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Properties

Label 16.28.e.a.5.3
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 5.3
Character \(\chi\) \(=\) 16.5
Dual form 16.28.e.a.13.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11565.4 - 677.061i) q^{2} +(663110. - 663110. i) q^{3} +(1.33301e8 + 1.56610e7i) q^{4} +(2.21940e8 + 2.21940e8i) q^{5} +(-8.11812e9 + 7.22019e9i) q^{6} +2.02008e11i q^{7} +(-1.53108e12 - 2.71379e11i) q^{8} +6.74617e12i q^{9} +O(q^{10})\) \(q+(-11565.4 - 677.061i) q^{2} +(663110. - 663110. i) q^{3} +(1.33301e8 + 1.56610e7i) q^{4} +(2.21940e8 + 2.21940e8i) q^{5} +(-8.11812e9 + 7.22019e9i) q^{6} +2.02008e11i q^{7} +(-1.53108e12 - 2.71379e11i) q^{8} +6.74617e12i q^{9} +(-2.41657e12 - 2.71710e12i) q^{10} +(-1.35048e14 - 1.35048e14i) q^{11} +(9.87782e13 - 7.80082e13i) q^{12} +(-8.89396e14 + 8.89396e14i) q^{13} +(1.36772e14 - 2.33631e15i) q^{14} +2.94342e14 q^{15} +(1.75239e16 + 4.17525e15i) q^{16} -1.92087e16 q^{17} +(4.56757e15 - 7.80224e16i) q^{18} +(8.59540e16 - 8.59540e16i) q^{19} +(2.61090e16 + 3.30606e16i) q^{20} +(1.33954e17 + 1.33954e17i) q^{21} +(1.47045e18 + 1.65332e18i) q^{22} -4.07622e18i q^{23} +(-1.19523e18 + 8.35320e17i) q^{24} -7.35207e18i q^{25} +(1.08884e19 - 9.68408e18i) q^{26} +(9.53006e18 + 9.53006e18i) q^{27} +(-3.16365e18 + 2.69279e19i) q^{28} +(-6.58791e19 + 6.58791e19i) q^{29} +(-3.40419e18 - 1.99287e17i) q^{30} +1.72400e20 q^{31} +(-1.99844e20 - 6.01534e19i) q^{32} -1.79103e20 q^{33} +(2.22157e20 + 1.30055e19i) q^{34} +(-4.48337e19 + 4.48337e19i) q^{35} +(-1.05652e20 + 8.99270e20i) q^{36} +(-7.86028e20 - 7.86028e20i) q^{37} +(-1.05229e21 + 9.35899e20i) q^{38} +1.17953e21i q^{39} +(-2.79578e20 - 4.00038e20i) q^{40} +3.80051e21i q^{41} +(-1.45854e21 - 1.63993e21i) q^{42} +(3.06808e21 + 3.06808e21i) q^{43} +(-1.58870e22 - 2.01170e22i) q^{44} +(-1.49725e21 + 1.49725e21i) q^{45} +(-2.75985e21 + 4.71433e22i) q^{46} -6.46916e22 q^{47} +(1.43889e22 - 8.85160e21i) q^{48} +2.49051e22 q^{49} +(-4.97780e21 + 8.50298e22i) q^{50} +(-1.27375e22 + 1.27375e22i) q^{51} +(-1.32486e23 + 1.04628e23i) q^{52} +(7.95642e22 + 7.95642e22i) q^{53} +(-1.03767e23 - 1.16672e23i) q^{54} -5.99451e22i q^{55} +(5.48208e22 - 3.09291e23i) q^{56} -1.13994e23i q^{57} +(8.06525e23 - 7.17317e23i) q^{58} +(9.06673e23 + 9.06673e23i) q^{59} +(3.92360e22 + 4.60969e21i) q^{60} +(1.36557e24 - 1.36557e24i) q^{61} +(-1.99388e24 - 1.16725e23i) q^{62} -1.36278e24 q^{63} +(2.27056e24 + 8.31007e23i) q^{64} -3.94785e23 q^{65} +(2.07141e24 + 1.21264e23i) q^{66} +(5.98561e24 - 5.98561e24i) q^{67} +(-2.56054e24 - 3.00827e23i) q^{68} +(-2.70299e24 - 2.70299e24i) q^{69} +(5.48877e23 - 4.88166e23i) q^{70} -1.14932e24i q^{71} +(1.83077e24 - 1.03289e25i) q^{72} +2.28648e25i q^{73} +(8.55857e24 + 9.62295e24i) q^{74} +(-4.87523e24 - 4.87523e24i) q^{75} +(1.28039e25 - 1.01116e25i) q^{76} +(2.72808e25 - 2.72808e25i) q^{77} +(7.98617e23 - 1.36418e25i) q^{78} +4.29420e25 q^{79} +(2.96259e24 + 4.81591e24i) q^{80} -3.88046e25 q^{81} +(2.57318e24 - 4.39546e25i) q^{82} +(1.59022e25 - 1.59022e25i) q^{83} +(1.57583e25 + 1.99540e25i) q^{84} +(-4.26318e24 - 4.26318e24i) q^{85} +(-3.34064e25 - 3.75609e25i) q^{86} +8.73702e25i q^{87} +(1.70120e26 + 2.43418e26i) q^{88} -1.45760e26i q^{89} +(1.83300e25 - 1.63026e25i) q^{90} +(-1.79665e26 - 1.79665e26i) q^{91} +(6.38378e25 - 5.43364e26i) q^{92} +(1.14320e26 - 1.14320e26i) q^{93} +(7.48187e26 + 4.38002e25i) q^{94} +3.81533e25 q^{95} +(-1.72407e26 + 9.26304e25i) q^{96} +1.15773e27 q^{97} +(-2.88038e26 - 1.68623e25i) q^{98} +(9.11056e26 - 9.11056e26i) 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

Display 100 coefficients 10 coefficients

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11565.4 − 677.061i −0.998291 − 0.0584417i
\(3\) 663110. − 663110.i 0.240131 − 0.240131i −0.576773 − 0.816904i \(-0.695688\pi\)
0.816904 + 0.576773i \(0.195688\pi\)
\(4\) 1.33301e8 + 1.56610e7i 0.993169 + 0.116684i
\(5\) 2.21940e8 + 2.21940e8i 0.0813094 + 0.0813094i 0.746592 − 0.665282i \(-0.231689\pi\)
−0.665282 + 0.746592i \(0.731689\pi\)
\(6\) −8.11812e9 + 7.22019e9i −0.253755 + 0.225687i
\(7\) 2.02008e11i 0.788035i 0.919103 + 0.394017i \(0.128915\pi\)
−0.919103 + 0.394017i \(0.871085\pi\)
\(8\) −1.53108e12 − 2.71379e11i −0.984652 − 0.174527i
\(9\) 6.74617e12i 0.884674i
\(10\) −2.41657e12 − 2.71710e12i −0.0764186 − 0.0859223i
\(11\) −1.35048e14 − 1.35048e14i −1.17947 − 1.17947i −0.979879 − 0.199590i \(-0.936039\pi\)
−0.199590 − 0.979879i \(-0.563961\pi\)
\(12\) 9.87782e13 − 7.80082e13i 0.266510 − 0.210472i
\(13\) −8.89396e14 + 8.89396e14i −0.814442 + 0.814442i −0.985296 − 0.170855i \(-0.945347\pi\)
0.170855 + 0.985296i \(0.445347\pi\)
\(14\) 1.36772e14 − 2.33631e15i 0.0460541 − 0.786688i
\(15\) 2.94342e14 0.0390499
\(16\) 1.75239e16 + 4.17525e15i 0.972770 + 0.231773i
\(17\) −1.92087e16 −0.470367 −0.235184 − 0.971951i \(-0.575569\pi\)
−0.235184 + 0.971951i \(0.575569\pi\)
\(18\) 4.56757e15 − 7.80224e16i 0.0517019 − 0.883162i
\(19\) 8.59540e16 − 8.59540e16i 0.468913 − 0.468913i −0.432649 − 0.901562i \(-0.642421\pi\)
0.901562 + 0.432649i \(0.142421\pi\)
\(20\) 2.61090e16 + 3.30606e16i 0.0712665 + 0.0902415i
\(21\) 1.33954e17 + 1.33954e17i 0.189232 + 0.189232i
\(22\) 1.47045e18 + 1.65332e18i 1.10852 + 1.24638i
\(23\) − 4.07622e18i − 1.68629i −0.537686 − 0.843145i \(-0.680701\pi\)
0.537686 − 0.843145i \(-0.319299\pi\)
\(24\) −1.19523e18 + 8.35320e17i −0.278355 + 0.194537i
\(25\) − 7.35207e18i − 0.986778i
\(26\) 1.08884e19 − 9.68408e18i 0.860647 − 0.765452i
\(27\) 9.53006e18 + 9.53006e18i 0.452569 + 0.452569i
\(28\) −3.16365e18 + 2.69279e19i −0.0919507 + 0.782652i
\(29\) −6.58791e19 + 6.58791e19i −1.19227 + 1.19227i −0.215843 + 0.976428i \(0.569250\pi\)
−0.976428 + 0.215843i \(0.930750\pi\)
\(30\) −3.40419e18 − 1.99287e17i −0.0389831 − 0.00228214i
\(31\) 1.72400e20 1.26810 0.634051 − 0.773291i \(-0.281391\pi\)
0.634051 + 0.773291i \(0.281391\pi\)
\(32\) −1.99844e20 − 6.01534e19i −0.957562 − 0.288227i
\(33\) −1.79103e20 −0.566455
\(34\) 2.22157e20 + 1.30055e19i 0.469563 + 0.0274891i
\(35\) −4.48337e19 + 4.48337e19i −0.0640746 + 0.0640746i
\(36\) −1.05652e20 + 8.99270e20i −0.103227 + 0.878631i
\(37\) −7.86028e20 − 7.86028e20i −0.530536 − 0.530536i 0.390196 − 0.920732i \(-0.372407\pi\)
