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Properties

Label 74.8.f.b.7.4
Level $74$
Weight $8$
Character 74.7
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.4
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(-36.4042 - 13.2501i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-1.10281 - 6.25436i) q^{5} -309.925 q^{6} +(125.532 + 711.929i) q^{7} +(256.000 - 443.405i) q^{8} +(-525.635 - 441.061i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(-36.4042 - 13.2501i) q^{3} +(49.0268 - 41.1384i) q^{4} +(-1.10281 - 6.25436i) q^{5} -309.925 q^{6} +(125.532 + 711.929i) q^{7} +(256.000 - 443.405i) q^{8} +(-525.635 - 441.061i) q^{9} +(-25.4034 - 43.9999i) q^{10} +(435.627 - 754.529i) q^{11} +(-2329.87 + 848.004i) q^{12} +(-8006.36 + 6718.13i) q^{13} +(2891.65 + 5008.48i) q^{14} +(-42.7236 + 242.297i) q^{15} +(711.263 - 4033.77i) q^{16} +(21500.3 + 18040.9i) q^{17} +(-5158.30 - 1877.47i) q^{18} +(565.620 + 205.869i) q^{19} +(-311.362 - 261.263i) q^{20} +(4863.19 - 27580.5i) q^{21} +(1210.33 - 6864.15i) q^{22} +(39917.9 + 69139.8i) q^{23} +(-15194.6 + 12749.8i) q^{24} +(73375.6 - 26706.5i) q^{25} +(-41806.2 + 72410.5i) q^{26} +(55654.1 + 96395.7i) q^{27} +(35442.1 + 29739.4i) q^{28} +(-70292.1 + 121749. i) q^{29} +(341.789 + 1938.38i) q^{30} +150217. q^{31} +(-5690.10 - 32270.2i) q^{32} +(-25856.2 + 21695.9i) q^{33} +(210992. + 76794.8i) q^{34} +(4314.22 - 1570.25i) q^{35} -43914.8 q^{36} +(39761.3 + 305534. i) q^{37} +4815.37 q^{38} +(380481. - 138484. i) q^{39} +(-3055.53 - 1112.12i) q^{40} +(-60819.7 + 51033.8i) q^{41} +(-38905.5 - 220644. i) q^{42} -646286. q^{43} +(-9682.67 - 54913.2i) q^{44} +(-2178.87 + 3773.92i) q^{45} +(489262. + 410539. i) q^{46} +(-413470. - 716151. i) q^{47} +(-79340.7 + 137422. i) q^{48} +(282793. - 102928. i) q^{49} +(478531. - 401535. i) q^{50} +(-543658. - 941644. i) q^{51} +(-116153. + 658738. i) q^{52} +(-217169. + 1.23163e6i) q^{53} +(682136. + 572380. i) q^{54} +(-5199.51 - 1892.47i) q^{55} +(347809. + 126592. i) q^{56} +(-17863.2 - 14989.0i) q^{57} +(-195297. + 1.10759e6i) q^{58} +(-313710. + 1.77914e6i) q^{59} +(7873.13 + 13636.7i) q^{60} +(1.69067e6 - 1.41864e6i) q^{61} +(1.12926e6 - 411018. i) q^{62} +(248019. - 429582. i) q^{63} +(-131072. - 227023. i) q^{64} +(50847.1 + 42665.8i) q^{65} +(-135012. + 233847. i) q^{66} +(600356. + 3.40479e6i) q^{67} +1.79626e6 q^{68} +(-537073. - 3.04589e6i) q^{69} +(28135.9 - 23608.8i) q^{70} +(-3.86522e6 - 1.40682e6i) q^{71} +(-330131. + 120158. i) q^{72} -4.23800e6 q^{73} +(1.13490e6 + 2.18807e6i) q^{74} -3.02504e6 q^{75} +(36199.7 - 13175.6i) q^{76} +(591856. + 215418. i) q^{77} +(2.48137e6 - 2.08211e6i) q^{78} +(-333614. - 1.89202e6i) q^{79} -26013.0 q^{80} +(-488210. - 2.76878e6i) q^{81} +(-317578. + 550061. i) q^{82} +(-2.55806e6 - 2.14647e6i) q^{83} +(-896192. - 1.55225e6i) q^{84} +(89123.3 - 154366. i) q^{85} +(-4.85848e6 + 1.76834e6i) q^{86} +(4.17211e6 - 3.50082e6i) q^{87} +(-223041. - 386319. i) q^{88} +(1.85527e6 - 1.05217e7i) q^{89} +(-6053.72 + 34332.3i) q^{90} +(-5.78789e6 - 4.85661e6i) q^{91} +(4.80135e6 + 1.74755e6i) q^{92} +(-5.46853e6 - 1.99038e6i) q^{93} +(-5.06778e6 - 4.25237e6i) q^{94} +(663.805 - 3764.63i) q^{95} +(-220438. + 1.25017e6i) q^{96} +(-2.14726e6 - 3.71917e6i) q^{97} +(1.84428e6 - 1.54754e6i) q^{98} +(-561774. + 204469. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.51754 − 2.73616i 0.664463 − 0.241845i
\(3\) −36.4042 − 13.2501i −0.778444 − 0.283330i −0.0779204 − 0.996960i \(-0.524828\pi\)
−0.700524 + 0.713629i \(0.747050\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) −1.10281 − 6.25436i −0.00394554 − 0.0223763i 0.982771 − 0.184825i \(-0.0591719\pi\)
−0.986717 + 0.162449i \(0.948061\pi\)
\(6\) −309.925 −0.585769
\(7\) 125.532 + 711.929i 0.138329 + 0.784501i 0.972484 + 0.232971i \(0.0748447\pi\)
−0.834155 + 0.551530i \(0.814044\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) −525.635 − 441.061i −0.240345 − 0.201674i
\(10\) −25.4034 − 43.9999i −0.00803325 − 0.0139140i
\(11\) 435.627 − 754.529i 0.0986826 − 0.170923i −0.812457 − 0.583021i \(-0.801870\pi\)
0.911140 + 0.412098i \(0.135204\pi\)
\(12\) −2329.87 + 848.004i −0.389222 + 0.141665i
\(13\) −8006.36 + 6718.13i −1.01073 + 0.848100i −0.988434 − 0.151652i \(-0.951541\pi\)
−0.0222919 + 0.999752i \(0.507096\pi\)
\(14\) 2891.65 + 5008.48i 0.281642 + 0.487818i
\(15\) −42.7236 + 242.297i −0.00326850 + 0.0185366i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) 21500.3 + 18040.9i 1.06138 + 0.890608i 0.994244 − 0.107136i \(-0.0341680\pi\)
0.0671404 + 0.997744i \(0.478612\pi\)
\(18\) −5158.30 − 1877.47i −0.208474 − 0.0758785i
\(19\) 565.620 + 205.869i 0.0189185 + 0.00688578i 0.351462 − 0.936202i \(-0.385685\pi\)
−0.332544 + 0.943088i \(0.607907\pi\)
\(20\) −311.362 − 261.263i −0.00870282 − 0.00730254i
\(21\) 4863.19 − 27580.5i 0.114592 − 0.649883i
\(22\) 1210.33 − 6864.15i 0.0242340 − 0.137438i
\(23\) 39917.9 + 69139.8i 0.684101 + 1.18490i 0.973719 + 0.227755i \(0.0731384\pi\)
−0.289618 + 0.957142i \(0.593528\pi\)
\(24\) −15194.6 + 12749.8i −0.224363 + 0.188263i
\(25\) 73375.6 − 26706.5i 0.939207 − 0.341844i
\(26\) −41806.2 + 72410.5i −0.466481 + 0.807970i
\(27\) 55654.1 + 96395.7i 0.544157 + 0.942507i
\(28\) 35442.1 + 29739.4i 0.305117 + 0.256023i
\(29\) −70292.1 + 121749.i −0.535197 + 0.926988i 0.463957 + 0.885858i \(0.346429\pi\)
−0.999154 + 0.0411300i \(0.986904\pi\)
\(30\) 341.789 + 1938.38i 0.00231118 + 0.0131073i
\(31\) 150217. 0.905635 0.452817 − 0.891603i \(-0.350419\pi\)
0.452817 + 0.891603i \(0.350419\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) −25856.2 + 21695.9i −0.125247 + 0.105094i
\(34\) 210992. + 76794.8i 0.920640 + 0.335085i
\(35\) 4314.22 − 1570.25i 0.0170084 − 0.00619056i
\(36\) −43914.8 −0.156874
\(37\) 39761.3 + 305534.i 0.129049 + 0.991638i
\(38\) 4815.37 0.0142360
\(39\) 380481. − 138484.i 1.02709 − 0.373829i
\(40\) −3055.53 − 1112.12i −0.00754878 − 0.00274753i
\(41\) −60819.7 + 51033.8i −0.137816 + 0.115642i −0.709090 − 0.705118i \(-0.750894\pi\)
0.571274 + 0.820760i \(0.306450\pi\)
\(42\) −38905.5 − 220644.i −0.0810287 − 0.459536i
\(43\) −646286. −1.23961 −0.619805 − 0.784756i \(-0.712788\pi\)
−0.619805 + 0.784756i \(0.712788\pi\)
\(44\) −9682.67 − 54913.2i −0.0171361 − 0.0971834i
\(45\) −2178.87 + 3773.92i −0.00356441 + 0.00617375i
\(46\) 489262. + 410539.i 0.741121 + 0.621874i
\(47\) −413470. − 716151.i −0.580900 − 1.00615i −0.995373 − 0.0960868i \(-0.969367\pi\)
0.414473 − 0.910062i \(-0.363966\pi\)
