Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, 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("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.713538\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | ||||||||
\(3\) | −0.286462 | −0.165389 | −0.0826945 | − | 0.996575i | \(-0.526353\pi\) | ||||
−0.0826945 | + | 0.996575i | \(0.526353\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.286462 | −0.108272 | −0.0541362 | − | 0.998534i | \(-0.517241\pi\) | ||||
−0.0541362 | + | 0.998534i | \(0.517241\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91794 | −0.972646 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.26819 | 1.28691 | 0.643454 | − | 0.765485i | \(-0.277501\pi\) | ||||
0.643454 | + | 0.765485i | \(0.277501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.20440 | −0.888741 | −0.444371 | − | 0.895843i | \(-0.646573\pi\) | ||||
−0.444371 | + | 0.895843i | \(0.646573\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.286462 | −0.0694773 | −0.0347386 | − | 0.999396i | \(-0.511060\pi\) | ||||
−0.0347386 | + | 0.999396i | \(0.511060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0820605 | 0.0179071 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.936212 | −0.195214 | −0.0976069 | − | 0.995225i | \(-0.531119\pi\) | ||||
−0.0976069 | + | 0.995225i | \(0.531119\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.69527 | 0.326254 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.26819 | 0.421192 | 0.210596 | − | 0.977573i | \(-0.432460\pi\) | ||||
0.210596 | + | 0.977573i | \(0.432460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18613 | −0.751851 | −0.375925 | − | 0.926650i | \(-0.622675\pi\) | ||||
−0.375925 | + | 0.926650i | \(0.622675\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.22267 | −0.212840 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.67699 | −1.42649 | −0.713244 | − | 0.700915i | \(-0.752775\pi\) | ||||
−0.713244 | + | 0.700915i | \(0.752775\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.917939 | 0.146988 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08206 | 0.168989 | 0.0844947 | − | 0.996424i | \(-0.473072\pi\) | ||||
0.0844947 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.42708 | −0.675123 | −0.337561 | − | 0.941304i | \(-0.609602\pi\) | ||||
−0.337561 | + | 0.941304i | \(0.609602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.759053 | 0.110719 | 0.0553596 | − | 0.998466i | \(-0.482369\pi\) | ||||
0.0553596 | + | 0.998466i | \(0.482369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91794 | −0.988277 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0820605 | 0.0114908 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.42708 | −0.608106 | −0.304053 | − | 0.952655i | \(-0.598340\pi\) | ||||
−0.304053 | + | 0.952655i | \(0.598340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.286462 | 0.0379428 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.70050 | −0.611953 | −0.305976 | − | 0.952039i | \(-0.598983\pi\) | ||||
−0.305976 | + | 0.952039i | \(0.598983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1861 | 1.30420 | 0.652100 | − | 0.758133i | \(-0.273888\pi\) | ||||
0.652100 | + | 0.758133i | \(0.273888\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.835879 | 0.105311 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.82284 | −1.20005 | −0.600025 | − | 0.799981i | \(-0.704843\pi\) | ||||
−0.600025 | + | 0.799981i | \(0.704843\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.268189 | 0.0322862 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.83588 | 0.573913 | 0.286957 | − | 0.957944i | \(-0.407356\pi\) | ||||
0.286957 | + | 0.957944i | \(0.407356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4726 | −1.22572 | −0.612862 | − | 0.790190i | \(-0.709982\pi\) | ||||
−0.612862 | + | 0.790190i | \(0.709982\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.22267 | −0.139337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.10407 | 0.574253 | 0.287126 | − | 0.957893i | \(-0.407300\pi\) | ||||
0.287126 | + | 0.957893i | \(0.407300\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.26819 | 0.918688 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7355 | −1.72720 | −0.863600 | − | 0.504177i | \(-0.831796\pi\) | ||||
−0.863600 | + | 0.504177i | \(0.831796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.649750 | −0.0696605 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.75382 | −1.03390 | −0.516951 | − | 0.856015i | \(-0.672933\pi\) | ||||
−0.516951 | + | 0.856015i | \(0.672933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.917939 | 0.0962262 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.19917 | 0.124348 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.61320 | 0.976073 | 0.488037 | − | 0.872823i | \(-0.337713\pi\) | ||||
0.488037 | + | 0.872823i | \(0.337713\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.4543 | −1.25171 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.731811 | 0.0728179 | 0.0364089 | − | 0.999337i | \(-0.488408\pi\) | ||||
0.0364089 | + | 0.999337i | \(0.488408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.10407 | 0.305853 | 0.152926 | − | 0.988238i | \(-0.451130\pi\) | ||||
0.152926 | + | 0.988238i | \(0.451130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.1731 | −1.37016 | −0.685082 | − | 0.728466i | \(-0.740234\pi\) | ||||
−0.685082 | + | 0.728466i | \(0.740234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.61844 | −0.921279 | −0.460640 | − | 0.887587i | \(-0.652380\pi\) | ||||
