Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.2821 | 0.454411 | 0.227205 | − | 0.973847i | \(-0.427041\pi\) | ||||
0.227205 | + | 0.973847i | \(0.427041\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | −406.278 | −0.793511 | ||||||||
\(5\) | 1021.11 | 0.730650 | 0.365325 | − | 0.930880i | \(-0.380958\pi\) | ||||
0.365325 | + | 0.930880i | \(0.380958\pi\) | |||||||
\(6\) | 832.853 | 0.262354 | ||||||||
\(7\) | −5408.24 | −0.851363 | −0.425682 | − | 0.904873i | \(-0.639966\pi\) | ||||
−0.425682 | + | 0.904873i | \(0.639966\pi\) | |||||||
\(8\) | −9441.86 | −0.814991 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 10499.2 | 0.332015 | ||||||||
\(11\) | 83087.8 | 1.71108 | 0.855540 | − | 0.517737i | \(-0.173226\pi\) | ||||
0.855540 | + | 0.517737i | \(0.173226\pi\) | |||||||
\(12\) | −32908.5 | −0.458134 | ||||||||
\(13\) | 79756.4 | 0.774498 | 0.387249 | − | 0.921975i | \(-0.373425\pi\) | ||||
0.387249 | + | 0.921975i | \(0.373425\pi\) | |||||||
\(14\) | −55608.3 | −0.386868 | ||||||||
\(15\) | 82710.3 | 0.421841 | ||||||||
\(16\) | 110932. | 0.423171 | ||||||||
\(17\) | −3716.65 | −0.0107927 | −0.00539636 | − | 0.999985i | \(-0.501718\pi\) | ||||
−0.00539636 | + | 0.999985i | \(0.501718\pi\) | |||||||
\(18\) | 67461.1 | 0.151470 | ||||||||
\(19\) | −920691. | −1.62077 | −0.810387 | − | 0.585895i | \(-0.800743\pi\) | ||||
−0.810387 | + | 0.585895i | \(0.800743\pi\) | |||||||
\(20\) | −414856. | −0.579779 | ||||||||
\(21\) | −438067. | −0.491535 | ||||||||
\(22\) | 854320. | 0.777533 | ||||||||
\(23\) | −802158. | −0.597702 | −0.298851 | − | 0.954300i | \(-0.596603\pi\) | ||||
−0.298851 | + | 0.954300i | \(0.596603\pi\) | |||||||
\(24\) | −764791. | −0.470535 | ||||||||
\(25\) | −910449. | −0.466150 | ||||||||
\(26\) | 820066. | 0.351940 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 2.19725e6 | 0.675566 | ||||||||
\(29\) | 1.05704e6 | 0.277523 | 0.138762 | − | 0.990326i | \(-0.455688\pi\) | ||||
0.138762 | + | 0.990326i | \(0.455688\pi\) | |||||||
\(30\) | 850439. | 0.191689 | ||||||||
\(31\) | −4.68310e6 | −0.910763 | −0.455382 | − | 0.890296i | \(-0.650497\pi\) | ||||
−0.455382 | + | 0.890296i | \(0.650497\pi\) | |||||||
\(32\) | 5.97485e6 | 1.00728 | ||||||||
\(33\) | 6.73011e6 | 0.987892 | ||||||||
\(34\) | −38215.1 | −0.00490433 | ||||||||
\(35\) | −5.52244e6 | −0.622049 | ||||||||
\(36\) | −2.66559e6 | −0.264504 | ||||||||
\(37\) | 1.75608e7 | 1.54041 | 0.770206 | − | 0.637795i | \(-0.220153\pi\) | ||||
0.770206 | + | 0.637795i | \(0.220153\pi\) | |||||||
\(38\) | −9.46667e6 | −0.736497 | ||||||||
\(39\) | 6.46027e6 | 0.447157 | ||||||||
\(40\) | −9.64122e6 | −0.595473 | ||||||||
\(41\) | 2.26645e7 | 1.25262 | 0.626309 | − | 0.779575i | \(-0.284565\pi\) | ||||
0.626309 | + | 0.779575i | \(0.284565\pi\) | |||||||
\(42\) | −4.50427e6 | −0.223359 | ||||||||
\(43\) | 3.56651e7 | 1.59087 | 0.795436 | − | 0.606037i | \(-0.207242\pi\) | ||||
0.795436 | + | 0.606037i | \(0.207242\pi\) | |||||||
\(44\) | −3.37567e7 | −1.35776 | ||||||||
\(45\) | 6.69954e6 | 0.243550 | ||||||||
\(46\) | −8.24790e6 | −0.271602 | ||||||||
\(47\) | 1.91417e7 | 0.572189 | 0.286094 | − | 0.958201i | \(-0.407643\pi\) | ||||
0.286094 | + | 0.958201i | \(0.407643\pi\) | |||||||
\(48\) | 8.98546e6 | 0.244318 | ||||||||
\(49\) | −1.11045e7 | −0.275181 | ||||||||
\(50\) | −9.36137e6 | −0.211824 | ||||||||
\(51\) | −301048. | −0.00623118 | ||||||||
\(52\) | −3.24032e7 | −0.614573 | ||||||||
\(53\) | −4.74993e7 | −0.826886 | −0.413443 | − | 0.910530i | \(-0.635674\pi\) | ||||
−0.413443 | + | 0.910530i | \(0.635674\pi\) | |||||||
\(54\) | 5.46435e6 | 0.0874514 | ||||||||
\(55\) | 8.48422e7 | 1.25020 | ||||||||
\(56\) | 5.10638e7 | 0.693853 | ||||||||
\(57\) | −7.45759e7 | −0.935754 | ||||||||
\(58\) | 1.08686e7 | 0.126109 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −3.36033e7 | −0.334736 | ||||||||
\(61\) | −1.71221e7 | −0.158334 | −0.0791669 | − | 0.996861i | \(-0.525226\pi\) | ||||
−0.0791669 | + | 0.996861i | \(0.525226\pi\) | |||||||
\(62\) | −4.81523e7 | −0.413861 | ||||||||
\(63\) | −3.54835e7 | −0.283788 | ||||||||
\(64\) | 4.63722e6 | 0.0345500 | ||||||||
\(65\) | 8.14404e7 | 0.565887 | ||||||||
\(66\) | 6.91999e7 | 0.448909 | ||||||||
\(67\) | 2.36658e8 | 1.43477 | 0.717387 | − | 0.696674i | \(-0.245338\pi\) | ||||
0.717387 | + | 0.696674i | \(0.245338\pi\) | |||||||
\(68\) | 1.50999e6 | 0.00856415 | ||||||||
\(69\) | −6.49748e7 | −0.345083 | ||||||||
\(70\) | −5.67825e7 | −0.282666 | ||||||||
\(71\) | 3.46163e8 | 1.61666 | 0.808329 | − | 0.588731i | \(-0.200372\pi\) | ||||
0.808329 | + | 0.588731i | \(0.200372\pi\) | |||||||
\(72\) | −6.19480e7 | −0.271664 | ||||||||
\(73\) | 4.22598e8 | 1.74170 | 0.870852 | − | 0.491544i | \(-0.163567\pi\) | ||||
0.870852 | + | 0.491544i | \(0.163567\pi\) | |||||||
\(74\) | 1.80563e8 | 0.699980 | ||||||||
\(75\) | −7.37464e7 | −0.269132 | ||||||||
\(76\) | 3.74056e8 | 1.28610 | ||||||||
\(77\) | −4.49359e8 | −1.45675 | ||||||||
\(78\) | 6.64254e7 | 0.203193 | ||||||||
\(79\) | 5.45210e8 | 1.57486 | 0.787429 | − | 0.616405i | \(-0.211412\pi\) | ||||
0.787429 | + | 0.616405i | \(0.211412\pi\) | |||||||
\(80\) | 1.13274e8 | 0.309190 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 2.33040e8 | 0.569203 | ||||||||
\(83\) | −5.05775e7 | −0.116978 | −0.0584892 | − | 0.998288i | \(-0.518628\pi\) | ||||
−0.0584892 | + | 0.998288i | \(0.518628\pi\) | |||||||
\(84\) | 1.77977e8 | 0.390038 | ||||||||
\(85\) | −3.79512e6 | −0.00788571 | ||||||||
\(86\) | 3.66714e8 | 0.722909 | ||||||||
\(87\) | 8.56200e7 | 0.160228 | ||||||||
\(88\) | −7.84503e8 | −1.39451 | ||||||||
\(89\) | −1.50176e8 | −0.253715 | −0.126857 | − | 0.991921i | \(-0.540489\pi\) | ||||
−0.126857 | + | 0.991921i | \(0.540489\pi\) | |||||||
\(90\) | 6.88856e7 | 0.110672 | ||||||||
\(91\) | −4.31342e8 | −0.659379 | ||||||||
\(92\) | 3.25899e8 | 0.474283 | ||||||||
\(93\) | −3.79331e8 | −0.525829 | ||||||||
\(94\) | 1.96817e8 | 0.260009 | ||||||||
\(95\) | −9.40131e8 | −1.18422 | ||||||||
\(96\) | 4.83963e8 | 0.581556 | ||||||||
\(97\) | −1.06697e9 | −1.22371 | −0.611854 | − | 0.790970i | \(-0.709576\pi\) | ||||
−0.611854 | + | 0.790970i | \(0.709576\pi\) | |||||||
\(98\) | −1.14178e8 | −0.125045 | ||||||||
\(99\) | 5.45139e8 | 0.570360 | ||||||||
\(100\) | 3.69895e8 | 0.369895 | ||||||||
\(101\) | −3.63643e8 | −0.347720 | −0.173860 | − | 0.984770i | \(-0.555624\pi\) | ||||
−0.173860 | + | 0.984770i | \(0.555624\pi\) | |||||||
\(102\) | −3.09542e6 | −0.00283152 | ||||||||
\(103\) | 1.28954e9 | 1.12893 | 0.564467 | − | 0.825456i | \(-0.309082\pi\) | ||||
0.564467 | + | 0.825456i | \(0.309082\pi\) | |||||||
\(104\) | −7.53049e8 | −0.631209 | ||||||||
\(105\) | −4.47317e8 | −0.359140 | ||||||||
\(106\) | −4.88395e8 | −0.375746 | ||||||||
\(107\) | −8.78243e8 | −0.647720 | −0.323860 | − | 0.946105i | \(-0.604981\pi\) | ||||
−0.323860 | + | 0.946105i | \(0.604981\pi\) | |||||||
\(108\) | −2.15913e8 | −0.152711 | ||||||||
\(109\) | 2.59822e9 | 1.76302 | 0.881508 | − | 0.472169i | \(-0.156529\pi\) | ||||
0.881508 | + | 0.472169i | \(0.156529\pi\) | |||||||
\(110\) | 8.72359e8 | 0.568105 | ||||||||
\(111\) | 1.42243e9 | 0.889357 | ||||||||
\(112\) | −5.99945e8 | −0.360272 | ||||||||
\(113\) | −2.19142e7 | −0.0126437 | −0.00632183 | − | 0.999980i | \(-0.502012\pi\) | ||||
−0.00632183 | + | 0.999980i | \(0.502012\pi\) | |||||||
\(114\) | −7.66800e8 | −0.425217 | ||||||||
\(115\) | −8.19096e8 | −0.436711 | ||||||||
\(116\) | −4.29450e8 | −0.220218 | ||||||||