\(48\) −79340.7 + 137422.i −0.103550 + 0.179354i
\(49\) 282793. − 102928.i 0.343386 − 0.124982i
\(50\) 478531. − 401535.i 0.541396 − 0.454285i
\(51\) −543658. − 941644.i −0.573892 − 0.994011i
\(52\) −116153. + 658738.i −0.114556 + 0.649682i
\(53\) −217169. + 1.23163e6i −0.200370 + 1.13635i 0.704192 + 0.710010i \(0.251309\pi\)
−0.904562 + 0.426343i \(0.859802\pi\)
\(54\) 682136. + 572380.i 0.589512 + 0.494660i
\(55\) −5199.51 − 1892.47i −0.00421398 − 0.00153376i
\(56\) 347809. + 126592.i 0.264657 + 0.0963271i
\(57\) −17863.2 − 14989.0i −0.0127761 − 0.0107204i
\(58\) −195297. + 1.10759e6i −0.131431 + 0.745383i
\(59\) −313710. + 1.77914e6i −0.198859 + 1.12779i 0.707955 + 0.706258i \(0.249618\pi\)
−0.906814 + 0.421530i \(0.861493\pi\)
\(60\) 7873.13 + 13636.7i 0.00470563 + 0.00815039i
\(61\) 1.69067e6 − 1.41864e6i 0.953686 − 0.800237i −0.0262286 − 0.999656i \(-0.508350\pi\)
0.979914 + 0.199419i \(0.0639053\pi\)
\(62\) 1.12926e6 − 411018.i 0.601761 − 0.219023i
\(63\) 248019. − 429582.i 0.124967 − 0.216448i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) 50847.1 + 42665.8i 0.0229652 + 0.0192701i
\(66\) −135012. + 233847.i −0.0578052 + 0.100122i
\(67\) 600356. + 3.40479e6i 0.243864 + 1.38302i 0.823117 + 0.567871i \(0.192233\pi\)
−0.579254 + 0.815147i \(0.696656\pi\)
\(68\) 1.79626e6 0.692770
\(69\) −537073. − 3.04589e6i −0.196817 − 1.11620i
\(70\) 28135.9 − 23608.8i 0.00980431 − 0.00822679i
\(71\) −3.86522e6 − 1.40682e6i −1.28165 − 0.466483i −0.390673 − 0.920529i \(-0.627758\pi\)
−0.890978 + 0.454047i \(0.849980\pi\)
\(72\) −330131. + 120158.i −0.104237 + 0.0379392i
\(73\) −4.23800e6 −1.27506 −0.637531 − 0.770425i \(-0.720044\pi\)
−0.637531 + 0.770425i \(0.720044\pi\)
\(74\) 1.13490e6 + 2.18807e6i 0.325571 + 0.627697i
\(75\) −3.02504e6 −0.827975
\(76\) 36199.7 − 13175.6i 0.00945927 − 0.00344289i
\(77\) 591856. + 215418.i 0.147740 + 0.0537730i
\(78\) 2.48137e6 − 2.08211e6i 0.592052 − 0.496791i
\(79\) −333614. − 1.89202e6i −0.0761288 − 0.431748i −0.998921 − 0.0464491i \(-0.985209\pi\)
0.922792 − 0.385299i \(-0.125902\pi\)
\(80\) −26013.0 −0.00568036
\(81\) −488210. − 2.76878e6i −0.102073 − 0.578883i
\(82\) −317578. + 550061.i −0.0636066 + 0.110170i
\(83\) −2.55806e6 − 2.14647e6i −0.491063 − 0.412051i 0.363344 − 0.931655i \(-0.381635\pi\)
−0.854407 + 0.519604i \(0.826079\pi\)
\(84\) −896192. − 1.55225e6i −0.164977 − 0.285749i
\(85\) 89123.3 − 154366.i 0.0157407 − 0.0272638i
\(86\) −4.85848e6 + 1.76834e6i −0.823675 + 0.299793i
\(87\) 4.17211e6 − 3.50082e6i 0.679264 − 0.569971i
\(88\) −223041. − 386319.i −0.0348896 − 0.0604305i
\(89\) 1.85527e6 − 1.05217e7i 0.278959 − 1.58206i −0.447137 − 0.894465i \(-0.647557\pi\)
0.726097 − 0.687592i \(-0.241332\pi\)
\(90\) −6053.72 + 34332.3i −0.000875333 + 0.00496426i
\(91\) −5.78789e6 − 4.85661e6i −0.805147 − 0.675599i
\(92\) 4.80135e6 + 1.74755e6i 0.642844 + 0.233976i
\(93\) −5.46853e6 − 1.99038e6i −0.704986 − 0.256594i
\(94\) −5.06778e6 − 4.25237e6i −0.629318 − 0.528061i
\(95\) 663.805 − 3764.63i 7.94343e−5 − 0.000450494i
\(96\) −220438. + 1.25017e6i −0.0254294 + 0.144218i
\(97\) −2.14726e6 − 3.71917e6i −0.238882 − 0.413756i 0.721512 − 0.692402i \(-0.243448\pi\)
−0.960394 + 0.278646i \(0.910114\pi\)
\(98\) 1.84428e6 − 1.54754e6i 0.197941 − 0.166092i
\(99\) −561774. + 204469.i −0.0581887 + 0.0211789i
\(100\) 2.49871e6 − 4.32789e6i 0.249871 − 0.432789i
\(101\) 2.17976e6 + 3.77545e6i 0.210515 + 0.364623i 0.951876 − 0.306484i \(-0.0991526\pi\)
−0.741361 + 0.671107i \(0.765819\pi\)
\(102\) −6.66346e6 − 5.59131e6i −0.621727 − 0.521691i
\(103\) −4.69630e6 + 8.13423e6i −0.423473 + 0.733476i −0.996276 − 0.0862164i \(-0.972522\pi\)
0.572804 + 0.819692i \(0.305856\pi\)
\(104\) 929226. + 5.26990e6i 0.0810037 + 0.459395i
\(105\) −177862. −0.0149941
\(106\) 1.73735e6 + 9.85300e6i 0.141683 + 0.803522i
\(107\) −8.09118e6 + 6.78931e6i −0.638511 + 0.535775i −0.903561 − 0.428460i \(-0.859056\pi\)
0.265049 + 0.964235i \(0.414612\pi\)
\(108\) 6.69411e6 + 2.43646e6i 0.511340 + 0.186113i
\(109\) 1.06434e7 − 3.87388e6i 0.787205 − 0.286519i 0.0830316 − 0.996547i \(-0.473540\pi\)
0.704174 + 0.710028i \(0.251318\pi\)
\(110\) −44265.6 −0.00317097
\(111\) 2.60086e6 − 1.16496e7i 0.180504 − 0.808498i
\(112\) 2.96104e6 0.199151
\(113\) 4.00406e6 − 1.45736e6i 0.261051 − 0.0950148i −0.208179 − 0.978091i \(-0.566754\pi\)
0.469230 + 0.883076i \(0.344531\pi\)
\(114\) −175300. − 63803.9i −0.0110819 − 0.00403348i
\(115\) 388403. − 325909.i 0.0238144 − 0.0199827i
\(116\) 1.56238e6 + 8.86069e6i 0.0929359 + 0.527066i
\(117\) 7.17153e6 0.413963
\(118\) 2.50968e6 + 1.42331e7i 0.140615 + 0.797467i
\(119\) −1.01448e7 + 1.75714e7i −0.551862 + 0.955854i
\(120\) 96498.6 + 80972.0i 0.00509785 + 0.00427760i
\(121\) 9.36404e6 + 1.62190e7i 0.480523 + 0.832291i
\(122\) 8.82807e6 − 1.52907e7i 0.440156 − 0.762372i
\(123\) 2.89030e6 − 1.05198e6i 0.140047 − 0.0509730i
\(124\) 7.36466e6 − 6.17969e6i 0.346878 − 0.291065i
\(125\) −496031. − 859152.i −0.0227156 − 0.0393446i
\(126\) 689090. − 3.90802e6i 0.0306887 − 0.174044i
\(127\) −5.36091e6 + 3.04032e7i −0.232234 + 1.31706i 0.616128 + 0.787646i \(0.288701\pi\)
−0.848362 + 0.529417i \(0.822411\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) 2.35275e7 + 8.56332e6i 0.964967 + 0.351219i
\(130\) 498986. + 181616.i 0.0199199 + 0.00725024i
\(131\) 1.75300e7 + 1.47094e7i 0.681291 + 0.571671i 0.916383 − 0.400302i \(-0.131095\pi\)
−0.235092 + 0.971973i \(0.575539\pi\)
\(132\) −375112. + 2.12737e6i −0.0141956 + 0.0805070i
\(133\) −75560.4 + 428525.i −0.00278493 + 0.0157941i
\(134\) 1.38292e7 + 2.39530e7i 0.496514 + 0.859988i
\(135\) 541517. − 454387.i 0.0189428 − 0.0158949i
\(136\) 1.35035e7 − 4.91487e6i 0.460320 − 0.167543i
\(137\) −892863. + 1.54648e6i −0.0296663 + 0.0513835i −0.880477 − 0.474088i \(-0.842778\pi\)
0.850811 + 0.525472i \(0.176111\pi\)
\(138\) −1.23715e7 − 2.14281e7i −0.400725 − 0.694076i
\(139\) −4.04872e7 − 3.39728e7i −1.27869 − 1.07295i −0.993423 − 0.114503i \(-0.963472\pi\)
−0.285270 − 0.958447i \(-0.592083\pi\)
\(140\) 146915. − 254464.i 0.00452500 − 0.00783752i
\(141\) 5.56301e6 + 3.15494e7i 0.167126 + 0.947817i
\(142\) −3.29062e7 −0.964426
\(143\) 1.58123e6 + 8.96763e6i 0.0452189 + 0.256449i
\(144\) −2.15300e6 + 1.80658e6i −0.0600864 + 0.0504184i
\(145\) 838983. + 305365.i 0.0228542 + 0.00831824i
\(146\) −3.18594e7 + 1.15959e7i −0.847231 + 0.308367i
\(147\) −1.16587e7 −0.302718
\(148\) 1.45185e7 + 1.33436e7i 0.368135 + 0.338344i
