Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 26x^{8} + 82x^{7} + 211x^{6} - 340x^{5} - 593x^{4} + 192x^{3} + 423x^{2} + 126x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.19255\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.553287 | −0.247438 | −0.123719 | − | 0.992317i | \(-0.539482\pi\) | ||||
−0.123719 | + | 0.992317i | \(0.539482\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.19255 | −0.450741 | −0.225370 | − | 0.974273i | \(-0.572359\pi\) | ||||
−0.225370 | + | 0.974273i | \(0.572359\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.843505 | −0.254326 | −0.127163 | − | 0.991882i | \(-0.540587\pi\) | ||||
−0.127163 | + | 0.991882i | \(0.540587\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93872 | 0.815054 | 0.407527 | − | 0.913193i | \(-0.366391\pi\) | ||||
0.407527 | + | 0.913193i | \(0.366391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.89858 | −0.945544 | −0.472772 | − | 0.881185i | \(-0.656747\pi\) | ||||
−0.472772 | + | 0.881185i | \(0.656747\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.92245 | −0.899873 | −0.449936 | − | 0.893061i | \(-0.648553\pi\) | ||||
−0.449936 | + | 0.893061i | \(0.648553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.42491 | 0.714143 | 0.357072 | − | 0.934077i | \(-0.383775\pi\) | ||||
0.357072 | + | 0.934077i | \(0.383775\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69387 | −0.938775 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.30275 | 1.54178 | 0.770891 | − | 0.636968i | \(-0.219812\pi\) | ||||
0.770891 | + | 0.636968i | \(0.219812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.13278 | 1.28109 | 0.640543 | − | 0.767923i | \(-0.278709\pi\) | ||||
0.640543 | + | 0.767923i | \(0.278709\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.659822 | 0.111530 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.02924 | 0.826802 | 0.413401 | − | 0.910549i | \(-0.364341\pi\) | ||||
0.413401 | + | 0.910549i | \(0.364341\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.17577 | −1.27684 | −0.638420 | − | 0.769688i | \(-0.720412\pi\) | ||||
−0.638420 | + | 0.769688i | \(0.720412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.35576 | 1.42674 | 0.713370 | − | 0.700788i | \(-0.247168\pi\) | ||||
0.713370 | + | 0.700788i | \(0.247168\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.99954 | −1.02099 | −0.510494 | − | 0.859881i | \(-0.670537\pi\) | ||||
−0.510494 | + | 0.859881i | \(0.670537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.57783 | −0.796833 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.65547 | 0.639477 | 0.319739 | − | 0.947506i | \(-0.396405\pi\) | ||||
0.319739 | + | 0.947506i | \(0.396405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.466701 | 0.0629299 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.45570 | −0.710272 | −0.355136 | − | 0.934815i | \(-0.615565\pi\) | ||||
−0.355136 | + | 0.934815i | \(0.615565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.19050 | 0.152428 | 0.0762142 | − | 0.997091i | \(-0.475717\pi\) | ||||
0.0762142 | + | 0.997091i | \(0.475717\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.62595 | −0.201675 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.61950 | −0.686531 | −0.343265 | − | 0.939238i | \(-0.611533\pi\) | ||||
−0.343265 | + | 0.939238i | \(0.611533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1882 | −1.20912 | −0.604560 | − | 0.796559i | \(-0.706651\pi\) | ||||
−0.604560 | + | 0.796559i | \(0.706651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.81452 | 0.446456 | 0.223228 | − | 0.974766i | \(-0.428341\pi\) | ||||
0.223228 | + | 0.974766i | \(0.428341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00592 | 0.114635 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.65506 | 0.298718 | 0.149359 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149359 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.17199 | −0.787228 | −0.393614 | − | 0.919276i | \(-0.628775\pi\) | ||||
−0.393614 | + | 0.919276i | \(0.628775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.15703 | 0.233963 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0346287 | 0.00367063 | 0.00183531 | − | 0.999998i | \(-0.499416\pi\) | ||||
0.00183531 | + | 0.999998i | \(0.499416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50456 | −0.367378 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.17024 | 0.222662 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0201 | −1.62659 | −0.813296 | − | 0.581851i | \(-0.802329\pi\) | ||||
−0.813296 | + | 0.581851i | \(0.802329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.26340 | −0.324721 | −0.162360 | − | 0.986732i | \(-0.551911\pi\) | ||||
−0.162360 | + | 0.986732i | \(0.551911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.52096 | 0.346930 | 0.173465 | − | 0.984840i | \(-0.444504\pi\) | ||||
