Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,6,Mod(1,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(123.174773616\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 384) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 768.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 80.0000 | 1.43108 | 0.715542 | − | 0.698570i | \(-0.246180\pi\) | ||||
0.715542 | + | 0.698570i | \(0.246180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −36.0000 | −0.277688 | −0.138844 | − | 0.990314i | \(-0.544339\pi\) | ||||
−0.138844 | + | 0.990314i | \(0.544339\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 36.0000 | 0.0897059 | 0.0448529 | − | 0.998994i | \(-0.485718\pi\) | ||||
0.0448529 | + | 0.998994i | \(0.485718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 404.000 | 0.663014 | 0.331507 | − | 0.943453i | \(-0.392443\pi\) | ||||
0.331507 | + | 0.943453i | \(0.392443\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −720.000 | −0.826236 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.00167845 | −0.000839224 | − | 1.00000i | \(-0.500267\pi\) | ||||
−0.000839224 | 1.00000i | \(0.500267\pi\) | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2916.00 | −1.85312 | −0.926560 | − | 0.376147i | \(-0.877249\pi\) | ||||
−0.926560 | + | 0.376147i | \(0.877249\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 324.000 | 0.160323 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2808.00 | 1.10682 | 0.553411 | − | 0.832909i | \(-0.313326\pi\) | ||||
0.553411 | + | 0.832909i | \(0.313326\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3275.00 | 1.04800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4408.00 | −0.973300 | −0.486650 | − | 0.873597i | \(-0.661781\pi\) | ||||
−0.486650 | + | 0.873597i | \(0.661781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5796.00 | −1.08324 | −0.541619 | − | 0.840624i | \(-0.682189\pi\) | ||||
−0.541619 | + | 0.840624i | \(0.682189\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −324.000 | −0.0517917 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2880.00 | −0.397395 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2316.00 | 0.278121 | 0.139061 | − | 0.990284i | \(-0.455592\pi\) | ||||
0.139061 | + | 0.990284i | \(0.455592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3636.00 | −0.382792 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6874.00 | −0.638631 | −0.319315 | − | 0.947648i | \(-0.603453\pi\) | ||||
−0.319315 | + | 0.947648i | \(0.603453\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17244.0 | −1.42222 | −0.711110 | − | 0.703081i | \(-0.751807\pi\) | ||||
−0.711110 | + | 0.703081i | \(0.751807\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6480.00 | 0.477028 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5688.00 | 0.375591 | 0.187795 | − | 0.982208i | \(-0.439866\pi\) | ||||
0.187795 | + | 0.982208i | \(0.439866\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15511.0 | −0.922889 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.0000 | 0.000969052 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 32072.0 | 1.56833 | 0.784163 | − | 0.620555i | \(-0.213093\pi\) | ||||
0.784163 | + | 0.620555i | \(0.213093\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2880.00 | 0.128377 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26244.0 | 1.06990 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43308.0 | −1.61971 | −0.809857 | − | 0.586628i | \(-0.800455\pi\) | ||||
−0.809857 | + | 0.586628i | \(0.800455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18012.0 | 0.619780 | 0.309890 | − | 0.950772i | \(-0.399708\pi\) | ||||
0.309890 | + | 0.950772i | \(0.399708\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2916.00 | −0.0925627 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 32320.0 | 0.948829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11628.0 | 0.316459 | 0.158230 | − | 0.987402i | \(-0.449421\pi\) | ||||
0.158230 | + | 0.987402i | \(0.449421\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −25272.0 | −0.639024 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8712.00 | 0.205103 | 0.102551 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102551 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15846.0 | −0.348027 | −0.174013 | − | 0.984743i | \(-0.555674\pi\) | ||||
−0.174013 | + | 0.984743i | \(0.555674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −29475.0 | −0.605063 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1296.00 | −0.0249103 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40356.0 | −0.727512 | −0.363756 | − | 0.931494i | \(-0.618506\pi\) | ||||
−0.363756 | + | 0.931494i | \(0.618506\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 66204.0 | 1.05485 | 0.527423 | − | 0.849603i | \(-0.323158\pi\) | ||||
0.527423 | + | 0.849603i | \(0.323158\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −160.000 | −0.00240200 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 39672.0 | 0.561935 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −66086.0 | −0.884371 | −0.442185 | − | 0.896924i | \(-0.645797\pi\) | ||||
−0.442185 | + | 0.896924i | \(0.645797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14544.0 | −0.184111 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 52164.0 | 0.625408 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −233280. | −2.65197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −119682. | −1.29152 | −0.645758 | − | 0.763543i | \(-0.723458\pi\) | ||||
−0.645758 | + | 0.763543i | \(0.723458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2916.00 | 0.0299020 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 32392.0 | 0.315962 | 0.157981 | − | 0.987442i | \(-0.449502\pi\) | ||||
0.157981 | + | 0.987442i | \(0.449502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 109476. | 1.01678 | 0.508389 | − | 0.861128i | \(-0.330241\pi\) | ||||
0.508389 | + | 0.861128i | \(0.330241\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 25920.0 | 0.229436 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 106596. | 0.900081 | 0.450040 | − | 0.893008i | \(-0.351410\pi\) | ||||
0.450040 | + | 0.893008i | \(0.351410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 77524.0 | 0.624985 | 0.312493 | − | 0.949920i | \(-0.398836\pi\) | ||||
0.312493 | + | 0.949920i | \(0.398836\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20844.0 | −0.160573 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 179506. | 1.32246 | 0.661230 | − | 0.750183i | \(-0.270035\pi\) | ||||
