Properties

Label 27.10.e.a.4.18
Level $27$
Weight $10$
Character 27.4
Analytic conductor $13.906$
Analytic rank $0$
Dimension $156$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,10,Mod(4,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 27.e (of order \(9\), degree \(6\), 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: \(13.9059675764\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(26\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.18
Character \(\chi\) \(=\) 27.4
Dual form 27.10.e.a.7.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(17.4636 + 6.35623i) q^{2} +(-17.1474 + 139.244i) q^{3} +(-127.639 - 107.102i) q^{4} +(280.318 - 1589.76i) q^{5} +(-1184.52 + 2322.71i) q^{6} +(610.601 - 512.355i) q^{7} +(-6305.87 - 10922.1i) q^{8} +(-19094.9 - 4775.35i) q^{9} +(15000.2 - 25981.2i) q^{10} +(-4495.09 - 25492.9i) q^{11} +(17102.0 - 15936.5i) q^{12} +(106141. - 38632.3i) q^{13} +(13919.9 - 5066.44i) q^{14} +(216558. + 66292.8i) q^{15} +(-25886.0 - 146807. i) q^{16} +(64251.1 - 111286. i) q^{17} +(-303113. - 204767. i) q^{18} +(-175832. - 304550. i) q^{19} +(-206046. + 172893. i) q^{20} +(60872.3 + 93808.2i) q^{21} +(83538.4 - 473770. i) q^{22} +(-1965.39 - 1649.15i) q^{23} +(1.62897e6 - 690772. i) q^{24} +(-613422. - 223267. i) q^{25} +2.09916e6 q^{26} +(992367. - 2.57698e6i) q^{27} -132811. q^{28} +(-3.90737e6 - 1.42216e6i) q^{29} +(3.36051e6 + 2.53421e6i) q^{30} +(-4.10711e6 - 3.44627e6i) q^{31} +(-640209. + 3.63081e6i) q^{32} +(3.62682e6 - 188779. i) q^{33} +(1.82942e6 - 1.53506e6i) q^{34} +(-643359. - 1.11433e6i) q^{35} +(1.92581e6 + 2.65463e6i) q^{36} +(1.52669e6 - 2.64430e6i) q^{37} +(-1.13487e6 - 6.43617e6i) q^{38} +(3.55928e6 + 1.54420e7i) q^{39} +(-1.91312e7 + 6.96317e6i) q^{40} +(-2.20476e7 + 8.02467e6i) q^{41} +(466783. + 2.02515e6i) q^{42} +(3.33783e6 + 1.89298e7i) q^{43} +(-2.15659e6 + 3.73533e6i) q^{44} +(-1.29443e7 + 2.90178e7i) q^{45} +(-23840.3 - 41292.6i) q^{46} +(1.67023e7 - 1.40149e7i) q^{47} +(2.08859e7 - 1.08713e6i) q^{48} +(-6.89700e6 + 3.91149e7i) q^{49} +(-9.29341e6 - 7.79810e6i) q^{50} +(1.43942e7 + 1.08549e7i) q^{51} +(-1.76854e7 - 6.43695e6i) q^{52} +8.11126e7 q^{53} +(3.37102e7 - 3.86956e7i) q^{54} -4.17877e7 q^{55} +(-9.44636e6 - 3.43819e6i) q^{56} +(4.54219e7 - 1.92614e7i) q^{57} +(-5.91971e7 - 4.96722e7i) q^{58} +(3.01060e7 - 1.70740e8i) q^{59} +(-2.05412e7 - 3.16554e7i) q^{60} +(-7.48377e7 + 6.27963e7i) q^{61} +(-4.98196e7 - 8.62901e7i) q^{62} +(-1.41061e7 + 6.86755e6i) q^{63} +(-7.24209e7 + 1.25437e8i) q^{64} +(-3.16628e7 - 1.79568e8i) q^{65} +(6.45373e7 + 1.97562e7i) q^{66} +(2.17705e8 - 7.92381e7i) q^{67} +(-2.01199e7 + 7.32305e6i) q^{68} +(263337. - 245390. i) q^{69} +(-4.15242e6 - 2.35496e7i) q^{70} +(1.41531e8 - 2.45140e8i) q^{71} +(6.82535e7 + 2.38669e8i) q^{72} +(2.29279e8 + 3.97123e8i) q^{73} +(4.34693e7 - 3.64750e7i) q^{74} +(4.16073e7 - 8.15870e7i) q^{75} +(-1.01749e7 + 5.77045e7i) q^{76} +(-1.58061e7 - 1.32629e7i) q^{77} +(-3.59951e7 + 2.92297e8i) q^{78} +(-5.29687e8 - 1.92790e8i) q^{79} -2.40644e8 q^{80} +(3.41813e8 + 1.82370e8i) q^{81} -4.36037e8 q^{82} +(6.29101e7 + 2.28974e7i) q^{83} +(2.27736e6 - 1.84931e7i) q^{84} +(-1.58908e8 - 1.33339e8i) q^{85} +(-6.20314e7 + 3.51798e8i) q^{86} +(2.65029e8 - 5.19692e8i) q^{87} +(-2.50091e8 + 2.09851e8i) q^{88} +(2.71094e8 + 4.69549e8i) q^{89} +(-4.10498e8 + 4.24477e8i) q^{90} +(4.50165e7 - 7.79709e7i) q^{91} +(74232.5 + 420994. i) q^{92} +(5.50300e8 - 5.12797e8i) q^{93} +(3.80764e8 - 1.38587e8i) q^{94} +(-5.33450e8 + 1.94160e8i) q^{95} +(-4.94591e8 - 1.51404e8i) q^{96} +(1.23991e7 + 7.03187e7i) q^{97} +(-3.69070e8 + 6.39247e8i) q^{98} +(-3.59041e7 + 5.08251e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 17.4636 + 6.35623i 0.771789 + 0.280908i 0.697745 0.716347i \(-0.254187\pi\)
0.0740446 + 0.997255i \(0.476409\pi\)
\(3\) −17.1474 + 139.244i −0.122223 + 0.992503i
\(4\) −127.639 107.102i −0.249295 0.209184i
\(5\) 280.318 1589.76i 0.200579 1.13754i −0.703668 0.710529i \(-0.748456\pi\)
0.904247 0.427010i \(-0.140433\pi\)
\(6\) −1184.52 + 2322.71i −0.373132 + 0.731670i
\(7\) 610.601 512.355i 0.0961205 0.0806547i −0.593461 0.804863i \(-0.702239\pi\)
0.689582 + 0.724208i \(0.257794\pi\)
\(8\) −6305.87 10922.1i −0.544302 0.942760i
\(9\) −19094.9 4775.35i −0.970123 0.242613i
\(10\) 15000.2 25981.2i 0.474349 0.821597i
\(11\) −4495.09 25492.9i −0.0925702 0.524992i −0.995465 0.0951300i \(-0.969673\pi\)
0.902895 0.429862i \(-0.141438\pi\)
\(12\) 17102.0 15936.5i 0.238085 0.221859i
\(13\) 106141. 38632.3i 1.03072 0.375150i 0.229363 0.973341i \(-0.426336\pi\)
0.801354 + 0.598191i \(0.204114\pi\)
\(14\) 13919.9 5066.44i 0.0968414 0.0352474i
\(15\) 216558. + 66292.8i 1.10450 + 0.338108i
\(16\) −25886.0 146807.i −0.0987472 0.560023i
\(17\) 64251.1 111286.i 0.186578 0.323162i −0.757529 0.652801i \(-0.773594\pi\)
0.944107 + 0.329639i \(0.106927\pi\)
\(18\) −303113. 204767.i −0.680579 0.459762i
\(19\) −175832. 304550.i −0.309533 0.536127i 0.668727 0.743508i \(-0.266839\pi\)
−0.978260 + 0.207381i \(0.933506\pi\)
\(20\) −206046. + 172893.i −0.287958 + 0.241625i
\(21\) 60872.3 + 93808.2i 0.0683019 + 0.105258i
\(22\) 83538.4 473770.i 0.0760299 0.431187i
\(23\) −1965.39 1649.15i −0.00146444 0.00122881i 0.642055 0.766659i \(-0.278082\pi\)
−0.643520 + 0.765430i \(0.722526\pi\)
\(24\) 1.62897e6 690772.i 1.00222 0.424995i
\(25\) −613422. 223267.i −0.314072 0.114313i
\(26\) 2.09916e6 0.900879
\(27\) 992367. 2.57698e6i 0.359365 0.933197i
\(28\) −132811. −0.0408340
\(29\) −3.90737e6 1.42216e6i −1.02587 0.373387i −0.226364 0.974043i \(-0.572684\pi\)
−0.799508 + 0.600656i \(0.794906\pi\)
\(30\) 3.36051e6 + 2.53421e6i 0.757461 + 0.571210i
\(31\) −4.10711e6 3.44627e6i −0.798746 0.670227i 0.149147 0.988815i \(-0.452347\pi\)
−0.947893 + 0.318588i \(0.896792\pi\)
\(32\) −640209. + 3.63081e6i −0.107931 + 0.612108i
\(33\) 3.62682e6 188779.i 0.532370 0.0277103i
\(34\) 1.82942e6 1.53506e6i 0.234778 0.197002i
\(35\) −643359. 1.11433e6i −0.0724682 0.125519i
\(36\) 1.92581e6 + 2.65463e6i 0.191097 + 0.263416i
\(37\) 1.52669e6 2.64430e6i 0.133919 0.231955i −0.791265 0.611474i \(-0.790577\pi\)
0.925184 + 0.379519i \(0.123910\pi\)
\(38\) −1.13487e6 6.43617e6i −0.0882917 0.500727i
\(39\) 3.55928e6 + 1.54420e7i 0.246361 + 1.06884i
\(40\) −1.91312e7 + 6.96317e6i −1.18160 + 0.430068i
\(41\) −2.20476e7 + 8.02467e6i −1.21852 + 0.443507i −0.869653 0.493664i \(-0.835657\pi\)
−0.348872 + 0.937171i \(0.613435\pi\)
\(42\) 466783. + 2.02515e6i 0.0231469 + 0.100423i
\(43\) 3.33783e6 + 1.89298e7i 0.148887 + 0.844379i 0.964164 + 0.265308i \(0.0854735\pi\)
−0.815277 + 0.579071i \(0.803415\pi\)
\(44\) −2.15659e6 + 3.73533e6i −0.0867424 + 0.150242i
\(45\) −1.29443e7 + 2.90178e7i −0.470568 + 1.05489i
\(46\) −23840.3 41292.6i −0.000785058 0.00135976i
\(47\) 1.67023e7 1.40149e7i 0.499270 0.418937i −0.358065 0.933697i \(-0.616563\pi\)
0.857335 + 0.514760i \(0.172119\pi\)
\(48\) 2.08859e7 1.08713e6i 0.567893 0.0295593i
\(49\) −6.89700e6 + 3.91149e7i −0.170914 + 0.969303i
\(50\) −9.29341e6 7.79810e6i −0.210286 0.176451i
\(51\) 1.43942e7 + 1.08549e7i 0.297936 + 0.224677i
\(52\) −1.76854e7 6.43695e6i −0.335428 0.122086i
\(53\) 8.11126e7 1.41204 0.706020 0.708192i \(-0.250489\pi\)
0.706020 + 0.708192i \(0.250489\pi\)
\(54\) 3.37102e7 3.86956e7i 0.539497 0.619283i
\(55\) −4.17877e7 −0.615767
\(56\) −9.44636e6 3.43819e6i −0.128357 0.0467180i
\(57\) 4.54219e7 1.92614e7i 0.569939 0.241685i
\(58\) −5.91971e7 4.96722e7i −0.686869 0.576352i
\(59\) 3.01060e7 1.70740e8i 0.323459 1.83443i −0.196832 0.980437i \(-0.563065\pi\)
0.520291 0.853989i \(-0.325823\pi\)
\(60\) −2.05412e7 3.16554e7i −0.204619 0.315331i
\(61\) −7.48377e7 + 6.27963e7i −0.692048 + 0.580697i −0.919499 0.393092i \(-0.871405\pi\)
0.227451 + 0.973790i \(0.426961\pi\)
\(62\) −4.98196e7 8.62901e7i −0.428191 0.741649i
\(63\) −1.41061e7 + 6.86755e6i −0.112817 + 0.0549249i
\(64\) −7.24209e7 + 1.25437e8i −0.539577 + 0.934576i
\(65\) −3.16628e7 1.79568e8i −0.220008 1.24773i
\(66\) 6.45373e7 + 1.97562e7i 0.418662 + 0.128161i
\(67\) 2.17705e8 7.92381e7i 1.31987 0.480394i 0.416454 0.909157i \(-0.363273\pi\)
0.903417 + 0.428763i \(0.141051\pi\)
\(68\) −2.01199e7 + 7.32305e6i −0.114113 + 0.0415338i
\(69\) 263337. 245390.i 0.00139859 0.00130328i
\(70\) −4.15242e6 2.35496e7i −0.0206709 0.117231i
\(71\) 1.41531e8 2.45140e8i 0.660983 1.14486i −0.319375 0.947629i \(-0.603473\pi\)
0.980358 0.197228i \(-0.0631938\pi\)
\(72\) 6.82535e7 + 2.38669e8i 0.299315 + 1.04665i
