Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1158316930\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.50306 | −1.44514 | −0.722570 | − | 0.691298i | \(-0.757039\pi\) | ||||
−0.722570 | + | 0.691298i | \(0.757039\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0732871 | 0.0327750 | 0.0163875 | − | 0.999866i | \(-0.494783\pi\) | ||||
0.0163875 | + | 0.999866i | \(0.494783\pi\) | |||||||
\(6\) | −2.50306 | −1.02187 | ||||||||
\(7\) | −1.25699 | −0.475097 | −0.237548 | − | 0.971376i | \(-0.576344\pi\) | ||||
−0.237548 | + | 0.971376i | \(0.576344\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.26529 | 1.08843 | ||||||||
\(10\) | 0.0732871 | 0.0231754 | ||||||||
\(11\) | −2.84908 | −0.859030 | −0.429515 | − | 0.903060i | \(-0.641315\pi\) | ||||
−0.429515 | + | 0.903060i | \(0.641315\pi\) | |||||||
\(12\) | −2.50306 | −0.722570 | ||||||||
\(13\) | 1.61180 | 0.447033 | 0.223516 | − | 0.974700i | \(-0.428246\pi\) | ||||
0.223516 | + | 0.974700i | \(0.428246\pi\) | |||||||
\(14\) | −1.25699 | −0.335944 | ||||||||
\(15\) | −0.183442 | −0.0473644 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.27913 | −1.52291 | −0.761457 | − | 0.648216i | \(-0.775516\pi\) | ||||
−0.761457 | + | 0.648216i | \(0.775516\pi\) | |||||||
\(18\) | 3.26529 | 0.769636 | ||||||||
\(19\) | 7.93778 | 1.82105 | 0.910526 | − | 0.413452i | \(-0.135677\pi\) | ||||
0.910526 | + | 0.413452i | \(0.135677\pi\) | |||||||
\(20\) | 0.0732871 | 0.0163875 | ||||||||
\(21\) | 3.14631 | 0.686581 | ||||||||
\(22\) | −2.84908 | −0.607426 | ||||||||
\(23\) | −3.36070 | −0.700754 | −0.350377 | − | 0.936609i | \(-0.613946\pi\) | ||||
−0.350377 | + | 0.936609i | \(0.613946\pi\) | |||||||
\(24\) | −2.50306 | −0.510934 | ||||||||
\(25\) | −4.99463 | −0.998926 | ||||||||
\(26\) | 1.61180 | 0.316100 | ||||||||
\(27\) | −0.664031 | −0.127793 | ||||||||
\(28\) | −1.25699 | −0.237548 | ||||||||
\(29\) | 2.56226 | 0.475800 | 0.237900 | − | 0.971290i | \(-0.423541\pi\) | ||||
0.237900 | + | 0.971290i | \(0.423541\pi\) | |||||||
\(30\) | −0.183442 | −0.0334917 | ||||||||
\(31\) | −2.29991 | −0.413077 | −0.206538 | − | 0.978439i | \(-0.566220\pi\) | ||||
−0.206538 | + | 0.978439i | \(0.566220\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.13141 | 1.24142 | ||||||||
\(34\) | −6.27913 | −1.07686 | ||||||||
\(35\) | −0.0921209 | −0.0155713 | ||||||||
\(36\) | 3.26529 | 0.544215 | ||||||||
\(37\) | 4.83601 | 0.795035 | 0.397517 | − | 0.917595i | \(-0.369872\pi\) | ||||
0.397517 | + | 0.917595i | \(0.369872\pi\) | |||||||
\(38\) | 7.93778 | 1.28768 | ||||||||
\(39\) | −4.03443 | −0.646025 | ||||||||
\(40\) | 0.0732871 | 0.0115877 | ||||||||
\(41\) | −5.31870 | −0.830641 | −0.415321 | − | 0.909675i | \(-0.636331\pi\) | ||||
−0.415321 | + | 0.909675i | \(0.636331\pi\) | |||||||
\(42\) | 3.14631 | 0.485486 | ||||||||
\(43\) | 6.39401 | 0.975078 | 0.487539 | − | 0.873101i | \(-0.337895\pi\) | ||||
0.487539 | + | 0.873101i | \(0.337895\pi\) | |||||||
\(44\) | −2.84908 | −0.429515 | ||||||||
\(45\) | 0.239303 | 0.0356732 | ||||||||
\(46\) | −3.36070 | −0.495508 | ||||||||
\(47\) | 2.78599 | 0.406379 | 0.203189 | − | 0.979139i | \(-0.434869\pi\) | ||||
0.203189 | + | 0.979139i | \(0.434869\pi\) | |||||||
\(48\) | −2.50306 | −0.361285 | ||||||||
\(49\) | −5.41998 | −0.774283 | ||||||||
\(50\) | −4.99463 | −0.706347 | ||||||||
\(51\) | 15.7170 | 2.20082 | ||||||||
\(52\) | 1.61180 | 0.223516 | ||||||||
\(53\) | −10.7813 | −1.48092 | −0.740461 | − | 0.672099i | \(-0.765393\pi\) | ||||
−0.740461 | + | 0.672099i | \(0.765393\pi\) | |||||||
\(54\) | −0.664031 | −0.0903632 | ||||||||
\(55\) | −0.208801 | −0.0281547 | ||||||||
\(56\) | −1.25699 | −0.167972 | ||||||||
\(57\) | −19.8687 | −2.63167 | ||||||||
\(58\) | 2.56226 | 0.336442 | ||||||||
\(59\) | −7.89307 | −1.02759 | −0.513795 | − | 0.857913i | \(-0.671761\pi\) | ||||
−0.513795 | + | 0.857913i | \(0.671761\pi\) | |||||||
\(60\) | −0.183442 | −0.0236822 | ||||||||
\(61\) | 9.40976 | 1.20480 | 0.602398 | − | 0.798196i | \(-0.294212\pi\) | ||||
0.602398 | + | 0.798196i | \(0.294212\pi\) | |||||||
\(62\) | −2.29991 | −0.292089 | ||||||||
\(63\) | −4.10443 | −0.517109 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.118124 | 0.0146515 | ||||||||
\(66\) | 7.13141 | 0.877815 | ||||||||
\(67\) | 12.5474 | 1.53291 | 0.766455 | − | 0.642298i | \(-0.222019\pi\) | ||||
0.766455 | + | 0.642298i | \(0.222019\pi\) | |||||||
\(68\) | −6.27913 | −0.761457 | ||||||||
\(69\) | 8.41201 | 1.01269 | ||||||||
\(70\) | −0.0921209 | −0.0110106 | ||||||||
\(71\) | 2.58613 | 0.306917 | 0.153459 | − | 0.988155i | \(-0.450959\pi\) | ||||
0.153459 | + | 0.988155i | \(0.450959\pi\) | |||||||
\(72\) | 3.26529 | 0.384818 | ||||||||
\(73\) | 14.4787 | 1.69460 | 0.847300 | − | 0.531114i | \(-0.178227\pi\) | ||||
0.847300 | + | 0.531114i | \(0.178227\pi\) | |||||||
\(74\) | 4.83601 | 0.562174 | ||||||||
\(75\) | 12.5018 | 1.44359 | ||||||||
\(76\) | 7.93778 | 0.910526 | ||||||||
\(77\) | 3.58126 | 0.408122 | ||||||||
\(78\) | −4.03443 | −0.456809 | ||||||||
\(79\) | 7.54999 | 0.849441 | 0.424720 | − | 0.905325i | \(-0.360372\pi\) | ||||
0.424720 | + | 0.905325i | \(0.360372\pi\) | |||||||
\(80\) | 0.0732871 | 0.00819374 | ||||||||
\(81\) | −8.13376 | −0.903751 | ||||||||
\(82\) | −5.31870 | −0.587352 | ||||||||
\(83\) | −3.60097 | −0.395258 | −0.197629 | − | 0.980277i | \(-0.563324\pi\) | ||||
−0.197629 | + | 0.980277i | \(0.563324\pi\) | |||||||
\(84\) | 3.14631 | 0.343291 | ||||||||
\(85\) | −0.460179 | −0.0499134 | ||||||||
\(86\) | 6.39401 | 0.689484 | ||||||||
\(87\) | −6.41349 | −0.687598 | ||||||||
\(88\) | −2.84908 | −0.303713 | ||||||||
\(89\) | 2.95236 | 0.312950 | 0.156475 | − | 0.987682i | \(-0.449987\pi\) | ||||
0.156475 | + | 0.987682i | \(0.449987\pi\) | |||||||
\(90\) | 0.239303 | 0.0252248 | ||||||||
\(91\) | −2.02601 | −0.212384 | ||||||||
\(92\) | −3.36070 | −0.350377 | ||||||||
\(93\) | 5.75681 | 0.596953 | ||||||||
\(94\) | 2.78599 | 0.287353 | ||||||||
\(95\) | 0.581737 | 0.0596849 | ||||||||
\(96\) | −2.50306 | −0.255467 | ||||||||
\(97\) | 1.08941 | 0.110613 | 0.0553065 | − | 0.998469i | \(-0.482386\pi\) | ||||
0.0553065 | + | 0.998469i | \(0.482386\pi\) | |||||||
\(98\) | −5.41998 | −0.547501 | ||||||||
\(99\) | −9.30307 | −0.934993 | ||||||||
\(100\) | −4.99463 | −0.499463 | ||||||||
\(101\) | −11.4845 | −1.14276 | −0.571378 | − | 0.820687i | \(-0.693591\pi\) | ||||
−0.571378 | + | 0.820687i | \(0.693591\pi\) | |||||||
\(102\) | 15.7170 | 1.55622 | ||||||||
\(103\) | −0.617715 | −0.0608652 | −0.0304326 | − | 0.999537i | \(-0.509689\pi\) | ||||
−0.0304326 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(104\) | 1.61180 | 0.158050 | ||||||||
\(105\) | 0.230584 | 0.0225027 | ||||||||
\(106\) | −10.7813 | −1.04717 | ||||||||
\(107\) | 17.2253 | 1.66523 | 0.832616 | − | 0.553851i | \(-0.186842\pi\) | ||||
0.832616 | + | 0.553851i | \(0.186842\pi\) | |||||||
\(108\) | −0.664031 | −0.0638964 | ||||||||
\(109\) | 8.80570 | 0.843434 | 0.421717 | − | 0.906728i | \(-0.361428\pi\) | ||||
0.421717 | + | 0.906728i | \(0.361428\pi\) | |||||||
\(110\) | −0.208801 | −0.0199084 | ||||||||
\(111\) | −12.1048 | −1.14894 | ||||||||
