Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-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 | ||||||||
\(3\) | 13.4164 | 0.860663 | 0.430331 | − | 0.902671i | \(-0.358397\pi\) | ||||
0.430331 | + | 0.902671i | \(0.358397\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −138.636 | −1.06938 | −0.534689 | − | 0.845049i | \(-0.679571\pi\) | ||||
−0.534689 | + | 0.845049i | \(0.679571\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −63.0000 | −0.259259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 259.384 | 0.646340 | 0.323170 | − | 0.946341i | \(-0.395251\pi\) | ||||
0.323170 | + | 0.946341i | \(0.395251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −154.000 | −0.252733 | −0.126367 | − | 0.991984i | \(-0.540332\pi\) | ||||
−0.126367 | + | 0.991984i | \(0.540332\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 335.410 | 0.384900 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 178.000 | 0.149382 | 0.0746909 | − | 0.997207i | \(-0.476203\pi\) | ||||
0.0746909 | + | 0.997207i | \(0.476203\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 965.981 | 0.613882 | 0.306941 | − | 0.951729i | \(-0.400695\pi\) | ||||
0.306941 | + | 0.951729i | \(0.400695\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1860.00 | −0.920375 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2634.09 | −1.03827 | −0.519135 | − | 0.854692i | \(-0.673746\pi\) | ||||
−0.519135 | + | 0.854692i | \(0.673746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4105.42 | −1.08380 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4110.00 | −0.907500 | −0.453750 | − | 0.891129i | \(-0.649914\pi\) | ||||
−0.453750 | + | 0.891129i | \(0.649914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3157.33 | −0.590086 | −0.295043 | − | 0.955484i | \(-0.595334\pi\) | ||||
−0.295043 | + | 0.955484i | \(0.595334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3480.00 | 0.556281 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3465.91 | −0.478241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7442.00 | −0.893687 | −0.446843 | − | 0.894612i | \(-0.647452\pi\) | ||||
−0.446843 | + | 0.894612i | \(0.647452\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2066.13 | −0.217518 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7270.00 | 0.675421 | 0.337711 | − | 0.941250i | \(-0.390347\pi\) | ||||
0.337711 | + | 0.941250i | \(0.390347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17910.9 | −1.47722 | −0.738612 | − | 0.674131i | \(-0.764518\pi\) | ||||
−0.738612 | + | 0.674131i | \(0.764518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1575.00 | −0.115944 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7410.33 | 0.489320 | 0.244660 | − | 0.969609i | \(-0.421324\pi\) | ||||
0.244660 | + | 0.969609i | \(0.421324\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2413.00 | 0.143571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2388.12 | 0.128567 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −32226.0 | −1.57586 | −0.787928 | − | 0.615767i | \(-0.788846\pi\) | ||||
−0.787928 | + | 0.615767i | \(0.788846\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6484.60 | 0.289052 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12960.0 | 0.528345 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34041.9 | 1.27316 | 0.636581 | − | 0.771210i | \(-0.280348\pi\) | ||||
0.636581 | + | 0.771210i | \(0.280348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26770.0 | −0.921136 | −0.460568 | − | 0.887624i | \(-0.652354\pi\) | ||||
−0.460568 | + | 0.887624i | \(0.652354\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8734.08 | 0.277246 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3850.00 | −0.113026 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49806.2 | 1.35549 | 0.677745 | − | 0.735297i | \(-0.262957\pi\) | ||||
0.677745 | + | 0.735297i | \(0.262957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −35340.0 | −0.893601 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −54103.9 | −1.27375 | −0.636873 | − | 0.770969i | \(-0.719772\pi\) | ||||
−0.636873 | + | 0.770969i | \(0.719772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18534.0 | −0.407063 | −0.203532 | − | 0.979068i | \(-0.565242\pi\) | ||||
−0.203532 | + | 0.979068i | \(0.565242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8385.25 | 0.172133 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −35960.0 | −0.691183 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86741.5 | 1.56372 | 0.781861 | − | 0.623453i | \(-0.214271\pi\) | ||||
0.781861 | + | 0.623453i | \(0.214271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −39771.0 | −0.673525 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −78642.5 | −1.25303 | −0.626516 | − | 0.779409i | \(-0.715520\pi\) | ||||
−0.626516 | + | 0.779409i | \(0.715520\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4450.00 | 0.0668056 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −55141.4 | −0.781052 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −107590. | −1.43978 | −0.719891 | − | 0.694087i | \(-0.755808\pi\) | ||||
−0.719891 | + | 0.694087i | \(0.755808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21350.0 | 0.270268 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −42360.0 | −0.507865 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24149.5 | 0.274536 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −108838. | −1.17450 | −0.587248 | − | 0.809407i | \(-0.699788\pi\) | ||||
−0.587248 | + | 0.809407i | \(0.699788\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16341.2 | −0.167570 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −59198.0 | −0.577436 | −0.288718 | − | 0.957414i | \(-0.593229\pi\) | ||||
−0.288718 | + | 0.957414i | \(0.593229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 112908. | 1.04865 | 0.524326 | − | 0.851517i | \(-0.324317\pi\) | ||||
0.524326 | + | 0.851517i | \(0.324317\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46500.0 | −0.411604 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 40039.0 | 0.338084 | 0.169042 | − | 0.985609i | \(-0.445933\pi\) | ||||
0.169042 | + | 0.985609i | \(0.445933\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 139614. | 1.12554 | 0.562772 | − | 0.826612i | \(-0.309735\pi\) | ||||
0.562772 | + | 0.826612i | \(0.309735\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −99844.9 | −0.769163 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −43046.0 | −0.317130 | −0.158565 | − | 0.987349i | \(-0.550687\pi\) | ||||
