Properties

Label 3.19.b.b.2.1
Level $3$
Weight $19$
Character 3.2
Analytic conductor $6.162$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,19,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 19, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 19);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), 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: \(6.16158413129\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.601940665.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 123x^{2} - 1744x + 16016 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{11} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.1
Root \(-6.07949 - 12.9551i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.19.b.b.2.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-932.767i q^{2} +(-4234.02 + 19222.2i) q^{3} -607911. q^{4} +1.14247e6i q^{5} +(1.79299e7 + 3.94936e6i) q^{6} -9.81043e6 q^{7} +3.22520e8i q^{8} +(-3.51567e8 - 1.62775e8i) q^{9} +O(q^{10})\) \(q-932.767i q^{2} +(-4234.02 + 19222.2i) q^{3} -607911. q^{4} +1.14247e6i q^{5} +(1.79299e7 + 3.94936e6i) q^{6} -9.81043e6 q^{7} +3.22520e8i q^{8} +(-3.51567e8 - 1.62775e8i) q^{9} +1.06566e9 q^{10} +2.16393e9i q^{11} +(2.57391e9 - 1.16854e10i) q^{12} -1.47189e10 q^{13} +9.15085e9i q^{14} +(-2.19608e10 - 4.83724e9i) q^{15} +1.41476e11 q^{16} +1.36506e10i q^{17} +(-1.51831e11 + 3.27930e11i) q^{18} -2.38919e11 q^{19} -6.94520e11i q^{20} +(4.15376e10 - 1.88578e11i) q^{21} +2.01844e12 q^{22} -5.70649e11i q^{23} +(-6.19955e12 - 1.36556e12i) q^{24} +2.50946e12 q^{25} +1.37293e13i q^{26} +(4.61743e12 - 6.06870e12i) q^{27} +5.96387e12 q^{28} -1.35326e13i q^{29} +(-4.51202e12 + 2.04843e13i) q^{30} -1.17012e13 q^{31} -4.74176e13i q^{32} +(-4.15954e13 - 9.16211e12i) q^{33} +1.27329e13 q^{34} -1.12081e13i q^{35} +(2.13721e14 + 9.89525e13i) q^{36} -1.26080e14 q^{37} +2.22856e14i q^{38} +(6.23201e13 - 2.82930e14i) q^{39} -3.68470e14 q^{40} +3.28662e14i q^{41} +(-1.75900e14 - 3.87449e13i) q^{42} +8.40904e14 q^{43} -1.31547e15i q^{44} +(1.85965e14 - 4.01654e14i) q^{45} -5.32283e14 q^{46} +9.97479e14i q^{47} +(-5.99013e14 + 2.71948e15i) q^{48} -1.53217e15 q^{49} -2.34074e15i q^{50} +(-2.62395e14 - 5.77971e13i) q^{51} +8.94778e15 q^{52} +5.45882e15i q^{53} +(-5.66068e15 - 4.30699e15i) q^{54} -2.47222e15 q^{55} -3.16406e15i q^{56} +(1.01159e15 - 4.59255e15i) q^{57} -1.26228e16 q^{58} -8.03632e14i q^{59} +(1.33502e16 + 2.94061e15i) q^{60} +1.04106e16 q^{61} +1.09145e16i q^{62} +(3.44902e15 + 1.59689e15i) q^{63} -7.14245e15 q^{64} -1.68159e16i q^{65} +(-8.54612e15 + 3.87989e16i) q^{66} -1.50639e16 q^{67} -8.29836e15i q^{68} +(1.09691e16 + 2.41614e15i) q^{69} -1.04546e16 q^{70} -4.47214e16i q^{71} +(5.24981e16 - 1.13387e17i) q^{72} -3.92287e16 q^{73} +1.17603e17i q^{74} +(-1.06251e16 + 4.82374e16i) q^{75} +1.45241e17 q^{76} -2.12290e16i q^{77} +(-2.63908e17 - 5.81302e16i) q^{78} -7.20817e16 q^{79} +1.61632e17i q^{80} +(9.71035e16 + 1.14452e17i) q^{81} +3.06565e17 q^{82} -1.02835e17i q^{83} +(-2.52512e16 + 1.14639e17i) q^{84} -1.55954e16 q^{85} -7.84368e17i q^{86} +(2.60126e17 + 5.72973e16i) q^{87} -6.97910e17 q^{88} +5.12684e17i q^{89} +(-3.74650e17 - 1.73462e17i) q^{90} +1.44399e17 q^{91} +3.46904e17i q^{92} +(4.95431e16 - 2.24923e17i) q^{93} +9.30416e17 q^{94} -2.72957e17i q^{95} +(9.11471e17 + 2.00767e17i) q^{96} -7.28759e17 q^{97} +1.42916e18i q^{98} +(3.52232e17 - 7.60764e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9} + 1461136320 q^{10} + 7123171104 q^{12} - 5426221528 q^{13} - 68287821120 q^{15} + 201224008192 q^{16} - 624067623360 q^{18} + 191416649480 q^{19} - 843499414296 q^{21} + 6661732766400 q^{22} - 16917300997632 q^{24} + 11407599454180 q^{25} - 4632207691356 q^{27} + 5750860980032 q^{28} - 17181499602240 q^{30} + 35728415085608 q^{31} + 12242871023040 q^{33} - 97283346838272 q^{34} + 412657454022048 q^{36} - 475299833502232 q^{37} + 416909545005096 q^{39} - 967003294602240 q^{40} + 149151729948480 q^{42} + 15\!\cdots\!92 q^{43}+ \cdots + 30\!\cdots\!60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 932.767i 1.82181i −0.412615 0.910906i \(-0.635384\pi\)
0.412615 0.910906i \(-0.364616\pi\)
\(3\) −4234.02 + 19222.2i −0.215111 + 0.976590i
\(4\) −607911. −2.31900
\(5\) 1.14247e6i 0.584944i 0.956274 + 0.292472i \(0.0944779\pi\)
−0.956274 + 0.292472i \(0.905522\pi\)
\(6\) 1.79299e7 + 3.94936e6i 1.77916 + 0.391891i
\(7\) −9.81043e6 −0.243112 −0.121556 0.992585i \(-0.538788\pi\)
−0.121556 + 0.992585i \(0.538788\pi\)
\(8\) 3.22520e8i 2.40296i
\(9\) −3.51567e8 1.62775e8i −0.907455 0.420150i
\(10\) 1.06566e9 1.06566
\(11\) 2.16393e9i 0.917716i 0.888510 + 0.458858i \(0.151741\pi\)
−0.888510 + 0.458858i \(0.848259\pi\)
\(12\) 2.57391e9 1.16854e10i 0.498841 2.26471i
\(13\) −1.47189e10 −1.38799 −0.693993 0.719982i \(-0.744150\pi\)
−0.693993 + 0.719982i \(0.744150\pi\)
\(14\) 9.15085e9i 0.442903i
\(15\) −2.19608e10 4.83724e9i −0.571251 0.125828i
\(16\) 1.41476e11 2.05875
\(17\) 1.36506e10i 0.115110i 0.998342 + 0.0575549i \(0.0183304\pi\)
−0.998342 + 0.0575549i \(0.981670\pi\)
\(18\) −1.51831e11 + 3.27930e11i −0.765434 + 1.65321i
\(19\) −2.38919e11 −0.740402 −0.370201 0.928952i \(-0.620711\pi\)
−0.370201 + 0.928952i \(0.620711\pi\)
\(20\) 6.94520e11i 1.35648i
