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 | 1.15 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18.6113 | 0.822512 | 0.411256 | − | 0.911520i | \(-0.365090\pi\) | ||||
0.411256 | + | 0.911520i | \(0.365090\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −165.619 | −0.323475 | ||||||||
\(5\) | 1492.75 | 1.06813 | 0.534063 | − | 0.845445i | \(-0.320664\pi\) | ||||
0.534063 | + | 0.845445i | \(0.320664\pi\) | |||||||
\(6\) | −1507.52 | −0.474877 | ||||||||
\(7\) | 11801.9 | 1.85785 | 0.928924 | − | 0.370271i | \(-0.120735\pi\) | ||||
0.928924 | + | 0.370271i | \(0.120735\pi\) | |||||||
\(8\) | −12611.4 | −1.08857 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 27782.1 | 0.878546 | ||||||||
\(11\) | 54115.8 | 1.11444 | 0.557220 | − | 0.830365i | \(-0.311868\pi\) | ||||
0.557220 | + | 0.830365i | \(0.311868\pi\) | |||||||
\(12\) | 13415.1 | 0.186758 | ||||||||
\(13\) | 176081. | 1.70989 | 0.854945 | − | 0.518718i | \(-0.173591\pi\) | ||||
0.854945 | + | 0.518718i | \(0.173591\pi\) | |||||||
\(14\) | 219649. | 1.52810 | ||||||||
\(15\) | −120913. | −0.616683 | ||||||||
\(16\) | −149917. | −0.571889 | ||||||||
\(17\) | 108748. | 0.315791 | 0.157896 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157896 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(18\) | 122109. | 0.274171 | ||||||||
\(19\) | 54464.9 | 0.0958795 | 0.0479397 | − | 0.998850i | \(-0.484734\pi\) | ||||
0.0479397 | + | 0.998850i | \(0.484734\pi\) | |||||||
\(20\) | −247228. | −0.345512 | ||||||||
\(21\) | −955953. | −1.07263 | ||||||||
\(22\) | 1.00717e6 | 0.916640 | ||||||||
\(23\) | −2.05205e6 | −1.52902 | −0.764511 | − | 0.644611i | \(-0.777019\pi\) | ||||
−0.764511 | + | 0.644611i | \(0.777019\pi\) | |||||||
\(24\) | 1.02152e6 | 0.628488 | ||||||||
\(25\) | 275183. | 0.140894 | ||||||||
\(26\) | 3.27711e6 | 1.40640 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −1.95462e6 | −0.600967 | ||||||||
\(29\) | −3.15094e6 | −0.827272 | −0.413636 | − | 0.910442i | \(-0.635741\pi\) | ||||
−0.413636 | + | 0.910442i | \(0.635741\pi\) | |||||||
\(30\) | −2.25035e6 | −0.507229 | ||||||||
\(31\) | 5.67861e6 | 1.10437 | 0.552185 | − | 0.833722i | \(-0.313794\pi\) | ||||
0.552185 | + | 0.833722i | \(0.313794\pi\) | |||||||
\(32\) | 3.66687e6 | 0.618188 | ||||||||
\(33\) | −4.38338e6 | −0.643422 | ||||||||
\(34\) | 2.02394e6 | 0.259742 | ||||||||
\(35\) | 1.76173e7 | 1.98442 | ||||||||
\(36\) | −1.08663e6 | −0.107825 | ||||||||
\(37\) | 1.48233e7 | 1.30028 | 0.650139 | − | 0.759815i | \(-0.274711\pi\) | ||||
0.650139 | + | 0.759815i | \(0.274711\pi\) | |||||||
\(38\) | 1.01366e6 | 0.0788620 | ||||||||
\(39\) | −1.42626e7 | −0.987206 | ||||||||
\(40\) | −1.88257e7 | −1.16273 | ||||||||
\(41\) | −2.73520e7 | −1.51168 | −0.755842 | − | 0.654754i | \(-0.772772\pi\) | ||||
−0.755842 | + | 0.654754i | \(0.772772\pi\) | |||||||
\(42\) | −1.77915e7 | −0.882250 | ||||||||
\(43\) | 1.96666e7 | 0.877247 | 0.438623 | − | 0.898671i | \(-0.355466\pi\) | ||||
0.438623 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(44\) | −8.96260e6 | −0.360493 | ||||||||
\(45\) | 9.79394e6 | 0.356042 | ||||||||
\(46\) | −3.81914e7 | −1.25764 | ||||||||
\(47\) | −1.60710e7 | −0.480400 | −0.240200 | − | 0.970723i | \(-0.577213\pi\) | ||||
−0.240200 | + | 0.970723i | \(0.577213\pi\) | |||||||
\(48\) | 1.21433e7 | 0.330181 | ||||||||
\(49\) | 9.89308e7 | 2.45160 | ||||||||
\(50\) | 5.12152e6 | 0.115887 | ||||||||
\(51\) | −8.80857e6 | −0.182322 | ||||||||
\(52\) | −2.91624e7 | −0.553106 | ||||||||
\(53\) | −4.91083e7 | −0.854896 | −0.427448 | − | 0.904040i | \(-0.640587\pi\) | ||||
−0.427448 | + | 0.904040i | \(0.640587\pi\) | |||||||
\(54\) | −9.89081e6 | −0.158292 | ||||||||
\(55\) | 8.07814e7 | 1.19036 | ||||||||
\(56\) | −1.48838e8 | −2.02240 | ||||||||
\(57\) | −4.41166e6 | −0.0553561 | ||||||||
\(58\) | −5.86430e7 | −0.680441 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 2.00255e7 | 0.199481 | ||||||||
\(61\) | 9.09669e7 | 0.841200 | 0.420600 | − | 0.907246i | \(-0.361820\pi\) | ||||
0.420600 | + | 0.907246i | \(0.361820\pi\) | |||||||
\(62\) | 1.05686e8 | 0.908357 | ||||||||
\(63\) | 7.74322e7 | 0.619283 | ||||||||
\(64\) | 1.45003e8 | 1.08036 | ||||||||
\(65\) | 2.62846e8 | 1.82638 | ||||||||
\(66\) | −8.15804e7 | −0.529222 | ||||||||
\(67\) | −1.83319e7 | −0.111140 | −0.0555700 | − | 0.998455i | \(-0.517698\pi\) | ||||
−0.0555700 | + | 0.998455i | \(0.517698\pi\) | |||||||
\(68\) | −1.80107e7 | −0.102150 | ||||||||
\(69\) | 1.66216e8 | 0.882781 | ||||||||
\(70\) | 3.27881e8 | 1.63221 | ||||||||
\(71\) | −3.08979e8 | −1.44300 | −0.721500 | − | 0.692414i | \(-0.756547\pi\) | ||||
−0.721500 | + | 0.692414i | \(0.756547\pi\) | |||||||
\(72\) | −8.27433e7 | −0.362858 | ||||||||
\(73\) | 1.21812e7 | 0.0502039 | 0.0251019 | − | 0.999685i | \(-0.492009\pi\) | ||||
0.0251019 | + | 0.999685i | \(0.492009\pi\) | |||||||
\(74\) | 2.75880e8 | 1.06949 | ||||||||
\(75\) | −2.22898e7 | −0.0813451 | ||||||||
\(76\) | −9.02043e6 | −0.0310146 | ||||||||
\(77\) | 6.38668e8 | 2.07046 | ||||||||
\(78\) | −2.65446e8 | −0.811988 | ||||||||
\(79\) | −2.20744e8 | −0.637626 | −0.318813 | − | 0.947818i | \(-0.603284\pi\) | ||||
−0.318813 | + | 0.947818i | \(0.603284\pi\) | |||||||
\(80\) | −2.23789e8 | −0.610850 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −5.09056e8 | −1.24338 | ||||||||
\(83\) | 4.48981e8 | 1.03843 | 0.519215 | − | 0.854644i | \(-0.326224\pi\) | ||||
0.519215 | + | 0.854644i | \(0.326224\pi\) | |||||||
\(84\) | 1.58324e8 | 0.346968 | ||||||||
\(85\) | 1.62333e8 | 0.337305 | ||||||||
\(86\) | 3.66022e8 | 0.721546 | ||||||||
\(87\) | 2.55226e8 | 0.477626 | ||||||||
\(88\) | −6.82475e8 | −1.21315 | ||||||||
\(89\) | 7.18855e8 | 1.21447 | 0.607234 | − | 0.794523i | \(-0.292279\pi\) | ||||
0.607234 | + | 0.794523i | \(0.292279\pi\) | |||||||
\(90\) | 1.82278e8 | 0.292849 | ||||||||
\(91\) | 2.07809e9 | 3.17672 | ||||||||
\(92\) | 3.39859e8 | 0.494600 | ||||||||
\(93\) | −4.59968e8 | −0.637608 | ||||||||
\(94\) | −2.99103e8 | −0.395134 | ||||||||
\(95\) | 8.13026e7 | 0.102411 | ||||||||
\(96\) | −2.97016e8 | −0.356911 | ||||||||
\(97\) | −1.57982e9 | −1.81191 | −0.905953 | − | 0.423378i | \(-0.860844\pi\) | ||||
−0.905953 | + | 0.423378i | \(0.860844\pi\) | |||||||
\(98\) | 1.84123e9 | 2.01647 | ||||||||
\(99\) | 3.55054e8 | 0.371480 | ||||||||
\(100\) | −4.55756e7 | −0.0455756 | ||||||||
\(101\) | 4.78446e8 | 0.457495 | 0.228748 | − | 0.973486i | \(-0.426537\pi\) | ||||
0.228748 | + | 0.973486i | \(0.426537\pi\) | |||||||
\(102\) | −1.63939e8 | −0.149962 | ||||||||
\(103\) | 1.88156e9 | 1.64722 | 0.823608 | − | 0.567160i | \(-0.191958\pi\) | ||||
0.823608 | + | 0.567160i | \(0.191958\pi\) | |||||||
\(104\) | −2.22063e9 | −1.86134 | ||||||||
\(105\) | −1.42700e9 | −1.14570 | ||||||||
\(106\) | −9.13970e8 | −0.703162 | ||||||||
\(107\) | 1.55230e9 | 1.14485 | 0.572426 | − | 0.819956i | \(-0.306002\pi\) | ||||
0.572426 | + | 0.819956i | \(0.306002\pi\) | |||||||
\(108\) | 8.80167e7 | 0.0622527 | ||||||||
\(109\) | 2.26041e9 | 1.53380 | 0.766898 | − | 0.641769i | \(-0.221799\pi\) | ||||
0.766898 | + | 0.641769i | \(0.221799\pi\) | |||||||
\(110\) | 1.50345e9 | 0.979087 | ||||||||
\(111\) | −1.20068e9 | −0.750716 | ||||||||
\(112\) | −1.76931e9 | −1.06248 | ||||||||
\(113\) | 5.97898e8 | 0.344964 | 0.172482 | − | 0.985013i | \(-0.444821\pi\) | ||||
0.172482 | + | 0.985013i | \(0.444821\pi\) | |||||||
\(114\) | −8.21068e7 | −0.0455310 | ||||||||