\(149\) 2.51436e7 0.622695 0.311347 − 0.950296i \(-0.399220\pi\)
0.311347 + 0.950296i \(0.399220\pi\)
\(150\) −2.27409e7 + 8.27701e6i −0.550159 + 0.200241i
\(151\) 4.46339e7 + 1.62454e7i 1.05498 + 0.383983i 0.810542 − 0.585681i \(-0.199173\pi\)
0.244442 + 0.969664i \(0.421395\pi\)
\(152\) 236082. − 198096.i 0.00545269 − 0.00457535i
\(153\) −3.34419e6 − 1.89658e7i −0.0754868 − 0.428107i
\(154\) 5.03872e6 0.111173
\(155\) −165661. − 939511.i −0.00357322 − 0.0202647i
\(156\) 1.29568e7 − 2.24418e7i 0.273251 − 0.473284i
\(157\) 5.14435e7 + 4.31662e7i 1.06092 + 0.890216i 0.994199 − 0.107556i \(-0.0343024\pi\)
0.0667192 + 0.997772i \(0.478747\pi\)
\(158\) −7.68482e6 − 1.33105e7i −0.155001 − 0.268469i
\(159\) 2.42250e7 − 4.19589e7i 0.477940 − 0.827816i
\(160\) −195554. + 71175.9i −0.00377439 + 0.00137377i
\(161\) −4.42116e7 + 3.70980e7i −0.834922 + 0.700583i
\(162\) −1.12460e7 − 1.94786e7i −0.207823 − 0.359961i
\(163\) 2.57229e6 − 1.45882e7i 0.0465225 − 0.263842i −0.952671 − 0.304004i \(-0.901676\pi\)
0.999193 + 0.0401619i \(0.0127874\pi\)
\(164\) −882350. + 5.00405e6i −0.0156202 + 0.0885867i
\(165\) 164209. + 137787.i 0.00284579 + 0.00238790i
\(166\) −2.51034e7 − 9.13689e6i −0.425946 − 0.155032i
\(167\) 2.27257e7 + 8.27147e6i 0.377580 + 0.137428i 0.523837 − 0.851819i \(-0.324500\pi\)
−0.146256 + 0.989247i \(0.546722\pi\)
\(168\) −1.09844e7 − 9.21698e6i −0.178728 − 0.149971i
\(169\) 8.07231e6 − 4.57804e7i 0.128645 − 0.729585i
\(170\) 247618. − 1.40431e6i 0.00386554 − 0.0219226i
\(171\) −206509. − 357685.i −0.00315830 − 0.00547034i
\(172\) −3.16854e7 + 2.65872e7i −0.474798 + 0.398403i
\(173\) −6.22870e7 + 2.26706e7i −0.914610 + 0.332891i −0.756092 − 0.654465i \(-0.772894\pi\)
−0.158518 + 0.987356i \(0.550672\pi\)
\(174\) 2.17852e7 − 3.77331e7i 0.313502 − 0.543001i
\(175\) 2.82241e7 + 4.88857e7i 0.398096 + 0.689522i
\(176\) −2.73375e6 − 2.29389e6i −0.0377976 − 0.0317160i
\(177\) 3.49940e7 − 6.06115e7i 0.474338 − 0.821577i
\(178\) −1.48421e7 − 8.41739e7i −0.197254 − 1.11868i
\(179\) 8.10296e7 1.05599 0.527993 − 0.849249i \(-0.322945\pi\)
0.527993 + 0.849249i \(0.322945\pi\)
\(180\) 48429.7 + 274659.i 0.000618954 + 0.00351026i
\(181\) 7.05063e7 − 5.91618e7i 0.883798 − 0.741594i −0.0831586 − 0.996536i \(-0.526501\pi\)
0.966956 + 0.254942i \(0.0820564\pi\)
\(182\) −5.67992e7 − 2.06732e7i −0.698381 − 0.254190i
\(183\) −8.03448e7 + 2.92431e7i −0.969123 + 0.352732i
\(184\) 4.08759e7 0.483732
\(185\) 1.86707e6 − 585628.i 0.0216800 − 0.00680018i
\(186\) −4.65559e7 −0.530493
\(187\) 2.29785e7 − 8.36348e6i 0.256966 − 0.0935279i
\(188\) −4.97324e7 − 1.81011e7i −0.545868 − 0.198680i
\(189\) −6.16405e7 + 5.17225e7i −0.664125 + 0.557267i
\(190\) −5310.44 − 30117.0i −5.61685e−5 − 0.000318548i
\(191\) −1.55052e8 −1.61013 −0.805067 − 0.593184i \(-0.797871\pi\)
−0.805067 + 0.593184i \(0.797871\pi\)
\(192\) 1.76350e6 + 1.00013e7i 0.0179813 + 0.101977i
\(193\) −4.30546e6 + 7.45728e6i −0.0431092 + 0.0746672i −0.886775 − 0.462202i \(-0.847060\pi\)
0.843666 + 0.536869i \(0.180393\pi\)
\(194\) −2.63184e7 − 2.20837e7i −0.258793 − 0.217153i
\(195\) −1.28573e6 − 2.22694e6i −0.0124173 − 0.0215074i
\(196\) 9.63015e6 − 1.66799e7i 0.0913559 − 0.158233i
\(197\) 1.26723e8 − 4.61232e7i 1.18092 − 0.429821i 0.324396 − 0.945921i \(-0.394839\pi\)
0.856528 + 0.516100i \(0.172617\pi\)
\(198\) −3.66370e6 + 3.07421e6i −0.0335422 + 0.0281452i
\(199\) −6.91886e7 − 1.19838e8i −0.622370 − 1.07798i −0.989043 − 0.147627i \(-0.952836\pi\)
0.366673 − 0.930350i \(-0.380497\pi\)
\(200\) 6.94234e6 − 3.93720e7i 0.0613622 − 0.348002i
\(201\) 2.32581e7 − 1.31903e8i 0.202017 − 1.14570i
\(202\) 2.67166e7 + 2.24179e7i 0.228061 + 0.191366i
\(203\) −9.55008e7 − 3.47595e7i −0.801255 − 0.291633i
\(204\) −6.53916e7 − 2.38006e7i −0.539282 − 0.196283i
\(205\) 386256. + 324108.i 0.00313139 + 0.00262755i
\(206\) −1.30481e7 + 7.39992e7i −0.103995 + 0.589782i
\(207\) 9.51258e6 − 5.39485e7i 0.0745422 − 0.422750i
\(208\) 2.14048e7 + 3.70742e7i 0.164926 + 0.285660i
\(209\) 401734. − 337095.i 0.00304387 − 0.00255411i
\(210\) −1.33708e6 + 486658.i −0.00996301 + 0.00362624i
\(211\) −2.57966e7 + 4.46811e7i −0.189049 + 0.327443i −0.944933 − 0.327262i \(-0.893874\pi\)
0.755884 + 0.654705i \(0.227207\pi\)
\(212\) 4.00200e7 + 6.93167e7i 0.288471 + 0.499646i
\(213\) 1.22070e8 + 1.02429e8i 0.865525 + 0.726262i
\(214\) −4.22491e7 + 7.31776e7i −0.294693 + 0.510423i
\(215\) 712732. + 4.04210e6i 0.00489093 + 0.0277379i
\(216\) 5.69898e7 0.384777
\(217\) 1.88571e7 + 1.06944e8i 0.125275 + 0.710471i
\(218\) 6.94127e7 − 5.82442e7i 0.453776 − 0.380763i
\(219\) 1.54281e8 + 5.61538e7i 0.992564 + 0.361264i
\(220\) −332768. + 121118.i −0.00210699 + 0.000766882i
\(221\) −2.93340e8 −1.82809
\(222\) −1.23230e7 − 9.46924e7i −0.0755928 − 0.580871i
\(223\) −2.28141e8 −1.37764 −0.688822 − 0.724931i \(-0.741872\pi\)
−0.688822 + 0.724931i \(0.741872\pi\)
\(224\) 2.22598e7 − 8.10190e6i 0.132328 − 0.0481636i
\(225\) −5.03480e7 − 1.83252e7i −0.294675 − 0.107253i
\(226\) 2.61131e7 − 2.19115e7i 0.150480 − 0.126268i
\(227\) 1.75489e7 + 9.95246e7i 0.0995769 + 0.564729i 0.993248 + 0.116007i \(0.0370095\pi\)
−0.893672 + 0.448722i \(0.851879\pi\)
\(228\) −1.49240e6 −0.00833899
\(229\) 2.74132e7 + 1.55468e8i 0.150847 + 0.855494i 0.962485 + 0.271334i \(0.0874649\pi\)
−0.811638 + 0.584160i \(0.801424\pi\)
\(230\) 2.02810e6 − 3.51277e6i 0.0109911 − 0.0190371i
\(231\) −1.86918e7 − 1.56842e7i −0.0997719 − 0.0837185i
\(232\) 3.59895e7 + 6.23357e7i 0.189221 + 0.327740i
\(233\) 1.37409e8 − 2.37999e8i 0.711655 − 1.23262i −0.252581 − 0.967576i \(-0.581279\pi\)
0.964236 − 0.265046i \(-0.0853873\pi\)
\(234\) 5.39123e7 − 1.96225e7i 0.275063 − 0.100115i
\(235\) −4.02308e6 + 3.37577e6i −0.0202219 + 0.0169682i
\(236\) 5.78107e7 + 1.00131e8i 0.286297 + 0.495880i
\(237\) −1.29244e7 + 7.32978e7i −0.0630653 + 0.357661i
\(238\) −2.81861e7 + 1.59851e8i −0.135524 + 0.768594i
\(239\) 1.04434e8 + 8.76304e7i 0.494821 + 0.415204i 0.855750 − 0.517389i \(-0.173096\pi\)
−0.360929 + 0.932593i \(0.617540\pi\)
\(240\) 946985. + 344674.i 0.00442185 + 0.00160942i
\(241\) −1.74352e8 − 6.34589e7i −0.802356 − 0.292034i −0.0918934 − 0.995769i \(-0.529292\pi\)
−0.710462 + 0.703735i \(0.751514\pi\)
\(242\) 1.14772e8 + 9.63055e7i 0.520575 + 0.436815i
\(243\) 2.33578e7 − 1.32469e8i 0.104426 − 0.592231i
\(244\) 2.45277e7 − 1.39103e8i 0.108092 − 0.613017i
\(245\) −955618. − 1.65518e6i −0.00415148 − 0.00719058i
\(246\) 1.88495e7 − 1.58166e7i 0.0807286 − 0.0677394i
\(247\) −5.91162e6 + 2.15165e6i −0.0249613 + 0.00908516i
