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Properties

Label 71.10.g.a.2.9
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 2.9
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34663 + 29.9850i) q^{2} +(-129.450 - 113.097i) q^{3} +(-387.347 - 34.8619i) q^{4} +(459.484 + 1414.15i) q^{5} +(3565.52 - 3729.25i) q^{6} +(3763.22 + 1038.58i) q^{7} +(-495.923 + 3661.05i) q^{8} +(1324.22 + 9775.79i) q^{9} +O(q^{10})\) \(q+(-1.34663 + 29.9850i) q^{2} +(-129.450 - 113.097i) q^{3} +(-387.347 - 34.8619i) q^{4} +(459.484 + 1414.15i) q^{5} +(3565.52 - 3729.25i) q^{6} +(3763.22 + 1038.58i) q^{7} +(-495.923 + 3661.05i) q^{8} +(1324.22 + 9775.79i) q^{9} +(-43021.9 + 11873.3i) q^{10} +(25473.5 - 47337.6i) q^{11} +(46199.2 + 48320.5i) q^{12} +(-20275.0 - 37677.3i) q^{13} +(-36209.5 + 111441. i) q^{14} +(100455. - 235027. i) q^{15} +(-305032. - 55355.2i) q^{16} +(-402883. - 292712. i) q^{17} +(-294910. + 26542.4i) q^{18} +(-219647. - 513890. i) q^{19} +(-128680. - 563784. i) q^{20} +(-369687. - 560052. i) q^{21} +(1.38512e6 + 827568. i) q^{22} +(955839. + 1.19858e6i) q^{23} +(478250. - 417835. i) q^{24} +(-208570. + 151535. i) q^{25} +(1.15706e6 - 557210. i) q^{26} +(-929726. + 1.40847e6i) q^{27} +(-1.42146e6 - 533485. i) q^{28} +(-172218. + 102895. i) q^{29} +(6.91199e6 + 3.32864e6i) q^{30} +(9.82466e6 - 1.78291e6i) q^{31} +(1.64967e6 - 7.22769e6i) q^{32} +(-8.65126e6 + 3.24687e6i) q^{33} +(9.31949e6 - 1.16863e7i) q^{34} +(260431. + 5.79895e6i) q^{35} +(-172131. - 3.83279e6i) q^{36} +(9.60823e6 - 1.20483e7i) q^{37} +(1.57048e7 - 5.89410e6i) q^{38} +(-1.63659e6 + 7.17036e6i) q^{39} +(-5.40513e6 + 980886. i) q^{40} +(1.30113e7 + 6.26592e6i) q^{41} +(1.72910e7 - 1.03309e7i) q^{42} +(1.00735e7 + 3.78064e6i) q^{43} +(-1.15174e7 + 1.74480e7i) q^{44} +(-1.32159e7 + 6.36445e6i) q^{45} +(-3.72267e7 + 2.70468e7i) q^{46} +(-2.49710e7 + 2.18165e7i) q^{47} +(3.32258e7 + 4.16638e7i) q^{48} +(-2.15583e7 - 1.28805e7i) q^{49} +(-4.26291e6 - 6.45804e6i) q^{50} +(1.90483e7 + 8.34561e7i) q^{51} +(6.53998e6 + 1.53010e7i) q^{52} +(5.93456e6 - 534120. i) q^{53} +(-4.09811e7 - 2.97745e7i) q^{54} +(7.86469e7 + 1.42723e7i) q^{55} +(-5.66857e6 + 1.32623e7i) q^{56} +(-2.96861e7 + 9.13643e7i) q^{57} +(-2.85340e6 - 5.30251e6i) q^{58} +(-4.39772e7 - 4.59966e7i) q^{59} +(-4.71045e7 + 8.75348e7i) q^{60} +(1.64784e8 - 4.54776e7i) q^{61} +(4.02304e7 + 2.96993e8i) q^{62} +(-5.16963e6 + 3.81637e7i) q^{63} +(6.14935e7 + 1.69711e7i) q^{64} +(4.39652e7 - 4.59840e7i) q^{65} +(-8.57074e7 - 2.63780e8i) q^{66} +(8.15558e7 + 7.34016e6i) q^{67} +(1.45851e8 + 1.27426e8i) q^{68} +(1.18230e7 - 2.63259e8i) q^{69} -1.74232e8 q^{70} +(-3.65746e7 - 2.10976e8i) q^{71} -3.64464e7 q^{72} +(965780. - 2.15048e7i) q^{73} +(3.48331e8 + 3.04327e8i) q^{74} +(4.41375e7 + 3.97244e6i) q^{75} +(6.71646e7 + 2.06711e8i) q^{76} +(1.45026e8 - 1.51686e8i) q^{77} +(-2.12799e8 - 5.87289e7i) q^{78} +(-3.38824e7 + 2.50130e8i) q^{79} +(-6.18770e7 - 4.56795e8i) q^{80} +(4.66823e8 - 1.28835e8i) q^{81} +(-2.05405e8 + 3.81706e8i) q^{82} +(2.42428e8 + 2.53559e8i) q^{83} +(1.23673e8 + 2.29822e8i) q^{84} +(2.28819e8 - 7.04231e8i) q^{85} +(-1.26928e8 + 2.96962e8i) q^{86} +(3.39306e7 + 6.15750e6i) q^{87} +(1.60673e8 + 1.16736e8i) q^{88} +(6.49219e8 - 5.84307e7i) q^{89} +(-1.73041e8 - 4.04850e8i) q^{90} +(-3.71684e7 - 1.62845e8i) q^{91} +(-3.28457e8 - 4.97591e8i) q^{92} +(-1.47344e9 - 8.80339e8i) q^{93} +(-6.20540e8 - 7.78133e8i) q^{94} +(6.25791e8 - 5.46737e8i) q^{95} +(-1.03098e9 + 7.49049e8i) q^{96} +(2.27001e8 - 1.09318e8i) q^{97} +(4.15253e8 - 6.29082e8i) q^{98} +(4.96495e8 + 1.86338e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34663 + 29.9850i −0.0595131 + 1.32516i 0.717889 + 0.696158i \(0.245109\pi\)
−0.777402 + 0.629004i \(0.783463\pi\)
\(3\) −129.450 − 113.097i −0.922688 − 0.806129i 0.0586774 − 0.998277i \(-0.481312\pi\)
−0.981366 + 0.192148i \(0.938455\pi\)
\(4\) −387.347 − 34.8619i −0.756537 − 0.0680896i
\(5\) 459.484 + 1414.15i 0.328780 + 1.01188i 0.969705 + 0.244277i \(0.0785506\pi\)
−0.640926 + 0.767603i \(0.721449\pi\)
\(6\) 3565.52 − 3729.25i 1.12316 − 1.17474i
\(7\) 3763.22 + 1038.58i 0.592404 + 0.163493i 0.549368 − 0.835580i \(-0.314868\pi\)
0.0430360 + 0.999074i \(0.486297\pi\)
\(8\) −495.923 + 3661.05i −0.0428065 + 0.316010i
\(9\) 1324.22 + 9775.79i 0.0672774 + 0.496661i
\(10\) −43021.9 + 11873.3i −1.36047 + 0.375466i
\(11\) 25473.5 − 47337.6i 0.524591 − 0.974854i −0.471096 − 0.882082i \(-0.656142\pi\)
0.995687 − 0.0927719i \(-0.0295727\pi\)
\(12\) 46199.2 + 48320.5i 0.643159 + 0.672692i
\(13\) −20275.0 − 37677.3i −0.196887 − 0.365877i 0.762940 − 0.646469i \(-0.223755\pi\)
−0.959827 + 0.280592i \(0.909469\pi\)
\(14\) −36209.5 + 111441.i −0.251911 + 0.775301i
\(15\) 100455. − 235027.i 0.512344 − 1.19869i
\(16\) −305032. − 55355.2i −1.16361 − 0.211163i
\(17\) −402883. − 292712.i −1.16993 − 0.850002i −0.178927 − 0.983862i \(-0.557263\pi\)
−0.991000 + 0.133861i \(0.957263\pi\)
\(18\) −294910. + 26542.4i −0.662160 + 0.0595955i
\(19\) −219647. − 513890.i −0.386665 − 0.904647i −0.993916 − 0.110138i \(-0.964871\pi\)
0.607251 − 0.794510i \(-0.292272\pi\)
\(20\) −128680. − 563784.i −0.179836 − 0.787911i
\(21\) −369687. − 560052.i −0.414808 − 0.628407i
\(22\) 1.38512e6 + 827568.i 1.26062 + 0.753185i
\(23\) 955839. + 1.19858e6i 0.712213 + 0.893086i 0.997869 − 0.0652457i \(-0.0207831\pi\)
−0.285657 + 0.958332i \(0.592212\pi\)
\(24\) 478250. − 417835.i 0.294242 − 0.257071i
\(25\) −208570. + 151535.i −0.106788 + 0.0775860i
\(26\) 1.15706e6 − 557210.i 0.496564 − 0.239132i
\(27\) −929726. + 1.40847e6i −0.336681 + 0.510049i
\(28\) −1.42146e6 − 533485.i −0.437044 − 0.164025i
\(29\) −172218. + 102895.i −0.0452154 + 0.0270150i −0.535329 − 0.844644i \(-0.679812\pi\)
0.490114 + 0.871659i \(0.336955\pi\)
\(30\) 6.91199e6 + 3.32864e6i 1.55797 + 0.750276i
\(31\) 9.82466e6 − 1.78291e6i 1.91069 − 0.346739i 0.912616 − 0.408817i \(-0.134059\pi\)
0.998071 + 0.0620782i \(0.0197728\pi\)
\(32\) 1.64967e6 − 7.22769e6i 0.278114 − 1.21850i
\(33\) −8.65126e6 + 3.24687e6i −1.26989 + 0.476598i
\(34\) 9.31949e6 − 1.16863e7i 1.19602 − 1.49976i
\(35\) 260431. + 5.79895e6i 0.0293350 + 0.653195i
\(36\) −172131. − 3.83279e6i −0.0170804 − 0.380324i
\(37\) 9.60823e6 − 1.20483e7i 0.842821 − 1.05686i −0.154801 − 0.987946i \(-0.549474\pi\)
0.997622 − 0.0689189i \(-0.0219550\pi\)
\(38\) 1.57048e7 − 5.89410e6i 1.22182 − 0.458555i
\(39\) −1.63659e6 + 7.17036e6i −0.113279 + 0.496307i
\(40\) −5.40513e6 + 980886.i −0.333838 + 0.0605827i
\(41\) 1.30113e7 + 6.26592e6i 0.719108 + 0.346304i 0.757390 − 0.652963i \(-0.226474\pi\)
−0.0382822 + 0.999267i \(0.512189\pi\)
\(42\) 1.72910e7 − 1.03309e7i 0.857428 − 0.512289i
\(43\) 1.00735e7 + 3.78064e6i 0.449336 + 0.168639i 0.565776 − 0.824559i \(-0.308577\pi\)
−0.116440 + 0.993198i \(0.537148\pi\)
