Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,6,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1080.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(173.214525398\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 460x - 1125 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.47876\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 99.3349 | 0.766226 | 0.383113 | − | 0.923702i | \(-0.374852\pi\) | ||||
0.383113 | + | 0.923702i | \(0.374852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −377.165 | −0.939830 | −0.469915 | − | 0.882712i | \(-0.655715\pi\) | ||||
−0.469915 | + | 0.882712i | \(0.655715\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −388.245 | −0.637158 | −0.318579 | − | 0.947896i | \(-0.603206\pi\) | ||||
−0.318579 | + | 0.947896i | \(0.603206\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1158.43 | 0.972180 | 0.486090 | − | 0.873909i | \(-0.338423\pi\) | ||||
0.486090 | + | 0.873909i | \(0.338423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 246.899 | 0.156905 | 0.0784524 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784524 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −195.844 | −0.0771951 | −0.0385975 | − | 0.999255i | \(-0.512289\pi\) | ||||
−0.0385975 | + | 0.999255i | \(0.512289\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3268.26 | −0.721641 | −0.360821 | − | 0.932635i | \(-0.617503\pi\) | ||||
−0.360821 | + | 0.932635i | \(0.617503\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 160.538 | 0.0300036 | 0.0150018 | − | 0.999887i | \(-0.495225\pi\) | ||||
0.0150018 | + | 0.999887i | \(0.495225\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2483.37 | 0.342666 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9122.21 | −1.09546 | −0.547729 | − | 0.836656i | \(-0.684508\pi\) | ||||
−0.547729 | + | 0.836656i | \(0.684508\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12382.6 | 1.15041 | 0.575204 | − | 0.818010i | \(-0.304923\pi\) | ||||
0.575204 | + | 0.818010i | \(0.304923\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8303.37 | 0.684831 | 0.342416 | − | 0.939549i | \(-0.388755\pi\) | ||||
0.342416 | + | 0.939549i | \(0.388755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11023.0 | −0.727869 | −0.363935 | − | 0.931424i | \(-0.618567\pi\) | ||||
−0.363935 | + | 0.931424i | \(0.618567\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6939.58 | −0.412898 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6025.60 | 0.294653 | 0.147326 | − | 0.989088i | \(-0.452933\pi\) | ||||
0.147326 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9429.11 | −0.420305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1557.29 | 0.0582423 | 0.0291212 | − | 0.999576i | \(-0.490729\pi\) | ||||
0.0291212 | + | 0.999576i | \(0.490729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −50994.4 | −1.75468 | −0.877340 | − | 0.479869i | \(-0.840684\pi\) | ||||
−0.877340 | + | 0.479869i | \(0.840684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9706.11 | −0.284946 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15506.8 | 0.422021 | 0.211011 | − | 0.977484i | \(-0.432325\pi\) | ||||
0.211011 | + | 0.977484i | \(0.432325\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −50902.6 | −1.19838 | −0.599189 | − | 0.800608i | \(-0.704510\pi\) | ||||
−0.599189 | + | 0.800608i | \(0.704510\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25207.0 | −0.553624 | −0.276812 | − | 0.960924i | \(-0.589278\pi\) | ||||
−0.276812 | + | 0.960924i | \(0.589278\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −37465.6 | −0.720122 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16866.4 | 0.304056 | 0.152028 | − | 0.988376i | \(-0.451420\pi\) | ||||
0.152028 | + | 0.988376i | \(0.451420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −108648. | −1.73112 | −0.865561 | − | 0.500803i | \(-0.833038\pi\) | ||||
−0.865561 | + | 0.500803i | \(0.833038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28960.7 | 0.434772 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 46103.4 | 0.616962 | 0.308481 | − | 0.951231i | \(-0.400179\pi\) | ||||
0.308481 | + | 0.951231i | \(0.400179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38566.2 | −0.488207 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6172.49 | 0.0701699 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 178039. | 1.92126 | 0.960632 | − | 0.277825i | \(-0.0896136\pi\) | ||||
0.960632 | + | 0.277825i | \(0.0896136\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −22874.9 | −0.223129 | −0.111565 | − | 0.993757i | \(-0.535586\pi\) | ||||
−0.111565 | + | 0.993757i | \(0.535586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35513.2 | −0.329835 | −0.164918 | − | 0.986307i | \(-0.552736\pi\) | ||||
−0.164918 | + | 0.986307i | \(0.552736\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 181041. | 1.52868 | 0.764342 | − | 0.644811i | \(-0.223064\pi\) | ||||