\(112\) | −1.25699 | −0.118774 | ||||||||
\(113\) | 4.22222 | 0.397193 | 0.198597 | − | 0.980081i | \(-0.436362\pi\) | ||||
0.198597 | + | 0.980081i | \(0.436362\pi\) | |||||||
\(114\) | −19.8687 | −1.86088 | ||||||||
\(115\) | −0.246296 | −0.0229672 | ||||||||
\(116\) | 2.56226 | 0.237900 | ||||||||
\(117\) | 5.26299 | 0.486564 | ||||||||
\(118\) | −7.89307 | −0.726616 | ||||||||
\(119\) | 7.89279 | 0.723531 | ||||||||
\(120\) | −0.183442 | −0.0167459 | ||||||||
\(121\) | −2.88275 | −0.262068 | ||||||||
\(122\) | 9.40976 | 0.851920 | ||||||||
\(123\) | 13.3130 | 1.20039 | ||||||||
\(124\) | −2.29991 | −0.206538 | ||||||||
\(125\) | −0.732477 | −0.0655147 | ||||||||
\(126\) | −4.10443 | −0.365651 | ||||||||
\(127\) | 4.76056 | 0.422432 | 0.211216 | − | 0.977439i | \(-0.432258\pi\) | ||||
0.211216 | + | 0.977439i | \(0.432258\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.0046 | −1.40912 | ||||||||
\(130\) | 0.118124 | 0.0103602 | ||||||||
\(131\) | 12.1098 | 1.05804 | 0.529019 | − | 0.848610i | \(-0.322560\pi\) | ||||
0.529019 | + | 0.848610i | \(0.322560\pi\) | |||||||
\(132\) | 7.13141 | 0.620709 | ||||||||
\(133\) | −9.97769 | −0.865176 | ||||||||
\(134\) | 12.5474 | 1.08393 | ||||||||
\(135\) | −0.0486649 | −0.00418841 | ||||||||
\(136\) | −6.27913 | −0.538431 | ||||||||
\(137\) | 11.2786 | 0.963596 | 0.481798 | − | 0.876282i | \(-0.339984\pi\) | ||||
0.481798 | + | 0.876282i | \(0.339984\pi\) | |||||||
\(138\) | 8.41201 | 0.716078 | ||||||||
\(139\) | −16.4307 | −1.39363 | −0.696817 | − | 0.717249i | \(-0.745401\pi\) | ||||
−0.696817 | + | 0.717249i | \(0.745401\pi\) | |||||||
\(140\) | −0.0921209 | −0.00778564 | ||||||||
\(141\) | −6.97349 | −0.587274 | ||||||||
\(142\) | 2.58613 | 0.217023 | ||||||||
\(143\) | −4.59215 | −0.384015 | ||||||||
\(144\) | 3.26529 | 0.272107 | ||||||||
\(145\) | 0.187781 | 0.0155943 | ||||||||
\(146\) | 14.4787 | 1.19826 | ||||||||
\(147\) | 13.5665 | 1.11895 | ||||||||
\(148\) | 4.83601 | 0.397517 | ||||||||
\(149\) | −11.6150 | −0.951541 | −0.475771 | − | 0.879569i | \(-0.657831\pi\) | ||||
−0.475771 | + | 0.879569i | \(0.657831\pi\) | |||||||
\(150\) | 12.5018 | 1.02077 | ||||||||
\(151\) | 13.7458 | 1.11862 | 0.559309 | − | 0.828959i | \(-0.311066\pi\) | ||||
0.559309 | + | 0.828959i | \(0.311066\pi\) | |||||||
\(152\) | 7.93778 | 0.643839 | ||||||||
\(153\) | −20.5032 | −1.65758 | ||||||||
\(154\) | 3.58126 | 0.288586 | ||||||||
\(155\) | −0.168554 | −0.0135386 | ||||||||
\(156\) | −4.03443 | −0.323013 | ||||||||
\(157\) | 16.9202 | 1.35038 | 0.675188 | − | 0.737645i | \(-0.264062\pi\) | ||||
0.675188 | + | 0.737645i | \(0.264062\pi\) | |||||||
\(158\) | 7.54999 | 0.600645 | ||||||||
\(159\) | 26.9861 | 2.14014 | ||||||||
\(160\) | 0.0732871 | 0.00579385 | ||||||||
\(161\) | 4.22435 | 0.332926 | ||||||||
\(162\) | −8.13376 | −0.639048 | ||||||||
\(163\) | 4.60136 | 0.360406 | 0.180203 | − | 0.983629i | \(-0.442324\pi\) | ||||
0.180203 | + | 0.983629i | \(0.442324\pi\) | |||||||
\(164\) | −5.31870 | −0.415321 | ||||||||
\(165\) | 0.522640 | 0.0406874 | ||||||||
\(166\) | −3.60097 | −0.279489 | ||||||||
\(167\) | 22.5770 | 1.74706 | 0.873532 | − | 0.486767i | \(-0.161824\pi\) | ||||
0.873532 | + | 0.486767i | \(0.161824\pi\) | |||||||
\(168\) | 3.14631 | 0.242743 | ||||||||
\(169\) | −10.4021 | −0.800162 | ||||||||
\(170\) | −0.460179 | −0.0352941 | ||||||||
\(171\) | 25.9191 | 1.98209 | ||||||||
\(172\) | 6.39401 | 0.487539 | ||||||||
\(173\) | −0.748496 | −0.0569071 | −0.0284535 | − | 0.999595i | \(-0.509058\pi\) | ||||
−0.0284535 | + | 0.999595i | \(0.509058\pi\) | |||||||
\(174\) | −6.41349 | −0.486205 | ||||||||
\(175\) | 6.27819 | 0.474586 | ||||||||
\(176\) | −2.84908 | −0.214757 | ||||||||
\(177\) | 19.7568 | 1.48501 | ||||||||
\(178\) | 2.95236 | 0.221289 | ||||||||
\(179\) | −7.22728 | −0.540192 | −0.270096 | − | 0.962833i | \(-0.587055\pi\) | ||||
−0.270096 | + | 0.962833i | \(0.587055\pi\) | |||||||
\(180\) | 0.239303 | 0.0178366 | ||||||||
\(181\) | 3.01609 | 0.224184 | 0.112092 | − | 0.993698i | \(-0.464245\pi\) | ||||
0.112092 | + | 0.993698i | \(0.464245\pi\) | |||||||
\(182\) | −2.02601 | −0.150178 | ||||||||
\(183\) | −23.5532 | −1.74110 | ||||||||
\(184\) | −3.36070 | −0.247754 | ||||||||
\(185\) | 0.354417 | 0.0260572 | ||||||||
\(186\) | 5.75681 | 0.422110 | ||||||||
\(187\) | 17.8898 | 1.30823 | ||||||||
\(188\) | 2.78599 | 0.203189 | ||||||||
\(189\) | 0.834679 | 0.0607140 | ||||||||
\(190\) | 0.581737 | 0.0422036 | ||||||||
\(191\) | 10.6334 | 0.769406 | 0.384703 | − | 0.923041i | \(-0.374304\pi\) | ||||
0.384703 | + | 0.923041i | \(0.374304\pi\) | |||||||
\(192\) | −2.50306 | −0.180642 | ||||||||
\(193\) | −1.43622 | −0.103381 | −0.0516905 | − | 0.998663i | \(-0.516461\pi\) | ||||
−0.0516905 | + | 0.998663i | \(0.516461\pi\) | |||||||
\(194\) | 1.08941 | 0.0782153 | ||||||||
\(195\) | −0.295671 | −0.0211735 | ||||||||
\(196\) | −5.41998 | −0.387142 | ||||||||
\(197\) | 2.72603 | 0.194222 | 0.0971108 | − | 0.995274i | \(-0.469040\pi\) | ||||
0.0971108 | + | 0.995274i | \(0.469040\pi\) | |||||||
\(198\) | −9.30307 | −0.661140 | ||||||||
\(199\) | 7.68601 | 0.544847 | 0.272423 | − | 0.962177i | \(-0.412175\pi\) | ||||
0.272423 | + | 0.962177i | \(0.412175\pi\) | |||||||
\(200\) | −4.99463 | −0.353174 | ||||||||
\(201\) | −31.4069 | −2.21527 | ||||||||
\(202\) | −11.4845 | −0.808050 | ||||||||
\(203\) | −3.22073 | −0.226051 | ||||||||
\(204\) | 15.7170 | 1.10041 | ||||||||
\(205\) | −0.389792 | −0.0272242 | ||||||||
\(206\) | −0.617715 | −0.0430382 | ||||||||
\(207\) | −10.9736 | −0.762721 | ||||||||
\(208\) | 1.61180 | 0.111758 | ||||||||
\(209\) | −22.6154 | −1.56434 | ||||||||
\(210\) | 0.230584 | 0.0159118 | ||||||||
\(211\) | 13.3045 | 0.915917 | 0.457959 | − | 0.888974i | \(-0.348581\pi\) | ||||
0.457959 | + | 0.888974i | \(0.348581\pi\) | |||||||
\(212\) | −10.7813 | −0.740461 | ||||||||
\(213\) | −6.47323 | −0.443538 | ||||||||
\(214\) | 17.2253 | 1.17750 | ||||||||
\(215\) | 0.468598 | 0.0319581 | ||||||||
\(216\) | −0.664031 | −0.0451816 | ||||||||
\(217\) | 2.89096 | 0.196251 | ||||||||
\(218\) | 8.80570 | 0.596398 | ||||||||
\(219\) | −36.2409 | −2.44893 | ||||||||
\(220\) | −0.208801 | −0.0140773 | ||||||||
\(221\) | −10.1207 | −0.680792 | ||||||||
\(222\) | −12.1048 | −0.812421 | ||||||||
\(223\) | 5.60413 | 0.375281 | 0.187640 | − | 0.982238i | \(-0.439916\pi\) | ||||
0.187640 | + | 0.982238i | \(0.439916\pi\) | |||||||
\(224\) | −1.25699 | −0.0839860 | ||||||||
\(225\) | −16.3089 | −1.08726 | ||||||||
\(226\) | 4.22222 | 0.280858 | ||||||||
\(227\) | 26.0194 | 1.72697 | 0.863483 | − | 0.504378i | \(-0.168278\pi\) | ||||
0.863483 | + | 0.504378i | \(0.168278\pi\) | |||||||
\(228\) | −19.8687 | −1.31584 | ||||||||
\(229\) | 19.0513 | 1.25894 | 0.629472 | − | 0.777023i | \(-0.283271\pi\) | ||||
0.629472 | + | 0.777023i | \(0.283271\pi\) | |||||||
\(230\) | −0.246296 | −0.0162402 | ||||||||
\(231\) | −8.96409 | −0.589794 | ||||||||
\(232\) | 2.56226 | 0.168221 | ||||||||
\(233\) | 5.11960 | 0.335396 | 0.167698 | − | 0.985838i | \(-0.446367\pi\) | ||||
0.167698 | + | 0.985838i | \(0.446367\pi\) | |||||||
\(234\) | 5.26299 | 0.344053 | ||||||||
\(235\) | 0.204177 | 0.0133191 | ||||||||
