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Properties

Label 71.10.g.a.2.8
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 2.8
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.60524 + 35.7435i) q^{2} +(-201.017 - 175.623i) q^{3} +(-765.079 - 68.8584i) q^{4} +(-311.108 - 957.493i) q^{5} +(6600.05 - 6903.12i) q^{6} +(3843.59 + 1060.76i) q^{7} +(1230.34 - 9082.74i) q^{8} +(6922.16 + 51101.5i) q^{9} +O(q^{10})\) \(q+(-1.60524 + 35.7435i) q^{2} +(-201.017 - 175.623i) q^{3} +(-765.079 - 68.8584i) q^{4} +(-311.108 - 957.493i) q^{5} +(6600.05 - 6903.12i) q^{6} +(3843.59 + 1060.76i) q^{7} +(1230.34 - 9082.74i) q^{8} +(6922.16 + 51101.5i) q^{9} +(34723.5 - 9583.08i) q^{10} +(4226.01 - 7853.23i) q^{11} +(141701. + 148207. i) q^{12} +(-41577.8 - 77264.5i) q^{13} +(-44085.2 + 135680. i) q^{14} +(-105620. + 247110. i) q^{15} +(-64309.8 - 11670.5i) q^{16} +(376432. + 273494. i) q^{17} +(-1.83765e6 + 165392. i) q^{18} +(335268. + 784399. i) q^{19} +(172091. + 753981. i) q^{20} +(-586331. - 888254. i) q^{21} +(273918. + 163658. i) q^{22} +(-825037. - 1.03456e6i) q^{23} +(-1.84246e6 + 1.60971e6i) q^{24} +(760107. - 552250. i) q^{25} +(2.82844e6 - 1.36211e6i) q^{26} +(4.68873e6 - 7.10312e6i) q^{27} +(-2.86761e6 - 1.07623e6i) q^{28} +(-1.53976e6 + 919966. i) q^{29} +(-8.66302e6 - 4.17189e6i) q^{30} +(6.30595e6 - 1.14436e6i) q^{31} +(1.56463e6 - 6.85510e6i) q^{32} +(-2.22871e6 + 836448. i) q^{33} +(-1.03799e7 + 1.30160e7i) q^{34} +(-180099. - 4.01022e6i) q^{35} +(-1.77724e6 - 3.95733e7i) q^{36} +(-6.11430e6 + 7.66709e6i) q^{37} +(-2.85753e7 + 1.07245e7i) q^{38} +(-5.21159e6 + 2.28335e7i) q^{39} +(-9.07943e6 + 1.64767e6i) q^{40} +(-1.85245e6 - 892093. i) q^{41} +(3.26905e7 - 1.95316e7i) q^{42} +(-1.21929e7 - 4.57609e6i) q^{43} +(-3.77399e6 + 5.71735e6i) q^{44} +(4.67757e7 - 2.25260e7i) q^{45} +(3.83033e7 - 2.78290e7i) q^{46} +(1.54827e6 - 1.35269e6i) q^{47} +(1.08777e7 + 1.36403e7i) q^{48} +(-2.09935e7 - 1.25431e7i) q^{49} +(1.85192e7 + 2.80553e7i) q^{50} +(-2.76373e7 - 1.21087e8i) q^{51} +(2.64900e7 + 6.19764e7i) q^{52} +(-2.14783e7 + 1.93308e6i) q^{53} +(2.46363e8 + 1.78994e8i) q^{54} +(-8.83416e6 - 1.60316e6i) q^{55} +(1.43636e7 - 3.36052e7i) q^{56} +(7.03640e7 - 2.16558e8i) q^{57} +(-3.04111e7 - 5.65132e7i) q^{58} +(-5.35492e7 - 5.60081e7i) q^{59} +(9.78231e7 - 1.81786e8i) q^{60} +(6.49060e7 - 1.79129e7i) q^{61} +(3.07809e7 + 2.27233e8i) q^{62} +(-2.76006e7 + 2.03756e8i) q^{63} +(2.10255e8 + 5.80266e7i) q^{64} +(-6.10450e7 + 6.38481e7i) q^{65} +(-2.63199e7 - 8.10044e7i) q^{66} +(-3.01675e8 - 2.71513e7i) q^{67} +(-2.69168e8 - 2.35165e8i) q^{68} +(-1.58470e7 + 3.52860e8i) q^{69} +1.43628e8 q^{70} +(2.10167e8 + 4.09675e7i) q^{71} +4.72658e8 q^{72} +(1.91330e7 - 4.26029e8i) q^{73} +(-2.64233e8 - 2.30854e8i) q^{74} +(-2.49782e8 - 2.24808e7i) q^{75} +(-2.02494e8 - 6.23213e8i) q^{76} +(2.45734e7 - 2.57018e7i) q^{77} +(-8.07781e8 - 2.22933e8i) q^{78} +(3.80784e7 - 2.81106e8i) q^{79} +(8.83289e6 + 6.52070e7i) q^{80} +(-1.21155e9 + 3.34365e8i) q^{81} +(3.48601e7 - 6.47809e7i) q^{82} +(-3.32534e7 - 3.47804e7i) q^{83} +(3.87426e8 + 7.19958e8i) q^{84} +(1.44758e8 - 4.45518e8i) q^{85} +(1.83138e8 - 4.28472e8i) q^{86} +(4.71085e8 + 8.54894e7i) q^{87} +(-6.61294e7 - 4.80459e7i) q^{88} +(4.56452e8 - 4.10815e7i) q^{89} +(7.30071e8 + 1.70809e9i) q^{90} +(-7.78486e7 - 3.41077e8i) q^{91} +(5.59981e8 + 8.48334e8i) q^{92} +(-1.46858e9 - 8.77434e8i) q^{93} +(4.58643e7 + 5.75121e7i) q^{94} +(6.46752e8 - 5.65050e8i) q^{95} +(-1.51843e9 + 1.10320e9i) q^{96} +(-1.25837e9 + 6.05999e8i) q^{97} +(4.82032e8 - 7.30247e8i) q^{98} +(4.30565e8 + 1.61594e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.60524 + 35.7435i −0.0709423 + 1.57965i 0.576216 + 0.817297i \(0.304529\pi\)
−0.647159 + 0.762355i \(0.724043\pi\)
\(3\) −201.017 − 175.623i −1.43280 − 1.25180i −0.919210 − 0.393769i \(-0.871171\pi\)
−0.513594 − 0.858034i \(-0.671686\pi\)
\(4\) −765.079 − 68.8584i −1.49430 − 0.134489i
\(5\) −311.108 − 957.493i −0.222611 − 0.685126i −0.998525 − 0.0542880i \(-0.982711\pi\)
0.775914 − 0.630838i \(-0.217289\pi\)
\(6\) 6600.05 − 6903.12i 2.07906 − 2.17453i
\(7\) 3843.59 + 1060.76i 0.605056 + 0.166985i 0.555124 − 0.831768i \(-0.312671\pi\)
0.0499324 + 0.998753i \(0.484099\pi\)
\(8\) 1230.34 − 9082.74i 0.106199 − 0.783992i
\(9\) 6922.16 + 51101.5i 0.351682 + 2.59622i
\(10\) 34723.5 − 9583.08i 1.09805 − 0.303044i
\(11\) 4226.01 − 7853.23i 0.0870288 − 0.161727i −0.833361 − 0.552730i \(-0.813586\pi\)
0.920389 + 0.391003i \(0.127872\pi\)
\(12\) 141701. + 148207.i 1.97268 + 2.06326i
\(13\) −41577.8 − 77264.5i −0.403754 − 0.750300i 0.594811 − 0.803866i \(-0.297227\pi\)
−0.998564 + 0.0535659i \(0.982941\pi\)
\(14\) −44085.2 + 135680.i −0.306702 + 0.943932i
\(15\) −105620. + 247110.i −0.538685 + 1.26032i
\(16\) −64309.8 − 11670.5i −0.245323 − 0.0445195i
\(17\) 376432. + 273494.i 1.09312 + 0.794196i 0.979923 − 0.199376i \(-0.0638916\pi\)
0.113195 + 0.993573i \(0.463892\pi\)
\(18\) −1.83765e6 + 165392.i −4.12608 + 0.371354i
\(19\) 335268. + 784399.i 0.590203 + 1.38085i 0.902428 + 0.430840i \(0.141783\pi\)
−0.312226 + 0.950008i \(0.601075\pi\)
\(20\) 172091. + 753981.i 0.240505 + 1.05372i
\(21\) −586331. − 888254.i −0.657894 − 0.996667i
\(22\) 273918. + 163658.i 0.249298 + 0.148949i
\(23\) −825037. − 1.03456e6i −0.614750 − 0.770872i 0.372845 − 0.927893i \(-0.378382\pi\)
−0.987595 + 0.157022i \(0.949811\pi\)
\(24\) −1.84246e6 + 1.60971e6i −1.13357 + 0.990367i
\(25\) 760107. − 552250.i 0.389175 − 0.282752i
\(26\) 2.82844e6 − 1.36211e6i 1.21386 − 0.584562i
\(27\) 4.68873e6 − 7.10312e6i 1.69792 − 2.57224i
\(28\) −2.86761e6 − 1.07623e6i −0.881675 − 0.330898i
\(29\) −1.53976e6 + 919966.i −0.404262 + 0.241535i −0.700610 − 0.713545i \(-0.747089\pi\)
0.296347 + 0.955080i \(0.404231\pi\)
\(30\) −8.66302e6 − 4.17189e6i −1.95265 − 0.940345i
\(31\) 6.30595e6 − 1.14436e6i 1.22637 − 0.222554i 0.473545 − 0.880770i \(-0.342974\pi\)
0.752829 + 0.658216i \(0.228689\pi\)
\(32\) 1.56463e6 − 6.85510e6i 0.263777 − 1.15568i
\(33\) −2.22871e6 + 836448.i −0.327145 + 0.122780i
\(34\) −1.03799e7 + 1.30160e7i −1.33210 + 1.67040i
\(35\) −180099. − 4.01022e6i −0.0202864 − 0.451713i
\(36\) −1.77724e6 − 3.95733e7i −0.176354 − 3.92682i
\(37\) −6.11430e6 + 7.66709e6i −0.536338 + 0.672547i −0.973988 − 0.226599i \(-0.927239\pi\)
0.437650 + 0.899145i \(0.355811\pi\)
\(38\) −2.85753e7 + 1.07245e7i −2.22313 + 0.834355i
\(39\) −5.21159e6 + 2.28335e7i −0.360728 + 1.58045i
\(40\) −9.07943e6 + 1.64767e6i −0.560775 + 0.101766i
\(41\) −1.85245e6 − 892093.i −0.102381 − 0.0493040i 0.381992 − 0.924165i \(-0.375238\pi\)
−0.484373 + 0.874861i \(0.660952\pi\)
\(42\) 3.26905e7 − 1.95316e7i 1.62106 − 0.968539i
\(43\) −1.21929e7 − 4.57609e6i −0.543876 − 0.204120i 0.0642879 − 0.997931i \(-0.479522\pi\)