0.661230 | + | 0.750183i | \(0.270035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 224640. | 1.58395 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32724.0 | 0.221005 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 72.0000 | 0.000466085 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −159755. | −0.991953 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 61866.0 | 0.368714 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12000.0 | 0.0686920 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −339804. | −1.86947 | −0.934736 | − | 0.355342i | \(-0.884365\pi\) | ||||
−0.934736 | + | 0.355342i | \(0.884365\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 155196. | 0.821119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 334188. | 1.70142 | 0.850712 | − | 0.525632i | \(-0.176171\pi\) | ||||
0.850712 | + | 0.525632i | \(0.176171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104976. | 0.514589 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −58320.0 | −0.275412 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 393766. | 1.79241 | 0.896204 | − | 0.443643i | \(-0.146314\pi\) | ||||
0.896204 | + | 0.443643i | \(0.146314\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −244620. | −1.07388 | −0.536939 | − | 0.843621i | \(-0.680419\pi\) | ||||
−0.536939 | + | 0.843621i | \(0.680419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −51192.0 | −0.216847 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14544.0 | 0.0594763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −352640. | −1.39287 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 139599. | 0.532830 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −368240. | −1.35883 | −0.679415 | − | 0.733754i | \(-0.737766\pi\) | ||||
−0.679415 | + | 0.733754i | \(0.737766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −380052. | −1.35644 | −0.678220 | − | 0.734859i | \(-0.737248\pi\) | ||||
−0.678220 | + | 0.734859i | \(0.737248\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −162.000 | −0.000559482 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −463680. | −1.55020 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −513204. | −1.66166 | −0.830828 | − | 0.556530i | \(-0.812132\pi\) | ||||
−0.830828 | + | 0.556530i | \(0.812132\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −288648. | −0.905473 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −101088. | −0.307351 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31500.0 | 0.0928628 | 0.0464314 | − | 0.998921i | \(-0.485215\pi\) | ||||
0.0464314 | + | 0.998921i | \(0.485215\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25920.0 | −0.0741182 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 106560. | 0.295667 | 0.147834 | − | 0.989012i | \(-0.452770\pi\) | ||||
0.147834 | + | 0.989012i | \(0.452770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −208077. | −0.560412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −236196. | −0.617707 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 249680. | 0.634262 | 0.317131 | − | 0.948382i | \(-0.397281\pi\) | ||||
0.317131 | + | 0.948382i | \(0.397281\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −117900. | −0.291017 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 389772. | 0.935142 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −362916. | −0.846591 | −0.423295 | − | 0.905992i | \(-0.639127\pi\) | ||||
−0.423295 | + | 0.905992i | \(0.639127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 506644. | 1.14949 | 0.574747 | − | 0.818331i | \(-0.305101\pi\) | ||||
0.574747 | + | 0.818331i | \(0.305101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −162108. | −0.357830 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 185280. | 0.398015 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −72.0000 | −0.000150567 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26244.0 | 0.0534411 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −806256. | −1.59915 | −0.799576 | − | 0.600565i | \(-0.794942\pi\) | ||||
−0.799576 | + | 0.600565i | \(0.794942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −438418. | −0.847218 | −0.423609 | − | 0.905845i | \(-0.639237\pi\) | ||||
−0.423609 | + | 0.905845i | \(0.639237\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −290880. | −0.547807 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −334664. | −0.614389 | −0.307195 | − | 0.951647i | \(-0.599390\pi\) | ||||
−0.307195 | + | 0.951647i | \(0.599390\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −63324.0 | −0.113354 | −0.0566768 | − | 0.998393i | \(-0.518050\pi\) | ||||
−0.0566768 | + | 0.998393i | \(0.518050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −104652. | −0.182708 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 158688. | 0.270274 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −549920. | −0.913934 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 227448. | 0.368940 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −104976. | −0.166236 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −662436. | −1.02433 | −0.512163 | − | 0.858889i | \(-0.671155\pi\) | ||||
−0.512163 | + | 0.858889i | \(0.671155\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −78408.0 | −0.118416 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.37952e6 | −2.03532 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 208656. | 0.300803 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 142614. | 0.200933 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −808.000 | −0.00111283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.33038e6 | −1.79149 | −0.895743 | − | 0.444572i | \(-0.853356\pi\) | ||||
−0.895743 | + | 0.444572i | \(0.853356\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 265275. | 0.349333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −717156. | −0.923738 | −0.461869 | − | 0.886948i | \(-0.652821\pi\) | ||||
−0.461869 | + | 0.886948i | \(0.652821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −198316. | −0.249902 | −0.124951 | − | 0.992163i | \(-0.539877\pi\) | ||||
−0.124951 | + | 0.992163i | \(0.539877\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11664.0 | 0.0143819 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −860662. | −1.03859 | −0.519293 | − | 0.854596i | \(-0.673805\pi\) | ||||
−0.519293 | + | 0.854596i | \(0.673805\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 455040. | 0.537502 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 363204. | 0.420029 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −443520. | −0.502248 | −0.251124 | − | 0.967955i | \(-0.580800\pi\) | ||||
