250128i
\(429\) −2.51024e9 + 1.85689e8i −1.53502 + 0.113550i
\(430\) −1.01231e9 3.68450e8i −0.614006 0.223480i
\(431\) −2.00252e9 −1.20478 −0.602388 0.798203i \(-0.705784\pi\)
−0.602388 + 0.798203i \(0.705784\pi\)
\(432\) −4.18497e8 1.00085e9i −0.249746 0.597275i
\(433\) 1.99267e9 1.17958 0.589791 0.807556i \(-0.299210\pi\)
0.589791 + 0.807556i \(0.299210\pi\)
\(434\) −4.81745e8 1.75341e8i −0.282880 0.102960i
\(435\) 2.27004e9 + 3.33642e9i 1.32227 + 1.94343i
\(436\) −5.09229e8 4.27294e8i −0.294246 0.246902i
\(437\) −1.90833e8 + 1.08227e9i −0.109388 + 0.620369i
\(438\) −9.21798e8 2.60310e8i −0.524175 0.148024i
\(439\) −8.09326e8 + 6.79105e8i −0.456560 + 0.383099i −0.841863 0.539691i \(-0.818541\pi\)
0.385304 + 0.922790i \(0.374097\pi\)
\(440\) 2.47388e9 + 4.28488e9i 1.38450 + 2.39803i
\(441\) 5.62218e8 3.04767e8i 0.312154 0.169213i
\(442\) 7.66412e8 1.32746e9i 0.422167 0.731214i
\(443\) 2.92936e8 + 1.66132e9i 0.160088 + 0.907906i 0.953985 + 0.299853i \(0.0969378\pi\)
−0.793897 + 0.608052i \(0.791951\pi\)
\(444\) 1.72679e7 1.70908e8i 0.00936264 0.0926662i
\(445\) 1.48526e9 5.40589e8i 0.798990 0.290808i
\(446\) −1.54354e8 + 5.61804e7i −0.0823847 + 0.0299856i
\(447\) −2.36114e7 + 2.33692e8i −0.0125039 + 0.123757i
\(448\) −2.92611e8 1.65948e9i −0.153751 0.871964i
\(449\) 1.17286e9 2.03145e9i 0.611482 1.05912i −0.379509 0.925188i \(-0.623907\pi\)
0.990991 0.133930i \(-0.0427596\pi\)
\(450\) 8.38581e7 3.12175e9i 0.0433812 1.61493i
\(451\) −1.50246e9 2.60234e9i −0.771234 1.33582i
\(452\) −2.20197e8 + 1.84767e8i −0.112157 + 0.0941109i
\(453\) 5.32372e8 + 1.50339e8i 0.269074 + 0.0759849i
\(454\) 9.44223e7 5.35495e8i 0.0473564 0.268572i
\(455\) 2.16275e9 + 1.81476e9i 1.07638 + 0.903192i
\(456\) −6.97989e8 1.02588e9i −0.344724 0.506663i
\(457\) 2.27304e8 + 8.27320e7i 0.111404 + 0.0405478i 0.397121 0.917766i \(-0.370009\pi\)
−0.285717 + 0.958314i \(0.592232\pi\)
\(458\) 1.39138e9 0.676732
\(459\) −5.95311e8 + 1.91037e9i −0.287342 + 0.922090i
\(460\) −1.09605e9 −0.525021
\(461\) −3.22009e9 1.17202e9i −1.53079 0.557162i −0.566975 0.823735i \(-0.691886\pi\)
−0.963815 + 0.266573i \(0.914108\pi\)
\(462\) −2.16308e9 + 1.60009e8i −1.02053 + 0.0754914i
\(463\) 5.76008e8 + 4.83328e8i 0.269709 + 0.226312i 0.767604 0.640925i \(-0.221449\pi\)
−0.497895 + 0.867237i \(0.665893\pi\)
\(464\) 3.33966e8 1.89401e9i 0.155199 0.880177i
\(465\) −3.99864e8 1.57670e9i −0.184428 0.727217i
\(466\) −1.40663e9 + 1.18030e9i −0.643914 + 0.540308i
\(467\) −1.14815e8 1.98866e8i −0.0521663 0.0903548i 0.838763 0.544497i \(-0.183279\pi\)