−0.158565 | + | 0.987349i | \(0.550687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −65852.2 | −0.464329 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9702.00 | 0.0655234 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24677.2 | −0.159746 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −93771.0 | −0.582244 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 97537.3 | 0.581310 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 157370. | 0.865790 | 0.432895 | − | 0.901444i | \(-0.357492\pi\) | ||||
0.432895 | + | 0.901444i | \(0.357492\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −240300. | −1.27139 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −267729. | −1.36307 | −0.681533 | − | 0.731787i | \(-0.738686\pi\) | ||||
−0.681533 | + | 0.731787i | \(0.738686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −133920. | −0.656472 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −102636. | −0.484689 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −112158. | −0.510539 | −0.255269 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255269 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 147348. | 0.646855 | 0.323428 | − | 0.946253i | \(-0.395165\pi\) | ||||
0.323428 | + | 0.946253i | \(0.395165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 99420.0 | 0.421139 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −39945.1 | −0.163352 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −102750. | −0.405847 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 32373.8 | 0.123566 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 174566. | 0.644160 | 0.322080 | − | 0.946712i | \(-0.395618\pi\) | ||||
0.322080 | + | 0.946712i | \(0.395618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −345258. | −1.23226 | −0.616128 | − | 0.787646i | \(-0.711300\pi\) | ||||
−0.616128 | + | 0.787646i | \(0.711300\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11214.0 | −0.0387286 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −78933.2 | −0.263895 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26502.0 | 0.0858083 | 0.0429042 | − | 0.999079i | \(-0.486339\pi\) | ||||
0.0429042 | + | 0.999079i | \(0.486339\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −432357. | −1.35628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 365180. | 1.11030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 141709. | 0.417760 | 0.208880 | − | 0.977941i | \(-0.433018\pi\) | ||||
0.208880 | + | 0.977941i | \(0.433018\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 87000.0 | 0.248777 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 411047. | 1.14051 | 0.570257 | − | 0.821466i | \(-0.306844\pi\) | ||||
0.570257 | + | 0.821466i | \(0.306844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −347577. | −0.936126 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −60856.8 | −0.159155 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −595946. | −1.51388 | −0.756940 | − | 0.653484i | \(-0.773307\pi\) | ||||
−0.756940 | + | 0.653484i | \(0.773307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −86647.6 | −0.213876 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 456720. | 1.09576 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −300939. | −0.702014 | −0.351007 | − | 0.936373i | \(-0.614161\pi\) | ||||
−0.351007 | + | 0.936373i | \(0.614161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −217022. | −0.492388 | −0.246194 | − | 0.969221i | \(-0.579180\pi\) | ||||
−0.246194 | + | 0.969221i | \(0.579180\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −359157. | −0.792788 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −186050. | −0.399669 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 46170.3 | 0.0965515 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 569160. | 1.15899 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 916260. | 1.81734 | 0.908668 | − | 0.417519i | \(-0.137100\pi\) | ||||
0.908668 | + | 0.417519i | \(0.137100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 864114. | 1.66985 | 0.834926 | − | 0.550363i | \(-0.185511\pi\) | ||||
0.834926 | + | 0.550363i | \(0.185511\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −51653.2 | −0.0972771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −432522. | −0.794040 | −0.397020 | − | 0.917810i | \(-0.629956\pi\) | ||||
−0.397020 | + | 0.917810i | \(0.629956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 795182. | 1.42342 | 0.711711 | − | 0.702473i | \(-0.247921\pi\) | ||||
0.711711 | + | 0.702473i | \(0.247921\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 668220. | 1.16662 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 569795. | 0.970462 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 181750. | 0.302058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 165948. | 0.269181 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 250560. | 0.396777 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −453126. | −0.700669 | −0.350334 | − | 0.936625i | \(-0.613932\pi\) | ||||
−0.350334 | + | 0.936625i | \(0.613932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −725880. | −1.09627 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −447773. | −0.660635 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 437720. | 0.631026 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −248660. | −0.350344 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27412.0 | −0.0377537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 430358. | 0.579519 | 0.289760 | − | 0.957099i | \(-0.406425\pi\) | ||||
0.289760 | + | 0.957099i | \(0.406425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −39375.0 | −0.0518519 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.12403e6 | 1.44782 | 0.723909 | − | 0.689896i | \(-0.242344\pi\) | ||||
0.723909 | + | 0.689896i | \(0.242344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 812410. | 1.02373 | 0.511866 | − | 0.859065i | \(-0.328954\pi\) | ||||
0.511866 | + | 0.859065i | \(0.328954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −482454. | −0.594875 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 846194. | 1.02113 | 0.510564 | − | 0.859840i | \(-0.329437\pi\) | ||||
0.510564 | + | 0.859840i | \(0.329437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 185258. | 0.218831 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.16376e6 | 1.34584 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 56688.8 | 0.0641952 | 0.0320976 | − | 0.999485i | \(-0.489781\pi\) | ||||
