Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.41388\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.413878 | 0.185092 | 0.0925460 | − | 0.995708i | \(-0.470499\pi\) | ||||
0.0925460 | + | 0.995708i | \(0.470499\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72537 | 1.03009 | 0.515046 | − | 0.857162i | \(-0.327775\pi\) | ||||
0.515046 | + | 0.857162i | \(0.327775\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.29320 | −0.992938 | −0.496469 | − | 0.868054i | \(-0.665370\pi\) | ||||
−0.496469 | + | 0.868054i | \(0.665370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51462 | −0.974781 | −0.487391 | − | 0.873184i | \(-0.662051\pi\) | ||||
−0.487391 | + | 0.873184i | \(0.662051\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.413878 | 0.106863 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.04345 | −0.495611 | −0.247805 | − | 0.968810i | \(-0.579709\pi\) | ||||
−0.247805 | + | 0.968810i | \(0.579709\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.104243 | 0.0239150 | 0.0119575 | − | 0.999929i | \(-0.496194\pi\) | ||||
0.0119575 | + | 0.999929i | \(0.496194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.72537 | 0.594724 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.14941 | −1.49075 | −0.745377 | − | 0.666643i | \(-0.767731\pi\) | ||||
−0.745377 | + | 0.666643i | \(0.767731\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.82870 | −0.965741 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.94939 | 0.733383 | 0.366692 | − | 0.930343i | \(-0.380490\pi\) | ||||
0.366692 | + | 0.930343i | \(0.380490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.72301 | −1.20749 | −0.603744 | − | 0.797178i | \(-0.706325\pi\) | ||||
−0.603744 | + | 0.797178i | \(0.706325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.29320 | −0.573273 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.12797 | 0.190662 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8427 | −1.94693 | −0.973467 | − | 0.228828i | \(-0.926511\pi\) | ||||
−0.973467 | + | 0.228828i | \(0.926511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.51462 | −0.562790 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.68403 | 0.263001 | 0.131500 | − | 0.991316i | \(-0.458021\pi\) | ||||
0.131500 | + | 0.991316i | \(0.458021\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.25044 | −0.495687 | −0.247843 | − | 0.968800i | \(-0.579722\pi\) | ||||
−0.247843 | + | 0.968800i | \(0.579722\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.413878 | 0.0616973 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.28674 | −0.187691 | −0.0938453 | − | 0.995587i | \(-0.529916\pi\) | ||||
−0.0938453 | + | 0.995587i | \(0.529916\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.427633 | 0.0610904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.04345 | −0.286141 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.39006 | −0.328300 | −0.164150 | − | 0.986435i | \(-0.552488\pi\) | ||||
−0.164150 | + | 0.986435i | \(0.552488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.36298 | −0.183785 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.104243 | 0.0138073 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.83514 | 0.629482 | 0.314741 | − | 0.949178i | \(-0.398082\pi\) | ||||
0.314741 | + | 0.949178i | \(0.398082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.869119 | −0.111279 | −0.0556397 | − | 0.998451i | \(-0.517720\pi\) | ||||
−0.0556397 | + | 0.998451i | \(0.517720\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.72537 | 0.343364 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.45463 | −0.180424 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.884563 | 0.108067 | 0.0540333 | − | 0.998539i | \(-0.482792\pi\) | ||||
0.0540333 | + | 0.998539i | \(0.482792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.14941 | −0.860688 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.76105 | 0.683711 | 0.341856 | − | 0.939752i | \(-0.388945\pi\) | ||||
0.341856 | + | 0.939752i | \(0.388945\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.55384 | −1.11819 | −0.559096 | − | 0.829103i | \(-0.688852\pi\) | ||||
−0.559096 | + | 0.829103i | \(0.688852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.82870 | −0.557571 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.97519 | −1.02282 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.30282 | 0.934140 | 0.467070 | − | 0.884220i | \(-0.345310\pi\) | ||||
0.467070 | + | 0.884220i | \(0.345310\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.73510 | −1.06857 | −0.534283 | − | 0.845306i | \(-0.679418\pi\) | ||||
−0.534283 | + | 0.845306i | \(0.679418\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.845741 | −0.0917335 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.94939 | 0.423419 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7470 | 1.66917 | 0.834587 | − | 0.550876i | \(-0.185706\pi\) | ||||
0.834587 | + | 0.550876i | \(0.185706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.57864 | −1.00411 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.72301 | −0.697143 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0431440 | 0.00442648 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.3694 | −1.56052 | −0.780262 | − | 0.625453i | \(-0.784914\pi\) | ||||
−0.780262 | + | 0.625453i | \(0.784914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.29320 | −0.330979 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.3982 | 1.43268 | 0.716338 | − | 0.697753i | \(-0.245817\pi\) | ||||
0.716338 | + | 0.697753i | \(0.245817\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.67716 | −0.559387 | −0.279693 | − | 0.960089i | \(-0.590233\pi\) | ||||
−0.279693 | + | 0.960089i | \(0.590233\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.12797 | 0.110079 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.767992 | −0.0742446 | −0.0371223 | − | 0.999311i | \(-0.511819\pi\) | ||||
−0.0371223 | + | 0.999311i | \(0.511819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.64735 | 0.445136 | 0.222568 | − | 0.974917i | \(-0.428556\pi\) | ||||
0.222568 | + | 0.974917i | \(0.428556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.8427 | −1.12406 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.5981 | 1.84364 | 0.921819 | − | 0.387621i | \(-0.126703\pi\) | ||||
