Properties

Label 27.10.e.a.7.18
Level $27$
Weight $10$
Character 27.7
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 7.18
Character \(\chi\) \(=\) 27.7
Dual form 27.10.e.a.4.18

$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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 0.0740446 0.997255i \(-0.476409\pi\)
0.697745 + 0.716347i \(0.254187\pi\)
\(3\) −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 0.904247 + 0.427010i \(0.140433\pi\)
−0.703668 + 0.710529i \(0.748456\pi\)
\(6\) −1184.52 2322.71i −0.373132 0.731670i
\(7\) 610.601 + 512.355i 0.0961205 + 0.0806547i 0.689582 0.724208i \(-0.257794\pi\)
−0.593461 + 0.804863i \(0.702239\pi\)
\(8\) −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 0.902895 + 0.429862i \(0.141438\pi\)
−0.995465 + 0.0951300i \(0.969673\pi\)
\(12\) 17102.0 + 15936.5i 0.238085 + 0.221859i
\(13\) 106141. + 38632.3i 1.03072 + 0.375150i 0.801354 0.598191i \(-0.204114\pi\)
0.229363 + 0.973341i \(0.426336\pi\)
\(14\) 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 0.944107 0.329639i \(-0.106927\pi\)
−0.757529 + 0.652801i \(0.773594\pi\)
\(18\) −303113. + 204767.i −0.680579 + 0.459762i
\(19\) −175832. + 304550.i −0.309533 + 0.536127i −0.978260 0.207381i \(-0.933506\pi\)
0.668727 + 0.743508i \(0.266839\pi\)
\(20\) −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 −0.643520 0.765430i \(-0.722526\pi\)
0.642055 + 0.766659i \(0.278082\pi\)
\(24\) 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 −0.799508 0.600656i \(-0.794906\pi\)
−0.226364 + 0.974043i \(0.572684\pi\)
\(30\) 3.36051e6 2.53421e6i 0.757461 0.571210i
\(31\) −4.10711e6 + 3.44627e6i −0.798746 + 0.670227i −0.947893 0.318588i \(-0.896792\pi\)
0.149147 + 0.988815i \(0.452347\pi\)
\(32\) −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 0.925184 0.379519i \(-0.123910\pi\)
−0.791265 + 0.611474i \(0.790577\pi\)
\(38\) −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 −0.348872 0.937171i \(-0.613435\pi\)
−0.869653 + 0.493664i \(0.835657\pi\)
\(42\) 466783. 2.02515e6i 0.0231469 0.100423i
\(43\) 3.33783e6 1.89298e7i 0.148887 0.844379i −0.815277 0.579071i \(-0.803415\pi\)
0.964164 0.265308i \(-0.0854735\pi\)
\(44\) −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 0.857335 0.514760i \(-0.172119\pi\)
−0.358065 + 0.933697i \(0.616563\pi\)
\(48\) 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 0.520291 + 0.853989i \(0.325823\pi\)
−0.196832 + 0.980437i \(0.563065\pi\)
\(60\) −2.05412e7 + 3.16554e7i −0.204619 + 0.315331i
\(61\) −7.48377e7 6.27963e7i −0.692048 0.580697i 0.227451 0.973790i \(-0.426961\pi\)
−0.919499 + 0.393092i \(0.871405\pi\)
\(62\) −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 0.903417 0.428763i \(-0.141051\pi\)
0.416454 + 0.909157i \(0.363273\pi\)
\(68\) −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 0.980358 + 0.197228i \(0.0631938\pi\)
−0.319375 + 0.947629i \(0.603473\pi\)
\(72\) 6.82535e7 2.38669e8i 0.299315 1.04665i
\(73\) 2.29279e8 3.97123e8i 0.944957 1.63671i 0.189119 0.981954i \(-0.439437\pi\)
0.755837 0.654759i \(-0.227230\pi\)
\(74\) 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 −0.963627 0.267252i \(-0.913884\pi\)
−0.566394 + 0.824134i \(0.691662\pi\)
\(80\) −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 −0.268243 0.963351i \(-0.586443\pi\)
0.413745 + 0.910393i \(0.364221\pi\)
\(84\) 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 −0.540855 0.841116i \(-0.681899\pi\)
0.998855 + 0.0478365i \(0.0152326\pi\)
\(90\) −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 −0.976872 0.213827i \(-0.931407\pi\)
0.991092 + 0.133178i \(0.0425182\pi\)
\(98\) −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 0.694345 0.719642i \(-0.255694\pi\)