0.173465 | + | 0.984840i | \(0.444504\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.0090 | −1.25762 | −0.628811 | − | 0.777558i | \(-0.716458\pi\) | ||||
−0.628811 | + | 0.777558i | \(0.716458\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.62330 | −0.538615 | −0.269307 | − | 0.963054i | \(-0.586795\pi\) | ||||
−0.269307 | + | 0.963054i | \(0.586795\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.78699 | −0.638466 | −0.319233 | − | 0.947676i | \(-0.603425\pi\) | ||||
−0.319233 | + | 0.947676i | \(0.603425\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.89496 | −0.176706 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.64924 | 0.426196 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2885 | −0.935318 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.36350 | 0.479726 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5685 | −1.02654 | −0.513268 | − | 0.858228i | \(-0.671565\pi\) | ||||
−0.513268 | + | 0.858228i | \(0.671565\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6410 | −0.929708 | −0.464854 | − | 0.885387i | \(-0.653893\pi\) | ||||
−0.464854 | + | 0.885387i | \(0.653893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.67772 | 0.405609 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.4369 | 1.83147 | 0.915737 | − | 0.401777i | \(-0.131607\pi\) | ||||
0.915737 | + | 0.401777i | \(0.131607\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1597 | 1.20101 | 0.600506 | − | 0.799620i | \(-0.294966\pi\) | ||||
0.600506 | + | 0.799620i | \(0.294966\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.47882 | −0.207290 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.59380 | −0.381495 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.93561 | −0.486264 | −0.243132 | − | 0.969993i | \(-0.578175\pi\) | ||||
−0.243132 | + | 0.969993i | \(0.578175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.85158 | −0.232058 | −0.116029 | − | 0.993246i | \(-0.537017\pi\) | ||||
−0.116029 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.94648 | −0.316989 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.96471 | 0.635653 | 0.317827 | − | 0.948149i | \(-0.397047\pi\) | ||||
0.317827 | + | 0.948149i | \(0.397047\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.08437 | −0.321894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.00784 | −0.548896 | −0.274448 | − | 0.961602i | \(-0.588495\pi\) | ||||
−0.274448 | + | 0.961602i | \(0.588495\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.36394 | −0.335688 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.6960 | 1.95363 | 0.976814 | − | 0.214092i | \(-0.0686792\pi\) | ||||
0.976814 | + | 0.214092i | \(0.0686792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.59767 | 0.423144 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.29160 | −0.619743 | −0.309872 | − | 0.950778i | \(-0.600286\pi\) | ||||
−0.309872 | + | 0.950778i | \(0.600286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8881 | 1.84992 | 0.924960 | − | 0.380064i | \(-0.124098\pi\) | ||||
0.924960 | + | 0.380064i | \(0.124098\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.78261 | −0.204582 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.28847 | 0.240477 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.1554 | −1.74782 | −0.873910 | − | 0.486088i | \(-0.838424\pi\) | ||||
−0.873910 | + | 0.486088i | \(0.838424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.74862 | 0.413794 | 0.206897 | − | 0.978363i | \(-0.433663\pi\) | ||||
0.206897 | + | 0.978363i | \(0.433663\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.1007 | −1.50336 | −0.751682 | − | 0.659526i | \(-0.770757\pi\) | ||||
−0.751682 | + | 0.659526i | \(0.770757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.63118 | −0.540960 | −0.270480 | − | 0.962726i | \(-0.587182\pi\) | ||||
−0.270480 | + | 0.962726i | \(0.587182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.90143 | −0.694944 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.52355 | 0.315938 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.30861 | 0.228861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.88130 | 0.611414 | 0.305707 | − | 0.952126i | \(-0.401107\pi\) | ||||
0.305707 | + | 0.952126i | \(0.401107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.17642 | −0.353029 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.50619 | −0.577438 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4568 | −0.770669 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.98927 | 0.601966 | 0.300983 | − | 0.953629i | \(-0.402685\pi\) | ||||
0.300983 | + | 0.953629i | \(0.402685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7375 | −0.911791 | −0.455895 | − | 0.890033i | \(-0.650681\pi\) | ||||
−0.455895 | + | 0.890033i | \(0.650681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.18243 | 0.540710 | 0.270355 | − | 0.962761i | \(-0.412859\pi\) | ||||