0.921819 | + | 0.387621i | \(0.126703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.95898 | −0.275927 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.51462 | −0.324927 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.56917 | −0.510525 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.154818 | −0.0140744 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.68403 | 0.151844 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.06789 | −0.363843 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0424 | −1.42353 | −0.711766 | − | 0.702417i | \(-0.752104\pi\) | ||||
−0.711766 | + | 0.702417i | \(0.752104\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.25044 | −0.286185 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.16033 | −0.450860 | −0.225430 | − | 0.974259i | \(-0.572379\pi\) | ||||
−0.225430 | + | 0.974259i | \(0.572379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.284101 | 0.0246347 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.413878 | 0.0356210 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.88061 | −0.844158 | −0.422079 | − | 0.906559i | \(-0.638699\pi\) | ||||
−0.422079 | + | 0.906559i | \(0.638699\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9804 | 1.52508 | 0.762540 | − | 0.646941i | \(-0.223952\pi\) | ||||
0.762540 | + | 0.646941i | \(0.223952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.28674 | −0.108363 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5744 | 0.967897 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.63457 | 0.135743 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.427633 | 0.0352705 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.3576 | 1.25815 | 0.629073 | − | 0.777346i | \(-0.283435\pi\) | ||||
0.629073 | + | 0.777346i | \(0.283435\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7460 | 1.03725 | 0.518626 | − | 0.855001i | \(-0.326444\pi\) | ||||
0.518626 | + | 0.855001i | \(0.326444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.04345 | −0.165204 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.78251 | −0.223496 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3249 | 1.54230 | 0.771148 | − | 0.636656i | \(-0.219683\pi\) | ||||
0.771148 | + | 0.636656i | \(0.219683\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.39006 | −0.189544 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.4848 | −1.53562 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.3454 | 1.20195 | 0.600973 | − | 0.799269i | \(-0.294780\pi\) | ||||
0.600973 | + | 0.799269i | \(0.294780\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.36298 | −0.106108 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.647425 | −0.0498019 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.104243 | 0.00797167 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.18370 | −0.242053 | −0.121026 | − | 0.992649i | \(-0.538619\pi\) | ||||
−0.121026 | + | 0.992649i | \(0.538619\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.1600 | −0.994802 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.83514 | 0.363431 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.5301 | −0.787058 | −0.393529 | − | 0.919312i | \(-0.628746\pi\) | ||||
−0.393529 | + | 0.919312i | \(0.628746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5951 | 1.15918 | 0.579588 | − | 0.814910i | \(-0.303214\pi\) | ||||
0.579588 | + | 0.814910i | \(0.303214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.869119 | −0.0642471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.90145 | −0.360362 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.72951 | 0.492111 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.72537 | 0.198241 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.21547 | −0.0879483 | −0.0439741 | − | 0.999033i | \(-0.514002\pi\) | ||||
−0.0439741 | + | 0.999033i | \(0.514002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.45639 | −0.104833 | −0.0524165 | − | 0.998625i | \(-0.516692\pi\) | ||||
−0.0524165 | + | 0.998625i | \(0.516692\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.45463 | −0.104168 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.70373 | −0.691362 | −0.345681 | − | 0.938352i | \(-0.612352\pi\) | ||||
−0.345681 | + | 0.938352i | \(0.612352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.90201 | −0.701935 | −0.350967 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350967 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.884563 | 0.0623923 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7635 | 0.755452 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.696982 | 0.0486794 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.14941 | −0.496918 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.343294 | −0.0237461 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7202 | −0.944536 | −0.472268 | − | 0.881455i | \(-0.656564\pi\) | ||||
−0.472268 | + | 0.881455i | \(0.656564\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.76105 | 0.394741 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.34528 | −0.0917476 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.3227 | −1.24382 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.55384 | −0.645589 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.18197 | 0.483112 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.3126 | −1.69505 | −0.847527 | − | 0.530752i | \(-0.821910\pi\) | ||||
−0.847527 | + | 0.530752i | \(0.821910\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.82870 | −0.321914 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8035 | 0.849799 | 0.424899 | − | 0.905241i | \(-0.360309\pi\) | ||||
0.424899 | + | 0.905241i | \(0.360309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4832 | 1.68397 | 0.841987 | − | 0.539497i | \(-0.181386\pi\) | ||||
0.841987 | + | 0.539497i | \(0.181386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.97519 | −0.590524 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0993 | 1.05470 | 0.527351 | − | 0.849648i | \(-0.323185\pi\) | ||||
0.527351 | + | 0.849648i | \(0.323185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.532554 | −0.0347400 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.30282 | 0.539326 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.30980 | 0.0847238 | 0.0423619 | − | 0.999102i | \(-0.486512\pi\) | ||||