0.0320976 | + | 0.999485i | \(0.489781\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.27571e6 | 1.41485 | 0.707423 | − | 0.706790i | \(-0.249857\pi\) | ||||
0.707423 | + | 0.706790i | \(0.249857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 464033. | 0.504119 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60325.0 | 0.0642070 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −148761. | −0.155148 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.05510e6 | −1.07844 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −50937.6 | −0.0510334 | −0.0255167 | − | 0.999674i | \(-0.508123\pi\) | ||||
−0.0255167 | + | 0.999674i | \(0.508123\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −683240. | −0.671076 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 59703.0 | 0.0574971 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.64806e6 | 1.55647 | 0.778233 | − | 0.627976i | \(-0.216116\pi\) | ||||
0.778233 | + | 0.627976i | \(0.216116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.03173e6 | 0.955690 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 258930. | 0.235278 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −522994. | −0.466238 | −0.233119 | − | 0.972448i | \(-0.574893\pi\) | ||||
−0.233119 | + | 0.972448i | \(0.574893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −805650. | −0.704745 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.44347e6 | −1.23917 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.93789e6 | 1.63285 | 0.816427 | − | 0.577448i | \(-0.195951\pi\) | ||||
0.816427 | + | 0.577448i | \(0.195951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.00132e6 | −0.828228 | −0.414114 | − | 0.910225i | \(-0.635908\pi\) | ||||
−0.414114 | + | 0.910225i | \(0.635908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 286440. | 0.232609 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 162115. | 0.129268 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 445702. | 0.349016 | 0.174508 | − | 0.984656i | \(-0.444167\pi\) | ||||
0.174508 | + | 0.984656i | \(0.444167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 198912. | 0.152985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.24647e6 | 0.941708 | 0.470854 | − | 0.882211i | \(-0.343946\pi\) | ||||
0.470854 | + | 0.882211i | \(0.343946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.27900e6 | −1.69153 | −0.845764 | − | 0.533557i | \(-0.820855\pi\) | ||||
−0.845764 | + | 0.533557i | \(0.820855\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 324000. | 0.236283 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.00789e6 | −0.722281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.38817e6 | −0.977685 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.46021e6 | −1.01084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.45427e6 | −1.67014 | −0.835072 | − | 0.550140i | \(-0.814574\pi\) | ||||
−0.835072 | + | 0.550140i | \(0.814574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 851047. | 0.569375 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.06488e6 | −0.700502 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 405650. | 0.262406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.48310e6 | 1.57971 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −794225. | −0.496977 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −669250. | −0.411945 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20710.5 | −0.0125413 | −0.00627067 | − | 0.999980i | \(-0.501996\pi\) | ||||
−0.00627067 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.51482e6 | 0.902537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 47270.5 | 0.0277133 | 0.0138567 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138567 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.79169e6 | −1.61067 | −0.805333 | − | 0.592822i | \(-0.798014\pi\) | ||||
−0.805333 | + | 0.592822i | \(0.798014\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 218352. | 0.123988 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 471582. | 0.263578 | 0.131789 | − | 0.991278i | \(-0.457928\pi\) | ||||
0.131789 | + | 0.991278i | \(0.457928\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.06607e6 | −0.586554 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 537180. | 0.290976 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 171945. | 0.0917028 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −96250.0 | −0.0505466 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.87312e6 | 0.968715 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.02734e6 | −0.523268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.09092e6 | 1.55066 | 0.775331 | − | 0.631555i | \(-0.217583\pi\) | ||||
0.775331 | + | 0.631555i | \(0.217583\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 468846. | 0.231697 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.24515e6 | 0.606193 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −665838. | −0.319370 | −0.159685 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159685 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −577523. | −0.272942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −818960. | −0.381397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.99553e6 | 0.915847 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −883500. | −0.399631 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.80908e6 | −0.806556 | −0.403278 | − | 0.915078i | \(-0.632129\pi\) | ||||
−0.403278 | + | 0.915078i | \(0.632129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.36181e6 | 1.03796 | 0.518981 | − | 0.854786i | \(-0.326312\pi\) | ||||
0.518981 | + | 0.854786i | \(0.326312\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 632235. | 0.273912 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.14535e6 | 0.489215 | 0.244608 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244608 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.35260e6 | −0.569636 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −331080. | −0.137487 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 767275. | 0.314206 | 0.157103 | − | 0.987582i | \(-0.449784\pi\) | ||||
0.157103 | + | 0.987582i | \(0.449784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.54298e6 | −0.623149 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.25807e6 | −0.501116 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −463350. | −0.182044 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.99537e6 | −1.54843 | −0.774215 | − | 0.632923i | \(-0.781855\pi\) | ||||