\(21\) 4.15376e10 1.88578e11i 0.0522959 0.237420i
\(22\) 2.01844e12 1.67190
\(23\) 5.70649e11i 0.316824i −0.987373 0.158412i \(-0.949363\pi\)
0.987373 0.158412i \(-0.0506375\pi\)
\(24\) −6.19955e12 1.36556e12i −2.34671 0.516903i
\(25\) 2.50946e12 0.657840
\(26\) 1.37293e13i 2.52865i
\(27\) 4.61743e12 6.06870e12i 0.605517 0.795832i
\(28\) 5.96387e12 0.563775
\(29\) 1.35326e13i 0.932823i −0.884568 0.466411i \(-0.845547\pi\)
0.884568 0.466411i \(-0.154453\pi\)
\(30\) −4.51202e12 + 2.04843e13i −0.229235 + 1.04071i
\(31\) −1.17012e13 −0.442562 −0.221281 0.975210i \(-0.571024\pi\)
−0.221281 + 0.975210i \(0.571024\pi\)
\(32\) 4.74176e13i 1.34769i
\(33\) −4.15954e13 9.16211e12i −0.896232 0.197410i
\(34\) 1.27329e13 0.209708
\(35\) 1.12081e13i 0.142207i
\(36\) 2.13721e14 + 9.89525e13i 2.10438 + 0.974326i
\(37\) −1.26080e14 −0.970132 −0.485066 0.874478i \(-0.661204\pi\)
−0.485066 + 0.874478i \(0.661204\pi\)
\(38\) 2.22856e14i 1.34887i
\(39\) 6.23201e13 2.82930e14i 0.298571 1.35549i
\(40\) −3.68470e14 −1.40560
\(41\) 3.28662e14i 1.00391i 0.864894 + 0.501955i \(0.167386\pi\)
−0.864894 + 0.501955i \(0.832614\pi\)
\(42\) −1.75900e14 3.87449e13i −0.432535 0.0952733i
\(43\) 8.40904e14 1.67313 0.836566 0.547866i \(-0.184560\pi\)
0.836566 + 0.547866i \(0.184560\pi\)
\(44\) 1.31547e15i 2.12818i
\(45\) 1.85965e14 4.01654e14i 0.245764 0.530811i
\(46\) −5.32283e14 −0.577194
\(47\) 9.97479e14i 0.891298i 0.895208 + 0.445649i \(0.147027\pi\)
−0.895208 + 0.445649i \(0.852973\pi\)
\(48\) −5.99013e14 + 2.71948e15i −0.442859 + 2.01055i
\(49\) −1.53217e15 −0.940897
\(50\) 2.34074e15i 1.19846i
\(51\) −2.62395e14 5.77971e13i −0.112415 0.0247613i
\(52\) 8.94778e15 3.21873
\(53\) 5.45882e15i 1.65431i 0.561977 + 0.827153i \(0.310041\pi\)
−0.561977 + 0.827153i \(0.689959\pi\)
\(54\) −5.66068e15 4.30699e15i −1.44986 1.10314i
\(55\) −2.47222e15 −0.536813
\(56\) 3.16406e15i 0.584188i
\(57\) 1.01159e15 4.59255e15i 0.159268 0.723069i
\(58\) −1.26228e16 −1.69943
\(59\) 8.03632e14i 0.0927660i −0.998924 0.0463830i \(-0.985231\pi\)
0.998924 0.0463830i \(-0.0147695\pi\)
\(60\) 1.33502e16 + 2.94061e15i 1.32473 + 0.291794i
\(61\) 1.04106e16 0.890243 0.445121 0.895470i \(-0.353161\pi\)
0.445121 + 0.895470i \(0.353161\pi\)
\(62\) 1.09145e16i 0.806265i
\(63\) 3.44902e15 + 1.59689e15i 0.220613 + 0.102143i
\(64\) −7.14245e15 −0.396486
\(65\) 1.68159e16i 0.811894i
\(66\) −8.54612e15 + 3.87989e16i −0.359645 + 1.63276i
\(67\) −1.50639e16 −0.553685 −0.276843 0.960915i \(-0.589288\pi\)
−0.276843 + 0.960915i \(0.589288\pi\)
\(68\) 8.29836e15i 0.266939i
\(69\) 1.09691e16 + 2.41614e15i 0.309407 + 0.0681523i
\(70\) −1.04546e16 −0.259074
\(71\) 4.47214e16i 0.975417i −0.873007 0.487709i \(-0.837833\pi\)
0.873007 0.487709i \(-0.162167\pi\)
\(72\) 5.24981e16 1.13387e17i 1.00960 2.18058i
\(73\) −3.92287e16 −0.666344 −0.333172 0.942866i \(-0.608119\pi\)
−0.333172 + 0.942866i \(0.608119\pi\)
\(74\) 1.17603e17i 1.76740i
\(75\) −1.06251e16 + 4.82374e16i −0.141508 + 0.642440i
\(76\) 1.45241e17 1.71699
\(77\) 2.12290e16i 0.223107i
\(78\) −2.63908e17 5.81302e16i −2.46945 0.543939i
\(79\) −7.20817e16 −0.601425 −0.300712 0.953715i \(-0.597224\pi\)
−0.300712 + 0.953715i \(0.597224\pi\)
\(80\) 1.61632e17i 1.20425i
\(81\) 9.71035e16 + 1.14452e17i 0.646948 + 0.762534i
\(82\) 3.06565e17 1.82893
\(83\) 1.02835e17i 0.550093i −0.961431 0.275047i \(-0.911307\pi\)
0.961431 0.275047i \(-0.0886933\pi\)
\(84\) −2.52512e16 + 1.14639e17i −0.121274 + 0.550577i
\(85\) −1.55954e16 −0.0673328
\(86\) 7.84368e17i 3.04813i
\(87\) 2.60126e17 + 5.72973e16i 0.910985 + 0.200660i
\(88\) −6.97910e17 −2.20524
\(89\) 5.12684e17i 1.46332i 0.681669 + 0.731661i \(0.261254\pi\)
−0.681669 + 0.731661i \(0.738746\pi\)
\(90\) −3.74650e17 1.73462e17i −0.967037 0.447736i
\(91\) 1.44399e17 0.337435
\(92\) 3.46904e17i 0.734715i
\(93\) 4.95431e16 2.24923e17i 0.0951999 0.432202i
\(94\) 9.30416e17 1.62378
\(95\) 2.72957e17i 0.433094i
\(96\) 9.11471e17 + 2.00767e17i 1.31614 + 0.289902i
\(97\) −7.28759e17 −0.958602 −0.479301 0.877651i \(-0.659110\pi\)
−0.479301 + 0.877651i \(0.659110\pi\)
\(98\) 1.42916e18i 1.71414i
\(99\) 3.52232e17 7.60764e17i 0.385578 0.832785i
\(100\) −1.52553e18 −1.52553
\(101\) 1.15126e18i 1.05264i 0.850286 + 0.526321i \(0.176429\pi\)
−0.850286 + 0.526321i \(0.823571\pi\)
\(102\) −5.39112e16 + 2.44754e17i −0.0451105 + 0.204799i
\(103\) −1.83618e18 −1.40728 −0.703638 0.710559i \(-0.748442\pi\)
−0.703638 + 0.710559i \(0.748442\pi\)
\(104\) 4.74714e18i 3.33528i
\(105\) 2.15445e17 + 4.74554e16i 0.138878 + 0.0305902i
\(106\) 5.09181e18 3.01383
\(107\) 1.30924e18i 0.712140i −0.934459 0.356070i \(-0.884117\pi\)
0.934459 0.356070i \(-0.115883\pi\)
\(108\) −2.80699e18 + 3.68923e18i −1.40419 + 1.84553i
\(109\) 9.37377e17 0.431594 0.215797 0.976438i \(-0.430765\pi\)
0.215797 + 0.976438i \(0.430765\pi\)
\(110\) 2.30601e18i 0.977971i
\(111\) 5.33826e17 2.42354e18i 0.208686 0.947420i
\(112\) −1.38794e18 −0.500506
\(113\) 5.05201e17i 0.168174i −0.996458 0.0840868i \(-0.973203\pi\)
0.996458 0.0840868i \(-0.0267973\pi\)
\(114\) −4.28378e18 9.43576e17i −1.31730 0.290157i
\(115\) 6.51949e17 0.185325
\(116\) 8.22661e18i 2.16321i
\(117\) 5.17467e18 + 2.39586e18i 1.25953 + 0.583162i
\(118\) −7.49601e17 −0.169002
\(119\) 1.33918e17i 0.0279845i
