Properties

Label 27.10.e.a.4.15
Level $27$
Weight $10$
Character 27.4
Analytic conductor $13.906$
Analytic rank $0$
Dimension $156$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,10,Mod(4,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 27.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.9059675764\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(26\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.15
Character \(\chi\) \(=\) 27.4
Dual form 27.10.e.a.7.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.82322 + 1.75551i) q^{2} +(-137.543 + 27.6597i) q^{3} +(-372.033 - 312.173i) q^{4} +(203.603 - 1154.69i) q^{5} +(-711.954 - 108.048i) q^{6} +(-440.948 + 369.999i) q^{7} +(-2560.36 - 4434.68i) q^{8} +(18152.9 - 7608.76i) q^{9} +(3009.09 - 5211.90i) q^{10} +(12328.1 + 69916.4i) q^{11} +(59805.0 + 32646.7i) q^{12} +(-143827. + 52348.7i) q^{13} +(-2776.32 + 1010.50i) q^{14} +(3934.29 + 164451. i) q^{15} +(38614.5 + 218993. i) q^{16} +(164482. - 284892. i) q^{17} +(100913. - 4831.19i) q^{18} +(140625. + 243570. i) q^{19} +(-436210. + 366024. i) q^{20} +(50415.0 - 63087.1i) q^{21} +(-63277.4 + 358864. i) q^{22} +(821687. + 689477. i) q^{23} +(474820. + 539138. i) q^{24} +(543480. + 197811. i) q^{25} -785607. q^{26} +(-2.28634e6 + 1.54863e6i) q^{27} +279551. q^{28} +(1.62591e6 + 591785. i) q^{29} +(-269718. + 800088. i) q^{30} +(4.00947e6 + 3.36434e6i) q^{31} +(-653471. + 3.70602e6i) q^{32} +(-3.62951e6 - 9.27548e6i) q^{33} +(1.29346e6 - 1.08535e6i) q^{34} +(337456. + 584492. i) q^{35} +(-9.12872e6 - 2.83613e6i) q^{36} +(3.24063e6 - 5.61294e6i) q^{37} +(250677. + 1.42166e6i) q^{38} +(1.83344e7 - 1.11784e7i) q^{39} +(-5.64198e6 + 2.05351e6i) q^{40} +(-1.80717e7 + 6.57754e6i) q^{41} +(353913. - 215779. i) q^{42} +(-5.74575e6 - 3.25858e7i) q^{43} +(1.72395e7 - 2.98597e7i) q^{44} +(-5.08979e6 - 2.25101e7i) q^{45} +(2.75279e6 + 4.76797e6i) q^{46} +(-2.17446e7 + 1.82459e7i) q^{47} +(-1.13684e7 - 2.90528e7i) q^{48} +(-6.94979e6 + 3.94142e7i) q^{49} +(2.27407e6 + 1.90817e6i) q^{50} +(-1.47433e7 + 4.37343e7i) q^{51} +(6.98503e7 + 2.54234e7i) q^{52} -5.03334e7 q^{53} +(-1.37461e7 + 3.45570e6i) q^{54} +8.32418e7 q^{55} +(2.76981e6 + 1.00813e6i) q^{56} +(-2.60790e7 - 2.96116e7i) q^{57} +(6.80326e6 + 5.70861e6i) q^{58} +(-1.89454e7 + 1.07445e8i) q^{59} +(4.98734e7 - 6.24093e7i) q^{60} +(-3.81453e7 + 3.20077e7i) q^{61} +(1.34324e7 + 2.32656e7i) q^{62} +(-5.18924e6 + 1.00716e7i) q^{63} +(4.72694e7 - 8.18730e7i) q^{64} +(3.11630e7 + 1.76734e8i) q^{65} +(-1.22273e6 - 5.11093e7i) q^{66} +(1.99585e8 - 7.26431e7i) q^{67} +(-1.50128e8 + 5.46423e7i) q^{68} +(-1.32088e8 - 7.21048e7i) q^{69} +(601546. + 3.41154e6i) q^{70} +(-1.75242e8 + 3.03528e8i) q^{71} +(-8.02204e7 - 6.10210e7i) q^{72} +(1.92455e8 + 3.33341e8i) q^{73} +(2.54838e7 - 2.13835e7i) q^{74} +(-8.02230e7 - 1.21749e7i) q^{75} +(2.37187e7 - 1.34516e8i) q^{76} +(-3.13051e7 - 2.62681e7i) q^{77} +(1.08054e8 - 2.17296e7i) q^{78} +(4.56193e7 + 1.66041e7i) q^{79} +2.60732e8 q^{80} +(2.71634e8 - 2.76242e8i) q^{81} -9.87104e7 q^{82} +(-1.67411e8 - 6.09326e7i) q^{83} +(-3.84502e7 + 7.73229e6i) q^{84} +(-2.95473e8 - 2.47931e8i) q^{85} +(2.94916e7 - 1.67255e8i) q^{86} +(-2.40001e8 - 3.64233e7i) q^{87} +(2.78492e8 - 2.33682e8i) q^{88} +(-3.40131e8 - 5.89124e8i) q^{89} +(1.49676e7 - 1.17506e8i) q^{90} +(4.40512e7 - 7.62990e7i) q^{91} +(-9.04587e7 - 5.13017e8i) q^{92} +(-6.44529e8 - 3.51839e8i) q^{93} +(-1.36910e8 + 4.98311e7i) q^{94} +(3.09880e8 - 1.12787e8i) q^{95} +(-1.26272e7 - 5.27810e8i) q^{96} +(2.16877e8 + 1.22997e9i) q^{97} +(-1.02712e8 + 1.77903e8i) q^{98} +(7.55768e8 + 1.17538e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 2382 q^{5} - 6822 q^{6} - 6 q^{7} + 36861 q^{8} + 2538 q^{9} - 3 q^{10} - 121767 q^{11} + 319935 q^{12} - 6 q^{13} - 720417 q^{14} - 706356 q^{15} + 1530 q^{16} + 1002249 q^{17}+ \cdots + 5248107342 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.82322 + 1.75551i 0.213158 + 0.0775832i 0.446392 0.894837i \(-0.352709\pi\)
−0.233234 + 0.972421i \(0.574931\pi\)
\(3\) −137.543 + 27.6597i −0.980373 + 0.197152i
\(4\) −372.033 312.173i −0.726627 0.609713i
\(5\) 203.603 1154.69i 0.145687 0.826230i −0.821127 0.570746i \(-0.806654\pi\)
0.966813 0.255484i \(-0.0822347\pi\)
\(6\) −711.954 108.048i −0.224270 0.0340359i
\(7\) −440.948 + 369.999i −0.0694139 + 0.0582452i −0.676834 0.736135i \(-0.736649\pi\)
0.607421 + 0.794380i \(0.292204\pi\)
\(8\) −2560.36 4434.68i −0.221002 0.382787i
\(9\) 18152.9 7608.76i 0.922262 0.386565i
\(10\) 3009.09 5211.90i 0.0951558 0.164815i
\(11\) 12328.1 + 69916.4i 0.253881 + 1.43983i 0.798928 + 0.601426i \(0.205401\pi\)
−0.545047 + 0.838405i \(0.683488\pi\)
\(12\) 59805.0 + 32646.7i 0.832572 + 0.454490i
\(13\) −143827. + 52348.7i −1.39667 + 0.508348i −0.927190 0.374592i \(-0.877783\pi\)
−0.469485 + 0.882940i \(0.655560\pi\)
\(14\) −2776.32 + 1010.50i −0.0193150 + 0.00703008i
\(15\) 3934.29 + 164451.i 0.0200658 + 0.838735i
\(16\) 38614.5 + 218993.i 0.147302 + 0.835394i
\(17\) 164482. 284892.i 0.477639 0.827294i −0.522033 0.852925i \(-0.674826\pi\)
0.999671 + 0.0256311i \(0.00815951\pi\)
\(18\) 100913. 4831.19i 0.226579 0.0108475i
\(19\) 140625. + 243570.i 0.247555 + 0.428779i 0.962847 0.270048i \(-0.0870394\pi\)
−0.715292 + 0.698826i \(0.753706\pi\)
\(20\) −436210. + 366024.i −0.609622 + 0.511534i
\(21\) 50415.0 63087.1i 0.0565683 0.0707871i
\(22\) −63277.4 + 358864.i −0.0575899 + 0.326609i
\(23\) 821687. + 689477.i 0.612253 + 0.513741i 0.895358 0.445348i \(-0.146920\pi\)
−0.283105 + 0.959089i \(0.591364\pi\)
\(24\) 474820. + 539138.i 0.292132 + 0.331703i
\(25\) 543480. + 197811.i 0.278262 + 0.101279i
\(26\) −785607. −0.337152
\(27\) −2.28634e6 + 1.54863e6i −0.827949 + 0.560804i
\(28\) 279551. 0.0859508
\(29\) 1.62591e6 + 591785.i 0.426881 + 0.155372i 0.546521 0.837445i \(-0.315952\pi\)
−0.119640 + 0.992817i \(0.538174\pi\)
\(30\) −269718. + 800088.i −0.0607946 + 0.180340i
\(31\) 4.00947e6 + 3.36434e6i 0.779756 + 0.654293i 0.943187 0.332262i \(-0.107812\pi\)
−0.163431 + 0.986555i \(0.552256\pi\)
\(32\) −653471. + 3.70602e6i −0.110167 + 0.624788i
\(33\) −3.62951e6 9.27548e6i −0.532764 1.36152i
\(34\) 1.29346e6 1.08535e6i 0.165997 0.139288i
\(35\) 337456. + 584492.i 0.0380112 + 0.0658373i
\(36\) −9.12872e6 2.83613e6i −0.905834 0.281426i
\(37\) 3.24063e6 5.61294e6i 0.284264 0.492360i −0.688167 0.725553i \(-0.741584\pi\)
0.972430 + 0.233193i \(0.0749175\pi\)
\(38\) 250677. + 1.42166e6i 0.0195024 + 0.110604i
\(39\) 1.83344e7 1.11784e7i 1.26904 0.773728i
\(40\) −5.64198e6 + 2.05351e6i −0.348467 + 0.126832i
\(41\) −1.80717e7 + 6.57754e6i −0.998781 + 0.363527i −0.789114 0.614246i \(-0.789460\pi\)
−0.209667 + 0.977773i \(0.567238\pi\)
\(42\) 353913. 215779.i 0.0175499 0.0107001i
\(43\) −5.74575e6 3.25858e7i −0.256294 1.45352i −0.792728 0.609575i \(-0.791340\pi\)
0.536434 0.843942i \(-0.319771\pi\)
\(44\) 1.72395e7 2.98597e7i 0.693407 1.20102i
\(45\) −5.08979e6 2.25101e7i −0.185030 0.818317i
\(46\) 2.75279e6 + 4.76797e6i 0.0906490 + 0.157009i
\(47\) −2.17446e7 + 1.82459e7i −0.649996 + 0.545412i −0.907070 0.420980i \(-0.861686\pi\)
0.257073 + 0.966392i \(0.417242\pi\)
\(48\) −1.13684e7 2.90528e7i −0.309111 0.789956i
\(49\) −6.94979e6 + 3.94142e7i −0.172222 + 0.976722i
\(50\) 2.27407e6 + 1.90817e6i 0.0514562 + 0.0431769i
\(51\) −1.47433e7 + 4.37343e7i −0.305161 + 0.905224i
\(52\) 6.98503e7 + 2.54234e7i 1.32481 + 0.482191i
\(53\) −5.03334e7 −0.876223 −0.438112 0.898921i \(-0.644353\pi\)
−0.438112 + 0.898921i \(0.644353\pi\)
\(54\) −1.37461e7 + 3.45570e6i −0.219993 + 0.0553050i
\(55\) 8.32418e7 1.22662
\(56\) 2.76981e6 + 1.00813e6i 0.0376361 + 0.0136984i
\(57\) −2.60790e7 2.96116e7i −0.327231 0.371557i
\(58\) 6.80326e6 + 5.70861e6i 0.0789389 + 0.0662376i
\(59\) −1.89454e7 + 1.07445e8i −0.203549 + 1.15438i 0.696158 + 0.717889i \(0.254891\pi\)
−0.899707 + 0.436495i \(0.856220\pi\)
\(60\) 4.98734e7 6.24093e7i 0.496807 0.621682i
\(61\) −3.81453e7 + 3.20077e7i −0.352742 + 0.295985i −0.801890 0.597472i \(-0.796172\pi\)
0.449148 + 0.893457i \(0.351728\pi\)
\(62\) 1.34324e7 + 2.32656e7i 0.115449 + 0.199964i
\(63\) −5.18924e6 + 1.00716e7i −0.0415022 + 0.0805503i
\(64\) 4.72694e7 8.18730e7i 0.352184 0.610001i
\(65\) 3.11630e7 + 1.76734e8i 0.216535 + 1.22803i
\(66\) −1.22273e6 5.11093e7i −0.00793200 0.331552i
\(67\) 1.99585e8 7.26431e7i 1.21002 0.440411i 0.343308 0.939223i \(-0.388453\pi\)
0.866710 + 0.498812i \(0.166230\pi\)
\(68\) −1.50128e8 + 5.46423e7i −0.851477 + 0.309912i
\(69\) −1.32088e8 7.21048e7i −0.701521 0.382951i
