Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.4936 | −0.994085 | −0.497043 | − | 0.867726i | \(-0.665581\pi\) | ||||
−0.497043 | + | 0.867726i | \(0.665581\pi\) | |||||||
\(3\) | −161.121 | −1.14844 | −0.574219 | − | 0.818702i | \(-0.694694\pi\) | ||||
−0.574219 | + | 0.818702i | \(0.694694\pi\) | |||||||
\(4\) | −6.03889 | −0.0117947 | ||||||||
\(5\) | −1284.66 | −0.919230 | −0.459615 | − | 0.888118i | \(-0.652013\pi\) | ||||
−0.459615 | + | 0.888118i | \(0.652013\pi\) | |||||||
\(6\) | 3624.20 | 1.14165 | ||||||||
\(7\) | −9354.17 | −1.47253 | −0.736265 | − | 0.676694i | \(-0.763412\pi\) | ||||
−0.736265 | + | 0.676694i | \(0.763412\pi\) | |||||||
\(8\) | 11652.5 | 1.00581 | ||||||||
\(9\) | 6277.10 | 0.318910 | ||||||||
\(10\) | 28896.7 | 0.913792 | ||||||||
\(11\) | −57101.0 | −1.17592 | −0.587959 | − | 0.808891i | \(-0.700068\pi\) | ||||
−0.587959 | + | 0.808891i | \(0.700068\pi\) | |||||||
\(12\) | 972.994 | 0.0135455 | ||||||||
\(13\) | −147205. | −1.42948 | −0.714739 | − | 0.699391i | \(-0.753455\pi\) | ||||
−0.714739 | + | 0.699391i | \(0.753455\pi\) | |||||||
\(14\) | 210409. | 1.46382 | ||||||||
\(15\) | 206987. | 1.05568 | ||||||||
\(16\) | −259016. | −0.988066 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −141194. | −0.317023 | ||||||||
\(19\) | −495550. | −0.872360 | −0.436180 | − | 0.899859i | \(-0.643669\pi\) | ||||
−0.436180 | + | 0.899859i | \(0.643669\pi\) | |||||||
\(20\) | 7757.93 | 0.0108420 | ||||||||
\(21\) | 1.50716e6 | 1.69111 | ||||||||
\(22\) | 1.28441e6 | 1.16896 | ||||||||
\(23\) | −2.06028e6 | −1.53515 | −0.767576 | − | 0.640958i | \(-0.778537\pi\) | ||||
−0.767576 | + | 0.640958i | \(0.778537\pi\) | |||||||
\(24\) | −1.87747e6 | −1.15511 | ||||||||
\(25\) | −302768. | −0.155017 | ||||||||
\(26\) | 3.31117e6 | 1.42102 | ||||||||
\(27\) | 2.15998e6 | 0.782190 | ||||||||
\(28\) | 56488.8 | 0.0173680 | ||||||||
\(29\) | −1.09429e6 | −0.287305 | −0.143652 | − | 0.989628i | \(-0.545885\pi\) | ||||
−0.143652 | + | 0.989628i | \(0.545885\pi\) | |||||||
\(30\) | −4.65587e6 | −1.04943 | ||||||||
\(31\) | −8.20471e6 | −1.59564 | −0.797822 | − | 0.602894i | \(-0.794014\pi\) | ||||
−0.797822 | + | 0.602894i | \(0.794014\pi\) | |||||||
\(32\) | −139917. | −0.0235882 | ||||||||
\(33\) | 9.20020e6 | 1.35047 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.20169e7 | 1.35359 | ||||||||
\(36\) | −37906.7 | −0.00376144 | ||||||||
\(37\) | −1.78074e7 | −1.56204 | −0.781019 | − | 0.624507i | \(-0.785300\pi\) | ||||
−0.781019 | + | 0.624507i | \(0.785300\pi\) | |||||||
\(38\) | 1.11467e7 | 0.867201 | ||||||||
\(39\) | 2.37179e7 | 1.64167 | ||||||||
\(40\) | −1.49696e7 | −0.924570 | ||||||||
\(41\) | 1.40060e7 | 0.774082 | 0.387041 | − | 0.922062i | \(-0.373497\pi\) | ||||
0.387041 | + | 0.922062i | \(0.373497\pi\) | |||||||
\(42\) | −3.39013e7 | −1.68111 | ||||||||
\(43\) | −2.12860e6 | −0.0949479 | −0.0474740 | − | 0.998872i | \(-0.515117\pi\) | ||||
−0.0474740 | + | 0.998872i | \(0.515117\pi\) | |||||||
\(44\) | 344827. | 0.0138696 | ||||||||
\(45\) | −8.06395e6 | −0.293151 | ||||||||
\(46\) | 4.63431e7 | 1.52607 | ||||||||
\(47\) | 1.57971e7 | 0.472212 | 0.236106 | − | 0.971727i | \(-0.424129\pi\) | ||||
0.236106 | + | 0.971727i | \(0.424129\pi\) | |||||||
\(48\) | 4.17330e7 | 1.13473 | ||||||||
\(49\) | 4.71468e7 | 1.16834 | ||||||||
\(50\) | 6.81033e6 | 0.154100 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 888955. | 0.0168603 | ||||||||
\(53\) | −3.85001e7 | −0.670225 | −0.335113 | − | 0.942178i | \(-0.608774\pi\) | ||||
−0.335113 | + | 0.942178i | \(0.608774\pi\) | |||||||
\(54\) | −4.85856e7 | −0.777564 | ||||||||
\(55\) | 7.33555e7 | 1.08094 | ||||||||
\(56\) | −1.09000e8 | −1.48108 | ||||||||
\(57\) | 7.98436e7 | 1.00185 | ||||||||
\(58\) | 2.46146e7 | 0.285605 | ||||||||
\(59\) | 6.56446e7 | 0.705285 | 0.352643 | − | 0.935758i | \(-0.385283\pi\) | ||||
0.352643 | + | 0.935758i | \(0.385283\pi\) | |||||||
\(60\) | −1.24997e6 | −0.0124514 | ||||||||
\(61\) | −4.06936e7 | −0.376307 | −0.188153 | − | 0.982140i | \(-0.560250\pi\) | ||||
−0.188153 | + | 0.982140i | \(0.560250\pi\) | |||||||
\(62\) | 1.84553e8 | 1.58621 | ||||||||
\(63\) | −5.87170e7 | −0.469604 | ||||||||
\(64\) | 1.35763e8 | 1.01151 | ||||||||
\(65\) | 1.89109e8 | 1.31402 | ||||||||
\(66\) | −2.06945e8 | −1.34248 | ||||||||
\(67\) | 1.29000e8 | 0.782083 | 0.391041 | − | 0.920373i | \(-0.372115\pi\) | ||||
0.391041 | + | 0.920373i | \(0.372115\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.31955e8 | 1.76303 | ||||||||
\(70\) | −2.70304e8 | −1.34559 | ||||||||
\(71\) | 1.56798e8 | 0.732280 | 0.366140 | − | 0.930560i | \(-0.380679\pi\) | ||||
0.366140 | + | 0.930560i | \(0.380679\pi\) | |||||||
\(72\) | 7.31442e7 | 0.320762 | ||||||||
\(73\) | −2.48477e8 | −1.02408 | −0.512039 | − | 0.858962i | \(-0.671110\pi\) | ||||
−0.512039 | + | 0.858962i | \(0.671110\pi\) | |||||||
\(74\) | 4.00551e8 | 1.55280 | ||||||||
\(75\) | 4.87823e7 | 0.178027 | ||||||||
\(76\) | 2.99257e6 | 0.0102892 | ||||||||
\(77\) | 5.34133e8 | 1.73157 | ||||||||
\(78\) | −5.33500e8 | −1.63196 | ||||||||
\(79\) | −5.41804e8 | −1.56502 | −0.782511 | − | 0.622637i | \(-0.786061\pi\) | ||||
−0.782511 | + | 0.622637i | \(0.786061\pi\) | |||||||
\(80\) | 3.32748e8 | 0.908260 | ||||||||
\(81\) | −4.71571e8 | −1.21721 | ||||||||
\(82\) | −3.15045e8 | −0.769504 | ||||||||
\(83\) | 7.51897e7 | 0.173903 | 0.0869515 | − | 0.996213i | \(-0.472287\pi\) | ||||
0.0869515 | + | 0.996213i | \(0.472287\pi\) | |||||||
\(84\) | −9.10155e6 | −0.0199461 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.78798e7 | 0.0943863 | ||||||||
\(87\) | 1.76314e8 | 0.329952 | ||||||||
\(88\) | −6.65373e8 | −1.18275 | ||||||||
\(89\) | 4.56857e8 | 0.771836 | 0.385918 | − | 0.922533i | \(-0.373885\pi\) | ||||
0.385918 | + | 0.922533i | \(0.373885\pi\) | |||||||
\(90\) | 1.81387e8 | 0.291417 | ||||||||
\(91\) | 1.37698e9 | 2.10495 | ||||||||
\(92\) | 1.24418e7 | 0.0181067 | ||||||||
\(93\) | 1.32195e9 | 1.83250 | ||||||||
\(94\) | −3.55333e8 | −0.469419 | ||||||||
\(95\) | 6.36614e8 | 0.801899 | ||||||||
\(96\) | 2.25436e7 | 0.0270896 | ||||||||
\(97\) | 1.00520e9 | 1.15287 | 0.576437 | − | 0.817142i | \(-0.304443\pi\) | ||||
0.576437 | + | 0.817142i | \(0.304443\pi\) | |||||||
\(98\) | −1.06050e9 | −1.16143 | ||||||||
\(99\) | −3.58429e8 | −0.375011 | ||||||||
\(100\) | 1.82838e6 | 0.00182838 | ||||||||
\(101\) | −7.94017e8 | −0.759248 | −0.379624 | − | 0.925141i | \(-0.623947\pi\) | ||||
−0.379624 | + | 0.925141i | \(0.623947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.53373e9 | 1.34271 | 0.671353 | − | 0.741138i | \(-0.265714\pi\) | ||||
0.671353 | + | 0.741138i | \(0.265714\pi\) | |||||||
\(104\) | −1.71531e9 | −1.43778 | ||||||||
\(105\) | −1.93619e9 | −1.55452 | ||||||||
\(106\) | 8.66006e8 | 0.666261 | ||||||||
\(107\) | 1.65042e9 | 1.21722 | 0.608609 | − | 0.793471i | \(-0.291728\pi\) | ||||
0.608609 | + | 0.793471i | \(0.291728\pi\) | |||||||
\(108\) | −1.30439e7 | −0.00922570 | ||||||||
\(109\) | 8.41832e8 | 0.571223 | 0.285612 | − | 0.958345i | \(-0.407803\pi\) | ||||
0.285612 | + | 0.958345i | \(0.407803\pi\) | |||||||
\(110\) | −1.65003e9 | −1.07454 | ||||||||
\(111\) | 2.86915e9 | 1.79390 | ||||||||
\(112\) | 2.42288e9 | 1.45496 | ||||||||
\(113\) | 2.33505e9 | 1.34723 | 0.673617 | − | 0.739081i | \(-0.264740\pi\) | ||||
0.673617 | + | 0.739081i | \(0.264740\pi\) | |||||||