−0.608164 + 0.793811i \(0.708094\pi\)
\(44\) −3.77399e6 + 5.71735e6i −0.151797 + 0.229963i
\(45\) 4.67757e7 − 2.25260e7i 1.70045 − 0.818895i
\(46\) 3.83033e7 − 2.78290e7i 1.26132 − 0.916404i
\(47\) 1.54827e6 − 1.35269e6i 0.0462815 − 0.0404349i −0.634487 − 0.772933i \(-0.718789\pi\)
0.680769 + 0.732498i \(0.261646\pi\)
\(48\) 1.08777e7 + 1.36403e7i 0.295769 + 0.370883i
\(49\) −2.09935e7 − 1.25431e7i −0.520240 − 0.310829i
\(50\) 1.85192e7 + 2.80553e7i 0.419041 + 0.634820i
\(51\) −2.76373e7 − 1.21087e8i −0.572045 − 2.50629i
\(52\) 2.64900e7 + 6.19764e7i 0.502420 + 1.17547i
\(53\) −2.14783e7 + 1.93308e6i −0.373903 + 0.0336519i −0.274997 − 0.961445i \(-0.588677\pi\)
−0.0989054 + 0.995097i \(0.531534\pi\)
\(54\) 2.46363e8 + 1.78994e8i 3.94280 + 2.86461i
\(55\) −8.83416e6 − 1.60316e6i −0.130177 − 0.0236236i
\(56\) 1.43636e7 − 3.36052e7i 0.195171 − 0.456626i
\(57\) 7.03640e7 − 2.16558e8i 0.882904 − 2.71730i
\(58\) −3.04111e7 − 5.65132e7i −0.352863 − 0.655729i
\(59\) −5.35492e7 − 5.60081e7i −0.575333 − 0.601751i 0.369529 − 0.929219i \(-0.379519\pi\)
−0.944862 + 0.327468i \(0.893805\pi\)
\(60\) 9.78231e7 − 1.81786e8i 0.974453 − 1.81084i
\(61\) 6.49060e7 − 1.79129e7i 0.600206 − 0.165646i 0.0472872 − 0.998881i \(-0.484942\pi\)
0.552919 + 0.833235i \(0.313514\pi\)
\(62\) 3.07809e7 + 2.27233e8i 0.264556 + 1.95303i
\(63\) −2.76006e7 + 2.03756e8i −0.220742 + 1.62959i
\(64\) 2.10255e8 + 5.80266e7i 1.56652 + 0.432332i
\(65\) −6.10450e7 + 6.38481e7i −0.424170 + 0.443647i
\(66\) −2.63199e7 − 8.10044e7i −0.170741 − 0.525486i
\(67\) −3.01675e8 − 2.71513e7i −1.82896 − 0.164609i −0.878965 − 0.476886i \(-0.841765\pi\)
−0.949991 + 0.312277i \(0.898908\pi\)
\(68\) −2.69168e8 − 2.35165e8i −1.52663 − 1.33378i
\(69\) −1.58470e7 + 3.52860e8i −0.0841638 + 1.87405i
\(70\) 1.43628e8 0.714988
\(71\) 2.10167e8 + 4.09675e7i 0.981526 + 0.191327i
\(72\) 4.72658e8 2.07277
\(73\) 1.91330e7 − 4.26029e8i 0.0788552 − 1.75585i −0.437267 − 0.899332i \(-0.644053\pi\)
0.516122 − 0.856515i \(-0.327375\pi\)
\(74\) −2.64233e8 − 2.30854e8i −1.02434 − 0.894940i
\(75\) −2.49782e8 − 2.24808e7i −0.911560 − 0.0820419i
\(76\) −2.02494e8 − 6.23213e8i −0.696228 − 2.14277i
\(77\) 2.45734e7 − 2.57018e7i 0.0796632 − 0.0833212i
\(78\) −8.07781e8 − 2.22933e8i −2.47097 − 0.681945i
\(79\) 3.80784e7 − 2.81106e8i 0.109991 − 0.811984i −0.848969 − 0.528443i \(-0.822776\pi\)
0.958960 − 0.283542i \(-0.0915095\pi\)
\(80\) 8.83289e6 + 6.52070e7i 0.0241100 + 0.177987i
\(81\) −1.21155e9 + 3.34365e8i −3.12721 + 0.863055i
\(82\) 3.48601e7 − 6.47809e7i 0.0851464 − 0.158229i
\(83\) −3.32534e7 − 3.47804e7i −0.0769104 − 0.0804420i 0.683220 − 0.730213i \(-0.260579\pi\)
−0.760130 + 0.649771i \(0.774865\pi\)
\(84\) 3.87426e8 + 7.19958e8i 0.849048 + 1.57779i
\(85\) 1.44758e8 − 4.45518e8i 0.300785 − 0.925721i
\(86\) 1.83138e8 − 4.28472e8i 0.361023 − 0.844655i
\(87\) 4.71085e8 + 8.54894e7i 0.881583 + 0.159984i
\(88\) −6.61294e7 − 4.80459e7i −0.117550 − 0.0854051i
\(89\) 4.56452e8 − 4.10815e7i 0.771153 − 0.0694050i 0.302927 − 0.953014i \(-0.402036\pi\)
0.468226 + 0.883609i \(0.344893\pi\)
\(90\) 7.30071e8 + 1.70809e9i 1.17294 + 2.74422i
\(91\) −7.78486e7 − 3.41077e8i −0.119005 − 0.521394i
\(92\) 5.59981e8 + 8.48334e8i 0.814944 + 1.23459i
\(93\) −1.46858e9 − 8.77434e8i −2.03575 − 1.21630i
\(94\) 4.58643e7 + 5.75121e7i 0.0605898 + 0.0759772i
\(95\) 6.46752e8 − 5.65050e8i 0.814670 − 0.711755i
\(96\) −1.51843e9 + 1.10320e9i −1.82463 + 1.32567i
\(97\) −1.25837e9 + 6.05999e8i −1.44323 + 0.695023i −0.981405 − 0.191949i \(-0.938519\pi\)
−0.461824 + 0.886971i \(0.652805\pi\)
\(98\) 4.82032e8 − 7.30247e8i 0.527908 − 0.799747i
\(99\) 4.30565e8 + 1.61594e8i 0.450485 + 0.169070i
\(100\) −6.19569e8 + 3.70175e8i −0.619569 + 0.370175i
\(101\) −1.66729e9 − 8.02923e8i −1.59428 − 0.767764i −0.594926 − 0.803780i \(-0.702819\pi\)
−0.999351 + 0.0360169i \(0.988533\pi\)
\(102\) 4.37244e9 − 7.93480e8i 3.99966 − 0.725831i
\(103\) −2.20124e8 + 9.64424e8i −0.192708 + 0.844307i 0.782436 + 0.622732i \(0.213977\pi\)
−0.975143 + 0.221576i \(0.928880\pi\)
\(104\) −7.52928e8 + 2.82579e8i −0.631108 + 0.236859i
\(105\) −6.68084e8 + 8.37751e8i −0.536388 + 0.672610i
\(106\) −3.46172e7 − 7.70812e8i −0.0266327 − 0.593024i
\(107\) 1.86784e7 + 4.15906e8i 0.0137756 + 0.306739i 0.994038 + 0.109036i \(0.0347765\pi\)
−0.980262 + 0.197702i \(0.936652\pi\)
\(108\) −4.07636e9 + 5.11159e9i −2.88314 + 3.61534i
\(109\) −2.19610e9 + 8.24209e8i −1.49016 + 0.559266i −0.957846 − 0.287282i \(-0.907248\pi\)
−0.532312 + 0.846548i \(0.678677\pi\)
\(110\) 7.14836e7 − 3.13190e8i 0.0465521 − 0.203958i
\(111\) 2.57559e9 − 4.67401e8i 1.61036 − 0.292238i
\(112\) −2.34801e8 − 1.13074e8i −0.141000 − 0.0679020i
\(113\) 1.81959e9 − 1.08715e9i 1.04983 − 0.627246i 0.119076 − 0.992885i \(-0.462007\pi\)
0.930757 + 0.365639i \(0.119150\pi\)
\(114\) 7.62758e9 + 2.86268e9i 4.22976 + 1.58745i
\(115\) −7.33912e8 + 1.11183e9i −0.391295 + 0.592786i
\(116\) 1.24139e9 − 5.97821e8i 0.636571 − 0.306556i
\(117\) 3.66052e9 − 2.65952e9i 1.80595 − 1.31210i
\(118\) 2.08788e9 − 1.82413e9i 0.991373 − 0.866137i
\(119\) 1.15674e9 + 1.45050e9i 0.528779 + 0.663068i
\(120\) 2.11449e9 + 1.26335e9i 0.930871 + 0.556169i
\(121\) 1.25517e9 + 1.90150e9i 0.532315 + 0.806424i
\(122\) 5.36080e8 + 2.34872e9i 0.219084 + 0.959869i
\(123\) 2.15701e8 + 5.04658e8i 0.0849728 + 0.198804i
\(124\) −4.90335e9 + 4.41310e8i −1.86250 + 0.167628i
\(125\) −2.35606e9 − 1.71178e9i −0.863159 − 0.627121i
\(126\) −7.23863e9 − 1.31362e9i −2.55852 − 0.464303i
\(127\) 1.30745e9 − 3.05894e9i 0.445974 − 1.04341i −0.534216 − 0.845348i \(-0.679393\pi\)
0.980190 − 0.198059i \(-0.0634639\pi\)
\(128\) −1.29910e9 + 3.99822e9i −0.427757 + 1.31650i
\(129\) 1.64732e9 + 3.06123e9i 0.523750 + 0.973290i
\(130\) −2.18416e9 − 2.28445e9i −0.670717 − 0.701515i
\(131\) −1.24177e9 + 2.30760e9i −0.368401 + 0.684605i −0.995544 − 0.0943000i \(-0.969939\pi\)
0.627142 + 0.778905i \(0.284224\pi\)
\(132\) 1.76273e9 − 4.86483e8i 0.505364 − 0.139471i
\(133\) 4.56572e8 + 3.37055e9i 0.126525 + 0.934045i
\(134\) 1.45474e9 − 1.07393e10i 0.389775 − 2.87744i
\(135\) −8.25989e9 − 2.27958e9i −2.14029 − 0.590682i
\(136\) 2.94722e9 − 3.08255e9i 0.738732 − 0.772653i
\(137\) −1.85220e9 − 5.70048e9i −0.449205 − 1.38251i −0.877805 − 0.479018i \(-0.840993\pi\)
0.428600 − 0.903494i \(-0.359007\pi\)
\(138\) −1.25870e10 − 1.13285e9i −2.95438 − 0.265899i
\(139\) −1.32880e9 − 1.16094e9i −0.301922 − 0.263781i 0.493623 − 0.869676i \(-0.335672\pi\)
−0.795545 + 0.605895i \(0.792815\pi\)
\(140\) −1.38347e8 + 3.08054e9i −0.0304365 + 0.677720i
\(141\) −5.48792e8 −0.116929
\(142\) −1.80169e9 + 7.44633e9i −0.371862 + 1.53690i
\(143\) −7.82484e8 −0.156482
\(144\) 1.51217e8 − 3.36711e9i 0.0293069 − 0.652569i
\(145\) 1.35989e9 + 1.18810e9i 0.255475 + 0.223202i