\(236\) | −7.89307 | −0.513795 | ||||||||
\(237\) | −18.8981 | −1.22756 | ||||||||
\(238\) | 7.89279 | 0.511614 | ||||||||
\(239\) | −22.9400 | −1.48386 | −0.741932 | − | 0.670475i | \(-0.766090\pi\) | ||||
−0.741932 | + | 0.670475i | \(0.766090\pi\) | |||||||
\(240\) | −0.183442 | −0.0118411 | ||||||||
\(241\) | 16.2412 | 1.04619 | 0.523093 | − | 0.852275i | \(-0.324778\pi\) | ||||
0.523093 | + | 0.852275i | \(0.324778\pi\) | |||||||
\(242\) | −2.88275 | −0.185310 | ||||||||
\(243\) | 22.3513 | 1.43384 | ||||||||
\(244\) | 9.40976 | 0.602398 | ||||||||
\(245\) | −0.397215 | −0.0253771 | ||||||||
\(246\) | 13.3130 | 0.848806 | ||||||||
\(247\) | 12.7941 | 0.814070 | ||||||||
\(248\) | −2.29991 | −0.146045 | ||||||||
\(249\) | 9.01343 | 0.571203 | ||||||||
\(250\) | −0.732477 | −0.0463259 | ||||||||
\(251\) | 8.76594 | 0.553301 | 0.276651 | − | 0.960971i | \(-0.410776\pi\) | ||||
0.276651 | + | 0.960971i | \(0.410776\pi\) | |||||||
\(252\) | −4.10443 | −0.258555 | ||||||||
\(253\) | 9.57489 | 0.601968 | ||||||||
\(254\) | 4.76056 | 0.298704 | ||||||||
\(255\) | 1.15185 | 0.0721319 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.66192 | 0.290802 | 0.145401 | − | 0.989373i | \(-0.453553\pi\) | ||||
0.145401 | + | 0.989373i | \(0.453553\pi\) | |||||||
\(258\) | −16.0046 | −0.996401 | ||||||||
\(259\) | −6.07880 | −0.377718 | ||||||||
\(260\) | 0.118124 | 0.00732575 | ||||||||
\(261\) | 8.36653 | 0.517875 | ||||||||
\(262\) | 12.1098 | 0.748145 | ||||||||
\(263\) | −3.88618 | −0.239632 | −0.119816 | − | 0.992796i | \(-0.538231\pi\) | ||||
−0.119816 | + | 0.992796i | \(0.538231\pi\) | |||||||
\(264\) | 7.13141 | 0.438908 | ||||||||
\(265\) | −0.790128 | −0.0485372 | ||||||||
\(266\) | −9.97769 | −0.611772 | ||||||||
\(267\) | −7.38993 | −0.452257 | ||||||||
\(268\) | 12.5474 | 0.766455 | ||||||||
\(269\) | 12.1564 | 0.741187 | 0.370593 | − | 0.928795i | \(-0.379154\pi\) | ||||
0.370593 | + | 0.928795i | \(0.379154\pi\) | |||||||
\(270\) | −0.0486649 | −0.00296165 | ||||||||
\(271\) | 4.52991 | 0.275172 | 0.137586 | − | 0.990490i | \(-0.456066\pi\) | ||||
0.137586 | + | 0.990490i | \(0.456066\pi\) | |||||||
\(272\) | −6.27913 | −0.380728 | ||||||||
\(273\) | 5.07122 | 0.306924 | ||||||||
\(274\) | 11.2786 | 0.681365 | ||||||||
\(275\) | 14.2301 | 0.858107 | ||||||||
\(276\) | 8.41201 | 0.506344 | ||||||||
\(277\) | 0.700840 | 0.0421094 | 0.0210547 | − | 0.999778i | \(-0.493298\pi\) | ||||
0.0210547 | + | 0.999778i | \(0.493298\pi\) | |||||||
\(278\) | −16.4307 | −0.985448 | ||||||||
\(279\) | −7.50988 | −0.449605 | ||||||||
\(280\) | −0.0921209 | −0.00550528 | ||||||||
\(281\) | −11.0037 | −0.656424 | −0.328212 | − | 0.944604i | \(-0.606446\pi\) | ||||
−0.328212 | + | 0.944604i | \(0.606446\pi\) | |||||||
\(282\) | −6.97349 | −0.415266 | ||||||||
\(283\) | 18.9431 | 1.12605 | 0.563027 | − | 0.826439i | \(-0.309637\pi\) | ||||
0.563027 | + | 0.826439i | \(0.309637\pi\) | |||||||
\(284\) | 2.58613 | 0.153459 | ||||||||
\(285\) | −1.45612 | −0.0862531 | ||||||||
\(286\) | −4.59215 | −0.271539 | ||||||||
\(287\) | 6.68554 | 0.394635 | ||||||||
\(288\) | 3.26529 | 0.192409 | ||||||||
\(289\) | 22.4275 | 1.31927 | ||||||||
\(290\) | 0.187781 | 0.0110269 | ||||||||
\(291\) | −2.72686 | −0.159851 | ||||||||
\(292\) | 14.4787 | 0.847300 | ||||||||
\(293\) | 14.8903 | 0.869898 | 0.434949 | − | 0.900455i | \(-0.356766\pi\) | ||||
0.434949 | + | 0.900455i | \(0.356766\pi\) | |||||||
\(294\) | 13.5665 | 0.791215 | ||||||||
\(295\) | −0.578460 | −0.0336792 | ||||||||
\(296\) | 4.83601 | 0.281087 | ||||||||
\(297\) | 1.89188 | 0.109778 | ||||||||
\(298\) | −11.6150 | −0.672841 | ||||||||
\(299\) | −5.41677 | −0.313260 | ||||||||
\(300\) | 12.5018 | 0.721794 | ||||||||
\(301\) | −8.03719 | −0.463256 | ||||||||
\(302\) | 13.7458 | 0.790983 | ||||||||
\(303\) | 28.7465 | 1.65144 | ||||||||
\(304\) | 7.93778 | 0.455263 | ||||||||
\(305\) | 0.689614 | 0.0394872 | ||||||||
\(306\) | −20.5032 | −1.17209 | ||||||||
\(307\) | 21.9660 | 1.25367 | 0.626833 | − | 0.779153i | \(-0.284351\pi\) | ||||
0.626833 | + | 0.779153i | \(0.284351\pi\) | |||||||
\(308\) | 3.58126 | 0.204061 | ||||||||
\(309\) | 1.54617 | 0.0879588 | ||||||||
\(310\) | −0.168554 | −0.00957321 | ||||||||
\(311\) | −0.789869 | −0.0447894 | −0.0223947 | − | 0.999749i | \(-0.507129\pi\) | ||||
−0.0223947 | + | 0.999749i | \(0.507129\pi\) | |||||||
\(312\) | −4.03443 | −0.228404 | ||||||||
\(313\) | −7.71109 | −0.435857 | −0.217928 | − | 0.975965i | \(-0.569930\pi\) | ||||
−0.217928 | + | 0.975965i | \(0.569930\pi\) | |||||||
\(314\) | 16.9202 | 0.954860 | ||||||||
\(315\) | −0.300801 | −0.0169482 | ||||||||
\(316\) | 7.54999 | 0.424720 | ||||||||
\(317\) | 8.45844 | 0.475073 | 0.237537 | − | 0.971379i | \(-0.423660\pi\) | ||||
0.237537 | + | 0.971379i | \(0.423660\pi\) | |||||||
\(318\) | 26.9861 | 1.51331 | ||||||||
\(319\) | −7.30009 | −0.408727 | ||||||||
\(320\) | 0.0732871 | 0.00409687 | ||||||||
\(321\) | −43.1159 | −2.40649 | ||||||||
\(322\) | 4.22435 | 0.235414 | ||||||||
\(323\) | −49.8424 | −2.77330 | ||||||||
\(324\) | −8.13376 | −0.451875 | ||||||||
\(325\) | −8.05034 | −0.446553 | ||||||||
\(326\) | 4.60136 | 0.254846 | ||||||||
\(327\) | −22.0412 | −1.21888 | ||||||||
\(328\) | −5.31870 | −0.293676 | ||||||||
\(329\) | −3.50196 | −0.193069 | ||||||||
\(330\) | 0.522640 | 0.0287704 | ||||||||
\(331\) | −12.6610 | −0.695911 | −0.347955 | − | 0.937511i | \(-0.613124\pi\) | ||||
−0.347955 | + | 0.937511i | \(0.613124\pi\) | |||||||
\(332\) | −3.60097 | −0.197629 | ||||||||
\(333\) | 15.7910 | 0.865339 | ||||||||
\(334\) | 22.5770 | 1.23536 | ||||||||
\(335\) | 0.919563 | 0.0502411 | ||||||||
\(336\) | 3.14631 | 0.171645 | ||||||||
\(337\) | −9.53440 | −0.519372 | −0.259686 | − | 0.965693i | \(-0.583619\pi\) | ||||
−0.259686 | + | 0.965693i | \(0.583619\pi\) | |||||||
\(338\) | −10.4021 | −0.565800 | ||||||||
\(339\) | −10.5685 | −0.574000 | ||||||||
\(340\) | −0.460179 | −0.0249567 | ||||||||
\(341\) | 6.55263 | 0.354845 | ||||||||
\(342\) | 25.9191 | 1.40155 | ||||||||
\(343\) | 15.6118 | 0.842956 | ||||||||
\(344\) | 6.39401 | 0.344742 | ||||||||
\(345\) | 0.616492 | 0.0331908 | ||||||||
\(346\) | −0.748496 | −0.0402394 | ||||||||
\(347\) | −4.11913 | −0.221127 | −0.110563 | − | 0.993869i | \(-0.535266\pi\) | ||||
−0.110563 | + | 0.993869i | \(0.535266\pi\) | |||||||
\(348\) | −6.41349 | −0.343799 | ||||||||
\(349\) | −32.4434 | −1.73666 | −0.868328 | − | 0.495991i | \(-0.834805\pi\) | ||||
−0.868328 | + | 0.495991i | \(0.834805\pi\) | |||||||
\(350\) | 6.27819 | 0.335583 | ||||||||
\(351\) | −1.07029 | −0.0571276 | ||||||||
\(352\) | −2.84908 | −0.151856 | ||||||||
\(353\) | −1.98124 | −0.105451 | −0.0527254 | − | 0.998609i | \(-0.516791\pi\) | ||||
−0.0527254 | + | 0.998609i | \(0.516791\pi\) | |||||||
\(354\) | 19.7568 | 1.05006 | ||||||||
\(355\) | 0.189530 | 0.0100592 | ||||||||
\(356\) | 2.95236 | 0.156475 | ||||||||
\(357\) | −19.7561 | −1.04560 | ||||||||
\(358\) | −7.22728 | −0.381974 | ||||||||
\(359\) | −1.52429 | −0.0804490 | −0.0402245 | − | 0.999191i | \(-0.512807\pi\) | ||||
−0.0402245 | + | 0.999191i | \(0.512807\pi\) | |||||||
\(360\) | 0.239303 | 0.0126124 | ||||||||
