Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, 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("7500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.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: | \(59.8878015160\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 6x^{2} + 7x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.12233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7500.1 |
$q$-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 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.50430 | −0.568572 | −0.284286 | − | 0.958740i | \(-0.591756\pi\) | ||||
−0.284286 | + | 0.958740i | \(0.591756\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.17438 | −1.86164 | −0.930822 | − | 0.365473i | \(-0.880907\pi\) | ||||
−0.930822 | + | 0.365473i | \(0.880907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.55634 | 0.986352 | 0.493176 | − | 0.869930i | \(-0.335836\pi\) | ||||
0.493176 | + | 0.869930i | \(0.335836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.495700 | −0.120225 | −0.0601125 | − | 0.998192i | \(-0.519146\pi\) | ||||
−0.0601125 | + | 0.998192i | \(0.519146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.311674 | 0.0715030 | 0.0357515 | − | 0.999361i | \(-0.488618\pi\) | ||||
0.0357515 | + | 0.999361i | \(0.488618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50430 | −0.328265 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.06064 | 0.638188 | 0.319094 | − | 0.947723i | \(-0.396621\pi\) | ||||
0.319094 | + | 0.947723i | \(0.396621\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.122334 | −0.0227168 | −0.0113584 | − | 0.999935i | \(-0.503616\pi\) | ||||
−0.0113584 | + | 0.999935i | \(0.503616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.94362 | −0.528690 | −0.264345 | − | 0.964428i | \(-0.585156\pi\) | ||||
−0.264345 | + | 0.964428i | \(0.585156\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.17438 | −1.07482 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.36700 | 0.717930 | 0.358965 | − | 0.933351i | \(-0.383130\pi\) | ||||
0.358965 | + | 0.933351i | \(0.383130\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.55634 | 0.569470 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.25327 | 0.664249 | 0.332124 | − | 0.943236i | \(-0.392235\pi\) | ||||
0.332124 | + | 0.943236i | \(0.392235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.62663 | 0.553056 | 0.276528 | − | 0.961006i | \(-0.410816\pi\) | ||||
0.276528 | + | 0.961006i | \(0.410816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.28215 | −0.770480 | −0.385240 | − | 0.922816i | \(-0.625881\pi\) | ||||
−0.385240 | + | 0.922816i | \(0.625881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.73708 | −0.676726 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.495700 | −0.0694120 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.59978 | 1.18127 | 0.590636 | − | 0.806938i | \(-0.298877\pi\) | ||||
0.590636 | + | 0.806938i | \(0.298877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.311674 | 0.0412823 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8826 | 1.67717 | 0.838584 | − | 0.544772i | \(-0.183384\pi\) | ||||
0.838584 | + | 0.544772i | \(0.183384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3209 | −1.44950 | −0.724748 | − | 0.689014i | \(-0.758044\pi\) | ||||
−0.724748 | + | 0.689014i | \(0.758044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50430 | −0.189524 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2414 | −1.61769 | −0.808846 | − | 0.588020i | \(-0.799908\pi\) | ||||
−0.808846 | + | 0.588020i | \(0.799908\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.06064 | 0.368458 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.26823 | 0.387868 | 0.193934 | − | 0.981015i | \(-0.437875\pi\) | ||||
0.193934 | + | 0.981015i | \(0.437875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.9668 | −1.86877 | −0.934385 | − | 0.356264i | \(-0.884050\pi\) | ||||
−0.934385 | + | 0.356264i | \(0.884050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.28811 | 1.05848 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.52746 | −0.959414 | −0.479707 | − | 0.877429i | \(-0.659257\pi\) | ||||
−0.479707 | + | 0.877429i | \(0.659257\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3381 | −1.24452 | −0.622260 | − | 0.782810i | \(-0.713785\pi\) | ||||
−0.622260 | + | 0.782810i | \(0.713785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.122334 | −0.0131155 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.1326 | 1.49805 | 0.749024 | − | 0.662543i | \(-0.230523\pi\) | ||||
0.749024 | + | 0.662543i | \(0.230523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.34980 | −0.560812 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.94362 | −0.305239 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4828 | 1.16590 | 0.582949 | − | 0.812509i | \(-0.301899\pi\) | ||||
0.582949 | + | 0.812509i | \(0.301899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.17438 | −0.620548 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.8359 | −1.47622 | −0.738111 | − | 0.674679i | \(-0.764282\pi\) | ||||
−0.738111 | + | 0.674679i | \(0.764282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.2645 | −1.89819 | −0.949096 | − | 0.314987i | \(-0.898000\pi\) | ||||
−0.949096 | + | 0.314987i | \(0.898000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.63523 | −0.834799 | −0.417400 | − | 0.908723i | \(-0.637058\pi\) | ||||
−0.417400 | + | 0.908723i | \(0.637058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6893 | −1.79011 | −0.895055 | − | 0.445955i | \(-0.852864\pi\) | ||||
