Properties

Label 23.11.d.a.5.2
Level $23$
Weight $11$
Character 23.5
Analytic conductor $14.613$
Analytic rank $0$
Dimension $190$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [23,11,Mod(5,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.5");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 23.d (of order \(22\), degree \(10\), 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: \(14.6132168115\)
Analytic rank: \(0\)
Dimension: \(190\)
Relative dimension: \(19\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.2
Character \(\chi\) \(=\) 23.5
Dual form 23.11.d.a.14.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-55.1016 - 16.1793i) q^{2} +(-267.468 + 308.675i) q^{3} +(1912.97 + 1229.39i) q^{4} +(-1056.35 - 151.880i) q^{5} +(19732.1 - 12681.0i) q^{6} +(-3001.68 + 1370.82i) q^{7} +(-47007.4 - 54249.4i) q^{8} +(-15337.3 - 106673. i) q^{9} +O(q^{10})\) \(q+(-55.1016 - 16.1793i) q^{2} +(-267.468 + 308.675i) q^{3} +(1912.97 + 1229.39i) q^{4} +(-1056.35 - 151.880i) q^{5} +(19732.1 - 12681.0i) q^{6} +(-3001.68 + 1370.82i) q^{7} +(-47007.4 - 54249.4i) q^{8} +(-15337.3 - 106673. i) q^{9} +(55749.3 + 25459.9i) q^{10} +(5688.57 + 19373.5i) q^{11} +(-891142. + 261663. i) q^{12} +(259550. - 568335. i) q^{13} +(187576. - 26969.4i) q^{14} +(329422. - 285446. i) q^{15} +(745159. + 1.63167e6i) q^{16} +(1.38726e6 + 2.15862e6i) q^{17} +(-880789. + 6.12602e6i) q^{18} +(1.96021e6 - 3.05015e6i) q^{19} +(-1.83405e6 - 1.58921e6i) q^{20} +(379716. - 1.29319e6i) q^{21} -1.15955e6i q^{22} +(-2.67832e6 + 5.85262e6i) q^{23} +2.93184e7 q^{24} +(-8.27724e6 - 2.43042e6i) q^{25} +(-2.34969e7 + 2.71168e7i) q^{26} +(1.67405e7 + 1.07585e7i) q^{27} +(-7.42741e6 - 1.06790e6i) q^{28} +(-4.21321e6 + 2.70766e6i) q^{29} +(-2.27700e7 + 1.03987e7i) q^{30} +(3.77167e6 + 4.35274e6i) q^{31} +(-4.19932e6 - 2.92069e7i) q^{32} +(-7.50162e6 - 3.42588e6i) q^{33} +(-4.15154e7 - 1.41388e8i) q^{34} +(3.37903e6 - 992172. i) q^{35} +(1.01804e8 - 2.22919e8i) q^{36} +(-1.22651e7 + 1.76345e6i) q^{37} +(-1.57360e8 + 1.36353e8i) q^{38} +(1.06009e8 + 2.32128e8i) q^{39} +(4.14169e7 + 6.44459e7i) q^{40} +(2.81306e7 - 1.95653e8i) q^{41} +(-4.18459e7 + 6.51135e7i) q^{42} +(1.59175e8 + 1.37926e8i) q^{43} +(-1.29356e7 + 4.40545e7i) q^{44} +1.15014e8i q^{45} +(2.42271e8 - 2.79155e8i) q^{46} +1.07492e8 q^{47} +(-7.02962e8 - 2.06408e8i) q^{48} +(-1.77851e8 + 2.05251e8i) q^{49} +(4.16767e8 + 2.67840e8i) q^{50} +(-1.03736e9 - 1.49150e8i) q^{51} +(1.19522e9 - 7.68121e8i) q^{52} +(-4.66888e8 + 2.13221e8i) q^{53} +(-7.48366e8 - 8.63661e8i) q^{54} +(-3.06667e6 - 2.13292e7i) q^{55} +(2.15467e8 + 9.84007e7i) q^{56} +(4.17210e8 + 1.42089e9i) q^{57} +(2.75963e8 - 8.10299e7i) q^{58} +(-9.48362e7 + 2.07662e8i) q^{59} +(9.81101e8 - 1.41061e8i) q^{60} +(5.56382e8 - 4.82108e8i) q^{61} +(-1.37401e8 - 3.00866e8i) q^{62} +(1.92268e8 + 2.99175e8i) q^{63} +(2.02488e7 - 1.40834e8i) q^{64} +(-3.60495e8 + 5.60941e8i) q^{65} +(3.57923e8 + 3.10142e8i) q^{66} +(-1.58540e8 + 5.39936e8i) q^{67} +5.83488e9i q^{68} +(-1.09019e9 - 2.39212e9i) q^{69} -2.02243e8 q^{70} +(2.59270e8 + 7.61285e7i) q^{71} +(-5.06600e9 + 5.84648e9i) q^{72} +(-9.38541e6 - 6.03164e6i) q^{73} +(7.04357e8 + 1.01271e8i) q^{74} +(2.96411e9 - 1.90492e9i) q^{75} +(7.49968e9 - 3.42499e9i) q^{76} +(-4.36329e7 - 5.03550e7i) q^{77} +(-2.08562e9 - 1.45058e10i) q^{78} +(1.88062e9 + 8.58850e8i) q^{79} +(-5.39331e8 - 1.83679e9i) q^{80} +(-1.69248e9 + 4.96958e8i) q^{81} +(-4.71556e9 + 1.03256e10i) q^{82} +(7.48751e8 - 1.07654e8i) q^{83} +(2.31623e9 - 2.00703e9i) q^{84} +(-1.13758e9 - 2.49096e9i) q^{85} +(-6.53927e9 - 1.01753e10i) q^{86} +(2.91111e8 - 2.02472e9i) q^{87} +(7.83596e8 - 1.21930e9i) q^{88} +(2.84805e9 + 2.46785e9i) q^{89} +(1.86085e9 - 6.33746e9i) q^{90} +2.06176e9i q^{91} +(-1.23187e10 + 7.90319e9i) q^{92} -2.35238e9 q^{93} +(-5.92298e9 - 1.73914e9i) q^{94} +(-2.53393e9 + 2.92431e9i) q^{95} +(1.01386e10 + 6.51570e9i) q^{96} +(-1.22808e10 - 1.76571e9i) q^{97} +(1.31207e10 - 8.43216e9i) q^{98} +(1.97939e9 - 9.03957e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 190 q + 13 q^{2} - 71 q^{3} - 11699 q^{4} - 11 q^{5} + 3346 q^{6} - 11 q^{7} - 50582 q^{8} - 394850 q^{9} - 11 q^{10} - 11 q^{11} - 311414 q^{12} + 615881 q^{13} - 11 q^{14} - 4830144 q^{15} + 4888037 q^{16} + 1092014 q^{17} - 12368454 q^{18} - 2415644 q^{19} + 25028597 q^{20} + 26277196 q^{21} - 27677088 q^{23} - 86512102 q^{24} + 27883308 q^{25} + 19713282 q^{26} + 71519392 q^{27} + 43862005 q^{28} + 14189630 q^{29} - 270003723 q^{30} - 143915692 q^{31} + 282266229 q^{32} - 54918402 q^{33} - 124580401 q^{34} - 190738351 q^{35} + 455227393 q^{36} + 518658261 q^{37} - 208458646 q^{38} - 527477093 q^{39} - 1236125011 q^{40} + 306361793 q^{41} + 1644990919 q^{42} + 997299501 q^{43} + 1314948338 q^{44} - 983375619 q^{46} - 1197840554 q^{47} - 3164309566 q^{48} + 634842426 q^{49} - 1020294456 q^{50} + 2177981773 q^{51} + 7146448896 q^{52} + 679896965 q^{53} - 2477743998 q^{54} - 7228070785 q^{55} - 4503370696 q^{56} + 2289855898 q^{57} + 6681134963 q^{58} + 3429280247 q^{59} - 14840793781 q^{60} - 5311011871 q^{61} - 2481918590 q^{62} - 453734886 q^{63} + 9411259010 q^{64} + 10772645950 q^{65} + 12902167608 q^{66} + 2086349727 q^{67} - 722851896 q^{69} - 14032163318 q^{70} - 9791640554 q^{71} - 17117854769 q^{72} - 3808899929 q^{73} + 28336591052 q^{74} + 11315752564 q^{75} + 3533940894 q^{76} + 10258348964 q^{77} + 32629640016 q^{78} + 11295172361 q^{79} - 32343151082 q^{80} - 59771908210 q^{81} - 19730142428 q^{82} - 14758669948 q^{83} + 3906513611 q^{84} - 18216984945 q^{85} - 6838112941 q^{86} + 33011018419 q^{87} + 50131567101 q^{88} + 34310737417 q^{89} + 65550641882 q^{90} - 21333991814 q^{92} - 60352716136 q^{93} - 23758977011 q^{94} - 40681791604 q^{95} - 193570603643 q^{96} - 50355692024 q^{97} + 86096143637 q^{98} + 177617674300 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(e\left(\frac{1}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −55.1016 16.1793i −1.72193 0.505603i −0.736606 0.676323i \(-0.763573\pi\)
−0.985320 + 0.170720i \(0.945391\pi\)
\(3\) −267.468 + 308.675i −1.10069 + 1.27027i −0.140757 + 0.990044i \(0.544954\pi\)
−0.959935 + 0.280222i \(0.909592\pi\)
\(4\) 1912.97 + 1229.39i 1.86814 + 1.20058i
\(5\) −1056.35 151.880i −0.338032 0.0486017i −0.0287914 0.999585i \(-0.509166\pi\)
−0.309241 + 0.950984i \(0.600075\pi\)
\(6\) 19732.1 12681.0i 2.53756 1.63079i
\(7\) −3001.68 + 1370.82i −0.178597 + 0.0815625i −0.502707 0.864457i \(-0.667663\pi\)
0.324110 + 0.946019i \(0.394935\pi\)
\(8\) −47007.4 54249.4i −1.43455 1.65556i
\(9\) −15337.3 106673.i −0.259739 1.80652i
\(10\) 55749.3 + 25459.9i 0.557493 + 0.254599i
\(11\) 5688.57 + 19373.5i 0.0353215 + 0.120294i 0.975267 0.221031i \(-0.0709423\pi\)
−0.939945 + 0.341326i \(0.889124\pi\)
\(12\) −891142. + 261663.i −3.58130 + 1.05157i
\(13\) 259550. 568335.i 0.699043 1.53069i −0.142084 0.989855i \(-0.545380\pi\)
0.841128 0.540837i \(-0.181892\pi\)
\(14\) 187576. 26969.4i 0.348769 0.0501454i
\(15\) 329422. 285446.i 0.433807 0.375896i
\(16\) 745159. + 1.63167e6i 0.710639 + 1.55608i
\(17\) 1.38726e6 + 2.15862e6i 0.977044 + 1.52031i 0.848900 + 0.528554i \(0.177266\pi\)
0.128144 + 0.991756i \(0.459098\pi\)
\(18\) −880789. + 6.12602e6i −0.466133 + 3.24202i
\(19\) 1.96021e6 3.05015e6i 0.791654 1.23184i −0.177192 0.984176i \(-0.556701\pi\)
0.968847 0.247662i \(-0.0796622\pi\)
\(20\) −1.83405e6 1.58921e6i −0.573141 0.496629i
\(21\) 379716. 1.29319e6i 0.0929742 0.316641i
\(22\) 1.15955e6i 0.224996i
\(23\) −2.67832e6 + 5.85262e6i −0.416125 + 0.909308i
\(24\) 2.93184e7 3.68200
\(25\) −8.27724e6 2.43042e6i −0.847589 0.248875i
\(26\) −2.34969e7 + 2.71168e7i −1.97762 + 2.28230i
\(27\) 1.67405e7 + 1.07585e7i 1.16668 + 0.749778i
\(28\) −7.42741e6 1.06790e6i −0.431566 0.0620499i
\(29\) −4.21321e6 + 2.70766e6i −0.205411 + 0.132009i −0.639302 0.768956i \(-0.720777\pi\)
0.433891 + 0.900965i \(0.357140\pi\)
\(30\) −2.27700e7 + 1.03987e7i −0.937037 + 0.427930i
\(31\) 3.77167e6 + 4.35274e6i 0.131742 + 0.152039i 0.817788 0.575520i \(-0.195200\pi\)
−0.686045 + 0.727559i \(0.740655\pi\)
\(32\) −4.19932e6 2.92069e7i −0.125150 0.870434i
\(33\) −7.50162e6 3.42588e6i −0.191684 0.0875391i
\(34\) −4.15154e7 1.41388e8i −0.913723 3.11186i
\(35\) 3.37903e6 992172.i 0.0643356 0.0188906i
\(36\) 1.01804e8 2.22919e8i 1.68365 3.68667i
\(37\) −1.22651e7 + 1.76345e6i −0.176873 + 0.0254305i −0.230182 0.973148i \(-0.573932\pi\)
0.0533091 + 0.998578i \(0.483023\pi\)
\(38\) −1.57360e8 + 1.36353e8i −1.98599 + 1.72087i
\(39\) 1.06009e8 + 2.32128e8i 1.17495 + 2.57279i
\(40\) 4.14169e7 + 6.44459e7i 0.404462 + 0.629355i
\(41\) 2.81306e7 1.95653e8i 0.242806 1.68875i −0.395098 0.918639i \(-0.629290\pi\)
