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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.0004 | 0.574540 | 0.287270 | − | 0.957850i | \(-0.407252\pi\) | ||||
0.287270 | + | 0.957850i | \(0.407252\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −342.991 | −0.669904 | ||||||||
\(5\) | −5.38377 | −0.00385231 | −0.00192615 | − | 0.999998i | \(-0.500613\pi\) | ||||
−0.00192615 | + | 0.999998i | \(0.500613\pi\) | |||||||
\(6\) | −1053.03 | −0.331711 | ||||||||
\(7\) | −6261.56 | −0.985692 | −0.492846 | − | 0.870117i | \(-0.664043\pi\) | ||||
−0.492846 | + | 0.870117i | \(0.664043\pi\) | |||||||
\(8\) | −11115.2 | −0.959427 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −69.9909 | −0.00221331 | ||||||||
\(11\) | −43612.2 | −0.898133 | −0.449066 | − | 0.893498i | \(-0.648243\pi\) | ||||
−0.449066 | + | 0.893498i | \(0.648243\pi\) | |||||||
\(12\) | 27782.3 | 0.386769 | ||||||||
\(13\) | −69107.7 | −0.671091 | −0.335545 | − | 0.942024i | \(-0.608921\pi\) | ||||
−0.335545 | + | 0.942024i | \(0.608921\pi\) | |||||||
\(14\) | −81402.5 | −0.566319 | ||||||||
\(15\) | 436.085 | 0.00222413 | ||||||||
\(16\) | 31109.9 | 0.118675 | ||||||||
\(17\) | −325669. | −0.945707 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(18\) | 85295.3 | 0.191513 | ||||||||
\(19\) | −628064. | −1.10564 | −0.552819 | − | 0.833302i | \(-0.686448\pi\) | ||||
−0.552819 | + | 0.833302i | \(0.686448\pi\) | |||||||
\(20\) | 1846.58 | 0.00258068 | ||||||||
\(21\) | 507186. | 0.569090 | ||||||||
\(22\) | −566974. | −0.516013 | ||||||||
\(23\) | −408662. | −0.304501 | −0.152250 | − | 0.988342i | \(-0.548652\pi\) | ||||
−0.152250 | + | 0.988342i | \(0.548652\pi\) | |||||||
\(24\) | 900330. | 0.553925 | ||||||||
\(25\) | −1.95310e6 | −0.999985 | ||||||||
\(26\) | −898425. | −0.385569 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 2.14766e6 | 0.660319 | ||||||||
\(29\) | −7.39061e6 | −1.94039 | −0.970196 | − | 0.242323i | \(-0.922091\pi\) | ||||
−0.970196 | + | 0.242323i | \(0.922091\pi\) | |||||||
\(30\) | 5669.26 | 0.00127785 | ||||||||
\(31\) | 685788. | 0.133371 | 0.0666856 | − | 0.997774i | \(-0.478758\pi\) | ||||
0.0666856 | + | 0.997774i | \(0.478758\pi\) | |||||||
\(32\) | 6.09541e6 | 1.02761 | ||||||||
\(33\) | 3.53259e6 | 0.518537 | ||||||||
\(34\) | −4.23382e6 | −0.543346 | ||||||||
\(35\) | 33710.8 | 0.00379719 | ||||||||
\(36\) | −2.25036e6 | −0.223301 | ||||||||
\(37\) | 4.07607e6 | 0.357547 | 0.178774 | − | 0.983890i | \(-0.442787\pi\) | ||||
0.178774 | + | 0.983890i | \(0.442787\pi\) | |||||||
\(38\) | −8.16506e6 | −0.635233 | ||||||||
\(39\) | 5.59772e6 | 0.387455 | ||||||||
\(40\) | 59841.6 | 0.00369601 | ||||||||
\(41\) | −2.00366e6 | −0.110738 | −0.0553689 | − | 0.998466i | \(-0.517633\pi\) | ||||
−0.0553689 | + | 0.998466i | \(0.517633\pi\) | |||||||
\(42\) | 6.59360e6 | 0.326965 | ||||||||
\(43\) | 5.29965e6 | 0.236395 | 0.118198 | − | 0.992990i | \(-0.462288\pi\) | ||||
0.118198 | + | 0.992990i | \(0.462288\pi\) | |||||||
\(44\) | 1.49586e7 | 0.601663 | ||||||||
\(45\) | −35322.9 | −0.00128410 | ||||||||
\(46\) | −5.31275e6 | −0.174948 | ||||||||
\(47\) | −4.79365e7 | −1.43293 | −0.716467 | − | 0.697621i | \(-0.754242\pi\) | ||||
−0.716467 | + | 0.697621i | \(0.754242\pi\) | |||||||
\(48\) | −2.51990e6 | −0.0685170 | ||||||||
\(49\) | −1.14649e6 | −0.0284112 | ||||||||
\(50\) | −2.53909e7 | −0.574531 | ||||||||
\(51\) | 2.63792e7 | 0.546004 | ||||||||
\(52\) | 2.37033e7 | 0.449566 | ||||||||
\(53\) | 2.75368e7 | 0.479372 | 0.239686 | − | 0.970850i | \(-0.422956\pi\) | ||||
0.239686 | + | 0.970850i | \(0.422956\pi\) | |||||||
\(54\) | −6.90892e6 | −0.110570 | ||||||||
\(55\) | 234798. | 0.00345989 | ||||||||
\(56\) | 6.95984e7 | 0.945699 | ||||||||
\(57\) | 5.08732e7 | 0.638340 | ||||||||
\(58\) | −9.60806e7 | −1.11483 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | −149573. | −0.00148995 | ||||||||
\(61\) | −1.32205e8 | −1.22254 | −0.611271 | − | 0.791421i | \(-0.709342\pi\) | ||||
−0.611271 | + | 0.791421i | \(0.709342\pi\) | |||||||
\(62\) | 8.91549e6 | 0.0766271 | ||||||||
\(63\) | −4.10821e7 | −0.328564 | ||||||||
\(64\) | 6.33143e7 | 0.471728 | ||||||||
\(65\) | 372060. | 0.00258525 | ||||||||
\(66\) | 4.59249e7 | 0.297920 | ||||||||
\(67\) | −8.56509e7 | −0.519272 | −0.259636 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259636 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(68\) | 1.11702e8 | 0.633533 | ||||||||
\(69\) | 3.31016e7 | 0.175804 | ||||||||
\(70\) | 438252. | 0.00218164 | ||||||||
\(71\) | 1.57797e8 | 0.736949 | 0.368475 | − | 0.929638i | \(-0.379880\pi\) | ||||
0.368475 | + | 0.929638i | \(0.379880\pi\) | |||||||
\(72\) | −7.29267e7 | −0.319809 | ||||||||
\(73\) | 3.62252e8 | 1.49299 | 0.746497 | − | 0.665389i | \(-0.231734\pi\) | ||||
0.746497 | + | 0.665389i | \(0.231734\pi\) | |||||||
\(74\) | 5.29903e7 | 0.205425 | ||||||||
\(75\) | 1.58201e8 | 0.577342 | ||||||||
\(76\) | 2.15420e8 | 0.740671 | ||||||||
\(77\) | 2.73080e8 | 0.885282 | ||||||||
\(78\) | 7.27724e7 | 0.222608 | ||||||||
\(79\) | 1.14795e7 | 0.0331590 | 0.0165795 | − | 0.999863i | \(-0.494722\pi\) | ||||
0.0165795 | + | 0.999863i | \(0.494722\pi\) | |||||||
\(80\) | −167489. | −0.000457172 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −2.60482e7 | −0.0636233 | ||||||||
\(83\) | −4.93368e7 | −0.114109 | −0.0570545 | − | 0.998371i | \(-0.518171\pi\) | ||||
−0.0570545 | + | 0.998371i | \(0.518171\pi\) | |||||||
\(84\) | −1.73960e8 | −0.381235 | ||||||||
\(85\) | 1.75333e6 | 0.00364316 | ||||||||
\(86\) | 6.88973e7 | 0.135819 | ||||||||
\(87\) | 5.98639e8 | 1.12029 | ||||||||
\(88\) | 4.84757e8 | 0.861692 | ||||||||
\(89\) | 8.84760e8 | 1.49476 | 0.747378 | − | 0.664399i | \(-0.231312\pi\) | ||||
0.747378 | + | 0.664399i | \(0.231312\pi\) | |||||||
\(90\) | −459210. | −0.000737769 0 | ||||||||
\(91\) | 4.32722e8 | 0.661489 | ||||||||
\(92\) | 1.40167e8 | 0.203986 | ||||||||
\(93\) | −5.55488e7 | −0.0770019 | ||||||||
\(94\) | −6.23191e8 | −0.823277 | ||||||||
\(95\) | 3.38135e6 | 0.00425926 | ||||||||
\(96\) | −4.93729e8 | −0.593291 | ||||||||
\(97\) | −7.61382e8 | −0.873232 | −0.436616 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436616 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(98\) | −1.49048e7 | −0.0163234 | ||||||||
\(99\) | −2.86139e8 | −0.299378 | ||||||||
\(100\) | 6.69894e8 | 0.669894 | ||||||||
\(101\) | 9.88097e8 | 0.944830 | 0.472415 | − | 0.881376i | \(-0.343382\pi\) | ||||
0.472415 | + | 0.881376i | \(0.343382\pi\) | |||||||
\(102\) | 3.42939e8 | 0.313701 | ||||||||
\(103\) | −8.31308e8 | −0.727770 | −0.363885 | − | 0.931444i | \(-0.618550\pi\) | ||||
−0.363885 | + | 0.931444i | \(0.618550\pi\) | |||||||
\(104\) | 7.68145e8 | 0.643862 | ||||||||
\(105\) | −2.73057e6 | −0.00219231 | ||||||||
\(106\) | 3.57989e8 | 0.275418 | ||||||||
\(107\) | −9.36999e8 | −0.691054 | −0.345527 | − | 0.938409i | \(-0.612300\pi\) | ||||
−0.345527 | + | 0.938409i | \(0.612300\pi\) | |||||||
\(108\) | 1.82279e8 | 0.128923 | ||||||||
\(109\) | −5.10879e8 | −0.346656 | −0.173328 | − | 0.984864i | \(-0.555452\pi\) | ||||
−0.173328 | + | 0.984864i | \(0.555452\pi\) | |||||||
\(110\) | 3.05245e6 | 0.00198784 | ||||||||
\(111\) | −3.30161e8 | −0.206430 | ||||||||
\(112\) | −1.94797e8 | −0.116977 | ||||||||
\(113\) | −4.27921e8 | −0.246894 | −0.123447 | − | 0.992351i | \(-0.539395\pi\) | ||||
−0.123447 | + | 0.992351i | \(0.539395\pi\) | |||||||
\(114\) | 6.61369e8 | 0.366752 | ||||||||
\(115\) | 2.20014e6 | 0.00117303 | ||||||||