0.0423619 | + | 0.999102i | \(0.486512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.56647 | −0.616231 | −0.308115 | − | 0.951349i | \(-0.599698\pi\) | ||||
−0.308115 | + | 0.951349i | \(0.599698\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.176988 | 0.0113073 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.366375 | −0.0233119 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.73510 | −0.616937 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.83575 | −0.557707 | −0.278854 | − | 0.960334i | \(-0.589954\pi\) | ||||
−0.278854 | + | 0.960334i | \(0.589954\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.5445 | 1.48023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.845741 | −0.0529624 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.44156 | −0.588949 | −0.294474 | − | 0.955659i | \(-0.595145\pi\) | ||||
−0.294474 | + | 0.955659i | \(0.595145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.2758 | −2.00552 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.94939 | 0.244461 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.1240 | −0.994248 | −0.497124 | − | 0.867680i | \(-0.665611\pi\) | ||||
−0.497124 | + | 0.867680i | \(0.665611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.989192 | −0.0607656 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.7470 | 0.963698 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.94717 | −0.545519 | −0.272759 | − | 0.962082i | \(-0.587936\pi\) | ||||
−0.272759 | + | 0.962082i | \(0.587936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.65772 | 0.100699 | 0.0503496 | − | 0.998732i | \(-0.483966\pi\) | ||||
0.0503496 | + | 0.998732i | \(0.483966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.57864 | −0.579726 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.9019 | 0.958921 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.8633 | −1.49389 | −0.746945 | − | 0.664885i | \(-0.768480\pi\) | ||||
−0.746945 | + | 0.664885i | \(0.768480\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.72301 | −0.402496 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2065 | 0.966802 | 0.483401 | − | 0.875399i | \(-0.339401\pi\) | ||||
0.483401 | + | 0.875399i | \(0.339401\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.21553 | 0.0722555 | 0.0361278 | − | 0.999347i | \(-0.488498\pi\) | ||||
0.0361278 | + | 0.999347i | \(0.488498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0431440 | 0.00255563 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.58960 | 0.270915 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8243 | −0.754370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.3694 | −0.900969 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.99666 | −0.584011 | −0.292006 | − | 0.956417i | \(-0.594323\pi\) | ||||
−0.292006 | + | 0.956417i | \(0.594323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00116 | 0.116512 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.29320 | −0.191091 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.1275 | 1.45316 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.85863 | −0.510603 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.3982 | 0.827156 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.359709 | −0.0205969 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.87030 | −0.106744 | −0.0533720 | − | 0.998575i | \(-0.516997\pi\) | ||||
−0.0533720 | + | 0.998575i | \(0.516997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.67716 | −0.322962 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.7848 | −1.80235 | −0.901175 | − | 0.433455i | \(-0.857294\pi\) | ||||
−0.901175 | + | 0.433455i | \(0.857294\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.24201 | 0.465866 | 0.232933 | − | 0.972493i | \(-0.425168\pi\) | ||||
0.232933 | + | 0.972493i | \(0.425168\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.12797 | 0.0635539 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.89475 | −0.499579 | −0.249789 | − | 0.968300i | \(-0.580361\pi\) | ||||
−0.249789 | + | 0.968300i | \(0.580361\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.0061 | −0.728204 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.767992 | −0.0428652 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.213016 | −0.0118525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.9711 | 0.941386 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.64735 | 0.256999 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.50685 | −0.193339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2141 | −0.561417 | −0.280708 | − | 0.959793i | \(-0.590569\pi\) | ||||
−0.280708 | + | 0.959793i | \(0.590569\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.8427 | −0.648978 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.366101 | 0.0200022 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3679 | 0.619246 | 0.309623 | − | 0.950859i | \(-0.399797\pi\) | ||||
0.309623 | + | 0.950859i | \(0.399797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.5981 | 1.06442 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.1402 | 1.19896 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9121 | −0.967164 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.95898 | −0.159306 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.88839 | −0.316105 | −0.158053 | − | 0.987431i | \(-0.550522\pi\) | ||||
−0.158053 | + | 0.987431i | \(0.550522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.42996 | 0.344188 | 0.172094 | − | 0.985081i | \(-0.444947\pi\) | ||||
0.172094 | + | 0.985081i | \(0.444947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.51462 | −0.187597 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.5192 | 1.46470 | 0.732349 | − | 0.680929i | \(-0.238424\pi\) | ||||
0.732349 | + | 0.680929i | \(0.238424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.38437 | 0.126549 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.56917 | −0.294752 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3372 | 0.598354 | 0.299177 | − | 0.954198i | \(-0.403288\pi\) | ||||
