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Properties

Label 71.10.g.a.2.3
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 2.3
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.94237 + 43.2502i) q^{2} +(-65.2666 - 57.0217i) q^{3} +(-1356.87 - 122.121i) q^{4} +(57.5622 + 177.158i) q^{5} +(2592.98 - 2712.04i) q^{6} +(10262.9 + 2832.38i) q^{7} +(4941.81 - 36481.9i) q^{8} +(-1633.86 - 12061.6i) q^{9} +O(q^{10})\) \(q+(-1.94237 + 43.2502i) q^{2} +(-65.2666 - 57.0217i) q^{3} +(-1356.87 - 122.121i) q^{4} +(57.5622 + 177.158i) q^{5} +(2592.98 - 2712.04i) q^{6} +(10262.9 + 2832.38i) q^{7} +(4941.81 - 36481.9i) q^{8} +(-1633.86 - 12061.6i) q^{9} +(-7773.94 + 2145.47i) q^{10} +(-17350.6 + 32242.9i) q^{11} +(81594.8 + 85341.5i) q^{12} +(50178.1 + 93246.6i) q^{13} +(-142435. + 438371. i) q^{14} +(6344.98 - 14844.8i) q^{15} +(881936. + 160048. i) q^{16} +(-351550. - 255416. i) q^{17} +(524842. - 47236.6i) q^{18} +(426576. + 998025. i) q^{19} +(-56469.7 - 247410. i) q^{20} +(-508317. - 770068. i) q^{21} +(-1.36081e6 - 813046. i) q^{22} +(484403. + 607423. i) q^{23} +(-2.40280e6 + 2.09926e6i) q^{24} +(1.55204e6 - 1.12762e6i) q^{25} +(-4.13040e6 + 1.98910e6i) q^{26} +(-1.52090e6 + 2.30406e6i) q^{27} +(-1.35795e7 - 5.09648e6i) q^{28} +(3.16478e6 - 1.89087e6i) q^{29} +(629717. + 303256. i) q^{30} +(-3.81282e6 + 691925. i) q^{31} +(-4.44078e6 + 1.94563e7i) q^{32} +(2.97096e6 - 1.11502e6i) q^{33} +(1.17296e7 - 1.47085e7i) q^{34} +(88975.4 + 1.98119e6i) q^{35} +(743962. + 1.65656e7i) q^{36} +(6.04608e6 - 7.58154e6i) q^{37} +(-4.39934e7 + 1.65110e7i) q^{38} +(2.04213e6 - 8.94714e6i) q^{39} +(6.74753e6 - 1.22450e6i) q^{40} +(9.06735e6 + 4.36661e6i) q^{41} +(3.42929e7 - 2.04891e7i) q^{42} +(-1.77728e7 - 6.67025e6i) q^{43} +(2.74801e7 - 4.16305e7i) q^{44} +(2.04277e6 - 983745. i) q^{45} +(-2.72121e7 + 1.97707e7i) q^{46} +(-4.52970e7 + 3.95748e7i) q^{47} +(-4.84348e7 - 6.07353e7i) q^{48} +(6.26630e7 + 3.74394e7i) q^{49} +(4.57553e7 + 6.93163e7i) q^{50} +(8.38022e6 + 3.67161e7i) q^{51} +(-5.66979e7 - 1.32651e8i) q^{52} +(3.36685e6 - 303022. i) q^{53} +(-9.66971e7 - 7.02545e7i) q^{54} +(-6.71083e6 - 1.21784e6i) q^{55} +(1.54048e8 - 3.60413e8i) q^{56} +(2.90679e7 - 8.94619e7i) q^{57} +(7.56334e7 + 1.40550e8i) q^{58} +(-7.97113e7 - 8.33715e7i) q^{59} +(-1.04222e7 + 1.93676e7i) q^{60} +(-1.10913e8 + 3.06099e7i) q^{61} +(-2.25200e7 - 1.66249e8i) q^{62} +(1.73950e7 - 1.28415e8i) q^{63} +(-3.90476e8 - 1.07765e8i) q^{64} +(-1.36310e7 + 1.42569e7i) q^{65} +(4.24542e7 + 1.30661e8i) q^{66} +(-1.78263e7 - 1.60439e6i) q^{67} +(4.45816e8 + 3.89498e8i) q^{68} +(3.02092e6 - 6.72660e7i) q^{69} -8.58598e7 q^{70} +(3.96172e7 + 2.10426e8i) q^{71} -4.48105e8 q^{72} +(-2.09083e7 + 4.65560e8i) q^{73} +(3.16160e8 + 2.76220e8i) q^{74} +(-1.65595e8 - 1.49039e7i) q^{75} +(-4.56929e8 - 1.40628e9i) q^{76} +(-2.69392e8 + 2.81762e8i) q^{77} +(3.82999e8 + 1.05701e8i) q^{78} +(-1.81289e7 + 1.33833e8i) q^{79} +(2.24124e7 + 1.65455e8i) q^{80} +(-297995. + 82241.4i) q^{81} +(-2.06469e8 + 3.83684e8i) q^{82} +(7.39581e7 + 7.73541e7i) q^{83} +(5.95679e8 + 1.10696e9i) q^{84} +(2.50130e7 - 7.69822e7i) q^{85} +(3.23011e8 - 7.55722e8i) q^{86} +(-3.14375e8 - 5.70507e7i) q^{87} +(1.09054e9 + 7.92323e8i) q^{88} +(-5.41473e8 + 4.87334e7i) q^{89} +(3.85794e7 + 9.02609e7i) q^{90} +(2.50863e8 + 1.09910e9i) q^{91} +(-5.83094e8 - 8.83349e8i) q^{92} +(2.88305e8 + 1.72254e8i) q^{93} +(-1.62364e9 - 2.03597e9i) q^{94} +(-1.52254e8 + 1.33020e8i) q^{95} +(1.39927e9 - 1.01663e9i) q^{96} +(1.01168e8 - 4.87201e7i) q^{97} +(-1.74098e9 + 2.63747e9i) q^{98} +(4.17250e8 + 1.56597e8i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.94237 + 43.2502i −0.0858414 + 1.91141i 0.247970 + 0.968768i \(0.420237\pi\)
−0.333811 + 0.942640i \(0.608335\pi\)
\(3\) −65.2666 − 57.0217i −0.465206 − 0.406439i 0.393165 − 0.919468i \(-0.371380\pi\)
−0.858371 + 0.513030i \(0.828523\pi\)
\(4\) −1356.87 − 122.121i −2.65014 − 0.238517i
\(5\) 57.5622 + 177.158i 0.0411881 + 0.126764i 0.969536 − 0.244948i \(-0.0787709\pi\)
−0.928348 + 0.371712i \(0.878771\pi\)
\(6\) 2592.98 − 2712.04i 0.816804 − 0.854310i
\(7\) 10262.9 + 2832.38i 1.61558 + 0.445872i 0.952963 − 0.303087i \(-0.0980171\pi\)
0.662617 + 0.748958i \(0.269446\pi\)
\(8\) 4941.81 − 36481.9i 0.426561 − 3.14900i
\(9\) −1633.86 − 12061.6i −0.0830086 − 0.612794i
\(10\) −7773.94 + 2145.47i −0.245833 + 0.0678457i
\(11\) −17350.6 + 32242.9i −0.357313 + 0.663998i −0.994270 − 0.106901i \(-0.965907\pi\)
0.636957 + 0.770899i \(0.280193\pi\)
\(12\) 81594.8 + 85341.5i 1.13592 + 1.18808i
\(13\) 50178.1 + 93246.6i 0.487270 + 0.905499i 0.998927 + 0.0463094i \(0.0147460\pi\)
−0.511657 + 0.859190i \(0.670968\pi\)
\(14\) −142435. + 438371.i −0.990927 + 3.04976i
\(15\) 6344.98 − 14844.8i 0.0323608 − 0.0757119i
\(16\) 881936. + 160048.i 3.36432 + 0.610534i
\(17\) −351550. − 255416.i −1.02086 − 0.741699i −0.0544022 − 0.998519i \(-0.517325\pi\)
−0.966459 + 0.256820i \(0.917325\pi\)
\(18\) 524842. − 47236.6i 1.17843 − 0.106060i
\(19\) 426576. + 998025.i 0.750941 + 1.75691i 0.647216 + 0.762307i \(0.275933\pi\)
0.103725 + 0.994606i \(0.466924\pi\)
\(20\) −56469.7 − 247410.i −0.0789189 − 0.345766i
\(21\) −508317. − 770068.i −0.570359 − 0.864056i
\(22\) −1.36081e6 − 813046.i −1.23850 − 0.739969i
\(23\) 484403. + 607423.i 0.360937 + 0.452601i 0.928833 − 0.370500i \(-0.120814\pi\)
−0.567895 + 0.823101i \(0.692242\pi\)
\(24\) −2.40280e6 + 2.09926e6i −1.47831 + 1.29156i
\(25\) 1.55204e6 − 1.12762e6i 0.794644 − 0.577343i
\(26\) −4.13040e6 + 1.98910e6i −1.77261 + 0.853642i
\(27\) −1.52090e6 + 2.30406e6i −0.550761 + 0.834367i
\(28\) −1.35795e7 − 5.09648e6i −4.17516 − 1.56696i
\(29\) 3.16478e6 − 1.89087e6i 0.830908 − 0.496444i −0.0333794 − 0.999443i \(-0.510627\pi\)
0.864287 + 0.502998i \(0.167770\pi\)
\(30\) 629717. + 303256.i 0.141938 + 0.0683539i
\(31\) −3.81282e6 + 691925.i −0.741513 + 0.134565i −0.536152 − 0.844122i \(-0.680123\pi\)
−0.205361 + 0.978686i \(0.565837\pi\)
\(32\) −4.44078e6 + 1.94563e7i −0.748659 + 3.28009i
\(33\) 2.97096e6 − 1.11502e6i 0.436098 − 0.163670i
\(34\) 1.17296e7 − 1.47085e7i 1.50532 − 1.88761i
\(35\) 88975.4 + 1.98119e6i 0.0100222 + 0.223162i
\(36\) 743962. + 1.65656e7i 0.0738226 + 1.64379i
\(37\) 6.04608e6 − 7.58154e6i 0.530354 − 0.665043i −0.442417 − 0.896809i \(-0.645879\pi\)
0.972771 + 0.231766i \(0.0744505\pi\)
\(38\) −4.39934e7 + 1.65110e7i −3.42264 + 1.28454i
\(39\) 2.04213e6 − 8.94714e6i 0.141349 − 0.619289i
\(40\) 6.74753e6 − 1.22450e6i 0.416749 − 0.0756288i
\(41\) 9.06735e6 + 4.36661e6i 0.501133 + 0.241333i 0.667334 − 0.744759i \(-0.267436\pi\)
−0.166200 + 0.986092i \(0.553150\pi\)
\(42\) 3.42929e7 − 2.04891e7i 1.70052 − 1.01602i
\(43\) −1.77728e7 − 6.67025e6i −0.792772 − 0.297532i −0.0780575 − 0.996949i \(-0.524872\pi\)