−0.774215 | + | 0.632923i | \(0.781855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −458010. | −0.175109 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.46769e6 | 1.68519 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.68131e6 | −1.74219 | −0.871094 | − | 0.491117i | \(-0.836589\pi\) | ||||
−0.871094 | + | 0.491117i | \(0.836589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 209631. | 0.0769800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 632940. | 0.229356 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 337271. | 0.120609 | 0.0603046 | − | 0.998180i | \(-0.480793\pi\) | ||||
0.0603046 | + | 0.998180i | \(0.480793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.11134e6 | 0.745153 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 598689. | 0.208547 | 0.104274 | − | 0.994549i | \(-0.466748\pi\) | ||||
0.104274 | + | 0.994549i | \(0.466748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −899000. | −0.309106 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.12839e6 | 0.382984 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.97243e6 | −1.33101 | −0.665506 | − | 0.746393i | \(-0.731784\pi\) | ||||
−0.665506 | + | 0.746393i | \(0.731784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −468868. | −0.155099 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.59196e6 | −1.17314 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.16854e6 | 0.699318 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 179398. | 0.0571270 | 0.0285635 | − | 0.999592i | \(-0.490907\pi\) | ||||
0.0285635 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.79673e6 | −0.565001 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.14504e6 | 1.90838 | 0.954188 | − | 0.299208i | \(-0.0967224\pi\) | ||||
0.954188 | + | 0.299208i | \(0.0967224\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 486229. | 0.149134 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −994275. | −0.301210 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.93033e6 | −0.577626 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.64503e6 | −0.781847 | −0.390923 | − | 0.920423i | \(-0.627844\pi\) | ||||
−0.390923 | + | 0.920423i | \(0.627844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50476e6 | −0.439402 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.71944e6 | −1.36149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.96606e6 | −0.560373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.97688e6 | 0.556724 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.15984e6 | −0.601018 | −0.300509 | − | 0.953779i | \(-0.597157\pi\) | ||||
−0.300509 | + | 0.953779i | \(0.597157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.47209e6 | −0.404789 | −0.202395 | − | 0.979304i | \(-0.564872\pi\) | ||||
−0.202395 | + | 0.979304i | \(0.564872\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −466851. | −0.126861 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 111250. | 0.0298764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.71129e6 | 0.985043 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −535920. | −0.140591 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.63748e6 | 1.72112 | 0.860558 | − | 0.509352i | \(-0.170115\pi\) | ||||
0.860558 | + | 0.509352i | \(0.170115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.27853e6 | −1.60931 | −0.804653 | − | 0.593746i | \(-0.797649\pi\) | ||||
−0.804653 | + | 0.593746i | \(0.797649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.37854e6 | −0.349297 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.54448e6 | −0.637376 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.44021e6 | 0.604319 | 0.302160 | − | 0.953257i | \(-0.402292\pi\) | ||||
0.302160 | + | 0.953257i | \(0.402292\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −152019. | −0.0372221 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.30646e6 | −0.558390 | −0.279195 | − | 0.960234i | \(-0.590068\pi\) | ||||
−0.279195 | + | 0.960234i | \(0.590068\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.68975e6 | −0.643890 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.34205e6 | 0.554405 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.60241e6 | 1.77965 | 0.889826 | − | 0.456300i | \(-0.150825\pi\) | ||||
0.889826 | + | 0.456300i | \(0.150825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.88572e6 | 0.436552 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.63212e6 | −1.06056 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 533749. | 0.120867 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.56938e6 | −0.351510 | −0.175755 | − | 0.984434i | \(-0.556237\pi\) | ||||
−0.175755 | + | 0.984434i | \(0.556237\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −730765. | −0.161900 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 562602. | 0.123296 | 0.0616480 | − | 0.998098i | \(-0.480364\pi\) | ||||
0.0616480 | + | 0.998098i | \(0.480364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.87382e6 | 1.05662 | 0.528308 | − | 0.849053i | \(-0.322827\pi\) | ||||
0.528308 | + | 0.849053i | \(0.322827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.05900e6 | −0.227124 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.11862e6 | −1.08608 | −0.543039 | − | 0.839708i | \(-0.682726\pi\) | ||||
−0.543039 | + | 0.839708i | \(0.682726\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.90494e6 | −1.44953 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 355562. | 0.0738521 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.64580e6 | −0.954790 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 603738. | 0.122776 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.03024e6 | 0.408555 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.00179e6 | −0.796922 | −0.398461 | − | 0.917185i | \(-0.630456\pi\) | ||||
−0.398461 | + | 0.917185i | \(0.630456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.14607e6 | 0.225864 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.89940e6 | 0.955598 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.72095e6 | −0.525250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.68175e6 | −0.321321 | −0.160661 | − | 0.987010i | \(-0.551362\pi\) | ||||
−0.160661 | + | 0.987010i | \(0.551362\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.90122e6 | 0.359551 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 115927. | 0.0217010 | 0.0108505 | − | 0.999941i | \(-0.496546\pi\) | ||||