\(248\) 3.84555e7 − 6.66070e7i 0.160095 − 0.277293i
\(249\) 6.46834e7 + 1.12035e8i 0.265519 + 0.459892i
\(250\) −6.07971e6 − 5.10149e6i −0.0246089 − 0.0206494i
\(251\) 1.01523e8 − 1.75844e8i 0.405236 − 0.701889i −0.589113 − 0.808051i \(-0.700523\pi\)
0.994349 + 0.106162i \(0.0338561\pi\)
\(252\) −5.51272e6 − 3.12642e7i −0.0217002 − 0.123068i
\(253\) 6.95573e7 0.270035
\(254\) 4.28873e7 + 2.43226e8i 0.164214 + 0.931305i
\(255\) −5.28983e6 + 4.43869e6i −0.0199779 + 0.0167635i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) 1.02121e8 − 3.71691e7i 0.375275 − 0.136589i −0.147495 − 0.989063i \(-0.547121\pi\)
0.522770 + 0.852474i \(0.324899\pi\)
\(258\) 2.00300e8 0.726126
\(259\) −2.12527e8 + 6.66615e7i −0.760090 + 0.238411i
\(260\) 4.24808e6 0.0149894
\(261\) 9.06469e7 − 3.29928e7i 0.315581 − 0.114862i
\(262\) 1.72030e8 + 6.26138e7i 0.590948 + 0.215088i
\(263\) 1.78512e8 − 1.49789e8i 0.605092 − 0.507732i −0.287986 − 0.957635i \(-0.592986\pi\)
0.893078 + 0.449902i \(0.148541\pi\)
\(264\) 3.00090e6 + 1.70189e7i 0.0100378 + 0.0569271i
\(265\) 7.94252e6 0.0262179
\(266\) 604484. + 3.42820e6i 0.00196924 + 0.0111681i
\(267\) −2.06953e8 + 3.58453e8i −0.665399 + 1.15251i
\(268\) 1.69501e8 + 1.42228e8i 0.537899 + 0.451351i
\(269\) −5.29204e7 − 9.16608e7i −0.165764 − 0.287112i 0.771162 − 0.636638i \(-0.219676\pi\)
−0.936926 + 0.349527i \(0.886342\pi\)
\(270\) 2.82760e6 − 4.89755e6i 0.00874269 − 0.0151428i
\(271\) −1.65272e8 + 6.01542e7i −0.504438 + 0.183600i −0.581689 − 0.813411i \(-0.697608\pi\)
0.0772510 + 0.997012i \(0.475386\pi\)
\(272\) 8.80651e7 − 7.38954e7i 0.265346 − 0.222652i
\(273\) 1.46353e8 + 2.53491e8i 0.435344 + 0.754039i
\(274\) −2.48070e6 + 1.40688e7i −0.00728531 + 0.0413170i
\(275\) 1.18136e7 − 6.69981e7i 0.0342544 − 0.194266i
\(276\) −1.51634e8 − 1.27236e8i −0.434126 − 0.364275i
\(277\) 3.74534e8 + 1.36319e8i 1.05880 + 0.385370i 0.811976 − 0.583691i \(-0.198392\pi\)
0.246820 + 0.969061i \(0.420614\pi\)
\(278\) −3.97319e8 − 1.44612e8i −1.10913 − 0.403691i
\(279\) −7.89594e7 − 6.62548e7i −0.217665 − 0.182643i
\(280\) 408184. − 2.31493e6i 0.00111123 − 0.00630209i
\(281\) 7.70508e7 − 4.36977e8i 0.207160 − 1.17486i −0.686845 − 0.726804i \(-0.741005\pi\)
0.894005 − 0.448057i \(-0.147884\pi\)
\(282\) 1.28144e8 + 2.21953e8i 0.340273 + 0.589371i
\(283\) −1.87057e8 + 1.56960e8i −0.490594 + 0.411657i −0.854239 − 0.519880i \(-0.825976\pi\)
0.363645 + 0.931537i \(0.381532\pi\)
\(284\) −2.47374e8 + 9.00368e7i −0.640826 + 0.233241i
\(285\) −74046.8 + 128253.i −0.000189474 + 0.000328178i
\(286\) 3.64239e7 + 6.30880e7i 0.0920672 + 0.159465i
\(287\) −4.39673e7 − 3.68929e7i −0.109785 − 0.0921205i
\(288\) −1.12422e7 + 1.94720e7i −0.0277317 + 0.0480328i
\(289\) 6.55342e7 + 3.71663e8i 0.159708 + 0.905747i
\(290\) 7.14262e6 0.0171975
\(291\) 2.88902e7 + 1.63845e8i 0.0687267 + 0.389769i
\(292\) −2.07776e8 + 1.74345e8i −0.488377 + 0.409797i
\(293\) −1.42181e8 − 5.17496e7i −0.330221 − 0.120190i 0.171589 − 0.985169i \(-0.445110\pi\)
−0.501810 + 0.864978i \(0.667332\pi\)
\(294\) −8.76445e7 + 3.19000e7i −0.201145 + 0.0732108i
\(295\) 1.14733e7 0.0260203
\(296\) 1.45654e8 + 6.05863e7i 0.326439 + 0.135786i
\(297\) 9.69777e7 0.214795
\(298\) 1.89018e8 − 6.87969e7i 0.413758 − 0.150596i
\(299\) −7.84087e8 − 2.85384e8i −1.69635 − 0.617421i
\(300\) −1.48308e8 + 1.24446e8i −0.317133 + 0.266106i
\(301\) −8.11297e7 − 4.60110e8i −0.171474 − 0.972475i
\(302\) 3.79987e8 0.793862
\(303\) −2.93274e7 − 1.66324e8i −0.0605654 − 0.343484i
\(304\) 1.23273e6 − 2.13516e6i 0.00251659 − 0.00435885i
\(305\) −1.07372e7 − 9.00958e6i −0.0216691 − 0.0181826i
\(306\) −7.70337e7 − 1.33426e8i −0.153694 − 0.266205i
\(307\) −1.28294e8 + 2.22212e8i −0.253059 + 0.438312i −0.964367 − 0.264569i \(-0.914770\pi\)
0.711307 + 0.702881i \(0.248103\pi\)
\(308\) 3.78788e7 − 1.37867e7i 0.0738700 − 0.0268865i
\(309\) 2.78744e8 − 2.33894e8i 0.537466 − 0.450987i
\(310\) −3.81602e6 − 6.60953e6i −0.00727519 − 0.0126010i
\(311\) 5.50954e7 − 3.12462e8i 0.103861 − 0.589027i −0.887808 − 0.460215i \(-0.847772\pi\)
0.991669 − 0.128812i \(-0.0411165\pi\)
\(312\) 3.59987e7 − 2.04159e8i 0.0671037 − 0.380564i
\(313\) 3.60069e8 + 3.02134e8i 0.663714 + 0.556922i 0.911197 − 0.411970i \(-0.135159\pi\)
−0.247483 + 0.968892i \(0.579604\pi\)
\(314\) 5.04839e8 + 1.83746e8i 0.920235 + 0.334938i
\(315\) −2.96028e6 − 1.07745e6i −0.00533637 − 0.00194228i
\(316\) −9.41906e7 − 7.90353e7i −0.167920 − 0.140902i
\(317\) −2.18828e7 + 1.24104e8i −0.0385830 + 0.218815i −0.998003 − 0.0631658i \(-0.979880\pi\)
0.959420 + 0.281981i \(0.0909914\pi\)
\(318\) 6.73059e7 − 3.81711e8i 0.117370 − 0.665640i
\(319\) 6.12423e7 + 1.06075e8i 0.105629 + 0.182955i
\(320\) −1.27534e6 + 1.07014e6i −0.00217571 + 0.00182563i
\(321\) 3.84512e8 − 1.39951e8i 0.648847 − 0.236161i
\(322\) −2.30857e8 + 3.99855e8i −0.385342 + 0.667433i
\(323\) 8.44694e6 + 1.46305e7i 0.0139473 + 0.0241575i
\(324\) −1.37839e8 − 1.15660e8i −0.225145 − 0.188919i
\(325\) −4.08053e8 + 7.06769e8i −0.659364 + 1.14205i
\(326\) −2.05783e7 − 1.16705e8i −0.0328964 − 0.186565i
\(327\) −4.38794e8 −0.693975
\(328\) 7.05880e6 + 4.00324e7i 0.0110452 + 0.0626402i
\(329\) 4.57945e8 − 3.84261e8i 0.708969 − 0.594896i
\(330\) 1.61145e6 + 586522.i 0.00246842 + 0.000898432i
\(331\) −8.17383e8 + 2.97503e8i −1.23888 + 0.450914i −0.876628 − 0.481168i \(-0.840213\pi\)
−0.362247 + 0.932082i \(0.617990\pi\)
\(332\) −2.13716e8 −0.320519
\(333\) 1.13859e8 − 1.78137e8i 0.168971 − 0.264361i
\(334\) 1.93473e8 0.284124
\(335\) 2.06327e7 − 7.50968e6i 0.0299846 − 0.0109135i
\(336\) −1.07795e8 − 3.92340e7i −0.155028 − 0.0564255i
\(337\) 7.13584e8 − 5.98768e8i 1.01564 − 0.852224i 0.0265678 − 0.999647i \(-0.491542\pi\)
0.989074 + 0.147423i \(0.0470978\pi\)
\(338\) −6.45785e7 − 3.66243e8i −0.0909661 − 0.515894i
\(339\) −1.65075e8 −0.230134
\(340\) −1.98094e6 − 1.12345e7i −0.00273335 − 0.0155016i
\(341\) 6.54386e7 − 1.13343e8i 0.0893704 − 0.154794i
\(342\) −2.53113e6 − 2.12387e6i −0.00342155 − 0.00287102i
\(343\) 4.06452e8 + 7.03995e8i 0.543850 + 0.941976i
\(344\) −1.65449e8 + 2.86566e8i −0.219134 + 0.379552i
\(345\) −1.84578e7 + 6.71810e6i −0.0241999 + 0.00880804i
\(346\) −4.06215e8 + 3.40855e8i −0.527217 + 0.442387i
\(347\) −7.07056e8 − 1.22466e9i −0.908449 − 1.57348i −0.816219 − 0.577742i \(-0.803934\pi\)
−0.0922295 − 0.995738i \(-0.529399\pi\)
\(348\) 6.05275e7 − 3.43268e8i 0.0769884 − 0.436623i
\(349\) −1.68121e8 + 9.53461e8i −0.211706 + 1.20064i 0.674826 + 0.737976i \(0.264218\pi\)
