Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3311,2,Mod(1,3311)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3311, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3311.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3311 = 7 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3311.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: | \(26.4384681092\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 3311.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66765 | −1.88631 | −0.943156 | − | 0.332351i | \(-0.892158\pi\) | ||||
−0.943156 | + | 0.332351i | \(0.892158\pi\) | |||||||
\(3\) | 0.718543 | 0.414851 | 0.207425 | − | 0.978251i | \(-0.433492\pi\) | ||||
0.207425 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(4\) | 5.11634 | 2.55817 | ||||||||
\(5\) | 4.04126 | 1.80731 | 0.903653 | − | 0.428265i | \(-0.140875\pi\) | ||||
0.903653 | + | 0.428265i | \(0.140875\pi\) | |||||||
\(6\) | −1.91682 | −0.782538 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −8.31331 | −2.93920 | ||||||||
\(9\) | −2.48370 | −0.827899 | ||||||||
\(10\) | −10.7807 | −3.40914 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.67631 | 1.06126 | ||||||||
\(13\) | 5.51938 | 1.53080 | 0.765400 | − | 0.643555i | \(-0.222541\pi\) | ||||
0.765400 | + | 0.643555i | \(0.222541\pi\) | |||||||
\(14\) | −2.66765 | −0.712959 | ||||||||
\(15\) | 2.90382 | 0.749763 | ||||||||
\(16\) | 11.9443 | 2.98607 | ||||||||
\(17\) | −4.96805 | −1.20493 | −0.602465 | − | 0.798145i | \(-0.705815\pi\) | ||||
−0.602465 | + | 0.798145i | \(0.705815\pi\) | |||||||
\(18\) | 6.62563 | 1.56167 | ||||||||
\(19\) | 4.54206 | 1.04202 | 0.521010 | − | 0.853551i | \(-0.325555\pi\) | ||||
0.521010 | + | 0.853551i | \(0.325555\pi\) | |||||||
\(20\) | 20.6765 | 4.62340 | ||||||||
\(21\) | 0.718543 | 0.156799 | ||||||||
\(22\) | −2.66765 | −0.568744 | ||||||||
\(23\) | 5.54439 | 1.15609 | 0.578043 | − | 0.816006i | \(-0.303817\pi\) | ||||
0.578043 | + | 0.816006i | \(0.303817\pi\) | |||||||
\(24\) | −5.97347 | −1.21933 | ||||||||
\(25\) | 11.3318 | 2.26636 | ||||||||
\(26\) | −14.7238 | −2.88757 | ||||||||
\(27\) | −3.94027 | −0.758306 | ||||||||
\(28\) | 5.11634 | 0.966898 | ||||||||
\(29\) | −4.35655 | −0.808991 | −0.404496 | − | 0.914540i | \(-0.632553\pi\) | ||||
−0.404496 | + | 0.914540i | \(0.632553\pi\) | |||||||
\(30\) | −7.74637 | −1.41429 | ||||||||
\(31\) | −4.05602 | −0.728483 | −0.364241 | − | 0.931305i | \(-0.618672\pi\) | ||||
−0.364241 | + | 0.931305i | \(0.618672\pi\) | |||||||
\(32\) | −15.2365 | −2.69346 | ||||||||
\(33\) | 0.718543 | 0.125082 | ||||||||
\(34\) | 13.2530 | 2.27287 | ||||||||
\(35\) | 4.04126 | 0.683098 | ||||||||
\(36\) | −12.7074 | −2.11791 | ||||||||
\(37\) | 6.45896 | 1.06185 | 0.530924 | − | 0.847420i | \(-0.321845\pi\) | ||||
0.530924 | + | 0.847420i | \(0.321845\pi\) | |||||||
\(38\) | −12.1166 | −1.96557 | ||||||||
\(39\) | 3.96591 | 0.635054 | ||||||||
\(40\) | −33.5962 | −5.31203 | ||||||||
\(41\) | −5.14577 | −0.803634 | −0.401817 | − | 0.915720i | \(-0.631621\pi\) | ||||
−0.401817 | + | 0.915720i | \(0.631621\pi\) | |||||||
\(42\) | −1.91682 | −0.295772 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 5.11634 | 0.771318 | ||||||||
\(45\) | −10.0373 | −1.49627 | ||||||||
\(46\) | −14.7905 | −2.18074 | ||||||||
\(47\) | 6.28439 | 0.916672 | 0.458336 | − | 0.888779i | \(-0.348446\pi\) | ||||
0.458336 | + | 0.888779i | \(0.348446\pi\) | |||||||
\(48\) | 8.58248 | 1.23877 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −30.2292 | −4.27506 | ||||||||
\(51\) | −3.56976 | −0.499866 | ||||||||
\(52\) | 28.2390 | 3.91605 | ||||||||
\(53\) | −8.65248 | −1.18851 | −0.594255 | − | 0.804277i | \(-0.702553\pi\) | ||||
−0.594255 | + | 0.804277i | \(0.702553\pi\) | |||||||
\(54\) | 10.5113 | 1.43040 | ||||||||
\(55\) | 4.04126 | 0.544924 | ||||||||
\(56\) | −8.31331 | −1.11091 | ||||||||
\(57\) | 3.26366 | 0.432283 | ||||||||
\(58\) | 11.6217 | 1.52601 | ||||||||
\(59\) | 5.41422 | 0.704871 | 0.352436 | − | 0.935836i | \(-0.385354\pi\) | ||||
0.352436 | + | 0.935836i | \(0.385354\pi\) | |||||||
\(60\) | 14.8569 | 1.91802 | ||||||||
\(61\) | −9.21586 | −1.17997 | −0.589985 | − | 0.807414i | \(-0.700866\pi\) | ||||
−0.589985 | + | 0.807414i | \(0.700866\pi\) | |||||||
\(62\) | 10.8200 | 1.37415 | ||||||||
\(63\) | −2.48370 | −0.312916 | ||||||||
\(64\) | 16.7571 | 2.09464 | ||||||||
\(65\) | 22.3052 | 2.76662 | ||||||||
\(66\) | −1.91682 | −0.235944 | ||||||||
\(67\) | 4.74573 | 0.579783 | 0.289891 | − | 0.957060i | \(-0.406381\pi\) | ||||
0.289891 | + | 0.957060i | \(0.406381\pi\) | |||||||
\(68\) | −25.4183 | −3.08242 | ||||||||
\(69\) | 3.98388 | 0.479603 | ||||||||
\(70\) | −10.7807 | −1.28854 | ||||||||
\(71\) | 16.4133 | 1.94789 | 0.973947 | − | 0.226774i | \(-0.0728178\pi\) | ||||
0.973947 | + | 0.226774i | \(0.0728178\pi\) | |||||||
\(72\) | 20.6477 | 2.43336 | ||||||||
\(73\) | −1.37440 | −0.160861 | −0.0804304 | − | 0.996760i | \(-0.525629\pi\) | ||||
−0.0804304 | + | 0.996760i | \(0.525629\pi\) | |||||||
\(74\) | −17.2302 | −2.00297 | ||||||||
\(75\) | 8.14238 | 0.940201 | ||||||||
\(76\) | 23.2387 | 2.66567 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −10.5796 | −1.19791 | ||||||||
\(79\) | 7.80555 | 0.878193 | 0.439096 | − | 0.898440i | \(-0.355299\pi\) | ||||
0.439096 | + | 0.898440i | \(0.355299\pi\) | |||||||
\(80\) | 48.2700 | 5.39675 | ||||||||
\(81\) | 4.61983 | 0.513315 | ||||||||
\(82\) | 13.7271 | 1.51590 | ||||||||
\(83\) | −4.75614 | −0.522054 | −0.261027 | − | 0.965331i | \(-0.584061\pi\) | ||||
−0.261027 | + | 0.965331i | \(0.584061\pi\) | |||||||
\(84\) | 3.67631 | 0.401119 | ||||||||
\(85\) | −20.0772 | −2.17768 | ||||||||
\(86\) | −2.66765 | −0.287660 | ||||||||
\(87\) | −3.13037 | −0.335611 | ||||||||
\(88\) | −8.31331 | −0.886201 | ||||||||
\(89\) | 8.49796 | 0.900782 | 0.450391 | − | 0.892832i | \(-0.351285\pi\) | ||||
0.450391 | + | 0.892832i | \(0.351285\pi\) | |||||||
\(90\) | 26.7759 | 2.82243 | ||||||||
\(91\) | 5.51938 | 0.578588 | ||||||||
\(92\) | 28.3670 | 2.95747 | ||||||||
\(93\) | −2.91443 | −0.302212 | ||||||||
\(94\) | −16.7645 | −1.72913 | ||||||||
\(95\) | 18.3556 | 1.88325 | ||||||||
\(96\) | −10.9481 | −1.11739 | ||||||||
\(97\) | −2.08406 | −0.211604 | −0.105802 | − | 0.994387i | \(-0.533741\pi\) | ||||
−0.105802 | + | 0.994387i | \(0.533741\pi\) | |||||||
\(98\) | −2.66765 | −0.269473 | ||||||||
\(99\) | −2.48370 | −0.249621 | ||||||||
\(100\) | 57.9773 | 5.79773 | ||||||||
\(101\) | 1.94049 | 0.193086 | 0.0965429 | − | 0.995329i | \(-0.469221\pi\) | ||||
0.0965429 | + | 0.995329i | \(0.469221\pi\) | |||||||
\(102\) | 9.52286 | 0.942904 | ||||||||
\(103\) | −6.58984 | −0.649316 | −0.324658 | − | 0.945831i | \(-0.605249\pi\) | ||||
−0.324658 | + | 0.945831i | \(0.605249\pi\) | |||||||
\(104\) | −45.8843 | −4.49932 | ||||||||
\(105\) | 2.90382 | 0.283384 | ||||||||
\(106\) | 23.0818 | 2.24190 | ||||||||
\(107\) | −3.33886 | −0.322780 | −0.161390 | − | 0.986891i | \(-0.551598\pi\) | ||||
−0.161390 | + | 0.986891i | \(0.551598\pi\) | |||||||
\(108\) | −20.1598 | −1.93988 | ||||||||
