Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8038,2,Mod(1,8038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8038, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8038 = 2 \cdot 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8038.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: | \(64.1837531447\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8038.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.46931 | −1.42566 | −0.712828 | − | 0.701339i | \(-0.752586\pi\) | ||||
−0.712828 | + | 0.701339i | \(0.752586\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.696459 | 0.311466 | 0.155733 | − | 0.987799i | \(-0.450226\pi\) | ||||
0.155733 | + | 0.987799i | \(0.450226\pi\) | |||||||
\(6\) | −2.46931 | −1.00809 | ||||||||
\(7\) | −2.94189 | −1.11193 | −0.555965 | − | 0.831206i | \(-0.687651\pi\) | ||||
−0.555965 | + | 0.831206i | \(0.687651\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.09749 | 1.03250 | ||||||||
\(10\) | 0.696459 | 0.220240 | ||||||||
\(11\) | 6.47128 | 1.95116 | 0.975582 | − | 0.219637i | \(-0.0704872\pi\) | ||||
0.975582 | + | 0.219637i | \(0.0704872\pi\) | |||||||
\(12\) | −2.46931 | −0.712828 | ||||||||
\(13\) | 0.247100 | 0.0685332 | 0.0342666 | − | 0.999413i | \(-0.489090\pi\) | ||||
0.0342666 | + | 0.999413i | \(0.489090\pi\) | |||||||
\(14\) | −2.94189 | −0.786253 | ||||||||
\(15\) | −1.71977 | −0.444044 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.32305 | −1.04849 | −0.524247 | − | 0.851567i | \(-0.675653\pi\) | ||||
−0.524247 | + | 0.851567i | \(0.675653\pi\) | |||||||
\(18\) | 3.09749 | 0.730085 | ||||||||
\(19\) | 5.40761 | 1.24059 | 0.620296 | − | 0.784368i | \(-0.287013\pi\) | ||||
0.620296 | + | 0.784368i | \(0.287013\pi\) | |||||||
\(20\) | 0.696459 | 0.155733 | ||||||||
\(21\) | 7.26444 | 1.58523 | ||||||||
\(22\) | 6.47128 | 1.37968 | ||||||||
\(23\) | −7.44793 | −1.55300 | −0.776501 | − | 0.630116i | \(-0.783007\pi\) | ||||
−0.776501 | + | 0.630116i | \(0.783007\pi\) | |||||||
\(24\) | −2.46931 | −0.504046 | ||||||||
\(25\) | −4.51494 | −0.902989 | ||||||||
\(26\) | 0.247100 | 0.0484603 | ||||||||
\(27\) | −0.240730 | −0.0463284 | ||||||||
\(28\) | −2.94189 | −0.555965 | ||||||||
\(29\) | −9.62171 | −1.78671 | −0.893353 | − | 0.449355i | \(-0.851654\pi\) | ||||
−0.893353 | + | 0.449355i | \(0.851654\pi\) | |||||||
\(30\) | −1.71977 | −0.313986 | ||||||||
\(31\) | 1.40003 | 0.251452 | 0.125726 | − | 0.992065i | \(-0.459874\pi\) | ||||
0.125726 | + | 0.992065i | \(0.459874\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −15.9796 | −2.78169 | ||||||||
\(34\) | −4.32305 | −0.741397 | ||||||||
\(35\) | −2.04891 | −0.346328 | ||||||||
\(36\) | 3.09749 | 0.516248 | ||||||||
\(37\) | 10.6398 | 1.74917 | 0.874584 | − | 0.484874i | \(-0.161135\pi\) | ||||
