Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14940 | −0.812749 | −0.406375 | − | 0.913707i | \(-0.633207\pi\) | ||||
−0.406375 | + | 0.913707i | \(0.633207\pi\) | |||||||
\(3\) | 0.361587 | 0.208762 | 0.104381 | − | 0.994537i | \(-0.466714\pi\) | ||||
0.104381 | + | 0.994537i | \(0.466714\pi\) | |||||||
\(4\) | −0.678878 | −0.339439 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.415609 | −0.169672 | ||||||||
\(7\) | −3.63700 | −1.37466 | −0.687328 | − | 0.726347i | \(-0.741216\pi\) | ||||
−0.687328 | + | 0.726347i | \(0.741216\pi\) | |||||||
\(8\) | 3.07910 | 1.08863 | ||||||||
\(9\) | −2.86925 | −0.956418 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.31008 | −0.998027 | −0.499013 | − | 0.866594i | \(-0.666304\pi\) | ||||
−0.499013 | + | 0.866594i | \(0.666304\pi\) | |||||||
\(12\) | −0.245473 | −0.0708621 | ||||||||
\(13\) | 3.42302 | 0.949375 | 0.474687 | − | 0.880155i | \(-0.342561\pi\) | ||||
0.474687 | + | 0.880155i | \(0.342561\pi\) | |||||||
\(14\) | 4.18037 | 1.11725 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.18137 | −0.545342 | ||||||||
\(17\) | −0.605765 | −0.146919 | −0.0734597 | − | 0.997298i | \(-0.523404\pi\) | ||||
−0.0734597 | + | 0.997298i | \(0.523404\pi\) | |||||||
\(18\) | 3.29792 | 0.777328 | ||||||||
\(19\) | −1.21792 | −0.279411 | −0.139705 | − | 0.990193i | \(-0.544616\pi\) | ||||
−0.139705 | + | 0.990193i | \(0.544616\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.31509 | −0.286976 | ||||||||
\(22\) | 3.80461 | 0.811146 | ||||||||
\(23\) | 6.22482 | 1.29797 | 0.648983 | − | 0.760803i | \(-0.275195\pi\) | ||||
0.648983 | + | 0.760803i | \(0.275195\pi\) | |||||||
\(24\) | 1.11336 | 0.227265 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.93442 | −0.771603 | ||||||||
\(27\) | −2.12225 | −0.408427 | ||||||||
\(28\) | 2.46908 | 0.466611 | ||||||||
\(29\) | 3.29498 | 0.611863 | 0.305931 | − | 0.952054i | \(-0.401032\pi\) | ||||
0.305931 | + | 0.952054i | \(0.401032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.187069 | 0.0335986 | 0.0167993 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0167993 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(32\) | −3.65094 | −0.645401 | ||||||||
\(33\) | −1.19688 | −0.208351 | ||||||||
\(34\) | 0.696266 | 0.119409 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94787 | 0.324645 | ||||||||
\(37\) | −0.174751 | −0.0287289 | −0.0143645 | − | 0.999897i | \(-0.504573\pi\) | ||||
−0.0143645 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(38\) | 1.39988 | 0.227091 | ||||||||
\(39\) | 1.23772 | 0.198194 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.28617 | 1.45026 | 0.725128 | − | 0.688614i | \(-0.241780\pi\) | ||||
0.725128 | + | 0.688614i | \(0.241780\pi\) | |||||||
\(42\) | 1.51157 | 0.233240 | ||||||||
\(43\) | −5.81664 | −0.887030 | −0.443515 | − | 0.896267i | \(-0.646269\pi\) | ||||
−0.443515 | + | 0.896267i | \(0.646269\pi\) | |||||||
\(44\) | 2.24714 | 0.338769 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.15482 | −1.05492 | ||||||||
\(47\) | −3.12220 | −0.455420 | −0.227710 | − | 0.973729i | \(-0.573124\pi\) | ||||
−0.227710 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(48\) | −0.788755 | −0.113847 | ||||||||
\(49\) | 6.22774 | 0.889677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.219037 | −0.0306713 | ||||||||
\(52\) | −2.32381 | −0.322255 | ||||||||
\(53\) | 2.23321 | 0.306755 | 0.153378 | − | 0.988168i | \(-0.450985\pi\) | ||||
0.153378 | + | 0.988168i | \(0.450985\pi\) | |||||||
\(54\) | 2.43931 | 0.331948 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −11.1987 | −1.49649 | ||||||||
\(57\) | −0.440386 | −0.0583305 | ||||||||
\(58\) | −3.78725 | −0.497291 | ||||||||
\(59\) | 6.04532 | 0.787034 | 0.393517 | − | 0.919317i | \(-0.371258\pi\) | ||||
0.393517 | + | 0.919317i | \(0.371258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.39259 | 0.306340 | 0.153170 | − | 0.988200i | \(-0.451052\pi\) | ||||
0.153170 | + | 0.988200i | \(0.451052\pi\) | |||||||
\(62\) | −0.215017 | −0.0273072 | ||||||||
\(63\) | 10.4355 | 1.31475 | ||||||||
\(64\) | 8.55913 | 1.06989 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.37570 | 0.169337 | ||||||||
\(67\) | 5.48219 | 0.669756 | 0.334878 | − | 0.942261i | \(-0.391305\pi\) | ||||
0.334878 | + | 0.942261i | \(0.391305\pi\) | |||||||
\(68\) | 0.411240 | 0.0498702 | ||||||||
\(69\) | 2.25082 | 0.270966 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.38307 | 0.757531 | 0.378765 | − | 0.925493i | \(-0.376349\pi\) | ||||
0.378765 | + | 0.925493i | \(0.376349\pi\) | |||||||
\(72\) | −8.83473 | −1.04118 | ||||||||
\(73\) | −0.625385 | −0.0731957 | −0.0365979 | − | 0.999330i | \(-0.511652\pi\) | ||||
−0.0365979 | + | 0.999330i | \(0.511652\pi\) | |||||||
\(74\) | 0.200859 | 0.0233494 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.826821 | 0.0948429 | ||||||||
\(77\) | 12.0388 | 1.37194 | ||||||||
\(78\) | −1.42264 | −0.161082 | ||||||||
\(79\) | 6.61180 | 0.743886 | 0.371943 | − | 0.928256i | \(-0.378692\pi\) | ||||
0.371943 | + | 0.928256i | \(0.378692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.84039 | 0.871154 | ||||||||
\(82\) | −10.6735 | −1.17869 | ||||||||
\(83\) | −13.1244 | −1.44059 | −0.720297 | − | 0.693666i | \(-0.755994\pi\) | ||||
−0.720297 | + | 0.693666i | \(0.755994\pi\) | |||||||
\(84\) | 0.892786 | 0.0974109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.68566 | 0.720933 | ||||||||
\(87\) | 1.19142 | 0.127734 | ||||||||
\(88\) | −10.1921 | −1.08648 | ||||||||
\(89\) | −1.26185 | −0.133756 | −0.0668779 | − | 0.997761i | \(-0.521304\pi\) | ||||
−0.0668779 | + | 0.997761i | \(0.521304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4495 | −1.30506 | ||||||||
\(92\) | −4.22589 | −0.440580 | ||||||||
\(93\) | 0.0676417 | 0.00701412 | ||||||||
\(94\) | 3.58866 | 0.370143 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.32013 | −0.134736 | ||||||||
\(97\) | 0.489708 | 0.0497223 | 0.0248612 | − | 0.999691i | \(-0.492086\pi\) | ||||
0.0248612 | + | 0.999691i | \(0.492086\pi\) | |||||||
\(98\) | −7.15817 | −0.723085 | ||||||||
\(99\) | 9.49746 | 0.954531 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.80782 | −0.279388 | −0.139694 | − | 0.990195i | \(-0.544612\pi\) | ||||
−0.139694 | + | 0.990195i | \(0.544612\pi\) | |||||||
\(102\) | 0.251761 | 0.0249281 | ||||||||
\(103\) | −13.1100 | −1.29177 | −0.645884 | − | 0.763436i | \(-0.723511\pi\) | ||||
−0.645884 | + | 0.763436i | \(0.723511\pi\) | |||||||
\(104\) | 10.5398 | 1.03352 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.56686 | −0.249315 | ||||||||
\(107\) | −3.36714 | −0.325514 | −0.162757 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162757 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(108\) | 1.44075 | 0.138636 | ||||||||
\(109\) | 7.11162 | 0.681170 | 0.340585 | − | 0.940214i | \(-0.389375\pi\) | ||||
