Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{130}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 130 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-11.4018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −15.8035 | −1.01380 | −0.506898 | − | 0.862006i | \(-0.669208\pi\) | ||||
−0.506898 | + | 0.862006i | \(0.669208\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21.0000 | −0.375659 | −0.187830 | − | 0.982202i | \(-0.560145\pi\) | ||||
−0.187830 | + | 0.982202i | \(0.560145\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.75088 | 0.0277814 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 625.874 | 1.55957 | 0.779785 | − | 0.626047i | \(-0.215328\pi\) | ||||
0.779785 | + | 0.626047i | \(0.215328\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −206.821 | −0.339419 | −0.169710 | − | 0.985494i | \(-0.554283\pi\) | ||||
−0.169710 | + | 0.985494i | \(0.554283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 331.874 | 0.380842 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1061.46 | 0.890805 | 0.445402 | − | 0.895330i | \(-0.353061\pi\) | ||||
0.445402 | + | 0.895330i | \(0.353061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1883.98 | 1.19727 | 0.598635 | − | 0.801022i | \(-0.295710\pi\) | ||||
0.598635 | + | 0.801022i | \(0.295710\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3717.37 | −1.46526 | −0.732632 | − | 0.680625i | \(-0.761708\pi\) | ||||
−0.732632 | + | 0.680625i | \(0.761708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2684.00 | −0.858880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3733.56 | 0.985631 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −123.747 | −0.0273238 | −0.0136619 | − | 0.999907i | \(-0.504349\pi\) | ||||
−0.0136619 | + | 0.999907i | \(0.504349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9109.26 | 1.70247 | 0.851234 | − | 0.524786i | \(-0.175855\pi\) | ||||
0.851234 | + | 0.524786i | \(0.175855\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9891.00 | −1.58109 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6028.73 | −0.723971 | −0.361986 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361986 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3268.50 | 0.344102 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −17201.9 | −1.59814 | −0.799071 | − | 0.601236i | \(-0.794675\pi\) | ||||
−0.799071 | + | 0.601236i | \(0.794675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5401.98 | −0.445535 | −0.222767 | − | 0.974872i | \(-0.571509\pi\) | ||||
−0.222767 | + | 0.974872i | \(0.571509\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −141.769 | −0.0104363 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1875.24 | −0.123826 | −0.0619131 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619131 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16774.8 | −0.903094 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18707.2 | 0.914787 | 0.457393 | − | 0.889264i | \(-0.348783\pi\) | ||||
0.457393 | + | 0.889264i | \(0.348783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13143.3 | −0.585867 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −29773.5 | −1.21379 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2534.78 | 0.0948004 | 0.0474002 | − | 0.998876i | \(-0.484906\pi\) | ||||
0.0474002 | + | 0.998876i | \(0.484906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2094.71 | −0.0720773 | −0.0360386 | − | 0.999350i | \(-0.511474\pi\) | ||||
−0.0360386 | + | 0.999350i | \(0.511474\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4343.24 | 0.127506 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −58620.8 | −1.59538 | −0.797691 | − | 0.603067i | \(-0.793945\pi\) | ||||
−0.797691 | + | 0.603067i | \(0.793945\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 58747.5 | 1.48548 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 31279.5 | 0.736401 | 0.368201 | − | 0.929746i | \(-0.379974\pi\) | ||||
0.368201 | + | 0.929746i | \(0.379974\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7150.47 | −0.157046 | −0.0785231 | − | 0.996912i | \(-0.525020\pi\) | ||||
−0.0785231 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 42416.6 | 0.870729 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2979.81 | −0.0537181 | −0.0268591 | − | 0.999639i | \(-0.508551\pi\) | ||||
−0.0268591 | + | 0.999639i | \(0.508551\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −60643.9 | −1.02701 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −45954.6 | −0.732207 | −0.366103 | − | 0.930574i | \(-0.619308\pi\) | ||||
−0.366103 | + | 0.930574i | \(0.619308\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22290.7 | −0.334639 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1955.64 | 0.0277007 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 99040.0 | 1.32536 | 0.662682 | − | 0.748900i | \(-0.269418\pi\) | ||||
0.662682 | + | 0.748900i | \(0.269418\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −143958. | −1.72595 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −39563.6 | −0.449766 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −115548. | −1.24691 | −0.623454 | − | 0.781860i | \(-0.714271\pi\) | ||||
−0.623454 | + | 0.781860i | \(0.714271\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4225.20 | 0.0433271 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10951.5 | 0.106824 | 0.0534120 | − | 0.998573i | \(-0.482990\pi\) | ||||
0.0534120 | + | 0.998573i | \(0.482990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 137724. | 1.27914 | 0.639570 | − | 0.768733i | \(-0.279113\pi\) | ||||
0.639570 | + | 0.768733i | \(0.279113\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −75573.0 | −0.638127 | −0.319064 | − | 0.947733i | \(-0.603368\pi\) | ||||
−0.319064 | + | 0.947733i | \(0.603368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 44526.3 | 0.358963 | 0.179482 | − | 0.983761i | \(-0.442558\pi\) | ||||