\(70\) 601546. + 3.41154e6i 0.00299452 + 0.0169828i
\(71\) −1.75242e8 + 3.03528e8i −0.818419 + 1.41754i 0.0884276 + 0.996083i \(0.471816\pi\)
−0.906847 + 0.421461i \(0.861518\pi\)
\(72\) −8.02204e7 6.10210e7i −0.351794 0.267598i
\(73\) 1.92455e8 + 3.33341e8i 0.793186 + 1.37384i 0.923984 + 0.382430i \(0.124913\pi\)
−0.130798 + 0.991409i \(0.541754\pi\)
\(74\) 2.54838e7 2.13835e7i 0.0987920 0.0828963i
\(75\) −8.02230e7 1.21749e7i −0.292768 0.0444313i
\(76\) 2.37187e7 1.34516e8i 0.0815512 0.462500i
\(77\) −3.13051e7 2.62681e7i −0.101486 0.0851569i
\(78\) 1.08054e8 2.17296e7i 0.330535 0.0664702i
\(79\) 4.56193e7 + 1.66041e7i 0.131773 + 0.0479615i 0.407065 0.913399i \(-0.366552\pi\)
−0.275292 + 0.961361i \(0.588774\pi\)
\(80\) 2.60732e8 0.711687
\(81\) 2.71634e8 2.76242e8i 0.701135 0.713029i
\(82\) −9.87104e7 −0.241102
\(83\) −1.67411e8 6.09326e7i −0.387197 0.140928i 0.141084 0.989998i \(-0.454941\pi\)
−0.528281 + 0.849069i \(0.677163\pi\)
\(84\) −3.84502e7 + 7.73229e6i −0.0842638 + 0.0169454i
\(85\) −2.95473e8 2.47931e8i −0.613949 0.515165i
\(86\) 2.94916e7 1.67255e8i 0.0581373 0.329713i
\(87\) −2.40001e8 3.64233e7i −0.449134 0.0681620i
\(88\) 2.78492e8 2.33682e8i 0.495040 0.415388i
\(89\) −3.40131e8 5.89124e8i −0.574634 0.995295i −0.996081 0.0884419i \(-0.971811\pi\)
0.421448 0.906853i \(-0.361522\pi\)
\(90\) 1.49676e7 1.17506e8i 0.0240470 0.188786i
\(91\) 4.40512e7 7.62990e7i 0.0673398 0.116636i
\(92\) −9.04587e7 5.13017e8i −0.131645 0.746597i
\(93\) −6.44529e8 3.51839e8i −0.893447 0.487721i
\(94\) −1.36910e8 + 4.98311e7i −0.180867 + 0.0658301i
\(95\) 3.09880e8 1.12787e8i 0.390335 0.142070i
\(96\) −1.26272e7 5.27810e8i −0.0151736 0.634245i
\(97\) 2.16877e8 + 1.22997e9i 0.248737 + 1.41066i 0.811650 + 0.584144i \(0.198569\pi\)
−0.562913 + 0.826516i \(0.690319\pi\)
\(98\) −1.02712e8 + 1.77903e8i −0.112488 + 0.194835i
\(99\) 7.55768e8 + 1.17538e9i 0.790734 + 1.22976i
\(100\) −1.40442e8 2.43252e8i −0.140442 0.243252i
\(101\) −1.70877e8 + 1.43383e8i −0.163395 + 0.137104i −0.720819 0.693123i \(-0.756234\pi\)
0.557424 + 0.830228i \(0.311790\pi\)
\(102\) −1.47886e8 + 1.85058e8i −0.135278 + 0.169281i
\(103\) 1.03428e8 5.86567e8i 0.0905460 0.513512i −0.905476 0.424399i \(-0.860486\pi\)
0.996021 0.0891133i \(-0.0284033\pi\)
\(104\) 6.00399e8 + 5.03794e8i 0.503257 + 0.422283i
\(105\) −6.25815e7 7.10585e7i −0.0502451 0.0570511i
\(106\) −2.42769e8 8.83606e7i −0.186774 0.0679802i
\(107\) 1.08574e9 0.800754 0.400377 0.916351i \(-0.368879\pi\)
0.400377 + 0.916351i \(0.368879\pi\)
\(108\) 1.33403e9 + 1.37590e8i 0.943539 + 0.0973152i
\(109\) −1.86453e9 −1.26517 −0.632587 0.774489i \(-0.718007\pi\)
−0.632587 + 0.774489i \(0.718007\pi\)
\(110\) 4.01493e8 + 1.46132e8i 0.261464 + 0.0951650i
\(111\) −2.90472e8 + 8.61652e8i −0.181615 + 0.538739i
\(112\) −9.80544e7 8.22774e7i −0.0588825 0.0494083i
\(113\) −2.47881e8 + 1.40580e9i −0.143018 + 0.811095i 0.825919 + 0.563788i \(0.190657\pi\)
−0.968937 + 0.247307i \(0.920454\pi\)
\(114\) −7.38015e7 1.88605e8i −0.0409254 0.104588i
\(115\) 9.63431e8 8.08414e8i 0.513665 0.431016i
\(116\) −4.20155e8 7.27730e8i −0.215451 0.373172i
\(117\) −2.21257e9 + 2.04463e9i −1.09159 + 1.00874i
\(118\) −2.79997e8 + 4.84970e8i −0.132949 + 0.230274i
\(119\) 3.28816e7 + 1.86481e8i 0.0150311 + 0.0852458i
\(120\) 7.19212e8 4.38501e8i 0.316622 0.193043i
\(121\) −2.52057e9 + 9.17412e8i −1.06897 + 0.389072i
\(122\) −2.40173e8 + 8.74158e7i −0.0981532 + 0.0357249i
\(123\) 2.30369e9 1.40455e9i 0.907508 0.553304i
\(124\) −4.41398e8 2.50329e9i −0.167661 0.950855i
\(125\) 1.48409e9 2.57052e9i 0.543707 0.941727i
\(126\) −4.27097e7 + 3.94679e7i −0.0150959 + 0.0139501i
\(127\) 2.21753e9 + 3.84088e9i 0.756402 + 1.31013i 0.944674 + 0.328010i \(0.106378\pi\)
−0.188272 + 0.982117i \(0.560289\pi\)
\(128\) 1.84770e9 1.55040e9i 0.608396 0.510505i
\(129\) 1.69160e9 + 4.32301e9i 0.537828 + 1.37446i
\(130\) −1.59952e8 + 9.07134e8i −0.0491185 + 0.278565i
\(131\) −1.64912e9 1.38378e9i −0.489251 0.410530i 0.364507 0.931201i \(-0.381237\pi\)
−0.853758 + 0.520671i \(0.825682\pi\)
\(132\) −1.54526e9 + 4.58382e9i −0.443014 + 1.31415i
\(133\) −1.52129e8 5.53705e7i −0.0421580 0.0153443i
\(134\) 1.09017e9 0.292094
\(135\) 1.32269e9 + 2.95532e9i 0.342732 + 0.765777i
\(136\) −1.68454e9 −0.422236
\(137\) 3.56983e9 + 1.29931e9i 0.865775 + 0.315116i 0.736455 0.676487i \(-0.236498\pi\)
0.129320 + 0.991603i \(0.458721\pi\)
\(138\) −5.10506e8 5.79658e8i −0.119824 0.136055i
\(139\) −4.78102e9 4.01175e9i −1.08631 0.911523i −0.0898811 0.995953i \(-0.528649\pi\)
−0.996429 + 0.0844297i \(0.973093\pi\)
\(140\) 5.69175e7 3.22795e8i 0.0125219 0.0710151i
\(141\) 2.48613e9 3.11103e9i 0.529710 0.662855i
\(142\) −1.37808e9 + 1.15634e9i −0.284430 + 0.238665i
\(143\) −5.43315e9 9.41050e9i −1.08653 1.88192i
\(144\) 2.36723e9 + 3.68155e9i 0.458786 + 0.713510i
\(145\) 1.01437e9 1.75694e9i 0.190564 0.330066i
\(146\) 3.43067e8 + 1.94563e9i 0.0624873 + 0.354383i
\(147\) −1.34293e8 5.61336e9i −0.0237206 0.991506i
\(148\) −2.95783e9 + 1.07656e9i −0.506752 + 0.184443i
\(149\) −4.70352e9 + 1.71194e9i −0.781780 + 0.284545i −0.701915 0.712261i \(-0.747671\pi\)
−0.0798651 + 0.996806i \(0.525449\pi\)
\(150\) −3.65560e8 1.99554e8i −0.0589587 0.0321848i
\(151\) −5.60010e8 3.17597e9i −0.0876595 0.497142i −0.996751 0.0805453i \(-0.974334\pi\)
0.909091 0.416597i \(-0.136777\pi\)
\(152\) 7.20103e8 1.24726e9i 0.109421 0.189522i
\(153\) 8.18155e8 6.42312e9i 0.120705 0.947621i
\(154\) −1.04877e8 1.81653e8i −0.0150258 0.0260255i
\(155\) 4.70111e9 3.94470e9i 0.654196 0.548936i
\(156\) −1.03106e10 1.56476e9i −1.39387 0.211538i
\(157\) 8.02176e8 4.54936e9i 0.105371 0.597589i −0.885701 0.464257i \(-0.846321\pi\)
0.991071 0.133332i \(-0.0425675\pi\)
\(158\) 1.90883e8 + 1.60170e8i 0.0243675 + 0.0204468i
\(159\) 6.92298e9 1.39221e9i 0.859025 0.172749i
\(160\) 4.14626e9 + 1.50911e9i 0.500169 + 0.182047i
\(161\) −6.17427e8 −0.0724218
\(162\) 1.79509e9 8.55520e8i 0.204772 0.0975916i
\(163\) 4.02954e9 0.447107 0.223553 0.974692i \(-0.428234\pi\)
0.223553 + 0.974692i \(0.428234\pi\)
\(164\) 8.77658e9 + 3.19442e9i 0.947389 + 0.344821i
\(165\) −1.14493e10 + 2.30244e9i −1.20254 + 0.241830i
\(166\) −7.00491e8 5.87782e8i −0.0716006 0.0600800i
\(167\) −1.78494e9 + 1.01229e10i −0.177583 + 1.00712i 0.757538 + 0.652791i \(0.226402\pi\)
−0.935120 + 0.354330i \(0.884709\pi\)
\(168\) −4.08852e8 6.20485e7i −0.0395981 0.00600952i
\(169\) 9.82229e9 8.24188e9i 0.926238 0.777206i
\(170\) −9.89885e8 1.71453e9i −0.0909002 0.157444i
\(171\) 4.40602e9 + 3.35152e9i 0.394062 + 0.299750i
\(172\) −8.03479e9 + 1.39167e10i −0.699997 + 1.21243i
\(173\) 1.57684e9 + 8.94273e9i 0.133839 + 0.759037i 0.975661 + 0.219283i \(0.0703716\pi\)
−0.841823 + 0.539754i \(0.818517\pi\)
\(174\) −1.09364e9 5.97001e8i −0.0904484 0.0493746i
\(175\) −3.12836e8 + 1.13863e8i −0.0252143 + 0.00917724i
\(176\) −1.48352e10 + 5.39956e9i −1.16543 + 0.424182i
\(177\) −3.66088e8 1.53022e10i −0.0280353 1.17186i
\(178\) −6.06314e8 3.43857e9i −0.0452697 0.256737i
\(179\) −9.77182e9 + 1.69253e10i −0.711438 + 1.23225i 0.252880 + 0.967498i \(0.418622\pi\)
−0.964318 + 0.264748i \(0.914711\pi\)
\(180\) −5.13349e9 + 9.96341e9i −0.364490 + 0.707427i
\(181\) 1.29853e10 + 2.24912e10i 0.899289 + 1.55761i 0.828405 + 0.560129i \(0.189248\pi\)
0.0708832 + 0.997485i \(0.477418\pi\)
\(182\) 3.46412e8 2.90674e8i 0.0234030 0.0196375i
\(183\) 4.36128e9 5.45751e9i 0.287464 0.359720i
\(184\) 9.53792e8 5.40922e9i 0.0613442 0.347900i
\(185\) −5.82140e9 4.88474e9i −0.365389 0.306597i
\(186\) −2.49104e9 2.82847e9i −0.152607 0.173278i
\(187\) 2.19464e10 + 7.98783e9i 1.31243 + 0.477685i
\(188\) 1.37856e10 0.804850
\(189\) 4.35163e8 1.52881e9i 0.0248070 0.0871516i
\(190\) 1.69262e9 0.0942253
\(191\) 1.30602e10 + 4.75351e9i 0.710065 + 0.258443i 0.671702 0.740821i \(-0.265563\pi\)
0.0383631 + 0.999264i \(0.487786\pi\)
\(192\) −4.23697e9 + 1.25685e10i −0.225009 + 0.667463i
\(193\) −3.44582e8 2.89139e8i −0.0178766 0.0150002i 0.633806 0.773492i \(-0.281492\pi\)
−0.651682 + 0.758492i \(0.725936\pi\)
\(194\) −1.11318e9 + 6.31315e9i −0.0564231 + 0.319991i
\(195\) −9.17464e9 2.34465e10i −0.454395 1.16124i
\(196\) 1.48896e10 1.24939e10i 0.720661 0.604706i
\(197\) −1.48978e10 2.58038e10i −0.704734 1.22063i −0.966788 0.255581i \(-0.917733\pi\)
0.262054 0.965053i \(-0.415600\pi\)
\(198\) 1.58184e9 + 6.99588e9i 0.0731426 + 0.323481i
\(199\) −1.10366e10 + 1.91160e10i −0.498881 + 0.864086i −0.999999 0.00129214i \(-0.999589\pi\)
0.501119 + 0.865379i \(0.332922\pi\)