\(120\) 1.56011e18 7.08280e18i 0.302360 1.37269i
\(121\) 8.77344e17 0.157798
\(122\) 9.71069e18i 1.62185i
\(123\) −6.31761e18 1.39156e18i −0.980408 0.215952i
\(124\) 7.11328e18 1.02630
\(125\) 7.22516e18i 0.969744i
\(126\) 1.48953e18 3.21713e18i 0.186086 0.401915i
\(127\) −8.86372e18 −1.03129 −0.515647 0.856801i \(-0.672448\pi\)
−0.515647 + 0.856801i \(0.672448\pi\)
\(128\) 5.76799e18i 0.625366i
\(129\) −3.56041e18 + 1.61640e19i −0.359909 + 1.63396i
\(130\) −1.56853e19 −1.47912
\(131\) 1.50395e19i 1.32371i −0.749632 0.661855i \(-0.769769\pi\)
0.749632 0.661855i \(-0.230231\pi\)
\(132\) 2.52863e19 + 5.56975e18i 2.07836 + 0.457794i
\(133\) 2.34389e18 0.180000
\(134\) 1.40511e19i 1.00871i
\(135\) 6.93330e18 + 5.27527e18i 0.465518 + 0.354194i
\(136\) −4.40260e18 −0.276604
\(137\) 7.91047e18i 0.465283i 0.972563 + 0.232641i \(0.0747369\pi\)
−0.972563 + 0.232641i \(0.925263\pi\)
\(138\) 2.25370e18 1.02317e19i 0.124161 0.563682i
\(139\) 2.96560e19 1.53102 0.765508 0.643426i \(-0.222488\pi\)
0.765508 + 0.643426i \(0.222488\pi\)
\(140\) 6.81354e18i 0.329777i
\(141\) −1.91738e19 4.22335e18i −0.870433 0.191728i
\(142\) −4.17147e19 −1.77703
\(143\) 3.18506e19i 1.27378i
\(144\) −4.97383e19 2.30287e19i −1.86822 0.864983i
\(145\) 1.54606e19 0.545649
\(146\) 3.65913e19i 1.21395i
\(147\) 6.48724e18 2.94517e19i 0.202397 0.918870i
\(148\) 7.66454e19 2.24973
\(149\) 3.76072e19i 1.03895i 0.854486 + 0.519475i \(0.173872\pi\)
−0.854486 + 0.519475i \(0.826128\pi\)
\(150\) 4.49943e19 + 9.91076e18i 1.17040 + 0.257802i
\(151\) −3.02438e19 −0.741044 −0.370522 0.928824i \(-0.620821\pi\)
−0.370522 + 0.928824i \(0.620821\pi\)
\(152\) 7.70561e19i 1.77916i
\(153\) 2.22198e18 4.79910e18i 0.0483633 0.104457i
\(154\) −1.98018e19 −0.406459
\(155\) 1.33682e19i 0.258874i
\(156\) −3.78851e19 + 1.71996e20i −0.692384 + 3.14338i
\(157\) −1.60317e19 −0.276620 −0.138310 0.990389i \(-0.544167\pi\)
−0.138310 + 0.990389i \(0.544167\pi\)
\(158\) 6.72354e19i 1.09568i
\(159\) −1.04931e20 2.31128e19i −1.61558 0.355859i
\(160\) 5.41731e19 0.788323
\(161\) 5.59831e18i 0.0770237i
\(162\) 1.06757e20 9.05749e19i 1.38919 1.17862i
\(163\) 4.78329e19 0.588895 0.294448 0.955668i \(-0.404864\pi\)
0.294448 + 0.955668i \(0.404864\pi\)
\(164\) 1.99797e20i 2.32806i
\(165\) 1.04674e19 4.75215e19i 0.115474 0.524246i
\(166\) −9.59207e19 −1.00217
\(167\) 1.25413e20i 1.24135i 0.784067 + 0.620676i \(0.213142\pi\)
−0.784067 + 0.620676i \(0.786858\pi\)
\(168\) 6.08203e19 + 1.33967e19i 0.570512 + 0.125665i
\(169\) 1.04190e20 0.926503
\(170\) 1.45469e19i 0.122668i
\(171\) 8.39958e19 + 3.88899e19i 0.671881 + 0.311080i
\(172\) −5.11195e20 −3.87999
\(173\) 1.32712e19i 0.0956085i 0.998857 + 0.0478042i \(0.0152224\pi\)
−0.998857 + 0.0478042i \(0.984778\pi\)
\(174\) 5.34451e19 2.42637e20i 0.365565 1.65964i
\(175\) −2.46189e19 −0.159929
\(176\) 3.06144e20i 1.88935i
\(177\) 1.54476e19 + 3.40260e18i 0.0905943 + 0.0199550i
\(178\) 4.78215e20 2.66590
\(179\) 3.08776e19i 0.163669i −0.996646 0.0818345i \(-0.973922\pi\)
0.996646 0.0818345i \(-0.0260779\pi\)
\(180\) −1.13050e20 + 2.44170e20i −0.569927 + 1.23095i
\(181\) 6.94280e18 0.0332987 0.0166494 0.999861i \(-0.494700\pi\)
0.0166494 + 0.999861i \(0.494700\pi\)
\(182\) 1.34690e20i 0.614743i
\(183\) −4.40789e19 + 2.00115e20i −0.191501 + 0.869402i
\(184\) 1.84046e20 0.761317
\(185\) 1.44043e20i 0.567473i
\(186\) −2.09800e20 4.62122e19i −0.787390 0.173436i
\(187\) −2.95389e19 −0.105638
\(188\) 6.06379e20i 2.06692i
\(189\) −4.52990e19 + 5.95365e19i −0.147208 + 0.193476i
\(190\) −2.54606e20 −0.789016
\(191\) 3.84936e19i 0.113786i 0.998380 + 0.0568930i \(0.0181194\pi\)
−0.998380 + 0.0568930i \(0.981881\pi\)
\(192\) 3.02413e19 1.37294e20i 0.0852884 0.387204i
\(193\) −5.08300e20 −1.36806 −0.684028 0.729455i \(-0.739774\pi\)
−0.684028 + 0.729455i \(0.739774\pi\)
\(194\) 6.79762e20i 1.74639i
\(195\) 3.23238e20 + 7.11989e19i 0.792887 + 0.174647i
\(196\) 9.31422e20 2.18194
\(197\) 6.30050e20i 1.40987i −0.709272 0.704935i \(-0.750976\pi\)
0.709272 0.704935i \(-0.249024\pi\)
\(198\) −7.09616e20 3.28551e20i −1.51718 0.702451i
\(199\) 1.14335e19 0.0233615 0.0116807 0.999932i \(-0.496282\pi\)
0.0116807 + 0.999932i \(0.496282\pi\)
\(200\) 8.09352e20i 1.58077i
\(201\) 6.37807e19 2.89561e20i 0.119104 0.540723i
\(202\) 1.07386e21 1.91771
\(203\) 1.32761e20i 0.226780i
\(204\) 1.59513e20 + 3.51355e19i 0.260690 + 0.0574215i
\(205\) −3.75486e20 −0.587231
\(206\) 1.71272e21i 2.56379i
\(207\) −9.28872e19 + 2.00621e20i −0.133114 + 0.287504i
\(208\) −2.08237e21 −2.85751
\(209\) 5.17002e20i 0.679479i
\(210\) 4.42649e19 2.00960e20i 0.0557296 0.253009i
\(211\) 6.41724e20 0.774117 0.387058 0.922055i \(-0.373491\pi\)
0.387058 + 0.922055i \(0.373491\pi\)
\(212\) 3.31847e21i 3.83633i
\(213\) 8.59645e20 + 1.89352e20i 0.952582 + 0.209823i
\(214\) −1.22122e21 −1.29738
\(215\) 9.60707e20i 0.978690i
\(216\) 1.95728e21 + 1.48921e21i 1.91236 + 1.45504i
\(217\) 1.14794e20 0.107592
\(218\) 8.74355e20i 0.786284i
\(219\) 1.66095e20 7.54063e20i 0.143338 0.650744i
\(220\) 1.50289e21 1.24487
\(221\) 2.00922e20i 0.159771i
\(222\) −2.26060e21 4.97935e20i −1.72602 0.380186i
\(223\) −8.65729e20 −0.634802 −0.317401 0.948291i \(-0.602810\pi\)
−0.317401 + 0.948291i \(0.602810\pi\)
