Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, 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("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.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: | \(64.1278578633\) |
Analytic rank: | \(1\) |
Dimension: | \(102\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71515 | −1.91990 | −0.959949 | − | 0.280175i | \(-0.909608\pi\) | ||||
−0.959949 | + | 0.280175i | \(0.909608\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.37202 | 2.68601 | ||||||||
\(5\) | 0.694821 | 0.310734 | 0.155367 | − | 0.987857i | \(-0.450344\pi\) | ||||
0.155367 | + | 0.987857i | \(0.450344\pi\) | |||||||
\(6\) | 2.71515 | 1.10845 | ||||||||
\(7\) | 4.70425 | 1.77804 | 0.889020 | − | 0.457868i | \(-0.151387\pi\) | ||||
0.889020 | + | 0.457868i | \(0.151387\pi\) | |||||||
\(8\) | −9.15552 | −3.23697 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.88654 | −0.596577 | ||||||||
\(11\) | −2.64356 | −0.797063 | −0.398532 | − | 0.917155i | \(-0.630480\pi\) | ||||
−0.398532 | + | 0.917155i | \(0.630480\pi\) | |||||||
\(12\) | −5.37202 | −1.55077 | ||||||||
\(13\) | 3.34489 | 0.927706 | 0.463853 | − | 0.885912i | \(-0.346467\pi\) | ||||
0.463853 | + | 0.885912i | \(0.346467\pi\) | |||||||
\(14\) | −12.7727 | −3.41366 | ||||||||
\(15\) | −0.694821 | −0.179402 | ||||||||
\(16\) | 14.1145 | 3.52863 | ||||||||
\(17\) | 2.32220 | 0.563216 | 0.281608 | − | 0.959530i | \(-0.409132\pi\) | ||||
0.281608 | + | 0.959530i | \(0.409132\pi\) | |||||||
\(18\) | −2.71515 | −0.639966 | ||||||||
\(19\) | −1.75052 | −0.401598 | −0.200799 | − | 0.979632i | \(-0.564354\pi\) | ||||
−0.200799 | + | 0.979632i | \(0.564354\pi\) | |||||||
\(20\) | 3.73259 | 0.834633 | ||||||||
\(21\) | −4.70425 | −1.02655 | ||||||||
\(22\) | 7.17765 | 1.53028 | ||||||||
\(23\) | −0.201020 | −0.0419155 | −0.0209578 | − | 0.999780i | \(-0.506672\pi\) | ||||
−0.0209578 | + | 0.999780i | \(0.506672\pi\) | |||||||
\(24\) | 9.15552 | 1.86886 | ||||||||
\(25\) | −4.51722 | −0.903445 | ||||||||
\(26\) | −9.08187 | −1.78110 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 25.2713 | 4.77583 | ||||||||
\(29\) | 5.37029 | 0.997237 | 0.498619 | − | 0.866821i | \(-0.333841\pi\) | ||||
0.498619 | + | 0.866821i | \(0.333841\pi\) | |||||||
\(30\) | 1.88654 | 0.344434 | ||||||||
\(31\) | −5.14363 | −0.923824 | −0.461912 | − | 0.886926i | \(-0.652836\pi\) | ||||
−0.461912 | + | 0.886926i | \(0.652836\pi\) | |||||||
\(32\) | −20.0120 | −3.53765 | ||||||||
\(33\) | 2.64356 | 0.460185 | ||||||||
\(34\) | −6.30511 | −1.08132 | ||||||||
\(35\) | 3.26861 | 0.552497 | ||||||||
\(36\) | 5.37202 | 0.895336 | ||||||||
\(37\) | −0.104230 | −0.0171353 | −0.00856765 | − | 0.999963i | \(-0.502727\pi\) | ||||
−0.00856765 | + | 0.999963i | \(0.502727\pi\) | |||||||
\(38\) | 4.75293 | 0.771027 | ||||||||
\(39\) | −3.34489 | −0.535612 | ||||||||
\(40\) | −6.36145 | −1.00583 | ||||||||
\(41\) | −4.61915 | −0.721389 | −0.360695 | − | 0.932684i | \(-0.617460\pi\) | ||||
−0.360695 | + | 0.932684i | \(0.617460\pi\) | |||||||
\(42\) | 12.7727 | 1.97088 | ||||||||
\(43\) | −8.09619 | −1.23466 | −0.617329 | − | 0.786705i | \(-0.711785\pi\) | ||||
−0.617329 | + | 0.786705i | \(0.711785\pi\) | |||||||
\(44\) | −14.2012 | −2.14092 | ||||||||
\(45\) | 0.694821 | 0.103578 | ||||||||
\(46\) | 0.545798 | 0.0804735 | ||||||||
\(47\) | −9.79368 | −1.42856 | −0.714278 | − | 0.699862i | \(-0.753245\pi\) | ||||
−0.714278 | + | 0.699862i | \(0.753245\pi\) | |||||||
\(48\) | −14.1145 | −2.03726 | ||||||||
\(49\) | 15.1300 | 2.16143 | ||||||||
\(50\) | 12.2649 | 1.73452 | ||||||||
\(51\) | −2.32220 | −0.325173 | ||||||||
\(52\) | 17.9688 | 2.49183 | ||||||||
\(53\) | −7.08677 | −0.973443 | −0.486722 | − | 0.873557i | \(-0.661807\pi\) | ||||
−0.486722 | + | 0.873557i | \(0.661807\pi\) | |||||||
\(54\) | 2.71515 | 0.369485 | ||||||||
\(55\) | −1.83680 | −0.247674 | ||||||||
\(56\) | −43.0699 | −5.75545 | ||||||||
\(57\) | 1.75052 | 0.231863 | ||||||||
\(58\) | −14.5811 | −1.91459 | ||||||||
\(59\) | −1.46332 | −0.190509 | −0.0952543 | − | 0.995453i | \(-0.530366\pi\) | ||||
−0.0952543 | + | 0.995453i | \(0.530366\pi\) | |||||||
\(60\) | −3.73259 | −0.481876 | ||||||||
\(61\) | 11.9421 | 1.52903 | 0.764514 | − | 0.644607i | \(-0.222979\pi\) | ||||
0.764514 | + | 0.644607i | \(0.222979\pi\) | |||||||
\(62\) | 13.9657 | 1.77365 | ||||||||
\(63\) | 4.70425 | 0.592680 | ||||||||
\(64\) | 26.1064 | 3.26330 | ||||||||
\(65\) | 2.32410 | 0.288270 | ||||||||
\(66\) | −7.17765 | −0.883508 | ||||||||
\(67\) | 5.44194 | 0.664839 | 0.332420 | − | 0.943132i | \(-0.392135\pi\) | ||||
0.332420 | + | 0.943132i | \(0.392135\pi\) | |||||||
\(68\) | 12.4749 | 1.51280 | ||||||||
\(69\) | 0.201020 | 0.0241999 | ||||||||
\(70\) | −8.87477 | −1.06074 | ||||||||
\(71\) | 6.97388 | 0.827647 | 0.413824 | − | 0.910357i | \(-0.364193\pi\) | ||||
0.413824 | + | 0.910357i | \(0.364193\pi\) | |||||||
\(72\) | −9.15552 | −1.07899 | ||||||||
\(73\) | −6.65620 | −0.779049 | −0.389524 | − | 0.921016i | \(-0.627361\pi\) | ||||
−0.389524 | + | 0.921016i | \(0.627361\pi\) | |||||||
\(74\) | 0.283000 | 0.0328980 | ||||||||
\(75\) | 4.51722 | 0.521604 | ||||||||
\(76\) | −9.40385 | −1.07870 | ||||||||
\(77\) | −12.4360 | −1.41721 | ||||||||
\(78\) | 9.08187 | 1.02832 | ||||||||
\(79\) | 6.48188 | 0.729269 | 0.364634 | − | 0.931151i | \(-0.381194\pi\) | ||||
0.364634 | + | 0.931151i | \(0.381194\pi\) | |||||||
\(80\) | 9.80708 | 1.09647 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.5417 | 1.38499 | ||||||||
\(83\) | −0.672215 | −0.0737851 | −0.0368926 | − | 0.999319i | \(-0.511746\pi\) | ||||
−0.0368926 | + | 0.999319i | \(0.511746\pi\) | |||||||
\(84\) | −25.2713 | −2.75733 | ||||||||
\(85\) | 1.61351 | 0.175010 | ||||||||
\(86\) | 21.9823 | 2.37042 | ||||||||
\(87\) | −5.37029 | −0.575755 | ||||||||
\(88\) | 24.2032 | 2.58007 | ||||||||
\(89\) | −8.94870 | −0.948560 | −0.474280 | − | 0.880374i | \(-0.657292\pi\) | ||||
−0.474280 | + | 0.880374i | \(0.657292\pi\) | |||||||
\(90\) | −1.88654 | −0.198859 | ||||||||
\(91\) | 15.7352 | 1.64950 | ||||||||
\(92\) | −1.07988 | −0.112585 | ||||||||
\(93\) | 5.14363 | 0.533370 | ||||||||
\(94\) | 26.5913 | 2.74268 | ||||||||
\(95\) | −1.21630 | −0.124790 | ||||||||
\(96\) | 20.0120 | 2.04247 | ||||||||
\(97\) | −17.9487 | −1.82242 | −0.911209 | − | 0.411944i | \(-0.864850\pi\) | ||||
−0.911209 | + | 0.411944i | \(0.864850\pi\) | |||||||
\(98\) | −41.0801 | −4.14972 | ||||||||
\(99\) | −2.64356 | −0.265688 | ||||||||
\(100\) | −24.2666 | −2.42666 | ||||||||
\(101\) | −16.3936 | −1.63122 | −0.815611 | − | 0.578601i | \(-0.803599\pi\) | ||||
−0.815611 | + | 0.578601i | \(0.803599\pi\) | |||||||
\(102\) | 6.30511 | 0.624299 | ||||||||
\(103\) | 6.23122 | 0.613980 | 0.306990 | − | 0.951713i | \(-0.400678\pi\) | ||||
0.306990 | + | 0.951713i | \(0.400678\pi\) | |||||||
\(104\) | −30.6242 | −3.00295 | ||||||||
\(105\) | −3.26861 | −0.318984 | ||||||||
\(106\) | 19.2416 | 1.86891 | ||||||||
\(107\) | −0.208802 | −0.0201857 | −0.0100928 | − | 0.999949i | \(-0.503213\pi\) | ||||
−0.0100928 | + | 0.999949i | \(0.503213\pi\) | |||||||
\(108\) | −5.37202 | −0.516923 | ||||||||