\(44\) −1.15174e7 + 1.74480e7i −0.463250 + 0.701794i
\(45\) −1.32159e7 + 6.36445e6i −0.480442 + 0.231369i
\(46\) −3.72267e7 + 2.70468e7i −1.22587 + 0.890646i
\(47\) −2.49710e7 + 2.18165e7i −0.746440 + 0.652145i −0.944674 − 0.328010i \(-0.893622\pi\)
0.198234 + 0.980155i \(0.436479\pi\)
\(48\) 3.32258e7 + 4.16638e7i 0.903420 + 1.13285i
\(49\) −2.15583e7 − 1.28805e7i −0.534236 − 0.319191i
\(50\) −4.26291e6 − 6.45804e6i −0.0964587 − 0.146129i
\(51\) 1.90483e7 + 8.34561e7i 0.394267 + 1.72740i
\(52\) 6.53998e6 + 1.53010e7i 0.124040 + 0.290206i
\(53\) 5.93456e6 − 534120.i 0.103311 − 0.00929817i −0.0378631 − 0.999283i \(-0.512055\pi\)
0.141174 + 0.989985i \(0.454912\pi\)
\(54\) −4.09811e7 − 2.97745e7i −0.655861 − 0.476511i
\(55\) 7.86469e7 + 1.42723e7i 1.15891 + 0.210311i
\(56\) −5.66857e6 + 1.32623e7i −0.0770243 + 0.180207i
\(57\) −2.96861e7 + 9.13643e7i −0.372491 + 1.14641i
\(58\) −2.85340e6 − 5.30251e6i −0.0331083 − 0.0615255i
\(59\) −4.39772e7 − 4.59966e7i −0.472491 − 0.494187i 0.443002 − 0.896521i \(-0.353913\pi\)
−0.915493 + 0.402334i \(0.868199\pi\)
\(60\) −4.71045e7 + 8.75348e7i −0.469226 + 0.871967i
\(61\) 1.64784e8 − 4.54776e7i 1.52381 − 0.420546i 0.598932 − 0.800800i \(-0.295592\pi\)
0.924882 + 0.380254i \(0.124163\pi\)
\(62\) 4.02304e7 + 2.96993e8i 0.345774 + 2.55261i
\(63\) −5.16963e6 + 3.81637e7i −0.0413454 + 0.305224i
\(64\) 6.14935e7 + 1.69711e7i 0.458162 + 0.126445i
\(65\) 4.39652e7 − 4.59840e7i 0.305491 − 0.319519i
\(66\) −8.57074e7 − 2.63780e8i −0.555995 − 1.71118i
\(67\) 8.15558e7 + 7.34016e6i 0.494445 + 0.0445009i 0.334057 − 0.942553i \(-0.391582\pi\)
0.160389 + 0.987054i \(0.448725\pi\)
\(68\) 1.45851e8 + 1.27426e8i 0.827217 + 0.722718i
\(69\) 1.18230e7 − 2.63259e8i 0.0627921 − 1.39818i
\(70\) −1.74232e8 −0.867335
\(71\) −3.65746e7 − 2.10976e8i −0.170811 − 0.985304i
\(72\) −3.64464e7 −0.159830
\(73\) 965780. − 2.15048e7i 0.00398039 − 0.0886302i −0.996019 − 0.0891358i \(-0.971589\pi\)
1.00000 0.000505563i \(0.000160926\pi\)
\(74\) 3.48331e8 + 3.04327e8i 1.35036 + 1.17977i
\(75\) 4.41375e7 + 3.97244e6i 0.161076 + 0.0144971i
\(76\) 6.71646e7 + 2.06711e8i 0.230929 + 0.710727i
\(77\) 1.45026e8 − 1.51686e8i 0.470152 − 0.491740i
\(78\) −2.12799e8 − 5.87289e7i −0.650945 − 0.179649i
\(79\) −3.38824e7 + 2.50130e8i −0.0978705 + 0.722509i 0.873820 + 0.486250i \(0.161636\pi\)
−0.971690 + 0.236259i \(0.924079\pi\)
\(80\) −6.18770e7 − 4.56795e8i −0.168898 − 1.24686i
\(81\) 4.66823e8 − 1.28835e8i 1.20495 − 0.332546i
\(82\) −2.05405e8 + 3.81706e8i −0.501705 + 0.932324i
\(83\) 2.42428e8 + 2.53559e8i 0.560700 + 0.586446i 0.940996 − 0.338419i \(-0.109892\pi\)
−0.380296 + 0.924865i \(0.624178\pi\)
\(84\) 1.23673e8 + 2.29822e8i 0.271030 + 0.503658i
\(85\) 2.28819e8 − 7.04231e8i 0.475451 − 1.46329i
\(86\) −1.26928e8 + 2.96962e8i −0.250215 + 0.585407i
\(87\) 3.39306e7 + 6.15750e6i 0.0634973 + 0.0115231i
\(88\) 1.60673e8 + 1.16736e8i 0.285608 + 0.207506i
\(89\) 6.49219e8 − 5.84307e7i 1.09682 − 0.0987157i 0.473584 − 0.880749i \(-0.342960\pi\)
0.623237 + 0.782033i \(0.285817\pi\)
\(90\) −1.73041e8 − 4.04850e8i −0.278008 − 0.650433i
\(91\) −3.71684e7 − 1.62845e8i −0.0568182 − 0.248937i
\(92\) −3.28457e8 − 4.97591e8i −0.478006 − 0.724147i
\(93\) −1.47344e9 − 8.80339e8i −2.04249 − 1.22033i
\(94\) −6.20540e8 − 7.78133e8i −0.819775 − 1.02797i
\(95\) 6.25791e8 − 5.46737e8i 0.788267 − 0.688688i
\(96\) −1.03098e9 + 7.49049e8i −1.23888 + 0.900098i
\(97\) 2.27001e8 − 1.09318e8i 0.260349 − 0.125377i −0.299157 − 0.954204i \(-0.596705\pi\)
0.559505 + 0.828827i \(0.310991\pi\)
\(98\) 4.15253e8 − 6.29082e8i 0.454774 − 0.688953i
\(99\) 4.96495e8 + 1.86338e8i 0.519465 + 0.194959i
\(100\) 8.60719e7 − 5.14255e7i 0.0860719 − 0.0514255i
\(101\) 1.68209e9 + 8.10053e8i 1.60844 + 0.774582i 0.999822 − 0.0188845i \(-0.00601148\pi\)
0.608614 + 0.793466i \(0.291726\pi\)
\(102\) −2.52808e9 + 4.58779e8i −2.31255 + 0.419665i
\(103\) 2.46689e8 − 1.08081e9i 0.215964 − 0.946200i −0.744462 − 0.667665i \(-0.767294\pi\)
0.960426 − 0.278535i \(-0.0898489\pi\)
\(104\) 1.47994e8 − 5.55429e7i 0.124049 − 0.0465563i
\(105\) 6.22129e8 − 7.80125e8i 0.499492 − 0.626344i
\(106\) 8.02394e6 + 1.78667e8i 0.00617322 + 0.137457i
\(107\) 3.99474e7 + 8.89497e8i 0.0294619 + 0.656021i 0.958339 + 0.285633i \(0.0922038\pi\)
−0.928877 + 0.370388i \(0.879225\pi\)
\(108\) 4.09229e8 − 5.13157e8i 0.289440 − 0.362947i
\(109\) −4.05172e8 + 1.52064e8i −0.274929 + 0.103183i −0.485031 − 0.874497i \(-0.661192\pi\)
0.210102 + 0.977679i \(0.432620\pi\)
\(110\) −5.33863e8 + 2.33901e9i −0.347667 + 1.52323i
\(111\) −2.60641e9 + 4.72993e8i −1.62963 + 0.295734i
\(112\) −1.09041e9 − 5.25115e8i −0.654801 − 0.315336i
\(113\) −2.91764e9 + 1.74321e9i −1.68337 + 1.00576i −0.740811 + 0.671713i \(0.765559\pi\)
−0.942555 + 0.334052i \(0.891584\pi\)
\(114\) −2.69958e9 − 1.01317e9i −1.49701 − 0.561837i
\(115\) −1.25578e9 + 1.90243e9i −0.669535 + 1.01430i
\(116\) 7.02951e7 − 3.38524e7i 0.0360466 − 0.0173591i
\(117\) 3.41477e8 − 2.48098e8i 0.168471 − 0.122401i
\(118\) 1.43843e9 − 1.25672e9i 0.682997 − 0.596716i
\(119\) −1.21213e9 − 1.51996e9i −0.554100 − 0.694820i
\(120\) 8.10627e8 + 4.84327e8i 0.356866 + 0.213218i
\(121\) −2.92968e8 − 4.43827e8i −0.124247 − 0.188226i
\(122\) 1.14174e9 + 5.00230e9i 0.466605 + 2.04433i
\(123\) −9.75655e8 − 2.28266e9i −0.384347 − 0.899224i
\(124\) −3.86771e9 + 3.48100e8i −1.46912 + 0.132223i
\(125\) 2.03937e9 + 1.48169e9i 0.747139 + 0.542828i
\(126\) −1.13738e9 − 2.06404e8i −0.402010 − 0.0729541i
\(127\) 3.39106e8 − 7.93377e8i 0.115669 − 0.270622i −0.851683 − 0.524057i \(-0.824418\pi\)
0.967352 + 0.253436i \(0.0815606\pi\)
\(128\) 5.81262e8 − 1.78894e9i 0.191393 − 0.589048i
\(129\) −8.76429e8 − 1.62868e9i −0.278653 − 0.517823i
\(130\) 1.31962e9 + 1.38022e9i 0.405233 + 0.423841i
\(131\) 1.67501e9 − 3.11269e9i 0.496931 − 0.923452i −0.501373 − 0.865231i \(-0.667172\pi\)
0.998304 − 0.0582208i \(-0.0185428\pi\)
\(132\) 3.46423e9 − 9.56068e8i 0.993172 − 0.274098i
\(133\) −2.92863e8 − 2.16200e9i −0.0811582 − 0.599134i
\(134\) −3.29920e8 + 2.43557e9i −0.0883968 + 0.652572i
\(135\) −2.41898e9 − 6.67597e8i −0.626802 − 0.172986i
\(136\) 1.27143e9 − 1.32981e9i 0.318690 − 0.333323i
\(137\) 4.28774e8 + 1.31963e9i 0.103989 + 0.320044i 0.989492 − 0.144589i \(-0.0461861\pi\)
−0.885503 + 0.464633i \(0.846186\pi\)
\(138\) 7.87788e9 + 7.09022e8i 1.84907 + 0.166419i
\(139\) 4.91742e8 + 4.29622e8i 0.111730 + 0.0976158i 0.711991 − 0.702189i \(-0.247794\pi\)
−0.600261 + 0.799804i \(0.704937\pi\)
\(140\) 1.01285e8 − 2.25528e9i 0.0222828 − 0.496164i
\(141\) 5.69985e9 1.21444
\(142\) 6.37536e9 − 8.12583e8i 1.31585 − 0.167714i
\(143\) −2.30003e9 −0.459962
\(144\) 1.37211e8 − 3.05523e9i 0.0265923 − 0.592124i
\(145\) −2.24640e8 − 1.96262e8i −0.0422018 − 0.0368706i
\(146\) 6.43519e8 + 5.79178e7i 0.117212 + 0.0105493i
