Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96796 | −1.39156 | −0.695780 | − | 0.718255i | \(-0.744941\pi\) | ||||
−0.695780 | + | 0.718255i | \(0.744941\pi\) | |||||||
\(3\) | −0.967508 | −0.558591 | −0.279295 | − | 0.960205i | \(-0.590101\pi\) | ||||
−0.279295 | + | 0.960205i | \(0.590101\pi\) | |||||||
\(4\) | 1.87288 | 0.936439 | ||||||||
\(5\) | 0.188751 | 0.0844121 | 0.0422060 | − | 0.999109i | \(-0.486561\pi\) | ||||
0.0422060 | + | 0.999109i | \(0.486561\pi\) | |||||||
\(6\) | 1.90402 | 0.777313 | ||||||||
\(7\) | −4.91446 | −1.85749 | −0.928745 | − | 0.370720i | \(-0.879111\pi\) | ||||
−0.928745 | + | 0.370720i | \(0.879111\pi\) | |||||||
\(8\) | 0.250172 | 0.0884493 | ||||||||
\(9\) | −2.06393 | −0.687976 | ||||||||
\(10\) | −0.371455 | −0.117464 | ||||||||
\(11\) | −1.60871 | −0.485045 | −0.242522 | − | 0.970146i | \(-0.577975\pi\) | ||||
−0.242522 | + | 0.970146i | \(0.577975\pi\) | |||||||
\(12\) | −1.81202 | −0.523086 | ||||||||
\(13\) | 3.63672 | 1.00864 | 0.504322 | − | 0.863515i | \(-0.331742\pi\) | ||||
0.504322 | + | 0.863515i | \(0.331742\pi\) | |||||||
\(14\) | 9.67146 | 2.58481 | ||||||||
\(15\) | −0.182618 | −0.0471518 | ||||||||
\(16\) | −4.23808 | −1.05952 | ||||||||
\(17\) | 3.34454 | 0.811171 | 0.405585 | − | 0.914057i | \(-0.367068\pi\) | ||||
0.405585 | + | 0.914057i | \(0.367068\pi\) | |||||||
\(18\) | 4.06173 | 0.957360 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.353508 | 0.0790467 | ||||||||
\(21\) | 4.75477 | 1.03758 | ||||||||
\(22\) | 3.16589 | 0.674969 | ||||||||
\(23\) | 2.14601 | 0.447474 | 0.223737 | − | 0.974650i | \(-0.428174\pi\) | ||||
0.223737 | + | 0.974650i | \(0.428174\pi\) | |||||||
\(24\) | −0.242044 | −0.0494070 | ||||||||
\(25\) | −4.96437 | −0.992875 | ||||||||
\(26\) | −7.15693 | −1.40359 | ||||||||
\(27\) | 4.89939 | 0.942888 | ||||||||
\(28\) | −9.20417 | −1.73943 | ||||||||
\(29\) | −3.45241 | −0.641097 | −0.320549 | − | 0.947232i | \(-0.603867\pi\) | ||||
−0.320549 | + | 0.947232i | \(0.603867\pi\) | |||||||
\(30\) | 0.359386 | 0.0656146 | ||||||||
\(31\) | 3.44285 | 0.618354 | 0.309177 | − | 0.951005i | \(-0.399946\pi\) | ||||
0.309177 | + | 0.951005i | \(0.399946\pi\) | |||||||
\(32\) | 7.84005 | 1.38594 | ||||||||
\(33\) | 1.55644 | 0.270942 | ||||||||
\(34\) | −6.58193 | −1.12879 | ||||||||
\(35\) | −0.927609 | −0.156795 | ||||||||
\(36\) | −3.86548 | −0.644247 | ||||||||
\(37\) | −5.13774 | −0.844639 | −0.422319 | − | 0.906447i | \(-0.638784\pi\) | ||||
−0.422319 | + | 0.906447i | \(0.638784\pi\) | |||||||
\(38\) | 1.96796 | 0.319246 | ||||||||
\(39\) | −3.51856 | −0.563420 | ||||||||
\(40\) | 0.0472203 | 0.00746619 | ||||||||
\(41\) | −11.7806 | −1.83983 | −0.919914 | − | 0.392121i | \(-0.871741\pi\) | ||||
−0.919914 | + | 0.392121i | \(0.871741\pi\) | |||||||
\(42\) | −9.35722 | −1.44385 | ||||||||
\(43\) | −3.74167 | −0.570600 | −0.285300 | − | 0.958438i | \(-0.592093\pi\) | ||||
−0.285300 | + | 0.958438i | \(0.592093\pi\) | |||||||
\(44\) | −3.01292 | −0.454215 | ||||||||
\(45\) | −0.389569 | −0.0580735 | ||||||||
\(46\) | −4.22327 | −0.622687 | ||||||||
\(47\) | 5.82681 | 0.849928 | 0.424964 | − | 0.905210i | \(-0.360287\pi\) | ||||
0.424964 | + | 0.905210i | \(0.360287\pi\) | |||||||
\(48\) | 4.10038 | 0.591839 | ||||||||
\(49\) | 17.1519 | 2.45027 | ||||||||
\(50\) | 9.76970 | 1.38164 | ||||||||
\(51\) | −3.23587 | −0.453113 | ||||||||
\(52\) | 6.81113 | 0.944534 | ||||||||
\(53\) | −10.8588 | −1.49157 | −0.745785 | − | 0.666186i | \(-0.767926\pi\) | ||||
−0.745785 | + | 0.666186i | \(0.767926\pi\) | |||||||
\(54\) | −9.64182 | −1.31209 | ||||||||
\(55\) | −0.303646 | −0.0409436 | ||||||||
\(56\) | −1.22946 | −0.164294 | ||||||||
\(57\) | 0.967508 | 0.128150 | ||||||||
\(58\) | 6.79422 | 0.892125 | ||||||||
\(59\) | 5.17048 | 0.673139 | 0.336569 | − | 0.941659i | \(-0.390733\pi\) | ||||
0.336569 | + | 0.941659i | \(0.390733\pi\) | |||||||
\(60\) | −0.342022 | −0.0441548 | ||||||||
\(61\) | 9.16826 | 1.17387 | 0.586937 | − | 0.809632i | \(-0.300333\pi\) | ||||
0.586937 | + | 0.809632i | \(0.300333\pi\) | |||||||
\(62\) | −6.77540 | −0.860477 | ||||||||
\(63\) | 10.1431 | 1.27791 | ||||||||
\(64\) | −6.95275 | −0.869094 | ||||||||
\(65\) | 0.686435 | 0.0851418 | ||||||||
\(66\) | −3.06302 | −0.377032 | ||||||||
\(67\) | 13.8922 | 1.69720 | 0.848601 | − | 0.529034i | \(-0.177445\pi\) | ||||
0.848601 | + | 0.529034i | \(0.177445\pi\) | |||||||
\(68\) | 6.26392 | 0.759612 | ||||||||
\(69\) | −2.07628 | −0.249955 | ||||||||
\(70\) | 1.82550 | 0.218189 | ||||||||
\(71\) | −7.81496 | −0.927465 | −0.463733 | − | 0.885975i | \(-0.653490\pi\) | ||||
−0.463733 | + | 0.885975i | \(0.653490\pi\) | |||||||
\(72\) | −0.516338 | −0.0608510 | ||||||||
\(73\) | 7.15869 | 0.837861 | 0.418931 | − | 0.908018i | \(-0.362405\pi\) | ||||
0.418931 | + | 0.908018i | \(0.362405\pi\) | |||||||
\(74\) | 10.1109 | 1.17537 | ||||||||
\(75\) | 4.80307 | 0.554611 | ||||||||
\(76\) | −1.87288 | −0.214834 | ||||||||
\(77\) | 7.90594 | 0.900966 | ||||||||
\(78\) | 6.92439 | 0.784032 | ||||||||
\(79\) | 14.7823 | 1.66314 | 0.831571 | − | 0.555419i | \(-0.187442\pi\) | ||||
0.831571 | + | 0.555419i | \(0.187442\pi\) | |||||||
\(80\) | −0.799943 | −0.0894364 | ||||||||
\(81\) | 1.45159 | 0.161287 | ||||||||
\(82\) | 23.1839 | 2.56023 | ||||||||
\(83\) | 8.05904 | 0.884595 | 0.442297 | − | 0.896868i | \(-0.354164\pi\) | ||||
0.442297 | + | 0.896868i | \(0.354164\pi\) | |||||||
\(84\) | 8.90511 | 0.971627 | ||||||||
\(85\) | 0.631286 | 0.0684726 | ||||||||
\(86\) | 7.36348 | 0.794024 | ||||||||
\(87\) | 3.34024 | 0.358111 | ||||||||
\(88\) | −0.402456 | −0.0429019 | ||||||||
\(89\) | 0.0958099 | 0.0101558 | 0.00507792 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507792 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(90\) | 0.766657 | 0.0808127 | ||||||||
\(91\) | −17.8725 | −1.87355 | ||||||||
\(92\) | 4.01921 | 0.419032 | ||||||||
\(93\) | −3.33098 | −0.345407 | ||||||||
\(94\) | −11.4670 | −1.18273 | ||||||||
\(95\) | −0.188751 | −0.0193655 | ||||||||
\(96\) | −7.58531 | −0.774172 | ||||||||
\(97\) | −3.34440 | −0.339572 | −0.169786 | − | 0.985481i | \(-0.554308\pi\) | ||||
−0.169786 | + | 0.985481i | \(0.554308\pi\) | |||||||
\(98\) | −33.7542 | −3.40969 | ||||||||
\(99\) | 3.32027 | 0.333699 | ||||||||
\(100\) | −9.29766 | −0.929766 | ||||||||
\(101\) | −5.26784 | −0.524170 | −0.262085 | − | 0.965045i | \(-0.584410\pi\) | ||||
−0.262085 | + | 0.965045i | \(0.584410\pi\) | |||||||
\(102\) | 6.36807 | 0.630533 | ||||||||
\(103\) | 1.78581 | 0.175961 | 0.0879805 | − | 0.996122i | \(-0.471959\pi\) | ||||
0.0879805 | + | 0.996122i | \(0.471959\pi\) | |||||||
\(104\) | 0.909807 | 0.0892139 | ||||||||
\(105\) | 0.897469 | 0.0875840 | ||||||||
\(106\) | 21.3697 | 2.07561 | ||||||||
\(107\) | −11.9476 | −1.15502 | −0.577508 | − | 0.816385i | \(-0.695975\pi\) | ||||
−0.577508 | + | 0.816385i | \(0.695975\pi\) | |||||||
\(108\) | 9.17596 | 0.882957 | ||||||||
\(109\) | 10.7995 | 1.03441 | 0.517204 | − | 0.855862i | \(-0.326973\pi\) | ||||
0.517204 | + | 0.855862i | \(0.326973\pi\) | |||||||
\(110\) | 0.597564 | 0.0569755 | ||||||||
\(111\) | 4.97080 | 0.471808 | ||||||||
