Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,8,Mod(99,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.99");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.c (of order \(2\), degree \(1\), 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: | \(109.334758919\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{8761})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4381x^{2} + 4796100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.3 | ||
Root | \(-46.3001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.99 |
Dual form | 350.8.c.i.99.2 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000i | 0.707107i | ||||||||
\(3\) | − 44.3001i | − 0.947284i | −0.880717 | − | 0.473642i | \(-0.842939\pi\) | ||||
0.880717 | − | 0.473642i | \(-0.157061\pi\) | |||||||
\(4\) | −64.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 354.401 | 0.669831 | ||||||||
\(7\) | 343.000i | 0.377964i | ||||||||
\(8\) | − 512.000i | − 0.353553i | ||||||||
\(9\) | 224.501 | 0.102652 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8294.71 | 1.87900 | 0.939500 | − | 0.342548i | \(-0.111290\pi\) | ||||
0.939500 | + | 0.342548i | \(0.111290\pi\) | |||||||
\(12\) | 2835.21i | 0.473642i | ||||||||
\(13\) | − 2086.69i | − 0.263425i | −0.991288 | − | 0.131713i | \(-0.957952\pi\) | ||||
0.991288 | − | 0.131713i | \(-0.0420476\pi\) | |||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 22276.5i | 1.09970i | 0.835262 | + | 0.549852i | \(0.185316\pi\) | ||||
−0.835262 | + | 0.549852i | \(0.814684\pi\) | |||||||
\(18\) | 1796.00i | 0.0725861i | ||||||||
\(19\) | −22693.4 | −0.759035 | −0.379518 | − | 0.925184i | \(-0.623910\pi\) | ||||
−0.379518 | + | 0.925184i | \(0.623910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15194.9 | 0.358040 | ||||||||
\(22\) | 66357.7i | 1.32865i | ||||||||
\(23\) | 51846.8i | 0.888534i | 0.895894 | + | 0.444267i | \(0.146536\pi\) | ||||
−0.895894 | + | 0.444267i | \(0.853464\pi\) | |||||||
\(24\) | −22681.7 | −0.334916 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 16693.6 | 0.186270 | ||||||||
\(27\) | − 106830.i | − 1.04453i | ||||||||
\(28\) | − 21952.0i | − 0.188982i | ||||||||
\(29\) | 69360.5 | 0.528103 | 0.264052 | − | 0.964509i | \(-0.414941\pi\) | ||||
0.264052 | + | 0.964509i | \(0.414941\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 54654.7 | 0.329505 | 0.164752 | − | 0.986335i | \(-0.447318\pi\) | ||||
0.164752 | + | 0.986335i | \(0.447318\pi\) | |||||||
\(32\) | 32768.0i | 0.176777i | ||||||||
\(33\) | − 367457.i | − 1.77995i | ||||||||
\(34\) | −178212. | −0.777608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −14368.0 | −0.0513261 | ||||||||
\(37\) | 301929.i | 0.979938i | 0.871740 | + | 0.489969i | \(0.162992\pi\) | ||||
−0.871740 | + | 0.489969i | \(0.837008\pi\) | |||||||
\(38\) | − 181547.i | − 0.536719i | ||||||||
\(39\) | −92440.8 | −0.249538 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −120041. | −0.272010 | −0.136005 | − | 0.990708i | \(-0.543426\pi\) | ||||
−0.136005 | + | 0.990708i | \(0.543426\pi\) | |||||||
\(42\) | 121559.i | 0.253172i | ||||||||
\(43\) | 260607.i | 0.499859i | 0.968264 | + | 0.249929i | \(0.0804074\pi\) | ||||
−0.968264 | + | 0.249929i | \(0.919593\pi\) | |||||||
\(44\) | −530862. | −0.939500 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −414774. | −0.628289 | ||||||||
\(47\) | − 282025.i | − 0.396228i | −0.980179 | − | 0.198114i | \(-0.936518\pi\) | ||||
0.980179 | − | 0.198114i | \(-0.0634816\pi\) | |||||||
\(48\) | − 181453.i | − 0.236821i | ||||||||
\(49\) | −117649. | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 986852. | 1.04173 | ||||||||
\(52\) | 133548.i | 0.131713i | ||||||||
\(53\) | − 413071.i | − 0.381118i | −0.981676 | − | 0.190559i | \(-0.938970\pi\) | ||||
0.981676 | − | 0.190559i | \(-0.0610300\pi\) | |||||||
\(54\) | 854638. | 0.738591 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | 1.00532e6i | 0.719022i | ||||||||
\(58\) | 554884.i | 0.373426i | ||||||||
\(59\) | −961690. | −0.609611 | −0.304806 | − | 0.952415i | \(-0.598591\pi\) | ||||
−0.304806 | + | 0.952415i | \(0.598591\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.52312e6 | −1.42326 | −0.711630 | − | 0.702555i | \(-0.752043\pi\) | ||||
−0.711630 | + | 0.702555i | \(0.752043\pi\) | |||||||
\(62\) | 437238.i | 0.232995i | ||||||||
\(63\) | 77003.7i | 0.0387989i | ||||||||
\(64\) | −262144. | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.93965e6 | 1.25861 | ||||||||
\(67\) | − 133835.i | − 0.0543637i | −0.999631 | − | 0.0271819i | \(-0.991347\pi\) | ||||
0.999631 | − | 0.0271819i | \(-0.00865332\pi\) | |||||||
\(68\) | − 1.42570e6i | − 0.549852i | ||||||||
\(69\) | 2.29682e6 | 0.841695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.71568e6 | −1.89524 | −0.947619 | − | 0.319404i | \(-0.896517\pi\) | ||||
−0.947619 | + | 0.319404i | \(0.896517\pi\) | |||||||
\(72\) | − 114944.i | − 0.0362931i | ||||||||
\(73\) | − 28628.0i | − 0.00861314i | −0.999991 | − | 0.00430657i | \(-0.998629\pi\) | ||||
0.999991 | − | 0.00430657i | \(-0.00137083\pi\) | |||||||
\(74\) | −2.41543e6 | −0.692921 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.45238e6 | 0.379518 | ||||||||
\(77\) | 2.84509e6i | 0.710196i | ||||||||
\(78\) | − 739526.i | − 0.176450i | ||||||||
\(79\) | 7.61428e6 | 1.73754 | 0.868768 | − | 0.495219i | \(-0.164912\pi\) | ||||
0.868768 | + | 0.495219i | \(0.164912\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.24159e6 | −0.886810 | ||||||||
\(82\) | − 960326.i | − 0.192340i | ||||||||
\(83\) | 2.64843e6i | 0.508411i | 0.967150 | + | 0.254206i | \(0.0818140\pi\) | ||||
−0.967150 | + | 0.254206i | \(0.918186\pi\) | |||||||
\(84\) | −972476. | −0.179020 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.08486e6 | −0.353453 | ||||||||
\(87\) | − 3.07268e6i | − 0.500264i | ||||||||
\(88\) | − 4.24689e6i | − 0.664327i | ||||||||
\(89\) | 7.82855e6 | 1.17711 | 0.588554 | − | 0.808458i | \(-0.299697\pi\) | ||||
0.588554 | + | 0.808458i | \(0.299697\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 715736. | 0.0995653 | ||||||||
\(92\) | − 3.31819e6i | − 0.444267i | ||||||||
\(93\) | − 2.42121e6i | − 0.312135i | ||||||||
\(94\) | 2.25620e6 | 0.280175 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.45163e6 | 0.167458 | ||||||||
\(97\) | 9.84758e6i | 1.09554i | 0.836629 | + | 0.547770i | \(0.184523\pi\) | ||||
−0.836629 | + | 0.547770i | \(0.815477\pi\) | |||||||
\(98\) | − 941192.i | − 0.101015i | ||||||||
\(99\) | 1.86217e6 | 0.192884 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.89329e7 | 1.82848 | 0.914242 | − | 0.405168i | \(-0.132787\pi\) | ||||
0.914242 | + | 0.405168i | \(0.132787\pi\) | |||||||
\(102\) | 7.89481e6i | 0.736616i | ||||||||
\(103\) | 1.88723e7i | 1.70174i | 0.525374 | + | 0.850871i | \(0.323925\pi\) | ||||
−0.525374 | + | 0.850871i | \(0.676075\pi\) | |||||||
\(104\) | −1.06839e6 | −0.0931348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.30457e6 | 0.269491 | ||||||||
\(107\) | − 1.75676e6i | − 0.138634i | −0.997595 | − | 0.0693168i | \(-0.977918\pi\) | ||||
0.997595 | − | 0.0693168i | \(-0.0220819\pi\) | |||||||
\(108\) | 6.83710e6i | 0.522263i | ||||||||
\(109\) | 1.51030e7 | 1.11704 | 0.558521 | − | 0.829490i | \(-0.311369\pi\) | ||||
