Properties

Label 18.9.d.a.11.6
Level $18$
Weight $9$
Character 18.11
Analytic conductor $7.333$
Analytic rank $0$
Dimension $16$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [18,9,Mod(5,18)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(18, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("18.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 18.d (of order \(6\), 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: \(7.33281498110\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 5476 x^{14} - 38192 x^{13} + 11414542 x^{12} - 67991120 x^{11} + \cdots + 19\!\cdots\!29 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{28}\cdot 3^{22} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.6
Root \(0.500000 + 11.5235i\) of defining polynomial
Character \(\chi\) \(=\) 18.11
Dual form 18.9.d.a.5.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(9.79796 + 5.65685i) q^{2} +(7.38176 + 80.6629i) q^{3} +(64.0000 + 110.851i) q^{4} +(935.250 - 539.967i) q^{5} +(-383.972 + 832.090i) q^{6} +(-2056.09 + 3561.25i) q^{7} +1448.15i q^{8} +(-6452.02 + 1190.87i) q^{9} +12218.1 q^{10} +(8419.53 + 4861.02i) q^{11} +(-8469.15 + 5980.71i) q^{12} +(-4116.02 - 7129.16i) q^{13} +(-40291.0 + 23262.0i) q^{14} +(50459.1 + 71454.1i) q^{15} +(-8192.00 + 14189.0i) q^{16} -87809.9i q^{17} +(-69953.2 - 24830.0i) q^{18} +123643. q^{19} +(119712. + 69115.7i) q^{20} +(-302439. - 139562. i) q^{21} +(54996.1 + 95256.1i) q^{22} +(92029.4 - 53133.2i) q^{23} +(-116812. + 10689.9i) q^{24} +(387816. - 671717. i) q^{25} -93134.9i q^{26} +(-143686. - 511648. i) q^{27} -526359. q^{28} +(430885. + 248772. i) q^{29} +(90190.8 + 985544. i) q^{30} +(-577977. - 1.00109e6i) q^{31} +(-160530. + 92681.9i) q^{32} +(-329953. + 715027. i) q^{33} +(496728. - 860358. i) q^{34} +4.44088e6i q^{35} +(-544939. - 638999. i) q^{36} +1.20145e6 q^{37} +(1.21145e6 + 699428. i) q^{38} +(544675. - 384636. i) q^{39} +(781955. + 1.35439e6i) q^{40} +(1.53952e6 - 888843. i) q^{41} +(-2.17380e6 - 3.07827e6i) q^{42} +(-528726. + 915780. i) q^{43} +1.24442e6i q^{44} +(-5.39122e6 + 4.59764e6i) q^{45} +1.20227e6 q^{46} +(-3.80689e6 - 2.19791e6i) q^{47} +(-1.20499e6 - 556051. i) q^{48} +(-5.57261e6 - 9.65205e6i) q^{49} +(7.59961e6 - 4.38763e6i) q^{50} +(7.08301e6 - 648192. i) q^{51} +(526851. - 912532. i) q^{52} +1.04810e6i q^{53} +(1.48649e6 - 5.82592e6i) q^{54} +1.04991e7 q^{55} +(-5.15724e6 - 2.97754e6i) q^{56} +(912700. + 9.97337e6i) q^{57} +(2.81453e6 + 4.87491e6i) q^{58} +(-8.70048e6 + 5.02323e6i) q^{59} +(-4.69139e6 + 1.01665e7i) q^{60} +(-4.15770e6 + 7.20135e6i) q^{61} -1.30781e7i q^{62} +(9.02495e6 - 2.54258e7i) q^{63} -2.09715e6 q^{64} +(-7.69902e6 - 4.44503e6i) q^{65} +(-7.27767e6 + 5.13931e6i) q^{66} +(6.19183e6 + 1.07246e7i) q^{67} +(9.73384e6 - 5.61983e6i) q^{68} +(4.96522e6 + 7.03114e6i) q^{69} +(-2.51214e7 + 4.35116e7i) q^{70} -1.69579e7i q^{71} +(-1.72456e6 - 9.34352e6i) q^{72} -2.42736e7 q^{73} +(1.17718e7 + 6.79644e6i) q^{74} +(5.70454e7 + 2.63239e7i) q^{75} +(7.91313e6 + 1.37059e7i) q^{76} +(-3.46226e7 + 1.99894e7i) q^{77} +(7.51254e6 - 687500. i) q^{78} +(6.39004e6 - 1.10679e7i) q^{79} +1.76936e7i q^{80} +(4.02104e7 - 1.53670e7i) q^{81} +2.01122e7 q^{82} +(-2.79188e7 - 1.61189e7i) q^{83} +(-3.88546e6 - 4.24577e7i) q^{84} +(-4.74144e7 - 8.21242e7i) q^{85} +(-1.03609e7 + 5.98185e6i) q^{86} +(-1.68860e7 + 3.65928e7i) q^{87} +(-7.03950e6 + 1.21928e7i) q^{88} +2.10088e7i q^{89} +(-7.88311e7 + 1.45501e7i) q^{90} +3.38516e7 q^{91} +(1.17798e7 + 6.80105e6i) q^{92} +(7.64841e7 - 5.40111e7i) q^{93} +(-2.48665e7 - 4.30700e7i) q^{94} +(1.15637e8 - 6.67629e7i) q^{95} +(-8.66099e6 - 1.22646e7i) q^{96} +(-4.46651e7 + 7.73622e7i) q^{97} -1.26094e8i q^{98} +(-6.01118e7 - 2.13368e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 126 q^{3} + 1024 q^{4} - 882 q^{5} + 384 q^{6} - 1846 q^{7} - 28662 q^{9} + 45756 q^{11} + 5376 q^{12} - 3370 q^{13} - 94464 q^{14} + 128754 q^{15} - 131072 q^{16} - 236544 q^{18} + 362180 q^{19}+ \cdots + 366888330 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).

\(n\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.79796 + 5.65685i 0.612372 + 0.353553i
\(3\) 7.38176 + 80.6629i 0.0911329 + 0.995839i
\(4\) 64.0000 + 110.851i 0.250000 + 0.433013i
\(5\) 935.250 539.967i 1.49640 0.863947i 0.496408 0.868089i \(-0.334652\pi\)
0.999991 + 0.00414227i \(0.00131853\pi\)
\(6\) −383.972 + 832.090i −0.296275 + 0.642045i
\(7\) −2056.09 + 3561.25i −0.856347 + 1.48324i 0.0190419 + 0.999819i \(0.493938\pi\)
−0.875389 + 0.483419i \(0.839395\pi\)
\(8\) 1448.15i 0.353553i
\(9\) −6452.02 + 1190.87i −0.983390 + 0.181507i
\(10\) 12218.1 1.22181
\(11\) 8419.53 + 4861.02i 0.575065 + 0.332014i 0.759170 0.650893i \(-0.225605\pi\)
−0.184105 + 0.982907i \(0.558939\pi\)
\(12\) −8469.15 + 5980.71i −0.408428 + 0.288421i
\(13\) −4116.02 7129.16i −0.144113 0.249612i 0.784928 0.619586i \(-0.212700\pi\)
−0.929042 + 0.369975i \(0.879366\pi\)
\(14\) −40291.0 + 23262.0i −1.04881 + 0.605529i
\(15\) 50459.1 + 71454.1i 0.996723 + 1.41144i
\(16\) −8192.00 + 14189.0i −0.125000 + 0.216506i
\(17\) 87809.9i 1.05135i −0.850685 0.525676i \(-0.823813\pi\)
0.850685 0.525676i \(-0.176187\pi\)
\(18\) −69953.2 24830.0i −0.666373 0.236531i
\(19\) 123643. 0.948754 0.474377 0.880322i \(-0.342673\pi\)
0.474377 + 0.880322i \(0.342673\pi\)
\(20\) 119712. + 69115.7i 0.748200 + 0.431973i
\(21\) −302439. 139562.i −1.55511 0.717612i
\(22\) 54996.1 + 95256.1i 0.234769 + 0.406632i
\(23\) 92029.4 53133.2i 0.328863 0.189869i −0.326473 0.945206i \(-0.605860\pi\)
0.655336 + 0.755337i \(0.272527\pi\)
\(24\) −116812. + 10689.9i −0.352082 + 0.0322203i
\(25\) 387816. 671717.i 0.992808 1.71959i
\(26\) 93134.9i 0.203807i
\(27\) −143686. 511648.i −0.270371 0.962756i
\(28\) −526359. −0.856347
\(29\) 430885. + 248772.i 0.609213 + 0.351729i 0.772657 0.634823i \(-0.218927\pi\)
−0.163444 + 0.986553i \(0.552260\pi\)
\(30\) 90190.8 + 985544.i 0.111347 + 1.21672i
\(31\) −577977. 1.00109e6i −0.625841 1.08399i −0.988378 0.152019i \(-0.951422\pi\)
0.362536 0.931970i \(-0.381911\pi\)
\(32\) −160530. + 92681.9i −0.153093 + 0.0883883i
\(33\) −329953. + 715027.i −0.278225 + 0.602929i
\(34\) 496728. 860358.i 0.371709 0.643819i
\(35\) 4.44088e6i 2.95935i
\(36\) −544939. 638999.i −0.324442 0.380443i
\(37\) 1.20145e6 0.641061 0.320531 0.947238i \(-0.396139\pi\)
0.320531 + 0.947238i \(0.396139\pi\)
\(38\) 1.21145e6 + 699428.i 0.580991 + 0.335435i
\(39\) 544675. 384636.i 0.235439 0.166261i
\(40\) 781955. + 1.35439e6i 0.305451 + 0.529057i
\(41\) 1.53952e6 888843.i 0.544816 0.314550i −0.202212 0.979342i \(-0.564813\pi\)
0.747029 + 0.664792i \(0.231480\pi\)
\(42\) −2.17380e6 3.07827e6i −0.698590 0.989259i
\(43\) −528726. + 915780.i −0.154652 + 0.267866i −0.932932 0.360052i \(-0.882759\pi\)
0.778280 + 0.627917i \(0.216092\pi\)
\(44\) 1.24442e6i 0.332014i
\(45\) −5.39122e6 + 4.59764e6i −1.31473 + 1.12120i
\(46\) 1.20227e6 0.268516
\(47\) −3.80689e6 2.19791e6i −0.780151 0.450420i 0.0563327 0.998412i \(-0.482059\pi\)
−0.836484 + 0.547992i \(0.815393\pi\)
\(48\) −1.20499e6 556051.i −0.226997 0.104749i
\(49\) −5.57261e6 9.65205e6i −0.966662 1.67431i
\(50\) 7.59961e6 4.38763e6i 1.21594 0.702021i
\(51\) 7.08301e6 648192.i 1.04698 0.0958127i
\(52\) 526851. 912532.i 0.0720567 0.124806i
\(53\) 1.04810e6i 0.132831i 0.997792 + 0.0664157i \(0.0211563\pi\)
−0.997792 + 0.0664157i \(0.978844\pi\)
\(54\) 1.48649e6 5.82592e6i 0.174818 0.685156i
\(55\) 1.04991e7 1.14737
\(56\) −5.15724e6 2.97754e6i −0.524404 0.302765i
\(57\) 912700. + 9.97337e6i 0.0864627 + 0.944806i
\(58\) 2.81453e6 + 4.87491e6i 0.248710 + 0.430779i
\(59\) −8.70048e6 + 5.02323e6i −0.718018 + 0.414548i −0.814023 0.580833i \(-0.802727\pi\)
0.0960047 + 0.995381i \(0.469394\pi\)
\(60\) −4.69139e6 + 1.01665e7i −0.361990 + 0.784453i
\(61\) −4.15770e6 + 7.20135e6i −0.300285 + 0.520109i −0.976200 0.216870i \(-0.930415\pi\)
0.675915 + 0.736979i \(0.263749\pi\)
\(62\) 1.30781e7i 0.885073i
\(63\) 9.02495e6 2.54258e7i 0.572905 1.61403i
\(64\) −2.09715e6 −0.125000