0.179482 | + | 0.983761i | \(0.442558\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 95275.0 | 0.733959 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 90456.5 | 0.666413 | 0.333207 | − | 0.942854i | \(-0.391869\pi\) | ||||
0.333207 | + | 0.942854i | \(0.391869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 78064.7 | 0.550440 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1396.22 | −0.00942954 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 230667. | 1.43226 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 271850. | 1.62019 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 121989. | 0.698306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −187707. | −1.03269 | −0.516346 | − | 0.856380i | \(-0.672708\pi\) | ||||
−0.516346 | + | 0.856380i | \(0.672708\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 85370.2 | 0.451681 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −154412. | −0.786147 | −0.393073 | − | 0.919507i | \(-0.628588\pi\) | ||||
−0.393073 | + | 0.919507i | \(0.628588\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −78404.9 | −0.370262 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 109238. | 0.497246 | 0.248623 | − | 0.968600i | \(-0.420022\pi\) | ||||
0.248623 | + | 0.968600i | \(0.420022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 204695. | 0.898609 | 0.449305 | − | 0.893379i | \(-0.351672\pi\) | ||||
0.449305 | + | 0.893379i | \(0.351672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29635.4 | 0.125534 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −129444. | −0.529348 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2598.69 | 0.0102644 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −406308. | −1.49930 | −0.749651 | − | 0.661833i | \(-0.769779\pi\) | ||||
−0.749651 | + | 0.661833i | \(0.769779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 416838. | 1.48773 | 0.743866 | − | 0.668328i | \(-0.232990\pi\) | ||||
0.743866 | + | 0.668328i | \(0.232990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7165.81 | 0.0247478 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −191295. | −0.639548 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 119291. | 0.386240 | 0.193120 | − | 0.981175i | \(-0.438139\pi\) | ||||
0.193120 | + | 0.981175i | \(0.438139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −295640. | −0.927407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −47372.4 | −0.139655 | −0.0698275 | − | 0.997559i | \(-0.522245\pi\) | ||||
−0.0698275 | + | 0.997559i | \(0.522245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 207711. | 0.593950 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 231669. | 0.642802 | 0.321401 | − | 0.946943i | \(-0.395846\pi\) | ||||
0.321401 | + | 0.946943i | \(0.395846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328518. | −0.884795 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12718.5 | 0.0332618 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 134339. | 0.341262 | 0.170631 | − | 0.985335i | \(-0.445419\pi\) | ||||
0.170631 | + | 0.985335i | \(0.445419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −40058.4 | −0.0961082 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −46584.4 | −0.108669 | −0.0543347 | − | 0.998523i | \(-0.517304\pi\) | ||||
−0.0543347 | + | 0.998523i | \(0.517304\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 829210. | 1.88134 | 0.940672 | − | 0.339317i | \(-0.110196\pi\) | ||||
0.940672 | + | 0.339317i | \(0.110196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33103.7 | 0.0730716 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 126603. | 0.271967 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 664342. | 1.38927 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 471917. | 0.936013 | 0.468006 | − | 0.883725i | \(-0.344972\pi\) | ||||
0.468006 | + | 0.883725i | \(0.344972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 688354. | 1.33021 | 0.665103 | − | 0.746752i | \(-0.268388\pi\) | ||||
0.665103 | + | 0.746752i | \(0.268388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −68638.5 | −0.129265 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 311915. | 0.572625 | 0.286313 | − | 0.958136i | \(-0.407570\pi\) | ||||
0.286313 | + | 0.958136i | \(0.407570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 287212. | 0.514126 | 0.257063 | − | 0.966395i | \(-0.417245\pi\) | ||||
0.257063 | + | 0.966395i | \(0.417245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 926414. | 1.61739 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 361239. | 0.600357 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25095.5 | −0.0407071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.17913e6 | 1.86723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 460493. | 0.712061 | 0.356031 | − | 0.934474i | \(-0.384130\pi\) | ||||
0.356031 | + | 0.934474i | \(0.384130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −494326. | −0.746560 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 113442. | 0.167369 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 113003. | 0.159213 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −219533. | −0.302356 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19776e6 | 1.61290 | 0.806449 | − | 0.591304i | \(-0.201387\pi\) | ||||
0.806449 | + | 0.591304i | \(0.201387\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18119.4 | −0.0238609 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −894561. | −1.15225 | −0.576123 | − | 0.817363i | \(-0.695435\pi\) | ||||
−0.576123 | + | 0.817363i | \(0.695435\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −259256. | −0.326693 | −0.163347 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163347 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 211315. | 0.255000 | 0.127500 | − | 0.991839i | \(-0.459305\pi\) | ||||