−0.460640 | + | 0.887587i | \(0.652380\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.48563 | 0.235925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.77733 | −0.825701 | −0.412851 | − | 0.910799i | \(-0.635467\pi\) | ||||
−0.412851 | + | 0.910799i | \(0.635467\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.35025 | 0.864431 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0820605 | 0.00752248 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.21744 | 0.656131 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.309969 | −0.0279490 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.77209 | −0.600926 | −0.300463 | − | 0.953793i | \(-0.597141\pi\) | ||||
−0.300463 | + | 0.953793i | \(0.597141\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.26819 | 0.111658 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.91794 | −0.254942 | −0.127471 | − | 0.991842i | \(-0.540686\pi\) | ||||
−0.127471 | + | 0.991842i | \(0.540686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.286462 | 0.0248394 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4360 | 1.23335 | 0.616677 | − | 0.787216i | \(-0.288478\pi\) | ||||
0.616677 | + | 0.787216i | \(0.288478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.29950 | −0.195041 | −0.0975205 | − | 0.995234i | \(-0.531091\pi\) | ||||
−0.0975205 | + | 0.995234i | \(0.531091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.217440 | −0.0183117 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.6770 | −1.14373 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.98173 | 0.163450 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.75382 | 0.553294 | 0.276647 | − | 0.960972i | \(-0.410777\pi\) | ||||
0.276647 | + | 0.960972i | \(0.410777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8866 | −0.967320 | −0.483660 | − | 0.875256i | \(-0.660693\pi\) | ||||
−0.483660 | + | 0.875256i | \(0.660693\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.835879 | 0.0675768 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1731 | 1.13114 | 0.565568 | − | 0.824702i | \(-0.308657\pi\) | ||||
0.565568 | + | 0.824702i | \(0.308657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.26819 | 0.100574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.268189 | 0.0211363 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.89443 | −0.618340 | −0.309170 | − | 0.951007i | \(-0.600051\pi\) | ||||
−0.309170 | + | 0.951007i | \(0.600051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.4726 | −1.58422 | −0.792108 | − | 0.610381i | \(-0.791017\pi\) | ||||
−0.792108 | + | 0.610381i | \(0.791017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.73181 | −0.210139 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.91794 | 0.223140 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.0492 | 1.82843 | 0.914215 | − | 0.405229i | \(-0.132808\pi\) | ||||
0.914215 | + | 0.405229i | \(0.132808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.34651 | 0.101210 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.6718 | 1.39559 | 0.697796 | − | 0.716296i | \(-0.254164\pi\) | ||||
0.697796 | + | 0.716296i | \(0.254164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.53638 | −0.262857 | −0.131428 | − | 0.991326i | \(-0.541956\pi\) | ||||
−0.131428 | + | 0.991326i | \(0.541956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.91794 | −0.215700 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.22267 | −0.0894108 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.485629 | −0.0353243 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2682 | −1.03241 | −0.516205 | − | 0.856465i | \(-0.672656\pi\) | ||||
−0.516205 | + | 0.856465i | \(0.672656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.18089 | 0.588874 | 0.294437 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294437 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.6404 | −0.900595 | −0.450297 | − | 0.892879i | \(-0.648682\pi\) | ||||
−0.450297 | + | 0.892879i | \(0.648682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.10407 | −0.290930 | −0.145465 | − | 0.989363i | \(-0.546468\pi\) | ||||
−0.145465 | + | 0.989363i | \(0.546468\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.81387 | 0.198475 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.649750 | −0.0456035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.73181 | 0.189874 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.26819 | −0.295237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.53638 | 0.105769 | 0.0528843 | − | 0.998601i | \(-0.483159\pi\) | ||||
0.0528843 | + | 0.998601i | \(0.483159\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.38530 | −0.0949189 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.19917 | 0.0814048 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.00000 | 0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.917939 | 0.0617473 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.40880 | −0.0943404 | −0.0471702 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471702 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.9179 | −1.52112 | −0.760559 | − | 0.649269i | \(-0.775075\pi\) | ||||
−0.760559 | + | 0.649269i | \(0.775075\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.78513 | 0.250128 | 0.125064 | − | 0.992149i | \(-0.460086\pi\) | ||||
0.125064 | + | 0.992149i | \(0.460086\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.350250 | 0.0230447 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.26819 | −0.148594 | −0.0742970 | − | 0.997236i | \(-0.523671\pi\) | ||||
