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Properties

Label 71.10.g.a.2.10
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
CM no
Inner twists $2$

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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 2.10
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.33405 + 29.7049i) q^{2} +(-5.04413 - 4.40692i) q^{3} +(-370.660 - 33.3600i) q^{4} +(-108.717 - 334.598i) q^{5} +(137.636 - 143.956i) q^{6} +(8583.36 + 2368.86i) q^{7} +(-558.163 + 4120.53i) q^{8} +(-2636.09 - 19460.4i) q^{9} +O(q^{10})\) \(q+(-1.33405 + 29.7049i) q^{2} +(-5.04413 - 4.40692i) q^{3} +(-370.660 - 33.3600i) q^{4} +(-108.717 - 334.598i) q^{5} +(137.636 - 143.956i) q^{6} +(8583.36 + 2368.86i) q^{7} +(-558.163 + 4120.53i) q^{8} +(-2636.09 - 19460.4i) q^{9} +(10084.2 - 2783.07i) q^{10} +(-17851.3 + 33173.2i) q^{11} +(1722.64 + 1801.74i) q^{12} +(-91701.3 - 170410. i) q^{13} +(-81817.2 + 251807. i) q^{14} +(-926.162 + 2166.86i) q^{15} +(-309138. - 56100.3i) q^{16} +(94406.7 + 68590.5i) q^{17} +(581585. - 52343.6i) q^{18} +(-272307. - 637093. i) q^{19} +(29135.0 + 127649. i) q^{20} +(-32856.2 - 49775.0i) q^{21} +(-961591. - 574524. i) q^{22} +(-726540. - 911053. i) q^{23} +(20974.3 - 18324.7i) q^{24} +(1.47998e6 - 1.07526e6i) q^{25} +(5.18432e6 - 2.49664e6i) q^{26} +(-145093. + 219807. i) q^{27} +(-3.10248e6 - 1.16438e6i) q^{28} +(3.53825e6 - 2.11401e6i) q^{29} +(-63130.8 - 30402.2i) q^{30} +(-7.05508e6 + 1.28031e6i) q^{31} +(1.60511e6 - 7.03246e6i) q^{32} +(236236. - 88660.8i) q^{33} +(-2.16341e6 + 2.71284e6i) q^{34} +(-140546. - 3.12951e6i) q^{35} +(327895. + 7.30114e6i) q^{36} +(-1.94533e6 + 2.43937e6i) q^{37} +(1.92880e7 - 7.23892e6i) q^{38} +(-288429. + 1.26369e6i) q^{39} +(1.43940e6 - 261213. i) q^{40} +(-1.18114e6 - 568807. i) q^{41} +(1.52239e6 - 909587. i) q^{42} +(-1.25420e7 - 4.70709e6i) q^{43} +(7.72341e6 - 1.17005e7i) q^{44} +(-6.22482e6 + 2.99771e6i) q^{45} +(2.80319e7 - 2.03664e7i) q^{46} +(2.57321e7 - 2.24815e7i) q^{47} +(1.31210e6 + 1.64533e6i) q^{48} +(3.34211e7 + 1.99682e7i) q^{49} +(2.99662e7 + 4.53969e7i) q^{50} +(-173927. - 762023. i) q^{51} +(2.83051e7 + 6.62232e7i) q^{52} +(-567123. + 51042.0i) q^{53} +(-6.33576e6 - 4.60320e6i) q^{54} +(1.30404e7 + 2.36649e6i) q^{55} +(-1.45519e7 + 3.40458e7i) q^{56} +(-1.43407e6 + 4.41361e6i) q^{57} +(5.80761e7 + 1.07923e8i) q^{58} +(9.74925e7 + 1.01969e8i) q^{59} +(415578. - 772273. i) q^{60} +(5.95067e7 - 1.64228e7i) q^{61} +(-2.86196e7 - 2.11278e8i) q^{62} +(2.34724e7 - 1.73280e8i) q^{63} +(5.16903e7 + 1.42656e7i) q^{64} +(-4.70491e7 + 4.92095e7i) q^{65} +(2.31851e6 + 7.13563e6i) q^{66} +(1.80547e8 + 1.62495e7i) q^{67} +(-3.27046e7 - 2.85732e7i) q^{68} +(-350176. + 7.79728e6i) q^{69} +9.31491e7 q^{70} +(1.36935e8 - 1.64613e8i) q^{71} +8.16585e7 q^{72} +(-4.20782e6 + 9.36945e7i) q^{73} +(-6.98660e7 - 6.10401e7i) q^{74} +(-1.22038e7 - 1.09836e6i) q^{75} +(7.96798e7 + 2.45229e8i) q^{76} +(-2.31806e8 + 2.42450e8i) q^{77} +(-3.71529e7 - 1.02536e7i) q^{78} +(6.51228e7 - 4.80756e8i) q^{79} +(1.48377e7 + 1.09536e8i) q^{80} +(-3.70907e8 + 1.02364e8i) q^{81} +(1.84720e7 - 3.43268e7i) q^{82} +(-5.65009e8 - 5.90953e8i) q^{83} +(1.05180e7 + 1.95457e7i) q^{84} +(1.26866e7 - 3.90453e7i) q^{85} +(1.56555e8 - 3.66278e8i) q^{86} +(-2.71637e7 - 4.92948e6i) q^{87} +(-1.26727e8 - 9.20727e7i) q^{88} +(-4.85314e7 + 4.36791e6i) q^{89} +(-8.07425e7 - 1.88906e8i) q^{90} +(-3.83429e8 - 1.67991e9i) q^{91} +(2.38907e8 + 3.61929e8i) q^{92} +(4.12289e7 + 2.46331e7i) q^{93} +(6.33481e8 + 7.94360e8i) q^{94} +(-1.83565e8 + 1.60376e8i) q^{95} +(-3.90879e7 + 2.83991e7i) q^{96} +(-8.00753e8 + 3.85623e8i) q^{97} +(-6.37736e8 + 9.66129e8i) q^{98} +(6.92621e8 + 2.59945e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33405 + 29.7049i −0.0589571 + 1.31278i 0.723607 + 0.690212i \(0.242483\pi\)
−0.782564 + 0.622570i \(0.786089\pi\)
\(3\) −5.04413 − 4.40692i −0.0359535 − 0.0314116i 0.639775 − 0.768563i \(-0.279028\pi\)
−0.675728 + 0.737151i \(0.736171\pi\)
\(4\) −370.660 − 33.3600i −0.723946 − 0.0651563i
\(5\) −108.717 − 334.598i −0.0777918 − 0.239419i 0.904597 − 0.426269i \(-0.140172\pi\)
−0.982388 + 0.186850i \(0.940172\pi\)
\(6\) 137.636 − 143.956i 0.0433563 − 0.0453471i
\(7\) 8583.36 + 2368.86i 1.35119 + 0.372904i 0.865361 − 0.501150i \(-0.167089\pi\)
0.485828 + 0.874054i \(0.338518\pi\)
\(8\) −558.163 + 4120.53i −0.0481789 + 0.355671i
\(9\) −2636.09 − 19460.4i −0.133927 − 0.988691i
\(10\) 10084.2 − 2783.07i 0.318891 − 0.0880083i
\(11\) −17851.3 + 33173.2i −0.367622 + 0.683156i −0.995459 − 0.0951883i \(-0.969655\pi\)
0.627837 + 0.778345i \(0.283940\pi\)
\(12\) 1722.64 + 1801.74i 0.0239817 + 0.0250829i
\(13\) −91701.3 − 170410.i −0.890492 − 1.65481i −0.746656 − 0.665211i \(-0.768342\pi\)
−0.143837 − 0.989601i \(-0.545944\pi\)
\(14\) −81817.2 + 251807.i −0.569204 + 1.75183i
\(15\) −926.162 + 2166.86i −0.00472363 + 0.0110515i
\(16\) −309138. − 56100.3i −1.17927 − 0.214006i
\(17\) 94406.7 + 68590.5i 0.274147 + 0.199179i 0.716360 − 0.697731i \(-0.245807\pi\)
−0.442214 + 0.896910i \(0.645807\pi\)
\(18\) 581585. − 52343.6i 1.30583 − 0.117527i
\(19\) −272307. − 637093.i −0.479366 − 1.12153i −0.968430 − 0.249284i \(-0.919805\pi\)
0.489065 − 0.872248i \(-0.337338\pi\)
\(20\) 29135.0 + 127649.i 0.0407174 + 0.178395i
\(21\) −32856.2 − 49775.0i −0.0368664 − 0.0558502i
\(22\) −961591. − 574524.i −0.875161 − 0.522885i
\(23\) −726540. − 911053.i −0.541358 − 0.678841i 0.433632 − 0.901090i \(-0.357232\pi\)
−0.974990 + 0.222249i \(0.928660\pi\)
\(24\) 20974.3 − 18324.7i 0.0129044 − 0.0112742i
\(25\) 1.47998e6 − 1.07526e6i 0.757747 − 0.550536i
\(26\) 5.18432e6 − 2.49664e6i 2.22491 − 1.07146i
\(27\) −145093. + 219807.i −0.0525424 + 0.0795983i
\(28\) −3.10248e6 − 1.16438e6i −0.953890 − 0.358001i
\(29\) 3.53825e6 − 2.11401e6i 0.928962 − 0.555029i 0.0331440 − 0.999451i \(-0.489448\pi\)
0.895818 + 0.444422i \(0.146591\pi\)
\(30\) −63130.8 − 30402.2i −0.0142297 − 0.00685267i
\(31\) −7.05508e6 + 1.28031e6i −1.37206 + 0.248993i −0.814028 − 0.580825i \(-0.802730\pi\)
−0.558035 + 0.829818i \(0.688444\pi\)
\(32\) 1.60511e6 − 7.03246e6i 0.270602 − 1.18558i
\(33\) 236236. − 88660.8i 0.0346763 − 0.0130142i
\(34\) −2.16341e6 + 2.71284e6i −0.277642 + 0.348152i
\(35\) −140546. − 3.12951e6i −0.0158312 − 0.352509i
\(36\) 327895. + 7.30114e6i 0.0325367 + 0.724485i
\(37\) −1.94533e6 + 2.43937e6i −0.170642 + 0.213978i −0.859797 − 0.510635i \(-0.829410\pi\)
0.689155 + 0.724614i \(0.257982\pi\)
\(38\) 1.92880e7 − 7.23892e6i 1.50059 − 0.563180i
\(39\) −288429. + 1.26369e6i −0.0199640 + 0.0874680i
\(40\) 1.43940e6 − 261213.i 0.0889021 − 0.0161333i
\(41\) −1.18114e6 − 568807.i −0.0652790 − 0.0314367i 0.400959 − 0.916096i \(-0.368677\pi\)
−0.466238 + 0.884659i \(0.654391\pi\)
\(42\) 1.52239e6 − 909587.i 0.0754927 − 0.0451048i
