Properties

Label 16.28.e.a.5.5
Level $16$
Weight $28$
Character 16.5
Analytic conductor $73.897$
Analytic rank $0$
Dimension $106$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,28,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 28, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 28);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 28 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(73.8968919741\)
Analytic rank: \(0\)
Dimension: \(106\)
Relative dimension: \(53\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 16.5
Dual form 16.28.e.a.13.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11221.9 + 2878.54i) q^{2} +(3.13170e6 - 3.13170e6i) q^{3} +(1.17646e8 - 6.46055e7i) q^{4} +(2.99171e9 + 2.99171e9i) q^{5} +(-2.61290e10 + 4.41585e10i) q^{6} +3.77678e11i q^{7} +(-1.13424e12 + 1.06365e12i) q^{8} -1.19895e13i q^{9} +O(q^{10})\) \(q+(-11221.9 + 2878.54i) q^{2} +(3.13170e6 - 3.13170e6i) q^{3} +(1.17646e8 - 6.46055e7i) q^{4} +(2.99171e9 + 2.99171e9i) q^{5} +(-2.61290e10 + 4.41585e10i) q^{6} +3.77678e11i q^{7} +(-1.13424e12 + 1.06365e12i) q^{8} -1.19895e13i q^{9} +(-4.21845e13 - 2.49610e13i) q^{10} +(8.16634e13 + 8.16634e13i) q^{11} +(1.66106e14 - 5.70757e14i) q^{12} +(1.00097e15 - 1.00097e15i) q^{13} +(-1.08716e15 - 4.23828e15i) q^{14} +1.87383e16 q^{15} +(9.66665e15 - 1.52011e16i) q^{16} -4.15045e16 q^{17} +(3.45124e16 + 1.34546e17i) q^{18} +(-6.12129e16 + 6.12129e16i) q^{19} +(5.45242e17 + 1.58681e17i) q^{20} +(1.18278e18 + 1.18278e18i) q^{21} +(-1.15149e18 - 6.81350e17i) q^{22} -2.23390e18i q^{23} +(-2.21088e17 + 6.88314e18i) q^{24} +1.04500e19i q^{25} +(-8.35152e18 + 1.41142e19i) q^{26} +(-1.36666e19 - 1.36666e19i) q^{27} +(2.44001e19 + 4.44322e19i) q^{28} +(6.99374e19 - 6.99374e19i) q^{29} +(-2.10280e20 + 5.39388e19i) q^{30} +1.12013e20 q^{31} +(-6.47215e19 + 1.98412e20i) q^{32} +5.11492e20 q^{33} +(4.65760e20 - 1.19472e20i) q^{34} +(-1.12990e21 + 1.12990e21i) q^{35} +(-7.74591e20 - 1.41052e21i) q^{36} +(7.62043e20 + 7.62043e20i) q^{37} +(5.10724e20 - 8.63131e20i) q^{38} -6.26951e21i q^{39} +(-6.57544e21 - 2.11205e20i) q^{40} +4.26521e21i q^{41} +(-1.66777e22 - 9.86836e21i) q^{42} +(-5.47987e21 - 5.47987e21i) q^{43} +(1.48833e22 + 4.33145e21i) q^{44} +(3.58692e22 - 3.58692e22i) q^{45} +(6.43037e21 + 2.50687e22i) q^{46} -1.88547e22 q^{47} +(-1.73323e22 - 7.78785e22i) q^{48} -7.69282e22 q^{49} +(-3.00808e22 - 1.17269e23i) q^{50} +(-1.29980e23 + 1.29980e23i) q^{51} +(5.30919e22 - 1.82429e23i) q^{52} +(1.66919e23 + 1.66919e23i) q^{53} +(1.92706e23 + 1.14026e23i) q^{54} +4.88626e23i q^{55} +(-4.01716e23 - 4.28379e23i) q^{56} +3.83402e23i q^{57} +(-5.83515e23 + 9.86150e23i) q^{58} +(7.00589e23 + 7.00589e23i) q^{59} +(2.20448e24 - 1.21060e24i) q^{60} +(-1.14353e24 + 1.14353e24i) q^{61} +(-1.25700e24 + 3.22433e23i) q^{62} +4.52819e24 q^{63} +(1.55164e23 - 2.41287e24i) q^{64} +5.98924e24 q^{65} +(-5.73992e24 + 1.47235e24i) q^{66} +(4.64819e23 - 4.64819e23i) q^{67} +(-4.88282e24 + 2.68142e24i) q^{68} +(-6.99592e24 - 6.99592e24i) q^{69} +(9.42721e24 - 1.59321e25i) q^{70} +1.39337e25i q^{71} +(1.27526e25 + 1.35991e25i) q^{72} -1.41951e25i q^{73} +(-1.07452e25 - 6.35802e24i) q^{74} +(3.27264e25 + 3.27264e25i) q^{75} +(-3.24675e24 + 1.11561e25i) q^{76} +(-3.08425e25 + 3.08425e25i) q^{77} +(1.80470e25 + 7.03560e25i) q^{78} -2.71335e24 q^{79} +(7.43971e25 - 1.65575e25i) q^{80} +5.82794e24 q^{81} +(-1.22776e25 - 4.78639e25i) q^{82} +(5.76649e24 - 5.76649e24i) q^{83} +(2.15562e26 + 6.27347e25i) q^{84} +(-1.24169e26 - 1.24169e26i) q^{85} +(7.72688e25 + 4.57207e25i) q^{86} -4.38047e26i q^{87} +(-1.79487e26 - 5.76517e24i) q^{88} +2.71721e26i q^{89} +(-2.99271e26 + 5.05773e26i) q^{90} +(3.78046e26 + 3.78046e26i) q^{91} +(-1.44322e26 - 2.62809e26i) q^{92} +(3.50791e26 - 3.50791e26i) q^{93} +(2.11586e26 - 5.42739e25i) q^{94} -3.66262e26 q^{95} +(4.18679e26 + 8.24056e26i) q^{96} +6.54574e26 q^{97} +(8.63283e26 - 2.21441e26i) q^{98} +(9.79108e26 - 9.79108e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11221.9 + 2878.54i −0.968641 + 0.248466i
\(3\) 3.13170e6 3.13170e6i 1.13408 1.13408i 0.144588 0.989492i \(-0.453814\pi\)
0.989492 0.144588i \(-0.0461858\pi\)
\(4\) 1.17646e8 6.46055e7i 0.876529 0.481349i
\(5\) 2.99171e9 + 2.99171e9i 1.09603 + 1.09603i 0.994870 + 0.101164i \(0.0322565\pi\)
0.101164 + 0.994870i \(0.467743\pi\)
\(6\) −2.61290e10 + 4.41585e10i −0.816736 + 1.38030i
\(7\) 3.77678e11i 1.47332i 0.676262 + 0.736662i \(0.263599\pi\)
−0.676262 + 0.736662i \(0.736401\pi\)
\(8\) −1.13424e12 + 1.06365e12i −0.729443 + 0.684042i
\(9\) 1.19895e13i 1.57228i
\(10\) −4.21845e13 2.49610e13i −1.33399 0.789335i
\(11\) 8.16634e13 + 8.16634e13i 0.713225 + 0.713225i 0.967209 0.253984i \(-0.0817410\pi\)
−0.253984 + 0.967209i \(0.581741\pi\)
\(12\) 1.66106e14 5.70757e14i 0.448167 1.53994i
\(13\) 1.00097e15 1.00097e15i 0.916617 0.916617i −0.0801650 0.996782i \(-0.525545\pi\)
0.996782 + 0.0801650i \(0.0255447\pi\)
\(14\) −1.08716e15 4.23828e15i −0.366071 1.42712i
\(15\) 1.87383e16 2.48598
\(16\) 9.66665e15 1.52011e16i 0.536607 0.843832i
\(17\) −4.15045e16 −1.01633 −0.508165 0.861260i \(-0.669676\pi\)
−0.508165 + 0.861260i \(0.669676\pi\)
\(18\) 3.45124e16 + 1.34546e17i 0.390657 + 1.52297i
\(19\) −6.12129e16 + 6.12129e16i −0.333941 + 0.333941i −0.854081 0.520140i \(-0.825880\pi\)
0.520140 + 0.854081i \(0.325880\pi\)
\(20\) 5.45242e17 + 1.58681e17i 1.48828 + 0.433131i
\(21\) 1.18278e18 + 1.18278e18i 1.67087 + 1.67087i
\(22\) −1.15149e18 6.81350e17i −0.868071 0.513646i
\(23\) 2.23390e18i 0.924141i −0.886843 0.462071i \(-0.847107\pi\)
0.886843 0.462071i \(-0.152893\pi\)
\(24\) −2.21088e17 + 6.88314e18i −0.0514889 + 1.60301i
\(25\) 1.04500e19i 1.40258i
\(26\) −8.35152e18 + 1.41142e19i −0.660124 + 1.11562i
\(27\) −1.36666e19 1.36666e19i −0.649008 0.649008i
\(28\) 2.44001e19 + 4.44322e19i 0.709182 + 1.29141i
\(29\) 6.99374e19 6.99374e19i 1.26572 1.26572i 0.317438 0.948279i \(-0.397178\pi\)
0.948279 0.317438i \(-0.102822\pi\)
\(30\) −2.10280e20 + 5.39388e19i −2.40802 + 0.617682i
\(31\) 1.12013e20 0.823919 0.411960 0.911202i \(-0.364844\pi\)