\(109\) | 15.7840 | 1.51183 | 0.755915 | − | 0.654670i | \(-0.227192\pi\) | ||||
0.755915 | + | 0.654670i | \(0.227192\pi\) | |||||||
\(110\) | −10.7807 | −1.02790 | ||||||||
\(111\) | 4.64104 | 0.440508 | ||||||||
\(112\) | 11.9443 | 1.12863 | ||||||||
\(113\) | −1.63450 | −0.153761 | −0.0768804 | − | 0.997040i | \(-0.524496\pi\) | ||||
−0.0768804 | + | 0.997040i | \(0.524496\pi\) | |||||||
\(114\) | −8.70630 | −0.815420 | ||||||||
\(115\) | 22.4063 | 2.08940 | ||||||||
\(116\) | −22.2896 | −2.06954 | ||||||||
\(117\) | −13.7085 | −1.26735 | ||||||||
\(118\) | −14.4432 | −1.32961 | ||||||||
\(119\) | −4.96805 | −0.455421 | ||||||||
\(120\) | −24.1403 | −2.20370 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 24.5847 | 2.22579 | ||||||||
\(123\) | −3.69746 | −0.333388 | ||||||||
\(124\) | −20.7520 | −1.86358 | ||||||||
\(125\) | 25.5884 | 2.28870 | ||||||||
\(126\) | 6.62563 | 0.590258 | ||||||||
\(127\) | 4.27072 | 0.378965 | 0.189482 | − | 0.981884i | \(-0.439319\pi\) | ||||
0.189482 | + | 0.981884i | \(0.439319\pi\) | |||||||
\(128\) | −14.2290 | −1.25768 | ||||||||
\(129\) | 0.718543 | 0.0632642 | ||||||||
\(130\) | −59.5025 | −5.21872 | ||||||||
\(131\) | −8.48525 | −0.741359 | −0.370680 | − | 0.928761i | \(-0.620875\pi\) | ||||
−0.370680 | + | 0.928761i | \(0.620875\pi\) | |||||||
\(132\) | 3.67631 | 0.319982 | ||||||||
\(133\) | 4.54206 | 0.393846 | ||||||||
\(134\) | −12.6599 | −1.09365 | ||||||||
\(135\) | −15.9237 | −1.37049 | ||||||||
\(136\) | 41.3010 | 3.54153 | ||||||||
\(137\) | 12.5750 | 1.07436 | 0.537179 | − | 0.843468i | \(-0.319490\pi\) | ||||
0.537179 | + | 0.843468i | \(0.319490\pi\) | |||||||
\(138\) | −10.6276 | −0.904681 | ||||||||
\(139\) | −12.9013 | −1.09427 | −0.547137 | − | 0.837043i | \(-0.684282\pi\) | ||||
−0.547137 | + | 0.837043i | \(0.684282\pi\) | |||||||
\(140\) | 20.6765 | 1.74748 | ||||||||
\(141\) | 4.51560 | 0.380282 | ||||||||
\(142\) | −43.7848 | −3.67434 | ||||||||
\(143\) | 5.51938 | 0.461554 | ||||||||
\(144\) | −29.6660 | −2.47216 | ||||||||
\(145\) | −17.6060 | −1.46210 | ||||||||
\(146\) | 3.66640 | 0.303434 | ||||||||
\(147\) | 0.718543 | 0.0592644 | ||||||||
\(148\) | 33.0463 | 2.71639 | ||||||||
\(149\) | −11.0637 | −0.906375 | −0.453187 | − | 0.891415i | \(-0.649713\pi\) | ||||
−0.453187 | + | 0.891415i | \(0.649713\pi\) | |||||||
\(150\) | −21.7210 | −1.77351 | ||||||||
\(151\) | 23.0736 | 1.87771 | 0.938853 | − | 0.344317i | \(-0.111890\pi\) | ||||
0.938853 | + | 0.344317i | \(0.111890\pi\) | |||||||
\(152\) | −37.7595 | −3.06270 | ||||||||
\(153\) | 12.3391 | 0.997560 | ||||||||
\(154\) | −2.66765 | −0.214965 | ||||||||
\(155\) | −16.3914 | −1.31659 | ||||||||
\(156\) | 20.2910 | 1.62458 | ||||||||
\(157\) | 3.59102 | 0.286594 | 0.143297 | − | 0.989680i | \(-0.454230\pi\) | ||||
0.143297 | + | 0.989680i | \(0.454230\pi\) | |||||||
\(158\) | −20.8225 | −1.65655 | ||||||||
\(159\) | −6.21718 | −0.493054 | ||||||||
\(160\) | −61.5748 | −4.86791 | ||||||||
\(161\) | 5.54439 | 0.436959 | ||||||||
\(162\) | −12.3241 | −0.968272 | ||||||||
\(163\) | −23.6797 | −1.85473 | −0.927367 | − | 0.374153i | \(-0.877933\pi\) | ||||
−0.927367 | + | 0.374153i | \(0.877933\pi\) | |||||||
\(164\) | −26.3275 | −2.05583 | ||||||||
\(165\) | 2.90382 | 0.226062 | ||||||||
\(166\) | 12.6877 | 0.984757 | ||||||||
\(167\) | −21.4040 | −1.65629 | −0.828144 | − | 0.560516i | \(-0.810603\pi\) | ||||
−0.828144 | + | 0.560516i | \(0.810603\pi\) | |||||||
\(168\) | −5.97347 | −0.460863 | ||||||||
\(169\) | 17.4635 | 1.34335 | ||||||||
\(170\) | 53.5589 | 4.10778 | ||||||||
\(171\) | −11.2811 | −0.862687 | ||||||||
\(172\) | 5.11634 | 0.390118 | ||||||||
\(173\) | −2.77519 | −0.210994 | −0.105497 | − | 0.994420i | \(-0.533643\pi\) | ||||
−0.105497 | + | 0.994420i | \(0.533643\pi\) | |||||||
\(174\) | 8.35072 | 0.633067 | ||||||||
\(175\) | 11.3318 | 0.856603 | ||||||||
\(176\) | 11.9443 | 0.900334 | ||||||||
\(177\) | 3.89035 | 0.292416 | ||||||||
\(178\) | −22.6696 | −1.69915 | ||||||||
\(179\) | −3.19007 | −0.238437 | −0.119219 | − | 0.992868i | \(-0.538039\pi\) | ||||
−0.119219 | + | 0.992868i | \(0.538039\pi\) | |||||||
\(180\) | −51.3541 | −3.82771 | ||||||||
\(181\) | 10.9975 | 0.817436 | 0.408718 | − | 0.912661i | \(-0.365976\pi\) | ||||
0.408718 | + | 0.912661i | \(0.365976\pi\) | |||||||
\(182\) | −14.7238 | −1.09140 | ||||||||
\(183\) | −6.62199 | −0.489512 | ||||||||
\(184\) | −46.0922 | −3.39796 | ||||||||
\(185\) | 26.1024 | 1.91908 | ||||||||
\(186\) | 7.77466 | 0.570066 | ||||||||
\(187\) | −4.96805 | −0.363300 | ||||||||
\(188\) | 32.1531 | 2.34501 | ||||||||
\(189\) | −3.94027 | −0.286613 | ||||||||
\(190\) | −48.9664 | −3.55239 | ||||||||
\(191\) | −20.1120 | −1.45526 | −0.727628 | − | 0.685972i | \(-0.759377\pi\) | ||||
−0.727628 | + | 0.685972i | \(0.759377\pi\) | |||||||
\(192\) | 12.0407 | 0.868963 | ||||||||
\(193\) | 18.0089 | 1.29631 | 0.648155 | − | 0.761508i | \(-0.275541\pi\) | ||||
0.648155 | + | 0.761508i | \(0.275541\pi\) | |||||||
\(194\) | 5.55954 | 0.399152 | ||||||||
\(195\) | 16.0273 | 1.14774 | ||||||||
\(196\) | 5.11634 | 0.365453 | ||||||||
\(197\) | 3.97398 | 0.283134 | 0.141567 | − | 0.989929i | \(-0.454786\pi\) | ||||
0.141567 | + | 0.989929i | \(0.454786\pi\) | |||||||
\(198\) | 6.62563 | 0.470863 | ||||||||
\(199\) | 11.0924 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(200\) | −94.2046 | −6.66127 | ||||||||
\(201\) | 3.41001 | 0.240523 | ||||||||
\(202\) | −5.17654 | −0.364220 | ||||||||
\(203\) | −4.35655 | −0.305770 | ||||||||
\(204\) | −18.2641 | −1.27874 | ||||||||
\(205\) | −20.7954 | −1.45241 | ||||||||
\(206\) | 17.5794 | 1.22481 | ||||||||
\(207\) | −13.7706 | −0.957122 | ||||||||
\(208\) | 65.9250 | 4.57108 | ||||||||
\(209\) | 4.54206 | 0.314181 | ||||||||
\(210\) | −7.74637 | −0.534550 | ||||||||
\(211\) | −26.1500 | −1.80024 | −0.900119 | − | 0.435645i | \(-0.856520\pi\) | ||||
−0.900119 | + | 0.435645i | \(0.856520\pi\) | |||||||
\(212\) | −44.2691 | −3.04041 | ||||||||
\(213\) | 11.7936 | 0.808086 | ||||||||
\(214\) | 8.90691 | 0.608864 | ||||||||
\(215\) | 4.04126 | 0.275612 | ||||||||
\(216\) | 32.7567 | 2.22881 | ||||||||
\(217\) | −4.05602 | −0.275341 | ||||||||
\(218\) | −42.1060 | −2.85178 | ||||||||
\(219\) | −0.987562 | −0.0667333 | ||||||||
\(220\) | 20.6765 | 1.39401 | ||||||||
\(221\) | −27.4206 | −1.84451 | ||||||||
\(222\) | −12.3807 | −0.830936 | ||||||||
\(223\) | −26.5212 | −1.77599 | −0.887996 | − | 0.459852i | \(-0.847902\pi\) | ||||
−0.887996 | + | 0.459852i | \(0.847902\pi\) | |||||||
\(224\) | −15.2365 | −1.01803 | ||||||||
\(225\) | −28.1447 | −1.87631 | ||||||||
\(226\) | 4.36027 | 0.290041 | ||||||||
\(227\) | −9.71559 | −0.644847 | −0.322423 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322423 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(228\) | 16.6980 | 1.10585 | ||||||||
\(229\) | −10.0568 | −0.664574 | −0.332287 | − | 0.943178i | \(-0.607820\pi\) | ||||
−0.332287 | + | 0.943178i | \(0.607820\pi\) | |||||||
\(230\) | −59.7722 | −3.94126 | ||||||||
\(231\) | 0.718543 | 0.0472767 | ||||||||
\(232\) | 36.2173 | 2.37779 | ||||||||