0.270355 | + | 0.962761i | \(0.412859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.6304 | −1.48256 | −0.741282 | − | 0.671194i | \(-0.765782\pi\) | ||||
−0.741282 | + | 0.671194i | \(0.765782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.87275 | 0.252631 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.1846 | −1.30563 | −0.652817 | − | 0.757516i | \(-0.726413\pi\) | ||||
−0.652817 | + | 0.757516i | \(0.726413\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5196 | 0.935291 | 0.467646 | − | 0.883916i | \(-0.345102\pi\) | ||||
0.467646 | + | 0.883916i | \(0.345102\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.08614 | 0.197166 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.5270 | −0.733445 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.5054 | −1.04181 | −0.520905 | − | 0.853615i | \(-0.674405\pi\) | ||||
−0.520905 | + | 0.853615i | \(0.674405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.88893 | −0.181625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.8128 | −1.11113 | −0.555566 | − | 0.831473i | \(-0.687498\pi\) | ||||
−0.555566 | + | 0.831473i | \(0.687498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.99761 | −0.372673 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.29983 | −0.141814 | −0.0709068 | − | 0.997483i | \(-0.522589\pi\) | ||||
−0.0709068 | + | 0.997483i | \(0.522589\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.57581 | −0.158231 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.03212 | 0.306814 | 0.153407 | − | 0.988163i | \(-0.450975\pi\) | ||||
0.153407 | + | 0.988163i | \(0.450975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.85768 | 0.295083 | 0.147541 | − | 0.989056i | \(-0.452864\pi\) | ||||
0.147541 | + | 0.989056i | \(0.452864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.95931 | 0.238755 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6282 | −0.758753 | −0.379377 | − | 0.925242i | \(-0.623862\pi\) | ||||
−0.379377 | + | 0.925242i | \(0.623862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.7600 | −1.05948 | −0.529738 | − | 0.848161i | \(-0.677710\pi\) | ||||
−0.529738 | + | 0.848161i | \(0.677710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.43500 | −0.263633 | −0.131817 | − | 0.991274i | \(-0.542081\pi\) | ||||
−0.131817 | + | 0.991274i | \(0.542081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.75000 | 0.575524 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.80108 | −0.105946 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.8983 | −1.10405 | −0.552025 | − | 0.833828i | \(-0.686145\pi\) | ||||
−0.552025 | + | 0.833828i | \(0.686145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.01857 | 0.175748 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0648 | 0.582065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.1572 | −0.643090 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.658690 | −0.0377165 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.5138 | −1.28493 | −0.642467 | − | 0.766314i | \(-0.722089\pi\) | ||||
−0.642467 | + | 0.766314i | \(0.722089\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.5228 | −1.39056 | −0.695281 | − | 0.718738i | \(-0.744720\pi\) | ||||
−0.695281 | + | 0.718738i | \(0.744720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8723 | 0.897153 | 0.448576 | − | 0.893744i | \(-0.351931\pi\) | ||||
0.448576 | + | 0.893744i | \(0.351931\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.97332 | 0.279329 | 0.139665 | − | 0.990199i | \(-0.455398\pi\) | ||||
0.139665 | + | 0.990199i | \(0.455398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.00341 | −0.392116 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.2920 | 0.850869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.7940 | −0.765152 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.34729 | 0.460201 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.1768 | −1.54874 | −0.774368 | − | 0.632736i | \(-0.781932\pi\) | ||||
−0.774368 | + | 0.632736i | \(0.781932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.10920 | 0.169874 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.2227 | −1.64633 | −0.823167 | − | 0.567799i | \(-0.807795\pi\) | ||||
−0.823167 | + | 0.567799i | \(0.807795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.01654 | −0.325814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.9997 | 0.809906 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4230 | 1.09636 | 0.548182 | − | 0.836359i | \(-0.315320\pi\) | ||||
0.548182 | + | 0.836359i | \(0.315320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.59387 | −0.406490 | −0.203245 | − | 0.979128i | \(-0.565149\pi\) | ||||
−0.203245 | + | 0.979128i | \(0.565149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.7547 | −1.90303 | −0.951517 | − | 0.307597i | \(-0.900475\pi\) | ||||