0.764342 | + | 0.644811i | \(0.223064\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −135116. | −1.08928 | −0.544641 | − | 0.838669i | \(-0.683334\pi\) | ||||
−0.544641 | + | 0.838669i | \(0.683334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 25161.8 | 0.185373 | 0.0926863 | − | 0.995695i | \(-0.470455\pi\) | ||||
0.0926863 | + | 0.995695i | \(0.470455\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4896.09 | −0.0345227 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 115072. | 0.744909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18797.9 | −0.116720 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 199066. | 1.09519 | 0.547594 | − | 0.836744i | \(-0.315544\pi\) | ||||
0.547594 | + | 0.836744i | \(0.315544\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −156929. | −0.798962 | −0.399481 | − | 0.916741i | \(-0.630810\pi\) | ||||
−0.399481 | + | 0.916741i | \(0.630810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24525.7 | 0.120224 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 111075. | 0.505611 | 0.252806 | − | 0.967517i | \(-0.418647\pi\) | ||||
0.252806 | + | 0.967517i | \(0.418647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −38994.0 | −0.171183 | −0.0855915 | − | 0.996330i | \(-0.527278\pi\) | ||||
−0.0855915 | + | 0.996330i | \(0.527278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 146432. | 0.598820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −81706.5 | −0.322728 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128256. | 0.473272 | 0.236636 | − | 0.971598i | \(-0.423955\pi\) | ||||
0.236636 | + | 0.971598i | \(0.423955\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −40903.4 | −0.145988 | −0.0729939 | − | 0.997332i | \(-0.523255\pi\) | ||||
−0.0729939 | + | 0.997332i | \(0.523255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4013.45 | 0.0134180 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −278801. | −0.902705 | −0.451352 | − | 0.892346i | \(-0.649058\pi\) | ||||
−0.451352 | + | 0.892346i | \(0.649058\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19454.1 | −0.0591488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −407634. | −1.20171 | −0.600857 | − | 0.799357i | \(-0.705174\pi\) | ||||
−0.600857 | + | 0.799357i | \(0.705174\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −63166.6 | −0.175265 | −0.0876327 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876327 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −220559. | −0.594030 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −37294.0 | −0.0947380 | −0.0473690 | − | 0.998877i | \(-0.515084\pi\) | ||||
−0.0473690 | + | 0.998877i | \(0.515084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 62084.3 | 0.153245 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 88336.1 | 0.206066 | 0.103033 | − | 0.994678i | \(-0.467145\pi\) | ||||
0.103033 | + | 0.994678i | \(0.467145\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −205793. | −0.466910 | −0.233455 | − | 0.972368i | \(-0.575003\pi\) | ||||
−0.233455 | + | 0.972368i | \(0.575003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −228055. | −0.489904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −436918. | −0.913684 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2274.66 | −0.00451162 | −0.00225581 | − | 0.999997i | \(-0.500718\pi\) | ||||
−0.00225581 | + | 0.999997i | \(0.500718\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −537826. | −1.03932 | −0.519659 | − | 0.854374i | \(-0.673941\pi\) | ||||
−0.519659 | + | 0.854374i | \(0.673941\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −463032. | −0.850052 | −0.425026 | − | 0.905181i | \(-0.639735\pi\) | ||||
−0.425026 | + | 0.905181i | \(0.639735\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −550731. | −0.985841 | −0.492920 | − | 0.870074i | \(-0.664071\pi\) | ||||
−0.492920 | + | 0.870074i | \(0.664071\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −324652. | −0.552940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 309565. | 0.514478 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −93121.7 | −0.147464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28057.4 | −0.0433851 | −0.0216926 | − | 0.999765i | \(-0.506905\pi\) | ||||
−0.0216926 | + | 0.999765i | \(0.506905\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 207584. | 0.306266 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15947.0 | 0.0229895 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −449753. | −0.619432 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 52686.4 | 0.0709473 | 0.0354737 | − | 0.999371i | \(-0.488706\pi\) | ||||
0.0354737 | + | 0.999371i | \(0.488706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 996201. | 1.28316 | 0.641582 | − | 0.767054i | \(-0.278278\pi\) | ||||
0.641582 | + | 0.767054i | \(0.278278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −822292. | −1.03619 | −0.518093 | − | 0.855325i | \(-0.673358\pi\) | ||||