\(65\) −7.69902e6 4.44503e6i −0.431302 0.249013i
\(66\) −7.27767e6 + 5.13931e6i −0.383545 + 0.270850i
\(67\) 6.19183e6 + 1.07246e7i 0.307270 + 0.532207i 0.977764 0.209708i \(-0.0672513\pi\)
−0.670494 + 0.741915i \(0.733918\pi\)
\(68\) 9.73384e6 5.61983e6i 0.455248 0.262838i
\(69\) 4.96522e6 + 7.03114e6i 0.219049 + 0.310191i
\(70\) −2.51214e7 + 4.35116e7i −1.04629 + 1.81223i
\(71\) 1.69579e7i 0.667328i −0.942692 0.333664i \(-0.891715\pi\)
0.942692 0.333664i \(-0.108285\pi\)
\(72\) −1.72456e6 9.34352e6i −0.0641725 0.347681i
\(73\) −2.42736e7 −0.854757 −0.427378 0.904073i \(-0.640563\pi\)
−0.427378 + 0.904073i \(0.640563\pi\)
\(74\) 1.17718e7 + 6.79644e6i 0.392568 + 0.226649i
\(75\) 5.70454e7 + 2.63239e7i 1.80292 + 0.831965i
\(76\) 7.91313e6 + 1.37059e7i 0.237189 + 0.410823i
\(77\) −3.46226e7 + 1.99894e7i −0.984911 + 0.568639i
\(78\) 7.51254e6 687500.i 0.202959 0.0185735i
\(79\) 6.39004e6 1.10679e7i 0.164057 0.284155i −0.772263 0.635303i \(-0.780875\pi\)
0.936320 + 0.351148i \(0.114209\pi\)
\(80\) 1.76936e7i 0.431973i
\(81\) 4.02104e7 1.53670e7i 0.934110 0.356985i
\(82\) 2.01122e7 0.444841
\(83\) −2.79188e7 1.61189e7i −0.588281 0.339644i 0.176136 0.984366i \(-0.443640\pi\)
−0.764418 + 0.644722i \(0.776973\pi\)
\(84\) −3.88546e6 4.24577e7i −0.0780414 0.852784i
\(85\) −4.74144e7 8.21242e7i −0.908312 1.57324i
\(86\) −1.03609e7 + 5.98185e6i −0.189410 + 0.109356i
\(87\) −1.68860e7 + 3.65928e7i −0.294746 + 0.638732i
\(88\) −7.03950e6 + 1.21928e7i −0.117385 + 0.203316i
\(89\) 2.10088e7i 0.334843i 0.985885 + 0.167422i \(0.0535441\pi\)
−0.985885 + 0.167422i \(0.946456\pi\)
\(90\) −7.88311e7 + 1.45501e7i −1.20151 + 0.221767i
\(91\) 3.38516e7 0.493644
\(92\) 1.17798e7 + 6.80105e6i 0.164432 + 0.0949346i
\(93\) 7.64841e7 5.40111e7i 1.02244 0.722024i
\(94\) −2.48665e7 4.30700e7i −0.318495 0.551650i
\(95\) 1.15637e8 6.67629e7i 1.41972 0.819673i
\(96\) −8.66099e6 1.22646e7i −0.101972 0.144401i
\(97\) −4.46651e7 + 7.73622e7i −0.504523 + 0.873860i 0.495463 + 0.868629i \(0.334998\pi\)
−0.999986 + 0.00523116i \(0.998335\pi\)
\(98\) 1.26094e8i 1.36707i
\(99\) −6.01118e7 2.13368e7i −0.625776 0.222121i
\(100\) 9.92808e7 0.992808
\(101\) −3.08430e7 1.78072e7i −0.296395 0.171124i 0.344427 0.938813i \(-0.388073\pi\)
−0.640822 + 0.767689i \(0.721406\pi\)
\(102\) 7.30657e7 + 3.37166e7i 0.675014 + 0.311489i
\(103\) −4.35300e6 7.53962e6i −0.0386759 0.0669886i 0.846040 0.533120i \(-0.178981\pi\)
−0.884715 + 0.466132i \(0.845647\pi\)
\(104\) 1.03241e7 5.96064e6i 0.0882510 0.0509518i
\(105\) −3.58215e8 + 3.27815e7i −2.94704 + 0.269694i
\(106\) −5.92897e6 + 1.02693e7i −0.0469630 + 0.0813422i
\(107\) 2.34341e8i 1.78778i 0.448290 + 0.893888i \(0.352033\pi\)
−0.448290 + 0.893888i \(0.647967\pi\)
\(108\) 4.75209e7 4.86733e7i 0.349293 0.357763i
\(109\) 2.66492e8 1.88789 0.943947 0.330098i \(-0.107082\pi\)
0.943947 + 0.330098i \(0.107082\pi\)
\(110\) 1.02870e8 + 5.93921e7i 0.702617 + 0.405656i
\(111\) 8.86883e6 + 9.69126e7i 0.0584217 + 0.638393i
\(112\) −3.36870e7 5.83476e7i −0.214087 0.370809i
\(113\) −2.47560e8 + 1.42929e8i −1.51833 + 0.876610i −0.518565 + 0.855038i \(0.673534\pi\)
−0.999767 + 0.0215714i \(0.993133\pi\)
\(114\) −4.74753e7 + 1.02882e8i −0.281092 + 0.609142i
\(115\) 5.73803e7 9.93856e7i 0.328074 0.568241i
\(116\) 6.36855e7i 0.351729i
\(117\) 3.50465e7 + 4.10958e7i 0.187026 + 0.219308i
\(118\) −1.13663e8 −0.586259
\(119\) 3.12713e8 + 1.80545e8i 1.55940 + 0.900322i
\(120\) −1.03477e8 + 7.30726e7i −0.499019 + 0.352395i
\(121\) −5.99205e7 1.03785e8i −0.279534 0.484166i
\(122\) −8.14740e7 + 4.70390e7i −0.367773 + 0.212334i
\(123\) 8.30610e7 + 1.17621e8i 0.362892 + 0.513883i
\(124\) 7.39811e7 1.28139e8i 0.312921 0.541994i
\(125\) 4.15781e8i 1.70304i
\(126\) 2.32256e8 1.98068e8i 0.921478 0.785837i
\(127\) −8.18752e7 −0.314730 −0.157365 0.987541i \(-0.550300\pi\)
−0.157365 + 0.987541i \(0.550300\pi\)
\(128\) −2.05478e7 1.18633e7i −0.0765466 0.0441942i
\(129\) −7.77724e7 3.58885e7i −0.280845 0.129597i
\(130\) −5.02898e7 8.71044e7i −0.176078 0.304977i
\(131\) 3.27800e8 1.89256e8i 1.11308 0.642634i 0.173451 0.984843i \(-0.444508\pi\)
0.939624 + 0.342208i \(0.111175\pi\)
\(132\) −1.00379e8 + 9.18601e6i −0.330632 + 0.0302574i
\(133\) −2.54220e8 + 4.40322e8i −0.812463 + 1.40723i
\(134\) 1.40105e8i 0.434545i
\(135\) −4.10656e8 4.00933e8i −1.23635 1.20708i
\(136\) 1.27162e8 0.371709
\(137\) 8.36881e7 + 4.83174e7i 0.237565 + 0.137158i 0.614057 0.789262i \(-0.289537\pi\)
−0.376492 + 0.926420i \(0.622870\pi\)
\(138\) 8.87485e6 + 9.69784e7i 0.0244706 + 0.267398i
\(139\) −2.13230e8 3.69325e8i −0.571200 0.989348i −0.996443 0.0842686i \(-0.973145\pi\)
0.425243 0.905079i \(-0.360189\pi\)
\(140\) −4.92277e8 + 2.84216e8i −1.28144 + 0.739839i
\(141\) 1.49188e8 3.23299e8i 0.377449 0.817953i
\(142\) 9.59286e7 1.66153e8i 0.235936 0.408653i
\(143\) 8.00322e7i 0.191391i
\(144\) 3.59577e7 1.01303e8i 0.0836262 0.235599i
\(145\) 5.37313e8 1.21550
\(146\) −2.37832e8 1.37312e8i −0.523429 0.302202i
\(147\) 7.37427e8 5.20752e8i 1.57925 1.11522i
\(148\) 7.68929e7 + 1.33182e8i 0.160265 + 0.277588i
\(149\) 3.73436e8 2.15603e8i 0.757653 0.437431i −0.0707992 0.997491i \(-0.522555\pi\)
0.828453 + 0.560059i \(0.189222\pi\)
\(150\) 4.10018e8 + 5.80618e8i 0.809912 + 1.14690i
\(151\) −4.20280e8 + 7.27947e8i −0.808409 + 1.40021i 0.105556 + 0.994413i \(0.466338\pi\)
−0.913965 + 0.405793i \(0.866996\pi\)
\(152\) 1.79054e8i 0.335435i
\(153\) 1.04570e8 + 5.66551e8i 0.190828 + 1.03389i
\(154\) −4.52308e8 −0.804176
\(155\) −1.08111e9 6.24177e8i −1.87302 1.08139i
\(156\) 7.74966e7 + 3.57612e7i 0.130853 + 0.0603829i
\(157\) 2.10919e8 + 3.65323e8i 0.347150 + 0.601282i 0.985742 0.168264i \(-0.0538160\pi\)
−0.638592 + 0.769546i \(0.720483\pi\)
\(158\) 1.25219e8 7.22951e7i 0.200928 0.116006i
\(159\) −8.45431e7 + 7.73685e6i −0.132279 + 0.0121053i
\(160\) −1.00090e8 + 1.73361e8i −0.152726 + 0.264529i
\(161\) 4.36987e8i 0.650376i
\(162\) 4.80909e8 + 7.68988e7i 0.698237 + 0.111650i
\(163\) −5.50818e8 −0.780293 −0.390146 0.920753i \(-0.627576\pi\)
−0.390146 + 0.920753i \(0.627576\pi\)
\(164\) 1.97059e8 + 1.13772e8i 0.272408 + 0.157275i
\(165\) 7.75022e7 + 8.46892e8i 0.104563 + 1.14259i
\(166\) −1.82365e8 3.15866e8i −0.240165 0.415978i
\(167\) 5.25550e8 3.03427e8i 0.675691 0.390111i −0.122538 0.992464i \(-0.539103\pi\)
0.798230 + 0.602353i \(0.205770\pi\)
\(168\) 2.02107e8 4.37978e8i 0.253714 0.549813i
\(169\) 3.73982e8 6.47756e8i 0.458463 0.794081i
\(170\) 1.07287e9i 1.28455i
\(171\) −7.97744e8 + 1.47242e8i −0.932995 + 0.172206i
\(172\) −1.35354e8 −0.154652
\(173\) −8.26617e8 4.77248e8i −0.922826 0.532794i −0.0382907 0.999267i \(-0.512191\pi\)
−0.884536 + 0.466473i \(0.845525\pi\)
\(174\) −3.72448e8 + 2.63014e8i −0.406321 + 0.286933i
\(175\) 1.59477e9 + 2.76222e9i 1.70038 + 2.94514i
\(176\) −1.37946e8 + 7.96429e7i −0.143766 + 0.0830035i
\(177\) −4.69413e8 6.64726e8i −0.478258 0.677251i
\(178\) −1.18844e8 + 2.05844e8i −0.118385 + 0.205049i
\(179\) 9.44019e8i 0.919536i 0.888039 + 0.459768i \(0.152067\pi\)
−0.888039 + 0.459768i \(0.847933\pi\)
\(180\) −8.54692e8 3.03375e8i −0.814178 0.288994i
\(181\) −8.68230e8 −0.808948 −0.404474 0.914550i \(-0.632545\pi\)
−0.404474 + 0.914550i \(0.632545\pi\)
\(182\) 3.31677e8 + 1.91494e8i 0.302294 + 0.174530i
\(183\) −6.11573e8 2.82214e8i −0.545311 0.251637i
\(184\) 7.69451e7 + 1.33273e8i 0.0671289 + 0.116271i
\(185\) 1.12366e9 6.48744e8i 0.959284 0.553843i
\(186\) 1.05492e9 9.65397e7i 0.881390 0.0806593i
\(187\) 4.26845e8 7.39318e8i 0.349063 0.604595i
\(188\) 5.62665e8i 0.450420i
\(189\) 2.11754e9 + 5.40291e8i 1.65953 + 0.423429i
\(190\) 1.51067e9 1.15919
\(191\) −6.09956e7 3.52159e7i −0.0458316 0.0264609i 0.476909 0.878953i \(-0.341757\pi\)
−0.522741 + 0.852492i \(0.675090\pi\)
\(192\) −1.54807e7 1.69162e8i −0.0113916 0.124480i
\(193\) −1.36871e9 2.37068e9i −0.986467 1.70861i −0.635225 0.772327i \(-0.719093\pi\)
−0.351242 0.936285i \(-0.614241\pi\)
\(194\) −8.75254e8 + 5.05328e8i −0.617913 + 0.356752i
\(195\) 3.01717e8 6.53838e8i 0.208671 0.452201i
\(196\) 7.13294e8 1.23546e9i 0.483331 0.837154i