−0.890929 + 0.454142i \(0.849946\pi\)
\(468\) 1.99361e8 + 5.97170e8i 0.0899043 + 0.269301i
\(469\) 4.37286e8 7.57401e8i 0.195731 0.339017i
\(470\) 2.95952e6 + 1.67843e7i 0.00131486 + 0.00745694i
\(471\) 3.50070e8 + 2.52194e8i 0.154377 + 0.111214i
\(472\) −3.32014e9 + 1.20843e9i −1.45331 + 0.528963i
\(473\) −1.46132e9 + 5.31877e8i −0.634938 + 0.231098i
\(474\) −1.94678e9 + 8.76168e8i −0.839639 + 0.377888i
\(475\) −4.34732e8 2.46549e9i −0.186120 1.05554i
\(476\) −2.52116e8 + 4.36678e8i −0.107146 + 0.185582i
\(477\) −2.51834e9 3.17039e9i −1.06243 1.33751i
\(478\) −1.34766e9 2.33421e9i −0.564393 0.977558i
\(479\) −1.76057e9 + 1.47729e9i −0.731945 + 0.614174i −0.930661 0.365883i \(-0.880767\pi\)
0.198716 + 0.980057i \(0.436323\pi\)
\(480\) 1.58150e9 1.53959e9i 0.652718 0.635420i
\(481\) 1.46820e8 8.32657e8i 0.0601557 0.341160i
\(482\) 2.75942e9 + 2.31543e9i 1.12242 + 0.941818i
\(483\) 9.64966e8 1.99885e9i 0.389670 0.807172i
\(484\) 8.05303e8 + 2.93106e8i 0.322850 + 0.117508i
\(485\) 3.47967e9 1.38498
\(486\) 1.11372e9 + 1.84237e9i 0.440099 + 0.728033i
\(487\) 2.56009e9 1.00439 0.502196 0.864754i \(-0.332526\pi\)
0.502196 + 0.864754i \(0.332526\pi\)
\(488\) −1.27209e9 4.63003e8i −0.495505 0.180349i
\(489\) −3.85753e8 + 7.99058e8i −0.149186 + 0.309028i
\(490\) −1.02603e9 8.60944e8i −0.393981 0.330589i
\(491\) −8.32972e8 + 4.72402e9i −0.317574 + 1.80105i 0.239834 + 0.970814i \(0.422907\pi\)
−0.557408 + 0.830238i \(0.688204\pi\)
\(492\) −5.38539e8 + 5.24266e8i −0.203863 + 0.198461i
\(493\) −2.71750e9 + 2.28026e9i −1.02142 + 0.857077i
\(494\) −6.61041e8 1.14496e9i −0.246708 0.427312i
\(495\) −4.28046e9 5.38875e9i −1.58625 1.99696i
\(496\) −3.87610e8 + 6.71361e8i −0.142629 + 0.247042i
\(497\) −2.69469e8 1.52824e9i −0.0984605 0.558397i
\(498\) 4.79233e8 2.15684e8i 0.173878 0.0782555i
\(499\) 2.27849e9 8.29304e8i 0.820911 0.298787i 0.102788 0.994703i \(-0.467224\pi\)
0.718123 + 0.695916i \(0.245002\pi\)
\(500\) 1.11075e9 4.04281e8i 0.397395 0.144640i
\(501\) 5.46670e8 + 3.93827e8i 0.194220 + 0.139918i
\(502\) 4.24844e8 + 2.40941e9i 0.149888 + 0.850057i
\(503\) 2.83625e8 4.91252e8i 0.0993701 0.172114i −0.812054 0.583582i \(-0.801651\pi\)
0.911424 + 0.411468i \(0.134984\pi\)
\(504\) 7.93584e8 + 2.37711e9i 0.276113 + 0.827071i
\(505\) −2.30535e9 3.99299e9i −0.796558 1.37968i
\(506\) 3.17493e9 2.66408e9i 1.08945 0.914157i
\(507\) 4.03940e7 + 1.59277e8i 0.0137654 + 0.0542783i
\(508\) −2.46412e8 + 1.39747e9i −0.0833948 + 0.472955i