\(109\) | −14.3945 | −1.37874 | −0.689372 | − | 0.724407i | \(-0.742114\pi\) | ||||
−0.689372 | + | 0.724407i | \(0.742114\pi\) | |||||||
\(110\) | 4.98718 | 0.475509 | ||||||||
\(111\) | 0.104230 | 0.00989307 | ||||||||
\(112\) | 66.3983 | 6.27405 | ||||||||
\(113\) | −7.27734 | −0.684595 | −0.342298 | − | 0.939592i | \(-0.611205\pi\) | ||||
−0.342298 | + | 0.939592i | \(0.611205\pi\) | |||||||
\(114\) | −4.75293 | −0.445153 | ||||||||
\(115\) | −0.139673 | −0.0130246 | ||||||||
\(116\) | 28.8493 | 2.67859 | ||||||||
\(117\) | 3.34489 | 0.309235 | ||||||||
\(118\) | 3.97314 | 0.365757 | ||||||||
\(119\) | 10.9242 | 1.00142 | ||||||||
\(120\) | 6.36145 | 0.580718 | ||||||||
\(121\) | −4.01159 | −0.364690 | ||||||||
\(122\) | −32.4245 | −2.93558 | ||||||||
\(123\) | 4.61915 | 0.416494 | ||||||||
\(124\) | −27.6317 | −2.48140 | ||||||||
\(125\) | −6.61277 | −0.591464 | ||||||||
\(126\) | −12.7727 | −1.13789 | ||||||||
\(127\) | −0.992677 | −0.0880858 | −0.0440429 | − | 0.999030i | \(-0.514024\pi\) | ||||
−0.0440429 | + | 0.999030i | \(0.514024\pi\) | |||||||
\(128\) | −30.8587 | −2.72755 | ||||||||
\(129\) | 8.09619 | 0.712830 | ||||||||
\(130\) | −6.31028 | −0.553448 | ||||||||
\(131\) | −10.6911 | −0.934087 | −0.467044 | − | 0.884234i | \(-0.654681\pi\) | ||||
−0.467044 | + | 0.884234i | \(0.654681\pi\) | |||||||
\(132\) | 14.2012 | 1.23606 | ||||||||
\(133\) | −8.23491 | −0.714057 | ||||||||
\(134\) | −14.7757 | −1.27642 | ||||||||
\(135\) | −0.694821 | −0.0598007 | ||||||||
\(136\) | −21.2609 | −1.82311 | ||||||||
\(137\) | −9.20017 | −0.786024 | −0.393012 | − | 0.919533i | \(-0.628567\pi\) | ||||
−0.393012 | + | 0.919533i | \(0.628567\pi\) | |||||||
\(138\) | −0.545798 | −0.0464614 | ||||||||
\(139\) | −5.90304 | −0.500690 | −0.250345 | − | 0.968157i | \(-0.580544\pi\) | ||||
−0.250345 | + | 0.968157i | \(0.580544\pi\) | |||||||
\(140\) | 17.5591 | 1.48401 | ||||||||
\(141\) | 9.79368 | 0.824777 | ||||||||
\(142\) | −18.9351 | −1.58900 | ||||||||
\(143\) | −8.84242 | −0.739441 | ||||||||
\(144\) | 14.1145 | 1.17621 | ||||||||
\(145\) | 3.73139 | 0.309875 | ||||||||
\(146\) | 18.0725 | 1.49569 | ||||||||
\(147\) | −15.1300 | −1.24790 | ||||||||
\(148\) | −0.559925 | −0.0460256 | ||||||||
\(149\) | −17.8884 | −1.46547 | −0.732737 | − | 0.680512i | \(-0.761757\pi\) | ||||
−0.732737 | + | 0.680512i | \(0.761757\pi\) | |||||||
\(150\) | −12.2649 | −1.00143 | ||||||||
\(151\) | 23.7802 | 1.93521 | 0.967603 | − | 0.252476i | \(-0.0812448\pi\) | ||||
0.967603 | + | 0.252476i | \(0.0812448\pi\) | |||||||
\(152\) | 16.0270 | 1.29996 | ||||||||
\(153\) | 2.32220 | 0.187739 | ||||||||
\(154\) | 33.7655 | 2.72090 | ||||||||
\(155\) | −3.57391 | −0.287063 | ||||||||
\(156\) | −17.9688 | −1.43866 | ||||||||
\(157\) | −14.1681 | −1.13074 | −0.565369 | − | 0.824838i | \(-0.691266\pi\) | ||||
−0.565369 | + | 0.824838i | \(0.691266\pi\) | |||||||
\(158\) | −17.5993 | −1.40012 | ||||||||
\(159\) | 7.08677 | 0.562018 | ||||||||
\(160\) | −13.9048 | −1.09927 | ||||||||
\(161\) | −0.945648 | −0.0745275 | ||||||||
\(162\) | −2.71515 | −0.213322 | ||||||||
\(163\) | −4.28033 | −0.335262 | −0.167631 | − | 0.985850i | \(-0.553612\pi\) | ||||
−0.167631 | + | 0.985850i | \(0.553612\pi\) | |||||||
\(164\) | −24.8141 | −1.93766 | ||||||||
\(165\) | 1.83680 | 0.142995 | ||||||||
\(166\) | 1.82516 | 0.141660 | ||||||||
\(167\) | 1.26633 | 0.0979912 | 0.0489956 | − | 0.998799i | \(-0.484398\pi\) | ||||
0.0489956 | + | 0.998799i | \(0.484398\pi\) | |||||||
\(168\) | 43.0699 | 3.32291 | ||||||||
\(169\) | −1.81169 | −0.139361 | ||||||||
\(170\) | −4.38093 | −0.336002 | ||||||||
\(171\) | −1.75052 | −0.133866 | ||||||||
\(172\) | −43.4929 | −3.31630 | ||||||||
\(173\) | 4.54297 | 0.345396 | 0.172698 | − | 0.984975i | \(-0.444752\pi\) | ||||
0.172698 | + | 0.984975i | \(0.444752\pi\) | |||||||
\(174\) | 14.5811 | 1.10539 | ||||||||
\(175\) | −21.2502 | −1.60636 | ||||||||
\(176\) | −37.3126 | −2.81254 | ||||||||
\(177\) | 1.46332 | 0.109990 | ||||||||
\(178\) | 24.2970 | 1.82114 | ||||||||
\(179\) | −7.62596 | −0.569991 | −0.284995 | − | 0.958529i | \(-0.591992\pi\) | ||||
−0.284995 | + | 0.958529i | \(0.591992\pi\) | |||||||
\(180\) | 3.73259 | 0.278211 | ||||||||
\(181\) | −11.8129 | −0.878043 | −0.439021 | − | 0.898477i | \(-0.644675\pi\) | ||||
−0.439021 | + | 0.898477i | \(0.644675\pi\) | |||||||
\(182\) | −42.7234 | −3.16687 | ||||||||
\(183\) | −11.9421 | −0.882785 | ||||||||
\(184\) | 1.84044 | 0.135679 | ||||||||
\(185\) | −0.0724212 | −0.00532451 | ||||||||
\(186\) | −13.9657 | −1.02402 | ||||||||
\(187\) | −6.13887 | −0.448919 | ||||||||
\(188\) | −52.6118 | −3.83711 | ||||||||
\(189\) | −4.70425 | −0.342184 | ||||||||
\(190\) | 3.30244 | 0.239584 | ||||||||
\(191\) | −13.7707 | −0.996411 | −0.498205 | − | 0.867059i | \(-0.666007\pi\) | ||||
−0.498205 | + | 0.867059i | \(0.666007\pi\) | |||||||
\(192\) | −26.1064 | −1.88407 | ||||||||
\(193\) | 2.01737 | 0.145213 | 0.0726067 | − | 0.997361i | \(-0.476868\pi\) | ||||
0.0726067 | + | 0.997361i | \(0.476868\pi\) | |||||||
\(194\) | 48.7334 | 3.49886 | ||||||||
\(195\) | −2.32410 | −0.166432 | ||||||||
\(196\) | 81.2785 | 5.80561 | ||||||||
\(197\) | 20.7633 | 1.47933 | 0.739663 | − | 0.672977i | \(-0.234985\pi\) | ||||
0.739663 | + | 0.672977i | \(0.234985\pi\) | |||||||
\(198\) | 7.17765 | 0.510093 | ||||||||
\(199\) | −20.6345 | −1.46274 | −0.731370 | − | 0.681980i | \(-0.761119\pi\) | ||||
−0.731370 | + | 0.681980i | \(0.761119\pi\) | |||||||
\(200\) | 41.3575 | 2.92442 | ||||||||
\(201\) | −5.44194 | −0.383845 | ||||||||
\(202\) | 44.5110 | 3.13178 | ||||||||
\(203\) | 25.2632 | 1.77313 | ||||||||
\(204\) | −12.4749 | −0.873417 | ||||||||
\(205\) | −3.20948 | −0.224160 | ||||||||
\(206\) | −16.9187 | −1.17878 | ||||||||
\(207\) | −0.201020 | −0.0139718 | ||||||||
\(208\) | 47.2116 | 3.27354 | ||||||||
\(209\) | 4.62761 | 0.320099 | ||||||||
\(210\) | 8.87477 | 0.612417 | ||||||||
\(211\) | −23.6283 | −1.62664 | −0.813319 | − | 0.581818i | \(-0.802342\pi\) | ||||
−0.813319 | + | 0.581818i | \(0.802342\pi\) | |||||||
\(212\) | −38.0703 | −2.61468 | ||||||||
\(213\) | −6.97388 | −0.477842 | ||||||||
\(214\) | 0.566928 | 0.0387544 | ||||||||
\(215\) | −5.62541 | −0.383650 | ||||||||
\(216\) | 9.15552 | 0.622954 | ||||||||
\(217\) | −24.1969 | −1.64260 | ||||||||
\(218\) | 39.0832 | 2.64705 | ||||||||
\(219\) | 6.65620 | 0.449784 | ||||||||
\(220\) | −9.86733 | −0.665255 | ||||||||
\(221\) | 7.76751 | 0.522499 | ||||||||
\(222\) | −0.283000 | −0.0189937 | ||||||||
\(223\) | 6.82897 | 0.457302 | 0.228651 | − | 0.973508i | \(-0.426569\pi\) | ||||
0.228651 | + | 0.973508i | \(0.426569\pi\) | |||||||
\(224\) | −94.1415 | −6.29009 | ||||||||
\(225\) | −4.51722 | −0.301148 | ||||||||
\(226\) | 19.7591 | 1.31435 | ||||||||
\(227\) | 28.9229 | 1.91968 | 0.959840 | − | 0.280549i | \(-0.0905164\pi\) | ||||
0.959840 | + | 0.280549i | \(0.0905164\pi\) | |||||||
\(228\) | 9.40385 | 0.622785 | ||||||||
\(229\) | −2.66664 | −0.176216 | −0.0881082 | − | 0.996111i | \(-0.528082\pi\) | ||||
−0.0881082 | + | 0.996111i | \(0.528082\pi\) | |||||||
\(230\) | 0.379232 | 0.0250058 | ||||||||
\(231\) | 12.4360 | 0.818227 | ||||||||
