Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,6,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(4.33036313495\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.6847 | −1.88880 | −0.944399 | − | 0.328801i | \(-0.893356\pi\) | ||||
−0.944399 | + | 0.328801i | \(0.893356\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 82.1619 | 2.56756 | ||||||||
\(5\) | 25.8466 | 0.462358 | 0.231179 | − | 0.972911i | \(-0.425742\pi\) | ||||
0.231179 | + | 0.972911i | \(0.425742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −115.324 | −0.889558 | −0.444779 | − | 0.895640i | \(-0.646718\pi\) | ||||
−0.444779 | + | 0.895640i | \(0.646718\pi\) | |||||||
\(8\) | −535.963 | −2.96081 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −276.162 | −0.873301 | ||||||||
\(11\) | −63.0909 | −0.157212 | −0.0786059 | − | 0.996906i | \(-0.525047\pi\) | ||||
−0.0786059 | + | 0.996906i | \(0.525047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −797.295 | −1.30846 | −0.654231 | − | 0.756295i | \(-0.727007\pi\) | ||||
−0.654231 | + | 0.756295i | \(0.727007\pi\) | |||||||
\(14\) | 1232.20 | 1.68020 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3097.40 | 3.02481 | ||||||||
\(17\) | −1147.02 | −0.962608 | −0.481304 | − | 0.876554i | \(-0.659837\pi\) | ||||
−0.481304 | + | 0.876554i | \(0.659837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −752.057 | −0.477933 | −0.238966 | − | 0.971028i | \(-0.576809\pi\) | ||||
−0.238966 | + | 0.971028i | \(0.576809\pi\) | |||||||
\(20\) | 2123.61 | 1.18713 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 674.105 | 0.296941 | ||||||||
\(23\) | 265.386 | 0.104607 | 0.0523033 | − | 0.998631i | \(-0.483344\pi\) | ||||
0.0523033 | + | 0.998631i | \(0.483344\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2456.95 | −0.786225 | ||||||||
\(26\) | 8518.83 | 2.47142 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9475.23 | −2.28399 | ||||||||
\(29\) | −7183.76 | −1.58620 | −0.793098 | − | 0.609094i | \(-0.791533\pi\) | ||||
−0.793098 | + | 0.609094i | \(0.791533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2696.39 | 0.503940 | 0.251970 | − | 0.967735i | \(-0.418922\pi\) | ||||
0.251970 | + | 0.967735i | \(0.418922\pi\) | |||||||
\(32\) | −15943.8 | −2.75244 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12255.5 | 1.81817 | ||||||||
\(35\) | −2980.73 | −0.411294 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11181.4 | 1.34274 | 0.671372 | − | 0.741121i | \(-0.265705\pi\) | ||||
0.671372 | + | 0.741121i | \(0.265705\pi\) | |||||||
\(38\) | 8035.47 | 0.902719 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13852.8 | −1.36895 | ||||||||
\(41\) | 9945.87 | 0.924024 | 0.462012 | − | 0.886874i | \(-0.347128\pi\) | ||||
0.462012 | + | 0.886874i | \(0.347128\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9965.85 | 0.821946 | 0.410973 | − | 0.911648i | \(-0.365189\pi\) | ||||
0.410973 | + | 0.911648i | \(0.365189\pi\) | |||||||
\(44\) | −5183.67 | −0.403651 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2835.56 | −0.197581 | ||||||||
\(47\) | −20250.0 | −1.33715 | −0.668574 | − | 0.743646i | \(-0.733095\pi\) | ||||
−0.668574 | + | 0.743646i | \(0.733095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3507.41 | −0.208687 | ||||||||
\(50\) | 26251.7 | 1.48502 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −65507.3 | −3.35955 | ||||||||
\(53\) | −15738.2 | −0.769600 | −0.384800 | − | 0.923000i | \(-0.625730\pi\) | ||||
−0.384800 | + | 0.923000i | \(0.625730\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1630.69 | −0.0726881 | ||||||||
\(56\) | 61809.3 | 2.63381 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 76756.0 | 2.99601 | ||||||||
\(59\) | 40290.0 | 1.50684 | 0.753419 | − | 0.657540i | \(-0.228403\pi\) | ||||
0.753419 | + | 0.657540i | \(0.228403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10702.5 | −0.368267 | −0.184133 | − | 0.982901i | \(-0.558948\pi\) | ||||
−0.184133 | + | 0.982901i | \(0.558948\pi\) | |||||||
\(62\) | −28810.0 | −0.951841 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 71237.8 | 2.17400 | ||||||||
\(65\) | −20607.4 | −0.604977 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54262.5 | −1.47677 | −0.738385 | − | 0.674379i | \(-0.764411\pi\) | ||||
−0.738385 | + | 0.674379i | \(0.764411\pi\) | |||||||
\(68\) | −94241.6 | −2.47156 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 31848.1 | 0.776851 | ||||||||
\(71\) | 51165.1 | 1.20456 | 0.602279 | − | 0.798286i | \(-0.294260\pi\) | ||||
0.602279 | + | 0.798286i | \(0.294260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7578.37 | 0.166444 | 0.0832220 | − | 0.996531i | \(-0.473479\pi\) | ||||
0.0832220 | + | 0.996531i | \(0.473479\pi\) | |||||||
\(74\) | −119470. | −2.53617 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −61790.4 | −1.22712 | ||||||||
\(77\) | 7275.89 | 0.139849 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −26589.2 | −0.479333 | −0.239666 | − | 0.970855i | \(-0.577038\pi\) | ||||
−0.239666 | + | 0.970855i | \(0.577038\pi\) | |||||||
\(80\) | 80057.2 | 1.39854 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −106268. | −1.74530 | ||||||||
\(83\) | 91718.4 | 1.46137 | 0.730686 | − | 0.682713i | \(-0.239200\pi\) | ||||
0.730686 | + | 0.682713i | \(0.239200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −29646.6 | −0.445069 | ||||||||
\(86\) | −106482. | −1.55249 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 33814.4 | 0.465474 | ||||||||
\(89\) | −45378.2 | −0.607256 | −0.303628 | − | 0.952791i | \(-0.598198\pi\) | ||||
−0.303628 | + | 0.952791i | \(0.598198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 91947.2 | 1.16395 | ||||||||
\(92\) | 21804.7 | 0.268584 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 216364. | 2.52560 | ||||||||
\(95\) | −19438.1 | −0.220976 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 376.873 | 0.00406692 | 0.00203346 | − | 0.999998i | \(-0.499353\pi\) | ||||
0.00203346 | + | 0.999998i | \(0.499353\pi\) | |||||||
\(98\) | 37475.5 | 0.394168 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −201868. | −2.01868 | ||||||||
\(101\) | −1626.35 | −0.0158639 | −0.00793195 | − | 0.999969i | \(-0.502525\pi\) | ||||
−0.00793195 | + | 0.999969i | \(0.502525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59635.7 | 0.553876 | 0.276938 | − | 0.960888i | \(-0.410680\pi\) | ||||
0.276938 | + | 0.960888i | \(0.410680\pi\) | |||||||
\(104\) | 427321. | 3.87410 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 168157. | 1.45362 | ||||||||
\(107\) | 113386. | 0.957412 | 0.478706 | − | 0.877975i | \(-0.341106\pi\) | ||||
0.478706 | + | 0.877975i | \(0.341106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 167511. | 1.35044 | 0.675221 | − | 0.737615i | \(-0.264048\pi\) | ||||
0.675221 | + | 0.737615i | \(0.264048\pi\) | |||||||