\(197\) 5.47276e8i 0.363364i 0.983357 + 0.181682i \(0.0581541\pi\)
−0.983357 + 0.181682i \(0.941846\pi\)
\(198\) −4.68274e8 5.49101e8i −0.304676 0.357266i
\(199\) −2.66467e9 −1.69915 −0.849574 0.527469i \(-0.823141\pi\)
−0.849574 + 0.527469i \(0.823141\pi\)
\(200\) 9.72749e8 + 5.61617e8i 0.607968 + 0.351011i
\(201\) −8.19368e8 + 5.78617e8i −0.501990 + 0.354493i
\(202\) −2.01465e8 3.48948e8i −0.121003 0.209583i
\(203\) −1.77188e9 + 1.02299e9i −1.04340 + 0.602405i
\(204\) 5.25165e8 + 7.43676e8i 0.303232 + 0.429401i
\(205\) 9.59891e8 1.66258e9i 0.543509 0.941385i
\(206\) 9.84972e7i 0.0546959i
\(207\) −5.30501e8 + 4.52411e8i −0.288938 + 0.246406i
\(208\) 1.34874e8 0.0720567
\(209\) 1.04101e9 + 6.01029e8i 0.545595 + 0.315000i
\(210\) −3.69521e9 1.70518e9i −1.90004 0.876782i
\(211\) −9.39137e8 1.62663e9i −0.473804 0.820653i 0.525746 0.850642i \(-0.323786\pi\)
−0.999550 + 0.0299884i \(0.990453\pi\)
\(212\) −1.16184e8 + 6.70786e7i −0.0575176 + 0.0332078i
\(213\) 1.36788e9 1.25179e8i 0.664551 0.0608155i
\(214\) −1.32563e9 + 2.29606e9i −0.632074 + 1.09478i
\(215\) 1.14198e9i 0.534446i
\(216\) 7.40946e8 2.08080e8i 0.340386 0.0955906i
\(217\) 4.75349e9 2.14375
\(218\) 2.61107e9 + 1.50750e9i 1.15609 + 0.667471i
\(219\) −1.79182e8 1.95798e9i −0.0778964 0.851200i
\(220\) 6.71945e8 + 1.16384e9i 0.286842 + 0.496826i
\(221\) −6.26011e8 + 3.61427e8i −0.262430 + 0.151514i
\(222\) −4.61324e8 + 9.99716e8i −0.189930 + 0.411590i
\(223\) 1.45052e9 2.51237e9i 0.586548 1.01593i −0.408132 0.912923i \(-0.633820\pi\)
0.994680 0.103009i \(-0.0328470\pi\)
\(224\) 7.62249e8i 0.302765i
\(225\) −1.70227e9 + 4.79577e9i −0.664198 + 1.87123i
\(226\) −3.23411e9 −1.23971
\(227\) 3.60966e9 + 2.08404e9i 1.35945 + 0.784877i 0.989549 0.144195i \(-0.0460594\pi\)
0.369898 + 0.929072i \(0.379393\pi\)
\(228\) −1.04715e9 + 7.39470e8i −0.387497 + 0.273641i
\(229\) 1.80018e9 + 3.11801e9i 0.654599 + 1.13380i 0.981994 + 0.188911i \(0.0604957\pi\)
−0.327396 + 0.944887i \(0.606171\pi\)
\(230\) 1.12442e9 6.49184e8i 0.401807 0.231983i
\(231\) −1.86798e9 2.64520e9i −0.656030 0.928991i
\(232\) −3.60260e8 + 6.23988e8i −0.124355 + 0.215389i
\(233\) 2.86365e9i 0.971618i 0.874065 + 0.485809i \(0.161475\pi\)
−0.874065 + 0.485809i \(0.838525\pi\)
\(234\) 1.10912e8 + 6.00908e8i 0.0369925 + 0.200422i
\(235\) −4.74719e9 −1.55656
\(236\) −1.11366e9 6.42973e8i −0.359009 0.207274i
\(237\) 9.39937e8 + 4.33739e8i 0.297924 + 0.137479i
\(238\) 2.04263e9 + 3.53795e9i 0.636624 + 1.10266i
\(239\) 1.21500e9 7.01479e8i 0.372378 0.214992i −0.302119 0.953270i \(-0.597694\pi\)
0.674497 + 0.738278i \(0.264361\pi\)
\(240\) −1.42722e9 + 1.30610e8i −0.430176 + 0.0393670i
\(241\) 2.21808e9 3.84182e9i 0.657519 1.13886i −0.323737 0.946147i \(-0.604939\pi\)
0.981256 0.192709i \(-0.0617273\pi\)
\(242\) 1.35585e9i 0.395320i
\(243\) 1.53637e9 + 3.13005e9i 0.440627 + 0.897690i
\(244\) −1.06437e9 −0.300285
\(245\) −1.04236e10 6.01805e9i −2.89303 1.67029i
\(246\) 1.48464e8 + 1.62231e9i 0.0405396 + 0.442990i
\(247\) −5.08916e8 8.81468e8i −0.136728 0.236820i
\(248\) 1.44973e9 8.37001e8i 0.383248 0.221268i
\(249\) 1.09411e9 2.37100e9i 0.284619 0.616786i
\(250\) 2.35201e9 4.07381e9i 0.602116 1.04290i
\(251\) 2.42084e9i 0.609916i −0.952366 0.304958i \(-0.901357\pi\)
0.952366 0.304958i \(-0.0986425\pi\)
\(252\) 3.39608e9 6.26825e8i 0.842123 0.155433i
\(253\) 1.03313e9 0.252157
\(254\) −8.02210e8 4.63156e8i −0.192732 0.111274i
\(255\) 6.27438e9 4.43081e9i 1.48392 1.04791i
\(256\) −1.34218e8 2.32472e8i −0.0312500 0.0541266i
\(257\) −2.08915e9 + 1.20617e9i −0.478891 + 0.276488i −0.719954 0.694022i \(-0.755837\pi\)
0.241063 + 0.970509i \(0.422504\pi\)
\(258\) −5.58995e8 7.91581e8i −0.126162 0.178656i
\(259\) −2.47029e9 + 4.27867e9i −0.548971 + 0.950846i
\(260\) 1.13793e9i 0.249013i
\(261\) −3.07633e9 1.09195e9i −0.662935 0.235310i
\(262\) 4.28237e9 0.908822
\(263\) 5.65030e9 + 3.26220e9i 1.18100 + 0.681849i 0.956245 0.292567i \(-0.0945096\pi\)
0.224752 + 0.974416i \(0.427843\pi\)
\(264\) −1.03547e9 4.77823e8i −0.213168 0.0983674i
\(265\) 5.65941e8 + 9.80238e8i 0.114759 + 0.198769i
\(266\) −4.98168e9 + 2.87617e9i −0.995060 + 0.574498i
\(267\) −1.69463e9 + 1.55082e8i −0.333450 + 0.0305152i
\(268\) −7.92554e8 + 1.37274e9i −0.153635 + 0.266103i
\(269\) 6.64127e9i 1.26836i −0.773186 0.634180i \(-0.781338\pi\)
0.773186 0.634180i \(-0.218662\pi\)
\(270\) −1.75557e9 6.25134e9i −0.330341 1.17630i
\(271\) −2.72229e9 −0.504728 −0.252364 0.967632i \(-0.581208\pi\)
−0.252364 + 0.967632i \(0.581208\pi\)
\(272\) 1.24593e9 + 7.19339e8i 0.227624 + 0.131419i
\(273\) 2.49885e8 + 2.73057e9i 0.0449872 + 0.491590i
\(274\) 5.46649e8 + 9.46823e8i 0.0969853 + 0.167983i
\(275\) 6.53045e9 3.77036e9i 1.14186 0.659252i
\(276\) −4.61637e8 + 1.00039e9i −0.0795544 + 0.172399i
\(277\) −5.00946e9 + 8.67663e9i −0.850886 + 1.47378i 0.0295233 + 0.999564i \(0.490601\pi\)
−0.880410 + 0.474214i \(0.842732\pi\)
\(278\) 4.82484e9i 0.807799i
\(279\) 4.92128e9 + 5.77073e9i 0.812198 + 0.952388i
\(280\) −6.43108e9 −1.04629
\(281\) −6.83019e9 3.94341e9i −1.09549 0.632480i −0.160456 0.987043i \(-0.551296\pi\)
−0.935032 + 0.354563i \(0.884630\pi\)
\(282\) 3.29060e9 2.32374e9i 0.520329 0.367444i
\(283\) 4.86855e8 + 8.43258e8i 0.0759021 + 0.131466i 0.901478 0.432824i \(-0.142483\pi\)
−0.825576 + 0.564291i \(0.809150\pi\)
\(284\) 1.87981e9 1.08531e9i 0.288962 0.166832i
\(285\) 6.23889e9 + 8.83477e9i 0.945645 + 1.33911i
\(286\) 4.52730e8 7.84152e8i 0.0676668 0.117202i
\(287\) 7.31016e9i 1.07746i
\(288\) 9.25369e8 7.89155e8i 0.134507 0.114708i
\(289\) −7.34822e8 −0.105339
\(290\) 5.26458e9 + 3.03950e9i 0.744340 + 0.429745i
\(291\) −6.56997e9 3.03175e9i −0.916203 0.422787i
\(292\) −1.55351e9 2.69076e9i −0.213689 0.370121i
\(293\) −4.59420e9 + 2.65246e9i −0.623361 + 0.359898i −0.778176 0.628046i \(-0.783855\pi\)
0.154815 + 0.987943i \(0.450522\pi\)
\(294\) 1.01711e10 9.30795e8i 1.36138 0.124585i
\(295\) −5.42475e9 + 9.39595e9i −0.716295 + 1.24066i
\(296\) 1.73989e9i 0.226649i
\(297\) 1.27736e9 5.00630e9i 0.164167 0.643414i
\(298\) 4.87854e9 0.618621
\(299\) −7.57590e8 4.37395e8i −0.0947871 0.0547254i
\(300\) 7.32868e8 + 8.00828e9i 0.0904775 + 0.988677i
\(301\) −2.17422e9 3.76585e9i −0.264872 0.458772i
\(302\) −8.23578e9 + 4.75493e9i −0.990095 + 0.571632i
\(303\) 1.20871e9 2.61933e9i 0.143400 0.310756i
\(304\) −1.01288e9 + 1.75436e9i −0.118594 + 0.205411i
\(305\) 8.98008e9i 1.03772i
\(306\) −2.18032e9 + 6.14258e9i −0.248677 + 0.700592i
\(307\) 1.34241e10 1.51124 0.755618 0.655013i \(-0.227337\pi\)
0.755618 + 0.655013i \(0.227337\pi\)
\(308\) −4.43169e9 2.55864e9i −0.492455 0.284319i
\(309\) 5.76035e8 4.06782e8i 0.0631852 0.0446198i
\(310\) −7.06176e9 1.22313e10i −0.764656 1.32442i
\(311\) 1.98291e9 1.14483e9i 0.211964 0.122377i −0.390260 0.920705i \(-0.627615\pi\)
0.602224 + 0.798327i \(0.294282\pi\)
\(312\) 5.57013e8 + 7.88774e8i 0.0587823 + 0.0832404i
\(313\) 8.94161e9 1.54873e10i 0.931619 1.61361i 0.151065 0.988524i \(-0.451730\pi\)
0.780555 0.625088i \(-0.214937\pi\)
\(314\) 4.77256e9i 0.490945i
\(315\) −5.28851e9 2.86527e10i −0.537144 2.91020i
\(316\) 1.63585e9 0.164057
\(317\) 5.77404e9 + 3.33364e9i 0.571798 + 0.330128i 0.757867 0.652409i \(-0.226242\pi\)
−0.186069 + 0.982537i \(0.559575\pi\)
\(318\) −8.72116e8 4.02442e8i −0.0852836 0.0393546i
\(319\) 2.41856e9 + 4.18908e9i 0.233558 + 0.404535i
\(320\) −1.96136e9 + 1.13239e9i −0.187050 + 0.107993i
\(321\) −1.89026e10 + 1.72985e9i −1.78034 + 0.162925i
\(322\) −2.47197e9 + 4.28158e9i −0.229943 + 0.398272i
\(323\) 1.08570e10i 0.997474i
\(324\) 4.27692e9 + 3.47388e9i 0.388106 + 0.315235i
\(325\) −6.38503e9 −0.572308
\(326\) −5.39689e9 3.11590e9i −0.477830 0.275875i
\(327\) 1.96718e9 + 2.14960e10i 0.172049 + 1.88004i
\(328\) 1.28718e9 + 2.22946e9i 0.111210 + 0.192622i
\(329\) 1.56546e10 9.03820e9i 1.33616 0.771433i
\(330\) −4.03138e9 + 8.73623e9i −0.339937 + 0.736662i
\(331\) −7.84292e9 + 1.35843e10i −0.653380 + 1.13169i 0.328918 + 0.944359i \(0.393316\pi\)
−0.982297 + 0.187328i \(0.940017\pi\)
\(332\) 4.12645e9i 0.339644i
