Properties

Label 27.8.e.a.4.14
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 4.14
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.14

$q$-expansion

\(f(q)\) \(=\) \(q+(7.46251 + 2.71613i) q^{2} +(42.7022 + 19.0664i) q^{3} +(-49.7420 - 41.7385i) q^{4} +(71.4552 - 405.243i) q^{5} +(266.878 + 258.268i) q^{6} +(898.235 - 753.709i) q^{7} +(-766.085 - 1326.90i) q^{8} +(1459.95 + 1628.35i) q^{9} +O(q^{10})\) \(q+(7.46251 + 2.71613i) q^{2} +(42.7022 + 19.0664i) q^{3} +(-49.7420 - 41.7385i) q^{4} +(71.4552 - 405.243i) q^{5} +(266.878 + 258.268i) q^{6} +(898.235 - 753.709i) q^{7} +(-766.085 - 1326.90i) q^{8} +(1459.95 + 1628.35i) q^{9} +(1633.93 - 2830.04i) q^{10} +(1289.55 + 7313.38i) q^{11} +(-1328.29 - 2730.72i) q^{12} +(-3791.99 + 1380.17i) q^{13} +(8750.26 - 3184.83i) q^{14} +(10777.8 - 15942.3i) q^{15} +(-669.609 - 3797.54i) q^{16} +(7380.03 - 12782.6i) q^{17} +(6472.06 + 16117.0i) q^{18} +(-1194.93 - 2069.69i) q^{19} +(-20468.5 + 17175.2i) q^{20} +(52727.1 - 15058.9i) q^{21} +(-10240.9 + 58078.8i) q^{22} +(-782.904 - 656.935i) q^{23} +(-7414.36 - 71267.9i) q^{24} +(-85702.2 - 31193.0i) q^{25} -32046.4 q^{26} +(31296.2 + 97369.9i) q^{27} -76138.7 q^{28} +(-127204. - 46298.5i) q^{29} +(123731. - 89695.9i) q^{30} +(123510. + 103637. i) q^{31} +(-28737.8 + 162980. i) q^{32} +(-84373.2 + 336884. i) q^{33} +(89792.7 - 75345.0i) q^{34} +(-241251. - 417860. i) q^{35} +(-4655.87 - 141933. i) q^{36} +(-120547. + 208793. i) q^{37} +(-3295.66 - 18690.6i) q^{38} +(-188241. - 13363.1i) q^{39} +(-592456. + 215636. i) q^{40} +(154404. - 56198.5i) q^{41} +(434378. + 30836.3i) q^{42} +(177068. + 1.00420e6i) q^{43} +(241105. - 417606. i) q^{44} +(764197. - 475279. i) q^{45} +(-4058.11 - 7028.85i) q^{46} +(797496. - 669179. i) q^{47} +(43811.6 - 174930. i) q^{48} +(95742.7 - 542984. i) q^{49} +(-554829. - 465557. i) q^{50} +(558861. - 405134. i) q^{51} +(246227. + 89619.4i) q^{52} -749747. q^{53} +(-30921.2 + 811628. i) q^{54} +3.05584e6 q^{55} +(-1.68822e6 - 614461. i) q^{56} +(-11564.9 - 111163. i) q^{57} +(-823509. - 691006. i) q^{58} +(50040.2 - 283792. i) q^{59} +(-1.20152e6 + 343155. i) q^{60} +(-1.80233e6 + 1.51233e6i) q^{61} +(640202. + 1.10886e6i) q^{62} +(2.53868e6 + 362265. i) q^{63} +(-903924. + 1.56564e6i) q^{64} +(288346. + 1.63529e6i) q^{65} +(-1.54466e6 + 2.28483e6i) q^{66} +(-2.96301e6 + 1.07845e6i) q^{67} +(-900624. + 327800. i) q^{68} +(-20906.3 - 42979.6i) q^{69} +(-665379. - 3.77355e6i) q^{70} +(968628. - 1.67771e6i) q^{71} +(1.04221e6 - 3.18466e6i) q^{72} +(-1.90937e6 - 3.30713e6i) q^{73} +(-1.46669e6 + 1.23070e6i) q^{74} +(-3.06493e6 - 2.96604e6i) q^{75} +(-26947.2 + 152825. i) q^{76} +(6.67048e6 + 5.59720e6i) q^{77} +(-1.36845e6 - 611009. i) q^{78} +(5.86605e6 + 2.13507e6i) q^{79} -1.58677e6 q^{80} +(-520074. + 4.75461e6i) q^{81} +1.30488e6 q^{82} +(3.52512e6 + 1.28304e6i) q^{83} +(-3.25129e6 - 1.45169e6i) q^{84} +(-4.65271e6 - 3.90408e6i) q^{85} +(-1.40617e6 + 7.97480e6i) q^{86} +(-4.54914e6 - 4.40236e6i) q^{87} +(8.71621e6 - 7.31377e6i) q^{88} +(-4.12096e6 - 7.13772e6i) q^{89} +(6.99375e6 - 1.47111e6i) q^{90} +(-2.36585e6 + 4.09777e6i) q^{91} +(11523.8 + 65354.5i) q^{92} +(3.29816e6 + 6.78042e6i) q^{93} +(7.76890e6 - 2.82765e6i) q^{94} +(-924109. + 336348. i) q^{95} +(-4.33461e6 + 6.41168e6i) q^{96} +(-1.50671e6 - 8.54498e6i) q^{97} +(2.18930e6 - 3.79197e6i) q^{98} +(-1.00261e7 + 1.27770e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.46251 + 2.71613i 0.659599 + 0.240074i 0.650063 0.759880i \(-0.274742\pi\)
0.00953567 + 0.999955i \(0.496965\pi\)
\(3\) 42.7022 + 19.0664i 0.913115 + 0.407703i
\(4\) −49.7420 41.7385i −0.388610 0.326082i
\(5\) 71.4552 405.243i 0.255646 1.44984i −0.538763 0.842457i \(-0.681108\pi\)
0.794409 0.607383i \(-0.207781\pi\)
\(6\) 266.878 + 258.268i 0.504411 + 0.488136i
\(7\) 898.235 753.709i 0.989799 0.830540i 0.00426019 0.999991i \(-0.498644\pi\)
0.985539 + 0.169451i \(0.0541995\pi\)
\(8\) −766.085 1326.90i −0.529008 0.916268i
\(9\) 1459.95 + 1628.35i 0.667557 + 0.744558i
\(10\) 1633.93 2830.04i 0.516693 0.894939i
\(11\) 1289.55 + 7313.38i 0.292121 + 1.65670i 0.678679 + 0.734435i \(0.262553\pi\)
−0.386558 + 0.922265i \(0.626336\pi\)
\(12\) −1328.29 2730.72i −0.221901 0.456188i
\(13\) −3791.99 + 1380.17i −0.478702 + 0.174233i −0.570090 0.821582i \(-0.693092\pi\)
0.0913885 + 0.995815i \(0.470869\pi\)
\(14\) 8750.26 3184.83i 0.852261 0.310198i
\(15\) 10777.8 15942.3i 0.824537 1.21964i
\(16\) −669.609 3797.54i −0.0408697 0.231784i
\(17\) 7380.03 12782.6i 0.364323 0.631026i −0.624344 0.781149i \(-0.714634\pi\)
0.988667 + 0.150123i \(0.0479670\pi\)
\(18\) 6472.06 + 16117.0i 0.261571 + 0.651373i
\(19\) −1194.93 2069.69i −0.0399674 0.0692256i 0.845350 0.534213i \(-0.179392\pi\)
−0.885317 + 0.464988i \(0.846059\pi\)
\(20\) −20468.5 + 17175.2i −0.572113 + 0.480060i
\(21\) 52727.1 15058.9i 1.24241 0.354835i
\(22\) −10240.9 + 58078.8i −0.205049 + 1.16289i
\(23\) −782.904 656.935i −0.0134172 0.0112583i 0.636054 0.771644i \(-0.280565\pi\)
−0.649472 + 0.760386i \(0.725010\pi\)
\(24\) −7414.36 71267.9i −0.109480 1.05234i
\(25\) −85702.2 31193.0i −1.09699 0.399271i
\(26\) −32046.4 −0.357580
\(27\) 31296.2 + 97369.9i 0.305998 + 0.952032i
\(28\) −76138.7 −0.655469
\(29\) −127204. 46298.5i −0.968519 0.352512i −0.191153 0.981560i \(-0.561223\pi\)
−0.777366 + 0.629048i \(0.783445\pi\)
\(30\) 123731. 89695.9i 0.836669 0.606525i
\(31\) 123510. + 103637.i 0.744623 + 0.624813i 0.934075 0.357077i \(-0.116227\pi\)
−0.189452 + 0.981890i \(0.560671\pi\)
\(32\) −28737.8 + 162980.i −0.155035 + 0.879246i
\(33\) −84373.2 + 336884.i −0.408701 + 1.63186i
\(34\) 89792.7 75345.0i 0.391800 0.328760i
\(35\) −241251. 417860.i −0.951112 1.64737i
\(36\) −4655.87 141933.i −0.0166319 0.507021i
\(37\) −120547. + 208793.i −0.391246 + 0.677658i −0.992614 0.121314i \(-0.961289\pi\)
0.601368 + 0.798972i \(0.294622\pi\)
\(38\) −3295.66 18690.6i −0.00974317 0.0552563i
\(39\) −188241. 13363.1i −0.508145 0.0360730i
\(40\) −592456. + 215636.i −1.46368 + 0.532736i
\(41\) 154404. 56198.5i 0.349877 0.127345i −0.161103 0.986938i \(-0.551505\pi\)
0.510980 + 0.859593i \(0.329283\pi\)
\(42\) 434378. + 30836.3i 0.904681 + 0.0642230i
\(43\) 177068. + 1.00420e6i 0.339625 + 1.92611i 0.375655 + 0.926759i \(0.377418\pi\)
−0.0360301 + 0.999351i \(0.511471\pi\)