−0.951517 | + | 0.307597i | \(0.900475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.63702 | 0.299182 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.91617 | 0.312244 | 0.156122 | − | 0.987738i | \(-0.450101\pi\) | ||||
0.156122 | + | 0.987738i | \(0.450101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.61435 | −0.190229 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.11053 | −0.110470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7218 | 1.44707 | 0.723534 | − | 0.690289i | \(-0.242516\pi\) | ||||
0.723534 | + | 0.690289i | \(0.242516\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.55187 | −0.288239 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.77432 | −0.402539 | −0.201270 | − | 0.979536i | \(-0.564507\pi\) | ||||
−0.201270 | + | 0.979536i | \(0.564507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.3994 | 1.25663 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.3173 | −1.04363 | −0.521816 | − | 0.853058i | \(-0.674745\pi\) | ||||
−0.521816 | + | 0.853058i | \(0.674745\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.49960 | 0.281016 | 0.140508 | − | 0.990080i | \(-0.455126\pi\) | ||||
0.140508 | + | 0.990080i | \(0.455126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.556563 | −0.0283651 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6983 | 0.694530 | 0.347265 | − | 0.937767i | \(-0.387110\pi\) | ||||
0.347265 | + | 0.937767i | \(0.387110\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.3523 | −0.675254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.46901 | −0.0739140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.48233 | 0.475905 | 0.237952 | − | 0.971277i | \(-0.423524\pi\) | ||||
0.237952 | + | 0.971277i | \(0.423524\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.61248 | 0.230337 | 0.115168 | − | 0.993346i | \(-0.463259\pi\) | ||||
0.115168 | + | 0.993346i | \(0.463259\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9612 | 1.04415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.24219 | −0.210278 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.1759 | 1.78879 | 0.894393 | − | 0.447282i | \(-0.147608\pi\) | ||||
0.894393 | + | 0.447282i | \(0.147608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.50619 | 0.320149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.96817 | 0.194790 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.80836 | −0.332610 | −0.166305 | − | 0.986074i | \(-0.553184\pi\) | ||||
−0.166305 | + | 0.986074i | \(0.553184\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.28706 | −0.111464 | −0.0557322 | − | 0.998446i | \(-0.517749\pi\) | ||||
−0.0557322 | + | 0.998446i | \(0.517749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.2994 | 0.887653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.41973 | −0.0687057 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.1173 | 0.872681 | 0.436340 | − | 0.899782i | \(-0.356274\pi\) | ||||
0.436340 | + | 0.899782i | \(0.356274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.9195 | 1.43784 | 0.718920 | − | 0.695093i | \(-0.244637\pi\) | ||||
0.718920 | + | 0.695093i | \(0.244637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.4341 | −0.642638 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.9704 | 1.76450 | 0.882250 | − | 0.470780i | \(-0.156028\pi\) | ||||
0.882250 | + | 0.470780i | \(0.156028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.0326 | −1.52191 | −0.760957 | − | 0.648803i | \(-0.775270\pi\) | ||||
−0.760957 | + | 0.648803i | \(0.775270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0191596 | −0.000908252 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1504 | 0.809379 | 0.404690 | − | 0.914454i | \(-0.367380\pi\) | ||||
0.404690 | + | 0.914454i | \(0.367380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.89630 | 0.324734 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.93903 | 0.0909031 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.8100 | −0.646005 | −0.323002 | − | 0.946398i | \(-0.604692\pi\) | ||||
−0.323002 | + | 0.946398i | \(0.604692\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.0964 | −0.749686 | −0.374843 | − | 0.927088i | \(-0.622303\pi\) | ||||
−0.374843 | + | 0.927088i | \(0.622303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.1389 | −1.67952 | −0.839758 | − | 0.542961i | \(-0.817303\pi\) | ||||
−0.839758 | + | 0.542961i | \(0.817303\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.9562 | −0.692092 | −0.346046 | − | 0.938218i | \(-0.612476\pi\) | ||||
−0.346046 | + | 0.938218i | \(0.612476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.70152 | 0.309448 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.89163 | −0.362858 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.4115 | 0.844778 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.11705 | 0.370878 | 0.185439 | − | 0.982656i | \(-0.440629\pi\) | ||||