\(147\) 1.33398e9 + 4.10556e9i 0.235624 + 0.725177i
\(148\) −4.14175e9 + 4.33193e9i −0.709587 + 0.742170i
\(149\) −1.10340e10 − 3.04520e9i −1.83398 − 0.506148i −0.834960 − 0.550310i \(-0.814509\pi\)
−0.999024 + 0.0441628i \(0.985938\pi\)
\(150\) −1.78550e8 + 1.31811e9i −0.0287972 + 0.212589i
\(151\) −6.60517e8 − 4.87614e9i −0.103392 − 0.763272i −0.966210 − 0.257757i \(-0.917017\pi\)
0.862818 − 0.505515i \(-0.168698\pi\)
\(152\) 1.99031e9 − 5.49290e8i 0.302430 − 0.0834653i
\(153\) 2.32798e9 − 4.32611e9i 0.343453 − 0.638243i
\(154\) 4.35299e9 + 4.55287e9i 0.623655 + 0.652292i
\(155\) 7.03557e9 + 1.30743e10i 0.979053 + 1.81939i
\(156\) 8.83900e8 − 2.72036e9i 0.119493 − 0.367761i
\(157\) 3.00637e9 − 7.03375e9i 0.394906 − 0.923929i −0.597607 − 0.801789i \(-0.703882\pi\)
0.992513 − 0.122140i \(-0.0389756\pi\)
\(158\) −7.45451e9 − 1.35279e9i −0.951617 − 0.172693i
\(159\) −8.28634e8 − 6.02038e8i −0.102820 − 0.0747028i
\(160\) 1.09790e10 − 9.88128e8i 1.32441 − 0.119199i
\(161\) 2.35220e9 + 5.50325e9i 0.275904 + 0.645510i
\(162\) 3.23448e9 + 1.41712e10i 0.368966 + 1.61655i
\(163\) −5.27873e9 − 7.99693e9i −0.585713 − 0.887318i 0.414023 − 0.910266i \(-0.364123\pi\)
−0.999737 + 0.0229486i \(0.992695\pi\)
\(164\) −4.82145e9 − 2.88068e9i −0.520452 − 0.310956i
\(165\) −8.56666e9 − 1.07423e10i −0.899775 − 1.12828i
\(166\) −7.92943e9 + 6.92774e9i −0.810505 + 0.708117i
\(167\) −9.08871e9 + 6.60333e9i −0.904228 + 0.656960i −0.939548 − 0.342416i \(-0.888755\pi\)
0.0353204 + 0.999376i \(0.488755\pi\)
\(168\) 2.23372e9 − 1.07570e9i 0.216340 − 0.104184i
\(169\) 4.83348e9 − 7.32241e9i 0.455795 − 0.690500i
\(170\) 2.08082e10 + 7.80946e9i 1.91080 + 0.717135i
\(171\) 4.73282e9 − 2.82773e9i 0.423290 − 0.252904i
\(172\) −3.77013e9 − 1.81560e9i −0.328457 − 0.158177i
\(173\) −4.93597e8 + 8.95746e7i −0.0418952 + 0.00760287i −0.199464 − 0.979905i \(-0.563920\pi\)
0.157569 + 0.987508i \(0.449634\pi\)
\(174\) −2.30325e8 + 1.00912e9i −0.0190488 + 0.0834584i
\(175\) −9.42277e8 + 3.53642e8i −0.0759464 + 0.0285032i
\(176\) −1.03906e10 + 1.30294e10i −0.816270 + 1.02357i
\(177\) 4.90773e8 + 1.09279e10i 0.0375838 + 0.836869i
\(178\) 8.77789e8 + 1.95455e10i 0.0655391 + 1.45934i
\(179\) 8.79279e9 − 1.10258e10i 0.640159 − 0.802734i −0.350864 − 0.936427i \(-0.614112\pi\)
0.991023 + 0.133692i \(0.0426834\pi\)
\(180\) 5.34103e9 − 2.00452e9i 0.379226 − 0.142326i
\(181\) 1.08799e9 − 4.76681e9i 0.0753482 − 0.330122i −0.923179 − 0.384370i \(-0.874419\pi\)
0.998528 + 0.0542475i \(0.0172760\pi\)
\(182\) 4.93297e9 − 8.95202e8i 0.333263 − 0.0604783i
\(183\) −2.64747e10 − 1.27495e10i −1.74502 − 0.840357i
\(184\) −4.86210e9 + 2.90497e9i −0.312712 + 0.186837i
\(185\) 2.14529e10 + 8.05142e9i 1.34652 + 0.505358i
\(186\) 2.83811e10 − 4.29956e10i 1.73869 − 2.63400i
\(187\) −2.41191e10 + 1.16151e10i −1.44236 + 0.694604i
\(188\) 1.04330e10 − 7.58002e9i 0.609114 − 0.442547i
\(189\) −4.96158e9 + 4.33480e9i −0.282841 + 0.247110i
\(190\) 1.55512e10 + 1.95006e10i 0.865711 + 1.08557i
\(191\) 2.54863e9 + 1.52273e9i 0.138566 + 0.0827892i 0.580509 − 0.814254i \(-0.302854\pi\)
−0.441943 + 0.897043i \(0.645711\pi\)
\(192\) −6.04093e9 − 9.15161e9i −0.320810 − 0.486007i
\(193\) −1.89140e9 − 8.28675e9i −0.0981238 − 0.429909i 0.901874 − 0.431999i \(-0.142192\pi\)
−0.999998 + 0.00209060i \(0.999335\pi\)
\(194\) 2.97221e9 + 6.95384e9i 0.150651 + 0.352466i
\(195\) −1.08919e10 + 9.80290e8i −0.539447 + 0.0485511i
\(196\) 7.90153e9 + 5.74079e9i 0.382436 + 0.277856i
\(197\) 3.84058e10 + 6.96962e9i 1.81676 + 0.329694i 0.976997 − 0.213253i \(-0.0684059\pi\)
0.839767 + 0.542947i \(0.182692\pi\)
\(198\) −6.25593e9 + 1.46365e10i −0.289267 + 0.676773i
\(199\) 3.25596e9 − 1.00208e10i 0.147177 − 0.452964i −0.850108 − 0.526609i \(-0.823463\pi\)
0.997285 + 0.0736450i \(0.0234632\pi\)
\(200\) −4.51343e8 − 8.38736e8i −0.0199467 − 0.0370673i
\(201\) −9.72722e9 − 1.01739e10i −0.420346 − 0.439647i
\(202\) −2.65546e10 + 4.93467e10i −1.12217 + 2.08534i
\(203\) −7.54958e8 + 2.08355e8i −0.0312026 + 0.00861137i
\(204\) −4.46887e9 − 3.29906e10i −0.180660 − 1.33369i
\(205\) −2.88243e9 + 2.12790e10i −0.113990 + 0.841508i
\(206\) 3.20760e10 + 8.85240e9i 1.24102 + 0.342499i
\(207\) −1.04514e10 + 1.09313e10i −0.395646 + 0.413813i
\(208\) 4.09890e9 + 1.26151e10i 0.151839 + 0.467312i
\(209\) −2.99215e10 − 2.69299e9i −1.08474 − 0.0976284i
\(210\) 2.25543e10 + 1.97051e10i 0.800280 + 0.699184i
\(211\) −1.55482e9 + 3.46208e10i −0.0540020 + 1.20245i 0.770819 + 0.637054i \(0.219847\pi\)
−0.824821 + 0.565394i \(0.808724\pi\)
\(212\) −2.31736e9 −0.0787919
\(213\) −1.91261e10 + 3.14472e10i −0.636676 + 1.04682i
\(214\) −2.67254e10 −0.871087
\(215\) −7.17775e8 + 1.59825e10i −0.0229095 + 0.510119i
\(216\) −4.69543e9 − 4.10227e9i −0.146769 − 0.128228i
\(217\) 3.88240e10 + 3.49423e9i 1.18859 + 0.106975i
\(218\) −4.01401e9 − 1.23539e10i −0.120372 − 0.370466i
\(219\) −2.55714e9 + 2.67456e9i −0.0751200 + 0.0785694i
\(220\) −2.99661e10 − 8.27012e9i −0.862439 − 0.238018i
\(221\) −2.86013e9 + 2.11143e10i −0.0806529 + 0.595404i
\(222\) −1.06728e10 − 7.87901e10i −0.294911 − 2.17712i
\(223\) −1.07997e10 + 2.98052e9i −0.292441 + 0.0807086i −0.409179 − 0.912454i \(-0.634185\pi\)
0.116738 + 0.993163i \(0.462756\pi\)
\(224\) 1.37146e10 − 2.54860e10i 0.363972 − 0.676373i
\(225\) −1.75757e9 − 1.83827e9i −0.0457184 − 0.0478177i
\(226\) −4.83411e10 − 8.98328e10i −1.23262 − 2.29059i
\(227\) 2.07093e10 − 6.37368e10i 0.517666 − 1.59321i −0.260712 − 0.965417i \(-0.583957\pi\)
0.778378 − 0.627796i \(-0.216043\pi\)
\(228\) 1.46839e10 − 3.43548e10i 0.359862 − 0.841939i
\(229\) −4.29483e10 − 7.79397e9i −1.03202 − 0.187283i −0.363976 − 0.931408i \(-0.618581\pi\)
−0.668040 + 0.744125i \(0.732867\pi\)
\(230\) −5.53531e10 − 4.02164e10i −1.30427 − 0.947606i
\(231\) −3.59287e10 + 3.23364e9i −0.830210 + 0.0747202i
\(232\) −2.91298e8 − 6.81526e8i −0.00660149 − 0.0154450i
\(233\) 2.12534e9 + 9.31172e9i 0.0472418 + 0.206980i 0.993040 − 0.117774i \(-0.0375757\pi\)
−0.945799 + 0.324754i \(0.894719\pi\)
\(234\) 6.97936e9 + 1.05733e10i 0.152175 + 0.230536i
\(235\) −4.23254e10 − 2.52883e10i −0.905307 − 0.540896i
\(236\) 1.54309e10 + 1.93498e10i 0.323808 + 0.406043i
\(237\) 3.26749e10 − 2.85472e10i 0.672739 − 0.587755i
\(238\) 4.72084e10 − 3.42989e10i 0.953725 − 0.692921i
\(239\) 2.54638e10 − 1.22627e10i 0.504815 − 0.243106i −0.164102 − 0.986443i \(-0.552473\pi\)
0.668917 + 0.743337i \(0.266758\pi\)
\(240\) −4.36520e10 + 6.61300e10i −0.849285 + 1.28661i
\(241\) −9.81763e9 − 3.68462e9i −0.187469 − 0.0703584i 0.255875 − 0.966710i \(-0.417637\pi\)
−0.443344 + 0.896352i \(0.646208\pi\)
\(242\) 1.37027e10 − 8.18697e9i 0.256824 − 0.153445i
\(243\) −4.50723e10 − 2.17057e10i −0.829243 − 0.399342i
\(244\) −6.54142e10 + 1.18709e10i −1.18146 + 0.214403i