0.411960 + 0.911202i \(0.364844\pi\)
\(32\) −6.47215e19 + 1.98412e20i −0.310116 + 0.950699i
\(33\) 5.11492e20 1.61771
\(34\) 4.65760e20 1.19472e20i 0.984458 0.252523i
\(35\) −1.12990e21 + 1.12990e21i −1.61481 + 1.61481i
\(36\) −7.74591e20 1.41052e21i −0.756813 1.37815i
\(37\) 7.62043e20 + 7.62043e20i 0.514347 + 0.514347i 0.915855 0.401509i \(-0.131514\pi\)
−0.401509 + 0.915855i \(0.631514\pi\)
\(38\) 5.10724e20 8.63131e20i 0.240496 0.406442i
\(39\) 6.26951e21i 2.07903i
\(40\) −6.57544e21 2.11205e20i −1.54923 0.0497615i
\(41\) 4.26521e21i 0.720043i 0.932944 + 0.360022i \(0.117231\pi\)
−0.932944 + 0.360022i \(0.882769\pi\)
\(42\) −1.66777e22 9.86836e21i −2.03362 1.20332i
\(43\) −5.47987e21 5.47987e21i −0.486347 0.486347i 0.420804 0.907151i \(-0.361748\pi\)
−0.907151 + 0.420804i \(0.861748\pi\)
\(44\) 1.48833e22 + 4.33145e21i 0.968472 + 0.281853i
\(45\) 3.58692e22 3.58692e22i 1.72327 1.72327i
\(46\) 6.43037e21 + 2.50687e22i 0.229618 + 0.895161i
\(47\) −1.88547e22 −0.503614 −0.251807 0.967777i \(-0.581025\pi\)
−0.251807 + 0.967777i \(0.581025\pi\)
\(48\) −1.73323e22 7.78785e22i −0.348418 1.56553i
\(49\) −7.69282e22 −1.17068
\(50\) −3.00808e22 1.17269e23i −0.348493 1.35859i
\(51\) −1.29980e23 + 1.29980e23i −1.15260 + 1.15260i
\(52\) 5.30919e22 1.82429e23i 0.362229 1.24465i
\(53\) 1.66919e23 + 1.66919e23i 0.880607 + 0.880607i 0.993596 0.112990i \(-0.0360427\pi\)
−0.112990 + 0.993596i \(0.536043\pi\)
\(54\) 1.92706e23 + 1.14026e23i 0.789912 + 0.467399i
\(55\) 4.88626e23i 1.56344i
\(56\) −4.01716e23 4.28379e23i −1.00781 1.07471i
\(57\) 3.83402e23i 0.757431i
\(58\) −5.83515e23 + 9.86150e23i −0.911537 + 1.54051i
\(59\) 7.00589e23 + 7.00589e23i 0.868882 + 0.868882i 0.992349 0.123467i \(-0.0394012\pi\)
−0.123467 + 0.992349i \(0.539401\pi\)
\(60\) 2.20448e24 1.21060e24i 2.17903 1.19662i
\(61\) −1.14353e24 + 1.14353e24i −0.904260 + 0.904260i −0.995801 0.0915416i \(-0.970821\pi\)
0.0915416 + 0.995801i \(0.470821\pi\)
\(62\) −1.25700e24 + 3.22433e23i −0.798082 + 0.204716i
\(63\) 4.52819e24 2.31647
\(64\) 1.55164e23 2.41287e24i 0.0641743 0.997939i
\(65\) 5.98924e24 2.00928
\(66\) −5.73992e24 + 1.47235e24i −1.56698 + 0.401946i
\(67\) 4.64819e23 4.64819e23i 0.103580 0.103580i −0.653418 0.756997i \(-0.726666\pi\)
0.756997 + 0.653418i \(0.226666\pi\)
\(68\) −4.88282e24 + 2.68142e24i −0.890842 + 0.489209i
\(69\) −6.99592e24 6.99592e24i −1.04805 1.04805i
\(70\) 9.42721e24 1.59321e25i 1.16295 1.96540i
\(71\) 1.39337e25i 1.41931i 0.704548 + 0.709657i \(0.251150\pi\)
−0.704548 + 0.709657i \(0.748850\pi\)
\(72\) 1.27526e25 + 1.35991e25i 1.07550 + 1.14689i
\(73\) 1.41951e25i 0.993756i −0.867820 0.496878i \(-0.834480\pi\)
0.867820 0.496878i \(-0.165520\pi\)
\(74\) −1.07452e25 6.35802e24i −0.626015 0.370419i
\(75\) 3.27264e25 + 3.27264e25i 1.59064 + 1.59064i
\(76\) −3.24675e24 + 1.11561e25i −0.131967 + 0.453451i
\(77\) −3.08425e25 + 3.08425e25i −1.05081 + 1.05081i
\(78\) 1.80470e25 + 7.03560e25i 0.516569 + 2.01384i
\(79\) −2.71335e24 −0.0653942 −0.0326971 0.999465i \(-0.510410\pi\)
−0.0326971 + 0.999465i \(0.510410\pi\)
\(80\) 7.43971e25 1.65575e25i 1.51301 0.336729i
\(81\) 5.82794e24 0.100223
\(82\) −1.22776e25 4.78639e25i −0.178906 0.697463i
\(83\) 5.76649e24 5.76649e24i 0.0713440 0.0713440i −0.670534 0.741878i \(-0.733935\pi\)
0.741878 + 0.670534i \(0.233935\pi\)
\(84\) 2.15562e26 + 6.27347e25i 2.26883 + 0.660294i
\(85\) −1.24169e26 1.24169e26i −1.11393 1.11393i
\(86\) 7.72688e25 + 4.57207e25i 0.591936 + 0.350255i
\(87\) 4.38047e26i 2.87085i
\(88\) −1.79487e26 5.76517e24i −1.00813 0.0323814i
\(89\) 2.71721e26i 1.31026i 0.755515 + 0.655131i \(0.227387\pi\)
−0.755515 + 0.655131i \(0.772613\pi\)
\(90\) −2.99271e26 + 5.05773e26i −1.24105 + 2.09740i
\(91\) 3.78046e26 + 3.78046e26i 1.35047 + 1.35047i
\(92\) −1.44322e26 2.62809e26i −0.444834 0.810037i
\(93\) 3.50791e26 3.50791e26i 0.934391 0.934391i
\(94\) 2.11586e26 5.42739e25i 0.487821 0.125131i
\(95\) −3.66262e26 −0.732021
\(96\) 4.18679e26 + 8.24056e26i 0.726473 + 1.42986i
\(97\) 6.54574e26 0.987507 0.493753 0.869602i \(-0.335625\pi\)
0.493753 + 0.869602i \(0.335625\pi\)
\(98\) 8.63283e26 2.21441e26i 1.13397 0.290875i
\(99\) 9.79108e26 9.79108e26i 1.12139 1.12139i
\(100\) 6.75129e26 + 1.22940e27i 0.675129 + 1.22940i
\(101\) 8.73679e26 + 8.73679e26i 0.763859 + 0.763859i 0.977018 0.213158i \(-0.0683751\pi\)
−0.213158 + 0.977018i \(0.568375\pi\)
\(102\) 1.08447e27 1.83277e27i 0.830072 1.40284i
\(103\) 1.91785e27i 1.28681i 0.765528 + 0.643403i \(0.222478\pi\)
−0.765528 + 0.643403i \(0.777522\pi\)
\(104\) −7.06655e25 + 2.20003e27i −0.0416157 + 1.29562i
\(105\) 7.07703e27i 3.66265i
\(106\) −2.35364e27 1.39267e27i −1.07179 0.634190i
\(107\) −1.51836e27 1.51836e27i −0.609105 0.609105i 0.333607 0.942712i \(-0.391734\pi\)
−0.942712 + 0.333607i \(0.891734\pi\)
\(108\) −2.49076e27 7.24880e26i −0.881273 0.256475i
\(109\) −2.68650e27 + 2.68650e27i −0.839323 + 0.839323i −0.988770 0.149447i \(-0.952251\pi\)
0.149447 + 0.988770i \(0.452251\pi\)
\(110\) −1.40653e27 5.48333e27i −0.388461 1.51441i
\(111\) 4.77298e27 1.16662
\(112\) 5.74113e27 + 3.65088e27i 1.24324 + 0.790596i
\(113\) −3.40909e27 −0.654755 −0.327378 0.944894i \(-0.606165\pi\)
−0.327378 + 0.944894i \(0.606165\pi\)
\(114\) −1.10364e27 4.30251e27i −0.188196 0.733679i
\(115\) 6.68318e27 6.68318e27i 1.01289 1.01289i
\(116\) 3.70950e27 1.27462e28i 0.500187 1.71869i
\(117\) −1.20012e28 1.20012e28i −1.44117 1.44117i
\(118\) −9.87863e27 5.84529e27i −1.05752 0.625747i
\(119\) 1.56753e28i 1.49738i
\(120\) −2.12538e28 + 1.99309e28i −1.81338 + 1.70051i
\(121\) 2.27842e26i 0.0173793i
\(122\) 9.54088e27 1.61242e28i 0.651225 1.10058i
\(123\) 1.33574e28 + 1.33574e28i 0.816587 + 0.816587i
\(124\) 1.31778e28 7.23664e27i 0.722189 0.396592i
\(125\) −8.97345e27 + 8.97345e27i −0.441239 + 0.441239i
\(126\) −5.08150e28 + 1.30346e28i −2.24383 + 0.575565i
\(127\) 2.75899e28 1.09496 0.547482 0.836818i \(-0.315587\pi\)
0.547482 + 0.836818i \(0.315587\pi\)
\(128\) 5.20429e27 + 2.75237e28i 0.185792 + 0.982589i
\(129\) −3.43227e28 −1.10311
