Properties

Label 162.11.d.d.107.4
Level $162$
Weight $11$
Character 162.107
Analytic conductor $102.928$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 162.d (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(102.927874933\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17318914560000.97
Defining polynomial: \( x^{8} - 4x^{7} - 82x^{6} + 260x^{5} + 2477x^{4} - 5392x^{3} - 31616x^{2} + 34356x + 161859 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{24}\cdot 3^{16} \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.4
Root \(-2.88503 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 162.107
Dual form 162.11.d.d.53.4

$q$-expansion

\(f(q)\) \(=\) \(q+(19.5959 + 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(3144.08 - 1815.24i) q^{5} +(11613.3 - 20114.8i) q^{7} +11585.2i q^{8} +O(q^{10})\) \(q+(19.5959 + 11.3137i) q^{2} +(256.000 + 443.405i) q^{4} +(3144.08 - 1815.24i) q^{5} +(11613.3 - 20114.8i) q^{7} +11585.2i q^{8} +82148.2 q^{10} +(54076.9 + 31221.3i) q^{11} +(85080.3 + 147363. i) q^{13} +(455145. - 262778. i) q^{14} +(-131072. + 227023. i) q^{16} +2.66626e6i q^{17} +766825. q^{19} +(1.60977e6 + 929401. i) q^{20} +(706458. + 1.22362e6i) q^{22} +(-1.21526e6 + 701633. i) q^{23} +(1.70736e6 - 2.95723e6i) q^{25} +3.85029e6i q^{26} +1.18920e7 q^{28} +(4.18503e6 + 2.41623e6i) q^{29} +(2.09149e7 + 3.62256e7i) q^{31} +(-5.13695e6 + 2.96582e6i) q^{32} +(-3.01653e7 + 5.22478e7i) q^{34} -8.43233e7i q^{35} +5.01619e7 q^{37} +(1.50266e7 + 8.67564e6i) q^{38} +(2.10299e7 + 3.64249e7i) q^{40} +(1.29245e8 - 7.46194e7i) q^{41} +(9.93595e7 - 1.72096e8i) q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} +(-1.34285e8 - 7.75293e7i) q^{47} +(-1.28498e8 - 2.22565e8i) q^{49} +(6.69144e7 - 3.86331e7i) q^{50} +(-4.35611e7 + 7.54501e7i) q^{52} -4.21541e7i q^{53} +2.26696e8 q^{55} +(2.33034e8 + 1.34542e8i) q^{56} +(5.46730e7 + 9.46964e7i) q^{58} +(-2.52902e8 + 1.46013e8i) q^{59} +(2.65363e8 - 4.59623e8i) q^{61} +9.46499e8i q^{62} -1.34218e8 q^{64} +(5.34999e8 + 3.08882e8i) q^{65} +(-2.61047e8 - 4.52146e8i) q^{67} +(-1.18223e9 + 6.82563e8i) q^{68} +(9.54009e8 - 1.65239e9i) q^{70} -5.71364e8i q^{71} +2.18588e9 q^{73} +(9.82968e8 + 5.67517e8i) q^{74} +(1.96307e8 + 3.40014e8i) q^{76} +(1.25602e9 - 7.25163e8i) q^{77} +(-9.82961e8 + 1.70254e9i) q^{79} +9.51707e8i q^{80} +3.37689e9 q^{82} +(-1.89277e9 - 1.09279e9i) q^{83} +(4.83989e9 + 8.38294e9i) q^{85} +(3.89408e9 - 2.24825e9i) q^{86} +(-3.61707e8 + 6.26494e8i) q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} +(-6.22215e8 - 3.59236e8i) q^{92} +(-1.75429e9 - 3.03852e9i) q^{94} +(2.41096e9 - 1.39197e9i) q^{95} +(4.42056e9 - 7.65664e9i) q^{97} -5.81517e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2048 q^{4} + 45112 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2048 q^{4} + 45112 q^{7} - 107520 q^{10} - 275240 q^{13} - 1048576 q^{16} - 3137456 q^{19} - 7730688 q^{22} + 33732380 q^{25} + 46194688 q^{28} + 21785848 q^{31} - 151087104 q^{34} - 142028336 q^{37} - 27525120 q^{40} + 470688664 q^{43} + 377628672 q^{46} + 50058420 q^{49} + 140922880 q^{52} + 5402718720 q^{55} + 1564177920 q^{58} + 1184038744 q^{61} - 1073741824 q^{64} + 297365848 q^{67} + 3962250240 q^{70} + 13068538000 q^{73} - 803188736 q^{76} - 199282568 q^{79} + 16757336064 q^{82} + 12880512000 q^{85} + 3958112256 q^{88} + 16634464160 q^{91} - 8505477120 q^{94} + 39176355064 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 19.5959 + 11.3137i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 256.000 + 443.405i 0.250000 + 0.433013i
\(5\) 3144.08 1815.24i 1.00611 0.580876i 0.0960570 0.995376i \(-0.469377\pi\)
0.910049 + 0.414500i \(0.136044\pi\)
\(6\) 0 0
\(7\) 11613.3 20114.8i 0.690978 1.19681i −0.280540 0.959842i \(-0.590514\pi\)
0.971518 0.236966i \(-0.0761531\pi\)
\(8\) 11585.2i 0.353553i
\(9\) 0 0
\(10\) 82148.2 0.821482
\(11\) 54076.9 + 31221.3i 0.335775 + 0.193860i 0.658402 0.752666i \(-0.271233\pi\)
−0.322627 + 0.946526i \(0.604566\pi\)
\(12\) 0 0
\(13\) 85080.3 + 147363.i 0.229146 + 0.396892i 0.957555 0.288250i \(-0.0930734\pi\)
−0.728409 + 0.685142i \(0.759740\pi\)
\(14\) 455145. 262778.i 0.846272 0.488595i
\(15\) 0 0
\(16\) −131072. + 227023.i −0.125000 + 0.216506i
\(17\) 2.66626e6i 1.87784i 0.344139 + 0.938919i \(0.388171\pi\)
−0.344139 + 0.938919i \(0.611829\pi\)
\(18\) 0 0
\(19\) 766825. 0.309691 0.154845 0.987939i \(-0.450512\pi\)
0.154845 + 0.987939i \(0.450512\pi\)
\(20\) 1.60977e6 + 929401.i 0.503053 + 0.290438i
\(21\) 0 0
\(22\) 706458. + 1.22362e6i 0.137080 + 0.237429i
\(23\) −1.21526e6 + 701633.i −0.188813 + 0.109011i −0.591427 0.806359i \(-0.701435\pi\)
0.402614 + 0.915370i \(0.368102\pi\)
\(24\) 0 0
\(25\) 1.70736e6 2.95723e6i 0.174833 0.302820i
\(26\) 3.85029e6i 0.324061i
\(27\) 0 0
\(28\) 1.18920e7 0.690978
\(29\) 4.18503e6 + 2.41623e6i 0.204037 + 0.117801i 0.598537 0.801095i \(-0.295749\pi\)
−0.394500 + 0.918896i \(0.629082\pi\)
\(30\) 0 0
