↑

Properties

Label 71.10.g.a.2.12
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [71,10,Mod(2,71)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(71, base_ring=CyclotomicField(70))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("71.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 71.g (of order \(35\), degree \(24\), 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: \(36.5675443676\)
Analytic rank: \(0\)
Dimension: \(1272\)
Relative dimension: \(53\) over \(\Q(\zeta_{35})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label 2.12
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22566 + 27.2915i) q^{2} +(89.6817 + 78.3526i) q^{3} +(-233.387 - 21.0052i) q^{4} +(-738.642 - 2273.31i) q^{5} +(-2248.28 + 2351.52i) q^{6} +(2604.45 + 718.783i) q^{7} +(-1018.25 + 7517.03i) q^{8} +(-738.425 - 5451.27i) q^{9} +O(q^{10})\) \(q+(-1.22566 + 27.2915i) q^{2} +(89.6817 + 78.3526i) q^{3} +(-233.387 - 21.0052i) q^{4} +(-738.642 - 2273.31i) q^{5} +(-2248.28 + 2351.52i) q^{6} +(2604.45 + 718.783i) q^{7} +(-1018.25 + 7517.03i) q^{8} +(-738.425 - 5451.27i) q^{9} +(62947.3 - 17372.4i) q^{10} +(-38479.3 + 71506.4i) q^{11} +(-19284.7 - 20170.2i) q^{12} +(58068.0 + 107908. i) q^{13} +(-22808.9 + 70198.5i) q^{14} +(111877. - 261749. i) q^{15} +(-321952. - 58425.7i) q^{16} +(-373275. - 271200. i) q^{17} +(149679. - 13471.3i) q^{18} +(300.518 + 703.098i) q^{19} +(124638. + 546074. i) q^{20} +(177253. + 268527. i) q^{21} +(-1.90436e6 - 1.13780e6i) q^{22} +(-1.53944e6 - 1.93039e6i) q^{23} +(-680297. + 594358. i) q^{24} +(-3.04222e6 + 2.21030e6i) q^{25} +(-3.01616e6 + 1.45250e6i) q^{26} +(1.65221e6 - 2.50298e6i) q^{27} +(-592746. - 222461. i) q^{28} +(-3.34310e6 + 1.99741e6i) q^{29} +(7.00639e6 + 3.37410e6i) q^{30} +(4.90487e6 - 890103. i) q^{31} +(1.12489e6 - 4.92846e6i) q^{32} +(-9.05360e6 + 3.39787e6i) q^{33} +(7.85897e6 - 9.85484e6i) q^{34} +(-289743. - 6.45164e6i) q^{35} +(57833.6 + 1.28776e6i) q^{36} +(-4.91293e6 + 6.16062e6i) q^{37} +(-19557.0 + 7339.85i) q^{38} +(-3.24726e6 + 1.42272e7i) q^{39} +(1.78406e7 - 3.23760e6i) q^{40} +(-1.14505e7 - 5.51425e6i) q^{41} +(-7.54577e6 + 4.50839e6i) q^{42} +(2.76927e6 + 1.03933e6i) q^{43} +(1.04825e7 - 1.58804e7i) q^{44} +(-1.18470e7 + 5.70520e6i) q^{45} +(5.45702e7 - 3.96476e7i) q^{46} +(-3.90820e7 + 3.41449e7i) q^{47} +(-2.42954e7 - 3.04655e7i) q^{48} +(-2.83750e7 - 1.69533e7i) q^{49} +(-5.65937e7 - 8.57358e7i) q^{50} +(-1.22267e7 - 5.35687e7i) q^{51} +(-1.12857e7 - 2.64041e7i) q^{52} +(1.31978e7 - 1.18782e6i) q^{53} +(6.62852e7 + 4.81590e7i) q^{54} +(1.90978e8 + 3.46575e7i) q^{55} +(-8.05509e6 + 1.88458e7i) q^{56} +(-28138.5 + 86601.4i) q^{57} +(-5.04148e7 - 9.36864e7i) q^{58} +(-1.17385e8 - 1.22775e8i) q^{59} +(-3.16086e7 + 5.87386e7i) q^{60} +(1.27790e8 - 3.52677e7i) q^{61} +(1.82805e7 + 1.34952e8i) q^{62} +(1.99509e6 - 1.47283e7i) q^{63} +(-2.83679e7 - 7.82903e6i) q^{64} +(2.02417e8 - 2.11712e8i) q^{65} +(-8.16365e7 - 2.51251e8i) q^{66} +(-2.28281e8 - 2.05457e7i) q^{67} +(8.14207e7 + 7.11351e7i) q^{68} +(1.31919e7 - 2.93740e8i) q^{69} +1.76430e8 q^{70} +(1.65192e8 + 1.36235e8i) q^{71} +4.17293e7 q^{72} +(-7.56547e6 + 1.68458e8i) q^{73} +(-1.62111e8 - 1.41632e8i) q^{74} +(-4.46014e8 - 4.01420e7i) q^{75} +(-55368.3 - 170406. i) q^{76} +(-1.51615e8 + 1.58577e8i) q^{77} +(-3.84302e8 - 1.06061e8i) q^{78} +(-1.51090e7 + 1.11539e8i) q^{79} +(1.04988e8 + 7.75051e8i) q^{80} +(2.39913e8 - 6.62116e7i) q^{81} +(1.64527e8 - 3.05742e8i) q^{82} +(2.59699e8 + 2.71623e8i) q^{83} +(-3.57281e7 - 6.63939e7i) q^{84} +(-3.40804e8 + 1.04889e9i) q^{85} +(-3.17590e7 + 7.43038e7i) q^{86} +(-4.56317e8 - 8.28093e7i) q^{87} +(-4.98334e8 - 3.62061e8i) q^{88} +(-4.76186e8 + 4.28575e7i) q^{89} +(-1.41183e8 - 3.30315e8i) q^{90} +(7.36725e7 + 3.22780e8i) q^{91} +(3.18736e8 + 4.82864e8i) q^{92} +(5.09619e8 + 3.04483e8i) q^{93} +(-8.83965e8 - 1.10846e9i) q^{94} +(1.37638e6 - 1.20251e6i) q^{95} +(4.87040e8 - 3.53855e8i) q^{96} +(-3.16602e8 + 1.52468e8i) q^{97} +(4.97459e8 - 7.53618e8i) q^{98} +(4.18215e8 + 1.56959e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{35}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22566 + 27.2915i −0.0541672 + 1.20613i 0.769347 + 0.638831i \(0.220582\pi\)
−0.823514 + 0.567296i \(0.807990\pi\)
\(3\) 89.6817 + 78.3526i 0.639232 + 0.558480i 0.915358 − 0.402641i \(-0.131908\pi\)
−0.276126 + 0.961121i \(0.589051\pi\)
\(4\) −233.387 − 21.0052i −0.455833 − 0.0410257i
\(5\) −738.642 − 2273.31i −0.528529 − 1.62665i −0.757230 − 0.653148i \(-0.773448\pi\)
0.228701 − 0.973497i \(-0.426552\pi\)
\(6\) −2248.28 + 2351.52i −0.708223 + 0.740743i
\(7\) 2604.45 + 718.783i 0.409992 + 0.113150i 0.464947 − 0.885338i \(-0.346073\pi\)
−0.0549558 + 0.998489i \(0.517502\pi\)
\(8\) −1018.25 + 7517.03i −0.0878921 + 0.648845i
\(9\) −738.425 − 5451.27i −0.0375159 − 0.276953i
\(10\) 62947.3 − 17372.4i 1.99057 − 0.549362i
\(11\) −38479.3 + 71506.4i −0.792428 + 1.47258i 0.0868263 + 0.996223i \(0.472328\pi\)
−0.879254 + 0.476354i \(0.841958\pi\)
\(12\) −19284.7 − 20170.2i −0.268471 − 0.280799i
\(13\) 58068.0 + 107908.i 0.563887 + 1.04788i 0.989712 + 0.143072i \(0.0456979\pi\)
−0.425826 + 0.904805i \(0.640016\pi\)
\(14\) −22808.9 + 70198.5i −0.158682 + 0.488373i
\(15\) 111877. − 261749.i 0.570596 − 1.33498i
\(16\) −321952. − 58425.7i −1.22815 − 0.222876i
\(17\) −373275. − 271200.i −1.08395 − 0.787534i −0.105581 − 0.994411i \(-0.533670\pi\)
−0.978367 + 0.206877i \(0.933670\pi\)
\(18\) 149679. − 13471.3i 0.336073 − 0.0302471i
\(19\) 300.518 + 703.098i 0.000529030 + 0.00123773i 0.919792 − 0.392406i \(-0.128357\pi\)
−0.919263 + 0.393644i \(0.871214\pi\)
\(20\) 124638. + 546074.i 0.174187 + 0.763162i
\(21\) 177253. + 268527.i 0.198887 + 0.301302i
\(22\) −1.90436e6 − 1.13780e6i −1.73319 − 1.03553i
\(23\) −1.53944e6 − 1.93039e6i −1.14706 − 1.43837i −0.880180 − 0.474640i \(-0.842578\pi\)
−0.266881 − 0.963730i \(-0.585993\pi\)
\(24\) −680297. + 594358.i −0.418551 + 0.365677i
\(25\) −3.04222e6 + 2.21030e6i −1.55761 + 1.13167i
\(26\) −3.01616e6 + 1.45250e6i −1.29442 + 0.623358i
\(27\) 1.65221e6 − 2.50298e6i 0.598311 − 0.906402i
\(28\) −592746. − 222461.i −0.182246 − 0.0683979i
\(29\) −3.34310e6 + 1.99741e6i −0.877724 + 0.524416i −0.879671 − 0.475582i \(-0.842237\pi\)
0.00194713 + 0.999998i \(0.499380\pi\)
\(30\) 7.00639e6 + 3.37410e6i 1.57924 + 0.760523i
\(31\) 4.90487e6 − 890103.i 0.953894 − 0.173106i 0.320770 − 0.947157i \(-0.396058\pi\)
0.633123 + 0.774051i \(0.281773\pi\)
\(32\) 1.12489e6 − 4.92846e6i 0.189642 − 0.830876i
\(33\) −9.05360e6 + 3.39787e6i −1.32895 + 0.498763i
\(34\) 7.85897e6 − 9.85484e6i 1.00858 − 1.26472i
\(35\) −289743. − 6.45164e6i −0.0326368 − 0.726714i
\(36\) 57833.6 + 1.28776e6i 0.00573877 + 0.127784i
\(37\) −4.91293e6 + 6.16062e6i −0.430956 + 0.540402i −0.949135 − 0.314871i \(-0.898039\pi\)
0.518178 + 0.855273i \(0.326610\pi\)