0.127500 | + | 0.991839i | \(0.459305\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 39380.1 | 0.0465165 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 47091.5 | 0.0544592 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −463.018 | −0.000524328 0 | −0.000262164 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000262164 | 1.00000i | \(0.500083\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 286395. | 0.317631 | 0.158815 | − | 0.987308i | \(-0.449233\pi\) | ||||
0.158815 | + | 0.987308i | \(0.449233\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 51129.9 | 0.0555469 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −389647. | −0.406376 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 726244. | 0.742308 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.37168e6 | 1.37426 | 0.687129 | − | 0.726535i | \(-0.258870\pi\) | ||||
0.687129 | + | 0.726535i | \(0.258870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.32660e6 | −2.28518 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 352272. | 0.339256 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −759223. | −0.717029 | −0.358515 | − | 0.933524i | \(-0.616717\pi\) | ||||
−0.358515 | + | 0.933524i | \(0.616717\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −835.404 | −0.000759093 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.07244e6 | 0.956061 | 0.478030 | − | 0.878343i | \(-0.341351\pi\) | ||||
0.478030 | + | 0.878343i | \(0.341351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −392852. | −0.343648 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.56518e6 | −1.34365 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.76611e6 | −1.48812 | −0.744059 | − | 0.668114i | \(-0.767102\pi\) | ||||
−0.744059 | + | 0.668114i | \(0.767102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.05171e6 | 1.69704 | 0.848522 | − | 0.529160i | \(-0.177493\pi\) | ||||
0.848522 | + | 0.529160i | \(0.177493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.67984e6 | −1.33948 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 870682. | 0.681805 | 0.340903 | − | 0.940099i | \(-0.389267\pi\) | ||||
0.340903 | + | 0.940099i | \(0.389267\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 61495.6 | 0.0472970 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.35412e6 | 1.77854 | 0.889270 | − | 0.457383i | \(-0.151213\pi\) | ||||
0.889270 | + | 0.457383i | \(0.151213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.19035e6 | 1.62573 | 0.812863 | − | 0.582454i | \(-0.197908\pi\) | ||||
0.812863 | + | 0.582454i | \(0.197908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 625243. | 0.455970 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −293153. | −0.206467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.82607e6 | 1.26411 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −807700. | −0.549644 | −0.274822 | − | 0.961495i | \(-0.588619\pi\) | ||||
−0.274822 | + | 0.961495i | \(0.588619\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −53230.4 | −0.0356127 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.33674e6 | 1.53716 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 768830. | 0.497339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −173072. | −0.108298 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43988.8 | 0.0270765 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −211516. | −0.128085 | −0.0640424 | − | 0.997947i | \(-0.520399\pi\) | ||||
−0.0640424 | + | 0.997947i | \(0.520399\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.17653e6 | −1.29679 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 291709. | 0.171021 | 0.0855104 | − | 0.996337i | \(-0.472748\pi\) | ||||
0.0855104 | + | 0.996337i | \(0.472748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.99598e6 | −1.15158 | −0.575791 | − | 0.817597i | \(-0.695306\pi\) | ||||
−0.575791 | + | 0.817597i | \(0.695306\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.80957e6 | −1.57033 | −0.785167 | − | 0.619285i | \(-0.787423\pi\) | ||||
−0.785167 | + | 0.619285i | \(0.787423\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −77450.2 | −0.0426134 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19432e6 | 0.646930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.99977e6 | 1.06653 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 555108. | 0.291520 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −703671. | −0.363916 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.38050e6 | −0.692572 | −0.346286 | − | 0.938129i | \(-0.612557\pi\) | ||||
−0.346286 | + | 0.938129i | \(0.612557\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40699.2 | −0.0201129 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.23104e6 | 0.599320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 566429. | 0.271688 | 0.135844 | − | 0.990730i | \(-0.456625\pi\) | ||||
0.135844 | + | 0.990730i | \(0.456625\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.42953e6 | −0.675607 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.70125e6 | 2.65512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.23370e6 | −0.558034 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −540207. | −0.240845 | −0.120422 | − | 0.992723i | \(-0.538425\pi\) | ||||
−0.120422 | + | 0.992723i | \(0.538425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73807e6 | 0.763841 | 0.381921 | − | 0.924195i | \(-0.375263\pi\) | ||||
0.381921 | + | 0.924195i | \(0.375263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −772180. | −0.334542 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.07422e6 | 0.458834 | 0.229417 | − | 0.973328i | \(-0.426318\pi\) | ||||
0.229417 | + | 0.973328i | \(0.426318\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −656870. | −0.276636 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −121204. | −0.0496341 | −0.0248170 | − | 0.999692i | \(-0.507900\pi\) | ||||
−0.0248170 | + | 0.999692i | \(0.507900\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.07328e6 | 0.433455 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.64535e6 | −1.45202 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 150160. | 0.0589959 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 553829. | 0.214640 | 0.107320 | − | 0.994225i | \(-0.465773\pi\) | ||||
