Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 24x^{4} + x^{3} - 35x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.78665\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −1.78665 | −1.03152 | −0.515761 | − | 0.856732i | \(-0.672491\pi\) | ||||
−0.515761 | + | 0.856732i | \(0.672491\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.75578 | −0.663622 | −0.331811 | − | 0.943346i | \(-0.607660\pi\) | ||||
−0.331811 | + | 0.943346i | \(0.607660\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.192116 | 0.0640385 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77574 | 1.43994 | 0.719970 | − | 0.694005i | \(-0.244155\pi\) | ||||
0.719970 | + | 0.694005i | \(0.244155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.72967 | 0.479724 | 0.239862 | − | 0.970807i | \(-0.422898\pi\) | ||||
0.239862 | + | 0.970807i | \(0.422898\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.81453 | −1.89530 | −0.947651 | − | 0.319309i | \(-0.896549\pi\) | ||||
−0.947651 | + | 0.319309i | \(0.896549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.43970 | 0.559706 | 0.279853 | − | 0.960043i | \(-0.409714\pi\) | ||||
0.279853 | + | 0.960043i | \(0.409714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.13696 | 0.684541 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.01670 | 0.965465 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.86235 | 1.46000 | 0.730001 | − | 0.683446i | \(-0.239520\pi\) | ||||
0.730001 | + | 0.683446i | \(0.239520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.14217 | −1.10317 | −0.551583 | − | 0.834120i | \(-0.685976\pi\) | ||||
−0.551583 | + | 0.834120i | \(0.685976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.53258 | −1.48533 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.83324 | −1.12338 | −0.561689 | − | 0.827349i | \(-0.689848\pi\) | ||||
−0.561689 | + | 0.827349i | \(0.689848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.09031 | −0.494846 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50416 | −0.391084 | −0.195542 | − | 0.980695i | \(-0.562647\pi\) | ||||
−0.195542 | + | 0.980695i | \(0.562647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.26755 | 0.498297 | 0.249148 | − | 0.968465i | \(-0.419849\pi\) | ||||
0.249148 | + | 0.968465i | \(0.419849\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.46487 | −1.23473 | −0.617364 | − | 0.786678i | \(-0.711799\pi\) | ||||
−0.617364 | + | 0.786678i | \(0.711799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.91724 | −0.559605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.9618 | 1.95505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.76559 | −0.379883 | −0.189942 | − | 0.981795i | \(-0.560830\pi\) | ||||
−0.189942 | + | 0.981795i | \(0.560830\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.35889 | −0.577349 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.91706 | −0.249580 | −0.124790 | − | 0.992183i | \(-0.539826\pi\) | ||||
−0.124790 | + | 0.992183i | \(0.539826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50364 | −0.448595 | −0.224297 | − | 0.974521i | \(-0.572009\pi\) | ||||
−0.224297 | + | 0.974521i | \(0.572009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.337313 | −0.0424974 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7649 | 1.55948 | 0.779741 | − | 0.626102i | \(-0.215351\pi\) | ||||
0.779741 | + | 0.626102i | \(0.215351\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.78665 | −0.215087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3973 | 1.58997 | 0.794984 | − | 0.606630i | \(-0.207479\pi\) | ||||
0.794984 | + | 0.606630i | \(0.207479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0111737 | 0.00130778 | 0.000653890 | − | 1.00000i | \(-0.499792\pi\) | ||||
0.000653890 | 1.00000i | \(0.499792\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.38515 | −0.955577 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.6960 | 1.87844 | 0.939222 | − | 0.343310i | \(-0.111548\pi\) | ||||
0.939222 | + | 0.343310i | \(0.111548\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.53944 | −1.05994 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.64145 | 0.289937 | 0.144969 | − | 0.989436i | \(-0.453692\pi\) | ||||
0.144969 | + | 0.989436i | \(0.453692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.0473 | −1.50602 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1729 | −1.39632 | −0.698160 | − | 0.715942i | \(-0.745998\pi\) | ||||
−0.698160 | + | 0.715942i | \(0.745998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.03692 | −0.318356 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9739 | 1.13794 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8568 | 1.61001 | 0.805005 | − | 0.593268i | \(-0.202162\pi\) | ||||
0.805005 | + | 0.593268i | \(0.202162\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.917494 | 0.0922117 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6987 | 1.56208 | 0.781040 | − | 0.624481i | \(-0.214689\pi\) | ||||
0.781040 | + | 0.624481i | \(0.214689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.37467 | −0.825180 | −0.412590 | − | 0.910917i | \(-0.635376\pi\) | ||||
−0.412590 | + | 0.910917i | \(0.635376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.52262 | 0.630565 | 0.315283 | − | 0.948998i | \(-0.397901\pi\) | ||||
0.315283 | + | 0.948998i | \(0.397901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.11474 | −0.777251 | −0.388626 | − | 0.921396i | \(-0.627050\pi\) | ||||