\(110\) | 17423.3 | 0.137293 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −357204. | −2.69074 | ||||||||
\(113\) | −181432. | −1.33665 | −0.668326 | − | 0.743868i | \(-0.732989\pi\) | ||||
−0.668326 | + | 0.743868i | \(0.732989\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6859.33 | 0.0483657 | ||||||||
\(116\) | −590232. | −4.07265 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −430484. | −2.84611 | ||||||||
\(119\) | 132279. | 0.856296 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157071. | −0.975284 | ||||||||
\(122\) | 114353. | 0.695582 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 221541. | 1.29390 | ||||||||
\(125\) | −144274. | −0.825875 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 65774.9 | 0.361868 | 0.180934 | − | 0.983495i | \(-0.442088\pi\) | ||||
0.180934 | + | 0.983495i | \(0.442088\pi\) | |||||||
\(128\) | −250948. | −1.35381 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 220183. | 1.14268 | ||||||||
\(131\) | −88139.0 | −0.448735 | −0.224367 | − | 0.974505i | \(-0.572032\pi\) | ||||
−0.224367 | + | 0.974505i | \(0.572032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 86730.1 | 0.425149 | ||||||||
\(134\) | 579776. | 2.78932 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 614762. | 2.85010 | ||||||||
\(137\) | −45228.8 | −0.205880 | −0.102940 | − | 0.994688i | \(-0.532825\pi\) | ||||
−0.102940 | + | 0.994688i | \(0.532825\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −71637.5 | −0.314488 | −0.157244 | − | 0.987560i | \(-0.550261\pi\) | ||||
−0.157244 | + | 0.987560i | \(0.550261\pi\) | |||||||
\(140\) | −244902. | −1.05602 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −546681. | −2.27517 | ||||||||
\(143\) | 50302.1 | 0.205706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −185676. | −0.733390 | ||||||||
\(146\) | −80972.2 | −0.314379 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 918688. | 3.44757 | ||||||||
\(149\) | −461330. | −1.70234 | −0.851169 | − | 0.524891i | \(-0.824106\pi\) | ||||
−0.851169 | + | 0.524891i | \(0.824106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −364935. | −1.30249 | −0.651243 | − | 0.758869i | \(-0.725752\pi\) | ||||
−0.651243 | + | 0.758869i | \(0.725752\pi\) | |||||||
\(152\) | 403075. | 1.41507 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −77740.4 | −0.264147 | ||||||||
\(155\) | 69692.5 | 0.233001 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −270764. | −0.876681 | −0.438341 | − | 0.898809i | \(-0.644434\pi\) | ||||
−0.438341 | + | 0.898809i | \(0.644434\pi\) | |||||||
\(158\) | 284096. | 0.905363 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −412094. | −1.27261 | ||||||||
\(161\) | −30605.4 | −0.0930536 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −119086. | −0.351069 | −0.175535 | − | 0.984473i | \(-0.556165\pi\) | ||||
−0.175535 | + | 0.984473i | \(0.556165\pi\) | |||||||
\(164\) | 817172. | 2.37249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −979979. | −2.76024 | ||||||||
\(167\) | 402672. | 1.11728 | 0.558638 | − | 0.829412i | \(-0.311324\pi\) | ||||
0.558638 | + | 0.829412i | \(0.311324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 264387. | 0.712071 | ||||||||
\(170\) | 316764. | 0.840647 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 818814. | 2.11040 | ||||||||
\(173\) | −467534. | −1.18768 | −0.593839 | − | 0.804584i | \(-0.702388\pi\) | ||||
−0.593839 | + | 0.804584i | \(0.702388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 283345. | 0.699393 | ||||||||
\(176\) | −195418. | −0.475535 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 484850. | 1.14698 | ||||||||
\(179\) | −49932.9 | −0.116481 | −0.0582404 | − | 0.998303i | \(-0.518549\pi\) | ||||
−0.0582404 | + | 0.998303i | \(0.518549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 82498.4 | 0.187176 | 0.0935878 | − | 0.995611i | \(-0.470166\pi\) | ||||
0.0935878 | + | 0.995611i | \(0.470166\pi\) | |||||||
\(182\) | −982424. | −2.19847 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −142237. | −0.309720 | ||||||||
\(185\) | 289002. | 0.620828 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72366.7 | 0.151333 | ||||||||
\(188\) | −1.66378e6 | −3.43321 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 207689. | 0.417379 | ||||||||
\(191\) | 344744. | 0.683775 | 0.341887 | − | 0.939741i | \(-0.388934\pi\) | ||||
0.341887 | + | 0.939741i | \(0.388934\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 591965. | 1.14394 | 0.571970 | − | 0.820275i | \(-0.306179\pi\) | ||||
0.571970 | + | 0.820275i | \(0.306179\pi\) | |||||||
\(194\) | −4026.75 | −0.00768158 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −288175. | −0.535817 | ||||||||
\(197\) | −236171. | −0.433572 | −0.216786 | − | 0.976219i | \(-0.569557\pi\) | ||||
−0.216786 | + | 0.976219i | \(0.569557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 36776.0 | 0.0658313 | 0.0329156 | − | 0.999458i | \(-0.489521\pi\) | ||||
0.0329156 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(200\) | 1.31684e6 | 2.32786 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17377.0 | 0.0299637 | ||||||||
\(203\) | 828459. | 1.41101 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 257067. | 0.427230 | ||||||||
\(206\) | −637187. | −1.04616 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.46954e6 | −3.95784 | ||||||||
\(209\) | 47448.0 | 0.0751367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 526111. | 0.813525 | 0.406763 | − | 0.913534i | \(-0.366658\pi\) | ||||
0.406763 | + | 0.913534i | \(0.366658\pi\) | |||||||
\(212\) | −1.29308e6 | −1.97599 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.21149e6 | −1.80836 | ||||||||
\(215\) | 257583. | 0.380033 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −310958. | −0.448284 | ||||||||
\(218\) | −1.78979e6 | −2.55071 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −133980. | −0.186631 | ||||||||
\(221\) | 914516. | 1.25954 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 172656. | 0.232498 | 0.116249 | − | 0.993220i | \(-0.462913\pi\) | ||||
0.116249 | + | 0.993220i | \(0.462913\pi\) | |||||||
\(224\) | 1.83871e6 | 2.44846 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.93854e6 | 2.52467 | ||||||||
\(227\) | −1.13692e6 | −1.46442 | −0.732208 | − | 0.681081i | \(-0.761510\pi\) | ||||
−0.732208 | + | 0.681081i | \(0.761510\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −783946. | −0.987865 | −0.493933 | − | 0.869500i | \(-0.664441\pi\) | ||||
−0.493933 | + | 0.869500i | \(0.664441\pi\) | |||||||
\(230\) | −73289.6 | −0.0913530 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.85023e6 | 4.69642 | ||||||||
\(233\) | 852850. | 1.02916 | 0.514580 | − | 0.857442i | \(-0.327948\pi\) | ||||
0.514580 | + | 0.857442i | \(0.327948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −523392. | −0.618241 | ||||||||
