Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,12,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(98.3479271116\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 33.5 | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.12.e.b.97.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −367.824 | − | 367.824i | −0.873923 | − | 0.873923i | 0.118974 | − | 0.992897i | \(-0.462039\pi\) |
−0.992897 | + | 0.118974i | \(0.962039\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 502.344 | − | 502.344i | 0.0718896 | − | 0.0718896i | −0.670248 | − | 0.742137i | \(-0.733812\pi\) |
0.742137 | + | 0.670248i | \(0.233812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33063.2i | 0.743542i | 0.928325 | + | 0.371771i | \(0.121249\pi\) | ||||
−0.928325 | + | 0.371771i | \(0.878751\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 93442.1i | 0.527483i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −335681. | + | 335681.i | −0.628444 | + | 0.628444i | −0.947677 | − | 0.319232i | \(-0.896575\pi\) |
0.319232 | + | 0.947677i | \(0.396575\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −568061. | − | 568061.i | −0.424333 | − | 0.424333i | 0.462360 | − | 0.886692i | \(-0.347003\pi\) |
−0.886692 | + | 0.462360i | \(0.847003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −369548. | −0.125652 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.78457e6 | −1.15892 | −0.579460 | − | 0.815001i | \(-0.696736\pi\) | ||||
−0.579460 | + | 0.815001i | \(0.696736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.33879e6 | − | 1.33879e6i | −0.124042 | − | 0.124042i | 0.642361 | − | 0.766402i | \(-0.277955\pi\) |
−0.766402 | + | 0.642361i | \(0.777955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.21614e7 | − | 1.21614e7i | 0.649798 | − | 0.649798i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.07133e6i | − | 0.0347074i | −0.999849 | − | 0.0173537i | \(-0.994476\pi\) | ||
0.999849 | − | 0.0173537i | \(-0.00552412\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.83234e7i | 0.989664i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.07887e7 | + | 3.07887e7i | −0.412943 | + | 0.412943i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.01359e7 | − | 5.01359e7i | −0.453899 | − | 0.453899i | 0.442747 | − | 0.896647i | \(-0.354004\pi\) |
−0.896647 | + | 0.442747i | \(0.854004\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.95969e8 | 1.85676 | 0.928382 | − | 0.371628i | \(-0.121200\pi\) | ||||
0.928382 | + | 0.371628i | \(0.121200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.46943e8 | 1.09842 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.66091e7 | + | 1.66091e7i | 0.0534529 | + | 0.0534529i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.11883e8 | + | 5.11883e8i | −1.21356 | + | 1.21356i | −0.243711 | + | 0.969848i | \(0.578365\pi\) |
−0.969848 | + | 0.243711i | \(0.921635\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.17893e8i | 0.741669i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.31803e8i | 1.25607i | 0.778186 | + | 0.628034i | \(0.216140\pi\) | ||||
−0.778186 | + | 0.628034i | \(0.783860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.27362e9 | − | 1.27362e9i | 1.32118 | − | 1.32118i | 0.408358 | − | 0.912822i | \(-0.366101\pi\) |
0.912822 | − | 0.408358i | \(-0.133899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.69401e7 | + | 4.69401e7i | 0.0379206 | + | 0.0379206i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.80739e7 | −0.0114951 | −0.00574756 | − | 0.999983i | \(-0.501830\pi\) | ||||
−0.00574756 | + | 0.999983i | \(0.501830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.84154e8 | 0.447146 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.49553e9 | + | 2.49553e9i | 1.01281 | + | 1.01281i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.29607e9 | + | 2.29607e9i | −0.754168 | + | 0.754168i | −0.975254 | − | 0.221086i | \(-0.929040\pi\) |
0.221086 | + | 0.975254i | \(0.429040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.37255e8i | 0.0903572i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.84878e8i | 0.216806i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.81453e8 | − | 4.81453e8i | 0.0876734 | − | 0.0876734i | −0.661910 | − | 0.749583i | \(-0.730254\pi\) |
0.749583 | + | 0.661910i | \(0.230254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30887e9 | − | 1.30887e9i | −0.198419 | − | 0.198419i | 0.600903 | − | 0.799322i | \(-0.294808\pi\) |
−0.799322 | + | 0.600903i | \(0.794808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.08949e9 | −0.392206 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.70724e8 | −0.0610103 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.42251e9 | + | 9.42251e9i | 0.852619 | + | 0.852619i | 0.990455 | − | 0.137836i | \(-0.0440147\pi\) |
−0.137836 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.94062e8 | + | 3.94062e8i | −0.0303316 | + | 0.0303316i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.74203e10i | − | 1.14587i | −0.819601 | − | 0.572934i | \(-0.805805\pi\) | ||
0.819601 | − | 0.572934i | \(-0.194195\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.91310e9i | − | 0.503215i | −0.967829 | − | 0.251607i | \(-0.919041\pi\) | ||
0.967829 | − | 0.251607i | \(-0.0809591\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.77745e10 | − | 1.77745e10i | 0.864890 | − | 0.864890i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.10987e10 | − | 1.10987e10i | −0.467274 | − | 0.467274i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.07466e10 | −1.48985 | −0.744924 | − | 0.667149i | \(-0.767514\pi\) | ||||
−0.744924 | + | 0.667149i | \(0.767514\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.92026e10 | 1.24924 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.16461e10 | − | 1.16461e10i | −0.324527 | − | 0.324527i | 0.525974 | − | 0.850501i | \(-0.323701\pi\) |
−0.850501 | + | 0.525974i | \(0.823701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.40819e9 | + | 3.40819e9i | −0.0833143 | + | 0.0833143i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.68824e10i | 0.793346i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.96706e10i | − | 1.51235i | −0.654368 | − | 0.756176i | \(-0.727065\pi\) | ||
0.654368 | − | 0.756176i | \(-0.272935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.87819e10 | − | 1.87819e10i | 0.315509 | − | 0.315509i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.08864e11 | − | 1.08864e11i | −1.62267 | − | 1.62267i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.34507e9 | −0.0178346 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.03397e10 | −0.122254 | −0.0611269 | − | 0.998130i | \(-0.519469\pi\) | ||||
−0.0611269 | + | 0.998130i | \(0.519469\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.13667e10 | − | 3.13667e10i | −0.331494 | − | 0.331494i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.36018e10 | − | 3.36018e10i | 0.318123 | − | 0.318123i | −0.529923 | − | 0.848046i | \(-0.677779\pi\) |
0.848046 | + | 0.529923i | \(0.177779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.27041e10i | − | 0.787942i | −0.919123 | − | 0.393971i | \(-0.871101\pi\) | ||
0.919123 | − | 0.393971i | \(-0.128899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.22184e10i | − | 0.0934275i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.88146e10 | + | 2.88146e10i | −0.198610 | + | 0.198610i | −0.799404 | − | 0.600794i | \(-0.794851\pi\) |
0.600794 | + | 0.799404i | \(0.294851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.21468e10 | + | 2.21468e10i | 0.137868 | + | 0.137868i | 0.772673 | − | 0.634804i | \(-0.218919\pi\) |
