Properties

Label 54.9.f.a.5.9
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
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("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\), degree \(6\), 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: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.9
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(61.3803 + 52.8531i) q^{3} +(-22.2270 + 126.055i) q^{4} +(209.630 + 575.954i) q^{5} +(11.6907 - 916.336i) q^{6} +(358.863 + 2035.21i) q^{7} +(1254.14 - 724.077i) q^{8} +(974.093 + 6488.29i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(61.3803 + 52.8531i) q^{3} +(-22.2270 + 126.055i) q^{4} +(209.630 + 575.954i) q^{5} +(11.6907 - 916.336i) q^{6} +(358.863 + 2035.21i) q^{7} +(1254.14 - 724.077i) q^{8} +(974.093 + 6488.29i) q^{9} +(3467.19 - 6005.34i) q^{10} +(-1876.37 + 5155.27i) q^{11} +(-8026.72 + 6562.56i) q^{12} +(-427.513 - 358.726i) q^{13} +(15029.0 - 17910.9i) q^{14} +(-17573.8 + 46431.9i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-62437.1 - 36048.1i) q^{17} +(49148.8 - 55627.1i) q^{18} +(-75841.5 - 131361. i) q^{19} +(-77261.6 + 13623.3i) q^{20} +(-85540.2 + 143889. i) q^{21} +(58325.3 - 21228.7i) q^{22} +(-12116.4 - 2136.45i) q^{23} +(115249. + 21841.0i) q^{24} +(11457.8 - 9614.25i) q^{25} +6313.94i q^{26} +(-283136. + 449737. i) q^{27} -264526. q^{28} +(83917.4 + 100009. i) q^{29} +(530218. - 185358. i) q^{30} +(-173088. + 981632. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-387644. + 217261. i) q^{33} +(141640. + 803282. i) q^{34} +(-1.09696e6 + 633330. i) q^{35} +(-839535. - 21425.2i) q^{36} +(-1.08580e6 + 1.88067e6i) q^{37} +(-586940. + 1.61260e6i) q^{38} +(-7281.10 - 44614.1i) q^{39} +(679941. + 570538. i) q^{40} +(-1.67092e6 + 1.99132e6i) q^{41} +(1.86913e6 - 305046. i) q^{42} +(6.15302e6 + 2.23951e6i) q^{43} +(-608144. - 351112. i) q^{44} +(-3.53276e6 + 1.92117e6i) q^{45} +(69598.2 + 120548. i) q^{46} +(-4.51540e6 + 796186. i) q^{47} +(-648836. - 1.15768e6i) q^{48} +(1.40384e6 - 510956. i) q^{49} +(-166650. - 29384.8i) q^{50} +(-1.92716e6 - 5.51264e6i) q^{51} +(54721.7 - 45916.9i) q^{52} -8.48466e6i q^{53} +(5.95684e6 - 816744. i) q^{54} -3.36254e6 q^{55} +(1.92371e6 + 2.29259e6i) q^{56} +(2.28768e6 - 1.20715e7i) q^{57} +(256484. - 1.45459e6i) q^{58} +(-6.50099e6 - 1.78613e7i) q^{59} +(-5.46237e6 - 3.24731e6i) q^{60} +(2.29174e6 + 1.29971e7i) q^{61} +(9.76636e6 - 5.63861e6i) q^{62} +(-1.28555e7 + 4.31089e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(116990. - 321428. i) q^{65} +(4.70203e6 + 1.77965e6i) q^{66} +(-602495. - 505554. i) q^{67} +(5.93184e6 - 7.06929e6i) q^{68} +(-630792. - 771527. i) q^{69} +(1.34664e7 + 4.90136e6i) q^{70} +(1.88839e7 + 1.09027e7i) q^{71} +(5.91967e6 + 7.43189e6i) q^{72} +(7.76455e6 + 1.34486e7i) q^{73} +(2.41957e7 - 4.26635e6i) q^{74} +(1.21143e6 + 15455.5i) q^{75} +(1.82445e7 - 6.64046e6i) q^{76} +(-1.11654e7 - 1.96877e6i) q^{77} +(-333711. + 387552. i) q^{78} +(-926580. + 777493. i) q^{79} -1.00420e7i q^{80} +(-4.11490e7 + 1.26404e7i) q^{81} +2.94099e7 q^{82} +(-2.24413e7 - 2.67445e7i) q^{83} +(-1.62367e7 - 1.39810e7i) q^{84} +(7.67333e6 - 4.35176e7i) q^{85} +(-2.53372e7 - 6.96134e7i) q^{86} +(-134903. + 1.05739e7i) q^{87} +(1.37959e6 + 7.82406e6i) q^{88} +(-3.19449e7 + 1.84434e7i) q^{89} +(4.23417e7 + 1.66463e7i) q^{90} +(576665. - 998813. i) q^{91} +(538622. - 1.47985e6i) q^{92} +(-6.25065e7 + 5.11047e7i) q^{93} +(3.97378e7 + 3.33439e7i) q^{94} +(5.97594e7 - 7.12185e7i) q^{95} +(-5.31482e6 + 1.40423e7i) q^{96} +(1.53373e8 + 5.58232e7i) q^{97} +(-1.46375e7 - 8.45098e6i) q^{98} +(-3.52766e7 - 7.15268e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) 61.3803 + 52.8531i 0.757782 + 0.652508i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) 209.630 + 575.954i 0.335408 + 0.921527i 0.986679 + 0.162681i \(0.0520141\pi\)
−0.651271 + 0.758846i \(0.725764\pi\)
\(6\) 11.6907 916.336i 0.00902061 0.707049i
\(7\) 358.863 + 2035.21i 0.149464 + 0.847651i 0.963674 + 0.267081i \(0.0860592\pi\)
−0.814210 + 0.580570i \(0.802830\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) 974.093 + 6488.29i 0.148467 + 0.988917i
\(10\) 3467.19 6005.34i 0.346719 0.600534i
\(11\) −1876.37 + 5155.27i −0.128158 + 0.352112i −0.987132 0.159908i \(-0.948880\pi\)
0.858974 + 0.512020i \(0.171103\pi\)
\(12\) −8026.72 + 6562.56i −0.387091 + 0.316481i
\(13\) −427.513 358.726i −0.0149684 0.0125600i 0.635273 0.772288i \(-0.280888\pi\)
−0.650241 + 0.759728i \(0.725332\pi\)
\(14\) 15029.0 17910.9i 0.391218 0.466235i
\(15\) −17573.8 + 46431.9i −0.347137 + 0.917173i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) −62437.1 36048.1i −0.747561 0.431605i 0.0772508 0.997012i \(-0.475386\pi\)
−0.824812 + 0.565407i \(0.808719\pi\)
\(18\) 49148.8 55627.1i 0.468191 0.529903i
\(19\) −75841.5 131361.i −0.581959 1.00798i −0.995247 0.0973821i \(-0.968953\pi\)
0.413288 0.910600i \(-0.364380\pi\)
\(20\) −77261.6 + 13623.3i −0.482885 + 0.0851456i
\(21\) −85540.2 + 143889.i −0.439838 + 0.739861i
\(22\) 58325.3 21228.7i 0.248981 0.0906216i
\(23\) −12116.4 2136.45i −0.0432975 0.00763452i 0.151957 0.988387i \(-0.451442\pi\)
−0.195255 + 0.980753i \(0.562553\pi\)
\(24\) 115249. + 21841.0i 0.347371 + 0.0658307i
\(25\) 11457.8 9614.25i 0.0293320 0.0246125i
\(26\) 6313.94i 0.0138168i
\(27\) −283136. + 449737.i −0.532770 + 0.846260i
\(28\) −264526. −0.430364
\(29\) 83917.4 + 100009.i 0.118648 + 0.141399i 0.822099 0.569345i \(-0.192803\pi\)
−0.703451 + 0.710744i \(0.748359\pi\)
\(30\) 530218. 185358.i 0.654590 0.228837i
\(31\) −173088. + 981632.i −0.187422 + 1.06292i 0.735382 + 0.677653i \(0.237003\pi\)
−0.922804 + 0.385270i \(0.874108\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) −387644. + 217261.i −0.326872 + 0.183200i
\(34\) 141640. + 803282.i 0.105992 + 0.601108i
\(35\) −1.09696e6 + 633330.i −0.731002 + 0.422044i
\(36\) −839535. 21425.2i −0.499837 0.0127560i
\(37\) −1.08580e6 + 1.88067e6i −0.579355 + 1.00347i 0.416198 + 0.909274i \(0.363362\pi\)
−0.995553 + 0.0941985i \(0.969971\pi\)
\(38\) −586940. + 1.61260e6i −0.281487 + 0.773380i
\(39\) −7281.10 44614.1i −0.00314730 0.0192848i
\(40\) 679941. + 570538.i 0.265602 + 0.222866i
\(41\) −1.67092e6 + 1.99132e6i −0.591317 + 0.704704i −0.975858 0.218404i \(-0.929915\pi\)
0.384542 + 0.923108i \(0.374359\pi\)
\(42\) 1.86913e6 305046.i 0.600679 0.0980319i
\(43\) 6.15302e6 + 2.23951e6i 1.79976 + 0.655058i 0.998380 + 0.0569009i \(0.0181219\pi\)