−0.886532 + 0.462667i \(0.846893\pi\)
\(350\) 3.45935e8 + 2.90274e8i 0.431277 + 0.361885i
\(351\) −1.09319e9 − 3.97887e8i −1.34933 − 0.491117i
\(352\) −2.68275e7 − 9.76442e6i −0.0327855 − 0.0119329i
\(353\) 4.43597e8 + 3.72222e8i 0.536756 + 0.450392i 0.870427 − 0.492298i \(-0.163843\pi\)
−0.333671 + 0.942690i \(0.608287\pi\)
\(354\) 9.72264e7 − 5.51398e8i 0.116486 − 0.660624i
\(355\) −4.53617e6 + 2.57259e7i −0.00538134 + 0.0305191i
\(356\) −3.41890e8 − 5.92170e8i −0.401616 − 0.695619i
\(357\) 6.02137e8 − 5.05253e8i 0.700416 − 0.587719i
\(358\) 6.09143e8 − 2.21710e8i 0.701663 − 0.255385i
\(359\) −1.55797e7 + 2.69848e7i −0.0177717 + 0.0307814i −0.874774 − 0.484530i \(-0.838991\pi\)
0.857003 + 0.515312i \(0.172324\pi\)
\(360\) 1.11558e6 + 1.93225e6i 0.00126021 + 0.00218275i
\(361\) −6.84468e8 − 5.74337e8i −0.765734 − 0.642527i
\(362\) 3.68158e8 − 6.37668e8i 0.407900 − 0.706504i
\(363\) −1.25988e8 − 7.14514e8i −0.138247 − 0.784039i
\(364\) −4.83555e8 −0.525522
\(365\) 4.67372e6 + 2.65060e7i 0.00503081 + 0.0285311i
\(366\) −5.23981e8 + 4.39672e8i −0.558640 + 0.468755i
\(367\) 2.86450e6 + 1.04259e6i 0.00302494 + 0.00110099i 0.343532 − 0.939141i \(-0.388377\pi\)
−0.340507 + 0.940242i \(0.610599\pi\)
\(368\) 3.07286e8 − 1.11843e8i 0.321422 − 0.116988i
\(369\) 5.44780e7 0.0564454
\(370\) 1.24334e7 − 9.51108e6i 0.0127610 − 0.00976166i
\(371\) −9.04091e8 −0.919186
\(372\) −3.49986e8 + 1.27385e8i −0.352493 + 0.128297i
\(373\) −4.19649e8 − 1.52740e8i −0.418702 − 0.152395i 0.124073 − 0.992273i \(-0.460404\pi\)
−0.542775 + 0.839878i \(0.682626\pi\)
\(374\) 1.49858e8 − 1.25746e8i 0.148125 − 0.124292i
\(375\) 6.67383e6 + 3.78492e7i 0.00653531 + 0.0370636i
\(376\) −4.23393e8 −0.410758
\(377\) −2.55145e8 − 1.44700e9i −0.245241 − 1.39083i
\(378\) −3.21864e8 + 5.57484e8i −0.306514 + 0.530898i
\(379\) 1.42460e9 + 1.19538e9i 1.34417 + 1.12789i 0.980533 + 0.196353i \(0.0629098\pi\)
0.363638 + 0.931541i \(0.381535\pi\)
\(380\) −122326. − 211876.i −0.000114361 − 0.000198079i
\(381\) 5.98004e8 − 1.03577e9i 0.553945 − 0.959461i
\(382\) −1.16561e9 + 4.24249e8i −1.06987 + 0.389402i
\(383\) 5.10819e8 − 4.28628e8i 0.464591 − 0.389839i −0.380226 − 0.924894i \(-0.624154\pi\)
0.844817 + 0.535055i \(0.179709\pi\)
\(384\) 4.06224e7 + 7.03601e7i 0.0366106 + 0.0634114i
\(385\) 694595. − 3.93924e6i 0.000620325 − 0.00351804i
\(386\) −1.19622e7 + 6.78409e7i −0.0105866 + 0.0600393i
\(387\) 3.39711e8 + 2.85051e8i 0.297935 + 0.249997i
\(388\) −2.58274e8 − 9.40041e7i −0.224476 − 0.0817026i
\(389\) 1.34630e9 + 4.90013e8i 1.15963 + 0.422070i 0.848964 − 0.528451i \(-0.177227\pi\)
0.310663 + 0.950520i \(0.399449\pi\)
\(390\) −1.57588e7 − 1.32232e7i −0.0134523 − 0.0112878i
\(391\) −3.89097e8 + 2.20668e9i −0.329184 + 1.86690i
\(392\) 2.67561e7 − 1.51742e8i 0.0224348 − 0.127234i
\(393\) −4.43266e8 − 7.67759e8i −0.368375 − 0.638044i
\(394\) 8.26441e8 − 6.93466e8i 0.680730 − 0.571201i
\(395\) −1.14654e7 + 4.17308e6i −0.00936054 + 0.00340696i
\(396\) −1.91305e7 + 3.31349e7i −0.0154808 + 0.0268135i
\(397\) 6.46929e8 + 1.12051e9i 0.518907 + 0.898774i 0.999759 + 0.0219718i \(0.00699439\pi\)
−0.480851 + 0.876802i \(0.659672\pi\)
\(398\) −8.48025e8 − 7.11577e8i −0.674245 − 0.565759i
\(399\) 8.42869e6 − 1.45989e7i 0.00664286 − 0.0115058i
\(400\) −5.55387e7 − 3.14976e8i −0.0433896 − 0.246075i
\(401\) 8.27509e7 0.0640866 0.0320433 − 0.999486i \(-0.489799\pi\)
0.0320433 + 0.999486i \(0.489799\pi\)
\(402\) −1.86065e8 − 1.05523e9i −0.142848 − 0.810130i
\(403\) −1.20269e9 + 1.00918e9i −0.915348 + 0.768068i
\(404\) 2.62182e8 + 9.54266e7i 0.197819 + 0.0720004i
\(405\) −1.67785e7 + 6.10689e6i −0.0125505 + 0.00456801i
\(406\) −8.13039e8 −0.602935
\(407\) 2.47855e8 + 1.03098e8i 0.182229 + 0.0758000i
\(408\) −5.56706e8 −0.405803
\(409\) 1.95167e9 − 7.10351e8i 1.41051 − 0.513383i 0.479229 − 0.877690i \(-0.340916\pi\)
0.931279 + 0.364307i \(0.118694\pi\)
\(410\) 3.79051e6 + 1.37963e6i 0.00271615 + 0.000988598i
\(411\) 5.29950e7 − 4.44681e7i 0.0376520 − 0.0315938i
\(412\) 1.04384e8 + 5.91994e8i 0.0735352 + 0.417039i
\(413\) −1.30600e9 −0.912259
\(414\) −7.61006e7 − 4.31588e8i −0.0527093 − 0.298929i
\(415\) −1.06037e7 + 1.83662e7i −0.00728265 + 0.0126139i
\(416\) 2.62352e8 + 2.20140e8i 0.178673 + 0.149924i
\(417\) 1.02376e9 + 1.77321e9i 0.691391 + 1.19752i
\(418\) 2.09770e6 − 3.63333e6i 0.00140484 − 0.00243326i
\(419\) 4.86676e8 − 1.77136e8i 0.323215 − 0.117641i −0.175317 − 0.984512i \(-0.556095\pi\)
0.498532 + 0.866871i \(0.333873\pi\)
\(420\) −8.71999e6 + 7.31694e6i −0.00574306 + 0.00481900i
\(421\) 1.25936e9 + 2.18128e9i 0.822551 + 1.42470i 0.903777 + 0.428004i \(0.140783\pi\)
−0.0812264 + 0.996696i \(0.525884\pi\)
\(422\) −7.16727e7 + 4.06476e8i −0.0464259 + 0.263294i
\(423\) −9.85314e7 + 5.58800e8i −0.0632971 + 0.358975i
\(424\) 4.90514e8 + 4.11590e8i 0.312515 + 0.262231i
\(425\) 2.05940e9 + 7.49562e8i 1.30131 + 0.473638i
\(426\) 1.19793e9 + 4.36009e8i 0.750752 + 0.273251i
\(427\) 1.22221e9 + 1.02555e9i 0.759709 + 0.637471i
\(428\) −1.17384e8 + 6.65716e8i −0.0723694 + 0.410427i
\(429\) 6.12579e7 − 3.47411e8i 0.0374595 − 0.212443i
\(430\) 1.64178e7 + 2.84365e7i 0.00995810 + 0.0172479i
\(431\) −2.71960e8 + 2.28201e8i −0.163619 + 0.137293i −0.720921 − 0.693017i \(-0.756281\pi\)
0.557302 + 0.830310i \(0.311837\pi\)
\(432\) 4.28423e8 − 1.55933e8i 0.255670 − 0.0930563i
\(433\) −5.23718e8 + 9.07105e8i −0.310020 + 0.536970i −0.978366 − 0.206880i \(-0.933669\pi\)
0.668346 + 0.743850i \(0.267002\pi\)
\(434\) 4.34374e8 + 7.52358e8i 0.255064 + 0.441785i
\(435\) −2.64964e7 − 2.22332e7i −0.0154339 − 0.0129506i
\(436\) 3.62447e8 − 6.27777e8i 0.209432 − 0.362746i
\(437\) 8.34463e6 + 4.73247e7i 0.00478324 + 0.0271271i
\(438\) 1.31346e9 0.746892
\(439\) −9.56915e7 − 5.42694e8i −0.0539818 − 0.306146i 0.945848 − 0.324611i \(-0.105233\pi\)
−0.999830 + 0.0184646i \(0.994122\pi\)
\(440\) −2.17020e6 + 1.82102e6i −0.00121455 + 0.00101913i
\(441\) −1.94044e8 − 7.06261e7i −0.107737 − 0.0392130i
\(442\) −2.20520e9 + 8.02625e8i −1.21470 + 0.442115i
\(443\) 2.96415e9 1.61990 0.809948 − 0.586502i \(-0.199495\pi\)
0.809948 + 0.586502i \(0.199495\pi\)
\(444\) −3.51732e8 − 6.78137e8i −0.190709 − 0.367686i
\(445\) −6.78527e7 −0.0365012
\(446\) −1.71506e9 + 6.24231e8i −0.915393 + 0.333176i
\(447\) −9.15333e8 − 3.33154e8i −0.484733 − 0.176428i
\(448\) 1.45171e8 − 1.21813e8i 0.0762792 − 0.0640058i
\(449\) 2.99521e8 + 1.69867e9i 0.156158 + 0.885618i 0.957719 + 0.287705i \(0.0928923\pi\)
−0.801561 + 0.597913i \(0.795997\pi\)
