Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6021,2,Mod(1,6021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6021 = 3^{3} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6021.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: | \(48.0779270570\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.874032 | 0.390879 | 0.195440 | − | 0.980716i | \(-0.437387\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.23607 | −0.390879 | ||||||||
\(11\) | 1.74806 | 0.527061 | 0.263531 | − | 0.964651i | \(-0.415113\pi\) | ||||
0.263531 | + | 0.964651i | \(0.415113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −1.41421 | −0.377964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −0.333851 | −0.0809706 | −0.0404853 | − | 0.999180i | \(-0.512890\pi\) | ||||
−0.0404853 | + | 0.999180i | \(0.512890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.70820 | 1.53897 | 0.769484 | − | 0.638666i | \(-0.220514\pi\) | ||||
0.769484 | + | 0.638666i | \(0.220514\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.47214 | −0.527061 | ||||||||
\(23\) | −1.20788 | −0.251861 | −0.125930 | − | 0.992039i | \(-0.540192\pi\) | ||||
−0.125930 | + | 0.992039i | \(0.540192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23607 | −0.847214 | ||||||||
\(26\) | −1.41421 | −0.277350 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.62210 | −0.486911 | −0.243456 | − | 0.969912i | \(-0.578281\pi\) | ||||
−0.243456 | + | 0.969912i | \(0.578281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76393 | −0.496417 | −0.248208 | − | 0.968707i | \(-0.579842\pi\) | ||||
−0.248208 | + | 0.968707i | \(0.579842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.472136 | 0.0809706 | ||||||||
\(35\) | 0.874032 | 0.147738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.00000 | −1.47959 | −0.739795 | − | 0.672832i | \(-0.765078\pi\) | ||||
−0.739795 | + | 0.672832i | \(0.765078\pi\) | |||||||
\(38\) | −9.48683 | −1.53897 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.47214 | 0.390879 | ||||||||
\(41\) | −5.11667 | −0.799090 | −0.399545 | − | 0.916714i | \(-0.630832\pi\) | ||||
−0.399545 | + | 0.916714i | \(0.630832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.472136 | −0.0720001 | −0.0360000 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360000 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.70820 | 0.251861 | ||||||||
\(47\) | −6.73722 | −0.982724 | −0.491362 | − | 0.870955i | \(-0.663501\pi\) | ||||
−0.491362 | + | 0.870955i | \(0.663501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 5.99070 | 0.847214 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7735 | 1.47986 | 0.739929 | − | 0.672685i | \(-0.234859\pi\) | ||||
0.739929 | + | 0.672685i | \(0.234859\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.52786 | 0.206017 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.70820 | 0.486911 | ||||||||
\(59\) | −5.24419 | −0.682736 | −0.341368 | − | 0.939930i | \(-0.610890\pi\) | ||||
−0.341368 | + | 0.939930i | \(0.610890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.7082 | −1.37105 | −0.685523 | − | 0.728051i | \(-0.740426\pi\) | ||||
−0.685523 | + | 0.728051i | \(0.740426\pi\) | |||||||
\(62\) | 3.90879 | 0.496417 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0.874032 | 0.108410 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00000 | −1.09952 | −0.549762 | − | 0.835321i | \(-0.685282\pi\) | ||||
−0.549762 | + | 0.835321i | \(0.685282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.23607 | −0.147738 | ||||||||
\(71\) | −6.65841 | −0.790207 | −0.395104 | − | 0.918637i | \(-0.629291\pi\) | ||||
−0.395104 | + | 0.918637i | \(0.629291\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.18034 | −1.07448 | −0.537239 | − | 0.843430i | \(-0.680533\pi\) | ||||
−0.537239 | + | 0.843430i | \(0.680533\pi\) | |||||||
\(74\) | 12.7279 | 1.47959 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.74806 | 0.199210 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2361 | 1.15165 | 0.575824 | − | 0.817574i | \(-0.304681\pi\) | ||||
0.575824 | + | 0.817574i | \(0.304681\pi\) | |||||||
\(80\) | −3.49613 | −0.390879 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.23607 | 0.799090 | ||||||||
\(83\) | 4.37016 | 0.479687 | 0.239844 | − | 0.970812i | \(-0.422904\pi\) | ||||
0.239844 | + | 0.970812i | \(0.422904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.291796 | −0.0316497 | ||||||||
\(86\) | 0.667701 | 0.0720001 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.94427 | 0.527061 | ||||||||
\(89\) | −1.74806 | −0.185294 | −0.0926472 | − | 0.995699i | \(-0.529533\pi\) | ||||
−0.0926472 | + | 0.995699i | \(0.529533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.52786 | 0.982724 | ||||||||
\(95\) | 5.86319 | 0.601550 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7082 | −1.08725 | −0.543627 | − | 0.839327i | \(-0.682949\pi\) | ||||
−0.543627 | + | 0.839327i | \(0.682949\pi\) | |||||||
\(98\) | 8.48528 | 0.857143 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9374 | 1.48632 | 0.743161 | − | 0.669112i | \(-0.233326\pi\) | ||||
0.743161 | + | 0.669112i | \(0.233326\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.47214 | −0.342120 | −0.171060 | − | 0.985261i | \(-0.554719\pi\) | ||||
−0.171060 | + | 0.985261i | \(0.554719\pi\) | |||||||
\(104\) | 2.82843 | 0.277350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.2361 | −1.47986 | ||||||||
\(107\) | 0.874032 | 0.0844959 | 0.0422479 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422479 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4164 | −1.28506 | −0.642529 | − | 0.766261i | \(-0.722115\pi\) | ||||
−0.642529 | + | 0.766261i | \(0.722115\pi\) | |||||||
\(110\) | −2.16073 | −0.206017 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 5.65685 | 0.532152 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.05573 | −0.0984472 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.41641 | 0.682736 | ||||||||