0.185439 | + | 0.982656i | \(0.440629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.7795 | 0.673888 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.86370 | 0.402480 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4148 | −0.517256 | −0.258628 | − | 0.965977i | \(-0.583270\pi\) | ||||
−0.258628 | + | 0.965977i | \(0.583270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.17339 | 0.188342 | 0.0941712 | − | 0.995556i | \(-0.469980\pi\) | ||||
0.0941712 | + | 0.995556i | \(0.469980\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.3689 | −1.45782 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1500 | 0.545000 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7796 | −0.840692 | −0.420346 | − | 0.907364i | \(-0.638091\pi\) | ||||
−0.420346 | + | 0.907364i | \(0.638091\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6242 | 0.652063 | 0.326031 | − | 0.945359i | \(-0.394289\pi\) | ||||
0.326031 | + | 0.945359i | \(0.394289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.80560 | 0.0803481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.72936 | 0.386922 | 0.193461 | − | 0.981108i | \(-0.438029\pi\) | ||||
0.193461 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.54900 | −0.201236 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.94810 | −0.0858436 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.90415 | 0.259664 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.8308 | 1.65740 | 0.828698 | − | 0.559696i | \(-0.189082\pi\) | ||||
0.828698 | + | 0.559696i | \(0.189082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.8820 | 0.738198 | 0.369099 | − | 0.929390i | \(-0.379666\pi\) | ||||
0.369099 | + | 0.929390i | \(0.379666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.8077 | −1.21132 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2700 | −0.490000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0263 | −1.04069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.19769 | 0.311183 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.70493 | 0.202656 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8584 | 1.54167 | 0.770836 | − | 0.637033i | \(-0.219839\pi\) | ||||
0.770836 | + | 0.637033i | \(0.219839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.11130 | 0.133273 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6738 | −0.926703 | −0.463352 | − | 0.886174i | \(-0.653353\pi\) | ||||
−0.463352 | + | 0.886174i | \(0.653353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.5671 | −1.38741 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.16629 | −0.134644 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.434369 | −0.0184048 | −0.00920241 | − | 0.999958i | \(-0.502929\pi\) | ||||
−0.00920241 | + | 0.999958i | \(0.502929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.4939 | 1.16287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.17536 | 0.302405 | 0.151203 | − | 0.988503i | \(-0.451685\pi\) | ||||
0.151203 | + | 0.988503i | \(0.451685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.75515 | 0.157980 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.8314 | −1.75366 | −0.876832 | − | 0.480796i | \(-0.840348\pi\) | ||||
−0.876832 | + | 0.480796i | \(0.840348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.69600 | 0.154673 | 0.0773364 | − | 0.997005i | \(-0.475358\pi\) | ||||
0.0773364 | + | 0.997005i | \(0.475358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0761 | −0.670419 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.3267 | 1.34578 | 0.672890 | − | 0.739743i | \(-0.265053\pi\) | ||||
0.672890 | + | 0.739743i | \(0.265053\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.55294 | 0.354836 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.92691 | −0.162636 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.757694 | −0.0312734 | −0.0156367 | − | 0.999878i | \(-0.504978\pi\) | ||||
−0.0156367 | + | 0.999878i | \(0.504978\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.9780 | −1.15281 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.7840 | 1.14095 | 0.570475 | − | 0.821315i | \(-0.306759\pi\) | ||||
0.570475 | + | 0.821315i | \(0.306759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.57237 | −0.105457 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.0577 | −0.778679 | −0.389339 | − | 0.921094i | \(-0.627297\pi\) | ||||
−0.389339 | + | 0.921094i | \(0.627297\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.5642 | −1.57307 | −0.786533 | − | 0.617548i | \(-0.788126\pi\) | ||||
−0.786533 | + | 0.617548i | \(0.788126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.69249 | 0.231433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.93884 | 0.241050 | 0.120525 | − | 0.992710i | \(-0.461542\pi\) | ||||