\(450\) −4.28634e8 −0.221739
\(451\) 1.20117e7 + 6.81219e7i 0.00616578 + 0.0349679i
\(452\) 1.36353e8 − 2.36170e8i 0.0694512 − 0.120293i
\(453\) −1.40961e9 − 1.18280e9i −0.712452 − 0.597818i
\(454\) 4.04240e8 + 7.00164e8i 0.202742 + 0.351159i
\(455\) −2.39921e7 + 4.15555e7i −0.0119406 + 0.0206818i
\(456\) −1.12192e7 + 4.08345e6i −0.00554095 + 0.00201674i
\(457\) 1.38846e9 − 1.16506e9i 0.680498 − 0.571006i −0.235654 − 0.971837i \(-0.575723\pi\)
0.916152 + 0.400831i \(0.131279\pi\)
\(458\) 6.31466e8 + 1.09373e9i 0.307129 + 0.531963i
\(459\) −5.42485e8 + 3.07658e9i −0.261844 + 1.48499i
\(460\) 5.63480e6 − 3.19566e7i 0.00269915 − 0.0153076i
\(461\) 1.65509e9 + 1.38878e9i 0.786806 + 0.660209i 0.944953 − 0.327207i \(-0.106107\pi\)
−0.158147 + 0.987416i \(0.550552\pi\)
\(462\) −1.83431e8 − 6.67633e7i −0.0865416 − 0.0314986i
\(463\) 4.43654e8 + 1.61477e8i 0.207736 + 0.0756096i 0.443792 − 0.896130i \(-0.353633\pi\)
−0.236056 + 0.971739i \(0.575855\pi\)
\(464\) 4.41113e8 + 3.70138e8i 0.204992 + 0.172009i
\(465\) −6.41780e6 + 3.63972e7i −0.00296006 + 0.0167874i
\(466\) 3.81773e8 − 2.16514e9i 0.174765 − 0.991142i
\(467\) −1.45207e9 − 2.51506e9i −0.659750 − 1.14272i −0.980680 − 0.195617i \(-0.937329\pi\)
0.320931 − 0.947103i \(-0.396004\pi\)
\(468\) 3.51597e8 − 2.95025e8i 0.158557 − 0.133045i
\(469\) −2.34860e9 + 8.54821e8i −1.05125 + 0.382622i
\(470\) −2.10071e7 + 3.63853e7i −0.00933303 + 0.0161653i
\(471\) −1.30081e9 − 2.25306e9i −0.573640 − 0.993574i
\(472\) 7.08569e8 + 5.94560e8i 0.310159 + 0.260255i
\(473\) −2.81540e8 + 4.87641e8i −0.122328 + 0.211878i
\(474\) 1.03395e8 + 5.86383e8i 0.0445939 + 0.252905i
\(475\) 4.70008e7 0.0201223
\(476\) 2.25489e8 + 1.27881e9i 0.0958299 + 0.543478i
\(477\) 6.57373e8 − 5.51601e8i 0.277330 − 0.232708i
\(478\) 1.02486e9 + 3.73017e8i 0.429206 + 0.156218i
\(479\) −2.01530e9 + 7.33511e8i −0.837850 + 0.304953i −0.725077 − 0.688668i \(-0.758196\pi\)
−0.112774 + 0.993621i \(0.535974\pi\)
\(480\) 8.06208e6 0.00332738
\(481\) −2.37096e9 − 2.17909e9i −0.971441 − 0.892828i
\(482\) −1.48433e9 −0.603762
\(483\) 2.10104e9 − 7.64716e8i 0.848436 − 0.308806i
\(484\) 1.12631e9 + 4.09945e8i 0.451544 + 0.164349i
\(485\) −2.08930e7 + 1.75313e7i −0.00831580 + 0.00697779i
\(486\) −1.86862e8 − 1.05975e9i −0.0738405 − 0.418771i
\(487\) 1.13768e9 0.446344 0.223172 − 0.974779i \(-0.428359\pi\)
0.223172 + 0.974779i \(0.428359\pi\)
\(488\) −1.96221e8 − 1.11283e9i −0.0764322 − 0.433469i
\(489\) −2.86937e8 + 4.96989e8i −0.110970 + 0.192205i
\(490\) −1.17127e7 − 9.82815e6i −0.00449751 − 0.00377386i
\(491\) −2.39856e9 − 4.15442e9i −0.914461 − 1.58389i −0.807689 − 0.589609i \(-0.799282\pi\)
−0.106772 − 0.994284i \(-0.534051\pi\)
\(492\) 9.84252e7 − 1.70478e8i 0.0372588 − 0.0645341i
\(493\) −3.70777e9 + 1.34952e9i −1.39363 + 0.507240i
\(494\) −3.85535e7 + 3.23503e7i −0.0143886 + 0.0120735i
\(495\) 1.89835e6 + 3.28804e6i 0.000703491 + 0.00121848i
\(496\) 1.06844e8 − 6.05941e8i 0.0393155 − 0.222969i
\(497\) 5.16349e8 − 2.92836e9i 0.188667 − 1.06998i
\(498\) 7.92806e8 + 6.65243e8i 0.287650 + 0.241367i
\(499\) −1.46323e9 − 5.32570e8i −0.527180 − 0.191878i 0.0646985 − 0.997905i \(-0.479391\pi\)
−0.591879 + 0.806027i \(0.701614\pi\)
\(500\) −5.96630e7 − 2.17155e7i −0.0213457 − 0.00776919i
\(501\) −7.17714e8 − 6.02233e8i −0.254988 − 0.213960i
\(502\) 2.82069e8 − 1.59970e9i 0.0995160 − 0.564383i
\(503\) 8.52519e8 − 4.83488e9i 0.298687 − 1.69394i −0.353140 − 0.935570i \(-0.614886\pi\)
0.651827 − 0.758368i \(-0.274003\pi\)
\(504\) −1.26986e8 − 2.19946e8i −0.0441823 − 0.0765261i
\(505\) 2.12091e7 − 1.77966e7i 0.00732830 − 0.00614917i
\(506\) 5.22900e8 − 1.90320e8i 0.179429 − 0.0653066i
\(507\) −9.00459e8 + 1.55964e9i −0.306857 + 0.531492i
\(508\) 9.87912e8 + 1.71111e9i 0.334345 + 0.579103i
\(509\) −4.13818e9 − 3.47234e9i −1.39090 − 1.16711i −0.964973 − 0.262350i \(-0.915502\pi\)
−0.425930 − 0.904756i \(-0.640053\pi\)
\(510\) −2.76215e7 + 4.78418e7i −0.00922044 + 0.0159703i
\(511\) −5.32006e8 − 3.01716e9i −0.176378 − 1.00029i
\(512\) −1.34218e8 −0.0441942
\(513\) 1.16342e7 + 6.59808e7i 0.00380475 + 0.0215778i
\(514\) 6.66000e8 − 5.58840e8i 0.216323 − 0.181517i
\(515\) 5.60535e7 + 2.04018e7i 0.0180833 + 0.00658178i
\(516\) 1.50576e9 − 5.48053e8i 0.482484 − 0.175610i
\(517\) −7.20475e8 −0.229299
\(518\) −1.41528e9 + 1.08264e9i −0.447393 + 0.342239i
\(519\) 2.56790e9 0.806291
\(520\) 3.19351e7 − 1.16234e7i 0.00995993 − 0.00362512i
\(521\) −4.31186e9 − 1.56939e9i −1.33577 − 0.486182i −0.427295 − 0.904112i \(-0.640533\pi\)
−0.908479 + 0.417930i \(0.862756\pi\)
\(522\) 5.91168e8 − 4.96049e8i 0.181913 − 0.152643i
\(523\) −7.68916e7 − 4.36074e8i −0.0235030 − 0.133292i 0.970799 − 0.239896i \(-0.0771134\pi\)
−0.994302 + 0.106604i \(0.966002\pi\)
\(524\) 1.46456e9 0.444681
\(525\) −3.79741e8 − 2.15362e9i −0.114533 − 0.649547i
\(526\) 9.32121e8 − 1.61448e9i 0.279269 − 0.483708i
\(527\) 3.22971e9 + 2.71005e9i 0.961227 + 0.806565i
\(528\) 6.91259e7 + 1.19730e8i 0.0204372 + 0.0353983i
\(529\) −1.48446e9 + 2.57116e9i −0.435987 + 0.755152i
\(530\) 5.97082e7 − 2.17320e7i 0.0174208 − 0.00634066i
\(531\) 9.49604e8 − 7.96813e8i 0.275240 − 0.230954i
\(532\) 1.39243e7 + 2.41176e7i 0.00400944 + 0.00694455i
\(533\) 1.44093e8 − 8.17190e8i 0.0412189 − 0.233764i
\(534\) −5.74992e8 + 3.26094e9i −0.163406 + 0.926721i
\(535\) 5.13858e7 + 4.31178e7i 0.0145079 + 0.0121736i
\(536\) 1.66339e9 + 6.05425e8i 0.466571 + 0.169818i
\(537\) −2.94982e9 − 1.07365e9i −0.822026 − 0.299193i
\(538\) −6.48630e8 − 5.44265e8i −0.179580 − 0.150686i
\(539\) 4.55301e7 − 2.58214e8i 0.0125238 − 0.0710263i
\(540\) 7.85613e6 − 4.45543e7i 0.00214699 − 0.0121762i
\(541\) 3.23065e9 + 5.59566e9i 0.877203 + 1.51936i 0.854398 + 0.519620i \(0.173926\pi\)
0.0228052 + 0.999740i \(0.492740\pi\)
\(542\) −1.07785e9 + 9.04424e8i −0.290778 + 0.243991i
\(543\) −3.35062e9 + 1.21953e9i −0.898103 + 0.326883i
\(544\) 4.59843e8 − 7.96472e8i 0.122466 − 0.212117i
\(545\) −3.59663e7 − 6.22955e7i −0.00951719 − 0.0164842i
\(546\) 1.79381e9 + 1.50518e9i 0.471630 + 0.395745i
\(547\) −6.65158e8 + 1.15209e9i −0.173768 + 0.300975i −0.939734 − 0.341906i \(-0.888928\pi\)
0.765966 + 0.642881i \(0.222261\pi\)
\(548\) 1.98456e7 + 1.12550e8i 0.00515149 + 0.0292156i
\(549\) −1.51439e9 −0.390601
\(550\) −9.45085e7 − 5.35985e8i −0.0242215 − 0.137367i
\(551\) −6.48231e7 + 5.43930e7i −0.0165082 + 0.0138520i
\(552\) −1.48806e9 − 5.41608e8i −0.376558 − 0.137056i
\(553\) 1.30510e9 − 4.75018e8i 0.328176 − 0.119446i
\(554\) 3.18857e9 0.796731