\(115\) | −3.06321e9 | −1.63319 | ||||||||
\(116\) | 5.21855e8 | 0.267602 | ||||||||
\(117\) | 1.15527e9 | 0.569964 | ||||||||
\(118\) | 2.25520e8 | 0.107082 | ||||||||
\(119\) | 1.28343e9 | 0.586692 | ||||||||
\(120\) | 1.52488e9 | 0.671305 | ||||||||
\(121\) | 5.70570e8 | 0.241977 | ||||||||
\(122\) | 1.69301e9 | 0.691897 | ||||||||
\(123\) | 2.21551e9 | 0.872771 | ||||||||
\(124\) | −9.40486e8 | −0.357236 | ||||||||
\(125\) | −2.50475e9 | −0.917634 | ||||||||
\(126\) | 1.44111e9 | 0.509367 | ||||||||
\(127\) | −1.45243e9 | −0.495425 | −0.247712 | − | 0.968834i | \(-0.579679\pi\) | ||||
−0.247712 | + | 0.968834i | \(0.579679\pi\) | |||||||
\(128\) | 8.21259e8 | 0.270418 | ||||||||
\(129\) | −1.59300e9 | −0.506479 | ||||||||
\(130\) | 4.89191e9 | 1.50222 | ||||||||
\(131\) | 6.58148e8 | 0.195255 | 0.0976276 | − | 0.995223i | \(-0.468875\pi\) | ||||
0.0976276 | + | 0.995223i | \(0.468875\pi\) | |||||||
\(132\) | 7.25971e8 | 0.208131 | ||||||||
\(133\) | 6.42789e8 | 0.178129 | ||||||||
\(134\) | −3.41180e8 | −0.0914139 | ||||||||
\(135\) | −7.93310e8 | −0.205561 | ||||||||
\(136\) | −1.37146e9 | −0.343762 | ||||||||
\(137\) | −2.80147e9 | −0.679429 | −0.339714 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339714 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(138\) | 3.09351e9 | 0.726098 | ||||||||
\(139\) | −8.04977e9 | −1.82901 | −0.914507 | − | 0.404571i | \(-0.867421\pi\) | ||||
−0.914507 | + | 0.404571i | \(0.867421\pi\) | |||||||
\(140\) | −2.91776e9 | −0.641908 | ||||||||
\(141\) | 1.30175e9 | 0.277359 | ||||||||
\(142\) | −5.75051e9 | −1.18688 | ||||||||
\(143\) | 9.52878e9 | 1.90557 | ||||||||
\(144\) | −9.83608e8 | −0.190630 | ||||||||
\(145\) | −4.70356e9 | −0.883631 | ||||||||
\(146\) | 2.26708e8 | 0.0412933 | ||||||||
\(147\) | −8.01340e9 | −1.41543 | ||||||||
\(148\) | −2.45501e9 | −0.420607 | ||||||||
\(149\) | −1.17236e9 | −0.194861 | −0.0974304 | − | 0.995242i | \(-0.531062\pi\) | ||||
−0.0974304 | + | 0.995242i | \(0.531062\pi\) | |||||||
\(150\) | −4.14843e8 | −0.0669072 | ||||||||
\(151\) | 1.25208e9 | 0.195991 | 0.0979954 | − | 0.995187i | \(-0.468757\pi\) | ||||
0.0979954 | + | 0.995187i | \(0.468757\pi\) | |||||||
\(152\) | −6.86878e8 | −0.104372 | ||||||||
\(153\) | 7.13494e8 | 0.105264 | ||||||||
\(154\) | 1.18865e10 | 1.70298 | ||||||||
\(155\) | 8.47676e9 | 1.17961 | ||||||||
\(156\) | 2.36216e9 | 0.319336 | ||||||||
\(157\) | 6.13909e9 | 0.806410 | 0.403205 | − | 0.915110i | \(-0.367896\pi\) | ||||
0.403205 | + | 0.915110i | \(0.367896\pi\) | |||||||
\(158\) | −4.10833e9 | −0.524455 | ||||||||
\(159\) | 3.97777e9 | 0.493575 | ||||||||
\(160\) | 5.47372e9 | 0.660302 | ||||||||
\(161\) | −2.42181e10 | −2.84069 | ||||||||
\(162\) | 8.01156e8 | 0.0913902 | ||||||||
\(163\) | 1.04317e10 | 1.15748 | 0.578738 | − | 0.815513i | \(-0.303545\pi\) | ||||
0.578738 | + | 0.815513i | \(0.303545\pi\) | |||||||
\(164\) | 4.53000e9 | 0.488992 | ||||||||
\(165\) | −6.54330e9 | −0.687256 | ||||||||
\(166\) | 8.35613e9 | 0.854120 | ||||||||
\(167\) | 6.18162e9 | 0.615004 | 0.307502 | − | 0.951547i | \(-0.400507\pi\) | ||||
0.307502 | + | 0.951547i | \(0.400507\pi\) | |||||||
\(168\) | 1.20559e10 | 1.16764 | ||||||||
\(169\) | 2.04002e10 | 1.92373 | ||||||||
\(170\) | 3.02124e9 | 0.277437 | ||||||||
\(171\) | 3.57344e8 | 0.0319598 | ||||||||
\(172\) | −3.25717e9 | −0.283767 | ||||||||
\(173\) | −1.19474e10 | −1.01407 | −0.507033 | − | 0.861927i | \(-0.669258\pi\) | ||||
−0.507033 | + | 0.861927i | \(0.669258\pi\) | |||||||
\(174\) | 4.75009e9 | 0.392853 | ||||||||
\(175\) | 3.24768e9 | 0.261759 | ||||||||
\(176\) | −8.11290e9 | −0.637337 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 1.33788e10 | 0.998914 | ||||||||
\(179\) | 1.17881e10 | 0.858230 | 0.429115 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429115 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(180\) | −1.62206e9 | −0.115171 | ||||||||
\(181\) | 1.59490e10 | 1.10453 | 0.552266 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552266 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(182\) | 3.86760e10 | 2.61289 | ||||||||
\(183\) | −7.36832e9 | −0.485667 | ||||||||
\(184\) | 2.58792e10 | 1.66445 | ||||||||
\(185\) | 2.21275e10 | 1.38886 | ||||||||
\(186\) | −8.56060e9 | −0.524440 | ||||||||
\(187\) | 5.88497e9 | 0.351931 | ||||||||
\(188\) | 2.66166e9 | 0.155397 | ||||||||
\(189\) | −6.27200e9 | −0.357543 | ||||||||
\(190\) | 1.51315e9 | 0.0842346 | ||||||||
\(191\) | −2.20091e10 | −1.19661 | −0.598305 | − | 0.801269i | \(-0.704159\pi\) | ||||
−0.598305 | + | 0.801269i | \(0.704159\pi\) | |||||||
\(192\) | −1.17452e10 | −0.623744 | ||||||||
\(193\) | −2.16486e10 | −1.12311 | −0.561556 | − | 0.827439i | \(-0.689797\pi\) | ||||
−0.561556 | + | 0.827439i | \(0.689797\pi\) | |||||||
\(194\) | −2.94026e10 | −1.49031 | ||||||||
\(195\) | −2.12905e10 | −1.05446 | ||||||||
\(196\) | −1.63848e10 | −0.793030 | ||||||||
\(197\) | 1.45366e10 | 0.687647 | 0.343823 | − | 0.939034i | \(-0.388278\pi\) | ||||
0.343823 | + | 0.939034i | \(0.388278\pi\) | |||||||
\(198\) | 6.60801e9 | 0.305547 | ||||||||
\(199\) | −2.43774e10 | −1.10192 | −0.550958 | − | 0.834533i | \(-0.685737\pi\) | ||||
−0.550958 | + | 0.834533i | \(0.685737\pi\) | |||||||
\(200\) | −3.47044e9 | −0.153373 | ||||||||
\(201\) | 1.48488e9 | 0.0641667 | ||||||||
\(202\) | 8.90450e9 | 0.376295 | ||||||||
\(203\) | −3.71870e10 | −1.53695 | ||||||||
\(204\) | 1.45887e9 | 0.0589766 | ||||||||
\(205\) | −4.08297e10 | −1.61467 | ||||||||
\(206\) | 3.50183e10 | 1.35485 | ||||||||
\(207\) | −1.34635e10 | −0.509674 | ||||||||
\(208\) | −2.63977e10 | −0.977868 | ||||||||
\(209\) | 2.94741e9 | 0.106852 | ||||||||
\(210\) | −2.65583e10 | −0.942354 | ||||||||
\(211\) | −1.54719e10 | −0.537370 | −0.268685 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268685 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(212\) | 8.13327e9 | 0.276537 | ||||||||
\(213\) | 2.50273e10 | 0.833117 | ||||||||
\(214\) | 2.88904e10 | 0.941655 | ||||||||
\(215\) | 2.93574e10 | 0.937010 | ||||||||
\(216\) | 6.70220e9 | 0.209496 | ||||||||
\(217\) | 6.70183e10 | 2.05175 | ||||||||
\(218\) | 4.20691e10 | 1.26156 | ||||||||
\(219\) | −9.86678e8 | −0.0289852 | ||||||||
\(220\) | −1.33789e10 | −0.385052 | ||||||||
\(221\) | 1.91485e10 | 0.539969 | ||||||||
\(222\) | −2.23463e10 | −0.617472 | ||||||||
\(223\) | −2.66817e10 | −0.722505 | −0.361253 | − | 0.932468i | \(-0.617651\pi\) | ||||
−0.361253 | + | 0.932468i | \(0.617651\pi\) | |||||||
\(224\) | 4.32759e10 | 1.14850 | ||||||||
\(225\) | 1.80548e9 | 0.0469646 | ||||||||
\(226\) | 1.11277e10 | 0.283737 | ||||||||
\(227\) | −2.11753e10 | −0.529315 | −0.264657 | − | 0.964343i | \(-0.585259\pi\) | ||||
−0.264657 | + | 0.964343i | \(0.585259\pi\) | |||||||
\(228\) | 7.30655e8 | 0.0179063 | ||||||||
\(229\) | −3.86876e10 | −0.929634 | −0.464817 | − | 0.885407i | \(-0.653880\pi\) | ||||
−0.464817 | + | 0.885407i | \(0.653880\pi\) | |||||||
\(230\) | −5.70103e10 | −1.34332 | ||||||||
\(231\) | −5.17321e10 | −1.19538 | ||||||||
\(232\) | 3.97376e10 | 0.900547 | ||||||||
\(233\) | −2.74168e10 | −0.609418 | −0.304709 | − | 0.952446i | \(-0.598559\pi\) | ||||
−0.304709 | + | 0.952446i | \(0.598559\pi\) | |||||||
\(234\) | 2.15011e10 | 0.468802 | ||||||||
\(235\) | −2.39900e10 | −0.513128 | ||||||||
\(236\) | −2.00687e9 | −0.0421128 | ||||||||
\(237\) | 1.78802e10 | 0.368134 | ||||||||
\(238\) | 2.38863e10 | 0.482561 | ||||||||