\(116\) | 2.53491e9 | 1.29988 | ||||||||
\(117\) | −4.53416e8 | −0.223697 | ||||||||
\(118\) | 1.57530e8 | 0.0747987 | ||||||||
\(119\) | 2.03920e9 | 0.932176 | ||||||||
\(120\) | −4.84717e6 | −0.00213389 | ||||||||
\(121\) | −4.55927e8 | −0.193357 | ||||||||
\(122\) | −1.71871e9 | −0.702400 | ||||||||
\(123\) | 1.62296e8 | 0.0639345 | ||||||||
\(124\) | −2.35219e8 | −0.0893459 | ||||||||
\(125\) | 2.10302e7 | 0.00770456 | ||||||||
\(126\) | −5.34082e8 | −0.188773 | ||||||||
\(127\) | 2.84159e9 | 0.969270 | 0.484635 | − | 0.874716i | \(-0.338952\pi\) | ||||
0.484635 | + | 0.874716i | \(0.338952\pi\) | |||||||
\(128\) | −2.29774e9 | −0.756583 | ||||||||
\(129\) | −4.29271e8 | −0.136483 | ||||||||
\(130\) | 4.83691e6 | 0.00148533 | ||||||||
\(131\) | 2.87084e9 | 0.851704 | 0.425852 | − | 0.904793i | \(-0.359974\pi\) | ||||
0.425852 | + | 0.904793i | \(0.359974\pi\) | |||||||
\(132\) | −1.21164e9 | −0.347370 | ||||||||
\(133\) | 3.93266e9 | 1.08982 | ||||||||
\(134\) | −1.11349e9 | −0.298343 | ||||||||
\(135\) | 2.86115e6 | 0.000741377 0 | ||||||||
\(136\) | 3.61987e9 | 0.907336 | ||||||||
\(137\) | −2.90047e9 | −0.703438 | −0.351719 | − | 0.936106i | \(-0.614403\pi\) | ||||
−0.351719 | + | 0.936106i | \(0.614403\pi\) | |||||||
\(138\) | 4.30332e8 | 0.101006 | ||||||||
\(139\) | −1.76889e9 | −0.401916 | −0.200958 | − | 0.979600i | \(-0.564405\pi\) | ||||
−0.200958 | + | 0.979600i | \(0.564405\pi\) | |||||||
\(140\) | −1.15625e7 | −0.00254375 | ||||||||
\(141\) | 3.88286e9 | 0.827304 | ||||||||
\(142\) | 2.05142e9 | 0.423407 | ||||||||
\(143\) | 3.01394e9 | 0.602729 | ||||||||
\(144\) | 2.04112e8 | 0.0395583 | ||||||||
\(145\) | 3.97893e7 | 0.00747499 | ||||||||
\(146\) | 4.70940e9 | 0.857784 | ||||||||
\(147\) | 9.28660e7 | 0.0164032 | ||||||||
\(148\) | −1.39805e9 | −0.239522 | ||||||||
\(149\) | −3.34952e9 | −0.556730 | −0.278365 | − | 0.960475i | \(-0.589793\pi\) | ||||
−0.278365 | + | 0.960475i | \(0.589793\pi\) | |||||||
\(150\) | 2.05667e9 | 0.331706 | ||||||||
\(151\) | 4.36665e9 | 0.683521 | 0.341760 | − | 0.939787i | \(-0.388977\pi\) | ||||
0.341760 | + | 0.939787i | \(0.388977\pi\) | |||||||
\(152\) | 6.98105e9 | 1.06078 | ||||||||
\(153\) | −2.13672e9 | −0.315236 | ||||||||
\(154\) | 3.55014e9 | 0.508630 | ||||||||
\(155\) | −3.69212e6 | −0.000513787 0 | ||||||||
\(156\) | −1.91997e9 | −0.259557 | ||||||||
\(157\) | −6.73348e9 | −0.884486 | −0.442243 | − | 0.896895i | \(-0.645817\pi\) | ||||
−0.442243 | + | 0.896895i | \(0.645817\pi\) | |||||||
\(158\) | 1.49238e8 | 0.0190512 | ||||||||
\(159\) | −2.23048e9 | −0.276766 | ||||||||
\(160\) | −3.28163e7 | −0.00395867 | ||||||||
\(161\) | 2.55886e9 | 0.300144 | ||||||||
\(162\) | 5.59623e8 | 0.0638378 | ||||||||
\(163\) | −9.26677e9 | −1.02822 | −0.514108 | − | 0.857726i | \(-0.671877\pi\) | ||||
−0.514108 | + | 0.857726i | \(0.671877\pi\) | |||||||
\(164\) | 6.87235e8 | 0.0741837 | ||||||||
\(165\) | −1.90186e7 | −0.00199757 | ||||||||
\(166\) | −6.41396e8 | −0.0655602 | ||||||||
\(167\) | 1.00723e10 | 1.00209 | 0.501043 | − | 0.865422i | \(-0.332950\pi\) | ||||
0.501043 | + | 0.865422i | \(0.332950\pi\) | |||||||
\(168\) | −5.63747e9 | −0.546000 | ||||||||
\(169\) | −5.82862e9 | −0.549637 | ||||||||
\(170\) | 2.27939e7 | 0.00209314 | ||||||||
\(171\) | −4.12073e9 | −0.368546 | ||||||||
\(172\) | −1.81773e9 | −0.158362 | ||||||||
\(173\) | 1.80552e9 | 0.153248 | 0.0766240 | − | 0.997060i | \(-0.475586\pi\) | ||||
0.0766240 | + | 0.997060i | \(0.475586\pi\) | |||||||
\(174\) | 7.78253e9 | 0.643649 | ||||||||
\(175\) | 1.22294e10 | 0.985677 | ||||||||
\(176\) | −1.35677e9 | −0.106586 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 1.15022e10 | 0.858797 | ||||||||
\(179\) | −2.22042e9 | −0.161658 | −0.0808289 | − | 0.996728i | \(-0.525757\pi\) | ||||
−0.0808289 | + | 0.996728i | \(0.525757\pi\) | |||||||
\(180\) | 1.21154e7 | 0.000860226 0 | ||||||||
\(181\) | −3.48123e8 | −0.0241090 | −0.0120545 | − | 0.999927i | \(-0.503837\pi\) | ||||
−0.0120545 | + | 0.999927i | \(0.503837\pi\) | |||||||
\(182\) | 5.62554e9 | 0.380052 | ||||||||
\(183\) | 1.07086e10 | 0.705835 | ||||||||
\(184\) | 4.54235e9 | 0.292146 | ||||||||
\(185\) | −2.19446e7 | −0.00137738 | ||||||||
\(186\) | −7.22155e8 | −0.0442407 | ||||||||
\(187\) | 1.42031e10 | 0.849370 | ||||||||
\(188\) | 1.64418e10 | 0.959927 | ||||||||
\(189\) | 3.32765e9 | 0.189697 | ||||||||
\(190\) | 4.39587e7 | 0.00244711 | ||||||||
\(191\) | −1.65843e10 | −0.901671 | −0.450835 | − | 0.892607i | \(-0.648874\pi\) | ||||
−0.450835 | + | 0.892607i | \(0.648874\pi\) | |||||||
\(192\) | −5.12846e9 | −0.272352 | ||||||||
\(193\) | 3.25642e9 | 0.168940 | 0.0844701 | − | 0.996426i | \(-0.473080\pi\) | ||||
0.0844701 | + | 0.996426i | \(0.473080\pi\) | |||||||
\(194\) | −9.89824e9 | −0.501707 | ||||||||
\(195\) | −3.01368e7 | −0.00149259 | ||||||||
\(196\) | 3.93237e8 | 0.0190328 | ||||||||
\(197\) | 9.55814e8 | 0.0452143 | 0.0226071 | − | 0.999744i | \(-0.492803\pi\) | ||||
0.0226071 | + | 0.999744i | \(0.492803\pi\) | |||||||
\(198\) | −3.71991e9 | −0.172004 | ||||||||
\(199\) | −2.28494e10 | −1.03285 | −0.516423 | − | 0.856333i | \(-0.672737\pi\) | ||||
−0.516423 | + | 0.856333i | \(0.672737\pi\) | |||||||
\(200\) | 2.17090e10 | 0.959412 | ||||||||
\(201\) | 6.93772e9 | 0.299802 | ||||||||
\(202\) | 1.28456e10 | 0.542842 | ||||||||
\(203\) | 4.62767e10 | 1.91263 | ||||||||
\(204\) | −9.04782e9 | −0.365770 | ||||||||
\(205\) | 1.07872e7 | 0.000426596 0 | ||||||||
\(206\) | −1.08073e10 | −0.418133 | ||||||||
\(207\) | −2.68123e9 | −0.101500 | ||||||||
\(208\) | −2.14993e9 | −0.0796417 | ||||||||
\(209\) | 2.73912e10 | 0.993009 | ||||||||
\(210\) | −3.54984e7 | −0.00125957 | ||||||||
\(211\) | 2.10406e10 | 0.730781 | 0.365390 | − | 0.930854i | \(-0.380936\pi\) | ||||
0.365390 | + | 0.930854i | \(0.380936\pi\) | |||||||
\(212\) | −9.44488e9 | −0.321133 | ||||||||
\(213\) | −1.27816e10 | −0.425478 | ||||||||
\(214\) | −1.21813e10 | −0.397038 | ||||||||
\(215\) | −2.85321e7 | −0.000910668 0 | ||||||||
\(216\) | 5.90706e9 | 0.184642 | ||||||||
\(217\) | −4.29410e9 | −0.131463 | ||||||||
\(218\) | −6.64161e9 | −0.199168 | ||||||||
\(219\) | −2.93424e10 | −0.861980 | ||||||||
\(220\) | −8.05334e7 | −0.00231779 | ||||||||
\(221\) | 2.25063e10 | 0.634655 | ||||||||
\(222\) | −4.29222e9 | −0.118602 | ||||||||
\(223\) | −2.84613e10 | −0.770696 | −0.385348 | − | 0.922771i | \(-0.625919\pi\) | ||||
−0.385348 | + | 0.922771i | \(0.625919\pi\) | |||||||
\(224\) | −3.81668e10 | −1.01291 | ||||||||
\(225\) | −1.28143e10 | −0.333328 | ||||||||
\(226\) | −5.56313e9 | −0.141851 | ||||||||
\(227\) | −2.93030e10 | −0.732479 | −0.366240 | − | 0.930521i | \(-0.619355\pi\) | ||||
−0.366240 | + | 0.930521i | \(0.619355\pi\) | |||||||
\(228\) | −1.74490e10 | −0.427626 | ||||||||
\(229\) | 2.53540e10 | 0.609238 | 0.304619 | − | 0.952474i | \(-0.401471\pi\) | ||||
0.304619 | + | 0.952474i | \(0.401471\pi\) | |||||||
\(230\) | 2.86026e7 | 0.000673954 0 | ||||||||
\(231\) | −2.21195e10 | −0.511118 | ||||||||
\(232\) | 8.21480e10 | 1.86166 | ||||||||
\(233\) | −5.06606e10 | −1.12608 | −0.563039 | − | 0.826430i | \(-0.690368\pi\) | ||||
−0.563039 | + | 0.826430i | \(0.690368\pi\) | |||||||
\(234\) | −5.89457e9 | −0.128523 | ||||||||
\(235\) | 2.58079e8 | 0.00552010 | ||||||||
\(236\) | −4.15614e9 | −0.0872140 | ||||||||
\(237\) | −9.29840e8 | −0.0191444 | ||||||||
\(238\) | 2.65103e10 | 0.535572 | ||||||||
\(239\) | 2.41312e10 | 0.478397 | 0.239198 | − | 0.970971i | \(-0.423115\pi\) | ||||
0.239198 | + | 0.970971i | \(0.423115\pi\) | |||||||