\(236\) | 3.31030e6 | 3.86890 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.41336e6 | −1.61737 | ||||||||
\(239\) | −625959. | −0.708845 | −0.354423 | − | 0.935085i | \(-0.615323\pi\) | ||||
−0.354423 | + | 0.935085i | \(0.615323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −114154. | −0.126604 | −0.0633021 | − | 0.997994i | \(-0.520163\pi\) | ||||
−0.0633021 | + | 0.997994i | \(0.520163\pi\) | |||||||
\(242\) | 1.67825e6 | 1.84212 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −879342. | −0.945547 | ||||||||
\(245\) | −90654.5 | −0.0964882 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 599612. | 0.625356 | ||||||||
\(248\) | −1.44517e6 | −1.49207 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.54152e6 | 1.55991 | ||||||||
\(251\) | −572829. | −0.573906 | −0.286953 | − | 0.957945i | \(-0.592642\pi\) | ||||
−0.286953 | + | 0.957945i | \(0.592642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16743.5 | −0.0164454 | ||||||||
\(254\) | −702782. | −0.683496 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 401685. | 0.383077 | ||||||||
\(257\) | 286863. | 0.270920 | 0.135460 | − | 0.990783i | \(-0.456749\pi\) | ||||
0.135460 | + | 0.990783i | \(0.456749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.28949e6 | −1.19445 | ||||||||
\(260\) | −1.69314e6 | −1.55332 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 941735. | 0.847569 | ||||||||
\(263\) | 296534. | 0.264353 | 0.132177 | − | 0.991226i | \(-0.457803\pi\) | ||||
0.132177 | + | 0.991226i | \(0.457803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −406778. | −0.355830 | ||||||||
\(266\) | −926681. | −0.803020 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.45831e6 | −3.79170 | ||||||||
\(269\) | 60270.2 | 0.0507835 | 0.0253917 | − | 0.999678i | \(-0.491917\pi\) | ||||
0.0253917 | + | 0.999678i | \(0.491917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.18183e6 | −1.80467 | −0.902335 | − | 0.431036i | \(-0.858148\pi\) | ||||
−0.902335 | + | 0.431036i | \(0.858148\pi\) | |||||||
\(272\) | −3.55279e6 | −2.91170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 483254. | 0.388866 | ||||||||
\(275\) | 155012. | 0.123604 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −39559.4 | −0.0309778 | −0.0154889 | − | 0.999880i | \(-0.504930\pi\) | ||||
−0.0154889 | + | 0.999880i | \(0.504930\pi\) | |||||||
\(278\) | 765422. | 0.594004 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.59756e6 | 1.21776 | ||||||||
\(281\) | 955918. | 0.722196 | 0.361098 | − | 0.932528i | \(-0.382402\pi\) | ||||
0.361098 | + | 0.932528i | \(0.382402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.38449e6 | 1.76982 | 0.884911 | − | 0.465759i | \(-0.154219\pi\) | ||||
0.884911 | + | 0.465759i | \(0.154219\pi\) | |||||||
\(284\) | 4.20382e6 | 3.09277 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −537461. | −0.388536 | ||||||||
\(287\) | −1.14700e6 | −0.821973 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −104196. | −0.0733849 | ||||||||
\(290\) | 1.98388e6 | 1.38523 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 622653. | 0.427355 | ||||||||
\(293\) | −2.31380e6 | −1.57455 | −0.787276 | − | 0.616600i | \(-0.788510\pi\) | ||||
−0.787276 | + | 0.616600i | \(0.788510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.04136e6 | 0.696699 | ||||||||
\(296\) | −5.99283e6 | −3.97560 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.92915e6 | 3.21537 | ||||||||
\(299\) | −211591. | −0.136874 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.14930e6 | −0.731168 | ||||||||
\(302\) | 3.89921e6 | 2.46013 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.32942e6 | −1.44565 | ||||||||
\(305\) | −276624. | −0.170271 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 175518. | 0.106286 | 0.0531430 | − | 0.998587i | \(-0.483076\pi\) | ||||
0.0531430 | + | 0.998587i | \(0.483076\pi\) | |||||||
\(308\) | 597801. | 0.359071 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −744641. | −0.440091 | ||||||||
\(311\) | −3.31716e6 | −1.94476 | −0.972379 | − | 0.233408i | \(-0.925012\pi\) | ||||
−0.972379 | + | 0.233408i | \(0.925012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.15765e6 | 1.82181 | 0.910904 | − | 0.412617i | \(-0.135385\pi\) | ||||
0.910904 | + | 0.412617i | \(0.135385\pi\) | |||||||
\(314\) | 2.89302e6 | 1.65587 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.18462e6 | −1.23072 | ||||||||
\(317\) | 1.25137e6 | 0.699420 | 0.349710 | − | 0.936858i | \(-0.386280\pi\) | ||||
0.349710 | + | 0.936858i | \(0.386280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 453230. | 0.249369 | ||||||||
\(320\) | 1.84125e6 | 1.00517 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 327008. | 0.175759 | ||||||||
\(323\) | 862626. | 0.460062 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.95892e6 | 1.02875 | ||||||||
\(326\) | 1.27240e6 | 0.663100 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.33062e6 | −2.73586 | ||||||||
\(329\) | 2.33530e6 | 1.18947 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.47582e6 | −1.24208 | −0.621039 | − | 0.783780i | \(-0.713289\pi\) | ||||
−0.621039 | + | 0.783780i | \(0.713289\pi\) | |||||||
\(332\) | 7.53576e6 | 3.75216 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.30241e6 | −2.11031 | ||||||||
\(335\) | −1.40250e6 | −0.682796 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.03952e6 | −0.498607 | −0.249304 | − | 0.968425i | \(-0.580202\pi\) | ||||
−0.249304 | + | 0.968425i | \(0.580202\pi\) | |||||||
\(338\) | −2.82488e6 | −1.34496 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.43582e6 | −1.14274 | ||||||||
\(341\) | −170118. | −0.0792253 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.34274e6 | 1.07520 | ||||||||
\(344\) | −5.34133e6 | −2.43362 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.99545e6 | 2.24328 | ||||||||
\(347\) | −3.47924e6 | −1.55118 | −0.775588 | − | 0.631240i | \(-0.782546\pi\) | ||||
−0.775588 | + | 0.631240i | \(0.782546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.20547e6 | 0.969252 | 0.484626 | − | 0.874721i | \(-0.338956\pi\) | ||||
0.484626 | + | 0.874721i | \(0.338956\pi\) | |||||||
\(350\) | −3.02745e6 | −1.32101 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00591e6 | 0.432716 | ||||||||
\(353\) | 3.67997e6 | 1.57184 | 0.785920 | − | 0.618329i | \(-0.212190\pi\) | ||||
0.785920 | + | 0.618329i | \(0.212190\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.32244e6 | 0.556937 | ||||||||
\(356\) | −3.72836e6 | −1.55917 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 533516. | 0.220009 | ||||||||
\(359\) | −1.30796e6 | −0.535620 | −0.267810 | − | 0.963472i | \(-0.586300\pi\) | ||||
−0.267810 | + | 0.963472i | \(0.586300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91051e6 | −0.771580 | ||||||||
\(362\) | −881467. | −0.353537 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.55456e6 | 2.98852 | ||||||||