0.120525 | + | 0.992710i | \(0.461542\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.5697 | −0.832160 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.21906 | −0.372354 | −0.186177 | − | 0.982516i | \(-0.559610\pi\) | ||||
−0.186177 | + | 0.982516i | \(0.559610\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.11101 | −0.205761 | −0.102881 | − | 0.994694i | \(-0.532806\pi\) | ||||
−0.102881 | + | 0.994694i | \(0.532806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.2033 | −1.25417 | −0.627083 | − | 0.778952i | \(-0.715751\pi\) | ||||
−0.627083 | + | 0.778952i | \(0.715751\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0412963 | −0.00165450 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.5018 | 0.820073 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.6069 | −0.781778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51818 | −0.0604378 | −0.0302189 | − | 0.999543i | \(-0.509620\pi\) | ||||
−0.0302189 | + | 0.999543i | \(0.509620\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.40069 | 0.254004 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3917 | −0.649461 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.9404 | 1.93303 | 0.966515 | − | 0.256609i | \(-0.0826053\pi\) | ||||
0.966515 | + | 0.256609i | \(0.0826053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.0494 | −0.514620 | −0.257310 | − | 0.966329i | \(-0.582836\pi\) | ||||
−0.257310 | + | 0.966329i | \(0.582836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.21609 | 0.283694 | 0.141847 | − | 0.989889i | \(-0.454696\pi\) | ||||
0.141847 | + | 0.989889i | \(0.454696\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.60191 | 0.180641 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.8951 | 0.778556 | 0.389278 | − | 0.921120i | \(-0.372724\pi\) | ||||
0.389278 | + | 0.921120i | \(0.372724\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.88752 | 0.230045 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.9877 | −0.934430 | −0.467215 | − | 0.884144i | \(-0.654743\pi\) | ||||
−0.467215 | + | 0.884144i | \(0.654743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.49867 | −0.174978 | −0.0874890 | − | 0.996165i | \(-0.527884\pi\) | ||||
−0.0874890 | + | 0.996165i | \(0.527884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.58812 | −0.100363 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.4362 | 1.10105 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.00420 | −0.0387666 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8519 | 0.649592 | 0.324796 | − | 0.945784i | \(-0.394704\pi\) | ||||
0.324796 | + | 0.945784i | \(0.394704\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.4746 | −1.13280 | −0.566401 | − | 0.824130i | \(-0.691665\pi\) | ||||
−0.566401 | + | 0.824130i | \(0.691665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1047 | 0.733171 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.5730 | 1.59075 | 0.795373 | − | 0.606120i | \(-0.207275\pi\) | ||||
0.795373 | + | 0.606120i | \(0.207275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.8607 | −0.453176 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.6811 | 0.521208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7341 | 1.05506 | 0.527528 | − | 0.849538i | \(-0.323119\pi\) | ||||
0.527528 | + | 0.849538i | \(0.323119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.83439 | −0.297175 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.8739 | 1.20731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.66547 | 0.100673 | 0.0503367 | − | 0.998732i | \(-0.483971\pi\) | ||||
0.0503367 | + | 0.998732i | \(0.483971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.7270 | −0.744016 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.89177 | 0.146365 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.3193 | −1.32644 | −0.663222 | − | 0.748423i | \(-0.730811\pi\) | ||||
−0.663222 | + | 0.748423i | \(0.730811\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.4291 | 0.914878 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.37150 | 0.0512912 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5636 | 0.393954 | 0.196977 | − | 0.980408i | \(-0.436888\pi\) | ||||
0.196977 | + | 0.980408i | \(0.436888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.19891 | −0.156376 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −38.9720 | −1.44739 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.55384 | 0.0947167 | 0.0473584 | − | 0.998878i | \(-0.484920\pi\) | ||||
0.0473584 | + | 0.998878i | \(0.484920\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.4742 | −1.34905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.9050 | −0.882953 | −0.441476 | − | 0.897273i | \(-0.645545\pi\) | ||||
−0.441476 | + | 0.897273i | \(0.645545\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.74008 | 0.174603 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.2160 | 1.66330 | 0.831648 | − | 0.555303i | \(-0.187398\pi\) | ||||