\(232\) | −49.1678 | −3.22802 | ||||||||
\(233\) | −4.95531 | −0.324633 | −0.162317 | − | 0.986739i | \(-0.551897\pi\) | ||||
−0.162317 | + | 0.986739i | \(0.551897\pi\) | |||||||
\(234\) | −9.08187 | −0.593701 | ||||||||
\(235\) | −6.80486 | −0.443900 | ||||||||
\(236\) | −7.86100 | −0.511708 | ||||||||
\(237\) | −6.48188 | −0.421043 | ||||||||
\(238\) | −29.6608 | −1.92263 | ||||||||
\(239\) | −3.42150 | −0.221318 | −0.110659 | − | 0.993858i | \(-0.535296\pi\) | ||||
−0.110659 | + | 0.993858i | \(0.535296\pi\) | |||||||
\(240\) | −9.80708 | −0.633045 | ||||||||
\(241\) | −18.5558 | −1.19528 | −0.597640 | − | 0.801764i | \(-0.703895\pi\) | ||||
−0.597640 | + | 0.801764i | \(0.703895\pi\) | |||||||
\(242\) | 10.8921 | 0.700169 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 64.1531 | 4.10698 | ||||||||
\(245\) | 10.5126 | 0.671628 | ||||||||
\(246\) | −12.5417 | −0.799627 | ||||||||
\(247\) | −5.85532 | −0.372565 | ||||||||
\(248\) | 47.0926 | 2.99039 | ||||||||
\(249\) | 0.672215 | 0.0425999 | ||||||||
\(250\) | 17.9546 | 1.13555 | ||||||||
\(251\) | 11.4910 | 0.725308 | 0.362654 | − | 0.931924i | \(-0.381871\pi\) | ||||
0.362654 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(252\) | 25.2713 | 1.59194 | ||||||||
\(253\) | 0.531408 | 0.0334093 | ||||||||
\(254\) | 2.69526 | 0.169116 | ||||||||
\(255\) | −1.61351 | −0.101042 | ||||||||
\(256\) | 31.5731 | 1.97332 | ||||||||
\(257\) | −9.69760 | −0.604919 | −0.302460 | − | 0.953162i | \(-0.597808\pi\) | ||||
−0.302460 | + | 0.953162i | \(0.597808\pi\) | |||||||
\(258\) | −21.9823 | −1.36856 | ||||||||
\(259\) | −0.490324 | −0.0304673 | ||||||||
\(260\) | 12.4851 | 0.774295 | ||||||||
\(261\) | 5.37029 | 0.332412 | ||||||||
\(262\) | 29.0279 | 1.79335 | ||||||||
\(263\) | 3.40660 | 0.210060 | 0.105030 | − | 0.994469i | \(-0.466506\pi\) | ||||
0.105030 | + | 0.994469i | \(0.466506\pi\) | |||||||
\(264\) | −24.2032 | −1.48960 | ||||||||
\(265\) | −4.92404 | −0.302481 | ||||||||
\(266\) | 22.3590 | 1.37092 | ||||||||
\(267\) | 8.94870 | 0.547651 | ||||||||
\(268\) | 29.2342 | 1.78576 | ||||||||
\(269\) | 16.5341 | 1.00810 | 0.504052 | − | 0.863673i | \(-0.331842\pi\) | ||||
0.504052 | + | 0.863673i | \(0.331842\pi\) | |||||||
\(270\) | 1.88654 | 0.114811 | ||||||||
\(271\) | 11.8992 | 0.722824 | 0.361412 | − | 0.932406i | \(-0.382295\pi\) | ||||
0.361412 | + | 0.932406i | \(0.382295\pi\) | |||||||
\(272\) | 32.7768 | 1.98738 | ||||||||
\(273\) | −15.7352 | −0.952339 | ||||||||
\(274\) | 24.9798 | 1.50909 | ||||||||
\(275\) | 11.9415 | 0.720102 | ||||||||
\(276\) | 1.07988 | 0.0650013 | ||||||||
\(277\) | 5.82588 | 0.350043 | 0.175022 | − | 0.984565i | \(-0.444000\pi\) | ||||
0.175022 | + | 0.984565i | \(0.444000\pi\) | |||||||
\(278\) | 16.0276 | 0.961273 | ||||||||
\(279\) | −5.14363 | −0.307941 | ||||||||
\(280\) | −29.9259 | −1.78841 | ||||||||
\(281\) | −0.240212 | −0.0143299 | −0.00716493 | − | 0.999974i | \(-0.502281\pi\) | ||||
−0.00716493 | + | 0.999974i | \(0.502281\pi\) | |||||||
\(282\) | −26.5913 | −1.58349 | ||||||||
\(283\) | 19.2408 | 1.14374 | 0.571872 | − | 0.820343i | \(-0.306217\pi\) | ||||
0.571872 | + | 0.820343i | \(0.306217\pi\) | |||||||
\(284\) | 37.4638 | 2.22307 | ||||||||
\(285\) | 1.21630 | 0.0720475 | ||||||||
\(286\) | 24.0085 | 1.41965 | ||||||||
\(287\) | −21.7296 | −1.28266 | ||||||||
\(288\) | −20.0120 | −1.17922 | ||||||||
\(289\) | −11.6074 | −0.682788 | ||||||||
\(290\) | −10.1313 | −0.594929 | ||||||||
\(291\) | 17.9487 | 1.05217 | ||||||||
\(292\) | −35.7572 | −2.09253 | ||||||||
\(293\) | 3.98884 | 0.233031 | 0.116515 | − | 0.993189i | \(-0.462828\pi\) | ||||
0.116515 | + | 0.993189i | \(0.462828\pi\) | |||||||
\(294\) | 41.0801 | 2.39584 | ||||||||
\(295\) | −1.01675 | −0.0591974 | ||||||||
\(296\) | 0.954280 | 0.0554664 | ||||||||
\(297\) | 2.64356 | 0.153395 | ||||||||
\(298\) | 48.5696 | 2.81356 | ||||||||
\(299\) | −0.672390 | −0.0388853 | ||||||||
\(300\) | 24.2666 | 1.40103 | ||||||||
\(301\) | −38.0865 | −2.19527 | ||||||||
\(302\) | −64.5668 | −3.71540 | ||||||||
\(303\) | 16.3936 | 0.941786 | ||||||||
\(304\) | −24.7078 | −1.41709 | ||||||||
\(305\) | 8.29762 | 0.475120 | ||||||||
\(306\) | −6.30511 | −0.360439 | ||||||||
\(307\) | 11.3947 | 0.650331 | 0.325165 | − | 0.945657i | \(-0.394580\pi\) | ||||
0.325165 | + | 0.945657i | \(0.394580\pi\) | |||||||
\(308\) | −66.8062 | −3.80664 | ||||||||
\(309\) | −6.23122 | −0.354482 | ||||||||
\(310\) | 9.70368 | 0.551132 | ||||||||
\(311\) | −17.2381 | −0.977481 | −0.488741 | − | 0.872429i | \(-0.662544\pi\) | ||||
−0.488741 | + | 0.872429i | \(0.662544\pi\) | |||||||
\(312\) | 30.6242 | 1.73376 | ||||||||
\(313\) | −15.0796 | −0.852351 | −0.426176 | − | 0.904640i | \(-0.640139\pi\) | ||||
−0.426176 | + | 0.904640i | \(0.640139\pi\) | |||||||
\(314\) | 38.4685 | 2.17090 | ||||||||
\(315\) | 3.26861 | 0.184166 | ||||||||
\(316\) | 34.8208 | 1.95882 | ||||||||
\(317\) | 2.06313 | 0.115877 | 0.0579384 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579384 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(318\) | −19.2416 | −1.07902 | ||||||||
\(319\) | −14.1967 | −0.794861 | ||||||||
\(320\) | 18.1393 | 1.01402 | ||||||||
\(321\) | 0.208802 | 0.0116542 | ||||||||
\(322\) | 2.56757 | 0.143085 | ||||||||
\(323\) | −4.06507 | −0.226186 | ||||||||
\(324\) | 5.37202 | 0.298445 | ||||||||
\(325\) | −15.1096 | −0.838131 | ||||||||
\(326\) | 11.6217 | 0.643668 | ||||||||
\(327\) | 14.3945 | 0.796019 | ||||||||
\(328\) | 42.2907 | 2.33511 | ||||||||
\(329\) | −46.0719 | −2.54003 | ||||||||
\(330\) | −4.98718 | −0.274535 | ||||||||
\(331\) | 13.0867 | 0.719311 | 0.359655 | − | 0.933085i | \(-0.382894\pi\) | ||||
0.359655 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(332\) | −3.61115 | −0.198188 | ||||||||
\(333\) | −0.104230 | −0.00571177 | ||||||||
\(334\) | −3.43826 | −0.188133 | ||||||||
\(335\) | 3.78118 | 0.206588 | ||||||||
\(336\) | −66.3983 | −3.62233 | ||||||||
\(337\) | 31.7844 | 1.73141 | 0.865703 | − | 0.500558i | \(-0.166872\pi\) | ||||
0.865703 | + | 0.500558i | \(0.166872\pi\) | |||||||
\(338\) | 4.91900 | 0.267559 | ||||||||
\(339\) | 7.27734 | 0.395251 | ||||||||
\(340\) | 8.66783 | 0.470079 | ||||||||
\(341\) | 13.5975 | 0.736346 | ||||||||
\(342\) | 4.75293 | 0.257009 | ||||||||
\(343\) | 38.2455 | 2.06506 | ||||||||
\(344\) | 74.1248 | 3.99654 | ||||||||
\(345\) | 0.139673 | 0.00751973 | ||||||||
\(346\) | −12.3348 | −0.663124 | ||||||||
\(347\) | −9.62339 | −0.516611 | −0.258305 | − | 0.966063i | \(-0.583164\pi\) | ||||
−0.258305 | + | 0.966063i | \(0.583164\pi\) | |||||||
\(348\) | −28.8493 | −1.54648 | ||||||||
\(349\) | −8.91464 | −0.477190 | −0.238595 | − | 0.971119i | \(-0.576687\pi\) | ||||
−0.238595 | + | 0.971119i | \(0.576687\pi\) | |||||||
\(350\) | 57.6973 | 3.08405 | ||||||||
\(351\) | −3.34489 | −0.178537 | ||||||||
\(352\) | 52.9029 | 2.81973 | ||||||||
\(353\) | −3.61671 | −0.192498 | −0.0962491 | − | 0.995357i | \(-0.530685\pi\) | ||||
−0.0962491 | + | 0.995357i | \(0.530685\pi\) | |||||||
\(354\) | −3.97314 | −0.211170 | ||||||||
\(355\) | 4.84560 | 0.257178 | ||||||||
\(356\) | −48.0726 | −2.54784 | ||||||||
\(357\) | −10.9242 | −0.578171 | ||||||||
