Properties

Label 9.10.c.a.4.2
Level $9$
Weight $10$
Character 9.4
Analytic conductor $4.635$
Analytic rank $0$
Dimension $16$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9,10,Mod(4,9)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9, base_ring=CyclotomicField(6))
 
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("9.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 9.c (of order \(3\), degree \(2\), 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: \(4.63532252547\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{28}\cdot 17^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.2
Root \(0.500000 + 15.6774i\) of defining polynomial
Character \(\chi\) \(=\) 9.4
Dual form 9.10.c.a.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-12.8270 - 22.2170i) q^{2} +(-90.7998 - 106.950i) q^{3} +(-73.0637 + 126.550i) q^{4} +(-353.226 + 611.805i) q^{5} +(-1211.43 + 3389.15i) q^{6} +(2284.21 + 3956.36i) q^{7} -9386.09 q^{8} +(-3193.79 + 19422.2i) q^{9} +18123.3 q^{10} +(-35716.7 - 61863.1i) q^{11} +(20168.8 - 3676.53i) q^{12} +(13201.0 - 22864.9i) q^{13} +(58599.1 - 101497. i) q^{14} +(97505.6 - 17774.1i) q^{15} +(157804. + 273325. i) q^{16} -314759. q^{17} +(472469. - 178171. i) q^{18} -904019. q^{19} +(-51616.0 - 89401.5i) q^{20} +(215729. - 603534. i) q^{21} +(-916276. + 1.58704e6i) q^{22} +(55921.2 - 96858.3i) q^{23} +(852255. + 1.00385e6i) q^{24} +(727026. + 1.25925e6i) q^{25} -677318. q^{26} +(2.36720e6 - 1.42195e6i) q^{27} -667571. q^{28} +(-2.19402e6 - 3.80015e6i) q^{29} +(-1.64559e6 - 1.93829e6i) q^{30} +(4.94392e6 - 8.56313e6i) q^{31} +(1.64546e6 - 2.85003e6i) q^{32} +(-3.37322e6 + 9.43708e6i) q^{33} +(4.03742e6 + 6.99301e6i) q^{34} -3.22736e6 q^{35} +(-2.22452e6 - 1.82323e6i) q^{36} -6.32122e6 q^{37} +(1.15959e7 + 2.00846e7i) q^{38} +(-3.64406e6 + 664268. i) q^{39} +(3.31541e6 - 5.74246e6i) q^{40} +(-2.68019e6 + 4.64223e6i) q^{41} +(-1.61759e7 + 2.94867e6i) q^{42} +(-1.12275e7 - 1.94466e7i) q^{43} +1.04384e7 q^{44} +(-1.07544e7 - 8.81438e6i) q^{45} -2.86920e6 q^{46} +(2.23644e7 + 3.87363e7i) q^{47} +(1.49036e7 - 4.16950e7i) q^{48} +(9.74159e6 - 1.68729e7i) q^{49} +(1.86511e7 - 3.23047e7i) q^{50} +(2.85801e7 + 3.36636e7i) q^{51} +(1.92903e6 + 3.34118e6i) q^{52} -4.00972e7 q^{53} +(-6.19556e7 - 3.43528e7i) q^{54} +5.04642e7 q^{55} +(-2.14398e7 - 3.71348e7i) q^{56} +(8.20848e7 + 9.66852e7i) q^{57} +(-5.62853e7 + 9.74890e7i) q^{58} +(4.79118e7 - 8.29857e7i) q^{59} +(-4.87481e6 + 1.36380e7i) q^{60} +(-1.01113e7 - 1.75132e7i) q^{61} -2.53663e8 q^{62} +(-8.41364e7 + 3.17284e7i) q^{63} +7.71659e7 q^{64} +(9.32588e6 + 1.61529e7i) q^{65} +(2.52932e8 - 4.61065e7i) q^{66} +(-9.12489e7 + 1.58048e8i) q^{67} +(2.29975e7 - 3.98328e7i) q^{68} +(-1.54367e7 + 2.81392e6i) q^{69} +(4.13974e7 + 7.17024e7i) q^{70} +1.38543e8 q^{71} +(2.99772e7 - 1.82298e8i) q^{72} -2.17970e8 q^{73} +(8.10823e7 + 1.40439e8i) q^{74} +(6.86631e7 - 1.92095e8i) q^{75} +(6.60510e7 - 1.14404e8i) q^{76} +(1.63169e8 - 2.82617e8i) q^{77} +(6.15004e7 + 7.24395e7i) q^{78} +(-1.97294e8 - 3.41722e8i) q^{79} -2.22962e8 q^{80} +(-3.67020e8 - 1.24061e8i) q^{81} +1.37515e8 q^{82} +(2.36638e8 + 4.09870e8i) q^{83} +(6.06153e7 + 7.13970e7i) q^{84} +(1.11181e8 - 1.92571e8i) q^{85} +(-2.88030e8 + 4.98883e8i) q^{86} +(-2.07211e8 + 5.79704e8i) q^{87} +(3.35240e8 + 5.80653e8i) q^{88} +2.60507e8 q^{89} +(-5.78820e7 + 3.51994e8i) q^{90} +1.20616e8 q^{91} +(8.17161e6 + 1.41537e7i) q^{92} +(-1.36474e9 + 2.48775e8i) q^{93} +(5.73736e8 - 9.93741e8i) q^{94} +(3.19323e8 - 5.53083e8i) q^{95} +(-4.54219e8 + 8.27988e7i) q^{96} +(-2.87421e8 - 4.97828e8i) q^{97} -4.99822e8 q^{98} +(1.31559e9 - 4.96118e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 15 q^{2} - 3 q^{3} - 1793 q^{4} + 453 q^{5} + 2439 q^{6} - 343 q^{7} - 14478 q^{8} - 15669 q^{9} + 1020 q^{10} + 99150 q^{11} - 241212 q^{12} + 32435 q^{13} + 394824 q^{14} + 723843 q^{15} - 328193 q^{16}+ \cdots + 1672014609 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.8270 22.2170i −0.566879 0.981862i −0.996872 0.0790305i \(-0.974818\pi\)
0.429994 0.902832i \(-0.358516\pi\)
\(3\) −90.7998 106.950i −0.647201 0.762319i
\(4\) −73.0637 + 126.550i −0.142703 + 0.247168i
\(5\) −353.226 + 611.805i −0.252748 + 0.437772i −0.964281 0.264880i \(-0.914668\pi\)
0.711534 + 0.702652i \(0.248001\pi\)
\(6\) −1211.43 + 3389.15i −0.381608 + 1.06760i
\(7\) 2284.21 + 3956.36i 0.359579 + 0.622809i 0.987891 0.155153i \(-0.0495870\pi\)
−0.628311 + 0.777962i \(0.716254\pi\)
\(8\) −9386.09 −0.810177
\(9\) −3193.79 + 19422.2i −0.162261 + 0.986748i
\(10\) 18123.3 0.573109
\(11\) −35716.7 61863.1i −0.735537 1.27399i −0.954487 0.298251i \(-0.903597\pi\)
0.218951 0.975736i \(-0.429737\pi\)
\(12\) 20168.8 3676.53i 0.280778 0.0511826i
\(13\) 13201.0 22864.9i 0.128193 0.222036i −0.794784 0.606893i \(-0.792416\pi\)
0.922976 + 0.384857i \(0.125749\pi\)
\(14\) 58599.1 101497.i 0.407675 0.706114i
\(15\) 97505.6 17774.1i 0.497301 0.0906520i
\(16\) 157804. + 273325.i 0.601975 + 1.04265i
\(17\) −314759. −0.914026 −0.457013 0.889460i \(-0.651081\pi\)
−0.457013 + 0.889460i \(0.651081\pi\)
\(18\) 472469. 178171.i 1.06083 0.400048i
\(19\) −904019. −1.59143 −0.795713 0.605674i \(-0.792904\pi\)
−0.795713 + 0.605674i \(0.792904\pi\)
\(20\) −51616.0 89401.5i −0.0721355 0.124942i
\(21\) 215729. 603534.i 0.242059 0.677197i
\(22\) −916276. + 1.58704e6i −0.833920 + 1.44439i
\(23\) 55921.2 96858.3i 0.0416678 0.0721708i −0.844439 0.535651i \(-0.820066\pi\)
0.886107 + 0.463480i \(0.153400\pi\)
\(24\) 852255. + 1.00385e6i 0.524347 + 0.617614i
\(25\) 727026. + 1.25925e6i 0.372237 + 0.644734i
\(26\) −677318. −0.290678
\(27\) 2.36720e6 1.42195e6i 0.857233 0.514929i
\(28\) −667571. −0.205251
\(29\) −2.19402e6 3.80015e6i −0.576035 0.997722i −0.995928 0.0901485i \(-0.971266\pi\)
0.419893 0.907573i \(-0.362067\pi\)
\(30\) −1.64559e6 1.93829e6i −0.370917 0.436892i
\(31\) 4.94392e6 8.56313e6i 0.961488 1.66535i 0.242721 0.970096i \(-0.421960\pi\)
0.718767 0.695251i \(-0.244707\pi\)
\(32\) 1.64546e6 2.85003e6i 0.277404 0.480478i
\(33\) −3.37322e6 + 9.43708e6i −0.495145 + 1.38524i
\(34\) 4.03742e6 + 6.99301e6i 0.518142 + 0.897448i
\(35\) −3.22736e6 −0.363531
\(36\) −2.22452e6 1.82323e6i −0.220737 0.180917i
\(37\) −6.32122e6 −0.554489 −0.277245 0.960799i \(-0.589421\pi\)
−0.277245 + 0.960799i \(0.589421\pi\)
\(38\) 1.15959e7 + 2.00846e7i 0.902145 + 1.56256i
\(39\) −3.64406e6 + 664268.i −0.252229 + 0.0459783i
\(40\) 3.31541e6 5.74246e6i 0.204770 0.354673i
\(41\) −2.68019e6 + 4.64223e6i −0.148128 + 0.256566i −0.930536 0.366201i \(-0.880658\pi\)
0.782407 + 0.622767i \(0.213992\pi\)
\(42\) −1.61759e7 + 2.94867e6i −0.802133 + 0.146219i
\(43\) −1.12275e7 1.94466e7i −0.500812 0.867432i −1.00000 0.000938191i \(-0.999701\pi\)
0.499187 0.866494i \(-0.333632\pi\)
\(44\) 1.04384e7 0.419852
\(45\) −1.07544e7 8.81438e6i −0.390959 0.320432i
\(46\) −2.86920e6 −0.0944824
\(47\) 2.23644e7 + 3.87363e7i 0.668524 + 1.15792i 0.978317 + 0.207114i \(0.0664069\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(48\) 1.49036e7 4.16950e7i 0.405234 1.13370i
\(49\) 9.74159e6 1.68729e7i 0.241406 0.418127i
\(50\) 1.86511e7 3.23047e7i 0.422027 0.730971i
\(51\) 2.85801e7 + 3.36636e7i 0.591559 + 0.696779i
\(52\) 1.92903e6 + 3.34118e6i 0.0365868 + 0.0633702i
\(53\) −4.00972e7 −0.698027 −0.349013 0.937118i \(-0.613483\pi\)
−0.349013 + 0.937118i \(0.613483\pi\)
\(54\) −6.19556e7 3.43528e7i −0.991537 0.549782i
\(55\) 5.04642e7 0.743621
\(56\) −2.14398e7 3.71348e7i −0.291323 0.504586i
\(57\) 8.20848e7 + 9.66852e7i 1.02997 + 1.21317i
\(58\) −5.62853e7 + 9.74890e7i −0.653084 + 1.13117i
\(59\) 4.79118e7 8.29857e7i 0.514764 0.891598i −0.485089 0.874465i \(-0.661213\pi\)
0.999853 0.0171331i \(-0.00545391\pi\)
\(60\) −4.87481e6 + 1.36380e7i −0.0485598 + 0.135853i
\(61\) −1.01113e7 1.75132e7i −0.0935020 0.161950i 0.815480 0.578785i \(-0.196473\pi\)
−0.908982 + 0.416834i \(0.863139\pi\)
\(62\) −2.53663e8 −2.18019
\(63\) −8.41364e7 + 3.17284e7i −0.672901 + 0.253756i
\(64\) 7.71659e7 0.574931
\(65\) 9.32588e6 + 1.61529e7i 0.0648007 + 0.112238i