−0.251124 | + | 0.967955i | \(0.580800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −34242.0 | −0.0379766 | −0.0189883 | − | 0.999820i | \(-0.506045\pi\) | ||||
−0.0189883 | + | 0.999820i | \(0.506045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.24088e6 | −1.32073 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17806e6 | −1.22865 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −595836. | −0.609016 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 236052. | 0.236496 | 0.118248 | − | 0.992984i | \(-0.462272\pi\) | ||||
0.118248 | + | 0.992984i | \(0.462272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 101088. | 0.0992884 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1440.00 | 0.00138679 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 929282. | 0.877637 | 0.438818 | − | 0.898576i | \(-0.355397\pi\) | ||||
0.438818 | + | 0.898576i | \(0.355397\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −83376.0 | −0.0772310 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −357048. | −0.324433 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.69070e6 | −1.50723 | −0.753613 | − | 0.657319i | \(-0.771691\pi\) | ||||
−0.753613 | + | 0.657319i | \(0.771691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.56576e6 | 2.24441 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 594774. | 0.510592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −900056. | −0.758383 | −0.379192 | − | 0.925318i | \(-0.623798\pi\) | ||||
−0.379192 | + | 0.925318i | \(0.623798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.58389e6 | 1.31009 | 0.655047 | − | 0.755588i | \(-0.272649\pi\) | ||||
0.655047 | + | 0.755588i | \(0.272649\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 130896. | 0.106297 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 117900. | 0.0940117 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.95466e6 | 1.53064 | 0.765318 | − | 0.643653i | \(-0.222582\pi\) | ||||
0.765318 | + | 0.643653i | \(0.222582\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −469476. | −0.361080 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.16081e6 | −1.63249 | −0.816244 | − | 0.577707i | \(-0.803947\pi\) | ||||
−0.816244 | + | 0.577707i | \(0.803947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 659556. | 0.489537 | 0.244769 | − | 0.969582i | \(-0.421288\pi\) | ||||
0.244769 | + | 0.969582i | \(0.421288\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.09952e6 | 1.53112 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 247464. | 0.177340 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41985e6 | −0.999997 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.07714e6 | 0.745657 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 802664. | 0.546216 | 0.273108 | − | 0.961983i | \(-0.411948\pi\) | ||||
0.273108 | + | 0.961983i | \(0.411948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.46464e6 | −2.31794 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26244.0 | −0.0172639 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.13443e6 | 0.733839 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 620784. | 0.394934 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −291528. | −0.182421 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.44096e6 | 0.886957 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −178452. | −0.108063 | −0.0540313 | − | 0.998539i | \(-0.517207\pi\) | ||||
−0.0540313 | + | 0.998539i | \(0.517207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −985284. | −0.587037 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.25827e6 | −0.737689 | −0.368845 | − | 0.929491i | \(-0.620247\pi\) | ||||
−0.368845 | + | 0.929491i | \(0.620247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 923062. | 0.532562 | 0.266281 | − | 0.963895i | \(-0.414205\pi\) | ||||
0.266281 | + | 0.963895i | \(0.414205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −233280. | −0.132465 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 568408. | 0.317696 | 0.158848 | − | 0.987303i | \(-0.449222\pi\) | ||||
0.158848 | + | 0.987303i | \(0.449222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −158688. | −0.0873107 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −959364. | −0.519662 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5832.00 | 0.00311036 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.32310e6 | 0.694839 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −697716. | −0.360836 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −204768. | −0.104297 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.60644e6 | 1.30761 | 0.653803 | − | 0.756665i | \(-0.273172\pi\) | ||||
0.653803 | + | 0.756665i | \(0.273172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 187596. | 0.0927071 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 930240. | 0.452880 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 232002. | 0.111280 | 0.0556400 | − | 0.998451i | \(-0.482280\pi\) | ||||
0.0556400 | + | 0.998451i | \(0.482280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.61555e6 | −0.763523 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −208656. | −0.0971728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.16345e6 | 0.533964 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.02176e6 | −0.914496 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.21973e6 | 1.43548 | 0.717738 | − | 0.696313i | \(-0.245177\pi\) | ||||
0.717738 | + | 0.696313i | \(0.245177\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.40341e6 | −1.93520 | −0.967600 | − | 0.252489i | \(-0.918751\pi\) | ||||
−0.967600 | + | 0.252489i | \(0.918751\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −294516. | −0.127597 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −556766. | −0.237813 | −0.118907 | − | 0.992905i | \(-0.537939\pi\) | ||||
−0.118907 | + | 0.992905i | \(0.537939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 696960. | 0.293520 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −648.000 | −0.000269094 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.86314e6 | 0.762975 | 0.381487 | − | 0.924374i | \(-0.375412\pi\) | ||||
0.381487 | + | 0.924374i | \(0.375412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.02696e6 | 2.43405 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.43780e6 | 0.572704 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.26768e6 | −0.498055 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.19936e6 | −1.62749 | −0.813745 | − | 0.581222i | \(-0.802575\pi\) | ||||