\(200\) −5.14280e8 2.91663e9i −0.0227282 0.128898i
\(201\) −2.54422e10 + 1.55120e10i −1.09944 + 0.670324i
\(202\) −1.07589e9 + 3.91591e8i −0.0454659 + 0.0165482i
\(203\) −9.35904e8 + 3.40641e8i −0.0386811 + 0.0140788i
\(204\) 1.91377e10 1.16681e10i 0.773665 0.471700i
\(205\) 3.91558e9 + 2.22064e10i 0.154847 + 0.878184i
\(206\) 1.52858e9 2.64757e9i 0.0591405 0.102434i
\(207\) 2.01620e10 + 6.26398e9i 0.763252 + 0.237128i
\(208\) −1.70178e10 2.94758e10i −0.630404 1.09189i
\(209\) −1.52959e10 + 1.28348e10i −0.554519 + 0.465297i
\(210\) −1.77100e8 4.52593e8i −0.00628394 0.0160591i
\(211\) 1.04654e9 5.93525e9i 0.0363485 0.206143i −0.961225 0.275766i \(-0.911069\pi\)
0.997573 + 0.0696232i \(0.0221797\pi\)
\(212\) 1.87257e10 + 1.57127e10i 0.636688 + 0.534244i
\(213\) 1.57077e10 4.65952e10i 0.522884 1.55107i
\(214\) 5.23676e9 + 1.90602e9i 0.170687 + 0.0621250i
\(215\) −3.87964e10 −1.23828
\(216\) 1.27215e10 + 6.17411e9i 0.397647 + 0.192989i
\(217\) −3.01277e9 −0.0922353
\(218\) −8.99303e9 3.27320e9i −0.269682 0.0981562i
\(219\) −3.56908e10 4.05253e10i −1.04847 1.19050i
\(220\) −3.09687e10 2.59858e10i −0.891294 0.747885i
\(221\) −8.74328e9 + 4.95856e10i −0.246552 + 1.39827i
\(222\) −2.91365e9 + 3.64601e9i −0.0805098 + 0.100746i
\(223\) 4.79845e10 4.02638e10i 1.29936 1.09029i 0.309104 0.951028i \(-0.399971\pi\)
0.990255 0.139264i \(-0.0444736\pi\)
\(224\) −1.08308e9 1.87595e9i −0.0287438 0.0497857i
\(225\) 1.13708e10 5.44379e8i 0.295781 0.0141606i
\(226\) −3.66348e9 + 6.34534e9i −0.0934128 + 0.161796i
\(227\) 2.56021e9 + 1.45197e10i 0.0639969 + 0.362944i 0.999942 + 0.0107977i \(0.00343709\pi\)
−0.935945 + 0.352147i \(0.885452\pi\)
\(228\) 4.58325e8 + 1.91577e10i 0.0112322 + 0.469500i
\(229\) 4.91315e9 1.78824e9i 0.118059 0.0429701i −0.282315 0.959322i \(-0.591102\pi\)
0.400374 + 0.916352i \(0.368880\pi\)
\(230\) 6.06601e9 2.20785e9i 0.142932 0.0520228i
\(231\) 5.03235e9 + 2.74709e9i 0.116283 + 0.0634774i
\(232\) −1.53856e9 8.72559e9i −0.0348672 0.197742i
\(233\) 3.50624e10 6.07298e10i 0.779363 1.34990i −0.152947 0.988234i \(-0.548876\pi\)
0.932310 0.361661i \(-0.117790\pi\)
\(234\) −1.42610e10 + 5.97750e9i −0.310942 + 0.130331i
\(235\) 1.66411e10 + 2.88232e10i 0.355940 + 0.616505i
\(236\) 4.05896e10 3.40587e10i 0.851747 0.714700i
\(237\) −6.73386e9 1.02195e9i −0.138642 0.0210408i
\(238\) −1.68774e8 + 9.57162e8i −0.00340964 + 0.0193370i
\(239\) −4.76010e10 3.99420e10i −0.943681 0.791842i 0.0345410 0.999403i \(-0.489003\pi\)
−0.978222 + 0.207561i \(0.933448\pi\)
\(240\) −3.58617e10 + 7.21176e9i −0.697719 + 0.140311i
\(241\) −1.98105e10 7.21044e9i −0.378285 0.137684i 0.145878 0.989303i \(-0.453399\pi\)
−0.524163 + 0.851618i \(0.675622\pi\)
\(242\) −1.37678e10 −0.258045
\(243\) −2.97204e10 + 4.55083e10i −0.546798 + 0.837264i
\(244\) 2.41832e10 0.436778
\(245\) 4.40963e10 + 1.60497e10i 0.781906 + 0.284590i
\(246\) 1.35769e10 2.73030e9i 0.236370 0.0475338i
\(247\) −3.29763e10 2.76704e10i −0.563723 0.473020i
\(248\) 4.65408e9 2.63946e10i 0.0781271 0.443081i
\(249\) 2.47115e10 + 3.75029e9i 0.407382 + 0.0618255i
\(250\) 1.16706e10 9.79283e9i 0.188958 0.158554i
\(251\) 2.25558e10 + 3.90679e10i 0.358697 + 0.621281i 0.987743 0.156087i \(-0.0498879\pi\)
−0.629047 + 0.777368i \(0.716555\pi\)
\(252\) 5.07466e9 2.12704e9i 0.0792692 0.0332256i
\(253\) −3.80758e10 + 6.59493e10i −0.584261 + 1.01197i
\(254\) 3.95295e9 + 2.24183e10i 0.0595894 + 0.337948i
\(255\) 4.74978e10 + 2.59284e10i 0.703465 + 0.384012i
\(256\) −3.38512e10 + 1.23208e10i −0.492599 + 0.179291i
\(257\) −7.93532e10 + 2.88822e10i −1.13466 + 0.412982i −0.839982 0.542614i \(-0.817435\pi\)
−0.294678 + 0.955597i \(0.595212\pi\)
\(258\) 5.69875e8 + 2.38204e10i 0.00800739 + 0.334704i
\(259\) 6.47833e8 + 3.67404e9i 0.00894570 + 0.0507336i
\(260\) 4.35779e10 7.54792e10i 0.591407 1.02435i
\(261\) 3.40178e10 1.62860e9i 0.453757 0.0217237i
\(262\) −5.52483e9 9.56929e9i −0.0724375 0.125465i
\(263\) 4.66786e10 3.91680e10i 0.601612 0.504812i −0.290351 0.956920i \(-0.593772\pi\)
0.891963 + 0.452108i \(0.149328\pi\)
\(264\) −3.18409e10 + 3.98443e10i −0.403429 + 0.504834i
\(265\) −1.02480e10 + 5.81195e10i −0.127654 + 0.723961i
\(266\) −6.36549e8 5.34128e8i −0.00779587 0.00654151i
\(267\) 6.30774e10 + 7.16217e10i 0.759580 + 0.862470i
\(268\) −9.69295e10 3.52795e10i −1.14776 0.417749i
\(269\) −1.46201e10 −0.170242 −0.0851209 0.996371i \(-0.527128\pi\)
−0.0851209 + 0.996371i \(0.527128\pi\)
\(270\) 1.19151e9 + 1.65761e10i 0.0136446 + 0.189822i
\(271\) 2.22347e10 0.250420 0.125210 0.992130i \(-0.460039\pi\)
0.125210 + 0.992130i \(0.460039\pi\)
\(272\) 6.87409e10 + 2.50196e10i 0.761474 + 0.277154i
\(273\) −3.94851e9 + 1.17128e10i −0.0430231 + 0.127623i
\(274\) 1.49371e10 + 1.25337e10i 0.160099 + 0.134339i
\(275\) −7.13010e9 + 4.04368e10i −0.0751794 + 0.426363i
\(276\) 2.66318e10 + 6.80595e10i 0.276254 + 0.705989i
\(277\) −1.16713e11 + 9.79335e10i −1.19113 + 0.999476i −0.191290 + 0.981534i \(0.561267\pi\)
−0.999839 + 0.0179427i \(0.994288\pi\)
\(278\) −1.60172e10 2.77427e10i −0.160837 0.278578i
\(279\) 9.83818e10 + 3.05654e10i 0.972067 + 0.302003i
\(280\) 1.72802e9 2.99302e9i 0.0168011 0.0291004i
\(281\) −8.09146e9 4.58890e10i −0.0774192 0.439066i −0.998736 0.0502543i \(-0.983997\pi\)
0.921317 0.388812i \(-0.127114\pi\)
\(282\) 1.74526e10 1.06408e10i 0.164338 0.100196i
\(283\) −1.08318e11 + 3.94245e10i −1.00383 + 0.365365i −0.791061 0.611737i \(-0.790471\pi\)
−0.212771 + 0.977102i \(0.568249\pi\)
\(284\) 1.59949e11 5.82167e10i 1.45898 0.531025i
\(285\) −3.95020e10 + 2.40842e10i −0.354664 + 0.216237i
\(286\) −9.68508e9 5.49268e10i −0.0855965 0.485442i
\(287\) 5.53497e9 9.58685e9i 0.0481556 0.0834080i
\(288\) 1.63358e10 + 7.22471e10i 0.139919 + 0.618805i
\(289\) 5.18499e9 + 8.98066e9i 0.0437227 + 0.0757300i
\(290\) 7.97685e9 6.69337e9i 0.0662278 0.0555717i
\(291\) −6.38504e10 1.63175e11i −0.521970 1.33393i
\(292\) 3.24606e10 1.84093e11i 0.261296 1.48188i
\(293\) 1.29042e10 + 1.08279e10i 0.102288 + 0.0858299i 0.692497 0.721420i \(-0.256510\pi\)
−0.590209 + 0.807250i \(0.700955\pi\)
\(294\) 9.20658e9 2.73102e10i 0.0718679 0.213188i
\(295\) 1.20208e11 + 4.37521e10i 0.924132 + 0.336356i
\(296\) −3.31887e10 −0.251292
\(297\) −1.36461e11 1.40761e11i −1.01766 1.04973i
\(298\) −2.56914e10 −0.188719
\(299\) −1.54274e11 5.61511e10i −1.11628 0.406292i
\(300\) 2.60450e10 + 2.95729e10i 0.185643 + 0.210789i
\(301\) 1.45903e10 + 1.22427e10i 0.102451 + 0.0859664i
\(302\) 2.87440e9 1.63015e10i 0.0198845 0.112771i
\(303\) 1.95369e10 2.44476e10i 0.133157 0.166627i
\(304\) −4.79101e10 + 4.02014e10i −0.321733 + 0.269966i
\(305\) 2.91925e10 + 5.05629e10i 0.193162 + 0.334567i
\(306\) 1.52220e10 2.95438e10i 0.0992486 0.192628i
\(307\) 1.28073e11 2.21829e11i 0.822878 1.42527i −0.0806528 0.996742i \(-0.525701\pi\)
0.903531 0.428524i \(-0.140966\pi\)
\(308\) 3.44634e9 + 1.95452e10i 0.0218213 + 0.123755i
\(309\) 1.99857e9 + 8.35387e10i 0.0124711 + 0.521284i
\(310\) 2.95995e10 1.07733e10i 0.182035 0.0662555i
\(311\) 6.65416e10 2.42192e10i 0.403340 0.146804i −0.132381 0.991199i \(-0.542262\pi\)
0.535721 + 0.844395i \(0.320040\pi\)
\(312\) −9.65151e10 5.26863e10i −0.576633 0.314776i
\(313\) 3.00272e9 + 1.70293e10i 0.0176834 + 0.100287i 0.992372 0.123279i \(-0.0393411\pi\)
−0.974689 + 0.223567i \(0.928230\pi\)
\(314\) 1.18555e10 2.05343e10i 0.0688235 0.119206i
\(315\) 1.05731e10 + 8.04258e9i 0.0605067 + 0.0460255i
\(316\) −1.17886e10 2.04184e10i −0.0665072 0.115194i
\(317\) −1.80799e11 + 1.51709e11i −1.00561 + 0.843807i −0.987752 0.156033i \(-0.950129\pi\)
−0.0178587 + 0.999841i \(0.505685\pi\)
\(318\) 3.58351e10 + 5.43843e9i 0.196511 + 0.0298230i
\(319\) −2.13309e10 + 1.20974e11i −0.115332 + 0.654083i
\(320\) −8.49138e10 7.12511e10i −0.452693 0.379854i
\(321\) −1.49335e11 + 3.00312e10i −0.785037 + 0.157870i
\(322\) −2.97799e9 1.08390e9i −0.0154373 0.00561871i
\(323\) 9.25216e10 0.472968
\(324\) −1.87292e11 + 1.79744e10i −0.944206 + 0.0906156i
\(325\) −8.85223e10 −0.440127
\(326\) 1.94353e10 + 7.07389e9i 0.0953044 + 0.0346880i
\(327\) 2.56452e11 5.15723e10i 1.24034 0.249432i
\(328\) 7.54392e10 + 6.33010e10i 0.359886 + 0.301980i
\(329\) 2.83727e9 1.60910e10i 0.0133512 0.0757183i
\(330\) −5.92644e10 8.99414e9i −0.275094 0.0417491i
\(331\) 1.82248e11 1.52924e11i 0.834519 0.700244i −0.121805 0.992554i \(-0.538868\pi\)
0.956324 + 0.292310i \(0.0944238\pi\)
\(332\) 4.32609e10 + 7.49301e10i 0.195422 + 0.338481i
\(333\) 1.61193e10 1.26548e11i 0.0718367 0.563971i
\(334\) −2.63800e10 + 4.56916e10i −0.115989 + 0.200899i