\(224\) 4.65187e20i 0.327639i
\(225\) −8.82242e20 4.08477e20i −0.596960 0.276391i
\(226\) −4.71235e20 −0.306381
\(227\) 2.48692e21i 1.55392i 0.629547 + 0.776962i \(0.283240\pi\)
−0.629547 + 0.776962i \(0.716760\pi\)
\(228\) −6.14955e20 + 2.79186e21i −0.369343 + 1.67679i
\(229\) −4.47185e20 −0.258207 −0.129103 0.991631i \(-0.541210\pi\)
−0.129103 + 0.991631i \(0.541210\pi\)
\(230\) 6.08117e20i 0.337627i
\(231\) 4.08069e20 + 8.98843e19i 0.217884 + 0.0479928i
\(232\) 4.36454e21 2.24154
\(233\) 2.20802e21i 1.09094i 0.838131 + 0.545468i \(0.183648\pi\)
−0.838131 + 0.545468i \(0.816352\pi\)
\(234\) 2.23478e21 4.82676e21i 1.06241 2.29463i
\(235\) −1.13959e21 −0.521360
\(236\) 4.88537e20i 0.215124i
\(237\) 3.05196e20 1.38557e21i 0.129373 0.587345i
\(238\) −1.24915e20 −0.0509825
\(239\) 1.30522e21i 0.512983i −0.966547 0.256491i \(-0.917434\pi\)
0.966547 0.256491i \(-0.0825665\pi\)
\(240\) −3.10693e21 6.84355e20i −1.17606 0.259048i
\(241\) 1.77386e21 0.646795 0.323398 0.946263i \(-0.395175\pi\)
0.323398 + 0.946263i \(0.395175\pi\)
\(242\) 8.18358e20i 0.287478i
\(243\) −2.61116e21 + 1.38195e21i −0.883848 + 0.467774i
\(244\) −6.32874e21 −2.06447
\(245\) 1.75046e21i 0.550372i
\(246\) −1.29800e21 + 5.89286e21i −0.393423 + 1.78612i
\(247\) 3.51662e21 1.02767
\(248\) 3.77387e21i 1.06346i
\(249\) 1.97671e21 + 4.35404e20i 0.537215 + 0.118331i
\(250\) 6.73939e21 1.76669
\(251\) 4.95925e21i 1.25416i −0.778956 0.627079i \(-0.784250\pi\)
0.778956 0.627079i \(-0.215750\pi\)
\(252\) −2.09670e21 9.70767e20i −0.511600 0.236870i
\(253\) 1.23484e21 0.290755
\(254\) 8.26779e21i 1.87882i
\(255\) 6.60314e19 2.99778e20i 0.0144840 0.0657565i
\(256\) −7.25254e21 −1.53579
\(257\) 7.24122e20i 0.148052i 0.997256 + 0.0740259i \(0.0235847\pi\)
−0.997256 + 0.0740259i \(0.976415\pi\)
\(258\) 1.50773e22 + 3.32103e21i 2.97677 + 0.655686i
\(259\) 1.23690e21 0.235850
\(260\) 1.02226e22i 1.88278i
\(261\) −2.20276e21 + 4.75761e21i −0.391925 + 0.846494i
\(262\) −1.40284e22 −2.41155
\(263\) 1.13671e22i 1.88821i −0.329650 0.944103i \(-0.606931\pi\)
0.329650 0.944103i \(-0.393069\pi\)
\(264\) 2.95497e21 1.34154e22i 0.474370 2.15361i
\(265\) −6.23653e21 −0.967676
\(266\) 2.18631e21i 0.327927i
\(267\) −9.85492e21 2.17072e21i −1.42906 0.314776i
\(268\) 9.15748e21 1.28399
\(269\) 9.09091e21i 1.23264i 0.787495 + 0.616321i \(0.211377\pi\)
−0.787495 + 0.616321i \(0.788623\pi\)
\(270\) 4.92060e21 6.46716e21i 0.645275 0.848085i
\(271\) 5.59132e21 0.709235 0.354618 0.935011i \(-0.384611\pi\)
0.354618 + 0.935011i \(0.384611\pi\)
\(272\) 1.93124e21i 0.236982i
\(273\) −6.11387e20 + 2.77566e21i −0.0725860 + 0.329536i
\(274\) 7.37863e21 0.847658
\(275\) 5.43029e21i 0.603710i
\(276\) −6.66826e21 1.46880e21i −0.717515 0.158045i
\(277\) −3.61235e21 −0.376246 −0.188123 0.982145i \(-0.560240\pi\)
−0.188123 + 0.982145i \(0.560240\pi\)
\(278\) 2.76622e22i 2.78922i
\(279\) 4.11374e21 + 1.90466e21i 0.401605 + 0.185942i
\(280\) 3.61484e21 0.341718
\(281\) 3.75694e20i 0.0343936i 0.999852 + 0.0171968i \(0.00547418\pi\)
−0.999852 + 0.0171968i \(0.994526\pi\)
\(282\) −3.93940e21 + 1.78847e22i −0.349292 + 1.58576i
\(283\) 4.33569e21 0.372375 0.186187 0.982514i \(-0.440387\pi\)
0.186187 + 0.982514i \(0.440387\pi\)
\(284\) 2.71866e22i 2.26199i
\(285\) 5.24684e21 + 1.15571e21i 0.422955 + 0.0931632i
\(286\) −2.97092e22 −2.32058
\(287\) 3.22431e21i 0.244062i
\(288\) −7.71838e21 + 1.66704e22i −0.566231 + 1.22297i
\(289\) 1.38767e22 0.986750
\(290\) 1.44211e22i 0.994070i
\(291\) 3.08558e21 1.40084e22i 0.206205 0.936160i
\(292\) 2.38476e22 1.54525
\(293\) 1.01590e22i 0.638326i 0.947700 + 0.319163i \(0.103402\pi\)
−0.947700 + 0.319163i \(0.896598\pi\)
\(294\) −2.74716e22 6.05109e21i −1.67401 0.368729i
\(295\) 9.18125e20 0.0542630
\(296\) 4.06633e22i 2.33119i
\(297\) 1.31322e22 + 9.99178e21i 0.730348 + 0.555693i
\(298\) 3.50788e22 1.89277
\(299\) 8.39932e21i 0.439748i
\(300\) 6.45913e21 2.93240e22i 0.328158 1.48982i
\(301\) −8.24963e21 −0.406758
\(302\) 2.82105e22i 1.35004i
\(303\) −2.21297e22 4.87446e21i −1.02800 0.226434i
\(304\) −3.38013e22 −1.52430
\(305\) 1.18938e22i 0.520742i
\(306\) −4.47645e21 2.07259e21i −0.190301 0.0881089i
\(307\) −3.56186e22 −1.47039 −0.735194 0.677857i \(-0.762909\pi\)
−0.735194 + 0.677857i \(0.762909\pi\)
\(308\) 1.29054e22i 0.517385i
\(309\) 7.77441e21 3.52954e22i 0.302720 1.37433i
\(310\) −1.24695e22 −0.471620
\(311\) 9.62119e21i 0.353497i 0.984256 + 0.176748i \(0.0565579\pi\)
−0.984256 + 0.176748i \(0.943442\pi\)
\(312\) 9.12505e22 + 2.00995e22i 3.25720 + 0.717454i
\(313\) −2.06842e22 −0.717364 −0.358682 0.933460i \(-0.616774\pi\)
−0.358682 + 0.933460i \(0.616774\pi\)
\(314\) 1.49539e22i 0.503949i
\(315\) −1.82440e21 + 3.94040e21i −0.0597481 + 0.129046i
\(316\) 4.38193e22 1.39470
\(317\) 4.70774e22i 1.45640i −0.685367 0.728198i \(-0.740358\pi\)
0.685367 0.728198i \(-0.259642\pi\)
\(318\) −2.15588e22 + 9.78758e22i −0.648308 + 2.94328i
\(319\) 2.92835e22 0.856066
\(320\) 8.16003e21i 0.231922i
\(321\) 2.51665e22 + 5.54335e21i 0.695468 + 0.153189i
\(322\) 5.22192e21 0.140323
\(323\) 3.26139e21i 0.0852275i
\(324\) −5.90303e22 6.95768e22i −1.50027 1.76831i
\(325\) −3.69365e22 −0.913072
\(326\) 4.46170e22i 1.07286i
\(327\) −3.96888e21 + 1.80185e22i −0.0928406 + 0.421491i
\(328\) −1.06000e23 −2.41236