\(245\) 8.30921e9 − 3.64050e10i 0.147337 − 0.645526i
\(246\) 6.97593e10 − 2.61811e10i 1.21449 − 0.455806i
\(247\) −1.49087e10 + 1.86949e10i −0.254861 + 0.319585i
\(248\) 1.65506e9 + 3.68528e10i 0.0277831 + 0.618639i
\(249\) −2.70542e9 − 6.02409e10i −0.0446003 − 0.993103i
\(250\) −4.71747e10 + 5.91553e10i −0.763800 + 0.957775i
\(251\) −4.79986e10 + 1.80142e10i −0.763303 + 0.286472i −0.702506 − 0.711678i \(-0.747936\pi\)
−0.0607968 + 0.998150i \(0.519364\pi\)
\(252\) 3.33290e9 − 1.46024e10i 0.0520619 − 0.228098i
\(253\) 8.10867e10 − 1.47151e10i 1.24425 − 0.225798i
\(254\) 2.33327e10 + 1.12365e10i 0.351734 + 0.169386i
\(255\) −1.09267e11 + 6.52838e10i −1.61829 + 0.966885i
\(256\) 8.34376e10 + 3.13147e10i 1.21418 + 0.455688i
\(257\) 5.16956e10 − 7.83156e10i 0.739188 − 1.11982i −0.249286 − 0.968430i \(-0.580196\pi\)
0.988474 − 0.151392i \(-0.0483756\pi\)
\(258\) 5.00161e10 − 2.40865e10i 0.702783 − 0.338443i
\(259\) 4.86710e10 − 3.53616e10i 0.672081 − 0.488296i
\(260\) −1.86329e10 + 1.62791e10i −0.252871 + 0.220927i
\(261\) −1.23394e9 − 1.54731e9i −0.0164593 − 0.0206393i
\(262\) 9.10782e10 + 5.44167e10i 1.19415 + 0.713471i
\(263\) 1.75273e10 + 2.65528e10i 0.225899 + 0.342223i 0.929793 − 0.368082i \(-0.119986\pi\)
−0.703894 + 0.710305i \(0.748557\pi\)
\(264\) −7.59661e9 − 3.32829e10i −0.0962503 − 0.421700i
\(265\) 3.48216e9 + 8.14691e9i 0.0433752 + 0.101481i
\(266\) 6.52220e10 − 5.87009e9i 0.798779 − 0.0718915i
\(267\) −9.06494e10 − 6.58607e10i −1.09160 − 0.793095i
\(268\) −3.13345e10 − 5.68638e9i −0.371036 − 0.0673332i
\(269\) 2.62316e10 − 6.13718e10i 0.305449 − 0.714634i −0.694539 − 0.719455i \(-0.744392\pi\)
0.999988 + 0.00482068i \(0.00153447\pi\)
\(270\) 2.32753e10 − 7.16341e10i 0.266538 − 0.820320i
\(271\) −3.68823e10 − 6.85389e10i −0.415391 − 0.771925i 0.583810 − 0.811890i \(-0.301561\pi\)
−0.999201 + 0.0399649i \(0.987275\pi\)
\(272\) 1.06689e11 + 1.11588e11i 1.18184 + 1.23611i
\(273\) −1.36058e10 + 2.52839e10i −0.148250 + 0.275494i
\(274\) −4.01465e10 + 1.10797e10i −0.430299 + 0.118755i
\(275\) 1.86031e9 + 1.37333e10i 0.0196150 + 0.144804i
\(276\) −1.37573e10 + 1.01560e11i −0.142706 + 1.05350i
\(277\) 8.95132e10 + 2.47041e10i 0.913542 + 0.252121i 0.691045 − 0.722812i \(-0.257151\pi\)
0.222497 + 0.974933i \(0.428579\pi\)
\(278\) −1.35444e10 + 1.41663e10i −0.136006 + 0.142251i
\(279\) 3.04394e10 + 9.36828e10i 0.300758 + 0.925637i
\(280\) −2.13594e10 − 1.92238e9i −0.207672 − 0.0186908i
\(281\) −5.53616e9 − 4.83680e9i −0.0529700 − 0.0462785i 0.631047 − 0.775745i \(-0.282626\pi\)
−0.684017 + 0.729466i \(0.739768\pi\)
\(282\) −7.67558e9 + 1.70910e11i −0.0722753 + 1.60934i
\(283\) −1.63338e11 −1.51373 −0.756863 − 0.653573i \(-0.773269\pi\)
−0.756863 + 0.653573i \(0.773269\pi\)
\(284\) 6.81205e9 + 8.29959e10i 0.0621363 + 0.757050i
\(285\) −1.42843e11 −1.28250
\(286\) 3.09729e9 − 6.89664e10i 0.0273737 − 0.609524i
\(287\) 4.24567e10 + 3.70933e10i 0.369384 + 0.322721i
\(288\) 7.28409e10 + 6.55580e9i 0.623891 + 0.0561512i
\(289\) 3.99889e10 + 1.23073e11i 0.337209 + 1.03782i
\(290\) 6.18742e9 − 6.47154e9i 0.0513711 − 0.0537300i
\(291\) −4.17487e10 − 1.15219e10i −0.341291 − 0.0941903i
\(292\) −1.12379e9 + 8.29614e9i −0.00904611 + 0.0667810i
\(293\) −6.83900e9 − 5.04875e10i −0.0542111 − 0.400202i −0.997642 − 0.0686331i \(-0.978136\pi\)
0.943431 − 0.331569i \(-0.107578\pi\)
\(294\) −1.24901e11 + 3.44706e10i −0.974999 + 0.269083i
\(295\) 4.48390e10 − 8.33248e10i 0.344712 − 0.640583i
\(296\) 3.93447e10 + 4.11513e10i 0.297902 + 0.311581i
\(297\) 4.29905e10 + 7.98898e10i 0.320604 + 0.595782i
\(298\) 1.06169e11 − 3.26754e11i 0.779873 − 2.40020i
\(299\) 2.57798e10 − 6.03148e10i 0.186535 − 0.436419i
\(300\) −1.69580e10 − 3.07743e9i −0.120873 − 0.0219352i
\(301\) 3.39822e10 + 2.46895e10i 0.238617 + 0.173366i
\(302\) 1.47100e11 − 1.32393e10i 1.01761 − 0.0915868i
\(303\) −1.26132e11 − 2.95100e11i −0.859673 − 2.01130i
\(304\) 3.85530e10 + 1.68912e11i 0.258897 + 1.13430i
\(305\) 1.40028e11 + 2.12133e11i 0.926541 + 1.40365i
\(306\) 1.26583e11 + 7.56301e10i 0.825336 + 0.493115i
\(307\) 1.99537e10 + 2.50211e10i 0.128204 + 0.160762i 0.841790 − 0.539805i \(-0.181502\pi\)
−0.713587 + 0.700567i \(0.752930\pi\)
\(308\) −6.14635e10 + 5.36991e10i −0.389170 + 0.340008i
\(309\) −1.54170e11 + 1.12011e11i −0.962027 + 0.698953i
\(310\) −4.01506e11 + 1.93355e11i −2.46925 + 1.18913i
\(311\) 2.81084e9 − 4.25823e9i 0.0170378 − 0.0258112i −0.825955 − 0.563737i \(-0.809363\pi\)
0.842992 + 0.537926i \(0.180792\pi\)
\(312\) −2.54394e10 − 9.54758e9i −0.151989 − 0.0570424i
\(313\) −6.82631e10 + 4.07853e10i −0.402010 + 0.240190i −0.699646 − 0.714490i \(-0.746659\pi\)
0.297636 + 0.954679i \(0.403802\pi\)
\(314\) 2.06858e11 + 9.96178e10i 1.20085 + 0.578300i
\(315\) −5.63444e10 + 1.02250e10i −0.322443 + 0.0585148i
\(316\) 2.18442e10 − 9.57058e10i 0.123238 − 0.539941i
\(317\) 5.31396e10 − 1.99436e10i 0.295564 − 0.110927i −0.199188 − 0.979961i \(-0.563830\pi\)
0.494752 + 0.869034i \(0.335259\pi\)
\(318\) 1.91680e10 − 2.40359e10i 0.105112 − 0.131807i
\(319\) 4.83837e8 + 1.07735e10i 0.00261602 + 0.0582503i
\(320\) 4.25562e9 + 9.47586e10i 0.0226875 + 0.505177i
\(321\) 9.54280e10 − 1.19663e11i 0.501653 − 0.629053i
\(322\) −1.68182e11 + 6.31199e10i −0.871825 + 0.327201i
\(323\) −6.19295e10 + 2.71331e11i −0.316582 + 1.38704i
\(324\) −1.85314e11 + 3.36295e10i −0.934234 + 0.169539i
\(325\) 9.93821e9 + 4.78599e9i 0.0494121 + 0.0237956i
\(326\) 2.46896e11 − 1.47514e11i 1.21070 − 0.723358i
\(327\) 6.96473e10 + 2.61391e10i 0.336852 + 0.126423i
\(328\) −2.93925e10 + 4.45277e10i −0.140218 + 0.212421i
\(329\) −1.16629e11 + 5.61658e10i −0.548816 + 0.264296i
\(330\) 3.33642e11 − 2.42405e11i 1.54870 − 1.12520i
\(331\) −1.87780e10 + 1.64058e10i −0.0859850 + 0.0751229i −0.699858 − 0.714282i \(-0.746753\pi\)
0.613873 + 0.789405i \(0.289611\pi\)
\(332\) −8.50641e10 − 1.06667e11i −0.384260 − 0.481846i
\(333\) 1.30505e11 + 7.79733e10i 0.581607 + 0.347494i
\(334\) −1.85762e11 − 2.81417e11i −0.816765 − 1.23735i
\(335\) 2.70935e10 + 1.18704e11i 0.117534 + 0.514950i
\(336\) 8.17646e10 + 1.91298e11i 0.349976 + 0.818810i
\(337\) −3.56295e11 + 3.20671e10i −1.50479 + 0.135433i −0.811127 − 0.584870i \(-0.801146\pi\)
−0.693659 + 0.720303i \(0.744003\pi\)
\(338\) 2.13054e11 + 1.54792e11i 0.887899 + 0.645096i
\(339\) 5.74838e11 + 1.04318e11i 2.36400 + 0.429002i
\(340\) −1.13183e11 + 2.64805e11i −0.459331 + 1.07466i
\(341\) 1.65869e11 − 5.10493e11i 0.664310 − 2.04454i
\(342\) 7.84161e10 + 1.45721e11i 0.309947 + 0.575978i
\(343\) −1.76619e11 − 1.84729e11i −0.688991 − 0.720628i
\(344\) −1.88368e10 + 3.50046e10i −0.0725260 + 0.134776i
\(345\) 3.77718e11 − 1.04244e11i 1.43543 − 0.396154i
\(346\) −2.02120e9 − 1.49211e10i −0.00758171 − 0.0559704i
\(347\) 3.56694e10 − 2.63322e11i 0.132073 − 0.974999i −0.796707 − 0.604366i \(-0.793426\pi\)