\(361\) | 44.0084 | 2.31623 | ||||||||
\(362\) | 3.01609 | 0.158522 | ||||||||
\(363\) | 7.21567 | 0.378725 | ||||||||
\(364\) | −2.02601 | −0.106192 | ||||||||
\(365\) | 1.06110 | 0.0555405 | ||||||||
\(366\) | −23.5532 | −1.23114 | ||||||||
\(367\) | −28.7275 | −1.49956 | −0.749782 | − | 0.661685i | \(-0.769841\pi\) | ||||
−0.749782 | + | 0.661685i | \(0.769841\pi\) | |||||||
\(368\) | −3.36070 | −0.175188 | ||||||||
\(369\) | −17.3671 | −0.904094 | ||||||||
\(370\) | 0.354417 | 0.0184252 | ||||||||
\(371\) | 13.5519 | 0.703581 | ||||||||
\(372\) | 5.75681 | 0.298477 | ||||||||
\(373\) | −7.34260 | −0.380185 | −0.190093 | − | 0.981766i | \(-0.560879\pi\) | ||||
−0.190093 | + | 0.981766i | \(0.560879\pi\) | |||||||
\(374\) | 17.8898 | 0.925057 | ||||||||
\(375\) | 1.83343 | 0.0946780 | ||||||||
\(376\) | 2.78599 | 0.143677 | ||||||||
\(377\) | 4.12986 | 0.212698 | ||||||||
\(378\) | 0.834679 | 0.0429313 | ||||||||
\(379\) | −13.9457 | −0.716342 | −0.358171 | − | 0.933656i | \(-0.616600\pi\) | ||||
−0.358171 | + | 0.933656i | \(0.616600\pi\) | |||||||
\(380\) | 0.581737 | 0.0298425 | ||||||||
\(381\) | −11.9160 | −0.610473 | ||||||||
\(382\) | 10.6334 | 0.544052 | ||||||||
\(383\) | −6.06270 | −0.309789 | −0.154895 | − | 0.987931i | \(-0.549504\pi\) | ||||
−0.154895 | + | 0.987931i | \(0.549504\pi\) | |||||||
\(384\) | −2.50306 | −0.127734 | ||||||||
\(385\) | 0.262460 | 0.0133762 | ||||||||
\(386\) | −1.43622 | −0.0731015 | ||||||||
\(387\) | 20.8783 | 1.06130 | ||||||||
\(388\) | 1.08941 | 0.0553065 | ||||||||
\(389\) | 30.2018 | 1.53129 | 0.765645 | − | 0.643263i | \(-0.222420\pi\) | ||||
0.765645 | + | 0.643263i | \(0.222420\pi\) | |||||||
\(390\) | −0.295671 | −0.0149719 | ||||||||
\(391\) | 21.1023 | 1.06719 | ||||||||
\(392\) | −5.41998 | −0.273750 | ||||||||
\(393\) | −30.3115 | −1.52901 | ||||||||
\(394\) | 2.72603 | 0.137335 | ||||||||
\(395\) | 0.553317 | 0.0278404 | ||||||||
\(396\) | −9.30307 | −0.467497 | ||||||||
\(397\) | −17.9251 | −0.899636 | −0.449818 | − | 0.893120i | \(-0.648511\pi\) | ||||
−0.449818 | + | 0.893120i | \(0.648511\pi\) | |||||||
\(398\) | 7.68601 | 0.385265 | ||||||||
\(399\) | 24.9747 | 1.25030 | ||||||||
\(400\) | −4.99463 | −0.249731 | ||||||||
\(401\) | −26.5773 | −1.32721 | −0.663603 | − | 0.748085i | \(-0.730974\pi\) | ||||
−0.663603 | + | 0.748085i | \(0.730974\pi\) | |||||||
\(402\) | −31.4069 | −1.56643 | ||||||||
\(403\) | −3.70700 | −0.184659 | ||||||||
\(404\) | −11.4845 | −0.571378 | ||||||||
\(405\) | −0.596099 | −0.0296204 | ||||||||
\(406\) | −3.22073 | −0.159842 | ||||||||
\(407\) | −13.7782 | −0.682958 | ||||||||
\(408\) | 15.7170 | 0.778108 | ||||||||
\(409\) | −3.04631 | −0.150630 | −0.0753151 | − | 0.997160i | \(-0.523996\pi\) | ||||
−0.0753151 | + | 0.997160i | \(0.523996\pi\) | |||||||
\(410\) | −0.389792 | −0.0192504 | ||||||||
\(411\) | −28.2310 | −1.39253 | ||||||||
\(412\) | −0.617715 | −0.0304326 | ||||||||
\(413\) | 9.92149 | 0.488205 | ||||||||
\(414\) | −10.9736 | −0.539325 | ||||||||
\(415\) | −0.263904 | −0.0129546 | ||||||||
\(416\) | 1.61180 | 0.0790250 | ||||||||
\(417\) | 41.1269 | 2.01400 | ||||||||
\(418\) | −22.6154 | −1.10615 | ||||||||
\(419\) | 16.8127 | 0.821352 | 0.410676 | − | 0.911781i | \(-0.365293\pi\) | ||||
0.410676 | + | 0.911781i | \(0.365293\pi\) | |||||||
\(420\) | 0.230584 | 0.0112513 | ||||||||
\(421\) | −40.3056 | −1.96438 | −0.982188 | − | 0.187899i | \(-0.939832\pi\) | ||||
−0.982188 | + | 0.187899i | \(0.939832\pi\) | |||||||
\(422\) | 13.3045 | 0.647651 | ||||||||
\(423\) | 9.09707 | 0.442315 | ||||||||
\(424\) | −10.7813 | −0.523585 | ||||||||
\(425\) | 31.3619 | 1.52128 | ||||||||
\(426\) | −6.47323 | −0.313629 | ||||||||
\(427\) | −11.8280 | −0.572395 | ||||||||
\(428\) | 17.2253 | 0.832616 | ||||||||
\(429\) | 11.4944 | 0.554955 | ||||||||
\(430\) | 0.468598 | 0.0225978 | ||||||||
\(431\) | 16.8867 | 0.813405 | 0.406702 | − | 0.913561i | \(-0.366679\pi\) | ||||
0.406702 | + | 0.913561i | \(0.366679\pi\) | |||||||
\(432\) | −0.664031 | −0.0319482 | ||||||||
\(433\) | −1.01520 | −0.0487873 | −0.0243937 | − | 0.999702i | \(-0.507766\pi\) | ||||
−0.0243937 | + | 0.999702i | \(0.507766\pi\) | |||||||
\(434\) | 2.89096 | 0.138771 | ||||||||
\(435\) | −0.470026 | −0.0225360 | ||||||||
\(436\) | 8.80570 | 0.421717 | ||||||||
\(437\) | −26.6765 | −1.27611 | ||||||||
\(438\) | −36.2409 | −1.73166 | ||||||||
\(439\) | 29.8989 | 1.42700 | 0.713499 | − | 0.700657i | \(-0.247109\pi\) | ||||
0.713499 | + | 0.700657i | \(0.247109\pi\) | |||||||
\(440\) | −0.208801 | −0.00995418 | ||||||||
\(441\) | −17.6978 | −0.842753 | ||||||||
\(442\) | −10.1207 | −0.481393 | ||||||||
\(443\) | 15.6699 | 0.744500 | 0.372250 | − | 0.928132i | \(-0.378586\pi\) | ||||
0.372250 | + | 0.928132i | \(0.378586\pi\) | |||||||
\(444\) | −12.1048 | −0.574468 | ||||||||
\(445\) | 0.216370 | 0.0102569 | ||||||||
\(446\) | 5.60413 | 0.265363 | ||||||||
\(447\) | 29.0731 | 1.37511 | ||||||||
\(448\) | −1.25699 | −0.0593871 | ||||||||
\(449\) | −7.05157 | −0.332784 | −0.166392 | − | 0.986060i | \(-0.553212\pi\) | ||||
−0.166392 | + | 0.986060i | \(0.553212\pi\) | |||||||
\(450\) | −16.3089 | −0.768809 | ||||||||
\(451\) | 15.1534 | 0.713546 | ||||||||
\(452\) | 4.22222 | 0.198597 | ||||||||
\(453\) | −34.4065 | −1.61656 | ||||||||
\(454\) | 26.0194 | 1.22115 | ||||||||
\(455\) | −0.148480 | −0.00696087 | ||||||||
\(456\) | −19.8687 | −0.930438 | ||||||||
\(457\) | −31.4584 | −1.47156 | −0.735781 | − | 0.677220i | \(-0.763185\pi\) | ||||
−0.735781 | + | 0.677220i | \(0.763185\pi\) | |||||||
\(458\) | 19.0513 | 0.890208 | ||||||||
\(459\) | 4.16954 | 0.194617 | ||||||||
\(460\) | −0.246296 | −0.0114836 | ||||||||
\(461\) | −10.7377 | −0.500103 | −0.250051 | − | 0.968233i | \(-0.580448\pi\) | ||||
−0.250051 | + | 0.968233i | \(0.580448\pi\) | |||||||
\(462\) | −8.96409 | −0.417047 | ||||||||
\(463\) | 13.4944 | 0.627139 | 0.313569 | − | 0.949565i | \(-0.398475\pi\) | ||||
0.313569 | + | 0.949565i | \(0.398475\pi\) | |||||||
\(464\) | 2.56226 | 0.118950 | ||||||||
\(465\) | 0.421900 | 0.0195651 | ||||||||
\(466\) | 5.11960 | 0.237161 | ||||||||
\(467\) | −10.4824 | −0.485068 | −0.242534 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242534 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(468\) | 5.26299 | 0.243282 | ||||||||
\(469\) | −15.7719 | −0.728280 | ||||||||
\(470\) | 0.204177 | 0.00941799 | ||||||||
\(471\) | −42.3521 | −1.95148 | ||||||||
\(472\) | −7.89307 | −0.363308 | ||||||||
\(473\) | −18.2171 | −0.837621 | ||||||||
\(474\) | −18.8981 | −0.868016 | ||||||||
\(475\) | −39.6463 | −1.81910 | ||||||||
\(476\) | 7.89279 | 0.361766 | ||||||||
\(477\) | −35.2040 | −1.61188 | ||||||||
\(478\) | −22.9400 | −1.04925 | ||||||||
\(479\) | 33.1021 | 1.51247 | 0.756236 | − | 0.654299i | \(-0.227036\pi\) | ||||
0.756236 | + | 0.654299i | \(0.227036\pi\) | |||||||
\(480\) | −0.183442 | −0.00837293 | ||||||||
\(481\) | 7.79468 | 0.355407 | ||||||||
\(482\) | 16.2412 | 0.739766 | ||||||||
\(483\) | −10.5738 | −0.481124 | ||||||||
\(484\) | −2.88275 | −0.131034 | ||||||||
\(485\) | 0.0798398 | 0.00362534 | ||||||||
\(486\) | 22.3513 | 1.01388 | ||||||||