−0.388626 | + | 0.921396i | \(0.627050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2086 | 1.15879 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9224 | −1.21563 | −0.607817 | − | 0.794077i | \(-0.707955\pi\) | ||||
−0.607817 | + | 0.794077i | \(0.707955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.332296 | 0.0307208 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.7206 | 1.25776 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8077 | 1.07343 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.47406 | 0.403412 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.05406 | −0.625947 | −0.312973 | − | 0.949762i | \(-0.601325\pi\) | ||||
−0.312973 | + | 0.949762i | \(0.601325\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.83797 | −0.514004 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1585 | 0.974923 | 0.487461 | − | 0.873145i | \(-0.337923\pi\) | ||||
0.487461 | + | 0.873145i | \(0.337923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.28358 | −0.371434 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.71462 | 0.231926 | 0.115963 | − | 0.993254i | \(-0.463005\pi\) | ||||
0.115963 | + | 0.993254i | \(0.463005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0913 | −1.11039 | −0.555197 | − | 0.831719i | \(-0.687357\pi\) | ||||
−0.555197 | + | 0.831719i | \(0.687357\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.1238 | 1.27365 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.26046 | 0.690774 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.99873 | 0.577245 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0898 | −0.990435 | −0.495217 | − | 0.868769i | \(-0.664912\pi\) | ||||
−0.495217 | + | 0.868769i | \(0.664912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9430 | −1.21604 | −0.608021 | − | 0.793921i | \(-0.708036\pi\) | ||||
−0.608021 | + | 0.793921i | \(0.708036\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50129 | −0.121372 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.78395 | 0.381800 | 0.190900 | − | 0.981609i | \(-0.438859\pi\) | ||||
0.190900 | + | 0.981609i | \(0.438859\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.94114 | 0.391858 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.75578 | −0.138375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.49063 | −0.430059 | −0.215030 | − | 0.976608i | \(-0.568985\pi\) | ||||
−0.215030 | + | 0.976608i | \(0.568985\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.26932 | 0.562517 | 0.281258 | − | 0.959632i | \(-0.409248\pi\) | ||||
0.281258 | + | 0.959632i | \(0.409248\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0082 | −0.769865 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.468705 | 0.0358427 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50892 | −0.570893 | −0.285446 | − | 0.958395i | \(-0.592142\pi\) | ||||
−0.285446 | + | 0.958395i | \(0.592142\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.42511 | 0.257447 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.73414 | 0.428590 | 0.214295 | − | 0.976769i | \(-0.431255\pi\) | ||||
0.214295 | + | 0.976769i | \(0.431255\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.2262 | 1.87505 | 0.937523 | − | 0.347923i | \(-0.113113\pi\) | ||||
0.937523 | + | 0.347923i | \(0.113113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.25977 | 0.462736 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −37.3202 | −2.72912 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.80823 | −0.640704 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.63151 | −0.262767 | −0.131383 | − | 0.991332i | \(-0.541942\pi\) | ||||
−0.131383 | + | 0.991332i | \(0.541942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7050 | 1.56236 | 0.781179 | − | 0.624307i | \(-0.214619\pi\) | ||||
0.781179 | + | 0.624307i | \(0.214619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.26526 | 0.517628 | 0.258814 | − | 0.965927i | \(-0.416668\pi\) | ||||
0.258814 | + | 0.965927i | \(0.416668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.52705 | −0.462690 | −0.231345 | − | 0.972872i | \(-0.574313\pi\) | ||||
−0.231345 | + | 0.972872i | \(0.574313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.8064 | −1.60864 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8046 | −0.968890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.192116 | 0.0133530 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6514 | 0.805944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7856 | 1.56863 | 0.784313 | − | 0.620365i | \(-0.213016\pi\) | ||||
0.784313 | + | 0.620365i | \(0.213016\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.9363 | −1.64009 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.7843 | 0.732086 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0199634 | −0.00134900 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5165 | −0.909221 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.86315 | −0.459591 | −0.229795 | − | 0.973239i | \(-0.573806\pi\) | ||||
−0.229795 | + | 0.973239i | \(0.573806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.5001 | −1.16152 | −0.580761 | − | 0.814074i | \(-0.697245\pi\) | ||||
−0.580761 | + | 0.814074i | \(0.697245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.8643 | −1.57700 | −0.788498 | − | 0.615038i | \(-0.789141\pi\) | ||||
−0.788498 | + | 0.615038i | \(0.789141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.9813 | 0.985699 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.8957 | −1.43444 | −0.717218 | − | 0.696849i | \(-0.754585\pi\) | ||||