\(112\) | 20.8279 | 1.96805 | ||||||||
\(113\) | 18.0149 | 1.69470 | 0.847350 | − | 0.531034i | \(-0.178197\pi\) | ||||
0.847350 | + | 0.531034i | \(0.178197\pi\) | |||||||
\(114\) | −1.90402 | −0.178328 | ||||||||
\(115\) | 0.405062 | 0.0377722 | ||||||||
\(116\) | −6.46595 | −0.600348 | ||||||||
\(117\) | −7.50593 | −0.693923 | ||||||||
\(118\) | −10.1753 | −0.936713 | ||||||||
\(119\) | −16.4366 | −1.50674 | ||||||||
\(120\) | −0.0456861 | −0.00417055 | ||||||||
\(121\) | −8.41205 | −0.764731 | ||||||||
\(122\) | −18.0428 | −1.63352 | ||||||||
\(123\) | 11.3979 | 1.02771 | ||||||||
\(124\) | 6.44803 | 0.579051 | ||||||||
\(125\) | −1.88079 | −0.168223 | ||||||||
\(126\) | −19.9612 | −1.77829 | ||||||||
\(127\) | −14.8043 | −1.31367 | −0.656836 | − | 0.754033i | \(-0.728106\pi\) | ||||
−0.656836 | + | 0.754033i | \(0.728106\pi\) | |||||||
\(128\) | −1.99734 | −0.176541 | ||||||||
\(129\) | 3.62010 | 0.318732 | ||||||||
\(130\) | −1.35088 | −0.118480 | ||||||||
\(131\) | 10.0720 | 0.879996 | 0.439998 | − | 0.897999i | \(-0.354979\pi\) | ||||
0.439998 | + | 0.897999i | \(0.354979\pi\) | |||||||
\(132\) | 2.91502 | 0.253720 | ||||||||
\(133\) | 4.91446 | 0.426137 | ||||||||
\(134\) | −27.3393 | −2.36176 | ||||||||
\(135\) | 0.924765 | 0.0795911 | ||||||||
\(136\) | 0.836712 | 0.0717475 | ||||||||
\(137\) | 10.9503 | 0.935543 | 0.467772 | − | 0.883849i | \(-0.345057\pi\) | ||||
0.467772 | + | 0.883849i | \(0.345057\pi\) | |||||||
\(138\) | 4.08604 | 0.347827 | ||||||||
\(139\) | 14.7580 | 1.25175 | 0.625877 | − | 0.779922i | \(-0.284741\pi\) | ||||
0.625877 | + | 0.779922i | \(0.284741\pi\) | |||||||
\(140\) | −1.73730 | −0.146828 | ||||||||
\(141\) | −5.63749 | −0.474762 | ||||||||
\(142\) | 15.3796 | 1.29062 | ||||||||
\(143\) | −5.85044 | −0.489238 | ||||||||
\(144\) | 8.74710 | 0.728925 | ||||||||
\(145\) | −0.651647 | −0.0541163 | ||||||||
\(146\) | −14.0880 | −1.16593 | ||||||||
\(147\) | −16.5946 | −1.36870 | ||||||||
\(148\) | −9.62235 | −0.790952 | ||||||||
\(149\) | 14.6769 | 1.20238 | 0.601188 | − | 0.799108i | \(-0.294694\pi\) | ||||
0.601188 | + | 0.799108i | \(0.294694\pi\) | |||||||
\(150\) | −9.45226 | −0.771774 | ||||||||
\(151\) | −9.88759 | −0.804641 | −0.402320 | − | 0.915499i | \(-0.631796\pi\) | ||||
−0.402320 | + | 0.915499i | \(0.631796\pi\) | |||||||
\(152\) | −0.250172 | −0.0202917 | ||||||||
\(153\) | −6.90290 | −0.558066 | ||||||||
\(154\) | −15.5586 | −1.25375 | ||||||||
\(155\) | 0.649842 | 0.0521965 | ||||||||
\(156\) | −6.58982 | −0.527608 | ||||||||
\(157\) | −6.72897 | −0.537030 | −0.268515 | − | 0.963275i | \(-0.586533\pi\) | ||||
−0.268515 | + | 0.963275i | \(0.586533\pi\) | |||||||
\(158\) | −29.0911 | −2.31436 | ||||||||
\(159\) | 10.5060 | 0.833178 | ||||||||
\(160\) | 1.47982 | 0.116990 | ||||||||
\(161\) | −10.5465 | −0.831178 | ||||||||
\(162\) | −2.85667 | −0.224441 | ||||||||
\(163\) | −5.75158 | −0.450498 | −0.225249 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225249 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(164\) | −22.0637 | −1.72289 | ||||||||
\(165\) | 0.293780 | 0.0228708 | ||||||||
\(166\) | −15.8599 | −1.23097 | ||||||||
\(167\) | 0.849574 | 0.0657420 | 0.0328710 | − | 0.999460i | \(-0.489535\pi\) | ||||
0.0328710 | + | 0.999460i | \(0.489535\pi\) | |||||||
\(168\) | 1.18951 | 0.0917730 | ||||||||
\(169\) | 0.225734 | 0.0173641 | ||||||||
\(170\) | −1.24235 | −0.0952837 | ||||||||
\(171\) | 2.06393 | 0.157833 | ||||||||
\(172\) | −7.00770 | −0.534332 | ||||||||
\(173\) | 14.2419 | 1.08279 | 0.541395 | − | 0.840768i | \(-0.317896\pi\) | ||||
0.541395 | + | 0.840768i | \(0.317896\pi\) | |||||||
\(174\) | −6.57347 | −0.498333 | ||||||||
\(175\) | 24.3972 | 1.84425 | ||||||||
\(176\) | 6.81786 | 0.513915 | ||||||||
\(177\) | −5.00248 | −0.376009 | ||||||||
\(178\) | −0.188550 | −0.0141324 | ||||||||
\(179\) | 8.03224 | 0.600358 | 0.300179 | − | 0.953883i | \(-0.402954\pi\) | ||||
0.300179 | + | 0.953883i | \(0.402954\pi\) | |||||||
\(180\) | −0.729615 | −0.0543823 | ||||||||
\(181\) | 2.09618 | 0.155808 | 0.0779040 | − | 0.996961i | \(-0.475177\pi\) | ||||
0.0779040 | + | 0.996961i | \(0.475177\pi\) | |||||||
\(182\) | 35.1724 | 2.60715 | ||||||||
\(183\) | −8.87036 | −0.655716 | ||||||||
\(184\) | 0.536872 | 0.0395788 | ||||||||
\(185\) | −0.969754 | −0.0712977 | ||||||||
\(186\) | 6.55525 | 0.480654 | ||||||||
\(187\) | −5.38041 | −0.393454 | ||||||||
\(188\) | 10.9129 | 0.795906 | ||||||||
\(189\) | −24.0778 | −1.75140 | ||||||||
\(190\) | 0.371455 | 0.0269482 | ||||||||
\(191\) | −1.76351 | −0.127603 | −0.0638014 | − | 0.997963i | \(-0.520322\pi\) | ||||
−0.0638014 | + | 0.997963i | \(0.520322\pi\) | |||||||
\(192\) | 6.72684 | 0.485468 | ||||||||
\(193\) | −0.887799 | −0.0639052 | −0.0319526 | − | 0.999489i | \(-0.510173\pi\) | ||||
−0.0319526 | + | 0.999489i | \(0.510173\pi\) | |||||||
\(194\) | 6.58166 | 0.472535 | ||||||||
\(195\) | −0.664131 | −0.0475594 | ||||||||
\(196\) | 32.1233 | 2.29452 | ||||||||
\(197\) | 14.4349 | 1.02844 | 0.514221 | − | 0.857658i | \(-0.328081\pi\) | ||||
0.514221 | + | 0.857658i | \(0.328081\pi\) | |||||||
\(198\) | −6.53416 | −0.464363 | ||||||||
\(199\) | 0.796173 | 0.0564392 | 0.0282196 | − | 0.999602i | \(-0.491016\pi\) | ||||
0.0282196 | + | 0.999602i | \(0.491016\pi\) | |||||||
\(200\) | −1.24195 | −0.0878191 | ||||||||
\(201\) | −13.4408 | −0.948042 | ||||||||
\(202\) | 10.3669 | 0.729414 | ||||||||
\(203\) | 16.9667 | 1.19083 | ||||||||
\(204\) | −6.06039 | −0.424312 | ||||||||
\(205\) | −2.22361 | −0.155304 | ||||||||
\(206\) | −3.51441 | −0.244860 | ||||||||
\(207\) | −4.42921 | −0.307851 | ||||||||
\(208\) | −15.4127 | −1.06868 | ||||||||
\(209\) | 1.60871 | 0.111277 | ||||||||
\(210\) | −1.76619 | −0.121878 | ||||||||
\(211\) | 4.91514 | 0.338372 | 0.169186 | − | 0.985584i | \(-0.445886\pi\) | ||||
0.169186 | + | 0.985584i | \(0.445886\pi\) | |||||||
\(212\) | −20.3372 | −1.39676 | ||||||||
\(213\) | 7.56104 | 0.518074 | ||||||||
\(214\) | 23.5124 | 1.60727 | ||||||||
\(215\) | −0.706245 | −0.0481655 | ||||||||
\(216\) | 1.22569 | 0.0833978 | ||||||||
\(217\) | −16.9197 | −1.14859 | ||||||||
\(218\) | −21.2531 | −1.43944 | ||||||||
\(219\) | −6.92609 | −0.468022 | ||||||||
\(220\) | −0.568692 | −0.0383412 | ||||||||
\(221\) | 12.1632 | 0.818183 | ||||||||
\(222\) | −9.78235 | −0.656548 | ||||||||
\(223\) | 11.1315 | 0.745424 | 0.372712 | − | 0.927947i | \(-0.378428\pi\) | ||||
0.372712 | + | 0.927947i | \(0.378428\pi\) | |||||||
\(224\) | −38.5296 | −2.57436 | ||||||||
\(225\) | 10.2461 | 0.683074 | ||||||||
\(226\) | −35.4527 | −2.35828 | ||||||||
\(227\) | −22.8786 | −1.51851 | −0.759253 | − | 0.650796i | \(-0.774435\pi\) | ||||
−0.759253 | + | 0.650796i | \(0.774435\pi\) | |||||||
\(228\) | 1.81202 | 0.120004 | ||||||||
\(229\) | −23.5220 | −1.55438 | −0.777189 | − | 0.629267i | \(-0.783355\pi\) | ||||
−0.777189 | + | 0.629267i | \(0.783355\pi\) | |||||||
\(230\) | −0.797146 | −0.0525623 | ||||||||
\(231\) | −7.64906 | −0.503271 | ||||||||
\(232\) | −0.863699 | −0.0567046 | ||||||||
\(233\) | −10.1296 | −0.663613 | −0.331806 | − | 0.943347i | \(-0.607658\pi\) | ||||
−0.331806 | + | 0.943347i | \(0.607658\pi\) | |||||||