\(73\) 2.29279e8 + 3.97123e8i 0.944957 + 1.63671i 0.755837 + 0.654759i \(0.227230\pi\)
0.189119 + 0.981954i \(0.439437\pi\)
\(74\) 4.34693e7 3.64750e7i 0.168515 0.141401i
\(75\) 4.16073e7 8.15870e7i 0.151843 0.297746i
\(76\) −1.01749e7 + 5.77045e7i −0.0349838 + 0.198403i
\(77\) −1.58061e7 1.32629e7i −0.0512410 0.0429963i
\(78\) −3.59951e7 + 2.92297e8i −0.110108 + 0.894125i
\(79\) −5.29687e8 1.92790e8i −1.53002 0.556882i −0.566394 0.824134i \(-0.691662\pi\)
−0.963627 + 0.267252i \(0.913884\pi\)
\(80\) −2.40644e8 −0.656855
\(81\) 3.41813e8 + 1.82370e8i 0.882278 + 0.470728i
\(82\) −4.36037e8 −1.06503
\(83\) 6.29101e7 + 2.28974e7i 0.145502 + 0.0529584i 0.413745 0.910393i \(-0.364221\pi\)
−0.268243 + 0.963351i \(0.586443\pi\)
\(84\) 2.27736e6 1.84931e7i 0.00499085 0.0405279i
\(85\) −1.58908e8 1.33339e8i −0.330187 0.277059i
\(86\) −6.20314e7 + 3.51798e8i −0.122284 + 0.693506i
\(87\) 2.65029e8 5.19692e8i 0.495972 0.972544i
\(88\) −2.50091e8 + 2.09851e8i −0.444555 + 0.373026i
\(89\) 2.71094e8 + 4.69549e8i 0.458000 + 0.793279i 0.998855 0.0478365i \(-0.0152326\pi\)
−0.540855 + 0.841116i \(0.681899\pi\)
\(90\) −4.10498e8 + 4.24477e8i −0.659507 + 0.681967i
\(91\) 4.50165e7 7.79709e7i 0.0688154 0.119192i
\(92\) 74232.5 + 420994.i 0.000108031 + 0.000612675i
\(93\) 5.50300e8 5.12797e8i 0.762827 0.710841i
\(94\) 3.80764e8 1.38587e8i 0.503014 0.183082i
\(95\) −5.33450e8 + 1.94160e8i −0.671951 + 0.244570i
\(96\) −4.94591e8 1.51404e8i −0.594327 0.181935i
\(97\) 1.23991e7 + 7.03187e7i 0.0142206 + 0.0806488i 0.991092 0.133178i \(-0.0425182\pi\)
−0.976872 + 0.213827i \(0.931407\pi\)
\(98\) −3.69070e8 + 6.39247e8i −0.404195 + 0.700086i
\(99\) −3.59041e7 + 5.08251e8i −0.0375652 + 0.531766i
\(100\) 5.43843e7 + 9.41964e7i 0.0543843 + 0.0941964i
\(101\) 1.11072e8 9.32004e7i 0.106208 0.0891192i −0.588137 0.808761i \(-0.700138\pi\)
0.694345 + 0.719642i \(0.255694\pi\)
\(102\) 1.82379e8 + 2.81058e8i 0.166830 + 0.257096i
\(103\) 2.46300e8 1.39683e9i 0.215624 1.22286i −0.664198 0.747557i \(-0.731227\pi\)
0.879821 0.475305i \(-0.157662\pi\)
\(104\) −1.09126e9 9.15675e8i −0.914698 0.767523i
\(105\) 1.66196e8 7.04762e7i 0.133435 0.0565836i
\(106\) 1.41652e9 + 5.15571e8i 1.08980 + 0.396654i
\(107\) 2.27609e9 1.67866 0.839328 0.543625i \(-0.182949\pi\)
0.839328 + 0.543625i \(0.182949\pi\)
\(108\) −4.02664e8 + 2.22639e8i −0.284797 + 0.157468i
\(109\) −7.56560e8 −0.513362 −0.256681 0.966496i \(-0.582629\pi\)
−0.256681 + 0.966496i \(0.582629\pi\)
\(110\) −7.29763e8 2.65612e8i −0.475242 0.172974i
\(111\) 3.42025e8 + 2.57925e8i 0.213848 + 0.161265i
\(112\) −9.10231e7 7.63774e7i −0.0546601 0.0458653i
\(113\) −3.43870e8 + 1.95018e9i −0.198400 + 1.12518i 0.709093 + 0.705115i \(0.249105\pi\)
−0.907493 + 0.420067i \(0.862007\pi\)
\(114\) 9.15660e8 4.76608e7i 0.507764 0.0264295i
\(115\) −3.17269e6 + 2.66221e6i −0.00169156 + 0.00141939i
\(116\) 3.46416e8 + 6.00011e8i 0.177639 + 0.307679i
\(117\) −2.21124e9 + 2.30819e8i −1.09094 + 0.113877i
\(118\) 1.61102e9 2.79037e9i 0.764948 1.32493i
\(119\) −1.77862e7 1.00871e8i −0.00813060 0.0461109i
\(120\) −6.41533e8 2.78330e9i −0.282425 1.22531i
\(121\) 1.58606e9 5.77280e8i 0.672645 0.244823i
\(122\) −1.70608e9 + 6.20964e8i −0.697238 + 0.253774i
\(123\) −7.39331e8 3.20761e9i −0.291250 1.26360i
\(124\) 1.55125e8 + 8.79759e8i 0.0589230 + 0.334169i
\(125\) 1.04956e9 1.81788e9i 0.384512 0.665995i
\(126\) −2.89994e8 + 3.02709e7i −0.102500 + 0.0106994i
\(127\) 1.94110e9 + 3.36209e9i 0.662112 + 1.14681i 0.980060 + 0.198703i \(0.0636731\pi\)
−0.317948 + 0.948108i \(0.602994\pi\)
\(128\) −6.16009e8 + 5.16893e8i −0.202835 + 0.170198i
\(129\) −2.69310e9 + 1.40178e8i −0.856245 + 0.0445683i
\(130\) 5.88433e8 3.33717e9i 0.180697 1.02479i
\(131\) 8.75614e8 + 7.34727e8i 0.259772 + 0.217974i 0.763366 0.645966i \(-0.223545\pi\)
−0.503595 + 0.863940i \(0.667990\pi\)
\(132\) −4.83143e8 3.64344e8i −0.138514 0.104455i
\(133\) −2.63401e8 9.58701e7i −0.0729936 0.0265675i
\(134\) 4.30556e9 1.15361
\(135\) −3.81860e9 2.30000e9i −0.989468 0.595971i
\(136\) −1.62064e9 −0.406219
\(137\) 2.92900e9 + 1.06607e9i 0.710356 + 0.258549i 0.671826 0.740709i \(-0.265510\pi\)
0.0385301 + 0.999257i \(0.487732\pi\)
\(138\) 6.15856e6 2.61157e6i 0.00144552 0.000612978i
\(139\) 1.22616e9 + 1.02887e9i 0.278599 + 0.233772i 0.771370 0.636387i \(-0.219572\pi\)
−0.492771 + 0.870159i \(0.664016\pi\)
\(140\) −3.72292e7 + 2.11137e8i −0.00819045 + 0.0464503i
\(141\) 1.66509e9 + 2.56601e9i 0.354774 + 0.546730i
\(142\) 4.02981e9 3.38141e9i 0.831739 0.697912i
\(143\) −1.46196e9 2.53220e9i −0.292364 0.506390i
\(144\) −2.06762e8 + 2.92688e9i −0.0400718 + 0.567249i
\(145\) −3.35620e9 + 5.81312e9i −0.630511 + 1.09208i
\(146\) 1.47983e9 + 8.39256e9i 0.269541 + 1.52864i
\(147\) −5.32825e9 1.63109e9i −0.941146 0.288104i
\(148\) −4.78075e8 + 1.74005e8i −0.0819065 + 0.0298115i
\(149\) −4.49393e8 + 1.63566e8i −0.0746945 + 0.0271866i −0.379097 0.925357i \(-0.623765\pi\)
0.304403 + 0.952543i \(0.401543\pi\)
\(150\) 1.24520e9 1.16034e9i 0.200830 0.187143i
\(151\) 1.20387e9 + 6.82747e9i 0.188444 + 1.06872i 0.921450 + 0.388497i \(0.127006\pi\)
−0.733006 + 0.680222i \(0.761883\pi\)
\(152\) −2.21755e9 + 3.84091e9i −0.336959 + 0.583630i
\(153\) −1.75830e9 + 1.81818e9i −0.259407 + 0.268241i
\(154\) −1.91730e8 3.32086e8i −0.0274692 0.0475781i
\(155\) −6.63004e9 + 5.56327e9i −0.922622 + 0.774172i
\(156\) 1.19957e9 2.35221e9i 0.162167 0.317992i
\(157\) 1.25829e9 7.13614e9i 0.165285 0.937379i −0.783485 0.621411i \(-0.786560\pi\)
0.948770 0.315968i \(-0.102329\pi\)
\(158\) −8.02482e9 6.73362e9i −1.02442 0.859591i
\(159\) −1.39087e9 + 1.12945e10i −0.172583 + 1.40145i
\(160\) 5.59265e9 + 2.03556e9i 0.674648 + 0.245552i
\(161\) −2.04502e6 −0.000239873
\(162\) 4.81009e9 + 5.35747e9i 0.548701 + 0.611142i
\(163\) −1.48150e10 −1.64383 −0.821915 0.569610i \(-0.807094\pi\)
−0.821915 + 0.569610i \(0.807094\pi\)
\(164\) 3.67360e9 + 1.33708e9i 0.396547 + 0.144331i
\(165\) 7.16549e8 5.81870e9i 0.0752607 0.611150i
\(166\) 9.53096e8 + 7.99743e8i 0.0974205 + 0.0817455i
\(167\) 3.07828e9 1.74578e10i 0.306256 1.73686i −0.311278 0.950319i \(-0.600757\pi\)
0.617534 0.786544i \(-0.288132\pi\)
\(168\) 6.40729e8 1.25640e9i 0.0620558 0.121684i
\(169\) 1.65000e9 1.38451e9i 0.155594 0.130559i
\(170\) −1.92756e9 3.33864e9i −0.177006 0.306584i
\(171\) 1.90317e9 + 6.65502e9i 0.170214 + 0.595206i
\(172\) 1.60138e9 2.77367e9i 0.139513 0.241644i
\(173\) 2.08583e9 + 1.18294e10i 0.177040 + 1.00405i 0.935762 + 0.352631i \(0.114713\pi\)
−0.758722 + 0.651414i \(0.774176\pi\)
\(174\) 7.93165e9 7.39110e9i 0.655982 0.611276i
\(175\) −4.88948e8 + 1.77962e8i −0.0394086 + 0.0143436i
\(176\) −3.62617e9 + 1.31982e9i −0.284867 + 0.103683i
\(177\) 2.32583e10 + 7.11982e9i 1.78114 + 0.545242i
\(178\) 1.74972e9 + 9.92316e9i 0.130641 + 0.740900i
\(179\) 1.07814e10 1.86739e10i 0.784939 1.35955i −0.144097 0.989564i \(-0.546028\pi\)
0.929036 0.369990i \(-0.120639\pi\)
\(180\) 4.76006e9 2.31744e9i 0.337976 0.164544i
\(181\) −1.09960e10 1.90457e10i −0.761522 1.31900i −0.942066 0.335428i \(-0.891119\pi\)
0.180543 0.983567i \(-0.442214\pi\)
\(182\) 1.28175e9 1.07552e9i 0.0865929 0.0726601i
\(183\) −7.46075e9 1.14975e10i −0.491760 0.757834i
\(184\) −5.61875e6 + 3.18655e7i −0.000361376 + 0.00204946i
\(185\) −3.77585e9 3.16831e9i −0.236996 0.198864i
\(186\) 1.28697e10 5.45745e9i 0.788423 0.334335i
\(187\) −3.12582e9 1.13771e9i −0.186929 0.0680367i
\(188\) −3.63289e9 −0.212100
\(189\) −7.14386e8 2.08195e9i −0.0407244 0.118684i
\(190\) −1.05501e10 −0.587307
\(191\) 4.20187e9 + 1.52936e9i 0.228451 + 0.0831493i 0.453709 0.891150i \(-0.350100\pi\)
−0.225259 + 0.974299i \(0.572323\pi\)
\(192\) −1.62245e10 1.22351e10i −0.861620 0.649758i
\(193\) −2.16606e10 1.81754e10i −1.12373 0.942921i −0.124943 0.992164i \(-0.539875\pi\)
−0.998787 + 0.0492430i \(0.984319\pi\)
\(194\) −2.30429e8 + 1.30683e9i −0.0116797 + 0.0662386i
\(195\) 2.55468e10 1.32973e9i 1.26526 0.0658580i
\(196\) 5.06961e9 4.25391e9i 0.245370 0.205890i
\(197\) −8.39382e9 1.45385e10i −0.397065 0.687737i 0.596297 0.802764i \(-0.296638\pi\)
−0.993362 + 0.115027i \(0.963305\pi\)
\(198\) −3.85758e9 + 8.64768e9i −0.178370 + 0.399859i
\(199\) −1.43606e10 + 2.48733e10i −0.649134 + 1.12433i 0.334196 + 0.942504i \(0.391535\pi\)
−0.983330 + 0.181830i \(0.941798\pi\)
\(200\) 1.42961e9 + 8.10775e9i 0.0631806 + 0.358315i
\(201\) 7.30038e9 + 3.16729e10i 0.315474 + 1.36869i
\(202\) 2.53212e9 9.21615e8i 0.107005 0.0389465i
\(203\) −3.11449e9 + 1.13358e9i −0.128723 + 0.0468512i