\(240\) | 1.35666e7 | 0.000263949 0 | ||||||||
\(241\) | −5.41759e10 | −1.03450 | −0.517249 | − | 0.855835i | \(-0.673044\pi\) | ||||
−0.517249 | + | 0.855835i | \(0.673044\pi\) | |||||||
\(242\) | −5.92721e9 | −0.111092 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 4.53451e10 | 0.818986 | ||||||||
\(245\) | 6.17246e6 | 0.000109449 0 | ||||||||
\(246\) | 2.10991e9 | 0.0367329 | ||||||||
\(247\) | 4.34041e10 | 0.741983 | ||||||||
\(248\) | −7.62266e9 | −0.127960 | ||||||||
\(249\) | 3.99628e9 | 0.0658808 | ||||||||
\(250\) | 2.73400e8 | 0.00442658 | ||||||||
\(251\) | −2.51631e10 | −0.400158 | −0.200079 | − | 0.979780i | \(-0.564120\pi\) | ||||
−0.200079 | + | 0.979780i | \(0.564120\pi\) | |||||||
\(252\) | 1.40908e10 | 0.220106 | ||||||||
\(253\) | 1.78226e10 | 0.273482 | ||||||||
\(254\) | 3.69417e10 | 0.556884 | ||||||||
\(255\) | −1.42019e8 | −0.00210338 | ||||||||
\(256\) | −6.22884e10 | −0.906415 | ||||||||
\(257\) | −9.81242e10 | −1.40306 | −0.701531 | − | 0.712639i | \(-0.747500\pi\) | ||||
−0.701531 | + | 0.712639i | \(0.747500\pi\) | |||||||
\(258\) | −5.58068e9 | −0.0784149 | ||||||||
\(259\) | −2.55225e10 | −0.352432 | ||||||||
\(260\) | −1.27613e8 | −0.00173187 | ||||||||
\(261\) | −4.84898e10 | −0.646797 | ||||||||
\(262\) | 3.73220e10 | 0.489338 | ||||||||
\(263\) | 6.22591e10 | 0.802420 | 0.401210 | − | 0.915986i | \(-0.368590\pi\) | ||||
0.401210 | + | 0.915986i | \(0.368590\pi\) | |||||||
\(264\) | −3.92653e10 | −0.497498 | ||||||||
\(265\) | −1.48252e8 | −0.00184669 | ||||||||
\(266\) | 5.11260e10 | 0.626144 | ||||||||
\(267\) | −7.16655e10 | −0.862998 | ||||||||
\(268\) | 2.93775e10 | 0.347863 | ||||||||
\(269\) | −8.07261e10 | −0.940002 | −0.470001 | − | 0.882666i | \(-0.655746\pi\) | ||||
−0.470001 | + | 0.882666i | \(0.655746\pi\) | |||||||
\(270\) | 3.71960e7 | 0.000425951 0 | ||||||||
\(271\) | −1.34610e11 | −1.51605 | −0.758026 | − | 0.652224i | \(-0.773836\pi\) | ||||
−0.758026 | + | 0.652224i | \(0.773836\pi\) | |||||||
\(272\) | −1.01315e10 | −0.112232 | ||||||||
\(273\) | −3.50505e10 | −0.381911 | ||||||||
\(274\) | −3.77072e10 | −0.404153 | ||||||||
\(275\) | 8.51787e10 | 0.898119 | ||||||||
\(276\) | −1.13535e10 | −0.117772 | ||||||||
\(277\) | −1.24234e11 | −1.26789 | −0.633944 | − | 0.773379i | \(-0.718565\pi\) | ||||
−0.633944 | + | 0.773379i | \(0.718565\pi\) | |||||||
\(278\) | −2.29962e10 | −0.230917 | ||||||||
\(279\) | 4.49946e9 | 0.0444571 | ||||||||
\(280\) | −3.74701e8 | −0.00364313 | ||||||||
\(281\) | −9.46201e10 | −0.905326 | −0.452663 | − | 0.891682i | \(-0.649526\pi\) | ||||
−0.452663 | + | 0.891682i | \(0.649526\pi\) | |||||||
\(282\) | 5.04785e10 | 0.475319 | ||||||||
\(283\) | −5.75537e10 | −0.533377 | −0.266689 | − | 0.963783i | \(-0.585930\pi\) | ||||
−0.266689 | + | 0.963783i | \(0.585930\pi\) | |||||||
\(284\) | −5.41231e10 | −0.493685 | ||||||||
\(285\) | −2.73889e8 | −0.00245908 | ||||||||
\(286\) | 3.91823e10 | 0.346292 | ||||||||
\(287\) | 1.25460e10 | 0.109153 | ||||||||
\(288\) | 3.99920e10 | 0.342537 | ||||||||
\(289\) | −1.25275e10 | −0.105639 | ||||||||
\(290\) | 5.17275e8 | 0.00429468 | ||||||||
\(291\) | 6.16719e10 | 0.504161 | ||||||||
\(292\) | −1.24249e11 | −1.00016 | ||||||||
\(293\) | −2.37210e11 | −1.88030 | −0.940152 | − | 0.340754i | \(-0.889318\pi\) | ||||
−0.940152 | + | 0.340754i | \(0.889318\pi\) | |||||||
\(294\) | 1.20729e9 | 0.00942430 | ||||||||
\(295\) | −6.52370e7 | −0.000501528 0 | ||||||||
\(296\) | −4.53062e10 | −0.343040 | ||||||||
\(297\) | 2.31773e10 | 0.172846 | ||||||||
\(298\) | −4.35450e10 | −0.319864 | ||||||||
\(299\) | 2.82417e10 | 0.204348 | ||||||||
\(300\) | −5.42614e10 | −0.386763 | ||||||||
\(301\) | −3.31840e10 | −0.233013 | ||||||||
\(302\) | 5.67680e10 | 0.392710 | ||||||||
\(303\) | −8.00359e10 | −0.545498 | ||||||||
\(304\) | −1.95390e10 | −0.131211 | ||||||||
\(305\) | 7.11762e8 | 0.00470961 | ||||||||
\(306\) | −2.77781e10 | −0.181115 | ||||||||
\(307\) | −8.86156e10 | −0.569360 | −0.284680 | − | 0.958623i | \(-0.591887\pi\) | ||||
−0.284680 | + | 0.958623i | \(0.591887\pi\) | |||||||
\(308\) | −9.36640e10 | −0.593054 | ||||||||
\(309\) | 6.73359e10 | 0.420178 | ||||||||
\(310\) | −4.79989e7 | −0.000295191 0 | ||||||||
\(311\) | −1.52131e11 | −0.922137 | −0.461068 | − | 0.887365i | \(-0.652534\pi\) | ||||
−0.461068 | + | 0.887365i | \(0.652534\pi\) | |||||||
\(312\) | −6.22197e10 | −0.371734 | ||||||||
\(313\) | 2.58244e11 | 1.52083 | 0.760415 | − | 0.649438i | \(-0.224996\pi\) | ||||
0.760415 | + | 0.649438i | \(0.224996\pi\) | |||||||
\(314\) | −8.75376e10 | −0.508172 | ||||||||
\(315\) | 2.21176e8 | 0.00126573 | ||||||||
\(316\) | −3.93736e9 | −0.0222133 | ||||||||
\(317\) | −3.16618e11 | −1.76104 | −0.880521 | − | 0.474008i | \(-0.842807\pi\) | ||||
−0.880521 | + | 0.474008i | \(0.842807\pi\) | |||||||
\(318\) | −2.89971e10 | −0.159013 | ||||||||
\(319\) | 3.22321e11 | 1.74273 | ||||||||
\(320\) | −3.40869e8 | −0.00181724 | ||||||||
\(321\) | 7.58969e10 | 0.398980 | ||||||||
\(322\) | 3.32661e10 | 0.172445 | ||||||||
\(323\) | 2.04541e11 | 1.04561 | ||||||||
\(324\) | −1.47646e10 | −0.0744338 | ||||||||
\(325\) | 1.34974e11 | 0.671081 | ||||||||
\(326\) | −1.20471e11 | −0.590751 | ||||||||
\(327\) | 4.13812e10 | 0.200142 | ||||||||
\(328\) | 2.22710e10 | 0.106245 | ||||||||
\(329\) | 3.00157e11 | 1.41243 | ||||||||
\(330\) | −2.47249e8 | −0.00114768 | ||||||||
\(331\) | 1.66007e11 | 0.760153 | 0.380077 | − | 0.924955i | \(-0.375898\pi\) | ||||
0.380077 | + | 0.924955i | \(0.375898\pi\) | |||||||
\(332\) | 1.69221e10 | 0.0764420 | ||||||||
\(333\) | 2.67431e10 | 0.119182 | ||||||||
\(334\) | 1.30944e11 | 0.575739 | ||||||||
\(335\) | 4.61124e8 | 0.00200040 | ||||||||
\(336\) | 1.57785e10 | 0.0675367 | ||||||||
\(337\) | −3.96343e11 | −1.67393 | −0.836963 | − | 0.547259i | \(-0.815671\pi\) | ||||
−0.836963 | + | 0.547259i | \(0.815671\pi\) | |||||||
\(338\) | −7.57742e10 | −0.315788 | ||||||||
\(339\) | 3.46616e10 | 0.142544 | ||||||||
\(340\) | −6.01375e8 | −0.00244056 | ||||||||
\(341\) | −2.99087e10 | −0.119785 | ||||||||
\(342\) | −5.35709e10 | −0.211744 | ||||||||
\(343\) | 2.59855e11 | 1.01370 | ||||||||
\(344\) | −5.89066e10 | −0.226804 | ||||||||
\(345\) | −1.78211e8 | −0.000677250 0 | ||||||||
\(346\) | 2.34724e10 | 0.0880472 | ||||||||
\(347\) | 2.17182e11 | 0.804158 | 0.402079 | − | 0.915605i | \(-0.368288\pi\) | ||||
0.402079 | + | 0.915605i | \(0.368288\pi\) | |||||||
\(348\) | −2.05328e11 | −0.750484 | ||||||||
\(349\) | −2.10061e11 | −0.757933 | −0.378966 | − | 0.925410i | \(-0.623720\pi\) | ||||
−0.378966 | + | 0.925410i | \(0.623720\pi\) | |||||||
\(350\) | 1.58987e11 | 0.566311 | ||||||||
\(351\) | 3.67267e10 | 0.129152 | ||||||||
\(352\) | −2.65834e11 | −0.922930 | ||||||||
\(353\) | 6.15837e10 | 0.211096 | 0.105548 | − | 0.994414i | \(-0.466340\pi\) | ||||
0.105548 | + | 0.994414i | \(0.466340\pi\) | |||||||
\(354\) | −1.27599e10 | −0.0431851 | ||||||||
\(355\) | −8.49545e8 | −0.00283896 | ||||||||
\(356\) | −3.03464e11 | −1.00134 | ||||||||
\(357\) | −1.65175e11 | −0.538192 | ||||||||
\(358\) | −2.88663e10 | −0.0928789 | ||||||||
\(359\) | 2.41244e11 | 0.766535 | 0.383268 | − | 0.923637i | \(-0.374799\pi\) | ||||
0.383268 | + | 0.923637i | \(0.374799\pi\) | |||||||
\(360\) | 3.92620e8 | 0.00123200 | ||||||||
\(361\) | 7.17766e10 | 0.222434 | ||||||||
\(362\) | −4.52572e9 | −0.0138516 | ||||||||
\(363\) | 3.69301e10 | 0.111635 | ||||||||
\(364\) | −1.48420e11 | −0.443134 | ||||||||
\(365\) | −1.95028e9 | −0.00575147 | ||||||||