−0.634804 | + | 0.772673i | \(0.718919\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.76565e11 | 2.12111 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.71538e11 | −0.875849 | −0.437924 | − | 0.899012i | \(-0.644286\pi\) | ||||
−0.437924 | + | 0.899012i | \(0.644286\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.38178e8 | − | 5.38178e8i | −0.00249510 | − | 0.00249510i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.30808e10 | − | 5.30808e10i | 0.223829 | − | 0.223829i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.24319e11i | − | 0.861705i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.99484e10i | 0.210116i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.42740e11 | − | 3.42740e11i | 1.09771 | − | 1.09771i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.88035e10 | + | 4.88035e10i | 0.143036 | + | 0.143036i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.54635e11 | 1.48966 | 0.744830 | − | 0.667254i | \(-0.232531\pi\) | ||||
0.744830 | + | 0.667254i | \(0.232531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.36933e11 | −2.30922 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50085e11 | + | 4.50085e11i | 1.01930 | + | 1.01930i | 0.999810 | + | 0.0194915i | \(0.00620473\pi\) |
0.0194915 | + | 0.999810i | \(0.493795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.42646e10 | − | 4.42646e10i | 0.0922301 | − | 0.0922301i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.09330e10i | 0.0593727i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.75745e11i | − | 1.37327i | −0.727002 | − | 0.686635i | \(-0.759087\pi\) | ||
0.727002 | − | 0.686635i | \(-0.240913\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.80649e11 | − | 3.80649e11i | 0.622219 | − | 0.622219i | −0.323880 | − | 0.946098i | \(-0.604987\pi\) |
0.946098 | + | 0.323880i | \(0.104987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.64802e9 | + | 6.64802e9i | 0.0100459 | + | 0.0100459i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.81374e11 | 0.533339 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.03709e10 | −0.0652613 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.25213e11 | − | 3.25213e11i | −0.390771 | − | 0.390771i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.21482e11 | − | 1.21482e11i | 0.135515 | − | 0.135515i | −0.636095 | − | 0.771610i | \(-0.719451\pi\) |
0.771610 | + | 0.636095i | \(0.219451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.18981e11i | − | 0.434331i | −0.976135 | − | 0.217166i | \(-0.930319\pi\) | ||
0.976135 | − | 0.217166i | \(-0.0696812\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.33965e11i | − | 0.611311i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.48678e11 | − | 1.48678e11i | 0.133482 | − | 0.133482i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.64950e12 | − | 1.64950e12i | −1.38008 | − | 1.38008i | −0.844456 | − | 0.535626i | \(-0.820076\pi\) |
−0.535626 | − | 0.844456i | \(-0.679924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.68910e12 | 1.31817 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.54217e10 | 0.0258064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07698e12 | − | 1.07698e12i | −0.733121 | − | 0.733121i | 0.238116 | − | 0.971237i | \(-0.423470\pi\) |
−0.971237 | + | 0.238116i | \(0.923470\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.24050e11 | − | 1.24050e11i | 0.0789653 | − | 0.0789653i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.59845e12i | − | 0.952268i | −0.879373 | − | 0.476134i | \(-0.842038\pi\) | ||
0.879373 | − | 0.476134i | \(-0.157962\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.14677e12i | − | 0.639883i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.25099e11 | − | 1.25099e11i | 0.0654299 | − | 0.0654299i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.45486e12 | − | 1.45486e12i | −0.713785 | − | 0.713785i | 0.253540 | − | 0.967325i | \(-0.418405\pi\) |
−0.967325 | + | 0.253540i | \(0.918405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.59773e12 | −0.735856 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.54180e11 | −0.153240 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.30891e12 | + | 1.30891e12i | 0.532376 | + | 0.532376i | 0.921279 | − | 0.388903i | \(-0.127146\pi\) |
−0.388903 | + | 0.921279i | \(0.627146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.38152e12 | − | 2.38152e12i | 0.911219 | − | 0.911219i | −0.0851488 | − | 0.996368i | \(-0.527137\pi\) |
0.996368 | + | 0.0851488i | \(0.0271366\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.62869e11i | 0.346806i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.14282e11i | 0.174485i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.27745e12 | − | 2.27745e12i | 0.728316 | − | 0.728316i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.01797e12 | − | 1.01797e12i | −0.307040 | − | 0.307040i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.52280e12 | −1.00278 | −0.501388 | − | 0.865223i | \(-0.667177\pi\) | ||||
−0.501388 | + | 0.865223i | \(0.667177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.01739e12 | 1.07989 | 0.539944 | − | 0.841701i | \(-0.318445\pi\) | ||||
0.539944 | + | 0.841701i | \(0.318445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.09926e11 | + | 2.09926e11i | 0.0533183 | + | 0.0533183i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.98851e12 | + | 3.98851e12i | −0.957737 | + | 0.957737i | −0.999142 | − | 0.0414057i | \(-0.986816\pi\) |
0.0414057 | + | 0.999142i | \(0.486816\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.41250e11i | − | 0.0320846i | −0.999871 | − | 0.0160423i | \(-0.994893\pi\) | ||
0.999871 | − | 0.0160423i | \(-0.00510665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.93165e12i | − | 1.49025i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.65765e12 | − | 1.65765e12i | 0.337493 | − | 0.337493i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.68086e11 | + | 4.68086e11i | 0.0902982 | + | 0.0902982i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00108e11 | 0.0183076 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.98812e11 | 0.155907 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.64182e12 | + | 3.64182e12i | 0.599466 | + | 0.599466i | 0.940170 | − | 0.340704i | \(-0.110666\pi\) |
−0.340704 | + | 0.940170i | \(0.610666\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.40761e12 | + | 6.40761e12i | −1.00140 | + | 1.00140i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.27959e12i | − | 0.189958i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.78567e12i | 1.38058i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.27845e12 | + | 3.27845e12i | −0.439771 | + | 0.439771i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.85405e12 | + | 3.85405e12i | 0.491768 | + | 0.491768i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.31451e12 | −0.645337 | −0.322668 | − | 0.946512i | \(-0.604580\pi\) | ||||
−0.322668 | + | 0.946512i | \(0.604580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.51544e12 | −0.522031 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.88964e12 | + | 4.88964e12i | 0.538437 | + | 0.538437i | 0.923070 | − | 0.384633i | \(-0.125672\pi\) |
−0.384633 | + | 0.923070i | \(0.625672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.07133e12 | − | 7.07133e12i | 0.742003 | − | 0.742003i | −0.230960 | − | 0.972963i | \(-0.574187\pi\) |
0.972963 | + | 0.230960i | \(0.0741867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.16472e12i | 0.816724i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.54810e13i | 1.47687i | 0.674324 | + | 0.738435i | \(0.264435\pi\) | ||||
−0.674324 | + | 0.738435i | \(0.735565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.07932e9 | + | 9.07932e9i | −0.000826380 | + | 0.000826380i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.49876e13 | + | 1.49876e13i | 1.30201 | + | 1.30201i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.47869e13 | 1.22656 | 0.613280 | − | 0.789866i | \(-0.289850\pi\) | ||||