0.637905 0.770115i \(-0.279801\pi\)
\(42\) −4.18459e7 + 6.51135e7i −0.320189 + 0.498224i
\(43\) 1.59175e8 + 1.37926e8i 1.08276 + 0.938219i 0.998304 0.0582077i \(-0.0185386\pi\)
0.0844583 + 0.996427i \(0.473084\pi\)
\(44\) −1.29356e7 + 4.40545e7i −0.0784372 + 0.267132i
\(45\) 1.15014e8i 0.623287i
\(46\) 2.42271e8 2.79155e8i 1.17628 1.35537i
\(47\) 1.07492e8 0.468691 0.234345 0.972153i \(-0.424705\pi\)
0.234345 + 0.972153i \(0.424705\pi\)
\(48\) −7.02962e8 2.06408e8i −2.75883 0.810067i
\(49\) −1.77851e8 + 2.05251e8i −0.629616 + 0.726616i
\(50\) 4.16767e8 + 2.67840e8i 1.33365 + 0.857087i
\(51\) −1.03736e9 1.49150e8i −3.00662 0.432287i
\(52\) 1.19522e9 7.68121e8i 3.14363 2.02029i
\(53\) −4.66888e8 + 2.13221e8i −1.11643 + 0.509859i −0.886212 0.463279i \(-0.846673\pi\)
−0.230222 + 0.973138i \(0.573945\pi\)
\(54\) −7.48366e8 8.63661e8i −1.62984 1.88094i
\(55\) −3.06667e6 2.13292e7i −0.00609332 0.0423800i
\(56\) 2.15467e8 + 9.84007e7i 0.391238 + 0.178673i
\(57\) 4.17210e8 + 1.42089e9i 0.693395 + 2.36149i
\(58\) 2.75963e8 8.10299e7i 0.420446 0.123454i
\(59\) −9.48362e7 + 2.07662e8i −0.132652 + 0.290468i −0.964289 0.264852i \(-0.914677\pi\)
0.831637 + 0.555320i \(0.187404\pi\)
\(60\) 9.81101e8 1.41061e8i 1.26170 0.181406i
\(61\) 5.56382e8 4.82108e8i 0.658755 0.570815i −0.260016 0.965604i \(-0.583728\pi\)
0.918772 + 0.394789i \(0.129182\pi\)
\(62\) −1.37401e8 3.00866e8i −0.149979 0.328409i
\(63\) 1.92268e8 + 2.99175e8i 0.193733 + 0.301455i
\(64\) 2.02488e7 1.40834e8i 0.0188582 0.131161i
\(65\) −3.60495e8 + 5.60941e8i −0.310693 + 0.483448i
\(66\) 3.57923e8 + 3.10142e8i 0.285805 + 0.247652i
\(67\) −1.58540e8 + 5.39936e8i −0.117426 + 0.399916i −0.997139 0.0755890i \(-0.975916\pi\)
0.879713 + 0.475505i \(0.157734\pi\)
\(68\) 5.83488e9i 4.01317i
\(69\) −1.09019e9 2.39212e9i −0.697038 1.52946i
\(70\) −2.02243e8 −0.120332
\(71\) 2.59270e8 + 7.61285e7i 0.143701 + 0.0421945i 0.352792 0.935702i \(-0.385232\pi\)
−0.209091 + 0.977896i \(0.567050\pi\)
\(72\) −5.06600e9 + 5.84648e9i −2.61820 + 3.02157i
\(73\) −9.38541e6 6.03164e6i −0.00452730 0.00290952i 0.538375 0.842705i \(-0.319038\pi\)
−0.542903 + 0.839796i \(0.682675\pi\)
\(74\) 7.04357e8 + 1.01271e8i 0.317420 + 0.0456381i
\(75\) 2.96411e9 1.90492e9i 1.24907 0.802730i
\(76\) 7.49968e9 3.42499e9i 2.95784 1.35080i
\(77\) −4.36329e7 5.03550e7i −0.0161198 0.0186033i
\(78\) −2.08562e9 1.45058e10i −0.722373 5.02422i
\(79\) 1.88062e9 + 8.58850e8i 0.611175 + 0.279114i 0.696859 0.717208i \(-0.254580\pi\)
−0.0856841 + 0.996322i \(0.527308\pi\)
\(80\) −5.39331e8 1.83679e9i −0.164591 0.560544i
\(81\) −1.69248e9 + 4.96958e8i −0.485400 + 0.142526i
\(82\) −4.71556e9 + 1.03256e10i −1.27193 + 2.78514i
\(83\) 7.48751e8 1.07654e8i 0.190085 0.0273301i −0.0466149 0.998913i \(-0.514843\pi\)
0.236700 + 0.971583i \(0.423934\pi\)
\(84\) 2.31623e9 2.00703e9i 0.553841 0.479906i
\(85\) −1.13758e9 2.49096e9i −0.256383 0.561400i
\(86\) −6.53927e9 1.01753e10i −1.39007 2.16299i
\(87\) 2.91111e8 2.02472e9i 0.0584068 0.406228i
\(88\) 7.83596e8 1.21930e9i 0.148484 0.231045i
\(89\) 2.84805e9 + 2.46785e9i 0.510032 + 0.441946i 0.871469 0.490451i \(-0.163168\pi\)
−0.361436 + 0.932397i \(0.617713\pi\)
\(90\) 1.86085e9 6.33746e9i 0.315136 1.07325i
\(91\) 2.06176e9i 0.330393i
\(92\) −1.23187e10 + 7.90319e9i −1.86907 + 1.19912i
\(93\) −2.35238e9 −0.338138
\(94\) −5.92298e9 1.73914e9i −0.807051 0.236971i
\(95\) −2.53393e9 + 2.92431e9i −0.327474 + 0.377925i
\(96\) 1.01386e10 + 6.51570e9i 1.24343 + 0.799107i
\(97\) −1.22808e10 1.76571e9i −1.43010 0.205617i −0.616643 0.787243i \(-0.711508\pi\)
−0.813457 + 0.581626i \(0.802417\pi\)
\(98\) 1.31207e10 8.43216e9i 1.45153 0.932842i
\(99\) 1.97939e9 9.03957e8i 0.208140 0.0950543i
\(100\) −1.28462e10 1.48253e10i −1.28462 1.48253i
\(101\) 4.38754e8 + 3.05160e9i 0.0417460 + 0.290350i 0.999990 + 0.00439900i \(0.00140025\pi\)
−0.958244 + 0.285951i \(0.907691\pi\)
\(102\) 5.47471e10 + 2.50022e10i 4.95861 + 2.26452i
\(103\) 5.07291e9 + 1.72767e10i 0.437593 + 1.49031i 0.823258 + 0.567667i \(0.192154\pi\)
−0.385665 + 0.922639i \(0.626028\pi\)
\(104\) −4.30326e10 + 1.26355e10i −3.53697 + 1.03855i
\(105\) −5.97524e8 + 1.30840e9i −0.0468176 + 0.102516i
\(106\) 2.91760e10 4.19488e9i 2.18020 0.313466i
\(107\) 2.88357e8 2.49863e8i 0.0205595 0.0178149i −0.644520 0.764587i \(-0.722943\pi\)
0.665080 + 0.746772i \(0.268397\pi\)
\(108\) 1.87978e10 + 4.11614e10i 1.27935 + 2.80138i
\(109\) 4.40358e9 + 6.85211e9i 0.286203 + 0.445340i 0.954351 0.298688i \(-0.0965491\pi\)
−0.668148 + 0.744028i \(0.732913\pi\)
\(110\) −1.76112e8 + 1.22489e9i −0.0109352 + 0.0760560i
\(111\) 2.73619e9 4.25759e9i 0.162379 0.252667i
\(112\) −4.47346e9 3.87627e9i −0.253836 0.219950i
\(113\) −5.32880e9 + 1.81482e10i −0.289226 + 0.985014i 0.678833 + 0.734293i \(0.262486\pi\)
−0.968059 + 0.250721i \(0.919332\pi\)
\(114\) 8.50434e10i 4.41689i
\(115\) 3.71815e9 5.77563e9i 0.184858 0.287151i
\(116\) −1.13885e10 −0.542223
\(117\) −6.46070e10 1.89703e10i −2.94680 0.865258i
\(118\) 8.58545e9 9.90814e9i 0.375278 0.433094i
\(119\) −7.12320e9 4.57780e9i −0.298497 0.191833i
\(120\) −3.09705e10 4.45289e9i −1.24464 0.178952i
\(121\) 2.14770e10 1.38024e10i 0.828030 0.532143i
\(122\) −3.84577e10 + 1.75631e10i −1.42293 + 0.649832i
\(123\) 5.28690e10 + 6.10141e10i 1.87791 + 2.16723i
\(124\) 1.86388e9 + 1.29636e10i 0.0635783 + 0.442197i
\(125\) 1.78547e10 + 8.15398e9i 0.585064 + 0.267190i
\(126\) −5.75384e9 1.95958e10i −0.181178 0.617035i
\(127\) 3.54206e10 1.04004e10i 1.07211 0.314799i 0.302389 0.953185i \(-0.402216\pi\)
0.769716 + 0.638386i \(0.220398\pi\)
\(128\) −1.59463e10 + 3.49175e10i −0.464098 + 1.01623i
\(129\) −8.51487e10 + 1.22425e10i −2.38358 + 0.342707i
\(130\) 2.89395e10 2.50762e10i 0.779424 0.675375i
\(131\) 1.63927e10 + 3.58950e10i 0.424907 + 0.930417i 0.994126 + 0.108231i \(0.0345186\pi\)
−0.569218 + 0.822186i \(0.692754\pi\)
\(132\) −1.01387e10 1.57761e10i −0.252994 0.393667i
\(133\) −1.70272e9 + 1.18427e10i −0.0409153 + 0.284572i
\(134\) 1.74716e10 2.71863e10i 0.404397 0.629254i
\(135\) −1.60499e10 1.39073e10i −0.357934 0.310152i
\(136\) 5.18924e10 1.76729e11i 1.11535 3.79852i
\(137\) 2.83021e10i 0.586429i −0.956047 0.293215i \(-0.905275\pi\)
0.956047 0.293215i \(-0.0947250\pi\)
\(138\) 2.13684e10 + 1.49448e11i 0.426949 + 2.98603i
\(139\) 6.54685e9 0.126171 0.0630853 0.998008i \(-0.479906\pi\)
0.0630853 + 0.998008i \(0.479906\pi\)
\(140\) 7.68376e9 + 2.25616e9i 0.142868 + 0.0419497i
\(141\) −2.87507e10 + 3.31800e10i −0.515884 + 0.595362i
\(142\) −1.30545e10 8.38961e9i −0.226109 0.145311i
\(143\) 1.24871e10 + 1.79537e9i 0.208825 + 0.0300244i
\(144\) 1.62627e11 1.04514e11i 2.62652 1.68796i
\(145\) 4.86187e9 2.22034e9i 0.0758513 0.0346401i
\(146\) 4.19563e8 + 4.84202e8i 0.00632460 + 0.00729898i
\(147\) −1.57863e10 1.09796e11i −0.229982 1.59956i
\(148\) −2.56308e10 1.17052e10i −0.360955 0.164843i
\(149\) 1.80132e10 + 6.13472e10i 0.245278 + 0.835341i 0.986455 + 0.164031i \(0.0524498\pi\)
−0.741177 + 0.671310i \(0.765732\pi\)
\(150\) −1.94147e11 + 5.70068e10i −2.55667 + 0.750706i
\(151\) 1.07686e10 2.35799e10i 0.137174 0.300370i −0.828561 0.559899i \(-0.810840\pi\)
0.965735 + 0.259529i \(0.0835672\pi\)
\(152\) −2.57614e11 + 3.70392e10i −3.17505 + 0.456504i
\(153\) 2.08991e11 1.81091e11i 2.49270 2.15994i
\(154\) 1.58953e9 + 3.48059e9i 0.0183513 + 0.0401836i
\(155\) −3.32311e9 5.17087e9i −0.0371438 0.0577969i
\(156\) −8.25837e10 + 5.74382e11i −0.893864 + 6.21696i
\(157\) −8.31445e10 + 1.29375e11i −0.871636 + 1.35629i 0.0620025 + 0.998076i \(0.480251\pi\)
−0.933639 + 0.358216i \(0.883385\pi\)
\(158\) −8.97296e10 7.77511e10i −0.911277 0.789626i
\(159\) 5.90619e10 2.01146e11i 0.581195 1.97937i
\(160\) 3.14906e10i 0.300317i
\(161\) 1.65761e7 2.12392e10i 0.000153233 0.196340i
\(162\) 1.01299e11 0.907883
\(163\) 1.57463e11 + 4.62352e10i 1.36848 + 0.401823i 0.881746 0.471724i \(-0.156368\pi\)
0.486738 + 0.873548i \(0.338186\pi\)
\(164\) 2.94347e11 3.39695e11i 2.48108 2.86332i
\(165\) 7.40402e9 + 4.75828e9i 0.0605408 + 0.0389072i
\(166\) −4.29992e10 6.18235e9i −0.341130 0.0490471i
\(167\) 1.09931e11 7.06485e10i 0.846328 0.543902i −0.0440992 0.999027i \(-0.514042\pi\)
0.890428 + 0.455125i \(0.150405\pi\)
\(168\) −8.80045e10 + 4.01903e10i −0.657595 + 0.300314i
\(169\) −1.65360e11 1.90836e11i −1.19949 1.38429i
\(170\) 2.23807e10 + 1.55661e11i 0.157626 + 1.09632i
\(171\) −3.55435e11 1.62322e11i −2.43097 1.11019i
\(172\) 1.34933e11 + 4.59538e11i 0.896344 + 3.05267i
\(173\) 4.13523e10 1.21421e10i 0.266851 0.0783545i −0.145570 0.989348i \(-0.546502\pi\)
0.412421 + 0.910993i \(0.364683\pi\)
\(174\) −4.87993e10 + 1.06856e11i −0.305962 + 0.669963i
\(175\) 2.81773e10 4.05128e9i 0.171676 0.0246832i