\(117\) | 5.23282e8 | 0.258166 | ||||||||
\(118\) | −1.24592e8 | −0.0591592 | ||||||||
\(119\) | 2.01005e7 | 0.00918853 | ||||||||
\(120\) | −7.80939e8 | −0.343797 | ||||||||
\(121\) | 4.54563e9 | 1.92779 | ||||||||
\(122\) | −1.76052e8 | −0.0719485 | ||||||||
\(123\) | 1.83582e9 | 0.723200 | ||||||||
\(124\) | 1.90264e9 | 0.722701 | ||||||||
\(125\) | −2.92404e9 | −1.07124 | ||||||||
\(126\) | −3.64846e8 | −0.128956 | ||||||||
\(127\) | −3.69422e9 | −1.26010 | −0.630052 | − | 0.776553i | \(-0.716967\pi\) | ||||
−0.630052 | + | 0.776553i | \(0.716967\pi\) | |||||||
\(128\) | −3.01144e9 | −0.991584 | ||||||||
\(129\) | 2.88887e9 | 0.918491 | ||||||||
\(130\) | 8.37382e8 | 0.257145 | ||||||||
\(131\) | 3.85636e8 | 0.114408 | 0.0572040 | − | 0.998363i | \(-0.481781\pi\) | ||||
0.0572040 | + | 0.998363i | \(0.481781\pi\) | |||||||
\(132\) | −2.73429e9 | −0.783903 | ||||||||
\(133\) | 4.97932e9 | 1.37987 | ||||||||
\(134\) | 2.43335e9 | 0.651977 | ||||||||
\(135\) | 5.42662e8 | 0.140614 | ||||||||
\(136\) | 3.50921e7 | 0.00879597 | ||||||||
\(137\) | 6.21695e9 | 1.50777 | 0.753885 | − | 0.657007i | \(-0.228178\pi\) | ||||
0.753885 | + | 0.657007i | \(0.228178\pi\) | |||||||
\(138\) | −6.68080e8 | −0.156810 | ||||||||
\(139\) | 3.62783e9 | 0.824290 | 0.412145 | − | 0.911118i | \(-0.364780\pi\) | ||||
0.412145 | + | 0.911118i | \(0.364780\pi\) | |||||||
\(140\) | 2.24364e9 | 0.493603 | ||||||||
\(141\) | 1.55047e9 | 0.330353 | ||||||||
\(142\) | 3.55930e9 | 0.734627 | ||||||||
\(143\) | 6.62678e9 | 1.32523 | ||||||||
\(144\) | 7.27822e8 | 0.141057 | ||||||||
\(145\) | 1.07936e9 | 0.202772 | ||||||||
\(146\) | 4.34521e9 | 0.791449 | ||||||||
\(147\) | −8.99468e8 | −0.158876 | ||||||||
\(148\) | −7.13457e9 | −1.22233 | ||||||||
\(149\) | 8.69055e8 | 0.144447 | 0.0722236 | − | 0.997388i | \(-0.476990\pi\) | ||||
0.0722236 | + | 0.997388i | \(0.476990\pi\) | |||||||
\(150\) | −7.58271e8 | −0.122296 | ||||||||
\(151\) | 4.90512e9 | 0.767809 | 0.383904 | − | 0.923373i | \(-0.374579\pi\) | ||||
0.383904 | + | 0.923373i | \(0.374579\pi\) | |||||||
\(152\) | 8.69303e9 | 1.32092 | ||||||||
\(153\) | −2.43849e7 | −0.00359758 | ||||||||
\(154\) | −4.62037e9 | −0.661963 | ||||||||
\(155\) | −4.78198e9 | −0.665450 | ||||||||
\(156\) | −2.62466e9 | −0.354824 | ||||||||
\(157\) | −9.75892e9 | −1.28190 | −0.640949 | − | 0.767583i | \(-0.721459\pi\) | ||||
−0.640949 | + | 0.767583i | \(0.721459\pi\) | |||||||
\(158\) | 5.60592e9 | 0.715632 | ||||||||
\(159\) | −3.84744e9 | −0.477403 | ||||||||
\(160\) | 6.10100e9 | 0.735972 | ||||||||
\(161\) | 4.33826e9 | 0.508861 | ||||||||
\(162\) | 4.42612e8 | 0.0504901 | ||||||||
\(163\) | 9.82042e9 | 1.08965 | 0.544823 | − | 0.838551i | \(-0.316597\pi\) | ||||
0.544823 | + | 0.838551i | \(0.316597\pi\) | |||||||
\(164\) | −9.20808e9 | −0.993966 | ||||||||
\(165\) | 6.87222e9 | 0.721804 | ||||||||
\(166\) | −5.20045e8 | −0.0531563 | ||||||||
\(167\) | 1.77473e10 | 1.76566 | 0.882831 | − | 0.469690i | \(-0.155634\pi\) | ||||
0.882831 | + | 0.469690i | \(0.155634\pi\) | |||||||
\(168\) | 4.13617e9 | 0.400596 | ||||||||
\(169\) | −4.24342e9 | −0.400152 | ||||||||
\(170\) | −3.90220e7 | −0.00358335 | ||||||||
\(171\) | −6.04065e9 | −0.540258 | ||||||||
\(172\) | −1.44899e10 | −1.26237 | ||||||||
\(173\) | −2.02008e9 | −0.171460 | −0.0857298 | − | 0.996318i | \(-0.527322\pi\) | ||||
−0.0857298 | + | 0.996318i | \(0.527322\pi\) | |||||||
\(174\) | 8.80357e8 | 0.0728093 | ||||||||
\(175\) | 4.92393e9 | 0.396863 | ||||||||
\(176\) | 9.21706e9 | 0.724078 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | −1.54413e9 | −0.115291 | ||||||||
\(179\) | −5.99197e9 | −0.436245 | −0.218123 | − | 0.975921i | \(-0.569993\pi\) | ||||
−0.218123 | + | 0.975921i | \(0.569993\pi\) | |||||||
\(180\) | −2.72187e9 | −0.193260 | ||||||||
\(181\) | 1.86075e10 | 1.28865 | 0.644324 | − | 0.764753i | \(-0.277139\pi\) | ||||
0.644324 | + | 0.764753i | \(0.277139\pi\) | |||||||
\(182\) | −4.43512e9 | −0.299629 | ||||||||
\(183\) | −1.38689e9 | −0.0914140 | ||||||||
\(184\) | 7.57386e9 | 0.487122 | ||||||||
\(185\) | 1.79316e10 | 1.12550 | ||||||||
\(186\) | −3.90033e9 | −0.238943 | ||||||||
\(187\) | −3.08808e8 | −0.0184672 | ||||||||
\(188\) | −7.77683e9 | −0.454038 | ||||||||
\(189\) | −2.87416e9 | −0.163845 | ||||||||
\(190\) | −9.66656e9 | −0.538122 | ||||||||
\(191\) | −1.08703e10 | −0.591004 | −0.295502 | − | 0.955342i | \(-0.595487\pi\) | ||||
−0.295502 | + | 0.955342i | \(0.595487\pi\) | |||||||
\(192\) | 3.75615e8 | 0.0199474 | ||||||||
\(193\) | −3.52554e10 | −1.82902 | −0.914510 | − | 0.404564i | \(-0.867423\pi\) | ||||
−0.914510 | + | 0.404564i | \(0.867423\pi\) | |||||||
\(194\) | −1.09707e10 | −0.556066 | ||||||||
\(195\) | 6.59668e9 | 0.326715 | ||||||||
\(196\) | 4.51153e9 | 0.218359 | ||||||||
\(197\) | −3.49511e10 | −1.65334 | −0.826670 | − | 0.562687i | \(-0.809768\pi\) | ||||
−0.826670 | + | 0.562687i | \(0.809768\pi\) | |||||||
\(198\) | 5.60520e9 | 0.259178 | ||||||||
\(199\) | 8.09055e9 | 0.365712 | 0.182856 | − | 0.983140i | \(-0.441466\pi\) | ||||
0.182856 | + | 0.983140i | \(0.441466\pi\) | |||||||
\(200\) | 8.59633e9 | 0.379908 | ||||||||
\(201\) | 1.91693e10 | 0.828368 | ||||||||
\(202\) | −3.73903e9 | −0.158007 | ||||||||
\(203\) | −5.71671e9 | −0.236273 | ||||||||
\(204\) | 1.22309e8 | 0.00494451 | ||||||||
\(205\) | 2.31431e10 | 0.915226 | ||||||||
\(206\) | 1.32593e10 | 0.513000 | ||||||||
\(207\) | −5.26296e9 | −0.199234 | ||||||||
\(208\) | 8.84751e9 | 0.327745 | ||||||||
\(209\) | −7.64981e10 | −2.77327 | ||||||||
\(210\) | −4.59938e9 | −0.163197 | ||||||||
\(211\) | 1.92887e9 | 0.0669934 | 0.0334967 | − | 0.999439i | \(-0.489336\pi\) | ||||
0.0334967 | + | 0.999439i | \(0.489336\pi\) | |||||||
\(212\) | 1.92979e10 | 0.656143 | ||||||||
\(213\) | 2.80392e10 | 0.933378 | ||||||||
\(214\) | −9.03021e9 | −0.294331 | ||||||||
\(215\) | 3.64182e10 | 1.16237 | ||||||||
\(216\) | −5.01779e9 | −0.156845 | ||||||||
\(217\) | 2.53273e10 | 0.775390 | ||||||||
\(218\) | 2.67152e10 | 0.801133 | ||||||||
\(219\) | 3.42304e10 | 1.00557 | ||||||||
\(220\) | −3.44695e10 | −0.992048 | ||||||||
\(221\) | −2.96426e8 | −0.00835895 | ||||||||
\(222\) | 1.46256e10 | 0.404133 | ||||||||
\(223\) | −2.36958e9 | −0.0641653 | −0.0320827 | − | 0.999485i | \(-0.510214\pi\) | ||||
−0.0320827 | + | 0.999485i | \(0.510214\pi\) | |||||||
\(224\) | −3.23134e10 | −0.857564 | ||||||||
\(225\) | −5.97346e9 | −0.155383 | ||||||||
\(226\) | −2.25325e8 | −0.00574542 | ||||||||
\(227\) | −5.19431e10 | −1.29841 | −0.649205 | − | 0.760614i | \(-0.724898\pi\) | ||||
−0.649205 | + | 0.760614i | \(0.724898\pi\) | |||||||
\(228\) | 3.02985e10 | 0.742531 | ||||||||
\(229\) | 3.55924e9 | 0.0855260 | 0.0427630 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427630 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(230\) | −8.42206e9 | −0.198446 | ||||||||
\(231\) | −3.63981e10 | −0.841055 | ||||||||
\(232\) | −9.98039e9 | −0.226179 | ||||||||
\(233\) | 1.10887e10 | 0.246478 | 0.123239 | − | 0.992377i | \(-0.460672\pi\) | ||||
0.123239 | + | 0.992377i | \(0.460672\pi\) | |||||||
\(234\) | 5.38046e9 | 0.117313 | ||||||||
\(235\) | 1.95458e10 | 0.418070 | ||||||||
\(236\) | 4.92301e9 | 0.103306 | ||||||||
\(237\) | 4.41620e10 | 0.909245 | ||||||||
\(238\) | 2.06676e8 | 0.00417537 | ||||||||
\(239\) | −8.65942e10 | −1.71671 | −0.858357 | − | 0.513052i | \(-0.828515\pi\) | ||||
−0.858357 | + | 0.513052i | \(0.828515\pi\) | |||||||