−0.895055 | + | 0.445955i | \(0.852864\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.36700 | 0.414497 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.05638 | −0.569736 | −0.284868 | − | 0.958567i | \(-0.591950\pi\) | ||||
−0.284868 | + | 0.958567i | \(0.591950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.55634 | 0.328784 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.745682 | 0.0683566 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.1229 | 2.46572 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.25327 | 0.383504 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.24565 | 0.820418 | 0.410209 | − | 0.911991i | \(-0.365456\pi\) | ||||
0.410209 | + | 0.911991i | \(0.365456\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.62663 | 0.319307 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.0155 | 1.66140 | 0.830698 | − | 0.556724i | \(-0.187942\pi\) | ||||
0.830698 | + | 0.556724i | \(0.187942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.468851 | −0.0406546 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.86205 | −0.671700 | −0.335850 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335850 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8004 | −1.17053 | −0.585266 | − | 0.810842i | \(-0.699010\pi\) | ||||
−0.585266 | + | 0.810842i | \(0.699010\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.28215 | −0.444837 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.9582 | −1.83624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.73708 | −0.390708 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.12168 | 0.419585 | 0.209792 | − | 0.977746i | \(-0.432721\pi\) | ||||
0.209792 | + | 0.977746i | \(0.432721\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9476 | −1.05366 | −0.526829 | − | 0.849972i | \(-0.676619\pi\) | ||||
−0.526829 | + | 0.849972i | \(0.676619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.495700 | −0.0400750 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.02750 | 0.321429 | 0.160715 | − | 0.987001i | \(-0.448620\pi\) | ||||
0.160715 | + | 0.987001i | \(0.448620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.59978 | 0.682007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.60412 | −0.362856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.6190 | −1.22338 | −0.611688 | − | 0.791099i | \(-0.709509\pi\) | ||||
−0.611688 | + | 0.791099i | \(0.709509\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.8445 | −0.916551 | −0.458276 | − | 0.888810i | \(-0.651533\pi\) | ||||
−0.458276 | + | 0.888810i | \(0.651533\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.352437 | −0.0271105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.311674 | 0.0238343 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8305 | −1.12754 | −0.563772 | − | 0.825930i | \(-0.690651\pi\) | ||||
−0.563772 | + | 0.825930i | \(0.690651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.8826 | 0.968314 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.957535 | −0.0715695 | −0.0357848 | − | 0.999360i | \(-0.511393\pi\) | ||||
−0.0357848 | + | 0.999360i | \(0.511393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.14123 | 0.307815 | 0.153908 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153908 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3209 | −0.836867 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.06064 | 0.223816 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.50430 | −0.109422 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6305 | −1.27570 | −0.637849 | − | 0.770162i | \(-0.720176\pi\) | ||||
−0.637849 | + | 0.770162i | \(0.720176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.25392 | −0.378185 | −0.189093 | − | 0.981959i | \(-0.560555\pi\) | ||||
−0.189093 | + | 0.981959i | \(0.560555\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.11597 | 0.150756 | 0.0753782 | − | 0.997155i | \(-0.475984\pi\) | ||||
0.0753782 | + | 0.997155i | \(0.475984\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.07029 | 0.642976 | 0.321488 | − | 0.946914i | \(-0.395817\pi\) | ||||
0.321488 | + | 0.946914i | \(0.395817\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.2414 | −0.933975 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.184026 | 0.0129161 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.06064 | 0.212729 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.92439 | −0.133113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.8149 | −1.36412 | −0.682058 | − | 0.731298i | \(-0.738915\pi\) | ||||
−0.682058 | + | 0.731298i | \(0.738915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.26823 | 0.223936 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.42809 | 0.300598 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.9668 | −1.07894 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.76288 | −0.118584 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.58214 | −0.440773 | −0.220386 | − | 0.975413i | \(-0.570732\pi\) | ||||
−0.220386 | + | 0.975413i | \(0.570732\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7821 | −0.782006 | −0.391003 | − | 0.920389i | \(-0.627872\pi\) | ||||
−0.391003 | + | 0.920389i | \(0.627872\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.8899 | 0.785705 | 0.392853 | − | 0.919601i | \(-0.371488\pi\) | ||||
0.392853 | + | 0.919601i | \(0.371488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.28811 | 0.611113 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.05001 | 0.330837 | 0.165419 | − | 0.986223i | \(-0.447102\pi\) | ||||