−0.714714 + 0.699417i \(0.753443\pi\)
\(44\) 2.74801e7 − 4.16305e7i 1.10530 − 1.67446i
\(45\) 2.04277e6 − 983745.i 0.0742613 − 0.0357624i
\(46\) −2.72121e7 + 1.97707e7i −0.896089 + 0.651047i
\(47\) −4.52970e7 + 3.95748e7i −1.35403 + 1.18298i −0.388882 + 0.921288i \(0.627139\pi\)
−0.965151 + 0.261695i \(0.915719\pi\)
\(48\) −4.84348e7 − 6.07353e7i −1.31696 − 1.65141i
\(49\) 6.26630e7 + 3.74394e7i 1.55285 + 0.927784i
\(50\) 4.57553e7 + 6.93163e7i 1.03532 + 1.56845i
\(51\) 8.38022e6 + 3.67161e7i 0.173456 + 0.759961i
\(52\) −5.66979e7 − 1.32651e8i −1.07536 − 2.51592i
\(53\) 3.36685e6 − 303022.i 0.0586114 − 0.00527512i −0.0602948 − 0.998181i \(-0.519204\pi\)
0.118906 + 0.992905i \(0.462061\pi\)
\(54\) −9.66971e7 − 7.02545e7i −1.54754 − 1.12435i
\(55\) −6.71083e6 − 1.21784e6i −0.0988881 − 0.0179455i
\(56\) 1.54048e8 − 3.60413e8i 2.09319 − 4.89727i
\(57\) 2.90679e7 − 8.94619e7i 0.364735 − 1.12254i
\(58\) 7.56334e7 + 1.40550e8i 0.877581 + 1.63082i
\(59\) −7.97113e7 − 8.33715e7i −0.856419 − 0.895744i 0.139103 − 0.990278i \(-0.455578\pi\)
−0.995522 + 0.0945343i \(0.969864\pi\)
\(60\) −1.04222e7 + 1.93676e7i −0.103819 + 0.192928i
\(61\) −1.10913e8 + 3.06099e7i −1.02564 + 0.283060i −0.738088 − 0.674704i \(-0.764271\pi\)
−0.287556 + 0.957764i \(0.592843\pi\)
\(62\) −2.25200e7 − 1.66249e8i −0.193556 − 1.42888i
\(63\) 1.73950e7 − 1.28415e8i 0.139121 − 1.02703i
\(64\) −3.90476e8 − 1.07765e8i −2.90928 − 0.802909i
\(65\) −1.36310e7 + 1.42569e7i −0.0947150 + 0.0990641i
\(66\) 4.24542e7 + 1.30661e8i 0.275406 + 0.847612i
\(67\) −1.78263e7 − 1.60439e6i −0.108075 − 0.00972689i 0.0354700 − 0.999371i \(-0.488707\pi\)
−0.143545 + 0.989644i \(0.545850\pi\)
\(68\) 4.45816e8 + 3.89498e8i 2.52852 + 2.20910i
\(69\) 3.02092e6 − 6.72660e7i 0.0160442 − 0.357252i
\(70\) −8.58598e7 −0.427414
\(71\) 3.96172e7 + 2.10426e8i 0.185021 + 0.982735i
\(72\) −4.48105e8 −1.96510
\(73\) −2.09083e7 + 4.65560e8i −0.0861721 + 1.91877i 0.235422 + 0.971893i \(0.424353\pi\)
−0.321594 + 0.946878i \(0.604219\pi\)
\(74\) 3.16160e8 + 2.76220e8i 1.22564 + 1.07081i
\(75\) −1.65595e8 − 1.49039e7i −0.604328 − 0.0543905i
\(76\) −4.56929e8 − 1.40628e9i −1.57104 − 4.83517i
\(77\) −2.69392e8 + 2.81762e8i −0.873325 + 0.913426i
\(78\) 3.82999e8 + 1.05701e8i 1.17158 + 0.323336i
\(79\) −1.81289e7 + 1.33833e8i −0.0523661 + 0.386582i 0.945733 + 0.324946i \(0.105346\pi\)
−0.998099 + 0.0616361i \(0.980368\pi\)
\(80\) 2.24124e7 + 1.65455e8i 0.0611763 + 0.451621i
\(81\) −297995. + 82241.4i −0.000769177 + 0.000212279i
\(82\) −2.06469e8 + 3.83684e8i −0.504304 + 0.937154i
\(83\) 7.39581e7 + 7.73541e7i 0.171054 + 0.178909i 0.802765 − 0.596295i \(-0.203361\pi\)
−0.631711 + 0.775204i \(0.717647\pi\)
\(84\) 5.95679e8 + 1.10696e9i 1.30544 + 2.42591i
\(85\) 2.50130e7 − 7.69822e7i 0.0519734 − 0.159958i
\(86\) 3.23011e8 − 7.55722e8i 0.636758 − 1.48977i
\(87\) −3.14375e8 − 5.70507e7i −0.588318 − 0.106764i
\(88\) 1.09054e9 + 7.92323e8i 1.93851 + 1.40841i
\(89\) −5.41473e8 + 4.87334e7i −0.914791 + 0.0823326i −0.537023 − 0.843568i \(-0.680451\pi\)
−0.377768 + 0.925900i \(0.623308\pi\)
\(90\) 3.85794e7 + 9.02609e7i 0.0619818 + 0.145014i
\(91\) 2.50863e8 + 1.09910e9i 0.383487 + 1.68017i
\(92\) −5.83094e8 − 8.83349e8i −0.848581 − 1.28555i
\(93\) 2.88305e8 + 1.72254e8i 0.399649 + 0.238779i
\(94\) −1.62364e9 − 2.03597e9i −2.14493 − 2.68966i
\(95\) −1.52254e8 + 1.33020e8i −0.191784 + 0.167556i
\(96\) 1.39927e9 − 1.01663e9i 1.68144 − 1.22163i
\(97\) 1.01168e8 − 4.87201e7i 0.116030 − 0.0558772i −0.374968 − 0.927038i \(-0.622346\pi\)
0.490998 + 0.871160i \(0.336632\pi\)
\(98\) −1.74098e9 + 2.63747e9i −1.90667 + 2.88848i
\(99\) 4.17250e8 + 1.56597e8i 0.436554 + 0.163842i
\(100\) −2.24362e9 + 1.34050e9i −2.24362 + 1.34050i
\(101\) −8.38931e8 − 4.04008e8i −0.802196 − 0.386317i −0.0125815 − 0.999921i \(-0.504005\pi\)
−0.789614 + 0.613604i \(0.789719\pi\)
\(102\) −1.60426e9 + 2.91130e8i −1.46748 + 0.266309i
\(103\) −2.42255e8 + 1.06139e9i −0.212083 + 0.929196i 0.751066 + 0.660227i \(0.229540\pi\)
−0.963149 + 0.268969i \(0.913317\pi\)
\(104\) 3.64979e9 − 1.36979e9i 3.05927 − 1.14816i
\(105\) 1.07164e8 − 1.34379e8i 0.0860393 − 0.107890i
\(106\) 6.56610e6 + 1.46206e8i 0.00505162 + 0.112483i
\(107\) −5.88004e7 − 1.30929e9i −0.0433664 − 0.965627i −0.896256 − 0.443536i \(-0.853724\pi\)
0.852890 − 0.522091i \(-0.174848\pi\)
\(108\) 2.34503e9 − 2.94058e9i 1.65860 − 2.07982i
\(109\) −6.47408e8 + 2.42976e8i −0.439298 + 0.164871i −0.561217 − 0.827669i \(-0.689667\pi\)
0.121919 + 0.992540i \(0.461095\pi\)
\(110\) 6.57066e7 − 2.87879e8i 0.0427900 − 0.187475i
\(111\) −8.26920e8 + 1.50064e8i −0.517023 + 0.0938259i
\(112\) 8.59790e9 + 4.14053e9i 5.16311 + 2.48642i
\(113\) 1.36189e9 − 8.13690e8i 0.785757 − 0.469468i −0.0631537 − 0.998004i \(-0.520116\pi\)
0.848911 + 0.528536i \(0.177259\pi\)
\(114\) 3.81279e9 + 1.43096e9i 2.11432 + 0.793517i
\(115\) −7.97266e7 + 1.20781e8i −0.0425072 + 0.0643957i
\(116\) −4.52511e9 + 2.17918e9i −2.32043 + 1.11746i
\(117\) 1.04272e9 − 7.57582e8i 0.514437 − 0.373760i
\(118\) 3.76067e9 − 3.28560e9i 1.78565 − 1.56007i
\(119\) −2.88448e9 − 3.61703e9i −1.31858 − 1.65345i
\(120\) −5.10211e8 − 3.04837e8i −0.224613 − 0.134200i
\(121\) 5.60427e8 + 8.49011e8i 0.237676 + 0.360064i
\(122\) −1.10845e9 − 4.85645e9i −0.453000 − 1.98472i
\(123\) −3.42804e8 − 8.02030e8i −0.135043 − 0.315950i
\(124\) 5.25800e9 − 4.73229e8i 1.99721 − 0.179752i
\(125\) 5.83442e8 + 4.23895e8i 0.213748 + 0.155297i
\(126\) 5.52018e9 + 1.00177e9i 1.95113 + 0.354078i
\(127\) −2.20972e9 + 5.16989e9i −0.753737 + 1.76346i −0.115933 + 0.993257i \(0.536986\pi\)
−0.637804 + 0.770199i \(0.720157\pi\)
\(128\) 2.26182e9 − 6.96115e9i 0.744753 − 2.29211i
\(129\) 7.79623e8 + 1.44878e9i 0.247874 + 0.460627i
\(130\) −5.90139e8 − 6.17237e8i −0.181221 − 0.189543i
\(131\) −1.34166e9 + 2.49322e9i −0.398035 + 0.739672i −0.998185 − 0.0602145i \(-0.980822\pi\)
0.600151 + 0.799887i \(0.295107\pi\)
\(132\) −4.16738e9 + 1.15012e9i −1.19476 + 0.329732i
\(133\) 1.55112e9 + 1.14508e10i 0.429847 + 3.17326i
\(134\) 1.04015e8 − 7.67873e8i 0.0278693 − 0.205740i
\(135\) −4.95730e8 − 1.36813e8i −0.128453 − 0.0354507i
\(136\) −1.10554e10 + 1.15630e10i −2.77107 + 2.89831i
\(137\) −8.42301e8 − 2.59234e9i −0.204279 − 0.628707i −0.999742 − 0.0227050i \(-0.992772\pi\)
0.795463 − 0.606002i \(-0.207228\pi\)
\(138\) 2.90340e9 + 2.61311e8i 0.681477 + 0.0613340i
\(139\) −3.55497e9 − 3.10588e9i −0.807735 − 0.705697i 0.151453 − 0.988464i \(-0.451605\pi\)
−0.959189 + 0.282767i \(0.908748\pi\)
\(140\) 1.21216e8 − 2.69909e9i 0.0266676 − 0.593801i
\(141\) 5.21301e9 1.11071
\(142\) −9.17791e9 + 1.30473e9i −1.89429 + 0.269291i
\(143\) −3.87716e9 −0.775357
\(144\) 4.89478e8 − 1.08991e10i 0.0948641 − 2.11231i
\(145\) 5.17155e8 + 4.51824e8i 0.0971548 + 0.0848816i