0.928779 − 0.370633i \(-0.120859\pi\)
\(348\) −1.29283e10 − 3.56798e9i −0.0472535 − 0.0130411i
\(349\) 3.69527e11 − 3.86495e11i 1.33331 − 1.39453i 0.476260 − 0.879305i \(-0.341992\pi\)
0.857052 − 0.515230i \(-0.172293\pi\)
\(350\) −9.33507e9 − 2.87304e10i −0.0332515 − 0.102338i
\(351\) 7.19178e10 + 6.47272e9i 0.252903 + 0.0227617i
\(352\) −3.00119e11 − 2.62206e11i −1.04196 − 0.910333i
\(353\) 1.20841e10 − 2.69073e11i 0.0414217 − 0.922326i −0.865470 − 0.500961i \(-0.832980\pi\)
0.906891 − 0.421365i \(-0.138449\pi\)
\(354\) −3.28334e11 −1.11122
\(355\) 2.81545e11 − 1.48662e11i 0.940850 − 0.496789i
\(356\) −2.53510e11 −0.836508
\(357\) −1.49931e10 + 3.33847e11i −0.0488522 + 1.08778i
\(358\) 3.18768e11 + 2.78499e11i 1.02565 + 0.896088i
\(359\) −2.84230e11 − 2.55811e10i −0.903118 − 0.0812821i −0.371662 − 0.928368i \(-0.621212\pi\)
−0.531456 + 0.847086i \(0.678355\pi\)
\(360\) −1.67465e10 − 5.15405e10i −0.0525489 − 0.161729i
\(361\) 7.15896e9 − 7.48769e9i 0.0221854 − 0.0232041i
\(362\) 1.41468e11 + 3.90426e10i 0.432981 + 0.119495i
\(363\) −1.22708e10 + 9.05870e10i −0.0370932 + 0.273833i
\(364\) 8.71997e9 + 6.43734e10i 0.0260351 + 0.192199i
\(365\) 3.08546e10 − 8.51533e9i 0.0909918 − 0.0251121i
\(366\) 4.17946e11 − 7.76673e11i 1.21746 − 2.26242i
\(367\) 1.03693e11 + 1.08454e11i 0.298368 + 0.312068i 0.854936 − 0.518734i \(-0.173596\pi\)
−0.556568 + 0.830802i \(0.687882\pi\)
\(368\) −2.25214e11 − 4.18517e11i −0.640147 − 1.18959i
\(369\) −4.40244e10 + 1.35493e11i −0.123616 + 0.380451i
\(370\) −2.70311e11 + 6.32423e11i −0.749817 + 1.75428i
\(371\) 2.28878e10 + 4.15352e9i 0.0627222 + 0.0113824i
\(372\) 5.40042e11 + 3.92364e11i 1.46212 + 1.06230i
\(373\) −3.41174e11 + 3.07062e10i −0.912612 + 0.0821366i −0.535984 − 0.844228i \(-0.680059\pi\)
−0.376628 + 0.926365i \(0.622916\pi\)
\(374\) −3.15801e11 − 7.38852e11i −0.834624 − 1.95270i
\(375\) −9.64216e10 − 4.22451e11i −0.251787 − 1.10315i
\(376\) −6.74876e10 − 1.02239e11i −0.174132 − 0.263799i
\(377\) 7.36854e9 + 4.40250e9i 0.0187865 + 0.0112244i
\(378\) −1.23298e11 − 1.54610e11i −0.310628 − 0.389516i
\(379\) −6.80209e10 + 5.94281e10i −0.169343 + 0.147950i −0.738438 − 0.674321i \(-0.764436\pi\)
0.569096 + 0.822271i \(0.307293\pi\)
\(380\) −2.61459e11 + 1.89961e11i −0.643246 + 0.467346i
\(381\) −1.33625e11 + 6.43506e10i −0.324883 + 0.156455i
\(382\) −4.90912e10 + 7.43699e10i −0.117956 + 0.178695i
\(383\) 6.29206e11 + 2.36145e11i 1.49416 + 0.560769i 0.958857 − 0.283888i \(-0.0916243\pi\)
0.535307 + 0.844657i \(0.320196\pi\)
\(384\) −2.77567e11 + 1.65839e11i −0.651445 + 0.389220i
\(385\) 2.81143e11 + 1.35391e11i 0.652159 + 0.314063i
\(386\) 2.51025e11 − 4.55543e10i 0.575538 − 0.104445i
\(387\) −2.36192e10 + 1.03483e11i −0.0535261 + 0.234513i
\(388\) −9.17393e10 + 3.44303e10i −0.205500 + 0.0771256i
\(389\) −3.15338e11 + 3.95421e11i −0.698237 + 0.875561i −0.996890 − 0.0788003i \(-0.974891\pi\)
0.298654 + 0.954362i \(0.403462\pi\)
\(390\) −1.47266e10 − 3.27914e11i −0.0322339 − 0.717743i
\(391\) −3.42518e10 − 7.62675e11i −0.0741118 − 1.65023i
\(392\) 5.78475e10 − 7.25385e10i 0.123736 − 0.155161i
\(393\) −5.68864e11 + 2.13498e11i −1.20293 + 0.451468i
\(394\) −2.60702e11 + 1.14221e12i −0.545019 + 2.38788i
\(395\) −3.69288e11 + 6.70159e10i −0.763270 + 0.138513i
\(396\) −1.85820e11 − 8.94861e10i −0.379720 − 0.182864i
\(397\) −1.39982e9 + 8.36351e8i −0.00282822 + 0.00168978i −0.514313 − 0.857603i \(-0.671953\pi\)
0.511484 + 0.859293i \(0.329096\pi\)
\(398\) 2.96089e11 + 1.11124e11i 0.591492 + 0.221991i
\(399\) −2.06604e11 + 3.12992e11i −0.408095 + 0.618238i
\(400\) 7.20089e10 − 3.46776e10i 0.140642 − 0.0677298i
\(401\) −6.12329e10 + 4.44883e10i −0.118259 + 0.0859204i −0.645343 − 0.763893i \(-0.723285\pi\)
0.527084 + 0.849813i \(0.323285\pi\)
\(402\) 3.18162e11 − 2.77970e11i 0.607619 − 0.530861i
\(403\) −2.66371e11 − 3.34018e11i −0.503053 − 0.630809i
\(404\) −6.23314e11 − 3.72413e11i −1.16410 − 0.695518i
\(405\) 3.96689e11 + 6.00958e11i 0.732660 + 1.10993i
\(406\) −5.23088e9 − 2.29180e10i −0.00955449 − 0.0418610i
\(407\) −3.25585e11 − 7.61744e11i −0.588152 − 1.37605i
\(408\) −3.14984e11 + 2.83491e10i −0.562753 + 0.0506487i
\(409\) 2.34592e11 + 1.70441e11i 0.414533 + 0.301176i 0.775434 − 0.631428i \(-0.217531\pi\)
−0.360902 + 0.932604i \(0.617531\pi\)
\(410\) −6.34168e11 − 1.15085e11i −1.10835 − 0.201136i
\(411\) 9.37413e10 − 2.19319e11i 0.162048 − 0.379129i
\(412\) −1.33233e11 + 4.10050e11i −0.227811 + 0.701131i
\(413\) −1.17725e11 − 2.18769e11i −0.199110 − 0.370008i
\(414\) −3.13700e11 − 3.28104e11i −0.524823 − 0.548922i
\(415\) −2.47178e11 + 4.59334e11i −0.409066 + 0.760173i
\(416\) −3.05767e11 + 8.43864e10i −0.500577 + 0.138151i
\(417\) −1.50670e10 − 1.11229e11i −0.0244013 − 0.180138i
\(418\) 1.21042e11 − 8.93570e11i 0.193930 − 1.43165i
\(419\) −1.11477e12 − 3.07657e11i −1.76694 − 0.487645i −0.777047 − 0.629443i \(-0.783283\pi\)
−0.989896 + 0.141798i \(0.954712\pi\)
\(420\) −2.68177e11 + 2.80491e11i −0.420532 + 0.439842i
\(421\) 2.98408e11 + 9.18406e11i 0.462958 + 1.42484i 0.861533 + 0.507702i \(0.169505\pi\)
−0.398575 + 0.917136i \(0.630495\pi\)
\(422\) −1.03601e12 − 9.32427e10i −1.59022 − 0.143123i
\(423\) −2.46340e11 − 2.15221e11i −0.374114 − 0.326853i
\(424\) −9.87645e8 + 2.19916e10i −0.00148407 + 0.0330454i
\(425\) 1.28385e11 0.190882
\(426\) −9.17188e11 − 6.15844e11i −1.34932 − 0.905998i
\(427\) 6.67352e11 0.971471
\(428\) 1.55360e10 − 3.45937e11i 0.0223791 − 0.498310i
\(429\) 2.97738e11 + 2.60126e11i 0.424401 + 0.370788i
\(430\) −4.78268e11 − 4.30449e10i −0.674627 − 0.0607175i
\(431\) 3.48010e11 + 1.07106e12i 0.485784 + 1.49509i 0.830842 + 0.556509i \(0.187859\pi\)
−0.345057 + 0.938582i \(0.612141\pi\)
\(432\) 3.61563e11 − 3.78165e11i 0.499467 − 0.522401i
\(433\) 6.63759e11 + 1.83186e11i 0.907434 + 0.250436i 0.688443 − 0.725291i \(-0.258295\pi\)
0.218991 + 0.975727i \(0.429723\pi\)
\(434\) −1.57056e11 + 1.15943e12i −0.212496 + 1.56871i
\(435\) 6.88297e9 + 5.08121e10i 0.00921667 + 0.0680402i
\(436\) 1.62244e11 − 4.47764e10i 0.215020 − 0.0593417i
\(437\) 4.05994e11 − 7.54463e11i 0.532541 − 0.989626i
\(438\) −7.67530e10 − 8.02774e10i −0.0996465 − 0.104222i
\(439\) 2.25441e11 + 4.18939e11i 0.289695 + 0.538344i 0.983296 − 0.182016i \(-0.0582622\pi\)
−0.693600 + 0.720360i \(0.743976\pi\)
\(440\) −9.12545e10 + 2.80853e11i −0.116069 + 0.357225i
\(441\) 9.73691e10 − 2.27806e11i 0.122588 − 0.286809i
\(442\) −6.29260e11 − 1.14194e11i −0.784206 − 0.142312i
\(443\) 1.06297e12 + 7.72293e11i 1.31131 + 0.952721i 0.999997 + 0.00241219i \(0.000767825\pi\)
0.311310 + 0.950308i \(0.399232\pi\)
\(444\) 1.02607e12 − 9.23484e10i 1.25301 − 0.112773i
\(445\) 3.80935e11 + 8.91242e11i 0.460501 + 1.07740i
\(446\) −7.48276e10 − 3.27841e11i −0.0895478 − 0.392335i
