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Properties

Label 71.10.g.a.2.13
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
CM no
Inner twists $2$

Related objects

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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 2.13
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.21652 + 27.0880i) q^{2} +(-157.432 - 137.544i) q^{3} +(-222.342 - 20.0111i) q^{4} +(0.550643 + 1.69470i) q^{5} +(3917.33 - 4097.20i) q^{6} +(-7924.62 - 2187.06i) q^{7} +(-1051.02 + 7758.94i) q^{8} +(3224.33 + 23803.0i) q^{9} +O(q^{10})\) \(q+(-1.21652 + 27.0880i) q^{2} +(-157.432 - 137.544i) q^{3} +(-222.342 - 20.0111i) q^{4} +(0.550643 + 1.69470i) q^{5} +(3917.33 - 4097.20i) q^{6} +(-7924.62 - 2187.06i) q^{7} +(-1051.02 + 7758.94i) q^{8} +(3224.33 + 23803.0i) q^{9} +(-46.5760 + 12.8542i) q^{10} +(-37674.5 + 70010.9i) q^{11} +(32251.4 + 33732.3i) q^{12} +(50366.1 + 93595.9i) q^{13} +(68883.5 - 212002. i) q^{14} +(146.408 - 342.539i) q^{15} +(-321358. - 58317.9i) q^{16} +(-359470. - 261170. i) q^{17} +(-648698. + 58383.9i) q^{18} +(-165.701 - 387.678i) q^{19} +(-88.5180 - 387.823i) q^{20} +(946774. + 1.43430e6i) q^{21} +(-1.85062e6 - 1.10570e6i) q^{22} +(-60614.3 - 76008.0i) q^{23} +(1.23266e6 - 1.07695e6i) q^{24} +(1.58011e6 - 1.14802e6i) q^{25} +(-2.59660e6 + 1.25046e6i) q^{26} +(499523. - 756745. i) q^{27} +(1.71821e6 + 644855. i) q^{28} +(1.66570e6 - 995208. i) q^{29} +(9100.59 + 4382.61i) q^{30} +(-5.58001e6 + 1.01262e6i) q^{31} +(1.07860e6 - 4.72566e6i) q^{32} +(1.55608e7 - 5.84006e6i) q^{33} +(7.51189e6 - 9.41961e6i) q^{34} +(-657.222 - 14634.2i) q^{35} +(-240580. - 5.35693e6i) q^{36} +(4.80566e6 - 6.02610e6i) q^{37} +(10703.0 - 4016.90i) q^{38} +(4.94435e6 - 2.16626e7i) q^{39} +(-13727.8 + 2491.24i) q^{40} +(-7.86947e6 - 3.78973e6i) q^{41} +(-4.00041e7 + 2.39014e7i) q^{42} +(1.04599e7 + 3.92567e6i) q^{43} +(9.77761e6 - 1.48124e7i) q^{44} +(-38563.6 + 18571.2i) q^{45} +(2.13264e6 - 1.54946e6i) q^{46} +(1.44608e7 - 1.26340e7i) q^{47} +(4.25708e7 + 5.33821e7i) q^{48} +(2.33749e7 + 1.39659e7i) q^{49} +(2.91752e7 + 4.41986e7i) q^{50} +(2.06697e7 + 9.05597e7i) q^{51} +(-9.32554e6 - 2.18182e7i) q^{52} +(5.23923e7 - 4.71539e6i) q^{53} +(1.98910e7 + 1.44517e7i) q^{54} +(-139393. - 25296.1i) q^{55} +(2.52982e7 - 5.91880e7i) q^{56} +(-27236.2 + 83824.3i) q^{57} +(2.49319e7 + 4.63311e7i) q^{58} +(1.02723e8 + 1.07439e8i) q^{59} +(-39407.3 + 73231.0i) q^{60} +(-8.96444e7 + 2.47403e7i) q^{61} +(-2.06417e7 - 1.52383e8i) q^{62} +(2.65069e7 - 1.95682e8i) q^{63} +(-3.44998e7 - 9.52134e6i) q^{64} +(-130884. + 136894. i) q^{65} +(1.39266e8 + 4.28615e8i) q^{66} +(-1.50273e8 - 1.35248e7i) q^{67} +(7.46989e7 + 6.52625e7i) q^{68} +(-911821. + 2.03033e7i) q^{69} +397210. q^{70} +(1.30151e8 - 1.70027e8i) q^{71} -1.88075e8 q^{72} +(1.80447e7 - 4.01797e8i) q^{73} +(1.57389e8 + 1.37507e8i) q^{74} +(-4.06663e8 - 3.66004e7i) q^{75} +(29084.5 + 89512.9i) q^{76} +(4.51674e8 - 4.72414e8i) q^{77} +(5.80782e8 + 1.60286e8i) q^{78} +(5.00966e7 - 3.69828e8i) q^{79} +(-78121.9 - 576719. i) q^{80} +(2.73028e8 - 7.53509e7i) q^{81} +(1.12230e8 - 2.08558e8i) q^{82} +(1.88211e8 + 1.96854e8i) q^{83} +(-1.81806e8 - 3.37851e8i) q^{84} +(244667. - 753007. i) q^{85} +(-1.19063e8 + 2.78562e8i) q^{86} +(-3.99120e8 - 7.24296e7i) q^{87} +(-5.03614e8 - 3.65897e8i) q^{88} +(-7.35201e8 + 6.61693e7i) q^{89} +(-456145. - 1.06720e6i) q^{90} +(-1.94433e8 - 8.51866e8i) q^{91} +(1.19561e7 + 1.81127e7i) q^{92} +(1.01775e9 + 6.08080e8i) q^{93} +(3.24638e8 + 4.07083e8i) q^{94} +(565.757 - 494.287i) q^{95} +(-8.19795e8 + 5.95616e8i) q^{96} +(1.01922e9 - 4.90829e8i) q^{97} +(-4.06743e8 + 6.16190e8i) q^{98} +(-1.78794e9 - 6.71026e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.21652 + 27.0880i −0.0537633 + 1.19713i 0.772934 + 0.634486i \(0.218788\pi\)
−0.826698 + 0.562647i \(0.809783\pi\)
\(3\) −157.432 − 137.544i −1.12214 − 0.980387i −0.122216 − 0.992504i \(-0.539000\pi\)
−0.999927 + 0.0121170i \(0.996143\pi\)
\(4\) −222.342 − 20.0111i −0.434262 − 0.0390843i
\(5\) 0.550643 + 1.69470i 0.000394008 + 0.00121263i 0.951253 − 0.308411i \(-0.0997971\pi\)
−0.950859 + 0.309623i \(0.899797\pi\)
\(6\) 3917.33 − 4097.20i 1.23398 − 1.29064i
\(7\) −7924.62 − 2187.06i −1.24749 − 0.344286i −0.420909 − 0.907103i \(-0.638289\pi\)
−0.826581 + 0.562817i \(0.809718\pi\)
\(8\) −1051.02 + 7758.94i −0.0907206 + 0.669727i
\(9\) 3224.33 + 23803.0i 0.163813 + 1.20932i
\(10\) −46.5760 + 12.8542i −0.00147286 + 0.000406485i
\(11\) −37674.5 + 70010.9i −0.775854 + 1.44178i 0.117807 + 0.993036i \(0.462413\pi\)
−0.893661 + 0.448742i \(0.851872\pi\)
\(12\) 32251.4 + 33732.3i 0.448986 + 0.469602i
\(13\) 50366.1 + 93595.9i 0.489095 + 0.908891i 0.998821 + 0.0485539i \(0.0154613\pi\)
−0.509725 + 0.860337i \(0.670253\pi\)
\(14\) 68883.5 − 212002.i 0.479225 − 1.47490i
\(15\) 146.408 − 342.539i 0.000746715 − 0.00174703i
\(16\) −321358. − 58317.9i −1.22588 − 0.222465i
\(17\) −359470. − 261170.i −1.04386 − 0.758409i −0.0728250 − 0.997345i \(-0.523201\pi\)
−0.971035 + 0.238936i \(0.923201\pi\)
\(18\) −648698. + 58383.9i −1.45652 + 0.131089i
\(19\) −165.701 − 387.678i −0.000291699 − 0.000682464i 0.919382 − 0.393366i \(-0.128690\pi\)
−0.919674 + 0.392684i \(0.871547\pi\)
\(20\) −88.5180 − 387.823i −0.000123708 − 0.000541999i
\(21\) 946774. + 1.43430e6i 1.06233 + 1.60936i
\(22\) −1.85062e6 − 1.10570e6i −1.68429 − 1.00631i
\(23\) −60614.3 − 76008.0i −0.0451648 − 0.0566349i 0.758736 − 0.651398i \(-0.225817\pi\)
−0.803901 + 0.594763i \(0.797246\pi\)
\(24\) 1.23266e6 − 1.07695e6i 0.758392 − 0.662587i
\(25\) 1.58011e6 − 1.14802e6i 0.809016 − 0.587784i
\(26\) −2.59660e6 + 1.25046e6i −1.11436 + 0.536647i
\(27\) 499523. − 756745.i 0.180892 − 0.274039i
\(28\) 1.71821e6 + 644855.i 0.528281 + 0.198267i
\(29\) 1.66570e6 − 995208.i 0.437326 − 0.261290i −0.277318 − 0.960778i \(-0.589446\pi\)
0.714644 + 0.699488i \(0.246589\pi\)
\(30\) 9100.59 + 4382.61i 0.00205128 + 0.000987842i
\(31\) −5.58001e6 + 1.01262e6i −1.08519 + 0.196934i −0.691549 − 0.722329i \(-0.743072\pi\)
−0.393644 + 0.919263i \(0.628786\pi\)
\(32\) 1.07860e6 − 4.72566e6i 0.181839 − 0.796687i
\(33\) 1.55608e7 − 5.84006e6i 2.28412 − 0.857244i
\(34\) 7.51189e6 − 9.41961e6i 0.964037 − 1.20886i
\(35\) −657.222 − 14634.2i −7.40296e−5 − 0.00164840i
\(36\) −240580. − 5.35693e6i −0.0238725 − 0.531563i
\(37\) 4.80566e6 − 6.02610e6i 0.421546 − 0.528602i −0.525029 − 0.851084i \(-0.675946\pi\)
0.946576 + 0.322482i \(0.104517\pi\)
\(38\) 10703.0 − 4016.90i 0.000832683 − 0.000312511i
\(39\) 4.94435e6 − 2.16626e7i 0.342230 − 1.49941i
\(40\) −13727.8 + 2491.24i −0.000847876 + 0.000153867i
\(41\) −7.86947e6 − 3.78973e6i −0.434929 − 0.209451i 0.203591 − 0.979056i \(-0.434739\pi\)
−0.638520 + 0.769605i \(0.720453\pi\)
\(42\) −4.00041e7 + 2.39014e7i −1.98373 + 1.18522i