−0.920732 + 0.390196i \(0.872407\pi\)
\(38\) −1.05229e21 + 9.35899e20i −0.495516 + 0.440708i
\(39\) 1.17953e21i 0.391146i
\(40\) −2.79578e20 − 4.00038e20i −0.0658708 − 0.0942522i
\(41\) 3.80051e21i 0.641594i 0.947148 + 0.320797i \(0.103951\pi\)
−0.947148 + 0.320797i \(0.896049\pi\)
\(42\) −1.45854e21 − 1.63993e21i −0.177849 − 0.199967i
\(43\) 3.06808e21 + 3.06808e21i 0.272297 + 0.272297i 0.830024 − 0.557728i \(-0.188327\pi\)
−0.557728 + 0.830024i \(0.688327\pi\)
\(44\) −1.58870e22 − 2.01170e22i −1.03379 − 1.30904i
\(45\) −1.49725e21 + 1.49725e21i −0.0719323 + 0.0719323i
\(46\) −2.75985e21 + 4.71433e22i −0.0985497 + 1.68341i
\(47\) −6.46916e22 −1.72793 −0.863967 − 0.503549i \(-0.832027\pi\)
−0.863967 + 0.503549i \(0.832027\pi\)
\(48\) 1.43889e22 − 8.85160e21i 0.289248 − 0.177936i
\(49\) 2.49051e22 0.379001
\(50\) −4.97780e21 + 8.50298e22i −0.0576690 + 0.985091i
\(51\) −1.27375e22 + 1.27375e22i −0.112950 + 0.112950i
\(52\) −1.32486e23 + 1.04628e23i −0.903910 + 0.713846i
\(53\) 7.95642e22 + 7.95642e22i 0.419753 + 0.419753i 0.885118 − 0.465366i \(-0.154077\pi\)
−0.465366 + 0.885118i \(0.654077\pi\)
\(54\) −1.03767e23 − 1.16672e23i −0.425347 − 0.478245i
\(55\) − 5.99451e22i − 0.191804i
\(56\) 5.48208e22 − 3.09291e23i 0.137533 − 0.775940i
\(57\) − 1.13994e23i − 0.225201i
\(58\) 8.06525e23 − 7.17317e23i 1.25991 − 1.12055i
\(59\) 9.06673e23 + 9.06673e23i 1.12447 + 1.12447i 0.991061 + 0.133411i \(0.0425930\pi\)
0.133411 + 0.991061i \(0.457407\pi\)
\(60\) 3.92360e22 + 4.60969e21i 0.0387831 + 0.00455648i
\(61\) 1.36557e24 − 1.36557e24i 1.07984 − 1.07984i 0.0833191 − 0.996523i \(-0.473448\pi\)
0.996523 − 0.0833191i \(-0.0265521\pi\)
\(62\) −1.99388e24 − 1.16725e23i −1.26594 − 0.0741101i
\(63\) −1.36278e24 −0.697154
\(64\) 2.27056e24 + 8.31007e23i 0.939081 + 0.343696i
\(65\) −3.94785e23 −0.132444
\(66\) 2.07141e24 + 1.21264e23i 0.565487 + 0.0331046i
\(67\) 5.98561e24 − 5.98561e24i 1.33383 − 1.33383i 0.431907 − 0.901918i \(-0.357841\pi\)
0.901918 − 0.431907i \(-0.142159\pi\)
\(68\) −2.56054e24 − 3.00827e23i −0.467154 − 0.0548842i
\(69\) −2.70299e24 − 2.70299e24i −0.404931 − 0.404931i
\(70\) 5.48877e23 − 4.88166e23i 0.0677097 − 0.0602205i
\(71\) − 1.14932e24i − 0.117072i −0.998285 − 0.0585361i \(-0.981357\pi\)
0.998285 − 0.0585361i \(-0.0186433\pi\)
\(72\) 1.83077e24 − 1.03289e25i 0.154399 − 0.871096i
\(73\) 2.28648e25i 1.60069i 0.599537 + 0.800347i \(0.295351\pi\)
−0.599537 + 0.800347i \(0.704649\pi\)
\(74\) 8.55857e24 + 9.62295e24i 0.498624 + 0.560635i
\(75\) −4.87523e24 − 4.87523e24i −0.236956 − 0.236956i
\(76\) 1.28039e25 − 1.01116e25i 0.520424 − 0.410996i
\(77\) 2.72808e25 − 2.72808e25i 0.929463 − 0.929463i
\(78\) 7.98617e23 − 1.36418e25i 0.0228592 − 0.390477i
\(79\) 4.29420e25 1.03494 0.517472 − 0.855700i \(-0.326873\pi\)
0.517472 + 0.855700i \(0.326873\pi\)
\(80\) 2.96259e24 + 4.81591e24i 0.0602500 + 0.0979407i
\(81\) −3.88046e25 −0.667322
\(82\) 2.57318e24 − 4.39546e25i 0.0374959 − 0.640498i
\(83\) 1.59022e25 − 1.59022e25i 0.196745 − 0.196745i −0.601858 − 0.798603i \(-0.705573\pi\)
0.798603 + 0.601858i \(0.205573\pi\)
\(84\) 1.57583e25 + 1.99540e25i 0.165859 + 0.210019i
\(85\) −4.26318e24 − 4.26318e24i −0.0382453 − 0.0382453i
\(86\) −3.34064e25 − 3.75609e25i −0.255918 − 0.287745i
\(87\) 8.73702e25i 0.572603i
\(88\) 1.70120e26 + 2.43418e26i 0.955519 + 1.36722i
\(89\) − 1.45760e26i − 0.702868i −0.936213 − 0.351434i \(-0.885694\pi\)
0.936213 − 0.351434i \(-0.114306\pi\)
\(90\) 1.83300e25 − 1.63026e25i 0.0760132 − 0.0676055i
\(91\) −1.79665e26 − 1.79665e26i −0.641808 − 0.641808i
\(92\) 6.38378e25 − 5.43364e26i 0.196762 − 1.67477i
\(93\) 1.14320e26 − 1.14320e26i 0.304511 − 0.304511i
\(94\) 7.48187e26 + 4.38002e25i 1.72498 + 0.100983i
\(95\) 3.81533e25 0.0762541
\(96\) −1.72407e26 + 9.26304e25i −0.299153 + 0.160728i
\(97\) 1.15773e27 1.74658 0.873288 − 0.487204i \(-0.161983\pi\)
0.873288 + 0.487204i \(0.161983\pi\)
\(98\) −2.88038e26 − 1.68623e25i −0.378354 − 0.0221495i
\(99\) 9.11056e26 − 9.11056e26i 1.04345 − 1.04345i
\(100\) 1.15141e26 − 9.80037e26i 0.115141 − 0.980037i
\(101\) 1.30801e26 + 1.30801e26i 0.114359 + 0.114359i 0.761971 − 0.647611i \(-0.224232\pi\)
−0.647611 + 0.761971i \(0.724232\pi\)
\(102\) 1.55938e26 − 1.38690e26i 0.119358 − 0.106156i
\(103\) − 9.63147e26i − 0.646234i −0.946359 − 0.323117i \(-0.895269\pi\)
0.946359 − 0.323117i \(-0.104731\pi\)
\(104\) 1.60310e27 − 1.12037e27i 0.944084 − 0.659800i
\(105\) 5.94594e25i 0.0307726i
\(106\) −8.66325e26 − 9.74064e26i −0.394504 − 0.443566i
\(107\) 1.76213e27 + 1.76213e27i 0.706898 + 0.706898i 0.965882 − 0.258984i \(-0.0833877\pi\)
−0.258984 + 0.965882i \(0.583388\pi\)
\(108\) 1.12112e27 + 1.41962e27i 0.396670 + 0.502285i
\(109\) −1.02498e27 + 1.02498e27i −0.320227 + 0.320227i −0.848854 − 0.528627i \(-0.822707\pi\)
0.528627 + 0.848854i \(0.322707\pi\)
\(110\) −4.05865e25 + 6.93292e26i −0.0112094 + 0.191476i
\(111\) −1.04245e27 −0.254797
\(112\) −8.43435e26 + 3.53996e27i −0.182645 + 0.766576i
\(113\) −1.75140e27 −0.336378 −0.168189 − 0.985755i \(-0.553792\pi\)
−0.168189 + 0.985755i \(0.553792\pi\)
\(114\) −7.71808e25 + 1.31839e27i −0.0131612 + 0.224816i
\(115\) 9.04678e26 − 9.04678e26i 0.137111 − 0.137111i
\(116\) −9.81348e27 + 7.75001e27i −1.32325 + 1.04501i
\(117\) −6.00001e27 − 6.00001e27i −0.720515 − 0.720515i
\(118\) −9.87220e27 − 1.10999e28i −1.05683 − 1.18827i
\(119\) − 3.88031e27i − 0.370666i
\(120\) −4.50660e26 − 7.98782e25i −0.0384505 − 0.00681524i
\(121\) 2.33659e28i 1.78230i
\(122\) −1.67179e28 + 1.48688e28i −1.14110 + 1.01489i
\(123\) 2.52016e27 + 2.52016e27i 0.154067 + 0.154067i
\(124\) 2.29811e28 + 2.69996e27i 1.25944 + 0.147967i
\(125\) 3.28530e27 − 3.28530e27i 0.161544 − 0.161544i
\(126\) 1.57612e28 + 9.22686e26i 0.695962 + 0.0407429i
\(127\) −2.33146e28 −0.925291 −0.462645 − 0.886543i \(-0.653100\pi\)
−0.462645 + 0.886543i \(0.653100\pi\)
\(128\) −2.56974e28 − 1.11483e28i −0.917390 − 0.397990i
\(129\) 4.06895e27 0.130774
\(130\) 4.56586e27 + 2.67294e26i 0.132217 + 0.00774023i
\(131\) −6.64628e27 + 6.64628e27i −0.173547 + 0.173547i −0.788536 − 0.614989i \(-0.789160\pi\)
0.614989 + 0.788536i \(0.289160\pi\)
\(132\) −2.38746e28 − 2.80494e27i −0.562586 − 0.0660960i
\(133\) 1.73634e28 + 1.73634e28i 0.369520 + 0.369520i
\(134\) −7.32789e28 + 6.51736e28i −1.40950 + 1.25359i