\(365\) | 195875. | 0.0769567 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.37650e6 | −1.69614 | −0.848069 | − | 0.529885i | \(-0.822235\pi\) | ||||
−0.848069 | + | 0.529885i | \(0.822235\pi\) | |||||||
\(368\) | 822008. | 0.316414 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.08789e6 | −1.17262 | ||||||||
\(371\) | 1.81499e6 | 0.684603 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.02935e6 | −1.12740 | −0.563699 | − | 0.825980i | \(-0.690622\pi\) | ||||
−0.563699 | + | 0.825980i | \(0.690622\pi\) | |||||||
\(374\) | −773214. | −0.285838 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.08532e7 | 3.95903 | ||||||||
\(377\) | 5.72758e6 | 2.07548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 833764. | 0.298157 | 0.149078 | − | 0.988825i | \(-0.452369\pi\) | ||||
0.149078 | + | 0.988825i | \(0.452369\pi\) | |||||||
\(380\) | −1.59707e6 | −0.567369 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.68347e6 | −1.29151 | ||||||||
\(383\) | 1.63521e6 | 0.569609 | 0.284804 | − | 0.958586i | \(-0.408071\pi\) | ||||
0.284804 | + | 0.958586i | \(0.408071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 188057. | 0.0646603 | ||||||||
\(386\) | −6.32495e6 | −2.16067 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30964.6 | 0.0104421 | ||||||||
\(389\) | −4.48524e6 | −1.50284 | −0.751418 | − | 0.659827i | \(-0.770630\pi\) | ||||
−0.751418 | + | 0.659827i | \(0.770630\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −304404. | −0.100695 | ||||||||
\(392\) | 1.87984e6 | 0.617883 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.52341e6 | 0.818930 | ||||||||
\(395\) | −687240. | −0.221623 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.08717e6 | −0.664632 | −0.332316 | − | 0.943168i | \(-0.607830\pi\) | ||||
−0.332316 | + | 0.943168i | \(0.607830\pi\) | |||||||
\(398\) | −392939. | −0.124342 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.61017e6 | −2.37818 | ||||||||
\(401\) | 4.02831e6 | 1.25101 | 0.625506 | − | 0.780219i | \(-0.284892\pi\) | ||||
0.625506 | + | 0.780219i | \(0.284892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.14982e6 | −0.659386 | ||||||||
\(404\) | −133624. | −0.0407315 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.85180e6 | −2.66512 | ||||||||
\(407\) | −705447. | −0.211095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.31168e6 | −1.27450 | −0.637248 | − | 0.770658i | \(-0.719927\pi\) | ||||
−0.637248 | + | 0.770658i | \(0.719927\pi\) | |||||||
\(410\) | −2.74667e6 | −0.806951 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.89978e6 | 1.42211 | ||||||||
\(413\) | −4.64639e6 | −1.34042 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.37061e6 | 0.675677 | ||||||||
\(416\) | 1.27120e7 | 3.60146 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −506965. | −0.141918 | ||||||||
\(419\) | 4.33250e6 | 1.20560 | 0.602800 | − | 0.797892i | \(-0.294052\pi\) | ||||
0.602800 | + | 0.797892i | \(0.294052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 249525. | 0.0686135 | 0.0343067 | − | 0.999411i | \(-0.489078\pi\) | ||||
0.0343067 | + | 0.999411i | \(0.489078\pi\) | |||||||
\(422\) | −5.62131e6 | −1.53659 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.43509e6 | 2.27864 | ||||||||
\(425\) | 2.81818e6 | 0.756827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.23426e6 | 0.327594 | ||||||||
\(428\) | 9.31599e6 | 2.45821 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.75219e6 | −0.717806 | ||||||||
\(431\) | 4.16691e6 | 1.08049 | 0.540245 | − | 0.841508i | \(-0.318332\pi\) | ||||
0.540245 | + | 0.841508i | \(0.318332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.75137e6 | 1.73050 | 0.865251 | − | 0.501340i | \(-0.167159\pi\) | ||||
0.865251 | + | 0.501340i | \(0.167159\pi\) | |||||||
\(434\) | 3.32248e6 | 0.846717 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.37630e7 | 3.46734 | ||||||||
\(437\) | −199586. | −0.0499949 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −343561. | −0.0850831 | −0.0425415 | − | 0.999095i | \(-0.513545\pi\) | ||||
−0.0425415 | + | 0.999095i | \(0.513545\pi\) | |||||||
\(440\) | 873987. | 0.215215 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.77129e6 | −2.37901 | ||||||||
\(443\) | −5.17293e6 | −1.25235 | −0.626177 | − | 0.779681i | \(-0.715381\pi\) | ||||
−0.626177 | + | 0.779681i | \(0.715381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.17287e6 | −0.280770 | ||||||||
\(446\) | −1.84477e6 | −0.439141 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.21541e6 | −1.93390 | ||||||||
\(449\) | −913932. | −0.213943 | −0.106972 | − | 0.994262i | \(-0.534115\pi\) | ||||
−0.106972 | + | 0.994262i | \(0.534115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −627494. | −0.145268 | ||||||||
\(452\) | −1.49068e7 | −3.43194 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.21476e7 | 2.76599 | ||||||||
\(455\) | 2.37652e6 | 0.538162 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.96268e6 | 0.439602 | 0.219801 | − | 0.975545i | \(-0.429459\pi\) | ||||
0.219801 | + | 0.975545i | \(0.429459\pi\) | |||||||
\(458\) | 8.37620e6 | 1.86588 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 563576. | 0.124182 | ||||||||
\(461\) | −2.23347e6 | −0.489472 | −0.244736 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244736 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.27635e6 | 1.36068 | 0.680338 | − | 0.732898i | \(-0.261833\pi\) | ||||
0.680338 | + | 0.732898i | \(0.261833\pi\) | |||||||
\(464\) | −2.22510e7 | −4.79793 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.11241e6 | −1.94388 | ||||||||
\(467\) | −4.69184e6 | −0.995522 | −0.497761 | − | 0.867314i | \(-0.665844\pi\) | ||||
−0.497761 | + | 0.867314i | \(0.665844\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.25776e6 | 1.31367 | ||||||||
\(470\) | 5.59227e6 | 1.16773 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.15939e7 | −4.46146 | ||||||||
\(473\) | −628755. | −0.129220 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.84777e6 | 0.375763 | ||||||||
\(476\) | 1.08683e7 | 2.19859 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.68816e6 | 1.33887 | ||||||||
\(479\) | 2.04271e6 | 0.406788 | 0.203394 | − | 0.979097i | \(-0.434803\pi\) | ||||
0.203394 | + | 0.979097i | \(0.434803\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.91490e6 | −1.75693 | ||||||||
\(482\) | 1.21969e6 | 0.239130 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.29052e7 | −2.50410 | ||||||||
\(485\) | 9740.87 | 0.00188037 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.45535e6 | −1.23338 | −0.616690 | − | 0.787206i | \(-0.711527\pi\) | ||||
−0.616690 | + | 0.787206i | \(0.711527\pi\) | |||||||
\(488\) | 5.73617e6 | 1.09037 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 968613. | 0.182247 | ||||||||