\(43\) 1.04599e7 + 3.92567e6i 0.466573 + 0.175108i 0.573578 − 0.819151i \(-0.305555\pi\)
−0.107005 + 0.994258i \(0.534126\pi\)
\(44\) 9.77761e6 − 1.48124e7i 0.393274 − 0.595785i
\(45\) −38563.6 + 18571.2i −0.00140191 + 0.000675126i
\(46\) 2.13264e6 − 1.54946e6i 0.0702277 − 0.0510234i
\(47\) 1.44608e7 − 1.26340e7i 0.432266 − 0.377659i −0.414126 − 0.910219i \(-0.635913\pi\)
0.846392 + 0.532560i \(0.178770\pi\)
\(48\) 4.25708e7 + 5.33821e7i 1.15751 + 1.45148i
\(49\) 2.33749e7 + 1.39659e7i 0.579252 + 0.346087i
\(50\) 2.91752e7 + 4.41986e7i 0.660160 + 1.00010i
\(51\) 2.06697e7 + 9.05597e7i 0.427826 + 1.87443i
\(52\) −9.32554e6 − 2.18182e7i −0.176872 − 0.413812i
\(53\) 5.23923e7 − 4.71539e6i 0.912066 − 0.0820874i 0.376342 − 0.926481i \(-0.377182\pi\)
0.535724 + 0.844393i \(0.320039\pi\)
\(54\) 1.98910e7 + 1.44517e7i 0.318336 + 0.231285i
\(55\) −139393. − 25296.1i −0.00205404 − 0.000372753i
\(56\) 2.52982e7 − 5.91880e7i 0.343750 − 0.804244i
\(57\) −27236.2 + 83824.3i −0.000341750 + 0.00105180i
\(58\) 2.49319e7 + 4.63311e7i 0.289287 + 0.537585i
\(59\) 1.02723e8 + 1.07439e8i 1.10365 + 1.15433i 0.986927 + 0.161165i \(0.0515252\pi\)
0.116725 + 0.993164i \(0.462761\pi\)
\(60\) −39407.3 + 73231.0i −0.000392551 + 0.000729481i
\(61\) −8.96444e7 + 2.47403e7i −0.828970 + 0.228781i −0.654673 − 0.755912i \(-0.727194\pi\)
−0.174297 + 0.984693i \(0.555765\pi\)
\(62\) −2.06417e7 − 1.52383e8i −0.177412 − 1.30971i
\(63\) 2.65069e7 − 1.95682e8i 0.211995 − 1.56501i
\(64\) −3.44998e7 − 9.52134e6i −0.257044 − 0.0709395i
\(65\) −130884. + 136894.i −0.000909443 + 0.000951203i
\(66\) 1.39266e8 + 4.28615e8i 0.903433 + 2.78048i
\(67\) −1.50273e8 − 1.35248e7i −0.911056 − 0.0819965i −0.375814 − 0.926695i \(-0.622637\pi\)
−0.535242 + 0.844699i \(0.679780\pi\)
\(68\) 7.46989e7 + 6.52625e7i 0.423667 + 0.370146i
\(69\) −911821. + 2.03033e7i −0.00484271 + 0.107831i
\(70\) 397210. 0.00197733
\(71\) 1.30151e8 − 1.70027e8i 0.607833 − 0.794065i
\(72\) −1.88075e8 −0.824773
\(73\) 1.80447e7 − 4.01797e8i 0.0743699 − 1.65597i −0.521764 − 0.853090i \(-0.674726\pi\)
0.596134 − 0.802885i \(-0.296703\pi\)
\(74\) 1.57389e8 + 1.37507e8i 0.610143 + 0.533066i
\(75\) −4.06663e8 − 3.66004e7i −1.48409 − 0.133570i
\(76\) 29084.5 + 89512.9i 0.000100000 + 0.000307769i
\(77\) 4.51674e8 − 4.72414e8i 1.46425 − 1.53149i
\(78\) 5.80782e8 + 1.60286e8i 1.77659 + 0.490308i
\(79\) 5.00966e7 − 3.69828e8i 0.144706 − 1.06826i −0.762324 − 0.647196i \(-0.775942\pi\)
0.907030 − 0.421066i \(-0.138344\pi\)
\(80\) −78121.9 − 576719.i −0.000213240 − 0.00157420i
\(81\) 2.73028e8 − 7.53509e7i 0.704733 − 0.194494i
\(82\) 1.12230e8 − 2.08558e8i 0.274123 − 0.509406i
\(83\) 1.88211e8 + 1.96854e8i 0.435306 + 0.455294i 0.903663 − 0.428245i \(-0.140868\pi\)
−0.468357 + 0.883540i \(0.655154\pi\)
\(84\) −1.81806e8 − 3.37851e8i −0.398428 − 0.740404i
\(85\) 244667. − 753007.i 0.000508381 − 0.00156464i
\(86\) −1.19063e8 + 2.78562e8i −0.234712 + 0.549136i
\(87\) −3.99120e8 − 7.24296e7i −0.746907 − 0.135544i
\(88\) −5.03614e8 − 3.65897e8i −0.895211 − 0.650409i
\(89\) −7.35201e8 + 6.61693e7i −1.24208 + 0.111790i −0.691120 − 0.722740i \(-0.742883\pi\)
−0.550964 + 0.834529i \(0.685740\pi\)
\(90\) −456145. − 1.06720e6i −0.000732843 − 0.00171457i
\(91\) −1.94433e8 − 8.51866e8i −0.297224 − 1.30222i
\(92\) 1.19561e7 + 1.81127e7i 0.0173998 + 0.0263596i
\(93\) 1.01775e9 + 6.08080e8i 1.41081 + 0.842922i
\(94\) 3.24638e8 + 4.07083e8i 0.428868 + 0.537784i
\(95\) 565.757 − 494.287i 7.12646e−7 − 6.22620e-7i
\(96\) −8.19795e8 + 5.95616e8i −0.985110 + 0.715724i
\(97\) 1.01922e9 − 4.90829e8i 1.16894 − 0.562934i 0.254273 − 0.967132i \(-0.418164\pi\)
0.914671 + 0.404199i \(0.132450\pi\)
\(98\) −4.06743e8 + 6.16190e8i −0.445454 + 0.674835i
\(99\) −1.78794e9 − 6.71026e8i −1.87066 − 0.702071i
\(100\) −3.74298e8 + 2.23632e8i −0.374298 + 0.223632i
\(101\) −6.33200e8 − 3.04933e8i −0.605473 − 0.291581i 0.105920 − 0.994375i \(-0.466221\pi\)
−0.711393 + 0.702794i \(0.751936\pi\)
\(102\) −2.47823e9 + 4.49732e8i −2.26694 + 0.411389i
\(103\) 2.85345e6 − 1.25018e7i 0.00249806 − 0.0109447i −0.973664 − 0.227990i \(-0.926785\pi\)
0.976162 + 0.217045i \(0.0696419\pi\)
\(104\) −7.79141e8 + 2.92417e8i −0.653079 + 0.245105i
\(105\) −1.90938e6 + 2.39429e6i −0.00153300 + 0.00192232i
\(106\) 6.39941e7 + 1.42494e9i 0.0492338 + 1.09628i
\(107\) 6.63061e7 + 1.47642e9i 0.0489020 + 1.08889i 0.862048 + 0.506827i \(0.169182\pi\)
−0.813146 + 0.582060i \(0.802247\pi\)
\(108\) −1.26208e8 + 1.58260e8i −0.0892650 + 0.111935i
\(109\) 1.40166e9 − 5.26052e8i 0.951095 − 0.356952i 0.172875 − 0.984944i \(-0.444694\pi\)
0.778220 + 0.627992i \(0.216123\pi\)
\(110\) 854796. − 3.74510e6i 0.000556667 − 0.00243892i
\(111\) −1.58542e9 + 2.87712e8i −0.991269 + 0.179889i
\(112\) 2.41910e9 + 1.16498e9i 1.45269 + 0.699577i
\(113\) 1.74256e9 − 1.04113e9i 1.00539 − 0.600692i 0.0869329 − 0.996214i \(-0.472293\pi\)
0.918457 + 0.395522i \(0.129436\pi\)
\(114\) −2.23750e6 − 839748.i −0.00124077 − 0.000465669i
\(115\) 95434.2 − 144577.i 5.08819e−5 − 7.70829e-5i
\(116\) −3.90270e8 + 1.87944e8i −0.200126 + 0.0963757i
\(117\) −2.06547e9 + 1.50065e9i −1.01902 + 0.740360i
\(118\) −3.03529e9 + 2.65185e9i −1.44122 + 1.25916i
\(119\) 2.27747e9 + 2.85586e9i 1.04110 + 1.30549i
\(120\) 2.50386e6 + 1.49599e6i 0.00110229 + 0.000658586i
\(121\) −2.18317e9 − 3.30737e9i −0.925878 − 1.40265i
\(122\) −5.61111e8 − 2.45839e9i −0.229313 − 1.00469i
\(123\) 7.17651e8 + 1.67903e9i 0.282709 + 0.661431i
\(124\) 1.26093e9 − 1.13486e8i 0.478955 − 0.0431067i
\(125\) 5.63125e6 + 4.09134e6i 0.00206305 + 0.00149889i
\(126\) 5.26838e9 + 9.56070e8i 1.86213 + 0.337926i
\(127\) −1.05818e9 + 2.47574e9i −0.360947 + 0.844478i 0.636377 + 0.771378i \(0.280432\pi\)
−0.997325 + 0.0731001i \(0.976711\pi\)
\(128\) 1.06679e9 − 3.28324e9i 0.351265 − 1.08108i
\(129\) −1.10677e9 − 2.05673e9i −0.351888 − 0.653918i
\(130\) −3.54895e6 − 3.71191e6i −0.00108982 − 0.00113986i
\(131\) −9.95948e8 + 1.85078e9i −0.295472 + 0.549078i −0.984442 − 0.175711i \(-0.943777\pi\)
0.688970 + 0.724790i \(0.258063\pi\)
\(132\) −3.57668e9 + 9.87101e8i −1.02541 + 0.282995i
\(133\) 465248. + 3.43460e6i 0.000128929 + 0.000951795i
\(134\) 5.49172e8 − 4.05415e9i 0.147142 − 1.08625i
\(135\) 1.55752e6 + 429848.i 0.000403581 + 0.000111381i
\(136\) 2.40421e9 − 2.51461e9i 0.602626 − 0.630298i
\(137\) 7.89925e8 + 2.43114e9i 0.191577 + 0.589613i 0.999999 + 0.00101067i \(0.000321707\pi\)
−0.808423 + 0.588603i \(0.799678\pi\)
\(138\) −5.48866e8 − 4.93988e7i −0.128828 − 0.0115947i
\(139\) −5.42814e9 − 4.74243e9i −1.23335 − 1.07754i −0.994309 − 0.106530i \(-0.966026\pi\)
−0.239036 − 0.971011i \(-0.576831\pi\)
\(140\) −146719. + 3.26694e6i −3.22782e−5 + 0.000718729i
\(141\) −4.01433e9 −0.855316
\(142\) 4.44737e9 + 3.73237e9i 0.917922 + 0.770348i
\(143\) −8.45025e9 −1.68989
\(144\) 3.51975e8 − 7.83732e9i 0.0682150 − 1.51893i