\(204\) −6.74689e8 2.92716e9i −0.0272752 0.118334i
\(205\) 6.57697e9 + 3.72999e10i 0.260096 + 1.47508i
\(206\) 1.31799e10 2.28282e10i 0.509928 0.883221i
\(207\) 2.96536e7 + 4.08759e7i 0.00112256 + 0.00154739i
\(208\) −8.41904e9 1.45822e10i −0.311873 0.540180i
\(209\) −6.97349e9 + 5.85145e9i −0.252809 + 0.212132i
\(210\) 3.35034e9 1.74388e8i 0.118878 0.00618771i
\(211\) −1.83777e9 + 1.04225e10i −0.0638294 + 0.361995i 0.936117 + 0.351687i \(0.114392\pi\)
−0.999947 + 0.0103071i \(0.996719\pi\)
\(212\) −1.03532e10 8.68732e9i −0.352015 0.295376i
\(213\) 3.17074e10 + 2.39109e10i 1.05549 + 0.795955i
\(214\) 3.97487e10 + 1.44673e10i 1.29557 + 0.471548i
\(215\) 3.10294e10 0.990378
\(216\) −3.44037e10 + 5.41135e9i −1.07538 + 0.169147i
\(217\) −4.27352e9 −0.130833
\(218\) −1.32123e10 4.80887e9i −0.396208 0.144208i
\(219\) −5.92287e10 + 2.51162e10i −1.73994 + 0.737829i
\(220\) 5.33375e9 + 4.47555e9i 0.153508 + 0.128808i
\(221\) 2.52046e9 1.42942e10i 0.0710745 0.403084i
\(222\) 4.33356e9 + 6.67830e9i 0.119745 + 0.184534i
\(223\) 4.93800e9 4.14348e9i 0.133715 0.112200i −0.573477 0.819221i \(-0.694406\pi\)
0.707192 + 0.707021i \(0.249962\pi\)
\(224\) 1.46935e9 + 2.54499e9i 0.0389950 + 0.0675413i
\(225\) 1.06471e10 + 7.19258e9i 0.276955 + 0.187095i
\(226\) −1.84010e10 + 3.18715e10i −0.469196 + 0.812671i
\(227\) 5.28046e8 + 2.99470e9i 0.0131994 + 0.0748578i 0.990696 0.136094i \(-0.0434549\pi\)
−0.977497 + 0.210952i \(0.932344\pi\)
\(228\) −7.86055e9 2.40627e9i −0.192640 0.0589709i
\(229\) 1.65307e10 6.01668e9i 0.397220 0.144576i −0.135684 0.990752i \(-0.543323\pi\)
0.532904 + 0.846176i \(0.321101\pi\)
\(230\) −7.23282e7 + 2.63253e7i −0.00170425 + 0.000620295i
\(231\) 2.11782e9 1.97349e9i 0.0489367 0.0456017i
\(232\) 9.10634e9 + 5.16446e10i 0.206371 + 1.17039i
\(233\) 2.16335e9 3.74704e9i 0.0480868 0.0832887i −0.840980 0.541066i \(-0.818021\pi\)
0.889067 + 0.457777i \(0.151354\pi\)
\(234\) −4.00834e10 1.00242e10i −0.873963 0.218565i
\(235\) −1.75983e10 3.04812e10i −0.376415 0.651969i
\(236\) −2.21293e10 + 1.85687e10i −0.464369 + 0.389651i
\(237\) 3.59277e10 7.04500e10i 0.739710 1.45049i
\(238\) 3.30546e8 1.87462e9i 0.00667783 0.0378719i
\(239\) −5.29871e10 4.44615e10i −1.05046 0.881442i −0.0573191 0.998356i \(-0.518255\pi\)
−0.993142 + 0.116914i \(0.962700\pi\)
\(240\) 4.12641e9 3.35083e10i 0.0802826 0.651930i
\(241\) −3.12649e10 1.13795e10i −0.597007 0.217293i 0.0258013 0.999667i \(-0.491786\pi\)
−0.622809 + 0.782374i \(0.714008\pi\)
\(242\) 3.13677e10 0.587913
\(243\) −3.12551e10 + 4.44683e10i −0.575034 + 0.818130i
\(244\) 1.62778e10 0.293997
\(245\) 6.02499e10 + 2.19292e10i 1.06834 + 0.388843i
\(246\) 7.47689e9 6.07157e10i 0.130171 1.05704i
\(247\) −3.04285e10 2.55325e10i −0.520169 0.436473i
\(248\) −1.17416e10 + 6.65900e10i −0.197104 + 1.11783i
\(249\) −4.26708e9 + 8.36725e9i −0.0703450 + 0.137939i
\(250\) 2.98839e10 2.50756e10i 0.483846 0.405995i
\(251\) 1.43058e10 + 2.47784e10i 0.227500 + 0.394042i 0.957067 0.289868i \(-0.0936114\pi\)
−0.729566 + 0.683910i \(0.760278\pi\)
\(252\) 2.53601e9 + 6.34218e8i 0.0396140 + 0.00990686i
\(253\) −3.32072e7 + 5.75166e7i −0.000509554 + 0.000882573i
\(254\) 1.25284e10 + 7.10522e10i 0.188862 + 1.07109i
\(255\) 2.12916e10 1.98405e10i 0.315338 0.293848i
\(256\) 5.56434e10 2.02525e10i 0.809718 0.294713i
\(257\) 1.28810e10 4.68831e9i 0.184184 0.0670374i −0.248282 0.968688i \(-0.579866\pi\)
0.432466 + 0.901650i \(0.357644\pi\)
\(258\) −4.79222e10 1.46699e10i −0.673361 0.206129i
\(259\) −4.22624e8 2.39682e9i −0.00583586 0.0330968i
\(260\) −1.51907e10 + 2.63111e10i −0.206157 + 0.357075i
\(261\) 6.78196e10 + 4.58152e10i 0.904634 + 0.611121i
\(262\) 1.06213e10 + 1.83966e10i 0.139258 + 0.241202i
\(263\) 1.54430e10 1.29582e10i 0.199036 0.167011i −0.537822 0.843058i \(-0.680753\pi\)
0.736858 + 0.676047i \(0.236308\pi\)
\(264\) −2.49322e10 3.84221e10i −0.315895 0.486814i
\(265\) 2.27373e10 1.28950e11i 0.283226 1.60625i
\(266\) −3.99055e9 3.34847e9i −0.0488726 0.0410090i
\(267\) −7.00306e10 + 2.96968e10i −0.843310 + 0.357609i
\(268\) −3.62742e10 1.32027e10i −0.429528 0.156335i
\(269\) −1.53806e10 −0.179096 −0.0895481 0.995982i \(-0.528542\pi\)
−0.0895481 + 0.995982i \(0.528542\pi\)
\(270\) −5.20671e10 6.44381e10i −0.596247 0.737914i
\(271\) 5.60281e10 0.631022 0.315511 0.948922i \(-0.397824\pi\)
0.315511 + 0.948922i \(0.397824\pi\)
\(272\) −1.80007e10 6.55174e9i −0.199402 0.0725766i
\(273\) 1.00851e10 + 7.60529e9i 0.109887 + 0.0828674i
\(274\) 4.43746e10 + 3.72347e10i 0.475617 + 0.399090i
\(275\) −2.93435e9 + 1.66415e10i −0.0309396 + 0.175467i
\(276\) −5.98938e7 + 3.11752e6i −0.000621286 + 3.23384e-5i
\(277\) 1.30917e11 1.09852e11i 1.33609 1.12111i 0.353478 0.935443i \(-0.384999\pi\)
0.982612 0.185670i \(-0.0594456\pi\)
\(278\) 1.48734e10 + 2.57615e10i 0.149351 + 0.258684i
\(279\) 6.19678e10 + 8.54193e10i 0.612276 + 0.843989i
\(280\) −8.11388e9 + 1.40537e10i −0.0788892 + 0.136640i
\(281\) −9.07283e9 5.14545e10i −0.0868089 0.492318i −0.996952 0.0780227i \(-0.975139\pi\)
0.910143 0.414295i \(-0.135972\pi\)
\(282\) 1.27683e10 + 5.53955e10i 0.120230 + 0.521620i
\(283\) 6.89819e10 2.51073e10i 0.639287 0.232681i −0.00198143 0.999998i \(-0.500631\pi\)
0.641268 + 0.767317i \(0.278408\pi\)
\(284\) −4.43199e10 + 1.61311e10i −0.404265 + 0.147140i
\(285\) −1.78884e10 7.76092e10i −0.160609 0.696805i
\(286\) −9.43593e9 5.35138e10i −0.0833946 0.472954i
\(287\) −9.35081e9 + 1.61961e10i −0.0813543 + 0.140910i
\(288\) 2.95631e10 6.62728e10i 0.253212 0.567635i
\(289\) 5.10375e10 + 8.83996e10i 0.430377 + 0.745435i
\(290\) −9.55609e10 + 8.01851e10i −0.793395 + 0.665737i
\(291\) −1.00041e10 + 5.20721e8i −0.0817823 + 0.00425683i
\(292\) 1.32677e10 7.52448e10i 0.106800 0.605694i
\(293\) −1.75418e10 1.47193e10i −0.139050 0.116676i 0.570610 0.821221i \(-0.306707\pi\)
−0.709660 + 0.704545i \(0.751151\pi\)
\(294\) −8.26829e10 6.23522e10i −0.645436 0.486731i
\(295\) −2.62996e11 9.57226e10i −2.02185 0.735894i
\(296\) −3.85084e10 −0.291570
\(297\) −7.01554e10 1.37146e10i −0.523188 0.102277i
\(298\) −8.88769e9 −0.0652853
\(299\) −2.72319e8 9.91161e7i −0.00197042 0.000717173i
\(300\) −1.40489e10 + 5.95748e9i −0.100137 + 0.0424636i
\(301\) 1.17368e10 + 9.84838e9i 0.0824142 + 0.0691537i
\(302\) −2.23731e10 + 1.26884e11i −0.154773 + 0.877761i
\(303\) 1.10730e10 + 1.70643e10i 0.0754700 + 0.116304i
\(304\) −4.01584e10 + 3.36969e10i −0.269678 + 0.226287i
\(305\) 7.88527e10 + 1.36577e11i 0.521756 + 0.903708i
\(306\) −4.22630e10 + 2.05758e10i −0.275559 + 0.134156i
\(307\) −2.68079e9 + 4.64326e9i −0.0172242 + 0.0298333i −0.874509 0.485009i \(-0.838816\pi\)
0.857285 + 0.514842i \(0.172150\pi\)
\(308\) 5.96997e8 + 3.38574e9i 0.00378002 + 0.0214375i
\(309\) 1.90278e11 + 5.82478e10i 1.18734 + 0.363468i
\(310\) −1.51146e11 + 5.50126e10i −0.929541 + 0.338325i
\(311\) 6.13619e9 2.23339e9i 0.0371944 0.0135376i −0.323356 0.946277i \(-0.604811\pi\)
0.360550 + 0.932740i \(0.382589\pi\)
\(312\) 1.46215e11 1.36250e11i 0.873565 0.814031i
\(313\) 4.11967e10 + 2.33638e11i 0.242612 + 1.37592i 0.825973 + 0.563709i \(0.190626\pi\)
−0.583361 + 0.812213i \(0.698263\pi\)
\(314\) 6.73333e10 1.16625e11i 0.390883 0.677029i
\(315\) 6.96359e9 + 2.43503e10i 0.0398507 + 0.139350i
\(316\) 4.69606e10 + 8.13381e10i 0.264936 + 0.458883i
\(317\) 2.09537e11 1.75822e11i 1.16545 0.977929i 0.165485 0.986212i \(-0.447081\pi\)
0.999966 + 0.00828314i \(0.00263663\pi\)
\(318\) −9.60798e10 + 1.88401e11i −0.526878 + 1.03315i
\(319\) −1.86912e10 + 1.06003e11i −0.101060 + 0.573139i
\(320\) 1.79113e11 + 1.50294e11i 0.954889 + 0.801247i
\(321\) −3.90289e10 + 3.16932e11i −0.205170 + 1.66607i
\(322\) −3.57134e7 1.29986e7i −0.000185131 6.73822e-5i
\(323\) −4.51896e10 −0.231008
\(324\) −2.40965e10 5.98864e10i −0.121479 0.301908i
\(325\) −7.37347e10 −0.366604
\(326\) −2.58723e11 9.41674e10i −1.26869 0.461765i
\(327\) 1.29730e10 1.05347e11i 0.0627445 0.509514i
\(328\) 2.26676e11 + 1.90204e11i 1.08137 + 0.907374i
\(329\) 3.01783e9 1.71150e10i 0.0142008 0.0805369i
\(330\) 4.94985e10 9.70608e10i 0.229763 0.450538i
\(331\) −1.45802e11 + 1.22342e11i −0.667631 + 0.560209i −0.912363 0.409382i \(-0.865744\pi\)
0.244732 + 0.969591i \(0.421300\pi\)
\(332\) −5.57744e9 9.66041e9i −0.0251950 0.0436389i
\(333\) −4.17795e10 + 4.32023e10i −0.186193 + 0.192534i
\(334\) 1.64724e11 2.85310e11i 0.724264 1.25446i
\(335\) −6.49430e10 3.68310e11i −0.281729 1.59776i
\(336\) 1.21959e10 1.13648e10i 0.0522021 0.0486445i