\(38\) −19557.0 + 7339.85i −0.00152151 + 0.000571033i
\(39\) −3.24726e6 + 1.42272e7i −0.224764 + 0.984756i
\(40\) 1.78406e7 − 3.23760e6i 1.10189 − 0.199964i
\(41\) −1.14505e7 − 5.51425e6i −0.632842 − 0.304761i 0.0898241 − 0.995958i \(-0.471369\pi\)
−0.722667 + 0.691197i \(0.757084\pi\)
\(42\) −7.54577e6 + 4.50839e6i −0.374181 + 0.223563i
\(43\) 2.76927e6 + 1.03933e6i 0.123526 + 0.0463600i 0.412372 − 0.911015i \(-0.364700\pi\)
−0.288847 + 0.957375i \(0.593272\pi\)
\(44\) 1.04825e7 − 1.58804e7i 0.421628 − 0.638739i
\(45\) −1.18470e7 + 5.70520e6i −0.430677 + 0.207403i
\(46\) 5.45702e7 − 3.96476e7i 1.79699 − 1.30559i
\(47\) −3.90820e7 + 3.41449e7i −1.16825 + 1.02067i −0.168864 + 0.985639i \(0.554010\pi\)
−0.999386 + 0.0350302i \(0.988847\pi\)
\(48\) −2.42954e7 − 3.04655e7i −0.660600 − 0.828367i
\(49\) −2.83750e7 − 1.69533e7i −0.703159 − 0.420118i
\(50\) −5.65937e7 − 8.57358e7i −1.28057 − 1.93998i
\(51\) −1.22267e7 − 5.35687e7i −0.253072 − 1.10878i
\(52\) −1.12857e7 − 2.64041e7i −0.214048 − 0.500791i
\(53\) 1.31978e7 − 1.18782e6i 0.229752 − 0.0206781i 0.0258352 − 0.999666i \(-0.491776\pi\)
0.203917 + 0.978988i \(0.434633\pi\)
\(54\) 6.62852e7 + 4.81590e7i 1.06083 + 0.770736i
\(55\) 1.90978e8 + 3.46575e7i 2.81418 + 0.510699i
\(56\) −8.05509e6 + 1.88458e7i −0.109452 + 0.256076i
\(57\) −28138.5 + 86601.4i −0.000353073 + 0.00108665i
\(58\) −5.04148e7 − 9.36864e7i −0.584968 − 1.08705i
\(59\) −1.17385e8 − 1.22775e8i −1.26118 − 1.31909i −0.926278 − 0.376842i \(-0.877010\pi\)
−0.334905 − 0.942252i \(-0.608704\pi\)
\(60\) −3.16086e7 + 5.87386e7i −0.314865 + 0.585117i
\(61\) 1.27790e8 − 3.52677e7i 1.18171 − 0.326131i 0.380652 − 0.924718i \(-0.375699\pi\)
0.801058 + 0.598587i \(0.204271\pi\)
\(62\) 1.82805e7 + 1.34952e8i 0.157118 + 1.15989i
\(63\) 1.99509e6 − 1.47283e7i 0.0159562 − 0.117793i
\(64\) −2.83679e7 − 7.82903e6i −0.211357 − 0.0583308i
\(65\) 2.02417e8 − 2.11712e8i 1.40649 − 1.47108i
\(66\) −8.16365e7 − 2.51251e8i −0.529586 − 1.62990i
\(67\) −2.28281e8 − 2.05457e7i −1.38399 − 0.124562i −0.627527 − 0.778595i \(-0.715933\pi\)
−0.756466 + 0.654033i \(0.773076\pi\)
\(68\) 8.14207e7 + 7.11351e7i 0.461790 + 0.403454i
\(69\) 1.31919e7 − 2.93740e8i 0.0700625 − 1.56006i
\(70\) 1.76430e8 0.878277
\(71\) 1.65192e8 + 1.36235e8i 0.771485 + 0.636247i
\(72\) 4.17293e7 0.182997
\(73\) −7.56547e6 + 1.68458e8i −0.0311805 + 0.694288i 0.921148 + 0.389213i \(0.127253\pi\)
−0.952328 + 0.305075i \(0.901318\pi\)
\(74\) −1.62111e8 − 1.41632e8i −0.628449 − 0.549060i
\(75\) −4.46014e8 − 4.01420e7i −1.62769 − 0.146495i
\(76\) −55368.3 − 170406.i −0.000190371 − 0.000585900i
\(77\) −1.51615e8 + 1.58577e8i −0.491511 + 0.514081i
\(78\) −3.84302e8 − 1.06061e8i −1.17557 − 0.324435i
\(79\) −1.51090e7 + 1.11539e8i −0.0436430 + 0.322185i 0.955947 + 0.293540i \(0.0948335\pi\)
−0.999590 + 0.0286450i \(0.990881\pi\)
\(80\) 1.04988e8 + 7.75051e8i 0.286572 + 2.11556i
\(81\) 2.39913e8 − 6.62116e7i 0.619256 − 0.170904i
\(82\) 1.64527e8 − 3.05742e8i 0.401860 − 0.746780i
\(83\) 2.59699e8 + 2.71623e8i 0.600646 + 0.628226i 0.951295 − 0.308281i \(-0.0997536\pi\)
−0.350650 + 0.936507i \(0.614039\pi\)
\(84\) −3.57281e7 − 6.63939e7i −0.0782983 − 0.145503i
\(85\) −3.40804e8 + 1.04889e9i −0.708141 + 2.17943i
\(86\) −3.17590e7 + 7.43038e7i −0.0626071 + 0.146477i
\(87\) −4.56317e8 − 8.28093e7i −0.853945 − 0.154968i
\(88\) −4.98334e8 − 3.62061e8i −0.885827 − 0.643591i
\(89\) −4.76186e8 + 4.28575e7i −0.804491 + 0.0724055i −0.484249 − 0.874930i \(-0.660907\pi\)
−0.320242 + 0.947336i \(0.603764\pi\)
\(90\) −1.41183e8 − 3.30315e8i −0.226826 − 0.530685i
\(91\) 7.36725e7 + 3.22780e8i 0.112621 + 0.493425i
\(92\) 3.18736e8 + 4.82864e8i 0.463858 + 0.702715i
\(93\) 5.09619e8 + 3.04483e8i 0.706435 + 0.422076i
\(94\) −8.83965e8 − 1.10846e9i −1.16778 − 1.46434i
\(95\) 1.37638e6 − 1.20251e6i 0.00173373 − 0.00151472i
\(96\) 4.87040e8 − 3.53855e8i 0.585253 − 0.425211i
\(97\) −3.16602e8 + 1.52468e8i −0.363112 + 0.174866i −0.606539 − 0.795054i \(-0.707443\pi\)
0.243427 + 0.969919i \(0.421728\pi\)
\(98\) 4.97459e8 − 7.53618e8i 0.544803 − 0.825342i
\(99\) 4.18215e8 + 1.56959e8i 0.437564 + 0.164220i
\(100\) 7.56440e8 − 4.51952e8i 0.756440 − 0.451952i
\(101\) 1.47206e9 + 7.08906e8i 1.40760 + 0.677864i 0.974687 − 0.223572i \(-0.0717719\pi\)
0.432912 + 0.901436i \(0.357486\pi\)
\(102\) 1.47696e9 − 2.68028e8i 1.35104 − 0.245177i
\(103\) 1.62080e8 − 7.10121e8i 0.141894 − 0.621677i −0.853101 − 0.521746i \(-0.825281\pi\)
0.994994 − 0.0999307i \(-0.0318621\pi\)
\(104\) −8.70278e8 + 3.26621e8i −0.729471 + 0.273775i
\(105\) 4.79518e8 − 6.01296e8i 0.384993 − 0.482766i
\(106\) 1.62415e7 + 3.61644e8i 0.0124954 + 0.278231i
\(107\) 3.06806e6 + 6.83156e7i 0.00226275 + 0.0503840i 0.999807 − 0.0196586i \(-0.00625792\pi\)
−0.997544 + 0.0700426i \(0.977686\pi\)
\(108\) −4.38178e8 + 5.49458e8i −0.309916 + 0.388622i
\(109\) −7.27841e8 + 2.73163e8i −0.493875 + 0.185354i −0.585870 − 0.810405i \(-0.699247\pi\)
0.0919949 + 0.995759i \(0.470676\pi\)
\(110\) −1.17993e9 + 5.16961e9i −0.768404 + 3.36660i
\(111\) −9.23301e8 + 1.67554e8i −0.577285 + 0.104762i
\(112\) −7.96513e8 − 3.83580e8i −0.478312 − 0.230343i
\(113\) 1.08586e9 − 6.48771e8i 0.626500 − 0.374316i −0.164283 − 0.986413i \(-0.552531\pi\)
0.790783 + 0.612097i \(0.209674\pi\)
\(114\) −2.32900e6 − 874087.i −0.00129151 − 0.000484711i
\(115\) −3.25128e9 + 4.92548e9i −1.73346 + 2.62608i
\(116\) 8.22190e8 − 3.95946e8i 0.421610 − 0.203037i
\(117\) 5.45359e8 − 3.96227e8i 0.269058 − 0.195482i
\(118\) 3.49459e9 − 3.05313e9i 1.65931 − 1.44969i
\(119\) −7.77242e8 − 9.74630e8i −0.355300 − 0.445532i
\(120\) 1.85365e9 + 1.10751e9i 0.816042 + 0.487563i
\(121\) −2.33353e9 − 3.53515e9i −0.989645 − 1.49925i
\(122\) 8.05882e8 + 3.53080e9i 0.329346 + 1.44296i
\(123\) −5.94841e8 − 1.39170e9i −0.234330 − 0.548243i
\(124\) −1.16343e9 + 1.04710e8i −0.441918 + 0.0397733i
\(125\) 3.49486e9 + 2.53917e9i 1.28037 + 0.930242i
\(126\) 3.99514e8 + 7.25010e7i 0.141210 + 0.0256258i
\(127\) −2.18876e7 + 5.12086e7i −0.00746589 + 0.0174673i −0.923219 − 0.384274i \(-0.874452\pi\)
0.915753 + 0.401741i \(0.131595\pi\)
\(128\) 1.04825e9 − 3.22619e9i 0.345161 − 1.06230i
\(129\) 1.66919e8 + 3.10188e8i 0.0530705 + 0.0986215i
\(130\) 5.52985e9 + 5.78377e9i 1.69812 + 1.77609i
\(131\) 3.97894e8 − 7.39411e8i 0.118045 − 0.219364i −0.814716 − 0.579860i \(-0.803107\pi\)
0.932761 + 0.360497i \(0.117393\pi\)
\(132\) 2.18436e9 − 6.02845e8i 0.626241 − 0.172832i
\(133\) 277311. + 2.04719e6i 7.68484e−5 + 0.000567317i
\(134\) 8.40520e8 − 6.20497e9i 0.225204 − 1.66252i
\(135\) −6.91044e9 − 1.90716e9i −1.79062 − 0.494180i
\(136\) 2.41870e9 − 2.52977e9i 0.606258 − 0.634097i
\(137\) 1.37121e9 + 4.22015e9i 0.332553 + 1.02349i 0.967915 + 0.251278i \(0.0808510\pi\)
−0.635362 + 0.772215i \(0.719149\pi\)
\(138\) 8.00044e9 + 7.20053e8i 1.87784 + 0.169008i
\(139\) 5.45086e9 + 4.76227e9i 1.23851 + 1.08205i 0.993653 + 0.112491i \(0.0358831\pi\)