\(145\) 2.60379e6 + 2.27486e6i 0.000489158 + 0.000427365i
\(146\) 1.08619e10 + 9.77591e8i 1.97842 + 0.178061i
\(147\) −1.75904e9 − 5.41376e9i −0.310704 − 0.956250i
\(148\) −1.18909e9 + 1.24369e9i −0.203721 + 0.213076i
\(149\) 4.21938e9 + 1.16447e9i 0.701310 + 0.193549i 0.598466 − 0.801148i \(-0.295777\pi\)
0.102844 + 0.994697i \(0.467206\pi\)
\(150\) 1.48615e9 − 1.09712e10i 0.239691 − 1.76947i
\(151\) 4.18403e8 + 3.08878e9i 0.0654936 + 0.483493i 0.993757 + 0.111569i \(0.0355876\pi\)
−0.928263 + 0.371924i \(0.878698\pi\)
\(152\) 3.18212e6 − 878211.i 0.000483527 − 0.000133445i
\(153\) 5.05758e9 − 9.39856e9i 0.746159 − 1.38660i
\(154\) 1.22473e10 + 1.28096e10i 1.75467 + 1.83524i
\(155\) −4.78869e6 − 8.89887e6i −0.000666383 − 0.00123835i
\(156\) −1.53283e9 + 4.71756e9i −0.207221 + 0.637759i
\(157\) −1.69356e9 + 3.96228e9i −0.222460 + 0.520472i −0.993165 − 0.116721i \(-0.962762\pi\)
0.770704 + 0.637193i \(0.219905\pi\)
\(158\) 9.95696e9 + 1.80692e9i 1.27107 + 0.230665i
\(159\) −8.89681e9 − 6.46391e9i −1.10395 − 0.802063i
\(160\) 8.60252e6 − 774241.i 0.00103773 − 9.33977e-5i
\(161\) 3.14112e8 + 7.34901e8i 0.0368441 + 0.0862011i
\(162\) 1.70896e9 + 7.48745e9i 0.194946 + 0.854115i
\(163\) 4.18293e9 + 6.33687e9i 0.464127 + 0.703122i 0.988976 − 0.148073i \(-0.0473070\pi\)
−0.524850 + 0.851195i \(0.675878\pi\)
\(164\) 1.67388e9 + 1.00009e9i 0.180687 + 0.107955i
\(165\) 1.84656e7 + 2.31551e7i 0.00193948 + 0.00243203i
\(166\) −5.56134e9 + 4.85880e9i −0.568451 + 0.496641i
\(167\) 1.45649e10 − 1.05820e10i 1.44905 − 1.05280i 0.462996 − 0.886360i \(-0.346774\pi\)
0.986052 − 0.166435i \(-0.0532256\pi\)
\(168\) −1.21237e10 + 5.83848e9i −1.17421 + 0.565468i
\(169\) −3.81465e8 + 5.77894e8i −0.0359720 + 0.0544952i
\(170\) 2.00998e7 + 7.54359e6i 0.00184575 + 0.000692720i
\(171\) 8.69362e6 − 5.19419e6i 0.000777531 − 0.000464553i
\(172\) −2.24712e9 − 1.08216e9i −0.195771 − 0.0942783i
\(173\) −1.82547e10 + 3.31275e9i −1.54942 + 0.281178i −0.884787 − 0.465995i \(-0.845697\pi\)
−0.664630 + 0.747173i \(0.731411\pi\)
\(174\) 2.44751e9 − 1.07233e10i 0.202420 − 0.886860i
\(175\) −1.50325e10 + 5.64181e9i −1.21161 + 0.454723i
\(176\) 1.61899e10 − 2.03015e10i 1.27185 − 1.59485i
\(177\) −1.39416e9 − 3.10434e10i −0.106766 − 2.37733i
\(178\) −8.98005e8 − 1.99956e10i −0.0670484 − 1.49295i
\(179\) −1.70129e10 + 2.13335e10i −1.23863 + 1.55319i −0.528969 + 0.848641i \(0.677421\pi\)
−0.709657 + 0.704547i \(0.751150\pi\)
\(180\) 8.94593e6 − 3.35746e6i 0.000635184 − 0.000238388i
\(181\) −4.86005e9 + 2.12933e10i −0.336579 + 1.47465i 0.469548 + 0.882907i \(0.344417\pi\)
−0.806127 + 0.591742i \(0.798440\pi\)
\(182\) 2.33119e10 − 4.23048e9i 1.57491 − 0.285804i
\(183\) 1.75158e10 + 8.43517e9i 1.15452 + 0.555986i
\(184\) 6.53448e8 − 3.90417e8i 0.0420273 − 0.0251101i
\(185\) 1.28587e7 + 4.82594e6i 0.000807092 + 0.000302907i
\(186\) −1.77098e10 + 2.68292e10i −1.08494 + 1.64361i
\(187\) 3.18276e10 − 1.53274e10i 1.90334 − 0.916601i
\(188\) −3.46806e9 + 2.51969e9i −0.202477 + 0.147108i
\(189\) −5.61358e9 + 4.90443e9i −0.320009 + 0.279583i
\(190\) 12701.0 + 15926.5i 7.07044e−7 + 8.86605e-7i
\(191\) 4.65047e9 + 2.77853e9i 0.252841 + 0.151065i 0.633727 − 0.773556i \(-0.281524\pi\)
−0.380887 + 0.924622i \(0.624381\pi\)
\(192\) 4.12178e9 + 6.24422e9i 0.218891 + 0.331606i
\(193\) 6.26409e8 + 2.74448e9i 0.0324975 + 0.142381i 0.988574 − 0.150736i \(-0.0481645\pi\)
−0.956076 + 0.293117i \(0.905307\pi\)
\(194\) 1.20557e10 + 2.82057e10i 0.611060 + 1.42965i
\(195\) 3.94343e7 − 3.54915e6i 0.00195307 − 0.000175780i
\(196\) −4.91775e9 − 3.57295e9i −0.238020 − 0.172932i
\(197\) 3.44925e10 + 6.25947e9i 1.63165 + 0.296101i 0.915643 − 0.401992i \(-0.131682\pi\)
0.716007 + 0.698093i \(0.245968\pi\)
\(198\) 2.03519e10 − 4.76155e10i 0.941046 − 2.20169i
\(199\) 1.31089e9 − 4.03451e9i 0.0592554 − 0.182370i −0.917047 − 0.398778i \(-0.869434\pi\)
0.976303 + 0.216409i \(0.0694343\pi\)
\(200\) 7.24666e9 + 1.34666e10i 0.320260 + 0.595143i
\(201\) 2.17976e10 + 2.27985e10i 0.941946 + 0.985198i
\(202\) 9.03034e9 − 1.67812e10i 0.381613 − 0.709155i
\(203\) −1.53766e10 + 4.24367e9i −0.635518 + 0.175392i
\(204\) −2.78353e9 − 2.05488e10i −0.112528 − 0.830714i
\(205\) 2.08922e6 − 1.54232e7i 8.26211e−5 − 0.000609933i
\(206\) 3.35177e8 + 9.25030e7i 0.0129680 + 0.00357893i
\(207\) 1.61378e9 − 1.68788e9i 0.0610909 − 0.0638961i
\(208\) −1.07272e10 − 3.30151e10i −0.397377 − 1.22300i
\(209\) 3.33844e7 + 3.00465e6i 0.00121028 + 0.000108927i
\(210\) −6.25337e7 − 5.46341e7i −0.00221885 − 0.00193855i
\(211\) −1.04491e9 + 2.32667e10i −0.0362916 + 0.808096i 0.895491 + 0.445080i \(0.146825\pi\)
−0.931783 + 0.363017i \(0.881747\pi\)
\(212\) −1.17434e10 −0.399283
\(213\) −4.38762e10 + 8.86628e9i −1.46057 + 0.295144i
\(214\) −4.00740e10 −1.30617
\(215\) −893175. + 1.98881e7i −2.85078e−5 + 0.000634775i
\(216\) 5.34653e9 + 4.67112e9i 0.167121 + 0.146009i
\(217\) 4.64341e10 + 4.17915e9i 1.42157 + 0.127944i
\(218\) 1.25446e10 + 3.86082e10i 0.376185 + 1.15778i
\(219\) −5.81057e10 + 6.07738e10i −1.70695 + 1.78533i
\(220\) 3.04867e7 + 8.41379e6i 0.000877421 + 0.000242153i
\(221\) 6.33936e9 − 4.67990e10i 0.178764 − 1.31969i
\(222\) −5.86484e9 − 4.32960e10i −0.162057 − 1.19635i
\(223\) −2.77448e10 + 7.65707e9i −0.751293 + 0.207344i −0.620652 − 0.784086i \(-0.713132\pi\)
−0.130641 + 0.991430i \(0.541703\pi\)
\(224\) −1.88828e10 + 3.50901e10i −0.501130 + 0.931255i
\(225\) 3.24210e10 + 3.39097e10i 0.843345 + 0.882070i
\(226\) 2.60823e10 + 4.84690e10i 0.665055 + 1.23588i
\(227\) 9.20339e9 − 2.83251e10i 0.230055 − 0.708036i −0.767684 − 0.640828i \(-0.778591\pi\)
0.997739 − 0.0672075i \(-0.0214090\pi\)
\(228\) 7.73316e6 − 1.80926e7i 0.000189518 − 0.000443399i
\(229\) −6.20478e10 − 1.12600e10i −1.49096 − 0.270570i −0.628946 − 0.777449i \(-0.716513\pi\)
−0.862017 + 0.506879i \(0.830799\pi\)
\(230\) 3.80020e6 + 2.76100e6i 8.95428e−5 + 6.50567e-5i
\(231\) −1.36086e11 + 1.22479e10i −3.14455 + 0.283015i
\(232\) 5.97108e9 + 1.39700e10i 0.135318 + 0.316593i
\(233\) −1.24095e10 − 5.43695e10i −0.275837 − 1.20852i −0.903003 − 0.429634i \(-0.858642\pi\)
0.627166 − 0.778885i \(-0.284215\pi\)
\(234\) −3.81369e10 − 5.77750e10i −0.831523 − 1.25970i
\(235\) 2.93736e7 + 1.75499e7i 0.000628278 + 0.000375379i
\(236\) −2.06896e10 − 2.59439e10i −0.434158 − 0.544416i
\(237\) −5.87546e10 + 5.13323e10i −1.20969 + 1.05687i
\(238\) −8.01301e10 + 5.82179e10i −1.61882 + 1.17614i
\(239\) 5.02434e10 − 2.41959e10i 0.996067 − 0.479680i 0.136465 − 0.990645i \(-0.456426\pi\)
0.859602 + 0.510964i \(0.170712\pi\)
\(240\) −6.70256e7 + 1.01539e8i −0.00130404 + 0.00197553i
\(241\) 4.68404e10 + 1.75795e10i 0.894424 + 0.335683i 0.755909 − 0.654677i \(-0.227195\pi\)
0.138516 + 0.990360i \(0.455767\pi\)
\(242\) 9.22459e10 − 5.51143e10i 1.72893 − 1.03299i
\(243\) −6.94275e10 − 3.34345e10i −1.27733 − 0.615130i
\(244\) 2.04268e10 − 3.70692e9i 0.368932 − 0.0669512i