\(66\) 2.52932e8 4.61065e7i 1.64080 0.299099i
\(67\) −9.12489e7 + 1.58048e8i −0.553211 + 0.958190i 0.444829 + 0.895615i \(0.353264\pi\)
−0.998040 + 0.0625744i \(0.980069\pi\)
\(68\) 2.29975e7 3.98328e7i 0.130434 0.225918i
\(69\) −1.54367e7 + 2.81392e6i −0.0819847 + 0.0149448i
\(70\) 4.13974e7 + 7.17024e7i 0.206078 + 0.356938i
\(71\) 1.38543e8 0.647025 0.323512 0.946224i \(-0.395136\pi\)
0.323512 + 0.946224i \(0.395136\pi\)
\(72\) 2.99772e7 1.82298e8i 0.131460 0.799440i
\(73\) −2.17970e8 −0.898347 −0.449173 0.893445i \(-0.648281\pi\)
−0.449173 + 0.893445i \(0.648281\pi\)
\(74\) 8.10823e7 + 1.40439e8i 0.314328 + 0.544432i
\(75\) 6.86631e7 1.92095e8i 0.250581 0.701036i
\(76\) 6.60510e7 1.14404e8i 0.227101 0.393350i
\(77\) 1.63169e8 2.82617e8i 0.528967 0.916198i
\(78\) 6.15004e7 + 7.24395e7i 0.188127 + 0.221590i
\(79\) −1.97294e8 3.41722e8i −0.569890 0.987078i −0.996576 0.0826785i \(-0.973653\pi\)
0.426686 0.904400i \(-0.359681\pi\)
\(80\) −2.22962e8 −0.608591
\(81\) −3.67020e8 1.24061e8i −0.947343 0.320222i
\(82\) 1.37515e8 0.335883
\(83\) 2.36638e8 + 4.09870e8i 0.547310 + 0.947969i 0.998458 + 0.0555197i \(0.0176816\pi\)
−0.451147 + 0.892450i \(0.648985\pi\)
\(84\) 6.06153e7 + 7.13970e7i 0.132839 + 0.156467i
\(85\) 1.11181e8 1.92571e8i 0.231018 0.400135i
\(86\) −2.88030e8 + 4.98883e8i −0.567799 + 0.983458i
\(87\) −2.07211e8 + 5.79704e8i −0.387772 + 1.08485i
\(88\) 3.35240e8 + 5.80653e8i 0.595915 + 1.03215i
\(89\) 2.60507e8 0.440113 0.220057 0.975487i \(-0.429376\pi\)
0.220057 + 0.975487i \(0.429376\pi\)
\(90\) −5.78820e7 + 3.51994e8i −0.0929934 + 0.565514i
\(91\) 1.20616e8 0.184381
\(92\) 8.17161e6 + 1.41537e7i 0.0118922 + 0.0205979i
\(93\) −1.36474e9 + 2.48775e8i −1.89180 + 0.344853i
\(94\) 5.73736e8 9.93741e8i 0.757944 1.31280i
\(95\) 3.19323e8 5.53083e8i 0.402229 0.696682i
\(96\) −4.54219e8 + 8.27988e7i −0.545814 + 0.0994955i
\(97\) −2.87421e8 4.97828e8i −0.329644 0.570961i 0.652797 0.757533i \(-0.273595\pi\)
−0.982441 + 0.186572i \(0.940262\pi\)
\(98\) −4.99822e8 −0.547391
\(99\) 1.31559e9 4.96118e8i 1.37645 0.519070i
\(100\) −2.12477e8 −0.212477
\(101\) −7.03860e7 1.21912e8i −0.0673039 0.116574i 0.830410 0.557153i \(-0.188106\pi\)
−0.897714 + 0.440579i \(0.854773\pi\)
\(102\) 3.81309e8 1.06677e9i 0.348800 0.975818i
\(103\) 1.70819e7 2.95867e7i 0.0149544 0.0259017i −0.858451 0.512895i \(-0.828573\pi\)
0.873406 + 0.486993i \(0.161906\pi\)
\(104\) −1.23906e8 + 2.14612e8i −0.103859 + 0.179888i
\(105\) 2.93044e8 + 3.45168e8i 0.235278 + 0.277127i
\(106\) 5.14326e8 + 8.90839e8i 0.395696 + 0.685366i
\(107\) 1.61837e9 1.19358 0.596790 0.802397i \(-0.296443\pi\)
0.596790 + 0.802397i \(0.296443\pi\)
\(108\) 6.99129e6 + 4.03463e8i 0.00494482 + 0.285362i
\(109\) −8.56262e8 −0.581015 −0.290508 0.956873i \(-0.593824\pi\)
−0.290508 + 0.956873i \(0.593824\pi\)
\(110\) −6.47305e8 1.12116e9i −0.421543 0.730133i
\(111\) 5.73966e8 + 6.76057e8i 0.358866 + 0.422698i
\(112\) −7.20914e8 + 1.24866e9i −0.432915 + 0.749831i
\(113\) −9.66311e8 + 1.67370e9i −0.557524 + 0.965661i 0.440178 + 0.897911i \(0.354915\pi\)
−0.997702 + 0.0677501i \(0.978418\pi\)
\(114\) 1.09516e9 3.06386e9i 0.607301 1.69901i
\(115\) 3.95056e7 + 6.84257e7i 0.0210629 + 0.0364820i
\(116\) 6.41212e8 0.328807
\(117\) 4.01923e8 + 3.29418e8i 0.198293 + 0.162522i
\(118\) −2.45826e9 −1.16724
\(119\) −7.18976e8 1.24530e9i −0.328665 0.569264i
\(120\) −9.15197e8 + 1.66830e8i −0.402901 + 0.0734442i
\(121\) −1.37239e9 + 2.37705e9i −0.582028 + 1.00810i
\(122\) −2.59394e8 + 4.49284e8i −0.106009 + 0.183612i
\(123\) 7.39849e8 1.34866e8i 0.291454 0.0531287i
\(124\) 7.22443e8 + 1.25131e9i 0.274414 + 0.475298i
\(125\) −2.40700e9 −0.881824
\(126\) 1.78413e9 + 1.46228e9i 0.630607 + 0.516848i
\(127\) 4.98705e9 1.70109 0.850545 0.525903i \(-0.176272\pi\)
0.850545 + 0.525903i \(0.176272\pi\)
\(128\) −1.83228e9 3.17361e9i −0.603320 1.04498i
\(129\) −1.06037e9 + 2.96653e9i −0.337134 + 0.943182i
\(130\) 2.39246e8 4.14387e8i 0.0734683 0.127251i
\(131\) 9.58360e7 1.65993e8i 0.0284320 0.0492457i −0.851459 0.524421i \(-0.824282\pi\)
0.879891 + 0.475175i \(0.157615\pi\)
\(132\) −9.47803e8 1.11639e9i −0.271729 0.320061i
\(133\) −2.06497e9 3.57663e9i −0.572243 0.991155i
\(134\) 4.68180e9 1.25441
\(135\) 3.37993e7 + 1.95054e9i 0.00875802 + 0.505420i
\(136\) 2.95436e9 0.740523
\(137\) −5.00385e8 8.66692e8i −0.121356 0.210195i 0.798947 0.601402i \(-0.205391\pi\)
−0.920303 + 0.391207i \(0.872058\pi\)
\(138\) 2.60523e8 + 3.06862e8i 0.0611491 + 0.0720257i
\(139\) 6.75119e8 1.16934e9i 0.153396 0.265689i −0.779078 0.626927i \(-0.784312\pi\)
0.932474 + 0.361238i \(0.117646\pi\)
\(140\) 2.35803e8 4.08423e8i 0.0518768 0.0898533i
\(141\) 2.11218e9 5.90913e9i 0.450033 1.25903i
\(142\) −1.77709e9 3.07800e9i −0.366785 0.635290i
\(143\) −1.88599e9 −0.377161
\(144\) −5.81255e9 + 2.19195e9i −1.12651 + 0.424815i
\(145\) 3.09993e9 0.582366
\(146\) 2.79590e9 + 4.84264e9i 0.509253 + 0.882053i
\(147\) −2.68910e9 + 4.90192e8i −0.474984 + 0.0865840i
\(148\) 4.61852e8 7.99951e8i 0.0791270 0.137052i
\(149\) −1.76496e9 + 3.05700e9i −0.293357 + 0.508110i −0.974601 0.223947i \(-0.928106\pi\)
0.681244 + 0.732056i \(0.261439\pi\)
\(150\) −5.14852e9 + 9.38514e8i −0.830370 + 0.151367i
\(151\) −2.86323e8 4.95926e8i −0.0448188 0.0776284i 0.842746 0.538312i \(-0.180938\pi\)
−0.887565 + 0.460683i \(0.847604\pi\)
\(152\) 8.48521e9 1.28934
\(153\) 1.00528e9 6.11330e9i 0.148311 0.901913i
\(154\) −8.37186e9 −1.19944
\(155\) 3.49264e9 + 6.04943e9i 0.486028 + 0.841825i
\(156\) 1.82185e8 5.09689e8i 0.0246293 0.0689041i
\(157\) −4.20086e8 + 7.27610e8i −0.0551810 + 0.0955763i −0.892296 0.451450i \(-0.850907\pi\)
0.837115 + 0.547026i \(0.184240\pi\)
\(158\) −5.06137e9 + 8.76654e9i −0.646117 + 1.11911i
\(159\) 3.64081e9 + 4.28841e9i 0.451764 + 0.532119i
\(160\) 1.16244e9 + 2.01340e9i 0.140227 + 0.242880i
\(161\) 5.10942e8 0.0599315
\(162\) 1.95151e9 + 9.74541e9i 0.222614 + 1.11169i
\(163\) −7.00425e9 −0.777173 −0.388586 0.921412i \(-0.627037\pi\)
−0.388586 + 0.921412i \(0.627037\pi\)
\(164\) −3.91650e8 6.78357e8i −0.0422766 0.0732253i
\(165\) −4.58214e9 5.39717e9i −0.481272 0.566876i
\(166\) 6.07072e9 1.05148e10i 0.620517 1.07477i
\(167\) 4.63508e9 8.02820e9i 0.461141 0.798719i −0.537877 0.843023i \(-0.680774\pi\)
0.999018 + 0.0443040i \(0.0141070\pi\)
\(168\) −2.02485e9 + 5.66483e9i −0.196111 + 0.548649i
\(169\) 4.95372e9 + 8.58009e9i 0.467133 + 0.809099i
\(170\) −5.70448e9 −0.523836
\(171\) 2.88725e9 1.75580e10i 0.258227 1.57034i
\(172\) 3.28129e9 0.285869
\(173\) −4.13667e9 7.16492e9i −0.351110 0.608141i 0.635334 0.772237i \(-0.280862\pi\)
−0.986444 + 0.164097i \(0.947529\pi\)
\(174\) 1.55372e10 2.83224e9i 1.28499 0.234239i
\(175\) −3.32136e9 + 5.75276e9i −0.267697 + 0.463665i
\(176\) 1.12725e10 1.95245e10i 0.885549 1.53382i
\(177\) −1.32257e10 + 2.41090e9i −1.01284 + 0.184628i
\(178\) −3.34152e9 5.78769e9i −0.249491 0.432131i
\(179\) −2.36310e10 −1.72046 −0.860229 0.509907i \(-0.829680\pi\)
−0.860229 + 0.509907i \(0.829680\pi\)
\(180\) 1.90122e9 7.16964e8i 0.134991 0.0509062i
\(181\) 1.40618e10 0.973841 0.486921 0.873446i \(-0.338120\pi\)
0.486921 + 0.873446i \(0.338120\pi\)
\(182\) −1.54714e9 2.67972e9i −0.104522 0.181037i
\(183\) −9.54946e8 + 2.67160e9i −0.0629432 + 0.176093i
\(184\) −5.24881e8 + 9.09121e8i −0.0337583 + 0.0584711i
\(185\) 2.23282e9 3.86735e9i 0.140146 0.242740i
\(186\) 2.30325e10 + 2.71293e10i 1.41102 + 1.66200i
\(187\) 1.12422e10 + 1.94720e10i 0.672299 + 1.16446i
\(188\) −6.53611e9 −0.381600
\(189\) 1.10329e10 + 6.11749e9i 0.628946 + 0.348735i
\(190\) −1.63838e10 −0.912061
\(191\) 4.87596e9 + 8.44541e9i 0.265100 + 0.459167i 0.967590 0.252527i \(-0.0812616\pi\)
−0.702490 + 0.711694i \(0.747928\pi\)
\(192\) −7.00665e9 8.25293e9i −0.372096 0.438281i
\(193\) −4.97588e9 + 8.61847e9i −0.258144 + 0.447118i −0.965745 0.259494i \(-0.916444\pi\)
0.707601 + 0.706612i \(0.249778\pi\)
\(194\) −7.37349e9 + 1.27713e10i −0.373737 + 0.647331i
\(195\) 8.80772e8 2.46409e9i 0.0436222 0.122040i
\(196\) 1.42351e9 + 2.46560e9i 0.0688984 + 0.119336i