\(234\) | 14.7714 | 0.965636 | ||||||||
\(235\) | 1.09982 | 0.0717442 | ||||||||
\(236\) | 9.68367 | 0.630353 | ||||||||
\(237\) | −14.3020 | −0.929016 | ||||||||
\(238\) | 32.3466 | 2.09672 | ||||||||
\(239\) | −4.49190 | −0.290557 | −0.145278 | − | 0.989391i | \(-0.546408\pi\) | ||||
−0.145278 | + | 0.989391i | \(0.546408\pi\) | |||||||
\(240\) | 0.773951 | 0.0499584 | ||||||||
\(241\) | −6.25584 | −0.402974 | −0.201487 | − | 0.979491i | \(-0.564577\pi\) | ||||
−0.201487 | + | 0.979491i | \(0.564577\pi\) | |||||||
\(242\) | 16.5546 | 1.06417 | ||||||||
\(243\) | −16.1026 | −1.03298 | ||||||||
\(244\) | 17.1710 | 1.09926 | ||||||||
\(245\) | 3.23743 | 0.206832 | ||||||||
\(246\) | −22.4306 | −1.43012 | ||||||||
\(247\) | −3.63672 | −0.231399 | ||||||||
\(248\) | 0.861306 | 0.0546930 | ||||||||
\(249\) | −7.79719 | −0.494127 | ||||||||
\(250\) | 3.70132 | 0.234092 | ||||||||
\(251\) | −7.32121 | −0.462111 | −0.231055 | − | 0.972941i | \(-0.574218\pi\) | ||||
−0.231055 | + | 0.972941i | \(0.574218\pi\) | |||||||
\(252\) | 18.9968 | 1.19668 | ||||||||
\(253\) | −3.45231 | −0.217045 | ||||||||
\(254\) | 29.1344 | 1.82805 | ||||||||
\(255\) | −0.610774 | −0.0382482 | ||||||||
\(256\) | 17.8362 | 1.11476 | ||||||||
\(257\) | −17.8582 | −1.11396 | −0.556981 | − | 0.830525i | \(-0.688040\pi\) | ||||
−0.556981 | + | 0.830525i | \(0.688040\pi\) | |||||||
\(258\) | −7.12422 | −0.443535 | ||||||||
\(259\) | 25.2492 | 1.56891 | ||||||||
\(260\) | 1.28561 | 0.0797301 | ||||||||
\(261\) | 7.12554 | 0.441060 | ||||||||
\(262\) | −19.8213 | −1.22457 | ||||||||
\(263\) | 11.6234 | 0.716728 | 0.358364 | − | 0.933582i | \(-0.383335\pi\) | ||||
0.358364 | + | 0.933582i | \(0.383335\pi\) | |||||||
\(264\) | 0.389379 | 0.0239646 | ||||||||
\(265\) | −2.04961 | −0.125907 | ||||||||
\(266\) | −9.67146 | −0.592996 | ||||||||
\(267\) | −0.0926969 | −0.00567296 | ||||||||
\(268\) | 26.0184 | 1.58933 | ||||||||
\(269\) | 21.0073 | 1.28084 | 0.640419 | − | 0.768025i | \(-0.278761\pi\) | ||||
0.640419 | + | 0.768025i | \(0.278761\pi\) | |||||||
\(270\) | −1.81990 | −0.110756 | ||||||||
\(271\) | −3.97821 | −0.241659 | −0.120830 | − | 0.992673i | \(-0.538555\pi\) | ||||
−0.120830 | + | 0.992673i | \(0.538555\pi\) | |||||||
\(272\) | −14.1745 | −0.859453 | ||||||||
\(273\) | 17.2918 | 1.04655 | ||||||||
\(274\) | −21.5497 | −1.30186 | ||||||||
\(275\) | 7.98625 | 0.481589 | ||||||||
\(276\) | −3.88862 | −0.234067 | ||||||||
\(277\) | −5.35621 | −0.321824 | −0.160912 | − | 0.986969i | \(-0.551443\pi\) | ||||
−0.160912 | + | 0.986969i | \(0.551443\pi\) | |||||||
\(278\) | −29.0431 | −1.74189 | ||||||||
\(279\) | −7.10579 | −0.425413 | ||||||||
\(280\) | −0.232062 | −0.0138684 | ||||||||
\(281\) | 17.6593 | 1.05346 | 0.526732 | − | 0.850032i | \(-0.323417\pi\) | ||||
0.526732 | + | 0.850032i | \(0.323417\pi\) | |||||||
\(282\) | 11.0944 | 0.660660 | ||||||||
\(283\) | −3.63125 | −0.215856 | −0.107928 | − | 0.994159i | \(-0.534422\pi\) | ||||
−0.107928 | + | 0.994159i | \(0.534422\pi\) | |||||||
\(284\) | −14.6365 | −0.868514 | ||||||||
\(285\) | 0.182618 | 0.0108174 | ||||||||
\(286\) | 11.5134 | 0.680804 | ||||||||
\(287\) | 57.8954 | 3.41746 | ||||||||
\(288\) | −16.1813 | −0.953492 | ||||||||
\(289\) | −5.81404 | −0.342002 | ||||||||
\(290\) | 1.28242 | 0.0753061 | ||||||||
\(291\) | 3.23573 | 0.189682 | ||||||||
\(292\) | 13.4073 | 0.784606 | ||||||||
\(293\) | −7.40251 | −0.432459 | −0.216230 | − | 0.976343i | \(-0.569376\pi\) | ||||
−0.216230 | + | 0.976343i | \(0.569376\pi\) | |||||||
\(294\) | 32.6575 | 1.90462 | ||||||||
\(295\) | 0.975933 | 0.0568210 | ||||||||
\(296\) | −1.28532 | −0.0747077 | ||||||||
\(297\) | −7.88171 | −0.457343 | ||||||||
\(298\) | −28.8835 | −1.67318 | ||||||||
\(299\) | 7.80443 | 0.451342 | ||||||||
\(300\) | 8.99556 | 0.519359 | ||||||||
\(301\) | 18.3883 | 1.05988 | ||||||||
\(302\) | 19.4584 | 1.11971 | ||||||||
\(303\) | 5.09668 | 0.292797 | ||||||||
\(304\) | 4.23808 | 0.243071 | ||||||||
\(305\) | 1.73052 | 0.0990892 | ||||||||
\(306\) | 13.5846 | 0.776582 | ||||||||
\(307\) | −13.0501 | −0.744807 | −0.372404 | − | 0.928071i | \(-0.621466\pi\) | ||||
−0.372404 | + | 0.928071i | \(0.621466\pi\) | |||||||
\(308\) | 14.8069 | 0.843699 | ||||||||
\(309\) | −1.72778 | −0.0982902 | ||||||||
\(310\) | −1.27886 | −0.0726346 | ||||||||
\(311\) | 33.5659 | 1.90335 | 0.951673 | − | 0.307113i | \(-0.0993629\pi\) | ||||
0.951673 | + | 0.307113i | \(0.0993629\pi\) | |||||||
\(312\) | −0.880246 | −0.0498341 | ||||||||
\(313\) | −19.6588 | −1.11118 | −0.555592 | − | 0.831455i | \(-0.687508\pi\) | ||||
−0.555592 | + | 0.831455i | \(0.687508\pi\) | |||||||
\(314\) | 13.2424 | 0.747310 | ||||||||
\(315\) | 1.91452 | 0.107871 | ||||||||
\(316\) | 27.6855 | 1.55743 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | −20.6754 | −1.15942 | ||||||||
\(319\) | 5.55394 | 0.310961 | ||||||||
\(320\) | −1.31234 | −0.0733620 | ||||||||
\(321\) | 11.5594 | 0.645182 | ||||||||
\(322\) | 20.7550 | 1.15663 | ||||||||
\(323\) | −3.34454 | −0.186095 | ||||||||
\(324\) | 2.71864 | 0.151036 | ||||||||
\(325\) | −18.0540 | −1.00146 | ||||||||
\(326\) | 11.3189 | 0.626895 | ||||||||
\(327\) | −10.4486 | −0.577811 | ||||||||
\(328\) | −2.94719 | −0.162731 | ||||||||
\(329\) | −28.6356 | −1.57873 | ||||||||
\(330\) | −0.578148 | −0.0318260 | ||||||||
\(331\) | 27.0196 | 1.48513 | 0.742565 | − | 0.669774i | \(-0.233609\pi\) | ||||
0.742565 | + | 0.669774i | \(0.233609\pi\) | |||||||
\(332\) | 15.0936 | 0.828369 | ||||||||
\(333\) | 10.6039 | 0.581091 | ||||||||
\(334\) | −1.67193 | −0.0914840 | ||||||||
\(335\) | 2.62217 | 0.143264 | ||||||||
\(336\) | −20.1511 | −1.09933 | ||||||||
\(337\) | −6.55603 | −0.357130 | −0.178565 | − | 0.983928i | \(-0.557145\pi\) | ||||
−0.178565 | + | 0.983928i | \(0.557145\pi\) | |||||||
\(338\) | −0.444235 | −0.0241632 | ||||||||
\(339\) | −17.4296 | −0.946644 | ||||||||
\(340\) | 1.18232 | 0.0641204 | ||||||||
\(341\) | −5.53855 | −0.299929 | ||||||||
\(342\) | −4.06173 | −0.219633 | ||||||||
\(343\) | −49.8909 | −2.69386 | ||||||||
\(344\) | −0.936064 | −0.0504692 | ||||||||
\(345\) | −0.391900 | −0.0210992 | ||||||||
\(346\) | −28.0275 | −1.50677 | ||||||||
\(347\) | −16.5458 | −0.888227 | −0.444113 | − | 0.895971i | \(-0.646481\pi\) | ||||
−0.444113 | + | 0.895971i | \(0.646481\pi\) | |||||||
\(348\) | 6.25586 | 0.335349 | ||||||||
\(349\) | −35.4680 | −1.89856 | −0.949279 | − | 0.314436i | \(-0.898184\pi\) | ||||
−0.949279 | + | 0.314436i | \(0.898184\pi\) | |||||||
\(350\) | −48.0128 | −2.56639 | ||||||||
\(351\) | 17.8177 | 0.951039 | ||||||||
\(352\) | −12.6124 | −0.672242 | ||||||||
\(353\) | −5.82385 | −0.309973 | −0.154986 | − | 0.987917i | \(-0.549533\pi\) | ||||
−0.154986 | + | 0.987917i | \(0.549533\pi\) | |||||||
\(354\) | 9.84469 | 0.523239 | ||||||||
\(355\) | −1.47508 | −0.0782893 | ||||||||
\(356\) | 0.179440 | 0.00951031 | ||||||||
\(357\) | 15.9025 | 0.841652 | ||||||||
\(358\) | −15.8071 | −0.835434 | ||||||||
\(359\) | 23.3455 | 1.23213 | 0.616063 | − | 0.787697i | \(-0.288727\pi\) | ||||
0.616063 | + | 0.787697i | \(0.288727\pi\) | |||||||