\(130\) −6.72109e28 + 1.72403e28i −1.94627 + 0.499239i
\(131\) −1.31168e28 + 1.31168e28i −0.342504 + 0.342504i −0.857308 0.514804i \(-0.827865\pi\)
0.514804 + 0.857308i \(0.327865\pi\)
\(132\) 6.01748e28 3.30452e28i 1.41797 0.778682i
\(133\) −2.31188e28 2.31188e28i −0.492003 0.492003i
\(134\) −3.87817e27 + 6.55417e27i −0.0745954 + 0.126067i
\(135\) 8.17729e28i 1.42267i
\(136\) 4.70762e28 4.41461e28i 0.741354 0.695211i
\(137\) 5.22657e26i 0.00745572i −0.999993 0.00372786i \(-0.998813\pi\)
0.999993 0.00372786i \(-0.00118662\pi\)
\(138\) 9.86458e28 + 5.83697e28i 1.27559 + 0.754779i
\(139\) −3.85785e28 3.85785e28i −0.452528 0.452528i 0.443665 0.896193i \(-0.353678\pi\)
−0.896193 + 0.443665i \(0.853678\pi\)
\(140\) −5.99302e28 + 2.05926e29i −0.638142 + 2.19272i
\(141\) −5.90473e28 + 5.90473e28i −0.571139 + 0.571139i
\(142\) −4.01086e28 1.56363e29i −0.352651 1.37480i
\(143\) 1.63486e29 1.30751
\(144\) −1.82255e29 1.15899e29i −1.32674 0.843695i
\(145\) 4.18464e29 2.77454
\(146\) 4.08611e28 + 1.59296e29i 0.246915 + 0.962593i
\(147\) −2.40917e29 + 2.40917e29i −1.32765 + 1.32765i
\(148\) 1.38883e29 + 4.04189e28i 0.698420 + 0.203260i
\(149\) −2.13398e29 2.13398e29i −0.979888 0.979888i 0.0199133 0.999802i \(-0.493661\pi\)
−0.999802 + 0.0199133i \(0.993661\pi\)
\(150\) −4.61457e29 2.73049e29i −1.93597 1.14554i
\(151\) 1.63581e29i 0.627398i −0.949522 0.313699i \(-0.898432\pi\)
0.949522 0.313699i \(-0.101568\pi\)
\(152\) 4.32143e27 1.34539e29i 0.0151614 0.472020i
\(153\) 4.97620e29i 1.59795i
\(154\) 2.57331e29 4.34893e29i 0.756767 1.27895i
\(155\) 3.35109e29 + 3.35109e29i 0.903043 + 0.903043i
\(156\) −4.05045e29 7.37582e29i −1.00074 1.82233i
\(157\) −6.63366e28 + 6.63366e28i −0.150351 + 0.150351i −0.778275 0.627924i \(-0.783905\pi\)
0.627924 + 0.778275i \(0.283905\pi\)
\(158\) 3.04490e28 7.81047e27i 0.0633435 0.0162482i
\(159\) 1.04548e30 1.99736
\(160\) −7.87218e29 + 3.99962e29i −1.38189 + 0.702101i
\(161\) 8.43696e29 1.36156
\(162\) −6.54007e28 + 1.67759e28i −0.0970800 + 0.0249020i
\(163\) −7.39399e28 + 7.39399e28i −0.101006 + 0.101006i −0.755804 0.654798i \(-0.772754\pi\)
0.654798 + 0.755804i \(0.272754\pi\)
\(164\) 2.75556e29 + 5.01784e29i 0.346592 + 0.631139i
\(165\) 1.53023e30 + 1.53023e30i 1.77306 + 1.77306i
\(166\) −4.81121e28 + 8.13103e28i −0.0513802 + 0.0868333i
\(167\) 7.93389e29i 0.781293i 0.920541 + 0.390646i \(0.127748\pi\)
−0.920541 + 0.390646i \(0.872252\pi\)
\(168\) −2.59961e30 8.35001e28i −2.36174 0.0758598i
\(169\) 8.11366e29i 0.680372i
\(170\) 1.75084e30 + 1.03599e30i 1.35577 + 0.802224i
\(171\) 7.33915e29 + 7.33915e29i 0.525047 + 0.525047i
\(172\) −9.98714e29 2.90654e29i −0.660400 0.192195i
\(173\) 2.02867e30 2.02867e30i 1.24048 1.24048i 0.280679 0.959802i \(-0.409440\pi\)
0.959802 0.280679i \(-0.0905596\pi\)
\(174\) 1.26093e30 + 4.91573e30i 0.713309 + 2.78082i
\(175\) −3.94674e30 −2.06645
\(176\) 2.03079e30 4.51965e29i 0.984564 0.219121i
\(177\) 4.38807e30 1.97076
\(178\) −7.82159e29 3.04923e30i −0.325556 1.26917i
\(179\) 8.39006e28 8.39006e28i 0.0323780 0.0323780i −0.690732 0.723110i \(-0.742712\pi\)
0.723110 + 0.690732i \(0.242712\pi\)
\(180\) 1.90251e30 6.53721e30i 0.681002 2.33999i
\(181\) −2.12428e30 2.12428e30i −0.705588 0.705588i 0.260017 0.965604i \(-0.416272\pi\)
−0.965604 + 0.260017i \(0.916272\pi\)
\(182\) −5.33062e30 3.15419e30i −1.64367 0.972576i
\(183\) 7.16237e30i 2.05101i
\(184\) 2.37608e30 + 2.53379e30i 0.632151 + 0.674109i
\(185\) 4.55961e30i 1.12748i
\(186\) −2.92679e30 + 4.94632e30i −0.672924 + 1.13725i
\(187\) −3.38940e30 3.38940e30i −0.724871 0.724871i
\(188\) −2.21817e30 + 1.21812e30i −0.441433 + 0.242414i
\(189\) 5.16157e30 5.16157e30i 0.956198 0.956198i
\(190\) 4.11017e30 1.05430e30i 0.709065 0.181882i
\(191\) 4.37011e30 0.702331 0.351166 0.936313i \(-0.385785\pi\)
0.351166 + 0.936313i \(0.385785\pi\)
\(192\) −7.07046e30 8.04232e30i −1.05896 1.20452i
\(193\) −1.93792e30 −0.270591 −0.135295 0.990805i \(-0.543198\pi\)
−0.135295 + 0.990805i \(0.543198\pi\)
\(194\) −7.34558e30 + 1.88422e30i −0.956539 + 0.245362i
\(195\) 1.87565e31 1.87565e31i 2.27869 2.27869i
\(196\) −9.05028e30 + 4.96999e30i −1.02614 + 0.563506i
\(197\) −1.15203e31 1.15203e31i −1.21946 1.21946i −0.967821 0.251641i \(-0.919030\pi\)
−0.251641 0.967821i \(-0.580970\pi\)
\(198\) −8.16908e30 + 1.38059e31i −0.807594 + 1.36485i
\(199\) 1.51292e31i 1.39733i 0.715448 + 0.698666i \(0.246223\pi\)
−0.715448 + 0.698666i \(0.753777\pi\)
\(200\) −1.11151e31 1.18529e31i −0.959422 1.02310i
\(201\) 2.91135e30i 0.234935i
\(202\) −1.23193e31 7.28945e30i −0.929698 0.550112i
\(203\) 2.64138e31 + 2.64138e31i 1.86481 + 1.86481i
\(204\) −6.89416e30 + 2.36890e31i −0.455485 + 1.56509i
\(205\) −1.27603e31 + 1.27603e31i −0.789192 + 0.789192i
\(206\) −5.52062e30 2.15220e31i −0.319728 1.24645i
\(207\) −2.67835e31 −1.45301
\(208\) −5.53987e30 2.48920e31i −0.281608 1.26533i
\(209\) −9.99772e30 −0.476350
\(210\) −2.03715e31 7.94180e31i −0.910045 3.54779i
\(211\) 1.31463e31 1.31463e31i 0.550797 0.550797i −0.375874 0.926671i \(-0.622657\pi\)
0.926671 + 0.375874i \(0.122657\pi\)
\(212\) 3.04212e31 + 8.85343e30i 1.19576 + 0.347999i
\(213\) 4.36362e31 + 4.36362e31i 1.60962 + 1.60962i
\(214\) 2.14095e31 + 1.26682e31i 0.741346 + 0.438662i
\(215\) 3.27883e31i 1.06611i
\(216\) 3.00377e31 + 9.64818e29i 0.917362 + 0.0294659i
\(217\) 4.23047e31i 1.21390i
\(218\) 2.24145e31 3.78809e31i 0.604459 1.02155i
\(219\) −4.44549e31 4.44549e31i −1.12700 1.12700i
\(220\) 3.15679e31 + 5.74848e31i 0.752558 + 1.37040i
\(221\) −4.15449e31 + 4.15449e31i −0.931584 + 0.931584i
\(222\) −5.35621e31 + 1.37392e31i −1.13004 + 0.289866i
\(223\) −5.43366e30 −0.107889 −0.0539444 0.998544i \(-0.517179\pi\)
−0.0539444 + 0.998544i \(0.517179\pi\)
\(224\) −7.49358e31 2.44439e31i −1.40069 0.456901i
\(225\) 1.25291e32 2.20524
\(226\) 3.82565e31 9.81319e30i 0.634223 0.162684i
\(227\) 6.60671e31 6.60671e31i 1.03190 1.03190i 0.0324226 0.999474i \(-0.489678\pi\)
0.999474 0.0324226i \(-0.0103222\pi\)
\(228\) 2.47699e31 + 4.51056e31i 0.364589 + 0.663911i
\(229\) −8.84126e31 8.84126e31i −1.22669 1.22669i −0.965208 0.261482i \(-0.915789\pi\)