\(197\) −3.23117e9 −0.152849 −0.0764244 0.997075i \(-0.524350\pi\)
−0.0764244 + 0.997075i \(0.524350\pi\)
\(198\) −2.78973e10 2.28647e10i −1.28994 1.05724i
\(199\) −2.90155e10 −1.31157 −0.655785 0.754947i \(-0.727662\pi\)
−0.655785 + 0.754947i \(0.727662\pi\)
\(200\) −6.82393e9 1.18194e10i −0.301578 0.522348i
\(201\) 2.51887e10 4.59159e9i 1.08849 0.198418i
\(202\) −1.80568e9 + 3.12754e9i −0.0763063 + 0.132166i
\(203\) 1.00232e10 1.73607e10i 0.414260 0.717520i
\(204\) −6.34830e9 + 1.15722e9i −0.256639 + 0.0467822i
\(205\) −1.89343e9 3.27951e9i −0.0748783 0.129693i
\(206\) −8.76437e8 −0.0339092
\(207\) 1.70260e9 + 1.39545e9i 0.0644533 + 0.0528262i
\(208\) 8.33270e9 0.308675
\(209\) 3.22886e10 + 5.59255e10i 1.17055 + 2.02746i
\(210\) 3.90972e9 1.09380e10i 0.138726 0.388108i
\(211\) 2.12768e9 3.68525e9i 0.0738985 0.127996i −0.826708 0.562631i \(-0.809789\pi\)
0.900607 + 0.434635i \(0.143123\pi\)
\(212\) 2.92965e9 5.07430e9i 0.0996102 0.172530i
\(213\) −1.25796e10 1.48172e10i −0.418755 0.493240i
\(214\) −2.07589e10 3.59554e10i −0.676615 1.17193i
\(215\) 1.58634e10 0.506317
\(216\) −2.22188e10 + 1.33466e10i −0.694510 + 0.417184i
\(217\) 4.51718e10 1.38292
\(218\) 1.09833e10 + 1.90236e10i 0.329365 + 0.570477i
\(219\) 1.97916e10 + 2.33120e10i 0.581411 + 0.684827i
\(220\) −3.68710e9 + 6.38625e9i −0.106117 + 0.183799i
\(221\) −4.15515e9 + 7.19692e9i −0.117171 + 0.202947i
\(222\) 7.65772e9 2.14236e10i 0.211598 0.591975i
\(223\) −2.11759e10 3.66777e10i −0.573416 0.993185i −0.996212 0.0869601i \(-0.972285\pi\)
0.422796 0.906225i \(-0.361049\pi\)
\(224\) 1.50343e10 0.398995
\(225\) −2.67792e10 + 1.00986e10i −0.696589 + 0.262689i
\(226\) 4.95795e10 1.26419
\(227\) −2.96301e10 5.13208e10i −0.740656 1.28285i −0.952197 0.305485i \(-0.901181\pi\)
0.211541 0.977369i \(-0.432152\pi\)
\(228\) −1.82329e10 + 3.32365e9i −0.446838 + 0.0814532i
\(229\) 3.07523e10 5.32645e10i 0.738954 1.27991i −0.214013 0.976831i \(-0.568653\pi\)
0.952967 0.303075i \(-0.0980133\pi\)
\(230\) 1.01348e9 1.75539e9i 0.0238802 0.0413617i
\(231\) −4.50417e10 + 8.21056e9i −1.04078 + 0.189723i
\(232\) 2.05932e10 + 3.56685e10i 0.466690 + 0.808331i
\(233\) −4.69389e10 −1.04335 −0.521677 0.853143i \(-0.674693\pi\)
−0.521677 + 0.853143i \(0.674693\pi\)
\(234\) 2.16321e9 1.31550e10i 0.0471659 0.286826i
\(235\) −3.15987e10 −0.675872
\(236\) 7.00123e9 + 1.21265e10i 0.146916 + 0.254467i
\(237\) −1.86331e10 + 5.21290e10i −0.383635 + 1.07328i
\(238\) −1.84446e10 + 3.19470e10i −0.372626 + 0.645407i
\(239\) −5.22440e9 + 9.04892e9i −0.103573 + 0.179393i −0.913154 0.407614i \(-0.866361\pi\)
0.809581 + 0.587008i \(0.199694\pi\)
\(240\) 2.02449e10 + 2.38459e10i 0.393881 + 0.463940i
\(241\) −1.49700e10 2.59288e10i −0.285854 0.495114i 0.686962 0.726693i \(-0.258944\pi\)
−0.972816 + 0.231580i \(0.925611\pi\)
\(242\) 7.04147e10 1.31976
\(243\) 2.00570e10 + 5.05176e10i 0.369010 + 0.929426i
\(244\) 2.95507e9 0.0533719
\(245\) 6.88196e9 + 1.19199e10i 0.122030 + 0.211361i
\(246\) −1.24864e10 1.47073e10i −0.217384 0.256050i
\(247\) −1.19340e10 + 2.06703e10i −0.204009 + 0.353354i
\(248\) −4.64041e10 + 8.03743e10i −0.778976 + 1.34923i
\(249\) 2.23490e10 6.25246e10i 0.368435 1.03075i
\(250\) 3.08746e10 + 5.34764e10i 0.499887 + 0.865830i
\(251\) −1.50652e9 −0.0239576 −0.0119788 0.999928i \(-0.503813\pi\)
−0.0119788 + 0.999928i \(0.503813\pi\)
\(252\) 2.13208e9 1.29657e10i 0.0333044 0.202531i
\(253\) −7.98928e9 −0.122593
\(254\) −6.39689e10 1.10797e11i −0.964311 1.67024i
\(255\) −3.06908e10 + 5.59457e9i −0.454546 + 0.0828583i
\(256\) −2.72509e10 + 4.72000e10i −0.396553 + 0.686850i
\(257\) 4.35790e10 7.54811e10i 0.623130 1.07929i −0.365770 0.930705i \(-0.619194\pi\)
0.988899 0.148587i \(-0.0474725\pi\)
\(258\) 7.95088e10 1.44935e10i 1.11719 0.203650i
\(259\) −1.44390e10 2.50090e10i −0.199383 0.345341i
\(260\) −2.72553e9 −0.0369889
\(261\) 8.08143e10 3.04757e10i 1.07797 0.406510i
\(262\) −4.91715e9 −0.0644700
\(263\) 2.10643e10 + 3.64844e10i 0.271485 + 0.470226i 0.969242 0.246108i \(-0.0791519\pi\)
−0.697757 + 0.716334i \(0.745819\pi\)
\(264\) 3.16614e10 8.85773e10i 0.401155 1.12229i
\(265\) 1.41633e10 2.45316e10i 0.176425 0.305577i
\(266\) −5.29747e10 + 9.17548e10i −0.648785 + 1.12373i
\(267\) −2.36540e10 2.78613e10i −0.284842 0.335507i
\(268\) −1.33340e10 2.30951e10i −0.157889 0.273472i
\(269\) 6.32241e10 0.736202 0.368101 0.929786i \(-0.380008\pi\)
0.368101 + 0.929786i \(0.380008\pi\)
\(270\) 4.29015e10 2.57704e10i 0.491288 0.295111i
\(271\) −1.63811e11 −1.84493 −0.922467 0.386075i \(-0.873831\pi\)
−0.922467 + 0.386075i \(0.873831\pi\)
\(272\) −4.96703e10 8.60314e10i −0.550220 0.953009i
\(273\) −1.09519e10 1.28999e10i −0.119332 0.140557i
\(274\) −1.28369e10 + 2.22341e10i −0.137588 + 0.238310i
\(275\) 5.19339e10 8.99522e10i 0.547588 0.948451i
\(276\) 7.71758e8 2.15911e9i 0.00800553 0.0223967i
\(277\) 8.63022e10 + 1.49480e11i 0.880771 + 1.52554i 0.850485 + 0.525999i \(0.176308\pi\)
0.0302857 + 0.999541i \(0.490358\pi\)
\(278\) −3.46390e10 −0.347827
\(279\) 1.50525e11 + 1.23370e11i 1.48726 + 1.21897i
\(280\) 3.02923e10 0.294525
\(281\) 1.27714e10 + 2.21208e10i 0.122197 + 0.211652i 0.920634 0.390427i \(-0.127673\pi\)
−0.798437 + 0.602079i \(0.794339\pi\)
\(282\) −1.58376e11 + 2.88701e10i −1.49131 + 0.271849i
\(283\) 3.69467e10 6.39936e10i 0.342402 0.593058i −0.642476 0.766306i \(-0.722093\pi\)
0.984878 + 0.173248i \(0.0554261\pi\)
\(284\) −1.01224e10 + 1.75326e10i −0.0923321 + 0.159924i
\(285\) −8.81469e10 + 1.60681e10i −0.791417 + 0.144266i
\(286\) 2.41916e10 + 4.19010e10i 0.213805 + 0.370320i
\(287\) −2.44885e10 −0.213056
\(288\) 5.00984e10 + 4.10608e10i 0.429099 + 0.351691i
\(289\) −1.95145e10 −0.164557
\(290\) −3.97628e10 6.88712e10i −0.330131 0.571803i
\(291\) −2.71451e10 + 7.59424e10i −0.221908 + 0.620821i
\(292\) 1.59257e10 2.75841e10i 0.128196 0.222043i
\(293\) −1.01768e11 + 1.76267e11i −0.806687 + 1.39722i 0.108459 + 0.994101i \(0.465408\pi\)
−0.915146 + 0.403122i \(0.867925\pi\)
\(294\) 4.53837e10 + 5.34561e10i 0.354272 + 0.417287i
\(295\) 3.38474e10 + 5.86253e10i 0.260211 + 0.450699i
\(296\) 5.93316e10 0.449234
\(297\) −1.72515e11 9.56553e10i −1.28654 0.713354i
\(298\) 9.05566e10 0.665192
\(299\) −1.47643e9 2.55726e9i −0.0106830 0.0185035i
\(300\) 1.92929e10 + 2.27245e10i 0.137515 + 0.161975i
\(301\) 5.12919e10 8.88401e10i 0.360163 0.623821i
\(302\) −7.34533e9 + 1.27225e10i −0.0508136 + 0.0880118i
\(303\) −6.64752e9 + 1.85974e10i −0.0453073 + 0.126754i
\(304\) −1.42658e11 2.47091e11i −0.957998 1.65930i
\(305\) 1.42862e10 0.0945297
\(306\) −1.48714e11 + 5.60811e10i −0.969629 + 0.365654i
\(307\) 8.22523e10 0.528476 0.264238 0.964457i \(-0.414880\pi\)
0.264238 + 0.964457i \(0.414880\pi\)
\(308\) 2.38434e10 + 4.12980e10i 0.150970 + 0.261488i
\(309\) −4.71534e9 + 8.59550e8i −0.0294239 + 0.00536362i
\(310\) 8.96002e10 1.55192e11i 0.551038 0.954425i
\(311\) 1.16047e11 2.00999e11i 0.703415 1.21835i −0.263846 0.964565i \(-0.584991\pi\)
0.967261 0.253785i \(-0.0816756\pi\)
\(312\) 3.42035e10 6.23489e9i 0.204350 0.0372506i
\(313\) −3.15040e10 5.45665e10i −0.185531 0.321349i 0.758224 0.651994i \(-0.226067\pi\)
−0.943755 + 0.330645i \(0.892734\pi\)
\(314\) 2.15537e10 0.125124
\(315\) 1.03075e10 6.26824e10i 0.0589871 0.358714i
\(316\) 5.76600e10 0.325299
\(317\) 1.15735e11 + 2.00459e11i 0.643722 + 1.11496i 0.984595 + 0.174850i \(0.0559439\pi\)
−0.340873 + 0.940109i \(0.610723\pi\)
\(318\) 4.85749e10 1.35895e11i 0.266373 0.745217i
\(319\) −1.56726e11 + 2.71458e11i −0.847390 + 1.46772i
\(320\) −2.72570e10 + 4.72105e10i −0.145312 + 0.251689i
\(321\) −1.46948e11 1.73086e11i −0.772486 0.909889i
\(322\) −6.55385e9 1.13516e10i −0.0339739 0.0588445i
\(323\) 2.84548e11 1.45460
\(324\) 4.25157e10 3.73821e10i 0.214337 0.188456i
\(325\) 3.83899e10 0.190872
\(326\) 8.98436e10 + 1.55614e11i 0.440563 + 0.763077i
\(327\) 7.77484e10 + 9.15776e10i 0.376034 + 0.442919i
\(328\) 2.51565e10 4.35724e10i 0.120010 0.207864i
\(329\) −1.02170e11 + 1.76963e11i −0.480775 + 0.832726i
\(330\) −6.11339e10 + 1.71031e11i −0.283772 + 0.793893i