\(245\) −1.07968e7 + 4.73037e7i −0.000191446 + 0.000838780i
\(246\) −4.63546e10 + 1.73972e10i −0.807020 + 0.302880i
\(247\) 2.79393e7 − 3.50348e7i 0.000477617 − 0.000598913i
\(248\) −1.99218e9 − 4.43592e10i −0.0334422 − 0.744649i
\(249\) −2.55442e9 − 5.68786e10i −0.0421110 − 0.937673i
\(250\) −1.17677e8 + 1.47562e8i −0.00190529 + 0.00238916i
\(251\) 4.49400e10 − 1.68662e10i 0.714662 − 0.268217i 0.0325556 − 0.999470i \(-0.489635\pi\)
0.682107 + 0.731253i \(0.261064\pi\)
\(252\) −9.80940e9 + 4.29778e10i −0.153229 + 0.671338i
\(253\) 7.60500e9 − 1.38010e9i 0.116696 − 0.0211772i
\(254\) −6.57756e10 − 3.16759e10i −0.991546 − 0.477504i
\(255\) −1.42090e8 + 8.48950e7i −0.00210443 + 0.00125734i
\(256\) 7.04830e10 + 2.64527e10i 1.02566 + 0.384938i
\(257\) 5.38868e10 − 8.16350e10i 0.770519 − 1.16729i −0.211291 − 0.977423i \(-0.567767\pi\)
0.981811 − 0.189863i \(-0.0608045\pi\)
\(258\) 5.70591e10 − 2.74782e10i 0.801745 − 0.386100i
\(259\) −5.12625e10 + 3.72444e10i −0.707865 + 0.514294i
\(260\) 3.18403e7 − 2.78181e7i 0.000432113 − 0.000377526i
\(261\) 2.90597e10 + 3.64397e10i 0.387622 + 0.486063i
\(262\) −4.89224e10 − 2.92298e10i −0.641434 − 0.383239i
\(263\) −2.15555e10 − 3.26552e10i −0.277817 − 0.420874i 0.668699 − 0.743534i \(-0.266852\pi\)
−0.946515 + 0.322660i \(0.895423\pi\)
\(264\) 2.89580e10 + 1.26873e11i 0.366902 + 1.60750i
\(265\) 3.68406e7 + 8.61930e7i 0.000458903 + 0.00107366i
\(266\) −9.36025e7 + 8.42437e6i −0.00114636 + 0.000103174i
\(267\) 1.24846e11 + 9.07056e10i 1.50339 + 1.09228i
\(268\) 3.31414e10 + 6.01428e9i 0.392432 + 0.0712159i
\(269\) 3.93197e10 − 9.19929e10i 0.457851 − 1.07120i −0.518514 − 0.855069i \(-0.673515\pi\)
0.976365 − 0.216127i \(-0.0693426\pi\)
\(270\) −1.35385e7 + 4.16672e7i −0.000155036 + 0.000477152i
\(271\) −5.76953e10 − 1.07216e11i −0.649799 − 1.20753i −0.965928 − 0.258812i \(-0.916669\pi\)
0.316129 − 0.948716i \(-0.397617\pi\)
\(272\) 1.00288e11 + 1.04893e11i 1.11093 + 1.16194i
\(273\) −8.65594e10 + 1.60854e11i −0.943153 + 1.75267i
\(274\) −6.68157e10 + 1.84400e10i −0.716145 + 0.197643i
\(275\) 2.08439e10 + 1.53876e11i 0.219777 + 1.62246i
\(276\) 6.09028e8 − 4.49602e9i 0.00631751 − 0.0466378i
\(277\) −5.94376e10 − 1.64037e10i −0.606600 − 0.167411i −0.0507750 − 0.998710i \(-0.516169\pi\)
−0.555825 + 0.831299i \(0.687598\pi\)
\(278\) 1.35066e11 − 1.41268e11i 1.35627 − 1.41855i
\(279\) −4.20953e10 − 1.29556e11i −0.415924 − 1.28008i
\(280\) 1.14236e8 + 1.02815e7i 0.00111069 + 9.99641e-5i
\(281\) −1.02632e11 − 8.96666e10i −0.981981 − 0.857931i 0.00787992 − 0.999969i \(-0.497492\pi\)
−0.989861 + 0.142038i \(0.954635\pi\)
\(282\) 4.88353e9 − 1.08740e11i 0.0459846 − 1.02393i
\(283\) 1.05955e11 0.981935 0.490968 − 0.871178i \(-0.336643\pi\)
0.490968 + 0.871178i \(0.336643\pi\)
\(284\) −3.23404e10 + 3.51997e10i −0.294994 + 0.321075i
\(285\) −157055. −1.41010e−6
\(286\) 1.02799e10 − 2.28901e11i 0.0908538 − 2.02302i
\(287\) 5.40742e10 + 4.72432e10i 0.470459 + 0.411027i
\(288\) 1.15963e11 + 1.04368e10i 0.993235 + 0.0893927i
\(289\) 2.43631e10 + 7.49819e10i 0.205443 + 0.632290i
\(290\) −6.47890e7 + 6.77640e7i −0.000537911 + 0.000562611i
\(291\) −2.27968e11 − 6.29153e10i −1.86362 − 0.514325i
\(292\) −1.20525e10 + 8.89752e10i −0.0970185 + 0.716219i
\(293\) −2.17584e9 − 1.60627e10i −0.0172474 − 0.127325i 0.980279 − 0.197619i \(-0.0633207\pi\)
−0.997526 + 0.0702934i \(0.977606\pi\)
\(294\) 1.48788e11 − 4.10629e10i 1.16146 − 0.320543i
\(295\) −1.25515e8 + 2.33245e8i −0.000964929 + 0.00179314i
\(296\) 4.17053e10 + 4.36204e10i 0.315776 + 0.330276i
\(297\) 3.41611e10 + 6.34820e10i 0.254758 + 0.473420i
\(298\) −3.66763e10 + 1.12878e11i −0.269409 + 0.829156i
\(299\) 4.06113e9 − 9.50148e9i 0.0293850 − 0.0687497i
\(300\) 8.96859e10 + 1.62756e10i 0.639261 + 0.116009i
\(301\) −7.43051e10 − 5.39858e10i −0.521759 − 0.379080i
\(302\) −8.41779e10 + 7.57614e9i −0.582327 + 0.0524103i
\(303\) 5.77443e10 + 1.35099e11i 0.393566 + 0.920793i
\(304\) 3.06410e7 + 1.34247e8i 0.000205765 + 0.000901515i
\(305\) −9.12895e7 − 1.38298e8i −0.000604048 − 0.000915094i
\(306\) 2.48436e11 + 1.48433e11i 1.61982 + 0.967799i
\(307\) 1.81871e11 + 2.28059e11i 1.16853 + 1.46530i 0.857192 + 0.514997i \(0.172207\pi\)
0.311342 + 0.950298i \(0.399221\pi\)
\(308\) −1.09880e11 + 9.59989e10i −0.695727 + 0.607838i
\(309\) −2.16878e9 + 1.57571e9i −0.0135332 + 0.00983247i
\(310\) 2.46878e8 − 1.18890e8i 0.00151829 − 0.000731171i
\(311\) −3.01291e10 + 4.56436e10i −0.182627 + 0.276668i −0.914342 − 0.404943i \(-0.867291\pi\)
0.731715 + 0.681610i \(0.238720\pi\)
\(312\) 1.62882e11 + 6.11307e10i 0.973146 + 0.365228i
\(313\) −9.08424e10 + 5.42758e10i −0.534982 + 0.319637i −0.754855 − 0.655892i \(-0.772293\pi\)
0.219873 + 0.975528i \(0.429436\pi\)
\(314\) −1.05270e11 − 5.06954e10i −0.611114 − 0.294297i
\(315\) 3.46218e8 − 6.28293e7i 0.00198131 − 0.000359555i
\(316\) −1.85392e10 + 8.12257e10i −0.104592 + 0.458249i
\(317\) 1.59884e11 − 6.00055e10i 0.889279 − 0.333752i 0.135420 − 0.990788i \(-0.456762\pi\)
0.753859 + 0.657036i \(0.228190\pi\)
\(318\) 1.85918e11 − 2.33134e11i 1.01953 − 1.27845i
\(319\) 6.92113e9 + 1.54111e11i 0.0374213 + 0.833250i
\(320\) −2.86121e6 − 6.37098e7i −1.52537e−5 − 0.000339650i
\(321\) 1.92635e11 − 2.41556e11i 1.01266 − 1.26983i
\(322\) −2.02891e10 + 7.61465e9i −0.105175 + 0.0394728i
\(323\) −4.16852e7 + 1.82635e8i −0.000213094 + 0.000933624i
\(324\) −6.22134e10 + 1.12901e10i −0.313640 + 0.0569173i
\(325\) 1.87034e11 + 9.00706e10i 0.929918 + 0.447825i
\(326\) −1.76742e11 + 1.05598e11i −0.866683 + 0.517819i
\(327\) −2.93022e11 − 1.09973e11i −1.41721 − 0.531890i
\(328\) 3.76753e10 − 5.70756e10i 0.179732 − 0.272282i
\(329\) −1.42227e11 + 6.84931e10i −0.669270 + 0.322304i
\(330\) −6.49691e8 + 4.72028e8i −0.00301574 + 0.00219106i
\(331\) −1.94977e11 + 1.70346e11i −0.892807 + 0.780022i −0.976285 − 0.216488i \(-0.930540\pi\)
0.0834784 + 0.996510i \(0.473397\pi\)
\(332\) −3.79080e10 − 4.75352e10i −0.171242 − 0.214730i
\(333\) 1.58934e11 + 9.49589e10i 0.708303 + 0.423191i
\(334\) 2.68927e11 + 4.07407e11i 1.18243 + 1.79130i
\(335\) −5.98263e7 − 2.62116e8i −0.000259532 − 0.00113708i
\(336\) −2.20608e11 − 5.16138e11i −0.944266 − 2.20922i
\(337\) −1.48386e11 + 1.33550e10i −0.626699 + 0.0564040i −0.398437 − 0.917196i \(-0.630447\pi\)
−0.228262 + 0.973600i \(0.573304\pi\)
\(338\) −1.51900e10 − 1.10361e10i −0.0633040 − 0.0459931i
\(339\) −4.17537e11 − 7.57717e10i −1.71710 − 0.311608i
\(340\) −6.94682e7 + 1.62529e8i −0.000281923 + 0.000659592i
\(341\) 1.39329e11 − 4.28811e11i 0.558017 − 1.71740i
\(342\) 1.30124e8 + 2.41812e8i 0.000514329 + 0.000955784i
\(343\) 7.45614e10 + 7.79851e10i 0.290864 + 0.304220i
\(344\) −4.14526e10 + 7.70318e10i −0.159602 + 0.296591i
\(345\) −3.49101e7 + 9.63458e6i −0.000132668 + 3.66140e-5i
\(346\) −6.75285e10 − 4.98515e11i −0.253305 − 1.86998i