\(43\) −1.25420e7 − 4.70709e6i −0.559446 − 0.209964i 0.0556023 − 0.998453i \(-0.482292\pi\)
−0.615048 + 0.788489i \(0.710864\pi\)
\(44\) 7.72341e6 − 1.17005e7i 0.310650 − 0.470615i
\(45\) −6.22482e6 + 2.99771e6i −0.226293 + 0.108977i
\(46\) 2.80319e7 − 2.03664e7i 0.923088 − 0.670662i
\(47\) 2.57321e7 − 2.24815e7i 0.769192 − 0.672023i −0.181071 − 0.983470i \(-0.557957\pi\)
0.950263 + 0.311447i \(0.100814\pi\)
\(48\) 1.31210e6 + 1.64533e6i 0.0356765 + 0.0447369i
\(49\) 3.34211e7 + 1.99682e7i 0.828205 + 0.494829i
\(50\) 2.99662e7 + 4.53969e7i 0.678059 + 1.02721i
\(51\) −173927. − 762023.i −0.00359998 − 0.0157726i
\(52\) 2.83051e7 + 6.62232e7i 0.536847 + 1.25602i
\(53\) −567123. + 51042.0i −0.00987271 + 0.000888560i −0.0945746 − 0.995518i \(-0.530149\pi\)
0.0847019 + 0.996406i \(0.473006\pi\)
\(54\) −6.33576e6 − 4.60320e6i −0.101397 − 0.0736696i
\(55\) 1.30404e7 + 2.36649e6i 0.192158 + 0.0348716i
\(56\) −1.45519e7 + 3.40458e7i −0.197730 + 0.462612i
\(57\) −1.43407e6 + 4.41361e6i −0.0179942 + 0.0553806i
\(58\) 5.80761e7 + 1.07923e8i 0.673863 + 1.25225i
\(59\) 9.74925e7 + 1.01969e8i 1.04746 + 1.09556i 0.995292 + 0.0969180i \(0.0308985\pi\)
0.0521668 + 0.998638i \(0.483387\pi\)
\(60\) 415578. − 772273.i 0.00413973 − 0.00769291i
\(61\) 5.95067e7 − 1.64228e7i 0.550278 − 0.151867i 0.0201688 − 0.999797i \(-0.493580\pi\)
0.530109 + 0.847930i \(0.322151\pi\)
\(62\) −2.86196e7 − 2.11278e8i −0.245980 − 1.81590i
\(63\) 2.34724e7 − 1.73280e8i 0.187726 − 1.38585i
\(64\) 5.16903e7 + 1.42656e7i 0.385123 + 0.106287i
\(65\) −4.70491e7 + 4.92095e7i −0.326920 + 0.341931i
\(66\) 2.31851e6 + 7.13563e6i 0.0150404 + 0.0462897i
\(67\) 1.80547e8 + 1.62495e7i 1.09460 + 0.0985154i 0.622191 − 0.782866i \(-0.286243\pi\)
0.472406 + 0.881381i \(0.343386\pi\)
\(68\) −3.27046e7 − 2.85732e7i −0.185489 − 0.162057i
\(69\) −350176. + 7.79728e6i −0.00185980 + 0.0414116i
\(70\) 9.31491e7 0.463700
\(71\) 1.36935e8 − 1.64613e8i 0.639517 − 0.768777i
\(72\) 8.16585e7 0.358101
\(73\) −4.20782e6 + 9.36945e7i −0.0173422 + 0.386154i 0.971486 + 0.237096i \(0.0761956\pi\)
−0.988828 + 0.149058i \(0.952376\pi\)
\(74\) −6.98660e7 − 6.10401e7i −0.270846 − 0.236631i
\(75\) −1.22038e7 − 1.09836e6i −0.0445368 − 0.00400839i
\(76\) 7.96798e7 + 2.45229e8i 0.273960 + 0.843162i
\(77\) −2.31806e8 + 2.42450e8i −0.751479 + 0.785985i
\(78\) −3.71529e7 − 1.02536e7i −0.113649 − 0.0313652i
\(79\) 6.51228e7 − 4.80756e8i 0.188110 − 1.38868i −0.612962 − 0.790113i \(-0.710022\pi\)
0.801071 − 0.598569i \(-0.204264\pi\)
\(80\) 1.48377e7 + 1.09536e8i 0.0405005 + 0.298987i
\(81\) −3.70907e8 + 1.02364e8i −0.957376 + 0.264219i
\(82\) 1.84720e7 − 3.43268e7i 0.0451182 − 0.0838437i
\(83\) −5.65009e8 − 5.90953e8i −1.30678 − 1.36679i −0.888773 − 0.458347i \(-0.848442\pi\)
−0.418011 − 0.908442i \(-0.637273\pi\)
\(84\) 1.05180e7 + 1.95457e7i 0.0230503 + 0.0428346i
\(85\) 1.26866e7 − 3.90453e7i 0.0263608 − 0.0811303i
\(86\) 1.56555e8 − 3.66278e8i 0.308620 − 0.722052i
\(87\) −2.71637e7 − 4.92948e6i −0.0508337 − 0.00922496i
\(88\) −1.26727e8 − 9.20727e7i −0.225267 − 0.163666i
\(89\) −4.85314e7 + 4.36791e6i −0.0819913 + 0.00737935i −0.130559 − 0.991441i \(-0.541677\pi\)
0.0485677 + 0.998820i \(0.484534\pi\)
\(90\) −8.07425e7 − 1.88906e8i −0.129721 − 0.303498i
\(91\) −3.83429e8 − 1.67991e9i −0.586137 − 2.56803i
\(92\) 2.38907e8 + 3.61929e8i 0.347683 + 0.526717i
\(93\) 4.12289e7 + 2.46331e7i 0.0571517 + 0.0341465i
\(94\) 6.33481e8 + 7.94360e8i 0.836870 + 1.04940i
\(95\) −1.83565e8 + 1.60376e8i −0.231225 + 0.202015i
\(96\) −3.90879e7 + 2.83991e7i −0.0469702 + 0.0341258i
\(97\) −8.00753e8 + 3.85623e8i −0.918388 + 0.442272i −0.832495 − 0.554032i \(-0.813088\pi\)
−0.0858924 + 0.996304i \(0.527374\pi\)
\(98\) −6.37736e8 + 9.66129e8i −0.698432 + 1.05808i
\(99\) 6.92621e8 + 2.59945e8i 0.724665 + 0.271971i
\(100\) −5.84439e8 + 3.49186e8i −0.584439 + 0.349186i
\(101\) 6.35931e8 + 3.06248e8i 0.608084 + 0.292838i 0.712474 − 0.701699i \(-0.247575\pi\)
−0.104390 + 0.994536i \(0.533289\pi\)
\(102\) 2.28678e7 − 4.14990e6i 0.0209182 − 0.00379609i
\(103\) 8.75174e7 − 3.83439e8i 0.0766173 − 0.335682i −0.922063 − 0.387040i \(-0.873498\pi\)
0.998680 + 0.0513574i \(0.0163548\pi\)
\(104\) 7.53361e8 − 2.82741e8i 0.631471 − 0.236995i
\(105\) −1.30826e7 + 1.64050e7i −0.0105037 + 0.0131712i
\(106\) −759627. − 1.69144e7i −0.000584419 − 0.0130131i
\(107\) 473204. + 1.05367e7i 0.000348997 + 0.00777102i 0.999160 − 0.0409790i \(-0.0130477\pi\)
−0.998811 + 0.0487500i \(0.984476\pi\)
\(108\) 6.11130e7 − 7.66333e7i 0.0432242 − 0.0542014i
\(109\) −9.93310e7 + 3.72795e7i −0.0674008 + 0.0252960i −0.384848 − 0.922980i \(-0.625746\pi\)
0.317447 + 0.948276i \(0.397175\pi\)
\(110\) −8.76927e7 + 3.84207e8i −0.0571079 + 0.250206i
\(111\) 2.05626e7 − 3.73157e6i 0.0128566 − 0.00233312i
\(112\) −2.52055e9 − 1.21383e9i −1.51361 − 0.728916i
\(113\) −4.37616e8 + 2.61463e8i −0.252488 + 0.150854i −0.633567 − 0.773688i \(-0.718410\pi\)
0.381079 + 0.924542i \(0.375553\pi\)
\(114\) −1.29193e8 − 4.84868e7i −0.0716417 − 0.0268876i
\(115\) −2.25849e8 + 3.42146e8i −0.120414 + 0.182419i
\(116\) −1.38201e9 + 6.65542e8i −0.708681 + 0.341283i
\(117\) −3.07451e9 + 2.23376e9i −1.51684 + 1.10205i
\(118\) −3.15904e9 + 2.75997e9i −1.49998 + 1.31049i
\(119\) 6.47846e8 + 8.12373e8i 0.296149 + 0.371359i
\(120\) −8.41167e6 − 5.02574e6i −0.00370311 − 0.00221251i
\(121\) 5.17193e8 + 7.83514e8i 0.219340 + 0.332286i
\(122\) 4.08453e8 + 1.78955e9i 0.166925 + 0.731348i
\(123\) 3.45113e6 + 8.07432e6i 0.00135953 + 0.00318078i
\(124\) 2.65775e9 − 2.39202e8i 1.00952 − 0.0908587i
\(125\) −1.07659e9 − 7.82188e8i −0.394417 − 0.286560i
\(126\) 5.11595e9 + 9.28408e8i 1.80825 + 0.328149i
\(127\) −1.46279e9 + 3.42236e9i −0.498959 + 1.16737i 0.461043 + 0.887378i \(0.347475\pi\)
−0.960002 + 0.279994i \(0.909668\pi\)
\(128\) 6.48552e8 − 1.99604e9i 0.213550 − 0.657240i
\(129\) 4.25196e7 + 7.90147e7i 0.0135187 + 0.0251220i
\(130\) −1.39900e9 − 1.46323e9i −0.429607 − 0.449334i
\(131\) 1.67355e9 − 3.10997e9i 0.496498 − 0.922647i −0.501837 − 0.864962i \(-0.667342\pi\)
0.998335 − 0.0576853i \(-0.0183720\pi\)
\(132\) −9.05210e7 + 2.49822e7i −0.0259517 + 0.00716222i
\(133\) −8.28123e8 − 6.11345e9i −0.229489 − 1.69416i
\(134\) −7.23549e8 + 5.34145e9i −0.193864 + 1.43116i
\(135\) 8.93209e7 + 2.46510e7i 0.0231447 + 0.00638753i
\(136\) −3.35324e8 + 3.50721e8i −0.0840502 + 0.0879097i
\(137\) −1.64341e9 − 5.05790e9i −0.398569 − 1.22667i −0.926147 − 0.377163i \(-0.876900\pi\)
0.527577 − 0.849507i \(-0.323100\pi\)
\(138\) −2.31150e8 − 2.08039e7i −0.0542548 − 0.00488302i
\(139\) −2.79508e9 − 2.44199e9i −0.635078 − 0.554851i 0.279050 − 0.960277i \(-0.409981\pi\)
−0.914128 + 0.405426i \(0.867123\pi\)
\(140\) −5.23055e7 + 1.16467e9i −0.0115072 + 0.256229i
\(141\) −2.28870e8 −0.0487644
\(142\) 4.70712e9 + 4.28724e9i 0.971533 + 0.884871i
\(143\) 7.29001e9 1.45786
\(144\) −2.76818e8 + 6.16384e9i −0.0536492 + 1.19459i