0.613280 | + | 0.789866i | \(0.289850\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.70990e12 | −0.293946 | −0.146973 | − | 0.989140i | \(-0.546953\pi\) | ||||
−0.146973 | + | 0.989140i | \(0.546953\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.96555e12 | − | 8.96555e12i | −0.678801 | − | 0.678801i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.44149e11 | − | 4.44149e11i | 0.0321452 | − | 0.0321452i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.52103e12i | 0.105270i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.56743e12i | 0.567223i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64619e13 | + | 1.64619e13i | −1.04297 | + | 1.04297i | −0.0439391 | + | 0.999034i | \(0.513991\pi\) |
−0.999034 | + | 0.0439391i | \(0.986009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.59626e11 | + | 3.59626e11i | 0.0218116 | + | 0.0218116i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.50723e12 | 0.145621 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.20187e13 | 1.22506 | 0.612532 | − | 0.790446i | \(-0.290151\pi\) | ||||
0.612532 | + | 0.790446i | \(0.290151\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.69245e13 | − | 1.69245e13i | −0.902331 | − | 0.902331i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.68480e12 | − | 4.68480e12i | 0.239424 | − | 0.239424i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.64085e12i | 0.227426i | 0.993514 | + | 0.113713i | \(0.0362745\pi\) | ||||
−0.993514 | + | 0.113713i | \(0.963726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.30684e12i | 0.108434i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.93047e13 | + | 2.93047e13i | −1.32168 | + | 1.32168i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.23177e12 | + | 3.23177e12i | 0.139895 | + | 0.139895i | 0.773586 | − | 0.633691i | \(-0.218461\pi\) |
−0.633691 | + | 0.773586i | \(0.718461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.04462e13 | −1.26533 | −0.632663 | − | 0.774427i | \(-0.718038\pi\) | ||||
−0.632663 | + | 0.774427i | \(0.718038\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.38169e13 | −0.551461 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.62212e13 | − | 1.62212e13i | −0.621949 | − | 0.621949i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.12987e13 | + | 1.12987e13i | −0.416282 | + | 0.416282i | −0.883920 | − | 0.467638i | \(-0.845105\pi\) |
0.467638 | + | 0.883920i | \(0.345105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.76559e13i | 0.979412i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.01696e13i | − | 0.686772i | −0.939194 | − | 0.343386i | \(-0.888426\pi\) | ||
0.939194 | − | 0.343386i | \(-0.111574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.67176e12 | − | 2.67176e12i | 0.0874929 | − | 0.0874929i | −0.662006 | − | 0.749499i | \(-0.730295\pi\) |
0.749499 | + | 0.662006i | \(0.230295\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.94748e11 | + | 4.94748e11i | 0.0155861 | + | 0.0155861i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.08084e13 | −0.933938 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.17585e13 | 0.343095 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.80318e12 | + | 3.80318e12i | 0.106840 | + | 0.106840i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.85320e13 | − | 3.85320e13i | 1.04244 | − | 1.04244i | 0.0433791 | − | 0.999059i | \(-0.486188\pi\) |
0.999059 | − | 0.0433791i | \(-0.0138123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.83710e11i | − | 0.0126056i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.06703e13i | − | 0.519024i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.08583e11 | + | 6.08583e11i | −0.0147275 | + | 0.0147275i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.21098e13 | + | 4.21098e13i | 0.982352 | + | 0.982352i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.47191e13 | −0.556031 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.31501e12 | −0.0285285 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.24055e13 | + | 3.24055e13i | 0.678199 | + | 0.678199i | 0.959593 | − | 0.281393i | \(-0.0907966\pi\) |
−0.281393 | + | 0.959593i | \(0.590797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.40988e13 | + | 3.40988e13i | −0.688601 | + | 0.688601i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.32038e13i | − | 1.03696i | −0.855091 | − | 0.518478i | \(-0.826499\pi\) | ||
0.855091 | − | 0.518478i | \(-0.173501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.41435e13i | 1.39502i | 0.716577 | + | 0.697508i | \(0.245708\pi\) | ||||
−0.716577 | + | 0.697508i | \(0.754292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.55199e12 | + | 1.55199e12i | −0.0281955 | + | 0.0281955i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.45432e12 | − | 6.45432e12i | −0.113246 | − | 0.113246i | 0.648213 | − | 0.761459i | \(-0.275517\pi\) |
−0.761459 | + | 0.648213i | \(0.775517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.36593e13 | 0.570501 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.11974e13 | 0.347140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.08312e12 | + | 9.08312e12i | 0.143754 | + | 0.143754i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.74507e13 | − | 2.74507e13i | 0.419947 | − | 0.419947i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.62922e13i | − | 0.240973i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.97580e11i | − | 0.00854710i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.80148e13 | − | 5.80148e13i | 0.802574 | − | 0.802574i | −0.180923 | − | 0.983497i | \(-0.557909\pi\) |
0.983497 | + | 0.180923i | \(0.0579085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.78314e13 | − | 4.78314e13i | −0.640132 | − | 0.640132i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.46668e12 | 0.122589 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.30225e13 | −0.915150 | −0.457575 | − | 0.889171i | \(-0.651282\pi\) | ||||
−0.457575 | + | 0.889171i | \(0.651282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.30958e13 | + | 6.30958e13i | 0.765425 | + | 0.765425i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.93510e13 | + | 9.93510e13i | −1.16687 | + | 1.16687i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.46096e13i | 1.07601i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.95910e11i | 0.00436105i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.07174e13 | − | 4.07174e13i | 0.434478 | − | 0.434478i | −0.455670 | − | 0.890149i | \(-0.650600\pi\) |
0.890149 | + | 0.455670i | \(0.150600\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.50423e13 | − | 7.50423e13i | −0.775829 | − | 0.775829i | 0.203290 | − | 0.979119i | \(-0.434837\pi\) |
−0.979119 | + | 0.203290i | \(0.934837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.49797e13 | 0.350451 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.92000e14 | 1.86441 | 0.932205 | − | 0.361931i | \(-0.117882\pi\) | ||||
0.932205 | + | 0.361931i | \(0.117882\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.75099e12 | − | 8.75099e12i | −0.0823761 | − | 0.0823761i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.25101e13 | + | 8.25101e13i | −0.753064 | + | 0.753064i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.04811e13i | − | 0.535304i | −0.963516 | − | 0.267652i | \(-0.913752\pi\) | ||
0.963516 | − | 0.267652i | \(-0.0862477\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.12906e14i | − | 0.969227i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.20505e13 | − | 2.20505e13i | 0.183625 | − | 0.183625i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.47744e12 | − | 4.47744e12i | −0.0361759 | − | 0.0361759i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.73489e13 | 0.606444 | 0.303222 | − | 0.952920i | \(-0.401938\pi\) | ||||
