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Properties

Label 74.8.f.b.7.9
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 7.9
Character \(\chi\) \(=\) 74.7
Dual form 74.8.f.b.53.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 - 2.73616i) q^{2} +(46.7880 + 17.0295i) q^{3} +(49.0268 - 41.1384i) q^{4} +(58.4927 + 331.728i) q^{5} +398.326 q^{6} +(201.162 + 1140.85i) q^{7} +(256.000 - 443.405i) q^{8} +(223.779 + 187.773i) q^{9} +O(q^{10})\) \(q+(7.51754 - 2.73616i) q^{2} +(46.7880 + 17.0295i) q^{3} +(49.0268 - 41.1384i) q^{4} +(58.4927 + 331.728i) q^{5} +398.326 q^{6} +(201.162 + 1140.85i) q^{7} +(256.000 - 443.405i) q^{8} +(223.779 + 187.773i) q^{9} +(1347.38 + 2333.74i) q^{10} +(59.0140 - 102.215i) q^{11} +(2994.43 - 1089.89i) q^{12} +(-10230.8 + 8584.64i) q^{13} +(4633.78 + 8025.94i) q^{14} +(-2912.40 + 16517.0i) q^{15} +(711.263 - 4033.77i) q^{16} +(-23683.1 - 19872.5i) q^{17} +(2196.05 + 799.296i) q^{18} +(44947.2 + 16359.4i) q^{19} +(16514.5 + 13857.3i) q^{20} +(-10016.0 + 56803.6i) q^{21} +(163.963 - 929.880i) q^{22} +(-6066.20 - 10507.0i) q^{23} +(19528.7 - 16386.5i) q^{24} +(-33208.9 + 12087.0i) q^{25} +(-53421.3 + 92528.5i) q^{26} +(-47173.7 - 81707.3i) q^{27} +(56794.9 + 47656.6i) q^{28} +(28453.0 - 49282.0i) q^{29} +(23299.2 + 132136. i) q^{30} +211983. q^{31} +(-5690.10 - 32270.2i) q^{32} +(4501.82 - 3777.48i) q^{33} +(-232413. - 84591.4i) q^{34} +(-366684. + 133462. i) q^{35} +18695.9 q^{36} +(162944. + 261498. i) q^{37} +382654. q^{38} +(-624870. + 227434. i) q^{39} +(162064. + 58986.5i) q^{40} +(144658. - 121383. i) q^{41} +(80128.1 + 454429. i) q^{42} +994755. q^{43} +(-1311.70 - 7439.04i) q^{44} +(-49200.2 + 85217.3i) q^{45} +(-74351.7 - 62388.5i) q^{46} +(668647. + 1.15813e6i) q^{47} +(101972. - 176620. i) q^{48} +(-487185. + 177321. i) q^{49} +(-216577. + 181730. i) q^{50} +(-769669. - 1.33311e6i) q^{51} +(-148424. + 841756. i) q^{52} +(158871. - 901001. i) q^{53} +(-578195. - 485163. i) q^{54} +(37359.6 + 13597.8i) q^{55} +(557354. + 202860. i) q^{56} +(1.82440e6 + 1.53085e6i) q^{57} +(79052.9 - 448332. i) q^{58} +(19524.9 - 110731. i) q^{59} +(536698. + 929589. i) q^{60} +(-1.12444e6 + 943517. i) q^{61} +(1.59359e6 - 580020. i) q^{62} +(-169204. + 293070. i) q^{63} +(-131072. - 227023. i) q^{64} +(-3.44620e6 - 2.89170e6i) q^{65} +(23506.8 - 40715.0i) q^{66} +(-427209. - 2.42282e6i) q^{67} -1.97863e6 q^{68} +(-104898. - 594905. i) q^{69} +(-2.39139e6 + 2.00662e6i) q^{70} +(2.47134e6 + 899495. i) q^{71} +(140547. - 51154.9i) q^{72} -4.62325e6 q^{73} +(1.94044e6 + 1.51998e6i) q^{74} -1.75961e6 q^{75} +(2.87662e6 - 1.04700e6i) q^{76} +(128483. + 46764.1i) q^{77} +(-4.07519e6 + 3.41949e6i) q^{78} +(-402008. - 2.27990e6i) q^{79} +1.37972e6 q^{80} +(-926675. - 5.25543e6i) q^{81} +(755351. - 1.30831e6i) q^{82} +(2.04743e6 + 1.71800e6i) q^{83} +(1.84576e6 + 3.19694e6i) q^{84} +(5.20698e6 - 9.01875e6i) q^{85} +(7.47811e6 - 2.72181e6i) q^{86} +(2.17051e6 - 1.82127e6i) q^{87} +(-30215.2 - 52334.2i) q^{88} +(1.71628e6 - 9.73353e6i) q^{89} +(-136696. + 775244. i) q^{90} +(-1.18518e7 - 9.94484e6i) q^{91} +(-729647. - 265570. i) q^{92} +(9.91828e6 + 3.60996e6i) q^{93} +(8.19541e6 + 6.87677e6i) q^{94} +(-2.79781e6 + 1.58672e7i) q^{95} +(283315. - 1.60676e6i) q^{96} +(-4.09025e6 - 7.08452e6i) q^{97} +(-3.17726e6 + 2.66603e6i) q^{98} +(32399.4 - 11792.4i) 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
\(3\) 46.7880 + 17.0295i 1.00048 + 0.364147i 0.789771 − 0.613401i \(-0.210199\pi\)
0.210713 + 0.977548i \(0.432421\pi\)
\(4\) 49.0268 − 41.1384i 0.383022 − 0.321394i
\(5\) 58.4927 + 331.728i 0.209270 + 1.18683i 0.890578 + 0.454831i \(0.150300\pi\)
−0.681308 + 0.731997i \(0.738589\pi\)
\(6\) 398.326 0.752852
\(7\) 201.162 + 1140.85i 0.221668 + 1.25714i 0.868954 + 0.494893i \(0.164793\pi\)
−0.647286 + 0.762247i \(0.724096\pi\)
\(8\) 256.000 − 443.405i 0.176777 − 0.306186i
\(9\) 223.779 + 187.773i 0.102322 + 0.0858588i
\(10\) 1347.38 + 2333.74i 0.426080 + 0.737992i
\(11\) 59.0140 − 102.215i 0.0133684 − 0.0231548i −0.859264 − 0.511533i \(-0.829078\pi\)
0.872632 + 0.488378i \(0.162411\pi\)
\(12\) 2994.43 − 1089.89i 0.500242 − 0.182073i
\(13\) −10230.8 + 8584.64i −1.29154 + 1.08373i −0.299996 + 0.953940i \(0.596985\pi\)
−0.991542 + 0.129788i \(0.958570\pi\)
\(14\) 4633.78 + 8025.94i 0.451323 + 0.781714i
\(15\) −2912.40 + 16517.0i −0.222808 + 1.26361i
\(16\) 711.263 − 4033.77i 0.0434120 − 0.246202i
\(17\) −23683.1 − 19872.5i −1.16914 − 0.981027i −0.169153 − 0.985590i \(-0.554103\pi\)
−0.999990 + 0.00456281i \(0.998548\pi\)
\(18\) 2196.05 + 799.296i 0.0887540 + 0.0323038i
\(19\) 44947.2 + 16359.4i 1.50337 + 0.547181i 0.956930 − 0.290320i \(-0.0937617\pi\)
0.546437 + 0.837500i \(0.315984\pi\)
\(20\) 16514.5 + 13857.3i 0.461594 + 0.387323i
\(21\) −10016.0 + 56803.6i −0.236008 + 1.33847i
\(22\) 163.963 − 929.880i 0.00328296 − 0.0186186i
\(23\) −6066.20 − 10507.0i −0.103961 − 0.180065i 0.809352 − 0.587323i \(-0.199818\pi\)
−0.913313 + 0.407258i \(0.866485\pi\)
\(24\) 19528.7 − 16386.5i 0.288359 − 0.241962i
\(25\) −33208.9 + 12087.0i −0.425073 + 0.154714i
\(26\) −53421.3 + 92528.5i −0.596085 + 1.03245i
\(27\) −47173.7 − 81707.3i −0.461240 − 0.798891i
\(28\) 56794.9 + 47656.6i 0.488941 + 0.410270i
\(29\) 28453.0 − 49282.0i 0.216638 − 0.375228i −0.737140 − 0.675740i \(-0.763824\pi\)
0.953778 + 0.300512i \(0.0971575\pi\)
\(30\) 23299.2 + 132136.i 0.157549 + 0.893506i
\(31\) 211983. 1.27801 0.639007 − 0.769201i \(-0.279346\pi\)
0.639007 + 0.769201i \(0.279346\pi\)
\(32\) −5690.10 − 32270.2i −0.0306970 − 0.174091i
\(33\) 4501.82 − 3777.48i 0.0218067 − 0.0182980i
\(34\) −232413. − 84591.4i −1.01411 − 0.369105i
\(35\) −366684. + 133462.i −1.44562 + 0.526163i
\(36\) 18695.9 0.0667863
\(37\) 162944. + 261498.i 0.528851 + 0.848715i
\(38\) 382654. 1.13126
\(39\) −624870. + 227434.i −1.68680 + 0.613945i
\(40\) 162064. + 58986.5i 0.400384 + 0.145728i
\(41\) 144658. − 121383.i 0.327793 − 0.275051i −0.464007 − 0.885832i \(-0.653589\pi\)
0.791800 + 0.610781i \(0.209144\pi\)
\(42\) 80128.1 + 454429.i 0.166883 + 0.946441i
\(43\) 994755. 1.90799 0.953996 − 0.299818i \(-0.0969261\pi\)
0.953996 + 0.299818i \(0.0969261\pi\)
\(44\) −1311.70 − 7439.04i −0.00232141 − 0.0131653i
\(45\) −49200.2 + 85217.3i −0.0804865 + 0.139407i
\(46\) −74351.7 − 62388.5i −0.112626 − 0.0945044i
\(47\) 668647. + 1.15813e6i 0.939408 + 1.62710i 0.766578 + 0.642151i \(0.221958\pi\)
0.172830 + 0.984952i \(0.444709\pi\)