\(114\) | −1.79597e9 | −0.995926 | ||||||||
\(115\) | 2.64677e9 | 1.41116 | ||||||||
\(116\) | 6.60832e6 | 0.00338867 | ||||||||
\(117\) | −9.24020e8 | −0.455874 | ||||||||
\(118\) | −1.47658e9 | −0.701114 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.41192e9 | 1.06181 | ||||||||
\(121\) | 9.02580e8 | 0.382782 | ||||||||
\(122\) | 9.15344e8 | 0.374081 | ||||||||
\(123\) | −2.25667e9 | −0.888985 | ||||||||
\(124\) | 4.95474e7 | 0.0188201 | ||||||||
\(125\) | 2.89806e9 | 1.06173 | ||||||||
\(126\) | 1.32076e9 | 0.466826 | ||||||||
\(127\) | −1.32135e9 | −0.450715 | −0.225357 | − | 0.974276i | \(-0.572355\pi\) | ||||
−0.225357 | + | 0.974276i | \(0.572355\pi\) | |||||||
\(128\) | −2.98216e9 | −0.981944 | ||||||||
\(129\) | 3.42963e8 | 0.109042 | ||||||||
\(130\) | −4.25373e9 | −1.30625 | ||||||||
\(131\) | −5.89659e9 | −1.74936 | −0.874681 | − | 0.484698i | \(-0.838929\pi\) | ||||
−0.874681 | + | 0.484698i | \(0.838929\pi\) | |||||||
\(132\) | −5.55590e7 | −0.0159284 | ||||||||
\(133\) | 4.63545e9 | 1.28458 | ||||||||
\(134\) | −2.90167e9 | −0.777457 | ||||||||
\(135\) | −2.77484e9 | −0.719012 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.07749e9 | −0.988896 | −0.494448 | − | 0.869207i | \(-0.664630\pi\) | ||||
−0.494448 | + | 0.869207i | \(0.664630\pi\) | |||||||
\(138\) | −7.46687e9 | −1.75260 | ||||||||
\(139\) | −8.32735e9 | −1.89208 | −0.946041 | − | 0.324046i | \(-0.894957\pi\) | ||||
−0.946041 | + | 0.324046i | \(0.894957\pi\) | |||||||
\(140\) | −7.25690e7 | −0.0159652 | ||||||||
\(141\) | −2.54525e9 | −0.542306 | ||||||||
\(142\) | −3.52694e9 | −0.727949 | ||||||||
\(143\) | 8.40556e9 | 1.68095 | ||||||||
\(144\) | −1.62587e9 | −0.315104 | ||||||||
\(145\) | 1.40580e9 | 0.264099 | ||||||||
\(146\) | 5.58913e9 | 1.01802 | ||||||||
\(147\) | −7.59636e9 | −1.34177 | ||||||||
\(148\) | 1.07537e8 | 0.0184238 | ||||||||
\(149\) | 1.09294e10 | 1.81660 | 0.908301 | − | 0.418317i | \(-0.137380\pi\) | ||||
0.908301 | + | 0.418317i | \(0.137380\pi\) | |||||||
\(150\) | −1.09729e9 | −0.176974 | ||||||||
\(151\) | −1.08934e10 | −1.70517 | −0.852586 | − | 0.522586i | \(-0.824967\pi\) | ||||
−0.852586 | + | 0.522586i | \(0.824967\pi\) | |||||||
\(152\) | −5.77442e9 | −0.877429 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.20146e10 | −1.72133 | ||||||||
\(155\) | 1.05403e10 | 1.46676 | ||||||||
\(156\) | −1.43230e8 | −0.0193630 | ||||||||
\(157\) | 3.77707e7 | 0.00496143 | 0.00248072 | − | 0.999997i | \(-0.499210\pi\) | ||||
0.00248072 | + | 0.999997i | \(0.499210\pi\) | |||||||
\(158\) | 1.21871e10 | 1.55576 | ||||||||
\(159\) | 6.20320e9 | 0.769712 | ||||||||
\(160\) | 1.79746e8 | 0.0216829 | ||||||||
\(161\) | 1.92722e10 | 2.26056 | ||||||||
\(162\) | 1.06073e10 | 1.21001 | ||||||||
\(163\) | −4.13858e9 | −0.459205 | −0.229603 | − | 0.973284i | \(-0.573743\pi\) | ||||
−0.229603 | + | 0.973284i | \(0.573743\pi\) | |||||||
\(164\) | −8.45807e7 | −0.00913007 | ||||||||
\(165\) | −1.18191e10 | −1.24139 | ||||||||
\(166\) | −1.69129e9 | −0.172874 | ||||||||
\(167\) | −1.30060e10 | −1.29396 | −0.646978 | − | 0.762508i | \(-0.723968\pi\) | ||||
−0.646978 | + | 0.762508i | \(0.723968\pi\) | |||||||
\(168\) | 1.75622e10 | 1.70093 | ||||||||
\(169\) | 1.10648e10 | 1.04341 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.11061e9 | −0.278204 | ||||||||
\(172\) | 1.28544e7 | 0.00111988 | ||||||||
\(173\) | 4.63053e9 | 0.393028 | 0.196514 | − | 0.980501i | \(-0.437038\pi\) | ||||
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(174\) | −3.96593e9 | −0.328000 | ||||||||
\(175\) | 2.83214e9 | 0.228267 | ||||||||
\(176\) | 1.47901e10 | 1.16188 | ||||||||
\(177\) | −1.05767e10 | −0.809976 | ||||||||
\(178\) | −1.02763e10 | −0.767271 | ||||||||
\(179\) | −1.45886e9 | −0.106212 | −0.0531062 | − | 0.998589i | \(-0.516912\pi\) | ||||
−0.0531062 | + | 0.998589i | \(0.516912\pi\) | |||||||
\(180\) | 4.86973e7 | 0.00345763 | ||||||||
\(181\) | −7.76243e9 | −0.537582 | −0.268791 | − | 0.963199i | \(-0.586624\pi\) | ||||
−0.268791 | + | 0.963199i | \(0.586624\pi\) | |||||||
\(182\) | −3.09732e10 | −2.09250 | ||||||||
\(183\) | 6.55661e9 | 0.432165 | ||||||||
\(184\) | −2.40075e10 | −1.54407 | ||||||||
\(185\) | 2.28764e10 | 1.43587 | ||||||||
\(186\) | −2.97355e10 | −1.82166 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.53969e7 | −0.00556960 | ||||||||
\(189\) | −2.02048e10 | −1.15180 | ||||||||
\(190\) | −1.43197e10 | −0.797156 | ||||||||
\(191\) | −3.61087e9 | −0.196319 | −0.0981595 | − | 0.995171i | \(-0.531296\pi\) | ||||
−0.0981595 | + | 0.995171i | \(0.531296\pi\) | |||||||
\(192\) | −2.18744e10 | −1.16166 | ||||||||
\(193\) | −1.09453e10 | −0.567833 | −0.283917 | − | 0.958849i | \(-0.591634\pi\) | ||||
−0.283917 | + | 0.958849i | \(0.591634\pi\) | |||||||
\(194\) | −2.26106e10 | −1.14605 | ||||||||
\(195\) | −3.04695e10 | −1.50907 | ||||||||
\(196\) | −2.84714e8 | −0.0137803 | ||||||||
\(197\) | −3.82220e9 | −0.180807 | −0.0904034 | − | 0.995905i | \(-0.528816\pi\) | ||||
−0.0904034 | + | 0.995905i | \(0.528816\pi\) | |||||||
\(198\) | 8.06234e9 | 0.372793 | ||||||||
\(199\) | 1.97634e10 | 0.893352 | 0.446676 | − | 0.894696i | \(-0.352608\pi\) | ||||
0.446676 | + | 0.894696i | \(0.352608\pi\) | |||||||
\(200\) | −3.52802e9 | −0.155918 | ||||||||
\(201\) | −2.07846e10 | −0.898174 | ||||||||
\(202\) | 1.78603e10 | 0.754757 | ||||||||
\(203\) | 1.02362e10 | 0.423065 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.79930e10 | −0.711559 | ||||||||
\(206\) | −3.44990e10 | −1.33476 | ||||||||
\(207\) | −1.29326e10 | −0.489575 | ||||||||
\(208\) | 3.81284e10 | 1.41242 | ||||||||
\(209\) | 2.82964e10 | 1.02582 | ||||||||
\(210\) | 4.35518e10 | 1.54532 | ||||||||
\(211\) | −4.98585e9 | −0.173168 | −0.0865840 | − | 0.996245i | \(-0.527595\pi\) | ||||
−0.0865840 | + | 0.996245i | \(0.527595\pi\) | |||||||
\(212\) | 2.32498e8 | 0.00790511 | ||||||||
\(213\) | −2.52635e10 | −0.840978 | ||||||||
\(214\) | −3.71239e10 | −1.21002 | ||||||||
\(215\) | 2.73453e9 | 0.0872790 | ||||||||
\(216\) | 2.51692e10 | 0.786735 | ||||||||
\(217\) | 7.67483e10 | 2.34963 | ||||||||
\(218\) | −1.89358e10 | −0.567845 | ||||||||
\(219\) | 4.00349e10 | 1.17609 | ||||||||
\(220\) | −4.42986e8 | −0.0127493 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.45374e10 | −1.78329 | ||||||||
\(223\) | −6.96358e10 | −1.88565 | −0.942824 | − | 0.333291i | \(-0.891841\pi\) | ||||
−0.942824 | + | 0.333291i | \(0.891841\pi\) | |||||||
\(224\) | 1.30880e9 | 0.0347343 | ||||||||
\(225\) | −1.90050e9 | −0.0494364 | ||||||||
\(226\) | −5.25236e10 | −1.33927 | ||||||||
\(227\) | −2.88086e10 | −0.720122 | −0.360061 | − | 0.932929i | \(-0.617244\pi\) | ||||
−0.360061 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(228\) | −4.82167e8 | −0.0118165 | ||||||||
\(229\) | −7.61079e9 | −0.182882 | −0.0914408 | − | 0.995811i | \(-0.529147\pi\) | ||||
−0.0914408 | + | 0.995811i | \(0.529147\pi\) | |||||||
\(230\) | −5.95353e10 | −1.40281 | ||||||||
\(231\) | −8.60602e10 | −1.98860 | ||||||||
\(232\) | −1.27513e10 | −0.288974 | ||||||||
\(233\) | −6.47083e10 | −1.43833 | −0.719165 | − | 0.694839i | \(-0.755475\pi\) | ||||
−0.719165 | + | 0.694839i | \(0.755475\pi\) | |||||||
\(234\) | 2.07845e10 | 0.453178 | ||||||||
\(235\) | −2.02939e10 | −0.434071 | ||||||||
\(236\) | −3.96420e8 | −0.00831863 | ||||||||