\(337\) −2.47427e11 + 9.00562e10i −1.04499 + 0.380346i −0.806771 0.590865i \(-0.798787\pi\)
−0.238221 + 0.971211i \(0.576564\pi\)
\(338\) 3.76152e10 1.36908e10i 0.156761 0.0570564i
\(339\) −2.65656e11 8.13225e10i −1.09250 0.334435i
\(340\) 6.00193e9 + 3.40386e10i 0.0243577 + 0.138139i
\(341\) −6.93938e10 + 1.20194e11i −0.277924 + 0.481378i
\(342\) −9.06466e9 + 1.28318e11i −0.0358289 + 0.507188i
\(343\) 3.19120e10 + 5.52731e10i 0.124489 + 0.215621i
\(344\) 1.85705e11 1.55825e11i 0.715007 0.599962i
\(345\) −3.16294e8 4.87429e8i −0.00120200 0.00185236i
\(346\) −3.87639e10 + 2.19841e11i −0.145407 + 0.824644i
\(347\) −1.87218e11 1.57095e11i −0.693210 0.581673i 0.226623 0.973983i \(-0.427232\pi\)
−0.919833 + 0.392310i \(0.871676\pi\)
\(348\) −8.94882e10 + 3.79479e10i −0.327084 + 0.138701i
\(349\) −1.11185e11 4.04679e10i −0.401172 0.146015i 0.133551 0.991042i \(-0.457362\pi\)
−0.534723 + 0.845027i \(0.679584\pi\)
\(350\) −9.66996e9 −0.0344444
\(351\) 5.77674e9 3.11861e11i 0.0203142 1.09668i
\(352\) 9.54377e10 0.331343
\(353\) 8.80596e10 + 3.20511e10i 0.301850 + 0.109864i 0.488505 0.872561i \(-0.337542\pi\)
−0.186655 + 0.982425i \(0.559765\pi\)
\(354\) 3.60918e11 + 2.72173e11i 1.22150 + 0.921149i
\(355\) −3.50039e11 2.93718e11i −1.16974 0.981528i
\(356\) 1.56874e10 8.89676e10i 0.0517638 0.293567i
\(357\) 1.43507e10 7.46963e8i 0.0467590 0.00243384i
\(358\) 3.06977e11 2.57584e11i 0.987717 0.828793i
\(359\) −8.91130e10 1.54348e11i −0.283150 0.490430i 0.689009 0.724753i \(-0.258046\pi\)
−0.972159 + 0.234323i \(0.924713\pi\)
\(360\) 3.98560e11 4.16034e10i 1.25064 0.130547i
\(361\) 9.95100e10 1.72356e11i 0.308379 0.534128i
\(362\) −7.09716e10 4.02500e11i −0.217218 1.23190i
\(363\) 5.31861e10 + 2.30749e11i 0.160775 + 0.697525i
\(364\) −1.40967e10 + 5.13078e9i −0.0420883 + 0.0153189i
\(365\) 6.95602e11 2.53178e11i 2.05136 0.746636i
\(366\) −5.72108e10 2.48210e11i −0.166653 0.723027i
\(367\) −2.64512e10 1.50012e11i −0.0761111 0.431647i −0.998923 0.0463968i \(-0.985226\pi\)
0.922812 0.385251i \(-0.125885\pi\)
\(368\) −1.91231e8 + 3.31222e8i −0.000543554 + 0.000941464i
\(369\) 4.59318e11 4.79457e10i 1.28972 0.134627i
\(370\) −4.58014e10 7.93303e10i −0.127049 0.220055i
\(371\) 4.95274e10 4.15585e10i 0.135726 0.113888i
\(372\) −1.25161e11 + 6.51475e9i −0.338865 + 0.0176382i
\(373\) −1.18121e11 + 6.69899e11i −0.315965 + 1.79193i 0.250793 + 0.968041i \(0.419309\pi\)
−0.566758 + 0.823884i \(0.691802\pi\)
\(374\) −4.73566e10 3.97369e10i −0.125158 0.105020i
\(375\) 2.35133e11 + 1.77317e11i 0.614006 + 0.463029i
\(376\) −2.58394e11 9.40478e10i −0.666711 0.242663i
\(377\) −4.69674e11 −1.19746
\(378\) 7.57592e8 4.08991e10i 0.00190863 0.103039i
\(379\) −1.34945e11 −0.335954 −0.167977 0.985791i \(-0.553723\pi\)
−0.167977 + 0.985791i \(0.553723\pi\)
\(380\) 8.88841e10 + 3.23512e10i 0.218674 + 0.0795910i
\(381\) −5.01436e11 + 2.12636e11i −1.21914 + 0.516982i
\(382\) 6.36589e10 + 5.34161e10i 0.152959 + 0.128347i
\(383\) −6.63858e10 + 3.76492e11i −0.157645 + 0.894050i 0.798683 + 0.601753i \(0.205531\pi\)
−0.956328 + 0.292297i \(0.905580\pi\)
\(384\) −6.14114e10 9.46390e10i −0.144131 0.222116i
\(385\) −2.55156e10 + 2.14101e10i −0.0591878 + 0.0496645i
\(386\) −2.62744e11 4.55087e11i −0.602408 1.04340i
\(387\) 2.66606e10 3.77402e11i 0.0604185 0.855273i
\(388\) 5.94867e9 1.03034e10i 0.0133253 0.0230801i
\(389\) 7.26294e10 + 4.11902e11i 0.160820 + 0.912054i 0.953270 + 0.302118i \(0.0976937\pi\)
−0.792451 + 0.609936i \(0.791195\pi\)
\(390\) 4.54591e11 + 1.39160e11i 0.995017 + 0.304595i
\(391\) −3.09806e8 + 1.12760e8i −0.000670339 + 0.000243984i
\(392\) 4.70708e11 1.71324e11i 1.00685 0.366463i
\(393\) −1.17321e11 + 1.09326e11i −0.248090 + 0.231183i
\(394\) −5.41761e10 3.07248e11i −0.113260 0.642327i
\(395\) −4.54971e11 + 7.88033e11i −0.940365 + 1.62876i
\(396\) 5.90175e10 6.10274e10i 0.120601 0.124709i
\(397\) 2.77084e11 + 4.79923e11i 0.559827 + 0.969649i 0.997510 + 0.0705199i \(0.0224658\pi\)
−0.437683 + 0.899129i \(0.644201\pi\)
\(398\) −4.08889e11 + 3.43099e11i −0.816830 + 0.685401i
\(399\) 1.78660e10 3.50331e10i 0.0352898 0.0691992i
\(400\) −1.68981e10 + 9.58339e10i −0.0330041 + 0.187176i
\(401\) 7.45020e10 + 6.25146e10i 0.143886 + 0.120735i 0.711890 0.702291i \(-0.247840\pi\)
−0.568004 + 0.823026i \(0.692284\pi\)
\(402\) −7.38291e10 + 5.99525e11i −0.140997 + 1.14496i
\(403\) −5.69071e11 2.07125e11i −1.07472 0.391165i
\(404\) −2.41591e10 −0.0451195
\(405\) 3.85740e11 4.92279e11i 0.712439 0.909208i
\(406\) −6.15956e10 −0.112508
\(407\) −7.42736e10 2.70334e10i −0.134171 0.0488344i
\(408\) 2.77897e10 2.25664e11i 0.0496492 0.403174i
\(409\) 2.35442e11 + 1.97559e11i 0.416033 + 0.349093i 0.826652 0.562714i \(-0.190243\pi\)
−0.410618 + 0.911807i \(0.634687\pi\)
\(410\) −1.22229e11 + 6.93195e11i −0.213622 + 1.21151i
\(411\) −1.98668e11 + 3.89566e11i −0.343432 + 0.673430i
\(412\) −1.81041e11 + 1.51912e11i −0.309556 + 0.259749i
\(413\) −6.90965e10 1.19679e11i −0.116864 0.202414i
\(414\) 2.58043e8 + 9.02326e8i 0.000431708 + 0.00150960i
\(415\) 5.40362e10 9.35935e10i 0.0894270 0.154892i
\(416\) 7.23136e10 + 4.10111e11i 0.118386 + 0.671400i
\(417\) −1.64289e11 + 1.53093e11i −0.266071 + 0.247938i
\(418\) −1.58975e11 + 5.78623e10i −0.254705 + 0.0927049i
\(419\) 7.46444e11 2.71683e11i 1.18313 0.430626i 0.325827 0.945430i \(-0.394357\pi\)
0.857308 + 0.514804i \(0.172135\pi\)
\(420\) −2.87613e10 8.80440e9i −0.0451010 0.0138063i
\(421\) −6.14953e10 3.48757e11i −0.0954053 0.541070i −0.994622 0.103568i \(-0.966974\pi\)
0.899217 0.437503i \(-0.144137\pi\)
\(422\) −9.83421e10 + 1.70334e11i −0.150950 + 0.261453i
\(423\) −3.85855e11 + 1.87854e11i −0.585993 + 0.285291i
\(424\) −5.11486e11 8.85920e11i −0.768577 1.33121i
\(425\) −6.42596e10 + 5.39202e10i −0.0955405 + 0.0801680i
\(426\) 4.01742e11 + 6.19111e11i 0.591022 + 0.910804i
\(427\) −1.35220e10 + 7.66869e10i −0.0196841 + 0.111634i
\(428\) −2.90518e11 2.43773e11i −0.418481 0.351147i
\(429\) 3.77663e11 1.60150e11i 0.538327 0.228280i
\(430\) 5.41886e11 + 1.97230e11i 0.764363 + 0.278205i
\(431\) −4.28096e11 −0.597576 −0.298788 0.954319i \(-0.596582\pi\)
−0.298788 + 0.954319i \(0.596582\pi\)
\(432\) −4.04006e11 7.89786e10i −0.558098 0.109102i
\(433\) 1.26300e12 1.72666 0.863330 0.504639i \(-0.168375\pi\)
0.863330 + 0.504639i \(0.168375\pi\)
\(434\) −7.46310e10 2.71635e10i −0.100975 0.0367520i
\(435\) −7.51893e11 5.67012e11i −1.00683 0.759260i
\(436\) 9.65667e10 + 8.10291e10i 0.127979 + 0.107387i
\(437\) −1.56672e8 + 8.88533e8i −0.000205507 + 0.00116549i
\(438\) −1.19399e12 + 6.21482e10i −1.55013 + 0.0806854i
\(439\) 6.80449e11 5.70965e11i 0.874390 0.733701i −0.0906275 0.995885i \(-0.528887\pi\)
0.965018 + 0.262184i \(0.0844428\pi\)
\(440\) 2.63508e11 + 4.56409e11i 0.335163 + 0.580520i
\(441\) 3.18485e11 7.13960e11i 0.400973 0.898877i
\(442\) 1.34874e11 2.33608e11i 0.168084 0.291130i
\(443\) −4.14262e9 2.34940e10i −0.00511044 0.0289827i 0.982146 0.188121i \(-0.0602396\pi\)
−0.987256 + 0.159138i \(0.949129\pi\)
\(444\) −1.60315e10 6.95530e10i −0.0195772 0.0849361i
\(445\) 8.22463e11 2.99352e11i 0.994252 0.361878i
\(446\) 1.12572e11 4.09729e10i 0.134718 0.0490332i
\(447\) −1.50697e10 6.53802e10i −0.0178534 0.0774573i
\(448\) 2.00478e10 + 1.13697e11i 0.0235134 + 0.133351i
\(449\) 2.17348e11 3.76458e11i 0.252375 0.437127i −0.711804 0.702378i \(-0.752122\pi\)
0.964179 + 0.265251i \(0.0854549\pi\)
\(450\) 1.40219e11 + 1.93283e11i 0.161194 + 0.222197i
\(451\) 3.03679e11 + 5.25987e11i 0.345637 + 0.598660i
\(452\) 2.52760e11 2.12091e11i 0.284830 0.239001i
\(453\) −9.71329e11 + 5.05584e10i −1.08374 + 0.0564094i
\(454\) −9.81341e9 + 5.56546e10i −0.0108410 + 0.0614823i
\(455\) −1.11336e11 9.34221e10i −0.121782 0.102188i
\(456\) −4.96799e11 3.74643e11i −0.538071 0.405766i
\(457\) 1.03488e12 + 3.76664e11i 1.10985 + 0.403954i 0.830940 0.556362i \(-0.187803\pi\)
0.278914 + 0.960316i \(0.410026\pi\)
\(458\) 3.26929e11 0.347183
\(459\) −2.23021e11 2.76010e11i −0.234525 0.290247i
\(460\) 6.90087e8 0.000718611
\(461\) −6.56893e10 2.39090e10i −0.0677393 0.0246551i 0.307928 0.951410i \(-0.400364\pi\)
−0.375668 + 0.926754i \(0.622587\pi\)
\(462\) 4.95287e10 2.10029e10i 0.0505787 0.0214482i
\(463\) −4.84959e11 4.06929e11i −0.490445 0.411532i 0.363741 0.931500i \(-0.381499\pi\)
−0.854186 + 0.519968i \(0.825944\pi\)
\(464\) −1.07637e11 + 6.10441e11i −0.107803 + 0.611383i
\(465\) −6.60965e11 1.01859e12i −0.655602 1.01033i
\(466\) 6.15969e10 5.16860e10i 0.0605094 0.0507734i
\(467\) 5.33198e11 + 9.23527e11i 0.518756 + 0.898511i 0.999762 + 0.0217944i \(0.00693792\pi\)