−0.588137 + 0.808761i \(0.700138\pi\)
\(102\) 1.82379e8 2.81058e8i 0.166830 0.257096i
\(103\) 2.46300e8 + 1.39683e9i 0.215624 + 1.22286i 0.879821 + 0.475305i \(0.157662\pi\)
−0.664198 + 0.747557i \(0.731227\pi\)
\(104\) −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 −0.907493 0.420067i \(-0.862007\pi\)
0.709093 0.705115i \(-0.249105\pi\)
\(114\) 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 −0.317948 0.948108i \(-0.602994\pi\)
0.980060 0.198703i \(-0.0636731\pi\)
\(128\) −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 −0.503595 0.863940i \(-0.667990\pi\)
0.763366 + 0.645966i \(0.223545\pi\)
\(132\) −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 0.0385301 0.999257i \(-0.487732\pi\)
0.671826 + 0.740709i \(0.265510\pi\)
\(138\) 6.15856e6 + 2.61157e6i 0.00144552 + 0.000612978i
\(139\) 1.22616e9 1.02887e9i 0.278599 0.233772i −0.492771 0.870159i \(-0.664016\pi\)
0.771370 + 0.636387i \(0.219572\pi\)
\(140\) −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 0.304403 0.952543i \(-0.401543\pi\)
−0.379097 + 0.925357i \(0.623765\pi\)
\(150\) 1.24520e9 + 1.16034e9i 0.200830 + 0.187143i
\(151\) 1.20387e9 6.82747e9i 0.188444 1.06872i −0.733006 0.680222i \(-0.761883\pi\)
0.921450 0.388497i \(-0.127006\pi\)
\(152\) −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 0.948770 + 0.315968i \(0.102329\pi\)
−0.783485 + 0.621411i \(0.786560\pi\)
\(158\) −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 0.617534 + 0.786544i \(0.288132\pi\)
−0.311278 + 0.950319i \(0.600757\pi\)
\(168\) 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 −0.758722 0.651414i \(-0.774176\pi\)
0.935762 0.352631i \(-0.114713\pi\)
\(174\) 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 0.929036 + 0.369990i \(0.120639\pi\)
−0.144097 + 0.989564i \(0.546028\pi\)
\(180\) 4.76006e9 + 2.31744e9i 0.337976 + 0.164544i
\(181\) −1.09960e10 + 1.90457e10i −0.761522 + 1.31900i 0.180543 + 0.983567i \(0.442214\pi\)
−0.942066 + 0.335428i \(0.891119\pi\)
\(182\) 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 −0.225259 0.974299i \(-0.572323\pi\)
0.453709 + 0.891150i \(0.350100\pi\)
\(192\) −1.62245e10 + 1.22351e10i −0.861620 + 0.649758i
\(193\) −2.16606e10 + 1.81754e10i −1.12373 + 0.942921i −0.998787 0.0492430i \(-0.984319\pi\)
−0.124943 + 0.992164i \(0.539875\pi\)
\(194\) −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 −0.993362 0.115027i \(-0.963305\pi\)
0.596297 + 0.802764i \(0.296638\pi\)
\(198\) −3.85758e9 8.64768e9i −0.178370 0.399859i
\(199\) −1.43606e10 2.48733e10i −0.649134 1.12433i −0.983330 0.181830i \(-0.941798\pi\)
0.334196 0.942504i \(-0.391535\pi\)
\(200\) 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 −0.999947 0.0103071i \(-0.996719\pi\)
0.936117 0.351687i \(-0.114392\pi\)
\(212\) −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 0.707192 0.707021i \(-0.249962\pi\)
−0.573477 + 0.819221i \(0.694406\pi\)
\(224\) 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 −0.977497 0.210952i \(-0.932344\pi\)
0.990696 + 0.136094i \(0.0434549\pi\)
\(228\) −7.86055e9 + 2.40627e9i −0.192640 + 0.0589709i
\(229\) 1.65307e10 + 6.01668e9i 0.397220 + 0.144576i 0.532904 0.846176i \(-0.321101\pi\)
−0.135684 + 0.990752i \(0.543323\pi\)
\(230\) −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 0.889067 0.457777i \(-0.151354\pi\)
−0.840980 + 0.541066i \(0.818021\pi\)
\(234\) −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 −0.993142 0.116914i \(-0.962700\pi\)
−0.0573191 + 0.998356i \(0.518255\pi\)
\(240\) 4.12641e9 + 3.35083e10i 0.0802826 + 0.651930i
\(241\) −3.12649e10 + 1.13795e10i −0.597007 + 0.217293i −0.622809 0.782374i \(-0.714008\pi\)