\(491\) | 5.68549e6 | 1.06430 | 0.532150 | − | 0.846650i | \(-0.321384\pi\) | ||||
0.532150 | + | 0.846650i | \(0.321384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.23994e6 | 1.52689 | ||||||||
\(494\) | −6.40664e6 | −1.18117 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.35180e6 | 1.52432 | ||||||||
\(497\) | −5.90055e6 | −1.07152 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 202061. | 0.0363272 | 0.0181636 | − | 0.999835i | \(-0.494218\pi\) | ||||
0.0181636 | + | 0.999835i | \(0.494218\pi\) | |||||||
\(500\) | −1.18539e7 | −2.12048 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.12048e6 | 1.08399 | ||||||||
\(503\) | 1.48616e6 | 0.261906 | 0.130953 | − | 0.991389i | \(-0.458196\pi\) | ||||
0.130953 | + | 0.991389i | \(0.458196\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42035.5 | −0.00733480 | ||||||||
\(506\) | 178898. | 0.0310620 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.40419e6 | 0.929119 | ||||||||
\(509\) | −8.86109e6 | −1.51598 | −0.757989 | − | 0.652268i | \(-0.773818\pi\) | ||||
−0.757989 | + | 0.652268i | \(0.773818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −873966. | −0.148062 | ||||||||
\(512\) | 3.73847e6 | 0.630258 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.06503e6 | −0.511714 | ||||||||
\(515\) | 1.54138e6 | 0.256089 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.27759e6 | 0.210215 | ||||||||
\(518\) | 1.37777e7 | 2.25607 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.10448e7 | 1.79122 | ||||||||
\(521\) | −885212. | −0.142874 | −0.0714370 | − | 0.997445i | \(-0.522758\pi\) | ||||
−0.0714370 | + | 0.997445i | \(0.522758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.19649e6 | 0.510998 | 0.255499 | − | 0.966809i | \(-0.417760\pi\) | ||||
0.255499 | + | 0.966809i | \(0.417760\pi\) | |||||||
\(524\) | −7.24167e6 | −1.15215 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.16836e6 | −0.499310 | ||||||||
\(527\) | −3.09282e6 | −0.485097 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.36591e6 | −0.989057 | ||||||||
\(530\) | 4.34629e6 | 0.672092 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.12591e6 | 1.09159 | ||||||||
\(533\) | −7.92980e6 | −1.20905 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.93063e6 | 0.442667 | ||||||||
\(536\) | 2.90827e7 | 4.37243 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −643967. | −0.0959197 | ||||||||
\(539\) | 221286. | 0.0328081 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.95533e6 | −1.02170 | −0.510851 | − | 0.859669i | \(-0.670670\pi\) | ||||
−0.510851 | + | 0.859669i | \(0.670670\pi\) | |||||||
\(542\) | 2.33121e7 | 3.40866 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.82880e7 | 2.64952 | ||||||||
\(545\) | 4.32958e6 | 0.624388 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.48749e6 | −1.35576 | −0.677880 | − | 0.735173i | \(-0.737101\pi\) | ||||
−0.677880 | + | 0.735173i | \(0.737101\pi\) | |||||||
\(548\) | −3.71609e6 | −0.528609 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.65625e6 | −0.233463 | ||||||||
\(551\) | 5.40260e6 | 0.758095 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.06637e6 | 0.426394 | ||||||||
\(554\) | 422678. | 0.0585107 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.88588e6 | −0.807466 | ||||||||
\(557\) | −8.41675e6 | −1.14949 | −0.574747 | − | 0.818331i | \(-0.694899\pi\) | ||||
−0.574747 | + | 0.818331i | \(0.694899\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.94573e6 | −1.07548 | ||||||||
\(560\) | −9.23251e6 | −1.24408 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.02137e7 | −1.36408 | ||||||||
\(563\) | −7.81759e6 | −1.03945 | −0.519723 | − | 0.854335i | \(-0.673965\pi\) | ||||
−0.519723 | + | 0.854335i | \(0.673965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.68941e6 | −0.618012 | ||||||||
\(566\) | −2.54775e7 | −3.34284 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.74226e7 | −3.56646 | ||||||||
\(569\) | 9.22271e6 | 1.19420 | 0.597101 | − | 0.802166i | \(-0.296319\pi\) | ||||
0.597101 | + | 0.802166i | \(0.296319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.37099e6 | −0.561035 | −0.280518 | − | 0.959849i | \(-0.590506\pi\) | ||||
−0.280518 | + | 0.959849i | \(0.590506\pi\) | |||||||
\(572\) | 4.13292e6 | 0.528161 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.22553e7 | 1.55254 | ||||||||
\(575\) | −652042. | −0.0822443 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.98397e6 | 0.623212 | 0.311606 | − | 0.950211i | \(-0.399133\pi\) | ||||
0.311606 | + | 0.950211i | \(0.399133\pi\) | |||||||
\(578\) | 1.11330e6 | 0.138609 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.52555e7 | −1.88302 | ||||||||
\(581\) | −1.05773e7 | −1.29998 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 992937. | 0.120990 | ||||||||
\(584\) | −4.06172e6 | −0.492809 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.47222e7 | 2.97401 | ||||||||
\(587\) | 9.17700e6 | 1.09927 | 0.549636 | − | 0.835404i | \(-0.314766\pi\) | ||||
0.549636 | + | 0.835404i | \(0.314766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.02784e6 | −0.240849 | ||||||||
\(590\) | −1.11266e7 | −1.31592 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.46334e7 | 4.06154 | ||||||||
\(593\) | 1.25421e7 | 1.46465 | 0.732327 | − | 0.680953i | \(-0.238434\pi\) | ||||
0.732327 | + | 0.680953i | \(0.238434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.41896e6 | 0.395915 | ||||||||
\(596\) | −3.79038e7 | −4.37086 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.26078e6 | 0.258527 | ||||||||
\(599\) | 8.28426e6 | 0.943380 | 0.471690 | − | 0.881765i | \(-0.343644\pi\) | ||||
0.471690 | + | 0.881765i | \(0.343644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.27223e6 | 0.934193 | 0.467096 | − | 0.884206i | \(-0.345300\pi\) | ||||
0.467096 | + | 0.884206i | \(0.345300\pi\) | |||||||
\(602\) | 1.22799e7 | 1.38103 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.99838e7 | −3.34421 | ||||||||
\(605\) | −4.05974e6 | −0.450930 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.18488e6 | 0.681333 | 0.340666 | − | 0.940184i | \(-0.389347\pi\) | ||||
0.340666 | + | 0.940184i | \(0.389347\pi\) | |||||||
\(608\) | 1.19907e7 | 1.31548 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.95564e6 | 0.321608 | ||||||||
\(611\) | 1.61452e7 | 1.74961 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.25753e7 | −1.35166 | −0.675829 | − | 0.737059i | \(-0.736214\pi\) | ||||
−0.675829 | + | 0.737059i | \(0.736214\pi\) | |||||||
\(614\) | −1.87535e6 | −0.200753 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.89961e6 | −0.414066 | ||||||||
\(617\) | −6.68148e6 | −0.706577 | −0.353289 | − | 0.935514i | \(-0.614937\pi\) | ||||
−0.353289 | + | 0.935514i | \(0.614937\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.04346e7 | 1.09458 | 0.547292 | − | 0.836942i | \(-0.315659\pi\) | ||||