0.801379 + 0.598158i \(0.204100\pi\)
\(44\) −608144. 351112.i −0.162254 0.0936775i
\(45\) −3.53276e6 + 1.92117e6i −0.861516 + 0.468507i
\(46\) 69598.2 + 120548.i 0.0155441 + 0.0269232i
\(47\) −4.51540e6 + 796186.i −0.925347 + 0.163164i −0.615964 0.787774i \(-0.711233\pi\)
−0.309383 + 0.950938i \(0.600122\pi\)
\(48\) −648836. 1.15768e6i −0.122228 0.218083i
\(49\) 1.40384e6 510956.i 0.243519 0.0886338i
\(50\) −166650. 29384.8i −0.0266639 0.00470157i
\(51\) −1.92716e6 5.51264e6i −0.284863 0.814852i
\(52\) 54721.7 45916.9i 0.00748421 0.00628000i
\(53\) 8.48466e6i 1.07530i −0.843167 0.537652i \(-0.819311\pi\)
0.843167 0.537652i \(-0.180689\pi\)
\(54\) 5.95684e6 816744.i 0.700553 0.0960530i
\(55\) −3.36254e6 −0.367466
\(56\) 1.92371e6 + 2.29259e6i 0.195609 + 0.233117i
\(57\) 2.28768e6 1.20715e7i 0.216718 1.14356i
\(58\) 256484. 1.45459e6i 0.0226646 0.128537i
\(59\) −6.50099e6 1.78613e7i −0.536502 1.47403i −0.851203 0.524837i \(-0.824126\pi\)
0.314700 0.949191i \(-0.398096\pi\)
\(60\) −5.46237e6 3.24731e6i −0.421480 0.250564i
\(61\) 2.29174e6 + 1.29971e7i 0.165519 + 0.938703i 0.948528 + 0.316693i \(0.102572\pi\)
−0.783009 + 0.622010i \(0.786316\pi\)
\(62\) 9.76636e6 5.63861e6i 0.660946 0.381597i
\(63\) −1.28555e7 + 4.31089e6i −0.816067 + 0.273656i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) 116990. 321428.i 0.00655384 0.0180065i
\(66\) 4.70203e6 + 1.77965e6i 0.247805 + 0.0937905i
\(67\) −602495. 505554.i −0.0298988 0.0250881i 0.627716 0.778443i \(-0.283990\pi\)
−0.657615 + 0.753355i \(0.728434\pi\)
\(68\) 5.93184e6 7.06929e6i 0.277430 0.330628i
\(69\) −630792. 771527.i −0.0278285 0.0340373i
\(70\) 1.34664e7 + 4.90136e6i 0.560865 + 0.204138i
\(71\) 1.88839e7 + 1.09027e7i 0.743121 + 0.429041i 0.823203 0.567747i \(-0.192185\pi\)
−0.0800822 + 0.996788i \(0.525518\pi\)
\(72\) 5.91967e6 + 7.43189e6i 0.220276 + 0.276547i
\(73\) 7.76455e6 + 1.34486e7i 0.273416 + 0.473571i 0.969734 0.244162i \(-0.0785130\pi\)
−0.696318 + 0.717733i \(0.745180\pi\)
\(74\) 2.41957e7 4.26635e6i 0.806884 0.142275i
\(75\) 1.21143e6 + 15455.5i 0.0382871 + 0.000488471i
\(76\) 1.82445e7 6.64046e6i 0.546863 0.199042i
\(77\) −1.11654e7 1.96877e6i −0.317623 0.0560056i
\(78\) −333711. + 387552.i −0.00901556 + 0.0104701i
\(79\) −926580. + 777493.i −0.0237889 + 0.0199613i −0.654605 0.755971i \(-0.727165\pi\)
0.630816 + 0.775933i \(0.282720\pi\)
\(80\) 1.00420e7i 0.245167i
\(81\) −4.11490e7 + 1.26404e7i −0.955915 + 0.293644i
\(82\) 2.94099e7 0.650486
\(83\) −2.24413e7 2.67445e7i −0.472862 0.563536i 0.475911 0.879494i \(-0.342119\pi\)
−0.948773 + 0.315958i \(0.897674\pi\)
\(84\) −1.62367e7 1.39810e7i −0.326122 0.280816i
\(85\) 7.67333e6 4.35176e7i 0.146997 0.833661i
\(86\) −2.53372e7 6.96134e7i −0.463196 1.27262i
\(87\) −134903. + 1.05739e7i −0.00235474 + 0.184568i
\(88\) 1.37959e6 + 7.82406e6i 0.0230049 + 0.130467i
\(89\) −3.19449e7 + 1.84434e7i −0.509146 + 0.293955i −0.732482 0.680786i \(-0.761638\pi\)
0.223337 + 0.974741i \(0.428305\pi\)
\(90\) 4.23417e7 + 1.66463e7i 0.645355 + 0.253716i
\(91\) 576665. 998813.i 0.00840926 0.0145653i
\(92\) 538622. 1.47985e6i 0.00751853 0.0206570i
\(93\) −6.25065e7 + 5.11047e7i −0.835591 + 0.683170i
\(94\) 3.97378e7 + 3.33439e7i 0.508970 + 0.427076i
\(95\) 5.97594e7 7.12185e7i 0.733689 0.874376i
\(96\) −5.31482e6 + 1.40423e7i −0.0625754 + 0.165331i
\(97\) 1.53373e8 + 5.58232e7i 1.73246 + 0.630563i 0.998801 0.0489589i \(-0.0155903\pi\)
0.733656 + 0.679521i \(0.237813\pi\)
\(98\) −1.46375e7 8.45098e6i −0.158695 0.0916226i
\(99\) −3.52766e7 7.15268e6i −0.367237 0.0744609i
\(100\) 957255. + 1.65801e6i 0.00957255 + 0.0165801i
\(101\) 6.04415e7 1.06575e7i 0.580831 0.102416i 0.124489 0.992221i \(-0.460271\pi\)
0.456341 + 0.889805i \(0.349160\pi\)
\(102\) −3.37621e7 + 5.67919e7i −0.311909 + 0.524669i
\(103\) −1.36149e8 + 4.95541e7i −1.20966 + 0.440282i −0.866587 0.499026i \(-0.833691\pi\)
−0.343077 + 0.939307i \(0.611469\pi\)
\(104\) −795906. 140340.i −0.00680344 0.00119963i
\(105\) −1.00805e8 1.91037e7i −0.829327 0.157167i
\(106\) −7.35349e7 + 6.17031e7i −0.582465 + 0.488747i
\(107\) 3.13078e7i 0.238846i −0.992843 0.119423i \(-0.961896\pi\)
0.992843 0.119423i \(-0.0381044\pi\)
\(108\) −5.03985e7 4.56871e7i −0.370444 0.335814i
\(109\) 3.10455e7 0.219934 0.109967 0.993935i \(-0.464925\pi\)
0.109967 + 0.993935i \(0.464925\pi\)
\(110\) 2.44535e7 + 2.91425e7i 0.167020 + 0.199047i
\(111\) −1.66046e8 + 5.80479e7i −1.09380 + 0.382380i
\(112\) 5.87960e6 3.33449e7i 0.0373659 0.211913i
\(113\) −5.73174e6 1.57478e7i −0.0351539 0.0965844i 0.920874 0.389860i \(-0.127477\pi\)
−0.956028 + 0.293276i \(0.905255\pi\)
\(114\) −1.21258e8 + 6.79605e7i −0.717943 + 0.402381i
\(115\) −1.30947e6 7.42636e6i −0.00748693 0.0424605i
\(116\) −1.44719e7 + 8.35535e6i −0.0799269 + 0.0461458i
\(117\) 1.91108e6 3.12326e6i 0.0101985 0.0166673i
\(118\) −1.07523e8 + 1.86236e8i −0.554594 + 0.960585i
\(119\) 5.09591e7 1.40009e8i 0.254117 0.698181i
\(120\) 1.15803e7 + 7.09568e7i 0.0558462 + 0.342191i
\(121\) 1.41152e8 + 1.18441e8i 0.658486 + 0.552535i
\(122\) 9.59773e7 1.14381e8i 0.433241 0.516316i
\(123\) −2.07809e8 + 3.39148e7i −0.907914 + 0.148173i
\(124\) −1.19893e8 4.36374e7i −0.507115 0.184575i
\(125\) 2.15284e8 + 1.24294e8i 0.881803 + 0.509109i
\(126\) 1.30851e8 + 8.00657e7i 0.519151 + 0.317661i
\(127\) 8.11111e7 + 1.40489e8i 0.311792 + 0.540040i 0.978750 0.205055i \(-0.0657374\pi\)
−0.666958 + 0.745095i \(0.732404\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) 2.59309e8 + 4.62668e8i 0.936394 + 1.67075i
\(130\) −3.63654e6 + 1.32359e6i −0.0127325 + 0.00463426i
\(131\) 2.88786e8 + 5.09207e7i 0.980597 + 0.172906i 0.640896 0.767628i \(-0.278563\pi\)
0.339701 + 0.940533i \(0.389674\pi\)
\(132\) −1.87707e7 5.36937e7i −0.0618280 0.176859i
\(133\) 2.40131e8 2.01494e8i 0.767436 0.643955i
\(134\) 8.89825e6i 0.0275985i
\(135\) −3.18382e8 6.87949e7i −0.958546 0.207120i
\(136\) −1.04406e8 −0.305191
\(137\) −2.71128e8 3.23118e8i −0.769649 0.917232i 0.228768 0.973481i \(-0.426530\pi\)
−0.998417 + 0.0562489i \(0.982086\pi\)
\(138\) −2.09936e6 + 1.10777e7i −0.00578855 + 0.0305446i
\(139\) −2.61714e7 + 1.48426e8i −0.0701081 + 0.397603i 0.929479 + 0.368875i \(0.120257\pi\)
−0.999587 + 0.0287282i \(0.990854\pi\)
\(140\) −5.54526e7 1.52355e8i −0.144348 0.396592i
\(141\) −3.19238e8 1.89783e8i −0.807677 0.480154i
\(142\) −4.28388e7 2.42951e8i −0.105362 0.597538i
\(143\) 2.65150e6 1.53085e6i 0.00634085 0.00366089i