\(360\) | −0.0974594 | −0.00513656 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −4.12521 | −0.216816 | ||||||||
\(363\) | 8.13872 | 0.427172 | ||||||||
\(364\) | −33.4730 | −1.75446 | ||||||||
\(365\) | 1.35121 | 0.0707256 | ||||||||
\(366\) | 17.4565 | 0.912468 | ||||||||
\(367\) | −0.883059 | −0.0460953 | −0.0230477 | − | 0.999734i | \(-0.507337\pi\) | ||||
−0.0230477 | + | 0.999734i | \(0.507337\pi\) | |||||||
\(368\) | −9.09497 | −0.474108 | ||||||||
\(369\) | 24.3144 | 1.26576 | ||||||||
\(370\) | 1.90844 | 0.0992150 | ||||||||
\(371\) | 53.3651 | 2.77058 | ||||||||
\(372\) | −6.23852 | −0.323452 | ||||||||
\(373\) | 5.06087 | 0.262042 | 0.131021 | − | 0.991380i | \(-0.458174\pi\) | ||||
0.131021 | + | 0.991380i | \(0.458174\pi\) | |||||||
\(374\) | 10.5884 | 0.547515 | ||||||||
\(375\) | 1.81968 | 0.0939677 | ||||||||
\(376\) | 1.45771 | 0.0751756 | ||||||||
\(377\) | −12.5555 | −0.646639 | ||||||||
\(378\) | 47.3843 | 2.43718 | ||||||||
\(379\) | 2.77259 | 0.142418 | 0.0712092 | − | 0.997461i | \(-0.477314\pi\) | ||||
0.0712092 | + | 0.997461i | \(0.477314\pi\) | |||||||
\(380\) | −0.353508 | −0.0181346 | ||||||||
\(381\) | 14.3233 | 0.733806 | ||||||||
\(382\) | 3.47051 | 0.177567 | ||||||||
\(383\) | 10.3211 | 0.527382 | 0.263691 | − | 0.964607i | \(-0.415060\pi\) | ||||
0.263691 | + | 0.964607i | \(0.415060\pi\) | |||||||
\(384\) | 1.93244 | 0.0986144 | ||||||||
\(385\) | 1.49226 | 0.0760524 | ||||||||
\(386\) | 1.74716 | 0.0889279 | ||||||||
\(387\) | 7.72255 | 0.392559 | ||||||||
\(388\) | −6.26365 | −0.317989 | ||||||||
\(389\) | −10.0931 | −0.511740 | −0.255870 | − | 0.966711i | \(-0.582362\pi\) | ||||
−0.255870 | + | 0.966711i | \(0.582362\pi\) | |||||||
\(390\) | 1.30699 | 0.0661818 | ||||||||
\(391\) | 7.17742 | 0.362978 | ||||||||
\(392\) | 4.29093 | 0.216724 | ||||||||
\(393\) | −9.74475 | −0.491558 | ||||||||
\(394\) | −28.4073 | −1.43114 | ||||||||
\(395\) | 2.79018 | 0.140389 | ||||||||
\(396\) | 6.21845 | 0.312489 | ||||||||
\(397\) | 4.21868 | 0.211729 | 0.105865 | − | 0.994381i | \(-0.466239\pi\) | ||||
0.105865 | + | 0.994381i | \(0.466239\pi\) | |||||||
\(398\) | −1.56684 | −0.0785385 | ||||||||
\(399\) | −4.75477 | −0.238036 | ||||||||
\(400\) | 21.0394 | 1.05197 | ||||||||
\(401\) | −22.5470 | −1.12594 | −0.562971 | − | 0.826477i | \(-0.690342\pi\) | ||||
−0.562971 | + | 0.826477i | \(0.690342\pi\) | |||||||
\(402\) | 26.4510 | 1.31926 | ||||||||
\(403\) | 12.5207 | 0.623699 | ||||||||
\(404\) | −9.86603 | −0.490853 | ||||||||
\(405\) | 0.273988 | 0.0136146 | ||||||||
\(406\) | −33.3899 | −1.65711 | ||||||||
\(407\) | 8.26514 | 0.409688 | ||||||||
\(408\) | −0.809526 | −0.0400775 | ||||||||
\(409\) | 28.8575 | 1.42691 | 0.713456 | − | 0.700700i | \(-0.247129\pi\) | ||||
0.713456 | + | 0.700700i | \(0.247129\pi\) | |||||||
\(410\) | 4.37598 | 0.216114 | ||||||||
\(411\) | −10.5945 | −0.522586 | ||||||||
\(412\) | 3.34460 | 0.164777 | ||||||||
\(413\) | −25.4101 | −1.25035 | ||||||||
\(414\) | 8.71652 | 0.428393 | ||||||||
\(415\) | 1.52115 | 0.0746705 | ||||||||
\(416\) | 28.5121 | 1.39792 | ||||||||
\(417\) | −14.2784 | −0.699218 | ||||||||
\(418\) | −3.16589 | −0.154849 | ||||||||
\(419\) | −1.85598 | −0.0906707 | −0.0453354 | − | 0.998972i | \(-0.514436\pi\) | ||||
−0.0453354 | + | 0.998972i | \(0.514436\pi\) | |||||||
\(420\) | 1.68085 | 0.0820171 | ||||||||
\(421\) | −27.4874 | −1.33965 | −0.669827 | − | 0.742517i | \(-0.733632\pi\) | ||||
−0.669827 | + | 0.742517i | \(0.733632\pi\) | |||||||
\(422\) | −9.67282 | −0.470865 | ||||||||
\(423\) | −12.0261 | −0.584730 | ||||||||
\(424\) | −2.71657 | −0.131928 | ||||||||
\(425\) | −16.6036 | −0.805391 | ||||||||
\(426\) | −14.8798 | −0.720931 | ||||||||
\(427\) | −45.0570 | −2.18046 | ||||||||
\(428\) | −22.3764 | −1.08160 | ||||||||
\(429\) | 5.66034 | 0.273284 | ||||||||
\(430\) | 1.38986 | 0.0670252 | ||||||||
\(431\) | −12.9904 | −0.625727 | −0.312863 | − | 0.949798i | \(-0.601288\pi\) | ||||
−0.312863 | + | 0.949798i | \(0.601288\pi\) | |||||||
\(432\) | −20.7640 | −0.999010 | ||||||||
\(433\) | −11.7942 | −0.566793 | −0.283397 | − | 0.959003i | \(-0.591461\pi\) | ||||
−0.283397 | + | 0.959003i | \(0.591461\pi\) | |||||||
\(434\) | 33.2974 | 1.59833 | ||||||||
\(435\) | 0.630474 | 0.0302289 | ||||||||
\(436\) | 20.2262 | 0.968659 | ||||||||
\(437\) | −2.14601 | −0.102658 | ||||||||
\(438\) | 13.6303 | 0.651280 | ||||||||
\(439\) | −6.60344 | −0.315165 | −0.157582 | − | 0.987506i | \(-0.550370\pi\) | ||||
−0.157582 | + | 0.987506i | \(0.550370\pi\) | |||||||
\(440\) | −0.0759639 | −0.00362144 | ||||||||
\(441\) | −35.4002 | −1.68573 | ||||||||
\(442\) | −23.9367 | −1.13855 | ||||||||
\(443\) | −3.92798 | −0.186624 | −0.0933120 | − | 0.995637i | \(-0.529745\pi\) | ||||
−0.0933120 | + | 0.995637i | \(0.529745\pi\) | |||||||
\(444\) | 9.30970 | 0.441819 | ||||||||
\(445\) | 0.0180842 | 0.000857275 0 | ||||||||
\(446\) | −21.9065 | −1.03730 | ||||||||
\(447\) | −14.2000 | −0.671637 | ||||||||
\(448\) | 34.1690 | 1.61433 | ||||||||
\(449\) | −13.5326 | −0.638644 | −0.319322 | − | 0.947646i | \(-0.603455\pi\) | ||||
−0.319322 | + | 0.947646i | \(0.603455\pi\) | |||||||
\(450\) | −20.1640 | −0.950538 | ||||||||
\(451\) | 18.9517 | 0.892399 | ||||||||
\(452\) | 33.7397 | 1.58698 | ||||||||
\(453\) | 9.56632 | 0.449465 | ||||||||
\(454\) | 45.0242 | 2.11309 | ||||||||
\(455\) | −3.37345 | −0.158150 | ||||||||
\(456\) | 0.242044 | 0.0113347 | ||||||||
\(457\) | 7.58845 | 0.354973 | 0.177486 | − | 0.984123i | \(-0.443203\pi\) | ||||
0.177486 | + | 0.984123i | \(0.443203\pi\) | |||||||
\(458\) | 46.2905 | 2.16301 | ||||||||
\(459\) | 16.3862 | 0.764843 | ||||||||
\(460\) | 0.758631 | 0.0353713 | ||||||||
\(461\) | −5.04183 | −0.234822 | −0.117411 | − | 0.993083i | \(-0.537459\pi\) | ||||
−0.117411 | + | 0.993083i | \(0.537459\pi\) | |||||||
\(462\) | 15.0531 | 0.700332 | ||||||||
\(463\) | 10.1341 | 0.470970 | 0.235485 | − | 0.971878i | \(-0.424332\pi\) | ||||
0.235485 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(464\) | 14.6316 | 0.679256 | ||||||||
\(465\) | −0.628727 | −0.0291565 | ||||||||
\(466\) | 19.9347 | 0.923457 | ||||||||
\(467\) | 22.4356 | 1.03820 | 0.519098 | − | 0.854715i | \(-0.326268\pi\) | ||||
0.519098 | + | 0.854715i | \(0.326268\pi\) | |||||||
\(468\) | −14.0577 | −0.649817 | ||||||||
\(469\) | −68.2726 | −3.15253 | ||||||||
\(470\) | −2.16440 | −0.0998363 | ||||||||
\(471\) | 6.51033 | 0.299980 | ||||||||
\(472\) | 1.29351 | 0.0595387 | ||||||||
\(473\) | 6.01928 | 0.276767 | ||||||||
\(474\) | 28.1458 | 1.29278 | ||||||||
\(475\) | 4.96437 | 0.227781 | ||||||||
\(476\) | −30.7837 | −1.41097 | ||||||||
\(477\) | 22.4118 | 1.02617 | ||||||||
\(478\) | 8.83990 | 0.404327 | ||||||||
\(479\) | −15.6650 | −0.715752 | −0.357876 | − | 0.933769i | \(-0.616499\pi\) | ||||
−0.357876 | + | 0.933769i | \(0.616499\pi\) | |||||||
\(480\) | −1.43174 | −0.0653495 | ||||||||
\(481\) | −18.6845 | −0.851940 | ||||||||
\(482\) | 12.3113 | 0.560762 | ||||||||
\(483\) | 10.2038 | 0.464288 | ||||||||
\(484\) | −15.7547 | −0.716124 | ||||||||
\(485\) | −0.631259 | −0.0286640 | ||||||||
\(486\) | 31.6893 | 1.43746 | ||||||||
\(487\) | 29.6945 | 1.34559 | 0.672793 | − | 0.739831i | \(-0.265094\pi\) | ||||