0.340585 | + | 0.940214i | \(0.389375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0631879 | −0.00599753 | ||||||||
\(112\) | 7.93363 | 0.749658 | ||||||||
\(113\) | 11.2316 | 1.05658 | 0.528291 | − | 0.849064i | \(-0.322833\pi\) | ||||
0.528291 | + | 0.849064i | \(0.322833\pi\) | |||||||
\(114\) | 0.506180 | 0.0474081 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.23689 | −0.207690 | ||||||||
\(117\) | −9.82151 | −0.907999 | ||||||||
\(118\) | −6.94850 | −0.639661 | ||||||||
\(119\) | 2.20316 | 0.201964 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0433654 | −0.00394231 | ||||||||
\(122\) | −2.75005 | −0.248978 | ||||||||
\(123\) | 3.35776 | 0.302759 | ||||||||
\(124\) | −0.126997 | −0.0114047 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.9945 | −1.06856 | ||||||||
\(127\) | 19.1172 | 1.69638 | 0.848189 | − | 0.529693i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529693i | \(0.177693\pi\) | |||||||
\(128\) | −2.53600 | −0.224152 | ||||||||
\(129\) | −2.10322 | −0.185179 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.46608 | 0.827055 | 0.413528 | − | 0.910492i | \(-0.364296\pi\) | ||||
0.413528 | + | 0.910492i | \(0.364296\pi\) | |||||||
\(132\) | 0.812537 | 0.0707223 | ||||||||
\(133\) | 4.42959 | 0.384094 | ||||||||
\(134\) | −6.30123 | −0.544344 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.86521 | −0.159941 | ||||||||
\(137\) | −16.7033 | −1.42706 | −0.713528 | − | 0.700626i | \(-0.752904\pi\) | ||||
−0.713528 | + | 0.700626i | \(0.752904\pi\) | |||||||
\(138\) | −2.58709 | −0.220228 | ||||||||
\(139\) | −8.45064 | −0.716774 | −0.358387 | − | 0.933573i | \(-0.616673\pi\) | ||||
−0.358387 | + | 0.933573i | \(0.616673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.12895 | −0.0950747 | ||||||||
\(142\) | −7.33670 | −0.615682 | ||||||||
\(143\) | −11.3305 | −0.947501 | ||||||||
\(144\) | 6.25891 | 0.521576 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.718818 | 0.0594898 | ||||||||
\(147\) | 2.25187 | 0.185731 | ||||||||
\(148\) | 0.118635 | 0.00975172 | ||||||||
\(149\) | −8.57298 | −0.702326 | −0.351163 | − | 0.936314i | \(-0.614214\pi\) | ||||
−0.351163 | + | 0.936314i | \(0.614214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.1314 | −1.39413 | −0.697066 | − | 0.717007i | \(-0.745511\pi\) | ||||
−0.697066 | + | 0.717007i | \(0.745511\pi\) | |||||||
\(152\) | −3.75012 | −0.304175 | ||||||||
\(153\) | 1.73809 | 0.140516 | ||||||||
\(154\) | −13.8374 | −1.11505 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.840260 | −0.0672747 | ||||||||
\(157\) | −14.1271 | −1.12746 | −0.563732 | − | 0.825958i | \(-0.690635\pi\) | ||||
−0.563732 | + | 0.825958i | \(0.690635\pi\) | |||||||
\(158\) | −7.59961 | −0.604592 | ||||||||
\(159\) | 0.807501 | 0.0640390 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.6397 | −1.78425 | ||||||||
\(162\) | −9.01175 | −0.708030 | ||||||||
\(163\) | −9.98079 | −0.781756 | −0.390878 | − | 0.920443i | \(-0.627829\pi\) | ||||
−0.390878 | + | 0.920443i | \(0.627829\pi\) | |||||||
\(164\) | −6.30418 | −0.492273 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0852 | 1.17084 | ||||||||
\(167\) | −1.72404 | −0.133410 | −0.0667050 | − | 0.997773i | \(-0.521249\pi\) | ||||
−0.0667050 | + | 0.997773i | \(0.521249\pi\) | |||||||
\(168\) | −4.04930 | −0.312411 | ||||||||
\(169\) | −1.28294 | −0.0986879 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.49453 | 0.267234 | ||||||||
\(172\) | 3.94879 | 0.301092 | ||||||||
\(173\) | 17.0426 | 1.29572 | 0.647862 | − | 0.761758i | \(-0.275663\pi\) | ||||
0.647862 | + | 0.761758i | \(0.275663\pi\) | |||||||
\(174\) | −1.36942 | −0.103816 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.22051 | 0.544266 | ||||||||
\(177\) | 2.18591 | 0.164303 | ||||||||
\(178\) | 1.45037 | 0.108710 | ||||||||
\(179\) | −13.9513 | −1.04277 | −0.521384 | − | 0.853322i | \(-0.674584\pi\) | ||||
−0.521384 | + | 0.853322i | \(0.674584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1649 | 0.978536 | 0.489268 | − | 0.872133i | \(-0.337264\pi\) | ||||
0.489268 | + | 0.872133i | \(0.337264\pi\) | |||||||
\(182\) | 14.3095 | 1.06069 | ||||||||
\(183\) | 0.865131 | 0.0639523 | ||||||||
\(184\) | 19.1669 | 1.41300 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0777474 | −0.00570072 | ||||||||
\(187\) | 2.00513 | 0.146630 | ||||||||
\(188\) | 2.11959 | 0.154587 | ||||||||
\(189\) | 7.71861 | 0.561446 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1886 | 1.60551 | 0.802756 | − | 0.596308i | \(-0.203366\pi\) | ||||
0.802756 | + | 0.596308i | \(0.203366\pi\) | |||||||
\(192\) | 3.09487 | 0.223353 | ||||||||
\(193\) | −5.06056 | −0.364267 | −0.182134 | − | 0.983274i | \(-0.558300\pi\) | ||||
−0.182134 | + | 0.983274i | \(0.558300\pi\) | |||||||
\(194\) | −0.562871 | −0.0404118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.22787 | −0.301991 | ||||||||
\(197\) | 3.62547 | 0.258304 | 0.129152 | − | 0.991625i | \(-0.458775\pi\) | ||||
0.129152 | + | 0.991625i | \(0.458775\pi\) | |||||||
\(198\) | −10.9164 | −0.775794 | ||||||||
\(199\) | −0.289466 | −0.0205197 | −0.0102599 | − | 0.999947i | \(-0.503266\pi\) | ||||
−0.0102599 | + | 0.999947i | \(0.503266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.98229 | 0.139820 | ||||||||
\(202\) | 3.22731 | 0.227073 | ||||||||
\(203\) | −11.9838 | −0.841100 | ||||||||
\(204\) | 0.148699 | 0.0104110 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.0687 | 1.04988 | ||||||||
\(207\) | −17.8606 | −1.24140 | ||||||||
\(208\) | −7.46687 | −0.517734 | ||||||||
\(209\) | 4.03143 | 0.278860 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8956 | −1.23198 | −0.615992 | − | 0.787752i | \(-0.711245\pi\) | ||||
−0.615992 | + | 0.787752i | \(0.711245\pi\) | |||||||
\(212\) | −1.51608 | −0.104125 | ||||||||
\(213\) | 2.30803 | 0.158144 | ||||||||
\(214\) | 3.87019 | 0.264561 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.53462 | −0.444625 | ||||||||
\(217\) | −0.680369 | −0.0461864 | ||||||||
\(218\) | −8.17410 | −0.553620 | ||||||||
\(219\) | −0.226131 | −0.0152805 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.07354 | −0.139482 | ||||||||
\(222\) | 0.0726282 | 0.00487448 | ||||||||
\(223\) | −24.3454 | −1.63029 | −0.815145 | − | 0.579257i | \(-0.803343\pi\) | ||||
−0.815145 | + | 0.579257i | \(0.803343\pi\) | |||||||
\(224\) | 13.2785 | 0.887204 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.9096 | −0.858735 | ||||||||
\(227\) | −7.75396 | −0.514648 | −0.257324 | − | 0.966325i | \(-0.582841\pi\) | ||||
−0.257324 | + | 0.966325i | \(0.582841\pi\) | |||||||
\(228\) | 0.298968 | 0.0197996 | ||||||||
\(229\) | 24.1455 | 1.59558 | 0.797790 | − | 0.602935i | \(-0.206002\pi\) | ||||
0.797790 | + | 0.602935i | \(0.206002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.35306 | 0.286410 | ||||||||
\(232\) | 10.1456 | 0.666091 | ||||||||