0.0108505 | + | 0.999941i | \(0.496546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −731580. | −0.135564 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −408530. | −0.0749395 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.50076e6 | 1.36212 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.98867e6 | −1.43623 | −0.718113 | − | 0.695926i | \(-0.754994\pi\) | ||||
−0.718113 | + | 0.695926i | \(0.754994\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.51478e6 | 0.981598 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.07650e6 | −1.42332 | −0.711661 | − | 0.702523i | \(-0.752057\pi\) | ||||
−0.711661 | + | 0.702523i | \(0.752057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.47995e6 | −0.258237 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.66323e6 | −0.805689 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.83427e6 | −0.484894 | −0.242447 | − | 0.970165i | \(-0.577950\pi\) | ||||
−0.242447 | + | 0.970165i | \(0.577950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.56948e6 | 0.435305 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.96576e6 | −0.665324 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.82270e6 | 0.468972 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.92212e6 | 0.316267 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.99545e6 | −1.30294 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.97526e6 | 0.480209 | 0.240105 | − | 0.970747i | \(-0.422818\pi\) | ||||
0.240105 | + | 0.970747i | \(0.422818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.72888e6 | 1.23556 | 0.617778 | − | 0.786352i | \(-0.288033\pi\) | ||||
0.617778 | + | 0.786352i | \(0.288033\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.16250e6 | −0.184075 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −562004. | −0.0881481 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 502077. | 0.0780066 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.14464e6 | −0.330079 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.11958e6 | −0.170701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.00098e6 | 0.151196 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.03752e6 | −0.604198 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 625893. | 0.0927958 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.83660e6 | 1.44495 | 0.722474 | − | 0.691399i | \(-0.243005\pi\) | ||||
0.722474 | + | 0.691399i | \(0.243005\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.91166e6 | −0.423780 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.49035e6 | 0.503359 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.45608e6 | −0.493873 | −0.246937 | − | 0.969032i | \(-0.579424\pi\) | ||||
−0.246937 | + | 0.969032i | \(0.579424\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.68651e6 | 0.238813 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.97018e6 | −0.557098 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.20255e7 | −1.67221 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.49612e6 | −0.343980 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.05760e6 | 0.963871 | 0.481936 | − | 0.876207i | \(-0.339934\pi\) | ||||
0.481936 | + | 0.876207i | \(0.339934\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.75828e6 | 0.373344 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 619440. | 0.0830983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.32495e6 | 0.309131 | 0.154566 | − | 0.987983i | \(-0.450602\pi\) | ||||
0.154566 | + | 0.987983i | \(0.450602\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.07615e6 | −0.141825 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.51370e6 | 0.720254 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.01947e7 | 1.32006 | 0.660029 | − | 0.751240i | \(-0.270544\pi\) | ||||
0.660029 | + | 0.751240i | \(0.270544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.21297e7 | −1.55689 | −0.778446 | − | 0.627712i | \(-0.783992\pi\) | ||||
−0.778446 | + | 0.627712i | \(0.783992\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.22929e7 | 1.56411 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.64631e6 | −0.207654 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.46358e6 | 0.183011 | 0.0915053 | − | 0.995805i | \(-0.470832\pi\) | ||||
0.0915053 | + | 0.995805i | \(0.470832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.15933e7 | 1.43718 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.09027e7 | 1.33997 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.35891e6 | −1.01854 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 242550. | 0.0293030 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.18425e6 | 0.620998 | 0.310499 | − | 0.950574i | \(-0.399504\pi\) | ||||
0.310499 | + | 0.950574i | \(0.399504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.04992e6 | −0.362243 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.80289e6 | −0.683401 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.02722e7 | −1.19957 | −0.599785 | − | 0.800161i | \(-0.704747\pi\) | ||||
−0.599785 | + | 0.800161i | \(0.704747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −616931. | −0.0714405 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.06685e7 | 1.22509 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.39289e7 | 1.58617 | 0.793085 | − | 0.609111i | \(-0.208474\pi\) | ||||
0.793085 | + | 0.609111i | \(0.208474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.81441e6 | −0.543697 | −0.271848 | − | 0.962340i | \(-0.587635\pi\) | ||||
−0.271848 | + | 0.962340i | \(0.587635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.13779e6 | −0.351423 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.34427e6 | −0.260387 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.04800e7 | 1.15449 | 0.577245 | − | 0.816571i | \(-0.304128\pi\) | ||||
0.577245 | + | 0.816571i | \(0.304128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.64460e6 | 0.835240 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.14119e6 | −0.123667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.07977e6 | 0.331029 | 0.165515 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165515 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.43843e6 | 0.259970 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.15522e6 | 0.122166 | 0.0610831 | − | 0.998133i | \(-0.480545\pi\) | ||||
0.0610831 | + | 0.998133i | \(0.480545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.76853e7 | 1.85517 | 0.927587 | − | 0.373606i | \(-0.121879\pi\) | ||||