\(366\) | 1.39216e11 | 0.405531 | ||||||||
\(367\) | 4.54037e11 | 1.30645 | 0.653227 | − | 0.757162i | \(-0.273415\pi\) | ||||
0.653227 | + | 0.757162i | \(0.273415\pi\) | |||||||
\(368\) | −1.27134e10 | −0.0361366 | ||||||||
\(369\) | −1.31460e10 | −0.0369126 | ||||||||
\(370\) | −2.85288e8 | −0.000791362 0 | ||||||||
\(371\) | −1.72424e11 | −0.472513 | ||||||||
\(372\) | 1.90527e10 | 0.0515839 | ||||||||
\(373\) | 3.76935e11 | 1.00827 | 0.504134 | − | 0.863625i | \(-0.331812\pi\) | ||||
0.504134 | + | 0.863625i | \(0.331812\pi\) | |||||||
\(374\) | 1.84646e11 | 0.487997 | ||||||||
\(375\) | −1.70344e9 | −0.00444823 | ||||||||
\(376\) | 5.32823e11 | 1.37479 | ||||||||
\(377\) | 5.10748e11 | 1.30218 | ||||||||
\(378\) | 4.32606e10 | 0.108988 | ||||||||
\(379\) | 5.70349e11 | 1.41992 | 0.709961 | − | 0.704241i | \(-0.248712\pi\) | ||||
0.709961 | + | 0.704241i | \(0.248712\pi\) | |||||||
\(380\) | −1.15977e9 | −0.00285329 | ||||||||
\(381\) | −2.30169e11 | −0.559608 | ||||||||
\(382\) | −2.15602e11 | −0.518046 | ||||||||
\(383\) | 1.35501e11 | 0.321772 | 0.160886 | − | 0.986973i | \(-0.448565\pi\) | ||||
0.160886 | + | 0.986973i | \(0.448565\pi\) | |||||||
\(384\) | 1.86117e11 | 0.436814 | ||||||||
\(385\) | −1.47020e9 | −0.00341038 | ||||||||
\(386\) | 4.23347e10 | 0.0970629 | ||||||||
\(387\) | 3.47710e10 | 0.0787984 | ||||||||
\(388\) | 2.61147e11 | 0.584982 | ||||||||
\(389\) | 2.72102e11 | 0.602503 | 0.301251 | − | 0.953545i | \(-0.402596\pi\) | ||||
0.301251 | + | 0.953545i | \(0.402596\pi\) | |||||||
\(390\) | −3.91790e8 | −0.000857555 0 | ||||||||
\(391\) | 1.33088e11 | 0.287969 | ||||||||
\(392\) | 1.27435e10 | 0.0272584 | ||||||||
\(393\) | −2.32538e11 | −0.491731 | ||||||||
\(394\) | 1.24259e10 | 0.0259774 | ||||||||
\(395\) | −6.18030e7 | −0.000127739 0 | ||||||||
\(396\) | 9.81432e10 | 0.200554 | ||||||||
\(397\) | 3.58106e11 | 0.723526 | 0.361763 | − | 0.932270i | \(-0.382175\pi\) | ||||
0.361763 | + | 0.932270i | \(0.382175\pi\) | |||||||
\(398\) | −2.97050e11 | −0.593412 | ||||||||
\(399\) | −3.18545e11 | −0.629207 | ||||||||
\(400\) | −6.07607e10 | −0.118673 | ||||||||
\(401\) | −6.62237e11 | −1.27898 | −0.639490 | − | 0.768799i | \(-0.720854\pi\) | ||||
−0.639490 | + | 0.768799i | \(0.720854\pi\) | |||||||
\(402\) | 9.01929e10 | 0.172248 | ||||||||
\(403\) | −4.73932e10 | −0.0895043 | ||||||||
\(404\) | −3.38908e11 | −0.632945 | ||||||||
\(405\) | −2.31753e8 | −0.000428034 0 | ||||||||
\(406\) | 6.01614e11 | 1.09888 | ||||||||
\(407\) | −1.77766e11 | −0.321125 | ||||||||
\(408\) | −2.93210e11 | −0.523851 | ||||||||
\(409\) | 3.42205e11 | 0.604688 | 0.302344 | − | 0.953199i | \(-0.402231\pi\) | ||||
0.302344 | + | 0.953199i | \(0.402231\pi\) | |||||||
\(410\) | 1.40238e8 | 0.000245097 0 | ||||||||
\(411\) | 2.34938e11 | 0.406130 | ||||||||
\(412\) | 2.85131e11 | 0.487536 | ||||||||
\(413\) | −7.58736e10 | −0.128326 | ||||||||
\(414\) | −3.48569e10 | −0.0583160 | ||||||||
\(415\) | 2.65618e8 | 0.000439583 0 | ||||||||
\(416\) | −4.21240e11 | −0.689620 | ||||||||
\(417\) | 1.43280e11 | 0.232046 | ||||||||
\(418\) | 3.56096e11 | 0.570523 | ||||||||
\(419\) | −9.70797e11 | −1.53874 | −0.769370 | − | 0.638803i | \(-0.779430\pi\) | ||||
−0.769370 | + | 0.638803i | \(0.779430\pi\) | |||||||
\(420\) | 9.36561e8 | 0.00146864 | ||||||||
\(421\) | 2.64923e11 | 0.411008 | 0.205504 | − | 0.978656i | \(-0.434117\pi\) | ||||
0.205504 | + | 0.978656i | \(0.434117\pi\) | |||||||
\(422\) | 2.73535e11 | 0.419863 | ||||||||
\(423\) | −3.14511e11 | −0.477644 | ||||||||
\(424\) | −3.06077e11 | −0.459922 | ||||||||
\(425\) | 6.36063e11 | 0.945693 | ||||||||
\(426\) | −1.66165e11 | −0.244454 | ||||||||
\(427\) | 8.27810e11 | 1.20505 | ||||||||
\(428\) | 3.21382e11 | 0.462940 | ||||||||
\(429\) | −2.44129e11 | −0.347986 | ||||||||
\(430\) | −3.70927e8 | −0.000523215 0 | ||||||||
\(431\) | −5.88050e11 | −0.820855 | −0.410427 | − | 0.911893i | \(-0.634620\pi\) | ||||
−0.410427 | + | 0.911893i | \(0.634620\pi\) | |||||||
\(432\) | −1.65331e10 | −0.0228390 | ||||||||
\(433\) | 1.45666e12 | 1.99142 | 0.995711 | − | 0.0925180i | \(-0.0294916\pi\) | ||||
0.995711 | + | 0.0925180i | \(0.0294916\pi\) | |||||||
\(434\) | −5.58249e10 | −0.0755308 | ||||||||
\(435\) | −3.22294e9 | −0.00431569 | ||||||||
\(436\) | 1.75227e11 | 0.232226 | ||||||||
\(437\) | 2.56666e11 | 0.336668 | ||||||||
\(438\) | −3.81462e11 | −0.495242 | ||||||||
\(439\) | 6.78683e11 | 0.872121 | 0.436060 | − | 0.899917i | \(-0.356373\pi\) | ||||
0.436060 | + | 0.899917i | \(0.356373\pi\) | |||||||
\(440\) | −2.60982e9 | −0.00331951 | ||||||||
\(441\) | −7.52215e9 | −0.00947040 | ||||||||
\(442\) | 2.92589e11 | 0.364635 | ||||||||
\(443\) | −9.72292e11 | −1.19944 | −0.599722 | − | 0.800208i | \(-0.704722\pi\) | ||||
−0.599722 | + | 0.800208i | \(0.704722\pi\) | |||||||
\(444\) | 1.13242e11 | 0.138288 | ||||||||
\(445\) | −4.76334e9 | −0.00575826 | ||||||||
\(446\) | −3.70007e11 | −0.442795 | ||||||||
\(447\) | 2.71311e11 | 0.321428 | ||||||||
\(448\) | −3.96446e11 | −0.464979 | ||||||||
\(449\) | 5.40504e11 | 0.627611 | 0.313806 | − | 0.949487i | \(-0.398396\pi\) | ||||
0.313806 | + | 0.949487i | \(0.398396\pi\) | |||||||
\(450\) | −1.66590e11 | −0.191510 | ||||||||
\(451\) | 8.73838e10 | 0.0994572 | ||||||||
\(452\) | 1.46773e11 | 0.165395 | ||||||||
\(453\) | −3.53698e11 | −0.394631 | ||||||||
\(454\) | −3.80949e11 | −0.420839 | ||||||||
\(455\) | −2.32967e9 | −0.00254826 | ||||||||
\(456\) | −5.65465e11 | −0.612440 | ||||||||
\(457\) | 1.70451e12 | 1.82801 | 0.914003 | − | 0.405708i | \(-0.132975\pi\) | ||||
0.914003 | + | 0.405708i | \(0.132975\pi\) | |||||||
\(458\) | 3.29611e11 | 0.350032 | ||||||||
\(459\) | 1.73074e11 | 0.182001 | ||||||||
\(460\) | −7.54627e8 | −0.000785818 0 | ||||||||
\(461\) | −9.89439e11 | −1.02032 | −0.510158 | − | 0.860081i | \(-0.670413\pi\) | ||||
−0.510158 | + | 0.860081i | \(0.670413\pi\) | |||||||
\(462\) | −2.87561e11 | −0.293658 | ||||||||
\(463\) | −4.94694e11 | −0.500290 | −0.250145 | − | 0.968208i | \(-0.580478\pi\) | ||||
−0.250145 | + | 0.968208i | \(0.580478\pi\) | |||||||
\(464\) | −2.29921e11 | −0.230276 | ||||||||
\(465\) | 2.99062e8 | 0.000296635 0 | ||||||||
\(466\) | −6.58606e11 | −0.646977 | ||||||||
\(467\) | 8.03745e11 | 0.781974 | 0.390987 | − | 0.920396i | \(-0.372134\pi\) | ||||
0.390987 | + | 0.920396i | \(0.372134\pi\) | |||||||
\(468\) | 1.55517e11 | 0.149855 | ||||||||
\(469\) | 5.36308e11 | 0.511843 | ||||||||
\(470\) | 3.35512e9 | 0.00317152 | ||||||||
\(471\) | 5.45412e11 | 0.510658 | ||||||||
\(472\) | −1.34687e11 | −0.124907 | ||||||||
\(473\) | −2.31129e11 | −0.212314 | ||||||||
\(474\) | −1.20883e10 | −0.0109992 | ||||||||
\(475\) | 1.22667e12 | 1.10562 | ||||||||
\(476\) | −6.99426e11 | −0.624468 | ||||||||
\(477\) | 1.80669e11 | 0.159791 | ||||||||
\(478\) | 3.13714e11 | 0.274858 | ||||||||
\(479\) | −1.44136e12 | −1.25101 | −0.625507 | − | 0.780219i | \(-0.715108\pi\) | ||||
−0.625507 | + | 0.780219i | \(0.715108\pi\) | |||||||
\(480\) | 2.65812e9 | 0.00228554 | ||||||||
\(481\) | −2.81688e11 | −0.239947 | ||||||||
\(482\) | −7.04306e11 | −0.594360 | ||||||||
\(483\) | −2.07268e11 | −0.173288 | ||||||||
\(484\) | 1.56379e11 | 0.129531 | ||||||||
\(485\) | 4.09910e9 | 0.00336396 | ||||||||
\(486\) | −4.53294e10 | −0.0368568 | ||||||||
\(487\) | 3.24854e10 | 0.0261703 | 0.0130851 | − | 0.999914i | \(-0.495835\pi\) | ||||
0.0130851 | + | 0.999914i | \(0.495835\pi\) | |||||||
\(488\) | 1.46948e12 | 1.17294 | ||||||||
\(489\) | 7.50608e11 | 0.593640 | ||||||||