\(329\) 9.78570e21i 0.216685i
\(330\) −4.43265e22 9.76368e21i −0.955077 0.210372i
\(331\) 6.94207e22 1.45558 0.727791 0.685799i \(-0.240547\pi\)
0.727791 + 0.685799i \(0.240547\pi\)
\(332\) 6.25143e22i 1.27566i
\(333\) 4.43255e22 + 2.05226e22i 0.880350 + 0.407601i
\(334\) 1.16981e23 2.26151
\(335\) 1.72100e22i 0.323875i
\(336\) 5.87658e21 2.66793e22i 0.107664 0.488789i
\(337\) −7.20588e22 −1.28534 −0.642670 0.766143i \(-0.722173\pi\)
−0.642670 + 0.766143i \(0.722173\pi\)
\(338\) 9.71853e22i 1.68791i
\(339\) 9.71107e21 + 2.13903e21i 0.164237 + 0.0361759i
\(340\) 9.48063e21 0.156145
\(341\) 2.53205e22i 0.406146i
\(342\) 3.62752e22 7.83486e22i 0.566729 1.22404i
\(343\) 3.10067e22 0.471854
\(344\) 2.71209e23i 4.02048i
\(345\) −2.76037e21 + 1.25319e22i −0.0398653 + 0.180986i
\(346\) 1.23790e22 0.174181
\(347\) 7.97053e22i 1.09275i 0.837540 + 0.546376i \(0.183993\pi\)
−0.837540 + 0.546376i \(0.816007\pi\)
\(348\) −1.58134e23 3.48317e22i −2.11257 0.465330i
\(349\) −2.86134e22 −0.372513 −0.186256 0.982501i \(-0.559635\pi\)
−0.186256 + 0.982501i \(0.559635\pi\)
\(350\) 2.29637e22i 0.291360i
\(351\) −6.79635e22 + 8.93245e22i −0.840449 + 1.10460i
\(352\) 1.02608e23 1.23679
\(353\) 4.43974e22i 0.521657i −0.965385 0.260829i \(-0.916004\pi\)
0.965385 0.260829i \(-0.0839957\pi\)
\(354\) 3.17383e21 1.44090e22i 0.0363542 0.165046i
\(355\) 5.10928e22 0.570565
\(356\) 3.11666e23i 3.39344i
\(357\) 2.57421e21 + 5.67014e20i 0.0273294 + 0.00601977i
\(358\) −2.88016e22 −0.298174
\(359\) 4.97330e22i 0.502105i 0.967973 + 0.251052i \(0.0807767\pi\)
−0.967973 + 0.251052i \(0.919223\pi\)
\(360\) 1.29542e23 + 5.99775e22i 1.27552 + 0.590563i
\(361\) −4.70452e22 −0.451805
\(362\) 6.47602e21i 0.0606640i
\(363\) −3.71470e21 + 1.68645e22i −0.0339441 + 0.154104i
\(364\) −8.77815e22 −0.782511
\(365\) 4.48176e22i 0.389774i
\(366\) 1.86661e23 + 4.11153e22i 1.58389 + 0.348878i
\(367\) −6.92177e22 −0.573090 −0.286545 0.958067i \(-0.592507\pi\)
−0.286545 + 0.958067i \(0.592507\pi\)
\(368\) 8.07332e22i 0.652262i
\(369\) 5.34978e22 1.15547e23i 0.421792 0.911003i
\(370\) −1.34358e23 −1.03383
\(371\) 5.35533e22i 0.402181i
\(372\) −3.01178e22 + 1.36733e23i −0.220768 + 1.00227i
\(373\) 8.88028e22 0.635400 0.317700 0.948191i \(-0.397090\pi\)
0.317700 + 0.948191i \(0.397090\pi\)
\(374\) 2.75529e22i 0.192453i
\(375\) −1.38884e23 3.05915e22i −0.947042 0.208602i
\(376\) −3.21707e23 −2.14176
\(377\) 1.99185e23i 1.29474i
\(378\) 5.55337e22 + 4.22534e22i 0.352477 + 0.268186i
\(379\) 2.92079e23 1.81028 0.905142 0.425109i \(-0.139764\pi\)
0.905142 + 0.425109i \(0.139764\pi\)
\(380\) 1.65934e23i 1.00434i
\(381\) 3.75292e22 1.70380e23i 0.221842 1.00715i
\(382\) 3.59056e22 0.207297
\(383\) 1.19044e23i 0.671306i 0.941986 + 0.335653i \(0.108957\pi\)
−0.941986 + 0.335653i \(0.891043\pi\)
\(384\) 1.10873e23 + 2.44218e22i 0.610726 + 0.134523i
\(385\) 2.42535e22 0.130505
\(386\) 4.74126e23i 2.49234i
\(387\) −2.95634e23 1.36878e23i −1.51829 0.702966i
\(388\) 4.43020e23 2.22299
\(389\) 3.20490e23i 1.57133i −0.618650 0.785666i \(-0.712320\pi\)
0.618650 0.785666i \(-0.287680\pi\)
\(390\) 6.64120e22 3.01506e23i 0.318174 1.44449i
\(391\) 7.78971e21 0.0364696
\(392\) 4.94156e23i 2.26094i
\(393\) 2.89093e23 + 6.36778e22i 1.29272 + 0.284744i
\(394\) −5.87690e23 −2.56852
\(395\) 8.23511e22i 0.351800i
\(396\) −2.14126e23 + 4.62477e23i −0.894154 + 1.93123i
\(397\) −3.68991e23 −1.50626 −0.753132 0.657870i \(-0.771458\pi\)
−0.753132 + 0.657870i \(0.771458\pi\)
\(398\) 1.06648e22i 0.0425602i
\(399\) −9.92411e21 + 4.50548e22i −0.0387200 + 0.175786i
\(400\) 3.55029e23 1.35433
\(401\) 4.34713e23i 1.62145i 0.585429 + 0.810724i \(0.300926\pi\)
−0.585429 + 0.810724i \(0.699074\pi\)
\(402\) −2.70093e23 5.94926e22i −0.985096 0.216984i
\(403\) 1.72228e23 0.614270
\(404\) 6.99863e23i 2.44107i
\(405\) −1.30758e23 + 1.10938e23i −0.446040 + 0.378429i
\(406\) 1.23835e23 0.413150
\(407\) 2.72828e23i 0.890305i
\(408\) 1.86407e22 8.46277e22i 0.0595006 0.270129i
\(409\) 1.61875e22 0.0505440 0.0252720 0.999681i \(-0.491955\pi\)
0.0252720 + 0.999681i \(0.491955\pi\)
\(410\) 3.50241e23i 1.06982i
\(411\) −1.52057e23 3.34931e22i −0.454391 0.100087i
\(412\) 1.11623e24 3.26347
\(413\) 7.88397e21i 0.0225525i
\(414\) 1.87133e23 + 8.66422e22i 0.523778 + 0.242508i
\(415\) 1.17485e23 0.321774
\(416\) 6.97934e23i 1.87057i
\(417\) −1.25564e23 + 5.70055e23i −0.329338 + 1.49518i
\(418\) −4.82243e23 −1.23788
\(419\) 1.48601e23i 0.373333i 0.982423 + 0.186666i \(0.0597684\pi\)
−0.982423 + 0.186666i \(0.940232\pi\)
\(420\) −1.30971e23 2.88487e22i −0.322057 0.0709386i
\(421\) −2.10694e23 −0.507123 −0.253562 0.967319i \(-0.581602\pi\)
−0.253562 + 0.967319i \(0.581602\pi\)
\(422\) 5.98580e23i 1.41029i
\(423\) 1.62364e23 3.50680e23i 0.374479 0.808813i
\(424\) −1.76058e24 −3.97523
\(425\) 3.42557e22i 0.0757238i
\(426\) 1.76621e23 8.01848e23i 0.382257 1.73543i
\(427\) −1.02133e23 −0.216428
\(428\) 7.95901e23i 1.65145i
\(429\) 6.12239e23 + 1.34856e23i 1.24396 + 0.274003i
\(430\) 8.96116e23 1.78299
\(431\) 1.45530e23i 0.283567i −0.989898 0.141783i \(-0.954716\pi\)
0.989898 0.141783i \(-0.0452837\pi\)
\(432\) 6.53256e23 8.58576e23i 1.24661 1.63842i
\(433\) 2.76937e23 0.517594 0.258797 0.965932i \(-0.416674\pi\)