0.0258013 + 0.999667i \(0.491786\pi\)
\(242\) 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 −0.729566 0.683910i \(-0.760278\pi\)
0.957067 + 0.289868i \(0.0936114\pi\)
\(252\) 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 0.432466 0.901650i \(-0.357644\pi\)
−0.248282 + 0.968688i \(0.579866\pi\)
\(258\) −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 0.736858 0.676047i \(-0.236308\pi\)
−0.537822 + 0.843058i \(0.680753\pi\)
\(264\) −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 0.982612 + 0.185670i \(0.0594456\pi\)
0.353478 + 0.935443i \(0.384999\pi\)
\(278\) 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 0.910143 + 0.414295i \(0.135972\pi\)
−0.996952 + 0.0780227i \(0.975139\pi\)
\(282\) 1.27683e10 5.53955e10i 0.120230 0.521620i
\(283\) 6.89819e10 + 2.51073e10i 0.639287 + 0.232681i 0.641268 0.767317i \(-0.278408\pi\)
−0.00198143 + 0.999998i \(0.500631\pi\)
\(284\) −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 −0.709660 0.704545i \(-0.751151\pi\)
0.570610 + 0.821221i \(0.306707\pi\)
\(294\) −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 0.857285 0.514842i \(-0.172150\pi\)
−0.874509 + 0.485009i \(0.838816\pi\)
\(308\) 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 0.360550 0.932740i \(-0.382589\pi\)
−0.323356 + 0.946277i \(0.604811\pi\)
\(312\) 1.46215e11 + 1.36250e11i 0.873565 + 0.814031i
\(313\) 4.11967e10 2.33638e11i 0.242612 1.37592i −0.583361 0.812213i \(-0.698263\pi\)
0.825973 0.563709i \(-0.190626\pi\)
\(314\) 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 0.999966 0.00828314i \(-0.00263663\pi\)
0.165485 + 0.986212i \(0.447081\pi\)
\(318\) −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 0.244732 0.969591i \(-0.421300\pi\)
−0.912363 + 0.409382i \(0.865744\pi\)
\(332\) −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 −0.238221 0.971211i \(-0.576564\pi\)
−0.806771 + 0.590865i \(0.798787\pi\)
\(338\) 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 −0.919833 0.392310i \(-0.871676\pi\)
0.226623 + 0.973983i \(0.427232\pi\)
\(348\) −8.94882e10 3.79479e10i −0.327084 0.138701i
\(349\) −1.11185e11 + 4.04679e10i −0.401172 + 0.146015i −0.534723 0.845027i \(-0.679584\pi\)
0.133551 + 0.991042i \(0.457362\pi\)
\(350\) −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 −0.186655 0.982425i \(-0.559765\pi\)
0.488505 + 0.872561i \(0.337542\pi\)
\(354\) 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 −0.972159 0.234323i \(-0.924713\pi\)
0.689009 + 0.724753i \(0.258046\pi\)
\(360\) 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 0.922812 + 0.385251i \(0.125885\pi\)
−0.998923 + 0.0463968i \(0.985226\pi\)
\(368\) −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 −0.566758 0.823884i \(-0.691802\pi\)
0.250793 0.968041i \(-0.419309\pi\)
\(374\) −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 −0.956328 0.292297i \(-0.905580\pi\)
0.798683 0.601753i \(-0.205531\pi\)
\(384\) −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 −0.792451 0.609936i \(-0.791195\pi\)
0.953270 0.302118i \(-0.0976937\pi\)
\(390\) 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 −0.437683 0.899129i \(-0.644201\pi\)
0.997510 0.0705199i \(-0.0224658\pi\)
\(398\) −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 −0.568004 0.823026i \(-0.692284\pi\)
0.711890 + 0.702291i \(0.247840\pi\)
\(402\) −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 −0.410618 0.911807i \(-0.634687\pi\)
0.826652 + 0.562714i \(0.190243\pi\)
\(410\) −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 0.857308 0.514804i \(-0.172135\pi\)
0.325827 + 0.945430i \(0.394357\pi\)
\(420\) −2.87613e10 + 8.80440e9i −0.0451010 + 0.0138063i