\(176\) −2.73723e10 + 2.37182e10i −0.162087 + 0.140449i
\(177\) −3.87344e10 8.48166e10i −0.222962 0.488219i
\(178\) −1.17004e11 1.82062e11i −0.654789 1.01887i
\(179\) 1.02010e10 7.09494e10i 0.0555108 0.386086i −0.943059 0.332625i \(-0.892066\pi\)
0.998570 0.0534608i \(-0.0170252\pi\)
\(180\) −1.41397e11 + 2.20019e11i −0.748306 + 1.16439i
\(181\) 1.82540e11 + 1.58172e11i 0.939649 + 0.814210i 0.982765 0.184860i \(-0.0591831\pi\)
−0.0431162 + 0.999070i \(0.513729\pi\)
\(182\) 3.33578e10 1.13606e11i 0.167047 0.568911i
\(183\) 3.00690e11i 1.46509i
\(184\) 4.43402e11 1.29819e11i 2.10237 0.615529i
\(185\) 1.32241e10 0.0610248
\(186\) 1.29620e11 + 3.80599e10i 0.582248 + 0.170963i
\(187\) −3.39285e10 + 3.91556e10i −0.148374 + 0.171232i
\(188\) 2.05629e11 + 1.32150e11i 0.875580 + 0.562701i
\(189\) −6.49977e10 9.34526e9i −0.269519 0.0387510i
\(190\) 1.86937e11 1.20137e11i 0.754966 0.485187i
\(191\) −3.08335e11 + 1.40812e11i −1.21299 + 0.553952i −0.916096 0.400960i \(-0.868677\pi\)
−0.296890 + 0.954912i \(0.595949\pi\)
\(192\) 3.80558e10 + 4.39188e10i 0.145853 + 0.168323i
\(193\) −6.17880e9 4.29745e10i −0.0230737 0.160481i 0.975027 0.222087i \(-0.0712869\pi\)
−0.998101 + 0.0616058i \(0.980378\pi\)
\(194\) 6.48121e11 + 2.95987e11i 2.35856 + 1.07712i
\(195\) −7.67274e10 2.61309e11i −0.272131 0.926792i
\(196\) −5.92559e11 + 1.73991e11i −2.04857 + 0.601515i
\(197\) 6.26035e10 1.37083e11i 0.210993 0.462010i −0.774314 0.632801i \(-0.781905\pi\)
0.985307 + 0.170791i \(0.0546324\pi\)
\(198\) −1.23693e11 + 1.77844e10i −0.406461 + 0.0584403i
\(199\) −3.81305e11 + 3.30403e11i −1.22182 + 1.05871i −0.225393 + 0.974268i \(0.572367\pi\)
−0.996428 + 0.0844458i \(0.973088\pi\)
\(200\) 2.57243e11 + 5.63283e11i 0.803884 + 1.76026i
\(201\) −1.24260e11 1.93353e11i −0.378750 0.589346i
\(202\) 2.51967e10 1.75247e11i 0.0749182 0.521067i
\(203\) 8.93498e9 1.39031e10i 0.0259187 0.0403303i
\(204\) −1.80108e12 1.56064e12i −5.09779 4.41726i
\(205\) −5.94316e10 + 2.02405e11i −0.164153 + 0.559053i
\(206\) 1.03405e12i 2.78744i
\(207\) 6.65397e11 + 1.95942e11i 1.75077 + 0.515557i
\(208\) 1.12074e12 2.87865
\(209\) 7.02429e10 + 2.06252e10i 0.176145 + 0.0517209i
\(210\) 5.40934e10 6.24272e10i 0.132449 0.152854i
\(211\) 3.57558e11 + 2.29789e11i 0.854938 + 0.549435i 0.893111 0.449836i \(-0.148518\pi\)
−0.0381736 + 0.999271i \(0.512154\pi\)
\(212\) −1.15528e12 1.66104e11i −2.69778 0.387882i
\(213\) −9.28454e10 + 5.96681e10i −0.211769 + 0.136096i
\(214\) −1.99315e10 + 9.10243e9i −0.0444091 + 0.0202810i
\(215\) −1.47197e11 1.69874e11i −0.320410 0.369773i
\(216\) −2.03287e11 1.41389e12i −0.432356 3.00710i
\(217\) −1.72882e10 7.89525e9i −0.0359295 0.0164084i
\(218\) −1.31782e11 4.48809e11i −0.267654 0.911547i
\(219\) 4.37211e9 1.28377e9i 0.00867902 0.00254839i
\(220\) 2.03555e10 4.45723e10i 0.0394974 0.0864872i
\(221\) 1.58688e12 2.28160e11i 3.01012 0.432790i
\(222\) −2.19653e11 + 1.90330e11i −0.407354 + 0.352974i
\(223\) −3.06421e11 6.70968e11i −0.555641 1.21668i −0.954097 0.299496i \(-0.903181\pi\)
0.398457 0.917187i \(-0.369546\pi\)
\(224\) 5.26425e10 + 8.19133e10i 0.0933462 + 0.145249i
\(225\) −1.32310e11 + 9.20237e11i −0.229446 + 1.59583i
\(226\) 5.87251e11 9.13781e11i 0.996052 1.54989i
\(227\) 1.10236e11 + 9.55200e10i 0.182892 + 0.158476i 0.741495 0.670958i \(-0.234117\pi\)
−0.558603 + 0.829435i \(0.688663\pi\)
\(228\) −9.48718e11 + 3.23104e12i −1.53979 + 5.24406i
\(229\) 5.48941e11i 0.871662i 0.900029 + 0.435831i \(0.143545\pi\)
−0.900029 + 0.435831i \(0.856455\pi\)
\(230\) −2.98321e11 + 2.58090e11i −0.463495 + 0.400988i
\(231\) 2.72137e10 0.0413741
\(232\) 3.44941e11 + 1.01284e11i 0.513222 + 0.150696i
\(233\) −5.78496e11 + 6.67620e11i −0.842404 + 0.972186i −0.999882 0.0153361i \(-0.995118\pi\)
0.157478 + 0.987522i \(0.449664\pi\)
\(234\) 3.25303e12 + 2.09059e12i 4.63669 + 2.97982i
\(235\) −1.13549e11 1.63259e10i −0.158433 0.0227792i
\(236\) −4.36718e11 + 2.80662e11i −0.596542 + 0.383374i
\(237\) −7.68111e11 + 3.50785e11i −1.02727 + 0.469136i
\(238\) 3.18434e11 + 3.67493e11i 0.416999 + 0.481242i
\(239\) 3.82128e10 + 2.65776e11i 0.0490027 + 0.340821i 0.999543 + 0.0302207i \(0.00962101\pi\)
−0.950541 + 0.310600i \(0.899470\pi\)
\(240\) 7.11225e11 + 3.24806e11i 0.893205 + 0.407913i
\(241\) 1.82170e11 + 6.20416e11i 0.224075 + 0.763128i 0.992398 + 0.123067i \(0.0392730\pi\)
−0.768324 + 0.640061i \(0.778909\pi\)
\(242\) −1.40673e12 + 4.13053e11i −1.69486 + 0.497656i
\(243\) −1.88845e11 + 4.13513e11i −0.222882 + 0.488043i
\(244\) 1.65705e12 2.38247e11i 1.91595 0.275473i
\(245\) 2.19047e11 1.89805e11i 0.248145 0.215019i
\(246\) −1.92600e12 4.21736e12i −2.13787 4.68128i
\(247\) −1.22474e12 1.90573e12i −1.33216 2.07289i
\(248\) 5.88373e10 4.09222e11i 0.0627183 0.436215i
\(249\) −1.67037e11 + 2.59915e11i −0.174508 + 0.271540i
\(250\) −8.51899e11 7.38174e11i −0.872344 0.755891i
\(251\) −2.06011e11 + 7.01608e11i −0.206786 + 0.704248i 0.789151 + 0.614199i \(0.210521\pi\)
−0.995937 + 0.0900495i \(0.971297\pi\)
\(252\) 8.08686e11i 0.795751i
\(253\) −1.28621e11 1.85954e10i −0.124083 0.0179392i
\(254\) −2.12000e12 −2.00525
\(255\) 1.07316e12 + 3.15109e11i 0.995326 + 0.292254i
\(256\) 1.34819e12 1.55590e12i 1.22618 1.41508i
\(257\) 9.13294e11 + 5.86939e11i 0.814601 + 0.523512i 0.880350 0.474324i \(-0.157307\pi\)
−0.0657493 + 0.997836i \(0.520944\pi\)
\(258\) 4.88990e12 + 7.03062e11i 4.27762 + 0.615028i
\(259\) 3.43985e10 2.21065e10i 0.0295148 0.0189680i
\(260\) −1.37923e12 + 6.29875e11i −1.16084 + 0.530136i
\(261\) 3.53455e11 + 4.07909e11i 0.291831 + 0.336791i
\(262\) −3.22509e11 2.24310e12i −0.261237 1.81694i
\(263\) −6.84828e11 3.12751e11i −0.544256 0.248553i 0.124262 0.992249i \(-0.460344\pi\)
−0.668518 + 0.743696i \(0.733071\pi\)
\(264\) 1.66780e11 + 5.68000e11i 0.130054 + 0.442924i
\(265\) 5.25582e11 1.54325e11i 0.402171 0.118088i
\(266\) 2.85429e11 6.25002e11i 0.214333 0.469325i
\(267\) −1.52353e12 + 2.19050e11i −1.12278 + 0.161431i
\(268\) −9.67076e11 + 8.37976e11i −0.699498 + 0.606119i
\(269\) −3.83958e11 8.40750e11i −0.272597 0.596905i 0.722978 0.690871i \(-0.242773\pi\)
−0.995575 + 0.0939659i \(0.970046\pi\)
\(270\) 6.59364e11 + 1.02599e12i 0.459522 + 0.715031i
\(271\) 1.23961e11 8.62166e11i 0.0848082 0.589854i −0.902458 0.430778i \(-0.858239\pi\)
0.987266 0.159076i \(-0.0508515\pi\)
\(272\) −2.48843e12 + 3.87207e12i −1.67140 + 2.60075i
\(273\) −6.36412e11 5.51454e11i −0.419687 0.363661i
\(274\) −4.57908e11 + 1.55949e12i −0.296500 + 1.00979i
\(275\) 1.74185e11i 0.110751i
\(276\) 8.55353e11 5.91633e12i 0.534072 3.69409i
\(277\) −6.40895e11 −0.392996 −0.196498 0.980504i \(-0.562957\pi\)
−0.196498 + 0.980504i \(0.562957\pi\)
\(278\) −3.60742e11 1.05923e11i −0.217256 0.0637922i
\(279\) 4.06475e11 4.69097e11i 0.240443 0.277486i
\(280\) −2.12664e11 1.36671e11i −0.123567 0.0794120i
\(281\) −2.44452e12 3.51469e11i −1.39528 0.200611i −0.596685 0.802476i \(-0.703516\pi\)
−0.798598 + 0.601864i \(0.794425\pi\)
\(282\) 2.12104e12 1.36311e12i 1.18933 0.764337i
\(283\) 2.46476e12 1.12562e12i 1.35782 0.620097i 0.402435 0.915449i \(-0.368164\pi\)
0.955389 + 0.295351i \(0.0954367\pi\)
\(284\) 4.02385e11 + 4.64377e11i 0.217796 + 0.251350i
\(285\) −2.24916e11 1.56432e12i −0.119618 0.831959i
\(286\) −6.59011e11 3.00960e11i −0.344400 0.157282i
\(287\) 1.83766e11 + 6.25849e11i 0.0943746 + 0.321410i
\(288\) −3.05120e12 + 8.95912e11i −1.53995 + 0.452171i
\(289\) −1.89768e12 + 4.15534e12i −0.941312 + 2.06119i
\(290\) −3.03820e11 + 4.36827e10i −0.148124 + 0.0212971i
\(291\) 3.82974e12 3.31849e12i 1.83529 1.59029i
\(292\) −1.05388e10 2.30767e10i −0.00496451 0.0108708i
\(293\) −4.44523e11 6.91692e11i −0.205853 0.320313i 0.722941 0.690909i \(-0.242790\pi\)
−0.928794 + 0.370596i \(0.879153\pi\)
\(294\) −9.06574e11 + 6.30536e12i −0.412731 + 2.87060i
\(295\) 1.31720e11 2.04961e11i 0.0589579 0.0917403i
\(296\) 6.72216e11 + 5.82478e11i 0.295835 + 0.256343i
\(297\) −1.13200e11 + 3.85523e11i −0.0489851 + 0.166828i
\(298\) 3.67177e12i 1.56241i
\(299\) 2.63109e12 + 3.04123e12i 1.10098 + 1.27260i
\(300\) 8.01215e12 3.29718
\(301\) −6.66865e11 1.95809e11i −0.269902 0.0792503i
\(302\) −9.74871e11 + 1.12506e12i −0.388072 + 0.447859i
\(303\) −1.05931e12 6.80775e11i −0.414771 0.266557i
\(304\) 6.43752e12 + 9.25575e11i 2.47942 + 0.356487i
\(305\) −6.60958e11 + 4.24772e11i −0.250423 + 0.160937i
\(306\) −1.44457e13 + 6.59711e12i −5.38431 + 2.45893i
\(307\) 1.70544e12 + 1.96818e12i 0.625379 + 0.721726i 0.976719 0.214522i \(-0.0688193\pi\)
−0.351340 + 0.936248i \(0.614274\pi\)
\(308\) −2.15624e10 1.49970e11i −0.00777935 0.0541066i
\(309\) −6.68973e12 3.05510e12i −2.37474 1.08451i
\(310\) 9.94480e10 + 3.38689e11i 0.0347366 + 0.118302i