\(240\) | 9.17519e9 | 0.178511 | ||||||||
\(241\) | −1.31367e10 | −0.250848 | −0.125424 | − | 0.992103i | \(-0.540029\pi\) | ||||
−0.125424 | + | 0.992103i | \(0.540029\pi\) | |||||||
\(242\) | 4.67388e10 | 0.876009 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 6.95634e9 | 0.125640 | ||||||||
\(245\) | −1.13390e10 | −0.201061 | ||||||||
\(246\) | 1.88762e10 | 0.328630 | ||||||||
\(247\) | −7.34310e10 | −1.25529 | ||||||||
\(248\) | 4.42171e10 | 0.742263 | ||||||||
\(249\) | −4.09678e9 | −0.0675376 | ||||||||
\(250\) | −3.00654e10 | −0.486784 | ||||||||
\(251\) | 1.25306e11 | 1.99268 | 0.996342 | − | 0.0854528i | \(-0.0272337\pi\) | ||||
0.996342 | + | 0.0854528i | \(0.0272337\pi\) | |||||||
\(252\) | 1.44161e10 | 0.225189 | ||||||||
\(253\) | −6.66495e10 | −1.02272 | ||||||||
\(254\) | −3.79845e10 | −0.572605 | ||||||||
\(255\) | −3.07405e8 | −0.00455282 | ||||||||
\(256\) | −3.33383e10 | −0.485136 | ||||||||
\(257\) | 9.80273e10 | 1.40168 | 0.700838 | − | 0.713320i | \(-0.252809\pi\) | ||||
0.700838 | + | 0.713320i | \(0.252809\pi\) | |||||||
\(258\) | 2.97038e10 | 0.417372 | ||||||||
\(259\) | −9.49731e10 | −1.31145 | ||||||||
\(260\) | −3.30874e10 | −0.449038 | ||||||||
\(261\) | 6.93522e9 | 0.0925077 | ||||||||
\(262\) | 3.96516e9 | 0.0519882 | ||||||||
\(263\) | −1.02117e11 | −1.31613 | −0.658065 | − | 0.752961i | \(-0.728625\pi\) | ||||
−0.658065 | + | 0.752961i | \(0.728625\pi\) | |||||||
\(264\) | −6.35448e10 | −0.805123 | ||||||||
\(265\) | −4.85023e10 | −0.604165 | ||||||||
\(266\) | 5.11980e10 | 0.627026 | ||||||||
\(267\) | −1.21643e10 | −0.146482 | ||||||||
\(268\) | −9.61487e10 | −1.13851 | ||||||||
\(269\) | 6.03682e10 | 0.702948 | 0.351474 | − | 0.936198i | \(-0.385681\pi\) | ||||
0.351474 | + | 0.936198i | \(0.385681\pi\) | |||||||
\(270\) | 5.57973e9 | 0.0638964 | ||||||||
\(271\) | 8.51802e10 | 0.959350 | 0.479675 | − | 0.877446i | \(-0.340755\pi\) | ||||
0.479675 | + | 0.877446i | \(0.340755\pi\) | |||||||
\(272\) | −4.12294e8 | −0.00456716 | ||||||||
\(273\) | −3.49387e10 | −0.380693 | ||||||||
\(274\) | 6.39236e10 | 0.685147 | ||||||||
\(275\) | −7.56472e10 | −0.797620 | ||||||||
\(276\) | 2.63978e10 | 0.273827 | ||||||||
\(277\) | 1.02318e10 | 0.104422 | 0.0522112 | − | 0.998636i | \(-0.483373\pi\) | ||||
0.0522112 | + | 0.998636i | \(0.483373\pi\) | |||||||
\(278\) | 3.73018e10 | 0.374566 | ||||||||
\(279\) | −3.07258e10 | −0.303588 | ||||||||
\(280\) | 5.21421e10 | 0.506964 | ||||||||
\(281\) | 3.22800e10 | 0.308855 | 0.154428 | − | 0.988004i | \(-0.450647\pi\) | ||||
0.154428 | + | 0.988004i | \(0.450647\pi\) | |||||||
\(282\) | 1.59422e10 | 0.150116 | ||||||||
\(283\) | 1.78367e11 | 1.65301 | 0.826507 | − | 0.562926i | \(-0.190324\pi\) | ||||
0.826507 | + | 0.562926i | \(0.190324\pi\) | |||||||
\(284\) | −1.40638e11 | −1.28284 | ||||||||
\(285\) | −7.61506e10 | −0.683709 | ||||||||
\(286\) | 6.81375e10 | 0.602198 | ||||||||
\(287\) | −1.22575e11 | −1.06643 | ||||||||
\(288\) | 3.92010e10 | 0.335761 | ||||||||
\(289\) | −1.18574e11 | −0.999884 | ||||||||
\(290\) | 1.10981e10 | 0.0921419 | ||||||||
\(291\) | −8.64243e10 | −0.706509 | ||||||||
\(292\) | −1.71692e11 | −1.38206 | ||||||||
\(293\) | −1.22710e11 | −0.972689 | −0.486345 | − | 0.873767i | \(-0.661670\pi\) | ||||
−0.486345 | + | 0.873767i | \(0.661670\pi\) | |||||||
\(294\) | −9.24845e9 | −0.0721948 | ||||||||
\(295\) | −1.23732e10 | −0.0951226 | ||||||||
\(296\) | −1.65807e11 | −1.25542 | ||||||||
\(297\) | 4.41563e10 | 0.329297 | ||||||||
\(298\) | 8.93575e9 | 0.0656383 | ||||||||
\(299\) | −6.39772e10 | −0.462919 | ||||||||
\(300\) | 2.99615e10 | 0.213559 | ||||||||
\(301\) | −1.92885e11 | −1.35441 | ||||||||
\(302\) | 5.04351e10 | 0.348900 | ||||||||
\(303\) | −2.94551e10 | −0.200756 | ||||||||
\(304\) | −1.02134e11 | −0.685864 | ||||||||
\(305\) | −1.74837e10 | −0.115687 | ||||||||
\(306\) | −2.50729e8 | −0.00163478 | ||||||||
\(307\) | 4.87069e10 | 0.312945 | 0.156473 | − | 0.987682i | \(-0.449988\pi\) | ||||
0.156473 | + | 0.987682i | \(0.449988\pi\) | |||||||
\(308\) | 1.82564e11 | 1.15595 | ||||||||
\(309\) | 1.04453e11 | 0.651791 | ||||||||
\(310\) | −4.91690e10 | −0.302387 | ||||||||
\(311\) | 2.92063e10 | 0.177033 | 0.0885165 | − | 0.996075i | \(-0.471787\pi\) | ||||
0.0885165 | + | 0.996075i | \(0.471787\pi\) | |||||||
\(312\) | −6.09969e10 | −0.364429 | ||||||||
\(313\) | −2.12156e11 | −1.24941 | −0.624706 | − | 0.780860i | \(-0.714781\pi\) | ||||
−0.624706 | + | 0.780860i | \(0.714781\pi\) | |||||||
\(314\) | −1.00343e11 | −0.582508 | ||||||||
\(315\) | −3.62327e10 | −0.207350 | ||||||||
\(316\) | −2.21506e11 | −1.24967 | ||||||||
\(317\) | 9.39993e9 | 0.0522827 | 0.0261413 | − | 0.999658i | \(-0.491678\pi\) | ||||
0.0261413 | + | 0.999658i | \(0.491678\pi\) | |||||||
\(318\) | −3.95600e10 | −0.216937 | ||||||||
\(319\) | 8.78269e10 | 0.474864 | ||||||||
\(320\) | 4.73513e9 | 0.0252440 | ||||||||
\(321\) | −7.11376e10 | −0.373961 | ||||||||
\(322\) | 4.46066e10 | 0.231232 | ||||||||
\(323\) | 3.42188e9 | 0.0174926 | ||||||||
\(324\) | −1.74889e10 | −0.0881679 | ||||||||
\(325\) | −7.26141e10 | −0.361032 | ||||||||
\(326\) | 1.00975e11 | 0.495147 | ||||||||
\(327\) | 2.10456e11 | 1.01788 | ||||||||
\(328\) | −2.13995e11 | −1.02087 | ||||||||
\(329\) | −1.03523e11 | −0.487140 | ||||||||
\(330\) | 7.06611e10 | 0.327995 | ||||||||
\(331\) | −2.23051e11 | −1.02136 | −0.510680 | − | 0.859771i | \(-0.670606\pi\) | ||||
−0.510680 | + | 0.859771i | \(0.670606\pi\) | |||||||
\(332\) | 2.05485e10 | 0.0928237 | ||||||||
\(333\) | 1.15217e11 | 0.513471 | ||||||||
\(334\) | 1.82480e11 | 0.802336 | ||||||||
\(335\) | 2.41655e11 | 1.04832 | ||||||||
\(336\) | −4.85955e10 | −0.208003 | ||||||||
\(337\) | −2.53877e11 | −1.07223 | −0.536117 | − | 0.844144i | \(-0.680109\pi\) | ||||
−0.536117 | + | 0.844144i | \(0.680109\pi\) | |||||||
\(338\) | −4.36314e10 | −0.181834 | ||||||||
\(339\) | −1.77505e9 | −0.00729982 | ||||||||
\(340\) | 1.54187e9 | 0.00625740 | ||||||||
\(341\) | −3.89108e11 | −1.55839 | ||||||||
\(342\) | −6.21108e10 | −0.245499 | ||||||||
\(343\) | 2.78298e11 | 1.08564 | ||||||||
\(344\) | −3.36745e11 | −1.29655 | ||||||||
\(345\) | −6.63468e10 | −0.252135 | ||||||||
\(346\) | −2.07708e10 | −0.0779131 | ||||||||
\(347\) | 2.33811e11 | 0.865729 | 0.432864 | − | 0.901459i | \(-0.357503\pi\) | ||||
0.432864 | + | 0.901459i | \(0.357503\pi\) | |||||||
\(348\) | −3.47855e10 | −0.127143 | ||||||||
\(349\) | −4.83086e10 | −0.174305 | −0.0871525 | − | 0.996195i | \(-0.527777\pi\) | ||||
−0.0871525 | + | 0.996195i | \(0.527777\pi\) | |||||||
\(350\) | 5.06285e10 | 0.180339 | ||||||||
\(351\) | 4.23858e10 | 0.149052 | ||||||||
\(352\) | 4.96437e11 | 1.72354 | ||||||||
\(353\) | 1.95997e11 | 0.671834 | 0.335917 | − | 0.941892i | \(-0.390954\pi\) | ||||
0.335917 | + | 0.941892i | \(0.390954\pi\) | |||||||
\(354\) | −1.00920e10 | −0.0341556 | ||||||||
\(355\) | 3.53472e11 | 1.18121 | ||||||||
\(356\) | 6.10132e10 | 0.201325 | ||||||||
\(357\) | 1.62814e9 | 0.00530500 | ||||||||
\(358\) | −6.16103e10 | −0.198235 | ||||||||
\(359\) | 1.10952e10 | 0.0352543 | 0.0176271 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176271 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(360\) | −6.32561e10 | −0.198491 | ||||||||
\(361\) | 5.24983e11 | 1.62691 | ||||||||
\(362\) | 1.91325e11 | 0.585575 | ||||||||
\(363\) | 3.68196e11 | 1.11301 | ||||||||
\(364\) | 1.75244e11 | 0.523225 | ||||||||
\(365\) | 4.31521e11 | 1.27258 | ||||||||