\(487\) | 17.3503 | 0.786218 | 0.393109 | − | 0.919492i | \(-0.371400\pi\) | ||||
0.393109 | + | 0.919492i | \(0.371400\pi\) | |||||||
\(488\) | 9.40976 | 0.425960 | ||||||||
\(489\) | −11.5175 | −0.520838 | ||||||||
\(490\) | −0.397215 | −0.0179443 | ||||||||
\(491\) | −32.5188 | −1.46755 | −0.733776 | − | 0.679391i | \(-0.762244\pi\) | ||||
−0.733776 | + | 0.679391i | \(0.762244\pi\) | |||||||
\(492\) | 13.3130 | 0.600196 | ||||||||
\(493\) | −16.0888 | −0.724603 | ||||||||
\(494\) | 12.7941 | 0.575635 | ||||||||
\(495\) | −0.681794 | −0.0306444 | ||||||||
\(496\) | −2.29991 | −0.103269 | ||||||||
\(497\) | −3.25073 | −0.145815 | ||||||||
\(498\) | 9.01343 | 0.403901 | ||||||||
\(499\) | −36.3677 | −1.62804 | −0.814022 | − | 0.580835i | \(-0.802726\pi\) | ||||
−0.814022 | + | 0.580835i | \(0.802726\pi\) | |||||||
\(500\) | −0.732477 | −0.0327574 | ||||||||
\(501\) | −56.5116 | −2.52475 | ||||||||
\(502\) | 8.76594 | 0.391243 | ||||||||
\(503\) | −22.4027 | −0.998886 | −0.499443 | − | 0.866347i | \(-0.666462\pi\) | ||||
−0.499443 | + | 0.866347i | \(0.666462\pi\) | |||||||
\(504\) | −4.10443 | −0.182826 | ||||||||
\(505\) | −0.841669 | −0.0374538 | ||||||||
\(506\) | 9.57489 | 0.425656 | ||||||||
\(507\) | 26.0370 | 1.15635 | ||||||||
\(508\) | 4.76056 | 0.211216 | ||||||||
\(509\) | 16.7812 | 0.743814 | 0.371907 | − | 0.928270i | \(-0.378704\pi\) | ||||
0.371907 | + | 0.928270i | \(0.378704\pi\) | |||||||
\(510\) | 1.15185 | 0.0510050 | ||||||||
\(511\) | −18.1995 | −0.805099 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.27093 | −0.232717 | ||||||||
\(514\) | 4.66192 | 0.205628 | ||||||||
\(515\) | −0.0452705 | −0.00199486 | ||||||||
\(516\) | −16.0046 | −0.704562 | ||||||||
\(517\) | −7.93751 | −0.349091 | ||||||||
\(518\) | −6.07880 | −0.267087 | ||||||||
\(519\) | 1.87353 | 0.0822387 | ||||||||
\(520\) | 0.118124 | 0.00518008 | ||||||||
\(521\) | −33.1730 | −1.45334 | −0.726668 | − | 0.686989i | \(-0.758932\pi\) | ||||
−0.726668 | + | 0.686989i | \(0.758932\pi\) | |||||||
\(522\) | 8.36653 | 0.366193 | ||||||||
\(523\) | −8.17339 | −0.357397 | −0.178699 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178699 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(524\) | 12.1098 | 0.529019 | ||||||||
\(525\) | −15.7146 | −0.685844 | ||||||||
\(526\) | −3.88618 | −0.169446 | ||||||||
\(527\) | 14.4415 | 0.629080 | ||||||||
\(528\) | 7.13141 | 0.310355 | ||||||||
\(529\) | −11.7057 | −0.508944 | ||||||||
\(530\) | −0.790128 | −0.0343210 | ||||||||
\(531\) | −25.7732 | −1.11846 | ||||||||
\(532\) | −9.97769 | −0.432588 | ||||||||
\(533\) | −8.57268 | −0.371324 | ||||||||
\(534\) | −7.38993 | −0.319794 | ||||||||
\(535\) | 1.26239 | 0.0545779 | ||||||||
\(536\) | 12.5474 | 0.541966 | ||||||||
\(537\) | 18.0903 | 0.780653 | ||||||||
\(538\) | 12.1564 | 0.524098 | ||||||||
\(539\) | 15.4420 | 0.665132 | ||||||||
\(540\) | −0.0486649 | −0.00209420 | ||||||||
\(541\) | −6.26310 | −0.269272 | −0.134636 | − | 0.990895i | \(-0.542986\pi\) | ||||
−0.134636 | + | 0.990895i | \(0.542986\pi\) | |||||||
\(542\) | 4.52991 | 0.194576 | ||||||||
\(543\) | −7.54943 | −0.323977 | ||||||||
\(544\) | −6.27913 | −0.269216 | ||||||||
\(545\) | 0.645344 | 0.0276435 | ||||||||
\(546\) | 5.07122 | 0.217028 | ||||||||
\(547\) | 16.7450 | 0.715963 | 0.357982 | − | 0.933729i | \(-0.383465\pi\) | ||||
0.357982 | + | 0.933729i | \(0.383465\pi\) | |||||||
\(548\) | 11.2786 | 0.481798 | ||||||||
\(549\) | 30.7256 | 1.31134 | ||||||||
\(550\) | 14.2301 | 0.606773 | ||||||||
\(551\) | 20.3387 | 0.866457 | ||||||||
\(552\) | 8.41201 | 0.358039 | ||||||||
\(553\) | −9.49025 | −0.403566 | ||||||||
\(554\) | 0.700840 | 0.0297759 | ||||||||
\(555\) | −0.887125 | −0.0376563 | ||||||||
\(556\) | −16.4307 | −0.696817 | ||||||||
\(557\) | 39.1167 | 1.65743 | 0.828713 | − | 0.559673i | \(-0.189073\pi\) | ||||
0.828713 | + | 0.559673i | \(0.189073\pi\) | |||||||
\(558\) | −7.50988 | −0.317918 | ||||||||
\(559\) | 10.3059 | 0.435892 | ||||||||
\(560\) | −0.0921209 | −0.00389282 | ||||||||
\(561\) | −44.7790 | −1.89057 | ||||||||
\(562\) | −11.0037 | −0.464162 | ||||||||
\(563\) | −12.8152 | −0.540096 | −0.270048 | − | 0.962847i | \(-0.587040\pi\) | ||||
−0.270048 | + | 0.962847i | \(0.587040\pi\) | |||||||
\(564\) | −6.97349 | −0.293637 | ||||||||
\(565\) | 0.309434 | 0.0130180 | ||||||||
\(566\) | 18.9431 | 0.796240 | ||||||||
\(567\) | 10.2240 | 0.429369 | ||||||||
\(568\) | 2.58613 | 0.108512 | ||||||||
\(569\) | 3.48635 | 0.146155 | 0.0730777 | − | 0.997326i | \(-0.476718\pi\) | ||||
0.0730777 | + | 0.997326i | \(0.476718\pi\) | |||||||
\(570\) | −1.45612 | −0.0609901 | ||||||||
\(571\) | −20.4225 | −0.854654 | −0.427327 | − | 0.904097i | \(-0.640545\pi\) | ||||
−0.427327 | + | 0.904097i | \(0.640545\pi\) | |||||||
\(572\) | −4.59215 | −0.192007 | ||||||||
\(573\) | −26.6160 | −1.11190 | ||||||||
\(574\) | 6.68554 | 0.279049 | ||||||||
\(575\) | 16.7854 | 0.700001 | ||||||||
\(576\) | 3.26529 | 0.136054 | ||||||||
\(577\) | −12.8232 | −0.533838 | −0.266919 | − | 0.963719i | \(-0.586006\pi\) | ||||
−0.266919 | + | 0.963719i | \(0.586006\pi\) | |||||||
\(578\) | 22.4275 | 0.932862 | ||||||||
\(579\) | 3.59493 | 0.149400 | ||||||||
\(580\) | 0.187781 | 0.00779717 | ||||||||
\(581\) | 4.52637 | 0.187786 | ||||||||
\(582\) | −2.72686 | −0.113032 | ||||||||
\(583\) | 30.7167 | 1.27216 | ||||||||
\(584\) | 14.4787 | 0.599132 | ||||||||
\(585\) | 0.385709 | 0.0159471 | ||||||||
\(586\) | 14.8903 | 0.615111 | ||||||||
\(587\) | 8.20589 | 0.338693 | 0.169347 | − | 0.985557i | \(-0.445834\pi\) | ||||
0.169347 | + | 0.985557i | \(0.445834\pi\) | |||||||
\(588\) | 13.5665 | 0.559474 | ||||||||
\(589\) | −18.2562 | −0.752234 | ||||||||
\(590\) | −0.578460 | −0.0238148 | ||||||||
\(591\) | −6.82341 | −0.280677 | ||||||||
\(592\) | 4.83601 | 0.198759 | ||||||||
\(593\) | −9.57242 | −0.393092 | −0.196546 | − | 0.980495i | \(-0.562973\pi\) | ||||
−0.196546 | + | 0.980495i | \(0.562973\pi\) | |||||||
\(594\) | 1.89188 | 0.0776247 | ||||||||
\(595\) | 0.578439 | 0.0237137 | ||||||||
\(596\) | −11.6150 | −0.475771 | ||||||||
\(597\) | −19.2385 | −0.787380 | ||||||||
\(598\) | −5.41677 | −0.221508 | ||||||||
\(599\) | −34.6804 | −1.41700 | −0.708502 | − | 0.705709i | \(-0.750629\pi\) | ||||
−0.708502 | + | 0.705709i | \(0.750629\pi\) | |||||||
\(600\) | 12.5018 | 0.510385 | ||||||||
\(601\) | 22.7332 | 0.927306 | 0.463653 | − | 0.886017i | \(-0.346538\pi\) | ||||
0.463653 | + | 0.886017i | \(0.346538\pi\) | |||||||
\(602\) | −8.03719 | −0.327572 | ||||||||
\(603\) | 40.9709 | 1.66846 | ||||||||
\(604\) | 13.7458 | 0.559309 | ||||||||
\(605\) | −0.211268 | −0.00858926 | ||||||||
\(606\) | 28.7465 | 1.16775 | ||||||||
\(607\) | 13.7497 | 0.558084 | 0.279042 | − | 0.960279i | \(-0.409983\pi\) | ||||
0.279042 | + | 0.960279i | \(0.409983\pi\) | |||||||
\(608\) | 7.93778 | 0.321920 | ||||||||
\(609\) | 8.06167 | 0.326675 | ||||||||
\(610\) | 0.689614 | 0.0279216 | ||||||||
\(611\) | 4.49046 | 0.181665 | ||||||||
\(612\) | −20.5032 | −0.828792 | ||||||||
\(613\) | −21.1720 | −0.855127 | −0.427564 | − | 0.903985i | \(-0.640628\pi\) | ||||
−0.427564 | + | 0.903985i | \(0.640628\pi\) | |||||||