−0.261482 0.965208i \(-0.584211\pi\)
\(230\) −5.57604e31 + 9.42360e31i −0.729458 + 1.23280i
\(231\) 1.93179e32i 2.38341i
\(232\) −4.93735e30 + 1.53715e32i −0.0574654 + 1.78907i
\(233\) 2.06242e31i 0.226503i −0.993566 0.113251i \(-0.963873\pi\)
0.993566 0.113251i \(-0.0361265\pi\)
\(234\) 1.69223e32 + 1.00131e32i 1.75406 + 1.03790i
\(235\) −5.64076e31 5.64076e31i −0.551978 0.551978i
\(236\) 1.27683e32 + 3.71594e31i 1.17984 + 0.343365i
\(237\) −8.49740e30 + 8.49740e30i −0.0741623 + 0.0741623i
\(238\) 4.51220e31 + 1.75907e32i 0.372048 + 1.45042i
\(239\) 1.28995e32 1.00508 0.502542 0.864553i \(-0.332398\pi\)
0.502542 + 0.864553i \(0.332398\pi\)
\(240\) 1.81136e32 2.84843e32i 1.33399 2.09775i
\(241\) −9.30064e31 −0.647564 −0.323782 0.946132i \(-0.604954\pi\)
−0.323782 + 0.946132i \(0.604954\pi\)
\(242\) −6.55853e29 2.55683e30i −0.00431816 0.0168343i
\(243\) 1.22467e32 1.22467e32i 0.762669 0.762669i
\(244\) −6.06529e31 + 2.08409e32i −0.357346 + 1.22787i
\(245\) −2.30147e32 2.30147e32i −1.28311 1.28311i
\(246\) −1.88345e32 1.11446e32i −0.993873 0.588085i
\(247\) 1.22545e32i 0.612191i
\(248\) −1.27050e32 + 1.19142e32i −0.601002 + 0.563595i
\(249\) 3.61179e31i 0.161820i
\(250\) 7.48690e31 1.26530e32i 0.317769 0.537035i
\(251\) −1.02833e32 1.02833e32i −0.413557 0.413557i 0.469419 0.882976i \(-0.344463\pi\)
−0.882976 + 0.469419i \(0.844463\pi\)
\(252\) 5.32722e32 2.92546e32i 2.03046 1.11503i
\(253\) 1.82428e32 1.82428e32i 0.659121 0.659121i
\(254\) −3.09612e32 + 7.94185e31i −1.06063 + 0.272061i
\(255\) −7.77722e32 −2.52657
\(256\) −1.37630e32 2.93888e32i −0.424106 0.905613i
\(257\) 2.65715e31 0.0776819 0.0388409 0.999245i \(-0.487633\pi\)
0.0388409 + 0.999245i \(0.487633\pi\)
\(258\) 3.85167e32 9.87992e31i 1.06852 0.274086i
\(259\) −2.87807e32 + 2.87807e32i −0.757799 + 0.757799i
\(260\) 7.04609e32 3.86938e32i 1.76120 0.967166i
\(261\) −8.38518e32 8.38518e32i −1.99006 1.99006i
\(262\) 1.09439e32 1.84953e32i 0.246663 0.416864i
\(263\) 4.78124e32i 1.02362i 0.859099 + 0.511809i \(0.171025\pi\)
−0.859099 + 0.511809i \(0.828975\pi\)
\(264\) −5.80156e32 + 5.44046e32i −1.18003 + 1.10658i
\(265\) 9.98746e32i 1.93035i
\(266\) 3.25986e32 + 1.92889e32i 0.598820 + 0.354328i
\(267\) 8.50950e32 + 8.50950e32i 1.48594 + 1.48594i
\(268\) 2.46541e31 8.47138e31i 0.0409326 0.140648i
\(269\) 3.46601e32 3.46601e32i 0.547235 0.547235i −0.378405 0.925640i \(-0.623527\pi\)
0.925640 + 0.378405i \(0.123527\pi\)
\(270\) 2.35386e32 + 9.17650e32i 0.353485 + 1.37805i
\(271\) −8.20273e32 −1.17185 −0.585926 0.810364i \(-0.699269\pi\)
−0.585926 + 0.810364i \(0.699269\pi\)
\(272\) −4.01209e32 + 6.30915e32i −0.545369 + 0.857611i
\(273\) 2.36786e33 3.06309
\(274\) 1.50449e30 + 5.86523e30i 0.00185249 + 0.00722191i
\(275\) −8.53385e32 + 8.53385e32i −1.00035 + 1.00035i
\(276\) −1.27502e33 3.71065e32i −1.42312 0.414169i
\(277\) −7.41105e32 7.41105e32i −0.787776 0.787776i 0.193353 0.981129i \(-0.438064\pi\)
−0.981129 + 0.193353i \(0.938064\pi\)
\(278\) 5.43974e32 + 3.21875e32i 0.550774 + 0.325899i
\(279\) 1.34298e33i 1.29543i
\(280\) 7.97673e31 2.48340e33i 0.0733148 2.28251i
\(281\) 1.17693e33i 1.03090i −0.856920 0.515449i \(-0.827625\pi\)
0.856920 0.515449i \(-0.172375\pi\)
\(282\) 4.92655e32 8.32594e32i 0.411320 0.695137i
\(283\) −1.40700e33 1.40700e33i −1.11989 1.11989i −0.991757 0.128136i \(-0.959101\pi\)
−0.128136 0.991757i \(-0.540899\pi\)
\(284\) 9.00193e32 + 1.63924e33i 0.683184 + 1.24407i
\(285\) −1.14702e33 + 1.14702e33i −0.830170 + 0.830170i
\(286\) −1.83463e33 + 4.70601e32i −1.26650 + 0.324871i
\(287\) −1.61088e33 −1.06086
\(288\) 2.37887e33 + 7.75981e32i 1.49476 + 0.487588i
\(289\) 5.49090e31 0.0329248
\(290\) −4.69598e33 + 1.20457e33i −2.68753 + 0.689378i
\(291\) 2.04993e33 2.04993e33i 1.11991 1.11991i
\(292\) −9.17082e32 1.66999e33i −0.478343 0.871056i
\(293\) −9.79971e32 9.79971e32i −0.488091 0.488091i 0.419613 0.907703i \(-0.362166\pi\)
−0.907703 + 0.419613i \(0.862166\pi\)
\(294\) 2.01006e33 3.39704e33i 0.956137 1.61589i
\(295\) 4.19191e33i 1.90465i
\(296\) −1.67489e33 5.37977e31i −0.727021 0.0233521i
\(297\) 2.23212e33i 0.925777i
\(298\) 3.00902e33 + 1.78047e33i 1.19263 + 0.705691i
\(299\) −2.23608e33 2.23608e33i −0.847083 0.847083i
\(300\) 5.96443e33 + 1.73582e33i 2.15989 + 0.628589i
\(301\) 2.06963e33 2.06963e33i 0.716547 0.716547i
\(302\) 4.70873e32 + 1.83569e33i 0.155887 + 0.607723i
\(303\) 5.47221e33 1.73256
\(304\) 3.38782e32 + 1.52223e33i 0.102595 + 0.460985i
\(305\) −6.84218e33 −1.98220
\(306\) −1.43242e33 5.58425e33i −0.397036 1.54784i
\(307\) −2.78215e33 + 2.78215e33i −0.737927 + 0.737927i −0.972176 0.234250i \(-0.924737\pi\)
0.234250 + 0.972176i \(0.424737\pi\)
\(308\) −1.63589e33 + 5.62108e33i −0.415260 + 1.42687i
\(309\) 6.00615e33 + 6.00615e33i 1.45934 + 1.45934i
\(310\) −4.72520e33 2.79595e33i −1.09910 0.650349i
\(311\) 1.72573e33i 0.384332i −0.981362 0.192166i \(-0.938449\pi\)
0.981362 0.192166i \(-0.0615512\pi\)
\(312\) 6.66854e33 + 7.11115e33i 1.42215 + 1.51654i
\(313\) 3.35883e33i 0.686024i −0.939331 0.343012i \(-0.888553\pi\)
0.939331 0.343012i \(-0.111447\pi\)
\(314\) 5.53472e32 9.35377e32i 0.108279 0.182994i
\(315\) 1.35470e34 + 1.35470e34i 2.53893 + 2.53893i
\(316\) −3.19214e32 + 1.75297e32i −0.0573199 + 0.0314774i
\(317\) 9.80948e32 9.80948e32i 0.168790 0.168790i −0.617657 0.786447i \(-0.711918\pi\)
0.786447 + 0.617657i \(0.211918\pi\)
\(318\) −1.17323e34 + 3.00946e33i −1.93472 + 0.496275i
\(319\) 1.14227e34 1.80548
\(320\) 7.68279e33 6.75439e33i 1.16411 1.02344i
\(321\) −9.51008e33 −1.38155
\(322\) −9.46789e33 + 2.42861e33i −1.31886 + 0.338301i
\(323\) 2.54061e33 2.54061e33i 0.339394 0.339394i
\(324\) 6.85632e32 3.76517e32i 0.0878483 0.0482422i
\(325\) 1.04602e34 + 1.04602e34i 1.28563 + 1.28563i
\(326\) 6.16909e32 1.04259e33i 0.0727418 0.122935i
\(327\) 1.68267e34i 1.90372i
\(328\) −4.53668e33 4.83779e33i −0.492540 0.525231i
\(329\) 7.12099e33i 0.741986i
\(330\) −2.15770e34 1.27673e34i −2.15801 1.27691i
\(331\) 1.85950e33 + 1.85950e33i 0.178532 + 0.178532i 0.790716 0.612183i \(-0.209709\pi\)