\(145\) −1.09201e9 − 9.54062e8i −0.205150 − 0.179234i
\(146\) −2.77757e9 − 2.49986e8i −0.505914 − 0.0455331i
\(147\) −8.05821e7 − 2.48006e8i −0.0142335 − 0.0438061i
\(148\) 8.02435e8 − 8.39281e8i 0.137478 − 0.143790i
\(149\) 1.13504e9 + 3.13251e8i 0.188657 + 0.0520660i 0.359088 − 0.933304i \(-0.383088\pi\)
−0.170432 + 0.985370i \(0.554516\pi\)
\(150\) 4.89071e7 − 3.61047e8i 0.00788790 − 0.0582308i
\(151\) −1.17911e9 − 8.70456e9i −0.184569 − 1.36254i −0.811902 − 0.583794i \(-0.801568\pi\)
0.627333 − 0.778751i \(-0.284147\pi\)
\(152\) 2.77715e9 − 7.66445e8i 0.421991 − 0.116462i
\(153\) 1.08593e9 − 2.01800e9i 0.160211 − 0.297722i
\(154\) −6.89271e9 − 7.20921e9i −0.987522 − 1.03287i
\(155\) 1.19540e9 + 2.22142e9i 0.166349 + 0.309128i
\(156\) 1.49066e8 − 4.58777e8i 0.0201519 − 0.0620213i
\(157\) 3.46161e9 − 8.09884e9i 0.454705 − 1.06383i −0.522711 − 0.852510i \(-0.675079\pi\)
0.977416 − 0.211325i \(-0.0677778\pi\)
\(158\) 1.41939e10 + 2.57581e9i 1.81195 + 0.328820i
\(159\) 3.08558e6 + 2.24181e6i 0.000382869 + 0.000278171i
\(160\) −2.52755e9 + 2.27484e8i −0.304902 + 0.0274416i
\(161\) −4.07800e9 − 9.54096e9i −0.478334 − 1.11912i
\(162\) −2.54590e9 − 1.11543e10i −0.290418 − 1.27240i
\(163\) 3.43012e9 + 5.19641e9i 0.380597 + 0.576579i 0.973498 − 0.228696i \(-0.0734461\pi\)
−0.592901 + 0.805275i \(0.702018\pi\)
\(164\) 4.18826e8 + 2.50237e8i 0.0452102 + 0.0270118i
\(165\) −5.53486e7 − 6.94050e7i −0.00581339 − 0.00728975i
\(166\) 1.83079e10 − 1.59952e10i 1.87134 − 1.63494i
\(167\) −1.02939e10 + 7.47895e9i −1.02413 + 0.744075i −0.967126 − 0.254299i \(-0.918155\pi\)
−0.0570057 + 0.998374i \(0.518155\pi\)
\(168\) 2.23439e8 − 1.07602e8i 0.0216405 − 0.0104215i
\(169\) −1.47883e10 + 2.24033e10i −1.39453 + 2.11262i
\(170\) 1.14291e9 + 4.28941e8i 0.104952 + 0.0393892i
\(171\) −1.16803e10 + 6.97863e9i −1.04465 + 0.624148i
\(172\) 4.49179e9 + 2.16313e9i 0.391328 + 0.188454i
\(173\) 3.40415e9 − 6.17762e8i 0.288936 − 0.0524341i −0.0321538 − 0.999483i \(-0.510237\pi\)
0.321090 + 0.947049i \(0.395951\pi\)
\(174\) 1.82667e8 − 8.00317e8i 0.0151074 − 0.0661897i
\(175\) 1.52503e10 − 5.72354e9i 1.22916 − 0.461310i
\(176\) 7.37953e9 − 9.25364e9i 0.579724 − 0.726951i
\(177\) −4.23945e7 − 9.43988e8i −0.00324661 − 0.0722914i
\(178\) −6.50049e7 − 1.44745e9i −0.00485351 − 0.108072i
\(179\) −8.14932e9 + 1.02189e10i −0.593312 + 0.743989i −0.984319 − 0.176398i \(-0.943555\pi\)
0.391007 + 0.920388i \(0.372127\pi\)
\(180\) 2.40730e9 − 9.03473e8i 0.170924 − 0.0641489i
\(181\) −3.84049e9 + 1.68263e10i −0.265970 + 1.16529i 0.648685 + 0.761057i \(0.275319\pi\)
−0.914655 + 0.404235i \(0.867538\pi\)
\(182\) 5.04131e10 − 9.14863e9i 3.40582 − 0.618066i
\(183\) −3.72534e8 − 1.79403e8i −0.0245548 − 0.0118250i
\(184\) 4.15955e9 − 2.48521e9i 0.267526 − 0.159839i
\(185\) 1.02770e9 + 3.85702e8i 0.0645050 + 0.0242091i
\(186\) −7.86726e8 + 1.19184e9i −0.0481964 + 0.0730145i
\(187\) −3.96064e9 + 1.90735e9i −0.236853 + 0.114062i
\(188\) −1.02878e10 + 7.47456e9i −0.600640 + 0.436390i
\(189\) −1.76608e9 + 1.54297e9i −0.100677 + 0.0879590i
\(190\) −4.51907e9 − 5.66673e9i −0.251569 − 0.315458i
\(191\) −1.97429e9 − 1.17958e9i −0.107340 − 0.0641324i 0.458226 − 0.888836i \(-0.348485\pi\)
−0.565566 + 0.824703i \(0.691342\pi\)
\(192\) −1.97865e8 − 2.99753e8i −0.0105078 − 0.0159187i
\(193\) 7.27579e9 + 3.18773e10i 0.377461 + 1.65376i 0.705209 + 0.708999i \(0.250853\pi\)
−0.327748 + 0.944765i \(0.606290\pi\)
\(194\) −1.03866e10 − 2.43007e10i −0.526461 − 1.23172i
\(195\) 4.54184e8 − 4.08773e7i 0.0224945 − 0.00202454i
\(196\) −1.17217e10 − 8.51633e9i −0.567334 − 0.412192i
\(197\) −1.40265e10 − 2.54544e9i −0.663517 − 0.120411i −0.163658 − 0.986517i \(-0.552329\pi\)
−0.499859 + 0.866107i \(0.666615\pi\)
\(198\) −8.64562e9 + 2.02274e10i −0.399763 + 0.935293i
\(199\) 5.01733e9 − 1.54418e10i 0.226795 − 0.698004i −0.771309 − 0.636461i \(-0.780398\pi\)
0.998104 − 0.0615432i \(-0.0196022\pi\)
\(200\) 3.60459e9 + 6.69845e9i 0.159302 + 0.296033i
\(201\) −8.39093e8 − 8.77622e8i −0.0362600 − 0.0379250i
\(202\) −9.94542e9 + 1.84817e10i −0.420283 + 0.781017i
\(203\) 3.53779e10 − 9.76367e9i 1.46218 − 0.403535i
\(204\) 3.90466e7 + 2.88254e8i 0.00157851 + 0.0116530i
\(205\) −6.19110e7 + 4.57045e8i −0.00244836 + 0.0180745i
\(206\) 1.12732e10 + 3.11122e9i 0.436160 + 0.120373i
\(207\) −1.58142e10 + 1.65404e10i −0.598662 + 0.626151i
\(208\) 1.87883e10 + 5.78245e10i 0.695990 + 2.14204i
\(209\) 2.59954e10 + 2.33963e9i 0.942407 + 0.0848182i
\(210\) −4.69856e8 − 4.10501e8i −0.0166716 − 0.0145656i
\(211\) 1.38464e8 − 3.08314e9i 0.00480912 − 0.107083i −0.995153 − 0.0983421i \(-0.968646\pi\)
0.999962 − 0.00874139i \(-0.00278251\pi\)
\(212\) 2.11913e8 0.00720520
\(213\) −1.41615e9 + 2.26865e8i −0.0471414 + 0.00755195i
\(214\) −3.13623e8 −0.0102222
\(215\) −2.11448e8 + 4.70826e9i −0.00674887 + 0.150275i
\(216\) −8.24734e8 − 7.20548e8i −0.0257793 − 0.0225227i
\(217\) −6.35891e10 − 5.72312e9i −1.94677 − 0.175212i
\(218\) −9.74871e8 − 3.00034e9i −0.0292343 − 0.0899740i
\(219\) 4.34129e8 − 4.54064e8i 0.0127532 − 0.0133388i
\(220\) −4.75462e9 − 1.31219e9i −0.136840 − 0.0377655i
\(221\) 3.03126e9 − 2.23776e10i 0.0854786 − 0.631029i
\(222\) 8.34142e7 + 6.15788e8i 0.00230490 + 0.0170154i
\(223\) −5.79815e10 + 1.60019e10i −1.57007 + 0.433311i −0.939422 − 0.342762i \(-0.888638\pi\)
−0.630644 + 0.776073i \(0.717209\pi\)
\(224\) 3.04362e10 − 5.65599e10i 0.807744 − 1.50104i
\(225\) −2.48264e10 − 2.59664e10i −0.645793 − 0.675446i
\(226\) −7.18293e9 − 1.33481e10i −0.183153 − 0.340355i
\(227\) 6.73213e9 − 2.07194e10i 0.168281 − 0.517917i −0.830982 − 0.556300i \(-0.812221\pi\)
0.999263 + 0.0383830i \(0.0122207\pi\)
\(228\) 6.78791e8 − 1.58811e9i 0.0166353 − 0.0389201i
\(229\) 6.74171e10 + 1.22344e10i 1.61998 + 0.293984i 0.911362 − 0.411606i \(-0.135032\pi\)
0.708621 + 0.705590i \(0.249318\pi\)
\(230\) −9.86211e9 − 7.16524e9i −0.232378 − 0.168832i
\(231\) 2.23772e9 − 2.01399e8i 0.0517073 − 0.00465374i
\(232\) 6.73590e9 + 1.57594e10i 0.152651 + 0.357145i
\(233\) 1.92711e10 + 8.44323e10i 0.428356 + 1.87675i 0.478631 + 0.878016i \(0.341133\pi\)
−0.0502744 + 0.998735i \(0.516010\pi\)
\(234\) −6.22520e10 − 9.43077e10i −1.35732 − 2.05625i
\(235\) −1.03198e10 − 6.16577e9i −0.220732 − 0.131881i
\(236\) −3.27349e10 − 4.10483e10i −0.686921 − 0.861372i
\(237\) −2.44714e9 + 2.13800e9i −0.0503839 + 0.0440191i
\(238\) −2.49957e10 + 1.81604e10i −0.504974 + 0.366885i
\(239\) −6.20571e10 + 2.98851e10i −1.23027 + 0.592467i −0.932154 − 0.362062i \(-0.882073\pi\)
−0.298117 + 0.954529i \(0.596359\pi\)
\(240\) 4.07874e8 − 6.17902e8i 0.00793551 − 0.0120218i
\(241\) −6.72316e10 − 2.52324e10i −1.28380 − 0.481818i −0.386112 − 0.922452i \(-0.626182\pi\)
−0.897687 + 0.440634i \(0.854754\pi\)
\(242\) −2.39641e10 + 1.43179e10i −0.449151 + 0.268355i
\(243\) 6.99266e9 + 3.36749e9i 0.128651 + 0.0619552i