\(239\) | 7.19297e10 | 1.42599 | 0.712997 | − | 0.701167i | \(-0.247337\pi\) | ||||
0.712997 | + | 0.701167i | \(0.247337\pi\) | |||||||
\(240\) | 1.81269e10 | 0.352675 | ||||||||
\(241\) | 1.36309e10 | 0.260283 | 0.130142 | − | 0.991495i | \(-0.458457\pi\) | ||||
0.130142 | + | 0.991495i | \(0.458457\pi\) | |||||||
\(242\) | 1.06191e10 | 0.199029 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −1.50658e10 | −0.272107 | ||||||||
\(245\) | 1.47679e11 | 2.61862 | ||||||||
\(246\) | 4.12335e10 | 0.717864 | ||||||||
\(247\) | 9.59026e9 | 0.163943 | ||||||||
\(248\) | −7.16151e10 | −1.20219 | ||||||||
\(249\) | −3.63675e10 | −0.599538 | ||||||||
\(250\) | −4.66167e10 | −0.754765 | ||||||||
\(251\) | 2.60960e10 | 0.414994 | 0.207497 | − | 0.978236i | \(-0.433468\pi\) | ||||
0.207497 | + | 0.978236i | \(0.433468\pi\) | |||||||
\(252\) | −1.28242e10 | −0.200322 | ||||||||
\(253\) | −1.11049e11 | −1.70400 | ||||||||
\(254\) | −2.70316e10 | −0.407493 | ||||||||
\(255\) | −1.31490e10 | −0.194743 | ||||||||
\(256\) | −5.89568e10 | −0.857934 | ||||||||
\(257\) | −7.00925e10 | −1.00224 | −0.501121 | − | 0.865377i | \(-0.667079\pi\) | ||||
−0.501121 | + | 0.865377i | \(0.667079\pi\) | |||||||
\(258\) | −2.96478e10 | −0.416585 | ||||||||
\(259\) | 1.74942e11 | 2.41572 | ||||||||
\(260\) | −4.35323e10 | −0.590787 | ||||||||
\(261\) | −2.06733e10 | −0.275757 | ||||||||
\(262\) | 1.22490e10 | 0.160600 | ||||||||
\(263\) | 1.15879e11 | 1.49350 | 0.746750 | − | 0.665105i | \(-0.231613\pi\) | ||||
0.746750 | + | 0.665105i | \(0.231613\pi\) | |||||||
\(264\) | 5.52804e10 | 0.700413 | ||||||||
\(265\) | −7.33065e10 | −0.913137 | ||||||||
\(266\) | 1.19631e10 | 0.146514 | ||||||||
\(267\) | −5.82272e10 | −0.701173 | ||||||||
\(268\) | 3.03611e9 | 0.0359510 | ||||||||
\(269\) | 1.49016e11 | 1.73519 | 0.867597 | − | 0.497268i | \(-0.165663\pi\) | ||||
0.867597 | + | 0.497268i | \(0.165663\pi\) | |||||||
\(270\) | −1.47645e10 | −0.169076 | ||||||||
\(271\) | −1.47037e11 | −1.65602 | −0.828009 | − | 0.560715i | \(-0.810526\pi\) | ||||
−0.828009 | + | 0.560715i | \(0.810526\pi\) | |||||||
\(272\) | −1.63032e10 | −0.180598 | ||||||||
\(273\) | −1.68325e11 | −1.83408 | ||||||||
\(274\) | −5.21391e10 | −0.558838 | ||||||||
\(275\) | 1.48918e10 | 0.157018 | ||||||||
\(276\) | −2.75286e10 | −0.285557 | ||||||||
\(277\) | 1.15628e11 | 1.18006 | 0.590032 | − | 0.807380i | \(-0.299115\pi\) | ||||
0.590032 | + | 0.807380i | \(0.299115\pi\) | |||||||
\(278\) | −1.49817e11 | −1.50438 | ||||||||
\(279\) | 3.72574e10 | 0.368123 | ||||||||
\(280\) | −2.22178e11 | −2.16018 | ||||||||
\(281\) | −1.10467e11 | −1.05695 | −0.528476 | − | 0.848948i | \(-0.677236\pi\) | ||||
−0.528476 | + | 0.848948i | \(0.677236\pi\) | |||||||
\(282\) | 2.42273e10 | 0.228131 | ||||||||
\(283\) | −1.39797e11 | −1.29557 | −0.647783 | − | 0.761825i | \(-0.724303\pi\) | ||||
−0.647783 | + | 0.761825i | \(0.724303\pi\) | |||||||
\(284\) | 5.11728e10 | 0.466774 | ||||||||
\(285\) | −6.58551e9 | −0.0591273 | ||||||||
\(286\) | 1.77343e11 | 1.56735 | ||||||||
\(287\) | −3.22805e11 | −2.80848 | ||||||||
\(288\) | 2.40583e10 | 0.206063 | ||||||||
\(289\) | −1.06762e11 | −0.900276 | ||||||||
\(290\) | −8.75395e10 | −0.726797 | ||||||||
\(291\) | 1.27966e11 | 1.04610 | ||||||||
\(292\) | −2.01744e9 | −0.0162397 | ||||||||
\(293\) | −2.95432e10 | −0.234182 | −0.117091 | − | 0.993121i | \(-0.537357\pi\) | ||||
−0.117091 | + | 0.993121i | \(0.537357\pi\) | |||||||
\(294\) | −1.49140e11 | −1.16421 | ||||||||
\(295\) | 1.80882e10 | 0.139058 | ||||||||
\(296\) | −1.86942e11 | −1.41545 | ||||||||
\(297\) | −2.87593e10 | −0.214474 | ||||||||
\(298\) | −2.18192e10 | −0.160275 | ||||||||
\(299\) | −3.61329e11 | −2.61446 | ||||||||
\(300\) | 3.69162e9 | 0.0263131 | ||||||||
\(301\) | 2.32103e11 | 1.62979 | ||||||||
\(302\) | 2.33029e10 | 0.161205 | ||||||||
\(303\) | −3.87541e10 | −0.264135 | ||||||||
\(304\) | −8.16524e9 | −0.0548325 | ||||||||
\(305\) | 1.35791e11 | 0.898508 | ||||||||
\(306\) | 1.32791e10 | 0.0865807 | ||||||||
\(307\) | −5.96724e9 | −0.0383399 | −0.0191700 | − | 0.999816i | \(-0.506102\pi\) | ||||
−0.0191700 | + | 0.999816i | \(0.506102\pi\) | |||||||
\(308\) | −1.05776e11 | −0.669742 | ||||||||
\(309\) | −1.52406e11 | −0.951021 | ||||||||
\(310\) | 1.57764e11 | 0.970240 | ||||||||
\(311\) | −2.69967e11 | −1.63640 | −0.818199 | − | 0.574934i | \(-0.805028\pi\) | ||||
−0.818199 | + | 0.574934i | \(0.805028\pi\) | |||||||
\(312\) | 1.79871e11 | 1.07465 | ||||||||
\(313\) | −3.88607e10 | −0.228855 | −0.114428 | − | 0.993432i | \(-0.536503\pi\) | ||||
−0.114428 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(314\) | 1.14257e11 | 0.663281 | ||||||||
\(315\) | 1.15587e11 | 0.661472 | ||||||||
\(316\) | 3.65593e10 | 0.206256 | ||||||||
\(317\) | −2.23628e11 | −1.24383 | −0.621913 | − | 0.783086i | \(-0.713644\pi\) | ||||
−0.621913 | + | 0.783086i | \(0.713644\pi\) | |||||||
\(318\) | 7.40316e10 | 0.405971 | ||||||||
\(319\) | −1.70515e11 | −0.921946 | ||||||||
\(320\) | 2.16453e11 | 1.15396 | ||||||||
\(321\) | −1.25737e11 | −0.660981 | ||||||||
\(322\) | −4.50731e11 | −2.33650 | ||||||||
\(323\) | 5.92294e9 | 0.0302779 | ||||||||
\(324\) | −7.12936e9 | −0.0359416 | ||||||||
\(325\) | 4.84546e10 | 0.240913 | ||||||||
\(326\) | 1.94148e11 | 0.952038 | ||||||||
\(327\) | −1.83093e11 | −0.885537 | ||||||||
\(328\) | 3.44946e11 | 1.64558 | ||||||||
\(329\) | −1.89668e11 | −0.892510 | ||||||||
\(330\) | −1.21779e11 | −0.565276 | ||||||||
\(331\) | 3.56601e11 | 1.63289 | 0.816444 | − | 0.577425i | \(-0.195942\pi\) | ||||
0.816444 | + | 0.577425i | \(0.195942\pi\) | |||||||
\(332\) | −7.43599e10 | −0.335906 | ||||||||
\(333\) | 9.72554e10 | 0.433426 | ||||||||
\(334\) | 1.15048e11 | 0.505848 | ||||||||
\(335\) | −2.73649e10 | −0.118712 | ||||||||
\(336\) | 1.43314e11 | 0.613425 | ||||||||
\(337\) | 4.09649e11 | 1.73012 | 0.865061 | − | 0.501666i | \(-0.167279\pi\) | ||||
0.865061 | + | 0.501666i | \(0.167279\pi\) | |||||||
\(338\) | 3.79674e11 | 1.58229 | ||||||||
\(339\) | −4.84298e10 | −0.199165 | ||||||||
\(340\) | −2.68855e10 | −0.109110 | ||||||||
\(341\) | 3.07303e11 | 1.23075 | ||||||||
\(342\) | 6.65065e9 | 0.0262873 | ||||||||
\(343\) | 6.91322e11 | 2.69685 | ||||||||
\(344\) | −2.48023e11 | −0.954947 | ||||||||
\(345\) | 2.48120e11 | 0.942922 | ||||||||
\(346\) | −2.22357e11 | −0.834081 | ||||||||
\(347\) | 2.00285e11 | 0.741595 | 0.370797 | − | 0.928714i | \(-0.379084\pi\) | ||||
0.370797 | + | 0.928714i | \(0.379084\pi\) | |||||||
\(348\) | −4.22702e10 | −0.154500 | ||||||||
\(349\) | 4.58740e11 | 1.65521 | 0.827603 | − | 0.561314i | \(-0.189704\pi\) | ||||
0.827603 | + | 0.561314i | \(0.189704\pi\) | |||||||
\(350\) | 6.04436e10 | 0.215300 | ||||||||
\(351\) | −9.35769e10 | −0.329069 | ||||||||
\(352\) | 1.98435e11 | 0.688933 | ||||||||
\(353\) | 2.90410e11 | 0.995463 | 0.497732 | − | 0.867331i | \(-0.334166\pi\) | ||||
0.497732 | + | 0.867331i | \(0.334166\pi\) | |||||||
\(354\) | −1.82671e10 | −0.0618238 | ||||||||
\(355\) | −4.61229e11 | −1.54131 | ||||||||
\(356\) | −1.19056e11 | −0.392850 | ||||||||
\(357\) | −1.03958e11 | −0.338727 | ||||||||
\(358\) | 2.19391e11 | 0.705904 | ||||||||
\(359\) | 8.27981e10 | 0.263084 | 0.131542 | − | 0.991311i | \(-0.458007\pi\) | ||||
0.131542 | + | 0.991311i | \(0.458007\pi\) | |||||||
\(360\) | −1.23515e11 | −0.387578 | ||||||||
\(361\) | −3.19721e11 | −0.990807 | ||||||||
\(362\) | 2.96831e11 | 0.908491 | ||||||||
\(363\) | −4.62162e10 | −0.139706 | ||||||||