\(311\) 3.27533e12 9.61722e11i 1.12578 0.330558i 0.334731 0.942314i \(-0.391355\pi\)
0.791047 + 0.611756i \(0.209537\pi\)
\(312\) 7.60959e12 1.66627e13i 2.57388 5.63601i
\(313\) 8.39938e11 1.20765e11i 0.279592 0.0401993i −0.00109214 0.999999i \(-0.500348\pi\)
0.280684 + 0.959800i \(0.409439\pi\)
\(314\) 6.67460e12 5.78357e12i 2.18664 1.89473i
\(315\) −1.57664e11 3.45235e11i −0.0508369 0.111317i
\(316\) 2.54171e12 + 3.95498e12i 0.806661 + 1.25519i
\(317\) 4.60718e11 3.20437e12i 0.143926 1.00103i −0.781988 0.623293i \(-0.785794\pi\)
0.925914 0.377734i \(-0.123297\pi\)
\(318\) −6.50881e12 + 1.01279e13i −2.00155 + 3.11447i
\(319\) −7.64240e10 6.62218e10i −0.0231354 0.0200469i
\(320\) −4.27797e10 + 1.45694e11i −0.0127493 + 0.0434203i
\(321\) 1.55839e11i 0.0457247i
\(322\) −3.44548e11 + 1.17004e12i −0.0995338 + 0.338005i
\(323\) 9.30346e12 2.64626
\(324\) −3.84863e12 1.13006e12i −1.07791 0.316502i
\(325\) −3.52965e12 + 4.07343e12i −0.973452 + 1.12342i
\(326\) −7.92840e12 5.09527e12i −2.15326 1.38382i
\(327\) −3.29289e12 4.73446e11i −0.880722 0.126629i
\(328\) −1.19364e13 + 7.67105e12i −3.14415 + 2.02063i
\(329\) −3.22656e11 + 1.47352e11i −0.0837068 + 0.0382276i
\(330\) −3.30988e11 3.81980e11i −0.0845751 0.0976049i
\(331\) 4.06070e11 + 2.82428e12i 0.102202 + 0.710833i 0.974912 + 0.222593i \(0.0714520\pi\)
−0.872709 + 0.488240i \(0.837639\pi\)
\(332\) 1.56469e12 + 7.14570e11i 0.387916 + 0.177156i
\(333\) 3.76227e11 + 1.28131e12i 0.0918816 + 0.312920i
\(334\) −7.20043e12 + 2.11424e12i −1.73231 + 0.508653i
\(335\) 2.49479e11 5.46283e11i 0.0591303 0.129477i
\(336\) 2.39302e12 3.44064e11i 0.558791 0.0803420i
\(337\) 8.34571e11 7.23160e11i 0.192006 0.166374i −0.553553 0.832814i \(-0.686728\pi\)
0.745558 + 0.666440i \(0.232183\pi\)
\(338\) 6.02403e12 + 1.31908e13i 1.36554 + 2.99011i
\(339\) −4.17662e12 6.49895e12i −0.932881 1.45159i
\(340\) 8.86203e11 6.16368e12i 0.195047 1.35658i
\(341\) −6.28724e10 + 9.78313e10i −0.0136360 + 0.0212181i
\(342\) 1.69588e13 + 1.46949e13i 3.62463 + 3.14076i
\(343\) 5.15102e11 1.75428e12i 0.108498 0.369511i
\(344\) 1.51187e13i 3.13850i
\(345\) 7.88306e11 + 2.69250e12i 0.161287 + 0.550883i
\(346\) −2.47503e12 −0.499114
\(347\) −4.23892e11 1.24466e11i −0.0842574 0.0247402i 0.239332 0.970938i \(-0.423072\pi\)
−0.323590 + 0.946198i \(0.604890\pi\)
\(348\) 3.04607e12 3.51535e12i 0.596821 0.688768i
\(349\) 6.53953e11 + 4.20270e11i 0.126305 + 0.0811710i 0.602268 0.798294i \(-0.294264\pi\)
−0.475963 + 0.879465i \(0.657900\pi\)
\(350\) −1.61816e12 2.32656e11i −0.308093 0.0442970i
\(351\) 1.04594e13 6.72187e12i 1.96324 1.26170i
\(352\) 5.41952e11 2.47501e11i 0.100288 0.0457999i
\(353\) 6.39269e12 + 7.37755e12i 1.16630 + 1.34598i 0.927012 + 0.375032i \(0.122368\pi\)
0.239287 + 0.970949i \(0.423086\pi\)
\(354\) 7.62058e11 + 5.30023e12i 0.137079 + 0.953407i
\(355\) −2.62318e11 1.19796e11i −0.0465249 0.0212472i
\(356\) 2.41429e12 + 8.22231e12i 0.422220 + 1.43795i
\(357\) 3.31828e12 9.74336e11i 0.572232 0.168023i
\(358\) −1.71000e12 + 3.74438e12i −0.290791 + 0.636744i
\(359\) −5.55037e11 + 7.98023e10i −0.0930786 + 0.0133827i −0.188697 0.982035i \(-0.560426\pi\)
0.0956181 + 0.995418i \(0.469517\pi\)
\(360\) 6.23945e12 5.40651e12i 1.03189 0.894138i
\(361\) −2.91406e12 6.38089e12i −0.475293 1.04075i
\(362\) −7.49914e12 1.16689e13i −1.20634 1.87710i
\(363\) −1.48395e12 + 1.03211e13i −0.235443 + 1.63754i
\(364\) −2.53471e12 + 3.94409e12i −0.396663 + 0.617219i
\(365\) 8.99820e9 + 7.79698e9i 0.00138896 + 0.00120354i
\(366\) 4.86495e12 1.65685e13i 0.740752 2.52277i
\(367\) 4.73940e12i 0.711858i −0.934513 0.355929i \(-0.884164\pi\)
0.934513 0.355929i \(-0.115836\pi\)
\(368\) −1.15453e13 9.01051e9i −1.71067 0.00133509i
\(369\) −2.13024e13 −3.11384
\(370\) −7.28667e11 2.13956e11i −0.105080 0.0308543i
\(371\) 1.10916e12 1.28004e12i 0.157807 0.182118i
\(372\) −4.50005e12 2.89201e12i −0.631688 0.405961i
\(373\) 5.00365e12 + 7.19416e11i 0.693015 + 0.0996406i 0.479817 0.877368i \(-0.340703\pi\)
0.213198 + 0.977009i \(0.431612\pi\)
\(374\) 2.50302e12 1.60860e12i 0.342064 0.219831i
\(375\) −7.29250e12 + 3.33037e12i −0.983377 + 0.449093i
\(376\) −5.05292e12 5.83138e12i −0.672362 0.775947i
\(377\) 4.45323e11 + 3.09729e12i 0.0584747 + 0.406701i
\(378\) 3.43028e12 + 1.56656e12i 0.444499 + 0.202996i
\(379\) 2.46370e12 + 8.39058e12i 0.315058 + 1.07299i 0.953016 + 0.302919i \(0.0979611\pi\)
−0.637958 + 0.770071i \(0.720221\pi\)
\(380\) −8.44248e12 + 2.47894e12i −1.06550 + 0.312858i
\(381\) −6.26354e12 + 1.37152e13i −0.780180 + 1.70836i
\(382\) 1.92680e13 2.77032e12i 2.36875 0.340575i
\(383\) 9.74634e12 8.44526e12i 1.18263 1.02475i 0.183498 0.983020i \(-0.441258\pi\)
0.999129 0.0417323i \(-0.0132877\pi\)
\(384\) −6.51302e12 1.42615e13i −0.780057 1.70809i
\(385\) 3.84437e10 + 5.98195e10i 0.00454487 + 0.00707195i
\(386\) −3.54835e11 + 2.46793e12i −0.0414086 + 0.288003i
\(387\) 1.22717e13 1.90952e13i 1.41368 2.19973i
\(388\) −2.13220e13 1.84756e13i −2.42476 2.10107i
\(389\) −2.79803e11 + 9.52921e11i −0.0314126 + 0.106982i −0.973707 0.227804i \(-0.926846\pi\)
0.942294 + 0.334785i \(0.108664\pi\)
\(390\) 1.56400e13i 1.73346i
\(391\) −1.63491e13 + 2.33763e12i −1.78900 + 0.255795i
\(392\) 1.94951e13 2.10617
\(393\) −1.54644e13 4.54076e12i −1.64957 0.484358i
\(394\) −5.66745e12 + 6.54059e12i −0.596907 + 0.688867i
\(395\) −1.85615e12 1.19288e12i −0.193031 0.124054i
\(396\) 4.89784e12 + 7.04203e11i 0.502954 + 0.0723139i
\(397\) −5.49298e12 + 3.53012e12i −0.557000 + 0.357962i −0.788655 0.614836i \(-0.789222\pi\)
0.231655 + 0.972798i \(0.425586\pi\)
\(398\) 2.63562e13 1.20365e13i 2.63917 1.20527i
\(399\) −3.20011e12 3.69313e12i −0.316447 0.365199i
\(400\) −2.20222e12 1.53168e13i −0.215061 1.49578i
\(401\) 5.62891e12 + 2.57064e12i 0.542878 + 0.247924i 0.667928 0.744226i \(-0.267182\pi\)
−0.125049 + 0.992151i \(0.539909\pi\)
\(402\) 3.71863e12 + 1.26645e13i 0.354204 + 1.20631i
\(403\) 3.45275e12 1.01382e12i 0.324818 0.0953752i
\(404\) −2.91230e12 + 6.37704e12i −0.270601 + 0.592533i
\(405\) 1.86333e12 2.67907e11i 0.171008 0.0245872i
\(406\) −7.17274e11 + 6.21521e11i −0.0650212 + 0.0563412i
\(407\) −1.03935e11 2.27586e11i −0.00930657 0.0203786i
\(408\) 4.06723e13 + 6.32874e13i 3.59748 + 5.59779i
\(409\) 9.00424e11 6.26258e12i 0.0786738 0.547189i −0.911922 0.410365i \(-0.865401\pi\)
0.990595 0.136824i \(-0.0436895\pi\)
\(410\) 6.54955e12 1.01913e13i 0.565317 0.879651i
\(411\) 8.73614e12 + 7.56991e12i 0.744921 + 0.645478i
\(412\) −1.15356e13 + 3.92865e13i −0.971746 + 3.30946i
\(413\) 7.53339e11i 0.0626961i
\(414\) −3.34942e13 2.15624e13i −2.75403 1.77294i
\(415\) −8.07295e11 −0.0655831
\(416\) −1.76893e13 5.19403e12i −1.41985 0.416906i
\(417\) −1.75107e12 + 2.02085e12i −0.138875 + 0.160270i
\(418\) −3.53680e12 2.27296e12i −0.277159 0.178119i
\(419\) 2.02928e13 + 2.91766e12i 1.57134 + 0.225925i 0.872234 0.489089i \(-0.162671\pi\)
0.699110 + 0.715014i \(0.253580\pi\)
\(420\) −2.75158e12 + 1.76833e12i −0.210541 + 0.135306i
\(421\) 1.02011e13 4.65867e12i 0.771321 0.352251i 0.00943001 0.999956i \(-0.496998\pi\)
0.761891 + 0.647705i \(0.224271\pi\)
\(422\) −1.59842e13 1.84468e13i −1.19434 1.37834i
\(423\) −1.64864e12 1.14665e13i −0.121737 0.846701i
\(424\) 3.35143e13 + 1.53055e13i 2.44569 + 1.11691i
\(425\) −6.23635e12 2.12391e13i −0.449765 1.53176i
\(426\) 6.08132e12 1.78564e12i 0.433461 0.127276i
\(427\) −1.00920e12 + 2.20983e12i −0.0710946 + 0.155676i
\(428\) 8.58799e11 1.23477e11i 0.0597961 0.00859738i
\(429\) −3.89409e12 + 3.37425e12i −0.267991 + 0.232215i
\(430\) 5.36233e12 + 1.17419e13i 0.364764 + 0.798721i
\(431\) −5.91872e12 9.20970e12i −0.397962 0.619240i 0.583223 0.812312i \(-0.301791\pi\)
−0.981185 + 0.193072i \(0.938155\pi\)
\(432\) −5.07995e12 + 3.53318e13i −0.337630 + 2.34827i
\(433\) 6.77560e12 1.05430e13i 0.445152 0.692670i −0.544079 0.839034i \(-0.683121\pi\)
0.989231 + 0.146364i \(0.0467570\pi\)
\(434\) 8.24867e11 + 7.14751e11i 0.0535717 + 0.0464201i
\(435\) −6.15032e11 + 2.09461e12i −0.0394867 + 0.134479i
\(436\) 1.85216e13i 1.17557i
\(437\) 1.26013e13 + 1.96417e13i 0.790693 + 1.23246i
\(438\) −2.61681e11 −0.0162331
\(439\) 5.59496e12 + 1.64283e12i 0.343143 + 0.100756i 0.448763 0.893651i \(-0.351865\pi\)
−0.105621 + 0.994407i \(0.533683\pi\)
\(440\) −1.01294e12 + 1.16900e12i −0.0614215 + 0.0708842i
\(441\) 2.46226e13 + 1.58240e13i 1.47618 + 0.948686i
\(442\) −9.11313e13 1.31027e13i −5.40202 0.776694i
\(443\) 7.37255e11 4.73805e11i 0.0432115 0.0277703i −0.518857 0.854861i \(-0.673642\pi\)
0.562068 + 0.827091i \(0.310006\pi\)
\(444\) 1.04685e13 4.78081e12i 0.606694 0.277068i
\(445\) −2.63372e12 3.03948e12i −0.150928 0.174180i
\(446\) 6.02849e12 + 4.19291e13i 0.341613 + 2.37597i