−0.481007 + 0.876717i \(0.659729\pi\)
\(468\) 3.06962e11 + 2.07367e11i 0.295787 + 0.199817i
\(469\) 9.23327e10 1.59925e11i 0.0881207 0.152629i
\(470\) −1.13585e11 6.44171e11i −0.107369 0.608921i
\(471\) 9.72091e11 + 2.97576e11i 0.910150 + 0.278615i
\(472\) −2.05468e12 + 7.47842e11i −1.90548 + 0.693539i
\(473\) 4.67571e11 1.70182e11i 0.429509 0.156329i
\(474\) 1.07522e12 1.00195e12i 0.978354 0.911679i
\(475\) 3.98632e10 + 2.26075e11i 0.0359294 + 0.203766i
\(476\) −8.53324e9 + 1.47800e10i −0.00761873 + 0.0131960i
\(477\) −1.54884e12 3.87341e11i −1.36985 0.342579i
\(478\) −6.42739e11 1.11326e12i −0.563130 0.975370i
\(479\) 5.72842e11 4.80671e11i 0.497193 0.417194i −0.359403 0.933182i \(-0.617020\pi\)
0.856596 + 0.515988i \(0.172575\pi\)
\(480\) −3.79339e11 + 7.43840e11i −0.326168 + 0.639578i
\(481\) 5.98893e10 3.39649e11i 0.0510148 0.289319i
\(482\) −4.73666e11 3.97453e11i −0.399724 0.335409i
\(483\) 3.50667e7 2.84757e8i 2.93179e−5 0.000238074i
\(484\) −2.64271e11 9.61870e10i −0.218900 0.0796732i
\(485\) 1.15266e11 0.0945936
\(486\) −8.28478e11 + 5.77911e11i −0.673624 + 0.469892i
\(487\) 6.87914e11 0.554184 0.277092 0.960843i \(-0.410629\pi\)
0.277092 + 0.960843i \(0.410629\pi\)
\(488\) 1.15778e12 + 4.21399e11i 0.924141 + 0.336360i
\(489\) 2.54038e11 2.06290e12i 0.200913 1.63151i
\(490\) 9.12793e11 + 7.65924e11i 0.715303 + 0.600210i
\(491\) −3.57819e11 + 2.02929e12i −0.277841 + 1.57572i 0.451948 + 0.892045i \(0.350729\pi\)
−0.729789 + 0.683672i \(0.760382\pi\)
\(492\) −2.49173e11 + 4.88600e11i −0.191716 + 0.375933i
\(493\) −4.09320e11 + 3.43460e11i −0.312070 + 0.261858i
\(494\) −3.69100e11 6.39300e11i −0.278852 0.482985i
\(495\) 7.97933e11 + 1.99551e11i 0.597370 + 0.149393i
\(496\) −3.99619e11 + 6.92161e11i −0.296469 + 0.513499i
\(497\) −3.91793e10 2.22197e11i −0.0288040 0.163356i
\(498\) −1.27703e11 + 1.19000e11i −0.0930396 + 0.0866989i
\(499\) 2.01988e12 7.35175e11i 1.45839 0.530809i 0.513466 0.858110i \(-0.328361\pi\)
0.944920 + 0.327300i \(0.106139\pi\)
\(500\) −3.28663e11 + 1.19624e11i −0.235172 + 0.0855957i
\(501\) 2.37812e12 + 7.27989e11i 1.68641 + 0.516244i
\(502\) 9.23340e10 + 5.23652e11i 0.0648925 + 0.368024i
\(503\) −7.52953e10 + 1.30415e11i −0.0524460 + 0.0908391i −0.891057 0.453892i \(-0.850035\pi\)
0.838611 + 0.544731i \(0.183368\pi\)
\(504\) 1.63959e11 + 1.10762e11i 0.113187 + 0.0764632i
\(505\) −1.17031e11 2.02703e11i −0.0800735 0.138691i
\(506\) −9.45506e8 + 7.93373e8i −0.000641190 + 0.000538022i
\(507\) 1.64493e11 + 2.53494e11i 0.110563 + 0.170385i
\(508\) 1.12326e11 6.37030e11i 0.0748328 0.424398i
\(509\) −1.00277e12 8.41426e11i −0.662174 0.555630i 0.248563 0.968616i \(-0.420042\pi\)
−0.910738 + 0.412985i \(0.864486\pi\)
\(510\) 4.97939e11 2.11153e11i 0.325919 0.138208i
\(511\) 3.43466e11 + 1.25011e11i 0.222838 + 0.0811065i
\(512\) 1.51218e12 0.972501
\(513\) −9.59308e11 + 1.50889e11i −0.611547 + 0.0961901i
\(514\) 2.54749e11 0.160982
\(515\) −2.15159e12 7.83114e11i −1.34780 0.490561i
\(516\) 3.58758e11 + 2.70544e11i 0.222781 + 0.168002i
\(517\) −4.32358e11 3.62792e11i −0.266156 0.223332i
\(518\) 7.85420e9 4.45434e10i 0.00479312 0.0271831i
\(519\) −1.68294e12 + 8.75982e10i −1.01816 + 0.0529958i
\(520\) −1.76160e12 + 1.47816e12i −1.05656 + 0.886556i
\(521\) −5.73452e10 9.93248e10i −0.0340979 0.0590593i 0.848473 0.529239i \(-0.177522\pi\)
−0.882571 + 0.470180i \(0.844189\pi\)
\(522\) 8.93162e11 + 1.23117e12i 0.526518 + 0.725775i
\(523\) −1.53405e12 + 2.65706e12i −0.896566 + 1.55290i −0.0647127 + 0.997904i \(0.520613\pi\)
−0.831854 + 0.554995i \(0.812720\pi\)
\(524\) −3.30719e10 1.87560e11i −0.0191632 0.108680i
\(525\) −1.63961e10 7.11348e10i −0.00941940 0.0408663i
\(526\) 3.52056e11 1.28138e11i 0.200529 0.0729865i
\(527\) −6.47409e11 + 2.35638e11i −0.365621 + 0.133075i
\(528\) −1.21598e11 5.27555e11i −0.0680884 0.295403i
\(529\) −3.12766e11 1.77378e12i −0.173648 0.984804i
\(530\) 1.21671e12 2.10740e12i 0.669800 1.16013i
\(531\) −1.39021e12 + 3.11650e12i −0.758850 + 1.70114i
\(532\) 2.33524e10 + 4.04475e10i 0.0126395 + 0.0218922i
\(533\) −2.03015e12 + 1.70350e12i −1.08957 + 0.914259i
\(534\) −1.41175e12 + 7.34825e10i −0.751313 + 0.0391064i
\(535\) 6.38027e11 3.61843e12i 0.336703 1.90954i
\(536\) −2.23826e12 1.87813e12i −1.17130 0.982841i
\(537\) 2.41536e12 + 1.82145e12i 1.25342 + 0.945222i
\(538\) −2.68600e11 9.77623e10i −0.138225 0.0503096i
\(539\) 1.02815e12 0.524698
\(540\) 2.41068e11 + 7.02549e11i 0.122002 + 0.355553i
\(541\) −2.16618e12 −1.08719 −0.543597 0.839346i \(-0.682938\pi\)
−0.543597 + 0.839346i \(0.682938\pi\)
\(542\) 9.78453e11 + 3.56128e11i 0.487016 + 0.177259i
\(543\) 2.84056e12 1.20455e12i 1.40218 0.594602i
\(544\) 3.62924e11 + 3.04530e11i 0.177673 + 0.149085i
\(545\) −2.12077e11 + 1.20275e12i −0.102970 + 0.583970i
\(546\) 1.27781e11 + 1.96919e11i 0.0615317 + 0.0948244i
\(547\) −2.55652e12 + 2.14518e12i −1.22098 + 1.02452i −0.222202 + 0.975001i \(0.571324\pi\)
−0.998773 + 0.0495193i \(0.984231\pi\)
\(548\) −2.59677e11 4.49773e11i −0.123004 0.213050i
\(549\) 1.72890e12 8.41715e11i 0.812256 0.395448i
\(550\) −1.57022e11 + 2.71970e11i −0.0731691 + 0.126733i
\(551\) 2.53920e11 + 1.44005e12i 0.117358 + 0.665573i
\(552\) −4.34074e9 1.32879e9i −0.00198993 0.000609158i
\(553\) −4.22204e11 + 1.53670e11i −0.191982 + 0.0698756i
\(554\) 2.98452e12 1.08628e12i 1.34611 0.489944i
\(555\) 5.05915e11 4.71437e11i 0.226339 0.210914i
\(556\) −4.63118e10 2.62648e11i −0.0205521 0.116557i
\(557\) −1.36006e12 + 2.35570e12i −0.598702 + 1.03698i 0.394311 + 0.918977i \(0.370983\pi\)
−0.993013 + 0.118006i \(0.962350\pi\)
\(558\) 5.39237e11 + 1.88561e12i 0.235465 + 0.823375i
\(559\) 1.08558e12 + 1.88028e12i 0.470229 + 0.814460i
\(560\) −1.46937e11 + 1.23295e11i −0.0631372 + 0.0529784i
\(561\) 2.12019e11 4.15744e11i 0.0903736 0.177212i
\(562\) 1.68613e11 9.56250e11i 0.0712979 0.404351i
\(563\) −2.02498e12 1.69916e12i −0.849441 0.712766i 0.110225 0.993907i \(-0.464843\pi\)
−0.959667 + 0.281141i \(0.909287\pi\)
\(564\) 6.22944e10 5.05859e11i 0.0259235 0.210510i
\(565\) 3.00393e12 + 1.09334e12i 1.24014 + 0.451376i
\(566\) 1.36426e12 0.558757
\(567\) 3.02149e11 6.37742e10i 0.122771 0.0259132i
\(568\) −3.56992e12 −1.43910
\(569\) 1.25065e12 + 4.55200e11i 0.500186 + 0.182053i 0.579778 0.814775i \(-0.303139\pi\)
−0.0795917 + 0.996828i \(0.525362\pi\)
\(570\) 1.80906e11 1.46904e12i 0.0717822 0.582903i
\(571\) −1.49100e12 1.25110e12i −0.586969 0.492526i 0.300258 0.953858i \(-0.402927\pi\)
−0.887227 + 0.461332i \(0.847372\pi\)
\(572\) −8.45994e10 + 4.79787e11i −0.0330434 + 0.187399i
\(573\) −2.85005e11 + 5.58862e11i −0.110448 + 0.216575i
\(574\) −2.66245e11 + 2.23406e11i −0.102371 + 0.0858996i
\(575\) 8.37409e8 + 1.45043e9i 0.000319471 + 0.000553341i
\(576\) 1.98187e12 2.04937e12i 0.750197 0.775745i
\(577\) −8.98161e11 + 1.55566e12i −0.337336 + 0.584283i −0.983931 0.178550i \(-0.942859\pi\)
0.646595 + 0.762834i \(0.276193\pi\)
\(578\) 3.29411e11 + 1.86818e12i 0.122762 + 0.696216i
\(579\) 2.90224e12 2.70445e12i 1.07320 1.00006i
\(580\) 1.05098e12 3.82525e11i 0.385628 0.140357i
\(581\) 5.01446e10 1.82511e10i 0.0182571 0.00664504i
\(582\) −1.78017e11 5.44946e10i −0.0643145 0.0196879i
\(583\) −3.64609e11 2.06780e12i −0.130713 0.741310i
\(584\) 2.89161e12 5.00842e12i 1.02868 1.78173i
\(585\) −2.52903e11 + 3.58005e12i −0.0892797 + 1.26383i
\(586\) −2.12783e11 3.68552e11i −0.0745416 0.129110i
\(587\) 3.44036e12 2.88680e12i 1.19600 1.00357i 0.196268 0.980550i \(-0.437118\pi\)
0.999735 0.0230158i \(-0.00732681\pi\)
\(588\) 5.05402e11 + 7.78857e11i 0.174357 + 0.268695i
\(589\) −3.27401e11 + 1.85679e12i −0.112089 + 0.635687i
\(590\) −3.98442e12 3.34332e12i −1.35373 1.13591i
\(591\) 2.16834e12 9.19494e11i 0.731111 0.310031i
\(592\) −4.27721e11 1.55678e11i −0.143124 0.0520929i
\(593\) −2.68424e12 −0.891407 −0.445703 0.895181i \(-0.647046\pi\)
−0.445703 + 0.895181i \(0.647046\pi\)
\(594\) −1.13799e12 6.85431e11i −0.375060 0.225904i
\(595\) −1.65346e11 −0.0540838
\(596\) 7.48784e10 + 2.72535e10i 0.0243080 + 0.00884738i
\(597\) −3.21722e12 2.42615e12i −1.03657 0.781687i
\(598\) −4.12567e9 3.46185e9i −0.00131929 0.00110701i
\(599\) 8.87977e10 5.03597e11i 0.0281826 0.159832i −0.967469 0.252991i \(-0.918586\pi\)
0.995651 + 0.0931597i \(0.0296967\pi\)
\(600\) −1.15347e12 + 6.00391e10i −0.363351 + 0.0189127i
\(601\) 2.07245e12 1.73900e12i 0.647962 0.543705i −0.258490 0.966014i \(-0.583225\pi\)
0.906452 + 0.422309i \(0.138780\pi\)
\(602\) 1.42369e11 + 2.46590e11i 0.0441805 + 0.0765229i