\(146\) 1.51970e10 + 1.36776e9i 2.76803 + 0.249128i
\(147\) 2.01720e9 + 6.20832e9i 0.356305 + 1.09659i
\(148\) 5.20586e9 − 5.44491e9i 0.891898 − 0.932852i
\(149\) −1.84631e9 − 5.09548e8i −0.306878 − 0.0846929i 0.109206 − 0.994019i \(-0.465169\pi\)
−0.416084 + 0.909326i \(0.636598\pi\)
\(150\) 1.20450e9 − 8.89198e9i 0.194266 − 1.43413i
\(151\) −1.20405e7 − 8.88867e7i −0.00188473 − 0.0139136i 0.989983 − 0.141187i \(-0.0450918\pi\)
−0.991868 + 0.127273i \(0.959378\pi\)
\(152\) 7.53698e9 − 2.08008e9i 1.14525 − 0.316070i
\(153\) −1.13702e10 + 2.11294e10i −1.67748 + 3.11728i
\(154\) 8.79225e8 + 9.19598e8i 0.125967 + 0.131751i
\(155\) −3.05755e9 − 5.68188e9i −0.425482 − 0.790678i
\(156\) 5.55956e9 − 1.71106e10i 0.751587 − 2.31315i
\(157\) 4.13700e8 − 9.67899e8i 0.0543422 − 0.127140i −0.890157 − 0.455655i \(-0.849405\pi\)
0.944499 + 0.328515i \(0.106548\pi\)
\(158\) 9.98656e9 + 1.81229e9i 1.27485 + 0.231351i
\(159\) 4.65699e9 + 3.38350e9i 0.577854 + 0.419836i
\(160\) −7.05048e9 + 6.34554e8i −0.850508 + 0.0765471i
\(161\) −2.07368e9 − 4.85161e9i −0.243234 − 0.569075i
\(162\) −1.00065e10 − 4.38416e10i −1.14148 − 5.00113i
\(163\) 4.98130e9 + 7.54634e9i 0.552711 + 0.837322i 0.998322 − 0.0579050i \(-0.0184420\pi\)
−0.445611 + 0.895227i \(0.647013\pi\)
\(164\) 1.35584e9 + 8.10078e8i 0.146356 + 0.0874439i
\(165\) 1.49426e9 + 1.87375e9i 0.156946 + 0.196804i
\(166\) 1.29655e9 − 1.13276e9i 0.132527 − 0.115785i
\(167\) −4.48735e9 + 3.26025e9i −0.446442 + 0.324359i −0.788190 − 0.615433i \(-0.788981\pi\)
0.341747 + 0.939792i \(0.388981\pi\)
\(168\) −8.78916e9 + 4.23264e9i −0.851247 + 0.409939i
\(169\) 1.60090e9 − 2.42526e9i 0.150964 − 0.228701i
\(170\) 1.56920e10 + 5.88930e9i 1.44098 + 0.540808i
\(171\) −3.77631e10 + 2.25624e10i −3.37742 + 2.01792i
\(172\) 9.01346e9 + 4.34065e9i 0.785260 + 0.378161i
\(173\) 1.12249e8 − 2.03701e7i 0.00952739 − 0.00172897i −0.173791 − 0.984783i \(-0.555602\pi\)
0.183318 + 0.983054i \(0.441316\pi\)
\(174\) −3.81189e9 + 1.67010e10i −0.315260 + 1.38124i
\(175\) 3.50734e9 − 1.31633e9i 0.282688 − 0.106094i
\(176\) −3.63425e8 + 4.55721e8i −0.0285501 + 0.0358007i
\(177\) 9.27979e8 + 2.06630e10i 0.0710654 + 1.58239i
\(178\) 7.35678e8 + 1.63811e10i 0.0549285 + 1.22308i
\(179\) 1.18687e10 − 1.48829e10i 0.864104 − 1.08355i −0.131632 − 0.991299i \(-0.542022\pi\)
0.995736 − 0.0922531i \(-0.0294069\pi\)
\(180\) −3.73383e10 + 1.40133e10i −2.65111 + 0.994978i
\(181\) 2.95028e9 − 1.29260e10i 0.204320 − 0.895183i −0.763950 − 0.645275i \(-0.776743\pi\)
0.968270 − 0.249908i \(-0.0804003\pi\)
\(182\) 1.23162e10 − 2.23507e9i 0.832064 − 0.150997i
\(183\) −1.61931e10 − 7.79819e9i −1.06733 − 0.514001i
\(184\) −1.04118e10 + 6.22073e9i −0.669643 + 0.400093i
\(185\) 9.24339e9 + 3.46910e9i 0.580174 + 0.217743i
\(186\) 3.37200e10 − 5.10836e10i 2.06575 − 3.12948i
\(187\) 3.73862e9 − 1.80042e9i 0.223575 − 0.107668i
\(188\) −1.27770e9 + 9.28301e8i −0.0745963 + 0.0541974i
\(189\) 2.55563e10 − 2.23278e10i 1.45686 − 1.27282i
\(190\) 1.91587e10 + 2.40242e10i 1.06653 + 1.33739i
\(191\) 6.80260e9 + 4.06436e9i 0.369849 + 0.220975i 0.685782 − 0.727807i \(-0.259460\pi\)
−0.315933 + 0.948782i \(0.602317\pi\)
\(192\) −3.20739e10 − 4.85899e10i −1.70332 − 2.58042i
\(193\) −3.52761e9 − 1.54555e10i −0.183009 − 0.801815i −0.980188 − 0.198071i \(-0.936532\pi\)
0.797179 − 0.603744i \(-0.206325\pi\)
\(194\) −1.96405e10 − 4.59512e10i −0.995508 − 2.32911i
\(195\) 2.34843e10 − 2.11362e9i 1.16311 − 0.104682i
\(196\) 1.51980e10 + 1.10420e10i 0.735589 + 0.534437i
\(197\) 1.81539e10 + 3.29446e9i 0.858762 + 0.155842i 0.590039 − 0.807375i \(-0.299112\pi\)
0.268724 + 0.963217i \(0.413398\pi\)
\(198\) −6.46708e9 + 1.51305e10i −0.299030 + 0.699615i
\(199\) −5.72319e9 + 1.76142e10i −0.258702 + 0.796201i 0.734376 + 0.678743i \(0.237475\pi\)
−0.993078 + 0.117459i \(0.962525\pi\)
\(200\) −4.08075e9 − 7.58330e9i −0.180345 − 0.335138i
\(201\) 5.58734e10 + 5.84390e10i 2.41448 + 2.52534i
\(202\) 3.13756e10 − 5.83057e10i 1.32590 − 2.46394i
\(203\) −6.89408e9 + 1.90265e9i −0.284934 + 0.0786368i
\(204\) 1.28069e10 + 9.45443e10i 0.517736 + 3.82208i
\(205\) −2.77860e8 + 2.05125e9i −0.0109884 + 0.0811195i
\(206\) −3.41185e10 − 9.41611e9i −1.32004 − 0.364308i
\(207\) 4.71567e10 − 4.93220e10i 1.78516 − 1.86713i
\(208\) 1.77214e9 + 5.45410e9i 0.0656469 + 0.202040i
\(209\) 7.57691e9 + 6.81935e8i 0.274684 + 0.0247220i
\(210\) −2.88717e10 − 2.52244e10i −1.02444 − 0.895024i
\(211\) −8.06779e8 + 1.79643e10i −0.0280210 + 0.623936i 0.935022 + 0.354589i \(0.115379\pi\)
−0.963043 + 0.269347i \(0.913192\pi\)
\(212\) 1.65657e10 0.563247
\(213\) −3.50522e10 − 4.51453e10i −1.16683 − 1.50281i
\(214\) −1.48959e10 −0.485518
\(215\) −5.88246e8 + 1.30983e10i −0.0187753 + 0.418064i
\(216\) −5.87470e10 − 5.13257e10i −1.83630 − 1.60433i
\(217\) 2.54514e10 + 2.29067e9i 0.779188 + 0.0701282i
\(218\) −2.59348e10 − 7.98192e10i −0.777730 − 2.39361i
\(219\) −7.86666e10 + 8.22788e10i −2.31096 + 2.41707i
\(220\) 6.64844e9 + 1.83485e9i 0.191345 + 0.0528080i
\(221\) 5.48016e9 − 4.04561e10i 0.154535 − 1.14083i
\(222\) 1.25721e10 + 9.28109e10i 0.347391 + 2.56455i
\(223\) 1.09426e10 − 3.01997e9i 0.296312 − 0.0817770i −0.114720 − 0.993398i \(-0.536597\pi\)
0.411032 + 0.911621i \(0.365168\pi\)
\(224\) 1.32854e10 − 2.46885e10i 0.352582 − 0.655206i
\(225\) 3.34823e10 + 3.50198e10i 0.870953 + 0.910945i
\(226\) 3.59378e10 + 6.67835e10i 0.916353 + 1.70287i
\(227\) 2.03251e10 − 6.25543e10i 0.508062 − 1.56365i −0.287498 − 0.957781i \(-0.592824\pi\)
0.795561 − 0.605874i \(-0.207176\pi\)
\(228\) −6.87459e10 + 1.60839e11i −1.68477 + 3.94171i
\(229\) −5.22992e10 − 9.49090e9i −1.25671 − 0.228059i −0.490951 − 0.871187i \(-0.663351\pi\)
−0.765759 + 0.643128i \(0.777636\pi\)
\(230\) −3.85625e10 − 2.80173e10i −0.908636 − 0.660163i
\(231\) −9.45350e9 + 8.50831e8i −0.218443 + 0.0196603i
\(232\) 6.46138e9 + 1.51171e10i 0.146430 + 0.342589i
\(233\) −3.61450e9 − 1.58362e10i −0.0803427 − 0.352004i 0.918738 − 0.394867i \(-0.129209\pi\)
−0.999081 + 0.0428627i \(0.986352\pi\)
\(234\) 8.91845e10 + 1.35109e11i 1.94455 + 2.94586i
\(235\) −1.77687e9 − 1.06163e9i −0.0380058 − 0.0227074i
\(236\) 3.71128e10 + 4.65380e10i 0.778789 + 0.976570i
\(237\) −5.70230e10 + 4.98195e10i −1.17404 + 1.02573i
\(238\) −5.37029e10 + 3.90174e10i −1.08493 + 0.788247i
\(239\) −7.19938e10 + 3.46704e10i −1.42726 + 0.687334i −0.978487 − 0.206309i \(-0.933855\pi\)
−0.448778 + 0.893643i \(0.648141\pi\)
\(240\) 9.67630e9 − 1.46590e10i 0.188260 − 0.285202i
\(241\) 6.62212e9 + 2.48532e9i 0.126450 + 0.0474576i 0.413798 − 0.910369i \(-0.364202\pi\)
−0.287347 + 0.957826i \(0.592773\pi\)
\(242\) −6.99812e10 + 4.18118e10i −1.31163 + 0.783664i
\(243\) 1.51330e11 + 7.28765e10i 2.78417 + 1.34079i
\(244\) −5.08917e10 + 9.23548e9i −0.919163 + 0.166804i