\(509\) −1.36830e9 1.14814e9i −0.459905 0.385906i 0.383191 0.923669i \(-0.374825\pi\)
−0.843096 + 0.537763i \(0.819270\pi\)
\(510\) 4.17944e9 3.09165e8i 1.39515 0.103204i
\(511\) 1.45736e9 + 5.30437e8i 0.483164 + 0.175857i
\(512\) −3.18661e9 −1.04926
\(513\) 1.17024e9 + 1.26853e9i 0.382704 + 0.414850i
\(514\) 4.91749e9 1.59725
\(515\) 4.24009e9 + 1.54327e9i 1.36789 + 0.497870i
\(516\) 2.18799e8 + 3.21583e8i 0.0701086 + 0.103043i
\(517\) 1.88468e7 + 1.58144e7i 0.00599821 + 0.00503310i
\(518\) 1.26515e8 7.17502e8i 0.0399933 0.226813i
\(519\) −3.45502e8 9.75677e7i −0.108484 0.0306352i
\(520\) 4.66608e9 3.91531e9i 1.45526 1.22111i
\(521\) 3.03435e8 + 5.25565e8i 0.0940013 + 0.162815i 0.909191 0.416379i \(-0.136701\pi\)
−0.815190 + 0.579194i \(0.803368\pi\)
\(522\) −1.02489e8 + 3.81530e9i −0.0315377 + 1.17404i
\(523\) −1.95781e8 + 3.39103e8i −0.0598432 + 0.103651i −0.894395 0.447278i \(-0.852393\pi\)
0.834552 + 0.550930i \(0.185727\pi\)
\(524\) −2.41003e8 1.36680e9i −0.0731751 0.414997i
\(525\) −5.08290e8 + 5.03077e9i −0.153304 + 1.51732i
\(526\) −1.99167e9 + 7.24910e8i −0.596717 + 0.217187i
\(527\) 1.34368e9 4.89060e8i 0.399907 0.145554i
\(528\) −3.29703e8 + 3.26321e9i −0.0974773 + 0.964776i
\(529\) 1.45248e8 + 8.23742e8i 0.0426594 + 0.241934i
\(530\) −4.23999e9 + 7.34388e9i −1.23708 + 2.14269i
\(531\) 4.32047e9 2.34204e9i 1.25228 0.678834i
\(532\) 2.17454e8 + 3.76641e8i 0.0626147 + 0.108452i
\(533\) −2.83386e9 + 2.37789e9i −0.810651 + 0.680217i
\(534\) 1.43863e9 + 4.06261e8i 0.408841 + 0.115454i
\(535\) −1.47495e9 + 8.36485e9i −0.416427 + 2.36167i
\(536\) −1.44542e9 1.21286e9i −0.405433 0.340198i
\(537\) −9.22865e8 1.35639e9i −0.257175 0.377986i
\(538\) 7.82701e8 + 2.84880e8i 0.216699 + 0.0788721i
\(539\) −1.93348e9 −0.531838
\(540\) −1.04328e9 + 1.36909e9i −0.285115 + 0.374158i
\(541\) −2.13678e9 −0.580188 −0.290094 0.956998i \(-0.593687\pi\)
−0.290094 + 0.956998i \(0.593687\pi\)
\(542\) −1.97395e9 7.18460e8i −0.532524 0.193823i
\(543\) −6.45146e9 + 4.77233e8i −1.72925 + 0.127918i
\(544\) 1.48631e9 + 1.24716e9i 0.395835 + 0.332145i
\(545\) 1.55342e9 8.80986e9i 0.411055 2.33121i
\(546\) 6.56409e8 + 2.58828e9i 0.172584 + 0.680515i
\(547\) 4.25584e9 3.57108e9i 1.11181 0.932918i 0.113646 0.993521i \(-0.463747\pi\)
0.998162 + 0.0606035i \(0.0193025\pi\)
\(548\) −4.03488e8 6.98862e8i −0.104737 0.181409i
\(549\) 1.84488e9 + 3.76643e8i 0.475843 + 0.0971465i
\(550\) −4.72082e9 + 8.17671e9i −1.20990 + 2.09560i
\(551\) 5.31316e8 + 3.01324e9i 0.135308 + 0.767368i
