Properties

Label 27.8.e.a.4.18
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 4.18
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.18

$q$-expansion

\(f(q)\) \(=\) \(q+(16.7921 + 6.11184i) q^{2} +(46.7511 - 1.15397i) q^{3} +(146.567 + 122.985i) q^{4} +(-21.3907 + 121.313i) q^{5} +(792.104 + 266.358i) q^{6} +(-285.632 + 239.674i) q^{7} +(565.850 + 980.080i) q^{8} +(2184.34 - 107.899i) q^{9} +O(q^{10})\) \(q+(16.7921 + 6.11184i) q^{2} +(46.7511 - 1.15397i) q^{3} +(146.567 + 122.985i) q^{4} +(-21.3907 + 121.313i) q^{5} +(792.104 + 266.358i) q^{6} +(-285.632 + 239.674i) q^{7} +(565.850 + 980.080i) q^{8} +(2184.34 - 107.899i) q^{9} +(-1100.64 + 1906.36i) q^{10} +(-803.430 - 4556.48i) q^{11} +(6994.12 + 5580.54i) q^{12} +(933.323 - 339.702i) q^{13} +(-6261.21 + 2278.89i) q^{14} +(-860.050 + 5696.20i) q^{15} +(-740.959 - 4202.19i) q^{16} +(-11166.2 + 19340.4i) q^{17} +(37339.1 + 11538.5i) q^{18} +(-13878.2 - 24037.7i) q^{19} +(-18054.8 + 15149.8i) q^{20} +(-13077.0 + 11534.6i) q^{21} +(14357.1 - 81423.4i) q^{22} +(23315.9 + 19564.3i) q^{23} +(27585.1 + 45166.9i) q^{24} +(59154.2 + 21530.4i) q^{25} +17748.7 q^{26} +(101996. - 7565.05i) q^{27} -71340.5 q^{28} +(-146453. - 53304.7i) q^{29} +(-49256.3 + 90394.8i) q^{30} +(-245544. - 206036. i) q^{31} +(38395.0 - 217749. i) q^{32} +(-42819.3 - 212093. i) q^{33} +(-305710. + 256521. i) q^{34} +(-22965.6 - 39777.6i) q^{35} +(333423. + 252826. i) q^{36} +(-88195.2 + 152759. i) q^{37} +(-86129.5 - 488465. i) q^{38} +(43241.9 - 16958.5i) q^{39} +(-131000. + 47680.2i) q^{40} +(456882. - 166292. i) q^{41} +(-290089. + 113766. i) q^{42} +(109246. + 619565. i) q^{43} +(442620. - 766641. i) q^{44} +(-33635.0 + 267296. i) q^{45} +(271949. + 471029. i) q^{46} +(-78494.2 + 65864.5i) q^{47} +(-39489.9 - 195602. i) q^{48} +(-118865. + 674115. i) q^{49} +(861736. + 723082. i) q^{50} +(-499714. + 917072. i) q^{51} +(178573. + 64995.2i) q^{52} +2.07437e6 q^{53} +(1.75896e6 + 496348. i) q^{54} +569945. q^{55} +(-396524. - 144323. i) q^{56} +(-676558. - 1.10777e6i) q^{57} +(-2.13347e6 - 1.79020e6i) q^{58} +(-442381. + 2.50887e6i) q^{59} +(-826600. + 729104. i) q^{60} +(-1.00139e6 + 840264. i) q^{61} +(-2.86395e6 - 4.96051e6i) q^{62} +(-598056. + 554347. i) q^{63} +(1.70249e6 - 2.94880e6i) q^{64} +(21245.7 + 120491. i) q^{65} +(577253. - 3.82320e6i) q^{66} +(-2.45376e6 + 893094. i) q^{67} +(-4.01517e6 + 1.46140e6i) q^{68} +(1.11262e6 + 887749. i) q^{69} +(-142527. - 808313. i) q^{70} +(429648. - 744172. i) q^{71} +(1.34176e6 + 2.07977e6i) q^{72} +(1.52805e6 + 2.64665e6i) q^{73} +(-2.41462e6 + 2.02611e6i) q^{74} +(2.79037e6 + 938308. i) q^{75} +(922180. - 5.22994e6i) q^{76} +(1.32155e6 + 1.10891e6i) q^{77} +(829771. - 20481.4i) q^{78} +(-642214. - 233747. i) q^{79} +525629. q^{80} +(4.75968e6 - 471375. i) q^{81} +8.68838e6 q^{82} +(1.46994e6 + 535013. i) q^{83} +(-3.33525e6 + 82324.8i) q^{84} +(-2.10739e6 - 1.76831e6i) q^{85} +(-1.95221e6 + 1.10715e7i) q^{86} +(-6.90837e6 - 2.32305e6i) q^{87} +(4.01109e6 - 3.36571e6i) q^{88} +(-1.37382e6 - 2.37952e6i) q^{89} +(-2.19847e6 + 4.28290e6i) q^{90} +(-185169. + 320722. i) q^{91} +(1.01123e6 + 5.73499e6i) q^{92} +(-1.17172e7 - 9.34907e6i) q^{93} +(-1.72064e6 + 626261. i) q^{94} +(3.21294e6 - 1.16942e6i) q^{95} +(1.54374e6 - 1.02243e7i) q^{96} +(145687. + 826233. i) q^{97} +(-6.11607e6 + 1.05933e7i) q^{98} +(-2.24660e6 - 9.86619e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.7921 + 6.11184i 1.48423 + 0.540215i 0.951923 0.306337i \(-0.0991035\pi\)
0.532306 + 0.846552i \(0.321326\pi\)
\(3\) 46.7511 1.15397i 0.999696 0.0246757i
\(4\) 146.567 + 122.985i 1.14506 + 0.960818i
\(5\) −21.3907 + 121.313i −0.0765298 + 0.434022i 0.922335 + 0.386391i \(0.126278\pi\)
−0.998865 + 0.0476313i \(0.984833\pi\)
\(6\) 792.104 + 266.358i 1.49711 + 0.503426i
\(7\) −285.632 + 239.674i −0.314748 + 0.264105i −0.786451 0.617652i \(-0.788084\pi\)
0.471703 + 0.881758i \(0.343639\pi\)
\(8\) 565.850 + 980.080i 0.390738 + 0.676779i
\(9\) 2184.34 107.899i 0.998782 0.0493364i
\(10\) −1100.64 + 1906.36i −0.348053 + 0.602846i
\(11\) −803.430 4556.48i −0.182001 1.03218i −0.929748 0.368195i \(-0.879976\pi\)
0.747747 0.663983i \(-0.231135\pi\)
\(12\) 6994.12 + 5580.54i 1.16842 + 0.932270i
\(13\) 933.323 339.702i 0.117823 0.0428841i −0.282436 0.959286i \(-0.591142\pi\)
0.400259 + 0.916402i \(0.368920\pi\)
\(14\) −6261.21 + 2278.89i −0.609832 + 0.221961i
\(15\) −860.050 + 5696.20i −0.0657967 + 0.435778i
\(16\) −740.959 4202.19i −0.0452245 0.256481i
\(17\) −11166.2 + 19340.4i −0.551231 + 0.954761i 0.446955 + 0.894557i \(0.352508\pi\)
−0.998186 + 0.0602040i \(0.980825\pi\)
\(18\) 37339.1 + 11538.5i 1.50907 + 0.466331i
\(19\) −13878.2 24037.7i −0.464188 0.803998i 0.534976 0.844867i \(-0.320321\pi\)
−0.999164 + 0.0408696i \(0.986987\pi\)
\(20\) −18054.8 + 15149.8i −0.504647 + 0.423449i
\(21\) −13077.0 + 11534.6i −0.308135 + 0.271791i
\(22\) 14357.1 81423.4i 0.287467 1.63031i
\(23\) 23315.9 + 19564.3i 0.399580 + 0.335288i 0.820331 0.571888i \(-0.193789\pi\)
−0.420751 + 0.907176i \(0.638233\pi\)
\(24\) 27585.1 + 45166.9i 0.407319 + 0.666931i
\(25\) 59154.2 + 21530.4i 0.757174 + 0.275589i
\(26\) 17748.7 0.198043
\(27\) 101996. 7565.05i 0.997261 0.0739671i
\(28\) −71340.5 −0.614162
\(29\) −146453. 53304.7i −1.11508 0.405856i −0.282226 0.959348i \(-0.591073\pi\)
−0.832855 + 0.553492i \(0.813295\pi\)
\(30\) −49256.3 + 90394.8i −0.333071 + 0.611250i
\(31\) −245544. 206036.i −1.48035 1.24216i −0.905812 0.423679i \(-0.860738\pi\)
−0.574535 0.818480i \(-0.694817\pi\)
\(32\) 38395.0 217749.i 0.207133 1.17471i
\(33\) −42819.3 212093.i −0.207415 1.02737i
\(34\) −305710. + 256521.i −1.33393 + 1.11930i
\(35\) −22965.6 39777.6i −0.0905399 0.156820i
\(36\) 333423. + 252826.i 1.19107 + 0.903155i
\(37\) −88195.2 + 152759.i −0.286246 + 0.495792i −0.972911 0.231182i \(-0.925741\pi\)
0.686665 + 0.726974i \(0.259074\pi\)
\(38\) −86129.5 488465.i −0.254630 1.44408i
\(39\) 43241.9 16958.5i 0.116729 0.0457784i
\(40\) −131000. + 47680.2i −0.323640 + 0.117795i
\(41\) 456882. 166292.i 1.03529 0.376814i 0.232196 0.972669i \(-0.425409\pi\)
0.803092 + 0.595855i \(0.203187\pi\)
\(42\) −290089. + 113766.i −0.604169 + 0.236941i
\(43\) 109246. + 619565.i 0.209540 + 1.18836i 0.890134 + 0.455698i \(0.150610\pi\)
−0.680595 + 0.732660i \(0.738278\pi\)