\(31\) 2.09149e7 + 3.62256e7i 0.730544 + 1.26534i 0.956651 + 0.291237i \(0.0940670\pi\)
−0.226106 + 0.974103i \(0.572600\pi\)
\(32\) −5.13695e6 + 2.96582e6i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −3.01653e7 + 5.22478e7i −0.663916 + 1.14994i
\(35\) 8.43233e7i 1.60549i
\(36\) 0 0
\(37\) 5.01619e7 0.723378 0.361689 0.932299i \(-0.382200\pi\)
0.361689 + 0.932299i \(0.382200\pi\)
\(38\) 1.50266e7 + 8.67564e6i 0.189646 + 0.109492i
\(39\) 0 0
\(40\) 2.10299e7 + 3.64249e7i 0.205371 + 0.355712i
\(41\) 1.29245e8 7.46194e7i 1.11556 0.644069i 0.175296 0.984516i \(-0.443912\pi\)
0.940264 + 0.340447i \(0.110578\pi\)
\(42\) 0 0
\(43\) 9.93595e7 1.72096e8i 0.675876 1.17065i −0.300336 0.953834i \(-0.597099\pi\)
0.976212 0.216818i \(-0.0695680\pi\)
\(44\) 3.19706e7i 0.193860i
\(45\) 0 0
\(46\) −3.17523e7 −0.154165
\(47\) −1.34285e8 7.75293e7i −0.585514 0.338047i 0.177808 0.984065i \(-0.443099\pi\)
−0.763322 + 0.646019i \(0.776433\pi\)
\(48\) 0 0
\(49\) −1.28498e8 2.22565e8i −0.454901 0.787911i
\(50\) 6.69144e7 3.86331e7i 0.214126 0.123626i
\(51\) 0 0
\(52\) −4.35611e7 + 7.54501e7i −0.114573 + 0.198446i
\(53\) 4.21541e7i 0.100800i −0.998729 0.0503999i \(-0.983950\pi\)
0.998729 0.0503999i \(-0.0160496\pi\)
\(54\) 0 0
\(55\) 2.26696e8 0.450434
\(56\) 2.33034e8 + 1.34542e8i 0.423136 + 0.244298i
\(57\) 0 0
\(58\) 5.46730e7 + 9.46964e7i 0.0832976 + 0.144276i
\(59\) −2.52902e8 + 1.46013e8i −0.353746 + 0.204236i −0.666334 0.745653i \(-0.732138\pi\)
0.312588 + 0.949889i \(0.398804\pi\)
\(60\) 0 0
\(61\) 2.65363e8 4.59623e8i 0.314190 0.544192i −0.665075 0.746776i \(-0.731601\pi\)
0.979265 + 0.202584i \(0.0649339\pi\)
\(62\) 9.46499e8i 1.03315i
\(63\) 0 0
\(64\) −1.34218e8 −0.125000
\(65\) 5.34999e8 + 3.08882e8i 0.461090 + 0.266211i
\(66\) 0 0
\(67\) −2.61047e8 4.52146e8i −0.193350 0.334892i 0.753008 0.658011i \(-0.228602\pi\)
−0.946358 + 0.323119i \(0.895269\pi\)
\(68\) −1.18223e9 + 6.82563e8i −0.813128 + 0.469459i
\(69\) 0 0
\(70\) 9.54009e8 1.65239e9i 0.567626 0.983157i
\(71\) 5.71364e8i 0.316681i −0.987385 0.158340i \(-0.949386\pi\)
0.987385 0.158340i \(-0.0506143\pi\)
\(72\) 0 0
\(73\) 2.18588e9 1.05441 0.527207 0.849737i \(-0.323239\pi\)
0.527207 + 0.849737i \(0.323239\pi\)
\(74\) 9.82968e8 + 5.67517e8i 0.442977 + 0.255753i
\(75\) 0 0
\(76\) 1.96307e8 + 3.40014e8i 0.0774227 + 0.134100i
\(77\) 1.25602e9 7.25163e8i 0.464026 0.267906i
\(78\) 0 0
\(79\) −9.82961e8 + 1.70254e9i −0.319449 + 0.553301i −0.980373 0.197151i \(-0.936831\pi\)
0.660924 + 0.750452i \(0.270164\pi\)
\(80\) 9.51707e8i 0.290438i
\(81\) 0 0
\(82\) 3.37689e9 0.910851
\(83\) −1.89277e9 1.09279e9i −0.480514 0.277425i 0.240116 0.970744i \(-0.422814\pi\)
−0.720631 + 0.693319i \(0.756148\pi\)
\(84\) 0 0
\(85\) 4.83989e9 + 8.38294e9i 1.09079 + 1.88930i
\(86\) 3.89408e9 2.24825e9i 0.827776 0.477917i
\(87\) 0 0
\(88\) −3.61707e8 + 6.26494e8i −0.0685398 + 0.118714i
\(89\) 2.38742e8i 0.0427542i 0.999771 + 0.0213771i \(0.00680506\pi\)
−0.999771 + 0.0213771i \(0.993195\pi\)
\(90\) 0 0
\(91\) 3.95224e9 0.633339
\(92\) −6.22215e8 3.59236e8i −0.0944064 0.0545056i
\(93\) 0 0
\(94\) −1.75429e9 3.03852e9i −0.239035 0.414021i
\(95\) 2.41096e9 1.39197e9i 0.311582 0.179892i
\(96\) 0 0
\(97\) 4.42056e9 7.65664e9i 0.514776 0.891619i −0.485076 0.874472i \(-0.661208\pi\)
0.999853 0.0171473i \(-0.00545843\pi\)
\(98\) 5.81517e9i 0.643327i
\(99\) 0 0
\(100\) 1.74833e9 0.174833
\(101\) 1.45430e10 + 8.39641e9i 1.38372 + 0.798890i 0.992598 0.121450i \(-0.0387543\pi\)
0.391120 + 0.920340i \(0.372088\pi\)
\(102\) 0 0
\(103\) −4.18432e9 7.24746e9i −0.360944 0.625173i 0.627173 0.778880i \(-0.284212\pi\)
−0.988116 + 0.153708i \(0.950879\pi\)
\(104\) −1.70724e9 + 9.85675e8i −0.140323 + 0.0810153i
\(105\) 0 0
\(106\) 4.76919e8 8.26048e8i 0.0356381 0.0617271i
\(107\) 1.43555e10i 1.02353i 0.859126 + 0.511764i \(0.171008\pi\)
−0.859126 + 0.511764i \(0.828992\pi\)
\(108\) 0 0
\(109\) −4.72564e9 −0.307134 −0.153567 0.988138i \(-0.549076\pi\)
−0.153567 + 0.988138i \(0.549076\pi\)
\(110\) 4.44233e9 + 2.56478e9i 0.275833 + 0.159253i
\(111\) 0 0
\(112\) 3.04435e9 + 5.27296e9i 0.172744 + 0.299202i
\(113\) 1.14452e10 6.60792e9i 0.621202 0.358651i −0.156135 0.987736i \(-0.549903\pi\)
0.777337 + 0.629084i \(0.216570\pi\)
\(114\) 0 0
\(115\) −2.54726e9 + 4.41199e9i −0.126644 + 0.219354i
\(116\) 2.47422e9i 0.117801i
\(117\) 0 0
\(118\) −6.60779e9 −0.288833
\(119\) 5.36312e10 + 3.09640e10i 2.24741 + 1.29754i
\(120\) 0 0
\(121\) −1.10192e10 1.90858e10i −0.424837 0.735839i
\(122\) 1.04001e10 6.00449e9i 0.384802 0.222166i
\(123\) 0 0
\(124\) −1.07084e10 + 1.85475e10i −0.365272 + 0.632670i
\(125\) 2.30568e10i 0.755526i
\(126\) 0 0
\(127\) −3.17814e10 −0.961953 −0.480976 0.876733i \(-0.659718\pi\)
−0.480976 + 0.876733i \(0.659718\pi\)
\(128\) −2.63012e9 1.51850e9i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 6.98920e9 + 1.21056e10i 0.188239 + 0.326040i
\(131\) 4.33960e10 2.50547e10i 1.12485 0.649430i 0.182213 0.983259i \(-0.441674\pi\)
0.942634 + 0.333829i \(0.108341\pi\)
\(132\) 0 0