\(335\) −4.32441e10 2.45250e11i −0.187597 1.06391i
\(336\) 1.57624e10 + 8.60449e9i 0.0674677 + 0.0368297i
\(337\) 3.87477e11 1.41030e11i 1.63648 0.595631i 0.650064 0.759879i \(-0.274742\pi\)
0.986419 + 0.164248i \(0.0525197\pi\)
\(338\) 6.18437e10 2.25093e10i 0.257733 0.0938072i
\(339\) −4.78989e9 2.00214e11i −0.0196982 0.823372i
\(340\) 3.25283e10 + 1.84477e11i 0.132010 + 0.748665i
\(341\) −1.85793e11 + 3.21803e11i −0.744107 + 1.28883i
\(342\) 1.53676e10 + 2.38999e10i 0.0607419 + 0.0944667i
\(343\) −2.31329e10 4.00673e10i −0.0902414 0.156303i
\(344\) −1.29796e11 + 1.08912e11i −0.499746 + 0.419336i
\(345\) −1.10152e11 + 1.37840e11i −0.418608 + 0.523827i
\(346\) −8.09357e9 + 4.59009e10i −0.0303597 + 0.172178i
\(347\) −8.58760e8 7.20585e8i −0.00317972 0.00266810i 0.641196 0.767377i \(-0.278438\pi\)
−0.644376 + 0.764709i \(0.722883\pi\)
\(348\) 7.79180e10 + 8.84724e10i 0.284794 + 0.323371i
\(349\) −2.74997e11 1.00091e11i −0.992231 0.361143i −0.205647 0.978626i \(-0.565930\pi\)
−0.786584 + 0.617484i \(0.788152\pi\)
\(350\) −1.70877e9 −0.00608662
\(351\) 2.47768e11 3.42422e11i 0.871291 1.20415i
\(352\) −2.67168e11 −0.927559
\(353\) −4.45541e11 1.62164e11i −1.52722 0.555862i −0.564281 0.825583i \(-0.690846\pi\)
−0.962939 + 0.269721i \(0.913069\pi\)
\(354\) 2.50974e10 7.44486e10i 0.0849405 0.251966i
\(355\) 3.14801e11 + 2.64150e11i 1.05198 + 0.882719i
\(356\) −5.73686e10 + 3.25353e11i −0.189299 + 1.07357i
\(357\) −9.68062e9 2.47396e10i −0.0315425 0.0806093i
\(358\) −7.68441e10 + 6.44798e10i −0.247250 + 0.207468i
\(359\) 2.51241e11 + 4.35163e11i 0.798300 + 1.38270i 0.920722 + 0.390218i \(0.127600\pi\)
−0.122422 + 0.992478i \(0.539066\pi\)
\(360\) −8.67935e10 + 8.02056e10i −0.272349 + 0.251677i
\(361\) 1.21793e11 2.10951e11i 0.377433 0.653733i
\(362\) 2.31475e10 + 1.31276e11i 0.0708460 + 0.401788i
\(363\) 3.21310e11 1.95901e11i 0.971280 0.592185i
\(364\) −4.02070e10 + 1.46341e10i −0.120045 + 0.0436929i
\(365\) 4.24090e11 1.54356e11i 1.25066 0.455204i
\(366\) 3.06161e10 1.86665e10i 0.0891835 0.0543748i
\(367\) 8.92505e10 + 5.06165e11i 0.256811 + 1.45645i 0.791382 + 0.611323i \(0.209362\pi\)
−0.534571 + 0.845124i \(0.679527\pi\)
\(368\) −1.19262e11 + 2.06568e11i −0.338990 + 0.587148i
\(369\) −2.78006e11 + 2.56904e11i −0.780611 + 0.721361i
\(370\) −1.95027e10 3.37797e10i −0.0540987 0.0937017i
\(371\) 2.21944e10 1.86233e10i 0.0608220 0.0510357i
\(372\) 1.29951e11 + 3.32100e11i 0.351834 + 0.899137i
\(373\) −3.61006e10 + 2.04737e11i −0.0965661 + 0.547653i 0.897690 + 0.440627i \(0.145244\pi\)
−0.994256 + 0.107026i \(0.965867\pi\)
\(374\) 9.18294e10 + 7.70540e10i 0.242694 + 0.203645i
\(375\) −1.33026e11 + 3.94605e11i −0.347372 + 1.03044i
\(376\) 1.36589e11 + 4.97142e10i 0.352427 + 0.128273i
\(377\) −2.64830e11 −0.675197
\(378\) 4.78272e9 6.60985e9i 0.0120493 0.0166525i
\(379\) 5.11931e11 1.27449 0.637243 0.770663i \(-0.280075\pi\)
0.637243 + 0.770663i \(0.280075\pi\)
\(380\) −1.50495e11 5.47756e10i −0.370250 0.134760i
\(381\) −4.11242e11 4.66947e11i −0.999851 1.13529i
\(382\) 5.46472e10 + 4.58544e10i 0.131305 + 0.110178i
\(383\) 6.18978e10 3.51040e11i 0.146988 0.833608i −0.818762 0.574133i \(-0.805339\pi\)
0.965750 0.259475i \(-0.0835496\pi\)
\(384\) −2.11253e11 + 2.64353e11i −0.495808 + 0.620432i
\(385\) −3.67053e10 + 3.07994e10i −0.0851443 + 0.0714446i
\(386\) −1.15441e9 1.99950e9i −0.00264677 0.00458435i
\(387\) −3.52240e11 5.47808e11i −0.798250 1.24145i
\(388\) 3.03278e11 5.25293e11i 0.679358 1.17668i
\(389\) 6.84736e10 + 3.88333e11i 0.151618 + 0.859866i 0.961813 + 0.273707i \(0.0882498\pi\)
−0.810196 + 0.586160i \(0.800639\pi\)
\(390\) −3.09081e9 1.29194e11i −0.00676521 0.282781i
\(391\) 3.31579e11 1.20685e11i 0.717451 0.261131i
\(392\) 1.92583e11 7.00946e10i 0.411938 0.149933i
\(393\) 2.65099e11 + 1.44714e11i 0.560585 + 0.306016i
\(394\) −2.65567e10 1.50611e11i −0.0555190 0.314864i
\(395\) 2.84608e10 4.92955e10i 0.0588248 0.101887i
\(396\) 8.57514e10 6.73211e11i 0.175232 1.37570i
\(397\) −6.50349e10 1.12644e11i −0.131398 0.227588i 0.792818 0.609459i \(-0.208613\pi\)
−0.924216 + 0.381871i \(0.875280\pi\)
\(398\) −8.67901e10 + 7.28256e10i −0.173379 + 0.145482i
\(399\) 2.24558e10 + 3.40795e9i 0.0443558 + 0.00673156i
\(400\) −2.23331e10 + 1.26657e11i −0.0436192 + 0.247377i
\(401\) −7.62899e11 6.40148e11i −1.47339 1.23632i −0.912917 0.408145i \(-0.866176\pi\)
−0.560471 0.828174i \(-0.689380\pi\)
\(402\) −1.49945e11 + 3.01537e10i −0.286361 + 0.0575869i
\(403\) −7.52788e11 2.73993e11i −1.42167 0.517447i
\(404\) 1.08332e11 0.202321
\(405\) −2.63669e11 3.69897e11i −0.486980 0.683177i
\(406\) −5.11207e9 −0.00933747
\(407\) 4.32387e11 + 1.57376e11i 0.781084 + 0.284291i
\(408\) 2.31696e11 4.65938e10i 0.413949 0.0832448i
\(409\) −1.81185e11 1.52032e11i −0.320160 0.268646i 0.468516 0.883455i \(-0.344789\pi\)
−0.788676 + 0.614809i \(0.789233\pi\)
\(410\) −2.00978e10 + 1.13980e11i −0.0351253 + 0.199206i
\(411\) −5.26942e11 7.99703e10i −0.910908 0.138242i
\(412\) −2.21589e11 + 1.85935e11i −0.378888 + 0.317925i
\(413\) −3.14005e10 5.43872e10i −0.0531081 0.0919860i
\(414\) 8.62495e10 + 6.56071e10i 0.144296 + 0.109761i
\(415\) −1.04444e11 + 1.80902e11i −0.172849 + 0.299382i
\(416\) −1.00019e11 5.67234e11i −0.163742 0.928629i
\(417\) 7.68557e11 + 4.19545e11i 1.24470 + 0.679464i
\(418\) −9.63070e10 + 3.50529e10i −0.154300 + 0.0561604i
\(419\) 5.69703e11 2.07355e11i 0.902995 0.328663i 0.151543 0.988451i \(-0.451576\pi\)
0.751452 + 0.659787i \(0.229354\pi\)
\(420\) 1.09983e9 + 4.59724e10i 0.00172467 + 0.0720900i
\(421\) −1.59940e11 9.07063e11i −0.248134 1.40724i −0.813100 0.582124i \(-0.802222\pi\)
0.564966 0.825114i \(-0.308889\pi\)
\(422\) 1.54671e10 2.67898e10i 0.0237412 0.0411209i
\(423\) −2.55899e11 + 4.96665e11i −0.388630 + 0.754279i
\(424\) 1.28872e11 + 2.23212e11i 0.193647 + 0.335407i
\(425\) 1.45748e11 1.22297e11i 0.216696 0.181830i
\(426\) 1.57560e11 1.97164e11i 0.231794 0.290057i
\(427\) 4.97726e9 2.82275e10i 0.00724545 0.0410910i
\(428\) −4.03931e11 3.38939e11i −0.581849 0.488230i
\(429\) 1.00758e12 + 1.14406e12i 1.43622 + 1.63077i
\(430\) −1.87123e11 6.81073e10i −0.263949 0.0960695i
\(431\) 1.12321e12 1.56788 0.783941 0.620836i \(-0.213207\pi\)
0.783941 + 0.620836i \(0.213207\pi\)
\(432\) −4.27426e11 4.40893e11i −0.590451 0.609055i
\(433\) −2.33971e11 −0.319864 −0.159932 0.987128i \(-0.551128\pi\)
−0.159932 + 0.987128i \(0.551128\pi\)
\(434\) −1.45312e10 5.28894e9i −0.0196607 0.00715591i
\(435\) −9.09225e10 + 2.69711e11i −0.121750 + 0.361158i
\(436\) 6.93667e11 + 5.82056e11i 0.919310 + 0.771392i
\(437\) −5.23861e10 + 2.97096e11i −0.0687147 + 0.389700i
\(438\) −1.01002e11 2.58118e11i −0.131128 0.335108i
\(439\) −9.14258e11 + 7.67153e11i −1.17484 + 0.985807i −0.174839 + 0.984597i \(0.555941\pi\)
−0.999999 + 0.00120975i \(0.999615\pi\)
\(440\) −2.13129e11 3.69151e11i −0.271085 0.469533i
\(441\) 1.73735e11 + 7.68362e11i 0.218732 + 0.967369i
\(442\) −1.29219e11 + 2.23813e11i −0.161037 + 0.278924i
\(443\) −6.46091e10 3.66417e11i −0.0797035 0.452021i −0.998374 0.0569970i \(-0.981847\pi\)
0.918671 0.395024i \(-0.129264\pi\)
\(444\) 3.77050e11 2.29886e11i 0.460442 0.280730i
\(445\) −7.49508e11 + 2.72798e11i −0.906058 + 0.329778i
\(446\) 3.02123e11 1.09964e11i 0.361557 0.131596i
\(447\) 5.99582e11 3.65562e11i 0.710337 0.433089i
\(448\) 9.44961e9 + 5.35914e10i 0.0110831 + 0.0628556i
\(449\) −5.94911e11 + 1.03042e12i −0.690786 + 1.19648i 0.280794 + 0.959768i \(0.409402\pi\)
−0.971581 + 0.236709i \(0.923931\pi\)
\(450\) 5.57997e10 + 1.73359e10i 0.0641468 + 0.0199292i
\(451\) −6.82668e11 1.18242e12i −0.776989 1.34578i
\(452\) 5.31074e11 4.45624e11i 0.598456 0.502164i
\(453\) 1.64872e11 + 4.21342e11i 0.183952 + 0.470102i
\(454\) −1.31409e10 + 7.45260e10i −0.0145169 + 0.0823296i
\(455\) −7.91327e10 6.64003e10i −0.0865575 0.0726304i
\(456\) −6.45461e10 + 1.91469e11i −0.0699083 + 0.207375i
\(457\) 4.38390e11 + 1.59561e11i 0.470151 + 0.171121i 0.566221 0.824254i \(-0.308405\pi\)
−0.0960696 + 0.995375i \(0.530627\pi\)
\(458\) 2.68365e10 0.0284991
\(459\) 6.51303e10 + 9.06082e11i 0.0684898 + 0.952819i
\(460\) −6.10793e11 −0.636039
\(461\) −4.28880e11 1.56100e11i −0.442264 0.160971i 0.111283 0.993789i \(-0.464504\pi\)
−0.553547 + 0.832818i \(0.686726\pi\)
\(462\) 1.94496e10 + 2.20841e10i 0.0198619 + 0.0225523i
\(463\) −6.66831e11 5.59538e11i −0.674375 0.565868i 0.239982 0.970777i \(-0.422859\pi\)
−0.914357 + 0.404909i \(0.867303\pi\)
\(464\) −6.68131e10 + 3.78916e11i −0.0669161 + 0.379500i
\(465\) −5.37494e11 + 6.72596e11i −0.533133 + 0.667138i