0.927587 | + | 0.373606i | \(0.121879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08140e7 | 1.12528 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.49159e7 | 1.53967 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.36162e6 | 0.341491 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.32468e6 | −0.133501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.42541e6 | 0.542449 | 0.271225 | − | 0.962516i | \(-0.412571\pi\) | ||||
0.271225 | + | 0.962516i | \(0.412571\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.07932e6 | −0.603039 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.93425e6 | 0.387193 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −371602. | −0.0362852 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.40855e6 | 0.330230 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.16005e7 | 1.11515 | 0.557573 | − | 0.830128i | \(-0.311733\pi\) | ||||
0.557573 | + | 0.830128i | \(0.311733\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.57873e6 | −0.913651 | −0.456826 | − | 0.889556i | \(-0.651014\pi\) | ||||
−0.456826 | + | 0.889556i | \(0.651014\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00750e6 | −0.568584 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.28130e7 | −1.20334 | −0.601671 | − | 0.798744i | \(-0.705498\pi\) | ||||
−0.601671 | + | 0.798744i | \(0.705498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.82992e6 | 0.822896 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.87263e6 | 0.543100 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.58665e6 | 0.145613 | 0.0728064 | − | 0.997346i | \(-0.476804\pi\) | ||||
0.0728064 | + | 0.997346i | \(0.476804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.69322e6 | −0.609582 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.16764e6 | 0.105535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.95559e7 | −1.75414 | −0.877071 | − | 0.480361i | \(-0.840506\pi\) | ||||
−0.877071 | + | 0.480361i | \(0.840506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.46471e6 | 0.664522 | 0.332261 | − | 0.943188i | \(-0.392189\pi\) | ||||
0.332261 | + | 0.943188i | \(0.392189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −367771. | −0.0324933 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.34800e6 | −0.293583 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.08261e7 | 0.942231 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.77386e6 | 0.498771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.94371e6 | −0.595367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.09694e7 | −0.933568 | −0.466784 | − | 0.884371i | \(-0.654587\pi\) | ||||
−0.466784 | + | 0.884371i | \(0.654587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.56589e6 | −0.216760 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.52708e6 | 0.547327 | 0.273664 | − | 0.961825i | \(-0.411764\pi\) | ||||
0.273664 | + | 0.961825i | \(0.411764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.50889e7 | 1.25598 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50805e7 | 1.24608 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.54389e7 | −1.26638 | −0.633191 | − | 0.773995i | \(-0.718255\pi\) | ||||
−0.633191 | + | 0.773995i | \(0.718255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.80395e6 | −0.228320 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08996e7 | 0.881089 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.96280e6 | 0.398271 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.78757e6 | −0.381435 | −0.190717 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190717 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.26548e6 | 0.179196 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.68370e6 | 0.289282 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.29406e6 | 0.100896 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.13529e7 | 0.878847 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.31891e6 | 0.255094 | 0.127547 | − | 0.991833i | \(-0.459290\pi\) | ||||
0.127547 | + | 0.991833i | \(0.459290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.18883e6 | −0.548618 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.48550e6 | 0.188339 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.20699e6 | 0.617497 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.60044e7 | −1.19570 | −0.597852 | − | 0.801607i | \(-0.703979\pi\) | ||||
−0.597852 | + | 0.801607i | \(0.703979\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.46472e6 | −0.405409 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.31668e6 | 0.612669 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −998628. | −0.0730531 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 760560. | 0.0552504 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.56006e7 | −1.12543 | −0.562715 | − | 0.826651i | \(-0.690243\pi\) | ||||
−0.562715 | + | 0.826651i | \(0.690243\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.56531e7 | −1.12141 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.71154e7 | 1.21771 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.56875e6 | −0.181500 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.14545e7 | −0.803783 | −0.401891 | − | 0.915687i | \(-0.631647\pi\) | ||||
−0.401891 | + | 0.915687i | \(0.631647\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.58900e7 | 1.10740 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.18814e6 | −0.220670 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.13267e7 | −0.778650 | −0.389325 | − | 0.921101i | \(-0.627292\pi\) | ||||
−0.389325 | + | 0.921101i | \(0.627292\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 809345. | 0.0552606 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.29189e7 | 0.876108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.31055e7 | −0.882756 | −0.441378 | − | 0.897321i | \(-0.645510\pi\) | ||||
−0.441378 | + | 0.897321i | \(0.645510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.99584e6 | −0.133530 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.16787e6 | 0.276976 | 0.138488 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138488 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.36415e6 | 0.288077 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.95448e6 | 0.324860 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.55086e6 | −0.361539 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.89308e7 | −1.87180 | −0.935902 | − | 0.352260i | \(-0.885413\pi\) | ||||
−0.935902 | + | 0.352260i | \(0.885413\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −683400. | −0.0439225 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.63145e6 | −0.551082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.32870e6 | −0.528247 | −0.264124 | − | 0.964489i | \(-0.585083\pi\) | ||||