\(144\) 2.13611e7 1.05352e8i 0.0496790 0.245014i
\(145\) −4.00089e7 + 6.92974e7i −0.0905075 + 0.156764i
\(146\) 6.00901e7 1.65096e8i 0.132249 0.363350i
\(147\) 1.13174e8 + 4.28347e7i 0.242369 + 0.0917332i
\(148\) −2.12934e8 1.78673e8i −0.443812 0.372402i
\(149\) 2.35050e7 2.80122e7i 0.0476887 0.0568332i −0.741673 0.670762i \(-0.765967\pi\)
0.789362 + 0.613929i \(0.210412\pi\)
\(150\) −8.67593e6 1.06116e7i −0.0171376 0.0209612i
\(151\) 7.92027e8 + 2.88274e8i 1.52346 + 0.554496i 0.962011 0.273012i \(-0.0880200\pi\)
0.561454 + 0.827508i \(0.310242\pi\)
\(152\) −1.90231e8 1.09830e8i −0.356376 0.205754i
\(153\) 1.73071e8 4.40224e8i 0.315833 0.803355i
\(154\) 6.41355e7 + 1.11086e8i 0.114029 + 0.197504i
\(155\) −6.01659e8 + 1.06089e8i −1.04237 + 0.183799i
\(156\) 5.78569e6 + 73814.4i 0.00976915 + 0.000124636i
\(157\) 9.55069e8 3.47617e8i 1.57194 0.572139i 0.598509 0.801116i \(-0.295760\pi\)
0.973432 + 0.228977i \(0.0735380\pi\)
\(158\) 1.34768e7 + 2.37632e6i 0.0216250 + 0.00381308i
\(159\) 4.48441e8 5.20792e8i 0.701644 0.814846i
\(160\) −8.70324e7 + 7.30288e7i −0.132801 + 0.111433i
\(161\) 2.54262e7i 0.0378423i
\(162\) 4.08800e8 + 2.64705e8i 0.593541 + 0.384329i
\(163\) 4.35974e6 0.00617605 0.00308802 0.999995i \(-0.499017\pi\)
0.00308802 + 0.999995i \(0.499017\pi\)
\(164\) −2.13878e8 2.54890e8i −0.295658 0.352352i
\(165\) −2.06394e8 1.77721e8i −0.278459 0.239774i
\(166\) −6.85891e7 + 3.88988e8i −0.0903280 + 0.512276i
\(167\) −5.83854e7 1.60412e8i −0.0750651 0.206240i 0.896485 0.443074i \(-0.146112\pi\)
−0.971550 + 0.236835i \(0.923890\pi\)
\(168\) −3.09249e6 + 2.42394e8i −0.00388214 + 0.304288i
\(169\) −1.41596e8 8.03031e8i −0.173582 0.984432i
\(170\) −4.32962e8 + 2.49971e8i −0.518387 + 0.299291i
\(171\) 7.78433e8 6.20039e8i 0.910409 0.725162i
\(172\) −4.19066e8 + 7.25843e8i −0.478816 + 0.829333i
\(173\) −2.83342e8 + 7.78475e8i −0.316320 + 0.869081i 0.675025 + 0.737795i \(0.264133\pi\)
−0.991345 + 0.131286i \(0.958089\pi\)
\(174\) 9.26227e7 7.57273e7i 0.101046 0.0826144i
\(175\) 2.36788e7 + 1.98689e7i 0.0252469 + 0.0211846i
\(176\) 5.77768e7 6.88557e7i 0.0602147 0.0717611i
\(177\) 5.44994e8 1.43993e9i 0.555263 1.46706i
\(178\) 3.92159e8 + 1.42734e8i 0.390645 + 0.142183i
\(179\) 1.50419e9 + 8.68446e8i 1.46518 + 0.845923i 0.999243 0.0388952i \(-0.0123838\pi\)
0.465937 + 0.884818i \(0.345717\pi\)
\(180\) −1.63652e8 4.88025e8i −0.155895 0.464892i
\(181\) −5.94377e8 1.02949e9i −0.553793 0.959197i −0.997996 0.0632715i \(-0.979847\pi\)
0.444203 0.895926i \(-0.353487\pi\)
\(182\) −1.28502e7 + 2.26584e6i −0.0117118 + 0.00206511i
\(183\) −5.46271e8 + 9.18894e8i −0.487084 + 0.819334i
\(184\) −1.67426e7 + 6.09382e6i −0.0146067 + 0.00531641i
\(185\) −1.31080e9 2.31129e8i −1.11905 0.197318i
\(186\) 8.97481e8 + 1.70083e8i 0.749849 + 0.142105i
\(187\) 3.02992e8 2.54241e8i 0.247779 0.207912i
\(188\) 5.86887e8i 0.469811i
\(189\) −1.01692e9 4.14848e8i −0.796963 0.325118i
\(190\) −1.05183e9 −0.807104
\(191\) 1.50409e9 + 1.79250e9i 1.13016 + 1.34687i 0.930195 + 0.367066i \(0.119638\pi\)
0.199963 + 0.979803i \(0.435918\pi\)
\(192\) 1.60353e8 5.60577e7i 0.117997 0.0412506i
\(193\) 1.94286e8 1.10185e9i 0.140027 0.794132i −0.831200 0.555974i \(-0.812345\pi\)
0.971226 0.238158i \(-0.0765435\pi\)
\(194\) −6.31568e8 1.73522e9i −0.445875 1.22503i
\(195\) 2.41694e7 1.35460e7i 0.0167158 0.00936859i
\(196\) 3.32057e7 + 1.88319e8i 0.0225003 + 0.127605i
\(197\) −2.12594e9 + 1.22741e9i −1.41152 + 0.814940i −0.995531 0.0944317i \(-0.969897\pi\)
−0.415985 + 0.909371i \(0.636563\pi\)
\(198\) 1.94552e8 + 3.57752e8i 0.126583 + 0.232767i
\(199\) −1.09908e9 + 1.90366e9i −0.700837 + 1.21389i 0.267336 + 0.963603i \(0.413857\pi\)
−0.968173 + 0.250282i \(0.919477\pi\)
\(200\) 7.40823e6 2.03539e7i 0.00463014 0.0127212i
\(201\) −1.02613e7 6.28748e7i −0.00628662 0.0385205i
\(202\) −5.31915e8 4.46330e8i −0.319475 0.268072i
\(203\) −1.73424e8 + 2.06679e8i −0.102124 + 0.121706i
\(204\) 7.37732e8 1.20399e8i 0.425969 0.0695189i
\(205\) −1.49719e9 5.44931e8i −0.847736 0.308551i
\(206\) 1.41959e9 + 8.19602e8i 0.788305 + 0.455128i
\(207\) 2.05939e6 8.06959e7i 0.00112165 0.0439511i
\(208\) 4.57178e6 + 7.91856e6i 0.00244249 + 0.00423051i
\(209\) 8.19510e8 1.44502e8i 0.429506 0.0757334i
\(210\) 5.67519e8 + 1.01259e9i 0.291812 + 0.520661i
\(211\) −1.46917e8 + 5.34735e7i −0.0741213 + 0.0269779i −0.378815 0.925473i \(-0.623668\pi\)
0.304693 + 0.952450i \(0.401446\pi\)
\(212\) 1.06954e9 + 1.88588e8i 0.529484 + 0.0933623i
\(213\) 5.82864e8 + 1.66728e9i 0.283171 + 0.810012i
\(214\) −2.71339e8 + 2.27680e8i −0.129377 + 0.108560i
\(215\) 4.01332e9i 1.87824i
\(216\) −2.94475e7 + 7.69045e8i −0.0135280 + 0.353294i
\(217\) −2.05994e9 −0.929001
\(218\) −2.25772e8 2.69065e8i −0.0999643 0.119133i
\(219\) −2.34209e8 + 1.23586e9i −0.101819 + 0.537270i
\(220\) 7.47391e7 4.23867e8i 0.0319049 0.180942i
\(221\) 1.37613e7 + 3.78088e7i 0.00576886 + 0.0158498i
\(222\) 1.71063e9 + 1.01695e9i 0.704278 + 0.418684i
\(223\) 1.31016e7 + 7.43029e7i 0.00529792 + 0.0300460i 0.987342 0.158605i \(-0.0506996\pi\)
−0.982044 + 0.188651i \(0.939589\pi\)
\(224\) −3.31752e8 + 1.91537e8i −0.131771 + 0.0760783i
\(225\) 7.35410e7 + 6.49764e7i 0.0286945 + 0.0253528i
\(226\) −9.48004e7 + 1.64199e8i −0.0363393 + 0.0629415i
\(227\) −1.18038e9 + 3.24306e9i −0.444546 + 1.22138i 0.491925 + 0.870637i \(0.336293\pi\)
−0.936472 + 0.350744i \(0.885929\pi\)
\(228\) 1.47082e9 + 5.56686e8i 0.544279 + 0.206002i
\(229\) −2.28950e8 1.92112e8i −0.0832528 0.0698574i 0.600211 0.799841i \(-0.295083\pi\)
−0.683464 + 0.729984i \(0.739528\pi\)
\(230\) −5.48400e7 + 6.53557e7i −0.0195968 + 0.0233546i
\(231\) −5.81282e8 7.10971e8i −0.204145 0.249692i
\(232\) 1.77658e8 + 6.46623e7i 0.0613244 + 0.0223203i
\(233\) 6.83338e8 + 3.94525e8i 0.231853 + 0.133860i 0.611426 0.791301i \(-0.290596\pi\)
−0.379574 + 0.925161i \(0.623929\pi\)
\(234\) −4.09666e7 + 6.15037e6i −0.0136637 + 0.00205134i
\(235\) −1.40513e9 2.43376e9i −0.460729 0.798005i
\(236\) 2.39601e9 4.22482e8i 0.772399 0.136195i
\(237\) −9.79667e7 1.24987e6i −0.0310517 0.000396161i
\(238\) −1.58402e9 + 5.76536e8i −0.493688 + 0.179688i
\(239\) −3.90748e9 6.88994e8i −1.19758 0.211166i −0.460928 0.887437i \(-0.652483\pi\)
−0.736652 + 0.676272i \(0.763595\pi\)
\(240\) 5.30753e8 6.16384e8i 0.159973 0.185783i
\(241\) 3.42039e9 2.87004e9i 1.01393 0.850786i 0.0250751 0.999686i \(-0.492018\pi\)
0.988852 + 0.148899i \(0.0475731\pi\)
\(242\) 2.08468e9i 0.607824i
\(243\) −3.19382e9 1.39898e9i −0.915980 0.401224i