0.107320 | + | 0.994225i | \(0.465773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −116128. | −0.0443986 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −501478. | −0.186629 | −0.0933146 | − | 0.995637i | \(-0.529746\pi\) | ||||
−0.0933146 | + | 0.995637i | \(0.529746\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.92785e6 | −0.707939 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25593.6 | 0.00927422 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −999004. | −0.357248 | −0.178624 | − | 0.983917i | \(-0.557165\pi\) | ||||
−0.178624 | + | 0.983917i | \(0.557165\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.96643e6 | 1.04694 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −652464. | −0.227279 | −0.113640 | − | 0.993522i | \(-0.536251\pi\) | ||||
−0.113640 | + | 0.993522i | \(0.536251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −36468.1 | −0.0123776 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −79253.0 | −0.0265547 | −0.0132774 | − | 0.999912i | \(-0.504226\pi\) | ||||
−0.0132774 | + | 0.999912i | \(0.504226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.94585e6 | −1.30526 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.44026e6 | 0.796992 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 62576.0 | 0.0201797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00886e6 | 1.27657 | 0.638284 | − | 0.769801i | \(-0.279644\pi\) | ||||
0.638284 | + | 0.769801i | \(0.279644\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 674418. | 0.209444 | 0.104722 | − | 0.994502i | \(-0.466605\pi\) | ||||
0.104722 | + | 0.994502i | \(0.466605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.88399e6 | −0.577850 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.27352e6 | 0.385806 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.77322e6 | −1.12908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.85413e6 | −0.843656 | −0.421828 | − | 0.906676i | \(-0.638611\pi\) | ||||
−0.421828 | + | 0.906676i | \(0.638611\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.72634e6 | −0.504106 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 965047. | 0.275060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.23490e6 | −0.911006 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.66553e6 | 1.29827 | 0.649136 | − | 0.760672i | \(-0.275130\pi\) | ||||
0.649136 | + | 0.760672i | \(0.275130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.73317e6 | −1.02653 | −0.513266 | − | 0.858229i | \(-0.671565\pi\) | ||||
−0.513266 | + | 0.858229i | \(0.671565\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12659.5 | −0.00344007 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.84897e6 | −0.765095 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.04567e6 | 0.536651 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −964670. | −0.250141 | −0.125071 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125071 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.18096e6 | −1.58429 | −0.792147 | − | 0.610330i | \(-0.791037\pi\) | ||||
−0.792147 | + | 0.610330i | \(0.791037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41068.5 | −0.0104060 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.00344e6 | −1.75432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 215135. | 0.0532782 | 0.0266391 | − | 0.999645i | \(-0.491520\pi\) | ||||
0.0266391 | + | 0.999645i | \(0.491520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.19867e6 | 1.74278 | 0.871391 | − | 0.490589i | \(-0.163218\pi\) | ||||
0.871391 | + | 0.490589i | \(0.163218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.07984e6 | −0.497886 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.42109e6 | 1.51999 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.92153e6 | 0.917994 | 0.458997 | − | 0.888438i | \(-0.348209\pi\) | ||||
0.458997 | + | 0.888438i | \(0.348209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07662e7 | −2.49242 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.58750e6 | −1.50826 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.32168e6 | 0.296030 | 0.148015 | − | 0.988985i | \(-0.452712\pi\) | ||||
0.148015 | + | 0.988985i | \(0.452712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.96304e6 | 0.878005 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −75459.1 | −0.0165371 | −0.00826855 | − | 0.999966i | \(-0.502632\pi\) | ||||
−0.00826855 | + | 0.999966i | \(0.502632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.28757e6 | 0.712727 | 0.356363 | − | 0.934347i | \(-0.384016\pi\) | ||||
0.356363 | + | 0.934347i | \(0.384016\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.02312e6 | 0.648371 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 643382. | 0.136514 | 0.0682569 | − | 0.997668i | \(-0.478256\pi\) | ||||
0.0682569 | + | 0.997668i | \(0.478256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.88521e6 | −0.391568 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.38096e6 | −0.694843 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.05660e6 | −1.02831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 126290. | 0.0254141 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.42648e6 | 1.47892 | 0.739459 | − | 0.673202i | \(-0.235081\pi\) | ||||
0.739459 | + | 0.673202i | \(0.235081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24687e6 | 0.245730 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.42652e6 | 0.468413 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.17085e6 | 0.796896 | 0.398448 | − | 0.917191i | \(-0.369549\pi\) | ||||
0.398448 | + | 0.917191i | \(0.369549\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 748651. | 0.141582 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.73674e6 | 0.699502 | 0.349751 | − | 0.936843i | \(-0.386266\pi\) | ||||