0.547292 | + | 0.836942i | \(0.315659\pi\) | |||||||
\(620\) | 5.72607e6 | 0.598243 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.54427e7 | 3.67326 | ||||||||
\(623\) | 5.23318e6 | 0.540189 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.94898e6 | 0.404376 | ||||||||
\(626\) | −3.37384e7 | −3.44103 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.22465e7 | −2.25093 | ||||||||
\(629\) | −1.28254e7 | −1.29254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.36703e6 | 0.436629 | 0.218315 | − | 0.975878i | \(-0.429944\pi\) | ||||
0.218315 | + | 0.975878i | \(0.429944\pi\) | |||||||
\(632\) | 1.42508e7 | 1.41921 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.33705e7 | −1.32106 | ||||||||
\(635\) | 1.70006e6 | 0.167313 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.79644e6 | 0.273059 | ||||||||
\(638\) | −4.84261e6 | −0.471007 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.48615e6 | −0.625946 | ||||||||
\(641\) | 9.99391e6 | 0.960705 | 0.480353 | − | 0.877075i | \(-0.340509\pi\) | ||||
0.480353 | + | 0.877075i | \(0.340509\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.03306e7 | 0.985364 | 0.492682 | − | 0.870209i | \(-0.336017\pi\) | ||||
0.492682 | + | 0.870209i | \(0.336017\pi\) | |||||||
\(644\) | −2.51460e6 | −0.238921 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.21687e6 | −0.868964 | ||||||||
\(647\) | 404393. | 0.0379790 | 0.0189895 | − | 0.999820i | \(-0.493955\pi\) | ||||
0.0189895 | + | 0.999820i | \(0.493955\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.54193e6 | −0.236893 | ||||||||
\(650\) | −2.09304e7 | −1.94309 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.78437e6 | −0.901392 | ||||||||
\(653\) | −8.98734e6 | −0.824799 | −0.412399 | − | 0.911003i | \(-0.635309\pi\) | ||||
−0.412399 | + | 0.911003i | \(0.635309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.27809e6 | −0.207476 | ||||||||
\(656\) | 3.08064e7 | 2.79499 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.49519e7 | −2.24667 | ||||||||
\(659\) | 2.91006e6 | 0.261028 | 0.130514 | − | 0.991446i | \(-0.458337\pi\) | ||||
0.130514 | + | 0.991446i | \(0.458337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.38558e7 | 1.23347 | 0.616733 | − | 0.787173i | \(-0.288456\pi\) | ||||
0.616733 | + | 0.787173i | \(0.288456\pi\) | |||||||
\(662\) | 2.64533e7 | 2.34603 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.91577e7 | −4.32684 | ||||||||
\(665\) | 2.24168e6 | 0.196571 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.90647e6 | −0.165927 | ||||||||
\(668\) | 3.30843e7 | 2.86867 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.49852e7 | 1.28966 | ||||||||
\(671\) | 675234. | 0.0578959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.27036e6 | 0.703861 | 0.351930 | − | 0.936026i | \(-0.385525\pi\) | ||||
0.351930 | + | 0.936026i | \(0.385525\pi\) | |||||||
\(674\) | 1.11069e7 | 0.941769 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.17225e7 | 1.82829 | ||||||||
\(677\) | −1.34494e6 | −0.112780 | −0.0563899 | − | 0.998409i | \(-0.517959\pi\) | ||||
−0.0563899 | + | 0.998409i | \(0.517959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43462.4 | −0.00361776 | ||||||||
\(680\) | 1.58895e7 | 1.31776 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.81765e6 | 0.149641 | ||||||||
\(683\) | 8.12622e6 | 0.666556 | 0.333278 | − | 0.942829i | \(-0.391845\pi\) | ||||
0.333278 | + | 0.942829i | \(0.391845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.16901e6 | −0.0951901 | ||||||||
\(686\) | −2.50313e7 | −2.03083 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.08682e7 | 2.48623 | ||||||||
\(689\) | 1.25480e7 | 1.00699 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.43559e7 | −1.14376 | −0.571881 | − | 0.820337i | \(-0.693786\pi\) | ||||
−0.571881 | + | 0.820337i | \(0.693786\pi\) | |||||||
\(692\) | −3.84135e7 | −3.04943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.71745e7 | 2.92986 | ||||||||
\(695\) | −1.85159e6 | −0.145406 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.14081e7 | −0.889473 | ||||||||
\(698\) | −2.35646e7 | −1.83072 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.32802e7 | 1.79573 | ||||||||
\(701\) | −2.70976e6 | −0.208274 | −0.104137 | − | 0.994563i | \(-0.533208\pi\) | ||||
−0.104137 | + | 0.994563i | \(0.533208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.40907e6 | −0.641741 | ||||||||
\(704\) | −4.49446e6 | −0.341779 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.93193e7 | −2.96889 | ||||||||
\(707\) | 187557. | 0.0141119 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.76568e6 | −0.131916 | −0.0659578 | − | 0.997822i | \(-0.521010\pi\) | ||||
−0.0659578 | + | 0.997822i | \(0.521010\pi\) | |||||||
\(710\) | −1.41298e7 | −1.05194 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.43210e7 | 1.79797 | ||||||||
\(713\) | 715586. | 0.0527154 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.30014e6 | 0.0951096 | ||||||||
\(716\) | −4.10258e6 | −0.299071 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.39751e7 | 1.01168 | ||||||||
\(719\) | −2.06759e7 | −1.49157 | −0.745783 | − | 0.666189i | \(-0.767924\pi\) | ||||
−0.745783 | + | 0.666189i | \(0.767924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.87741e6 | −0.492705 | ||||||||
\(722\) | 2.04131e7 | 1.45736 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.77823e6 | 0.480585 | ||||||||
\(725\) | 1.76502e7 | 1.24711 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.77199e7 | 1.24344 | 0.621720 | − | 0.783240i | \(-0.286434\pi\) | ||||
0.621720 | + | 0.783240i | \(0.286434\pi\) | |||||||
\(728\) | −4.92803e7 | −3.44623 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.09286e6 | −0.145356 | ||||||||
\(731\) | −1.14311e7 | −0.791212 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.13488e6 | −0.352996 | −0.176498 | − | 0.984301i | \(-0.556477\pi\) | ||||
−0.176498 | + | 0.984301i | \(0.556477\pi\) | |||||||
\(734\) | 4.67614e7 | 3.20366 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.23128e6 | −0.287924 | ||||||||
\(737\) | 3.42347e6 | 0.232166 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.41879e6 | −0.567072 | −0.283536 | − | 0.958962i | \(-0.591508\pi\) | ||||
−0.283536 | + | 0.958962i | \(0.591508\pi\) | |||||||
\(740\) | 2.37449e7 | 1.59401 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.93925e7 | −1.29308 | ||||||||
\(743\) | −3.63942e6 | −0.241858 | −0.120929 | − | 0.992661i | \(-0.538587\pi\) | ||||
−0.120929 | + | 0.992661i | \(0.538587\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.19238e7 | −0.787090 | ||||||||
\(746\) | 3.23676e7 | 2.12943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.94579e6 | 0.388558 | ||||||||
\(749\) | −1.30761e7 | −0.851673 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.91843e7 | −1.24121 | −0.620605 | − | 0.784123i | \(-0.713113\pi\) | ||||