−0.717218 | + | 0.696849i | \(0.754585\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.8299 | −1.93766 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3443 | 1.25128 | 0.625639 | − | 0.780113i | \(-0.284838\pi\) | ||||
0.625639 | + | 0.780113i | \(0.284838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4761 | 0.739240 | 0.369620 | − | 0.929183i | \(-0.379488\pi\) | ||||
0.369620 | + | 0.929183i | \(0.379488\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.99352 | 0.127884 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.21988 | 0.268504 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.71935 | −0.299077 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.0040 | −1.07328 | −0.536641 | − | 0.843811i | \(-0.680307\pi\) | ||||
−0.536641 | + | 0.843811i | \(0.680307\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.77574 | 0.300248 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.6462 | −0.913607 | −0.456803 | − | 0.889568i | \(-0.651006\pi\) | ||||
−0.456803 | + | 0.889568i | \(0.651006\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9977 | 0.745499 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.51048 | 0.0934964 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.2641 | −0.632912 | −0.316456 | − | 0.948607i | \(-0.602493\pi\) | ||||
−0.316456 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.5353 | 1.44034 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.61485 | −0.159430 | −0.0797150 | − | 0.996818i | \(-0.525401\pi\) | ||||
−0.0797150 | + | 0.996818i | \(0.525401\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.87492 | −0.599859 | −0.299929 | − | 0.953961i | \(-0.596963\pi\) | ||||
−0.299929 | + | 0.953961i | \(0.596963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.42591 | 0.328391 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.21949 | −0.253525 | −0.126762 | − | 0.991933i | \(-0.540459\pi\) | ||||
−0.126762 | + | 0.991933i | \(0.540459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.18001 | −0.0706451 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4058 | −0.799724 | −0.399862 | − | 0.916575i | \(-0.630942\pi\) | ||||
−0.399862 | + | 0.916575i | \(0.630942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.66084 | 0.336502 | 0.168251 | − | 0.985744i | \(-0.446188\pi\) | ||||
0.168251 | + | 0.985744i | \(0.446188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.39676 | 0.259532 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.0668 | 2.59217 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.3305 | −1.66076 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.70404 | 0.333233 | 0.166617 | − | 0.986022i | \(-0.446716\pi\) | ||||
0.166617 | + | 0.986022i | \(0.446716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.9585 | 1.39021 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.72967 | 0.100029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.73710 | −0.330681 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.0481 | −1.61132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.8943 | −0.850065 | −0.425033 | − | 0.905178i | \(-0.639737\pi\) | ||||
−0.425033 | + | 0.905178i | \(0.639737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9626 | 0.851192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0355 | 0.569059 | 0.284530 | − | 0.958667i | \(-0.408163\pi\) | ||||
0.284530 | + | 0.958667i | \(0.408163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5043 | −1.32854 | −0.664272 | − | 0.747491i | \(-0.731258\pi\) | ||||
−0.664272 | + | 0.747491i | \(0.731258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.94093 | −0.446007 | −0.223004 | − | 0.974818i | \(-0.571586\pi\) | ||||
−0.223004 | + | 0.974818i | \(0.571586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.5486 | 2.10232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.6536 | −0.650442 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.0651 | −1.06081 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.4982 | 0.801752 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8625 | 0.819393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.31442 | −0.347072 | −0.173536 | − | 0.984828i | \(-0.555519\pi\) | ||||
−0.173536 | + | 0.984828i | \(0.555519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.31277 | −0.0719394 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.4516 | 1.27749 | 0.638746 | − | 0.769418i | \(-0.279453\pi\) | ||||
0.638746 | + | 0.769418i | \(0.279453\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.0877 | 1.25395 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.3334 | −1.58849 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1683 | 1.03499 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4757 | 0.830780 | 0.415390 | − | 0.909643i | \(-0.363645\pi\) | ||||
0.415390 | + | 0.909643i | \(0.363645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.5514 | −1.36773 | −0.683867 | − | 0.729607i | \(-0.739703\pi\) | ||||
−0.683867 | + | 0.729607i | \(0.739703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.67724 | 0.463157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.5917 | 1.25566 | 0.627829 | − | 0.778352i | \(-0.283944\pi\) | ||||
0.627829 | + | 0.778352i | \(0.283944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.5139 | −1.29741 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.14840 | −0.166166 | −0.0830832 | − | 0.996543i | \(-0.526477\pi\) | ||||