\(552\) −3.88545e9 2.79912e9i −0.983228 0.708328i
\(553\) 3.24818e9 1.18224e9i 0.816775 0.297282i
\(554\) −1.29205e7 + 4.70267e6i −0.00322846 + 0.00117506i
\(555\) 2.10801e9 9.48732e8i 0.523416 0.235569i
\(556\) −7.64969e7 4.33836e8i −0.0188748 0.107044i
\(557\) 3.35190e9 5.80565e9i 0.821859 1.42350i −0.0824372 0.996596i \(-0.526270\pi\)
0.904296 0.426905i \(-0.140396\pi\)
\(558\) 5.64807e8 1.43101e9i 0.137620 0.348676i
\(559\) 9.57239e8 + 1.65799e9i 0.231782 + 0.401457i
\(560\) 2.81811e9 2.36467e9i 0.678109 0.569001i
\(561\) 4.33486e9 4.21998e9i 1.03658 1.00911i
\(562\) 7.21361e8 4.09104e9i 0.171426 0.972203i
\(563\) 3.53059e8 + 2.96251e8i 0.0833811 + 0.0699651i 0.683526 0.729927i \(-0.260446\pi\)
−0.600144 + 0.799892i \(0.704890\pi\)
\(564\) 2.67527e6 5.54162e6i 0.000627900 0.00130065i
\(565\) −3.63497e9 1.32302e9i −0.847874 0.308601i
\(566\) −1.83929e9 −0.426377
\(567\) −1.57830e9 3.10797e9i −0.363621 0.716039i
\(568\) −3.34800e9 −0.766596
\(569\) 5.00513e9 + 1.82172e9i 1.13900 + 0.414561i 0.841551 0.540178i \(-0.181643\pi\)
0.297445 + 0.954739i \(0.403865\pi\)
\(570\) 1.57148e9 3.25520e9i 0.355424 0.736234i
\(571\) −9.81547e8 8.23616e8i −0.220640 0.185139i 0.525767 0.850629i \(-0.323778\pi\)
−0.746407 + 0.665490i \(0.768223\pi\)
\(572\) 3.30527e8 1.87451e9i 0.0738449 0.418795i
\(573\) −9.67435e7 + 9.41797e7i −0.0214823 + 0.0209130i
\(574\) −2.44195e9 + 2.04904e9i −0.538945 + 0.452228i
\(575\) −4.83097e9 8.36748e9i −1.05973 1.83551i
\(576\) 5.00168e9 7.44049e8i 1.09053 0.162227i
\(577\) 6.17263e8 1.06913e9i 0.133769 0.231694i −0.791358 0.611353i \(-0.790625\pi\)
0.925126 + 0.379659i \(0.123959\pi\)
\(578\) −4.60756e7 2.61307e8i −0.00992483 0.0562865i
\(579\) −9.36886e8 + 4.21655e8i −0.200591 + 0.0902781i
\(580\) −2.86757e9 + 1.04371e9i −0.610261 + 0.222117i
\(581\) −7.99596e8 + 2.91029e8i −0.169143 + 0.0615631i
\(582\) 2.67027e9 + 1.92369e9i 0.561469 + 0.404488i
\(583\) 2.12568e9 + 1.20553e10i 0.444281 + 2.51965i
\(584\) 1.67301e9 2.89774e9i 0.347579 0.602024i
\(585\) −5.61820e9 + 6.34158e9i −1.16025 + 1.30964i
\(586\) 1.19026e9 + 2.06160e9i 0.244344 + 0.423216i
\(587\) −3.98986e9 + 3.34789e9i −0.814188 + 0.683185i −0.951603 0.307329i \(-0.900565\pi\)
0.137415 + 0.990513i \(0.456120\pi\)
\(588\) 1.18881e8 + 4.68757e8i 0.0241152 + 0.0950884i
\(589\) 2.14164e8 1.21459e9i 0.0431860 0.244920i
\(590\) −7.88474e9 6.61608e9i −1.58054 1.32623i
\(591\) −2.19346e9 + 1.62257e8i −0.437093 + 0.0323330i
\(592\) −1.03526e9 3.76806e8i −0.205081 0.0746434i