0.244855 + 0.969560i \(0.421260\pi\)
\(140\) −6.78955e7 + 1.51181e9i −0.0149371 + 0.332599i
\(141\) −6.18028e9 −1.31681
\(142\) −3.92053e9 + 4.34138e9i −0.809184 + 0.896045i
\(143\) −9.95056e9 −1.98992
\(144\) −8.07569e7 + 1.79819e9i −0.0156512 + 0.348502i
\(145\) 7.01007e9 + 6.12451e9i 1.31694 + 1.15058i
\(146\) −4.58821e9 − 4.12947e8i −0.835710 − 0.0752153i
\(147\) −1.21639e9 − 3.74365e9i −0.214854 − 0.661253i
\(148\) 1.27602e9 − 1.33461e9i 0.218614 − 0.228653i
\(149\) −5.52780e9 − 1.52558e9i −0.918785 − 0.253569i −0.225509 − 0.974241i \(-0.572405\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(150\) 1.64220e9 − 1.21232e10i 0.264859 − 1.95527i
\(151\) −1.13619e9 − 8.38768e9i −0.177850 − 1.31294i −0.831237 − 0.555918i \(-0.812367\pi\)
0.653387 − 0.757024i \(-0.273348\pi\)
\(152\) −5.59121e6 + 1.54308e6i −0.000849591 + 0.000234472i
\(153\) −1.20275e9 + 2.23508e9i −0.177445 + 0.329748i
\(154\) −4.14197e9 − 4.33216e9i −0.593423 − 0.620671i
\(155\) −5.64642e9 − 1.04928e10i −0.785743 − 1.46015i
\(156\) 1.05671e9 − 3.25223e9i 0.142855 − 0.439663i
\(157\) −1.30045e9 + 3.04255e9i −0.170822 + 0.399659i −0.982963 − 0.183803i \(-0.941159\pi\)
0.812141 + 0.583462i \(0.198302\pi\)
\(158\) −3.02556e9 − 5.49058e8i −0.386232 − 0.0700909i
\(159\) 1.27667e9 + 9.27555e8i 0.158413 + 0.115094i
\(160\) −1.20348e10 + 1.08315e9i −1.45177 + 0.130662i
\(161\) −2.62185e9 − 6.13413e9i −0.307533 − 0.719510i
\(162\) 1.51297e9 + 6.62873e9i 0.172588 + 0.756159i
\(163\) −4.68892e9 − 7.10341e9i −0.520270 − 0.788175i 0.475533 − 0.879698i \(-0.342255\pi\)
−0.995803 + 0.0915226i \(0.970827\pi\)
\(164\) 2.55656e9 + 1.52747e9i 0.275968 + 0.164883i
\(165\) 1.44118e10 + 1.80718e10i 1.51370 + 1.89812i
\(166\) −7.73132e9 + 6.75465e9i −0.790255 + 0.690425i
\(167\) −1.07618e10 + 7.81892e9i −1.07068 + 0.777898i −0.976035 − 0.217613i \(-0.930173\pi\)
−0.0946493 + 0.995511i \(0.530173\pi\)
\(168\) −2.19901e9 + 1.05899e9i −0.212979 + 0.102565i
\(169\) −2.43035e9 + 3.68182e9i −0.229181 + 0.347194i
\(170\) −2.82080e10 − 1.05866e10i −2.59031 − 0.972161i
\(171\) 3.61087e6 − 2.15739e6i 0.000322945 − 0.000192951i
\(172\) −6.24480e8 − 3.00734e8i −0.0544052 − 0.0262002i
\(173\) 1.34969e10 − 2.44933e9i 1.14558 − 0.207893i 0.427610 − 0.903963i \(-0.359356\pi\)
0.717974 + 0.696070i \(0.245070\pi\)
\(174\) 2.81928e9 − 1.23521e10i 0.233167 − 1.02157i
\(175\) −9.51203e9 + 3.56992e9i −0.766658 + 0.287732i
\(176\) 1.65663e10 − 2.07735e10i 1.30142 − 1.63193i
\(177\) −9.07546e8 − 2.02081e10i −0.0695006 − 1.54755i
\(178\) −5.86003e8 − 1.30484e10i −0.0437532 − 0.974240i
\(179\) 6.70211e9 − 8.40418e9i 0.487947 − 0.611867i −0.475516 − 0.879707i \(-0.657739\pi\)
0.963463 + 0.267840i \(0.0863100\pi\)
\(180\) 2.88476e9 − 1.08267e9i 0.204826 − 0.0768723i
\(181\) −5.89628e9 + 2.58333e10i −0.408342 + 1.78907i 0.183509 + 0.983018i \(0.441254\pi\)
−0.591851 + 0.806047i \(0.701603\pi\)
\(182\) −8.89947e9 + 1.61502e9i −0.601233 + 0.109108i
\(183\) 1.42237e10 + 6.84977e9i 0.937525 + 0.451488i
\(184\) 1.60783e10 − 9.60637e9i 1.03410 − 0.617844i
\(185\) 1.76339e10 + 6.61811e9i 1.10682 + 0.415395i
\(186\) −8.93444e9 + 1.35351e10i −0.547342 + 0.829188i
\(187\) 3.37559e10 − 1.62560e10i 2.01865 − 0.972133i
\(188\) 9.83842e9 − 7.14803e9i 0.574401 − 0.417327i
\(189\) 6.10219e9 − 5.33132e9i 0.347862 − 0.303918i
\(190\) 3.11313e7 + 3.90374e7i 0.00173303 + 0.00217315i
\(191\) −3.21068e9 − 1.91829e9i −0.174561 − 0.104295i 0.422961 − 0.906148i \(-0.360991\pi\)
−0.597522 + 0.801853i \(0.703848\pi\)
\(192\) −1.93065e9 − 2.92482e9i −0.102530 − 0.155326i
\(193\) 2.65953e9 + 1.16521e10i 0.137974 + 0.604502i 0.995879 + 0.0906942i \(0.0289086\pi\)
−0.857905 + 0.513808i \(0.828234\pi\)
\(194\) −3.77302e9 − 8.82743e9i −0.191241 − 0.447431i
\(195\) 3.47413e10 − 3.12678e9i 1.72064 − 0.154861i
\(196\) 6.26623e9 + 4.55269e9i 0.303287 + 0.220351i
\(197\) 1.87635e10 + 3.40508e9i 0.887599 + 0.161076i 0.603162 − 0.797619i \(-0.293907\pi\)
0.284438 + 0.958695i \(0.408193\pi\)
\(198\) −4.79624e9 + 1.12214e10i −0.221772 + 0.518862i
\(199\) 6.15491e8 − 1.89429e9i 0.0278216 − 0.0856262i −0.936182 − 0.351517i \(-0.885666\pi\)
0.964003 + 0.265891i \(0.0856660\pi\)
\(200\) −1.35171e10 − 2.51191e10i −0.597379 − 1.11012i
\(201\) −1.88629e10 − 1.97290e10i −0.815127 − 0.852556i
\(202\) −2.11514e10 + 3.93059e10i −0.893835 + 1.66102i
\(203\) −1.01426e10 + 2.79919e9i −0.419197 + 0.115691i
\(204\) 1.72833e9 + 1.27590e10i 0.0698700 + 0.515801i
\(205\) −4.07779e9 + 3.01035e10i −0.161262 + 1.19049i
\(206\) 1.91816e10 + 5.29379e9i 0.742135 + 0.204816i
\(207\) −9.38634e9 + 9.81734e9i −0.355328 + 0.371644i
\(208\) −1.23905e10 − 3.81340e10i −0.458990 − 1.41263i
\(209\) −6.18398e7 − 5.56568e6i −0.00224187 − 0.000201772i
\(210\) 1.58226e10 + 1.38238e10i 0.561423 + 0.490500i
\(211\) −1.05974e9 + 2.35970e10i −0.0368070 + 0.819571i 0.892674 + 0.450702i \(0.148826\pi\)
−0.929481 + 0.368869i \(0.879745\pi\)
\(212\) −3.10514e9 −0.105577
\(213\) 4.14040e9 + 2.51610e10i 0.137827 + 0.837569i
\(214\) −1.86820e9 −0.0608921
\(215\) 3.17204e8 − 7.06309e9i 0.0101243 − 0.225435i
\(216\) 1.71326e10 + 1.49683e10i 0.535528 + 0.467877i
\(217\) 1.34143e10 + 1.20731e9i 0.410675 + 0.0369615i
\(218\) −6.56295e9 − 2.01987e10i −0.196809 − 0.605716i
\(219\) −1.38776e10 + 1.45149e10i −0.407677 + 0.426397i
\(220\) −4.38438e10 − 1.21001e10i −1.26185 − 0.348247i
\(221\) 7.58944e9 − 5.60275e10i 0.214015 − 1.57992i
\(222\) −3.44116e9 − 2.54037e10i −0.0950860 − 0.701953i
\(223\) −9.62528e9 + 2.65641e9i −0.260640 + 0.0719322i −0.393915 − 0.919147i \(-0.628879\pi\)
0.133274 + 0.991079i \(0.457451\pi\)
\(224\) 6.47221e9 − 1.20274e10i 0.171766 − 0.319194i
\(225\) 1.42954e10 + 1.49518e10i 0.371856 + 0.388931i
\(226\) 1.63751e10 + 3.04300e10i 0.417537 + 0.775914i
\(227\) −2.28531e10 + 7.03345e10i −0.571253 + 1.75814i 0.0773454 + 0.997004i \(0.475356\pi\)
−0.648598 + 0.761131i \(0.724644\pi\)
\(228\) 8.38623e6 − 1.96206e7i 0.000205523 − 0.000480844i
\(229\) 6.65701e10 + 1.20807e10i 1.59963 + 0.290290i 0.903813 − 0.427928i \(-0.140756\pi\)
0.695818 + 0.718218i \(0.255042\pi\)
\(230\) −1.30439e11 − 9.47694e10i −3.07349 − 2.23302i
\(231\) −2.60220e10 + 2.34202e9i −0.601294 + 0.0541174i
\(232\) −1.16105e10 − 2.71640e10i −0.263120 − 0.615599i
\(233\) −1.05585e9 − 4.62597e9i −0.0234693 − 0.102826i 0.961837 − 0.273624i \(-0.0882224\pi\)
−0.985306 + 0.170799i \(0.945365\pi\)
\(234\) 1.01452e10 + 1.53693e10i 0.221202 + 0.335107i
\(235\) 1.06489e11 + 6.36244e10i 2.27772 + 1.36088i
\(236\) 2.48171e10 + 3.11197e10i 0.520772 + 0.653027i
\(237\) −1.00944e10 + 8.81921e9i −0.207832 + 0.181577i
\(238\) 2.75518e10 − 2.00175e10i 0.556613 − 0.404403i
\(239\) −5.62295e10 + 2.70787e10i −1.11474 + 0.536830i −0.898263 − 0.439458i \(-0.855171\pi\)
−0.216476 + 0.976288i \(0.569456\pi\)
\(240\) −5.13118e10 + 7.77340e10i −0.998312 + 1.51238i