0.831648 | + | 0.555303i | \(0.187398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.3530 | −1.55378 | −0.776890 | − | 0.629636i | \(-0.783204\pi\) | ||||
−0.776890 | + | 0.629636i | \(0.783204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.28410 | 0.120320 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.5138 | 0.566862 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.78671 | −0.320632 | −0.160316 | − | 0.987066i | \(-0.551251\pi\) | ||||
−0.160316 | + | 0.987066i | \(0.551251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.57774 | 0.0574198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5182 | 0.927474 | 0.463737 | − | 0.885973i | \(-0.346508\pi\) | ||||
0.463737 | + | 0.885973i | \(0.346508\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7547 | −1.22361 | −0.611804 | − | 0.791010i | \(-0.709556\pi\) | ||||
−0.611804 | + | 0.791010i | \(0.709556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.70606 | 0.242776 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.0328 | −0.578910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.3898 | −1.60074 | −0.800369 | − | 0.599507i | \(-0.795363\pi\) | ||||
−0.800369 | + | 0.599507i | \(0.795363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.30404 | 0.154806 | 0.0774028 | − | 0.997000i | \(-0.475337\pi\) | ||||
0.0774028 | + | 0.997000i | \(0.475337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.4804 | −1.20265 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.0691 | 1.14899 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.59382 | 0.307511 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.40677 | −0.157284 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0547106 | 0.00195022 | 0.000975112 | − | 1.00000i | \(-0.499690\pi\) | ||||
0.000975112 | 1.00000i | \(0.499690\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.09381 | 0.287783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.49855 | 0.124237 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.0615 | −0.391818 | −0.195909 | − | 0.980622i | \(-0.562766\pi\) | ||||
−0.195909 | + | 0.980622i | \(0.562766\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.2883 | 0.965389 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.21757 | −0.113546 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.25983 | 0.0796485 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.3733 | 1.59524 | 0.797620 | − | 0.603160i | \(-0.206092\pi\) | ||||
0.797620 | + | 0.603160i | \(0.206092\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.8301 | −0.836787 | −0.418394 | − | 0.908266i | \(-0.637407\pi\) | ||||
−0.418394 | + | 0.908266i | \(0.637407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.87735 | 0.135818 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.6975 | −1.28388 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.6841 | 1.73399 | 0.866994 | − | 0.498319i | \(-0.166049\pi\) | ||||
0.866994 | + | 0.498319i | \(0.166049\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.8208 | −0.934916 | −0.467458 | − | 0.884015i | \(-0.654830\pi\) | ||||
−0.467458 | + | 0.884015i | \(0.654830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.8347 | −1.87202 | −0.936009 | − | 0.351977i | \(-0.885509\pi\) | ||||
−0.936009 | + | 0.351977i | \(0.885509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.71959 | 0.198649 | 0.0993247 | − | 0.995055i | \(-0.468332\pi\) | ||||
0.0993247 | + | 0.995055i | \(0.468332\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.7456 | 0.753441 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.553287 | −0.0191473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.3026 | 0.597352 | 0.298676 | − | 0.954355i | \(-0.403455\pi\) | ||||
0.298676 | + | 0.954355i | \(0.403455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.9356 | 1.37709 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.41451 | 0.0830617 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2695 | 0.421586 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.2247 | 0.590455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.07488 | 0.0368033 | 0.0184016 | − | 0.999831i | \(-0.494142\pi\) | ||||
0.0184016 | + | 0.999831i | \(0.494142\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.7863 | 0.607568 | 0.303784 | − | 0.952741i | \(-0.401750\pi\) | ||||
0.303784 | + | 0.952741i | \(0.401750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.4455 | 1.75530 | 0.877649 | − | 0.479305i | \(-0.159111\pi\) | ||||
0.877649 | + | 0.479305i | \(0.159111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2535 | 0.621357 | 0.310678 | − | 0.950515i | \(-0.399444\pi\) | ||||
0.310678 | + | 0.950515i | \(0.399444\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.2172 | −0.483401 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.23956 | −0.0759719 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.5141 | −0.559560 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.39623 | −0.216232 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1122 | −0.544072 | −0.272036 | − | 0.962287i | \(-0.587697\pi\) | ||||