−0.518093 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 379890. | 0.458424 | 0.229212 | − | 0.973376i | \(-0.426385\pi\) | ||||
0.229212 | + | 0.973376i | \(0.426385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −275574. | −0.325513 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 514548. | 0.582682 | 0.291341 | − | 0.956619i | \(-0.405899\pi\) | ||||
0.291341 | + | 0.956619i | \(0.405899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.02435e6 | −1.13608 | −0.568038 | − | 0.823003i | \(-0.692297\pi\) | ||||
−0.568038 | + | 0.823003i | \(0.692297\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −173490. | −0.184654 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −95857.4 | −0.0999731 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −572497. | −0.573574 | −0.286787 | − | 0.957994i | \(-0.592587\pi\) | ||||
−0.286787 | + | 0.957994i | \(0.592587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 73865.2 | 0.0725502 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 687168. | 0.648978 | 0.324489 | − | 0.945889i | \(-0.394808\pi\) | ||||
0.324489 | + | 0.945889i | \(0.394808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −906154. | −0.839368 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 185741. | 0.165584 | 0.0827921 | − | 0.996567i | \(-0.473616\pi\) | ||||
0.0827921 | + | 0.996567i | \(0.473616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 150640. | 0.131773 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −443456. | −0.373654 | −0.186827 | − | 0.982393i | \(-0.559820\pi\) | ||||
−0.186827 | + | 0.982393i | \(0.559820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −130669. | −0.108081 | −0.0540403 | − | 0.998539i | \(-0.517210\pi\) | ||||
−0.0540403 | + | 0.998539i | \(0.517210\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −235728. | −0.187966 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.63482e6 | −1.28018 | −0.640090 | − | 0.768300i | \(-0.721103\pi\) | ||||
−0.640090 | + | 0.768300i | \(0.721103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.42734e6 | −1.07835 | −0.539176 | − | 0.842193i | \(-0.681264\pi\) | ||||
−0.539176 | + | 0.842193i | \(0.681264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.02228e6 | −0.758757 | −0.379379 | − | 0.925242i | \(-0.623862\pi\) | ||||
−0.379379 | + | 0.925242i | \(0.623862\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.23002e6 | 0.881471 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −77902.6 | −0.0548665 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 505763. | 0.344174 | 0.172087 | − | 0.985082i | \(-0.444949\pi\) | ||||
0.172087 | + | 0.985082i | \(0.444949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38932.2 | 0.0260468 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 76035.2 | 0.0491854 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 824815. | 0.524735 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.27486e6 | −0.784717 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.88839e6 | −1.14353 | −0.571763 | − | 0.820419i | \(-0.693740\pi\) | ||||
−0.571763 | + | 0.820419i | \(0.693740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 356728. | 0.209139 | 0.104570 | − | 0.994518i | \(-0.466653\pi\) | ||||
0.104570 | + | 0.994518i | \(0.466653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −706711. | −0.407738 | −0.203869 | − | 0.978998i | \(-0.565352\pi\) | ||||
−0.203869 | + | 0.978998i | \(0.565352\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.36781e6 | −0.764502 | −0.382251 | − | 0.924058i | \(-0.624851\pi\) | ||||
−0.382251 | + | 0.924058i | \(0.624851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.23267e6 | 0.678220 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 286015. | 0.152540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −242653. | −0.127432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.09496e6 | −0.557712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −935015. | −0.469082 | −0.234541 | − | 0.972106i | \(-0.575359\pi\) | ||||
−0.234541 | + | 0.972106i | \(0.575359\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 387669. | 0.188734 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.11603e6 | −0.535304 | −0.267652 | − | 0.963516i | \(-0.586248\pi\) | ||||
−0.267652 | + | 0.963516i | \(0.586248\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −60549.3 | −0.0281983 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.35886e6 | −1.08260 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.64476e6 | −1.17913 | −0.589566 | − | 0.807721i | \(-0.700701\pi\) | ||||
−0.589566 | + | 0.807721i | \(0.700701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.93475e6 | −0.850279 | −0.425139 | − | 0.905128i | \(-0.639775\pi\) | ||||
−0.425139 | + | 0.905128i | \(0.639775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 793356. | 0.338869 | 0.169434 | − | 0.985541i | \(-0.445806\pi\) | ||||