0.558521 | + | 0.829490i | \(0.311369\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.33755e7 | 0.928280 | ||||||||
\(112\) | 1.40493e6i | 0.0944911i | ||||||||
\(113\) | 9.05559e6i | 0.590394i | 0.955436 | + | 0.295197i | \(0.0953854\pi\) | ||||
−0.955436 | + | 0.295197i | \(0.904615\pi\) | |||||||
\(114\) | −8.04256e6 | −0.508426 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.43907e6 | −0.264052 | ||||||||
\(117\) | − 468464.i | − 0.0270412i | ||||||||
\(118\) | − 7.69352e6i | − 0.431060i | ||||||||
\(119\) | −7.64084e6 | −0.415649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.93151e7 | 2.53064 | ||||||||
\(122\) | − 2.01850e7i | − 1.00640i | ||||||||
\(123\) | 5.31782e6i | 0.257671i | ||||||||
\(124\) | −3.49790e6 | −0.164752 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −616029. | −0.0274350 | ||||||||
\(127\) | 3.51254e7i | 1.52163i | 0.648971 | + | 0.760813i | \(0.275200\pi\) | ||||
−0.648971 | + | 0.760813i | \(0.724800\pi\) | |||||||
\(128\) | − 2.09715e6i | − 0.0883883i | ||||||||
\(129\) | 1.15449e7 | 0.473508 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.78958e7 | 1.86143 | 0.930717 | − | 0.365740i | \(-0.119184\pi\) | ||||
0.930717 | + | 0.365740i | \(0.119184\pi\) | |||||||
\(132\) | 2.35172e7i | 0.889974i | ||||||||
\(133\) | − 7.78384e6i | − 0.286888i | ||||||||
\(134\) | 1.07068e6 | 0.0384409 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.14056e7 | 0.388804 | ||||||||
\(137\) | − 3.21903e6i | − 0.106955i | −0.998569 | − | 0.0534777i | \(-0.982969\pi\) | ||||
0.998569 | − | 0.0534777i | \(-0.0170306\pi\) | |||||||
\(138\) | 1.83745e7i | 0.595168i | ||||||||
\(139\) | −2.92523e7 | −0.923866 | −0.461933 | − | 0.886915i | \(-0.652844\pi\) | ||||
−0.461933 | + | 0.886915i | \(0.652844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.24937e7 | −0.375341 | ||||||||
\(142\) | − 4.57254e7i | − 1.34014i | ||||||||
\(143\) | − 1.73085e7i | − 0.494976i | ||||||||
\(144\) | 919554. | 0.0256631 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 229024. | 0.00609041 | ||||||||
\(147\) | 5.21186e6i | 0.135326i | ||||||||
\(148\) | − 1.93234e7i | − 0.489969i | ||||||||
\(149\) | −2.12164e7 | −0.525436 | −0.262718 | − | 0.964873i | \(-0.584619\pi\) | ||||
−0.262718 | + | 0.964873i | \(0.584619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.71361e7 | −0.641398 | −0.320699 | − | 0.947181i | \(-0.603918\pi\) | ||||
−0.320699 | + | 0.947181i | \(0.603918\pi\) | |||||||
\(152\) | 1.16190e7i | 0.268360i | ||||||||
\(153\) | 5.00109e6i | 0.112887i | ||||||||
\(154\) | −2.27607e7 | −0.502184 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.91621e6 | 0.124769 | ||||||||
\(157\) | − 1.51261e7i | − 0.311944i | −0.987761 | − | 0.155972i | \(-0.950149\pi\) | ||||
0.987761 | − | 0.155972i | \(-0.0498510\pi\) | |||||||
\(158\) | 6.09142e7i | 1.22862i | ||||||||
\(159\) | −1.82991e7 | −0.361027 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.77834e7 | −0.335834 | ||||||||
\(162\) | − 3.39327e7i | − 0.627070i | ||||||||
\(163\) | 1.01081e8i | 1.82816i | 0.405536 | + | 0.914079i | \(0.367085\pi\) | ||||
−0.405536 | + | 0.914079i | \(0.632915\pi\) | |||||||
\(164\) | 7.68261e6 | 0.136005 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.11874e7 | −0.359501 | ||||||||
\(167\) | − 4.83737e7i | − 0.803714i | −0.915702 | − | 0.401857i | \(-0.868365\pi\) | ||||
0.915702 | − | 0.401857i | \(-0.131635\pi\) | |||||||
\(168\) | − 7.77981e6i | − 0.126586i | ||||||||
\(169\) | 5.83942e7 | 0.930607 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.09468e6 | −0.0779167 | ||||||||
\(172\) | − 1.66789e7i | − 0.249929i | ||||||||
\(173\) | − 6.02289e6i | − 0.0884390i | −0.999022 | − | 0.0442195i | \(-0.985920\pi\) | ||||
0.999022 | − | 0.0442195i | \(-0.0140801\pi\) | |||||||
\(174\) | 2.45814e7 | 0.353740 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.39751e7 | 0.469750 | ||||||||
\(177\) | 4.26030e7i | 0.577475i | ||||||||
\(178\) | 6.26284e7i | 0.832341i | ||||||||
\(179\) | 1.04527e7 | 0.136221 | 0.0681103 | − | 0.997678i | \(-0.478303\pi\) | ||||
0.0681103 | + | 0.997678i | \(0.478303\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.01810e8 | 1.27619 | 0.638095 | − | 0.769958i | \(-0.279723\pi\) | ||||
0.638095 | + | 0.769958i | \(0.279723\pi\) | |||||||
\(182\) | 5.72589e6i | 0.0704033i | ||||||||
\(183\) | 1.11775e8i | 1.34823i | ||||||||
\(184\) | 2.65455e7 | 0.314144 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.93697e7 | 0.220712 | ||||||||
\(187\) | 1.84777e8i | 2.06635i | ||||||||
\(188\) | 1.80496e7i | 0.198114i | ||||||||
\(189\) | 3.66426e7 | 0.394793 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.16808e8 | 1.21299 | 0.606495 | − | 0.795088i | \(-0.292575\pi\) | ||||
0.606495 | + | 0.795088i | \(0.292575\pi\) | |||||||
\(192\) | 1.16130e7i | 0.118411i | ||||||||
\(193\) | 1.72514e8i | 1.72732i | 0.504073 | + | 0.863661i | \(0.331834\pi\) | ||||
−0.504073 | + | 0.863661i | \(0.668166\pi\) | |||||||
\(194\) | −7.87807e7 | −0.774664 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | − 1.13246e8i | − 1.05534i | −0.849450 | − | 0.527669i | \(-0.823066\pi\) | ||||
0.849450 | − | 0.527669i | \(-0.176934\pi\) | |||||||
\(198\) | 1.48973e7i | 0.136389i | ||||||||
\(199\) | −1.87994e8 | −1.69106 | −0.845529 | − | 0.533930i | \(-0.820715\pi\) | ||||
−0.845529 | + | 0.533930i | \(0.820715\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.92892e6 | −0.0514979 | ||||||||
\(202\) | 1.51463e8i | 1.29293i | ||||||||
\(203\) | 2.37906e7i | 0.199604i | ||||||||
\(204\) | −6.31585e7 | −0.520866 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.50978e8 | −1.20331 | ||||||||
\(207\) | 1.16396e7i | 0.0912101i | ||||||||
\(208\) | − 8.54710e6i | − 0.0658563i | ||||||||
\(209\) | −1.88235e8 | −1.42623 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.04724e7 | −0.150031 | −0.0750155 | − | 0.997182i | \(-0.523901\pi\) | ||||
−0.0750155 | + | 0.997182i | \(0.523901\pi\) | |||||||
\(212\) | 2.64365e7i | 0.190559i | ||||||||
\(213\) | 2.53205e8i | 1.79533i | ||||||||
\(214\) | 1.40541e7 | 0.0980287 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.46968e7 | −0.369295 | ||||||||
\(217\) | 1.87466e7i | 0.124541i | ||||||||
\(218\) | 1.20824e8i | 0.789868i | ||||||||
\(219\) | −1.26823e6 | −0.00815910 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.64843e7 | 0.289690 | ||||||||
\(222\) | 1.07004e8i | 0.656393i | ||||||||
\(223\) | − 1.96181e8i | − 1.18465i | −0.805698 | − | 0.592326i | \(-0.798210\pi\) | ||||
0.805698 | − | 0.592326i | \(-0.201790\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.24447e7 | −0.417472 | ||||||||
\(227\) | 9.92114e7i | 0.562951i | 0.959568 | + | 0.281476i | \(0.0908239\pi\) | ||||
−0.959568 | + | 0.281476i | \(0.909176\pi\) | |||||||
\(228\) | − 6.43405e7i | − 0.359511i | ||||||||
\(229\) | −2.80737e7 | −0.154481 | −0.0772407 | − | 0.997012i | \(-0.524611\pi\) | ||||
−0.0772407 | + | 0.997012i | \(0.524611\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.26038e8 | 0.672757 | ||||||||
\(232\) | − 3.55126e7i | − 0.186713i | ||||||||
\(233\) | 2.59746e7i | 0.134525i | 0.997735 | + | 0.0672626i | \(0.0214265\pi\) | ||||
−0.997735 | + | 0.0672626i | \(0.978573\pi\) | |||||||
\(234\) | 3.74771e6 | 0.0191210 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.15481e7 | 0.304806 | ||||||||