\(44\) 442620. 766641.i 0.783334 1.35677i
\(45\) −33635.0 + 267296.i −0.0550235 + 0.437269i
\(46\) 271949. + 471029.i 0.411941 + 0.713503i
\(47\) −78494.2 + 65864.5i −0.110280 + 0.0925356i −0.696260 0.717790i \(-0.745154\pi\)
0.585980 + 0.810325i \(0.300710\pi\)
\(48\) −39489.9 195602.i −0.0515396 0.255287i
\(49\) −118865. + 674115.i −0.144333 + 0.818554i
\(50\) 861736. + 723082.i 0.974943 + 0.818074i
\(51\) −499714. + 917072.i −0.527504 + 0.968072i
\(52\) 178573. + 64995.2i 0.176118 + 0.0641017i
\(53\) 2.07437e6 1.91391 0.956953 0.290242i \(-0.0937358\pi\)
0.956953 + 0.290242i \(0.0937358\pi\)
\(54\) 1.75896e6 + 496348.i 1.52012 + 0.428951i
\(55\) 569945. 0.461917
\(56\) −396524. 144323.i −0.301725 0.109819i
\(57\) −676558. 1.10777e6i −0.483886 0.792299i
\(58\) −2.13347e6 1.79020e6i −1.43579 1.20477i
\(59\) −442381. + 2.50887e6i −0.280424 + 1.59036i 0.440764 + 0.897623i \(0.354708\pi\)
−0.721188 + 0.692740i \(0.756404\pi\)
\(60\) −826600. + 729104.i −0.494045 + 0.435773i
\(61\) −1.00139e6 + 840264.i −0.564869 + 0.473981i −0.879939 0.475087i \(-0.842417\pi\)
0.315070 + 0.949069i \(0.397972\pi\)
\(62\) −2.86395e6 4.96051e6i −1.52614 2.64335i
\(63\) −598056. + 554347.i −0.301335 + 0.279312i
\(64\) 1.70249e6 2.94880e6i 0.811812 1.40610i
\(65\) 21245.7 + 120491.i 0.00959566 + 0.0544197i
\(66\) 577253. 3.82320e6i 0.247151 1.63691i
\(67\) −2.45376e6 + 893094.i −0.996712 + 0.362773i −0.788316 0.615271i \(-0.789047\pi\)
−0.208396 + 0.978044i \(0.566824\pi\)
\(68\) −4.01517e6 + 1.46140e6i −1.54854 + 0.563624i
\(69\) 1.11262e6 + 887749.i 0.407732 + 0.325326i
\(70\) −142527. 808313.i −0.0496655 0.281667i
\(71\) 429648. 744172.i 0.142465 0.246757i −0.785959 0.618278i \(-0.787830\pi\)
0.928424 + 0.371522i \(0.121164\pi\)
\(72\) 1.34176e6 + 2.07977e6i 0.423652 + 0.656677i
\(73\) 1.52805e6 + 2.64665e6i 0.459734 + 0.796282i 0.998947 0.0458875i \(-0.0146116\pi\)
−0.539213 + 0.842169i \(0.681278\pi\)
\(74\) −2.41462e6 + 2.02611e6i −0.692689 + 0.581235i
\(75\) 2.79037e6 + 938308.i 0.763744 + 0.256821i
\(76\) 922180. 5.22994e6i 0.240973 1.36662i
\(77\) 1.32155e6 + 1.10891e6i 0.329888 + 0.276809i
\(78\) 829771. 20481.4i 0.197983 0.00488686i
\(79\) −642214. 233747.i −0.146550 0.0533397i 0.267704 0.963501i \(-0.413735\pi\)
−0.414254 + 0.910162i \(0.635957\pi\)
\(80\) 525629. 0.114779
\(81\) 4.75968e6 471375.i 0.995132 0.0985527i
\(82\) 8.68838e6 1.74016
\(83\) 1.46994e6 + 535013.i 0.282179 + 0.102705i 0.479233 0.877688i \(-0.340915\pi\)
−0.197053 + 0.980393i \(0.563137\pi\)
\(84\) −3.33525e6 + 82324.8i −0.613975 + 0.0151549i
\(85\) −2.10739e6 1.76831e6i −0.372202 0.312314i
\(86\) −1.95221e6 + 1.10715e7i −0.330964 + 1.87699i
\(87\) −6.90837e6 2.32305e6i −1.12476 0.378217i
\(88\) 4.01109e6 3.36571e6i 0.627442 0.526486i
\(89\) −1.37382e6 2.37952e6i −0.206568 0.357787i 0.744063 0.668110i \(-0.232896\pi\)
−0.950631 + 0.310323i \(0.899563\pi\)
\(90\) −2.19847e6 + 4.28290e6i −0.317887 + 0.619283i
\(91\) −185169. + 320722.i −0.0257587 + 0.0446154i
\(92\) 1.01123e6 + 5.73499e6i 0.135392 + 0.767848i
\(93\) −1.17172e7 9.34907e6i −1.51055 1.20525i
\(94\) −1.72064e6 + 626261.i −0.213669 + 0.0777693i
\(95\) 3.21294e6 1.16942e6i 0.384477 0.139938i
\(96\) 1.54374e6 1.02243e7i 0.178083 1.17947i
\(97\) 145687. + 826233.i 0.0162077 + 0.0919182i 0.991839 0.127500i \(-0.0406952\pi\)
−0.975631 + 0.219418i \(0.929584\pi\)
\(98\) −6.11607e6 + 1.05933e7i −0.656419 + 1.13695i
\(99\) −2.24660e6 9.86619e6i −0.232703 1.02194i
\(100\) 6.02218e6 + 1.04307e7i 0.602218 + 1.04307i
\(101\) 7.18886e6 6.03217e6i 0.694281 0.582571i −0.225860 0.974160i \(-0.572519\pi\)
0.920140 + 0.391589i \(0.128075\pi\)
\(102\) −1.39963e7 + 1.23454e7i −1.30590 + 1.15187i
\(103\) 375312. 2.12850e6i 0.0338425 0.191930i −0.963200 0.268787i \(-0.913377\pi\)
0.997042 + 0.0768565i \(0.0244883\pi\)
\(104\) 861056. + 722512.i 0.0750610 + 0.0629837i
\(105\) −1.11957e6 1.83315e6i −0.0943819 0.154538i
\(106\) 3.48331e7 + 1.26782e7i 2.84068 + 1.03392i
\(107\) 1.80236e7 1.42232 0.711160 0.703030i \(-0.248170\pi\)
0.711160 + 0.703030i \(0.248170\pi\)
\(108\) 1.58796e7 + 1.14351e7i 1.21299 + 0.873489i
\(109\) −1.98533e7 −1.46838 −0.734191 0.678943i \(-0.762438\pi\)
−0.734191 + 0.678943i \(0.762438\pi\)
\(110\) 9.57060e6 + 3.48341e6i 0.685590 + 0.249534i
\(111\) −3.94695e6 + 7.24341e6i −0.273925 + 0.502705i
\(112\) 1.21879e6 + 1.02269e6i 0.0819723 + 0.0687830i
\(113\) 2.41988e6 1.37238e7i 0.157768 0.894748i −0.798443 0.602071i \(-0.794343\pi\)
0.956211 0.292678i \(-0.0945463\pi\)
\(114\) −4.59033e6 2.27369e7i −0.290186 1.43735i
\(115\) −2.87215e6 + 2.41002e6i −0.176102 + 0.147767i
\(116\) −1.49096e7 2.58243e7i −0.886879 1.53612i
\(117\) 2.00204e6 842728.i 0.115564 0.0486448i
\(118\) −2.27623e7 + 3.94255e7i −1.27535 + 2.20897i
\(119\) −1.44597e6 8.20048e6i −0.0786581 0.446092i
\(120\) −6.06939e6 + 2.38027e6i −0.320635 + 0.125746i
\(121\) −1.80404e6 + 656617.i −0.0925758 + 0.0336948i
\(122\) −2.19510e7 + 7.98951e6i −1.09445 + 0.398346i
\(123\) 2.11679e7 8.30155e6i 1.02567 0.402246i
\(124\) −1.06495e7 6.03964e7i −0.501595 2.84469i
\(125\) −8.68915e6 + 1.50501e7i −0.397917 + 0.689212i
\(126\) −1.34307e7 + 5.65345e6i −0.598139 + 0.251777i
\(127\) −3.70882e6 6.42387e6i −0.160666 0.278281i 0.774442 0.632645i \(-0.218031\pi\)
−0.935108 + 0.354364i \(0.884697\pi\)
\(128\) 2.49306e7 2.09193e7i 1.05075 0.881681i
\(129\) 5.82234e6 + 2.88393e7i 0.238799 + 1.18283i
\(130\) −379657. + 2.15314e6i −0.0151562 + 0.0859550i
\(131\) −7.21665e6 6.05548e6i −0.280470 0.235342i 0.491690 0.870770i \(-0.336379\pi\)
−0.772160 + 0.635428i \(0.780824\pi\)
\(132\) 1.98083e7 3.63521e7i 0.749616 1.37569i
\(133\) 9.72523e6 + 3.53970e6i 0.358442 + 0.130462i
\(134\) −4.66622e7 −1.67532
\(135\) −1.26402e6 + 1.25352e7i −0.0442168 + 0.438494i
\(136\) −2.52735e7 −0.861549
\(137\) 3.37379e7 + 1.22796e7i 1.12098 + 0.408002i 0.835008 0.550238i \(-0.185463\pi\)
0.285967 + 0.958239i \(0.407685\pi\)
\(138\) 1.32575e7 + 2.17073e7i 0.429422 + 0.703121i
\(139\) −1.68732e7 1.41583e7i −0.532901 0.447157i 0.336201 0.941790i \(-0.390858\pi\)
−0.869102 + 0.494633i \(0.835302\pi\)
\(140\) 1.52603e6 8.65452e6i 0.0470017 0.266560i
\(141\) −3.59369e6 + 3.16982e6i −0.107963 + 0.0952286i
\(142\) 1.17630e7 9.87029e6i 0.344752 0.289282i
\(143\) −2.29770e6 3.97974e6i −0.0657079 0.113809i
\(144\) −2.07191e6 9.09904e6i −0.0578233 0.253938i