\(44\) 241105. 417606.i 0.426699 0.739065i
\(45\) 764197. 475279.i 1.25015 0.777508i
\(46\) −4058.11 7028.85i −0.00614711 0.0106471i
\(47\) 797496. 669179.i 1.12043 0.940155i 0.121807 0.992554i \(-0.461131\pi\)
0.998626 + 0.0523986i \(0.0166866\pi\)
\(48\) 43811.6 174930.i 0.0571801 0.228308i
\(49\) 95742.7 542984.i 0.116257 0.659327i
\(50\) −554829. 465557.i −0.627717 0.526717i
\(51\) 558861. 405134.i 0.589940 0.427664i
\(52\) 246227. + 89619.4i 0.242842 + 0.0883874i
\(53\) −749747. −0.691750 −0.345875 0.938281i \(-0.612418\pi\)
−0.345875 + 0.938281i \(0.612418\pi\)
\(54\) −30921.2 + 811628.i −0.0267225 + 0.701422i
\(55\) 3.05584e6 2.47663
\(56\) −1.68822e6 614461.i −1.28461 0.467559i
\(57\) −11564.9 111163.i −0.00827139 0.0795057i
\(58\) −823509. 691006.i −0.554205 0.465033i
\(59\) 50040.2 283792.i 0.0317203 0.179895i −0.964831 0.262870i \(-0.915331\pi\)
0.996552 + 0.0829750i \(0.0264422\pi\)
\(60\) −1.20152e6 + 343155.i −0.718127 + 0.205098i
\(61\) −1.80233e6 + 1.51233e6i −1.01667 + 0.853086i −0.989205 0.146537i \(-0.953187\pi\)
−0.0274630 + 0.999623i \(0.508743\pi\)
\(62\) 640202. + 1.10886e6i 0.341151 + 0.590890i
\(63\) 2.53868e6 + 362265.i 1.27913 + 0.182530i
\(64\) −903924. + 1.56564e6i −0.431025 + 0.746557i
\(65\) 288346. + 1.63529e6i 0.130232 + 0.738583i
\(66\) −1.54466e6 + 2.28483e6i −0.661345 + 0.978252i
\(67\) −2.96301e6 + 1.07845e6i −1.20357 + 0.438063i −0.864469 0.502687i \(-0.832345\pi\)
−0.339100 + 0.940750i \(0.610123\pi\)
\(68\) −900624. + 327800.i −0.347346 + 0.126424i
\(69\) −20906.3 42979.6i −0.00766136 0.0157504i
\(70\) −665379. 3.77355e6i −0.231860 1.31494i
\(71\) 968628. 1.67771e6i 0.321183 0.556306i −0.659549 0.751661i \(-0.729253\pi\)
0.980732 + 0.195356i \(0.0625861\pi\)
\(72\) 1.04221e6 3.18466e6i 0.329072 1.00554i
\(73\) −1.90937e6 3.30713e6i −0.574460 0.994995i −0.996100 0.0882312i \(-0.971879\pi\)
0.421640 0.906764i \(-0.361455\pi\)
\(74\) −1.46669e6 + 1.23070e6i −0.420754 + 0.353054i
\(75\) −3.06493e6 2.96604e6i −0.838892 0.811825i
\(76\) −26947.2 + 152825.i −0.00704151 + 0.0399344i
\(77\) 6.67048e6 + 5.59720e6i 1.66510 + 1.39718i
\(78\) −1.36845e6 611009.i −0.326512 0.145786i
\(79\) 5.86605e6 + 2.13507e6i 1.33860 + 0.487211i 0.909372 0.415985i \(-0.136563\pi\)
0.429229 + 0.903196i \(0.358785\pi\)
\(80\) −1.58677e6 −0.346497
\(81\) −520074. + 4.75461e6i −0.108735 + 0.994071i
\(82\) 1.30488e6 0.261351
\(83\) 3.52512e6 + 1.28304e6i 0.676707 + 0.246301i 0.657433 0.753513i \(-0.271642\pi\)
0.0192742 + 0.999814i \(0.493864\pi\)
\(84\) −3.25129e6 1.45169e6i −0.598519 0.267237i
\(85\) −4.65271e6 3.90408e6i −0.821749 0.689530i
\(86\) −1.40617e6 + 7.97480e6i −0.238393 + 1.35200i
\(87\) −4.54914e6 4.40236e6i −0.740649 0.716752i
\(88\) 8.71621e6 7.31377e6i 1.36345 1.14407i
\(89\) −4.12096e6 7.13772e6i −0.619632 1.07323i −0.989553 0.144171i \(-0.953949\pi\)
0.369921 0.929063i \(-0.379385\pi\)
\(90\) 6.99375e6 1.47111e6i 1.01126 0.212715i
\(91\) −2.36585e6 + 4.09777e6i −0.329111 + 0.570037i
\(92\) 11523.8 + 65354.5i 0.00154290 + 0.00875020i
\(93\) 3.29816e6 + 6.78042e6i 0.425188 + 0.874110i
\(94\) 7.76890e6 2.82765e6i 0.964744 0.351138i
\(95\) −924109. + 336348.i −0.110584 + 0.0402491i
\(96\) −4.33461e6 + 6.41168e6i −0.500035 + 0.739644i
\(97\) −1.50671e6 8.54498e6i −0.167621 0.950627i −0.946321 0.323230i \(-0.895231\pi\)
0.778699 0.627397i \(-0.215880\pi\)
\(98\) 2.18930e6 3.79197e6i 0.234970 0.406981i
\(99\) −1.00261e7 + 1.27770e7i −1.03850 + 1.32344i
\(100\) 2.96105e6 + 5.12869e6i 0.296105 + 0.512869i
\(101\) 8.19828e6 6.87918e6i 0.791768 0.664373i −0.154414 0.988006i \(-0.549349\pi\)
0.946182 + 0.323634i \(0.104905\pi\)
\(102\) 5.27090e6 1.50537e6i 0.491795 0.140457i
\(103\) −729870. + 4.13930e6i −0.0658135 + 0.373247i 0.934057 + 0.357125i \(0.116243\pi\)
−0.999870 + 0.0161218i \(0.994868\pi\)
\(104\) 4.73633e6 + 3.97425e6i 0.412881 + 0.346448i
\(105\) −2.33489e6 2.24433e7i −0.196836 1.89201i
\(106\) −5.59500e6 2.03641e6i −0.456278 0.166072i
\(107\) −1.27099e7 −1.00300 −0.501498 0.865159i \(-0.667218\pi\)
−0.501498 + 0.865159i \(0.667218\pi\)
\(108\) 2.50734e6 6.14963e6i 0.191527 0.469749i
\(109\) 2.03485e7 1.50501 0.752506 0.658585i \(-0.228845\pi\)
0.752506 + 0.658585i \(0.228845\pi\)
\(110\) 2.28042e7 + 8.30006e6i 1.63358 + 0.594575i
\(111\) −9.12854e6 + 6.61753e6i −0.633535 + 0.459267i
\(112\) −3.46371e6 2.90640e6i −0.232958 0.195475i
\(113\) −404160. + 2.29211e6i −0.0263499 + 0.149438i −0.995144 0.0984288i \(-0.968618\pi\)
0.968794 + 0.247867i \(0.0797294\pi\)
\(114\) 215631. 860967.i 0.0136315 0.0544276i
\(115\) −322160. + 270325.i −0.0197528 + 0.0165746i
\(116\) 4.39496e6 + 7.61229e6i 0.261428 + 0.452806i
\(117\) −7.78350e6 4.15970e6i −0.449288 0.240111i
\(118\) 1.14424e6 1.98189e6i 0.0641108 0.111043i
\(119\) −3.00535e6 1.70442e7i −0.163486 0.927174i
\(120\) −2.94106e7 2.08784e6i −1.55371 0.110297i
\(121\) −3.35107e7 + 1.21969e7i −1.71963 + 0.625894i
\(122\) −1.75576e7 + 6.39044e6i −0.875397 + 0.318619i
\(123\) 7.66489e6 + 544128.i 0.371397 + 0.0263653i
\(124\) −1.81797e6 1.03102e7i −0.0856272 0.485616i
\(125\) −2.69063e6 + 4.66031e6i −0.123217 + 0.213417i
\(126\) 1.79609e7 + 9.59879e6i 0.799894 + 0.427484i
\(127\) 1.35005e7 + 2.33836e7i 0.584840 + 1.01297i 0.994895 + 0.100912i \(0.0321761\pi\)
−0.410055 + 0.912061i \(0.634491\pi\)
\(128\) 5.22932e6 4.38792e6i 0.220399 0.184937i
\(129\) −1.15853e7 + 4.62576e7i −0.475163 + 1.89723i
\(130\) −2.28988e6 + 1.29866e7i −0.0914138 + 0.518434i
\(131\) −2.88021e7 2.41678e7i −1.11937 0.939264i −0.120799 0.992677i \(-0.538546\pi\)
−0.998573 + 0.0534125i \(0.982990\pi\)
\(132\) 1.82579e7 1.32357e7i 0.690944 0.500885i
\(133\) −2.63327e6 958432.i −0.0970543 0.0353249i
\(134\) −2.50407e7 −0.899040
\(135\) 4.16947e7 5.72497e6i 1.45852 0.200265i
\(136\) −2.26149e7 −0.770919
\(137\) 1.80096e7 + 6.55497e6i 0.598388 + 0.217796i 0.623415 0.781891i \(-0.285745\pi\)
−0.0250266 + 0.999687i \(0.507967\pi\)
\(138\) −39275.4 377520.i −0.00127217 0.0122282i
\(139\) −1.35167e7 1.13418e7i −0.426892 0.358205i 0.403885 0.914810i \(-0.367659\pi\)
−0.830778 + 0.556604i \(0.812104\pi\)
\(140\) −5.44051e6 + 3.08546e7i −0.167568 + 0.950326i
\(141\) 4.68136e7 1.33700e7i 1.40639 0.401666i
\(142\) 1.17853e7 9.88903e6i 0.345407 0.289831i
\(143\) −1.49837e7 2.59524e7i −0.428491 0.742168i
\(144\) 5.20613e6 6.63457e6i 0.145294 0.185159i