−0.0830832 | + | 0.996543i | \(0.526477\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0479 | −0.686729 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0963 | −1.10727 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.4297 | −1.69282 | −0.846408 | − | 0.532534i | \(-0.821240\pi\) | ||||
−0.846408 | + | 0.532534i | \(0.821240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.481088 | −0.0250445 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.85577 | 0.252099 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.99302 | −0.413863 | −0.206931 | − | 0.978355i | \(-0.566348\pi\) | ||||
−0.206931 | + | 0.978355i | \(0.566348\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5993 | 0.700398 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.96061 | −0.460275 | −0.230138 | − | 0.973158i | \(-0.573918\pi\) | ||||
−0.230138 | + | 0.973158i | \(0.573918\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6031 | 0.645678 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.7195 | −1.87628 | −0.938141 | − | 0.346255i | \(-0.887453\pi\) | ||||
−0.938141 | + | 0.346255i | \(0.887453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.627747 | 0.0319102 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0627294 | 0.00318051 | 0.00159025 | − | 0.999999i | \(-0.499494\pi\) | ||||
0.00159025 | + | 0.999999i | \(0.499494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.81453 | −0.395198 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.9363 | −1.00565 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.9714 | −1.05252 | −0.526262 | − | 0.850323i | \(-0.676407\pi\) | ||||
−0.526262 | + | 0.850323i | \(0.676407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.65326 | 0.383142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8567 | −0.691972 | −0.345986 | − | 0.938240i | \(-0.612456\pi\) | ||||
−0.345986 | + | 0.938240i | \(0.612456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.6239 | −0.529215 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.6338 | −1.61760 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.5868 | 0.622378 | 0.311189 | − | 0.950348i | \(-0.399273\pi\) | ||||
0.311189 | + | 0.950348i | \(0.399273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.85007 | −0.239236 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.36593 | 0.165627 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.3896 | 1.14540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.4927 | 1.58737 | 0.793685 | − | 0.608328i | \(-0.208160\pi\) | ||||
0.793685 | + | 0.608328i | \(0.208160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8356 | 0.917992 | 0.458996 | − | 0.888438i | \(-0.348209\pi\) | ||||
0.458996 | + | 0.888438i | \(0.348209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.62623 | −0.0790702 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.15162 | 0.297698 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.7585 | −0.712549 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.66739 | −0.0803155 | −0.0401577 | − | 0.999193i | \(-0.512786\pi\) | ||||
−0.0401577 | + | 0.999193i | \(0.512786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.83595 | −0.280458 | −0.140229 | − | 0.990119i | \(-0.544784\pi\) | ||||
−0.140229 | + | 0.990119i | \(0.544784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.43970 | 0.116707 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.5742 | −1.45923 | −0.729614 | − | 0.683860i | \(-0.760300\pi\) | ||||
−0.729614 | + | 0.683860i | \(0.760300\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.752562 | −0.0358363 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.9173 | −1.65897 | −0.829485 | − | 0.558530i | \(-0.811366\pi\) | ||||
−0.829485 | + | 0.558530i | \(0.811366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.6002 | 1.02166 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.1265 | −1.56334 | −0.781668 | − | 0.623694i | \(-0.785631\pi\) | ||||
−0.781668 | + | 0.623694i | \(0.785631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9592 | −0.563138 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.6978 | 1.25437 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.27252 | 0.199860 | 0.0999299 | − | 0.994994i | \(-0.468138\pi\) | ||||
0.0999299 | + | 0.994994i | \(0.468138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −39.2032 | −1.82985 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.4702 | −1.79173 | −0.895867 | − | 0.444322i | \(-0.853444\pi\) | ||||
−0.895867 | + | 0.444322i | \(0.853444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.94727 | 0.415815 | 0.207908 | − | 0.978148i | \(-0.433335\pi\) | ||||
0.207908 | + | 0.978148i | \(0.433335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.3171 | 0.755064 | 0.377532 | − | 0.925996i | \(-0.376773\pi\) | ||||
0.377532 | + | 0.925996i | \(0.376773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.4124 | −1.03491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.54723 | −0.393836 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.6050 | 0.717518 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.531313 | −0.0243272 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.9574 | −0.546349 | −0.273174 | − | 0.961965i | \(-0.588074\pi\) | ||||
−0.273174 | + | 0.961965i | \(0.588074\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8192 | −0.538911 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.13696 | 0.142737 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.19495 | −0.0541484 | −0.0270742 | − | 0.999633i | \(-0.508619\pi\) | ||||