0.299177 | + | 0.954198i | \(0.403288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9891 | −0.999428 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.154818 | −0.00812583 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.95413 | −0.206968 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7364 | −1.03023 | −0.515116 | − | 0.857120i | \(-0.672251\pi\) | ||||
−0.515116 | + | 0.857120i | \(0.672251\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.68403 | 0.0876670 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.51378 | −0.338179 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5585 | −0.909143 | −0.454571 | − | 0.890710i | \(-0.650208\pi\) | ||||
−0.454571 | + | 0.890710i | \(0.650208\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.06789 | −0.210065 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.8806 | −0.714888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.9151 | −1.17707 | −0.588535 | − | 0.808471i | \(-0.700295\pi\) | ||||
−0.588535 | + | 0.808471i | \(0.700295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0424 | −0.821876 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.0263 | −1.48318 | −0.741588 | − | 0.670856i | \(-0.765927\pi\) | ||||
−0.741588 | + | 0.670856i | \(0.765927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.71463 | −0.189315 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.25044 | −0.165229 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6204 | −0.893390 | −0.446695 | − | 0.894686i | \(-0.647399\pi\) | ||||
−0.446695 | + | 0.894686i | \(0.647399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6095 | 0.738834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.16033 | −0.260304 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.43635 | 0.172902 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.09900 | 0.205723 | 0.102862 | − | 0.994696i | \(-0.467200\pi\) | ||||
0.102862 | + | 0.994696i | \(0.467200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.284101 | 0.0142228 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.1968 | 1.70771 | 0.853855 | − | 0.520512i | \(-0.174259\pi\) | ||||
0.853855 | + | 0.520512i | \(0.174259\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.6288 | 1.17704 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.413878 | 0.0205658 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.0005 | 1.93318 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9430 | 1.72782 | 0.863911 | − | 0.503645i | \(-0.168008\pi\) | ||||
0.863911 | + | 0.503645i | \(0.168008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.88061 | −0.487375 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.1775 | 0.648424 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.02914 | −0.197783 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.9804 | 0.880506 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1622 | 0.496456 | 0.248228 | − | 0.968702i | \(-0.420152\pi\) | ||||
0.248228 | + | 0.968702i | \(0.420152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.04565 | 0.0996988 | 0.0498494 | − | 0.998757i | \(-0.484126\pi\) | ||||
0.0498494 | + | 0.998757i | \(0.484126\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.28674 | −0.0625635 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.86724 | 0.478631 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.36867 | −0.114628 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.5744 | 0.558816 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.7674 | −1.72285 | −0.861427 | − | 0.507881i | \(-0.830429\pi\) | ||||
−0.861427 | + | 0.507881i | \(0.830429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.18675 | 0.0570317 | 0.0285158 | − | 0.999593i | \(-0.490922\pi\) | ||||
0.0285158 | + | 0.999593i | \(0.490922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.63457 | 0.0783714 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.745277 | −0.0356514 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.60398 | −0.0765537 | −0.0382768 | − | 0.999267i | \(-0.512187\pi\) | ||||
−0.0382768 | + | 0.999267i | \(0.512187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.427633 | 0.0203635 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.90700 | −0.233139 | −0.116569 | − | 0.993183i | \(-0.537190\pi\) | ||||
−0.116569 | + | 0.993183i | \(0.537190\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.51732 | 0.308951 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.3576 | 0.726391 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6462 | 0.502423 | 0.251212 | − | 0.967932i | \(-0.419171\pi\) | ||||
0.251212 | + | 0.967932i | \(0.419171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.54584 | −0.261144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.7460 | 0.598858 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.96439 | −0.185854 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.35862 | −0.0635535 | −0.0317768 | − | 0.999495i | \(-0.510117\pi\) | ||||
−0.0317768 | + | 0.999495i | \(0.510117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.04345 | −0.0953803 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.30249 | −0.433260 | −0.216630 | − | 0.976254i | \(-0.569507\pi\) | ||||
−0.216630 | + | 0.976254i | \(0.569507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.4887 | −1.23103 | −0.615517 | − | 0.788123i | \(-0.711053\pi\) | ||||
−0.615517 | + | 0.788123i | \(0.711053\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.78251 | −0.129036 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3061 | 0.615731 | 0.307865 | − | 0.951430i | \(-0.400385\pi\) | ||||
0.307865 | + | 0.951430i | \(0.400385\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.41076 | 0.111319 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.3249 | 0.890445 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.7043 | 0.492186 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.503359 | −0.0230957 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.39006 | −0.109433 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.2772 | −1.47478 | −0.737391 | − | 0.675467i | \(-0.763942\pi\) | ||||
−0.737391 | + | 0.675467i | \(0.763942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.6228 | 1.89783 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.4848 | −0.886588 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.36105 | −0.288840 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.2588 | −1.00864 | −0.504322 | − | 0.863516i | \(-0.668257\pi\) | ||||