0.169434 | + | 0.985541i | \(0.445806\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.27256e6 | −0.535931 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.04612e6 | 0.837906 | 0.418953 | − | 0.908008i | \(-0.362397\pi\) | ||||
0.418953 | + | 0.908008i | \(0.362397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.41514e6 | −0.975381 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −630176. | −0.247588 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.79742e6 | −1.47171 | −0.735857 | − | 0.677137i | \(-0.763220\pi\) | ||||
−0.735857 | + | 0.677137i | \(0.763220\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 598552. | 0.225771 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00590e6 | 0.746511 | 0.373256 | − | 0.927729i | \(-0.378241\pi\) | ||||
0.373256 | + | 0.927729i | \(0.378241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.26888e6 | 0.459800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.33518e6 | 0.835070 | 0.417535 | − | 0.908661i | \(-0.362894\pi\) | ||||
0.417535 | + | 0.908661i | \(0.362894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 109725. | 0.0382217 | 0.0191108 | − | 0.999817i | \(-0.493916\pi\) | ||||
0.0191108 | + | 0.999817i | \(0.493916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −936640. | −0.322048 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.39896e6 | −1.13887 | −0.569433 | − | 0.822038i | \(-0.692837\pi\) | ||||
−0.569433 | + | 0.822038i | \(0.692837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −226871. | −0.0750475 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 421659. | 0.135978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.56111e6 | 1.45243 | 0.726213 | − | 0.687470i | \(-0.241279\pi\) | ||||
0.726213 | + | 0.687470i | \(0.241279\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.11367e6 | 0.656412 | 0.328206 | − | 0.944606i | \(-0.393556\pi\) | ||||
0.328206 | + | 0.944606i | \(0.393556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −62328.0 | −0.0191170 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.44058e6 | 1.02954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.71857e6 | −0.507995 | −0.253997 | − | 0.967205i | \(-0.581745\pi\) | ||||
−0.253997 | + | 0.967205i | \(0.581745\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 154693. | 0.0446268 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.71621e6 | −0.774182 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.57529e6 | 0.994892 | 0.497446 | − | 0.867495i | \(-0.334271\pi\) | ||||
0.497446 | + | 0.867495i | \(0.334271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.89801e6 | −1.34683 | −0.673417 | − | 0.739263i | \(-0.735174\pi\) | ||||
−0.673417 | + | 0.739263i | \(0.735174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 724017. | 0.194436 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.06552e6 | −1.34448 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −557438. | −0.144545 | −0.0722726 | − | 0.997385i | \(-0.523025\pi\) | ||||
−0.0722726 | + | 0.997385i | \(0.523025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.44495e6 | −1.39564 | −0.697821 | − | 0.716272i | \(-0.745847\pi\) | ||||
−0.697821 | + | 0.716272i | \(0.745847\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −48353.7 | −0.0121123 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −658765. | −0.163143 | −0.0815716 | − | 0.996667i | \(-0.525994\pi\) | ||||
−0.0815716 | + | 0.996667i | \(0.525994\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.02447e6 | −0.490118 | −0.245059 | − | 0.969508i | \(-0.578807\pi\) | ||||
−0.245059 | + | 0.969508i | \(0.578807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.15259e6 | 0.275914 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.98151e6 | −0.932034 | −0.466017 | − | 0.884776i | \(-0.654311\pi\) | ||||
−0.466017 | + | 0.884776i | \(0.654311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.67027e6 | −1.08119 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −964156. | −0.218333 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.69421e6 | −0.603449 | −0.301725 | − | 0.953395i | \(-0.597562\pi\) | ||||
−0.301725 | + | 0.953395i | \(0.597562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.99662e6 | 0.437565 | 0.218782 | − | 0.975774i | \(-0.429792\pi\) | ||||
0.218782 | + | 0.975774i | \(0.429792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 485244. | 0.105198 | 0.0525990 | − | 0.998616i | \(-0.483249\pi\) | ||||
0.0525990 | + | 0.998616i | \(0.483249\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.14247e6 | −1.30332 | −0.651660 | − | 0.758511i | \(-0.725927\pi\) | ||||
−0.651660 | + | 0.758511i | \(0.725927\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.54036e6 | 0.323364 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.13174e6 | −0.643625 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 154312. | 0.0313810 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.22475e6 | 1.04046 | 0.520232 | − | 0.854025i | \(-0.325845\pi\) | ||||