\(135\) 4.23021e27i 0.0735963i
\(136\) 2.94100e28 + 5.21284e27i 0.463148 + 0.0820917i
\(137\) − 9.10738e28i − 1.29917i −0.760289 − 0.649585i \(-0.774943\pi\)
0.760289 − 0.649585i \(-0.225057\pi\)
\(138\) 2.94311e28 + 3.30913e28i 0.380574 + 0.427904i
\(139\) −4.72427e28 − 4.72427e28i −0.554159 − 0.554159i 0.373479 − 0.927638i \(-0.378165\pi\)
−0.927638 + 0.373479i \(0.878165\pi\)
\(140\) −6.67852e27 + 5.27423e27i −0.0711134 + 0.0561605i
\(141\) −4.28977e28 + 4.28977e28i −0.414931 + 0.414931i
\(142\) −7.78160e26 + 1.32924e28i −0.00684189 + 0.116872i
\(143\) 2.40222e29 1.92122
\(144\) −2.81670e28 + 1.18219e29i −0.205044 + 0.860584i
\(145\) −2.92425e28 −0.193886
\(146\) 1.54808e28 − 2.64441e29i 0.0935473 − 1.59796i
\(147\) 1.65148e28 − 1.65148e28i 0.0910101 − 0.0910101i
\(148\) −9.24683e28 − 1.17088e29i −0.465007 − 0.588817i
\(149\) 9.86696e28 + 9.86696e28i 0.453074 + 0.453074i 0.896373 − 0.443300i \(-0.146192\pi\)
−0.443300 + 0.896373i \(0.646192\pi\)
\(150\) 5.30833e28 + 5.96850e28i 0.222703 + 0.250399i
\(151\) − 1.00038e29i − 0.383686i −0.981426 − 0.191843i \(-0.938554\pi\)
0.981426 − 0.191843i \(-0.0614464\pi\)
\(152\) −1.54929e29 + 1.08276e29i −0.543554 + 0.379879i
\(153\) − 1.29585e29i − 0.416122i
\(154\) −3.33985e29 + 2.97043e29i −0.982194 + 0.873555i
\(155\) 3.82625e28 + 3.82625e28i 0.103109 + 0.103109i
\(156\) −1.84727e28 + 1.57233e29i −0.0456403 + 0.388474i
\(157\) 3.16820e29 − 3.16820e29i 0.718071 − 0.718071i −0.250139 − 0.968210i \(-0.580476\pi\)
0.968210 + 0.250139i \(0.0804764\pi\)
\(158\) −4.96643e29 − 2.90744e28i −1.03317 − 0.0604839i
\(159\) 1.05520e29 0.201591
\(160\) −3.10030e28 − 5.77039e28i −0.0544232 − 0.101294i
\(161\) 8.23431e29 1.32886
\(162\) 4.48792e29 + 2.62731e28i 0.666181 + 0.0389994i
\(163\) 4.14863e29 − 4.14863e29i 0.566724 − 0.566724i −0.364485 − 0.931209i \(-0.618755\pi\)
0.931209 + 0.364485i \(0.118755\pi\)
\(164\) −5.95199e28 + 5.06612e29i −0.0748635 + 0.637211i
\(165\) −3.97502e28 − 3.97502e28i −0.0460581 − 0.0460581i
\(166\) −1.94683e29 + 1.73149e29i −0.207907 + 0.184910i
\(167\) − 4.22711e29i − 0.416266i −0.978101 − 0.208133i \(-0.933261\pi\)
0.978101 − 0.208133i \(-0.0667387\pi\)
\(168\) −1.68741e29 − 2.41446e29i −0.153302 − 0.219354i
\(169\) − 3.89517e29i − 0.326630i
\(170\) 4.64191e28 + 5.21919e28i 0.0359448 + 0.0404150i
\(171\) 5.79860e29 + 5.79860e29i 0.414835 + 0.414835i
\(172\) 3.60928e29 + 4.57027e29i 0.238664 + 0.302209i
\(173\) 2.05397e30 − 2.05397e30i 1.25595 − 1.25595i 0.302941 − 0.953009i \(-0.402031\pi\)
0.953009 − 0.302941i \(-0.0979685\pi\)
\(174\) 5.91550e28 − 1.01048e30i 0.0334639 − 0.571624i
\(175\) 1.48518e30 0.777615
\(176\) −1.80270e30 − 2.93042e30i −0.873983 − 1.42072i
\(177\) 1.20245e30 0.540042
\(178\) −9.86885e28 + 1.68578e30i −0.0410768 + 0.701667i
\(179\) 2.28929e30 − 2.28929e30i 0.883455 − 0.883455i −0.110429 − 0.993884i \(-0.535222\pi\)
0.993884 + 0.110429i \(0.0352224\pi\)
\(180\) −2.23033e29 + 1.76136e29i −0.0798343 + 0.0630476i
\(181\) −1.91433e30 − 1.91433e30i −0.635853 − 0.635853i 0.313677 − 0.949530i \(-0.398439\pi\)
−0.949530 + 0.313677i \(0.898439\pi\)
\(182\) 1.95626e30 + 2.19955e30i 0.603203 + 0.678220i
\(183\) − 1.81104e30i − 0.518608i
\(184\) −1.10620e30 + 6.24102e30i −0.294303 + 1.66041i
\(185\) − 3.48902e29i − 0.0862752i
\(186\) −1.39956e30 + 1.24476e30i −0.321787 + 0.286194i
\(187\) 2.59409e30 + 2.59409e30i 0.554784 + 0.554784i
\(188\) −8.62345e30 − 1.01314e30i −1.71613 − 0.201622i
\(189\) −1.92515e30 + 1.92515e30i −0.356640 + 0.356640i
\(190\) −4.41259e29 − 2.58321e28i −0.0761238 − 0.00445642i
\(191\) −5.92432e30 −0.952112 −0.476056 − 0.879415i \(-0.657934\pi\)
−0.476056 + 0.879415i \(0.657934\pi\)
\(192\) 2.05668e30 − 9.54581e29i 0.308035 − 0.142970i
\(193\) 8.66032e30 1.20923 0.604617 − 0.796517i \(-0.293326\pi\)
0.604617 + 0.796517i \(0.293326\pi\)
\(194\) −1.33896e31 − 7.83851e29i −1.74359 − 0.102073i
\(195\) −2.61786e29 + 2.61786e29i −0.0318038 + 0.0318038i
\(196\) 3.31987e30 + 3.90039e29i 0.376413 + 0.0442233i
\(197\) 3.19524e30 + 3.19524e30i 0.338228 + 0.338228i 0.855700 − 0.517472i \(-0.173127\pi\)
−0.517472 + 0.855700i \(0.673127\pi\)
\(198\) −1.11536e31 + 9.91992e30i −1.10264 + 0.980682i
\(199\) 1.03044e31i 0.951715i 0.879522 + 0.475857i \(0.157862\pi\)
−0.879522 + 0.475857i \(0.842138\pi\)
\(200\) −1.99520e30 + 1.12566e31i −0.172219 + 0.971633i
\(201\) − 7.93824e30i − 0.640586i
\(202\) −1.42421e30 − 1.60133e30i −0.107480 − 0.120847i
\(203\) −1.33081e31 − 1.33081e31i −0.939551 − 0.939551i
\(204\) −1.89740e30 + 1.49843e30i −0.125358 + 0.0989990i
\(205\) −8.43487e29 + 8.43487e29i −0.0521676 + 0.0521676i
\(206\) −6.52109e29 + 1.11392e31i −0.0377670 + 0.645130i
\(207\) 2.74989e31 1.49182
\(208\) −1.92991e31 + 1.18722e31i −0.981030 + 0.603498i
\(209\) −2.32158e31 −1.10614
\(210\) 4.02576e28 − 6.87674e29i 0.00179841 − 0.0307201i
\(211\) 1.42399e31 − 1.42399e31i 0.596615 − 0.596615i −0.342795 − 0.939410i \(-0.611374\pi\)
0.939410 + 0.342795i \(0.111374\pi\)
\(212\) 9.35992e30 + 1.18520e31i 0.367907 + 0.465864i
\(213\) −7.62126e29 − 7.62126e29i −0.0281127 − 0.0281127i
\(214\) −1.91867e31 − 2.15729e31i −0.664377 − 0.747002i
\(215\) 1.36186e30i 0.0442805i
\(216\) −1.20050e31 − 1.71775e31i −0.366638 − 0.524609i
\(217\) 3.48262e31i 0.999309i
\(218\) 1.25483e31 − 1.11604e31i 0.338394 − 0.300965i
\(219\) 1.51619e31 + 1.51619e31i 0.384377 + 0.384377i
\(220\) 9.38802e29 − 7.99074e30i 0.0223804 − 0.190494i
\(221\) 1.70841e31 − 1.70841e31i 0.383087 − 0.383087i
\(222\) 1.20564e31 + 7.05800e29i 0.254361 + 0.0148907i
\(223\) −1.60517e31 −0.318718 −0.159359 − 0.987221i \(-0.550943\pi\)
−0.159359 + 0.987221i \(0.550943\pi\)
\(224\) 1.21515e31 − 4.03702e31i 0.227133 − 0.754592i
\(225\) 4.95983e31 0.872976
\(226\) 2.02558e31 + 1.18581e30i 0.335803 + 0.0196585i
\(227\) 6.53451e30 − 6.53451e30i 0.102062 − 0.102062i −0.654232 − 0.756294i \(-0.727008\pi\)
0.756294 + 0.654232i \(0.227008\pi\)
\(228\) 1.78526e30 − 1.51955e31i 0.0262773 − 0.223663i
\(229\) −2.13448e31 − 2.13448e31i −0.296151 − 0.296151i 0.543353 − 0.839504i \(-0.317155\pi\)
−0.839504 + 0.543353i \(0.817155\pi\)
\(230\) −1.10755e31 + 9.85047e30i −0.144890 + 0.128864i
\(231\) − 3.61803e31i − 0.446386i
\(232\) 1.18744e32 − 8.29880e31i 1.38206 − 0.965889i
\(233\) − 6.29729e31i − 0.691590i −0.938310 − 0.345795i \(-0.887609\pi\)