\(447\) −2.37543e13 1.08482e13i −1.33108 0.607885i
\(448\) 1.32277e11 + 4.50495e11i 0.00732984 + 0.0249632i
\(449\) 8.57434e12 2.51765e12i 0.469861 0.137964i −0.0382267 0.999269i \(-0.512171\pi\)
0.508087 + 0.861306i \(0.330353\pi\)
\(450\) 2.21793e13 4.85659e13i 1.20195 2.63190i
\(451\) 3.95050e12 5.67996e11i 0.211724 0.0304412i
\(452\) −3.25052e13 + 2.81659e13i −1.72290 + 1.49290i
\(453\) 4.39826e12 + 9.63085e12i 0.230563 + 0.504863i
\(454\) −4.52873e12 7.04684e12i −0.234800 0.365355i
\(455\) 3.13140e11 2.17794e12i 0.0160576 0.111683i
\(456\) 5.74704e13 8.94257e13i 2.91487 4.53563i
\(457\) 4.56993e12 + 3.95987e12i 0.229260 + 0.198655i 0.761914 0.647678i \(-0.224260\pi\)
−0.532654 + 0.846333i \(0.678805\pi\)
\(458\) 8.88147e12 3.02475e13i 0.440715 1.50094i
\(459\) 5.10614e13i 2.50628i
\(460\) 1.42132e13 6.47757e12i 0.690087 0.314502i
\(461\) −3.03834e13 −1.45926 −0.729630 0.683843i \(-0.760307\pi\)
−0.729630 + 0.683843i \(0.760307\pi\)
\(462\) −1.49952e12 4.40299e11i −0.0712430 0.0209188i
\(463\) −1.80748e13 + 2.08594e13i −0.849508 + 0.980385i −0.999966 0.00823186i \(-0.997380\pi\)
0.150458 + 0.988616i \(0.451925\pi\)
\(464\) −7.55753e12 4.85693e12i −0.351390 0.225825i
\(465\) 2.48494e12 + 3.57281e11i 0.114301 + 0.0164341i
\(466\) 4.26777e13 2.74273e13i 1.94210 1.24811i
\(467\) −1.16386e13 + 5.31517e12i −0.523982 + 0.239295i −0.659803 0.751439i \(-0.729360\pi\)
0.135821 + 0.990733i \(0.456633\pi\)
\(468\) −1.00270e14 1.15717e14i −4.46622 5.15429i
\(469\) −2.64271e11 1.83804e12i −0.0116462 0.0810013i
\(470\) 5.99260e12 + 2.73673e12i 0.261292 + 0.119328i
\(471\) −1.76964e13 6.02684e13i −0.763450 2.60007i
\(472\) 1.57236e13 4.61685e12i 0.671183 0.197077i
\(473\) −1.76663e12 + 3.86838e12i −0.0746174 + 0.163389i
\(474\) 4.79996e13 6.90130e12i 2.00607 0.288429i
\(475\) −2.36383e13 + 2.04827e13i −0.977571 + 0.847070i
\(476\) −7.99857e12 1.75144e13i −0.327324 0.716740i
\(477\) 2.99058e13 + 4.65343e13i 1.21105 + 1.88444i
\(478\) 2.19448e12 1.52629e13i 0.0879412 0.611644i
\(479\) −7.51307e12 + 1.16906e13i −0.297948 + 0.463616i −0.957660 0.287903i \(-0.907042\pi\)
0.659712 + 0.751519i \(0.270678\pi\)
\(480\) −9.72034e12 8.42273e12i −0.381483 0.330557i
\(481\) −2.18117e12 + 7.42838e12i −0.0847157 + 0.288515i
\(482\) 3.71333e13i 1.42734i
\(483\) 6.55156e12 + 5.68592e12i 0.249235 + 0.216304i
\(484\) 5.80535e13 2.18576
\(485\) 1.27046e13 + 3.73041e12i 0.473427 + 0.139011i
\(486\) 1.70960e13 1.97298e13i 0.630541 0.727683i
\(487\) −3.39802e11 2.18377e11i −0.0124045 0.00797191i 0.534424 0.845217i \(-0.320529\pi\)
−0.546828 + 0.837245i \(0.684165\pi\)
\(488\) −5.23082e13 7.52078e12i −1.89004 0.271746i
\(489\) −5.63879e13 + 3.62383e13i −2.01670 + 1.29606i
\(490\) −1.51407e13 + 6.91454e12i −0.536002 + 0.244784i
\(491\) 2.57600e12 + 2.97286e12i 0.0902688 + 0.104176i 0.799087 0.601216i \(-0.205317\pi\)
−0.708818 + 0.705391i \(0.750771\pi\)
\(492\) 2.61267e13 + 1.81715e14i 0.906273 + 6.30326i
\(493\) −1.16896e13 5.33848e12i −0.401390 0.183309i
\(494\) 3.66516e13 + 1.24824e14i 1.24583 + 4.24290i
\(495\) −2.22822e12 + 6.54265e11i −0.0749778 + 0.0220155i
\(496\) −4.29175e12 + 9.39761e12i −0.142964 + 0.313047i
\(497\) −8.82604e11 + 1.26899e11i −0.0291061 + 0.00418482i
\(498\) 1.34092e13 1.16192e13i 0.437782 0.379340i
\(499\) −8.32592e12 1.82312e13i −0.269110 0.589268i 0.726039 0.687654i \(-0.241359\pi\)
−0.995148 + 0.0983859i \(0.968632\pi\)
\(500\) 2.41312e13 + 3.75488e13i 0.772198 + 1.20156i
\(501\) −7.59570e12 + 5.28293e13i −0.240646 + 1.67373i
\(502\) 2.27030e13 3.53266e13i 0.712140 1.10811i
\(503\) −3.46433e13 3.00186e13i −1.07592 0.932290i −0.0780123 0.996952i \(-0.524857\pi\)
−0.997907 + 0.0646628i \(0.979403\pi\)
\(504\) 7.19204e12 2.44938e13i 0.221156 0.753190i
\(505\) 3.29020e12i 0.100176i
\(506\) 6.78639e12 + 3.10564e12i 0.204591 + 0.0936265i
\(507\) 1.03135e14 3.07869
\(508\) 8.05449e13 + 2.36501e13i 2.38078 + 0.699061i
\(509\) 2.39578e13 2.76487e13i 0.701225 0.809257i −0.287692 0.957723i \(-0.592888\pi\)
0.988918 + 0.148466i \(0.0474335\pi\)
\(510\) −5.40348e13 3.47261e13i −1.56611 1.00648i
\(511\) 3.64403e10 + 5.23932e9i 0.00104587 + 0.000150373i
\(512\) −6.63933e13 + 4.26684e13i −1.88701 + 1.21271i
\(513\) 6.56301e13 2.99723e13i 1.84721 0.843593i
\(514\) −4.08277e13 4.71177e13i −1.13799 1.31331i
\(515\) −2.73477e12 1.90208e13i −0.0754893 0.525039i
\(516\) −1.77938e14 8.12616e13i −4.86430 2.22145i
\(517\) 6.11475e11 + 2.08249e12i 0.0165549 + 0.0563808i
\(518\) −2.25308e12 + 6.61564e11i −0.0604126 + 0.0177387i
\(519\) −7.31245e12 + 1.60120e13i −0.194190 + 0.425216i
\(520\) 4.73766e13 6.81173e12i 1.24608 0.179160i
\(521\) 4.21041e13 3.64834e13i 1.09682 0.950401i 0.0978255 0.995204i \(-0.468811\pi\)
0.998996 + 0.0448025i \(0.0142658\pi\)
\(522\) −1.28763e13 2.81951e13i −0.332229 0.727480i
\(523\) 2.37774e12 + 3.69984e12i 0.0607653 + 0.0945527i 0.870307 0.492510i \(-0.163921\pi\)
−0.809541 + 0.587063i \(0.800284\pi\)
\(524\) −1.27703e13 + 8.88193e13i −0.323254 + 2.24828i
\(525\) −6.28600e12 + 9.78121e12i −0.157608 + 0.245243i
\(526\) 3.26750e13 + 2.83131e13i 0.811498 + 0.703167i
\(527\) −4.16363e12 + 1.41800e13i −0.102428 + 0.348838i
\(528\) 1.47930e13i 0.360484i
\(529\) −2.70797e13 3.13504e13i −0.653680 0.756771i
\(530\) −3.14572e13 −0.752214
\(531\) 2.36066e13 + 6.93152e12i 0.559191 + 0.164193i
\(532\) −1.78166e13 + 2.05614e13i −0.418087 + 0.482498i
\(533\) −1.03895e14 6.67692e13i −2.41523 1.55217i
\(534\) 8.74928e13 + 1.25796e13i 2.01496 + 0.289707i
\(535\) −3.42556e11 + 2.20147e11i −0.00781560 + 0.00502278i
\(536\) 3.67438e13 1.67803e13i 0.830538 0.379294i
\(537\) 1.91719e13 + 2.21255e13i 0.429332 + 0.495475i
\(538\) 7.55394e12 + 5.25388e13i 0.167595 + 1.16565i
\(539\) −4.98815e12 2.27801e12i −0.109647 0.0500740i
\(540\) −1.36055e13 4.63359e13i −0.296309 1.00913i
\(541\) 6.11580e13 1.79576e13i 1.31967 0.387491i 0.455299 0.890339i \(-0.349532\pi\)
0.864375 + 0.502847i \(0.167714\pi\)
\(542\) −2.07797e13 + 4.55011e13i −0.444265 + 0.972805i
\(543\) −9.76474e13 + 1.40396e13i −2.06853 + 0.297409i
\(544\) 5.72212e13 4.95824e13i 1.20105 1.04072i
\(545\) −3.61103e12 7.90705e12i −0.0751015 0.164449i
\(546\) 2.61452e13 + 4.06827e13i 0.538801 + 0.838391i
\(547\) 1.17466e13 8.16996e13i 0.239870 1.66834i −0.412898 0.910777i \(-0.635483\pi\)
0.652768 0.757558i \(-0.273608\pi\)
\(548\) 3.47944e13 5.41411e13i 0.704055 1.09553i
\(549\) −5.99615e13 5.19570e13i −1.20229 1.04179i
\(550\) −2.81818e12 + 9.59785e12i −0.0559959 + 0.190704i
\(551\) 1.81585e13i 0.357538i
\(552\) −7.85242e13 + 1.71589e14i −1.53217 + 3.34807i
\(553\) −6.82235e12 −0.131919
\(554\) 3.53143e13 + 1.03692e13i 0.676709 + 0.198700i
\(555\) −3.53702e12 + 4.08193e12i −0.0671695 + 0.0775177i
\(556\) 1.25239e13 + 8.04865e12i 0.235704 + 0.151478i
\(557\) 2.13581e13 + 3.07083e12i 0.398369 + 0.0572769i 0.338588 0.940935i \(-0.390051\pi\)
0.0597811 + 0.998212i \(0.480960\pi\)
\(558\) −2.99870e13 + 1.92715e13i −0.554323 + 0.356242i
\(559\) 1.19702e14 5.46662e13i 2.19302 1.00152i
\(560\) 4.13681e12 + 4.77413e12i 0.0751148 + 0.0866871i
\(561\) −3.01154e12 2.09458e13i −0.0541970 0.376948i
\(562\) 1.29011e14 + 5.89172e13i 2.30114 + 1.05090i
\(563\) 2.70847e13 + 9.22419e13i 0.478830 + 1.63075i 0.745175 + 0.666869i \(0.232366\pi\)
−0.266345 + 0.963878i \(0.585816\pi\)
\(564\) −9.57906e13 + 2.81267e13i −1.67852 + 0.492859i
\(565\) 8.38545e12 1.83616e13i 0.145641 0.318910i
\(566\) −1.54024e14 + 2.21453e13i −2.65159 + 0.381242i
\(567\) 4.39905e12 3.81180e12i 0.0750661 0.0650451i
\(568\) −8.05768e12 1.76439e13i −0.136291 0.298436i
\(569\) 4.48340e13 + 6.97631e13i 0.751703 + 1.16967i 0.980561 + 0.196213i \(0.0628645\pi\)
−0.228858 + 0.973460i \(0.573499\pi\)
\(570\) −1.29164e13 + 8.98356e13i −0.214668 + 1.49305i
\(571\) −2.62049e13 + 4.07756e13i −0.431720 + 0.671769i −0.987150 0.159794i \(-0.948917\pi\)
0.555430 + 0.831563i \(0.312553\pi\)
\(572\) 2.16803e13 + 1.87861e13i 0.354066 + 0.306800i
\(573\) 3.90047e13 1.32838e14i 0.631457 2.15054i
\(574\) 3.74585e13i 0.601161i
\(575\) 3.63934e13 4.19341e13i 0.579007 0.667156i
\(576\) −1.53338e13 −0.241844
\(577\) −8.85267e13 2.59938e13i −1.38419 0.406435i −0.496964 0.867771i \(-0.665552\pi\)
−0.887225 + 0.461337i \(0.847370\pi\)
\(578\) 1.71796e14 1.98263e14i 2.66301 3.07328i
\(579\) 1.49178e13 + 9.58708e12i 0.229251 + 0.147331i
\(580\) 1.20303e13 + 1.72970e12i 0.183289 + 0.0263530i
\(581\) −2.09994e12 + 1.34955e12i −0.0317194 + 0.0203849i
\(582\) −2.64716e14 + 1.20892e14i −3.96428 + 1.81043i
\(583\) −6.78675e12 7.83233e12i −0.100767 0.116292i
\(584\) 1.13971e11 + 7.92685e11i 0.00167776 + 0.0116691i
\(585\) 6.53665e13 + 2.98519e13i 0.954060 + 0.435705i
\(586\) 1.33029e13 + 4.53054e13i 0.192512 + 0.655635i