\(241\) −7.76020e10 − 2.91245e10i −1.48182 − 0.556137i −0.526104 − 0.850420i \(-0.676348\pi\)
−0.955718 + 0.294283i \(0.904919\pi\)
\(242\) 9.93397e10 − 5.93527e10i 1.86189 − 1.11243i
\(243\) −2.64820e10 − 1.27531e10i −0.487218 − 0.234632i
\(244\) −3.05652e10 + 5.54676e9i −0.552042 + 0.100181i
\(245\) −1.75810e10 + 7.70274e10i −0.311743 + 1.36583i
\(246\) 3.87107e10 − 1.45284e10i 0.673943 − 0.252935i
\(247\) −5.84197e7 + 7.32560e7i −0.000998672 + 0.00125230i
\(248\) 1.69654e9 + 3.77764e10i 0.0284794 + 0.634144i
\(249\) 2.00783e9 + 4.47077e10i 0.0331001 + 0.737031i
\(250\) −7.35812e10 + 9.22680e10i −1.19134 + 1.49390i
\(251\) −3.98991e10 + 1.49744e10i −0.634499 + 0.238132i −0.647836 − 0.761779i \(-0.724326\pi\)
0.0133371 + 0.999911i \(0.495755\pi\)
\(252\) −7.74998e8 + 3.39549e9i −0.0121059 + 0.0530396i
\(253\) 1.97272e11 − 3.57996e10i 3.02707 − 0.549333i
\(254\) −1.37073e9 − 6.60111e8i −0.0206634 − 0.00995096i
\(255\) −1.12747e11 + 6.73631e10i −1.66984 + 0.997681i
\(256\) 7.26564e10 + 2.72684e10i 1.05729 + 0.396807i
\(257\) 3.41838e10 − 5.17862e10i 0.488788 − 0.740483i −0.503559 − 0.863961i \(-0.667976\pi\)
0.992347 + 0.123478i \(0.0394049\pi\)
\(258\) −8.67010e9 + 4.17530e9i −0.121825 + 0.0586677i
\(259\) −1.72236e10 + 1.25137e10i −0.237835 + 0.172797i
\(260\) −5.16885e10 + 4.51589e10i −0.701478 + 0.612863i
\(261\) 1.33570e10 + 1.67492e10i 0.178167 + 0.223415i
\(262\) 1.96920e10 + 1.17654e10i 0.258186 + 0.154259i
\(263\) 1.13338e10 + 1.71699e10i 0.146074 + 0.221293i 0.900243 − 0.435388i \(-0.143389\pi\)
−0.754169 + 0.656680i \(0.771960\pi\)
\(264\) −1.63231e10 − 7.15161e10i −0.206816 − 0.906120i
\(265\) −1.24487e10 − 2.91253e10i −0.155067 − 0.362797i
\(266\) −5.62109e7 + 5.05907e6i −0.000688419 + 6.19589e-5i
\(267\) −4.60632e10 − 3.34668e10i −0.554694 − 0.403008i
\(268\) 5.28462e10 + 9.59018e9i 0.625760 + 0.113559i
\(269\) −2.28183e9 + 5.33862e9i −0.0265704 + 0.0621646i −0.932288 − 0.361718i \(-0.882190\pi\)
0.905717 + 0.423883i \(0.139333\pi\)
\(270\) 6.05192e10 − 1.86259e11i 0.693036 − 2.13295i
\(271\) −4.37364e10 − 8.12758e10i −0.492585 − 0.915376i −0.998602 − 0.0528526i \(-0.983169\pi\)
0.506018 − 0.862523i \(-0.331117\pi\)
\(272\) 1.04331e11 + 1.09122e11i 1.15573 + 1.20880i
\(273\) −1.86836e10 + 3.47199e10i −0.203577 + 0.378309i
\(274\) −1.16855e11 + 3.22499e10i −1.25248 + 0.345661i
\(275\) −4.09884e10 − 3.02589e11i −0.432179 − 3.19048i
\(276\) −9.24886e9 + 6.82778e10i −0.0959395 + 0.708254i
\(277\) 8.37852e10 + 2.31233e10i 0.855084 + 0.235988i 0.665980 − 0.745969i \(-0.268013\pi\)
0.189103 + 0.981957i \(0.439442\pi\)
\(278\) −1.36651e11 + 1.42925e11i −1.37218 + 1.43518i
\(279\) −8.47407e9 − 2.60805e10i −0.0837285 − 0.257690i
\(280\) 4.87922e10 + 4.39137e9i 0.474394 + 0.0426962i
\(281\) 7.83361e10 + 6.84402e10i 0.749520 + 0.654836i 0.945445 − 0.325783i \(-0.105628\pi\)
−0.195924 + 0.980619i \(0.562771\pi\)
\(282\) 7.57494e9 − 1.68669e11i 0.0713277 − 1.58824i
\(283\) 1.70855e11 1.58340 0.791699 − 0.610912i \(-0.209197\pi\)
0.791699 + 0.610912i \(0.209197\pi\)
\(284\) −3.56921e10 − 3.52653e10i −0.325566 − 0.321673i
\(285\) 2.17656e8 0.00195420
\(286\) 1.21960e10 − 2.71566e11i 0.107788 − 2.40009i
\(287\) −2.58586e10 − 2.25920e10i −0.224976 − 0.196556i
\(288\) −2.76970e10 − 2.49278e9i −0.237229 − 0.0213510i
\(289\) 2.91389e10 + 8.96803e10i 0.245716 + 0.756235i
\(290\) −1.75739e11 + 1.83809e11i −1.45908 + 1.52607i
\(291\) −4.03397e10 − 1.11330e10i −0.329772 − 0.0910113i
\(292\) 5.30417e9 − 3.91570e10i 0.0426968 − 0.315200i
\(293\) −1.89619e9 − 1.39982e10i −0.0150306 − 0.110961i 0.981880 − 0.189503i \(-0.0606877\pi\)
−0.996911 + 0.0785424i \(0.974973\pi\)
\(294\) 1.03661e11 − 2.86086e10i 0.809193 − 0.223323i
\(295\) −1.92400e11 + 3.57538e11i −1.47913 + 2.74868i
\(296\) −4.13070e10 − 4.32037e10i −0.312760 − 0.327121i
\(297\) 1.15404e11 + 2.14456e11i 0.860629 + 1.59932i
\(298\) 4.84105e10 − 1.48992e11i 0.355604 − 1.09444i
\(299\) 1.18914e11 − 2.78212e11i 0.860421 − 2.01306i
\(300\) 1.03250e11 + 1.87372e10i 0.735947 + 0.133555i
\(301\) 6.46538e9 + 4.69738e9i 0.0453989 + 0.0329842i
\(302\) 2.30305e11 − 2.07278e10i 1.59321 − 0.143391i
\(303\) 7.64722e10 + 1.78916e11i 0.521209 + 1.21943i
\(304\) −5.56736e7 − 2.43922e8i −0.000373868 − 0.00163802i
\(305\) −1.74565e11 − 2.64455e11i −1.15507 − 1.74985i
\(306\) −5.95247e10 − 3.55643e10i −0.388106 − 0.231883i
\(307\) 8.30461e10 + 1.04137e11i 0.533576 + 0.669084i 0.973430 − 0.228986i \(-0.0735410\pi\)
−0.439853 + 0.898070i \(0.644970\pi\)
\(308\) 3.87158e10 − 3.38250e10i 0.245138 − 0.214170i
\(309\) 7.01755e10 − 5.09855e10i 0.437897 − 0.318151i
\(310\) 2.93285e11 − 1.41239e11i 1.80369 − 0.868613i
\(311\) 1.31222e11 − 1.98792e11i 0.795397 − 1.20498i −0.179814 − 0.983701i \(-0.557550\pi\)
0.975211 − 0.221275i \(-0.0710218\pi\)
\(312\) −1.03640e11 − 3.88966e10i −0.619199 − 0.232389i
\(313\) −2.33103e9 + 1.39273e9i −0.0137277 + 0.00820194i −0.519747 − 0.854320i \(-0.673974\pi\)
0.506019 + 0.862522i \(0.331117\pi\)
\(314\) −8.14420e10 − 3.92204e10i −0.472786 − 0.227682i
\(315\) −3.49557e10 + 6.34352e9i −0.200042 + 0.0363022i
\(316\) 5.86914e9 − 2.57144e10i 0.0331118 − 0.145072i
\(317\) −1.59618e11 + 5.99055e10i −0.887798 + 0.333196i −0.753268 − 0.657714i \(-0.771524\pi\)
−0.134530 + 0.990910i \(0.542952\pi\)
\(318\) −2.68792e10 + 3.37054e10i −0.147399 + 0.184832i
\(319\) −1.41876e10 − 3.15912e11i −0.0767099 − 1.70808i
\(320\) 3.15590e9 + 7.02717e10i 0.0168248 + 0.374632i
\(321\) −5.07755e9 + 6.36705e9i −0.0266920 + 0.0334708i
\(322\) 1.70623e11 − 6.40360e10i 0.884478 − 0.331950i
\(323\) 7.85042e7 − 3.43949e8i 0.000401311 − 0.00175826i
\(324\) −5.73831e10 + 1.04135e10i −0.289289 + 0.0524982i
\(325\) −4.15165e11 − 1.99933e11i −2.06417 − 0.994053i
\(326\) 1.99610e11 − 1.19261e11i 0.978821 − 0.584818i
\(327\) −8.66771e10 − 3.25304e10i −0.419217 − 0.157335i
\(328\) 5.31102e10 − 8.04585e10i 0.253365 − 0.383831i
\(329\) −1.26330e11 + 6.08372e10i −0.594462 + 0.286278i
\(330\) −5.10871e11 + 3.71169e11i −2.37136 + 1.72290i
\(331\) −9.44507e10 + 8.25191e10i −0.432493 + 0.377858i −0.846476 − 0.532427i \(-0.821280\pi\)
0.413983 + 0.910285i \(0.364137\pi\)
\(332\) −5.49047e10 − 6.88483e10i −0.248021 − 0.311008i
\(333\) 3.72111e10 + 2.22326e10i 0.165834 + 0.0990811i
\(334\) −2.00200e11 − 3.03290e11i −0.880247 − 1.33352i
\(335\) 1.21912e11 + 5.34129e11i 0.528863 + 2.31710i
\(336\) −4.13781e10 − 9.68090e10i −0.177110 − 0.414371i
\(337\) −1.23252e11 + 1.10929e10i −0.520548 + 0.0468502i −0.346798 − 0.937940i \(-0.612731\pi\)
−0.173750 + 0.984790i \(0.555588\pi\)
\(338\) −9.75037e10 − 7.08406e10i −0.406346 − 0.295228i
\(339\) 1.48215e11 + 2.68970e10i 0.609527 + 0.110613i
\(340\) 1.01571e11 − 2.37637e11i 0.412207 − 0.964406i
\(341\) −1.25088e11 + 3.84980e11i −0.500979 + 1.54186i
\(342\) 5.44529e7 + 1.01190e8i 0.000215230 + 0.000399965i