\(237\) | 8.72962e10 | 1.79733 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.98151e10 | 0.789328 | 0.394664 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(240\) | −5.36128e10 | −1.04308 | ||||||||
\(241\) | −6.98581e10 | −1.33395 | −0.666975 | − | 0.745080i | \(-0.732411\pi\) | ||||
−0.666975 | + | 0.745080i | \(0.732411\pi\) | |||||||
\(242\) | −2.03023e10 | −0.380518 | ||||||||
\(243\) | 3.34653e10 | 0.615696 | ||||||||
\(244\) | 2.45744e8 | 0.00443842 | ||||||||
\(245\) | −6.05678e10 | −1.07397 | ||||||||
\(246\) | 5.07605e10 | 0.883727 | ||||||||
\(247\) | 7.29474e10 | 1.24702 | ||||||||
\(248\) | −9.56058e10 | −1.60491 | ||||||||
\(249\) | −1.21147e10 | −0.199717 | ||||||||
\(250\) | −6.51878e10 | −1.05545 | ||||||||
\(251\) | 9.47934e10 | 1.50746 | 0.753731 | − | 0.657183i | \(-0.228252\pi\) | ||||
0.753731 | + | 0.657183i | \(0.228252\pi\) | |||||||
\(252\) | 3.54586e8 | 0.00553884 | ||||||||
\(253\) | 1.17644e11 | 1.80521 | ||||||||
\(254\) | 2.97219e10 | 0.448049 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.43124e9 | −0.0353792 | ||||||||
\(257\) | 3.19715e10 | 0.457156 | 0.228578 | − | 0.973526i | \(-0.426592\pi\) | ||||
0.228578 | + | 0.973526i | \(0.426592\pi\) | |||||||
\(258\) | −7.71446e9 | −0.108397 | ||||||||
\(259\) | 1.66573e11 | 2.30015 | ||||||||
\(260\) | −1.14201e9 | −0.0154985 | ||||||||
\(261\) | −6.86898e9 | −0.0916242 | ||||||||
\(262\) | 1.32635e11 | 1.73902 | ||||||||
\(263\) | −1.28301e11 | −1.65360 | −0.826798 | − | 0.562498i | \(-0.809840\pi\) | ||||
−0.826798 | + | 0.562498i | \(0.809840\pi\) | |||||||
\(264\) | 1.07206e11 | 1.35831 | ||||||||
\(265\) | 4.94597e10 | 0.616091 | ||||||||
\(266\) | −1.04268e11 | −1.27698 | ||||||||
\(267\) | −7.36094e10 | −0.886406 | ||||||||
\(268\) | −7.79016e8 | −0.00922444 | ||||||||
\(269\) | −3.10336e10 | −0.361366 | −0.180683 | − | 0.983541i | \(-0.557831\pi\) | ||||
−0.180683 | + | 0.983541i | \(0.557831\pi\) | |||||||
\(270\) | 6.24161e10 | 0.714759 | ||||||||
\(271\) | −1.15285e11 | −1.29841 | −0.649203 | − | 0.760615i | \(-0.724897\pi\) | ||||
−0.649203 | + | 0.760615i | \(0.724897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.21861e11 | −2.41740 | ||||||||
\(274\) | 9.17174e10 | 0.983047 | ||||||||
\(275\) | 1.72883e10 | 0.182287 | ||||||||
\(276\) | −2.00464e9 | −0.0207944 | ||||||||
\(277\) | −1.43535e11 | −1.46487 | −0.732436 | − | 0.680835i | \(-0.761617\pi\) | ||||
−0.732436 | + | 0.680835i | \(0.761617\pi\) | |||||||
\(278\) | 1.87312e11 | 1.88089 | ||||||||
\(279\) | −5.15018e10 | −0.508866 | ||||||||
\(280\) | 1.40028e11 | 1.36146 | ||||||||
\(281\) | 9.65223e10 | 0.923526 | 0.461763 | − | 0.887003i | \(-0.347217\pi\) | ||||
0.461763 | + | 0.887003i | \(0.347217\pi\) | |||||||
\(282\) | 5.72517e10 | 0.539098 | ||||||||
\(283\) | 1.85654e10 | 0.172055 | 0.0860273 | − | 0.996293i | \(-0.472583\pi\) | ||||
0.0860273 | + | 0.996293i | \(0.472583\pi\) | |||||||
\(284\) | −9.46885e8 | −0.00863703 | ||||||||
\(285\) | −1.02572e11 | −0.920932 | ||||||||
\(286\) | −1.89071e11 | −1.67101 | ||||||||
\(287\) | −1.31015e11 | −1.13986 | ||||||||
\(288\) | −8.78270e8 | −0.00752249 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −3.16214e10 | −0.262537 | ||||||||
\(291\) | −1.61960e11 | −1.32400 | ||||||||
\(292\) | 1.50052e9 | 0.0120787 | ||||||||
\(293\) | −6.88004e10 | −0.545364 | −0.272682 | − | 0.962104i | \(-0.587911\pi\) | ||||
−0.272682 | + | 0.962104i | \(0.587911\pi\) | |||||||
\(294\) | 1.70869e11 | 1.33383 | ||||||||
\(295\) | −8.43311e10 | −0.648319 | ||||||||
\(296\) | −2.07501e11 | −1.57111 | ||||||||
\(297\) | −1.23337e11 | −0.919791 | ||||||||
\(298\) | −2.45842e11 | −1.80586 | ||||||||
\(299\) | 3.03284e11 | 2.19447 | ||||||||
\(300\) | −2.94591e8 | −0.00209978 | ||||||||
\(301\) | 1.99113e10 | 0.139814 | ||||||||
\(302\) | 2.45032e11 | 1.69509 | ||||||||
\(303\) | 1.27933e11 | 0.871949 | ||||||||
\(304\) | 1.28355e11 | 0.861950 | ||||||||
\(305\) | 5.22775e10 | 0.345912 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.12146e10 | 0.586059 | 0.293030 | − | 0.956103i | \(-0.405337\pi\) | ||||
0.293030 | + | 0.956103i | \(0.405337\pi\) | |||||||
\(308\) | −3.22557e9 | −0.0204234 | ||||||||
\(309\) | −2.47116e11 | −1.54201 | ||||||||
\(310\) | −2.37089e11 | −1.45809 | ||||||||
\(311\) | 2.25280e11 | 1.36553 | 0.682763 | − | 0.730640i | \(-0.260778\pi\) | ||||
0.682763 | + | 0.730640i | \(0.260778\pi\) | |||||||
\(312\) | 2.76374e11 | 1.65121 | ||||||||
\(313\) | 1.70381e11 | 1.00340 | 0.501699 | − | 0.865043i | \(-0.332709\pi\) | ||||
0.501699 | + | 0.865043i | \(0.332709\pi\) | |||||||
\(314\) | −8.49599e8 | −0.00493209 | ||||||||
\(315\) | 7.54315e10 | 0.431674 | ||||||||
\(316\) | 3.27190e9 | 0.0184590 | ||||||||
\(317\) | −1.59870e11 | −0.889203 | −0.444602 | − | 0.895728i | \(-0.646655\pi\) | ||||
−0.444602 | + | 0.895728i | \(0.646655\pi\) | |||||||
\(318\) | −1.39532e11 | −0.765160 | ||||||||
\(319\) | 6.24853e10 | 0.337847 | ||||||||
\(320\) | −1.74410e11 | −0.929814 | ||||||||
\(321\) | −2.65918e11 | −1.39790 | ||||||||
\(322\) | −4.33501e11 | −2.24719 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.84776e9 | 0.0143566 | ||||||||
\(325\) | 4.45689e10 | 0.221594 | ||||||||
\(326\) | 9.30914e10 | 0.456489 | ||||||||
\(327\) | −1.35637e11 | −0.656015 | ||||||||
\(328\) | 1.63206e11 | 0.778580 | ||||||||
\(329\) | −1.47769e11 | −0.695345 | ||||||||
\(330\) | 2.65855e11 | 1.23405 | ||||||||
\(331\) | 1.59564e11 | 0.730648 | 0.365324 | − | 0.930880i | \(-0.380958\pi\) | ||||
0.365324 | + | 0.930880i | \(0.380958\pi\) | |||||||
\(332\) | −4.54062e8 | −0.00205113 | ||||||||
\(333\) | −1.11778e11 | −0.498149 | ||||||||
\(334\) | 2.92552e11 | 1.28630 | ||||||||
\(335\) | −1.65721e11 | −0.718914 | ||||||||
\(336\) | −3.90377e11 | −1.67093 | ||||||||
\(337\) | 1.20392e11 | 0.508466 | 0.254233 | − | 0.967143i | \(-0.418177\pi\) | ||||
0.254233 | + | 0.967143i | \(0.418177\pi\) | |||||||
\(338\) | −2.48888e11 | −1.03724 | ||||||||
\(339\) | −3.76226e11 | −1.54721 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.68498e11 | 1.87634 | ||||||||
\(342\) | 6.99688e10 | 0.276559 | ||||||||
\(343\) | −6.35449e10 | −0.247889 | ||||||||
\(344\) | −2.48036e10 | −0.0954996 | ||||||||
\(345\) | −4.26451e11 | −1.62063 | ||||||||
\(346\) | −1.04157e11 | −0.390703 | ||||||||
\(347\) | 1.84318e11 | 0.682472 | 0.341236 | − | 0.939978i | \(-0.389155\pi\) | ||||
0.341236 | + | 0.939978i | \(0.389155\pi\) | |||||||
\(348\) | −1.06474e9 | −0.00389168 | ||||||||
\(349\) | −3.67126e10 | −0.132465 | −0.0662325 | − | 0.997804i | \(-0.521098\pi\) | ||||
−0.0662325 | + | 0.997804i | \(0.521098\pi\) | |||||||
\(350\) | −6.37050e10 | −0.226917 | ||||||||
\(351\) | −3.17960e11 | −1.11812 | ||||||||
\(352\) | 7.98938e9 | 0.0277378 | ||||||||
\(353\) | 2.10064e11 | 0.720055 | 0.360027 | − | 0.932942i | \(-0.382767\pi\) | ||||
0.360027 | + | 0.932942i | \(0.382767\pi\) | |||||||
\(354\) | 2.37909e11 | 0.805185 | ||||||||
\(355\) | −2.01432e11 | −0.673134 | ||||||||
\(356\) | −2.75891e9 | −0.00910358 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.28150e10 | 0.105584 | ||||||||
\(359\) | −4.88942e11 | −1.55358 | −0.776788 | − | 0.629762i | \(-0.783152\pi\) | ||||
−0.776788 | + | 0.629762i | \(0.783152\pi\) | |||||||
\(360\) | −9.39656e10 | −0.294854 | ||||||||
\(361\) | −7.71182e10 | −0.238987 | ||||||||
\(362\) | 1.74605e11 | 0.534402 | ||||||||
\(363\) | −1.45425e11 | −0.439601 | ||||||||