\(587\) −8.75890e13 + 2.57185e13i −1.25678 + 0.369024i −0.841295 0.540576i \(-0.818206\pi\)
−0.415485 + 0.909600i \(0.636388\pi\)
\(588\) 1.04784e14 2.29445e14i 1.49076 3.26431i
\(589\) 2.06698e13 2.97187e12i 0.291582 0.0419231i
\(590\) −1.05741e13 + 9.16251e12i −0.147905 + 0.128161i
\(591\) 2.55695e13 + 5.59893e13i 0.354637 + 0.776547i
\(592\) −1.20168e13 1.86985e13i −0.165265 0.257157i
\(593\) −3.97869e12 + 2.76724e13i −0.0542584 + 0.377375i 0.944541 + 0.328393i \(0.106507\pi\)
−0.998800 + 0.0489825i \(0.984402\pi\)
\(594\) 1.24750e13 1.94115e13i 0.168697 0.262498i
\(595\) 6.82932e12 + 5.91764e12i 0.0915783 + 0.0793531i
\(596\) −4.09612e13 + 1.39501e14i −0.544680 + 1.85501i
\(597\) 2.06072e14i 2.71736i
\(598\) −9.57722e13 2.10146e14i −1.25237 2.74799i
\(599\) 4.55768e13 0.591030 0.295515 0.955338i \(-0.404509\pi\)
0.295515 + 0.955338i \(0.404509\pi\)
\(600\) −2.42676e14 7.12560e13i −3.12083 0.916358i
\(601\) −2.72488e13 + 3.14468e13i −0.347516 + 0.401055i −0.902419 0.430861i \(-0.858210\pi\)
0.554903 + 0.831915i \(0.312756\pi\)
\(602\) 3.35773e13 + 2.15788e13i 0.424681 + 0.272926i
\(603\) 6.00284e13 + 8.63078e12i 0.752957 + 0.108259i
\(604\) 4.95889e13 3.18689e13i 0.616879 0.396444i
\(605\) −2.47835e13 + 1.13183e13i −0.305764 + 0.139638i
\(606\) 4.73550e13 + 5.46506e13i 0.579432 + 0.668701i
\(607\) −1.25050e13 8.69744e13i −0.151754 1.05548i −0.913278 0.407338i \(-0.866457\pi\)
0.761523 0.648138i \(-0.224452\pi\)
\(608\) −9.73172e13 4.44433e13i −1.17131 0.534919i
\(609\) 1.90171e12 + 6.47664e12i 0.0227017 + 0.0773149i
\(610\) 4.32923e13 1.27118e13i 0.512580 0.150507i
\(611\) 2.78995e13 6.10914e13i 0.327635 0.717421i
\(612\) 6.22426e14 8.94914e13i 7.24988 1.04238i
\(613\) −3.26017e13 + 2.82495e13i −0.376649 + 0.326369i −0.822528 0.568725i \(-0.807437\pi\)
0.445878 + 0.895094i \(0.352891\pi\)
\(614\) −6.21285e13 1.36042e14i −0.711949 1.55895i
\(615\) −4.65814e13 7.24820e13i −0.529464 0.823863i
\(616\) −6.80663e11 + 4.73412e12i −0.00767412 + 0.0533747i
\(617\) 2.29723e13 3.57455e13i 0.256908 0.399757i −0.688709 0.725037i \(-0.741822\pi\)
0.945618 + 0.325281i \(0.105459\pi\)
\(618\) 3.19186e14 + 2.76576e14i 3.54080 + 3.06812i
\(619\) −3.93652e13 + 1.34066e14i −0.433171 + 1.47524i 0.397043 + 0.917800i \(0.370036\pi\)
−0.830214 + 0.557445i \(0.811782\pi\)
\(620\) 1.39771e13i 0.152567i
\(621\) −1.07802e14 + 6.91613e13i −1.16726 + 0.748867i
\(622\) −1.96036e14 −2.10564
\(623\) −1.19319e13 3.50353e12i −0.127136 0.0373306i
\(624\) −2.99763e14 + 3.45945e14i −3.16851 + 3.65665i
\(625\) 5.32489e13 + 3.42210e13i 0.558355 + 0.358833i
\(626\) −4.82358e13 6.93526e12i −0.501762 0.0721425i
\(627\) −2.51542e13 + 1.61656e13i −0.259581 + 0.166823i
\(628\) −3.18106e14 + 1.45274e14i −3.25667 + 1.48727i
\(629\) −2.08215e13 2.40293e13i −0.211475 0.244055i
\(630\) 3.10186e12 + 2.15739e13i 0.0312550 + 0.217383i
\(631\) 9.52149e13 + 4.34832e13i 0.951827 + 0.434685i 0.829936 0.557859i \(-0.188377\pi\)
0.121891 + 0.992543i \(0.461104\pi\)
\(632\) −4.18109e13 1.42395e14i −0.414672 1.41224i
\(633\) −1.66565e14 + 4.89080e13i −1.63895 + 0.481240i
\(634\) −7.72307e13 + 1.69112e14i −0.753952 + 1.65092i
\(635\) −3.89962e13 + 5.60681e12i −0.377706 + 0.0543059i
\(636\) 3.60272e14 3.12177e14i 3.46214 2.99996i
\(637\) 7.04901e13 + 1.54352e14i 0.672096 + 1.47168i
\(638\) 3.13967e12 + 4.88541e12i 0.0297016 + 0.0462166i
\(639\) 4.14438e12 2.88248e13i 0.0389005 0.270559i
\(640\) 2.21481e13 3.44632e13i 0.206271 0.320963i
\(641\) −7.57894e13 6.56719e13i −0.700355 0.606861i 0.230143 0.973157i \(-0.426081\pi\)
−0.930499 + 0.366295i \(0.880626\pi\)
\(642\) 2.52136e12 8.58697e12i 0.0231185 0.0787345i
\(643\) 1.49447e14i 1.35967i 0.733367 + 0.679833i \(0.237948\pi\)
−0.733367 + 0.679833i \(0.762052\pi\)
\(644\) 2.61430e13 4.06096e13i 0.236008 0.366606i
\(645\) 9.18063e13 0.822382
\(646\) −5.12635e14 1.50523e14i −4.55665 1.33795i
\(647\) −7.81434e13 + 9.01823e13i −0.689241 + 0.795426i −0.987257 0.159134i \(-0.949130\pi\)
0.298016 + 0.954561i \(0.403675\pi\)
\(648\) 1.06519e14 + 6.84556e13i 0.932292 + 0.599147i
\(649\) −4.56263e12 6.56007e11i −0.0396270 0.00569751i
\(650\) 2.60394e14 1.67345e14i 2.24422 1.44227i
\(651\) 7.06110e12 3.22470e12i 0.0603904 0.0275794i
\(652\) 2.44381e14 + 2.82031e14i 2.07410 + 2.39364i
\(653\) −2.22632e13 1.54844e14i −0.187508 1.30415i −0.838432 0.545007i \(-0.816527\pi\)
0.650923 0.759143i \(-0.274382\pi\)
\(654\) 1.73784e14 + 7.93643e13i 1.45251 + 0.663340i
\(655\) −1.18647e13 4.04075e13i −0.0984126 0.335162i
\(656\) 3.40202e14 9.98925e13i 2.80039 0.822268i
\(657\) −4.99468e11 + 1.09368e12i −0.00408020 + 0.00893438i
\(658\) 2.01629e13 2.89899e12i 0.163465 0.0235027i
\(659\) 2.75403e13 2.38638e13i 0.221586 0.192005i −0.536993 0.843587i \(-0.680440\pi\)
0.758578 + 0.651582i \(0.225894\pi\)
\(660\) 8.31391e12 + 1.82049e13i 0.0663874 + 0.145368i
\(661\) 1.20938e14 + 1.88183e14i 0.958417 + 1.49133i 0.868688 + 0.495359i \(0.164964\pi\)
0.0897283 + 0.995966i \(0.471400\pi\)
\(662\) 2.33197e13 1.62192e14i 0.183414 1.27568i
\(663\) −3.54014e14 + 5.50857e14i −2.76346 + 4.30002i
\(664\) −4.10370e13 3.55588e13i −0.317933 0.275490i
\(665\) 3.59734e12 1.22514e13i 0.0276614 0.0942059i
\(666\) 7.66894e13i 0.585281i
\(667\) −4.56259e12 3.19103e13i −0.0345607 0.241714i
\(668\) 2.97151e14 2.23406
\(669\) 2.89069e14 + 8.48782e13i 2.15710 + 0.633382i
\(670\) −2.25852e13 + 2.60647e13i −0.167282 + 0.193054i
\(671\) 1.25051e13 + 8.03656e12i 0.0919339 + 0.0590823i
\(672\) −3.93648e13 5.65980e12i −0.287251 0.0413004i
\(673\) −1.54513e13 + 9.92996e12i −0.111915 + 0.0719237i −0.595401 0.803429i \(-0.703007\pi\)
0.483486 + 0.875352i \(0.339371\pi\)
\(674\) −5.76864e13 + 2.63445e13i −0.414738 + 0.189405i
\(675\) −1.12418e14 1.29737e14i −0.802262 0.925860i
\(676\) −8.17175e13 5.68358e14i −0.578871 4.02613i
\(677\) −2.30983e13 1.05486e13i −0.162419 0.0741742i 0.332547 0.943087i \(-0.392092\pi\)
−0.494966 + 0.868913i \(0.664819\pi\)
\(678\) 1.24990e14 + 4.25677e14i 0.872423 + 2.97120i
\(679\) 3.92834e13 1.15346e13i 0.272182 0.0799199i
\(680\) −8.16583e13 + 1.78807e14i −0.561637 + 1.22981i
\(681\) −5.89692e13 + 8.47849e12i −0.402615 + 0.0578873i
\(682\) 5.04721e12 4.37343e12i 0.0342082 0.0296415i
\(683\) 6.16316e13 + 1.34954e14i 0.414667 + 0.907995i 0.995570 + 0.0940220i \(0.0299724\pi\)
−0.580903 + 0.813973i \(0.697300\pi\)
\(684\) −4.80380e14 7.47486e14i −3.20852 4.99255i
\(685\) −4.29853e12 + 2.98969e13i −0.0285015 + 0.198232i
\(686\) −5.67659e13 + 8.83295e13i −0.373652 + 0.581414i
\(687\) −1.69444e14 1.46824e14i −1.10724 0.959431i
\(688\) −1.06439e14 + 3.62499e14i −0.690493 + 2.35160i
\(689\) 3.20690e14i 2.06533i
\(690\) 1.25742e11 1.61115e14i 0.000803960 1.03013i
\(691\) 1.88258e14 1.19499 0.597494 0.801874i \(-0.296163\pi\)
0.597494 + 0.801874i \(0.296163\pi\)
\(692\) 9.40332e13 + 2.76106e13i 0.592585 + 0.173999i
\(693\) −4.70233e12 + 5.42678e12i −0.0294203 + 0.0339528i
\(694\) 2.13434e13 + 1.37165e13i 0.132576 + 0.0852015i
\(695\) −6.91577e12 9.94338e11i −0.0426498 0.00613211i
\(696\) −1.23525e14 + 7.93844e13i −0.756323 + 0.486059i
\(697\) 4.61365e14 2.10698e14i 2.80466 1.28085i
\(698\) −2.92342e13 3.37380e13i −0.176447 0.203630i
\(699\) −5.13481e13 3.57134e14i −0.307708 2.14016i
\(700\) 5.88830e13 + 2.68910e13i 0.350348 + 0.159999i
\(701\) −4.60981e13 1.56996e14i −0.272328 0.927464i −0.976152 0.217090i \(-0.930344\pi\)
0.703824 0.710375i \(-0.251475\pi\)
\(702\) −6.85087e14 + 2.01160e14i −4.01846 + 1.17993i
\(703\) −1.86634e13 + 4.08671e13i −0.108696 + 0.238011i
\(704\) 2.84362e12 4.08851e11i 0.0164441 0.00236430i
\(705\) 3.54102e13 3.06831e13i 0.203321 0.176179i
\(706\) −2.32884e14 5.09944e14i −1.32775 2.90736i
\(707\) −5.50020e12 8.55848e12i −0.0311374 0.0484507i
\(708\) 3.01750e13 2.09872e14i 0.169622 1.17974i
\(709\) 9.92931e13 1.54503e14i 0.554227 0.862395i −0.445227 0.895418i \(-0.646877\pi\)
0.999455 + 0.0330229i \(0.0105134\pi\)
\(710\) 1.25159e13 + 1.08451e13i 0.0693698 + 0.0601093i
\(711\) 6.27728e13 2.13785e14i 0.345481 1.17660i
\(712\) 2.70512e14i 1.47838i
\(713\) −3.55767e13 + 1.04161e13i −0.193071 + 0.0565272i
\(714\) −1.98607e14 −1.07029
\(715\) −1.29181e13 3.79309e12i −0.0691302 0.0202985i
\(716\) 1.06739e14 1.23183e14i 0.567229 0.654617i
\(717\) −9.22591e13 5.92913e13i −0.486871 0.312893i
\(718\) 3.18746e13 + 4.58287e12i 0.167041 + 0.0240168i
\(719\) 2.34555e13 1.50740e13i 0.122068 0.0784482i −0.478182 0.878261i \(-0.658704\pi\)
0.600250 + 0.799812i \(0.295068\pi\)
\(720\) −1.87665e14 + 8.57037e13i −0.969886 + 0.442932i
\(721\) −3.89105e13 4.49052e13i −0.199706 0.230473i
\(722\) 5.73308e13 + 3.98745e14i 0.292215 + 2.03240i
\(723\) −2.40231e14 1.09710e14i −1.21601 0.555335i