−0.620605 | + | 0.784123i | \(0.713113\pi\) | |||||||
\(752\) | −6.27222e7 | −4.04461 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.11972e7 | −3.92016 | ||||||||
\(755\) | −9.43233e6 | −0.602215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 213745. | 0.0135567 | 0.00677837 | − | 0.999977i | \(-0.497842\pi\) | ||||
0.00677837 | + | 0.999977i | \(0.497842\pi\) | |||||||
\(758\) | −8.90848e6 | −0.563158 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.04181e7 | 0.654267 | ||||||||
\(761\) | 1.67486e7 | 1.04838 | 0.524189 | − | 0.851602i | \(-0.324369\pi\) | ||||
0.524189 | + | 0.851602i | \(0.324369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.93180e7 | −1.20130 | ||||||||
\(764\) | 2.83248e7 | 1.75563 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.74717e7 | −1.07588 | ||||||||
\(767\) | −3.21230e7 | −1.97164 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.56362e7 | 0.953486 | 0.476743 | − | 0.879043i | \(-0.341817\pi\) | ||||
0.476743 | + | 0.879043i | \(0.341817\pi\) | |||||||
\(770\) | −2.00932e6 | −0.122130 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.86370e7 | 2.93713 | ||||||||
\(773\) | 7.70701e6 | 0.463913 | 0.231957 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231957 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.62491e6 | −0.396210 | ||||||||
\(776\) | −201990. | −0.0120413 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.79232e7 | 2.83855 | ||||||||
\(779\) | −7.47986e6 | −0.441621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.22805e6 | −0.189371 | ||||||||
\(782\) | 3.25245e6 | 0.190193 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.08639e7 | −0.631239 | ||||||||
\(785\) | −6.99832e6 | −0.405340 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.41953e7 | 0.816974 | 0.408487 | − | 0.912764i | \(-0.366057\pi\) | ||||
0.408487 | + | 0.912764i | \(0.366057\pi\) | |||||||
\(788\) | −1.94043e7 | −1.11322 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.34292e6 | 0.418602 | ||||||||
\(791\) | 2.09235e7 | 1.18903 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.53309e6 | 0.481863 | ||||||||
\(794\) | 2.23007e7 | 1.25536 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.02159e6 | 0.169026 | ||||||||
\(797\) | −1.72207e6 | −0.0960297 | −0.0480149 | − | 0.998847i | \(-0.515289\pi\) | ||||
−0.0480149 | + | 0.998847i | \(0.515289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.32272e7 | 1.28715 | ||||||||
\(800\) | 3.91733e7 | 2.16404 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.30411e7 | −2.36291 | ||||||||
\(803\) | −478126. | −0.0261670 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −791044. | −0.0430240 | ||||||||
\(806\) | 2.29701e7 | 1.24545 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 871663. | 0.0469699 | ||||||||
\(809\) | −2.11981e7 | −1.13874 | −0.569372 | − | 0.822080i | \(-0.692813\pi\) | ||||
−0.569372 | + | 0.822080i | \(0.692813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.62522e7 | 1.40157 | 0.700784 | − | 0.713374i | \(-0.252834\pi\) | ||||
0.700784 | + | 0.713374i | \(0.252834\pi\) | |||||||
\(812\) | 6.80678e7 | 3.62286 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.53746e6 | 0.398716 | ||||||||
\(815\) | −3.07798e6 | −0.162320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.49489e6 | −0.392835 | ||||||||
\(818\) | 4.60689e7 | 2.40727 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.11211e7 | 1.09694 | ||||||||
\(821\) | 1.03058e7 | 0.533608 | 0.266804 | − | 0.963751i | \(-0.414032\pi\) | ||||
0.266804 | + | 0.963751i | \(0.414032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.59771e7 | −1.85151 | −0.925756 | − | 0.378121i | \(-0.876570\pi\) | ||||
−0.925756 | + | 0.378121i | \(0.876570\pi\) | |||||||
\(824\) | −3.19625e7 | −1.63992 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.96451e7 | 2.53178 | ||||||||
\(827\) | −2.68608e7 | −1.36570 | −0.682850 | − | 0.730558i | \(-0.739260\pi\) | ||||
−0.682850 | + | 0.730558i | \(0.739260\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.79726e7 | 0.908290 | 0.454145 | − | 0.890928i | \(-0.349945\pi\) | ||||
0.454145 | + | 0.890928i | \(0.349945\pi\) | |||||||
\(830\) | −2.53291e7 | −1.27622 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.67975e7 | −2.84460 | ||||||||
\(833\) | 4.02308e6 | 0.200884 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.04077e7 | 0.516581 | ||||||||
\(836\) | 3.89842e6 | 0.192918 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.62912e7 | −2.27714 | ||||||||
\(839\) | −6.90706e6 | −0.338757 | −0.169378 | − | 0.985551i | \(-0.554176\pi\) | ||||
−0.169378 | + | 0.985551i | \(0.554176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.10953e7 | 1.51602 | ||||||||
\(842\) | −2.66609e6 | −0.129597 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.32263e7 | 2.08877 | ||||||||
\(845\) | 6.83350e6 | 0.329232 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.81140e7 | 0.867572 | ||||||||
\(848\) | −4.87475e7 | −2.32789 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.01113e7 | −1.42949 | ||||||||
\(851\) | 2.96740e6 | 0.140460 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.22992e7 | −1.04934 | −0.524671 | − | 0.851305i | \(-0.675812\pi\) | ||||
−0.524671 | + | 0.851305i | \(0.675812\pi\) | |||||||
\(854\) | −1.31876e7 | −0.618760 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.07705e7 | −2.83471 | ||||||||
\(857\) | −1.43986e6 | −0.0669683 | −0.0334842 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334842 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.21807e7 | −1.48803 | −0.744017 | − | 0.668161i | \(-0.767082\pi\) | ||||
−0.744017 | + | 0.668161i | \(0.767082\pi\) | |||||||
\(860\) | 2.11635e7 | 0.975758 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.45220e7 | −2.04083 | ||||||||
\(863\) | −1.47425e6 | −0.0673818 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.20842e7 | −0.549132 | ||||||||
\(866\) | −7.21360e7 | −3.26857 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.55489e7 | −1.15099 | ||||||||
\(869\) | 1.67754e6 | 0.0753568 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.32632e7 | 1.93230 | ||||||||
\(872\) | −8.97795e7 | −3.99840 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.13250e6 | 0.0944303 | ||||||||
\(875\) | 1.66383e7 | 0.734663 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.33628e6 | 0.322090 | 0.161045 | − | 0.986947i | \(-0.448514\pi\) | ||||
0.161045 | + | 0.986947i | \(0.448514\pi\) | |||||||
\(878\) | 3.67084e6 | 0.160705 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.05088e6 | −0.219867 | ||||||||
\(881\) | 3.95062e7 | 1.71485 | 0.857424 | − | 0.514610i | \(-0.172063\pi\) | ||||
0.857424 | + | 0.514610i | \(0.172063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.54183e7 | 1.09709 | 0.548547 | − | 0.836120i | \(-0.315181\pi\) | ||||