\(466\) 2.75725e11 2.31361e11i 0.270857 0.227276i
\(467\) −6.42551e11 1.11293e12i −0.625146 1.08279i −0.988513 0.151139i \(-0.951706\pi\)
0.363366 0.931646i \(-0.381627\pi\)
\(468\) 1.46142e12 6.99658e10i 1.40822 0.0674185i
\(469\) −6.11288e10 + 1.05878e11i −0.0583403 + 0.101048i
\(470\) 2.96642e10 + 1.68234e11i 0.0280409 + 0.159028i
\(471\) 1.55007e10 + 6.47919e11i 0.0145130 + 0.606634i
\(472\) 5.24989e11 1.91080e11i 0.486868 0.177205i
\(473\) 2.20745e12 8.03444e11i 2.02775 0.738041i
\(474\) −3.06848e10 1.67504e10i −0.0279204 0.0152413i
\(475\) 2.82463e10 + 1.60193e11i 0.0254590 + 0.144385i
\(476\) 4.59812e10 7.96418e10i 0.0410534 0.0711066i
\(477\) −9.13696e11 + 3.82975e11i −0.808107 + 0.338717i
\(478\) −1.59471e11 2.76213e11i −0.139720 0.242001i
\(479\) −9.49325e11 + 7.96578e11i −0.823958 + 0.691383i −0.953895 0.300139i \(-0.902967\pi\)
0.129937 + 0.991522i \(0.458522\pi\)
\(480\) −6.12028e11 9.28832e10i −0.526243 0.0798641i
\(481\) −1.72260e11 + 9.76935e11i −0.146734 + 0.832171i
\(482\) −8.28924e10 6.95550e10i −0.0699525 0.0586971i
\(483\) 8.49225e10 1.70778e10i 0.0710004 0.0142781i
\(484\) 1.22413e12 + 4.45546e11i 1.01396 + 0.369052i
\(485\) 1.46439e12 1.20177
\(486\) −2.23238e11 + 1.67322e11i −0.181512 + 0.136047i
\(487\) 1.32515e12 1.06754 0.533769 0.845630i \(-0.320775\pi\)
0.533769 + 0.845630i \(0.320775\pi\)
\(488\) 2.39610e11 + 8.72107e10i 0.191256 + 0.0696115i
\(489\) −5.54233e11 + 1.11456e11i −0.438331 + 0.0881481i
\(490\) 1.84510e11 + 1.54823e11i 0.144590 + 0.121326i
\(491\) −3.50397e11 + 1.98720e12i −0.272078 + 1.54303i 0.476015 + 0.879437i \(0.342081\pi\)
−0.748093 + 0.663594i \(0.769030\pi\)
\(492\) −1.29551e12 1.96610e11i −0.996776 0.151274i
\(493\) 4.36029e11 3.65872e11i 0.332433 0.278945i
\(494\) −1.10476e11 1.91351e11i −0.0834637 0.144563i
\(495\) 1.51108e12 6.33367e11i 1.13126 0.474168i
\(496\) −5.81945e11 + 1.00796e12i −0.431732 + 0.747783i
\(497\) −3.50326e10 1.98680e11i −0.0257554 0.146066i
\(498\) 1.12605e11 + 6.14697e10i 0.0820402 + 0.0447846i
\(499\) −4.82759e11 + 1.75710e11i −0.348560 + 0.126865i −0.510366 0.859957i \(-0.670490\pi\)
0.161806 + 0.986823i \(0.448268\pi\)
\(500\) −1.35458e12 + 4.93025e11i −0.969255 + 0.352780i
\(501\) −3.44911e10 1.44170e12i −0.0244589 1.02237i
\(502\) 4.02078e10 + 2.28030e11i 0.0282581 + 0.160260i
\(503\) 7.16695e11 1.24135e12i 0.499204 0.864647i −0.500795 0.865566i \(-0.666959\pi\)
1.00000 0.000918437i \(0.000292348\pi\)
\(504\) 5.79507e10 2.77439e9i 0.0400057 0.00191527i
\(505\) 1.30772e11 + 2.26503e11i 0.0894753 + 0.154976i
\(506\) −2.99423e11 + 2.51245e11i −0.203052 + 0.170381i
\(507\) −1.12301e12 + 1.40529e12i −0.754831 + 0.944562i
\(508\) 3.74022e11 2.12119e12i 0.249179 1.41316i
\(509\) −7.35298e11 6.16988e11i −0.485549 0.407424i 0.366879 0.930269i \(-0.380426\pi\)
−0.852428 + 0.522845i \(0.824871\pi\)
\(510\) 1.83575e11 + 2.08441e11i 0.120156 + 0.136432i
\(511\) −2.08198e11 7.57780e10i −0.135078 0.0491642i
\(512\) −1.41984e12 −0.913116
\(513\) −6.98717e11 3.39107e11i −0.445424 0.216176i
\(514\) −4.33441e11 −0.273902
\(515\) −6.56246e11 2.38854e11i −0.411087 0.149624i
\(516\) 7.20195e11 2.13637e12i 0.447225 1.32664i
\(517\) −1.54376e12 1.29537e12i −0.950323 0.797416i
\(518\) −3.32517e9 + 1.88580e10i −0.00202923 + 0.0115083i
\(519\) −4.64236e11 1.18639e12i −0.280857 0.717752i
\(520\) 7.03970e11 5.90701e11i 0.422220 0.354285i
\(521\) 1.14586e12 + 1.98469e12i 0.681336 + 1.18011i 0.974573 + 0.224069i \(0.0719340\pi\)
−0.293238 + 0.956040i \(0.594733\pi\)
\(522\) 1.66934e11 + 5.18634e10i 0.0984075 + 0.0305734i
\(523\) −4.98633e11 + 8.63657e11i −0.291422 + 0.504759i −0.974146 0.225918i \(-0.927462\pi\)
0.682724 + 0.730677i \(0.260795\pi\)
\(524\) 1.81550e11 + 1.02962e12i 0.105197 + 0.596604i
\(525\) 3.98789e10 2.43140e10i 0.0229101 0.0139682i
\(526\) 2.93900e11 1.06971e11i 0.167403 0.0609299i
\(527\) 1.61796e12 5.88889e11i 0.913735 0.332572i
\(528\) 1.89112e12 1.15301e12i 1.05893 0.645623i
\(529\) −1.12976e11 6.40721e11i −0.0627245 0.355728i
\(530\) −1.51458e11 + 2.62332e11i −0.0833777 + 0.144414i
\(531\) 4.73607e11 + 2.09458e12i 0.258519 + 1.14333i
\(532\) 3.93120e10 + 6.80903e10i 0.0212776 + 0.0368539i
\(533\) 2.25486e12 1.89206e12i 1.21017 1.01546i
\(534\) 1.78504e11 + 4.56180e11i 0.0949974 + 0.242773i
\(535\) 2.21060e11 1.25369e12i 0.116659 0.661606i
\(536\) −8.33159e11 6.99103e11i −0.436000 0.365847i
\(537\) 8.75892e11 2.59823e12i 0.454534 1.34832i
\(538\) −7.05161e10 2.56658e10i −0.0362884 0.0132079i
\(539\) −2.84138e12 −1.45004
\(540\) 4.30488e11 1.51238e12i 0.217866 0.765402i
\(541\) 2.03546e11 0.102159 0.0510794 0.998695i \(-0.483734\pi\)
0.0510794 + 0.998695i \(0.483734\pi\)
\(542\) 1.07243e11 + 3.90332e10i 0.0533791 + 0.0194284i
\(543\) −2.40813e12 2.73433e12i −1.18873 1.34975i
\(544\) 9.48331e11 + 7.95744e11i 0.464264 + 0.389564i
\(545\) −3.79624e11 + 2.15296e12i −0.184319 + 1.04532i
\(546\) −3.96064e10 + 4.95617e10i −0.0190721 + 0.0238660i
\(547\) 5.09924e11 4.27877e11i 0.243536 0.204351i −0.512847 0.858480i \(-0.671409\pi\)
0.756383 + 0.654129i \(0.226965\pi\)
\(548\) −9.22485e11 1.59779e12i −0.436965 0.756846i
\(549\) −4.48908e11 + 8.71271e11i −0.210903 + 0.409334i
\(550\) −1.05377e11 + 1.82519e11i −0.0491037 + 0.0850501i
\(551\) 8.45037e10 + 4.79244e11i 0.0390565 + 0.221501i
\(552\) 1.84304e10 + 7.70380e11i 0.00844909 + 0.353166i
\(553\) −2.62592e10 + 9.55758e9i −0.0119404 + 0.00434595i
\(554\) −7.34853e11 + 2.67465e11i −0.331441 + 0.120635i
\(555\) 9.35801e11 + 5.10841e11i 0.418663 + 0.228543i
\(556\) 5.26338e11 + 2.98501e12i 0.233576 + 1.32467i
\(557\) 4.51240e11 7.81571e11i 0.198637 0.344049i −0.749450 0.662061i \(-0.769682\pi\)
0.948087 + 0.318012i \(0.103015\pi\)
\(558\) 4.20859e11 + 3.20134e11i 0.183774 + 0.139790i
\(559\) 2.53222e12 + 4.38593e12i 1.09685 + 1.89980i
\(560\) −1.14969e11 + 9.64706e10i −0.0494009 + 0.0414523i
\(561\) −3.23950e12 4.91636e11i −1.38085 0.209561i
\(562\) 4.15315e10 2.35537e11i 0.0175616 0.0995969i
\(563\) −3.00202e12 2.51899e12i −1.25929 1.05667i −0.995757 0.0920186i \(-0.970668\pi\)
−0.263532 0.964651i \(-0.584887\pi\)
\(564\) −1.89610e12 + 3.81305e11i −0.789053 + 0.158678i
\(565\) 1.57280e12 + 5.72452e11i 0.649315 + 0.236331i
\(566\) −5.91651e11 −0.242321
\(567\) −1.75671e10 + 2.22313e11i −0.00713799 + 0.0903318i
\(568\) 1.79473e12 0.723489
\(569\) 3.73460e12 + 1.35928e12i 1.49361 + 0.543631i 0.954398 0.298536i \(-0.0964984\pi\)
0.539216 + 0.842168i \(0.318721\pi\)
\(570\) −2.32807e11 + 4.68173e10i −0.0923760 + 0.0185767i
\(571\) −7.88821e11 6.61899e11i −0.310539 0.260573i 0.474176 0.880430i \(-0.342746\pi\)
−0.784715 + 0.619857i \(0.787191\pi\)
\(572\) −9.16389e11 + 5.19710e12i −0.357930 + 2.02992i
\(573\) −1.92781e12 2.92570e11i −0.747081 0.113379i
\(574\) 4.35262e10 3.65228e10i 0.0167358 0.0140430i
\(575\) 3.10185e11 + 5.37256e11i 0.118335 + 0.204963i
\(576\) 2.35124e11 1.84589e12i 0.0890010 0.698723i
\(577\) 8.29829e11 1.43731e12i 0.311672 0.539832i −0.667053 0.745011i \(-0.732444\pi\)
0.978724 + 0.205179i \(0.0657777\pi\)
\(578\) 9.24270e9 + 5.24180e10i 0.00344448 + 0.0195346i
\(579\) 5.53922e10 + 3.02378e10i 0.0204831 + 0.0111814i
\(580\) −9.25848e11 + 3.36981e11i −0.339714 + 0.123646i
\(581\) 9.63645e10 3.50738e10i 0.0350852 0.0127700i
\(582\) −2.15103e10 8.99117e11i −0.00777129 0.324835i
\(583\) −6.20517e11 3.51913e12i −0.222457 1.26161i
\(584\) 9.85506e11 1.70695e12i 0.350592 0.607243i
\(585\) 1.91043e12 + 2.97112e12i 0.674417 + 1.04886i
\(586\) 4.32311e10 + 7.48785e10i 0.0151446 + 0.0262312i
\(587\) −2.56726e12 + 2.15418e12i −0.892478 + 0.748878i −0.968706 0.248212i \(-0.920157\pi\)
0.0762274 + 0.997090i \(0.475713\pi\)
\(588\) −1.70238e12 + 2.13028e12i −0.587297 + 0.734918i
\(589\) −2.55621e11 + 1.44970e12i −0.0875140 + 0.496317i
\(590\) 5.02982e11 + 4.22052e11i 0.170891 + 0.143394i
\(591\) 2.76281e12 + 3.13705e12i 0.931552 + 1.05774i
\(592\) 1.35433e12 + 4.92936e11i 0.453187 + 0.164947i
\(593\) 1.51807e11 0.0504135 0.0252067 0.999682i \(-0.491976\pi\)
0.0252067 + 0.999682i \(0.491976\pi\)
\(594\) −4.11075e11 9.18477e11i −0.135482 0.302712i
\(595\) 2.22023e11 0.0726225
\(596\) 2.28428e12 + 8.31412e11i 0.741553 + 0.269903i
\(597\) 9.89261e11 2.93453e12i 0.318732 0.945482i
\(598\) −6.45523e11 5.41658e11i −0.206422 0.173209i
\(599\) −9.76595e11 + 5.53854e12i −0.309951 + 1.75782i 0.289278 + 0.957245i \(0.406585\pi\)
−0.599230 + 0.800577i \(0.704526\pi\)
\(600\) 1.51408e11 + 3.86935e11i 0.0476946 + 0.121887i