\(490\) | 8.02441e7 | 6.28827e−5 0 | ||||||||
\(491\) | −1.66719e12 | −1.29455 | −0.647276 | − | 0.762256i | \(-0.724092\pi\) | ||||
−0.647276 | + | 0.762256i | \(0.724092\pi\) | |||||||
\(492\) | −5.56661e10 | −0.0428300 | ||||||||
\(493\) | 2.40689e12 | 1.83504 | ||||||||
\(494\) | 5.64268e11 | 0.426299 | ||||||||
\(495\) | 1.54051e9 | 0.00115330 | ||||||||
\(496\) | 2.13348e10 | 0.0158278 | ||||||||
\(497\) | −9.88058e11 | −0.726405 | ||||||||
\(498\) | 5.19531e10 | 0.0378512 | ||||||||
\(499\) | 2.24713e12 | 1.62247 | 0.811235 | − | 0.584720i | \(-0.198796\pi\) | ||||
0.811235 | + | 0.584720i | \(0.198796\pi\) | |||||||
\(500\) | −7.21316e9 | −0.00516132 | ||||||||
\(501\) | −8.15858e11 | −0.578555 | ||||||||
\(502\) | −3.27129e11 | −0.229907 | ||||||||
\(503\) | 7.88688e11 | 0.549350 | 0.274675 | − | 0.961537i | \(-0.411430\pi\) | ||||
0.274675 | + | 0.961537i | \(0.411430\pi\) | |||||||
\(504\) | 4.56635e11 | 0.315233 | ||||||||
\(505\) | −5.31969e9 | −0.00363978 | ||||||||
\(506\) | 2.31700e11 | 0.157126 | ||||||||
\(507\) | 4.72119e11 | 0.317333 | ||||||||
\(508\) | −9.74639e11 | −0.649318 | ||||||||
\(509\) | 8.56844e11 | 0.565811 | 0.282906 | − | 0.959148i | \(-0.408702\pi\) | ||||
0.282906 | + | 0.959148i | \(0.408702\pi\) | |||||||
\(510\) | −1.84630e9 | −0.00120847 | ||||||||
\(511\) | −2.26826e12 | −1.47163 | ||||||||
\(512\) | 3.66674e11 | 0.235811 | ||||||||
\(513\) | 3.33779e11 | 0.212780 | ||||||||
\(514\) | −1.27565e12 | −0.806115 | ||||||||
\(515\) | 4.47557e9 | 0.00280360 | ||||||||
\(516\) | 1.47236e11 | 0.0914304 | ||||||||
\(517\) | 2.09061e12 | 1.28696 | ||||||||
\(518\) | −3.31802e11 | −0.202486 | ||||||||
\(519\) | −1.46247e11 | −0.0884778 | ||||||||
\(520\) | −4.13551e9 | −0.00248036 | ||||||||
\(521\) | 5.21995e10 | 0.0310382 | 0.0155191 | − | 0.999880i | \(-0.495060\pi\) | ||||
0.0155191 | + | 0.999880i | \(0.495060\pi\) | |||||||
\(522\) | −6.30385e11 | −0.371611 | ||||||||
\(523\) | −1.08408e12 | −0.633585 | −0.316793 | − | 0.948495i | \(-0.602606\pi\) | ||||
−0.316793 | + | 0.948495i | \(0.602606\pi\) | |||||||
\(524\) | −9.84673e11 | −0.570560 | ||||||||
\(525\) | −9.90583e11 | −0.569081 | ||||||||
\(526\) | 8.09390e11 | 0.461022 | ||||||||
\(527\) | −2.23340e11 | −0.126130 | ||||||||
\(528\) | 1.09898e11 | 0.0615374 | ||||||||
\(529\) | −1.63415e12 | −0.907279 | ||||||||
\(530\) | −1.92733e9 | −0.00106100 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −1.34887e12 | −0.730073 | ||||||||
\(533\) | 1.38468e11 | 0.0743151 | ||||||||
\(534\) | −9.31677e11 | −0.495827 | ||||||||
\(535\) | 5.04458e9 | 0.00266216 | ||||||||
\(536\) | 9.52025e11 | 0.498204 | ||||||||
\(537\) | 1.79854e11 | 0.0933332 | ||||||||
\(538\) | −1.04947e12 | −0.540069 | ||||||||
\(539\) | 5.00011e10 | 0.0255170 | ||||||||
\(540\) | −9.81349e8 | −0.000496651 0 | ||||||||
\(541\) | −1.26617e12 | −0.635482 | −0.317741 | − | 0.948178i | \(-0.602924\pi\) | ||||
−0.317741 | + | 0.948178i | \(0.602924\pi\) | |||||||
\(542\) | −1.74997e12 | −0.871033 | ||||||||
\(543\) | 2.81979e10 | 0.0139193 | ||||||||
\(544\) | −1.98509e12 | −0.971818 | ||||||||
\(545\) | 2.75045e9 | 0.00133543 | ||||||||
\(546\) | −4.55669e11 | −0.219423 | ||||||||
\(547\) | 1.17605e12 | 0.561673 | 0.280836 | − | 0.959756i | \(-0.409388\pi\) | ||||
0.280836 | + | 0.959756i | \(0.409388\pi\) | |||||||
\(548\) | 9.94835e11 | 0.471236 | ||||||||
\(549\) | −8.67398e11 | −0.407514 | ||||||||
\(550\) | 1.10735e12 | 0.516006 | ||||||||
\(551\) | 4.64178e12 | 2.14537 | ||||||||
\(552\) | −3.67930e11 | −0.168671 | ||||||||
\(553\) | −7.18796e10 | −0.0326846 | ||||||||
\(554\) | −1.61508e12 | −0.728452 | ||||||||
\(555\) | 1.77751e9 | 0.000795233 0 | ||||||||
\(556\) | 6.06714e11 | 0.269245 | ||||||||
\(557\) | −1.12035e12 | −0.493178 | −0.246589 | − | 0.969120i | \(-0.579310\pi\) | ||||
−0.246589 | + | 0.969120i | \(0.579310\pi\) | |||||||
\(558\) | 5.84945e10 | 0.0255424 | ||||||||
\(559\) | −3.66246e11 | −0.158643 | ||||||||
\(560\) | 1.04874e9 | 0.000450631 0 | ||||||||
\(561\) | −1.15045e12 | −0.490384 | ||||||||
\(562\) | −1.23010e12 | −0.520146 | ||||||||
\(563\) | 1.73855e12 | 0.729290 | 0.364645 | − | 0.931147i | \(-0.381190\pi\) | ||||
0.364645 | + | 0.931147i | \(0.381190\pi\) | |||||||
\(564\) | −1.33178e12 | −0.554214 | ||||||||
\(565\) | 2.30383e9 | 0.000951113 0 | ||||||||
\(566\) | −7.48219e11 | −0.306447 | ||||||||
\(567\) | −2.69540e11 | −0.109521 | ||||||||
\(568\) | −1.75395e12 | −0.707048 | ||||||||
\(569\) | −1.86209e11 | −0.0744723 | −0.0372361 | − | 0.999306i | \(-0.511855\pi\) | ||||
−0.0372361 | + | 0.999306i | \(0.511855\pi\) | |||||||
\(570\) | −3.56066e9 | −0.00141284 | ||||||||
\(571\) | 1.86548e12 | 0.734391 | 0.367195 | − | 0.930144i | \(-0.380318\pi\) | ||||
0.367195 | + | 0.930144i | \(0.380318\pi\) | |||||||
\(572\) | −1.03375e12 | −0.403770 | ||||||||
\(573\) | 1.34333e12 | 0.520580 | ||||||||
\(574\) | 1.63103e11 | 0.0627130 | ||||||||
\(575\) | 7.98155e11 | 0.304496 | ||||||||
\(576\) | 4.15405e11 | 0.157243 | ||||||||
\(577\) | −4.30621e12 | −1.61735 | −0.808675 | − | 0.588256i | \(-0.799815\pi\) | ||||
−0.808675 | + | 0.588256i | \(0.799815\pi\) | |||||||
\(578\) | −1.62861e11 | −0.0606936 | ||||||||
\(579\) | −2.63770e11 | −0.0975376 | ||||||||
\(580\) | −1.36474e10 | −0.00500752 | ||||||||
\(581\) | 3.08925e11 | 0.112476 | ||||||||
\(582\) | 8.01757e11 | 0.289661 | ||||||||
\(583\) | −1.20094e12 | −0.430540 | ||||||||
\(584\) | −4.02650e12 | −1.43242 | ||||||||
\(585\) | 2.44108e9 | 0.000861750 0 | ||||||||
\(586\) | −3.08381e12 | −1.08031 | ||||||||
\(587\) | 2.77522e12 | 0.964775 | 0.482387 | − | 0.875958i | \(-0.339770\pi\) | ||||
0.482387 | + | 0.875958i | \(0.339770\pi\) | |||||||
\(588\) | −3.18522e10 | −0.0109886 | ||||||||
\(589\) | −4.30719e11 | −0.147460 | ||||||||
\(590\) | −8.48105e8 | −0.000288148 0 | ||||||||
\(591\) | −7.74209e10 | −0.0261045 | ||||||||
\(592\) | 1.26806e11 | 0.0424319 | ||||||||
\(593\) | −2.32710e11 | −0.0772802 | −0.0386401 | − | 0.999253i | \(-0.512303\pi\) | ||||
−0.0386401 | + | 0.999253i | \(0.512303\pi\) | |||||||
\(594\) | 3.01313e11 | 0.0993068 | ||||||||
\(595\) | −1.09786e10 | −0.00359103 | ||||||||
\(596\) | 1.14886e12 | 0.372956 | ||||||||
\(597\) | 1.85080e12 | 0.596314 | ||||||||
\(598\) | 3.67152e11 | 0.117406 | ||||||||
\(599\) | −3.06957e12 | −0.974220 | −0.487110 | − | 0.873341i | \(-0.661949\pi\) | ||||
−0.487110 | + | 0.873341i | \(0.661949\pi\) | |||||||
\(600\) | −1.75843e12 | −0.553917 | ||||||||
\(601\) | 4.30421e12 | 1.34573 | 0.672866 | − | 0.739764i | \(-0.265063\pi\) | ||||
0.672866 | + | 0.739764i | \(0.265063\pi\) | |||||||
\(602\) | −4.31404e11 | −0.133875 | ||||||||
\(603\) | −5.61956e11 | −0.173091 | ||||||||
\(604\) | −1.49772e12 | −0.457893 | ||||||||
\(605\) | 2.45460e9 | 0.000744873 0 | ||||||||
\(606\) | −1.04049e12 | −0.313410 | ||||||||
\(607\) | −1.31155e12 | −0.392134 | −0.196067 | − | 0.980590i | \(-0.562817\pi\) | ||||
−0.196067 | + | 0.980590i | \(0.562817\pi\) | |||||||
\(608\) | −3.82831e12 | −1.13616 | ||||||||
\(609\) | −3.74842e12 | −1.10426 | ||||||||
\(610\) | 9.25315e9 | 0.00270586 | ||||||||
\(611\) | 3.31278e12 | 0.961628 | ||||||||
\(612\) | 7.32874e11 | 0.211178 | ||||||||
\(613\) | −5.03412e12 | −1.43996 | −0.719982 | − | 0.693993i | \(-0.755850\pi\) | ||||
−0.719982 | + | 0.693993i | \(0.755850\pi\) | |||||||
\(614\) | −1.15203e12 | −0.327120 | ||||||||
\(615\) | −8.73765e8 | −0.000246295 0 | ||||||||
\(616\) | −3.03534e12 | −0.849363 | ||||||||