0.165419 | + | 0.986223i | \(0.447102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.52746 | −0.553918 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.67932 | 0.173311 | 0.0866556 | − | 0.996238i | \(-0.472382\pi\) | ||||
0.0866556 | + | 0.996238i | \(0.472382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6561 | 0.815250 | 0.407625 | − | 0.913149i | \(-0.366357\pi\) | ||||
0.407625 | + | 0.913149i | \(0.366357\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.10842 | 0.0705271 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.3381 | −0.718524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.9068 | −1.44586 | −0.722932 | − | 0.690919i | \(-0.757206\pi\) | ||||
−0.722932 | + | 0.690919i | \(0.757206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.8975 | −1.18808 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.7764 | 1.73264 | 0.866322 | − | 0.499486i | \(-0.166478\pi\) | ||||
0.866322 | + | 0.499486i | \(0.166478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.56928 | −0.408195 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.122334 | −0.00757225 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.7115 | −0.722161 | −0.361081 | − | 0.932535i | \(-0.617592\pi\) | ||||
−0.361081 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.1326 | 0.864899 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.20621 | 0.256457 | 0.128229 | − | 0.991745i | \(-0.459071\pi\) | ||||
0.128229 | + | 0.991745i | \(0.459071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5659 | −0.763325 | −0.381663 | − | 0.924302i | \(-0.624648\pi\) | ||||
−0.381663 | + | 0.924302i | \(0.624648\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.34980 | −0.323785 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.8653 | −1.91460 | −0.957299 | − | 0.289100i | \(-0.906644\pi\) | ||||
−0.957299 | + | 0.289100i | \(0.906644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.94362 | −0.176230 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.2998 | 0.972364 | 0.486182 | − | 0.873858i | \(-0.338389\pi\) | ||||
0.486182 | + | 0.873858i | \(0.338389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6305 | 0.810249 | 0.405124 | − | 0.914262i | \(-0.367228\pi\) | ||||
0.405124 | + | 0.914262i | \(0.367228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.39819 | −0.377673 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7543 | −0.985546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4828 | 0.673132 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.2652 | −1.47601 | −0.738004 | − | 0.674796i | \(-0.764232\pi\) | ||||
−0.738004 | + | 0.674796i | \(0.764232\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.17438 | −0.358274 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.8847 | 0.629477 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.45554 | −0.314452 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.8359 | −0.852297 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.01023 | 0.400095 | 0.200047 | − | 0.979786i | \(-0.435890\pi\) | ||||
0.200047 | + | 0.979786i | \(0.435890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.2645 | −1.09592 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5118 | 0.822891 | 0.411446 | − | 0.911434i | \(-0.365024\pi\) | ||||
0.411446 | + | 0.911434i | \(0.365024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.9197 | −1.23897 | −0.619486 | − | 0.785008i | \(-0.712659\pi\) | ||||
−0.619486 | + | 0.785008i | \(0.712659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.7178 | 1.89378 | 0.946890 | − | 0.321559i | \(-0.104207\pi\) | ||||
0.946890 | + | 0.321559i | \(0.104207\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.755333 | 0.0422905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.63523 | −0.481972 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.154497 | −0.00859645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.6893 | −1.03352 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.94593 | 0.438073 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.5950 | 1.84655 | 0.923275 | − | 0.384139i | \(-0.125502\pi\) | ||||
0.923275 | + | 0.384139i | \(0.125502\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.36700 | 0.239310 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.08526 | −0.168065 | −0.0840323 | − | 0.996463i | \(-0.526780\pi\) | ||||
−0.0840323 | + | 0.996463i | \(0.526780\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.05638 | −0.328937 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.1750 | 0.984233 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6561 | 0.953339 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5739 | −0.675005 | −0.337502 | − | 0.941325i | \(-0.609582\pi\) | ||||
−0.337502 | + | 0.941325i | \(0.609582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3100 | 0.712466 | 0.356233 | − | 0.934397i | \(-0.384061\pi\) | ||||
0.356233 | + | 0.934397i | \(0.384061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.55634 | 0.189823 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2914 | 0.600980 | 0.300490 | − | 0.953785i | \(-0.402850\pi\) | ||||
0.300490 | + | 0.953785i | \(0.402850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.745682 | 0.0394657 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.4072 | 1.02427 | 0.512135 | − | 0.858905i | \(-0.328855\pi\) | ||||
0.512135 | + | 0.858905i | \(0.328855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9029 | −0.994887 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.1229 | 1.42358 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.5703 | −0.917160 | −0.458580 | − | 0.888653i | \(-0.651642\pi\) | ||||