\(119\) | −0.333851 | −0.0306040 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.94427 | −0.722207 | ||||||||
\(122\) | 15.1437 | 1.37105 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.07262 | −0.722037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.23607 | −0.819569 | −0.409784 | − | 0.912182i | \(-0.634396\pi\) | ||||
−0.409784 | + | 0.912182i | \(0.634396\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.23607 | −0.108410 | ||||||||
\(131\) | 0.127520 | 0.0111414 | 0.00557072 | − | 0.999984i | \(-0.498227\pi\) | ||||
0.00557072 | + | 0.999984i | \(0.498227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.70820 | 0.581675 | ||||||||
\(134\) | 12.7279 | 1.09952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.944272 | −0.0809706 | ||||||||
\(137\) | 0.333851 | 0.0285228 | 0.0142614 | − | 0.999898i | \(-0.495460\pi\) | ||||
0.0142614 | + | 0.999898i | \(0.495460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00000 | 0.254457 | 0.127228 | − | 0.991873i | \(-0.459392\pi\) | ||||
0.127228 | + | 0.991873i | \(0.459392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.41641 | 0.790207 | ||||||||
\(143\) | 1.74806 | 0.146180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.29180 | −0.190323 | ||||||||
\(146\) | 12.9830 | 1.07448 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.28825 | −0.187460 | −0.0937302 | − | 0.995598i | \(-0.529879\pi\) | ||||
−0.0937302 | + | 0.995598i | \(0.529879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9443 | −1.29753 | −0.648763 | − | 0.760990i | \(-0.724713\pi\) | ||||
−0.648763 | + | 0.760990i | \(0.724713\pi\) | |||||||
\(152\) | 18.9737 | 1.53897 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.47214 | −0.199210 | ||||||||
\(155\) | −2.41577 | −0.194039 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4164 | 1.07075 | 0.535373 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535373 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(158\) | −14.4760 | −1.15165 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.20788 | −0.0951945 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7082 | 0.995383 | 0.497692 | − | 0.867354i | \(-0.334181\pi\) | ||||
0.497692 | + | 0.867354i | \(0.334181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.18034 | −0.479687 | ||||||||
\(167\) | 2.62210 | 0.202904 | 0.101452 | − | 0.994840i | \(-0.467651\pi\) | ||||
0.101452 | + | 0.994840i | \(0.467651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0.412662 | 0.0316497 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.5563 | −1.18273 | −0.591364 | − | 0.806405i | \(-0.701410\pi\) | ||||
−0.591364 | + | 0.806405i | \(0.701410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.23607 | −0.320217 | ||||||||
\(176\) | −6.99226 | −0.527061 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.47214 | 0.185294 | ||||||||
\(179\) | 23.0888 | 1.72574 | 0.862868 | − | 0.505429i | \(-0.168666\pi\) | ||||
0.862868 | + | 0.505429i | \(0.168666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6525 | −1.46076 | −0.730379 | − | 0.683043i | \(-0.760656\pi\) | ||||
−0.730379 | + | 0.683043i | \(0.760656\pi\) | |||||||
\(182\) | −1.41421 | −0.104828 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.41641 | −0.251861 | ||||||||
\(185\) | −7.86629 | −0.578341 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.583592 | −0.0426765 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.29180 | −0.601550 | ||||||||
\(191\) | 8.81913 | 0.638130 | 0.319065 | − | 0.947733i | \(-0.396631\pi\) | ||||
0.319065 | + | 0.947733i | \(0.396631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00000 | 0.647834 | 0.323917 | − | 0.946085i | \(-0.395000\pi\) | ||||
0.323917 | + | 0.946085i | \(0.395000\pi\) | |||||||
\(194\) | 15.1437 | 1.08725 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7990 | 1.41062 | 0.705310 | − | 0.708899i | \(-0.250808\pi\) | ||||
0.705310 | + | 0.708899i | \(0.250808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.23607 | −0.442063 | −0.221032 | − | 0.975267i | \(-0.570942\pi\) | ||||
−0.221032 | + | 0.975267i | \(0.570942\pi\) | |||||||
\(200\) | −11.9814 | −0.847214 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.1246 | −1.48632 | ||||||||
\(203\) | −2.62210 | −0.184035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.47214 | −0.312348 | ||||||||
\(206\) | 4.91034 | 0.342120 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 11.7264 | 0.811130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.76393 | −0.121434 | −0.0607170 | − | 0.998155i | \(-0.519339\pi\) | ||||
−0.0607170 | + | 0.998155i | \(0.519339\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.23607 | −0.0844959 | ||||||||
\(215\) | −0.412662 | −0.0281433 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.76393 | −0.187628 | ||||||||
\(218\) | 18.9737 | 1.28506 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.333851 | −0.0224572 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | −22.4698 | −1.49137 | −0.745686 | − | 0.666297i | \(-0.767878\pi\) | ||||
−0.745686 | + | 0.666297i | \(0.767878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.47214 | 0.163363 | 0.0816817 | − | 0.996658i | \(-0.473971\pi\) | ||||
0.0816817 | + | 0.996658i | \(0.473971\pi\) | |||||||
\(230\) | 1.49302 | 0.0984472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.41641 | −0.486911 | ||||||||
\(233\) | 20.0053 | 1.31059 | 0.655296 | − | 0.755372i | \(-0.272544\pi\) | ||||
0.655296 | + | 0.755372i | \(0.272544\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.88854 | −0.384126 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.472136 | 0.0306040 | ||||||||
\(239\) | −12.3941 | −0.801706 | −0.400853 | − | 0.916142i | \(-0.631286\pi\) | ||||
−0.400853 | + | 0.916142i | \(0.631286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.58359 | 0.102008 | 0.0510041 | − | 0.998698i | \(-0.483758\pi\) | ||||
0.0510041 | + | 0.998698i | \(0.483758\pi\) | |||||||