\(364\) | −8.31544e9 | −0.0248273 | ||||||||
\(365\) | 3.19209e11 | 0.941362 | ||||||||
\(366\) | −1.47482e11 | −0.429608 | ||||||||
\(367\) | 2.50484e11 | 0.720748 | 0.360374 | − | 0.932808i | \(-0.382649\pi\) | ||||
0.360374 | + | 0.932808i | \(0.382649\pi\) | |||||||
\(368\) | 5.33645e11 | 1.51683 | ||||||||
\(369\) | 8.79171e10 | 0.246862 | ||||||||
\(370\) | −5.14573e11 | −1.42738 | ||||||||
\(371\) | 3.60137e11 | 0.986926 | ||||||||
\(372\) | −7.98314e9 | −0.0216138 | ||||||||
\(373\) | 3.12819e11 | 0.836766 | 0.418383 | − | 0.908271i | \(-0.362597\pi\) | ||||
0.418383 | + | 0.908271i | \(0.362597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.66939e11 | −1.21933 | ||||||||
\(376\) | 1.84076e11 | 0.474955 | ||||||||
\(377\) | 1.61086e11 | 0.410696 | ||||||||
\(378\) | 4.54478e11 | 1.14499 | ||||||||
\(379\) | 1.31869e11 | 0.328298 | 0.164149 | − | 0.986436i | \(-0.447512\pi\) | ||||
0.164149 | + | 0.986436i | \(0.447512\pi\) | |||||||
\(380\) | −3.84444e9 | −0.00945817 | ||||||||
\(381\) | 2.12898e11 | 0.517618 | ||||||||
\(382\) | 8.12215e10 | 0.195158 | ||||||||
\(383\) | 4.82378e11 | 1.14549 | 0.572747 | − | 0.819732i | \(-0.305878\pi\) | ||||
0.572747 | + | 0.819732i | \(0.305878\pi\) | |||||||
\(384\) | 4.80490e11 | 1.12770 | ||||||||
\(385\) | −6.86180e11 | −1.59171 | ||||||||
\(386\) | 2.46200e11 | 0.564475 | ||||||||
\(387\) | −1.33614e10 | −0.0302798 | ||||||||
\(388\) | −6.07032e9 | −0.0135978 | ||||||||
\(389\) | −5.41960e10 | −0.120004 | −0.0600018 | − | 0.998198i | \(-0.519111\pi\) | ||||
−0.0600018 | + | 0.998198i | \(0.519111\pi\) | |||||||
\(390\) | 6.85367e11 | 1.50014 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.49381e11 | 1.17513 | ||||||||
\(393\) | 9.50066e11 | 2.00903 | ||||||||
\(394\) | 8.59749e10 | 0.179737 | ||||||||
\(395\) | 6.96035e11 | 1.43861 | ||||||||
\(396\) | 2.16451e9 | 0.00442315 | ||||||||
\(397\) | 6.99376e11 | 1.41304 | 0.706519 | − | 0.707694i | \(-0.250265\pi\) | ||||
0.706519 | + | 0.707694i | \(0.250265\pi\) | |||||||
\(398\) | −4.44550e11 | −0.888068 | ||||||||
\(399\) | −7.46871e11 | −1.47526 | ||||||||
\(400\) | 7.84216e10 | 0.153167 | ||||||||
\(401\) | 2.39362e10 | 0.0462280 | 0.0231140 | − | 0.999733i | \(-0.492642\pi\) | ||||
0.0231140 | + | 0.999733i | \(0.492642\pi\) | |||||||
\(402\) | 4.67521e11 | 0.892861 | ||||||||
\(403\) | 1.20778e12 | 2.28094 | ||||||||
\(404\) | 4.79498e9 | 0.00895510 | ||||||||
\(405\) | 6.05809e11 | 1.11889 | ||||||||
\(406\) | −2.30249e11 | −0.420562 | ||||||||
\(407\) | 1.01682e12 | 1.83683 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.57952e11 | 0.632514 | 0.316257 | − | 0.948674i | \(-0.397574\pi\) | ||||
0.316257 | + | 0.948674i | \(0.397574\pi\) | |||||||
\(410\) | 4.04727e11 | 0.707350 | ||||||||
\(411\) | 6.56971e11 | 1.13569 | ||||||||
\(412\) | −9.26201e9 | −0.0158368 | ||||||||
\(413\) | −6.14050e11 | −1.03855 | ||||||||
\(414\) | 2.90900e11 | 0.486679 | ||||||||
\(415\) | −9.65934e10 | −0.159857 | ||||||||
\(416\) | 2.05964e10 | 0.0337188 | ||||||||
\(417\) | 1.34171e12 | 2.17294 | ||||||||
\(418\) | −6.36487e11 | −1.01976 | ||||||||
\(419\) | 1.71160e11 | 0.271293 | 0.135646 | − | 0.990757i | \(-0.456689\pi\) | ||||
0.135646 | + | 0.990757i | \(0.456689\pi\) | |||||||
\(420\) | 1.16924e10 | 0.0183351 | ||||||||
\(421\) | 1.13078e11 | 0.175432 | 0.0877159 | − | 0.996146i | \(-0.472043\pi\) | ||||
0.0877159 | + | 0.996146i | \(0.472043\pi\) | |||||||
\(422\) | 1.12150e11 | 0.172144 | ||||||||
\(423\) | 9.91598e10 | 0.150593 | ||||||||
\(424\) | −4.48625e11 | −0.674119 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.68266e11 | 0.836004 | ||||||||
\(427\) | 3.80655e11 | 0.554122 | ||||||||
\(428\) | −9.96672e9 | −0.0143567 | ||||||||
\(429\) | −1.35432e12 | −1.93047 | ||||||||
\(430\) | −6.15094e10 | −0.0867627 | ||||||||
\(431\) | −1.20420e12 | −1.68093 | −0.840466 | − | 0.541864i | \(-0.817719\pi\) | ||||
−0.840466 | + | 0.541864i | \(0.817719\pi\) | |||||||
\(432\) | −5.59468e11 | −0.772856 | ||||||||
\(433\) | 2.53234e11 | 0.346200 | 0.173100 | − | 0.984904i | \(-0.444622\pi\) | ||||
0.173100 | + | 0.984904i | \(0.444622\pi\) | |||||||
\(434\) | −1.72634e12 | −2.33573 | ||||||||
\(435\) | −2.26504e11 | −0.303301 | ||||||||
\(436\) | −5.08373e9 | −0.00673741 | ||||||||
\(437\) | 1.02097e12 | 1.33921 | ||||||||
\(438\) | −9.00528e11 | −1.16913 | ||||||||
\(439\) | −6.92143e11 | −0.889417 | −0.444709 | − | 0.895675i | \(-0.646693\pi\) | ||||
−0.444709 | + | 0.895675i | \(0.646693\pi\) | |||||||
\(440\) | 8.54779e11 | 1.08722 | ||||||||
\(441\) | 2.95945e11 | 0.372595 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.01866e11 | 0.495752 | 0.247876 | − | 0.968792i | \(-0.420267\pi\) | ||||
0.247876 | + | 0.968792i | \(0.420267\pi\) | |||||||
\(444\) | −1.73265e10 | −0.0211586 | ||||||||
\(445\) | −5.86907e11 | −0.709495 | ||||||||
\(446\) | 1.56636e12 | 1.87449 | ||||||||
\(447\) | −1.76097e12 | −2.08625 | ||||||||
\(448\) | −1.26995e12 | −1.48949 | ||||||||
\(449\) | 1.26065e11 | 0.146381 | 0.0731907 | − | 0.997318i | \(-0.476682\pi\) | ||||
0.0731907 | + | 0.997318i | \(0.476682\pi\) | |||||||
\(450\) | 4.27491e10 | 0.0491440 | ||||||||
\(451\) | −7.99758e11 | −0.910257 | ||||||||
\(452\) | −1.41011e10 | −0.0158902 | ||||||||
\(453\) | 1.75516e12 | 1.95828 | ||||||||
\(454\) | 6.48009e11 | 0.715863 | ||||||||
\(455\) | −1.76896e12 | −1.93493 | ||||||||
\(456\) | 9.30382e11 | 1.00767 | ||||||||
\(457\) | 1.28002e12 | 1.37276 | 0.686380 | − | 0.727243i | \(-0.259199\pi\) | ||||
0.686380 | + | 0.727243i | \(0.259199\pi\) | |||||||
\(458\) | 1.71194e11 | 0.181800 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.59835e10 | −0.0166442 | ||||||||
\(461\) | −2.46980e11 | −0.254687 | −0.127344 | − | 0.991859i | \(-0.540645\pi\) | ||||
−0.127344 | + | 0.991859i | \(0.540645\pi\) | |||||||
\(462\) | 1.93580e12 | 1.97684 | ||||||||
\(463\) | −1.06166e12 | −1.07367 | −0.536833 | − | 0.843688i | \(-0.680380\pi\) | ||||
−0.536833 | + | 0.843688i | \(0.680380\pi\) | |||||||
\(464\) | 2.83439e11 | 0.283876 | ||||||||
\(465\) | −1.69827e12 | −1.68449 | ||||||||
\(466\) | 1.45552e12 | 1.42982 | ||||||||
\(467\) | 2.02752e11 | 0.197260 | 0.0986302 | − | 0.995124i | \(-0.468554\pi\) | ||||
0.0986302 | + | 0.995124i | \(0.468554\pi\) | |||||||
\(468\) | 5.58006e9 | 0.00537690 | ||||||||
\(469\) | −1.20669e12 | −1.15164 | ||||||||
\(470\) | 4.56483e11 | 0.431503 | ||||||||
\(471\) | −6.08567e9 | −0.00569790 | ||||||||
\(472\) | 7.64927e11 | 0.709383 | ||||||||
\(473\) | 1.21545e11 | 0.111651 | ||||||||
\(474\) | −1.96360e12 | −1.78670 | ||||||||
\(475\) | 1.50036e11 | 0.135231 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.41669e11 | −0.213741 | ||||||||
\(478\) | −8.95585e11 | −0.784659 | ||||||||
\(479\) | 1.25765e12 | 1.09157 | 0.545783 | − | 0.837927i | \(-0.316232\pi\) | ||||
0.545783 | + | 0.837927i | \(0.316232\pi\) | |||||||
\(480\) | −2.89609e10 | −0.0249015 | ||||||||
\(481\) | 2.62133e12 | 2.23290 | ||||||||
\(482\) | 1.57136e12 | 1.32606 | ||||||||
\(483\) | −3.10517e12 | −2.59611 | ||||||||
\(484\) | −5.45058e9 | −0.00451480 | ||||||||
\(485\) | −1.29135e12 | −1.05976 | ||||||||
\(486\) | −7.52754e11 | −0.612054 | ||||||||
\(487\) | −3.15297e11 | −0.254003 | −0.127002 | − | 0.991903i | \(-0.540535\pi\) | ||||
−0.127002 | + | 0.991903i | \(0.540535\pi\) | |||||||
\(488\) | −4.74184e11 | −0.378493 | ||||||||