0.349751 | + | 0.936843i | \(0.386266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −131353. | −0.0243402 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −88729.2 | −0.0162762 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.70862e6 | −1.56566 | −0.782831 | − | 0.622235i | \(-0.786225\pi\) | ||||
−0.782831 | + | 0.622235i | \(0.786225\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.66119e6 | −0.651670 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.28384e6 | −0.578711 | −0.289355 | − | 0.957222i | \(-0.593441\pi\) | ||||
−0.289355 | + | 0.957222i | \(0.593441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −229981. | −0.0401294 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.19174e6 | 0.897001 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.43703e6 | −1.61451 | −0.807255 | − | 0.590203i | \(-0.799048\pi\) | ||||
−0.807255 | + | 0.590203i | \(0.799048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.03396e6 | 1.18007 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.89221e6 | −0.480521 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.17366e6 | −0.193116 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.12303e6 | −0.345970 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.90726e6 | 0.953437 | 0.476719 | − | 0.879056i | \(-0.341826\pi\) | ||||
0.476719 | + | 0.879056i | \(0.341826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −654337. | −0.104604 | −0.0523019 | − | 0.998631i | \(-0.516656\pi\) | ||||
−0.0523019 | + | 0.998631i | \(0.516656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.66915e6 | 1.51657 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.38248e6 | 1.14700 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17112.0 | 0.00263369 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55771e6 | 0.542440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.58703e6 | 0.239718 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 736196. | 0.110169 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −863115. | −0.126787 | −0.0633936 | − | 0.997989i | \(-0.520192\pi\) | ||||
−0.0633936 | + | 0.997989i | \(0.520192\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.31044e7 | −1.90730 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −935052. | −0.134848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.45692e6 | 0.779794 | 0.389897 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389897 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14141.1 | −0.00200241 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −233137. | −0.0327139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.00078e6 | −0.275719 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.11776e7 | 1.52655 | 0.763275 | − | 0.646074i | \(-0.223590\pi\) | ||||
0.763275 | + | 0.646074i | \(0.223590\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.11724e6 | 0.151223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.04989e7 | −1.40844 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −880265. | −0.117042 | −0.0585211 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585211 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.89959e6 | −0.250344 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.54972e6 | −0.200665 | −0.100332 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100332 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09701e7 | 1.40806 | 0.704032 | − | 0.710168i | \(-0.251381\pi\) | ||||
0.704032 | + | 0.710168i | \(0.251381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.45794e6 | −0.948926 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.97742e6 | 1.25849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.25868e7 | −1.57390 | −0.786948 | − | 0.617019i | \(-0.788340\pi\) | ||||
−0.786948 | + | 0.617019i | \(0.788340\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.08784e7 | −1.34856 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17084e7 | 1.42667 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29320.7 | 0.00354230 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.19962e7 | −1.43697 | −0.718484 | − | 0.695544i | \(-0.755164\pi\) | ||||
−0.718484 | + | 0.695544i | \(0.755164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.71617e7 | 2.03831 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.92935e6 | −0.580525 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.32309e6 | 0.621623 | 0.310811 | − | 0.950472i | \(-0.399399\pi\) | ||||
0.310811 | + | 0.950472i | \(0.399399\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.53895e6 | −0.521218 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.55513e6 | −0.860350 | −0.430175 | − | 0.902746i | \(-0.641548\pi\) | ||||
−0.430175 | + | 0.902746i | \(0.641548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.44758e6 | 0.502270 | 0.251135 | − | 0.967952i | \(-0.419196\pi\) | ||||
0.251135 | + | 0.967952i | \(0.419196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −395742. | −0.0443219 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.84400e6 | −0.538042 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.57320e6 | −0.613950 | −0.306975 | − | 0.951718i | \(-0.599317\pi\) | ||||
−0.306975 | + | 0.951718i | \(0.599317\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 387840. | 0.0420290 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.11265e7 | −1.19593 | −0.597965 | − | 0.801522i | \(-0.704024\pi\) | ||||
−0.597965 | + | 0.801522i | \(0.704024\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.70884e6 | −0.608640 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.07454e7 | −1.13634 | −0.568170 | − | 0.822911i | \(-0.692349\pi\) | ||||
−0.568170 | + | 0.822911i | \(0.692349\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.35756e7 | −1.42408 | −0.712038 | − | 0.702141i | \(-0.752228\pi\) | ||||
−0.712038 | + | 0.702141i | \(0.752228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38790e7 | −1.44421 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.82573e6 | 0.596555 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.86344e7 | −1.89299 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.39927e6 | −0.644917 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.27986e7 | −1.27964 | −0.639820 | − | 0.768525i | \(-0.720991\pi\) | ||||