0.303222 | + | 0.952920i | \(0.401938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.70696e13 | −0.662555 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.59154e13 | − | 7.59154e13i | −0.560755 | − | 0.560755i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.33207e13 | − | 7.33207e13i | 0.525809 | − | 0.525809i | −0.393511 | − | 0.919320i | \(-0.628740\pi\) |
0.919320 | + | 0.393511i | \(0.128740\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3.59022e13i | − | 0.250005i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.69605e13i | 0.385209i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.92106e14 | − | 1.92106e14i | 1.26190 | − | 1.26190i | 0.311734 | − | 0.950169i | \(-0.399090\pi\) |
0.950169 | − | 0.311734i | \(-0.100910\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.04008e14 | − | 2.04008e14i | −1.30185 | − | 1.30185i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.28679e14 | 0.797836 | 0.398918 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398918 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.11507e13 | −0.0671844 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.19009e14 | + | 1.19009e14i | 0.696900 | + | 0.696900i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.00352e14 | − | 2.00352e14i | 1.14044 | − | 1.14044i | 0.152068 | − | 0.988370i | \(-0.451407\pi\) |
0.988370 | − | 0.152068i | \(-0.0485934\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.26854e12i | 0.0402230i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.31104e14i | − | 1.78158i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.04688e13 | + | 2.04688e13i | −0.107105 | + | 0.107105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.54966e14 | + | 1.54966e14i | 0.788657 | + | 0.788657i | 0.981274 | − | 0.192617i | \(-0.0616974\pi\) |
−0.192617 | + | 0.981274i | \(0.561697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.25632e13 | −0.161204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.58680e14 | −1.72748 | −0.863740 | − | 0.503938i | \(-0.831884\pi\) | ||||
−0.863740 | + | 0.503938i | \(0.831884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68128e14 | − | 1.68128e14i | −0.787886 | − | 0.787886i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.96932e13 | − | 1.96932e13i | 0.0898077 | − | 0.0898077i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.43658e14i | − | 1.52531i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.56728e13i | 0.197324i | 0.995121 | + | 0.0986618i | \(0.0314562\pi\) | ||||
−0.995121 | + | 0.0986618i | \(0.968544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.85338e14 | + | 2.85338e14i | −1.20013 | + | 1.20013i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.59184e13 | + | 1.59184e13i | 0.0651888 | + | 0.0651888i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.17007e13 | −0.0466602 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.80024e14 | −1.08754 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.11630e13 | − | 2.11630e13i | −0.0800572 | − | 0.0800572i | 0.665944 | − | 0.746001i | \(-0.268029\pi\) |
−0.746001 | + | 0.665944i | \(0.768029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.92706e14 | − | 1.92706e14i | 0.710138 | − | 0.710138i | −0.256426 | − | 0.966564i | \(-0.582545\pi\) |
0.966564 | + | 0.256426i | \(0.0825450\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.68886e12i | − | 0.00606349i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.27854e14i | − | 1.14694i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.32754e13 | − | 4.32754e13i | 0.147533 | − | 0.147533i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.40279e14 | − | 1.40279e14i | −0.466097 | − | 0.466097i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.15533e14 | 1.02193 | 0.510964 | − | 0.859602i | \(-0.329289\pi\) | ||||
0.510964 | + | 0.859602i | \(0.329289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.43423e13 | 0.297867 | 0.148934 | − | 0.988847i | \(-0.452416\pi\) | ||||
0.148934 | + | 0.988847i | \(0.452416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.85276e13 | + | 1.85276e13i | 0.0570334 | + | 0.0570334i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.43429e12 | + | 1.43429e12i | −0.00430516 | + | 0.00430516i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.26118e12i | − | 0.0124731i | −0.999981 | − | 0.00623655i | \(-0.998015\pi\) | ||
0.999981 | − | 0.00623655i | \(-0.00198517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.26172e13i | 0.235862i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.07675e13 | + | 1.07675e13i | −0.0299843 | + | 0.0299843i | −0.721940 | − | 0.691956i | \(-0.756749\pi\) |
0.691956 | + | 0.721940i | \(0.256749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00220e13 | − | 4.00220e13i | −0.108722 | − | 0.108722i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.93681e13 | −0.236860 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.49573e14 | 0.386811 | 0.193405 | − | 0.981119i | \(-0.438047\pi\) | ||||
0.193405 | + | 0.981119i | \(0.438047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.12788e14 | − | 3.12788e14i | −0.789368 | − | 0.789368i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.54111e14 | + | 1.54111e14i | −0.379572 | + | 0.379572i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.88700e13i | − | 0.0453637i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.73073e13i | − | 0.134484i | −0.997737 | − | 0.0672420i | \(-0.978580\pi\) | ||
0.997737 | − | 0.0672420i | \(-0.0214200\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.08888e14 | − | 2.08888e14i | 0.478568 | − | 0.478568i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.04689e14 | + | 5.04689e14i | 1.12893 | + | 1.12893i | 0.990351 | + | 0.138583i | \(0.0442548\pi\) |
0.138583 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.04606e14 | −0.228487 | −0.114243 | − | 0.993453i | \(-0.536444\pi\) | ||||
−0.114243 | + | 0.993453i | \(0.536444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.09375e14 | −0.233306 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.83143e14 | + | 5.83143e14i | 1.21488 | + | 1.21488i | 0.969404 | + | 0.245472i | \(0.0789430\pi\) |
0.245472 | + | 0.969404i | \(0.421057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.11538e14 | + | 3.11538e14i | −0.633958 | + | 0.633958i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.21345e15i | 2.41217i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.55057e14i | 1.66058i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.46949e13 | − | 6.46949e13i | 0.122760 | − | 0.122760i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.14550e14 | − | 2.14550e14i | −0.397811 | − | 0.397811i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.29337e12 | −0.0168394 | −0.00841972 | − | 0.999965i | \(-0.502680\pi\) | ||||
−0.00841972 | + | 0.999965i | \(0.502680\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.81561e14 | 1.02991 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.30289e13 | − | 1.30289e13i | −0.0225528 | − | 0.0225528i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.19407e12 | + | 5.19407e12i | −0.00878878 | + | 0.00878878i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.67485e14i | − | 0.442477i | −0.975220 | − | 0.221238i | \(-0.928990\pi\) | ||
0.975220 | − | 0.221238i | \(-0.0710099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.92278e14i | 1.28138i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.39834e13 | + | 3.39834e13i | −0.0537425 | + | 0.0537425i | −0.733467 | − | 0.679725i | \(-0.762099\pi\) |