\(347\) 4.50265e10 − 3.32399e11i 0.166719 − 1.23077i −0.693353 − 0.720598i \(-0.743867\pi\)
0.860072 − 0.510173i \(-0.170418\pi\)
\(348\) 8.72917e10 + 2.40910e10i 0.319056 + 0.0880537i
\(349\) 8.24166e10 − 8.62010e10i 0.297372 − 0.311027i −0.557181 − 0.830391i \(-0.688117\pi\)
0.854553 + 0.519364i \(0.173831\pi\)
\(350\) −1.34538e11 − 4.14065e11i −0.479224 − 1.47490i
\(351\) 9.59873e10 + 8.63901e9i 0.337545 + 0.0303796i
\(352\) 2.90212e11 + 2.53551e11i 1.00757 + 0.880284i
\(353\) −1.08361e9 + 2.41285e10i −0.00371440 + 0.0827075i −0.999994 − 0.00347263i \(-0.998895\pi\)
0.996280 + 0.0861801i \(0.0274661\pi\)
\(354\) 8.42599e11 2.85172
\(355\) 3.59813e8 + 1.26943e8i 0.00120240 + 0.000424209i
\(356\) 1.64790e11 0.543759
\(357\) 3.42599e10 − 7.62857e11i 0.111630 − 2.48563i
\(358\) −5.57186e11 − 4.86799e11i −1.79278 − 1.56630i
\(359\) 5.17187e11 + 4.65477e10i 1.64332 + 0.147902i 0.872321 − 0.488933i \(-0.162614\pi\)
0.771000 + 0.636835i \(0.219757\pi\)
\(360\) −1.03562e8 − 3.18731e8i −0.000324967 − 0.00100015i
\(361\) 2.22997e11 − 2.33237e11i 0.691062 − 0.722794i
\(362\) −5.70880e11 − 1.57553e11i −1.74726 − 0.482212i
\(363\) −1.11208e11 + 8.20969e11i −0.336167 + 2.48169i
\(364\) 2.61838e10 + 1.93296e11i 0.0781764 + 0.577122i
\(365\) 6.90863e8 − 1.90666e8i 0.00203739 − 0.000562284i
\(366\) −2.49800e11 + 4.64207e11i −0.727659 + 1.35222i
\(367\) −4.05218e11 − 4.23825e11i −1.16598 − 1.21952i −0.971095 − 0.238695i \(-0.923281\pi\)
−0.194886 − 0.980826i \(-0.562434\pi\)
\(368\) 1.50463e10 + 2.79607e10i 0.0427675 + 0.0794754i
\(369\) 6.48332e10 − 1.99536e11i 0.182045 − 0.560277i
\(370\) −1.46368e8 + 3.42445e8i −0.000406011 + 0.000949911i
\(371\) −4.25502e11 − 7.72172e10i −1.16606 − 0.211608i
\(372\) −2.14121e11 − 1.55568e11i −0.579717 − 0.421189i
\(373\) 1.78889e11 − 1.61003e10i 0.478513 − 0.0430669i 0.152242 − 0.988343i \(-0.451351\pi\)
0.326271 + 0.945276i \(0.394208\pi\)
\(374\) 3.76469e11 + 8.80793e11i 0.994963 + 2.32783i
\(375\) −3.23799e8 − 1.41866e9i −0.000845542 − 0.00370456i
\(376\) 8.28278e10 + 1.25479e11i 0.213713 + 0.323761i
\(377\) 1.77042e11 + 1.05778e11i 0.451378 + 0.269686i
\(378\) −1.26022e11 − 1.58027e11i −0.317493 − 0.398124i
\(379\) −4.34748e11 + 3.79828e11i −1.08233 + 0.945606i −0.998704 − 0.0508913i \(-0.983794\pi\)
−0.0836286 + 0.996497i \(0.526651\pi\)
\(380\) −135683. + 98579.3i −3.33809e−7 + 2.42527e-7i
\(381\) 5.07116e11 − 2.44214e11i 1.23295 − 0.593757i
\(382\) −8.09222e10 + 1.22592e11i −0.194439 + 0.294562i
\(383\) −2.14409e11 − 8.04692e10i −0.509154 − 0.191089i 0.0835583 − 0.996503i \(-0.473372\pi\)
−0.592712 + 0.805414i \(0.701943\pi\)
\(384\) −6.19539e11 + 3.70157e11i −1.45405 + 0.868752i
\(385\) 1.04931e9 + 5.05322e8i 0.00243406 + 0.00117218i
\(386\) −7.51045e10 + 1.36295e10i −0.172196 + 0.0312490i
\(387\) −5.97164e10 + 2.61635e11i −0.135330 + 0.592920i
\(388\) −2.36437e11 + 8.87362e10i −0.529630 + 0.198773i
\(389\) 3.12301e11 − 3.91613e11i 0.691513 − 0.867130i −0.304845 − 0.952402i \(-0.598605\pi\)
0.996358 + 0.0852724i \(0.0271760\pi\)
\(390\) 4.81666e7 + 1.07251e9i 0.000105428 + 0.00234753i
\(391\) 1.93801e9 + 4.31532e10i 0.00419335 + 0.0933723i
\(392\) −1.32928e11 + 1.66686e11i −0.284334 + 0.356543i
\(393\) 4.11359e11 − 1.54386e11i 0.869870 − 0.326468i
\(394\) −2.11518e11 + 9.26720e11i −0.442195 + 1.93738i
\(395\) 6.54334e8 − 1.18744e8i 0.00135242 − 0.000245429i
\(396\) 3.84107e11 + 1.84976e11i 0.784917 + 0.377996i
\(397\) −1.71488e11 + 1.02459e11i −0.346479 + 0.207011i −0.675586 − 0.737281i \(-0.736109\pi\)
0.329107 + 0.944293i \(0.393252\pi\)
\(398\) 1.07692e11 + 4.04176e10i 0.215135 + 0.0807414i
\(399\) 3.99165e8 − 6.04709e8i 0.000788450 − 0.00119445i
\(400\) −5.74731e11 + 2.76776e11i −1.12252 + 0.540578i
\(401\) −3.38993e11 + 2.46293e11i −0.654699 + 0.475667i −0.864869 − 0.501998i \(-0.832598\pi\)
0.210170 + 0.977665i \(0.432598\pi\)
\(402\) −6.44083e11 + 5.62718e11i −1.23006 + 1.07467i
\(403\) −3.75821e11 − 4.71264e11i −0.709754 − 0.890004i
\(404\) 1.34685e11 + 8.04705e10i 0.251538 + 0.150287i
\(405\) 2.78038e8 + 4.21210e8i 0.000513520 + 0.000777949i
\(406\) −9.62467e10 − 4.21684e11i −0.175800 − 0.770229i
\(407\) 2.40842e11 + 5.63479e11i 0.435069 + 1.01789i
\(408\) −7.24372e11 + 6.51946e10i −1.29417 + 0.116477i
\(409\) −5.07898e11 − 3.69009e11i −0.897473 − 0.652053i 0.0403425 − 0.999186i \(-0.487155\pi\)
−0.937816 + 0.347133i \(0.887155\pi\)
\(410\) 4.15243e8 + 7.53554e7i 0.000725729 + 0.000131700i
\(411\) 2.10030e11 − 4.91389e11i 0.363072 − 0.849450i
\(412\) −8.84617e8 + 2.72257e9i −0.00151258 + 0.00465523i
\(413\) −5.79062e11 − 1.07608e12i −0.979377 − 1.81999i
\(414\) 4.37581e10 + 4.57674e10i 0.0732077 + 0.0765692i
\(415\) −2.29972e8 + 4.27359e8i −0.000380590 + 0.000707255i
\(416\) 4.96628e11 − 1.37061e11i 0.813038 − 0.224384i
\(417\) 2.02271e11 + 1.49322e12i 0.327582 + 2.41831i
\(418\) −1.22003e8 + 9.00662e8i −0.000195469 + 0.00144301i
\(419\) 3.25186e11 + 8.97455e10i 0.515428 + 0.142249i 0.514067 − 0.857750i \(-0.328138\pi\)
0.00136108 + 0.999999i \(0.499567\pi\)
\(420\) 4.72448e8 − 4.94142e8i 0.000740853 − 0.000774872i
\(421\) 2.16175e11 + 6.65317e11i 0.335379 + 1.03219i 0.966535 + 0.256534i \(0.0825805\pi\)
−0.631157 + 0.775655i \(0.717420\pi\)
\(422\) −6.28977e11 − 5.66089e10i −0.965447 − 0.0868918i
\(423\) 3.47353e11 + 3.03473e11i 0.527521 + 0.460881i
\(424\) −1.84789e10 + 4.11465e11i −0.0277671 + 0.618282i
\(425\) −8.67829e11 −1.29028
\(426\) −1.86793e11 − 1.19931e12i −0.274801 − 1.76436i
\(427\) 7.64506e11 1.11290
\(428\) 1.48022e10 − 3.29597e11i 0.0213221 − 0.474773i
\(429\) 1.33034e12 + 1.16228e12i 1.89629 + 1.65674i
\(430\) −5.37642e8 − 4.83887e7i −0.000758377 − 6.82552e-5i
\(431\) −2.16750e11 − 6.67088e11i −0.302560 − 0.931183i −0.980577 − 0.196137i \(-0.937160\pi\)
0.678017 − 0.735046i \(-0.262840\pi\)
\(432\) −2.04658e11 + 2.14055e11i −0.282716 + 0.295698i
\(433\) 1.12328e12 + 3.10005e11i 1.53565 + 0.423812i 0.928670 − 0.370906i \(-0.120953\pi\)
0.606979 + 0.794718i \(0.292381\pi\)
\(434\) −1.69693e11 + 1.25272e12i −0.229594 + 1.69493i
\(435\) −9.70258e7 − 7.16273e8i −0.000129923 − 0.000959129i
\(436\) −3.22175e11 + 8.89147e10i −0.426975 + 0.117838i
\(437\) −1.94227e7 + 3.60935e7i −2.54767e−5 + 4.73437e-5i
\(438\) −1.57556e12 − 1.64790e12i −2.04550 − 2.13943i
\(439\) −1.57874e11 − 2.93379e11i −0.202871 − 0.376997i 0.758749 − 0.651383i \(-0.225811\pi\)
−0.961620 + 0.274386i \(0.911525\pi\)
\(440\) 3.42776e8 − 1.05495e9i 0.000435986 − 0.00134183i
\(441\) −2.57061e11 + 6.01423e11i −0.323640 + 0.757193i
\(442\) 1.25998e12 + 2.28653e11i 1.57023 + 0.284955i
\(443\) 3.12532e11 + 2.27068e11i 0.385547 + 0.280116i 0.763628 − 0.645656i \(-0.223416\pi\)
−0.378081 + 0.925772i \(0.623416\pi\)
\(444\) 3.58263e11 − 3.22443e10i 0.437501 − 0.0393758i
\(445\) −5.16970e8 − 1.20951e9i −0.000624951 − 0.00146214i
\(446\) −1.73663e11 − 7.60866e11i −0.207826 − 0.910545i