\(364\) | −3.44172e11 | −1.02759 | ||||||||
\(365\) | 1.81835e10 | 0.0536241 | ||||||||
\(366\) | −1.37134e11 | −0.399467 | ||||||||
\(367\) | 3.34608e11 | 0.962808 | 0.481404 | − | 0.876499i | \(-0.340127\pi\) | ||||
0.481404 | + | 0.876499i | \(0.340127\pi\) | |||||||
\(368\) | 3.07639e11 | 0.874431 | ||||||||
\(369\) | −1.79456e11 | −0.503895 | ||||||||
\(370\) | 4.11821e11 | 1.14235 | ||||||||
\(371\) | −5.79570e11 | −1.58827 | ||||||||
\(372\) | 7.61794e10 | 0.206250 | ||||||||
\(373\) | 4.59899e11 | 1.23019 | 0.615096 | − | 0.788453i | \(-0.289117\pi\) | ||||
0.615096 | + | 0.788453i | \(0.289117\pi\) | |||||||
\(374\) | 1.09527e11 | 0.289467 | ||||||||
\(375\) | 2.02885e11 | 0.529796 | ||||||||
\(376\) | 2.02678e11 | 0.522950 | ||||||||
\(377\) | −5.54821e11 | −1.41455 | ||||||||
\(378\) | −1.16730e11 | −0.294083 | ||||||||
\(379\) | −4.64799e10 | −0.115715 | −0.0578574 | − | 0.998325i | \(-0.518427\pi\) | ||||
−0.0578574 | + | 0.998325i | \(0.518427\pi\) | |||||||
\(380\) | −1.34653e10 | −0.0331275 | ||||||||
\(381\) | 1.17647e11 | 0.286034 | ||||||||
\(382\) | −4.09618e11 | −0.984225 | ||||||||
\(383\) | −3.29063e11 | −0.781419 | −0.390710 | − | 0.920514i | \(-0.627770\pi\) | ||||
−0.390710 | + | 0.920514i | \(0.627770\pi\) | |||||||
\(384\) | −6.65220e10 | −0.156126 | ||||||||
\(385\) | 9.53373e11 | 2.21151 | ||||||||
\(386\) | −4.02910e11 | −0.923772 | ||||||||
\(387\) | 1.29033e11 | 0.292416 | ||||||||
\(388\) | 2.61649e11 | 0.586106 | ||||||||
\(389\) | −1.15550e11 | −0.255857 | −0.127929 | − | 0.991783i | \(-0.540833\pi\) | ||||
−0.127929 | + | 0.991783i | \(0.540833\pi\) | |||||||
\(390\) | −3.96244e11 | −0.867306 | ||||||||
\(391\) | −2.23156e11 | −0.482852 | ||||||||
\(392\) | −1.24765e12 | −2.66874 | ||||||||
\(393\) | −5.33100e10 | −0.112731 | ||||||||
\(394\) | 2.70546e11 | 0.565598 | ||||||||
\(395\) | −3.29515e11 | −0.681065 | ||||||||
\(396\) | −5.88036e10 | −0.120164 | ||||||||
\(397\) | −3.49147e11 | −0.705425 | −0.352713 | − | 0.935732i | \(-0.614741\pi\) | ||||
−0.352713 | + | 0.935732i | \(0.614741\pi\) | |||||||
\(398\) | −4.53695e11 | −0.906338 | ||||||||
\(399\) | −5.20659e10 | −0.102843 | ||||||||
\(400\) | −4.12547e10 | −0.0805757 | ||||||||
\(401\) | 5.89365e11 | 1.13824 | 0.569122 | − | 0.822253i | \(-0.307283\pi\) | ||||
0.569122 | + | 0.822253i | \(0.307283\pi\) | |||||||
\(402\) | 2.76356e10 | 0.0527778 | ||||||||
\(403\) | 9.99898e11 | 1.88835 | ||||||||
\(404\) | −7.92397e10 | −0.147988 | ||||||||
\(405\) | 6.42581e10 | 0.118681 | ||||||||
\(406\) | −6.92098e11 | −1.26416 | ||||||||
\(407\) | 8.02173e11 | 1.44908 | ||||||||
\(408\) | 1.11088e11 | 0.198471 | ||||||||
\(409\) | 3.27083e11 | 0.577967 | 0.288983 | − | 0.957334i | \(-0.406683\pi\) | ||||
0.288983 | + | 0.957334i | \(0.406683\pi\) | |||||||
\(410\) | −7.59894e11 | −1.32808 | ||||||||
\(411\) | 2.26919e11 | 0.392268 | ||||||||
\(412\) | −3.11622e11 | −0.532833 | ||||||||
\(413\) | 1.43008e11 | 0.241871 | ||||||||
\(414\) | −2.50574e11 | −0.419213 | ||||||||
\(415\) | 6.70218e11 | 1.10917 | ||||||||
\(416\) | 6.45667e11 | 1.05703 | ||||||||
\(417\) | 6.52031e11 | 1.05598 | ||||||||
\(418\) | 5.48552e10 | 0.0878870 | ||||||||
\(419\) | 4.85479e11 | 0.769497 | 0.384749 | − | 0.923021i | \(-0.374288\pi\) | ||||
0.384749 | + | 0.923021i | \(0.374288\pi\) | |||||||
\(420\) | 2.36338e11 | 0.370606 | ||||||||
\(421\) | −6.01168e9 | −0.00932667 | −0.00466333 | − | 0.999989i | \(-0.501484\pi\) | ||||
−0.00466333 | + | 0.999989i | \(0.501484\pi\) | |||||||
\(422\) | −2.87953e11 | −0.441993 | ||||||||
\(423\) | −1.05442e11 | −0.160133 | ||||||||
\(424\) | 6.19323e11 | 0.930617 | ||||||||
\(425\) | 2.99255e10 | 0.0444930 | ||||||||
\(426\) | 4.65791e11 | 0.685248 | ||||||||
\(427\) | 1.07358e12 | 1.56282 | ||||||||
\(428\) | −2.57091e11 | −0.370331 | ||||||||
\(429\) | −7.71831e11 | −1.10018 | ||||||||
\(430\) | 5.46379e11 | 0.770702 | ||||||||
\(431\) | 2.61315e11 | 0.364768 | 0.182384 | − | 0.983227i | \(-0.441619\pi\) | ||||
0.182384 | + | 0.983227i | \(0.441619\pi\) | |||||||
\(432\) | 7.96722e10 | 0.110060 | ||||||||
\(433\) | −1.12179e12 | −1.53361 | −0.766805 | − | 0.641881i | \(-0.778154\pi\) | ||||
−0.766805 | + | 0.641881i | \(0.778154\pi\) | |||||||
\(434\) | 1.24730e12 | 1.68759 | ||||||||
\(435\) | 3.80989e11 | 0.510165 | ||||||||
\(436\) | −3.74366e11 | −0.496144 | ||||||||
\(437\) | −1.11765e11 | −0.146602 | ||||||||
\(438\) | −1.83634e10 | −0.0238407 | ||||||||
\(439\) | 2.31501e11 | 0.297483 | 0.148742 | − | 0.988876i | \(-0.452478\pi\) | ||||
0.148742 | + | 0.988876i | \(0.452478\pi\) | |||||||
\(440\) | −1.01877e12 | −1.29580 | ||||||||
\(441\) | 6.49085e11 | 0.817199 | ||||||||
\(442\) | 3.56378e11 | 0.444130 | ||||||||
\(443\) | 2.00771e11 | 0.247676 | 0.123838 | − | 0.992302i | \(-0.460480\pi\) | ||||
0.123838 | + | 0.992302i | \(0.460480\pi\) | |||||||
\(444\) | 1.98856e11 | 0.242837 | ||||||||
\(445\) | 1.07307e12 | 1.29721 | ||||||||
\(446\) | −4.96581e11 | −0.594269 | ||||||||
\(447\) | 9.49615e10 | 0.112503 | ||||||||
\(448\) | 1.71131e12 | 2.00714 | ||||||||
\(449\) | −3.68935e11 | −0.428392 | −0.214196 | − | 0.976791i | \(-0.568713\pi\) | ||||
−0.214196 | + | 0.976791i | \(0.568713\pi\) | |||||||
\(450\) | 3.36023e10 | 0.0386289 | ||||||||
\(451\) | −1.48017e12 | −1.68468 | ||||||||
\(452\) | −9.90233e10 | −0.111587 | ||||||||
\(453\) | −1.01418e11 | −0.113155 | ||||||||
\(454\) | −3.94101e11 | −0.435368 | ||||||||
\(455\) | 3.10208e12 | 3.39313 | ||||||||
\(456\) | 5.56371e10 | 0.0602591 | ||||||||
\(457\) | −1.37268e12 | −1.47213 | −0.736066 | − | 0.676910i | \(-0.763319\pi\) | ||||
−0.736066 | + | 0.676910i | \(0.763319\pi\) | |||||||
\(458\) | −7.20027e11 | −0.764634 | ||||||||
\(459\) | −5.77930e10 | −0.0607741 | ||||||||
\(460\) | 5.07326e11 | 0.528295 | ||||||||
\(461\) | 4.80655e11 | 0.495654 | 0.247827 | − | 0.968804i | \(-0.420283\pi\) | ||||
0.247827 | + | 0.968804i | \(0.420283\pi\) | |||||||
\(462\) | −9.62803e11 | −0.983215 | ||||||||
\(463\) | 2.39475e11 | 0.242185 | 0.121092 | − | 0.992641i | \(-0.461360\pi\) | ||||
0.121092 | + | 0.992641i | \(0.461360\pi\) | |||||||
\(464\) | 4.72380e11 | 0.473108 | ||||||||
\(465\) | −6.86617e11 | −0.681046 | ||||||||
\(466\) | −5.10263e11 | −0.501253 | ||||||||
\(467\) | −1.22103e12 | −1.18796 | −0.593980 | − | 0.804480i | \(-0.702444\pi\) | ||||
−0.593980 | + | 0.804480i | \(0.702444\pi\) | |||||||
\(468\) | −1.91335e11 | −0.184369 | ||||||||
\(469\) | −2.16351e11 | −0.206481 | ||||||||
\(470\) | −4.46486e11 | −0.422053 | ||||||||
\(471\) | −4.97266e11 | −0.465581 | ||||||||
\(472\) | −1.52817e11 | −0.141720 | ||||||||
\(473\) | 1.06427e12 | 0.977639 | ||||||||
\(474\) | 3.32775e11 | 0.302794 | ||||||||
\(475\) | 1.49878e10 | 0.0135088 | ||||||||
\(476\) | −2.12560e11 | −0.189780 | ||||||||
\(477\) | −3.22199e11 | −0.284965 | ||||||||
\(478\) | 1.33871e12 | 1.17290 | ||||||||
\(479\) | 1.73521e12 | 1.50606 | 0.753028 | − | 0.657988i | \(-0.228592\pi\) | ||||
0.753028 | + | 0.657988i | \(0.228592\pi\) | |||||||
\(480\) | −4.43372e11 | −0.381226 | ||||||||
\(481\) | 2.61010e12 | 2.22333 | ||||||||
\(482\) | 2.53688e11 | 0.214086 | ||||||||
\(483\) | 1.96167e12 | 1.64007 | ||||||||
\(484\) | −9.44973e10 | −0.0782736 | ||||||||
\(485\) | −2.35828e12 | −1.93534 | ||||||||
\(486\) | −6.48936e10 | −0.0527641 | ||||||||
\(487\) | −1.80440e12 | −1.45363 | −0.726815 | − | 0.686834i | \(-0.759000\pi\) | ||||
−0.726815 | + | 0.686834i | \(0.759000\pi\) | |||||||