0.679725 | + | 0.733467i | \(0.262099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.40150e14 | + | 3.40150e14i | 0.526033 | + | 0.526033i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.15138e13 | −0.0476619 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.75970e14 | 0.852001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.03300e14 | − | 1.03300e14i | −0.149468 | − | 0.149468i | 0.628412 | − | 0.777880i | \(-0.283705\pi\) |
−0.777880 | + | 0.628412i | \(0.783705\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.87949e14 | + | 5.87949e14i | −0.832209 | + | 0.832209i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.03966e15i | − | 1.43969i | −0.694136 | − | 0.719843i | \(-0.744214\pi\) | ||
0.694136 | − | 0.719843i | \(-0.255786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.37594e13i | − | 0.0457395i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.21811e14 | + | 4.21811e14i | −0.559209 | + | 0.559209i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.30191e14 | − | 5.30191e14i | −0.687835 | − | 0.687835i | 0.273918 | − | 0.961753i | \(-0.411680\pi\) |
−0.961753 | + | 0.273918i | \(0.911680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.94695e14 | 0.374161 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.24391e13 | 0.102444 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.65693e13 | − | 4.65693e13i | −0.0566448 | − | 0.0566448i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.06706e12 | − | 6.06706e12i | 0.00722405 | − | 0.00722405i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.07026e15i | 1.24759i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.25048e14i | 0.827484i | 0.910394 | + | 0.413742i | \(0.135778\pi\) | ||||
−0.910394 | + | 0.413742i | \(0.864222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.35477e14 | + | 6.35477e14i | −0.710134 | + | 0.710134i | −0.966563 | − | 0.256429i | \(-0.917454\pi\) |
0.256429 | + | 0.966563i | \(0.417454\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.87682e14 | + | 5.87682e14i | 0.643082 | + | 0.643082i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.00802e15 | −2.15184 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.51662e14 | 0.998795 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.49880e13 | + | 4.49880e13i | 0.0462463 | + | 0.0462463i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.29321e14 | − | 5.29321e14i | 0.532991 | − | 0.532991i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.89497e13i | 0.0285560i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.62898e14i | − | 0.930511i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.96793e14 | + | 2.96793e14i | −0.281006 | + | 0.281006i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.14149e15 | + | 1.14149e15i | 1.05898 | + | 1.05898i | 0.998148 | + | 0.0608311i | \(0.0193751\pi\) |
0.0608311 | + | 0.998148i | \(0.480625\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.75196e15 | −1.59267 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.22506e13 | 0.0198226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.92097e14 | + | 7.92097e14i | 0.691589 | + | 0.691589i | 0.962581 | − | 0.270993i | \(-0.0873519\pi\) |
−0.270993 | + | 0.962581i | \(0.587352\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.22304e14 | − | 1.22304e14i | 0.104663 | − | 0.104663i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.34243e14i | 0.112605i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.34721e15i | − | 1.10776i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.89165e14 | − | 1.89165e14i | 0.152486 | − | 0.152486i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.32985e15 | − | 1.32985e15i | −1.05099 | − | 1.05099i | −0.998628 | − | 0.0523642i | \(-0.983324\pi\) |
−0.0523642 | − | 0.998628i | \(-0.516676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.44698e15 | −1.12124 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.67540e15 | −1.27299 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.09588e14 | − | 6.09588e14i | −0.454193 | − | 0.454193i | 0.442551 | − | 0.896743i | \(-0.354074\pi\) |
−0.896743 | + | 0.442551i | \(0.854074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.61711e13 | + | 8.61711e13i | −0.0629644 | + | 0.0629644i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.29616e15i | 0.928865i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.37610e15i | 0.967234i | 0.875280 | + | 0.483617i | \(0.160677\pi\) | ||||
−0.875280 | + | 0.483617i | \(0.839323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.57011e14 | − | 4.57011e14i | 0.315085 | − | 0.315085i | −0.531790 | − | 0.846876i | \(-0.678481\pi\) |
0.846876 | + | 0.531790i | \(0.178481\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.29577e15 | + | 1.29577e15i | 0.876349 | + | 0.876349i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.17705e13 | 0.0343486 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.10753e15 | 0.720921 | 0.360460 | − | 0.932775i | \(-0.382620\pi\) | ||||
0.360460 | + | 0.932775i | \(0.382620\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.47769e15 | − | 1.47769e15i | −0.943740 | − | 0.943740i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.85057e14 | − | 3.85057e14i | 0.241299 | − | 0.241299i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.54149e15i | − | 0.947905i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.33297e13i | − | 0.0321819i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.20142e14 | + | 7.20142e14i | −0.426490 | + | 0.426490i | −0.887431 | − | 0.460941i | \(-0.847512\pi\) |
0.460941 | + | 0.887431i | \(0.347512\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.96240e14 | − | 3.96240e14i | −0.230316 | − | 0.230316i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.93414e15 | 1.67398 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.05889e15 | 0.592996 | 0.296498 | − | 0.955034i | \(-0.404181\pi\) | ||||
0.296498 | + | 0.955034i | \(0.404181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.12686e14 | − | 1.12686e14i | −0.0619476 | − | 0.0619476i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.19552e13 | + | 5.19552e13i | −0.0280395 | + | 0.0280395i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.03403e14i | − | 0.425682i | −0.977087 | − | 0.212841i | \(-0.931728\pi\) | ||
0.977087 | − | 0.212841i | \(-0.0682717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.38624e15i | − | 0.721155i | −0.932729 | − | 0.360578i | \(-0.882580\pi\) | ||
0.932729 | − | 0.360578i | \(-0.117420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.80459e14 | + | 8.80459e14i | −0.449742 | + | 0.449742i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.01147e13 | + | 3.01147e13i | 0.0151051 | + | 0.0151051i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.18636e15 | 1.56948 | 0.784742 | − | 0.619823i | \(-0.212796\pi\) | ||||
0.784742 | + | 0.619823i | \(0.212796\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.21945e15 | −0.589886 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.02671e13 | + | 1.02671e13i | 0.00487776 | + | 0.00487776i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.13972e15 | + | 1.13972e15i | −0.531820 | + | 0.531820i | −0.921114 | − | 0.389294i | \(-0.872719\pi\) |
0.389294 | + | 0.921114i | \(0.372719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 3.44346e14i | − | 0.157827i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.02609e15i | 1.81265i | 0.422578 | + | 0.906326i | \(0.361125\pi\) | ||||
−0.422578 | + | 0.906326i | \(0.638875\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.12455e14 | + | 1.12455e14i | −0.0497370 | + | 0.0497370i | −0.731538 | − | 0.681801i | \(-0.761197\pi\) |