\(146\) −2.00950e10 − 1.80858e9i −3.66016 − 0.329420i
\(147\) −1.95495e9 − 6.01670e9i −0.345308 − 1.06275i
\(148\) −9.12960e9 + 9.54881e9i −1.56413 + 1.63596i
\(149\) 4.39597e9 + 1.21321e9i 0.730662 + 0.201650i 0.611522 − 0.791227i \(-0.290558\pi\)
0.119140 + 0.992877i \(0.461986\pi\)
\(150\) 9.66243e8 − 7.13309e9i 0.155839 − 1.15045i
\(151\) 8.46800e8 + 6.25133e9i 0.132551 + 0.978534i 0.928018 + 0.372536i \(0.121512\pi\)
−0.795466 + 0.605998i \(0.792774\pi\)
\(152\) 3.85179e10 − 1.06303e10i 5.85284 − 1.61528i
\(153\) −2.50635e9 + 4.65758e9i −0.369769 + 0.687145i
\(154\) −1.16630e10 − 1.21985e10i −1.67096 − 1.74769i
\(155\) −3.42054e8 − 6.35643e8i −0.0475995 − 0.0884547i
\(156\) −3.86353e9 + 1.18907e10i −0.522304 + 1.60749i
\(157\) 3.47506e9 − 8.13030e9i 0.456471 − 1.06797i −0.520358 − 0.853948i \(-0.674202\pi\)
0.976829 − 0.214019i \(-0.0686556\pi\)
\(158\) −5.75310e9 − 1.04403e9i −0.734421 − 0.133278i
\(159\) −2.37022e8 − 1.72206e8i −0.0294104 − 0.0213679i
\(160\) −3.70247e9 + 3.33228e8i −0.446633 + 0.0401977i
\(161\) 3.25093e9 + 7.60593e9i 0.381321 + 0.892145i
\(162\) −2.97814e6 − 1.30481e7i −0.000339725 − 0.00148843i
\(163\) 6.84231e9 + 1.03657e10i 0.759204 + 1.15014i 0.984420 + 0.175836i \(0.0562627\pi\)
−0.225216 + 0.974309i \(0.572309\pi\)
\(164\) −1.17700e10 − 7.03223e9i −1.27051 − 0.759094i
\(165\) 3.68550e8 + 4.62147e8i 0.0387096 + 0.0485403i
\(166\) −3.48924e9 + 3.04845e9i −0.356651 + 0.311597i
\(167\) −7.00562e9 + 5.08988e9i −0.696983 + 0.506388i −0.878948 − 0.476917i \(-0.841754\pi\)
0.181965 + 0.983305i \(0.441754\pi\)
\(168\) −3.06055e10 + 1.47389e10i −2.96421 + 1.42749i
\(169\) −3.35099e8 + 5.07653e8i −0.0315997 + 0.0478715i
\(170\) 3.28091e9 + 1.23135e9i 0.301283 + 0.113073i
\(171\) 1.13408e10 − 6.77584e9i 1.01429 − 0.606011i
\(172\) 2.33008e10 + 1.12211e10i 2.02999 + 0.977590i
\(173\) −1.10063e9 + 1.99735e8i −0.0934189 + 0.0169530i −0.225065 − 0.974344i \(-0.572259\pi\)
0.131646 + 0.991297i \(0.457974\pi\)
\(174\) 3.07809e9 − 1.34860e10i 0.254571 − 1.11535i
\(175\) 1.91223e10 − 7.17671e9i 1.54123 − 0.578434i
\(176\) −2.04626e10 + 2.56592e10i −1.60751 + 2.01575i
\(177\) 4.48501e8 + 9.98666e9i 0.0343466 + 0.764787i
\(178\) −1.05599e9 − 2.35135e10i −0.0788443 − 1.75561i
\(179\) 3.61996e9 − 4.53929e9i 0.263551 − 0.330483i −0.632394 − 0.774647i \(-0.717928\pi\)
0.895946 + 0.444164i \(0.146499\pi\)
\(180\) −2.89190e9 + 1.08535e9i −0.205333 + 0.0770626i
\(181\) 2.97863e9 − 1.30502e10i 0.206283 − 0.903783i −0.760733 − 0.649065i \(-0.775160\pi\)
0.967015 − 0.254718i \(-0.0819826\pi\)
\(182\) −4.80237e10 + 8.71502e9i −3.24440 + 0.588772i
\(183\) 8.98432e9 + 4.32662e9i 0.592182 + 0.285180i
\(184\) 2.45538e10 − 1.46702e10i 1.57920 − 0.943530i
\(185\) 1.69116e9 + 6.34702e8i 0.106148 + 0.0398379i
\(186\) −8.01002e9 + 1.21347e10i −0.490711 + 0.743395i
\(187\) 1.43350e10 − 6.90335e9i 0.857254 − 0.412832i
\(188\) 6.62950e10 − 4.81662e10i 3.87053 − 2.81211i
\(189\) −2.21348e10 + 1.93386e10i −1.26182 + 1.10242i
\(190\) −5.45741e9 − 6.84338e9i −0.303805 − 0.380960i
\(191\) 2.75648e9 + 1.64692e9i 0.149867 + 0.0895412i 0.585875 − 0.810401i \(-0.300751\pi\)
−0.436008 + 0.899943i \(0.643608\pi\)
\(192\) 1.93402e10 + 2.92991e10i 1.02708 + 1.55596i
\(193\) −3.41594e8 − 1.49662e9i −0.0177216 − 0.0776433i 0.965294 − 0.261166i \(-0.0841070\pi\)
−0.983015 + 0.183523i \(0.941250\pi\)
\(194\) 1.91065e9 + 4.47018e9i 0.0968440 + 0.226578i
\(195\) 1.70261e9 − 1.53237e8i 0.0843255 − 0.00758943i
\(196\) −8.04535e10 − 5.84529e10i −3.89397 − 2.82913i
\(197\) 1.42057e10 + 2.57796e9i 0.671995 + 0.121949i 0.503821 − 0.863808i \(-0.331927\pi\)
0.168174 + 0.985757i \(0.446213\pi\)
\(198\) −7.58329e9 + 1.77420e10i −0.350642 + 0.820369i
\(199\) −8.27461e8 + 2.54666e9i −0.0374032 + 0.115115i −0.968015 − 0.250893i \(-0.919276\pi\)
0.930612 + 0.366008i \(0.119276\pi\)
\(200\) −3.34679e10 − 6.21939e10i −1.47909 − 2.74861i
\(201\) 1.07197e9 + 1.12120e9i 0.0463236 + 0.0484507i
\(202\) 1.91030e10 − 3.54992e10i 0.807271 − 1.50016i
\(203\) 3.78355e10 − 1.04419e10i 1.56375 − 0.431567i
\(204\) −6.88707e9 − 5.08424e10i −0.278419 − 2.05537i
\(205\) −2.51643e8 + 1.85771e9i −0.00995161 + 0.0734657i
\(206\) −4.54348e10 − 1.25392e10i −1.75787 − 0.485140i
\(207\) 6.53506e9 − 6.83514e9i 0.247391 − 0.258750i
\(208\) 2.93300e10 + 9.02684e10i 1.08649 + 3.34388i
\(209\) −3.95806e10 − 3.56232e9i −1.43491 − 0.129144i
\(210\) 5.60378e9 + 4.89588e9i 0.198836 + 0.173718i
\(211\) −4.14572e8 + 9.23116e9i −0.0143989 + 0.320616i 0.978847 + 0.204591i \(0.0655866\pi\)
−0.993246 + 0.116025i \(0.962985\pi\)
\(212\) −4.60538e9 −0.156587
\(213\) 9.41316e9 − 1.59928e10i 0.313348 − 0.532374i
\(214\) 5.67414e10 1.84943
\(215\) 1.58647e8 − 3.53255e9i 0.00506360 − 0.112750i
\(216\) 7.65406e10 + 6.68715e10i 2.39249 + 2.09025i
\(217\) −4.10904e10 − 3.69820e9i −1.25797 − 0.113220i
\(218\) −9.25128e9 − 2.84725e10i −0.277426 − 0.853830i
\(219\) 2.79117e10 − 2.91933e10i 0.819950 − 0.857601i
\(220\) 8.95700e9 + 2.47198e9i 0.257787 + 0.0711446i
\(221\) 6.17655e9 − 4.55971e10i 0.174173 − 1.28580i
\(222\) −4.88411e9 − 3.60559e10i −0.134957 − 0.996296i
\(223\) −2.72170e10 + 7.51142e9i −0.737002 + 0.203400i −0.614332 − 0.789048i \(-0.710574\pi\)
−0.122670 + 0.992447i \(0.539146\pi\)
\(224\) −1.00683e11 + 1.87100e11i −2.67202 + 4.96544i
\(225\) −1.61368e10 − 1.68777e10i −0.419755 − 0.439029i
\(226\) 3.25470e10 + 6.04825e10i 0.829895 + 1.54220i
\(227\) −9.14058e9 + 2.81318e10i −0.228485 + 0.703204i 0.769434 + 0.638726i \(0.220538\pi\)
−0.997919 + 0.0644781i \(0.979462\pi\)
\(228\) −5.03665e10 + 1.17838e11i −1.23434 + 2.88788i
\(229\) 3.49881e10 + 6.34940e9i 0.840737 + 0.152571i 0.581809 − 0.813325i \(-0.302345\pi\)
0.258928 + 0.965897i \(0.416631\pi\)
\(230\) −5.06893e9 − 3.68279e9i −0.119438 − 0.0867765i
\(231\) 3.36488e10 − 3.02845e9i 0.777528 − 0.0699788i
\(232\) −5.33428e10 − 1.24802e11i −1.20887 − 2.82829i
\(233\) 5.28496e8 + 2.31549e9i 0.0117474 + 0.0514685i 0.980462 − 0.196709i \(-0.0630255\pi\)
−0.968715 + 0.248178i \(0.920168\pi\)
\(234\) 3.07402e10 + 4.65695e10i 0.670248 + 1.01538i
\(235\) −9.61839e9 − 5.74672e9i −0.205730 − 0.122918i
\(236\) 9.79766e10 + 1.22859e11i 2.05598 + 2.57811i
\(237\) 8.81461e9 − 7.70109e9i 0.181483 − 0.158557i
\(238\) 1.62040e11 − 1.17729e11i 3.27360 − 2.37841i
\(239\) 8.04401e10 − 3.87379e10i 1.59471 − 0.767973i 0.595342 − 0.803472i \(-0.297017\pi\)
0.999370 + 0.0354996i \(0.0113023\pi\)
\(240\) 7.97174e9 − 1.20767e10i 0.155097 − 0.234962i
\(241\) −5.63643e9 − 2.11539e9i −0.107629 − 0.0403937i 0.296980 − 0.954884i \(-0.404021\pi\)
−0.404608 + 0.914490i \(0.632592\pi\)
\(242\) −3.78085e10 + 2.25895e10i −0.708631 + 0.423387i
\(243\) 4.89829e10 + 2.35889e10i 0.901191 + 0.433991i
\(244\) 1.54232e11 − 2.79890e10i 2.78561 − 0.505514i