\(601\) 3.63412e12 3.04939e12i 1.13622 0.953405i 0.136915 0.990583i \(-0.456281\pi\)
0.999309 + 0.0371781i \(0.0118369\pi\)
\(602\) 4.88800e10 + 8.46627e10i 0.0151687 + 0.0262729i
\(603\) 3.07032e12 2.83728e12i 0.945706 0.873925i
\(604\) −7.83110e11 + 1.35639e12i −0.239418 + 0.414684i
\(605\) 5.46131e11 + 3.09727e12i 0.165729 + 0.939895i
\(606\) 1.37149e11 8.36191e10i 0.0413110 0.0251871i
\(607\) −1.67977e12 + 6.11388e11i −0.502229 + 0.182796i −0.580696 0.814120i \(-0.697220\pi\)
0.0784673 + 0.996917i \(0.474997\pi\)
\(608\) −9.94571e11 + 3.61994e11i −0.295168 + 0.107432i
\(609\) 1.19305e11 7.27394e10i 0.0351463 0.0214285i
\(610\) 5.20382e10 + 2.95123e11i 0.0152173 + 0.0863017i
\(611\) 2.17231e12 3.76255e12i 0.630575 1.09219i
\(612\) −2.30950e12 + 2.13421e12i −0.665484 + 0.614972i
\(613\) 8.97771e11 + 1.55498e12i 0.256799 + 0.444789i 0.965383 0.260838i \(-0.0839988\pi\)
−0.708584 + 0.705627i \(0.750665\pi\)
\(614\) 1.00715e12 8.45097e11i 0.285980 0.239966i
\(615\) −1.15278e12 2.94602e12i −0.324944 0.830419i
\(616\) −3.63381e10 + 2.06084e11i −0.0101683 + 0.0576674i
\(617\) −4.09727e12 3.43802e12i −1.13818 0.955048i −0.138804 0.990320i \(-0.544326\pi\)
−0.999378 + 0.0352723i \(0.988770\pi\)
\(618\) −1.37013e11 + 4.06434e11i −0.0377846 + 0.112084i
\(619\) 4.64841e11 + 1.69188e11i 0.127261 + 0.0463193i 0.404866 0.914376i \(-0.367318\pi\)
−0.277604 + 0.960695i \(0.589540\pi\)
\(620\) −2.98040e12 −0.810050
\(621\) −2.94640e12 3.03887e11i −0.795022 0.0819974i
\(622\) 3.63461e11 0.0973647
\(623\) 3.67955e11 + 1.33925e11i 0.0978586 + 0.0356176i
\(624\) 3.15597e12 + 3.58346e12i 0.833300 + 0.946176i
\(625\) −1.80065e12 1.51093e12i −0.472031 0.396081i
\(626\) −1.54122e10 + 8.74072e10i −0.00401126 + 0.0227490i
\(627\) 1.74883e12 2.18841e12i 0.451901 0.565489i
\(628\) −1.71862e12 + 1.44210e12i −0.440923 + 0.369978i
\(629\) −1.06605e12 1.84646e12i −0.271551 0.470340i
\(630\) 3.68774e10 + 5.73522e10i 0.00932669 + 0.0145050i
\(631\) −6.83547e11 + 1.18394e12i −0.171647 + 0.297301i −0.938996 0.343929i \(-0.888242\pi\)
0.767349 + 0.641230i \(0.221575\pi\)
\(632\) −4.31682e10 2.44819e11i −0.0107631 0.0610406i
\(633\) 2.02227e10 + 8.45296e11i 0.00500637 + 0.209263i
\(634\) −1.13836e12 + 4.14329e11i −0.279819 + 0.101846i
\(635\) 4.88652e12 1.77855e12i 1.19266 0.434094i
\(636\) −3.01019e12 1.64322e12i −0.729519 0.398234i
\(637\) −1.06372e12 6.03264e12i −0.255976 1.45171i
\(638\) −3.15254e11 + 5.46036e11i −0.0753299 + 0.130475i
\(639\) −8.71675e11 + 6.84329e12i −0.206824 + 1.62372i
\(640\) −1.41404e12 2.44919e12i −0.333159 0.577048i
\(641\) 3.06971e12 2.57580e12i 0.718186 0.602630i −0.208697 0.977980i \(-0.566922\pi\)
0.926883 + 0.375351i \(0.122478\pi\)
\(642\) −7.72997e11 1.17312e11i −0.179585 0.0272544i
\(643\) −1.68695e11 + 9.56716e11i −0.0389182 + 0.220716i −0.998064 0.0621965i \(-0.980189\pi\)
0.959146 + 0.282912i \(0.0913006\pi\)
\(644\) 2.29703e11 + 1.92744e11i 0.0526236 + 0.0441565i
\(645\) 5.33615e12 1.07309e12i 1.21397 0.244129i
\(646\) 4.46252e11 + 1.62422e11i 0.100817 + 0.0366944i
\(647\) 2.07885e12 0.466395 0.233198 0.972429i \(-0.425081\pi\)
0.233198 + 0.972429i \(0.425081\pi\)
\(648\) −1.92052e12 4.97329e11i −0.427890 0.110804i
\(649\) −7.74569e12 −1.71380
\(650\) −4.26962e11 1.55402e11i −0.0938165 0.0341464i
\(651\) 4.14384e11 8.33323e10i 0.0904250 0.0181844i
\(652\) −1.49912e12 1.25791e12i −0.324880 0.272607i
\(653\) 3.38608e11 1.92034e12i 0.0728766 0.413304i −0.926443 0.376434i \(-0.877150\pi\)
0.999320 0.0368699i \(-0.0117387\pi\)
\(654\) 1.32746e12 + 2.01459e11i 0.283741 + 0.0430613i
\(655\) −1.93360e12 + 1.62248e12i −0.410469 + 0.344425i
\(656\) −2.13827e12 3.70359e12i −0.450811 0.780827i
\(657\) 6.02992e12 + 4.58676e12i 1.26260 + 0.960421i
\(658\) 4.19326e10 7.26294e10i 0.00872038 0.0151041i
\(659\) −1.07304e12 6.08551e12i −0.221631 1.25693i −0.869021 0.494775i \(-0.835250\pi\)
0.647390 0.762159i \(-0.275861\pi\)
\(660\) 4.97828e12 + 2.71757e12i 1.02125 + 0.557485i
\(661\) 1.19594e12 4.35288e11i 0.243671 0.0886891i −0.217298 0.976105i \(-0.569724\pi\)
0.460969 + 0.887416i \(0.347502\pi\)
\(662\) 1.14748e12 4.17648e11i 0.232212 0.0845181i
\(663\) −1.68949e11 7.06196e12i −0.0339583 1.41943i
\(664\) 1.58416e11 + 8.98422e11i 0.0316259 + 0.179359i
\(665\) −9.49099e10 + 1.64389e11i −0.0188198 + 0.0325968i
\(666\) 2.99903e11 5.82072e11i 0.0590673 0.114642i
\(667\) 9.27970e11 + 1.60729e12i 0.181538 + 0.314433i
\(668\) 3.82416e12 3.20885e12i 0.743091 0.623527i
\(669\) −5.48623e12 + 6.86522e12i −1.05890 + 1.32506i
\(670\) 2.21962e11 1.25881e12i 0.0425541 0.241336i
\(671\) −2.70812e12 2.27238e12i −0.515724 0.432743i
\(672\) 2.00857e11 + 2.28065e11i 0.0379950 + 0.0431416i
\(673\) 2.80815e11 + 1.02208e11i 0.0527658 + 0.0192052i 0.368268 0.929720i \(-0.379951\pi\)
−0.315502 + 0.948925i \(0.602173\pi\)
\(674\) 2.11647e12 0.395041
\(675\) −1.54892e12 + 3.89389e11i −0.287184 + 0.0721966i
\(676\) −6.22711e12 −1.14690
\(677\) −4.73930e12 1.72497e12i −0.867093 0.315596i −0.130103 0.991500i \(-0.541531\pi\)
−0.736989 + 0.675905i \(0.763753\pi\)
\(678\) 3.28375e11 9.74085e11i 0.0596810 0.177037i
\(679\) −5.50720e11 4.62109e11i −0.0994299 0.0834316i
\(680\) −3.42977e11 + 1.94512e12i −0.0615142 + 0.348864i
\(681\) −7.53747e11 1.92626e12i −0.134296 0.343204i
\(682\) −1.46105e12 + 1.22597e12i −0.258604 + 0.216995i
\(683\) 1.13832e12 + 1.97163e12i 0.200158 + 0.346683i 0.948579 0.316540i \(-0.102521\pi\)
−0.748422 + 0.663223i \(0.769188\pi\)
\(684\) −5.92934e11 2.62232e12i −0.103575 0.458071i
\(685\) 2.22713e12 3.85751e12i 0.386490 0.669421i
\(686\) −4.12364e10 2.33863e11i −0.00710922 0.0403184i
\(687\) −6.26305e11 + 3.81855e11i −0.107271 + 0.0654024i
\(688\) 6.91421e12 2.51656e12i 1.17651 0.428213i
\(689\) 7.23930e12 2.63489e12i 1.22380 0.445426i
\(690\) −7.73266e11 + 4.71457e11i −0.129870 + 0.0791810i
\(691\) 2.12817e11 + 1.20695e12i 0.0355104 + 0.201389i 0.997401 0.0720434i \(-0.0229520\pi\)
−0.961891 + 0.273433i \(0.911841\pi\)
\(692\) 2.20504e12 3.81924e12i 0.365543 0.633140i
\(693\) −7.68145e11 2.38648e11i −0.126515 0.0393060i
\(694\) −2.87699e9 4.98310e9i −0.000470783 0.000815421i
\(695\) −5.60576e12 + 4.70379e12i −0.911388 + 0.764745i
\(696\) 4.52964e11 + 1.15758e12i 0.0731681 + 0.186987i
\(697\) −1.09858e12 + 6.23036e12i −0.176313 + 0.999921i
\(698\) −1.15066e12 9.65517e11i −0.183484 0.153961i
\(699\) −3.14280e12 + 9.32274e12i −0.497931 + 1.47705i
\(700\) 1.51931e11 + 5.52982e10i 0.0239168 + 0.00870502i
\(701\) 1.15369e12 0.180450 0.0902252 0.995921i \(-0.471241\pi\)
0.0902252 + 0.995921i \(0.471241\pi\)
\(702\) 1.79616e12 1.21662e12i 0.279144 0.189076i
\(703\) 1.82286e12 0.281484
\(704\) 6.30701e12 + 2.29556e12i 0.967712 + 0.352218i
\(705\) −3.08610e12 3.50413e12i −0.470499 0.534231i
\(706\) −1.86426e12 1.56430e12i −0.282414 0.236973i
\(707\) 2.22963e10 1.26449e11i 0.00335619 0.0190339i
\(708\) −4.64074e12 + 5.80721e12i −0.694125 + 0.868597i
\(709\) 4.61341e11 3.87111e11i 0.0685669 0.0575344i −0.607860 0.794044i \(-0.707972\pi\)
0.676427 + 0.736510i \(0.263527\pi\)
\(710\) 1.05464e12 + 1.82669e12i 0.155755 + 0.269775i
\(711\) 9.54458e11 4.56947e10i 0.140070 0.00670584i
\(712\) −1.74172e12 + 3.01674e12i −0.253990 + 0.439924i
\(713\) 9.74889e11 + 5.52887e12i 0.141271 + 0.801186i
\(714\) −3.26127e9 1.36319e11i −0.000469617 0.0196297i
\(715\) −1.19724e13 + 4.35760e12i −1.71319 + 0.623549i
\(716\) 8.91906e12 3.24627e12i 1.26827 0.461611i
\(717\) 7.65194e12 + 4.17709e12i 1.08127 + 0.590252i
\(718\) 4.47860e11 + 2.53994e12i 0.0628901 + 0.356668i
\(719\) −6.43613e12 + 1.11477e13i −0.898141 + 1.55563i −0.0682726 + 0.997667i \(0.521749\pi\)
−0.829868 + 0.557959i \(0.811585\pi\)
\(720\) 4.73303e12 1.98385e12i 0.656362 0.275113i
\(721\) 1.71423e11 + 2.96914e11i 0.0236244 + 0.0409187i
\(722\) 9.57760e11 8.03656e11i 0.131172 0.110066i
\(723\) 2.92423e12 + 4.43789e11i 0.398005 + 0.0604024i
\(724\) 2.19018e12 1.24211e13i 0.296249 1.68011i
\(725\) 7.66592e11 + 6.43247e11i 0.103049 + 0.0864682i
\(726\) 1.89365e12 3.80812e11i 0.252980 0.0508740i
\(727\) −1.65453e11 6.02198e10i −0.0219669 0.00799530i 0.331013 0.943626i \(-0.392609\pi\)
−0.352980 + 0.935631i \(0.614832\pi\)
\(728\) −4.51148e11 −0.0595289
\(729\) 2.82908e12 7.08139e12i 0.370998 0.928634i
\(730\) 2.31645e12 0.301905
\(731\) −1.02285e13 3.72287e12i −1.32490 0.482225i
\(732\) −3.32622e12 + 6.68901e11i −0.428205 + 0.0861117i
\(733\) 1.10709e13 + 9.28958e12i 1.41649 + 1.18858i 0.953187 + 0.302381i \(0.0977814\pi\)
0.463306 + 0.886198i \(0.346663\pi\)
\(734\) −4.58101e11 + 2.59802e12i −0.0582545 + 0.330378i