\(244\) −1.68930e9 −0.476592
\(245\) 5.88574e8 + 7.01436e8i 0.163357 + 0.194681i
\(246\) 1.80519e9 + 1.55440e9i 0.492926 + 0.424447i
\(247\) −1.46995e7 + 8.33650e7i −0.00394925 + 0.0223973i
\(248\) 4.93701e8 + 1.35643e9i 0.130514 + 0.358584i
\(249\) 3.60758e7 2.82767e9i 0.00938465 0.735584i
\(250\) −4.88378e8 2.76973e9i −0.125025 0.709051i
\(251\) −5.78760e9 + 3.34147e9i −1.45815 + 0.841865i −0.998921 0.0464503i \(-0.985209\pi\)
−0.459233 + 0.888316i \(0.651876\pi\)
\(252\) −2.57673e8 1.71632e9i −0.0638949 0.425594i
\(253\) 3.37488e7 5.84547e7i 0.00823714 0.0142671i
\(254\) 6.27721e8 1.72465e9i 0.150811 0.414349i
\(255\) 2.77104e9 2.26557e9i 0.655362 0.535817i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 3.45809e9 4.12119e9i 0.792690 0.944691i −0.206742 0.978396i \(-0.566286\pi\)
0.999432 + 0.0337043i \(0.0107304\pi\)
\(258\) 2.12408e9 5.61205e9i 0.479394 1.26661i
\(259\) −4.21721e9 1.53494e9i −0.937187 0.341108i
\(260\) 3.79174e7 + 2.18916e7i 0.00829745 + 0.00479054i
\(261\) −5.67143e8 + 6.41898e8i −0.122217 + 0.138326i
\(262\) −1.65882e9 2.87316e9i −0.352042 0.609754i
\(263\) 8.07348e9 1.42357e9i 1.68748 0.297548i 0.754183 0.656664i \(-0.228033\pi\)
0.933293 + 0.359116i \(0.116922\pi\)
\(264\) −3.28846e8 + 5.53159e8i −0.0676982 + 0.113877i
\(265\) 4.88678e9 1.77864e9i 0.990921 0.360666i
\(266\) −3.49262e9 6.15843e8i −0.697629 0.123011i
\(267\) −2.93558e9 5.56327e8i −0.577630 0.109467i
\(268\) 7.71194e7 6.47109e7i 0.0149494 0.0125441i
\(269\) 2.57842e8i 0.0492431i 0.999697 + 0.0246215i \(0.00783807\pi\)
−0.999697 + 0.0246215i \(0.992162\pi\)
\(270\) 1.71914e9 + 3.25965e9i 0.323486 + 0.613361i
\(271\) 3.57905e9 0.663575 0.331788 0.943354i \(-0.392348\pi\)
0.331788 + 0.943354i \(0.392348\pi\)
\(272\) 7.59275e8 + 9.04869e8i 0.138715 + 0.165314i
\(273\) 8.81862e7 3.08289e7i 0.0158763 0.00555019i
\(274\) −8.28672e8 + 4.69963e9i −0.147021 + 0.833800i
\(275\) 2.80650e7 + 7.71080e7i 0.00490721 + 0.0134824i
\(276\) 1.11276e8 6.23660e7i 0.0191763 0.0107476i
\(277\) −1.13222e9 6.42112e9i −0.192314 1.09067i −0.916193 0.400738i \(-0.868754\pi\)
0.723879 0.689927i \(-0.242357\pi\)
\(278\) 1.47670e9 8.52574e8i 0.247237 0.142742i
\(279\) −6.53771e9 1.66845e8i −1.07897 0.0275357i
\(280\) −9.17160e8 + 1.58857e9i −0.149215 + 0.258448i
\(281\) 1.75169e9 4.81272e9i 0.280952 0.771908i −0.716298 0.697794i \(-0.754165\pi\)
0.997250 0.0741139i \(-0.0236128\pi\)
\(282\) 6.76786e8 + 4.14693e9i 0.107018 + 0.655738i
\(283\) 9.09122e9 + 7.62844e9i 1.41735 + 1.18930i 0.952743 + 0.303777i \(0.0982478\pi\)
0.464604 + 0.885519i \(0.346197\pi\)
\(284\) −1.79407e9 + 2.13809e9i −0.275782 + 0.328664i
\(285\) 7.43217e9 1.21294e9i 1.12651 0.183849i
\(286\) −3.25501e7 1.18473e7i −0.00486506 0.00177074i
\(287\) −4.65240e9 2.68606e9i −0.685724 0.395903i
\(288\) −1.06841e9 + 5.81018e8i −0.155298 + 0.0844539i
\(289\) −8.88954e8 1.53971e9i −0.127435 0.220724i
\(290\) 8.91544e8 1.57203e8i 0.126052 0.0222264i
\(291\) 6.46366e9 + 1.15327e10i 0.901377 + 1.60827i
\(292\) −1.86785e9 + 6.79842e8i −0.256927 + 0.0935139i
\(293\) 5.81364e9 + 1.02510e9i 0.788820 + 0.139090i 0.553524 0.832834i \(-0.313283\pi\)
0.235296 + 0.971924i \(0.424394\pi\)
\(294\) −4.51795e8 1.29236e9i −0.0604718 0.172980i
\(295\) 8.92450e9 7.48855e9i 1.17841 0.988803i
\(296\) 3.14483e9i 0.409666i
\(297\) −1.78725e9 2.30352e9i −0.229699 0.296050i
\(298\) −4.13712e8 −0.0524606
\(299\) 4.41353e6 + 5.25984e6i 0.000552206 + 0.000658093i
\(300\) −2.88746e7 + 1.52363e8i −0.00356477 + 0.0188103i
\(301\) −2.34980e9 + 1.33264e10i −0.286262 + 1.62348i
\(302\) −3.26145e9 8.96076e9i −0.392088 1.07725i
\(303\) 4.27320e9 + 2.54036e9i 0.506970 + 0.301387i
\(304\) 4.31546e8 + 2.44742e9i 0.0505281 + 0.286559i
\(305\) −7.00533e9 + 4.04453e9i −0.809523 + 0.467378i
\(306\) −5.07396e9 + 1.70148e9i −0.578710 + 0.194062i
\(307\) −2.23954e9 + 3.87900e9i −0.252119 + 0.436683i −0.964109 0.265507i \(-0.914461\pi\)
0.711990 + 0.702190i \(0.247794\pi\)
\(308\) 4.96347e8 1.36370e9i 0.0551547 0.151536i
\(309\) −1.09759e10 4.15424e9i −1.20395 0.455678i
\(310\) 5.29491e9 + 4.44295e9i 0.573339 + 0.481089i
\(311\) 4.06207e9 4.84099e9i 0.434216 0.517479i −0.503918 0.863752i \(-0.668109\pi\)
0.938134 + 0.346273i \(0.112553\pi\)
\(312\) −4.14356e7 5.06802e7i −0.00437276 0.00534835i
\(313\) −8.65906e9 3.15164e9i −0.902180 0.328367i −0.151054 0.988525i \(-0.548267\pi\)
−0.751126 + 0.660159i \(0.770489\pi\)
\(314\) −9.95828e9 5.74942e9i −1.02439 0.591433i
\(315\) −5.17777e9 6.50047e9i −0.525896 0.660241i
\(316\) −7.74121e7 1.34082e8i −0.00776355 0.0134469i
\(317\) 1.52319e10 2.68580e9i 1.50840 0.265972i 0.642540 0.766252i \(-0.277881\pi\)
0.865864 + 0.500280i \(0.166769\pi\)
\(318\) −7.77480e9 9.91917e7i −0.760293 0.00969989i
\(319\) −6.73033e8 + 2.44964e8i −0.0649940 + 0.0236559i
\(320\) 1.26585e9 + 2.23204e8i 0.120721 + 0.0212864i
\(321\) 1.65472e9 1.92168e9i 0.155849 0.180993i
\(322\) −2.20363e8 + 1.84907e8i −0.0204982 + 0.0172000i
\(323\) 1.09357e10i 1.00470i
\(324\) −6.78772e8 5.46801e9i −0.0615948 0.496192i
\(325\) −8.34724e6 −0.000748186
\(326\) −3.17054e7 3.77850e7i −0.00280713 0.00334541i
\(327\) 1.90558e9 + 1.64085e9i 0.166662 + 0.143509i
\(328\) −6.53692e8 + 3.70727e9i −0.0564778 + 0.320302i
\(329\) −3.24081e9 8.90406e9i −0.276612 0.759984i
\(330\) −3.93105e7 + 3.08122e9i −0.00331477 + 0.259817i
\(331\) 1.08256e9 + 6.13950e9i 0.0901861 + 0.511471i 0.996117 + 0.0880443i \(0.0280617\pi\)
−0.905930 + 0.423427i \(0.860827\pi\)
\(332\) 3.87008e9 2.23439e9i 0.318543 0.183911i
\(333\) −1.32600e10 5.21306e9i −1.07837 0.423952i
\(334\) −9.65667e8 + 1.67258e9i −0.0775964 + 0.134401i
\(335\) 1.64874e8 4.52989e8i 0.0130910 0.0359673i
\(336\) 2.12327e9 1.73597e9i 0.166590 0.136202i
\(337\) 1.73679e10 + 1.45734e10i 1.34657 + 1.12990i 0.979886 + 0.199557i \(0.0639501\pi\)
0.366680 + 0.930347i \(0.380494\pi\)
\(338\) −5.92998e9 + 7.06708e9i −0.454346 + 0.541468i
\(339\) 4.80506e8 1.26955e9i 0.0363831 0.0961281i
\(340\) 5.31508e9 + 1.93453e9i 0.397735 + 0.144764i
\(341\) −4.73580e9 2.73422e9i −0.350248 0.202216i
\(342\) −1.10348e10 2.23741e9i −0.806601 0.163546i
\(343\) 7.50048e9 + 1.29912e10i 0.541892 + 0.938584i
\(344\) 9.33832e9 1.64660e9i 0.666860 0.117585i
\(345\) 3.12131e8 5.25042e8i 0.0220323 0.0370611i
\(346\) 8.80744e9 3.20565e9i 0.614533 0.223672i
\(347\) −2.57563e10 4.54153e9i −1.77650 0.313245i −0.813264 0.581895i \(-0.802312\pi\)
−0.963238 + 0.268650i \(0.913423\pi\)