−0.0270742 | + | 0.999633i | \(0.508619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.80982 | 0.443616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.6912 | 0.617874 | 0.308937 | − | 0.951083i | \(-0.400027\pi\) | ||||
0.308937 | + | 0.951083i | \(0.400027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −61.4406 | −2.76714 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.5227 | −1.05514 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.9774 | −0.536184 | −0.268092 | − | 0.963393i | \(-0.586393\pi\) | ||||
−0.268092 | + | 0.963393i | \(0.586393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9877 | −0.580249 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.3666 | −1.44316 | −0.721578 | − | 0.692333i | \(-0.756583\pi\) | ||||
−0.721578 | + | 0.692333i | \(0.756583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8812 | 0.794133 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6507 | 0.693706 | 0.346853 | − | 0.937919i | \(-0.387250\pi\) | ||||
0.346853 | + | 0.937919i | \(0.387250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0196185 | −0.000867872 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.2393 | 0.540377 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.4261 | −1.77794 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.4158 | 0.588889 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7184 | 0.951499 | 0.475749 | − | 0.879581i | \(-0.342177\pi\) | ||||
0.475749 | + | 0.879581i | \(0.342177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.89014 | −0.388739 | −0.194369 | − | 0.980928i | \(-0.562266\pi\) | ||||
−0.194369 | + | 0.980928i | \(0.562266\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.9981 | 2.09083 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.368297 | −0.0159827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.33137 | −0.187613 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.2449 | −0.442100 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.7077 | −0.805798 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0112 | −1.24729 | −0.623645 | − | 0.781708i | \(-0.714349\pi\) | ||||
−0.623645 | + | 0.781708i | \(0.714349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −45.0703 | −1.93415 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9089 | −1.06503 | −0.532514 | − | 0.846421i | \(-0.678753\pi\) | ||||
−0.532514 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.673103 | −0.0287273 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.1818 | 0.817172 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.3145 | −1.24658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.3536 | 0.650552 | 0.325276 | − | 0.945619i | \(-0.394543\pi\) | ||||
0.325276 | + | 0.945619i | \(0.394543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.65178 | 0.239045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 66.6781 | 2.81515 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.8264 | 0.709146 | 0.354573 | − | 0.935028i | \(-0.384626\pi\) | ||||
0.354573 | + | 0.935028i | \(0.384626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.7492 | 0.703398 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.75646 | 0.0736344 | 0.0368172 | − | 0.999322i | \(-0.488278\pi\) | ||||
0.0368172 | + | 0.999322i | \(0.488278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.4273 | −0.561913 | −0.280956 | − | 0.959721i | \(-0.590652\pi\) | ||||
−0.280956 | + | 0.959721i | \(0.590652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.48823 | 0.271050 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.4806 | −0.852620 | −0.426310 | − | 0.904577i | \(-0.640187\pi\) | ||||
−0.426310 | + | 0.904577i | \(0.640187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.7792 | −1.61161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.63781 | −0.192409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.2078 | −0.547010 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.3569 | −1.87208 | −0.936040 | − | 0.351893i | \(-0.885538\pi\) | ||||
−0.936040 | + | 0.351893i | \(0.885538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.9851 | −0.617449 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9805 | −0.533945 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.8520 | −1.18481 | −0.592404 | − | 0.805641i | \(-0.701821\pi\) | ||||
−0.592404 | + | 0.805641i | \(0.701821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.6615 | 0.477275 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.78767 | −0.359054 | −0.179527 | − | 0.983753i | \(-0.557457\pi\) | ||||
−0.179527 | + | 0.983753i | \(0.557457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.7810 | −1.82665 | −0.913327 | − | 0.407227i | \(-0.866496\pi\) | ||||
−0.913327 | + | 0.407227i | \(0.866496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.45234 | 0.0998669 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.96387 | −0.282655 | −0.141327 | − | 0.989963i | \(-0.545137\pi\) | ||||
−0.141327 | + | 0.989963i | \(0.545137\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.6639 | 0.999432 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6414 | −0.592329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.6214 | 1.23679 | 0.618393 | − | 0.785869i | \(-0.287784\pi\) | ||||
0.618393 | + | 0.785869i | \(0.287784\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6041 | 0.426905 | 0.213452 | − | 0.976953i | \(-0.431529\pi\) | ||||