−0.0742970 | + | 0.997236i | \(0.523671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.46212 | −0.0949750 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.18613 | −0.141409 | −0.0707045 | − | 0.997497i | \(-0.522525\pi\) | ||||
−0.0707045 | + | 0.997497i | \(0.522525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.9907 | 1.28771 | 0.643857 | − | 0.765146i | \(-0.277333\pi\) | ||||
0.643857 | + | 0.765146i | \(0.277333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.45432 | −0.478195 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.20440 | 0.203891 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.50764 | 0.285660 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.35025 | 0.0852270 | 0.0426135 | − | 0.999092i | \(-0.486432\pi\) | ||||
0.0426135 | + | 0.999092i | \(0.486432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.99593 | −0.251222 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.9582 | 0.745933 | 0.372967 | − | 0.927845i | \(-0.378341\pi\) | ||||
0.372967 | + | 0.927845i | \(0.378341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.48563 | 0.154449 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.61844 | −0.409671 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.31370 | 0.512645 | 0.256322 | − | 0.966591i | \(-0.417489\pi\) | ||||
0.256322 | + | 0.966591i | \(0.417489\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.79410 | 0.170996 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.02201 | −0.306197 | −0.153099 | − | 0.988211i | \(-0.548925\pi\) | ||||
−0.153099 | + | 0.988211i | \(0.548925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.96869 | 0.423318 | 0.211659 | − | 0.977344i | \(-0.432113\pi\) | ||||
0.211659 | + | 0.977344i | \(0.432113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.262955 | −0.0159148 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7083 | 0.763568 | 0.381784 | − | 0.924252i | \(-0.375310\pi\) | ||||
0.381784 | + | 0.924252i | \(0.375310\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.2149 | 0.731285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5364 | −0.986478 | −0.493239 | − | 0.869894i | \(-0.664187\pi\) | ||||
−0.493239 | + | 0.869894i | \(0.664187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1548 | 1.55474 | 0.777371 | − | 0.629042i | \(-0.216553\pi\) | ||||
0.777371 | + | 0.629042i | \(0.216553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.309969 | −0.0182969 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9179 | −0.995173 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.75382 | −0.161432 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.95449 | 0.231023 | 0.115512 | − | 0.993306i | \(-0.463149\pi\) | ||||
0.115512 | + | 0.993306i | \(0.463149\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.23571 | 0.419859 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | 0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26819 | 0.0730972 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.209636 | −0.0120433 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7355 | 1.18344 | 0.591720 | − | 0.806144i | \(-0.298449\pi\) | ||||
0.591720 | + | 0.806144i | \(0.298449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.889198 | −0.0505847 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.97799 | −0.112162 | −0.0560808 | − | 0.998426i | \(-0.517860\pi\) | ||||
−0.0560808 | + | 0.998426i | \(0.517860\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.67699 | 0.490453 | 0.245226 | − | 0.969466i | \(-0.421138\pi\) | ||||
0.245226 | + | 0.969466i | \(0.421138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.34502 | 0.131709 | 0.0658546 | − | 0.997829i | \(-0.479023\pi\) | ||||
0.0658546 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.68106 | 0.542035 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.06005 | 0.226610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.286462 | 0.0159392 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.75532 | 0.152369 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.217440 | −0.0119878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8579 | −1.25638 | −0.628192 | − | 0.778059i | \(-0.716205\pi\) | ||||
−0.628192 | + | 0.778059i | \(0.716205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.3189 | 1.38747 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.386795 | 0.0210701 | 0.0105350 | − | 0.999945i | \(-0.496647\pi\) | ||||
0.0105350 | + | 0.999945i | \(0.496647\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.51437 | 0.136562 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.8672 | −0.967563 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.98696 | 0.215276 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.1406 | −0.759108 | −0.379554 | − | 0.925170i | \(-0.623923\pi\) | ||||
−0.379554 | + | 0.925170i | \(0.623923\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.81387 | −0.150623 | −0.0753115 | − | 0.997160i | \(-0.523995\pi\) | ||||
−0.0753115 | + | 0.997160i | \(0.523995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.43231 | −0.289955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3137 | 0.708617 | 0.354308 | − | 0.935129i | \(-0.384716\pi\) | ||||
0.354308 | + | 0.935129i | \(0.384716\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0235072 | −0.00124413 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.1861 | 0.748715 | 0.374358 | − | 0.927284i | \(-0.377863\pi\) | ||||