\(333\) −7.75179e9 + 1.43077e9i −0.630413 + 0.116357i
\(334\) 6.86576e9 0.551700
\(335\) 1.15818e10 + 6.68676e9i 0.919597 + 0.530929i
\(336\) 4.45782e9 3.14800e9i 0.349756 0.246989i
\(337\) −1.29188e9 2.23761e9i −0.100162 0.173486i 0.811589 0.584229i \(-0.198603\pi\)
−0.911751 + 0.410743i \(0.865270\pi\)
\(338\) 7.32852e9 4.23112e9i 0.561500 0.324182i
\(339\) −1.33565e10 1.89139e10i −1.01133 1.43213i
\(340\) 6.06905e9 1.05119e10i 0.454156 0.786621i
\(341\) 1.12382e10i 0.831152i
\(342\) −8.64919e9 3.07005e9i −0.632224 0.224409i
\(343\) 2.21253e10 1.59850
\(344\) −1.32619e9 7.65677e8i −0.0947049 0.0546779i
\(345\) 8.44030e9 + 3.89482e9i 0.595774 + 0.274923i
\(346\) −5.39944e9 9.35211e9i −0.376742 0.652537i
\(347\) 1.45626e10 8.40775e9i 1.00444 0.579912i 0.0948784 0.995489i \(-0.469754\pi\)
0.909558 + 0.415577i \(0.136420\pi\)
\(348\) −5.13706e9 + 4.70111e8i −0.350266 + 0.0320541i
\(349\) 1.22366e10 2.11945e10i 0.824822 1.42863i −0.0772336 0.997013i \(-0.524609\pi\)
0.902055 0.431620i \(-0.142058\pi\)
\(350\) 3.60855e10i 2.40470i
\(351\) −3.05620e9 + 3.13032e9i −0.201351 + 0.206234i
\(352\) −1.80211e9 −0.117385
\(353\) −9.05088e9 5.22553e9i −0.582897 0.336536i 0.179387 0.983779i \(-0.442589\pi\)
−0.762284 + 0.647243i \(0.775922\pi\)
\(354\) −8.39031e8 9.16836e9i −0.0534275 0.583820i
\(355\) −9.15672e9 1.58599e10i −0.576536 0.998590i
\(356\) −2.32885e9 + 1.34456e9i −0.144991 + 0.0837108i
\(357\) −1.22549e10 + 2.65571e10i −0.754463 + 1.63496i
\(358\) −5.34018e9 + 9.24946e9i −0.325105 + 0.563098i
\(359\) 2.37497e10i 1.42982i 0.699219 + 0.714908i \(0.253531\pi\)
−0.699219 + 0.714908i \(0.746469\pi\)
\(360\) −6.65809e9 7.80732e9i −0.396405 0.464828i
\(361\) −1.69607e9 −0.0998656
\(362\) −8.50688e9 4.91145e9i −0.495377 0.286006i
\(363\) 7.92931e9 5.59948e9i 0.456677 0.322494i
\(364\) 2.16651e9 + 3.75250e9i 0.123411 + 0.213754i
\(365\) −2.27019e10 + 1.31069e10i −1.27906 + 0.738464i
\(366\) −4.39573e9 6.22470e9i −0.244966 0.346892i
\(367\) −5.17433e9 + 8.96220e9i −0.285226 + 0.494027i −0.972664 0.232217i \(-0.925402\pi\)
0.687438 + 0.726243i \(0.258735\pi\)
\(368\) 1.74107e9i 0.0949346i
\(369\) −8.87452e9 + 7.56820e9i −0.478674 + 0.408213i
\(370\) 1.46794e10 0.783252
\(371\) −3.73256e9 2.15499e9i −0.197020 0.113750i
\(372\) 1.08822e10 + 5.02164e9i 0.568256 + 0.262225i
\(373\) 4.02672e9 + 6.97448e9i 0.208025 + 0.360310i 0.951092 0.308907i \(-0.0999631\pi\)
−0.743067 + 0.669217i \(0.766630\pi\)
\(374\) 8.36443e9 4.82920e9i 0.427513 0.246825i
\(375\) 3.35382e10 3.06920e9i 1.69595 0.155203i
\(376\) 3.18291e9 5.51296e9i 0.159248 0.275825i
\(377\) 4.09580e9i 0.202756i
\(378\) 1.76912e10 + 1.72724e10i 0.866544 + 0.846028i
\(379\) −2.63218e10 −1.27573 −0.637864 0.770149i \(-0.720182\pi\)
−0.637864 + 0.770149i \(0.720182\pi\)
\(380\) 1.48015e10 + 8.54565e9i 0.709858 + 0.409837i
\(381\) −6.04383e8 6.60429e9i −0.0286822 0.313420i
\(382\) −3.98422e8 6.90087e8i −0.0187107 0.0324079i
\(383\) −2.64941e10 + 1.52964e10i −1.23127 + 0.710876i −0.967295 0.253653i \(-0.918368\pi\)
−0.263978 + 0.964529i \(0.585035\pi\)
\(384\) 8.05248e8 1.74502e9i 0.0370344 0.0802556i
\(385\) −2.15872e10 + 3.73901e10i −0.982547 + 1.70182i
\(386\) 3.09704e10i 1.39508i
\(387\) 2.32077e9 6.53827e9i 0.103464 0.291487i
\(388\) −1.14343e10 −0.504523
\(389\) 3.76791e10 + 2.17540e10i 1.64552 + 0.950039i 0.978824 + 0.204704i \(0.0656233\pi\)
0.666691 + 0.745334i \(0.267710\pi\)
\(390\) 6.65487e9 4.69951e9i 0.287661 0.203139i
\(391\) −4.66562e9 8.08109e9i −0.199619 0.345751i
\(392\) 1.39777e10 8.07001e9i 0.591957 0.341767i
\(393\) 1.76857e10 + 2.50443e10i 0.741398 + 1.04988i
\(394\) −3.09586e9 + 5.36219e9i −0.128468 + 0.222514i
\(395\) 1.38016e10i 0.566947i
\(396\) −1.48194e9 8.02902e9i −0.0602629 0.326499i
\(397\) 4.31419e10 1.73675 0.868375 0.495908i \(-0.165165\pi\)
0.868375 + 0.495908i \(0.165165\pi\)
\(398\) −2.61083e10 1.50737e10i −1.04051 0.600740i
\(399\) −3.73943e10 1.72558e10i −1.47541 0.680838i
\(400\) 6.35397e9 + 1.10054e10i 0.248202 + 0.429899i
\(401\) −1.57455e10 + 9.09069e9i −0.608948 + 0.351576i −0.772554 0.634950i \(-0.781021\pi\)
0.163606 + 0.986526i \(0.447688\pi\)
\(402\) −1.13013e10 + 1.03422e9i −0.432737 + 0.0396013i
\(403\) −4.75794e9 + 8.24099e9i −0.180384 + 0.312434i
\(404\) 4.55864e9i 0.171124i
\(405\) 2.93091e10 3.60843e10i 1.08939 1.34121i
\(406\) −2.31477e10 −0.851930
\(407\) 1.01157e10 + 5.84028e9i 0.368652 + 0.212841i
\(408\) 9.38682e8 + 1.02573e10i 0.0338749 + 0.370162i
\(409\) 3.23724e9 + 5.60707e9i 0.115686 + 0.200374i 0.918054 0.396456i \(-0.129760\pi\)
−0.802368 + 0.596830i \(0.796427\pi\)
\(410\) 1.88099e10 1.08599e10i 0.665659 0.384319i
\(411\) −3.27965e9 + 7.10720e9i −0.114937 + 0.249076i
\(412\) 5.57184e8 9.65071e8i 0.0193379 0.0334943i
\(413\) 4.13128e10i 1.41999i
\(414\) −7.75705e9 + 1.43174e9i −0.264055 + 0.0487375i
\(415\) −3.48148e10 −1.17374
\(416\) 1.32149e9 + 7.62961e8i 0.0441255 + 0.0254759i
\(417\) 2.82168e10 1.99260e10i 0.933176 0.658985i
\(418\) 6.79986e9 + 1.17777e10i 0.222738 + 0.385794i
\(419\) −3.28096e10 + 1.89427e10i −1.06450 + 0.614589i −0.926673 0.375868i \(-0.877345\pi\)
−0.137826 + 0.990456i \(0.544011\pi\)
\(420\) −2.65596e10 3.76105e10i −0.853541 1.20868i
\(421\) 2.38781e10 4.13581e10i 0.760102 1.31654i −0.182696 0.983170i \(-0.558482\pi\)
0.942798 0.333366i \(-0.108184\pi\)
\(422\) 2.12502e10i 0.670061i
\(423\) 2.71795e10 + 9.64744e9i 0.848947 + 0.301336i
\(424\) −1.51782e9 −0.0469630
\(425\) −5.89834e10 3.40541e10i −1.80790 1.04379i
\(426\) 1.41105e10 + 6.51138e9i 0.428454 + 0.197713i
\(427\) −1.70972e10 2.96133e10i −0.514297 0.890789i
\(428\) −2.59770e10 + 1.49978e10i −0.774130 + 0.446944i
\(429\) 6.45563e9 5.90779e8i 0.190594 0.0174420i
\(430\) −6.46000e9 + 1.11890e10i −0.188955 + 0.327280i
\(431\) 2.73395e10i 0.792285i −0.918189 0.396143i \(-0.870349\pi\)
0.918189 0.396143i \(-0.129651\pi\)
\(432\) 8.43683e9 + 2.15266e9i 0.242239 + 0.0618075i
\(433\) −6.96958e9 −0.198269 −0.0991345 0.995074i \(-0.531607\pi\)
−0.0991345 + 0.995074i \(0.531607\pi\)
\(434\) 4.65745e10 + 2.68898e10i 1.31277 + 0.757930i
\(435\) 3.96632e9 + 4.33413e10i 0.110772 + 1.21044i
\(436\) 1.70555e10 + 2.95409e10i 0.471973 + 0.817482i
\(437\) 1.13788e10 6.56953e9i 0.312010 0.180139i
\(438\) 9.32038e9 2.01978e10i 0.253243 0.548792i
\(439\) 4.26214e9 7.38223e9i 0.114754 0.198760i −0.802927 0.596077i \(-0.796725\pi\)
0.917682 + 0.397317i \(0.130059\pi\)
\(440\) 1.52044e10i 0.405656i
\(441\) 4.74489e10 + 5.56389e10i 1.25450 + 1.47104i
\(442\) −8.17817e9 −0.214273
\(443\) −1.77214e10 1.02315e10i −0.460134 0.265658i 0.251967 0.967736i \(-0.418923\pi\)
−0.712101 + 0.702077i \(0.752256\pi\)
\(444\) −1.01753e10 + 7.18553e9i −0.261827 + 0.184896i
\(445\) 1.13441e10 + 1.96485e10i 0.289287 + 0.501060i
\(446\) 2.84242e10 1.64107e10i 0.718372 0.414752i
\(447\) 2.01478e10 + 2.85309e10i 0.504658 + 0.714636i
\(448\) 4.31193e9 7.46849e9i 0.107043 0.185405i
\(449\) 1.52992e10i 0.376430i 0.982128 + 0.188215i \(0.0602702\pi\)
−0.982128 + 0.188215i \(0.939730\pi\)
\(450\) −4.38077e10 + 3.73592e10i −1.06832 + 0.911062i
\(451\) 1.72827e10 0.417740
\(452\) −3.16877e10 1.82949e10i −0.759166 0.438305i
\(453\) −6.18207e10 2.85275e10i −1.46805 0.677440i
\(454\) 2.35782e10 + 4.08386e10i 0.554992 + 0.961274i
\(455\) 3.16597e10 1.82788e10i 0.738689 0.426483i
\(456\) −1.44430e10 + 1.32173e9i −0.334039 + 0.0305692i
\(457\) −1.20106e10 + 2.08029e10i −0.275359 + 0.476935i −0.970226 0.242203i \(-0.922130\pi\)
0.694867 + 0.719138i \(0.255463\pi\)
\(458\) 4.07335e10i 0.925742i
\(459\) −4.49278e10 + 1.26171e10i −1.01219 + 0.284255i
\(460\) 1.46894e10 0.328074
\(461\) 4.96796e10 + 2.86825e10i 1.09995 + 0.635058i 0.936209 0.351445i \(-0.114310\pi\)
0.163744 + 0.986503i \(0.447643\pi\)
\(462\) −3.33883e9 3.64845e10i −0.0732869 0.800830i
\(463\) 3.03202e10 + 5.25162e10i 0.659795 + 1.14280i 0.980669 + 0.195676i \(0.0626900\pi\)
−0.320874 + 0.947122i \(0.603977\pi\)
\(464\) −7.05962e9 + 4.07587e9i −0.152303 + 0.0879324i
\(465\) 4.23675e10 9.18128e10i 0.906194 1.96377i
\(466\) −1.61992e10 + 2.80579e10i −0.343519 + 0.594992i