\(145\) 9.59929e6 1.66265e7i 0.261488 0.452910i
\(146\) 9.48323e6 + 5.37821e7i 0.252186 + 1.43022i
\(147\) −4.77915e6 + 3.16528e7i −0.124091 + 0.821867i
\(148\) −3.17135e7 + 1.15428e7i −0.804134 + 0.292681i
\(149\) −4.46405e7 + 1.62478e7i −1.10555 + 0.402386i −0.829358 0.558718i \(-0.811294\pi\)
−0.276188 + 0.961104i \(0.589071\pi\)
\(150\) 4.11215e7 + 3.28105e7i 0.994832 + 0.793767i
\(151\) −1.37273e7 7.78516e7i −0.324465 1.84013i −0.513412 0.858143i \(-0.671619\pi\)
0.188947 0.981987i \(-0.439493\pi\)
\(152\) 1.57059e7 2.72034e7i 0.362752 0.628305i
\(153\) −2.23039e7 + 4.34508e7i −0.503455 + 0.980794i
\(154\) 1.54142e7 + 2.66981e7i 0.340093 + 0.589059i
\(155\) 3.02472e7 2.53804e7i 0.652415 0.547441i
\(156\) 8.42349e6 + 2.83253e6i 0.177646 + 0.0597364i
\(157\) −7.23863e6 + 4.10523e7i −0.149282 + 0.846621i 0.814546 + 0.580098i \(0.196986\pi\)
−0.963829 + 0.266523i \(0.914125\pi\)
\(158\) −9.35551e6 7.85021e6i −0.188698 0.158337i
\(159\) 9.69792e7 2.39376e6i 1.91332 0.0472270i
\(160\) 2.55945e7 + 9.31563e6i 0.493999 + 0.179801i
\(161\) −1.13488e7 −0.214318
\(162\) 8.28062e7 + 2.11750e7i 1.53024 + 0.391310i
\(163\) 3.29063e7 0.595145 0.297572 0.954699i \(-0.403823\pi\)
0.297572 + 0.954699i \(0.403823\pi\)
\(164\) 8.74154e7 + 3.18166e7i 1.54751 + 0.563249i
\(165\) 2.66456e7 657700.i 0.461776 0.0113981i
\(166\) 2.14135e7 + 1.79680e7i 0.363336 + 0.304875i
\(167\) −2.44163e6 + 1.38472e7i −0.0405670 + 0.230067i −0.998350 0.0574261i \(-0.981711\pi\)
0.957783 + 0.287493i \(0.0928218\pi\)
\(168\) −1.87045e7 6.28968e6i −0.304343 0.102340i
\(169\) −4.73125e7 + 3.96999e7i −0.754001 + 0.632682i
\(170\) −2.45799e7 4.25737e7i −0.383715 0.664615i
\(171\) −3.29082e7 5.10089e7i −0.503289 0.780117i
\(172\) −6.01851e7 + 1.04244e8i −0.901861 + 1.56207i
\(173\) −1.67728e7 9.51231e7i −0.246288 1.39677i −0.817482 0.575954i \(-0.804631\pi\)
0.571194 0.820815i \(-0.306480\pi\)
\(174\) −1.01808e8 8.12318e7i −1.46508 1.16897i
\(175\) −2.20566e7 + 8.02794e6i −0.311104 + 0.113233i
\(176\) −1.85519e7 + 6.75233e6i −0.256503 + 0.0933596i
\(177\) −1.77867e7 + 1.17803e8i −0.241095 + 1.59680i
\(178\) −8.52608e6 4.83538e7i −0.113313 0.642629i
\(179\) 4.83086e7 8.36729e7i 0.629562 1.09043i −0.358077 0.933692i \(-0.616568\pi\)
0.987640 0.156742i \(-0.0500991\pi\)
\(180\) −3.78031e7 + 3.50403e7i −0.483141 + 0.447831i
\(181\) −5.41120e6 9.37248e6i −0.0678295 0.117484i 0.830116 0.557591i \(-0.188274\pi\)
−0.897946 + 0.440106i \(0.854941\pi\)
\(182\) −5.06959e6 + 4.25389e6i −0.0623337 + 0.0523042i
\(183\) −4.58464e7 + 4.04389e7i −0.553001 + 0.487776i
\(184\) −5.98134e6 + 3.39219e7i −0.0707842 + 0.401437i
\(185\) −1.66450e7 1.39668e7i −0.193278 0.162180i
\(186\) −1.39617e8 2.28605e8i −1.59090 2.60489i
\(187\) 9.70954e7 + 3.53398e7i 1.08581 + 0.395202i
\(188\) −1.96050e7 −0.215186
\(189\) −2.73201e7 + 2.66065e7i −0.294351 + 0.286663i
\(190\) 6.10994e7 0.646248
\(191\) −5.06380e7 1.84307e7i −0.525847 0.191393i 0.0654360 0.997857i \(-0.479156\pi\)
−0.591283 + 0.806464i \(0.701378\pi\)
\(192\) 7.61906e7 1.39825e8i 0.776868 1.42570i
\(193\) −1.17237e8 9.83735e7i −1.17385 0.984981i −1.00000 0.000209353i \(-0.999933\pi\)
−0.173854 0.984771i \(-0.555622\pi\)
\(194\) −2.60340e6 + 1.47646e7i −0.0255997 + 0.145183i
\(195\) 1.13230e6 + 5.60855e6i 0.0109356 + 0.0541664i
\(196\) −1.00327e8 + 8.41848e7i −0.951752 + 0.798615i
\(197\) 9.88162e7 + 1.71155e8i 0.920866 + 1.59499i 0.798079 + 0.602553i \(0.205850\pi\)
0.122787 + 0.992433i \(0.460817\pi\)
\(198\) 2.25754e7 1.79405e8i 0.206684 1.64251i
\(199\) 5.71709e7 9.90229e7i 0.514268 0.890738i −0.485595 0.874184i \(-0.661397\pi\)
0.999863 0.0165540i \(-0.00526955\pi\)
\(200\) 1.23709e7 + 7.01589e7i 0.109344 + 0.620123i
\(201\) −1.13685e8 + 4.45847e7i −0.987457 + 0.387258i
\(202\) 1.57584e8 5.73558e7i 1.34518 0.489607i
\(203\) 5.46075e7 1.98755e7i 0.458159 0.166756i
\(204\) −1.86028e8 + 7.29557e7i −1.53416 + 0.601663i
\(205\) 1.04003e7 + 5.89828e7i 0.0843152 + 0.478175i
\(206\) 1.93114e7 3.34483e7i 0.153914 0.266586i
\(207\) 5.30407e7 + 4.02193e7i 0.415636 + 0.315165i
\(208\) −2.11904e6 3.67029e6i −0.0163274 0.0282800i
\(209\) −9.83770e7 + 8.25481e7i −0.745386 + 0.625453i
\(210\) −7.59608e6 3.76251e7i −0.0566008 0.280356i
\(211\) 3.95214e7 2.24137e8i 0.289630 1.64257i −0.398631 0.917111i \(-0.630515\pi\)
0.688261 0.725463i \(-0.258374\pi\)
\(212\) 3.04035e8 + 2.55116e8i 2.19153 + 1.83892i
\(213\) 1.92278e7 3.52867e7i 0.136333 0.250197i
\(214\) 3.02654e8 + 1.10157e8i 2.11105 + 0.768359i
\(215\) −7.74981e7 −0.531810
\(216\) 6.51286e7 + 9.56833e7i 0.439727 + 0.646023i
\(217\) 1.19517e8 0.793998
\(218\) −3.33379e8 1.21340e8i −2.17941 0.793242i
\(219\) 7.44920e7 + 1.21971e8i 0.479242 + 0.784695i
\(220\) 8.35354e7 + 7.00946e7i 0.528922 + 0.443818i
\(221\) −3.85169e6 + 2.18440e7i −0.0240037 + 0.136132i
\(222\) −1.10548e8 + 9.75092e7i −0.678135 + 0.598150i
\(223\) −2.24956e8 + 1.88760e8i −1.35841 + 1.13984i −0.381935 + 0.924189i \(0.624742\pi\)
−0.976471 + 0.215649i \(0.930813\pi\)
\(224\) 4.12219e7 + 7.13983e7i 0.245053 + 0.424444i
\(225\) 1.31536e8 + 4.06469e7i 0.769849 + 0.237897i
\(226\) 1.24513e8 2.15662e8i 0.717521 1.24278i
\(227\) −3.10201e6 1.75923e7i −0.0176016 0.0998236i 0.974741 0.223337i \(-0.0716950\pi\)
−0.992343 + 0.123513i \(0.960584\pi\)
\(228\) 3.70777e7 2.45570e8i 0.207177 1.37215i
\(229\) −1.72955e8 + 6.29503e7i −0.951717 + 0.346397i −0.770783 0.637098i \(-0.780135\pi\)
−0.180935 + 0.983495i \(0.557912\pi\)
\(230\) −6.29591e7 + 2.29152e7i −0.341202 + 0.124187i
\(231\) 6.30637e7 + 5.03180e7i 0.336618 + 0.268585i
\(232\) −3.06277e7 1.73699e8i −0.161030 0.913247i
\(233\) 4.28350e7 7.41925e7i 0.221847 0.384250i −0.733522 0.679666i \(-0.762125\pi\)
0.955369 + 0.295416i \(0.0954581\pi\)
\(234\) 3.87691e7 1.91506e6i 0.197802 0.00977073i
\(235\) −6.31116e6 1.09313e7i −0.0317228 0.0549455i
\(236\) −3.73391e8 + 3.13313e8i −1.84915 + 1.55162i
\(237\) −3.02939e7 1.01868e7i −0.147821 0.0497072i
\(238\) 2.58391e7 1.46541e8i 0.124239 0.704595i
\(239\) 2.49912e6 + 2.09701e6i 0.0118412 + 0.00993592i 0.648689 0.761054i \(-0.275318\pi\)
−0.636848 + 0.770990i \(0.719762\pi\)
\(240\) 2.45737e7 606560.i 0.114745 0.00283227i
\(241\) 1.04385e8 + 3.79929e7i 0.480372 + 0.174841i 0.570845 0.821058i \(-0.306616\pi\)
−0.0904733 + 0.995899i \(0.528838\pi\)