0.374358 | + | 0.927284i | \(0.377863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.06752 | −0.108517 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0272 | 1.46301 | 0.731505 | − | 0.681836i | \(-0.238818\pi\) | ||||
0.731505 | + | 0.681836i | \(0.238818\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.15739 | −0.164367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.26819 | 0.0658411 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3502 | 1.26081 | 0.630404 | − | 0.776267i | \(-0.282889\pi\) | ||||
0.630404 | + | 0.776267i | \(0.282889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.26819 | −0.374331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.8866 | 1.48381 | 0.741903 | − | 0.670507i | \(-0.233923\pi\) | ||||
0.741903 | + | 0.670507i | \(0.233923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.93995 | 0.0993865 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3398 | 0.528338 | 0.264169 | − | 0.964476i | \(-0.414902\pi\) | ||||
0.264169 | + | 0.964476i | \(0.414902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.9179 | 0.656656 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.9086 | 1.71924 | 0.859618 | − | 0.510937i | \(-0.170702\pi\) | ||||
0.859618 | + | 0.510937i | \(0.170702\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.268189 | 0.0135629 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.835879 | 0.0421645 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.8866 | 1.70072 | 0.850361 | − | 0.526200i | \(-0.176384\pi\) | ||||
0.850361 | + | 0.526200i | \(0.176384\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0820605 | −0.00410816 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5051 | −0.524598 | −0.262299 | − | 0.964987i | \(-0.584481\pi\) | ||||
−0.262299 | + | 0.964987i | \(0.584481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.4140 | 0.668201 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.0350 | −1.83576 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.78256 | −0.335376 | −0.167688 | − | 0.985840i | \(-0.553630\pi\) | ||||
−0.167688 | + | 0.985840i | \(0.553630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.13538 | −0.203983 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.34651 | 0.0662577 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.658720 | 0.0322576 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.6498 | 0.911100 | 0.455550 | − | 0.890210i | \(-0.349443\pi\) | ||||
0.455550 | + | 0.890210i | \(0.349443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.64975 | 0.470300 | 0.235150 | − | 0.971959i | \(-0.424442\pi\) | ||||
0.235150 | + | 0.971959i | \(0.424442\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.21487 | −0.107691 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.91794 | −0.141209 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.91794 | 0.189160 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7758 | −1.62692 | −0.813462 | − | 0.581618i | \(-0.802420\pi\) | ||||
−0.813462 | + | 0.581618i | \(0.802420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.08986 | −0.0523755 | −0.0261878 | − | 0.999657i | \(-0.508337\pi\) | ||||
−0.0261878 | + | 0.999657i | \(0.508337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.936212 | 0.0447851 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.9687 | −0.618962 | −0.309481 | − | 0.950906i | \(-0.600155\pi\) | ||||
−0.309481 | + | 0.950906i | \(0.600155\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.1861 | 0.961244 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.9437 | 1.51769 | 0.758845 | − | 0.651271i | \(-0.225764\pi\) | ||||
0.758845 | + | 0.651271i | \(0.225764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.93471 | −0.0915088 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.05075 | −0.238360 | −0.119180 | − | 0.992873i | \(-0.538026\pi\) | ||||
−0.119180 | + | 0.992873i | \(0.538026\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.61844 | 0.217474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.40507 | 0.159984 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.0948 | −1.64166 | −0.820832 | − | 0.571170i | \(-0.806490\pi\) | ||||
−0.820832 | + | 0.571170i | \(0.806490\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.485629 | −0.0226672 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.8866 | −1.29881 | −0.649405 | − | 0.760443i | \(-0.724982\pi\) | ||||
−0.649405 | + | 0.760443i | \(0.724982\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.0037 | 1.30144 | 0.650722 | − | 0.759316i | \(-0.274466\pi\) | ||||
0.650722 | + | 0.759316i | \(0.274466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.4543 | −0.807690 | −0.403845 | − | 0.914828i | \(-0.632326\pi\) | ||||
−0.403845 | + | 0.914828i | \(0.632326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.81387 | 0.129933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.06005 | −0.187077 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.8956 | −0.868821 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.9179 | 0.591472 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.0440 | 1.18998 | 0.594991 | − | 0.803733i | \(-0.297156\pi\) | ||||
0.594991 | + | 0.803733i | \(0.297156\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.8046 | 1.26778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0768261 | −0.00349571 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.9907 | 0.996494 | 0.498247 | − | 0.867035i | \(-0.333977\pi\) | ||||