−0.458580 | + | 0.888653i | \(0.651642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.25327 | 0.221416 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.9367 | −0.671637 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2065 | 1.46048 | 0.730238 | − | 0.683193i | \(-0.239409\pi\) | ||||
0.730238 | + | 0.683193i | \(0.239409\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.435060 | −0.0224067 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.62822 | 0.186369 | 0.0931845 | − | 0.995649i | \(-0.470295\pi\) | ||||
0.0931845 | + | 0.995649i | \(0.470295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.24565 | 0.473669 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.8348 | 0.706925 | 0.353463 | − | 0.935449i | \(-0.385004\pi\) | ||||
0.353463 | + | 0.935449i | \(0.385004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.62663 | 0.184352 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.9014 | −1.05974 | −0.529871 | − | 0.848079i | \(-0.677759\pi\) | ||||
−0.529871 | + | 0.848079i | \(0.677759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.51716 | −0.0767261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0155 | 0.959207 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4522 | 0.775523 | 0.387761 | − | 0.921760i | \(-0.373248\pi\) | ||||
0.387761 | + | 0.921760i | \(0.373248\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.468851 | −0.0234719 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.25590 | 0.112654 | 0.0563271 | − | 0.998412i | \(-0.482061\pi\) | ||||
0.0563271 | + | 0.998412i | \(0.482061\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.4685 | −0.521474 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.9635 | −1.33653 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.33260 | −0.115340 | −0.0576699 | − | 0.998336i | \(-0.518367\pi\) | ||||
−0.0576699 | + | 0.998336i | \(0.518367\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.86205 | −0.387806 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.3793 | −0.953591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.8004 | −0.675806 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.04076 | −0.246257 | −0.123129 | − | 0.992391i | \(-0.539293\pi\) | ||||
−0.123129 | + | 0.992391i | \(0.539293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9386 | 0.630587 | 0.315293 | − | 0.948994i | \(-0.397897\pi\) | ||||
0.315293 | + | 0.948994i | \(0.397897\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.28215 | −0.256827 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0301 | 0.824142 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.9582 | −1.06015 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.56501 | 0.0753841 | 0.0376920 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376920 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.8729 | −1.24337 | −0.621687 | − | 0.783266i | \(-0.713552\pi\) | ||||
−0.621687 | + | 0.783266i | \(0.713552\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.953923 | 0.0456323 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3713 | 0.781358 | 0.390679 | − | 0.920527i | \(-0.372240\pi\) | ||||
0.390679 | + | 0.920527i | \(0.372240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.73708 | −0.225575 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.1180 | −1.33593 | −0.667963 | − | 0.744194i | \(-0.732834\pi\) | ||||
−0.667963 | + | 0.744194i | \(0.732834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.12168 | 0.242247 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.65681 | −0.125383 | −0.0626914 | − | 0.998033i | \(-0.519968\pi\) | ||||
−0.0626914 | + | 0.998033i | \(0.519968\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.2613 | −1.23659 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.9476 | −0.608329 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.321574 | 0.0150426 | 0.00752129 | − | 0.999972i | \(-0.497606\pi\) | ||||
0.00752129 | + | 0.999972i | \(0.497606\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.495700 | −0.0231373 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.68562 | −0.357955 | −0.178977 | − | 0.983853i | \(-0.557279\pi\) | ||||
−0.178977 | + | 0.983853i | \(0.557279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.1041 | −0.887842 | −0.443921 | − | 0.896066i | \(-0.646413\pi\) | ||||
−0.443921 | + | 0.896066i | \(0.646413\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.41944 | 0.297056 | 0.148528 | − | 0.988908i | \(-0.452546\pi\) | ||||
0.148528 | + | 0.988908i | \(0.452546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.9190 | 0.919774 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.02750 | 0.185577 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.3922 | −1.02959 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.59978 | 0.393757 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.5609 | 1.53344 | 0.766719 | − | 0.641983i | \(-0.221888\pi\) | ||||
0.766719 | + | 0.641983i | \(0.221888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.5305 | 0.708132 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.60412 | −0.209495 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9105 | 0.539715 | 0.269858 | − | 0.962900i | \(-0.413023\pi\) | ||||
0.269858 | + | 0.962900i | \(0.413023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.6190 | −0.706316 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6130 | 0.704607 | 0.352303 | − | 0.935886i | \(-0.385398\pi\) | ||||