\(133\) 8.90535e9 1.54245e10i 0.213990 0.370641i
\(134\) 1.18136e10i 0.273438i
\(135\) 0 0
\(136\) −3.08893e10 −0.663916
\(137\) −2.37935e10 1.37372e10i −0.493010 0.284639i 0.232812 0.972522i \(-0.425207\pi\)
−0.725822 + 0.687882i \(0.758540\pi\)
\(138\) 0 0
\(139\) −3.16244e10 5.47751e10i −0.609464 1.05562i −0.991329 0.131405i \(-0.958051\pi\)
0.381865 0.924218i \(-0.375282\pi\)
\(140\) 3.73894e10 2.15868e10i 0.695197 0.401372i
\(141\) 0 0
\(142\) 6.46425e9 1.11964e10i 0.111963 0.193926i
\(143\) 1.06253e10i 0.177689i
\(144\) 0 0
\(145\) 1.75441e10 0.273710
\(146\) 4.28342e10 + 2.47304e10i 0.645694 + 0.372792i
\(147\) 0 0
\(148\) 1.28414e10 + 2.22420e10i 0.180845 + 0.313232i
\(149\) −2.93131e10 + 1.69239e10i −0.399145 + 0.230446i −0.686115 0.727493i \(-0.740685\pi\)
0.286970 + 0.957940i \(0.407352\pi\)
\(150\) 0 0
\(151\) −6.11931e10 + 1.05990e11i −0.779503 + 1.35014i 0.152726 + 0.988269i \(0.451195\pi\)
−0.932229 + 0.361870i \(0.882139\pi\)
\(152\) 8.88385e9i 0.109492i
\(153\) 0 0
\(154\) 3.28171e10 0.378876
\(155\) 1.31516e11 + 7.59309e10i 1.47001 + 0.848711i
\(156\) 0 0
\(157\) 7.94857e10 + 1.37673e11i 0.833279 + 1.44328i 0.895424 + 0.445215i \(0.146873\pi\)
−0.0621448 + 0.998067i \(0.519794\pi\)
\(158\) −3.85241e10 + 2.22419e10i −0.391243 + 0.225884i
\(159\) 0 0
\(160\) −1.07673e10 + 1.86496e10i −0.102685 + 0.177856i
\(161\) 3.25930e10i 0.301297i
\(162\) 0 0
\(163\) −9.20831e10 −0.800280 −0.400140 0.916454i \(-0.631038\pi\)
−0.400140 + 0.916454i \(0.631038\pi\)
\(164\) 6.61732e10 + 3.82051e10i 0.557780 + 0.322034i
\(165\) 0 0
\(166\) −2.47270e10 4.28284e10i −0.196169 0.339775i
\(167\) 1.83958e11 1.06208e11i 1.41623 0.817663i 0.420269 0.907400i \(-0.361936\pi\)
0.995966 + 0.0897362i \(0.0286024\pi\)
\(168\) 0 0
\(169\) 5.44519e10 9.43135e10i 0.394984 0.684133i
\(170\) 2.19029e11i 1.54261i
\(171\) 0 0
\(172\) 1.01744e11 0.675876
\(173\) 2.63386e11 + 1.52066e11i 1.69966 + 0.981300i 0.946072 + 0.323956i \(0.105013\pi\)
0.753590 + 0.657345i \(0.228320\pi\)
\(174\) 0 0
\(175\) −3.96560e10 6.86861e10i −0.241612 0.418484i
\(176\) −1.41759e10 + 8.18449e9i −0.0839438 + 0.0484650i
\(177\) 0 0
\(178\) −2.70106e9 + 4.67837e9i −0.0151159 + 0.0261815i
\(179\) 7.07114e9i 0.0384791i −0.999815 0.0192395i \(-0.993875\pi\)
0.999815 0.0192395i \(-0.00612451\pi\)
\(180\) 0 0
\(181\) −1.27309e11 −0.655337 −0.327669 0.944793i \(-0.606263\pi\)
−0.327669 + 0.944793i \(0.606263\pi\)
\(182\) 7.74478e10 + 4.47145e10i 0.387839 + 0.223919i
\(183\) 0 0
\(184\) −8.12859e9 1.40791e10i −0.0385413 0.0667554i
\(185\) 1.57713e11 9.10557e10i 0.727795 0.420193i
\(186\) 0 0
\(187\) −8.32442e10 + 1.44183e11i −0.364037 + 0.630531i
\(188\) 7.93900e10i 0.338047i
\(189\) 0 0
\(190\) 6.29934e10 0.254406
\(191\) −1.78799e11 1.03230e11i −0.703394 0.406105i 0.105216 0.994449i \(-0.466447\pi\)
−0.808610 + 0.588345i \(0.799780\pi\)
\(192\) 0 0
\(193\) −1.55803e11 2.69859e11i −0.581821 1.00774i −0.995264 0.0972136i \(-0.969007\pi\)
0.413442 0.910530i \(-0.364326\pi\)
\(194\) 1.73250e11 1.00026e11i 0.630470 0.364002i
\(195\) 0 0
\(196\) 6.57911e10 1.13954e11i 0.227450 0.393956i
\(197\) 1.51694e11i 0.511255i 0.966775 + 0.255628i \(0.0822821\pi\)
−0.966775 + 0.255628i \(0.917718\pi\)
\(198\) 0 0
\(199\) −1.11692e11 −0.357895 −0.178947 0.983859i \(-0.557269\pi\)
−0.178947 + 0.983859i \(0.557269\pi\)
\(200\) 3.42602e10 + 1.97801e10i 0.107063 + 0.0618129i
\(201\) 0 0
\(202\) 1.89989e11 + 3.29071e11i 0.564901 + 0.978436i
\(203\) 9.72037e10 5.61206e10i 0.281970 0.162795i
\(204\) 0 0
\(205\) 2.70904e11 4.69219e11i 0.748248 1.29600i
\(206\) 1.89361e11i 0.510451i
\(207\) 0 0
\(208\) −4.46066e10 −0.114573
\(209\) 4.14676e10 + 2.39413e10i 0.103987 + 0.0600367i
\(210\) 0 0
\(211\) −7.65329e10 1.32559e11i −0.182994 0.316954i 0.759905 0.650034i \(-0.225245\pi\)
−0.942899 + 0.333080i \(0.891912\pi\)
\(212\) 1.86913e10 1.07914e10i 0.0436476 0.0252000i
\(213\) 0 0
\(214\) −1.62414e11 + 2.81310e11i −0.361872 + 0.626781i
\(215\) 7.21444e11i 1.57040i
\(216\) 0 0
\(217\) 9.71560e11 2.01916
\(218\) −9.26033e10 5.34645e10i −0.188081 0.108588i
\(219\) 0 0
\(220\) 5.80343e10 + 1.00518e11i 0.112609 + 0.195044i
\(221\) −3.92909e11 + 2.26846e11i −0.745300 + 0.430299i
\(222\) 0 0
\(223\) 3.02880e11 5.24603e11i 0.549219 0.951276i −0.449109 0.893477i \(-0.648259\pi\)
0.998328 0.0577987i \(-0.0184082\pi\)
\(224\) 1.37771e11i 0.244298i
\(225\) 0 0
\(226\) 2.99040e11 0.507210
\(227\) 5.80746e11 + 3.35294e11i 0.963512 + 0.556284i 0.897252 0.441519i \(-0.145560\pi\)
0.0662598 + 0.997802i \(0.478893\pi\)
\(228\) 0 0
\(229\) −1.76678e11 3.06015e11i −0.280547 0.485921i 0.690973 0.722881i \(-0.257182\pi\)
−0.971520 + 0.236960i \(0.923849\pi\)
\(230\) −9.98318e10 + 5.76379e10i −0.155106 + 0.0895508i
\(231\) 0 0
\(232\) −2.79926e10 + 4.84845e10i −0.0416488 + 0.0721379i
\(233\) 1.12390e12i 1.63662i 0.574779 + 0.818309i \(0.305088\pi\)
−0.574779 + 0.818309i \(0.694912\pi\)
\(234\) 0 0
\(235\) −5.62936e11 −0.785452
\(236\) −1.29486e11 7.47586e10i −0.176873 0.102118i