\(447\) 1.08395e12 + 1.64211e12i 1.28418 + 1.94544i
\(448\) 2.13787e11 + 1.27732e11i 0.250744 + 0.149813i
\(449\) −1.08573e11 − 1.36146e11i −0.126070 − 0.158087i 0.714791 − 0.699339i \(-0.246522\pi\)
−0.840861 + 0.541252i \(0.817951\pi\)
\(450\) 5.74873e10 − 5.02252e10i 0.0660870 − 0.0577385i
\(451\) 6.28057e11 − 4.56310e11i 0.714833 − 0.519357i
\(452\) 1.19091e12 − 5.73512e11i 1.34201 − 0.646279i
\(453\) −4.65971e11 + 7.05916e11i −0.519897 + 0.787610i
\(454\) 1.88326e12 + 7.06799e11i 2.08046 + 0.780808i
\(455\) 2.13209e11 − 1.27386e11i 0.233213 − 0.139339i
\(456\) −3.19768e11 − 1.53992e11i −0.346332 − 0.166785i
\(457\) −1.24224e12 + 2.25432e11i −1.33224 + 0.241765i −0.797533 − 0.603275i \(-0.793862\pi\)
−0.534702 + 0.845040i \(0.679576\pi\)
\(458\) 2.91537e11 − 1.27731e12i 0.309599 − 1.35644i
\(459\) 7.86848e11 − 2.95309e11i 0.827434 − 0.310541i
\(460\) 5.52745e11 − 6.93120e11i 0.575592 − 0.721769i
\(461\) −2.22089e10 − 4.94519e11i −0.0229019 − 0.509951i −0.977357 − 0.211597i \(-0.932134\pi\)
0.954455 − 0.298354i \(-0.0964377\pi\)
\(462\) −4.85782e10 − 1.08168e12i −0.0496081 − 1.10461i
\(463\) −3.26535e11 + 4.09462e11i −0.330229 + 0.414094i −0.919032 − 0.394182i \(-0.871028\pi\)
0.588803 + 0.808276i \(0.299599\pi\)
\(464\) 5.82277e10 − 2.18532e10i 0.0583175 − 0.0218869i
\(465\) 5.67906e11 − 2.48816e12i 0.563298 − 2.46797i
\(466\) −2.82074e11 + 5.11889e10i −0.277093 + 0.0502850i
\(467\) 3.54010e11 + 1.70482e11i 0.344421 + 0.165865i 0.598095 − 0.801425i \(-0.295925\pi\)
−0.253674 + 0.967290i \(0.581639\pi\)
\(468\) −1.40919e11 + 8.41954e10i −0.135789 + 0.0811301i
\(469\) 2.99289e11 + 1.12325e11i 0.285636 + 0.107201i
\(470\) 8.15265e11 − 1.23507e12i 0.770652 − 1.16749i
\(471\) −1.18467e12 + 5.70506e11i −1.10918 + 0.534153i
\(472\) 1.90205e11 − 1.38192e11i 0.176394 − 0.128158i
\(473\) 4.35573e11 − 3.80548e11i 0.400116 − 0.349571i
\(474\) 8.11987e11 + 1.01820e12i 0.738833 + 0.926467i
\(475\) 1.23684e11 + 7.38980e10i 0.111479 + 0.0666057i
\(476\) 4.16527e11 + 6.31011e11i 0.371887 + 0.563385i
\(477\) 1.30801e10 + 5.73077e10i 0.0115685 + 0.0506851i
\(478\) 3.33407e11 + 7.80044e11i 0.292112 + 0.683429i
\(479\) −8.28003e11 + 7.45216e10i −0.718657 + 0.0646803i −0.442931 − 0.896556i \(-0.646061\pi\)
−0.275727 + 0.961236i \(0.588918\pi\)
\(480\) −1.53298e12 − 1.11378e12i −1.31811 − 0.957662i
\(481\) −6.48757e11 − 1.17732e11i −0.552623 − 0.100286i
\(482\) 1.23704e11 − 2.89420e11i 0.104393 − 0.244240i
\(483\) 3.17908e11 − 9.78420e11i 0.265790 − 0.818019i
\(484\) 9.80076e10 + 1.82129e11i 0.0811812 + 0.150860i
\(485\) 2.58895e11 + 2.70783e11i 0.212464 + 0.222220i
\(486\) 7.11541e11 − 1.32226e12i 0.578544 − 1.07512i
\(487\) −5.90446e11 + 1.62953e11i −0.475664 + 0.131275i −0.495645 − 0.868525i \(-0.665068\pi\)
0.0199806 + 0.999800i \(0.493640\pi\)
\(488\) 8.47755e10 + 6.25838e11i 0.0676677 + 0.499543i
\(489\) −2.21097e11 + 1.63221e12i −0.174861 + 1.29088i
\(490\) 1.08041e12 + 2.98176e11i 0.846658 + 0.233663i
\(491\) 1.22120e12 − 1.27728e12i 0.948248 − 0.991789i −0.0517288 − 0.998661i \(-0.516473\pi\)
0.999976 + 0.00687195i \(0.00218743\pi\)
\(492\) 2.98339e11 + 9.18194e11i 0.229545 + 0.706466i
\(493\) 9.95022e10 + 8.95536e9i 0.0758615 + 0.00682766i
\(494\) −5.40489e11 − 4.72211e11i −0.408334 − 0.356751i
\(495\) −3.53772e10 + 7.87735e11i −0.0264850 + 0.589735i
\(496\) −3.09553e12 −2.29650
\(497\) 8.14776e10 − 8.31934e11i 0.0599010 − 0.611625i
\(498\) 1.80997e12 1.31868
\(499\) −8.15944e10 + 1.81684e12i −0.0589126 + 1.31179i 0.724061 + 0.689736i \(0.242273\pi\)
−0.782974 + 0.622055i \(0.786298\pi\)
\(500\) −7.38290e11 − 6.45025e11i −0.528278 − 0.461542i
\(501\) 1.92334e12 + 1.73104e11i 1.36392 + 0.122755i
\(502\) −4.75519e11 − 1.46350e12i −0.334196 − 1.02855i
\(503\) 5.79998e10 − 6.06630e10i 0.0403990 − 0.0422540i −0.702287 − 0.711894i \(-0.747837\pi\)
0.742686 + 0.669640i \(0.233552\pi\)
\(504\) −1.37156e11 − 3.78526e10i −0.0946840 − 0.0261311i
\(505\) −3.72639e11 + 2.75093e12i −0.254963 + 1.88221i
\(506\) 3.32038e11 + 2.45120e12i 0.225170 + 1.66227i
\(507\) −1.45383e12 + 4.01232e11i −0.977189 + 0.269687i
\(508\) −1.59010e11 + 2.95490e11i −0.105935 + 0.196860i
\(509\) −1.90788e12 − 1.99548e12i −1.25985 − 1.31770i −0.927159 − 0.374669i \(-0.877756\pi\)
−0.332695 − 0.943035i \(-0.607958\pi\)
\(510\) −1.81039e12 − 3.36427e12i −1.18497 − 2.20204i
\(511\) 2.59689e10 − 7.99241e10i 0.0168484 − 0.0518541i
\(512\) −6.72817e11 + 1.57413e12i −0.432695 + 1.01234i
\(513\) 9.28014e11 + 1.68410e11i 0.591597 + 0.107359i
\(514\) 2.27868e12 + 1.65556e12i 1.43995 + 1.04619i
\(515\) 1.64178e12 − 1.47762e11i 1.02845 − 0.0925618i
\(516\) 2.82704e11 + 6.61418e11i 0.175553 + 0.410726i
\(517\) 3.96643e11 + 1.73781e12i 0.244170 + 1.06978i
\(518\) 9.94775e11 + 1.50702e12i 0.607073 + 0.919676i
\(519\) 7.40265e10 + 4.42288e10i 0.0447851 + 0.0267579i
\(520\) 1.46546e11 + 1.83763e11i 0.0878942 + 0.110216i
\(521\) 2.00859e10 − 1.75485e10i 0.0119432 − 0.0104345i −0.651946 − 0.758265i \(-0.726047\pi\)
0.663890 + 0.747831i \(0.268904\pi\)
\(522\) 4.80576e10 − 3.49159e10i 0.0283299 − 0.0205829i
\(523\) −8.19665e11 + 3.94730e11i −0.479048 + 0.230697i −0.657794 − 0.753198i \(-0.728510\pi\)
0.178746 + 0.983895i \(0.442796\pi\)
\(524\) −7.57323e11 + 1.14730e12i −0.438824 + 0.664790i
\(525\) 1.61973e11 + 6.07895e10i 0.0930521 + 0.0349230i
\(526\) −8.19788e11 + 4.89800e11i −0.466945 + 0.278987i
\(527\) −4.48006e12 − 2.15749e12i −2.53009 − 1.21843i
\(528\) 2.81864e12 − 5.11508e11i 1.57829 − 0.286418i
\(529\) −1.22182e11 + 5.35315e11i −0.0678355 + 0.297207i
\(530\) −2.48974e11 + 9.34416e10i −0.137061 + 0.0514397i
\(531\) 3.91417e11 − 4.90821e11i 0.213656 − 0.267916i
\(532\) 3.80683e10 + 8.47656e11i 0.0206044 + 0.458793i
\(533\) −2.77218e10 − 6.17274e11i −0.0148781 − 0.331288i
\(534\) 2.09690e12 − 2.62943e12i 1.11594 − 1.39935i
\(535\) −1.23952e12 + 4.65201e11i −0.654128 + 0.245498i
\(536\) −6.73181e10 + 2.94940e11i −0.0352282 + 0.154345i
\(537\) −2.38521e12 + 4.32851e11i −1.23777 + 0.224623i
\(538\) 1.80491e12 + 8.69199e11i 0.928828 + 0.447300i
\(539\) −1.15890e12 + 6.92410e11i −0.591420 + 0.353357i
\(540\) 9.13712e11 + 3.42922e11i 0.462421 + 0.173549i
\(541\) 1.07142e12 − 1.62313e12i 0.537739 − 0.814639i −0.459556 − 0.888149i \(-0.651991\pi\)
0.997295 + 0.0735097i \(0.0234200\pi\)
\(542\) 2.10480e12 − 1.01362e12i 1.04765 − 0.504520i
\(543\) −6.79951e11 + 4.94013e11i −0.335644 + 0.243859i
\(544\) −2.78025e12 + 2.42903e12i −1.36110 + 1.18916i
\(545\) −4.01210e11 − 5.03102e11i −0.194799 − 0.244271i
\(546\) −7.39815e11 − 4.42019e11i −0.356251 − 0.212850i
\(547\) 2.00013e12 + 3.03006e12i 0.955245 + 1.44713i 0.893511 + 0.449042i \(0.148235\pi\)
0.0617347 + 0.998093i \(0.480337\pi\)
\(548\) −1.20080e11 − 5.26103e11i −0.0568796 − 0.249206i
\(549\) 6.62790e11 + 1.55068e12i 0.311387 + 0.728526i