\(233\) | −1.75180 | −0.114764 | −0.0573820 | − | 0.998352i | \(-0.518275\pi\) | ||||
−0.0573820 | + | 0.998352i | \(0.518275\pi\) | |||||||
\(234\) | 36.5693 | 2.39061 | ||||||||
\(235\) | 25.3969 | 1.65671 | ||||||||
\(236\) | 27.7010 | 1.80318 | ||||||||
\(237\) | 5.60862 | 0.364319 | ||||||||
\(238\) | 13.2530 | 0.859066 | ||||||||
\(239\) | 13.0129 | 0.841735 | 0.420867 | − | 0.907122i | \(-0.361726\pi\) | ||||
0.420867 | + | 0.907122i | \(0.361726\pi\) | |||||||
\(240\) | 34.6840 | 2.23885 | ||||||||
\(241\) | 19.3503 | 1.24646 | 0.623230 | − | 0.782039i | \(-0.285820\pi\) | ||||
0.623230 | + | 0.782039i | \(0.285820\pi\) | |||||||
\(242\) | −2.66765 | −0.171483 | ||||||||
\(243\) | 15.1404 | 0.971255 | ||||||||
\(244\) | −47.1515 | −3.01857 | ||||||||
\(245\) | 4.04126 | 0.258187 | ||||||||
\(246\) | 9.86351 | 0.628874 | ||||||||
\(247\) | 25.0693 | 1.59512 | ||||||||
\(248\) | 33.7189 | 2.14116 | ||||||||
\(249\) | −3.41749 | −0.216575 | ||||||||
\(250\) | −68.2609 | −4.31720 | ||||||||
\(251\) | 12.7283 | 0.803402 | 0.401701 | − | 0.915771i | \(-0.368419\pi\) | ||||
0.401701 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(252\) | −12.7074 | −0.800494 | ||||||||
\(253\) | 5.54439 | 0.348573 | ||||||||
\(254\) | −11.3928 | −0.714846 | ||||||||
\(255\) | −14.4263 | −0.903412 | ||||||||
\(256\) | 4.44380 | 0.277737 | ||||||||
\(257\) | 8.99621 | 0.561168 | 0.280584 | − | 0.959829i | \(-0.409472\pi\) | ||||
0.280584 | + | 0.959829i | \(0.409472\pi\) | |||||||
\(258\) | −1.91682 | −0.119336 | ||||||||
\(259\) | 6.45896 | 0.401341 | ||||||||
\(260\) | 114.121 | 7.07750 | ||||||||
\(261\) | 10.8203 | 0.669763 | ||||||||
\(262\) | 22.6356 | 1.39843 | ||||||||
\(263\) | 0.691192 | 0.0426207 | 0.0213104 | − | 0.999773i | \(-0.493216\pi\) | ||||
0.0213104 | + | 0.999773i | \(0.493216\pi\) | |||||||
\(264\) | −5.97347 | −0.367641 | ||||||||
\(265\) | −34.9669 | −2.14800 | ||||||||
\(266\) | −12.1166 | −0.742917 | ||||||||
\(267\) | 6.10615 | 0.373690 | ||||||||
\(268\) | 24.2808 | 1.48318 | ||||||||
\(269\) | −12.4212 | −0.757335 | −0.378668 | − | 0.925533i | \(-0.623618\pi\) | ||||
−0.378668 | + | 0.925533i | \(0.623618\pi\) | |||||||
\(270\) | 42.4787 | 2.58517 | ||||||||
\(271\) | 5.61315 | 0.340975 | 0.170487 | − | 0.985360i | \(-0.445466\pi\) | ||||
0.170487 | + | 0.985360i | \(0.445466\pi\) | |||||||
\(272\) | −59.3399 | −3.59801 | ||||||||
\(273\) | 3.96591 | 0.240028 | ||||||||
\(274\) | −33.5458 | −2.02657 | ||||||||
\(275\) | 11.3318 | 0.683333 | ||||||||
\(276\) | 20.3829 | 1.22691 | ||||||||
\(277\) | 28.9996 | 1.74242 | 0.871210 | − | 0.490911i | \(-0.163336\pi\) | ||||
0.871210 | + | 0.490911i | \(0.163336\pi\) | |||||||
\(278\) | 34.4161 | 2.06414 | ||||||||
\(279\) | 10.0739 | 0.603110 | ||||||||
\(280\) | −33.5962 | −2.00776 | ||||||||
\(281\) | 2.30609 | 0.137570 | 0.0687848 | − | 0.997632i | \(-0.478088\pi\) | ||||
0.0687848 | + | 0.997632i | \(0.478088\pi\) | |||||||
\(282\) | −12.0460 | −0.717331 | ||||||||
\(283\) | −4.99388 | −0.296856 | −0.148428 | − | 0.988923i | \(-0.547421\pi\) | ||||
−0.148428 | + | 0.988923i | \(0.547421\pi\) | |||||||
\(284\) | 83.9758 | 4.98305 | ||||||||
\(285\) | 13.1893 | 0.781268 | ||||||||
\(286\) | −14.7238 | −0.870634 | ||||||||
\(287\) | −5.14577 | −0.303745 | ||||||||
\(288\) | 37.8429 | 2.22991 | ||||||||
\(289\) | 7.68156 | 0.451857 | ||||||||
\(290\) | 46.9665 | 2.75797 | ||||||||
\(291\) | −1.49749 | −0.0877842 | ||||||||
\(292\) | −7.03188 | −0.411510 | ||||||||
\(293\) | 25.4346 | 1.48591 | 0.742953 | − | 0.669343i | \(-0.233424\pi\) | ||||
0.742953 | + | 0.669343i | \(0.233424\pi\) | |||||||
\(294\) | −1.91682 | −0.111791 | ||||||||
\(295\) | 21.8803 | 1.27392 | ||||||||
\(296\) | −53.6953 | −3.12098 | ||||||||
\(297\) | −3.94027 | −0.228638 | ||||||||
\(298\) | 29.5141 | 1.70971 | ||||||||
\(299\) | 30.6016 | 1.76974 | ||||||||
\(300\) | 41.6592 | 2.40519 | ||||||||
\(301\) | 1.00000 | 0.0576390 | ||||||||
\(302\) | −61.5524 | −3.54194 | ||||||||
\(303\) | 1.39432 | 0.0801018 | ||||||||
\(304\) | 54.2516 | 3.11154 | ||||||||
\(305\) | −37.2437 | −2.13257 | ||||||||
\(306\) | −32.9165 | −1.88171 | ||||||||
\(307\) | −0.258332 | −0.0147438 | −0.00737188 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737188 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(308\) | 5.11634 | 0.291531 | ||||||||
\(309\) | −4.73508 | −0.269369 | ||||||||
\(310\) | 43.7266 | 2.48350 | ||||||||
\(311\) | 23.8530 | 1.35258 | 0.676289 | − | 0.736636i | \(-0.263587\pi\) | ||||
0.676289 | + | 0.736636i | \(0.263587\pi\) | |||||||
\(312\) | −32.9698 | −1.86655 | ||||||||
\(313\) | −29.0283 | −1.64078 | −0.820388 | − | 0.571807i | \(-0.806243\pi\) | ||||
−0.820388 | + | 0.571807i | \(0.806243\pi\) | |||||||
\(314\) | −9.57957 | −0.540607 | ||||||||
\(315\) | −10.0373 | −0.565536 | ||||||||
\(316\) | 39.9359 | 2.24657 | ||||||||
\(317\) | −20.6165 | −1.15794 | −0.578968 | − | 0.815350i | \(-0.696544\pi\) | ||||
−0.578968 | + | 0.815350i | \(0.696544\pi\) | |||||||
\(318\) | 16.5852 | 0.930054 | ||||||||
\(319\) | −4.35655 | −0.243920 | ||||||||
\(320\) | 67.7199 | 3.78566 | ||||||||
\(321\) | −2.39912 | −0.133906 | ||||||||
\(322\) | −14.7905 | −0.824241 | ||||||||
\(323\) | −22.5652 | −1.25556 | ||||||||
\(324\) | 23.6367 | 1.31315 | ||||||||
\(325\) | 62.5444 | 3.46934 | ||||||||
\(326\) | 63.1690 | 3.49861 | ||||||||
\(327\) | 11.3415 | 0.627184 | ||||||||
\(328\) | 42.7784 | 2.36204 | ||||||||
\(329\) | 6.28439 | 0.346470 | ||||||||
\(330\) | −7.74637 | −0.426423 | ||||||||
\(331\) | 30.8442 | 1.69535 | 0.847676 | − | 0.530515i | \(-0.178001\pi\) | ||||
0.847676 | + | 0.530515i | \(0.178001\pi\) | |||||||
\(332\) | −24.3341 | −1.33550 | ||||||||
\(333\) | −16.0421 | −0.879102 | ||||||||
\(334\) | 57.0982 | 3.12427 | ||||||||
\(335\) | 19.1787 | 1.04785 | ||||||||
\(336\) | 8.58248 | 0.468213 | ||||||||
\(337\) | −8.60361 | −0.468668 | −0.234334 | − | 0.972156i | \(-0.575291\pi\) | ||||
−0.234334 | + | 0.972156i | \(0.575291\pi\) | |||||||
\(338\) | −46.5865 | −2.53397 | ||||||||
\(339\) | −1.17446 | −0.0637878 | ||||||||
\(340\) | −102.722 | −5.57088 | ||||||||
\(341\) | −4.05602 | −0.219646 | ||||||||
\(342\) | 30.0940 | 1.62730 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.31331 | −0.448223 | ||||||||
\(345\) | 16.0999 | 0.866790 | ||||||||
\(346\) | 7.40322 | 0.398000 | ||||||||
\(347\) | −35.2002 | −1.88965 | −0.944823 | − | 0.327582i | \(-0.893766\pi\) | ||||
−0.944823 | + | 0.327582i | \(0.893766\pi\) | |||||||
\(348\) | −16.0160 | −0.858550 | ||||||||
\(349\) | 32.3400 | 1.73112 | 0.865560 | − | 0.500805i | \(-0.166963\pi\) | ||||
0.865560 | + | 0.500805i | \(0.166963\pi\) | |||||||
\(350\) | −30.2292 | −1.61582 | ||||||||
\(351\) | −21.7478 | −1.16081 | ||||||||
\(352\) | −15.2365 | −0.812110 | ||||||||
\(353\) | −30.5999 | −1.62867 | −0.814335 | − | 0.580395i | \(-0.802898\pi\) | ||||
−0.814335 | + | 0.580395i | \(0.802898\pi\) | |||||||
\(354\) | −10.3781 | −0.551589 | ||||||||
\(355\) | 66.3302 | 3.52044 | ||||||||
\(356\) | 43.4785 | 2.30435 | ||||||||
\(357\) | −3.56976 | −0.188932 | ||||||||
\(358\) | 8.50999 | 0.449767 | ||||||||