\(237\) 0 0
\(238\) 7.00635e11 + 1.21354e12i 0.917502 + 1.58916i
\(239\) 2.29153e11 1.32302e11i 0.293857 0.169658i −0.345823 0.938300i \(-0.612400\pi\)
0.639680 + 0.768641i \(0.279067\pi\)
\(240\) 0 0
\(241\) −4.43384e11 + 7.67964e11i −0.545375 + 0.944617i 0.453209 + 0.891404i \(0.350279\pi\)
−0.998583 + 0.0532121i \(0.983054\pi\)
\(242\) 4.98671e11i 0.600810i
\(243\) 0 0
\(244\) 2.71732e11 0.314190
\(245\) −8.08018e11 4.66509e11i −0.915357 0.528482i
\(246\) 0 0
\(247\) 6.52417e10 + 1.13002e11i 0.0709644 + 0.122914i
\(248\) −4.19682e11 + 2.42304e11i −0.447365 + 0.258286i
\(249\) 0 0
\(250\) −2.60858e11 + 4.51820e11i −0.267119 + 0.462663i
\(251\) 8.59494e11i 0.862729i 0.902178 + 0.431364i \(0.141968\pi\)
−0.902178 + 0.431364i \(0.858032\pi\)
\(252\) 0 0
\(253\) −8.76237e10 −0.0845316
\(254\) −6.22785e11 3.59565e11i −0.589073 0.340102i
\(255\) 0 0
\(256\) −3.43597e10 5.95128e10i −0.0312500 0.0541266i
\(257\) −1.88707e12 + 1.08950e12i −1.68315 + 0.971764i −0.723596 + 0.690224i \(0.757512\pi\)
−0.959549 + 0.281540i \(0.909155\pi\)
\(258\) 0 0
\(259\) 5.82543e11 1.00899e12i 0.499838 0.865745i
\(260\) 3.16295e11i 0.266211i
\(261\) 0 0
\(262\) 1.13385e12 0.918433
\(263\) −1.19461e12 6.89708e11i −0.949395 0.548134i −0.0565021 0.998402i \(-0.517995\pi\)
−0.892893 + 0.450269i \(0.851328\pi\)
\(264\) 0 0
\(265\) −7.65196e10 1.32536e11i −0.0585522 0.101415i
\(266\) 3.49017e11 2.01505e11i 0.262083 0.151313i
\(267\) 0 0
\(268\) 1.33656e11 2.31499e11i 0.0966750 0.167446i
\(269\) 1.18129e12i 0.838680i −0.907829 0.419340i \(-0.862262\pi\)
0.907829 0.419340i \(-0.137738\pi\)
\(270\) 0 0
\(271\) −1.42251e12 −0.973213 −0.486606 0.873621i \(-0.661765\pi\)
−0.486606 + 0.873621i \(0.661765\pi\)
\(272\) −6.05304e11 3.49472e11i −0.406564 0.234730i
\(273\) 0 0
\(274\) −3.10837e11 5.38385e11i −0.201270 0.348611i
\(275\) 1.84657e11 1.06612e11i 0.117409 0.0677863i
\(276\) 0 0
\(277\) −2.64980e11 + 4.58959e11i −0.162485 + 0.281433i −0.935759 0.352639i \(-0.885284\pi\)
0.773274 + 0.634072i \(0.218618\pi\)
\(278\) 1.43116e12i 0.861913i
\(279\) 0 0
\(280\) 9.76905e11 0.567626
\(281\) −1.97835e12 1.14220e12i −1.12920 0.651946i −0.185469 0.982650i \(-0.559381\pi\)
−0.943735 + 0.330704i \(0.892714\pi\)
\(282\) 0 0
\(283\) −1.15637e12 2.00289e12i −0.637038 1.10338i −0.986079 0.166275i \(-0.946826\pi\)
0.349042 0.937107i \(-0.386507\pi\)
\(284\) 2.53346e11 1.46269e11i 0.137127 0.0791701i
\(285\) 0 0
\(286\) −1.20211e11 + 2.08212e11i −0.0628225 + 0.108812i
\(287\) 3.46630e12i 1.78015i
\(288\) 0 0
\(289\) −5.09295e12 −2.52627
\(290\) 3.43793e11 + 1.98489e11i 0.167613 + 0.0967712i
\(291\) 0 0
\(292\) 5.59584e11 + 9.69228e11i 0.263604 + 0.456575i
\(293\) −9.17894e11 + 5.29947e11i −0.425064 + 0.245411i −0.697242 0.716836i \(-0.745590\pi\)
0.272177 + 0.962247i \(0.412256\pi\)
\(294\) 0 0
\(295\) −5.30096e11 + 9.18153e11i −0.237271 + 0.410965i
\(296\) 5.81138e11i 0.255753i
\(297\) 0 0
\(298\) −7.65890e11 −0.325900
\(299\) −2.06790e11 1.19390e11i −0.0865314 0.0499589i
\(300\) 0 0
\(301\) −2.30778e12 3.99719e12i −0.934031 1.61779i
\(302\) −2.39827e12 + 1.38464e12i −0.954692 + 0.551192i
\(303\) 0 0
\(304\) −1.00509e11 + 1.74087e11i −0.0387114 + 0.0670501i
\(305\) 1.92679e12i 0.730020i
\(306\) 0 0
\(307\) 6.89209e11 0.252731 0.126366 0.991984i \(-0.459669\pi\)
0.126366 + 0.991984i \(0.459669\pi\)
\(308\) 6.43082e11 + 3.71284e11i 0.232013 + 0.133953i
\(309\) 0 0
\(310\) 1.71812e12 + 2.97587e12i 0.600129 + 1.03945i
\(311\) 1.69458e12 9.78369e11i 0.582454 0.336280i −0.179654 0.983730i \(-0.557498\pi\)
0.762108 + 0.647450i \(0.224165\pi\)
\(312\) 0 0
\(313\) 1.24410e11 2.15485e11i 0.0414128 0.0717291i −0.844576 0.535436i \(-0.820147\pi\)
0.885989 + 0.463707i \(0.153481\pi\)
\(314\) 3.59711e12i 1.17843i
\(315\) 0 0
\(316\) −1.00655e12 −0.319449
\(317\) −4.01555e12 2.31838e12i −1.25444 0.724249i −0.282448 0.959283i \(-0.591147\pi\)
−0.971987 + 0.235034i \(0.924480\pi\)
\(318\) 0 0
\(319\) 1.50876e11 + 2.61324e11i 0.0456737 + 0.0791091i
\(320\) −4.21992e11 + 2.43637e11i −0.125763 + 0.0726095i
\(321\) 0 0
\(322\) −3.68748e11 + 6.38690e11i −0.106525 + 0.184506i
\(323\) 2.04456e12i 0.581549i
\(324\) 0 0
\(325\) 5.81050e11 0.160249
\(326\) −1.80445e12 1.04180e12i −0.490069 0.282942i
\(327\) 0 0
\(328\) 8.64483e11 + 1.49733e12i 0.227713 + 0.394410i
\(329\) −3.11897e12 + 1.80074e12i −0.809154 + 0.467165i
\(330\) 0 0
\(331\) 7.07216e11 1.22493e12i 0.177997 0.308300i −0.763197 0.646165i \(-0.776372\pi\)
0.941194 + 0.337866i \(0.109705\pi\)
\(332\) 1.11902e12i 0.277425i
\(333\) 0 0
\(334\) 4.80642e12 1.15635
\(335\) −1.64150e12 9.47723e11i −0.389061 0.224625i
\(336\) 0 0
\(337\) −4.33878e11 7.51498e11i −0.0998201 0.172893i 0.811790 0.583949i \(-0.198493\pi\)
−0.911610 + 0.411056i \(0.865160\pi\)
\(338\) 2.13407e12 1.23211e12i 0.483755 0.279296i
\(339\) 0 0
\(340\) −2.47803e12 + 4.29207e12i −0.545395 + 0.944652i
\(341\) 2.61196e12i 0.566493i
\(342\) 0 0
\(343\) 5.91785e11 0.124650