0.681801 | + | 0.731538i | \(0.261197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.29849e13 | + | 3.29849e13i | 0.0143322 | + | 0.0143322i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.63416e15 | 1.12450 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.31051e15 | −0.969098 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.30605e14 | − | 3.30605e14i | −0.136250 | − | 0.136250i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.47290e15 | − | 3.47290e15i | 1.40642 | − | 1.40642i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.54561e15i | 1.41101i | 0.708706 | + | 0.705504i | \(0.249279\pi\) | ||||
−0.708706 | + | 0.705504i | \(0.750721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.67910e15i | − | 1.04777i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.78618e14 | − | 2.78618e14i | 0.107091 | − | 0.107091i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.02253e14 | − | 5.02253e14i | −0.189739 | − | 0.189739i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.62779e15 | 0.604427 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.99466e15 | −1.45801 | −0.729005 | − | 0.684509i | \(-0.760017\pi\) | ||||
−0.729005 | + | 0.684509i | \(0.760017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.20860e14 | + | 7.20860e14i | 0.258637 | + | 0.258637i | 0.824500 | − | 0.565863i | \(-0.191457\pi\) |
−0.565863 | + | 0.824500i | \(0.691457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.70663e14 | + | 4.70663e14i | −0.166009 | + | 0.166009i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 2.38050e15i | − | 0.825458i | −0.910854 | − | 0.412729i | \(-0.864576\pi\) | ||
0.910854 | − | 0.412729i | \(-0.135424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.23229e14i | 0.110196i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.59940e15 | − | 3.59940e15i | 1.20652 | − | 1.20652i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.05366e15 | − | 3.05366e15i | −1.00646 | − | 1.00646i | −0.999979 | − | 0.00648374i | \(-0.997936\pi\) |
−0.00648374 | − | 0.999979i | \(-0.502064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.52195e14 | 0.146554 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.32859e14 | 0.265437 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.38786e15 | + | 3.38786e15i | 1.06183 | + | 1.06183i | 0.997958 | + | 0.0638750i | \(0.0203459\pi\) |
0.0638750 | + | 0.997958i | \(0.479654\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.17225e15 | + | 2.17225e15i | −0.669580 | + | 0.669580i | −0.957619 | − | 0.288039i | \(-0.906997\pi\) |
0.288039 | + | 0.957619i | \(0.406997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.83523e15i | − | 0.859534i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4.44722e13i | − | 0.0132608i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.37122e13 | + | 5.37122e13i | −0.0157536 | + | 0.0157536i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.95480e15 | + | 1.95480e15i | 0.563975 | + | 0.563975i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.78726e14 | 0.249390 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.38223e14 | −0.0665121 | −0.0332561 | − | 0.999447i | \(-0.510588\pi\) | ||||
−0.0332561 | + | 0.999447i | \(0.510588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.48781e15 | − | 1.48781e15i | −0.408675 | − | 0.408675i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.90659e15 | + | 1.90659e15i | −0.515252 | + | 0.515252i | −0.916131 | − | 0.400879i | \(-0.868705\pi\) |
0.400879 | + | 0.916131i | \(0.368705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.41862e14i | − | 0.0909007i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 3.59706e15i | − | 0.941106i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.55329e15 | − | 2.55329e15i | 0.657334 | − | 0.657334i | −0.297415 | − | 0.954748i | \(-0.596124\pi\) |
0.954748 | + | 0.297415i | \(0.0961243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.89691e14 | − | 3.89691e14i | −0.0987239 | − | 0.0987239i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.20201e15 | −1.29691 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.60862e15 | 0.640037 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.73213e14 | + | 4.73213e14i | 0.114269 | + | 0.114269i | 0.761929 | − | 0.647660i | \(-0.224252\pi\) |
−0.647660 | + | 0.761929i | \(0.724252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.03708e15 | − | 1.03708e15i | 0.246479 | − | 0.246479i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.82433e14i | − | 0.0894621i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.32188e15i | − | 1.45568i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.69430e15 | − | 5.69430e15i | 1.29067 | − | 1.29067i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.29380e14 | − | 4.29380e14i | −0.0958061 | − | 0.0958061i | 0.657579 | − | 0.753385i | \(-0.271580\pi\) |
−0.753385 | + | 0.657579i | \(0.771580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.37061e15 | 0.301064 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.67918e12 | 0.00144439 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.11098e15 | + | 1.11098e15i | 0.236538 | + | 0.236538i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.83229e14 | − | 1.83229e14i | 0.0384097 | − | 0.0384097i | −0.687641 | − | 0.726051i | \(-0.741354\pi\) |
0.726051 | + | 0.687641i | \(0.241354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3.80744e15i | − | 0.785870i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.17081e14i | − | 0.0644433i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.91581e14 | − | 1.91581e14i | 0.0383415 | − | 0.0383415i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.43898e15 | − | 5.43898e15i | −1.07192 | − | 1.07192i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.63852e15 | −0.900265 | −0.450133 | − | 0.892962i | \(-0.648623\pi\) | ||||
−0.450133 | + | 0.892962i | \(0.648623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.06509e15 | 0.585867 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.36459e15 | + | 1.36459e15i | 0.256887 | + | 0.256887i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.42274e15 | − | 2.42274e15i | 0.449208 | − | 0.449208i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.43021e15i | 0.626442i | 0.949680 | + | 0.313221i | \(0.101408\pi\) | ||||
−0.949680 | + | 0.313221i | \(0.898592\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 3.49140e14i | − | 0.0628055i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.64094e15 | + | 8.64094e15i | −1.53114 | + | 1.53114i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.05712e15 | − | 4.05712e15i | −0.708184 | − | 0.708184i | 0.257969 | − | 0.966153i | \(-0.416947\pi\) |
−0.966153 | + | 0.257969i | \(0.916947\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.26738e14 | −0.0561848 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.32591e15 | −1.07165 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.67030e15 | − | 1.67030e15i | −0.278772 | − | 0.278772i | 0.553846 | − | 0.832619i | \(-0.313159\pi\) |
−0.832619 | + | 0.553846i | \(0.813159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.59471e14 | − | 5.59471e14i | 0.0919978 | − | 0.0919978i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.61265e15i | − | 0.747330i | −0.927564 | − | 0.373665i | \(-0.878101\pi\) | ||
0.927564 | − | 0.373665i | \(-0.121899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.22052e14i | − | 0.0194843i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.08824e15 | − | 1.08824e15i | 0.171183 | − | 0.171183i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.52701e14 | − | 9.52701e14i | −0.147675 | − | 0.147675i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.38439e14 | −0.0975214 | −0.0487607 | − | 0.998810i | \(-0.515527\pi\) | ||||