\(724\) 1.54739e14 + 5.26992e14i 0.777870 + 2.64918i
\(725\) 4.14545e13 1.21721e13i 0.206958 0.0607682i
\(726\) 2.48756e14 5.44700e14i 1.23336 2.70069i
\(727\) −6.11407e12 + 8.79071e11i −0.0301064 + 0.00432864i −0.157352 0.987543i \(-0.550296\pi\)
0.127245 + 0.991871i \(0.459386\pi\)
\(728\) 1.11849e14 9.69178e13i 0.546985 0.473965i
\(729\) −1.20400e14 2.63639e14i −0.584775 1.28048i
\(730\) −3.69665e11 5.75211e11i −0.00178318 0.00277468i
\(731\) −7.69126e13 + 5.34939e14i −0.368477 + 2.56282i
\(732\) −3.69666e14 + 5.75212e14i −1.75895 + 2.73698i
\(733\) 8.46008e13 + 7.33070e13i 0.399811 + 0.346438i 0.831441 0.555612i \(-0.187516\pi\)
−0.431631 + 0.902050i \(0.642062\pi\)
\(734\) −7.66802e13 + 2.61149e14i −0.359917 + 1.22577i
\(735\) 1.18381e14i 0.551881i
\(736\) 1.82184e14 + 5.36485e13i 0.843570 + 0.248410i
\(737\) −1.13623e13 −0.0522552
\(738\) 1.17380e15 + 3.44657e14i 5.36180 + 1.57437i
\(739\) −1.02690e14 + 1.18510e14i −0.465913 + 0.537692i −0.939270 0.343178i \(-0.888496\pi\)
0.473357 + 0.880870i \(0.343042\pi\)
\(740\) 2.52973e13 + 1.62576e13i 0.114003 + 0.0732651i
\(741\) 9.15827e14 + 1.31676e14i 4.09942 + 0.589408i
\(742\) −8.18267e13 + 5.25868e13i −0.363811 + 0.233807i
\(743\) −2.50844e14 + 1.14557e14i −1.10780 + 0.505913i −0.883416 0.468589i \(-0.844763\pi\)
−0.224379 + 0.974502i \(0.572035\pi\)
\(744\) 1.10579e14 + 1.27616e14i 0.485076 + 0.559808i
\(745\) −9.71080e12 6.75401e13i −0.0423130 0.294293i
\(746\) −2.64070e14 1.20597e14i −1.14294 0.521964i
\(747\) −2.29677e13 7.82207e13i −0.0987448 0.336294i
\(748\) −1.13042e14 + 3.31921e13i −0.482761 + 0.141751i
\(749\) −5.23038e11 + 1.14529e12i −0.00221883 + 0.00485856i
\(750\) 4.55712e14 6.55214e13i 1.92037 0.276107i
\(751\) 2.71635e14 2.35373e14i 1.13707 0.985273i 0.137080 0.990560i \(-0.456228\pi\)
0.999986 + 0.00528651i \(0.00168276\pi\)
\(752\) 8.00986e13 + 1.75391e14i 0.333070 + 0.729322i
\(753\) −1.61467e14 2.51248e14i −0.666975 1.03783i
\(754\) 2.55739e13 1.77870e14i 0.104940 0.729873i
\(755\) −1.49567e13 + 2.32731e13i −0.0609679 + 0.0948679i
\(756\) −1.12850e14 9.77850e13i −0.456975 0.395971i
\(757\) −2.82171e13 + 9.60987e13i −0.113510 + 0.386579i −0.996577 0.0826673i \(-0.973656\pi\)
0.883067 + 0.469246i \(0.155474\pi\)
\(758\) 5.02195e14i 2.00690i
\(759\) 4.01421e13 3.47285e13i 0.159364 0.137872i
\(760\) 2.77756e14 1.09546
\(761\) −2.96626e14 8.70971e13i −1.16221 0.341256i −0.356920 0.934135i \(-0.616173\pi\)
−0.805292 + 0.592879i \(0.797991\pi\)
\(762\) 5.67034e14 6.54392e14i 2.20716 2.54720i
\(763\) −2.26112e13 1.45313e13i −0.0874380 0.0561930i
\(764\) −7.62949e14 1.09696e14i −2.93109 0.421427i
\(765\) −2.48272e14 + 1.59555e14i −0.947589 + 0.608979i
\(766\) −6.73677e14 + 3.07658e14i −2.55451 + 1.16661i
\(767\) 9.34070e13 + 1.07797e14i 0.351887 + 0.406099i
\(768\) 1.19668e14 + 8.32307e14i 0.447890 + 3.11514i
\(769\) 1.95889e14 + 8.94595e13i 0.728414 + 0.332655i 0.744870 0.667209i \(-0.232511\pi\)
−0.0164567 + 0.999865i \(0.505239\pi\)
\(770\) −1.15047e12 3.91814e12i −0.00425032 0.0144753i
\(771\) −4.25450e14 + 1.24923e14i −1.56163 + 0.458535i
\(772\) 4.10127e13 8.98053e13i 0.149566 0.327503i
\(773\) −5.19464e14 + 7.46876e13i −1.88217 + 0.270615i −0.985190 0.171465i \(-0.945150\pi\)
−0.896976 + 0.442079i \(0.854241\pi\)
\(774\) −9.85139e14 + 8.53628e14i −3.54644 + 3.07301i
\(775\) −2.06401e13 4.51954e13i −0.0738248 0.161654i
\(776\) 4.81498e14 + 7.49225e14i 1.71114 + 2.66259i
\(777\) −2.37676e12 + 1.65307e13i −0.00839229 + 0.0583697i
\(778\) 3.08352e13 4.79804e13i 0.108180 0.168332i
\(779\) −5.41628e14 4.69324e14i −1.88805 1.63601i
\(780\) 1.74475e14 5.94206e14i 0.604310 2.05809i
\(781\) 5.45603e12i 0.0187768i
\(782\) 9.38684e14 + 1.35710e14i 3.20986 + 0.464065i
\(783\) −9.96618e13 −0.338626
\(784\) −4.67429e14 1.37250e14i −1.57810 0.463373i
\(785\) 1.07479e14 1.24038e14i 0.360559 0.416108i
\(786\) 7.78648e14 + 5.00407e14i 2.59554 + 1.66805i
\(787\) 2.95139e14 + 4.24346e13i 0.977581 + 0.140555i 0.612543 0.790437i \(-0.290147\pi\)
0.365039 + 0.930992i \(0.381056\pi\)
\(788\) 2.88287e14 1.85271e14i 0.948843 0.609784i
\(789\) 2.79708e14 1.27738e14i 0.914787 0.417769i
\(790\) 8.29771e13 + 9.57606e13i 0.269664 + 0.311209i
\(791\) −8.88263e12 6.17800e13i −0.0286853 0.199511i
\(792\) −1.42085e14 6.48881e13i −0.455956 0.208228i
\(793\) −1.29590e14 4.41343e14i −0.413243 1.40738i
\(794\) 3.59787e14 1.05643e14i 1.14010 0.334764i
\(795\) −9.29402e13 + 2.03511e14i −0.292663 + 0.640843i
\(796\) −1.13562e15 + 1.63278e14i −3.55360 + 0.510931i
\(797\) −1.30803e14 + 1.13341e14i −0.406748 + 0.352449i −0.834078 0.551647i \(-0.814000\pi\)
0.427330 + 0.904096i \(0.359454\pi\)
\(798\) 1.16579e14 + 2.55273e14i 0.360252 + 0.788842i
\(799\) 1.49119e14 + 2.32034e14i 0.457931 + 0.712555i
\(800\) −3.62262e13 + 2.51959e14i −0.110554 + 0.768917i
\(801\) 2.19573e14 3.41662e14i 0.665910 1.03618i
\(802\) −2.68571e14 2.32718e14i −0.809445 0.701388i
\(803\) 6.34643e10 2.16140e11i 0.000190087 0.000647376i
\(804\) 5.22644e14i 1.55570i
\(805\) −3.24332e12 + 2.24335e13i −0.00959425 + 0.0663617i
\(806\) −2.06655e14 −0.607534
\(807\) 3.62215e14 + 1.06356e14i 1.05827 + 0.310738i
\(808\) 1.44923e14 1.67250e14i 0.420805 0.485635i
\(809\) 1.76971e14 + 1.13732e14i 0.510692 + 0.328202i 0.770480 0.637464i \(-0.220017\pi\)
−0.259789 + 0.965666i \(0.583653\pi\)
\(810\) −1.07007e14 1.53853e13i −0.306894 0.0441247i
\(811\) −1.45231e14 + 9.33342e13i −0.413956 + 0.266034i −0.731000 0.682377i \(-0.760946\pi\)
0.317044 + 0.948411i \(0.397310\pi\)
\(812\) 3.41847e13 1.56117e13i 0.0968394 0.0442251i
\(813\) 2.32973e14 + 2.68865e14i 0.655924 + 0.756976i
\(814\) 2.04481e12 + 1.42219e13i 0.00572177 + 0.0397958i
\(815\) −1.59314e14 7.27561e13i −0.443063 0.202340i
\(816\) −5.29635e14 1.80377e15i −1.46395 4.98575i
\(817\) 7.32713e14 2.15144e14i 2.01291 0.591043i
\(818\) −1.50939e14 + 3.30510e14i −0.412131 + 0.902440i
\(819\) 2.19935e14 3.16218e13i 0.596862 0.0858158i
\(820\) −3.62527e14 + 3.14131e14i −0.977847 + 0.847309i
\(821\) −8.27021e13 1.81092e14i −0.221718 0.485495i 0.765785 0.643097i \(-0.222351\pi\)
−0.987503 + 0.157602i \(0.949624\pi\)
\(822\) −3.58900e14 5.58459e14i −0.956343 1.48810i
\(823\) −2.72071e13 + 1.89230e14i −0.0720582 + 0.501175i 0.921547 + 0.388266i \(0.126926\pi\)
−0.993605 + 0.112909i \(0.963983\pi\)
\(824\) 6.98789e14 1.08734e15i 1.83954 2.86238i
\(825\) 5.37664e13 + 4.65888e13i 0.140683 + 0.121902i
\(826\) −1.21885e13 + 4.15102e13i −0.0316993 + 0.107958i
\(827\) 4.93688e14i 1.27622i −0.769945 0.638110i \(-0.779717\pi\)
0.769945 0.638110i \(-0.220283\pi\)
\(828\) 1.03200e15 + 1.19287e15i 2.65171 + 3.06507i
\(829\) −7.48622e13 −0.191201 −0.0956005 0.995420i \(-0.530477\pi\)
−0.0956005 + 0.995420i \(0.530477\pi\)
\(830\) 4.44832e13 + 1.30615e13i 0.112929 + 0.0331590i
\(831\) 1.71419e14 1.97828e14i 0.432567 0.499209i
\(832\) −7.47850e13 4.80614e13i −0.187585 0.120554i
\(833\) −6.89785e14 9.91762e13i −1.71984 0.247276i
\(834\) 1.29183e14 8.30208e13i 0.320166 0.205758i
\(835\) −1.26856e14 + 5.79333e13i −0.312521 + 0.142724i
\(836\) 1.09016e14 + 1.25812e14i 0.266969 + 0.308098i
\(837\) 1.63109e13 + 1.13445e14i 0.0397055 + 0.276158i
\(838\) −1.07096e15 4.89091e14i −2.59151 1.18350i
\(839\) 1.38288e14 + 4.70966e14i 0.332641 + 1.13287i 0.940774 + 0.339035i \(0.110100\pi\)
−0.608133 + 0.793835i \(0.708081\pi\)
\(840\) 9.90678e13 2.90889e13i 0.236884 0.0695554i
\(841\) −1.64348e14 + 3.59873e14i −0.390648 + 0.855400i
\(842\) −6.37469e14 + 9.16543e13i −1.50626 + 0.216567i
\(843\) 7.62322e14 6.60556e14i 1.79061 1.55157i
\(844\) 4.01499e14 + 8.79159e14i 0.937501 + 2.05284i
\(845\) 1.45694e14 + 2.26705e14i 0.338189 + 0.526232i
\(846\) −9.46777e13 + 6.58498e14i −0.218472 + 1.51951i
\(847\) −4.55464e13 + 7.08715e13i −0.104481 + 0.162575i
\(848\) −6.95811e14 6.02924e14i −1.58676 1.37494i
\(849\) −3.11796e14 + 1.06188e15i −0.706857 + 2.40733i
\(850\) 1.27121e15i 2.86498i
\(851\) 2.25290e13 7.65059e13i 0.0504771 0.171414i
\(852\) −2.50966e14 −0.559008
\(853\) 1.18058e14 + 3.46649e13i 0.261427 + 0.0767618i 0.409819 0.912167i \(-0.365592\pi\)
−0.148393 + 0.988929i \(0.547410\pi\)
\(854\) 9.13620e13 1.05437e14i 0.201130 0.232116i
\(855\) 3.50810e14 + 2.25452e14i 0.767789 + 0.493428i
\(856\) −2.71098e13 3.89781e12i −0.0589872 0.00848108i
\(857\) 2.01031e14 1.29195e14i 0.434869 0.279473i −0.304836 0.952405i \(-0.598602\pi\)
0.739705 + 0.672932i \(0.234965\pi\)
\(858\) 2.69164e14 1.22923e14i 0.578868 0.264360i
\(859\) −5.96539e13 6.88443e13i −0.127548 0.147198i 0.688383 0.725347i \(-0.258321\pi\)
−0.815931 + 0.578149i \(0.803775\pi\)
\(860\) −7.27414e13 5.05927e14i −0.154628 1.07546i
\(861\) −2.42335e14 1.10671e14i −0.512154 0.233893i
\(862\) 1.77124e14 + 6.03230e14i 0.372170 + 1.26750i