0.258797 + 0.965932i \(0.416674\pi\)
\(434\) 1.07076e23i 0.196012i
\(435\) −6.54605e22 + 2.97187e23i −0.117375 + 0.532876i
\(436\) −5.69842e23 −1.00087
\(437\) 1.36339e23i 0.234577i
\(438\) −7.03365e23 1.54928e23i −1.18553 0.261134i
\(439\) 7.04854e23 1.16391 0.581954 0.813222i \(-0.302288\pi\)
0.581954 + 0.813222i \(0.302288\pi\)
\(440\) 7.97341e23i 1.28994i
\(441\) 5.38659e23 + 2.49398e23i 0.853821 + 0.395318i
\(442\) −1.87413e23 −0.291072
\(443\) 1.22387e24i 1.86252i −0.364351 0.931262i \(-0.618709\pi\)
0.364351 0.931262i \(-0.381291\pi\)
\(444\) −3.24519e23 + 1.47329e24i −0.483941 + 2.19706i
\(445\) −5.85726e23 −0.855962
\(446\) 8.07524e23i 1.15649i
\(447\) −7.22894e23 1.59230e23i −1.01463 0.223489i
\(448\) 7.00705e22 0.0963903
\(449\) 4.92165e23i 0.663580i 0.943353 + 0.331790i \(0.107653\pi\)
−0.943353 + 0.331790i \(0.892347\pi\)
\(450\) −3.81014e23 + 8.22927e23i −0.503533 + 1.08755i
\(451\) −7.11200e23 −0.921304
\(452\) 3.07117e23i 0.389994i
\(453\) 1.28053e23 5.81353e23i 0.159407 0.723696i
\(454\) 2.31972e24 2.83096
\(455\) 1.64971e23i 0.197381i
\(456\) 1.48119e24 + 3.26257e23i 1.73751 + 0.382716i
\(457\) −1.39981e24 −1.60999 −0.804994 0.593284i \(-0.797831\pi\)
−0.804994 + 0.593284i \(0.797831\pi\)
\(458\) 4.17120e23i 0.470404i
\(459\) 8.28415e22 + 6.30308e22i 0.0916080 + 0.0697009i
\(460\) −3.96327e23 −0.429767
\(461\) 1.15752e24i 1.23090i −0.788177 0.615449i \(-0.788975\pi\)
0.788177 0.615449i \(-0.211025\pi\)
\(462\) 8.38411e22 3.80634e23i 0.0874338 0.396944i
\(463\) 1.06888e23 0.109320 0.0546602 0.998505i \(-0.482592\pi\)
0.0546602 + 0.998505i \(0.482592\pi\)
\(464\) 1.91454e24i 1.92045i
\(465\) 2.56967e23 + 5.66015e22i 0.252814 + 0.0556867i
\(466\) 2.05957e24 1.98748
\(467\) 1.19933e24i 1.13524i 0.823291 + 0.567619i \(0.192135\pi\)
−0.823291 + 0.567619i \(0.807865\pi\)
\(468\) −3.14574e24 1.45647e24i −2.92085 1.35235i
\(469\) 1.47783e23 0.134607
\(470\) 1.06297e24i 0.949819i
\(471\) 6.78788e22 3.08165e23i 0.0595039 0.270144i
\(472\) 2.59187e23 0.222913
\(473\) 1.81965e24i 1.53546i
\(474\) −1.29241e24 2.84677e23i −1.07003 0.235693i
\(475\) −5.99557e23 −0.487066
\(476\) 8.14105e22i 0.0648960i
\(477\) 8.88557e23 1.91914e24i 0.695056 1.50121i
\(478\) −1.21747e24 −0.934557
\(479\) 8.59327e23i 0.647350i −0.946168 0.323675i \(-0.895082\pi\)
0.946168 0.323675i \(-0.104918\pi\)
\(480\) −2.29370e23 + 1.04133e24i −0.169577 + 0.769868i
\(481\) 1.85576e24 1.34653
\(482\) 1.65460e24i 1.17834i
\(483\) −1.07612e23 2.37034e22i −0.0752205 0.0165686i
\(484\) −5.33347e23 −0.365933
\(485\) 8.32585e23i 0.560729i
\(486\) 1.28904e24 + 2.43561e24i 0.852195 + 1.61020i
\(487\) 9.68317e23 0.628430 0.314215 0.949352i \(-0.398259\pi\)
0.314215 + 0.949352i \(0.398259\pi\)
\(488\) 3.35764e24i 2.13922i
\(489\) −2.02526e23 + 9.19454e23i −0.126678 + 0.575109i
\(490\) −1.63277e24 −1.00267
\(491\) 1.67063e24i 1.00727i 0.863916 + 0.503635i \(0.168004\pi\)
−0.863916 + 0.503635i \(0.831996\pi\)
\(492\) 3.84054e24 + 8.45946e23i 2.27356 + 0.500791i
\(493\) 1.84728e23 0.107377
\(494\) 3.28019e24i 1.87222i
\(495\) 8.69149e23 + 4.02415e23i 0.487133 + 0.225542i
\(496\) −1.65544e24 −0.911125
\(497\) 4.38736e23i 0.237135i
\(498\) 4.06131e23 1.84381e24i 0.215577 0.978705i
\(499\) 3.00033e23 0.156410 0.0782050 0.996937i \(-0.475081\pi\)
0.0782050 + 0.996937i \(0.475081\pi\)
\(500\) 4.39225e24i 2.24883i
\(501\) −2.41072e24 5.31002e23i −1.21229 0.267028i
\(502\) −4.62582e24 −2.28484
\(503\) 3.08864e24i 1.49850i 0.662289 + 0.749248i \(0.269585\pi\)
−0.662289 + 0.749248i \(0.730415\pi\)
\(504\) −5.15029e23 + 1.11238e24i −0.245447 + 0.530124i
\(505\) −1.31528e24 −0.615737
\(506\) 1.15182e24i 0.529700i
\(507\) −4.41144e23 + 2.00277e24i −0.199301 + 0.904813i
\(508\) 5.38835e24 2.39157
\(509\) 3.85870e24i 1.68260i −0.540569 0.841299i \(-0.681791\pi\)
0.540569 0.841299i \(-0.318209\pi\)
\(510\) −2.79624e23 6.15919e22i −0.119796 0.0263871i
\(511\) 3.84851e23 0.161996
\(512\) 5.25289e24i 2.17254i
\(513\) −1.10319e24 + 1.44992e24i −0.448326 + 0.589236i
\(514\) 6.75437e23 0.269722
\(515\) 2.09777e24i 0.823178i
\(516\) 2.16441e24 9.82630e24i 0.834627 3.78916i
\(517\) −2.15847e24 −0.817958
\(518\) 1.15374e24i 0.429675i
\(519\) −2.55103e23 5.61907e22i −0.0933702 0.0205664i
\(520\) 5.42346e24 1.95095
\(521\) 1.16274e24i 0.411097i 0.978647 + 0.205549i \(0.0658979\pi\)
−0.978647 + 0.205549i \(0.934102\pi\)
\(522\) 4.43774e24 + 2.05467e24i 1.54215 + 0.714014i
\(523\) 1.12148e24 0.383069 0.191534 0.981486i \(-0.438654\pi\)
0.191534 + 0.981486i \(0.438654\pi\)
\(524\) 9.14270e24i 3.06968i
\(525\) 1.04237e23 4.73230e23i 0.0344023 0.156185i
\(526\) −1.06029e25 −3.43996
\(527\) 1.59728e23i 0.0509432i
\(528\) −5.88476e24 1.29622e24i −1.84512 0.406419i
\(529\) 2.91851e24 0.899622
\(530\) 5.81723e24i 1.76292i
\(531\) −1.30811e23 + 2.82530e23i −0.0389756 + 0.0841810i
\(532\) −1.42488e24 −0.417420
\(533\) 4.83754e24i 1.39341i
\(534\) −2.02477e24 + 9.19235e24i −0.573463 + 2.60349i
\(535\) 1.49577e24 0.416562
\(536\) 4.85840e24i 1.33049i
\(537\) 5.93536e23 + 1.30737e23i 0.159837 + 0.0352070i
\(538\) 8.47970e24 2.24564
\(539\) 3.31550e24i 0.863476i
\(540\) −4.21483e24 3.20690e24i −1.07953 0.821375i
\(541\) 2.23337e24 0.562582 0.281291 0.959622i \(-0.409237\pi\)
0.281291 + 0.959622i \(0.409237\pi\)