\(488\) | −1.14722e12 | −0.915708 | ||||||||
\(489\) | −8.44970e11 | −0.668269 | ||||||||
\(490\) | 2.74850e12 | 2.15384 | ||||||||
\(491\) | −1.81935e12 | −1.41270 | −0.706351 | − | 0.707862i | \(-0.749660\pi\) | ||||
−0.706351 | + | 0.707862i | \(0.749660\pi\) | |||||||
\(492\) | −3.66930e11 | −0.282319 | ||||||||
\(493\) | −3.42657e11 | −0.261245 | ||||||||
\(494\) | 1.78487e11 | 0.134845 | ||||||||
\(495\) | 5.30007e11 | 0.396788 | ||||||||
\(496\) | −8.51323e11 | −0.631578 | ||||||||
\(497\) | −3.64653e12 | −2.68088 | ||||||||
\(498\) | −6.76847e11 | −0.493127 | ||||||||
\(499\) | −3.19828e11 | −0.230921 | −0.115461 | − | 0.993312i | \(-0.536834\pi\) | ||||
−0.115461 | + | 0.993312i | \(0.536834\pi\) | |||||||
\(500\) | 4.14834e11 | 0.296831 | ||||||||
\(501\) | −5.00711e11 | −0.355073 | ||||||||
\(502\) | 4.85680e11 | 0.341337 | ||||||||
\(503\) | 8.65153e11 | 0.602611 | 0.301305 | − | 0.953528i | \(-0.402578\pi\) | ||||
0.301305 | + | 0.953528i | \(0.402578\pi\) | |||||||
\(504\) | −9.76526e11 | −0.674134 | ||||||||
\(505\) | 7.14201e11 | 0.488663 | ||||||||
\(506\) | −2.06676e12 | −1.40156 | ||||||||
\(507\) | −1.65241e12 | −1.11066 | ||||||||
\(508\) | 2.40550e11 | 0.160257 | ||||||||
\(509\) | 1.81057e12 | 1.19560 | 0.597798 | − | 0.801647i | \(-0.296042\pi\) | ||||
0.597798 | + | 0.801647i | \(0.296042\pi\) | |||||||
\(510\) | −2.44720e11 | −0.160178 | ||||||||
\(511\) | 1.43761e11 | 0.0932712 | ||||||||
\(512\) | −1.51775e12 | −0.976079 | ||||||||
\(513\) | −2.89449e10 | −0.0184520 | ||||||||
\(514\) | −1.30451e12 | −0.824356 | ||||||||
\(515\) | 2.80870e12 | 1.75943 | ||||||||
\(516\) | 2.63831e11 | 0.163833 | ||||||||
\(517\) | −8.69695e11 | −0.535377 | ||||||||
\(518\) | 3.25591e12 | 1.98696 | ||||||||
\(519\) | 9.67740e11 | 0.585471 | ||||||||
\(520\) | −3.31485e12 | −1.98815 | ||||||||
\(521\) | −2.25238e12 | −1.33928 | −0.669640 | − | 0.742686i | \(-0.733552\pi\) | ||||
−0.669640 | + | 0.742686i | \(0.733552\pi\) | |||||||
\(522\) | −3.84757e11 | −0.226814 | ||||||||
\(523\) | −3.18471e11 | −0.186128 | −0.0930640 | − | 0.995660i | \(-0.529666\pi\) | ||||
−0.0930640 | + | 0.995660i | \(0.529666\pi\) | |||||||
\(524\) | −1.09002e11 | −0.0631601 | ||||||||
\(525\) | −2.63062e11 | −0.151127 | ||||||||
\(526\) | 2.15667e12 | 1.22842 | ||||||||
\(527\) | 6.17536e11 | 0.348750 | ||||||||
\(528\) | 6.57145e11 | 0.367967 | ||||||||
\(529\) | 2.40978e12 | 1.33791 | ||||||||
\(530\) | −1.36433e12 | −0.751066 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −1.06458e11 | −0.0576204 | ||||||||
\(533\) | −4.81617e12 | −2.58481 | ||||||||
\(534\) | −1.08369e12 | −0.576723 | ||||||||
\(535\) | 2.31720e12 | 1.22285 | ||||||||
\(536\) | 2.31190e11 | 0.120984 | ||||||||
\(537\) | −9.54833e11 | −0.495499 | ||||||||
\(538\) | 2.77339e12 | 1.42722 | ||||||||
\(539\) | 5.35372e12 | 2.73216 | ||||||||
\(540\) | 1.31387e11 | 0.0664938 | ||||||||
\(541\) | −1.83667e11 | −0.0921816 | −0.0460908 | − | 0.998937i | \(-0.514676\pi\) | ||||
−0.0460908 | + | 0.998937i | \(0.514676\pi\) | |||||||
\(542\) | −2.73655e12 | −1.36209 | ||||||||
\(543\) | −1.29187e12 | −0.637702 | ||||||||
\(544\) | 3.98764e11 | 0.195218 | ||||||||
\(545\) | 3.37423e12 | 1.63829 | ||||||||
\(546\) | −3.13276e12 | −1.50855 | ||||||||
\(547\) | 1.87270e12 | 0.894386 | 0.447193 | − | 0.894437i | \(-0.352424\pi\) | ||||
0.447193 | + | 0.894437i | \(0.352424\pi\) | |||||||
\(548\) | 4.63977e11 | 0.219778 | ||||||||
\(549\) | 5.96834e11 | 0.280400 | ||||||||
\(550\) | 2.77155e11 | 0.129149 | ||||||||
\(551\) | −1.71615e11 | −0.0793185 | ||||||||
\(552\) | −2.09622e12 | −0.960972 | ||||||||
\(553\) | −2.60519e12 | −1.18461 | ||||||||
\(554\) | 2.15200e12 | 0.970617 | ||||||||
\(555\) | −1.79232e12 | −0.801859 | ||||||||
\(556\) | 1.33320e12 | 0.591640 | ||||||||
\(557\) | −3.46768e12 | −1.52648 | −0.763239 | − | 0.646116i | \(-0.776392\pi\) | ||||
−0.763239 | + | 0.646116i | \(0.776392\pi\) | |||||||
\(558\) | 6.93409e11 | 0.302786 | ||||||||
\(559\) | 3.46293e12 | 1.50000 | ||||||||
\(560\) | −2.64114e12 | −1.13487 | ||||||||
\(561\) | −4.76683e11 | −0.203187 | ||||||||
\(562\) | −2.05594e12 | −0.869355 | ||||||||
\(563\) | −1.63273e12 | −0.684898 | −0.342449 | − | 0.939536i | \(-0.611256\pi\) | ||||
−0.342449 | + | 0.939536i | \(0.611256\pi\) | |||||||
\(564\) | −2.15595e11 | −0.0897186 | ||||||||
\(565\) | 8.92514e11 | 0.368466 | ||||||||
\(566\) | −2.60181e12 | −1.06562 | ||||||||
\(567\) | 5.08032e11 | 0.206428 | ||||||||
\(568\) | 3.89665e12 | 1.57081 | ||||||||
\(569\) | −2.02549e12 | −0.810075 | −0.405038 | − | 0.914300i | \(-0.632742\pi\) | ||||
−0.405038 | + | 0.914300i | \(0.632742\pi\) | |||||||
\(570\) | −1.22565e11 | −0.0486329 | ||||||||
\(571\) | 1.28759e12 | 0.506893 | 0.253447 | − | 0.967349i | \(-0.418436\pi\) | ||||
0.253447 | + | 0.967349i | \(0.418436\pi\) | |||||||
\(572\) | −1.57815e12 | −0.616404 | ||||||||
\(573\) | 1.78274e12 | 0.690863 | ||||||||
\(574\) | −6.00782e12 | −2.31001 | ||||||||
\(575\) | −5.64691e11 | −0.215430 | ||||||||
\(576\) | 9.51364e11 | 0.360119 | ||||||||
\(577\) | −4.89310e12 | −1.83778 | −0.918889 | − | 0.394515i | \(-0.870913\pi\) | ||||
−0.918889 | + | 0.394515i | \(0.870913\pi\) | |||||||
\(578\) | −1.98698e12 | −0.740487 | ||||||||
\(579\) | 1.75354e12 | 0.648429 | ||||||||
\(580\) | 7.79000e11 | 0.285832 | ||||||||
\(581\) | 5.29883e12 | 1.92924 | ||||||||
\(582\) | 2.38161e12 | 0.860433 | ||||||||
\(583\) | −2.65753e12 | −0.952731 | ||||||||
\(584\) | −1.53622e11 | −0.0546506 | ||||||||
\(585\) | 1.72453e12 | 0.608793 | ||||||||
\(586\) | −5.49838e11 | −0.192617 | ||||||||
\(587\) | −1.75813e12 | −0.611195 | −0.305598 | − | 0.952161i | \(-0.598856\pi\) | ||||
−0.305598 | + | 0.952161i | \(0.598856\pi\) | |||||||
\(588\) | 1.32717e12 | 0.457856 | ||||||||
\(589\) | 3.09285e11 | 0.105886 | ||||||||
\(590\) | 3.36645e11 | 0.114377 | ||||||||
\(591\) | −1.17747e12 | −0.397013 | ||||||||
\(592\) | −2.22226e12 | −0.743615 | ||||||||
\(593\) | −1.62832e12 | −0.540745 | −0.270372 | − | 0.962756i | \(-0.587147\pi\) | ||||
−0.270372 | + | 0.962756i | \(0.587147\pi\) | |||||||
\(594\) | −5.35249e11 | −0.176407 | ||||||||
\(595\) | 1.91584e12 | 0.626661 | ||||||||
\(596\) | 1.94166e11 | 0.0630325 | ||||||||
\(597\) | 1.97457e12 | 0.636191 | ||||||||
\(598\) | −6.72480e12 | −2.15042 | ||||||||
\(599\) | 2.05355e12 | 0.651754 | 0.325877 | − | 0.945412i | \(-0.394340\pi\) | ||||
0.325877 | + | 0.945412i | \(0.394340\pi\) | |||||||
\(600\) | 2.81106e11 | 0.0885500 | ||||||||
\(601\) | −4.87509e12 | −1.52422 | −0.762110 | − | 0.647448i | \(-0.775836\pi\) | ||||
−0.762110 | + | 0.647448i | \(0.775836\pi\) | |||||||
\(602\) | 4.31974e12 | 1.34052 | ||||||||
\(603\) | −1.20275e11 | −0.0370467 | ||||||||
\(604\) | −2.07368e11 | −0.0633981 | ||||||||
\(605\) | 8.51720e11 | 0.258462 | ||||||||
\(606\) | −7.21265e11 | −0.217254 | ||||||||
\(607\) | −3.47527e12 | −1.03906 | −0.519528 | − | 0.854453i | \(-0.673892\pi\) | ||||
−0.519528 | + | 0.854453i | \(0.673892\pi\) | |||||||
\(608\) | 1.99716e11 | 0.0592715 | ||||||||
\(609\) | 3.01214e12 | 0.887356 | ||||||||
\(610\) | 2.52725e12 | 0.739033 | ||||||||
\(611\) | −2.82981e12 | −0.821431 | ||||||||
\(612\) | −1.18168e11 | −0.0340502 | ||||||||
\(613\) | 2.62214e12 | 0.750038 | 0.375019 | − | 0.927017i | \(-0.377636\pi\) | ||||
0.375019 | + | 0.927017i | \(0.377636\pi\) | |||||||
\(614\) | −1.11058e11 | −0.0315350 | ||||||||
\(615\) | 3.30720e12 | 0.932230 | ||||||||
\(616\) | −8.05449e12 | −2.25385 | ||||||||