\(489\) | 6.66813e11 | 0.527369 | ||||||||
\(490\) | 1.36239e12 | 1.06762 | ||||||||
\(491\) | −1.29498e12 | −1.00553 | −0.502765 | − | 0.864423i | \(-0.667684\pi\) | ||||
−0.502765 | + | 0.864423i | \(0.667684\pi\) | |||||||
\(492\) | 1.36278e10 | 0.0104853 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.64085e12 | −1.23964 | ||||||||
\(495\) | 4.60460e11 | 0.344721 | ||||||||
\(496\) | 2.12515e12 | 1.57660 | ||||||||
\(497\) | −1.46671e12 | −1.07830 | ||||||||
\(498\) | 2.72502e11 | 0.198535 | ||||||||
\(499\) | −2.19676e12 | −1.58610 | −0.793050 | − | 0.609157i | \(-0.791508\pi\) | ||||
−0.793050 | + | 0.609157i | \(0.791508\pi\) | |||||||
\(500\) | −1.75011e10 | −0.0125227 | ||||||||
\(501\) | 2.09554e12 | 1.48603 | ||||||||
\(502\) | −2.13224e12 | −1.49855 | ||||||||
\(503\) | 8.02912e10 | 0.0559258 | 0.0279629 | − | 0.999609i | \(-0.491098\pi\) | ||||
0.0279629 | + | 0.999609i | \(0.491098\pi\) | |||||||
\(504\) | −6.84203e11 | −0.472332 | ||||||||
\(505\) | 1.02004e12 | 0.697923 | ||||||||
\(506\) | −2.64624e12 | −1.79453 | ||||||||
\(507\) | −1.78278e12 | −1.19829 | ||||||||
\(508\) | 7.97949e9 | 0.00531605 | ||||||||
\(509\) | −2.24252e12 | −1.48083 | −0.740417 | − | 0.672148i | \(-0.765372\pi\) | ||||
−0.740417 | + | 0.672148i | \(0.765372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.32429e12 | 1.50798 | ||||||||
\(512\) | 1.58155e12 | 1.01711 | ||||||||
\(513\) | −1.07038e12 | −0.682352 | ||||||||
\(514\) | −7.19154e11 | −0.454452 | ||||||||
\(515\) | −1.97032e12 | −1.23425 | ||||||||
\(516\) | −2.07111e9 | −0.00128612 | ||||||||
\(517\) | −9.02030e11 | −0.555282 | ||||||||
\(518\) | −3.74682e12 | −2.28654 | ||||||||
\(519\) | −7.46078e11 | −0.451368 | ||||||||
\(520\) | 2.20360e12 | 1.32165 | ||||||||
\(521\) | 4.21783e11 | 0.250795 | 0.125398 | − | 0.992107i | \(-0.459979\pi\) | ||||
0.125398 | + | 0.992107i | \(0.459979\pi\) | |||||||
\(522\) | 1.54508e11 | 0.0910823 | ||||||||
\(523\) | 6.85779e11 | 0.400799 | 0.200399 | − | 0.979714i | \(-0.435776\pi\) | ||||
0.200399 | + | 0.979714i | \(0.435776\pi\) | |||||||
\(524\) | 3.56088e10 | 0.0206332 | ||||||||
\(525\) | −4.56318e11 | −0.262151 | ||||||||
\(526\) | 2.88595e12 | 1.64382 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.38299e12 | −1.33435 | ||||||||
\(529\) | 2.44361e12 | 1.35669 | ||||||||
\(530\) | −1.11253e12 | −0.612447 | ||||||||
\(531\) | 4.12057e11 | 0.224922 | ||||||||
\(532\) | −2.79930e10 | −0.0151512 | ||||||||
\(533\) | −2.06176e12 | −1.10653 | ||||||||
\(534\) | 1.65574e12 | 0.881163 | ||||||||
\(535\) | −2.12024e12 | −1.11890 | ||||||||
\(536\) | 1.50318e12 | 0.786627 | ||||||||
\(537\) | 2.35054e11 | 0.121978 | ||||||||
\(538\) | 6.98057e11 | 0.359228 | ||||||||
\(539\) | −2.69213e12 | −1.37387 | ||||||||
\(540\) | 1.67570e10 | 0.00848054 | ||||||||
\(541\) | −1.41665e12 | −0.711011 | −0.355505 | − | 0.934674i | \(-0.615691\pi\) | ||||
−0.355505 | + | 0.934674i | \(0.615691\pi\) | |||||||
\(542\) | 2.59317e12 | 1.29073 | ||||||||
\(543\) | 1.25069e12 | 0.617379 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.08147e12 | −0.525085 | ||||||||
\(546\) | 4.99045e12 | 2.40310 | ||||||||
\(547\) | 1.74223e12 | 0.832076 | 0.416038 | − | 0.909347i | \(-0.363418\pi\) | ||||
0.416038 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(548\) | 2.46235e10 | 0.0116637 | ||||||||
\(549\) | −2.55438e11 | −0.120008 | ||||||||
\(550\) | −3.88877e11 | −0.181209 | ||||||||
\(551\) | 5.42277e11 | 0.250633 | ||||||||
\(552\) | 3.86813e12 | 1.77327 | ||||||||
\(553\) | 5.06813e12 | 2.30454 | ||||||||
\(554\) | 3.22862e12 | 1.45621 | ||||||||
\(555\) | −3.68588e12 | −1.64901 | ||||||||
\(556\) | 5.02879e10 | 0.0223166 | ||||||||
\(557\) | 9.15412e11 | 0.402966 | 0.201483 | − | 0.979492i | \(-0.435424\pi\) | ||||
0.201483 | + | 0.979492i | \(0.435424\pi\) | |||||||
\(558\) | 1.15846e12 | 0.505856 | ||||||||
\(559\) | 3.13340e11 | 0.135726 | ||||||||
\(560\) | −3.11258e12 | −1.33744 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.17113e12 | −0.918064 | ||||||||
\(563\) | −3.05435e12 | −1.28124 | −0.640620 | − | 0.767858i | \(-0.721323\pi\) | ||||
−0.640620 | + | 0.767858i | \(0.721323\pi\) | |||||||
\(564\) | 1.53705e10 | 0.00639634 | ||||||||
\(565\) | −2.99975e12 | −1.23842 | ||||||||
\(566\) | −4.17603e11 | −0.171037 | ||||||||
\(567\) | 4.41115e12 | 1.79237 | ||||||||
\(568\) | 1.82709e12 | 0.736535 | ||||||||
\(569\) | −2.05865e11 | −0.0823335 | −0.0411668 | − | 0.999152i | \(-0.513107\pi\) | ||||
−0.0411668 | + | 0.999152i | \(0.513107\pi\) | |||||||
\(570\) | 2.30721e12 | 0.915485 | ||||||||
\(571\) | 1.37439e12 | 0.541062 | 0.270531 | − | 0.962711i | \(-0.412801\pi\) | ||||
0.270531 | + | 0.962711i | \(0.412801\pi\) | |||||||
\(572\) | −5.07603e10 | −0.0198263 | ||||||||
\(573\) | 5.81789e11 | 0.225460 | ||||||||
\(574\) | 2.94699e12 | 1.13312 | ||||||||
\(575\) | 6.23787e11 | 0.237975 | ||||||||
\(576\) | 8.52199e11 | 0.322582 | ||||||||
\(577\) | −1.39056e12 | −0.522275 | −0.261138 | − | 0.965302i | \(-0.584098\pi\) | ||||
−0.261138 | + | 0.965302i | \(0.584098\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.76353e12 | 0.652121 | ||||||||
\(580\) | −8.48946e9 | −0.00311497 | ||||||||
\(581\) | −7.03337e11 | −0.256077 | ||||||||
\(582\) | 3.64306e12 | 1.31617 | ||||||||
\(583\) | 2.19840e12 | 0.788130 | ||||||||
\(584\) | −2.89539e12 | −1.03003 | ||||||||
\(585\) | 1.18705e12 | 0.419053 | ||||||||
\(586\) | 1.54757e12 | 0.542138 | ||||||||
\(587\) | −2.02089e12 | −0.702539 | −0.351269 | − | 0.936274i | \(-0.614250\pi\) | ||||
−0.351269 | + | 0.936274i | \(0.614250\pi\) | |||||||
\(588\) | 4.58736e10 | 0.0158258 | ||||||||
\(589\) | 4.06584e12 | 1.39198 | ||||||||
\(590\) | 1.89691e12 | 0.644484 | ||||||||
\(591\) | 6.15837e11 | 0.207645 | ||||||||
\(592\) | 4.61238e12 | 1.54340 | ||||||||
\(593\) | −2.56146e12 | −0.850630 | −0.425315 | − | 0.905045i | \(-0.639837\pi\) | ||||
−0.425315 | + | 0.905045i | \(0.639837\pi\) | |||||||
\(594\) | 2.77429e12 | 0.914351 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.60017e10 | −0.0214263 | ||||||||
\(597\) | −3.18431e12 | −1.02596 | ||||||||
\(598\) | −6.82194e12 | −2.18149 | ||||||||
\(599\) | −1.66546e12 | −0.528583 | −0.264291 | − | 0.964443i | \(-0.585138\pi\) | ||||
−0.264291 | + | 0.964443i | \(0.585138\pi\) | |||||||
\(600\) | 5.68439e11 | 0.179062 | ||||||||
\(601\) | 2.30323e12 | 0.720114 | 0.360057 | − | 0.932930i | \(-0.382757\pi\) | ||||
0.360057 | + | 0.932930i | \(0.382757\pi\) | |||||||
\(602\) | −4.47875e11 | −0.138987 | ||||||||
\(603\) | 8.09745e11 | 0.249414 | ||||||||
\(604\) | 6.57842e10 | 0.0201120 | ||||||||
\(605\) | −1.15951e12 | −0.351865 | ||||||||
\(606\) | −2.87767e12 | −0.866791 | ||||||||
\(607\) | −5.08694e12 | −1.52092 | −0.760461 | − | 0.649383i | \(-0.775027\pi\) | ||||
−0.760461 | + | 0.649383i | \(0.775027\pi\) | |||||||
\(608\) | 6.93356e10 | 0.0205774 | ||||||||
\(609\) | −1.64927e12 | −0.485863 | ||||||||
\(610\) | −1.17591e12 | −0.343866 | ||||||||
\(611\) | −2.32541e12 | −0.675016 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.87867e12 | 1.68154 | 0.840770 | − | 0.541393i | \(-0.182103\pi\) | ||||
0.840770 | + | 0.541393i | \(0.182103\pi\) | |||||||
\(614\) | −2.05174e12 | −0.582593 | ||||||||
\(615\) | 2.89906e12 | 0.817182 | ||||||||
\(616\) | 6.22401e12 | 1.74163 | ||||||||