\(555\) −7.57288e7 − 3.41944e6i −0.0188034 − 0.000849044i
\(556\) −3.38255e9 −0.834607
\(557\) −3.88091e9 + 1.41254e9i −0.951569 + 0.346343i −0.770724 − 0.637169i \(-0.780105\pi\)
−0.180845 + 0.983512i \(0.557883\pi\)
\(558\) −7.74864e8 − 2.82027e8i −0.188802 − 0.0687182i
\(559\) 5.17440e9 − 4.34184e9i 1.25291 − 1.05131i
\(560\) −3.26548e6 − 1.85194e7i −0.000785757 − 0.00445625i
\(561\) −9.47330e8 −0.226533
\(562\) −6.16407e8 − 3.49582e9i −0.146484 − 0.830752i
\(563\) −1.04915e9 + 1.81719e9i −0.247777 + 0.429162i −0.962909 − 0.269828i \(-0.913033\pi\)
0.715132 + 0.698989i \(0.246367\pi\)
\(564\) 1.57063e9 + 1.31792e9i 0.368635 + 0.309322i
\(565\) −1.35306e7 − 2.34356e7i −0.00315607 − 0.00546647i
\(566\) −9.76744e8 + 1.69177e9i −0.226424 + 0.392178i
\(567\) 1.90989e9 − 6.95142e8i 0.440014 − 0.160152i
\(568\) −1.61329e9 + 1.35371e9i −0.369397 + 0.309961i
\(569\) 1.14261e9 + 1.97906e9i 0.260019 + 0.450367i 0.966247 − 0.257618i \(-0.0829377\pi\)
−0.706227 + 0.707985i \(0.749604\pi\)
\(570\) −205730. + 1.16675e6i −4.65302e−5 + 0.000263886i
\(571\) −2.99823e8 + 1.70038e9i −0.0673966 + 0.382225i 0.932388 + 0.361460i \(0.117721\pi\)
−0.999784 + 0.0207656i \(0.993390\pi\)
\(572\) 4.46437e8 + 3.74605e8i 0.0997411 + 0.0836927i
\(573\) 5.64457e9 + 2.05445e9i 1.25340 + 0.456200i
\(574\) −4.31471e8 − 1.57042e8i −0.0952269 − 0.0346598i
\(575\) 4.77548e9 + 4.00710e9i 1.04756 + 0.879009i
\(576\) −3.12350e7 + 1.77142e8i −0.00681024 + 0.0386228i
\(577\) 1.46831e9 − 8.32720e9i 0.318202 − 1.80461i −0.235475 − 0.971880i \(-0.575665\pi\)
0.553677 − 0.832732i \(-0.313224\pi\)
\(578\) 1.50959e9 + 2.61468e9i 0.325170 + 0.563211i
\(579\) 2.55547e8 − 2.14429e8i 0.0547136 − 0.0459101i
\(580\) 5.36949e7 − 1.95434e7i 0.0114271 − 0.00415912i
\(581\) 1.20701e9 − 2.09061e9i 0.255326 − 0.442238i
\(582\) 6.65489e8 + 1.15266e9i 0.139930 + 0.242366i
\(583\) 8.34692e8 + 7.00389e8i 0.174456 + 0.146386i
\(584\) −1.08493e9 + 1.87915e9i −0.225401 + 0.390406i
\(585\) −7.90885e6 − 4.48533e7i −0.00163331 − 0.00926294i
\(586\) −1.21045e9 −0.248487
\(587\) 2.14299e8 + 1.21535e9i 0.0437308 + 0.248010i 0.998835 − 0.0482612i \(-0.0153680\pi\)
−0.955104 + 0.296271i \(0.904257\pi\)
\(588\) −5.71588e8 + 4.79619e8i −0.115948 + 0.0972917i
\(589\) 8.49658e7 + 3.09250e7i 0.0171333 + 0.00623600i
\(590\) 8.62512e7 − 3.13929e7i 0.0172895 − 0.00629287i
\(591\) −5.22437e9 −1.04106
\(592\) 1.26073e9 + 5.69270e7i 0.249746 + 0.0112770i
\(593\) −8.65489e9 −1.70439 −0.852197 − 0.523221i \(-0.824730\pi\)
−0.852197 + 0.523221i \(0.824730\pi\)
\(594\) 7.29034e8 − 2.65347e8i 0.142723 − 0.0519471i
\(595\) 1.21086e8 + 4.40715e7i 0.0235658 + 0.00857726i
\(596\) 1.23271e9 − 1.03437e9i 0.238506 − 0.200130i
\(597\) 9.30895e8 + 5.27937e9i 0.179057 + 1.01548i
\(598\) −6.67527e9 −1.27648
\(599\) −8.17151e8 − 4.63430e9i −0.155349 − 0.881028i −0.958466 − 0.285207i \(-0.907938\pi\)
0.803117 − 0.595821i \(-0.203173\pi\)
\(600\) −7.74411e8 + 1.34132e9i −0.146367 + 0.253515i
\(601\) −3.68345e7 − 3.09078e7i −0.00692141 − 0.00580775i 0.639320 − 0.768941i \(-0.279216\pi\)
−0.646242 + 0.763133i \(0.723660\pi\)
\(602\) −1.86883e9 − 3.23691e9i −0.349126 − 0.604704i
\(603\) 1.18615e9 − 2.05447e9i 0.220307 − 0.381583i
\(604\) 2.85657e9 − 1.03971e9i 0.527492 − 0.191991i
\(605\) 9.11126e7 − 7.64526e7i 0.0167276 − 0.0140362i
\(606\) −6.75560e8 − 1.17010e9i −0.123313 − 0.213585i
\(607\) −6.71139e8 + 3.80622e9i −0.121801 + 0.690770i 0.861355 + 0.508004i \(0.169616\pi\)
−0.983156 + 0.182766i \(0.941495\pi\)
\(608\) 3.42499e6 − 1.94241e7i 0.000618012 − 0.00350492i
\(609\) 3.01607e9 + 2.53078e9i 0.541104 + 0.454040i
\(610\) −1.05369e8 − 3.83512e7i −0.0187957 − 0.00684107i
\(611\) 8.12159e9 + 2.95602e9i 1.44044 + 0.524279i
\(612\) −9.44180e8 − 7.92261e8i −0.166504 − 0.139713i
\(613\) 1.24108e9 − 7.03850e9i 0.217614 − 1.23415i −0.658698 − 0.752407i \(-0.728892\pi\)
0.876312 − 0.481744i \(-0.159996\pi\)
\(614\) −3.56449e8 + 2.02152e9i −0.0621452 + 0.352443i
\(615\) −9.76692e6 − 1.69168e7i −0.00169315 − 0.00293262i
\(616\) 2.47032e8 − 2.07285e8i 0.0425816 − 0.0357302i
\(617\) −4.95444e9 + 1.80327e9i −0.849174 + 0.309074i −0.729703 − 0.683764i \(-0.760342\pi\)
−0.119470 + 0.992838i \(0.538120\pi\)
\(618\) 1.45550e9 − 2.52100e9i 0.248057 − 0.429648i
\(619\) −1.13889e8 − 1.97262e8i −0.0193003 − 0.0334292i 0.856214 − 0.516621i \(-0.172811\pi\)
−0.875514 + 0.483192i \(0.839477\pi\)
\(620\) −4.67718e7 − 3.92462e7i −0.00788158 − 0.00661343i
\(621\) −4.44319e9 + 7.69582e9i −0.744516 + 1.28954i
\(622\) −4.40763e8 − 2.49969e9i −0.0734411 − 0.416505i
\(623\) 7.72362e9 1.27971
\(624\) −2.87990e8 − 1.63327e9i −0.0474495 − 0.269099i
\(625\) 4.66832e9 − 3.91719e9i 0.764858 − 0.641792i
\(626\) 3.53352e9 + 1.28610e9i 0.575702 + 0.209538i
\(627\) −1.90913e7 + 6.94867e6i −0.00309314 + 0.00112581i
\(628\) 4.29790e9 0.692465
\(629\) −4.65722e9 + 7.28639e9i −0.746190 + 1.16744i
\(630\) −2.52021e7 −0.00401555
\(631\) −1.26060e9 + 4.58821e8i −0.199745 + 0.0727011i −0.439955 − 0.898020i \(-0.645006\pi\)
0.240211 + 0.970721i \(0.422783\pi\)
\(632\) −9.24335e8 − 3.36430e8i −0.145653 − 0.0530134i
\(633\) 1.53113e9 − 1.28477e9i 0.239939 − 0.201332i
\(634\) 1.75062e8 + 9.92829e8i 0.0272823 + 0.154726i
\(635\) 1.96065e8 0.0303873
\(636\) −5.38447e8 − 3.05369e9i −0.0829934 − 0.470679i
\(637\) −1.57266e9 + 2.72392e9i −0.241072 + 0.417548i
\(638\) 7.50629e8 + 6.29852e8i 0.114433 + 0.0960210i
\(639\) 1.41120e9 + 2.44427e9i 0.213962 + 0.370592i
\(640\) −6.65934e6 + 1.15343e7i −0.00100416 + 0.00173925i
\(641\) −5.98527e8 + 2.17846e8i −0.0897596 + 0.0326698i −0.386510 − 0.922285i \(-0.626319\pi\)
0.296750 + 0.954955i \(0.404097\pi\)
\(642\) 2.50765e9 − 2.10417e9i 0.374020 − 0.313840i
\(643\) 1.64682e9 + 2.85238e9i 0.244291 + 0.423125i 0.961932 − 0.273288i \(-0.0881113\pi\)
−0.717641 + 0.696413i \(0.754778\pi\)
\(644\) −6.41405e8 + 3.63759e9i −0.0946307 + 0.536677i
\(645\) 2.76116e7 − 1.56593e8i 0.00405166 − 0.0229781i
\(646\) 1.03532e8 + 8.68734e7i 0.0151098 + 0.0126786i
\(647\) 5.30178e8 + 1.92969e8i 0.0769585 + 0.0280106i 0.380213 − 0.924899i \(-0.375851\pi\)
−0.303254 + 0.952910i \(0.598073\pi\)
\(648\) −1.35267e9 − 4.92332e8i −0.195290 − 0.0710798i
\(649\) 1.20575e9 + 1.01174e9i 0.173141 + 0.145283i
\(650\) −1.13372e9 + 6.42966e9i −0.161924 + 0.918315i
\(651\) 7.30534e8 − 4.14306e9i 0.103778 − 0.588556i
\(652\) −4.74023e8 − 8.21033e8i −0.0669782 − 0.116010i
\(653\) −6.63367e8 + 5.56631e8i −0.0932305 + 0.0782296i −0.688212 − 0.725510i \(-0.741604\pi\)