\(366\) | −1.42602e10 | −0.0415395 | ||||||||
\(367\) | 1.41329e11 | 0.406663 | 0.203331 | − | 0.979110i | \(-0.434823\pi\) | ||||
0.203331 | + | 0.979110i | \(0.434823\pi\) | |||||||
\(368\) | −8.89847e10 | −0.252930 | ||||||||
\(369\) | 1.48702e11 | 0.417539 | ||||||||
\(370\) | 1.84375e11 | 0.511440 | ||||||||
\(371\) | 2.56888e11 | 0.703981 | ||||||||
\(372\) | 1.54114e11 | 0.417251 | ||||||||
\(373\) | −2.00258e11 | −0.535673 | −0.267836 | − | 0.963464i | \(-0.586309\pi\) | ||||
−0.267836 | + | 0.963464i | \(0.586309\pi\) | |||||||
\(374\) | −3.17521e9 | −0.00839170 | ||||||||
\(375\) | −2.36847e11 | −0.618482 | ||||||||
\(376\) | −1.80733e11 | −0.466328 | ||||||||
\(377\) | 8.43055e10 | 0.214941 | ||||||||
\(378\) | −2.95525e10 | −0.0744529 | ||||||||
\(379\) | −7.47339e11 | −1.86055 | −0.930274 | − | 0.366865i | \(-0.880431\pi\) | ||||
−0.930274 | + | 0.366865i | \(0.880431\pi\) | |||||||
\(380\) | 3.81954e11 | 0.939691 | ||||||||
\(381\) | −2.99232e11 | −0.727522 | ||||||||
\(382\) | −1.11770e11 | −0.268558 | ||||||||
\(383\) | 5.64880e11 | 1.34141 | 0.670705 | − | 0.741724i | \(-0.265992\pi\) | ||||
0.670705 | + | 0.741724i | \(0.265992\pi\) | |||||||
\(384\) | −2.43927e11 | −0.572491 | ||||||||
\(385\) | −4.58847e11 | −1.06437 | ||||||||
\(386\) | −3.62501e11 | −0.831126 | ||||||||
\(387\) | 2.33999e11 | 0.530291 | ||||||||
\(388\) | 4.33485e11 | 0.971026 | ||||||||
\(389\) | 3.37311e11 | 0.746890 | 0.373445 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373445 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(390\) | 6.78280e10 | 0.148463 | ||||||||
\(391\) | 2.98134e9 | 0.00645084 | ||||||||
\(392\) | 1.04848e11 | 0.224270 | ||||||||
\(393\) | 3.12365e10 | 0.0660535 | ||||||||
\(394\) | −3.59372e11 | −0.751296 | ||||||||
\(395\) | 5.56722e11 | 1.15067 | ||||||||
\(396\) | −2.21478e11 | −0.452587 | ||||||||
\(397\) | −3.78094e11 | −0.763911 | −0.381956 | − | 0.924181i | \(-0.624749\pi\) | ||||
−0.381956 | + | 0.924181i | \(0.624749\pi\) | |||||||
\(398\) | 8.31882e10 | 0.166183 | ||||||||
\(399\) | 4.03325e11 | 0.796667 | ||||||||
\(400\) | −1.00998e11 | −0.197261 | ||||||||
\(401\) | 2.23371e11 | 0.431397 | 0.215698 | − | 0.976460i | \(-0.430797\pi\) | ||||
0.215698 | + | 0.976460i | \(0.430797\pi\) | |||||||
\(402\) | 1.97101e11 | 0.376419 | ||||||||
\(403\) | −3.73507e11 | −0.705385 | ||||||||
\(404\) | 1.47740e11 | 0.275919 | ||||||||
\(405\) | 4.39557e10 | 0.0811834 | ||||||||
\(406\) | −5.87800e10 | −0.107365 | ||||||||
\(407\) | 1.45909e12 | 2.63577 | ||||||||
\(408\) | 2.84246e9 | 0.00507836 | ||||||||
\(409\) | −7.63055e11 | −1.34834 | −0.674172 | − | 0.738574i | \(-0.735500\pi\) | ||||
−0.674172 | + | 0.738574i | \(0.735500\pi\) | |||||||
\(410\) | 2.37960e11 | 0.415889 | ||||||||
\(411\) | 5.03573e11 | 0.870511 | ||||||||
\(412\) | −5.23913e11 | −0.895822 | ||||||||
\(413\) | 6.55336e10 | 0.110838 | ||||||||
\(414\) | −5.41145e10 | −0.0905341 | ||||||||
\(415\) | −5.16455e10 | −0.0854704 | ||||||||
\(416\) | 4.76532e11 | 0.780139 | ||||||||
\(417\) | 2.93854e11 | 0.475904 | ||||||||
\(418\) | −7.86565e11 | −1.26020 | ||||||||
\(419\) | −8.80094e11 | −1.39497 | −0.697487 | − | 0.716598i | \(-0.745698\pi\) | ||||
−0.697487 | + | 0.716598i | \(0.745698\pi\) | |||||||
\(420\) | 1.81735e11 | 0.284982 | ||||||||
\(421\) | 2.56266e11 | 0.397577 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(422\) | 1.98329e10 | 0.0304425 | ||||||||
\(423\) | 1.25588e11 | 0.190730 | ||||||||
\(424\) | 4.48482e11 | 0.673905 | ||||||||
\(425\) | 3.38382e9 | 0.00503103 | ||||||||
\(426\) | 2.88303e11 | 0.424137 | ||||||||
\(427\) | 9.26006e10 | 0.134799 | ||||||||
\(428\) | 3.56810e11 | 0.513973 | ||||||||
\(429\) | 5.36769e11 | 0.765121 | ||||||||
\(430\) | 3.74457e11 | 0.528194 | ||||||||
\(431\) | −3.10399e11 | −0.433284 | −0.216642 | − | 0.976251i | \(-0.569510\pi\) | ||||
−0.216642 | + | 0.976251i | \(0.569510\pi\) | |||||||
\(432\) | 5.89536e10 | 0.0814392 | ||||||||
\(433\) | −8.40602e10 | −0.114920 | −0.0574599 | − | 0.998348i | \(-0.518300\pi\) | ||||
−0.0574599 | + | 0.998348i | \(0.518300\pi\) | |||||||
\(434\) | 2.60419e11 | 0.352346 | ||||||||
\(435\) | 8.74279e10 | 0.117071 | ||||||||
\(436\) | −1.05560e12 | −1.39897 | ||||||||
\(437\) | 7.38539e11 | 0.968740 | ||||||||
\(438\) | 3.51962e11 | 0.456943 | ||||||||
\(439\) | 3.22184e11 | 0.414012 | 0.207006 | − | 0.978340i | \(-0.433628\pi\) | ||||
0.207006 | + | 0.978340i | \(0.433628\pi\) | |||||||
\(440\) | −8.01068e11 | −1.01890 | ||||||||
\(441\) | −7.28569e10 | −0.0917270 | ||||||||
\(442\) | −3.04790e9 | −0.00379840 | ||||||||
\(443\) | 9.07439e11 | 1.11944 | 0.559720 | − | 0.828682i | \(-0.310909\pi\) | ||||
0.559720 | + | 0.828682i | \(0.310909\pi\) | |||||||
\(444\) | −5.77900e11 | −0.705715 | ||||||||
\(445\) | −1.53347e11 | −0.185377 | ||||||||
\(446\) | −2.43644e10 | −0.0291574 | ||||||||
\(447\) | 7.03935e10 | 0.0833966 | ||||||||
\(448\) | −2.50792e10 | −0.0294146 | ||||||||
\(449\) | 1.17081e12 | 1.35950 | 0.679750 | − | 0.733444i | \(-0.262088\pi\) | ||||
0.679750 | + | 0.733444i | \(0.262088\pi\) | |||||||
\(450\) | −6.14199e10 | −0.0706078 | ||||||||
\(451\) | 1.88314e12 | 2.14333 | ||||||||
\(452\) | 8.90326e9 | 0.0100329 | ||||||||
\(453\) | 3.97314e11 | 0.443295 | ||||||||
\(454\) | −5.34087e11 | −0.590011 | ||||||||
\(455\) | −4.40450e11 | −0.481776 | ||||||||
\(456\) | 7.04135e11 | 0.762631 | ||||||||
\(457\) | −1.29882e12 | −1.39292 | −0.696458 | − | 0.717597i | \(-0.745242\pi\) | ||||
−0.696458 | + | 0.717597i | \(0.745242\pi\) | |||||||
\(458\) | 3.65966e10 | 0.0388639 | ||||||||
\(459\) | −1.97518e9 | −0.00207706 | ||||||||
\(460\) | 3.32780e11 | 0.346535 | ||||||||
\(461\) | −9.50693e11 | −0.980362 | −0.490181 | − | 0.871621i | \(-0.663069\pi\) | ||||
−0.490181 | + | 0.871621i | \(0.663069\pi\) | |||||||
\(462\) | −3.74250e11 | −0.382184 | ||||||||
\(463\) | −1.14359e12 | −1.15652 | −0.578261 | − | 0.815852i | \(-0.696269\pi\) | ||||
−0.578261 | + | 0.815852i | \(0.696269\pi\) | |||||||
\(464\) | 1.17259e11 | 0.117440 | ||||||||
\(465\) | −3.87340e11 | −0.384198 | ||||||||
\(466\) | 1.14015e11 | 0.112002 | ||||||||
\(467\) | −1.38510e12 | −1.34758 | −0.673792 | − | 0.738921i | \(-0.735336\pi\) | ||||
−0.673792 | + | 0.738921i | \(0.735336\pi\) | |||||||
\(468\) | −2.12598e11 | −0.204858 | ||||||||
\(469\) | −1.27990e12 | −1.22151 | ||||||||
\(470\) | 2.00973e11 | 0.189975 | ||||||||
\(471\) | −7.90473e11 | −0.740104 | ||||||||
\(472\) | 1.14410e11 | 0.106103 | ||||||||
\(473\) | 2.96333e12 | 2.72211 | ||||||||
\(474\) | 4.54080e11 | 0.413171 | ||||||||
\(475\) | 8.38242e11 | 0.755524 | ||||||||
\(476\) | −8.16639e9 | −0.00729120 | ||||||||
\(477\) | −3.11643e11 | −0.275629 | ||||||||
\(478\) | −8.90373e11 | −0.780093 | ||||||||
\(479\) | −1.68282e12 | −1.46059 | −0.730295 | − | 0.683132i | \(-0.760617\pi\) | ||||
−0.730295 | + | 0.683132i | \(0.760617\pi\) | |||||||
\(480\) | 4.94181e11 | 0.424914 | ||||||||
\(481\) | 1.40059e12 | 1.19305 | ||||||||
\(482\) | −1.35073e11 | −0.113988 | ||||||||
\(483\) | 3.51399e11 | 0.293791 | ||||||||
\(484\) | −1.84679e12 | −1.52972 | ||||||||
\(485\) | −1.08950e12 | −0.894103 | ||||||||
\(486\) | 3.58516e10 | 0.0291505 | ||||||||
\(487\) | −3.61535e11 | −0.291253 | −0.145626 | − | 0.989340i | \(-0.546520\pi\) | ||||
−0.145626 | + | 0.989340i | \(0.546520\pi\) | |||||||
\(488\) | 1.61665e11 | 0.129040 | ||||||||
\(489\) | 7.95454e11 | 0.629108 | ||||||||
\(490\) | −1.16589e11 | −0.0913643 | ||||||||