\(344\) 1.99377e12 + 1.15110e12i 0.413888 + 0.238958i
\(345\) 0 0
\(346\) 3.44086e12 + 5.95975e12i 0.693884 + 1.20184i
\(347\) −4.50950e12 + 2.60356e12i −0.896357 + 0.517512i −0.876017 0.482281i \(-0.839808\pi\)
−0.0203407 + 0.999793i \(0.506475\pi\)
\(348\) 0 0
\(349\) −5.59765e11 + 9.69541e11i −0.108113 + 0.187257i −0.915006 0.403441i \(-0.867814\pi\)
0.806893 + 0.590698i \(0.201148\pi\)
\(350\) 1.79462e12i 0.341691i
\(351\) 0 0
\(352\) −3.70388e11 −0.0685398
\(353\) 3.23852e12 + 1.86976e12i 0.590844 + 0.341124i 0.765431 0.643518i \(-0.222526\pi\)
−0.174587 + 0.984642i \(0.555859\pi\)
\(354\) 0 0
\(355\) −1.03716e12 1.79642e12i −0.183952 0.318614i
\(356\) −1.05859e11 + 6.11180e10i −0.0185131 + 0.0106886i
\(357\) 0 0
\(358\) 8.00009e10 1.38566e11i 0.0136044 0.0235635i
\(359\) 3.54489e12i 0.594471i −0.954804 0.297235i \(-0.903935\pi\)
0.954804 0.297235i \(-0.0960646\pi\)
\(360\) 0 0
\(361\) −5.54305e12 −0.904092
\(362\) −2.49473e12 1.44033e12i −0.401310 0.231697i
\(363\) 0 0
\(364\) 1.01177e12 + 1.75244e12i 0.158335 + 0.274244i
\(365\) 6.87257e12 3.96788e12i 1.06085 0.612484i
\(366\) 0 0
\(367\) 5.05807e12 8.76083e12i 0.759722 1.31588i −0.183271 0.983062i \(-0.558669\pi\)
0.942992 0.332814i \(-0.107998\pi\)
\(368\) 3.67858e11i 0.0545056i
\(369\) 0 0
\(370\) 4.12071e12 0.594242
\(371\) −8.47919e11 4.89546e11i −0.120638 0.0696505i
\(372\) 0 0
\(373\) −1.90528e12 3.30004e12i −0.263885 0.457062i 0.703386 0.710808i \(-0.251670\pi\)
−0.967271 + 0.253746i \(0.918337\pi\)
\(374\) −3.26249e12 + 1.88360e12i −0.445853 + 0.257413i
\(375\) 0 0
\(376\) 8.98195e11 1.55572e12i 0.119518 0.207010i
\(377\) 8.22293e11i 0.107974i
\(378\) 0 0
\(379\) 1.11052e13 1.42014 0.710069 0.704132i \(-0.248664\pi\)
0.710069 + 0.704132i \(0.248664\pi\)
\(380\) 1.23441e12 + 7.12688e11i 0.155791 + 0.0899460i
\(381\) 0 0
\(382\) −2.33582e12 4.04576e12i −0.287159 0.497375i
\(383\) −3.71671e12 + 2.14585e12i −0.450988 + 0.260378i −0.708247 0.705964i \(-0.750514\pi\)
0.257259 + 0.966342i \(0.417181\pi\)
\(384\) 0 0
\(385\) 2.63269e12 4.55995e12i 0.311240 0.539083i
\(386\) 7.05084e12i 0.822820i
\(387\) 0 0
\(388\) 4.52665e12 0.514776
\(389\) 1.30384e13 + 7.52771e12i 1.46378 + 0.845113i 0.999183 0.0404106i \(-0.0128666\pi\)
0.464595 + 0.885523i \(0.346200\pi\)
\(390\) 0 0
\(391\) −1.87074e12 3.24021e12i −0.204705 0.354560i
\(392\) 2.57847e12 1.48868e12i 0.278569 0.160832i
\(393\) 0 0
\(394\) −1.71622e12 + 2.97259e12i −0.180756 + 0.313079i
\(395\) 7.13723e12i 0.742240i
\(396\) 0 0
\(397\) −1.11669e13 −1.13235 −0.566174 0.824286i \(-0.691577\pi\)
−0.566174 + 0.824286i \(0.691577\pi\)
\(398\) −2.18870e12 1.26365e12i −0.219165 0.126535i
\(399\) 0 0
\(400\) 4.47573e11 + 7.75220e11i 0.0437083 + 0.0757050i
\(401\) 1.00186e13 5.78426e12i 0.966243 0.557861i 0.0681541 0.997675i \(-0.478289\pi\)
0.898089 + 0.439814i \(0.144956\pi\)
\(402\) 0 0
\(403\) −3.55889e12 + 6.16417e12i −0.334803 + 0.579895i
\(404\) 8.59793e12i 0.798890i
\(405\) 0 0
\(406\) 2.53973e12 0.230227
\(407\) 2.71260e12 + 1.56612e12i 0.242892 + 0.140234i
\(408\) 0 0
\(409\) 5.37056e12 + 9.30209e12i 0.469249 + 0.812763i 0.999382 0.0351516i \(-0.0111914\pi\)
−0.530133 + 0.847914i \(0.677858\pi\)
\(410\) 1.06172e13 6.12985e12i 0.916413 0.529091i
\(411\) 0 0
\(412\) 2.14237e12 3.71070e12i 0.180472 0.312586i
\(413\) 6.78275e12i 0.564489i
\(414\) 0 0
\(415\) −7.93468e12 −0.644598
\(416\) −8.74107e11 5.04666e11i −0.0701613 0.0405077i
\(417\) 0 0
\(418\) 5.41730e11 + 9.38304e11i 0.0424523 + 0.0735296i
\(419\) 7.63589e12 4.40859e12i 0.591275 0.341373i −0.174326 0.984688i \(-0.555775\pi\)
0.765602 + 0.643315i \(0.222441\pi\)
\(420\) 0 0
\(421\) 2.84871e12 4.93410e12i 0.215396 0.373076i −0.737999 0.674802i \(-0.764229\pi\)
0.953395 + 0.301725i \(0.0975625\pi\)
\(422\) 3.46348e12i 0.258792i
\(423\) 0 0
\(424\) 4.88365e11 0.0356381
\(425\) 7.88474e12 + 4.55226e12i 0.568647 + 0.328309i
\(426\) 0 0
\(427\) −6.16347e12 1.06754e13i −0.434196 0.752050i
\(428\) −6.36531e12 + 3.67501e12i −0.443201 + 0.255882i
\(429\) 0 0
\(430\) 8.16221e12 1.41374e13i 0.555220 0.961670i
\(431\) 1.80323e13i 1.21245i 0.795293 + 0.606226i \(0.207317\pi\)
−0.795293 + 0.606226i \(0.792683\pi\)
\(432\) 0 0
\(433\) 2.06339e13 1.35563 0.677816 0.735232i \(-0.262927\pi\)
0.677816 + 0.735232i \(0.262927\pi\)
\(434\) 1.90386e13 + 1.09919e13i 1.23648 + 0.713881i
\(435\) 0 0
\(436\) −1.20976e12 2.09537e12i −0.0767836 0.132993i
\(437\) −9.31896e11 + 5.38030e11i −0.0584736 + 0.0337598i
\(438\) 0 0
\(439\) −9.76567e12 + 1.69146e13i −0.598935 + 1.03739i 0.394044 + 0.919092i \(0.371076\pi\)
−0.992979 + 0.118294i \(0.962258\pi\)
\(440\) 2.62633e12i 0.159253i
\(441\) 0 0
\(442\) −1.02659e13 −0.608535
\(443\) 2.57616e13 + 1.48735e13i 1.50992 + 0.871753i 0.999933 + 0.0115703i \(0.00368303\pi\)
0.509987 + 0.860182i \(0.329650\pi\)
\(444\) 0 0
\(445\) 4.33373e11 + 7.50625e11i 0.0248349 + 0.0430153i
\(446\) 1.18704e13 6.85338e12i 0.672653 0.388357i
\(447\) 0 0
\(448\) −1.55871e12 + 2.69976e12i −0.0863722 + 0.149601i