\(467\) 1.01091e10i 0.212543i 0.994337 + 0.106271i \(0.0338912\pi\)
−0.994337 + 0.106271i \(0.966109\pi\)
\(468\) −2.31254e9 + 6.51509e9i −0.0482066 + 0.135812i
\(469\) −5.09238e10 −1.05252
\(470\) −4.65128e10 2.68542e10i −0.953193 0.550326i
\(471\) −2.79111e10 + 1.97101e10i −0.567143 + 0.400502i
\(472\) −7.27441e9 1.25996e10i −0.146565 0.253858i
\(473\) −8.90324e9 + 5.14029e9i −0.177870 + 0.102693i
\(474\) 6.75587e9 + 9.56684e9i 0.133834 + 0.189520i
\(475\) 4.79505e10 8.30528e10i 0.941931 1.63147i
\(476\) 4.62195e10i 0.900322i
\(477\) −1.24815e9 6.76238e9i −0.0241099 0.130625i
\(478\) 1.58727e10 0.304045
\(479\) 1.87971e10 + 1.08525e10i 0.357067 + 0.206153i 0.667793 0.744347i \(-0.267239\pi\)
−0.310727 + 0.950499i \(0.600572\pi\)
\(480\) −1.47227e10 6.79386e9i −0.277346 0.127983i
\(481\) −4.94520e9 8.56534e9i −0.0923855 0.160016i
\(482\) 4.34652e10 2.50947e10i 0.805293 0.464936i
\(483\) −3.52486e10 + 3.22573e9i −0.647670 + 0.0592706i
\(484\) 7.66982e9 1.32845e10i 0.139767 0.242083i
\(485\) 9.64707e10i 1.74353i
\(486\) −2.65293e9 + 3.93592e10i −0.0475533 + 0.705506i
\(487\) −5.82792e9 −0.103609 −0.0518045 0.998657i \(-0.516497\pi\)
−0.0518045 + 0.998657i \(0.516497\pi\)
\(488\) −1.04287e10 6.02100e9i −0.183886 0.106167i
\(489\) −4.06601e9 4.44306e10i −0.0711103 0.777046i
\(490\) −6.80865e10 1.17929e11i −1.18107 2.04568i
\(491\) −2.15718e10 + 1.24545e10i −0.371159 + 0.214288i −0.673964 0.738764i \(-0.735410\pi\)
0.302806 + 0.953052i \(0.402077\pi\)
\(492\) −7.72253e9 + 1.67352e10i −0.131795 + 0.285607i
\(493\) 2.18446e10 3.78360e10i 0.369791 0.640497i
\(494\) 1.15154e10i 0.193363i
\(495\) −6.77407e10 + 1.25031e10i −1.12831 + 0.208256i
\(496\) 1.89392e10 0.312921
\(497\) 6.03915e10 + 3.48670e10i 0.989806 + 0.571465i
\(498\) 2.41325e10 1.70417e10i 0.392360 0.277075i
\(499\) −8.19755e9 1.41986e10i −0.132215 0.229004i 0.792315 0.610112i \(-0.208876\pi\)
−0.924530 + 0.381109i \(0.875542\pi\)
\(500\) 4.60899e10 2.66100e10i 0.737438 0.425760i
\(501\) 2.83548e10 + 4.01526e10i 0.450065 + 0.637328i
\(502\) 1.36943e10 2.37192e10i 0.215638 0.373496i
\(503\) 4.61285e10i 0.720606i −0.932835 0.360303i \(-0.882673\pi\)
0.932835 0.360303i \(-0.117327\pi\)
\(504\) 3.68205e10 + 1.30695e10i 0.570647 + 0.202552i
\(505\) −3.84612e10 −0.591367
\(506\) 1.01225e10 + 5.84424e9i 0.154414 + 0.0891509i
\(507\) 5.50105e10 + 2.53849e10i 0.832557 + 0.384188i
\(508\) −5.24001e9 9.07597e9i −0.0786824 0.136282i
\(509\) −6.69443e9 + 3.86503e9i −0.0997339 + 0.0575814i −0.549037 0.835798i \(-0.685006\pi\)
0.449303 + 0.893379i \(0.351672\pi\)
\(510\) 8.65405e10 7.91964e9i 1.27920 0.117064i
\(511\) 4.99087e10 8.64444e10i 0.731969 1.26781i
\(512\) 3.03700e9i 0.0441942i
\(513\) −1.77657e10 6.32615e10i −0.256516 0.913419i
\(514\) −2.72925e10 −0.391013
\(515\) −8.14229e9 4.70095e9i −0.115749 0.0668278i
\(516\) −9.99150e8 1.09180e10i −0.0140939 0.154009i
\(517\) −2.13681e10 3.70107e10i −0.299092 0.518042i
\(518\) −4.84077e10 + 2.79482e10i −0.672349 + 0.388181i
\(519\) 3.23943e10 7.02003e10i 0.446477 0.967541i
\(520\) 6.43709e9 1.11494e10i 0.0880392 0.152488i
\(521\) 3.97902e10i 0.540039i 0.962855 + 0.270019i \(0.0870301\pi\)
−0.962855 + 0.270019i \(0.912970\pi\)
\(522\) −2.39648e10 2.81013e10i −0.322769 0.378481i
\(523\) −3.49978e10 −0.467772 −0.233886 0.972264i \(-0.575144\pi\)
−0.233886 + 0.972264i \(0.575144\pi\)
\(524\) 4.19585e10 + 2.42247e10i 0.556538 + 0.321317i
\(525\) −2.11037e11 + 1.49029e11i −2.77792 + 1.96170i
\(526\) 3.69076e10 + 6.39259e10i 0.482140 + 0.835091i
\(527\) −8.79053e10 + 5.07521e10i −1.13965 + 0.657979i
\(528\) −7.44251e9 1.05392e10i −0.0957599 0.135604i
\(529\) −3.35092e10 + 5.80397e10i −0.427899 + 0.741143i
\(530\) 1.28058e10i 0.162294i
\(531\) 5.01537e10 4.27711e10i 0.630848 0.537988i
\(532\) −6.50804e10 −0.812463
\(533\) −1.26734e10 7.31699e9i −0.157031 0.0906617i
\(534\) −1.74812e10 8.06681e9i −0.214984 0.0992057i
\(535\) 1.26536e11 + 2.19167e11i 1.54454 + 2.67523i
\(536\) −1.55308e10 + 8.96673e9i −0.188163 + 0.108636i
\(537\) −7.61474e10 + 6.96853e9i −0.915709 + 0.0838000i
\(538\) 3.75687e10 6.50709e10i 0.448433 0.776708i
\(539\) 1.08354e11i 1.28378i
\(540\) 1.81620e10 7.11814e10i 0.213593 0.837127i
\(541\) 2.34001e10 0.273168 0.136584 0.990629i \(-0.456388\pi\)
0.136584 + 0.990629i \(0.456388\pi\)
\(542\) −2.66729e10 1.53996e10i −0.309081 0.178448i
\(543\) −6.40907e9 7.00340e10i −0.0737218 0.805582i
\(544\) 8.13839e9 + 1.40961e10i 0.0929272 + 0.160955i
\(545\) 2.49236e11 1.43897e11i 2.82504 1.63104i
\(546\) −1.29981e10 + 2.81676e10i −0.146254 + 0.316942i
\(547\) −1.16091e10 + 2.01075e10i −0.129673 + 0.224600i −0.923550 0.383478i \(-0.874726\pi\)
0.793877 + 0.608078i \(0.208059\pi\)
\(548\) 1.23692e10i 0.137158i
\(549\) 1.82497e10 5.14145e10i 0.200894 0.565974i
\(550\) 8.53134e10 0.932324
\(551\) 5.32757e10 + 3.07588e10i 0.577994 + 0.333705i
\(552\) −1.01822e10 + 7.19040e9i −0.109669 + 0.0774456i
\(553\) 2.62770e10 + 4.55131e10i 0.280980 + 0.486671i
\(554\) −9.81649e10 + 5.66755e10i −1.04212 + 0.601667i
\(555\) 6.06242e10 + 8.58486e10i 0.638960 + 0.904819i
\(556\) 2.72934e10 4.72735e10i 0.285600 0.494674i
\(557\) 3.65617e10i 0.379844i −0.981799 0.189922i \(-0.939176\pi\)
0.981799 0.189922i \(-0.0608236\pi\)
\(558\) 1.55744e10 + 8.43804e10i 0.160647 + 0.870372i
\(559\) 8.70499e9 0.0891499
\(560\) −6.30115e10 3.63797e10i −0.640719 0.369919i
\(561\) 6.27864e10 + 2.89731e10i 0.633891 + 0.292512i
\(562\) −4.46146e10 7.72748e10i −0.447231 0.774627i
\(563\) −1.15433e11 + 6.66450e10i −1.14893 + 0.663337i −0.948627 0.316397i \(-0.897527\pi\)
−0.200306 + 0.979733i \(0.564194\pi\)
\(564\) 4.53862e10 4.15346e9i 0.448546 0.0410481i
\(565\) −1.54354e11 + 2.67348e11i −1.51469 + 2.62352i
\(566\) 1.10163e10i 0.107342i
\(567\) −2.79503e10 + 1.74795e11i −0.270430 + 1.69121i
\(568\) 2.45577e10 0.235936
\(569\) −1.42643e11 8.23549e10i −1.36082 0.785670i −0.371087 0.928598i \(-0.621015\pi\)
−0.989733 + 0.142928i \(0.954348\pi\)
\(570\) 1.11514e10 + 1.21855e11i 0.105641 + 1.15437i
\(571\) −6.84597e10 1.18576e11i −0.644007 1.11545i −0.984530 0.175216i \(-0.943937\pi\)
0.340523 0.940236i \(-0.389396\pi\)
\(572\) 8.87167e9 5.12206e9i 0.0828745 0.0478476i
\(573\) 2.39036e9 5.18004e9i 0.0221740 0.0480524i
\(574\) −4.13525e10 + 7.16247e10i −0.380938 + 0.659804i
\(575\) 8.24235e10i 0.754015i
\(576\) 1.35309e10 2.49743e9i 0.122924 0.0226884i
\(577\) −1.01555e11 −0.916218 −0.458109 0.888896i \(-0.651473\pi\)
−0.458109 + 0.888896i \(0.651473\pi\)
\(578\) −7.19976e9 4.15678e9i −0.0645070 0.0372431i
\(579\) 1.81122e11 1.27904e11i 1.61160 1.13807i
\(580\) 3.43881e10 + 5.95619e10i 0.303876 + 0.526328i
\(581\) 1.14807e11 6.62840e10i 1.00755 0.581707i
\(582\) −4.72222e10 6.68703e10i −0.411580 0.582829i
\(583\) −5.09485e9 + 8.82453e9i −0.0441018 + 0.0763866i
\(584\) 3.51519e10i 0.302202i
\(585\) 5.49677e10 + 1.95109e10i 0.469336 + 0.166592i
\(586\) −6.00184e10 −0.508972
\(587\) −3.25669e10 1.88025e10i −0.274299 0.158367i 0.356541 0.934280i \(-0.383956\pi\)
−0.630840 + 0.775913i \(0.717289\pi\)
\(588\) 1.04921e11 + 4.84165e10i 0.877717 + 0.405027i
\(589\) −7.14626e10 1.23777e11i −0.593769 1.02844i
\(590\) −1.06303e11 + 6.13741e10i −0.877278 + 0.506497i
\(591\) −4.41449e10 + 4.03986e9i −0.361852 + 0.0331144i
\(592\) −9.84229e9 + 1.70474e10i −0.0801326 + 0.138794i
\(593\) 1.30215e11i 1.05304i 0.850163 + 0.526519i \(0.176503\pi\)
−0.850163 + 0.526519i \(0.823497\pi\)
\(594\) 4.08354e10 4.18256e10i 0.328013 0.335967i
\(595\) 3.89953e11 3.11132
\(596\) 4.77998e10 + 2.75972e10i 0.378827 + 0.218716i
\(597\) −1.96700e10 2.14940e11i −0.154848 1.69208i
\(598\) −4.94856e9 8.57115e9i −0.0386967 0.0670246i
\(599\) 1.13848e11 6.57304e10i 0.884341 0.510575i 0.0122537 0.999925i \(-0.496099\pi\)
0.872087 + 0.489350i \(0.162766\pi\)
\(600\) −3.81211e10 + 8.26106e10i −0.294144 + 0.637427i
\(601\) 2.15092e10 3.72550e10i 0.164864 0.285553i −0.771743 0.635935i \(-0.780615\pi\)
0.936607 + 0.350382i \(0.113948\pi\)
\(602\) 4.91969e10i 0.374586i