\(735\) −6.50904e12 9.87831e11i −0.822667 0.124850i
\(736\) −3.09216e12 + 2.59463e12i −0.388430 + 0.325931i
\(737\) 7.53946e12 + 1.30587e13i 0.941318 + 1.63041i
\(738\) −1.79188e12 + 7.51064e11i −0.222359 + 0.0932016i
\(739\) −3.65737e11 + 6.33476e11i −0.0451096 + 0.0781322i −0.887699 0.460425i \(-0.847697\pi\)
0.842589 + 0.538557i \(0.181030\pi\)
\(740\) 6.40872e11 + 3.63457e12i 0.0785650 + 0.445564i
\(741\) 5.30100e12 + 2.89374e12i 0.645916 + 0.352597i
\(742\) 1.39742e11 5.08619e10i 0.0169242 0.00615991i
\(743\) −3.62672e12 + 1.32002e12i −0.436581 + 0.158902i −0.550954 0.834535i \(-0.685736\pi\)
0.114374 + 0.993438i \(0.463514\pi\)
\(744\) 8.99324e10 + 3.75911e12i 0.0107606 + 0.449787i
\(745\) 1.01911e12 + 5.77966e12i 0.121204 + 0.687384i
\(746\) −5.33538e11 + 9.24114e11i −0.0630725 + 0.109245i
\(747\) −3.50261e12 + 1.67688e11i −0.411575 + 0.0197042i
\(748\) −5.67120e12 9.82280e12i −0.662396 1.14730i
\(749\) −4.78755e11 + 4.01723e11i −0.0555834 + 0.0466400i
\(750\) −1.33434e12 + 1.66974e12i −0.153990 + 0.192696i
\(751\) −4.82128e11 + 2.73429e12i −0.0553074 + 0.313664i −0.999893 0.0146003i \(-0.995352\pi\)
0.944586 + 0.328264i \(0.106464\pi\)
\(752\) −4.83538e12 4.05737e12i −0.551380 0.462662i
\(753\) −4.18299e12 4.74961e12i −0.474143 0.538369i
\(754\) −1.27733e12 4.64910e11i −0.143924 0.0523839i
\(755\) −3.78129e12 −0.423524
\(756\) −6.39148e11 + 4.32922e11i −0.0711629 + 0.0482016i
\(757\) 1.43220e13 1.58516 0.792581 0.609767i \(-0.208737\pi\)
0.792581 + 0.609767i \(0.208737\pi\)
\(758\) 2.46916e12 + 8.98699e11i 0.271667 + 0.0988787i
\(759\) 3.41291e12 1.01240e13i 0.373282 1.10730i
\(760\) −1.29358e12 1.08544e12i −0.140647 0.118017i
\(761\) 1.37154e12 7.77841e12i 0.148244 0.840736i −0.816460 0.577402i \(-0.804067\pi\)
0.964705 0.263334i \(-0.0848222\pi\)
\(762\) −1.16378e12 2.97413e12i −0.125047 0.319567i
\(763\) 8.22161e11 6.89875e11i 0.0878206 0.0736902i
\(764\) −3.37490e12 5.84549e12i −0.358377 0.620727i
\(765\) −7.25014e12 2.25248e12i −0.765367 0.237785i
\(766\) 9.14800e11 1.58448e12i 0.0960056 0.166287i
\(767\) −2.89973e12 1.64452e13i −0.302537 1.71577i
\(768\) 4.31518e12 2.63095e12i 0.447583 0.272889i
\(769\) 1.36410e13 4.96493e12i 1.40663 0.511970i 0.476489 0.879180i \(-0.341909\pi\)
0.930138 + 0.367210i \(0.119687\pi\)
\(770\) −2.31106e11 + 8.41158e10i −0.0236921 + 0.00862322i
\(771\) 1.01156e13 6.16742e12i 1.03097 0.628577i
\(772\) 3.79347e10 + 2.15138e11i 0.00384378 + 0.0217992i
\(773\) −1.96630e12 + 3.40574e12i −0.198081 + 0.343086i −0.947906 0.318550i \(-0.896804\pi\)
0.749825 + 0.661636i \(0.230138\pi\)
\(774\) −7.37247e11 3.26056e12i −0.0738378 0.326556i
\(775\) 1.51356e12 + 2.62157e12i 0.150710 + 0.261038i
\(776\) 4.89924e12 4.11095e12i 0.485010 0.406972i
\(777\) −1.90727e11 4.87418e11i −0.0187724 0.0479742i
\(778\) −3.51458e11 + 1.99322e12i −0.0343927 + 0.195050i
\(779\) −4.14343e12 3.47675e12i −0.403126 0.338263i
\(780\) −3.90609e12 + 1.15869e13i −0.377847 + 1.12084i
\(781\) −2.33820e13 8.51035e12i −2.24881 0.818498i
\(782\) 1.81114e12 0.173190
\(783\) −4.63385e12 + 1.16492e12i −0.440569 + 0.110757i
\(784\) −8.89982e12 −0.841316
\(785\) −5.08978e12 1.85253e12i −0.478394 0.174121i
\(786\) 1.02458e12 + 1.16337e12i 0.0957515 + 0.108722i
\(787\) 1.19610e13 + 1.00364e13i 1.11143 + 0.932596i 0.998140 0.0609660i \(-0.0194181\pi\)
0.113285 + 0.993562i \(0.463863\pi\)
\(788\) −2.51276e12 + 1.42506e13i −0.232158 + 1.31663i
\(789\) −5.33691e12 + 6.67837e12i −0.490279 + 0.613514i
\(790\) 2.23811e11 1.87800e11i 0.0204437 0.0171543i
\(791\) −4.10844e11 7.11602e11i −0.0373149 0.0646313i
\(792\) 3.27740e12 6.36099e12i 0.295982 0.574462i
\(793\) 3.81076e12 6.60043e12i 0.342202 0.592711i
\(794\) −1.15931e11 6.57475e11i −0.0103516 0.0587066i
\(795\) −1.98026e11 8.27736e12i −0.0175821 0.734919i
\(796\) 1.00735e13 3.66644e12i 0.889345 0.323695i
\(797\) 6.32997e12 2.30392e12i 0.555698 0.202258i −0.0488781 0.998805i \(-0.515565\pi\)
0.604576 + 0.796547i \(0.293342\pi\)
\(798\) 1.02326e11 + 5.58586e10i 0.00893253 + 0.00487615i
\(799\) 1.62150e12 + 9.19599e12i 0.140753 + 0.798248i
\(800\) −1.08824e12 + 1.88489e12i −0.0939333 + 0.162697i
\(801\) −1.06569e13 8.10632e12i −0.914709 0.695789i
\(802\) −2.55584e12 4.42685e12i −0.218147 0.377842i
\(803\) −2.09334e13 + 1.75652e13i −1.77672 + 1.49085i
\(804\) 1.43078e13 + 2.17139e12i 1.20759 + 0.183267i
\(805\) −1.25710e11 + 7.12937e11i −0.0105509 + 0.0598370i
\(806\) −3.14987e12 2.64305e12i −0.262896 0.220596i
\(807\) 2.01089e12 4.04388e11i 0.166900 0.0335635i
\(808\) 1.07336e12 + 3.90673e11i 0.0885923 + 0.0322450i
\(809\) 8.17110e12 0.670675 0.335338 0.942098i \(-0.391150\pi\)
0.335338 + 0.942098i \(0.391150\pi\)
\(810\) −6.22374e11 2.24697e12i −0.0508006 0.183406i
\(811\) 2.07621e13 1.68530 0.842651 0.538460i \(-0.180994\pi\)
0.842651 + 0.538460i \(0.180994\pi\)
\(812\) 4.54526e11 + 1.65434e11i 0.0366908 + 0.0133543i
\(813\) −3.05822e12 + 6.15005e11i −0.245505 + 0.0493709i
\(814\) 1.80922e12 + 1.51812e12i 0.144438 + 0.121198i
\(815\) 8.20427e11 4.65287e12i 0.0651375 0.369413i
\(816\) −1.01468e13 1.53991e12i −0.801170 0.121588i
\(817\) 7.12893e12 5.98188e12i 0.559790 0.469719i
\(818\) −6.07001e11 1.05136e12i −0.0474023 0.0821032i
\(819\) 2.19116e11 1.72022e12i 0.0170175 0.133600i
\(820\) 5.47550e12 9.48385e12i 0.422923 0.732525i
\(821\) 3.56272e12 + 2.02052e13i 0.273676 + 1.55210i 0.743135 + 0.669142i \(0.233338\pi\)
−0.469458 + 0.882955i \(0.655551\pi\)
\(822\) −2.40117e12 1.31076e12i −0.183442 0.100139i
\(823\) −1.30605e13 + 4.75362e12i −0.992336 + 0.361181i −0.786625 0.617432i \(-0.788173\pi\)
−0.205712 + 0.978613i \(0.565951\pi\)
\(824\) −2.86605e12 + 1.04316e12i −0.216576 + 0.0788274i
\(825\) −1.37777e11 5.75900e12i −0.0103546 0.432817i
\(826\) −5.59742e10 3.17445e11i −0.00418386 0.0237279i
\(827\) −7.13700e12 + 1.23617e13i −0.530568 + 0.918971i 0.468796 + 0.883307i \(0.344688\pi\)
−0.999364 + 0.0356643i \(0.988645\pi\)
\(828\) −5.54551e12 8.62445e12i −0.410020 0.637668i
\(829\) −3.70442e12 6.41625e12i −0.272411 0.471830i 0.697067 0.717006i \(-0.254488\pi\)
−0.969479 + 0.245175i \(0.921154\pi\)
\(830\) −8.21329e11 + 6.89177e11i −0.0600711 + 0.0504056i
\(831\) 1.33441e13 1.66983e13i 0.970702 1.21469i
\(832\) −2.51267e12 + 1.42500e13i −0.181794 + 1.03101i
\(833\) 1.00857e13 + 8.46289e12i 0.725776 + 0.608999i
\(834\) 2.97040e12 + 3.37276e12i 0.212603 + 0.241401i
\(835\) 1.13254e13 + 4.12212e12i 0.806242 + 0.293448i
\(836\) 9.69725e12 0.686626
\(837\) −1.43771e13 1.48283e12i −1.01253 0.104431i
\(838\) 3.11181e12 0.217979
\(839\) −1.28307e13 4.67001e12i −0.893970 0.325378i −0.146136 0.989264i \(-0.546684\pi\)
−0.747834 + 0.663886i \(0.768906\pi\)
\(840\) −1.54890e11 + 4.59464e11i −0.0107341 + 0.0318416i
\(841\) −8.81973e12 7.40063e12i −0.607958 0.510137i
\(842\) 8.20932e11 4.65573e12i 0.0562863 0.319215i
\(843\) 2.38219e12 + 6.08788e12i 0.162462 + 0.415185i
\(844\) −2.24217e12 + 1.88141e12i −0.152100 + 0.127627i
\(845\) −7.51697e12 1.30198e13i −0.507210 0.878514i
\(846\) −2.10615e12 + 1.94629e12i −0.141359 + 0.130629i
\(847\) 7.71998e11 1.33714e12i 0.0515396 0.0892692i
\(848\) −1.94360e12 1.10227e13i −0.129070 0.731991i
\(849\) 1.38078e13 8.41858e12i 0.912097 0.556102i
\(850\) 9.17666e11 3.34003e11i 0.0602975 0.0219465i
\(851\) 6.53277e12 2.37773e12i 0.426987 0.155410i
\(852\) −2.03895e13 + 1.24314e13i −1.32565 + 0.808244i
\(853\) −3.48320e12 1.97542e13i −0.225272 1.27758i −0.862164 0.506628i \(-0.830892\pi\)
0.636892 0.770953i \(-0.280220\pi\)
\(854\) 7.35600e10 1.27410e11i 0.00473240 0.00819675i
\(855\) 4.76705e12 4.40522e12i 0.305072 0.281916i
\(856\) −2.77989e12 4.81491e12i −0.176968 0.306518i
\(857\) −1.19917e13 + 1.00623e13i −0.759396 + 0.637209i −0.937970 0.346718i \(-0.887296\pi\)
0.178574 + 0.983927i \(0.442852\pi\)
\(858\) 2.85137e12 + 7.28689e12i 0.179622 + 0.459039i
\(859\) −1.80369e12 + 1.02293e13i −0.113030 + 0.641025i 0.874677 + 0.484707i \(0.161074\pi\)
−0.987707 + 0.156318i \(0.950037\pi\)
\(860\) 1.44335e13 + 1.21112e13i 0.899766 + 0.754993i
\(861\) −4.96125e11 + 1.47170e12i −0.0307664 + 0.0912649i
\(862\) 5.41749e12 + 1.97180e12i 0.334207 + 0.121641i
\(863\) 1.57454e13 0.966288 0.483144 0.875541i \(-0.339495\pi\)
0.483144 + 0.875541i \(0.339495\pi\)
\(864\) −4.24520e12 9.48520e12i −0.259171 0.579075i
\(865\) 1.06471e13 0.646637
\(866\) −1.12849e12 4.10737e11i −0.0681817 0.0248161i
\(867\) −9.61559e11 1.09181e12i −0.0577949 0.0656236i
\(868\) 1.12085e12 + 9.40505e11i 0.0670207 + 0.0562370i
\(869\) −5.98495e11 + 3.39423e12i −0.0356018 + 0.201908i