\(348\) −1.32990e9 2.52030e8i −0.0906777 0.0171845i
\(349\) −1.55726e9 + 1.30670e9i −0.104969 + 0.0880793i −0.693762 0.720205i \(-0.744048\pi\)
0.588793 + 0.808284i \(0.299603\pi\)
\(350\) 3.49712e8i 0.0233044i
\(351\) 2.82377e8 9.07002e7i 0.0186038 0.00597558i
\(352\) −1.01693e9 −0.0662400
\(353\) −4.86605e9 5.79914e9i −0.313385 0.373478i 0.586243 0.810135i \(-0.300606\pi\)
−0.899628 + 0.436658i \(0.856162\pi\)
\(354\) −1.64430e10 + 5.74828e9i −1.04705 + 0.366037i
\(355\) −2.32078e9 + 1.31618e10i −0.146124 + 0.828709i
\(356\) −1.61485e9 4.43677e9i −0.100539 0.276228i
\(357\) 1.05278e10 5.90045e9i 0.648133 0.363255i
\(358\) −3.41231e9 1.93521e10i −0.207738 1.17814i
\(359\) 6.51994e9 3.76429e9i 0.392524 0.226624i −0.290729 0.956805i \(-0.593898\pi\)
0.683253 + 0.730182i \(0.260565\pi\)
\(360\) −3.03949e9 + 4.96741e9i −0.180963 + 0.295747i
\(361\) −3.01208e9 + 5.21707e9i −0.177352 + 0.307183i
\(362\) −4.59990e9 + 1.26381e10i −0.267864 + 0.735950i
\(363\) 2.40401e9 + 1.47303e10i 0.138455 + 0.848369i
\(364\) 1.13088e8 + 9.48923e7i 0.00644187 + 0.00540537i
\(365\) −6.11809e9 + 7.29125e9i −0.344702 + 0.410800i
\(366\) 1.19365e10 1.94806e9i 0.665202 0.108562i
\(367\) −1.37482e9 5.00394e8i −0.0757848 0.0275834i 0.303850 0.952720i \(-0.401728\pi\)
−0.379634 + 0.925137i \(0.623950\pi\)
\(368\) 1.74571e8 + 1.00789e8i 0.00951880 + 0.00549568i
\(369\) −1.45479e10 8.90167e9i −0.784685 0.480138i
\(370\) 7.52937e9 + 1.30413e10i 0.401746 + 0.695845i
\(371\) 1.72681e10 3.04483e9i 0.911483 0.160719i
\(372\) −5.05269e9 9.01519e9i −0.263846 0.470764i
\(373\) 2.96376e10 1.07872e10i 1.53112 0.557280i 0.567221 0.823566i \(-0.308019\pi\)
0.963894 + 0.266285i \(0.0857963\pi\)
\(374\) −4.40691e9 7.77057e8i −0.225241 0.0397161i
\(375\) 6.64486e9 + 1.90076e10i 0.336017 + 0.961177i
\(376\) −5.08643e9 + 4.26803e9i −0.254485 + 0.213538i
\(377\) 7.28584e7i 0.00360674i
\(378\) 3.79993e9 + 1.18303e10i 0.186127 + 0.579468i
\(379\) −2.49091e10 −1.20726 −0.603631 0.797264i \(-0.706280\pi\)
−0.603631 + 0.797264i \(0.706280\pi\)
\(380\) 7.64920e9 + 9.11597e9i 0.366844 + 0.437188i
\(381\) −2.44663e9 + 1.29102e10i −0.116110 + 0.612680i
\(382\) 4.59706e9 2.60712e10i 0.215887 1.22436i
\(383\) −9.16902e9 2.51917e10i −0.426116 1.17074i −0.948151 0.317820i \(-0.897049\pi\)
0.522035 0.852924i \(-0.325173\pi\)
\(384\) −1.65198e9 9.82080e8i −0.0759765 0.0451671i
\(385\) −1.20669e9 6.84348e9i −0.0549229 0.311483i
\(386\) −1.09624e10 + 6.32915e9i −0.493806 + 0.285099i
\(387\) −8.53700e9 + 4.21040e10i −0.380594 + 1.87707i
\(388\) −1.04458e10 + 1.80927e10i −0.460910 + 0.798320i
\(389\) 6.46268e9 1.77561e10i 0.282237 0.775441i −0.714858 0.699270i \(-0.753508\pi\)
0.997095 0.0761704i \(-0.0242693\pi\)
\(390\) −2.93168e8 1.10960e8i −0.0126724 0.00479632i
\(391\) 6.79499e8 + 5.70167e8i 0.0290724 + 0.0243947i
\(392\) 1.39064e9 1.65730e9i 0.0588939 0.0701870i
\(393\) 1.50345e10 + 1.83888e10i 0.630257 + 0.770872i
\(394\) 2.60982e10 + 9.49898e9i 1.08299 + 0.394178i
\(395\) −6.42039e8 3.70682e8i −0.0263738 0.0152269i
\(396\) 1.68573e9 4.28783e9i 0.0685499 0.174364i
\(397\) −1.89328e10 3.27925e10i −0.762171 1.32012i −0.941729 0.336372i \(-0.890800\pi\)
0.179558 0.983747i \(-0.442533\pi\)
\(398\) 2.44915e10 4.31852e9i 0.976076 0.172108i
\(399\) 2.53889e10 + 3.23915e8i 1.00173 + 0.0127802i
\(400\) −2.30279e8 + 8.38145e7i −0.00899526 + 0.00327401i
\(401\) 1.86431e10 + 3.28728e9i 0.721008 + 0.127133i 0.522099 0.852885i \(-0.325149\pi\)
0.198909 + 0.980018i \(0.436260\pi\)
\(402\) −4.70300e8 + 5.46178e8i −0.0180082 + 0.0209136i
\(403\) 4.26134e8 3.57569e8i 0.0161557 0.0135563i
\(404\) 7.85586e9i 0.294896i
\(405\) −1.59064e10 2.10501e10i −0.591222 0.782411i
\(406\) 3.05244e9 0.112342
\(407\) −7.65799e9 9.12644e9i −0.279086 0.332601i
\(408\) −6.40850e9 5.51820e9i −0.231268 0.199139i
\(409\) −2.30423e9 + 1.30680e10i −0.0823443 + 0.466998i 0.915554 + 0.402195i \(0.131753\pi\)
−0.997898 + 0.0648022i \(0.979358\pi\)
\(410\) 6.16519e9 + 1.69387e10i 0.218178 + 0.599440i
\(411\) 4.35856e8 3.41631e10i 0.0152748 1.19726i
\(412\) −3.22039e9 1.82637e10i −0.111768 0.633870i
\(413\) 3.40186e10 1.96407e10i 1.16927 0.675081i
\(414\) −7.14352e8 + 5.68997e8i −0.0243170 + 0.0193691i
\(415\) 1.06992e10 1.85316e10i 0.360711 0.624770i
\(416\) 3.53812e7 9.72089e7i 0.00118140 0.00324588i
\(417\) −9.45117e9 + 7.72717e9i −0.312566 + 0.255550i
\(418\) −7.21210e9 6.05167e9i −0.236242 0.198230i
\(419\) 3.02319e10 3.60290e10i 0.980865 1.16895i −0.00475730 0.999989i \(-0.501514\pi\)
0.985623 0.168961i \(-0.0540413\pi\)
\(420\) 4.64872e9 1.22824e10i 0.149395 0.394718i
\(421\) −2.18560e10 7.95494e9i −0.695733 0.253226i −0.0301450 0.999546i \(-0.509597\pi\)
−0.665588 + 0.746319i \(0.731819\pi\)
\(422\) 1.53187e9 + 8.84427e8i 0.0483029 + 0.0278877i
\(423\) −9.56430e9 2.85216e10i −0.298739 0.890867i
\(424\) −6.14355e9 1.06409e10i −0.190089 0.329243i
\(425\) −1.06197e9 + 1.87253e8i −0.0325503 + 0.00573950i
\(426\) 1.02113e10 1.71766e10i 0.310056 0.521553i
\(427\) −2.56295e10 + 9.32837e9i −0.770954 + 0.280604i
\(428\) 3.94652e9 + 6.95878e8i 0.117609 + 0.0207376i
\(429\) 2.43660e8 + 4.61764e7i 0.00719375 + 0.00136330i
\(430\) 3.47827e10 2.91861e10i 1.01739 0.853695i
\(431\) 1.75369e10i 0.508211i 0.967177 + 0.254105i \(0.0817810\pi\)
−0.967177 + 0.254105i \(0.918219\pi\)
\(432\) 6.87931e9 5.33752e9i 0.197520 0.153251i
\(433\) −4.92821e10 −1.40197 −0.700983 0.713178i \(-0.747255\pi\)
−0.700983 + 0.713178i \(0.747255\pi\)
\(434\) 1.49805e10 + 1.78531e10i 0.422249 + 0.503217i
\(435\) −6.11835e9 + 2.13890e9i −0.170874 + 0.0597358i
\(436\) −6.90047e8 + 3.91345e9i −0.0190956 + 0.108296i
\(437\) 6.38280e8 + 1.75366e9i 0.0175019 + 0.0480861i
\(438\) 1.24142e10 6.95771e9i 0.337304 0.189047i
\(439\) −2.23872e9 1.26964e10i −0.0602756 0.341840i 0.939724 0.341933i \(-0.111082\pi\)
−1.00000 9.29709e-5i \(0.999970\pi\)
\(440\) −4.21710e9 + 2.43474e9i −0.112513 + 0.0649594i
\(441\) 4.68270e9 + 8.61080e9i 0.123806 + 0.227661i
\(442\) 2.27605e8 3.94224e8i 0.00596339 0.0103289i
\(443\) −1.94414e10 + 5.34149e10i −0.504793 + 1.38691i 0.381751 + 0.924265i \(0.375321\pi\)
−0.886545 + 0.462643i \(0.846901\pi\)
\(444\) −3.62655e9 2.22213e10i −0.0933172 0.571790i
\(445\) −1.73192e10 1.45325e10i −0.441659 0.370596i
\(446\) 5.48690e8 6.53903e8i 0.0138672 0.0165262i
\(447\) 2.92328e9 4.77084e8i 0.0732217 0.0119499i
\(448\) 4.07262e9 + 1.48231e9i 0.101102 + 0.0367983i
\(449\) −8.87105e9 5.12170e9i −0.218268 0.126017i 0.386880 0.922130i \(-0.373553\pi\)