0.938310 − 0.345795i \(-0.112391\pi\)
\(234\) 6.53304e31 + 7.34552e31i 0.677176 + 0.761392i
\(235\) −1.43577e31 − 1.43577e31i −0.140497 − 0.140497i
\(236\) 1.06661e32 + 1.35060e32i 0.985583 + 1.24800i
\(237\) 2.84753e31 − 2.84753e31i 0.248522 − 0.248522i
\(238\) −2.62721e30 + 4.48775e31i −0.0216623 + 0.370032i
\(239\) −6.70350e31 −0.522312 −0.261156 − 0.965297i \(-0.584104\pi\)
−0.261156 + 0.965297i \(0.584104\pi\)
\(240\) 5.15800e30 + 1.22895e30i 0.0379865 + 0.00905071i
\(241\) −2.94270e31 −0.204888 −0.102444 − 0.994739i \(-0.532666\pi\)
−0.102444 + 0.994739i \(0.532666\pi\)
\(242\) 1.58202e31 − 2.70237e32i 0.104161 − 1.77925i
\(243\) −9.84041e31 + 9.84041e31i −0.612814 + 0.612814i
\(244\) 2.03417e32 − 1.60645e32i 1.19847 − 0.946466i
\(245\) 5.52744e30 + 5.52744e30i 0.0308164 + 0.0308164i
\(246\) −2.74404e31 − 3.08531e31i −0.144800 − 0.162807i
\(247\) 1.52894e32i 0.763805i
\(248\) −2.63958e32 − 4.67858e31i −1.24864 − 0.221318i
\(249\) − 2.10898e31i − 0.0944892i
\(250\) −4.02203e31 + 3.57716e31i −0.170708 + 0.151827i
\(251\) 9.76128e31 + 9.76128e31i 0.392565 + 0.392565i 0.875601 − 0.483036i \(-0.160466\pi\)
−0.483036 + 0.875601i \(0.660466\pi\)
\(252\) −1.81660e32 − 2.13425e31i −0.692392 − 0.0813464i
\(253\) −5.50486e32 + 5.50486e32i −1.98893 + 1.98893i
\(254\) 2.69644e32 + 1.57854e31i 0.923709 + 0.0540756i
\(255\) −5.65391e30 −0.0183678
\(256\) 2.89653e32 + 1.46333e32i 0.892562 + 0.450924i
\(257\) −7.05290e31 −0.206192 −0.103096 − 0.994671i \(-0.532875\pi\)
−0.103096 + 0.994671i \(0.532875\pi\)
\(258\) −4.70591e31 − 2.75492e30i −0.130550 − 0.00764265i
\(259\) 1.58784e32 − 1.58784e32i 0.418081 − 0.418081i
\(260\) −5.26252e31 − 6.18274e30i −0.131539 − 0.0154540i
\(261\) −4.44432e32 − 4.44432e32i −1.05477 − 1.05477i
\(262\) 8.13671e31 − 7.23672e31i 0.183392 − 0.163108i
\(263\) 4.56818e32i 0.978004i 0.872283 + 0.489002i \(0.162639\pi\)
−0.872283 + 0.489002i \(0.837361\pi\)
\(264\) 2.74222e32 + 4.86049e31i 0.557761 + 0.0988616i
\(265\) 3.53170e31i 0.0682597i
\(266\) −1.89059e32 − 2.12571e32i −0.347293 − 0.390484i
\(267\) −9.66550e31 − 9.66550e31i −0.168781 − 0.168781i
\(268\) 8.91629e32 − 7.04147e32i 1.48035 − 1.16908i
\(269\) 6.44816e32 − 6.44816e32i 1.01808 − 1.01808i 0.0182416 − 0.999834i \(-0.494193\pi\)
0.999834 − 0.0182416i \(-0.00580679\pi\)
\(270\) 2.86411e30 − 4.89242e31i 0.00430109 − 0.0734705i
\(271\) −2.20087e32 −0.314419 −0.157209 − 0.987565i \(-0.550250\pi\)
−0.157209 + 0.987565i \(0.550250\pi\)
\(272\) −3.36610e32 − 8.02011e31i −0.457559 − 0.109019i
\(273\) −2.38276e32 −0.308236
\(274\) −6.16625e31 + 1.05331e33i −0.0759257 + 1.29695i
\(275\) −9.92882e32 + 9.92882e32i −1.16387 + 1.16387i
\(276\) −3.17979e32 − 4.02642e32i −0.354916 − 0.449414i
\(277\) −2.92280e31 − 2.92280e31i −0.0310686 − 0.0310686i 0.691402 − 0.722470i \(-0.256993\pi\)
−0.722470 + 0.691402i \(0.756993\pi\)
\(278\) 5.14396e32 + 5.78368e32i 0.520826 + 0.585598i
\(279\) 1.16304e33i 1.12186i
\(280\) 8.08109e31 − 5.64770e31i 0.0742740 − 0.0519085i
\(281\) 1.10242e33i 0.965635i 0.875721 + 0.482817i \(0.160387\pi\)
−0.875721 + 0.482817i \(0.839613\pi\)
\(282\) 5.25175e32 − 4.67086e32i 0.438471 − 0.389972i
\(283\) −3.12691e32 − 3.12691e32i −0.248885 − 0.248885i 0.571628 − 0.820513i \(-0.306312\pi\)
−0.820513 + 0.571628i \(0.806312\pi\)
\(284\) 1.79995e31 − 1.53205e32i 0.0136604 − 0.116272i
\(285\) 2.52998e31 − 2.52998e31i 0.0183110 − 0.0183110i
\(286\) −2.77828e33 − 1.62645e32i −1.91793 − 0.112279i
\(287\) −7.67735e32 −0.505598
\(288\) 4.05805e32 − 1.34818e33i 0.254987 − 0.847130i
\(289\) −1.29874e33 −0.778755
\(290\) 3.38202e32 + 1.97989e31i 0.193554 + 0.0113310i
\(291\) 7.67700e32 − 7.67700e32i 0.419407 − 0.419407i
\(292\) −3.58085e32 + 3.04789e33i −0.186775 + 1.58976i
\(293\) −1.18705e33 − 1.18705e33i −0.591232 − 0.591232i 0.346732 − 0.937964i \(-0.387291\pi\)
−0.937964 + 0.346732i \(0.887291\pi\)
\(294\) −2.02183e32 + 1.79819e32i −0.0961733 + 0.0855358i
\(295\) 4.02454e32i 0.182860i
\(296\) 9.90160e32 + 1.41678e33i 0.429801 + 0.614986i
\(297\) − 2.57403e33i − 1.06758i
\(298\) −1.07435e33 − 1.20796e33i −0.425821 − 0.478778i
\(299\) 3.62538e33 + 3.62538e33i 1.37338 + 1.37338i
\(300\) −5.73521e32 − 7.26223e32i −0.207689 − 0.262986i
\(301\) −6.19777e32 + 6.19777e32i −0.214579 + 0.214579i
\(302\) −6.77317e31 + 1.15698e33i −0.0224232 + 0.383030i
\(303\) 1.73470e32 0.0549225
\(304\) 1.86513e33 − 1.14737e33i 0.564826 − 0.347463i
\(305\) 6.06148e32 0.175603
\(306\) −8.77370e31 + 1.49871e33i −0.0243189 + 0.415411i
\(307\) 1.51049e33 − 1.51049e33i 0.400635 − 0.400635i −0.477822 − 0.878457i \(-0.658573\pi\)
0.878457 + 0.477822i \(0.158573\pi\)
\(308\) 4.06380e33 − 3.20931e33i 1.03157 − 0.814661i
\(309\) −6.38672e32 − 6.38672e32i −0.155181 − 0.155181i
\(310\) −4.16616e32 − 4.68428e32i −0.0969066 − 0.108958i
\(311\) − 3.63876e33i − 0.810379i −0.914233 − 0.405190i \(-0.867206\pi\)
0.914233 − 0.405190i \(-0.132794\pi\)
\(312\) 3.20101e32 − 1.80596e33i 0.0682654 − 0.385143i
\(313\) − 6.14360e33i − 1.25480i −0.778697 − 0.627400i \(-0.784119\pi\)
0.778697 − 0.627400i \(-0.215881\pi\)
\(314\) −3.87867e33 + 3.44965e33i −0.758809 + 0.674878i
\(315\) −3.02456e32 − 3.02456e32i −0.0566852 − 0.0566852i
\(316\) 5.72421e33 + 6.72515e32i 1.02787 + 0.120761i
\(317\) 2.73410e33 − 2.73410e33i 0.470451 − 0.470451i −0.431610 − 0.902060i \(-0.642054\pi\)
0.902060 + 0.431610i \(0.142054\pi\)
\(318\) −1.22038e33 − 7.14432e31i −0.201247 − 0.0117813i
\(319\) 1.77937e34 2.81250
\(320\) 3.19494e32 + 6.88362e32i 0.0484104 + 0.104302i
\(321\) 2.33697e33 0.339497
\(322\) −9.52333e33 − 5.57513e32i −1.32658 − 0.0776606i
\(323\) −1.65106e33 + 1.65106e33i −0.220561 + 0.220561i
\(324\) −5.17269e33 − 6.07719e32i −0.662764 − 0.0778655i
\(325\) 6.53890e33 + 6.53890e33i 0.803673 + 0.803673i
\(326\) −5.07896e33 + 4.51718e33i −0.598876 + 0.532635i
\(327\) 1.35935e33i 0.153793i
\(328\) 1.03138e33 − 5.81889e33i 0.111975 − 0.631747i
\(329\) − 1.30682e34i − 1.36167i
\(330\) 4.32815e32 + 4.86642e32i 0.0432877 + 0.0486711i
\(331\) 2.13037e33 + 2.13037e33i 0.204539 + 0.204539i 0.801942 − 0.597402i \(-0.203800\pi\)
−0.597402 + 0.801942i \(0.703800\pi\)
\(332\) 2.36882e33 − 1.87073e33i 0.218358 − 0.172444i
\(333\) 5.30268e33 − 5.30268e33i 0.469351 − 0.469351i
\(334\) −2.86201e32 + 4.88884e33i −0.0243273 + 0.415555i