\(593\) 2.73328e8 0.0538261 0.0269131 0.999638i \(-0.491432\pi\)
0.0269131 + 0.999638i \(0.491432\pi\)
\(594\) −3.05689e8 6.50168e9i −0.0598449 1.27284i
\(595\) −6.78561e9 −1.32062
\(596\) −1.66906e8 6.07490e7i −0.0322932 0.0117538i
\(597\) −8.66533e8 1.27360e9i −0.166677 0.244976i
\(598\) −3.90863e9 3.27973e9i −0.747431 0.627169i
\(599\) −5.43963e8 + 3.08497e9i −0.103413 + 0.586485i 0.888429 + 0.459014i \(0.151797\pi\)
−0.991842 + 0.127471i \(0.959314\pi\)
\(600\) 1.04985e10 + 2.96470e9i 1.98425 + 0.560340i
\(601\) −1.57067e8 + 1.31795e8i −0.0295137 + 0.0247650i −0.657425 0.753520i \(-0.728354\pi\)
0.627911 + 0.778285i \(0.283910\pi\)
\(602\) 8.24854e8 + 1.42869e9i 0.154095 + 0.266901i
\(603\) 2.23681e9 + 1.37280e9i 0.415450 + 0.254975i
\(604\) −2.09162e8 + 3.62280e8i −0.0386237 + 0.0668982i
\(605\) 2.00263e9 + 1.13575e10i 0.367670 + 2.08516i
\(606\) 4.38363e8 4.33867e9i 0.0800165 0.791959i
\(607\) 8.01974e9 2.91895e9i 1.45546 0.529744i 0.511349 0.859373i \(-0.329146\pi\)
0.944110 + 0.329629i \(0.106924\pi\)
\(608\) 1.57256e9 5.72367e8i 0.283757 0.103279i
\(609\) 6.21217e8 6.14846e9i 0.111451 1.10308i
\(610\) −6.84802e8 3.88370e9i −0.122155 0.692774i
\(611\) 1.51442e7 2.62305e7i 0.00268597 0.00465224i
\(612\) −1.28963e9 7.91486e8i −0.227423 0.139577i
\(613\) 7.64294e7 + 1.32380e8i 0.0134014 + 0.0232118i 0.872648 0.488349i \(-0.162401\pi\)
−0.859247 + 0.511561i \(0.829067\pi\)
\(614\) −5.46752e9 + 4.58780e9i −0.953238 + 0.799862i
\(615\) −9.73363e9 2.74872e9i −1.68738 0.476505i
\(616\) 1.31571e9 7.46174e9i 0.226791 1.28620i
\(617\) 3.62446e9 + 3.04128e9i 0.621219 + 0.521265i 0.898186 0.439615i \(-0.144885\pi\)
−0.276968 + 0.960879i \(0.589329\pi\)
\(618\) 2.40064e9 + 3.52837e9i 0.409135 + 0.601332i
\(619\) 1.23431e9 + 4.49250e8i 0.209173 + 0.0761327i 0.444482 0.895788i \(-0.353388\pi\)
−0.235309 + 0.971921i \(0.575610\pi\)
\(620\) 1.23005e9 0.207277
\(621\) 5.91840e9 + 3.05578e9i 0.991708 + 0.512036i
\(622\) 4.23012e9 0.704833
\(623\) −2.27448e9 8.27842e8i −0.376854 0.137164i
\(624\) 4.02677e9 2.97872e8i 0.663454 0.0490776i
\(625\) 3.30661e9 + 2.77457e9i 0.541755 + 0.454586i
\(626\) 3.48186e8 1.97466e9i 0.0567285 0.321724i
\(627\) −1.28271e9 5.05786e9i −0.207823 0.819465i
\(628\) −2.49933e8 + 2.09718e8i −0.0402684 + 0.0337892i
\(629\) 1.01606e9 + 1.75987e9i 0.162796 + 0.281971i
\(630\) −4.84122e9 + 5.46455e9i −0.771370 + 0.870688i
\(631\) 1.85172e9 3.20728e9i 0.293409 0.508199i −0.681204 0.732093i \(-0.738544\pi\)
0.974614 + 0.223894i \(0.0718769\pi\)