0.352303 | + | 0.935886i | \(0.385398\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0606408 | 0.00273112 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.91640 | −0.220531 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9130 | 1.38386 | 0.691929 | − | 0.721966i | \(-0.256761\pi\) | ||||
0.691929 | + | 0.721966i | \(0.256761\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8445 | −0.529171 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.0396 | −1.38399 | −0.691994 | − | 0.721903i | \(-0.743268\pi\) | ||||
−0.691994 | + | 0.721903i | \(0.743268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.352437 | −0.0156523 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.3428 | −0.591409 | −0.295704 | − | 0.955280i | \(-0.595554\pi\) | ||||
−0.295704 | + | 0.955280i | \(0.595554\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0188 | 1.06253 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.311674 | 0.0137608 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.6139 | 1.43436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.8305 | −0.650988 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.5176 | 1.16176 | 0.580879 | − | 0.813990i | \(-0.302709\pi\) | ||||
0.580879 | + | 0.813990i | \(0.302709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.4147 | 0.761492 | 0.380746 | − | 0.924680i | \(-0.375667\pi\) | ||||
0.380746 | + | 0.924680i | \(0.375667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.45915 | 0.0635618 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.6325 | −0.592716 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.8826 | 0.559056 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.1261 | 0.655183 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.957535 | −0.0413207 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.2485 | 1.25982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.46682 | 0.235037 | 0.117519 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117519 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.14123 | 0.177717 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6459 | −0.925510 | −0.462755 | − | 0.886486i | \(-0.653139\pi\) | ||||
−0.462755 | + | 0.886486i | \(0.653139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.3209 | −0.483165 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0381282 | −0.00162432 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.8279 | 0.545496 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.58830 | 0.109670 | 0.0548349 | − | 0.998495i | \(-0.482537\pi\) | ||||
0.0548349 | + | 0.998495i | \(0.482537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8975 | 0.545508 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.06064 | 0.129220 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.8939 | −0.838426 | −0.419213 | − | 0.907888i | \(-0.637694\pi\) | ||||
−0.419213 | + | 0.907888i | \(0.637694\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.50430 | −0.0631746 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.4303 | 1.35955 | 0.679775 | − | 0.733421i | \(-0.262077\pi\) | ||||
0.679775 | + | 0.733421i | \(0.262077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7182 | 0.574088 | 0.287044 | − | 0.957917i | \(-0.407327\pi\) | ||||
0.287044 | + | 0.957917i | \(0.407327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.6305 | −0.736524 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.6432 | −1.02591 | −0.512955 | − | 0.858415i | \(-0.671449\pi\) | ||||
−0.512955 | + | 0.858415i | \(0.671449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.25392 | −0.218345 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.0559 | 0.707599 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −53.0983 | −2.19911 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.32165 | −0.343471 | −0.171736 | − | 0.985143i | \(-0.554938\pi\) | ||||
−0.171736 | + | 0.985143i | \(0.554938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.917451 | −0.0378029 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.11597 | 0.0870393 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.7904 | −0.894826 | −0.447413 | − | 0.894328i | \(-0.647654\pi\) | ||||
−0.447413 | + | 0.894328i | \(0.647654\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.07029 | 0.371222 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.6482 | 0.435074 | 0.217537 | − | 0.976052i | \(-0.430198\pi\) | ||||
0.217537 | + | 0.976052i | \(0.430198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.60740 | 0.106358 | 0.0531791 | − | 0.998585i | \(-0.483065\pi\) | ||||
0.0531791 | + | 0.998585i | \(0.483065\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2414 | −0.539231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.9820 | −1.33870 | −0.669349 | − | 0.742948i | \(-0.733427\pi\) | ||||
−0.669349 | + | 0.742948i | \(0.733427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.184026 | 0.00745712 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.7851 | −0.759964 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7891 | 0.758886 | 0.379443 | − | 0.925215i | \(-0.376116\pi\) | ||||
0.379443 | + | 0.925215i | \(0.376116\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.3278 | −1.58328 | −0.791639 | − | 0.610990i | \(-0.790772\pi\) | ||||
−0.791639 | + | 0.610990i | \(0.790772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0365 | −0.644560 | −0.322280 | − | 0.946644i | \(-0.604449\pi\) | ||||
−0.322280 | + | 0.946644i | \(0.604449\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.06064 | 0.122819 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.2596 | −0.851748 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.92439 | −0.0768529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.16472 | −0.0863132 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.82685 | 0.192154 | 0.0960770 | − | 0.995374i | \(-0.469371\pi\) | ||||