\(542\) 5.21540e24i 1.29209i
\(543\) −2.93960e22 + 1.33456e23i −0.00716291 + 0.0325192i
\(544\) 6.47279e23 0.155132
\(545\) 1.07092e24i 0.252459i
\(546\) 2.58905e24 + 5.70282e23i 0.600352 + 0.132238i
\(547\) 2.13233e24 0.486372 0.243186 0.969980i \(-0.421808\pi\)
0.243186 + 0.969980i \(0.421808\pi\)
\(548\) 4.80886e24i 1.07899i
\(549\) −3.66003e24 1.69459e24i −0.807855 0.374035i
\(550\) 5.06519e24 1.09985
\(551\) 3.23319e24i 0.690664i
\(552\) −7.79255e23 + 3.53777e24i −0.163768 + 0.743495i
\(553\) 7.07152e23 0.146213
\(554\) 3.36949e24i 0.685450i
\(555\) 2.76882e24 + 6.09880e23i 0.554188 + 0.122070i
\(556\) −1.80282e25 −3.55042
\(557\) 4.28440e24i 0.830221i −0.909771 0.415111i \(-0.863743\pi\)
0.909771 0.415111i \(-0.136257\pi\)
\(558\) 1.77660e24 3.83717e24i 0.338752 0.731649i
\(559\) −1.23772e25 −2.32228
\(560\) 1.58568e24i 0.292768i
\(561\) 1.25069e23 5.67804e23i 0.0227239 0.103165i
\(562\) 3.50435e23 0.0626587
\(563\) 6.48683e24i 1.14145i 0.821141 + 0.570725i \(0.193338\pi\)
−0.821141 + 0.570725i \(0.806662\pi\)
\(564\) 1.16559e25 + 2.56742e24i 2.01853 + 0.444616i
\(565\) 5.77176e23 0.0983722
\(566\) 4.04419e24i 0.678396i
\(567\) −9.52627e23 1.12283e24i −0.157281 0.185381i
\(568\) 1.44236e25 2.34389
\(569\) 1.13256e25i 1.81155i 0.423762 + 0.905774i \(0.360709\pi\)
−0.423762 + 0.905774i \(0.639291\pi\)
\(570\) 1.07801e24 4.89409e24i 0.169726 0.770545i
\(571\) 3.22177e23 0.0499309 0.0249654 0.999688i \(-0.492052\pi\)
0.0249654 + 0.999688i \(0.492052\pi\)
\(572\) 1.93623e25i 2.95388i
\(573\) −7.39933e23 1.62983e23i −0.111122 0.0244766i
\(574\) −3.00754e24 −0.444635
\(575\) 1.43202e24i 0.208420i
\(576\) 2.51105e24 + 1.16261e24i 0.359793 + 0.166583i
\(577\) 1.04474e25 1.47375 0.736877 0.676027i \(-0.236300\pi\)
0.736877 + 0.676027i \(0.236300\pi\)
\(578\) 1.29438e25i 1.79767i
\(579\) 2.15215e24 9.77065e24i 0.294284 1.33603i
\(580\) −9.39866e24 −1.26536
\(581\) 1.00885e24i 0.133734i
\(582\) −1.30665e25 2.87813e24i −1.70551 0.375667i
\(583\) −1.18125e25 −1.51818
\(584\) 1.26521e25i 1.60120i
\(585\) −2.73720e24 + 5.91190e24i −0.341117 + 0.736757i
\(586\) 9.47598e24 1.16291
\(587\) 1.94521e24i 0.235084i −0.993068 0.117542i \(-0.962498\pi\)
0.993068 0.117542i \(-0.0375015\pi\)
\(588\) −3.94367e24 + 1.79040e25i −0.469358 + 2.13086i
\(589\) 2.79563e24 0.327674
\(590\) 8.56397e23i 0.0988569i
\(591\) 1.21110e25 + 2.66765e24i 1.37686 + 0.303278i
\(592\) −1.78373e25 −1.99726
\(593\) 1.02435e25i 1.12968i 0.825200 + 0.564841i \(0.191063\pi\)
−0.825200 + 0.564841i \(0.808937\pi\)
\(594\) 9.32000e24 1.22493e25i 1.01237 1.33056i
\(595\) 1.52998e23 0.0163694
\(596\) 2.28618e25i 2.40932i
\(597\) −4.84096e22 + 2.19777e23i −0.00502531 + 0.0228146i
\(598\) 7.83461e24 0.801137
\(599\) 8.10173e24i 0.816086i −0.912963 0.408043i \(-0.866211\pi\)
0.912963 0.408043i \(-0.133789\pi\)
\(600\) −1.55575e25 3.42682e24i −1.54376 0.340040i
\(601\) −4.00759e24 −0.391754 −0.195877 0.980628i \(-0.562755\pi\)
−0.195877 + 0.980628i \(0.562755\pi\)
\(602\) 7.69499e24i 0.741036i
\(603\) 5.29595e24 + 2.45201e24i 0.502444 + 0.232631i
\(604\) 1.83856e25 1.71848
\(605\) 1.00234e24i 0.0923031i
\(606\) −4.54673e24 + 2.06419e25i −0.412521 + 1.87282i
\(607\) 1.18663e25 1.06076 0.530378 0.847761i \(-0.322050\pi\)
0.530378 + 0.847761i \(0.322050\pi\)
\(608\) 1.13289e25i 0.997832i
\(609\) −2.55195e24 5.62112e23i −0.221471 0.0487828i
\(610\) 1.10942e25 0.948695
\(611\) 1.46818e25i 1.23711i
\(612\) −1.35076e24 + 2.91743e24i −0.112154 + 0.242235i
\(613\) −1.12607e25 −0.921345 −0.460673 0.887570i \(-0.652392\pi\)
−0.460673 + 0.887570i \(0.652392\pi\)
\(614\) 3.32239e25i 2.67877i
\(615\) 1.58982e24 7.21768e24i 0.126320 0.573484i
\(616\) 6.84679e24 0.536119
\(617\) 2.90545e23i 0.0224206i 0.999937 + 0.0112103i \(0.00356842\pi\)
−0.999937 + 0.0112103i \(0.996432\pi\)
\(618\) −3.29224e25 7.25172e24i −2.50377 0.551499i
\(619\) −1.42594e25 −1.06877 −0.534385 0.845241i \(-0.679457\pi\)
−0.534385 + 0.845241i \(0.679457\pi\)
\(620\) 8.12670e24i 0.600329i
\(621\) −3.46310e24 2.63493e24i −0.252139 0.191843i
\(622\) 8.97433e24 0.644004
\(623\) 5.02965e24i 0.355750i
\(624\) 8.81681e24 4.00278e25i 0.614682 2.79062i
\(625\) 1.31831e24 0.0905936
\(626\) 1.92935e25i 1.30690i
\(627\) 9.93793e24 + 2.18900e24i 0.663572 + 0.146163i
\(628\) 9.74587e24 0.641481
\(629\) 1.72107e24i 0.111672i
\(630\) 3.67548e24 + 1.70174e24i 0.235098 + 0.108850i
\(631\) −1.34151e25 −0.845923 −0.422961 0.906148i \(-0.639009\pi\)
−0.422961 + 0.906148i \(0.639009\pi\)
\(632\) 2.32478e25i 1.44520i
\(633\) −2.71708e24 + 1.23354e25i −0.166521 + 0.755995i
\(634\) −4.39123e25 −2.65328
\(635\) 1.01265e25i 0.603249i
\(636\) 6.37884e25 + 1.40505e25i 3.74652 + 0.825235i
\(637\) 2.25518e25 1.30595
\(638\) 2.73147e25i 1.55959i
\(639\) −7.27951e24 + 1.57226e25i −0.409821 + 0.885147i
\(640\) 6.58975e24 0.365805
\(641\) 5.98895e24i 0.327815i 0.986476 + 0.163907i \(0.0524098\pi\)
−0.986476 + 0.163907i \(0.947590\pi\)
\(642\) 5.17066e24 2.34745e25i 0.279081 1.26701i
\(643\) −1.54893e25 −0.824391 −0.412196 0.911095i \(-0.635238\pi\)
−0.412196 + 0.911095i \(0.635238\pi\)
\(644\) 3.40328e24i 0.178618i
\(645\) −1.84669e25 4.06766e24i −0.955778 0.210527i
\(646\) −3.04212e24 −0.155268
\(647\) 1.51080e25i 0.760447i −0.924895 0.380223i \(-0.875847\pi\)