\(603\) −5.27213e10 6.18214e10i −0.398765 0.467595i
\(604\) −1.07592e11 −0.808409
\(605\) −1.12081e11 6.47102e10i −0.836588 0.483004i
\(606\) 2.66600e10 1.88266e10i 0.197683 0.139599i
\(607\) −1.29606e10 2.24485e10i −0.0954710 0.165361i 0.814334 0.580396i \(-0.197102\pi\)
−0.909805 + 0.415036i \(0.863769\pi\)
\(608\) −1.98483e10 + 1.14594e10i −0.145248 + 0.0838588i
\(609\) −9.55972e10 1.35373e11i −0.694986 0.984156i
\(610\) −5.07990e10 + 8.79865e10i −0.366890 + 0.635472i
\(611\) 3.61866e10i 0.259646i
\(612\) −5.61104e10 + 4.78510e10i −0.399980 + 0.341103i
\(613\) 1.28485e11 0.909933 0.454967 0.890508i \(-0.349651\pi\)
0.454967 + 0.890508i \(0.349651\pi\)
\(614\) 1.31529e11 + 7.59383e10i 0.925439 + 0.534303i
\(615\) 1.41194e11 + 6.51549e10i 0.986999 + 0.455456i
\(616\) −2.89477e10 5.01389e10i −0.201044 0.348219i
\(617\) −1.02289e11 + 5.90563e10i −0.705808 + 0.407498i −0.809507 0.587110i \(-0.800265\pi\)
0.103699 + 0.994609i \(0.466932\pi\)
\(618\) 7.94507e9 7.27083e8i 0.0544683 0.00498460i
\(619\) −6.40218e10 + 1.10889e11i −0.436079 + 0.755312i −0.997383 0.0722982i \(-0.976967\pi\)
0.561304 + 0.827610i \(0.310300\pi\)
\(620\) 1.59789e11i 1.08139i
\(621\) −4.04089e10 3.94521e10i −0.271713 0.265280i
\(622\) 2.59046e10 0.173068
\(623\) −7.48177e10 4.31960e10i −0.496652 0.286742i
\(624\) 9.95606e8 + 1.08793e10i 0.00656673 + 0.0717568i
\(625\) −7.30176e10 1.26470e11i −0.478528 0.828835i
\(626\) 1.75219e11 1.01163e11i 1.14100 0.658754i
\(627\) −4.07962e10 + 8.84077e10i −0.263967 + 0.572032i
\(628\) −2.69977e10 + 4.67613e10i −0.173575 + 0.300641i
\(629\) 1.05499e11i 0.673980i
\(630\) 1.10267e11 3.10654e11i 0.699978 1.97203i
\(631\) −2.40613e11 −1.51775 −0.758877 0.651233i \(-0.774252\pi\)
−0.758877 + 0.651233i \(0.774252\pi\)
\(632\) 1.60280e10 + 9.25377e9i 0.100464 + 0.0580030i
\(633\) 1.24277e11 8.77610e10i 0.774059 0.546621i
\(634\) 3.77159e10 + 6.53258e10i 0.233436 + 0.404322i
\(635\) −7.65738e10 + 4.42099e10i −0.470961 + 0.271910i
\(636\) −6.26840e9 8.87655e9i −0.0383114 0.0542520i
\(637\) −4.58740e10 + 7.94561e10i −0.278618 + 0.482580i
\(638\) 5.47259e10i 0.330301i
\(639\) 2.01947e10 + 1.09413e11i 0.121125 + 0.656244i
\(640\) −2.56231e10 −0.152726
\(641\) 1.87111e11 + 1.08029e11i 1.10833 + 0.639893i 0.938396 0.345563i \(-0.112312\pi\)
0.169932 + 0.985456i \(0.445645\pi\)
\(642\) −1.94993e11 8.99804e10i −1.14783 0.529673i
\(643\) −1.85669e10 3.21588e10i −0.108616 0.188129i 0.806594 0.591106i \(-0.201309\pi\)
−0.915210 + 0.402977i \(0.867975\pi\)
\(644\) −4.84405e10 + 2.79671e10i −0.281621 + 0.162594i
\(645\) −9.21153e10 + 8.42981e9i −0.532222 + 0.0487056i
\(646\) 6.14167e10 1.06377e11i 0.352660 0.610825i
\(647\) 5.88598e10i 0.335894i 0.985796 + 0.167947i \(0.0537137\pi\)
−0.985796 + 0.167947i \(0.946286\pi\)
\(648\) 2.22538e10 + 5.82309e10i 0.126213 + 0.330258i
\(649\) −9.76719e10 −0.550543
\(650\) −6.25603e10 3.61192e10i −0.350465 0.202341i
\(651\) 3.50892e10 + 3.83431e11i 0.195366 + 2.13483i
\(652\) −3.52523e10 6.10588e10i −0.195073 0.337877i
\(653\) −1.48938e11 + 8.59893e10i −0.819129 + 0.472925i −0.850116 0.526595i \(-0.823468\pi\)
0.0309867 + 0.999520i \(0.490135\pi\)
\(654\) −1.02325e11 + 2.21745e11i −0.559335 + 1.21211i
\(655\) 2.04384e11 3.54003e11i 1.11040 1.92328i
\(656\) 2.91256e10i 0.157275i
\(657\) 1.56614e11 2.89067e10i 0.840559 0.155145i
\(658\) 2.04511e11 1.09097
\(659\) 2.34850e11 + 1.35591e11i 1.24523 + 0.718934i 0.970154 0.242489i \(-0.0779639\pi\)
0.275075 + 0.961423i \(0.411297\pi\)
\(660\) −8.89189e10 + 6.27923e10i −0.468617 + 0.330926i
\(661\) 1.21597e11 + 2.10613e11i 0.636968 + 1.10326i 0.986095 + 0.166185i \(0.0531451\pi\)
−0.349126 + 0.937076i \(0.613522\pi\)
\(662\) −1.53689e11 + 8.87325e10i −0.800223 + 0.462009i
\(663\) −3.37749e10 4.78279e10i −0.174799 0.247530i
\(664\) 2.33427e10 4.04308e10i 0.120082 0.207989i
\(665\) 5.49082e11i 2.80770i
\(666\) −8.40454e10 2.98321e10i −0.427186 0.151631i
\(667\) 5.28721e10 0.267130
\(668\) 6.72704e10 + 3.88386e10i 0.337846 + 0.195055i
\(669\) 2.13363e11 + 9.84574e10i 1.06516 + 0.491523i
\(670\) 7.56521e10 + 1.31033e11i 0.375424 + 0.650253i
\(671\) −7.00118e10 + 4.04213e10i −0.345367 + 0.199398i
\(672\) 6.14853e10 5.62674e9i 0.301505 0.0275918i
\(673\) 1.44609e10 2.50471e10i 0.0704914 0.122095i −0.828625 0.559804i \(-0.810877\pi\)
0.899117 + 0.437709i \(0.144210\pi\)
\(674\) 2.92320e10i 0.141651i
\(675\) −3.99406e11 1.01909e11i −1.92398 0.490904i
\(676\) 9.57394e10 0.458463
\(677\) 1.58076e11 + 9.12654e10i 0.752509 + 0.434462i 0.826600 0.562790i \(-0.190272\pi\)
−0.0740905 + 0.997252i \(0.523605\pi\)
\(678\) −2.38734e10 2.60873e11i −0.112979 1.23455i
\(679\) −1.83671e11 3.18127e11i −0.864095 1.49666i
\(680\) 1.18929e11 6.86634e10i 0.556225 0.321137i
\(681\) −1.41459e11 + 3.06549e11i −0.657721 + 1.42532i
\(682\) 6.35730e10 1.10112e11i 0.293857 0.508974i
\(683\) 3.71514e11i 1.70723i −0.520903 0.853616i \(-0.674405\pi\)
0.520903 0.853616i \(-0.325595\pi\)
\(684\) −6.73776e10 7.90075e10i −0.307816 0.360947i
\(685\) 1.04359e11 0.473989
\(686\) 2.16783e11 + 1.25159e11i 0.978876 + 0.565155i
\(687\) −2.38219e11 + 1.68225e11i −1.06942 + 0.755201i
\(688\) −8.66264e9 1.50041e10i −0.0386631 0.0669665i
\(689\) 7.47209e9 4.31401e9i 0.0331562 0.0191428i
\(690\) 6.06653e10 + 8.59069e10i 0.267636 + 0.378993i
\(691\) −9.88238e10 + 1.71168e11i −0.433460 + 0.750775i −0.997169 0.0751987i \(-0.976041\pi\)
0.563708 + 0.825974i \(0.309374\pi\)
\(692\) 1.22175e11i 0.532794i
\(693\) 1.99581e11 1.70203e11i 0.865339 0.737962i
\(694\) 1.90246e11 0.820119
\(695\) −3.98846e11 2.30274e11i −1.70949 0.986973i
\(696\) −5.29921e10 2.44535e10i −0.225826 0.104209i
\(697\) −7.80492e10 1.35185e11i −0.330702 0.572793i
\(698\) 2.39788e11 1.38442e11i 1.01020 0.583237i
\(699\) −2.30990e11 + 2.11388e10i −0.967575 + 0.0885464i
\(700\) −2.04130e11 + 3.53564e11i −0.850189 + 1.47257i
\(701\) 6.70096e10i 0.277501i −0.990327 0.138751i \(-0.955691\pi\)
0.990327 0.138751i \(-0.0443087\pi\)
\(702\) −4.76523e10 + 1.33822e10i −0.196217 + 0.0551035i
\(703\) 1.48551e11 0.608209
\(704\) −1.76570e10 1.01943e10i −0.0718831 0.0415017i
\(705\) −3.50426e10 3.82922e11i −0.141854 1.55008i
\(706\) −5.91201e10 1.02399e11i −0.237967 0.412170i
\(707\) 1.26832e11 7.32264e10i 0.507634 0.293083i
\(708\) 4.36433e10 9.45775e10i 0.173694 0.376405i
\(709\) 5.70291e10 9.87774e10i 0.225690 0.390906i −0.730836 0.682553i \(-0.760870\pi\)
0.956526 + 0.291647i \(0.0942031\pi\)
\(710\) 2.07193e11i 0.815345i
\(711\) −2.80483e10 + 7.90198e10i −0.109756 + 0.309213i
\(712\) −3.04240e10 −0.118385
\(713\) −1.06382e11 6.14196e10i −0.411632 0.237656i
\(714\) −2.70303e11 + 1.90881e11i −1.04006 + 0.734464i
\(715\) −4.32147e10 7.48501e10i −0.165351 0.286397i
\(716\) −1.04646e11 + 6.04172e10i −0.398171 + 0.229884i
\(717\) 6.55522e10 + 9.28271e10i 0.248034 + 0.351235i
\(718\) −1.34348e11 + 2.32698e11i −0.505516 + 0.875580i
\(719\) 2.31072e11i 0.864633i 0.901722 + 0.432317i \(0.142304\pi\)
−0.901722 + 0.432317i \(0.857696\pi\)
\(720\) −2.10708e10 1.14160e11i −0.0784063 0.424798i
\(721\) 3.58007e10 0.132480
\(722\) −1.66181e10 9.59444e9i −0.0611549 0.0353078i
\(723\) 3.26266e11 + 1.50557e11i 1.19404 + 0.550995i
\(724\) −5.55667e10 9.62444e10i −0.202237 0.350285i
\(725\) 3.34208e11 1.92955e11i 1.20966 0.698400i
\(726\) 1.09367e11 1.00085e10i 0.393675 0.0360267i
\(727\) 1.70637e11 2.95551e11i 0.610850 1.05802i −0.380248 0.924885i \(-0.624161\pi\)
0.991097 0.133138i \(-0.0425055\pi\)
\(728\) 4.90224e10i 0.174530i
\(729\) −2.41138e11 + 1.47034e11i −0.853799 + 0.520603i
\(730\) −2.96576e11 −1.04435
\(731\) 8.04145e10 + 4.64274e10i 0.281621 + 0.162594i
\(732\) −7.85694e9 8.58554e10i −0.0273659 0.299036i
\(733\) 2.07203e11 + 3.58887e11i 0.717763 + 1.24320i 0.961884 + 0.273457i \(0.0881670\pi\)
−0.244122 + 0.969745i \(0.578500\pi\)
\(734\) −1.01396e11 + 5.85408e10i −0.349330 + 0.201685i
\(735\) 4.08489e11 8.85220e11i 1.39969 3.03320i
\(736\) −9.84897e9 + 1.70589e10i −0.0335645 + 0.0581353i
\(737\) 1.20394e11i 0.408071i
\(738\) −1.29764e11 + 2.39510e10i −0.437452 + 0.0807418i