\(237\) | − 3.37313e8i | − 1.64594i | ||||||||
\(238\) | − 6.11267e7i | − 0.293908i | ||||||||
\(239\) | 2.89625e8 | 1.37228 | 0.686142 | − | 0.727468i | \(-0.259303\pi\) | ||||
0.686142 | + | 0.727468i | \(0.259303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.35224e8 | −1.08248 | −0.541242 | − | 0.840867i | \(-0.682046\pi\) | ||||
−0.541242 | + | 0.840867i | \(0.682046\pi\) | |||||||
\(242\) | 3.94521e8i | 1.78944i | ||||||||
\(243\) | − 4.57339e7i | − 0.204464i | ||||||||
\(244\) | 1.61480e8 | 0.711630 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.25426e7 | −0.182201 | ||||||||
\(247\) | 4.73542e7i | 0.199949i | ||||||||
\(248\) | − 2.79832e7i | − 0.116497i | ||||||||
\(249\) | 1.17326e8 | 0.481610 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.71067e8 | 1.48113 | 0.740566 | − | 0.671984i | \(-0.234558\pi\) | ||||
0.740566 | + | 0.671984i | \(0.234558\pi\) | |||||||
\(252\) | − 4.92824e6i | − 0.0193995i | ||||||||
\(253\) | 4.30054e8i | 1.66956i | ||||||||
\(254\) | −2.81003e8 | −1.07595 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 2.53506e8i | 0.931585i | 0.884894 | + | 0.465792i | \(0.154231\pi\) | ||||
−0.884894 | + | 0.465792i | \(0.845769\pi\) | |||||||
\(258\) | 9.23595e7i | 0.334821i | ||||||||
\(259\) | −1.03562e8 | −0.370382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.55715e7 | 0.0542110 | ||||||||
\(262\) | 3.83166e8i | 1.31623i | ||||||||
\(263\) | − 3.39492e8i | − 1.15076i | −0.817887 | − | 0.575379i | \(-0.804855\pi\) | ||||
0.817887 | − | 0.575379i | \(-0.195145\pi\) | |||||||
\(264\) | −1.88138e8 | −0.629307 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.22707e7 | 0.202861 | ||||||||
\(267\) | − 3.46806e8i | − 1.11506i | ||||||||
\(268\) | 8.56546e6i | 0.0271819i | ||||||||
\(269\) | −1.51784e8 | −0.475436 | −0.237718 | − | 0.971334i | \(-0.576399\pi\) | ||||
−0.237718 | + | 0.971334i | \(0.576399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.09610e7 | 0.186063 | 0.0930314 | − | 0.995663i | \(-0.470344\pi\) | ||||
0.0930314 | + | 0.995663i | \(0.470344\pi\) | |||||||
\(272\) | 9.12446e7i | 0.274926i | ||||||||
\(273\) | − 3.17072e7i | − 0.0943167i | ||||||||
\(274\) | 2.57522e7 | 0.0756289 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.46996e8 | −0.420847 | ||||||||
\(277\) | − 2.27766e8i | − 0.643888i | −0.946759 | − | 0.321944i | \(-0.895664\pi\) | ||||
0.946759 | − | 0.321944i | \(-0.104336\pi\) | |||||||
\(278\) | − 2.34019e8i | − 0.653272i | ||||||||
\(279\) | 1.22700e7 | 0.0338244 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.86914e8 | 1.30912 | 0.654560 | − | 0.756010i | \(-0.272854\pi\) | ||||
0.654560 | + | 0.756010i | \(0.272854\pi\) | |||||||
\(282\) | − 9.99499e7i | − 0.265406i | ||||||||
\(283\) | 2.62185e8i | 0.687631i | 0.939037 | + | 0.343815i | \(0.111719\pi\) | ||||
−0.939037 | + | 0.343815i | \(0.888281\pi\) | |||||||
\(284\) | 3.65803e8 | 0.947619 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.38468e8 | 0.350001 | ||||||||
\(287\) | − 4.11740e7i | − 0.102810i | ||||||||
\(288\) | 7.35643e6i | 0.0181465i | ||||||||
\(289\) | −8.59041e7 | −0.209349 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.36249e8 | 1.03779 | ||||||||
\(292\) | 1.83219e6i | 0.00430657i | ||||||||
\(293\) | − 7.42829e7i | − 0.172525i | −0.996272 | − | 0.0862625i | \(-0.972508\pi\) | ||||
0.996272 | − | 0.0862625i | \(-0.0274924\pi\) | |||||||
\(294\) | −4.16949e7 | −0.0956902 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.54588e8 | 0.346460 | ||||||||
\(297\) | − 8.86122e8i | − 1.96266i | ||||||||
\(298\) | − 1.69731e8i | − 0.371539i | ||||||||
\(299\) | 1.08188e8 | 0.234062 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.93883e7 | −0.188929 | ||||||||
\(302\) | − 2.17089e8i | − 0.453537i | ||||||||
\(303\) | − 8.38728e8i | − 1.73210i | ||||||||
\(304\) | −9.29522e7 | −0.189759 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00087e7 | −0.0798233 | ||||||||
\(307\) | − 4.64592e8i | − 0.916404i | −0.888848 | − | 0.458202i | \(-0.848494\pi\) | ||||
0.888848 | − | 0.458202i | \(-0.151506\pi\) | |||||||
\(308\) | − 1.82086e8i | − 0.355098i | ||||||||
\(309\) | 8.36043e8 | 1.61203 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.84752e8 | −1.29084 | −0.645419 | − | 0.763829i | \(-0.723317\pi\) | ||||
−0.645419 | + | 0.763829i | \(0.723317\pi\) | |||||||
\(312\) | 4.73297e7i | 0.0882252i | ||||||||
\(313\) | 2.85953e8i | 0.527096i | 0.964646 | + | 0.263548i | \(0.0848927\pi\) | ||||
−0.964646 | + | 0.263548i | \(0.915107\pi\) | |||||||
\(314\) | 1.21009e8 | 0.220578 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.87314e8 | −0.868768 | ||||||||
\(317\) | 8.17943e8i | 1.44217i | 0.692848 | + | 0.721084i | \(0.256356\pi\) | ||||
−0.692848 | + | 0.721084i | \(0.743644\pi\) | |||||||
\(318\) | − 1.46393e8i | − 0.255284i | ||||||||
\(319\) | 5.75325e8 | 0.992307 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.78245e7 | −0.131325 | ||||||||
\(322\) | − 1.42268e8i | − 0.237471i | ||||||||
\(323\) | − 5.05530e8i | − 0.834714i | ||||||||
\(324\) | 2.71461e8 | 0.443405 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.08649e8 | −1.29270 | ||||||||
\(327\) | − 6.69063e8i | − 1.05816i | ||||||||
\(328\) | 6.14609e7i | 0.0961702i | ||||||||
\(329\) | 9.67346e7 | 0.149760 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.47073e8 | 1.43544 | 0.717720 | − | 0.696331i | \(-0.245186\pi\) | ||||
0.717720 | + | 0.696331i | \(0.245186\pi\) | |||||||
\(332\) | − 1.69499e8i | − 0.254206i | ||||||||
\(333\) | 6.77832e7i | 0.100593i | ||||||||
\(334\) | 3.86990e8 | 0.568312 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.22385e7 | 0.0895100 | ||||||||
\(337\) | − 1.36535e9i | − 1.94330i | −0.236415 | − | 0.971652i | \(-0.575973\pi\) | ||||
0.236415 | − | 0.971652i | \(-0.424027\pi\) | |||||||
\(338\) | 4.67154e8i | 0.658039i | ||||||||
\(339\) | 4.01164e8 | 0.559271 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.53345e8 | 0.619139 | ||||||||
\(342\) | − 4.07574e7i | − 0.0550954i | ||||||||
\(343\) | − 4.03536e7i | − 0.0539949i | ||||||||
\(344\) | 1.33431e8 | 0.176727 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.81831e7 | 0.0625358 | ||||||||
\(347\) | 9.66351e8i | 1.24160i | 0.783969 | + | 0.620800i | \(0.213192\pi\) | ||||
−0.783969 | + | 0.620800i | \(0.786808\pi\) | |||||||
\(348\) | 1.96651e8i | 0.250132i | ||||||||
\(349\) | −6.50882e8 | −0.819621 | −0.409811 | − | 0.912171i | \(-0.634405\pi\) | ||||
−0.409811 | + | 0.912171i | \(0.634405\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.22921e8 | −0.275154 | ||||||||
\(352\) | 2.71801e8i | 0.332164i | ||||||||
\(353\) | − 6.03836e8i | − 0.730647i | −0.930881 | − | 0.365323i | \(-0.880958\pi\) | ||||
0.930881 | − | 0.365323i | \(-0.119042\pi\) | |||||||
\(354\) | −3.40824e8 | −0.408337 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.01027e8 | −0.588554 | ||||||||
\(357\) | 3.38490e8i | 0.393738i | ||||||||
\(358\) | 8.36216e7i | 0.0963225i | ||||||||
\(359\) | −8.56904e7 | −0.0977466 | −0.0488733 | − | 0.998805i | \(-0.515563\pi\) | ||||
−0.0488733 | + | 0.998805i | \(0.515563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.78881e8 | −0.423865 | ||||||||
\(362\) | 8.14480e8i | 0.902403i | ||||||||