\(245\) −3.02568e9 + 1.32564e10i −0.0536507 + 0.235059i
\(246\) 3.53538e10 − 1.32685e10i 0.615501 − 0.231001i
\(247\) −7.16577e10 + 8.98559e10i −1.22497 + 1.53607i
\(248\) 6.40051e9 + 1.42518e11i 0.107444 + 2.39242i
\(249\) −4.16130e8 − 9.26586e9i −0.00686013 − 0.152753i
\(250\) −1.94668e10 + 2.44106e10i −0.315185 + 0.395229i
\(251\) −2.49454e10 + 9.36215e9i −0.396696 + 0.148883i −0.541747 − 0.840542i \(-0.682237\pi\)
0.145051 + 0.989424i \(0.453665\pi\)
\(252\) −3.92848e10 + 1.72118e11i −0.613652 + 2.68859i
\(253\) −2.79898e10 + 5.07939e9i −0.429494 + 0.0779416i
\(254\) −2.19307e11 − 1.05613e11i −3.30598 − 1.59208i
\(255\) −6.02218e9 + 3.59808e9i −0.0891914 + 0.0532894i
\(256\) 1.02505e11 + 3.84708e10i 1.49164 + 0.559823i
\(257\) 7.91559e8 − 1.19916e9i 0.0113184 − 0.0171466i −0.828870 − 0.559441i \(-0.811016\pi\)
0.840188 + 0.542295i \(0.182444\pi\)
\(258\) −6.41744e10 + 3.09048e10i −0.901724 + 0.434247i
\(259\) 8.35240e10 − 6.06837e10i 1.15335 − 0.837960i
\(260\) 2.02366e10 − 1.76802e10i 0.274636 − 0.239942i
\(261\) −2.79778e10 − 3.50830e10i −0.373191 − 0.467966i
\(262\) −1.05226e11 − 6.28698e10i −1.37965 − 0.824301i
\(263\) 3.03773e10 + 4.60196e10i 0.391515 + 0.593119i 0.975863 − 0.218384i \(-0.0700784\pi\)
−0.584348 + 0.811503i \(0.698650\pi\)
\(264\) −2.59962e10 − 1.13897e11i −0.329376 − 1.44309i
\(265\) 2.47486e8 + 5.79022e8i 0.00308279 + 0.00721255i
\(266\) −4.98265e11 + 4.48446e10i −6.10229 + 0.549216i
\(267\) 3.81190e10 + 2.76951e10i 0.459030 + 0.333504i
\(268\) 2.39920e10 + 4.35390e9i 0.284092 + 0.0515552i
\(269\) −3.03764e9 + 7.10690e9i −0.0353712 + 0.0827551i −0.936282 − 0.351249i \(-0.885757\pi\)
0.900911 + 0.434004i \(0.142900\pi\)
\(270\) 6.88007e9 − 2.11747e10i 0.0787872 − 0.242482i
\(271\) 1.02551e10 + 1.90572e10i 0.115499 + 0.214633i 0.931781 − 0.363020i \(-0.118254\pi\)
−0.816282 + 0.577653i \(0.803969\pi\)
\(272\) −2.69166e11 − 2.81525e11i −2.98167 − 3.11858i
\(273\) 4.62998e10 − 8.60394e10i 0.504484 − 0.937488i
\(274\) 1.13755e11 − 3.13944e10i 1.21925 − 0.336492i
\(275\) 9.42894e9 + 6.96072e10i 0.0994181 + 0.733934i
\(276\) −1.23136e10 + 9.09023e10i −0.127730 + 0.942940i
\(277\) 1.68048e11 + 4.63782e10i 1.71504 + 0.473320i 0.979041 − 0.203665i \(-0.0652855\pi\)
0.735996 + 0.676986i \(0.236714\pi\)
\(278\) 1.41235e11 − 1.47720e11i 1.41821 − 1.48333i
\(279\) 1.45754e10 + 4.48583e10i 0.144012 + 0.443225i
\(280\) 7.27174e10 + 6.54468e9i 0.707012 + 0.0636323i
\(281\) −2.39399e10 − 2.09156e10i −0.229057 − 0.200121i 0.535757 − 0.844372i \(-0.320026\pi\)
−0.764814 + 0.644251i \(0.777169\pi\)
\(282\) −1.01256e10 + 2.25464e11i −0.0953453 + 2.12303i
\(283\) −1.60087e11 −1.48361 −0.741803 − 0.670618i \(-0.766029\pi\)
−0.741803 + 0.670618i \(0.766029\pi\)
\(284\) −2.80580e10 − 2.90358e11i −0.255932 − 2.64851i
\(285\) 1.75221e10 0.157320
\(286\) 7.53088e9 − 1.67688e11i 0.0665578 − 1.48202i
\(287\) 8.06894e10 + 7.04962e10i 0.702017 + 0.613334i
\(288\) 2.41930e11 + 2.17741e10i 2.07216 + 0.186498i
\(289\) 2.17044e10 + 6.67991e10i 0.183023 + 0.563288i
\(290\) −2.05460e10 + 2.14894e10i −0.170583 + 0.178416i
\(291\) −9.38101e9 − 2.58900e9i −0.0766887 − 0.0211647i
\(292\) 8.52244e10 − 6.29152e11i 0.686027 − 5.06445i
\(293\) 3.05301e10 + 2.25382e11i 0.242005 + 1.78655i 0.550000 + 0.835164i \(0.314628\pi\)
−0.307995 + 0.951388i \(0.599658\pi\)
\(294\) 2.64021e11 − 7.28651e10i 2.06099 − 0.568796i
\(295\) 1.01816e10 − 1.89206e10i 0.0782738 − 0.145457i
\(296\) −2.46710e11 − 2.58039e11i −1.86799 − 1.95377i
\(297\) −4.79011e10 − 8.90151e10i −0.357224 − 0.663834i
\(298\) −6.10103e10 + 1.87770e11i −0.448157 + 1.37928i
\(299\) −3.23336e10 + 7.56483e10i −0.233956 + 0.547367i
\(300\) 2.22871e11 + 4.04452e10i 1.58858 + 0.288285i
\(301\) −1.63508e11 − 1.18795e11i −1.14813 − 0.834162i
\(302\) −2.72016e11 + 2.44819e10i −1.88176 + 0.169361i
\(303\) 3.17170e10 + 7.42056e10i 0.216172 + 0.505760i
\(304\) 2.16481e11 + 9.48467e11i 1.45375 + 6.36929i
\(305\) −1.18072e10 − 1.78871e10i −0.0781261 − 0.118356i
\(306\) −1.96573e11 − 1.17447e11i −1.28167 − 0.765764i
\(307\) 2.95278e10 + 3.70267e10i 0.189718 + 0.237899i 0.867589 − 0.497282i \(-0.165669\pi\)
−0.677871 + 0.735181i \(0.737097\pi\)
\(308\) 3.99938e11 − 3.49416e11i 2.53230 − 2.21240i
\(309\) 7.63334e10 − 5.54595e10i 0.476323 − 0.346069i
\(310\) 2.81561e10 − 1.35593e10i 0.173159 − 0.0833890i
\(311\) 5.07260e10 − 7.68466e10i 0.307474 − 0.465804i −0.647680 − 0.761913i \(-0.724261\pi\)
0.955154 + 0.296109i \(0.0956892\pi\)
\(312\) −3.16317e11 − 1.18716e11i −1.88985 − 0.709272i
\(313\) −4.93037e10 + 2.94576e10i −0.290356 + 0.173479i −0.650689 − 0.759344i \(-0.725520\pi\)
0.360334 + 0.932823i \(0.382663\pi\)
\(314\) 3.44887e11 + 1.66089e11i 2.00214 + 0.964179i
\(315\) 2.37510e10 − 4.31018e9i 0.135920 − 0.0246659i
\(316\) 4.09424e10 − 1.79380e11i 0.230984 − 1.01200i
\(317\) 2.14988e11 − 8.06865e10i 1.19577 − 0.448781i 0.327492 − 0.944854i \(-0.393797\pi\)
0.868281 + 0.496073i \(0.165225\pi\)
\(318\) 7.90835e9 − 9.91676e9i 0.0433674 − 0.0543811i
\(319\) 6.05610e9 + 1.34850e11i 0.0327442 + 0.729107i
\(320\) −3.38529e9 − 7.53792e10i −0.0180476 − 0.401862i
\(321\) −7.08204e10 + 8.88060e10i −0.372294 + 0.466842i
\(322\) −3.35273e11 + 1.25830e11i −1.73799 + 0.652277i
\(323\) 1.04949e11 − 4.59810e11i 0.536495 − 2.35054i
\(324\) 4.14384e8 − 7.51996e7i 0.00208906 − 0.000379108i
\(325\) 1.83025e11 + 8.81404e10i 0.909990 + 0.438228i
\(326\) −4.61607e11 + 2.75797e11i −2.26357 + 1.35242i
\(327\) 5.61091e10 + 2.10581e10i 0.271374 + 0.101848i
\(328\) 2.04111e11 − 3.09215e11i 0.973722 − 1.47513i
\(329\) −5.76969e11 + 2.77854e11i −2.71501 + 1.30748i
\(330\) −2.07038e10 + 1.50422e10i −0.0961032 + 0.0698231i
\(331\) −1.51900e11 + 1.32711e11i −0.695556 + 0.607689i −0.931355 − 0.364113i \(-0.881372\pi\)
0.235799 + 0.971802i \(0.424229\pi\)
\(332\) −9.09050e10 − 1.13991e11i −0.410645 − 0.514932i
\(333\) −1.01324e11 − 6.05384e10i −0.451558 − 0.269794i
\(334\) −2.06531e11 − 3.12881e11i −0.908084 − 1.37569i
\(335\) −7.41887e8 − 3.25042e9i −0.00321837 − 0.0141006i
\(336\) −3.25056e11 − 7.60505e11i −1.39133 − 3.25518i
\(337\) −4.60560e10 + 4.14511e9i −0.194514 + 0.0175066i −0.186468 − 0.982461i \(-0.559704\pi\)
−0.00804622 + 0.999968i \(0.502561\pi\)
\(338\) −2.13052e10 − 1.54791e10i −0.0887893 − 0.0645092i
\(339\) −1.35284e11 − 2.45504e10i −0.556349 − 0.100963i
\(340\) −4.33406e10 + 1.01400e11i −0.175889 + 0.411513i
\(341\) 4.38452e10 − 1.34942e11i 0.175601 − 0.540445i
\(342\) 2.71028e11 + 5.03655e11i 1.07127 + 1.99075i
\(343\) 2.40162e11 + 2.51190e11i 0.936873 + 0.979893i
\(344\) −3.31173e11 + 6.15423e11i −1.27509 + 2.36952i
\(345\) 1.20906e10 − 3.33679e9i 0.0459475 − 0.0126807i
\(346\) −6.50076e9 − 4.79905e10i −0.0243849 − 0.180017i
\(347\) 2.16954e10 − 1.60162e11i 0.0803312 − 0.593028i −0.905382 − 0.424597i \(-0.860416\pi\)