\(449\) 1.37505e13i 0.753509i −0.926313 0.376754i \(-0.877040\pi\)
0.926313 0.376754i \(-0.122960\pi\)
\(450\) 0 0
\(451\) 9.31887e12 0.499437
\(452\) 5.85997e12 + 3.38325e12i 0.310601 + 0.179326i
\(453\) 0 0
\(454\) 7.58684e12 + 1.31408e13i 0.393352 + 0.681306i
\(455\) 1.24262e13 7.17425e12i 0.637207 0.367891i
\(456\) 0 0
\(457\) −2.05112e11 + 3.55265e11i −0.0102899 + 0.0178226i −0.871124 0.491062i \(-0.836609\pi\)
0.860835 + 0.508885i \(0.169942\pi\)
\(458\) 7.99554e12i 0.396753i
\(459\) 0 0
\(460\) −2.60840e12 −0.126644
\(461\) 1.82657e11 + 1.05457e11i 0.00877266 + 0.00506490i 0.504380 0.863482i \(-0.331721\pi\)
−0.495607 + 0.868547i \(0.665054\pi\)
\(462\) 0 0
\(463\) 9.83688e12 + 1.70380e13i 0.462330 + 0.800779i 0.999077 0.0429642i \(-0.0136801\pi\)
−0.536746 + 0.843744i \(0.680347\pi\)
\(464\) −1.09708e12 + 6.33399e11i −0.0510092 + 0.0294502i
\(465\) 0 0
\(466\) −1.27155e13 + 2.20238e13i −0.578632 + 1.00222i
\(467\) 1.21902e13i 0.548815i −0.961614 0.274407i \(-0.911518\pi\)
0.961614 0.274407i \(-0.0884817\pi\)
\(468\) 0 0
\(469\) −1.21264e13 −0.534402
\(470\) −1.10312e13 6.36889e12i −0.480989 0.277699i
\(471\) 0 0
\(472\) −1.69159e12 2.92993e12i −0.0722082 0.125068i
\(473\) 1.07461e13 6.20427e12i 0.453885 0.262051i
\(474\) 0 0
\(475\) 1.30924e12 2.26768e12i 0.0541443 0.0937806i
\(476\) 3.17071e13i 1.29754i
\(477\) 0 0
\(478\) 5.98729e12 0.239933
\(479\) −4.33780e12 2.50443e12i −0.172025 0.0993187i 0.411515 0.911403i \(-0.365000\pi\)
−0.583540 + 0.812084i \(0.698333\pi\)
\(480\) 0 0
\(481\) 4.26779e12 + 7.39203e12i 0.165759 + 0.287103i
\(482\) −1.73770e13 + 1.00326e13i −0.667945 + 0.385638i
\(483\) 0 0
\(484\) 5.64181e12 9.77191e12i 0.212418 0.367919i
\(485\) 3.20975e13i 1.19608i
\(486\) 0 0
\(487\) −4.17000e13 −1.52227 −0.761134 0.648595i \(-0.775357\pi\)
−0.761134 + 0.648595i \(0.775357\pi\)
\(488\) 5.32484e12 + 3.07430e12i 0.192401 + 0.111083i
\(489\) 0 0
\(490\) −1.05559e13 1.82834e13i −0.373693 0.647255i
\(491\) −1.82160e12 + 1.05170e12i −0.0638331 + 0.0368540i −0.531577 0.847010i \(-0.678400\pi\)
0.467744 + 0.883864i \(0.345067\pi\)
\(492\) 0 0
\(493\) −6.44229e12 + 1.11584e13i −0.221211 + 0.383148i
\(494\) 2.95250e12i 0.100359i
\(495\) 0 0
\(496\) −1.09654e13 −0.365272
\(497\) −1.14929e13 6.63541e12i −0.379006 0.218819i
\(498\) 0 0
\(499\) −1.37241e13 2.37708e13i −0.443589 0.768319i 0.554363 0.832275i \(-0.312962\pi\)
−0.997953 + 0.0639553i \(0.979628\pi\)
\(500\) −1.02235e13 + 5.90255e12i −0.327152 + 0.188881i
\(501\) 0 0
\(502\) −9.72406e12 + 1.68426e13i −0.305021 + 0.528311i
\(503\) 2.26985e13i 0.704949i 0.935822 + 0.352474i \(0.114660\pi\)
−0.935822 + 0.352474i \(0.885340\pi\)
\(504\) 0 0
\(505\) 6.09659e13 1.85622
\(506\) −1.71707e12 9.91349e11i −0.0517648 0.0298864i
\(507\) 0 0
\(508\) −8.13603e12 1.40920e13i −0.240488 0.416538i
\(509\) 3.64995e13 2.10730e13i 1.06831 0.616791i 0.140593 0.990068i \(-0.455099\pi\)
0.927720 + 0.373277i \(0.121766\pi\)
\(510\) 0 0
\(511\) 2.53852e13 4.39684e13i 0.728577 1.26193i
\(512\) 1.55494e12i 0.0441942i
\(513\) 0 0
\(514\) −4.93051e13 −1.37428
\(515\) −2.63117e13 1.51911e13i −0.726295 0.419327i
\(516\) 0 0
\(517\) −4.84114e12 8.38509e12i −0.131067 0.227015i
\(518\) 2.28309e13 1.31815e13i 0.612174 0.353439i
\(519\) 0 0
\(520\) −3.57847e12 + 6.19809e12i −0.0941197 + 0.163020i
\(521\) 6.54420e13i 1.70478i 0.522907 + 0.852390i \(0.324848\pi\)
−0.522907 + 0.852390i \(0.675152\pi\)
\(522\) 0 0
\(523\) −6.14531e13 −1.57049 −0.785245 0.619185i \(-0.787463\pi\)
−0.785245 + 0.619185i \(0.787463\pi\)
\(524\) 2.22188e13 + 1.28280e13i 0.562423 + 0.324715i
\(525\) 0 0
\(526\) −1.56063e13 2.70309e13i −0.387589 0.671324i
\(527\) −9.65869e13 + 5.57645e13i −2.37610 + 1.37184i
\(528\) 0 0
\(529\) −1.97287e13 + 3.41711e13i −0.476233 + 0.824860i
\(530\) 3.46288e12i 0.0828053i
\(531\) 0 0
\(532\) 9.11907e12 0.213990
\(533\) 2.19923e13 + 1.26973e13i 0.511252 + 0.295172i
\(534\) 0 0
\(535\) 2.60587e13 + 4.51349e13i 0.594543 + 1.02978i
\(536\) 5.23822e12 3.02429e12i 0.118402 0.0683595i
\(537\) 0 0
\(538\) 1.33648e13 2.31485e13i 0.296518 0.513584i
\(539\) 1.60475e13i 0.352748i
\(540\) 0 0
\(541\) 1.50207e13 0.324118 0.162059 0.986781i \(-0.448187\pi\)
0.162059 + 0.986781i \(0.448187\pi\)
\(542\) −2.78753e13 1.60938e13i −0.595969 0.344083i
\(543\) 0 0
\(544\) −7.90765e12 1.36965e13i −0.165979 0.287484i
\(545\) −1.48578e13 + 8.57816e12i −0.309010 + 0.178407i
\(546\) 0 0
\(547\) −3.57548e13 + 6.19292e13i −0.730127 + 1.26462i 0.226702 + 0.973964i \(0.427206\pi\)
−0.956829 + 0.290652i \(0.906128\pi\)
\(548\) 1.40669e13i 0.284639i
\(549\) 0 0
\(550\) 4.82470e12 0.0958644
\(551\) 3.20919e12 + 1.85282e12i 0.0631883 + 0.0364818i
\(552\) 0 0
\(553\) 2.28308e13 + 3.95441e13i 0.441464 + 0.764638i
\(554\) −1.03851e13 + 5.99581e12i −0.199003 + 0.114894i
\(555\) 0 0
\(556\) 1.61917e13 2.80448e13i 0.304732 0.527811i
\(557\) 7.34107e13i 1.36925i −0.728895 0.684626i \(-0.759966\pi\)
0.728895 0.684626i \(-0.240034\pi\)
\(558\) 0 0