\(242\) | 11.2349 | 0.722207 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.24419 | −0.335039 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.70820 | 0.426833 | ||||||||
\(248\) | −7.81758 | −0.496417 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.4164 | 0.722037 | ||||||||
\(251\) | 29.8747 | 1.88568 | 0.942838 | − | 0.333253i | \(-0.108146\pi\) | ||||
0.942838 | + | 0.333253i | \(0.108146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.11146 | −0.132746 | ||||||||
\(254\) | 13.0618 | 0.819569 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.5927 | −1.22216 | −0.611078 | − | 0.791570i | \(-0.709264\pi\) | ||||
−0.611078 | + | 0.791570i | \(0.709264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00000 | −0.559233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.180340 | −0.0111414 | ||||||||
\(263\) | 30.2874 | 1.86760 | 0.933800 | − | 0.357796i | \(-0.116472\pi\) | ||||
0.933800 | + | 0.357796i | \(0.116472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.41641 | 0.578445 | ||||||||
\(266\) | −9.48683 | −0.581675 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.9358 | 0.849681 | 0.424841 | − | 0.905268i | \(-0.360330\pi\) | ||||
0.424841 | + | 0.905268i | \(0.360330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8885 | 1.39038 | 0.695190 | − | 0.718826i | \(-0.255320\pi\) | ||||
0.695190 | + | 0.718826i | \(0.255320\pi\) | |||||||
\(272\) | 1.33540 | 0.0809706 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.472136 | −0.0285228 | ||||||||
\(275\) | −7.40492 | −0.446533 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.3607 | 1.82420 | 0.912098 | − | 0.409972i | \(-0.134461\pi\) | ||||
0.912098 | + | 0.409972i | \(0.134461\pi\) | |||||||
\(278\) | −4.24264 | −0.254457 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.47214 | 0.147738 | ||||||||
\(281\) | 3.03476 | 0.181038 | 0.0905192 | − | 0.995895i | \(-0.471147\pi\) | ||||
0.0905192 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.70820 | 0.101542 | 0.0507711 | − | 0.998710i | \(-0.483832\pi\) | ||||
0.0507711 | + | 0.998710i | \(0.483832\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.47214 | −0.146180 | ||||||||
\(287\) | −5.11667 | −0.302028 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8885 | −0.993444 | ||||||||
\(290\) | 3.24109 | 0.190323 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.9535 | −1.74990 | −0.874952 | − | 0.484210i | \(-0.839107\pi\) | ||||
−0.874952 | + | 0.484210i | \(0.839107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.58359 | −0.266867 | ||||||||
\(296\) | −25.4558 | −1.47959 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.23607 | 0.187460 | ||||||||
\(299\) | −1.20788 | −0.0698537 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.472136 | −0.0272135 | ||||||||
\(302\) | 22.5486 | 1.29753 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.8328 | −1.53897 | ||||||||
\(305\) | −9.35931 | −0.535913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.41641 | 0.423277 | 0.211638 | − | 0.977348i | \(-0.432120\pi\) | ||||
0.211638 | + | 0.977348i | \(0.432120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.41641 | 0.194039 | ||||||||
\(311\) | −24.6305 | −1.39667 | −0.698334 | − | 0.715772i | \(-0.746075\pi\) | ||||
−0.698334 | + | 0.715772i | \(0.746075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.2918 | −0.751297 | −0.375648 | − | 0.926762i | \(-0.622580\pi\) | ||||
−0.375648 | + | 0.926762i | \(0.622580\pi\) | |||||||
\(314\) | −18.9737 | −1.07075 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.6367 | −0.934411 | −0.467205 | − | 0.884149i | \(-0.654739\pi\) | ||||
−0.467205 | + | 0.884149i | \(0.654739\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.58359 | −0.256632 | ||||||||
\(320\) | 6.99226 | 0.390879 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.70820 | 0.0951945 | ||||||||
\(323\) | −2.23954 | −0.124611 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.23607 | −0.234975 | ||||||||
\(326\) | −17.9721 | −0.995383 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.4721 | −0.799090 | ||||||||
\(329\) | −6.73722 | −0.371435 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.9443 | −0.766447 | −0.383223 | − | 0.923656i | \(-0.625186\pi\) | ||||
−0.383223 | + | 0.923656i | \(0.625186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.70820 | −0.202904 | ||||||||
\(335\) | −7.86629 | −0.429781 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2361 | −0.666541 | −0.333271 | − | 0.942831i | \(-0.608152\pi\) | ||||
−0.333271 | + | 0.942831i | \(0.608152\pi\) | |||||||
\(338\) | 16.9706 | 0.923077 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.83153 | −0.261642 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −1.33540 | −0.0720001 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.0000 | 1.18273 | ||||||||
\(347\) | 30.9064 | 1.65914 | 0.829570 | − | 0.558402i | \(-0.188585\pi\) | ||||
0.829570 | + | 0.558402i | \(0.188585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.4164 | 0.878750 | 0.439375 | − | 0.898304i | \(-0.355200\pi\) | ||||
0.439375 | + | 0.898304i | \(0.355200\pi\) | |||||||
\(350\) | 5.99070 | 0.320217 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.7348 | −1.79552 | −0.897761 | − | 0.440483i | \(-0.854807\pi\) | ||||
−0.897761 | + | 0.440483i | \(0.854807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.81966 | −0.308875 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −32.6525 | −1.72574 | ||||||||
\(359\) | −7.61125 | −0.401706 | −0.200853 | − | 0.979621i | \(-0.564371\pi\) | ||||
−0.200853 | + | 0.979621i | \(0.564371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | 27.7928 | 1.46076 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.02391 | −0.419991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2918 | −1.00702 | −0.503512 | − | 0.863988i | \(-0.667959\pi\) | ||||
−0.503512 | + | 0.863988i | \(0.667959\pi\) | |||||||