\(603\) −4.53545e12 + 4.73430e11i −1.39699 + 0.145824i
\(604\) 5.77575e11 1.00039e12i 0.176580 0.305846i
\(605\) −4.73135e11 2.68328e12i −0.143577 0.814267i
\(606\) 8.49105e10 + 3.68386e11i 0.0255761 + 0.110963i
\(607\) −4.72762e10 + 1.72071e10i −0.0141349 + 0.00514470i −0.349078 0.937094i \(-0.613505\pi\)
0.334943 + 0.942238i \(0.391283\pi\)
\(608\) 1.21833e12 4.43436e11i 0.361576 0.131603i
\(609\) −1.04440e11 4.53113e11i −0.0307671 0.133484i
\(610\) 5.08938e11 + 2.88633e12i 0.148827 + 0.844038i
\(611\) 1.23137e12 2.13280e12i 0.357441 0.619107i
\(612\) 4.19159e11 4.37536e10i 0.120781 0.0126076i
\(613\) 6.02886e9 + 1.04423e10i 0.00172450 + 0.00298692i 0.866886 0.498506i \(-0.166118\pi\)
−0.865162 + 0.501493i \(0.832784\pi\)
\(614\) −7.63299e10 + 6.40484e10i −0.0216739 + 0.0181866i
\(615\) −5.30657e12 + 2.76211e11i −1.49581 + 0.0778580i
\(616\) −4.51874e10 + 2.56270e11i −0.0126446 + 0.0717109i
\(617\) −3.43937e12 2.88597e12i −0.955422 0.801694i 0.0247802 0.999693i \(-0.492111\pi\)
−0.980202 + 0.197999i \(0.936556\pi\)
\(618\) 2.95270e12 + 2.22667e12i 0.814275 + 0.614054i
\(619\) 6.52254e12 + 2.37401e12i 1.78570 + 0.649942i 0.999488 + 0.0319882i \(0.0101839\pi\)
0.786214 + 0.617954i \(0.212038\pi\)
\(620\) 1.44209e12 0.391949
\(621\) −6.20022e9 + 3.42819e9i −0.00167300 + 0.000925022i
\(622\) 1.21356e11 0.0325091
\(623\) 4.06106e11 + 1.47811e11i 0.108005 + 0.0393106i
\(624\) 2.17485e12 9.22257e11i 0.574248 0.243513i
\(625\) −3.57248e12 2.99767e12i −0.936504 0.785821i
\(626\) −7.65614e11 + 4.34201e12i −0.199262 + 1.13007i
\(627\) −6.95204e11 1.07136e12i −0.179642 0.276841i
\(628\) −9.24903e11 + 7.76086e11i −0.237289 + 0.199109i
\(629\) −1.96183e11 3.39799e11i −0.0499727 0.0865553i
\(630\) −3.31671e10 + 4.69507e11i −0.00838831 + 0.118743i
\(631\) 2.17006e12 3.75865e12i 0.544928 0.943843i −0.453684 0.891163i \(-0.649890\pi\)
0.998611 0.0526798i \(-0.0167763\pi\)
\(632\) 1.23447e12 + 7.00100e12i 0.307788 + 1.74555i
\(633\) −1.41976e12 4.34618e11i −0.351479 0.107595i
\(634\) 4.77684e12 1.73863e12i 1.17419 0.427370i
\(635\) 5.88904e12 2.14343e12i 1.43735 0.523152i
\(636\) 1.38719e12 1.29265e12i 0.336185 0.313274i
\(637\) 7.79039e11 + 4.41815e12i 0.187470 + 1.06319i
\(638\) −1.00019e12 + 1.73239e12i −0.238996 + 0.413954i
\(639\) −3.87316e12 + 4.00506e12i −0.918992 + 0.950289i
\(640\) 6.49057e11 + 1.12420e12i 0.152923 + 0.264871i
\(641\) −6.22809e12 + 5.22599e12i −1.45712 + 1.22267i −0.529942 + 0.848034i \(0.677786\pi\)
−0.927174 + 0.374631i \(0.877769\pi\)
\(642\) −2.69608e12 + 5.28670e12i −0.626361 + 1.22822i
\(643\) −7.54498e11 + 4.27897e12i −0.174064 + 0.987165i 0.765155 + 0.643846i \(0.222662\pi\)
−0.939219 + 0.343319i \(0.888449\pi\)
\(644\) 2.61025e8 + 2.19026e8i 5.97991e−5 + 5.01774e-5i
\(645\) −5.32073e11 + 4.32067e12i −0.121047 + 0.982953i
\(646\) −7.89173e11 2.87235e11i −0.178290 0.0648921i
\(647\) 5.86334e12 1.31545 0.657727 0.753256i \(-0.271518\pi\)
0.657727 + 0.753256i \(0.271518\pi\)
\(648\) −1.63567e11 4.88331e12i −0.0364424 1.08799i
\(649\) −4.48798e12 −0.993002
\(650\) −1.28767e12 4.68675e11i −0.282941 0.102982i
\(651\) 7.32796e10 5.95063e11i 0.0159907 0.129852i
\(652\) 1.89097e12 + 1.58671e12i 0.409799 + 0.343862i
\(653\) −1.16333e12 + 6.59756e12i −0.250376 + 1.41995i 0.557293 + 0.830316i \(0.311840\pi\)
−0.807669 + 0.589636i \(0.799271\pi\)
\(654\) 8.96163e11 1.75727e12i 0.191552 0.375612i
\(655\) 1.41349e12 1.18606e12i 0.300059 0.251780i
\(656\) 1.74880e12 + 3.02901e12i 0.368700 + 0.638607i
\(657\) −2.48167e12 8.67793e12i −0.519637 1.81707i
\(658\) 1.61489e11 2.79707e11i 0.0335835 0.0581684i
\(659\) −4.47489e10 2.53783e11i −0.00924267 0.0524178i 0.979838 0.199796i \(-0.0640278\pi\)
−0.989080 + 0.147378i \(0.952917\pi\)
\(660\) −7.14654e11 + 6.65950e11i −0.146605 + 0.136614i
\(661\) −4.08951e12 + 1.48846e12i −0.833229 + 0.303271i −0.723184 0.690656i \(-0.757322\pi\)
−0.110046 + 0.993927i \(0.535100\pi\)
\(662\) −3.32386e12 + 1.20978e12i −0.672638 + 0.244820i
\(663\) 1.94717e12 + 5.96067e11i 0.391375 + 0.119808i
\(664\) −1.46616e11 8.31499e11i −0.0292701 0.165999i
\(665\) −2.26246e11 + 3.91870e11i −0.0448626 + 0.0777042i
\(666\) −1.00422e12 + 4.88908e11i −0.197786 + 0.0962926i
\(667\) 5.33411e9 + 9.23895e9i 0.00104351 + 0.00180741i
\(668\) −2.26268e12 + 1.89861e12i −0.439671 + 0.368928i
\(669\) 4.92282e11 + 7.58639e11i 0.0950159 + 0.146426i
\(670\) 1.20693e12 6.84481e12i 0.231390 1.31228i
\(671\) 1.93726e12 + 1.62556e12i 0.368924 + 0.309564i
\(672\) −3.79570e11 + 1.60959e11i −0.0718010 + 0.0304476i
\(673\) 4.63098e12 + 1.68554e12i 0.870173 + 0.316717i 0.738237 0.674541i \(-0.235659\pi\)
0.131936 + 0.991258i \(0.457881\pi\)
\(674\) −4.89339e12 −0.913356
\(675\) −1.18409e12 + 1.35921e12i −0.219543 + 0.252011i
\(676\) −3.58889e11 −0.0660998
\(677\) 8.07971e11 + 2.94078e11i 0.147825 + 0.0538038i 0.414873 0.909879i \(-0.363826\pi\)
−0.267048 + 0.963683i \(0.586048\pi\)
\(678\) −4.12240e12 3.10875e12i −0.749232 0.565005i
\(679\) 4.35990e10 + 3.65839e10i 0.00787160 + 0.00660505i
\(680\) −4.54293e11 + 2.57642e12i −0.0814790 + 0.462091i
\(681\) −4.26049e11 + 2.21762e10i −0.0759098 + 0.00395117i
\(682\) −1.97584e12 + 1.65793e12i −0.349722 + 0.293451i
\(683\) 2.19930e12 + 3.80931e12i 0.386716 + 0.669812i 0.992006 0.126194i \(-0.0402761\pi\)
−0.605290 + 0.796005i \(0.706943\pi\)
\(684\) 4.69847e11 1.05327e12i 0.0820737 0.183988i
\(685\) 2.51584e12 4.35756e12i 0.436592 0.756199i
\(686\) 2.05969e11 + 1.16811e12i 0.0355094 + 0.201384i
\(687\) 5.54330e11 + 2.40497e12i 0.0949431 + 0.411913i
\(688\) 2.69261e12 9.80031e11i 0.458169 0.166760i
\(689\) 8.60940e12 3.13356e12i 1.45541 0.529727i
\(690\) −2.42541e9 1.05227e10i −0.000407347 0.00176728i
\(691\) −1.08407e12 6.14808e12i −0.180887 1.02586i −0.931127 0.364695i \(-0.881173\pi\)
0.750240 0.661166i \(-0.229938\pi\)
\(692\) 1.00071e12 1.73329e12i 0.165895 0.287338i
\(693\) 2.38482e11 + 3.28734e11i 0.0392786 + 0.0541434i
\(694\) −2.27097e12 3.93344e12i −0.371616 0.643657i
\(695\) 1.97937e12 1.66088e12i 0.321806 0.270027i
\(696\) −7.34736e12 + 3.82436e11i −1.18683 + 0.0617757i
\(697\) −5.23548e11 + 2.96919e12i −0.0840251 + 0.476530i
\(698\) −1.68446e12 1.41343e12i −0.268603 0.225385i
\(699\) 4.84658e11 + 3.65486e11i 0.0767870 + 0.0579060i
\(700\) 8.14691e10 + 2.96523e10i 0.0128248 + 0.00466785i
\(701\) −1.23156e13 −1.92630 −0.963150 0.268965i \(-0.913319\pi\)
−0.963150 + 0.268965i \(0.913319\pi\)
\(702\) 2.08314e12 5.40949e12i 0.323744 0.840697i
\(703\) −1.07376e12 −0.165810
\(704\) 3.52329e12 + 1.28237e12i 0.540593 + 0.196760i
\(705\) 4.54610e12 1.92780e12i 0.693088 0.293907i
\(706\) 1.33411e12 + 1.11945e12i 0.202102 + 0.169584i
\(707\) 2.00689e10 1.13816e11i 0.00302090 0.0171324i
\(708\) −2.20612e12 3.39978e12i −0.329974 0.508511i
\(709\) 6.51478e12 5.46655e12i 0.968259 0.812466i −0.0140180 0.999902i \(-0.504462\pi\)
0.982277 + 0.187436i \(0.0600178\pi\)
\(710\) −4.24601e12 7.35430e12i −0.627073 1.08612i
\(711\) 9.19370e12 + 6.21076e12i 1.34920 + 0.911447i
\(712\) 3.41897e12 5.92184e12i 0.498581 0.863568i
\(713\) 2.38862e9 + 1.35465e10i 0.000346133 + 0.00196302i
\(714\) 2.55362e11 + 7.81714e10i 0.0367718 + 0.0112566i
\(715\) −4.43540e12 + 1.61435e12i −0.634681 + 0.231005i
\(716\) −3.37614e12 + 1.22881e12i −0.480078 + 0.174734i
\(717\) 7.09960e12 6.61576e12i 1.00322 0.934853i
\(718\) −5.75161e11 3.26190e12i −0.0807661 0.458047i
\(719\) −3.51879e12 + 6.09472e12i −0.491036 + 0.850499i −0.999947 0.0103202i \(-0.996715\pi\)
0.508911 + 0.860819i \(0.330048\pi\)
\(720\) 4.59508e12 + 1.14916e12i 0.637230 + 0.159361i
\(721\) −5.65284e11 9.79101e11i −0.0779037 0.134933i
\(722\) 2.83334e12 2.37745e12i 0.388044 0.325608i
\(723\) 2.12064e12 4.15832e12i 0.288632 0.565973i
\(724\) −6.36307e11 + 3.60868e12i −0.0860683 + 0.488117i
\(725\) 2.07934e12 + 1.74477e12i 0.279515 + 0.234541i
\(726\) −5.37873e11 + 4.36777e12i −0.0718563 + 0.583505i
\(727\) −6.18464e12 2.25102e12i −0.821125 0.298865i −0.102914 0.994690i \(-0.532817\pi\)
−0.718211 + 0.695825i \(0.755039\pi\)
\(728\) −1.13547e12 −0.149826
\(729\) −5.65601e12 5.11461e12i −0.741714 0.670716i
\(730\) 1.37570e13 1.79296
\(731\) 2.32108e12 + 8.44804e11i 0.300650 + 0.109428i
\(732\) −2.79122e11 + 2.26660e12i −0.0359331 + 0.291792i
\(733\) 3.20204e12 + 2.68683e12i 0.409693 + 0.343773i 0.824226 0.566261i \(-0.191611\pi\)
−0.414533 + 0.910034i \(0.636055\pi\)
\(734\) 4.91579e11 2.78788e12i 0.0625116 0.354521i
\(735\) −4.08664e12 + 8.01342e12i −0.516503 + 1.01280i