\(447\) −5.04099e11 − 7.63678e11i −0.597217 − 0.904745i
\(448\) 2.52574e11 + 1.50906e11i 0.296236 + 0.176993i
\(449\) 7.20303e11 + 9.03232e11i 0.836386 + 1.04880i 0.998079 + 0.0619541i \(0.0197333\pi\)
−0.161693 + 0.986841i \(0.551695\pi\)
\(450\) −9.57988e11 + 8.36969e11i −1.10130 + 0.962173i
\(451\) 5.61801e11 − 4.08172e11i 0.639422 − 0.464567i
\(452\) −4.08278e11 + 1.96616e11i −0.460080 + 0.221563i
\(453\) 3.58974e11 − 5.43822e11i 0.400517 − 0.606757i
\(454\) 7.56075e11 + 2.83760e11i 0.835244 + 0.313472i
\(455\) 1.33660e9 − 7.98580e8i 0.00146201 − 0.000873508i
\(456\) −6.21762e8 − 2.99425e8i −0.000673414 − 0.000324299i
\(457\) 1.00245e12 − 1.81918e11i 1.07508 − 0.195098i 0.387984 − 0.921666i \(-0.373172\pi\)
0.687094 + 0.726568i \(0.258886\pi\)
\(458\) 3.80494e11 − 1.66705e12i 0.404067 − 1.77033i
\(459\) −3.77203e11 + 1.41567e11i −0.396659 + 0.148869i
\(460\) −2.41122e7 + 3.02357e7i −2.51088e−5 + 3.14854e-5i
\(461\) 9.55489e9 + 2.12756e11i 0.00985307 + 0.219396i 0.997878 + 0.0651043i \(0.0207380\pi\)
−0.988025 + 0.154291i \(0.950691\pi\)
\(462\) −1.66221e11 − 3.70120e12i −0.169745 − 3.77966i
\(463\) 1.12700e12 − 1.41321e12i 1.13975 − 1.42920i 0.252690 − 0.967547i \(-0.418685\pi\)
0.887060 − 0.461654i \(-0.152744\pi\)
\(464\) −5.93324e11 + 2.22678e11i −0.594239 + 0.223022i
\(465\) −4.70096e8 + 2.05963e9i −0.000466282 + 0.00204291i
\(466\) 1.48786e12 − 2.70007e11i 1.46159 − 0.265239i
\(467\) −1.48235e11 − 7.13862e10i −0.144220 − 0.0694525i 0.360382 − 0.932805i \(-0.382646\pi\)
−0.504602 + 0.863352i \(0.668361\pi\)
\(468\) 4.89269e11 − 2.92325e11i 0.471457 − 0.281682i
\(469\) 1.16128e12 + 4.35835e11i 1.10830 + 0.415953i
\(470\) −5.11126e8 + 7.74323e8i −0.000483156 + 0.000731950i
\(471\) 8.11611e11 − 3.90851e11i 0.759896 − 0.365947i
\(472\) −9.41580e11 + 6.84098e11i −0.873209 + 0.634424i
\(473\) −6.68911e11 + 5.84410e11i −0.614459 + 0.536837i
\(474\) −1.31901e12 − 1.65399e12i −1.20018 − 1.50498i
\(475\) −7.06887e8 − 4.22345e8i −0.000637131 − 0.000380668i
\(476\) −4.49228e11 − 6.80551e11i −0.401084 − 0.607617i
\(477\) 2.81171e11 + 1.23189e12i 0.248678 + 1.08953i
\(478\) 5.94298e11 + 1.39043e12i 0.520689 + 1.21821i
\(479\) −9.36157e11 + 8.42557e10i −0.812529 + 0.0731290i −0.488107 − 0.872784i \(-0.662313\pi\)
−0.324422 + 0.945913i \(0.605170\pi\)
\(480\) −1.46081e9 − 1.06134e9i −0.00125605 − 0.000912574i
\(481\) 8.06061e11 + 1.46279e11i 0.686618 + 0.124603i
\(482\) −5.33176e11 + 1.24743e12i −0.449944 + 1.05270i
\(483\) 5.16302e10 − 1.58902e11i 0.0431660 − 0.132851i
\(484\) 4.19227e11 + 7.79054e11i 0.347252 + 0.645303i
\(485\) 1.39303e9 + 1.45700e9i 0.00114320 + 0.00119570i
\(486\) 9.90135e11 − 1.83998e12i 0.805066 − 1.49606i
\(487\) −1.11699e12 + 3.08271e11i −0.899851 + 0.248343i −0.685206 − 0.728349i \(-0.740288\pi\)
−0.214645 + 0.976692i \(0.568859\pi\)
\(488\) −9.77403e10 − 7.21548e11i −0.0780162 − 0.575938i
\(489\) 2.13073e11 − 1.57297e12i 0.168515 − 1.24403i
\(490\) −1.26823e9 − 3.50009e8i −0.000993838 − 0.000274282i
\(491\) 7.51079e11 − 7.85567e11i 0.583202 − 0.609981i −0.363695 − 0.931518i \(-0.618485\pi\)
0.946897 + 0.321537i \(0.104199\pi\)
\(492\) −1.25965e11 − 3.87679e11i −0.0969183 − 0.298284i
\(493\) −8.58687e11 − 7.72832e10i −0.654672 − 0.0589215i
\(494\) 9.15035e8 + 7.99442e8i 0.000691299 + 0.000603970i
\(495\) 1.52673e8 − 3.39953e9i 0.000114298 − 0.00254505i
\(496\) 1.85224e12 1.37413
\(497\) −1.40325e12 + 1.06276e12i −1.03165 + 0.781321i
\(498\) 1.54384e12 1.12478
\(499\) 4.14239e10 − 9.22375e11i 0.0299088 − 0.665971i −0.926910 − 0.375285i \(-0.877545\pi\)
0.956818 − 0.290686i \(-0.0938836\pi\)
\(500\) −1.17019e9 − 1.02237e9i −0.000837321 − 0.000731545i
\(501\) −3.74848e12 − 3.37369e11i −2.65819 − 0.239241i
\(502\) 4.02203e11 + 1.23785e12i 0.282669 + 0.869966i
\(503\) 1.40116e12 − 1.46550e12i 0.975962 − 1.02078i −0.0238159 − 0.999716i \(-0.507582\pi\)
0.999778 − 0.0210602i \(-0.00670415\pi\)
\(504\) 1.49042e12 + 4.11330e11i 1.02890 + 0.283957i
\(505\) 1.68104e8 − 1.24100e9i 0.000115019 − 0.000849101i
\(506\) 2.81326e10 + 2.07683e11i 0.0190780 + 0.140839i
\(507\) 1.39541e11 − 3.85109e10i 0.0937920 − 0.0258850i
\(508\) 2.84821e11 − 5.29285e11i 0.189751 − 0.352617i
\(509\) −1.27369e12 − 1.33218e12i −0.841076 − 0.879697i 0.153017 − 0.988223i \(-0.451101\pi\)
−0.994094 + 0.108527i \(0.965387\pi\)
\(510\) −2.12678e9 − 3.95222e9i −0.00139206 − 0.00258688i
\(511\) −1.02175e12 + 3.14462e12i −0.662904 + 2.04021i
\(512\) −1.07612e11 + 2.51771e11i −0.0692064 + 0.161916i
\(513\) −3.76145e8 − 6.82603e7i −0.000239788 − 4.35151e-5i
\(514\) 2.14578e12 + 1.55900e12i 1.35597 + 0.985171i
\(515\) 2.27581e7 − 2.04826e6i 1.42562e−5 − 1.28308e-6i
\(516\) 2.04925e11 + 4.79445e11i 0.127254 + 0.297725i
\(517\) 3.39715e11 + 1.48839e12i 0.209126 + 0.916240i
\(518\) −9.46514e11 − 1.43391e12i −0.577621 − 0.875058i
\(519\) 3.32954e12 + 1.98931e12i 2.01433 + 1.20351i
\(520\) −9.24588e8 − 1.15940e9i −0.000554540 − 0.000695372i
\(521\) −2.03052e12 + 1.77401e12i −1.20736 + 1.05484i −0.210344 + 0.977627i \(0.567459\pi\)
−0.997015 + 0.0772107i \(0.975399\pi\)
\(522\) −1.02243e12 + 7.42840e11i −0.602722 + 0.437903i
\(523\) −1.13743e12 + 5.47759e11i −0.664765 + 0.320134i −0.735661 − 0.677350i \(-0.763128\pi\)
0.0708963 + 0.997484i \(0.477414\pi\)
\(524\) 2.58477e11 − 3.91576e11i 0.149772 − 0.226895i
\(525\) 3.14261e12 + 1.17944e12i 1.80540 + 0.677577i
\(526\) 9.10789e11 − 5.44171e11i 0.518778 − 0.309956i
\(527\) 2.27031e12 + 1.09332e12i 1.28215 + 0.617449i
\(528\) −5.34116e12 + 9.69278e11i −2.99077 + 0.542745i
\(529\) 3.98691e11 − 1.74678e12i 0.221353 − 0.969812i
\(530\) −2.37961e9 + 8.93084e8i −0.00130998 + 0.000491644i
\(531\) −2.22617e12 + 2.79153e12i −1.21516 + 1.52376i
\(532\) −3.47139e7 − 7.72965e8i −1.87889e−5 − 0.000418367i
\(533\) −4.16507e10 − 9.27424e11i −0.0223537 − 0.497744i
\(534\) −2.60891e12 + 3.27147e12i −1.38843 + 1.74104i
\(535\) −2.46558e9 + 9.25349e8i −0.00130115 + 0.000488330i
\(536\) 2.62878e11 − 1.15175e12i 0.137567 − 0.602719i
\(537\) 5.61269e12 − 1.01855e12i 2.91264 − 0.528566i
\(538\) 2.44407e12 + 1.17700e12i 1.25775 + 0.605700i
\(539\) −1.85840e12 + 1.11034e12i −0.948396 + 0.566640i
\(540\) −3.37700e8 − 1.26741e8i −0.000170907 − 6.41423e-5i
\(541\) 5.30110e10 − 8.03082e10i 0.0266059 − 0.0403062i −0.821027 − 0.570889i \(-0.806598\pi\)
0.847633 + 0.530583i \(0.178027\pi\)
\(542\) 2.97445e12 − 1.43242e12i 1.48051 − 0.712974i
\(543\) 3.69390e12 − 2.68377e12i 1.82342 − 1.32479i
\(544\) −1.62193e12 + 1.41703e12i −0.794029 + 0.693722i
\(545\) 1.66332e9 + 2.08573e9i 0.000807590 + 0.00101269i
\(546\) −4.25192e12 − 2.54041e12i −2.04747 − 1.22331i
\(547\) −2.27404e11 − 3.44502e11i −0.108606 − 0.164532i 0.776206 − 0.630480i \(-0.217142\pi\)
−0.884812 + 0.465948i \(0.845713\pi\)
\(548\) −1.26984e11 − 5.56352e11i −0.0601499 − 0.263534i
\(549\) −8.77936e11 − 2.05403e12i −0.412465 − 0.965010i