\(335\) 2.65690e33 0.216905
\(336\) 1.78809e33 + 2.90668e33i 0.140220 + 0.227938i
\(337\) −3.11876e32 −0.0234951 −0.0117476 − 0.999931i \(-0.503739\pi\)
−0.0117476 + 0.999931i \(0.503739\pi\)
\(338\) −2.63727e32 + 4.50494e33i −0.0190888 + 0.326072i
\(339\) −1.16137e33 + 1.16137e33i −0.0807748 + 0.0807748i
\(340\) −5.01520e32 − 6.35051e32i −0.0335214 − 0.0424466i
\(341\) −2.32823e34 − 2.32823e34i −1.49569 − 1.49569i
\(342\) −6.31373e33 − 7.09893e33i −0.389882 − 0.438370i
\(343\) 1.83055e34i 1.08670i
\(344\) −3.86486e33 − 5.53008e33i −0.220594 − 0.315640i
\(345\) − 1.19980e33i − 0.0658494i
\(346\) −2.51458e34 + 2.23644e34i −1.32720 + 1.18040i
\(347\) 1.97855e34 + 1.97855e34i 1.00438 + 1.00438i 0.999990 + 0.00439146i \(0.00139785\pi\)
0.00439146 + 0.999990i \(0.498602\pi\)
\(348\) −1.36831e33 + 1.16465e34i −0.0668134 + 0.568692i
\(349\) 1.37407e34 − 1.37407e34i 0.645455 − 0.645455i −0.306436 − 0.951891i \(-0.599137\pi\)
0.951891 + 0.306436i \(0.0991365\pi\)
\(350\) −1.71767e34 − 1.00556e33i −0.776286 − 0.0454451i
\(351\) −1.69520e34 −0.737182
\(352\) 1.88650e34 + 3.51121e34i 0.789460 + 1.46937i
\(353\) −3.34923e34 −1.34892 −0.674461 − 0.738311i \(-0.735624\pi\)
−0.674461 + 0.738311i \(0.735624\pi\)
\(354\) −1.39068e34 − 8.14131e32i −0.539119 − 0.0315610i
\(355\) 2.55080e32 − 2.55080e32i 0.00951906 − 0.00951906i
\(356\) 2.28275e33 − 1.94300e34i 0.0820132 − 0.698067i
\(357\) −2.57307e33 − 2.57307e33i −0.0890084 − 0.0890084i
\(358\) −2.80266e34 + 2.49266e34i −0.933576 + 0.830315i
\(359\) 2.73910e34i 0.878683i 0.898320 + 0.439342i \(0.144788\pi\)
−0.898320 + 0.439342i \(0.855212\pi\)
\(360\) 2.69872e33 − 1.88608e33i 0.0833824 − 0.0582742i
\(361\) 1.88244e34i 0.560241i
\(362\) 2.08440e34 + 2.34362e34i 0.597606 + 0.671926i
\(363\) 1.54942e34 + 1.54942e34i 0.427986 + 0.427986i
\(364\) −2.11358e34 − 2.67633e34i −0.562536 − 0.712313i
\(365\) −5.07461e33 + 5.07461e33i −0.130151 + 0.130151i
\(366\) −1.22619e33 + 2.09455e34i −0.0303083 + 0.517721i
\(367\) −8.52015e33 −0.202981 −0.101490 − 0.994837i \(-0.532361\pi\)
−0.101490 + 0.994837i \(0.532361\pi\)
\(368\) 1.70193e34 − 7.14312e34i 0.390837 − 1.64037i
\(369\) −2.56389e34 −0.567602
\(370\) −2.36228e32 + 4.03521e33i −0.00504207 + 0.0861277i
\(371\) −1.60726e34 + 1.60726e34i −0.330780 + 0.330780i
\(372\) 1.70294e34 − 1.34486e34i 0.337962 − 0.266900i
\(373\) −2.27237e34 − 2.27237e34i −0.434920 − 0.434920i 0.455378 − 0.890298i \(-0.349504\pi\)
−0.890298 + 0.455378i \(0.849504\pi\)
\(374\) −2.82455e34 − 3.17582e34i −0.521413 − 0.586258i
\(375\) − 4.35703e33i − 0.0775834i
\(376\) 9.90481e34 + 1.75560e34i 1.70141 + 0.301571i
\(377\) − 1.17185e35i − 1.94207i
\(378\) 2.35686e34 − 2.09618e34i 0.376873 − 0.335188i
\(379\) 3.97346e34 + 3.97346e34i 0.613111 + 0.613111i 0.943755 − 0.330644i \(-0.107266\pi\)
−0.330644 + 0.943755i \(0.607266\pi\)
\(380\) 5.08587e33 + 5.97519e32i 0.0757332 + 0.00889761i
\(381\) −1.54602e34 + 1.54602e34i −0.222191 + 0.222191i
\(382\) 6.85174e34 + 4.01113e33i 0.950485 + 0.0556431i
\(383\) 7.64494e34 1.02374 0.511871 − 0.859062i \(-0.328953\pi\)
0.511871 + 0.859062i \(0.328953\pi\)
\(384\) −2.44327e34 + 9.64765e33i −0.315864 + 0.124724i
\(385\) 1.21094e34 0.151148
\(386\) −1.00160e35 − 5.86356e33i −1.20717 − 0.0706697i
\(387\) −2.06978e34 + 2.06978e34i −0.240894 + 0.240894i
\(388\) 1.54326e35 + 1.81312e34i 1.73465 + 0.203797i
\(389\) −6.16888e34 − 6.16888e34i −0.669710 − 0.669710i 0.287939 − 0.957649i \(-0.407030\pi\)
−0.957649 + 0.287939i \(0.907030\pi\)
\(390\) 3.20492e33 − 2.85043e33i 0.0336081 − 0.0298908i
\(391\) 7.82989e34i 0.793176i
\(392\) −3.81317e34 − 6.75872e33i −0.373185 − 0.0661459i
\(393\) 8.81443e33i 0.0833480i
\(394\) −3.47910e34 − 3.91178e34i −0.317884 − 0.357417i
\(395\) 9.53055e33 + 9.53055e33i 0.0841506 + 0.0841506i
\(396\) 1.35713e35 − 1.07177e35i 1.15807 − 0.914565i
\(397\) 1.99385e34 − 1.99385e34i 0.164445 − 0.164445i −0.620088 − 0.784533i \(-0.712903\pi\)
0.784533 + 0.620088i \(0.212903\pi\)
\(398\) 6.97672e33 − 1.19175e35i 0.0556198 − 0.950088i
\(399\) 2.30277e34 0.177466
\(400\) 3.06967e34 − 1.28837e35i 0.228709 − 0.959907i
\(401\) −2.90815e34 −0.209492 −0.104746 − 0.994499i \(-0.533403\pi\)
−0.104746 + 0.994499i \(0.533403\pi\)
\(402\) −5.37468e33 + 9.18093e34i −0.0374370 + 0.639491i
\(403\) −1.53332e35 + 1.53332e35i −1.03280 + 1.03280i
\(404\) 1.53874e34 + 1.94843e34i 0.100234 + 0.126922i
\(405\) −8.61230e33 − 8.61230e33i −0.0542596 − 0.0542596i
\(406\) 1.44904e35 + 1.62925e35i 0.883036 + 0.992854i
\(407\) 2.12303e35i 1.25150i
\(408\) 2.29588e34 − 1.60454e34i 0.130929 − 0.0915036i
\(409\) − 1.38603e35i − 0.764732i −0.924011 − 0.382366i \(-0.875109\pi\)
0.924011 − 0.382366i \(-0.124891\pi\)
\(410\) 1.03264e34 − 9.18420e33i 0.0551272 − 0.0490297i
\(411\) −6.03920e34 − 6.03920e34i −0.311971 − 0.311971i
\(412\) 1.50839e34 − 1.28388e35i 0.0754049 − 0.641820i
\(413\) −1.83155e35 + 1.83155e35i −0.886123 + 0.886123i
\(414\) −3.18037e35 − 1.86184e34i −1.48927 − 0.0871843i
\(415\) 7.05868e33 0.0319944
\(416\) 2.31241e35 − 1.24240e35i 1.01462 − 0.545134i
\(417\) −6.26542e34 −0.266142
\(418\) 2.68501e35 + 1.57185e34i 1.10425 + 0.0646446i
\(419\) 2.02377e35 − 2.02377e35i 0.805882 − 0.805882i −0.178125 − 0.984008i \(-0.557003\pi\)
0.984008 + 0.178125i \(0.0570033\pi\)
\(420\) −9.31194e32 + 7.92599e33i −0.00359066 + 0.0305624i
\(421\) 1.02197e35 + 1.02197e35i 0.381618 + 0.381618i 0.871685 − 0.490067i \(-0.163028\pi\)
−0.490067 + 0.871685i \(0.663028\pi\)
\(422\) −1.74332e35 + 1.55049e35i −0.630462 + 0.560728i
\(423\) − 4.36421e35i − 1.52866i
\(424\) −1.00227e35 − 1.43411e35i −0.340052 − 0.486568i
\(425\) 1.41224e35i 0.464148i
\(426\) 8.29831e33 + 9.33033e33i 0.0264217 + 0.0297076i
\(427\) 2.75856e35 + 2.75856e35i 0.850953 + 0.850953i
\(428\) 2.07297e35 + 2.62490e35i 0.619586 + 0.784552i
\(429\) 1.59294e35 − 1.59294e35i 0.461345 − 0.461345i
\(430\) 9.22062e32 − 1.57505e34i 0.00258783 − 0.0442049i
\(431\) −3.92304e35 −1.06704 −0.533518 − 0.845789i \(-0.679130\pi\)
−0.533518 + 0.845789i \(0.679130\pi\)
\(432\) 1.27213e35 + 2.06794e35i 0.335352 + 0.545139i
\(433\) −6.26470e35 −1.60071 −0.800357 − 0.599523i \(-0.795357\pi\)
−0.800357 + 0.599523i \(0.795357\pi\)
\(434\) 2.35795e34 − 4.02780e35i 0.0584013 − 0.997601i