\(550\) −4.14299e11 + 3.72876e10i −0.193055 + 0.0173753i
\(551\) 9.07041e10 + 6.59004e10i 0.0419222 + 0.0304583i
\(552\) 9.57940e11 + 1.73841e11i 0.439150 + 0.0796939i
\(553\) −3.87287e11 + 9.06103e11i −0.176104 + 0.412016i
\(554\) −8.61293e11 + 2.65079e12i −0.388469 + 1.19559i
\(555\) −1.86648e12 − 3.46851e12i −0.835037 − 1.55176i
\(556\) −1.75497e11 − 1.83556e11i −0.0778815 − 0.0814576i
\(557\) −1.50338e12 + 2.79375e12i −0.661791 + 1.22981i 0.299452 + 0.954111i \(0.403196\pi\)
−0.961243 + 0.275702i \(0.911090\pi\)
\(558\) −2.85007e12 + 7.86568e11i −1.24452 + 0.343465i
\(559\) −6.17957e10 − 4.56194e11i −0.0267673 − 0.197604i
\(560\) 2.41562e11 − 1.78328e12i 0.103796 − 0.766256i
\(561\) 4.43584e12 + 1.22421e12i 1.89079 + 0.521825i
\(562\) 1.52486e11 − 1.59488e11i 0.0644789 − 0.0674396i
\(563\) −1.00859e12 − 3.10412e12i −0.423084 − 1.30212i −0.904817 − 0.425802i \(-0.859992\pi\)
0.481732 − 0.876319i \(-0.340008\pi\)
\(564\) −2.20782e12 − 1.98708e11i −0.918773 − 0.0826910i
\(565\) −3.80576e12 − 3.32499e12i −1.57117 − 1.37269i
\(566\) 2.19955e11 − 4.89768e12i 0.0900865 − 2.00593i
\(567\) 1.89056e12 0.768188
\(568\) 7.90532e11 − 2.92737e10i 0.318678 − 0.0118008i
\(569\) 3.23558e12 1.29404 0.647018 − 0.762474i \(-0.276016\pi\)
0.647018 + 0.762474i \(0.276016\pi\)
\(570\) 1.92356e11 − 4.28314e12i 0.0763253 − 1.69951i
\(571\) −9.01595e11 − 7.87700e11i −0.354935 − 0.310097i 0.461941 − 0.886911i \(-0.347153\pi\)
−0.816876 + 0.576813i \(0.804296\pi\)
\(572\) 8.90911e11 + 8.01834e10i 0.347978 + 0.0313186i
\(573\) −1.57702e11 − 4.85358e11i −0.0611143 − 0.188090i
\(574\) −1.16942e12 + 1.22311e12i −0.449641 + 0.470288i
\(575\) −3.80987e11 − 1.05146e11i −0.145347 − 0.0401131i
\(576\) −8.44751e10 + 6.23620e11i −0.0319763 + 0.236058i
\(577\) 2.33074e10 + 1.72062e11i 0.00875393 + 0.0646241i 0.994800 − 0.101850i \(-0.0324761\pi\)
−0.986046 + 0.166474i \(0.946762\pi\)
\(578\) −3.74420e12 + 1.03333e12i −1.39535 + 0.385093i
\(579\) −6.92363e11 + 1.28663e12i −0.256024 + 0.475772i
\(580\) 8.01716e10 + 8.38529e10i 0.0294168 + 0.0307675i
\(581\) 6.48965e11 + 1.20598e12i 0.236281 + 0.439084i
\(582\) 4.01704e11 − 1.23632e12i 0.145129 − 0.446660i
\(583\) 1.25890e11 − 2.94534e11i 0.0451318 − 0.105591i
\(584\) 7.82511e10 + 1.42005e10i 0.0278377 + 0.00505179i
\(585\) 5.07749e11 + 3.68901e11i 0.179245 + 0.130229i
\(586\) 1.52308e12 − 1.37079e11i 0.533559 − 0.0480212i
\(587\) 5.85435e11 + 1.36969e12i 0.203520 + 0.476159i 0.989932 − 0.141543i \(-0.0452064\pi\)
−0.786412 + 0.617703i \(0.788064\pi\)
\(588\) −3.73584e11 − 1.63678e12i −0.128882 − 0.564667i
\(589\) −3.07418e12 − 4.65718e12i −1.05247 − 1.59443i
\(590\) 2.43811e12 + 1.45670e12i 0.828361 + 0.494923i
\(591\) −4.18337e12 − 5.24578e12i −1.41053 − 1.76875i
\(592\) −3.59776e12 + 3.14326e12i −1.20388 + 1.05180i
\(593\) 3.73085e12 − 2.71062e12i 1.23897 − 0.900167i 0.241444 − 0.970415i \(-0.422379\pi\)
0.997530 + 0.0702482i \(0.0223791\pi\)
\(594\) −2.45339e12 + 1.18149e12i −0.808587 + 0.389395i
\(595\) 1.59250e12 − 2.41253e12i 0.520897 − 0.789126i
\(596\) 4.16784e12 + 1.56421e12i 1.35301 + 0.507795i
\(597\) −1.55480e12 + 9.28951e11i −0.500946 + 0.299301i
\(598\) 1.77382e12 + 8.54229e11i 0.567225 + 0.273161i
\(599\) −2.90368e12 + 5.26939e11i −0.921568 + 0.167240i −0.618550 − 0.785745i \(-0.712280\pi\)
−0.303017 + 0.952985i \(0.597994\pi\)
\(600\) −3.64321e10 + 1.59620e11i −0.0114764 + 0.0502812i
\(601\) −5.11402e11 + 1.91932e11i −0.159892 + 0.0600085i −0.430037 − 0.902811i \(-0.641500\pi\)
0.270145 + 0.962820i \(0.412928\pi\)
\(602\) −7.86075e11 + 9.85707e11i −0.243938 + 0.305889i
\(603\) 3.62421e10 + 8.06992e11i 0.0111631 + 0.248566i
\(604\) 8.58583e10 + 1.91178e12i 0.0262492 + 0.584484i
\(605\) 4.93022e11 − 6.18231e11i 0.149612 − 0.187608i
\(606\) 9.01843e12 − 3.38467e12i 2.71646 − 1.01951i
\(607\) 1.12544e12 − 4.93088e12i 0.336491 − 1.47427i −0.469814 − 0.882766i \(-0.655679\pi\)
0.806305 − 0.591500i \(-0.201464\pi\)
\(608\) −4.07659e12 + 7.39791e11i −1.20985 + 0.219555i
\(609\) 1.21293e11 + 5.84118e10i 0.0357321 + 0.0172077i
\(610\) −6.54937e12 + 3.91307e12i −1.91520 + 1.14428i
\(611\) 1.32827e12 + 4.98510e11i 0.385569 + 0.144707i
\(612\) −1.05255e12 + 1.59455e12i −0.303293 + 0.459469i
\(613\) 2.17919e12 − 1.04944e12i 0.623336 − 0.300183i −0.0954286 − 0.995436i \(-0.530422\pi\)
0.718765 + 0.695253i \(0.244708\pi\)
\(614\) −7.77128e11 + 5.64617e11i −0.220666 + 0.160323i
\(615\) 2.77971e12 − 2.42856e12i 0.783541 − 0.684559i
\(616\) 4.83407e11 + 6.06173e11i 0.135269 + 0.169623i
\(617\) 4.11049e12 + 2.45591e12i 1.14185 + 0.682226i 0.953951 − 0.299961i \(-0.0969737\pi\)
0.187903 + 0.982188i \(0.439831\pi\)
\(618\) −3.15104e12 − 4.77363e12i −0.868973 − 1.31644i
\(619\) 1.40102e12 + 6.13829e12i 0.383564 + 1.68050i 0.686212 + 0.727402i \(0.259272\pi\)
−0.302648 + 0.953102i \(0.597871\pi\)
\(620\) −2.26941e12 − 5.30955e12i −0.616809 − 1.44310i
\(621\) −2.57684e12 + 2.31920e11i −0.695306 + 0.0625787i
\(622\) 1.23898e11 + 9.00171e10i 0.0331900 + 0.0241139i
\(623\) 2.50384e12 + 4.54379e11i 0.665901 + 0.120843i
\(624\) 8.96128e11 − 2.09660e12i 0.236613 − 0.553585i
\(625\) −1.31387e12 + 4.04367e12i −0.344422 + 1.06002i
\(626\) −1.13102e12 − 2.10179e12i −0.294365 − 0.547023i
\(627\) 3.56876e12 + 3.73263e12i 0.922176 + 0.964520i
\(628\) −1.40972e12 + 2.61970e12i −0.361671 + 0.672098i
\(629\) −7.39768e12 + 2.04163e12i −1.88438 + 0.520055i
\(630\) −2.30722e11 − 1.70326e12i −0.0583520 − 0.430772i
\(631\) 1.00353e12 − 7.40834e12i 0.251998 − 1.86032i −0.215731 − 0.976453i \(-0.569214\pi\)
0.467729 − 0.883872i \(-0.345072\pi\)
\(632\) −8.98935e11 − 2.48090e11i −0.224131 − 0.0618561i
\(633\) 4.11677e12 − 4.30581e12i 1.01916 − 1.06595i
\(634\) 5.26450e11 + 1.62025e12i 0.129406 + 0.398272i
\(635\) 1.27776e12 + 1.15001e11i 0.311867 + 0.0280685i
\(636\) 2.99981e11 + 2.62085e11i 0.0727003 + 0.0635164i
\(637\) −4.82071e10 + 1.07341e12i −0.0116007 + 0.258309i
\(638\) −3.23694e11 −0.0773467
\(639\) 2.01402e12 − 6.36924e11i 0.477871 − 0.151124i
\(640\) 2.79690e12 0.658973
\(641\) 3.72717e11 − 8.29920e12i 0.0872004 − 1.94167i −0.191918 − 0.981411i \(-0.561471\pi\)
0.279118 − 0.960257i \(-0.409958\pi\)
\(642\) 3.45959e12 + 3.02255e12i 0.803742 + 0.702208i
\(643\) 9.73531e7 + 8.76193e6i 2.24595e−5 + 2.02139e-6i 0.0896505 − 0.995973i \(-0.471425\pi\)
−0.0896281 + 0.995975i \(0.528568\pi\)
\(644\) −7.19265e11 − 2.21367e12i −0.164779 − 0.507139i
\(645\) 1.90048e12 − 1.98775e12i 0.432360 − 0.452213i
\(646\) −8.05246e12 − 2.22234e12i −1.81921 − 0.502069i
\(647\) −3.98700e11 + 2.94332e12i −0.0894492 + 0.660341i 0.889604 + 0.456734i \(0.150981\pi\)
−0.979053 + 0.203607i \(0.934734\pi\)
\(648\) 2.40163e11 + 1.77296e12i 0.0535080 + 0.395012i
\(649\) −3.29762e12 + 9.10085e11i −0.729625 + 0.201364i
\(650\) −1.56891e11 + 2.91552e11i −0.0344737 + 0.0640628i