\(145\) −2.78515e7 + 4.82402e7i −0.758684 + 1.31408i
\(146\) −5.26610e6 2.98656e7i −0.140041 0.794210i
\(147\) 1.44411e7 2.13611e7i 0.374965 0.554643i
\(148\) 1.47110e7 5.35435e6i 0.373014 0.135766i
\(149\) −2.54922e7 + 9.27840e6i −0.631328 + 0.229785i −0.637809 0.770194i \(-0.720159\pi\)
0.00648111 + 0.999979i \(0.497937\pi\)
\(150\) −1.48159e7 3.04588e7i −0.358434 0.736875i
\(151\) −9.77375e6 5.54297e7i −0.231016 1.31016i −0.850844 0.525418i \(-0.823909\pi\)
0.619828 0.784738i \(-0.287202\pi\)
\(152\) −1.83084e6 + 3.17111e6i −0.0422861 + 0.0732418i
\(153\) 3.15890e7 6.64464e6i 0.713043 0.149986i
\(154\) 3.45758e7 + 5.98870e7i 0.762868 + 1.32133i
\(155\) 5.08236e7 4.26461e7i 1.09624 0.919853i
\(156\) 8.80572e6 + 8.52160e6i 0.185707 + 0.179715i
\(157\) 2.82266e6 1.60081e7i 0.0582116 0.330134i −0.941770 0.336259i \(-0.890838\pi\)
0.999981 + 0.00612431i \(0.00194944\pi\)
\(158\) 3.79763e7 + 3.18659e7i 0.765973 + 0.642727i
\(159\) −3.20158e7 1.42950e7i −0.631648 0.282028i
\(160\) 6.39931e7 + 2.32916e7i 1.23513 + 0.449551i
\(161\) −1.19837e6 −0.0226308
\(162\) −1.67952e7 + 3.40687e7i −0.310372 + 0.629584i
\(163\) −6.74542e7 −1.21998 −0.609990 0.792409i \(-0.708827\pi\)
−0.609990 + 0.792409i \(0.708827\pi\)
\(164\) −1.00260e7 3.64917e6i −0.177490 0.0646012i
\(165\) 1.30491e8 + 5.82637e7i 2.26145 + 1.00973i
\(166\) 2.28214e7 + 1.91494e7i 0.387225 + 0.324920i
\(167\) 7.11829e6 4.03698e7i 0.118268 0.670733i −0.866812 0.498636i \(-0.833835\pi\)
0.985080 0.172097i \(-0.0550543\pi\)
\(168\) −6.03750e7 5.84270e7i −0.982370 0.950673i
\(169\) −3.55939e7 + 2.98668e7i −0.567246 + 0.475976i
\(170\) −2.41169e7 4.17716e7i −0.376487 0.652094i
\(171\) 1.62563e6 4.96740e6i 0.0248620 0.0759701i
\(172\) 3.31062e7 5.73415e7i 0.496089 0.859250i
\(173\) 8.83323e6 + 5.00957e7i 0.129705 + 0.735596i 0.978401 + 0.206715i \(0.0662772\pi\)
−0.848696 + 0.528881i \(0.822612\pi\)
\(174\) −2.19906e7 4.52088e7i −0.316457 0.650579i
\(175\) −1.00491e8 + 3.65758e7i −1.41741 + 0.515894i
\(176\) 2.69094e7 9.79422e6i 0.372057 0.135418i
\(177\) 7.54771e6 1.11645e7i 0.102308 0.151332i
\(178\) −1.13657e7 6.44583e7i −0.151053 0.856661i
\(179\) 9.62002e6 1.66624e7i 0.125369 0.217146i −0.796508 0.604628i \(-0.793322\pi\)
0.921877 + 0.387482i \(0.126655\pi\)
\(180\) −5.78502e7 8.25512e6i −0.739351 0.105504i
\(181\) 1.22175e7 + 2.11614e7i 0.153147 + 0.265258i 0.932383 0.361473i \(-0.117726\pi\)
−0.779236 + 0.626731i \(0.784393\pi\)
\(182\) −2.87852e7 + 2.41537e7i −0.353932 + 0.296984i
\(183\) −1.05798e8 + 3.02160e7i −1.27614 + 0.364467i
\(184\) −271914. + 1.54210e6i −0.00321788 + 0.0182495i
\(185\) 7.59982e7 + 6.37701e7i 0.882475 + 0.740484i
\(186\) 6.19604e6 + 5.95572e7i 0.0706023 + 0.678639i
\(187\) 1.03001e8 + 3.74892e7i 1.15185 + 0.419238i
\(188\) −6.75996e7 −0.741979
\(189\) 1.01500e8 + 6.38728e7i 1.09358 + 0.688177i
\(190\) −7.80974e6 −0.0826036
\(191\) −1.06937e8 3.89219e7i −1.11048 0.404182i −0.279311 0.960201i \(-0.590106\pi\)
−0.831170 + 0.556019i \(0.812328\pi\)
\(192\) −6.84506e7 + 4.96218e7i −0.697948 + 0.505962i
\(193\) 2.99836e7 + 2.51592e7i 0.300215 + 0.251910i 0.780434 0.625238i \(-0.214998\pi\)
−0.480219 + 0.877149i \(0.659443\pi\)
\(194\) 1.19655e7 6.78594e7i 0.117658 0.667274i
\(195\) −1.88661e7 + 7.53283e7i −0.182205 + 0.727507i
\(196\) −2.74258e7 + 2.30130e7i −0.260173 + 0.218311i
\(197\) −2.08522e7 3.61170e7i −0.194321 0.336573i 0.752357 0.658756i \(-0.228917\pi\)
−0.946678 + 0.322182i \(0.895584\pi\)
\(198\) −1.09524e8 + 6.81163e7i −1.00272 + 0.623624i
\(199\) 6.83716e7 1.18423e8i 0.615021 1.06525i −0.375360 0.926879i \(-0.622481\pi\)
0.990381 0.138368i \(-0.0441857\pi\)
\(200\) 2.42652e7 + 1.37615e8i 0.214476 + 1.21635i
\(201\) −1.47089e8 1.04418e7i −1.27760 0.0906961i
\(202\) 7.98645e7 2.90683e7i 0.681748 0.248136i
\(203\) −1.49155e8 + 5.42879e7i −1.25141 + 0.455477i
\(204\) −4.47085e7 3.17384e6i −0.368710 0.0261746i
\(205\) −1.17410e7 6.65868e7i −0.0951850 0.539821i
\(206\) −1.66895e7 + 2.89071e7i −0.133018 + 0.230393i
\(207\) −73280.1 2.23393e6i −0.000574235 0.0175055i
\(208\) 7.78041e6 + 1.34761e7i 0.0599488 + 0.103834i
\(209\) 1.35955e7 1.14080e7i 0.103011 0.0864363i
\(210\) 4.35348e7 1.73825e8i 0.324391 1.29522i
\(211\) 3.09369e6 1.75452e7i 0.0226719 0.128579i −0.971371 0.237567i \(-0.923650\pi\)
0.994043 + 0.108988i \(0.0347611\pi\)
\(212\) 3.72940e7 + 3.12933e7i 0.268821 + 0.225567i
\(213\) 7.33504e7 5.31738e7i 0.520084 0.377024i
\(214\) −9.48479e7 3.45218e7i −0.661575 0.240794i
\(215\) 4.19597e8 2.87938
\(216\) 1.05224e8 1.16121e8i 0.710441 0.784009i
\(217\) 1.89053e8 1.25596
\(218\) 1.51851e8 + 5.52692e7i 0.992704 + 0.361315i
\(219\) −1.84794e7 1.77626e8i −0.118886 1.14275i
\(220\) −1.52004e8 1.27546e8i −0.962442 0.807585i
\(221\) −1.03428e7 + 5.86571e7i −0.0644564 + 0.365551i
\(222\) −8.60959e7 + 2.45891e7i −0.528137 + 0.150837i
\(223\) −9.93408e7 + 8.33569e7i −0.599875 + 0.503355i −0.891405 0.453207i \(-0.850280\pi\)
0.291530 + 0.956562i \(0.405836\pi\)
\(224\) 9.70264e7 + 1.68055e8i 0.576795 + 0.999039i
\(225\) −7.43275e7 1.85093e8i −0.435022 1.08331i
\(226\) −9.24171e6 + 1.60071e7i −0.0532565 + 0.0922430i
\(227\) −3.02196e7 1.71384e8i −0.171474 0.972479i −0.942135 0.335233i \(-0.891185\pi\)
0.770661 0.637245i \(-0.219926\pi\)
\(228\) −4.06452e6 + 6.01218e6i −0.0227111 + 0.0335938i
\(229\) 9.95192e7 3.62220e7i 0.547624 0.199319i −0.0533664 0.998575i \(-0.516995\pi\)
0.600991 + 0.799256i \(0.294773\pi\)
\(230\) −3.13836e6 + 1.14227e6i −0.0170081 + 0.00619044i
\(231\) 1.78126e8 + 3.66194e8i 0.950790 + 1.95465i
\(232\) 3.60157e7 + 2.04255e8i 0.189358 + 1.07390i
\(233\) −5.72793e7 + 9.92107e7i −0.296655 + 0.513822i −0.975369 0.220581i \(-0.929205\pi\)
0.678713 + 0.734403i \(0.262538\pi\)
\(234\) −4.67861e7 5.21828e7i −0.238705 0.266239i
\(235\) −2.14194e8 3.70996e8i −1.07664 1.86480i
\(236\) −1.43342e7 + 1.20278e7i −0.0709873 + 0.0595654i
\(237\) 2.09785e8 + 2.03016e8i 1.02366 + 0.990630i
\(238\) 2.38668e7 1.35355e8i 0.114756 0.650812i
\(239\) 1.12338e8 + 9.42625e7i 0.532271 + 0.446628i 0.868885 0.495014i \(-0.164837\pi\)
−0.336614 + 0.941643i \(0.609282\pi\)
\(240\) −6.77586e7 3.02540e7i −0.316392 0.141268i
\(241\) 1.05544e7 + 3.84149e6i 0.0485706 + 0.0176783i 0.366191 0.930540i \(-0.380662\pi\)
−0.317621 + 0.948218i \(0.602884\pi\)