\(614\) | 21.9660 | 0.886476 | ||||||||
\(615\) | 0.975671 | 0.0393428 | ||||||||
\(616\) | 3.58126 | 0.144293 | ||||||||
\(617\) | 40.0853 | 1.61377 | 0.806887 | − | 0.590706i | \(-0.201151\pi\) | ||||
0.806887 | + | 0.590706i | \(0.201151\pi\) | |||||||
\(618\) | 1.54617 | 0.0621963 | ||||||||
\(619\) | 8.25566 | 0.331823 | 0.165911 | − | 0.986141i | \(-0.446943\pi\) | ||||
0.165911 | + | 0.986141i | \(0.446943\pi\) | |||||||
\(620\) | −0.168554 | −0.00676929 | ||||||||
\(621\) | 2.23161 | 0.0895513 | ||||||||
\(622\) | −0.789869 | −0.0316709 | ||||||||
\(623\) | −3.71108 | −0.148681 | ||||||||
\(624\) | −4.03443 | −0.161506 | ||||||||
\(625\) | 24.9195 | 0.996779 | ||||||||
\(626\) | −7.71109 | −0.308197 | ||||||||
\(627\) | 56.6075 | 2.26069 | ||||||||
\(628\) | 16.9202 | 0.675188 | ||||||||
\(629\) | −30.3659 | −1.21077 | ||||||||
\(630\) | −0.300801 | −0.0119842 | ||||||||
\(631\) | −11.9847 | −0.477103 | −0.238552 | − | 0.971130i | \(-0.576673\pi\) | ||||
−0.238552 | + | 0.971130i | \(0.576673\pi\) | |||||||
\(632\) | 7.54999 | 0.300323 | ||||||||
\(633\) | −33.3018 | −1.32363 | ||||||||
\(634\) | 8.45844 | 0.335928 | ||||||||
\(635\) | 0.348888 | 0.0138452 | ||||||||
\(636\) | 26.9861 | 1.07007 | ||||||||
\(637\) | −8.73593 | −0.346130 | ||||||||
\(638\) | −7.30009 | −0.289013 | ||||||||
\(639\) | 8.44446 | 0.334058 | ||||||||
\(640\) | 0.0732871 | 0.00289693 | ||||||||
\(641\) | 1.26732 | 0.0500561 | 0.0250280 | − | 0.999687i | \(-0.492032\pi\) | ||||
0.0250280 | + | 0.999687i | \(0.492032\pi\) | |||||||
\(642\) | −43.1159 | −1.70165 | ||||||||
\(643\) | −30.7094 | −1.21106 | −0.605531 | − | 0.795822i | \(-0.707039\pi\) | ||||
−0.605531 | + | 0.795822i | \(0.707039\pi\) | |||||||
\(644\) | 4.22435 | 0.166463 | ||||||||
\(645\) | −1.17293 | −0.0461840 | ||||||||
\(646\) | −49.8424 | −1.96102 | ||||||||
\(647\) | −28.7450 | −1.13008 | −0.565042 | − | 0.825062i | \(-0.691140\pi\) | ||||
−0.565042 | + | 0.825062i | \(0.691140\pi\) | |||||||
\(648\) | −8.13376 | −0.319524 | ||||||||
\(649\) | 22.4880 | 0.882731 | ||||||||
\(650\) | −8.05034 | −0.315760 | ||||||||
\(651\) | −7.23624 | −0.283611 | ||||||||
\(652\) | 4.60136 | 0.180203 | ||||||||
\(653\) | 3.32212 | 0.130005 | 0.0650024 | − | 0.997885i | \(-0.479295\pi\) | ||||
0.0650024 | + | 0.997885i | \(0.479295\pi\) | |||||||
\(654\) | −22.0412 | −0.861878 | ||||||||
\(655\) | 0.887491 | 0.0346771 | ||||||||
\(656\) | −5.31870 | −0.207660 | ||||||||
\(657\) | 47.2770 | 1.84445 | ||||||||
\(658\) | −3.50196 | −0.136521 | ||||||||
\(659\) | 13.7205 | 0.534475 | 0.267237 | − | 0.963631i | \(-0.413889\pi\) | ||||
0.267237 | + | 0.963631i | \(0.413889\pi\) | |||||||
\(660\) | 0.522640 | 0.0203437 | ||||||||
\(661\) | −30.3360 | −1.17993 | −0.589966 | − | 0.807428i | \(-0.700859\pi\) | ||||
−0.589966 | + | 0.807428i | \(0.700859\pi\) | |||||||
\(662\) | −12.6610 | −0.492083 | ||||||||
\(663\) | 25.3327 | 0.983840 | ||||||||
\(664\) | −3.60097 | −0.139745 | ||||||||
\(665\) | −0.731236 | −0.0283561 | ||||||||
\(666\) | 15.7910 | 0.611887 | ||||||||
\(667\) | −8.61099 | −0.333419 | ||||||||
\(668\) | 22.5770 | 0.873532 | ||||||||
\(669\) | −14.0275 | −0.542333 | ||||||||
\(670\) | 0.919563 | 0.0355258 | ||||||||
\(671\) | −26.8092 | −1.03496 | ||||||||
\(672\) | 3.14631 | 0.121372 | ||||||||
\(673\) | 11.1832 | 0.431082 | 0.215541 | − | 0.976495i | \(-0.430849\pi\) | ||||
0.215541 | + | 0.976495i | \(0.430849\pi\) | |||||||
\(674\) | −9.53440 | −0.367252 | ||||||||
\(675\) | 3.31659 | 0.127656 | ||||||||
\(676\) | −10.4021 | −0.400081 | ||||||||
\(677\) | 9.03682 | 0.347313 | 0.173657 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173657 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(678\) | −10.5685 | −0.405879 | ||||||||
\(679\) | −1.36938 | −0.0525519 | ||||||||
\(680\) | −0.460179 | −0.0176471 | ||||||||
\(681\) | −65.1279 | −2.49571 | ||||||||
\(682\) | 6.55263 | 0.250913 | ||||||||
\(683\) | 34.0205 | 1.30176 | 0.650880 | − | 0.759181i | \(-0.274400\pi\) | ||||
0.650880 | + | 0.759181i | \(0.274400\pi\) | |||||||
\(684\) | 25.9191 | 0.991043 | ||||||||
\(685\) | 0.826576 | 0.0315818 | ||||||||
\(686\) | 15.6118 | 0.596060 | ||||||||
\(687\) | −47.6864 | −1.81935 | ||||||||
\(688\) | 6.39401 | 0.243769 | ||||||||
\(689\) | −17.3773 | −0.662021 | ||||||||
\(690\) | 0.616492 | 0.0234694 | ||||||||
\(691\) | −23.4507 | −0.892106 | −0.446053 | − | 0.895007i | \(-0.647171\pi\) | ||||
−0.446053 | + | 0.895007i | \(0.647171\pi\) | |||||||
\(692\) | −0.748496 | −0.0284535 | ||||||||
\(693\) | 11.6938 | 0.444212 | ||||||||
\(694\) | −4.11913 | −0.156360 | ||||||||
\(695\) | −1.20416 | −0.0456763 | ||||||||
\(696\) | −6.41349 | −0.243103 | ||||||||
\(697\) | 33.3968 | 1.26499 | ||||||||
\(698\) | −32.4434 | −1.22800 | ||||||||
\(699\) | −12.8147 | −0.484695 | ||||||||
\(700\) | 6.27819 | 0.237293 | ||||||||
\(701\) | 18.4243 | 0.695876 | 0.347938 | − | 0.937518i | \(-0.386882\pi\) | ||||
0.347938 | + | 0.937518i | \(0.386882\pi\) | |||||||
\(702\) | −1.07029 | −0.0403953 | ||||||||
\(703\) | 38.3872 | 1.44780 | ||||||||
\(704\) | −2.84908 | −0.107379 | ||||||||
\(705\) | −0.511067 | −0.0192479 | ||||||||
\(706\) | −1.98124 | −0.0745649 | ||||||||
\(707\) | 14.4359 | 0.542919 | ||||||||
\(708\) | 19.7568 | 0.742506 | ||||||||
\(709\) | −28.8670 | −1.08412 | −0.542061 | − | 0.840339i | \(-0.682356\pi\) | ||||
−0.542061 | + | 0.840339i | \(0.682356\pi\) | |||||||
\(710\) | 0.189530 | 0.00711293 | ||||||||
\(711\) | 24.6529 | 0.924556 | ||||||||
\(712\) | 2.95236 | 0.110645 | ||||||||
\(713\) | 7.72931 | 0.289465 | ||||||||
\(714\) | −19.7561 | −0.739353 | ||||||||
\(715\) | −0.336545 | −0.0125861 | ||||||||
\(716\) | −7.22728 | −0.270096 | ||||||||
\(717\) | 57.4201 | 2.14439 | ||||||||
\(718\) | −1.52429 | −0.0568860 | ||||||||
\(719\) | 9.34232 | 0.348410 | 0.174205 | − | 0.984709i | \(-0.444264\pi\) | ||||
0.174205 | + | 0.984709i | \(0.444264\pi\) | |||||||
\(720\) | 0.239303 | 0.00891831 | ||||||||
\(721\) | 0.776460 | 0.0289169 | ||||||||
\(722\) | 44.0084 | 1.63782 | ||||||||
\(723\) | −40.6526 | −1.51189 | ||||||||
\(724\) | 3.01609 | 0.112092 | ||||||||
\(725\) | −12.7976 | −0.475289 | ||||||||
\(726\) | 7.21567 | 0.267799 | ||||||||
\(727\) | −3.57659 | −0.132649 | −0.0663243 | − | 0.997798i | \(-0.521127\pi\) | ||||
−0.0663243 | + | 0.997798i | \(0.521127\pi\) | |||||||
\(728\) | −2.02601 | −0.0750890 | ||||||||
\(729\) | −31.5454 | −1.16835 | ||||||||
\(730\) | 1.06110 | 0.0392730 | ||||||||
\(731\) | −40.1489 | −1.48496 | ||||||||
\(732\) | −23.5532 | −0.870550 | ||||||||
\(733\) | 22.2760 | 0.822784 | 0.411392 | − | 0.911459i | \(-0.365043\pi\) | ||||
0.411392 | + | 0.911459i | \(0.365043\pi\) | |||||||
\(734\) | −28.7275 | −1.06035 | ||||||||
\(735\) | 0.994250 | 0.0366735 | ||||||||
\(736\) | −3.36070 | −0.123877 | ||||||||
\(737\) | −35.7486 | −1.31682 | ||||||||
\(738\) | −17.3671 | −0.639291 | ||||||||
\(739\) | −20.8011 | −0.765180 | −0.382590 | − | 0.923918i | \(-0.624968\pi\) | ||||
−0.382590 | + | 0.923918i | \(0.624968\pi\) | |||||||
\(740\) | 0.354417 | 0.0130286 | ||||||||
\(741\) | −32.0244 | −1.17645 | ||||||||
\(742\) | 13.5519 | 0.497507 | ||||||||