0.213452 | + | 0.976953i | \(0.431529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.0095 | −0.844445 | −0.422223 | − | 0.906492i | \(-0.638750\pi\) | ||||
−0.422223 | + | 0.906492i | \(0.638750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.01670 | 0.201313 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.1286 | 0.926629 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.8170 | −0.831349 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.3985 | 2.12914 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.45489 | −0.217156 | −0.108578 | − | 0.994088i | \(-0.534630\pi\) | ||||
−0.108578 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −40.7099 | −1.61807 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.77552 | −0.268456 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.57383 | 0.101819 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.7734 | −1.13648 | −0.568241 | − | 0.822862i | \(-0.692376\pi\) | ||||
−0.568241 | + | 0.822862i | \(0.692376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5319 | 0.454775 | 0.227388 | − | 0.973804i | \(-0.426982\pi\) | ||||
0.227388 | + | 0.973804i | \(0.426982\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.18564 | 0.125240 | 0.0626202 | − | 0.998037i | \(-0.480054\pi\) | ||||
0.0626202 | + | 0.998037i | \(0.480054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.15538 | −0.359380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.2678 | −0.755163 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.6814 | −1.12239 | −0.561194 | − | 0.827684i | \(-0.689658\pi\) | ||||
−0.561194 | + | 0.827684i | \(0.689658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.00214664 | 8.37483e−5 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.0012 | −0.934954 | −0.467477 | − | 0.884005i | \(-0.654837\pi\) | ||||
−0.467477 | + | 0.884005i | \(0.654837\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.9043 | 1.24093 | 0.620467 | − | 0.784232i | \(-0.286943\pi\) | ||||
0.620467 | + | 0.784232i | \(0.286943\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.1493 | 0.937882 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.86235 | 0.304431 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.2620 | 0.474078 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.7325 | −0.645950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.87848 | −0.0724101 | −0.0362051 | − | 0.999344i | \(-0.511527\pi\) | ||||
−0.0362051 | + | 0.999344i | \(0.511527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.6119 | 1.33024 | 0.665121 | − | 0.746736i | \(-0.268380\pi\) | ||||
0.665121 | + | 0.746736i | \(0.268380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.8410 | −1.06844 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.2665 | 1.19814 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0493 | 0.614110 | 0.307055 | − | 0.951692i | \(-0.400656\pi\) | ||||
0.307055 | + | 0.951692i | \(0.400656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.6371 | 1.62671 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.78356 | −0.182239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5985 | 0.745564 | 0.372782 | − | 0.927919i | \(-0.378404\pi\) | ||||
0.372782 | + | 0.927919i | \(0.378404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.61092 | −0.0611937 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.5688 | 0.741223 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.1199 | 1.47965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.5536 | −1.94715 | −0.973575 | − | 0.228366i | \(-0.926662\pi\) | ||||
−0.973575 | + | 0.228366i | \(0.926662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6711 | −0.628761 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.5635 | −1.03663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.64772 | 0.324772 | 0.162386 | − | 0.986727i | \(-0.448081\pi\) | ||||
0.162386 | + | 0.986727i | \(0.448081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.20756 | 0.120293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.14217 | −0.230026 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.5615 | −1.29072 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.50754 | 0.279984 | 0.139992 | − | 0.990153i | \(-0.455292\pi\) | ||||
0.139992 | + | 0.990153i | \(0.455292\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7041 | 0.547608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.5037 | −0.762543 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.79852 | −0.103791 | −0.0518956 | − | 0.998653i | \(-0.516526\pi\) | ||||
−0.0518956 | + | 0.998653i | \(0.516526\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.0566 | 0.928022 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.5344 | −0.944423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.38900 | −0.0513038 | −0.0256519 | − | 0.999671i | \(-0.508166\pi\) | ||||
−0.0256519 | + | 0.999671i | \(0.508166\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.9619 | 2.24556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.31935 | −0.232461 | −0.116230 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116230 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.53944 | −0.276968 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7611 | 1.45869 | 0.729347 | − | 0.684144i | \(-0.239824\pi\) | ||||
0.729347 | + | 0.684144i | \(0.239824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.507464 | 0.0185671 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.4523 | −0.418457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.27267 | −0.265384 | −0.132692 | − | 0.991157i | \(-0.542362\pi\) | ||||