\(421\) −6.14953e10 + 3.48757e11i −0.0954053 + 0.541070i 0.899217 + 0.437503i \(0.144137\pi\)
−0.994622 + 0.103568i \(0.966974\pi\)
\(422\) −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 0.965018 0.262184i \(-0.0844428\pi\)
−0.0906275 + 0.995885i \(0.528887\pi\)
\(440\) 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 −0.987256 0.159138i \(-0.949129\pi\)
0.982146 + 0.188121i \(0.0602396\pi\)
\(444\) −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 0.964179 0.265251i \(-0.0854549\pi\)
−0.711804 + 0.702378i \(0.752122\pi\)
\(450\) 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 0.278914 0.960316i \(-0.410026\pi\)
0.830940 + 0.556362i \(0.187803\pi\)
\(458\) 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 −0.375668 0.926754i \(-0.622587\pi\)
0.307928 + 0.951410i \(0.400364\pi\)
\(462\) 4.95287e10 + 2.10029e10i 0.0505787 + 0.0214482i
\(463\) −4.84959e11 + 4.06929e11i −0.490445 + 0.411532i −0.854186 0.519968i \(-0.825944\pi\)
0.363741 + 0.931500i \(0.381499\pi\)
\(464\) −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 −0.481007 0.876717i \(-0.659729\pi\)
0.999762 0.0217944i \(-0.00693792\pi\)
\(468\) 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 0.856596 0.515988i \(-0.172575\pi\)
−0.359403 + 0.933182i \(0.617020\pi\)
\(480\) −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 −0.729789 0.683672i \(-0.760382\pi\)
0.451948 0.892045i \(-0.350729\pi\)
\(492\) −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 0.944920 0.327300i \(-0.106139\pi\)
0.513466 + 0.858110i \(0.328361\pi\)
\(500\) −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 0.838611 0.544731i \(-0.183368\pi\)
−0.891057 + 0.453892i \(0.850035\pi\)
\(504\) 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 −0.910738 0.412985i \(-0.864486\pi\)
0.248563 + 0.968616i \(0.420042\pi\)
\(510\) 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 −0.882571 0.470180i \(-0.844189\pi\)
0.848473 + 0.529239i \(0.177522\pi\)
\(522\) 8.93162e11 1.23117e12i 0.526518 0.725775i
\(523\) −1.53405e12 2.65706e12i −0.896566 1.55290i −0.831854 0.554995i \(-0.812720\pi\)
−0.0647127 0.997904i \(-0.520613\pi\)
\(524\) −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 −0.998773 0.0495193i \(-0.984231\pi\)
−0.222202 0.975001i \(-0.571324\pi\)
\(548\) −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 −0.993013 0.118006i \(-0.962350\pi\)
0.394311 0.918977i \(-0.370983\pi\)
\(558\) 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 −0.959667 0.281141i \(-0.909287\pi\)
0.110225 + 0.993907i \(0.464843\pi\)
\(564\) 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 −0.0795917 0.996828i \(-0.525362\pi\)
0.579778 + 0.814775i \(0.303139\pi\)
\(570\) 1.80906e11 + 1.46904e12i 0.0717822 + 0.582903i
\(571\) −1.49100e12 + 1.25110e12i −0.586969 + 0.492526i −0.887227 0.461332i \(-0.847372\pi\)
0.300258 + 0.953858i \(0.402927\pi\)
\(572\) −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 0.646595 0.762834i \(-0.276193\pi\)
−0.983931 + 0.178550i \(0.942859\pi\)
\(578\) 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 0.999735 + 0.0230158i \(0.00732681\pi\)
0.196268 + 0.980550i \(0.437118\pi\)
\(588\) 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 0.995651 0.0931597i \(-0.0296967\pi\)
−0.967469 + 0.252991i \(0.918586\pi\)
\(600\) −1.15347e12 6.00391e10i −0.363351 0.0189127i
\(601\) 2.07245e12 + 1.73900e12i 0.647962 + 0.543705i 0.906452 0.422309i \(-0.138780\pi\)
−0.258490 + 0.966014i \(0.583225\pi\)
\(602\) 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 0.334943 0.942238i \(-0.391283\pi\)
−0.349078 + 0.937094i \(0.613505\pi\)
\(608\) 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 −0.865162 0.501493i \(-0.832784\pi\)