−0.813745 | + | 0.581222i | \(0.802575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −556794. | −0.212877 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.15459e6 | −0.435506 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.74152e6 | 1.39244 | 0.696218 | − | 0.717830i | \(-0.254864\pi\) | ||||
0.696218 | + | 0.717830i | \(0.254864\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −108000. | −0.0396593 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.78083e6 | −0.645312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.47100e6 | −0.883640 | −0.441820 | − | 0.897104i | \(-0.645667\pi\) | ||||
−0.441820 | + | 0.897104i | \(0.645667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.05824e6 | 1.07934 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 472176. | 0.164478 | 0.0822388 | − | 0.996613i | \(-0.473793\pi\) | ||||
0.0822388 | + | 0.996613i | \(0.473793\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −103680. | −0.0356487 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.39676e6 | −0.474073 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.39157e6 | −1.13639 | −0.568194 | − | 0.822895i | \(-0.692358\pi\) | ||||
−0.568194 | + | 0.822895i | \(0.692358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5616.00 | −0.00185774 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00769e6 | −0.982318 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.22848e6 | −1.04113 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.94950e6 | 1.25767 | 0.628834 | − | 0.777540i | \(-0.283533\pi\) | ||||
0.628834 | + | 0.777540i | \(0.283533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −944784. | −0.297098 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −200354. | −0.0622210 | −0.0311105 | − | 0.999516i | \(-0.509904\pi\) | ||||
−0.0311105 | + | 0.999516i | \(0.509904\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.34158e6 | −0.718203 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 524880. | 0.159009 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 83376.0 | 0.0249491 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.29357e6 | 0.973552 | 0.486776 | − | 0.873527i | \(-0.338173\pi\) | ||||
0.486776 | + | 0.873527i | \(0.338173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.54389e6 | −1.03485 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.55909e6 | 0.449775 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.29632e6 | 1.50957 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.20158e6 | 0.620004 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −970740. | −0.270127 | −0.135063 | − | 0.990837i | \(-0.543124\pi\) | ||||
−0.135063 | + | 0.990837i | \(0.543124\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.40490e6 | 1.48622 | 0.743109 | − | 0.669171i | \(-0.233350\pi\) | ||||
0.743109 | + | 0.669171i | \(0.233350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 460728. | 0.125197 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6550.00 | −0.00175901 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −648432. | −0.172106 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −130896. | −0.0343386 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.46646e6 | −1.41747 | −0.708733 | − | 0.705477i | \(-0.750733\pi\) | ||||
−0.708733 | + | 0.705477i | \(0.750733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.99423e6 | −0.767476 | −0.383738 | − | 0.923442i | \(-0.625363\pi\) | ||||
−0.383738 | + | 0.923442i | \(0.625363\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.17376e6 | 0.804176 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.18813e6 | −2.05107 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.04469e6 | 0.506368 | 0.253184 | − | 0.967418i | \(-0.418522\pi\) | ||||
0.253184 | + | 0.967418i | \(0.418522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.25639e6 | −0.307630 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.49344e6 | −1.81414 | −0.907072 | − | 0.420976i | \(-0.861688\pi\) | ||||
−0.907072 | + | 0.420976i | \(0.861688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.28688e6 | −1.26561 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.31416e6 | 0.784521 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.92095e6 | −0.449676 | −0.224838 | − | 0.974396i | \(-0.572185\pi\) | ||||
−0.224838 | + | 0.974396i | \(0.572185\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −247464. | −0.0572889 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.42047e6 | 0.783141 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.16352e6 | −0.263479 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.20241e6 | −1.38922 | −0.694608 | − | 0.719388i | \(-0.744422\pi\) | ||||
−0.694608 | + | 0.719388i | \(0.744422\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1458.00 | 0.000323017 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.10840e6 | −0.900369 | −0.450184 | − | 0.892936i | \(-0.648642\pi\) | ||||
−0.450184 | + | 0.892936i | \(0.648642\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5940.00 | 0.00128776 | 0.000643879 | − | 1.00000i | \(-0.499795\pi\) | ||||
0.000643879 | 1.00000i | \(0.499795\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.17312e6 | 0.895011 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.12715e6 | 0.875705 | 0.437853 | − | 0.899047i | \(-0.355739\pi\) | ||||
0.437853 | + | 0.899047i | \(0.355739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −418608. | −0.0878770 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.61884e6 | 0.959357 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −620784. | −0.127581 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.54990e6 | −1.94207 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.59783e6 | 0.522775 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.34297e6 | 0.864864 | 0.432432 | − | 0.901667i | \(-0.357656\pi\) | ||||
0.432432 | + | 0.901667i | \(0.357656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 935664. | 0.184398 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 909792. | 0.177449 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.57456e6 | −1.84827 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.15822e6 | 1.74980 | 0.874901 | − | 0.484303i | \(-0.160927\pi\) | ||||
0.874901 | + | 0.484303i | \(0.160927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −283500. | −0.0536143 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.33205e6 | 0.623746 | 0.311873 | − | 0.950124i | \(-0.399044\pi\) | ||||