\(617\) | −3.35752e12 | −0.932685 | −0.466342 | − | 0.884604i | \(-0.654429\pi\) | ||||
−0.466342 | + | 0.884604i | \(0.654429\pi\) | |||||||
\(618\) | −2.83648e12 | −0.782225 | ||||||||
\(619\) | 3.47281e12 | 0.950766 | 0.475383 | − | 0.879779i | \(-0.342309\pi\) | ||||
0.475383 | + | 0.879779i | \(0.342309\pi\) | |||||||
\(620\) | −1.40391e12 | −0.381573 | ||||||||
\(621\) | 1.09055e12 | 0.294260 | ||||||||
\(622\) | −5.02444e12 | −1.34596 | ||||||||
\(623\) | 8.48384e12 | 2.25630 | ||||||||
\(624\) | 2.13821e12 | 0.564573 | ||||||||
\(625\) | −4.27644e12 | −1.12104 | ||||||||
\(626\) | −7.23249e11 | −0.188236 | ||||||||
\(627\) | −2.38740e11 | −0.0616910 | ||||||||
\(628\) | −1.01675e12 | −0.260853 | ||||||||
\(629\) | 1.61200e12 | 0.410616 | ||||||||
\(630\) | 2.15123e12 | 0.544068 | ||||||||
\(631\) | −2.45725e12 | −0.617045 | −0.308523 | − | 0.951217i | \(-0.599835\pi\) | ||||
−0.308523 | + | 0.951217i | \(0.599835\pi\) | |||||||
\(632\) | 2.78388e12 | 0.694103 | ||||||||
\(633\) | 1.25323e12 | 0.310251 | ||||||||
\(634\) | −4.16201e12 | −1.02306 | ||||||||
\(635\) | −2.16811e12 | −0.529176 | ||||||||
\(636\) | −6.58795e11 | −0.159659 | ||||||||
\(637\) | 1.74199e13 | 4.19197 | ||||||||
\(638\) | −3.17351e12 | −0.758311 | ||||||||
\(639\) | −2.02721e12 | −0.481000 | ||||||||
\(640\) | 1.22594e12 | 0.288840 | ||||||||
\(641\) | 5.98365e12 | 1.39992 | 0.699962 | − | 0.714180i | \(-0.253200\pi\) | ||||
0.699962 | + | 0.714180i | \(0.253200\pi\) | |||||||
\(642\) | −2.34012e12 | −0.543665 | ||||||||
\(643\) | 4.95464e12 | 1.14304 | 0.571522 | − | 0.820587i | \(-0.306353\pi\) | ||||
0.571522 | + | 0.820587i | \(0.306353\pi\) | |||||||
\(644\) | 4.01098e12 | 0.918891 | ||||||||
\(645\) | −2.37795e12 | −0.540983 | ||||||||
\(646\) | 1.10234e11 | 0.0249039 | ||||||||
\(647\) | −7.46826e12 | −1.67552 | −0.837761 | − | 0.546037i | \(-0.816136\pi\) | ||||
−0.837761 | + | 0.546037i | \(0.816136\pi\) | |||||||
\(648\) | −5.42879e11 | −0.120953 | ||||||||
\(649\) | 6.55740e11 | 0.145088 | ||||||||
\(650\) | 9.01804e11 | 0.198154 | ||||||||
\(651\) | −5.42848e12 | −1.18458 | ||||||||
\(652\) | −1.72769e12 | −0.374414 | ||||||||
\(653\) | −5.31545e12 | −1.14401 | −0.572007 | − | 0.820249i | \(-0.693835\pi\) | ||||
−0.572007 | + | 0.820249i | \(0.693835\pi\) | |||||||
\(654\) | −3.40760e12 | −0.728365 | ||||||||
\(655\) | 9.82452e11 | 0.208557 | ||||||||
\(656\) | 4.10053e12 | 0.864516 | ||||||||
\(657\) | 7.99209e10 | 0.0167346 | ||||||||
\(658\) | −3.52997e12 | −0.734099 | ||||||||
\(659\) | 3.34203e12 | 0.690282 | 0.345141 | − | 0.938551i | \(-0.387831\pi\) | ||||
0.345141 | + | 0.938551i | \(0.387831\pi\) | |||||||
\(660\) | 1.08369e12 | 0.222310 | ||||||||
\(661\) | −1.03490e12 | −0.210859 | −0.105430 | − | 0.994427i | \(-0.533622\pi\) | ||||
−0.105430 | + | 0.994427i | \(0.533622\pi\) | |||||||
\(662\) | 6.63681e12 | 1.34307 | ||||||||
\(663\) | −1.55102e12 | −0.311751 | ||||||||
\(664\) | −5.66228e12 | −1.13041 | ||||||||
\(665\) | 9.59524e11 | 0.190265 | ||||||||
\(666\) | 1.81005e12 | 0.356498 | ||||||||
\(667\) | 6.46589e12 | 1.26492 | ||||||||
\(668\) | −1.02379e12 | −0.198938 | ||||||||
\(669\) | 2.16121e12 | 0.417138 | ||||||||
\(670\) | −5.09297e11 | −0.0976416 | ||||||||
\(671\) | 4.92274e12 | 0.937467 | ||||||||
\(672\) | −3.50535e12 | −0.663086 | ||||||||
\(673\) | 2.81027e12 | 0.528056 | 0.264028 | − | 0.964515i | \(-0.414949\pi\) | ||||
0.264028 | + | 0.964515i | \(0.414949\pi\) | |||||||
\(674\) | 7.62410e12 | 1.42305 | ||||||||
\(675\) | −1.46244e11 | −0.0271150 | ||||||||
\(676\) | −3.37865e12 | −0.622277 | ||||||||
\(677\) | 3.12734e12 | 0.572172 | 0.286086 | − | 0.958204i | \(-0.407646\pi\) | ||||
0.286086 | + | 0.958204i | \(0.407646\pi\) | |||||||
\(678\) | −9.01341e11 | −0.163816 | ||||||||
\(679\) | −1.86449e13 | −3.36625 | ||||||||
\(680\) | −2.04725e12 | −0.367181 | ||||||||
\(681\) | 1.71520e12 | 0.305600 | ||||||||
\(682\) | 5.71930e12 | 1.01231 | ||||||||
\(683\) | 8.96063e12 | 1.57560 | 0.787799 | − | 0.615933i | \(-0.211221\pi\) | ||||
0.787799 | + | 0.615933i | \(0.211221\pi\) | |||||||
\(684\) | −5.91830e10 | −0.0103382 | ||||||||
\(685\) | −4.18190e12 | −0.725715 | ||||||||
\(686\) | 1.28664e13 | 2.21819 | ||||||||
\(687\) | 3.13369e12 | 0.536724 | ||||||||
\(688\) | −2.94837e12 | −0.501688 | ||||||||
\(689\) | −8.64706e12 | −1.46178 | ||||||||
\(690\) | 4.61784e12 | 0.775564 | ||||||||
\(691\) | 3.78288e11 | 0.0631206 | 0.0315603 | − | 0.999502i | \(-0.489952\pi\) | ||||
0.0315603 | + | 0.999502i | \(0.489952\pi\) | |||||||
\(692\) | 1.97872e12 | 0.328025 | ||||||||
\(693\) | 4.19030e12 | 0.690154 | ||||||||
\(694\) | 3.72757e12 | 0.609970 | ||||||||
\(695\) | −1.20163e13 | −1.95362 | ||||||||
\(696\) | −3.21875e12 | −0.519931 | ||||||||
\(697\) | −2.97446e12 | −0.477377 | ||||||||
\(698\) | 8.53775e12 | 1.36143 | ||||||||
\(699\) | 2.22076e12 | 0.351848 | ||||||||
\(700\) | −5.37877e11 | −0.0846725 | ||||||||
\(701\) | −5.57092e12 | −0.871356 | −0.435678 | − | 0.900103i | \(-0.643491\pi\) | ||||
−0.435678 | + | 0.900103i | \(0.643491\pi\) | |||||||
\(702\) | −1.74159e12 | −0.270663 | ||||||||
\(703\) | 8.07348e11 | 0.124670 | ||||||||
\(704\) | 7.84695e12 | 1.20399 | ||||||||
\(705\) | 1.94319e12 | 0.296254 | ||||||||
\(706\) | 5.40491e12 | 0.818780 | ||||||||
\(707\) | 5.64656e12 | 0.849956 | ||||||||
\(708\) | 1.62556e11 | 0.0243138 | ||||||||
\(709\) | 4.49290e12 | 0.667757 | 0.333879 | − | 0.942616i | \(-0.391642\pi\) | ||||
0.333879 | + | 0.942616i | \(0.391642\pi\) | |||||||
\(710\) | −8.58408e12 | −1.26774 | ||||||||
\(711\) | −1.44830e12 | −0.212542 | ||||||||
\(712\) | −9.06575e12 | −1.32204 | ||||||||
\(713\) | −1.16528e13 | −1.68861 | ||||||||
\(714\) | −1.93479e12 | −0.278607 | ||||||||
\(715\) | 1.42241e13 | 2.03539 | ||||||||
\(716\) | −1.95233e12 | −0.277616 | ||||||||
\(717\) | −5.82631e12 | −0.823298 | ||||||||
\(718\) | 1.54098e12 | 0.216390 | ||||||||
\(719\) | −3.51348e12 | −0.490295 | −0.245148 | − | 0.969486i | \(-0.578836\pi\) | ||||
−0.245148 | + | 0.969486i | \(0.578836\pi\) | |||||||
\(720\) | −1.46828e12 | −0.203617 | ||||||||
\(721\) | 2.22059e13 | 3.06028 | ||||||||
\(722\) | −5.95043e12 | −0.814950 | ||||||||
\(723\) | −1.10410e12 | −0.150275 | ||||||||
\(724\) | −2.64145e12 | −0.357288 | ||||||||
\(725\) | −8.67084e11 | −0.116558 | ||||||||
\(726\) | −8.60144e11 | −0.114910 | ||||||||
\(727\) | 2.85192e12 | 0.378646 | 0.189323 | − | 0.981915i | \(-0.439371\pi\) | ||||
0.189323 | + | 0.981915i | \(0.439371\pi\) | |||||||
\(728\) | −2.62076e13 | −3.45809 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 3.38419e11 | 0.0441064 | ||||||||
\(731\) | 2.13870e12 | 0.277027 | ||||||||
\(732\) | 1.22033e12 | 0.157101 | ||||||||
\(733\) | −6.61645e12 | −0.846559 | −0.423279 | − | 0.905999i | \(-0.639121\pi\) | ||||
−0.423279 | + | 0.905999i | \(0.639121\pi\) | |||||||
\(734\) | 6.22750e12 | 0.791921 | ||||||||
\(735\) | −1.19620e13 | −1.51186 | ||||||||
\(736\) | −7.52461e12 | −0.945222 | ||||||||
\(737\) | −9.92044e11 | −0.123859 | ||||||||
\(738\) | −3.33992e12 | −0.414459 | ||||||||
\(739\) | 6.98786e12 | 0.861875 | 0.430937 | − | 0.902382i | \(-0.358183\pi\) | ||||
0.430937 | + | 0.902382i | \(0.358183\pi\) | |||||||
\(740\) | −3.66473e12 | −0.449261 | ||||||||
\(741\) | −7.76811e11 | −0.0946528 | ||||||||
\(742\) | −1.07866e13 | −1.30637 | ||||||||
\(743\) | −1.02827e13 | −1.23783 | −0.618913 | − | 0.785460i | \(-0.712427\pi\) | ||||