\(242\) −3.43068e7 −0.155606
\(243\) 2.21977e8 2.75298e7i 0.992397 0.123078i
\(244\) −2.50110e8 −1.10222
\(245\) −7.92362e7 2.88396e7i −0.344225 0.125288i
\(246\) 4.06191e8 1.00261e7i 1.73963 0.0429398i
\(247\) −2.11184e7 1.77205e7i −0.0891708 0.0748232i
\(248\) 6.29908e7 3.57238e8i 0.262238 1.48723i
\(249\) 6.93386e7 + 2.33162e7i 0.284628 + 0.0957106i
\(250\) −2.37893e8 + 1.99616e8i −0.962923 + 0.807988i
\(251\) 1.40256e8 + 2.42930e8i 0.559839 + 0.969670i 0.997509 + 0.0705344i \(0.0224705\pi\)
−0.437670 + 0.899136i \(0.644196\pi\)
\(252\) −1.55832e8 + 7.69755e6i −0.613414 + 0.0303006i
\(253\) 7.04118e7 1.21957e8i 0.273353 0.473461i
\(254\) −2.30174e7 1.30538e8i −0.0881330 0.499827i
\(255\) −1.00563e8 8.02385e7i −0.379795 0.303035i
\(256\) 1.36939e8 4.98418e7i 0.510139 0.185675i
\(257\) −2.73861e8 + 9.96772e7i −1.00638 + 0.366294i −0.792043 0.610465i \(-0.790983\pi\)
−0.214341 + 0.976759i \(0.568760\pi\)
\(258\) −7.84917e7 + 5.19859e8i −0.284547 + 1.88459i
\(259\) −1.14208e7 6.47708e7i −0.0408459 0.231649i
\(260\) −1.17046e7 + 2.02729e7i −0.0412998 + 0.0715334i
\(261\) −3.25655e8 1.00633e8i −1.13375 0.350348i
\(262\) −8.41727e7 1.45791e8i −0.289146 0.500815i
\(263\) 3.64900e8 3.06187e8i 1.23688 1.03787i 0.239122 0.970990i \(-0.423140\pi\)
0.997761 0.0668785i \(-0.0213040\pi\)
\(264\) 1.83639e8 1.61979e8i 0.614259 0.541809i
\(265\) −4.43723e7 + 2.51648e8i −0.146471 + 0.830678i
\(266\) 1.41673e8 + 1.18878e8i 0.461533 + 0.387272i
\(267\) −6.69734e7 1.09660e8i −0.215334 0.352581i
\(268\) −4.69478e8 1.70876e8i −1.48985 0.542262i
\(269\) 4.80231e8 1.50424 0.752121 0.659025i \(-0.229031\pi\)
0.752121 + 0.659025i \(0.229031\pi\)
\(270\) −9.78388e7 + 2.02767e8i −0.302509 + 0.626939i
\(271\) 3.90431e8 1.19166 0.595830 0.803111i \(-0.296823\pi\)
0.595830 + 0.803111i \(0.296823\pi\)
\(272\) 8.95457e7 + 3.25920e7i 0.269807 + 0.0982018i
\(273\) −8.28677e6 + 1.52078e7i −0.0246499 + 0.0452374i
\(274\) 4.91480e8 + 4.12401e8i 1.44338 + 1.21114i
\(275\) 5.05764e7 2.86833e8i 0.146651 0.831697i
\(276\) 5.38943e7 + 2.66950e8i 0.154298 + 0.764273i
\(277\) −1.45473e8 + 1.22066e8i −0.411247 + 0.345077i −0.824821 0.565393i \(-0.808724\pi\)
0.413575 + 0.910470i \(0.364280\pi\)
\(278\) −1.96804e8 3.40875e8i −0.549386 0.951565i
\(279\) −5.58582e8 4.23558e8i −1.53983 1.16761i
\(280\) 2.59902e7 4.50163e7i 0.0707548 0.122551i
\(281\) −6.21788e6 3.52633e7i −0.0167174 0.0948094i 0.975307 0.220852i \(-0.0708836\pi\)
−0.992025 + 0.126042i \(0.959773\pi\)
\(282\) −7.97191e7 + 3.12640e7i −0.211685 + 0.0830180i
\(283\) −2.07839e8 + 7.56471e7i −0.545097 + 0.198399i −0.599867 0.800100i \(-0.704780\pi\)
0.0547696 + 0.998499i \(0.482558\pi\)
\(284\) 1.54494e8 5.62313e7i 0.400219 0.145668i
\(285\) 1.48859e8 5.83791e7i 0.380907 0.149383i
\(286\) −1.42598e7 8.08715e7i −0.0360440 0.204416i
\(287\) −9.06445e7 + 1.57001e8i −0.226337 + 0.392026i
\(288\) 6.03728e7 4.79780e8i 0.148925 1.18350i
\(289\) −4.41983e7 7.65537e7i −0.107712 0.186562i
\(290\) 2.62811e8 2.20524e8i 0.632776 0.530962i
\(291\) 7.76449e6 + 3.84592e7i 0.0184709 + 0.0914903i
\(292\) −1.01536e8 + 5.75839e8i −0.238660 + 1.35351i
\(293\) −1.74642e8 1.46542e8i −0.405613 0.340350i 0.417045 0.908886i \(-0.363066\pi\)
−0.822658 + 0.568536i \(0.807510\pi\)
\(294\) −2.73709e8 + 5.02309e8i −0.628164 + 1.15280i
\(295\) −2.94895e8 1.07333e8i −0.668792 0.243420i
\(296\) −1.99621e8 −0.447389
\(297\) −1.16416e8 4.58663e8i −0.257850 1.01589i
\(298\) −8.48913e8 −1.85826
\(299\) 2.84073e7 + 1.03394e7i 0.0614583 + 0.0223690i
\(300\) 2.93580e8 + 4.80699e8i 0.627773 + 1.02789i
\(301\) −1.79698e8 1.50784e8i −0.379804 0.318693i
\(302\) 2.45305e8 1.39119e9i 0.512486 2.90645i
\(303\) 3.29126e8 2.90306e8i 0.679694 0.599525i
\(304\) −9.07276e7 + 7.61295e7i −0.185217 + 0.155416i
\(305\) −8.05144e7 1.39455e8i −0.162489 0.281439i
\(306\) −6.40094e8 + 5.93313e8i −1.27708 + 1.18375i
\(307\) −1.55480e8 + 2.69299e8i −0.306683 + 0.531190i −0.977635 0.210311i \(-0.932552\pi\)
0.670952 + 0.741501i \(0.265886\pi\)
\(308\) 5.73171e7 + 3.25061e8i 0.111778 + 0.633925i
\(309\) 1.50901e7 9.99430e7i 0.0290962 0.192707i
\(310\) 6.63036e8 2.41325e8i 1.26407 0.460084i
\(311\) 6.01550e6 2.18946e6i 0.0113399 0.00412740i −0.336344 0.941739i \(-0.609190\pi\)
0.347684 + 0.937612i \(0.386968\pi\)
\(312\) 4.10891e7 + 3.27846e7i 0.0765923 + 0.0611123i
\(313\) 1.05376e8 + 5.97617e8i 0.194239 + 1.10158i 0.913498 + 0.406842i \(0.133370\pi\)
−0.719259 + 0.694742i \(0.755519\pi\)
\(314\) −3.72457e8 + 6.45115e8i −0.678926 + 1.17593i
\(315\) −5.44566e7 8.44097e7i −0.0981665 0.152162i
\(316\) −6.53804e7 1.13242e8i −0.116558 0.201885i
\(317\) 1.63022e6 1.36791e6i 0.00287434 0.00241186i −0.641349 0.767249i \(-0.721625\pi\)
0.644224 + 0.764837i \(0.277181\pi\)
\(318\) 1.64312e9 + 5.52524e8i 2.86532 + 0.963511i
\(319\) −1.25217e8 + 7.10138e8i −0.215970 + 1.22483i
\(320\) 3.21310e8 + 2.69611e8i 0.548150 + 0.459953i
\(321\) 8.42622e8 2.07986e7i 1.42189 0.0350968i
\(322\) −1.90571e8 6.93620e7i −0.318098 0.115778i
\(323\) 6.19864e8 1.02350
\(324\) 7.55587e8 + 5.16280e8i 1.23418 + 0.843292i
\(325\) 6.25239e7 0.101031
\(326\) 5.52567e8 + 2.01118e8i 0.883331 + 0.321506i
\(327\) −9.28162e8 + 2.29101e7i −1.46793 + 0.0362334i
\(328\) 4.21506e8 + 3.53686e8i 0.659546 + 0.553425i
\(329\) 6.63448e6 3.76260e7i 0.0102712 0.0582508i
\(330\) 4.51456e8 + 1.51809e8i 0.691539 + 0.232541i
\(331\) 8.86662e8 7.43998e8i 1.34388 1.12765i 0.363268 0.931685i \(-0.381661\pi\)
0.980611 0.195964i \(-0.0627836\pi\)
\(332\) 1.49646e8 + 2.59195e8i 0.224431 + 0.388726i
\(333\) −1.76166e8 + 3.43192e8i −0.261437 + 0.509311i
\(334\) −1.25632e8 + 2.17601e8i −0.184496 + 0.319557i
\(335\) −5.58562e7 3.16776e8i −0.0811735 0.460358i
\(336\) 5.81602e7 + 4.64055e7i 0.0836446 + 0.0667393i
\(337\) 5.15855e8 1.87756e8i 0.734214 0.267232i 0.0522665 0.998633i \(-0.483355\pi\)
0.681947 + 0.731401i \(0.261133\pi\)
\(338\) −1.03712e9 + 3.77479e8i −1.46089 + 0.531722i
\(339\) 9.72953e7 6.44397e8i 0.135642 0.898369i
\(340\) −9.13996e7 5.18353e8i −0.126115 0.715236i
\(341\) −7.41521e8 + 1.28435e9i −1.01271 + 1.75406i
\(342\) −2.40841e8 1.05768e9i −0.325565 1.42976i
\(343\) −2.81151e8 4.86969e8i −0.376193 0.651586i
\(344\) −5.45407e8 + 4.57651e8i −0.722381 + 0.606149i
\(345\) −1.31495e8 + 1.15985e8i −0.172402 + 0.152068i
\(346\) 2.99726e8 1.69983e9i 0.389008 2.20617i