0.594981 + 0.803740i \(0.297159\pi\)
\(654\) −3.29865e9 + 1.20061e9i −0.461121 + 0.167834i
\(655\) 7.26657e7 − 1.25861e8i 0.0101038 − 0.0175003i
\(656\) 1.62600e8 + 2.81631e8i 0.0224883 + 0.0389509i
\(657\) 2.22764e9 + 1.86922e9i 0.306455 + 0.257146i
\(658\) 2.39122e9 − 4.14171e9i 0.327211 − 0.566747i
\(659\) 1.14716e9 + 6.50585e9i 0.156143 + 0.885533i 0.957733 + 0.287659i \(0.0928768\pi\)
−0.801590 + 0.597875i \(0.796012\pi\)
\(660\) 1.37190e7 0.00185746
\(661\) 2.23844e8 + 1.26948e9i 0.0301467 + 0.170971i 0.996164 − 0.0875075i \(-0.0278902\pi\)
−0.966017 + 0.258478i \(0.916779\pi\)
\(662\) −5.33070e9 + 4.47299e9i −0.714136 + 0.599231i
\(663\) 1.06788e10 + 3.88677e9i 1.42307 + 0.517954i
\(664\) −1.60662e9 + 5.84761e8i −0.212973 + 0.0775158i
\(665\) 2.76347e6 0.000364401
\(666\) 3.68529e8 − 1.65069e9i 0.0483406 − 0.216523i
\(667\) −1.12236e10 −1.46451
\(668\) 1.45444e9 − 5.29374e8i 0.188790 − 0.0687140i
\(669\) 8.30531e9 + 3.02288e9i 1.07242 + 0.390328i
\(670\) 1.34559e8 − 1.12909e8i 0.0172843 − 0.0145033i
\(671\) −3.33904e8 − 1.89366e9i −0.0426670 − 0.241977i
\(672\) −9.17700e8 −0.116656
\(673\) 6.42469e8 + 3.64362e9i 0.0812456 + 0.460766i 0.998104 + 0.0615535i \(0.0196055\pi\)
−0.916858 + 0.399213i \(0.869283\pi\)
\(674\) 3.72607e9 − 6.45374e9i 0.468750 − 0.811899i
\(675\) 6.65805e9 + 5.58676e9i 0.833266 + 0.699193i
\(676\) −1.48757e9 − 2.57655e9i −0.185210 − 0.320793i
\(677\) 5.54053e9 − 9.59649e9i 0.686264 − 1.18864i −0.286774 − 0.957998i \(-0.592583\pi\)
0.973038 − 0.230646i \(-0.0740839\pi\)
\(678\) −1.24096e9 + 4.51671e8i −0.152916 + 0.0556568i
\(679\) 2.37823e9 − 1.99557e9i 0.291548 − 0.244638i
\(680\) −4.56311e7 − 7.90355e7i −0.00556519 − 0.00963919i
\(681\) 6.79853e8 − 3.85564e9i 0.0824898 − 0.467823i
\(682\) 1.81813e8 − 1.03111e9i 0.0219472 − 0.124469i
\(683\) −5.83240e9 − 4.89396e9i −0.700446 − 0.587744i 0.221455 − 0.975171i \(-0.428920\pi\)
−0.921901 + 0.387427i \(0.873364\pi\)
\(684\) −2.48391e7 − 9.04069e6i −0.00296783 − 0.00108020i
\(685\) 1.06569e7 + 3.87880e6i 0.00126682 + 0.000461085i
\(686\) 4.98176e9 + 4.18019e9i 0.589180 + 0.494381i
\(687\) 1.06200e9 − 6.02292e9i 0.124962 − 0.708694i
\(688\) −4.59679e8 + 2.60697e9i −0.0538140 + 0.305194i
\(689\) −6.53549e9 − 1.13198e10i −0.761221 − 1.31847i
\(690\) −1.20376e8 + 1.01007e8i −0.0139498 + 0.0117052i
\(691\) 6.20007e9 − 2.25664e9i 0.714864 − 0.260189i 0.0411201 − 0.999154i \(-0.486907\pi\)
0.673744 + 0.738965i \(0.264685\pi\)
\(692\) −2.12110e9 + 3.67386e9i −0.243327 + 0.421455i
\(693\) −2.16088e8 − 3.74275e8i −0.0246641 − 0.0427194i
\(694\) −8.66618e9 − 7.27179e9i −0.984169 − 0.825816i
\(695\) −1.67828e8 + 2.90687e8i −0.0189635 + 0.0328457i
\(696\) −4.84220e8 − 2.74615e9i −0.0544390 − 0.308739i
\(697\) −2.22834e9 −0.249268
\(698\) 1.34497e9 + 7.62769e9i 0.149699 + 0.848983i
\(699\) −8.15577e9 + 6.84350e9i −0.903223 + 0.757894i
\(700\) 3.39482e9 + 1.23561e9i 0.374088 + 0.136157i
\(701\) 2.38178e9 − 8.66899e8i 0.261150 − 0.0950507i −0.208127 − 0.978102i \(-0.566737\pi\)
0.469277 + 0.883051i \(0.344515\pi\)
\(702\) −9.30675e9 −1.01536
\(703\) −4.04102e7 + 1.81002e8i −0.00438679 + 0.0196489i
\(704\) −2.28394e8 −0.0246707
\(705\) 1.91186e8 − 6.95862e7i 0.0205492 − 0.00747930i
\(706\) 4.35322e9 + 1.58444e9i 0.465579 + 0.169457i
\(707\) −2.41422e9 + 2.02577e9i −0.256926 + 0.215587i
\(708\) −7.77811e8 − 4.41119e9i −0.0823679 − 0.467131i
\(709\) −6.43599e9 −0.678193 −0.339097 − 0.940752i \(-0.610121\pi\)
−0.339097 + 0.940752i \(0.610121\pi\)
\(710\) 3.62894e7 + 2.05807e8i 0.00380518 + 0.0215803i
\(711\) −6.59135e8 + 1.14166e9i −0.0687750 + 0.119122i
\(712\) −4.19044e9 − 3.51620e9i −0.435091 − 0.365084i
\(713\) 5.99634e9 + 1.03860e10i 0.619545 + 1.07308i
\(714\) 3.14413e9 − 5.44580e9i 0.323264 − 0.559910i
\(715\) 5.43430e7 − 1.97792e7i 0.00555997 − 0.00202366i
\(716\) 3.97262e9 − 3.33343e9i 0.404466 − 0.339387i
\(717\) −2.64073e9 − 4.57387e9i −0.267551 − 0.463411i
\(718\) −4.32862e7 + 2.45488e8i −0.00436429 + 0.0247511i
\(719\) −2.21042e9 + 1.25359e10i −0.221780 + 1.25778i 0.646965 + 0.762520i \(0.276038\pi\)
−0.868745 + 0.495259i \(0.835073\pi\)
\(720\) 1.36734e7 + 1.14733e7i 0.00136525 + 0.00114558i
\(721\) −6.38053e9 − 2.32232e9i −0.633991 − 0.230754i
\(722\) −6.71699e9 − 2.44479e9i −0.664194 − 0.241747i
\(723\) 5.50631e9 + 4.62034e9i 0.541847 + 0.454664i
\(724\) 1.02288e9 − 5.80103e9i 0.100170 − 0.568094i
\(725\) −1.90622e9 + 1.08107e10i −0.185776 + 1.05359i
\(726\) −2.90215e9 − 5.02667e9i −0.281476 − 0.487531i
\(727\) 1.24976e10 − 1.04867e10i 1.20630 − 1.01221i 0.206876 − 0.978367i \(-0.433670\pi\)
0.999427 − 0.0338416i \(-0.0107742\pi\)
\(728\) −3.63515e9 + 1.32309e9i −0.349190 + 0.127095i
\(729\) −5.67991e9 + 9.83789e9i −0.542994 + 0.940493i
\(730\) 1.07660e8 + 1.86472e8i 0.0102429 + 0.0177412i
\(731\) −1.38953e10 − 1.16596e10i −1.31570 − 1.10401i
\(732\) −2.73604e9 + 4.73895e9i −0.257830 + 0.446574i
\(733\) −3.25916e9 − 1.84836e10i −0.305663 − 1.73350i −0.620370 − 0.784310i \(-0.713017\pi\)
0.314707 − 0.949189i \(-0.398094\pi\)
\(734\) 2.43867e7 0.00227623
\(735\) 1.28573e7 + 7.29175e7i 0.00119439 + 0.00677370i
\(736\) 2.00402e9 − 1.68157e9i 0.185280 − 0.155469i
\(737\) 2.83054e9 + 1.03023e9i 0.260455 + 0.0947980i
\(738\) 4.09541e8 − 1.49061e8i 0.0375059 − 0.0136510i
\(739\) 4.55534e9 0.415207 0.207604 − 0.978213i \(-0.433434\pi\)
0.207604 + 0.978213i \(0.433434\pi\)
\(740\) 6.74447e7 − 1.05520e8i 0.00611838 − 0.00957244i
\(741\) 2.43717e8 0.0220051
\(742\) −6.79654e9 + 2.47374e9i −0.610765 + 0.222300i
\(743\) 8.39606e9 + 3.05592e9i 0.750957 + 0.273326i 0.689008 − 0.724754i \(-0.258046\pi\)
0.0619483 + 0.998079i \(0.480269\pi\)
\(744\) −2.28249e9 + 1.91524e9i −0.203191 + 0.170497i
\(745\) −2.77287e7 − 1.57257e8i −0.00245687 − 0.0139336i
\(746\) −3.57265e9 −0.315068
\(747\) 3.97885e8 + 2.25652e9i 0.0349249 + 0.198069i
\(748\) 7.82501e8 − 1.35533e9i 0.0683643 − 0.118410i
\(749\) −5.84920e9 − 4.90807e9i −0.508640 − 0.426800i
\(750\) 1.53732e8 + 2.66272e8i 0.0133061 + 0.0230468i
\(751\) 7.70174e9 − 1.33398e10i 0.663513 − 1.14924i −0.316173 − 0.948701i \(-0.602398\pi\)
0.979686 − 0.200536i \(-0.0642685\pi\)
\(752\) −3.18288e9 + 1.15847e9i −0.272934 + 0.0993398i
\(753\) −6.02581e9 + 5.05626e9i −0.514320 + 0.431566i
\(754\) −5.87729e9 − 1.01798e10i −0.499319 − 0.864845i
\(755\) 5.23818e7 − 2.97072e8i 0.00442962 − 0.0251216i
\(756\) −8.94257e8 + 5.07158e9i −0.0752724 + 0.426891i
\(757\) −4.32122e9 − 3.62593e9i −0.362052 − 0.303797i 0.443556 − 0.896247i \(-0.353717\pi\)