Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6024,2,Mod(1,6024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6024 = 2^{3} \cdot 3 \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6024.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1018821776\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 43 x^{12} + 119 x^{11} + 679 x^{10} - 1667 x^{9} - 4890 x^{8} + 9662 x^{7} + 16575 x^{6} - 20277 x^{5} - 25196 x^{4} + 8040 x^{3} + 10776 x^{2} + \cdots - 416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.42255\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6024.1 |
$q$-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 | ||||||||
\(5\) | −3.42255 | −1.53061 | −0.765305 | − | 0.643667i | \(-0.777412\pi\) | ||||
−0.765305 | + | 0.643667i | \(0.777412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.90388 | −1.47553 | −0.737763 | − | 0.675059i | \(-0.764118\pi\) | ||||
−0.737763 | + | 0.675059i | \(0.764118\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.19109 | −1.26366 | −0.631830 | − | 0.775107i | \(-0.717696\pi\) | ||||
−0.631830 | + | 0.775107i | \(0.717696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.32382 | −0.367163 | −0.183581 | − | 0.983005i | \(-0.558769\pi\) | ||||
−0.183581 | + | 0.983005i | \(0.558769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.42255 | 0.883699 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.02268 | 0.490572 | 0.245286 | − | 0.969451i | \(-0.421118\pi\) | ||||
0.245286 | + | 0.969451i | \(0.421118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.592230 | −0.135867 | −0.0679334 | − | 0.997690i | \(-0.521641\pi\) | ||||
−0.0679334 | + | 0.997690i | \(0.521641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.90388 | 0.851896 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.66343 | 0.555363 | 0.277682 | − | 0.960673i | \(-0.410434\pi\) | ||||
0.277682 | + | 0.960673i | \(0.410434\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.71385 | 1.34277 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.79017 | 1.26090 | 0.630451 | − | 0.776229i | \(-0.282870\pi\) | ||||
0.630451 | + | 0.776229i | \(0.282870\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.654960 | 0.117634 | 0.0588171 | − | 0.998269i | \(-0.481267\pi\) | ||||
0.0588171 | + | 0.998269i | \(0.481267\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.19109 | 0.729575 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.3612 | 2.25846 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.41699 | 1.21935 | 0.609673 | − | 0.792653i | \(-0.291301\pi\) | ||||
0.609673 | + | 0.792653i | \(0.291301\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.32382 | 0.211982 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.06823 | 1.10387 | 0.551936 | − | 0.833886i | \(-0.313889\pi\) | ||||
0.551936 | + | 0.833886i | \(0.313889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.29612 | 0.960149 | 0.480075 | − | 0.877228i | \(-0.340610\pi\) | ||||
0.480075 | + | 0.877228i | \(0.340610\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.42255 | −0.510204 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.83861 | 0.705784 | 0.352892 | − | 0.935664i | \(-0.385198\pi\) | ||||
0.352892 | + | 0.935664i | \(0.385198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.24026 | 1.17718 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.02268 | −0.283232 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.29738 | −0.178209 | −0.0891046 | − | 0.996022i | \(-0.528401\pi\) | ||||
−0.0891046 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.3442 | 1.93417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.592230 | 0.0784427 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.96586 | −1.29744 | −0.648722 | − | 0.761025i | \(-0.724696\pi\) | ||||
−0.648722 | + | 0.761025i | \(0.724696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.18394 | −0.151589 | −0.0757943 | − | 0.997123i | \(-0.524149\pi\) | ||||
−0.0757943 | + | 0.997123i | \(0.524149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.90388 | −0.491842 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.53085 | 0.561983 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19525 | −0.634701 | −0.317351 | − | 0.948308i | \(-0.602793\pi\) | ||||
−0.317351 | + | 0.948308i | \(0.602793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.66343 | −0.320639 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.71718 | −0.915861 | −0.457930 | − | 0.888988i | \(-0.651409\pi\) | ||||
−0.457930 | + | 0.888988i | \(0.651409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.9445 | −1.74913 | −0.874563 | − | 0.484912i | \(-0.838852\pi\) | ||||
−0.874563 | + | 0.484912i | \(0.838852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.71385 | −0.775248 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.3615 | 1.86457 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.29169 | 0.707871 | 0.353935 | − | 0.935270i | \(-0.384843\pi\) | ||||
0.353935 | + | 0.935270i | \(0.384843\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.1069 | −1.54844 | −0.774219 | − | 0.632918i | \(-0.781857\pi\) | ||||
−0.774219 | + | 0.632918i | \(0.781857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.92272 | −0.750875 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.79017 | −0.727983 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.06762 | 0.113167 | 0.0565836 | − | 0.998398i | \(-0.481979\pi\) | ||||
0.0565836 | + | 0.998398i | \(0.481979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.16805 | 0.541759 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.654960 | −0.0679162 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.02694 | 0.207959 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.41590 | 0.549902 | 0.274951 | − | 0.961458i | \(-0.411338\pi\) | ||||
0.274951 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.19109 | −0.421220 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.01940 | −0.797960 | −0.398980 | − | 0.916960i | \(-0.630636\pi\) | ||||
−0.398980 | + | 0.916960i | \(0.630636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0264 | 1.28353 | 0.641765 | − | 0.766901i | \(-0.278202\pi\) | ||||
0.641765 | + | 0.766901i | \(0.278202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.3612 | −1.30392 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.57643 | −0.442420 | −0.221210 | − | 0.975226i | \(-0.571001\pi\) | ||||