\(347\) −1.06854e8 8.96612e7i −0.137290 0.115200i 0.571557 0.820562i \(-0.306340\pi\)
−0.708846 + 0.705363i \(0.750784\pi\)
\(348\) −7.26843e8 1.19011e9i −0.924513 1.51377i
\(349\) −5.05463e7 1.83974e7i −0.0636503 0.0231668i 0.309999 0.950737i \(-0.399671\pi\)
−0.373649 + 0.927570i \(0.621894\pi\)
\(350\) −4.19443e8 −0.522919
\(351\) 9.26251e7 4.17088e7i 0.114328 0.0514816i
\(352\) −1.02302e9 −1.25021
\(353\) −1.04945e9 3.81968e8i −1.26984 0.462185i −0.382782 0.923838i \(-0.625034\pi\)
−0.887060 + 0.461654i \(0.847256\pi\)
\(354\) −1.01867e9 + 1.86945e9i −1.22045 + 2.23977i
\(355\) 8.10871e7 + 6.80402e7i 0.0961950 + 0.0807172i
\(356\) 9.12878e7 5.17719e8i 0.107235 0.608162i
\(357\) −7.70636e7 3.81713e8i −0.0896418 0.444016i
\(358\) 1.32260e9 1.10979e9i 1.52348 1.27835i
\(359\) 5.58954e8 + 9.68136e8i 0.637595 + 1.10435i 0.985959 + 0.166988i \(0.0534041\pi\)
−0.348364 + 0.937359i \(0.613263\pi\)
\(360\) −2.81004e8 + 1.18284e8i −0.317434 + 0.133619i
\(361\) 6.17296e7 1.06919e8i 0.0690587 0.119613i
\(362\) −3.35826e7 1.90456e8i −0.0372078 0.211016i
\(363\) −8.35832e7 + 3.27794e7i −0.0917162 + 0.0359690i
\(364\) −6.65837e7 + 2.42345e7i −0.0723625 + 0.0263378i
\(365\) −3.53759e8 + 1.28758e8i −0.380787 + 0.138595i
\(366\) −1.01701e9 + 3.98849e8i −1.08428 + 0.425231i
\(367\) −1.03863e7 5.89036e7i −0.0109680 0.0622029i 0.978832 0.204663i \(-0.0656098\pi\)
−0.989801 + 0.142460i \(0.954499\pi\)
\(368\) 6.49369e7 1.12474e8i 0.0679241 0.117648i
\(369\) 9.80042e8 4.12534e8i 1.01544 0.427432i
\(370\) −1.94142e8 3.36265e8i −0.199257 0.345124i
\(371\) −5.92506e8 + 4.97172e8i −0.602399 + 0.505473i
\(372\) −5.67572e8 2.81131e9i −0.571638 2.83145i
\(373\) −7.34937e7 + 4.16803e8i −0.0733279 + 0.415863i 0.925942 + 0.377665i \(0.123273\pi\)
−0.999270 + 0.0381981i \(0.987838\pi\)
\(374\) 1.41445e9 + 1.18686e9i 1.39809 + 1.17314i
\(375\) −3.88860e8 + 7.13634e8i −0.380789 + 0.698821i
\(376\) −1.08968e8 3.96613e7i −0.105717 0.0384777i
\(377\) −1.54796e8 −0.148787
\(378\) −6.21377e8 + 2.79804e8i −0.591744 + 0.266460i
\(379\) 1.60275e9 1.51227 0.756133 0.654418i \(-0.227086\pi\)
0.756133 + 0.654418i \(0.227086\pi\)
\(380\) 6.14733e8 + 2.23744e8i 0.574704 + 0.209175i
\(381\) −1.80805e8 2.96043e8i −0.167484 0.274232i
\(382\) −7.37674e8 6.18982e8i −0.677084 0.568141i
\(383\) 1.74349e7 9.88780e7i 0.0158571 0.0899299i −0.975852 0.218432i \(-0.929906\pi\)
0.991709 + 0.128502i \(0.0410169\pi\)
\(384\) 1.14139e9 1.00677e9i 1.02867 0.907341i
\(385\) −1.62795e8 + 1.36601e8i −0.145388 + 0.121995i
\(386\) −1.36742e9 2.36843e9i −1.21017 2.09607i
\(387\) 3.05481e8 + 1.34155e9i 0.267914 + 1.17657i
\(388\) −8.02610e7 + 1.39016e8i −0.0697579 + 0.120824i
\(389\) 1.37843e8 + 7.81744e8i 0.118730 + 0.673350i 0.984836 + 0.173490i \(0.0555043\pi\)
−0.866106 + 0.499861i \(0.833385\pi\)
\(390\) −1.52647e7 + 1.01100e8i −0.0130306 + 0.0863029i
\(391\) −6.38731e8 + 2.32479e8i −0.540381 + 0.196682i
\(392\) −7.27946e8 + 2.64951e8i −0.610377 + 0.222159i
\(393\) −3.44374e8 2.74773e8i −0.286191 0.228350i
\(394\) 6.13265e8 + 3.47800e9i 0.505140 + 2.86479i
\(395\) 4.20939e7 7.29088e7i 0.0343660 0.0595237i
\(396\) 8.84112e8 1.72236e9i 0.715442 1.39377i
\(397\) 1.02221e9 + 1.77051e9i 0.819920 + 1.42014i 0.905741 + 0.423832i \(0.139315\pi\)
−0.0858208 + 0.996311i \(0.527351\pi\)
\(398\) 1.56523e9 1.31339e9i 1.24448 1.04424i
\(399\) 4.58750e8 + 1.54262e8i 0.361552 + 0.121578i
\(400\) 4.66438e7 2.64530e8i 0.0364405 0.206664i
\(401\) 4.36462e8 + 3.66235e8i 0.338019 + 0.283632i 0.795958 0.605352i \(-0.206968\pi\)
−0.457939 + 0.888984i \(0.651412\pi\)
\(402\) −2.18151e9 + 5.38468e7i −1.67481 + 0.0413398i
\(403\) −2.99163e8 1.08886e8i −0.227688 0.0828716i
\(404\) 1.79552e9 1.35474
\(405\) −4.46293e7 + 5.87494e8i −0.0333832 + 0.439451i
\(406\) 1.03845e9 0.770096
\(407\) 7.66900e8 + 2.79129e8i 0.563843 + 0.205222i
\(408\) −1.18157e9 + 2.91649e7i −0.861287 + 0.0212594i
\(409\) 3.87627e8 + 3.25258e8i 0.280145 + 0.235069i 0.772023 0.635595i \(-0.219245\pi\)
−0.491878 + 0.870664i \(0.663689\pi\)
\(410\) −1.85851e8 + 1.05401e9i −0.133174 + 0.755270i
\(411\) 1.59146e9 + 5.35152e8i 1.13070 + 0.380217i
\(412\) 3.16782e8 2.65812e8i 0.223162 0.187255i
\(413\) −4.74952e8 8.22640e8i −0.331760 0.574625i
\(414\) 6.44852e8 + 9.99544e8i 0.446641 + 0.692310i
\(415\) −9.63470e7 + 1.66878e8i −0.0661713 + 0.114612i
\(416\) −3.81348e7 2.16273e8i −0.0259714 0.147291i
\(417\) −8.05181e8 6.42447e8i −0.543773 0.433871i
\(418\) −2.15648e9 + 7.84894e8i −1.44420 + 0.525647i
\(419\) −1.66171e9 + 6.04812e8i −1.10358 + 0.401671i −0.828636 0.559788i \(-0.810883\pi\)
−0.274947 + 0.961459i \(0.588660\pi\)
\(420\) 6.13564e7 4.06370e8i 0.0404098 0.267639i
\(421\) −3.50467e6 1.98760e7i −0.00228908 0.0129820i 0.983642 0.180135i \(-0.0576536\pi\)
−0.985931 + 0.167153i \(0.946542\pi\)
\(422\) 2.03354e9 3.52219e9i 1.31722 2.28149i
\(423\) −1.64351e8 + 1.52340e8i −0.105580 + 0.0978637i
\(424\) 1.17378e9 + 2.03305e9i 0.747837 + 1.29529i
\(425\) −1.07693e9 + 9.03655e8i −0.680500 + 0.571007i
\(426\) 5.38542e8 4.75021e8i 0.337509 0.297701i
\(427\) 8.46391e7 4.80012e8i 0.0526106 0.298370i
\(428\) 2.64167e9 + 2.21662e9i 1.62864 + 1.36659i
\(429\) −1.12013e8 1.83406e8i −0.0684963 0.112153i
\(430\) −1.30136e9 4.73656e8i −0.789328 0.287292i
\(431\) −1.40740e9 −0.846735 −0.423367 0.905958i \(-0.639152\pi\)
−0.423367 + 0.905958i \(0.639152\pi\)
\(432\) −1.07364e8 4.23000e8i −0.0640718 0.252433i
\(433\) 2.36842e9 1.40201 0.701006 0.713155i \(-0.252735\pi\)
0.701006 + 0.713155i \(0.252735\pi\)
\(434\) 2.00694e9 + 7.30466e8i 1.17847 + 0.428930i
\(435\) 4.29591e8 7.88383e8i 0.250232 0.459224i
\(436\) −2.90984e9 2.44165e9i −1.68138 1.41085i
\(437\) 1.46700e8 8.31976e8i 0.0840900 0.476898i
\(438\) 5.05415e8 + 2.50343e9i 0.287401 + 1.42356i
\(439\) 1.00116e9 8.40076e8i 0.564780 0.473906i −0.315129 0.949049i \(-0.602048\pi\)
0.879909 + 0.475142i \(0.157603\pi\)
\(440\) 3.22503e8 + 5.58592e8i 0.180489 + 0.312616i
\(441\) −1.86904e8 + 1.48532e9i −0.103773 + 0.824678i
\(442\) −1.98185e8 + 3.43267e8i −0.109167 + 0.189084i
\(443\) −2.12817e6 1.20694e7i −0.00116304 0.00659590i 0.984221 0.176945i \(-0.0566215\pi\)
−0.985384 + 0.170349i \(0.945510\pi\)
\(444\) −1.46932e9 + 5.76234e8i −0.796667 + 0.312434i
\(445\) 3.18053e8 1.15762e8i 0.171096 0.0622739i
\(446\) −4.93115e9 + 1.79479e9i −2.63194 + 0.957949i