\(48\) 101972. − 176620.i 0.133087 − 0.230513i
\(49\) −487185. + 177321.i −0.591572 + 0.215315i
\(50\) −216577. + 181730.i −0.245029 + 0.205604i
\(51\) −769669. − 1.33311e6i −0.812471 − 1.40724i
\(52\) −148424. + 841756.i −0.146384 + 0.830184i
\(53\) 158871. − 901001.i 0.146581 − 0.831303i −0.819503 − 0.573075i \(-0.805750\pi\)
0.966084 − 0.258228i \(-0.0831386\pi\)
\(54\) −578195. − 485163.i −0.499684 − 0.419285i
\(55\) 37359.6 + 13597.8i 0.0302784 + 0.0110204i
\(56\) 557354. + 202860.i 0.424105 + 0.154361i
\(57\) 1.82440e6 + 1.53085e6i 1.30484 + 1.09489i
\(58\) 79052.9 − 448332.i 0.0532010 − 0.301718i
\(59\) 19524.9 − 110731.i 0.0123768 − 0.0701921i −0.977994 − 0.208634i \(-0.933098\pi\)
0.990371 + 0.138442i \(0.0442094\pi\)
\(60\) 536698. + 929589.i 0.320775 + 0.555599i
\(61\) −1.12444e6 + 943517.i −0.634281 + 0.532225i −0.902256 − 0.431201i \(-0.858090\pi\)
0.267975 + 0.963426i \(0.413646\pi\)
\(62\) 1.59359e6 − 580020.i 0.849193 − 0.309081i
\(63\) −169204. + 293070.i −0.0852549 + 0.147666i
\(64\) −131072. − 227023.i −0.0625000 − 0.108253i
\(65\) −3.44620e6 − 2.89170e6i −1.55648 − 1.30604i
\(66\) 23506.8 − 40715.0i 0.0100645 − 0.0174322i
\(67\) −427209. − 2.42282e6i −0.173532 − 0.984147i −0.939825 − 0.341656i \(-0.889012\pi\)
0.766293 − 0.642491i \(-0.222099\pi\)
\(68\) −1.97863e6 −0.763104
\(69\) −104898. − 594905.i −0.0384410 − 0.218010i
\(70\) −2.39139e6 + 2.00662e6i −0.833312 + 0.699231i
\(71\) 2.47134e6 + 899495.i 0.819461 + 0.298260i 0.717526 − 0.696532i \(-0.245274\pi\)
0.101935 + 0.994791i \(0.467497\pi\)
\(72\) 140547. − 51154.9i 0.0443770 − 0.0161519i
\(73\) −4.62325e6 −1.39097 −0.695485 − 0.718541i \(-0.744810\pi\)
−0.695485 + 0.718541i \(0.744810\pi\)
\(74\) 1.94044e6 + 1.51998e6i 0.556659 + 0.436040i
\(75\) −1.75961e6 −0.481618
\(76\) 2.87662e6 − 1.04700e6i 0.751683 − 0.273590i
\(77\) 128483. + 46764.1i 0.0320722 + 0.0116733i
\(78\) −4.07519e6 + 3.41949e6i −0.972337 + 0.815887i
\(79\) −402008. − 2.27990e6i −0.0917360 − 0.520261i −0.995699 − 0.0926495i \(-0.970466\pi\)
0.903963 − 0.427611i \(-0.140645\pi\)
\(80\) 1.37972e6 0.301284
\(81\) −926675. − 5.25543e6i −0.193745 − 1.09878i
\(82\) 755351. − 1.30831e6i 0.151287 − 0.262036i
\(83\) 2.04743e6 + 1.71800e6i 0.393040 + 0.329799i 0.817796 − 0.575508i \(-0.195196\pi\)
−0.424756 + 0.905308i \(0.639640\pi\)
\(84\) 1.84576e6 + 3.19694e6i 0.339779 + 0.588515i
\(85\) 5.20698e6 − 9.01875e6i 0.919644 − 1.59287i
\(86\) 7.47811e6 − 2.72181e6i 1.26779 − 0.461438i
\(87\) 2.17051e6 − 1.82127e6i 0.353381 − 0.296522i
\(88\) −30215.2 − 52334.2i −0.00472646 − 0.00818647i
\(89\) 1.71628e6 − 9.73353e6i 0.258062 − 1.46354i −0.530026 − 0.847981i \(-0.677818\pi\)
0.788088 − 0.615562i \(-0.211071\pi\)
\(90\) −136696. + 775244.i −0.0197655 + 0.112096i
\(91\) −1.18518e7 − 9.94484e6i −1.64869 − 1.38342i
\(92\) −729647. − 265570.i −0.0976912 − 0.0355567i
\(93\) 9.91828e6 + 3.60996e6i 1.27863 + 0.465384i
\(94\) 8.19541e6 + 6.87677e6i 1.01771 + 0.853959i
\(95\) −2.79781e6 + 1.58672e7i −0.334800 + 1.89875i
\(96\) 283315. − 1.60676e6i 0.0326828 − 0.185354i
\(97\) −4.09025e6 − 7.08452e6i −0.455039 − 0.788151i 0.543651 − 0.839311i \(-0.317041\pi\)
−0.998690 + 0.0511604i \(0.983708\pi\)
\(98\) −3.17726e6 + 2.66603e6i −0.341005 + 0.286137i
\(99\) 32399.4 − 11792.4i 0.00335594 − 0.00122146i
\(100\) −1.13088e6 + 1.95875e6i −0.113088 + 0.195875i
\(101\) −2.95129e6 − 5.11179e6i −0.285028 − 0.493683i 0.687588 − 0.726101i \(-0.258670\pi\)
−0.972616 + 0.232418i \(0.925336\pi\)
\(102\) −9.43361e6 − 7.91573e6i −0.880191 − 0.738568i
\(103\) 6.27784e6 − 1.08735e7i 0.566083 − 0.980485i −0.430865 − 0.902416i \(-0.641791\pi\)
0.996948 − 0.0780681i \(-0.0248752\pi\)
\(104\) 1.18739e6 + 6.73405e6i 0.103509 + 0.587029i
\(105\) −1.94292e7 −1.63792
\(106\) −1.27097e6 − 7.20801e6i −0.103649 − 0.587820i
\(107\) 1.96998e6 − 1.65301e6i 0.155460 − 0.130446i −0.561740 − 0.827314i \(-0.689868\pi\)
0.717200 + 0.696868i \(0.245423\pi\)
\(108\) −5.67409e6 − 2.06520e6i −0.433424 − 0.157753i
\(109\) −1.70868e7 + 6.21909e6i −1.26377 + 0.459975i −0.885033 − 0.465529i \(-0.845864\pi\)
−0.378738 + 0.925504i \(0.623642\pi\)
\(110\) 318058. 0.0227841
\(111\) 3.17069e6 + 1.50098e7i 0.220051 + 1.04171i
\(112\) 4.74499e6 0.319133
\(113\) −1.26112e7 + 4.59010e6i −0.822208 + 0.299259i −0.718657 − 0.695365i \(-0.755243\pi\)
−0.103551 + 0.994624i \(0.533020\pi\)
\(114\) 1.79036e7 + 6.51639e6i 1.13181 + 0.411946i
\(115\) 3.13063e6 − 2.62691e6i 0.191951 − 0.161066i
\(116\) −632424. − 3.58665e6i −0.0376188 − 0.213347i
\(117\) −3.90140e6 −0.225201
\(118\) −156199. − 885850.i −0.00875169 − 0.0496333i
\(119\) 1.79073e7 − 3.10164e7i 0.974127 − 1.68724i
\(120\) 6.57816e6 + 5.51973e6i 0.347512 + 0.291597i
\(121\) 9.73662e6 + 1.68643e7i 0.499643 + 0.865406i
\(122\) −5.87141e6 + 1.01696e7i −0.292740 + 0.507041i
\(123\) 8.83535e6 − 3.21580e6i 0.428111 − 0.155819i
\(124\) 1.03929e7 − 8.72065e6i 0.489508 − 0.410746i
\(125\) 7.20595e6 + 1.24811e7i 0.329994 + 0.571567i
\(126\) −470112. + 2.66614e6i −0.0209365 + 0.118737i
\(127\) −6.22308e6 + 3.52928e7i −0.269583 + 1.52888i 0.486077 + 0.873916i \(0.338427\pi\)
−0.755660 + 0.654964i \(0.772684\pi\)
\(128\) −1.60651e6 − 1.34802e6i −0.0677094 − 0.0568149i
\(129\) 4.65427e7 + 1.69401e7i 1.90892 + 0.694789i
\(130\) −3.38191e7 − 1.23091e7i −1.35008 − 0.491390i
\(131\) −1.34227e7 − 1.12630e7i −0.521662 − 0.437727i 0.343548 − 0.939135i \(-0.388371\pi\)
−0.865211 + 0.501408i \(0.832815\pi\)
\(132\) 65310.7 − 370396.i 0.00247159 − 0.0140171i
\(133\) −9.62193e6 + 5.45687e7i −0.354635 + 2.01123i
\(134\) −9.84080e6 − 1.70448e7i −0.353316 − 0.611961i
\(135\) 2.43453e7 − 2.04281e7i 0.851622 − 0.714596i
\(136\) −1.48744e7 + 5.41385e6i −0.507054 + 0.184553i
\(137\) 681929. − 1.18114e6i 0.0226578 − 0.0392444i −0.854474 − 0.519494i \(-0.826121\pi\)
0.877132 + 0.480249i \(0.159454\pi\)
\(138\) −2.41633e6 − 4.18520e6i −0.0782671 − 0.135563i
\(139\) 2.80600e7 + 2.35451e7i 0.886209 + 0.743617i 0.967446 − 0.253077i \(-0.0814427\pi\)
−0.0812373 + 0.996695i \(0.525887\pi\)
\(140\) −1.24870e7 + 2.16280e7i −0.384599 + 0.666145i
\(141\) 1.15624e7 + 6.55734e7i 0.347360 + 1.96997i
\(142\) 2.10396e7 0.616634
\(143\) 273722. + 1.55236e6i 0.00782770 + 0.0443931i
\(144\) 916600. − 769119.i 0.0255806 − 0.0214647i
\(145\) 1.80125e7 + 6.55603e6i 0.490667 + 0.178588i
\(146\) −3.47555e7 + 1.26500e7i −0.924248 + 0.336399i
\(147\) −2.58141e7 −0.670265
\(148\) 1.87462e7 + 6.11713e6i 0.475333 + 0.155107i