−0.221210 | + | 0.975226i | \(0.571001\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.22019 | −0.595786 | −0.297893 | − | 0.954599i | \(-0.596284\pi\) | ||||
−0.297893 | + | 0.954599i | \(0.596284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.41699 | −0.703990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.37635 | 0.129476 | 0.0647379 | − | 0.997902i | \(-0.479379\pi\) | ||||
0.0647379 | + | 0.997902i | \(0.479379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.11572 | −0.850045 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.32382 | −0.122388 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.89630 | −0.723852 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.56522 | 0.596839 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.06823 | −0.637321 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.86572 | −0.524646 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2459 | 0.997916 | 0.498958 | − | 0.866626i | \(-0.333716\pi\) | ||||
0.498958 | + | 0.866626i | \(0.333716\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.29612 | −0.554342 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.91756 | −0.604390 | −0.302195 | − | 0.953246i | \(-0.597719\pi\) | ||||
−0.302195 | + | 0.953246i | \(0.597719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.31199 | 0.200475 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.42255 | 0.294566 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.468996 | 0.0400691 | 0.0200345 | − | 0.999799i | \(-0.493622\pi\) | ||||
0.0200345 | + | 0.999799i | \(0.493622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3818 | 0.965393 | 0.482696 | − | 0.875788i | \(-0.339657\pi\) | ||||
0.482696 | + | 0.875788i | \(0.339657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.83861 | −0.407485 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.54827 | 0.463969 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.2397 | −1.92995 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.24026 | −0.679645 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.9159 | 1.05811 | 0.529054 | − | 0.848588i | \(-0.322547\pi\) | ||||
0.529054 | + | 0.848588i | \(0.322547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.99361 | 0.406374 | 0.203187 | − | 0.979140i | \(-0.434870\pi\) | ||||
0.203187 | + | 0.979140i | \(0.434870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.02268 | 0.163524 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.24163 | −0.180052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4359 | 1.47134 | 0.735671 | − | 0.677339i | \(-0.236867\pi\) | ||||
0.735671 | + | 0.677339i | \(0.236867\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.29738 | 0.102889 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3977 | −0.819454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.47891 | 0.350815 | 0.175408 | − | 0.984496i | \(-0.443876\pi\) | ||||
0.175408 | + | 0.984496i | \(0.443876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.3442 | −1.11670 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0001 | −0.928594 | −0.464297 | − | 0.885680i | \(-0.653693\pi\) | ||||
−0.464297 | + | 0.885680i | \(0.653693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2475 | −0.865191 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.592230 | −0.0452889 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.01711 | −0.685558 | −0.342779 | − | 0.939416i | \(-0.611368\pi\) | ||||
−0.342779 | + | 0.939416i | \(0.611368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.2100 | −1.98129 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.96586 | 0.749080 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.47311 | 0.633310 | 0.316655 | − | 0.948541i | \(-0.397440\pi\) | ||||
0.316655 | + | 0.948541i | \(0.397440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0206 | 1.04214 | 0.521072 | − | 0.853513i | \(-0.325532\pi\) | ||||
0.521072 | + | 0.853513i | \(0.325532\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.18394 | 0.0875197 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.3850 | −1.86634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.47723 | −0.619917 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.90388 | 0.283965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.96559 | −0.648727 | −0.324364 | − | 0.945932i | \(-0.605150\pi\) | ||||
−0.324364 | + | 0.945932i | \(0.605150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0671 | 0.724645 | 0.362323 | − | 0.932053i | \(-0.381984\pi\) | ||||
0.362323 | + | 0.932053i | \(0.381984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.53085 | −0.324461 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.5224 | −1.03468 | −0.517340 | − | 0.855780i | \(-0.673078\pi\) | ||||
−0.517340 | + | 0.855780i | \(0.673078\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7736 | −1.18905 | −0.594525 | − | 0.804077i | \(-0.702660\pi\) | ||||
−0.594525 | + | 0.804077i | \(0.702660\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.19525 | 0.366445 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.5080 | −1.86050 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.1914 | −1.68960 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.66343 | 0.185121 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.48209 | 0.171690 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.01992 | 0.276743 | 0.138371 | − | 0.990380i | \(-0.455813\pi\) | ||||
0.138371 | + | 0.990380i | \(0.455813\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.71718 | 0.528772 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.5488 | −1.46961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.55688 | −0.173573 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.9445 | 1.00986 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.67767 | −0.180120 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.04684 | 0.538856 | 0.269428 | − | 0.963021i | \(-0.413165\pi\) | ||||
0.269428 | + | 0.963021i | \(0.413165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.71385 | 0.447590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.2181 | −1.27555 | −0.637776 | − | 0.770222i | \(-0.720145\pi\) | ||||
−0.637776 | + | 0.770222i | \(0.720145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.84628 | 0.122006 | 0.0610029 | − | 0.998138i | \(-0.480570\pi\) | ||||