0.520232 | + | 0.854025i | \(0.325845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.54165e6 | 0.697980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.45099e6 | 0.859215 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 526301. | 0.100557 | 0.0502784 | − | 0.998735i | \(-0.483989\pi\) | ||||
0.0502784 | + | 0.998735i | \(0.483989\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.79599e6 | 1.45938 | 0.729689 | − | 0.683779i | \(-0.239665\pi\) | ||||
0.729689 | + | 0.683779i | \(0.239665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.78604e6 | −0.701565 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.05640e6 | −0.918227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.85501e6 | −0.513283 | −0.256642 | − | 0.966507i | \(-0.582616\pi\) | ||||
−0.256642 | + | 0.966507i | \(0.582616\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.58697e6 | 1.51328 | 0.756641 | − | 0.653830i | \(-0.226839\pi\) | ||||
0.756641 | + | 0.653830i | \(0.226839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −571874. | −0.0997865 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.78163e6 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.50394e6 | −0.424201 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −887831. | −0.147507 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.15747e6 | 0.684073 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.16124e6 | −0.994429 | −0.497215 | − | 0.867628i | \(-0.665644\pi\) | ||||
−0.497215 | + | 0.867628i | \(0.665644\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.56908e6 | 1.36987 | 0.684936 | − | 0.728604i | \(-0.259830\pi\) | ||||
0.684936 | + | 0.728604i | \(0.259830\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 185972. | 0.0291689 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.39799e6 | −0.994041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.80747e6 | −0.732991 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.52603e6 | 0.683648 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.61737e6 | 0.388054 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.18531e6 | −0.761695 | −0.380848 | − | 0.924638i | \(-0.624368\pi\) | ||||
−0.380848 | + | 0.924638i | \(0.624368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.37790e6 | −0.487142 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.67763e6 | 0.668433 | 0.334216 | − | 0.942496i | \(-0.391528\pi\) | ||||
0.334216 | + | 0.942496i | \(0.391528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −806931. | −0.113229 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.67542e6 | 0.232976 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.26986e6 | −1.12943 | −0.564716 | − | 0.825285i | \(-0.691014\pi\) | ||||
−0.564716 | + | 0.825285i | \(0.691014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.22374e6 | −0.436345 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.98649e6 | 0.530054 | 0.265027 | − | 0.964241i | \(-0.414619\pi\) | ||||
0.265027 | + | 0.964241i | \(0.414619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 629045. | 0.0829012 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 225037. | 0.0291389 | 0.0145695 | − | 0.999894i | \(-0.495362\pi\) | ||||
0.0145695 | + | 0.999894i | \(0.495362\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.22720e7 | 1.57516 | 0.787582 | − | 0.616210i | \(-0.211333\pi\) | ||||
0.787582 | + | 0.616210i | \(0.211333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −122402. | −0.0154390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.11245e6 | −0.389191 | −0.194596 | − | 0.980884i | \(-0.562339\pi\) | ||||
−0.194596 | + | 0.980884i | \(0.562339\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.07926e7 | −1.32643 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.27264e6 | −0.276923 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.10819e6 | 0.611888 | 0.305944 | − | 0.952050i | \(-0.401028\pi\) | ||||
0.305944 | + | 0.952050i | \(0.401028\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39636.8 | 0.00470771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.08828e7 | −1.27087 | −0.635437 | − | 0.772153i | \(-0.719180\pi\) | ||||
−0.635437 | + | 0.772153i | \(0.719180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.87681e6 | 0.333133 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.72892e6 | −0.196883 | −0.0984414 | − | 0.995143i | \(-0.531386\pi\) | ||||
−0.0984414 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18839e7 | 1.34206 | 0.671030 | − | 0.741430i | \(-0.265852\pi\) | ||||
0.671030 | + | 0.741430i | \(0.265852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −469947. | −0.0521988 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.75410e6 | 0.193234 | 0.0966170 | − | 0.995322i | \(-0.469198\pi\) | ||||
0.0966170 | + | 0.995322i | \(0.469198\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.27960e6 | 0.463768 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −500215. | −0.0537658 | −0.0268829 | − | 0.999639i | \(-0.508558\pi\) | ||||