\(358\) | 20.7056 | 1.09432 | ||||||||
\(359\) | 35.8872 | 1.89406 | 0.947028 | − | 0.321151i | \(-0.104070\pi\) | ||||
0.947028 | + | 0.321151i | \(0.104070\pi\) | |||||||
\(360\) | −6.36145 | −0.335278 | ||||||||
\(361\) | −15.9357 | −0.838719 | ||||||||
\(362\) | 32.0736 | 1.68575 | ||||||||
\(363\) | 4.01159 | 0.210554 | ||||||||
\(364\) | 84.5299 | 4.43057 | ||||||||
\(365\) | −4.62487 | −0.242077 | ||||||||
\(366\) | 32.4245 | 1.69486 | ||||||||
\(367\) | 10.3566 | 0.540611 | 0.270305 | − | 0.962775i | \(-0.412875\pi\) | ||||
0.270305 | + | 0.962775i | \(0.412875\pi\) | |||||||
\(368\) | −2.83730 | −0.147905 | ||||||||
\(369\) | −4.61915 | −0.240463 | ||||||||
\(370\) | 0.196634 | 0.0102225 | ||||||||
\(371\) | −33.3380 | −1.73082 | ||||||||
\(372\) | 27.6317 | 1.43264 | ||||||||
\(373\) | −5.81641 | −0.301162 | −0.150581 | − | 0.988598i | \(-0.548114\pi\) | ||||
−0.150581 | + | 0.988598i | \(0.548114\pi\) | |||||||
\(374\) | 16.6679 | 0.861878 | ||||||||
\(375\) | 6.61277 | 0.341482 | ||||||||
\(376\) | 89.6663 | 4.62418 | ||||||||
\(377\) | 17.9630 | 0.925143 | ||||||||
\(378\) | 12.7727 | 0.656958 | ||||||||
\(379\) | −8.52681 | −0.437993 | −0.218996 | − | 0.975726i | \(-0.570278\pi\) | ||||
−0.218996 | + | 0.975726i | \(0.570278\pi\) | |||||||
\(380\) | −6.53399 | −0.335187 | ||||||||
\(381\) | 0.992677 | 0.0508564 | ||||||||
\(382\) | 37.3894 | 1.91301 | ||||||||
\(383\) | 17.0306 | 0.870224 | 0.435112 | − | 0.900376i | \(-0.356709\pi\) | ||||
0.435112 | + | 0.900376i | \(0.356709\pi\) | |||||||
\(384\) | 30.8587 | 1.57475 | ||||||||
\(385\) | −8.64078 | −0.440375 | ||||||||
\(386\) | −5.47745 | −0.278795 | ||||||||
\(387\) | −8.09619 | −0.411552 | ||||||||
\(388\) | −96.4209 | −4.89503 | ||||||||
\(389\) | −29.8811 | −1.51503 | −0.757516 | − | 0.652817i | \(-0.773587\pi\) | ||||
−0.757516 | + | 0.652817i | \(0.773587\pi\) | |||||||
\(390\) | 6.31028 | 0.319533 | ||||||||
\(391\) | −0.466808 | −0.0236075 | ||||||||
\(392\) | −138.523 | −6.99646 | ||||||||
\(393\) | 10.6911 | 0.539295 | ||||||||
\(394\) | −56.3755 | −2.84016 | ||||||||
\(395\) | 4.50375 | 0.226608 | ||||||||
\(396\) | −14.2012 | −0.713640 | ||||||||
\(397\) | −16.5730 | −0.831774 | −0.415887 | − | 0.909416i | \(-0.636529\pi\) | ||||
−0.415887 | + | 0.909416i | \(0.636529\pi\) | |||||||
\(398\) | 56.0257 | 2.80831 | ||||||||
\(399\) | 8.23491 | 0.412261 | ||||||||
\(400\) | −63.7585 | −3.18793 | ||||||||
\(401\) | 33.7378 | 1.68479 | 0.842393 | − | 0.538863i | \(-0.181146\pi\) | ||||
0.842393 | + | 0.538863i | \(0.181146\pi\) | |||||||
\(402\) | 14.7757 | 0.736943 | ||||||||
\(403\) | −17.2049 | −0.857037 | ||||||||
\(404\) | −88.0666 | −4.38148 | ||||||||
\(405\) | 0.694821 | 0.0345260 | ||||||||
\(406\) | −68.5932 | −3.40422 | ||||||||
\(407\) | 0.275538 | 0.0136579 | ||||||||
\(408\) | 21.2609 | 1.05257 | ||||||||
\(409\) | −12.5278 | −0.619461 | −0.309731 | − | 0.950824i | \(-0.600239\pi\) | ||||
−0.309731 | + | 0.950824i | \(0.600239\pi\) | |||||||
\(410\) | 8.71421 | 0.430364 | ||||||||
\(411\) | 9.20017 | 0.453811 | ||||||||
\(412\) | 33.4742 | 1.64916 | ||||||||
\(413\) | −6.88384 | −0.338732 | ||||||||
\(414\) | 0.545798 | 0.0268245 | ||||||||
\(415\) | −0.467069 | −0.0229275 | ||||||||
\(416\) | −66.9380 | −3.28190 | ||||||||
\(417\) | 5.90304 | 0.289073 | ||||||||
\(418\) | −12.5646 | −0.614557 | ||||||||
\(419\) | 20.9173 | 1.02188 | 0.510938 | − | 0.859618i | \(-0.329298\pi\) | ||||
0.510938 | + | 0.859618i | \(0.329298\pi\) | |||||||
\(420\) | −17.5591 | −0.856794 | ||||||||
\(421\) | 32.0033 | 1.55974 | 0.779872 | − | 0.625939i | \(-0.215284\pi\) | ||||
0.779872 | + | 0.625939i | \(0.215284\pi\) | |||||||
\(422\) | 64.1542 | 3.12298 | ||||||||
\(423\) | −9.79368 | −0.476185 | ||||||||
\(424\) | 64.8831 | 3.15100 | ||||||||
\(425\) | −10.4899 | −0.508835 | ||||||||
\(426\) | 18.9351 | 0.917409 | ||||||||
\(427\) | 56.1786 | 2.71867 | ||||||||
\(428\) | −1.12169 | −0.0542188 | ||||||||
\(429\) | 8.84242 | 0.426916 | ||||||||
\(430\) | 15.2738 | 0.736568 | ||||||||
\(431\) | 34.0717 | 1.64118 | 0.820588 | − | 0.571520i | \(-0.193646\pi\) | ||||
0.820588 | + | 0.571520i | \(0.193646\pi\) | |||||||
\(432\) | −14.1145 | −0.679086 | ||||||||
\(433\) | 2.23556 | 0.107434 | 0.0537171 | − | 0.998556i | \(-0.482893\pi\) | ||||
0.0537171 | + | 0.998556i | \(0.482893\pi\) | |||||||
\(434\) | 65.6982 | 3.15362 | ||||||||
\(435\) | −3.73139 | −0.178906 | ||||||||
\(436\) | −77.3276 | −3.70332 | ||||||||
\(437\) | 0.351890 | 0.0168332 | ||||||||
\(438\) | −18.0725 | −0.863539 | ||||||||
\(439\) | −30.9655 | −1.47790 | −0.738951 | − | 0.673759i | \(-0.764679\pi\) | ||||
−0.738951 | + | 0.673759i | \(0.764679\pi\) | |||||||
\(440\) | 16.8169 | 0.801713 | ||||||||
\(441\) | 15.1300 | 0.720475 | ||||||||
\(442\) | −21.0899 | −1.00315 | ||||||||
\(443\) | −16.1963 | −0.769509 | −0.384755 | − | 0.923019i | \(-0.625714\pi\) | ||||
−0.384755 | + | 0.923019i | \(0.625714\pi\) | |||||||
\(444\) | 0.559925 | 0.0265729 | ||||||||
\(445\) | −6.21775 | −0.294749 | ||||||||
\(446\) | −18.5417 | −0.877973 | ||||||||
\(447\) | 17.8884 | 0.846092 | ||||||||
\(448\) | 122.811 | 5.80228 | ||||||||
\(449\) | 37.8328 | 1.78544 | 0.892721 | − | 0.450611i | \(-0.148794\pi\) | ||||
0.892721 | + | 0.450611i | \(0.148794\pi\) | |||||||
\(450\) | 12.2649 | 0.578174 | ||||||||
\(451\) | 12.2110 | 0.574993 | ||||||||
\(452\) | −39.0940 | −1.83883 | ||||||||
\(453\) | −23.7802 | −1.11729 | ||||||||
\(454\) | −78.5299 | −3.68559 | ||||||||
\(455\) | 10.9332 | 0.512555 | ||||||||
\(456\) | −16.0270 | −0.750531 | ||||||||
\(457\) | 29.5581 | 1.38267 | 0.691334 | − | 0.722536i | \(-0.257023\pi\) | ||||
0.691334 | + | 0.722536i | \(0.257023\pi\) | |||||||
\(458\) | 7.24031 | 0.338318 | ||||||||
\(459\) | −2.32220 | −0.108391 | ||||||||
\(460\) | −0.750325 | −0.0349841 | ||||||||
\(461\) | −5.28732 | −0.246255 | −0.123128 | − | 0.992391i | \(-0.539292\pi\) | ||||
−0.123128 | + | 0.992391i | \(0.539292\pi\) | |||||||
\(462\) | −33.7655 | −1.57091 | ||||||||
\(463\) | −37.5153 | −1.74348 | −0.871742 | − | 0.489966i | \(-0.837009\pi\) | ||||
−0.871742 | + | 0.489966i | \(0.837009\pi\) | |||||||
\(464\) | 75.7991 | 3.51889 | ||||||||
\(465\) | 3.57391 | 0.165736 | ||||||||
\(466\) | 13.4544 | 0.623263 | ||||||||
\(467\) | 24.9227 | 1.15329 | 0.576643 | − | 0.816996i | \(-0.304362\pi\) | ||||
0.576643 | + | 0.816996i | \(0.304362\pi\) | |||||||
\(468\) | 17.9688 | 0.830609 | ||||||||
\(469\) | 25.6003 | 1.18211 | ||||||||
\(470\) | 18.4762 | 0.852243 | ||||||||
\(471\) | 14.1681 | 0.652832 | ||||||||
\(472\) | 13.3975 | 0.616670 | ||||||||
\(473\) | 21.4028 | 0.984100 | ||||||||
\(474\) | 17.5993 | 0.808361 | ||||||||
\(475\) | 7.90751 | 0.362821 | ||||||||
\(476\) | 58.6851 | 2.68983 | ||||||||
\(477\) | −7.08677 | −0.324481 | ||||||||
\(478\) | 9.28987 | 0.424909 | ||||||||
\(479\) | −15.4505 | −0.705952 | −0.352976 | − | 0.935632i | \(-0.614830\pi\) | ||||
−0.352976 | + | 0.935632i | \(0.614830\pi\) | |||||||
\(480\) | 13.9048 | 0.634663 | ||||||||
\(481\) | −0.348638 | −0.0158965 | ||||||||
\(482\) | 50.3816 | 2.29482 | ||||||||
\(483\) | 0.945648 | 0.0430285 | ||||||||