\(244\) −2.26046e10 + 4.10214e9i −0.408266 + 0.0740894i
\(245\) 3.04785e9 − 1.33535e10i 0.0540438 − 0.236781i
\(246\) −2.44451e8 + 9.17439e7i −0.00425582 + 0.00159724i
\(247\) −8.35958e10 + 1.04826e11i −1.42905 + 1.79198i
\(248\) −1.33766e9 − 2.97853e10i −0.0224550 − 0.499999i
\(249\) 2.45694e8 + 5.47080e9i 0.00405039 + 0.0901890i
\(250\) 2.46710e10 − 3.09365e10i 0.399445 − 0.500888i
\(251\) 4.67955e10 − 1.75626e10i 0.744170 − 0.279292i 0.0496514 − 0.998767i \(-0.484189\pi\)
0.694518 + 0.719475i \(0.255618\pi\)
\(252\) −1.44809e10 + 6.34450e10i −0.226200 + 0.991049i
\(253\) 4.31922e10 − 7.83823e9i 0.662770 − 0.120275i
\(254\) −9.97093e10 − 4.80175e10i −1.50309 − 0.723849i
\(255\) −2.36062e8 + 1.41041e8i −0.00349620 + 0.00208888i
\(256\) 8.41310e10 + 3.15749e10i 1.22427 + 0.459475i
\(257\) 5.60947e9 − 8.49799e9i 0.0802090 − 0.121511i −0.792254 − 0.610191i \(-0.791093\pi\)
0.872463 + 0.488680i \(0.162521\pi\)
\(258\) −2.40384e9 + 1.15763e9i −0.0337767 + 0.0162660i
\(259\) −2.24760e10 + 1.63298e10i −0.310363 + 0.225492i
\(260\) 1.90809e10 − 1.66704e10i 0.258951 − 0.226239i
\(261\) −5.04666e10 − 6.32831e10i −0.673165 − 0.844123i
\(262\) 9.01487e10 + 5.38614e10i 1.18196 + 0.706190i
\(263\) −8.05269e10 − 1.21993e11i −1.03786 − 1.57230i −0.799082 − 0.601222i \(-0.794681\pi\)
−0.238781 − 0.971074i \(-0.576748\pi\)
\(264\) 2.33471e8 + 1.02290e9i 0.00295812 + 0.0129604i
\(265\) 7.87347e7 + 1.84209e8i 0.000980753 + 0.00229459i
\(266\) 1.82704e11 − 1.64437e10i 2.23759 − 0.201387i
\(267\) 2.64048e8 + 1.91842e8i 0.00317967 + 0.00231017i
\(268\) −6.63796e10 − 1.20461e10i −0.786010 − 0.142640i
\(269\) −1.73098e10 + 4.04983e10i −0.201561 + 0.471576i −0.989564 − 0.144096i \(-0.953973\pi\)
0.788002 + 0.615672i \(0.211115\pi\)
\(270\) −8.51413e8 + 2.62038e9i −0.00974997 + 0.0300073i
\(271\) −6.01709e10 − 1.11816e11i −0.677680 − 1.25934i −0.954441 − 0.298401i \(-0.903547\pi\)
0.276761 − 0.960939i \(-0.410739\pi\)
\(272\) −2.53368e10 − 2.65002e10i −0.280667 − 0.293555i
\(273\) −5.46918e9 + 1.01634e10i −0.0595924 + 0.110741i
\(274\) 1.52437e11 − 4.20698e10i 1.63385 − 0.450914i
\(275\) 9.25055e9 + 6.82903e10i 0.0975373 + 0.720049i
\(276\) 3.89914e8 − 2.87846e9i 0.00404462 − 0.0298586i
\(277\) 1.55684e11 + 4.29660e10i 1.58886 + 0.438497i 0.945113 − 0.326744i \(-0.105951\pi\)
0.643744 + 0.765241i \(0.277380\pi\)
\(278\) 7.62676e10 − 7.97697e10i 0.765841 − 0.801007i
\(279\) 4.35131e10 + 1.33920e11i 0.429934 + 1.32320i
\(280\) 1.29737e10 + 1.16765e9i 0.126140 + 0.0113528i
\(281\) 1.16309e11 + 1.01616e11i 1.11284 + 0.972260i 0.999773 − 0.0213271i \(-0.00678913\pi\)
0.113069 + 0.993587i \(0.463932\pi\)
\(282\) 3.05323e8 − 6.79856e9i 0.00287501 − 0.0640170i
\(283\) −7.35895e10 −0.681989 −0.340994 − 0.940065i \(-0.610764\pi\)
−0.340994 + 0.940065i \(0.610764\pi\)
\(284\) −5.62479e10 + 5.64472e10i −0.513066 + 0.514884i
\(285\) 1.63269e9 0.0146589
\(286\) −9.72521e9 + 2.16549e11i −0.0859512 + 1.91385i
\(287\) −8.79072e9 − 7.68022e9i −0.0764814 − 0.0668198i
\(288\) −1.41086e11 − 1.26980e10i −1.20842 − 0.108760i
\(289\) −3.24377e10 − 9.98330e10i −0.273533 − 0.841848i
\(290\) 2.97971e10 − 3.11653e10i 0.247390 − 0.258750i
\(291\) 5.73851e9 + 1.58373e9i 0.0469117 + 0.0129468i
\(292\) 4.68532e9 − 3.45884e10i 0.0377152 − 0.278425i
\(293\) −3.27491e9 − 2.41764e10i −0.0259594 − 0.191640i 0.973326 − 0.229424i \(-0.0736844\pi\)
−0.999286 + 0.0377842i \(0.987970\pi\)
\(294\) 7.47449e9 − 2.06283e9i 0.0583470 − 0.0161027i
\(295\) 2.35195e10 − 4.37066e10i 0.180813 − 0.336007i
\(296\) −8.96568e9 − 9.37736e9i −0.0678845 − 0.0710016i
\(297\) −4.70159e9 − 8.73702e9i −0.0350623 − 0.0651568i
\(298\) −1.08193e10 + 3.32983e10i −0.0794739 + 0.244596i
\(299\) −8.86274e10 + 2.07354e11i −0.641280 + 1.50035i
\(300\) 4.48682e9 + 8.14238e8i 0.0319811 + 0.00580371i
\(301\) −9.65019e10 − 7.01128e10i −0.677621 − 0.492320i
\(302\) 2.60141e11 − 2.34131e10i 1.79961 − 0.161967i
\(303\) −1.85811e9 − 4.34725e9i −0.0126642 − 0.0296294i
\(304\) 4.84392e10 + 2.12226e11i 0.325287 + 1.42517i
\(305\) −1.19645e10 − 1.81254e10i −0.0791669 − 0.119933i
\(306\) 5.84958e10 + 3.49496e10i 0.381398 + 0.227875i
\(307\) 1.05181e10 + 1.31893e10i 0.0675793 + 0.0847418i 0.814472 − 0.580203i \(-0.197027\pi\)
−0.746893 + 0.664944i \(0.768455\pi\)
\(308\) 9.40095e10 − 8.21336e10i 0.595242 − 0.520047i
\(309\) −2.13123e9 + 1.54843e9i −0.0132990 + 0.00966227i
\(310\) −6.75817e10 + 3.25456e10i −0.415625 + 0.200154i
\(311\) 1.06172e11 − 1.60844e11i 0.643558 − 0.974949i −0.355629 − 0.934627i \(-0.615733\pi\)
0.999187 − 0.0403216i \(-0.0128382\pi\)
\(312\) −5.04607e9 − 1.89382e9i −0.0301480 − 0.0113147i
\(313\) −1.49444e11 + 8.92884e10i −0.880092 + 0.525830i −0.880434 − 0.474170i \(-0.842748\pi\)
0.000341707 1.00000i \(0.499891\pi\)
\(314\) 2.35957e11 + 1.13631e11i 1.36978 + 0.659649i
\(315\) −6.05310e10 + 1.09848e10i −0.346402 + 0.0628627i
\(316\) −4.01765e10 + 1.76025e11i −0.226663 + 0.993074i
\(317\) 1.32897e11 − 4.98770e10i 0.739176 − 0.277417i 0.0467503 − 0.998907i \(-0.485113\pi\)
0.692426 + 0.721489i \(0.256542\pi\)
\(318\) −7.07089e7 + 8.86662e7i −0.000387750 + 0.000486223i
\(319\) 6.96612e9 + 1.55113e11i 0.0376646 + 0.838667i
\(320\) −8.46391e8 − 1.88464e10i −0.00451228 − 0.100474i
\(321\) 4.40476e7 − 5.52340e7i 0.000231553 − 0.000290358i
\(322\) 2.88853e11 − 1.08408e11i 1.49736 − 0.561968i
\(323\) 1.79910e10 − 7.88235e10i 0.0919693 − 0.402944i
\(324\) 1.40895e11 − 2.55687e10i 0.710304 − 0.128901i
\(325\) −3.18951e11 − 1.53599e11i −1.58580 − 0.763682i
\(326\) −1.58935e11 + 9.49590e10i −0.779362 + 0.465647i
\(327\) 6.65326e8 + 2.49701e8i 0.00321788 + 0.00120769i
\(328\) 3.00305e9 − 4.54943e9i 0.0143262 − 0.0217032i
\(329\) 2.74123e11 − 1.32011e11i 1.28992 − 0.621195i
\(330\) 2.13550e9 − 1.55153e9i 0.00991260 − 0.00720192i
\(331\) 2.75282e11 − 2.40507e11i 1.26053 − 1.10129i 0.270162 − 0.962815i \(-0.412923\pi\)
0.990366 − 0.138475i \(-0.0442200\pi\)
\(332\) 1.89712e11 + 2.37892e11i 0.856986 + 1.07463i
\(333\) 5.25992e10 + 3.14266e10i 0.234412 + 0.140055i
\(334\) −2.08429e11 − 3.15756e11i −0.916428 − 1.38833i
\(335\) −1.41916e10 − 6.21773e10i −0.0615642 − 0.269730i
\(336\) 7.36471e9 + 1.72306e10i 0.0315231 + 0.0737520i
\(337\) 1.83508e11 − 1.65160e10i 0.775033 − 0.0697542i 0.304940 − 0.952371i \(-0.401363\pi\)
0.470092 + 0.882617i \(0.344221\pi\)
\(338\) −6.45759e11 − 4.69171e11i −2.69119 − 1.95527i
\(339\) 3.35964e9 + 6.09685e8i 0.0138164 + 0.00250730i
\(340\) −6.00496e9 + 1.40493e10i −0.0243700 + 0.0570164i
\(341\) 8.34701e10 − 2.56894e11i 0.334300 − 1.02887i
\(342\) −1.91717e11 − 3.56270e11i −0.757781 − 1.40819i
\(343\) −8.74820e9 − 9.14990e9i −0.0341268 − 0.0356938i
\(344\) 2.63962e10 − 4.90523e10i 0.101631 − 0.188863i
\(345\) 2.64702e9 − 7.30532e8i 0.0100594 − 0.00277621i
\(346\) 1.38092e10 + 1.01944e11i 0.0517997 + 0.382401i