0.311873 | + | 0.950124i | \(0.399044\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8816.00 | 0.00163363 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 233280. | 0.0427922 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −313632. | −0.0569547 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.36028e6 | 0.783905 | 0.391952 | − | 0.919985i | \(-0.371800\pi\) | ||||
0.391952 | + | 0.919985i | \(0.371800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −959040. | −0.170703 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.82474e6 | 1.37896 | 0.689478 | − | 0.724307i | \(-0.257840\pi\) | ||||
0.689478 | + | 0.724307i | \(0.257840\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.59136e6 | 0.452167 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.87269e6 | 0.323554 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.18598e6 | 0.373982 | 0.186991 | − | 0.982362i | \(-0.440126\pi\) | ||||
0.186991 | + | 0.982362i | \(0.440126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 570456. | 0.0966429 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.12576e6 | 0.356633 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.75808e6 | 1.45509 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 204768. | 0.0336927 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.24712e6 | −0.366191 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.42385e6 | 0.714012 | 0.357006 | − | 0.934102i | \(-0.383798\pi\) | ||||
0.357006 | + | 0.934102i | \(0.383798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.86866e6 | 0.458590 | 0.229295 | − | 0.973357i | \(-0.426358\pi\) | ||||
0.229295 | + | 0.973357i | \(0.426358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.06110e6 | 0.168019 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11592.0 | 0.00181816 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.44852e6 | 0.225053 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.50795e6 | −0.539904 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.77710e6 | −0.423421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.52768e6 | 1.28809 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.26624e6 | 0.488779 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −558396. | −0.0827886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.40059e6 | −0.646424 | −0.323212 | − | 0.946327i | \(-0.604763\pi\) | ||||
−0.323212 | + | 0.946327i | \(0.604763\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.55980e6 | −0.663660 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.20192e6 | 0.894406 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.05280e6 | 1.00784 | 0.503922 | − | 0.863749i | \(-0.331890\pi\) | ||||
0.503922 | + | 0.863749i | \(0.331890\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.45897e6 | 0.206593 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.28537e7 | 1.80364 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.45282e6 | 0.202022 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.66752e6 | −0.229794 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.08665e7 | −1.48406 | −0.742028 | − | 0.670369i | \(-0.766136\pi\) | ||||
−0.742028 | + | 0.670369i | \(0.766136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.96658e6 | −0.942953 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 648.000 | 8.69296e−5 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50709e6 | −0.599274 | −0.299637 | − | 0.954053i | \(-0.596866\pi\) | ||||
−0.299637 | + | 0.954053i | \(0.596866\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.43605e7 | 1.89255 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −236196. | −0.0308542 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.57873e6 | −0.333907 | −0.166953 | − | 0.985965i | \(-0.553393\pi\) | ||||
−0.166953 | + | 0.985965i | \(0.553393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.02212e6 | 0.772963 | 0.386482 | − | 0.922297i | \(-0.373690\pi\) | ||||
0.386482 | + | 0.922297i | \(0.373690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.25630e6 | 0.923270 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.19620e6 | 1.15995 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.51475e7 | −1.89409 | −0.947047 | − | 0.321095i | \(-0.895949\pi\) | ||||
−0.947047 | + | 0.321095i | \(0.895949\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.94576e6 | 0.489141 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.38334e6 | −0.292918 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.15459e6 | 0.140688 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.61792e6 | 0.316276 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.30090e7 | 1.55829 | 0.779145 | − | 0.626843i | \(-0.215653\pi\) | ||||
0.779145 | + | 0.626843i | \(0.215653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.69011e7 | 2.00737 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.01198e6 | 0.354718 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 900818. | 0.105196 | 0.0525981 | − | 0.998616i | \(-0.483250\pi\) | ||||
0.0525981 | + | 0.998616i | \(0.483250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5760.00 | 0.000667007 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 569916. | 0.0654448 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.39649e7 | 1.59027 | 0.795135 | − | 0.606432i | \(-0.207400\pi\) | ||||
0.795135 | + | 0.606432i | \(0.207400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.28411e7 | −1.45017 | −0.725083 | − | 0.688662i | \(-0.758198\pi\) | ||||
−0.725083 | + | 0.688662i | \(0.758198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 941868. | 0.105486 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.27804e7 | −1.41957 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.62023e6 | 0.839453 | 0.419726 | − | 0.907651i | \(-0.362126\pi\) | ||||
0.419726 | + | 0.907651i | \(0.362126\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.42819e6 | −0.156043 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.29795e6 | 0.249022 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.50444e7 | −1.61705 | −0.808527 | − | 0.588459i | \(-0.799735\pi\) | ||||
−0.808527 | + | 0.588459i | \(0.799735\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.94928e6 | 0.527660 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.25329e6 | 0.132537 | 0.0662687 | − | 0.997802i | \(-0.478891\pi\) | ||||
0.0662687 | + | 0.997802i | \(0.478891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.56551e6 | 0.793618 | 0.396809 | − | 0.917901i | \(-0.370118\pi\) | ||||