\(617\) | 2.77401e12 | 0.770592 | 0.385296 | − | 0.922793i | \(-0.374099\pi\) | ||||
0.385296 | + | 0.922793i | \(0.374099\pi\) | |||||||
\(618\) | 5.55853e12 | 1.53289 | ||||||||
\(619\) | −1.51857e12 | −0.415744 | −0.207872 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207872 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(620\) | −6.36516e10 | −0.0173000 | ||||||||
\(621\) | −4.45016e12 | −1.20078 | ||||||||
\(622\) | −5.06734e12 | −1.35745 | ||||||||
\(623\) | −4.27351e12 | −1.13655 | ||||||||
\(624\) | −6.14330e12 | −1.62208 | ||||||||
\(625\) | −3.13169e12 | −0.820953 | ||||||||
\(626\) | −3.83249e12 | −0.997462 | ||||||||
\(627\) | −4.55915e12 | −1.17810 | ||||||||
\(628\) | −2.28093e8 | −5.85186e−5 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.69672e12 | −0.429120 | ||||||||
\(631\) | −6.49509e12 | −1.63100 | −0.815499 | − | 0.578759i | \(-0.803537\pi\) | ||||
−0.815499 | + | 0.578759i | \(0.803537\pi\) | |||||||
\(632\) | −6.31340e12 | −1.57411 | ||||||||
\(633\) | 8.03326e11 | 0.198873 | ||||||||
\(634\) | 3.59605e12 | 0.883944 | ||||||||
\(635\) | 1.69749e12 | 0.414310 | ||||||||
\(636\) | −3.74604e10 | −0.00907853 | ||||||||
\(637\) | −6.94025e12 | −1.67012 | ||||||||
\(638\) | −1.40552e12 | −0.335848 | ||||||||
\(639\) | 9.84235e11 | 0.233531 | ||||||||
\(640\) | 3.83107e12 | 0.902632 | ||||||||
\(641\) | 4.72982e12 | 1.10658 | 0.553291 | − | 0.832988i | \(-0.313372\pi\) | ||||
0.553291 | + | 0.832988i | \(0.313372\pi\) | |||||||
\(642\) | 5.98145e12 | 1.38963 | ||||||||
\(643\) | −9.58308e11 | −0.221083 | −0.110542 | − | 0.993872i | \(-0.535259\pi\) | ||||
−0.110542 | + | 0.993872i | \(0.535259\pi\) | |||||||
\(644\) | −1.16383e11 | −0.0266626 | ||||||||
\(645\) | −4.40591e11 | −0.100234 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.17064e12 | 0.262635 | 0.131317 | − | 0.991340i | \(-0.458079\pi\) | ||||
0.131317 | + | 0.991340i | \(0.458079\pi\) | |||||||
\(648\) | −5.49500e12 | −1.22428 | ||||||||
\(649\) | −3.74837e12 | −0.829357 | ||||||||
\(650\) | −1.00251e12 | −0.220283 | ||||||||
\(651\) | −1.23658e13 | −2.69841 | ||||||||
\(652\) | 2.49924e10 | 0.00541619 | ||||||||
\(653\) | 5.02539e12 | 1.08158 | 0.540792 | − | 0.841156i | \(-0.318125\pi\) | ||||
0.540792 | + | 0.841156i | \(0.318125\pi\) | |||||||
\(654\) | 3.05096e12 | 0.652134 | ||||||||
\(655\) | 7.57512e12 | 1.60807 | ||||||||
\(656\) | −3.62778e12 | −0.764844 | ||||||||
\(657\) | −1.55971e12 | −0.326588 | ||||||||
\(658\) | 3.32384e12 | 0.691232 | ||||||||
\(659\) | −3.15795e12 | −0.652261 | −0.326130 | − | 0.945325i | \(-0.605745\pi\) | ||||
−0.326130 | + | 0.945325i | \(0.605745\pi\) | |||||||
\(660\) | 7.13745e10 | 0.0146418 | ||||||||
\(661\) | −1.46675e12 | −0.298846 | −0.149423 | − | 0.988773i | \(-0.547742\pi\) | ||||
−0.149423 | + | 0.988773i | \(0.547742\pi\) | |||||||
\(662\) | −3.58916e12 | −0.726326 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.76152e11 | 0.174913 | ||||||||
\(665\) | −5.95499e12 | −1.18082 | ||||||||
\(666\) | 2.51430e12 | 0.495202 | ||||||||
\(667\) | 2.25455e12 | 0.441057 | ||||||||
\(668\) | 7.85418e10 | 0.0152618 | ||||||||
\(669\) | 1.12198e13 | 2.16555 | ||||||||
\(670\) | 3.72767e12 | 0.714661 | ||||||||
\(671\) | 2.32365e12 | 0.442505 | ||||||||
\(672\) | −2.10876e11 | −0.0398902 | ||||||||
\(673\) | −7.74648e12 | −1.45558 | −0.727791 | − | 0.685799i | \(-0.759453\pi\) | ||||
−0.727791 | + | 0.685799i | \(0.759453\pi\) | |||||||
\(674\) | −2.70804e12 | −0.505459 | ||||||||
\(675\) | −6.53971e11 | −0.121253 | ||||||||
\(676\) | −6.68193e10 | −0.0123067 | ||||||||
\(677\) | −7.62527e12 | −1.39510 | −0.697551 | − | 0.716535i | \(-0.745727\pi\) | ||||
−0.697551 | + | 0.716535i | \(0.745727\pi\) | |||||||
\(678\) | 8.46268e12 | 1.53806 | ||||||||
\(679\) | −9.40285e12 | −1.69764 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.64169e12 | 0.827016 | ||||||||
\(682\) | −1.05382e13 | −1.86525 | ||||||||
\(683\) | −6.54245e12 | −1.15040 | −0.575198 | − | 0.818014i | \(-0.695075\pi\) | ||||
−0.575198 | + | 0.818014i | \(0.695075\pi\) | |||||||
\(684\) | 1.87846e10 | 0.00328134 | ||||||||
\(685\) | 5.23820e12 | 0.909023 | ||||||||
\(686\) | 1.42935e12 | 0.246423 | ||||||||
\(687\) | 1.22626e12 | 0.210028 | ||||||||
\(688\) | 5.51340e11 | 0.0938148 | ||||||||
\(689\) | 5.66742e12 | 0.958073 | ||||||||
\(690\) | 9.59240e12 | 1.61104 | ||||||||
\(691\) | 4.12042e12 | 0.687528 | 0.343764 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343764 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(692\) | −2.79633e10 | −0.00463565 | ||||||||
\(693\) | 3.35280e12 | 0.552215 | ||||||||
\(694\) | −4.14597e12 | −0.678435 | ||||||||
\(695\) | 1.06978e13 | 1.73926 | ||||||||
\(696\) | 2.05451e12 | 0.331869 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 8.25798e11 | 0.131681 | ||||||||
\(699\) | 1.04259e13 | 1.65183 | ||||||||
\(700\) | −1.71030e10 | −0.00269234 | ||||||||
\(701\) | −8.29792e12 | −1.29789 | −0.648945 | − | 0.760835i | \(-0.724789\pi\) | ||||
−0.648945 | + | 0.760835i | \(0.724789\pi\) | |||||||
\(702\) | 7.15205e12 | 1.11151 | ||||||||
\(703\) | 8.82443e12 | 1.36266 | ||||||||
\(704\) | −7.75222e12 | −1.18946 | ||||||||
\(705\) | 3.26978e12 | 0.498503 | ||||||||
\(706\) | −4.72509e12 | −0.715796 | ||||||||
\(707\) | 7.42736e12 | 1.11801 | ||||||||
\(708\) | 6.38718e10 | 0.00955343 | ||||||||
\(709\) | −9.99767e12 | −1.48590 | −0.742952 | − | 0.669345i | \(-0.766575\pi\) | ||||
−0.742952 | + | 0.669345i | \(0.766575\pi\) | |||||||
\(710\) | 4.53093e12 | 0.669152 | ||||||||
\(711\) | −3.40096e12 | −0.499100 | ||||||||
\(712\) | 5.32355e12 | 0.776321 | ||||||||
\(713\) | 1.69040e13 | 2.44956 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07983e13 | −1.54518 | ||||||||
\(716\) | 8.80989e9 | 0.00125274 | ||||||||
\(717\) | −6.41507e12 | −0.906494 | ||||||||
\(718\) | 1.09981e13 | 1.54439 | ||||||||
\(719\) | −4.37408e12 | −0.610389 | −0.305194 | − | 0.952290i | \(-0.598721\pi\) | ||||
−0.305194 | + | 0.952290i | \(0.598721\pi\) | |||||||
\(720\) | 2.08869e12 | 0.289653 | ||||||||
\(721\) | −1.43467e13 | −1.97717 | ||||||||
\(722\) | 1.73467e12 | 0.237574 | ||||||||
\(723\) | 1.12556e13 | 1.53196 | ||||||||
\(724\) | 4.68765e10 | 0.00634062 | ||||||||
\(725\) | 3.31317e11 | 0.0445371 | ||||||||
\(726\) | 3.27113e12 | 0.437001 | ||||||||
\(727\) | 3.97360e12 | 0.527568 | 0.263784 | − | 0.964582i | \(-0.415029\pi\) | ||||
0.263784 | + | 0.964582i | \(0.415029\pi\) | |||||||
\(728\) | 1.60453e13 | 2.11718 | ||||||||
\(729\) | 3.88995e12 | 0.510118 | ||||||||
\(730\) | −7.18014e12 | −0.935794 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.95946e10 | −0.00509726 | ||||||||
\(733\) | 7.96904e12 | 1.01962 | 0.509810 | − | 0.860287i | \(-0.329716\pi\) | ||||
0.509810 | + | 0.860287i | \(0.329716\pi\) | |||||||
\(734\) | −5.63429e12 | −0.716485 | ||||||||
\(735\) | 9.75876e12 | 1.23339 | ||||||||
\(736\) | 2.88268e11 | 0.0362114 | ||||||||
\(737\) | −7.36603e12 | −0.919665 | ||||||||
\(738\) | −1.97757e12 | −0.245402 | ||||||||
\(739\) | −3.39911e12 | −0.419243 | −0.209621 | − | 0.977783i | \(-0.567223\pi\) | ||||
−0.209621 | + | 0.977783i | \(0.567223\pi\) | |||||||
\(740\) | −1.38148e11 | −0.0169357 | ||||||||
\(741\) | −1.17534e13 | −1.43213 | ||||||||
\(742\) | −8.10076e12 | −0.981089 | ||||||||
\(743\) | −7.05502e12 | −0.849276 | −0.424638 | − | 0.905363i | \(-0.639599\pi\) | ||||