\(447\) −2.06824e9 + 8.11117e8i −1.09528 + 0.429543i
\(448\) 2.20464e8 + 1.25031e9i 0.115842 + 0.656971i
\(449\) 1.69912e9 2.94296e9i 0.885854 1.53434i 0.0411218 0.999154i \(-0.486907\pi\)
0.844732 0.535190i \(-0.179760\pi\)
\(450\) 1.96034e9 + 1.48647e9i 1.01412 + 0.768978i
\(451\) −1.12478e9 1.94817e9i −0.577363 1.00002i
\(452\) 2.04250e9 1.71386e9i 1.04034 0.872952i
\(453\) −7.31607e8 3.62381e9i −0.369772 1.83156i
\(454\) 5.54323e7 3.14372e8i 0.0278014 0.157670i
\(455\) −3.49469e7 2.93239e7i −0.0173927 0.0145942i
\(456\) 7.02877e8 1.28991e9i 0.347138 0.637065i
\(457\) −2.35354e9 8.56617e8i −1.15349 0.419836i −0.306723 0.951799i \(-0.599233\pi\)
−0.846768 + 0.531962i \(0.821455\pi\)
\(458\) −3.28902e9 −1.59969
\(459\) −9.92592e8 + 2.05711e9i −0.479100 + 0.992918i
\(460\) −7.17359e8 −0.343624
\(461\) −2.88321e9 1.04940e9i −1.37064 0.498872i −0.451313 0.892366i \(-0.649044\pi\)
−0.919328 + 0.393493i \(0.871267\pi\)
\(462\) 7.51439e8 + 1.23038e9i 0.354525 + 0.580487i
\(463\) −3.19236e8 2.67871e8i −0.149479 0.125427i 0.564982 0.825103i \(-0.308883\pi\)
−0.714460 + 0.699676i \(0.753328\pi\)
\(464\) −1.15480e8 + 6.54921e8i −0.0536654 + 0.304352i
\(465\) 1.38480e9 1.22147e9i 0.638708 0.563374i
\(466\) 1.17274e9 9.84049e8i 0.536849 0.450470i
\(467\) 1.69549e8 + 2.93668e8i 0.0770348 + 0.133428i 0.901969 0.431800i \(-0.142121\pi\)
−0.824935 + 0.565228i \(0.808788\pi\)
\(468\) 3.97076e8 + 1.22704e8i 0.179066 + 0.0553346i
\(469\) 4.86820e8 8.43197e8i 0.217903 0.377419i
\(470\) −3.91678e7 2.22132e8i −0.0174015 0.0986889i
\(471\) −2.91041e8 + 1.92760e9i −0.128346 + 0.850047i
\(472\) −2.70922e9 + 9.86074e8i −1.18590 + 0.431631i
\(473\) 2.73526e9 9.95555e8i 1.18846 0.432565i
\(474\) −4.46440e8 3.56210e8i −0.192548 0.153632i
\(475\) −3.03411e8 1.72073e9i −0.129899 0.736691i
\(476\) 7.96602e8 1.37975e9i 0.338545 0.586378i
\(477\) 4.53112e9 2.23822e8i 1.91158 0.0944253i
\(478\) 2.91490e7 + 5.04875e7i 0.0122075 + 0.0211439i
\(479\) −1.76063e9 + 1.47734e9i −0.731971 + 0.614196i −0.930668 0.365864i \(-0.880773\pi\)
0.198697 + 0.980061i \(0.436329\pi\)
\(480\) 1.20732e9 + 4.05981e8i 0.498285 + 0.167556i
\(481\) −3.04223e7 + 1.72533e8i −0.0124648 + 0.0706911i
\(482\) 1.52064e9 + 1.27596e9i 0.618530 + 0.519008i
\(483\) −5.30569e8 + 1.30962e7i −0.214253 + 0.00528846i
\(484\) −3.45168e8 1.25631e8i −0.138379 0.0503659i
\(485\) −1.03349e8 −0.0411349
\(486\) 3.89572e9 + 8.94401e8i 1.53943 + 0.353431i
\(487\) −2.02240e9 −0.793442 −0.396721 0.917939i \(-0.629852\pi\)
−0.396721 + 0.917939i \(0.629852\pi\)
\(488\) −1.39016e9 5.05977e8i −0.541497 0.197089i
\(489\) 1.53841e9 3.79729e7i 0.594964 0.0146856i
\(490\) −1.15428e9 9.68557e8i −0.443226 0.371911i
\(491\) 3.09187e8 1.75349e9i 0.117879 0.668525i −0.867405 0.497602i \(-0.834214\pi\)
0.985284 0.170923i \(-0.0546750\pi\)
\(492\) 4.12349e9 + 1.38659e9i 1.56094 + 0.524892i
\(493\) 2.66626e9 2.23726e9i 1.00216 0.840915i
\(494\) −2.46319e8 4.26637e8i −0.0919292 0.159226i
\(495\) 1.24495e9 6.14964e7i 0.461354 0.0227893i
\(496\) −6.83864e8 + 1.18449e9i −0.251642 + 0.435857i
\(497\) 5.56372e7 + 3.15534e8i 0.0203291 + 0.115292i
\(498\) 1.02184e9 + 8.15315e8i 0.370748 + 0.295817i
\(499\) −1.59256e9 + 5.79645e8i −0.573779 + 0.208838i −0.612580 0.790409i \(-0.709868\pi\)
0.0388013 + 0.999247i \(0.487646\pi\)
\(500\) −3.12447e9 + 1.13722e9i −1.11785 + 0.406862i
\(501\) −9.81698e7 + 6.50189e8i −0.0348776 + 0.230998i
\(502\) 8.70446e8 + 4.93654e9i 0.307099 + 1.74165i
\(503\) −6.38921e8 + 1.10664e9i −0.223851 + 0.387722i −0.955974 0.293451i \(-0.905196\pi\)
0.732123 + 0.681173i \(0.238530\pi\)
\(504\) −8.81714e8 2.72465e8i −0.306776 0.0947992i
\(505\) 5.78005e8 + 1.00113e9i 0.199715 + 0.345917i
\(506\) 1.92774e9 1.61757e9i 0.661489 0.555055i
\(507\) −2.16610e9 + 1.91061e9i −0.738160 + 0.651095i
\(508\) 2.46445e8 1.39766e9i 0.0834059 0.473019i
\(509\) −1.52843e9 1.28250e9i −0.513727 0.431068i 0.348711 0.937230i \(-0.386619\pi\)
−0.862438 + 0.506162i \(0.831064\pi\)
\(510\) −1.19827e9 1.96200e9i −0.399998 0.654944i
\(511\) −1.07079e9 3.89736e8i −0.355003 0.129210i
\(512\) −1.56158e9 −0.514185
\(513\) −1.59736e9 2.34675e9i −0.522386 0.767460i
\(514\) −5.20792e9 −1.69158
\(515\) 2.50187e8 + 9.10605e7i 0.0807121 + 0.0293768i
\(516\) −2.69343e9 + 4.94296e9i −0.863041 + 1.58385i
\(517\) 3.63175e8 + 3.04740e8i 0.115584 + 0.0969867i
\(518\) 2.04088e8 1.15744e9i 0.0645155 0.365885i
\(519\) −8.93915e8 4.42776e9i −0.280679 1.39027i
\(520\) −1.06069e8 + 8.90021e7i −0.0330807 + 0.0277580i
\(521\) 4.49772e8 + 7.79027e8i 0.139335 + 0.241335i 0.927245 0.374455i \(-0.122170\pi\)
−0.787910 + 0.615790i \(0.788837\pi\)
\(522\) −4.85339e9 3.68020e9i −1.49348 1.13246i
\(523\) −1.81103e9 + 3.13680e9i −0.553567 + 0.958805i 0.444447 + 0.895805i \(0.353400\pi\)
−0.998014 + 0.0630003i \(0.979933\pi\)
\(524\) −3.12993e8 1.77507e9i −0.0950333 0.538961i
\(525\) −1.02191e9 + 4.00768e8i −0.308215 + 0.120875i
\(526\) 7.99881e9 2.91133e9i 2.39649 0.872251i
\(527\) 6.72661e9 2.44829e9i 2.00198 0.728661i
\(528\) −8.59529e8 + 3.37087e8i −0.254122 + 0.0996606i
\(529\) −4.30375e8 2.44078e9i −0.126402 0.716859i
\(530\) −2.28314e9 + 3.95451e9i −0.666141 + 1.15379i
\(531\) −6.95606e8 + 5.52795e9i −0.201620 + 1.60226i
\(532\) 9.90075e8 + 1.71486e9i 0.285087 + 0.493785i
\(533\) 3.69929e8 3.10408e8i 0.105821 0.0887947i
\(534\) −4.54402e8 2.25076e9i −0.129136 0.639637i
\(535\) −3.85537e8 + 2.18649e9i −0.108850 + 0.617318i
\(536\) −2.26376e9 1.89952e9i −0.634971 0.532804i
\(537\) 2.16192e9 3.96755e9i 0.602463 1.10564i
\(538\) 8.06411e9 + 2.93510e9i 2.23264 + 0.812614i
\(539\) 3.16709e9 0.871163
\(540\) −1.72690e9 + 1.68180e9i −0.471944 + 0.459617i
\(541\) 2.40561e8 0.0653182 0.0326591 0.999467i \(-0.489602\pi\)
0.0326591 + 0.999467i \(0.489602\pi\)
\(542\) 6.55617e9 + 2.38625e9i 1.76870 + 0.643752i
\(543\) −2.63795e8 4.31930e8i −0.0707079 0.115775i
\(544\) 3.78263e9 + 3.17400e9i 1.00739 + 0.845301i
\(545\) 4.24676e8 2.40846e9i 0.112375 0.637310i
\(546\) −2.32100e8 + 2.04724e8i −0.0610241 + 0.0538264i
\(547\) −2.72198e9 + 2.28401e9i −0.711098 + 0.596682i −0.924907 0.380193i \(-0.875857\pi\)
0.213809 + 0.976876i \(0.431413\pi\)
\(548\) 3.43468e9 + 5.94903e9i 0.891567 + 1.54424i
\(549\) −2.09670e9 + 1.94347e9i −0.540797 + 0.501273i
\(550\) 2.60236e9 4.50743e9i 0.666958 1.15521i