\(863\) 2.13931e14 6.28158e13i 0.446910 0.131225i −0.0505310 0.998722i \(-0.516091\pi\)
0.497441 + 0.867498i \(0.334273\pi\)
\(864\) 2.43924e14 5.34118e14i 0.506623 1.10935i
\(865\) −4.55266e13 + 6.54574e12i −0.0940124 + 0.0135169i
\(866\) −5.43926e14 + 4.71314e14i −1.11673 + 0.967656i
\(867\) −7.75079e14 1.69719e15i −1.58216 3.46445i
\(868\) −2.33655e13 3.63574e13i −0.0474216 0.0737894i
\(869\) −5.94089e12 + 4.13198e13i −0.0119882 + 0.0833795i
\(870\) 6.77785e13 1.05465e14i 0.135986 0.211599i
\(871\) 2.65716e14 + 2.30244e14i 0.530062 + 0.459301i
\(872\) 1.64722e14 5.60992e14i 0.326715 1.11269i
\(873\) 1.33711e15i 2.63692i
\(874\) −3.76563e14 1.28617e15i −0.738380 2.52197i
\(875\) −6.47718e13 −0.126283
\(876\) 9.94199e12 + 2.91923e12i 0.0192732 + 0.00565911i
\(877\) 5.04813e14 5.82585e14i 0.973044 1.12295i −0.0193453 0.999813i \(-0.506158\pi\)
0.992389 0.123140i \(-0.0392963\pi\)
\(878\) −2.81712e14 1.81045e14i −0.539923 0.346988i
\(879\) 3.32404e14 + 4.77924e13i 0.633463 + 0.0910783i
\(880\) 3.25171e13 2.08974e13i 0.0616166 0.0395986i
\(881\) 3.49692e14 1.59699e14i 0.658880 0.300900i −0.0577735 0.998330i \(-0.518400\pi\)
0.716654 + 0.697429i \(0.245673\pi\)
\(882\) −1.10072e15 1.27030e15i −2.06222 2.37993i
\(883\) 4.03380e13 + 2.80557e14i 0.0751468 + 0.522658i 0.992274 + 0.124063i \(0.0395927\pi\)
−0.917127 + 0.398594i \(0.869498\pi\)
\(884\) 3.31617e15 + 1.51444e15i 6.14292 + 2.80538i
\(885\) 2.80352e13 + 9.54791e13i 0.0516401 + 0.175870i
\(886\) −4.82898e13 + 1.41792e13i −0.0884477 + 0.0259706i
\(887\) −3.78995e14 + 8.29883e14i −0.690264 + 1.51147i 0.161125 + 0.986934i \(0.448488\pi\)
−0.851390 + 0.524534i \(0.824240\pi\)
\(888\) −3.59593e14 + 5.17016e13i −0.651248 + 0.0936353i
\(889\) −9.20642e13 + 7.97741e13i −0.165799 + 0.143666i
\(890\) 9.59458e13 + 2.10092e14i 0.171821 + 0.376235i
\(891\) −1.92556e13 2.99623e13i −0.0342901 0.0533565i
\(892\) 2.38709e14 1.66026e15i 0.422712 2.94002i
\(893\) 2.10707e14 3.27867e14i 0.371041 0.577351i
\(894\) 1.13338e15 + 9.82082e14i 1.98467 + 1.71973i
\(895\) −2.15517e13 + 7.33982e13i −0.0375289 + 0.127812i
\(896\) 1.26671e14i 0.219349i
\(897\) −1.64248e15 1.28187e12i −2.82839 0.00220741i
\(898\) −5.13194e14 −0.878819
\(899\) −2.76766e13 8.12658e12i −0.0471318 0.0138392i
\(900\) −1.38444e15 + 1.59773e15i −2.34456 + 2.70577i
\(901\) −1.10796e15 7.12042e14i −1.86595 1.19917i
\(902\) −2.26869e14 3.26188e13i −0.379963 0.0546305i
\(903\) 2.38807e14 1.53472e14i 0.397748 0.255617i
\(904\) 1.23503e15 5.64017e14i 2.04566 0.934222i
\(905\) −1.68803e14 1.94809e14i −0.278060 0.320898i
\(906\) −8.65310e13 6.01836e14i −0.141752 0.985910i
\(907\) 2.83767e13 + 1.29592e13i 0.0462302 + 0.0211126i 0.438396 0.898782i \(-0.355547\pi\)
−0.392166 + 0.919895i \(0.628274\pi\)
\(908\) 9.34468e13 + 3.18251e14i 0.151403 + 0.515632i
\(909\) 3.18796e14 9.36069e13i 0.513680 0.150830i
\(910\) −5.24920e13 + 1.14941e14i −0.0841175 + 0.184192i
\(911\) 1.85813e14 2.67158e13i 0.296131 0.0425772i 0.00735175 0.999973i \(-0.497660\pi\)
0.288779 + 0.957396i \(0.406751\pi\)
\(912\) −2.00753e15 + 1.73954e15i −3.18191 + 2.75714i
\(913\) 6.34496e12 + 1.38935e13i 0.0100017 + 0.0219007i
\(914\) −1.87743e14 2.92133e14i −0.294328 0.457984i
\(915\) 4.56689e13 3.17634e14i 0.0712057 0.495247i
\(916\) −6.74864e14 + 1.05011e15i −1.04650 + 1.62839i
\(917\) −9.84113e13 8.52739e13i −0.151774 0.131513i
\(918\) 8.26137e14 2.81356e15i 1.26718 4.31562i
\(919\) 1.58351e14i 0.241571i −0.992679 0.120785i \(-0.961459\pi\)
0.992679 0.120785i \(-0.0385413\pi\)
\(920\) −4.88105e14 + 6.97901e13i −0.740584 + 0.105890i
\(921\) −1.06368e15 −1.60513
\(922\) 1.67418e15 + 4.91583e14i 2.51273 + 0.737806i
\(923\) 1.10560e14 1.27593e14i 0.165040 0.190466i
\(924\) 5.20591e13 + 3.34564e13i 0.0772925 + 0.0496728i
\(925\) 1.05807e14 + 1.52127e13i 0.156245 + 0.0224646i
\(926\) 1.33344e15 8.56949e14i 1.95847 1.25864i
\(927\) 1.76516e15 8.06123e14i 2.57861 1.17761i
\(928\) 9.67752e13 + 1.11685e14i 0.140613 + 0.162276i
\(929\) −3.76590e13 2.61924e14i −0.0544239 0.378527i −0.998770 0.0495743i \(-0.984214\pi\)
0.944347 0.328952i \(-0.106696\pi\)
\(930\) −1.31144e14 5.98914e13i −0.188509 0.0860894i
\(931\) 2.77421e14 + 9.44809e14i 0.396635 + 1.35081i
\(932\) −1.92741e15 + 5.65940e14i −2.74092 + 0.804805i
\(933\) −5.79186e14 + 1.26824e15i −0.819237 + 1.79388i
\(934\) 7.27301e14 1.04570e14i 1.02325 0.147121i
\(935\) 4.17874e13 3.62090e13i 0.0584773 0.0506708i
\(936\) 2.00788e15 + 4.39664e15i 2.79485 + 6.11986i
\(937\) −4.44857e14 6.92212e14i −0.615918 0.958387i −0.999393 0.0348357i \(-0.988909\pi\)
0.383475 0.923551i \(-0.374727\pi\)
\(938\) −1.51765e13 + 1.05555e14i −0.0209005 + 0.145366i
\(939\) −1.87380e14 + 2.91568e14i −0.256681 + 0.399404i
\(940\) −1.97146e14 1.70828e14i −0.268626 0.232766i
\(941\) 3.98548e14 1.35733e15i 0.540172 1.83966i −0.00293701 0.999996i \(-0.500935\pi\)
0.543109 0.839662i \(-0.317247\pi\)
\(942\) 3.60720e15i 4.86313i
\(943\) 1.06974e15 + 6.88658e14i 1.43456 + 0.923518i
\(944\) −4.09504e14 −0.546259
\(945\) 6.72411e13 + 1.97438e13i 0.0892227 + 0.0261982i
\(946\) 1.59932e14 1.84571e14i 0.211096 0.243618i
\(947\) 7.21747e14 + 4.63838e14i 0.947622 + 0.608999i 0.920546 0.390634i \(-0.127744\pi\)
0.0270755 + 0.999633i \(0.491381\pi\)
\(948\) −1.90063e15 2.73269e14i −2.48231 0.356902i
\(949\) −5.86397e12 + 3.76855e12i −0.00761835 + 0.00489601i
\(950\) 1.63390e15 7.46179e14i 2.11158 0.964328i
\(951\) 8.65879e14 + 9.99278e14i 1.11315 + 1.28465i
\(952\) 8.64999e13 + 6.01620e14i 0.110619 + 0.769374i
\(953\) −6.21360e14 2.83765e14i −0.790458 0.360990i −0.0210748 0.999778i \(-0.506709\pi\)
−0.769383 + 0.638788i \(0.779436\pi\)
\(954\) −8.94964e14 3.04797e15i −1.13257 3.85717i
\(955\) 3.47096e14 1.01917e14i 0.436951 0.128300i
\(956\) −2.53643e14 + 5.55401e14i −0.317639 + 0.695533i
\(957\) 4.08820e13 5.87794e12i 0.0509299 0.00732261i
\(958\) 6.03127e14 5.22613e14i 0.747449 0.647668i
\(959\) 3.87971e13 + 8.49538e13i 0.0478306 + 0.104734i
\(960\) −3.35299e13 5.21736e13i −0.0411222 0.0639874i
\(961\) 1.11924e14 7.78451e14i 0.136555 0.949762i
\(962\) 2.40372e14 3.74026e14i 0.291748 0.453969i
\(963\) −3.10763e13 2.69278e13i −0.0375231 0.0325139i
\(964\) −4.14248e14 + 1.41080e15i −0.497594 + 1.69465i
\(965\) 4.63346e13i 0.0553693i
\(966\) −2.69008e14 4.19303e14i −0.319800 0.498474i
\(967\) −4.59640e14 −0.543607 −0.271804 0.962353i \(-0.587620\pi\)
−0.271804 + 0.962353i \(0.587620\pi\)
\(968\) −1.75835e15 5.16298e14i −2.06885 0.607469i
\(969\) −2.48838e15 + 2.87174e15i −2.91271 + 3.36145i
\(970\) −6.39689e14 4.11103e14i −0.744921 0.478732i
\(971\) −7.06790e14 1.01621e14i −0.818831 0.117730i −0.279845 0.960045i \(-0.590283\pi\)
−0.538986 + 0.842315i \(0.681192\pi\)
\(972\) −8.69626e14 + 5.58875e14i −1.00231 + 0.644144i
\(973\) −1.96515e13 + 8.97456e12i −0.0225337 + 0.0102908i
\(974\) 1.51904e13 + 1.75307e13i 0.0173291 + 0.0199988i
\(975\) −3.13297e14 2.17903e15i −0.355576 2.47309i
\(976\) 1.20123e15 + 5.48586e14i 1.35637 + 0.619434i
\(977\) 2.64462e14 + 9.00676e14i 0.297092 + 1.01180i 0.963832 + 0.266512i \(0.0858711\pi\)
−0.666740 + 0.745291i \(0.732311\pi\)
\(978\) 3.69338e15 1.08447e15i 4.12790 1.21206i
\(979\) −3.16095e13 + 6.92153e13i −0.0351483 + 0.0769641i
\(980\) 6.52376e14 9.37975e13i 0.721718 0.103767i
\(981\) 6.63399e14 5.74838e14i 0.730179 0.632704i
\(982\) −9.38428e13 2.05487e14i −0.102765 0.225023i
\(983\) −6.75811e14 1.05158e15i −0.736304 1.14571i −0.984223 0.176931i \(-0.943383\pi\)
0.247919 0.968781i \(-0.420253\pi\)
\(984\) 8.24745e14 5.73623e15i 0.894013 6.21800i
\(985\) −8.69514e13 + 1.35299e14i −0.0937768 + 0.145920i
\(986\) 5.57745e14 + 4.83289e14i 0.598482 + 0.518588i
\(987\) 4.08164e13 1.39008e14i 0.0435762 0.148407i
\(988\) 5.15128e15i 5.47181i
\(989\) −1.23355e15 + 5.62181e14i −1.30369 + 0.594148i
\(990\) 1.33364e14 0.140237
\(991\) −3.35668e14 9.85611e13i −0.351190 0.103119i 0.101379 0.994848i \(-0.467674\pi\)
−0.452569 + 0.891729i \(0.649493\pi\)
\(992\) 1.11292e14 1.28438e14i 0.115852 0.133701i
\(993\) −9.80395e14 6.30061e14i −1.01544 0.652584i
\(994\) 5.06860e13 + 7.28755e12i 0.0522344 + 0.00751017i
\(995\) 4.52974e14 2.91109e14i 0.464470 0.298497i
\(996\) −6.39075e14 + 2.91856e14i −0.652011 + 0.297764i
\(997\) −4.47974e14 5.16990e14i −0.454755 0.524815i 0.481354 0.876526i \(-0.340145\pi\)
−0.936108 + 0.351712i \(0.885600\pi\)
\(998\) 1.63803e14 + 1.13928e15i 0.165451 + 1.15074i
\(999\) −2.24296e14 1.02433e14i −0.225421 0.102946i
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 23.11.d.a.5.2 190
23.14 odd 22 inner 23.11.d.a.14.2 yes 190
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.11.d.a.5.2 190 1.1 even 1 trivial
23.11.d.a.14.2 yes 190 23.14 odd 22 inner