−0.612183 + 0.790716i \(0.709709\pi\)
\(332\) 3.05856e32 1.05095e33i 0.0281938 0.0968765i
\(333\) 9.13655e33 9.13655e33i 0.808695 0.808695i
\(334\) −2.28380e33 8.90336e33i −0.194125 0.756792i
\(335\) 2.78120e33 0.227053
\(336\) 2.94130e34 6.54605e33i 2.30653 0.513333i
\(337\) 9.82014e33 0.739799 0.369900 0.929072i \(-0.379392\pi\)
0.369900 + 0.929072i \(0.379392\pi\)
\(338\) 2.33555e33 + 9.10510e33i 0.169049 + 0.659036i
\(339\) −1.06763e34 + 1.06763e34i −0.742545 + 0.742545i
\(340\) −2.26300e34 6.58596e33i −1.51258 0.440204i
\(341\) 9.14735e33 + 9.14735e33i 0.587640 + 0.587640i
\(342\) −1.03486e34 6.12334e33i −0.639039 0.378126i
\(343\) 4.23599e33i 0.251469i
\(344\) 1.20442e34 + 3.86861e32i 0.687444 + 0.0220809i
\(345\) 4.18595e34i 2.29740i
\(346\) −1.69260e34 + 2.86053e34i −0.893363 + 1.50980i
\(347\) −5.31478e32 5.31478e32i −0.0269797 0.0269797i 0.693488 0.720468i \(-0.256073\pi\)
−0.720468 + 0.693488i \(0.756073\pi\)
\(348\) −2.83002e34 5.15343e34i −1.38188 2.51638i
\(349\) −2.18417e33 + 2.18417e33i −0.102599 + 0.102599i −0.756543 0.653944i \(-0.773113\pi\)
0.653944 + 0.756543i \(0.273113\pi\)
\(350\) 4.42901e34 1.13609e34i 2.00165 0.513443i
\(351\) −2.73598e34 −1.18978
\(352\) −2.14884e34 + 1.09176e34i −0.899244 + 0.456880i
\(353\) 2.47069e33 0.0995084 0.0497542 0.998761i \(-0.484156\pi\)
0.0497542 + 0.998761i \(0.484156\pi\)
\(354\) −4.92427e34 + 1.26312e34i −1.90896 + 0.489668i
\(355\) −4.16855e34 + 4.16855e34i −1.55561 + 1.55561i
\(356\) 1.75547e34 + 3.19668e34i 0.630693 + 1.14848i
\(357\) −4.90905e34 4.90905e34i −1.69815 1.69815i
\(358\) −7.00016e32 + 1.18304e33i −0.0233178 + 0.0394074i
\(359\) 4.81366e34i 1.54419i −0.635508 0.772094i \(-0.719209\pi\)
0.635508 0.772094i \(-0.280791\pi\)
\(360\) −2.53225e33 + 7.88365e34i −0.0782389 + 2.43581i
\(361\) 2.61066e34i 0.776967i
\(362\) 2.99533e34 + 1.77237e34i 0.858775 + 0.508146i
\(363\) 7.13535e32 + 7.13535e32i 0.0197095 + 0.0197095i
\(364\) 6.88994e34 + 2.00516e34i 1.83378 + 0.533681i
\(365\) 4.24676e34 4.24676e34i 1.08919 1.08919i
\(366\) −2.06172e34 8.03756e34i −0.509605 1.98669i
\(367\) −1.49278e34 −0.355634 −0.177817 0.984064i \(-0.556903\pi\)
−0.177817 + 0.984064i \(0.556903\pi\)
\(368\) −3.39578e34 2.15944e34i −0.779820 0.495901i
\(369\) 5.11380e34 1.13211
\(370\) −1.31250e34 5.11677e34i −0.280141 1.09213i
\(371\) −6.30417e34 + 6.30417e34i −1.29742 + 1.29742i
\(372\) 1.86060e34 6.39321e34i 0.369253 1.26879i
\(373\) 2.02249e34 + 2.02249e34i 0.387095 + 0.387095i 0.873650 0.486555i \(-0.161747\pi\)
−0.486555 + 0.873650i \(0.661747\pi\)
\(374\) 4.77921e34 + 2.82791e34i 0.882245 + 0.522034i
\(375\) 5.62044e34i 1.00080i
\(376\) 2.13858e34 2.00547e34i 0.367358 0.344493i
\(377\) 1.40011e35i 2.32035i
\(378\) −4.30650e34 + 7.27806e34i −0.688629 + 1.16379i
\(379\) 6.53646e34 + 6.53646e34i 1.00859 + 1.00859i 0.999963 + 0.00862339i \(0.00274494\pi\)
0.00862339 + 0.999963i \(0.497255\pi\)
\(380\) −4.30892e34 + 2.36626e34i −0.641637 + 0.352357i
\(381\) 8.64034e34 8.64034e34i 1.24178 1.24178i
\(382\) −4.90411e34 + 1.25795e34i −0.680307 + 0.174505i
\(383\) 1.12805e35 1.51058 0.755292 0.655389i \(-0.227495\pi\)
0.755292 + 0.655389i \(0.227495\pi\)
\(384\) 1.02494e35 + 6.98977e34i 1.32504 + 0.903632i
\(385\) −1.84543e35 −2.30345
\(386\) 2.17472e34 5.57838e33i 0.262105 0.0672326i
\(387\) −6.57012e34 + 6.57012e34i −0.764672 + 0.764672i
\(388\) 7.70078e34 4.22891e34i 0.865579 0.475335i
\(389\) −8.87777e34 8.87777e34i −0.963794 0.963794i 0.0355729 0.999367i \(-0.488674\pi\)
−0.999367 + 0.0355729i \(0.988674\pi\)
\(390\) −1.56493e35 + 2.64476e35i −1.64105 + 2.77341i
\(391\) 9.27169e34i 0.939232i
\(392\) 8.72553e34 8.18245e34i 0.853945 0.800795i
\(393\) 8.21559e34i 0.776854i
\(394\) 1.62441e35 + 9.61180e34i 1.48421 + 0.878225i
\(395\) −8.11753e33 8.11753e33i −0.0716742 0.0716742i
\(396\) 5.19321e34 1.78444e35i 0.443150 1.52271i
\(397\) −9.59636e34 + 9.59636e34i −0.791470 + 0.791470i −0.981733 0.190263i \(-0.939066\pi\)
0.190263 + 0.981733i \(0.439066\pi\)
\(398\) −4.35500e34 1.69779e35i −0.347190 1.35351i
\(399\) −1.44802e35 −1.11594
\(400\) 1.58852e35 + 1.01017e35i 1.18354 + 0.752633i
\(401\) 2.64669e35 1.90657 0.953287 0.302066i \(-0.0976764\pi\)
0.953287 + 0.302066i \(0.0976764\pi\)
\(402\) 8.38044e33 + 3.26710e34i 0.0583734 + 0.227568i
\(403\) 1.12122e35 1.12122e35i 0.755218 0.755218i
\(404\) 1.59229e35 + 4.63401e34i 1.03723 + 0.301862i
\(405\) 1.74355e34 + 1.74355e34i 0.109848 + 0.109848i
\(406\) −3.72447e35 2.20381e35i −2.26967 1.34299i
\(407\) 1.24462e35i 0.733690i
\(408\) 9.17614e33 2.85681e35i 0.0523297 1.62918i
\(409\) 7.01740e34i 0.387179i −0.981083 0.193589i \(-0.937987\pi\)
0.981083 0.193589i \(-0.0620130\pi\)
\(410\) 1.06464e35 1.79926e35i 0.568356 0.960530i
\(411\) −1.63681e33 1.63681e33i −0.00845538 0.00845538i
\(412\) 1.23904e35 + 2.25627e35i 0.619402 + 1.12792i
\(413\) −2.64597e35 + 2.64597e35i −1.28014 + 1.28014i
\(414\) 3.00562e35 7.70973e34i 1.40744 0.361023i
\(415\) 3.45033e34 0.156391
\(416\) 1.33821e35 + 2.63390e35i 0.587169 + 1.15568i
\(417\) −2.41633e35 −1.02641
\(418\) 1.12194e35 2.87788e34i 0.461412 0.118357i
\(419\) −1.69063e35 + 1.69063e35i −0.673222 + 0.673222i −0.958457 0.285236i \(-0.907928\pi\)
0.285236 + 0.958457i \(0.407928\pi\)
\(420\) 4.57215e35 + 8.32583e35i 1.76301 + 3.21042i
\(421\) −2.38107e35 2.38107e35i −0.889127 0.889127i 0.105312 0.994439i \(-0.466416\pi\)
−0.994439 + 0.105312i \(0.966416\pi\)
\(422\) −1.09685e35 + 1.85369e35i −0.396670 + 0.670378i
\(423\) 2.26059e35i 0.791821i
\(424\) −3.66870e35 1.17839e34i −1.24472 0.0399808i
\(425\) 4.33723e35i 1.42548i
\(426\) −6.15291e35 3.64074e35i −1.95907 1.15920i
\(427\) −4.31884e35 4.31884e35i −1.33227 1.33227i
\(428\) −2.76722e35 8.05340e34i −0.827091 0.240707i
\(429\) 5.11990e35 5.11990e35i 1.48282 1.48282i
\(430\) 9.43825e34 + 3.67948e35i 0.264891 + 1.03267i
\(431\) −4.80569e34 −0.130711 −0.0653556 0.997862i \(-0.520818\pi\)
−0.0653556 + 0.997862i \(0.520818\pi\)
\(432\) −3.39858e35 + 7.56375e34i −0.895916 + 0.199392i
\(433\) −3.31020e34 −0.0845799 −0.0422900 0.999105i \(-0.513465\pi\)