\(245\) −5.47863e9 + 2.40034e10i −0.0971459 + 0.425624i
\(246\) −1.83845e10 + 6.89981e9i −0.320069 + 0.120124i
\(247\) 4.66665e10 − 5.85179e10i 0.797754 − 1.00035i
\(248\) −2.63547e9 − 5.86833e10i −0.0442410 − 0.985103i
\(249\) 5.76263e8 + 1.28315e10i 0.00950001 + 0.211534i
\(250\) 6.49668e10 − 8.14658e10i 1.05187 − 1.31900i
\(251\) −8.30847e10 + 3.11822e10i −1.32126 + 0.495878i −0.909610 − 0.415462i \(-0.863620\pi\)
−0.411653 + 0.911341i \(0.635048\pi\)
\(252\) 3.51469e10 − 1.53989e11i 0.549016 − 2.40540i
\(253\) −1.16113e10 + 2.10714e9i −0.178171 + 0.0323333i
\(254\) 1.07238e11 + 5.16432e10i 1.61658 + 0.778505i
\(255\) −1.07342e11 + 6.41338e10i −1.58978 + 0.949852i
\(256\) −3.62708e10 − 1.36126e10i −0.527809 − 0.198090i
\(257\) 6.26437e10 − 9.49012e10i 0.895733 − 1.35698i −0.0381027 − 0.999274i \(-0.512131\pi\)
0.933835 − 0.357703i \(-0.116440\pi\)
\(258\) −1.12063e11 + 5.39668e10i −1.57462 + 0.758295i
\(259\) −3.16338e10 + 2.29833e10i −0.436820 + 0.317368i
\(260\) 5.11008e10 − 4.46454e10i 0.693501 − 0.605894i
\(261\) −5.76701e10 − 7.23160e10i −0.769252 − 0.964611i
\(262\) −8.04883e10 − 4.80895e10i −1.05530 − 0.630514i
\(263\) −5.10635e10 − 7.73579e10i −0.658127 − 0.997019i −0.998392 − 0.0566898i \(-0.981945\pi\)
0.340265 − 0.940330i \(-0.389483\pi\)
\(264\) 4.85517e9 + 2.12719e10i 0.0615158 + 0.269518i
\(265\) 8.53300e9 + 1.99639e10i 0.106291 + 0.248679i
\(266\) −1.21208e11 + 1.09089e10i −1.48444 + 0.133602i
\(267\) −9.89694e10 − 7.19055e10i −1.19179 − 0.865887i
\(268\) 2.28936e11 + 4.15458e10i 2.71086 + 0.491949i
\(269\) 3.43176e10 − 8.02899e10i 0.399605 − 0.934923i −0.592038 − 0.805910i \(-0.701676\pi\)
0.991643 − 0.129013i \(-0.0411808\pi\)
\(270\) 9.47393e10 − 2.91578e11i 1.08491 − 3.33901i
\(271\) 7.40930e10 + 1.37688e11i 0.834479 + 1.55072i 0.834689 + 0.550722i \(0.185647\pi\)
−0.000210216 1.00000i \(0.500067\pi\)
\(272\) −2.10165e10 − 2.19815e10i −0.232809 − 0.243499i
\(273\) −4.42521e10 + 8.22342e10i −0.482172 + 0.896026i
\(274\) 2.06728e11 − 5.70533e10i 2.21576 − 0.611510i
\(275\) −1.12473e9 − 8.30311e9i −0.0118591 − 0.0875474i
\(276\) 3.64216e10 − 2.68875e11i 0.377805 − 2.78907i
\(277\) −1.71401e11 − 4.73037e10i −1.74926 − 0.482765i −0.762782 − 0.646656i \(-0.776167\pi\)
−0.986478 + 0.163891i \(0.947596\pi\)
\(278\) 4.36291e10 − 4.56325e10i 0.438102 − 0.458218i
\(279\) 1.02129e11 + 3.14322e11i 1.00909 + 3.10567i
\(280\) −3.66454e10 − 3.29814e9i −0.356294 − 0.0320670i
\(281\) −1.17208e11 − 1.02401e11i −1.12144 − 0.979775i −0.121525 − 0.992588i \(-0.538779\pi\)
−0.999918 + 0.0128130i \(0.995921\pi\)
\(282\) 8.80943e8 − 1.96157e10i 0.00829520 − 0.184707i
\(283\) 1.28450e11 1.19040 0.595201 − 0.803577i \(-0.297072\pi\)
0.595201 + 0.803577i \(0.297072\pi\)
\(284\) −1.57973e11 − 4.58151e10i −1.44096 − 0.417904i
\(285\) −2.29244e11 −2.05824
\(286\) 1.25608e9 − 2.79687e10i 0.0111012 − 0.247187i
\(287\) −6.17375e9 − 5.39385e9i −0.0537132 − 0.0469278i
\(288\) 3.61136e11 + 3.25028e10i 3.09318 + 0.278391i
\(289\) 3.02566e10 + 9.31204e10i 0.255141 + 0.785244i
\(290\) −4.46499e10 + 4.67001e10i −0.370706 + 0.387728i
\(291\) 3.59381e11 + 9.91827e10i 2.93789 + 0.810807i
\(292\) −4.39740e10 + 3.24629e11i −0.353975 + 2.61315i
\(293\) −2.00998e10 − 1.48383e11i −0.159327 − 1.17620i −0.877236 − 0.480059i \(-0.840615\pi\)
0.717909 − 0.696137i \(-0.245099\pi\)
\(294\) −2.25145e11 + 6.21360e10i −1.75751 + 0.485043i
\(295\) −3.69678e10 + 6.86976e10i −0.284200 + 0.528132i
\(296\) 6.21155e10 + 6.49677e10i 0.470313 + 0.491909i
\(297\) −3.59679e10 − 6.68395e10i −0.268232 − 0.498459i
\(298\) 2.11768e10 − 6.51754e10i 0.155556 − 0.478752i
\(299\) −4.56318e10 + 1.06761e11i −0.330178 + 0.772489i
\(300\) 1.89555e11 + 3.43991e10i 1.35111 + 0.245190i
\(301\) −4.20105e10 − 3.05224e10i −0.294991 − 0.214323i
\(302\) 3.19645e9 − 2.87685e8i 0.0221124 − 0.00199015i
\(303\) 1.94141e11 + 4.54215e11i 1.32320 + 3.09577i
\(304\) −1.24067e10 − 5.43573e10i −0.0833154 − 0.365029i
\(305\) −3.73443e10 − 5.65742e10i −0.247101 − 0.374342i
\(306\) −7.36986e11 − 4.40329e11i −4.80522 − 2.87098i
\(307\) −3.57821e10 − 4.48693e10i −0.229902 − 0.288288i 0.653478 − 0.756946i \(-0.273309\pi\)
−0.883380 + 0.468657i \(0.844738\pi\)
\(308\) −2.05704e10 + 1.79718e10i −0.130246 + 0.113793i
\(309\) 2.13624e11 − 1.55207e11i 1.33302 − 0.968494i
\(310\) 2.07998e11 − 1.00167e11i 1.27918 − 0.616021i
\(311\) 1.64233e11 − 2.48802e11i 0.995494 − 1.50811i 0.140096 − 0.990138i \(-0.455259\pi\)
0.855398 − 0.517971i \(-0.173312\pi\)
\(312\) 2.00978e11 + 7.54285e10i 1.20075 + 0.450650i
\(313\) 6.76190e9 − 4.04005e9i 0.0398217 − 0.0237923i −0.492850 − 0.870114i \(-0.664045\pi\)
0.532672 + 0.846322i \(0.321188\pi\)
\(314\) 3.39320e10 + 1.63408e10i 0.196982 + 0.0948614i
\(315\) 2.03682e11 − 3.69627e10i 1.16561 − 0.211527i
\(316\) −4.84894e10 + 2.12446e11i −0.273562 + 1.19855i
\(317\) 2.71288e11 − 1.01816e11i 1.50891 − 0.566305i 0.546398 − 0.837526i \(-0.315999\pi\)
0.962517 + 0.271221i \(0.0874274\pi\)
\(318\) −1.28414e11 + 1.61026e11i −0.704189 + 0.883025i
\(319\) 7.17658e8 + 1.59799e10i 0.00388025 + 0.0864005i
\(320\) −9.85192e9 − 2.19370e11i −0.0525226 − 1.16951i
\(321\) 6.92880e10 − 8.68845e10i 0.364238 − 0.456740i
\(322\) 1.76742e11 − 6.63324e10i 0.916196 − 0.343854i
\(323\) −8.83227e10 + 3.86967e11i −0.451503 + 1.97817i
\(324\) 9.49952e11 − 1.72391e11i 4.78905 − 0.869084i
\(325\) −7.42728e10 − 3.57679e10i −0.369279 − 0.177836i
\(326\) −2.77729e11 + 1.65935e11i −1.36189 + 0.813690i
\(327\) 5.86202e11 + 2.20005e11i 2.83519 + 1.06407i
\(328\) −1.03818e10 + 1.57277e10i −0.0495267 + 0.0750298i
\(329\) 7.38581e9 − 3.55682e9i 0.0347549 − 0.0167371i
\(330\) −6.93728e10 + 5.04023e10i −0.322015 + 0.233958i
\(331\) −3.08257e11 + 2.69316e11i −1.41152 + 1.23321i −0.476232 + 0.879320i \(0.657998\pi\)
−0.935288 + 0.353888i \(0.884859\pi\)
\(332\) 2.30466e10 + 2.88995e10i 0.104108 + 0.130548i
\(333\) −4.34123e11 − 2.59377e11i −1.93470 − 1.15593i
\(334\) −1.09329e11 − 1.65627e11i −0.480704 − 0.728235i
\(335\) 6.78566e10 + 2.97299e11i 0.294368 + 1.28971i
\(336\) 2.73405e10 + 6.39662e10i 0.117025 + 0.273794i
\(337\) −1.24034e11 + 1.11632e10i −0.523848 + 0.0471471i −0.348408 − 0.937343i \(-0.613278\pi\)
−0.175440 + 0.984490i \(0.556135\pi\)
\(338\) 8.41172e10 + 6.11148e10i 0.350558 + 0.254695i
\(339\) −5.56697e11 − 1.01026e11i −2.28939 − 0.415463i
\(340\) −1.41429e11 + 3.30889e11i −0.573961 + 1.34285i
\(341\) 1.76620e10 − 5.43582e10i 0.0707369 − 0.217706i
\(342\) −7.45840e11 − 1.38600e12i −2.94801 − 5.47831i
\(343\) −1.78578e11 − 1.86778e11i −0.696634 − 0.728622i
\(344\) −5.65649e10 + 1.05115e11i −0.217788 + 0.404718i
\(345\) 3.42791e11 − 9.46044e10i 1.30270 − 0.359522i
\(346\) 5.47913e8 + 4.04486e9i 0.00205527 + 0.0151726i
\(347\) 1.45456e10 − 1.07380e11i 0.0538578 − 0.397594i −0.943875 − 0.330301i \(-0.892850\pi\)