0.0610029 | + | 0.998138i | \(0.480570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.3615 | −1.07651 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.372758 | −0.0244202 | −0.0122101 | − | 0.999925i | \(-0.503887\pi\) | ||||
−0.0122101 | + | 0.999925i | \(0.503887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.5604 | −1.08028 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.29169 | −0.408689 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.9151 | 1.61162 | 0.805812 | − | 0.592171i | \(-0.201729\pi\) | ||||
0.805812 | + | 0.592171i | \(0.201729\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3473 | 0.859774 | 0.429887 | − | 0.902883i | \(-0.358553\pi\) | ||||
0.429887 | + | 0.902883i | \(0.358553\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.2027 | −1.80180 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.784008 | 0.0498852 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.1069 | 0.893991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1627 | −0.701791 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.92272 | 0.433518 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2700 | 0.827757 | 0.413879 | − | 0.910332i | \(-0.364174\pi\) | ||||
0.413879 | + | 0.910332i | \(0.364174\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.9550 | −1.79918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.79017 | 0.420301 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.30949 | 0.389060 | 0.194530 | − | 0.980897i | \(-0.437682\pi\) | ||||
0.194530 | + | 0.980897i | \(0.437682\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.44035 | 0.272769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.06762 | −0.0653371 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.3581 | −0.875432 | −0.437716 | − | 0.899113i | \(-0.644212\pi\) | ||||
−0.437716 | + | 0.899113i | \(0.644212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.4332 | 1.36272 | 0.681361 | − | 0.731948i | \(-0.261388\pi\) | ||||
0.681361 | + | 0.731948i | \(0.261388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.16805 | −0.312784 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.1383 | −1.69680 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3951 | 0.985087 | 0.492544 | − | 0.870288i | \(-0.336067\pi\) | ||||
0.492544 | + | 0.870288i | \(0.336067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.654960 | 0.0392114 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.1631 | 0.964208 | 0.482104 | − | 0.876114i | \(-0.339873\pi\) | ||||
0.482104 | + | 0.876114i | \(0.339873\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6630 | −0.752735 | −0.376368 | − | 0.926470i | \(-0.622827\pi\) | ||||
−0.376368 | + | 0.926470i | \(0.622827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.02694 | −0.120065 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.5935 | −1.62879 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9088 | −0.759339 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.41590 | −0.317486 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.7646 | 0.979396 | 0.489698 | − | 0.871892i | \(-0.337107\pi\) | ||||
0.489698 | + | 0.871892i | \(0.337107\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.1087 | 1.98588 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.19109 | 0.243192 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.52591 | −0.203909 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.5793 | −1.41673 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.01940 | 0.460702 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.05211 | 0.232023 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.4014 | −1.22144 | −0.610722 | − | 0.791845i | \(-0.709121\pi\) | ||||
−0.610722 | + | 0.791845i | \(0.709121\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0264 | −0.741047 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.73908 | −0.438843 | −0.219422 | − | 0.975630i | \(-0.570417\pi\) | ||||
−0.219422 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.66051 | 0.319951 | 0.159976 | − | 0.987121i | \(-0.448858\pi\) | ||||
0.159976 | + | 0.987121i | \(0.448858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.3612 | 0.752819 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.88564 | 0.105908 | 0.0529539 | − | 0.998597i | \(-0.483136\pi\) | ||||
0.0529539 | + | 0.998597i | \(0.483136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.4582 | −1.59335 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.57643 | 0.255432 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.19789 | −0.0666525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.88795 | −0.493015 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.22019 | 0.343977 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.8893 | −1.04140 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8190 | −1.25425 | −0.627123 | − | 0.778920i | \(-0.715768\pi\) | ||||
−0.627123 | + | 0.778920i | \(0.715768\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.41699 | 0.406449 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.7810 | 0.971481 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.08711 | 0.386059 | 0.193030 | − | 0.981193i | \(-0.438169\pi\) | ||||
0.193030 | + | 0.981193i | \(0.438169\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.37635 | −0.0747528 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.74500 | −0.148650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.84181 | −0.261433 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.11572 | 0.490774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.7890 | 0.686552 | 0.343276 | − | 0.939235i | \(-0.388463\pi\) | ||||
0.343276 | + | 0.939235i | \(0.388463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4637 | −1.52363 | −0.761814 | − | 0.647796i | \(-0.775691\pi\) | ||||
−0.761814 | + | 0.647796i | \(0.775691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.32382 | 0.0706605 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.2046 | −1.28828 | −0.644142 | − | 0.764906i | \(-0.722785\pi\) | ||||
−0.644142 | + | 0.764906i | \(0.722785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.4124 | 1.40183 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.89630 | 0.417916 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.0683 | −1.16472 | −0.582361 | − | 0.812930i | \(-0.697871\pi\) | ||||