\(233\) | −9.06363 | −0.593778 | −0.296889 | − | 0.954912i | \(-0.595949\pi\) | ||||
−0.296889 | + | 0.954912i | \(0.595949\pi\) | |||||||
\(234\) | 11.2889 | 0.737976 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.10403 | −0.267150 | ||||||||
\(237\) | 2.39074 | 0.155295 | ||||||||
\(238\) | −2.53232 | −0.164146 | ||||||||
\(239\) | −13.0403 | −0.843504 | −0.421752 | − | 0.906711i | \(-0.638585\pi\) | ||||
−0.421752 | + | 0.906711i | \(0.638585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 0.0498442 | 0.00320411 | ||||||||
\(243\) | 9.20172 | 0.590291 | ||||||||
\(244\) | −1.62428 | −0.103984 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.85941 | −0.246067 | ||||||||
\(247\) | −4.16898 | −0.265266 | ||||||||
\(248\) | 0.576005 | 0.0365763 | ||||||||
\(249\) | −4.74563 | −0.300742 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.42229 | −0.531610 | −0.265805 | − | 0.964027i | \(-0.585638\pi\) | ||||
−0.265805 | + | 0.964027i | \(0.585638\pi\) | |||||||
\(252\) | −7.08441 | −0.446276 | ||||||||
\(253\) | −20.6047 | −1.29540 | ||||||||
\(254\) | −21.9733 | −1.37873 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.2034 | −0.887712 | ||||||||
\(257\) | −2.04403 | −0.127503 | −0.0637517 | − | 0.997966i | \(-0.520307\pi\) | ||||
−0.0637517 | + | 0.997966i | \(0.520307\pi\) | |||||||
\(258\) | 2.41745 | 0.150504 | ||||||||
\(259\) | 0.635570 | 0.0394924 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.45414 | −0.585197 | ||||||||
\(262\) | −10.8803 | −0.672189 | ||||||||
\(263\) | −26.0710 | −1.60761 | −0.803805 | − | 0.594893i | \(-0.797194\pi\) | ||||
−0.803805 | + | 0.594893i | \(0.797194\pi\) | |||||||
\(264\) | −3.68533 | −0.226816 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.09137 | −0.312172 | ||||||||
\(267\) | −0.456269 | −0.0279232 | ||||||||
\(268\) | −3.72174 | −0.227341 | ||||||||
\(269\) | 8.87038 | 0.540837 | 0.270418 | − | 0.962743i | \(-0.412838\pi\) | ||||
0.270418 | + | 0.962743i | \(0.412838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.842226 | 0.0511616 | 0.0255808 | − | 0.999673i | \(-0.491856\pi\) | ||||
0.0255808 | + | 0.999673i | \(0.491856\pi\) | |||||||
\(272\) | 1.32140 | 0.0801214 | ||||||||
\(273\) | −4.50158 | −0.272448 | ||||||||
\(274\) | 19.1988 | 1.15984 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.52803 | −0.0919765 | ||||||||
\(277\) | −13.3430 | −0.801704 | −0.400852 | − | 0.916143i | \(-0.631286\pi\) | ||||
−0.400852 | + | 0.916143i | \(0.631286\pi\) | |||||||
\(278\) | 9.71317 | 0.582557 | ||||||||
\(279\) | −0.536748 | −0.0321343 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8691 | 0.708054 | 0.354027 | − | 0.935235i | \(-0.384812\pi\) | ||||
0.354027 | + | 0.935235i | \(0.384812\pi\) | |||||||
\(282\) | 1.29762 | 0.0772719 | ||||||||
\(283\) | 25.4643 | 1.51369 | 0.756847 | − | 0.653592i | \(-0.226739\pi\) | ||||
0.756847 | + | 0.653592i | \(0.226739\pi\) | |||||||
\(284\) | −4.33332 | −0.257135 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.0233 | 0.770081 | ||||||||
\(287\) | −33.7738 | −1.99360 | ||||||||
\(288\) | 10.4755 | 0.617273 | ||||||||
\(289\) | −16.6330 | −0.978415 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.177072 | 0.0103802 | ||||||||
\(292\) | 0.424560 | 0.0248455 | ||||||||
\(293\) | 31.0311 | 1.81285 | 0.906427 | − | 0.422362i | \(-0.138799\pi\) | ||||
0.906427 | + | 0.422362i | \(0.138799\pi\) | |||||||
\(294\) | −2.58830 | −0.150953 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.538078 | −0.0312751 | ||||||||
\(297\) | 7.02481 | 0.407621 | ||||||||
\(298\) | 9.85379 | 0.570815 | ||||||||
\(299\) | 21.3077 | 1.23226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.1551 | 1.21936 | ||||||||
\(302\) | 19.6908 | 1.13308 | ||||||||
\(303\) | −1.01527 | −0.0583258 | ||||||||
\(304\) | 2.65674 | 0.152375 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.99777 | −0.114205 | ||||||||
\(307\) | −3.24000 | −0.184916 | −0.0924582 | − | 0.995717i | \(-0.529472\pi\) | ||||
−0.0924582 | + | 0.995717i | \(0.529472\pi\) | |||||||
\(308\) | −8.17284 | −0.465691 | ||||||||
\(309\) | −4.74041 | −0.269673 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.66898 | 0.264754 | 0.132377 | − | 0.991199i | \(-0.457739\pi\) | ||||
0.132377 | + | 0.991199i | \(0.457739\pi\) | |||||||
\(312\) | 3.81107 | 0.215759 | ||||||||
\(313\) | −27.9019 | −1.57711 | −0.788554 | − | 0.614965i | \(-0.789170\pi\) | ||||
−0.788554 | + | 0.614965i | \(0.789170\pi\) | |||||||
\(314\) | 16.2377 | 0.916345 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.48860 | −0.252504 | ||||||||
\(317\) | −23.5760 | −1.32416 | −0.662080 | − | 0.749434i | \(-0.730326\pi\) | ||||
−0.662080 | + | 0.749434i | \(0.730326\pi\) | |||||||
\(318\) | −0.928142 | −0.0520476 | ||||||||
\(319\) | −10.9067 | −0.610655 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.21751 | −0.0679550 | ||||||||
\(322\) | 26.0220 | 1.45015 | ||||||||
\(323\) | 0.737775 | 0.0410509 | ||||||||
\(324\) | −5.32266 | −0.295704 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.4719 | 0.635371 | ||||||||
\(327\) | 2.57147 | 0.142203 | ||||||||
\(328\) | 28.5931 | 1.57879 | ||||||||
\(329\) | 11.3554 | 0.626046 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0029 | −0.604773 | −0.302387 | − | 0.953185i | \(-0.597783\pi\) | ||||
−0.302387 | + | 0.953185i | \(0.597783\pi\) | |||||||
\(332\) | 8.90988 | 0.488993 | ||||||||
\(333\) | 0.501406 | 0.0274769 | ||||||||
\(334\) | 1.98161 | 0.108429 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.86870 | 0.156500 | ||||||||
\(337\) | −6.84048 | −0.372625 | −0.186312 | − | 0.982491i | \(-0.559654\pi\) | ||||
−0.186312 | + | 0.982491i | \(0.559654\pi\) | |||||||
\(338\) | 1.47462 | 0.0802085 | ||||||||
\(339\) | 4.06121 | 0.220574 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.619213 | −0.0335323 | ||||||||
\(342\) | −4.01662 | −0.217194 | ||||||||
\(343\) | 2.80870 | 0.151656 | ||||||||
\(344\) | −17.9101 | −0.965645 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.5888 | −1.05310 | ||||||||
\(347\) | 7.59996 | 0.407987 | 0.203994 | − | 0.978972i | \(-0.434608\pi\) | ||||
0.203994 | + | 0.978972i | \(0.434608\pi\) | |||||||
\(348\) | −0.808830 | −0.0433579 | ||||||||
\(349\) | 10.5572 | 0.565112 | 0.282556 | − | 0.959251i | \(-0.408818\pi\) | ||||
0.282556 | + | 0.959251i | \(0.408818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.26449 | −0.387750 | ||||||||
\(352\) | 12.0849 | 0.644128 | ||||||||
\(353\) | −31.2951 | −1.66567 | −0.832834 | − | 0.553523i | \(-0.813283\pi\) | ||||
−0.832834 | + | 0.553523i | \(0.813283\pi\) | |||||||
\(354\) | −2.51249 | −0.133537 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.856641 | 0.0454019 | ||||||||
\(357\) | 0.796636 | 0.0421624 | ||||||||
\(358\) | 16.0356 | 0.847509 | ||||||||
\(359\) | 12.2270 | 0.645319 | 0.322659 | − | 0.946515i | \(-0.395423\pi\) | ||||