0.672793 | + | 0.739831i | \(0.265094\pi\) | |||||||
\(488\) | 2.29365 | 0.103828 | ||||||||
\(489\) | 5.56470 | 0.251644 | ||||||||
\(490\) | −6.37115 | −0.287819 | ||||||||
\(491\) | −6.71702 | −0.303135 | −0.151567 | − | 0.988447i | \(-0.548432\pi\) | ||||
−0.151567 | + | 0.988447i | \(0.548432\pi\) | |||||||
\(492\) | 21.3468 | 0.962388 | ||||||||
\(493\) | −11.5467 | −0.520039 | ||||||||
\(494\) | 7.15693 | 0.322005 | ||||||||
\(495\) | 0.626704 | 0.0281682 | ||||||||
\(496\) | −14.5911 | −0.655159 | ||||||||
\(497\) | 38.4063 | 1.72276 | ||||||||
\(498\) | 15.3446 | 0.687607 | ||||||||
\(499\) | 27.2615 | 1.22039 | 0.610197 | − | 0.792250i | \(-0.291090\pi\) | ||||
0.610197 | + | 0.792250i | \(0.291090\pi\) | |||||||
\(500\) | −3.52248 | −0.157530 | ||||||||
\(501\) | −0.821970 | −0.0367229 | ||||||||
\(502\) | 14.4079 | 0.643055 | ||||||||
\(503\) | −14.3469 | −0.639698 | −0.319849 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319849 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(504\) | 2.53752 | 0.113030 | ||||||||
\(505\) | −0.994311 | −0.0442463 | ||||||||
\(506\) | 6.79402 | 0.302031 | ||||||||
\(507\) | −0.218399 | −0.00969944 | ||||||||
\(508\) | −27.7267 | −1.23017 | ||||||||
\(509\) | −6.37551 | −0.282590 | −0.141295 | − | 0.989968i | \(-0.545127\pi\) | ||||
−0.141295 | + | 0.989968i | \(0.545127\pi\) | |||||||
\(510\) | 1.20198 | 0.0532246 | ||||||||
\(511\) | −35.1811 | −1.55632 | ||||||||
\(512\) | −31.1063 | −1.37472 | ||||||||
\(513\) | −4.89939 | −0.216313 | ||||||||
\(514\) | 35.1442 | 1.55015 | ||||||||
\(515\) | 0.337073 | 0.0148532 | ||||||||
\(516\) | 6.78000 | 0.298473 | ||||||||
\(517\) | −9.37366 | −0.412253 | ||||||||
\(518\) | −49.6894 | −2.18323 | ||||||||
\(519\) | −13.7791 | −0.604837 | ||||||||
\(520\) | 0.171727 | 0.00753073 | ||||||||
\(521\) | −15.5851 | −0.682796 | −0.341398 | − | 0.939919i | \(-0.610900\pi\) | ||||
−0.341398 | + | 0.939919i | \(0.610900\pi\) | |||||||
\(522\) | −14.0228 | −0.613761 | ||||||||
\(523\) | −26.4795 | −1.15787 | −0.578933 | − | 0.815375i | \(-0.696531\pi\) | ||||
−0.578933 | + | 0.815375i | \(0.696531\pi\) | |||||||
\(524\) | 18.8636 | 0.824062 | ||||||||
\(525\) | −23.6045 | −1.03018 | ||||||||
\(526\) | −22.8744 | −0.997370 | ||||||||
\(527\) | 11.5148 | 0.501591 | ||||||||
\(528\) | −6.59633 | −0.287069 | ||||||||
\(529\) | −18.3946 | −0.799767 | ||||||||
\(530\) | 4.03356 | 0.175207 | ||||||||
\(531\) | −10.6715 | −0.463103 | ||||||||
\(532\) | 9.20417 | 0.399051 | ||||||||
\(533\) | −42.8429 | −1.85573 | ||||||||
\(534\) | 0.182424 | 0.00789426 | ||||||||
\(535\) | −2.25512 | −0.0974973 | ||||||||
\(536\) | 3.47545 | 0.150116 | ||||||||
\(537\) | −7.77125 | −0.335354 | ||||||||
\(538\) | −41.3416 | −1.78236 | ||||||||
\(539\) | −27.5924 | −1.18849 | ||||||||
\(540\) | 1.73197 | 0.0745322 | ||||||||
\(541\) | −9.54249 | −0.410264 | −0.205132 | − | 0.978734i | \(-0.565762\pi\) | ||||
−0.205132 | + | 0.978734i | \(0.565762\pi\) | |||||||
\(542\) | 7.82898 | 0.336283 | ||||||||
\(543\) | −2.02807 | −0.0870329 | ||||||||
\(544\) | 26.2214 | 1.12423 | ||||||||
\(545\) | 2.03842 | 0.0873165 | ||||||||
\(546\) | −34.0296 | −1.45633 | ||||||||
\(547\) | −18.2343 | −0.779641 | −0.389820 | − | 0.920891i | \(-0.627463\pi\) | ||||
−0.389820 | + | 0.920891i | \(0.627463\pi\) | |||||||
\(548\) | 20.5085 | 0.876079 | ||||||||
\(549\) | −18.9226 | −0.807598 | ||||||||
\(550\) | −15.7166 | −0.670160 | ||||||||
\(551\) | 3.45241 | 0.147078 | ||||||||
\(552\) | −0.519428 | −0.0221083 | ||||||||
\(553\) | −72.6471 | −3.08927 | ||||||||
\(554\) | 10.5408 | 0.447837 | ||||||||
\(555\) | 0.938244 | 0.0398263 | ||||||||
\(556\) | 27.6398 | 1.17219 | ||||||||
\(557\) | 6.84967 | 0.290230 | 0.145115 | − | 0.989415i | \(-0.453645\pi\) | ||||
0.145115 | + | 0.989415i | \(0.453645\pi\) | |||||||
\(558\) | 13.9839 | 0.591987 | ||||||||
\(559\) | −13.6074 | −0.575533 | ||||||||
\(560\) | 3.93129 | 0.166127 | ||||||||
\(561\) | 5.20559 | 0.219780 | ||||||||
\(562\) | −34.7528 | −1.46596 | ||||||||
\(563\) | −38.4048 | −1.61857 | −0.809284 | − | 0.587418i | \(-0.800145\pi\) | ||||
−0.809284 | + | 0.587418i | \(0.800145\pi\) | |||||||
\(564\) | −10.5583 | −0.444586 | ||||||||
\(565\) | 3.40033 | 0.143053 | ||||||||
\(566\) | 7.14617 | 0.300376 | ||||||||
\(567\) | −7.13375 | −0.299589 | ||||||||
\(568\) | −1.95509 | −0.0820337 | ||||||||
\(569\) | −4.08204 | −0.171128 | −0.0855639 | − | 0.996333i | \(-0.527269\pi\) | ||||
−0.0855639 | + | 0.996333i | \(0.527269\pi\) | |||||||
\(570\) | −0.359386 | −0.0150530 | ||||||||
\(571\) | −1.39252 | −0.0582752 | −0.0291376 | − | 0.999575i | \(-0.509276\pi\) | ||||
−0.0291376 | + | 0.999575i | \(0.509276\pi\) | |||||||
\(572\) | −10.9571 | −0.458141 | ||||||||
\(573\) | 1.70621 | 0.0712778 | ||||||||
\(574\) | −113.936 | −4.75560 | ||||||||
\(575\) | −10.6536 | −0.444285 | ||||||||
\(576\) | 14.3500 | 0.597916 | ||||||||
\(577\) | −36.8132 | −1.53255 | −0.766277 | − | 0.642511i | \(-0.777893\pi\) | ||||
−0.766277 | + | 0.642511i | \(0.777893\pi\) | |||||||
\(578\) | 11.4418 | 0.475916 | ||||||||
\(579\) | 0.858952 | 0.0356968 | ||||||||
\(580\) | −1.22046 | −0.0506766 | ||||||||
\(581\) | −39.6058 | −1.64313 | ||||||||
\(582\) | −6.36780 | −0.263954 | ||||||||
\(583\) | 17.4687 | 0.723479 | ||||||||
\(584\) | 1.79091 | 0.0741083 | ||||||||
\(585\) | −1.41675 | −0.0585755 | ||||||||
\(586\) | 14.5679 | 0.601793 | ||||||||
\(587\) | 2.29919 | 0.0948978 | 0.0474489 | − | 0.998874i | \(-0.484891\pi\) | ||||
0.0474489 | + | 0.998874i | \(0.484891\pi\) | |||||||
\(588\) | −31.0796 | −1.28170 | ||||||||
\(589\) | −3.44285 | −0.141860 | ||||||||
\(590\) | −1.92060 | −0.0790699 | ||||||||
\(591\) | −13.9658 | −0.574478 | ||||||||
\(592\) | 21.7742 | 0.894913 | ||||||||
\(593\) | 29.5571 | 1.21377 | 0.606883 | − | 0.794791i | \(-0.292420\pi\) | ||||
0.606883 | + | 0.794791i | \(0.292420\pi\) | |||||||
\(594\) | 15.5109 | 0.636420 | ||||||||
\(595\) | −3.10243 | −0.127187 | ||||||||
\(596\) | 27.4880 | 1.12595 | ||||||||
\(597\) | −0.770304 | −0.0315264 | ||||||||
\(598\) | −15.3588 | −0.628069 | ||||||||
\(599\) | −28.0205 | −1.14488 | −0.572442 | − | 0.819945i | \(-0.694004\pi\) | ||||
−0.572442 | + | 0.819945i | \(0.694004\pi\) | |||||||
\(600\) | 1.20160 | 0.0490550 | ||||||||
\(601\) | −30.6197 | −1.24900 | −0.624501 | − | 0.781024i | \(-0.714698\pi\) | ||||
−0.624501 | + | 0.781024i | \(0.714698\pi\) | |||||||
\(602\) | −36.1875 | −1.47489 | ||||||||
\(603\) | −28.6725 | −1.16763 | ||||||||
\(604\) | −18.5182 | −0.753497 | ||||||||
\(605\) | −1.58778 | −0.0645526 | ||||||||
\(606\) | −10.0301 | −0.407444 | ||||||||
\(607\) | −0.931814 | −0.0378212 | −0.0189106 | − | 0.999821i | \(-0.506020\pi\) | ||||
−0.0189106 | + | 0.999821i | \(0.506020\pi\) | |||||||
\(608\) | −7.84005 | −0.317956 | ||||||||
\(609\) | −16.4155 | −0.665188 | ||||||||
\(610\) | −3.40560 | −0.137889 | ||||||||
\(611\) | 21.1905 | 0.857275 | ||||||||
\(612\) | −12.9283 | −0.522595 | ||||||||
\(613\) | −46.0062 | −1.85817 | −0.929086 | − | 0.369864i | \(-0.879404\pi\) | ||||
−0.929086 | + | 0.369864i | \(0.879404\pi\) | |||||||