\(632\) −1.29500e9 7.34433e9i −0.204062 1.15729i
\(633\) 8.31154e9 + 5.98772e9i 1.30247 + 0.938314i
\(634\) −9.21718e9 + 3.35478e9i −1.43643 + 0.522819i
\(635\) −1.79447e10 + 6.53133e9i −2.78117 + 1.01226i
\(636\) 2.79202e9 1.25658e9i 0.430347 0.193682i
\(637\) 4.13334e8 + 2.34413e9i 0.0633597 + 0.359331i
\(638\) 5.76965e9 9.99332e9i 0.879583 1.52348i
\(639\) 4.60612e9 6.85205e8i 0.698364 0.103889i
\(640\) −2.27486e9 3.94016e9i −0.343023 0.594134i
\(641\) 4.10853e9 3.44747e9i 0.616146 0.517008i −0.280443 0.959871i \(-0.590482\pi\)
0.896589 + 0.442863i \(0.146037\pi\)
\(642\) −5.75626e9 + 5.60371e9i −0.858555 + 0.835802i
\(643\) 3.40206e7 1.92940e8i 0.00504665 0.0286210i −0.982180 0.187940i \(-0.939819\pi\)
0.987227 + 0.159319i \(0.0509300\pi\)
\(644\) 1.28577e9 + 1.07889e9i 0.189698 + 0.159176i
\(645\) −2.27562e9 + 4.71378e9i −0.333919 + 0.691688i
\(646\) 2.98594e9 + 1.08679e9i 0.435779 + 0.158611i
\(647\) 5.19682e9 0.754349 0.377175 0.926142i \(-0.376896\pi\)
0.377175 + 0.926142i \(0.376896\pi\)
\(648\) −7.19481e9 + 2.18904e9i −1.03874 + 0.316039i
\(649\) −1.48582e10 −2.13358
\(650\) 1.09226e10 + 3.97549e9i 1.56001 + 0.567798i
\(651\) −1.08294e9 + 2.24323e9i −0.153841 + 0.318669i
\(652\) −5.13997e8 4.31295e8i −0.0726263 0.0609407i
\(653\) −1.11094e9 + 6.30045e9i −0.156133 + 0.885473i 0.801610 + 0.597847i \(0.203977\pi\)
−0.957743 + 0.287626i \(0.907134\pi\)
\(654\) 6.06250e9 5.90183e9i 0.847480 0.825020i
\(655\) 1.43075e10 1.20054e10i 1.98939 1.66930i
\(656\) 2.41016e9 + 4.17452e9i 0.333336 + 0.577356i
\(657\) −1.70864e9 + 4.32905e9i −0.235057 + 0.595545i
\(658\) 1.30498e7 2.26028e7i 0.00178571 0.00309295i
\(659\) −4.86961e8 2.76170e9i −0.0662820 0.375904i −0.999847 0.0174956i \(-0.994431\pi\)
0.933565 0.358408i \(-0.116680\pi\)
\(660\) 4.74564e9 2.13583e9i 0.642527 0.289176i
\(661\) −9.56276e9 + 3.48056e9i −1.28789 + 0.468753i −0.893033 0.449991i \(-0.851427\pi\)
−0.394855 + 0.918744i \(0.629205\pi\)
\(662\) 2.94084e9 1.07038e9i 0.393974 0.143395i
\(663\) −6.04295e9 4.35340e9i −0.805289 0.580138i
\(664\) 3.18788e8 + 1.80793e9i 0.0422584 + 0.239659i
\(665\) −2.92634e9 + 5.06857e9i −0.385877 + 0.668359i
\(666\) 2.14217e9 + 4.37337e8i 0.280991 + 0.0573662i
\(667\) 5.90426e9 + 1.02265e10i 0.770415 + 1.33440i
\(668\) −3.90296e8 + 3.27497e8i −0.0506613 + 0.0425098i
\(669\) 1.96198e8 + 7.73628e8i 0.0253340 + 0.0998943i
\(670\) 9.54498e8 5.41322e9i 0.122606 0.695335i
\(671\) −4.36096e9 3.65928e9i −0.557254 0.467591i
\(672\) −3.37075e9 + 2.49344e8i −0.428484 + 0.0316962i