\(491\) | −1.88832e12 | −1.46625 | −0.733127 | − | 0.680092i | \(-0.761940\pi\) | ||||
−0.733127 | + | 0.680092i | \(0.761940\pi\) | |||||||
\(492\) | −7.45854e11 | −0.573867 | ||||||||
\(493\) | −3.92863e9 | −0.00299523 | ||||||||
\(494\) | −7.55027e11 | −0.570416 | ||||||||
\(495\) | 5.56650e11 | 0.416734 | ||||||||
\(496\) | −5.19504e11 | −0.385408 | ||||||||
\(497\) | −1.87213e12 | −1.37636 | ||||||||
\(498\) | −4.21236e10 | −0.0306898 | ||||||||
\(499\) | 2.16118e12 | 1.56041 | 0.780205 | − | 0.625524i | \(-0.215115\pi\) | ||||
0.780205 | + | 0.625524i | \(0.215115\pi\) | |||||||
\(500\) | 1.18797e12 | 0.850043 | ||||||||
\(501\) | 1.43753e12 | 1.01941 | ||||||||
\(502\) | 1.28841e12 | 0.905497 | ||||||||
\(503\) | 1.35300e12 | 0.942416 | 0.471208 | − | 0.882022i | \(-0.343818\pi\) | ||||
0.471208 | + | 0.882022i | \(0.343818\pi\) | |||||||
\(504\) | 3.35030e11 | 0.231284 | ||||||||
\(505\) | −3.71321e11 | −0.254061 | ||||||||
\(506\) | −6.85300e11 | −0.464733 | ||||||||
\(507\) | −3.43717e11 | −0.231028 | ||||||||
\(508\) | 1.50088e12 | 0.999907 | ||||||||
\(509\) | 1.28269e12 | 0.847019 | 0.423509 | − | 0.905892i | \(-0.360798\pi\) | ||||
0.423509 | + | 0.905892i | \(0.360798\pi\) | |||||||
\(510\) | −3.16078e9 | −0.00206885 | ||||||||
\(511\) | −2.28551e12 | −1.48282 | ||||||||
\(512\) | 1.19907e12 | 0.771133 | ||||||||
\(513\) | −4.89293e11 | −0.311918 | ||||||||
\(514\) | 1.00793e12 | 0.636937 | ||||||||
\(515\) | 1.31677e12 | 0.824856 | ||||||||
\(516\) | −1.17368e12 | −0.728832 | ||||||||
\(517\) | 1.59044e12 | 0.979060 | ||||||||
\(518\) | −9.76527e11 | −0.595937 | ||||||||
\(519\) | −1.63627e11 | −0.0989923 | ||||||||
\(520\) | −7.68949e11 | −0.461193 | ||||||||
\(521\) | 2.70756e12 | 1.60993 | 0.804967 | − | 0.593320i | \(-0.202183\pi\) | ||||
0.804967 | + | 0.593320i | \(0.202183\pi\) | |||||||
\(522\) | 7.13089e10 | 0.0420365 | ||||||||
\(523\) | 1.55055e12 | 0.906208 | 0.453104 | − | 0.891458i | \(-0.350317\pi\) | ||||
0.453104 | + | 0.891458i | \(0.350317\pi\) | |||||||
\(524\) | −1.56675e11 | −0.0907840 | ||||||||
\(525\) | 3.98838e11 | 0.229129 | ||||||||
\(526\) | −1.04998e12 | −0.598063 | ||||||||
\(527\) | 1.74054e10 | 0.00982962 | ||||||||
\(528\) | 7.46582e11 | 0.418047 | ||||||||
\(529\) | −1.15769e12 | −0.642752 | ||||||||
\(530\) | −4.98707e11 | −0.274539 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −2.02298e12 | −1.09494 | ||||||||
\(533\) | 1.80764e12 | 0.970151 | ||||||||
\(534\) | −1.25075e11 | −0.0665631 | ||||||||
\(535\) | −8.96787e11 | −0.473257 | ||||||||
\(536\) | −2.23449e12 | −1.16933 | ||||||||
\(537\) | −4.85350e11 | −0.251866 | ||||||||
\(538\) | 6.20715e11 | 0.319427 | ||||||||
\(539\) | −9.22652e11 | −0.470856 | ||||||||
\(540\) | −2.20472e11 | −0.111579 | ||||||||
\(541\) | −3.07338e12 | −1.54251 | −0.771257 | − | 0.636524i | \(-0.780372\pi\) | ||||
−0.771257 | + | 0.636524i | \(0.780372\pi\) | |||||||
\(542\) | 8.75835e11 | 0.435939 | ||||||||
\(543\) | 1.50721e12 | 0.744001 | ||||||||
\(544\) | −2.22064e10 | −0.0108713 | ||||||||
\(545\) | 2.65308e12 | 1.28815 | ||||||||
\(546\) | −3.59244e11 | −0.172991 | ||||||||
\(547\) | −2.55306e12 | −1.21932 | −0.609661 | − | 0.792663i | \(-0.708694\pi\) | ||||
−0.609661 | + | 0.792663i | \(0.708694\pi\) | |||||||
\(548\) | −2.52581e12 | −1.19643 | ||||||||
\(549\) | −1.12338e11 | −0.0527779 | ||||||||
\(550\) | −7.77815e11 | −0.362447 | ||||||||
\(551\) | −9.73204e11 | −0.449802 | ||||||||
\(552\) | 6.13483e11 | 0.281240 | ||||||||
\(553\) | −2.94862e12 | −1.34078 | ||||||||
\(554\) | 1.05205e11 | 0.0474506 | ||||||||
\(555\) | 1.45246e12 | 0.649809 | ||||||||
\(556\) | −1.47391e12 | −0.654083 | ||||||||
\(557\) | −2.18123e12 | −0.960182 | −0.480091 | − | 0.877219i | \(-0.659396\pi\) | ||||
−0.480091 | + | 0.877219i | \(0.659396\pi\) | |||||||
\(558\) | −3.15927e11 | −0.137954 | ||||||||
\(559\) | 2.84452e12 | 1.23213 | ||||||||
\(560\) | −6.12613e11 | −0.263233 | ||||||||
\(561\) | −2.50134e10 | −0.0106620 | ||||||||
\(562\) | 3.31907e11 | 0.140347 | ||||||||
\(563\) | −2.74986e12 | −1.15351 | −0.576756 | − | 0.816916i | \(-0.695682\pi\) | ||||
−0.576756 | + | 0.816916i | \(0.695682\pi\) | |||||||
\(564\) | −6.29923e11 | −0.262139 | ||||||||
\(565\) | −2.23769e10 | −0.00923810 | ||||||||
\(566\) | 1.83400e12 | 0.751147 | ||||||||
\(567\) | −2.32807e11 | −0.0945959 | ||||||||
\(568\) | −3.26842e12 | −1.31756 | ||||||||
\(569\) | −1.19313e12 | −0.477179 | −0.238590 | − | 0.971120i | \(-0.576685\pi\) | ||||
−0.238590 | + | 0.971120i | \(0.576685\pi\) | |||||||
\(570\) | −7.82991e11 | −0.310685 | ||||||||
\(571\) | 4.05845e12 | 1.59771 | 0.798854 | − | 0.601525i | \(-0.205440\pi\) | ||||
0.798854 | + | 0.601525i | \(0.205440\pi\) | |||||||
\(572\) | −2.69231e12 | −1.05158 | ||||||||
\(573\) | −8.80492e11 | −0.341216 | ||||||||
\(574\) | −1.26033e12 | −0.484599 | ||||||||
\(575\) | 7.30324e11 | 0.278619 | ||||||||
\(576\) | 3.04248e10 | 0.0115167 | ||||||||
\(577\) | 1.91055e12 | 0.717573 | 0.358787 | − | 0.933420i | \(-0.383191\pi\) | ||||
0.358787 | + | 0.933420i | \(0.383191\pi\) | |||||||
\(578\) | −1.21920e12 | −0.454358 | ||||||||
\(579\) | −2.85569e12 | −1.05598 | ||||||||
\(580\) | −4.38518e11 | −0.160902 | ||||||||
\(581\) | 2.73535e11 | 0.0995912 | ||||||||
\(582\) | −8.88627e11 | −0.321045 | ||||||||
\(583\) | −3.94661e12 | −1.41487 | ||||||||
\(584\) | −3.99011e12 | −1.41947 | ||||||||
\(585\) | 5.34331e11 | 0.188629 | ||||||||
\(586\) | −1.26172e12 | −0.442000 | ||||||||
\(587\) | 3.64868e12 | 1.26842 | 0.634212 | − | 0.773159i | \(-0.281324\pi\) | ||||
0.634212 | + | 0.773159i | \(0.281324\pi\) | |||||||
\(588\) | 3.65434e11 | 0.126070 | ||||||||
\(589\) | 4.31168e12 | 1.47614 | ||||||||
\(590\) | −1.27223e11 | −0.0432247 | ||||||||
\(591\) | −2.83104e12 | −0.954557 | ||||||||
\(592\) | 1.94805e12 | 0.651857 | ||||||||
\(593\) | −6.85524e11 | −0.227655 | −0.113827 | − | 0.993501i | \(-0.536311\pi\) | ||||
−0.113827 | + | 0.993501i | \(0.536311\pi\) | |||||||
\(594\) | 4.54021e11 | 0.149636 | ||||||||
\(595\) | 2.05249e10 | 0.00671360 | ||||||||
\(596\) | −3.53078e11 | −0.114620 | ||||||||
\(597\) | 6.55335e11 | 0.211144 | ||||||||
\(598\) | −6.57823e11 | −0.210355 | ||||||||
\(599\) | 5.21431e12 | 1.65492 | 0.827459 | − | 0.561526i | \(-0.189786\pi\) | ||||
0.827459 | + | 0.561526i | \(0.189786\pi\) | |||||||
\(600\) | 6.96303e11 | 0.219340 | ||||||||
\(601\) | 2.91650e12 | 0.911857 | 0.455928 | − | 0.890016i | \(-0.349307\pi\) | ||||
0.455928 | + | 0.890016i | \(0.349307\pi\) | |||||||
\(602\) | −1.98327e12 | −0.615458 | ||||||||
\(603\) | 1.55271e12 | 0.478258 | ||||||||
\(604\) | −1.99284e12 | −0.609265 | ||||||||
\(605\) | 4.64161e12 | 1.40854 | ||||||||
\(606\) | −3.02861e11 | −0.0912257 | ||||||||
\(607\) | 3.45121e12 | 1.03186 | 0.515932 | − | 0.856630i | \(-0.327446\pi\) | ||||
0.515932 | + | 0.856630i | \(0.327446\pi\) | |||||||
\(608\) | −5.50098e12 | −1.63258 | ||||||||
\(609\) | −4.63053e11 | −0.136412 | ||||||||
\(610\) | −1.79769e11 | −0.0525692 | ||||||||
\(611\) | 1.52667e12 | 0.443159 | ||||||||
\(612\) | 9.90705e9 | 0.00285472 | ||||||||
\(613\) | 3.13362e11 | 0.0896343 | 0.0448171 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448171 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(614\) | 5.00812e11 | 0.142206 | ||||||||
\(615\) | 1.87459e12 | 0.528406 | ||||||||
\(616\) | 4.24278e12 | 1.18724 | ||||||||
\(617\) | 3.57799e12 | 0.993930 | 0.496965 | − | 0.867770i | \(-0.334448\pi\) | ||||