0.997733 − 0.0672927i \(-0.0214361\pi\)
\(348\) −3.54531e11 − 9.78443e10i −1.29583 − 0.357626i
\(349\) 1.58895e11 − 1.66191e11i 0.573319 − 0.599645i −0.371017 − 0.928626i \(-0.620991\pi\)
0.944337 + 0.328981i \(0.106705\pi\)
\(350\) 4.14200e10 + 1.27478e11i 0.147538 + 0.454075i
\(351\) −7.43766e11 − 6.69401e10i −2.61550 − 0.235399i
\(352\) −4.72225e10 − 4.12571e10i −0.163948 − 0.143237i
\(353\) −4.36124e9 + 9.71106e10i −0.0149494 + 0.332874i 0.977556 + 0.210675i \(0.0675662\pi\)
−0.992506 + 0.122199i \(0.961005\pi\)
\(354\) −7.40058e11 −2.50467
\(355\) −2.61586e10 − 2.13979e11i −0.0874153 − 0.715061i
\(356\) −3.52051e11 −1.16166
\(357\) 2.22182e10 − 4.94726e11i 0.0723937 − 1.61197i
\(358\) 5.12915e11 + 4.48120e11i 1.65033 + 1.44185i
\(359\) −3.10354e11 − 2.79324e10i −0.986127 − 0.0887530i −0.415179 − 0.909740i \(-0.636281\pi\)
−0.570947 + 0.820987i \(0.693424\pi\)
\(360\) −1.47048e11 − 4.52567e11i −0.461421 − 1.42011i
\(361\) −2.79880e11 + 2.92731e11i −0.867339 + 0.907165i
\(362\) 4.57285e11 + 1.26203e11i 1.39958 + 0.386260i
\(363\) 8.16374e10 − 6.02671e11i 0.246780 − 1.82180i
\(364\) 3.60743e10 + 2.66312e11i 0.107707 + 0.795122i
\(365\) −4.13873e11 + 1.14222e11i −1.22053 + 0.336845i
\(366\) 3.04728e11 − 5.66280e11i 0.887662 − 1.64955i
\(367\) 7.40359e10 + 7.74354e10i 0.213032 + 0.222814i 0.820673 − 0.571397i \(-0.193599\pi\)
−0.607641 + 0.794211i \(0.707884\pi\)
\(368\) 4.09841e10 + 7.61613e10i 0.116493 + 0.216481i
\(369\) 3.27643e10 − 1.00838e11i 0.0919987 − 0.283143i
\(370\) −1.38836e11 + 3.24822e11i −0.385117 + 0.901027i
\(371\) −8.46043e10 − 1.53534e10i −0.231852 − 0.0420748i
\(372\) 1.06316e12 + 7.72431e11i 2.87843 + 2.09130i
\(373\) −2.63378e11 + 2.37045e10i −0.704515 + 0.0634075i −0.436103 − 0.899897i \(-0.643642\pi\)
−0.268412 + 0.963304i \(0.586499\pi\)
\(374\) 5.83520e10 + 1.36521e11i 0.154217 + 0.360810i
\(375\) 1.72980e11 + 7.57873e11i 0.451704 + 1.97905i
\(376\) −1.03812e10 − 1.57268e10i −0.0267856 − 0.0405785i
\(377\) 1.35101e11 + 8.07189e10i 0.344446 + 0.205797i
\(378\) 7.57050e11 + 9.49311e11i 1.90727 + 2.39164i
\(379\) 3.02833e11 − 2.64578e11i 0.753924 − 0.658683i −0.192615 − 0.981274i \(-0.561697\pi\)
0.946538 + 0.322591i \(0.104554\pi\)
\(380\) −5.33725e11 + 3.87774e11i −1.31308 + 0.954009i
\(381\) −8.00040e11 + 3.85279e11i −1.94513 + 0.936726i
\(382\) −1.56194e11 + 2.36624e11i −0.375301 + 0.568557i
\(383\) 1.35666e11 + 5.09164e10i 0.322164 + 0.120910i 0.507217 − 0.861818i \(-0.330674\pi\)
−0.185053 + 0.982729i \(0.559246\pi\)
\(384\) 9.63319e11 − 5.75556e11i 2.26089 − 1.35082i
\(385\) −3.22543e10 − 1.55329e10i −0.0748195 − 0.0360312i
\(386\) 5.58094e11 − 1.01279e11i 1.27957 − 0.232208i
\(387\) 1.49443e11 − 6.54753e11i 0.338670 − 1.48381i
\(388\) 1.00448e12 − 3.76988e11i 2.25008 − 0.844470i
\(389\) 4.02783e11 − 5.05074e11i 0.891863 − 1.11836i −0.100491 − 0.994938i \(-0.532041\pi\)
0.992354 − 0.123423i \(-0.0393872\pi\)
\(390\) 3.78503e10 + 8.42802e11i 0.0828473 + 1.84474i
\(391\) −2.76236e10 − 6.15086e11i −0.0597701 − 1.33089i
\(392\) −1.39755e11 + 1.75247e11i −0.298936 + 0.374854i
\(393\) 6.54885e11 − 2.45782e11i 1.38484 − 0.519738i
\(394\) −1.46897e11 + 6.43596e11i −0.307099 + 1.34549i
\(395\) −2.81003e11 + 5.09946e10i −0.580797 + 0.105399i
\(396\) −3.18289e11 − 1.53280e11i −0.650419 − 0.313225i
\(397\) −7.46658e11 + 4.46108e11i −1.50857 + 0.901327i −0.509399 + 0.860530i \(0.670132\pi\)
−0.999167 + 0.0407966i \(0.987010\pi\)
\(398\) −6.20404e11 − 2.32841e11i −1.23937 − 0.465143i
\(399\) 5.00167e11 − 7.57721e11i 0.987955 − 1.49669i
\(400\) −5.53274e10 + 2.66443e10i −0.108061 + 0.0520396i
\(401\) 2.80671e11 − 2.03920e11i 0.542062 − 0.393831i −0.282789 − 0.959182i \(-0.591259\pi\)
0.824850 + 0.565352i \(0.191259\pi\)
\(402\) −2.17850e12 + 1.90330e12i −4.16045 + 3.63488i
\(403\) −3.50606e11 − 4.39646e11i −0.662135 − 0.830291i
\(404\) 1.22032e12 + 7.29106e11i 2.27907 + 1.36168i
\(405\) 6.97074e11 + 1.05602e12i 1.28745 + 1.95041i
\(406\) −5.69405e10 − 2.49473e11i −0.104005 − 0.455676i
\(407\) 3.43724e10 + 8.04182e10i 0.0620919 + 0.145271i
\(408\) −1.13381e12 + 1.02044e11i −2.02567 + 0.182313i
\(409\) 1.62984e11 + 1.18415e11i 0.287999 + 0.209243i 0.722399 − 0.691477i \(-0.243040\pi\)
−0.434400 + 0.900720i \(0.643040\pi\)
\(410\) −7.28726e10 − 1.32244e10i −0.127361 − 0.0231126i
\(411\) −6.28813e11 + 1.47118e12i −1.08701 + 2.54318i
\(412\) 2.34821e11 − 7.22704e11i 0.401512 − 1.23573i
\(413\) −1.46410e11 − 2.72075e11i −0.247625 − 0.460165i
\(414\) 1.68724e12 + 1.76472e12i 2.82277 + 2.95239i
\(415\) −2.29565e10 + 4.26604e10i −0.0379918 + 0.0706006i
\(416\) −5.94709e11 + 1.64129e11i −0.973610 + 0.268699i
\(417\) 6.32239e10 + 4.66737e11i 0.102393 + 0.755893i
\(418\) −3.65375e10 + 2.69730e11i −0.0585390 + 0.432152i
\(419\) 9.13575e10 + 2.52131e10i 0.144804 + 0.0399634i 0.337687 − 0.941258i \(-0.390355\pi\)
−0.192883 + 0.981222i \(0.561784\pi\)
\(420\) 5.68824e11 − 5.94943e11i 0.891981 − 0.932939i
\(421\) −7.55844e10 − 2.32625e11i −0.117264 − 0.360900i 0.875149 − 0.483854i \(-0.160763\pi\)
−0.992412 + 0.122954i \(0.960763\pi\)
\(422\) −6.40812e11 − 5.76742e10i −0.983614 − 0.0885269i
\(423\) 7.98416e10 + 6.97555e10i 0.121254 + 0.105937i
\(424\) −8.86795e9 + 1.97460e11i −0.0133253 + 0.296711i
\(425\) 4.37166e11 0.649974
\(426\) 1.66992e12 − 1.18042e12i 2.45670 − 1.73657i
\(427\) 2.68473e11 0.390819
\(428\) 1.43482e10 − 3.19487e11i 0.0206681 − 0.460211i
\(429\) 1.57292e11 + 1.37422e11i 0.224207 + 0.195884i
\(430\) −4.67235e11 − 4.20519e10i −0.659063 − 0.0593168i
\(431\) 1.77230e10 + 5.45459e10i 0.0247395 + 0.0761402i 0.962664 − 0.270699i \(-0.0872549\pi\)
−0.937925 + 0.346839i \(0.887255\pi\)
\(432\) −3.84428e11 + 4.02080e11i −0.531054 + 0.555439i
\(433\) 5.45297e10 + 1.50492e10i 0.0745482 + 0.0205740i 0.303112 − 0.952955i \(-0.401974\pi\)
−0.228564 + 0.973529i \(0.573403\pi\)
\(434\) −1.22732e11 + 9.06043e11i −0.166056 + 1.22587i
\(435\) −6.47031e10 − 4.77658e11i −0.0866410 − 0.639610i
\(436\) 1.73694e12 − 4.79366e11i 2.30195 − 0.635298i
\(437\) 5.34902e11 − 9.94015e11i 0.701630 − 1.30385i
\(438\) −2.81465e12 − 2.94389e12i −3.65419 − 3.82198i
\(439\) −5.00454e10 − 9.30000e10i −0.0643094 − 0.119507i 0.846411 − 0.532530i \(-0.178759\pi\)
−0.910721 + 0.413023i \(0.864473\pi\)
\(440\) −2.54302e10 + 7.82660e10i −0.0323454 + 0.0995488i
\(441\) 4.95648e11 − 1.15963e12i 0.624022 − 1.45997i
\(442\) 1.43725e12 + 2.60822e11i 1.79115 + 0.325045i
\(443\) −4.90866e11 − 3.56635e11i −0.605545 − 0.439954i 0.242298 − 0.970202i \(-0.422099\pi\)
−0.847843 + 0.530248i \(0.822099\pi\)
\(444\) −2.00272e12 + 1.80248e11i −2.44566 + 0.220113i
\(445\) −1.81341e11 − 4.24269e11i −0.219218 − 0.512887i
\(446\) 9.03787e10 + 3.95975e11i 0.108158 + 0.473872i