−0.639820 | + | 0.768525i | \(0.720991\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.27741e6 | −0.721885 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.94184e6 | 0.387941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 211164. | 0.0204583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −884833. | −0.0850582 | −0.0425291 | − | 0.999095i | \(-0.513542\pi\) | ||||
−0.0425291 | + | 0.999095i | \(0.513542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.66271e6 | −0.635511 | −0.317756 | − | 0.948173i | \(-0.602929\pi\) | ||||
−0.317756 | + | 0.948173i | \(0.602929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.79277e6 | −0.169678 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.69177e7 | 1.58885 | 0.794423 | − | 0.607365i | \(-0.207773\pi\) | ||||
0.794423 | + | 0.607365i | \(0.207773\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.58645e6 | 0.147848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.49307e6 | 0.871212 | 0.435606 | − | 0.900137i | \(-0.356534\pi\) | ||||
0.435606 | + | 0.900137i | \(0.356534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.24266e6 | 0.295323 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −48272.0 | −0.00436297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.97563e6 | 0.446308 | 0.223154 | − | 0.974783i | \(-0.428365\pi\) | ||||
0.223154 | + | 0.974783i | \(0.428365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.11531e7 | 1.88309 | 0.941543 | − | 0.336894i | \(-0.109376\pi\) | ||||
0.941543 | + | 0.336894i | \(0.109376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.46939e6 | 0.306527 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 460015. | 0.0400366 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.89288e7 | −1.63515 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.31102e6 | −0.112410 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 417573. | 0.0355382 | 0.0177691 | − | 0.999842i | \(-0.494344\pi\) | ||||
0.0177691 | + | 0.999842i | \(0.494344\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00209e7 | −0.846539 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.62468e6 | 0.220092 | 0.110046 | − | 0.993926i | \(-0.464900\pi\) | ||||
0.110046 | + | 0.993926i | \(0.464900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41372e7 | 1.16814 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.74455e6 | 0.717275 | 0.358637 | − | 0.933477i | \(-0.383241\pi\) | ||||
0.358637 | + | 0.933477i | \(0.383241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.29399e6 | −0.186795 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.09716e6 | 0.331200 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.86905e6 | −0.310496 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.39667e6 | −0.350291 | −0.175146 | − | 0.984543i | \(-0.556040\pi\) | ||||
−0.175146 | + | 0.984543i | \(0.556040\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.29860e6 | −0.337571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.82591e7 | −1.42363 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.33951e6 | −0.258518 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.51339e6 | 0.500624 | 0.250312 | − | 0.968165i | \(-0.419467\pi\) | ||||
0.250312 | + | 0.968165i | \(0.419467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.13580e7 | −0.866789 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −622343. | −0.0471582 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04651e7 | −0.781859 | −0.390929 | − | 0.920421i | \(-0.627846\pi\) | ||||
−0.390929 | + | 0.920421i | \(0.627846\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20116.3 | −0.00149237 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.38625e7 | −2.49457 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.71832e6 | 0.198855 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7317.31 | 0.000531562 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.68149e7 | 1.21303 | 0.606516 | − | 0.795071i | \(-0.292567\pi\) | ||||
0.606516 | + | 0.795071i | \(0.292567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.52605e6 | −0.322013 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 332138. | 0.0234679 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.71928e7 | 1.20646 | 0.603228 | − | 0.797569i | \(-0.293881\pi\) | ||||
0.603228 | + | 0.797569i | \(0.293881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.39284e7 | 0.970696 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.73400e6 | −0.396885 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.97365e7 | 1.35679 | 0.678393 | − | 0.734700i | \(-0.262677\pi\) | ||||
0.678393 | + | 0.734700i | \(0.262677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.66892e7 | −2.48811 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.28719e7 | −0.867022 | −0.433511 | − | 0.901148i | \(-0.642725\pi\) | ||||
−0.433511 | + | 0.901148i | \(0.642725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.15778e6 | 0.411983 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.45606e7 | −1.63218 | −0.816089 | − | 0.577927i | \(-0.803862\pi\) | ||||
−0.816089 | + | 0.577927i | \(0.803862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.53246e6 | 0.563227 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −310234. | −0.0203417 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 325965. | 0.0210898 | 0.0105449 | − | 0.999944i | \(-0.496643\pi\) | ||||
0.0105449 | + | 0.999944i | \(0.496643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.16774e7 | −1.39322 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.75360e6 | −0.558881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.84659e7 | 1.17120 | 0.585599 | − | 0.810601i | \(-0.300859\pi\) | ||||