0.496965 | + | 0.867770i | \(0.334448\pi\) | |||||||
\(618\) | 1.07400e12 | 0.296181 | ||||||||
\(619\) | −6.72065e11 | −0.183994 | −0.0919969 | − | 0.995759i | \(-0.529325\pi\) | ||||
−0.0919969 | + | 0.995759i | \(0.529325\pi\) | |||||||
\(620\) | 1.94281e12 | 0.528042 | ||||||||
\(621\) | −4.26300e11 | −0.115028 | ||||||||
\(622\) | 3.00303e11 | 0.0804457 | ||||||||
\(623\) | 8.12188e11 | 0.216003 | ||||||||
\(624\) | 7.16648e11 | 0.189224 | ||||||||
\(625\) | −1.20756e12 | −0.316554 | ||||||||
\(626\) | −2.18142e12 | −0.567746 | ||||||||
\(627\) | −6.19635e12 | −1.60115 | ||||||||
\(628\) | 3.96483e12 | 1.01720 | ||||||||
\(629\) | −6.52674e10 | −0.0166252 | ||||||||
\(630\) | −3.72550e11 | −0.0942219 | ||||||||
\(631\) | −5.53679e11 | −0.139035 | −0.0695177 | − | 0.997581i | \(-0.522146\pi\) | ||||
−0.0695177 | + | 0.997581i | \(0.522146\pi\) | |||||||
\(632\) | −5.14779e12 | −1.28349 | ||||||||
\(633\) | 1.56239e11 | 0.0386787 | ||||||||
\(634\) | 9.66514e10 | 0.0237578 | ||||||||
\(635\) | −3.77223e12 | −0.920696 | ||||||||
\(636\) | 1.56313e12 | 0.378825 | ||||||||
\(637\) | −8.85658e11 | −0.213127 | ||||||||
\(638\) | 9.03048e11 | 0.215783 | ||||||||
\(639\) | 2.27118e12 | 0.538886 | ||||||||
\(640\) | −3.07503e12 | −0.724501 | ||||||||
\(641\) | 2.23104e12 | 0.521970 | 0.260985 | − | 0.965343i | \(-0.415953\pi\) | ||||
0.260985 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(642\) | −7.31447e11 | −0.169932 | ||||||||
\(643\) | −1.66757e12 | −0.384711 | −0.192355 | − | 0.981325i | \(-0.561613\pi\) | ||||
−0.192355 | + | 0.981325i | \(0.561613\pi\) | |||||||
\(644\) | −1.76254e12 | −0.403787 | ||||||||
\(645\) | 2.94987e12 | 0.671096 | ||||||||
\(646\) | 3.51843e10 | 0.00794881 | ||||||||
\(647\) | −2.62265e12 | −0.588397 | −0.294199 | − | 0.955744i | \(-0.595053\pi\) | ||||
−0.294199 | + | 0.955744i | \(0.595053\pi\) | |||||||
\(648\) | −4.06441e11 | −0.0905545 | ||||||||
\(649\) | −1.00680e12 | −0.222764 | ||||||||
\(650\) | −7.46629e11 | −0.164057 | ||||||||
\(651\) | 2.05151e12 | 0.447672 | ||||||||
\(652\) | −3.98982e12 | −0.864647 | ||||||||
\(653\) | 4.14476e12 | 0.892052 | 0.446026 | − | 0.895020i | \(-0.352839\pi\) | ||||
0.446026 | + | 0.895020i | \(0.352839\pi\) | |||||||
\(654\) | 2.16393e12 | 0.462535 | ||||||||
\(655\) | 3.93778e11 | 0.0835923 | ||||||||
\(656\) | 2.51421e12 | 0.530071 | ||||||||
\(657\) | 2.77267e12 | 0.580568 | ||||||||
\(658\) | −1.06443e12 | −0.221362 | ||||||||
\(659\) | −3.06194e12 | −0.632429 | −0.316215 | − | 0.948688i | \(-0.602412\pi\) | ||||
−0.316215 | + | 0.948688i | \(0.602412\pi\) | |||||||
\(660\) | −2.79203e12 | −0.572759 | ||||||||
\(661\) | 2.31516e11 | 0.0471710 | 0.0235855 | − | 0.999722i | \(-0.492492\pi\) | ||||
0.0235855 | + | 0.999722i | \(0.492492\pi\) | |||||||
\(662\) | −2.29345e12 | −0.464117 | ||||||||
\(663\) | −2.40105e10 | −0.00482604 | ||||||||
\(664\) | 4.77546e11 | 0.0953364 | ||||||||
\(665\) | 5.08445e12 | 1.00820 | ||||||||
\(666\) | 1.18467e12 | 0.233327 | ||||||||
\(667\) | −8.47911e11 | −0.165876 | ||||||||
\(668\) | −7.21032e12 | −1.40107 | ||||||||
\(669\) | −1.91936e11 | −0.0370459 | ||||||||
\(670\) | 2.48473e12 | 0.476367 | ||||||||
\(671\) | −1.42264e12 | −0.270921 | ||||||||
\(672\) | −2.61739e12 | −0.495115 | ||||||||
\(673\) | −4.40918e12 | −0.828495 | −0.414248 | − | 0.910164i | \(-0.635955\pi\) | ||||
−0.414248 | + | 0.910164i | \(0.635955\pi\) | |||||||
\(674\) | −2.61040e12 | −0.487234 | ||||||||
\(675\) | −4.83850e11 | −0.0897106 | ||||||||
\(676\) | 1.72401e12 | 0.317525 | ||||||||
\(677\) | −3.29730e12 | −0.603266 | −0.301633 | − | 0.953424i | \(-0.597532\pi\) | ||||
−0.301633 | + | 0.953424i | \(0.597532\pi\) | |||||||
\(678\) | −1.82513e10 | −0.00331712 | ||||||||
\(679\) | 5.77041e12 | 1.04182 | ||||||||
\(680\) | 3.58330e10 | 0.00642678 | ||||||||
\(681\) | −4.20739e12 | −0.749637 | ||||||||
\(682\) | −4.00086e12 | −0.708148 | ||||||||
\(683\) | −8.57985e12 | −1.50864 | −0.754322 | − | 0.656505i | \(-0.772034\pi\) | ||||
−0.754322 | + | 0.656505i | \(0.772034\pi\) | |||||||
\(684\) | 2.45418e12 | 0.428701 | ||||||||
\(685\) | 6.34822e12 | 1.10165 | ||||||||
\(686\) | 2.86150e12 | 0.493327 | ||||||||
\(687\) | 2.88299e11 | 0.0493784 | ||||||||
\(688\) | 3.95639e12 | 0.673210 | ||||||||
\(689\) | −3.78837e12 | −0.640422 | ||||||||
\(690\) | −6.82187e11 | −0.114573 | ||||||||
\(691\) | 3.91597e12 | 0.653414 | 0.326707 | − | 0.945126i | \(-0.394061\pi\) | ||||
0.326707 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(692\) | 8.20715e11 | 0.136055 | ||||||||
\(693\) | −2.94824e12 | −0.485583 | ||||||||
\(694\) | 2.40407e12 | 0.393396 | ||||||||
\(695\) | 3.70443e12 | 0.602268 | ||||||||
\(696\) | −8.08412e11 | −0.130584 | ||||||||
\(697\) | −8.42360e10 | −0.0135192 | ||||||||
\(698\) | −4.96716e11 | −0.0792061 | ||||||||
\(699\) | 8.98182e11 | 0.142304 | ||||||||
\(700\) | −2.00048e12 | −0.314915 | ||||||||
\(701\) | 5.83452e12 | 0.912587 | 0.456293 | − | 0.889829i | \(-0.349177\pi\) | ||||
0.456293 | + | 0.889829i | \(0.349177\pi\) | |||||||
\(702\) | 4.35817e11 | 0.0677309 | ||||||||
\(703\) | −1.61681e13 | −2.49666 | ||||||||
\(704\) | 3.85296e11 | 0.0591177 | ||||||||
\(705\) | 1.58321e12 | 0.241373 | ||||||||
\(706\) | 2.01526e12 | 0.305289 | ||||||||
\(707\) | 1.96667e12 | 0.296036 | ||||||||
\(708\) | 3.98764e11 | 0.0596439 | ||||||||
\(709\) | −5.16653e12 | −0.767875 | −0.383938 | − | 0.923359i | \(-0.625432\pi\) | ||||
−0.383938 | + | 0.923359i | \(0.625432\pi\) | |||||||
\(710\) | 3.63445e12 | 0.536755 | ||||||||
\(711\) | 3.57712e12 | 0.524953 | ||||||||
\(712\) | 1.41794e12 | 0.206775 | ||||||||
\(713\) | 3.75658e12 | 0.544365 | ||||||||
\(714\) | 1.67408e10 | 0.00241065 | ||||||||
\(715\) | 6.76671e12 | 0.968278 | ||||||||
\(716\) | 2.43440e12 | 0.346166 | ||||||||
\(717\) | −7.01413e12 | −0.991146 | ||||||||
\(718\) | 1.14083e11 | 0.0160199 | ||||||||
\(719\) | −1.32221e13 | −1.84510 | −0.922548 | − | 0.385882i | \(-0.873897\pi\) | ||||
−0.922548 | + | 0.385882i | \(0.873897\pi\) | |||||||
\(720\) | 7.43190e11 | 0.103063 | ||||||||
\(721\) | −6.97416e12 | −0.961133 | ||||||||
\(722\) | 5.39795e12 | 0.739285 | ||||||||
\(723\) | −1.06407e12 | −0.144827 | ||||||||
\(724\) | −7.55981e12 | −1.02256 | ||||||||
\(725\) | −9.62378e11 | −0.129367 | ||||||||
\(726\) | 3.78585e12 | 0.505764 | ||||||||
\(727\) | 4.22774e12 | 0.561311 | 0.280656 | − | 0.959809i | \(-0.409448\pi\) | ||||
0.280656 | + | 0.959809i | \(0.409448\pi\) | |||||||
\(728\) | 4.07267e12 | 0.537388 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 4.43696e12 | 0.578273 | ||||||||
\(731\) | −1.32555e11 | −0.0171699 | ||||||||
\(732\) | 5.63463e11 | 0.0725380 | ||||||||
\(733\) | 9.98133e12 | 1.27709 | 0.638544 | − | 0.769586i | \(-0.279537\pi\) | ||||
0.638544 | + | 0.769586i | \(0.279537\pi\) | |||||||
\(734\) | 1.45317e12 | 0.184792 | ||||||||
\(735\) | −9.18460e11 | −0.116083 | ||||||||
\(736\) | −4.79277e12 | −0.602056 | ||||||||
\(737\) | 1.96634e13 | 2.45501 | ||||||||
\(738\) | 1.52897e12 | 0.189734 | ||||||||
\(739\) | 5.83082e12 | 0.719166 | 0.359583 | − | 0.933113i | \(-0.382919\pi\) | ||||
0.359583 | + | 0.933113i | \(0.382919\pi\) | |||||||
\(740\) | −7.28521e12 | −0.893099 | ||||||||
\(741\) | −5.94791e12 | −0.724740 | ||||||||
\(742\) | 2.64136e12 | 0.319896 | ||||||||
\(743\) | −1.00539e13 | −1.21028 | −0.605142 | − | 0.796118i | \(-0.706884\pi\) | ||||
−0.605142 | + | 0.796118i | \(0.706884\pi\) | |||||||
\(744\) | 3.58159e12 | 0.428546 | ||||||||