0.0960770 | + | 0.995374i | \(0.469371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.8149 | −0.787572 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.8467 | −0.667490 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.26823 | 0.129289 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.5645 | −1.44421 | −0.722106 | − | 0.691782i | \(-0.756826\pi\) | ||||
−0.722106 | + | 0.691782i | \(0.756826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3769 | 0.724714 | 0.362357 | − | 0.932039i | \(-0.381972\pi\) | ||||
0.362357 | + | 0.932039i | \(0.381972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.1338 | 1.61714 | 0.808568 | − | 0.588403i | \(-0.200243\pi\) | ||||
0.808568 | + | 0.588403i | \(0.200243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −79.5419 | −3.12229 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.42809 | 0.173550 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9447 | 0.858761 | 0.429381 | − | 0.903124i | \(-0.358732\pi\) | ||||
0.429381 | + | 0.903124i | \(0.358732\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.9668 | −0.622924 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.2048 | 0.826020 | 0.413010 | − | 0.910726i | \(-0.364477\pi\) | ||||
0.413010 | + | 0.910726i | \(0.364477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9442 | 0.697948 | 0.348974 | − | 0.937132i | \(-0.386530\pi\) | ||||
0.348974 | + | 0.937132i | \(0.386530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.76288 | −0.0684646 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.374419 | −0.0144976 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.58214 | −0.254480 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 69.8996 | 2.69845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.3014 | −1.32222 | −0.661111 | − | 0.750288i | \(-0.729915\pi\) | ||||
−0.661111 | + | 0.750288i | \(0.729915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.14695 | 0.159380 | 0.0796901 | − | 0.996820i | \(-0.474607\pi\) | ||||
0.0796901 | + | 0.996820i | \(0.474607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.2735 | −0.662897 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.7821 | −0.451491 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.11840 | −0.0810583 | −0.0405291 | − | 0.999178i | \(-0.512904\pi\) | ||||
−0.0405291 | + | 0.999178i | \(0.512904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.8899 | 0.453627 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.5838 | 1.16515 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.97453 | −0.151198 | −0.0755991 | − | 0.997138i | \(-0.524087\pi\) | ||||
−0.0755991 | + | 0.997138i | \(0.524087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.28811 | 0.352826 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.10835 | −0.0798593 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.05001 | 0.191009 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.1954 | −0.385076 | −0.192538 | − | 0.981289i | \(-0.561672\pi\) | ||||
−0.192538 | + | 0.981289i | \(0.561672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.36108 | 0.0513342 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.3176 | 0.839338 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.8413 | 1.12071 | 0.560357 | − | 0.828251i | \(-0.310664\pi\) | ||||
0.560357 | + | 0.828251i | \(0.310664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.52746 | −0.319805 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.00937 | −0.337404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.67932 | 0.100061 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.43434 | 0.277254 | 0.138627 | − | 0.990345i | \(-0.455731\pi\) | ||||
0.138627 | + | 0.990345i | \(0.455731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.9796 | 1.07926 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.6561 | 0.470685 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9195 | 0.590420 | 0.295210 | − | 0.955432i | \(-0.404610\pi\) | ||||
0.295210 | + | 0.955432i | \(0.404610\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79772 | −0.0664912 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6103 | −1.13062 | −0.565308 | − | 0.824880i | \(-0.691243\pi\) | ||||
−0.565308 | + | 0.824880i | \(0.691243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 81.7573 | 3.01157 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9379 | 0.954141 | 0.477071 | − | 0.878865i | \(-0.341699\pi\) | ||||
0.477071 | + | 0.878865i | \(0.341699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.10842 | 0.0407188 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.2136 | −0.631504 | −0.315752 | − | 0.948842i | \(-0.602257\pi\) | ||||
−0.315752 | + | 0.948842i | \(0.602257\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.3381 | −0.414840 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.9900 | 0.474643 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4020 | 0.379576 | 0.189788 | − | 0.981825i | \(-0.439220\pi\) | ||||
0.189788 | + | 0.981825i | \(0.439220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9068 | −0.834770 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.9118 | 0.614669 | 0.307335 | − | 0.951601i | \(-0.400563\pi\) | ||||
0.307335 | + | 0.951601i | \(0.400563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.8975 | −0.685937 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.522347 | 0.0189351 | 0.00946753 | − | 0.999955i | \(-0.496986\pi\) | ||||