−0.0422900 + 0.999105i \(0.513465\pi\)
\(434\) −1.21776e35 4.74741e35i −0.301613 1.17583i
\(435\) 1.31051e36 1.31051e36i 3.14655 3.14655i
\(436\) −1.42493e35 + 4.89618e35i −0.331684 + 1.13970i
\(437\) 1.36744e35 + 1.36744e35i 0.308609 + 0.308609i
\(438\) 6.26834e35 + 3.70904e35i 1.37168 + 0.811636i
\(439\) 7.92134e35i 1.68084i −0.541932 0.840422i \(-0.682307\pi\)
0.541932 0.840422i \(-0.317693\pi\)
\(440\) −5.19725e35 5.54221e35i −1.06946 1.14044i
\(441\) 9.22335e35i 1.84063i
\(442\) 3.46625e35 5.85803e35i 0.670903 1.13384i
\(443\) 4.84742e35 + 4.84742e35i 0.910040 + 0.910040i 0.996275 0.0862350i \(-0.0274836\pi\)
−0.0862350 + 0.996275i \(0.527484\pi\)
\(444\) 5.61521e35 3.08361e35i 1.02258 0.561551i
\(445\) −8.12909e35 + 8.12909e35i −1.43609 + 1.43609i
\(446\) 6.09761e34 1.56410e34i 0.104506 0.0268067i
\(447\) −1.33660e36 −2.22254
\(448\) 9.11287e35 + 5.86019e34i 1.47029 + 0.0945494i
\(449\) 9.85150e34 0.154233 0.0771164 0.997022i \(-0.475429\pi\)
0.0771164 + 0.997022i \(0.475429\pi\)
\(450\) −1.40601e36 + 3.60655e35i −2.13609 + 0.547928i
\(451\) −3.48312e35 + 3.48312e35i −0.513553 + 0.513553i
\(452\) −4.01065e35 + 2.20246e35i −0.573912 + 0.315166i
\(453\) −5.12286e35 5.12286e35i −0.711520 0.711520i
\(454\) −5.51224e35 + 9.31577e35i −0.743146 + 1.25593i
\(455\) 2.26200e36i 2.96033i
\(456\) −4.07804e35 4.34871e35i −0.518115 0.552503i
\(457\) 4.84383e35i 0.597476i 0.954335 + 0.298738i \(0.0965657\pi\)
−0.954335 + 0.298738i \(0.903434\pi\)
\(458\) 1.24666e36 + 7.37661e35i 1.49301 + 0.883431i
\(459\) 5.67225e35 + 5.67225e35i 0.659605 + 0.659605i
\(460\) 3.54477e35 1.21802e36i 0.400274 1.37538i
\(461\) 4.63789e35 4.63789e35i 0.508579 0.508579i −0.405511 0.914090i \(-0.632906\pi\)
0.914090 + 0.405511i \(0.132906\pi\)
\(462\) −5.56073e35 2.16784e36i −0.592196 2.30867i
\(463\) 3.00115e34 0.0310416 0.0155208 0.999880i \(-0.495059\pi\)
0.0155208 + 0.999880i \(0.495059\pi\)
\(464\) −3.87067e35 1.73919e36i −0.388860 1.74725i
\(465\) 2.09893e36 2.04825
\(466\) 5.93677e34 + 2.31444e35i 0.0562782 + 0.219400i
\(467\) −1.91323e35 + 1.91323e35i −0.176193 + 0.176193i −0.789694 0.613501i \(-0.789761\pi\)
0.613501 + 0.789694i \(0.289761\pi\)
\(468\) −2.18724e36 6.36548e35i −1.95694 0.569524i
\(469\) 1.75552e35 + 1.75552e35i 0.152606 + 0.152606i
\(470\) 7.95374e35 + 4.70631e35i 0.671816 + 0.397520i
\(471\) 4.15493e35i 0.341021i
\(472\) −1.53982e36 4.94593e34i −1.22815 0.0394485i
\(473\) 8.95011e35i 0.693750i
\(474\) 7.08971e34 1.19817e35i 0.0534098 0.0902634i
\(475\) −6.39676e35 6.39676e35i −0.468378 0.468378i
\(476\) −1.01271e36 1.84413e36i −0.720762 1.31250i
\(477\) 2.00129e36 2.00129e36i 1.38456 1.38456i
\(478\) −1.44758e36 + 3.71318e35i −0.973564 + 0.249729i
\(479\) −1.37145e36 −0.896704 −0.448352 0.893857i \(-0.647989\pi\)
−0.448352 + 0.893857i \(0.647989\pi\)
\(480\) −1.21277e36 + 3.71790e36i −0.770941 + 2.36342i
\(481\) 1.52557e36 0.942917
\(482\) 1.04371e36 2.67723e35i 0.627257 0.160898i
\(483\) 2.64221e36 2.64221e36i 1.54412 1.54412i
\(484\) 1.47199e34 + 2.68047e34i 0.00836550 + 0.0152335i
\(485\) 1.95829e36 + 1.95829e36i 1.08234 + 1.08234i
\(486\) −1.02179e36 + 1.72685e36i −0.549254 + 0.928249i
\(487\) 7.45130e35i 0.389575i −0.980845 0.194787i \(-0.937598\pi\)
0.980845 0.194787i \(-0.0624017\pi\)
\(488\) 8.07292e34 2.51334e36i 0.0410547 1.27816i
\(489\) 4.63116e35i 0.229097i
\(490\) 3.24518e36 + 1.92020e36i 1.56168 + 0.924060i
\(491\) 1.35757e36 + 1.35757e36i 0.635566 + 0.635566i 0.949458 0.313893i \(-0.101633\pi\)
−0.313893 + 0.949458i \(0.601633\pi\)
\(492\) 2.43440e36 + 7.08479e35i 1.10883 + 0.322699i
\(493\) −2.90271e36 + 2.90271e36i −1.28638 + 1.28638i
\(494\) −3.52751e35 1.37519e36i −0.152109 0.592993i
\(495\) 5.85840e36 2.45815
\(496\) 1.08279e36 1.70272e36i 0.442121 0.695250i
\(497\) −5.26244e36 −2.09111
\(498\) 1.03967e35 + 4.05313e35i 0.0402067 + 0.156745i
\(499\) −3.19342e36 + 3.19342e36i −1.20199 + 1.20199i −0.228423 + 0.973562i \(0.573357\pi\)
−0.973562 + 0.228423i \(0.926643\pi\)
\(500\) −4.75954e35 + 1.63542e36i −0.174369 + 0.599149i
\(501\) 2.48466e36 + 2.48466e36i 0.886049 + 0.886049i
\(502\) 1.44999e36 + 8.57972e35i 0.503343 + 0.297833i
\(503\) 4.92464e36i 1.66420i −0.554622 0.832102i \(-0.687137\pi\)
0.554622 0.832102i \(-0.312863\pi\)
\(504\) −5.13607e36 + 4.81639e36i −1.68973 + 1.58456i
\(505\) 5.22758e36i 1.67443i
\(506\) −1.52207e36 + 2.57232e36i −0.474682 + 0.802220i
\(507\) −2.54096e36 2.54096e36i −0.771596 0.771596i
\(508\) 3.24583e36 1.78246e36i 0.959768 0.527059i
\(509\) 6.62858e35 6.62858e35i 0.190867 0.190867i −0.605204 0.796071i \(-0.706908\pi\)
0.796071 + 0.605204i \(0.206908\pi\)
\(510\) 8.72754e36 2.23870e36i 2.44734 0.627768i
\(511\) 5.36118e36 1.46412
\(512\) 2.39044e36 + 2.90182e36i 0.635820 + 0.771837i
\(513\) 1.67315e36 0.433460
\(514\) −2.98184e35 + 7.64872e34i −0.0752458 + 0.0193013i
\(515\) −5.73765e36 + 5.73765e36i −1.41038 + 1.41038i
\(516\) −4.03792e36 + 2.21744e36i −0.966911 + 0.530982i
\(517\) −1.53974e36 1.53974e36i −0.359190 0.359190i
\(518\) 2.40128e36 4.05821e36i 0.545747 0.922322i
\(519\) 1.27064e37i 2.81361i
\(520\) −6.79326e36 + 6.37044e36i −1.46566 + 1.37443i
\(521\) 7.74557e36i 1.62834i −0.580629 0.814169i \(-0.697193\pi\)
0.580629 0.814169i \(-0.302807\pi\)
\(522\) 1.18235e37 + 6.99608e36i 2.42211 + 1.43319i
\(523\) −9.70340e35 9.70340e35i −0.193710 0.193710i 0.603587 0.797297i \(-0.293737\pi\)
−0.797297 + 0.603587i \(0.793737\pi\)
\(524\) −6.95719e35 + 2.39055e36i −0.135351 + 0.465079i
\(525\) −1.23600e37 + 1.23600e37i −2.34352 + 2.34352i
\(526\) −1.37630e36 5.36548e36i −0.254334 0.991519i
\(527\) −4.64903e36 −0.837373
\(528\) 4.94441e36 7.77525e36i 0.868074 1.36507i
\(529\) 8.52890e35 0.145963
\(530\) −2.87493e36 1.12079e37i −0.479626 1.86981i
\(531\) 8.39974e36 8.39974e36i 1.36612 1.36612i
\(532\) −4.21343e36 1.22623e36i −0.668080 0.194430i
\(533\) 4.26937e36 + 4.26937e36i 0.660004 + 0.660004i
\(534\) −1.19988e37 7.09981e36i −1.80855 1.07014i
\(535\) 9.08495e36i 1.33520i
\(536\) −3.28147e34 + 1.02162e36i −0.00470266 + 0.146408i