\(343\) −1.37061e11 − 1.43354e11i −0.534675 − 0.559226i
\(344\) −1.06325e10 + 1.97584e10i −0.0409374 + 0.0760745i
\(345\) −6.77504e11 + 1.86979e11i −2.57470 + 0.710571i
\(346\) 5.03032e10 + 3.71353e11i 0.188692 + 1.39298i
\(347\) 7.30934e9 − 5.39598e10i 0.0270642 − 0.199796i −0.972369 − 0.233448i \(-0.924999\pi\)
0.999434 + 0.0336513i \(0.0107136\pi\)
\(348\) 1.04759e11 + 2.89116e10i 0.382899 + 0.105673i
\(349\) −2.38280e11 + 2.49221e11i −0.859752 + 0.899230i −0.995808 − 0.0914708i \(-0.970843\pi\)
0.136055 + 0.990701i \(0.456557\pi\)
\(350\) −8.57701e10 − 2.63973e11i −0.305513 − 0.940273i
\(351\) 3.66033e11 + 3.29436e10i 1.28718 + 0.115848i
\(352\) 3.09132e11 + 2.70080e11i 1.07325 + 0.937672i
\(353\) 1.21341e10 − 2.70187e11i 0.0415931 − 0.926142i −0.864388 − 0.502825i \(-0.832294\pi\)
0.905981 − 0.423317i \(-0.139134\pi\)
\(354\) 5.52622e11 1.87031
\(355\) 1.87685e11 − 4.76162e11i 0.627196 − 1.59121i
\(356\) 1.12036e11 0.369684
\(357\) 6.66040e9 − 1.48305e11i 0.0217017 − 0.483226i
\(358\) 2.21148e11 + 1.93212e11i 0.711558 + 0.621669i
\(359\) −1.93340e11 − 1.74009e10i −0.614321 − 0.0552899i −0.221891 − 0.975072i \(-0.571223\pi\)
−0.392431 + 0.919782i \(0.628366\pi\)
\(360\) −3.08230e10 − 9.48634e10i −0.0967194 − 0.297672i
\(361\) 2.22997e11 − 2.33237e11i 0.691061 − 0.722794i
\(362\) −6.97803e11 − 1.92581e11i −2.13572 − 0.589421i
\(363\) 6.77129e10 − 4.99876e11i 0.204688 − 1.51106i
\(364\) −1.04141e10 − 7.68801e10i −0.0310933 − 0.229540i
\(365\) 3.88545e11 − 1.07232e11i 1.14584 − 0.316232i
\(366\) −2.04374e11 + 3.79791e11i −0.595335 + 1.10632i
\(367\) −9.33530e10 − 9.76395e10i −0.268615 − 0.280950i 0.574705 − 0.818361i \(-0.305117\pi\)
−0.843321 + 0.537411i \(0.819402\pi\)
\(368\) 3.82840e11 + 7.11436e11i 1.08818 + 2.02218i
\(369\) −2.16044e10 + 6.64914e10i −0.0606629 + 0.186701i
\(370\) −2.02231e11 + 4.73144e11i −0.560972 + 1.31246i
\(371\) 3.52268e10 + 6.39272e9i 0.0965363 + 0.0175188i
\(372\) −1.12543e11 − 8.17669e10i −0.304701 − 0.221378i
\(373\) −9.82981e10 + 8.84699e9i −0.262939 + 0.0236650i −0.220325 − 0.975427i \(-0.570712\pi\)
−0.0426147 + 0.999092i \(0.513569\pi\)
\(374\) 4.02277e11 + 9.41174e11i 1.06317 + 2.48741i
\(375\) 1.14475e11 + 5.01548e11i 0.298931 + 1.30970i
\(376\) −2.16873e11 − 3.28548e11i −0.559577 − 0.847723i
\(377\) −4.09664e11 − 2.44763e11i −1.04446 − 0.624036i
\(378\) 1.38021e11 + 1.73072e11i 0.347721 + 0.436029i
\(379\) −1.33360e11 + 1.16513e11i −0.332007 + 0.290066i −0.807758 − 0.589514i \(-0.799319\pi\)
0.475751 + 0.879580i \(0.342176\pi\)
\(380\) −3.46488e8 + 2.51738e8i −0.000852436 + 0.000619331i
\(381\) −5.97524e9 + 2.87752e9i −0.0145276 + 0.00699611i
\(382\) 5.62883e10 − 8.52732e10i 0.135249 − 0.204893i
\(383\) −7.16005e10 − 2.68721e10i −0.170028 − 0.0638127i 0.264909 − 0.964273i \(-0.414658\pi\)
−0.434937 + 0.900461i \(0.643230\pi\)
\(384\) 3.46790e11 − 2.07197e11i 0.813909 − 0.486288i
\(385\) 4.72483e11 + 2.27536e11i 1.09600 + 0.527808i
\(386\) −3.21265e11 + 5.83009e10i −0.736580 + 0.133670i
\(387\) 3.62075e9 − 1.58635e10i 0.00820538 − 0.0359501i
\(388\) 7.70933e10 − 2.89336e10i 0.172693 − 0.0648126i
\(389\) 4.39698e11 − 5.51364e11i 0.973602 − 1.22086i −0.00170309 − 0.999999i \(-0.500542\pi\)
0.975305 − 0.220860i \(-0.0708865\pi\)
\(390\) 4.27533e10 + 9.51976e11i 0.0935791 + 2.08370i
\(391\) 5.11104e10 + 1.13806e12i 0.110590 + 2.46247i
\(392\) 1.56331e11 − 1.96033e11i 0.334394 − 0.419316i
\(393\) 9.36186e10 − 3.51356e10i 0.197968 − 0.0742987i
\(394\) −1.15928e11 + 5.07912e11i −0.242356 + 1.06183i
\(395\) 2.64723e11 − 4.80401e10i 0.547148 − 0.0992927i
\(396\) −9.43088e10 − 4.54167e10i −0.192719 − 0.0928085i
\(397\) −5.68333e11 + 3.39563e11i −1.14827 + 0.686062i −0.955444 − 0.295171i \(-0.904623\pi\)
−0.192829 + 0.981232i \(0.561766\pi\)
\(398\) 5.09436e10 + 1.91194e10i 0.101769 + 0.0381945i
\(399\) −1.35533e8 + 2.05324e8i −0.000267712 + 0.000405566i
\(400\) 1.10859e12 − 5.33867e11i 2.16521 − 1.04271i
\(401\) −1.12352e11 + 8.16283e10i −0.216985 + 0.157649i −0.690968 − 0.722885i \(-0.742816\pi\)
0.473983 + 0.880534i \(0.342816\pi\)
\(402\) 5.61554e11 − 4.90615e11i 1.07244 − 0.936966i
\(403\) 3.80866e11 + 4.77590e11i 0.719282 + 0.901951i
\(404\) −3.28668e11 − 1.96370e11i −0.613820 − 0.366741i
\(405\) −3.27729e11 − 4.96488e11i −0.605295 − 0.916982i
\(406\) −6.39627e10 − 2.80239e11i −0.116831 − 0.511872i
\(407\) −2.51478e11 − 5.88363e11i −0.454282 − 1.06285i
\(408\) 4.15127e11 − 3.73621e10i 0.741670 − 0.0667515i
\(409\) −6.49034e10 − 4.71551e10i −0.114687 − 0.0833247i 0.528964 − 0.848645i \(-0.322581\pi\)
−0.643650 + 0.765320i \(0.722581\pi\)
\(410\) −8.16571e11 − 1.48186e11i −1.42714 − 0.258988i
\(411\) −2.07687e11 + 4.85908e11i −0.359022 + 0.839973i
\(412\) −5.27436e10 + 1.62328e11i −0.0901846 + 0.277560i
\(413\) −2.17475e11 − 4.04135e11i −0.367818 − 0.683521i
\(414\) −2.56426e11 − 2.68200e11i −0.429003 − 0.448702i
\(415\) 4.25659e11 − 7.91007e11i 0.704442 − 1.30907i
\(416\) 5.97142e11 − 1.64801e11i 0.977593 − 0.269798i
\(417\) 1.15706e11 + 8.54178e11i 0.187389 + 1.38336i
\(418\) 2.27691e8 − 1.68088e9i 0.000364798 − 0.00269304i
\(419\) −5.82233e11 − 1.60686e11i −0.922856 − 0.254692i −0.227850 − 0.973696i \(-0.573170\pi\)
−0.695006 + 0.719004i \(0.744598\pi\)
\(420\) −1.24543e11 + 1.30262e11i −0.195298 + 0.204266i
\(421\) −1.65143e11 − 5.08257e11i −0.256207 − 0.788523i −0.993590 − 0.113048i \(-0.963939\pi\)
0.737383 − 0.675475i \(-0.236061\pi\)
\(422\) −6.42701e11 − 5.78441e10i −0.986513 − 0.0887878i
\(423\) 2.14992e11 + 1.87833e11i 0.326506 + 0.285260i
\(424\) −4.50977e9 + 1.00418e11i −0.00677653 + 0.150891i
\(425\) 1.73502e12 2.57960
\(426\) −6.91758e11 + 8.21588e10i −1.01768 + 0.120868i
\(427\) 3.58171e11 0.521393
\(428\) 7.18937e8 − 1.60084e10i 0.00103560 − 0.0230595i
\(429\) −8.92383e11 − 7.79652e11i −1.27202 − 1.11133i
\(430\) 1.92374e11 + 1.73140e10i 0.271355 + 0.0244224i
\(431\) −2.96985e11 − 9.14027e11i −0.414560 − 1.27588i −0.912644 − 0.408756i \(-0.865963\pi\)
0.498084 − 0.867129i \(-0.334037\pi\)
\(432\) −6.78169e11 + 7.09309e11i −0.936831 + 0.979848i
\(433\) 8.11515e11 + 2.23964e11i 1.10943 + 0.306184i 0.772290 − 0.635270i \(-0.219111\pi\)
0.337142 + 0.941454i \(0.390540\pi\)
\(434\) −4.93907e10 + 3.64617e11i −0.0668253 + 0.493324i
\(435\) 1.48804e11 + 1.09851e12i 0.199256 + 1.47097i
\(436\) 1.75606e11 − 4.84642e10i 0.232729 − 0.0642291i
\(437\) 8.94626e8 − 1.66249e9i 0.00117348 − 0.00218069i
\(438\) −3.79123e11 − 3.96532e11i −0.492206 − 0.514807i
\(439\) −2.99958e11 − 5.57416e11i −0.385452 − 0.716291i 0.611749 − 0.791052i \(-0.290466\pi\)
−0.997201 + 0.0747613i \(0.976181\pi\)
\(440\) −4.54985e11 + 1.40030e12i −0.578709 + 1.78108i
\(441\) −7.14641e10 + 1.67199e11i −0.0899734 + 0.210503i
\(442\) 1.51977e12 + 2.75798e11i 1.89400 + 0.343709i
\(443\) −2.71775e11 − 1.97456e11i −0.335269 − 0.243587i 0.407394 − 0.913252i \(-0.366437\pi\)
−0.742663 + 0.669666i \(0.766437\pi\)