0.00946753 | + | 0.999955i | \(0.496986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.1143 | 1.01781 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45.8148 | 1.65428 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.0791 | −1.37317 | −0.686584 | − | 0.727050i | \(-0.740891\pi\) | ||||
−0.686584 | + | 0.727050i | \(0.740891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.7764 | 1.00034 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.6913 | 0.816151 | 0.408075 | − | 0.912948i | \(-0.366200\pi\) | ||||
0.408075 | + | 0.912948i | \(0.366200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.56928 | −0.235671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.32563 | 0.0474957 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.1793 | −0.722072 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.122334 | −0.00437184 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.27911 | −0.0812415 | −0.0406207 | − | 0.999175i | \(-0.512934\pi\) | ||||
−0.0406207 | + | 0.999175i | \(0.512934\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.7115 | −0.416940 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.11061 | 0.323936 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.2611 | −1.42971 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.6409 | −0.695715 | −0.347858 | − | 0.937547i | \(-0.613091\pi\) | ||||
−0.347858 | + | 0.937547i | \(0.613091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.61836 | 0.0926310 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.1326 | 0.499349 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 98.5849 | 3.47899 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.20621 | 0.148066 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.1951 | 0.393599 | 0.196799 | − | 0.980444i | \(-0.436945\pi\) | ||||
0.196799 | + | 0.980444i | \(0.436945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.2989 | −0.677677 | −0.338839 | − | 0.940844i | \(-0.610034\pi\) | ||||
−0.338839 | + | 0.940844i | \(0.610034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.5659 | −0.440706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.13033 | 0.0395452 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.34980 | −0.186937 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.1255 | −1.67959 | −0.839797 | − | 0.542901i | \(-0.817326\pi\) | ||||
−0.839797 | + | 0.542901i | \(0.817326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.9012 | −1.21658 | −0.608289 | − | 0.793716i | \(-0.708144\pi\) | ||||
−0.608289 | + | 0.793716i | \(0.708144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.1640 | −0.805491 | −0.402746 | − | 0.915312i | \(-0.631944\pi\) | ||||
−0.402746 | + | 0.915312i | \(0.631944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7129 | 0.754121 | 0.377060 | − | 0.926189i | \(-0.376935\pi\) | ||||
0.377060 | + | 0.926189i | \(0.376935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.8653 | −1.10539 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.34817 | 0.0813594 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.94362 | −0.101746 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.3890 | 0.358668 | 0.179334 | − | 0.983788i | \(-0.442606\pi\) | ||||
0.179334 | + | 0.983788i | \(0.442606\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9850 | −0.999484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.2998 | 0.561395 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40.8010 | −1.40194 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.6305 | 0.467797 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.3658 | 0.458174 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.6101 | −1.15079 | −0.575395 | − | 0.817876i | \(-0.695152\pi\) | ||||
−0.575395 | + | 0.817876i | \(0.695152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.0078 | −1.57160 | −0.785799 | − | 0.618482i | \(-0.787748\pi\) | ||||
−0.785799 | + | 0.618482i | \(0.787748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.3516 | −1.03558 | −0.517791 | − | 0.855507i | \(-0.673245\pi\) | ||||
−0.517791 | + | 0.855507i | \(0.673245\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.39819 | −0.218050 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.32052 | 0.249193 | 0.124597 | − | 0.992207i | \(-0.460236\pi\) | ||||
0.124597 | + | 0.992207i | \(0.460236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.7543 | −0.569005 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.6518 | 1.78609 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.0909 | −1.59561 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.4828 | 0.388633 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.5437 | 1.57167 | 0.785834 | − | 0.618438i | \(-0.212234\pi\) | ||||
0.785834 | + | 0.618438i | \(0.212234\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.2652 | −0.852174 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.9721 | −0.504423 | −0.252211 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252211 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.74240 | 0.294205 | 0.147103 | − | 0.989121i | \(-0.453005\pi\) | ||||
0.147103 | + | 0.989121i | \(0.453005\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.4865 | −0.553563 | −0.276782 | − | 0.960933i | \(-0.589268\pi\) | ||||