\(331\) −7.72274e10 1.33762e11i −0.353627 0.612500i 0.633255 0.773943i \(-0.281718\pi\)
−0.986882 + 0.161443i \(0.948385\pi\)
\(332\) −6.91587e10 −0.312410
\(333\) 2.01886e10 1.22772e11i 0.0899722 0.547141i
\(334\) −2.37817e11 −1.04564
\(335\) −6.44629e10 1.11653e11i −0.279646 0.484361i
\(336\) 1.99004e11 3.62760e10i 0.851793 0.155272i
\(337\) −6.76249e10 + 1.17130e11i −0.285609 + 0.494690i −0.972757 0.231828i \(-0.925529\pi\)
0.687148 + 0.726518i \(0.258863\pi\)
\(338\) 1.27083e11 2.20113e11i 0.529616 0.917321i
\(339\) 2.66744e11 4.86242e10i 1.09697 0.199965i
\(340\) 1.62466e10 + 2.81399e10i 0.0659337 + 0.114201i
\(341\) −7.06323e11 −2.82884
\(342\) −4.27121e11 + 1.61070e11i −1.68824 + 0.636647i
\(343\) 2.73359e11 1.06638
\(344\) 1.05382e11 + 1.82528e11i 0.405747 + 0.702774i
\(345\) 3.73106e9 1.04382e10i 0.0141790 0.0396679i
\(346\) −1.06122e11 + 1.83809e11i −0.398074 + 0.689484i
\(347\) 1.41753e11 2.45523e11i 0.524867 0.909096i −0.474714 0.880140i \(-0.657449\pi\)
0.999581 0.0289556i \(-0.00921813\pi\)
\(348\) −5.82219e10 6.85779e10i −0.212804 0.250656i
\(349\) −4.86799e10 8.43160e10i −0.175645 0.304225i 0.764740 0.644340i \(-0.222868\pi\)
−0.940384 + 0.340114i \(0.889534\pi\)
\(350\) 1.70412e11 0.607008
\(351\) −1.26318e9 7.28970e10i −0.00444203 0.256347i
\(352\) −2.35082e11 −0.816164
\(353\) −1.91861e10 3.32314e10i −0.0657660 0.113910i 0.831268 0.555873i \(-0.187616\pi\)
−0.897034 + 0.441962i \(0.854282\pi\)
\(354\) 2.23209e11 + 2.62912e11i 0.755436 + 0.889806i
\(355\) −4.89368e10 + 8.47611e10i −0.163534 + 0.283249i
\(356\) −1.90336e10 + 3.29672e10i −0.0628053 + 0.108782i
\(357\) −6.79028e10 + 1.89968e11i −0.221249 + 0.618975i
\(358\) 3.03115e11 + 5.25011e11i 0.975291 + 1.68925i
\(359\) −4.48036e11 −1.42360 −0.711800 0.702383i \(-0.752120\pi\)
−0.711800 + 0.702383i \(0.752120\pi\)
\(360\) 1.00942e11 + 8.27326e10i 0.316746 + 0.259606i
\(361\) 4.94563e11 1.53264
\(362\) −1.80371e11 3.12412e11i −0.552050 0.956178i
\(363\) 3.78840e11 6.90580e10i 1.14519 0.208754i
\(364\) −8.81262e9 + 1.52639e10i −0.0263117 + 0.0455732i
\(365\) 7.69926e10 1.33355e11i 0.227055 0.393271i
\(366\) 7.16041e10 1.30526e10i 0.208580 0.0380217i
\(367\) 3.74037e10 + 6.47850e10i 0.107626 + 0.186414i 0.914808 0.403889i \(-0.132342\pi\)
−0.807182 + 0.590302i \(0.799008\pi\)
\(368\) 3.52983e10 0.100332
\(369\) −8.16021e10 6.68814e10i −0.229130 0.187796i
\(370\) −1.14561e11 −0.317783
\(371\) −9.15902e10 1.58639e11i −0.250996 0.434738i
\(372\) 6.82302e10 1.90884e11i 0.184728 0.516805i
\(373\) 1.39696e11 2.41961e11i 0.373675 0.647225i −0.616452 0.787392i \(-0.711431\pi\)
0.990128 + 0.140167i \(0.0447641\pi\)
\(374\) 2.88406e11 4.99535e11i 0.762224 1.32021i
\(375\) 2.18556e11 + 2.57430e11i 0.570717 + 0.672231i
\(376\) −2.09914e11 3.63582e11i −0.541623 0.938118i
\(377\) −1.15853e11 −0.295374
\(378\) −5.60720e9 3.23588e11i −0.0141265 0.815228i
\(379\) −6.40616e11 −1.59485 −0.797427 0.603415i \(-0.793806\pi\)
−0.797427 + 0.603415i \(0.793806\pi\)
\(380\) 4.66618e10 + 8.08206e10i 0.114798 + 0.198836i
\(381\) −4.52823e11 5.33367e11i −1.10095 1.29677i
\(382\) 1.25088e11 2.16659e11i 0.300559 0.520584i
\(383\) −1.66528e11 + 2.88435e11i −0.395451 + 0.684942i −0.993159 0.116772i \(-0.962745\pi\)
0.597707 + 0.801714i \(0.296079\pi\)
\(384\) −1.73048e11 + 4.84127e11i −0.406140 + 1.13624i
\(385\) 1.15271e11 + 1.99655e11i 0.267390 + 0.463134i
\(386\) 2.55302e11 0.585345
\(387\) 4.13553e11 1.55954e11i 0.937199 0.353425i
\(388\) 8.40002e10 0.188164
\(389\) 8.15796e10 + 1.41300e11i 0.180638 + 0.312873i 0.942098 0.335338i \(-0.108851\pi\)
−0.761460 + 0.648212i \(0.775517\pi\)
\(390\) −6.60423e10 + 1.20387e10i −0.144555 + 0.0263506i
\(391\) −1.76017e10 + 3.04870e10i −0.0380855 + 0.0659660i
\(392\) −9.14355e10 + 1.58371e11i −0.195581 + 0.338757i
\(393\) −2.64549e10 + 4.82241e9i −0.0559422 + 0.0101976i
\(394\) 4.14462e10 + 7.17870e10i 0.0866467 + 0.150076i
\(395\) 2.78757e11 0.576153
\(396\) −3.33380e10 + 2.02736e11i −0.0681257 + 0.414288i
\(397\) 2.79119e11 0.563939 0.281969 0.959423i \(-0.409012\pi\)
0.281969 + 0.959423i \(0.409012\pi\)
\(398\) 3.72182e11 + 6.44638e11i 0.743501 + 1.28778i
\(399\) −1.95023e11 + 5.45606e11i −0.385220 + 1.07771i
\(400\) −2.29455e11 + 3.97428e11i −0.448155 + 0.776227i
\(401\) −3.79966e11 + 6.58121e11i −0.733830 + 1.27103i 0.221405 + 0.975182i \(0.428936\pi\)
−0.955235 + 0.295848i \(0.904398\pi\)
\(402\) −4.25106e11 5.00720e11i −0.811858 0.956264i
\(403\) −1.30530e11 2.26084e11i −0.246511 0.426970i
\(404\) 2.05707e10 0.0384178
\(405\) 2.05542e11 1.80723e11i 0.379623 0.333785i
\(406\) −5.14269e11 −0.939341
\(407\) 2.25773e11 + 3.91051e11i 0.407847 + 0.706412i
\(408\) −2.68255e11 3.15970e11i −0.479267 0.564515i
\(409\) 1.89971e10 3.29039e10i 0.0335685 0.0581423i −0.848753 0.528789i \(-0.822646\pi\)
0.882322 + 0.470647i \(0.155979\pi\)
\(410\) −4.85739e10 + 8.41325e10i −0.0848938 + 0.147040i
\(411\) −4.72583e10 + 1.32212e11i −0.0816939 + 0.228551i
\(412\) 2.49613e9 + 4.32342e9i 0.00426805 + 0.00739248i
\(413\) 4.37762e11 0.740394
\(414\) 9.16363e9 5.57261e10i 0.0153308 0.0932303i
\(415\) −3.34347e11 −0.553326
\(416\) −4.34436e10 7.52465e10i −0.0711223 0.123187i
\(417\) −1.86362e11 + 3.39716e10i −0.301818 + 0.0550179i
\(418\) 8.28331e11 1.43471e12i 1.32712 2.29864i
\(419\) 3.66823e11 6.35355e11i 0.581424 1.00706i −0.413887 0.910328i \(-0.635829\pi\)
0.995311 0.0967277i \(-0.0308376\pi\)
\(420\) −6.50919e10 + 1.18655e10i −0.102072 + 0.0186065i
\(421\) 1.60716e11 + 2.78368e11i 0.249339 + 0.431867i 0.963342 0.268275i \(-0.0864535\pi\)
−0.714004 + 0.700142i \(0.753120\pi\)
\(422\) −1.09167e11 −0.167566
\(423\) −8.23770e11 + 3.10649e11i −1.25105 + 0.471779i
\(424\) 3.76356e11 0.565525
\(425\) −2.28838e11 3.96359e11i −0.340234 0.589303i
\(426\) −1.67835e11 + 4.69542e11i −0.246910 + 0.690767i
\(427\) 4.61924e10 8.00077e10i 0.0672428 0.116468i
\(428\) −1.18244e11 + 2.04805e11i −0.170327 + 0.295015i
\(429\) 1.71247e11 + 2.01707e11i 0.244099 + 0.287517i
\(430\) −2.03479e11 3.52437e11i −0.287020 0.497133i
\(431\) 3.86098e11 0.538952 0.269476 0.963007i \(-0.413150\pi\)
0.269476 + 0.963007i \(0.413150\pi\)
\(432\) 7.62208e11 + 4.22625e11i 1.05292 + 0.583820i
\(433\) 5.48808e11 0.750282 0.375141 0.926968i \(-0.377594\pi\)
0.375141 + 0.926968i \(0.377594\pi\)
\(434\) −5.79418e11 1.00358e12i −0.783950 1.35784i
\(435\) −2.81473e11 3.31539e11i −0.376908 0.443949i
\(436\) 6.25617e10 1.08360e11i 0.0829123 0.143608i
\(437\) −5.05538e10 + 8.75617e10i −0.0663113 + 0.114854i
\(438\) 2.64055e11 7.38734e11i 0.342816 0.959079i
\(439\) 1.50050e11 + 2.59895e11i 0.192817 + 0.333969i 0.946183 0.323633i \(-0.104904\pi\)
−0.753365 + 0.657602i \(0.771571\pi\)
\(440\) −4.73662e11 −0.602465
\(441\) 2.96596e11 + 2.43091e11i 0.373415 + 0.306052i
\(442\) 2.13192e11 0.265687
\(443\) −2.11330e11 3.66034e11i −0.260702 0.451549i 0.705727 0.708484i \(-0.250621\pi\)
−0.966429 + 0.256935i \(0.917287\pi\)
\(444\) −1.27491e11 + 2.32401e10i −0.155689 + 0.0283802i
\(445\) −9.20178e10 + 1.59379e11i −0.111238 + 0.192669i
\(446\) −5.43246e11 + 9.40929e11i −0.650114 + 1.12603i
\(447\) 4.87206e11 8.88118e10i 0.577203 0.105217i
\(448\) 1.76263e11 + 3.05296e11i 0.206733 + 0.358072i
\(449\) 1.63406e12 1.89741 0.948704 0.316165i \(-0.102395\pi\)
0.948704 + 0.316165i \(0.102395\pi\)
\(450\) 5.67859e11 + 4.65419e11i 0.652806 + 0.535042i
\(451\) 3.82911e11 0.435816
\(452\) −1.41205e11 2.44573e11i −0.159120 0.275605i
\(453\) −2.70414e10 + 7.56524e10i −0.0301709 + 0.0844074i
\(454\) −7.60130e11 + 1.31658e12i −0.839724 + 1.45445i
\(455\) −4.26045e10 + 7.37932e10i −0.0466020 + 0.0807170i
\(456\) −7.70455e11 9.07497e11i −0.834460 0.982886i
\(457\) −6.23184e11 1.07939e12i −0.668334 1.15759i −0.978370 0.206863i \(-0.933675\pi\)
0.310036 0.950725i \(-0.399659\pi\)
\(458\) −1.57784e12 −1.67559
\(459\) −7.45099e11 + 4.47572e11i −0.783533 + 0.470659i
\(460\) −1.15457e10 −0.0120229
\(461\) −1.44026e11 2.49459e11i −0.148520 0.257244i 0.782161 0.623077i \(-0.214118\pi\)
−0.930681 + 0.365833i \(0.880784\pi\)
\(462\) 7.60163e11 + 8.95374e11i 0.776279 + 0.914357i