0.498247 | + | 0.867035i | \(0.333977\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.26146 | 0.102267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.9907 | −1.53398 | −0.766989 | − | 0.641660i | \(-0.778246\pi\) | ||||
−0.766989 | + | 0.641660i | \(0.778246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.649750 | −0.0292633 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.38530 | −0.0621390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.83331 | 0.305901 | 0.152950 | − | 0.988234i | \(-0.451123\pi\) | ||||
0.152950 | + | 0.988234i | \(0.451123\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.86462 | 0.262012 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.4685 | −1.53688 | −0.768438 | − | 0.639925i | \(-0.778966\pi\) | ||||
−0.768438 | + | 0.639925i | \(0.778966\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.782560 | 0.0347547 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.9179 | 0.838523 | 0.419261 | − | 0.907866i | \(-0.362289\pi\) | ||||
0.419261 | + | 0.907866i | \(0.362289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | 0.132712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.69527 | −0.0748478 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.23978 | 0.142485 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.88920 | −0.302402 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.62774 | −0.0713127 | −0.0356563 | − | 0.999364i | \(-0.511352\pi\) | ||||
−0.0356563 | + | 0.999364i | \(0.511352\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.16669 | 0.0510158 | 0.0255079 | − | 0.999675i | \(-0.491880\pi\) | ||||
0.0255079 | + | 0.999675i | \(0.491880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.19917 | 0.0522365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1235 | −0.961892 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.7158 | 0.595214 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.46736 | −0.150188 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.34875 | −0.230816 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.5271 | −1.27182 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9399 | −1.02926 | −0.514629 | − | 0.857413i | \(-0.672070\pi\) | ||||
−0.514629 | + | 0.857413i | \(0.672070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.01304 | 0.0434736 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8139 | −0.633395 | −0.316698 | − | 0.948527i | \(-0.602574\pi\) | ||||
−0.316698 | + | 0.948527i | \(0.602574\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.7225 | −1.26853 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.26819 | −0.0966281 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.46212 | −0.0621757 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.3592 | 1.66770 | 0.833852 | − | 0.551988i | \(-0.186131\pi\) | ||||
0.833852 | + | 0.551988i | \(0.186131\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.1861 | 0.600009 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.350250 | 0.0147876 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.55722 | −0.402789 | −0.201394 | − | 0.979510i | \(-0.564547\pi\) | ||||
−0.201394 | + | 0.979510i | \(0.564547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.36852 | −0.0994686 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.2995 | 0.892922 | 0.446461 | − | 0.894803i | \(-0.352684\pi\) | ||||
0.446461 | + | 0.894803i | \(0.352684\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4543 | −0.730440 | −0.365220 | − | 0.930921i | \(-0.619006\pi\) | ||||
−0.365220 | + | 0.930921i | \(0.619006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.08729 | 0.170749 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.2861 | 1.55224 | 0.776121 | − | 0.630584i | \(-0.217185\pi\) | ||||
0.776121 | + | 0.630584i | \(0.217185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.34352 | −0.0973932 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.50764 | 0.187008 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8956 | −0.782576 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.73181 | 0.319126 | 0.159563 | − | 0.987188i | \(-0.448991\pi\) | ||||
0.159563 | + | 0.987188i | \(0.448991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.18613 | 0.172486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.62101 | 0.148948 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.74858 | 0.277131 | 0.138566 | − | 0.990353i | \(-0.455751\pi\) | ||||
0.138566 | + | 0.990353i | \(0.455751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.17566 | 0.0481166 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.9687 | −0.693322 | −0.346661 | − | 0.937991i | \(-0.612685\pi\) | ||||
−0.346661 | + | 0.937991i | \(0.612685\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7251 | 1.29409 | 0.647046 | − | 0.762451i | \(-0.276004\pi\) | ||||
0.647046 | + | 0.762451i | \(0.276004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.6625 | 1.16723 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.84518 | −0.156071 | −0.0780356 | − | 0.996951i | \(-0.524865\pi\) | ||||
−0.0780356 | + | 0.996951i | \(0.524865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.186129 | 0.00754232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.43231 | −0.0984007 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1208 | 1.29735 | 0.648674 | − | 0.761066i | \(-0.275324\pi\) | ||||
0.648674 | + | 0.761066i | \(0.275324\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.2630 | −1.41963 | −0.709817 | − | 0.704387i | \(-0.751222\pi\) | ||||