−0.504322 | + | 0.863516i | \(0.668257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.3454 | 0.693944 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.40910 | 0.379497 | 0.189749 | − | 0.981833i | \(-0.439233\pi\) | ||||
0.189749 | + | 0.981833i | \(0.439233\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.07040 | −0.363472 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.36298 | −0.0612616 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.7010 | 0.704286 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.47029 | −0.110585 | −0.0552927 | − | 0.998470i | \(-0.517609\pi\) | ||||
−0.0552927 | + | 0.998470i | \(0.517609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.9349 | 1.73602 | 0.868011 | − | 0.496545i | \(-0.165398\pi\) | ||||
0.868011 | + | 0.496545i | \(0.165398\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.95911 | 0.265177 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.647425 | −0.0287532 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0390 | 0.976864 | 0.488432 | − | 0.872602i | \(-0.337569\pi\) | ||||
0.488432 | + | 0.872602i | \(0.337569\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.0377 | −1.15184 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.104243 | 0.00460245 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.34965 | −0.103538 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.23750 | 0.186365 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.18370 | −0.139749 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.635065 | −0.0278227 | −0.0139114 | − | 0.999903i | \(-0.504428\pi\) | ||||
−0.0139114 | + | 0.999903i | \(0.504428\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.1785 | 1.27589 | 0.637944 | − | 0.770083i | \(-0.279785\pi\) | ||||
0.637944 | + | 0.770083i | \(0.279785\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.1600 | −0.574349 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.7382 | 0.598444 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.1141 | 1.22235 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.83514 | 0.209827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.91872 | −0.256368 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.317855 | −0.0137421 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.5301 | −0.454408 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40828 | −0.0606590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8099 | 1.53959 | 0.769793 | − | 0.638294i | \(-0.220359\pi\) | ||||
0.769793 | + | 0.638294i | \(0.220359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.5951 | 0.669250 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.92344 | 0.0823910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.1170 | −0.945653 | −0.472827 | − | 0.881156i | \(-0.656766\pi\) | ||||
−0.472827 | + | 0.881156i | \(0.656766\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.869119 | −0.0370931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.411697 | 0.0175389 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.6282 | 0.962250 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.90145 | −0.208055 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9219 | 1.64917 | 0.824586 | − | 0.565737i | \(-0.191408\pi\) | ||||
0.824586 | + | 0.565737i | \(0.191408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4241 | 0.483186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.72951 | 0.284120 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.4736 | 0.905006 | 0.452503 | − | 0.891763i | \(-0.350531\pi\) | ||||
0.452503 | + | 0.891763i | \(0.350531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.11124 | 0.341242 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.72537 | 0.114455 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.5335 | −1.02850 | −0.514248 | − | 0.857642i | \(-0.671929\pi\) | ||||
−0.514248 | + | 0.857642i | \(0.671929\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.9527 | 1.58827 | 0.794136 | − | 0.607740i | \(-0.207924\pi\) | ||||
0.794136 | + | 0.607740i | \(0.207924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.21547 | −0.0507770 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.5224 | 1.43968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0677 | 1.12684 | 0.563421 | − | 0.826170i | \(-0.309485\pi\) | ||||
0.563421 | + | 0.826170i | \(0.309485\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.45639 | −0.0605253 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.5317 | −1.10072 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.87094 | 0.325981 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.45463 | −0.0601414 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.7964 | −0.775812 | −0.387906 | − | 0.921699i | \(-0.626802\pi\) | ||||
−0.387906 | + | 0.921699i | \(0.626802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.700827 | −0.0288771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.70373 | −0.399158 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.2880 | −1.40804 | −0.704020 | − | 0.710180i | \(-0.748614\pi\) | ||||
−0.704020 | + | 0.710180i | \(0.748614\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.30496 | −0.0944940 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.90201 | −0.405262 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.9335 | −0.487592 | −0.243796 | − | 0.969827i | \(-0.578393\pi\) | ||||
−0.243796 | + | 0.969827i | \(0.578393\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.4330 | −0.507152 | −0.253576 | − | 0.967315i | \(-0.581607\pi\) | ||||
−0.253576 | + | 0.967315i | \(0.581607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.884563 | 0.0360222 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0640758 | −0.00260505 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.2350 | −0.780726 | −0.390363 | − | 0.920661i | \(-0.627650\pi\) | ||||
−0.390363 | + | 0.920661i | \(0.627650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.7635 | 0.436161 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.52241 | 0.182957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4268 | −0.421135 | −0.210568 | − | 0.977579i | \(-0.567531\pi\) | ||||