−0.424638 | + | 0.905363i | \(0.639599\pi\) | |||||||
\(744\) | 1.54041e13 | 1.84314 | ||||||||
\(745\) | −1.40406e13 | −1.66987 | ||||||||
\(746\) | −7.03643e12 | −0.831816 | ||||||||
\(747\) | 4.71973e11 | 0.0554593 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.54383e13 | −1.79239 | ||||||||
\(750\) | 1.05031e13 | 1.21211 | ||||||||
\(751\) | 1.65358e13 | 1.89690 | 0.948452 | − | 0.316920i | \(-0.102649\pi\) | ||||
0.948452 | + | 0.316920i | \(0.102649\pi\) | |||||||
\(752\) | −4.09169e12 | −0.466576 | ||||||||
\(753\) | −1.52732e13 | −1.73123 | ||||||||
\(754\) | −3.62339e12 | −0.408267 | ||||||||
\(755\) | 1.39944e13 | 1.56745 | ||||||||
\(756\) | 1.22015e11 | 0.0135851 | ||||||||
\(757\) | −5.91466e11 | −0.0654634 | −0.0327317 | − | 0.999464i | \(-0.510421\pi\) | ||||
−0.0327317 | + | 0.999464i | \(0.510421\pi\) | |||||||
\(758\) | −2.96622e12 | −0.326356 | ||||||||
\(759\) | −1.89550e13 | −2.07317 | ||||||||
\(760\) | 7.41818e12 | 0.806559 | ||||||||
\(761\) | −4.42291e12 | −0.478054 | −0.239027 | − | 0.971013i | \(-0.576829\pi\) | ||||
−0.239027 | + | 0.971013i | \(0.576829\pi\) | |||||||
\(762\) | −4.78884e12 | −0.514556 | ||||||||
\(763\) | −7.87463e12 | −0.841143 | ||||||||
\(764\) | 2.18057e10 | 0.00231552 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.08504e13 | −1.13872 | ||||||||
\(767\) | −9.66321e12 | −1.00819 | ||||||||
\(768\) | 3.91724e11 | 0.0406308 | ||||||||
\(769\) | −3.54128e12 | −0.365167 | −0.182583 | − | 0.983190i | \(-0.558446\pi\) | ||||
−0.182583 | + | 0.983190i | \(0.558446\pi\) | |||||||
\(770\) | 1.54346e13 | 1.58230 | ||||||||
\(771\) | −5.15130e12 | −0.525015 | ||||||||
\(772\) | 6.60976e10 | 0.00669743 | ||||||||
\(773\) | −1.02567e13 | −1.03323 | −0.516617 | − | 0.856217i | \(-0.672809\pi\) | ||||
−0.516617 | + | 0.856217i | \(0.672809\pi\) | |||||||
\(774\) | 3.00546e11 | 0.0301007 | ||||||||
\(775\) | 2.48412e12 | 0.247352 | ||||||||
\(776\) | 1.17132e13 | 1.15957 | ||||||||
\(777\) | −2.68385e13 | −2.64158 | ||||||||
\(778\) | 1.21906e12 | 0.119294 | ||||||||
\(779\) | −6.94067e12 | −0.675279 | ||||||||
\(780\) | 1.84002e11 | 0.0177990 | ||||||||
\(781\) | −8.95332e12 | −0.861101 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.36365e12 | −0.224727 | ||||||||
\(784\) | −1.22118e13 | −1.15440 | ||||||||
\(785\) | −4.85227e10 | −0.00456070 | ||||||||
\(786\) | −2.13704e13 | −1.99715 | ||||||||
\(787\) | 9.34742e11 | 0.0868571 | 0.0434285 | − | 0.999057i | \(-0.486172\pi\) | ||||
0.0434285 | + | 0.999057i | \(0.486172\pi\) | |||||||
\(788\) | 2.30818e10 | 0.00213256 | ||||||||
\(789\) | 2.06721e13 | 1.89905 | ||||||||
\(790\) | −1.56563e13 | −1.43011 | ||||||||
\(791\) | −2.18424e13 | −1.98384 | ||||||||
\(792\) | −4.17661e12 | −0.377190 | ||||||||
\(793\) | 5.99030e12 | 0.537922 | ||||||||
\(794\) | −1.57315e13 | −1.40468 | ||||||||
\(795\) | −7.96901e12 | −0.707542 | ||||||||
\(796\) | −1.19349e11 | −0.0105368 | ||||||||
\(797\) | 1.26917e13 | 1.11418 | 0.557091 | − | 0.830452i | \(-0.311918\pi\) | ||||
0.557091 | + | 0.830452i | \(0.311918\pi\) | |||||||
\(798\) | 1.67998e13 | 1.46653 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.23622e10 | 0.00365657 | ||||||||
\(801\) | 2.86773e12 | 0.246146 | ||||||||
\(802\) | −5.38411e11 | −0.0459546 | ||||||||
\(803\) | 1.41883e13 | 1.20423 | ||||||||
\(804\) | 1.25516e11 | 0.0105937 | ||||||||
\(805\) | −2.47583e13 | −2.07797 | ||||||||
\(806\) | −2.71672e13 | −2.26745 | ||||||||
\(807\) | 5.00018e12 | 0.415006 | ||||||||
\(808\) | −9.25232e12 | −0.763659 | ||||||||
\(809\) | −6.05218e11 | −0.0496757 | −0.0248378 | − | 0.999691i | \(-0.507907\pi\) | ||||
−0.0248378 | + | 0.999691i | \(0.507907\pi\) | |||||||
\(810\) | −1.36268e13 | −1.11227 | ||||||||
\(811\) | 2.19232e13 | 1.77955 | 0.889774 | − | 0.456402i | \(-0.150862\pi\) | ||||
0.889774 | + | 0.456402i | \(0.150862\pi\) | |||||||
\(812\) | −6.18153e10 | −0.00498992 | ||||||||
\(813\) | 1.85749e13 | 1.49114 | ||||||||
\(814\) | −2.28719e13 | −1.82596 | ||||||||
\(815\) | 5.31668e12 | 0.422115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05483e12 | 0.0828288 | ||||||||
\(818\) | −8.05163e12 | −0.628773 | ||||||||
\(819\) | 8.64344e12 | 0.671288 | ||||||||
\(820\) | 1.08658e11 | 0.00839263 | ||||||||
\(821\) | 3.11270e12 | 0.239107 | 0.119554 | − | 0.992828i | \(-0.461854\pi\) | ||||
0.119554 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(822\) | −1.47776e13 | −1.12897 | ||||||||
\(823\) | 2.30422e13 | 1.75075 | 0.875375 | − | 0.483444i | \(-0.160614\pi\) | ||||
0.875375 | + | 0.483444i | \(0.160614\pi\) | |||||||
\(824\) | 1.78718e13 | 1.35051 | ||||||||
\(825\) | −2.78552e12 | −0.209346 | ||||||||
\(826\) | 1.38122e13 | 1.03241 | ||||||||
\(827\) | 1.32673e13 | 0.986297 | 0.493148 | − | 0.869945i | \(-0.335846\pi\) | ||||
0.493148 | + | 0.869945i | \(0.335846\pi\) | |||||||
\(828\) | 7.80985e10 | 0.00577439 | ||||||||
\(829\) | 7.58786e12 | 0.557987 | 0.278994 | − | 0.960293i | \(-0.409999\pi\) | ||||
0.278994 | + | 0.960293i | \(0.409999\pi\) | |||||||
\(830\) | 2.17273e12 | 0.158911 | ||||||||
\(831\) | 2.31266e13 | 1.68232 | ||||||||
\(832\) | −1.99850e13 | −1.44594 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.01799e13 | −2.16009 | ||||||||
\(835\) | 1.67083e13 | 1.18944 | ||||||||
\(836\) | −1.70879e11 | −0.0120993 | ||||||||
\(837\) | −1.77220e13 | −1.24810 | ||||||||
\(838\) | −3.84999e12 | −0.269688 | ||||||||
\(839\) | −2.06984e13 | −1.44214 | −0.721070 | − | 0.692862i | \(-0.756349\pi\) | ||||
−0.721070 | + | 0.692862i | \(0.756349\pi\) | |||||||
\(840\) | −2.25615e13 | −1.56355 | ||||||||
\(841\) | −1.33097e13 | −0.917456 | ||||||||
\(842\) | −2.54353e12 | −0.174394 | ||||||||
\(843\) | −1.55518e13 | −1.06061 | ||||||||
\(844\) | 3.01090e10 | 0.00204247 | ||||||||
\(845\) | −1.42146e13 | −0.959133 | ||||||||
\(846\) | −2.23046e12 | −0.149702 | ||||||||
\(847\) | −8.44289e12 | −0.563658 | ||||||||
\(848\) | 9.97214e12 | 0.662227 | ||||||||
\(849\) | −2.99129e12 | −0.197594 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.66882e13 | 2.39797 | ||||||||
\(852\) | 1.52563e11 | 0.00991909 | ||||||||
\(853\) | 7.03835e12 | 0.455198 | 0.227599 | − | 0.973755i | \(-0.426913\pi\) | ||||
0.227599 | + | 0.973755i | \(0.426913\pi\) | |||||||
\(854\) | −8.56228e12 | −0.550845 | ||||||||
\(855\) | 3.99609e12 | 0.255733 | ||||||||
\(856\) | 1.92316e13 | 1.22429 | ||||||||
\(857\) | −1.87674e13 | −1.18848 | −0.594239 | − | 0.804289i | \(-0.702547\pi\) | ||||
−0.594239 | + | 0.804289i | \(0.702547\pi\) | |||||||
\(858\) | 3.04634e13 | 1.91905 | ||||||||
\(859\) | −4.63544e12 | −0.290484 | −0.145242 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145242 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(860\) | −1.65135e10 | −0.00102943 | ||||||||
\(861\) | 2.11092e13 | 1.30906 | ||||||||
\(862\) | 2.70867e13 | 1.67099 | ||||||||
\(863\) | 2.59525e13 | 1.59269 | 0.796343 | − | 0.604845i | \(-0.206765\pi\) | ||||
0.796343 | + | 0.604845i | \(0.206765\pi\) | |||||||
\(864\) | −3.02217e11 | −0.0184504 | ||||||||
\(865\) | −5.94867e12 | −0.361283 | ||||||||
\(866\) | −5.69614e12 | −0.344152 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.63474e11 | −0.0277132 | ||||||||
\(869\) | 3.09376e13 | 1.84034 | ||||||||
\(870\) | 5.09489e12 | 0.301507 | ||||||||
\(871\) | −1.89894e13 | −1.11797 | ||||||||
\(872\) | 9.80948e12 | 0.574542 | ||||||||