0.985713 − 0.168431i \(-0.0538701\pi\)
\(348\) 4.19600e11 + 1.15802e11i 1.53366 + 0.423263i
\(349\) −2.19651e10 + 2.29737e10i −0.0792537 + 0.0828928i −0.761232 − 0.648479i \(-0.775405\pi\)
0.681979 + 0.731372i \(0.261120\pi\)
\(350\) 2.73252e11 + 8.40982e11i 0.973322 + 2.99558i
\(351\) −2.91162e11 − 2.62050e10i −1.02389 − 0.0921516i
\(352\) −5.50277e11 − 4.80763e11i −1.91047 − 1.66913i
\(353\) 1.66796e10 − 3.71400e11i 0.0571742 − 1.27308i −0.741350 − 0.671119i \(-0.765814\pi\)
0.798524 − 0.601963i \(-0.205614\pi\)
\(354\) −4.32796e11 −1.46477
\(355\) −3.49982e10 + 1.91311e10i −0.116955 + 0.0639310i
\(356\) 7.40660e11 2.44396
\(357\) −1.79887e10 + 4.00550e11i −0.0586128 + 1.30512i
\(358\) 1.89294e11 + 1.65381e11i 0.609064 + 0.532123i
\(359\) −4.79409e11 − 4.31476e10i −1.52328 − 0.137098i −0.703882 − 0.710317i \(-0.748552\pi\)
−0.819402 + 0.573219i \(0.805694\pi\)
\(360\) −2.57939e10 − 7.93855e10i −0.0809387 − 0.249104i
\(361\) −5.91089e11 + 6.18231e11i −1.83177 + 1.91588i
\(362\) 5.58639e11 + 1.54175e11i 1.70979 + 0.471872i
\(363\) 1.18349e10 − 8.73686e10i 0.0357754 − 0.264104i
\(364\) −2.06166e11 − 1.52198e12i −0.615545 − 4.54414i
\(365\) −8.36813e10 + 2.30946e10i −0.246780 + 0.0681071i
\(366\) −2.04578e11 + 3.80170e11i −0.595929 + 1.10742i
\(367\) 1.38748e11 + 1.45119e11i 0.399235 + 0.417567i 0.891601 − 0.452821i \(-0.149582\pi\)
−0.492367 + 0.870388i \(0.663868\pi\)
\(368\) 3.29996e11 + 6.13236e11i 0.937980 + 1.74306i
\(369\) 3.78536e10 − 1.16501e11i 0.106289 − 0.327124i
\(370\) −3.07358e10 + 7.19101e10i −0.0852584 + 0.199472i
\(371\) 3.54119e10 + 6.42631e9i 0.0970435 + 0.0176108i
\(372\) −3.70156e11 − 2.68934e11i −1.00217 − 0.728120i
\(373\) −2.86825e11 + 2.58147e10i −0.767234 + 0.0690523i −0.466340 − 0.884605i \(-0.654428\pi\)
−0.300894 + 0.953658i \(0.597285\pi\)
\(374\) 2.70728e11 + 6.33399e11i 0.715502 + 1.67400i
\(375\) −1.39080e10 − 6.09351e10i −0.0363183 − 0.159121i
\(376\) 1.21992e12 + 1.84809e12i 3.14763 + 4.76846i
\(377\) 3.35120e11 + 2.00225e11i 0.854406 + 0.510484i
\(378\) −7.93404e11 − 9.94897e11i −1.99885 − 2.50648i
\(379\) 5.37949e10 − 4.69992e10i 0.133926 − 0.117008i −0.588370 − 0.808592i \(-0.700230\pi\)
0.722295 + 0.691585i \(0.243087\pi\)
\(380\) 2.22833e11 − 1.61898e11i 0.548218 − 0.398303i
\(381\) 4.39017e11 − 2.11419e11i 1.06738 − 0.514023i
\(382\) −7.65839e10 + 1.16020e11i −0.184015 + 0.278770i
\(383\) 3.69114e11 + 1.38531e11i 0.876528 + 0.328966i 0.748763 − 0.662838i \(-0.230648\pi\)
0.127765 + 0.991804i \(0.459220\pi\)
\(384\) −5.44558e11 + 3.25358e11i −1.27807 + 0.763610i
\(385\) −6.54231e10 − 3.15061e10i −0.151760 − 0.0730839i
\(386\) 6.53927e10 − 1.18670e10i 0.149929 − 0.0272081i
\(387\) −5.14158e10 + 2.25267e11i −0.116519 + 0.510504i
\(388\) −1.43222e11 + 5.37521e10i −0.320824 + 0.120407i
\(389\) −1.59100e11 + 1.99505e11i −0.352288 + 0.441755i −0.926126 − 0.377214i \(-0.876882\pi\)
0.573839 + 0.818968i \(0.305454\pi\)
\(390\) 3.32046e9 + 7.39358e10i 0.00726788 + 0.161832i
\(391\) −1.51465e10 − 3.37264e11i −0.0327731 − 0.729750i
\(392\) 1.67553e12 − 2.10105e12i 3.58398 − 4.49416i
\(393\) 2.29733e11 − 8.62203e10i 0.485800 − 0.182324i
\(394\) −1.39090e11 + 6.09394e11i −0.290779 + 1.27399i
\(395\) −2.47532e10 + 4.49204e9i −0.0511615 + 0.00928445i
\(396\) −5.47031e11 − 2.63436e11i −1.11785 − 0.538328i
\(397\) −2.51884e10 + 1.50494e10i −0.0508912 + 0.0304061i −0.538120 − 0.842869i \(-0.680865\pi\)
0.487228 + 0.873275i \(0.338008\pi\)
\(398\) −1.08537e11 − 4.07345e10i −0.216821 − 0.0813744i
\(399\) 5.51711e11 − 8.35806e11i 1.08977 − 1.65093i
\(400\) 1.54927e12 − 7.46091e11i 3.02592 − 1.45721i
\(401\) 2.91431e11 − 2.11737e11i 0.562841 − 0.408928i −0.269657 − 0.962957i \(-0.586910\pi\)
0.832498 + 0.554029i \(0.186910\pi\)
\(402\) −5.05742e10 + 4.41854e10i −0.0965855 + 0.0843842i
\(403\) −2.55840e11 − 3.20813e11i −0.483165 − 0.605870i
\(404\) 1.08898e12 + 6.50637e11i 2.03379 + 1.21513i
\(405\) −3.17230e7 − 4.80582e7i −5.85904e−5 − 8.87606e-5i
\(406\) 3.78125e11 + 1.65667e12i 0.690667 + 3.02601i
\(407\) 1.39547e11 + 3.26487e11i 0.252085 + 0.589782i
\(408\) 1.38089e12 − 1.24282e11i 2.46711 − 0.222044i
\(409\) 3.79346e11 + 2.75611e11i 0.670317 + 0.487014i 0.870131 − 0.492820i \(-0.164034\pi\)
−0.199814 + 0.979834i \(0.564034\pi\)
\(410\) −7.98575e10 − 1.44920e10i −0.139569 − 0.0253280i
\(411\) −9.28453e10 + 2.17222e11i −0.160499 + 0.375506i
\(412\) 4.58326e11 − 1.41058e12i 0.783677 − 2.41191i
\(413\) −5.81929e11 − 1.08141e12i −0.984226 − 1.82900i
\(414\) 2.82928e11 + 2.95919e11i 0.473341 + 0.495076i
\(415\) −9.44672e9 + 1.75549e10i −0.0156338 + 0.0290525i
\(416\) −2.03707e12 + 5.62194e11i −3.33492 + 0.920379i
\(417\) 5.49180e10 + 4.05421e11i 0.0889411 + 0.656590i
\(418\) 2.30951e11 − 1.70495e12i 0.370021 − 2.73161i
\(419\) −1.09348e12 − 3.01780e11i −1.73319 − 0.478330i −0.750080 − 0.661347i \(-0.769985\pi\)
−0.983110 + 0.183017i \(0.941414\pi\)
\(420\) −1.61818e11 + 1.69248e11i −0.253749 + 0.265401i
\(421\) −2.96581e11 − 9.12782e11i −0.460123 − 1.41611i −0.865014 − 0.501747i \(-0.832691\pi\)
0.404892 − 0.914365i \(-0.367309\pi\)
\(422\) −3.98445e11 − 3.58607e10i −0.611592 − 0.0550443i
\(423\) 5.51345e11 + 4.81696e11i 0.837321 + 0.731546i
\(424\) 5.58351e9 − 1.24327e11i 0.00838998 − 0.186818i
\(425\) −8.33632e11 −1.23944
\(426\) 6.73409e11 + 4.38185e11i 0.990686 + 0.644636i
\(427\) −1.22498e12 −1.78322
\(428\) −8.01069e10 + 1.78372e12i −0.115391 + 2.56939i
\(429\) 2.53049e11 + 2.21083e11i 0.360701 + 0.315135i
\(430\) 1.52476e11 + 1.37230e10i 0.215076 + 0.0193572i
\(431\) 4.05721e11 + 1.24868e12i 0.566343 + 1.74303i 0.663926 + 0.747798i \(0.268889\pi\)
−0.0975826 + 0.995227i \(0.531111\pi\)
\(432\) −1.71009e12 + 1.78862e12i −2.36235 + 2.47082i
\(433\) 4.60729e11 + 1.27153e11i 0.629869 + 0.173833i 0.566373 − 0.824149i \(-0.308346\pi\)
0.0634963 + 0.997982i \(0.479775\pi\)
\(434\) 2.39761e11 − 1.76998e12i 0.324395 − 2.39478i
\(435\) −7.98913e9 − 5.89781e10i −0.0106979 − 0.0789749i
\(436\) 9.08121e11 − 2.50626e11i 1.20352 − 0.332152i
\(437\) −3.99588e11 + 7.42559e11i −0.524138 + 0.974012i
\(438\) 1.20840e12 + 1.26389e12i 1.56884 + 1.64088i
\(439\) −1.17291e11 − 2.17964e11i −0.150722 − 0.280088i 0.794028 − 0.607882i \(-0.207980\pi\)
−0.944749 + 0.327794i \(0.893695\pi\)
\(440\) −7.75926e10 + 2.38806e11i −0.0986923 + 0.303744i
\(441\) 3.49198e11 − 8.16989e11i 0.439641 − 1.02859i
\(442\) 1.96009e12 + 3.55704e11i 2.44273 + 0.443290i
\(443\) −8.60509e11 − 6.25197e11i −1.06155 − 0.771258i −0.0871721 − 0.996193i \(-0.527783\pi\)
−0.974374 + 0.224935i \(0.927783\pi\)
\(444\) 1.14035e12 − 1.02633e11i 1.39256 − 0.125333i
\(445\) −3.98019e10 − 9.31211e10i −0.0481153 − 0.112571i
\(446\) −2.72005e11 − 1.19173e12i −0.325514 − 1.42617i
\(447\) −2.17731e11 − 3.29848e11i −0.257950 − 0.390778i