0.924895 0.380223i \(-0.124153\pi\)
\(648\) −3.69132e25 + 3.13178e25i −1.83234 + 1.55459i
\(649\) 1.73900e24 0.0851328
\(650\) 3.44531e25i 1.66345i
\(651\) −4.86039e23 + 2.20659e24i −0.0231442 + 0.105073i
\(652\) −2.90781e25 −1.36565
\(653\) 2.12528e25i 0.984457i −0.870466 0.492228i \(-0.836182\pi\)
0.870466 0.492228i \(-0.163818\pi\)
\(654\) 1.68070e25 + 3.70204e24i 0.767877 + 0.169138i
\(655\) 1.71822e25 0.774297
\(656\) 4.64978e25i 2.06680i
\(657\) 1.37915e25 + 6.38544e24i 0.604677 + 0.279964i
\(658\) −9.12778e24 −0.394759
\(659\) 4.11576e25i 1.75583i 0.478820 + 0.877913i \(0.341064\pi\)
−0.478820 + 0.877913i \(0.658936\pi\)
\(660\) −6.36327e24 + 2.88889e25i −0.267784 + 1.21572i
\(661\) 3.24714e25 1.34799 0.673996 0.738735i \(-0.264576\pi\)
0.673996 + 0.738735i \(0.264576\pi\)
\(662\) 6.47533e25i 2.65180i
\(663\) 3.86217e24 + 8.50709e23i 0.156030 + 0.0343684i
\(664\) 3.31662e25 1.32185
\(665\) 2.67783e24i 0.105290i
\(666\) 1.91428e25 4.13454e25i 0.742571 1.60383i
\(667\) −7.72236e24 −0.295541
\(668\) 7.62400e25i 2.87869i
\(669\) 3.66552e24 1.66412e25i 0.136553 0.619941i
\(670\) −1.60529e25 −0.590039
\(671\) 2.25278e25i 0.816990i
\(672\) −8.94192e24 1.96961e24i −0.319969 0.0704786i
\(673\) 1.10390e25 0.389758 0.194879 0.980827i \(-0.437569\pi\)
0.194879 + 0.980827i \(0.437569\pi\)
\(674\) 6.72141e25i 2.34165i
\(675\) 1.15873e25 1.52292e25i 0.398334 0.523530i
\(676\) −6.33384e25 −2.14856
\(677\) 2.74075e25i 0.917427i 0.888584 + 0.458714i \(0.151690\pi\)
−0.888584 + 0.458714i \(0.848310\pi\)
\(678\) 1.99522e24 9.05817e24i 0.0659058 0.299208i
\(679\) 7.14944e24 0.233047
\(680\) 5.02984e24i 0.161798i
\(681\) −4.78042e25 1.05297e25i −1.51755 0.334266i
\(682\) −2.36181e25 −0.739922
\(683\) 3.99739e25i 1.23592i 0.786210 + 0.617960i \(0.212041\pi\)
−0.786210 + 0.617960i \(0.787959\pi\)
\(684\) −5.10620e25 2.36416e25i −1.55809 0.721393i
\(685\) −9.03747e24 −0.272165
\(686\) 2.89220e25i 0.859630i
\(687\) 1.89339e24 8.59589e24i 0.0555431 0.252162i
\(688\) 1.18968e26 3.44456
\(689\) 8.03477e25i 2.29615i
\(690\) 1.16894e25 + 2.57478e24i 0.329723 + 0.0726271i
\(691\) −1.02801e25 −0.286218 −0.143109 0.989707i \(-0.545710\pi\)
−0.143109 + 0.989707i \(0.545710\pi\)
\(692\) 8.06773e24i 0.221716i
\(693\) −3.45555e24 + 7.46342e24i −0.0937385 + 0.202460i
\(694\) 7.43465e25 1.99079
\(695\) 3.38811e25i 0.895560i
\(696\) −1.84796e25 + 8.38960e25i −0.482179 + 2.18906i
\(697\) −4.48644e24 −0.115560
\(698\) 2.66897e25i 0.678648i
\(699\) −4.24430e25 9.34881e24i −1.06540 0.234672i
\(700\) 1.49661e25 0.370874
\(701\) 2.02392e25i 0.495143i 0.968870 + 0.247572i \(0.0796325\pi\)
−0.968870 + 0.247572i \(0.920367\pi\)
\(702\) 8.33189e25 + 6.33941e25i 2.01238 + 1.53114i
\(703\) 3.01229e25 0.718288
\(704\) 1.54557e25i 0.363861i
\(705\) 4.82505e24 2.19054e25i 0.112150 0.509155i
\(706\) −4.14124e25 −0.950361
\(707\) 1.12943e25i 0.255909i
\(708\) −9.39075e24 2.06848e24i −0.210088 0.0462755i
\(709\) −8.66215e25 −1.91342 −0.956708 0.291048i \(-0.905996\pi\)
−0.956708 + 0.291048i \(0.905996\pi\)
\(710\) 4.76577e25i 1.03946i
\(711\) 2.53415e25 + 1.17331e25i 0.545766 + 0.252688i
\(712\) −1.65351e26 −3.51631
\(713\) 6.67727e24i 0.140215i
\(714\) 5.28892e23 2.40114e24i 0.0109669 0.0497890i
\(715\) 3.63883e25 0.745088
\(716\) 1.87708e25i 0.379548i
\(717\) 2.50892e25 + 5.52633e24i 0.500973 + 0.110348i
\(718\) 4.63893e25 0.914740
\(719\) 8.53805e25i 1.66264i −0.555793 0.831320i \(-0.687585\pi\)
0.555793 0.831320i \(-0.312415\pi\)
\(720\) 2.63096e25 5.68245e25i 0.505967 1.09281i
\(721\) 1.80137e25 0.342125
\(722\) 4.38822e25i 0.823103i
\(723\) −7.51058e24 + 3.40976e25i −0.139133 + 0.631653i
\(724\) −4.22060e24 −0.0772196
\(725\) 3.39595e25i 0.613648i
\(726\) 1.57307e25 + 3.46495e24i 0.280748 + 0.0618397i
\(727\) 1.83358e25 0.323215 0.161607 0.986855i \(-0.448332\pi\)
0.161607 + 0.986855i \(0.448332\pi\)
\(728\) 4.65715e25i 0.810845i
\(729\) −1.55084e25 5.60436e25i −0.266698 0.963780i
\(730\) −4.18044e25 −0.710095
\(731\) 1.14789e25i 0.192594i
\(732\) 2.67960e25 1.21652e26i 0.444090 2.01614i
\(733\) 9.99901e25 1.63690 0.818449 0.574580i \(-0.194834\pi\)
0.818449 + 0.574580i \(0.194834\pi\)
\(734\) 6.45640e25i 1.04406i
\(735\) 3.36476e25 + 7.41148e24i 0.537488 + 0.118391i
\(736\) −2.70588e25 −0.426981
\(737\) 3.25971e25i 0.508126i
\(738\) −1.07778e26 4.99010e25i −1.65967 0.768426i
\(739\) 7.21830e24 0.109808 0.0549041 0.998492i \(-0.482515\pi\)
0.0549041 + 0.998492i \(0.482515\pi\)
\(740\) 8.75650e25i 1.31597i
\(741\) −1.48894e25 + 6.75972e25i −0.221062 + 1.00361i
\(742\) −4.99528e25 −0.732697
\(743\) 4.78088e25i 0.692802i 0.938087 + 0.346401i \(0.112596\pi\)
−0.938087 + 0.346401i \(0.887404\pi\)
\(744\) 7.25421e25 + 1.59786e25i 1.03856 + 0.228762i
\(745\) −4.29651e25 −0.607728
\(746\) 8.28324e25i 1.15758i
\(747\) −1.67389e25 + 3.61532e25i −0.231122 + 0.499185i
\(748\) 1.79570e25 0.244974
\(749\) 1.28442e25i 0.173129i
\(750\) −2.85348e25 + 1.29546e26i −0.380034 + 1.72533i
\(751\) −1.09528e26 −1.44134 −0.720670 0.693278i \(-0.756166\pi\)
−0.720670 + 0.693278i \(0.756166\pi\)
\(752\) 1.41119e26i 1.83496i
\(753\) 9.53277e25 + 2.09976e25i 1.22480 + 0.269783i
\(754\) 1.85793e26 2.35878
\(755\) 3.45527e25i 0.433470i
\(756\) 2.75378e25 3.61929e25i 0.34