−0.582361 | + | 0.812930i | \(0.697871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6493 | −0.981540 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.56522 | −0.344585 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 51.1484 | 2.67723 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0165 | 1.30585 | 0.652925 | − | 0.757423i | \(-0.273542\pi\) | ||||
0.652925 | + | 0.757423i | \(0.273542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.06823 | 0.367957 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.06482 | 0.262952 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.9992 | 1.19085 | 0.595427 | − | 0.803409i | \(-0.296983\pi\) | ||||
0.595427 | + | 0.803409i | \(0.296983\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.86572 | 0.302905 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.98899 | −0.462957 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.40672 | −0.277725 | −0.138862 | − | 0.990312i | \(-0.544345\pi\) | ||||
−0.138862 | + | 0.990312i | \(0.544345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.2459 | −0.576147 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.0852658 | 0.00435688 | 0.00217844 | − | 0.999998i | \(-0.499307\pi\) | ||||
0.00217844 | + | 0.999998i | \(0.499307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −55.9980 | −2.85392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.29612 | 0.320050 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −38.2372 | −1.93870 | −0.969351 | − | 0.245680i | \(-0.920989\pi\) | ||||
−0.969351 | + | 0.245680i | \(0.920989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.38727 | 0.272446 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.91756 | 0.348945 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.5336 | −1.08347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.5580 | 0.780835 | 0.390417 | − | 0.920638i | \(-0.372331\pi\) | ||||
0.390417 | + | 0.920638i | \(0.372331\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.31199 | −0.115744 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1348 | 0.705860 | 0.352930 | − | 0.935650i | \(-0.385185\pi\) | ||||
0.352930 | + | 0.935650i | \(0.385185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.867052 | −0.0431909 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.42255 | −0.170068 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.0853 | −1.54084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.1895 | 1.39388 | 0.696940 | − | 0.717130i | \(-0.254544\pi\) | ||||
0.696940 | + | 0.717130i | \(0.254544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.468996 | −0.0231339 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.9055 | 1.91441 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48.2817 | 2.37005 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3818 | −0.557370 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.13793 | 0.104445 | 0.0522224 | − | 0.998635i | \(-0.483370\pi\) | ||||
0.0522224 | + | 0.998635i | \(0.483370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.4041 | −1.14065 | −0.570324 | − | 0.821420i | \(-0.693182\pi\) | ||||
−0.570324 | + | 0.821420i | \(0.693182\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.83861 | 0.235261 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.5800 | 0.658725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.62197 | 0.223673 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.54827 | −0.267873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.07250 | 0.244334 | 0.122167 | − | 0.992510i | \(-0.461016\pi\) | ||||
0.122167 | + | 0.992510i | \(0.461016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.7359 | −0.515933 | −0.257967 | − | 0.966154i | \(-0.583052\pi\) | ||||
−0.257967 | + | 0.966154i | \(0.583052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.2397 | 1.11426 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.57736 | −0.0754554 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.61779 | −0.459032 | −0.229516 | − | 0.973305i | \(-0.573714\pi\) | ||||
−0.229516 | + | 0.973305i | \(0.573714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.24026 | 0.392393 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.06313 | 0.240557 | 0.120278 | − | 0.992740i | \(-0.461621\pi\) | ||||
0.120278 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.65397 | −0.173215 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.9159 | −0.610899 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9630 | −0.706147 | −0.353074 | − | 0.935596i | \(-0.614863\pi\) | ||||
−0.353074 | + | 0.935596i | \(0.614863\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.6236 | −1.39492 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.99361 | −0.234620 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.6879 | −0.829222 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.1616 | 1.13023 | 0.565116 | − | 0.825012i | \(-0.308831\pi\) | ||||
0.565116 | + | 0.825012i | \(0.308831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.02268 | −0.0944106 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3181 | 0.806582 | 0.403291 | − | 0.915072i | \(-0.367866\pi\) | ||||
0.403291 | + | 0.915072i | \(0.367866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.45093 | −0.253326 | −0.126663 | − | 0.991946i | \(-0.540427\pi\) | ||||
−0.126663 | + | 0.991946i | \(0.540427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.24163 | 0.103953 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.7328 | −1.88489 | −0.942445 | − | 0.334362i | \(-0.891479\pi\) | ||||
−0.942445 | + | 0.334362i | \(0.891479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.2816 | 0.936519 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.4359 | −0.849480 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.3876 | −1.21330 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.97614 | −0.182438 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.29738 | −0.0594030 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.7273 | −1.40397 | −0.701984 | − | 0.712193i | \(-0.747702\pi\) | ||||