\(149\) −5.23124e7 −1.29555 −0.647773 − 0.761833i \(-0.724299\pi\)
−0.647773 + 0.761833i \(0.724299\pi\)
\(150\) −1.32280e7 + 4.81458e6i −0.320017 + 0.116477i
\(151\) 822468. + 299354.i 0.0194402 + 0.00707564i 0.351722 − 0.936105i \(-0.385596\pi\)
−0.332282 + 0.943180i \(0.607818\pi\)
\(152\) 1.87603e7 − 1.57418e7i 0.433299 − 0.363581i
\(153\) −1.56827e6 − 8.89410e6i −0.0353998 − 0.200762i
\(154\) 1.09383e6 0.0241339
\(155\) 1.23995e7 + 7.03208e7i 0.267450 + 1.51678i
\(156\) −2.12791e7 + 3.68565e7i −0.448764 + 0.777282i
\(157\) −5.45054e6 − 4.57354e6i −0.112406 − 0.0943200i 0.584852 − 0.811140i \(-0.301153\pi\)
−0.697258 + 0.716820i \(0.745597\pi\)
\(158\) −9.26029e6 − 1.60393e7i −0.186777 − 0.323508i
\(159\) 2.27768e7 − 3.94506e7i 0.449369 − 0.778329i
\(160\) 1.03721e7 − 3.77514e6i 0.200192 − 0.0728640i
\(161\) 1.07665e7 − 9.03420e6i 0.203323 − 0.170608i
\(162\) −2.13460e7 − 3.69724e7i −0.394470 − 0.683243i
\(163\) 6.77752e6 − 3.84372e7i 0.122578 − 0.695177i −0.860138 − 0.510061i \(-0.829623\pi\)
0.982717 − 0.185116i \(-0.0592660\pi\)
\(164\) 2.09865e6 − 1.19020e7i 0.0371523 − 0.210701i
\(165\) 1.51642e6 + 1.27243e6i 0.0262800 + 0.0220516i
\(166\) 2.00924e7 + 7.31303e6i 0.340920 + 0.124085i
\(167\) −1.67689e7 − 6.10338e6i −0.278610 − 0.101406i 0.198936 − 0.980012i \(-0.436251\pi\)
−0.477546 + 0.878607i \(0.658474\pi\)
\(168\) 2.26229e7 + 1.89829e7i 0.368100 + 0.308873i
\(169\) 2.00766e7 − 1.13860e8i 0.319953 − 1.81455i
\(170\) 1.44669e7 − 8.20460e7i 0.225842 − 1.28081i
\(171\) 6.98639e6 + 1.21008e7i 0.106848 + 0.185066i
\(172\) 4.87697e7 − 4.09227e7i 0.730804 − 0.613217i
\(173\) −3.01267e6 + 1.09652e6i −0.0442375 + 0.0161011i −0.364044 − 0.931382i \(-0.618604\pi\)
0.319807 + 0.947483i \(0.396382\pi\)
\(174\) 1.13336e7 − 1.96303e7i 0.163096 − 0.282491i
\(175\) −2.04698e7 − 3.54547e7i −0.288722 − 0.500082i
\(176\) −370339. − 310751.i −0.00512041 − 0.00429653i
\(177\) 2.79922e6 − 4.84840e6i 0.0379430 − 0.0657191i
\(178\) −1.37303e7 − 7.78683e7i −0.182477 − 1.03488i
\(179\) −2.24741e7 −0.292885 −0.146442 − 0.989219i \(-0.546782\pi\)
−0.146442 + 0.989219i \(0.546782\pi\)
\(180\) 1.09357e6 + 6.20195e6i 0.0139763 + 0.0792638i
\(181\) 3.10122e7 − 2.60223e7i 0.388738 − 0.326190i −0.427383 − 0.904071i \(-0.640564\pi\)
0.816121 + 0.577881i \(0.196120\pi\)
\(182\) −1.16307e8 − 4.23323e7i −1.43007 − 0.520502i
\(183\) −6.86779e7 + 2.49967e7i −0.828396 + 0.301512i
\(184\) −6.21179e6 −0.0735114
\(185\) −7.72151e7 + 6.93490e7i −0.896605 + 0.805265i
\(186\) 8.44385e7 0.962155
\(187\) −3.42891e6 + 1.24802e6i −0.0383451 + 0.0139565i
\(188\) 8.04253e7 + 2.92724e7i 0.882755 + 0.321297i
\(189\) 8.37258e7 − 7.02543e7i 0.902076 − 0.756932i
\(190\) 2.23825e7 + 1.26937e8i 0.236739 + 1.34262i
\(191\) −1.69668e8 −1.76191 −0.880953 − 0.473204i \(-0.843097\pi\)
−0.880953 + 0.473204i \(0.843097\pi\)
\(192\) −2.26652e6 − 1.28541e7i −0.0231103 − 0.131065i
\(193\) −2.73358e7 + 4.73470e7i −0.273704 + 0.474070i −0.969807 − 0.243872i \(-0.921582\pi\)
0.696103 + 0.717942i \(0.254916\pi\)
\(194\) −5.01330e7 − 4.20666e7i −0.492967 − 0.413648i
\(195\) −1.11997e8 − 1.93984e8i −1.08164 − 1.87346i
\(196\) −1.65905e7 + 2.87355e7i −0.157384 + 0.272598i
\(197\) 1.37564e8 − 5.00690e7i 1.28195 − 0.466592i 0.390874 − 0.920444i \(-0.372173\pi\)
0.891077 + 0.453852i \(0.149951\pi\)
\(198\) 211298. − 177300.i 0.00193449 − 0.00162323i
\(199\) 6.96991e7 + 1.20722e8i 0.626962 + 1.08593i 0.988158 + 0.153440i \(0.0490353\pi\)
−0.361196 + 0.932490i \(0.617631\pi\)
\(200\) −3.14202e6 + 1.78193e7i −0.0277718 + 0.157501i
\(201\) 2.12711e7 − 1.20634e8i 0.184758 − 1.04781i
\(202\) −3.61731e7 − 3.03529e7i −0.308785 − 0.259101i
\(203\) 6.19468e7 + 2.25468e7i 0.519736 + 0.189168i
\(204\) −9.25762e7 − 3.36950e7i −0.763473 − 0.277882i
\(205\) 4.87275e7 + 4.08872e7i 0.395035 + 0.331474i
\(206\) 1.74422e7 − 9.89195e7i 0.139016 − 0.788400i
\(207\) 615436. − 3.49031e6i 0.00482266 − 0.0273507i
\(208\) 2.73517e7 + 4.73746e7i 0.210748 + 0.365026i
\(209\) 4.32470e6 − 3.62885e6i 0.0327675 − 0.0274952i
\(210\) −1.46060e8 + 5.31615e7i −1.08834 + 0.396123i
\(211\) 8.39449e7 − 1.45397e8i 0.615185 − 1.06553i −0.375167 − 0.926957i \(-0.622415\pi\)
0.990352 − 0.138575i \(-0.0442521\pi\)
\(212\) −2.92768e7 − 5.07089e7i −0.211032 − 0.365518i
\(213\) 1.00311e8 + 8.41712e7i 0.711248 + 0.596808i
\(214\) 1.02865e7 − 1.78167e7i 0.0717496 − 0.124274i
\(215\) 5.81859e7 + 3.29989e8i 0.399285 + 2.26446i
\(216\) −4.83059e7 −0.326146
\(217\) 4.26429e7 + 2.41840e8i 0.283294 + 1.60664i
\(218\) −1.11434e8 + 9.35046e7i −0.728487 + 0.611273i
\(219\) −2.16313e8 − 7.87315e7i −1.39164 − 0.506517i
\(220\) 2.39101e6 − 870258.i 0.0151392 − 0.00551022i
\(221\) 4.12895e8 2.57316
\(222\) 6.49051e7 + 1.04161e8i 0.398147 + 0.638957i
\(223\) −1.56936e8 −0.947665 −0.473833 − 0.880615i \(-0.657130\pi\)
−0.473833 + 0.880615i \(0.657130\pi\)
\(224\) 3.56707e7 − 1.29831e7i 0.212052 − 0.0771807i
\(225\) −9.70107e6 − 3.53090e6i −0.0567781 − 0.0206655i
\(226\) −8.22459e7 + 6.90125e7i −0.473952 + 0.397693i
\(227\) −1.45063e7 − 8.22694e7i −0.0823127 − 0.466818i −0.997904 − 0.0647087i \(-0.979388\pi\)
0.915592 − 0.402110i \(-0.131723\pi\)
\(228\) 1.52421e8 0.851675
\(229\) −2.88837e7 − 1.63808e8i −0.158939 − 0.901386i −0.955096 − 0.296296i \(-0.904248\pi\)
0.796158 − 0.605089i \(-0.206863\pi\)
\(230\) 1.63470e7 − 2.83138e7i 0.0885912 − 0.153444i
\(231\) 5.21511e6 + 4.37600e6i 0.0278370 + 0.0233580i
\(232\) −1.45679e7 − 2.52324e7i −0.0765931 − 0.132663i
\(233\) 5.49273e7 − 9.51368e7i 0.284474 − 0.492723i −0.688008 − 0.725703i \(-0.741514\pi\)
0.972481 + 0.232980i \(0.0748478\pi\)
\(234\) −2.93290e7 + 1.06749e7i −0.149638 + 0.0544637i
\(235\) −3.45074e8 + 2.89551e8i −1.73450 + 1.45542i
\(236\) −3.59806e6 − 6.23202e6i −0.0178187 − 0.0308629i
\(237\) 2.00163e7 − 1.13518e8i 0.0976707 − 0.553918i
\(238\) 4.97531e7 − 2.82164e8i 0.239222 − 1.35669i
\(239\) −6.15168e7 − 5.16187e7i −0.291475 − 0.244576i 0.485311 − 0.874342i \(-0.338707\pi\)
−0.776785 + 0.629765i \(0.783151\pi\)
\(240\) 6.45544e7 + 2.34959e7i 0.301430 + 0.109712i
\(241\) 1.79943e8 + 6.54939e7i 0.828086 + 0.301399i 0.721073 − 0.692859i \(-0.243649\pi\)
0.107013 + 0.994258i \(0.465871\pi\)
\(242\) 1.19339e8 + 1.00137e8i 0.541288 + 0.454195i
\(243\) 1.03097e7 − 5.84691e7i 0.0460917 − 0.261399i
\(244\) −1.63129e7 + 9.25153e7i −0.0718899 + 0.407708i
\(245\) −8.73191e7 − 1.51241e8i −0.379340 − 0.657035i
\(246\) 5.76212e7 − 4.83499e7i 0.246779 − 0.207073i