\(537\) 5.25504e35i 0.0734384i
\(538\) −2.89183e36 + 4.88723e36i −0.394105 + 0.666043i
\(539\) −6.28222e36 6.28222e36i −0.834959 0.834959i
\(540\) −5.28298e36 9.62024e36i −0.684799 1.24701i
\(541\) −1.75599e36 + 1.75599e36i −0.222003 + 0.222003i −0.809341 0.587339i \(-0.800176\pi\)
0.587339 + 0.809341i \(0.300176\pi\)
\(542\) 9.20505e36 2.36119e36i 1.13510 0.291166i
\(543\) −1.33052e37 −1.60039
\(544\) 2.68623e36 8.23498e36i 0.315180 0.966223i
\(545\) −1.60744e37 −1.83985
\(546\) −2.65719e37 + 6.81596e36i −2.96703 + 0.761074i
\(547\) 5.24181e36 5.24181e36i 0.571021 0.571021i −0.361392 0.932414i \(-0.617699\pi\)
0.932414 + 0.361392i \(0.117699\pi\)
\(548\) −3.37666e34 6.14884e34i −0.00358880 0.00653515i
\(549\) 1.37104e37 + 1.37104e37i 1.42175 + 1.42175i
\(550\) 7.12013e36 1.20331e37i 0.720429 1.21754i
\(551\) 8.56215e36i 0.845349i
\(552\) 1.53763e37 + 4.93889e35i 1.48140 + 0.0475830i
\(553\) 1.02477e36i 0.0963468i
\(554\) 1.04499e37 + 6.18333e36i 0.958808 + 0.567337i
\(555\) 1.42794e37 + 1.42794e37i 1.27866 + 1.27866i
\(556\) −7.03097e36 2.04621e36i −0.614477 0.178830i
\(557\) 4.03049e36 4.03049e36i 0.343805 0.343805i −0.513991 0.857796i \(-0.671833\pi\)
0.857796 + 0.513991i \(0.171833\pi\)
\(558\) 3.86583e36 + 1.50709e37i 0.321870 + 1.25481i
\(559\) −1.09704e37 −0.891588
\(560\) 6.25341e36 + 2.80981e37i 0.496111 + 2.22915i
\(561\) −2.12292e37 −1.64412
\(562\) 3.38784e36 + 1.32074e37i 0.256143 + 0.998569i
\(563\) 4.13227e36 4.13227e36i 0.305018 0.305018i −0.537955 0.842973i \(-0.680803\pi\)
0.842973 + 0.537955i \(0.180803\pi\)
\(564\) −3.13188e36 + 1.07614e37i −0.225703 + 0.775537i
\(565\) −1.01990e37 1.01990e37i −0.717634 0.717634i
\(566\) 1.98393e37 + 1.17391e37i 1.36303 + 0.806518i
\(567\) 2.20108e36i 0.147661i
\(568\) −1.48205e37 1.58042e37i −0.970869 1.03531i
\(569\) 1.26345e37i 0.808245i 0.914705 + 0.404123i \(0.132423\pi\)
−0.914705 + 0.404123i \(0.867577\pi\)
\(570\) 9.57008e36 1.61736e37i 0.597867 1.01041i
\(571\) 5.83670e36 + 5.83670e36i 0.356107 + 0.356107i 0.862376 0.506269i \(-0.168976\pi\)
−0.506269 + 0.862376i \(0.668976\pi\)
\(572\) 1.92334e37 1.05621e37i 1.14607 0.629367i
\(573\) 1.36859e37 1.36859e37i 0.796500 0.796500i
\(574\) 1.80771e37 4.63697e36i 1.02759 0.263587i
\(575\) 2.33443e37 1.29618
\(576\) −2.89292e37 1.86034e36i −1.56904 0.100900i
\(577\) −2.58987e37 −1.37216 −0.686080 0.727526i \(-0.740670\pi\)
−0.686080 + 0.727526i \(0.740670\pi\)
\(578\) −6.16185e35 + 1.58058e35i −0.0318923 + 0.00818069i
\(579\) −6.06900e36 + 6.06900e36i −0.306872 + 0.306872i
\(580\) 4.92305e37 2.70351e37i 2.43196 1.33552i
\(581\) 2.17788e36 + 2.17788e36i 0.105113 + 0.105113i
\(582\) −1.71034e37 + 2.89050e37i −0.806532 + 1.36305i
\(583\) 2.72624e37i 1.25614i
\(584\) 1.50986e37 + 1.61007e37i 0.679771 + 0.724889i
\(585\) 7.18083e37i 3.15915i
\(586\) 1.38181e37 + 8.17629e36i 0.594058 + 0.351511i
\(587\) −2.30752e37 2.30752e37i −0.969464 0.969464i 0.0300831 0.999547i \(-0.490423\pi\)
−0.999547 + 0.0300831i \(0.990423\pi\)
\(588\) −1.27783e37 + 4.39073e37i −0.524660 + 1.80278i
\(589\) −6.85663e36 + 6.85663e36i −0.275140 + 0.275140i
\(590\) −1.20666e37 4.70413e37i −0.473240 1.84492i
\(591\) −7.21561e37 −2.76593
\(592\) 1.89503e37 4.21751e36i 0.710024 0.158020i
\(593\) 2.88143e37 1.05528 0.527642 0.849467i \(-0.323076\pi\)
0.527642 + 0.849467i \(0.323076\pi\)
\(594\) 6.42525e36 + 2.50487e37i 0.230024 + 0.896745i
\(595\) 4.68959e37 4.68959e37i 1.64118 1.64118i
\(596\) −3.88921e37 1.13187e37i −1.33057 0.387233i
\(597\) 4.73802e37 + 4.73802e37i 1.58469 + 1.58469i
\(598\) 3.15298e37 + 1.86565e37i 1.03099 + 0.610048i
\(599\) 2.55414e36i 0.0816551i 0.999166 + 0.0408275i \(0.0129994\pi\)
−0.999166 + 0.0408275i \(0.987001\pi\)
\(600\) −7.19290e37 2.31038e36i −2.24834 0.0722172i
\(601\) 2.21970e37i 0.678404i 0.940714 + 0.339202i \(0.110157\pi\)
−0.940714 + 0.339202i \(0.889843\pi\)
\(602\) −1.72677e37 + 2.91827e37i −0.516039 + 0.872114i
\(603\) −5.57297e36 5.57297e36i −0.162856 0.162856i
\(604\) −1.05682e37 1.92446e37i −0.301997 0.549933i
\(605\) −6.81638e35 + 6.81638e35i −0.0190483 + 0.0190483i
\(606\) −6.14087e37 + 1.57520e37i −1.67822 + 0.430481i
\(607\) 1.12387e37 0.300379 0.150189 0.988657i \(-0.452012\pi\)
0.150189 + 0.988657i \(0.452012\pi\)
\(608\) −8.18358e36 1.61072e37i −0.213917 0.421037i
\(609\) 1.65441e38 4.22969
\(610\) 7.67825e37 1.96955e37i 1.92004 0.492509i
\(611\) −1.88730e37 + 1.88730e37i −0.461621 + 0.461621i
\(612\) 3.21490e37 + 5.85429e37i 0.769171 + 1.40065i
\(613\) −9.54654e36 9.54654e36i −0.223424 0.223424i 0.586515 0.809939i \(-0.300500\pi\)
−0.809939 + 0.586515i \(0.800500\pi\)
\(614\) 2.32126e37 3.92297e37i 0.531436 0.898135i
\(615\) 7.99227e37i 1.79001i
\(616\) 2.17738e36 6.77884e37i 0.0477083 1.48530i
\(617\) 1.88273e37i 0.403587i −0.979428 0.201794i \(-0.935323\pi\)
0.979428 0.201794i \(-0.0646770\pi\)
\(618\) −8.46896e37 5.01117e37i −1.77617 1.05098i
\(619\) 5.64391e37 + 5.64391e37i 1.15813 + 1.15813i 0.984878 + 0.173250i \(0.0554269\pi\)
0.173250 + 0.984878i \(0.444573\pi\)
\(620\) 6.10741e37 + 1.77743e37i 1.22622 + 0.356865i
\(621\) −3.05299e37 + 3.05299e37i −0.599775 + 0.599775i
\(622\) 4.96757e36 + 1.93660e37i 0.0954934 + 0.372279i
\(623\) −1.02623e38 −1.93044
\(624\) −9.53037e37 6.06052e37i −1.75436 1.11562i
\(625\) 2.41669e37 0.435352
\(626\) 9.66851e36 + 3.76925e37i 0.170454 + 0.664510i
\(627\) −3.13099e37 + 3.13099e37i −0.540219 + 0.540219i
\(628\) −3.51851e36 + 1.20899e37i −0.0594160 + 0.204159i
\(629\) −3.16282e37 3.16282e37i −0.522745 0.522745i
\(630\) −1.91019e38 1.13028e38i −3.09015 1.82847i
\(631\) 3.51996e37i 0.557368i −0.960383 0.278684i \(-0.910102\pi\)
0.960383 0.278684i \(-0.0898982\pi\)
\(632\) 3.07759e36 2.88604e36i 0.0477014 0.0447324i
\(633\) 8.23408e37i 1.24930i
\(634\) −8.18444e36 + 1.38318e37i −0.121558 + 0.205435i
\(635\) 8.25408e37 + 8.25408e37i 1.20012 + 1.20012i
\(636\) 1.22997e38 6.75440e37i 1.75074 0.961425i
\(637\) −7.70032e37 + 7.70032e37i −1.07307 + 1.07307i
\(638\) −1.28184e38 + 3.28806e37i −1.74886 + 0.448601i
\(639\) 1.67059e38 2.23155