\(447\) 2.81650e11 + 4.26682e11i 0.333677 + 0.505499i
\(448\) 7.46580e11 + 4.46061e11i 0.875640 + 0.523170i
\(449\) −1.35141e11 − 1.69462e11i −0.156921 − 0.196772i 0.697156 − 0.716919i \(-0.254448\pi\)
−0.854077 + 0.520147i \(0.825877\pi\)
\(450\) −1.30548e12 + 1.14056e12i −1.50076 + 1.31118i
\(451\) −1.48343e10 + 1.07777e10i −0.0168839 + 0.0122668i
\(452\) −1.46699e12 + 7.06465e11i −1.65312 + 0.796100i
\(453\) −1.31902e10 + 1.99823e10i −0.0147167 + 0.0222948i
\(454\) 2.20328e12 + 8.26905e11i 2.43399 + 0.913491i
\(455\) −3.02360e11 + 1.80651e11i −0.330729 + 0.197602i
\(456\) −1.88037e12 − 9.05538e11i −2.03658 − 0.980765i
\(457\) 1.22815e12 − 2.22877e11i 1.31713 − 0.239024i 0.525903 − 0.850545i \(-0.323728\pi\)
0.791228 + 0.611521i \(0.209442\pi\)
\(458\) 4.23190e11 − 1.85412e12i 0.449408 − 1.96899i
\(459\) 3.70765e12 − 1.39150e12i 3.89890 − 1.46328i
\(460\) 6.38060e11 − 8.00101e11i 0.664433 − 0.833172i
\(461\) −7.38898e10 − 1.64528e12i −0.0761957 − 1.69663i −0.565686 − 0.824621i \(-0.691389\pi\)
0.489491 − 0.872009i \(-0.337183\pi\)
\(462\) −1.52365e10 − 3.39267e11i −0.0155595 − 0.346459i
\(463\) 1.59981e11 − 2.00610e11i 0.161791 − 0.202879i −0.694327 − 0.719659i \(-0.744298\pi\)
0.856118 + 0.516780i \(0.172869\pi\)
\(464\) 1.09758e11 − 4.11930e10i 0.109928 − 0.0412565i
\(465\) −3.83251e11 + 1.67913e12i −0.380141 + 1.66551i
\(466\) 5.71841e11 − 1.03774e11i 0.561744 − 0.101942i
\(467\) −5.70726e11 − 2.74847e11i −0.555267 − 0.267402i 0.135137 − 0.990827i \(-0.456853\pi\)
−0.690403 + 0.723425i \(0.742567\pi\)
\(468\) −2.98372e12 + 1.78269e12i −2.87509 + 1.71779i
\(469\) −1.13072e12 − 4.24364e11i −1.07913 − 0.405006i
\(470\) 4.07986e10 − 6.18073e10i 0.0385660 − 0.0584251i
\(471\) −2.53146e11 + 1.21909e11i −0.237016 + 0.114141i
\(472\) −5.74591e11 + 4.17465e11i −0.532868 + 0.387151i
\(473\) −8.74645e10 + 7.64154e10i −0.0803446 + 0.0701950i
\(474\) −1.68919e12 − 2.11817e12i −1.53700 − 1.92734i
\(475\) 6.88024e11 + 4.11075e11i 0.620129 + 0.370510i
\(476\) −7.85117e11 − 1.18940e12i −0.700976 − 1.06193i
\(477\) −2.47460e11 − 1.08419e12i −0.218863 − 0.958900i
\(478\) −1.12367e12 − 2.62896e12i −0.984496 − 2.30334i
\(479\) −1.84607e12 + 1.66150e11i −1.60228 + 0.144208i −0.854398 − 0.519620i \(-0.826074\pi\)
−0.747885 + 0.663828i \(0.768931\pi\)
\(480\) 1.52871e12 + 1.11067e12i 1.31443 + 0.954991i
\(481\) 8.46613e11 + 1.53638e11i 0.721160 + 0.130871i
\(482\) −9.94641e10 + 2.32708e11i −0.0839373 + 0.196381i
\(483\) −4.35210e11 + 1.33944e12i −0.363862 + 1.11985i
\(484\) −8.29372e11 − 1.54123e12i −0.686981 − 1.27663i
\(485\) 9.71729e11 + 1.01635e12i 0.797457 + 0.834075i
\(486\) −2.84778e12 + 5.29206e12i −2.31549 + 4.30290i
\(487\) 5.35246e11 − 1.47718e11i 0.431194 − 0.119002i −0.0437006 − 0.999045i \(-0.513915\pi\)
0.474895 + 0.880043i \(0.342486\pi\)
\(488\) −8.28419e10 − 6.11563e11i −0.0661242 − 0.488149i
\(489\) 3.23988e11 − 2.39177e12i 0.256235 − 1.89160i
\(490\) −8.49171e11 − 2.34356e11i −0.665446 − 0.183651i
\(491\) −1.14020e12 + 1.19255e12i −0.885345 + 0.925999i −0.997708 − 0.0676687i \(-0.978444\pi\)
0.112363 + 0.993667i \(0.464158\pi\)
\(492\) −1.30279e11 − 4.00956e11i −0.100237 − 0.308499i
\(493\) −8.31222e11 − 7.48114e10i −0.633733 − 0.0570370i
\(494\) 2.01672e12 + 1.76196e12i 1.52361 + 1.33114i
\(495\) 2.07725e10 − 4.62536e11i 0.0155513 − 0.346276i
\(496\) −4.18890e11 −0.310765
\(497\) 7.64339e11 + 3.80400e11i 0.561930 + 0.279664i
\(498\) −4.59567e11 −0.334824
\(499\) 1.63584e10 − 3.64248e11i 0.0118110 − 0.262993i −0.984395 − 0.175971i \(-0.943693\pi\)
0.996206 − 0.0870221i \(-0.0277351\pi\)
\(500\) 1.68470e12 + 1.47188e12i 1.20547 + 1.05319i
\(501\) 1.47461e12 + 1.32717e11i 1.04570 + 0.0941145i
\(502\) −9.81189e11 − 3.01979e12i −0.689582 − 2.12232i
\(503\) −6.55407e11 + 6.85502e11i −0.456515 + 0.477477i −0.910486 − 0.413539i \(-0.864293\pi\)
0.453971 + 0.891016i \(0.350007\pi\)
\(504\) 1.81670e12 + 5.01378e11i 1.25414 + 0.346121i
\(505\) −2.50086e11 + 1.84621e12i −0.171111 + 1.26319i
\(506\) −5.66775e10 − 4.18410e11i −0.0384356 − 0.283743i
\(507\) −7.47738e11 + 2.06363e11i −0.502590 + 0.138706i
\(508\) −1.21094e12 + 2.25030e12i −0.806743 + 1.49918i
\(509\) −9.12265e11 − 9.54155e11i −0.602409 − 0.630070i 0.349323 − 0.937003i \(-0.386412\pi\)
−0.951731 + 0.306932i \(0.900697\pi\)
\(510\) −2.12005e12 − 3.93972e12i −1.38765 − 2.57869i
\(511\) 5.25456e11 − 1.61719e12i 0.340912 − 1.04922i
\(512\) −3.01174e11 + 7.04632e11i −0.193688 + 0.453156i
\(513\) 7.14366e12 + 1.29638e12i 4.55400 + 0.826428i
\(514\) 3.29154e12 + 2.39144e12i 2.08001 + 1.51121i
\(515\) 9.91912e11 − 8.92737e10i 0.621356 − 0.0559231i
\(516\) −1.04954e12 − 2.45552e12i −0.651740 − 1.52482i
\(517\) −4.07995e9 − 1.78754e10i −0.00251158 − 0.0110040i
\(518\) −7.70723e11 − 1.16760e12i −0.470343 − 0.712539i
\(519\) −2.61413e10 − 1.56187e10i −0.0158152 − 0.00944914i
\(520\) 5.04809e11 + 6.33011e11i 0.302770 + 0.379661i
\(521\) −2.10248e12 + 1.83688e12i −1.25015 + 1.09222i −0.258135 + 0.966109i \(0.583108\pi\)
−0.992016 + 0.126115i \(0.959749\pi\)
\(522\) 2.67740e12 − 1.94524e12i 1.57832 − 1.14672i
\(523\) −7.48907e11 + 3.60655e11i −0.437694 + 0.210782i −0.639736 − 0.768595i \(-0.720956\pi\)
0.202042 + 0.979377i \(0.435242\pi\)
\(524\) 1.10895e12 − 1.67999e12i 0.642572 − 0.973456i
\(525\) −9.36212e11 − 3.51366e11i −0.537845 − 0.201857i
\(526\) 2.84701e12 − 1.70101e12i 1.62163 − 0.968881i
\(527\) 2.68674e12 + 1.29387e12i 1.51732 + 0.730704i
\(528\) 1.53090e11 − 2.77817e10i 0.0857221 − 0.0155563i
\(529\) 1.11579e10 − 4.88859e10i 0.00619485 − 0.0271414i
\(530\) −7.27278e11 + 2.72952e11i −0.400367 + 0.150260i
\(531\) 2.49142e12 − 3.12414e12i 1.35995 − 1.70532i
\(532\) −1.17223e11 − 2.61017e12i −0.0634469 − 1.41276i
\(533\) 8.09368e9 + 1.80220e11i 0.00434384 + 0.0967231i
\(534\) 2.72902e12 − 3.42208e12i 1.45235 − 1.82119i
\(535\) 3.92416e11 − 1.47276e11i 0.207088 − 0.0777215i
\(536\) −6.17771e11 + 2.70663e12i −0.323286 + 1.41641i
\(537\) −4.99960e12 + 9.07293e11i −2.59448 + 0.470829i
\(538\) 2.81475e12 + 1.35551e12i 1.44850 + 0.697563i
\(539\) −1.87222e11 + 1.11860e11i −0.0955451 + 0.0570856i
\(540\) 6.16250e12 + 2.31283e12i 3.11878 + 1.17050i
\(541\) −6.52397e11 + 9.88340e11i −0.327434 + 0.496042i −0.960585 − 0.277987i \(-0.910333\pi\)
0.633150 + 0.774029i \(0.281761\pi\)
\(542\) −5.04038e12 + 2.42732e12i −2.50880 + 1.20817i
\(543\) −2.86317e12 + 2.08021e12i −1.41334 + 1.02685i
\(544\) 2.46381e12 − 2.15256e12i 1.20618 − 1.05381i
\(545\) 1.47240e12 + 1.84633e12i 0.714893 + 0.896448i
\(546\) −2.86830e12 − 1.71373e12i −1.38120 − 0.825231i
\(547\) 1.78707e12 + 2.70729e12i 0.853489 + 1.29298i 0.954535 + 0.298099i \(0.0963525\pi\)
−0.101046 + 0.994882i \(0.532219\pi\)
\(548\) 1.02455e12 + 4.48886e12i 0.485313 + 2.12629i
\(549\) 1.36467e12 + 3.19279e12i 0.641137 + 1.50001i