\(559\) 3.38141e13 0.619497
\(560\) 1.91434e13 + 1.10524e13i 0.347599 + 0.200686i
\(561\) 0 0
\(562\) −2.58451e13 4.47650e13i −0.460996 0.798468i
\(563\) 4.13394e13 2.38673e13i 0.730840 0.421951i −0.0878892 0.996130i \(-0.528012\pi\)
0.818729 + 0.574179i \(0.194679\pi\)
\(564\) 0 0
\(565\) 2.39899e13 4.15517e13i 0.416664 0.721683i
\(566\) 5.23314e13i 0.900907i
\(567\) 0 0
\(568\) 6.61939e12 0.111963
\(569\) −1.65369e13 9.54756e12i −0.277263 0.160078i 0.354921 0.934896i \(-0.384508\pi\)
−0.632184 + 0.774819i \(0.717841\pi\)
\(570\) 0 0
\(571\) 1.04724e13 + 1.81387e13i 0.172530 + 0.298831i 0.939304 0.343087i \(-0.111472\pi\)
−0.766774 + 0.641918i \(0.778139\pi\)
\(572\) −4.71130e12 + 2.72007e12i −0.0769415 + 0.0444222i
\(573\) 0 0
\(574\) 3.92167e13 6.79253e13i 0.629378 1.09011i
\(575\) 4.79175e12i 0.0762351i
\(576\) 0 0
\(577\) 3.56688e13 0.557711 0.278855 0.960333i \(-0.410045\pi\)
0.278855 + 0.960333i \(0.410045\pi\)
\(578\) −9.98011e13 5.76202e13i −1.54702 0.893173i
\(579\) 0 0
\(580\) 4.49129e12 + 7.77914e12i 0.0684275 + 0.118520i
\(581\) −4.39624e13 + 2.53817e13i −0.664050 + 0.383389i
\(582\) 0 0
\(583\) 1.31611e12 2.27956e12i 0.0195411 0.0338461i
\(584\) 2.53239e13i 0.372792i
\(585\) 0 0
\(586\) −2.39826e13 −0.347064
\(587\) −1.12079e14 6.47090e13i −1.60818 0.928483i −0.989777 0.142621i \(-0.954447\pi\)
−0.618402 0.785862i \(-0.712220\pi\)
\(588\) 0 0
\(589\) 1.60381e13 + 2.77787e13i 0.226243 + 0.391864i
\(590\) −2.07754e13 + 1.19947e13i −0.290596 + 0.167776i
\(591\) 0 0
\(592\) −6.57482e12 + 1.13879e13i −0.0904223 + 0.156616i
\(593\) 3.96596e13i 0.540848i −0.962741 0.270424i \(-0.912836\pi\)
0.962741 0.270424i \(-0.0871639\pi\)
\(594\) 0 0
\(595\) 2.24828e14 3.01485
\(596\) −1.50083e13 8.66505e12i −0.199572 0.115223i
\(597\) 0 0
\(598\) −2.70150e12 4.67913e12i −0.0353263 0.0611870i
\(599\) 3.96254e13 2.28777e13i 0.513854 0.296674i −0.220562 0.975373i \(-0.570789\pi\)
0.734416 + 0.678699i \(0.237456\pi\)
\(600\) 0 0
\(601\) −5.30165e13 + 9.18273e13i −0.676143 + 1.17111i 0.299990 + 0.953942i \(0.403017\pi\)
−0.976133 + 0.217172i \(0.930317\pi\)
\(602\) 1.04438e14i 1.32092i
\(603\) 0 0
\(604\) −6.26617e13 −0.779503
\(605\) −6.92903e13 4.00048e13i −0.854862 0.493555i
\(606\) 0 0
\(607\) 4.77534e13 + 8.27112e13i 0.579509 + 1.00374i 0.995536 + 0.0943870i \(0.0300891\pi\)
−0.416026 + 0.909353i \(0.636578\pi\)
\(608\) −3.93915e12 + 2.27427e12i −0.0474115 + 0.0273731i
\(609\) 0 0
\(610\) 2.17991e13 3.77572e13i 0.258101 0.447044i
\(611\) 2.63849e13i 0.309848i
\(612\) 0 0
\(613\) −5.18411e13 −0.598924 −0.299462 0.954108i \(-0.596807\pi\)
−0.299462 + 0.954108i \(0.596807\pi\)
\(614\) 1.35057e13 + 7.79751e12i 0.154766 + 0.0893540i
\(615\) 0 0
\(616\) 8.40119e12 + 1.45513e13i 0.0947190 + 0.164058i
\(617\) −6.97534e13 + 4.02721e13i −0.780081 + 0.450380i −0.836459 0.548030i \(-0.815378\pi\)
0.0563782 + 0.998409i \(0.482045\pi\)
\(618\) 0 0
\(619\) 2.57473e13 4.45957e13i 0.283321 0.490726i −0.688880 0.724876i \(-0.741897\pi\)
0.972201 + 0.234149i \(0.0752305\pi\)
\(620\) 7.77532e13i 0.848711i
\(621\) 0 0
\(622\) 4.42759e13 0.475571
\(623\) 4.80224e12 + 2.77257e12i 0.0511686 + 0.0295422i
\(624\) 0 0
\(625\) 5.85270e13 + 1.01372e14i 0.613700 + 1.06296i
\(626\) 4.87587e12 2.81508e12i 0.0507201 0.0292833i
\(627\) 0 0
\(628\) −4.06967e13 + 7.04887e13i −0.416640 + 0.721641i
\(629\) 1.33745e14i 1.35839i
\(630\) 0 0
\(631\) −1.02922e13 −0.102887 −0.0514435 0.998676i \(-0.516382\pi\)
−0.0514435 + 0.998676i \(0.516382\pi\)
\(632\) −1.97243e13 1.13878e13i −0.195622 0.112942i
\(633\) 0 0
\(634\) −5.24589e13 9.08614e13i −0.512121 0.887020i
\(635\) −9.99232e13 + 5.76907e13i −0.967827 + 0.558775i
\(636\) 0 0
\(637\) 2.18653e13 3.78719e13i 0.208477 0.361093i
\(638\) 6.82785e12i 0.0645923i
\(639\) 0 0
\(640\) −1.10257e13 −0.102685
\(641\) −4.00494e13 2.31225e13i −0.370089 0.213671i 0.303408 0.952861i \(-0.401875\pi\)
−0.673497 + 0.739190i \(0.735209\pi\)
\(642\) 0 0
\(643\) −1.36551e13 2.36514e13i −0.124234 0.215180i 0.797199 0.603716i \(-0.206314\pi\)
−0.921433 + 0.388537i \(0.872981\pi\)
\(644\) −1.44519e13 + 8.34381e12i −0.130466 + 0.0753243i
\(645\) 0 0
\(646\) −2.31315e13 + 4.00650e13i −0.205609 + 0.356125i
\(647\) 1.34984e13i 0.119059i −0.998227 0.0595293i \(-0.981040\pi\)
0.998227 0.0595293i \(-0.0189600\pi\)
\(648\) 0 0
\(649\) −1.82349e13 −0.158372
\(650\) 1.13862e13 + 6.57382e12i 0.0981323 + 0.0566567i
\(651\) 0 0
\(652\) −2.35733e13 4.08301e13i −0.200070 0.346531i
\(653\) −7.29055e13 + 4.20920e13i −0.614037 + 0.354514i −0.774544 0.632520i \(-0.782020\pi\)
0.160507 + 0.987035i \(0.448687\pi\)
\(654\) 0 0
\(655\) 9.09604e13 1.57548e14i 0.754477 1.30679i
\(656\) 3.91220e13i 0.322034i
\(657\) 0 0
\(658\) −8.14920e13 −0.660672
\(659\) 1.43296e14 + 8.27319e13i 1.15294 + 0.665650i 0.949602 0.313458i \(-0.101488\pi\)
0.203338 + 0.979109i \(0.434821\pi\)
\(660\) 0 0
\(661\) −1.00840e14 1.74661e14i −0.799148 1.38416i −0.920172 0.391515i \(-0.871951\pi\)