\(363\) | − 2.18466e9i | − 2.39724i | ||||||||
\(364\) | −4.58071e7 | −0.0497827 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.94197e8 | −0.953343 | ||||||||
\(367\) | − 1.63658e9i | − 1.72825i | −0.503276 | − | 0.864126i | \(-0.667872\pi\) | ||||
0.503276 | − | 0.864126i | \(-0.332128\pi\) | |||||||
\(368\) | 2.12364e8i | 0.222134i | ||||||||
\(369\) | −2.69492e7 | −0.0279225 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.41683e8 | 0.144049 | ||||||||
\(372\) | 1.54957e8i | 0.156067i | ||||||||
\(373\) | 1.88055e9i | 1.87630i | 0.346223 | + | 0.938152i | \(0.387464\pi\) | ||||
−0.346223 | + | 0.938152i | \(0.612536\pi\) | |||||||
\(374\) | −1.47822e9 | −1.46113 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.44397e8 | −0.140088 | ||||||||
\(377\) | − 1.44734e8i | − 0.139116i | ||||||||
\(378\) | 2.93141e8i | 0.279161i | ||||||||
\(379\) | −6.07726e8 | −0.573417 | −0.286708 | − | 0.958018i | \(-0.592561\pi\) | ||||
−0.286708 | + | 0.958018i | \(0.592561\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.55606e9 | 1.44141 | ||||||||
\(382\) | 9.34467e8i | 0.857713i | ||||||||
\(383\) | 1.54124e8i | 0.140176i | 0.997541 | + | 0.0700882i | \(0.0223281\pi\) | ||||
−0.997541 | + | 0.0700882i | \(0.977672\pi\) | |||||||
\(384\) | −9.29041e7 | −0.0837289 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.38011e9 | −1.22140 | ||||||||
\(387\) | 5.85065e7i | 0.0513116i | ||||||||
\(388\) | − 6.30245e8i | − 0.547770i | ||||||||
\(389\) | 1.99567e9 | 1.71896 | 0.859480 | − | 0.511170i | \(-0.170788\pi\) | ||||
0.859480 | + | 0.511170i | \(0.170788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.15496e9 | −0.977125 | ||||||||
\(392\) | 6.02363e7i | 0.0505076i | ||||||||
\(393\) | − 2.12179e9i | − 1.76331i | ||||||||
\(394\) | 9.05968e8 | 0.746236 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.19179e8 | −0.0964419 | ||||||||
\(397\) | 6.91714e8i | 0.554830i | 0.960750 | + | 0.277415i | \(0.0894777\pi\) | ||||
−0.960750 | + | 0.277415i | \(0.910522\pi\) | |||||||
\(398\) | − 1.50395e9i | − 1.19576i | ||||||||
\(399\) | −3.44825e8 | −0.271765 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.80549e8 | −0.449608 | −0.224804 | − | 0.974404i | \(-0.572174\pi\) | ||||
−0.224804 | + | 0.974404i | \(0.572174\pi\) | |||||||
\(402\) | − 4.74314e7i | − 0.0364145i | ||||||||
\(403\) | − 1.14048e8i | − 0.0867998i | ||||||||
\(404\) | −1.21170e9 | −0.914242 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.90325e8 | −0.141142 | ||||||||
\(407\) | 2.50441e9i | 1.84130i | ||||||||
\(408\) | − 5.05268e8i | − 0.368308i | ||||||||
\(409\) | 1.05158e9 | 0.759997 | 0.379998 | − | 0.924987i | \(-0.375925\pi\) | ||||
0.379998 | + | 0.924987i | \(0.375925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.42603e8 | −0.101317 | ||||||||
\(412\) | − 1.20783e9i | − 0.850871i | ||||||||
\(413\) | − 3.29860e8i | − 0.230411i | ||||||||
\(414\) | −9.31170e7 | −0.0644953 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.83768e7 | 0.0465674 | ||||||||
\(417\) | 1.29588e9i | 0.875164i | ||||||||
\(418\) | − 1.50588e9i | − 1.00850i | ||||||||
\(419\) | −1.96750e9 | −1.30667 | −0.653335 | − | 0.757069i | \(-0.726631\pi\) | ||||
−0.653335 | + | 0.757069i | \(0.726631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.78313e8 | −0.181780 | −0.0908901 | − | 0.995861i | \(-0.528971\pi\) | ||||
−0.0908901 | + | 0.995861i | \(0.528971\pi\) | |||||||
\(422\) | − 1.63780e8i | − 0.106088i | ||||||||
\(423\) | − 6.33148e7i | − 0.0406737i | ||||||||
\(424\) | −2.11492e8 | −0.134745 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.02564e9 | −1.26949 | ||||||||
\(427\) | − 8.65431e8i | − 0.537941i | ||||||||
\(428\) | 1.12432e8i | 0.0693168i | ||||||||
\(429\) | −7.66770e8 | −0.468883 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.77969e9 | −1.67234 | −0.836172 | − | 0.548467i | \(-0.815212\pi\) | ||||
−0.836172 | + | 0.548467i | \(0.815212\pi\) | |||||||
\(432\) | − 4.37575e8i | − 0.261131i | ||||||||
\(433\) | − 1.40755e9i | − 0.833213i | −0.909087 | − | 0.416607i | \(-0.863219\pi\) | ||||
0.909087 | − | 0.416607i | \(-0.136781\pi\) | |||||||
\(434\) | −1.49972e8 | −0.0880638 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.66590e8 | −0.558521 | ||||||||
\(437\) | − 1.17658e9i | − 0.674429i | ||||||||
\(438\) | − 1.01458e7i | − 0.00576935i | ||||||||
\(439\) | 1.57299e9 | 0.887362 | 0.443681 | − | 0.896185i | \(-0.353672\pi\) | ||||
0.443681 | + | 0.896185i | \(0.353672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.64123e7 | −0.0146646 | ||||||||
\(442\) | 3.71874e8i | 0.204842i | ||||||||
\(443\) | − 1.33047e9i | − 0.727098i | −0.931575 | − | 0.363549i | \(-0.881565\pi\) | ||||
0.931575 | − | 0.363549i | \(-0.118435\pi\) | |||||||
\(444\) | −8.56031e8 | −0.464140 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.56945e9 | 0.837675 | ||||||||
\(447\) | 9.39888e8i | 0.497737i | ||||||||
\(448\) | − 8.99154e7i | − 0.0472456i | ||||||||
\(449\) | −2.75936e9 | −1.43862 | −0.719310 | − | 0.694689i | \(-0.755542\pi\) | ||||
−0.719310 | + | 0.694689i | \(0.755542\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.95704e8 | −0.511108 | ||||||||
\(452\) | − 5.79558e8i | − 0.295197i | ||||||||
\(453\) | 1.20213e9i | 0.607586i | ||||||||
\(454\) | −7.93691e8 | −0.398067 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.14724e8 | 0.254213 | ||||||||
\(457\) | − 4.55675e8i | − 0.223331i | −0.993746 | − | 0.111665i | \(-0.964381\pi\) | ||||
0.993746 | − | 0.111665i | \(-0.0356185\pi\) | |||||||
\(458\) | − 2.24590e8i | − 0.109235i | ||||||||
\(459\) | 2.37979e9 | 1.14867 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.27395e8 | −0.203178 | −0.101589 | − | 0.994826i | \(-0.532393\pi\) | ||||
−0.101589 | + | 0.994826i | \(0.532393\pi\) | |||||||
\(462\) | 1.00830e9i | 0.475711i | ||||||||
\(463\) | 4.30814e8i | 0.201724i | 0.994900 | + | 0.100862i | \(0.0321600\pi\) | ||||
−0.994900 | + | 0.100862i | \(0.967840\pi\) | |||||||
\(464\) | 2.84100e8 | 0.132026 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.07797e8 | −0.0951236 | ||||||||
\(467\) | − 3.54276e9i | − 1.60966i | −0.593508 | − | 0.804828i | \(-0.702257\pi\) | ||||
0.593508 | − | 0.804828i | \(-0.297743\pi\) | |||||||
\(468\) | 2.99817e7i | 0.0135206i | ||||||||
\(469\) | 4.59055e7 | 0.0205476 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.70086e8 | −0.295500 | ||||||||
\(472\) | 4.92385e8i | 0.215530i | ||||||||
\(473\) | 2.16166e9i | 0.939235i | ||||||||
\(474\) | 2.69851e9 | 1.16386 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.89014e8 | 0.207825 | ||||||||
\(477\) | − 9.27346e7i | − 0.0391226i | ||||||||
\(478\) | 2.31700e9i | 0.970351i | ||||||||
\(479\) | −2.18067e9 | −0.906601 | −0.453301 | − | 0.891358i | \(-0.649754\pi\) | ||||
−0.453301 | + | 0.891358i | \(0.649754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.30033e8 | 0.258140 | ||||||||
\(482\) | − 1.88179e9i | − 0.765432i | ||||||||
\(483\) | 7.87808e8i | 0.318131i | ||||||||
\(484\) | −3.15617e9 | −1.26532 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.65871e8 | 0.144578 | ||||||||
\(487\) | 8.94148e8i | 0.350799i | 0.984497 | + | 0.175399i | \(0.0561217\pi\) | ||||
−0.984497 | + | 0.175399i | \(0.943878\pi\) | |||||||