\(359\) | −26.3034 | −1.38824 | −0.694119 | − | 0.719860i | \(-0.744206\pi\) | ||||
−0.694119 | + | 0.719860i | \(0.744206\pi\) | |||||||
\(360\) | 83.4428 | 4.39782 | ||||||||
\(361\) | 1.63029 | 0.0858048 | ||||||||
\(362\) | −29.3374 | −1.54194 | ||||||||
\(363\) | 0.718543 | 0.0377137 | ||||||||
\(364\) | 28.2390 | 1.48013 | ||||||||
\(365\) | −5.55429 | −0.290725 | ||||||||
\(366\) | 17.6651 | 0.923372 | ||||||||
\(367\) | −21.6637 | −1.13083 | −0.565417 | − | 0.824805i | \(-0.691285\pi\) | ||||
−0.565417 | + | 0.824805i | \(0.691285\pi\) | |||||||
\(368\) | 66.2238 | 3.45215 | ||||||||
\(369\) | 12.7805 | 0.665328 | ||||||||
\(370\) | −69.6319 | −3.61999 | ||||||||
\(371\) | −8.65248 | −0.449215 | ||||||||
\(372\) | −14.9112 | −0.773110 | ||||||||
\(373\) | 6.51494 | 0.337331 | 0.168665 | − | 0.985673i | \(-0.446054\pi\) | ||||
0.168665 | + | 0.985673i | \(0.446054\pi\) | |||||||
\(374\) | 13.2530 | 0.685297 | ||||||||
\(375\) | 18.3864 | 0.949468 | ||||||||
\(376\) | −52.2440 | −2.69428 | ||||||||
\(377\) | −24.0454 | −1.23840 | ||||||||
\(378\) | 10.5113 | 0.540641 | ||||||||
\(379\) | −0.504547 | −0.0259168 | −0.0129584 | − | 0.999916i | \(-0.504125\pi\) | ||||
−0.0129584 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(380\) | 93.9138 | 4.81767 | ||||||||
\(381\) | 3.06869 | 0.157214 | ||||||||
\(382\) | 53.6519 | 2.74507 | ||||||||
\(383\) | −17.2899 | −0.883471 | −0.441735 | − | 0.897145i | \(-0.645637\pi\) | ||||
−0.441735 | + | 0.897145i | \(0.645637\pi\) | |||||||
\(384\) | −10.2242 | −0.521750 | ||||||||
\(385\) | 4.04126 | 0.205962 | ||||||||
\(386\) | −48.0415 | −2.44525 | ||||||||
\(387\) | −2.48370 | −0.126253 | ||||||||
\(388\) | −10.6628 | −0.541320 | ||||||||
\(389\) | −23.4726 | −1.19011 | −0.595054 | − | 0.803686i | \(-0.702869\pi\) | ||||
−0.595054 | + | 0.803686i | \(0.702869\pi\) | |||||||
\(390\) | −42.7551 | −2.16499 | ||||||||
\(391\) | −27.5448 | −1.39300 | ||||||||
\(392\) | −8.31331 | −0.419885 | ||||||||
\(393\) | −6.09701 | −0.307554 | ||||||||
\(394\) | −10.6012 | −0.534079 | ||||||||
\(395\) | 31.5443 | 1.58716 | ||||||||
\(396\) | −12.7074 | −0.638573 | ||||||||
\(397\) | 10.7754 | 0.540802 | 0.270401 | − | 0.962748i | \(-0.412844\pi\) | ||||
0.270401 | + | 0.962748i | \(0.412844\pi\) | |||||||
\(398\) | −29.5906 | −1.48324 | ||||||||
\(399\) | 3.26366 | 0.163388 | ||||||||
\(400\) | 135.350 | 6.76751 | ||||||||
\(401\) | 37.8190 | 1.88859 | 0.944294 | − | 0.329102i | \(-0.106746\pi\) | ||||
0.944294 | + | 0.329102i | \(0.106746\pi\) | |||||||
\(402\) | −9.09670 | −0.453702 | ||||||||
\(403\) | −22.3867 | −1.11516 | ||||||||
\(404\) | 9.92821 | 0.493947 | ||||||||
\(405\) | 18.6700 | 0.927718 | ||||||||
\(406\) | 11.6217 | 0.576777 | ||||||||
\(407\) | 6.45896 | 0.320159 | ||||||||
\(408\) | 29.6765 | 1.46921 | ||||||||
\(409\) | 22.3467 | 1.10497 | 0.552487 | − | 0.833522i | \(-0.313679\pi\) | ||||
0.552487 | + | 0.833522i | \(0.313679\pi\) | |||||||
\(410\) | 55.4748 | 2.73970 | ||||||||
\(411\) | 9.03570 | 0.445698 | ||||||||
\(412\) | −33.7159 | −1.66106 | ||||||||
\(413\) | 5.41422 | 0.266416 | ||||||||
\(414\) | 36.7351 | 1.80543 | ||||||||
\(415\) | −19.2208 | −0.943512 | ||||||||
\(416\) | −84.0961 | −4.12315 | ||||||||
\(417\) | −9.27014 | −0.453961 | ||||||||
\(418\) | −12.1166 | −0.592643 | ||||||||
\(419\) | −19.3391 | −0.944775 | −0.472388 | − | 0.881391i | \(-0.656608\pi\) | ||||
−0.472388 | + | 0.881391i | \(0.656608\pi\) | |||||||
\(420\) | 14.8569 | 0.724944 | ||||||||
\(421\) | −22.7545 | −1.10899 | −0.554494 | − | 0.832188i | \(-0.687088\pi\) | ||||
−0.554494 | + | 0.832188i | \(0.687088\pi\) | |||||||
\(422\) | 69.7589 | 3.39581 | ||||||||
\(423\) | −15.6085 | −0.758912 | ||||||||
\(424\) | 71.9307 | 3.49327 | ||||||||
\(425\) | −56.2969 | −2.73080 | ||||||||
\(426\) | −31.4612 | −1.52430 | ||||||||
\(427\) | −9.21586 | −0.445987 | ||||||||
\(428\) | −17.0828 | −0.825727 | ||||||||
\(429\) | 3.96591 | 0.191476 | ||||||||
\(430\) | −10.7807 | −0.519890 | ||||||||
\(431\) | 13.3893 | 0.644941 | 0.322470 | − | 0.946580i | \(-0.395487\pi\) | ||||
0.322470 | + | 0.946580i | \(0.395487\pi\) | |||||||
\(432\) | −47.0637 | −2.26435 | ||||||||
\(433\) | 8.99946 | 0.432486 | 0.216243 | − | 0.976340i | \(-0.430620\pi\) | ||||
0.216243 | + | 0.976340i | \(0.430620\pi\) | |||||||
\(434\) | 10.8200 | 0.519378 | ||||||||
\(435\) | −12.6506 | −0.606552 | ||||||||
\(436\) | 80.7562 | 3.86752 | ||||||||
\(437\) | 25.1830 | 1.20466 | ||||||||
\(438\) | 2.63447 | 0.125880 | ||||||||
\(439\) | −14.6762 | −0.700458 | −0.350229 | − | 0.936664i | \(-0.613896\pi\) | ||||
−0.350229 | + | 0.936664i | \(0.613896\pi\) | |||||||
\(440\) | −33.5962 | −1.60164 | ||||||||
\(441\) | −2.48370 | −0.118271 | ||||||||
\(442\) | 73.1484 | 3.47932 | ||||||||
\(443\) | −38.5012 | −1.82925 | −0.914623 | − | 0.404309i | \(-0.867512\pi\) | ||||
−0.914623 | + | 0.404309i | \(0.867512\pi\) | |||||||
\(444\) | 23.7452 | 1.12690 | ||||||||
\(445\) | 34.3425 | 1.62799 | ||||||||
\(446\) | 70.7492 | 3.35007 | ||||||||
\(447\) | −7.94976 | −0.376011 | ||||||||
\(448\) | 16.7571 | 0.791699 | ||||||||
\(449\) | −15.3942 | −0.726496 | −0.363248 | − | 0.931692i | \(-0.618332\pi\) | ||||
−0.363248 | + | 0.931692i | \(0.618332\pi\) | |||||||
\(450\) | 75.0802 | 3.53931 | ||||||||
\(451\) | −5.14577 | −0.242305 | ||||||||
\(452\) | −8.36266 | −0.393347 | ||||||||
\(453\) | 16.5794 | 0.778968 | ||||||||
\(454\) | 25.9178 | 1.21638 | ||||||||
\(455\) | 22.3052 | 1.04569 | ||||||||
\(456\) | −27.1318 | −1.27056 | ||||||||
\(457\) | 19.6770 | 0.920451 | 0.460225 | − | 0.887802i | \(-0.347769\pi\) | ||||
0.460225 | + | 0.887802i | \(0.347769\pi\) | |||||||
\(458\) | 26.8281 | 1.25359 | ||||||||
\(459\) | 19.5755 | 0.913705 | ||||||||
\(460\) | 114.639 | 5.34505 | ||||||||
\(461\) | −39.2452 | −1.82783 | −0.913915 | − | 0.405905i | \(-0.866956\pi\) | ||||
−0.913915 | + | 0.405905i | \(0.866956\pi\) | |||||||
\(462\) | −1.91682 | −0.0891785 | ||||||||
\(463\) | 3.25597 | 0.151318 | 0.0756589 | − | 0.997134i | \(-0.475894\pi\) | ||||
0.0756589 | + | 0.997134i | \(0.475894\pi\) | |||||||
\(464\) | −52.0359 | −2.41571 | ||||||||
\(465\) | −11.7780 | −0.546190 | ||||||||
\(466\) | 4.67318 | 0.216481 | ||||||||
\(467\) | −12.6213 | −0.584043 | −0.292022 | − | 0.956412i | \(-0.594328\pi\) | ||||
−0.292022 | + | 0.956412i | \(0.594328\pi\) | |||||||
\(468\) | −70.1372 | −3.24209 | ||||||||
\(469\) | 4.74573 | 0.219137 | ||||||||
\(470\) | −67.7499 | −3.12507 | ||||||||
\(471\) | 2.58030 | 0.118894 | ||||||||
\(472\) | −45.0100 | −2.07176 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −14.9618 | −0.687220 | ||||||||
\(475\) | 51.4696 | 2.36159 | ||||||||
\(476\) | −25.4183 | −1.16504 | ||||||||
\(477\) | 21.4901 | 0.983966 | ||||||||
\(478\) | −34.7138 | −1.58777 | ||||||||
\(479\) | 40.0532 | 1.83008 | 0.915038 | − | 0.403368i | \(-0.132161\pi\) | ||||
0.915038 | + | 0.403368i | \(0.132161\pi\) | |||||||
\(480\) | −44.2441 | −2.01946 | ||||||||
\(481\) | 35.6495 | 1.62548 | ||||||||
\(482\) | −51.6196 | −2.35121 | ||||||||
\(483\) | 3.98388 | 0.181273 | ||||||||
\(484\) | 5.11634 | 0.232561 | ||||||||