0.396809 | + | 0.917901i | \(0.370118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.04703e6 | −0.213008 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.37910e6 | 0.245579 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.27438e6 | −0.949696 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 944784. | 0.0959762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4632.00 | −0.000466812 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00600e6 | −0.800465 | −0.400233 | − | 0.916414i | \(-0.631071\pi\) | ||||
−0.400233 | + | 0.916414i | \(0.631071\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.96192e6 | 0.591394 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.71843e7 | −2.67537 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.26644e6 | −0.611889 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 705672. | 0.0683677 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.20862e6 | 0.500700 | 0.250350 | − | 0.968155i | \(-0.419454\pi\) | ||||
0.250350 | + | 0.968155i | \(0.419454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.08288e6 | 0.484822 | 0.242411 | − | 0.970174i | \(-0.422062\pi\) | ||||
0.242411 | + | 0.970174i | \(0.422062\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.24157e7 | 1.17509 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.02670e7 | −0.964233 | −0.482117 | − | 0.876107i | \(-0.660132\pi\) | ||||
−0.482117 | + | 0.876107i | \(0.660132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.55909e6 | −0.145298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.87790e6 | −0.173668 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.06434e7 | −1.89452 | −0.947259 | − | 0.320469i | \(-0.896160\pi\) | ||||
−0.947259 | + | 0.320469i | \(0.896160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.67350e7 | 2.43488 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.28353e6 | −0.116009 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.87552e6 | −0.527027 | −0.263514 | − | 0.964656i | \(-0.584881\pi\) | ||||
−0.263514 | + | 0.964656i | \(0.584881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.07688e6 | 0.451953 | 0.225976 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225976 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7272.00 | 0.000642495 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.39808e6 | 0.736421 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.23777e7 | −1.07727 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.19734e7 | 1.03432 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 648432. | 0.0555979 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.12989e6 | 0.521693 | 0.260846 | − | 0.965380i | \(-0.415998\pi\) | ||||
0.260846 | + | 0.965380i | \(0.415998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.38748e6 | −0.201688 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.14086e6 | 0.263377 | 0.131688 | − | 0.991291i | \(-0.457960\pi\) | ||||
0.131688 | + | 0.991291i | \(0.457960\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.30855e6 | 0.358638 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.45440e6 | 0.533321 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.57417e7 | 1.29122 | 0.645609 | − | 0.763668i | \(-0.276604\pi\) | ||||
0.645609 | + | 0.763668i | \(0.276604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.15013e7 | 2.56509 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.78484e6 | 0.144281 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.29571e7 | 1.03982 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.05145e7 | −0.837708 | −0.418854 | − | 0.908054i | \(-0.637568\pi\) | ||||
−0.418854 | + | 0.908054i | \(0.637568\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −104976. | −0.00830342 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.95696e7 | −1.53681 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13748.0 | 0.00107191 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.74596e6 | 0.599628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.86967e6 | −0.451148 | −0.225574 | − | 0.974226i | \(-0.572426\pi\) | ||||
−0.225574 | + | 0.974226i | \(0.572426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.75346e6 | −0.515392 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.09536e6 | −0.310327 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.16611e6 | −0.0877388 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.27697e7 | 0.954037 | 0.477018 | − | 0.878893i | \(-0.341718\pi\) | ||||
0.477018 | + | 0.878893i | \(0.341718\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.26884e6 | −0.242504 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.62752e7 | −1.19895 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.16352e6 | 0.0851155 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.99168e6 | 0.289973 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.43243e7 | 1.75476 | 0.877380 | − | 0.479797i | \(-0.159290\pi\) | ||||
0.877380 | + | 0.479797i | \(0.159290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.94114e6 | −0.282347 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 308178. | 0.0219258 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.44362e7 | −1.02002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.65775e7 | 1.16328 | 0.581639 | − | 0.813447i | \(-0.302411\pi\) | ||||
0.581639 | + | 0.813447i | \(0.302411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34488.0 | 0.00238712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.50948e7 | 1.03769 | 0.518844 | − | 0.854869i | \(-0.326363\pi\) | ||||
0.518844 | + | 0.854869i | \(0.326363\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.11679e7 | 0.762525 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 418608. | 0.0283883 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.81265e7 | −1.22096 | −0.610481 | − | 0.792031i | \(-0.709024\pi\) | ||||
−0.610481 | + | 0.792031i | \(0.709024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.06026e7 | 0.709359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.97038e6 | 0.396762 | 0.198381 | − | 0.980125i | \(-0.436432\pi\) | ||||
0.198381 | + | 0.980125i | \(0.436432\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.94592e7 | −1.94460 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.36252e6 | 0.351615 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.83746e6 | −0.249942 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.93672e6 | 0.319402 | 0.159701 | − | 0.987165i | \(-0.448947\pi\) | ||||