−0.701984 | + | 0.712193i | \(0.747702\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.81879 | −0.447698 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.3977 | 0.473112 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.5362 | −0.841685 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.0244 | 1.40585 | 0.702924 | − | 0.711265i | \(-0.251877\pi\) | ||||
0.702924 | + | 0.711265i | \(0.251877\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.47891 | −0.202543 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.8207 | −0.533461 | −0.266730 | − | 0.963771i | \(-0.585943\pi\) | ||||
−0.266730 | + | 0.963771i | \(0.585943\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.7343 | 0.618564 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.3442 | 0.644724 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.1269 | 1.35138 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.5459 | 1.00930 | 0.504648 | − | 0.863325i | \(-0.331622\pi\) | ||||
0.504648 | + | 0.863325i | \(0.331622\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.0001 | 0.536124 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0088 | −1.60555 | −0.802775 | − | 0.596281i | \(-0.796644\pi\) | ||||
−0.802775 | + | 0.596281i | \(0.796644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.4468 | 1.22137 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2475 | 0.499519 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.10751 | −0.137738 | −0.0688691 | − | 0.997626i | \(-0.521939\pi\) | ||||
−0.0688691 | + | 0.997626i | \(0.521939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 58.3416 | 2.58088 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.592230 | 0.0261476 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −44.5835 | −1.96459 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.2791 | −0.891872 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.01711 | 0.395807 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6481 | 0.729365 | 0.364682 | − | 0.931132i | \(-0.381178\pi\) | ||||
0.364682 | + | 0.931132i | \(0.381178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.66216 | −0.422497 | −0.211248 | − | 0.977432i | \(-0.567753\pi\) | ||||
−0.211248 | + | 0.977432i | \(0.567753\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.2100 | 1.14390 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.32477 | 0.0577081 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9061 | −0.691571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.96586 | −0.432481 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.35710 | −0.405301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.6631 | 0.677173 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.47311 | −0.365642 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.5356 | −1.48756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.9248 | −0.469692 | −0.234846 | − | 0.972033i | \(-0.575459\pi\) | ||||
−0.234846 | + | 0.972033i | \(0.575459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.0206 | −0.601682 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.2889 | 0.911917 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.5636 | −1.90540 | −0.952701 | − | 0.303908i | \(-0.901708\pi\) | ||||
−0.952701 | + | 0.303908i | \(0.901708\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.18394 | −0.0505295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.02134 | −0.171315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.5620 | −1.04448 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.3850 | 1.07753 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.626224 | −0.0265340 | −0.0132670 | − | 0.999912i | \(-0.504223\pi\) | ||||
−0.0132670 | + | 0.999912i | \(0.504223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.33496 | −0.352531 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.47723 | 0.357909 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.6656 | 0.702372 | 0.351186 | − | 0.936306i | \(-0.385779\pi\) | ||||
0.351186 | + | 0.936306i | \(0.385779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.71061 | −0.198177 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.90388 | −0.163947 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.34649 | −0.266059 | −0.133029 | − | 0.991112i | \(-0.542470\pi\) | ||||
−0.133029 | + | 0.991112i | \(0.542470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.53134 | −0.147782 | −0.0738909 | − | 0.997266i | \(-0.523542\pi\) | ||||
−0.0738909 | + | 0.997266i | \(0.523542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.96559 | 0.374543 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.8819 | 0.745725 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4936 | 1.39436 | 0.697179 | − | 0.716898i | \(-0.254438\pi\) | ||||
0.697179 | + | 0.716898i | \(0.254438\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.0671 | −0.418374 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 55.0717 | 2.28476 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.43744 | 0.225196 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.53085 | 0.187328 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.3552 | −1.83073 | −0.915367 | − | 0.402621i | \(-0.868099\pi\) | ||||
−0.915367 | + | 0.402621i | \(0.868099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.387887 | −0.0159826 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5224 | 0.597372 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0365 | 0.740669 | 0.370335 | − | 0.928898i | \(-0.379243\pi\) | ||||
0.370335 | + | 0.928898i | \(0.379243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.0255 | 1.10794 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.7736 | 0.686498 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.89875 | 0.159299 | 0.0796493 | − | 0.996823i | \(-0.474620\pi\) | ||||
0.0796493 | + | 0.996823i | \(0.474620\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.5753 | −1.08403 | −0.542014 | − | 0.840370i | \(-0.682338\pi\) | ||||
−0.542014 | + | 0.840370i | \(0.682338\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.19525 | −0.211567 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.4698 | −0.913528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.31269 | 0.337402 | 0.168701 | − | 0.985667i | \(-0.446043\pi\) | ||||
0.168701 | + | 0.985667i | \(0.446043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.5080 | 1.07416 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.40547 | −0.259138 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.82520 | 0.194888 | 0.0974439 | − | 0.995241i | \(-0.468933\pi\) | ||||