0.874584 | + | 0.484874i | \(0.161135\pi\) | |||||||
\(38\) | 5.40761 | 0.877230 | ||||||||
\(39\) | −0.610166 | −0.0977048 | ||||||||
\(40\) | 0.696459 | 0.110120 | ||||||||
\(41\) | −0.621738 | −0.0970991 | −0.0485495 | − | 0.998821i | \(-0.515460\pi\) | ||||
−0.0485495 | + | 0.998821i | \(0.515460\pi\) | |||||||
\(42\) | 7.26444 | 1.12093 | ||||||||
\(43\) | −1.89591 | −0.289123 | −0.144562 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144562 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(44\) | 6.47128 | 0.975582 | ||||||||
\(45\) | 2.15727 | 0.321588 | ||||||||
\(46\) | −7.44793 | −1.09814 | ||||||||
\(47\) | 2.21454 | 0.323024 | 0.161512 | − | 0.986871i | \(-0.448363\pi\) | ||||
0.161512 | + | 0.986871i | \(0.448363\pi\) | |||||||
\(48\) | −2.46931 | −0.356414 | ||||||||
\(49\) | 1.65472 | 0.236389 | ||||||||
\(50\) | −4.51494 | −0.638510 | ||||||||
\(51\) | 10.6749 | 1.49479 | ||||||||
\(52\) | 0.247100 | 0.0342666 | ||||||||
\(53\) | −5.99737 | −0.823802 | −0.411901 | − | 0.911229i | \(-0.635135\pi\) | ||||
−0.411901 | + | 0.911229i | \(0.635135\pi\) | |||||||
\(54\) | −0.240730 | −0.0327591 | ||||||||
\(55\) | 4.50698 | 0.607721 | ||||||||
\(56\) | −2.94189 | −0.393127 | ||||||||
\(57\) | −13.3531 | −1.76866 | ||||||||
\(58\) | −9.62171 | −1.26339 | ||||||||
\(59\) | −3.90307 | −0.508137 | −0.254068 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254068 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(60\) | −1.71977 | −0.222022 | ||||||||
\(61\) | 9.72924 | 1.24570 | 0.622851 | − | 0.782341i | \(-0.285974\pi\) | ||||
0.622851 | + | 0.782341i | \(0.285974\pi\) | |||||||
\(62\) | 1.40003 | 0.177803 | ||||||||
\(63\) | −9.11247 | −1.14806 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.172095 | 0.0213458 | ||||||||
\(66\) | −15.9796 | −1.96695 | ||||||||
\(67\) | −7.84645 | −0.958597 | −0.479298 | − | 0.877652i | \(-0.659109\pi\) | ||||
−0.479298 | + | 0.877652i | \(0.659109\pi\) | |||||||
\(68\) | −4.32305 | −0.524247 | ||||||||
\(69\) | 18.3913 | 2.21405 | ||||||||
\(70\) | −2.04891 | −0.244891 | ||||||||
\(71\) | −8.12981 | −0.964831 | −0.482415 | − | 0.875943i | \(-0.660240\pi\) | ||||
−0.482415 | + | 0.875943i | \(0.660240\pi\) | |||||||
\(72\) | 3.09749 | 0.365043 | ||||||||
\(73\) | 9.56163 | 1.11910 | 0.559552 | − | 0.828795i | \(-0.310973\pi\) | ||||
0.559552 | + | 0.828795i | \(0.310973\pi\) | |||||||
\(74\) | 10.6398 | 1.23685 | ||||||||
\(75\) | 11.1488 | 1.28735 | ||||||||
\(76\) | 5.40761 | 0.620296 | ||||||||
\(77\) | −19.0378 | −2.16956 | ||||||||
\(78\) | −0.610166 | −0.0690878 | ||||||||
\(79\) | 13.6598 | 1.53685 | 0.768424 | − | 0.639941i | \(-0.221041\pi\) | ||||
0.768424 | + | 0.639941i | \(0.221041\pi\) | |||||||