\(435\) −1.93910e34 + 1.93910e34i −0.0465580 + 0.0465580i
\(436\) −1.52683e35 + 1.20579e35i −0.355405 + 0.280674i
\(437\) −3.50368e35 − 3.50368e35i −0.790724 − 0.790724i
\(438\) −1.65088e35 − 1.85619e35i −0.361256 − 0.406183i
\(439\) 8.59413e35i 1.82361i 0.410628 + 0.911803i \(0.365310\pi\)
−0.410628 + 0.911803i \(0.634690\pi\)
\(440\) −1.62679e34 + 9.17808e34i −0.0334749 + 0.188860i
\(441\) 1.68014e35i 0.335293i
\(442\) −2.09152e35 + 1.86018e35i −0.404820 + 0.360044i
\(443\) −2.16005e35 − 2.16005e35i −0.405521 − 0.405521i 0.474653 − 0.880173i \(-0.342574\pi\)
−0.880173 + 0.474653i \(0.842574\pi\)
\(444\) −1.38959e35 − 1.63258e34i −0.253056 − 0.0297306i
\(445\) 3.23500e34 − 3.23500e34i 0.0571498 − 0.0571498i
\(446\) 1.85645e35 + 1.08680e34i 0.318173 + 0.0186264i
\(447\) 1.30858e35 0.217594
\(448\) −1.67870e35 + 4.58671e35i −0.270845 + 0.740028i
\(449\) 1.18330e36 1.85255 0.926277 − 0.376844i \(-0.122991\pi\)
0.926277 + 0.376844i \(0.122991\pi\)
\(450\) −5.73626e35 − 3.35811e34i −0.871484 − 0.0510182i
\(451\) 5.13252e35 − 5.13252e35i 0.756741 − 0.756741i
\(452\) −2.33464e35 − 2.74288e34i −0.334080 − 0.0392498i
\(453\) −6.63361e34 − 6.63361e34i −0.0921349 − 0.0921349i
\(454\) −7.99987e34 + 7.11502e34i −0.107852 + 0.0959229i
\(455\) − 7.97499e34i − 0.104370i
\(456\) −3.09356e34 + 1.74534e35i −0.0393037 + 0.221745i
\(457\) 1.24346e35i 0.153378i 0.997055 + 0.0766892i \(0.0244349\pi\)
−0.997055 + 0.0766892i \(0.975565\pi\)
\(458\) 2.32411e35 + 2.61314e35i 0.278338 + 0.312953i
\(459\) −1.83060e35 − 1.83060e35i −0.212874 − 0.212874i
\(460\) 1.34763e35 − 1.06426e35i 0.152173 − 0.120176i
\(461\) 2.19680e35 − 2.19680e35i 0.240895 − 0.240895i −0.576325 − 0.817220i \(-0.695514\pi\)
0.817220 + 0.576325i \(0.195514\pi\)
\(462\) −2.44963e34 + 4.18441e35i −0.0260876 + 0.445623i
\(463\) −9.14490e34 −0.0945879 −0.0472939 − 0.998881i \(-0.515060\pi\)
−0.0472939 + 0.998881i \(0.515060\pi\)
\(464\) −1.42952e36 + 8.79395e35i −1.43614 + 0.883469i
\(465\) 5.07445e34 0.0495192
\(466\) −4.26365e34 + 7.28309e35i −0.0404177 + 0.690408i
\(467\) −2.10427e35 + 2.10427e35i −0.193786 + 0.193786i −0.797330 − 0.603544i \(-0.793755\pi\)
0.603544 + 0.797330i \(0.293755\pi\)
\(468\) −7.05841e35 − 8.93774e35i −0.631521 − 0.799666i
\(469\) 1.20914e36 + 1.20914e36i 1.05110 + 1.05110i
\(470\) 1.56332e35 + 1.75774e35i 0.132046 + 0.148468i
\(471\) − 4.20173e35i − 0.344862i
\(472\) −1.14214e36 − 1.63424e36i −0.910963 − 1.30346i
\(473\) − 8.28675e35i − 0.642331i
\(474\) −3.48609e35 + 3.10050e35i −0.262622 + 0.233573i
\(475\) −6.31939e35 − 6.31939e35i −0.462713 − 0.462713i
\(476\) 6.07696e34 − 5.17249e35i 0.0432506 − 0.368134i
\(477\) −5.36753e35 + 5.36753e35i −0.371344 + 0.371344i
\(478\) 7.75289e35 + 4.53868e34i 0.521419 + 0.0305248i
\(479\) 5.84796e35 0.382362 0.191181 − 0.981555i \(-0.438768\pi\)
0.191181 + 0.981555i \(0.438768\pi\)
\(480\) −5.88225e34 − 1.77056e34i −0.0373927 − 0.0112552i
\(481\) 1.39818e36 0.864181
\(482\) 3.40336e35 + 1.99239e34i 0.204537 + 0.0119740i
\(483\) 5.46025e35 − 5.46025e35i 0.319100 − 0.319100i
\(484\) −3.65934e35 + 3.11470e36i −0.207965 + 1.77012i
\(485\) 2.56946e35 + 2.56946e35i 0.142013 + 0.142013i
\(486\) 1.20471e36 − 1.07146e36i 0.647581 − 0.575953i
\(487\) − 2.40241e36i − 1.25605i −0.778194 − 0.628024i \(-0.783864\pi\)
0.778194 − 0.628024i \(-0.216136\pi\)
\(488\) −2.46138e36 + 1.72021e36i −1.25173 + 0.874808i
\(489\) − 5.50199e35i − 0.272176i
\(490\) −6.01848e34 − 6.76696e34i −0.0289627 − 0.0325647i
\(491\) 1.07313e36 + 1.07313e36i 0.502403 + 0.502403i 0.912184 − 0.409781i \(-0.134395\pi\)
−0.409781 + 0.912184i \(0.634395\pi\)
\(492\) 2.96471e35 + 3.75408e35i 0.135037 + 0.170991i
\(493\) 1.26545e36 − 1.26545e36i 0.560805 − 0.560805i
\(494\) 1.03519e35 − 1.76829e36i 0.0446380 − 0.762499i
\(495\) 4.04400e35 0.169684
\(496\) 3.02111e36 + 7.19814e35i 1.23357 + 0.293912i
\(497\) 2.32172e35 0.0922569
\(498\) −1.42791e34 + 2.43913e35i −0.00552211 + 0.0943277i
\(499\) 2.45324e36 − 2.45324e36i 0.923386 − 0.923386i −0.0738807 − 0.997267i \(-0.523538\pi\)
0.997267 + 0.0738807i \(0.0235384\pi\)
\(500\) 4.89385e35 − 3.86483e35i 0.179290 − 0.141591i
\(501\) −2.80304e35 − 2.80304e35i −0.0999585 − 0.0999585i
\(502\) −1.06284e36 − 1.19502e36i −0.368952 − 0.414836i
\(503\) − 1.43604e36i − 0.485289i −0.970115 − 0.242644i \(-0.921985\pi\)
0.970115 − 0.242644i \(-0.0780148\pi\)
\(504\) 2.08653e36 + 3.69830e35i 0.686454 + 0.121672i
\(505\) 5.80598e34i 0.0185970i
\(506\) 6.73932e36 − 5.99390e36i 2.10177 − 1.86929i
\(507\) −2.58293e35 − 2.58293e35i −0.0784341 − 0.0784341i
\(508\) −3.10786e36 − 3.65131e35i −0.918970 − 0.107966i
\(509\) −1.32222e36 + 1.32222e36i −0.380726 + 0.380726i −0.871364 − 0.490637i \(-0.836764\pi\)
0.490637 + 0.871364i \(0.336764\pi\)
\(510\) 6.53900e34 + 3.82804e33i 0.0183364 + 0.00107344i
\(511\) −4.61887e36 −1.26140
\(512\) −3.25089e36 − 1.88852e36i −0.864684 − 0.502316i
\(513\) 1.63829e36 0.424431
\(514\) 8.15699e35 + 4.77525e34i 0.205839 + 0.0120502i
\(515\) 2.13761e35 − 2.13761e35i 0.0525449 − 0.0525449i
\(516\) 5.42394e35 + 6.37238e34i 0.129881 + 0.0152592i
\(517\) 8.73648e36 + 8.73648e36i 2.03805 + 2.03805i
\(518\) −1.94391e36 + 1.72890e36i −0.441800 + 0.392933i
\(519\) − 2.72402e36i − 0.603186i
\(520\) 6.04448e35 + 1.07137e35i 0.130411 + 0.0231149i
\(521\) 7.08770e36i 1.49003i 0.667046 + 0.745017i \(0.267558\pi\)
−0.667046 + 0.745017i \(0.732442\pi\)
\(522\) 4.83914e36 + 5.44095e36i 0.991326 + 1.11461i
\(523\) −4.86887e36 − 4.86887e36i −0.971976 − 0.971976i 0.0276418 − 0.999618i \(-0.491200\pi\)
−0.999618 + 0.0276418i \(0.991200\pi\)
\(524\) −9.90043e35 + 7.81868e35i −0.192611 + 0.152111i
\(525\) 9.84836e35 − 9.84836e35i 0.186730 − 0.186730i
\(526\) 3.09294e35 − 5.28330e36i 0.0571562 − 0.976333i
\(527\) −3.31158e36 −0.596474
\(528\) −3.13858e36 − 7.47802e35i −0.551031 − 0.131289i
\(529\) −1.07724e37 −1.84357
\(530\) 2.39117e34 − 4.08456e35i 0.00398921 − 0.0681430i
\(531\) −6.11657e36 + 6.11657e36i −0.994791 + 0.994791i
\(532\) 2.04263e36 + 2.58649e36i 0.323879 + 0.410113i
\(533\) −3.38016e36 − 3.38016e36i −0.522541 − 0.522541i
\(534\) 1.05242e36 + 1.18330e36i 0.158628 + 0.178356i
\(535\) 7.82174e35i 0.114955i
\(536\) −1.07888e37 + 7.54008e36i −1.54614 + 1.08057i
\(537\) − 3.03610e36i − 0.424290i
\(538\) −7.89415e36 + 7.02100e36i −1.07583 + 0.956837i