0.548547 | + | 0.836120i | \(0.315181\pi\) | |||||||
\(884\) | 7.51384e7 | 3.23393 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.52710e7 | 2.36544 | ||||||||
\(887\) | 6.65524e6 | 0.284024 | 0.142012 | − | 0.989865i | \(-0.454643\pi\) | ||||
0.142012 | + | 0.989865i | \(0.454643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.58541e6 | −0.321903 | ||||||||
\(890\) | 1.25317e7 | 0.530317 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.41857e7 | 0.596952 | ||||||||
\(893\) | 1.52291e7 | 0.639067 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.29060e6 | −0.0538558 | ||||||||
\(896\) | 2.89403e7 | 1.20429 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.76505e6 | 0.404095 | ||||||||
\(899\) | −1.93702e7 | −0.799348 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.80521e7 | 0.740823 | ||||||||
\(902\) | 6.70456e6 | 0.274381 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.72410e7 | 3.95757 | ||||||||
\(905\) | 2.13230e6 | 0.0865421 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.02162e7 | −0.815984 | −0.407992 | − | 0.912986i | \(-0.633771\pi\) | ||||
−0.407992 | + | 0.912986i | \(0.633771\pi\) | |||||||
\(908\) | −9.34114e7 | −3.75998 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.53923e7 | −1.01648 | ||||||||
\(911\) | −2.75967e6 | −0.110170 | −0.0550848 | − | 0.998482i | \(-0.517543\pi\) | ||||
−0.0550848 | + | 0.998482i | \(0.517543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.78660e6 | −0.229745 | ||||||||
\(914\) | −2.09706e7 | −0.830320 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.44105e7 | −2.53640 | ||||||||
\(917\) | 1.01645e7 | 0.399175 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.47471e7 | −0.966575 | −0.483288 | − | 0.875462i | \(-0.660557\pi\) | ||||
−0.483288 | + | 0.875462i | \(0.660557\pi\) | |||||||
\(920\) | −3.67635e6 | −0.143201 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.38638e7 | 0.924513 | ||||||||
\(923\) | −4.07937e7 | −1.57612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.74723e7 | −1.05570 | ||||||||
\(926\) | −6.70607e7 | −2.57004 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.14537e8 | 4.36591 | ||||||||
\(929\) | 4.64223e7 | 1.76477 | 0.882383 | − | 0.470531i | \(-0.155938\pi\) | ||||
0.882383 | + | 0.470531i | \(0.155938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63777e6 | 0.0997385 | ||||||||
\(932\) | 7.00718e7 | 2.64243 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.01307e7 | 1.88034 | ||||||||
\(935\) | 1.87043e6 | 0.0699702 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.80567e7 | −0.671877 | −0.335939 | − | 0.941884i | \(-0.609054\pi\) | ||||
−0.335939 | + | 0.941884i | \(0.609054\pi\) | |||||||
\(938\) | −6.68620e7 | −2.48126 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.30029e7 | −1.58737 | ||||||||
\(941\) | 9.37905e6 | 0.345291 | 0.172645 | − | 0.984984i | \(-0.444769\pi\) | ||||
0.172645 | + | 0.984984i | \(0.444769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.63950e6 | 0.0966590 | ||||||||
\(944\) | 1.24794e8 | 4.55789 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.71803e6 | 0.244070 | ||||||||
\(947\) | 4.35017e6 | 0.157627 | 0.0788137 | − | 0.996889i | \(-0.474887\pi\) | ||||
0.0788137 | + | 0.996889i | \(0.474887\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.04220e6 | −0.217786 | ||||||||
\(950\) | −1.97428e7 | −0.709740 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.08967e7 | −2.53532 | ||||||||
\(953\) | 1.60322e7 | 0.571822 | 0.285911 | − | 0.958256i | \(-0.407704\pi\) | ||||
0.285911 | + | 0.958256i | \(0.407704\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.91045e6 | 0.316148 | ||||||||
\(956\) | −5.14300e7 | −1.82000 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.18257e7 | −0.768340 | ||||||||
\(959\) | 5.21596e6 | 0.183142 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.13586e7 | −0.746045 | ||||||||
\(962\) | 9.52527e7 | 3.31848 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.37910e6 | −0.325064 | ||||||||
\(965\) | 1.53003e7 | 0.528909 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.05998e7 | −1.39623 | −0.698116 | − | 0.715984i | \(-0.745978\pi\) | ||||
−0.698116 | + | 0.715984i | \(0.745978\pi\) | |||||||
\(968\) | 8.41840e7 | 2.88763 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −104078. | −0.00355164 | ||||||||
\(971\) | −1.54267e6 | −0.0525080 | −0.0262540 | − | 0.999655i | \(-0.508358\pi\) | ||||
−0.0262540 | + | 0.999655i | \(0.508358\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.26152e6 | 0.279755 | ||||||||
\(974\) | 6.89732e7 | 2.32961 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.31501e7 | −1.11394 | ||||||||
\(977\) | −5.14968e7 | −1.72601 | −0.863006 | − | 0.505193i | \(-0.831421\pi\) | ||||
−0.863006 | + | 0.505193i | \(0.831421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.86295e6 | 0.0954678 | ||||||||
\(980\) | −7.44835e6 | −0.247739 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.07476e7 | −2.01025 | ||||||||
\(983\) | 2.71081e7 | 0.894777 | 0.447389 | − | 0.894340i | \(-0.352354\pi\) | ||||
0.447389 | + | 0.894340i | \(0.352354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.10421e6 | −0.200465 | ||||||||
\(986\) | −8.80409e7 | −2.88398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.92652e7 | 1.60564 | ||||||||
\(989\) | 2.64480e6 | 0.0859809 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.04379e7 | −0.984534 | −0.492267 | − | 0.870444i | \(-0.663832\pi\) | ||||
−0.492267 | + | 0.870444i | \(0.663832\pi\) | |||||||
\(992\) | −4.29909e7 | −1.38707 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.30454e7 | 2.02389 | ||||||||
\(995\) | 950535. | 0.0304376 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.27678e7 | 1.04402 | 0.522010 | − | 0.852939i | \(-0.325182\pi\) | ||||
0.522010 | + | 0.852939i | \(0.325182\pi\) | |||||||
\(998\) | −2.15896e6 | −0.0686147 | ||||||||
\(999\) | 0 | 0 |
(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 | 27.6.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 27.6.a.d.1.2 | yes | 2 | ||
4.3 | odd | 2 | 432.6.a.k.1.2 | 2 | |||
5.4 | even | 2 | 675.6.a.n.1.2 | 2 | |||
9.2 | odd | 6 | 81.6.c.d.28.1 | 4 | |||
9.4 | even | 3 | 81.6.c.h.55.2 | 4 | |||
9.5 | odd | 6 | 81.6.c.d.55.1 | 4 | |||
9.7 | even | 3 | 81.6.c.h.28.2 | 4 | |||
12.11 | even | 2 | 432.6.a.v.1.1 | 2 | |||
15.14 | odd | 2 | 675.6.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.6.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
27.6.a.d.1.2 | yes | 2 | 3.2 | odd | 2 | ||
81.6.c.d.28.1 | 4 | 9.2 | odd | 6 | |||
81.6.c.d.55.1 | 4 | 9.5 | odd | 6 | |||
81.6.c.h.28.2 | 4 | 9.7 | even | 3 | |||
81.6.c.h.55.2 | 4 | 9.4 | even | 3 | |||
432.6.a.k.1.2 | 2 | 4.3 | odd | 2 | |||
432.6.a.v.1.1 | 2 | 12.11 | even | 2 | |||
675.6.a.f.1.1 | 2 | 15.14 | odd | 2 | |||
675.6.a.n.1.2 | 2 | 5.4 | even | 2 |