\(550\) −4.19355e12 + 3.77426e11i −1.95411 + 0.175873i
\(551\) −6.61829e8 − 4.80847e8i −0.000305889 − 0.000222241i
\(552\) −1.56574e11 − 2.84139e10i −0.0717782 − 0.0130258i
\(553\) −1.20583e12 + 2.82118e12i −0.548306 + 1.28283i
\(554\) 5.16652e11 − 1.59009e12i 0.233026 − 0.717180i
\(555\) −1.36059e9 − 2.52840e9i −0.000608707 − 0.00113117i
\(556\) 1.11200e12 + 1.16306e12i 0.493480 + 0.516139i
\(557\) −8.92788e10 + 1.65908e11i −0.0393007 + 0.0730329i −0.899488 − 0.436945i \(-0.856061\pi\)
0.860188 + 0.509978i \(0.170346\pi\)
\(558\) 3.56062e12 − 9.82669e11i 1.55479 − 0.429095i
\(559\) 1.59398e11 + 1.17673e12i 0.0690447 + 0.509709i
\(560\) −6.42231e8 + 4.74114e9i −0.000275959 + 0.00203721i
\(561\) −7.11888e12 − 1.96469e12i −3.03444 − 0.837453i
\(562\) 2.55375e12 − 2.67101e12i 1.07985 − 1.12944i
\(563\) 7.24142e11 + 2.22868e12i 0.303764 + 0.934889i 0.980136 + 0.198328i \(0.0635512\pi\)
−0.676372 + 0.736560i \(0.736449\pi\)
\(564\) 8.92553e11 + 8.03312e10i 0.371431 + 0.0334294i
\(565\) 2.72393e9 + 2.37983e9i 0.00112455 + 0.000982490i
\(566\) −1.28897e11 + 2.87011e12i −0.0527921 + 1.17551i
\(567\) −2.32844e12 −0.946109
\(568\) 1.18244e12 + 1.18853e12i 0.476664 + 0.479120i
\(569\) 5.80854e11 0.232307 0.116153 − 0.993231i \(-0.462944\pi\)
0.116153 + 0.993231i \(0.462944\pi\)
\(570\) 191061. − 4.25430e6i 7.58115e−8 − 1.68807e-6i
\(571\) 4.52071e11 + 3.94963e11i 0.177969 + 0.155487i 0.742314 − 0.670052i \(-0.233728\pi\)
−0.564345 + 0.825539i \(0.690871\pi\)
\(572\) 1.87885e12 + 1.69099e11i 0.733853 + 0.0660479i
\(573\) −3.49963e11 − 1.07708e12i −0.135621 − 0.417398i
\(574\) −1.34551e12 + 1.40729e12i −0.517347 + 0.541103i
\(575\) −1.83036e11 − 5.05146e10i −0.0698281 − 0.0192713i
\(576\) 1.15398e11 − 8.51899e11i 0.0436813 − 0.322468i
\(577\) 6.18523e10 + 4.56612e11i 0.0232308 + 0.171497i 0.998848 − 0.0479813i \(-0.0152788\pi\)
−0.975617 + 0.219478i \(0.929565\pi\)
\(578\) −2.06075e12 + 5.68730e11i −0.767980 + 0.211949i
\(579\) 2.78870e11 − 5.18228e11i 0.103121 − 0.191632i
\(580\) −5.33409e8 − 5.57902e8i −0.000195720 − 0.000204707i
\(581\) −1.06097e12 − 1.97162e12i −0.386289 − 0.717845i
\(582\) 1.98158e12 − 6.09867e12i 0.715909 − 2.20334i
\(583\) −1.64372e12 + 3.84568e12i −0.589278 + 1.37868i
\(584\) 3.09855e12 + 5.62304e11i 1.10230 + 0.200039i
\(585\) −3.68049e9 − 2.67403e9i −0.00129928 − 0.000943985i
\(586\) 4.37754e11 − 3.93985e10i 0.153352 − 0.0138020i
\(587\) −1.93434e12 − 4.52560e12i −0.672450 − 1.57328i −0.812389 − 0.583116i \(-0.801833\pi\)
0.139939 − 0.990160i \(-0.455309\pi\)
\(588\) 2.82772e11 + 1.23891e12i 0.0975527 + 0.427406i
\(589\) 1.31719e9 + 1.99545e9i 0.000450950 + 0.000683160i
\(590\) −6.16546e9 − 3.68369e9i −0.00209475 − 0.00125155i
\(591\) −4.56928e12 − 5.72970e12i −1.54065 − 1.93192i
\(592\) −1.89577e12 + 1.65628e12i −0.634362 + 0.554226i
\(593\) −2.71627e12 + 1.97349e12i −0.902043 + 0.655373i −0.938990 − 0.343944i \(-0.888237\pi\)
0.0369466 + 0.999317i \(0.488237\pi\)
\(594\) −1.76116e12 + 8.48130e11i −0.580443 + 0.279527i
\(595\) −3.58576e9 + 5.43219e9i −0.00117288 + 0.00177684i
\(596\) −9.14842e11 − 3.43346e11i −0.296987 − 0.111461i
\(597\) −7.61301e11 + 4.54856e11i −0.245286 + 0.146551i
\(598\) 2.52436e11 + 1.21567e11i 0.0807227 + 0.0388740i
\(599\) −1.69454e12 + 3.07514e11i −0.537813 + 0.0975986i −0.440665 − 0.897671i \(-0.645257\pi\)
−0.0971472 + 0.995270i \(0.530972\pi\)
\(600\) 7.11391e11 − 3.11681e12i 0.224093 − 0.981815i
\(601\) 1.35470e12 − 5.08428e11i 0.423553 − 0.158962i −0.130491 − 0.991450i \(-0.541655\pi\)
0.554044 + 0.832487i \(0.313084\pi\)
\(602\) 1.55276e12 − 1.94710e12i 0.481860 − 0.604234i
\(603\) −1.62600e11 − 3.62056e12i −0.0500831 − 1.11519i
\(604\) −3.12187e10 − 6.95138e11i −0.00954439 − 0.212522i
\(605\) 4.40286e9 − 5.52101e9i 0.00133609 − 0.00167540i
\(606\) −3.72982e12 + 1.39983e12i −1.12347 + 0.421645i
\(607\) −6.20125e10 + 2.71694e11i −0.0185409 + 0.0812328i −0.983352 − 0.181711i \(-0.941836\pi\)
0.964811 + 0.262944i \(0.0846935\pi\)
\(608\) −2.01076e9 + 3.64899e8i −0.000596752 + 0.000108295i
\(609\) 3.00447e12 + 1.44687e12i 0.885094 + 0.426239i
\(610\) 3.85727e9 − 2.30461e9i 0.00112796 − 0.000673927i
\(611\) 1.91082e12 + 7.17144e11i 0.554670 + 0.208171i
\(612\) −1.31259e12 + 1.98849e12i −0.378222 + 0.572982i
\(613\) −4.83343e11 + 2.32766e11i −0.138256 + 0.0665805i −0.501733 − 0.865023i \(-0.667304\pi\)
0.363477 + 0.931603i \(0.381590\pi\)
\(614\) −6.39893e12 + 4.64909e12i −1.81698 + 1.32011i
\(615\) −2.45029e9 + 2.14075e9i −0.000690683 + 0.000603432i
\(616\) 3.19071e12 + 4.00103e12i 0.892841 + 1.11959i
\(617\) −1.20556e12 − 7.20290e11i −0.334893 − 0.200090i 0.335601 − 0.942004i \(-0.391061\pi\)
−0.670494 + 0.741915i \(0.733918\pi\)
\(618\) −4.00444e10 − 6.06647e10i −0.0110432 − 0.0167297i
\(619\) −1.02842e12 − 4.50579e12i −0.281554 − 1.23357i −0.895802 − 0.444454i \(-0.853398\pi\)
0.614248 − 0.789113i \(-0.289459\pi\)
\(620\) 8.86649e8 + 2.07442e9i 0.000240985 + 0.000563812i
\(621\) −8.77969e10 + 7.90187e9i −0.0236901 + 0.00213215i
\(622\) −1.19974e12 − 8.71664e11i −0.321389 − 0.233503i
\(623\) 5.97090e12 + 1.08356e12i 1.58798 + 0.288175i
\(624\) −2.85222e12 + 6.67311e12i −0.753100 + 1.76197i
\(625\) 1.17880e12 − 3.62797e12i 0.309015 − 0.951052i
\(626\) −1.35971e12 − 2.52677e12i −0.353885 − 0.657629i
\(627\) −4.84251e9 − 5.06486e9i −0.00125131 − 0.00130877i
\(628\) 4.55840e11 − 8.47092e11i 0.116948 − 0.217326i
\(629\) −3.30133e12 + 9.11109e11i −0.840932 + 0.232082i
\(630\) 1.28074e9 + 9.45480e9i 0.000323913 + 0.00239122i
\(631\) 9.13923e11 − 6.74685e12i 0.229497 − 1.69422i −0.399438 − 0.916760i \(-0.630795\pi\)
0.628935 − 0.777458i \(-0.283491\pi\)
\(632\) 2.81682e12 + 7.77393e11i 0.702315 + 0.193827i
\(633\) 3.36470e12 − 3.51920e12i 0.832971 − 0.871219i
\(634\) 1.43093e12 + 4.40394e12i 0.351735 + 1.08253i
\(635\) −4.77833e9 − 4.30057e8i −0.00116626 − 0.000104965i
\(636\) 1.84879e12 + 1.61523e12i 0.448053 + 0.391452i
\(637\) −1.29844e11 + 2.89120e12i −0.0312460 + 0.695746i
\(638\) −4.18298e12 −0.999523
\(639\) 4.46681e12 + 2.54975e12i 1.05985 + 0.604984i
\(640\) 6.15155e9 0.00144935
\(641\) 8.57555e10 − 1.90949e12i 0.0200632 − 0.446743i −0.963669 − 0.267100i \(-0.913935\pi\)
0.983732 − 0.179642i \(-0.0574940\pi\)
\(642\) 6.30893e12 + 5.51195e12i 1.46571 + 1.28055i
\(643\) 9.84354e11 + 8.85935e10i 0.227092 + 0.0204387i 0.202601 − 0.979261i \(-0.435061\pi\)
0.0244912 + 0.999700i \(0.492203\pi\)
\(644\) −5.51341e10 − 1.69685e11i −0.0126309 − 0.0388738i
\(645\) 2.87611e9 − 3.00818e9i 0.000654315 − 0.000684360i
\(646\) −4.89650e9 − 1.35135e9i −0.00110622 − 0.000305296i
\(647\) −9.92336e11 + 7.32572e12i −0.222633 + 1.64354i 0.442465 + 0.896786i \(0.354104\pi\)
−0.665098 + 0.746756i \(0.731610\pi\)
\(648\) 2.97686e11 + 2.19760e12i 0.0663239 + 0.489623i
\(649\) −1.13920e13 + 3.14398e12i −2.52056 + 0.695630i