0.322659 | + | 0.946515i | \(0.395423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5167 | −0.921930 | ||||||||
\(362\) | −15.1317 | −0.795305 | ||||||||
\(363\) | −0.0156804 | −0.000823006 0 | ||||||||
\(364\) | 8.45169 | 0.442989 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.994382 | −0.0519772 | ||||||||
\(367\) | −4.97683 | −0.259788 | −0.129894 | − | 0.991528i | \(-0.541464\pi\) | ||||
−0.129894 | + | 0.991528i | \(0.541464\pi\) | |||||||
\(368\) | −13.5786 | −0.707835 | ||||||||
\(369\) | −26.6444 | −1.38705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.12219 | −0.421683 | ||||||||
\(372\) | −0.0459204 | −0.00238086 | ||||||||
\(373\) | 14.0011 | 0.724951 | 0.362476 | − | 0.931993i | \(-0.381932\pi\) | ||||
0.362476 | + | 0.931993i | \(0.381932\pi\) | |||||||
\(374\) | −2.30470 | −0.119173 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.61359 | −0.495783 | ||||||||
\(377\) | 11.2788 | 0.580887 | ||||||||
\(378\) | −8.87177 | −0.456315 | ||||||||
\(379\) | 15.1424 | 0.777812 | 0.388906 | − | 0.921277i | \(-0.372853\pi\) | ||||
0.388906 | + | 0.921277i | \(0.372853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.91254 | 0.354140 | ||||||||
\(382\) | −25.5036 | −1.30488 | ||||||||
\(383\) | 15.3097 | 0.782291 | 0.391145 | − | 0.920329i | \(-0.372079\pi\) | ||||
0.391145 | + | 0.920329i | \(0.372079\pi\) | |||||||
\(384\) | −0.916984 | −0.0467946 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.81661 | 0.296058 | ||||||||
\(387\) | 16.6894 | 0.848372 | ||||||||
\(388\) | −0.332452 | −0.0168777 | ||||||||
\(389\) | 35.9486 | 1.82267 | 0.911334 | − | 0.411667i | \(-0.135053\pi\) | ||||
0.911334 | + | 0.411667i | \(0.135053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.77078 | −0.190696 | ||||||||
\(392\) | 19.1759 | 0.968528 | ||||||||
\(393\) | 3.42281 | 0.172658 | ||||||||
\(394\) | −4.16711 | −0.209936 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.44762 | −0.324005 | ||||||||
\(397\) | −12.6507 | −0.634919 | −0.317460 | − | 0.948272i | \(-0.602830\pi\) | ||||
−0.317460 | + | 0.948272i | \(0.602830\pi\) | |||||||
\(398\) | 0.332713 | 0.0166774 | ||||||||
\(399\) | 1.60168 | 0.0801844 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.7283 | 0.885308 | 0.442654 | − | 0.896692i | \(-0.354037\pi\) | ||||
0.442654 | + | 0.896692i | \(0.354037\pi\) | |||||||
\(402\) | −2.27845 | −0.113639 | ||||||||
\(403\) | 0.640340 | 0.0318976 | ||||||||
\(404\) | 1.90616 | 0.0948352 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.7742 | 0.683604 | ||||||||
\(407\) | 0.578441 | 0.0286723 | ||||||||
\(408\) | −0.674437 | −0.0333896 | ||||||||
\(409\) | −27.5554 | −1.36253 | −0.681264 | − | 0.732038i | \(-0.738569\pi\) | ||||
−0.681264 | + | 0.732038i | \(0.738569\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.03969 | −0.297916 | ||||||||
\(412\) | 8.90009 | 0.438476 | ||||||||
\(413\) | −21.9868 | −1.08190 | ||||||||
\(414\) | 20.5290 | 1.00894 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.4972 | −0.612727 | ||||||||
\(417\) | −3.05564 | −0.149635 | ||||||||
\(418\) | −4.63373 | −0.226643 | ||||||||
\(419\) | 6.46452 | 0.315813 | 0.157906 | − | 0.987454i | \(-0.449526\pi\) | ||||
0.157906 | + | 0.987454i | \(0.449526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5361 | −1.19582 | −0.597909 | − | 0.801564i | \(-0.704002\pi\) | ||||
−0.597909 | + | 0.801564i | \(0.704002\pi\) | |||||||
\(422\) | 20.5692 | 1.00129 | ||||||||
\(423\) | 8.95840 | 0.435572 | ||||||||
\(424\) | 6.87630 | 0.333942 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.65286 | −0.128531 | ||||||||
\(427\) | −8.70185 | −0.421112 | ||||||||
\(428\) | 2.28587 | 0.110492 | ||||||||
\(429\) | −4.09695 | −0.197803 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.1862 | −0.586986 | −0.293493 | − | 0.955961i | \(-0.594818\pi\) | ||||
−0.293493 | + | 0.955961i | \(0.594818\pi\) | |||||||
\(432\) | 4.62941 | 0.222732 | ||||||||
\(433\) | 1.90864 | 0.0917233 | 0.0458616 | − | 0.998948i | \(-0.485397\pi\) | ||||
0.0458616 | + | 0.998948i | \(0.485397\pi\) | |||||||
\(434\) | 0.782017 | 0.0375380 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.82792 | −0.231215 | ||||||||
\(437\) | −7.58136 | −0.362666 | ||||||||
\(438\) | 0.259915 | 0.0124192 | ||||||||
\(439\) | 15.4413 | 0.736973 | 0.368486 | − | 0.929633i | \(-0.379876\pi\) | ||||
0.368486 | + | 0.929633i | \(0.379876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.8690 | −0.850904 | ||||||||
\(442\) | 2.38333 | 0.113364 | ||||||||
\(443\) | −35.2713 | −1.67579 | −0.837894 | − | 0.545833i | \(-0.816213\pi\) | ||||
−0.837894 | + | 0.545833i | \(0.816213\pi\) | |||||||
\(444\) | 0.0428968 | 0.00203579 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.9827 | 1.32502 | ||||||||
\(447\) | −3.09988 | −0.146619 | ||||||||
\(448\) | −31.1295 | −1.47073 | ||||||||
\(449\) | −7.11761 | −0.335901 | −0.167950 | − | 0.985795i | \(-0.553715\pi\) | ||||
−0.167950 | + | 0.985795i | \(0.553715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.7380 | −1.44740 | ||||||||
\(452\) | −7.62489 | −0.358645 | ||||||||
\(453\) | −6.19448 | −0.291042 | ||||||||
\(454\) | 8.91241 | 0.418280 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.35599 | −0.0635002 | ||||||||
\(457\) | −2.85579 | −0.133588 | −0.0667941 | − | 0.997767i | \(-0.521277\pi\) | ||||
−0.0667941 | + | 0.997767i | \(0.521277\pi\) | |||||||
\(458\) | −27.7529 | −1.29681 | ||||||||
\(459\) | 1.28558 | 0.0600058 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6995 | −0.777772 | −0.388886 | − | 0.921286i | \(-0.627140\pi\) | ||||
−0.388886 | + | 0.921286i | \(0.627140\pi\) | |||||||
\(462\) | −5.00341 | −0.232780 | ||||||||
\(463\) | 10.8186 | 0.502784 | 0.251392 | − | 0.967885i | \(-0.419112\pi\) | ||||
0.251392 | + | 0.967885i | \(0.419112\pi\) | |||||||
\(464\) | −7.18757 | −0.333675 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.4177 | 0.482593 | ||||||||
\(467\) | −16.8745 | −0.780859 | −0.390430 | − | 0.920633i | \(-0.627674\pi\) | ||||
−0.390430 | + | 0.920633i | \(0.627674\pi\) | |||||||
\(468\) | 6.66761 | 0.308210 | ||||||||
\(469\) | −19.9387 | −0.920684 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.10817 | −0.235372 | ||||||||
\(472\) | 18.6142 | 0.856787 | ||||||||
\(473\) | 19.2536 | 0.885280 | ||||||||
\(474\) | −2.74792 | −0.126216 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.49568 | −0.0685543 | ||||||||
\(477\) | −6.40766 | −0.293386 | ||||||||
\(478\) | 14.9885 | 0.685557 | ||||||||
\(479\) | −3.17196 | −0.144931 | −0.0724653 | − | 0.997371i | \(-0.523087\pi\) | ||||
−0.0724653 | + | 0.997371i | \(0.523087\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.598177 | −0.0272745 | ||||||||
\(482\) | 1.14940 | 0.0523538 | ||||||||
\(483\) | −8.18621 | −0.372485 | ||||||||
\(484\) | 0.0294398 | 0.00133817 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.5765 | −0.479758 | ||||||||