\(444\) 2.19006e11 − 1.97109e10i 0.267443 − 0.0240703i
\(445\) 4.49159e11 + 1.05086e12i 0.542975 + 1.27035i
\(446\) −6.07001e10 − 2.65945e11i −0.0726411 − 0.318262i
\(447\) −3.76210e11 − 5.69933e11i −0.445704 − 0.675212i
\(448\) −6.82553e10 − 4.07807e10i −0.0800544 − 0.0478303i
\(449\) 2.21776e11 + 2.78098e11i 0.257517 + 0.322916i 0.893737 − 0.448592i \(-0.148074\pi\)
−0.636220 + 0.771508i \(0.719503\pi\)
\(450\) −4.25579e11 + 3.71817e11i −0.489242 + 0.427438i
\(451\) 8.34910e11 − 6.06597e11i 0.950266 − 0.690408i
\(452\) −2.67053e11 + 1.28606e11i −0.300936 + 0.144923i
\(453\) 5.55301e11 − 8.41245e11i 0.619565 − 0.938600i
\(454\) −1.89153e12 − 7.09902e11i −2.08959 − 0.784237i
\(455\) 6.79361e11 − 4.05899e11i 0.743104 − 0.443984i
\(456\) −6.22333e8 − 2.99700e8i −0.000674033 − 0.000324597i
\(457\) 1.27244e12 − 2.30913e11i 1.36462 − 0.247643i 0.553662 − 0.832741i \(-0.313230\pi\)
0.810962 + 0.585098i \(0.198944\pi\)
\(458\) −4.11293e11 + 1.80199e12i −0.436774 + 1.91363i
\(459\) −1.29554e12 + 4.86223e11i −1.36236 + 0.511303i
\(460\) 8.62266e11 − 1.08125e12i 0.897906 − 1.12594i
\(461\) 4.48758e10 + 9.99237e11i 0.0462762 + 1.03042i 0.879027 + 0.476772i \(0.158193\pi\)
−0.832751 + 0.553648i \(0.813235\pi\)
\(462\) −3.20231e10 − 7.13050e11i −0.0327020 − 0.728168i
\(463\) −5.48128e11 + 6.87331e11i −0.554329 + 0.695106i −0.977498 − 0.210944i \(-0.932346\pi\)
0.423169 + 0.906051i \(0.360918\pi\)
\(464\) 1.19302e12 − 4.47747e11i 1.19486 − 0.448437i
\(465\) 3.15758e11 − 1.38342e12i 0.313195 − 1.37220i
\(466\) 1.27544e11 − 2.31458e10i 0.125292 − 0.0227371i
\(467\) 3.49405e10 + 1.68265e10i 0.0339941 + 0.0163707i 0.450804 − 0.892623i \(-0.351137\pi\)
−0.416809 + 0.908994i \(0.636852\pi\)
\(468\) −1.35602e11 + 8.10186e10i −0.130665 + 0.0780690i
\(469\) −5.79780e11 − 2.17595e11i −0.553331 − 0.207669i
\(470\) −1.86693e12 + 2.82827e12i −1.76477 + 2.67351i
\(471\) −3.55018e11 + 1.70968e11i −0.332397 + 0.160074i
\(472\) 1.04243e12 − 7.57370e11i 0.966736 − 0.702375i
\(473\) −1.80878e11 + 1.58028e11i −0.166154 + 0.145164i
\(474\) −2.28317e11 − 2.86301e11i −0.207748 − 0.260507i
\(475\) −2.46830e9 − 1.47474e9i −0.00222473 − 0.00132921i
\(476\) 1.60925e11 + 2.43792e11i 0.143679 + 0.217664i
\(477\) −1.62207e10 − 7.10677e10i −0.0143462 − 0.0628549i
\(478\) −6.70100e11 − 1.56778e12i −0.587103 − 1.37360i
\(479\) −2.88854e11 + 2.59973e10i −0.250708 + 0.0225642i −0.214281 − 0.976772i \(-0.568741\pi\)
−0.0364277 + 0.999336i \(0.511598\pi\)
\(480\) −1.16417e12 − 8.45818e11i −1.00099 − 0.727263i
\(481\) −9.50067e11 − 1.72412e11i −0.809285 − 0.146864i
\(482\) 8.89967e11 − 2.08218e12i 0.751038 − 1.75714i
\(483\) 2.45493e11 − 7.55549e11i 0.205247 − 0.631685i
\(484\) 4.70358e11 + 8.74072e11i 0.389605 + 0.724008i
\(485\) 5.80461e11 + 6.07114e11i 0.476360 + 0.498233i
\(486\) 3.80509e11 − 7.07105e11i 0.309387 − 0.574937i
\(487\) 6.44518e11 − 1.77876e11i 0.519224 − 0.143297i 0.00340466 − 0.999994i \(-0.498916\pi\)
0.515819 + 0.856698i \(0.327488\pi\)
\(488\) 1.34986e11 + 9.96509e11i 0.107746 + 0.795412i
\(489\) 1.36060e11 − 1.00444e12i 0.107607 − 0.794387i
\(490\) −2.08065e12 − 5.74222e11i −1.63048 − 0.449985i
\(491\) −5.54907e11 + 5.80388e11i −0.430877 + 0.450662i −0.902213 − 0.431292i \(-0.858058\pi\)
0.471335 + 0.881954i \(0.343772\pi\)
\(492\) 1.09595e11 + 3.37299e11i 0.0843234 + 0.259521i
\(493\) 1.78959e12 + 1.61066e11i 1.36440 + 0.122798i
\(494\) −1.92766e9 − 1.68415e9i −0.00145633 − 0.00127236i
\(495\) 4.79041e10 − 1.06667e12i 0.0358632 − 0.798556i
\(496\) −1.63114e12 −1.21011
\(497\) 3.32312e11 + 4.73555e11i 0.244311 + 0.348150i
\(498\) −1.22260e12 −0.890745
\(499\) −6.16437e10 + 1.37260e12i −0.0445078 + 0.991044i 0.845182 + 0.534478i \(0.179492\pi\)
−0.889690 + 0.456565i \(0.849079\pi\)
\(500\) −7.62318e11 − 6.66017e11i −0.545470 − 0.476563i
\(501\) −1.57777e12 − 1.42002e11i −1.11886 − 0.100699i
\(502\) −3.59771e11 − 1.10726e12i −0.252848 − 0.778186i
\(503\) 4.89356e11 − 5.11826e11i 0.340854 − 0.356506i −0.530043 − 0.847971i \(-0.677824\pi\)
0.870897 + 0.491465i \(0.163538\pi\)
\(504\) 1.08682e11 + 2.99943e10i 0.0750273 + 0.0207062i
\(505\) 5.24236e11 − 3.87007e12i 0.358687 − 2.64793i
\(506\) 7.35236e11 + 5.42773e12i 0.498597 + 3.68079i
\(507\) −5.06438e11 + 1.39768e11i −0.340401 + 0.0939446i
\(508\) 6.18392e9 − 1.14916e10i 0.00411981 − 0.00765588i
\(509\) −1.31974e11 − 1.38034e11i −0.0871479 − 0.0911496i 0.677783 − 0.735262i \(-0.262941\pi\)
−0.764931 + 0.644113i \(0.777227\pi\)
\(510\) −1.70025e12 − 3.15960e12i −1.11288 − 2.06808i
\(511\) −1.40789e11 + 4.33303e11i −0.0913428 + 0.281124i
\(512\) −1.50636e11 + 3.52431e11i −0.0968756 + 0.226652i
\(513\) 2.25636e9 + 4.09469e8i 0.00143840 + 0.000261032i
\(514\) 1.37143e12 + 9.96400e11i 0.866640 + 0.629651i
\(515\) −1.73404e12 + 1.56067e11i −1.08624 + 0.0977636i
\(516\) −3.24412e10 − 7.58999e10i −0.0201453 − 0.0471322i
\(517\) −9.37734e11 − 4.10848e12i −0.577261 − 2.52915i
\(518\) −3.20408e11 − 4.85397e11i −0.195533 − 0.296219i
\(519\) 1.40234e12 + 8.37858e11i 0.848398 + 0.506894i
\(520\) 1.38533e12 + 1.73715e12i 0.830882 + 1.04189i
\(521\) 2.47208e11 − 2.15979e11i 0.146991 − 0.128423i −0.581302 − 0.813688i \(-0.697457\pi\)
0.728294 + 0.685265i \(0.240314\pi\)
\(522\) −4.73483e11 + 3.44005e11i −0.279117 + 0.202791i
\(523\) 1.61056e12 − 7.75605e11i 0.941281 − 0.453297i 0.100660 − 0.994921i \(-0.467905\pi\)
0.840621 + 0.541624i \(0.182190\pi\)
\(524\) −1.08395e11 + 1.64211e11i −0.0628082 + 0.0951504i
\(525\) −1.13277e12 − 4.25135e11i −0.650765 − 0.244236i
\(526\) −4.82485e11 + 2.88271e11i −0.274820 + 0.164197i
\(527\) −2.07226e12 − 9.97948e11i −1.17030 − 0.563586i
\(528\) 3.11335e12 − 5.64989e11i 1.74331 − 0.316364i
\(529\) −9.55756e11 + 4.18744e12i −0.530636 + 2.32487i
\(530\) 8.10131e11 − 3.04047e11i 0.445978 − 0.167378i
\(531\) −5.82600e11 + 7.30557e11i −0.318013 + 0.398776i
\(532\) −2.17190e7 − 4.83612e8i −1.17554e−5 − 0.000261755i
\(533\) −6.98712e10 − 1.55580e12i −0.0374995 − 0.834991i
\(534\) 9.69819e11 − 1.21612e12i 0.516125 − 0.647201i
\(535\) 1.53036e11 − 5.74354e10i 0.0807610 − 0.0303101i
\(536\) 3.86890e11 − 1.69508e12i 0.202463 − 0.887050i
\(537\) 1.25955e12 − 2.28574e11i 0.653627 − 0.118616i
\(538\) −1.42902e11 − 6.88181e10i −0.0735392 − 0.0354146i
\(539\) 2.30412e12 − 1.37665e12i 1.17586 − 0.702543i
\(540\) 1.57274e12 + 5.90260e11i 0.795950 + 0.298725i
\(541\) 6.96630e11 − 1.05535e12i 0.349635 − 0.529674i −0.616620 − 0.787261i \(-0.711499\pi\)
0.966255 + 0.257586i \(0.0829272\pi\)
\(542\) 2.27175e12 − 1.09402e12i 1.13074 − 0.544536i
\(543\) −2.55289e12 + 1.85479e12i −1.26018 + 0.915576i
\(544\) −1.75649e12 + 1.53460e12i −0.859906 + 0.751277i
\(545\) 1.15860e12 + 1.45283e12i 0.562533 + 0.705394i
\(546\) −9.24661e11 − 5.52459e11i −0.445262 − 0.266032i
\(547\) −1.15414e12 − 1.74845e12i −0.551209 − 0.835047i 0.447020 − 0.894524i \(-0.352485\pi\)