\(368\) | 4.83153 | 0.251861 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.1246 | 0.578341 | ||||||||
\(371\) | 10.7735 | 0.559334 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.70820 | −0.450894 | −0.225447 | − | 0.974255i | \(-0.572384\pi\) | ||||
−0.225447 | + | 0.974255i | \(0.572384\pi\) | |||||||
\(374\) | 0.825324 | 0.0426765 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.0557 | −0.982724 | ||||||||
\(377\) | −2.62210 | −0.135045 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.00000 | −0.256833 | −0.128416 | − | 0.991720i | \(-0.540989\pi\) | ||||
−0.128416 | + | 0.991720i | \(0.540989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.4721 | −0.638130 | ||||||||
\(383\) | −25.1707 | −1.28616 | −0.643081 | − | 0.765798i | \(-0.722344\pi\) | ||||
−0.643081 | + | 0.765798i | \(0.722344\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.52786 | 0.0778672 | ||||||||
\(386\) | −12.7279 | −0.647834 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4242 | 1.23836 | 0.619178 | − | 0.785251i | \(-0.287466\pi\) | ||||
0.619178 | + | 0.785251i | \(0.287466\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.403252 | 0.0203933 | ||||||||
\(392\) | −16.9706 | −0.857143 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −28.0000 | −1.41062 | ||||||||
\(395\) | 8.94665 | 0.450155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.58359 | −0.129667 | −0.0648334 | − | 0.997896i | \(-0.520652\pi\) | ||||
−0.0648334 | + | 0.997896i | \(0.520652\pi\) | |||||||
\(398\) | 8.81913 | 0.442063 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.9443 | 0.847214 | ||||||||
\(401\) | −14.1421 | −0.706225 | −0.353112 | − | 0.935581i | \(-0.614877\pi\) | ||||
−0.353112 | + | 0.935581i | \(0.614877\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.76393 | −0.137681 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.70820 | 0.184035 | ||||||||
\(407\) | −15.7326 | −0.779835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4164 | 1.70178 | 0.850891 | − | 0.525342i | \(-0.176063\pi\) | ||||
0.850891 | + | 0.525342i | \(0.176063\pi\) | |||||||
\(410\) | 6.32456 | 0.312348 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.24419 | −0.258050 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.81966 | 0.187500 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.5836 | −0.811130 | ||||||||
\(419\) | −25.7109 | −1.25606 | −0.628029 | − | 0.778190i | \(-0.716138\pi\) | ||||
−0.628029 | + | 0.778190i | \(0.716138\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.1246 | −1.66313 | −0.831566 | − | 0.555426i | \(-0.812555\pi\) | ||||
−0.831566 | + | 0.555426i | \(0.812555\pi\) | |||||||
\(422\) | 2.49458 | 0.121434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.4721 | 1.47986 | ||||||||
\(425\) | 1.41421 | 0.0685994 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.7082 | −0.518206 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.583592 | 0.0281433 | ||||||||
\(431\) | 0.874032 | 0.0421006 | 0.0210503 | − | 0.999778i | \(-0.493299\pi\) | ||||
0.0210503 | + | 0.999778i | \(0.493299\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.4164 | 1.22143 | 0.610717 | − | 0.791849i | \(-0.290881\pi\) | ||||
0.610717 | + | 0.791849i | \(0.290881\pi\) | |||||||
\(434\) | 3.90879 | 0.187628 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.10272 | −0.387606 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.1803 | 1.05861 | 0.529305 | − | 0.848432i | \(-0.322453\pi\) | ||||
0.529305 | + | 0.848432i | \(0.322453\pi\) | |||||||
\(440\) | 4.32145 | 0.206017 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.472136 | 0.0224572 | ||||||||
\(443\) | −3.44742 | −0.163792 | −0.0818959 | − | 0.996641i | \(-0.526098\pi\) | ||||
−0.0818959 | + | 0.996641i | \(0.526098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.52786 | −0.0724277 | ||||||||
\(446\) | −1.41421 | −0.0669650 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | −20.8005 | −0.981638 | −0.490819 | − | 0.871261i | \(-0.663302\pi\) | ||||
−0.490819 | + | 0.871261i | \(0.663302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.94427 | −0.421169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 31.7771 | 1.49137 | ||||||||
\(455\) | 0.874032 | 0.0409753 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.1246 | −1.54950 | −0.774752 | − | 0.632265i | \(-0.782125\pi\) | ||||
−0.774752 | + | 0.632265i | \(0.782125\pi\) | |||||||
\(458\) | −3.49613 | −0.163363 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.2526 | 1.26928 | 0.634640 | − | 0.772808i | \(-0.281148\pi\) | ||||
0.634640 | + | 0.772808i | \(0.281148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.7639 | −1.10440 | −0.552202 | − | 0.833710i | \(-0.686212\pi\) | ||||
−0.552202 | + | 0.833710i | \(0.686212\pi\) | |||||||
\(464\) | 10.4884 | 0.486911 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.2918 | −1.31059 | ||||||||
\(467\) | 13.3168 | 0.616229 | 0.308114 | − | 0.951349i | \(-0.400302\pi\) | ||||
0.308114 | + | 0.951349i | \(0.400302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.00000 | −0.415581 | ||||||||
\(470\) | 8.32766 | 0.384126 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.8328 | −0.682736 | ||||||||
\(473\) | −0.825324 | −0.0379484 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.4164 | −1.30383 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.5279 | 0.801706 | ||||||||
\(479\) | −15.3500 | −0.701360 | −0.350680 | − | 0.936495i | \(-0.614050\pi\) | ||||
−0.350680 | + | 0.936495i | \(0.614050\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | −0.410365 | ||||||||
\(482\) | −2.23954 | −0.102008 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.35931 | −0.424985 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7082 | 0.847750 | 0.423875 | − | 0.905721i | \(-0.360670\pi\) | ||||
0.423875 | + | 0.905721i | \(0.360670\pi\) | |||||||
\(488\) | −30.2874 | −1.37105 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.41641 | 0.335039 | ||||||||