\(247\) −6.00285e8 + 2.18486e8i −2.53465 + 0.922537i
\(248\) 5.42677e7 − 9.39944e7i 0.225923 − 0.391310i
\(249\) 6.65388e7 + 1.15249e8i 0.273135 + 0.473083i
\(250\) 8.83213e7 + 7.41104e7i 0.357499 + 0.299978i
\(251\) 1.04185e8 − 1.80454e8i 0.415860 − 0.720290i −0.579658 − 0.814860i \(-0.696814\pi\)
0.995518 + 0.0945692i \(0.0301474\pi\)
\(252\) 3.76090e6 + 2.13291e7i 0.0148044 + 0.0839597i
\(253\) −1.43196e6 −0.00555917
\(254\) 4.97846e7 + 2.82343e8i 0.190624 + 1.08108i
\(255\) 3.97209e8 − 3.33298e8i 1.50013 − 1.25876i
\(256\) −1.57654e7 − 5.73815e6i −0.0587308 − 0.0213763i
\(257\) −2.21856e7 + 8.07491e6i −0.0815278 + 0.0296737i −0.382462 − 0.923971i \(-0.624924\pi\)
0.300934 + 0.953645i \(0.402702\pi\)
\(258\) 3.96237e8 1.43644
\(259\) −2.65550e8 + 2.38498e8i −0.949724 + 0.852973i
\(260\) −2.87916e8 −1.01592
\(261\) 1.56210e7 − 5.68559e6i 0.0543836 − 0.0197940i
\(262\) −1.31723e8 − 4.79432e7i −0.452487 − 0.164692i
\(263\) −4.02743e8 + 3.37941e8i −1.36516 + 1.14550i −0.390806 + 0.920473i \(0.627804\pi\)
−0.974352 + 0.225030i \(0.927752\pi\)
\(264\) −522486. − 2.96316e6i −0.00174768 − 0.00991156i
\(265\) 3.08180e8 1.01729
\(266\) 7.69755e7 + 4.36549e8i 0.250765 + 1.42216i
\(267\) 2.46058e8 − 4.26186e8i 0.791132 − 1.37028i
\(268\) −1.20616e8 − 1.01209e8i −0.382765 − 0.321178i
\(269\) 1.28301e8 + 2.22224e8i 0.401881 + 0.696079i 0.993953 − 0.109806i \(-0.0350231\pi\)
−0.592072 + 0.805885i \(0.701690\pi\)
\(270\) 1.27122e8 − 2.20182e8i 0.393050 − 0.680783i
\(271\) 9.87149e7 − 3.59293e7i 0.301294 − 0.109662i −0.186950 − 0.982370i \(-0.559860\pi\)
0.488243 + 0.872708i \(0.337638\pi\)
\(272\) −9.70060e7 + 8.13977e7i −0.292286 + 0.245257i
\(273\) −3.85167e8 − 6.67129e8i −1.14572 − 1.98445i
\(274\) 1.89465e6 − 1.07451e7i 0.00556420 − 0.0315561i
\(275\) −724308. + 4.10776e6i −0.00210019 + 0.0119108i
\(276\) −2.96162e7 − 2.48510e7i −0.0847907 − 0.0711478i
\(277\) −3.82509e8 − 1.39222e8i −1.08134 − 0.393575i −0.260933 − 0.965357i \(-0.584030\pi\)
−0.820406 + 0.571781i \(0.806253\pi\)
\(278\) 2.75366e8 + 1.00225e8i 0.768693 + 0.279781i
\(279\) 4.74374e7 + 3.98047e7i 0.130770 + 0.109729i
\(280\) −3.46934e7 + 1.96756e8i −0.0944482 + 0.535642i
\(281\) 1.11273e7 − 6.31063e7i 0.0299171 − 0.169668i −0.966188 − 0.257837i \(-0.916990\pi\)
0.996106 + 0.0881685i \(0.0281014\pi\)
\(282\) 2.66340e8 + 4.61314e8i 0.707236 + 1.22497i
\(283\) 1.07143e8 − 8.99040e7i 0.281004 − 0.235791i −0.491381 − 0.870945i \(-0.663508\pi\)
0.772386 + 0.635154i \(0.219063\pi\)
\(284\) 1.58166e8 − 5.75677e7i 0.409731 − 0.149130i
\(285\) −4.01113e8 + 6.94748e8i −1.02638 + 1.77775i
\(286\) 6.30522e6 + 1.09210e7i 0.0159375 + 0.0276045i
\(287\) 1.67578e8 + 1.40615e8i 0.418439 + 0.351112i
\(288\) 4.78614e6 − 8.28985e6i 0.0118063 − 0.0204490i
\(289\) 9.47193e7 + 5.37180e8i 0.230832 + 1.30911i
\(290\) 1.53348e8 0.369221
\(291\) −7.07292e7 − 4.01125e8i −0.168257 − 0.954234i
\(292\) −2.26664e8 + 1.90193e8i −0.532772 + 0.447049i
\(293\) 5.25083e8 + 1.91115e8i 1.21953 + 0.443871i 0.869998 − 0.493054i \(-0.164120\pi\)
0.349528 + 0.936926i \(0.386342\pi\)
\(294\) −1.94059e8 + 7.06316e7i −0.445366 + 0.162100i
\(295\) 3.78747e7 0.0858959
\(296\) 1.57663e8 − 5.30700e6i 0.353353 − 0.0118940i
\(297\) −1.11356e7 −0.0246642
\(298\) −3.93261e8 + 1.43135e8i −0.860842 + 0.313321i
\(299\) 1.52261e8 + 5.54183e7i 0.329411 + 0.119896i
\(300\) −8.62683e7 + 7.23877e7i −0.184470 + 0.154789i
\(301\) 2.00107e8 + 1.13486e9i 0.422940 + 2.39861i
\(302\) 7.00202e6 0.0146285
\(303\) −5.10342e7 − 2.89429e8i −0.105393 − 0.597714i
\(304\) 9.79595e7 − 1.69671e8i 0.199981 − 0.346378i
\(305\) −3.78763e8 − 3.17820e8i −0.764395 − 0.641403i
\(306\) −3.61252e7 − 6.25707e7i −0.0720752 − 0.124838i
\(307\) 1.29394e8 − 2.24118e8i 0.255230 − 0.442071i −0.709728 − 0.704476i \(-0.751182\pi\)
0.964958 + 0.262405i \(0.0845155\pi\)
\(308\) 8.22293e6 − 2.99290e6i 0.0160361 − 0.00583666i
\(309\) 4.78898e8 − 4.01843e8i 0.923398 − 0.774823i
\(310\) 2.85623e8 + 4.94713e8i 0.544536 + 0.943164i
\(311\) 1.08954e8 − 6.17906e8i 0.205390 − 1.16483i −0.691434 − 0.722440i \(-0.743021\pi\)
0.896824 − 0.442387i \(-0.145868\pi\)
\(312\) −5.91213e7 + 3.35294e8i −0.110205 + 0.625006i
\(313\) 4.39926e8 + 3.69142e8i 0.810914 + 0.680437i 0.950826 − 0.309727i \(-0.100238\pi\)
−0.139912 + 0.990164i \(0.544682\pi\)
\(314\) −5.34886e7 − 1.94682e7i −0.0975006 − 0.0354873i
\(315\) −1.07117e8 − 3.89874e7i −0.193095 − 0.0702809i
\(316\) −1.13501e8 − 9.52383e7i −0.202345 − 0.169788i
\(317\) 1.13093e8 − 6.41383e8i 0.199402 − 1.13086i −0.706608 − 0.707605i \(-0.749776\pi\)
0.906010 − 0.423257i \(-0.139113\pi\)
\(318\) 6.32824e7 − 3.58892e8i 0.110354 − 0.625849i
\(319\) −3.35825e6 − 5.81666e6i −0.00579223 − 0.0100324i
\(320\) 6.76433e7 − 5.67595e7i 0.115399 − 0.0968308i
\(321\) 1.20321e8 − 4.37933e7i 0.203037 − 0.0738993i
\(322\) 5.62189e7 − 9.73740e7i 0.0938397 − 0.162535i
\(323\) −7.39386e8 − 1.28065e9i −1.22085 − 2.11458i
\(324\) −2.61632e8 − 2.19535e8i −0.427350 − 0.358589i
\(325\) 2.35990e8 − 4.08746e8i 0.381330 − 0.660483i
\(326\) −5.42201e7 − 3.07498e8i −0.0866760 − 0.491564i
\(327\) −9.05367e8 −1.43188
\(328\) −1.67892e7 − 9.52161e7i −0.0262706 − 0.148988i
\(329\) −1.18674e9 + 9.95795e8i −1.83726 + 1.54164i
\(330\) 1.48813e7 + 5.41636e6i 0.0227952 + 0.00829676i
\(331\) −7.21536e8 + 2.62618e8i −1.09360 + 0.398039i −0.824955 − 0.565199i \(-0.808799\pi\)
−0.268649 + 0.963238i \(0.586577\pi\)
\(332\) 1.71055e8 0.256538
\(333\) −1.26386e7 + 8.91143e7i −0.0187562 + 0.132249i
\(334\) −1.42761e8 −0.209651
\(335\) 7.78731e8 − 2.83435e8i 1.13170 − 0.411904i
\(336\) 2.22009e8 + 8.08046e7i 0.319288 + 0.116211i
\(337\) −8.10814e8 + 6.80354e8i −1.15403 + 0.968345i −0.999806 − 0.0196908i \(-0.993732\pi\)
−0.154223 + 0.988036i \(0.549287\pi\)
\(338\) −1.60613e8 − 9.10880e8i −0.226241 − 1.28308i
\(339\) −6.68220e8 −0.931580
\(340\) −1.15735e8 − 6.56368e8i −0.159694 − 0.905672i
\(341\) 1.25100e7 − 2.16679e7i 0.0170850 − 0.0295922i
\(342\) 8.56301e7 + 7.18522e7i 0.115754 + 0.0971289i
\(343\) 1.76716e8 + 3.06081e8i 0.236454 + 0.409550i
\(344\) 2.54657e8 − 4.41079e8i 0.337289 − 0.584201i
\(345\) 1.91211e8 − 6.95951e7i 0.250695 − 0.0912456i
\(346\) −1.96476e7 + 1.64863e7i −0.0255002 + 0.0213972i
\(347\) −4.52289e8 − 7.83388e8i −0.581117 − 1.00652i −0.995347 − 0.0963515i \(-0.969283\pi\)
0.414231 − 0.910172i \(-0.364051\pi\)
\(348\) 3.14889e7 − 1.78582e8i 0.0400525 − 0.227149i
\(349\) 1.17437e8 − 6.66018e8i 0.147882 − 0.838682i −0.817125 − 0.576460i \(-0.804434\pi\)