−0.0268829 | + | 0.999639i | \(0.508558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.27374e6 | −0.874962 | −0.437481 | − | 0.899228i | \(-0.644129\pi\) | ||||
−0.437481 | + | 0.899228i | \(0.644129\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.17094e7 | 1.22831 | 0.614153 | − | 0.789187i | \(-0.289498\pi\) | ||||
0.614153 | + | 0.789187i | \(0.289498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.57968e6 | 0.472732 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.05674e7 | −1.06498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −367210. | −0.0367148 | −0.0183574 | − | 0.999831i | \(-0.505844\pi\) | ||||
−0.0183574 | + | 0.999831i | \(0.505844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.97666e6 | 0.489783 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.69426e6 | 0.263081 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.59036e7 | 1.52880 | 0.764398 | − | 0.644745i | \(-0.223036\pi\) | ||||
0.764398 | + | 0.644745i | \(0.223036\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.08655e6 | 0.294405 | 0.147203 | − | 0.989106i | \(-0.452973\pi\) | ||||
0.147203 | + | 0.989106i | \(0.452973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.94249e6 | −0.370263 | −0.185131 | − | 0.982714i | \(-0.559271\pi\) | ||||
−0.185131 | + | 0.982714i | \(0.559271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −587354. | −0.0547379 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.83440e6 | −0.810763 | −0.405381 | − | 0.914148i | \(-0.632861\pi\) | ||||
−0.405381 | + | 0.914148i | \(0.632861\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.92324e6 | −0.357307 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.93767e6 | −0.353204 | −0.176602 | − | 0.984282i | \(-0.556511\pi\) | ||||
−0.176602 | + | 0.984282i | \(0.556511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.52284e6 | 0.847740 | 0.423870 | − | 0.905723i | \(-0.360671\pi\) | ||||
0.423870 | + | 0.905723i | \(0.360671\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 613143. | 0.0537660 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 640067. | 0.0557072 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.92333e7 | 1.64910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.47502e6 | −0.380853 | −0.190426 | − | 0.981701i | \(-0.560987\pi\) | ||||
−0.190426 | + | 0.981701i | \(0.560987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.60623e7 | −1.34690 | −0.673452 | − | 0.739231i | \(-0.735189\pi\) | ||||
−0.673452 | + | 0.739231i | \(0.735189\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76855e7 | 1.47212 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.64450e7 | 1.34891 | 0.674456 | − | 0.738315i | \(-0.264378\pi\) | ||||
0.674456 | + | 0.738315i | \(0.264378\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.77689e6 | 0.226116 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.33941e6 | −0.187740 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.86170e6 | −0.626357 | −0.313178 | − | 0.949694i | \(-0.601394\pi\) | ||||
−0.313178 | + | 0.949694i | \(0.601394\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −974849. | −0.0765553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.43443e7 | 1.11840 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.57224e7 | −1.20844 | −0.604219 | − | 0.796818i | \(-0.706515\pi\) | ||||
−0.604219 | + | 0.796818i | \(0.706515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.25227e6 | −0.171883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.27228e6 | −0.170967 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.42345e7 | −1.06347 | −0.531736 | − | 0.846910i | \(-0.678460\pi\) | ||||
−0.531736 | + | 0.846910i | \(0.678460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31440.3 | −0.00231613 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.66080e6 | 0.267800 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.51911e7 | 1.81729 | 0.908646 | − | 0.417568i | \(-0.137118\pi\) | ||||
0.908646 | + | 0.417568i | \(0.137118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.52770e6 | −0.252728 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.04266e6 | −0.144328 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.76666e6 | −0.404658 | −0.202329 | − | 0.979318i | \(-0.564851\pi\) | ||||
−0.202329 | + | 0.979318i | \(0.564851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.61886e6 | 0.665779 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.99042e6 | 0.686790 | 0.343395 | − | 0.939191i | \(-0.388423\pi\) | ||||
0.343395 | + | 0.939191i | \(0.388423\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.84861e6 | −0.396628 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.19691e7 | −1.47979 | −0.739895 | − | 0.672722i | \(-0.765125\pi\) | ||||
−0.739895 | + | 0.672722i | \(0.765125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.21995e7 | −0.810721 | −0.405361 | − | 0.914157i | \(-0.632854\pi\) | ||||