\(484\) | −21.5504 | −0.979562 | ||||||||
\(485\) | −12.4712 | −0.566287 | ||||||||
\(486\) | 2.71515 | 0.123162 | ||||||||
\(487\) | 1.04389 | 0.0473031 | 0.0236515 | − | 0.999720i | \(-0.492471\pi\) | ||||
0.0236515 | + | 0.999720i | \(0.492471\pi\) | |||||||
\(488\) | −109.336 | −4.94941 | ||||||||
\(489\) | 4.28033 | 0.193563 | ||||||||
\(490\) | −28.5433 | −1.28946 | ||||||||
\(491\) | −7.80621 | −0.352289 | −0.176145 | − | 0.984364i | \(-0.556363\pi\) | ||||
−0.176145 | + | 0.984364i | \(0.556363\pi\) | |||||||
\(492\) | 24.8141 | 1.11871 | ||||||||
\(493\) | 12.4709 | 0.561660 | ||||||||
\(494\) | 15.8980 | 0.715287 | ||||||||
\(495\) | −1.83680 | −0.0825581 | ||||||||
\(496\) | −72.6000 | −3.25984 | ||||||||
\(497\) | 32.8069 | 1.47159 | ||||||||
\(498\) | −1.82516 | −0.0817874 | ||||||||
\(499\) | 23.9499 | 1.07214 | 0.536072 | − | 0.844172i | \(-0.319908\pi\) | ||||
0.536072 | + | 0.844172i | \(0.319908\pi\) | |||||||
\(500\) | −35.5239 | −1.58868 | ||||||||
\(501\) | −1.26633 | −0.0565753 | ||||||||
\(502\) | −31.1998 | −1.39252 | ||||||||
\(503\) | 19.0365 | 0.848795 | 0.424397 | − | 0.905476i | \(-0.360486\pi\) | ||||
0.424397 | + | 0.905476i | \(0.360486\pi\) | |||||||
\(504\) | −43.0699 | −1.91848 | ||||||||
\(505\) | −11.3906 | −0.506875 | ||||||||
\(506\) | −1.44285 | −0.0641425 | ||||||||
\(507\) | 1.81169 | 0.0804600 | ||||||||
\(508\) | −5.33268 | −0.236599 | ||||||||
\(509\) | 9.11020 | 0.403802 | 0.201901 | − | 0.979406i | \(-0.435288\pi\) | ||||
0.201901 | + | 0.979406i | \(0.435288\pi\) | |||||||
\(510\) | 4.38093 | 0.193991 | ||||||||
\(511\) | −31.3124 | −1.38518 | ||||||||
\(512\) | −24.0082 | −1.06102 | ||||||||
\(513\) | 1.75052 | 0.0772875 | ||||||||
\(514\) | 26.3304 | 1.16138 | ||||||||
\(515\) | 4.32958 | 0.190784 | ||||||||
\(516\) | 43.4929 | 1.91467 | ||||||||
\(517\) | 25.8902 | 1.13865 | ||||||||
\(518\) | 1.33130 | 0.0584940 | ||||||||
\(519\) | −4.54297 | −0.199414 | ||||||||
\(520\) | −21.2784 | −0.933118 | ||||||||
\(521\) | 8.88422 | 0.389225 | 0.194612 | − | 0.980880i | \(-0.437655\pi\) | ||||
0.194612 | + | 0.980880i | \(0.437655\pi\) | |||||||
\(522\) | −14.5811 | −0.638198 | ||||||||
\(523\) | −38.1070 | −1.66630 | −0.833151 | − | 0.553046i | \(-0.813466\pi\) | ||||
−0.833151 | + | 0.553046i | \(0.813466\pi\) | |||||||
\(524\) | −57.4329 | −2.50897 | ||||||||
\(525\) | 21.2502 | 0.927433 | ||||||||
\(526\) | −9.24942 | −0.403294 | ||||||||
\(527\) | −11.9445 | −0.520312 | ||||||||
\(528\) | 37.3126 | 1.62382 | ||||||||
\(529\) | −22.9596 | −0.998243 | ||||||||
\(530\) | 13.3695 | 0.580734 | ||||||||
\(531\) | −1.46332 | −0.0635028 | ||||||||
\(532\) | −44.2381 | −1.91796 | ||||||||
\(533\) | −15.4506 | −0.669238 | ||||||||
\(534\) | −24.2970 | −1.05143 | ||||||||
\(535\) | −0.145080 | −0.00627236 | ||||||||
\(536\) | −49.8238 | −2.15206 | ||||||||
\(537\) | 7.62596 | 0.329084 | ||||||||
\(538\) | −44.8926 | −1.93546 | ||||||||
\(539\) | −39.9970 | −1.72279 | ||||||||
\(540\) | −3.73259 | −0.160625 | ||||||||
\(541\) | 8.60339 | 0.369889 | 0.184944 | − | 0.982749i | \(-0.440790\pi\) | ||||
0.184944 | + | 0.982749i | \(0.440790\pi\) | |||||||
\(542\) | −32.3080 | −1.38775 | ||||||||
\(543\) | 11.8129 | 0.506938 | ||||||||
\(544\) | −46.4718 | −1.99246 | ||||||||
\(545\) | −10.0016 | −0.428422 | ||||||||
\(546\) | 42.7234 | 1.82839 | ||||||||
\(547\) | 4.56804 | 0.195315 | 0.0976576 | − | 0.995220i | \(-0.468865\pi\) | ||||
0.0976576 | + | 0.995220i | \(0.468865\pi\) | |||||||
\(548\) | −49.4235 | −2.11127 | ||||||||
\(549\) | 11.9421 | 0.509676 | ||||||||
\(550\) | −32.4230 | −1.38252 | ||||||||
\(551\) | −9.40082 | −0.400488 | ||||||||
\(552\) | −1.84044 | −0.0783344 | ||||||||
\(553\) | 30.4924 | 1.29667 | ||||||||
\(554\) | −15.8181 | −0.672048 | ||||||||
\(555\) | 0.0724212 | 0.00307411 | ||||||||
\(556\) | −31.7113 | −1.34486 | ||||||||
\(557\) | 28.0010 | 1.18644 | 0.593220 | − | 0.805040i | \(-0.297856\pi\) | ||||
0.593220 | + | 0.805040i | \(0.297856\pi\) | |||||||
\(558\) | 13.9657 | 0.591216 | ||||||||
\(559\) | −27.0809 | −1.14540 | ||||||||
\(560\) | 46.1350 | 1.94956 | ||||||||
\(561\) | 6.13887 | 0.259183 | ||||||||
\(562\) | 0.652211 | 0.0275119 | ||||||||
\(563\) | −9.39898 | −0.396120 | −0.198060 | − | 0.980190i | \(-0.563464\pi\) | ||||
−0.198060 | + | 0.980190i | \(0.563464\pi\) | |||||||
\(564\) | 52.6118 | 2.21536 | ||||||||
\(565\) | −5.05646 | −0.212727 | ||||||||
\(566\) | −52.2414 | −2.19587 | ||||||||
\(567\) | 4.70425 | 0.197560 | ||||||||
\(568\) | −63.8495 | −2.67907 | ||||||||
\(569\) | −23.0858 | −0.967806 | −0.483903 | − | 0.875122i | \(-0.660781\pi\) | ||||
−0.483903 | + | 0.875122i | \(0.660781\pi\) | |||||||
\(570\) | −3.30244 | −0.138324 | ||||||||
\(571\) | 4.79264 | 0.200566 | 0.100283 | − | 0.994959i | \(-0.468025\pi\) | ||||
0.100283 | + | 0.994959i | \(0.468025\pi\) | |||||||
\(572\) | −47.5017 | −1.98614 | ||||||||
\(573\) | 13.7707 | 0.575278 | ||||||||
\(574\) | 58.9991 | 2.46258 | ||||||||
\(575\) | 0.908051 | 0.0378684 | ||||||||
\(576\) | 26.1064 | 1.08777 | ||||||||
\(577\) | −15.4567 | −0.643471 | −0.321736 | − | 0.946830i | \(-0.604266\pi\) | ||||
−0.321736 | + | 0.946830i | \(0.604266\pi\) | |||||||
\(578\) | 31.5158 | 1.31088 | ||||||||
\(579\) | −2.01737 | −0.0838390 | ||||||||
\(580\) | 20.0451 | 0.832327 | ||||||||
\(581\) | −3.16227 | −0.131193 | ||||||||
\(582\) | −48.7334 | −2.02007 | ||||||||
\(583\) | 18.7343 | 0.775895 | ||||||||
\(584\) | 60.9409 | 2.52175 | ||||||||
\(585\) | 2.32410 | 0.0960898 | ||||||||
\(586\) | −10.8303 | −0.447395 | ||||||||
\(587\) | 24.1678 | 0.997513 | 0.498757 | − | 0.866742i | \(-0.333790\pi\) | ||||
0.498757 | + | 0.866742i | \(0.333790\pi\) | |||||||
\(588\) | −81.2785 | −3.35187 | ||||||||
\(589\) | 9.00405 | 0.371006 | ||||||||
\(590\) | 2.76062 | 0.113653 | ||||||||
\(591\) | −20.7633 | −0.854089 | ||||||||
\(592\) | −1.47116 | −0.0604642 | ||||||||
\(593\) | 8.53973 | 0.350685 | 0.175342 | − | 0.984508i | \(-0.443897\pi\) | ||||
0.175342 | + | 0.984508i | \(0.443897\pi\) | |||||||
\(594\) | −7.17765 | −0.294503 | ||||||||
\(595\) | 7.59038 | 0.311175 | ||||||||
\(596\) | −96.0968 | −3.93628 | ||||||||
\(597\) | 20.6345 | 0.844514 | ||||||||
\(598\) | 1.82564 | 0.0746558 | ||||||||
\(599\) | −34.0494 | −1.39122 | −0.695610 | − | 0.718419i | \(-0.744866\pi\) | ||||
−0.695610 | + | 0.718419i | \(0.744866\pi\) | |||||||
\(600\) | −41.3575 | −1.68841 | ||||||||
\(601\) | −36.6314 | −1.49423 | −0.747114 | − | 0.664696i | \(-0.768561\pi\) | ||||
−0.747114 | + | 0.664696i | \(0.768561\pi\) | |||||||
\(602\) | 103.410 | 4.21470 | ||||||||
\(603\) | 5.44194 | 0.221613 | ||||||||
\(604\) | 127.748 | 5.19798 | ||||||||
\(605\) | −2.78734 | −0.113322 | ||||||||
\(606\) | −44.5110 | −1.80813 | ||||||||
\(607\) | −16.0934 | −0.653212 | −0.326606 | − | 0.945160i | \(-0.605905\pi\) | ||||
−0.326606 | + | 0.945160i | \(0.605905\pi\) | |||||||
\(608\) | 35.0315 | 1.42071 | ||||||||
\(609\) | −25.2632 | −1.02372 | ||||||||
\(610\) | −22.5293 | −0.912183 | ||||||||
\(611\) | −32.7588 | −1.32528 | ||||||||
\(612\) | 12.4749 | 0.504268 | ||||||||
\(613\) | 30.3571 | 1.22611 | 0.613055 | − | 0.790040i | \(-0.289940\pi\) | ||||