\(650\) −2.66737e12 + 4.95680e12i −0.586101 + 1.08916i
\(651\) −6.73541e12 − 7.04469e12i −1.46977 − 1.53726i
\(652\) −8.03234e11 − 1.49266e12i −0.174071 − 0.323479i
\(653\) 2.51114e11 − 7.72850e11i 0.0540458 − 0.166336i −0.920390 − 0.391001i \(-0.872129\pi\)
0.974436 + 0.224665i \(0.0721289\pi\)
\(654\) 3.33542e12 − 7.80361e12i 0.712937 − 1.66800i
\(655\) −3.68494e9 − 6.68718e8i −0.000782248 − 0.000141957i
\(656\) 2.30791e12 + 1.67679e12i 0.486576 + 0.353518i
\(657\) 9.62215e12 − 8.66009e11i 2.01478 − 0.181334i
\(658\) −1.68232e12 − 3.93598e12i −0.349858 − 0.818534i
\(659\) −1.23548e12 − 5.41298e12i −0.255182 − 1.11803i −0.926333 − 0.376706i \(-0.877057\pi\)
0.671150 − 0.741321i \(-0.265800\pi\)
\(660\) −3.64232e9 − 5.51788e9i −0.000747189 − 0.00113194i
\(661\) 1.42128e12 + 8.49178e11i 0.289584 + 0.173018i 0.650343 − 0.759641i \(-0.274625\pi\)
−0.360759 + 0.932659i \(0.617482\pi\)
\(662\) −4.37715e12 − 5.48877e12i −0.885789 − 1.11074i
\(663\) −7.43497e12 + 6.49574e12i −1.49440 + 1.30562i
\(664\) −1.72519e12 + 1.25342e12i −0.344414 + 0.250231i
\(665\) −5.56444e6 + 2.67969e6i −1.10338e−6 + 5.31359e-7i
\(666\) −2.76560e12 + 4.18970e12i −0.544696 + 0.825180i
\(667\) −1.76609e11 − 6.62824e10i −0.0345499 − 0.0129668i
\(668\) −3.45014e12 + 2.06136e12i −0.670414 + 0.400554i
\(669\) 5.42111e12 + 2.61067e12i 1.04633 + 0.503888i
\(670\) 7.17298e9 − 1.30170e9i 0.00137519 − 0.000249560i
\(671\) 1.64522e12 − 7.20816e12i 0.313308 − 1.37269i
\(672\) 7.79921e12 − 2.92709e12i 1.47533 − 0.553700i
\(673\) 2.93929e12 − 3.68576e12i 0.552300 − 0.692562i −0.424814 − 0.905281i \(-0.639660\pi\)
0.977113 + 0.212719i \(0.0682318\pi\)
\(674\) −1.81245e11 − 4.03574e12i −0.0338296 − 0.753275i
\(675\) −7.94549e10 − 1.76920e12i −0.0147317 − 0.328027i
\(676\) 9.63799e10 − 1.20857e11i 0.0177511 − 0.0222592i
\(677\) −2.88422e12 + 1.08247e12i −0.527691 + 0.198046i −0.600979 − 0.799265i \(-0.705222\pi\)
0.0732874 + 0.997311i \(0.476651\pi\)
\(678\) 2.56045e12 − 1.12181e13i 0.465353 − 2.03884i
\(679\) −9.15038e12 + 1.66055e12i −1.65206 + 0.299804i
\(680\) 5.58538e9 + 2.68978e9i 0.00100176 + 0.000482421i
\(681\) −5.34487e12 + 3.19341e12i −0.952303 + 0.568975i
\(682\) 1.14462e13 + 4.29581e12i 2.02596 + 0.760354i
\(683\) 4.98640e12 − 7.55407e12i 0.876786 − 1.32827i −0.0670122 − 0.997752i \(-0.521347\pi\)
0.943798 − 0.330522i \(-0.107225\pi\)
\(684\) −2.03690e9 + 9.80918e8i −0.000355809 + 0.000171348i
\(685\) −3.68510e9 + 2.67738e9i −0.000639501 + 0.000464625i
\(686\) −2.20317e12 + 1.92485e12i −0.379830 + 0.331847i
\(687\) 8.21958e12 + 1.03070e13i 1.40781 + 1.76534i
\(688\) −3.13244e12 − 1.87155e12i −0.533009 − 0.318458i
\(689\) 3.08014e12 + 4.66621e12i 0.520695 + 0.788820i
\(690\) −2.18513e8 − 9.57367e8i −3.66991e−5 − 0.000160789i
\(691\) −2.24334e12 − 5.24855e12i −0.374321 − 0.875767i −0.995733 − 0.0922830i \(-0.970584\pi\)
0.621412 − 0.783484i \(-0.286559\pi\)
\(692\) 4.12509e12 − 3.71265e11i 0.683842 − 0.0615469i
\(693\) 1.27012e13 + 9.22797e12i 2.09192 + 1.51987i
\(694\) 8.94926e12 + 1.62405e12i 1.46443 + 0.265755i
\(695\) 5.04804e9 − 1.18105e10i 0.000820713 − 0.00192015i
\(696\) 9.81460e11 − 3.02062e12i 0.158537 − 0.487927i
\(697\) 1.83907e12 + 3.41757e12i 0.295155 + 0.548491i
\(698\) 2.23475e12 + 2.33737e12i 0.356353 + 0.372716i
\(699\) −5.52457e12 + 1.02664e13i −0.875288 + 1.62656i
\(700\) 3.45526e12 − 9.53592e11i 0.543926 − 0.150114i
\(701\) 9.02766e11 + 6.66449e12i 0.141203 + 1.04240i 0.913413 + 0.407035i \(0.133437\pi\)
−0.772209 + 0.635368i \(0.780848\pi\)
\(702\) −3.50785e11 + 2.58960e12i −0.0545160 + 0.402453i
\(703\) −3.13249e9 − 8.64513e8i −0.000483717 − 0.000133497i
\(704\) 1.96636e12 − 2.05665e12i 0.301707 − 0.315561i
\(705\) −2.21046e9 − 6.80310e9i −0.000337001 − 0.00103718i
\(706\) −6.52276e11 − 5.87059e10i −0.0988121 − 0.00889325i
\(707\) 4.35097e12 + 3.80133e12i 0.654935 + 0.572200i
\(708\) −3.11233e11 + 6.93014e12i −0.0465518 + 1.03656i
\(709\) 2.73871e12 0.407040 0.203520 − 0.979071i \(-0.434762\pi\)
0.203520 + 0.979071i \(0.434762\pi\)
\(710\) −3.87635e9 + 9.59218e9i −0.000572479 + 0.00141662i
\(711\) 8.96454e12 1.31557
\(712\) 2.59307e11 − 5.77393e12i 0.0378142 − 0.841998i
\(713\) 4.15196e11 + 3.62746e11i 0.0601659 + 0.0525653i
\(714\) 2.06226e13 + 1.85607e12i 2.96962 + 0.267271i
\(715\) −4.65307e9 − 1.43207e10i −0.000665828 − 0.00204921i
\(716\) 4.20960e12 − 4.40289e12i 0.598593 − 0.626079i
\(717\) −1.12379e13 − 3.10148e12i −1.58800 − 0.438261i
\(718\) −1.89005e12 + 1.39529e13i −0.265408 + 1.95932i
\(719\) −1.39672e12 − 1.03110e13i −0.194908 − 1.43887i −0.778919 − 0.627125i \(-0.784232\pi\)
0.584011 − 0.811746i \(-0.301483\pi\)
\(720\) 1.34758e10 − 3.71907e9i 0.00186877 − 0.000515749i
\(721\) −4.99546e10 + 9.28312e10i −0.00688441 + 0.0127934i
\(722\) 6.04664e12 + 6.32429e12i 0.828127 + 0.866153i
\(723\) −4.95623e12 − 9.21021e12i −0.674573 − 1.25357i
\(724\) 1.50670e12 − 4.63713e12i 0.203799 − 0.627229i
\(725\) 1.48947e12 − 3.48478e12i 0.200221 − 0.468441i
\(726\) −2.21031e13 − 4.01113e12i −2.95284 − 0.535861i
\(727\) −9.10551e12 − 6.61554e12i −1.20892 − 0.878335i −0.213792 − 0.976879i \(-0.568581\pi\)
−0.995133 + 0.0985440i \(0.968581\pi\)
\(728\) 6.81393e12 − 6.13265e11i 0.899097 − 0.0809202i
\(729\) 4.14032e12 + 9.68675e12i 0.542950 + 1.27029i
\(730\) 4.32431e9 + 1.89461e10i 0.000563591 + 0.00246926i
\(731\) −2.73475e12 − 4.14298e12i −0.354234 − 0.536641i
\(732\) −3.72570e12 − 2.22600e12i −0.479632 − 0.286567i
\(733\) −3.35649e12 − 4.20890e12i −0.429454 − 0.538519i 0.519276 − 0.854607i \(-0.326202\pi\)
−0.948730 + 0.316088i \(0.897630\pi\)
\(734\) 1.19735e13 − 1.04610e13i 1.52261 − 1.33027i
\(735\) 8.20613e9 − 5.96210e9i 0.00103716 − 0.000753540i
\(736\) −4.24567e11 + 2.04461e11i −0.0533330 + 0.0256838i
\(737\) 6.60835e12 − 1.00112e13i 0.825067 − 1.24992i
\(738\) 5.32617e12 + 1.99894e12i 0.660939 + 0.248055i
\(739\) −6.23414e12 + 3.72472e12i −0.768911 + 0.459403i −0.843044 − 0.537845i \(-0.819238\pi\)
0.0741322 + 0.997248i \(0.476381\pi\)
\(740\) −2.76245e9 − 1.33033e9i −0.000338650 − 0.000163085i
\(741\) −9.21739e9 + 1.67271e9i −0.00112312 + 0.000203816i
\(742\) 2.60930e12 − 1.14321e13i 0.316014 − 1.38455i
\(743\) 2.54949e12 − 9.56841e11i 0.306905 − 0.115183i −0.193170 − 0.981165i \(-0.561877\pi\)
0.500075 + 0.865982i \(0.333306\pi\)
\(744\) −5.78773e12 + 7.25759e12i −0.692517 + 0.868389i
\(745\) 3.49930e8 + 7.79181e9i 4.16177e−5 + 0.000926691i
\(746\) 2.18502e11 + 4.86533e12i 0.0258304 + 0.575159i
\(747\) −4.07885e12 + 5.11472e12i −0.479287 + 0.601006i
\(748\) −7.38333e12 + 2.77101e12i −0.862373 + 0.323654i
\(749\) 2.70356e12 − 1.18451e13i 0.313883 − 1.37521i
\(750\) 3.88225e10 − 7.04525e9i 0.00448031 − 0.000813056i
\(751\) −9.21207e12 − 4.43630e12i −1.05676 − 0.508910i −0.176945 − 0.984221i \(-0.556621\pi\)
−0.879818 + 0.475310i \(0.842336\pi\)
\(752\) −5.38387e12 + 3.21671e12i