\(463\) −7.86329e11 + 1.36196e12i −0.795225 + 1.37737i 0.127472 + 0.991842i \(0.459314\pi\)
−0.922696 + 0.385527i \(0.874020\pi\)
\(464\) 6.92449e11 1.19936e12i 0.693517 1.20121i
\(465\) 3.29858e11 9.22827e11i 0.327182 0.915339i
\(466\) 6.02085e11 + 1.04284e12i 0.591454 + 1.02443i
\(467\) 2.12882e11 0.207116 0.103558 0.994623i \(-0.466977\pi\)
0.103558 + 0.994623i \(0.466977\pi\)
\(468\) −7.10539e10 + 2.67949e10i −0.0684670 + 0.0258194i
\(469\) −8.33726e11 −0.795693
\(470\) 4.05317e11 + 7.02029e11i 0.383137 + 0.663613i
\(471\) 1.15962e11 2.11385e10i 0.108573 0.0197915i
\(472\) −4.49705e11 + 7.78911e11i −0.417050 + 0.722352i
\(473\) −8.02019e11 + 1.38914e12i −0.736732 + 1.27606i
\(474\) 1.39716e12 2.54685e11i 1.27128 0.231740i
\(475\) −6.57245e11 1.13838e12i −0.592388 1.02605i
\(476\) 2.10124e11 0.187605
\(477\) 1.28062e11 7.78773e11i 0.113263 0.688777i
\(478\) 2.68053e11 0.234853
\(479\) −7.62418e11 1.32055e12i −0.661733 1.14616i −0.980160 0.198208i \(-0.936488\pi\)
0.318426 0.947948i \(-0.396846\pi\)
\(480\) 1.09785e11 3.07140e11i 0.0943970 0.264089i
\(481\) −8.34466e10 + 1.44534e11i −0.0710814 + 0.123117i
\(482\) −3.84040e11 + 6.65176e11i −0.324089 + 0.561339i
\(483\) −4.63934e10 5.46455e10i −0.0387877 0.0456869i
\(484\) −2.00544e11 3.47353e11i −0.166114 0.287718i
\(485\) 4.06098e11 0.333267
\(486\) 8.65079e11 1.09360e12i 0.703384 0.889188i
\(487\) −1.81008e12 −1.45820 −0.729101 0.684406i \(-0.760062\pi\)
−0.729101 + 0.684406i \(0.760062\pi\)
\(488\) 9.49052e10 + 1.64381e11i 0.0757532 + 0.131208i
\(489\) 6.35985e11 + 7.49108e11i 0.502987 + 0.592454i
\(490\) 1.76550e11 3.05793e11i 0.138352 0.239632i
\(491\) 5.76915e11 9.99245e11i 0.447966 0.775899i −0.550288 0.834975i \(-0.685482\pi\)
0.998254 + 0.0590757i \(0.0188153\pi\)
\(492\) −3.69889e10 + 1.03482e11i −0.0284595 + 0.0796198i
\(493\) 6.90587e11 + 1.19613e12i 0.526511 + 0.911944i
\(494\) 6.12309e11 0.462593
\(495\) −1.61172e11 + 9.80124e11i −0.120661 + 0.733766i
\(496\) 3.12068e12 2.31517
\(497\) 3.16460e11 + 5.48125e11i 0.232657 + 0.402973i
\(498\) −1.67578e12 + 3.05475e11i −1.22091 + 0.222558i
\(499\) 1.00972e12 1.74888e12i 0.729032 1.26272i −0.228260 0.973600i \(-0.573304\pi\)
0.957293 0.289121i \(-0.0933629\pi\)
\(500\) 1.75865e11 3.04607e11i 0.125839 0.217959i
\(501\) −1.27948e12 + 2.33235e11i −0.907330 + 0.165395i
\(502\) 1.93241e10 + 3.34703e10i 0.0135810 + 0.0235230i
\(503\) −7.16624e11 −0.499155 −0.249578 0.968355i \(-0.580292\pi\)
−0.249578 + 0.968355i \(0.580292\pi\)
\(504\) 7.89712e11 2.97806e11i 0.545169 0.205587i
\(505\) 9.94486e10 0.0680437
\(506\) 1.02478e11 + 1.77498e11i 0.0694953 + 0.120369i
\(507\) 4.67848e11 1.30887e12i 0.314462 0.879754i
\(508\) −3.64372e11 + 6.31112e11i −0.242750 + 0.420455i
\(509\) 7.90670e11 1.36948e12i 0.522114 0.904327i −0.477555 0.878602i \(-0.658477\pi\)
0.999669 0.0257257i \(-0.00818966\pi\)
\(510\) 5.17965e11 + 6.10096e11i 0.339028 + 0.399331i
\(511\) −4.97889e11 8.62369e11i −0.323027 0.559499i
\(512\) −4.78068e11 −0.307450
\(513\) −2.14000e12 + 1.28547e12i −1.36422 + 0.819472i
\(514\) −2.23595e12 −1.41296
\(515\) 1.20675e10 + 2.09015e10i 0.00755936 + 0.0130932i
\(516\) −2.97941e11 3.50935e11i −0.185015 0.217923i
\(517\) 1.59757e12 2.76707e12i 0.983448 1.70338i
\(518\) −3.70417e11 + 6.41582e11i −0.226052 + 0.391533i
\(519\) −3.90683e11 + 1.09299e12i −0.236358 + 0.661247i
\(520\) −8.75336e10 1.51613e11i −0.0525001 0.0909328i
\(521\) 1.03065e12 0.612834 0.306417 0.951897i \(-0.400870\pi\)
0.306417 + 0.951897i \(0.400870\pi\)
\(522\) −1.71368e12 1.40454e12i −1.01021 0.827975i
\(523\) 2.03811e12 1.19116 0.595579 0.803297i \(-0.296923\pi\)
0.595579 + 0.803297i \(0.296923\pi\)
\(524\) 1.40043e10 + 2.42561e10i 0.00811465 + 0.0140550i
\(525\) 9.16838e11 1.67129e11i 0.526715 0.0960140i
\(526\) 5.40383e11 9.35971e11i 0.307798 0.533122i
\(527\) −1.55615e12 + 2.69532e12i −0.878825 + 1.52217i
\(528\) −3.11169e12 + 5.67225e11i −1.74238 + 0.317616i
\(529\) 8.94322e11 + 1.54901e12i 0.496528 + 0.860011i
\(530\) −7.26693e11 −0.400046
\(531\) 1.45874e12 + 1.19559e12i 0.796256 + 0.652614i
\(532\) 6.03497e11 0.326642
\(533\) 7.07626e10 + 1.22564e11i 0.0379779 + 0.0657797i
\(534\) −3.15586e11 + 8.82898e11i −0.167951 + 0.469867i
\(535\) −5.71651e11 + 9.90128e11i −0.301675 + 0.522516i
\(536\) 8.56471e11 1.48345e12i 0.448199 0.776303i
\(537\) 2.14569e12 + 2.52735e12i 1.11348 + 1.31154i
\(538\) −8.10975e11 1.40465e12i −0.417337 0.722849i
\(539\) −1.39175e12 −0.710251
\(540\) −2.49310e11 1.38236e11i −0.126173 0.0699600i
\(541\) −1.53998e12 −0.772905 −0.386453 0.922309i \(-0.626300\pi\)
−0.386453 + 0.922309i \(0.626300\pi\)
\(542\) 2.10120e12 + 3.63939e12i 1.04585 + 1.81147i
\(543\) −1.27681e12 1.50392e12i −0.630271 0.742378i
\(544\) −5.17925e11 + 8.97072e11i −0.253555 + 0.439170i
\(545\) 3.02454e11 5.23865e11i 0.146850 0.254352i
\(546\) −1.46117e11 + 4.08785e11i −0.0703615 + 0.196846i
\(547\) 9.59604e11 + 1.66208e12i 0.458299 + 0.793797i 0.998871 0.0475005i \(-0.0151256\pi\)
−0.540572 + 0.841298i \(0.681792\pi\)
\(548\) 1.46240e11 0.0692713
\(549\) 3.72438e11 1.40449e11i 0.174976 0.0659847i
\(550\) −2.66463e12 −1.24166
\(551\) 1.98343e12 + 3.43541e12i 0.916717 + 1.58780i
\(552\) 1.44890e11 2.64117e10i 0.0664221 0.0121080i
\(553\) 9.01319e11 1.56113e12i 0.409841 0.709865i
\(554\) 2.21400e12 3.83475e12i 0.998580 1.72959i
\(555\) −6.16354e11 + 1.12354e11i −0.275748 + 0.0502656i
\(556\) 9.86533e10 + 1.70873e11i 0.0437799 + 0.0758291i
\(557\) −2.71058e11 −0.119320 −0.0596601 0.998219i \(-0.519002\pi\)
−0.0596601 + 0.998219i \(0.519002\pi\)
\(558\) 8.10146e11 4.92668e12i 0.353760 2.15130i
\(559\) −5.92858e11 −0.256802
\(560\) −5.09291e11 8.82118e11i −0.218836 0.379036i
\(561\) 1.06175e12 2.97041e12i 0.452575 1.26614i
\(562\) 3.27638e11 5.67486e11i 0.138542 0.239962i
\(563\) −1.54117e11 + 2.66939e11i −0.0646492 + 0.111976i −0.896538 0.442966i \(-0.853926\pi\)
0.831889 + 0.554942i \(0.187260\pi\)
\(564\) 5.93477e11 + 6.99039e11i 0.246972 + 0.290901i
\(565\) −6.82652e11 1.18239e12i −0.281826 0.488137i
\(566\) −1.89566e12 −0.776402
\(567\) −3.47521e11 1.73544e12i −0.141207 0.705159i
\(568\) −1.30037e12 −0.524205
\(569\) −1.79082e12 3.10180e12i −0.716222 1.24053i −0.962486 0.271330i \(-0.912536\pi\)
0.246264 0.969203i \(-0.420797\pi\)
\(570\) 1.48765e12 + 1.75226e12i 0.590287 + 0.695281i
\(571\) 4.45411e10 7.71475e10i 0.0175347 0.0303710i −0.857125 0.515109i \(-0.827752\pi\)
0.874660 + 0.484738i \(0.161085\pi\)
\(572\) 1.37797e11 2.38672e11i 0.0538219 0.0932222i
\(573\) 4.60504e11 1.28833e12i 0.178459 0.499265i
\(574\) 3.14113e11 + 5.44060e11i 0.120777 + 0.209191i
\(575\) 1.62624e11 0.0620413
\(576\) −2.46452e11 + 1.49873e12i −0.0932890 + 0.567312i
\(577\) −4.29975e11 −0.161492 −0.0807462 0.996735i \(-0.525730\pi\)
−0.0807462 + 0.996735i \(0.525730\pi\)
\(578\) 2.50312e11 + 4.33553e11i 0.0932838 + 0.161572i
\(579\) 1.37356e12 2.50383e11i 0.507918 0.0925874i
\(580\) −2.26493e11 + 3.92297e11i −0.0831051 + 0.143942i
\(581\) −1.08106e12 + 1.87245e12i −0.393603 + 0.681740i
\(582\) 2.03540e12 3.71030e11i 0.735355 0.134047i
\(583\) 1.43214e12 + 2.48054e12i 0.513424 + 0.889277i
\(584\) 2.04589e12 0.727820
\(585\) −3.43509e11 + 1.29540e11i −0.121265 + 0.0457301i
\(586\) 5.22149e12 1.82917
\(587\) −1.13503e12 1.96594e12i −0.394582 0.683436i 0.598466 0.801148i \(-0.295777\pi\)
−0.993048 + 0.117712i \(0.962444\pi\)
\(588\) 1.34442e11 3.76121e11i 0.0463807 0.129757i
\(589\) −4.46940e12 + 7.74123e12i −1.53014 + 2.65028i
\(590\) 8.68320e11 1.50397e12i 0.295016 0.510983i
\(591\) 2.93390e11 + 3.45575e11i 0.0989239 + 0.116520i
\(592\) −9.97514e11 1.72774e12i −0.333788 0.578138i
\(593\) −4.09944e12 −1.36138 −0.680688 0.732573i \(-0.738319\pi\)
−0.680688 + 0.732573i \(0.738319\pi\)
\(594\) 8.76763e10 + 5.05974e12i 0.0288964 + 1.66759i
\(595\) 1.01584e12 0.332277
\(596\) −2.57909e11 4.46712e11i −0.0837256 0.145017i
\(597\) 2.63460e12 + 3.10322e12i 0.848850 + 0.999836i
\(598\) −3.78764e10 + 6.56039e10i −0.0121119 + 0.0209785i
\(599\) 8.09154e11 1.40150e12i 0.256809 0.444806i −0.708576 0.705634i \(-0.750662\pi\)