−0.276782 | + | 0.960933i | \(0.589268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9082 | −0.466467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.17438 | −0.206849 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.64631 | −0.0550916 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.8847 | 0.363429 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.360104 | 0.0120101 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26292 | −0.142018 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.45554 | −0.181549 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.0243 | −0.864124 | −0.432062 | − | 0.901844i | \(-0.642214\pi\) | ||||
−0.432062 | + | 0.901844i | \(0.642214\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.8359 | −0.492074 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.6447 | −1.71107 | −0.855533 | − | 0.517748i | \(-0.826771\pi\) | ||||
−0.855533 | + | 0.517748i | \(0.826771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 70.0058 | 2.31685 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.6051 | −0.944623 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.6307 | −0.911452 | −0.455726 | − | 0.890120i | \(-0.650620\pi\) | ||||
−0.455726 | + | 0.890120i | \(0.650620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.01023 | 0.230995 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6229 | 0.382574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.2645 | −0.632731 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.7012 | 1.76188 | 0.880939 | − | 0.473230i | \(-0.156912\pi\) | ||||
0.880939 | + | 0.473230i | \(0.156912\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47643 | −0.0483879 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.5118 | 0.475097 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.3213 | 0.990552 | 0.495276 | − | 0.868736i | \(-0.335067\pi\) | ||||
0.495276 | + | 0.868736i | \(0.335067\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.9197 | −0.715321 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.3682 | 1.54416 | 0.772080 | − | 0.635525i | \(-0.219216\pi\) | ||||
0.772080 | + | 0.635525i | \(0.219216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.0177 | 0.423915 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.6419 | 0.703266 | 0.351633 | − | 0.936138i | \(-0.385627\pi\) | ||||
0.351633 | + | 0.936138i | \(0.385627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.7833 | −1.84327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.7178 | 1.09337 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.8917 | 1.48658 | 0.743289 | − | 0.668970i | \(-0.233265\pi\) | ||||
0.743289 | + | 0.668970i | \(0.233265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.755333 | 0.0244164 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.8269 | 0.381910 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.3351 | −0.720487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.63523 | −0.278266 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.9696 | 0.481391 | 0.240695 | − | 0.970601i | \(-0.422625\pi\) | ||||
0.240695 | + | 0.970601i | \(0.422625\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.154497 | −0.00496316 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.3795 | −0.718191 | −0.359096 | − | 0.933301i | \(-0.616915\pi\) | ||||
−0.359096 | + | 0.933301i | \(0.616915\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.7599 | 0.665531 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.3686 | 1.29150 | 0.645752 | − | 0.763547i | \(-0.276544\pi\) | ||||
0.645752 | + | 0.763547i | \(0.276544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −87.2597 | −2.78883 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6893 | −0.596704 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.3730 | 0.745482 | 0.372741 | − | 0.927935i | \(-0.378418\pi\) | ||||
0.372741 | + | 0.927935i | \(0.378418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.94593 | 0.252922 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0998 | 0.352954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.8454 | 1.07514 | 0.537568 | − | 0.843221i | \(-0.319343\pi\) | ||||
0.537568 | + | 0.843221i | \(0.319343\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.5950 | 1.06611 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.54503 | −0.175613 | −0.0878065 | − | 0.996138i | \(-0.527986\pi\) | ||||
−0.0878065 | + | 0.996138i | \(0.527986\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.36700 | 0.138166 |
(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 | 7500.2.a.f.1.2 | 4 | ||
5.2 | odd | 4 | 7500.2.d.c.1249.2 | 8 | |||
5.3 | odd | 4 | 7500.2.d.c.1249.7 | 8 | |||
5.4 | even | 2 | 7500.2.a.e.1.3 | 4 | |||
25.3 | odd | 20 | 1500.2.o.b.49.2 | 16 | |||
25.4 | even | 10 | 300.2.m.b.241.2 | yes | 8 | ||
25.6 | even | 5 | 1500.2.m.a.301.1 | 8 | |||
25.8 | odd | 20 | 1500.2.o.b.949.4 | 16 | |||
25.17 | odd | 20 | 1500.2.o.b.949.1 | 16 | |||
25.19 | even | 10 | 300.2.m.b.61.2 | ✓ | 8 | ||
25.21 | even | 5 | 1500.2.m.a.1201.1 | 8 | |||
25.22 | odd | 20 | 1500.2.o.b.49.3 | 16 | |||
75.29 | odd | 10 | 900.2.n.b.541.1 | 8 | |||
75.44 | odd | 10 | 900.2.n.b.361.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.b.61.2 | ✓ | 8 | 25.19 | even | 10 | ||
300.2.m.b.241.2 | yes | 8 | 25.4 | even | 10 | ||
900.2.n.b.361.1 | 8 | 75.44 | odd | 10 | |||
900.2.n.b.541.1 | 8 | 75.29 | odd | 10 | |||
1500.2.m.a.301.1 | 8 | 25.6 | even | 5 | |||
1500.2.m.a.1201.1 | 8 | 25.21 | even | 5 | |||
1500.2.o.b.49.2 | 16 | 25.3 | odd | 20 | |||
1500.2.o.b.49.3 | 16 | 25.22 | odd | 20 | |||
1500.2.o.b.949.1 | 16 | 25.17 | odd | 20 | |||
1500.2.o.b.949.4 | 16 | 25.8 | odd | 20 | |||
7500.2.a.e.1.3 | 4 | 5.4 | even | 2 | |||
7500.2.a.f.1.2 | 4 | 1.1 | even | 1 | trivial | ||
7500.2.d.c.1249.2 | 8 | 5.2 | odd | 4 | |||
7500.2.d.c.1249.7 | 8 | 5.3 | odd | 4 |