\(242\) −2.83202e8 −1.28453
\(243\) −1.12861e8 + 1.93116e8i −0.504572 + 0.863369i
\(244\) 1.52774e8 0.673263
\(245\) −2.13199e8 7.75981e7i −0.926198 0.337108i
\(246\) 5.57214e7 + 2.48794e7i 0.238643 + 0.106553i
\(247\) 7.38769e6 + 6.19901e6i 0.0311939 + 0.0261748i
\(248\) 4.28968e7 2.43280e8i 0.178585 1.01280i
\(249\) 1.26067e8 + 1.22000e8i 0.517494 + 0.500797i
\(250\) −3.27369e7 + 2.74695e7i −0.132509 + 0.111189i
\(251\) −2.31229e6 4.00501e6i −0.00922964 0.0159862i 0.861374 0.507972i \(-0.169605\pi\)
−0.870603 + 0.491986i \(0.836271\pi\)
\(252\) −1.11159e8 1.23980e8i −0.437563 0.488035i
\(253\) 3.79482e6 6.57283e6i 0.0147323 0.0255170i
\(254\) 3.72348e7 + 2.11169e8i 0.142571 + 0.808561i
\(255\) −1.24244e8 2.55423e8i −0.469229 0.964649i
\(256\) 2.68391e8 9.76864e7i 0.999835 0.363910i
\(257\) 1.44716e8 5.26723e7i 0.531802 0.193560i −0.0621405 0.998067i \(-0.519793\pi\)
0.593943 + 0.804507i \(0.297570\pi\)
\(258\) −2.12097e8 + 3.13730e8i −0.768892 + 1.13733i
\(259\) 4.90899e7 + 2.78403e8i 0.175567 + 0.995690i
\(260\) 5.39118e7 9.33780e7i 0.190229 0.329487i
\(261\) −1.10321e8 2.74726e8i −0.384076 0.956441i
\(262\) −1.49293e8 2.58583e8i −0.512843 0.888270i
\(263\) −4.34720e8 + 3.64774e8i −1.47355 + 1.23646i −0.560790 + 0.827958i \(0.689503\pi\)
−0.912760 + 0.408497i \(0.866053\pi\)
\(264\) 5.11648e8 1.46127e8i 1.71142 0.488785i
\(265\) −5.35734e7 + 3.03830e8i −0.176843 + 1.00293i
\(266\) −1.70476e7 1.43046e7i −0.0555363 0.0466005i
\(267\) −3.98837e7 3.83368e8i −0.128235 1.23261i
\(268\) 1.92399e8 + 7.00274e7i 0.610563 + 0.222227i
\(269\) 5.48496e7 0.171807 0.0859034 0.996303i \(-0.472622\pi\)
0.0859034 + 0.996303i \(0.472622\pi\)
\(270\) 3.26697e8 + 7.05256e7i 1.01012 + 0.218059i
\(271\) −3.42655e8 −1.04584 −0.522919 0.852382i \(-0.675157\pi\)
−0.522919 + 0.852382i \(0.675157\pi\)
\(272\) −5.34842e7 1.94666e7i −0.161151 0.0586543i
\(273\) −1.79156e8 + 1.29875e8i −0.532921 + 0.386329i
\(274\) 1.16593e8 + 9.78331e7i 0.342409 + 0.287315i
\(275\) 1.17610e8 6.66998e8i 0.341019 1.93402i
\(276\) −753983. + 3.01049e6i −0.00215864 + 0.00861898i
\(277\) −3.21375e8 + 2.69666e8i −0.908517 + 0.762336i −0.971836 0.235657i \(-0.924276\pi\)
0.0633195 + 0.997993i \(0.479831\pi\)
\(278\) −7.00624e7 1.21352e8i −0.195582 0.338758i
\(279\) 1.15606e7 + 3.52422e8i 0.0318688 + 0.971513i
\(280\) −3.69638e8 + 6.40232e8i −1.00629 + 1.74295i
\(281\) −7.23299e7 4.10203e8i −0.194467 1.10288i −0.913176 0.407565i \(-0.866378\pi\)
0.718709 0.695311i \(-0.244733\pi\)
\(282\) 3.85662e8 + 2.73780e7i 1.02408 + 0.0726992i
\(283\) −2.06159e8 + 7.50356e7i −0.540691 + 0.196795i −0.597906 0.801566i \(-0.704000\pi\)
0.0572147 + 0.998362i \(0.481778\pi\)
\(284\) −1.18207e8 + 4.30237e7i −0.306216 + 0.111454i
\(285\) −4.58744e7 3.25660e6i −0.117385 0.00833313i
\(286\) −4.13254e7 2.34368e8i −0.104457 0.592403i
\(287\) 9.63339e7 1.66855e8i 0.240543 0.416633i
\(288\) −3.07345e8 + 1.91148e8i −0.758144 + 0.471514i
\(289\) 9.62397e7 + 1.66692e8i 0.234537 + 0.406230i
\(290\) −3.38869e8 + 2.84345e8i −0.815904 + 0.684624i
\(291\) 9.85819e7 3.93617e8i 0.234516 0.936371i
\(292\) −4.30586e7 + 2.44197e8i −0.101209 + 0.573986i
\(293\) −2.69906e8 2.26478e8i −0.626868 0.526005i 0.273086 0.961990i \(-0.411956\pi\)
−0.899954 + 0.435985i \(0.856400\pi\)
\(294\) 1.65787e8 1.20183e8i 0.380482 0.275822i
\(295\) −1.11429e8 4.05569e7i −0.252709 0.0919787i
\(296\) 3.69396e8 0.827888
\(297\) −6.71746e8 + 3.54444e8i −1.48784 + 0.785056i
\(298\) −2.15437e8 −0.471589
\(299\) 3.87544e6 + 1.41055e6i 0.00838440 + 0.00305167i
\(300\) 2.86578e7 + 2.75462e8i 0.0612799 + 0.589031i
\(301\) 9.15924e8 + 7.68551e8i 1.93587 + 1.62439i
\(302\) 7.76176e7 4.40191e8i 0.162157 0.919638i
\(303\) 4.81245e8 1.37444e8i 0.993842 0.283842i
\(304\) −7.05958e6 + 5.92369e6i −0.0144119 + 0.0120930i
\(305\) 4.84076e8 + 8.38444e8i 0.976931 + 1.69209i
\(306\) 2.53781e8 + 3.62141e7i 0.506330 + 0.0722525i
\(307\) 1.62919e8 2.82183e8i 0.321356 0.556605i −0.659412 0.751782i \(-0.729195\pi\)
0.980768 + 0.195177i \(0.0625280\pi\)
\(308\) −9.81844e7 5.56832e8i −0.191476 1.08592i
\(309\) −1.10088e8 + 1.62841e8i −0.212269 + 0.313985i
\(310\) 4.95104e8 1.80203e8i 0.943910 0.343555i
\(311\) −7.80914e8 + 2.84230e8i −1.47212 + 0.535806i −0.948674 0.316255i \(-0.897574\pi\)
−0.523442 + 0.852061i \(0.675352\pi\)
\(312\) 1.26477e8 + 2.60014e8i 0.235760 + 0.484680i
\(313\) −6.41430e7 3.63773e8i −0.118234 0.670541i −0.985098 0.171995i \(-0.944979\pi\)
0.866863 0.498546i \(-0.166132\pi\)
\(314\) 6.45442e7 1.11794e8i 0.117653 0.203781i
\(315\) 3.28207e8 1.00289e9i 0.591645 1.80787i
\(316\) −2.02675e8 3.51043e8i −0.361322 0.625828i
\(317\) 2.87148e8 2.40946e8i 0.506290 0.424827i −0.353532 0.935423i \(-0.615019\pi\)
0.859821 + 0.510595i \(0.170575\pi\)
\(318\) −2.00091e8 1.93635e8i −0.348926 0.337668i
\(319\) 1.74563e8 9.89996e8i 0.301082 1.70752i
\(320\) 5.69875e8 + 4.78182e8i 0.972198 + 0.815771i
\(321\) −5.42741e8 2.42332e8i −0.915851 0.408924i
\(322\) −8.94284e6 3.25493e6i −0.0149273 0.00543308i
\(323\) −3.52746e7 −0.0582442
\(324\) 2.24320e8 2.14797e8i 0.366404 0.350849i
\(325\) 3.68033e8 0.594696
\(326\) −5.03378e8 1.83215e8i −0.804697 0.292886i
\(327\) 8.68925e8 + 3.87972e8i 1.37425 + 0.613597i
\(328\) −1.92856e8 1.61826e8i −0.301770 0.253215i
\(329\) 2.11973e8 1.20216e9i 0.328167 1.86113i
\(330\) 8.15538e8 + 7.89224e8i 1.24924 + 1.20893i
\(331\) −2.26648e8 + 1.90180e8i −0.343521 + 0.288249i −0.798182 0.602416i \(-0.794205\pi\)
0.454661 + 0.890665i \(0.349760\pi\)
\(332\) −1.21795e8 2.10954e8i −0.182660 0.316377i
\(333\) −5.15980e8 + 1.08535e8i −0.765735 + 0.161070i
\(334\) 1.62770e8 2.81926e8i 0.239035 0.414021i
\(335\) 2.25310e8 + 1.27780e9i 0.327434 + 1.85697i
\(336\) −9.24934e7 1.90150e8i −0.133022 0.273469i
\(337\) −5.31072e8 + 1.93295e8i −0.755873 + 0.275115i −0.691075 0.722783i \(-0.742863\pi\)
−0.0647983 + 0.997898i \(0.520640\pi\)
\(338\) −3.46742e8 + 1.26204e8i −0.488425 + 0.177772i
\(339\) −6.09606e7 + 9.01720e7i −0.0849866 + 0.125711i
\(340\) 6.84844e7 + 3.88394e8i 0.0944964 + 0.535916i
\(341\) −5.98667e8 + 1.03692e9i −0.817607 + 1.41614i
\(342\) 2.56234e7 3.26539e7i 0.0346374 0.0441411i
\(343\) 1.59576e8 + 2.76393e8i 0.213519 + 0.369826i
\(344\) 1.19682e9 1.00425e9i 1.58517 1.33011i
\(345\) −1.89110e7 + 5.40102e6i −0.0247941 + 0.00708123i