0.613055 | + | 0.790040i | \(0.289940\pi\) | |||||||
\(614\) | −30.9383 | −1.24857 | ||||||||
\(615\) | 3.20948 | 0.129419 | ||||||||
\(616\) | 113.858 | 4.58746 | ||||||||
\(617\) | −22.0089 | −0.886044 | −0.443022 | − | 0.896511i | \(-0.646094\pi\) | ||||
−0.443022 | + | 0.896511i | \(0.646094\pi\) | |||||||
\(618\) | 16.9187 | 0.680569 | ||||||||
\(619\) | −24.4297 | −0.981913 | −0.490957 | − | 0.871184i | \(-0.663353\pi\) | ||||
−0.490957 | + | 0.871184i | \(0.663353\pi\) | |||||||
\(620\) | −19.1991 | −0.771054 | ||||||||
\(621\) | 0.201020 | 0.00806665 | ||||||||
\(622\) | 46.8039 | 1.87666 | ||||||||
\(623\) | −42.0969 | −1.68658 | ||||||||
\(624\) | −47.2116 | −1.88998 | ||||||||
\(625\) | 17.9914 | 0.719657 | ||||||||
\(626\) | 40.9434 | 1.63643 | ||||||||
\(627\) | −4.62761 | −0.184809 | ||||||||
\(628\) | −76.1113 | −3.03717 | ||||||||
\(629\) | −0.242043 | −0.00965088 | ||||||||
\(630\) | −8.87477 | −0.353579 | ||||||||
\(631\) | 26.9703 | 1.07367 | 0.536835 | − | 0.843687i | \(-0.319620\pi\) | ||||
0.536835 | + | 0.843687i | \(0.319620\pi\) | |||||||
\(632\) | −59.3450 | −2.36062 | ||||||||
\(633\) | 23.6283 | 0.939140 | ||||||||
\(634\) | −5.60170 | −0.222472 | ||||||||
\(635\) | −0.689733 | −0.0273712 | ||||||||
\(636\) | 38.0703 | 1.50958 | ||||||||
\(637\) | 50.6082 | 2.00517 | ||||||||
\(638\) | 38.5460 | 1.52605 | ||||||||
\(639\) | 6.97388 | 0.275882 | ||||||||
\(640\) | −21.4413 | −0.847542 | ||||||||
\(641\) | −4.23018 | −0.167082 | −0.0835411 | − | 0.996504i | \(-0.526623\pi\) | ||||
−0.0835411 | + | 0.996504i | \(0.526623\pi\) | |||||||
\(642\) | −0.566928 | −0.0223749 | ||||||||
\(643\) | 5.56928 | 0.219631 | 0.109815 | − | 0.993952i | \(-0.464974\pi\) | ||||
0.109815 | + | 0.993952i | \(0.464974\pi\) | |||||||
\(644\) | −5.08004 | −0.200181 | ||||||||
\(645\) | 5.62541 | 0.221500 | ||||||||
\(646\) | 11.0372 | 0.434255 | ||||||||
\(647\) | 20.4314 | 0.803242 | 0.401621 | − | 0.915806i | \(-0.368447\pi\) | ||||
0.401621 | + | 0.915806i | \(0.368447\pi\) | |||||||
\(648\) | −9.15552 | −0.359663 | ||||||||
\(649\) | 3.86838 | 0.151847 | ||||||||
\(650\) | 41.0248 | 1.60913 | ||||||||
\(651\) | 24.1969 | 0.948353 | ||||||||
\(652\) | −22.9940 | −0.900516 | ||||||||
\(653\) | 9.19180 | 0.359703 | 0.179852 | − | 0.983694i | \(-0.442438\pi\) | ||||
0.179852 | + | 0.983694i | \(0.442438\pi\) | |||||||
\(654\) | −39.0832 | −1.52827 | ||||||||
\(655\) | −7.42842 | −0.290252 | ||||||||
\(656\) | −65.1971 | −2.54552 | ||||||||
\(657\) | −6.65620 | −0.259683 | ||||||||
\(658\) | 125.092 | 4.87660 | ||||||||
\(659\) | 34.0811 | 1.32761 | 0.663805 | − | 0.747905i | \(-0.268940\pi\) | ||||
0.663805 | + | 0.747905i | \(0.268940\pi\) | |||||||
\(660\) | 9.86733 | 0.384085 | ||||||||
\(661\) | 21.2239 | 0.825513 | 0.412757 | − | 0.910841i | \(-0.364566\pi\) | ||||
0.412757 | + | 0.910841i | \(0.364566\pi\) | |||||||
\(662\) | −35.5323 | −1.38100 | ||||||||
\(663\) | −7.76751 | −0.301665 | ||||||||
\(664\) | 6.15447 | 0.238840 | ||||||||
\(665\) | −5.72179 | −0.221881 | ||||||||
\(666\) | 0.283000 | 0.0109660 | ||||||||
\(667\) | −1.07953 | −0.0417997 | ||||||||
\(668\) | 6.80272 | 0.263205 | ||||||||
\(669\) | −6.82897 | −0.264023 | ||||||||
\(670\) | −10.2664 | −0.396628 | ||||||||
\(671\) | −31.5696 | −1.21873 | ||||||||
\(672\) | 94.1415 | 3.63159 | ||||||||
\(673\) | −9.35291 | −0.360528 | −0.180264 | − | 0.983618i | \(-0.557695\pi\) | ||||
−0.180264 | + | 0.983618i | \(0.557695\pi\) | |||||||
\(674\) | −86.2992 | −3.32412 | ||||||||
\(675\) | 4.51722 | 0.173868 | ||||||||
\(676\) | −9.73243 | −0.374324 | ||||||||
\(677\) | 22.7074 | 0.872717 | 0.436358 | − | 0.899773i | \(-0.356268\pi\) | ||||
0.436358 | + | 0.899773i | \(0.356268\pi\) | |||||||
\(678\) | −19.7591 | −0.758842 | ||||||||
\(679\) | −84.4354 | −3.24033 | ||||||||
\(680\) | −14.7726 | −0.566502 | ||||||||
\(681\) | −28.9229 | −1.10833 | ||||||||
\(682\) | −36.9192 | −1.41371 | ||||||||
\(683\) | −34.9077 | −1.33570 | −0.667852 | − | 0.744294i | \(-0.732786\pi\) | ||||
−0.667852 | + | 0.744294i | \(0.732786\pi\) | |||||||
\(684\) | −9.40385 | −0.359565 | ||||||||
\(685\) | −6.39248 | −0.244244 | ||||||||
\(686\) | −103.842 | −3.96471 | ||||||||
\(687\) | 2.66664 | 0.101739 | ||||||||
\(688\) | −114.274 | −4.35666 | ||||||||
\(689\) | −23.7045 | −0.903069 | ||||||||
\(690\) | −0.379232 | −0.0144371 | ||||||||
\(691\) | −32.0515 | −1.21930 | −0.609648 | − | 0.792673i | \(-0.708689\pi\) | ||||
−0.609648 | + | 0.792673i | \(0.708689\pi\) | |||||||
\(692\) | 24.4049 | 0.927735 | ||||||||
\(693\) | −12.4360 | −0.472403 | ||||||||
\(694\) | 26.1289 | 0.991840 | ||||||||
\(695\) | −4.10156 | −0.155581 | ||||||||
\(696\) | 49.1678 | 1.86370 | ||||||||
\(697\) | −10.7266 | −0.406298 | ||||||||
\(698\) | 24.2045 | 0.916155 | ||||||||
\(699\) | 4.95531 | 0.187427 | ||||||||
\(700\) | −114.156 | −4.31470 | ||||||||
\(701\) | −10.5591 | −0.398810 | −0.199405 | − | 0.979917i | \(-0.563901\pi\) | ||||
−0.199405 | + | 0.979917i | \(0.563901\pi\) | |||||||
\(702\) | 9.08187 | 0.342773 | ||||||||
\(703\) | 0.182457 | 0.00688150 | ||||||||
\(704\) | −69.0138 | −2.60106 | ||||||||
\(705\) | 6.80486 | 0.256286 | ||||||||
\(706\) | 9.81990 | 0.369577 | ||||||||
\(707\) | −77.1195 | −2.90038 | ||||||||
\(708\) | 7.86100 | 0.295435 | ||||||||
\(709\) | 11.5575 | 0.434049 | 0.217025 | − | 0.976166i | \(-0.430365\pi\) | ||||
0.217025 | + | 0.976166i | \(0.430365\pi\) | |||||||
\(710\) | −13.1565 | −0.493755 | ||||||||
\(711\) | 6.48188 | 0.243090 | ||||||||
\(712\) | 81.9300 | 3.07046 | ||||||||
\(713\) | 1.03397 | 0.0387226 | ||||||||
\(714\) | 29.6608 | 1.11003 | ||||||||
\(715\) | −6.14390 | −0.229769 | ||||||||
\(716\) | −40.9668 | −1.53100 | ||||||||
\(717\) | 3.42150 | 0.127778 | ||||||||
\(718\) | −97.4391 | −3.63639 | ||||||||
\(719\) | 6.12977 | 0.228602 | 0.114301 | − | 0.993446i | \(-0.463537\pi\) | ||||
0.114301 | + | 0.993446i | \(0.463537\pi\) | |||||||
\(720\) | 9.80708 | 0.365488 | ||||||||
\(721\) | 29.3132 | 1.09168 | ||||||||
\(722\) | 43.2677 | 1.61026 | ||||||||
\(723\) | 18.5558 | 0.690096 | ||||||||
\(724\) | −63.4589 | −2.35843 | ||||||||
\(725\) | −24.2588 | −0.900949 | ||||||||
\(726\) | −10.8921 | −0.404242 | ||||||||
\(727\) | 29.1765 | 1.08210 | 0.541049 | − | 0.840991i | \(-0.318027\pi\) | ||||
0.541049 | + | 0.840991i | \(0.318027\pi\) | |||||||
\(728\) | −144.064 | −5.33937 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.5572 | 0.464762 | ||||||||
\(731\) | −18.8010 | −0.695379 | ||||||||
\(732\) | −64.1531 | −2.37117 | ||||||||
\(733\) | 13.5952 | 0.502148 | 0.251074 | − | 0.967968i | \(-0.419216\pi\) | ||||
0.251074 | + | 0.967968i | \(0.419216\pi\) | |||||||
\(734\) | −28.1197 | −1.03792 | ||||||||
\(735\) | −10.5126 | −0.387764 | ||||||||
\(736\) | 4.02281 | 0.148283 | ||||||||
\(737\) | −14.3861 | −0.529919 | ||||||||
\(738\) | 12.5417 | 0.461665 | ||||||||
\(739\) | −9.75815 | −0.358959 | −0.179480 | − | 0.983762i | \(-0.557441\pi\) | ||||
−0.179480 | + | 0.983762i | \(0.557441\pi\) | |||||||
\(740\) | −0.389048 | −0.0143017 | ||||||||
\(741\) | 5.85532 | 0.215100 | ||||||||
\(742\) | 90.5174 | 3.32300 | ||||||||