\(617\) | −1.09480e11 | −0.0304125 | −0.0152062 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152062 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(618\) | 8.75391e11 | 0.241409 | ||||||||
\(619\) | 4.84630e12 | 1.32679 | 0.663395 | − | 0.748270i | \(-0.269115\pi\) | ||||
0.663395 | + | 0.748270i | \(0.269115\pi\) | |||||||
\(620\) | 1.26636e9 | 0.000344188 0 | ||||||||
\(621\) | 2.17180e11 | 0.0586012 | ||||||||
\(622\) | −1.97775e12 | −0.529805 | ||||||||
\(623\) | −5.53997e12 | −1.47337 | ||||||||
\(624\) | 1.74145e11 | 0.0459811 | ||||||||
\(625\) | 3.81453e12 | 0.999955 | ||||||||
\(626\) | 3.35726e12 | 0.873777 | ||||||||
\(627\) | −2.21869e12 | −0.573314 | ||||||||
\(628\) | 2.30952e12 | 0.592520 | ||||||||
\(629\) | −1.32745e12 | −0.338135 | ||||||||
\(630\) | 2.87537e9 | 0.000727213 0 | ||||||||
\(631\) | 4.13465e12 | 1.03826 | 0.519130 | − | 0.854695i | \(-0.326256\pi\) | ||||
0.519130 | + | 0.854695i | \(0.326256\pi\) | |||||||
\(632\) | −1.27597e11 | −0.0318136 | ||||||||
\(633\) | −1.70429e12 | −0.421916 | ||||||||
\(634\) | −4.11615e12 | −1.01179 | ||||||||
\(635\) | −1.52985e10 | −0.00373393 | ||||||||
\(636\) | 7.65035e11 | 0.185406 | ||||||||
\(637\) | 7.92316e10 | 0.0190665 | ||||||||
\(638\) | 4.19028e12 | 1.00127 | ||||||||
\(639\) | 1.03531e12 | 0.245650 | ||||||||
\(640\) | 1.23705e10 | 0.00291459 | ||||||||
\(641\) | 4.53660e12 | 1.06138 | 0.530688 | − | 0.847567i | \(-0.321934\pi\) | ||||
0.530688 | + | 0.847567i | \(0.321934\pi\) | |||||||
\(642\) | 9.86687e11 | 0.229230 | ||||||||
\(643\) | 6.06625e11 | 0.139949 | 0.0699747 | − | 0.997549i | \(-0.477708\pi\) | ||||
0.0699747 | + | 0.997549i | \(0.477708\pi\) | |||||||
\(644\) | −8.77665e11 | −0.201068 | ||||||||
\(645\) | 2.31110e9 | 0.000525774 0 | ||||||||
\(646\) | 2.65911e12 | 0.600744 | ||||||||
\(647\) | 1.16298e12 | 0.260917 | 0.130459 | − | 0.991454i | \(-0.458355\pi\) | ||||
0.130459 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(648\) | −4.78472e11 | −0.106603 | ||||||||
\(649\) | −5.28464e11 | −0.116927 | ||||||||
\(650\) | 1.75471e12 | 0.385563 | ||||||||
\(651\) | 3.47822e11 | 0.0759002 | ||||||||
\(652\) | 3.17842e12 | 0.688805 | ||||||||
\(653\) | −2.30996e12 | −0.497159 | −0.248579 | − | 0.968612i | \(-0.579964\pi\) | ||||
−0.248579 | + | 0.968612i | \(0.579964\pi\) | |||||||
\(654\) | 5.37971e11 | 0.114990 | ||||||||
\(655\) | −1.54559e10 | −0.00328103 | ||||||||
\(656\) | −6.23336e10 | −0.0131418 | ||||||||
\(657\) | 2.37674e12 | 0.497664 | ||||||||
\(658\) | 3.90215e12 | 0.811498 | ||||||||
\(659\) | −1.47955e12 | −0.305594 | −0.152797 | − | 0.988258i | \(-0.548828\pi\) | ||||
−0.152797 | + | 0.988258i | \(0.548828\pi\) | |||||||
\(660\) | 6.52321e9 | 0.00133818 | ||||||||
\(661\) | −7.87237e12 | −1.60398 | −0.801990 | − | 0.597337i | \(-0.796225\pi\) | ||||
−0.801990 | + | 0.597337i | \(0.796225\pi\) | |||||||
\(662\) | 2.15815e12 | 0.436738 | ||||||||
\(663\) | −1.82301e12 | −0.366418 | ||||||||
\(664\) | 5.48388e11 | 0.109479 | ||||||||
\(665\) | −2.11725e10 | −0.00419832 | ||||||||
\(666\) | 3.47670e11 | 0.0684751 | ||||||||
\(667\) | 3.02026e12 | 0.590851 | ||||||||
\(668\) | −3.45471e12 | −0.671302 | ||||||||
\(669\) | 2.30537e12 | 0.444961 | ||||||||
\(670\) | 5.99478e9 | 0.00114931 | ||||||||
\(671\) | 5.76575e12 | 1.09801 | ||||||||
\(672\) | 3.09151e12 | 0.584802 | ||||||||
\(673\) | 3.54705e12 | 0.666499 | 0.333249 | − | 0.942839i | \(-0.391855\pi\) | ||||
0.333249 | + | 0.942839i | \(0.391855\pi\) | |||||||
\(674\) | −5.15260e12 | −0.961738 | ||||||||
\(675\) | 1.03796e12 | 0.192447 | ||||||||
\(676\) | 1.99916e12 | 0.368204 | ||||||||
\(677\) | 7.97527e11 | 0.145914 | 0.0729569 | − | 0.997335i | \(-0.476756\pi\) | ||||
0.0729569 | + | 0.997335i | \(0.476756\pi\) | |||||||
\(678\) | 4.50613e11 | 0.0818975 | ||||||||
\(679\) | 4.76744e12 | 0.860738 | ||||||||
\(680\) | −1.94885e10 | −0.00349534 | ||||||||
\(681\) | 2.37354e12 | 0.422897 | ||||||||
\(682\) | −3.88824e11 | −0.0688213 | ||||||||
\(683\) | −4.33649e12 | −0.762509 | −0.381254 | − | 0.924470i | \(-0.624508\pi\) | ||||
−0.381254 | + | 0.924470i | \(0.624508\pi\) | |||||||
\(684\) | 1.41337e12 | 0.246890 | ||||||||
\(685\) | 1.56155e10 | 0.00270986 | ||||||||
\(686\) | 3.37821e12 | 0.582409 | ||||||||
\(687\) | −2.05368e12 | −0.351744 | ||||||||
\(688\) | 1.64872e11 | 0.0280542 | ||||||||
\(689\) | −1.90301e12 | −0.321702 | ||||||||
\(690\) | −2.31681e9 | −0.000389107 0 | ||||||||
\(691\) | −1.10521e13 | −1.84414 | −0.922070 | − | 0.387023i | \(-0.873503\pi\) | ||||
−0.922070 | + | 0.387023i | \(0.873503\pi\) | |||||||
\(692\) | −6.19277e11 | −0.102661 | ||||||||
\(693\) | 1.79168e12 | 0.295094 | ||||||||
\(694\) | 2.82344e12 | 0.462021 | ||||||||
\(695\) | 9.52330e9 | 0.00154830 | ||||||||
\(696\) | −6.65399e12 | −1.07483 | ||||||||
\(697\) | 6.52529e11 | 0.104725 | ||||||||
\(698\) | −2.73087e12 | −0.435463 | ||||||||
\(699\) | 4.10351e12 | 0.650142 | ||||||||
\(700\) | −4.19458e12 | −0.660309 | ||||||||
\(701\) | 5.98491e12 | 0.936109 | 0.468055 | − | 0.883700i | \(-0.344955\pi\) | ||||
0.468055 | + | 0.883700i | \(0.344955\pi\) | |||||||
\(702\) | 4.77460e11 | 0.0742027 | ||||||||
\(703\) | −2.56003e12 | −0.395318 | ||||||||
\(704\) | −2.76127e12 | −0.423675 | ||||||||
\(705\) | −2.09044e10 | −0.00318703 | ||||||||
\(706\) | 8.00609e11 | 0.121283 | ||||||||
\(707\) | −6.18703e12 | −0.931311 | ||||||||
\(708\) | 3.36648e11 | 0.0503531 | ||||||||
\(709\) | −1.03720e13 | −1.54154 | −0.770769 | − | 0.637114i | \(-0.780128\pi\) | ||||
−0.770769 | + | 0.637114i | \(0.780128\pi\) | |||||||
\(710\) | −1.10444e10 | −0.00163109 | ||||||||
\(711\) | 7.53170e10 | 0.0110530 | ||||||||
\(712\) | −9.83427e12 | −1.43411 | ||||||||
\(713\) | −2.80255e11 | −0.0406117 | ||||||||
\(714\) | −2.14733e12 | −0.309213 | ||||||||
\(715\) | −1.62263e10 | −0.00232190 | ||||||||
\(716\) | 7.61584e11 | 0.108295 | ||||||||
\(717\) | −1.95463e12 | −0.276202 | ||||||||
\(718\) | 3.13626e12 | 0.440405 | ||||||||
\(719\) | 1.20078e13 | 1.67565 | 0.837823 | − | 0.545942i | \(-0.183828\pi\) | ||||
0.837823 | + | 0.545942i | \(0.183828\pi\) | |||||||
\(720\) | −1.09889e9 | −0.000152391 0 | ||||||||
\(721\) | 5.20528e12 | 0.717358 | ||||||||
\(722\) | 9.33122e11 | 0.127797 | ||||||||
\(723\) | 4.38825e12 | 0.597267 | ||||||||
\(724\) | 1.19403e11 | 0.0161507 | ||||||||
\(725\) | 1.44346e13 | 1.94036 | ||||||||
\(726\) | 4.80104e11 | 0.0641388 | ||||||||
\(727\) | 1.07636e12 | 0.142907 | 0.0714536 | − | 0.997444i | \(-0.477236\pi\) | ||||
0.0714536 | + | 0.997444i | \(0.477236\pi\) | |||||||
\(728\) | −4.80978e12 | −0.634650 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −2.53543e10 | −0.00330445 | ||||||||
\(731\) | −1.72593e12 | −0.223561 | ||||||||
\(732\) | −3.67296e12 | −0.472842 | ||||||||
\(733\) | 2.05646e12 | 0.263118 | 0.131559 | − | 0.991308i | \(-0.458002\pi\) | ||||
0.131559 | + | 0.991308i | \(0.458002\pi\) | |||||||
\(734\) | 5.90264e12 | 0.750610 | ||||||||
\(735\) | −4.99969e8 | −6.31902e−5 0 | ||||||||
\(736\) | −2.49096e12 | −0.312908 | ||||||||
\(737\) | 3.73542e12 | 0.466376 | ||||||||
\(738\) | −1.70903e11 | −0.0212078 | ||||||||
\(739\) | 2.23059e12 | 0.275118 | 0.137559 | − | 0.990494i | \(-0.456074\pi\) | ||||
0.137559 | + | 0.990494i | \(0.456074\pi\) | |||||||
\(740\) | 7.52679e9 | 0.000922714 0 | ||||||||
\(741\) | −3.51573e12 | −0.428384 | ||||||||
\(742\) | −2.24157e12 | −0.271478 | ||||||||
\(743\) | 9.80053e12 | 1.17978 | 0.589888 | − | 0.807485i | \(-0.299172\pi\) | ||||
0.589888 | + | 0.807485i | \(0.299172\pi\) | |||||||