0.0974439 | + | 0.995241i | \(0.468933\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.1914 | 0.975490 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.4154 | −0.821895 | −0.410948 | − | 0.911659i | \(-0.634802\pi\) | ||||
−0.410948 | + | 0.911659i | \(0.634802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.3880 | −1.02043 | −0.510215 | − | 0.860047i | \(-0.670434\pi\) | ||||
−0.510215 | + | 0.860047i | \(0.670434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.66343 | −0.106880 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.16785 | −0.166981 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.4935 | −0.539740 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.48209 | −0.0991250 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.0022 | 0.598177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.9024 | 0.911729 | 0.455864 | − | 0.890049i | \(-0.349330\pi\) | ||||
0.455864 | + | 0.890049i | \(0.349330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.01992 | −0.159777 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.4898 | −1.52742 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9087 | −0.432217 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.71718 | −0.305287 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.30989 | −0.0912352 | −0.0456176 | − | 0.998959i | \(-0.514526\pi\) | ||||
−0.0456176 | + | 0.998959i | \(0.514526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.4908 | −0.413718 | −0.206859 | − | 0.978371i | \(-0.566324\pi\) | ||||
−0.206859 | + | 0.978371i | \(0.566324\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.5488 | 0.848482 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.285006 | 0.0112047 | 0.00560237 | − | 0.999984i | \(-0.498217\pi\) | ||||
0.00560237 | + | 0.999984i | \(0.498217\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.7678 | 1.63953 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.55688 | 0.100212 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.73617 | 0.107074 | 0.0535372 | − | 0.998566i | \(-0.482950\pi\) | ||||
0.0535372 | + | 0.998566i | \(0.482950\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.6757 | 0.925086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.9445 | −0.583042 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.9986 | 1.36335 | 0.681676 | − | 0.731655i | \(-0.261252\pi\) | ||||
0.681676 | + | 0.731655i | \(0.261252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.6372 | 1.34723 | 0.673616 | − | 0.739082i | \(-0.264740\pi\) | ||||
0.673616 | + | 0.739082i | \(0.264740\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.67767 | 0.103992 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.91291 | −0.306849 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0851 | 0.700259 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.04684 | −0.311109 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.96202 | 0.191557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.12234 | 0.120357 | 0.0601787 | − | 0.998188i | \(-0.480833\pi\) | ||||
0.0601787 | + | 0.998188i | \(0.480833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.71385 | −0.258416 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.5426 | 1.59661 | 0.798307 | − | 0.602251i | \(-0.205729\pi\) | ||||
0.798307 | + | 0.602251i | \(0.205729\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.1430 | −0.811395 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.2181 | 0.736440 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.46317 | −0.170778 | −0.0853892 | − | 0.996348i | \(-0.527213\pi\) | ||||
−0.0853892 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.60516 | −0.0613301 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.84628 | −0.0704401 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.71751 | 0.0654318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.8149 | −1.02009 | −0.510044 | − | 0.860148i | \(-0.670371\pi\) | ||||
−0.510044 | + | 0.860148i | \(0.670371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.3615 | 0.621522 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.9548 | −1.47764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.2968 | 0.541529 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.372758 | 0.0140990 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.53215 | −0.0956380 | −0.0478190 | − | 0.998856i | \(-0.515227\pi\) | ||||
−0.0478190 | + | 0.998856i | \(0.515227\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.39256 | −0.165669 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.5604 | 0.623700 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.3067 | 1.17741 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.8029 | 1.19438 | 0.597192 | − | 0.802098i | \(-0.296283\pi\) | ||||
0.597192 | + | 0.802098i | \(0.296283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.29169 | 0.235957 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.74444 | 0.0653298 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.9892 | −0.710156 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9151 | −0.930472 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.0081 | 1.75311 | 0.876554 | − | 0.481304i | \(-0.159837\pi\) | ||||
0.876554 | + | 0.481304i | \(0.159837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.8535 | −1.89388 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.3473 | −0.496391 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45.5882 | 1.69310 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.3615 | −1.08896 | −0.544479 | − | 0.838774i | \(-0.683273\pi\) | ||||
−0.544479 | + | 0.838774i | \(0.683273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7350 | 0.471022 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.7676 | 1.39498 | 0.697490 | − | 0.716595i | \(-0.254300\pi\) | ||||
0.697490 | + | 0.716595i | \(0.254300\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 28.2027 | 1.04027 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.7738 | 0.802047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.3273 | −1.00525 | −0.502626 | − | 0.864504i | \(-0.667633\pi\) | ||||
−0.502626 | + | 0.864504i | \(0.667633\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.784008 | −0.0288013 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.9503 | −1.39226 | −0.696131 | − | 0.717915i | \(-0.745097\pi\) | ||||