\(743\) | 0.318128 | 0.0116710 | 0.00583548 | − | 0.999983i | \(-0.498142\pi\) | ||||
0.00583548 | + | 0.999983i | \(0.498142\pi\) | |||||||
\(744\) | −47.0926 | −1.72650 | ||||||||
\(745\) | −12.4292 | −0.455372 | ||||||||
\(746\) | 15.7924 | 0.578201 | ||||||||
\(747\) | −0.672215 | −0.0245950 | ||||||||
\(748\) | −32.9781 | −1.20580 | ||||||||
\(749\) | −0.982257 | −0.0358909 | ||||||||
\(750\) | −17.9546 | −0.655611 | ||||||||
\(751\) | 20.4435 | 0.745992 | 0.372996 | − | 0.927833i | \(-0.378330\pi\) | ||||
0.372996 | + | 0.927833i | \(0.378330\pi\) | |||||||
\(752\) | −138.233 | −5.04085 | ||||||||
\(753\) | −11.4910 | −0.418756 | ||||||||
\(754\) | −48.7723 | −1.77618 | ||||||||
\(755\) | 16.5230 | 0.601334 | ||||||||
\(756\) | −25.2713 | −0.919109 | ||||||||
\(757\) | 28.9140 | 1.05090 | 0.525449 | − | 0.850825i | \(-0.323897\pi\) | ||||
0.525449 | + | 0.850825i | \(0.323897\pi\) | |||||||
\(758\) | 23.1515 | 0.840902 | ||||||||
\(759\) | −0.531408 | −0.0192889 | ||||||||
\(760\) | 11.1359 | 0.403941 | ||||||||
\(761\) | 27.2253 | 0.986917 | 0.493459 | − | 0.869769i | \(-0.335732\pi\) | ||||
0.493459 | + | 0.869769i | \(0.335732\pi\) | |||||||
\(762\) | −2.69526 | −0.0976390 | ||||||||
\(763\) | −67.7154 | −2.45146 | ||||||||
\(764\) | −73.9763 | −2.67637 | ||||||||
\(765\) | 1.61351 | 0.0583367 | ||||||||
\(766\) | −46.2406 | −1.67074 | ||||||||
\(767\) | −4.89466 | −0.176736 | ||||||||
\(768\) | −31.5731 | −1.13930 | ||||||||
\(769\) | −16.6087 | −0.598925 | −0.299462 | − | 0.954108i | \(-0.596807\pi\) | ||||
−0.299462 | + | 0.954108i | \(0.596807\pi\) | |||||||
\(770\) | 23.4610 | 0.845475 | ||||||||
\(771\) | 9.69760 | 0.349250 | ||||||||
\(772\) | 10.8373 | 0.390045 | ||||||||
\(773\) | 18.0431 | 0.648964 | 0.324482 | − | 0.945892i | \(-0.394810\pi\) | ||||
0.324482 | + | 0.945892i | \(0.394810\pi\) | |||||||
\(774\) | 21.9823 | 0.790139 | ||||||||
\(775\) | 23.2349 | 0.834624 | ||||||||
\(776\) | 164.330 | 5.89910 | ||||||||
\(777\) | 0.490324 | 0.0175903 | ||||||||
\(778\) | 81.1316 | 2.90871 | ||||||||
\(779\) | 8.08593 | 0.289708 | ||||||||
\(780\) | −12.4851 | −0.447039 | ||||||||
\(781\) | −18.4359 | −0.659687 | ||||||||
\(782\) | 1.26745 | 0.0453240 | ||||||||
\(783\) | −5.37029 | −0.191918 | ||||||||
\(784\) | 213.553 | 7.62688 | ||||||||
\(785\) | −9.84430 | −0.351358 | ||||||||
\(786\) | −29.0279 | −1.03539 | ||||||||
\(787\) | −26.8028 | −0.955417 | −0.477708 | − | 0.878519i | \(-0.658532\pi\) | ||||
−0.477708 | + | 0.878519i | \(0.658532\pi\) | |||||||
\(788\) | 111.541 | 3.97348 | ||||||||
\(789\) | −3.40660 | −0.121278 | ||||||||
\(790\) | −12.2283 | −0.435065 | ||||||||
\(791\) | −34.2345 | −1.21724 | ||||||||
\(792\) | 24.2032 | 0.860022 | ||||||||
\(793\) | 39.9450 | 1.41849 | ||||||||
\(794\) | 44.9981 | 1.59692 | ||||||||
\(795\) | 4.92404 | 0.174638 | ||||||||
\(796\) | −110.849 | −3.92893 | ||||||||
\(797\) | −48.1881 | −1.70691 | −0.853455 | − | 0.521166i | \(-0.825497\pi\) | ||||
−0.853455 | + | 0.521166i | \(0.825497\pi\) | |||||||
\(798\) | −22.3590 | −0.791499 | ||||||||
\(799\) | −22.7429 | −0.804585 | ||||||||
\(800\) | 90.3986 | 3.19607 | ||||||||
\(801\) | −8.94870 | −0.316187 | ||||||||
\(802\) | −91.6031 | −3.23462 | ||||||||
\(803\) | 17.5960 | 0.620951 | ||||||||
\(804\) | −29.2342 | −1.03101 | ||||||||
\(805\) | −0.657056 | −0.0231582 | ||||||||
\(806\) | 46.7138 | 1.64542 | ||||||||
\(807\) | −16.5341 | −0.582029 | ||||||||
\(808\) | 150.092 | 5.28021 | ||||||||
\(809\) | −25.0667 | −0.881299 | −0.440650 | − | 0.897679i | \(-0.645252\pi\) | ||||
−0.440650 | + | 0.897679i | \(0.645252\pi\) | |||||||
\(810\) | −1.88654 | −0.0662863 | ||||||||
\(811\) | −4.29712 | −0.150892 | −0.0754461 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754461 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(812\) | 135.714 | 4.76264 | ||||||||
\(813\) | −11.8992 | −0.417323 | ||||||||
\(814\) | −0.748126 | −0.0262218 | ||||||||
\(815\) | −2.97407 | −0.104177 | ||||||||
\(816\) | −32.7768 | −1.14742 | ||||||||
\(817\) | 14.1726 | 0.495836 | ||||||||
\(818\) | 34.0149 | 1.18930 | ||||||||
\(819\) | 15.7352 | 0.549833 | ||||||||
\(820\) | −17.2414 | −0.602096 | ||||||||
\(821\) | −1.14479 | −0.0399534 | −0.0199767 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199767 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(822\) | −24.9798 | −0.871271 | ||||||||
\(823\) | 32.2248 | 1.12329 | 0.561643 | − | 0.827380i | \(-0.310170\pi\) | ||||
0.561643 | + | 0.827380i | \(0.310170\pi\) | |||||||
\(824\) | −57.0501 | −1.98743 | ||||||||
\(825\) | −11.9415 | −0.415751 | ||||||||
\(826\) | 18.6906 | 0.650331 | ||||||||
\(827\) | 37.5829 | 1.30689 | 0.653443 | − | 0.756976i | \(-0.273324\pi\) | ||||
0.653443 | + | 0.756976i | \(0.273324\pi\) | |||||||
\(828\) | −1.07988 | −0.0375285 | ||||||||
\(829\) | −44.2771 | −1.53781 | −0.768904 | − | 0.639365i | \(-0.779197\pi\) | ||||
−0.768904 | + | 0.639365i | \(0.779197\pi\) | |||||||
\(830\) | 1.26816 | 0.0440185 | ||||||||
\(831\) | −5.82588 | −0.202098 | ||||||||
\(832\) | 87.3231 | 3.02739 | ||||||||
\(833\) | 35.1348 | 1.21735 | ||||||||
\(834\) | −16.0276 | −0.554991 | ||||||||
\(835\) | 0.879870 | 0.0304492 | ||||||||
\(836\) | 24.8596 | 0.859788 | ||||||||
\(837\) | 5.14363 | 0.177790 | ||||||||
\(838\) | −56.7934 | −1.96190 | ||||||||
\(839\) | −23.5186 | −0.811953 | −0.405976 | − | 0.913884i | \(-0.633068\pi\) | ||||
−0.405976 | + | 0.913884i | \(0.633068\pi\) | |||||||
\(840\) | 29.9259 | 1.03254 | ||||||||
\(841\) | −0.160023 | −0.00551803 | ||||||||
\(842\) | −86.8936 | −2.99455 | ||||||||
\(843\) | 0.240212 | 0.00827335 | ||||||||
\(844\) | −126.932 | −4.36916 | ||||||||
\(845\) | −1.25880 | −0.0433041 | ||||||||
\(846\) | 26.5913 | 0.914227 | ||||||||
\(847\) | −18.8716 | −0.648434 | ||||||||
\(848\) | −100.027 | −3.43492 | ||||||||
\(849\) | −19.2408 | −0.660341 | ||||||||
\(850\) | 28.4816 | 0.976911 | ||||||||
\(851\) | 0.0209523 | 0.000718235 0 | ||||||||
\(852\) | −37.4638 | −1.28349 | ||||||||
\(853\) | 11.6289 | 0.398165 | 0.199082 | − | 0.979983i | \(-0.436204\pi\) | ||||
0.199082 | + | 0.979983i | \(0.436204\pi\) | |||||||
\(854\) | −152.533 | −5.21958 | ||||||||
\(855\) | −1.21630 | −0.0415966 | ||||||||
\(856\) | 1.91169 | 0.0653403 | ||||||||
\(857\) | −35.4647 | −1.21145 | −0.605725 | − | 0.795674i | \(-0.707117\pi\) | ||||
−0.605725 | + | 0.795674i | \(0.707117\pi\) | |||||||
\(858\) | −24.0085 | −0.819636 | ||||||||
\(859\) | 10.0422 | 0.342634 | 0.171317 | − | 0.985216i | \(-0.445198\pi\) | ||||
0.171317 | + | 0.985216i | \(0.445198\pi\) | |||||||
\(860\) | −30.2198 | −1.03049 | ||||||||
\(861\) | 21.7296 | 0.740544 | ||||||||
\(862\) | −92.5096 | −3.15089 | ||||||||
\(863\) | −42.7025 | −1.45361 | −0.726805 | − | 0.686844i | \(-0.758996\pi\) | ||||
−0.726805 | + | 0.686844i | \(0.758996\pi\) | |||||||
\(864\) | 20.0120 | 0.680822 | ||||||||
\(865\) | 3.15655 | 0.107326 | ||||||||
\(866\) | −6.06987 | −0.206263 | ||||||||
\(867\) | 11.6074 | 0.394208 | ||||||||
\(868\) | −129.986 | −4.41203 | ||||||||
\(869\) | −17.1352 | −0.581273 | ||||||||
\(870\) | 10.1313 | 0.343482 | ||||||||
\(871\) | 18.2027 | 0.616775 | ||||||||