−0.998230 + 0.0594772i \(0.981057\pi\)
\(548\) −2.31377e11 − 1.01373e12i −0.109599 − 0.480185i
\(549\) −2.86617e11 − 6.70573e11i −0.134656 − 0.315044i
\(550\) 8.30835e12 − 7.47765e11i 3.87153 − 0.348444i
\(551\) −2.40904e9 − 1.75027e9i −0.00111343 − 0.000808951i
\(552\) 2.19462e12 + 3.98264e11i 1.00608 + 0.182577i
\(553\) −1.19523e11 + 2.79638e11i −0.0543487 + 0.127155i
\(554\) −7.33762e11 + 2.25829e12i −0.330949 + 1.01856i
\(555\) 1.06289e12 + 1.97518e12i 0.475522 + 0.883668i
\(556\) −1.17213e12 − 1.22595e12i −0.520161 − 0.544045i
\(557\) −1.17459e12 + 2.18275e12i −0.517055 + 0.960849i 0.479470 + 0.877558i \(0.340829\pi\)
−0.996525 + 0.0832913i \(0.973457\pi\)
\(558\) 7.22164e11 − 1.99304e11i 0.315342 − 0.0870288i
\(559\) 4.86541e10 + 3.59179e11i 0.0210750 + 0.155582i
\(560\) −2.83658e11 + 2.09405e12i −0.121885 + 0.899788i
\(561\) 4.30098e12 + 1.18700e12i 1.83331 + 0.505960i
\(562\) −1.96385e12 + 2.05403e12i −0.830415 + 0.868546i
\(563\) 5.54366e11 + 1.70616e12i 0.232546 + 0.715704i 0.997437 + 0.0715441i \(0.0227927\pi\)
−0.764891 + 0.644159i \(0.777207\pi\)
\(564\) 1.44239e12 + 1.29818e11i 0.600244 + 0.0540229i
\(565\) −2.27692e12 − 1.98928e12i −0.940003 − 0.821256i
\(566\) −2.09411e11 + 4.66291e12i −0.0857682 + 1.90978i
\(567\) 6.72432e11 0.273228
\(568\) −1.19229e12 + 1.10304e12i −0.480633 + 0.444654i
\(569\) −3.96140e12 −1.58432 −0.792161 − 0.610312i \(-0.791044\pi\)
−0.792161 + 0.610312i \(0.791044\pi\)
\(570\) −2.66773e8 + 5.94016e9i −0.000105853 + 0.00235701i
\(571\) −3.65378e11 − 3.19221e11i −0.143840 − 0.125669i 0.583011 − 0.812464i \(-0.301874\pi\)
−0.726851 + 0.686795i \(0.759017\pi\)
\(572\) 2.32233e12 + 2.09013e11i 0.907071 + 0.0816378i
\(573\) −1.37636e11 − 4.23601e11i −0.0533380 − 0.164158i
\(574\) 6.48264e11 − 6.78031e11i 0.249258 − 0.260703i
\(575\) 8.95004e12 + 2.47006e12i 3.41444 + 0.942326i
\(576\) −2.17306e10 + 1.60422e11i −0.00822567 + 0.0607244i
\(577\) −1.02526e11 − 7.56878e11i −0.0385073 − 0.284273i −0.999957 − 0.00929102i \(-0.997043\pi\)
0.961450 − 0.274982i \(-0.0886718\pi\)
\(578\) −2.48323e12 + 6.85327e11i −0.925425 + 0.255401i
\(579\) −6.74465e11 + 1.25337e12i −0.249405 + 0.463473i
\(580\) −1.50741e12 − 1.57663e12i −0.553102 − 0.578499i
\(581\) 4.81134e11 + 8.94097e11i 0.175176 + 0.325531i
\(582\) 3.53280e11 − 1.08729e12i 0.127634 − 0.392817i
\(583\) −4.22904e11 + 9.89434e11i −0.151612 + 0.354714i
\(584\) −1.25860e12 − 2.28403e11i −0.447745 − 0.0812537i
\(585\) −1.30357e12 − 9.47099e11i −0.460185 − 0.334344i
\(586\) 3.84357e11 − 3.45928e10i 0.134647 − 0.0121184i
\(587\) −1.85784e12 − 4.34663e12i −0.645857 − 1.51106i −0.847054 − 0.531508i \(-0.821626\pi\)
0.201196 − 0.979551i \(-0.435517\pi\)
\(588\) 2.05252e11 + 8.99268e11i 0.0708092 + 0.310235i
\(589\) 2.09983e9 + 3.18111e9i 0.000718896 + 0.00108908i
\(590\) −9.52195e12 − 5.68910e12i −3.23513 − 1.93290i
\(591\) 1.41595e12 + 1.77555e12i 0.477424 + 0.598671i
\(592\) 1.94167e12 − 1.69638e12i 0.649721 − 0.567644i
\(593\) −1.51912e12 + 1.10371e12i −0.504484 + 0.366529i −0.810727 − 0.585424i \(-0.800928\pi\)
0.306243 + 0.951953i \(0.400928\pi\)
\(594\) −5.99429e12 + 2.88670e12i −1.97560 + 0.951397i
\(595\) −1.64153e12 + 2.48681e12i −0.536936 + 0.813423i
\(596\) 1.25807e12 + 4.72161e11i 0.408410 + 0.153279i
\(597\) 2.03620e11 − 1.21658e11i 0.0656050 − 0.0391971i
\(598\) 7.44709e12 + 3.58633e12i 2.38139 + 1.14682i
\(599\) 8.08574e10 − 1.46735e10i 0.0256625 − 0.00465706i −0.165710 − 0.986174i \(-0.552992\pi\)
0.191373 + 0.981517i \(0.438706\pi\)
\(600\) 7.55902e11 − 3.31182e12i 0.238114 − 1.04325i
\(601\) 4.68321e12 − 1.75764e12i 1.46423 − 0.549534i 0.513099 − 0.858329i \(-0.328497\pi\)
0.951128 + 0.308795i \(0.0999258\pi\)
\(602\) −1.36123e11 + 1.70693e11i −0.0422423 + 0.0529701i
\(603\) 5.65685e10 + 1.25960e12i 0.0174240 + 0.387975i
\(604\) 8.89865e10 + 1.98144e12i 0.0272056 + 0.605779i
\(605\) −6.31283e12 + 7.91604e12i −1.91569 + 2.40220i
\(606\) −4.97661e12 + 1.86775e12i −1.49902 + 0.562591i
\(607\) −3.65860e11 + 1.60294e12i −0.109387 + 0.479257i 0.890326 + 0.455323i \(0.150476\pi\)
−0.999714 + 0.0239336i \(0.992381\pi\)
\(608\) 3.80324e9 − 6.90186e8i 0.00112872 − 0.000204833i
\(609\) −1.12893e12 − 5.43665e11i −0.332576 − 0.160160i
\(610\) 7.43133e12 − 4.44001e12i 2.17311 − 1.29837i
\(611\) −5.95393e12 − 2.23455e12i −1.72830 − 0.648641i
\(612\) 3.27654e11 − 4.96374e11i 0.0944134 − 0.143030i
\(613\) 6.45246e11 − 3.10734e11i 0.184567 − 0.0888826i −0.339318 − 0.940672i \(-0.610196\pi\)
0.523885 + 0.851789i \(0.324482\pi\)
\(614\) −2.94383e12 + 2.13882e12i −0.835902 + 0.607318i
\(615\) −2.72439e12 + 2.38022e12i −0.767946 + 0.670934i
\(616\) −1.03764e12 − 1.30116e12i −0.290359 − 0.364099i
\(617\) −1.72939e12 − 1.03326e12i −0.480407 − 0.287030i 0.252208 − 0.967673i \(-0.418843\pi\)
−0.732615 + 0.680643i \(0.761700\pi\)
\(618\) 1.30546e12 + 1.97769e12i 0.360011 + 0.545393i
\(619\) 7.02817e11 + 3.07924e12i 0.192413 + 0.843016i 0.975306 + 0.220860i \(0.0708862\pi\)
−0.782893 + 0.622157i \(0.786257\pi\)
\(620\) 1.09739e12 + 2.56748e12i 0.298264 + 0.697823i
\(621\) −7.37521e12 + 6.63781e11i −1.99004 + 0.179107i
\(622\) 5.26452e12 + 3.82490e12i 1.41027 + 1.02462i
\(623\) −1.27101e12 − 2.30654e11i −0.338027 − 0.0613429i
\(624\) 1.87670e12 − 4.39075e12i 0.495522 − 1.15933i
\(625\) 9.21272e11 − 2.83538e12i 0.241506 − 0.743279i
\(626\) −3.51526e10 − 6.53245e10i −0.00914899 − 0.0170017i
\(627\) −5.10981e9 − 5.34444e9i −0.00132039 − 0.00138102i
\(628\) 3.67417e11 − 6.82775e11i 0.0942628 − 0.175170i
\(629\) 3.50463e12 − 9.67218e11i 0.892719 − 0.246375i
\(630\) −1.30280e11 − 9.61769e11i −0.0329493 − 0.243242i
\(631\) −2.85444e11 + 2.10723e12i −0.0716784 + 0.529151i 0.919138 + 0.393936i \(0.128887\pi\)
−0.990816 + 0.135215i \(0.956827\pi\)
\(632\) −8.23059e11 − 2.27150e11i −0.205213 − 0.0566351i
\(633\) −1.94393e12 + 2.03319e12i −0.481242 + 0.503340i
\(634\) −1.43927e12 − 4.42963e12i −0.353787 − 1.08884i
\(635\) 1.32580e11 + 1.19324e10i 0.0323590 + 0.00291237i
\(636\) −2.78474e11 − 2.43296e11i −0.0674882 − 0.0589627i
\(637\) 1.81721e11 − 4.04634e12i 0.0437299 − 0.973722i
\(638\) 8.63910e12 2.06431
\(639\) 6.20671e11 − 1.00111e12i 0.147268 − 0.237535i
\(640\) −8.10841e12 −1.91041
\(641\) −1.88047e11 + 4.18720e12i −0.0439953 + 0.979631i 0.848673 + 0.528918i \(0.177402\pi\)
−0.892669 + 0.450714i \(0.851170\pi\)
\(642\) −1.67543e11 − 1.46378e11i −0.0389241 − 0.0340070i
\(643\) −5.94002e12 − 5.34611e11i −1.37037 − 0.123336i −0.620130 − 0.784499i \(-0.712920\pi\)
−0.750242 + 0.661164i \(0.770063\pi\)
\(644\) 4.83057e11 + 1.48670e12i 0.110665 + 0.340593i
\(645\) 5.81859e11 − 6.08577e11i 0.132373 − 0.138451i
\(646\) 9.29068e9 + 2.56407e9i 0.00209895 + 0.000579272i
\(647\) −8.62880e11 + 6.37003e12i −0.193589 + 1.42913i 0.589774 + 0.807568i \(0.299217\pi\)
−0.783363 + 0.621564i \(0.786498\pi\)
\(648\) 2.53424e11 + 1.87085e12i 0.0564625 + 0.416823i