\(487\) | 6.17755 | 0.279931 | 0.139966 | − | 0.990156i | \(-0.455301\pi\) | ||||
0.139966 | + | 0.990156i | \(0.455301\pi\) | |||||||
\(488\) | 7.36704 | 0.333490 | ||||||||
\(489\) | −3.60893 | −0.163201 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.4496 | −1.10340 | −0.551698 | − | 0.834044i | \(-0.686020\pi\) | ||||
−0.551698 | + | 0.834044i | \(0.686020\pi\) | |||||||
\(492\) | −2.27951 | −0.102768 | ||||||||
\(493\) | −1.99598 | −0.0898946 | ||||||||
\(494\) | 4.79183 | 0.215594 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.408066 | −0.0183227 | ||||||||
\(497\) | −23.2152 | −1.04134 | ||||||||
\(498\) | 5.45463 | 0.244428 | ||||||||
\(499\) | −2.03667 | −0.0911737 | −0.0455869 | − | 0.998960i | \(-0.514516\pi\) | ||||
−0.0455869 | + | 0.998960i | \(0.514516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.623390 | −0.0278510 | ||||||||
\(502\) | 9.68059 | 0.432066 | ||||||||
\(503\) | −36.6362 | −1.63353 | −0.816764 | − | 0.576971i | \(-0.804234\pi\) | ||||
−0.816764 | + | 0.576971i | \(0.804234\pi\) | |||||||
\(504\) | 32.1319 | 1.43127 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 23.6830 | 1.05284 | ||||||||
\(507\) | −0.463896 | −0.0206023 | ||||||||
\(508\) | −12.9782 | −0.575817 | ||||||||
\(509\) | 15.6418 | 0.693309 | 0.346655 | − | 0.937993i | \(-0.387318\pi\) | ||||
0.346655 | + | 0.937993i | \(0.387318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.27452 | 0.100619 | ||||||||
\(512\) | 21.3974 | 0.945640 | ||||||||
\(513\) | 2.58474 | 0.114119 | ||||||||
\(514\) | 2.34941 | 0.103628 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.42783 | 0.0628568 | ||||||||
\(517\) | 10.3347 | 0.454522 | ||||||||
\(518\) | −0.730525 | −0.0320974 | ||||||||
\(519\) | 6.16238 | 0.270498 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.0010 | 1.35818 | 0.679088 | − | 0.734056i | \(-0.262375\pi\) | ||||
0.679088 | + | 0.734056i | \(0.262375\pi\) | |||||||
\(522\) | 10.8666 | 0.475618 | ||||||||
\(523\) | 13.3801 | 0.585073 | 0.292537 | − | 0.956254i | \(-0.405501\pi\) | ||||
0.292537 | + | 0.956254i | \(0.405501\pi\) | |||||||
\(524\) | −6.42631 | −0.280735 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.9661 | 1.30658 | ||||||||
\(527\) | −0.113320 | −0.00493628 | ||||||||
\(528\) | 2.61084 | 0.113622 | ||||||||
\(529\) | 15.7484 | 0.684713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.3456 | −0.752734 | ||||||||
\(532\) | −3.00715 | −0.130376 | ||||||||
\(533\) | 31.7867 | 1.37684 | ||||||||
\(534\) | 0.524435 | 0.0226945 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 16.8802 | 0.729115 | ||||||||
\(537\) | −5.04461 | −0.217691 | ||||||||
\(538\) | −10.1956 | −0.439565 | ||||||||
\(539\) | −20.6143 | −0.887922 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.42663 | 0.405282 | 0.202641 | − | 0.979253i | \(-0.435047\pi\) | ||||
0.202641 | + | 0.979253i | \(0.435047\pi\) | |||||||
\(542\) | −0.968055 | −0.0415815 | ||||||||
\(543\) | 4.76025 | 0.204282 | ||||||||
\(544\) | 2.21161 | 0.0948220 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.17412 | 0.221432 | ||||||||
\(547\) | 36.1196 | 1.54436 | 0.772181 | − | 0.635402i | \(-0.219166\pi\) | ||||
0.772181 | + | 0.635402i | \(0.219166\pi\) | |||||||
\(548\) | 11.3395 | 0.484398 | ||||||||
\(549\) | −6.86496 | −0.292989 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.01304 | −0.170961 | ||||||||
\(552\) | 6.93050 | 0.294982 | ||||||||
\(553\) | −24.0471 | −1.02259 | ||||||||
\(554\) | 15.3365 | 0.651584 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.73695 | 0.243301 | ||||||||
\(557\) | −44.4300 | −1.88256 | −0.941281 | − | 0.337625i | \(-0.890376\pi\) | ||||
−0.941281 | + | 0.337625i | \(0.890376\pi\) | |||||||
\(558\) | 0.616939 | 0.0261171 | ||||||||
\(559\) | −19.9105 | −0.842124 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.725029 | 0.0306108 | ||||||||
\(562\) | −13.6424 | −0.575470 | ||||||||
\(563\) | −35.7024 | −1.50468 | −0.752338 | − | 0.658778i | \(-0.771074\pi\) | ||||
−0.752338 | + | 0.658778i | \(0.771074\pi\) | |||||||
\(564\) | 0.766418 | 0.0322720 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −29.2687 | −1.23025 | ||||||||
\(567\) | −28.5155 | −1.19754 | ||||||||
\(568\) | 19.6541 | 0.824669 | ||||||||
\(569\) | −25.6913 | −1.07704 | −0.538518 | − | 0.842614i | \(-0.681016\pi\) | ||||
−0.538518 | + | 0.842614i | \(0.681016\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.37401 | 0.308593 | 0.154296 | − | 0.988025i | \(-0.450689\pi\) | ||||
0.154296 | + | 0.988025i | \(0.450689\pi\) | |||||||
\(572\) | 7.69200 | 0.321619 | ||||||||
\(573\) | 8.02312 | 0.335171 | ||||||||
\(574\) | 38.8196 | 1.62030 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.5583 | −1.02326 | ||||||||
\(577\) | 5.58190 | 0.232377 | 0.116189 | − | 0.993227i | \(-0.462932\pi\) | ||||
0.116189 | + | 0.993227i | \(0.462932\pi\) | |||||||
\(578\) | 19.1180 | 0.795206 | ||||||||
\(579\) | −1.82983 | −0.0760453 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 47.7335 | 1.98032 | ||||||||
\(582\) | −0.203527 | −0.00843646 | ||||||||
\(583\) | −7.39211 | −0.306150 | ||||||||
\(584\) | −1.92562 | −0.0796829 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −35.6671 | −1.47340 | ||||||||
\(587\) | −10.0599 | −0.415217 | −0.207608 | − | 0.978212i | \(-0.566568\pi\) | ||||
−0.207608 | + | 0.978212i | \(0.566568\pi\) | |||||||
\(588\) | −1.52875 | −0.0630444 | ||||||||
\(589\) | −0.227836 | −0.00938781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.31092 | 0.0539241 | ||||||||
\(592\) | 0.381197 | 0.0156671 | ||||||||
\(593\) | −21.7142 | −0.891694 | −0.445847 | − | 0.895109i | \(-0.647097\pi\) | ||||
−0.445847 | + | 0.895109i | \(0.647097\pi\) | |||||||
\(594\) | −8.07432 | −0.331293 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.82000 | 0.238397 | ||||||||
\(597\) | −0.104667 | −0.00428375 | ||||||||
\(598\) | −24.4911 | −1.00151 | ||||||||
\(599\) | −40.5561 | −1.65708 | −0.828538 | − | 0.559933i | \(-0.810827\pi\) | ||||
−0.828538 | + | 0.559933i | \(0.810827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.4901 | 1.32530 | 0.662650 | − | 0.748929i | \(-0.269432\pi\) | ||||
0.662650 | + | 0.748929i | \(0.269432\pi\) | |||||||
\(602\) | −24.3157 | −0.991034 | ||||||||
\(603\) | −15.7298 | −0.640567 | ||||||||
\(604\) | 11.6301 | 0.473222 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.16695 | 0.0474042 | ||||||||
\(607\) | −17.7595 | −0.720836 | −0.360418 | − | 0.932791i | \(-0.617366\pi\) | ||||
−0.360418 | + | 0.932791i | \(0.617366\pi\) | |||||||
\(608\) | 4.44657 | 0.180332 | ||||||||
\(609\) | −4.33320 | −0.175590 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.6874 | −0.432365 | ||||||||
\(612\) | −1.17995 | −0.0476967 | ||||||||
\(613\) | −11.4399 | −0.462055 | −0.231027 | − | 0.972947i | \(-0.574209\pi\) | ||||
−0.231027 | + | 0.972947i | \(0.574209\pi\) | |||||||