\(347\) 3.62318e10 − 2.67474e11i 0.134155 − 0.990374i −0.791276 − 0.611459i \(-0.790583\pi\)
0.925431 − 0.378915i \(-0.123703\pi\)
\(348\) 9.90405e9 + 2.73334e9i 0.0361998 + 0.00999051i
\(349\) −1.77843e11 + 1.86009e11i −0.641685 + 0.671150i −0.961016 − 0.276493i \(-0.910828\pi\)
0.319331 + 0.947643i \(0.396542\pi\)
\(350\) 1.49672e11 + 4.60644e11i 0.533132 + 1.64081i
\(351\) 5.07623e10 + 4.56869e9i 0.178509 + 0.0160661i
\(352\) 2.04636e11 + 1.78785e11i 0.710461 + 0.620711i
\(353\) −5.69344e9 + 1.26774e11i −0.0195159 + 0.434555i 0.965320 + 0.261068i \(0.0840748\pi\)
−0.984836 + 0.173487i \(0.944497\pi\)
\(354\) 2.80976e10 0.0950943
\(355\) −6.99662e10 − 2.79219e10i −0.233809 − 0.0933077i
\(356\) 1.81344e10 0.0598381
\(357\) 3.12247e8 − 6.95272e9i 0.00101740 − 0.0226542i
\(358\) −2.92680e11 − 2.55707e11i −0.941716 − 0.822752i
\(359\) 3.05581e11 + 2.75028e10i 0.970959 + 0.0873879i 0.563748 − 0.825947i \(-0.309359\pi\)
0.407210 + 0.913334i \(0.366502\pi\)
\(360\) −8.87770e9 − 2.73228e10i −0.0278573 − 0.0857360i
\(361\) −1.08739e11 + 1.13732e11i −0.336979 + 0.352453i
\(362\) −4.94699e11 − 1.36528e11i −1.51409 − 0.417863i
\(363\) 8.44097e8 − 6.23138e9i 0.00255160 − 0.0188367i
\(364\) 8.60800e10 + 6.35468e11i 0.257008 + 1.89731i
\(365\) 3.18074e10 − 8.77829e9i 0.0938016 − 0.0258876i
\(366\) 5.82611e9 − 1.08267e10i 0.0169713 − 0.0315379i
\(367\) −3.17655e11 − 3.32241e11i −0.914025 − 0.955995i 0.0851597 − 0.996367i \(-0.472860\pi\)
−0.999185 + 0.0403721i \(0.987146\pi\)
\(368\) 1.73491e11 + 3.22400e11i 0.493130 + 0.916390i
\(369\) −7.95562e9 + 2.44849e10i −0.0223386 + 0.0687510i
\(370\) −1.28282e10 + 3.00131e10i −0.0355843 + 0.0832536i
\(371\) −4.98874e9 − 9.05322e8i −0.0136712 − 0.00248096i
\(372\) −1.44602e10 − 1.05059e10i −0.0391499 − 0.0284440i
\(373\) −1.83052e10 + 1.64750e9i −0.0489650 + 0.00440693i −0.114095 − 0.993470i \(-0.536397\pi\)
0.0651297 + 0.997877i \(0.479254\pi\)
\(374\) −5.13738e10 − 1.20195e11i −0.135775 − 0.317661i
\(375\) 1.98342e9 + 8.68991e9i 0.00517932 + 0.0226921i
\(376\) 7.82728e10 + 1.18578e11i 0.201960 + 0.305956i
\(377\) −6.84709e11 − 4.09095e11i −1.74570 − 1.04301i
\(378\) −4.34778e10 − 5.45194e10i −0.109535 − 0.137353i
\(379\) 1.72378e11 − 1.50602e11i 0.429145 − 0.374933i −0.416093 − 0.909322i \(-0.636601\pi\)
0.845239 + 0.534389i \(0.179458\pi\)
\(380\) 7.33905e10 − 5.33213e10i 0.180557 − 0.131182i
\(381\) 2.24606e10 − 1.08164e10i 0.0546083 − 0.0262980i
\(382\) 3.76731e10 − 5.70723e10i 0.0905203 − 0.137132i
\(383\) −6.05298e10 − 2.27172e10i −0.143739 − 0.0539462i 0.278468 − 0.960445i \(-0.410173\pi\)
−0.422208 + 0.906499i \(0.638745\pi\)
\(384\) −1.20678e10 + 7.21016e9i −0.0283228 + 0.0169221i
\(385\) 1.06325e11 + 5.12033e10i 0.246638 + 0.118775i
\(386\) −9.56617e11 + 1.73600e11i −2.19329 + 0.398023i
\(387\) −5.85400e10 + 2.56480e11i −0.132664 + 0.581239i
\(388\) 3.09672e11 − 1.16222e11i 0.693680 − 0.260342i
\(389\) −1.12852e11 + 1.41512e11i −0.249883 + 0.313343i −0.890914 − 0.454172i \(-0.849935\pi\)
0.641032 + 0.767514i \(0.278507\pi\)
\(390\) 6.08352e8 + 1.35460e10i 0.00133157 + 0.0296497i
\(391\) −6.10073e9 − 1.35843e11i −0.0132004 − 0.293929i
\(392\) −1.00934e11 + 1.26567e11i −0.215898 + 0.270728i
\(393\) −2.21470e10 + 8.31191e9i −0.0468326 + 0.0175766i
\(394\) 9.43239e10 − 4.13260e11i 0.197192 − 0.863954i
\(395\) −1.67940e11 + 3.04766e10i −0.347110 + 0.0629911i
\(396\) −2.48055e11 − 1.19457e11i −0.506898 − 0.244109i
\(397\) 3.67774e10 − 2.19735e10i 0.0743060 − 0.0443958i −0.475266 − 0.879842i \(-0.657648\pi\)
0.549572 + 0.835447i \(0.314791\pi\)
\(398\) 4.52002e11 + 1.69639e11i 0.902956 + 0.338885i
\(399\) −2.27644e10 + 3.44865e10i −0.0449653 + 0.0681195i
\(400\) −5.17839e11 + 2.49378e11i −1.01141 + 0.487067i
\(401\) 5.62195e10 − 4.08459e10i 0.108577 − 0.0788857i −0.532172 − 0.846636i \(-0.678624\pi\)
0.640749 + 0.767751i \(0.278624\pi\)
\(402\) 2.71890e10 − 2.37543e10i 0.0519250 − 0.0453655i
\(403\) 8.65136e11 + 1.08485e12i 1.63385 + 2.04878i
\(404\) −2.25498e11 − 1.34729e11i −0.421140 − 0.251619i
\(405\) 7.45748e10 + 1.12976e11i 0.137735 + 0.208660i
\(406\) 2.42833e11 + 1.06392e12i 0.443547 + 1.94331i
\(407\) −4.61950e10 − 1.08079e11i −0.0834489 − 0.195238i
\(408\) 3.23702e9 − 2.91337e8i 0.00578328 − 0.000520505i
\(409\) −1.25157e11 − 9.09321e10i −0.221157 − 0.160680i 0.471690 − 0.881764i \(-0.343644\pi\)
−0.692847 + 0.721084i \(0.743644\pi\)
\(410\) −1.34939e10 − 2.44878e9i −0.0235836 − 0.00427979i
\(411\) −1.40002e10 + 3.27551e10i −0.0242017 + 0.0566227i
\(412\) −4.52307e10 + 1.39206e11i −0.0773386 + 0.238024i
\(413\) 5.95263e11 + 1.10618e12i 1.00678 + 1.87091i
\(414\) −4.70233e11 − 4.91825e11i −0.786705 − 0.822828i
\(415\) −1.36305e11 + 2.53298e11i −0.225578 + 0.419193i
\(416\) −1.34559e12 + 3.71359e11i −2.20289 + 0.607959i
\(417\) 3.33709e9 + 2.46354e10i 0.00540450 + 0.0398976i
\(418\) −1.04177e11 + 7.69069e11i −0.166909 + 1.23217i
\(419\) 4.32117e11 + 1.19257e11i 0.684917 + 0.189025i 0.591141 − 0.806568i \(-0.298678\pi\)
0.0937762 + 0.995593i \(0.470106\pi\)
\(420\) 5.39646e9 − 5.64426e9i 0.00846228 − 0.00885085i
\(421\) −1.35945e11 − 4.18397e11i −0.210909 − 0.649111i −0.999419 − 0.0340886i \(-0.989147\pi\)
0.788510 − 0.615022i \(-0.210853\pi\)
\(422\) 9.13996e10 + 8.22611e9i 0.140294 + 0.0126267i
\(423\) −5.05330e11 − 4.41494e11i −0.767439 − 0.670491i
\(424\) 1.06227e8 − 2.36534e9i 0.000159621 − 0.00355424i
\(425\) 2.13473e11 0.317389
\(426\) −4.84978e9 − 4.23693e10i −0.00713475 − 0.0623316i
\(427\) 5.49671e11 0.800161
\(428\) 1.76107e8 − 3.92133e9i 0.000253676 − 0.00564854i
\(429\) −3.67718e10 − 3.21265e10i −0.0524151 − 0.0457937i
\(430\) −1.39576e11 − 1.25621e10i −0.196881 − 0.0177196i
\(431\) −2.74052e11 − 8.43447e11i −0.382548 − 1.17736i −0.938243 − 0.345976i \(-0.887548\pi\)
0.555696 − 0.831386i \(-0.312452\pi\)
\(432\) 5.71850e10 − 5.98108e10i 0.0789960 − 0.0826234i
\(433\) −2.03519e11 − 5.61678e10i −0.278234 − 0.0767877i 0.124135 − 0.992265i \(-0.460384\pi\)
−0.402369 + 0.915478i \(0.631813\pi\)
\(434\) 2.54835e11 − 1.88127e12i 0.344791 − 2.54535i
\(435\) 1.30377e9 + 9.62482e9i 0.00174582 + 0.0128882i
\(436\) 3.80617e10 − 1.05044e10i 0.0504428 − 0.0139213i
\(437\) −3.82584e11 + 7.10960e11i −0.501834 + 0.932563i
\(438\) 1.29087e10 + 1.35015e10i 0.0167591 + 0.0175286i
\(439\) 3.35568e11 + 6.23591e11i 0.431212 + 0.801326i 0.999773 − 0.0213152i \(-0.00678536\pi\)
−0.568561 + 0.822641i \(0.692500\pi\)
\(440\) −1.70299e10 + 5.24125e10i −0.0216608 + 0.0666650i
\(441\) 3.00487e11 − 7.03025e11i 0.378314 − 0.885110i
\(442\) 6.60681e11 + 1.19896e11i 0.823363 + 0.149418i
\(443\) 5.78693e11 + 4.20445e11i 0.713890 + 0.518672i 0.884426 − 0.466680i \(-0.154550\pi\)
−0.170536 + 0.985351i \(0.554550\pi\)
\(444\) −7.74623e9 + 6.97174e8i −0.00945948 + 0.000851369i
\(445\) 6.73770e9 + 1.57636e10i 0.00814501 + 0.0190562i
\(446\) −3.97984e11 − 1.74368e12i −0.476276 − 2.08670i