−0.0487607 | + | 0.998810i | \(0.515527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.21101e16 | 1.82296 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.10473e14 | − | 2.10473e14i | −0.0312239 | − | 0.0312239i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.03835e15 | − | 3.03835e15i | 0.444232 | − | 0.444232i | −0.449199 | − | 0.893432i | \(-0.648291\pi\) |
0.893432 | + | 0.449199i | \(0.148291\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2.64558e14i | − | 0.0381234i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.97530e15i | − | 0.422586i | −0.977423 | − | 0.211293i | \(-0.932233\pi\) | ||
0.977423 | − | 0.211293i | \(-0.0677674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.32242e14 | + | 7.32242e14i | −0.102511 | + | 0.102511i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.18468e14 | − | 3.18468e14i | −0.0439469 | − | 0.0439469i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.46989e14 | −0.0744054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.50036e15 | −0.603465 | −0.301733 | − | 0.953393i | \(-0.597565\pi\) | ||||
−0.301733 | + | 0.953393i | \(0.597565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.09899e15 | − | 8.09899e15i | −1.07061 | − | 1.07061i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.33340e15 | + | 6.33340e15i | −0.825372 | + | 0.825372i | −0.986873 | − | 0.161500i | \(-0.948367\pi\) |
0.161500 | + | 0.986873i | \(0.448367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.43022e16i | 1.83757i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.24504e16i | 1.57714i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.24749e15 | − | 1.24749e15i | 0.155805 | − | 0.155805i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.84766e15 | + | 5.84766e15i | 0.720115 | + | 0.720115i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.08723e15 | 0.374869 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.65723e15 | −0.198427 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.25291e15 | + | 3.25291e15i | 0.384071 | + | 0.384071i | 0.872566 | − | 0.488496i | \(-0.162454\pi\) |
−0.488496 | + | 0.872566i | \(0.662454\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.70702e15 | − | 1.70702e15i | 0.198753 | − | 0.198753i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.67159e15i | − | 0.651230i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.48704e15i | 0.168391i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.48510e14 | − | 8.48510e14i | 0.0947628 | − | 0.0947628i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.11952e15 | + | 2.11952e15i | 0.233462 | + | 0.233462i | 0.814136 | − | 0.580674i | \(-0.197211\pi\) |
−0.580674 | + | 0.814136i | \(0.697211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.22624e14 | 0.0133219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.44458e15 | 0.797740 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.99196e15 | + | 2.99196e15i | 0.316242 | + | 0.316242i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.77939e13 | − | 1.77939e13i | 0.00185521 | − | 0.00185521i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.37745e15i | − | 0.244515i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.90043e15i | 0.700098i | 0.936731 | + | 0.350049i | \(0.113835\pi\) | ||||
−0.936731 | + | 0.350049i | \(0.886165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.16275e15 | − | 1.16275e15i | 0.116378 | − | 0.116378i | −0.646519 | − | 0.762898i | \(-0.723776\pi\) |
0.762898 | + | 0.646519i | \(0.223776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.11989e16 | + | 1.11989e16i | 1.10580 | + | 1.10580i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.08203e15 | −0.105408 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.41021e15 | −0.327763 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.75502e15 | + | 1.75502e15i | 0.166426 | + | 0.166426i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.05348e15 | + | 8.05348e15i | −0.753523 | + | 0.753523i | −0.975135 | − | 0.221612i | \(-0.928868\pi\) |
0.221612 | + | 0.975135i | \(0.428868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.72899e16i | 1.59622i | 0.602510 | + | 0.798111i | \(0.294167\pi\) | ||||
−0.602510 | + | 0.798111i | \(0.705833\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.19331e16i | 1.08707i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.23292e16 | + | 1.23292e16i | −1.10829 | + | 1.10829i | −0.114913 | + | 0.993376i | \(0.536659\pi\) |
−0.993376 | + | 0.114913i | \(0.963341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.23351e16 | + | 1.23351e16i | 1.09419 | + | 1.09419i | 0.995076 | + | 0.0991110i | \(0.0315999\pi\) |
0.0991110 | + | 0.995076i | \(0.468400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.31183e15 | 0.727598 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.99860e15 | −0.518206 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.02973e14 | − | 8.02973e14i | −0.0684582 | − | 0.0684582i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.11249e15 | + | 9.11249e15i | −0.766738 | + | 0.766738i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.85813e15i | − | 0.486484i | −0.969966 | − | 0.243242i | \(-0.921789\pi\) | ||
0.969966 | − | 0.243242i | \(-0.0782109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.17330e15i | − | 0.587951i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.41886e15 | + | 7.41886e15i | −0.600186 | + | 0.600186i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.76075e14 | − | 5.76075e14i | −0.0460010 | − | 0.0460010i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.98209e15 | −0.156230 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.96548e15 | −0.152924 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.48397e14 | + | 5.48397e14i | 0.0421194 | + | 0.0421194i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.14683e16 | − | 1.14683e16i | 0.869522 | − | 0.869522i | −0.122898 | − | 0.992419i | \(-0.539219\pi\) |
0.992419 | + | 0.122898i | \(0.0392187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.25686e14i | − | 0.00940747i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.71190e15i | 0.274285i | 0.990551 | + | 0.137142i | \(0.0437918\pi\) | ||||
−0.990551 | + | 0.137142i | \(0.956208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.20180e15 | + | 1.20180e15i | −0.0876735 | + | 0.0876735i | −0.749583 | − | 0.661910i | \(-0.769746\pi\) |
0.661910 | + | 0.749583i | \(0.269746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.13321e16 | + | 1.13321e16i | 0.816190 | + | 0.816190i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.89836e15 | 0.348331 | 0.174165 | − | 0.984716i | \(-0.444277\pi\) | ||||
0.174165 | + | 0.984716i | \(0.444277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.46168e15 | −0.102627 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.32506e15 | − | 4.32506e15i | −0.299839 | − | 0.299839i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.36778e16 | − | 1.36778e16i | 0.936287 | − | 0.936287i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.07051e16i | − | 0.723589i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9.66161e14i | − | 0.0644868i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.61360e15 | + | 1.61360e15i | −0.106353 | + | 0.106353i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.94432e15 | − | 3.94432e15i | −0.256729 | − | 0.256729i | 0.566993 | − | 0.823722i | \(-0.308106\pi\) |
−0.823722 | + | 0.566993i | \(0.808106\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.83460e16 | −1.82202 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.41637e15 | −0.534266 | −0.267133 | − | 0.963660i | \(-0.586076\pi\) | ||||