0.965385 + 0.260828i \(0.0839955\pi\)
\(600\) −6.44478e11 + 1.80302e12i −0.203015 + 0.567963i
\(601\) −8.60804e11 1.49096e12i −0.269134 0.466155i 0.699504 0.714629i \(-0.253404\pi\)
−0.968639 + 0.248474i \(0.920071\pi\)
\(602\) −2.63168e12 −0.816675
\(603\) −2.77820e12 2.27702e12i −0.855727 0.701357i
\(604\) 8.36793e10 0.0255830
\(605\) −9.69528e11 1.67927e12i −0.294213 0.509591i
\(606\) 4.98447e11 9.08610e10i 0.150139 0.0273685i
\(607\) 2.07028e12 3.58583e12i 0.618985 1.07211i −0.370686 0.928758i \(-0.620877\pi\)
0.989671 0.143356i \(-0.0457894\pi\)
\(608\) −1.48753e12 + 2.57648e12i −0.441468 + 0.764646i
\(609\) −2.76683e12 + 5.04361e11i −0.815089 + 0.148581i
\(610\) −1.83249e11 3.17397e11i −0.0535869 0.0928152i
\(611\) 1.18093e12 0.342799
\(612\) 7.00190e11 + 5.73878e11i 0.201760 + 0.165363i
\(613\) 1.88290e12 0.538585 0.269292 0.963058i \(-0.413210\pi\)
0.269292 + 0.963058i \(0.413210\pi\)
\(614\) −1.05505e12 1.82740e12i −0.299582 0.518891i
\(615\) −1.78822e11 + 5.00281e11i −0.0504061 + 0.141019i
\(616\) −1.53152e12 + 2.65267e12i −0.428557 + 0.742283i
\(617\) 1.45653e12 2.52278e12i 0.404609 0.700803i −0.589667 0.807646i \(-0.700741\pi\)
0.994276 + 0.106844i \(0.0340744\pi\)
\(618\) 7.95803e10 + 9.37353e10i 0.0219461 + 0.0258497i
\(619\) 1.23748e12 + 2.14337e12i 0.338789 + 0.586799i 0.984205 0.177032i \(-0.0566495\pi\)
−0.645417 + 0.763831i \(0.723316\pi\)
\(620\) −1.02074e12 −0.277430
\(621\) −5.35096e9 3.08800e11i −0.00144384 0.0833231i
\(622\) −5.95413e12 −1.59500
\(623\) 5.95052e11 + 1.03066e12i 0.158255 + 0.274107i
\(624\) −7.56608e11 8.91186e11i −0.199775 0.235309i
\(625\) −5.69756e11 + 9.86847e11i −0.149358 + 0.258696i
\(626\) −8.08203e11 + 1.39985e12i −0.210347 + 0.364331i
\(627\) 3.04946e12 8.53130e12i 0.787986 2.20451i
\(628\) −6.13860e10 1.06324e11i −0.0157489 0.0272780i
\(629\) 1.98966e12 0.506817
\(630\) −1.52483e12 + 5.75024e11i −0.385646 + 0.145430i
\(631\) 5.10645e12 1.28229 0.641146 0.767419i \(-0.278459\pi\)
0.641146 + 0.767419i \(0.278459\pi\)
\(632\) 1.85182e12 + 3.20744e12i 0.461712 + 0.799708i
\(633\) −5.87333e11 + 1.07064e11i −0.145401 + 0.0265049i
\(634\) 2.96907e12 5.14257e12i 0.729824 1.26409i
\(635\) −1.76155e12 + 3.05110e12i −0.429946 + 0.744689i
\(636\) −8.08710e11 + 1.47418e11i −0.195991 + 0.0357268i
\(637\) −2.57198e11 4.45480e11i −0.0618928 0.107202i
\(638\) 8.04130e12 1.92147
\(639\) −4.42476e11 + 2.69080e12i −0.104987 + 0.638450i
\(640\) 2.58884e12 0.609951
\(641\) 3.03247e11 + 5.25239e11i 0.0709472 + 0.122884i 0.899317 0.437298i \(-0.144064\pi\)
−0.828370 + 0.560182i \(0.810731\pi\)
\(642\) −1.96055e12 + 5.48491e12i −0.455480 + 1.27427i
\(643\) 1.25492e12 2.17359e12i 0.289512 0.501450i −0.684181 0.729312i \(-0.739840\pi\)
0.973693 + 0.227862i \(0.0731736\pi\)
\(644\) −3.73313e10 + 6.46598e10i −0.00855238 + 0.0148132i
\(645\) −1.44039e12 1.69659e12i −0.327689 0.385975i
\(646\) −3.64990e12 6.32182e12i −0.824584 1.42822i
\(647\) 2.81592e12 0.631758 0.315879 0.948799i \(-0.397701\pi\)
0.315879 + 0.948799i \(0.397701\pi\)
\(648\) 3.44488e12 + 1.16444e12i 0.767515 + 0.259437i
\(649\) −6.84501e12 −1.51451
\(650\) −4.92428e11 8.52910e11i −0.108201 0.187410i
\(651\) −4.10159e12 4.83114e12i −0.895030 1.05423i
\(652\) 5.11757e11 8.86389e11i 0.110905 0.192092i
\(653\) −5.41859e10 + 9.38527e10i −0.0116621 + 0.0201994i −0.871798 0.489866i \(-0.837046\pi\)
0.860135 + 0.510066i \(0.170379\pi\)
\(654\) 1.03730e12 2.90200e12i 0.221720 0.620295i
\(655\) 6.77035e10 + 1.17266e11i 0.0143723 + 0.0248935i
\(656\) −1.69178e12 −0.356678
\(657\) 6.96150e11 4.23345e12i 0.145767 0.886441i
\(658\) 5.24213e12 1.09016
\(659\) 3.26356e12 + 5.65265e12i 0.674073 + 1.16753i 0.976739 + 0.214432i \(0.0687901\pi\)
−0.302666 + 0.953097i \(0.597877\pi\)
\(660\) 1.01780e12 1.85533e11i 0.208793 0.0380604i
\(661\) −2.14242e12 + 3.71079e12i −0.436515 + 0.756066i −0.997418 0.0718158i \(-0.977121\pi\)
0.560903 + 0.827881i \(0.310454\pi\)
\(662\) −1.98119e12 + 3.43153e12i −0.400927 + 0.694426i
\(663\) 1.14700e12 2.09085e11i 0.230543 0.0420253i
\(664\) −2.22111e12 3.84707e12i −0.443418 0.768023i
\(665\) 2.91760e12 0.578533
\(666\) −2.98658e12 + 1.12626e12i −0.588221 + 0.221822i
\(667\) −4.90768e11 −0.0960085
\(668\) 6.77313e11 + 1.17314e12i 0.131612 + 0.227959i
\(669\) −1.99993e12 + 5.59510e12i −0.386009 + 1.07992i
\(670\) −1.65373e12 + 2.86435e12i −0.317050 + 0.549147i
\(671\) −7.22282e11 + 1.25103e12i −0.137548 + 0.238241i
\(672\) −1.36511e12 1.60793e12i −0.258230 0.304162i
\(673\) −2.48556e12 4.30512e12i −0.467043 0.808942i 0.532248 0.846588i \(-0.321347\pi\)
−0.999291 + 0.0376463i \(0.988014\pi\)
\(674\) 3.46970e12 0.647623
\(675\) 3.51160e12 + 1.94710e12i 0.651086 + 0.361011i
\(676\) −1.44775e12 −0.266644
\(677\) −3.82144e12 6.61893e12i −0.699163 1.21099i −0.968757 0.248011i \(-0.920223\pi\)
0.269595 0.962974i \(-0.413110\pi\)
\(678\) −4.50181e12 5.30255e12i −0.818188 0.963720i
\(679\) 1.31306e12 2.27428e12i 0.237066 0.410611i
\(680\) −1.04356e12 + 1.80749e12i −0.187165 + 0.324180i
\(681\) −2.79838e12 + 7.82887e12i −0.498591 + 1.39488i
\(682\) 9.06000e12 + 1.56924e13i 1.60361 + 2.77753i
\(683\) −4.20646e12 −0.739646 −0.369823 0.929102i \(-0.620582\pi\)
−0.369823 + 0.929102i \(0.620582\pi\)
\(684\) 2.01101e12 + 1.64823e12i 0.351287 + 0.287916i
\(685\) 7.06995e11 0.122690
\(686\) −3.50638e12 6.07323e12i −0.604506 1.04703i
\(687\) −8.48896e12 + 1.54744e12i −1.45395 + 0.265038i
\(688\) 3.54349e12 6.13750e12i 0.602952 1.04434i
\(689\) −5.29324e11 + 9.16816e11i −0.0894818 + 0.154987i
\(690\) −2.79763e11 + 5.09975e10i −0.0469861 + 0.00856502i
\(691\) 1.16845e12 + 2.02381e12i 0.194966 + 0.337690i 0.946889 0.321560i \(-0.104207\pi\)
−0.751924 + 0.659250i \(0.770874\pi\)
\(692\) 1.20896e12 0.200417
\(693\) 4.96790e12 + 4.07171e12i 0.818225 + 0.670621i
\(694\) −7.27305e12 −1.19014
\(695\) 4.76938e11 + 8.26082e11i 0.0775409 + 0.134305i
\(696\) 1.94490e12 5.44115e12i 0.314164 0.878920i
\(697\) 8.43615e11 1.46118e12i 0.135393 0.234508i
\(698\) −1.24883e12 + 2.16304e12i −0.199138 + 0.344918i
\(699\) 4.26204e12 + 5.02014e12i 0.675259 + 0.795368i
\(700\) −4.85341e11 8.40635e11i −0.0764022 0.132333i
\(701\) 1.10126e12 0.172250 0.0861251 0.996284i \(-0.472552\pi\)
0.0861251 + 0.996284i \(0.472552\pi\)
\(702\) −1.60335e12 + 9.63113e11i −0.249179 + 0.149679i
\(703\) 5.71450e12 0.882429
\(704\) −2.75611e12 4.77373e12i −0.422883 0.732454i
\(705\) 2.86916e12 + 3.37950e12i 0.437425 + 0.515230i
\(706\) −4.92201e11 + 8.52518e11i −0.0745627 + 0.129146i
\(707\) 3.21553e11 5.56946e11i 0.0484022 0.0838350i
\(708\) 6.61222e11 1.84987e12i 0.0989004 0.276688i
\(709\) −6.57748e11 1.13925e12i −0.0977578 0.169322i 0.812998 0.582266i \(-0.197834\pi\)
−0.910756 + 0.412944i \(0.864500\pi\)
\(710\) 2.51085e12 0.370816
\(711\) 7.26710e12 2.74048e12i 1.06647 0.402173i
\(712\) −2.44514e12 −0.356570
\(713\) −5.52940e11 9.57720e11i −0.0801263 0.138783i
\(714\) 5.09151e12 9.28122e11i 0.733170 0.133648i
\(715\) 6.66180e11 1.15386e12i 0.0953266 0.165111i
\(716\) 1.72657e12 2.99051e12i 0.245514 0.425243i
\(717\) 1.44216e12 2.62889e11i 0.203787 0.0371480i
\(718\) 5.74695e12 + 9.95402e12i 0.807008 + 1.39778i
\(719\) −1.32450e13 −1.84830 −0.924151 0.382027i \(-0.875226\pi\)
−0.924151 + 0.382027i \(0.875226\pi\)
\(720\) 7.12093e11 4.33040e12i 0.0987507 0.600526i
\(721\) 1.56074e11 0.0215091
\(722\) −6.34376e12 1.09877e13i −0.868819 1.50484i
\(723\) −1.41382e12 + 3.95537e12i −0.192430 + 0.538350i
\(724\) −1.02741e12 + 1.77952e12i −0.138970 + 0.240702i
\(725\) 3.19021e12 5.52561e12i 0.428843 0.742778i
\(726\) −6.39364e12 7.53088e12i −0.854149 1.00608i
\(727\) −2.35848e12 4.08501e12i −0.313132 0.542360i 0.665907 0.746035i \(-0.268045\pi\)
−0.979039 + 0.203675i \(0.934712\pi\)
\(728\) −1.13211e12 −0.149382
\(729\) 3.58171e12 6.73209e12i 0.469695 0.882829i
\(730\) −3.95034e12 −0.514851
\(731\) 3.53396e12 + 6.12100e12i 0.457755 + 0.792855i
\(732\) −2.68319e11 3.16045e11i −0.0345424 0.0406864i
\(733\) −8.29559e11 + 1.43684e12i −0.106140 + 0.183840i −0.914203 0.405256i \(-0.867183\pi\)
0.808063 + 0.589096i \(0.200516\pi\)