\(551\) 7.51183e8 + 4.26017e9i 0.191300 + 1.08492i
\(552\) −2.40490e8 + 1.59279e9i −0.0608569 + 0.403062i
\(553\) 2.39459e8 8.71561e7i 0.0602135 0.0219159i
\(554\) −3.18884e9 + 1.16064e9i −0.796800 + 0.290011i
\(555\) −7.94291e8 6.33757e8i −0.197221 0.157361i
\(556\) −7.31810e8 4.15030e9i −0.180566 1.02404i
\(557\) −1.01299e9 + 1.75455e9i −0.248377 + 0.430202i −0.963076 0.269231i \(-0.913231\pi\)
0.714699 + 0.699433i \(0.246564\pi\)
\(558\) −6.79107e9 1.05264e10i −1.65470 2.56484i
\(559\) 3.12429e8 + 5.41144e8i 0.0756503 + 0.131030i
\(560\) −1.50136e8 + 1.25979e8i −0.0361267 + 0.0303139i
\(561\) 4.58010e9 + 1.54013e9i 1.09523 + 0.368288i
\(562\) 1.11112e8 6.30149e8i 0.0264049 0.149750i
\(563\) 3.25885e9 + 2.73450e9i 0.769635 + 0.645800i 0.940615 0.339474i \(-0.110249\pi\)
−0.170981 + 0.985274i \(0.554694\pi\)
\(564\) −9.16557e8 + 2.26236e7i −0.215121 + 0.00530988i
\(565\) 1.61311e9 + 5.87126e8i 0.376267 + 0.136950i
\(566\) −3.95240e9 −0.916227
\(567\) −1.24654e9 + 1.27541e9i −0.287188 + 0.293839i
\(568\) 9.72464e8 0.222666
\(569\) 3.08913e9 + 1.12435e9i 0.702980 + 0.255864i 0.668683 0.743548i \(-0.266858\pi\)
0.0342975 + 0.999412i \(0.489081\pi\)
\(570\) 2.85647e9 7.05069e7i 0.646052 0.0159467i
\(571\) 3.49918e9 + 2.93616e9i 0.786575 + 0.660014i 0.944895 0.327373i \(-0.106163\pi\)
−0.158321 + 0.987388i \(0.550608\pi\)
\(572\) 1.52678e8 8.65883e8i 0.0341108 0.193452i
\(573\) −2.38865e9 8.03222e8i −0.530410 0.178359i
\(574\) −2.48168e9 + 2.08237e9i −0.547714 + 0.459586i
\(575\) 9.58004e8 + 1.65931e9i 0.210150 + 0.363991i
\(576\) 3.40064e9 6.62488e9i 0.741451 1.44444i
\(577\) −4.25167e9 + 7.36410e9i −0.921391 + 1.59590i −0.124125 + 0.992267i \(0.539612\pi\)
−0.797266 + 0.603629i \(0.793721\pi\)
\(578\) −2.74300e8 1.55563e9i −0.0590852 0.335089i
\(579\) −5.59448e9 4.46379e9i −1.19780 0.955715i
\(580\) 3.45174e9 1.25633e9i 0.734582 0.267366i
\(581\) −5.48089e8 + 1.99488e8i −0.115940 + 0.0421988i
\(582\) −1.04674e8 + 6.93267e8i −0.0220094 + 0.145771i
\(583\) −1.66661e9 9.45182e9i −0.348333 1.97549i
\(584\) −1.72929e9 + 2.99521e9i −0.359271 + 0.622276i
\(585\) 5.94086e7 + 2.60900e8i 0.0122689 + 0.0538800i
\(586\) −2.03697e9 3.52813e9i −0.418160 0.724275i
\(587\) 7.72415e8 6.48133e8i 0.157622 0.132261i −0.560566 0.828110i \(-0.689416\pi\)
0.718188 + 0.695849i \(0.244972\pi\)
\(588\) −4.59328e9 + 4.05151e9i −0.931756 + 0.821857i
\(589\) −1.54493e9 + 8.76171e9i −0.311533 + 1.76679i
\(590\) −4.29592e9 3.60470e9i −0.861141 0.722583i
\(591\) 4.81728e9 + 7.88764e9i 0.959943 + 1.57178i
\(592\) 7.07269e8 + 2.57425e8i 0.140107 + 0.0509946i
\(593\) −2.37491e9 −0.467686 −0.233843 0.972274i \(-0.575130\pi\)
−0.233843 + 0.972274i \(0.575130\pi\)
\(594\) 8.48395e8 8.41345e9i 0.166091 1.64711i
\(595\) 1.02575e9 0.199634
\(596\) −8.54107e9 3.10870e9i −1.65253 0.601473i
\(597\) 2.55853e9 4.69541e9i 0.492132 0.903156i
\(598\) 4.13826e8 + 3.47241e8i 0.0791341 + 0.0664014i
\(599\) 1.57671e9 8.94197e9i 0.299749 1.69996i −0.347497 0.937681i \(-0.612968\pi\)
0.647246 0.762281i \(-0.275921\pi\)
\(600\) 6.59315e8 + 3.26573e9i 0.124613 + 0.617236i
\(601\) −7.06784e8 + 5.93062e8i −0.132809 + 0.111440i −0.706772 0.707441i \(-0.749849\pi\)
0.573964 + 0.818881i \(0.305405\pi\)
\(602\) −2.09594e9 3.63027e9i −0.391553 0.678190i
\(603\) −5.26347e9 + 2.21558e9i −0.977600 + 0.411506i
\(604\) 7.56258e9 1.30988e10i 1.39650 2.41881i
\(605\) −4.10664e7 2.32899e8i −0.00753950 0.0427586i
\(606\) 7.30104e9 2.86330e9i 1.33269 0.522652i
\(607\) −1.24277e9 + 4.52331e8i −0.225543 + 0.0820910i −0.452320 0.891856i \(-0.649403\pi\)
0.226777 + 0.973947i \(0.427181\pi\)
\(608\) −5.76703e9 + 2.09903e9i −1.04061 + 0.378753i
\(609\) 2.53002e9 9.92217e8i 0.453904 0.178011i
\(610\) −4.99682e8 2.83384e9i −0.0891332 0.505499i
\(611\) −5.08862e7 + 8.81375e7i −0.00902518 + 0.0156321i
\(612\) −8.61281e9 + 3.62543e9i −1.51885 + 0.639337i
\(613\) −4.79933e9 8.31269e9i −0.841529 1.45757i −0.888602 0.458680i \(-0.848323\pi\)
0.0470727 0.998891i \(-0.485011\pi\)
\(614\) −4.25675e9 + 3.57183e9i −0.742144 + 0.622733i
\(615\) 5.54288e8 + 2.74551e9i 0.0960888 + 0.475949i
\(616\) −3.39025e8 + 1.92271e9i −0.0584385 + 0.331421i
\(617\) −4.28770e8 3.59781e8i −0.0734897 0.0616651i 0.605303 0.795995i \(-0.293052\pi\)
−0.678793 + 0.734330i \(0.737496\pi\)
\(618\) 8.64230e8 1.58603e9i 0.147289 0.270303i
\(619\) −1.09196e10 3.97440e9i −1.85050 0.673525i −0.984987 0.172631i \(-0.944773\pi\)
−0.865508 0.500894i \(-0.833004\pi\)
\(620\) 7.55466e9 1.27304
\(621\) 2.52612e9 + 1.81909e9i 0.423286 + 0.304813i
\(622\) 1.14395e8 0.0190607
\(623\) 9.62714e8 + 3.50399e8i 0.159510 + 0.0580571i
\(624\) −1.03303e8 1.69145e8i −0.0170203 0.0278685i
\(625\) 2.12752e9 + 1.78520e9i 0.348573 + 0.292488i
\(626\) −1.88305e9 + 1.06793e10i −0.306797 + 1.73993i
\(627\) −4.50398e9 + 3.97274e9i −0.729726 + 0.643656i
\(628\) −6.10976e9 + 5.12670e9i −0.984386 + 0.825998i
\(629\) −1.96961e9 3.41146e9i −0.315575 0.546592i
\(630\) −3.98544e8 1.75025e9i −0.0635015 0.278874i
\(631\) −4.49642e8 + 7.78802e8i −0.0712466 + 0.123403i −0.899448 0.437028i \(-0.856031\pi\)
0.828201 + 0.560431i \(0.189364\pi\)
\(632\) −1.34306e8 7.61686e8i −0.0211634 0.120024i
\(633\) 1.58902e9 1.05243e10i 0.249010 1.64922i
\(634\) 3.57353e7 1.30066e7i 0.00556910 0.00202699i
\(635\) 8.58632e8 3.12517e8i 0.133076 0.0484356i
\(636\) 1.45084e10 + 1.15761e10i 2.23624 + 1.78428i
\(637\) 1.18059e8 + 6.69545e8i 0.0180972 + 0.102634i
\(638\) −6.44290e9 + 1.11594e10i −0.982221 + 1.70126i
\(639\) 8.58200e8 1.67188e9i 0.130117 0.253485i
\(640\) 2.00449e9 + 3.47188e9i 0.302256 + 0.523522i
\(641\) −3.79303e9 + 3.18273e9i −0.568831 + 0.477306i −0.881258 0.472636i \(-0.843303\pi\)
0.312427 + 0.949942i \(0.398858\pi\)
\(642\) 1.42765e10 + 4.80071e9i 2.12937 + 0.716033i
\(643\) 2.25317e9 1.27784e10i 0.334238 1.89556i −0.100389 0.994948i \(-0.532009\pi\)
0.434627 0.900611i \(-0.356880\pi\)
\(644\) −1.66337e9 1.39573e9i −0.245407 0.205921i
\(645\) −3.62312e9 + 8.94305e7i −0.531648 + 0.0131228i
\(646\) 1.04088e10 + 3.78851e9i 1.51911 + 0.552910i
\(647\) 1.05373e10 1.52955 0.764776 0.644296i \(-0.222850\pi\)
0.764776 + 0.644296i \(0.222850\pi\)
\(648\) 3.15525e9 + 4.39815e9i 0.455535 + 0.634976i
\(649\) 1.17870e10 1.69258
\(650\) 1.04991e9 + 3.82136e8i 0.149953 + 0.0545784i
\(651\) 5.58754e9 1.37919e8i 0.793756 0.0195925i