\(346\) −7.01485e7 + 3.97832e8i −0.0910442 + 0.516337i
\(347\) 5.68368e8 + 4.76918e8i 0.730259 + 0.612760i 0.930202 0.367048i \(-0.119631\pi\)
−0.199944 + 0.979807i \(0.564076\pi\)
\(348\) 4.25355e7 + 4.08857e8i 0.0541033 + 0.520049i
\(349\) −1.99505e8 7.26137e7i −0.251226 0.0914386i 0.213338 0.976978i \(-0.431566\pi\)
−0.464563 + 0.885540i \(0.653789\pi\)
\(350\) −8.49261e8 −1.05877
\(351\) −2.53062e8 3.26031e8i −0.312357 0.402424i
\(352\) −1.22900e9 −1.50194
\(353\) 1.12513e9 + 4.09516e8i 1.36142 + 0.495517i 0.916494 0.400048i \(-0.131007\pi\)
0.444929 + 0.895566i \(0.353229\pi\)
\(354\) 8.66490e7 6.28143e7i 0.103813 0.0752570i
\(355\) −6.10667e8 5.12411e8i −0.724445 0.607881i
\(356\) −9.29327e7 + 5.27047e8i −0.109168 + 0.619120i
\(357\) 1.96635e8 7.85123e8i 0.228730 0.913270i
\(358\) 1.17047e8 9.82138e7i 0.134824 0.113131i
\(359\) 6.38946e7 + 1.10669e8i 0.0728842 + 0.126239i 0.900164 0.435551i \(-0.143446\pi\)
−0.827280 + 0.561790i \(0.810113\pi\)
\(360\) −1.21609e9 6.49908e8i −1.37374 0.734164i
\(361\) 4.44080e8 7.69169e8i 0.496805 0.860492i
\(362\) 3.36963e7 + 1.91101e8i 0.0373338 + 0.211731i
\(363\) −1.66353e9 1.18093e8i −1.82540 0.129584i
\(364\) 2.88717e8 1.05084e8i 0.313774 0.114205i
\(365\) −1.47662e9 + 5.37447e8i −1.58944 + 0.578509i
\(366\) −8.71589e8 6.18738e7i −0.929240 0.0659664i
\(367\) 1.94065e8 + 1.10060e9i 0.204935 + 1.16224i 0.897542 + 0.440929i \(0.145351\pi\)
−0.692607 + 0.721315i \(0.743538\pi\)
\(368\) −1.97050e6 + 3.41300e6i −0.00206115 + 0.00357001i
\(369\) 3.16933e8 + 1.69377e8i 0.328379 + 0.175494i
\(370\) 3.93929e8 + 6.82306e8i 0.404308 + 0.700282i
\(371\) −6.73450e8 + 5.65091e8i −0.684694 + 0.574526i
\(372\) 1.18947e8 4.74932e8i 0.119799 0.478334i
\(373\) 9.72250e7 5.51391e8i 0.0970057 0.550147i −0.897109 0.441810i \(-0.854337\pi\)
0.994114 0.108336i \(-0.0345524\pi\)
\(374\) 6.66819e8 + 5.59528e8i 0.659109 + 0.553058i
\(375\) −2.03751e8 + 1.47705e8i −0.199522 + 0.144639i
\(376\) −1.49888e9 5.45548e8i −1.45415 0.529268i
\(377\) 5.46256e8 0.525051
\(378\) 5.83957e8 + 7.52339e8i 0.556109 + 0.716460i
\(379\) 1.60910e9 1.51826 0.759131 0.650938i \(-0.225624\pi\)
0.759131 + 0.650938i \(0.225624\pi\)
\(380\) 6.00057e7 + 2.18403e7i 0.0560983 + 0.0204181i
\(381\) 1.30661e8 + 1.25593e9i 0.121035 + 1.16340i
\(382\) −6.92301e8 5.80910e8i −0.635438 0.533196i
\(383\) 2.96979e6 1.68425e7i 0.00270104 0.0153183i −0.983427 0.181302i \(-0.941969\pi\)
0.986128 + 0.165984i \(0.0530799\pi\)
\(384\) 3.06965e8 8.76695e7i 0.276649 0.0790113i
\(385\) 2.74486e9 2.30321e9i 2.45137 2.05694i
\(386\) 1.55417e8 + 2.69190e8i 0.137544 + 0.238234i
\(387\) −1.37668e9 + 1.75441e9i −1.20738 + 1.53866i
\(388\) −2.81708e8 + 4.87933e8i −0.244843 + 0.424081i
\(389\) 2.70902e7 + 1.53636e8i 0.0233340 + 0.132334i 0.994249 0.107089i \(-0.0341530\pi\)
−0.970915 + 0.239423i \(0.923042\pi\)
\(390\) −3.45390e8 + 5.10895e8i −0.294838 + 0.436120i
\(391\) −1.41752e7 + 5.15934e6i −0.0119925 + 0.00436491i
\(392\) −7.93831e8 + 2.88931e8i −0.665621 + 0.242266i
\(393\) −7.69119e8 1.58117e9i −0.639174 1.31403i
\(394\) −5.75109e7 3.26161e8i −0.0473711 0.268655i
\(395\) 1.28438e9 2.22461e9i 1.04859 1.81620i
\(396\) 1.03201e9 2.17080e8i 0.835123 0.175666i
\(397\) 2.55273e8 + 4.42146e8i 0.204757 + 0.354649i 0.950055 0.312082i \(-0.101026\pi\)
−0.745299 + 0.666731i \(0.767693\pi\)
\(398\) 8.31876e8 6.98027e8i 0.661406 0.554985i
\(399\) −9.41725e7 9.11340e7i −0.0742197 0.0718250i
\(400\) −6.10700e7 + 3.46345e8i −0.0477109 + 0.270582i
\(401\) 1.34601e9 + 1.12943e9i 1.04242 + 0.874692i 0.992276 0.124050i \(-0.0395884\pi\)
0.0501412 + 0.998742i \(0.484033\pi\)
\(402\) −1.06929e9 4.77435e8i −0.820927 0.366541i
\(403\) −6.11385e8 2.22526e8i −0.465315 0.169361i
\(404\) −6.94926e8 −0.524329
\(405\) 1.88961e9 + 5.50498e8i 1.41345 + 0.411778i
\(406\) −1.26052e9 −0.934780
\(407\) −1.68244e9 6.12357e8i −1.23697 0.450219i
\(408\) −9.65706e8 4.31184e8i −0.703938 0.314306i
\(409\) 9.54709e8 + 8.01096e8i 0.689985 + 0.578966i 0.918905 0.394479i \(-0.129075\pi\)
−0.228920 + 0.973445i \(0.573519\pi\)
\(410\) 9.32408e7 5.28795e8i 0.0668132 0.378917i
\(411\) 6.44071e8 + 6.23290e8i 0.457601 + 0.442837i
\(412\) 2.09073e8 1.75433e8i 0.147285 0.123587i
\(413\) −1.68949e8 2.92628e8i −0.118013 0.204405i
\(414\) 5.52080e6 1.68698e7i 0.00382385 0.0116844i
\(415\) 7.71831e8 1.33685e9i 0.530095 0.918151i
\(416\) −1.15967e8 6.57682e8i −0.0789784 0.447909i
\(417\) −3.60944e8 7.42035e8i −0.243761 0.501128i
\(418\) 1.32442e8 4.82049e7i 0.0886969 0.0322830i
\(419\) 2.14322e9 7.80069e8i 1.42337 0.518065i 0.488347 0.872650i \(-0.337600\pi\)
0.935024 + 0.354585i \(0.115378\pi\)
\(420\) −8.20607e8 + 1.21383e9i −0.540459 + 0.799439i
\(421\) −2.54639e8 1.44413e9i −0.166318 0.943234i −0.947695 0.319176i \(-0.896594\pi\)
0.781378 0.624058i \(-0.214517\pi\)
\(422\) 7.07417e7 1.22528e8i 0.0458228 0.0793675i
\(423\) 2.25396e9 + 3.21636e8i 1.44795 + 0.206621i
\(424\) 5.74370e8 + 9.94838e8i 0.365941 + 0.633829i
\(425\) −1.03121e9 + 8.65290e8i −0.651609 + 0.546765i
\(426\) 6.91805e8 1.97580e8i 0.433561 0.123825i
\(427\) −4.79056e8 + 2.71686e9i −0.297775 + 1.68877i
\(428\) 6.32217e8 + 5.30493e8i 0.389774 + 0.327059i
\(429\) −1.45015e8 1.39391e9i −0.0886776 0.852381i
\(430\) 3.13125e9 + 1.13968e9i 1.89923 + 0.691264i
\(431\) −2.14893e8 −0.129286 −0.0646431 0.997908i \(-0.520591\pi\)
−0.0646431 + 0.997908i \(0.520591\pi\)
\(432\) 3.48810e8 1.84049e8i 0.208159 0.109835i
\(433\) 3.25358e7 0.0192599 0.00962993 0.999954i \(-0.496935\pi\)
0.00962993 + 0.999954i \(0.496935\pi\)
\(434\) 1.41081e9 + 5.13494e8i 0.828429 + 0.301523i
\(435\) −2.10909e9 + 1.52894e9i −1.22852 + 0.890588i
\(436\) −1.01218e9 8.49317e8i −0.584862 0.490758i
\(437\) −424130. + 2.40536e6i −0.000243116 + 0.00137878i
\(438\) 3.44554e8 1.37573e9i 0.195928 0.782300i
\(439\) −5.87509e7 + 4.92978e7i −0.0331427 + 0.0278101i −0.659209 0.751960i \(-0.729109\pi\)
0.626066 + 0.779770i \(0.284664\pi\)
\(440\) −2.34103e9 4.05479e9i −1.31016 2.26926i
\(441\) 1.02395e9 6.36826e8i 0.568516 0.353578i
\(442\) −2.36504e8 + 4.09636e8i −0.130275 + 0.225642i
\(443\) 1.72570e8 + 9.78692e8i 0.0943087 + 0.534851i 0.994957 + 0.100302i \(0.0319810\pi\)
−0.900648 + 0.434549i \(0.856908\pi\)
\(444\) 7.30278e8 + 5.18421e7i 0.395957 + 0.0281088i
\(445\) −3.18697e9 + 1.15996e9i −1.71442 + 0.623999i