−0.605148 + 0.796113i \(0.706886\pi\)
\(450\) 2.83249e7 1.10989e9i 0.000690746 0.0270665i
\(451\) −7.13056e9 1.23505e10i −0.172353 0.298523i
\(452\) 2.11250e9 3.72491e8i 0.0506108 0.00892404i
\(453\) 3.33787e10 + 5.95555e10i 0.792641 + 1.41426i
\(454\) 3.66910e10 1.33544e10i 0.863647 0.314342i
\(455\) 6.96156e8 + 1.22751e8i 0.0162428 + 0.00286405i
\(456\) −5.87160e9 1.67957e10i −0.135799 0.388454i
\(457\) −1.81131e10 + 1.51987e10i −0.415268 + 0.348451i −0.826359 0.563143i \(-0.809592\pi\)
0.411092 + 0.911594i \(0.365148\pi\)
\(458\) 3.38136e9i 0.0768475i
\(459\) 3.38903e10 1.78738e10i 0.763528 0.402685i
\(460\) 9.65239e8 0.0215578
\(461\) −3.27293e10 3.90053e10i −0.724659 0.863615i 0.270416 0.962744i \(-0.412839\pi\)
−0.995075 + 0.0991290i \(0.968394\pi\)
\(462\) −1.93458e9 + 1.02083e10i −0.0424638 + 0.224070i
\(463\) −1.23618e10 + 7.01075e10i −0.269004 + 1.52560i 0.488381 + 0.872630i \(0.337588\pi\)
−0.757385 + 0.652968i \(0.773524\pi\)
\(464\) −7.31570e8 2.00997e9i −0.0157828 0.0433629i
\(465\) −4.25372e10 2.52878e10i −0.909823 0.540878i
\(466\) −1.55017e9 8.79147e9i −0.0328728 0.186431i
\(467\) −6.07992e10 + 3.51025e10i −1.27829 + 0.738023i −0.976534 0.215361i \(-0.930907\pi\)
−0.301759 + 0.953384i \(0.597574\pi\)
\(468\) 3.51226e8 + 3.10323e8i 0.00732156 + 0.00646889i
\(469\) 8.12695e8 1.40763e9i 0.0167972 0.0290936i
\(470\) −1.08743e10 + 2.98770e10i −0.222850 + 0.612274i
\(471\) 7.69951e10 + 2.91415e10i 1.56451 + 0.592146i
\(472\) −2.10861e10 1.76934e10i −0.424844 0.356486i
\(473\) −2.30906e10 + 2.75183e10i −0.461308 + 0.549765i
\(474\) 7.01612e8 + 8.58148e8i 0.0138990 + 0.0170000i
\(475\) −2.13192e9 7.75954e8i −0.0418790 0.0152427i
\(476\) 1.65162e10 + 9.53564e9i 0.321723 + 0.185747i
\(477\) 5.50509e10 8.26485e9i 1.06339 0.159647i
\(478\) 2.24450e10 + 3.88759e10i 0.429941 + 0.744679i
\(479\) −1.40431e10 + 2.47618e9i −0.266760 + 0.0470371i −0.305428 0.952215i \(-0.598800\pi\)
0.0386679 + 0.999252i \(0.487689\pi\)
\(480\) −9.20188e9 1.17399e8i −0.173345 0.00221156i
\(481\) 1.13884e9 4.14504e8i 0.0212756 0.00774370i
\(482\) −4.97482e10 8.77195e9i −0.921700 0.162520i
\(483\) 1.34385e9 1.56067e9i 0.0246924 0.0286762i
\(484\) −1.80675e10 + 1.51604e10i −0.329243 + 0.276268i
\(485\) 1.00038e11i 1.80800i
\(486\) 1.11018e10 + 3.78541e10i 0.198998 + 0.678528i
\(487\) 3.07686e10 0.547005 0.273503 0.961871i \(-0.411818\pi\)
0.273503 + 0.961871i \(0.411818\pi\)
\(488\) 1.22851e10 + 1.46408e10i 0.216620 + 0.258158i
\(489\) 2.67603e8 + 2.30426e8i 0.00468010 + 0.00402992i
\(490\) 1.79891e9 1.02021e10i 0.0312050 0.176973i
\(491\) −1.40875e9 3.87051e9i −0.0242387 0.0665951i 0.926983 0.375103i \(-0.122393\pi\)
−0.951222 + 0.308508i \(0.900170\pi\)
\(492\) 3.43822e8 2.69493e10i 0.00586777 0.459925i
\(493\) −1.63443e9 9.26932e9i −0.0276681 0.156913i
\(494\) 8.29407e8 4.78858e8i 0.0139271 0.00804080i
\(495\) −3.27543e9 2.18171e10i −0.0545566 0.363393i
\(496\) 8.16558e9 1.41432e10i 0.134915 0.233680i
\(497\) −1.54125e10 + 4.23454e10i −0.252607 + 0.694033i
\(498\) −2.47693e10 + 2.02511e10i −0.402713 + 0.329254i
\(499\) −6.20527e10 5.20684e10i −1.00083 0.839792i −0.0137269 0.999906i \(-0.504370\pi\)
−0.987099 + 0.160113i \(0.948814\pi\)
\(500\) −2.04531e10 + 2.43750e10i −0.327249 + 0.390000i
\(501\) 4.89459e9 1.29320e10i 0.0776900 0.205265i
\(502\) 7.10491e10 + 2.58597e10i 1.11878 + 0.407202i
\(503\) 1.09420e10 + 6.31738e9i 0.170933 + 0.0986881i 0.583026 0.812454i \(-0.301869\pi\)
−0.412093 + 0.911142i \(0.635202\pi\)
\(504\) −1.30011e10 + 1.47148e10i −0.201492 + 0.228051i
\(505\) 1.88086e10 + 3.25774e10i 0.289195 + 0.500900i
\(506\) −7.52047e8 + 1.32606e8i −0.0114721 + 0.00202284i
\(507\) 3.37515e10 5.67741e10i 0.510812 0.859248i
\(508\) −1.95122e10 + 7.10186e9i −0.292989 + 0.106639i
\(509\) 5.12441e10 + 9.03572e9i 0.763436 + 0.134614i 0.541791 0.840513i \(-0.317746\pi\)
0.221645 + 0.975127i \(0.428857\pi\)
\(510\) −3.97871e10 7.54010e9i −0.588114 0.111454i
\(511\) −2.45843e10 + 2.06287e10i −0.360557 + 0.302544i
\(512\) 3.03700e9i 0.0441942i
\(513\) 8.05515e10 + 3.08439e9i 1.16307 + 0.0445349i
\(514\) −6.08658e10 −0.872009
\(515\) −5.70818e10 6.80274e10i −0.811462 0.967063i
\(516\) −6.40855e10 + 2.24036e10i −0.903984 + 0.316023i
\(517\) 4.36798e9 2.47720e10i 0.0611390 0.346737i
\(518\) 1.73659e10 + 4.77123e10i 0.241200 + 0.662691i
\(519\) −5.85364e10 + 3.28076e10i −0.806783 + 0.452173i
\(520\) −8.60167e7 4.87825e8i −0.00117644 0.00667192i
\(521\) −3.25987e10 + 1.88208e10i −0.442434 + 0.255440i −0.704630 0.709575i \(-0.748887\pi\)
0.262195 + 0.965015i \(0.415554\pi\)
\(522\) 9.68764e9 + 2.47232e8i 0.130478 + 0.00332984i
\(523\) 1.37783e10 2.38647e10i 0.184157 0.318969i −0.759135 0.650933i \(-0.774378\pi\)
0.943292 + 0.331964i \(0.107711\pi\)
\(524\) −1.28377e10 + 3.52712e10i −0.170279 + 0.467837i
\(525\) 4.03281e8 + 2.47106e9i 0.00530848 + 0.0325271i
\(526\) −7.10507e10 5.96186e10i −0.928165 0.778823i
\(527\) 4.61930e10 5.50507e10i 0.598872 0.713708i
\(528\) 7.18560e9 1.17270e9i 0.0924543 0.0150887i
\(529\) −7.34460e10 2.67322e10i −0.937876 0.341359i
\(530\) −5.09533e10 2.94179e10i −0.645757 0.372828i
\(531\) 1.09557e11 5.95789e10i 1.37804 0.749401i
\(532\) 2.00620e10 + 3.47484e10i 0.250454 + 0.433799i
\(533\) 1.42868e9 2.51915e8i 0.0177022 0.00312137i
\(534\) 1.65269e10 + 2.94879e10i 0.203248 + 0.362643i
\(535\) 1.80319e10 6.56306e9i 0.220103 0.0801109i
\(536\) −1.12167e9 1.97781e8i −0.0135896 0.00239621i
\(537\) 4.64278e10 + 1.32807e11i 0.558317 + 1.59707i
\(538\) 2.23467e9 1.87511e9i 0.0266738 0.0223819i
\(539\) 8.19592e9i 0.0971052i
\(540\) 1.57486e10 3.86046e10i 0.185211 0.454009i
\(541\) 4.57596e10 0.534186 0.267093 0.963671i \(-0.413937\pi\)
0.267093 + 0.963671i \(0.413937\pi\)
\(542\) −2.60279e10 3.10189e10i −0.301608 0.359442i
\(543\) 1.79288e10 9.46051e10i 0.206229 1.08822i
\(544\) 2.32064e9 1.31610e10i 0.0264979 0.150277i
\(545\) 6.50807e9 + 1.78808e10i 0.0737677 + 0.202675i
\(546\) −9.08506e8 5.40095e8i −0.0102225 0.00607715i
\(547\) 2.44999e10 + 1.38946e11i 0.273662 + 1.55201i 0.743180 + 0.669091i \(0.233317\pi\)
−0.469518 + 0.882923i \(0.655572\pi\)
\(548\) 4.67572e10 2.69953e10i 0.518473 0.299340i
\(549\) −8.20967e10 + 2.75299e10i −0.903725 + 0.303051i
\(550\) 4.64182e8 8.03987e8i 0.00507268 0.00878615i
\(551\) 6.77287e9 1.86083e10i 0.0734795 0.201883i
\(552\) −1.34975e9 5.10860e8i −0.0145377 0.00550231i
\(553\) −1.91488e9 1.60677e9i −0.0204758 0.0171812i