−0.696131 | + | 0.717915i | \(0.745097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.2052 | −1.61955 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1069 | −0.516146 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.8658 | 0.652803 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.8835 | −0.543108 | −0.271554 | − | 0.962423i | \(-0.587538\pi\) | ||||
−0.271554 | + | 0.962423i | \(0.587538\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.00000 | −0.0364420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.0909 | −0.622001 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.3672 | 1.43083 | 0.715413 | − | 0.698702i | \(-0.246238\pi\) | ||||
0.715413 | + | 0.698702i | \(0.246238\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.1627 | 0.405179 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.3941 | −0.449287 | −0.224643 | − | 0.974441i | \(-0.572122\pi\) | ||||
−0.224643 | + | 0.974441i | \(0.572122\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.2829 | 0.879098 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.92272 | −0.250292 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.1930 | 0.476373 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.4371 | −0.556677 | −0.278339 | − | 0.960483i | \(-0.589784\pi\) | ||||
−0.278339 | + | 0.960483i | \(0.589784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2700 | −0.477906 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.4766 | 1.67165 | 0.835823 | − | 0.548999i | \(-0.184991\pi\) | ||||
0.835823 | + | 0.548999i | \(0.184991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.39730 | 0.157956 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.9550 | 1.03876 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.18602 | −0.149980 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.3434 | 1.15734 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.79017 | −0.242661 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.0977 | −2.25205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.0653 | −1.78463 | −0.892317 | − | 0.451409i | \(-0.850922\pi\) | ||||
−0.892317 | + | 0.451409i | \(0.850922\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.30949 | −0.224624 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.37309 | −0.191045 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.56733 | 0.0556577 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.44035 | −0.157483 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.78837 | 0.0633473 | 0.0316737 | − | 0.999498i | \(-0.489916\pi\) | ||||
0.0316737 | + | 0.999498i | \(0.489916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.78697 | 0.346238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.06762 | 0.0377224 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 62.6339 | 2.21030 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.5866 | 1.25426 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.3581 | 0.505431 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.8439 | 0.908622 | 0.454311 | − | 0.890843i | \(-0.349886\pi\) | ||||
0.454311 | + | 0.890843i | \(0.349886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.2004 | −0.709332 | −0.354666 | − | 0.934993i | \(-0.615405\pi\) | ||||
−0.354666 | + | 0.934993i | \(0.615405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.4332 | −0.786768 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.3293 | −0.536961 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.72875 | −0.130452 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.16805 | 0.180586 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.7491 | −1.49195 | −0.745977 | − | 0.665971i | \(-0.768017\pi\) | ||||
−0.745977 | + | 0.665971i | \(0.768017\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5627 | 0.681913 | 0.340957 | − | 0.940079i | \(-0.389249\pi\) | ||||
0.340957 | + | 0.940079i | \(0.389249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 28.1383 | 0.979651 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.3179 | −1.64540 | −0.822702 | − | 0.568472i | \(-0.807535\pi\) | ||||
−0.822702 | + | 0.568472i | \(0.807535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.6109 | −0.542189 | −0.271095 | − | 0.962553i | \(-0.587386\pi\) | ||||
−0.271095 | + | 0.962553i | \(0.587386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.3951 | −0.568740 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.6674 | 0.577491 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.0708 | 1.42132 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.654960 | −0.0226387 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.8474 | −0.857828 | −0.428914 | − | 0.903345i | \(-0.641104\pi\) | ||||
−0.428914 | + | 0.903345i | \(0.641104\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.1064 | 0.589876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.1631 | −0.556686 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38.4951 | 1.32427 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.6298 | −0.880651 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.6630 | 0.434592 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7546 | 0.677180 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.5910 | −1.93764 | −0.968819 | − | 0.247769i | \(-0.920303\pi\) | ||||
−0.968819 | + | 0.247769i | \(0.920303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.02694 | 0.0693197 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.7125 | −0.502570 | −0.251285 | − | 0.967913i | \(-0.580853\pi\) | ||||
−0.251285 | + | 0.967913i | \(0.580853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.98566 | −0.0677497 | −0.0338749 | − | 0.999426i | \(-0.510785\pi\) | ||||
−0.0338749 | + | 0.999426i | \(0.510785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.5935 | 0.940384 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.1719 | −0.448378 | −0.224189 | − | 0.974546i | \(-0.571973\pi\) | ||||
−0.224189 | + | 0.974546i | \(0.571973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.8615 | 1.04932 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.9088 | 0.438405 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.3690 | −0.894508 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.87760 | 0.233039 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.41590 | 0.183301 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.8991 | 0.774130 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.4241 | −1.09488 | −0.547442 | − | 0.836844i | \(-0.684398\pi\) | ||||