\(446\) −9.67740e8 + 3.52229e8i −0.516519 + 0.187998i
\(447\) −1.26548e9 8.98357e7i −0.670159 0.0475743i
\(448\) 3.68102e8 + 2.08761e9i 0.193417 + 1.09692i
\(449\) −9.08229e8 + 1.57310e9i −0.473514 + 0.820151i −0.999540 0.0303177i \(-0.990348\pi\)
0.526026 + 0.850468i \(0.323681\pi\)
\(450\) −5.19322e7 1.58314e9i −0.0268654 0.818986i
\(451\) 6.10113e8 + 1.05675e9i 0.313179 + 0.542441i
\(452\) 1.15773e8 9.71450e7i 0.0589688 0.0494807i
\(453\) 6.39482e8 2.55332e9i 0.323210 1.29051i
\(454\) 2.39987e8 1.36104e9i 0.120363 0.682612i
\(455\) 1.49154e9 + 1.25155e9i 0.742326 + 0.622885i
\(456\) −1.38642e8 + 1.00506e8i −0.0684730 + 0.0496380i
\(457\) −2.07512e9 7.55280e8i −1.01703 0.370170i −0.220904 0.975296i \(-0.570901\pi\)
−0.796130 + 0.605125i \(0.793123\pi\)
\(458\) 8.41047e8 0.409064
\(459\) 1.47561e9 + 3.18546e8i 0.712240 + 0.153755i
\(460\) 2.73079e7 0.0130808
\(461\) −2.68736e8 9.78120e7i −0.127754 0.0464985i 0.277352 0.960768i \(-0.410543\pi\)
−0.405106 + 0.914270i \(0.632765\pi\)
\(462\) 3.34633e8 + 3.21654e9i 0.157878 + 1.51755i
\(463\) −3.05563e9 2.56397e9i −1.43076 1.20055i −0.945262 0.326312i \(-0.894194\pi\)
−0.485497 0.874238i \(-0.661361\pi\)
\(464\) −9.06435e7 + 5.14065e8i −0.0421235 + 0.238894i
\(465\) 2.98338e9 8.52058e8i 1.37602 0.392992i
\(466\) −6.96917e8 + 5.84783e8i −0.319029 + 0.267697i
\(467\) −4.82347e8 8.35449e8i −0.219154 0.379587i 0.735395 0.677638i \(-0.236997\pi\)
−0.954550 + 0.298052i \(0.903663\pi\)
\(468\) 2.13547e8 + 5.31784e8i 0.0963016 + 0.239814i
\(469\) −1.84864e9 + 3.20194e9i −0.827462 + 1.43321i
\(470\) −5.90755e8 3.35034e9i −0.262461 1.48849i
\(471\) 4.25750e8 6.29762e8i 0.187751 0.277718i
\(472\) −4.14898e8 + 1.51011e8i −0.181612 + 0.0661014i
\(473\) −7.11577e9 + 2.58993e9i −3.09178 + 1.12531i
\(474\) 1.01410e9 + 2.08481e9i 0.437379 + 0.899173i
\(475\) 3.78486e7 + 2.14650e8i 0.0162040 + 0.0918975i
\(476\) −5.61906e8 + 9.73250e8i −0.238803 + 0.413618i
\(477\) −1.09459e9 1.22085e9i −0.461783 0.515049i
\(478\) 5.82291e8 + 1.00856e9i 0.243861 + 0.422380i
\(479\) 1.59895e9 1.34168e9i 0.664755 0.557796i −0.246753 0.969078i \(-0.579364\pi\)
0.911508 + 0.411283i \(0.134919\pi\)
\(480\) 2.28856e9 + 2.21472e9i 0.944534 + 0.914058i
\(481\) 1.68942e8 9.58116e8i 0.0692196 0.392564i
\(482\) 6.83283e7 + 5.73343e7i 0.0277930 + 0.0233211i
\(483\) −5.11729e7 2.28485e7i −0.0206645 0.00922664i
\(484\) 2.17597e9 + 7.91988e8i 0.872357 + 0.317512i
\(485\) −3.57045e9 −1.42111
\(486\) −1.36676e9 + 1.13458e9i −0.540088 + 0.448343i
\(487\) 3.84291e9 1.50768 0.753839 0.657059i \(-0.228200\pi\)
0.753839 + 0.657059i \(0.228200\pi\)
\(488\) 3.38745e9 + 1.23293e9i 1.31948 + 0.480252i
\(489\) −2.88044e9 1.28611e9i −1.11398 0.497389i
\(490\) −1.38023e9 1.15815e9i −0.529988 0.444713i
\(491\) 4.53422e8 2.57149e9i 0.172869 0.980390i −0.767705 0.640803i \(-0.778602\pi\)
0.940575 0.339587i \(-0.110287\pi\)
\(492\) −3.58556e8 3.46987e8i −0.135731 0.131352i
\(493\) −1.53058e9 + 1.28431e9i −0.575298 + 0.482733i
\(494\) 3.82934e7 + 6.63261e7i 0.0142915 + 0.0247537i
\(495\) 4.46137e9 + 4.97597e9i 1.65329 + 1.84400i
\(496\) 3.10863e8 5.38431e8i 0.114389 0.198127i
\(497\) −3.94451e8 2.23704e9i −0.144127 0.817386i
\(498\) 6.09412e8 + 1.25284e9i 0.221110 + 0.454562i
\(499\) 8.22020e8 2.99191e8i 0.296163 0.107794i −0.189665 0.981849i \(-0.560740\pi\)
0.485828 + 0.874054i \(0.338518\pi\)
\(500\) 3.28352e8 1.19510e8i 0.117475 0.0427573i
\(501\) 1.07367e9 1.58816e9i 0.381452 0.564238i
\(502\) −6.37738e6 3.61679e7i −0.00224998 0.0127603i
\(503\) 7.41112e8 1.28364e9i 0.259654 0.449735i −0.706495 0.707718i \(-0.749725\pi\)
0.966149 + 0.257984i \(0.0830580\pi\)
\(504\) −1.46415e9 3.64609e9i −0.509424 1.26859i
\(505\) −2.20193e9 3.81385e9i −0.760822 1.31778i
\(506\) 4.61716e7 3.87425e7i 0.0158434 0.0132942i
\(507\) −2.08939e9 + 5.96731e8i −0.712018 + 0.203353i
\(508\) 3.04453e8 1.72664e9i 0.103038 0.584357i
\(509\) −1.10451e9 9.26796e8i −0.371243 0.311510i 0.438010 0.898970i \(-0.355683\pi\)
−0.809253 + 0.587460i \(0.800128\pi\)
\(510\) −2.33409e8 2.24356e9i −0.0779151 0.748931i
\(511\) −4.20767e9 1.53147e9i −1.39498 0.507732i
\(512\) 1.39442e9 0.459145
\(513\) 1.64128e8 1.81124e8i 0.0536751 0.0592332i
\(514\) 1.22301e9 0.397245
\(515\) 1.62527e9 + 5.91549e8i 0.524323 + 0.190838i
\(516\) 2.50700e9 1.81739e9i 0.803304 0.582338i
\(517\) 5.92237e9 + 4.96946e9i 1.88486 + 1.58158i
\(518\) −3.89844e8 + 2.21092e9i −0.123236 + 0.698905i
\(519\) −5.77945e8 + 2.30761e9i −0.181468 + 0.724565i
\(520\) 1.94897e9 1.63538e9i 0.607846 0.510043i
\(521\) 1.85636e9 + 3.21531e9i 0.575083 + 0.996073i 0.996033 + 0.0889887i \(0.0283635\pi\)
−0.420950 + 0.907084i \(0.638303\pi\)
\(522\) −7.70807e7 2.34979e9i −0.0237192 0.723074i
\(523\) −2.61830e9 + 4.53503e9i −0.800321 + 1.38620i 0.119085 + 0.992884i \(0.462004\pi\)
−0.919405 + 0.393312i \(0.871329\pi\)
\(524\) 4.23945e8 + 2.40431e9i 0.128721 + 0.730014i
\(525\) −4.98856e9 3.54136e8i −1.50459 0.106810i
\(526\) −4.23488e9 + 1.54137e9i −1.26879 + 0.461803i
\(527\) 2.23626e9 8.13932e8i 0.665557 0.242243i
\(528\) 1.33583e9 + 9.48301e7i 0.394941 + 0.0280367i
\(529\) −5.91060e8 3.35207e9i −0.173595 0.984506i
\(530\) −1.22503e9 + 2.12182e9i −0.357423 + 0.619074i
\(531\) 5.35169e8 3.32839e8i 0.155117 0.0964724i
\(532\) 9.09807e7 + 1.57583e8i 0.0261974 + 0.0453753i
\(533\) −5.07935e8 + 4.26208e8i −0.145299 + 0.121920i
\(534\) 7.43644e8 2.96921e9i 0.211335 0.843815i
\(535\) −9.08190e8 + 5.15060e9i −0.256412 + 1.45418i
\(536\) 3.70090e9 + 3.10543e9i 1.03808 + 0.871053i
\(537\) 7.28487e8 5.28100e8i 0.203007 0.147166i
\(538\) 4.09315e8 + 1.48979e8i 0.113324 + 0.0412464i
\(539\) 4.09451e9 1.12627
\(540\) −2.31293e9 1.45550e9i −0.632098 0.397773i
\(541\) 2.80583e9 0.761851 0.380926 0.924606i \(-0.375605\pi\)
0.380926 + 0.924606i \(0.375605\pi\)
\(542\) −2.55707e9 9.30696e8i −0.689834 0.251079i
\(543\) 1.18244e8 + 1.13658e9i 0.0316942 + 0.304649i
\(544\) 1.87122e9 + 1.57014e9i 0.498344 + 0.418161i
\(545\) 1.45401e9 8.24608e9i 0.384750 2.18203i
\(546\) −1.68971e9 + 4.82585e8i −0.444262 + 0.126882i
\(547\) 2.54860e9 2.13853e9i 0.665802 0.558674i −0.246017 0.969265i \(-0.579122\pi\)
0.911820 + 0.410591i \(0.134678\pi\)
\(548\) −6.22241e8 1.07775e9i −0.161520 0.279761i
\(549\) −5.09391e9 7.26893e8i −1.31386 0.187485i
\(550\) 2.68932e9 4.65803e9i 0.689243 1.19380i