\(614\) | 25.6821 | 1.03644 | ||||||||
\(615\) | 2.15136 | 0.0867512 | ||||||||
\(616\) | 1.97785 | 0.0796898 | ||||||||
\(617\) | −33.0705 | −1.33137 | −0.665685 | − | 0.746233i | \(-0.731861\pi\) | ||||
−0.665685 | + | 0.746233i | \(0.731861\pi\) | |||||||
\(618\) | 3.40022 | 0.136777 | ||||||||
\(619\) | 9.02535 | 0.362760 | 0.181380 | − | 0.983413i | \(-0.441944\pi\) | ||||
0.181380 | + | 0.983413i | \(0.441944\pi\) | |||||||
\(620\) | 1.21707 | 0.0488789 | ||||||||
\(621\) | 10.5141 | 0.421918 | ||||||||
\(622\) | −66.0564 | −2.64862 | ||||||||
\(623\) | −0.470854 | −0.0188644 | ||||||||
\(624\) | 14.9119 | 0.596955 | ||||||||
\(625\) | 24.4669 | 0.978675 | ||||||||
\(626\) | 38.6879 | 1.54628 | ||||||||
\(627\) | −1.55644 | −0.0621583 | ||||||||
\(628\) | −12.6025 | −0.502896 | ||||||||
\(629\) | −17.1834 | −0.685146 | ||||||||
\(630\) | −3.76770 | −0.150109 | ||||||||
\(631\) | −12.5967 | −0.501465 | −0.250733 | − | 0.968056i | \(-0.580672\pi\) | ||||
−0.250733 | + | 0.968056i | \(0.580672\pi\) | |||||||
\(632\) | 3.69813 | 0.147104 | ||||||||
\(633\) | −4.75544 | −0.189012 | ||||||||
\(634\) | 1.96796 | 0.0781578 | ||||||||
\(635\) | −2.79433 | −0.110890 | ||||||||
\(636\) | 19.6764 | 0.780220 | ||||||||
\(637\) | 62.3765 | 2.47145 | ||||||||
\(638\) | −10.9299 | −0.432721 | ||||||||
\(639\) | 16.1295 | 0.638074 | ||||||||
\(640\) | −0.377000 | −0.0149022 | ||||||||
\(641\) | 47.1585 | 1.86265 | 0.931324 | − | 0.364191i | \(-0.118655\pi\) | ||||
0.931324 | + | 0.364191i | \(0.118655\pi\) | |||||||
\(642\) | −22.7484 | −0.897809 | ||||||||
\(643\) | −43.1064 | −1.69995 | −0.849976 | − | 0.526821i | \(-0.823384\pi\) | ||||
−0.849976 | + | 0.526821i | \(0.823384\pi\) | |||||||
\(644\) | −19.7522 | −0.778347 | ||||||||
\(645\) | 0.683298 | 0.0269048 | ||||||||
\(646\) | 6.58193 | 0.258963 | ||||||||
\(647\) | 46.8352 | 1.84128 | 0.920640 | − | 0.390412i | \(-0.127667\pi\) | ||||
0.920640 | + | 0.390412i | \(0.127667\pi\) | |||||||
\(648\) | 0.363147 | 0.0142657 | ||||||||
\(649\) | −8.31781 | −0.326503 | ||||||||
\(650\) | 35.5297 | 1.39359 | ||||||||
\(651\) | 16.3700 | 0.641590 | ||||||||
\(652\) | −10.7720 | −0.421864 | ||||||||
\(653\) | −24.8394 | −0.972039 | −0.486020 | − | 0.873948i | \(-0.661552\pi\) | ||||
−0.486020 | + | 0.873948i | \(0.661552\pi\) | |||||||
\(654\) | 20.5625 | 0.804058 | ||||||||
\(655\) | 1.90110 | 0.0742823 | ||||||||
\(656\) | 49.9274 | 1.94934 | ||||||||
\(657\) | −14.7750 | −0.576428 | ||||||||
\(658\) | 56.3538 | 2.19690 | ||||||||
\(659\) | 40.5713 | 1.58043 | 0.790217 | − | 0.612827i | \(-0.209968\pi\) | ||||
0.790217 | + | 0.612827i | \(0.209968\pi\) | |||||||
\(660\) | 0.550214 | 0.0214171 | ||||||||
\(661\) | −9.50686 | −0.369774 | −0.184887 | − | 0.982760i | \(-0.559192\pi\) | ||||
−0.184887 | + | 0.982760i | \(0.559192\pi\) | |||||||
\(662\) | −53.1735 | −2.06665 | ||||||||
\(663\) | −11.7680 | −0.457030 | ||||||||
\(664\) | 2.01615 | 0.0782418 | ||||||||
\(665\) | 0.927609 | 0.0359711 | ||||||||
\(666\) | −20.8681 | −0.808623 | ||||||||
\(667\) | −7.40891 | −0.286874 | ||||||||
\(668\) | 1.59115 | 0.0615634 | ||||||||
\(669\) | −10.7699 | −0.416387 | ||||||||
\(670\) | −5.16033 | −0.199361 | ||||||||
\(671\) | −14.7491 | −0.569382 | ||||||||
\(672\) | 37.2777 | 1.43802 | ||||||||
\(673\) | −30.0316 | −1.15763 | −0.578816 | − | 0.815458i | \(-0.696485\pi\) | ||||
−0.578816 | + | 0.815458i | \(0.696485\pi\) | |||||||
\(674\) | 12.9020 | 0.496967 | ||||||||
\(675\) | −24.3224 | −0.936170 | ||||||||
\(676\) | 0.422771 | 0.0162604 | ||||||||
\(677\) | −13.3937 | −0.514761 | −0.257380 | − | 0.966310i | \(-0.582859\pi\) | ||||
−0.257380 | + | 0.966310i | \(0.582859\pi\) | |||||||
\(678\) | 34.3007 | 1.31731 | ||||||||
\(679\) | 16.4359 | 0.630752 | ||||||||
\(680\) | 0.157930 | 0.00605635 | ||||||||
\(681\) | 22.1352 | 0.848224 | ||||||||
\(682\) | 10.8997 | 0.417370 | ||||||||
\(683\) | −2.22871 | −0.0852793 | −0.0426396 | − | 0.999091i | \(-0.513577\pi\) | ||||
−0.0426396 | + | 0.999091i | \(0.513577\pi\) | |||||||
\(684\) | 3.86548 | 0.147801 | ||||||||
\(685\) | 2.06687 | 0.0789711 | ||||||||
\(686\) | 98.1834 | 3.74866 | ||||||||
\(687\) | 22.7577 | 0.868262 | ||||||||
\(688\) | 15.8575 | 0.604563 | ||||||||
\(689\) | −39.4904 | −1.50447 | ||||||||
\(690\) | 0.771245 | 0.0293608 | ||||||||
\(691\) | 25.7189 | 0.978391 | 0.489196 | − | 0.872174i | \(-0.337290\pi\) | ||||
0.489196 | + | 0.872174i | \(0.337290\pi\) | |||||||
\(692\) | 26.6733 | 1.01397 | ||||||||
\(693\) | −16.3173 | −0.619843 | ||||||||
\(694\) | 32.5616 | 1.23602 | ||||||||
\(695\) | 2.78558 | 0.105663 | ||||||||
\(696\) | 0.835636 | 0.0316747 | ||||||||
\(697\) | −39.4009 | −1.49241 | ||||||||
\(698\) | 69.7997 | 2.64196 | ||||||||
\(699\) | 9.80048 | 0.370688 | ||||||||
\(700\) | 45.6929 | 1.72703 | ||||||||
\(701\) | 10.8324 | 0.409135 | 0.204567 | − | 0.978853i | \(-0.434421\pi\) | ||||
0.204567 | + | 0.978853i | \(0.434421\pi\) | |||||||
\(702\) | −35.0646 | −1.32343 | ||||||||
\(703\) | 5.13774 | 0.193773 | ||||||||
\(704\) | 11.1850 | 0.421550 | ||||||||
\(705\) | −1.06408 | −0.0400757 | ||||||||
\(706\) | 11.4611 | 0.431345 | ||||||||
\(707\) | 25.8886 | 0.973640 | ||||||||
\(708\) | −9.36903 | −0.352110 | ||||||||
\(709\) | −7.60880 | −0.285755 | −0.142877 | − | 0.989740i | \(-0.545635\pi\) | ||||
−0.142877 | + | 0.989740i | \(0.545635\pi\) | |||||||
\(710\) | 2.90291 | 0.108944 | ||||||||
\(711\) | −30.5097 | −1.14420 | ||||||||
\(712\) | 0.0239690 | 0.000898277 0 | ||||||||
\(713\) | 7.38838 | 0.276697 | ||||||||
\(714\) | −31.2956 | −1.17121 | ||||||||
\(715\) | −1.10428 | −0.0412976 | ||||||||
\(716\) | 15.0434 | 0.562198 | ||||||||
\(717\) | 4.34595 | 0.162303 | ||||||||
\(718\) | −45.9430 | −1.71458 | ||||||||
\(719\) | −49.0630 | −1.82974 | −0.914870 | − | 0.403749i | \(-0.867707\pi\) | ||||
−0.914870 | + | 0.403749i | \(0.867707\pi\) | |||||||
\(720\) | 1.65103 | 0.0615301 | ||||||||
\(721\) | −8.77628 | −0.326846 | ||||||||
\(722\) | −1.96796 | −0.0732400 | ||||||||
\(723\) | 6.05257 | 0.225098 | ||||||||
\(724\) | 3.92589 | 0.145905 | ||||||||
\(725\) | 17.1391 | 0.636529 | ||||||||
\(726\) | −16.0167 | −0.594435 | ||||||||
\(727\) | −38.6064 | −1.43183 | −0.715915 | − | 0.698187i | \(-0.753990\pi\) | ||||
−0.715915 | + | 0.698187i | \(0.753990\pi\) | |||||||
\(728\) | −4.47121 | −0.165714 | ||||||||
\(729\) | 11.2246 | 0.415727 | ||||||||
\(730\) | −2.65913 | −0.0984189 | ||||||||
\(731\) | −12.5142 | −0.462854 | ||||||||
\(732\) | −16.6131 | −0.614038 | ||||||||
\(733\) | −21.7522 | −0.803436 | −0.401718 | − | 0.915763i | \(-0.631587\pi\) | ||||
−0.401718 | + | 0.915763i | \(0.631587\pi\) | |||||||
\(734\) | 1.73783 | 0.0641444 | ||||||||
\(735\) | −3.13224 | −0.115535 | ||||||||
\(736\) | 16.8248 | 0.620171 | ||||||||
\(737\) | −22.3485 | −0.823219 | ||||||||
\(738\) | −47.8498 | −1.76138 | ||||||||
\(739\) | 10.7551 | 0.395632 | 0.197816 | − | 0.980239i | \(-0.436615\pi\) | ||||
0.197816 | + | 0.980239i | \(0.436615\pi\) | |||||||
\(740\) | −1.81623 | −0.0667659 | ||||||||
\(741\) | 3.51856 | 0.129257 | ||||||||
\(742\) | −105.020 | −3.85542 | ||||||||