\(745\) | 8.87405e11 | 0.105540 | ||||||||
\(746\) | −2.05908e12 | −0.243415 | ||||||||
\(747\) | −3.31839e11 | −0.0389928 | ||||||||
\(748\) | 1.25462e11 | 0.0146539 | ||||||||
\(749\) | 4.74975e12 | 0.551445 | ||||||||
\(750\) | −2.43530e12 | −0.281045 | ||||||||
\(751\) | 1.25152e12 | 0.143568 | 0.0717842 | − | 0.997420i | \(-0.477131\pi\) | ||||
0.0717842 | + | 0.997420i | \(0.477131\pi\) | |||||||
\(752\) | 2.12342e12 | 0.242133 | ||||||||
\(753\) | 1.01497e13 | 1.15048 | ||||||||
\(754\) | 8.66840e11 | 0.0976716 | ||||||||
\(755\) | 5.00869e12 | 0.561000 | ||||||||
\(756\) | 1.16771e12 | 0.130013 | ||||||||
\(757\) | 1.29325e13 | 1.43136 | 0.715681 | − | 0.698427i | \(-0.246116\pi\) | ||||
0.715681 | + | 0.698427i | \(0.246116\pi\) | |||||||
\(758\) | −7.68424e12 | −0.845453 | ||||||||
\(759\) | −5.39861e12 | −0.590465 | ||||||||
\(760\) | 8.87658e12 | 0.965127 | ||||||||
\(761\) | −1.02245e13 | −1.10513 | −0.552563 | − | 0.833471i | \(-0.686350\pi\) | ||||
−0.552563 | + | 0.833471i | \(0.686350\pi\) | |||||||
\(762\) | −3.07675e12 | −0.330594 | ||||||||
\(763\) | −1.40518e13 | −1.50097 | ||||||||
\(764\) | 4.41635e12 | 0.468968 | ||||||||
\(765\) | −2.48998e10 | −0.00262857 | ||||||||
\(766\) | 5.80817e12 | 0.609551 | ||||||||
\(767\) | −9.66437e11 | −0.100831 | ||||||||
\(768\) | −2.70040e12 | −0.280094 | ||||||||
\(769\) | 1.09064e12 | 0.112464 | 0.0562319 | − | 0.998418i | \(-0.482091\pi\) | ||||
0.0562319 | + | 0.998418i | \(0.482091\pi\) | |||||||
\(770\) | −4.71793e12 | −0.483663 | ||||||||
\(771\) | 7.94021e12 | 0.809258 | ||||||||
\(772\) | 1.43235e13 | 1.45135 | ||||||||
\(773\) | −9.93713e12 | −1.00104 | −0.500522 | − | 0.865724i | \(-0.666859\pi\) | ||||
−0.500522 | + | 0.865724i | \(0.666859\pi\) | |||||||
\(774\) | 2.40601e12 | 0.240970 | ||||||||
\(775\) | 4.26372e12 | 0.424552 | ||||||||
\(776\) | 1.00741e13 | 0.997311 | ||||||||
\(777\) | −7.69282e12 | −0.757166 | ||||||||
\(778\) | 3.46828e12 | 0.339395 | ||||||||
\(779\) | −2.08670e13 | −2.03021 | ||||||||
\(780\) | −2.68008e12 | −0.259252 | ||||||||
\(781\) | 2.87619e13 | 2.76623 | ||||||||
\(782\) | 3.06545e10 | 0.00293133 | ||||||||
\(783\) | 5.61753e11 | 0.0534093 | ||||||||
\(784\) | −1.23184e12 | −0.116448 | ||||||||
\(785\) | −9.96498e12 | −0.936619 | ||||||||
\(786\) | 3.21178e11 | 0.0300154 | ||||||||
\(787\) | 6.66953e12 | 0.619739 | 0.309870 | − | 0.950779i | \(-0.399715\pi\) | ||||
0.309870 | + | 0.950779i | \(0.399715\pi\) | |||||||
\(788\) | 1.41998e13 | 1.31194 | ||||||||
\(789\) | −8.27151e12 | −0.759868 | ||||||||
\(790\) | 5.72429e12 | 0.522877 | ||||||||
\(791\) | 1.18517e11 | 0.0107643 | ||||||||
\(792\) | −5.14713e12 | −0.464838 | ||||||||
\(793\) | −1.36560e12 | −0.122629 | ||||||||
\(794\) | −3.88762e12 | −0.347130 | ||||||||
\(795\) | −3.92868e12 | −0.348815 | ||||||||
\(796\) | −3.28701e12 | −0.290196 | ||||||||
\(797\) | 1.12543e12 | 0.0987997 | 0.0493998 | − | 0.998779i | \(-0.484269\pi\) | ||||
0.0493998 | + | 0.998779i | \(0.484269\pi\) | |||||||
\(798\) | 4.14704e12 | 0.362014 | ||||||||
\(799\) | −7.11428e10 | −0.00617548 | ||||||||
\(800\) | −5.43979e12 | −0.469545 | ||||||||
\(801\) | −9.85305e11 | −0.0845716 | ||||||||
\(802\) | 2.29673e12 | 0.196031 | ||||||||
\(803\) | 3.51127e13 | 2.98020 | ||||||||
\(804\) | −7.78804e12 | −0.657319 | ||||||||
\(805\) | 4.42987e12 | 0.371800 | ||||||||
\(806\) | −3.84045e12 | −0.320534 | ||||||||
\(807\) | 4.88983e12 | 0.405847 | ||||||||
\(808\) | 3.43347e12 | 0.283388 | ||||||||
\(809\) | −8.12047e12 | −0.666520 | −0.333260 | − | 0.942835i | \(-0.608149\pi\) | ||||
−0.333260 | + | 0.942835i | \(0.608149\pi\) | |||||||
\(810\) | 4.51958e11 | 0.0368906 | ||||||||
\(811\) | −3.12578e12 | −0.253726 | −0.126863 | − | 0.991920i | \(-0.540491\pi\) | ||||
−0.126863 | + | 0.991920i | \(0.540491\pi\) | |||||||
\(812\) | 2.32257e12 | 0.187485 | ||||||||
\(813\) | 6.89960e12 | 0.553881 | ||||||||
\(814\) | 1.50026e13 | 1.19772 | ||||||||
\(815\) | 1.00278e13 | 0.796151 | ||||||||
\(816\) | −3.33958e10 | −0.00263685 | ||||||||
\(817\) | −3.28365e13 | −2.57844 | ||||||||
\(818\) | −7.84584e12 | −0.612702 | ||||||||
\(819\) | −2.83003e12 | −0.219793 | ||||||||
\(820\) | −9.40251e12 | −0.726242 | ||||||||
\(821\) | 1.34118e13 | 1.03025 | 0.515126 | − | 0.857114i | \(-0.327745\pi\) | ||||
0.515126 | + | 0.857114i | \(0.327745\pi\) | |||||||
\(822\) | 5.17781e12 | 0.395570 | ||||||||
\(823\) | 1.27209e13 | 0.966538 | 0.483269 | − | 0.875472i | \(-0.339449\pi\) | ||||
0.483269 | + | 0.875472i | \(0.339449\pi\) | |||||||
\(824\) | −1.21757e13 | −0.920071 | ||||||||
\(825\) | −6.12742e12 | −0.460506 | ||||||||
\(826\) | 6.73826e11 | 0.0503660 | ||||||||
\(827\) | 1.44497e13 | 1.07420 | 0.537100 | − | 0.843519i | \(-0.319520\pi\) | ||||
0.537100 | + | 0.843519i | \(0.319520\pi\) | |||||||
\(828\) | 2.13822e12 | 0.158094 | ||||||||
\(829\) | 2.04951e13 | 1.50714 | 0.753571 | − | 0.657366i | \(-0.228330\pi\) | ||||
0.753571 | + | 0.657366i | \(0.228330\pi\) | |||||||
\(830\) | −5.31026e11 | −0.0388387 | ||||||||
\(831\) | 8.28776e11 | 0.0602883 | ||||||||
\(832\) | 3.69848e11 | 0.0267589 | ||||||||
\(833\) | 4.12717e10 | 0.00296995 | ||||||||
\(834\) | 3.02145e12 | 0.216256 | ||||||||
\(835\) | 1.81220e13 | 1.29008 | ||||||||
\(836\) | 3.10795e13 | 2.20062 | ||||||||
\(837\) | −2.48879e12 | −0.175276 | ||||||||
\(838\) | −9.04925e12 | −0.633891 | ||||||||
\(839\) | 3.36903e11 | 0.0234734 | 0.0117367 | − | 0.999931i | \(-0.496264\pi\) | ||||
0.0117367 | + | 0.999931i | \(0.496264\pi\) | |||||||
\(840\) | 4.22351e12 | 0.292696 | ||||||||
\(841\) | −1.33898e13 | −0.922981 | ||||||||
\(842\) | 2.63496e12 | 0.180663 | ||||||||
\(843\) | 2.61468e12 | 0.178318 | ||||||||
\(844\) | −7.83657e11 | −0.0531600 | ||||||||
\(845\) | −4.33302e12 | −0.292372 | ||||||||
\(846\) | 1.29132e12 | 0.0866696 | ||||||||
\(847\) | −2.45839e13 | −1.64125 | ||||||||
\(848\) | −5.26917e12 | −0.349914 | ||||||||
\(849\) | 1.44478e13 | 0.954368 | ||||||||
\(850\) | 3.47929e10 | 0.00228615 | ||||||||
\(851\) | −1.40866e13 | −0.920707 | ||||||||
\(852\) | −1.13917e13 | −0.740646 | ||||||||
\(853\) | 2.53831e13 | 1.64162 | 0.820812 | − | 0.571199i | \(-0.193521\pi\) | ||||
0.820812 | + | 0.571199i | \(0.193521\pi\) | |||||||
\(854\) | 9.52132e11 | 0.0612543 | ||||||||
\(855\) | −6.16820e12 | −0.394740 | ||||||||
\(856\) | 8.29224e12 | 0.527886 | ||||||||
\(857\) | −7.76188e12 | −0.491534 | −0.245767 | − | 0.969329i | \(-0.579040\pi\) | ||||
−0.245767 | + | 0.969329i | \(0.579040\pi\) | |||||||
\(858\) | 5.51914e12 | 0.347679 | ||||||||
\(859\) | −1.33642e13 | −0.837477 | −0.418739 | − | 0.908107i | \(-0.637528\pi\) | ||||
−0.418739 | + | 0.908107i | \(0.637528\pi\) | |||||||
\(860\) | −1.47959e13 | −0.922355 | ||||||||
\(861\) | −9.92858e12 | −0.615705 | ||||||||
\(862\) | −3.19157e12 | −0.196889 | ||||||||
\(863\) | −3.15557e13 | −1.93655 | −0.968275 | − | 0.249886i | \(-0.919607\pi\) | ||||
−0.968275 | + | 0.249886i | \(0.919607\pi\) | |||||||
\(864\) | 3.17528e12 | 0.193852 | ||||||||
\(865\) | −2.06274e12 | −0.125277 | ||||||||
\(866\) | −8.64319e11 | −0.0522208 | ||||||||
\(867\) | −9.60450e12 | −0.577283 | ||||||||
\(868\) | −1.02899e13 | −0.615281 | ||||||||
\(869\) | 4.53003e13 | 2.69471 | ||||||||
\(870\) | 8.98945e11 | 0.0531982 | ||||||||
\(871\) | 1.88750e13 | 1.11123 | ||||||||
\(872\) | −2.45320e13 | −1.43684 | ||||||||
\(873\) | −7.00037e12 | −0.407903 | ||||||||
\(874\) | 7.59377e12 | 0.440206 | ||||||||