\(485\) | −8.42223 | −0.382434 | ||||||||
\(486\) | −40.3892 | −1.83209 | ||||||||
\(487\) | −13.9768 | −0.633348 | −0.316674 | − | 0.948534i | \(-0.602566\pi\) | ||||
−0.316674 | + | 0.948534i | \(0.602566\pi\) | |||||||
\(488\) | 76.6143 | 3.46817 | ||||||||
\(489\) | −17.0149 | −0.769438 | ||||||||
\(490\) | −10.7807 | −0.487021 | ||||||||
\(491\) | −16.9512 | −0.764999 | −0.382499 | − | 0.923956i | \(-0.624937\pi\) | ||||
−0.382499 | + | 0.923956i | \(0.624937\pi\) | |||||||
\(492\) | −18.9175 | −0.852865 | ||||||||
\(493\) | 21.6436 | 0.974778 | ||||||||
\(494\) | −66.8761 | −3.00890 | ||||||||
\(495\) | −10.0373 | −0.451141 | ||||||||
\(496\) | −48.4463 | −2.17530 | ||||||||
\(497\) | 16.4133 | 0.736235 | ||||||||
\(498\) | 9.11666 | 0.408528 | ||||||||
\(499\) | 38.3649 | 1.71745 | 0.858725 | − | 0.512437i | \(-0.171257\pi\) | ||||
0.858725 | + | 0.512437i | \(0.171257\pi\) | |||||||
\(500\) | 130.919 | 5.85488 | ||||||||
\(501\) | −15.3797 | −0.687112 | ||||||||
\(502\) | −33.9546 | −1.51547 | ||||||||
\(503\) | 2.55024 | 0.113710 | 0.0568548 | − | 0.998382i | \(-0.481893\pi\) | ||||
0.0568548 | + | 0.998382i | \(0.481893\pi\) | |||||||
\(504\) | 20.6477 | 0.919723 | ||||||||
\(505\) | 7.84202 | 0.348965 | ||||||||
\(506\) | −14.7905 | −0.657517 | ||||||||
\(507\) | 12.5483 | 0.557289 | ||||||||
\(508\) | 21.8505 | 0.969457 | ||||||||
\(509\) | 42.3211 | 1.87585 | 0.937924 | − | 0.346841i | \(-0.112746\pi\) | ||||
0.937924 | + | 0.346841i | \(0.112746\pi\) | |||||||
\(510\) | 38.4844 | 1.70412 | ||||||||
\(511\) | −1.37440 | −0.0607997 | ||||||||
\(512\) | 16.6036 | 0.733781 | ||||||||
\(513\) | −17.8969 | −0.790169 | ||||||||
\(514\) | −23.9987 | −1.05854 | ||||||||
\(515\) | −26.6312 | −1.17351 | ||||||||
\(516\) | 3.67631 | 0.161841 | ||||||||
\(517\) | 6.28439 | 0.276387 | ||||||||
\(518\) | −17.2302 | −0.757053 | ||||||||
\(519\) | −1.99409 | −0.0875309 | ||||||||
\(520\) | −185.430 | −8.13166 | ||||||||
\(521\) | 25.2903 | 1.10799 | 0.553994 | − | 0.832521i | \(-0.313103\pi\) | ||||
0.553994 | + | 0.832521i | \(0.313103\pi\) | |||||||
\(522\) | −28.8649 | −1.26338 | ||||||||
\(523\) | −20.0521 | −0.876818 | −0.438409 | − | 0.898776i | \(-0.644458\pi\) | ||||
−0.438409 | + | 0.898776i | \(0.644458\pi\) | |||||||
\(524\) | −43.4134 | −1.89652 | ||||||||
\(525\) | 8.14238 | 0.355362 | ||||||||
\(526\) | −1.84386 | −0.0803960 | ||||||||
\(527\) | 20.1505 | 0.877771 | ||||||||
\(528\) | 8.58248 | 0.373505 | ||||||||
\(529\) | 7.74029 | 0.336534 | ||||||||
\(530\) | 93.2795 | 4.05180 | ||||||||
\(531\) | −13.4473 | −0.583562 | ||||||||
\(532\) | 23.2387 | 1.00753 | ||||||||
\(533\) | −28.4014 | −1.23020 | ||||||||
\(534\) | −16.2890 | −0.704896 | ||||||||
\(535\) | −13.4932 | −0.583362 | ||||||||
\(536\) | −39.4527 | −1.70410 | ||||||||
\(537\) | −2.29220 | −0.0989159 | ||||||||
\(538\) | 33.1354 | 1.42857 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −81.4709 | −3.50595 | ||||||||
\(541\) | 20.8151 | 0.894910 | 0.447455 | − | 0.894306i | \(-0.352330\pi\) | ||||
0.447455 | + | 0.894306i | \(0.352330\pi\) | |||||||
\(542\) | −14.9739 | −0.643185 | ||||||||
\(543\) | 7.90216 | 0.339114 | ||||||||
\(544\) | 75.6959 | 3.24543 | ||||||||
\(545\) | 63.7871 | 2.73234 | ||||||||
\(546\) | −10.5796 | −0.452767 | ||||||||
\(547\) | −14.9240 | −0.638106 | −0.319053 | − | 0.947737i | \(-0.603365\pi\) | ||||
−0.319053 | + | 0.947737i | \(0.603365\pi\) | |||||||
\(548\) | 64.3382 | 2.74839 | ||||||||
\(549\) | 22.8894 | 0.976896 | ||||||||
\(550\) | −30.2292 | −1.28898 | ||||||||
\(551\) | −19.7877 | −0.842985 | ||||||||
\(552\) | −33.1192 | −1.40965 | ||||||||
\(553\) | 7.80555 | 0.331926 | ||||||||
\(554\) | −77.3608 | −3.28675 | ||||||||
\(555\) | 18.7557 | 0.796134 | ||||||||
\(556\) | −66.0075 | −2.79934 | ||||||||
\(557\) | 29.0292 | 1.23000 | 0.615002 | − | 0.788525i | \(-0.289155\pi\) | ||||
0.615002 | + | 0.788525i | \(0.289155\pi\) | |||||||
\(558\) | −26.8737 | −1.13765 | ||||||||
\(559\) | 5.51938 | 0.233445 | ||||||||
\(560\) | 48.2700 | 2.03978 | ||||||||
\(561\) | −3.56976 | −0.150715 | ||||||||
\(562\) | −6.15183 | −0.259499 | ||||||||
\(563\) | −8.06217 | −0.339780 | −0.169890 | − | 0.985463i | \(-0.554341\pi\) | ||||
−0.169890 | + | 0.985463i | \(0.554341\pi\) | |||||||
\(564\) | 23.1034 | 0.972828 | ||||||||
\(565\) | −6.60544 | −0.277893 | ||||||||
\(566\) | 13.3219 | 0.559962 | ||||||||
\(567\) | 4.61983 | 0.194015 | ||||||||
\(568\) | −136.448 | −5.72525 | ||||||||
\(569\) | −38.3710 | −1.60860 | −0.804298 | − | 0.594226i | \(-0.797458\pi\) | ||||
−0.804298 | + | 0.594226i | \(0.797458\pi\) | |||||||
\(570\) | −35.1844 | −1.47371 | ||||||||
\(571\) | −6.07796 | −0.254355 | −0.127177 | − | 0.991880i | \(-0.540592\pi\) | ||||
−0.127177 | + | 0.991880i | \(0.540592\pi\) | |||||||
\(572\) | 28.2390 | 1.18073 | ||||||||
\(573\) | −14.4514 | −0.603715 | ||||||||
\(574\) | 13.7271 | 0.572958 | ||||||||
\(575\) | 62.8279 | 2.62010 | ||||||||
\(576\) | −41.6196 | −1.73415 | ||||||||
\(577\) | −22.4641 | −0.935191 | −0.467595 | − | 0.883943i | \(-0.654880\pi\) | ||||
−0.467595 | + | 0.883943i | \(0.654880\pi\) | |||||||
\(578\) | −20.4917 | −0.852343 | ||||||||
\(579\) | 12.9402 | 0.537776 | ||||||||
\(580\) | −90.0781 | −3.74029 | ||||||||
\(581\) | −4.75614 | −0.197318 | ||||||||
\(582\) | 3.99477 | 0.165588 | ||||||||
\(583\) | −8.65248 | −0.358349 | ||||||||
\(584\) | 11.4258 | 0.472802 | ||||||||
\(585\) | −55.3994 | −2.29049 | ||||||||
\(586\) | −67.8506 | −2.80288 | ||||||||
\(587\) | 16.2393 | 0.670266 | 0.335133 | − | 0.942171i | \(-0.391219\pi\) | ||||
0.335133 | + | 0.942171i | \(0.391219\pi\) | |||||||
\(588\) | 3.67631 | 0.151609 | ||||||||
\(589\) | −18.4227 | −0.759093 | ||||||||
\(590\) | −58.3688 | −2.40301 | ||||||||
\(591\) | 2.85547 | 0.117459 | ||||||||
\(592\) | 77.1477 | 3.17075 | ||||||||
\(593\) | −32.2290 | −1.32348 | −0.661742 | − | 0.749731i | \(-0.730183\pi\) | ||||
−0.661742 | + | 0.749731i | \(0.730183\pi\) | |||||||
\(594\) | 10.5113 | 0.431282 | ||||||||
\(595\) | −20.0772 | −0.823085 | ||||||||
\(596\) | −56.6058 | −2.31866 | ||||||||
\(597\) | 7.97035 | 0.326205 | ||||||||
\(598\) | −81.6343 | −3.33827 | ||||||||
\(599\) | 12.6481 | 0.516786 | 0.258393 | − | 0.966040i | \(-0.416807\pi\) | ||||
0.258393 | + | 0.966040i | \(0.416807\pi\) | |||||||
\(600\) | −67.6901 | −2.76344 | ||||||||
\(601\) | 28.7633 | 1.17328 | 0.586639 | − | 0.809848i | \(-0.300451\pi\) | ||||
0.586639 | + | 0.809848i | \(0.300451\pi\) | |||||||
\(602\) | −2.66765 | −0.108725 | ||||||||
\(603\) | −11.7869 | −0.480001 | ||||||||
\(604\) | 118.053 | 4.80350 | ||||||||
\(605\) | 4.04126 | 0.164301 | ||||||||
\(606\) | −3.71957 | −0.151097 | ||||||||
\(607\) | 14.2489 | 0.578346 | 0.289173 | − | 0.957277i | \(-0.406620\pi\) | ||||
0.289173 | + | 0.957277i | \(0.406620\pi\) | |||||||
\(608\) | −69.2052 | −2.80664 | ||||||||
\(609\) | −3.13037 | −0.126849 | ||||||||
\(610\) | 99.3531 | 4.02269 | ||||||||
\(611\) | 34.6859 | 1.40324 | ||||||||
\(612\) | 63.1313 | 2.55193 | ||||||||
\(613\) | 28.5551 | 1.15333 | 0.576664 | − | 0.816981i | \(-0.304354\pi\) | ||||