\(743\) | 1.46444 | 0.0537253 | 0.0268626 | − | 0.999639i | \(-0.491448\pi\) | ||||
0.0268626 | + | 0.999639i | \(0.491448\pi\) | |||||||
\(744\) | −0.833321 | −0.0305510 | ||||||||
\(745\) | 2.77028 | 0.101495 | ||||||||
\(746\) | −9.95961 | −0.364647 | ||||||||
\(747\) | −16.6333 | −0.608580 | ||||||||
\(748\) | −10.0768 | −0.368446 | ||||||||
\(749\) | 58.7159 | 2.14543 | ||||||||
\(750\) | −3.58105 | −0.130762 | ||||||||
\(751\) | 40.9213 | 1.49324 | 0.746619 | − | 0.665252i | \(-0.231676\pi\) | ||||
0.746619 | + | 0.665252i | \(0.231676\pi\) | |||||||
\(752\) | −24.6945 | −0.900517 | ||||||||
\(753\) | 7.08333 | 0.258131 | ||||||||
\(754\) | 24.7087 | 0.899837 | ||||||||
\(755\) | −1.86629 | −0.0679214 | ||||||||
\(756\) | −45.0948 | −1.64008 | ||||||||
\(757\) | 36.9995 | 1.34477 | 0.672384 | − | 0.740202i | \(-0.265270\pi\) | ||||
0.672384 | + | 0.740202i | \(0.265270\pi\) | |||||||
\(758\) | −5.45635 | −0.198184 | ||||||||
\(759\) | 3.34014 | 0.121239 | ||||||||
\(760\) | −0.0472203 | −0.00171286 | ||||||||
\(761\) | 51.8764 | 1.88052 | 0.940259 | − | 0.340460i | \(-0.110583\pi\) | ||||
0.940259 | + | 0.340460i | \(0.110583\pi\) | |||||||
\(762\) | −28.1877 | −1.02113 | ||||||||
\(763\) | −53.0738 | −1.92140 | ||||||||
\(764\) | −3.30283 | −0.119492 | ||||||||
\(765\) | −1.30293 | −0.0471075 | ||||||||
\(766\) | −20.3115 | −0.733884 | ||||||||
\(767\) | 18.8036 | 0.678958 | ||||||||
\(768\) | −17.2567 | −0.622696 | ||||||||
\(769\) | −33.2617 | −1.19945 | −0.599724 | − | 0.800207i | \(-0.704723\pi\) | ||||
−0.599724 | + | 0.800207i | \(0.704723\pi\) | |||||||
\(770\) | −2.93670 | −0.105831 | ||||||||
\(771\) | 17.2779 | 0.622249 | ||||||||
\(772\) | −1.66274 | −0.0598433 | ||||||||
\(773\) | −19.9933 | −0.719109 | −0.359554 | − | 0.933124i | \(-0.617071\pi\) | ||||
−0.359554 | + | 0.933124i | \(0.617071\pi\) | |||||||
\(774\) | −15.1977 | −0.546270 | ||||||||
\(775\) | −17.0916 | −0.613948 | ||||||||
\(776\) | −0.836677 | −0.0300350 | ||||||||
\(777\) | −24.4288 | −0.876378 | ||||||||
\(778\) | 19.8628 | 0.712117 | ||||||||
\(779\) | 11.7806 | 0.422085 | ||||||||
\(780\) | −1.24384 | −0.0445365 | ||||||||
\(781\) | 12.5720 | 0.449862 | ||||||||
\(782\) | −14.1249 | −0.505105 | ||||||||
\(783\) | −16.9147 | −0.604483 | ||||||||
\(784\) | −72.6911 | −2.59611 | ||||||||
\(785\) | −1.27010 | −0.0453318 | ||||||||
\(786\) | 19.1773 | 0.684032 | ||||||||
\(787\) | 54.5076 | 1.94299 | 0.971493 | − | 0.237066i | \(-0.0761859\pi\) | ||||
0.971493 | + | 0.237066i | \(0.0761859\pi\) | |||||||
\(788\) | 27.0347 | 0.963072 | ||||||||
\(789\) | −11.2457 | −0.400358 | ||||||||
\(790\) | −5.49097 | −0.195360 | ||||||||
\(791\) | −88.5335 | −3.14789 | ||||||||
\(792\) | 0.830639 | 0.0295155 | ||||||||
\(793\) | 33.3424 | 1.18402 | ||||||||
\(794\) | −8.30220 | −0.294634 | ||||||||
\(795\) | 1.98301 | 0.0703303 | ||||||||
\(796\) | 1.49113 | 0.0528519 | ||||||||
\(797\) | −41.5152 | −1.47055 | −0.735273 | − | 0.677772i | \(-0.762946\pi\) | ||||
−0.735273 | + | 0.677772i | \(0.762946\pi\) | |||||||
\(798\) | 9.35722 | 0.331242 | ||||||||
\(799\) | 19.4880 | 0.689437 | ||||||||
\(800\) | −38.9209 | −1.37606 | ||||||||
\(801\) | −0.197745 | −0.00698697 | ||||||||
\(802\) | 44.3716 | 1.56682 | ||||||||
\(803\) | −11.5163 | −0.406400 | ||||||||
\(804\) | −25.1730 | −0.887783 | ||||||||
\(805\) | −1.99066 | −0.0701614 | ||||||||
\(806\) | −24.6402 | −0.867915 | ||||||||
\(807\) | −20.3247 | −0.715465 | ||||||||
\(808\) | −1.31787 | −0.0463625 | ||||||||
\(809\) | 36.3019 | 1.27631 | 0.638154 | − | 0.769909i | \(-0.279698\pi\) | ||||
0.638154 | + | 0.769909i | \(0.279698\pi\) | |||||||
\(810\) | −0.539199 | −0.0189455 | ||||||||
\(811\) | −7.54260 | −0.264856 | −0.132428 | − | 0.991193i | \(-0.542277\pi\) | ||||
−0.132428 | + | 0.991193i | \(0.542277\pi\) | |||||||
\(812\) | 31.7766 | 1.11514 | ||||||||
\(813\) | 3.84895 | 0.134989 | ||||||||
\(814\) | −16.2655 | −0.570105 | ||||||||
\(815\) | −1.08562 | −0.0380275 | ||||||||
\(816\) | 13.7139 | 0.480082 | ||||||||
\(817\) | 3.74167 | 0.130905 | ||||||||
\(818\) | −56.7905 | −1.98563 | ||||||||
\(819\) | 36.8876 | 1.28896 | ||||||||
\(820\) | −4.16455 | −0.145432 | ||||||||
\(821\) | −46.0521 | −1.60723 | −0.803614 | − | 0.595151i | \(-0.797092\pi\) | ||||
−0.803614 | + | 0.595151i | \(0.797092\pi\) | |||||||
\(822\) | 20.8495 | 0.727210 | ||||||||
\(823\) | −23.4774 | −0.818370 | −0.409185 | − | 0.912451i | \(-0.634187\pi\) | ||||
−0.409185 | + | 0.912451i | \(0.634187\pi\) | |||||||
\(824\) | 0.446760 | 0.0155636 | ||||||||
\(825\) | −7.72676 | −0.269011 | ||||||||
\(826\) | 50.0061 | 1.73993 | ||||||||
\(827\) | −5.68901 | −0.197826 | −0.0989132 | − | 0.995096i | \(-0.531537\pi\) | ||||
−0.0989132 | + | 0.995096i | \(0.531537\pi\) | |||||||
\(828\) | −8.29536 | −0.288284 | ||||||||
\(829\) | −0.0641062 | −0.00222650 | −0.00111325 | − | 0.999999i | \(-0.500354\pi\) | ||||
−0.00111325 | + | 0.999999i | \(0.500354\pi\) | |||||||
\(830\) | −2.99357 | −0.103908 | ||||||||
\(831\) | 5.18218 | 0.179768 | ||||||||
\(832\) | −25.2852 | −0.876607 | ||||||||
\(833\) | 57.3652 | 1.98758 | ||||||||
\(834\) | 28.0994 | 0.973004 | ||||||||
\(835\) | 0.160358 | 0.00554942 | ||||||||
\(836\) | 3.01292 | 0.104204 | ||||||||
\(837\) | 16.8679 | 0.583039 | ||||||||
\(838\) | 3.65251 | 0.126174 | ||||||||
\(839\) | −27.8242 | −0.960599 | −0.480300 | − | 0.877104i | \(-0.659472\pi\) | ||||
−0.480300 | + | 0.877104i | \(0.659472\pi\) | |||||||
\(840\) | 0.224522 | 0.00774675 | ||||||||
\(841\) | −17.0808 | −0.588994 | ||||||||
\(842\) | 54.0942 | 1.86421 | ||||||||
\(843\) | −17.0855 | −0.588455 | ||||||||
\(844\) | 9.20546 | 0.316865 | ||||||||
\(845\) | 0.0426075 | 0.00146574 | ||||||||
\(846\) | 23.6670 | 0.813687 | ||||||||
\(847\) | 41.3406 | 1.42048 | ||||||||
\(848\) | 46.0205 | 1.58035 | ||||||||
\(849\) | 3.51327 | 0.120575 | ||||||||
\(850\) | 32.6752 | 1.12075 | ||||||||
\(851\) | −11.0256 | −0.377954 | ||||||||
\(852\) | 14.1609 | 0.485144 | ||||||||
\(853\) | −40.4409 | −1.38467 | −0.692335 | − | 0.721577i | \(-0.743418\pi\) | ||||
−0.692335 | + | 0.721577i | \(0.743418\pi\) | |||||||
\(854\) | 88.6705 | 3.03424 | ||||||||
\(855\) | 0.389569 | 0.0133230 | ||||||||
\(856\) | −2.98896 | −0.102160 | ||||||||
\(857\) | −48.8738 | −1.66950 | −0.834749 | − | 0.550631i | \(-0.814387\pi\) | ||||
−0.834749 | + | 0.550631i | \(0.814387\pi\) | |||||||
\(858\) | −11.1393 | −0.380291 | ||||||||
\(859\) | −9.65359 | −0.329376 | −0.164688 | − | 0.986346i | \(-0.552662\pi\) | ||||
−0.164688 | + | 0.986346i | \(0.552662\pi\) | |||||||
\(860\) | −1.32271 | −0.0451041 | ||||||||
\(861\) | −56.0143 | −1.90896 | ||||||||
\(862\) | 25.5647 | 0.870736 | ||||||||
\(863\) | 50.9009 | 1.73269 | 0.866344 | − | 0.499448i | \(-0.166464\pi\) | ||||
0.866344 | + | 0.499448i | \(0.166464\pi\) | |||||||
\(864\) | 38.4115 | 1.30678 | ||||||||
\(865\) | 2.68817 | 0.0914006 | ||||||||
\(866\) | 23.2105 | 0.788726 | ||||||||
\(867\) | 5.62513 | 0.191039 | ||||||||
\(868\) | −31.6886 | −1.07558 | ||||||||
\(869\) | −23.7805 | −0.806698 | ||||||||
\(870\) | −1.24075 | −0.0420653 | ||||||||
\(871\) | 50.5220 | 1.71187 | ||||||||
\(872\) | 2.70175 | 0.0914927 | ||||||||