\(744\) | 6.17436e11 | 0.0738777 | ||||||||
\(745\) | 1.80330e10 | 0.00214470 | ||||||||
\(746\) | 4.90028e12 | 0.579291 | ||||||||
\(747\) | −3.23699e11 | −0.0380363 | ||||||||
\(748\) | −4.87154e12 | −0.568996 | ||||||||
\(749\) | 5.86707e12 | 0.681167 | ||||||||
\(750\) | −2.21454e10 | −0.00255569 | ||||||||
\(751\) | −7.83593e12 | −0.898899 | −0.449450 | − | 0.893306i | \(-0.648380\pi\) | ||||
−0.449450 | + | 0.893306i | \(0.648380\pi\) | |||||||
\(752\) | −1.49130e12 | −0.170053 | ||||||||
\(753\) | 2.03821e12 | 0.231032 | ||||||||
\(754\) | 6.63991e12 | 0.748154 | ||||||||
\(755\) | −2.35090e10 | −0.00263313 | ||||||||
\(756\) | −1.14135e12 | −0.127078 | ||||||||
\(757\) | −1.40537e12 | −0.155547 | −0.0777733 | − | 0.996971i | \(-0.524781\pi\) | ||||
−0.0777733 | + | 0.996971i | \(0.524781\pi\) | |||||||
\(758\) | 7.41475e12 | 0.815802 | ||||||||
\(759\) | −1.44363e12 | −0.157895 | ||||||||
\(760\) | −3.75843e10 | −0.00408644 | ||||||||
\(761\) | −5.80533e12 | −0.627475 | −0.313737 | − | 0.949510i | \(-0.601581\pi\) | ||||
−0.313737 | + | 0.949510i | \(0.601581\pi\) | |||||||
\(762\) | −2.99228e12 | −0.321517 | ||||||||
\(763\) | 3.19890e12 | 0.341696 | ||||||||
\(764\) | 5.68827e12 | 0.604033 | ||||||||
\(765\) | 1.15036e10 | 0.00121439 | ||||||||
\(766\) | 1.76156e12 | 0.184871 | ||||||||
\(767\) | −8.37403e11 | −0.0873686 | ||||||||
\(768\) | 5.04536e12 | 0.523319 | ||||||||
\(769\) | −1.55106e13 | −1.59942 | −0.799708 | − | 0.600390i | \(-0.795012\pi\) | ||||
−0.799708 | + | 0.600390i | \(0.795012\pi\) | |||||||
\(770\) | −1.91131e10 | −0.00195940 | ||||||||
\(771\) | 7.94806e12 | 0.810058 | ||||||||
\(772\) | −1.11692e12 | −0.113174 | ||||||||
\(773\) | −5.80456e11 | −0.0584738 | −0.0292369 | − | 0.999573i | \(-0.509308\pi\) | ||||
−0.0292369 | + | 0.999573i | \(0.509308\pi\) | |||||||
\(774\) | 4.52035e11 | 0.0452729 | ||||||||
\(775\) | −1.33941e12 | −0.133369 | ||||||||
\(776\) | 8.46290e12 | 0.837802 | ||||||||
\(777\) | 2.06733e12 | 0.203476 | ||||||||
\(778\) | 3.53743e12 | 0.346162 | ||||||||
\(779\) | 1.25842e12 | 0.122436 | ||||||||
\(780\) | 1.03367e10 | 0.000999895 0 | ||||||||
\(781\) | −6.88189e12 | −0.661878 | ||||||||
\(782\) | 1.73020e12 | 0.165449 | ||||||||
\(783\) | 3.92767e12 | 0.373428 | ||||||||
\(784\) | −3.56673e10 | −0.00337170 | ||||||||
\(785\) | 3.62515e10 | 0.00340731 | ||||||||
\(786\) | −3.02308e12 | −0.282519 | ||||||||
\(787\) | −1.09674e13 | −1.01910 | −0.509550 | − | 0.860441i | \(-0.670188\pi\) | ||||
−0.509550 | + | 0.860441i | \(0.670188\pi\) | |||||||
\(788\) | −3.27835e11 | −0.0302892 | ||||||||
\(789\) | −5.04299e12 | −0.463277 | ||||||||
\(790\) | −8.03461e8 | −7.33910e−5 0 | ||||||||
\(791\) | 2.67945e12 | 0.243362 | ||||||||
\(792\) | 3.18049e12 | 0.287231 | ||||||||
\(793\) | 9.13639e12 | 0.820437 | ||||||||
\(794\) | 4.65551e12 | 0.415695 | ||||||||
\(795\) | 1.20084e10 | 0.00106619 | ||||||||
\(796\) | 7.83713e12 | 0.691908 | ||||||||
\(797\) | 7.83453e12 | 0.687781 | 0.343891 | − | 0.939010i | \(-0.388255\pi\) | ||||
0.343891 | + | 0.939010i | \(0.388255\pi\) | |||||||
\(798\) | −4.14120e12 | −0.361504 | ||||||||
\(799\) | 1.56114e13 | 1.35513 | ||||||||
\(800\) | −1.19049e13 | −1.02759 | ||||||||
\(801\) | 5.80491e12 | 0.498252 | ||||||||
\(802\) | −8.60932e12 | −0.734825 | ||||||||
\(803\) | −1.57986e13 | −1.34091 | ||||||||
\(804\) | −2.37957e12 | −0.200839 | ||||||||
\(805\) | −1.37763e10 | −0.00115625 | ||||||||
\(806\) | −6.16129e11 | −0.0514238 | ||||||||
\(807\) | 6.53882e12 | 0.542711 | ||||||||
\(808\) | −1.09829e13 | −0.906495 | ||||||||
\(809\) | −1.37396e12 | −0.112773 | −0.0563867 | − | 0.998409i | \(-0.517958\pi\) | ||||
−0.0563867 | + | 0.998409i | \(0.517958\pi\) | |||||||
\(810\) | −3.01288e9 | −0.000245923 0 | ||||||||
\(811\) | −1.75453e13 | −1.42419 | −0.712095 | − | 0.702083i | \(-0.752254\pi\) | ||||
−0.712095 | + | 0.702083i | \(0.752254\pi\) | |||||||
\(812\) | −1.58725e13 | −1.28128 | ||||||||
\(813\) | 1.09034e13 | 0.875293 | ||||||||
\(814\) | −2.31102e12 | −0.184499 | ||||||||
\(815\) | 4.98901e10 | 0.00396100 | ||||||||
\(816\) | 8.20655e11 | 0.0647970 | ||||||||
\(817\) | −3.32852e12 | −0.261367 | ||||||||
\(818\) | 4.44878e12 | 0.347417 | ||||||||
\(819\) | 2.83909e12 | 0.220496 | ||||||||
\(820\) | −3.69992e9 | −0.000285778 0 | ||||||||
\(821\) | −2.09757e13 | −1.61128 | −0.805641 | − | 0.592405i | \(-0.798179\pi\) | ||||
−0.805641 | + | 0.592405i | \(0.798179\pi\) | |||||||
\(822\) | 3.05428e12 | 0.233338 | ||||||||
\(823\) | 1.73596e13 | 1.31898 | 0.659492 | − | 0.751712i | \(-0.270771\pi\) | ||||
0.659492 | + | 0.751712i | \(0.270771\pi\) | |||||||
\(824\) | 9.24014e12 | 0.698242 | ||||||||
\(825\) | −6.89948e12 | −0.518530 | ||||||||
\(826\) | −9.86383e11 | −0.0737285 | ||||||||
\(827\) | 1.37776e13 | 1.02423 | 0.512117 | − | 0.858916i | \(-0.328861\pi\) | ||||
0.512117 | + | 0.858916i | \(0.328861\pi\) | |||||||
\(828\) | 9.19637e11 | 0.0679954 | ||||||||
\(829\) | 5.24467e12 | 0.385676 | 0.192838 | − | 0.981231i | \(-0.438231\pi\) | ||||
0.192838 | + | 0.981231i | \(0.438231\pi\) | |||||||
\(830\) | 3.45313e9 | 0.000252558 0 | ||||||||
\(831\) | 1.00629e13 | 0.732015 | ||||||||
\(832\) | −4.37550e12 | −0.316572 | ||||||||
\(833\) | 3.73378e11 | 0.0268687 | ||||||||
\(834\) | 1.86269e12 | 0.133320 | ||||||||
\(835\) | −5.42270e10 | −0.00386035 | ||||||||
\(836\) | −9.39494e12 | −0.665221 | ||||||||
\(837\) | −3.64456e11 | −0.0256673 | ||||||||
\(838\) | −1.26207e13 | −0.884068 | ||||||||
\(839\) | −2.45026e13 | −1.70720 | −0.853599 | − | 0.520931i | \(-0.825585\pi\) | ||||
−0.853599 | + | 0.520931i | \(0.825585\pi\) | |||||||
\(840\) | 3.03508e10 | 0.00210336 | ||||||||
\(841\) | 4.01140e13 | 2.76512 | ||||||||
\(842\) | 3.44409e12 | 0.236140 | ||||||||
\(843\) | 7.66423e12 | 0.522690 | ||||||||
\(844\) | −7.21673e12 | −0.489553 | ||||||||
\(845\) | 3.13799e10 | 0.00211737 | ||||||||
\(846\) | −4.08876e12 | −0.274426 | ||||||||
\(847\) | 2.85481e12 | 0.190591 | ||||||||
\(848\) | 8.56669e11 | 0.0568894 | ||||||||
\(849\) | 4.66185e12 | 0.307945 | ||||||||
\(850\) | 8.26905e12 | 0.543338 | ||||||||
\(851\) | −1.66573e12 | −0.108873 | ||||||||
\(852\) | 4.38397e12 | 0.285029 | ||||||||
\(853\) | −1.15100e13 | −0.744396 | −0.372198 | − | 0.928153i | \(-0.621396\pi\) | ||||
−0.372198 | + | 0.928153i | \(0.621396\pi\) | |||||||
\(854\) | 1.07618e13 | 0.692350 | ||||||||
\(855\) | 2.21850e10 | 0.00141975 | ||||||||
\(856\) | 1.04149e13 | 0.663016 | ||||||||
\(857\) | −1.59723e13 | −1.01147 | −0.505737 | − | 0.862688i | \(-0.668779\pi\) | ||||
−0.505737 | + | 0.862688i | \(0.668779\pi\) | |||||||
\(858\) | −3.17376e12 | −0.199932 | ||||||||
\(859\) | 2.59977e13 | 1.62917 | 0.814583 | − | 0.580046i | \(-0.196966\pi\) | ||||
0.814583 | + | 0.580046i | \(0.196966\pi\) | |||||||
\(860\) | 9.78623e9 | 0.000610060 0 | ||||||||
\(861\) | −1.01623e12 | −0.0630197 | ||||||||
\(862\) | −7.64485e12 | −0.471614 | ||||||||
\(863\) | 1.59640e13 | 0.979698 | 0.489849 | − | 0.871807i | \(-0.337052\pi\) | ||||
0.489849 | + | 0.871807i | \(0.337052\pi\) | |||||||
\(864\) | −3.23935e12 | −0.197764 | ||||||||
\(865\) | −9.72050e9 | −0.000590359 0 | ||||||||
\(866\) | 1.89371e13 | 1.14415 | ||||||||
\(867\) | 1.01472e12 | 0.0609905 | ||||||||
\(868\) | 1.47284e12 | 0.0880676 | ||||||||
\(869\) | −5.00646e11 | −0.0297812 | ||||||||
\(870\) | −4.18993e10 | −0.00247953 | ||||||||
\(871\) | 5.91914e12 | 0.348479 | ||||||||
\(872\) | 5.67852e12 | 0.332591 | ||||||||
\(873\) | −4.99543e12 | −0.291077 | ||||||||