\(550\) 2.98587e11 − 2.68733e10i 0.139136 − 0.0125225i
\(551\) −1.23785e12 − 8.99354e11i −0.572120 − 0.415670i
\(552\) 3.18544e12 + 5.78072e11i 1.46030 + 0.265006i
\(553\) 4.44544e11 − 1.04006e12i 0.202140 − 0.472929i
\(554\) 1.96594e12 − 6.05053e12i 0.886698 − 2.72898i
\(555\) −1.24882e12 − 2.32070e12i −0.558704 − 1.03825i
\(556\) 9.36700e11 + 9.79712e11i 0.415685 + 0.434772i
\(557\) −5.11287e11 + 9.50131e11i −0.225070 + 0.418249i −0.967938 − 0.251188i \(-0.919179\pi\)
0.742869 + 0.669437i \(0.233465\pi\)
\(558\) −1.13989e13 + 3.14589e12i −4.97747 + 1.37369i
\(559\) 1.53387e11 + 1.13234e12i 0.0664407 + 0.490485i
\(560\) −3.52192e10 + 2.59999e11i −0.0151333 + 0.111718i
\(561\) −1.06772e12 − 2.94672e11i −0.455119 − 0.125605i
\(562\) 3.84832e12 − 4.02503e12i 1.62726 − 1.70198i
\(563\) −4.20546e11 − 1.29431e12i −0.176411 − 0.542937i 0.823284 − 0.567629i \(-0.192139\pi\)
−0.999695 + 0.0246924i \(0.992139\pi\)
\(564\) 4.19869e11 + 3.77889e10i 0.174726 + 0.0157256i
\(565\) −1.60703e12 − 1.40402e12i −0.663447 − 0.579636i
\(566\) −2.06192e11 + 4.59123e12i −0.0844499 + 1.88042i
\(567\) −5.01136e12 −2.03626
\(568\) 6.30674e11 − 1.85849e12i 0.254236 − 0.749190i
\(569\) 3.20738e12 1.28276 0.641379 − 0.767224i \(-0.278363\pi\)
0.641379 + 0.767224i \(0.278363\pi\)
\(570\) 3.67991e11 − 8.19396e12i 0.146016 − 3.25130i
\(571\) 2.45487e12 + 2.14476e12i 0.966422 + 0.844337i 0.987846 − 0.155433i \(-0.0496774\pi\)
−0.0214248 + 0.999770i \(0.506820\pi\)
\(572\) 5.98662e11 + 5.38806e10i 0.233830 + 0.0210451i
\(573\) −6.53640e11 − 2.01170e12i −0.253305 − 0.779591i
\(574\) 2.02705e11 − 2.12013e11i 0.0779401 − 0.0815190i
\(575\) −1.19845e12 − 3.30752e11i −0.457210 − 0.126182i
\(576\) −1.50983e12 + 1.11460e13i −0.571513 + 4.21908i
\(577\) 2.39355e11 + 1.76699e12i 0.0898983 + 0.663656i 0.978690 + 0.205344i \(0.0658313\pi\)
−0.888792 + 0.458312i \(0.848454\pi\)
\(578\) −3.37701e12 + 9.31996e11i −1.25851 + 0.347327i
\(579\) −2.00523e12 + 3.72634e12i −0.741498 + 1.37793i
\(580\) −9.58616e11 − 1.00263e12i −0.351738 − 0.367889i
\(581\) −9.09188e10 − 1.68955e11i −0.0331025 − 0.0615148i
\(582\) −4.12203e12 + 1.26863e13i −1.48921 + 4.58333i
\(583\) −7.55865e10 + 1.76843e11i −0.0270979 + 0.0633987i
\(584\) −3.84597e12 − 6.97941e11i −1.36820 − 0.248291i
\(585\) −3.68529e12 − 2.67752e12i −1.30098 − 0.945217i
\(586\) 5.33598e12 − 4.80247e11i 1.86928 − 0.168239i
\(587\) 2.06920e12 + 4.84114e12i 0.719336 + 1.68297i 0.730390 + 0.683031i \(0.239339\pi\)
−0.0110537 + 0.999939i \(0.503519\pi\)
\(588\) −1.11583e12 − 4.88875e12i −0.384945 − 1.68655i
\(589\) 3.01182e12 + 4.56271e12i 1.03112 + 1.56208i
\(590\) −2.39615e12 − 1.43163e12i −0.814104 − 0.486404i
\(591\) −3.07066e12 − 3.85049e12i −1.03535 − 1.29829i
\(592\) 4.82688e11 − 4.21712e11i 0.161517 − 0.141113i
\(593\) −3.35291e12 + 2.43603e12i −1.11346 + 0.808977i −0.983205 − 0.182503i \(-0.941580\pi\)
−0.130256 + 0.991480i \(0.541580\pi\)
\(594\) 2.44681e12 − 1.17832e12i 0.806420 − 0.388352i
\(595\) 1.02898e12 − 1.55883e12i 0.336573 − 0.509886i
\(596\) 1.37748e12 + 5.16978e11i 0.447176 + 0.167828i
\(597\) 4.24391e12 − 2.53562e12i 1.36736 − 0.816957i
\(598\) −3.74276e12 − 1.80242e12i −1.19684 − 0.576368i
\(599\) −2.23394e12 + 4.05401e11i −0.709009 + 0.128666i −0.521069 − 0.853515i \(-0.674467\pi\)
−0.187940 + 0.982181i \(0.560181\pi\)
\(600\) −5.11504e11 + 2.24104e12i −0.161127 + 0.705943i
\(601\) −4.98670e12 + 1.87154e12i −1.55911 + 0.585145i −0.974148 − 0.225912i \(-0.927464\pi\)
−0.584967 + 0.811057i \(0.698892\pi\)
\(602\) 1.15841e12 − 1.45260e12i 0.359484 − 0.450778i
\(603\) −7.00776e11 − 1.56040e13i −0.215850 − 4.80627i
\(604\) 3.09136e9 + 6.88345e10i 0.000945112 + 0.0210446i
\(605\) 1.43018e12 − 1.79339e12i 0.434003 − 0.544222i
\(606\) −1.65468e13 + 6.21013e12i −4.98412 + 1.87057i
\(607\) 7.34448e11 − 3.21783e12i 0.219590 − 0.962085i −0.738193 − 0.674590i \(-0.764320\pi\)
0.957782 − 0.287495i \(-0.0928224\pi\)
\(608\) 5.90170e12 − 1.07100e12i 1.75150 − 0.317851i
\(609\) 1.71997e12 + 8.28296e11i 0.506692 + 0.244010i
\(610\) 2.08210e12 − 1.24400e12i 0.608861 − 0.363777i
\(611\) −1.68888e11 − 6.33849e10i −0.0490246 − 0.0183993i
\(612\) 1.01541e13 − 1.53827e13i 2.92589 − 4.43254i
\(613\) 5.66674e12 − 2.72896e12i 1.62092 − 0.780593i 0.620923 − 0.783871i \(-0.286758\pi\)
0.999995 + 0.00327866i \(0.00104363\pi\)
\(614\) 1.66122e12 − 1.20695e12i 0.471705 − 0.342714i
\(615\) 4.16100e11 − 3.63536e11i 0.117290 − 0.102473i
\(616\) −2.03209e11 − 2.54816e11i −0.0568630 − 0.0713040i
\(617\) −1.65320e12 − 9.87743e11i −0.459243 − 0.274385i 0.264589 − 0.964361i \(-0.414764\pi\)
−0.723832 + 0.689976i \(0.757621\pi\)
\(618\) 5.20470e12 + 7.88479e12i 1.43532 + 2.17441i
\(619\) 2.14595e11 + 9.40202e11i 0.0587505 + 0.257403i 0.995771 − 0.0918721i \(-0.0292851\pi\)
−0.937020 + 0.349275i \(0.886428\pi\)
\(620\) 1.94802e12 + 4.55763e12i 0.529458 + 1.23873i
\(621\) −1.12170e13 + 1.00955e12i −3.02667 + 0.272405i
\(622\) 8.62942e12 + 6.26964e12i 2.31167 + 1.67952i
\(623\) 1.79799e12 + 3.26288e11i 0.478180 + 0.0867770i
\(624\) 6.01635e11 − 1.40759e12i 0.158856 − 0.371661i
\(625\) −3.38964e11 + 1.04322e12i −0.0888573 + 0.273475i
\(626\) 1.33551e11 + 2.48179e11i 0.0347586 + 0.0645923i
\(627\) −1.40332e12 − 1.46776e12i −0.362622 − 0.379272i
\(628\) −3.83161e11 + 7.12033e11i −0.0983022 + 0.182676i
\(629\) −4.39852e12 + 1.21392e12i −1.12042 + 0.309215i
\(630\) 9.94218e11 + 7.33962e12i 0.251449 + 1.85627i
\(631\) −3.22904e11 + 2.38378e12i −0.0810853 + 0.598595i 0.904128 + 0.427262i \(0.140522\pi\)
−0.985213 + 0.171333i \(0.945192\pi\)
\(632\) −2.50636e12 − 6.91711e11i −0.624909 − 0.172464i
\(633\) 3.31713e12 − 3.46944e12i 0.821193 − 0.858901i
\(634\) 3.20378e12 + 9.86023e12i 0.787520 + 2.42374i
\(635\) −3.33567e12 − 3.00216e11i −0.814144 − 0.0732743i
\(636\) −3.32999e12 − 2.90932e12i −0.807022 − 0.705074i
\(637\) −9.62678e10 + 2.14357e12i −0.0231661 + 0.515834i
\(638\) −5.72329e11 −0.136758
\(639\) −6.38687e11 + 1.10234e13i −0.151542 + 2.61555i
\(640\) 4.23242e12 0.997193
\(641\) −1.84051e10 + 4.09820e11i −0.00430602 + 0.0958810i 0.995689 + 0.0927536i \(0.0295669\pi\)
−0.999995 + 0.00312734i \(0.999005\pi\)
\(642\) 2.99433e12 + 2.61607e12i 0.695651 + 0.607772i
\(643\) −3.53432e12 − 3.18094e11i −0.815373 − 0.0733849i −0.325901 − 0.945404i \(-0.605668\pi\)
−0.489472 + 0.872019i \(0.662810\pi\)
\(644\) 1.25245e12 + 3.85465e12i 0.286929 + 0.883078i
\(645\) 2.41861e12 − 2.52967e12i 0.550234 − 0.575500i
\(646\) −1.36898e13 − 3.77813e12i −3.09278 − 0.853554i
\(647\) 7.54943e11 − 5.57321e12i 0.169373 − 1.25036i −0.684163 − 0.729329i \(-0.739832\pi\)
0.853536 − 0.521034i \(-0.174453\pi\)
\(648\) 1.54634e12 + 1.14155e13i 0.344522 + 2.54336i
\(649\) −6.66144e11 + 1.83844e11i −0.147390 + 0.0406770i