\(488\) | 1.29184e9i | 0.503198i | ||||||||
\(489\) | 4.47791e9 | 1.73179 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.17252e9 | 1.59079 | 0.795396 | − | 0.606090i | \(-0.207263\pi\) | ||||
0.795396 | + | 0.606090i | \(0.207263\pi\) | |||||||
\(492\) | − 3.40340e8i | − 0.128836i | ||||||||
\(493\) | 1.54511e9i | 0.580758i | ||||||||
\(494\) | −3.78834e8 | −0.141385 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.23866e8 | 0.0823762 | ||||||||
\(497\) | − 1.96048e9i | − 0.716332i | ||||||||
\(498\) | 9.38605e8i | 0.340550i | ||||||||
\(499\) | −8.93170e8 | −0.321797 | −0.160899 | − | 0.986971i | \(-0.551439\pi\) | ||||
−0.160899 | + | 0.986971i | \(0.551439\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.14296e9 | −0.761346 | ||||||||
\(502\) | 2.96853e9i | 1.04732i | ||||||||
\(503\) | 2.88740e9i | 1.01162i | 0.862644 | + | 0.505812i | \(0.168807\pi\) | ||||
−0.862644 | + | 0.505812i | \(0.831193\pi\) | |||||||
\(504\) | 3.94259e7 | 0.0137175 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.44043e9 | −1.18056 | ||||||||
\(507\) | − 2.58687e9i | − 0.881550i | ||||||||
\(508\) | − 2.24802e9i | − 0.760813i | ||||||||
\(509\) | 1.04446e9 | 0.351059 | 0.175529 | − | 0.984474i | \(-0.443836\pi\) | ||||
0.175529 | + | 0.984474i | \(0.443836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.81942e6 | 0.00325546 | ||||||||
\(512\) | 1.34218e8i | 0.0441942i | ||||||||
\(513\) | 2.42433e9i | 0.792832i | ||||||||
\(514\) | −2.02805e9 | −0.658730 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.38876e8 | −0.236754 | ||||||||
\(517\) | − 2.33932e9i | − 0.744513i | ||||||||
\(518\) | − 8.28493e8i | − 0.261899i | ||||||||
\(519\) | −2.66815e8 | −0.0837769 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.58851e9 | 0.492106 | 0.246053 | − | 0.969256i | \(-0.420866\pi\) | ||||
0.246053 | + | 0.969256i | \(0.420866\pi\) | |||||||
\(522\) | 1.24572e8i | 0.0383330i | ||||||||
\(523\) | 4.73420e9i | 1.44707i | 0.690286 | + | 0.723537i | \(0.257485\pi\) | ||||
−0.690286 | + | 0.723537i | \(0.742515\pi\) | |||||||
\(524\) | −3.06533e9 | −0.930717 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.71593e9 | 0.813709 | ||||||||
\(527\) | 1.21752e9i | 0.362358i | ||||||||
\(528\) | − 1.50510e9i | − 0.444987i | ||||||||
\(529\) | 7.16738e8 | 0.210507 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.15900e8 | −0.0625780 | ||||||||
\(532\) | 4.98166e8i | 0.143444i | ||||||||
\(533\) | 2.50488e8i | 0.0716543i | ||||||||
\(534\) | 2.77444e9 | 0.788464 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.85237e7 | −0.0192205 | ||||||||
\(537\) | − 4.63056e8i | − 0.129040i | ||||||||
\(538\) | − 1.21427e9i | − 0.336184i | ||||||||
\(539\) | −9.75865e8 | −0.268429 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.26233e9 | 1.15733 | 0.578665 | − | 0.815566i | \(-0.303574\pi\) | ||||
0.578665 | + | 0.815566i | \(0.303574\pi\) | |||||||
\(542\) | 4.87688e8i | 0.131566i | ||||||||
\(543\) | − 4.51019e9i | − 1.20891i | ||||||||
\(544\) | −7.29957e8 | −0.194402 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.53658e8 | 0.0666920 | ||||||||
\(547\) | − 5.20549e9i | − 1.35990i | −0.733260 | − | 0.679948i | \(-0.762002\pi\) | ||||
0.733260 | − | 0.679948i | \(-0.237998\pi\) | |||||||
\(548\) | 2.06018e8i | 0.0534777i | ||||||||
\(549\) | −5.66442e8 | −0.146101 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57402e9 | −0.400849 | ||||||||
\(552\) | − 1.17597e9i | − 0.297584i | ||||||||
\(553\) | 2.61170e9i | 0.656727i | ||||||||
\(554\) | 1.82213e9 | 0.455298 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.87215e9 | 0.461933 | ||||||||
\(557\) | − 1.04344e9i | − 0.255844i | −0.991784 | − | 0.127922i | \(-0.959169\pi\) | ||||
0.991784 | − | 0.127922i | \(-0.0408307\pi\) | |||||||
\(558\) | 9.81601e7i | 0.0239175i | ||||||||
\(559\) | 5.43808e8 | 0.131675 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.18565e9 | 1.95742 | ||||||||
\(562\) | 3.89531e9i | 0.925688i | ||||||||
\(563\) | − 8.23842e9i | − 1.94565i | −0.231541 | − | 0.972825i | \(-0.574377\pi\) | ||||
0.231541 | − | 0.972825i | \(-0.425623\pi\) | |||||||
\(564\) | 7.99599e8 | 0.187670 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.09748e9 | −0.486228 | ||||||||
\(567\) | − 1.45486e9i | − 0.335183i | ||||||||
\(568\) | 2.92643e9i | 0.670068i | ||||||||
\(569\) | −6.17425e9 | −1.40505 | −0.702525 | − | 0.711659i | \(-0.747944\pi\) | ||||
−0.702525 | + | 0.711659i | \(0.747944\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.44117e9 | 0.998324 | 0.499162 | − | 0.866509i | \(-0.333641\pi\) | ||||
0.499162 | + | 0.866509i | \(0.333641\pi\) | |||||||
\(572\) | 1.10775e9i | 0.247488i | ||||||||
\(573\) | − 5.17462e9i | − 1.14905i | ||||||||
\(574\) | 3.29392e8 | 0.0726978 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.88515e7 | −0.0128315 | ||||||||
\(577\) | 8.17132e9i | 1.77083i | 0.464801 | + | 0.885415i | \(0.346126\pi\) | ||||
−0.464801 | + | 0.885415i | \(0.653874\pi\) | |||||||
\(578\) | − 6.87233e8i | − 0.148032i | ||||||||
\(579\) | 7.64238e9 | 1.63626 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.08411e8 | −0.192161 | ||||||||
\(582\) | 3.48999e9i | 0.733827i | ||||||||
\(583\) | − 3.42630e9i | − 0.716120i | ||||||||
\(584\) | −1.46576e7 | −0.00304521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.94263e8 | 0.121994 | ||||||||
\(587\) | − 6.28754e9i | − 1.28306i | −0.767097 | − | 0.641531i | \(-0.778300\pi\) | ||||
0.767097 | − | 0.641531i | \(-0.221700\pi\) | |||||||
\(588\) | − 3.33559e8i | − 0.0676632i | ||||||||
\(589\) | −1.24030e9 | −0.250106 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.01681e9 | −0.999704 | ||||||||
\(592\) | 1.23670e9i | 0.244984i | ||||||||
\(593\) | 7.01629e9i | 1.38171i | 0.722995 | + | 0.690854i | \(0.242765\pi\) | ||||
−0.722995 | + | 0.690854i | \(0.757235\pi\) | |||||||
\(594\) | 7.08898e9 | 1.38781 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.35785e9 | 0.262718 | ||||||||
\(597\) | 8.32816e9i | 1.60191i | ||||||||
\(598\) | 8.65507e8i | 0.165507i | ||||||||
\(599\) | 9.38103e8 | 0.178343 | 0.0891716 | − | 0.996016i | \(-0.471578\pi\) | ||||
0.0891716 | + | 0.996016i | \(0.471578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.95585e9 | 0.555421 | 0.277711 | − | 0.960665i | \(-0.410424\pi\) | ||||
0.277711 | + | 0.960665i | \(0.410424\pi\) | |||||||
\(602\) | − 7.15107e8i | − 0.133593i | ||||||||
\(603\) | − 3.00461e7i | − 0.00558056i | ||||||||
\(604\) | 1.73671e9 | 0.320699 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.70982e9 | 1.22478 | ||||||||
\(607\) | − 4.76325e9i | − 0.864457i | −0.901764 | − | 0.432228i | \(-0.857727\pi\) | ||||
0.901764 | − | 0.432228i | \(-0.142273\pi\) | |||||||
\(608\) | − 7.43617e8i | − 0.134180i | ||||||||
\(609\) | 1.05393e9 | 0.189082 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.88500e8 | −0.104376 | ||||||||
\(612\) | − 3.20070e8i | − 0.0564436i | ||||||||
\(613\) | 2.32881e9i | 0.408340i | 0.978935 | + | 0.204170i | \(0.0654495\pi\) | ||||
−0.978935 | + | 0.204170i | \(0.934550\pi\) | |||||||
\(614\) | 3.71673e9 | 0.647996 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.45668e9 | 0.251092 | ||||||||
\(617\) | 9.82915e9i | 1.68468i | 0.538945 | + | 0.842341i | \(0.318823\pi\) | ||||
−0.538945 | + | 0.842341i | \(0.681177\pi\) | |||||||