−0.272036 | + | 0.962287i | \(0.587697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.2142 | 0.681034 | 0.340517 | − | 0.940238i | \(-0.389398\pi\) | ||||
0.340517 | + | 0.940238i | \(0.389398\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.6929 | −0.460803 | −0.230401 | − | 0.973096i | \(-0.574004\pi\) | ||||
−0.230401 | + | 0.973096i | \(0.574004\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −57.0860 | −1.91676 | −0.958380 | − | 0.285495i | \(-0.907842\pi\) | ||||
−0.958380 | + | 0.285495i | \(0.907842\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7960 | 0.462702 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.4554 | 0.918759 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.58763 | 0.153348 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.2217 | 1.97515 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1497 | −0.604654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7703 | −0.457740 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.6389 | 0.519280 | 0.259640 | − | 0.965706i | \(-0.416396\pi\) | ||||
0.259640 | + | 0.965706i | \(0.416396\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.7626 | 1.91376 | 0.956880 | − | 0.290483i | \(-0.0938159\pi\) | ||||
0.956880 | + | 0.290483i | \(0.0938159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.04961 | 0.200213 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6899 | 0.419057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.3839 | −0.969284 | −0.484642 | − | 0.874713i | \(-0.661050\pi\) | ||||
−0.484642 | + | 0.874713i | \(0.661050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.9403 | −0.985498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.6066 | −0.776181 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.9096 | −0.751639 | −0.375820 | − | 0.926693i | \(-0.622639\pi\) | ||||
−0.375820 | + | 0.926693i | \(0.622639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.8788 | 0.717048 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.81947 | −0.0595030 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5414 | −0.442377 | −0.221189 | − | 0.975231i | \(-0.570994\pi\) | ||||
−0.221189 | + | 0.975231i | \(0.570994\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.8442 | 0.875094 | 0.437547 | − | 0.899195i | \(-0.355847\pi\) | ||||
0.437547 | + | 0.899195i | \(0.355847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.0013 | −0.911847 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.9637 | 1.07118 | 0.535588 | − | 0.844480i | \(-0.320090\pi\) | ||||
0.535588 | + | 0.844480i | \(0.320090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.2098 | 0.363886 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.8888 | 1.84281 | 0.921404 | − | 0.388606i | \(-0.127043\pi\) | ||||
0.921404 | + | 0.388606i | \(0.127043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3648 | 0.432476 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.5645 | −0.825521 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.8766 | 0.641180 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.18064 | −0.102388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.0993 | −1.70756 | −0.853778 | − | 0.520636i | \(-0.825695\pi\) | ||||
−0.853778 | + | 0.520636i | \(0.825695\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.0178 | −1.25214 | −0.626070 | − | 0.779767i | \(-0.715338\pi\) | ||||
−0.626070 | + | 0.779767i | \(0.715338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.8862 | −0.541345 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.7115 | 0.822584 | 0.411292 | − | 0.911504i | \(-0.365078\pi\) | ||||
0.411292 | + | 0.911504i | \(0.365078\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0292094 | −0.000933538 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.9445 | −1.68867 | −0.844334 | − | 0.535817i | \(-0.820004\pi\) | ||||
−0.844334 | + | 0.535817i | \(0.820004\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6748 | 0.371989 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0426 | 1.01890 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.1464 | 1.02117 | 0.510583 | − | 0.859829i | \(-0.329430\pi\) | ||||
0.510583 | + | 0.859829i | \(0.329430\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.22224 | 0.133854 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.5417 | 1.31564 | 0.657819 | − | 0.753176i | \(-0.271479\pi\) | ||||
0.657819 | + | 0.753176i | \(0.271479\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6012.2.a.j.1.5 | ✓ | 10 | |
3.2 | odd | 2 | 6012.2.a.k.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.a.j.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6012.2.a.k.1.6 | yes | 10 | 3.2 | odd | 2 |