\(650\) 1.39769e12 − 2.59735e12i 0.307116 − 0.570717i
\(651\) −4.71386e12 − 4.93031e12i −1.02864 − 1.07587i
\(652\) −3.29146e12 − 6.11656e12i −0.713303 − 1.32554i
\(653\) 1.88417e12 − 5.79889e12i 0.405519 − 1.24806i −0.514942 − 0.857225i \(-0.672186\pi\)
0.920461 − 0.390835i \(-0.127814\pi\)
\(654\) −8.80475e12 + 2.05997e13i −1.88199 + 4.40313i
\(655\) 2.59584e12 + 4.71075e11i 0.551051 + 0.100001i
\(656\) 1.08720e11 + 7.89894e10i 0.0229214 + 0.0166533i
\(657\) 2.19032e13 − 1.97132e12i 4.58630 − 0.412775i
\(658\) 1.15277e11 + 2.69704e11i 0.0239732 + 0.0560881i
\(659\) 2.35127e11 + 1.03016e12i 0.0485644 + 0.212775i 0.993388 − 0.114805i \(-0.0366242\pi\)
−0.944824 + 0.327579i \(0.893767\pi\)
\(660\) −1.01421e12 − 1.53646e12i −0.208055 − 0.315190i
\(661\) 2.23109e12 + 1.33302e12i 0.454581 + 0.271600i 0.721885 − 0.692013i \(-0.243276\pi\)
−0.267304 + 0.963612i \(0.586133\pi\)
\(662\) −9.13146e12 − 1.14505e13i −1.84790 − 2.31720i
\(663\) −8.20663e12 + 7.16992e12i −1.64951 + 1.44113i
\(664\) −3.56814e11 + 2.59241e11i −0.0712337 + 0.0517543i
\(665\) 3.08523e12 − 1.48577e12i 0.611773 − 0.294615i
\(666\) 9.96789e12 − 1.51007e13i 1.96322 − 2.97415i
\(667\) 2.22213e12 + 8.33978e11i 0.434713 + 0.163150i
\(668\) 3.65767e12 − 2.18536e12i 0.710740 − 0.424647i
\(669\) −2.73003e12 − 1.31471e12i −0.526926 − 0.253754i
\(670\) −1.07354e13 + 1.94819e12i −2.05818 + 0.373504i
\(671\) 1.33619e11 − 5.85422e11i 0.0254458 − 0.111485i
\(672\) −7.00646e12 + 2.62957e12i −1.32537 + 0.497419i
\(673\) 2.07225e11 − 2.59852e11i 0.0389381 − 0.0488269i −0.761981 − 0.647599i \(-0.775773\pi\)
0.800919 + 0.598772i \(0.204345\pi\)
\(674\) −1.99909e11 − 4.45131e12i −0.0373132 − 0.830842i
\(675\) −3.58763e11 − 7.98847e12i −0.0665182 − 1.48114i
\(676\) −1.39181e12 + 1.74528e12i −0.256343 + 0.321443i
\(677\) 2.36440e12 − 8.87373e11i 0.432585 − 0.162352i −0.125577 − 0.992084i \(-0.540078\pi\)
0.558162 + 0.829732i \(0.311507\pi\)
\(678\) 4.50464e12 − 1.97361e13i 0.818703 − 3.58697i
\(679\) −5.47947e12 + 9.94378e11i −0.989293 + 0.179530i
\(680\) −3.86842e12 − 1.86293e12i −0.693815 − 0.334124i
\(681\) −1.50717e13 + 9.00490e12i −2.68534 + 1.60442i
\(682\) 1.91460e12 + 7.18561e11i 0.338882 + 0.127184i
\(683\) 1.00688e12 − 1.52535e12i 0.177045 − 0.268212i −0.735206 − 0.677844i \(-0.762914\pi\)
0.912251 + 0.409632i \(0.134343\pi\)
\(684\) 3.04454e13 − 1.46617e13i 5.31826 − 2.56114i
\(685\) −4.88194e12 + 3.54693e12i −0.847197 + 0.615525i
\(686\) 6.96275e12 − 6.08317e12i 1.20039 − 1.04875i
\(687\) 8.84618e12 + 1.10928e13i 1.51513 + 1.89992i
\(688\) 7.30721e11 + 4.36585e11i 0.124338 + 0.0742884i
\(689\) 1.04238e12 + 1.57914e12i 0.176214 + 0.266952i
\(690\) 2.83123e12 + 1.24044e13i 0.475503 + 2.08332i
\(691\) 3.14017e12 + 7.34680e12i 0.523965 + 1.22588i 0.947429 + 0.319965i \(0.103671\pi\)
−0.423464 + 0.905913i \(0.639186\pi\)
\(692\) −8.72818e10 + 7.85551e9i −0.0144693 + 0.00130226i
\(693\) 1.48350e12 + 1.07783e12i 0.244337 + 0.177521i
\(694\) 3.81478e12 + 6.92280e11i 0.624240 + 0.113283i
\(695\) −6.98191e11 + 1.63350e12i −0.113512 + 0.265575i
\(696\) 1.35607e12 − 4.17356e12i 0.219049 − 0.674164i
\(697\) −4.53340e11 − 8.42447e11i −0.0727573 − 0.135206i
\(698\) 5.68519e12 + 5.94624e12i 0.906558 + 0.948185i
\(699\) −2.05462e12 + 3.81812e12i −0.325525 + 0.604926i
\(700\) −2.77404e12 + 7.65585e11i −0.436688 + 0.120518i
\(701\) 5.03380e11 + 3.71610e12i 0.0787345 + 0.581241i 0.986743 + 0.162290i \(0.0518880\pi\)
−0.908009 + 0.418951i \(0.862398\pi\)
\(702\) 3.58659e12 − 2.64773e13i 0.557398 − 4.11488i
\(703\) −8.06398e12 − 2.22552e12i −1.24523 − 0.343663i
\(704\) 1.34423e12 − 1.40596e12i 0.206252 − 0.215723i
\(705\) 1.70734e11 + 5.25464e11i 0.0260296 + 0.0801110i
\(706\) −3.46407e12 − 3.11772e11i −0.524765 − 0.0472297i
\(707\) −5.55665e12 − 4.85470e12i −0.836422 − 0.730760i
\(708\) 7.12847e11 − 1.58728e13i 0.106622 − 2.37412i
\(709\) −9.46502e12 −1.40674 −0.703369 − 0.710824i \(-0.748322\pi\)
−0.703369 + 0.710824i \(0.748322\pi\)
\(710\) 7.69033e12 − 5.91513e11i 1.13575 − 0.0873578i
\(711\) 1.46285e13 2.14677
\(712\) 1.88460e11 − 4.19638e12i 0.0274826 − 0.611949i
\(713\) −6.38656e12 − 5.57977e12i −0.925474 − 0.808562i
\(714\) 1.76475e13 + 1.58831e12i 2.54122 + 0.228714i
\(715\) 2.43437e11 + 7.49223e11i 0.0348345 + 0.107210i
\(716\) −1.01053e13 + 1.05694e13i −1.43695 + 1.50293i
\(717\) 2.05609e13 + 5.67444e12i 2.90540 + 0.801838i
\(718\) 1.49659e12 − 1.10483e13i 0.210157 − 1.55144i
\(719\) 9.99157e11 + 7.37607e12i 0.139429 + 1.02931i 0.916540 + 0.399943i \(0.130970\pi\)
−0.777111 + 0.629364i \(0.783315\pi\)
\(720\) −3.27103e12 + 9.02747e11i −0.453616 + 0.125190i
\(721\) −1.86909e12 + 3.47335e12i −0.257586 + 0.478674i
\(722\) −1.00139e13 − 1.04738e13i −1.37148 − 1.43445i
\(723\) −8.94677e11 − 1.66259e12i −0.121771 − 0.226288i
\(724\) −3.14727e12 + 9.68629e12i −0.425706 + 1.31019i
\(725\) −6.62333e11 + 1.54961e12i −0.0890340 + 0.208305i
\(726\) 2.14105e13 + 3.88543e12i 2.86030 + 0.519069i
\(727\) 5.24974e11 + 3.81416e11i 0.0697000 + 0.0506400i 0.622090 − 0.782946i \(-0.286284\pi\)
−0.552390 + 0.833586i \(0.686284\pi\)
\(728\) −3.19369e12 + 2.87438e11i −0.421407 + 0.0379274i
\(729\) −7.89820e12 − 1.84788e13i −1.03575 − 2.42325i
\(730\) −3.41831e12 − 1.49766e13i −0.445511 − 1.95191i
\(731\) −3.33828e12 − 5.05728e12i −0.432409 − 0.655072i
\(732\) 1.18520e13 + 7.08126e12i 1.52578 + 0.911614i
\(733\) 1.92937e12 + 2.41936e12i 0.246859 + 0.309551i 0.889788 − 0.456375i \(-0.150852\pi\)
−0.642929 + 0.765926i \(0.722281\pi\)
\(734\) −2.88666e12 + 2.52200e12i −0.367082 + 0.320710i
\(735\) 5.31685e12 − 3.86292e12i 0.671988 − 0.488228i
\(736\) −8.38292e12 + 4.03700e12i −1.05304 + 0.507117i
\(737\) −1.48811e12 + 2.25439e12i −0.185794 + 0.281465i
\(738\) 3.55171e12 + 1.33298e12i 0.440741 + 0.165413i
\(739\) −1.10157e13 + 6.58155e12i −1.35866 + 0.811761i −0.992900 − 0.118949i \(-0.962048\pi\)
−0.365759 + 0.930710i \(0.619190\pi\)
\(740\) −6.83305e12 − 3.29062e12i −0.837668 − 0.403400i
\(741\) −1.96578e13 + 3.56737e12i −2.39527 + 0.434677i
\(742\) 6.84595e11 − 2.99941e12i 0.0829117 − 0.363260i
\(743\) 7.65908e12 − 2.87450e12i 0.921992 − 0.346029i 0.155169 − 0.987888i \(-0.450408\pi\)
0.766823 + 0.641859i \(0.221836\pi\)
\(744\) −9.77636e12 + 1.22592e13i −1.16977 + 1.46684i
\(745\) 8.65125e10 + 1.92635e12i 0.0102891 + 0.229104i
\(746\) −4.24495e11 − 9.45211e12i −0.0501820 − 1.11739i
\(747\) 1.54714e12 − 1.94005e12i 0.181797 − 0.227967i
\(748\) −2.98431e12 + 1.12003e12i −0.348568 + 0.130820i
\(749\) −3.69386e11 + 1.61839e12i −0.0428857 + 0.187894i
\(750\) −2.73667e13 + 4.96632e12i −3.15825 + 0.573138i
\(751\) 1.50561e12 + 7.25063e11i 0.172716 + 0.0831757i 0.518244 − 0.855233i \(-0.326586\pi\)
−0.345528 + 0.938408i \(0.612300\pi\)
\(752\) −1.15356e11 + 6.89219e10i −0.0131540 + 0.00785917i