0.965008 − 0.262222i \(-0.0844552\pi\)
\(350\) −2.50892e8 − 2.10524e8i −0.312787 − 0.262460i
\(351\) 1.18405e9 + 4.30960e8i 1.46149 + 0.531939i
\(352\) −3.63430e6 − 1.32278e6i −0.00444142 − 0.00161654i
\(353\) 1.16547e8 + 9.77942e7i 0.141022 + 0.118332i 0.710570 − 0.703626i \(-0.248437\pi\)
−0.569548 + 0.821958i \(0.692882\pi\)
\(354\) 7.77728e6 − 4.41072e7i 0.00931786 − 0.0528442i
\(355\) −1.53833e8 + 8.72428e8i −0.182494 + 1.03498i
\(356\) −3.16278e8 − 5.47810e8i −0.371530 − 0.643509i
\(357\) 1.36604e9 − 1.14624e9i 1.58900 − 1.33333i
\(358\) −1.68950e8 + 6.14927e7i −0.194611 + 0.0708326i
\(359\) 4.65871e8 − 8.06912e8i 0.531416 − 0.920440i −0.467911 − 0.883775i \(-0.654993\pi\)
0.999328 − 0.0366645i \(-0.0116733\pi\)
\(360\) 2.51905e7 + 4.36313e7i 0.0284563 + 0.0492877i
\(361\) 1.06787e9 + 8.96051e8i 1.19466 + 1.00244i
\(362\) 1.61934e8 − 2.80478e8i 0.179415 − 0.310756i
\(363\) 1.68367e8 + 9.54858e8i 0.184750 + 1.04777i
\(364\) −9.90171e8 −1.07611
\(365\) −2.70426e8 − 1.53366e9i −0.291088 − 1.65084i
\(366\) −4.47894e8 + 3.75828e8i −0.477520 + 0.400687i
\(367\) −5.39116e8 − 1.96222e8i −0.569313 − 0.207213i 0.0412937 − 0.999147i \(-0.486852\pi\)
−0.610607 + 0.791934i \(0.709074\pi\)
\(368\) −4.66974e7 + 1.69965e7i −0.0488456 + 0.0177783i
\(369\) 5.51639e7 0.0571561
\(370\) −3.90718e8 + 7.32607e8i −0.401012 + 0.751908i
\(371\) 1.05986e9 1.07756
\(372\) 6.34770e8 − 2.31037e8i 0.639316 − 0.232692i
\(373\) 7.29751e8 + 2.65608e8i 0.728105 + 0.265008i 0.679362 − 0.733803i \(-0.262256\pi\)
0.0487423 + 0.998811i \(0.484479\pi\)
\(374\) −2.23622e7 + 1.87641e7i −0.0221036 + 0.0185471i
\(375\) 1.24607e8 + 7.06679e8i 0.122020 + 0.692010i
\(376\) 6.84695e8 0.664262
\(377\) 1.31972e8 + 7.48452e8i 0.126849 + 0.719398i
\(378\) 4.37185e8 − 7.57227e8i 0.416336 − 0.721115i
\(379\) 2.24365e8 + 1.88265e8i 0.211699 + 0.177636i 0.742471 − 0.669878i \(-0.233654\pi\)
−0.530772 + 0.847514i \(0.678098\pi\)
\(380\) 5.15582e8 + 8.93014e8i 0.482009 + 0.834864i
\(381\) −8.92183e8 + 1.54531e9i −0.826450 + 1.43145i
\(382\) −1.27548e9 + 4.64239e8i −1.17072 + 0.426108i
\(383\) 1.12750e9 − 9.46085e8i 1.02547 − 0.860467i 0.0351607 − 0.999382i \(-0.488806\pi\)
0.990304 + 0.138914i \(0.0443612\pi\)
\(384\) −5.22094e7 − 9.04294e7i −0.0470533 − 0.0814986i
\(385\) −7.99764e6 + 4.53569e7i −0.00714249 + 0.0405071i
\(386\) −7.59490e7 + 4.30728e8i −0.0672151 + 0.381196i
\(387\) 2.22606e8 + 1.86788e8i 0.195231 + 0.163818i
\(388\) −4.91978e8 − 1.79065e8i −0.427597 − 0.155632i
\(389\) −1.14107e9 − 4.15317e8i −0.982857 − 0.357731i −0.199907 − 0.979815i \(-0.564064\pi\)
−0.782950 + 0.622084i \(0.786286\pi\)
\(390\) −1.37271e9 − 1.15184e9i −1.17180 − 0.983256i
\(391\) −6.51331e7 + 3.69388e8i −0.0551040 + 0.312510i
\(392\) −4.60944e7 + 2.61414e8i −0.0386498 + 0.219194i
\(393\) −4.36219e8 − 7.55553e8i −0.362519 − 0.627900i
\(394\) 8.97142e8 − 7.52792e8i 0.738966 − 0.620066i
\(395\) 7.32793e8 − 2.66715e8i 0.598262 − 0.217750i
\(396\) 1.10332e6 − 1.91100e6i 0.000892828 − 0.00154642i
\(397\) −7.26269e8 − 1.25794e9i −0.582547 − 1.00900i −0.995176 − 0.0981021i \(-0.968723\pi\)
0.412629 − 0.910899i \(-0.364610\pi\)
\(398\) 8.54282e8 + 7.16827e8i 0.679220 + 0.569933i
\(399\) −1.37947e9 + 2.38931e9i −1.08719 + 1.88307i
\(400\) 2.51361e7 + 1.42554e8i 0.0196376 + 0.111370i
\(401\) 2.04743e8 0.158563 0.0792817 − 0.996852i \(-0.474737\pi\)
0.0792817 + 0.996852i \(0.474737\pi\)
\(402\) −1.70169e8 − 9.65074e8i −0.130644 − 0.740917i
\(403\) −2.16875e9 + 1.81980e9i −1.65060 + 1.38502i
\(404\) −3.54983e8 − 1.29203e8i −0.267839 − 0.0974852i
\(405\) 1.68917e9 − 6.14809e8i 1.26352 − 0.459883i
\(406\) 5.27379e8 0.391095
\(407\) 3.63451e7 − 1.22339e6i 0.0267218 − 0.000899464i
\(408\) −7.88141e8 −0.574504
\(409\) 1.29889e9 − 4.72756e8i 0.938728 − 0.341669i 0.173065 − 0.984910i \(-0.444633\pi\)
0.765663 + 0.643241i \(0.222411\pi\)
\(410\) 4.78185e8 + 1.74045e8i 0.342651 + 0.124715i
\(411\) 5.20202e7 − 4.36502e7i 0.0369595 − 0.0310127i
\(412\) −1.39537e8 − 7.91356e8i −0.0982993 − 0.557483i
\(413\) 1.30255e8 0.0909848
\(414\) −4.92349e6 − 2.79225e7i −0.00341014 − 0.0193398i
\(415\) −4.50150e8 + 7.79682e8i −0.309164 + 0.535487i
\(416\) 3.35242e8 + 2.81302e8i 0.228314 + 0.191578i
\(417\) 9.11912e8 + 1.57948e9i 0.615853 + 1.06669i
\(418\) 2.25820e7 − 3.91131e7i 0.0151232 − 0.0261942i
\(419\) −2.66924e8 + 9.71523e7i −0.177271 + 0.0645214i −0.429131 − 0.903242i \(-0.641180\pi\)
0.251860 + 0.967764i \(0.418958\pi\)
\(420\) −9.52554e8 + 7.99288e8i −0.627360 + 0.526418i
\(421\) −3.10704e8 − 5.38155e8i −0.202936 − 0.351495i 0.746537 − 0.665344i \(-0.231715\pi\)
−0.949473 + 0.313848i \(0.898382\pi\)
\(422\) 2.33230e8 − 1.32271e9i 0.151074 − 0.856786i
\(423\) −6.78364e7 + 3.84720e8i −0.0435784 + 0.247146i
\(424\) −3.58837e8 − 3.01100e8i −0.228622 − 0.191836i
\(425\) 1.02669e9 + 3.73684e8i 0.648750 + 0.236126i
\(426\) 9.84400e8 + 3.58292e8i 0.616933 + 0.224545i
\(427\) −1.30260e9 − 1.09301e9i −0.809681 − 0.679403i
\(428\) 2.85797e7 − 1.62084e8i 0.0176199 − 0.0999276i
\(429\) −1.36289e7 + 7.72931e7i −0.00833410 + 0.0472650i
\(430\) 1.34032e9 + 2.32150e9i 0.812958 + 1.40808i
\(431\) −1.18755e9 + 9.96474e8i −0.714466 + 0.599509i −0.925848 − 0.377895i \(-0.876648\pi\)
0.211382 + 0.977404i \(0.432204\pi\)
\(432\) −3.63141e8 + 1.32173e8i −0.216712 + 0.0788767i
\(433\) −8.54323e8 + 1.47973e9i −0.505725 + 0.875942i 0.494253 + 0.869318i \(0.335442\pi\)
−0.999978 + 0.00662362i \(0.997892\pi\)
\(434\) 9.82283e8 + 1.70136e9i 0.576797 + 0.999041i
\(435\) 7.31126e8 + 6.13487e8i 0.425873 + 0.357350i
\(436\) −5.81869e8 + 1.00783e9i −0.336219 + 0.582349i
\(437\) −1.00771e8 − 5.71498e8i −0.0577629 − 0.327589i
\(438\) −1.84156e9 −1.04719
\(439\) 1.14435e8 + 6.48996e8i 0.0645557 + 0.366114i 0.999923 + 0.0124350i \(0.00395830\pi\)
−0.935367 + 0.353679i \(0.884931\pi\)
\(440\) 1.55934e7 − 1.30844e7i 0.00872682 − 0.00732267i
\(441\) −1.42318e8 − 5.17995e7i −0.0790178 − 0.0287601i
\(442\) 3.10395e9 − 1.12975e9i 1.70977 − 0.622305i
\(443\) 1.04369e9 0.570375 0.285187 − 0.958472i \(-0.407944\pi\)
0.285187 + 0.958472i \(0.407944\pi\)
\(444\) 7.72929e8 + 6.05447e8i 0.419082 + 0.328273i
\(445\) 3.32928e9 1.79098
\(446\) −1.17977e9 + 4.29402e8i −0.629688 + 0.229188i
\(447\) −2.44760e9 − 8.90852e8i −1.29617 − 0.471769i
\(448\) 2.32632e8 − 1.95201e8i 0.122235 − 0.102567i
\(449\) 2.83940e8 + 1.61031e9i 0.148035 + 0.839549i 0.964880 + 0.262691i \(0.0846101\pi\)