−0.709817 | + | 0.704387i | \(0.751222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.29020 | 0.373405 | 0.186702 | − | 0.982417i | \(-0.440220\pi\) | ||||
0.186702 | + | 0.982417i | \(0.440220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.58713 | −0.0636893 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.79410 | 0.111943 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.22267 | 0.0488289 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.48563 | 0.0991085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.5271 | −1.05603 | −0.528013 | − | 0.849236i | \(-0.677063\pi\) | ||||
−0.528013 | + | 0.849236i | \(0.677063\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.440114 | −0.0174930 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.1679 | 0.878322 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1108 | −0.558215 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.86462 | −0.310634 | −0.155317 | − | 0.987865i | \(-0.549640\pi\) | ||||
−0.155317 | + | 0.987865i | \(0.549640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.67176 | 0.0659277 | 0.0329638 | − | 0.999457i | \(-0.489505\pi\) | ||||
0.0329638 | + | 0.999457i | \(0.489505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.4909 | −1.51323 | −0.756616 | − | 0.653859i | \(-0.773149\pi\) | ||||
−0.756616 | + | 0.653859i | \(0.773149\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.0626 | −0.787527 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.343516 | −0.0134634 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9985 | 1.01740 | 0.508700 | − | 0.860944i | \(-0.330126\pi\) | ||||
0.508700 | + | 0.860944i | \(0.330126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.5584 | 1.19220 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 46.9594 | 1.82928 | 0.914639 | − | 0.404272i | \(-0.132475\pi\) | ||||
0.914639 | + | 0.404272i | \(0.132475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7225 | −1.38944 | −0.694722 | − | 0.719278i | \(-0.744473\pi\) | ||||
−0.694722 | + | 0.719278i | \(0.744473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.262955 | −0.0102123 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.12351 | −0.0822225 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.403569 | 0.0156029 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.4763 | 1.67838 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3450 | −1.05407 | −0.527036 | − | 0.849843i | \(-0.676697\pi\) | ||||
−0.527036 | + | 0.849843i | \(0.676697\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.9944 | 1.53711 | 0.768555 | − | 0.639783i | \(-0.220976\pi\) | ||||
0.768555 | + | 0.639783i | \(0.220976\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.75382 | −0.105682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.56512 | 0.251576 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.0130 | −0.804042 | −0.402021 | − | 0.915631i | \(-0.631692\pi\) | ||||
−0.402021 | + | 0.915631i | \(0.631692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.08430 | −0.0413685 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.1861 | 0.540448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.7445 | −0.408741 | −0.204370 | − | 0.978894i | \(-0.565515\pi\) | ||||
−0.204370 | + | 0.978894i | \(0.565515\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.56769 | 0.135525 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.309969 | −0.0117409 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.649750 | 0.0245758 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.3029 | 1.59776 | 0.798879 | − | 0.601491i | \(-0.205427\pi\) | ||||
0.798879 | + | 0.601491i | \(0.205427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.67699 | 0.327259 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.209636 | −0.00788417 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.5584 | −1.52320 | −0.761601 | − | 0.648046i | \(-0.775586\pi\) | ||||
−0.761601 | + | 0.648046i | \(0.775586\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.8934 | −0.558545 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.91911 | 0.146772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.626243 | 0.0233875 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.8866 | 0.629765 | 0.314882 | − | 0.949131i | \(-0.398035\pi\) | ||||
0.314882 | + | 0.949131i | \(0.398035\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.889198 | −0.0331155 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.72658 | −0.212974 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4398 | −1.01769 | −0.508843 | − | 0.860860i | \(-0.669926\pi\) | ||||
−0.508843 | + | 0.860860i | \(0.669926\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.6692 | −0.839600 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.26819 | 0.0469057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0078 | 0.517390 | 0.258695 | − | 0.965959i | \(-0.416708\pi\) | ||||
0.258695 | + | 0.965959i | \(0.416708\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.9257 | −1.54435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.7851 | −0.727808 | −0.363904 | − | 0.931437i | \(-0.618556\pi\) | ||||
−0.363904 | + | 0.931437i | \(0.618556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.917939 | −0.0337213 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.8344 | −1.53475 | −0.767377 | − | 0.641196i | \(-0.778439\pi\) | ||||