\(743\) | 37.3805 | 1.37136 | 0.685678 | − | 0.727905i | \(-0.259506\pi\) | ||||
0.685678 | + | 0.727905i | \(0.259506\pi\) | |||||||
\(744\) | 5.75681 | 0.211055 | ||||||||
\(745\) | −0.851232 | −0.0311867 | ||||||||
\(746\) | −7.34260 | −0.268832 | ||||||||
\(747\) | −11.7582 | −0.430210 | ||||||||
\(748\) | 17.8898 | 0.654114 | ||||||||
\(749\) | −21.6520 | −0.791146 | ||||||||
\(750\) | 1.83343 | 0.0669474 | ||||||||
\(751\) | −20.7970 | −0.758893 | −0.379446 | − | 0.925214i | \(-0.623885\pi\) | ||||
−0.379446 | + | 0.925214i | \(0.623885\pi\) | |||||||
\(752\) | 2.78599 | 0.101595 | ||||||||
\(753\) | −21.9416 | −0.799598 | ||||||||
\(754\) | 4.12986 | 0.150400 | ||||||||
\(755\) | 1.00739 | 0.0366627 | ||||||||
\(756\) | 0.834679 | 0.0303570 | ||||||||
\(757\) | −34.7018 | −1.26126 | −0.630629 | − | 0.776085i | \(-0.717203\pi\) | ||||
−0.630629 | + | 0.776085i | \(0.717203\pi\) | |||||||
\(758\) | −13.9457 | −0.506530 | ||||||||
\(759\) | −23.9665 | −0.869928 | ||||||||
\(760\) | 0.581737 | 0.0211018 | ||||||||
\(761\) | 40.3675 | 1.46332 | 0.731660 | − | 0.681670i | \(-0.238746\pi\) | ||||
0.731660 | + | 0.681670i | \(0.238746\pi\) | |||||||
\(762\) | −11.9160 | −0.431669 | ||||||||
\(763\) | −11.0687 | −0.400712 | ||||||||
\(764\) | 10.6334 | 0.384703 | ||||||||
\(765\) | −1.50262 | −0.0543273 | ||||||||
\(766\) | −6.06270 | −0.219054 | ||||||||
\(767\) | −12.7221 | −0.459367 | ||||||||
\(768\) | −2.50306 | −0.0903212 | ||||||||
\(769\) | 45.9918 | 1.65851 | 0.829253 | − | 0.558873i | \(-0.188766\pi\) | ||||
0.829253 | + | 0.558873i | \(0.188766\pi\) | |||||||
\(770\) | 0.262460 | 0.00945840 | ||||||||
\(771\) | −11.6690 | −0.420250 | ||||||||
\(772\) | −1.43622 | −0.0516905 | ||||||||
\(773\) | 30.8849 | 1.11085 | 0.555426 | − | 0.831566i | \(-0.312555\pi\) | ||||
0.555426 | + | 0.831566i | \(0.312555\pi\) | |||||||
\(774\) | 20.8783 | 0.750455 | ||||||||
\(775\) | 11.4872 | 0.412633 | ||||||||
\(776\) | 1.08941 | 0.0391076 | ||||||||
\(777\) | 15.2156 | 0.545856 | ||||||||
\(778\) | 30.2018 | 1.08279 | ||||||||
\(779\) | −42.2187 | −1.51264 | ||||||||
\(780\) | −0.295671 | −0.0105867 | ||||||||
\(781\) | −7.36809 | −0.263651 | ||||||||
\(782\) | 21.1023 | 0.754615 | ||||||||
\(783\) | −1.70142 | −0.0608039 | ||||||||
\(784\) | −5.41998 | −0.193571 | ||||||||
\(785\) | 1.24003 | 0.0442585 | ||||||||
\(786\) | −30.3115 | −1.08117 | ||||||||
\(787\) | −1.28596 | −0.0458397 | −0.0229198 | − | 0.999737i | \(-0.507296\pi\) | ||||
−0.0229198 | + | 0.999737i | \(0.507296\pi\) | |||||||
\(788\) | 2.72603 | 0.0971108 | ||||||||
\(789\) | 9.72733 | 0.346302 | ||||||||
\(790\) | 0.553317 | 0.0196861 | ||||||||
\(791\) | −5.30728 | −0.188705 | ||||||||
\(792\) | −9.30307 | −0.330570 | ||||||||
\(793\) | 15.1667 | 0.538584 | ||||||||
\(794\) | −17.9251 | −0.636138 | ||||||||
\(795\) | 1.97773 | 0.0701430 | ||||||||
\(796\) | 7.68601 | 0.272423 | ||||||||
\(797\) | 35.7631 | 1.26680 | 0.633398 | − | 0.773827i | \(-0.281660\pi\) | ||||
0.633398 | + | 0.773827i | \(0.281660\pi\) | |||||||
\(798\) | 24.9747 | 0.884095 | ||||||||
\(799\) | −17.4936 | −0.618880 | ||||||||
\(800\) | −4.99463 | −0.176587 | ||||||||
\(801\) | 9.64032 | 0.340624 | ||||||||
\(802\) | −26.5773 | −0.938476 | ||||||||
\(803\) | −41.2509 | −1.45571 | ||||||||
\(804\) | −31.4069 | −1.10763 | ||||||||
\(805\) | 0.309590 | 0.0109116 | ||||||||
\(806\) | −3.70700 | −0.130573 | ||||||||
\(807\) | −30.4281 | −1.07112 | ||||||||
\(808\) | −11.4845 | −0.404025 | ||||||||
\(809\) | −42.2133 | −1.48414 | −0.742070 | − | 0.670323i | \(-0.766156\pi\) | ||||
−0.742070 | + | 0.670323i | \(0.766156\pi\) | |||||||
\(810\) | −0.596099 | −0.0209448 | ||||||||
\(811\) | 31.1810 | 1.09491 | 0.547456 | − | 0.836835i | \(-0.315596\pi\) | ||||
0.547456 | + | 0.836835i | \(0.315596\pi\) | |||||||
\(812\) | −3.22073 | −0.113026 | ||||||||
\(813\) | −11.3386 | −0.397663 | ||||||||
\(814\) | −13.7782 | −0.482924 | ||||||||
\(815\) | 0.337220 | 0.0118123 | ||||||||
\(816\) | 15.7170 | 0.550206 | ||||||||
\(817\) | 50.7543 | 1.77567 | ||||||||
\(818\) | −3.04631 | −0.106512 | ||||||||
\(819\) | −6.61551 | −0.231165 | ||||||||
\(820\) | −0.389792 | −0.0136121 | ||||||||
\(821\) | −41.4792 | −1.44764 | −0.723818 | − | 0.689991i | \(-0.757614\pi\) | ||||
−0.723818 | + | 0.689991i | \(0.757614\pi\) | |||||||
\(822\) | −28.2310 | −0.984668 | ||||||||
\(823\) | −11.6353 | −0.405581 | −0.202790 | − | 0.979222i | \(-0.565001\pi\) | ||||
−0.202790 | + | 0.979222i | \(0.565001\pi\) | |||||||
\(824\) | −0.617715 | −0.0215191 | ||||||||
\(825\) | −35.6187 | −1.24008 | ||||||||
\(826\) | 9.92149 | 0.345213 | ||||||||
\(827\) | −10.3859 | −0.361154 | −0.180577 | − | 0.983561i | \(-0.557797\pi\) | ||||
−0.180577 | + | 0.983561i | \(0.557797\pi\) | |||||||
\(828\) | −10.9736 | −0.381360 | ||||||||
\(829\) | 30.3121 | 1.05278 | 0.526391 | − | 0.850242i | \(-0.323545\pi\) | ||||
0.526391 | + | 0.850242i | \(0.323545\pi\) | |||||||
\(830\) | −0.263904 | −0.00916026 | ||||||||
\(831\) | −1.75424 | −0.0608540 | ||||||||
\(832\) | 1.61180 | 0.0558791 | ||||||||
\(833\) | 34.0328 | 1.17917 | ||||||||
\(834\) | 41.1269 | 1.42411 | ||||||||
\(835\) | 1.65460 | 0.0572599 | ||||||||
\(836\) | −22.6154 | −0.782169 | ||||||||
\(837\) | 1.52721 | 0.0527882 | ||||||||
\(838\) | 16.8127 | 0.580784 | ||||||||
\(839\) | 32.2012 | 1.11171 | 0.555854 | − | 0.831280i | \(-0.312391\pi\) | ||||
0.555854 | + | 0.831280i | \(0.312391\pi\) | |||||||
\(840\) | 0.230584 | 0.00795590 | ||||||||
\(841\) | −22.4348 | −0.773614 | ||||||||
\(842\) | −40.3056 | −1.38902 | ||||||||
\(843\) | 27.5428 | 0.948624 | ||||||||
\(844\) | 13.3045 | 0.457959 | ||||||||
\(845\) | −0.762339 | −0.0262253 | ||||||||
\(846\) | 9.09707 | 0.312764 | ||||||||
\(847\) | 3.62357 | 0.124507 | ||||||||
\(848\) | −10.7813 | −0.370231 | ||||||||
\(849\) | −47.4157 | −1.62730 | ||||||||
\(850\) | 31.3619 | 1.07571 | ||||||||
\(851\) | −16.2523 | −0.557123 | ||||||||
\(852\) | −6.47323 | −0.221769 | ||||||||
\(853\) | −27.4465 | −0.939749 | −0.469874 | − | 0.882733i | \(-0.655701\pi\) | ||||
−0.469874 | + | 0.882733i | \(0.655701\pi\) | |||||||
\(854\) | −11.8280 | −0.404744 | ||||||||
\(855\) | 1.89954 | 0.0649628 | ||||||||
\(856\) | 17.2253 | 0.588748 | ||||||||
\(857\) | 11.0342 | 0.376922 | 0.188461 | − | 0.982081i | \(-0.439650\pi\) | ||||
0.188461 | + | 0.982081i | \(0.439650\pi\) | |||||||
\(858\) | 11.4944 | 0.392412 | ||||||||
\(859\) | −41.5261 | −1.41685 | −0.708426 | − | 0.705785i | \(-0.750595\pi\) | ||||
−0.708426 | + | 0.705785i | \(0.750595\pi\) | |||||||
\(860\) | 0.468598 | 0.0159791 | ||||||||
\(861\) | −16.7343 | −0.570303 | ||||||||
\(862\) | 16.8867 | 0.575164 | ||||||||
\(863\) | −4.04033 | −0.137535 | −0.0687673 | − | 0.997633i | \(-0.521907\pi\) | ||||
−0.0687673 | + | 0.997633i | \(0.521907\pi\) | |||||||
\(864\) | −0.664031 | −0.0225908 | ||||||||
\(865\) | −0.0548550 | −0.00186513 | ||||||||
\(866\) | −1.01520 | −0.0344978 | ||||||||
\(867\) | −56.1373 | −1.90652 | ||||||||
\(868\) | 2.89096 | 0.0981256 | ||||||||
\(869\) | −21.5105 | −0.729695 | ||||||||
\(870\) | −0.470026 | −0.0159354 | ||||||||
\(871\) | 20.2239 | 0.685261 | ||||||||
\(872\) | 8.80570 | 0.298199 | ||||||||