\(673\) 8.46165e9 + 3.07979e9i 1.07005 + 0.389465i 0.816194 0.577778i \(-0.196080\pi\)
0.253852 + 0.967243i \(0.418302\pi\)
\(674\) 6.80110e9 0.855598
\(675\) −1.50503e10 1.93016e9i −1.88358 0.241563i
\(676\) −1.24259e8 −0.0154708
\(677\) 8.41940e8 + 3.06441e8i 0.104285 + 0.0379565i 0.393636 0.919267i \(-0.371217\pi\)
−0.289351 + 0.957223i \(0.593439\pi\)
\(678\) −2.05803e9 3.02482e9i −0.253599 0.372731i
\(679\) −4.08200e9 3.42521e9i −0.500414 0.419897i
\(680\) −2.54217e9 + 1.44174e10i −0.310044 + 1.75835i
\(681\) −2.54260e9 7.18015e8i −0.308505 0.0871202i
\(682\) −3.56309e9 + 2.98979e9i −0.430112 + 0.360907i
\(683\) 7.35302e9 + 1.27358e10i 0.883067 + 1.52952i 0.847913 + 0.530135i \(0.177859\pi\)
0.0351534 + 0.999382i \(0.488808\pi\)
\(684\) −1.14737e9 + 6.21967e8i −0.137090 + 0.0743141i
\(685\) 5.42986e9 9.40480e9i 0.645464 1.11798i
\(686\) 1.35928e9 + 7.70884e9i 0.160758 + 0.911705i
\(687\) 6.79598e8 6.72628e9i 0.0799657 0.791455i
\(688\) 2.34416e9 8.53204e8i 0.274428 0.0998835i
\(689\) 1.41613e10 5.15431e9i 1.64944 0.600348i
\(690\) 1.40234e9 1.38796e10i 0.162511 1.60844i
\(691\) 7.00358e8 + 3.97193e9i 0.0807508 + 0.457960i 0.998193 + 0.0600912i \(0.0191391\pi\)
−0.917442 + 0.397869i \(0.869750\pi\)
\(692\) 1.35743e8 2.35114e8i 0.0155721 0.0269717i
\(693\) −2.82997e8 + 1.05350e10i −0.0323010 + 1.20245i
\(694\) 3.93176e9 + 6.81000e9i 0.446507 + 0.773373i
\(695\) 4.54136e9 3.81065e9i 0.513144 0.430579i
\(696\) −1.28309e10 3.62337e9i −1.44253 0.407362i
\(697\) 1.54394e9 8.75614e9i 0.172710 0.979485i
\(698\) 2.82539e9 + 2.37078e9i 0.314474 + 0.263875i
\(699\) 5.01882e9 + 7.37648e9i 0.555817 + 0.816919i
\(700\) −3.59305e9 1.30776e9i −0.395931 0.144107i
\(701\) 5.94143e9 0.651446 0.325723 0.945465i \(-0.394392\pi\)
0.325723 + 0.945465i \(0.394392\pi\)
\(702\) −7.81722e9 + 1.76052e9i −0.852850 + 0.192071i
\(703\) 1.75274e9 0.190271
\(704\) −1.43664e10 5.22895e9i −1.55183 0.564820i
\(705\) 8.25850e7 6.10905e6i 0.00887645 0.000656617i
\(706\) 3.21976e9 + 2.70170e9i 0.344355 + 0.288948i
\(707\) −1.22608e9 + 6.95344e9i −0.130482 + 0.740000i
\(708\) 9.13560e8 + 3.60225e9i 0.0967432 + 0.381468i
\(709\) −6.28298e9 + 5.27204e9i −0.662070 + 0.555542i −0.910706 0.413054i \(-0.864462\pi\)
0.248637 + 0.968597i \(0.420017\pi\)
\(710\) −4.87662e9 8.44655e9i −0.511345 0.885676i
\(711\) 3.28474e9 + 9.83916e9i 0.342734 + 1.02663i
\(712\) −2.61103e9 + 4.52244e9i −0.271102 + 0.469562i
\(713\) −8.26532e8 4.68749e9i −0.0853977 0.484314i
\(714\) −5.20722e9 3.75134e9i −0.535380 0.385693i