\(447\) −4.34481e9 − 6.58211e9i −0.00514739 − 0.00779797i
\(448\) 4.09883e11 + 2.44894e11i 0.480738 + 0.287228i
\(449\) −5.36460e10 − 6.72699e10i −0.0622915 − 0.0781110i 0.749710 − 0.661767i \(-0.230193\pi\)
−0.812001 + 0.583656i \(0.801622\pi\)
\(450\) 8.04449e11 − 7.02826e11i 0.924788 − 0.807963i
\(451\) 3.99539e10 − 2.90282e10i 0.0454742 − 0.0330389i
\(452\) 1.70929e11 − 8.23152e10i 0.192616 − 0.0927592i
\(453\) −3.24128e10 + 4.91032e10i −0.0361638 + 0.0547858i
\(454\) 6.06485e11 + 2.27617e11i 0.669990 + 0.251452i
\(455\) −5.20410e11 + 3.10930e11i −0.569238 + 0.340104i
\(456\) −1.73860e10 − 8.37265e9i −0.0188303 − 0.00906820i
\(457\) 1.67947e12 − 3.04778e11i 1.80115 − 0.326860i 0.828647 − 0.559771i \(-0.189111\pi\)
0.972498 + 0.232911i \(0.0748252\pi\)
\(458\) −4.53359e11 + 1.98629e12i −0.481446 + 2.10935i
\(459\) −2.87744e10 + 1.07992e10i −0.0302586 + 0.0113563i
\(460\) 9.51271e10 − 1.19286e11i 0.0990590 − 0.124216i
\(461\) −4.90958e10 − 1.09320e12i −0.0506280 − 1.12732i −0.850102 − 0.526618i \(-0.823460\pi\)
0.799474 − 0.600701i \(-0.205112\pi\)
\(462\) 2.99729e9 + 6.67399e10i 0.00306084 + 0.0681548i
\(463\) −2.69237e11 + 3.37613e11i −0.272283 + 0.341432i −0.899107 − 0.437729i \(-0.855783\pi\)
0.626824 + 0.779161i \(0.284354\pi\)
\(464\) −1.21240e12 + 4.55023e11i −1.21427 + 0.455725i
\(465\) 3.75989e9 − 1.64732e10i 0.00372938 − 0.0163395i
\(466\) −2.53376e12 + 4.59809e11i −2.48902 + 0.451691i
\(467\) 2.08563e11 + 1.00439e11i 0.202914 + 0.0977181i 0.532581 − 0.846379i \(-0.321222\pi\)
−0.329667 + 0.944097i \(0.606937\pi\)
\(468\) 1.21412e12 − 7.25400e11i 1.16991 − 0.698990i
\(469\) 1.51121e12 + 5.67166e11i 1.44227 + 0.541293i
\(470\) 1.96921e11 − 2.98322e11i 0.186145 − 0.281997i
\(471\) −5.31518e10 + 2.55965e10i −0.0497650 + 0.0239655i
\(472\) −4.74584e11 + 3.44805e11i −0.440123 + 0.319768i
\(473\) 3.80039e11 − 3.32030e11i 0.349103 − 0.305002i
\(474\) −6.02445e10 − 7.55442e10i −0.0548170 − 0.0687383i
\(475\) −1.08805e12 − 6.50080e11i −0.980681 − 0.585930i
\(476\) −2.13030e11 − 3.22727e11i −0.190199 − 0.288140i
\(477\) 2.48829e9 + 1.09019e10i 0.00220074 + 0.00964205i
\(478\) −8.04946e11 − 1.88327e12i −0.705247 − 1.65001i
\(479\) 8.06170e11 − 7.25566e10i 0.699708 − 0.0629748i 0.265927 − 0.963993i \(-0.414322\pi\)
0.433781 + 0.901018i \(0.357179\pi\)
\(480\) 1.37518e10 + 9.99126e9i 0.0118243 + 0.00859082i
\(481\) 5.94081e11 + 1.07810e11i 0.506049 + 0.0918344i
\(482\) 8.39216e11 − 1.96344e12i 0.708210 − 1.65694i
\(483\) −2.14763e10 + 6.60973e10i −0.0179555 + 0.0552614i
\(484\) −1.65565e11 − 3.07671e11i −0.137140 − 0.254849i
\(485\) 2.16084e11 + 2.26006e11i 0.177331 + 0.185474i
\(486\) −1.09359e11 + 2.03224e11i −0.0889186 + 0.165238i
\(487\) −3.81308e11 + 1.05234e11i −0.307182 + 0.0847769i −0.416229 − 0.909260i \(-0.636649\pi\)
0.109047 + 0.994037i \(0.465220\pi\)
\(488\) 3.44562e10 + 2.54366e11i 0.0275029 + 0.203034i
\(489\) 5.59821e9 − 4.13277e10i 0.00442751 − 0.0326852i
\(490\) 3.92598e11 + 1.08350e11i 0.307656 + 0.0849077i
\(491\) 4.95016e10 − 5.17746e10i 0.0384372 − 0.0402022i −0.703297 − 0.710896i \(-0.748289\pi\)
0.741734 + 0.670694i \(0.234004\pi\)
\(492\) −1.00984e9 − 3.10796e9i −0.000776978 − 0.00239129i
\(493\) 4.79036e11 + 4.31140e10i 0.365222 + 0.0328706i
\(494\) −3.00232e12 − 2.62305e12i −2.26822 − 1.98168i
\(495\) 1.16771e10 − 2.60010e11i 0.00874199 − 0.194656i
\(496\) 2.25282e12 1.67132
\(497\) 1.56531e12 − 1.08855e12i 1.15079 − 0.800284i
\(498\) −1.62837e11 −0.118637
\(499\) 1.90382e10 − 4.23919e11i 0.0137459 − 0.306077i −0.980328 − 0.197374i \(-0.936759\pi\)
0.994074 − 0.108703i \(-0.0346698\pi\)
\(500\) 3.72955e11 + 3.25841e11i 0.266865 + 0.233153i
\(501\) 8.48829e10 + 7.63960e9i 0.0601936 + 0.00541753i
\(502\) 4.59268e11 + 1.41348e12i 0.322775 + 0.993399i
\(503\) −1.73999e12 + 1.81988e12i −1.21197 + 1.26762i −0.258536 + 0.966002i \(0.583240\pi\)
−0.953430 + 0.301615i \(0.902474\pi\)
\(504\) 7.00904e11 + 1.93437e11i 0.483862 + 0.133537i
\(505\) 3.33332e10 − 2.46075e11i 0.0228069 − 0.168367i
\(506\) 1.75213e11 + 1.29347e12i 0.118820 + 0.877164i
\(507\) 1.73324e11 − 4.78343e10i 0.116499 − 0.0321517i
\(508\) 6.56367e11 − 1.21973e12i 0.437281 − 0.812603i
\(509\) 1.40642e12 + 1.47100e12i 0.928719 + 0.971364i 0.999659 − 0.0261170i \(-0.00831426\pi\)
−0.0709403 + 0.997481i \(0.522600\pi\)
\(510\) −3.87467e9 − 7.20035e9i −0.00253612 − 0.00471290i
\(511\) −2.58066e11 + 7.94245e11i −0.167431 + 0.515301i
\(512\) −6.27832e11 + 1.46888e12i −0.403765 + 0.944654i
\(513\) 1.79547e11 + 3.25830e10i 0.114459 + 0.0207712i
\(514\) 2.44948e11 + 1.77965e11i 0.154789 + 0.112461i
\(515\) −1.37812e11 + 1.24033e10i −0.0863288 + 0.00776973i
\(516\) −1.31244e10 − 3.07061e10i −0.00814997 − 0.0190678i
\(517\) 2.86431e11 + 1.25494e12i 0.176325 + 0.772529i
\(518\) −4.55090e11 − 6.89431e11i −0.277724 − 0.420733i
\(519\) −1.98934e10 − 1.18858e10i −0.0120353 − 0.00719075i
\(520\) −1.76508e11 − 2.21334e11i −0.105864 − 0.132750i
\(521\) −1.05110e12 + 9.18318e11i −0.624991 + 0.546038i −0.911114 − 0.412155i \(-0.864776\pi\)
0.286123 + 0.958193i \(0.407634\pi\)
\(522\) 1.94714e12 − 1.41468e12i 1.14784 − 0.833952i
\(523\) 9.48371e11 − 4.56711e11i 0.554269 − 0.266922i −0.135713 − 0.990748i \(-0.543333\pi\)
0.689982 + 0.723826i \(0.257618\pi\)
\(524\) −7.24066e11 + 1.09691e12i −0.419554 + 0.635597i
\(525\) −1.02148e11 − 3.83367e10i −0.0586829 − 0.0220241i
\(526\) 3.73121e12 − 2.22930e12i 2.12527 − 1.26979i
\(527\) −7.53864e11 − 3.63042e11i −0.425741 − 0.205026i
\(528\) −7.80034e10 + 1.41555e10i −0.0436778 + 0.00792635i
\(529\) 9.86378e10 − 4.32160e11i 0.0547637 − 0.239935i
\(530\) −5.57694e9 + 2.09306e9i −0.00307011 + 0.00115223i
\(531\) 1.72736e12 − 2.16604e12i 0.942883 − 1.18234i
\(532\) 1.03007e11 + 2.29364e12i 0.0557528 + 1.24143i
\(533\) 1.13819e10 + 2.53438e11i 0.00610861 + 0.136019i
\(534\) −6.05089e9 + 7.58758e9i −0.00322021 + 0.00403801i
\(535\) 3.47412e9 − 1.30386e9i 0.00183338 − 0.000688079i
\(536\) −1.67731e11 + 7.34880e11i −0.0877754 + 0.384569i
\(537\) 8.61403e10 − 1.56322e10i 0.0447015 − 0.00811213i
\(538\) −1.17990e12 − 5.68212e11i −0.607193 − 0.292409i
\(539\) −1.25902e12 + 7.52227e11i −0.642512 + 0.383883i
\(540\) −3.22853e10 − 1.21169e10i −0.0163393 − 0.00613224i
\(541\) −1.86842e12 + 2.83053e12i −0.937749 + 1.42063i −0.0307352 + 0.999528i \(0.509785\pi\)
−0.907014 + 0.421101i \(0.861644\pi\)
\(542\) 3.40176e12 − 1.63820e12i 1.69319 − 0.815399i
\(543\) 9.35241e10 − 6.79492e10i 0.0461662 − 0.0335417i
\(544\) 6.33894e11 − 5.53816e11i 0.310328 − 0.271126i
\(545\) 2.32726e10 + 2.91830e10i 0.0112996 + 0.0141692i
\(546\) −2.94608e11 − 1.76020e11i −0.141866 − 0.0847607i
\(547\) 2.13757e12 + 3.23827e12i 1.02088 + 1.54657i 0.824353 + 0.566076i \(0.191539\pi\)
0.196531 + 0.980498i \(0.437032\pi\)
\(548\) 4.40416e11 + 1.92959e12i 0.208617 + 0.914012i
\(549\) −4.76460e11 − 1.11473e12i −0.223847 − 0.523715i