\(614\) | 3.72406 | 0.150291 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.0686 | 1.49354 | ||||||||
\(617\) | −3.85094 | −0.155033 | −0.0775164 | − | 0.996991i | \(-0.524699\pi\) | ||||
−0.0775164 | + | 0.996991i | \(0.524699\pi\) | |||||||
\(618\) | 5.44863 | 0.219176 | ||||||||
\(619\) | −38.1133 | −1.53190 | −0.765951 | − | 0.642899i | \(-0.777732\pi\) | ||||
−0.765951 | + | 0.642899i | \(0.777732\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.2106 | −0.530124 | ||||||||
\(622\) | −5.36653 | −0.215178 | ||||||||
\(623\) | 4.58934 | 0.183868 | ||||||||
\(624\) | −2.69992 | −0.108083 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.0705 | 1.28179 | ||||||||
\(627\) | 1.45771 | 0.0582154 | ||||||||
\(628\) | 9.59056 | 0.382705 | ||||||||
\(629\) | 0.105858 | 0.00422084 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4812 | 0.695916 | 0.347958 | − | 0.937510i | \(-0.386875\pi\) | ||||
0.347958 | + | 0.937510i | \(0.386875\pi\) | |||||||
\(632\) | 20.3584 | 0.809814 | ||||||||
\(633\) | −6.47082 | −0.257192 | ||||||||
\(634\) | 27.0983 | 1.07621 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.548194 | −0.0217373 | ||||||||
\(637\) | 21.3177 | 0.844637 | ||||||||
\(638\) | 12.5361 | 0.496310 | ||||||||
\(639\) | −18.3146 | −0.724516 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7032 | 0.817728 | 0.408864 | − | 0.912595i | \(-0.365925\pi\) | ||||
0.408864 | + | 0.912595i | \(0.365925\pi\) | |||||||
\(642\) | 1.39941 | 0.0552304 | ||||||||
\(643\) | −30.8231 | −1.21555 | −0.607773 | − | 0.794111i | \(-0.707937\pi\) | ||||
−0.607773 | + | 0.794111i | \(0.707937\pi\) | |||||||
\(644\) | 15.3696 | 0.605645 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.848000 | −0.0333641 | ||||||||
\(647\) | 16.3330 | 0.642115 | 0.321058 | − | 0.947060i | \(-0.395962\pi\) | ||||
0.321058 | + | 0.947060i | \(0.395962\pi\) | |||||||
\(648\) | 24.1414 | 0.948363 | ||||||||
\(649\) | −20.0105 | −0.785481 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.246013 | −0.00964200 | ||||||||
\(652\) | 6.77573 | 0.265358 | ||||||||
\(653\) | 24.9915 | 0.977992 | 0.488996 | − | 0.872286i | \(-0.337363\pi\) | ||||
0.488996 | + | 0.872286i | \(0.337363\pi\) | |||||||
\(654\) | −2.95565 | −0.115575 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20.2566 | −0.790887 | ||||||||
\(657\) | 1.79439 | 0.0700057 | ||||||||
\(658\) | −13.0520 | −0.508818 | ||||||||
\(659\) | 6.70558 | 0.261212 | 0.130606 | − | 0.991434i | \(-0.458308\pi\) | ||||
0.130606 | + | 0.991434i | \(0.458308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.84172 | −0.266112 | −0.133056 | − | 0.991109i | \(-0.542479\pi\) | ||||
−0.133056 | + | 0.991109i | \(0.542479\pi\) | |||||||
\(662\) | 12.6467 | 0.491529 | ||||||||
\(663\) | −0.749767 | −0.0291185 | ||||||||
\(664\) | −40.4115 | −1.56827 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.576317 | −0.0223318 | ||||||||
\(667\) | 20.5107 | 0.794176 | ||||||||
\(668\) | 1.17041 | 0.0452845 | ||||||||
\(669\) | −8.80299 | −0.340343 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.91967 | −0.305736 | ||||||||
\(672\) | 4.80132 | 0.185215 | ||||||||
\(673\) | 21.1590 | 0.815620 | 0.407810 | − | 0.913067i | \(-0.366293\pi\) | ||||
0.407810 | + | 0.913067i | \(0.366293\pi\) | |||||||
\(674\) | 7.86246 | 0.302851 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.870961 | 0.0334985 | ||||||||
\(677\) | −44.9217 | −1.72648 | −0.863240 | − | 0.504793i | \(-0.831569\pi\) | ||||
−0.863240 | + | 0.504793i | \(0.831569\pi\) | |||||||
\(678\) | −4.66795 | −0.179272 | ||||||||
\(679\) | −1.78107 | −0.0683511 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.80373 | −0.107439 | ||||||||
\(682\) | 0.711724 | 0.0272533 | ||||||||
\(683\) | −2.48221 | −0.0949792 | −0.0474896 | − | 0.998872i | \(-0.515122\pi\) | ||||
−0.0474896 | + | 0.998872i | \(0.515122\pi\) | |||||||
\(684\) | −2.37236 | −0.0907095 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.22832 | −0.123258 | ||||||||
\(687\) | 8.73071 | 0.333097 | ||||||||
\(688\) | 12.6883 | 0.483735 | ||||||||
\(689\) | 7.64433 | 0.291226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.1466 | −0.652289 | −0.326144 | − | 0.945320i | \(-0.605750\pi\) | ||||
−0.326144 | + | 0.945320i | \(0.605750\pi\) | |||||||
\(692\) | −11.5698 | −0.439819 | ||||||||
\(693\) | −34.5422 | −1.31215 | ||||||||
\(694\) | −8.73540 | −0.331591 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.66852 | 0.139055 | ||||||||
\(697\) | −5.62524 | −0.213071 | ||||||||
\(698\) | −12.1344 | −0.459294 | ||||||||
\(699\) | −3.27729 | −0.123959 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.4818 | −1.41567 | −0.707835 | − | 0.706378i | \(-0.750328\pi\) | ||||
−0.707835 | + | 0.706378i | \(0.750328\pi\) | |||||||
\(702\) | 8.34981 | 0.315143 | ||||||||
\(703\) | 0.212834 | 0.00802718 | ||||||||
\(704\) | −28.3314 | −1.06778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.9706 | 1.35377 | ||||||||
\(707\) | 10.2120 | 0.384063 | ||||||||
\(708\) | −1.48397 | −0.0557709 | ||||||||
\(709\) | −39.0821 | −1.46776 | −0.733880 | − | 0.679279i | \(-0.762293\pi\) | ||||
−0.733880 | + | 0.679279i | \(0.762293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.9709 | −0.711466 | ||||||||
\(712\) | −3.88537 | −0.145610 | ||||||||
\(713\) | 1.16447 | 0.0436098 | ||||||||
\(714\) | −0.915654 | −0.0342675 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.47122 | 0.353956 | ||||||||
\(717\) | −4.71519 | −0.176092 | ||||||||
\(718\) | −14.0538 | −0.524482 | ||||||||
\(719\) | 1.23516 | 0.0460638 | 0.0230319 | − | 0.999735i | \(-0.492668\pi\) | ||||
0.0230319 | + | 0.999735i | \(0.492668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.6811 | 1.77574 | ||||||||
\(722\) | 20.1337 | 0.749297 | ||||||||
\(723\) | −0.361587 | −0.0134476 | ||||||||
\(724\) | −8.93733 | −0.332153 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0180230 | 0.000668897 0 | ||||||||
\(727\) | −20.6303 | −0.765136 | −0.382568 | − | 0.923927i | \(-0.624960\pi\) | ||||
−0.382568 | + | 0.923927i | \(0.624960\pi\) | |||||||
\(728\) | −38.3333 | −1.42073 | ||||||||
\(729\) | −20.1939 | −0.747924 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.52352 | 0.130322 | ||||||||
\(732\) | −0.587318 | −0.0217079 | ||||||||
\(733\) | 6.08021 | 0.224578 | 0.112289 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112289 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(734\) | 5.72037 | 0.211143 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.7265 | −0.837708 | ||||||||
\(737\) | −18.1465 | −0.668435 | ||||||||
\(738\) | 30.6251 | 1.12733 | ||||||||
\(739\) | −25.4962 | −0.937891 | −0.468946 | − | 0.883227i | \(-0.655366\pi\) | ||||
−0.468946 | + | 0.883227i | \(0.655366\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.50745 | −0.0553775 | ||||||||
\(742\) | 9.33565 | 0.342722 | ||||||||
\(743\) | 11.9936 | 0.440004 | 0.220002 | − | 0.975499i | \(-0.429394\pi\) | ||||