\(448\) −3.70219e12 − 2.21195e12i −4.34217 − 2.59433i
\(449\) −5.69512e11 − 7.14146e11i −0.661294 − 0.829236i 0.332190 − 0.943213i \(-0.392213\pi\)
−0.993483 + 0.113976i \(0.963641\pi\)
\(450\) 7.61310e11 − 6.65137e11i 0.875196 − 0.764636i
\(451\) −2.98116e11 + 2.16594e11i −0.339306 + 0.246520i
\(452\) −1.94727e12 + 9.37758e11i −2.19434 + 1.05674i
\(453\) 3.01194e11 − 4.56289e11i 0.336050 − 0.509094i
\(454\) −1.19895e12 − 4.49975e11i −1.32450 − 0.497092i
\(455\) −1.80275e11 + 1.07709e11i −0.197190 + 0.117815i
\(456\) −3.12009e12 − 1.50256e12i −3.37929 − 1.62738i
\(457\) 4.65084e11 − 8.44004e10i 0.498780 − 0.0905152i 0.0766637 − 0.997057i \(-0.475573\pi\)
0.422116 + 0.906542i \(0.361287\pi\)
\(458\) −3.42573e11 + 1.50091e12i −0.363796 + 1.59389i
\(459\) 1.12317e12 − 4.21531e11i 1.18110 − 0.443274i
\(460\) 1.22928e11 − 1.54147e11i 0.128009 − 0.160519i
\(461\) −3.53433e10 − 7.86980e11i −0.0364463 − 0.811539i −0.931097 − 0.364772i \(-0.881147\pi\)
0.894651 − 0.446767i \(-0.147425\pi\)
\(462\) 6.56226e10 + 1.46120e12i 0.0670139 + 1.49218i
\(463\) 9.86260e11 − 1.23673e12i 0.997417 − 1.25072i 0.0294709 − 0.999566i \(-0.490618\pi\)
0.967947 − 0.251156i \(-0.0808108\pi\)
\(464\) 3.09377e12 − 1.16111e12i 3.09854 − 1.16290i
\(465\) −1.39208e10 + 6.09909e10i −0.0138078 + 0.0604960i
\(466\) −1.01172e11 + 1.83600e10i −0.0993857 + 0.0180359i
\(467\) −1.79947e12 − 8.66578e11i −1.75073 − 0.843105i −0.978069 − 0.208280i \(-0.933213\pi\)
−0.772656 − 0.634825i \(-0.781072\pi\)
\(468\) −1.50735e12 + 9.00603e11i −1.45248 + 0.867814i
\(469\) −1.78405e11 − 6.69564e10i −0.170266 − 0.0639020i
\(470\) 2.67229e11 − 4.04835e11i 0.252606 − 0.382682i
\(471\) −6.90409e11 + 3.32484e11i −0.646417 + 0.311298i
\(472\) −3.43547e12 + 2.49602e12i −3.18601 + 2.31477i
\(473\) 5.23438e11 − 4.57314e11i 0.480828 − 0.420087i
\(474\) 3.15953e11 + 3.96192e11i 0.287488 + 0.360498i
\(475\) 1.78746e12 + 1.06796e12i 1.61107 + 0.962571i
\(476\) 3.47216e12 + 5.26009e12i 3.10004 + 4.69637i
\(477\) −9.15589e9 − 4.01146e10i −0.00809782 − 0.0354789i
\(478\) 1.51918e12 + 3.55430e12i 1.33102 + 3.11407i
\(479\) 1.15205e12 − 1.03686e11i 0.999908 − 0.0899933i 0.422426 − 0.906397i \(-0.361178\pi\)
0.577481 + 0.816404i \(0.304036\pi\)
\(480\) 2.60649e11 + 1.89372e11i 0.224115 + 0.162829i
\(481\) 1.01033e12 + 1.83349e11i 0.860621 + 0.156180i
\(482\) 1.02439e11 − 2.39668e11i 0.0864478 − 0.202255i
\(483\) 2.21526e11 − 6.81787e11i 0.185209 − 0.570015i
\(484\) −6.56745e11 − 1.22044e12i −0.543992 − 1.01091i
\(485\) 1.44546e10 + 1.51183e10i 0.0118623 + 0.0124070i
\(486\) −1.11537e12 + 2.07270e12i −0.906892 + 1.68529i
\(487\) 7.62819e11 − 2.10525e11i 0.614527 − 0.169599i 0.0551036 − 0.998481i \(-0.482451\pi\)
0.559424 + 0.828882i \(0.311023\pi\)
\(488\) 5.68600e11 + 4.19757e12i 0.453855 + 3.35049i
\(489\) 1.44493e11 − 1.06669e12i 0.114277 − 0.843624i
\(490\) −5.67464e11 − 1.56610e11i −0.444688 − 0.122726i
\(491\) 1.56184e12 − 1.63356e12i 1.21275 − 1.26843i 0.259671 − 0.965697i \(-0.416386\pi\)
0.953075 − 0.302735i \(-0.0978997\pi\)
\(492\) 3.67196e11 + 1.13011e12i 0.282524 + 0.869520i
\(493\) −1.59554e12 − 1.43601e11i −1.21645 − 0.109483i
\(494\) −3.74710e12 − 3.27374e12i −2.83090 − 2.47328i
\(495\) −3.72454e9 + 8.29333e10i −0.00278836 + 0.0620877i
\(496\) −3.47340e12 −2.57684
\(497\) −1.89419e11 + 2.27179e12i −0.139258 + 1.67018i
\(498\) 4.01559e11 0.292562
\(499\) 6.49621e10 − 1.44649e12i 0.0469038 − 1.04439i −0.828192 − 0.560444i \(-0.810630\pi\)
0.875096 − 0.483949i \(-0.160798\pi\)
\(500\) −7.39888e11 − 6.46421e11i −0.529421 − 0.462541i
\(501\) 7.47467e11 + 6.72733e10i 0.530057 + 0.0477060i
\(502\) −3.56462e11 − 1.09708e12i −0.250522 − 0.771029i
\(503\) 4.73248e11 − 4.94978e11i 0.329634 − 0.344771i −0.537120 − 0.843506i \(-0.680488\pi\)
0.866754 + 0.498735i \(0.166202\pi\)
\(504\) −4.59886e12 − 1.26920e12i −3.17477 − 0.876181i
\(505\) 2.32826e10 − 1.71879e11i 0.0159302 − 0.117601i
\(506\) −1.65318e11 − 1.22043e12i −0.112110 − 0.827629i
\(507\) 5.08180e10 − 1.40249e10i 0.0341572 − 0.00942678i
\(508\) 3.62965e12 − 6.74502e12i 2.41812 − 4.49362i
\(509\) 7.78605e11 + 8.14357e11i 0.514147 + 0.537756i 0.927996 − 0.372590i \(-0.121530\pi\)
−0.413849 + 0.910346i \(0.635816\pi\)
\(510\) −1.43921e11 − 2.67449e11i −0.0942014 − 0.175055i
\(511\) −1.53322e12 + 4.71877e12i −0.994744 + 3.06151i
\(512\) −3.90099e11 + 9.12682e11i −0.250877 + 0.586955i
\(513\) −2.94829e12 − 5.35036e11i −1.87950 − 0.341079i
\(514\) 5.03264e10 + 3.65643e10i 0.0318026 + 0.0231059i
\(515\) −2.01978e11 + 1.81784e10i −0.126524 + 0.0113874i
\(516\) −8.80921e11 − 2.06102e12i −0.547033 − 1.27985i
\(517\) −4.90074e11 − 2.14715e12i −0.301685 − 1.32177i
\(518\) 2.46235e12 + 3.73030e12i 1.50268 + 2.27646i
\(519\) 8.32238e10 + 4.97239e10i 0.0503494 + 0.0300824i
\(520\) 4.52759e11 + 5.67741e11i 0.271551 + 0.340514i
\(521\) 1.68175e12 − 1.46930e12i 0.999982 − 0.873658i 0.00799142 − 0.999968i \(-0.497456\pi\)
0.991991 + 0.126310i \(0.0403134\pi\)
\(522\) 1.57169e12 − 1.14190e12i 0.926510 − 0.673149i
\(523\) 2.37104e11 − 1.14183e11i 0.138574 − 0.0667336i −0.363312 − 0.931668i \(-0.618354\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(524\) 2.12493e12 − 3.21913e12i 1.23127 − 1.86530i
\(525\) −1.65727e12 − 6.21986e11i −0.952089 − 0.357325i
\(526\) −2.04936e12 + 1.22444e12i −1.16730 + 0.697430i
\(527\) 1.51713e12 + 7.30609e11i 0.856789 + 0.412608i
\(528\) 2.79866e12 − 5.07881e11i 1.56710 − 0.284387i
\(529\) 2.66479e11 − 1.16752e12i 0.147949 − 0.648206i
\(530\) −2.55235e10 + 9.57915e9i −0.0140508 + 0.00527334i
\(531\) −8.75359e11 + 1.09767e12i −0.477816 + 0.599163i
\(532\) −7.06289e11 − 1.57267e13i −0.382278 − 8.51209i
\(533\) 4.78116e10 + 1.06461e12i 0.0256603 + 0.571370i
\(534\) −1.27186e12 + 1.59486e12i −0.676867 + 0.848764i
\(535\) 2.28567e11 − 8.57826e10i 0.120621 − 0.0452697i
\(536\) −1.46625e11 + 6.42407e11i −0.0767304 + 0.336178i
\(537\) −4.95101e11 + 8.98476e10i −0.256927 + 0.0466253i
\(538\) −3.01475e11 − 1.45183e11i −0.155143 − 0.0747127i
\(539\) −2.29440e12 + 1.37084e12i −1.17090 + 0.699580i
\(540\) 6.55933e11 + 2.46176e11i 0.331961 + 0.124587i
\(541\) 1.45805e12 − 2.20885e12i 0.731788 − 1.10861i −0.258011 − 0.966142i \(-0.583067\pi\)
0.989799 − 0.142470i \(-0.0455044\pi\)
\(542\) −8.44147e11 + 4.06520e11i −0.420166 + 0.202341i
\(543\) −9.38551e11 + 6.81897e11i −0.463296 + 0.336604i
\(544\) 6.53061e12 − 5.70562e12i 3.19712 − 2.79324i
\(545\) −8.03115e10 − 1.00707e11i −0.0389936 − 0.0488964i
\(546\) 3.63129e12 + 2.16960e12i 1.74862 + 1.04475i
\(547\) −5.21800e10 − 7.90494e10i −0.0249208 − 0.0377533i 0.821899 − 0.569633i \(-0.192915\pi\)
−0.846820 + 0.531879i \(0.821486\pi\)
\(548\) 8.26315e11 + 3.62032e12i 0.391411 + 1.71488i
\(549\) 5.50421e11 + 1.28777e12i 0.258595 + 0.605012i