\(873\) | 6.90260 | 0.233618 | ||||||||
\(874\) | 4.22327 | 0.142854 | ||||||||
\(875\) | 9.24304 | 0.312472 | ||||||||
\(876\) | −12.9717 | −0.438274 | ||||||||
\(877\) | −33.6231 | −1.13537 | −0.567686 | − | 0.823245i | \(-0.692161\pi\) | ||||
−0.567686 | + | 0.823245i | \(0.692161\pi\) | |||||||
\(878\) | 12.9953 | 0.438571 | ||||||||
\(879\) | 7.16198 | 0.241568 | ||||||||
\(880\) | 1.28688 | 0.0433807 | ||||||||
\(881\) | 3.15075 | 0.106151 | 0.0530757 | − | 0.998590i | \(-0.483098\pi\) | ||||
0.0530757 | + | 0.998590i | \(0.483098\pi\) | |||||||
\(882\) | 69.6663 | 2.34579 | ||||||||
\(883\) | −48.8822 | −1.64502 | −0.822508 | − | 0.568753i | \(-0.807426\pi\) | ||||
−0.822508 | + | 0.568753i | \(0.807426\pi\) | |||||||
\(884\) | 22.7801 | 0.766178 | ||||||||
\(885\) | −0.944223 | −0.0317397 | ||||||||
\(886\) | 7.73012 | 0.259698 | ||||||||
\(887\) | 16.2806 | 0.546648 | 0.273324 | − | 0.961922i | \(-0.411877\pi\) | ||||
0.273324 | + | 0.961922i | \(0.411877\pi\) | |||||||
\(888\) | 1.24356 | 0.0417311 | ||||||||
\(889\) | 72.7552 | 2.44013 | ||||||||
\(890\) | −0.0355891 | −0.00119295 | ||||||||
\(891\) | −2.33518 | −0.0782316 | ||||||||
\(892\) | 20.8480 | 0.698044 | ||||||||
\(893\) | −5.82681 | −0.194987 | ||||||||
\(894\) | 27.9451 | 0.934622 | ||||||||
\(895\) | 1.51609 | 0.0506774 | ||||||||
\(896\) | 9.81582 | 0.327924 | ||||||||
\(897\) | −7.55085 | −0.252116 | ||||||||
\(898\) | 26.6317 | 0.888711 | ||||||||
\(899\) | −11.8861 | −0.396425 | ||||||||
\(900\) | 19.1897 | 0.639657 | ||||||||
\(901\) | −36.3177 | −1.20992 | ||||||||
\(902\) | −37.2962 | −1.24183 | ||||||||
\(903\) | −17.7908 | −0.592041 | ||||||||
\(904\) | 4.50684 | 0.149895 | ||||||||
\(905\) | 0.395657 | 0.0131521 | ||||||||
\(906\) | −18.8262 | −0.625457 | ||||||||
\(907\) | 31.3658 | 1.04148 | 0.520742 | − | 0.853714i | \(-0.325655\pi\) | ||||
0.520742 | + | 0.853714i | \(0.325655\pi\) | |||||||
\(908\) | −42.8488 | −1.42199 | ||||||||
\(909\) | 10.8725 | 0.360616 | ||||||||
\(910\) | 6.63883 | 0.220075 | ||||||||
\(911\) | −3.23866 | −0.107302 | −0.0536509 | − | 0.998560i | \(-0.517086\pi\) | ||||
−0.0536509 | + | 0.998560i | \(0.517086\pi\) | |||||||
\(912\) | −4.10038 | −0.135777 | ||||||||
\(913\) | −12.9647 | −0.429068 | ||||||||
\(914\) | −14.9338 | −0.493965 | ||||||||
\(915\) | −1.67429 | −0.0553503 | ||||||||
\(916\) | −44.0539 | −1.45558 | ||||||||
\(917\) | −49.4985 | −1.63458 | ||||||||
\(918\) | −32.2475 | −1.06433 | ||||||||
\(919\) | 44.9041 | 1.48125 | 0.740625 | − | 0.671918i | \(-0.234529\pi\) | ||||
0.740625 | + | 0.671918i | \(0.234529\pi\) | |||||||
\(920\) | 0.101335 | 0.00334092 | ||||||||
\(921\) | 12.6261 | 0.416043 | ||||||||
\(922\) | 9.92214 | 0.326768 | ||||||||
\(923\) | −28.4208 | −0.935483 | ||||||||
\(924\) | −14.3258 | −0.471283 | ||||||||
\(925\) | 25.5056 | 0.838620 | ||||||||
\(926\) | −19.9435 | −0.655383 | ||||||||
\(927\) | −3.68578 | −0.121057 | ||||||||
\(928\) | −27.0671 | −0.888521 | ||||||||
\(929\) | 43.0558 | 1.41261 | 0.706307 | − | 0.707906i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707906i | \(0.250360\pi\) | |||||||
\(930\) | 1.23731 | 0.0405730 | ||||||||
\(931\) | −17.1519 | −0.562130 | ||||||||
\(932\) | −18.9715 | −0.621433 | ||||||||
\(933\) | −32.4753 | −1.06319 | ||||||||
\(934\) | −44.1524 | −1.44471 | ||||||||
\(935\) | −1.01556 | −0.0332123 | ||||||||
\(936\) | −1.87778 | −0.0613771 | ||||||||
\(937\) | 21.2253 | 0.693399 | 0.346699 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346699 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(938\) | 134.358 | 4.38694 | ||||||||
\(939\) | 19.0201 | 0.620697 | ||||||||
\(940\) | 2.05982 | 0.0671840 | ||||||||
\(941\) | 9.73246 | 0.317269 | 0.158635 | − | 0.987337i | \(-0.449291\pi\) | ||||
0.158635 | + | 0.987337i | \(0.449291\pi\) | |||||||
\(942\) | −12.8121 | −0.417440 | ||||||||
\(943\) | −25.2814 | −0.823274 | ||||||||
\(944\) | −21.9129 | −0.713205 | ||||||||
\(945\) | −4.54472 | −0.147840 | ||||||||
\(946\) | −11.8457 | −0.385137 | ||||||||
\(947\) | −36.0309 | −1.17085 | −0.585423 | − | 0.810728i | \(-0.699071\pi\) | ||||
−0.585423 | + | 0.810728i | \(0.699071\pi\) | |||||||
\(948\) | −26.7859 | −0.869967 | ||||||||
\(949\) | 26.0341 | 0.845104 | ||||||||
\(950\) | −9.76970 | −0.316971 | ||||||||
\(951\) | 0.967508 | 0.0313736 | ||||||||
\(952\) | −4.11199 | −0.133270 | ||||||||
\(953\) | 17.6960 | 0.573228 | 0.286614 | − | 0.958046i | \(-0.407470\pi\) | ||||
0.286614 | + | 0.958046i | \(0.407470\pi\) | |||||||
\(954\) | −44.1056 | −1.42797 | ||||||||
\(955\) | −0.332864 | −0.0107712 | ||||||||
\(956\) | −8.41278 | −0.272089 | ||||||||
\(957\) | −5.37348 | −0.173700 | ||||||||
\(958\) | 30.8281 | 0.996012 | ||||||||
\(959\) | −53.8145 | −1.73776 | ||||||||
\(960\) | 1.26970 | 0.0409794 | ||||||||
\(961\) | −19.1468 | −0.617638 | ||||||||
\(962\) | 36.7704 | 1.18553 | ||||||||
\(963\) | 24.6590 | 0.794624 | ||||||||
\(964\) | −11.7164 | −0.377360 | ||||||||
\(965\) | −0.167573 | −0.00539437 | ||||||||
\(966\) | −20.0807 | −0.646085 | ||||||||
\(967\) | 1.36674 | 0.0439515 | 0.0219757 | − | 0.999759i | \(-0.493004\pi\) | ||||
0.0219757 | + | 0.999759i | \(0.493004\pi\) | |||||||
\(968\) | −2.10446 | −0.0676400 | ||||||||
\(969\) | 3.23587 | 0.103951 | ||||||||
\(970\) | 1.24229 | 0.0398877 | ||||||||
\(971\) | 43.9793 | 1.41136 | 0.705682 | − | 0.708529i | \(-0.250641\pi\) | ||||
0.705682 | + | 0.708529i | \(0.250641\pi\) | |||||||
\(972\) | −30.1582 | −0.967324 | ||||||||
\(973\) | −72.5273 | −2.32512 | ||||||||
\(974\) | −58.4377 | −1.87246 | ||||||||
\(975\) | 17.4674 | 0.559405 | ||||||||
\(976\) | −38.8558 | −1.24375 | ||||||||
\(977\) | 14.0611 | 0.449854 | 0.224927 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224927 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(978\) | −10.9511 | −0.350178 | ||||||||
\(979\) | −0.154131 | −0.00492603 | ||||||||
\(980\) | 6.06332 | 0.193686 | ||||||||
\(981\) | −22.2895 | −0.711648 | ||||||||
\(982\) | 13.2188 | 0.421830 | ||||||||
\(983\) | −56.3939 | −1.79869 | −0.899344 | − | 0.437242i | \(-0.855955\pi\) | ||||
−0.899344 | + | 0.437242i | \(0.855955\pi\) | |||||||
\(984\) | 2.85143 | 0.0909003 | ||||||||
\(985\) | 2.72460 | 0.0868129 | ||||||||
\(986\) | 22.7236 | 0.723666 | ||||||||
\(987\) | 27.7052 | 0.881866 | ||||||||
\(988\) | −6.81113 | −0.216691 | ||||||||
\(989\) | −8.02967 | −0.255329 | ||||||||
\(990\) | −1.23333 | −0.0391978 | ||||||||
\(991\) | 24.6063 | 0.781644 | 0.390822 | − | 0.920466i | \(-0.372191\pi\) | ||||
0.390822 | + | 0.920466i | \(0.372191\pi\) | |||||||
\(992\) | 26.9921 | 0.857000 | ||||||||
\(993\) | −26.1416 | −0.829580 | ||||||||
\(994\) | −75.5821 | −2.39732 | ||||||||
\(995\) | 0.150279 | 0.00476415 | ||||||||
\(996\) | −14.6032 | −0.462719 | ||||||||
\(997\) | 39.5072 | 1.25120 | 0.625602 | − | 0.780142i | \(-0.284853\pi\) | ||||
0.625602 | + | 0.780142i | \(0.284853\pi\) | |||||||
\(998\) | −53.6497 | −1.69825 | ||||||||
\(999\) | −25.1718 | −0.796400 |
(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 | 6023.2.a.b.1.17 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.17 | ✓ | 99 | 1.1 | even | 1 | trivial |