\(715\) 2.40702e10 8.76085e9i 2.46269 0.896345i
\(716\) 1.16579e9 4.24312e8i 0.118693 0.0432005i
\(717\) −1.19424e10 + 5.37480e9i −1.20997 + 0.544560i
\(718\) 3.77031e8 + 2.13825e9i 0.0380138 + 0.215587i
\(719\) 8.24797e9 1.42859e10i 0.827553 1.43336i −0.0723990 0.997376i \(-0.523065\pi\)
0.899952 0.435989i \(-0.143601\pi\)
\(720\) 6.86645e9 + 8.64431e9i 0.685597 + 0.863111i
\(721\) −3.45494e9 5.98412e9i −0.343294 0.594603i
\(722\) −4.49102e9 + 3.76841e9i −0.444083 + 0.372630i
\(723\) 1.25412e10 1.22088e10i 1.23411 1.20140i
\(724\) 8.49474e8 4.81761e9i 0.0831888 0.471787i
\(725\) −2.06071e10 1.72914e10i −2.00832 1.68518i
\(726\) −4.74204e9 + 9.82278e9i −0.459925 + 0.952701i
\(727\) −1.12806e10 4.10581e9i −1.08884 0.396304i −0.265647 0.964070i \(-0.585586\pi\)
−0.823190 + 0.567766i \(0.807808\pi\)
\(728\) −9.32780e9 −0.896024
\(729\) 9.45048e9 4.48414e9i 0.903457 0.428679i
\(730\) 9.74746e9 0.927388
\(731\) −4.32387e9 1.57376e9i −0.409413 0.149014i
\(732\) −6.19028e8 + 1.28227e9i −0.0583340 + 0.120834i
\(733\) −1.23607e10 1.03719e10i −1.15926 0.972733i −0.159362 0.987220i \(-0.550944\pi\)
−0.999895 + 0.0144876i \(0.995388\pi\)
\(734\) 1.23434e9 7.00026e9i 0.115212 0.653398i
\(735\) −4.66316e9 + 4.53958e9i −0.433187 + 0.421706i
\(736\) 4.94754e9 4.15148e9i 0.457422 0.383823i
\(737\) −3.96741e9 6.87176e9i −0.365066 0.632313i
\(738\) −5.94991e9 7.49046e9i −0.544896 0.685979i
\(739\) 3.73977e9 6.47747e9i 0.340871 0.590405i −0.643724 0.765258i \(-0.722612\pi\)
0.984595 + 0.174853i \(0.0559449\pi\)
\(740\) 3.03552e8 + 1.72153e9i 0.0275373 + 0.156172i
\(741\) −5.85788e9 + 2.63640e9i −0.528904 + 0.238039i
\(742\) 1.22029e10 4.44148e9i 1.09660 0.399129i
\(743\) 2.90736e9 1.05819e9i 0.260039 0.0946463i −0.208711 0.977977i \(-0.566927\pi\)
0.468750 + 0.883331i \(0.344705\pi\)
\(744\) 4.36048e9 + 3.14133e9i 0.388176 + 0.279646i
\(745\) −4.15064e8 2.35395e9i −0.0367763 0.208569i
\(746\) −4.27935e9 + 7.41206e9i −0.377392 + 0.653662i
\(747\) −8.08596e8 2.42208e9i −0.0709757 0.212602i
\(748\) 2.28740e9 + 3.96190e9i 0.199842 + 0.346137i
\(749\) 9.96417e9 8.36093e9i 0.866473 0.727057i
\(750\) 3.69839e9 + 1.45831e10i 0.320109 + 1.26222i
\(751\) −9.97413e7 + 5.65661e8i −0.00859281 + 0.0487323i −0.988803 0.149229i \(-0.952321\pi\)
0.980210 + 0.197961i \(0.0634320\pi\)
\(752\) −3.02330e7 2.53685e7i −0.00259250 0.00217536i
\(753\) 1.18552e10 8.76964e8i 1.01187 0.0748513i
\(754\) −1.33492e10 4.85872e9i −1.13411 0.412783i
\(755\) −5.62952e9 −0.476055
\(756\) 2.57153e9