−0.132692 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.3801 | 1.10711 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8682 | 0.576739 | 0.288369 | − | 0.957519i | \(-0.406887\pi\) | ||||
0.288369 | + | 0.957519i | \(0.406887\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.53258 | −0.309713 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.80457 | −0.174166 | −0.0870828 | − | 0.996201i | \(-0.527754\pi\) | ||||
−0.0870828 | + | 0.996201i | \(0.527754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2477 | 0.515801 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.31588 | −0.119729 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1358 | 1.08673 | 0.543363 | − | 0.839498i | \(-0.317151\pi\) | ||||
0.543363 | + | 0.839498i | \(0.317151\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.1677 | 0.942406 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.35253 | 0.120582 | 0.0602910 | − | 0.998181i | \(-0.480797\pi\) | ||||
0.0602910 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.4356 | −0.768999 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.10941 | −0.218892 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 63.9821 | 2.28946 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.4431 | 1.40958 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.36807 | −0.0844126 | −0.0422063 | − | 0.999109i | \(-0.513439\pi\) | ||||
−0.0422063 | + | 0.999109i | \(0.513439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.3384 | 0.652863 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.6888 | 0.806722 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.06013 | −0.215202 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0367 | −1.17022 | −0.585110 | − | 0.810954i | \(-0.698949\pi\) | ||||
−0.585110 | + | 0.810954i | \(0.698949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 66.1490 | 2.34018 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.53071 | −0.0894183 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0533626 | 0.00188313 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.67181 | 0.164456 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.7157 | −0.587692 | −0.293846 | − | 0.955853i | \(-0.594935\pi\) | ||||
−0.293846 | + | 0.955853i | \(0.594935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.85752 | 0.205685 | 0.102843 | − | 0.994698i | \(-0.467206\pi\) | ||||
0.102843 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.6430 | 0.618768 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.97185 | 0.278900 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.583439 | −0.0203870 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.3966 | 0.921249 | 0.460625 | − | 0.887595i | \(-0.347625\pi\) | ||||
0.460625 | + | 0.887595i | \(0.347625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5803 | 0.891672 | 0.445836 | − | 0.895115i | \(-0.352906\pi\) | ||||
0.445836 | + | 0.895115i | \(0.352906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.74132 | −0.338739 | −0.169369 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169369 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.7679 | −1.90217 | −0.951085 | − | 0.308931i | \(-0.900029\pi\) | ||||
−0.951085 | + | 0.308931i | \(0.900029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.53875 | 0.261516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.6114 | 1.06062 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.8134 | −1.06507 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.2171 | 1.76821 | 0.884106 | − | 0.467286i | \(-0.154768\pi\) | ||||
0.884106 | + | 0.467286i | \(0.154768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.8166 | 1.13161 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.9515 | 0.824933 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.7318 | −0.712352 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.1139 | −0.347109 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.83324 | −0.234240 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.2520 | −0.796135 | −0.398067 | − | 0.917356i | \(-0.630319\pi\) | ||||
−0.398067 | + | 0.917356i | \(0.630319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.8722 | 1.66944 | 0.834721 | − | 0.550674i | \(-0.185629\pi\) | ||||
0.834721 | + | 0.550674i | \(0.185629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7171 | 0.433903 | 0.216952 | − | 0.976182i | \(-0.430389\pi\) | ||||
0.216952 | + | 0.976182i | \(0.430389\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.85546 | −0.267713 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.5511 | 0.461285 | 0.230642 | − | 0.973039i | \(-0.425917\pi\) | ||||
0.230642 | + | 0.973039i | \(0.425917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −78.7320 | −2.67388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 79.7357 | 2.70485 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.0791 | 0.748121 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.04633 | 0.103103 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.88341 | −0.164901 | −0.0824505 | − | 0.996595i | \(-0.526275\pi\) | ||||
−0.0824505 | + | 0.996595i | \(0.526275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.1911 | −0.343738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.5717 | −0.760461 | −0.380230 | − | 0.924892i | \(-0.624155\pi\) | ||||
−0.380230 | + | 0.924892i | \(0.624155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.202906 | −0.00682834 | −0.00341417 | − | 0.999994i | \(-0.501087\pi\) | ||||