\(739\) 2.71838e11 0.911449 0.455725 0.890121i \(-0.349380\pi\)
0.455725 + 0.890121i \(0.349380\pi\)
\(740\) 1.43828e11 + 8.30392e10i 0.479642 + 0.276921i
\(741\) 6.73451e10 4.75574e10i 0.223374 0.157741i
\(742\) −2.43810e10 4.22291e10i −0.0804332 0.139314i
\(743\) −2.96676e11 + 1.71286e11i −0.973479 + 0.562039i −0.900295 0.435280i \(-0.856649\pi\)
−0.0731842 + 0.997318i \(0.523316\pi\)
\(744\) 7.82165e10 + 1.10761e11i 0.255274 + 0.361488i
\(745\) 2.32837e11 4.03286e11i 0.755835 1.30914i
\(746\) 9.11142e10i 0.294192i
\(747\) 1.99328e11 + 7.07521e10i 0.640157 + 0.227225i
\(748\) 1.09272e11 0.349063
\(749\) −8.34547e11 4.81826e11i −2.65170 1.53096i
\(750\) 3.45967e11 + 1.59649e11i 1.09343 + 0.504568i
\(751\) −5.25839e10 9.10780e10i −0.165308 0.286321i 0.771457 0.636282i \(-0.219528\pi\)
−0.936765 + 0.349960i \(0.886195\pi\)
\(752\) 6.23721e10 3.60105e10i 0.195038 0.112605i
\(753\) 1.95272e11 1.78700e10i 0.607378 0.0555834i
\(754\) 2.31693e10 4.01304e10i 0.0716849 0.124162i
\(755\) 9.07750e11i 2.79369i
\(756\) 7.56306e10 + 2.69311e11i 0.231532 + 0.824454i
\(757\) −4.23531e11 −1.28974 −0.644869 0.764293i \(-0.723088\pi\)
−0.644869 + 0.764293i \(0.723088\pi\)
\(758\) −2.57900e11 1.48898e11i −0.781221 0.451038i
\(759\) 7.62628e9 + 8.33349e10i 0.0229798 + 0.251108i
\(760\) 9.66830e10 + 1.67460e11i 0.289798 + 0.501945i
\(761\) 4.62418e11 2.66977e11i 1.37878 0.796041i 0.386770 0.922176i \(-0.373591\pi\)
0.992013 + 0.126135i \(0.0402574\pi\)
\(762\) 3.14378e10 6.81275e10i 0.0932465 0.202070i
\(763\) −5.47931e11 + 9.49044e11i −1.61669 + 2.80019i
\(764\) 9.01526e9i 0.0264609i
\(765\) 4.03718e11 + 4.73403e11i 1.17878 + 1.38224i
\(766\) −3.46118e11 −1.00533
\(767\) 7.16228e10 + 4.13514e10i 0.206952 + 0.119484i
\(768\) 1.77611e10 1.25424e10i 0.0510535 0.0360527i
\(769\) −5.66789e10 9.81707e10i −0.162075 0.280722i 0.773538 0.633750i \(-0.218485\pi\)
−0.935613 + 0.353028i \(0.885152\pi\)
\(770\) −4.23021e11 + 2.44231e11i −1.20337 + 0.694766i
\(771\) −1.12715e11 1.59613e11i −0.318980 0.451701i
\(772\) 1.75195e11 3.03447e11i 0.493234 0.854306i
\(773\) 2.83942e11i 0.795265i −0.917545 0.397632i \(-0.869832\pi\)
0.917545 0.397632i \(-0.130168\pi\)
\(774\) 5.97249e10 5.09334e10i 0.166415 0.141919i
\(775\) −8.96595e11 −2.48536
\(776\) −1.12032e11 6.46820e10i −0.308956 0.178376i
\(777\) −3.63365e11 1.67677e11i −0.996918 0.460033i
\(778\) 2.46119e11 + 4.26290e11i 0.671779 + 1.16355i
\(779\) 1.90350e11 1.09899e11i 0.516897 0.298430i
\(780\) 9.17886e10 8.39991e9i 0.247976 0.0226932i
\(781\) 8.24328e10 1.42778e11i 0.221562 0.383757i
\(782\) 1.05571e11i 0.282304i
\(783\) 6.53712e10 2.56207e11i 0.173916 0.681621i
\(784\) 1.82603e11 0.483331
\(785\) 3.94524e11 + 2.27779e11i 1.03895 + 0.599839i
\(786\) 3.16114e10 + 3.45428e11i 0.0828236 + 0.905040i
\(787\) 3.25568e11 + 5.63900e11i 0.848678 + 1.46995i 0.882389 + 0.470521i \(0.155934\pi\)
−0.0337110 + 0.999432i \(0.510733\pi\)
\(788\) −6.06662e10 + 3.50257e10i −0.157341 + 0.0908409i
\(789\) −2.21430e11 + 4.79851e11i −0.571384 + 1.23822i
\(790\) 7.80739e10 1.35228e11i 0.200446 0.347183i
\(791\) 1.17550e12i 3.00273i
\(792\) 3.08990e10 8.70512e10i 0.0785315 0.221245i
\(793\) 6.84528e10 0.173100
\(794\) 4.22703e11 + 2.44047e11i 1.06354 + 0.614034i
\(795\) −7.48913e10 + 5.28863e10i −0.187483 + 0.132396i
\(796\) −1.70539e11 2.95382e11i −0.424787 0.735753i
\(797\) 4.16469e11 2.40448e11i 1.03216 0.595921i 0.114561 0.993416i \(-0.463454\pi\)
0.917604 + 0.397496i \(0.130121\pi\)
\(798\) −2.68774e11 3.80606e11i −0.662790 0.938564i
\(799\) −1.92998e11 + 3.34283e11i −0.473550 + 0.820213i
\(800\) 1.43774e11i 0.351011i
\(801\) −2.50188e10 1.35549e11i −0.0607765 0.329281i
\(802\) −2.05699e11 −0.497204
\(803\) −2.04372e11 1.17994e11i −0.491541 0.283791i
\(804\) −1.16580e11 5.37965e10i −0.278997 0.128745i
\(805\) 2.35958e11 + 4.08692e11i 0.561890 + 0.973223i
\(806\) −9.32361e10 + 5.38299e10i −0.220925 + 0.127551i
\(807\) 5.35705e11 4.90243e10i 1.26308 0.115589i
\(808\) 2.57876e10 4.46654e10i 0.0605013 0.104791i
\(809\) 1.97505e11i 0.461089i 0.973062 + 0.230545i \(0.0740508\pi\)
−0.973062 + 0.230545i \(0.925949\pi\)
\(810\) 4.91293e11 1.87755e11i 1.14130 0.436166i
\(811\) −1.30697e11 −0.302121 −0.151061 0.988524i \(-0.548269\pi\)
−0.151061 + 0.988524i \(0.548269\pi\)
\(812\) −2.26800e11 1.30943e11i −0.521698 0.301203i
\(813\) −2.00953e10 2.19588e11i −0.0459973 0.502627i
\(814\) 6.60752e10 + 1.14446e11i 0.150501 + 0.260676i
\(815\) −5.15152e11 + 2.97423e11i −1.16763 + 0.674131i
\(816\) −4.88268e10 + 1.05810e11i −0.110128 + 0.238654i
\(817\) −6.53730e10 + 1.13229e11i −0.146727 + 0.254139i
\(818\) 7.32504e10i 0.163605i
\(819\) −2.18411e11 + 4.03129e10i −0.485445 + 0.0896001i
\(820\) 2.45732e11 0.543509
\(821\) 2.25465e10 + 1.30172e10i 0.0496256 + 0.0286514i 0.524608 0.851344i \(-0.324212\pi\)
−0.474982 + 0.879996i \(0.657545\pi\)
\(822\) −7.23383e10 + 5.10835e10i −0.158446 + 0.111891i
\(823\) 1.02310e11 + 1.77206e11i 0.223007 + 0.386260i 0.955720 0.294278i \(-0.0950792\pi\)
−0.732712 + 0.680539i \(0.761746\pi\)
\(824\) 1.09185e10 6.30382e9i 0.0236840 0.0136740i
\(825\) 3.52334e11 + 4.98933e11i 0.760570 + 1.07703i
\(826\) 2.33701e11 4.04781e11i 0.502042 0.869562i
\(827\) 2.31574e11i 0.495072i −0.968879 0.247536i \(-0.920379\pi\)
0.968879 0.247536i \(-0.0796208\pi\)
\(828\) −8.41024e10 2.98523e10i −0.178932 0.0635122i
\(829\) 7.98205e11 1.69004 0.845019 0.534736i \(-0.179589\pi\)
0.845019 + 0.534736i \(0.179589\pi\)
\(830\) −3.41114e11 1.96942e11i −0.718765 0.414979i
\(831\) −7.36861e11 3.40029e11i −1.54519 0.713036i
\(832\) 8.63192e9 + 1.49509e10i 0.0180142 + 0.0312015i
\(833\) −8.47545e11 + 4.89331e11i −1.76029 + 1.01630i
\(834\) 3.89185e11 3.56158e10i 0.804438 0.0736171i
\(835\) 3.27681e11 5.67559e11i 0.674070 1.16752i
\(836\) 1.53863e11i 0.315000i
\(837\) −4.29156e11 + 4.39563e11i −0.874407 + 0.895612i
\(838\) −4.28623e11 −0.869160
\(839\) 5.56790e11 + 3.21463e11i 1.12368 + 0.648758i 0.942338 0.334662i \(-0.108622\pi\)
0.181343 + 0.983420i \(0.441955\pi\)
\(840\) −4.74727e10 5.18750e11i −0.0953514 1.04194i
\(841\) −1.26349e11 2.18842e11i −0.252573 0.437469i
\(842\) 4.67914e11 2.70150e11i 0.930931 0.537473i
\(843\) 2.67669e11 5.80053e11i 0.530014 1.14857i
\(844\) 1.20210e11 2.08209e11i 0.236902 0.410327i
\(845\) 8.07752e11i 1.58435i
\(846\) 2.11730e11 + 2.48276e11i 0.413334 + 0.484678i
\(847\) 4.92808e11 0.957511
\(848\) −1.48715e10 8.58606e9i −0.0287588 0.0166039i
\(849\) −6.44258e10 + 4.54959e10i −0.124002 + 0.0875672i
\(850\) −3.85278e11 6.67321e11i −0.738071 1.27838i
\(851\) 1.10569e11 6.38370e10i 0.210821 0.121718i
\(852\) 1.01420e11 + 1.43619e11i 0.192472 + 0.272555i
\(853\) 9.75384e10 1.68942e11i 0.184238 0.319110i −0.759081 0.650996i \(-0.774352\pi\)
0.943320 + 0.331886i \(0.107685\pi\)
\(854\) 3.86866e11i 0.727326i
\(855\) −6.66584e11 + 5.68464e11i −1.24736 + 1.06375i
\(856\) −3.39362e11 −0.632074
\(857\) −3.84904e10 2.22224e10i −0.0713557 0.0411972i 0.463898 0.885889i \(-0.346451\pi\)
−0.535253 + 0.844692i \(0.679784\pi\)
\(858\) 6.65940e10 + 3.07301e10i 0.122881 + 0.0567042i
\(859\) −1.25294e11 2.17015e11i −0.230122 0.398582i 0.727722 0.685872i \(-0.240579\pi\)
−0.957844 + 0.287290i \(0.907246\pi\)
\(860\) −1.26590e11 + 7.30866e10i −0.231422 + 0.133611i
\(861\) −5.89659e11 + 5.39619e10i −1.07297 + 0.0981916i
\(862\) 1.54656e11 2.67871e11i 0.280115 0.485174i
\(863\) 3.91558e11i 0.705915i 0.935639 + 0.352958i \(0.114824\pi\)
−0.935639 + 0.352958i \(0.885176\pi\)
\(864\) 7.04864e10 + 6.88176e10i 0.126488 + 0.123494i
\(865\) −1.03079e12 −1.84122
\(866\) −6.82876e10 3.94259e10i −0.121415 0.0700987i
\(867\) −5.42428e9 5.92729e10i −0.00959988 0.104901i
\(868\) 3.04224e11 + 5.26931e11i 0.535937 + 0.928271i
\(869\) 1.07602e11 6.21242e10i 0.188687 0.108939i
\(870\) −2.06313e11 + 4.47093e11i −0.360123 + 0.780406i
\(871\) 5.09714e10 8.82851e10i 0.0885633 0.153396i
\(872\) 3.85921e11i 0.667471i
\(873\) 1.96052e11 5.52333e11i 0.337531 0.950920i
\(874\) 1.48651e11 0.254755
\(875\) 1.48070e12 + 8.54884e11i 2.52601 + 1.45839i