0.220002 | + | 0.975499i | \(0.429394\pi\) | |||||||
\(744\) | 0.208276 | 0.00763576 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −16.0929 | −0.589204 | ||||||||
\(747\) | 37.6573 | 1.37781 | ||||||||
\(748\) | −1.36124 | −0.0497718 | ||||||||
\(749\) | 12.2463 | 0.447469 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.0878 | 1.49932 | 0.749658 | − | 0.661825i | \(-0.230218\pi\) | ||||
0.749658 | + | 0.661825i | \(0.230218\pi\) | |||||||
\(752\) | 6.81068 | 0.248360 | ||||||||
\(753\) | −3.04539 | −0.110980 | ||||||||
\(754\) | −12.9638 | −0.472115 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.23999 | −0.190577 | ||||||||
\(757\) | 25.6422 | 0.931982 | 0.465991 | − | 0.884789i | \(-0.345698\pi\) | ||||
0.465991 | + | 0.884789i | \(0.345698\pi\) | |||||||
\(758\) | −17.4047 | −0.632166 | ||||||||
\(759\) | −7.45038 | −0.270432 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.85649 | −0.248548 | −0.124274 | − | 0.992248i | \(-0.539660\pi\) | ||||
−0.124274 | + | 0.992248i | \(0.539660\pi\) | |||||||
\(762\) | −7.94528 | −0.287827 | ||||||||
\(763\) | −25.8649 | −0.936374 | ||||||||
\(764\) | −15.0634 | −0.544973 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.5970 | −0.635806 | ||||||||
\(767\) | 20.6933 | 0.747190 | ||||||||
\(768\) | −5.13576 | −0.185321 | ||||||||
\(769\) | 54.2872 | 1.95765 | 0.978823 | − | 0.204707i | \(-0.0656240\pi\) | ||||
0.978823 | + | 0.204707i | \(0.0656240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.739097 | −0.0266179 | ||||||||
\(772\) | 3.43550 | 0.123646 | ||||||||
\(773\) | 44.2104 | 1.59014 | 0.795068 | − | 0.606520i | \(-0.207435\pi\) | ||||
0.795068 | + | 0.606520i | \(0.207435\pi\) | |||||||
\(774\) | −19.1829 | −0.689513 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.50786 | 0.0541291 | ||||||||
\(777\) | 0.229814 | 0.00824453 | ||||||||
\(778\) | −41.3194 | −1.48137 | ||||||||
\(779\) | −11.3099 | −0.405218 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.1285 | −0.756036 | ||||||||
\(782\) | 4.33413 | 0.154988 | ||||||||
\(783\) | −6.99276 | −0.249901 | ||||||||
\(784\) | −13.5850 | −0.485179 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.93418 | −0.140328 | ||||||||
\(787\) | 11.0923 | 0.395398 | 0.197699 | − | 0.980263i | \(-0.436653\pi\) | ||||
0.197699 | + | 0.980263i | \(0.436653\pi\) | |||||||
\(788\) | −2.46125 | −0.0876783 | ||||||||
\(789\) | −9.42696 | −0.335608 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.8493 | −1.45243 | ||||||||
\(792\) | 29.2437 | 1.03913 | ||||||||
\(793\) | 8.18989 | 0.290831 | ||||||||
\(794\) | 14.5407 | 0.516030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.196512 | 0.00696519 | ||||||||
\(797\) | 4.22546 | 0.149673 | 0.0748367 | − | 0.997196i | \(-0.476156\pi\) | ||||
0.0748367 | + | 0.997196i | \(0.476156\pi\) | |||||||
\(798\) | −1.84097 | −0.0651698 | ||||||||
\(799\) | 1.89132 | 0.0669101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.62057 | 0.127926 | ||||||||
\(802\) | −20.3769 | −0.719533 | ||||||||
\(803\) | 2.07007 | 0.0730513 | ||||||||
\(804\) | −1.34573 | −0.0474603 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.736008 | −0.0259248 | ||||||||
\(807\) | 3.20742 | 0.112906 | ||||||||
\(808\) | −8.64556 | −0.304150 | ||||||||
\(809\) | −23.3178 | −0.819812 | −0.409906 | − | 0.912128i | \(-0.634438\pi\) | ||||
−0.409906 | + | 0.912128i | \(0.634438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6244 | −0.478417 | −0.239208 | − | 0.970968i | \(-0.576888\pi\) | ||||
−0.239208 | + | 0.970968i | \(0.576888\pi\) | |||||||
\(812\) | 8.13556 | 0.285502 | ||||||||
\(813\) | 0.304538 | 0.0106806 | ||||||||
\(814\) | −0.664861 | −0.0233034 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.477800 | 0.0167263 | ||||||||
\(817\) | 7.08423 | 0.247846 | ||||||||
\(818\) | 31.6722 | 1.10739 | ||||||||
\(819\) | 35.7208 | 1.24819 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.7743 | 0.445825 | 0.222912 | − | 0.974838i | \(-0.428444\pi\) | ||||
0.222912 | + | 0.974838i | \(0.428444\pi\) | |||||||
\(822\) | 6.94202 | 0.242131 | ||||||||
\(823\) | −6.14329 | −0.214142 | −0.107071 | − | 0.994251i | \(-0.534147\pi\) | ||||
−0.107071 | + | 0.994251i | \(0.534147\pi\) | |||||||
\(824\) | −40.3671 | −1.40625 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.2717 | 0.879314 | ||||||||
\(827\) | −21.6909 | −0.754267 | −0.377133 | − | 0.926159i | \(-0.623090\pi\) | ||||
−0.377133 | + | 0.926159i | \(0.623090\pi\) | |||||||
\(828\) | 12.1252 | 0.421378 | ||||||||
\(829\) | −12.2263 | −0.424638 | −0.212319 | − | 0.977200i | \(-0.568102\pi\) | ||||
−0.212319 | + | 0.977200i | \(0.568102\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.82466 | −0.167366 | ||||||||
\(832\) | 29.2981 | 1.01573 | ||||||||
\(833\) | −3.77255 | −0.130711 | ||||||||
\(834\) | 3.51216 | 0.121616 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.73685 | −0.0946558 | ||||||||
\(837\) | −0.397006 | −0.0137225 | ||||||||
\(838\) | −7.43033 | −0.256677 | ||||||||
\(839\) | −24.4507 | −0.844130 | −0.422065 | − | 0.906566i | \(-0.638695\pi\) | ||||
−0.422065 | + | 0.906566i | \(0.638695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1431 | −0.625624 | ||||||||
\(842\) | 28.2019 | 0.971900 | ||||||||
\(843\) | 4.29173 | 0.147815 | ||||||||
\(844\) | 12.1489 | 0.418183 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.2968 | −0.354011 | ||||||||
\(847\) | 0.157720 | 0.00541931 | ||||||||
\(848\) | −4.87146 | −0.167287 | ||||||||
\(849\) | 9.20755 | 0.316002 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.08780 | −0.0372892 | ||||||||
\(852\) | −1.56687 | −0.0536802 | ||||||||
\(853\) | 29.8098 | 1.02067 | 0.510334 | − | 0.859976i | \(-0.329522\pi\) | ||||
0.510334 | + | 0.859976i | \(0.329522\pi\) | |||||||
\(854\) | 10.0019 | 0.342258 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.3678 | −0.354363 | ||||||||
\(857\) | 18.6128 | 0.635801 | 0.317900 | − | 0.948124i | \(-0.397022\pi\) | ||||
0.317900 | + | 0.948124i | \(0.397022\pi\) | |||||||
\(858\) | 4.70904 | 0.160764 | ||||||||
\(859\) | −49.9154 | −1.70309 | −0.851546 | − | 0.524281i | \(-0.824334\pi\) | ||||
−0.851546 | + | 0.524281i | \(0.824334\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2122 | −0.416189 | ||||||||
\(862\) | 14.0068 | 0.477073 | ||||||||
\(863\) | 28.4944 | 0.969960 | 0.484980 | − | 0.874525i | \(-0.338827\pi\) | ||||
0.484980 | + | 0.874525i | \(0.338827\pi\) | |||||||
\(864\) | 7.74820 | 0.263599 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.19379 | −0.0745480 | ||||||||
\(867\) | −6.01430 | −0.204256 | ||||||||
\(868\) | 0.461887 | 0.0156775 | ||||||||
\(869\) | −21.8856 | −0.742418 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7656 | 0.635849 | ||||||||
\(872\) | 21.8974 | 0.741540 | ||||||||
\(873\) | −1.40510 | −0.0475553 | ||||||||