\(551\) 5.61771e7 + 3.18596e8i 0.0143063 + 0.0811353i
\(552\) −4.10136e7 + 6.06666e7i −0.0103787 + 0.0153519i
\(553\) 6.87831e9 2.50350e9i 1.72959 0.629520i
\(554\) −3.13071e9 + 1.13949e9i −0.782274 + 0.284724i
\(555\) 2.02942e9 + 4.17213e9i 0.503903 + 1.03593i
\(556\) 1.98955e8 + 1.12833e9i 0.0490901 + 0.278404i
\(557\) 2.47502e9 4.28686e9i 0.606856 1.05111i −0.384899 0.922959i \(-0.625764\pi\)
0.991755 0.128147i \(-0.0409028\pi\)
\(558\) −8.70954e8 + 2.66135e9i −0.212215 + 0.648460i
\(559\) −2.05741e9 3.56353e9i −0.498171 0.862858i
\(560\) −1.42530e9 + 1.19597e9i −0.342963 + 0.287780i
\(561\) 3.68357e9 + 3.56472e9i 0.880845 + 0.852424i
\(562\) 5.74403e8 3.25760e9i 0.136502 0.774142i
\(563\) −1.46145e9 1.22630e9i −0.345146 0.289612i 0.453691 0.891159i \(-0.350107\pi\)
−0.798838 + 0.601547i \(0.794551\pi\)
\(564\) −2.88665e9 1.28888e9i −0.677512 0.302507i
\(565\) 8.99980e8 + 3.27566e8i 0.209925 + 0.0764063i
\(566\) −1.74227e9 −0.403885
\(567\) 3.11644e9 + 4.66274e9i 0.717990 + 1.07424i
\(568\) −2.96821e9 −0.679634
\(569\) −2.41126e9 8.77625e8i −0.548719 0.199717i 0.0527581 0.998607i \(-0.483199\pi\)
−0.601477 + 0.798890i \(0.705421\pi\)
\(570\) −3.33493e8 1.48903e8i −0.0754265 0.0336777i
\(571\) 7.48290e8 + 6.27890e8i 0.168207 + 0.141142i 0.723005 0.690843i \(-0.242760\pi\)
−0.554799 + 0.831985i \(0.687205\pi\)
\(572\) −3.37899e8 + 1.91632e9i −0.0754921 + 0.428137i
\(573\) −3.82434e9 3.70095e9i −0.849210 0.821810i
\(574\) 1.17209e9 9.83503e8i 0.258685 0.217062i
\(575\) 4.66048e7 + 8.07219e7i 0.0102234 + 0.0177074i
\(576\) −3.86910e9 + 8.13852e8i −0.843589 + 0.177446i
\(577\) −9.22146e8 + 1.59720e9i −0.199841 + 0.346135i −0.948477 0.316847i \(-0.897376\pi\)
0.748636 + 0.662982i \(0.230709\pi\)
\(578\) 2.65432e8 + 1.50534e9i 0.0571750 + 0.324255i
\(579\) 8.00668e8 + 1.64603e9i 0.171426 + 0.352422i
\(580\) 3.39887e9 1.23709e9i 0.723329 0.263270i
\(581\) 4.13343e9 1.50444e9i 0.874367 0.318244i
\(582\) 1.80478e9 2.66961e9i 0.379485 0.561328i
\(583\) −9.66834e8 5.48319e9i −0.202075 1.14602i
\(584\) −2.92548e9 + 5.06708e9i −0.607788 + 1.05272i
\(585\) −2.24186e9 + 2.85697e9i −0.462981 + 0.590012i
\(586\) −1.39903e9 2.42319e9i −0.287201 0.497447i
\(587\) 1.53175e9 1.28529e9i 0.312575 0.262282i −0.472980 0.881073i \(-0.656822\pi\)
0.785556 + 0.618791i \(0.212377\pi\)
\(588\) −1.60991e9 + 4.59793e8i −0.326574 + 0.0932700i
\(589\) 6.69102e7 3.79466e8i 0.0134924 0.0765191i
\(590\) −7.21383e8 6.05312e8i −0.144605 0.121338i
\(591\) −2.01812e8 1.93985e9i −0.0402153 0.386555i
\(592\) 8.73621e8 + 3.17972e8i 0.173060 + 0.0629887i
\(593\) 1.89048e9 0.372290 0.186145 0.982522i \(-0.440401\pi\)
0.186145 + 0.982522i \(0.440401\pi\)
\(594\) −5.97562e9 + 8.20494e8i −1.16985 + 0.160629i
\(595\) −7.12177e9 −1.38605
\(596\) 1.65530e9 + 6.02480e8i 0.320269 + 0.116568i
\(597\) 5.17751e9 3.75332e9i 0.995889 0.721948i
\(598\) 2.50893e7 + 2.10524e7i 0.00479771 + 0.00402576i
\(599\) −9.44111e8 + 5.35432e9i −0.179485 + 1.01791i 0.753353 + 0.657617i \(0.228435\pi\)
−0.932838 + 0.360296i \(0.882676\pi\)
\(600\) −1.58763e9 + 6.33909e9i −0.300069 + 1.19811i
\(601\) −5.33341e9 + 4.47526e9i −1.00218 + 0.840925i −0.987284 0.158964i \(-0.949185\pi\)
−0.0148915 + 0.999889i \(0.504740\pi\)
\(602\) 4.74760e9 + 8.22309e9i 0.886925 + 1.53620i
\(603\) −6.08192e9 3.25034e9i −1.12961 0.603695i
\(604\) −1.82739e9 + 3.16513e9i −0.337443 + 0.584469i
\(605\) 2.54819e9 + 1.44515e10i 0.467830 + 2.65319i
\(606\) 3.96461e9 + 2.81446e8i 0.723680 + 0.0513738i
\(607\) −3.62773e8 + 1.32039e8i −0.0658377 + 0.0239630i −0.374729 0.927134i \(-0.622264\pi\)
0.308891 + 0.951097i \(0.400042\pi\)
\(608\) 3.71658e8 1.35272e8i 0.0670627 0.0244088i
\(609\) −7.40430e9 5.25629e8i −1.32838 0.0943015i
\(610\) 1.33510e9 + 7.57171e9i 0.238154 + 1.35064i
\(611\) −2.10051e9 + 3.63820e9i −0.372547 + 0.645270i
\(612\) −1.84864e9 9.87959e8i −0.326003 0.174224i
\(613\) 2.53466e9 + 4.39015e9i 0.444434 + 0.769782i 0.998013 0.0630146i \(-0.0200715\pi\)
−0.553579 + 0.832797i \(0.686738\pi\)
\(614\) 1.98223e9 1.66329e9i 0.345593 0.289987i
\(615\) 7.68200e8 3.06726e9i 0.133172 0.531725i
\(616\) 2.31676e9 1.31390e10i 0.399344 2.26479i
\(617\) −3.81077e9 3.19762e9i −0.653153 0.548061i 0.254873 0.966975i \(-0.417966\pi\)
−0.908026 + 0.418914i \(0.862411\pi\)
\(618\) −1.26383e9 + 9.16188e8i −0.215392 + 0.156144i
\(619\) 1.14328e9 + 4.16121e8i 0.193748 + 0.0705184i 0.437072 0.899427i \(-0.356016\pi\)
−0.243324 + 0.969945i \(0.578238\pi\)
\(620\) −4.30806e9 −0.725956
\(621\) 3.94637e7 9.67909e7i 0.00661268 0.0162186i
\(622\) −6.59958e9 −1.09964
\(623\) −9.08135e9 3.30534e9i −1.50467 0.547657i
\(624\) 7.53007e7 + 7.23801e8i 0.0124066 + 0.119254i
\(625\) −3.76191e9 3.15662e9i −0.616352 0.517181i
\(626\) 5.09387e8 2.88888e9i 0.0829923 0.470673i
\(627\) 7.98065e8 2.27928e8i 0.129301 0.0369285i
\(628\) −8.08559e8 + 6.78461e8i −0.130273 + 0.109312i
\(629\) 1.77928e9 + 3.08180e9i 0.285080 + 0.493773i
\(630\) 5.17324e9 6.59266e9i 0.824272 1.05043i
\(631\) 4.93297e9 8.54416e9i 0.781639 1.35384i −0.149348 0.988785i \(-0.547718\pi\)
0.930987 0.365053i \(-0.118949\pi\)
\(632\) −1.66088e9 9.41929e9i −0.261714 1.48426i
\(633\) 4.66630e8 6.90232e8i 0.0731240 0.108164i
\(634\) 2.79729e9 1.01813e9i 0.435938 0.158669i
\(635\) 1.04407e10 3.80010e9i 1.61816 0.588962i
\(636\) 9.95882e8 + 2.04735e9i 0.153500 + 0.315568i
\(637\) 3.86355e8 + 2.19113e9i 0.0592241 + 0.335877i
\(638\) 3.99164e9 6.91372e9i 0.608526 1.05400i
\(639\) 4.14605e9 8.72109e8i 0.628610 0.132226i
\(640\) −1.40451e9 2.43268e9i −0.211785 0.366822i
\(641\) −5.17518e9 + 4.34249e9i −0.776108 + 0.651232i −0.942265 0.334867i \(-0.891308\pi\)
0.166157 + 0.986099i \(0.446864\pi\)
\(642\) −3.39200e9 3.28256e9i −0.505922 0.489598i
\(643\) −2.25179e9 + 1.27705e10i −0.334033 + 1.89439i 0.102546 + 0.994728i \(0.467301\pi\)
−0.436579 + 0.899666i \(0.643810\pi\)
\(644\) 5.96093e7 + 5.00182e7i 0.00879455 + 0.00737950i
\(645\) 1.79177e10 + 8.00020e9i 2.62920 + 1.17393i
\(646\) −2.63237e8 9.58104e7i −0.0384178 0.0139829i
\(647\) 9.52972e9 1.38330 0.691648 0.722235i \(-0.256885\pi\)
0.691648 + 0.722235i \(0.256885\pi\)
\(648\) 6.70730e9 2.95235e9i 0.968357 0.426241i
\(649\) 2.14001e9 0.307298
\(650\) 2.74645e9 + 9.99626e8i 0.392261 + 0.142771i
\(651\) 8.07298e9 + 3.60456e9i 1.14683 + 0.512057i
\(652\) 3.35531e9 + 2.81544e9i 0.474096 + 0.397814i