0.585599 | + | 0.810601i | \(0.300859\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.67685e7 | 2.31671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.12626e6 | 0.320877 | 0.160439 | − | 0.987046i | \(-0.448709\pi\) | ||||
0.160439 | + | 0.987046i | \(0.448709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −150482. | −0.00929675 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −524246. | −0.0321771 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.63432e6 | 0.0996602 | 0.0498301 | − | 0.998758i | \(-0.484132\pi\) | ||||
0.0498301 | + | 0.998758i | \(0.484132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19984e7 | 0.726921 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.28257e6 | −0.257784 | −0.128892 | − | 0.991659i | \(-0.541142\pi\) | ||||
−0.128892 | + | 0.991659i | \(0.541142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.44493e7 | −1.46222 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.24079e7 | −1.91341 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.95770e7 | 1.14847 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −462019. | −0.0269312 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.50510e6 | −0.145095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.82963e6 | 0.450614 | 0.225307 | − | 0.974288i | \(-0.427662\pi\) | ||||
0.225307 | + | 0.974288i | \(0.427662\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.69484e7 | −0.969250 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 433229. | 0.0244644 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.20844e6 | 0.348389 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.68238e6 | −0.205344 | −0.102672 | − | 0.994715i | \(-0.532739\pi\) | ||||
−0.102672 | + | 0.994715i | \(0.532739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.99050e6 | −0.110305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 668607. | 0.0368205 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.47529e6 | −0.244925 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.79108e7 | 1.50865 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.08181e7 | 1.11833 | 0.559165 | − | 0.829056i | \(-0.311122\pi\) | ||||
0.559165 | + | 0.829056i | \(0.311122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.03542e7 | −1.62057 | −0.810283 | − | 0.586039i | \(-0.800687\pi\) | ||||
−0.810283 | + | 0.586039i | \(0.800687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.24243e7 | −1.72046 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 994821. | 0.0524627 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.01772e7 | −0.533426 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.74387e7 | 1.42071 | 0.710355 | − | 0.703843i | \(-0.248534\pi\) | ||||
0.710355 | + | 0.703843i | \(0.248534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.59126e7 | −0.818919 | −0.409459 | − | 0.912328i | \(-0.634283\pi\) | ||||
−0.409459 | + | 0.912328i | \(0.634283\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.65474e7 | 1.35796 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.40824e7 | −0.716001 | −0.358001 | − | 0.933721i | \(-0.616541\pi\) | ||||
−0.358001 | + | 0.933721i | \(0.616541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.18883e7 | 1.10618 | 0.553089 | − | 0.833122i | \(-0.313449\pi\) | ||||
0.553089 | + | 0.833122i | \(0.313449\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.37598e7 | −0.691211 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.86505e6 | −0.241475 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.40100e7 | 1.67801 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.98669e7 | 0.974372 | 0.487186 | − | 0.873298i | \(-0.338023\pi\) | ||||
0.487186 | + | 0.873298i | \(0.338023\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04958e7 | −0.999253 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.72034e7 | −1.80308 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.89888e6 | 0.332381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.46152e7 | −1.64815 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.24110e7 | 1.06081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.75258e6 | 0.411873 | 0.205937 | − | 0.978565i | \(-0.433976\pi\) | ||||
0.205937 | + | 0.978565i | \(0.433976\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −267089. | −0.0124951 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.95477e6 | −0.0909166 | −0.0454583 | − | 0.998966i | \(-0.514475\pi\) | ||||
−0.0454583 | + | 0.998966i | \(0.514475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.98450e6 | −0.230483 | −0.115241 | − | 0.993338i | \(-0.536764\pi\) | ||||
−0.115241 | + | 0.993338i | \(0.536764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.69931e7 | 0.776685 | 0.388343 | − | 0.921515i | \(-0.373048\pi\) | ||||
0.388343 | + | 0.921515i | \(0.373048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.82112e6 | −0.128198 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.63285e6 | 0.209315 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.86498e6 | −0.0837772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.21240e7 | 0.541503 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −780054. | −0.0346409 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.81959e7 | 0.798869 | 0.399434 | − | 0.916762i | \(-0.369207\pi\) | ||||
0.399434 | + | 0.916762i | \(0.369207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.27645e7 | 0.557226 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.77637e7 | 0.771068 | 0.385534 | − | 0.922694i | \(-0.374017\pi\) | ||||
0.385534 | + | 0.922694i | \(0.374017\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.71479e6 | −0.0740131 | −0.0370065 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370065 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 841226. | 0.0361039 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.42436e7 | 1.03464 | 0.517318 | − | 0.855793i | \(-0.326930\pi\) | ||||