\(875\) | 1.58139e13 | 0.912017 | ||||||||
\(876\) | −1.39071e13 | −0.797934 | ||||||||
\(877\) | −1.90311e13 | −1.08634 | −0.543171 | − | 0.839622i | \(-0.682776\pi\) | ||||
−0.543171 | + | 0.839622i | \(0.682776\pi\) | |||||||
\(878\) | 3.31274e12 | 0.188131 | ||||||||
\(879\) | −9.93947e12 | −0.561582 | ||||||||
\(880\) | 9.41168e12 | 0.529048 | ||||||||
\(881\) | −2.06010e13 | −1.15211 | −0.576057 | − | 0.817409i | \(-0.695410\pi\) | ||||
−0.576057 | + | 0.817409i | \(0.695410\pi\) | |||||||
\(882\) | −7.49125e11 | −0.0416817 | ||||||||
\(883\) | −4.21821e12 | −0.233510 | −0.116755 | − | 0.993161i | \(-0.537249\pi\) | ||||
−0.116755 | + | 0.993161i | \(0.537249\pi\) | |||||||
\(884\) | 1.20431e11 | 0.00663292 | ||||||||
\(885\) | −1.00223e12 | −0.0549190 | ||||||||
\(886\) | 9.33041e12 | 0.508685 | ||||||||
\(887\) | 2.06824e12 | 0.112188 | 0.0560939 | − | 0.998426i | \(-0.482135\pi\) | ||||
0.0560939 | + | 0.998426i | \(0.482135\pi\) | |||||||
\(888\) | −1.34303e13 | −0.724818 | ||||||||
\(889\) | 1.99793e13 | 1.07281 | ||||||||
\(890\) | −1.57674e12 | −0.0842372 | ||||||||
\(891\) | 3.57666e12 | 0.190120 | ||||||||
\(892\) | 9.62709e11 | 0.0509159 | ||||||||
\(893\) | −1.76235e13 | −0.927389 | ||||||||
\(894\) | 7.23795e11 | 0.0378963 | ||||||||
\(895\) | −6.11849e12 | −0.318743 | ||||||||
\(896\) | 1.62866e13 | 0.844198 | ||||||||
\(897\) | −5.18216e12 | −0.267267 | ||||||||
\(898\) | 1.20385e13 | 0.617771 | ||||||||
\(899\) | −4.95021e12 | −0.252758 | ||||||||
\(900\) | 2.42688e12 | 0.123298 | ||||||||
\(901\) | 1.76538e11 | 0.00892436 | ||||||||
\(902\) | 1.93627e13 | 0.973952 | ||||||||
\(903\) | −1.56237e13 | −0.781969 | ||||||||
\(904\) | 2.06911e11 | 0.0103045 | ||||||||
\(905\) | 1.90004e13 | 0.941551 | ||||||||
\(906\) | 4.08524e12 | 0.201438 | ||||||||
\(907\) | −1.79596e13 | −0.881176 | −0.440588 | − | 0.897709i | \(-0.645230\pi\) | ||||
−0.440588 | + | 0.897709i | \(0.645230\pi\) | |||||||
\(908\) | 2.11033e13 | 1.03030 | ||||||||
\(909\) | −2.38586e12 | −0.115907 | ||||||||
\(910\) | −4.52876e12 | −0.218924 | ||||||||
\(911\) | 3.19918e13 | 1.53888 | 0.769442 | − | 0.638717i | \(-0.220535\pi\) | ||||
0.769442 | + | 0.638717i | \(0.220535\pi\) | |||||||
\(912\) | −8.27283e12 | −0.395984 | ||||||||
\(913\) | −4.20237e12 | −0.200159 | ||||||||
\(914\) | −1.33546e13 | −0.632956 | ||||||||
\(915\) | −1.41618e12 | −0.0667917 | ||||||||
\(916\) | −1.44604e12 | −0.0678658 | ||||||||
\(917\) | −2.08561e12 | −0.0974027 | ||||||||
\(918\) | −2.03091e10 | −0.000943839 0 | ||||||||
\(919\) | 1.61849e13 | 0.748496 | 0.374248 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374248 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(920\) | 7.73379e12 | 0.355916 | ||||||||
\(921\) | 3.94526e12 | 0.180679 | ||||||||
\(922\) | −9.77516e12 | −0.445487 | ||||||||
\(923\) | 2.76087e13 | 1.25210 | ||||||||
\(924\) | 1.47877e13 | 0.667386 | ||||||||
\(925\) | −1.59882e13 | −0.718063 | ||||||||
\(926\) | −1.17585e13 | −0.525536 | ||||||||
\(927\) | 8.46070e12 | 0.376311 | ||||||||
\(928\) | 6.31563e12 | 0.279545 | ||||||||
\(929\) | 3.56724e12 | 0.157131 | 0.0785654 | − | 0.996909i | \(-0.474966\pi\) | ||||
0.0785654 | + | 0.996909i | \(0.474966\pi\) | |||||||
\(930\) | −3.98269e12 | −0.174583 | ||||||||
\(931\) | 1.02238e13 | 0.446006 | ||||||||
\(932\) | −4.50508e12 | −0.195583 | ||||||||
\(933\) | 2.36571e12 | 0.102210 | ||||||||
\(934\) | −1.42418e13 | −0.612356 | ||||||||
\(935\) | −3.15328e11 | −0.0134931 | ||||||||
\(936\) | −4.94075e12 | −0.210403 | ||||||||
\(937\) | −4.09993e12 | −0.173759 | −0.0868797 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868797 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(938\) | −1.31601e13 | −0.555069 | ||||||||
\(939\) | −1.71846e13 | −0.721349 | ||||||||
\(940\) | −7.94104e12 | −0.331743 | ||||||||
\(941\) | −8.94587e12 | −0.371937 | −0.185968 | − | 0.982556i | \(-0.559542\pi\) | ||||
−0.185968 | + | 0.982556i | \(0.559542\pi\) | |||||||
\(942\) | −8.12775e12 | −0.336311 | ||||||||
\(943\) | −1.81805e13 | −0.748693 | ||||||||
\(944\) | −1.34420e12 | −0.0550921 | ||||||||
\(945\) | −2.93485e12 | −0.119713 | ||||||||
\(946\) | 3.04694e13 | 1.23696 | ||||||||
\(947\) | −5.04823e12 | −0.203969 | −0.101984 | − | 0.994786i | \(-0.532519\pi\) | ||||
−0.101984 | + | 0.994786i | \(0.532519\pi\) | |||||||
\(948\) | −1.79420e13 | −0.721496 | ||||||||
\(949\) | 3.37049e13 | 1.34895 | ||||||||
\(950\) | 8.61892e12 | 0.343318 | ||||||||
\(951\) | 7.61394e11 | 0.0301854 | ||||||||
\(952\) | −1.89786e11 | −0.00748856 | ||||||||
\(953\) | −3.63509e13 | −1.42757 | −0.713784 | − | 0.700366i | \(-0.753020\pi\) | ||||
−0.713784 | + | 0.700366i | \(0.753020\pi\) | |||||||
\(954\) | −3.20436e12 | −0.125249 | ||||||||
\(955\) | −1.10998e13 | −0.431817 | ||||||||
\(956\) | 3.51813e13 | 1.36223 | ||||||||
\(957\) | 7.11398e12 | 0.274163 | ||||||||
\(958\) | −1.73030e13 | −0.663708 | ||||||||
\(959\) | −3.36228e13 | −1.28366 | ||||||||
\(960\) | 3.83546e11 | 0.0145746 | ||||||||
\(961\) | −4.50822e12 | −0.170510 | ||||||||
\(962\) | 1.44010e13 | 0.542133 | ||||||||
\(963\) | −5.76215e12 | −0.215907 | ||||||||
\(964\) | 5.33715e12 | 0.199050 | ||||||||
\(965\) | −3.59999e13 | −1.33637 | ||||||||
\(966\) | 3.61314e12 | 0.133502 | ||||||||
\(967\) | 2.21272e13 | 0.813779 | 0.406889 | − | 0.913477i | \(-0.366613\pi\) | ||||
0.406889 | + | 0.913477i | \(0.366613\pi\) | |||||||
\(968\) | −4.29192e13 | −1.57113 | ||||||||
\(969\) | 2.77172e11 | 0.0100993 | ||||||||
\(970\) | −1.12023e13 | −0.406290 | ||||||||
\(971\) | 1.48279e13 | 0.535296 | 0.267648 | − | 0.963517i | \(-0.413754\pi\) | ||||
0.267648 | + | 0.963517i | \(0.413754\pi\) | |||||||
\(972\) | −1.41660e12 | −0.0509037 | ||||||||
\(973\) | −1.96202e13 | −0.701770 | ||||||||
\(974\) | −3.71735e12 | −0.132348 | ||||||||
\(975\) | −5.88175e12 | −0.208442 | ||||||||
\(976\) | −1.89938e12 | −0.0670022 | ||||||||
\(977\) | −4.50100e13 | −1.58046 | −0.790231 | − | 0.612810i | \(-0.790039\pi\) | ||||
−0.790231 | + | 0.612810i | \(0.790039\pi\) | |||||||
\(978\) | 8.17897e12 | 0.285873 | ||||||||
\(979\) | −1.24778e13 | −0.434126 | ||||||||
\(980\) | 4.60679e12 | 0.159544 | ||||||||
\(981\) | 1.70469e13 | 0.587672 | ||||||||
\(982\) | −1.94160e13 | −0.666281 | ||||||||
\(983\) | −3.84240e13 | −1.31254 | −0.656269 | − | 0.754527i | \(-0.727866\pi\) | ||||
−0.656269 | + | 0.754527i | \(0.727866\pi\) | |||||||
\(984\) | −1.73336e13 | −0.589401 | ||||||||
\(985\) | −3.56891e13 | −1.20801 | ||||||||
\(986\) | −4.03948e10 | −0.00136107 | ||||||||
\(987\) | −8.38534e12 | −0.281251 | ||||||||
\(988\) | 2.98334e13 | 0.996084 | ||||||||
\(989\) | −2.86090e13 | −0.950868 | ||||||||
\(990\) | 5.72355e12 | 0.189368 | ||||||||
\(991\) | −2.04665e13 | −0.674081 | −0.337040 | − | 0.941490i | \(-0.609426\pi\) | ||||
−0.337040 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(992\) | −2.79808e13 | −0.917397 | ||||||||
\(993\) | −1.80672e13 | −0.589683 | ||||||||
\(994\) | −1.92495e13 | −0.625434 | ||||||||
\(995\) | 8.26138e12 | 0.267208 | ||||||||
\(996\) | 1.66443e12 | 0.0535918 | ||||||||
\(997\) | −2.11028e13 | −0.676413 | −0.338206 | − | 0.941072i | \(-0.609820\pi\) | ||||
−0.338206 | + | 0.941072i | \(0.609820\pi\) | |||||||
\(998\) | 2.22216e13 | 0.709067 | ||||||||
\(999\) | 9.33254e12 | 0.296452 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.d.1.13 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.d.1.13 | ✓ | 22 | 1.1 | even | 1 | trivial |