\(736\) 7.24602e9 6.08013e9i 0.000910226 0.000763770i
\(737\) −2.99861e12 5.19375e12i −0.374384 0.648451i
\(738\) 8.32610e12 + 2.08223e12i 1.03321 + 0.258389i
\(739\) −3.48679e12 + 6.03931e12i −0.430057 + 0.744881i −0.996878 0.0789601i \(-0.974840\pi\)
0.566820 + 0.823841i \(0.308173\pi\)
\(740\) 1.42614e11 + 8.08802e11i 0.0174831 + 0.0991515i
\(741\) 4.07703e12 3.79918e12i 0.496777 0.462922i
\(742\) 1.12908e12 4.10952e11i 0.136744 0.0497707i
\(743\) 9.07412e12 3.30271e12i 1.09233 0.397577i 0.267848 0.963461i \(-0.413687\pi\)
0.824484 + 0.565885i \(0.191465\pi\)
\(744\) −9.07094e12 2.77680e12i −1.08536 0.332251i
\(745\) 1.34058e11 + 7.60278e11i 0.0159437 + 0.0904210i
\(746\) −6.32086e12 + 1.09480e13i −0.747225 + 1.29423i
\(747\) −1.09192e12 7.37642e11i −0.128307 0.0866769i
\(748\) 2.77127e11 + 4.79998e11i 0.0323684 + 0.0560638i
\(749\) 1.38978e12 1.16616e12i 0.161353 0.135392i
\(750\) 2.97920e12 + 4.59114e12i 0.343814 + 0.529840i
\(751\) 8.52907e11 4.83708e12i 0.0978413 0.554885i −0.895998 0.444057i \(-0.853539\pi\)
0.993840 0.110828i \(-0.0353503\pi\)
\(752\) −2.48983e12 2.08922e12i −0.283916 0.238234i
\(753\) −3.69556e12 + 1.56712e12i −0.418893 + 0.177634i
\(754\) −8.20220e12 2.98536e12i −0.924186 0.336376i
\(755\) 1.11915e13 1.25351
\(756\) −1.31797e11 + 3.42250e11i −0.0146743 + 0.0381062i
\(757\) −4.59607e12 −0.508692 −0.254346 0.967113i \(-0.581860\pi\)
−0.254346 + 0.967113i \(0.581860\pi\)
\(758\) −2.35662e12 8.57740e11i −0.259286 0.0943723i
\(759\) −7.43944e9 5.61017e9i −0.000813677 0.000613604i
\(760\) 5.48450e12 + 4.60205e12i 0.596316 + 0.500368i
\(761\) 1.02595e12 5.81848e12i 0.110891 0.628895i −0.877812 0.479006i \(-0.840997\pi\)
0.988703 0.149889i \(-0.0478917\pi\)
\(762\) −1.01084e13 + 5.26152e11i −1.08614 + 0.0565346i
\(763\) −4.61956e11 + 3.87627e11i −0.0493447 + 0.0414051i
\(764\) −3.72526e11 6.45235e11i −0.0395582 0.0685169i
\(765\) 2.39759e12 + 3.30494e12i 0.253103 + 0.348889i
\(766\) −3.55241e12 + 6.15295e12i −0.372815 + 0.645734i
\(767\) −3.40057e12 1.92856e13i −0.354791 2.01212i
\(768\) 1.86591e12 + 8.09530e12i 0.193538 + 0.839668i
\(769\) −1.45061e13 + 5.27977e12i −1.49583 + 0.544436i −0.954976 0.296684i \(-0.904119\pi\)
−0.540849 + 0.841119i \(0.681897\pi\)
\(770\) −5.81682e11 + 2.11715e11i −0.0596317 + 0.0217042i
\(771\) 4.31945e11 + 1.87400e12i 0.0440234 + 0.190996i
\(772\) 8.18118e11 + 4.63978e12i 0.0828969 + 0.470132i
\(773\) 5.05669e11 8.75844e11i 0.0509400 0.0882306i −0.839431 0.543466i \(-0.817112\pi\)
0.890371 + 0.455236i \(0.150445\pi\)
\(774\) 2.86444e12 6.42133e12i 0.286884 0.643118i
\(775\) 1.74995e12 + 3.03100e12i 0.174248 + 0.301807i
\(776\) 6.89841e11 5.78845e11i 0.0682922 0.0573039i
\(777\) 3.40990e11 1.77488e10i 0.0335620 0.00174693i
\(778\) −1.34977e12 + 7.65494e12i −0.132085 + 0.749089i
\(779\) 6.32059e12 + 5.30361e12i 0.614949 + 0.516004i
\(780\) −3.40319e12 2.56639e12i −0.329201 0.248254i
\(781\) −6.88552e12 2.50613e12i −0.662228 0.241031i
\(782\) −6.12706e9 −0.000585898
\(783\) −7.54243e12 + 8.65788e12i −0.717106 + 0.823158i
\(784\) 5.92086e12 0.559709
\(785\) −1.09920e13 4.00077e12i −1.03315 0.376037i
\(786\) −2.74375e12 + 1.16350e12i −0.256414 + 0.108734i
\(787\) −1.50781e12 1.26520e12i −0.140107 0.117564i 0.570041 0.821616i \(-0.306927\pi\)
−0.710148 + 0.704053i \(0.751372\pi\)
\(788\) −4.85725e11 + 2.75468e12i −0.0448768 + 0.254509i
\(789\) 1.53955e12 + 2.37255e12i 0.141432 + 0.217956i
\(790\) −1.29543e13 + 1.08700e13i −1.18330 + 0.992903i
\(791\) 7.89219e11 + 1.36697e12i 0.0716809 + 0.124155i
\(792\) 5.77758e12 2.81282e12i 0.521774 0.254026i
\(793\) −5.51741e12 + 9.55643e12i −0.495457 + 0.858156i
\(794\) 1.78838e12 + 1.01424e13i 0.159686 + 0.905625i
\(795\) 1.75656e13 + 5.37719e12i 1.55959 + 0.477423i
\(796\) 4.49696e12 1.63676e12i 0.397018 0.144503i
\(797\) 1.89101e13 6.88272e12i 1.66009 0.604223i 0.669713 0.742620i \(-0.266417\pi\)
0.990377 + 0.138396i \(0.0441947\pi\)
\(798\) 5.34683e11 4.98244e11i 0.0466749 0.0434940i
\(799\) −4.86522e11 2.75920e12i −0.0422320 0.239510i
\(800\) 1.20336e12 2.08428e12i 0.103870 0.179908i
\(801\) −2.93427e12 1.02606e13i −0.251857 0.880695i
\(802\) 9.03715e11 + 1.56528e12i 0.0771342 + 0.133600i
\(803\) 9.09321e12 7.63011e12i 0.771786 0.647606i
\(804\) 2.46041e12 4.82459e12i 0.207661 0.407200i
\(805\) −5.73255e8 + 3.25109e9i −4.81134e−5 + 0.000272865i
\(806\) −8.62150e12 7.23429e12i −0.719573 0.603794i
\(807\) 2.63736e11 2.14165e12i 0.0218896 0.177754i
\(808\) −1.71835e12 6.25428e11i −0.141827 0.0516209i
\(809\) −1.35819e12 −0.111479 −0.0557395 0.998445i \(-0.517752\pi\)
−0.0557395 + 0.998445i \(0.517752\pi\)
\(810\) 9.86545e12 6.14510e12i 0.805257 0.501587i
\(811\) 6.18683e12 0.502197 0.251099 0.967962i \(-0.419208\pi\)
0.251099 + 0.967962i \(0.419208\pi\)
\(812\) 5.18940e11 + 1.88879e11i 0.0418905 + 0.0152469i
\(813\) −9.60735e11 + 7.80160e12i −0.0771252 + 0.626291i
\(814\) −1.12525e12 9.44200e11i −0.0898340 0.0753797i
\(815\) −4.15290e12 + 2.35523e13i −0.329718 + 1.86992i
\(816\) 1.22096e12 2.39416e12i 0.0964039 0.189037i
\(817\) 5.17816e12 4.34500e12i 0.406609 0.341185i
\(818\) 2.85593e12 + 4.94661e12i 0.223027 + 0.386294i
\(819\) −1.23193e12 + 1.27388e12i −0.0956768 + 0.0989352i
\(820\) 3.15541e12 5.46533e12i 0.243721 0.422138i
\(821\) −4.48393e12 2.54296e13i −0.344441 1.95342i −0.298251 0.954488i \(-0.596403\pi\)
−0.0461901 0.998933i \(-0.514708\pi\)
\(822\) −5.94563e12 + 5.54044e12i −0.454229 + 0.423273i
\(823\) −6.41370e12 + 2.33440e12i −0.487315 + 0.177368i −0.573980 0.818869i \(-0.694601\pi\)
0.0866652 + 0.996237i \(0.472379\pi\)
\(824\) −1.68095e13 + 6.11815e12i −1.27023 + 0.462326i
\(825\) −2.26692e12 6.93950e11i −0.170370 0.0521537i
\(826\) −4.45969e11 2.52921e12i −0.0333345 0.189049i
\(827\) 6.35461e12 1.10065e13i 0.472404 0.818229i −0.527097 0.849805i \(-0.676719\pi\)
0.999501 + 0.0315767i \(0.0100528\pi\)
\(828\) 5.92925e8 8.39333e9i 4.38392e−5 0.000620580i
\(829\) 8.41727e12 + 1.45791e13i 0.618979 + 1.07210i 0.989672 + 0.143347i \(0.0457866\pi\)
−0.370694 + 0.928755i \(0.620880\pi\)
\(830\) 1.53857e12 1.29101e12i 0.112529 0.0944232i
\(831\) 1.30514e13 + 2.01131e13i 0.949407 + 1.46310i
\(832\) −2.84094e12 + 1.61118e13i −0.205545 + 1.16570i
\(833\) 3.90980e12 + 3.28071e12i 0.281353 + 0.236084i
\(834\) −3.84217e12 + 1.62929e12i −0.274998 + 0.116614i
\(835\) −2.68908e13 9.78746e12i −1.91432 0.696756i
\(836\) 1.51679e12 0.107398
\(837\) −1.29567e13 + 7.16395e12i −0.912496 + 0.504531i
\(838\) 1.47625e13 1.03410
\(839\) −2.09727e13 7.63342e12i −1.46125 0.531852i −0.515541 0.856865i \(-0.672409\pi\)
−0.945709 + 0.325013i \(0.894631\pi\)
\(840\) −1.81776e12 1.37079e12i −0.125974 0.0949983i
\(841\) 2.13183e12 + 1.78882e12i 0.146951 + 0.123306i
\(842\) 1.14285e12 6.48143e12i 0.0783584 0.444392i
\(843\) 7.32033e12 3.81029e11i 0.499237 0.0259857i
\(844\) 1.35085e12 1.13349e12i 0.0916357 0.0768915i
\(845\) −1.73852e12 3.01121e12i −0.117307 0.203182i
\(846\) −7.93246e12 + 8.28025e11i −0.532404 + 0.0555746i
\(847\) 6.72679e11 1.16511e12i 0.0449089 0.0777845i
\(848\) −2.09968e12 1.19079e13i −0.139435 0.790775i
\(849\) 2.31320e12 + 1.00359e13i 0.152802 + 0.662933i
\(850\) −1.46493e12 + 5.33192e11i −0.0962570 + 0.0350347i
\(851\) −7.36140e9 + 2.67933e9i −0.000481146 + 0.000175123i
\(852\) −1.48620e12 6.44790e12i −0.0966269 0.419218i
\(853\) 1.19454e12 + 6.77458e12i 0.0772556 + 0.438139i 0.998761 + 0.0497720i \(0.0158495\pi\)
−0.921505 + 0.388367i \(0.873039\pi\)
\(854\) −7.23582e11 + 1.25328e12i −0.0465508 + 0.0806284i
\(855\) 1.11134e13 1.16006e12i 0.711211 0.0742394i
\(856\) −1.43527e13 2.48596e13i −0.913697 1.58257i
\(857\) 9.37934e12 7.87020e12i 0.593962 0.498393i −0.295537 0.955331i \(-0.595498\pi\)
0.889498 + 0.456938i \(0.151054\pi\)
\(858\) 7.61330e12 3.96278e11i 0.479601 0.0249636i
\(859\) 7.76449e11 4.40346e12i 0.0486568 0.275946i −0.950766 0.309909i \(-0.899702\pi\)
0.999423 + 0.0339623i \(0.0108126\pi\)
\(860\) −3.96057e12 3.32331e12i −0.246896 0.207171i
\(861\) −2.09487e12 1.57977e12i −0.129910 0.0979667i
\(862\) −7.47609e12 2.72107e12i −0.461203 0.167864i
\(863\) −1.77022e13 −1.08637 −0.543185 0.839613i \(-0.682782\pi\)
−0.543185 + 0.839613i \(0.682782\pi\)
\(864\) 8.72118e12 + 5.25290e12i 0.532431 + 0.320691i
\(865\) 1.93905e13 1.17765
\(866\) 2.20565e13 + 8.02790e12i 1.33262 + 0.485033i
\(867\) −1.31843e13 + 5.59086e12i −0.792449 + 0.336042i
\(868\) 5.45469e11 + 4.57702e11i 0.0326160 + 0.0273681i
\(869\) −2.53380e12 + 1.43699e13i −0.150724 + 0.854799i