\(872\) | 131.789 | 4.46295 | ||||||||
\(873\) | −17.9487 | −0.607473 | ||||||||
\(874\) | −0.955433 | −0.0323180 | ||||||||
\(875\) | −31.1081 | −1.05165 | ||||||||
\(876\) | 35.7572 | 1.20812 | ||||||||
\(877\) | 41.3765 | 1.39719 | 0.698593 | − | 0.715519i | \(-0.253810\pi\) | ||||
0.698593 | + | 0.715519i | \(0.253810\pi\) | |||||||
\(878\) | 84.0758 | 2.83742 | ||||||||
\(879\) | −3.98884 | −0.134540 | ||||||||
\(880\) | −25.9256 | −0.873952 | ||||||||
\(881\) | 46.3699 | 1.56224 | 0.781120 | − | 0.624381i | \(-0.214649\pi\) | ||||
0.781120 | + | 0.624381i | \(0.214649\pi\) | |||||||
\(882\) | −41.0801 | −1.38324 | ||||||||
\(883\) | −37.9554 | −1.27730 | −0.638650 | − | 0.769497i | \(-0.720507\pi\) | ||||
−0.638650 | + | 0.769497i | \(0.720507\pi\) | |||||||
\(884\) | 41.7272 | 1.40344 | ||||||||
\(885\) | 1.01675 | 0.0341776 | ||||||||
\(886\) | 43.9753 | 1.47738 | ||||||||
\(887\) | 9.83731 | 0.330305 | 0.165152 | − | 0.986268i | \(-0.447188\pi\) | ||||
0.165152 | + | 0.986268i | \(0.447188\pi\) | |||||||
\(888\) | −0.954280 | −0.0320235 | ||||||||
\(889\) | −4.66980 | −0.156620 | ||||||||
\(890\) | 16.8821 | 0.565889 | ||||||||
\(891\) | −2.64356 | −0.0885626 | ||||||||
\(892\) | 36.6854 | 1.22832 | ||||||||
\(893\) | 17.1441 | 0.573705 | ||||||||
\(894\) | −48.5696 | −1.62441 | ||||||||
\(895\) | −5.29868 | −0.177115 | ||||||||
\(896\) | −145.167 | −4.84969 | ||||||||
\(897\) | 0.672390 | 0.0224504 | ||||||||
\(898\) | −102.722 | −3.42787 | ||||||||
\(899\) | −27.6228 | −0.921271 | ||||||||
\(900\) | −24.2666 | −0.808887 | ||||||||
\(901\) | −16.4569 | −0.548259 | ||||||||
\(902\) | −33.1546 | −1.10393 | ||||||||
\(903\) | 38.0865 | 1.26744 | ||||||||
\(904\) | 66.6279 | 2.21601 | ||||||||
\(905\) | −8.20783 | −0.272837 | ||||||||
\(906\) | 64.5668 | 2.14509 | ||||||||
\(907\) | 58.3583 | 1.93775 | 0.968877 | − | 0.247542i | \(-0.0796229\pi\) | ||||
0.968877 | + | 0.247542i | \(0.0796229\pi\) | |||||||
\(908\) | 155.374 | 5.15628 | ||||||||
\(909\) | −16.3936 | −0.543741 | ||||||||
\(910\) | −29.6851 | −0.984053 | ||||||||
\(911\) | 2.57894 | 0.0854442 | 0.0427221 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427221 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(912\) | 24.7078 | 0.818158 | ||||||||
\(913\) | 1.77704 | 0.0588114 | ||||||||
\(914\) | −80.2544 | −2.65458 | ||||||||
\(915\) | −8.29762 | −0.274311 | ||||||||
\(916\) | −14.3252 | −0.473319 | ||||||||
\(917\) | −50.2937 | −1.66084 | ||||||||
\(918\) | 6.30511 | 0.208100 | ||||||||
\(919\) | 16.3444 | 0.539152 | 0.269576 | − | 0.962979i | \(-0.413117\pi\) | ||||
0.269576 | + | 0.962979i | \(0.413117\pi\) | |||||||
\(920\) | 1.27878 | 0.0421601 | ||||||||
\(921\) | −11.3947 | −0.375469 | ||||||||
\(922\) | 14.3559 | 0.472785 | ||||||||
\(923\) | 23.3269 | 0.767814 | ||||||||
\(924\) | 66.8062 | 2.19776 | ||||||||
\(925\) | 0.470830 | 0.0154808 | ||||||||
\(926\) | 101.859 | 3.34731 | ||||||||
\(927\) | 6.23122 | 0.204660 | ||||||||
\(928\) | −107.470 | −3.52788 | ||||||||
\(929\) | −5.01148 | −0.164421 | −0.0822106 | − | 0.996615i | \(-0.526198\pi\) | ||||
−0.0822106 | + | 0.996615i | \(0.526198\pi\) | |||||||
\(930\) | −9.70368 | −0.318196 | ||||||||
\(931\) | −26.4854 | −0.868024 | ||||||||
\(932\) | −26.6200 | −0.871968 | ||||||||
\(933\) | 17.2381 | 0.564349 | ||||||||
\(934\) | −67.6688 | −2.21419 | ||||||||
\(935\) | −4.26542 | −0.139494 | ||||||||
\(936\) | −30.6242 | −1.00098 | ||||||||
\(937\) | −23.4916 | −0.767437 | −0.383718 | − | 0.923450i | \(-0.625357\pi\) | ||||
−0.383718 | + | 0.923450i | \(0.625357\pi\) | |||||||
\(938\) | −69.5085 | −2.26953 | ||||||||
\(939\) | 15.0796 | 0.492105 | ||||||||
\(940\) | −36.5558 | −1.19232 | ||||||||
\(941\) | −40.3552 | −1.31554 | −0.657770 | − | 0.753218i | \(-0.728500\pi\) | ||||
−0.657770 | + | 0.753218i | \(0.728500\pi\) | |||||||
\(942\) | −38.4685 | −1.25337 | ||||||||
\(943\) | 0.928540 | 0.0302374 | ||||||||
\(944\) | −20.6541 | −0.672235 | ||||||||
\(945\) | −3.26861 | −0.106328 | ||||||||
\(946\) | −58.1116 | −1.88937 | ||||||||
\(947\) | −14.6798 | −0.477028 | −0.238514 | − | 0.971139i | \(-0.576660\pi\) | ||||
−0.238514 | + | 0.971139i | \(0.576660\pi\) | |||||||
\(948\) | −34.8208 | −1.13093 | ||||||||
\(949\) | −22.2643 | −0.722729 | ||||||||
\(950\) | −21.4700 | −0.696580 | ||||||||
\(951\) | −2.06313 | −0.0669015 | ||||||||
\(952\) | −100.017 | −3.24156 | ||||||||
\(953\) | 12.0270 | 0.389593 | 0.194796 | − | 0.980844i | \(-0.437595\pi\) | ||||
0.194796 | + | 0.980844i | \(0.437595\pi\) | |||||||
\(954\) | 19.2416 | 0.622970 | ||||||||
\(955\) | −9.56816 | −0.309618 | ||||||||
\(956\) | −18.3804 | −0.594463 | ||||||||
\(957\) | 14.1967 | 0.458913 | ||||||||
\(958\) | 41.9504 | 1.35536 | ||||||||
\(959\) | −43.2799 | −1.39758 | ||||||||
\(960\) | −18.1393 | −0.585443 | ||||||||
\(961\) | −4.54304 | −0.146550 | ||||||||
\(962\) | 0.946603 | 0.0305197 | ||||||||
\(963\) | −0.208802 | −0.00672855 | ||||||||
\(964\) | −99.6818 | −3.21054 | ||||||||
\(965\) | 1.40171 | 0.0451227 | ||||||||
\(966\) | −2.56757 | −0.0826103 | ||||||||
\(967\) | −50.4236 | −1.62151 | −0.810756 | − | 0.585384i | \(-0.800944\pi\) | ||||
−0.810756 | + | 0.585384i | \(0.800944\pi\) | |||||||
\(968\) | 36.7282 | 1.18049 | ||||||||
\(969\) | 4.06507 | 0.130589 | ||||||||
\(970\) | 33.8610 | 1.08721 | ||||||||
\(971\) | 9.19189 | 0.294982 | 0.147491 | − | 0.989063i | \(-0.452880\pi\) | ||||
0.147491 | + | 0.989063i | \(0.452880\pi\) | |||||||
\(972\) | −5.37202 | −0.172308 | ||||||||
\(973\) | −27.7694 | −0.890246 | ||||||||
\(974\) | −2.83431 | −0.0908171 | ||||||||
\(975\) | 15.1096 | 0.483895 | ||||||||
\(976\) | 168.557 | 5.39538 | ||||||||
\(977\) | −6.24136 | −0.199679 | −0.0998394 | − | 0.995004i | \(-0.531833\pi\) | ||||
−0.0998394 | + | 0.995004i | \(0.531833\pi\) | |||||||
\(978\) | −11.6217 | −0.371622 | ||||||||
\(979\) | 23.6564 | 0.756062 | ||||||||
\(980\) | 56.4741 | 1.80400 | ||||||||
\(981\) | −14.3945 | −0.459582 | ||||||||
\(982\) | 21.1950 | 0.676359 | ||||||||
\(983\) | 23.2549 | 0.741717 | 0.370859 | − | 0.928689i | \(-0.379063\pi\) | ||||
0.370859 | + | 0.928689i | \(0.379063\pi\) | |||||||
\(984\) | −42.2907 | −1.34818 | ||||||||
\(985\) | 14.4268 | 0.459676 | ||||||||
\(986\) | −33.8603 | −1.07833 | ||||||||
\(987\) | 46.0719 | 1.46649 | ||||||||
\(988\) | −31.4549 | −1.00071 | ||||||||
\(989\) | 1.62749 | 0.0517513 | ||||||||
\(990\) | 4.98718 | 0.158503 | ||||||||
\(991\) | 24.0712 | 0.764645 | 0.382323 | − | 0.924029i | \(-0.375124\pi\) | ||||
0.382323 | + | 0.924029i | \(0.375124\pi\) | |||||||
\(992\) | 102.934 | 3.26817 | ||||||||
\(993\) | −13.0867 | −0.415294 | ||||||||
\(994\) | −89.0755 | −2.82530 | ||||||||
\(995\) | −14.3373 | −0.454523 | ||||||||
\(996\) | 3.61115 | 0.114424 | ||||||||
\(997\) | 33.9393 | 1.07487 | 0.537435 | − | 0.843305i | \(-0.319393\pi\) | ||||
0.537435 | + | 0.843305i | \(0.319393\pi\) | |||||||
\(998\) | −65.0274 | −2.05841 | ||||||||
\(999\) | 0.104230 | 0.00329769 |
(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 | 8031.2.a.b.1.2 | ✓ | 102 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8031.2.a.b.1.2 | ✓ | 102 | 1.1 | even | 1 | trivial |