\(491\) | 18.8461 | 0.850515 | 0.425257 | − | 0.905072i | \(-0.360184\pi\) | ||||
0.425257 | + | 0.905072i | \(0.360184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.875388 | 0.0394255 | ||||||||
\(494\) | −9.48683 | −0.426833 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.0557 | 0.496417 | ||||||||
\(497\) | −6.65841 | −0.298670 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.2918 | −0.908386 | −0.454193 | − | 0.890903i | \(-0.650072\pi\) | ||||
−0.454193 | + | 0.890903i | \(0.650072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −42.2492 | −1.88568 | ||||||||
\(503\) | 23.3438 | 1.04085 | 0.520425 | − | 0.853907i | \(-0.325774\pi\) | ||||
0.520425 | + | 0.853907i | \(0.325774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0557 | 0.580972 | ||||||||
\(506\) | 2.98605 | 0.132746 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.98915 | −0.221140 | −0.110570 | − | 0.993868i | \(-0.535268\pi\) | ||||
−0.110570 | + | 0.993868i | \(0.535268\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.18034 | −0.406114 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 27.7082 | 1.22216 | ||||||||
\(515\) | −3.03476 | −0.133727 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7771 | −0.517956 | ||||||||
\(518\) | 12.7279 | 0.559233 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.47214 | 0.108410 | ||||||||
\(521\) | −0.255039 | −0.0111735 | −0.00558673 | − | 0.999984i | \(-0.501778\pi\) | ||||
−0.00558673 | + | 0.999984i | \(0.501778\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.8885 | 0.825938 | 0.412969 | − | 0.910745i | \(-0.364492\pi\) | ||||
0.412969 | + | 0.910745i | \(0.364492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.8328 | −1.86760 | ||||||||
\(527\) | 0.922740 | 0.0401952 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5410 | −0.936566 | ||||||||
\(530\) | −13.3168 | −0.578445 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.11667 | −0.221628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.763932 | 0.0330277 | ||||||||
\(536\) | −25.4558 | −1.09952 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.7082 | −0.849681 | ||||||||
\(539\) | −10.4884 | −0.451767 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.52786 | 0.366642 | 0.183321 | − | 0.983053i | \(-0.441315\pi\) | ||||
0.183321 | + | 0.983053i | \(0.441315\pi\) | |||||||
\(542\) | −32.3693 | −1.39038 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.7264 | −0.502303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.23607 | 0.181121 | 0.0905606 | − | 0.995891i | \(-0.471134\pi\) | ||||
0.0905606 | + | 0.995891i | \(0.471134\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.4721 | 0.446533 | ||||||||
\(551\) | −17.5896 | −0.749340 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.2361 | 0.435282 | ||||||||
\(554\) | −42.9365 | −1.82420 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.5316 | 1.50552 | 0.752760 | − | 0.658295i | \(-0.228722\pi\) | ||||
0.752760 | + | 0.658295i | \(0.228722\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.472136 | −0.0199692 | ||||||||
\(560\) | −3.49613 | −0.147738 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.29180 | −0.181038 | ||||||||
\(563\) | 8.69161 | 0.366308 | 0.183154 | − | 0.983084i | \(-0.441369\pi\) | ||||
0.183154 | + | 0.983084i | \(0.441369\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.94427 | 0.208007 | ||||||||
\(566\) | −2.41577 | −0.101542 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.8328 | −0.790207 | ||||||||
\(569\) | 8.61280 | 0.361067 | 0.180534 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180534 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2918 | 0.472547 | 0.236273 | − | 0.971687i | \(-0.424074\pi\) | ||||
0.236273 | + | 0.971687i | \(0.424074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.23607 | 0.302028 | ||||||||
\(575\) | 5.11667 | 0.213380 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.7639 | −1.23909 | −0.619544 | − | 0.784962i | \(-0.712683\pi\) | ||||
−0.619544 | + | 0.784962i | \(0.712683\pi\) | |||||||
\(578\) | 23.8840 | 0.993444 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.37016 | 0.181305 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.8328 | 0.779976 | ||||||||
\(584\) | −25.9659 | −1.07448 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.3607 | 1.74990 | ||||||||
\(587\) | −45.4311 | −1.87514 | −0.937570 | − | 0.347796i | \(-0.886930\pi\) | ||||
−0.937570 | + | 0.347796i | \(0.886930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.5410 | −0.763969 | ||||||||
\(590\) | 6.48218 | 0.266867 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 36.0000 | 1.47959 | ||||||||
\(593\) | −18.9737 | −0.779155 | −0.389578 | − | 0.920994i | \(-0.627379\pi\) | ||||
−0.389578 | + | 0.920994i | \(0.627379\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.291796 | −0.0119625 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.70820 | 0.0698537 | ||||||||
\(599\) | −14.5548 | −0.594693 | −0.297346 | − | 0.954770i | \(-0.596102\pi\) | ||||
−0.297346 | + | 0.954770i | \(0.596102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.58359 | −0.350132 | −0.175066 | − | 0.984557i | \(-0.556014\pi\) | ||||
−0.175066 | + | 0.984557i | \(0.556014\pi\) | |||||||
\(602\) | 0.667701 | 0.0272135 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.94355 | −0.282295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.12461 | −0.329768 | −0.164884 | − | 0.986313i | \(-0.552725\pi\) | ||||
−0.164884 | + | 0.986313i | \(0.552725\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.2361 | 0.535913 | ||||||||
\(611\) | −6.73722 | −0.272559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7082 | 0.755617 | 0.377809 | − | 0.925884i | \(-0.376678\pi\) | ||||
0.377809 | + | 0.925884i | \(0.376678\pi\) | |||||||
\(614\) | −10.4884 | −0.423277 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.94427 | 0.199210 | ||||||||
\(617\) | −2.74962 | −0.110695 | −0.0553477 | − | 0.998467i | \(-0.517627\pi\) | ||||