\(652\) 4.82300e9 + 4.04697e9i 0.681476 + 0.571826i
\(653\) −3.69025e8 + 2.09284e9i −0.0518632 + 0.294131i −0.999696 0.0246356i \(-0.992157\pi\)
0.947833 + 0.318766i \(0.103269\pi\)
\(654\) −1.57258e10 5.28807e9i −2.19832 0.739222i
\(655\) 8.88978e8 7.45941e8i 0.123608 0.103719i
\(656\) −1.03732e9 1.79669e9i −0.143466 0.248490i
\(657\) 3.62334e9 + 5.61630e9i 0.498459 + 0.772631i
\(658\) 3.41371e8 5.91272e8i 0.0467128 0.0809089i
\(659\) 8.49358e8 + 4.81695e9i 0.115609 + 0.655651i 0.986447 + 0.164081i \(0.0524659\pi\)
−0.870838 + 0.491570i \(0.836423\pi\)
\(660\) 3.98626e9 + 3.18060e9i 0.539712 + 0.430631i
\(661\) −6.41537e9 + 2.33500e9i −0.864006 + 0.314472i −0.735737 0.677267i \(-0.763164\pi\)
−0.128269 + 0.991739i \(0.540942\pi\)
\(662\) 1.94361e10 7.07418e9i 2.60380 0.947705i
\(663\) −1.54864e8 + 1.02568e9i −0.0206373 + 0.136683i
\(664\) 3.07407e8 + 1.74339e9i 0.0407498 + 0.231104i
\(665\) −6.37441e8 + 1.10408e9i −0.0840551 + 0.145588i
\(666\) −5.05573e9 + 4.68624e9i −0.663169 + 0.614702i
\(667\) −2.37182e9 4.10811e9i −0.309486 0.536045i
\(668\) −2.06086e9 + 1.72926e9i −0.267504 + 0.224462i
\(669\) −1.02991e10 + 9.08434e9i −1.32987 + 1.17301i
\(670\) 9.98140e8 5.66073e9i 0.128212 0.727128i
\(671\) 4.63319e9 + 3.88771e9i 0.592040 + 0.496781i
\(672\) 2.00956e9 + 3.29038e9i 0.255452 + 0.418268i
\(673\) 5.98629e9 + 2.17883e9i 0.757015 + 0.275531i 0.691555 0.722324i \(-0.256926\pi\)
0.0654607 + 0.997855i \(0.479148\pi\)
\(674\) 9.80983e9 1.23410
\(675\) 6.19636e9 + 1.74850e9i 0.775485 + 0.218828i
\(676\) −1.18169e10 −1.47127
\(677\) −8.67542e9 3.15759e9i −1.07456 0.391107i −0.256679 0.966497i \(-0.582628\pi\)
−0.817880 + 0.575390i \(0.804850\pi\)
\(678\) 5.57225e9 1.02261e10i 0.686636 1.26011i
\(679\) −2.39639e8 2.01081e8i −0.0293774 0.0246506i
\(680\) 5.40620e8 3.06601e9i 0.0659342 0.373931i
\(681\) −1.65323e8 8.18882e8i −0.0200595 0.0993589i
\(682\) −2.03015e10 + 1.70350e10i −2.45065 + 2.05634i
\(683\) −2.39674e9 4.15128e9i −0.287839 0.498551i 0.685455 0.728115i \(-0.259603\pi\)
−0.973294 + 0.229564i \(0.926270\pi\)
\(684\) 1.45005e9 1.15235e10i 0.173255 1.37685i
\(685\) −2.21135e9 + 3.83017e9i −0.262870 + 0.455304i
\(686\) −1.74486e9 9.89559e9i −0.206360 1.17033i
\(687\) −8.01318e9 + 3.14258e9i −0.942880 + 0.369776i
\(688\) 2.52258e9 9.18145e8i 0.295315 0.107486i
\(689\) 1.93606e9 7.04667e8i 0.225502 0.0820761i
\(690\) −2.91697e9 + 1.14397e9i −0.338033 + 0.132569i
\(691\) −1.70425e8 9.66530e8i −0.0196499 0.111440i 0.973405 0.229090i \(-0.0735751\pi\)
−0.993055 + 0.117650i \(0.962464\pi\)
\(692\) 9.24034e9 1.60047e10i 1.06003 1.83602i
\(693\) 3.00637e9 + 2.27965e9i 0.343143 + 0.260197i
\(694\) −1.24631e9 2.15868e9i −0.141537 0.245149i
\(695\) 2.07852e9 1.74408e9i 0.234859 0.197070i
\(696\) −1.63232e9 8.08526e9i −0.183516 0.908995i
\(697\) −1.88549e9 + 1.06931e10i −0.210916 + 1.19616i
\(698\) −7.36339e8 6.17862e8i −0.0819566 0.0687697i
\(699\) 1.91697e9 3.51801e9i 0.212298 0.389607i
\(700\) −4.22009e9 1.53599e9i −0.465028 0.169256i
\(701\) −5.01902e9 −0.550308 −0.275154 0.961400i \(-0.588729\pi\)
−0.275154 + 0.961400i \(0.588729\pi\)
\(702\) 1.81029e9 1.34270e8i 0.197500 0.0146487i
\(703\) 4.89595e9 0.531488
\(704\) −1.48040e10 5.38821e9i −1.59910 0.582023i
\(705\) −3.07668e8 5.03765e8i −0.0330690 0.0541460i
\(706\) −1.52880e10 1.28281e10i −1.63506 1.37198i
\(707\) −6.07615e8 + 3.44596e9i −0.0646637 + 0.366726i
\(708\) −1.70949e10 + 1.50786e10i −1.81030 + 1.59678i
\(709\) −1.26803e10 + 1.06400e10i −1.33618 + 1.12119i −0.353595 + 0.935398i \(0.615041\pi\)
−0.982589 + 0.185793i \(0.940515\pi\)
\(710\) 9.45775e8 + 1.63813e9i 0.0991708 + 0.171769i
\(711\) −1.42803e9 4.41287e8i −0.149003 0.0460445i
\(712\) 1.55475e9 2.69290e9i 0.161428 0.279602i
\(713\) −1.69412e9 9.60781e9i −0.175037 0.992684i
\(714\) 1.03890e9 6.88078e9i 0.106815 0.707447i
\(715\) 5.31943e8 1.93611e8i 0.0544245 0.0198089i
\(716\) 1.73710e10 6.32251e9i 1.76859 0.643716i
\(717\) 1.19257e8 + 9.51537e7i 0.0120827 + 0.00964070i
\(718\) 3.46893e9 + 1.96733e10i 0.349752 + 1.98354i
\(719\) 4.15265e9 7.19260e9i 0.416652 0.721663i −0.578948 0.815365i \(-0.696537\pi\)
0.995600 + 0.0937014i \(0.0298699\pi\)
\(720\) 1.14815e9 5.67147e7i 0.114640 0.00566281i
\(721\) 4.02945e8 + 6.97921e8i 0.0400380 + 0.0693478i
\(722\) 1.69004e9 1.41811e9i 0.167116 0.140227i
\(723\) 4.92395e9 + 1.65576e9i 0.484540 + 0.162934i
\(724\) 3.59565e8 2.03920e9i 0.0352122 0.199698i
\(725\) −7.51567e9 6.30639e9i −0.732461 0.614608i
\(726\) −1.60388e9 + 3.95890e7i −0.155559 + 0.00383970i
\(727\) 1.77701e10 + 6.46778e9i 1.71522 + 0.624287i 0.997408 0.0719541i \(-0.0229235\pi\)
0.717808 + 0.696242i \(0.245146\pi\)
\(728\) −4.19112e8 −0.0402597
\(729\) 1.03459e10 1.54320e9i 0.989058 0.147529i
\(730\) −6.72731e9 −0.640047
\(731\) −1.32025e10 4.80532e9i −1.25010 0.455000i
\(732\) −1.16929e10 + 2.88620e8i −1.10188 + 0.0271980i
\(733\) −5.47152e8 4.59115e8i −0.0513149 0.0430583i 0.616770 0.787144i \(-0.288441\pi\)
−0.668084 + 0.744085i \(0.732886\pi\)
\(734\) 1.85601e8 1.05260e9i 0.0173238 0.0982484i
\(735\) −3.73766e9 1.25685e9i −0.347212 0.116755i
\(736\) 5.15533e9 4.32583e9i 0.476633 0.399942i
\(737\) 6.04079e9 + 1.04629e10i 0.555850 + 0.962760i
\(738\) 1.89783e10 9.37465e8i 1.73804 0.0858535i
\(739\) 9.91757e8 1.71777e9i 0.0903961 0.156571i −0.817282 0.576238i \(-0.804520\pi\)
0.907678 + 0.419668i \(0.137853\pi\)
\(740\) −7.21912e8 4.09417e9i −0.0654897 0.371411i
\(741\) −1.00776e9 8.04082e8i −0.0909899 0.0726000i
\(742\) −1.29881e10 + 4.72727e9i −1.16716 + 0.424812i
\(743\) 4.28075e9 1.55807e9i 0.382877 0.139356i −0.143409 0.989664i \(-0.545806\pi\)
0.526286 + 0.850308i \(0.323584\pi\)
\(744\) 2.53265e9 1.67740e10i 0.225460 1.49325i
\(745\) −1.01618e9 5.76302e9i −0.0900371 0.510626i
\(746\) −3.78155e9 + 6.54984e9i −0.333491 + 0.577623i
\(747\) 3.26856e9 + 1.01004e9i 0.286903 + 0.0886581i
\(748\) 9.88477e9 + 1.71209e10i 0.863597 + 1.49579i
\(749\) −5.14810e9 + 4.31977e9i −0.447673 + 0.375642i
\(750\) −1.08914e10 + 9.60679e9i −0.942692 + 0.831503i
\(751\) 2.00820e9 1.13891e10i 0.173008 0.981178i −0.767410 0.641157i \(-0.778455\pi\)
0.940418 0.340021i \(-0.110434\pi\)
\(752\) 3.34936e8 + 2.81045e8i 0.0287210 + 0.0240998i
\(753\) 6.83746e9 + 1.11954e10i 0.583596 + 0.955560i
\(754\) −2.59935e9 9.46088e8i −0.220834 0.0803770i
\(755\) 9.73804e9 0.823488