\(618\) | 6.68835e9i | 1.13988i | ||||||||
\(619\) | 5.94350e8 | 0.100722 | 0.0503611 | − | 0.998731i | \(-0.483963\pi\) | ||||
0.0503611 | + | 0.998731i | \(0.483963\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.53878e9 | 0.928097 | ||||||||
\(622\) | − 5.47801e9i | − 0.912760i | ||||||||
\(623\) | 2.68519e9i | 0.444905i | ||||||||
\(624\) | −3.78637e8 | −0.0623846 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.28763e9 | −0.372713 | ||||||||
\(627\) | 8.33884e9i | 1.35104i | ||||||||
\(628\) | 9.68068e8i | 0.155972i | ||||||||
\(629\) | −6.72592e9 | −1.07764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.06380e9 | 0.960820 | 0.480410 | − | 0.877044i | \(-0.340488\pi\) | ||||
0.480410 | + | 0.877044i | \(0.340488\pi\) | |||||||
\(632\) | − 3.89851e9i | − 0.614312i | ||||||||
\(633\) | 9.06931e8i | 0.142122i | ||||||||
\(634\) | −6.54354e9 | −1.01977 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.17114e9 | 0.180513 | ||||||||
\(637\) | 2.45498e8i | 0.0376322i | ||||||||
\(638\) | 4.60260e9i | 0.701667i | ||||||||
\(639\) | −1.28317e9 | −0.194550 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.74978e8 | −0.116221 | −0.0581107 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581107 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(642\) | − 6.22596e8i | − 0.0928611i | ||||||||
\(643\) | 1.39116e9i | 0.206366i | 0.994662 | + | 0.103183i | \(0.0329028\pi\) | ||||
−0.994662 | + | 0.103183i | \(0.967097\pi\) | |||||||
\(644\) | 1.13814e9 | 0.167917 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.04424e9 | 0.590232 | ||||||||
\(647\) | 8.16793e9i | 1.18562i | 0.805341 | + | 0.592812i | \(0.201982\pi\) | ||||
−0.805341 | + | 0.592812i | \(0.798018\pi\) | |||||||
\(648\) | 2.17169e9i | 0.313535i | ||||||||
\(649\) | −7.97694e9 | −1.14546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.30475e8 | 0.117976 | ||||||||
\(652\) | − 6.46920e9i | − 0.914079i | ||||||||
\(653\) | 3.75842e9i | 0.528213i | 0.964493 | + | 0.264107i | \(0.0850771\pi\) | ||||
−0.964493 | + | 0.264107i | \(0.914923\pi\) | |||||||
\(654\) | 5.35250e9 | 0.748230 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.91687e8 | −0.0680026 | ||||||||
\(657\) | − 6.42701e6i | 0 0.000884159i | ||||||||
\(658\) | 7.73877e8i | 0.105896i | ||||||||
\(659\) | 1.11612e10 | 1.51919 | 0.759594 | − | 0.650398i | \(-0.225398\pi\) | ||||
0.759594 | + | 0.650398i | \(0.225398\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.25634e8 | −0.0977265 | −0.0488632 | − | 0.998805i | \(-0.515560\pi\) | ||||
−0.0488632 | + | 0.998805i | \(0.515560\pi\) | |||||||
\(662\) | 7.57658e9i | 1.01501i | ||||||||
\(663\) | − 2.05926e9i | − 0.274419i | ||||||||
\(664\) | 1.35600e9 | 0.179750 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.42266e8 | −0.0711299 | ||||||||
\(667\) | 3.59612e9i | 0.469238i | ||||||||
\(668\) | 3.09592e9i | 0.401857i | ||||||||
\(669\) | −8.69086e9 | −1.12220 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.09286e10 | −2.67431 | ||||||||
\(672\) | 4.97908e8i | 0.0632931i | ||||||||
\(673\) | − 3.86734e9i | − 0.489057i | −0.969642 | − | 0.244528i | \(-0.921367\pi\) | ||||
0.969642 | − | 0.244528i | \(-0.0786331\pi\) | |||||||
\(674\) | 1.09228e10 | 1.37412 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.73723e9 | −0.465304 | ||||||||
\(677\) | 6.50913e9i | 0.806237i | 0.915148 | + | 0.403118i | \(0.132074\pi\) | ||||
−0.915148 | + | 0.403118i | \(0.867926\pi\) | |||||||
\(678\) | 3.20931e9i | 0.395465i | ||||||||
\(679\) | −3.37772e9 | −0.414076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.39507e9 | 0.533275 | ||||||||
\(682\) | 3.62676e9i | 0.437798i | ||||||||
\(683\) | 5.96614e9i | 0.716508i | 0.933624 | + | 0.358254i | \(0.116628\pi\) | ||||
−0.933624 | + | 0.358254i | \(0.883372\pi\) | |||||||
\(684\) | 3.26060e8 | 0.0389584 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | 1.24367e9i | 0.146338i | ||||||||
\(688\) | 1.06745e9i | 0.124965i | ||||||||
\(689\) | −8.61953e8 | −0.100396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.47683e9 | 0.516176 | 0.258088 | − | 0.966121i | \(-0.416908\pi\) | ||||
0.258088 | + | 0.966121i | \(0.416908\pi\) | |||||||
\(692\) | 3.85465e8i | 0.0442195i | ||||||||
\(693\) | 6.38724e8i | 0.0729032i | ||||||||
\(694\) | −7.73081e9 | −0.877944 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.57321e9 | −0.176870 | ||||||||
\(697\) | − 2.67409e9i | − 0.299131i | ||||||||
\(698\) | − 5.20706e9i | − 0.579560i | ||||||||
\(699\) | 1.15068e9 | 0.127434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.17249e9 | −0.567135 | −0.283568 | − | 0.958952i | \(-0.591518\pi\) | ||||
−0.283568 | + | 0.958952i | \(0.591518\pi\) | |||||||
\(702\) | − 1.78337e9i | − 0.194563i | ||||||||
\(703\) | − 6.85179e9i | − 0.743808i | ||||||||
\(704\) | −2.17441e9 | −0.234875 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.83069e9 | 0.516645 | ||||||||
\(707\) | 6.49397e9i | 0.691102i | ||||||||
\(708\) | − 2.72659e9i | − 0.288738i | ||||||||
\(709\) | 1.92689e8 | 0.0203046 | 0.0101523 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101523 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.70941e9 | 0.178362 | ||||||||
\(712\) | − 4.00822e9i | − 0.416171i | ||||||||
\(713\) | 2.83367e9i | 0.292776i | ||||||||
\(714\) | −2.70792e9 | −0.278415 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.68973e8 | −0.0681103 | ||||||||
\(717\) | − 1.28304e10i | − 1.29994i | ||||||||
\(718\) | − 6.85523e8i | − 0.0691173i | ||||||||
\(719\) | 9.94078e8 | 0.0997400 | 0.0498700 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498700 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.47319e9 | −0.643198 | ||||||||
\(722\) | − 3.03105e9i | − 0.299718i | ||||||||
\(723\) | 1.04204e10i | 1.02542i | ||||||||
\(724\) | −6.51584e9 | −0.638095 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.74773e10 | 1.69510 | ||||||||
\(727\) | − 2.06212e8i | − 0.0199042i | −0.999950 | − | 0.00995208i | \(-0.996832\pi\) | ||||
0.999950 | − | 0.00995208i | \(-0.00316790\pi\) | |||||||
\(728\) | − 3.66457e8i | − 0.0352017i | ||||||||
\(729\) | −1.13024e10 | −1.08050 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.80542e9 | −0.549697 | ||||||||
\(732\) | − 7.15358e9i | − 0.674116i | ||||||||
\(733\) | 8.04851e9i | 0.754834i | 0.926043 | + | 0.377417i | \(0.123188\pi\) | ||||
−0.926043 | + | 0.377417i | \(0.876812\pi\) | |||||||
\(734\) | 1.30927e10 | 1.22206 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.69891e9 | −0.157072 | ||||||||
\(737\) | − 1.11013e9i | − 0.102149i | ||||||||
\(738\) | − 2.15594e8i | − 0.0197442i | ||||||||
\(739\) | 5.35129e9 | 0.487756 | 0.243878 | − | 0.969806i | \(-0.421580\pi\) | ||||
0.243878 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.09780e9 | 0.189409 | ||||||||
\(742\) | 1.13347e9i | 0.101858i | ||||||||
\(743\) | 1.53558e10i | 1.37345i | 0.726919 | + | 0.686723i | \(0.240952\pi\) | ||||
−0.726919 | + | 0.686723i | \(0.759048\pi\) | |||||||
\(744\) | −1.23966e9 | −0.110356 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.50444e10 | −1.32675 | ||||||||
\(747\) | 5.94574e8i | 0.0521896i | ||||||||
\(748\) | − 1.18257e10i | − 1.03317i | ||||||||