−0.618913 | + | 0.785460i | \(0.712427\pi\) | |||||||
\(744\) | 5.80083e12 | 0.694083 | ||||||||
\(745\) | −1.75005e12 | −0.208136 | ||||||||
\(746\) | 8.55932e12 | 1.01185 | ||||||||
\(747\) | 2.94577e12 | 0.346143 | ||||||||
\(748\) | −9.74663e11 | −0.113841 | ||||||||
\(749\) | 1.83201e13 | 2.12696 | ||||||||
\(750\) | 3.77595e12 | 0.435764 | ||||||||
\(751\) | 6.20048e12 | 0.711289 | 0.355644 | − | 0.934621i | \(-0.384261\pi\) | ||||
0.355644 | + | 0.934621i | \(0.384261\pi\) | |||||||
\(752\) | 2.40932e12 | 0.274736 | ||||||||
\(753\) | −2.11377e12 | −0.239597 | ||||||||
\(754\) | −1.03259e13 | −1.16348 | ||||||||
\(755\) | 1.86904e12 | 0.209343 | ||||||||
\(756\) | 1.03876e12 | 0.115656 | ||||||||
\(757\) | −8.98211e10 | −0.00994139 | −0.00497069 | − | 0.999988i | \(-0.501582\pi\) | ||||
−0.00497069 | + | 0.999988i | \(0.501582\pi\) | |||||||
\(758\) | −8.65052e11 | −0.0951767 | ||||||||
\(759\) | 8.99493e12 | 0.983807 | ||||||||
\(760\) | −1.02534e12 | −0.111482 | ||||||||
\(761\) | −8.53129e12 | −0.922112 | −0.461056 | − | 0.887371i | \(-0.652529\pi\) | ||||
−0.461056 | + | 0.887371i | \(0.652529\pi\) | |||||||
\(762\) | 2.18956e12 | 0.235266 | ||||||||
\(763\) | 2.66771e13 | 2.84956 | ||||||||
\(764\) | 3.64513e12 | 0.387073 | ||||||||
\(765\) | 1.06507e12 | 0.112435 | ||||||||
\(766\) | −6.12429e12 | −0.642726 | ||||||||
\(767\) | 2.13364e12 | 0.222609 | ||||||||
\(768\) | 4.77550e12 | 0.495329 | ||||||||
\(769\) | −1.33335e13 | −1.37492 | −0.687458 | − | 0.726224i | \(-0.741274\pi\) | ||||
−0.687458 | + | 0.726224i | \(0.741274\pi\) | |||||||
\(770\) | 1.77435e13 | 1.81900 | ||||||||
\(771\) | 5.67750e12 | 0.578645 | ||||||||
\(772\) | 3.58543e12 | 0.363298 | ||||||||
\(773\) | −9.54484e12 | −0.961525 | −0.480763 | − | 0.876851i | \(-0.659640\pi\) | ||||
−0.480763 | + | 0.876851i | \(0.659640\pi\) | |||||||
\(774\) | 2.40147e12 | 0.240515 | ||||||||
\(775\) | 1.56266e12 | 0.155599 | ||||||||
\(776\) | 1.99238e13 | 1.97239 | ||||||||
\(777\) | −1.41703e13 | −1.39472 | ||||||||
\(778\) | −2.15054e12 | −0.210445 | ||||||||
\(779\) | −1.48972e12 | −0.144940 | ||||||||
\(780\) | 3.52611e12 | 0.341091 | ||||||||
\(781\) | −1.67206e13 | −1.60814 | ||||||||
\(782\) | −4.15323e12 | −0.397151 | ||||||||
\(783\) | 1.67454e12 | 0.159209 | ||||||||
\(784\) | −1.48315e13 | −1.40204 | ||||||||
\(785\) | 9.16414e12 | 0.861347 | ||||||||
\(786\) | −9.92169e11 | −0.0927223 | ||||||||
\(787\) | 7.44479e12 | 0.691777 | 0.345888 | − | 0.938276i | \(-0.387578\pi\) | ||||
0.345888 | + | 0.938276i | \(0.387578\pi\) | |||||||
\(788\) | −2.40754e12 | −0.222436 | ||||||||
\(789\) | −9.38622e12 | −0.862272 | ||||||||
\(790\) | −6.13271e12 | −0.560184 | ||||||||
\(791\) | 7.05633e12 | 0.640891 | ||||||||
\(792\) | −4.47772e12 | −0.404383 | ||||||||
\(793\) | 1.60176e13 | 1.43836 | ||||||||
\(794\) | −6.49808e12 | −0.580220 | ||||||||
\(795\) | 5.93783e12 | 0.527200 | ||||||||
\(796\) | 4.03736e12 | 0.356442 | ||||||||
\(797\) | 1.74579e13 | 1.53260 | 0.766301 | − | 0.642482i | \(-0.222095\pi\) | ||||
0.766301 | + | 0.642482i | \(0.222095\pi\) | |||||||
\(798\) | −9.69014e11 | −0.0845897 | ||||||||
\(799\) | −1.74769e12 | −0.151706 | ||||||||
\(800\) | 1.00906e12 | 0.0870988 | ||||||||
\(801\) | 4.71641e12 | 0.404823 | ||||||||
\(802\) | 1.09689e13 | 0.936218 | ||||||||
\(803\) | 6.59195e11 | 0.0559492 | ||||||||
\(804\) | −2.45925e11 | −0.0207563 | ||||||||
\(805\) | −3.61516e13 | −3.03422 | ||||||||
\(806\) | 1.86094e13 | 1.55319 | ||||||||
\(807\) | −1.20703e13 | −1.00181 | ||||||||
\(808\) | −6.03386e12 | −0.498017 | ||||||||
\(809\) | 7.20004e12 | 0.590971 | 0.295486 | − | 0.955347i | \(-0.404519\pi\) | ||||
0.295486 | + | 0.955347i | \(0.404519\pi\) | |||||||
\(810\) | 1.19593e12 | 0.0976163 | ||||||||
\(811\) | −1.08968e13 | −0.884517 | −0.442259 | − | 0.896888i | \(-0.645823\pi\) | ||||
−0.442259 | + | 0.896888i | \(0.645823\pi\) | |||||||
\(812\) | 6.15887e12 | 0.497163 | ||||||||
\(813\) | 1.19100e13 | 0.956102 | ||||||||
\(814\) | 1.49295e13 | 1.19189 | ||||||||
\(815\) | 1.55720e13 | 1.23633 | ||||||||
\(816\) | 1.32056e12 | 0.104268 | ||||||||
\(817\) | 1.07114e12 | 0.0841100 | ||||||||
\(818\) | 6.08744e12 | 0.475384 | ||||||||
\(819\) | 1.36344e13 | 1.05891 | ||||||||
\(820\) | 6.76217e12 | 0.522305 | ||||||||
\(821\) | −2.50890e13 | −1.92726 | −0.963629 | − | 0.267242i | \(-0.913888\pi\) | ||||
−0.963629 | + | 0.267242i | \(0.913888\pi\) | |||||||
\(822\) | 4.22327e12 | 0.322645 | ||||||||
\(823\) | −1.83804e13 | −1.39655 | −0.698274 | − | 0.715831i | \(-0.746048\pi\) | ||||
−0.698274 | + | 0.715831i | \(0.746048\pi\) | |||||||
\(824\) | −2.37291e13 | −1.79312 | ||||||||
\(825\) | −1.20623e12 | −0.0906542 | ||||||||
\(826\) | 2.66156e12 | 0.198942 | ||||||||
\(827\) | −5.81755e12 | −0.432480 | −0.216240 | − | 0.976340i | \(-0.569379\pi\) | ||||
−0.216240 | + | 0.976340i | \(0.569379\pi\) | |||||||
\(828\) | 2.22982e12 | 0.164867 | ||||||||
\(829\) | −7.71834e12 | −0.567582 | −0.283791 | − | 0.958886i | \(-0.591592\pi\) | ||||
−0.283791 | + | 0.958886i | \(0.591592\pi\) | |||||||
\(830\) | 1.24736e13 | 0.912308 | ||||||||
\(831\) | −9.36590e12 | −0.681311 | ||||||||
\(832\) | 2.55323e13 | 1.84729 | ||||||||
\(833\) | 1.07585e13 | 0.774193 | ||||||||
\(834\) | 1.21352e13 | 0.868557 | ||||||||
\(835\) | 9.22762e12 | 0.656902 | ||||||||
\(836\) | −4.88148e11 | −0.0345639 | ||||||||
\(837\) | −3.01785e12 | −0.212536 | ||||||||
\(838\) | 9.03540e12 | 0.632920 | ||||||||
\(839\) | 9.00347e12 | 0.627308 | 0.313654 | − | 0.949537i | \(-0.398447\pi\) | ||||
0.313654 | + | 0.949537i | \(0.398447\pi\) | |||||||
\(840\) | 1.79964e13 | 1.24718 | ||||||||
\(841\) | −4.57875e12 | −0.315620 | ||||||||
\(842\) | −1.11885e11 | −0.00767129 | ||||||||
\(843\) | 8.94785e12 | 0.610232 | ||||||||
\(844\) | 2.56245e12 | 0.173826 | ||||||||
\(845\) | 3.04524e13 | 2.05478 | ||||||||
\(846\) | −1.96241e12 | −0.131711 | ||||||||
\(847\) | 6.73380e12 | 0.449557 | ||||||||
\(848\) | 7.36219e12 | 0.488906 | ||||||||
\(849\) | 1.13236e13 | 0.747995 | ||||||||
\(850\) | 5.56954e11 | 0.0365960 | ||||||||
\(851\) | −3.04181e13 | −1.98815 | ||||||||
\(852\) | −4.14500e12 | −0.269492 | ||||||||
\(853\) | −3.36589e11 | −0.0217685 | −0.0108843 | − | 0.999941i | \(-0.503465\pi\) | ||||
−0.0108843 | + | 0.999941i | \(0.503465\pi\) | |||||||
\(854\) | 1.99807e13 | 1.28544 | ||||||||
\(855\) | 5.33427e11 | 0.0341371 | ||||||||
\(856\) | −1.95767e13 | −1.24626 | ||||||||
\(857\) | −2.49442e12 | −0.157963 | −0.0789816 | − | 0.996876i | \(-0.525167\pi\) | ||||
−0.0789816 | + | 0.996876i | \(0.525167\pi\) | |||||||
\(858\) | −1.43648e13 | −0.904913 | ||||||||
\(859\) | −2.48059e13 | −1.55448 | −0.777242 | − | 0.629202i | \(-0.783382\pi\) | ||||
−0.777242 | + | 0.629202i | \(0.783382\pi\) | |||||||
\(860\) | −4.86214e12 | −0.303099 | ||||||||
\(861\) | 2.61472e13 | 1.62148 | ||||||||
\(862\) | 4.86341e12 | 0.300026 | ||||||||
\(863\) | −1.49580e13 | −0.917962 | −0.458981 | − | 0.888446i | \(-0.651785\pi\) | ||||
−0.458981 | + | 0.888446i | \(0.651785\pi\) | |||||||
\(864\) | −1.94872e12 | −0.118970 | ||||||||
\(865\) | −1.78345e13 | −1.08315 | ||||||||
\(866\) | −2.08779e13 | −1.26141 | ||||||||
\(867\) | 8.64771e12 | 0.519775 | ||||||||
\(868\) | −1.10995e13 | −0.663690 | ||||||||
\(869\) | −1.19457e13 | −0.710596 | ||||||||
\(870\) | 7.09070e12 | 0.419616 | ||||||||
\(871\) | −3.22790e12 | −0.190037 | ||||||||
\(872\) | −2.85069e13 | −1.66965 | ||||||||