0.576664 | + | 0.816981i | \(0.304354\pi\) | |||||||
\(614\) | 0.689137 | 0.0278113 | ||||||||
\(615\) | −14.9424 | −0.602535 | ||||||||
\(616\) | −8.31331 | −0.334953 | ||||||||
\(617\) | 18.1765 | 0.731759 | 0.365880 | − | 0.930662i | \(-0.380768\pi\) | ||||
0.365880 | + | 0.930662i | \(0.380768\pi\) | |||||||
\(618\) | 12.6315 | 0.508115 | ||||||||
\(619\) | −46.0766 | −1.85197 | −0.925987 | − | 0.377556i | \(-0.876764\pi\) | ||||
−0.925987 | + | 0.377556i | \(0.876764\pi\) | |||||||
\(620\) | −83.8642 | −3.36807 | ||||||||
\(621\) | −21.8464 | −0.876666 | ||||||||
\(622\) | −63.6314 | −2.55139 | ||||||||
\(623\) | 8.49796 | 0.340463 | ||||||||
\(624\) | 47.3699 | 1.89632 | ||||||||
\(625\) | 46.7505 | 1.87002 | ||||||||
\(626\) | 77.4373 | 3.09502 | ||||||||
\(627\) | 3.26366 | 0.130338 | ||||||||
\(628\) | 18.3729 | 0.733158 | ||||||||
\(629\) | −32.0885 | −1.27945 | ||||||||
\(630\) | 26.7759 | 1.06678 | ||||||||
\(631\) | −16.0331 | −0.638269 | −0.319135 | − | 0.947709i | \(-0.603392\pi\) | ||||
−0.319135 | + | 0.947709i | \(0.603392\pi\) | |||||||
\(632\) | −64.8899 | −2.58118 | ||||||||
\(633\) | −18.7899 | −0.746830 | ||||||||
\(634\) | 54.9975 | 2.18423 | ||||||||
\(635\) | 17.2591 | 0.684906 | ||||||||
\(636\) | −31.8092 | −1.26132 | ||||||||
\(637\) | 5.51938 | 0.218686 | ||||||||
\(638\) | 11.6217 | 0.460109 | ||||||||
\(639\) | −40.7655 | −1.61266 | ||||||||
\(640\) | −57.5032 | −2.27301 | ||||||||
\(641\) | 4.25668 | 0.168129 | 0.0840644 | − | 0.996460i | \(-0.473210\pi\) | ||||
0.0840644 | + | 0.996460i | \(0.473210\pi\) | |||||||
\(642\) | 6.39999 | 0.252588 | ||||||||
\(643\) | −2.47779 | −0.0977145 | −0.0488572 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488572 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(644\) | 28.3670 | 1.11782 | ||||||||
\(645\) | 2.90382 | 0.114338 | ||||||||
\(646\) | 60.1960 | 2.36838 | ||||||||
\(647\) | 39.8310 | 1.56592 | 0.782959 | − | 0.622073i | \(-0.213709\pi\) | ||||
0.782959 | + | 0.622073i | \(0.213709\pi\) | |||||||
\(648\) | −38.4061 | −1.50873 | ||||||||
\(649\) | 5.41422 | 0.212527 | ||||||||
\(650\) | −166.846 | −6.54426 | ||||||||
\(651\) | −2.91443 | −0.114225 | ||||||||
\(652\) | −121.153 | −4.74473 | ||||||||
\(653\) | −28.3938 | −1.11113 | −0.555567 | − | 0.831472i | \(-0.687499\pi\) | ||||
−0.555567 | + | 0.831472i | \(0.687499\pi\) | |||||||
\(654\) | −30.2550 | −1.18306 | ||||||||
\(655\) | −34.2911 | −1.33986 | ||||||||
\(656\) | −61.4625 | −2.39971 | ||||||||
\(657\) | 3.41358 | 0.133176 | ||||||||
\(658\) | −16.7645 | −0.653550 | ||||||||
\(659\) | −37.1416 | −1.44683 | −0.723415 | − | 0.690414i | \(-0.757428\pi\) | ||||
−0.723415 | + | 0.690414i | \(0.757428\pi\) | |||||||
\(660\) | 14.8569 | 0.578306 | ||||||||
\(661\) | 5.24905 | 0.204165 | 0.102082 | − | 0.994776i | \(-0.467450\pi\) | ||||
0.102082 | + | 0.994776i | \(0.467450\pi\) | |||||||
\(662\) | −82.2815 | −3.19796 | ||||||||
\(663\) | −19.7029 | −0.765195 | ||||||||
\(664\) | 39.5393 | 1.53442 | ||||||||
\(665\) | 18.3556 | 0.711801 | ||||||||
\(666\) | 42.7947 | 1.65826 | ||||||||
\(667\) | −24.1544 | −0.935263 | ||||||||
\(668\) | −109.510 | −4.23707 | ||||||||
\(669\) | −19.0566 | −0.736772 | ||||||||
\(670\) | −51.1621 | −1.97656 | ||||||||
\(671\) | −9.21586 | −0.355774 | ||||||||
\(672\) | −10.9481 | −0.422332 | ||||||||
\(673\) | −33.2139 | −1.28030 | −0.640150 | − | 0.768250i | \(-0.721128\pi\) | ||||
−0.640150 | + | 0.768250i | \(0.721128\pi\) | |||||||
\(674\) | 22.9514 | 0.884055 | ||||||||
\(675\) | −44.6503 | −1.71859 | ||||||||
\(676\) | 89.3494 | 3.43652 | ||||||||
\(677\) | 21.1752 | 0.813830 | 0.406915 | − | 0.913466i | \(-0.366605\pi\) | ||||
0.406915 | + | 0.913466i | \(0.366605\pi\) | |||||||
\(678\) | 3.13304 | 0.120324 | ||||||||
\(679\) | −2.08406 | −0.0799789 | ||||||||
\(680\) | 166.908 | 6.40063 | ||||||||
\(681\) | −6.98107 | −0.267515 | ||||||||
\(682\) | 10.8200 | 0.414321 | ||||||||
\(683\) | 13.5577 | 0.518769 | 0.259385 | − | 0.965774i | \(-0.416480\pi\) | ||||
0.259385 | + | 0.965774i | \(0.416480\pi\) | |||||||
\(684\) | −57.7179 | −2.20690 | ||||||||
\(685\) | 50.8190 | 1.94169 | ||||||||
\(686\) | −2.66765 | −0.101851 | ||||||||
\(687\) | −7.22627 | −0.275699 | ||||||||
\(688\) | 11.9443 | 0.455372 | ||||||||
\(689\) | −47.7563 | −1.81937 | ||||||||
\(690\) | −42.9489 | −1.63504 | ||||||||
\(691\) | −16.7121 | −0.635759 | −0.317879 | − | 0.948131i | \(-0.602971\pi\) | ||||
−0.317879 | + | 0.948131i | \(0.602971\pi\) | |||||||
\(692\) | −14.1988 | −0.539758 | ||||||||
\(693\) | −2.48370 | −0.0943478 | ||||||||
\(694\) | 93.9017 | 3.56446 | ||||||||
\(695\) | −52.1375 | −1.97769 | ||||||||
\(696\) | 26.0237 | 0.986426 | ||||||||
\(697\) | 25.5645 | 0.968323 | ||||||||
\(698\) | −86.2717 | −3.26543 | ||||||||
\(699\) | −1.25874 | −0.0476100 | ||||||||
\(700\) | 57.9773 | 2.19134 | ||||||||
\(701\) | 46.2335 | 1.74621 | 0.873107 | − | 0.487529i | \(-0.162102\pi\) | ||||
0.873107 | + | 0.487529i | \(0.162102\pi\) | |||||||
\(702\) | 58.0156 | 2.18966 | ||||||||
\(703\) | 29.3370 | 1.10647 | ||||||||
\(704\) | 16.7571 | 0.631558 | ||||||||
\(705\) | 18.2487 | 0.687287 | ||||||||
\(706\) | 81.6298 | 3.07218 | ||||||||
\(707\) | 1.94049 | 0.0729796 | ||||||||
\(708\) | 19.9044 | 0.748051 | ||||||||
\(709\) | −19.9411 | −0.748904 | −0.374452 | − | 0.927246i | \(-0.622169\pi\) | ||||
−0.374452 | + | 0.927246i | \(0.622169\pi\) | |||||||
\(710\) | −176.946 | −6.64065 | ||||||||
\(711\) | −19.3866 | −0.727055 | ||||||||
\(712\) | −70.6461 | −2.64757 | ||||||||
\(713\) | −22.4882 | −0.842189 | ||||||||
\(714\) | 9.52286 | 0.356384 | ||||||||
\(715\) | 22.3052 | 0.834169 | ||||||||
\(716\) | −16.3215 | −0.609963 | ||||||||
\(717\) | 9.35033 | 0.349194 | ||||||||
\(718\) | 70.1681 | 2.61865 | ||||||||
\(719\) | 10.7564 | 0.401145 | 0.200573 | − | 0.979679i | \(-0.435720\pi\) | ||||
0.200573 | + | 0.979679i | \(0.435720\pi\) | |||||||
\(720\) | −119.888 | −4.46796 | ||||||||
\(721\) | −6.58984 | −0.245418 | ||||||||
\(722\) | −4.34904 | −0.161855 | ||||||||
\(723\) | 13.9040 | 0.517095 | ||||||||
\(724\) | 56.2669 | 2.09114 | ||||||||
\(725\) | −49.3675 | −1.83346 | ||||||||
\(726\) | −1.91682 | −0.0711398 | ||||||||
\(727\) | 31.8213 | 1.18019 | 0.590093 | − | 0.807335i | \(-0.299091\pi\) | ||||
0.590093 | + | 0.807335i | \(0.299091\pi\) | |||||||
\(728\) | −45.8843 | −1.70058 | ||||||||
\(729\) | −2.98050 | −0.110389 | ||||||||
\(730\) | 14.8169 | 0.548398 | ||||||||
\(731\) | −4.96805 | −0.183750 | ||||||||
\(732\) | −33.8804 | −1.25226 | ||||||||
\(733\) | 8.57434 | 0.316700 | 0.158350 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158350 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(734\) | 57.7910 | 2.13311 | ||||||||
\(735\) | 2.90382 | 0.107109 | ||||||||
\(736\) | −84.4773 | −3.11387 | ||||||||
\(737\) | 4.74573 | 0.174811 | ||||||||
\(738\) | −34.0939 | −1.25502 | ||||||||
\(739\) | 25.4431 | 0.935939 | 0.467970 | − | 0.883745i | \(-0.344986\pi\) | ||||
0.467970 | + | 0.883745i | \(0.344986\pi\) | |||||||
\(740\) | 133.549 | 4.90935 | ||||||||
\(741\) | 18.0134 | 0.661738 | ||||||||