−0.767377 | + | 0.641196i | \(0.778439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.9154 | 1.67996 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.06005 | 0.148351 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.4983 | 1.76973 | 0.884865 | − | 0.465848i | \(-0.154251\pi\) | ||||
0.884865 | + | 0.465848i | \(0.154251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.386795 | −0.0140956 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.2537 | −1.17228 | −0.586139 | − | 0.810210i | \(-0.699353\pi\) | ||||
−0.586139 | + | 0.810210i | \(0.699353\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.14468 | 0.0415493 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6184 | −0.928668 | −0.464334 | − | 0.885660i | \(-0.653706\pi\) | ||||
−0.464334 | + | 0.885660i | \(0.653706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.75532 | 0.0997492 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.0623 | 0.543868 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.3096 | 1.52572 | 0.762862 | − | 0.646561i | \(-0.223793\pi\) | ||||
0.762862 | + | 0.646561i | \(0.223793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.42558 | −0.123369 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.889198 | 0.0319822 | 0.0159911 | − | 0.999872i | \(-0.494910\pi\) | ||||
0.0159911 | + | 0.999872i | \(0.494910\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.712038 | −0.0255442 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.08206 | −0.0387688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.6404 | 0.738573 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.84518 | 0.137416 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.6650 | −1.80601 | −0.903007 | − | 0.429627i | \(-0.858645\pi\) | ||||
−0.903007 | + | 0.429627i | \(0.858645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.38156 | −0.0847858 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.51437 | 0.0894007 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.6404 | −1.15910 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.4909 | −1.18631 | −0.593154 | − | 0.805089i | \(-0.702117\pi\) | ||||
−0.593154 | + | 0.805089i | \(0.702117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.217440 | −0.00769247 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.4611 | 1.00562 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −44.6990 | −1.57739 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.43861 | 0.0506416 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.35025 | −0.223263 | −0.111631 | − | 0.993750i | \(-0.535608\pi\) | ||||
−0.111631 | + | 0.993750i | \(0.535608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.08463 | −0.0380865 | −0.0190433 | − | 0.999819i | \(-0.506062\pi\) | ||||
−0.0190433 | + | 0.999819i | \(0.506062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.99627 | −0.0700121 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.42708 | 0.154884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.67849 | −0.0935941 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3630 | −0.431470 | −0.215735 | − | 0.976452i | \(-0.569215\pi\) | ||||
−0.215735 | + | 0.976452i | \(0.569215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.0765 | −0.943827 | −0.471914 | − | 0.881645i | \(-0.656437\pi\) | ||||
−0.471914 | + | 0.881645i | \(0.656437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0765 | 0.593808 | 0.296904 | − | 0.954907i | \(-0.404046\pi\) | ||||
0.296904 | + | 0.954907i | \(0.404046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.5804 | −0.992638 | −0.496319 | − | 0.868140i | \(-0.665315\pi\) | ||||
−0.496319 | + | 0.868140i | \(0.665315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.64045 | −0.126286 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.98173 | 0.0686628 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.09660 | −0.245294 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.9019 | −1.92995 | −0.964974 | − | 0.262346i | \(-0.915504\pi\) | ||||
−0.964974 | + | 0.262346i | \(0.915504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8553 | −0.822597 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.73705 | 0.163153 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.06752 | −0.0710409 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.49236 | −0.257137 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.12351 | 0.278470 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.93214 | 0.168873 | 0.0844367 | − | 0.996429i | \(-0.473091\pi\) | ||||
0.0844367 | + | 0.996429i | \(0.473091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.9411 | −1.36436 | −0.682181 | − | 0.731183i | \(-0.738968\pi\) | ||||
−0.682181 | + | 0.731183i | \(0.738968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.99070 | 0.0679217 | 0.0339608 | − | 0.999423i | \(-0.489188\pi\) | ||||
0.0339608 | + | 0.999423i | \(0.489188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0887944 | 0.00302611 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.9817 | −1.08867 | −0.544335 | − | 0.838868i | \(-0.683218\pi\) | ||||
−0.544335 | + | 0.838868i | \(0.683218\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.84635 | 0.164591 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.7851 | 0.739010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.4763 | 1.06653 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.0507 | −0.949374 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.2917 | 0.752737 | 0.376369 | − | 0.926470i | \(-0.377173\pi\) | ||||