\(550\) −2.04090e12 + 1.83684e11i −0.951018 + 0.0855932i
\(551\) −2.31031e12 − 1.67854e12i −1.06779 − 0.775798i
\(552\) −3.19335e10 − 5.79507e9i −0.0146393 − 0.00265664i
\(553\) 1.69781e12 − 3.97223e12i 0.772017 − 1.80622i
\(554\) −1.48399e12 + 4.56725e12i −0.669325 + 2.05997i
\(555\) −3.48409e9 − 6.47452e9i −0.00155873 − 0.00289660i
\(556\) 9.54559e11 + 9.98391e11i 0.423610 + 0.443061i
\(557\) −1.06496e12 + 1.97904e12i −0.468799 + 0.871175i 0.530919 + 0.847423i \(0.321847\pi\)
−0.999718 + 0.0237521i \(0.992439\pi\)
\(558\) −4.03611e12 + 1.11390e12i −1.76242 + 0.486397i
\(559\) 3.47984e11 + 2.56892e12i 0.150732 + 1.11275i
\(560\) −1.32118e11 + 9.75335e11i −0.0567696 + 0.419090i
\(561\) 2.83835e10 + 7.83336e9i 0.0120986 + 0.00333899i
\(562\) −3.17364e12 + 3.31937e12i −1.34198 + 1.40360i
\(563\) −6.37034e11 − 1.96059e12i −0.267224 − 0.822430i −0.991173 − 0.132577i \(-0.957675\pi\)
0.723949 − 0.689853i \(-0.242325\pi\)
\(564\) 8.48331e10 + 7.63511e9i 0.0353028 + 0.00317731i
\(565\) 1.35061e11 + 1.18000e11i 0.0557588 + 0.0487150i
\(566\) 9.81719e10 − 2.18597e12i 0.0402081 − 0.895302i
\(567\) −3.42611e12 −1.39212
\(568\) 6.01859e11 + 6.56125e11i 0.242620 + 0.264496i
\(569\) −1.73998e12 −0.695889 −0.347945 − 0.937515i \(-0.613120\pi\)
−0.347945 + 0.937515i \(0.613120\pi\)
\(570\) −2.17809e9 + 4.84989e10i −0.000864249 + 0.0192440i
\(571\) 8.17658e11 + 7.14366e11i 0.321891 + 0.281228i 0.803683 − 0.595058i \(-0.202871\pi\)
−0.481792 + 0.876286i \(0.660014\pi\)
\(572\) −2.70212e12 − 2.43195e11i −1.05541 − 0.0949888i
\(573\) 4.76023e9 + 1.46505e10i 0.00184473 + 0.00567749i
\(574\) 2.39867e11 − 2.50881e11i 0.0922289 − 0.0964639i
\(575\) −2.05489e12 − 5.67112e11i −0.783939 − 0.216353i
\(576\) 1.41354e11 − 1.04352e12i 0.0535067 − 0.395002i
\(577\) 2.99348e11 + 2.20988e12i 0.112431 + 0.829998i 0.956081 + 0.293104i \(0.0946882\pi\)
−0.843650 + 0.536894i \(0.819598\pi\)
\(578\) 3.00880e12 − 8.30375e11i 1.12129 − 0.309456i
\(579\) 1.03781e11 − 1.92857e11i 0.0383764 − 0.0713152i
\(580\) 3.72938e11 + 3.90062e11i 0.136839 + 0.143123i
\(581\) −3.44979e12 − 6.41079e12i −1.25603 − 2.33410i
\(582\) −5.46999e10 + 1.68349e11i −0.0197621 + 0.0608215i
\(583\) 8.43064e9 − 1.97245e10i 0.00302240 − 0.00707126i
\(584\) −3.83722e11 − 6.96353e10i −0.136508 − 0.0247726i
\(585\) 1.08166e12 + 7.85874e11i 0.381848 + 0.277429i
\(586\) 7.22524e11 − 6.50284e10i 0.253112 − 0.0227805i
\(587\) −1.99705e12 − 4.67232e12i −0.694251 − 1.62428i −0.778355 − 0.627824i \(-0.783946\pi\)
0.0841044 − 0.996457i \(-0.473197\pi\)
\(588\) 2.15951e10 + 9.46142e10i 0.00745001 + 0.0326406i
\(589\) 2.73682e12 + 4.14610e12i 0.936973 + 1.41945i
\(590\) 1.26692e12 + 7.56950e11i 0.430443 + 0.257178i
\(591\) 5.95341e10 + 7.46534e10i 0.0200734 + 0.0251713i
\(592\) 7.38226e11 − 6.44968e11i 0.247025 − 0.215820i
\(593\) 2.93767e12 − 2.13434e12i 0.975567 − 0.708791i 0.0188532 − 0.999822i \(-0.493998\pi\)
0.956713 + 0.291032i \(0.0939985\pi\)
\(594\) 2.65804e11 − 1.28005e11i 0.0876038 − 0.0421878i
\(595\) 2.01386e11 − 3.05087e11i 0.0658723 − 0.0997923i
\(596\) −4.10264e11 − 1.53975e11i −0.133185 − 0.0499851i
\(597\) −9.33587e10 + 5.57792e10i −0.0300795 + 0.0179717i
\(598\) −6.04119e12 − 2.90928e12i −1.93182 − 0.930317i
\(599\) 3.86410e12 − 7.01230e11i 1.22639 − 0.222556i 0.473552 − 0.880766i \(-0.342972\pi\)
0.752835 + 0.658210i \(0.228686\pi\)
\(600\) 1.13375e10 − 4.96730e10i 0.00357140 − 0.0156473i
\(601\) −5.28801e12 + 1.98462e12i −1.65332 + 0.620502i −0.991611 − 0.129258i \(-0.958741\pi\)
−0.661710 + 0.749760i \(0.730169\pi\)
\(602\) 2.21143e12 − 2.77304e12i 0.686260 − 0.860543i
\(603\) −1.59716e11 − 3.55636e12i −0.0491950 − 1.09541i
\(604\) 1.46666e11 + 3.26577e12i 0.0448397 + 0.998434i
\(605\) 2.05934e11 − 2.58233e11i 0.0624927 − 0.0783633i
\(606\) 1.31613e11 − 4.93953e10i 0.0396436 − 0.0148785i
\(607\) −8.07344e11 + 3.53721e12i −0.241385 + 1.05757i 0.698373 + 0.715734i \(0.253908\pi\)
−0.939758 + 0.341841i \(0.888950\pi\)
\(608\) −4.91742e12 + 8.92379e11i −1.45939 + 0.264840i
\(609\) −2.21478e11 − 1.06658e11i −0.0652459 − 0.0314208i
\(610\) 5.54373e11 − 3.31222e11i 0.162113 − 0.0968580i
\(611\) −6.19072e12 − 2.32342e12i −1.79703 − 0.674437i
\(612\) −4.69833e11 + 7.11767e11i −0.135382 + 0.205096i
\(613\) 3.24237e12 − 1.56144e12i 0.927449 − 0.446636i 0.0917242 − 0.995784i \(-0.470762\pi\)
0.835725 + 0.549149i \(0.185048\pi\)
\(614\) −4.05817e11 + 2.94843e11i −0.115232 + 0.0837208i
\(615\) 2.32645e9 − 2.03256e9i 0.000655777 − 0.000572935i
\(616\) −8.69638e11 − 1.09049e12i −0.243347 − 0.305147i
\(617\) 4.43196e12 + 2.64797e12i 1.23115 + 0.735581i 0.973063 − 0.230540i \(-0.0740492\pi\)
0.258092 + 0.966120i \(0.416906\pi\)
\(618\) −4.31528e10 − 6.53737e10i −0.0119004 − 0.0180283i
\(619\) −6.09286e11 − 2.66945e12i −0.166807 − 0.730827i −0.987260 − 0.159114i \(-0.949136\pi\)
0.820454 − 0.571713i \(-0.193721\pi\)
\(620\) −3.68980e11 − 8.63271e11i −0.100286 − 0.234630i
\(621\) 3.05671e11 − 2.75109e10i 0.0824788 − 0.00742323i
\(622\) 4.63620e12 + 3.36839e12i 1.24195 + 0.902332i
\(623\) −4.26910e11 − 7.74727e10i −0.113538 − 0.0206040i
\(624\) 1.60058e11 − 3.74473e11i 0.0422616 − 0.0988758i
\(625\) 9.59428e11 − 2.95281e12i 0.251508 − 0.774063i
\(626\) −2.45294e12 − 4.55832e12i −0.638413 − 1.18637i
\(627\) −1.20814e11 − 1.26361e11i −0.0312185 − 0.0326520i
\(628\) −1.55326e12 + 2.88644e12i −0.398497 + 0.740532i
\(629\) −3.50970e11 + 9.68616e10i −0.0894010 + 0.0246731i
\(630\) −2.45549e11 − 1.81272e12i −0.0621021 − 0.458456i
\(631\) −1.65585e11 + 1.22240e12i −0.0415805 + 0.306960i 0.958202 + 0.286093i \(0.0923567\pi\)
−0.999782 + 0.0208663i \(0.993358\pi\)
\(632\) 1.94462e12 + 5.36681e11i 0.484850 + 0.133810i
\(633\) −1.42856e10 + 1.49416e10i −0.00353657 + 0.00369896i
\(634\) 1.30430e12 + 4.01422e12i 0.320609 + 0.986733i
\(635\) 1.30414e12 + 1.17375e11i 0.318305 + 0.0286480i
\(636\) −1.06892e9 − 9.33884e8i −0.000259052 − 0.000226327i
\(637\) 3.38010e11 − 7.52637e12i 0.0813395 − 1.81117i
\(638\) −4.61690e12 −1.10321
\(639\) −3.56440e12 − 2.23088e12i −0.845732 − 0.529324i
\(640\) −7.38378e11 −0.173968
\(641\) −4.80262e10 + 1.06939e12i −0.0112361 + 0.250192i 0.985512 + 0.169608i \(0.0542501\pi\)
−0.996748 + 0.0805843i \(0.974321\pi\)
\(642\) 1.58196e9 + 1.38211e9i 0.000367525 + 0.000321097i
\(643\) 2.21420e12 + 1.99282e11i 0.510820 + 0.0459747i 0.342052 − 0.939681i \(-0.388878\pi\)
0.168768 + 0.985656i \(0.446021\pi\)
\(644\) 1.19327e12 + 3.67250e12i 0.273370 + 0.841347i
\(645\) 2.18155e10 − 2.28172e10i 0.00496303 − 0.00519092i
\(646\) 2.31744e12 + 6.39573e11i 0.523555 + 0.144492i
\(647\) −2.13006e11 + 1.57248e12i −0.0477885 + 0.352789i 0.951230 + 0.308484i \(0.0998216\pi\)
−0.999018 + 0.0443050i \(0.985893\pi\)
\(648\) −2.14766e11 − 1.58547e12i −0.0478497 − 0.353240i
\(649\) −5.12301e12 + 1.41386e12i −1.13351 + 0.312828i