\(870\) −9.12019e11 + 1.14126e12i −0.0539718 + 0.0675379i
\(871\) −2.49030e13 + 2.08961e13i −1.46612 + 1.23022i
\(872\) 4.77387e12 + 8.26859e12i 0.279606 + 0.484292i
\(873\) 1.32955e13 + 2.06774e13i 0.774713 + 1.20484i
\(874\) −7.74224e11 + 1.34100e12i −0.0448813 + 0.0777367i
\(875\) 2.96683e11 + 1.68258e12i 0.0171103 + 0.0970372i
\(876\) 6.27246e11 + 2.62185e13i 0.0359890 + 1.50431i
\(877\) 1.03678e13 3.77357e12i 0.591818 0.215404i −0.0287108 0.999588i \(-0.509140\pi\)
0.620529 + 0.784184i \(0.286918\pi\)
\(878\) −5.75641e12 + 2.09516e12i −0.326908 + 0.118985i
\(879\) −2.07437e12 1.13237e12i −0.117202 0.0639790i
\(880\) 3.21434e12 + 1.82294e13i 0.180684 + 1.02471i
\(881\) −6.34675e12 + 1.09929e13i −0.354944 + 0.614781i −0.987108 0.160053i \(-0.948833\pi\)
0.632164 + 0.774834i \(0.282167\pi\)
\(882\) −5.10904e11 + 4.01097e12i −0.0284270 + 0.223172i
\(883\) −6.78125e11 1.17455e12i −0.0375394 0.0650201i 0.846645 0.532158i \(-0.178619\pi\)
−0.884185 + 0.467138i \(0.845285\pi\)
\(884\) 1.87321e13 1.57181e13i 1.03169 0.865693i
\(885\) −1.77439e13 2.69286e12i −0.972307 0.147560i
\(886\) 3.31623e11 1.88073e12i 0.0180798 0.102536i
\(887\) −1.03849e13 8.71394e12i −0.563306 0.472670i 0.316111 0.948722i \(-0.397623\pi\)
−0.879417 + 0.476052i \(0.842067\pi\)
\(888\) 4.56486e12 9.17990e11i 0.246360 0.0495427i
\(889\) −2.39894e12 8.73142e11i −0.128813 0.0468842i
\(890\) −4.09394e12 −0.218719
\(891\) 2.26626e13 + 1.55861e13i 1.20465 + 0.828491i
\(892\) −3.04211e13 −1.60891
\(893\) −7.50199e12 2.73050e12i −0.394771 0.143685i
\(894\) 3.53366e12 7.10616e11i 0.185015 0.0372063i
\(895\) 1.75539e13 + 1.47295e13i 0.914471 + 0.767332i
\(896\) −2.41091e11 + 1.36729e12i −0.0124967 + 0.0708722i
\(897\) 2.27723e13 + 3.45600e12i 1.17447 + 0.178241i
\(898\) −4.67829e12 + 3.92555e12i −0.240073 + 0.201445i
\(899\) 4.52808e12 + 7.84287e12i 0.231204 + 0.400458i
\(900\) −4.40027e12 3.34714e12i −0.223557 0.170052i
\(901\) −8.27896e12 + 1.43396e13i −0.418518 + 0.724894i
\(902\) −1.21692e12 6.90147e12i −0.0612112 0.347146i
\(903\) −2.34542e12 1.28033e12i −0.117388 0.0640807i
\(904\) 6.86895e12 2.50009e12i 0.342084 0.124508i
\(905\) 2.86143e13 1.04147e13i 1.41796 0.516095i
\(906\) 5.55429e10 + 2.32165e12i 0.00273874 + 0.114478i
\(907\) −4.77134e11 2.70596e12i −0.0234103 0.132766i 0.970863 0.239636i \(-0.0770282\pi\)
−0.994273 + 0.106870i \(0.965917\pi\)
\(908\) 3.58016e12 6.20102e12i 0.174790 0.302745i
\(909\) −2.01095e12 + 3.90298e12i −0.0976929 + 0.189609i
\(910\) −2.65108e11 4.59181e11i −0.0128155 0.0221972i
\(911\) 1.61221e13 1.35280e13i 0.775512 0.650732i −0.166602 0.986024i \(-0.553280\pi\)
0.942114 + 0.335292i \(0.108835\pi\)
\(912\) 5.47772e12 6.85457e12i 0.262194 0.328098i
\(913\) 2.19632e12 1.24559e13i 0.104611 0.593278i
\(914\) 1.83434e12 + 1.53919e12i 0.0869404 + 0.0729517i
\(915\) −5.41376e12 6.14709e12i −0.255331 0.289918i
\(916\) −2.38610e12 8.68468e11i −0.111985 0.0407590i
\(917\) 1.23917e12 0.0578721
\(918\) −1.27650e12 + 4.48457e12i −0.0593236 + 0.208415i
\(919\) −2.55574e13 −1.18194 −0.590972 0.806692i \(-0.701256\pi\)
−0.590972 + 0.806692i \(0.701256\pi\)
\(920\) −6.05179e12 2.20267e12i −0.278508 0.101369i
\(921\) −1.14798e13 + 3.40534e13i −0.525733 + 1.55952i
\(922\) −1.79455e12 1.50581e12i −0.0817836 0.0686246i
\(923\) 9.31522e12 5.28292e13i 0.422460 2.39589i
\(924\) −1.01463e12 2.59297e12i −0.0457915 0.117024i
\(925\) 2.87152e12 2.40949e12i 0.128966 0.108215i
\(926\) −2.23400e12 3.86940e12i −0.0998467 0.172940i
\(927\) −2.58554e12 1.14348e13i −0.114999 0.508594i
\(928\) −3.25565e12 + 5.63896e12i −0.144103 + 0.249593i
\(929\) −6.29727e12 3.57136e13i −0.277384 1.57312i −0.731285 0.682072i \(-0.761079\pi\)
0.453901 0.891052i \(-0.350032\pi\)
\(930\) −3.77320e12 + 2.30050e12i −0.165400 + 0.100844i
\(931\) −1.05775e13 + 3.84988e12i −0.461432 + 0.167947i
\(932\) −3.20026e13 + 1.16480e13i −1.38935 + 0.505684i
\(933\) −8.48240e12 + 5.17168e12i −0.366481 + 0.223442i
\(934\) −1.14540e12 6.49591e12i −0.0492491 0.279305i
\(935\) 1.36918e13 2.37149e13i 0.585880 1.01477i
\(936\) 1.47322e13 + 4.57703e12i 0.627375 + 0.194914i
\(937\) −2.55461e12 4.42471e12i −0.108267 0.187524i 0.806801 0.590823i \(-0.201197\pi\)
−0.915068 + 0.403299i \(0.867863\pi\)
\(938\) −4.80708e11 + 4.03362e11i −0.0202753 + 0.0170130i
\(939\) −8.84026e11 2.25919e12i −0.0371082 0.0948328i
\(940\) 2.80679e12 1.59181e13i 0.117256 0.664990i
\(941\) −3.82223e12 3.20723e12i −0.158914 0.133345i 0.559863 0.828585i \(-0.310854\pi\)
−0.718778 + 0.695240i \(0.755298\pi\)
\(942\) −1.06266e12 + 3.15227e12i −0.0439710 + 0.130435i
\(943\) −1.93843e13 7.05531e12i −0.798266 0.290545i
\(944\) −2.42612e13 −0.994348
\(945\) −1.67670e12 8.13750e11i −0.0683931 0.0331931i
\(946\) 1.20574e13 0.489491
\(947\) 2.70313e13 + 9.83859e12i 1.09217 + 0.397519i 0.824426 0.565970i \(-0.191498\pi\)
0.267749 + 0.963489i \(0.413720\pi\)
\(948\) 2.18619e12 + 2.48233e12i 0.0879125 + 0.0998209i
\(949\) −4.51301e13 3.78687e13i −1.80621 1.51559i
\(950\) −1.44982e11 + 8.22232e11i −0.00577506 + 0.0327520i
\(951\) 2.06714e13 2.58672e13i 0.819515 1.02550i
\(952\) 7.42794e11 6.23278e11i 0.0293091 0.0245932i
\(953\) 2.07896e13 + 3.60087e13i 0.816448 + 1.41413i 0.908284 + 0.418355i \(0.137393\pi\)
−0.0918357 + 0.995774i \(0.529273\pi\)
\(954\) −5.07927e12 + 2.43170e11i −0.198533 + 0.00950480i
\(955\) 8.14792e12 1.41126e13i 0.316980 0.549025i
\(956\) 5.24034e12 + 2.97195e13i 0.202908 + 1.15075i
\(957\) −4.12184e11 1.72290e13i −0.0158850 0.663983i
\(958\) −5.97720e12 + 2.17552e12i −0.229273 + 0.0834486i
\(959\) −2.05485e12 + 7.47906e11i −0.0784508 + 0.0285537i
\(960\) 1.36500e13 + 7.45137e12i 0.518697 + 0.283149i
\(961\) 1.65832e11 + 9.40478e11i 0.00627209 + 0.0355708i
\(962\) −2.54586e12 + 4.40956e12i −0.0958401 + 0.166000i
\(963\) 1.97093e13 8.26114e12i 0.738505 0.309543i
\(964\) 5.11926e12 + 8.86683e12i 0.190924 + 0.330690i
\(965\) −4.04024e11 + 3.39016e11i −0.0149980 + 0.0125848i
\(966\) 4.39580e11 + 6.67119e10i 0.0162420 + 0.00246494i
\(967\) 3.55453e12 2.01588e13i 0.130726 0.741386i −0.847014 0.531570i \(-0.821602\pi\)
0.977741 0.209816i \(-0.0672866\pi\)
\(968\) 1.05220e13 + 8.82900e12i 0.385176 + 0.323201i
\(969\) −1.27257e13 + 2.55912e12i −0.463685 + 0.0932467i
\(970\) 7.06309e12 + 2.57075e12i 0.256166 + 0.0932369i
\(971\) −2.70481e13 −0.976451 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(972\) 2.52635e13 7.65269e12i 0.907809 0.274989i
\(973\) 3.59253e12 0.128497
\(974\) 6.39147e12 + 2.32630e12i 0.227554 + 0.0828230i
\(975\) 1.21756e13 2.44850e12i 0.431488 0.0867719i
\(976\) −8.48244e12 7.11761e12i −0.299224 0.251079i
\(977\) −8.79943e11 + 4.99040e12i −0.0308979 + 0.175231i −0.996352 0.0853443i \(-0.972801\pi\)
0.965454 + 0.260575i \(0.0839121\pi\)
\(978\) −2.86885e12 4.35385e11i −0.100273 0.0152177i
\(979\) 3.69962e13 3.10435e13i 1.28717 1.08006i
\(980\) −1.13950e13 1.97367e13i −0.394636 0.683529i
\(981\) −3.38466e13 + 1.41868e13i −1.16682 + 0.489072i
\(982\) −5.17858e12 + 8.96957e12i −0.177709 + 0.307801i
\(983\) 1.60186e12 + 9.08461e12i 0.0547185 + 0.310324i 0.999867 0.0163173i \(-0.00519418\pi\)
−0.945148 + 0.326641i \(0.894083\pi\)
\(984\) −1.21270e13 6.61996e12i −0.412359 0.225101i
\(985\) −3.28287e13 + 1.19487e13i −1.11119 + 0.404442i
\(986\) 2.74535e12 9.99227e11i 0.0925022 0.0336681i
\(987\) 5.48255e10 + 2.29167e12i 0.00183889 + 0.0768644i
\(988\) 3.63033e12 + 2.05886e13i 0.121210 + 0.687418i
\(989\) 1.77459e13 3.07369e13i 0.589815 1.02159i
\(990\) 8.40015e12 4.02158e11i 0.277926 0.0133057i
\(991\) 2.01024e13 + 3.48184e13i 0.662090 + 1.14677i 0.980065 + 0.198675i \(0.0636638\pi\)
−0.317975 + 0.948099i \(0.603003\pi\)
\(992\) −1.50884e13 + 1.26607e13i −0.494698 + 0.415101i
\(993\) −2.08370e13 + 2.60745e13i −0.680085 + 0.851028i
\(994\) 1.79814e11 1.01977e12i 0.00584231 0.0331334i
\(995\) 1.98259e13 + 1.66359e13i 0.641254 + 0.538076i
\(996\) −8.02275e12 9.10949e12i −0.258319 0.293310i
\(997\) −1.53940e13 5.60295e12i −0.493427 0.179593i 0.0833084 0.996524i \(-0.473451\pi\)
−0.576735 + 0.816931i \(0.695674\pi\)
\(998\) −2.63691e12 −0.0841410
\(999\) 1.28320e12 + 1.78516e13i 0.0407613 + 0.567065i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 27.10.e.a.4.15 156
3.2 odd 2 81.10.e.a.64.12 156
27.7 even 9 inner 27.10.e.a.7.15 yes 156
27.20 odd 18 81.10.e.a.19.12 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.10.e.a.4.15 156 1.1 even 1 trivial
27.10.e.a.7.15 yes 156 27.7 even 9 inner
81.10.e.a.19.12 156 27.20 odd 18
81.10.e.a.64.12 156 3.2 odd 2