\(651\) −4.63057e12 − 4.84320e12i −1.01046 − 1.05686i
\(652\) 1.76591e12 + 3.28161e12i 0.382697 + 0.711170i
\(653\) −2.09048e12 + 6.43385e12i −0.449922 + 1.38472i 0.427072 + 0.904218i \(0.359545\pi\)
−0.876994 + 0.480501i \(0.840455\pi\)
\(654\) −8.77568e11 + 2.05317e12i −0.187578 + 0.438860i
\(655\) 5.17143e12 + 9.38476e11i 1.09780 + 0.199222i
\(656\) −3.62202e12 − 2.63155e12i −0.763631 − 0.554810i
\(657\) 2.11505e11 − 1.90358e10i 0.0442870 − 0.00398590i
\(658\) −1.52707e12 − 3.57277e12i −0.317573 − 0.742999i
\(659\) 6.07985e11 + 2.66375e12i 0.125576 + 0.550186i 0.998100 + 0.0616143i \(0.0196249\pi\)
−0.872524 + 0.488572i \(0.837518\pi\)
\(660\) 2.94378e12 + 4.45963e12i 0.603889 + 0.914853i
\(661\) 5.12532e11 + 3.06224e11i 0.104427 + 0.0623925i 0.564163 − 0.825663i \(-0.309199\pi\)
−0.459736 + 0.888056i \(0.652056\pi\)
\(662\) −4.66641e11 − 5.85150e11i −0.0944327 − 0.118415i
\(663\) 2.75820e12 − 2.40977e12i 0.554389 − 0.484355i
\(664\) −1.04852e12 + 7.61794e11i −0.209325 + 0.152083i
\(665\) 2.92282e12 − 1.40756e12i 0.579569 − 0.279106i
\(666\) −2.51377e12 + 3.80820e12i −0.495099 + 0.750042i
\(667\) −2.87941e11 − 1.08066e11i −0.0563297 − 0.0211409i
\(668\) 3.75069e12 − 2.24093e12i 0.728814 − 0.435446i
\(669\) 1.73510e12 + 8.35579e11i 0.334893 + 0.161276i
\(670\) −3.59584e12 + 6.52548e11i −0.689387 + 0.125105i
\(671\) 2.04483e12 − 8.95898e12i 0.389409 − 1.70611i
\(672\) −4.65774e12 + 1.74808e12i −0.881077 + 0.330674i
\(673\) 3.57482e12 − 4.48268e12i 0.671717 − 0.842306i −0.322845 − 0.946452i \(-0.604639\pi\)
0.994562 + 0.104146i \(0.0332108\pi\)
\(674\) −4.81736e11 − 1.07267e13i −0.0899164 − 2.00215i
\(675\) −1.95202e10 − 4.34652e11i −0.00361925 − 0.0805888i
\(676\) −2.12751e12 + 2.66781e12i −0.391842 + 0.491354i
\(677\) −6.21712e12 + 2.33333e12i −1.13747 + 0.426900i −0.847847 − 0.530240i \(-0.822102\pi\)
−0.289624 + 0.957140i \(0.593530\pi\)
\(678\) −3.90206e12 + 1.70960e13i −0.709186 + 3.10715i
\(679\) 9.67791e11 − 1.75628e11i 0.174730 − 0.0317088i
\(680\) 2.46475e12 + 1.18696e12i 0.442062 + 0.212886i
\(681\) −9.88923e12 + 5.90854e12i −1.76198 + 1.05273i
\(682\) 1.50838e13 + 5.66103e12i 2.66981 + 1.00200i
\(683\) −1.47427e12 + 2.23343e12i −0.259230 + 0.392716i −0.940760 − 0.339074i \(-0.889886\pi\)
0.681530 + 0.731790i \(0.261315\pi\)
\(684\) −1.93182e12 + 9.30318e11i −0.337455 + 0.162510i
\(685\) −1.66913e12 + 1.21270e12i −0.289657 + 0.210448i
\(686\) 5.77693e12 − 5.04716e12i 0.995953 − 0.870138i
\(687\) 4.67817e12 + 5.86624e12i 0.801255 + 1.00474i
\(688\) −2.86346e12 − 1.71083e12i −0.487239 − 0.291112i
\(689\) −1.40448e11 − 2.12769e11i −0.0237426 − 0.0359685i
\(690\) 2.61710e12 + 1.14663e13i 0.439541 + 1.92575i
\(691\) −1.28457e12 − 3.00539e12i −0.214341 − 0.501476i 0.777511 − 0.628869i \(-0.216482\pi\)
−0.991852 + 0.127393i \(0.959339\pi\)
\(692\) 1.94316e11 − 1.74888e10i 0.0322130 − 0.00289922i
\(693\) 1.67489e12 + 1.21688e12i 0.275859 + 0.200423i
\(694\) 7.84767e12 + 1.42414e12i 1.28417 + 0.233043i
\(695\) −3.81601e11 + 8.92799e11i −0.0620408 + 0.145152i
\(696\) −3.93699e10 + 1.21168e11i −0.00635950 + 0.0195725i
\(697\) −3.40793e12 − 6.33300e12i −0.546944 − 1.01639i
\(698\) 1.10914e13 + 1.16007e13i 1.76863 + 1.84985i
\(699\) 7.78001e11 − 1.44577e12i 0.123263 − 0.229061i
\(700\) 3.77317e11 − 1.04133e11i 0.0593971 − 0.0163925i
\(701\) 6.69276e11 + 4.94079e12i 0.104682 + 0.772797i 0.964853 + 0.262791i \(0.0846428\pi\)
−0.860170 + 0.510007i \(0.829643\pi\)
\(702\) −2.90931e11 + 2.14774e12i −0.0452140 + 0.333783i
\(703\) −8.30195e12 − 2.29119e12i −1.28198 − 0.353804i
\(704\) 2.36982e12 − 2.47864e12i 0.363613 − 0.380309i
\(705\) 2.61899e12 + 8.06042e12i 0.399285 + 1.22887i
\(706\) 8.05189e12 + 7.24683e11i 1.21977 + 0.109781i
\(707\) 5.48877e12 + 4.79540e12i 0.826205 + 0.721834i
\(708\) 1.90868e11 − 4.25000e12i 0.0285485 − 0.635682i
\(709\) −9.58397e12 −1.42442 −0.712209 − 0.701967i \(-0.752305\pi\)
−0.712209 + 0.701967i \(0.752305\pi\)
\(710\) 4.07848e12 + 8.64232e12i 0.602332 + 1.27634i
\(711\) −2.49008e12 −0.365427
\(712\) −1.08045e11 + 2.40580e12i −0.0157559 + 0.350832i
\(713\) 1.15278e13 + 1.00715e13i 1.67048 + 1.45946i
\(714\) −9.99020e12 − 8.99135e11i −1.43857 − 0.129474i
\(715\) −1.05683e12 − 3.25258e12i −0.151226 − 0.465426i
\(716\) −3.79024e12 + 3.96428e12i −0.538962 + 0.563710i
\(717\) −4.68315e12 − 1.29247e12i −0.661762 − 0.182635i
\(718\) 1.14980e12 − 8.48818e12i 0.161459 − 1.19194i
\(719\) −1.34627e12 − 9.93854e12i −0.187867 − 1.38689i −0.801828 − 0.597555i \(-0.796139\pi\)
0.613961 − 0.789337i \(-0.289575\pi\)
\(720\) 4.38359e12 − 1.20979e12i 0.607902 − 0.167770i
\(721\) 2.05086e12 − 3.81113e12i 0.282635 − 0.525224i
\(722\) 2.14878e11 + 2.24745e11i 0.0294289 + 0.0307802i
\(723\) 8.54170e11 + 1.58731e12i 0.116258 + 0.216043i
\(724\) −5.87611e11 + 1.80848e12i −0.0794816 + 0.244619i
\(725\) 2.03272e10 − 4.75579e10i 0.00273248 − 0.00639296i
\(726\) −2.69973e12 − 4.89928e11i −0.360666 − 0.0654512i
\(727\) 5.94239e12 + 4.31740e12i 0.788963 + 0.573215i 0.907656 − 0.419716i \(-0.137870\pi\)
−0.118693 + 0.992931i \(0.537870\pi\)
\(728\) 6.14618e11 − 5.53166e10i 0.0810988 − 0.00729902i
\(729\) −3.66555e11 − 8.57599e11i −0.0480691 − 0.112463i
\(730\) 2.13782e11 + 9.36642e11i 0.0278624 + 0.122073i
\(731\) −2.95179e12 − 4.47178e12i −0.382347 − 0.579231i
\(732\) 9.81041e12 + 5.86145e12i 1.26295 + 0.754579i
\(733\) −3.57339e12 − 4.48089e12i −0.457207 − 0.573319i 0.498780 − 0.866729i \(-0.333781\pi\)
−0.955987 + 0.293410i \(0.905210\pi\)
\(734\) −3.39164e12 + 2.96319e12i −0.431298 + 0.376814i
\(735\) −5.19291e12 + 3.77287e12i −0.656323 + 0.476847i
\(736\) 1.02398e13 − 4.93124e12i 1.28630 − 0.619449i
\(737\) 2.42498e12 − 3.67368e12i 0.302764 − 0.458667i
\(738\) −4.00348e12 − 1.50253e12i −0.496803 − 0.186453i
\(739\) 3.30608e11 − 1.97529e11i 0.0407769 − 0.0243631i −0.492366 − 0.870388i \(-0.663868\pi\)
0.533143 + 0.846025i \(0.321011\pi\)
\(740\) −8.02904e12 − 3.86658e12i −0.984285 − 0.474007i
\(741\) 4.04425e12 − 7.33923e11i 0.492783 − 0.0894270i
\(742\) −1.55365e11 + 6.80696e11i −0.0188163 + 0.0824396i
\(743\) −4.57558e12 + 1.71725e12i −0.550804 + 0.206720i −0.611231 − 0.791453i \(-0.709325\pi\)
0.0604269 + 0.998173i \(0.480754\pi\)
\(744\) 3.95368e12 − 4.95776e12i 0.473068 − 0.593208i
\(745\) −7.63602e11 − 1.70029e13i −0.0908164 − 2.02218i
\(746\) −4.61291e11 − 1.02714e13i −0.0545319 − 1.21425i
\(747\) −2.15771e12 + 2.70569e12i −0.253543 + 0.317933i
\(748\) 9.74739e12 − 3.65826e12i 1.13849 − 0.427284i
\(749\) −7.73485e11 + 3.38886e12i −0.0898015 + 0.393446i
\(750\) 1.27970e13 − 2.32232e12i 1.47684 − 0.268007i
\(751\) −8.75603e12 − 4.21668e12i −1.00445 − 0.483717i −0.142003 − 0.989866i \(-0.545354\pi\)
−0.862446 + 0.506149i \(0.831068\pi\)
\(752\) 8.82460e12 − 5.27245e12i 1.00627 − 0.601219i