\(650\) 4.98812e12 − 9.26949e12i 1.09604 − 2.03679i
\(651\) 2.95530e11 + 3.09101e11i 0.0644893 + 0.0674505i
\(652\) −1.09806e12 − 2.04053e12i −0.237964 − 0.442211i
\(653\) −1.82327e12 + 5.61146e12i −0.392412 + 1.20772i 0.538546 + 0.842596i \(0.318974\pi\)
−0.930958 + 0.365125i \(0.881026\pi\)
\(654\) −8.30492e9 + 1.94303e10i −0.00177515 + 0.00415317i
\(655\) −1.22253e12 − 2.21857e11i −0.259522 − 0.0470964i
\(656\) 3.33225e11 + 2.42102e11i 0.0702538 + 0.0510424i
\(657\) 1.83442e12 − 1.65101e11i 0.384110 − 0.0345705i
\(658\) 3.55567e12 + 8.31890e12i 0.739443 + 1.73001i
\(659\) 7.00973e11 + 3.07116e12i 0.144783 + 0.634335i 0.994286 + 0.106751i \(0.0340448\pi\)
−0.849503 + 0.527584i \(0.823098\pi\)
\(660\) 1.82002e10 + 2.75721e10i 0.00373360 + 0.00565617i
\(661\) −7.05533e12 − 4.21537e12i −1.43751 − 0.858872i −0.438309 − 0.898824i \(-0.644422\pi\)
−0.999202 + 0.0399519i \(0.987280\pi\)
\(662\) 6.77699e12 + 8.49807e12i 1.37144 + 1.71973i
\(663\) −1.13907e11 + 9.95172e10i −0.0228949 + 0.0200026i
\(664\) 2.75041e12 − 1.99829e12i 0.549086 − 0.398934i
\(665\) −1.95552e12 + 9.41727e11i −0.387761 + 0.186736i
\(666\) −1.00369e12 + 1.52053e12i −0.197682 + 0.299475i
\(667\) −4.49666e12 − 1.68762e12i −0.879677 − 0.330148i
\(668\) 4.06504e12 − 2.42875e12i 0.789897 − 0.471941i
\(669\) 3.62986e11 + 1.74805e11i 0.0700603 + 0.0337393i
\(670\) 1.86590e12 − 3.38611e11i 0.357727 − 0.0649178i
\(671\) −5.17473e11 + 2.26720e12i −0.0985453 + 0.431755i
\(672\) −4.02779e11 + 1.51166e11i −0.0761913 + 0.0285951i
\(673\) 4.34875e11 − 5.45316e11i 0.0817140 − 0.102466i −0.739294 − 0.673383i \(-0.764841\pi\)
0.821008 + 0.570917i \(0.193412\pi\)
\(674\) 2.45798e11 + 5.47311e12i 0.0458784 + 1.02156i
\(675\) 2.16162e10 + 4.81322e11i 0.00400786 + 0.0892418i
\(676\) 6.22881e12 − 7.81068e12i 1.14721 − 1.43856i
\(677\) 7.45856e12 − 2.79925e12i 1.36460 − 0.512144i 0.441695 − 0.897165i \(-0.354377\pi\)
0.922908 + 0.385021i \(0.125806\pi\)
\(678\) −2.25925e10 + 9.89843e10i −0.00410611 + 0.0179901i
\(679\) −7.78664e12 + 1.41307e12i −1.40584 + 0.255122i
\(680\) 1.53806e11 + 7.40690e10i 0.0275856 + 0.0132845i
\(681\) −1.25266e11 + 7.48432e10i −0.0223189 + 0.0133349i
\(682\) 7.51966e12 + 2.82218e12i 1.33097 + 0.499522i
\(683\) 1.93322e12 − 2.92870e12i 0.339928 − 0.514969i −0.623896 − 0.781507i \(-0.714451\pi\)
0.963824 + 0.266538i \(0.0858798\pi\)
\(684\) 4.56222e12 − 2.19705e12i 0.796936 − 0.383784i
\(685\) −1.51369e12 + 1.09976e12i −0.262682 + 0.190850i
\(686\) 2.83467e11 − 2.47658e11i 0.0488702 − 0.0426966i
\(687\) −2.86145e11 − 3.58814e11i −0.0490095 − 0.0614560i
\(688\) 3.61314e12 + 2.15875e12i 0.614804 + 0.367328i
\(689\) 6.07040e10 + 9.19626e10i 0.0102620 + 0.0155462i
\(690\) 1.81691e10 + 7.96040e10i 0.00305149 + 0.0133695i
\(691\) 8.94350e11 + 2.09244e12i 0.149230 + 0.349141i 0.977420 − 0.211307i \(-0.0677719\pi\)
−0.828190 + 0.560448i \(0.810629\pi\)
\(692\) −1.28239e12 + 1.15417e11i −0.212590 + 0.0191335i
\(693\) 5.32924e12 + 3.87192e12i 0.877740 + 0.637716i
\(694\) 7.89695e12 + 1.43308e12i 1.29224 + 0.234506i
\(695\) −5.13209e11 + 1.20071e12i −0.0834378 + 0.195212i
\(696\) 3.54738e10 − 1.09177e11i 0.00573016 − 0.0176356i
\(697\) −7.24927e10 − 1.34714e11i −0.0116345 − 0.0216205i
\(698\) −5.28812e12 − 5.53094e12i −0.843241 − 0.881961i
\(699\) 2.74881e11 − 5.10814e11i 0.0435509 − 0.0809311i
\(700\) −5.84362e12 + 1.61274e12i −0.919900 + 0.253876i
\(701\) −1.92618e11 − 1.42197e12i −0.0301278 − 0.222412i 0.969626 − 0.244591i \(-0.0786538\pi\)
−0.999754 + 0.0221793i \(0.992940\pi\)
\(702\) −2.03432e11 + 1.50179e12i −0.0316156 + 0.233396i
\(703\) 2.08383e12 + 5.75101e11i 0.321783 + 0.0888066i
\(704\) −1.39597e12 + 1.46007e12i −0.214190 + 0.224025i
\(705\) 2.48822e10 + 7.65794e10i 0.00379347 + 0.0116751i
\(706\) −3.75822e12 − 3.38246e11i −0.569326 − 0.0512402i
\(707\) 4.73296e12 + 4.13507e12i 0.712436 + 0.622436i
\(708\) −1.57775e10 + 3.51313e11i −0.00235987 + 0.0525466i
\(709\) −1.30646e11 −0.0194173 −0.00970863 − 0.999953i \(-0.503090\pi\)
−0.00970863 + 0.999953i \(0.503090\pi\)
\(710\) 9.22754e11 − 2.04109e12i 0.136277 − 0.301439i
\(711\) −9.52737e12 −1.39817
\(712\) 9.09038e9 − 2.02413e11i 0.00132563 − 0.0295174i
\(713\) 6.29223e12 + 5.49735e12i 0.911804 + 0.796619i
\(714\) 2.06113e11 + 1.85505e10i 0.0296800 + 0.00267125i
\(715\) −7.92551e11 − 2.43922e12i −0.113410 − 0.349039i
\(716\) 3.36153e12 − 3.51589e12i 0.478001 − 0.499950i
\(717\) 4.44725e11 + 1.22736e11i 0.0628428 + 0.0173435i
\(718\) −1.22462e12 + 9.04054e12i −0.171966 + 1.26950i
\(719\) 7.97665e11 + 5.88860e12i 0.111312 + 0.821735i 0.957415 + 0.288716i \(0.0932283\pi\)
−0.846103 + 0.533019i \(0.821057\pi\)
\(720\) 2.09250e12 − 5.77494e11i 0.290181 − 0.0800849i
\(721\) 1.65950e12 − 3.08388e12i 0.228702 − 0.424999i
\(722\) −3.23334e12 − 3.38180e12i −0.442826 − 0.463160i
\(723\) 2.27928e11 + 4.23560e11i 0.0310223 + 0.0576492i
\(724\) 1.98484e12 − 6.10872e12i 0.268474 − 0.826279i
\(725\) 2.96341e12 − 6.93324e12i 0.398355 − 0.931998i
\(726\) 1.83976e11 + 3.33867e10i 0.0245780 + 0.00446025i
\(727\) 8.88807e12 + 6.45756e12i 1.18006 + 0.857361i 0.992178 − 0.124832i \(-0.0398390\pi\)
0.187878 + 0.982192i \(0.439839\pi\)
\(728\) 7.13615e12 − 6.42265e11i 0.941613 − 0.0847467i
\(729\) 2.95614e12 + 6.91624e12i 0.387660 + 0.906976i
\(730\) 2.18325e11 + 9.56545e11i 0.0284545 + 0.124667i
\(731\) −8.61186e11 − 1.30464e12i −0.111550 − 0.168991i
\(732\) 1.32099e11 + 7.89252e10i 0.0170059 + 0.0101605i
\(733\) −7.87741e12 − 9.87796e12i −1.00790 − 1.26386i −0.964300 − 0.264811i \(-0.914690\pi\)
−0.0435950 − 0.999049i \(-0.513881\pi\)
\(734\) 1.02929e13 − 8.99267e12i 1.30890 − 1.14355i
\(735\) −7.42216e10 + 5.39251e10i −0.00938074 + 0.00681551i
\(736\) −7.57313e12 + 3.64703e12i −0.951317 + 0.458130i
\(737\) −3.76204e12 + 5.69925e12i −0.469699 + 0.711564i
\(738\) −7.16706e11 − 2.68984e11i −0.0889381 − 0.0333790i
\(739\) −7.75561e11 + 4.63376e11i −0.0956569 + 0.0571523i −0.559931 − 0.828539i \(-0.689172\pi\)
0.464274 + 0.885692i \(0.346315\pi\)
\(740\) −3.68060e11 − 1.77248e11i −0.0451207 − 0.0217290i
\(741\) 8.83628e11 − 1.60355e11i 0.107668 − 0.0195389i
\(742\) 3.35477e10 − 1.46982e11i 0.00406298 − 0.0178011i
\(743\) 9.00718e12 − 3.38045e12i 1.08427 − 0.406935i 0.255666 − 0.966765i \(-0.417705\pi\)
0.828607 + 0.559830i \(0.189134\pi\)
\(744\) −1.24514e11 + 1.56136e11i −0.0148984 + 0.0186820i
\(745\) −1.85855e10 − 4.13837e11i −0.00221040 − 0.0492183i
\(746\) −2.45187e10 − 5.45952e11i −0.00289850 − 0.0645401i
\(747\) −1.00108e13 + 1.25531e13i −1.17632 + 1.47506i
\(748\) 1.53168e12 − 5.74850e11i 0.178901 − 0.0671425i
\(749\) −2.08983e10 + 9.15614e10i −0.00242629 + 0.0106303i
\(750\) −2.60779e11 + 4.73243e10i −0.0300951 + 0.00546146i
\(751\) −1.23920e13 − 5.96768e12i −1.42155 − 0.684583i −0.444145 − 0.895955i \(-0.646493\pi\)
−0.977406 + 0.211372i \(0.932207\pi\)
\(752\) −9.21599e12