−0.405361 | + | 0.914157i | \(0.632854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.20639e6 | 0.211653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.79837e7 | 1.17132 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.89445e6 | 0.640165 | 0.320082 | − | 0.947390i | \(-0.396289\pi\) | ||||
0.320082 | + | 0.947390i | \(0.396289\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.02258e6 | −0.0652878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.59336e7 | 1.01059 | 0.505293 | − | 0.862948i | \(-0.331385\pi\) | ||||
0.505293 | + | 0.862948i | \(0.331385\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.00477e6 | 0.501057 | 0.250528 | − | 0.968109i | \(-0.419396\pi\) | ||||
0.250528 | + | 0.968109i | \(0.419396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.34217e7 | −0.834636 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −604608. | −0.0371096 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.46154e7 | 0.891238 | 0.445619 | − | 0.895223i | \(-0.352984\pi\) | ||||
0.445619 | + | 0.895223i | \(0.352984\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.74241e7 | 1.65076 | 0.825379 | − | 0.564579i | \(-0.190961\pi\) | ||||
0.825379 | + | 0.564579i | \(0.190961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 100336. | 0.00600073 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.05725e6 | 0.180504 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.91986e7 | 1.12627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.97003e6 | −0.403702 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.22194e7 | 1.27878 | 0.639388 | − | 0.768884i | \(-0.279188\pi\) | ||||
0.639388 | + | 0.768884i | \(0.279188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.49944e6 | 0.142037 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.97983e7 | 1.11801 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.54647e6 | −0.0862376 | −0.0431188 | − | 0.999070i | \(-0.513729\pi\) | ||||
−0.0431188 | + | 0.999070i | \(0.513729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.27693e7 | −0.707620 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.50720e6 | 0.520312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −486352. | −0.0264522 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.22034e7 | 0.655555 | 0.327778 | − | 0.944755i | \(-0.393700\pi\) | ||||
0.327778 | + | 0.944755i | \(0.393700\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.99193e6 | 0.319900 | 0.159950 | − | 0.987125i | \(-0.448867\pi\) | ||||
0.159950 | + | 0.987125i | \(0.448867\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.01908e7 | −0.537423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.05010e6 | 0.107453 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.38572e7 | −1.23527 | −0.617635 | − | 0.786465i | \(-0.711909\pi\) | ||||
−0.617635 | + | 0.786465i | \(0.711909\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.39131e7 | 1.23065 | 0.615327 | − | 0.788272i | \(-0.289024\pi\) | ||||
0.615327 | + | 0.788272i | \(0.289024\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.76663e6 | 0.0898216 | 0.0449108 | − | 0.998991i | \(-0.485700\pi\) | ||||
0.0449108 | + | 0.998991i | \(0.485700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.68441e7 | 0.851258 | 0.425629 | − | 0.904898i | \(-0.360053\pi\) | ||||
0.425629 | + | 0.904898i | \(0.360053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.03901e6 | −0.401412 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.57917e6 | −0.0783811 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.52232e7 | −1.23707 | −0.618537 | − | 0.785756i | \(-0.712274\pi\) | ||||
−0.618537 | + | 0.785756i | \(0.712274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82963e6 | −0.479234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.51398e6 | −0.265658 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.86728e6 | −0.0894338 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.78653e6 | 0.0845640 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.96723e7 | −0.925727 | −0.462864 | − | 0.886430i | \(-0.653178\pi\) | ||||
−0.462864 | + | 0.886430i | \(0.653178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.31831e7 | −1.07825 | −0.539126 | − | 0.842225i | \(-0.681245\pi\) | ||||
−0.539126 | + | 0.842225i | \(0.681245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.11763e7 | 1.90399 | 0.951995 | − | 0.306112i | \(-0.0990284\pi\) | ||||
0.951995 | + | 0.306112i | \(0.0990284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.85382e7 | 0.847307 | 0.423653 | − | 0.905824i | \(-0.360747\pi\) | ||||
0.423653 | + | 0.905824i | \(0.360747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −932351. | −0.0423681 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.36140e6 | −0.285761 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.02042e6 | −0.268894 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.55211e6 | 0.0685333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.32018e7 | 1.01865 | 0.509323 | − | 0.860576i | \(-0.329896\pi\) | ||||