\(539\) −3.36338e36 − 3.36338e36i −0.447021 − 0.447021i
\(540\) −6.62493e34 + 5.63890e35i −0.00858748 + 0.0730935i
\(541\) −9.25234e36 + 9.25234e36i −1.16974 + 1.16974i −0.187467 + 0.982271i \(0.560028\pi\)
−0.982271 + 0.187467i \(0.939972\pi\)
\(542\) 2.54540e36 + 1.49012e35i 0.313882 + 0.0183752i
\(543\) −2.53883e36 −0.305376
\(544\) 3.83874e36 + 1.15547e36i 0.450406 + 0.135573i
\(545\) −4.54968e35 −0.0520749
\(546\) 2.75576e36 + 1.61327e35i 0.307710 + 0.0180139i
\(547\) 1.78743e36 − 1.78743e36i 0.194715 − 0.194715i −0.603015 − 0.797730i \(-0.706034\pi\)
0.797730 + 0.603015i \(0.206034\pi\)
\(548\) 1.42631e36 − 1.21402e37i 0.151592 − 1.29030i
\(549\) 9.21234e36 + 9.21234e36i 0.955308 + 0.955308i
\(550\) 1.21554e37 − 1.08109e37i 1.22990 − 1.09387i
\(551\) 1.13251e37i 1.11814i
\(552\) 3.40495e36 + 4.87202e36i 0.328045 + 0.469388i
\(553\) 8.67463e36i 0.815571i
\(554\) 3.18245e35 + 3.57823e35i 0.0291998 + 0.0328312i
\(555\) −2.31361e35 − 2.31361e35i −0.0207174 − 0.0207174i
\(556\) −5.55762e36 − 7.03736e36i −0.485712 − 0.615035i
\(557\) −3.36687e36 + 3.36687e36i −0.287198 + 0.287198i −0.835971 − 0.548773i \(-0.815095\pi\)
0.548773 + 0.835971i \(0.315095\pi\)
\(558\) 7.87448e35 − 1.34511e37i 0.0655632 − 1.11994i
\(559\) −5.45747e36 −0.443539
\(560\) −9.72852e35 + 5.98468e35i −0.0771807 + 0.0474791i
\(561\) 3.44034e36 0.266442
\(562\) 7.46408e35 − 1.27500e37i 0.0564334 − 0.963985i
\(563\) 9.47911e36 − 9.47911e36i 0.699688 − 0.699688i −0.264655 − 0.964343i \(-0.585258\pi\)
0.964343 + 0.264655i \(0.0852582\pi\)
\(564\) −6.39012e36 + 5.04648e36i −0.460512 + 0.363681i
\(565\) −3.88707e35 − 3.88707e35i −0.0273507 − 0.0273507i
\(566\) 3.40470e36 + 3.82812e36i 0.233914 + 0.263005i
\(567\) − 7.83884e36i − 0.525873i
\(568\) −3.11902e35 + 1.75970e36i −0.0204322 + 0.115275i
\(569\) − 1.53048e37i − 0.979065i −0.871985 − 0.489533i \(-0.837167\pi\)
0.871985 − 0.489533i \(-0.162833\pi\)
\(570\) −3.09733e35 + 2.75474e35i −0.0193498 + 0.0172096i
\(571\) 9.14289e36 + 9.14289e36i 0.557822 + 0.557822i 0.928687 − 0.370865i \(-0.120939\pi\)
−0.370865 + 0.928687i \(0.620939\pi\)
\(572\) 3.20218e37 + 3.76212e36i 1.90809 + 0.224175i
\(573\) −3.92848e36 + 3.92848e36i −0.228632 + 0.228632i
\(574\) 8.87919e36 + 5.19803e35i 0.504734 + 0.0295480i
\(575\) −2.99687e37 −1.66399
\(576\) −5.60611e36 + 1.53176e37i −0.304059 + 0.830780i
\(577\) −7.27440e35 −0.0385410 −0.0192705 − 0.999814i \(-0.506134\pi\)
−0.0192705 + 0.999814i \(0.506134\pi\)
\(578\) 1.50205e37 + 8.79325e35i 0.777424 + 0.0455117i
\(579\) 5.74274e36 − 5.74274e36i 0.290375 − 0.290375i
\(580\) −3.89805e36 − 4.57966e35i −0.192561 − 0.0226233i
\(581\) 3.21238e36 + 3.21238e36i 0.155042 + 0.155042i
\(582\) −9.39856e36 + 8.35901e36i −0.443202 + 0.394180i
\(583\) − 2.14900e37i − 0.990171i
\(584\) 6.20503e36 − 3.50078e37i 0.279364 − 1.57613i
\(585\) − 2.66329e36i − 0.117169i
\(586\) 1.29251e37 + 1.45325e37i 0.555669 + 0.624774i
\(587\) −3.74258e36 − 3.74258e36i −0.157238 − 0.157238i 0.624104 − 0.781341i \(-0.285464\pi\)
−0.781341 + 0.624104i \(0.785464\pi\)
\(588\) 2.46008e36 − 1.94280e36i 0.101008 − 0.0797690i
\(589\) 1.48185e37 − 1.48185e37i 0.594630 − 0.594630i
\(590\) 2.72486e35 − 4.65456e36i 0.0106867 − 0.182548i
\(591\) 4.23760e36 0.162438
\(592\) −1.04924e37 − 1.70561e37i −0.393125 − 0.639054i
\(593\) 3.94354e36 0.144427 0.0722133 − 0.997389i \(-0.476994\pi\)
0.0722133 + 0.997389i \(0.476994\pi\)
\(594\) −1.74278e36 + 2.97698e37i −0.0623914 + 1.06576i
\(595\) 8.61197e35 − 8.61197e35i 0.0301386 − 0.0301386i
\(596\) 1.16075e37 + 1.46980e37i 0.397113 + 0.502845i
\(597\) 6.83296e36 + 6.83296e36i 0.228536 + 0.228536i
\(598\) −3.94745e37 − 4.43837e37i −1.29077 − 1.45130i
\(599\) 5.27054e37i 1.68497i 0.538718 + 0.842486i \(0.318909\pi\)
−0.538718 + 0.842486i \(0.681091\pi\)
\(600\) 6.14133e36 + 8.78740e36i 0.191964 + 0.274675i
\(601\) − 4.15084e37i − 1.26862i −0.773080 − 0.634308i \(-0.781285\pi\)
0.773080 − 0.634308i \(-0.218715\pi\)
\(602\) 7.58761e36 − 6.74836e36i 0.226753 − 0.201672i
\(603\) 4.03800e37 + 4.03800e37i 1.18000 + 1.18000i
\(604\) 1.56669e36 − 1.33351e37i 0.0447698 − 0.381065i
\(605\) −5.18584e36 + 5.18584e36i −0.144918 + 0.144918i
\(606\) −2.00626e36 − 1.17450e35i −0.0548286 − 0.00320976i
\(607\) −2.81996e36 −0.0753694 −0.0376847 − 0.999290i \(-0.511998\pi\)
−0.0376847 + 0.999290i \(0.511998\pi\)
\(608\) −2.23478e37 + 1.20070e37i −0.584167 + 0.313860i
\(609\) −1.76495e37 −0.451231
\(610\) −7.01037e36 − 4.10399e35i −0.175303 − 0.0102625i
\(611\) 5.75365e37 − 5.75365e37i 1.40730 − 1.40730i
\(612\) 2.02943e36 − 1.72738e37i 0.0485546 − 0.413279i
\(613\) 1.12567e37 + 1.12567e37i 0.263447 + 0.263447i 0.826453 − 0.563006i \(-0.190355\pi\)
−0.563006 + 0.826453i \(0.690355\pi\)
\(614\) −1.84921e37 + 1.64468e37i −0.423364 + 0.376537i
\(615\) 1.11865e36i 0.0250542i
\(616\) −4.91725e37 + 3.43656e37i −1.07741 + 0.752982i
\(617\) − 3.61524e37i − 0.774975i −0.921875 − 0.387488i \(-0.873343\pi\)
0.921875 − 0.387488i \(-0.126657\pi\)
\(618\) 6.95410e36 + 7.81894e36i 0.145847 + 0.163985i
\(619\) −2.26432e37 − 2.26432e37i −0.464636 − 0.464636i 0.435535 − 0.900172i \(-0.356559\pi\)
−0.900172 + 0.435535i \(0.856559\pi\)
\(620\) 4.50119e36 + 5.69965e36i 0.0903733 + 0.114435i
\(621\) 3.88467e37 − 3.88467e37i 0.763163 − 0.763163i
\(622\) −2.46366e36 + 4.20839e37i −0.0473599 + 0.808994i
\(623\) 2.94447e37 0.553884
\(624\) −4.92486e36 + 2.06700e37i −0.0906571 + 0.380495i
\(625\) −5.33189e37 −0.960508
\(626\) −4.15959e36 + 7.10535e37i −0.0733327 + 1.25266i
\(627\) −1.53946e37 + 1.53946e37i −0.265618 + 0.265618i
\(628\) 4.71941e37 − 3.72707e37i 0.796953 − 0.629379i
\(629\) 1.50986e37 + 1.50986e37i 0.249547 + 0.249547i
\(630\) 3.29325e36 + 3.70281e36i 0.0532755 + 0.0599011i
\(631\) 6.60565e37i 1.04597i 0.852342 + 0.522985i \(0.175182\pi\)
−0.852342 + 0.522985i \(0.824818\pi\)
\(632\) −6.57476e37 − 1.16536e37i −1.01906 − 0.180625i
\(633\) − 1.88853e37i − 0.286532i
\(634\) −3.34722e37 + 2.97699e37i −0.497141 + 0.442153i
\(635\) −5.17445e36 − 5.17445e36i −0.0752348 − 0.0752348i
\(636\) 1.40659e37 + 1.65254e36i 0.200214 + 0.0235224i
\(637\) −2.21505e37 + 2.21505e37i −0.308674 + 0.308674i
\(638\) −2.05792e38 − 1.20474e37i −2.80769 − 0.164367i
\(639\) 7.75351e36 0.103571
\(640\) −3.22903e36 − 8.17752e36i −0.0422321 − 0.106953i