\(873\) | 3.55725 | 0.120395 | ||||||||
\(874\) | −26.6765 | −0.902345 | ||||||||
\(875\) | 0.920714 | 0.0311258 | ||||||||
\(876\) | −36.2409 | −1.22447 | ||||||||
\(877\) | −34.6942 | −1.17154 | −0.585770 | − | 0.810477i | \(-0.699208\pi\) | ||||
−0.585770 | + | 0.810477i | \(0.699208\pi\) | |||||||
\(878\) | 29.8989 | 1.00904 | ||||||||
\(879\) | −37.2711 | −1.25712 | ||||||||
\(880\) | −0.208801 | −0.00703867 | ||||||||
\(881\) | 38.5988 | 1.30043 | 0.650213 | − | 0.759752i | \(-0.274679\pi\) | ||||
0.650213 | + | 0.759752i | \(0.274679\pi\) | |||||||
\(882\) | −17.6978 | −0.595916 | ||||||||
\(883\) | −33.9606 | −1.14287 | −0.571433 | − | 0.820649i | \(-0.693612\pi\) | ||||
−0.571433 | + | 0.820649i | \(0.693612\pi\) | |||||||
\(884\) | −10.1207 | −0.340396 | ||||||||
\(885\) | 1.44792 | 0.0486712 | ||||||||
\(886\) | 15.6699 | 0.526441 | ||||||||
\(887\) | −20.7795 | −0.697707 | −0.348853 | − | 0.937177i | \(-0.613429\pi\) | ||||
−0.348853 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(888\) | −12.1048 | −0.406210 | ||||||||
\(889\) | −5.98397 | −0.200696 | ||||||||
\(890\) | 0.216370 | 0.00725274 | ||||||||
\(891\) | 23.1737 | 0.776349 | ||||||||
\(892\) | 5.60413 | 0.187640 | ||||||||
\(893\) | 22.1146 | 0.740037 | ||||||||
\(894\) | 29.0731 | 0.972350 | ||||||||
\(895\) | −0.529666 | −0.0177048 | ||||||||
\(896\) | −1.25699 | −0.0419930 | ||||||||
\(897\) | 13.5585 | 0.452704 | ||||||||
\(898\) | −7.05157 | −0.235314 | ||||||||
\(899\) | −5.89298 | −0.196542 | ||||||||
\(900\) | −16.3089 | −0.543630 | ||||||||
\(901\) | 67.6971 | 2.25532 | ||||||||
\(902\) | 15.1534 | 0.504553 | ||||||||
\(903\) | 20.1175 | 0.669470 | ||||||||
\(904\) | 4.22222 | 0.140429 | ||||||||
\(905\) | 0.221040 | 0.00734762 | ||||||||
\(906\) | −34.4065 | −1.14308 | ||||||||
\(907\) | −14.3691 | −0.477118 | −0.238559 | − | 0.971128i | \(-0.576675\pi\) | ||||
−0.238559 | + | 0.971128i | \(0.576675\pi\) | |||||||
\(908\) | 26.0194 | 0.863483 | ||||||||
\(909\) | −37.5004 | −1.24381 | ||||||||
\(910\) | −0.148480 | −0.00492208 | ||||||||
\(911\) | 5.21961 | 0.172934 | 0.0864668 | − | 0.996255i | \(-0.472442\pi\) | ||||
0.0864668 | + | 0.996255i | \(0.472442\pi\) | |||||||
\(912\) | −19.8687 | −0.657919 | ||||||||
\(913\) | 10.2594 | 0.339538 | ||||||||
\(914\) | −31.4584 | −1.04055 | ||||||||
\(915\) | −1.72614 | −0.0570645 | ||||||||
\(916\) | 19.0513 | 0.629472 | ||||||||
\(917\) | −15.2219 | −0.502670 | ||||||||
\(918\) | 4.16954 | 0.137615 | ||||||||
\(919\) | 29.2774 | 0.965773 | 0.482887 | − | 0.875683i | \(-0.339588\pi\) | ||||
0.482887 | + | 0.875683i | \(0.339588\pi\) | |||||||
\(920\) | −0.246296 | −0.00812012 | ||||||||
\(921\) | −54.9822 | −1.81172 | ||||||||
\(922\) | −10.7377 | −0.353626 | ||||||||
\(923\) | 4.16833 | 0.137202 | ||||||||
\(924\) | −8.96409 | −0.294897 | ||||||||
\(925\) | −24.1541 | −0.794181 | ||||||||
\(926\) | 13.4944 | 0.443454 | ||||||||
\(927\) | −2.01702 | −0.0662475 | ||||||||
\(928\) | 2.56226 | 0.0841104 | ||||||||
\(929\) | 20.6112 | 0.676230 | 0.338115 | − | 0.941105i | \(-0.390211\pi\) | ||||
0.338115 | + | 0.941105i | \(0.390211\pi\) | |||||||
\(930\) | 0.421900 | 0.0138346 | ||||||||
\(931\) | −43.0226 | −1.41001 | ||||||||
\(932\) | 5.11960 | 0.167698 | ||||||||
\(933\) | 1.97709 | 0.0647269 | ||||||||
\(934\) | −10.4824 | −0.342995 | ||||||||
\(935\) | 1.31109 | 0.0428771 | ||||||||
\(936\) | 5.26299 | 0.172026 | ||||||||
\(937\) | −29.3351 | −0.958337 | −0.479169 | − | 0.877723i | \(-0.659062\pi\) | ||||
−0.479169 | + | 0.877723i | \(0.659062\pi\) | |||||||
\(938\) | −15.7719 | −0.514972 | ||||||||
\(939\) | 19.3013 | 0.629874 | ||||||||
\(940\) | 0.204177 | 0.00665953 | ||||||||
\(941\) | −30.5178 | −0.994853 | −0.497426 | − | 0.867506i | \(-0.665722\pi\) | ||||
−0.497426 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(942\) | −42.3521 | −1.37991 | ||||||||
\(943\) | 17.8745 | 0.582075 | ||||||||
\(944\) | −7.89307 | −0.256898 | ||||||||
\(945\) | 0.0611712 | 0.00198990 | ||||||||
\(946\) | −18.2171 | −0.592287 | ||||||||
\(947\) | −44.7324 | −1.45361 | −0.726805 | − | 0.686844i | \(-0.758995\pi\) | ||||
−0.726805 | + | 0.686844i | \(0.758995\pi\) | |||||||
\(948\) | −18.8981 | −0.613780 | ||||||||
\(949\) | 23.3367 | 0.757542 | ||||||||
\(950\) | −39.6463 | −1.28629 | ||||||||
\(951\) | −21.1719 | −0.686547 | ||||||||
\(952\) | 7.89279 | 0.255807 | ||||||||
\(953\) | 30.2784 | 0.980813 | 0.490406 | − | 0.871494i | \(-0.336848\pi\) | ||||
0.490406 | + | 0.871494i | \(0.336848\pi\) | |||||||
\(954\) | −35.2040 | −1.13977 | ||||||||
\(955\) | 0.779290 | 0.0252172 | ||||||||
\(956\) | −22.9400 | −0.741932 | ||||||||
\(957\) | 18.2725 | 0.590667 | ||||||||
\(958\) | 33.1021 | 1.06948 | ||||||||
\(959\) | −14.1771 | −0.457801 | ||||||||
\(960\) | −0.183442 | −0.00592055 | ||||||||
\(961\) | −25.7104 | −0.829368 | ||||||||
\(962\) | 7.79468 | 0.251310 | ||||||||
\(963\) | 56.2456 | 1.81249 | ||||||||
\(964\) | 16.2412 | 0.523093 | ||||||||
\(965\) | −0.105256 | −0.00338831 | ||||||||
\(966\) | −10.5738 | −0.340206 | ||||||||
\(967\) | −50.2270 | −1.61519 | −0.807596 | − | 0.589737i | \(-0.799232\pi\) | ||||
−0.807596 | + | 0.589737i | \(0.799232\pi\) | |||||||
\(968\) | −2.88275 | −0.0926549 | ||||||||
\(969\) | 124.758 | 4.00781 | ||||||||
\(970\) | 0.0798398 | 0.00256350 | ||||||||
\(971\) | 29.1281 | 0.934766 | 0.467383 | − | 0.884055i | \(-0.345197\pi\) | ||||
0.467383 | + | 0.884055i | \(0.345197\pi\) | |||||||
\(972\) | 22.3513 | 0.716920 | ||||||||
\(973\) | 20.6532 | 0.662110 | ||||||||
\(974\) | 17.3503 | 0.555940 | ||||||||
\(975\) | 20.1505 | 0.645331 | ||||||||
\(976\) | 9.40976 | 0.301199 | ||||||||
\(977\) | −47.1583 | −1.50873 | −0.754363 | − | 0.656457i | \(-0.772054\pi\) | ||||
−0.754363 | + | 0.656457i | \(0.772054\pi\) | |||||||
\(978\) | −11.5175 | −0.368288 | ||||||||
\(979\) | −8.41152 | −0.268833 | ||||||||
\(980\) | −0.397215 | −0.0126886 | ||||||||
\(981\) | 28.7532 | 0.918018 | ||||||||
\(982\) | −32.5188 | −1.03772 | ||||||||
\(983\) | −18.0619 | −0.576086 | −0.288043 | − | 0.957618i | \(-0.593005\pi\) | ||||
−0.288043 | + | 0.957618i | \(0.593005\pi\) | |||||||
\(984\) | 13.3130 | 0.424403 | ||||||||
\(985\) | 0.199783 | 0.00636561 | ||||||||
\(986\) | −16.0888 | −0.512372 | ||||||||
\(987\) | 8.76559 | 0.279012 | ||||||||
\(988\) | 12.7941 | 0.407035 | ||||||||
\(989\) | −21.4883 | −0.683289 | ||||||||
\(990\) | −0.681794 | −0.0216688 | ||||||||
\(991\) | −1.35471 | −0.0430337 | −0.0215169 | − | 0.999768i | \(-0.506850\pi\) | ||||
−0.0215169 | + | 0.999768i | \(0.506850\pi\) | |||||||
\(992\) | −2.29991 | −0.0730223 | ||||||||
\(993\) | 31.6912 | 1.00569 | ||||||||
\(994\) | −3.25073 | −0.103107 | ||||||||
\(995\) | 0.563285 | 0.0178573 | ||||||||
\(996\) | 9.01343 | 0.285601 | ||||||||
\(997\) | 56.2921 | 1.78279 | 0.891395 | − | 0.453227i | \(-0.149727\pi\) | ||||
0.891395 | + | 0.453227i | \(0.149727\pi\) | |||||||
\(998\) | −36.3677 | −1.15120 | ||||||||
\(999\) | −3.21126 | −0.101600 |
(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 | 4022.2.a.f.1.6 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.f.1.6 | ✓ | 50 | 1.1 | even | 1 | trivial |