−0.0553477 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.4164 | −1.94602 | −0.973010 | − | 0.230764i | \(-0.925878\pi\) | ||||
−0.973010 | + | 0.230764i | \(0.925878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.8328 | 1.39667 | ||||||||
\(623\) | −1.74806 | −0.0700347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.1246 | 0.564984 | ||||||||
\(626\) | 18.7974 | 0.751297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00465 | 0.119803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.34752 | −0.252691 | −0.126345 | − | 0.991986i | \(-0.540325\pi\) | ||||
−0.126345 | + | 0.991986i | \(0.540325\pi\) | |||||||
\(632\) | 28.9520 | 1.15165 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.5279 | 0.934411 | ||||||||
\(635\) | −8.07262 | −0.320352 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | −0.237729 | ||||||||
\(638\) | 6.48218 | 0.256632 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.88854 | −0.390879 | ||||||||
\(641\) | −4.03631 | −0.159425 | −0.0797123 | − | 0.996818i | \(-0.525400\pi\) | ||||
−0.0797123 | + | 0.996818i | \(0.525400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.88854 | 0.0744769 | 0.0372384 | − | 0.999306i | \(-0.488144\pi\) | ||||
0.0372384 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.16718 | 0.124611 | ||||||||
\(647\) | −36.5632 | −1.43745 | −0.718724 | − | 0.695295i | \(-0.755274\pi\) | ||||
−0.718724 | + | 0.695295i | \(0.755274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.16718 | −0.359843 | ||||||||
\(650\) | 5.99070 | 0.234975 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.03321 | 0.0795655 | 0.0397828 | − | 0.999208i | \(-0.487333\pi\) | ||||
0.0397828 | + | 0.999208i | \(0.487333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.111456 | 0.00435495 | ||||||||
\(656\) | 20.4667 | 0.799090 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.52786 | 0.371435 | ||||||||
\(659\) | 7.81758 | 0.304530 | 0.152265 | − | 0.988340i | \(-0.451343\pi\) | ||||
0.152265 | + | 0.988340i | \(0.451343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.83282 | 0.304661 | 0.152331 | − | 0.988330i | \(-0.451322\pi\) | ||||
0.152331 | + | 0.988330i | \(0.451322\pi\) | |||||||
\(662\) | 19.7202 | 0.766447 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.3607 | 0.479687 | ||||||||
\(665\) | 5.86319 | 0.227365 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.16718 | 0.122634 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.1246 | 0.429781 | ||||||||
\(671\) | −18.7186 | −0.722625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.4721 | 0.596407 | 0.298204 | − | 0.954502i | \(-0.403613\pi\) | ||||
0.298204 | + | 0.954502i | \(0.403613\pi\) | |||||||
\(674\) | 17.3044 | 0.666541 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0810 | 1.15611 | 0.578054 | − | 0.815998i | \(-0.303812\pi\) | ||||
0.578054 | + | 0.815998i | \(0.303812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7082 | −0.410943 | ||||||||
\(680\) | −0.825324 | −0.0316497 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.83282 | 0.261642 | ||||||||
\(683\) | −29.2070 | −1.11758 | −0.558788 | − | 0.829311i | \(-0.688733\pi\) | ||||
−0.558788 | + | 0.829311i | \(0.688733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.291796 | 0.0111490 | ||||||||
\(686\) | 18.3848 | 0.701934 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.88854 | 0.0720001 | ||||||||
\(689\) | 10.7735 | 0.410439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3607 | 1.15497 | 0.577487 | − | 0.816400i | \(-0.304033\pi\) | ||||
0.577487 | + | 0.816400i | \(0.304033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −43.7082 | −1.65914 | ||||||||
\(695\) | 2.62210 | 0.0994618 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.70820 | 0.0647028 | ||||||||
\(698\) | −23.2163 | −0.878750 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.4195 | −0.809005 | −0.404502 | − | 0.914537i | \(-0.632555\pi\) | ||||
−0.404502 | + | 0.914537i | \(0.632555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.3738 | −2.27704 | ||||||||
\(704\) | 13.9845 | 0.527061 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.7082 | 1.79552 | ||||||||
\(707\) | 14.9374 | 0.561777 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.87539 | −0.220655 | −0.110327 | − | 0.993895i | \(-0.535190\pi\) | ||||
−0.110327 | + | 0.993895i | \(0.535190\pi\) | |||||||
\(710\) | 8.23024 | 0.308875 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.94427 | −0.185294 | ||||||||
\(713\) | 3.33851 | 0.125028 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.52786 | 0.0571389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7639 | 0.401706 | ||||||||
\(719\) | 49.0848 | 1.83055 | 0.915277 | − | 0.402824i | \(-0.131971\pi\) | ||||
0.915277 | + | 0.402824i | \(0.131971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.47214 | −0.129309 | ||||||||
\(722\) | −36.7696 | −1.36842 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.1074 | 0.412518 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.4164 | 0.423411 | 0.211706 | − | 0.977333i | \(-0.432098\pi\) | ||||
0.211706 | + | 0.977333i | \(0.432098\pi\) | |||||||
\(728\) | 2.82843 | 0.104828 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.3475 | 0.419991 | ||||||||
\(731\) | 0.157623 | 0.00582989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.87539 | 0.253948 | 0.126974 | − | 0.991906i | \(-0.459473\pi\) | ||||
0.126974 | + | 0.991906i | \(0.459473\pi\) | |||||||
\(734\) | 27.2827 | 1.00702 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.7326 | −0.579517 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5836 | −0.610037 | −0.305019 | − | 0.952346i | \(-0.598663\pi\) | ||||
−0.305019 | + | 0.952346i | \(0.598663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.2361 | −0.559334 | ||||||||
\(743\) | −46.2263 | −1.69588 | −0.847939 | − | 0.530094i | \(-0.822157\pi\) | ||||