\(554\) −4.74167e10 + 5.65091e10i −0.503376 + 0.599900i
\(555\) −6.82412e10 8.34664e10i −0.719242 0.879711i
\(556\) −1.81281e10 6.59810e9i −0.189694 0.0690430i
\(557\) 1.33034e11 + 7.68070e10i 1.38210 + 0.797958i 0.992408 0.122986i \(-0.0392470\pi\)
0.389695 + 0.920944i \(0.372580\pi\)
\(558\) 4.60983e10 + 5.78744e10i 0.475497 + 0.596966i
\(559\) −1.82712e9 3.16467e9i −0.0187120 0.0324101i
\(560\) 2.04377e10 3.60371e9i 0.207816 0.0366436i
\(561\) 3.20352e10 + 4.08708e8i 0.323427 + 0.00412631i
\(562\) −5.44498e10 + 1.98181e10i −0.545822 + 0.198663i
\(563\) 8.51046e10 + 1.50062e10i 0.847071 + 0.149361i 0.580304 0.814400i \(-0.302934\pi\)
0.266766 + 0.963761i \(0.414045\pi\)
\(564\) 3.10188e10 3.60233e10i 0.306555 0.356014i
\(565\) 7.86849e9 6.60244e9i 0.0772142 0.0647904i
\(566\) 1.34268e11i 1.30830i
\(567\) −4.04927e10 7.92107e10i −0.391782 0.766394i
\(568\) 3.15775e10 0.303378
\(569\) −7.55986e10 9.00949e10i −0.721215 0.859510i 0.273534 0.961862i \(-0.411808\pi\)
−0.994748 + 0.102352i \(0.967363\pi\)
\(570\) −6.45614e10 5.55923e10i −0.611609 0.526641i
\(571\) 2.33331e10 1.32329e11i 0.219497 1.24483i −0.653434 0.756984i \(-0.726672\pi\)
0.872930 0.487845i \(-0.162217\pi\)
\(572\) 1.34036e8 + 3.68262e8i 0.00125210 + 0.00344011i
\(573\) −2.41791e9 + 1.89520e11i −0.0224296 + 1.75807i
\(574\) 1.05541e10 + 5.98553e10i 0.0972240 + 0.551385i
\(575\) −1.59368e8 + 9.20112e7i −0.00145791 + 0.000841723i
\(576\) 1.28054e10 + 5.03433e9i 0.116333 + 0.0457353i
\(577\) 2.60646e10 4.51452e10i 0.235151 0.407294i −0.724165 0.689626i \(-0.757775\pi\)
0.959317 + 0.282332i \(0.0911081\pi\)
\(578\) −6.87965e9 + 1.89017e10i −0.0616389 + 0.169351i
\(579\) 7.01615e10 5.73632e10i 0.624287 0.510410i
\(580\) −7.84604e9 6.58361e9i −0.0693327 0.0581771i
\(581\) 4.63773e10 5.52703e10i 0.407006 0.485051i
\(582\) 5.29459e10 1.39889e11i 0.461467 1.21924i
\(583\) 4.37408e10 + 1.59203e10i 0.378627 + 0.137809i
\(584\) 1.94756e10 + 1.12443e10i 0.167433 + 0.0966673i
\(585\) 2.19947e9 + 4.45965e8i 0.0187800 + 0.00380783i
\(586\) −3.33943e10 5.78405e10i −0.283192 0.490503i
\(587\) −2.02163e10 + 3.56468e9i −0.170275 + 0.0300240i −0.258135 0.966109i \(-0.583108\pi\)
0.0878608 + 0.996133i \(0.471997\pi\)
\(588\) −7.91506e9 + 1.33141e10i −0.0662132 + 0.111379i
\(589\) 1.42076e11 5.17113e10i 1.18048 0.429660i
\(590\) −1.29804e11 2.28879e10i −1.07122 0.188885i
\(591\) −1.95363e11 3.70236e10i −1.60138 0.303479i
\(592\) 2.72556e10 2.28702e10i 0.221906 0.186201i
\(593\) 1.69568e11i 1.37128i −0.727943 0.685638i \(-0.759523\pi\)
0.727943 0.685638i \(-0.240477\pi\)
\(594\) −6.96667e9 + 3.22416e10i −0.0559602 + 0.258983i
\(595\) 9.13212e10 0.728625
\(596\) 3.00864e9 + 3.58556e9i 0.0238443 + 0.0284166i
\(597\) −1.68076e11 + 5.87576e10i −1.32315 + 0.462559i
\(598\) 1.34894e7 7.65023e7i 0.000105485 0.000598232i
\(599\) −2.99353e10 8.22467e10i −0.232529 0.638868i 0.767469 0.641086i \(-0.221516\pi\)
−0.999998 + 0.00221858i \(0.999294\pi\)
\(600\) 1.53049e9 8.57784e8i 0.0118093 0.00661870i
\(601\) −6.33839e9 3.59468e10i −0.0485826 0.275526i 0.950833 0.309704i \(-0.100230\pi\)
−0.999416 + 0.0341779i \(0.989119\pi\)
\(602\) 1.32585e11 7.65482e10i 1.00951 0.582840i
\(603\) 2.69329e9 4.40162e9i 0.0203711 0.0332922i
\(604\) −5.39429e10 + 9.34318e10i −0.405309 + 0.702016i
\(605\) −3.86267e10 + 1.06126e11i −0.288314 + 0.792137i
\(606\) −9.05921e9 5.55093e10i −0.0671738 0.411600i
\(607\) 7.27875e10 + 6.10760e10i 0.536169 + 0.449900i 0.870225 0.492654i \(-0.163973\pi\)
−0.334056 + 0.942553i \(0.608417\pi\)
\(608\) 1.80730e10 2.15385e10i 0.132256 0.157616i
\(609\) −2.15685e10 + 3.52001e9i −0.156802 + 0.0255903i
\(610\) 8.59981e10 + 3.13007e10i 0.621111 + 0.226066i
\(611\) 2.21600e9 + 1.27941e9i 0.0159003 + 0.00918005i
\(612\) 5.16457e10 + 3.16013e10i 0.368153 + 0.225268i
\(613\) 3.10433e10 + 5.37686e10i 0.219850 + 0.380791i 0.954762 0.297371i \(-0.0961099\pi\)
−0.734912 + 0.678162i \(0.762777\pi\)
\(614\) 4.99052e10 8.79963e9i 0.351133 0.0619143i
\(615\) −6.30965e10 1.12579e11i −0.441067 0.786968i
\(616\) −1.54285e10 + 5.61553e9i −0.107152 + 0.0390003i
\(617\) 2.13904e11 + 3.77171e10i 1.47597 + 0.260254i 0.852968 0.521964i \(-0.174800\pi\)
0.623005 + 0.782218i \(0.285911\pi\)
\(618\) 4.38165e10 + 1.25337e11i 0.300389 + 0.859263i
\(619\) −5.01793e10 + 4.21054e10i −0.341792 + 0.286797i −0.797484 0.603340i \(-0.793836\pi\)
0.455692 + 0.890137i \(0.349392\pi\)
\(620\) 7.82005e10i 0.529228i
\(621\) 4.39144e9 4.84430e9i 0.0295284 0.0325735i
\(622\) −7.14965e10 −0.477665
\(623\) −4.90001e10 5.83960e10i −0.325270 0.387642i
\(624\) −1.37903e8 + 7.27677e8i −0.000909569 + 0.00479954i
\(625\) −2.54432e10 + 1.44296e11i −0.166745 + 0.945655i
\(626\) 3.56567e10 + 9.79661e10i 0.232190 + 0.637938i
\(627\) 5.79391e10 + 3.44441e10i 0.374888 + 0.222866i
\(628\) 2.25907e10 + 1.28118e11i 0.145241 + 0.823705i
\(629\) 1.35589e11 7.82823e10i 0.866207 0.500105i
\(630\) −1.86839e10 + 9.21481e10i −0.118606 + 0.584957i
\(631\) 7.02657e10 1.21704e11i 0.443227 0.767691i −0.554700 0.832050i \(-0.687167\pi\)
0.997927 + 0.0643593i \(0.0205004\pi\)
\(632\) −5.99095e8 + 1.64600e9i −0.00375515 + 0.0103172i
\(633\) −1.18441e10 4.48281e9i −0.0737711 0.0279213i
\(634\) −1.34049e11 1.12480e11i −0.829670 0.696175i
\(635\) −6.39116e10 + 7.61669e10i −0.393084 + 0.468459i
\(636\) 5.56811e10 + 6.81040e10i 0.340314 + 0.416241i
\(637\) −7.83453e8 2.85154e8i −0.00475834 0.00173189i
\(638\) 7.01756e9 + 4.05159e9i 0.0423549 + 0.0244536i
\(639\) −5.23448e10 + 1.33145e11i −0.313957 + 0.798583i
\(640\) −7.27121e9 1.25941e10i −0.0433398 0.0750668i
\(641\) −2.48613e11 + 4.38372e10i −1.47262 + 0.259663i −0.851626 0.524150i \(-0.824383\pi\)
−0.620997 + 0.783813i \(0.713272\pi\)
\(642\) −2.86885e10 3.66011e8i −0.168876 0.00215453i
\(643\) 5.79071e10 2.10765e10i 0.338757 0.123297i −0.167040 0.985950i \(-0.553421\pi\)
0.505797 + 0.862653i \(0.331199\pi\)
\(644\) 3.20510e9 + 5.65146e8i 0.0186337 + 0.00328562i
\(645\) −2.12117e11 + 2.46339e11i −1.22556 + 1.42329i
\(646\) 9.47780e10 7.95282e10i 0.544224 0.456658i
\(647\) 2.86294e11i 1.63378i −0.576791 0.816892i \(-0.695695\pi\)
0.576791 0.816892i \(-0.304305\pi\)
\(648\) −4.24539e10 + 4.56479e10i −0.240779 + 0.258893i
\(649\) 1.04278e11 0.587780
\(650\) 6.07038e7 + 7.23439e7i 0.000340065 + 0.000405274i
\(651\) −1.26440e11 1.08874e11i −0.703980 0.606181i
\(652\) −9.69039e7 + 5.49569e8i −0.000536230 + 0.00304111i