\(550\) −3.02884e12 + 2.72601e11i −1.41138 + 0.127027i
\(551\) 3.23716e12 + 2.35193e12i 1.49617 + 1.08703i
\(552\) −2.43906e12 − 4.42625e11i −1.11814 − 0.202913i
\(553\) −5.65121e11 + 1.32217e12i −0.256968 + 0.601206i
\(554\) −2.33228e12 + 7.17801e12i −1.05193 + 3.23750i
\(555\) −7.41843e10 − 1.37858e11i −0.0331890 − 0.0616754i
\(556\) 4.44434e12 + 4.64841e12i 1.97229 + 2.06285i
\(557\) −5.72116e11 + 1.06317e12i −0.251847 + 0.468009i −0.974858 − 0.222827i \(-0.928472\pi\)
0.723012 + 0.690836i \(0.242757\pi\)
\(558\) −1.96844e12 + 5.43256e11i −0.859546 + 0.237220i
\(559\) −2.69829e11 − 1.99196e12i −0.116879 − 0.862833i
\(560\) −2.38615e11 + 1.76152e12i −0.102530 + 0.756907i
\(561\) −1.32924e12 − 3.66846e11i −0.566590 − 0.156369i
\(562\) 9.51105e11 − 9.94778e11i 0.402175 − 0.420642i
\(563\) −2.24912e11 − 6.92208e11i −0.0943463 − 0.290368i 0.892736 − 0.450579i \(-0.148782\pi\)
−0.987083 + 0.160211i \(0.948782\pi\)
\(564\) −7.07337e12 − 6.36615e11i −2.94355 − 0.264924i
\(565\) 2.22545e11 + 1.94432e11i 0.0918756 + 0.0802693i
\(566\) 3.10949e11 − 6.92382e12i 0.127355 − 2.83577i
\(567\) −3.29123e9 −0.00133732
\(568\) 7.87251e12 − 4.05426e11i 3.17355 − 0.163435i
\(569\) 2.93540e12 1.17398 0.586991 − 0.809593i \(-0.300312\pi\)
0.586991 + 0.809593i \(0.300312\pi\)
\(570\) −3.40344e10 + 7.57835e11i −0.0135046 + 0.300703i
\(571\) 3.00273e12 + 2.62341e12i 1.18210 + 1.03277i 0.998763 + 0.0497194i \(0.0158327\pi\)
0.183337 + 0.983050i \(0.441310\pi\)
\(572\) 5.26081e12 + 4.73481e11i 2.05480 + 0.184936i
\(573\) −8.59961e10 − 2.64669e11i −0.0333260 − 0.102567i
\(574\) −3.20570e12 + 3.35290e12i −1.23259 + 1.28919i
\(575\) 1.43676e12 + 3.96520e11i 0.548123 + 0.151272i
\(576\) −6.61834e11 + 4.88585e12i −0.250523 + 1.84944i
\(577\) 4.45792e11 + 3.29097e12i 0.167433 + 1.23604i 0.858334 + 0.513091i \(0.171500\pi\)
−0.690901 + 0.722949i \(0.742786\pi\)
\(578\) −2.93123e12 + 8.08969e11i −1.09238 + 0.301479i
\(579\) −6.30452e10 + 1.17158e11i −0.0233130 + 0.0433229i
\(580\) −6.46535e11 − 6.76222e11i −0.237228 − 0.248121i
\(581\) 5.39928e11 + 1.00335e12i 0.196582 + 0.365310i
\(582\) 1.30196e11 − 4.00702e11i 0.0470375 − 0.144767i
\(583\) −4.86467e10 + 1.13815e11i −0.0174399 + 0.0408027i
\(584\) 1.68812e13 + 3.06349e12i 6.00545 + 1.08983i
\(585\) 1.94233e11 + 1.41119e11i 0.0685681 + 0.0498176i
\(586\) −9.80714e12 + 8.82659e11i −3.43560 + 0.309210i
\(587\) 2.13525e11 + 4.99566e11i 0.0742296 + 0.173669i 0.952533 − 0.304434i \(-0.0984674\pi\)
−0.878304 + 0.478103i \(0.841325\pi\)
\(588\) 1.91784e12 + 8.40262e12i 0.661630 + 2.89879i
\(589\) −2.31702e12 − 3.51013e12i −0.793251 − 1.20172i
\(590\) 7.98542e11 + 4.77107e11i 0.271309 + 0.162099i
\(591\) −7.80161e11 − 9.78291e11i −0.263051 − 0.329856i
\(592\) 6.54566e12 − 5.71877e12i 2.19031 − 1.91362i
\(593\) 2.23840e12 − 1.62630e12i 0.743348 − 0.540074i −0.150410 − 0.988624i \(-0.548059\pi\)
0.893758 + 0.448550i \(0.148059\pi\)
\(594\) 3.94296e12 − 1.89883e12i 1.29952 − 0.625817i
\(595\) 4.74749e11 − 7.19214e11i 0.155288 − 0.235251i
\(596\) −5.81661e12 − 2.18301e12i −1.88826 − 0.708675i
\(597\) 1.99221e11 − 1.19029e11i 0.0641875 − 0.0383502i
\(598\) −3.20900e12 − 1.54537e12i −1.02616 − 0.494172i
\(599\) 2.30227e12 − 4.17800e11i 0.730693 − 0.132601i 0.199555 − 0.979887i \(-0.436050\pi\)
0.531138 + 0.847285i \(0.321765\pi\)
\(600\) −1.36206e12 + 5.96759e12i −0.429058 + 1.87983i
\(601\) −5.21186e12 + 1.95604e12i −1.62951 + 0.611566i −0.987848 − 0.155422i \(-0.950326\pi\)
−0.641662 + 0.766987i \(0.721755\pi\)
\(602\) 5.45552e12 − 6.84100e12i 1.69298 − 2.12293i
\(603\) 9.77400e9 + 2.17635e11i 0.00301054 + 0.0670349i
\(604\) −3.85582e11 − 8.58565e12i −0.117883 − 2.62486i
\(605\) −1.18150e11 + 1.48155e11i −0.0358537 + 0.0449591i
\(606\) −3.27101e12 + 1.22763e12i −0.985271 + 0.369778i
\(607\) −8.72286e10 + 3.82174e11i −0.0260801 + 0.114265i −0.986293 − 0.165006i \(-0.947236\pi\)
0.960212 + 0.279271i \(0.0900927\pi\)
\(608\) −2.13122e13 + 3.86760e12i −6.32503 + 1.14782i
\(609\) −3.06481e12 − 1.47594e12i −0.902871 − 0.434800i
\(610\) 7.96555e11 − 4.75919e11i 0.232933 − 0.139171i
\(611\) −5.96314e12 − 2.23800e12i −1.73097 − 0.649644i
\(612\) 3.96958e12 − 6.01365e12i 1.14383 − 1.73283i
\(613\) −2.08870e11 + 1.00587e11i −0.0597454 + 0.0287718i −0.463518 − 0.886088i \(-0.653413\pi\)
0.403773 + 0.914859i \(0.367699\pi\)
\(614\) −1.65877e12 + 1.20516e12i −0.471007 + 0.342207i
\(615\) 1.22354e11 − 1.06897e11i 0.0344889 − 0.0301320i
\(616\) 8.94792e12 + 1.12203e13i 2.50385 + 3.13973i
\(617\) −3.55873e12 − 2.12624e12i −0.988580 − 0.590649i −0.0749465 − 0.997188i \(-0.523879\pi\)
−0.913634 + 0.406538i \(0.866736\pi\)
\(618\) 2.25037e12 + 3.40916e12i 0.620591 + 0.940155i
\(619\) 6.82036e11 + 2.98819e12i 0.186724 + 0.818089i 0.978329 + 0.207057i \(0.0663885\pi\)
−0.791605 + 0.611033i \(0.790754\pi\)
\(620\) 3.86498e11 + 9.04257e11i 0.105047 + 0.245770i
\(621\) −2.13627e12 + 1.92268e11i −0.576426 + 0.0518793i
\(622\) 3.22510e12 + 2.34317e12i 0.863947 + 0.627694i
\(623\) −5.69511e12 − 1.03351e12i −1.51463 − 0.274864i
\(624\) 3.23299e12 − 7.56397e12i 0.853639 − 1.99719i
\(625\) 1.11635e12 − 3.43578e12i 0.292645 − 0.900668i
\(626\) −1.17828e12 − 2.18961e12i −0.306665 − 0.569880i
\(627\) 2.38016e12 + 2.48945e12i 0.615039 + 0.643280i
\(628\) −5.70808e12 + 1.06074e13i −1.46444 + 2.72138i
\(629\) −4.06194e12 + 1.12103e12i −1.03468 + 0.285553i
\(630\) 1.40283e11 + 1.03561e12i 0.0354791 + 0.261917i
\(631\) −1.72528e11 + 1.27365e12i −0.0433239 + 0.319830i 0.956300 + 0.292389i \(0.0944501\pi\)
−0.999623 + 0.0274411i \(0.991264\pi\)
\(632\) 4.79290e12 + 1.32276e12i 1.19501 + 0.329802i
\(633\) 5.53435e11 − 5.78847e11i 0.137009 − 0.143300i
\(634\) 3.07212e12 + 9.45502e12i 0.755156 + 2.32413i
\(635\) −1.04308e12 − 9.38793e10i −0.254588 − 0.0229133i
\(636\) 3.00578e11 + 2.62607e11i 0.0728450 + 0.0636428i
\(637\) −3.46785e11 + 7.72176e12i −0.0834511 + 1.85818i
\(638\) −5.84403e12 −1.39643
\(639\) 2.47335e12 − 8.21653e11i 0.586856 − 0.194955i
\(640\) 1.36342e12 0.321233
\(641\) 1.65681e10 − 3.68917e11i 0.00387624 − 0.0863112i −0.996122 − 0.0879786i \(-0.971959\pi\)
0.999999 + 0.00166733i \(0.000530727\pi\)
\(642\) −3.70332e12 − 3.23549e12i −0.860366 − 0.751679i
\(643\) −4.10506e12 − 3.69462e11i −0.947045 − 0.0852356i −0.394662 − 0.918826i \(-0.629138\pi\)
−0.552383 + 0.833591i \(0.686281\pi\)
\(644\) −3.48225e12 − 1.07173e13i −0.797762 − 2.45526i
\(645\) −2.11787e11 + 2.21511e11i −0.0481815 + 0.0503939i
\(646\) 1.96830e13 + 5.43217e12i 4.44678 + 1.22723i
\(647\) −7.90396e11 + 5.83493e12i −0.177327 + 1.30908i 0.655351 + 0.755324i \(0.272521\pi\)
−0.832678 + 0.553757i \(0.813194\pi\)
\(648\) 1.52769e9 + 1.12778e10i 0.000340367 + 0.00251269i
\(649\) 4.07118e12 − 1.12357e12i 0.900781 − 0.248600i