0.509323 | + | 0.860576i | \(0.329896\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.30268e6 | −0.0565453 | −0.0282727 | − | 0.999600i | \(-0.509001\pi\) | ||||
−0.0282727 | + | 0.999600i | \(0.509001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.39367e7 | 1.46476 | 0.732382 | − | 0.680894i | \(-0.238409\pi\) | ||||
0.732382 | + | 0.680894i | \(0.238409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.47651e7 | 0.630124 | 0.315062 | − | 0.949071i | \(-0.397975\pi\) | ||||
0.315062 | + | 0.949071i | \(0.397975\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.97742e7 | 0.839161 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.72156e6 | −0.114206 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.20840e6 | 0.0921554 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −524680. | −0.0216519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.98022e6 | 0.286456 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.14482e6 | −0.208809 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.33294e7 | −0.538011 | −0.269006 | − | 0.963139i | \(-0.586695\pi\) | ||||
−0.269006 | + | 0.963139i | \(0.586695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.33053e7 | −0.930375 | −0.465187 | − | 0.885212i | \(-0.654013\pi\) | ||||
−0.465187 | + | 0.885212i | \(0.654013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.09783e7 | 1.62696 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.55886e7 | −0.612185 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.50929e7 | 1.76124 | 0.880622 | − | 0.473819i | \(-0.157125\pi\) | ||||
0.880622 | + | 0.473819i | \(0.157125\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.97626e7 | 0.763556 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.70138e6 | −0.219092 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.55017e7 | 1.34962 | 0.674808 | − | 0.737993i | \(-0.264226\pi\) | ||||
0.674808 | + | 0.737993i | \(0.264226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.71338e6 | −0.0647857 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.09229e7 | −0.408612 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.53866e7 | −0.944616 | −0.472308 | − | 0.881434i | \(-0.656579\pi\) | ||||
−0.472308 | + | 0.881434i | \(0.656579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.52084e6 | −0.129620 | −0.0648100 | − | 0.997898i | \(-0.520644\pi\) | ||||
−0.0648100 | + | 0.997898i | \(0.520644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.42505e6 | −0.0888058 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.87280e6 | −0.140330 | −0.0701650 | − | 0.997535i | \(-0.522353\pi\) | ||||
−0.0701650 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.78650e6 | 0.352746 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.66754e7 | −0.951435 | −0.475718 | − | 0.879598i | \(-0.657812\pi\) | ||||
−0.475718 | + | 0.879598i | \(0.657812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −56866.4 | −0.00201766 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.10337e7 | 0.387412 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86034e7 | −0.999100 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.34456e7 | −0.464797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.00067e7 | 1.03193 | 0.515967 | − | 0.856608i | \(-0.327433\pi\) | ||||
0.515967 | + | 0.856608i | \(0.327433\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.42664e7 | 0.825956 | 0.412978 | − | 0.910741i | \(-0.364489\pi\) | ||||
0.412978 | + | 0.910741i | \(0.364489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.87346e6 | −0.131165 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.67601e7 | 0.896915 | 0.448458 | − | 0.893804i | \(-0.351974\pi\) | ||||
0.448458 | + | 0.893804i | \(0.351974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.73886e7 | −0.579839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.48680e7 | 0.820839 | 0.410419 | − | 0.911897i | \(-0.365382\pi\) | ||||
0.410419 | + | 0.911897i | \(0.365382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.15758e7 | −0.380155 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.62616e6 | −0.0528656 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.05276e7 | 1.31089 | 0.655446 | − | 0.755242i | \(-0.272481\pi\) | ||||
0.655446 | + | 0.755242i | \(0.272481\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.37683e7 | −0.440881 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.07721e7 | −1.29905 | −0.649524 | − | 0.760341i | \(-0.725032\pi\) | ||||
−0.649524 | + | 0.760341i | \(0.725032\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1080.6.a.h.1.3 | yes | 3 | |
3.2 | odd | 2 | 1080.6.a.f.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.6.a.f.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
1080.6.a.h.1.3 | yes | 3 | 1.1 | even | 1 | trivial |