\(653\) 1.01407e11 + 2.78614e11i 0.557720 + 1.53232i 0.822935 + 0.568135i \(0.192335\pi\)
−0.265215 + 0.964189i \(0.585443\pi\)
\(654\) 3.62944e8 2.84481e10i 0.00198394 0.155504i
\(655\) 3.12102e10 + 1.77002e11i 0.169563 + 0.961640i
\(656\) 3.68841e10 2.12950e10i 0.199170 0.114991i
\(657\) −7.96949e10 + 6.34788e10i −0.427729 + 0.340696i
\(658\) −5.36016e10 + 9.28406e10i −0.285939 + 0.495261i
\(659\) 3.98751e9 1.09556e10i 0.0211427 0.0580890i −0.928672 0.370901i \(-0.879049\pi\)
0.949815 + 0.312812i \(0.101271\pi\)
\(660\) 2.69902e10 2.20669e10i 0.142243 0.116296i
\(661\) −1.90914e11 1.60196e11i −1.00007 0.839160i −0.0130777 0.999914i \(-0.504163\pi\)
−0.986994 + 0.160754i \(0.948607\pi\)
\(662\) 4.53371e10 5.40307e10i 0.236060 0.281325i
\(663\) −1.15364e9 + 3.04805e9i −0.00597059 + 0.0157749i
\(664\) −4.75095e10 1.72920e10i −0.244404 0.0889558i
\(665\) 1.66390e11 + 9.60653e10i 0.850826 + 0.491225i
\(666\) 5.12502e10 + 1.52833e11i 0.260495 + 0.776819i
\(667\) −8.03114e8 1.39103e9i −0.00405764 0.00702804i
\(668\) 2.15186e10 3.79431e9i 0.108071 0.0190558i
\(669\) −3.12296e9 + 5.25320e9i −0.0155906 + 0.0262252i
\(670\) −5.12498e9 + 1.86534e9i −0.0254327 + 0.00925676i
\(671\) −7.13039e10 1.25728e10i −0.351741 0.0620215i
\(672\) −3.04864e10 5.77752e9i −0.149496 0.0283311i
\(673\) −1.49719e11 + 1.25629e11i −0.729820 + 0.612392i −0.930083 0.367351i \(-0.880265\pi\)
0.200263 + 0.979742i \(0.435820\pi\)
\(674\) 2.56507e11i 1.24296i
\(675\) 1.07976e9 + 7.87514e9i 0.00520132 + 0.0379353i
\(676\) 1.04374e11 0.499809
\(677\) 5.25533e9 + 6.26306e9i 0.0250176 + 0.0298148i 0.778408 0.627758i \(-0.216027\pi\)
−0.753391 + 0.657573i \(0.771583\pi\)
\(678\) −1.44973e10 + 5.06810e9i −0.0686071 + 0.0239843i
\(679\) −5.85722e10 + 3.32180e11i −0.275558 + 1.56277i
\(680\) −2.18867e10 6.01332e10i −0.102363 0.281241i
\(681\) −2.43858e11 + 1.36673e11i −1.13383 + 0.635471i
\(682\) 1.07433e10 + 6.09284e10i 0.0496593 + 0.281632i
\(683\) −2.10590e11 + 1.21584e11i −0.967730 + 0.558719i −0.898543 0.438885i \(-0.855374\pi\)
−0.0691862 + 0.997604i \(0.522040\pi\)
\(684\) 6.08571e10 + 1.11907e11i 0.278027 + 0.511251i
\(685\) 1.29265e11 2.23893e11i 0.587107 1.01690i
\(686\) 5.80464e10 1.59481e11i 0.262107 0.720134i
\(687\) −3.89932e9 2.38926e10i −0.0175050 0.107260i
\(688\) −8.21819e10 6.89588e10i −0.366794 0.307777i
\(689\) −3.04367e9 + 3.62730e9i −0.0135058 + 0.0160956i
\(690\) −6.82035e9 + 1.11309e9i −0.0300892 + 0.00491061i
\(691\) −1.92368e11 7.00161e10i −0.843761 0.307104i −0.116267 0.993218i \(-0.537093\pi\)
−0.727494 + 0.686114i \(0.759315\pi\)
\(692\) −9.18331e10 5.30199e10i −0.400475 0.231214i
\(693\) 1.89775e9 7.43622e10i 0.00822823 0.322418i
\(694\) 1.47947e11 + 2.56252e11i 0.637778 + 1.10466i
\(695\) −9.09726e10 + 1.60409e10i −0.389916 + 0.0687528i
\(696\) 7.48712e9 + 1.33588e10i 0.0319064 + 0.0569285i
\(697\) 1.76111e11 6.40991e10i 0.746199 0.271594i
\(698\) 2.26498e10 + 3.99377e9i 0.0954208 + 0.0168253i
\(699\) 2.10916e10 + 6.03327e10i 0.0883489 + 0.252722i
\(700\) −3.03089e9 + 2.54322e9i −0.0126234 + 0.0105923i
\(701\) 6.11409e10i 0.253198i 0.991954 + 0.126599i \(0.0404061\pi\)
−0.991954 + 0.126599i \(0.959594\pi\)
\(702\) −2.83961e9 1.78770e9i −0.0116926 0.00736118i
\(703\) 3.29396e11 1.34864
\(704\) 7.39543e9 + 8.81353e9i 0.0301074 + 0.0358805i
\(705\) 4.23843e10 2.23650e11i 0.171573 0.905343i
\(706\) −1.48725e10 + 8.43463e10i −0.0598640 + 0.339506i
\(707\) 4.33804e10 + 1.19187e11i 0.173626 + 0.477034i
\(708\) 1.69398e11 + 1.00705e11i 0.674178 + 0.400790i
\(709\) 1.73375e9 + 9.83258e9i 0.00686122 + 0.0389119i 0.988046 0.154158i \(-0.0492666\pi\)
−0.981185 + 0.193070i \(0.938155\pi\)
\(710\) 1.30948e11 7.56030e10i 0.515307 0.297513i
\(711\) −5.94717e9 5.25457e9i −0.0232719 0.0205617i
\(712\) −2.67089e10 + 4.62612e10i −0.103929 + 0.180010i
\(713\) 4.19442e9 1.15241e10i 0.0162298 0.0445911i
\(714\) −1.27699e11 4.83324e10i −0.491356 0.185971i
\(715\) 1.43753e9 + 1.20623e9i 0.00550039 + 0.00461537i
\(716\) −1.42906e11 + 1.70309e11i −0.543749 + 0.648014i
\(717\) −2.03427e11 2.48813e11i −0.769718 0.941448i
\(718\) −8.00394e10 2.91320e10i −0.301166 0.109616i
\(719\) −1.16250e11 6.71170e10i −0.434989 0.251141i 0.266481 0.963840i \(-0.414139\pi\)
−0.701470 + 0.712699i \(0.747472\pi\)
\(720\) 6.51556e10 9.78188e9i 0.242450 0.0363993i
\(721\) −1.49712e11 2.59308e11i −0.554006 0.959567i
\(722\) 6.71200e10 1.18351e10i 0.247004 0.0435534i
\(723\) 3.61635e11 + 4.61378e9i 1.32348 + 0.0168851i
\(724\) 1.42984e11 5.20419e10i 0.520395 0.189408i
\(725\) 1.92302e9 + 3.39080e8i 0.00696036 + 0.00122730i
\(726\) 1.10182e11 1.27958e11i 0.396610 0.460598i
\(727\) −3.18134e11 + 2.66946e11i −1.13887 + 0.955622i −0.999401 0.0346055i \(-0.988983\pi\)
−0.139464 + 0.990227i \(0.544538\pi\)
\(728\) 1.67020e9i 0.00594625i
\(729\) −1.22097e11 2.54674e11i −0.432311 0.901724i
\(730\) 1.07684e11 0.379194
\(731\) −3.03446e11 3.61633e11i −1.06270 1.26648i
\(732\) −1.03690e11 8.92846e10i −0.361153 0.310980i
\(733\) −6.37458e10 + 3.61520e11i −0.220819 + 1.25232i 0.649701 + 0.760190i \(0.274894\pi\)
−0.870519 + 0.492134i \(0.836217\pi\)
\(734\) 5.66132e9 + 1.55543e10i 0.0195044 + 0.0535880i
\(735\) −9.46171e8 + 7.41624e10i −0.00324206 + 0.254117i
\(736\) −3.96021e8 2.24595e9i −0.00134960 0.00765399i
\(737\) 3.73677e9 2.15742e9i 0.0126656 0.00731249i
\(738\) 2.86480e10 + 1.90820e11i 0.0965758 + 0.643276i
\(739\) 2.31041e11 4.00175e11i 0.774661 1.34175i −0.160324 0.987064i \(-0.551254\pi\)
0.934985 0.354688i \(-0.115413\pi\)
\(740\) 5.82700e10 1.60096e11i 0.194320 0.533891i
\(741\) −5.30836e9 + 4.34006e9i −0.0176071 + 0.0143954i
\(742\) −1.51968e11 1.27516e11i −0.501344 0.420678i
\(743\) −2.16327e11 + 2.57808e11i −0.709832 + 0.845944i −0.993601 0.112948i \(-0.963971\pi\)
0.283769 + 0.958893i \(0.408415\pi\)
\(744\) −4.13881e10 + 1.09352e11i −0.135078 + 0.356890i
\(745\) 2.10611e10 + 7.66561e9i 0.0683684 + 0.0248841i
\(746\) −3.09025e11 1.78415e11i −0.997787 0.576072i
\(747\) 1.51666e11 1.71657e11i 0.487086 0.551288i
\(748\) 2.53138e10 + 4.38448e10i 0.0808633 + 0.140059i
\(749\) 6.37180e10 1.12352e10i 0.202458 0.0356988i
\(750\) 1.16412e11 1.95819e11i 0.367920 0.618885i
\(751\) 3.30825e11 1.20410e11i 1.04001 0.378534i 0.235128 0.971965i \(-0.424449\pi\)
0.804885 + 0.593431i \(0.202227\pi\)
\(752\) 7.39803e10 + 1.30447e10i 0.231337 + 0.0407909i
\(753\) −5.31852e11 1.00792e11i −1.65429 0.313506i
\(754\) −6.31450e8 + 5.29849e8i −0.00195368 + 0.00163933i
\(755\) 5.16602e11i 1.58990i