−0.816845 + 0.576858i \(0.804279\pi\)
\(450\) −8.25893e7 −0.0427248
\(451\) −3.87030e6 − 2.19496e7i −0.00198667 − 0.0112670i
\(452\) −4.29458e8 + 7.43842e8i −0.218744 + 0.378875i
\(453\) 3.33838e7 + 2.80124e7i 0.0168730 + 0.0141581i
\(454\) −3.34154e8 − 5.78772e8i −0.167591 − 0.290277i
\(455\) 2.60574e9 − 4.51328e9i 1.29686 − 2.24622i
\(456\) 1.14583e9 − 4.17049e8i 0.565906 − 0.205973i
\(457\) −2.53988e9 + 2.13121e9i −1.24482 + 1.04453i −0.247689 + 0.968840i \(0.579671\pi\)
−0.997131 + 0.0756890i \(0.975884\pi\)
\(458\) −6.65340e8 − 1.15240e9i −0.323604 − 0.560499i
\(459\) −5.06506e8 + 2.87254e9i −0.244478 + 1.38651i
\(460\) 4.54180e7 − 2.57578e8i 0.0217558 − 0.123384i
\(461\) −1.16944e9 − 9.81275e8i −0.555935 − 0.466485i 0.321010 − 0.947076i \(-0.395978\pi\)
−0.876945 + 0.480591i \(0.840422\pi\)
\(462\) 5.11783e7 + 1.86274e7i 0.0241456 + 0.00878829i
\(463\) −1.48009e9 − 5.38709e8i −0.693035 − 0.252244i −0.0286006 − 0.999591i \(-0.509105\pi\)
−0.664434 + 0.747347i \(0.731327\pi\)
\(464\) −1.78555e8 − 1.49825e8i −0.0829772 − 0.0696261i
\(465\) −6.17379e8 + 3.50133e9i −0.284752 + 1.61491i
\(466\) 1.52608e8 − 8.65485e8i 0.0698598 − 0.396195i
\(467\) 8.40405e8 + 1.45562e9i 0.381838 + 0.661364i 0.991325 − 0.131433i \(-0.0419577\pi\)
−0.609487 + 0.792796i \(0.708624\pi\)
\(468\) −1.91273e8 + 1.60497e8i −0.0862570 + 0.0723782i
\(469\) 2.67813e9 − 9.74759e8i 1.19874 − 0.436307i
\(470\) −1.80185e9 + 3.12089e9i −0.800526 + 1.38655i
\(471\) −1.77135e8 − 3.06807e8i −0.0781144 − 0.135298i
\(472\) −4.41004e7 − 3.70046e7i −0.0193039 − 0.0161979i
\(473\) 5.87045e7 − 1.01679e8i 0.0255069 − 0.0441792i
\(474\) −1.60130e8 − 9.08144e8i −0.0690636 − 0.391679i
\(475\) −1.69038e9 −0.723698
\(476\) −3.98025e8 − 2.25731e9i −0.169155 − 0.959328i
\(477\) 2.04736e8 − 1.71794e8i 0.0863732 − 0.0724758i
\(478\) −6.03692e8 − 2.19726e8i −0.252824 − 0.0920203i
\(479\) 2.41106e9 − 8.77552e8i 1.00238 − 0.364837i 0.211879 − 0.977296i \(-0.432042\pi\)
0.790502 + 0.612459i \(0.209820\pi\)
\(480\) 5.49579e8 0.226822
\(481\) −3.91191e9 − 1.27650e9i −1.60281 − 0.523016i
\(482\) 1.53193e9 0.623124
\(483\) 6.57593e8 − 2.39344e8i 0.265547 − 0.0966514i
\(484\) 1.17113e9 + 4.26255e8i 0.469510 + 0.170888i
\(485\) 2.11089e9 − 1.77124e9i 0.840173 − 0.704989i
\(486\) −8.24774e7 − 4.67753e8i −0.0325918 − 0.184837i
\(487\) −2.59975e9 −1.01995 −0.509976 − 0.860189i \(-0.670346\pi\)
−0.509976 + 0.860189i \(0.670346\pi\)
\(488\) 1.30504e8 + 7.40122e8i 0.0508338 + 0.288293i
\(489\) 9.71672e8 − 1.68298e9i 0.375784 − 0.650877i
\(490\) −1.07025e9 − 8.98042e8i −0.410958 − 0.344834i
\(491\) −1.29717e9 − 2.24676e9i −0.494551 − 0.856587i 0.505429 − 0.862868i \(-0.331334\pi\)
−0.999980 + 0.00628059i \(0.998001\pi\)
\(492\) 3.00876e8 − 5.21133e8i 0.113896 − 0.197274i
\(493\) −1.65321e9 + 6.01720e8i −0.621390 + 0.226167i
\(494\) −3.91485e9 + 3.28495e9i −1.46107 + 1.22598i
\(495\) 5.80701e6 + 1.00580e7i 0.00215196 + 0.00372730i
\(496\) 1.50776e8 − 8.55092e8i 0.0554812 − 0.314649i
\(497\) −5.29045e8 + 3.00036e9i −0.193306 + 1.09629i
\(498\) 8.15546e8 + 6.84325e8i 0.295901 + 0.248290i
\(499\) 1.41975e9 + 5.16748e8i 0.511518 + 0.186177i 0.584867 − 0.811129i \(-0.301147\pi\)
−0.0733493 + 0.997306i \(0.523369\pi\)
\(500\) 8.66737e8 + 3.15466e8i 0.310093 + 0.112865i
\(501\) −6.80647e8 − 5.71130e8i −0.241819 − 0.202910i
\(502\) 2.89464e8 − 1.64163e9i 0.102125 − 0.579180i
\(503\) 3.11706e8 − 1.76777e9i 0.109209 − 0.619353i −0.880247 − 0.474516i \(-0.842623\pi\)
0.989455 − 0.144837i \(-0.0462659\pi\)
\(504\) 8.66326e7 + 1.50052e8i 0.0301422 + 0.0522078i
\(505\) 1.52310e9 − 1.27803e9i 0.526268 − 0.441592i
\(506\) −1.07648e7 + 3.91808e6i −0.00369387 + 0.00134446i
\(507\) 2.87832e9 − 4.98539e9i 0.980869 − 1.69891i
\(508\) 1.14679e9 + 1.98630e9i 0.388116 + 0.672237i
\(509\) 4.49395e9 + 3.77087e9i 1.51048 + 1.26745i 0.862810 + 0.505528i \(0.168702\pi\)
0.647674 + 0.761918i \(0.275742\pi\)
\(510\) 2.07408e9 − 3.59241e9i 0.692356 − 1.19920i
\(511\) −9.30022e8 − 5.27442e9i −0.308333 − 1.74864i
\(512\) −1.34218e8 −0.0441942
\(513\) −7.83641e8 − 4.44425e9i −0.256275 − 1.45341i
\(514\) −1.44687e8 + 1.21407e8i −0.0469958 + 0.0394342i
\(515\) 3.97427e9 + 1.44652e9i 1.28213 + 0.466657i
\(516\) 2.97873e9 − 1.08417e9i 0.954459 − 0.347395i
\(517\) 1.57838e8 0.0502337
\(518\) −1.34372e9 + 2.51950e9i −0.424769 + 0.796455i
\(519\) −1.59630e8 −0.0501222
\(520\) −2.16442e9 + 7.87785e8i −0.675041 + 0.245695i
\(521\) −3.41307e9 − 1.24226e9i −1.05734 − 0.384839i −0.245910 − 0.969293i \(-0.579087\pi\)
−0.811427 + 0.584453i \(0.801309\pi\)
\(522\) 1.01875e8 − 8.54833e7i 0.0313488 − 0.0263048i
\(523\) 4.26261e8 + 2.41744e9i 0.130292 + 0.738925i 0.978023 + 0.208498i \(0.0668575\pi\)
−0.847730 + 0.530428i \(0.822031\pi\)
\(524\) −1.12141e9 −0.340491
\(525\) −3.53967e8 − 2.00745e9i −0.106759 − 0.605461i
\(526\) −2.10297e9 + 3.64246e9i −0.630063 + 1.09130i
\(527\) −5.02042e9 − 4.21263e9i −1.49418 − 1.25377i
\(528\) −1.20355e7 − 2.08461e7i −0.00355832 − 0.00616320i
\(529\) 1.62882e9 − 2.82119e9i 0.478384 − 0.828586i
\(530\) 2.31676e9 − 8.43231e8i 0.675951 − 0.246026i
\(531\) 2.51616e7 − 2.11131e7i 0.00729302 − 0.00611957i
\(532\) 1.77314e9 + 3.07116e9i 0.510565 + 0.884325i
\(533\) −4.37939e8 + 2.48368e9i −0.125276 + 0.710477i
\(534\) 6.83641e8 − 3.87712e9i 0.194283 − 1.10183i
\(535\) 6.63579e8 + 5.56809e8i 0.187350 + 0.157206i
\(536\) −1.18366e9 − 4.30816e8i −0.332009 − 0.120841i
\(537\) −1.05152e9 − 3.82722e8i −0.293027 − 0.106653i
\(538\) 1.57255e9 + 1.31953e9i 0.435378 + 0.365326i
\(539\) −1.06258e7 + 6.02622e7i −0.00292283 + 0.0165762i
\(540\) 3.53192e8 − 2.00305e9i 0.0965236 − 0.547412i
\(541\) −2.89385e8 − 5.01229e8i −0.0785752 − 0.136096i 0.824060 − 0.566502i \(-0.191704\pi\)
−0.902635 + 0.430406i \(0.858370\pi\)
\(542\) 6.43785e8 − 5.40200e8i 0.173677 − 0.145733i
\(543\) 1.89414e9 − 6.89412e8i 0.507708 − 0.184790i
\(544\) −5.06529e8 + 8.77335e8i −0.134899 + 0.233652i
\(545\) −3.06250e9 − 5.30441e9i −0.810380 − 1.40362i
\(546\) −4.72088e9 − 3.96129e9i −1.24122 − 1.04151i
\(547\) −1.01107e9 + 1.75123e9i −0.264136 + 0.457496i −0.967337 − 0.253495i \(-0.918420\pi\)
0.703201 + 0.710991i \(0.251753\pi\)
\(548\) −1.51572e7 − 8.59609e7i −0.00393448 − 0.0223136i
\(549\) −4.28793e8 −0.110597
\(550\) 5.79447e6 + 3.28621e7i 0.00148506 + 0.00842220i
\(551\) 2.08511e9 − 1.74961e9i 0.531004 − 0.445565i
\(552\) −2.90638e8 − 1.05783e8i −0.0735470 − 0.0267689i
\(553\) 2.52015e9 − 9.17258e8i 0.633706 − 0.230650i