\(734\) 9.59553e11 1.66199e12i 0.122022 0.211348i
\(735\) 6.49959e11 1.81835e12i 0.0821472 0.229819i
\(736\) −1.84032e11 3.18753e11i −0.0231177 0.0400410i
\(737\) 1.30364e13 1.62763
\(738\) −4.39195e11 + 2.67084e12i −0.0545009 + 0.331432i
\(739\) −5.72028e12 −0.705533 −0.352767 0.935711i \(-0.614759\pi\)
−0.352767 + 0.935711i \(0.614759\pi\)
\(740\) 3.26276e11 + 5.65126e11i 0.0399984 + 0.0692792i
\(741\) 3.29430e12 6.00511e11i 0.401403 0.0731711i
\(742\) −2.34966e12 + 4.06972e12i −0.284568 + 0.492887i
\(743\) 3.35872e12 5.81747e12i 0.404318 0.700300i −0.589923 0.807459i \(-0.700842\pi\)
0.994242 + 0.107159i \(0.0341754\pi\)
\(744\) 1.28096e13 2.33503e12i 1.53269 0.279392i
\(745\) −1.24686e12 2.15962e12i −0.148291 0.256847i
\(746\) −7.16752e12 −0.847314
\(747\) −8.71632e12 + 3.28699e12i −1.02421 + 0.386238i
\(748\) −3.28558e12 −0.383755
\(749\) 3.69670e12 + 6.40287e12i 0.429186 + 0.743373i
\(750\) 2.91592e12 8.15771e12i 0.336511 0.941439i
\(751\) −4.55508e12 + 7.88962e12i −0.522536 + 0.905058i 0.477121 + 0.878838i \(0.341680\pi\)
−0.999656 + 0.0262203i \(0.991653\pi\)
\(752\) −7.05839e12 + 1.22255e13i −0.804869 + 1.39407i
\(753\) 1.36792e11 + 1.61123e11i 0.0155054 + 0.0182633i
\(754\) 1.48605e12 + 2.57391e12i 0.167441 + 0.290016i
\(755\) 4.04547e11 0.0453114
\(756\) −1.58028e12 + 9.49253e11i −0.175948 + 0.105690i
\(757\) −4.86606e12 −0.538575 −0.269288 0.963060i \(-0.586788\pi\)
−0.269288 + 0.963060i \(0.586788\pi\)
\(758\) 8.21717e12 + 1.42326e13i 0.904089 + 1.56593i
\(759\) 7.25425e11 + 8.54457e11i 0.0793422 + 0.0934549i
\(760\) −2.99719e12 + 5.19129e12i −0.325877 + 0.564435i
\(761\) −1.85589e12 + 3.21450e12i −0.200596 + 0.347442i −0.948720 0.316116i \(-0.897621\pi\)
0.748125 + 0.663558i \(0.230954\pi\)
\(762\) −6.04146e12 + 1.69019e13i −0.649150 + 1.81609i
\(763\) −1.95588e12 3.38768e12i −0.208921 0.361862i
\(764\) −1.42502e12 −0.151322
\(765\) 3.38506e12 + 2.77441e12i 0.357347 + 0.292883i
\(766\) 8.54423e12 0.896692
\(767\) −1.26497e12 2.19099e12i −0.131978 0.228592i
\(768\) 7.52244e12 1.37125e12i 0.780249 0.142230i
\(769\) 3.31651e12 5.74436e12i 0.341989 0.592343i −0.642813 0.766023i \(-0.722233\pi\)
0.984802 + 0.173681i \(0.0555660\pi\)
\(770\) 2.95716e12 5.12194e12i 0.303156 0.525081i
\(771\) −1.20297e13 + 2.19287e12i −1.22606 + 0.223495i
\(772\) −7.27112e11 1.25940e12i −0.0736756 0.127610i
\(773\) −7.34772e12 −0.740193 −0.370096 0.928993i \(-0.620675\pi\)
−0.370096 + 0.928993i \(0.620675\pi\)
\(774\) −8.76947e12 7.18749e12i −0.878293 0.719852i
\(775\) 1.43774e13 1.43161
\(776\) 2.69776e12 + 4.67266e12i 0.267070 + 0.462579i
\(777\) −1.36367e12 + 3.81507e12i −0.134219 + 0.375498i
\(778\) 2.09284e12 3.62491e12i 0.204799 0.354723i
\(779\) 2.42295e12 4.19666e12i 0.235736 0.408306i
\(780\) 2.47478e11 + 2.91497e11i 0.0239393 + 0.0281974i
\(781\) −4.94829e12 8.57069e12i −0.475911 0.824301i
\(782\) 9.03108e11 0.0863593
\(783\) −1.05973e13 5.87594e12i −1.00755 0.558662i
\(784\) 6.14905e12 0.581281
\(785\) −2.96770e11 5.14021e11i −0.0278937 0.0483134i
\(786\) 4.46476e11 + 5.25892e11i 0.0417251 + 0.0491467i
\(787\) 1.90682e12 3.30271e12i 0.177184 0.306891i −0.763731 0.645535i \(-0.776635\pi\)
0.940915 + 0.338643i \(0.109968\pi\)
\(788\) 2.36081e11 4.08905e11i 0.0218119 0.0377793i
\(789\) 1.98939e12 5.56561e12i 0.182757 0.511289i
\(790\) −3.57561e12 6.19314e12i −0.326609 0.565703i
\(791\) −8.82902e12 −0.801897
\(792\) −1.23482e13 + 4.65661e12i −1.11517 + 0.420539i
\(793\) −5.33916e11 −0.0479451
\(794\) −3.58026e12 6.20119e12i −0.319685 0.553710i
\(795\) −3.90970e12 + 7.12692e11i −0.347129 + 0.0632775i
\(796\) 2.11998e12 3.67192e12i 0.187164 0.324178i
\(797\) 8.93658e12 1.54786e13i 0.784529 1.35884i −0.144751 0.989468i \(-0.546238\pi\)
0.929280 0.369376i \(-0.120428\pi\)
\(798\) 1.46233e13 2.66566e12i 1.27653 0.232697i
\(799\) −7.03941e12 1.21926e13i −0.611048 1.05837i
\(800\) 4.78518e12 0.413041
\(801\) −8.32005e11 + 5.05961e12i −0.0714133 + 0.434281i
\(802\) 1.94953e13 1.66397
\(803\) 7.78517e12 + 1.34843e13i 0.660767 + 1.14448i
\(804\) −1.25931e12 + 3.52310e12i −0.106287 + 0.297354i
\(805\) −1.80478e11 + 3.12597e11i −0.0151476 + 0.0262363i
\(806\) −3.34861e12 + 5.79996e12i −0.279484 + 0.484080i
\(807\) −5.74073e12 6.76184e12i −0.476471 0.561221i
\(808\) 6.60650e11 + 1.14428e12i 0.0545281 + 0.0944454i
\(809\) 1.16949e13 0.959908 0.479954 0.877294i \(-0.340653\pi\)
0.479954 + 0.877294i \(0.340653\pi\)
\(810\) −6.65161e12 2.24839e12i −0.542931 0.183522i
\(811\) −3.78089e12 −0.306902 −0.153451 0.988156i \(-0.549039\pi\)
−0.153451 + 0.988156i \(0.549039\pi\)
\(812\) 1.46466e12 + 2.53687e12i 0.118232 + 0.204784i
\(813\) 1.48740e13 + 1.75196e13i 1.19404 + 1.40643i
\(814\) 5.79198e12 1.00320e13i 0.462400 0.800900i
\(815\) 2.47408e12 4.28524e12i 0.196429 0.340224i
\(816\) −4.69105e12 + 1.31239e13i −0.370394 + 1.03623i
\(817\) 1.01499e13 + 1.75801e13i 0.797006 + 1.38045i
\(818\) −9.74701e11 −0.0761170
\(819\) −3.85221e11 + 2.34261e12i −0.0299180 + 0.181938i
\(820\) 5.53363e11 0.0427413
\(821\) −3.66299e12 6.34448e12i −0.281379 0.487362i 0.690346 0.723480i \(-0.257458\pi\)
−0.971725 + 0.236117i \(0.924125\pi\)
\(822\) 3.54353e12 6.45945e11i 0.270716 0.0493483i
\(823\) −3.23057e12 + 5.59552e12i −0.245460 + 0.425149i −0.962261 0.272129i \(-0.912272\pi\)
0.716801 + 0.697278i \(0.245606\pi\)
\(824\) −1.60332e11 + 2.77703e11i −0.0121157 + 0.0209850i
\(825\) −1.43360e13 + 2.61329e12i −1.07742 + 0.196401i
\(826\) −5.61517e12 9.72576e12i −0.419713 0.726965i
\(827\) −1.17187e13 −0.871176 −0.435588 0.900146i \(-0.643460\pi\)
−0.435588 + 0.900146i \(0.643460\pi\)
\(828\) −3.00993e11 + 1.13507e11i −0.0222546 + 0.00839237i
\(829\) −2.81041e12 −0.206669 −0.103334 0.994647i \(-0.532951\pi\)
−0.103334 + 0.994647i \(0.532951\pi\)
\(830\) 4.28867e12 + 7.42819e12i 0.313668 + 0.543290i
\(831\) 8.15071e12 2.28028e13i 0.592913 1.65876i
\(832\) 1.01867e12 1.76439e12i 0.0737018 0.127655i
\(833\) −3.06626e12 + 5.31091e12i −0.220651 + 0.382179i
\(834\) 3.14521e12 + 3.70465e12i 0.225114 + 0.265155i
\(835\) 3.27446e12 + 5.67153e12i 0.233105 + 0.403749i
\(836\) −9.43650e12 −0.668163
\(837\) −4.73072e11 2.73007e13i −0.0333168 1.92269i
\(838\) −1.88209e13 −1.31839
\(839\) 8.01390e12 + 1.38805e13i 0.558361 + 0.967109i 0.997634 + 0.0687556i \(0.0219029\pi\)
−0.439273 + 0.898354i \(0.644764\pi\)
\(840\) −2.75054e12 3.23978e12i −0.190617 0.224522i
\(841\) −2.37384e12 + 4.11162e12i −0.163633 + 0.283420i
\(842\) 4.12300e12 7.14125e12i 0.282689 0.489632i
\(843\) 1.20618e12 3.37447e12i 0.0822600 0.230135i
\(844\) 3.10913e11 + 5.38517e11i 0.0210910 + 0.0365307i
\(845\) −6.99912e12 −0.472268
\(846\) 1.74682e13 + 1.43170e13i 1.17241 + 0.960916i
\(847\) −1.25393e13 −0.837141
\(848\) −6.32749e12 1.09595e13i −0.420194 0.727798i
\(849\) −1.01989e13 + 1.85914e12i −0.673703 + 0.122808i
\(850\) −5.87061e12 + 1.01682e13i −0.385743 + 0.668127i
\(851\) −3.53490e11 + 6.12263e11i −0.0231044 + 0.0400179i
\(852\) 2.79423e12 5.09356e11i 0.181671 0.0331164i
\(853\) 8.96613e12 + 1.55298e13i 0.579875 + 1.00437i 0.995493 + 0.0948337i \(0.0302319\pi\)
−0.415618 + 0.909539i \(0.636435\pi\)
\(854\) −2.37004e12 −0.152474
\(855\) 9.72222e12 + 7.96837e12i 0.622183 + 0.509943i
\(856\) −1.51902e13 −0.967011
\(857\) 2.18082e12 + 3.77729e12i 0.138104 + 0.239203i 0.926779 0.375607i \(-0.122566\pi\)
−0.788675 + 0.614810i \(0.789233\pi\)
\(858\) 2.28474e12 6.39191e12i 0.143928 0.402659i
\(859\) −3.67580e12 + 6.36667e12i −0.230347 + 0.398973i −0.957910 0.287068i \(-0.907319\pi\)
0.727563 + 0.686041i \(0.240653\pi\)
\(860\) −1.15904e12 + 2.00751e12i −0.0722527 + 0.125145i
\(861\) 2.22355e12 + 2.61905e12i 0.137890 + 0.162416i
\(862\) −4.95248e12 8.57795e12i −0.305520 0.529177i
\(863\) 1.41639e13 0.869231 0.434615 0.900616i \(-0.356884\pi\)
0.434615 + 0.900616i \(0.356884\pi\)
\(864\) −1.57450e11 9.08636e12i −0.00961241 0.554725i
\(865\) 5.84471e12 0.354969
\(866\) −7.03956e12 1.21929e13i −0.425319 0.736674i
\(867\) 1.77191e12 + 2.08708e12i 0.106501 + 0.125445i
\(868\) −3.30042e12 + 5.71649e12i −0.197347 + 0.341815i