0.866886 + 0.498506i \(0.166118\pi\)
\(614\) −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 −0.980202 0.197999i \(-0.936556\pi\)
0.0247802 + 0.999693i \(0.492111\pi\)
\(618\) 2.95270e12 2.22667e12i 0.814275 0.614054i
\(619\) 6.52254e12 2.37401e12i 1.78570 0.649942i 0.786214 0.617954i \(-0.212038\pi\)
0.999488 0.0319882i \(-0.0101839\pi\)
\(620\) 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 0.998611 + 0.0526798i \(0.0167763\pi\)
−0.453684 + 0.891163i \(0.649890\pi\)
\(632\) 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 −0.927174 0.374631i \(-0.877769\pi\)
−0.529942 0.848034i \(-0.677786\pi\)
\(642\) −2.69608e12 5.28670e12i −0.626361 1.22822i
\(643\) −7.54498e11 4.27897e12i −0.174064 0.987165i −0.939219 0.343319i \(-0.888449\pi\)
0.765155 0.643846i \(-0.222662\pi\)
\(644\) 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 −0.807669 0.589636i \(-0.799271\pi\)
0.557293 0.830316i \(-0.311840\pi\)
\(654\) 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 −0.989080 0.147378i \(-0.952917\pi\)
0.979838 + 0.199796i \(0.0640278\pi\)
\(660\) −7.14654e11 6.65950e11i −0.146605 0.136614i
\(661\) −4.08951e12 1.48846e12i −0.833229 0.303271i −0.110046 0.993927i \(-0.535100\pi\)
−0.723184 + 0.690656i \(0.757322\pi\)
\(662\) −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 0.131936 0.991258i \(-0.457881\pi\)
0.738237 + 0.674541i \(0.235659\pi\)
\(674\) −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 −0.267048 0.963683i \(-0.586048\pi\)
0.414873 + 0.909879i \(0.363826\pi\)
\(678\) −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 −0.605290 0.796005i \(-0.706943\pi\)
0.992006 + 0.126194i \(0.0402761\pi\)
\(684\) 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 0.750240 + 0.661166i \(0.229938\pi\)
−0.931127 + 0.364695i \(0.881173\pi\)
\(692\) 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 0.982277 0.187436i \(-0.0600178\pi\)
−0.0140180 + 0.999902i \(0.504462\pi\)
\(710\) −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 0.508911 0.860819i \(-0.330048\pi\)
−0.999947 + 0.0103202i \(0.996715\pi\)
\(720\) 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 −0.718211 0.695825i \(-0.755039\pi\)
−0.102914 + 0.994690i \(0.532817\pi\)
\(728\) −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 −0.414533 0.910034i \(-0.636055\pi\)
0.824226 + 0.566261i \(0.191611\pi\)
\(734\) 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 0.566820 0.823841i \(-0.308173\pi\)
−0.996878 + 0.0789601i \(0.974840\pi\)
\(740\) 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 0.824484 0.565885i \(-0.191465\pi\)
0.267848 + 0.963461i \(0.413687\pi\)
\(744\) −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 0.993840 + 0.110828i \(0.0353503\pi\)
−0.895998 + 0.444057i \(0.853539\pi\)
\(752\) −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 0.988703 + 0.149889i \(0.0478917\pi\)
−0.877812 + 0.479006i \(0.840997\pi\)
\(762\) −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 −0.540849 0.841119i \(-0.681897\pi\)
−0.954976 + 0.296684i \(0.904119\pi\)
\(770\) −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 0.890371 0.455236i \(-0.150445\pi\)
−0.839431 + 0.543466i \(0.817112\pi\)
\(774\) 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 −0.710148 0.704053i \(-0.751372\pi\)
0.570041 + 0.821616i \(0.306927\pi\)
\(788\) −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 0.990377 0.138396i \(-0.0441947\pi\)
0.669713 + 0.742620i \(0.266417\pi\)
\(798\) 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 −0.0461901 + 0.998933i \(0.514708\pi\)
−0.298251 + 0.954488i \(0.596403\pi\)
\(822\) −5.94563e12 5.54044e12i −0.454229 0.423273i