\(873\) | −1.03652e13 | −0.603969 | ||||||||
\(874\) | −2.08009e12 | −0.120582 | ||||||||
\(875\) | −2.95608e13 | −1.70482 | ||||||||
\(876\) | 1.63413e11 | 0.00937599 | ||||||||
\(877\) | −6.24566e12 | −0.356517 | −0.178258 | − | 0.983984i | \(-0.557046\pi\) | ||||
−0.178258 | + | 0.983984i | \(0.557046\pi\) | |||||||
\(878\) | 4.30854e12 | 0.244684 | ||||||||
\(879\) | 2.39300e12 | 0.135205 | ||||||||
\(880\) | −1.21105e13 | −0.680756 | ||||||||
\(881\) | 2.33730e13 | 1.30714 | 0.653572 | − | 0.756864i | \(-0.273270\pi\) | ||||
0.653572 | + | 0.756864i | \(0.273270\pi\) | |||||||
\(882\) | 1.20803e13 | 0.672156 | ||||||||
\(883\) | 5.34930e12 | 0.296124 | 0.148062 | − | 0.988978i | \(-0.452696\pi\) | ||||
0.148062 | + | 0.988978i | \(0.452696\pi\) | |||||||
\(884\) | −3.17135e12 | −0.174666 | ||||||||
\(885\) | −1.46515e12 | −0.0802853 | ||||||||
\(886\) | 3.73661e12 | 0.203716 | ||||||||
\(887\) | −2.76665e12 | −0.150071 | −0.0750357 | − | 0.997181i | \(-0.523907\pi\) | ||||
−0.0750357 | + | 0.997181i | \(0.523907\pi\) | |||||||
\(888\) | 1.51423e13 | 0.817209 | ||||||||
\(889\) | −1.71414e13 | −0.920424 | ||||||||
\(890\) | 1.99713e13 | 1.06697 | ||||||||
\(891\) | 2.32951e12 | 0.123827 | ||||||||
\(892\) | 4.41899e12 | 0.233712 | ||||||||
\(893\) | −8.75306e11 | −0.0460605 | ||||||||
\(894\) | 1.76736e12 | 0.0925349 | ||||||||
\(895\) | 1.75966e13 | 0.916698 | ||||||||
\(896\) | 9.69240e12 | 0.502395 | ||||||||
\(897\) | 2.92676e13 | 1.50946 | ||||||||
\(898\) | −6.86636e12 | −0.352357 | ||||||||
\(899\) | −1.78929e13 | −0.913615 | ||||||||
\(900\) | −2.99021e11 | −0.0151919 | ||||||||
\(901\) | −5.34042e12 | −0.269969 | ||||||||
\(902\) | −2.75480e13 | −1.38567 | ||||||||
\(903\) | −1.88004e13 | −0.940960 | ||||||||
\(904\) | −7.54032e12 | −0.375519 | ||||||||
\(905\) | 2.38078e13 | 1.17978 | ||||||||
\(906\) | −1.88753e12 | −0.0930716 | ||||||||
\(907\) | −5.41718e12 | −0.265791 | −0.132896 | − | 0.991130i | \(-0.542428\pi\) | ||||
−0.132896 | + | 0.991130i | \(0.542428\pi\) | |||||||
\(908\) | 3.50704e12 | 0.171220 | ||||||||
\(909\) | 3.13908e12 | 0.152498 | ||||||||
\(910\) | 5.77337e13 | 2.79089 | ||||||||
\(911\) | −3.39211e13 | −1.63169 | −0.815844 | − | 0.578272i | \(-0.803727\pi\) | ||||
−0.815844 | + | 0.578272i | \(0.803727\pi\) | |||||||
\(912\) | 6.61384e11 | 0.0316575 | ||||||||
\(913\) | 2.42970e13 | 1.15727 | ||||||||
\(914\) | −2.55474e13 | −1.21085 | ||||||||
\(915\) | −1.09991e13 | −0.518754 | ||||||||
\(916\) | 6.40740e12 | 0.300713 | ||||||||
\(917\) | 7.76739e12 | 0.362755 | ||||||||
\(918\) | −1.07560e12 | −0.0499874 | ||||||||
\(919\) | 3.66041e13 | 1.69282 | 0.846409 | − | 0.532534i | \(-0.178760\pi\) | ||||
0.846409 | + | 0.532534i | \(0.178760\pi\) | |||||||
\(920\) | 3.86313e13 | 1.77785 | ||||||||
\(921\) | 4.83347e11 | 0.0221356 | ||||||||
\(922\) | 8.94561e12 | 0.407682 | ||||||||
\(923\) | −5.44055e13 | −2.46737 | ||||||||
\(924\) | 8.56782e12 | 0.386675 | ||||||||
\(925\) | 4.07911e12 | 0.183201 | ||||||||
\(926\) | 4.45695e12 | 0.199200 | ||||||||
\(927\) | 1.23449e13 | 0.549072 | ||||||||
\(928\) | −1.15541e13 | −0.511409 | ||||||||
\(929\) | 1.54600e13 | 0.680989 | 0.340494 | − | 0.940247i | \(-0.389406\pi\) | ||||
0.340494 | + | 0.940247i | \(0.389406\pi\) | |||||||
\(930\) | −1.27789e13 | −0.560168 | ||||||||
\(931\) | 5.38826e12 | 0.235058 | ||||||||
\(932\) | 4.54075e12 | 0.197131 | ||||||||
\(933\) | 2.18673e13 | 0.944775 | ||||||||
\(934\) | −2.27251e13 | −0.977111 | ||||||||
\(935\) | 8.78480e12 | 0.375906 | ||||||||
\(936\) | −1.45695e13 | −0.620447 | ||||||||
\(937\) | −3.37491e13 | −1.43032 | −0.715161 | − | 0.698960i | \(-0.753646\pi\) | ||||
−0.715161 | + | 0.698960i | \(0.753646\pi\) | |||||||
\(938\) | −4.02657e12 | −0.169833 | ||||||||
\(939\) | 3.14772e12 | 0.132130 | ||||||||
\(940\) | 3.97321e12 | 0.165984 | ||||||||
\(941\) | −2.38639e12 | −0.0992175 | −0.0496087 | − | 0.998769i | \(-0.515797\pi\) | ||||
−0.0496087 | + | 0.998769i | \(0.515797\pi\) | |||||||
\(942\) | −9.25478e12 | −0.382946 | ||||||||
\(943\) | 5.61277e13 | 2.31140 | ||||||||
\(944\) | −1.81660e12 | −0.0744537 | ||||||||
\(945\) | −9.36255e12 | −0.381901 | ||||||||
\(946\) | 1.98075e13 | 0.804120 | ||||||||
\(947\) | 1.40787e13 | 0.568837 | 0.284419 | − | 0.958700i | \(-0.408199\pi\) | ||||
0.284419 | + | 0.958700i | \(0.408199\pi\) | |||||||
\(948\) | −2.96131e12 | −0.119082 | ||||||||
\(949\) | 2.14488e12 | 0.0858432 | ||||||||
\(950\) | 2.78943e11 | 0.0111112 | ||||||||
\(951\) | 1.81139e13 | 0.718124 | ||||||||
\(952\) | −1.61858e13 | −0.638657 | ||||||||
\(953\) | 4.17831e12 | 0.164090 | 0.0820452 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820452 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(954\) | −5.99656e12 | −0.234387 | ||||||||
\(955\) | −3.28541e13 | −1.27813 | ||||||||
\(956\) | −1.19129e13 | −0.461273 | ||||||||
\(957\) | 1.38117e13 | 0.532286 | ||||||||
\(958\) | 3.22945e13 | 1.23875 | ||||||||
\(959\) | −3.30626e13 | −1.26227 | ||||||||
\(960\) | −1.75327e13 | −0.666237 | ||||||||
\(961\) | 5.80701e12 | 0.219633 | ||||||||
\(962\) | 4.85774e13 | 1.82872 | ||||||||
\(963\) | 1.01847e13 | 0.381618 | ||||||||
\(964\) | −2.25753e12 | −0.0841951 | ||||||||
\(965\) | −3.23161e13 | −1.19963 | ||||||||
\(966\) | 3.65092e13 | 1.34898 | ||||||||
\(967\) | −2.15220e13 | −0.791521 | −0.395761 | − | 0.918354i | \(-0.629519\pi\) | ||||
−0.395761 | + | 0.918354i | \(0.629519\pi\) | |||||||
\(968\) | −7.19568e12 | −0.263410 | ||||||||
\(969\) | −4.79758e11 | −0.0174810 | ||||||||
\(970\) | −4.38908e13 | −1.59184 | ||||||||
\(971\) | 3.09036e13 | 1.11564 | 0.557818 | − | 0.829963i | \(-0.311639\pi\) | ||||
0.557818 | + | 0.829963i | \(0.311639\pi\) | |||||||
\(972\) | 5.77478e11 | 0.0207509 | ||||||||
\(973\) | −9.50025e13 | −3.39803 | ||||||||
\(974\) | −3.35823e13 | −1.19563 | ||||||||
\(975\) | −3.92482e12 | −0.139091 | ||||||||
\(976\) | −1.36375e13 | −0.481073 | ||||||||
\(977\) | −4.38260e13 | −1.53889 | −0.769443 | − | 0.638715i | \(-0.779466\pi\) | ||||
−0.769443 | + | 0.638715i | \(0.779466\pi\) | |||||||
\(978\) | −1.57260e13 | −0.549659 | ||||||||
\(979\) | 3.89014e13 | 1.35345 | ||||||||
\(980\) | −2.44585e13 | −0.847056 | ||||||||
\(981\) | 1.48305e13 | 0.511265 | ||||||||
\(982\) | −3.38606e13 | −1.16196 | ||||||||
\(983\) | 1.32092e13 | 0.451219 | 0.225609 | − | 0.974218i | \(-0.427563\pi\) | ||||
0.225609 | + | 0.974218i | \(0.427563\pi\) | |||||||
\(984\) | −2.79406e13 | −0.950075 | ||||||||
\(985\) | 2.16996e13 | 0.734494 | ||||||||
\(986\) | −6.37730e12 | −0.214877 | ||||||||
\(987\) | 1.53631e13 | 0.515291 | ||||||||
\(988\) | −1.58833e12 | −0.0530316 | ||||||||
\(989\) | −4.03570e13 | −1.34133 | ||||||||
\(990\) | 9.86413e12 | 0.326362 | ||||||||
\(991\) | −4.72326e13 | −1.55565 | −0.777823 | − | 0.628483i | \(-0.783676\pi\) | ||||
−0.777823 | + | 0.628483i | \(0.783676\pi\) | |||||||
\(992\) | 2.08227e13 | 0.682708 | ||||||||
\(993\) | −2.88847e13 | −0.942748 | ||||||||
\(994\) | −6.78668e13 | −2.20505 | ||||||||
\(995\) | −3.63894e13 | −1.17699 | ||||||||
\(996\) | 6.02315e12 | 0.193935 | ||||||||
\(997\) | −1.97696e13 | −0.633681 | −0.316840 | − | 0.948479i | \(-0.602622\pi\) | ||||
−0.316840 | + | 0.948479i | \(0.602622\pi\) | |||||||
\(998\) | −5.95242e12 | −0.189936 | ||||||||
\(999\) | −7.87769e12 | −0.250239 |
(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.c.1.15 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.c.1.15 | ✓ | 22 | 1.1 | even | 1 | trivial |