\(874\) | 8.71402 | 0.294756 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.153515 | 0.00518680 | ||||||||
\(877\) | 37.6957 | 1.27289 | 0.636447 | − | 0.771320i | \(-0.280403\pi\) | ||||
0.636447 | + | 0.771320i | \(0.280403\pi\) | |||||||
\(878\) | −17.7482 | −0.598974 | ||||||||
\(879\) | 11.2204 | 0.378456 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.3287 | 1.45978 | 0.729891 | − | 0.683563i | \(-0.239571\pi\) | ||||
0.729891 | + | 0.683563i | \(0.239571\pi\) | |||||||
\(882\) | 20.5386 | 0.691571 | ||||||||
\(883\) | −16.8177 | −0.565960 | −0.282980 | − | 0.959126i | \(-0.591323\pi\) | ||||
−0.282980 | + | 0.959126i | \(0.591323\pi\) | |||||||
\(884\) | 1.40768 | 0.0473455 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.5408 | 1.36200 | ||||||||
\(887\) | −42.9652 | −1.44263 | −0.721316 | − | 0.692607i | \(-0.756462\pi\) | ||||
−0.721316 | + | 0.692607i | \(0.756462\pi\) | |||||||
\(888\) | −0.194562 | −0.00652907 | ||||||||
\(889\) | −69.5292 | −2.33194 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.9523 | −0.869435 | ||||||||
\(892\) | 16.5276 | 0.553384 | ||||||||
\(893\) | 3.80261 | 0.127249 | ||||||||
\(894\) | 3.56300 | 0.119165 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.22341 | 0.308132 | ||||||||
\(897\) | 7.70458 | 0.257249 | ||||||||
\(898\) | 8.18098 | 0.273003 | ||||||||
\(899\) | 0.616388 | 0.0205577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.35280 | −0.0450683 | ||||||||
\(902\) | 35.3303 | 1.17637 | ||||||||
\(903\) | 7.64942 | 0.254557 | ||||||||
\(904\) | 34.5833 | 1.15022 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.11994 | 0.236544 | ||||||||
\(907\) | 3.48910 | 0.115854 | 0.0579268 | − | 0.998321i | \(-0.481551\pi\) | ||||
0.0579268 | + | 0.998321i | \(0.481551\pi\) | |||||||
\(908\) | 5.26399 | 0.174692 | ||||||||
\(909\) | 8.05634 | 0.267212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.19869 | 0.0728459 | 0.0364230 | − | 0.999336i | \(-0.488404\pi\) | ||||
0.0364230 | + | 0.999336i | \(0.488404\pi\) | |||||||
\(912\) | 0.960644 | 0.0318101 | ||||||||
\(913\) | 43.4429 | 1.43775 | ||||||||
\(914\) | 3.28245 | 0.108574 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.3918 | −0.541602 | ||||||||
\(917\) | −34.4281 | −1.13692 | ||||||||
\(918\) | −1.47765 | −0.0487697 | ||||||||
\(919\) | −5.02474 | −0.165751 | −0.0828754 | − | 0.996560i | \(-0.526410\pi\) | ||||
−0.0828754 | + | 0.996560i | \(0.526410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.17154 | −0.0386036 | ||||||||
\(922\) | 19.1944 | 0.632134 | ||||||||
\(923\) | 21.8494 | 0.719180 | ||||||||
\(924\) | −2.95519 | −0.0972187 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.4349 | −0.408637 | ||||||||
\(927\) | 37.6160 | 1.23547 | ||||||||
\(928\) | −12.0298 | −0.394897 | ||||||||
\(929\) | 20.3424 | 0.667413 | 0.333706 | − | 0.942677i | \(-0.391701\pi\) | ||||
0.333706 | + | 0.942677i | \(0.391701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.58492 | −0.248586 | ||||||||
\(932\) | 6.15309 | 0.201551 | ||||||||
\(933\) | 1.68824 | 0.0552707 | ||||||||
\(934\) | 19.3956 | 0.634643 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −30.2415 | −0.988473 | ||||||||
\(937\) | −32.8768 | −1.07404 | −0.537018 | − | 0.843571i | \(-0.680449\pi\) | ||||
−0.537018 | + | 0.843571i | \(0.680449\pi\) | |||||||
\(938\) | 22.9176 | 0.748285 | ||||||||
\(939\) | −10.0890 | −0.329241 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.1409 | −0.754373 | −0.377186 | − | 0.926137i | \(-0.623108\pi\) | ||||
−0.377186 | + | 0.926137i | \(0.623108\pi\) | |||||||
\(942\) | 5.87134 | 0.191298 | ||||||||
\(943\) | 57.8048 | 1.88238 | ||||||||
\(944\) | −13.1871 | −0.429203 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.1301 | −0.719510 | ||||||||
\(947\) | −16.0089 | −0.520219 | −0.260110 | − | 0.965579i | \(-0.583759\pi\) | ||||
−0.260110 | + | 0.965579i | \(0.583759\pi\) | |||||||
\(948\) | −1.62302 | −0.0527133 | ||||||||
\(949\) | −2.14070 | −0.0694902 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.52477 | −0.276435 | ||||||||
\(952\) | 6.78377 | 0.219863 | ||||||||
\(953\) | −1.56075 | −0.0505577 | −0.0252789 | − | 0.999680i | \(-0.508047\pi\) | ||||
−0.0252789 | + | 0.999680i | \(0.508047\pi\) | |||||||
\(954\) | 7.36497 | 0.238450 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.85274 | 0.286318 | ||||||||
\(957\) | −3.94371 | −0.127482 | ||||||||
\(958\) | 3.64585 | 0.117792 | ||||||||
\(959\) | 60.7497 | 1.96171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9650 | −0.998871 | ||||||||
\(962\) | 0.687545 | 0.0221674 | ||||||||
\(963\) | 9.66118 | 0.311327 | ||||||||
\(964\) | 0.678878 | 0.0218652 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.40923 | 0.302737 | ||||||||
\(967\) | −18.4147 | −0.592175 | −0.296088 | − | 0.955161i | \(-0.595682\pi\) | ||||
−0.296088 | + | 0.955161i | \(0.595682\pi\) | |||||||
\(968\) | −0.133526 | −0.00429170 | ||||||||
\(969\) | 0.266770 | 0.00856989 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.699689 | −0.0224541 | −0.0112271 | − | 0.999937i | \(-0.503574\pi\) | ||||
−0.0112271 | + | 0.999937i | \(0.503574\pi\) | |||||||
\(972\) | −6.24685 | −0.200368 | ||||||||
\(973\) | 30.7349 | 0.985317 | ||||||||
\(974\) | −7.10048 | −0.227514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.21913 | −0.167060 | ||||||||
\(977\) | 13.0194 | 0.416527 | 0.208263 | − | 0.978073i | \(-0.433219\pi\) | ||||
0.208263 | + | 0.978073i | \(0.433219\pi\) | |||||||
\(978\) | 4.14810 | 0.132642 | ||||||||
\(979\) | 4.17682 | 0.133492 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.4050 | −0.651483 | ||||||||
\(982\) | 28.1024 | 0.896785 | ||||||||
\(983\) | −36.2357 | −1.15574 | −0.577870 | − | 0.816129i | \(-0.696116\pi\) | ||||
−0.577870 | + | 0.816129i | \(0.696116\pi\) | |||||||
\(984\) | 10.3389 | 0.329592 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.29418 | 0.0730617 | ||||||||
\(987\) | 4.10598 | 0.130695 | ||||||||
\(988\) | 2.83023 | 0.0900415 | ||||||||
\(989\) | −36.2076 | −1.15133 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.84413 | −0.217411 | −0.108705 | − | 0.994074i | \(-0.534671\pi\) | ||||
−0.108705 | + | 0.994074i | \(0.534671\pi\) | |||||||
\(992\) | −0.682977 | −0.0216845 | ||||||||
\(993\) | −3.97850 | −0.126254 | ||||||||
\(994\) | 26.6836 | 0.846351 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.22170 | 0.102083 | ||||||||
\(997\) | −2.65302 | −0.0840221 | −0.0420110 | − | 0.999117i | \(-0.513376\pi\) | ||||
−0.0420110 | + | 0.999117i | \(0.513376\pi\) | |||||||
\(998\) | 2.34095 | 0.0741014 | ||||||||
\(999\) | 0.370866 | 0.0117337 |
(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 | 6025.2.a.l.1.17 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.24 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.17 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.24 | yes | 40 | 5.4 | even | 2 |