\(870\) −9.52670e12 1.46813e13i −0.563775 0.868814i
\(871\) 2.00463e13 1.68209e13i 1.18019 0.990299i
\(872\) 4.77077e12 + 8.26322e12i 0.279424 + 0.483977i
\(873\) 9.90364e10 1.40194e12i 0.00577073 0.0816894i
\(874\) −8.38378e9 + 1.45211e10i −0.000486002 + 0.000841781i
\(875\) −2.90542e11 1.64775e12i −0.0167561 0.0950285i
\(876\) 1.02499e13 + 3.13770e12i 0.588100 + 0.180029i
\(877\) 1.81090e12 6.59112e11i 0.103370 0.0376237i −0.289817 0.957082i \(-0.593595\pi\)
0.393187 + 0.919458i \(0.371372\pi\)
\(878\) 1.55123e13 5.64601e12i 0.880948 0.320639i
\(879\) 2.35037e12 2.19020e12i 0.132797 0.123747i
\(880\) 1.08172e12 + 6.13471e12i 0.0608052 + 0.344844i
\(881\) −1.42842e13 + 2.47410e13i −0.798850 + 1.38365i 0.121515 + 0.992590i \(0.461225\pi\)
−0.920365 + 0.391059i \(0.872109\pi\)
\(882\) 1.01000e13 1.04439e13i 0.561969 0.581107i
\(883\) −1.57308e11 2.72466e11i −0.00870821 0.0150831i 0.861638 0.507523i \(-0.169439\pi\)
−0.870347 + 0.492440i \(0.836105\pi\)
\(884\) −1.85265e12 + 1.55456e12i −0.102037 + 0.0856192i
\(885\) 1.78385e13 3.49793e13i 0.977494 1.91675i
\(886\) 7.69880e10 4.36621e11i 0.00419731 0.0238041i
\(887\) 6.42115e12 + 5.38798e12i 0.348302 + 0.292260i 0.800108 0.599856i \(-0.204776\pi\)
−0.451806 + 0.892116i \(0.649220\pi\)
\(888\) 6.60318e11 5.36208e12i 0.0356365 0.289384i
\(889\) 2.90782e12 + 1.05836e12i 0.156138 + 0.0568297i
\(890\) 1.62659e13 0.869007
\(891\) 3.11266e12 9.53357e12i 0.165456 0.506764i
\(892\) −1.07406e12 −0.0568049
\(893\) −7.20503e12 2.62242e12i −0.379144 0.137997i
\(894\) 1.52400e11 1.23756e12i 0.00797935 0.0647959i
\(895\) −2.66648e13 2.23744e13i −1.38910 1.16560i
\(896\) −1.11303e11 + 6.31230e11i −0.00576926 + 0.0327191i
\(897\) 1.84709e10 3.62193e10i 0.000952625 0.00186799i
\(898\) 6.18853e12 5.19279e12i 0.317573 0.266476i
\(899\) 1.11468e13 + 1.93068e13i 0.569157 + 0.985809i
\(900\) −5.88644e11 2.05838e12i −0.0299062 0.104576i
\(901\) 5.21157e12 9.02671e12i 0.263456 0.456318i
\(902\) 1.96003e12 + 1.11159e13i 0.0985900 + 0.559132i
\(903\) −1.57259e12 + 1.46541e12i −0.0787081 + 0.0733441i
\(904\) 2.34685e13 8.54184e12i 1.16877 0.425396i
\(905\) −3.33605e13 + 1.21422e13i −1.65316 + 0.601699i
\(906\) −1.72843e13 5.29106e12i −0.852263 0.260895i
\(907\) −1.54084e12 8.73856e12i −0.0756007 0.428753i −0.998992 0.0448924i \(-0.985705\pi\)
0.923391 0.383860i \(-0.125406\pi\)
\(908\) 2.53339e11 4.38796e11i 0.0123685 0.0214228i
\(909\) −2.56597e12 + 1.24925e12i −0.124656 + 0.0606892i
\(910\) −1.35052e12 2.33916e12i −0.0652850 0.113077i
\(911\) −1.14696e13 + 9.62414e12i −0.551716 + 0.462945i −0.875522 0.483179i \(-0.839482\pi\)
0.323805 + 0.946124i \(0.395038\pi\)
\(912\) −4.00349e12 6.16964e12i −0.191629 0.295313i
\(913\) 3.00935e11 1.70669e12i 0.0143336 0.0812898i
\(914\) 1.56785e13 + 1.31558e13i 0.743099 + 0.623534i
\(915\) −2.03697e13 + 8.63785e12i −0.960703 + 0.407391i
\(916\) −2.75436e12 1.00251e12i −0.129268 0.0470497i
\(917\) 9.11092e11 0.0425501
\(918\) −2.14036e12 6.23770e12i −0.0994708 0.289890i
\(919\) −3.61739e13 −1.67292 −0.836461 0.548027i \(-0.815379\pi\)
−0.836461 + 0.548027i \(0.815379\pi\)
\(920\) 4.90835e10 + 1.78649e10i 0.00225886 + 0.000822159i
\(921\) −6.00579e11 4.52904e11i −0.0275044 0.0207414i
\(922\) −9.95201e11 8.35073e11i −0.0453546 0.0380570i
\(923\) 5.55203e12 3.14871e13i 0.251793 1.42799i
\(924\) −4.81681e11 + 2.50719e10i −0.0217388 + 0.00113152i
\(925\) −1.52689e12 + 1.28121e12i −0.0685757 + 0.0575418i
\(926\) −5.88259e12 1.01889e13i −0.262917 0.455386i
\(927\) −1.13734e13 + 2.54963e13i −0.505863 + 1.13401i
\(928\) 7.66513e12 1.32764e13i 0.339277 0.587644i
\(929\) 3.46775e12 + 1.96666e13i 0.152748 + 0.866280i 0.960815 + 0.277189i \(0.0894028\pi\)
−0.808067 + 0.589091i \(0.799486\pi\)
\(930\) −5.06843e12 2.19895e13i −0.222178 0.963923i
\(931\) 1.31251e13 4.77716e12i 0.572573 0.208399i
\(932\) −6.77444e11 + 2.46569e11i −0.0294104 + 0.0107045i
\(933\) 2.05767e11 + 8.92727e11i 0.00889015 + 0.0385701i
\(934\) 3.44141e12 + 1.95172e13i 0.147971 + 0.839184i
\(935\) −2.68490e12 + 4.65039e12i −0.114889 + 0.198993i
\(936\) 1.64649e13 + 2.26959e13i 0.701159 + 0.966509i
\(937\) 1.43376e13 + 2.48334e13i 0.607642 + 1.05247i 0.991628 + 0.129127i \(0.0412176\pi\)
−0.383986 + 0.923339i \(0.625449\pi\)
\(938\) 2.62898e12 2.20598e12i 0.110885 0.0930440i
\(939\) −3.32392e13 + 1.73012e12i −1.39526 + 0.0726243i
\(940\) −1.01836e12 + 5.77542e12i −0.0425429 + 0.241273i
\(941\) 2.00326e13 + 1.68093e13i 0.832881 + 0.698870i 0.955951 0.293528i \(-0.0948293\pi\)
−0.123069 + 0.992398i \(0.539274\pi\)
\(942\) 1.50847e13 + 1.13756e13i 0.624178 + 0.470701i
\(943\) 5.65660e10 + 2.05883e10i 0.00232945 + 0.000847850i
\(944\) −2.58450e13 −1.05926
\(945\) −3.51005e12 + 5.52095e11i −0.143176 + 0.0225201i
\(946\) 9.24719e12 0.375405
\(947\) 1.42502e13 + 5.18665e12i 0.575766 + 0.209562i 0.613458 0.789728i \(-0.289778\pi\)
−0.0376913 + 0.999289i \(0.512000\pi\)
\(948\) −1.21311e13 + 5.14426e12i −0.487824 + 0.206864i
\(949\) 3.96778e13 + 3.32936e13i 1.58800 + 1.33249i
\(950\) −7.40832e11 + 4.20147e12i −0.0295096 + 0.167357i
\(951\) 2.08892e13 + 3.21917e13i 0.828153 + 1.27624i
\(952\) −9.89562e11 + 8.30341e11i −0.0390460 + 0.0327635i
\(953\) −4.99811e12 8.65697e12i −0.196285 0.339976i 0.751036 0.660261i \(-0.229554\pi\)
−0.947321 + 0.320286i \(0.896221\pi\)
\(954\) −2.45863e13 1.66092e13i −0.961005 0.649202i
\(955\) 3.60917e12 6.25126e12i 0.140408 0.243194i
\(956\) 2.00132e12 + 1.13501e13i 0.0774919 + 0.439478i
\(957\) −1.44398e13 4.42031e12i −0.556490 0.170353i
\(958\) 1.30591e13 4.75314e12i 0.500921 0.182320i
\(959\) 2.33465e12 8.49744e11i 0.0891330 0.0324417i
\(960\) −2.39989e13 + 2.23634e13i −0.911949 + 0.849799i
\(961\) 4.00352e11 + 2.27051e12i 0.0151421 + 0.0858752i
\(962\) 3.20477e12 5.55082e12i 0.120645 0.208963i
\(963\) −4.34617e13 1.08691e13i −1.62850 0.407263i
\(964\) 2.77186e12 + 4.80099e12i 0.103377 + 0.179054i
\(965\) −3.49663e13 + 2.93402e13i −1.29801 + 1.08916i
\(966\) 2.42237e9 4.74999e9i 8.95043e−5 0.000175508i
\(967\) 2.08182e12 1.18066e13i 0.0765638 0.434215i −0.922296 0.386483i \(-0.873690\pi\)
0.998860 0.0477315i \(-0.0151992\pi\)
\(968\) −1.63066e13 1.36829e13i −0.596932 0.500885i
\(969\) 7.74883e11 6.29239e12i 0.0282344 0.229276i
\(970\) 2.01295e12 + 7.32654e11i 0.0730063 + 0.0265721i
\(971\) −1.18164e13 −0.426577 −0.213289 0.976989i \(-0.568417\pi\)
−0.213289 + 0.976989i \(0.568417\pi\)
\(972\) 8.75202e12 2.32841e12i 0.314492 0.0836683i
\(973\) 1.27584e12 0.0456339
\(974\) 1.20135e13 + 4.37254e12i 0.427713 + 0.155675i
\(975\) 1.26436e12 1.02671e13i 0.0448073 0.363855i
\(976\) 1.11562e13 + 9.36113e12i 0.393542 + 0.330221i
\(977\) 7.51419e12 4.26151e13i 0.263850 1.49637i −0.508441 0.861097i \(-0.669778\pi\)
0.772291 0.635269i \(-0.219111\pi\)
\(978\) 1.75487e13 3.44109e13i 0.613366 1.20274i
\(979\) 1.07516e13 9.02166e12i 0.374068 0.313880i
\(980\) −5.34159e12 9.25190e12i −0.184992 0.320416i
\(981\) 1.44465e13 + 3.61284e12i 0.498025 + 0.124548i
\(982\) −1.91475e13 + 3.31644e13i −0.657067 + 1.13807i
\(983\) 5.72807e12 + 3.24855e13i 0.195667 + 1.10968i 0.911466 + 0.411375i \(0.134951\pi\)
−0.715799 + 0.698306i \(0.753937\pi\)
\(984\) −3.03716e13 + 2.83018e13i −1.03274 + 0.962357i
\(985\) −2.54657e13 + 9.26876e12i −0.861971 + 0.313732i
\(986\) −9.33130e12 + 3.39632e12i −0.314410 + 0.114436i
\(987\) 2.33142e12 + 7.13693e11i 0.0781974 + 0.0239378i
\(988\) 1.14928e12 + 6.51790e12i 0.0383725 + 0.217621i
\(989\) 2.46580e10 4.27089e10i 0.000819548 0.00141950i
\(990\) 1.26664e13 + 8.55672e12i 0.419078 + 0.283106i
\(991\) 1.35439e12 + 2.34588e12i 0.0446080 + 0.0772634i 0.887467 0.460871i \(-0.152463\pi\)
−0.842859 + 0.538134i \(0.819129\pi\)
\(992\) 1.51422e13 1.27058e13i 0.496461 0.416580i
\(993\) −1.45353e13 2.23999e13i −0.474409 0.731096i
\(994\) 7.28122e11 4.12939e12i 0.0236573 0.134167i
\(995\) 3.55171e13 + 2.98024e13i 1.14877 + 0.963934i
\(996\) 1.44080e12 6.10976e11i 0.0463912 0.0196724i
\(997\) 3.57905e13 + 1.30267e13i 1.14720 + 0.417547i 0.844509 0.535541i \(-0.179892\pi\)
0.302692 + 0.953088i \(0.402115\pi\)
\(998\) 3.99473e13 1.27468
\(999\) −5.29927e12 6.55836e12i −0.168334 0.208329i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 27.10.e.a.4.18 156
3.2 odd 2 81.10.e.a.64.9 156
27.7 even 9 inner 27.10.e.a.7.18 yes 156
27.20 odd 18 81.10.e.a.19.9 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.10.e.a.4.18 156 1.1 even 1 trivial
27.10.e.a.7.18 yes 156 27.7 even 9 inner
81.10.e.a.19.9 156 27.20 odd 18
81.10.e.a.64.9 156 3.2 odd 2