−0.847939 | + | 0.530094i | \(0.822157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.00000 | −0.0732743 | ||||||||
\(746\) | 12.3153 | 0.450894 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.874032 | 0.0319364 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.94427 | 0.289891 | 0.144945 | − | 0.989440i | \(-0.453699\pi\) | ||||
0.144945 | + | 0.989440i | \(0.453699\pi\) | |||||||
\(752\) | 26.9489 | 0.982724 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.70820 | 0.135045 | ||||||||
\(755\) | −13.9358 | −0.507176 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.4721 | 0.562344 | 0.281172 | − | 0.959657i | \(-0.409277\pi\) | ||||
0.281172 | + | 0.959657i | \(0.409277\pi\) | |||||||
\(758\) | 7.07107 | 0.256833 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.5836 | 0.601550 | ||||||||
\(761\) | 10.0757 | 0.365245 | 0.182622 | − | 0.983183i | \(-0.441541\pi\) | ||||
0.182622 | + | 0.983183i | \(0.441541\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4164 | −0.485707 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.5967 | 1.28616 | ||||||||
\(767\) | −5.24419 | −0.189357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2361 | 0.369122 | 0.184561 | − | 0.982821i | \(-0.440914\pi\) | ||||
0.184561 | + | 0.982821i | \(0.440914\pi\) | |||||||
\(770\) | −2.16073 | −0.0778672 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.4497 | 1.20310 | 0.601550 | − | 0.798835i | \(-0.294550\pi\) | ||||
0.601550 | + | 0.798835i | \(0.294550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7082 | 0.420571 | ||||||||
\(776\) | −30.2874 | −1.08725 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.5410 | −1.23836 | ||||||||
\(779\) | −34.3237 | −1.22977 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.6393 | −0.416488 | ||||||||
\(782\) | −0.570285 | −0.0203933 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.0000 | 0.857143 | ||||||||
\(785\) | 11.7264 | 0.418532 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.81966 | −0.100510 | −0.0502550 | − | 0.998736i | \(-0.516003\pi\) | ||||
−0.0502550 | + | 0.998736i | \(0.516003\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.6525 | −0.450155 | ||||||||
\(791\) | 5.65685 | 0.201135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7082 | −0.380259 | ||||||||
\(794\) | 3.65375 | 0.129667 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.5285 | −1.18764 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.24922 | 0.0795718 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.0000 | 0.706225 | ||||||||
\(803\) | −16.0478 | −0.566315 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.05573 | −0.0372095 | ||||||||
\(806\) | 3.90879 | 0.137681 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 42.2492 | 1.48632 | ||||||||
\(809\) | 2.20943 | 0.0776796 | 0.0388398 | − | 0.999245i | \(-0.487634\pi\) | ||||
0.0388398 | + | 0.999245i | \(0.487634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.4164 | 0.400884 | 0.200442 | − | 0.979706i | \(-0.435762\pi\) | ||||
0.200442 | + | 0.979706i | \(0.435762\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.2492 | 0.779835 | ||||||||
\(815\) | 11.1074 | 0.389074 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.16718 | −0.110806 | ||||||||
\(818\) | −48.6722 | −1.70178 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.9929 | −1.25616 | −0.628081 | − | 0.778148i | \(-0.716159\pi\) | ||||
−0.628081 | + | 0.778148i | \(0.716159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.9574 | −1.70655 | −0.853274 | − | 0.521462i | \(-0.825387\pi\) | ||||
−0.853274 | + | 0.521462i | \(0.825387\pi\) | |||||||
\(824\) | −9.82068 | −0.342120 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.41641 | 0.258050 | ||||||||
\(827\) | −12.7279 | −0.442593 | −0.221297 | − | 0.975207i | \(-0.571029\pi\) | ||||
−0.221297 | + | 0.975207i | \(0.571029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.00000 | 0.173657 | 0.0868286 | − | 0.996223i | \(-0.472327\pi\) | ||||
0.0868286 | + | 0.996223i | \(0.472327\pi\) | |||||||
\(830\) | −5.40182 | −0.187500 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.00000 | 0.277350 | ||||||||
\(833\) | 2.00310 | 0.0694034 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.29180 | 0.0793109 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.3607 | 1.25606 | ||||||||
\(839\) | 43.3004 | 1.49490 | 0.747449 | − | 0.664320i | \(-0.231279\pi\) | ||||
0.747449 | + | 0.664320i | \(0.231279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1246 | −0.762918 | ||||||||
\(842\) | 48.2595 | 1.66313 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.4884 | −0.360811 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.94427 | −0.272968 | ||||||||
\(848\) | −43.0941 | −1.47986 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.00000 | −0.0685994 | ||||||||
\(851\) | 10.8709 | 0.372651 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7082 | 0.366642 | 0.183321 | − | 0.983053i | \(-0.441315\pi\) | ||||
0.183321 | + | 0.983053i | \(0.441315\pi\) | |||||||
\(854\) | 15.1437 | 0.518206 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.47214 | 0.0844959 | ||||||||
\(857\) | 50.0864 | 1.71092 | 0.855459 | − | 0.517871i | \(-0.173275\pi\) | ||||
0.855459 | + | 0.517871i | \(0.173275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9443 | −0.748729 | −0.374364 | − | 0.927282i | \(-0.622139\pi\) | ||||
−0.374364 | + | 0.927282i | \(0.622139\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.23607 | −0.0421006 | ||||||||
\(863\) | −20.9281 | −0.712399 | −0.356200 | − | 0.934410i | \(-0.615928\pi\) | ||||
−0.356200 | + | 0.934410i | \(0.615928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5967 | −0.462303 | ||||||||
\(866\) | −35.9442 | −1.22143 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8933 | 0.606989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00000 | −0.304953 | ||||||||
\(872\) | −37.9473 | −1.28506 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.4590 | 0.387606 | ||||||||