\(873\) | 6.30977e12 | 0.367662 | ||||||||
\(874\) | −2.29653e13 | −1.33128 | ||||||||
\(875\) | −2.71089e13 | −1.56342 | ||||||||
\(876\) | −2.41766e11 | −0.0138716 | ||||||||
\(877\) | −1.01903e13 | −0.581688 | −0.290844 | − | 0.956771i | \(-0.593936\pi\) | ||||
−0.290844 | + | 0.956771i | \(0.593936\pi\) | |||||||
\(878\) | 1.55688e13 | 0.884157 | ||||||||
\(879\) | 1.10852e13 | 0.626317 | ||||||||
\(880\) | −1.90002e13 | −1.06804 | ||||||||
\(881\) | −2.42334e12 | −0.135526 | −0.0677630 | − | 0.997701i | \(-0.521586\pi\) | ||||
−0.0677630 | + | 0.997701i | \(0.521586\pi\) | |||||||
\(882\) | −6.65687e12 | −0.370392 | ||||||||
\(883\) | −7.32457e12 | −0.405470 | −0.202735 | − | 0.979234i | \(-0.564983\pi\) | ||||
−0.202735 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.35875e13 | 0.744554 | ||||||||
\(886\) | −9.03941e12 | −0.492820 | ||||||||
\(887\) | −8.53993e12 | −0.463232 | −0.231616 | − | 0.972807i | \(-0.574401\pi\) | ||||
−0.231616 | + | 0.972807i | \(0.574401\pi\) | |||||||
\(888\) | 3.34329e13 | 1.80433 | ||||||||
\(889\) | 1.23601e13 | 0.663690 | ||||||||
\(890\) | 1.32016e13 | 0.705298 | ||||||||
\(891\) | 2.69272e13 | 1.43133 | ||||||||
\(892\) | 4.20523e11 | 0.0222407 | ||||||||
\(893\) | −7.82824e12 | −0.411939 | ||||||||
\(894\) | 3.96104e13 | 2.07391 | ||||||||
\(895\) | 1.87414e12 | 0.0976335 | ||||||||
\(896\) | 2.78957e13 | 1.44594 | ||||||||
\(897\) | −4.88655e13 | −2.52021 | ||||||||
\(898\) | −2.83565e12 | −0.145516 | ||||||||
\(899\) | 8.97836e12 | 0.458436 | ||||||||
\(900\) | 1.14769e10 | 0.000583088 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.79894e13 | 0.904873 | ||||||||
\(903\) | −3.20813e12 | −0.160567 | ||||||||
\(904\) | 2.72093e13 | 1.35506 | ||||||||
\(905\) | 9.97211e12 | 0.494161 | ||||||||
\(906\) | −3.94799e13 | −1.94670 | ||||||||
\(907\) | 7.40422e11 | 0.0363284 | 0.0181642 | − | 0.999835i | \(-0.494218\pi\) | ||||
0.0181642 | + | 0.999835i | \(0.494218\pi\) | |||||||
\(908\) | 1.73972e11 | 0.00849363 | ||||||||
\(909\) | −4.98412e12 | −0.242131 | ||||||||
\(910\) | 3.97901e13 | 1.92349 | ||||||||
\(911\) | −3.49415e12 | −0.168077 | −0.0840385 | − | 0.996463i | \(-0.526782\pi\) | ||||
−0.0840385 | + | 0.996463i | \(0.526782\pi\) | |||||||
\(912\) | −2.06807e13 | −0.989896 | ||||||||
\(913\) | −4.29341e12 | −0.204495 | ||||||||
\(914\) | −2.87923e13 | −1.36464 | ||||||||
\(915\) | −8.42303e12 | −0.397259 | ||||||||
\(916\) | 4.59607e10 | 0.00215704 | ||||||||
\(917\) | 5.51577e13 | 2.57599 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.01277e11 | −0.0324317 | −0.0162158 | − | 0.999869i | \(-0.505162\pi\) | ||||
−0.0162158 | + | 0.999869i | \(0.505162\pi\) | |||||||
\(920\) | 3.08416e13 | 1.41936 | ||||||||
\(921\) | −1.46966e13 | −0.673053 | ||||||||
\(922\) | 5.55546e12 | 0.253181 | ||||||||
\(923\) | −2.30814e13 | −1.04678 | ||||||||
\(924\) | 5.19708e11 | 0.0234550 | ||||||||
\(925\) | 5.39149e12 | 0.242143 | ||||||||
\(926\) | 2.38804e13 | 1.06732 | ||||||||
\(927\) | 9.62736e12 | 0.428202 | ||||||||
\(928\) | 1.53110e11 | 0.00677700 | ||||||||
\(929\) | −1.21293e13 | −0.534276 | −0.267138 | − | 0.963658i | \(-0.586078\pi\) | ||||
−0.267138 | + | 0.963658i | \(0.586078\pi\) | |||||||
\(930\) | 3.82001e13 | 1.67452 | ||||||||
\(931\) | −2.33636e13 | −1.01922 | ||||||||
\(932\) | 3.90766e11 | 0.0169647 | ||||||||
\(933\) | −3.62974e13 | −1.56822 | ||||||||
\(934\) | −4.56063e12 | −0.196094 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.07672e13 | −0.458523 | ||||||||
\(937\) | −2.23656e13 | −0.947879 | −0.473939 | − | 0.880558i | \(-0.657168\pi\) | ||||
−0.473939 | + | 0.880558i | \(0.657168\pi\) | |||||||
\(938\) | 2.71427e13 | 1.14483 | ||||||||
\(939\) | −2.74521e13 | −1.15234 | ||||||||
\(940\) | 1.22553e11 | 0.00511974 | ||||||||
\(941\) | 3.98663e13 | 1.65750 | 0.828748 | − | 0.559621i | \(-0.189053\pi\) | ||||
0.828748 | + | 0.559621i | \(0.189053\pi\) | |||||||
\(942\) | 1.36889e11 | 0.00566420 | ||||||||
\(943\) | −2.88563e13 | −1.18833 | ||||||||
\(944\) | −1.70030e13 | −0.696868 | ||||||||
\(945\) | 2.59563e13 | 1.05877 | ||||||||
\(946\) | −2.73399e12 | −0.110991 | ||||||||
\(947\) | −5.17204e12 | −0.208972 | −0.104486 | − | 0.994526i | \(-0.533320\pi\) | ||||
−0.104486 | + | 0.994526i | \(0.533320\pi\) | |||||||
\(948\) | −5.27172e11 | −0.0211990 | ||||||||
\(949\) | 3.65770e13 | 1.46390 | ||||||||
\(950\) | −3.37486e12 | −0.134431 | ||||||||
\(951\) | 2.57585e13 | 1.02119 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.55006e13 | 1.39417 | 0.697087 | − | 0.716986i | \(-0.254479\pi\) | ||||
0.697087 | + | 0.716986i | \(0.254479\pi\) | |||||||
\(954\) | 5.43600e12 | 0.212477 | ||||||||
\(955\) | 4.63875e12 | 0.180462 | ||||||||
\(956\) | −2.40439e11 | −0.00930990 | ||||||||
\(957\) | −1.00677e13 | −0.387996 | ||||||||
\(958\) | −2.82890e13 | −1.08511 | ||||||||
\(959\) | 3.81416e13 | 1.45618 | ||||||||
\(960\) | 2.81012e13 | 1.06783 | ||||||||
\(961\) | 4.08777e13 | 1.54608 | ||||||||
\(962\) | −5.89632e13 | −2.21969 | ||||||||
\(963\) | 1.03599e13 | 0.388182 | ||||||||
\(964\) | 4.21865e11 | 0.0157336 | ||||||||
\(965\) | 1.40611e13 | 0.521969 | ||||||||
\(966\) | 6.98463e13 | 2.58075 | ||||||||
\(967\) | −1.41239e13 | −0.519440 | −0.259720 | − | 0.965684i | \(-0.583630\pi\) | ||||
−0.259720 | + | 0.965684i | \(0.583630\pi\) | |||||||
\(968\) | 1.05174e13 | 0.385006 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.90470e13 | 1.05349 | ||||||||
\(971\) | 1.57589e13 | 0.568905 | 0.284452 | − | 0.958690i | \(-0.408188\pi\) | ||||
0.284452 | + | 0.958690i | \(0.408188\pi\) | |||||||
\(972\) | −2.02093e11 | −0.00726195 | ||||||||
\(973\) | 7.78954e13 | 2.78615 | ||||||||
\(974\) | 7.09215e12 | 0.252501 | ||||||||
\(975\) | −7.18101e12 | −0.254486 | ||||||||
\(976\) | 1.05403e13 | 0.371816 | ||||||||
\(977\) | 2.30148e13 | 0.808132 | 0.404066 | − | 0.914730i | \(-0.367597\pi\) | ||||
0.404066 | + | 0.914730i | \(0.367597\pi\) | |||||||
\(978\) | −1.49990e13 | −0.524250 | ||||||||
\(979\) | −2.60870e13 | −0.907616 | ||||||||
\(980\) | 3.65762e11 | 0.0126672 | ||||||||
\(981\) | 5.28426e12 | 0.182169 | ||||||||
\(982\) | 2.91287e13 | 0.999583 | ||||||||
\(983\) | 3.30550e11 | 0.0112914 | 0.00564568 | − | 0.999984i | \(-0.498203\pi\) | ||||
0.00564568 | + | 0.999984i | \(0.498203\pi\) | |||||||
\(984\) | −2.62959e13 | −0.894150 | ||||||||
\(985\) | 4.91023e12 | 0.166203 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.38087e13 | 0.798561 | ||||||||
\(988\) | −4.40521e11 | −0.0147082 | ||||||||
\(989\) | 4.38551e12 | 0.145760 | ||||||||
\(990\) | −1.03574e13 | −0.342683 | ||||||||
\(991\) | 2.41937e13 | 0.796839 | 0.398420 | − | 0.917203i | \(-0.369559\pi\) | ||||
0.398420 | + | 0.917203i | \(0.369559\pi\) | |||||||
\(992\) | 1.14798e12 | 0.0376383 | ||||||||
\(993\) | −2.57091e13 | −0.839104 | ||||||||
\(994\) | 3.29916e13 | 1.07193 | ||||||||
\(995\) | −2.53893e13 | −0.821196 | ||||||||
\(996\) | 7.31591e10 | 0.00235560 | ||||||||
\(997\) | 5.11973e13 | 1.64104 | 0.820519 | − | 0.571619i | \(-0.193685\pi\) | ||||
0.820519 | + | 0.571619i | \(0.193685\pi\) | |||||||
\(998\) | 4.94130e13 | 1.57672 | ||||||||
\(999\) | −3.84635e13 | −1.22181 |
(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 | 289.10.a.g.1.10 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.10 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.10 | yes | 36 | 17.16 | even | 2 |