−0.210568 | + | 0.977579i | \(0.567531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.696982 | 0.0281050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.7139 | −0.833911 | −0.416956 | − | 0.908927i | \(-0.636903\pi\) | ||||
−0.416956 | + | 0.908927i | \(0.636903\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.86053 | −0.114974 | −0.0574871 | − | 0.998346i | \(-0.518309\pi\) | ||||
−0.0574871 | + | 0.998346i | \(0.518309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.14941 | −0.286896 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 42.9163 | 1.71940 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4599 | 0.898397 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.343294 | −0.0137098 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.2001 | 0.964921 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9113 | 0.474180 | 0.237090 | − | 0.971488i | \(-0.423806\pi\) | ||||
0.237090 | + | 0.971488i | \(0.423806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.7202 | −0.545328 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.63959 | −0.263484 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50297 | −0.0595497 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.76105 | 0.227904 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.2323 | 0.522644 | 0.261322 | − | 0.965252i | \(-0.415842\pi\) | ||||
0.261322 | + | 0.965252i | \(0.415842\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7086 | −1.40821 | −0.704105 | − | 0.710096i | \(-0.748652\pi\) | ||||
−0.704105 | + | 0.710096i | \(0.748652\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.34528 | −0.0529705 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.04495 | −0.198337 | −0.0991687 | − | 0.995071i | \(-0.531618\pi\) | ||||
−0.0991687 | + | 0.995071i | \(0.531618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.9231 | −0.625036 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.3227 | −0.718122 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.5847 | −0.922939 | −0.461470 | − | 0.887156i | \(-0.652678\pi\) | ||||
−0.461470 | + | 0.887156i | \(0.652678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.13575 | −0.0834505 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.55384 | −0.372731 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.3871 | −0.677307 | −0.338653 | − | 0.940911i | \(-0.609971\pi\) | ||||
−0.338653 | + | 0.940911i | \(0.609971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.6429 | −1.38635 | −0.693174 | − | 0.720770i | \(-0.743788\pi\) | ||||
−0.693174 | + | 0.720770i | \(0.743788\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.18197 | 0.278925 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.117583 | 0.00455968 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.2358 | −1.09329 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.3126 | −0.978640 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.86219 | 0.110493 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.77695 | 0.107043 | 0.0535217 | − | 0.998567i | \(-0.482955\pi\) | ||||
0.0535217 | + | 0.998567i | \(0.482955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.82870 | −0.185857 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.941133 | 0.0361707 | 0.0180853 | − | 0.999836i | \(-0.494243\pi\) | ||||
0.0180853 | + | 0.999836i | \(0.494243\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.8872 | −1.60748 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.8035 | 0.490632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2667 | 0.660693 | 0.330347 | − | 0.943860i | \(-0.392834\pi\) | ||||
0.330347 | + | 0.943860i | \(0.392834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.08937 | −0.156247 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4832 | 0.972243 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.40015 | 0.320020 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.2233 | −0.807372 | −0.403686 | − | 0.914898i | \(-0.632271\pi\) | ||||
−0.403686 | + | 0.914898i | \(0.632271\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.97519 | −0.340939 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.44171 | 0.282280 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.44123 | −0.130346 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.0993 | 0.608932 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1597 | 0.421496 | 0.210748 | − | 0.977540i | \(-0.432410\pi\) | ||||
0.210748 | + | 0.977540i | \(0.432410\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.23452 | −0.0465610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.532554 | −0.0200572 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.2405 | 1.47579 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.0151 | −1.39013 | −0.695066 | − | 0.718946i | \(-0.744625\pi\) | ||||
−0.695066 | + | 0.718946i | \(0.744625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.30282 | 0.311380 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0655 | 1.80007 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.79038 | 0.179150 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.30980 | 0.0489153 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.2002 | 0.678754 | 0.339377 | − | 0.940650i | \(-0.389784\pi\) | ||||
0.339377 | + | 0.940650i | \(0.389784\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4723 | −0.576220 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.56647 | −0.355781 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.0704 | −0.708258 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9170 | −0.516152 | −0.258076 | − | 0.966125i | \(-0.583088\pi\) | ||||
−0.258076 | + | 0.966125i | \(0.583088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.64212 | 0.245668 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.0066 | 1.81010 | 0.905050 | − | 0.425305i | \(-0.139833\pi\) | ||||
0.905050 | + | 0.425305i | \(0.139833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.176988 | 0.00652829 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.91304 | −0.107303 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.12817 | −0.262214 | −0.131107 | − | 0.991368i | \(-0.541853\pi\) | ||||
−0.131107 | + | 0.991368i | \(0.541853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.366375 | −0.0134591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.4421 | −0.456456 | −0.228228 | − | 0.973608i | \(-0.573293\pi\) | ||||