0.159701 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.12447e6 | −0.136541 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.04042e7 | −1.94118 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.06262e7 | −0.673965 | −0.336982 | − | 0.941511i | \(-0.609406\pi\) | ||||
−0.336982 | + | 0.941511i | \(0.609406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −909792. | −0.0573242 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.05189e7 | 1.91032 | 0.955162 | − | 0.296085i | \(-0.0956813\pi\) | ||||
0.955162 | + | 0.296085i | \(0.0956813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.79086e6 | −0.173551 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12960.0 | −0.000800666 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.74964e7 | −1.07389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.25735e7 | 1.37652 | 0.688260 | − | 0.725464i | \(-0.258375\pi\) | ||||
0.688260 | + | 0.725464i | \(0.258375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.36354e6 | −0.506704 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.22743e6 | −0.495240 | −0.247620 | − | 0.968857i | \(-0.579648\pi\) | ||||
−0.247620 | + | 0.968857i | \(0.579648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.89819e7 | −1.13523 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 750384. | 0.0445893 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.00446e7 | 1.18346 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 313632. | 0.0183989 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.21343e6 | 0.187312 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.10563e7 | −2.37797 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.64585e7 | −1.52275 | −0.761373 | − | 0.648314i | \(-0.775474\pi\) | ||||
−0.761373 | + | 0.648314i | \(0.775474\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.52163e7 | 0.870197 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.46222e6 | −0.367232 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.27685e6 | 0.410923 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.30918e7 | −1.29581 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −599296. | −0.0334192 | −0.0167096 | − | 0.999860i | \(-0.505319\pi\) | ||||
−0.0167096 | + | 0.999860i | \(0.505319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11376.0 | −0.000630409 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.35297e6 | −0.294790 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −570456. | −0.0312200 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.08704e6 | −0.439845 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.10050e6 | 0.437853 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.97875e6 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551339\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.22959e7 | 1.72423 | 0.862116 | − | 0.506711i | \(-0.169139\pi\) | ||||
0.862116 | + | 0.506711i | \(0.169139\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.42550e7 | −0.756383 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.52000e6 | 0.132894 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.02835e7 | 2.63554 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.17806e6 | −0.0613704 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.94847e7 | −1.00887 | −0.504437 | − | 0.863449i | \(-0.668300\pi\) | ||||
−0.504437 | + | 0.863449i | \(0.668300\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.52634e7 | −1.30015 | −0.650073 | − | 0.759872i | \(-0.725262\pi\) | ||||
−0.650073 | + | 0.759872i | \(0.725262\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.06110e6 | −0.0542777 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.51164e6 | −0.331075 | −0.165538 | − | 0.986203i | \(-0.552936\pi\) | ||||
−0.165538 | + | 0.986203i | \(0.552936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.29742e7 | 0.655682 | 0.327841 | − | 0.944733i | \(-0.393679\pi\) | ||||
0.327841 | + | 0.944733i | \(0.393679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.75919e7 | −0.883713 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31022.0 | 0.00154902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.52480e6 | 0.423124 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.22528e6 | 0.208469 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 700056. | 0.0343343 | 0.0171671 | − | 0.999853i | \(-0.494535\pi\) | ||||
0.0171671 | + | 0.999853i | \(0.494535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.08068e6 | −0.0526877 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.94473e7 | 0.942517 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.66462e7 | −0.801996 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.75118e6 | 0.275454 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.93600e6 | −0.282634 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.50333e6 | 0.307831 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.98508e6 | 0.140470 | 0.0702351 | − | 0.997530i | \(-0.477625\pi\) | ||||
0.0702351 | + | 0.997530i | \(0.477625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.88957e7 | −0.883990 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.82849e7 | −0.850436 | −0.425218 | − | 0.905091i | \(-0.639803\pi\) | ||||
−0.425218 | + | 0.905091i | \(0.639803\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.64825e6 | −0.446134 | −0.223067 | − | 0.974803i | \(-0.571607\pi\) | ||||
−0.223067 | + | 0.974803i | \(0.571607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.22718e6 | −0.102387 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.02411e7 | −0.468081 | −0.234041 | − | 0.972227i | \(-0.575195\pi\) | ||||
−0.234041 | + | 0.972227i | \(0.575195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.99744e7 | 0.907681 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.27787e7 | 0.577349 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.45282e6 | −0.0652621 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.69771e6 | 0.209817 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.69424e6 | −0.430505 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −432000. | −0.0190750 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.42253e7 | 0.624545 | 0.312272 | − | 0.949993i | \(-0.398910\pi\) | ||||
0.312272 | + | 0.949993i | \(0.398910\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.22398e6 | −0.315358 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.91991e7 | −1.70152 | −0.850758 | − | 0.525558i | \(-0.823856\pi\) | ||||
−0.850758 | + | 0.525558i | \(0.823856\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.17875e7 | 0.940383 | 0.470191 | − | 0.882564i | \(-0.344185\pi\) | ||||