\(742\) | 23.0818 | 0.847359 | ||||||||
\(743\) | 10.4730 | 0.384219 | 0.192109 | − | 0.981374i | \(-0.438467\pi\) | ||||
0.192109 | + | 0.981374i | \(0.438467\pi\) | |||||||
\(744\) | 24.2285 | 0.888260 | ||||||||
\(745\) | −44.7114 | −1.63810 | ||||||||
\(746\) | −17.3796 | −0.636311 | ||||||||
\(747\) | 11.8128 | 0.432208 | ||||||||
\(748\) | −25.4183 | −0.929384 | ||||||||
\(749\) | −3.33886 | −0.121999 | ||||||||
\(750\) | −49.0484 | −1.79099 | ||||||||
\(751\) | 44.1902 | 1.61252 | 0.806261 | − | 0.591560i | \(-0.201488\pi\) | ||||
0.806261 | + | 0.591560i | \(0.201488\pi\) | |||||||
\(752\) | 75.0625 | 2.73725 | ||||||||
\(753\) | 9.14582 | 0.333292 | ||||||||
\(754\) | 64.1448 | 2.33602 | ||||||||
\(755\) | 93.2466 | 3.39359 | ||||||||
\(756\) | −20.1598 | −0.733204 | ||||||||
\(757\) | 17.8450 | 0.648589 | 0.324294 | − | 0.945956i | \(-0.394873\pi\) | ||||
0.324294 | + | 0.945956i | \(0.394873\pi\) | |||||||
\(758\) | 1.34595 | 0.0488872 | ||||||||
\(759\) | 3.98388 | 0.144606 | ||||||||
\(760\) | −152.596 | −5.53524 | ||||||||
\(761\) | −25.8790 | −0.938112 | −0.469056 | − | 0.883168i | \(-0.655406\pi\) | ||||
−0.469056 | + | 0.883168i | \(0.655406\pi\) | |||||||
\(762\) | −8.18619 | −0.296554 | ||||||||
\(763\) | 15.7840 | 0.571418 | ||||||||
\(764\) | −102.900 | −3.72280 | ||||||||
\(765\) | 49.8657 | 1.80290 | ||||||||
\(766\) | 46.1233 | 1.66650 | ||||||||
\(767\) | 29.8831 | 1.07902 | ||||||||
\(768\) | 3.19306 | 0.115220 | ||||||||
\(769\) | 24.2088 | 0.872993 | 0.436497 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436497 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(770\) | −10.7807 | −0.388508 | ||||||||
\(771\) | 6.46416 | 0.232801 | ||||||||
\(772\) | 92.1399 | 3.31619 | ||||||||
\(773\) | 50.6535 | 1.82188 | 0.910940 | − | 0.412539i | \(-0.135358\pi\) | ||||
0.910940 | + | 0.412539i | \(0.135358\pi\) | |||||||
\(774\) | 6.62563 | 0.238153 | ||||||||
\(775\) | −45.9620 | −1.65100 | ||||||||
\(776\) | 17.3254 | 0.621947 | ||||||||
\(777\) | 4.64104 | 0.166496 | ||||||||
\(778\) | 62.6166 | 2.24491 | ||||||||
\(779\) | −23.3724 | −0.837402 | ||||||||
\(780\) | 82.0010 | 2.93611 | ||||||||
\(781\) | 16.4133 | 0.587312 | ||||||||
\(782\) | 73.4799 | 2.62764 | ||||||||
\(783\) | 17.1660 | 0.613463 | ||||||||
\(784\) | 11.9443 | 0.426582 | ||||||||
\(785\) | 14.5122 | 0.517964 | ||||||||
\(786\) | 16.2647 | 0.580142 | ||||||||
\(787\) | −26.6822 | −0.951118 | −0.475559 | − | 0.879684i | \(-0.657754\pi\) | ||||
−0.475559 | + | 0.879684i | \(0.657754\pi\) | |||||||
\(788\) | 20.3322 | 0.724306 | ||||||||
\(789\) | 0.496651 | 0.0176812 | ||||||||
\(790\) | −84.1490 | −2.99389 | ||||||||
\(791\) | −1.63450 | −0.0581161 | ||||||||
\(792\) | 20.6477 | 0.733685 | ||||||||
\(793\) | −50.8658 | −1.80630 | ||||||||
\(794\) | −28.7450 | −1.02012 | ||||||||
\(795\) | −25.1252 | −0.891101 | ||||||||
\(796\) | 56.7524 | 2.01154 | ||||||||
\(797\) | −42.0793 | −1.49052 | −0.745262 | − | 0.666772i | \(-0.767676\pi\) | ||||
−0.745262 | + | 0.666772i | \(0.767676\pi\) | |||||||
\(798\) | −8.70630 | −0.308200 | ||||||||
\(799\) | −31.2212 | −1.10453 | ||||||||
\(800\) | −172.657 | −6.10435 | ||||||||
\(801\) | −21.1063 | −0.745756 | ||||||||
\(802\) | −100.888 | −3.56247 | ||||||||
\(803\) | −1.37440 | −0.0485014 | ||||||||
\(804\) | 17.4468 | 0.615300 | ||||||||
\(805\) | 22.4063 | 0.789720 | ||||||||
\(806\) | 59.7199 | 2.10354 | ||||||||
\(807\) | −8.92518 | −0.314181 | ||||||||
\(808\) | −16.1319 | −0.567517 | ||||||||
\(809\) | 4.33163 | 0.152292 | 0.0761461 | − | 0.997097i | \(-0.475738\pi\) | ||||
0.0761461 | + | 0.997097i | \(0.475738\pi\) | |||||||
\(810\) | −49.8049 | −1.74996 | ||||||||
\(811\) | −12.5576 | −0.440955 | −0.220478 | − | 0.975392i | \(-0.570762\pi\) | ||||
−0.220478 | + | 0.975392i | \(0.570762\pi\) | |||||||
\(812\) | −22.2896 | −0.782212 | ||||||||
\(813\) | 4.03329 | 0.141454 | ||||||||
\(814\) | −17.2302 | −0.603920 | ||||||||
\(815\) | −95.6957 | −3.35207 | ||||||||
\(816\) | −42.6382 | −1.49264 | ||||||||
\(817\) | 4.54206 | 0.158906 | ||||||||
\(818\) | −59.6131 | −2.08432 | ||||||||
\(819\) | −13.7085 | −0.479012 | ||||||||
\(820\) | −106.396 | −3.71552 | ||||||||
\(821\) | 51.2305 | 1.78796 | 0.893978 | − | 0.448111i | \(-0.147903\pi\) | ||||
0.893978 | + | 0.448111i | \(0.147903\pi\) | |||||||
\(822\) | −24.1041 | −0.840726 | ||||||||
\(823\) | −1.43072 | −0.0498717 | −0.0249359 | − | 0.999689i | \(-0.507938\pi\) | ||||
−0.0249359 | + | 0.999689i | \(0.507938\pi\) | |||||||
\(824\) | 54.7833 | 1.90847 | ||||||||
\(825\) | 8.14238 | 0.283481 | ||||||||
\(826\) | −14.4432 | −0.502544 | ||||||||
\(827\) | 26.0424 | 0.905582 | 0.452791 | − | 0.891617i | \(-0.350428\pi\) | ||||
0.452791 | + | 0.891617i | \(0.350428\pi\) | |||||||
\(828\) | −70.4550 | −2.44848 | ||||||||
\(829\) | −8.16785 | −0.283681 | −0.141841 | − | 0.989890i | \(-0.545302\pi\) | ||||
−0.141841 | + | 0.989890i | \(0.545302\pi\) | |||||||
\(830\) | 51.2743 | 1.77976 | ||||||||
\(831\) | 20.8375 | 0.722845 | ||||||||
\(832\) | 92.4888 | 3.20647 | ||||||||
\(833\) | −4.96805 | −0.172133 | ||||||||
\(834\) | 24.7295 | 0.856311 | ||||||||
\(835\) | −86.4989 | −2.99342 | ||||||||
\(836\) | 23.2387 | 0.803728 | ||||||||
\(837\) | 15.9818 | 0.552413 | ||||||||
\(838\) | 51.5898 | 1.78214 | ||||||||
\(839\) | 7.06951 | 0.244067 | 0.122033 | − | 0.992526i | \(-0.461059\pi\) | ||||
0.122033 | + | 0.992526i | \(0.461059\pi\) | |||||||
\(840\) | −24.1403 | −0.832921 | ||||||||
\(841\) | −10.0205 | −0.345533 | ||||||||
\(842\) | 60.7011 | 2.09190 | ||||||||
\(843\) | 1.65702 | 0.0570709 | ||||||||
\(844\) | −133.792 | −4.60532 | ||||||||
\(845\) | 70.5747 | 2.42784 | ||||||||
\(846\) | 41.6380 | 1.43154 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −103.348 | −3.54898 | ||||||||
\(849\) | −3.58832 | −0.123151 | ||||||||
\(850\) | 150.180 | 5.15115 | ||||||||
\(851\) | 35.8110 | 1.22759 | ||||||||
\(852\) | 60.3402 | 2.06722 | ||||||||
\(853\) | 4.83085 | 0.165405 | 0.0827025 | − | 0.996574i | \(-0.473645\pi\) | ||||
0.0827025 | + | 0.996574i | \(0.473645\pi\) | |||||||
\(854\) | 24.5847 | 0.841270 | ||||||||
\(855\) | −45.5898 | −1.55914 | ||||||||
\(856\) | 27.7570 | 0.948714 | ||||||||
\(857\) | −37.4447 | −1.27909 | −0.639543 | − | 0.768756i | \(-0.720876\pi\) | ||||
−0.639543 | + | 0.768756i | \(0.720876\pi\) | |||||||
\(858\) | −10.5796 | −0.361183 | ||||||||
\(859\) | −40.8105 | −1.39244 | −0.696218 | − | 0.717831i | \(-0.745135\pi\) | ||||
−0.696218 | + | 0.717831i | \(0.745135\pi\) | |||||||
\(860\) | 20.6765 | 0.705062 | ||||||||
\(861\) | −3.69746 | −0.126009 | ||||||||
\(862\) | −35.7180 | −1.21656 | ||||||||
\(863\) | −31.0252 | −1.05611 | −0.528055 | − | 0.849210i | \(-0.677078\pi\) | ||||
−0.528055 | + | 0.849210i | \(0.677078\pi\) | |||||||
\(864\) | 60.0360 | 2.04247 | ||||||||
\(865\) | −11.2153 | −0.381330 | ||||||||
\(866\) | −24.0074 | −0.815804 | ||||||||
\(867\) | 5.51953 | 0.187453 | ||||||||
\(868\) | −20.7520 | −0.704369 | ||||||||
\(869\) | 7.80555 | 0.264785 | ||||||||
\(870\) | 33.7474 | 1.14415 | ||||||||
\(871\) | 26.1935 | 0.887531 | ||||||||