\(653\) 9.82710e8 5.57322e9i 0.138111 0.783268i −0.834531 0.550961i \(-0.814261\pi\)
0.972642 0.232307i \(-0.0746275\pi\)
\(654\) 5.43058e9 + 5.25536e9i 0.759144 + 0.734650i
\(655\) −1.18519e10 + 9.94491e9i −1.64795 + 1.38279i
\(656\) −3.16807e8 5.48725e8i −0.0438158 0.0758912i
\(657\) 2.59758e9 7.93735e9i 0.357346 1.09194i
\(658\) 4.84707e9 8.39538e9i 0.663268 1.14881i
\(659\) −1.35503e9 7.68475e9i −0.184438 1.04600i −0.926676 0.375861i \(-0.877347\pi\)
0.742238 0.670136i \(-0.233764\pi\)
\(660\) −4.05904e9 8.34465e9i −0.549566 1.12981i
\(661\) 4.59509e9 1.67248e9i 0.618856 0.225245i −0.0135179 0.999909i \(-0.504303\pi\)
0.632374 + 0.774664i \(0.282081\pi\)
\(662\) −2.20792e9 + 8.03616e8i −0.295787 + 0.107658i
\(663\) −1.56004e9 + 2.30758e9i −0.207892 + 0.307511i
\(664\) −9.98080e8 5.66040e9i −0.132305 0.750341i
\(665\) −5.76559e8 + 9.98629e8i −0.0760270 + 0.131683i
\(666\) −4.14530e9 5.91528e8i −0.543746 0.0775917i
\(667\) 6.91735e7 + 1.19812e8i 0.00902609 + 0.0156336i
\(668\) −2.03906e9 + 1.71097e9i −0.264674 + 0.222088i
\(669\) −5.83138e9 + 1.66545e9i −0.752974 + 0.215050i
\(670\) −1.78929e9 + 1.01475e10i −0.229836 + 1.30346i
\(671\) −1.33845e10 1.12309e10i −1.71030 1.43511i
\(672\) 9.39045e8 + 9.02623e9i 0.119370 + 1.14740i
\(673\) 1.11074e10 + 4.04277e9i 1.40462 + 0.511241i 0.929547 0.368703i \(-0.120198\pi\)
0.475077 + 0.879944i \(0.342420\pi\)
\(674\) −4.48815e9 −0.564621
\(675\) 3.55110e8 9.32104e9i 0.0444426 1.16654i
\(676\) 3.01711e9 0.375645
\(677\) −3.14303e9 1.14397e9i −0.389304 0.141695i 0.139950 0.990159i \(-0.455306\pi\)
−0.529254 + 0.848464i \(0.677528\pi\)
\(678\) −6.99838e8 + 5.07332e8i −0.0862370 + 0.0625156i
\(679\) −7.79381e9 6.53978e9i −0.955445 0.801713i
\(680\) −1.61595e9 + 9.16453e9i −0.197082 + 1.11771i
\(681\) 1.97723e9 7.89465e9i 0.239906 0.957895i
\(682\) −7.28397e9 + 6.11198e9i −0.879271 + 0.737796i
\(683\) 2.88772e9 + 5.00168e9i 0.346803 + 0.600680i 0.985680 0.168629i \(-0.0539340\pi\)
−0.638877 + 0.769309i \(0.720601\pi\)
\(684\) −2.88194e8 + 1.79237e8i −0.0344341 + 0.0214157i
\(685\) 3.94324e9 6.82989e9i 0.468744 0.811889i
\(686\) 4.40115e8 + 2.49601e9i 0.0520513 + 0.295197i
\(687\) 4.94031e9 + 3.50711e8i 0.581307 + 0.0412667i
\(688\) 3.69493e9 1.34485e9i 0.432561 0.157439i
\(689\) 2.84303e9 1.03478e9i 0.331142 0.120526i
\(690\) −1.55794e8 1.10597e7i −0.0180542 0.00128166i
\(691\) −1.79484e8 1.01790e9i −0.0206944 0.117364i 0.972711 0.232021i \(-0.0745340\pi\)
−0.993405 + 0.114658i \(0.963423\pi\)
\(692\) 1.65154e9 2.86055e9i 0.189460 0.328154i
\(693\) 6.24359e8 + 1.90335e10i 0.0712637 + 2.17246i
\(694\) 2.94608e9 + 5.10276e9i 0.334570 + 0.579492i
\(695\) −5.56204e9 + 4.66710e9i −0.628473 + 0.527352i
\(696\) −2.35646e9 + 9.40884e9i −0.264928 + 1.05780i
\(697\) 4.21145e8 2.38843e9i 0.0471104 0.267176i
\(698\) −1.29158e9 1.08376e9i −0.143756 0.120626i
\(699\) −4.33754e9 + 3.14440e9i −0.480367 + 0.348232i
\(700\) 6.52526e9 + 2.37500e9i 0.719042 + 0.261710i
\(701\) 2.79968e9 0.306969 0.153485 0.988151i \(-0.450950\pi\)
0.153485 + 0.988151i \(0.450950\pi\)
\(702\) −1.00293e9 3.12036e9i −0.109419 0.340428i
\(703\) 5.76182e8 0.0625484
\(704\) −1.26158e10 4.59178e9i −1.36273 0.495994i
\(705\) −2.07303e9 1.99262e10i −0.222814 2.14172i
\(706\) 7.28403e9 + 6.11203e9i 0.779032 + 0.653685i
\(707\) 2.17909e9 1.23582e10i 0.231904 1.31519i
\(708\) −8.41426e8 + 2.40312e8i −0.0891045 + 0.0254484i
\(709\) −6.11326e9 + 5.12963e9i −0.644185 + 0.540536i −0.905300 0.424772i \(-0.860354\pi\)
0.261115 + 0.965308i \(0.415910\pi\)
\(710\) −3.16534e9 5.48252e9i −0.331906 0.574879i
\(711\) 5.08749e9 + 1.26691e10i 0.530836 + 1.32191i
\(712\) −6.31401e9 + 1.09362e10i −0.655580 + 1.13550i
\(713\) −2.86136e7 1.62276e8i −0.00295638 0.0167664i
\(714\) 3.59989e9 5.32490e9i 0.370123 0.547480i
\(715\) −1.15877e10 + 4.21758e9i −1.18557 + 0.431511i
\(716\) −1.17398e9 + 4.27295e8i −0.119527 + 0.0435043i
\(717\) 2.99982e9 + 6.16708e9i 0.303933 + 0.624831i
\(718\) 1.76223e8 + 9.99412e8i 0.0177676 + 0.100765i
\(719\) 3.42217e9 5.92737e9i 0.343361 0.594718i −0.641694 0.766961i \(-0.721768\pi\)
0.985055 + 0.172243i \(0.0551013\pi\)
\(720\) −2.31661e9 2.58382e9i −0.231307 0.257988i
\(721\) 2.46423e9 + 4.26817e9i 0.244854 + 0.424100i
\(722\) 5.40312e9 4.53375e9i 0.534274 0.448309i
\(723\) 3.77452e8 + 3.65274e8i 0.0371431 + 0.0359447i
\(724\) 2.75520e8 1.56255e9i 0.0269816 0.153020i
\(725\) 9.45748e9 + 7.93577e9i 0.921706 + 0.773403i
\(726\) −1.20933e10 5.39964e9i −1.17292 0.523705i
\(727\) −1.56029e10 5.67899e9i −1.50603 0.548152i −0.548420 0.836203i \(-0.684770\pi\)
−0.957615 + 0.288052i \(0.906993\pi\)
\(728\) 7.24976e9 0.696408
\(729\) −8.50145e9 + 6.09462e9i −0.812730 + 0.582640i
\(730\) −1.24791e10 −1.18728
\(731\) 1.41431e10 + 5.14765e9i 1.33916 + 0.487414i
\(732\) 6.52377e9 + 2.91284e9i 0.614766 + 0.274491i
\(733\) 4.93762e9 + 4.14316e9i 0.463078 + 0.388568i 0.844262 0.535931i \(-0.180039\pi\)
−0.381184 + 0.924499i \(0.624484\pi\)
\(734\) −1.54116e9 + 8.74033e9i −0.143850 + 0.815815i
\(735\) −7.62454e9 7.37853e9i −0.708285 0.685432i
\(736\) 1.29566e8 1.08719e8i 0.0119790 0.0100516i
\(737\) −1.17080e10 2.02789e10i −1.07733 1.86599i
\(738\) 1.90506e9 + 2.12481e9i 0.174467 + 0.194591i
\(739\) −1.30675e9 + 2.26335e9i −0.119107 + 0.206299i −0.919414 0.393291i \(-0.871336\pi\)
0.800307 + 0.599590i \(0.204670\pi\)
\(740\) −1.11864e9 6.34410e9i −0.101479 0.575518i
\(741\) 1.97278e8 + 4.05567e8i 0.0178121 + 0.0366184i
\(742\) −6.56048e9 + 2.38782e9i −0.589552 + 0.214579i
\(743\) 2.73895e9 9.96895e8i 0.244975 0.0891638i −0.216614 0.976257i \(-0.569501\pi\)
0.461590 + 0.887093i \(0.347279\pi\)
\(744\) 6.47025e9 9.57070e9i 0.575991 0.851997i
\(745\) 1.93845e9 + 1.09935e10i 0.171755 + 0.974068i
\(746\) 2.22319e9 3.85068e9i 0.196061 0.339587i
\(747\) 3.05726e9 + 7.61330e9i 0.268355 + 0.668268i
\(748\) −3.55873e9 6.16389e9i −0.310913 0.538517i
\(749\) −1.14165e10 + 9.57958e9i −0.992765 + 0.833029i
\(750\) −1.92168e9 + 5.48833e8i −0.166328 + 0.0475036i
\(751\) 2.19413e9 1.24435e10i 0.189026 1.07202i −0.731646 0.681685i \(-0.761247\pi\)
0.920672 0.390337i \(-0.127641\pi\)
\(752\) −3.07525e9 2.58044e9i −0.263704 0.221274i
\(753\) −2.23789e7 2.15110e8i −0.00191010 0.0183602i
\(754\) 4.07644e9 + 1.48370e9i 0.346323 + 0.126051i
\(755\) −2.31608e10 −1.95857