\(823\) −6.41370e12 2.33440e12i −0.487315 0.177368i 0.0866652 0.996237i \(-0.472379\pi\)
−0.573980 + 0.818869i \(0.694601\pi\)
\(824\) −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 0.999501 0.0315767i \(-0.0100528\pi\)
−0.527097 + 0.849805i \(0.676719\pi\)
\(828\) 5.92925e8 + 8.39333e9i 4.38392e−5 + 0.000620580i
\(829\) 8.41727e12 1.45791e13i 0.618979 1.07210i −0.370694 0.928755i \(-0.620880\pi\)
0.989672 0.143347i \(-0.0457866\pi\)
\(830\) 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 −0.945709 0.325013i \(-0.894631\pi\)
−0.515541 + 0.856865i \(0.672409\pi\)
\(840\) −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 −0.921505 0.388367i \(-0.873039\pi\)
0.998761 0.0497720i \(-0.0158495\pi\)
\(854\) −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 0.889498 0.456938i \(-0.151054\pi\)
−0.295537 + 0.955331i \(0.595498\pi\)
\(858\) 7.61330e12 + 3.96278e11i 0.479601 + 0.0249636i
\(859\) 7.76449e11 + 4.40346e12i 0.0486568 + 0.275946i 0.999423 0.0339623i \(-0.0108126\pi\)
−0.950766 + 0.309909i \(0.899702\pi\)
\(860\) −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 0.393187 0.919458i \(-0.371372\pi\)
−0.289817 + 0.957082i \(0.593595\pi\)
\(878\) 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 −0.920365 0.391059i \(-0.872109\pi\)
0.121515 0.992590i \(-0.461225\pi\)
\(882\) 1.01000e13 + 1.04439e13i 0.561969 + 0.581107i
\(883\) −1.57308e11 + 2.72466e11i −0.00870821 + 0.0150831i −0.870347 0.492440i \(-0.836105\pi\)
0.861638 + 0.507523i \(0.169439\pi\)
\(884\) −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 −0.451806 0.892116i \(-0.649220\pi\)
0.800108 + 0.599856i \(0.204776\pi\)
\(888\) 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 0.923391 + 0.383860i \(0.125406\pi\)
−0.998992 + 0.0448924i \(0.985705\pi\)
\(908\) 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 0.323805 0.946124i \(-0.395038\pi\)
−0.875522 + 0.483179i \(0.839482\pi\)
\(912\) −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 −0.808067 0.589091i \(-0.799486\pi\)
0.960815 0.277189i \(-0.0894028\pi\)
\(930\) −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 −0.383986 0.923339i \(-0.625449\pi\)
0.991628 0.129127i \(-0.0412176\pi\)
\(938\) 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 −0.123069 0.992398i \(-0.539274\pi\)
0.955951 + 0.293528i \(0.0948293\pi\)
\(942\) 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 −0.0376913 0.999289i \(-0.512000\pi\)
0.613458 + 0.789728i \(0.289778\pi\)
\(948\) −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 −0.947321 0.320286i \(-0.896221\pi\)
0.751036 + 0.660261i \(0.229554\pi\)
\(954\) −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 0.998860 + 0.0477315i \(0.0151992\pi\)
−0.922296 + 0.386483i \(0.873690\pi\)
\(968\) −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 0.772291 + 0.635269i \(0.219111\pi\)
−0.508441 + 0.861097i \(0.669778\pi\)
\(978\) 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 −0.715799 0.698306i \(-0.753937\pi\)
0.911466 0.411375i \(-0.134951\pi\)
\(984\) −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 −0.842859 0.538134i \(-0.819129\pi\)
0.887467 + 0.460871i \(0.152463\pi\)
\(992\) 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 0.302692 0.953088i \(-0.402115\pi\)
0.844509 + 0.535541i \(0.179892\pi\)
\(998\) 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.7.18 yes 156
3.2 odd 2 81.10.e.a.19.9 156
27.4 even 9 inner 27.10.e.a.4.18 156
27.23 odd 18 81.10.e.a.64.9 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.10.e.a.4.18 156 27.4 even 9 inner
27.10.e.a.7.18 yes 156 1.1 even 1 trivial
81.10.e.a.19.9 156 3.2 odd 2
81.10.e.a.64.9 156 27.23 odd 18