\(649\) 1.32961e13 − 3.66948e12i 2.94186 − 0.811903i
\(650\) 5.96533e12 − 1.10854e13i 1.31076 − 2.43581i
\(651\) 1.10842e12 + 1.15932e12i 0.241875 + 0.252981i
\(652\) 9.45123e11 + 1.75633e12i 0.204821 + 0.380621i
\(653\) 8.94752e11 − 2.75376e12i 0.192572 − 0.592676i −0.807424 − 0.589971i \(-0.799139\pi\)
0.999996 − 0.00270470i \(-0.000860935\pi\)
\(654\) 9.94042e11 − 2.32568e12i 0.212474 − 0.497107i
\(655\) −1.97481e12 − 3.58375e11i −0.419217 − 0.0760767i
\(656\) 3.36432e12 + 2.44433e12i 0.709301 + 0.515337i
\(657\) 9.23899e11 − 8.31524e10i 0.193455 − 0.0174113i
\(658\) −1.50550e12 − 3.52230e12i −0.313087 − 0.732503i
\(659\) −7.72245e11 − 3.38343e12i −0.159504 − 0.698831i −0.989913 − 0.141677i \(-0.954750\pi\)
0.830409 − 0.557154i \(-0.188107\pi\)
\(660\) −2.98391e12 − 4.52043e12i −0.612123 − 0.927326i
\(661\) −3.07247e12 − 1.83572e12i −0.626010 − 0.374023i 0.164585 − 0.986363i \(-0.447371\pi\)
−0.790595 + 0.612339i \(0.790229\pi\)
\(662\) −2.13631e12 − 2.67884e12i −0.432317 − 0.542109i
\(663\) 5.07053e12 − 4.42999e12i 1.01916 − 0.890414i
\(664\) −2.30624e12 + 1.67558e12i −0.460414 + 0.334510i
\(665\) 4.44906e9 − 2.14255e9i 0.000882208 − 0.000424849i
\(666\) −6.52369e11 + 9.88297e11i −0.128487 + 0.194650i
\(667\) 9.00227e12 + 3.37861e12i 1.76111 + 0.660954i
\(668\) 2.67590e12 − 1.59878e12i 0.519967 − 0.310666i
\(669\) −1.07135e12 − 5.15934e11i −0.206782 − 0.0995811i
\(670\) −1.47266e13 + 2.67249e12i −2.82336 + 0.512365i
\(671\) −2.39538e12 + 1.04948e13i −0.456166 + 1.99860i
\(672\) 1.52282e12 − 5.71522e11i 0.288062 − 0.108111i
\(673\) 3.63941e12 − 4.56367e12i 0.683853 − 0.857525i −0.311850 − 0.950131i \(-0.600949\pi\)
0.995703 + 0.0926069i \(0.0295200\pi\)
\(674\) −1.51677e11 − 3.37734e12i −0.0283106 − 0.630385i
\(675\) 5.05978e11 + 1.12665e13i 0.0938134 + 2.08892i
\(676\) 6.44548e11 − 8.08237e11i 0.118712 − 0.148860i
\(677\) −6.81633e11 + 2.55821e11i −0.124710 + 0.0468045i −0.412950 − 0.910754i \(-0.635501\pi\)
0.288240 + 0.957558i \(0.406930\pi\)
\(678\) −9.15722e11 + 4.01204e12i −0.166429 + 0.729175i
\(679\) −9.34166e11 + 1.69526e11i −0.168659 + 0.0306071i
\(680\) −7.53749e12 − 3.62986e12i −1.35188 − 0.651029i
\(681\) −7.56040e12 + 4.51713e12i −1.34705 + 0.804823i
\(682\) −1.03534e13 − 3.88569e12i −1.83254 − 0.687763i
\(683\) 1.94440e12 − 2.94564e12i 0.341895 − 0.517949i −0.622428 − 0.782677i \(-0.713854\pi\)
0.964323 + 0.264728i \(0.0852822\pi\)
\(684\) −8.88045e8 + 4.27660e8i −0.000155125 + 7.47043e-5i
\(685\) 8.58085e12 − 6.23435e12i 1.48910 − 1.08189i
\(686\) 4.08035e12 − 3.56489e12i 0.703459 − 0.614594i
\(687\) 5.02357e12 + 6.29936e12i 0.860414 + 1.07892i
\(688\) −8.30849e11 − 4.96409e11i −0.141376 − 0.0844680i
\(689\) 8.94546e11 + 1.35518e12i 0.151222 + 0.229092i
\(690\) −4.27256e12 − 1.87193e13i −0.717575 − 3.14390i
\(691\) 2.01568e12 + 4.71591e12i 0.336333 + 0.786890i 0.999270 + 0.0382145i \(0.0121670\pi\)
−0.662937 + 0.748676i \(0.730690\pi\)
\(692\) −3.20145e12 + 2.88135e11i −0.530724 + 0.0477660i
\(693\) 9.76402e11 + 7.09397e11i 0.160816 + 0.116840i
\(694\) 1.46369e12 + 2.65620e11i 0.239514 + 0.0434653i
\(695\) 6.79987e12 − 1.59091e13i 1.10553 − 2.58651i
\(696\) 1.08712e12 − 3.34583e12i 0.175605 − 0.540458i
\(697\) 2.77870e12 + 5.16369e12i 0.445959 + 0.828730i
\(698\) −6.50958e12 − 6.80849e12i −1.03802 − 1.08568i
\(699\) 2.67766e11 − 4.97593e11i 0.0424237 − 0.0788365i
\(700\) 2.29497e12 − 6.33370e11i 0.361273 − 0.0997049i
\(701\) 9.70680e10 + 7.16585e11i 0.0151826 + 0.112082i 0.996955 − 0.0779773i \(-0.0248462\pi\)
−0.981773 + 0.190060i \(0.939132\pi\)
\(702\) −1.34771e12 + 9.94923e12i −0.209450 + 1.54622i
\(703\) −5.80795e9 − 1.60289e9i −0.000896858 − 0.000247517i
\(704\) 1.65140e12 − 1.72723e12i 0.253382 − 0.265017i
\(705\) 4.56501e12 + 1.40497e13i 0.695970 + 2.14198i
\(706\) 7.35893e12 + 6.62316e11i 1.11479 + 0.100333i
\(707\) 3.32435e12 + 2.90440e12i 0.500403 + 0.437189i
\(708\) −2.12665e11 + 4.73536e12i −0.0318087 + 0.708277i
\(709\) −7.59851e12 −1.12933 −0.564664 − 0.825321i \(-0.690994\pi\)
−0.564664 + 0.825321i \(0.690994\pi\)
\(710\) 1.27651e13 + 5.70584e12i 1.88523 + 0.842669i
\(711\) 6.19188e11 0.0908676
\(712\) 1.62715e11 − 3.62314e12i 0.0237284 − 0.528354i
\(713\) −9.26899e12 − 8.09807e12i −1.34316 − 1.17349i
\(714\) 4.03932e12 + 3.63545e11i 0.581656 + 0.0523500i
\(715\) 7.34990e12 + 2.26207e13i 1.05173 + 3.23689i
\(716\) −1.74071e12 + 1.82064e12i −0.247525 + 0.258891i
\(717\) −7.16444e12 − 1.97726e12i −1.01239 − 0.279401i
\(718\) 7.11866e11 − 5.25520e12i 0.0999627 − 0.737955i
\(719\) −1.70267e12 − 1.25696e13i −0.237602 − 1.75405i −0.580111 − 0.814537i \(-0.696991\pi\)
0.342509 − 0.939515i \(-0.388723\pi\)
\(720\) 4.14749e12 − 1.14463e12i 0.575160 − 0.158734i
\(721\) 9.32553e11 − 1.73297e12i 0.128518 − 0.238827i
\(722\) 6.09206e12 + 6.37180e12i 0.834348 + 0.872659i
\(723\) −4.67750e12 − 8.69226e12i −0.636637 − 1.18307i
\(724\) 1.91875e12 − 5.90529e12i 0.259534 − 0.798763i
\(725\) 5.75555e12 − 1.34658e13i 0.773689 − 1.81013i
\(726\) 1.35594e13 + 2.46067e12i 1.81145 + 0.328729i
\(727\) 9.52622e11 + 6.92121e11i 0.126478 + 0.0918918i 0.649226 − 0.760596i \(-0.275093\pi\)
−0.522748 + 0.852487i \(0.675093\pi\)
\(728\) −2.50137e12 + 2.25127e11i −0.330055 + 0.0297055i
\(729\) −3.30104e12 − 7.72318e12i −0.432890 − 1.01280i
\(730\) 2.45029e12 + 1.07354e13i 0.319349 + 1.39916i
\(731\) −7.51834e11 − 1.13898e12i −0.0973854 − 0.147533i
\(732\) −3.17574e12 − 1.89742e12i −0.408832 − 0.244266i
\(733\) −4.50026e12 − 5.64315e12i −0.575798 − 0.722028i 0.405592 − 0.914054i \(-0.367065\pi\)
−0.981390 + 0.192027i \(0.938494\pi\)
\(734\) 2.77915e12 − 2.42807e12i 0.353411 − 0.308766i
\(735\) −7.61199e12 + 5.53044e12i −0.962067 + 0.698983i
\(736\) −1.12456e13 + 5.41558e12i −1.41264 + 0.680291i
\(737\) 1.02532e13 − 1.55330e13i 1.28014 − 1.93933i
\(738\) −1.78817e12 − 6.71113e11i −0.221899 − 0.0832802i
\(739\) 9.00829e12 − 5.38220e12i 1.11107 − 0.663835i 0.164516 − 0.986374i \(-0.447394\pi\)
0.946556 + 0.322540i \(0.104537\pi\)
\(740\) −3.97650e12 − 1.91498e12i −0.487481 − 0.234759i
\(741\) −1.09790e10 + 1.99239e9i −0.00133776 + 0.000242769i
\(742\) −2.17643e11 + 9.53558e11i −0.0263589 + 0.115486i
\(743\) −5.33119e12 + 2.00083e12i −0.641763 + 0.240858i −0.650974 − 0.759100i \(-0.725639\pi\)
0.00921101 + 0.999958i \(0.497068\pi\)
\(744\) −2.80773e12 + 3.52078e12i −0.335952 + 0.421270i
\(745\) 6.14964e11 + 1.36932e13i 0.0731385 + 1.62856i
\(746\) −1.20967e11 − 2.69355e12i −0.0143003 − 0.318420i
\(747\) 1.28893e12 − 1.61626e12i 0.151456 − 0.189919i
\(748\) −8.21963e12 + 3.08488e12i −0.960052 + 0.360314i
\(749\) −4.11135e10 + 1.80130e11i −0.00477327 + 0.0209131i
\(750\) −1.38283e13 + 2.50947e12i −1.59586 + 0.289605i
\(751\) −1.52632e13 − 7.35038e12i −1.75092 − 0.843199i −0.977973 − 0.208730i \(-0.933067\pi\)
−0.772948 − 0.634469i \(-0.781219\pi\)
\(752\) </