\(554\) −3.25646e9 −0.813694
\(555\) −4.79372e9 + 1.92977e9i −1.19027 + 0.479160i
\(556\) 2.34430e9 0.578432
\(557\) −2.40936e9 + 8.76937e8i −0.590758 + 0.215018i −0.620063 − 0.784552i \(-0.712893\pi\)
0.0293049 + 0.999571i \(0.490671\pi\)
\(558\) 4.65525e8 + 1.69437e8i 0.113429 + 0.0412847i
\(559\) −1.01771e10 + 8.53962e9i −2.46424 + 2.06775i
\(560\) 2.77547e8 + 1.57405e9i 0.0667850 + 0.378756i
\(561\) −1.81685e8 −0.0434459
\(562\) −8.90188e7 − 5.04851e8i −0.0211546 − 0.119974i
\(563\) −2.23065e8 + 3.86361e8i −0.0526809 + 0.0912460i −0.891163 − 0.453683i \(-0.850110\pi\)
0.838482 + 0.544929i \(0.183443\pi\)
\(564\) 3.26445e9 + 2.73920e9i 0.766184 + 0.642905i
\(565\) −2.26033e9 − 3.91500e9i −0.527232 − 0.913193i
\(566\) 5.59463e8 − 9.69019e8i 0.129692 − 0.224634i
\(567\) 5.80923e9 − 2.11439e9i 1.33837 − 0.487128i
\(568\) 1.03150e9 − 8.65534e8i 0.236185 − 0.198182i
\(569\) −2.55309e9 − 4.42208e9i −0.580996 − 1.00632i −0.995362 − 0.0962044i \(-0.969330\pi\)
0.414365 − 0.910111i \(-0.364004\pi\)
\(570\) −1.11444e9 + 6.32031e9i −0.252055 + 1.42947i
\(571\) 7.32131e8 − 4.15212e9i 0.164574 − 0.933348i −0.784928 − 0.619587i \(-0.787300\pi\)
0.949502 − 0.313760i \(-0.101589\pi\)
\(572\) 7.72812e7 + 6.48466e7i 0.0172658 + 0.0144878i
\(573\) −7.93843e9 − 2.88935e9i −1.76276 − 0.641592i
\(574\) 1.64452e9 + 5.98558e8i 0.362951 + 0.132104i
\(575\) 3.28450e8 + 2.75602e8i 0.0720496 + 0.0604568i
\(576\) 1.32977e7 − 7.54149e7i 0.00289933 − 0.0164429i
\(577\) −3.42515e8 + 1.94250e9i −0.0742275 + 0.420965i 0.924938 + 0.380118i \(0.124117\pi\)
−0.999165 + 0.0408469i \(0.986994\pi\)
\(578\) 2.18187e9 + 3.77910e9i 0.469981 + 0.814032i
\(579\) −2.08528e9 + 1.74976e9i −0.446468 + 0.374631i
\(580\) 1.15280e9 − 4.19586e8i 0.245334 − 0.0892941i
\(581\) −1.54811e9 + 2.68140e9i −0.327480 + 0.567212i
\(582\) −1.62925e9 − 2.82195e9i −0.342577 − 0.593361i
\(583\) −8.27204e7 − 6.94107e7i −0.0172891 − 0.0145073i
\(584\) −1.18355e9 + 2.04997e9i −0.245891 + 0.425896i
\(585\) −2.28203e8 − 1.29421e9i −0.0471277 − 0.267275i
\(586\) 4.47025e9 0.917678
\(587\) 6.64926e8 + 3.77099e9i 0.135688 + 0.769523i 0.974378 + 0.224915i \(0.0722104\pi\)
−0.838691 + 0.544608i \(0.816678\pi\)
\(588\) −1.26558e9 + 1.06195e9i −0.256726 + 0.215419i
\(589\) 9.52804e9 + 3.46792e9i 1.92132 + 0.699304i
\(590\) 2.84725e8 − 1.03631e8i 0.0570747 − 0.0207735i
\(591\) 7.28898e9 1.45248
\(592\) 1.17072e9 − 4.71287e8i 0.231914 − 0.0933598i
\(593\) 2.00567e9 0.394973 0.197487 − 0.980306i \(-0.436722\pi\)
0.197487 + 0.980306i \(0.436722\pi\)
\(594\) −8.37126e7 + 3.04689e7i −0.0163885 + 0.00596492i
\(595\) 1.13365e10 + 4.12613e9i 2.20632 + 0.803033i
\(596\) −2.56471e9 + 2.15205e9i −0.496223 + 0.416380i
\(597\) 1.20525e9 + 6.83530e9i 0.231828 + 1.31476i
\(598\) 1.29626e9 0.247878
\(599\) 9.72882e8 + 5.51749e9i 0.184955 + 1.04893i 0.926013 + 0.377491i \(0.123213\pi\)
−0.741058 + 0.671441i \(0.765676\pi\)
\(600\) −4.50461e8 + 7.80221e8i −0.0851388 + 0.147465i
\(601\) 3.99708e9 + 3.35395e9i 0.751074 + 0.630226i 0.935787 − 0.352567i \(-0.114691\pi\)
−0.184713 + 0.982793i \(0.559136\pi\)
\(602\) 4.60948e9 + 7.98385e9i 0.861121 + 1.49150i
\(603\) 3.59340e8 − 6.22396e8i 0.0667414 − 0.115600i
\(604\) 5.26380e7 − 1.91587e7i 0.00972008 − 0.00353782i
\(605\) −5.02485e9 + 4.21635e9i −0.922528 + 0.774093i
\(606\) −1.17558e9 − 2.03616e9i −0.214584 − 0.371670i
\(607\) 1.79960e9 − 1.02061e10i 0.326600 − 1.85224i −0.171585 − 0.985169i \(-0.554889\pi\)
0.498185 − 0.867071i \(-0.334000\pi\)
\(608\) 2.72168e8 − 1.54354e9i 0.0491105 − 0.278519i
\(609\) 2.51441e9 + 2.10984e9i 0.451103 + 0.378520i
\(610\) −3.71697e9 − 1.35287e9i −0.663032 − 0.241324i
\(611\) −1.67829e10 − 6.10848e9i −2.97662 − 1.08340i
\(612\) −4.42776e8 − 3.71534e8i −0.0780827 − 0.0655191i
\(613\) −1.34295e9 + 7.61625e9i −0.235477 + 1.33546i 0.606130 + 0.795366i \(0.292721\pi\)
−0.841607 + 0.540091i \(0.818390\pi\)
\(614\) 3.59506e8 − 2.03886e9i 0.0626782 − 0.355466i
\(615\) 1.58358e9 + 2.74284e9i 0.274521 + 0.475485i
\(616\) 5.36271e7 − 4.49985e7i 0.00924383 − 0.00775650i
\(617\) −6.22077e9 + 2.26418e9i −1.06622 + 0.388072i −0.814761 − 0.579797i \(-0.803132\pi\)
−0.251457 + 0.967868i \(0.580910\pi\)
\(618\) 2.50063e9 − 4.33122e9i 0.426177 − 0.738160i
\(619\) 5.05415e8 + 8.75404e8i 0.0856506 + 0.148351i 0.905668 − 0.423987i \(-0.139370\pi\)
−0.820018 + 0.572338i \(0.806036\pi\)
\(620\) 3.50079e9 + 2.93751e9i 0.589923 + 0.495004i
\(621\) −5.72331e8 + 9.91306e8i −0.0959017 + 0.166107i
\(622\) −8.71628e8 − 4.94325e9i −0.145233 − 0.823657i
\(623\) 1.14497e10 1.89708
\(624\) 4.72970e8 + 2.68235e9i 0.0779270 + 0.441946i
\(625\) −5.83384e9 + 4.89517e9i −0.955816 + 0.802025i
\(626\) 4.31720e9 + 1.57133e9i 0.703382 + 0.256010i
\(627\) 2.64142e8 − 9.61397e7i 0.0427957 − 0.0155764i
\(628\) −4.55371e8 −0.0733680
\(629\) 1.33758e9 − 9.43119e9i 0.214309 − 1.51109i
\(630\) −9.11932e8 −0.145302
\(631\) −4.06146e9 + 1.47825e9i −0.643547 + 0.234232i −0.643117 − 0.765768i \(-0.722359\pi\)
−0.000429759 1.00000i \(0.500137\pi\)
\(632\) −1.11383e9 − 4.05402e8i −0.175513 − 0.0638817i
\(633\) 6.40365e9 − 5.37330e9i 1.00349 − 0.842031i
\(634\) −9.04745e8 − 5.13106e9i −0.140998 − 0.799641i
\(635\) −1.20716e10 −1.87093
\(636\) −5.06259e8 − 2.87114e9i −0.0780321 − 0.442542i
\(637\) 3.46205e9 − 5.99644e9i 0.530695 − 0.919191i
\(638\) −4.11611e7 − 3.45383e7i −0.00627501 − 0.00526536i
\(639\) 3.84134e8 + 6.65340e8i 0.0582411 + 0.100877i
\(640\) 3.53208e8 − 6.11775e8i 0.0532600 − 0.0922490i
\(641\) 9.23306e9 − 3.36056e9i 1.38466 − 0.503974i 0.461071 − 0.887363i \(-0.347465\pi\)
0.923587 + 0.383389i \(0.125243\pi\)
\(642\) 7.84694e8 − 6.58437e8i 0.117038 − 0.0982068i
\(643\) 5.67174e9 + 9.82374e9i 0.841352 + 1.45726i 0.888752 + 0.458388i \(0.151573\pi\)
−0.0474001 + 0.998876i \(0.515094\pi\)
\(644\) 1.56197e8 − 8.85837e8i 0.0230447 − 0.130693i
\(645\) −2.89712e9 + 1.64304e10i −0.425116 + 2.41095i
\(646\) −9.06244e9 − 7.60429e9i −1.32261 − 1.10980i
\(647\) 6.70101e9 + 2.43897e9i 0.972692 + 0.354031i 0.778995 − 0.627031i \(-0.215730\pi\)
0.193697 + 0.981061i \(0.437952\pi\)
\(648\) −2.56751e9 − 9.34499e8i −0.370681 − 0.134917i
\(649\) −1.01662e7 − 8.53044e6i −0.00145983 − 0.00122494i
\(650\) 6.55667e8 − 3.71847e9i 0.0936454 − 0.531089i
\(651\) −2.12322e9 + 1.20414e10i −0.301622 + 1.71058i
\(652\) −1.24897e9 − 2.16327e9i −0.176475 − 0.305664i
\(653\) 1.72847e9 − 1.45036e9i 0.242921 − 0.203835i −0.513196 − 0.858272i \(-0.671539\pi\)
0.756117 + 0.654437i \(0.227094\pi\)