0.470191 | + | 0.882564i | \(0.344185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.11818e7 | 1.33827 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.95406e7 | −1.26070 | −0.630348 | − | 0.776313i | \(-0.717088\pi\) | ||||
−0.630348 | + | 0.776313i | \(0.717088\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.22329e7 | 0.519131 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 236196. | 0.00996732 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.65862e7 | −0.696015 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.90333e7 | −1.21154 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.02099e7 | −0.423682 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.55488e7 | 1.05432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64144.0 | −0.00263235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.58706e6 | −0.228015 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.05315e7 | 1.64502 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.26701e7 | 1.72229 | 0.861144 | − | 0.508362i | \(-0.169749\pi\) | ||||
0.861144 | + | 0.508362i | \(0.169749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.62375e6 | 0.105321 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.80109e7 | 1.11823 | 0.559115 | − | 0.829090i | \(-0.311141\pi\) | ||||
0.559115 | + | 0.829090i | \(0.311141\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.38334e6 | 0.0946258 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.29686e7 | −0.512085 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.20308e7 | −0.472465 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.94685e7 | −1.15098 | −0.575492 | − | 0.817808i | \(-0.695189\pi\) | ||||
−0.575492 | + | 0.817808i | \(0.695189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.60607e6 | 0.0623900 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.51965e6 | 0.135986 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.58490e6 | 0.291471 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.86756e6 | 0.338926 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.29283e7 | −0.871631 | −0.435816 | − | 0.900036i | \(-0.643540\pi\) | ||||
−0.435816 | + | 0.900036i | \(0.643540\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.52301e7 | 1.71022 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.13244e7 | 0.425905 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5760.00 | −0.000215473 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.94030e6 | 0.109406 | 0.0547032 | − | 0.998503i | \(-0.482579\pi\) | ||||
0.0547032 | + | 0.998503i | \(0.482579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.30756e6 | −0.307475 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.11062e7 | −1.14518 | −0.572589 | − | 0.819843i | \(-0.694061\pi\) | ||||
−0.572589 | + | 0.819843i | \(0.694061\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.93022e7 | −0.706850 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.09952e6 | 0.0764787 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.15022e7 | 0.779126 | 0.389563 | − | 0.921000i | \(-0.372626\pi\) | ||||
0.389563 | + | 0.921000i | \(0.372626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.40178e6 | −0.230747 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.11567e6 | −0.183422 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.04724e6 | −0.251355 | −0.125677 | − | 0.992071i | \(-0.540110\pi\) | ||||
−0.125677 | + | 0.992071i | \(0.540110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.45005e7 | −2.28852 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.42819e6 | 0.0504088 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.41756e7 | −0.497730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.96446e6 | 0.173406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.63428e6 | 0.300027 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.50734e7 | −1.21244 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.33230e7 | −0.458179 | −0.229090 | − | 0.973405i | \(-0.573575\pi\) | ||||
−0.229090 | + | 0.973405i | \(0.573575\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −52488.0 | −0.00179577 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.72053e7 | 0.585618 | 0.292809 | − | 0.956171i | \(-0.405410\pi\) | ||||
0.292809 | + | 0.956171i | \(0.405410\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.80632e6 | 0.298203 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.19079e7 | −0.401166 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.43520e7 | 1.15137 | 0.575686 | − | 0.817671i | \(-0.304735\pi\) | ||||
0.575686 | + | 0.817671i | \(0.304735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.37910e6 | −0.0793332 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.27944e6 | 0.208328 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.83486e7 | 0.605647 | 0.302824 | − | 0.953047i | \(-0.402071\pi\) | ||||
0.302824 | + | 0.953047i | \(0.402071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.67731e7 | −0.879242 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.84291e6 | 0.0602160 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.84212e7 | −1.57414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.27810e7 | −0.736866 | −0.368433 | − | 0.929654i | \(-0.620106\pi\) | ||||
−0.368433 | + | 0.929654i | \(0.620106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.34579e7 | −0.754947 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.06592e6 | −0.162219 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50268e7 | −0.797382 | −0.398691 | − | 0.917085i | \(-0.630535\pi\) | ||||
−0.398691 | + | 0.917085i | \(0.630535\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.68836e6 | −0.0535245 |
(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 | 768.6.a.e.1.1 | 1 | ||
4.3 | odd | 2 | 768.6.a.k.1.1 | 1 | |||
8.3 | odd | 2 | 768.6.a.b.1.1 | 1 | |||
8.5 | even | 2 | 768.6.a.h.1.1 | 1 | |||
16.3 | odd | 4 | 384.6.d.c.193.2 | yes | 2 | ||
16.5 | even | 4 | 384.6.d.d.193.2 | yes | 2 | ||
16.11 | odd | 4 | 384.6.d.c.193.1 | ✓ | 2 | ||
16.13 | even | 4 | 384.6.d.d.193.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.d.c.193.1 | ✓ | 2 | 16.11 | odd | 4 | ||
384.6.d.c.193.2 | yes | 2 | 16.3 | odd | 4 | ||
384.6.d.d.193.1 | yes | 2 | 16.13 | even | 4 | ||
384.6.d.d.193.2 | yes | 2 | 16.5 | even | 4 | ||
768.6.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
768.6.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
768.6.a.h.1.1 | 1 | 8.5 | even | 2 | |||
768.6.a.k.1.1 | 1 | 4.3 | odd | 2 |