−0.228228 | + | 0.973608i | \(0.573293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.35618 | 0.232873 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.73510 | −0.356189 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.09306 | −0.0764788 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.7220 | −1.52246 | −0.761228 | − | 0.648484i | \(-0.775403\pi\) | ||||
−0.761228 | + | 0.648484i | \(0.775403\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.83575 | −0.321992 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.27528 | 0.191987 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0972 | −1.38467 | −0.692333 | − | 0.721578i | \(-0.743417\pi\) | ||||
−0.692333 | + | 0.721578i | \(0.743417\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.5445 | 0.854610 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5395 | 0.889556 | 0.444778 | − | 0.895641i | \(-0.353283\pi\) | ||||
0.444778 | + | 0.895641i | \(0.353283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6657 | 0.458531 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.845741 | −0.0305778 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.9937 | −0.613607 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.4319 | 1.85468 | 0.927341 | − | 0.374218i | \(-0.122089\pi\) | ||||
0.927341 | + | 0.374218i | \(0.122089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.44156 | −0.340030 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.41003 | −0.230553 | −0.115276 | − | 0.993333i | \(-0.536775\pi\) | ||||
−0.115276 | + | 0.993333i | \(0.536775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.4634 | 1.16612 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.2758 | −1.15789 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.175548 | 0.00628967 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.9723 | −0.678883 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.94939 | 0.141140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.99816 | 0.285466 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.4276 | 0.656872 | 0.328436 | − | 0.944526i | \(-0.393479\pi\) | ||||
0.328436 | + | 0.944526i | \(0.393479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.1240 | −0.574029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 53.4121 | 1.89912 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.05463 | 0.108473 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.989192 | −0.0350830 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0923 | −0.605439 | −0.302720 | − | 0.953080i | \(-0.597895\pi\) | ||||
−0.302720 | + | 0.953080i | \(0.597895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62940 | 0.0930214 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.7470 | 0.556391 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.4627 | 1.11030 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.06432 | −0.284230 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.94717 | −0.314955 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.7133 | 1.60720 | 0.803598 | − | 0.595173i | \(-0.202916\pi\) | ||||
0.803598 | + | 0.595173i | \(0.202916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5328 | −1.28284 | −0.641419 | − | 0.767190i | \(-0.721654\pi\) | ||||
−0.641419 | + | 0.767190i | \(0.721654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.65772 | 0.0581387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.35113 | 0.222470 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.338836 | −0.0118544 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.57864 | −0.334705 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.0829 | 0.735797 | 0.367898 | − | 0.929866i | \(-0.380077\pi\) | ||||
0.367898 | + | 0.929866i | \(0.380077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.25974 | −0.113627 | −0.0568137 | − | 0.998385i | \(-0.518094\pi\) | ||||
−0.0568137 | + | 0.998385i | \(0.518094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.9019 | 0.553633 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.0262 | 1.28753 | 0.643764 | − | 0.765224i | \(-0.277372\pi\) | ||||
0.643764 | + | 0.765224i | \(0.277372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.6796 | −1.34340 | −0.671698 | − | 0.740825i | \(-0.734435\pi\) | ||||
−0.671698 | + | 0.740825i | \(0.734435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.8633 | −0.862498 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.873848 | −0.0302770 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.413878 | −0.0143228 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.72301 | −0.232381 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1061 | −1.03938 | −0.519690 | − | 0.854355i | \(-0.673952\pi\) | ||||
−0.519690 | + | 0.854355i | \(0.673952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4023 | −0.462149 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.2065 | 0.558183 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.267955 | −0.00921794 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.421936 | −0.0144979 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.21553 | 0.0417168 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 84.6686 | 2.90240 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8542 | 1.09067 | 0.545334 | − | 0.838219i | \(-0.316403\pi\) | ||||
0.545334 | + | 0.838219i | \(0.316403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0431440 | 0.00147549 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.0715 | 1.26634 | 0.633170 | − | 0.774013i | \(-0.281754\pi\) | ||||
0.633170 | + | 0.774013i | \(0.281754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9884 | 0.579638 | 0.289819 | − | 0.957081i | \(-0.406405\pi\) | ||||
0.289819 | + | 0.957081i | \(0.406405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.58960 | 0.156413 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.9003 | −1.29014 | −0.645071 | − | 0.764123i | \(-0.723172\pi\) | ||||
−0.645071 | + | 0.764123i | \(0.723172\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.31767 | −0.0448020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.8243 | −0.435536 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.3429 | −0.927543 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.10891 | −0.105341 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.3694 | −0.520175 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0865 | −0.374792 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4949 | 0.624529 | 0.312265 | − | 0.949995i | \(-0.398912\pi\) | ||||