\(749\) | 6.02568e8 | 0.0523986 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.05007e9 | 0.176615 | 0.0883077 | − | 0.996093i | \(-0.471854\pi\) | ||||
0.0883077 | + | 0.996093i | \(0.471854\pi\) | |||||||
\(752\) | − 1.15517e9i | − 0.0990570i | ||||||||
\(753\) | − 1.64383e10i | − 1.40305i | ||||||||
\(754\) | 1.15787e9 | 0.0983697 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.34513e9 | −0.197397 | ||||||||
\(757\) | − 1.05302e10i | − 0.882270i | −0.897441 | − | 0.441135i | \(-0.854576\pi\) | ||||
0.897441 | − | 0.441135i | \(-0.145424\pi\) | |||||||
\(758\) | − 4.86181e9i | − 0.405467i | ||||||||
\(759\) | 1.90514e10 | 1.58155 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.69743e10 | 1.39620 | 0.698098 | − | 0.716002i | \(-0.254030\pi\) | ||||
0.698098 | + | 0.716002i | \(0.254030\pi\) | |||||||
\(762\) | 1.24485e10i | 1.01923i | ||||||||
\(763\) | 5.18032e9i | 0.422202i | ||||||||
\(764\) | −7.47573e9 | −0.606495 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.23299e9 | −0.0991198 | ||||||||
\(767\) | 2.00675e9i | 0.160587i | ||||||||
\(768\) | − 7.43232e8i | − 0.0592053i | ||||||||
\(769\) | −3.02600e9 | −0.239953 | −0.119977 | − | 0.992777i | \(-0.538282\pi\) | ||||
−0.119977 | + | 0.992777i | \(0.538282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.12303e10 | 0.882476 | ||||||||
\(772\) | − 1.10409e10i | − 0.863661i | ||||||||
\(773\) | 1.38384e10i | 1.07760i | 0.842434 | + | 0.538799i | \(0.181122\pi\) | ||||
−0.842434 | + | 0.538799i | \(0.818878\pi\) | |||||||
\(774\) | −4.68052e8 | −0.0362828 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.04196e9 | 0.387332 | ||||||||
\(777\) | 4.58779e9i | 0.350857i | ||||||||
\(778\) | 1.59654e10i | 1.21549i | ||||||||
\(779\) | 2.72413e9 | 0.206465 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.74099e10 | −3.56115 | ||||||||
\(782\) | − 9.23972e9i | − 0.690932i | ||||||||
\(783\) | − 7.40976e9i | − 0.551617i | ||||||||
\(784\) | −4.81890e8 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.69743e10 | 1.24685 | ||||||||
\(787\) | − 9.83270e9i | − 0.719054i | −0.933135 | − | 0.359527i | \(-0.882938\pi\) | ||||
0.933135 | − | 0.359527i | \(-0.117062\pi\) | |||||||
\(788\) | 7.24775e9i | 0.527669i | ||||||||
\(789\) | −1.50395e10 | −1.09009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.10607e9 | −0.223148 | ||||||||
\(792\) | − 9.53430e8i | − 0.0681947i | ||||||||
\(793\) | 5.26499e9i | 0.374922i | ||||||||
\(794\) | −5.53371e9 | −0.392324 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.20316e10 | 0.845529 | ||||||||
\(797\) | 3.16521e9i | 0.221462i | 0.993850 | + | 0.110731i | \(0.0353191\pi\) | ||||
−0.993850 | + | 0.110731i | \(0.964681\pi\) | |||||||
\(798\) | − 2.75860e9i | − 0.192167i | ||||||||
\(799\) | 6.28253e9 | 0.435733 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.75751e9 | 0.120833 | ||||||||
\(802\) | − 4.64439e9i | − 0.317921i | ||||||||
\(803\) | − 2.37461e8i | − 0.0161841i | ||||||||
\(804\) | 3.79451e8 | 0.0257489 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.12381e8 | 0.0613767 | ||||||||
\(807\) | 6.72403e9i | 0.450373i | ||||||||
\(808\) | − 9.69362e9i | − 0.646467i | ||||||||
\(809\) | −2.18461e10 | −1.45062 | −0.725311 | − | 0.688422i | \(-0.758304\pi\) | ||||
−0.725311 | + | 0.688422i | \(0.758304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.11360e10 | 0.733090 | 0.366545 | − | 0.930400i | \(-0.380541\pi\) | ||||
0.366545 | + | 0.930400i | \(0.380541\pi\) | |||||||
\(812\) | − 1.52260e9i | − 0.0998022i | ||||||||
\(813\) | − 2.70058e9i | − 0.176254i | ||||||||
\(814\) | −2.00353e10 | −1.30200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.04214e9 | 0.260433 | ||||||||
\(817\) | − 5.91407e9i | − 0.379410i | ||||||||
\(818\) | 8.41266e9i | 0.537399i | ||||||||
\(819\) | 1.60683e8 | 0.0102206 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.08012e9 | 0.131186 | 0.0655931 | − | 0.997846i | \(-0.479106\pi\) | ||||
0.0655931 | + | 0.997846i | \(0.479106\pi\) | |||||||
\(822\) | − 1.14083e9i | − 0.0716421i | ||||||||
\(823\) | − 1.89553e10i | − 1.18531i | −0.805458 | − | 0.592653i | \(-0.798081\pi\) | ||||
0.805458 | − | 0.592653i | \(-0.201919\pi\) | |||||||
\(824\) | 9.66260e9 | 0.601657 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.63888e9 | 0.162925 | ||||||||
\(827\) | 2.12105e10i | 1.30401i | 0.758215 | + | 0.652005i | \(0.226072\pi\) | ||||
−0.758215 | + | 0.652005i | \(0.773928\pi\) | |||||||
\(828\) | − 7.44936e8i | − 0.0456050i | ||||||||
\(829\) | 1.14471e10 | 0.697840 | 0.348920 | − | 0.937152i | \(-0.386548\pi\) | ||||
0.348920 | + | 0.937152i | \(0.386548\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00901e10 | −0.609945 | ||||||||
\(832\) | 5.47014e8i | 0.0329281i | ||||||||
\(833\) | − 2.62081e9i | − 0.157101i | ||||||||
\(834\) | −1.03671e10 | −0.618834 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.20471e10 | 0.713114 | ||||||||
\(837\) | − 5.83875e9i | − 0.344176i | ||||||||
\(838\) | − 1.57400e10i | − 0.923956i | ||||||||
\(839\) | −3.31864e10 | −1.93996 | −0.969981 | − | 0.243179i | \(-0.921810\pi\) | ||||
−0.969981 | + | 0.243179i | \(0.921810\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.24390e10 | −0.721107 | ||||||||
\(842\) | − 2.22651e9i | − 0.128538i | ||||||||
\(843\) | − 2.15703e10i | − 1.24011i | ||||||||
\(844\) | 1.31024e9 | 0.0750155 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.06518e8 | 0.0287606 | ||||||||
\(847\) | 1.69151e10i | 0.956494i | ||||||||
\(848\) | − 1.69194e9i | − 0.0952794i | ||||||||
\(849\) | 1.16148e10 | 0.651382 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.56540e10 | −0.870709 | ||||||||
\(852\) | − 1.62051e10i | − 0.897664i | ||||||||
\(853\) | − 2.28601e10i | − 1.26112i | −0.776140 | − | 0.630560i | \(-0.782825\pi\) | ||||
0.776140 | − | 0.630560i | \(-0.217175\pi\) | |||||||
\(854\) | 6.92345e9 | 0.380382 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.99460e8 | −0.0490144 | ||||||||
\(857\) | 2.93946e10i | 1.59527i | 0.603140 | + | 0.797635i | \(0.293916\pi\) | ||||
−0.603140 | + | 0.797635i | \(0.706084\pi\) | |||||||
\(858\) | − 6.13416e9i | − 0.331550i | ||||||||
\(859\) | −1.12866e10 | −0.607558 | −0.303779 | − | 0.952743i | \(-0.598248\pi\) | ||||
−0.303779 | + | 0.952743i | \(0.598248\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.82401e9 | −0.0973905 | ||||||||
\(862\) | − 2.22375e10i | − 1.18253i | ||||||||
\(863\) | − 2.36165e10i | − 1.25077i | −0.780315 | − | 0.625387i | \(-0.784941\pi\) | ||||
0.780315 | − | 0.625387i | \(-0.215059\pi\) | |||||||
\(864\) | 3.50060e9 | 0.184648 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.12604e10 | 0.589171 | ||||||||
\(867\) | 3.80556e9i | 0.198313i | ||||||||
\(868\) | − 1.19978e9i | − 0.0622705i | ||||||||
\(869\) | 6.31583e10 | 3.26483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.79274e8 | −0.0143208 | ||||||||
\(872\) | − 7.73272e9i | − 0.394934i | ||||||||
\(873\) | 2.21079e9i | 0.112460i | ||||||||
\(874\) | 9.41264e9 | 0.476893 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.11664e7 | 0.00407955 | ||||||||
\(877\) | − 3.02456e9i | − 0.151413i | −0.997130 | − | 0.0757065i | \(-0.975879\pi\) | ||||
0.997130 | − | 0.0757065i | \(-0.0241212\pi\) | |||||||
\(878\) | 1.25839e10i | 0.627459i | ||||||||