−0.264124 | + | 0.964489i | \(0.585083\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.16663e6 | −0.577571 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.48292e6 | 0.280608 | 0.140304 | − | 0.990108i | \(-0.455192\pi\) | ||||
0.140304 | + | 0.990108i | \(0.455192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.93556e7 | −1.20363 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −280350. | −0.0173200 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.24245e6 | −0.321770 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.32141e6 | 0.0805790 | 0.0402895 | − | 0.999188i | \(-0.487172\pi\) | ||||
0.0402895 | + | 0.999188i | \(0.487172\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.21110e7 | 1.33959 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.24897e6 | 0.436342 | 0.218171 | − | 0.975911i | \(-0.429991\pi\) | ||||
0.218171 | + | 0.975911i | \(0.429991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.97333e6 | −0.118017 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.38421e7 | 0.822527 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.02268e6 | 0.414629 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.40337e7 | −0.823273 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.68733e7 | 0.983547 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 662550. | 0.0383747 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.98037e6 | 0.286632 | 0.143316 | − | 0.989677i | \(-0.454223\pi\) | ||||
0.143316 | + | 0.989677i | \(0.454223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.01670e6 | −0.401273 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.96773e6 | 0.339132 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.12258e6 | 0.232802 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.08089e7 | −0.606548 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.48673e7 | −0.829061 | −0.414530 | − | 0.910036i | \(-0.636054\pi\) | ||||
−0.414530 | + | 0.910036i | \(0.636054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.31904e6 | 0.0730955 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.77817e6 | 0.373277 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.80742e6 | −0.263101 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.12950e6 | 0.496543 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.59995e7 | 1.40534 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −684390. | −0.0367648 | −0.0183824 | − | 0.999831i | \(-0.505852\pi\) | ||||
−0.0183824 | + | 0.999831i | \(0.505852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.27890e7 | −1.75056 | −0.875279 | − | 0.483618i | \(-0.839323\pi\) | ||||
−0.875279 | + | 0.483618i | \(0.839323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.34341e7 | −0.712825 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.54271e6 | 0.186828 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.73016e7 | −0.906841 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.34505e6 | −0.0700694 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.17265e6 | −0.371383 | −0.185691 | − | 0.982608i | \(-0.559452\pi\) | ||||
−0.185691 | + | 0.982608i | \(0.559452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.32939e6 | −0.0684153 | −0.0342077 | − | 0.999415i | \(-0.510891\pi\) | ||||
−0.0342077 | + | 0.999415i | \(0.510891\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.17500e6 | 0.111256 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.92964e7 | −0.981099 | −0.490550 | − | 0.871413i | \(-0.663204\pi\) | ||||
−0.490550 | + | 0.871413i | \(0.663204\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.10811e6 | −0.359226 | −0.179613 | − | 0.983737i | \(-0.557485\pi\) | ||||
−0.179613 | + | 0.983737i | \(0.557485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.97972e6 | 0.300385 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 429514. | 0.0214469 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02762e7 | 0.510054 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.29622e7 | 0.639534 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.24538e6 | 0.404395 | 0.202198 | − | 0.979345i | \(-0.435192\pi\) | ||||
0.202198 | + | 0.979345i | \(0.435192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.61905e6 | −0.176443 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.67231e7 | 0.810493 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.68942e6 | −0.418648 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.30001e7 | 0.622640 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.05761e7 | −1.45584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.96029e7 | 0.927889 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.86921e7 | −0.879599 | −0.439800 | − | 0.898096i | \(-0.644951\pi\) | ||||
−0.439800 | + | 0.898096i | \(0.644951\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.52142e6 | −0.0711761 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.24473e7 | −1.04403 | −0.522013 | − | 0.852937i | \(-0.674819\pi\) | ||||
−0.522013 | + | 0.852937i | \(0.674819\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.24436e6 | 0.150019 | 0.0750094 | − | 0.997183i | \(-0.476101\pi\) | ||||
0.0750094 | + | 0.997183i | \(0.476101\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.35222e7 | −0.621641 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.01542e6 | 0.0464108 | 0.0232054 | − | 0.999731i | \(-0.492613\pi\) | ||||
0.0232054 | + | 0.999731i | \(0.492613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.48987e7 | −0.677028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.86243e7 | −0.841457 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.24994e7 | 1.01070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.67015e6 | −0.342577 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.85679e6 | 0.304499 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.16619e6 | −0.0956482 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.96764e7 | −1.74194 | −0.870970 | − | 0.491337i | \(-0.836508\pi\) | ||||
−0.870970 | + | 0.491337i | \(0.836508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.29275e7 | −1.43743 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.44584e7 | −1.06167 | −0.530833 | − | 0.847477i | \(-0.678121\pi\) | ||||
−0.530833 | + | 0.847477i | \(0.678121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.11179e7 | 1.34310 | 0.671549 | − | 0.740960i | \(-0.265629\pi\) | ||||