0.312265 | + | 0.949995i | \(0.398912\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.99666 | −0.337179 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.6699 | −0.932223 | −0.466111 | − | 0.884726i | \(-0.654345\pi\) | ||||
−0.466111 | + | 0.884726i | \(0.654345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2872 | 0.413499 | 0.206749 | − | 0.978394i | \(-0.433712\pi\) | ||||
0.206749 | + | 0.978394i | \(0.433712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.00116 | 0.0672682 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.6301 | 1.56569 | 0.782843 | − | 0.622219i | \(-0.213769\pi\) | ||||
0.782843 | + | 0.622219i | \(0.213769\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.7214 | −1.46637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.29320 | −0.110326 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.134134 | −0.00448862 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.35819 | −0.145678 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.1275 | 0.838982 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.5518 | −0.885551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.88397 | 0.162709 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.85863 | −0.294797 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.45448 | 0.214554 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.8370 | 0.725084 | 0.362542 | − | 0.931967i | \(-0.381909\pi\) | ||||
0.362542 | + | 0.931967i | \(0.381909\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.3982 | 0.477559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.8654 | 0.790698 | 0.395349 | − | 0.918531i | \(-0.370624\pi\) | ||||
0.395349 | + | 0.918531i | \(0.370624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0597 | 1.06102 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.359709 | −0.0118916 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.0638 | −0.464427 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8967 | 0.425422 | 0.212711 | − | 0.977115i | \(-0.431771\pi\) | ||||
0.212711 | + | 0.977115i | \(0.431771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.87030 | −0.0616286 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.2479 | −0.666469 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.1851 | 1.88023 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.67716 | −0.186462 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.1515 | 0.923621 | 0.461810 | − | 0.886979i | \(-0.347200\pi\) | ||||
0.461810 | + | 0.886979i | \(0.347200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0445778 | 0.00146098 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.7848 | −1.04059 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.78520 | 0.0910857 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.3504 | −1.38353 | −0.691764 | − | 0.722124i | \(-0.743166\pi\) | ||||
−0.691764 | + | 0.722124i | \(0.743166\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.24201 | 0.268968 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.5165 | −1.77719 | −0.888593 | − | 0.458696i | \(-0.848317\pi\) | ||||
−0.888593 | + | 0.458696i | \(0.848317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0398 | −0.392070 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.12797 | 0.0366929 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.10003 | 0.0682417 | 0.0341209 | − | 0.999418i | \(-0.489137\pi\) | ||||
0.0341209 | + | 0.999418i | \(0.489137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.5782 | 1.08999 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.89475 | −0.288432 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.3650 | 1.14559 | 0.572793 | − | 0.819700i | \(-0.305860\pi\) | ||||
0.572793 | + | 0.819700i | \(0.305860\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.503056 | −0.0162785 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.0061 | −0.420429 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.9283 | −0.869560 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1988 | 0.458027 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.767992 | −0.0247482 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.602766 | −0.0194037 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.6270 | 1.49942 | 0.749712 | − | 0.661764i | \(-0.230192\pi\) | ||||
0.749712 | + | 0.661764i | \(0.230192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.213016 | −0.00684306 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.30578 | 0.298637 | 0.149318 | − | 0.988789i | \(-0.452292\pi\) | ||||
0.149318 | + | 0.988789i | \(0.452292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.0033 | 1.57097 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.9711 | 0.543509 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.0655 | −0.418001 | −0.209001 | − | 0.977915i | \(-0.567021\pi\) | ||||
−0.209001 | + | 0.977915i | \(0.567021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.8579 | −1.65739 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.64735 | 0.148379 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.31552 | 0.233329 | 0.116664 | − | 0.993171i | \(-0.462780\pi\) | ||||
0.116664 | + | 0.993171i | \(0.462780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.01616 | −0.127966 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.50685 | −0.111624 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.2387 | 0.738947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.7439 | −0.817782 | −0.408891 | − | 0.912583i | \(-0.634084\pi\) | ||||
−0.408891 | + | 0.912583i | \(0.634084\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.2141 | −0.324134 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.09823 | −0.129922 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.6667 | 1.25626 | 0.628129 | − | 0.778109i | \(-0.283821\pi\) | ||||
0.628129 | + | 0.778109i | \(0.283821\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8427 | −0.374688 |
(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 | 4008.2.a.i.1.6 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.6 | 9 | 4.3 | odd | 2 |