\(876\) 2.05577e11 1.45173e11i 0.349106 0.246530i
\(877\) 3.99055e10 + 6.91184e10i 0.0674582 + 0.116841i 0.897782 0.440441i \(-0.145178\pi\)
−0.830324 + 0.557282i \(0.811844\pi\)
\(878\) 8.35204e10 4.82206e10i 0.140545 0.0811436i
\(879\) −2.47869e11 3.51002e11i −0.415209 0.587968i
\(880\) −8.60090e10 + 1.48972e11i −0.143421 + 0.248413i
\(881\) 5.84453e11i 0.970166i 0.874468 + 0.485083i \(0.161211\pi\)
−0.874468 + 0.485083i \(0.838789\pi\)
\(882\) 1.50161e11 + 8.13560e11i 0.248132 + 1.34436i
\(883\) 7.52384e10 0.123765 0.0618823 0.998083i \(-0.480290\pi\)
0.0618823 + 0.998083i \(0.480290\pi\)
\(884\) −8.01294e10 4.62627e10i −0.131215 0.0757569i
\(885\) −7.97949e11 3.68218e11i −1.30077 0.600249i
\(886\) −1.15756e11 2.00495e11i −0.187849 0.325364i
\(887\) 6.05896e11 3.49814e11i 0.978822 0.565123i 0.0769076 0.997038i \(-0.475495\pi\)
0.901914 + 0.431915i \(0.142162\pi\)
\(888\) −1.40344e11 + 1.28434e10i −0.225706 + 0.0206552i
\(889\) 1.68343e11 2.91578e11i 0.269518 0.466819i
\(890\) 2.56687e11i 0.409113i
\(891\) 4.13252e11 + 6.60802e10i 0.655698 + 0.104848i
\(892\) 3.71333e11 0.586548
\(893\) −4.70694e11 2.71755e11i −0.740172 0.427338i
\(894\) 3.60122e10 + 3.93518e11i 0.0563768 + 0.616047i
\(895\) 5.09739e11 + 8.82894e11i 0.794430 + 1.37599i
\(896\) 8.44963e10 4.87840e10i 0.131101 0.0756911i
\(897\) 2.96892e10 6.43382e10i 0.0458594 0.0993800i
\(898\) −8.65455e10 + 1.49901e11i −0.133088 + 0.230515i
\(899\) 5.75137e11i 0.880507i
\(900\) −6.40562e11 + 1.18230e11i −0.976317 + 0.180202i
\(901\) 9.20338e10 0.139652
\(902\) 1.69335e11 + 9.77658e10i 0.255812 + 0.147693i
\(903\) 2.87715e11 2.03177e11i 0.432725 0.305579i
\(904\) −2.06983e11 3.58505e11i −0.309928 0.536812i
\(905\) −8.12012e11 + 4.68815e11i −1.21051 + 0.698888i
\(906\) −4.44341e11 6.29222e11i −0.659483 0.933881i
\(907\) −5.79947e10 + 1.00450e11i −0.0856958 + 0.148429i −0.905687 0.423946i \(-0.860645\pi\)
0.819992 + 0.572375i \(0.193978\pi\)
\(908\) 5.33513e11i 0.784877i
\(909\) 2.20205e11 + 7.81624e10i 0.322532 + 0.114483i
\(910\) 4.13601e11 0.603137
\(911\) 9.81176e11 + 5.66482e11i 1.42454 + 0.822456i 0.996682 0.0813913i \(-0.0259363\pi\)
0.427854 + 0.903848i \(0.359270\pi\)
\(912\) −1.48989e11 6.87516e10i −0.215364 0.0993810i
\(913\) −1.56709e11 2.71428e11i −0.225533 0.390635i
\(914\) −2.35358e11 + 1.35884e11i −0.337244 + 0.194708i
\(915\) −7.24360e11 + 6.62889e10i −1.03340 + 0.0945706i
\(916\) −2.30424e11 + 3.99105e11i −0.327299 + 0.566899i
\(917\) 1.55651e12i 2.20127i
\(918\) −5.11573e11 1.30528e11i −0.720340 0.183795i
\(919\) −3.06256e11 −0.429361 −0.214680 0.976684i \(-0.568871\pi\)
−0.214680 + 0.976684i \(0.568871\pi\)
\(920\) 1.43926e11 + 8.30956e10i 0.200903 + 0.115992i
\(921\) 9.90936e10 + 1.08283e12i 0.137723 + 1.50495i
\(922\) 3.24506e11 + 5.62060e11i 0.449054 + 0.777784i
\(923\) −1.20896e11 + 6.97992e10i −0.166573 + 0.0961709i
\(924\) 1.73674e11 3.76361e11i 0.238257 0.516317i
\(925\) 4.65942e11 8.07035e11i 0.636451 1.10237i
\(926\) 6.86069e11i 0.933090i
\(927\) 3.70644e10 + 4.34619e10i 0.0501923 + 0.0588559i
\(928\) −9.22265e10 −0.124355
\(929\) −8.75115e11 5.05248e11i −1.17490 0.678331i −0.220074 0.975483i \(-0.570630\pi\)
−0.954830 + 0.297152i \(0.903963\pi\)
\(930\) 9.34486e11 6.59911e11i 1.24923 0.882173i
\(931\) −6.89012e11 1.19340e12i −0.917124 1.58851i
\(932\) −3.17439e11 + 1.83273e11i −0.420723 + 0.242905i
\(933\) 1.06983e11 + 1.51496e11i 0.141185 + 0.199929i
\(934\) −5.71858e10 + 9.90488e10i −0.0751452 + 0.130155i
\(935\) 9.21929e11i 1.20629i
\(936\) −5.95131e10 + 5.07528e10i −0.0775370 + 0.0661236i
\(937\) −3.80033e11 −0.493018 −0.246509 0.969141i \(-0.579283\pi\)
−0.246509 + 0.969141i \(0.579283\pi\)
\(938\) −4.98950e11 2.88069e11i −0.644533 0.372121i
\(939\) 1.31526e12 + 6.06933e11i 1.69180 + 0.780689i
\(940\) −3.03820e11 5.26232e11i −0.389139 0.674009i
\(941\) 4.20722e11 2.42904e11i 0.536583 0.309796i −0.207110 0.978318i \(-0.566406\pi\)
0.743693 + 0.668521i \(0.233072\pi\)
\(942\) −3.84969e11 + 3.52299e10i −0.488902 + 0.0447412i
\(943\) 9.44541e10 1.63599e11i 0.119447 0.206888i
\(944\) 1.64601e11i 0.207274i
\(945\) 2.27217e12 6.38094e11i 2.84914 0.800124i
\(946\) −1.16311e11 −0.145231
\(947\) 4.64773e9 + 2.68337e9i 0.00577885 + 0.00333642i 0.502887 0.864352i \(-0.332271\pi\)
−0.497108 + 0.867689i \(0.665605\pi\)
\(948\) 1.20755e10 + 1.31953e11i 0.0149510 + 0.163375i
\(949\) 9.99106e10 + 1.73050e11i 0.123182 + 0.213357i
\(950\) 9.39635e11 5.42498e11i 1.15363 0.666046i
\(951\) −2.26279e11 + 4.90359e11i −0.276644 + 0.599504i
\(952\) −2.61457e11 + 4.52857e11i −0.318312 + 0.551332i
\(953\) 2.87948e11i 0.349094i −0.984649 0.174547i \(-0.944154\pi\)
0.984649 0.174547i \(-0.0558462\pi\)
\(954\) 2.60244e10 7.33182e10i 0.0314187 0.0885152i
\(955\) −7.60616e10 −0.0914433
\(956\) 1.55520e11 + 8.97893e10i 0.186189 + 0.107496i
\(957\) −3.20050e11 + 2.26011e11i −0.381566 + 0.269453i
\(958\) 1.22782e11 + 2.12665e11i 0.145772 + 0.252484i
\(959\) −3.44141e11 + 1.98690e11i −0.406876 + 0.234910i
\(960\) −1.05820e11 1.49850e11i −0.124590 0.176430i
\(961\) −2.41670e11 + 4.18585e11i −0.283354 + 0.490784i
\(962\) 1.11897e11i 0.130653i
\(963\) −2.79069e11 1.51197e12i −0.324494 1.75808i
\(964\) 5.67827e11 0.657519
\(965\) −2.56017e12 1.47812e12i −2.95230 1.70451i
\(966\) −3.63612e11 1.67791e11i −0.417570 0.192690i
\(967\) −4.51417e11 7.81877e11i −0.516264 0.894195i −0.999822 0.0188827i \(-0.993989\pi\)
0.483558 0.875312i \(-0.339344\pi\)
\(968\) 1.50297e11 8.67741e10i 0.171179 0.0988300i
\(969\) 8.75761e11 8.01441e10i 0.993323 0.0909027i
\(970\) −5.45721e11 + 9.45216e11i −0.616429 + 1.06769i
\(971\) 8.08040e11i 0.908983i −0.890751 0.454492i \(-0.849821\pi\)
0.890751 0.454492i \(-0.150179\pi\)
\(972\) −2.48642e11 + 3.70632e11i −0.278554 + 0.415220i
\(973\) 1.75368e12 1.95658
\(974\) −5.71017e10 3.29677e10i −0.0634473 0.0366313i
\(975\) −4.71328e10 5.15035e11i −0.0521561 0.569926i
\(976\) −6.81198e10 1.17987e11i −0.0750713 0.130027i
\(977\) 1.39658e12 8.06317e11i 1.53281 0.884968i 0.533579 0.845750i \(-0.320847\pi\)
0.999231 0.0392176i \(-0.0124866\pi\)
\(978\) 2.11499e11 4.58330e11i 0.231181 0.500983i
\(979\) −1.02124e11 + 1.76884e11i −0.111173 + 0.192557i
\(980\) 1.54062e12i 1.67029i
\(981\) −1.71941e12 + 3.17357e11i −1.85653 + 0.342666i
\(982\) −2.81812e11 −0.303050
\(983\) 1.24469e12 + 7.18625e11i 1.33306 + 0.769641i 0.985767 0.168117i \(-0.0537687\pi\)
0.347290 + 0.937758i \(0.387102\pi\)
\(984\) −1.70333e11 + 1.20285e11i −0.181685 + 0.128302i
\(985\) 2.95511e11 + 5.11840e11i 0.313927 + 0.543737i
\(986\) 4.28065e11 2.47143e11i 0.452900 0.261482i
\(987\) 8.44606e11 + 1.19603e12i 0.889991 + 1.26030i
\(988\) 6.51412e10 1.12828e11i 0.0683641 0.118410i
\(989\) 1.12372e11i 0.117455i
\(990\) −7.34449e11 2.60694e11i −0.764576 0.271388i
\(991\) −1.11953e12 −1.16075 −0.580377 0.814348i \(-0.697095\pi\)
−0.580377 + 0.814348i \(0.697095\pi\)
\(992\) 1.85565e11 + 1.07136e11i 0.191624 + 0.110634i
\(993\) −1.15365e12 5.32356e11i −1.18652 0.547527i
\(994\) 3.94476e11 + 6.83252e11i 0.404087 + 0.699899i
\(995\) −2.49213e12 + 1.43883e12i −2.54261 + 1.46797i
\(996\) 3.32852e11 3.04605e10i 0.338231 0.0309528i
\(997\) −4.45668e11 + 7.71920e11i −0.451057 + 0.781253i −0.998452 0.0556212i \(-0.982286\pi\)
0.547395 + 0.836874i \(0.315619\pi\)
\(998\) 1.85489e11i 0.186981i
\(999\) −1.72632e11 6.14721e11i −0.173324 0.617186i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 18.9.d.a.11.6 yes 16
3.2 odd 2 54.9.d.a.35.1 16
4.3 odd 2 144.9.q.b.65.5 16
9.2 odd 6 162.9.b.c.161.9 16
9.4 even 3 54.9.d.a.17.1 16
9.5 odd 6 inner 18.9.d.a.5.6 16
9.7 even 3 162.9.b.c.161.8 16
12.11 even 2 432.9.q.c.305.1 16
36.23 even 6 144.9.q.b.113.5 16
36.31 odd 6 432.9.q.c.17.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
18.9.d.a.5.6 16 9.5 odd 6 inner
18.9.d.a.11.6 yes 16 1.1 even 1 trivial
54.9.d.a.17.1 16 9.4 even 3
54.9.d.a.35.1 16 3.2 odd 2
144.9.q.b.65.5 16 4.3 odd 2
144.9.q.b.113.5 16 36.23 even 6
162.9.b.c.161.8 16 9.7 even 3
162.9.b.c.161.9 16 9.2 odd 6
432.9.q.c.17.1 16 36.31 odd 6
432.9.q.c.305.1 16 12.11 even 2