0.671549 | + | 0.740960i | \(0.265629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.14180e7 | 0.490040 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.87514e7 | −0.800249 | −0.400124 | − | 0.916461i | \(-0.631033\pi\) | ||||
−0.400124 | + | 0.916461i | \(0.631033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.18172e7 | −0.925858 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.03160e7 | −0.435327 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.15824e6 | 0.300385 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.52347e6 | −0.313950 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.44236e6 | 0.225843 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.29766e7 | 0.535503 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.73623e6 | −0.235404 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.33143e7 | 1.35960 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.42555e6 | −0.220203 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.07504e6 | 0.204843 | 0.102421 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102421 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.72947e6 | 0.149706 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.83599e7 | 1.13216 | 0.566082 | − | 0.824349i | \(-0.308459\pi\) | ||||
0.566082 | + | 0.824349i | \(0.308459\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.03986e7 | −0.809885 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.97893e6 | −0.354545 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.71169e7 | 1.45763 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.58570e6 | −0.374399 | −0.187200 | − | 0.982322i | \(-0.559941\pi\) | ||||
−0.187200 | + | 0.982322i | \(0.559941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −277860. | −0.0107939 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.33200e6 | 0.321918 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.65125e6 | −0.178737 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.11321e6 | −0.271873 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.82212e7 | −1.45300 | −0.726500 | − | 0.687167i | \(-0.758854\pi\) | ||||
−0.726500 | + | 0.687167i | \(0.758854\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.33091e6 | 0.0881357 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 634200. | 0.0238519 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.15426e6 | 0.0431791 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.37422e6 | −0.348808 | −0.174404 | − | 0.984674i | \(-0.555800\pi\) | ||||
−0.174404 | + | 0.984674i | \(0.555800\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.74544e7 | −1.38624 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.04898e6 | −0.112249 | −0.0561243 | − | 0.998424i | \(-0.517874\pi\) | ||||
−0.0561243 | + | 0.998424i | \(0.517874\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.91498e7 | −0.701270 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.42290e7 | 0.518316 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.95948e7 | 1.07236 | 0.536180 | − | 0.844104i | \(-0.319867\pi\) | ||||
0.536180 | + | 0.844104i | \(0.319867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.85424e6 | 0.102878 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.32694e6 | 0.226852 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.58338e7 | 0.564744 | 0.282372 | − | 0.959305i | \(-0.408879\pi\) | ||||
0.282372 | + | 0.959305i | \(0.408879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.29065e7 | 0.812738 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.43028e7 | −0.504825 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.55492e7 | 0.545960 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.86604e7 | −0.651798 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.52246e6 | −0.0876513 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.16028e7 | 0.746780 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.69009e6 | −0.298853 | −0.149427 | − | 0.988773i | \(-0.547743\pi\) | ||||
−0.149427 | + | 0.988773i | \(0.547743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.30688e6 | 0.0789252 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.81474e7 | 0.958054 | 0.479027 | − | 0.877800i | \(-0.340990\pi\) | ||||
0.479027 | + | 0.877800i | \(0.340990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.04278e7 | −0.691733 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.29133e6 | −0.0435036 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.34090e7 | −1.45493 | −0.727467 | − | 0.686143i | \(-0.759303\pi\) | ||||
−0.727467 | + | 0.686143i | \(0.759303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.79071e7 | −0.930590 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.79568e6 | −0.291808 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.64172e7 | −1.53213 | −0.766065 | − | 0.642763i | \(-0.777788\pi\) | ||||
−0.766065 | + | 0.642763i | \(0.777788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.08131e7 | −0.355106 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.37832e7 | −0.450358 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.71789e7 | 1.53376 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.64577e7 | 1.50271 | 0.751353 | − | 0.659901i | \(-0.229402\pi\) | ||||
0.751353 | + | 0.659901i | \(0.229402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.14690e7 | 1.33460 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.98795e7 | 0.636574 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.35968e7 | −0.433211 | −0.216605 | − | 0.976259i | \(-0.569499\pi\) | ||||
−0.216605 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.05525e7 | 0.968576 |
(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 | 320.6.a.t.1.2 | 2 | ||
4.3 | odd | 2 | inner | 320.6.a.t.1.1 | 2 | ||
8.3 | odd | 2 | 160.6.a.b.1.2 | yes | 2 | ||
8.5 | even | 2 | 160.6.a.b.1.1 | ✓ | 2 | ||
40.3 | even | 4 | 800.6.c.h.449.4 | 4 | |||
40.13 | odd | 4 | 800.6.c.h.449.1 | 4 | |||
40.19 | odd | 2 | 800.6.a.i.1.1 | 2 | |||
40.27 | even | 4 | 800.6.c.h.449.2 | 4 | |||
40.29 | even | 2 | 800.6.a.i.1.2 | 2 | |||
40.37 | odd | 4 | 800.6.c.h.449.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.b.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
160.6.a.b.1.2 | yes | 2 | 8.3 | odd | 2 | ||
320.6.a.t.1.1 | 2 | 4.3 | odd | 2 | inner | ||
320.6.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
800.6.a.i.1.1 | 2 | 40.19 | odd | 2 | |||
800.6.a.i.1.2 | 2 | 40.29 | even | 2 | |||
800.6.c.h.449.1 | 4 | 40.13 | odd | 4 | |||
800.6.c.h.449.2 | 4 | 40.27 | even | 4 | |||
800.6.c.h.449.3 | 4 | 40.37 | odd | 4 | |||
800.6.c.h.449.4 | 4 | 40.3 | even | 4 |