\(654\) −6.80613e9 + 2.47723e9i −0.951433 + 0.346293i
\(655\) 2.95112e9 − 5.11148e9i 0.410338 − 0.710726i
\(656\) −3.86740e8 − 6.69853e8i −0.0534879 − 0.0926437i
\(657\) −1.03459e9 − 8.68123e8i −0.142327 − 0.119427i
\(658\) −6.19673e9 + 1.07330e10i −0.847953 + 1.46870i
\(659\) 3.60561e8 + 2.04484e9i 0.0490771 + 0.278330i 0.999464 − 0.0327405i \(-0.0104235\pi\)
−0.950387 + 0.311071i \(0.899312\pi\)
\(660\) 1.26691e8 0.0171531
\(661\) −2.35251e9 − 1.33418e10i −0.316831 − 1.79684i −0.561766 − 0.827296i \(-0.689878\pi\)
0.244935 − 0.969539i \(-0.421233\pi\)
\(662\) −4.70561e9 + 3.94848e9i −0.630396 + 0.528965i
\(663\) 1.93185e10 + 7.03137e9i 2.57441 + 0.937007i
\(664\) 1.28591e9 − 4.68034e8i 0.170460 − 0.0620425i
\(665\) −1.86648e10 −2.46120
\(666\) 1.48820e8 + 7.04502e8i 0.0195209 + 0.0924107i
\(667\) −6.90406e8 −0.0900874
\(668\) −1.07321e9 + 3.90616e8i −0.139305 + 0.0507029i
\(669\) −7.34272e9 − 2.67253e9i −0.948124 − 0.345089i
\(670\) 5.07862e9 − 4.26147e9i 0.652354 − 0.547390i
\(671\) 3.00841e7 + 1.70616e8i 0.00384422 + 0.0218017i
\(672\) 1.89005e9 0.240260
\(673\) −1.63507e9 − 9.27297e9i −0.206769 − 1.17264i −0.894632 − 0.446803i \(-0.852562\pi\)
0.687864 − 0.725840i \(-0.258549\pi\)
\(674\) −4.23377e9 + 7.33311e9i −0.532620 + 0.922525i
\(675\) 2.55418e9 + 2.14321e9i 0.319660 + 0.268227i
\(676\) −3.69973e9 − 6.40812e9i −0.460634 − 0.797842i
\(677\) 1.80787e9 − 3.13131e9i 0.223927 − 0.387852i −0.732070 − 0.681229i \(-0.761446\pi\)
0.955997 + 0.293377i \(0.0947791\pi\)
\(678\) −5.02337e9 + 1.82836e9i −0.619001 + 0.225298i
\(679\) 7.25954e9 − 6.09148e9i 0.889948 − 0.746755i
\(680\) −2.66597e9 − 4.61760e9i −0.325143 − 0.563165i
\(681\) 7.22281e8 − 4.09626e9i 0.0876378 − 0.497018i
\(682\) 3.47574e7 − 1.97119e8i 0.00419567 − 0.0237948i
\(683\) 7.09033e9 + 5.94950e9i 0.851519 + 0.714509i 0.960124 − 0.279576i \(-0.0901939\pi\)
−0.108605 + 0.994085i \(0.534638\pi\)
\(684\) 8.40327e8 + 3.05854e8i 0.100404 + 0.0365441i
\(685\) 4.31704e8 + 1.57128e8i 0.0513180 + 0.0186782i
\(686\) 2.16595e9 + 1.81745e9i 0.256162 + 0.214946i
\(687\) 1.43814e9 − 8.15612e9i 0.169221 − 0.959699i
\(688\) 7.07533e8 − 4.01262e9i 0.0828299 − 0.469751i
\(689\) 6.10940e9 + 1.05818e10i 0.711592 + 1.23251i
\(690\) 1.24701e9 − 1.04637e9i 0.144510 − 0.121259i
\(691\) 1.11370e9 − 4.05354e8i 0.128409 − 0.0467371i −0.277016 − 0.960865i \(-0.589346\pi\)
0.405425 + 0.914128i \(0.367123\pi\)
\(692\) −1.02593e8 + 1.77696e8i −0.0117691 + 0.0203848i
\(693\) 1.99708e7 + 3.45905e7i 0.00227945 + 0.00394812i
\(694\) −5.54358e9 − 4.65162e9i −0.629553 − 0.528258i
\(695\) −6.16929e9 + 1.06855e10i −0.697089 + 1.20739i
\(696\) −2.51911e8 − 1.42866e9i −0.0283214 − 0.160619i
\(697\) −5.83813e9 −0.653069
\(698\) −9.39496e8 − 5.32815e9i −0.104569 − 0.593038i
\(699\) 4.19007e9 − 3.51588e9i 0.464035 − 0.389372i
\(700\) −2.46212e9 − 8.96139e8i −0.271310 − 0.0987488i
\(701\) 1.17184e10 − 4.26514e9i 1.28486 − 0.467650i 0.392821 − 0.919615i \(-0.371499\pi\)
0.892036 + 0.451965i \(0.149277\pi\)
\(702\) 1.00803e10 1.09975
\(703\) 3.04594e9 + 1.44193e10i 0.330657 + 1.56531i
\(704\) −3.09403e7 −0.00334211
\(705\) −2.10762e10 + 7.67112e9i −2.26533 + 0.824512i
\(706\) 1.14372e9 + 4.16282e8i 0.122322 + 0.0445216i
\(707\) 5.23807e9 − 4.39526e9i 0.557447 − 0.467753i
\(708\) −6.22182e7 − 3.52857e8i −0.00658872 − 0.0373665i
\(709\) −5.07395e9 −0.534668 −0.267334 − 0.963604i \(-0.586143\pi\)
−0.267334 + 0.963604i \(0.586143\pi\)
\(710\) 1.23066e9 + 6.97942e9i 0.129043 + 0.731839i
\(711\) 3.38143e8 − 5.85681e8i 0.0352823 − 0.0611107i
\(712\) −3.87653e9 − 3.25279e9i −0.402497 − 0.337735i
\(713\) −1.28593e9 − 2.22730e9i −0.132863 − 0.230126i
\(714\) 7.13295e9 − 1.23546e10i 0.733374 − 1.27024i
\(715\) −4.98950e8 + 1.81603e8i −0.0510488 + 0.0185803i
\(716\) −1.10183e9 + 9.24548e8i −0.112181 + 0.0941313i
\(717\) −1.99921e9 − 3.46274e9i −0.202554 − 0.350834i
\(718\) 1.29436e9 − 7.34069e9i 0.130503 − 0.740118i
\(719\) −8.62845e8 + 4.89344e9i −0.0865729 + 0.490979i 0.910433 + 0.413656i \(0.135748\pi\)
−0.997006 + 0.0773231i \(0.975363\pi\)
\(720\) 3.08753e8 + 2.59074e8i 0.0308281 + 0.0258679i
\(721\) 1.36679e10 + 4.97471e9i 1.35809 + 0.494304i
\(722\) 1.04795e10 + 3.81423e9i 1.03624 + 0.377161i
\(723\) 7.30386e9 + 6.12866e9i 0.718734 + 0.603089i
\(724\) 4.49913e8 − 2.55158e9i 0.0440599 − 0.249876i
\(725\) −3.49218e8 + 1.98051e9i −0.0340340 + 0.193016i
\(726\) 3.87835e9 + 6.71750e9i 0.376157 + 0.651523i
\(727\) 3.07154e9 − 2.57733e9i 0.296474 − 0.248771i −0.482401 − 0.875950i \(-0.660235\pi\)
0.778875 + 0.627180i \(0.215791\pi\)
\(728\) −7.44365e9 + 2.70927e9i −0.715033 + 0.260251i
\(729\) −4.35740e9 + 7.54724e9i −0.416564 + 0.721509i
\(730\) −6.22929e9 − 1.07895e10i −0.592664 − 1.02652i
\(731\) −2.35589e10 − 1.97683e10i −2.23072 − 1.87179i
\(732\) −2.33874e9 + 4.05081e9i −0.220390 + 0.381727i
\(733\) 1.26777e9 + 7.18989e9i 0.118899 + 0.674308i 0.984746 + 0.173999i \(0.0556690\pi\)
−0.865847 + 0.500309i \(0.833220\pi\)
\(734\) −4.58972e9 −0.428401
\(735\) −1.50994e9 − 8.56328e9i −0.140266 − 0.795489i
\(736\) −3.04545e8 + 2.55543e8i −0.0281565 + 0.0236261i
\(737\) −2.72861e8 − 9.93132e7i −0.0251076 − 0.00913842i
\(738\) 4.14697e8 − 1.50937e8i 0.0379781 − 0.0138229i
\(739\) 1.46475e10 1.33508 0.667540 − 0.744574i \(-0.267347\pi\)
0.667540 + 0.744574i \(0.267347\pi\)
\(740\) −9.32707e8 + 6.57647e9i −0.0846124 + 0.596598i
\(741\) −3.18068e10 −2.87182
\(742\) 7.96755e9 − 2.89995e9i 0.715997 − 0.260602i
\(743\) 1.54263e10 + 5.61470e9i 1.37975 + 0.502188i 0.922102 − 0.386946i \(-0.126470\pi\)
0.457647 + 0.889134i \(0.348692\pi\)
\(744\) 4.13975e9 − 3.47366e9i 0.368527 − 0.309231i
\(745\) −3.05989e9 − 1.73535e10i −0.271119 − 1.53759i
\(746\) 6.21268e9 0.547890
\(747\) 1.35579e8 + 7.68906e8i 0.0119006 + 0.0674918i
\(748\) −1.16767e8 + 2.02246e8i −0.0102015 + 0.0176695i
\(749\) 2.28211e9 + 1.91492e9i 0.198450 + 0.166519i
\(750\) 2.87032e9 + 4.97154e9i 0.248437 + 0.430305i
\(751\) −5.60277e9 + 9.70428e9i −0.482684 + 0.836033i −0.999802 − 0.0198810i \(-0.993671\pi\)
0.517119 + 0.855914i \(0.327005\pi\)
\(752\) 5.14722e9 − 1.87343e9i 0.441378 − 0.160648i
\(753\) 7.94764e9 − 6.66886e9i 0.678353 − 0.569205i
\(754\) 3.03999e9 + 5.26542e9i 0.258269 + 0.447336i
\(755\) −5.11958e7 + 2.90346e8i −0.00432933 + 0.0245528i
\(756\) 1.21466e9 − 6.88869e9i 0.102242 − 0.579843i
\(757\) 7.59423e9 + 6.37231e9i 0.636280 + 0.533902i 0.902873 − 0.429907i \(-0.141454\pi\)
−0.266594 + 0.963809i