\(872\) | −131.217 | −4.44357 | ||||||||
\(873\) | 5.17617 | 0.175187 | ||||||||
\(874\) | −67.1792 | −2.27237 | ||||||||
\(875\) | 25.5884 | 0.865046 | ||||||||
\(876\) | −5.05271 | −0.170715 | ||||||||
\(877\) | 22.0408 | 0.744266 | 0.372133 | − | 0.928179i | \(-0.378626\pi\) | ||||
0.372133 | + | 0.928179i | \(0.378626\pi\) | |||||||
\(878\) | 39.1510 | 1.32128 | ||||||||
\(879\) | 18.2759 | 0.616430 | ||||||||
\(880\) | 48.2700 | 1.62718 | ||||||||
\(881\) | −25.4669 | −0.858002 | −0.429001 | − | 0.903304i | \(-0.641134\pi\) | ||||
−0.429001 | + | 0.903304i | \(0.641134\pi\) | |||||||
\(882\) | 6.62563 | 0.223096 | ||||||||
\(883\) | −40.3906 | −1.35925 | −0.679625 | − | 0.733560i | \(-0.737858\pi\) | ||||
−0.679625 | + | 0.733560i | \(0.737858\pi\) | |||||||
\(884\) | −140.293 | −4.71857 | ||||||||
\(885\) | 15.7219 | 0.528486 | ||||||||
\(886\) | 102.708 | 3.45053 | ||||||||
\(887\) | 39.6915 | 1.33271 | 0.666355 | − | 0.745635i | \(-0.267854\pi\) | ||||
0.666355 | + | 0.745635i | \(0.267854\pi\) | |||||||
\(888\) | −38.5824 | −1.29474 | ||||||||
\(889\) | 4.27072 | 0.143235 | ||||||||
\(890\) | −91.6136 | −3.07089 | ||||||||
\(891\) | 4.61983 | 0.154770 | ||||||||
\(892\) | −135.692 | −4.54329 | ||||||||
\(893\) | 28.5441 | 0.955191 | ||||||||
\(894\) | 21.2071 | 0.709273 | ||||||||
\(895\) | −12.8919 | −0.430929 | ||||||||
\(896\) | −14.2290 | −0.475358 | ||||||||
\(897\) | 21.9886 | 0.734177 | ||||||||
\(898\) | 41.0662 | 1.37040 | ||||||||
\(899\) | 17.6703 | 0.589336 | ||||||||
\(900\) | −143.998 | −4.79994 | ||||||||
\(901\) | 42.9860 | 1.43207 | ||||||||
\(902\) | 13.7271 | 0.457062 | ||||||||
\(903\) | 0.718543 | 0.0239116 | ||||||||
\(904\) | 13.5881 | 0.451933 | ||||||||
\(905\) | 44.4437 | 1.47736 | ||||||||
\(906\) | −44.2280 | −1.46938 | ||||||||
\(907\) | 11.5260 | 0.382715 | 0.191357 | − | 0.981520i | \(-0.438711\pi\) | ||||
0.191357 | + | 0.981520i | \(0.438711\pi\) | |||||||
\(908\) | −49.7083 | −1.64963 | ||||||||
\(909\) | −4.81958 | −0.159855 | ||||||||
\(910\) | −59.5025 | −1.97249 | ||||||||
\(911\) | 39.9163 | 1.32249 | 0.661243 | − | 0.750172i | \(-0.270029\pi\) | ||||
0.661243 | + | 0.750172i | \(0.270029\pi\) | |||||||
\(912\) | 38.9821 | 1.29083 | ||||||||
\(913\) | −4.75614 | −0.157405 | ||||||||
\(914\) | −52.4913 | −1.73626 | ||||||||
\(915\) | −26.7612 | −0.884698 | ||||||||
\(916\) | −51.4542 | −1.70010 | ||||||||
\(917\) | −8.48525 | −0.280208 | ||||||||
\(918\) | −52.2205 | −1.72353 | ||||||||
\(919\) | 26.1430 | 0.862377 | 0.431188 | − | 0.902262i | \(-0.358094\pi\) | ||||
0.431188 | + | 0.902262i | \(0.358094\pi\) | |||||||
\(920\) | −186.271 | −6.14116 | ||||||||
\(921\) | −0.185622 | −0.00611646 | ||||||||
\(922\) | 104.692 | 3.44786 | ||||||||
\(923\) | 90.5909 | 2.98184 | ||||||||
\(924\) | 3.67631 | 0.120942 | ||||||||
\(925\) | 73.1916 | 2.40653 | ||||||||
\(926\) | −8.68578 | −0.285432 | ||||||||
\(927\) | 16.3672 | 0.537568 | ||||||||
\(928\) | 66.3787 | 2.17899 | ||||||||
\(929\) | 3.08427 | 0.101192 | 0.0505958 | − | 0.998719i | \(-0.483888\pi\) | ||||
0.0505958 | + | 0.998719i | \(0.483888\pi\) | |||||||
\(930\) | 31.4194 | 1.03028 | ||||||||
\(931\) | 4.54206 | 0.148860 | ||||||||
\(932\) | −8.96280 | −0.293586 | ||||||||
\(933\) | 17.1394 | 0.561119 | ||||||||
\(934\) | 33.6691 | 1.10169 | ||||||||
\(935\) | −20.0772 | −0.656595 | ||||||||
\(936\) | 113.963 | 3.72498 | ||||||||
\(937\) | −9.73490 | −0.318025 | −0.159013 | − | 0.987277i | \(-0.550831\pi\) | ||||
−0.159013 | + | 0.987277i | \(0.550831\pi\) | |||||||
\(938\) | −12.6599 | −0.413361 | ||||||||
\(939\) | −20.8581 | −0.680678 | ||||||||
\(940\) | 129.939 | 4.23814 | ||||||||
\(941\) | −30.4428 | −0.992407 | −0.496204 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496204 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(942\) | −6.88333 | −0.224271 | ||||||||
\(943\) | −28.5302 | −0.929070 | ||||||||
\(944\) | 64.6689 | 2.10479 | ||||||||
\(945\) | −15.9237 | −0.517997 | ||||||||
\(946\) | −2.66765 | −0.0867327 | ||||||||
\(947\) | 17.0361 | 0.553600 | 0.276800 | − | 0.960928i | \(-0.410726\pi\) | ||||
0.276800 | + | 0.960928i | \(0.410726\pi\) | |||||||
\(948\) | 28.6956 | 0.931991 | ||||||||
\(949\) | −7.58581 | −0.246246 | ||||||||
\(950\) | −137.303 | −4.45469 | ||||||||
\(951\) | −14.8138 | −0.480371 | ||||||||
\(952\) | 41.3010 | 1.33857 | ||||||||
\(953\) | 2.74726 | 0.0889925 | 0.0444962 | − | 0.999010i | \(-0.485832\pi\) | ||||
0.0444962 | + | 0.999010i | \(0.485832\pi\) | |||||||
\(954\) | −57.3281 | −1.85607 | ||||||||
\(955\) | −81.2780 | −2.63010 | ||||||||
\(956\) | 66.5785 | 2.15330 | ||||||||
\(957\) | −3.13037 | −0.101190 | ||||||||
\(958\) | −106.848 | −3.45209 | ||||||||
\(959\) | 12.5750 | 0.406069 | ||||||||
\(960\) | 48.6596 | 1.57048 | ||||||||
\(961\) | −14.5487 | −0.469313 | ||||||||
\(962\) | −95.1002 | −3.06615 | ||||||||
\(963\) | 8.29272 | 0.267229 | ||||||||
\(964\) | 99.0025 | 3.18866 | ||||||||
\(965\) | 72.7788 | 2.34283 | ||||||||
\(966\) | −10.6276 | −0.341937 | ||||||||
\(967\) | −6.64655 | −0.213739 | −0.106869 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106869 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(968\) | −8.31331 | −0.267200 | ||||||||
\(969\) | −16.2141 | −0.520871 | ||||||||
\(970\) | 22.4675 | 0.721390 | ||||||||
\(971\) | 11.2351 | 0.360551 | 0.180276 | − | 0.983616i | \(-0.442301\pi\) | ||||
0.180276 | + | 0.983616i | \(0.442301\pi\) | |||||||
\(972\) | 77.4633 | 2.48464 | ||||||||
\(973\) | −12.9013 | −0.413597 | ||||||||
\(974\) | 37.2851 | 1.19469 | ||||||||
\(975\) | 44.9409 | 1.43926 | ||||||||
\(976\) | −110.077 | −3.52348 | ||||||||
\(977\) | −28.9480 | −0.926129 | −0.463065 | − | 0.886325i | \(-0.653250\pi\) | ||||
−0.463065 | + | 0.886325i | \(0.653250\pi\) | |||||||
\(978\) | 45.3896 | 1.45140 | ||||||||
\(979\) | 8.49796 | 0.271596 | ||||||||
\(980\) | 20.6765 | 0.660486 | ||||||||
\(981\) | −39.2026 | −1.25164 | ||||||||
\(982\) | 45.2199 | 1.44303 | ||||||||
\(983\) | 29.0305 | 0.925930 | 0.462965 | − | 0.886377i | \(-0.346786\pi\) | ||||
0.462965 | + | 0.886377i | \(0.346786\pi\) | |||||||
\(984\) | 30.7381 | 0.979894 | ||||||||
\(985\) | 16.0599 | 0.511710 | ||||||||
\(986\) | −57.7375 | −1.83874 | ||||||||
\(987\) | 4.51560 | 0.143733 | ||||||||
\(988\) | 128.263 | 4.08060 | ||||||||
\(989\) | 5.54439 | 0.176301 | ||||||||
\(990\) | 26.7759 | 0.850993 | ||||||||
\(991\) | −30.0705 | −0.955220 | −0.477610 | − | 0.878572i | \(-0.658497\pi\) | ||||
−0.477610 | + | 0.878572i | \(0.658497\pi\) | |||||||
\(992\) | 61.7997 | 1.96214 | ||||||||
\(993\) | 22.1629 | 0.703318 | ||||||||
\(994\) | −43.7848 | −1.38877 | ||||||||
\(995\) | 44.8272 | 1.42112 | ||||||||
\(996\) | −17.4851 | −0.554035 | ||||||||
\(997\) | 8.05959 | 0.255250 | 0.127625 | − | 0.991823i | \(-0.459265\pi\) | ||||
0.127625 | + | 0.991823i | \(0.459265\pi\) | |||||||
\(998\) | −102.344 | −3.23965 | ||||||||
\(999\) | −25.4501 | −0.805205 |
(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 | 3311.2.a.k.1.2 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3311.2.a.k.1.2 | ✓ | 38 | 1.1 | even | 1 | trivial |