\(641\) 1.17475e38 1.50439 0.752196 − 0.658940i \(-0.228995\pi\)
0.752196 + 0.658940i \(0.228995\pi\)
\(642\) −2.70281e37 − 1.58227e36i −0.338916 − 0.0198408i
\(643\) 1.43703e34 − 1.43703e34i 0.000176448 − 0.000176448i −0.707019 − 0.707195i \(-0.749960\pi\)
0.707195 + 0.707019i \(0.249960\pi\)
\(644\) 1.09764e38 + 1.28958e37i 1.31978 + 0.155056i
\(645\) 9.03062e35 + 9.03062e35i 0.0106331 + 0.0106331i
\(646\) 2.02131e37 − 1.79774e37i 0.233074 − 0.207294i
\(647\) 5.95952e37i 0.672982i 0.941687 + 0.336491i \(0.109240\pi\)
−0.941687 + 0.336491i \(0.890760\pi\)
\(648\) 5.94129e37 + 1.05308e37i 0.657080 + 0.116465i
\(649\) − 2.44889e38i − 2.65256i
\(650\) −7.11980e37 − 8.00524e37i −0.755331 − 0.849267i
\(651\) 2.30936e37 + 2.30936e37i 0.239965 + 0.239965i
\(652\) 6.17988e37 − 4.88044e37i 0.628981 − 0.496726i
\(653\) −9.39383e37 + 9.39383e37i −0.936515 + 0.936515i −0.998102 − 0.0615870i \(-0.980384\pi\)
0.0615870 + 0.998102i \(0.480384\pi\)
\(654\) 9.20362e35 − 1.57215e37i 0.00898792 − 0.153530i
\(655\) −2.95015e36 −0.0282220
\(656\) −1.58681e37 + 6.65997e37i −0.148704 + 0.624123i
\(657\) −1.54250e38 −1.41609
\(658\) −8.84799e36 + 1.51140e38i −0.0795784 + 1.35934i
\(659\) 1.46058e38 − 1.46058e38i 1.28698 − 1.28698i 0.350374 − 0.936610i \(-0.386055\pi\)
0.936610 − 0.350374i \(-0.113945\pi\)
\(660\) −4.67621e36 − 5.92127e36i −0.0403693 − 0.0511178i
\(661\) 5.37834e37 + 5.37834e37i 0.454914 + 0.454914i 0.896982 − 0.442068i \(-0.145755\pi\)
−0.442068 + 0.896982i \(0.645755\pi\)
\(662\) −2.31962e37 − 2.60810e37i −0.192236 − 0.216143i
\(663\) − 2.26573e37i − 0.183982i
\(664\) −2.86631e37 + 2.00320e37i −0.228063 + 0.159388i
\(665\) 7.70727e36i 0.0600909i
\(666\) −6.49180e37 + 5.77376e37i −0.495979 + 0.441120i
\(667\) 2.68538e38 + 2.68538e38i 2.01051 + 2.01051i
\(668\) 6.62008e36 − 5.63477e37i 0.0485714 − 0.413423i
\(669\) −1.06441e37 + 1.06441e37i −0.0765342 + 0.0765342i
\(670\) −3.07282e37 − 1.79888e36i −0.216534 − 0.0126763i
\(671\) −3.68834e38 −2.54728
\(672\) −1.87121e37 − 3.48276e37i −0.126659 − 0.235743i
\(673\) −1.03533e38 −0.686871 −0.343435 − 0.939176i \(-0.611591\pi\)
−0.343435 + 0.939176i \(0.611591\pi\)
\(674\) 3.60698e36 + 2.11159e35i 0.0234550 + 0.00137310i
\(675\) 7.00656e37 − 7.00656e37i 0.446585 − 0.446585i
\(676\) 6.10023e36 − 5.19230e37i 0.0381124 − 0.324399i
\(677\) −1.60846e38 − 1.60846e38i −0.985063 − 0.985063i 0.0148267 − 0.999890i \(-0.495280\pi\)
−0.999890 + 0.0148267i \(0.995280\pi\)
\(678\) 1.42181e37 − 1.26455e37i 0.0853574 − 0.0759162i
\(679\) 2.33870e38i 1.37636i
\(680\) 5.37033e36 + 7.68420e36i 0.0309835 + 0.0443331i
\(681\) − 8.66620e36i − 0.0490165i
\(682\) 2.53506e38 + 2.85033e38i 1.40572 + 1.58054i
\(683\) −1.16442e37 − 1.16442e37i −0.0633036 − 0.0633036i 0.674746 − 0.738050i \(-0.264253\pi\)
−0.738050 + 0.674746i \(0.764253\pi\)
\(684\) 6.82147e37 + 8.63770e37i 0.363597 + 0.460406i
\(685\) 2.02129e37 − 2.02129e37i 0.105635 − 0.105635i
\(686\) 1.23939e37 − 2.11711e38i 0.0635087 − 1.08484i
\(687\) −2.83080e37 −0.142230
\(688\) 4.09546e37 + 6.65746e37i 0.201771 + 0.327993i
\(689\) −1.41528e38 −0.683728
\(690\) −8.12339e35 + 1.38762e37i −0.00384835 + 0.0657369i
\(691\) 3.97328e37 − 3.97328e37i 0.184585 − 0.184585i −0.608766 − 0.793350i \(-0.708335\pi\)
0.793350 + 0.608766i \(0.208335\pi\)
\(692\) 3.05964e38 − 2.41629e38i 1.39392 − 1.10082i
\(693\) 1.84041e38 + 1.84041e38i 0.822272 + 0.822272i
\(694\) −2.15432e38 − 2.42224e38i −0.943967 − 1.06136i
\(695\) − 2.09701e37i − 0.0901167i
\(696\) 2.37105e37 − 1.33771e38i 0.0999345 − 0.563815i
\(697\) − 7.30029e37i − 0.301785i
\(698\) −1.68221e38 + 1.49614e38i −0.682074 + 0.606631i
\(699\) −4.17580e37 − 4.17580e37i −0.166072 − 0.166072i
\(700\) 1.97975e38 + 2.32594e37i 0.772303 + 0.0907349i
\(701\) 1.32355e38 − 1.32355e38i 0.506462 − 0.506462i −0.406977 − 0.913439i \(-0.633417\pi\)
0.913439 + 0.406977i \(0.133417\pi\)
\(702\) 1.96057e38 + 1.14775e37i 0.735922 + 0.0430822i
\(703\) −1.35125e38 −0.497551
\(704\) −1.94409e38 − 4.18860e38i −0.702238 − 1.51300i
\(705\) −1.90414e37 −0.0674756
\(706\) 3.87353e38 + 2.26763e37i 1.34662 + 0.0788333i
\(707\) −2.64228e37 + 2.64228e37i −0.0901190 + 0.0901190i
\(708\) 1.60287e38 + 1.88316e37i 0.536353 + 0.0630140i
\(709\) 1.37626e38 + 1.37626e38i 0.451831 + 0.451831i 0.895962 − 0.444131i \(-0.146488\pi\)
−0.444131 + 0.895962i \(0.646488\pi\)
\(710\) −3.12282e36 + 2.77741e36i −0.0100591 + 0.00894648i
\(711\) 2.89694e38i 0.915587i
\(712\) −3.95563e37 + 2.23170e38i −0.122669 + 0.692081i
\(713\) − 7.02741e38i − 2.13839i
\(714\) 2.80166e37 + 3.15008e37i 0.0836545 + 0.0940581i
\(715\) 5.33150e37 + 5.33150e37i 0.156213 + 0.156213i
\(716\) 3.41017e38 − 2.69312e38i 0.980505 − 0.774336i
\(717\) −4.44516e37 + 4.44516e37i −0.125423 + 0.125423i
\(718\) 1.85454e37 − 3.16789e38i 0.0513518 − 0.877182i
\(719\) −1.32493e38 −0.360043 −0.180022 − 0.983663i \(-0.557617\pi\)
−0.180022 + 0.983663i \(0.557617\pi\)
\(720\) −3.24889e37 + 1.99861e37i −0.0866456 + 0.0533016i
\(721\) 1.94563e38 0.509255
\(722\) 1.27453e37 − 2.17713e38i 0.0327414 − 0.559283i
\(723\) −1.95133e37 + 1.95133e37i −0.0491999 + 0.0491999i
\(724\) −2.25202e38 − 2.85163e38i −0.557316 − 0.705703i
\(725\) 4.84348e38 + 4.84348e38i 1.17651 + 1.17651i
\(726\) −1.68706e38 − 1.89687e38i −0.402242 − 0.452266i
\(727\) 3.56179e38i 0.833592i 0.909000 + 0.416796i \(0.136847\pi\)
−0.909000 + 0.416796i \(0.863153\pi\)
\(728\) 2.26324e38 + 3.23839e38i 0.519945 + 0.743971i
\(729\) − 1.65403e38i − 0.373010i
\(730\) 6.21259e37 − 5.52543e37i 0.137535 − 0.122323i
\(731\) −5.89337e37 − 5.89337e37i −0.128079 − 0.128079i
\(732\) 2.83628e37 − 2.41414e38i 0.0605130 − 0.515065i
\(733\) −5.15135e38 + 5.15135e38i −1.07899 + 1.07899i −0.0823891 + 0.996600i \(0.526255\pi\)
−0.996600 + 0.0823891i \(0.973745\pi\)
\(734\) 9.85392e37 + 5.76866e36i 0.202634 + 0.0118626i
\(735\) 7.33060e36 0.0148000
\(736\) −2.45199e38 + 8.14610e38i −0.486035 + 1.61473i
\(737\) −1.61669e39 −3.14641
\(738\) 2.96525e38 + 1.73591e37i 0.566631 + 0.0331716i
\(739\) 5.08337e38 − 5.08337e38i 0.953789 − 0.953789i −0.0451898 − 0.998978i \(-0.514389\pi\)
0.998978 + 0.0451898i \(0.0143892\pi\)
\(740\) 5.46417e36 − 4.65090e37i 0.0100669 − 0.0856858i
\(741\) 1.01386e38 + 1.01386e38i 0.183413 + 0.183413i
\(742\) 1.96769e38 − 1.75005e38i 0.349546