−0.267133 | + | 0.963660i | \(0.586076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.32184e15 | + | 4.32184e15i | 0.270947 | + | 0.270947i | 0.829482 | − | 0.558534i | \(-0.188636\pi\) |
−0.558534 | + | 0.829482i | \(0.688636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.77920e14 | + | 1.77920e14i | −0.0110163 | + | 0.0110163i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.87494e16i | 1.75812i | 0.476707 | + | 0.879062i | \(0.341830\pi\) | ||||
−0.476707 | + | 0.879062i | \(0.658170\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.83380e16i | 1.10762i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.31596e16 | + | 1.31596e16i | −0.785081 | + | 0.785081i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.41972e13 | + | 2.41972e13i | 0.00142587 | + | 0.00142587i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.31505e15 | 0.0765446 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.47703e14 | 0.0257414 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.48387e16 | − | 1.48387e16i | −0.842784 | − | 0.842784i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.55779e16 | − | 1.55779e16i | 0.874020 | − | 0.874020i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3.09780e16i | − | 1.71700i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.39269e15i | − | 0.131014i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.17663e15 | − | 5.17663e15i | 0.280031 | − | 0.280031i | −0.553090 | − | 0.833121i | \(-0.686551\pi\) |
0.833121 | + | 0.553090i | \(0.186551\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.13983e15 | + | 3.13983e15i | 0.167805 | + | 0.167805i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.22340e16 | −1.17400 | −0.586998 | − | 0.809588i | \(-0.699690\pi\) | ||||
−0.586998 | + | 0.809588i | \(0.699690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.81874e15 | 0.407894 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.83691e14 | + | 4.83691e14i | 0.0249317 | + | 0.0249317i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.48812e16 | + | 1.48812e16i | −0.757893 | + | 0.757893i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.58068e16i | 0.795444i | 0.917506 | + | 0.397722i | \(0.130199\pi\) | ||||
−0.917506 | + | 0.397722i | \(0.869801\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 2.38390e16i | − | 1.18539i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.89580e15 | + | 9.89580e15i | −0.486230 | + | 0.486230i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.47359e16 | − | 2.47359e16i | −1.20102 | − | 1.20102i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.66246e15 | 0.415626 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.46893e16 | 1.64479 | 0.822393 | − | 0.568920i | \(-0.192639\pi\) | ||||
0.822393 | + | 0.568920i | \(0.192639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.18370e15 | − | 1.18370e15i | −0.0554647 | − | 0.0554647i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.95696e16 | + | 1.95696e16i | −0.906220 | + | 0.906220i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.28813e15i | − | 0.104717i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.05502e16i | − | 0.929496i | −0.885443 | − | 0.464748i | \(-0.846145\pi\) | ||
0.885443 | − | 0.464748i | \(-0.153855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.72718e16 | − | 2.72718e16i | 1.21914 | − | 1.21914i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.82034e16 | − | 1.82034e16i | −0.804286 | − | 0.804286i | 0.179476 | − | 0.983762i | \(-0.442560\pi\) |
−0.983762 | + | 0.179476i | \(0.942560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.98271e14 | 0.0435948 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.02274e15 | −0.0441460 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.56323e15 | − | 2.56323e15i | −0.109361 | − | 0.109361i | 0.650309 | − | 0.759670i | \(-0.274640\pi\) |
−0.759670 | + | 0.650309i | \(0.774640\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.06319e15 | + | 5.06319e15i | −0.213530 | + | 0.213530i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.74811e15i | 0.197937i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.68907e15i | 0.316857i | 0.987370 | + | 0.158428i | \(0.0506427\pi\) | ||||
−0.987370 | + | 0.158428i | \(0.949357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.76966e15 | + | 1.76966e15i | −0.0720892 | + | 0.0720892i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.23807e16 | − | 1.23807e16i | −0.498574 | − | 0.498574i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.56486e16 | 1.02108 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.21890e16 | 2.44757 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.69249e15 | − | 2.69249e15i | −0.104764 | − | 0.104764i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.01811e15 | − | 2.01811e15i | 0.0776328 | − | 0.0776328i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.35131e16i | 0.894260i | 0.894469 | + | 0.447130i | \(0.147554\pi\) | ||||
−0.894469 | + | 0.447130i | \(0.852446\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.68198e15i | − | 0.251261i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.96572e16 | − | 2.96572e16i | 1.10262 | − | 1.10262i | 0.108522 | − | 0.994094i | \(-0.465388\pi\) |
0.994094 | − | 0.108522i | \(-0.0346117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.25855e16 | + | 1.25855e16i | 0.462645 | + | 0.462645i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.01940e16 | −0.734003 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.19671e16 | −1.14890 | −0.574450 | − | 0.818539i | \(-0.694784\pi\) | ||||
−0.574450 | + | 0.818539i | \(0.694784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.67439e16 | + | 2.67439e16i | 0.950429 | + | 0.950429i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.06944e15 | + | 2.06944e15i | −0.0727233 | + | 0.0727233i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 3.59807e16i | − | 1.25033i | −0.780492 | − | 0.625166i | \(-0.785031\pi\) | ||
0.780492 | − | 0.625166i | \(-0.214969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00721e15i | 0.137703i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.19804e14 | + | 2.19804e14i | −0.00746951 | + | 0.00746951i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.36447e15 | − | 1.36447e15i | −0.0458547 | − | 0.0458547i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.28338e16 | −0.758881 | −0.379441 | − | 0.925216i | \(-0.623884\pi\) | ||||
−0.379441 | + | 0.925216i | \(0.623884\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.26785e16 | −1.40278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.09562e13 | − | 7.09562e13i | −0.00230655 | − | 0.00230655i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.26548e16 | − | 2.26548e16i | 0.728346 | − | 0.728346i | −0.241945 | − | 0.970290i | \(-0.577785\pi\) |
0.970290 | + | 0.241945i | \(0.0777852\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 3.15204e16i | − | 1.00226i |
(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 | 128.12.e.b.33.5 | 42 | ||
4.3 | odd | 2 | 128.12.e.a.33.17 | 42 | |||
8.3 | odd | 2 | 64.12.e.a.17.5 | 42 | |||
8.5 | even | 2 | 16.12.e.a.13.14 | yes | 42 | ||
16.3 | odd | 4 | 64.12.e.a.49.5 | 42 | |||
16.5 | even | 4 | inner | 128.12.e.b.97.5 | 42 | ||
16.11 | odd | 4 | 128.12.e.a.97.17 | 42 | |||
16.13 | even | 4 | 16.12.e.a.5.14 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.14 | ✓ | 42 | 16.13 | even | 4 | ||
16.12.e.a.13.14 | yes | 42 | 8.5 | even | 2 | ||
64.12.e.a.17.5 | 42 | 8.3 | odd | 2 | |||
64.12.e.a.49.5 | 42 | 16.3 | odd | 4 | |||
128.12.e.a.33.17 | 42 | 4.3 | odd | 2 | |||
128.12.e.a.97.17 | 42 | 16.11 | odd | 4 | |||
128.12.e.b.33.5 | 42 | 1.1 | even | 1 | trivial | ||
128.12.e.b.97.5 | 42 | 16.5 | even | 4 | inner |