\(650\) −4.16760e12 + 7.74469e12i −0.915747 + 1.70174i
\(651\) 2.47095e12 + 2.58441e12i 0.539200 + 0.563959i
\(652\) −8.01826e12 − 1.49004e13i −1.73767 − 3.22912i
\(653\) −1.53537e12 + 4.72538e12i −0.330448 + 1.01701i 0.638473 + 0.769644i \(0.279566\pi\)
−0.968921 + 0.247370i \(0.920434\pi\)
\(654\) −1.01975e12 + 2.38583e12i −0.217969 + 0.509964i
\(655\) −5.18923e11 − 9.41706e10i −0.110158 − 0.0199908i
\(656\) 7.29796e12 + 5.30228e12i 1.53863 + 1.11788i
\(657\) 5.64958e12 − 5.08471e11i 1.18296 − 0.106469i
\(658\) −1.08965e13 − 2.54937e13i −2.26606 − 5.30172i
\(659\) 1.19138e12 + 5.21980e12i 0.246075 + 1.07813i 0.935377 + 0.353652i \(0.115060\pi\)
−0.689302 + 0.724474i \(0.742083\pi\)
\(660\) −4.43637e11 − 6.72081e11i −0.0910081 − 0.137871i
\(661\) −2.85552e9 − 1.70609e9i −0.000581806 − 0.000347613i 0.512608 − 0.858623i \(-0.328679\pi\)
−0.513190 + 0.858275i \(0.671536\pi\)
\(662\) −5.44474e12 − 6.82748e12i −1.10183 − 1.38166i
\(663\) −3.00315e12 + 2.62377e12i −0.603624 + 0.527370i
\(664\) 3.18751e12 − 2.31586e12i 0.636349 − 0.462335i
\(665\) −1.93932e12 + 9.33930e11i −0.384550 + 0.185190i
\(666\) 2.81511e12 − 4.26470e12i 0.554448 − 0.839953i
\(667\) 2.68159e12 + 1.00642e12i 0.524597 + 0.196885i
\(668\) 1.01273e13 − 6.05078e12i 1.96788 − 1.17576i
\(669\) 2.20468e12 + 1.06172e12i 0.425527 + 0.204923i
\(670\) 1.42022e11 − 2.57733e10i 0.0272283 − 0.00494120i
\(671\) 9.37451e11 − 4.10724e12i 0.178524 − 0.782166i
\(672\) 1.72400e13 − 6.47028e12i 3.26119 − 1.22394i
\(673\) −2.44997e12 + 3.07217e12i −0.460356 + 0.577268i −0.956780 − 0.290812i \(-0.906075\pi\)
0.496424 + 0.868080i \(0.334646\pi\)
\(674\) −8.98193e10 − 1.99998e12i −0.0167649 − 0.373299i
\(675\) 2.37619e11 + 5.29100e12i 0.0440569 + 0.981003i
\(676\) 5.16680e11 − 6.47897e11i 0.0951616 − 0.119329i
\(677\) 8.60613e12 − 3.22994e12i 1.57456 − 0.590942i 0.597119 − 0.802153i \(-0.296312\pi\)
0.977441 + 0.211211i \(0.0677406\pi\)
\(678\) 1.32458e12 − 5.80337e12i 0.240738 − 1.05474i
\(679\) 1.17627e12 − 2.13462e11i 0.212370 − 0.0385395i
\(680\) −2.68485e12 − 1.29295e12i −0.481537 − 0.231896i
\(681\) 2.20070e12 − 1.31486e12i 0.392102 − 0.234270i
\(682\) 5.75109e12 + 2.15842e12i 1.01794 + 0.382038i
\(683\) 2.65339e12 − 4.01972e12i 0.466561 − 0.706809i −0.522774 − 0.852472i \(-0.675103\pi\)
0.989334 + 0.145662i \(0.0465312\pi\)
\(684\) −1.62155e13 + 7.80898e12i −2.83256 + 1.36409i
\(685\) 4.10769e11 − 2.98441e11i 0.0712836 − 0.0517906i
\(686\) −1.13305e13 + 9.89916e12i −1.95340 + 1.70663i
\(687\) −1.92150e12 − 2.40948e12i −0.329105 − 0.412685i
\(688\) −1.46069e13 − 8.72723e12i −2.48548 − 1.48501i
\(689\) 1.97198e11 + 2.98742e11i 0.0333362 + 0.0505022i
\(690\) 1.20833e11 + 5.29403e11i 0.0202938 + 0.0889130i
\(691\) −2.09891e12 − 4.91065e12i −0.350222 − 0.819385i −0.998326 − 0.0578335i \(-0.981581\pi\)
0.648104 − 0.761552i \(-0.275562\pi\)
\(692\) 1.51781e12 − 1.36605e11i 0.251616 − 0.0226459i
\(693\) 3.83865e12 + 2.78894e12i 0.632236 + 0.459346i
\(694\) 6.88488e12 + 1.24942e12i 1.12662 + 0.204452i
\(695\) 3.45601e11 − 8.08573e11i 0.0561879 − 0.131458i
\(696\) −3.63490e12 + 1.11871e13i −0.587153 + 1.80707i
\(697\) −2.07233e12 − 3.85103e12i −0.332591 − 0.618058i
\(698\) −9.50954e11 − 9.94620e11i −0.151639 − 0.158602i
\(699\) 9.75402e10 − 1.81260e11i 0.0154538 − 0.0287181i
\(700\) −2.68229e13 + 7.40264e12i −4.22244 + 1.16532i
\(701\) 6.33725e11 + 4.67835e12i 0.0991220 + 0.731748i 0.970494 + 0.241125i \(0.0775164\pi\)
−0.871372 + 0.490623i \(0.836769\pi\)
\(702\) 1.69892e12 − 1.25419e13i 0.264031 − 1.94916i
\(703\) 1.01457e13 + 2.80003e12i 1.56669 + 0.432378i
\(704\) 1.02497e13 − 1.07203e13i 1.57265 − 1.64486i
\(705\) 3.00072e11 + 9.23527e11i 0.0457482 + 0.140799i
\(706\) 1.60308e13 + 1.44279e12i 2.42847 + 0.218566i
\(707\) −7.46556e12 − 6.52246e12i −1.12376 − 0.981803i
\(708\) 6.11018e11 − 1.36054e13i 0.0913912 − 2.03498i
\(709\) 1.05567e13 1.56899 0.784495 − 0.620136i \(-0.212922\pi\)
0.784495 + 0.620136i \(0.212922\pi\)
\(710\) −7.59443e11 − 1.55084e12i −0.112159 − 0.229036i
\(711\) 1.64386e12 0.241242
\(712\) −8.97967e11 + 1.99948e13i −0.130949 + 2.91580i
\(713\) −2.26723e12 − 1.98082e12i −0.328544 − 0.287040i
\(714\) −1.72889e13 − 1.55603e12i −2.48958 − 0.224066i
\(715\) −2.23178e11 − 6.86871e11i −0.0319355 − 0.0982874i
\(716\) −5.46616e12 + 5.71715e12i −0.777273 + 0.812964i
\(717\) −7.45896e12 − 2.05854e12i −1.05400 − 0.290887i
\(718\) 2.79733e12 − 2.06507e13i 0.392811 − 2.89985i
\(719\) 1.95486e11 + 1.44313e12i 0.0272794 + 0.201385i 0.999460 − 0.0328461i \(-0.0104571\pi\)
−0.972181 + 0.234231i \(0.924743\pi\)
\(720\) 1.95904e12 − 5.40660e11i 0.271673 − 0.0749769i
\(721\) −5.49249e12 + 1.02068e13i −0.756939 + 1.40663i
\(722\) −2.55905e13 − 2.67656e13i −3.50479 − 3.66572i
\(723\) 2.47248e11 + 4.59464e11i 0.0336520 + 0.0625358i
\(724\) −5.63531e12 + 1.73437e13i −0.762244 + 2.34595i
\(725\) 2.77968e12 − 6.50339e12i 0.373658 − 0.874216i
\(726\) 3.75573e12 + 6.81564e11i 0.501740 + 0.0910525i
\(727\) 6.92750e12 + 5.03312e12i 0.919754 + 0.668240i 0.943463 − 0.331479i \(-0.107548\pi\)
−0.0237090 + 0.999719i \(0.507548\pi\)
\(728\) 4.13371e13 − 3.72041e12i 5.45442 − 0.490907i
\(729\) −1.84948e12 − 4.32707e12i −0.242536 − 0.567440i
\(730\) −8.36306e11 − 3.66409e12i −0.108996 − 0.477544i
\(731\) 4.54434e12 + 6.88439e12i 0.588631 + 0.891737i
\(732\) −1.16622e13 − 6.96783e12i −1.50134 − 0.897011i
\(733\) 5.25288e11 + 6.58690e11i 0.0672093 + 0.0842779i 0.814300 − 0.580445i \(-0.197121\pi\)
−0.747090 + 0.664722i \(0.768550\pi\)
\(734\) −6.54591e12 + 5.71899e12i −0.832411 + 0.727256i
\(735\) 9.53377e11 − 6.92669e11i 0.120496 − 0.0875453i
\(736\) −1.39693e13 + 6.72728e12i −1.75479 + 0.845063i
\(737\) 3.61027e11 − 5.46933e11i 0.0450750 − 0.0682858i
\(738\) 4.96519e12 + 1.86347e12i 0.616144 + 0.231243i
\(739\) −5.87282e12 + 3.50885e12i −0.724347 + 0.432777i −0.827191 − 0.561920i \(-0.810063\pi\)
0.102844 + 0.994697i \(0.467206\pi\)
\(740\) −2.21717e12 − 1.06773e12i −0.271804 − 0.130894i
\(741\) 9.80059e12 − 1.77855e12i 1.19418 − 0.216712i
\(742\) −3.46722e11 + 1.51909e12i −0.0419918 + 0.183978i
\(743\) −9.15572e12 + 3.43620e12i −1.10216 + 0.413646i −0.835135 − 0.550045i \(-0.814611\pi\)
−0.267021 + 0.963691i \(0.586039\pi\)
\(744\) 7.70891e12 − 9.66666e12i 0.922390 − 1.15664i
\(745\) 3.81115e10 + 8.48617e11i 0.00453265 + 0.100927i
\(746\) −5.59373e11 − 1.24554e13i −0.0661267 − 1.47242i
\(747\) 8.12179e11 − 1.01844e12i 0.0954353 − 0.119672i
\(748\) −2.02937e13 + 7.61636e12i −2.37031 + 0.889591i
\(749\) 3.10495e12 − 1.36037e13i 0.360484 − 1.57938i
\(750\) 2.66247e12 − 4.83167e11i 0.307262 − 0.0557599i
\(751\) 1.54544e13 + 7.44247e12i 1.77286 + 0.853763i 0.964064 + 0.265671i \(0.0855934\pi\)
0.808794 + 0.588093i \(0.200121\pi\)
\(752\) −4.62829e13 + 2.76528e13i −5.27765 + 3.15325i