\(874\) | 3.33674e12 | 0.193429 | ||||||||
\(875\) | −1.31682e11 | −0.00759433 | ||||||||
\(876\) | 1.00642e13 | 0.577444 | ||||||||
\(877\) | 6.66416e11 | 0.0380406 | 0.0190203 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190203 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(878\) | 8.82312e12 | 0.501068 | ||||||||
\(879\) | 1.92140e13 | 1.08559 | ||||||||
\(880\) | 7.30454e9 | 0.000410602 0 | ||||||||
\(881\) | −4.71400e12 | −0.263632 | −0.131816 | − | 0.991274i | \(-0.542081\pi\) | ||||
−0.131816 | + | 0.991274i | \(0.542081\pi\) | |||||||
\(882\) | −9.77906e10 | −0.00544112 | ||||||||
\(883\) | −3.24260e12 | −0.179503 | −0.0897513 | − | 0.995964i | \(-0.528607\pi\) | ||||
−0.0897513 | + | 0.995964i | \(0.528607\pi\) | |||||||
\(884\) | −7.71944e12 | −0.425158 | ||||||||
\(885\) | 5.28420e9 | 0.000289557 0 | ||||||||
\(886\) | −1.26401e13 | −0.689129 | ||||||||
\(887\) | 1.15928e13 | 0.628829 | 0.314414 | − | 0.949286i | \(-0.398192\pi\) | ||||
0.314414 | + | 0.949286i | \(0.398192\pi\) | |||||||
\(888\) | 3.66981e12 | 0.198054 | ||||||||
\(889\) | −1.77928e13 | −0.955402 | ||||||||
\(890\) | −6.19251e10 | −0.00330835 | ||||||||
\(891\) | −1.87736e12 | −0.0997925 | ||||||||
\(892\) | 9.76196e12 | 0.516292 | ||||||||
\(893\) | 3.01072e13 | 1.58430 | ||||||||
\(894\) | 3.52714e12 | 0.184673 | ||||||||
\(895\) | 1.19542e10 | 0.000622756 0 | ||||||||
\(896\) | 1.43875e13 | 0.745758 | ||||||||
\(897\) | −2.28758e12 | −0.117980 | ||||||||
\(898\) | 7.02675e12 | 0.360588 | ||||||||
\(899\) | −5.06839e12 | −0.258792 | ||||||||
\(900\) | 4.39517e12 | 0.223298 | ||||||||
\(901\) | −8.96790e12 | −0.453345 | ||||||||
\(902\) | 1.13602e12 | 0.0571422 | ||||||||
\(903\) | 2.68791e12 | 0.134530 | ||||||||
\(904\) | 4.75642e12 | 0.236877 | ||||||||
\(905\) | 1.87421e9 | 9.28752e−5 0 | ||||||||
\(906\) | −4.59821e12 | −0.226731 | ||||||||
\(907\) | −3.56853e13 | −1.75088 | −0.875441 | − | 0.483325i | \(-0.839429\pi\) | ||||
−0.875441 | + | 0.483325i | \(0.839429\pi\) | |||||||
\(908\) | 1.00506e13 | 0.490691 | ||||||||
\(909\) | 6.48291e12 | 0.314943 | ||||||||
\(910\) | −3.02866e10 | −0.00146408 | ||||||||
\(911\) | −3.47841e12 | −0.167320 | −0.0836602 | − | 0.996494i | \(-0.526661\pi\) | ||||
−0.0836602 | + | 0.996494i | \(0.526661\pi\) | |||||||
\(912\) | 1.58266e12 | 0.0757549 | ||||||||
\(913\) | 2.15169e12 | 0.102485 | ||||||||
\(914\) | 2.21593e13 | 1.05026 | ||||||||
\(915\) | −5.76527e10 | −0.00271910 | ||||||||
\(916\) | −8.69620e12 | −0.408131 | ||||||||
\(917\) | −1.79760e13 | −0.839518 | ||||||||
\(918\) | 2.25002e12 | 0.104567 | ||||||||
\(919\) | 1.60113e13 | 0.740471 | 0.370235 | − | 0.928938i | \(-0.379277\pi\) | ||||
0.370235 | + | 0.928938i | \(0.379277\pi\) | |||||||
\(920\) | −2.44549e10 | −0.00112544 | ||||||||
\(921\) | 7.17786e12 | 0.328720 | ||||||||
\(922\) | −1.28631e13 | −0.586213 | ||||||||
\(923\) | −1.09050e13 | −0.494560 | ||||||||
\(924\) | 7.58678e12 | 0.342400 | ||||||||
\(925\) | −7.96095e12 | −0.357542 | ||||||||
\(926\) | −6.43119e12 | −0.287437 | ||||||||
\(927\) | −5.45421e12 | −0.242590 | ||||||||
\(928\) | −4.50488e13 | −1.99397 | ||||||||
\(929\) | −1.18366e13 | −0.521384 | −0.260692 | − | 0.965422i | \(-0.583951\pi\) | ||||
−0.260692 | + | 0.965422i | \(0.583951\pi\) | |||||||
\(930\) | 3.88791e9 | 0.000170429 0 | ||||||||
\(931\) | 7.20072e11 | 0.0314125 | ||||||||
\(932\) | 1.73761e13 | 0.754365 | ||||||||
\(933\) | 1.23226e13 | 0.532396 | ||||||||
\(934\) | 1.04490e13 | 0.449275 | ||||||||
\(935\) | −7.64664e10 | −0.00327204 | ||||||||
\(936\) | 5.03980e12 | 0.214621 | ||||||||
\(937\) | 1.91151e13 | 0.810118 | 0.405059 | − | 0.914291i | \(-0.367251\pi\) | ||||
0.405059 | + | 0.914291i | \(0.367251\pi\) | |||||||
\(938\) | 6.97220e12 | 0.294074 | ||||||||
\(939\) | −2.09178e13 | −0.878051 | ||||||||
\(940\) | −8.85187e10 | −0.00369794 | ||||||||
\(941\) | −1.05459e13 | −0.438462 | −0.219231 | − | 0.975673i | \(-0.570355\pi\) | ||||
−0.219231 | + | 0.975673i | \(0.570355\pi\) | |||||||
\(942\) | 7.09054e12 | 0.293393 | ||||||||
\(943\) | 8.18817e11 | 0.0337198 | ||||||||
\(944\) | 3.76970e11 | 0.0154502 | ||||||||
\(945\) | −1.79153e10 | −0.000730770 0 | ||||||||
\(946\) | −3.00476e12 | −0.121983 | ||||||||
\(947\) | −2.96110e13 | −1.19641 | −0.598203 | − | 0.801345i | \(-0.704118\pi\) | ||||
−0.598203 | + | 0.801345i | \(0.704118\pi\) | |||||||
\(948\) | 3.18927e11 | 0.0128249 | ||||||||
\(949\) | −2.50344e13 | −1.00193 | ||||||||
\(950\) | 1.59471e13 | 0.635223 | ||||||||
\(951\) | 2.56461e13 | 1.01674 | ||||||||
\(952\) | −2.26660e13 | −0.894354 | ||||||||
\(953\) | −4.92564e13 | −1.93439 | −0.967196 | − | 0.254031i | \(-0.918244\pi\) | ||||
−0.967196 | + | 0.254031i | \(0.918244\pi\) | |||||||
\(954\) | 2.34876e12 | 0.0918061 | ||||||||
\(955\) | 8.92862e10 | 0.00347352 | ||||||||
\(956\) | −8.27677e12 | −0.320480 | ||||||||
\(957\) | −2.61080e13 | −1.00617 | ||||||||
\(958\) | −1.87382e13 | −0.718757 | ||||||||
\(959\) | 1.81615e13 | 0.693374 | ||||||||
\(960\) | 2.76104e10 | 0.00104919 | ||||||||
\(961\) | −2.59693e13 | −0.982212 | ||||||||
\(962\) | −3.66204e12 | −0.137859 | ||||||||
\(963\) | −6.14765e12 | −0.230351 | ||||||||
\(964\) | 1.85818e13 | 0.693014 | ||||||||
\(965\) | −1.75318e10 | −0.000650810 0 | ||||||||
\(966\) | −2.69455e12 | −0.0995611 | ||||||||
\(967\) | −4.25456e13 | −1.56472 | −0.782359 | − | 0.622828i | \(-0.785984\pi\) | ||||
−0.782359 | + | 0.622828i | \(0.785984\pi\) | |||||||
\(968\) | 5.06771e12 | 0.185512 | ||||||||
\(969\) | −1.65678e13 | −0.603682 | ||||||||
\(970\) | 5.32898e10 | 0.00193273 | ||||||||
\(971\) | −5.03139e13 | −1.81636 | −0.908179 | − | 0.418582i | \(-0.862527\pi\) | ||||
−0.908179 | + | 0.418582i | \(0.862527\pi\) | |||||||
\(972\) | 1.19593e12 | 0.0429743 | ||||||||
\(973\) | 1.10760e13 | 0.396165 | ||||||||
\(974\) | 4.22322e11 | 0.0150359 | ||||||||
\(975\) | −1.09329e13 | −0.387449 | ||||||||
\(976\) | −4.11289e12 | −0.145085 | ||||||||
\(977\) | −3.70742e13 | −1.30181 | −0.650903 | − | 0.759161i | \(-0.725610\pi\) | ||||
−0.650903 | + | 0.759161i | \(0.725610\pi\) | |||||||
\(978\) | 9.75817e12 | 0.341070 | ||||||||
\(979\) | −3.85863e13 | −1.34249 | ||||||||
\(980\) | −2.11710e9 | −7.33201e−5 0 | ||||||||
\(981\) | −3.35188e12 | −0.115552 | ||||||||
\(982\) | −2.16741e13 | −0.743772 | ||||||||
\(983\) | −3.04886e13 | −1.04147 | −0.520734 | − | 0.853719i | \(-0.674342\pi\) | ||||
−0.520734 | + | 0.853719i | \(0.674342\pi\) | |||||||
\(984\) | −1.80395e12 | −0.0613404 | ||||||||
\(985\) | −5.14588e9 | −0.000174179 0 | ||||||||
\(986\) | 3.12905e13 | 1.05430 | ||||||||
\(987\) | −2.43127e13 | −0.815467 | ||||||||
\(988\) | −1.48872e13 | −0.497057 | ||||||||
\(989\) | −2.16576e12 | −0.0719826 | ||||||||
\(990\) | 2.00271e10 | 0.000662614 0 | ||||||||
\(991\) | 3.56051e13 | 1.17268 | 0.586341 | − | 0.810064i | \(-0.300568\pi\) | ||||
0.586341 | + | 0.810064i | \(0.300568\pi\) | |||||||
\(992\) | 4.18016e12 | 0.137054 | ||||||||
\(993\) | −1.34466e13 | −0.438875 | ||||||||
\(994\) | −1.28451e13 | −0.417349 | ||||||||
\(995\) | 1.23016e11 | 0.00397884 | ||||||||
\(996\) | −1.37069e12 | −0.0441338 | ||||||||
\(997\) | −1.70884e13 | −0.547738 | −0.273869 | − | 0.961767i | \(-0.588304\pi\) | ||||
−0.273869 | + | 0.961767i | \(0.588304\pi\) | |||||||
\(998\) | 2.92135e13 | 0.932174 | ||||||||
\(999\) | −2.16619e12 | −0.0688100 |
(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.1.13 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.c.1.13 | ✓ | 22 | 1.1 | even | 1 | trivial |