\(875\) | −8.07262 | −0.272904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.0132 | 1.21608 | 0.608039 | − | 0.793907i | \(-0.291956\pi\) | ||||
0.608039 | + | 0.793907i | \(0.291956\pi\) | |||||||
\(878\) | −31.3677 | −1.05861 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.11146 | −0.206017 | ||||||||
\(881\) | −56.9024 | −1.91709 | −0.958545 | − | 0.284941i | \(-0.908026\pi\) | ||||
−0.958545 | + | 0.284941i | \(0.908026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.87539 | 0.163792 | ||||||||
\(887\) | −2.82843 | −0.0949693 | −0.0474846 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474846 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.23607 | −0.309768 | ||||||||
\(890\) | 2.16073 | 0.0724277 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.1946 | −1.51238 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.1803 | 0.674554 | ||||||||
\(896\) | −11.3137 | −0.377964 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.4164 | 0.981638 | ||||||||
\(899\) | 7.24730 | 0.241711 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.59675 | −0.119825 | ||||||||
\(902\) | 12.6491 | 0.421169 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.0000 | 0.532152 | ||||||||
\(905\) | −17.1769 | −0.570979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.4164 | −1.40841 | −0.704207 | − | 0.709995i | \(-0.748697\pi\) | ||||
−0.704207 | + | 0.709995i | \(0.748697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.23607 | −0.0409753 | ||||||||
\(911\) | −36.3268 | −1.20356 | −0.601780 | − | 0.798662i | \(-0.705542\pi\) | ||||
−0.601780 | + | 0.798662i | \(0.705542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.63932 | 0.252825 | ||||||||
\(914\) | 46.8453 | 1.54950 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.127520 | 0.00421107 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.944272 | −0.0311487 | −0.0155743 | − | 0.999879i | \(-0.504958\pi\) | ||||
−0.0155743 | + | 0.999879i | \(0.504958\pi\) | |||||||
\(920\) | −2.98605 | −0.0984472 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −38.5410 | −1.26928 | ||||||||
\(923\) | −6.65841 | −0.219164 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.1246 | 1.25353 | ||||||||
\(926\) | 33.6073 | 1.10440 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.9163 | −1.76894 | −0.884469 | − | 0.466599i | \(-0.845479\pi\) | ||||
−0.884469 | + | 0.466599i | \(0.845479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.2492 | −1.31912 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.8328 | −0.616229 | ||||||||
\(935\) | −0.510078 | −0.0166813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.5410 | 1.35709 | 0.678543 | − | 0.734561i | \(-0.262612\pi\) | ||||
0.678543 | + | 0.734561i | \(0.262612\pi\) | |||||||
\(938\) | 12.7279 | 0.415581 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.48373 | 0.243963 | 0.121981 | − | 0.992532i | \(-0.461075\pi\) | ||||
0.121981 | + | 0.992532i | \(0.461075\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.18034 | 0.201260 | ||||||||
\(944\) | 20.9768 | 0.682736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.16718 | 0.0379484 | ||||||||
\(947\) | 39.1853 | 1.27335 | 0.636676 | − | 0.771132i | \(-0.280309\pi\) | ||||
0.636676 | + | 0.771132i | \(0.280309\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.18034 | −0.298006 | ||||||||
\(950\) | 40.1869 | 1.30383 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.944272 | −0.0306040 | ||||||||
\(953\) | 23.6290 | 0.765417 | 0.382709 | − | 0.923869i | \(-0.374991\pi\) | ||||
0.382709 | + | 0.923869i | \(0.374991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.70820 | 0.249432 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.7082 | 0.701360 | ||||||||
\(959\) | 0.333851 | 0.0107806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | 12.7279 | 0.410365 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.86629 | 0.253225 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4164 | 0.334969 | 0.167485 | − | 0.985875i | \(-0.446436\pi\) | ||||
0.167485 | + | 0.985875i | \(0.446436\pi\) | |||||||
\(968\) | −22.4698 | −0.722207 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.2361 | 0.424985 | ||||||||
\(971\) | −41.9836 | −1.34732 | −0.673660 | − | 0.739042i | \(-0.735279\pi\) | ||||
−0.673660 | + | 0.739042i | \(0.735279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.00000 | 0.0961756 | ||||||||
\(974\) | −26.4574 | −0.847750 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 42.8328 | 1.37105 | ||||||||
\(977\) | −8.61280 | −0.275548 | −0.137774 | − | 0.990464i | \(-0.543995\pi\) | ||||
−0.137774 | + | 0.990464i | \(0.543995\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.05573 | −0.0976615 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.6525 | −0.850515 | ||||||||
\(983\) | 8.69161 | 0.277219 | 0.138610 | − | 0.990347i | \(-0.455737\pi\) | ||||
0.138610 | + | 0.990347i | \(0.455737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.3050 | 0.551382 | ||||||||
\(986\) | −1.23799 | −0.0394255 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.570285 | 0.0181340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.70820 | −0.0860289 | −0.0430145 | − | 0.999074i | \(-0.513696\pi\) | ||||
−0.0430145 | + | 0.999074i | \(0.513696\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.41641 | 0.298670 | ||||||||
\(995\) | −5.45052 | −0.172793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0557 | 0.540160 | 0.270080 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270080 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(998\) | 28.6969 | 0.908386 | ||||||||
\(999\) | 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 | 6021.2.a.k.1.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 6021.2.a.k.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6021.2.a.k.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6021.2.a.k.1.3 | yes | 4 | 3.2 | odd | 2 | inner |