\(879\) | −3.29074e9 | −0.163430 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.09728e10 | −1.03333 | −0.516666 | − | 0.856187i | \(-0.672827\pi\) | ||||
−0.516666 | + | 0.856187i | \(0.672827\pi\) | |||||||
\(882\) | − 2.11298e8i | − 0.0103694i | ||||||||
\(883\) | 1.76578e10i | 0.863124i | 0.902083 | + | 0.431562i | \(0.142037\pi\) | ||||
−0.902083 | + | 0.431562i | \(0.857963\pi\) | |||||||
\(884\) | −2.97499e9 | −0.144845 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.06438e10 | 0.514136 | ||||||||
\(887\) | − 3.58732e10i | − 1.72599i | −0.505215 | − | 0.862993i | \(-0.668587\pi\) | ||||
0.505215 | − | 0.862993i | \(-0.331413\pi\) | |||||||
\(888\) | − 6.84825e9i | − 0.328197i | ||||||||
\(889\) | −1.20480e10 | −0.575121 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.51827e10 | −1.66632 | ||||||||
\(892\) | 1.25556e10i | 0.592326i | ||||||||
\(893\) | 6.40011e9i | 0.300751i | ||||||||
\(894\) | −7.51911e9 | −0.351953 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | − 4.79276e9i | − 0.221724i | ||||||||
\(898\) | − 2.20749e10i | − 1.01726i | ||||||||
\(899\) | 3.79087e9 | 0.174013 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.20177e9 | 0.419117 | ||||||||
\(902\) | − 7.96563e9i | − 0.361408i | ||||||||
\(903\) | 3.95991e9i | 0.178969i | ||||||||
\(904\) | 4.63646e9 | 0.208736 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.61704e9 | −0.429628 | ||||||||
\(907\) | − 1.65563e10i | − 0.736780i | −0.929671 | − | 0.368390i | \(-0.879909\pi\) | ||||
0.929671 | − | 0.368390i | \(-0.120091\pi\) | |||||||
\(908\) | − 6.34953e9i | − 0.281476i | ||||||||
\(909\) | 4.25044e9 | 0.187698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.04661e9 | 0.0896852 | 0.0448426 | − | 0.998994i | \(-0.485721\pi\) | ||||
0.0448426 | + | 0.998994i | \(0.485721\pi\) | |||||||
\(912\) | 4.11779e9i | 0.179756i | ||||||||
\(913\) | 2.19680e10i | 0.955305i | ||||||||
\(914\) | 3.64540e9 | 0.157919 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.79672e9 | 0.0772407 | ||||||||
\(917\) | 1.64283e10i | 0.703556i | ||||||||
\(918\) | 1.90383e10i | 0.812232i | ||||||||
\(919\) | −3.62621e10 | −1.54116 | −0.770582 | − | 0.637341i | \(-0.780034\pi\) | ||||
−0.770582 | + | 0.637341i | \(0.780034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.05815e10 | −0.868096 | ||||||||
\(922\) | − 3.41916e9i | − 0.143669i | ||||||||
\(923\) | 1.19269e10i | 0.499253i | ||||||||
\(924\) | −8.06641e9 | −0.336379 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.44652e9 | −0.142640 | ||||||||
\(927\) | 4.23683e9i | 0.174688i | ||||||||
\(928\) | 2.27280e9i | 0.0933564i | ||||||||
\(929\) | 1.05595e10 | 0.432105 | 0.216053 | − | 0.976382i | \(-0.430682\pi\) | ||||
0.216053 | + | 0.976382i | \(0.430682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.66986e9 | 0.108434 | ||||||||
\(932\) | − 1.66238e9i | − 0.0672626i | ||||||||
\(933\) | 3.03346e10i | 1.22279i | ||||||||
\(934\) | 2.83421e10 | 1.13820 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.39854e8 | −0.00956050 | ||||||||
\(937\) | − 5.66531e9i | − 0.224975i | −0.993653 | − | 0.112488i | \(-0.964118\pi\) | ||||
0.993653 | − | 0.112488i | \(-0.0358819\pi\) | |||||||
\(938\) | 3.67244e8i | 0.0145293i | ||||||||
\(939\) | 1.26678e10 | 0.499310 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.76376e10 | −1.47251 | −0.736255 | − | 0.676704i | \(-0.763408\pi\) | ||||
−0.736255 | + | 0.676704i | \(0.763408\pi\) | |||||||
\(942\) | − 5.36069e9i | − 0.208950i | ||||||||
\(943\) | − 6.22373e9i | − 0.241690i | ||||||||
\(944\) | −3.93908e9 | −0.152403 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.72933e10 | −0.664139 | ||||||||
\(947\) | 3.56031e10i | 1.36227i | 0.732159 | + | 0.681134i | \(0.238513\pi\) | ||||
−0.732159 | + | 0.681134i | \(0.761487\pi\) | |||||||
\(948\) | 2.15881e10i | 0.822970i | ||||||||
\(949\) | −5.97380e7 | −0.00226892 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.62350e10 | 1.36614 | ||||||||
\(952\) | 3.91211e9i | 0.146954i | ||||||||
\(953\) | − 3.27959e10i | − 1.22742i | −0.789530 | − | 0.613712i | \(-0.789675\pi\) | ||||
0.789530 | − | 0.613712i | \(-0.210325\pi\) | |||||||
\(954\) | 7.41877e8 | 0.0276638 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.85360e10 | −0.686142 | ||||||||
\(957\) | − 2.54870e10i | − 0.939997i | ||||||||
\(958\) | − 1.74454e10i | − 0.641064i | ||||||||
\(959\) | 1.10413e9 | 0.0404253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45255e10 | −0.891427 | ||||||||
\(962\) | 5.04027e9i | 0.182533i | ||||||||
\(963\) | − 3.94393e8i | − 0.0142311i | ||||||||
\(964\) | 1.50543e10 | 0.541242 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.30247e9 | −0.224952 | ||||||||
\(967\) | − 1.21805e10i | − 0.433184i | −0.976262 | − | 0.216592i | \(-0.930506\pi\) | ||||
0.976262 | − | 0.216592i | \(-0.0694941\pi\) | |||||||
\(968\) | − 2.52493e10i | − 0.894718i | ||||||||
\(969\) | −2.23950e10 | −0.790712 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.37312e10 | 0.831865 | 0.415933 | − | 0.909395i | \(-0.363455\pi\) | ||||
0.415933 | + | 0.909395i | \(0.363455\pi\) | |||||||
\(972\) | 2.92697e9i | 0.102232i | ||||||||
\(973\) | − 1.00336e10i | − 0.349188i | ||||||||
\(974\) | −7.15318e9 | −0.248052 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.03347e10 | −0.355815 | ||||||||
\(977\) | 3.44206e9i | 0.118083i | 0.998256 | + | 0.0590416i | \(0.0188044\pi\) | ||||
−0.998256 | + | 0.0590416i | \(0.981196\pi\) | |||||||
\(978\) | 3.58233e10i | 1.22456i | ||||||||
\(979\) | 6.49356e10 | 2.21179 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.39062e9 | 0.114667 | ||||||||
\(982\) | 3.33802e10i | 1.12486i | ||||||||
\(983\) | − 5.25354e10i | − 1.76407i | −0.471187 | − | 0.882033i | \(-0.656174\pi\) | ||||
0.471187 | − | 0.882033i | \(-0.343826\pi\) | |||||||
\(984\) | 2.72272e9 | 0.0911005 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.23609e10 | −0.410658 | ||||||||
\(987\) | − 4.28535e9i | − 0.141865i | ||||||||
\(988\) | − 3.03067e9i | − 0.0999745i | ||||||||
\(989\) | −1.35117e10 | −0.444142 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.03399e10 | 1.64306 | 0.821531 | − | 0.570163i | \(-0.193120\pi\) | ||||
0.821531 | + | 0.570163i | \(0.193120\pi\) | |||||||
\(992\) | 1.79092e9i | 0.0582487i | ||||||||
\(993\) | − 4.19554e10i | − 1.35977i | ||||||||
\(994\) | 1.56838e10 | 0.506524 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.50884e9 | −0.240805 | ||||||||
\(997\) | − 4.80693e9i | − 0.153615i | −0.997046 | − | 0.0768077i | \(-0.975527\pi\) | ||||
0.997046 | − | 0.0768077i | \(-0.0244727\pi\) | |||||||
\(998\) | − 7.14536e9i | − 0.227545i | ||||||||
\(999\) | 3.22550e10 | 1.02357 |
(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 | 350.8.c.i.99.3 | 4 | ||
5.2 | odd | 4 | 350.8.a.l.1.1 | 2 | |||
5.3 | odd | 4 | 70.8.a.g.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 350.8.c.i.99.2 | 4 | ||
20.3 | even | 4 | 560.8.a.h.1.1 | 2 | |||
35.13 | even | 4 | 490.8.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.8.a.g.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
350.8.a.l.1.1 | 2 | 5.2 | odd | 4 | |||
350.8.c.i.99.2 | 4 | 5.4 | even | 2 | inner | ||
350.8.c.i.99.3 | 4 | 1.1 | even | 1 | trivial | ||
490.8.a.k.1.1 | 2 | 35.13 | even | 4 | |||
560.8.a.h.1.1 | 2 | 20.3 | even | 4 |