−0.00341417 | + | 0.999994i | \(0.501087\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.1859 | −0.644201 | −0.322100 | − | 0.946705i | \(-0.604389\pi\) | ||||
−0.322100 | + | 0.946705i | \(0.604389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.3854 | 0.415392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.5579 | −1.52625 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.6518 | −0.691085 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.09031 | −0.103183 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.2919 | −1.61062 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.6118 | 0.719993 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.2502 | 0.341105 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9713 | 0.430704 | 0.215352 | − | 0.976536i | \(-0.430910\pi\) | ||||
0.215352 | + | 0.976536i | \(0.430910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.01597 | 0.100033 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3377 | −1.03826 | −0.519132 | − | 0.854694i | \(-0.673745\pi\) | ||||
−0.519132 | + | 0.854694i | \(0.673745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.6149 | 0.417492 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.5919 | −0.646980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.4577 | −1.26860 | −0.634302 | − | 0.773085i | \(-0.718712\pi\) | ||||
−0.634302 | + | 0.773085i | \(0.718712\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.6110 | 0.876861 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.1729 | 0.762746 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.60890 | −0.0528433 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.3396 | −1.78282 | −0.891412 | − | 0.453193i | \(-0.850285\pi\) | ||||
−0.891412 | + | 0.453193i | \(0.850285\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.55689 | −0.313215 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.9299 | −0.586998 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.1182 | −1.40861 | −0.704304 | − | 0.709898i | \(-0.748741\pi\) | ||||
−0.704304 | + | 0.709898i | \(0.748741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.9940 | 1.37042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.22344 | 0.300676 | 0.150338 | − | 0.988635i | \(-0.451964\pi\) | ||||
0.150338 | + | 0.988635i | \(0.451964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.50416 | −0.0815467 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.8127 | 1.48871 | 0.744357 | − | 0.667782i | \(-0.232756\pi\) | ||||
0.744357 | + | 0.667782i | \(0.232756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0193268 | 0.000627374 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1877 | 0.460066 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2363 | 0.687913 | 0.343956 | − | 0.938986i | \(-0.388233\pi\) | ||||
0.343956 | + | 0.938986i | \(0.388233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −67.0861 | −2.16859 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.76627 | −0.153911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.72623 | 0.216975 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.25310 | 0.0403805 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.88651 | −0.189297 | −0.0946486 | − | 0.995511i | \(-0.530173\pi\) | ||||
−0.0946486 | + | 0.995511i | \(0.530173\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.0627 | 1.09425 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.1841 | −0.872378 | −0.436189 | − | 0.899855i | \(-0.643672\pi\) | ||||
−0.436189 | + | 0.899855i | \(0.643672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.9855 | 0.736882 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.5280 | −1.55255 | −0.776274 | − | 0.630395i | \(-0.782893\pi\) | ||||
−0.776274 | + | 0.630395i | \(0.782893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.9102 | −2.01062 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.55897 | −0.0497740 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.7935 | −1.62006 | −0.810030 | − | 0.586388i | \(-0.800549\pi\) | ||||
−0.810030 | + | 0.586388i | \(0.800549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.5540 | −0.845223 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.26755 | 0.103902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.42740 | 0.299471 | 0.149736 | − | 0.988726i | \(-0.452158\pi\) | ||||
0.149736 | + | 0.988726i | \(0.452158\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.2816 | 0.358012 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.78817 | 0.214984 | 0.107492 | − | 0.994206i | \(-0.465718\pi\) | ||||
0.107492 | + | 0.994206i | \(0.465718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.2803 | −1.08458 |
(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 | 9200.2.a.cz.1.2 | 7 | ||
4.3 | odd | 2 | 4600.2.a.bi.1.6 | 7 | |||
5.2 | odd | 4 | 1840.2.e.g.369.12 | 14 | |||
5.3 | odd | 4 | 1840.2.e.g.369.3 | 14 | |||
5.4 | even | 2 | 9200.2.a.dc.1.6 | 7 | |||
20.3 | even | 4 | 920.2.e.b.369.12 | yes | 14 | ||
20.7 | even | 4 | 920.2.e.b.369.3 | ✓ | 14 | ||
20.19 | odd | 2 | 4600.2.a.bh.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.3 | ✓ | 14 | 20.7 | even | 4 | ||
920.2.e.b.369.12 | yes | 14 | 20.3 | even | 4 | ||
1840.2.e.g.369.3 | 14 | 5.3 | odd | 4 | |||
1840.2.e.g.369.12 | 14 | 5.2 | odd | 4 | |||
4600.2.a.bh.1.2 | 7 | 20.19 | odd | 2 | |||
4600.2.a.bi.1.6 | 7 | 4.3 | odd | 2 | |||
9200.2.a.cz.1.2 | 7 | 1.1 | even | 1 | trivial | ||
9200.2.a.dc.1.6 | 7 | 5.4 | even | 2 |