0.517318 | + | 0.855793i | \(0.326930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.79554e7 | −1.60169 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.53292e6 | −0.148253 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 978272. | 0.0408227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.21502e7 | −0.504200 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.12725e6 | −0.0465179 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.98570e7 | 0.814897 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.74134e7 | −0.706745 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.90432e7 | 0.768639 | 0.384319 | − | 0.923200i | \(-0.374436\pi\) | ||||
0.384319 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 73932.0 | 0.00296772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.18731e7 | 1.27242 | 0.636208 | − | 0.771518i | \(-0.280502\pi\) | ||||
0.636208 | + | 0.771518i | \(0.280502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.87618e7 | −1.14193 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −695178. | −0.0274500 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.94858e7 | 1.15166 | 0.575830 | − | 0.817569i | \(-0.304679\pi\) | ||||
0.575830 | + | 0.817569i | \(0.304679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.34270e6 | 0.129852 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.46927e6 | −0.249949 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.61811e7 | 0.621804 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 929761. | 0.0355363 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.73871e6 | −0.370222 | −0.185111 | − | 0.982718i | \(-0.559264\pi\) | ||||
−0.185111 | + | 0.982718i | \(0.559264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.61003e6 | −0.173380 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39512e7 | −0.521893 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.66734e7 | 0.992498 | 0.496249 | − | 0.868180i | \(-0.334710\pi\) | ||||
0.496249 | + | 0.868180i | \(0.334710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.15434e7 | 1.16747 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.22865e6 | 0.118863 | 0.0594315 | − | 0.998232i | \(-0.481071\pi\) | ||||
0.0594315 | + | 0.998232i | \(0.481071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.39456e7 | 2.34170 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.59244e6 | 0.166406 | 0.0832029 | − | 0.996533i | \(-0.473485\pi\) | ||||
0.0832029 | + | 0.996533i | \(0.473485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.47887e6 | 0.0533045 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.44011e7 | 1.59200 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.97125e7 | 1.05976 | 0.529880 | − | 0.848073i | \(-0.322237\pi\) | ||||
0.529880 | + | 0.848073i | \(0.322237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.91025e6 | −0.351622 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.22399e6 | 0.0432012 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.43495e7 | 1.89840 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −510184. | −0.0177281 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.44554e7 | −0.499704 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.64435e6 | −0.262890 | −0.131445 | − | 0.991323i | \(-0.541962\pi\) | ||||
−0.131445 | + | 0.991323i | \(0.541962\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.16034e7 | −1.08125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.99621e7 | 1.70056 | 0.850281 | − | 0.526329i | \(-0.176432\pi\) | ||||
0.850281 | + | 0.526329i | \(0.176432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.77265e6 | −0.295542 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.05394e7 | 1.35876 | 0.679378 | − | 0.733789i | \(-0.262250\pi\) | ||||
0.679378 | + | 0.733789i | \(0.262250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.19865e7 | 2.06700 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 300592. | 0.00997251 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.13056e7 | 1.36341 | 0.681703 | − | 0.731629i | \(-0.261239\pi\) | ||||
0.681703 | + | 0.731629i | \(0.261239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.55021e6 | −0.215112 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.00811e7 | 0.652826 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.84084e7 | 0.595431 | 0.297715 | − | 0.954655i | \(-0.403775\pi\) | ||||
0.297715 | + | 0.954655i | \(0.403775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.18167e7 | 0.702126 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.03144e6 | −0.193136 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.39708e7 | −1.08235 | −0.541175 | − | 0.840910i | \(-0.682020\pi\) | ||||
−0.541175 | + | 0.840910i | \(0.682020\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.25086e7 | −0.713568 |
(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 | 784.6.a.bc.1.1 | 2 | ||
4.3 | odd | 2 | 98.6.a.c.1.2 | 2 | |||
7.2 | even | 3 | 112.6.i.b.81.2 | 4 | |||
7.4 | even | 3 | 112.6.i.b.65.2 | 4 | |||
7.6 | odd | 2 | 784.6.a.r.1.2 | 2 | |||
12.11 | even | 2 | 882.6.a.bt.1.2 | 2 | |||
28.3 | even | 6 | 98.6.c.f.79.2 | 4 | |||
28.11 | odd | 6 | 14.6.c.b.9.1 | ✓ | 4 | ||
28.19 | even | 6 | 98.6.c.f.67.2 | 4 | |||
28.23 | odd | 6 | 14.6.c.b.11.1 | yes | 4 | ||
28.27 | even | 2 | 98.6.a.f.1.1 | 2 | |||
84.11 | even | 6 | 126.6.g.e.37.2 | 4 | |||
84.23 | even | 6 | 126.6.g.e.109.2 | 4 | |||
84.83 | odd | 2 | 882.6.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.b.9.1 | ✓ | 4 | 28.11 | odd | 6 | ||
14.6.c.b.11.1 | yes | 4 | 28.23 | odd | 6 | ||
98.6.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
98.6.a.f.1.1 | 2 | 28.27 | even | 2 | |||
98.6.c.f.67.2 | 4 | 28.19 | even | 6 | |||
98.6.c.f.79.2 | 4 | 28.3 | even | 6 | |||
112.6.i.b.65.2 | 4 | 7.4 | even | 3 | |||
112.6.i.b.81.2 | 4 | 7.2 | even | 3 | |||
126.6.g.e.37.2 | 4 | 84.11 | even | 6 | |||
126.6.g.e.109.2 | 4 | 84.23 | even | 6 | |||
784.6.a.r.1.2 | 2 | 7.6 | odd | 2 | |||
784.6.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
882.6.a.bl.1.2 | 2 | 84.83 | odd | 2 | |||
882.6.a.bt.1.2 | 2 | 12.11 | even | 2 |