0.376369 | + | 0.926470i | \(0.377173\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.13281 | −0.0382087 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.6912 | 1.20247 | 0.601233 | − | 0.799073i | \(-0.294676\pi\) | ||||
0.601233 | + | 0.799073i | \(0.294676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.9948 | −0.605572 | −0.302786 | − | 0.953059i | \(-0.597917\pi\) | ||||
−0.302786 | + | 0.953059i | \(0.597917\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.3566 | −0.817813 | −0.408907 | − | 0.912576i | \(-0.634090\pi\) | ||||
−0.408907 | + | 0.912576i | \(0.634090\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93995 | 0.0650637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.2902 | 1.18227 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.759053 | −0.0254007 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.859386 | −0.0286941 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.49493 | −0.316674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26819 | 0.0422495 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.363288 | −0.0120895 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.73821 | −0.190534 | −0.0952671 | − | 0.995452i | \(-0.530371\pi\) | ||||
−0.0952671 | + | 0.995452i | \(0.530371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.13538 | −0.0708261 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8291 | −1.55152 | −0.775759 | − | 0.631029i | \(-0.782633\pi\) | ||||
−0.775759 | + | 0.631029i | \(0.782633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67.1623 | −2.22275 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.835879 | 0.0276032 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.32151 | 0.0765795 | 0.0382897 | − | 0.999267i | \(-0.487809\pi\) | ||||
0.0382897 | + | 0.999267i | \(0.487809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.93995 | −0.195728 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.4961 | −0.510060 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.05748 | −0.297487 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.5610 | −0.838628 | −0.419314 | − | 0.907841i | \(-0.637729\pi\) | ||||
−0.419314 | + | 0.907841i | \(0.637729\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.91794 | 0.226726 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.566620 | 0.0185503 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.7501 | 0.841219 | 0.420609 | − | 0.907242i | \(-0.361816\pi\) | ||||
0.420609 | + | 0.907242i | \(0.361816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.48563 | −0.0811154 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.1261 | −0.949483 | −0.474741 | − | 0.880125i | \(-0.657458\pi\) | ||||
−0.474741 | + | 0.880125i | \(0.657458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.01304 | −0.0329891 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.21711 | 0.202029 | 0.101014 | − | 0.994885i | \(-0.467791\pi\) | ||||
0.101014 | + | 0.994885i | \(0.467791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.5584 | 1.08935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.671758 | −0.0217832 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8266 | −1.54925 | −0.774627 | − | 0.632418i | \(-0.782063\pi\) | ||||
−0.774627 | + | 0.632418i | \(0.782063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.77326 | −0.0896467 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.13538 | −0.133538 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4763 | −0.434720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.3562 | 1.33269 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.2301 | 1.19724 | 0.598620 | − | 0.801033i | \(-0.295716\pi\) | ||||
0.598620 | + | 0.801033i | \(0.295716\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0820605 | −0.00263616 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8359 | 1.21421 | 0.607106 | − | 0.794621i | \(-0.292331\pi\) | ||||
0.607106 | + | 0.794621i | \(0.292331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.658720 | 0.0211176 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55.8684 | −1.78739 | −0.893694 | − | 0.448678i | \(-0.851895\pi\) | ||||
−0.893694 | + | 0.448678i | \(0.851895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.6311 | −1.33054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.0660 | 0.896079 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.93738 | 0.221268 | 0.110634 | − | 0.993861i | \(-0.464712\pi\) | ||||
0.110634 | + | 0.993861i | \(0.464712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0622883 | 0.00198266 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.14468 | 0.131793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.5897 | 1.16231 | 0.581155 | − | 0.813793i | \(-0.302601\pi\) | ||||
0.581155 | + | 0.813793i | \(0.302601\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.54792 | 0.207792 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.7538 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.7098 | −0.465398 |
(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 | 1900.2.a.f.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 7600.2.a.by.1.2 | 3 | |||
5.2 | odd | 4 | 1900.2.c.g.1749.4 | 6 | |||
5.3 | odd | 4 | 1900.2.c.g.1749.3 | 6 | |||
5.4 | even | 2 | 1900.2.a.h.1.2 | yes | 3 | ||
20.19 | odd | 2 | 7600.2.a.bj.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1900.2.a.h.1.2 | yes | 3 | 5.4 | even | 2 | ||
1900.2.c.g.1749.3 | 6 | 5.3 | odd | 4 | |||
1900.2.c.g.1749.4 | 6 | 5.2 | odd | 4 | |||
7600.2.a.bj.1.2 | 3 | 20.19 | odd | 2 | |||
7600.2.a.by.1.2 | 3 | 4.3 | odd | 2 |