\(640\) −6.67730e37 + 9.79125e37i −0.873316 + 1.28058i
\(641\) −6.31267e37 −0.808407 −0.404203 0.914669i \(-0.632451\pi\)
−0.404203 + 0.914669i \(0.632451\pi\)
\(642\) 1.06721e38 2.73751e37i 1.33822 0.343268i
\(643\) 4.84842e37 4.84842e37i 0.595323 0.595323i −0.343742 0.939064i \(-0.611694\pi\)
0.939064 + 0.343742i \(0.111694\pi\)
\(644\) 9.92572e37 5.45074e37i 1.19345 0.655385i
\(645\) −1.02683e38 1.02683e38i −1.20905 1.20905i
\(646\) −2.11973e37 + 3.58238e37i −0.244423 + 0.413078i
\(647\) 6.88709e37i 0.777728i −0.921295 0.388864i \(-0.872868\pi\)
0.921295 0.388864i \(-0.127132\pi\)
\(648\) −6.61030e36 + 6.19887e36i −0.0731069 + 0.0685567i
\(649\) 1.14425e38i 1.23942i
\(650\) −1.47494e38 8.72736e37i −1.56474 0.925876i
\(651\) 1.32486e38 + 1.32486e38i 1.37666 + 1.37666i
\(652\) −3.92179e36 + 1.34756e37i −0.0399155 + 0.137153i
\(653\) 1.13996e38 1.13996e38i 1.13648 1.13648i 0.147404 0.989076i \(-0.452908\pi\)
0.989076 0.147404i \(-0.0470919\pi\)
\(654\) −4.84362e37 1.88828e38i −0.473010 1.84402i
\(655\) −7.84832e37 −0.750791
\(656\) 6.48361e37 + 4.12303e37i 0.607596 + 0.386380i
\(657\) −1.70193e38 −1.56246
\(658\) 2.04981e37 + 7.99113e37i 0.184358 + 0.718718i
\(659\) 1.21592e38 1.21592e38i 1.07140 1.07140i 0.0741496 0.997247i \(-0.476376\pi\)
0.997247 0.0741496i \(-0.0236242\pi\)
\(660\) 2.78887e38 + 8.11639e37i 2.40760 + 0.700680i
\(661\) −3.46152e37 3.46152e37i −0.292783 0.292783i 0.545395 0.838179i \(-0.316380\pi\)
−0.838179 + 0.545395i \(0.816380\pi\)
\(662\) −2.62198e37 1.55145e37i −0.217293 0.128575i
\(663\) 2.60213e38i 2.11298i
\(664\) −4.07096e35 + 1.26741e37i −0.00323912 + 0.100844i
\(665\) 1.38329e38i 1.07850i
\(666\) −7.62298e37 + 1.28830e38i −0.582402 + 0.984268i
\(667\) −1.56233e38 1.56233e38i −1.16970 1.16970i
\(668\) 5.12573e37 + 9.33388e37i 0.376074 + 0.684826i
\(669\) −1.70166e37 + 1.70166e37i −0.122355 + 0.122355i
\(670\) −3.12105e37 + 8.00580e36i −0.219933 + 0.0564150i
\(671\) −1.86769e38 −1.28988
\(672\) −3.11228e38 + 1.58126e38i −2.10665 + 1.07033i
\(673\) 5.66114e36 0.0375578 0.0187789 0.999824i \(-0.494022\pi\)
0.0187789 + 0.999824i \(0.494022\pi\)
\(674\) −1.10201e38 + 2.82676e37i −0.716600 + 0.183815i
\(675\) 1.42816e38 1.42816e38i 0.910284 0.910284i
\(676\) −5.24187e37 9.54538e37i −0.327496 0.596366i
\(677\) 4.22629e37 + 4.22629e37i 0.258829 + 0.258829i 0.824578 0.565749i \(-0.191413\pi\)
−0.565749 + 0.824578i \(0.691413\pi\)
\(678\) 8.90762e37 1.50540e38i 0.534762 0.903757i
\(679\) 2.47218e38i 1.45492i
\(680\) 2.72910e38 + 8.76593e36i 1.57452 + 0.0505741i
\(681\) 4.13805e38i 2.34051i
\(682\) −1.28982e38 7.63199e37i −0.715220 0.423203i
\(683\) 7.37223e37 + 7.37223e37i 0.400792 + 0.400792i 0.878512 0.477720i \(-0.158537\pi\)
−0.477720 + 0.878512i \(0.658537\pi\)
\(684\) 1.33757e38 + 3.89270e37i 0.712950 + 0.207489i
\(685\) 1.56364e36 1.56364e36i 0.00817172 0.00817172i
\(686\) 1.21935e37 + 4.75360e37i 0.0624815 + 0.243583i
\(687\) −5.53764e38 −2.78233
\(688\) −1.36272e38 + 3.03282e37i −0.671373 + 0.149418i
\(689\) 3.34164e38 1.61436
\(690\) 1.20494e38 + 4.69744e38i 0.570825 + 2.22535i
\(691\) 1.10919e38 1.10919e38i 0.515289 0.515289i −0.400853 0.916142i \(-0.631286\pi\)
0.916142 + 0.400853i \(0.131286\pi\)
\(692\) 1.07601e38 3.69729e38i 0.490214 1.68442i
\(693\) 3.69787e38 + 3.69787e38i 1.65217 + 1.65217i
\(694\) 7.49408e36 + 4.43433e36i 0.0328372 + 0.0194301i
\(695\) 2.30831e38i 0.991971i
\(696\) 4.65927e38 + 4.96851e38i 1.96378 + 2.09412i
\(697\) 1.77025e38i 0.731801i
\(698\) 1.82234e37 3.07978e37i 0.0738892 0.124874i
\(699\) −6.45890e37 6.45890e37i −0.256872 0.256872i
\(700\) −4.64318e38 + 2.54981e38i −1.81130 + 0.994683i
\(701\) −3.32141e38 + 3.32141e38i −1.27095 + 1.27095i −0.325365 + 0.945588i \(0.605487\pi\)
−0.945588 + 0.325365i \(0.894513\pi\)
\(702\) 3.07030e38 7.87563e37i 1.15247 0.295621i
\(703\) −9.32937e37 −0.343523
\(704\) 2.09714e38 1.84372e38i 0.757525 0.665984i
\(705\) −3.53304e38 −1.25197
\(706\) −2.77259e37 + 7.11198e36i −0.0963879 + 0.0247245i
\(707\) −3.29969e38 + 3.29969e38i −1.12541 + 1.12541i
\(708\) 5.16238e38 2.83494e38i 1.72743 0.948625i
\(709\) 9.28028e37 + 9.28028e37i 0.304675 + 0.304675i 0.842840 0.538165i \(-0.180882\pi\)
−0.538165 + 0.842840i \(0.680882\pi\)
\(710\) 3.47798e38 5.87785e38i 1.12031 1.89335i
\(711\) 3.25318e37i 0.102818i
\(712\) −2.89015e38 3.08198e38i −0.896274 0.955761i
\(713\) 2.50226e38i 0.761418i
\(714\) 6.92199e38 + 4.09581e38i 2.06683 + 1.22296i
\(715\) 4.89102e38 + 4.89102e38i 1.43307 + 1.43307i
\(716\) 4.45011e36 1.52910e37i 0.0127951 0.0439653i
\(717\) 4.03975e38 4.03975e38i 1.13985 1.13985i
\(718\) 1.38563e38 + 5.40185e38i 0.383678 + 1.49576i
\(719\) 3.56905e38 0.969869 0.484934 0.874551i \(-0.338843\pi\)
0.484934 + 0.874551i \(0.338843\pi\)
\(720\) −1.98517e38 8.91987e38i −0.529431 2.37887i
\(721\) −7.24331e38 −1.89588
\(722\) −7.51488e37 2.92966e38i −0.193050 0.752602i
\(723\) −2.91269e38 + 2.91269e38i −0.734390 + 0.734390i
\(724\) −3.87153e38 1.12672e38i −0.958102 0.278835i
\(725\) 7.30847e38 + 7.30847e38i 1.77527 + 1.77527i
\(726\) −1.00612e37 5.95331e36i −0.0239886 0.0141943i
\(727\) 3.75790e37i 0.0879491i 0.999033 + 0.0439745i \(0.0140020\pi\)
−0.999033 + 0.0439745i \(0.985998\pi\)
\(728\) −8.30903e38 2.66888e37i −1.90887 0.0613134i
\(729\) 7.22622e38i 1.62963i
\(730\) −3.54324e38 + 5.98813e38i −0.784407 + 1.32566i
\(731\) 2.27439e38 + 2.27439e38i 0.494289 + 0.494289i
\(732\) 4.62729e38 + 8.42622e38i 0.987249 + 1.79777i
\(733\) −5.63729e38 + 5.63729e38i −1.18077 + 1.18077i −0.201229 + 0.979544i \(0.564494\pi\)
−0.979544 + 0.201229i \(0.935506\pi\)
\(734\) 1.67518e38 4.29702e37i 0.344481 0.0883629i
\(735\) −1.44150e39 −2.91029
\(736\) 4.43233e38 + 1.44581e38i 0.878580 + 0.286591i
\(737\) 7.59174e37 0.147751
\(738\) −5.73867e38 + 1.47203e38i −1.09661 + 0.281290i
\(739\) 1.78384e38 1.78384e38i 0.334699 0.334699i −0.519669 0.854368i \(-0.673945\pi\)
0.854368 + 0.519669i \(0.173945\pi\)
\(740\) 2.94576e38 + 5.36419e38i 0.542712 + 0.988271i
\(741\) 3.83775e38 + 3.83775e38i 0.694274 + 0.694274i
\(742\) 5.25981e38 8.88917e38i 0.934367 1.57910i
\(743\)