\(869\) −1.40933e13 + 2.44104e13i −0.838350 + 1.45206i
\(870\) −3.75535e12 + 1.05061e13i −0.222236 + 0.621737i
\(871\) 2.40916e12 + 4.17278e12i 0.141835 + 0.245666i
\(872\) 8.03695e12 0.470725
\(873\) 1.05868e13 3.99238e12i 0.616883 0.232631i
\(874\) 2.59381e12 0.150362
\(875\) −5.49810e12 9.52299e12i −0.317085 0.549208i
\(876\) −4.39618e12 + 8.01372e11i −0.252236 + 0.0459797i
\(877\) 2.34330e12 4.05872e12i 0.133761 0.231681i −0.791362 0.611347i \(-0.790628\pi\)
0.925124 + 0.379666i \(0.123961\pi\)
\(878\) 3.84939e12 6.66733e12i 0.218608 0.378640i
\(879\) 2.80923e13 5.12089e12i 1.58722 0.289331i
\(880\) 7.96346e12 + 1.37931e13i 0.447641 + 0.775337i
\(881\) 1.22598e13 0.685635 0.342817 0.939402i \(-0.388619\pi\)
0.342817 + 0.939402i \(0.388619\pi\)
\(882\) 1.59633e12 9.70761e12i 0.0888204 0.540137i
\(883\) −6.77194e12 −0.374878 −0.187439 0.982276i \(-0.560019\pi\)
−0.187439 + 0.982276i \(0.560019\pi\)
\(884\) −6.07181e11 1.05167e12i −0.0334413 0.0579220i
\(885\) 3.19667e12 8.94316e12i 0.175167 0.490057i
\(886\) −5.42145e12 + 9.39023e12i −0.295573 + 0.511947i
\(887\) 1.08701e13 1.88276e13i 0.589627 1.02126i −0.404654 0.914470i \(-0.632608\pi\)
0.994281 0.106795i \(-0.0340587\pi\)
\(888\) −5.38729e12 6.34554e12i −0.290745 0.342460i
\(889\) 1.13915e13 + 1.97306e13i 0.611676 + 1.05945i
\(890\) 4.72125e12 0.252233
\(891\) 5.43396e12 + 2.71360e13i 0.288846 + 1.44244i
\(892\) 6.18875e12 0.327311
\(893\) −2.02179e13 3.50183e13i −1.06391 1.84274i
\(894\) −8.22252e12 9.68506e12i −0.430513 0.507088i
\(895\) 8.34709e12 1.44576e13i 0.434842 0.753169i
\(896\) 8.37063e12 1.44984e13i 0.433883 0.751507i
\(897\) −1.39440e11 + 3.90104e11i −0.00719153 + 0.0201194i
\(898\) −2.09601e13 3.63040e13i −1.07560 1.86299i
\(899\) −4.33882e13 −2.21540
\(900\) 6.78606e11 4.12676e12i 0.0344768 0.209661i
\(901\) 1.26210e13 0.638015
\(902\) −4.91159e12 8.50713e12i −0.247055 0.427911i
\(903\) −1.41588e13 + 2.58098e12i −0.708649 + 0.129178i
\(904\) 9.06989e12 1.57095e13i 0.451694 0.782356i
\(905\) −4.96700e12 + 8.60309e12i −0.246136 + 0.426320i
\(906\) 2.02763e12 3.69613e11i 0.0999797 0.0182251i
\(907\) 1.13948e13 + 1.97364e13i 0.559079 + 0.968354i 0.997574 + 0.0696198i \(0.0221786\pi\)
−0.438494 + 0.898734i \(0.644488\pi\)
\(908\) 8.65954e12 0.422774
\(909\) 2.59260e12 9.77687e11i 0.125950 0.0474966i
\(910\) 2.18595e12 0.105671
\(911\) 5.63882e12 + 9.76672e12i 0.271241 + 0.469803i 0.969180 0.246354i \(-0.0792326\pi\)
−0.697939 + 0.716157i \(0.745899\pi\)
\(912\) −1.34731e13 + 3.76931e13i −0.644900 + 1.80420i
\(913\) 1.69039e13 2.92784e13i 0.805134 1.39453i
\(914\) −1.59872e13 + 2.76906e13i −0.757728 + 1.31242i
\(915\) −1.29719e12 1.52792e12i −0.0611797 0.0720618i
\(916\) 4.49375e12 + 7.78340e12i 0.210901 + 0.365292i
\(917\) 8.75637e11 0.0408942
\(918\) 1.95011e13 + 1.08129e13i 0.906290 + 0.502515i
\(919\) −2.27954e12 −0.105421 −0.0527105 0.998610i \(-0.516786\pi\)
−0.0527105 + 0.998610i \(0.516786\pi\)
\(920\) −3.70803e11 6.42250e11i −0.0170647 0.0295569i
\(921\) −7.46849e12 8.79692e12i −0.342030 0.402867i
\(922\) −3.69483e12 + 6.39963e12i −0.168386 + 0.291653i
\(923\) 1.82891e12 3.16776e12i 0.0829438 0.143663i
\(924\) 2.25186e12 6.29992e12i 0.101629 0.284322i
\(925\) −4.59569e12 7.95997e12i −0.206402 0.357498i
\(926\) 4.03450e13 1.80318
\(927\) 5.20081e11 + 4.26260e11i 0.0231320 + 0.0189590i
\(928\) −1.44407e13 −0.639179
\(929\) 9.43673e12 + 1.63449e13i 0.415672 + 0.719965i 0.995499 0.0947745i \(-0.0302130\pi\)
−0.579827 + 0.814740i \(0.696880\pi\)
\(930\) −2.47335e13 + 4.50863e12i −1.08421 + 0.197639i
\(931\) −8.80659e12 + 1.52535e13i −0.384179 + 0.665418i
\(932\) 3.42953e12 5.94012e12i 0.148889 0.257884i
\(933\) −3.20340e13 + 5.83941e12i −1.38402 + 0.252291i
\(934\) −2.73064e12 4.72961e12i −0.117410 0.203359i
\(935\) −1.58841e13 −0.679689
\(936\) −3.77249e12 3.09195e12i −0.160652 0.131671i
\(937\) −1.08798e13 −0.461096 −0.230548 0.973061i \(-0.574052\pi\)
−0.230548 + 0.973061i \(0.574052\pi\)
\(938\) 1.06942e13 + 1.85229e13i 0.451061 + 0.781261i
\(939\) −2.97536e12 + 8.32399e12i −0.124895 + 0.349411i
\(940\) 2.30872e12 3.99882e12i 0.0964486 0.167054i
\(941\) −1.41900e13 + 2.45778e13i −0.589970 + 1.02186i 0.404266 + 0.914641i \(0.367527\pi\)
−0.994236 + 0.107216i \(0.965806\pi\)
\(942\) −1.95708e12 2.30518e12i −0.0809802 0.0953842i
\(943\) 2.99759e11 + 5.19198e11i 0.0123444 + 0.0213811i
\(944\) 3.02427e13 1.23950
\(945\) −7.63983e12 + 4.58915e12i −0.311631 + 0.187193i
\(946\) 4.11500e13 1.67055
\(947\) −1.79187e12 3.10361e12i −0.0723988 0.125398i 0.827553 0.561387i \(-0.189732\pi\)
−0.899952 + 0.435989i \(0.856399\pi\)
\(948\) −5.23552e12 6.16676e12i −0.210534 0.247982i
\(949\) −2.87743e12 + 4.98385e12i −0.115161 + 0.199465i
\(950\) −1.68610e13 + 2.92040e13i −0.671624 + 1.16329i
\(951\) 1.09305e13 3.05796e13i 0.433337 1.21232i
\(952\) 6.74837e12 + 1.16885e13i 0.266276 + 0.461204i
\(953\) 2.91182e12 0.114353 0.0571763 0.998364i \(-0.481790\pi\)
0.0571763 + 0.998364i \(0.481790\pi\)
\(954\) −1.89447e13 + 7.14417e12i −0.740490 + 0.279244i
\(955\) −6.88926e12 −0.268014
\(956\) −7.63428e11 1.32230e12i −0.0295602 0.0511998i
\(957\) 4.32632e13 7.88637e12i 1.66730 0.303930i
\(958\) −1.95591e13 + 3.38773e13i −0.750245 + 1.29946i
\(959\) 2.28597e12 3.95941e12i 0.0872743 0.151163i
\(960\) 7.52411e12 1.37156e12i 0.285913 0.0521186i
\(961\) −3.56649e13 6.17735e13i −1.34892 2.33640i
\(962\) 4.28148e12 0.161178
\(963\) −5.16874e12 + 3.14323e13i −0.193672 + 1.17776i
\(964\) 4.37505e12 0.163168
\(965\) −3.51522e12 6.08853e12i −0.130491 0.226016i
\(966\) −6.18971e11 + 1.73166e12i −0.0228704 + 0.0639832i
\(967\) 1.34163e13 2.32377e13i 0.493417 0.854623i −0.506555 0.862208i \(-0.669081\pi\)
0.999971 + 0.00758529i \(0.00241450\pi\)
\(968\) 1.28814e13 2.23112e13i 0.471546 0.816742i
\(969\) −2.58369e13 3.04326e13i −0.941422 1.10887i
\(970\) −5.20902e12 9.02228e12i −0.188922 0.327223i
\(971\) 5.18797e13 1.87288 0.936442 0.350824i \(-0.114098\pi\)
0.936442 + 0.350824i \(0.114098\pi\)
\(972\) −7.85845e12 1.15279e12i −0.282383 0.0414240i
\(973\) 6.16844e12 0.220632
\(974\) 2.32179e13 + 4.02146e13i 0.826624 + 1.43175i
\(975\) −3.48580e12 4.10582e12i −0.123533 0.145505i
\(976\) 3.19120e12 5.52731e12i 0.112572 0.194980i
\(977\) −2.77975e13 + 4.81466e13i −0.976067 + 1.69060i −0.299700 + 0.954034i \(0.596887\pi\)
−0.676367 + 0.736565i \(0.736447\pi\)
\(978\) 8.48516e12 2.37385e13i 0.296576 0.829714i
\(979\) −9.30445e12 1.61158e13i −0.323719 0.560698i
\(980\) −2.01129e12 −0.0696557
\(981\) 2.73472e12 1.66305e13i 0.0942763 0.573315i
\(982\) −2.96003e13 −1.01577
\(983\) −2.01121e13 3.48351e13i −0.687015 1.18994i −0.972799 0.231650i \(-0.925587\pi\)
0.285785 0.958294i \(-0.407746\pi\)
\(984\) −6.94429e12 + 1.26586e12i −0.236129 + 0.0430436i
\(985\) 1.14133e12 1.97685e12i 0.0386322 0.0669129i
\(986\) 1.77163e13 3.06856e13i 0.596935 1.03392i
\(987\) 2.82033e13 5.14113e12i 0.945961 0.172437i
\(988\) −1.74388e12 3.02049e12i −0.0582252 0.100849i
\(989\) −2.51142e12 −0.0834710
\(990\) 2.38428e13 8.99129e12i 0.788858 0.297484i
\(991\) 1.34682e13 0.443588 0.221794 0.975094i \(-0.428809\pi\)
0.221794 + 0.975094i \(0.428809\pi\)
\(992\) −1.62701e13 2.81806e13i −0.533442 0.923949i
\(993\) −7.29365e12 + 2.04051e13i −0.238053 + 0.665988i
\(994\) 8.11847e12 1.40616e13i 0.263776 0.456874i
\(995\) 1.02490e13 1.77518e13i 0.331496 0.574169i
\(996\) 6.27960e12 + 7.39655e12i 0.202192 + 0.238156i
\(997\) 1.87292e13 + 3.24399e13i 0.600331 + 1.03980i 0.992771 + 0.120026i \(0.0382977\pi\)
−0.392440 + 0.919778i \(0.628369\pi\)
\(998\) −5.18065e13 −1.65309
\(999\) −1.49636e13 + 8.98846e12i −0.475326 + 0.285523i
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 9.10.c.a.4.2 16
3.2 odd 2 27.10.c.a.10.7 16
9.2 odd 6 27.10.c.a.19.7 16
9.4 even 3 81.10.a.c.1.7 8
9.5 odd 6 81.10.a.d.1.2 8
9.7 even 3 inner 9.10.c.a.7.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.10.c.a.4.2 16 1.1 even 1 trivial
9.10.c.a.7.2 yes 16 9.7 even 3 inner
27.10.c.a.10.7 16 3.2 odd 2
27.10.c.a.19.7 16 9.2 odd 6
81.10.a.c.1.7 8 9.4 even 3
81.10.a.d.1.2 8 9.5 odd 6