−0.547442 | + | 0.836844i | \(0.684398\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.7646 | −0.565454 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.1840 | −1.69074 | −0.845372 | − | 0.534178i | \(-0.820621\pi\) | ||||
−0.845372 | + | 0.534178i | \(0.820621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2133 | 1.11772 | 0.558858 | − | 0.829263i | \(-0.311240\pi\) | ||||
0.558858 | + | 0.829263i | \(0.311240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.1087 | −1.14655 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.8362 | −0.565306 | −0.282653 | − | 0.959222i | \(-0.591214\pi\) | ||||
−0.282653 | + | 0.959222i | \(0.591214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.9028 | −1.47245 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.19109 | −0.140407 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.86557 | −0.0958926 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.9997 | −0.969352 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.52591 | 0.117727 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.44729 | 0.148325 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.62419 | −0.0874244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.5793 | 0.817947 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −47.9862 | −1.59512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.3866 | 1.70626 | 0.853131 | − | 0.521696i | \(-0.174701\pi\) | ||||
0.853131 | + | 0.521696i | \(0.174701\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.01940 | −0.265987 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.76579 | 0.157898 | 0.0789489 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789489 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.1234 | 1.95670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.05211 | −0.133959 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.0053 | 0.891794 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.2194 | −0.864897 | −0.432449 | − | 0.901659i | \(-0.642350\pi\) | ||||
−0.432449 | + | 0.901659i | \(0.642350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.4014 | 0.705201 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.2162 | 0.336270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.7965 | 1.63730 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.0264 | 0.427844 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.44801 | 0.145934 | 0.0729672 | − | 0.997334i | \(-0.476753\pi\) | ||||
0.0729672 | + | 0.997334i | \(0.476753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.88012 | −0.159940 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.73908 | 0.253366 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.0138 | 0.948851 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.1565 | 0.331798 | 0.165899 | − | 0.986143i | \(-0.446947\pi\) | ||||
0.165899 | + | 0.986143i | \(0.446947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.66051 | −0.184724 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1089 | −0.688131 | −0.344066 | − | 0.938946i | \(-0.611804\pi\) | ||||
−0.344066 | + | 0.938946i | \(0.611804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.8257 | 0.613050 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.3612 | −0.434640 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.4529 | 1.08707 | 0.543536 | − | 0.839386i | \(-0.317085\pi\) | ||||
0.543536 | + | 0.839386i | \(0.317085\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7839 | 0.642214 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.88564 | −0.0611460 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.24793 | −0.0404244 | −0.0202122 | − | 0.999796i | \(-0.506434\pi\) | ||||
−0.0202122 | + | 0.999796i | \(0.506434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.6852 | 0.992949 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.4582 | 0.919923 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.83090 | −0.0591230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5710 | −0.986162 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.57643 | −0.147473 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.4551 | −1.10915 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.5263 | 1.04597 | 0.522987 | − | 0.852340i | \(-0.324818\pi\) | ||||
0.522987 | + | 0.852340i | \(0.324818\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.19789 | 0.0384818 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.25222 | −0.264826 | −0.132413 | − | 0.991195i | \(-0.542273\pi\) | ||||
−0.132413 | + | 0.991195i | \(0.542273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.4332 | −1.42446 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.88795 | 0.284642 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.7036 | 1.39820 | 0.699101 | − | 0.715023i | \(-0.253584\pi\) | ||||
0.699101 | + | 0.715023i | \(0.253584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.47448 | −0.143005 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.22019 | −0.198595 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.0267 | −1.62750 | −0.813750 | − | 0.581215i | \(-0.802578\pi\) | ||||
−0.813750 | + | 0.581215i | \(0.802578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.7037 | 1.58369 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.8893 | 0.601255 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7693 | 0.533232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.2203 | −0.610554 | −0.305277 | − | 0.952264i | \(-0.598749\pi\) | ||||
−0.305277 | + | 0.952264i | \(0.598749\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.8190 | 0.724139 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.4085 | 1.81997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.7823 | −0.373149 | −0.186574 | − | 0.982441i | \(-0.559739\pi\) | ||||
−0.186574 | + | 0.982441i | \(0.559739\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.41699 | −0.234663 |
(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 | 6024.2.a.o.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6024.2.a.o.1.2 | ✓ | 14 | 1.1 | even | 1 | trivial |