0.121024 0.992650i \(-0.461382\pi\)
\(662\) 2.77171e13 1.60025e13i 0.218001 0.125863i
\(663\) 0 0
\(664\) 1.26602e13 2.19281e13i 0.0980846 0.169887i
\(665\) 6.46612e13i 0.497205i
\(666\) 0 0
\(667\) −6.78122e12 −0.0513664
\(668\) 9.41862e13 + 5.43785e13i 0.708117 + 0.408832i
\(669\) 0 0
\(670\) −2.14445e13 3.71430e13i −0.158834 0.275108i
\(671\) 2.87001e13 1.65700e13i 0.210994 0.121818i
\(672\) 0 0
\(673\) −3.02184e12 + 5.23398e12i −0.0218875 + 0.0379103i −0.876762 0.480925i \(-0.840301\pi\)
0.854874 + 0.518835i \(0.173634\pi\)
\(674\) 1.96351e13i 0.141167i
\(675\) 0 0
\(676\) 5.57588e13 0.394984
\(677\) −1.05200e14 6.07372e13i −0.739727 0.427082i 0.0822428 0.996612i \(-0.473792\pi\)
−0.821970 + 0.569530i \(0.807125\pi\)
\(678\) 0 0
\(679\) −1.02674e14 1.77837e14i −0.711398 1.23218i
\(680\) −9.71184e13 + 5.60713e13i −0.667970 + 0.385653i
\(681\) 0 0
\(682\) −2.95510e13 + 5.11838e13i −0.200286 + 0.346905i
\(683\) 1.51629e14i 1.02019i −0.860119 0.510094i \(-0.829611\pi\)
0.860119 0.510094i \(-0.170389\pi\)
\(684\) 0 0
\(685\) −9.97450e13 −0.661360
\(686\) 1.15966e13 + 6.69528e12i 0.0763324 + 0.0440705i
\(687\) 0 0
\(688\) 2.60465e13 + 4.51139e13i 0.168969 + 0.292663i
\(689\) 6.21197e12 3.58648e12i 0.0400067 0.0230979i
\(690\) 0 0
\(691\) −3.31124e13 + 5.73524e13i −0.210185 + 0.364051i −0.951772 0.306806i \(-0.900740\pi\)
0.741588 + 0.670856i \(0.234073\pi\)
\(692\) 1.55716e14i 0.981300i
\(693\) 0 0
\(694\) −1.17824e14 −0.731873
\(695\) −1.98859e14 1.14812e14i −1.22637 0.708046i
\(696\) 0 0
\(697\) 1.98955e14 + 3.44600e14i 1.20946 + 2.09484i
\(698\) −2.19382e13 + 1.26660e13i −0.132411 + 0.0764475i
\(699\) 0 0
\(700\) 2.03039e13 3.51673e13i 0.120806 0.209242i
\(701\) 5.78990e13i 0.342043i 0.985267 + 0.171022i \(0.0547068\pi\)
−0.985267 + 0.171022i \(0.945293\pi\)
\(702\) 0 0
\(703\) 3.84654e13 0.224024
\(704\) −7.25808e12 4.19046e12i −0.0419719 0.0242325i
\(705\) 0 0
\(706\) 4.23078e13 + 7.32793e13i 0.241211 + 0.417790i
\(707\) 3.37784e14 1.95020e14i 1.91224 1.10403i
\(708\) 0 0
\(709\) −1.35039e14 + 2.33894e14i −0.753750 + 1.30553i 0.192244 + 0.981347i \(0.438424\pi\)
−0.945994 + 0.324186i \(0.894910\pi\)
\(710\) 4.69366e13i 0.260148i
\(711\) 0 0
\(712\) −2.76588e12 −0.0151159
\(713\) −5.08342e13 2.93491e13i −0.275872 0.159275i
\(714\) 0 0
\(715\) 1.92874e13 + 3.34068e13i 0.103215 + 0.178774i
\(716\) 3.13538e12 1.81021e12i 0.0166619 0.00961977i
\(717\) 0 0
\(718\) 4.01059e13 6.94654e13i 0.210177 0.364038i
\(719\) 1.48102e14i 0.770755i −0.922759 0.385377i \(-0.874071\pi\)
0.922759 0.385377i \(-0.125929\pi\)
\(720\) 0 0
\(721\) −1.94375e14 −0.997616
\(722\) −1.08621e14 6.27124e13i −0.553641 0.319645i
\(723\) 0 0
\(724\) −3.25910e13 5.64493e13i −0.163834 0.283769i
\(725\) 1.42907e13 8.25072e12i 0.0713448 0.0411910i
\(726\) 0 0
\(727\) −2.60801e13 + 4.51720e13i −0.128421 + 0.222432i −0.923065 0.384644i \(-0.874324\pi\)
0.794644 + 0.607076i \(0.207658\pi\)
\(728\) 4.57876e13i 0.223919i
\(729\) 0 0
\(730\) 1.79566e14 0.866183
\(731\) 4.58852e14 + 2.64918e14i 2.19829 + 1.26919i
\(732\) 0 0
\(733\) −1.60891e14 2.78671e14i −0.760346 1.31696i −0.942672 0.333720i \(-0.891696\pi\)
0.182326 0.983238i \(-0.441637\pi\)
\(734\) 1.98235e14 1.14451e14i 0.930465 0.537204i
\(735\) 0 0
\(736\) 4.16184e12 7.20851e12i 0.0192706 0.0333777i
\(737\) 3.26009e13i 0.149931i
\(738\) 0 0
\(739\) 1.66542e14 0.755617 0.377809 0.925884i \(-0.376678\pi\)
0.377809 + 0.925884i \(0.376678\pi\)
\(740\) 8.07491e13 + 4.66205e13i 0.363898 + 0.210096i
\(741\) 0 0
\(742\) −1.10772e13 1.91862e13i −0.0492503 0.0853041i
\(743\) 9.84071e13 5.68154e13i 0.434593 0.250912i −0.266708 0.963777i \(-0.585936\pi\)
0.701301 + 0.712865i \(0.252603\pi\)
\(744\) 0 0
\(745\) −6.14419e13 + 1.06420e14i −0.267721 + 0.463707i
\(746\) 8.62230e13i 0.373189i
\(747\) 0 0
\(748\) −8.52421e13 −0.364037
\(749\) 2.88758e14 + 1.66714e14i 1.22497 + 0.707236i
\(750\) 0 0
\(751\) 8.24781e13 + 1.42856e14i 0.345254 + 0.597998i 0.985400 0.170256i \(-0.0544594\pi\)
−0.640146 + 0.768253i \(0.721126\pi\)
\(752\) 3.52019e13 2.03238e13i 0.146378 0.0845116i
\(753\) 0 0
\(754\) −9.30319e12 + 1.61136e13i −0.0381746 + 0.0661204i
\(755\) 4.44320e14i 1.81118i
\(756\) 0 0
\(757\) −2.67990e14 −1.07805 −0.539026 0.842289i \(-0.681207\pi\)
−0.539026 + 0.842289i \(0.681207\pi\)
\(758\) 2.17617e14 + 1.25641e14i 0.869653 + 0.502095i
\(759\) 0 0
\(760\) 1.61263e13 + 2.79316e13i 0.0636014 + 0.110161i
\(761\) −1.12405e14 + 6.48973e13i −0.440417 + 0.254275i −0.703774 0.710423i \(-0.748503\pi\)
0.263358 + 0.964698i \(0.415170\pi\)
\(762\) 0 0
\(763\) −5.48801e13 + 9.50552e13i −0.212223 + 0.367581i
\(764\) 1.05707e14i 0.406105i
\(765\) 0 0
\(766\) −9.71099e13 −0.368230
\(767\) −4.30339e13 2.48456e13i −0.162119 0.0935995i
\(768\) 0 0
\(769\) 1.09593e14 + 1.89820e14i 0.407521 + 0.705846i 0.994611 0.103675i \(-0.0330601\pi\)
−0.587091 + 0.809521i \(0.699727\pi\)
\(770\) 1.03180e14 5.95709e13i 0.381190 0.220080i
\(771\) 0 0
\(772\) 7.97712e13 1.38168e14i 0.290911 0.503872i