\(80\) | 0.696459 | 0.0778665 | ||||||||
\(81\) | −8.69803 | −0.966448 | ||||||||
\(82\) | −0.621738 | −0.0686594 | ||||||||
\(83\) | −13.2203 | −1.45112 | −0.725559 | − | 0.688160i | \(-0.758419\pi\) | ||||
−0.725559 | + | 0.688160i | \(0.758419\pi\) | |||||||
\(84\) | 7.26444 | 0.792615 | ||||||||
\(85\) | −3.01083 | −0.326570 | ||||||||
\(86\) | −1.89591 | −0.204441 | ||||||||
\(87\) | 23.7590 | 2.54723 | ||||||||
\(88\) | 6.47128 | 0.689840 | ||||||||
\(89\) | 5.90688 | 0.626128 | 0.313064 | − | 0.949732i | \(-0.398645\pi\) | ||||
0.313064 | + | 0.949732i | \(0.398645\pi\) | |||||||
\(90\) | 2.15727 | 0.227397 | ||||||||
\(91\) | −0.726941 | −0.0762042 | ||||||||
\(92\) | −7.44793 | −0.776501 | ||||||||
\(93\) | −3.45710 | −0.358484 | ||||||||
\(94\) | 2.21454 | 0.228412 | ||||||||
\(95\) | 3.76618 | 0.386402 | ||||||||
\(96\) | −2.46931 | −0.252023 | ||||||||
\(97\) | 4.65460 | 0.472603 | 0.236302 | − | 0.971680i | \(-0.424065\pi\) | ||||
0.236302 | + | 0.971680i | \(0.424065\pi\) | |||||||
\(98\) | 1.65472 | 0.167152 | ||||||||
\(99\) | 20.0447 | 2.01457 | ||||||||
\(100\) | −4.51494 | −0.451494 | ||||||||
\(101\) | −13.8748 | −1.38060 | −0.690299 | − | 0.723524i | \(-0.742521\pi\) | ||||
−0.690299 | + | 0.723524i | \(0.742521\pi\) | |||||||
\(102\) | 10.6749 | 1.05698 | ||||||||
\(103\) | −3.48612 | −0.343498 | −0.171749 | − | 0.985141i | \(-0.554942\pi\) | ||||
−0.171749 | + | 0.985141i | \(0.554942\pi\) | |||||||
\(104\) | 0.247100 | 0.0242302 | ||||||||
\(105\) | 5.05939 | 0.493745 | ||||||||
\(106\) | −5.99737 | −0.582516 | ||||||||
\(107\) | −10.7045 | −1.03484 | −0.517419 | − | 0.855732i | \(-0.673107\pi\) | ||||
−0.517419 | + | 0.855732i | \(0.673107\pi\) | |||||||
\(108\) | −0.240730 | −0.0231642 | ||||||||
\(109\) | 17.3569 | 1.66249 | 0.831247 | − | 0.555904i | \(-0.187628\pi\) | ||||
0.831247 | + | 0.555904i | \(0.187628\pi\) | |||||||
\(110\) | 4.50698 | 0.429724 | ||||||||
\(111\) | −26.2729 | −2.49371 | ||||||||
\(112\) | −2.94189 | −0.277983 | ||||||||
\(113\) | 12.1686 | 1.14473 | 0.572364 | − | 0.820000i | \(-0.306026\pi\) | ||||
0.572364 | + | 0.820000i | \(0.306026\pi\) | |||||||
\(114\) | −13.3531 | −1.25063 | ||||||||
\(115\) | −5.18718 | −0.483707 | ||||||||
\(116\) | −9.62171 | −0.893353 | ||||||||
\(117\) | 0.765390 | 0.0707603 | ||||||||
\(118\) | −3.90307 | −0.359307 | ||||||||
\(119\) | 12.7179 | 1.16585 | ||||||||
\(120\) | −1.71977 | −0.156993 | ||||||||
\(121\) | 30.8774 | 2.80704 | ||||||||
\(122\) | 9.72924 | 0.880844 | ||||||||
\(123\) | 1.53526 | 0.138430 | ||||||||
\(124\) | 1.40003 | 0.125726 | ||||||||
\(125\) | −6.62677 | −0.592716 | ||||||||
\(126\) | −9.11247 | −0.811804 | ||||||||
\(127\) | 2.44248 | 0.216735 | 0.108368 | − | 0.994111i | \(-0.465438\pi\) | ||||
0.108368 | + | 0.994111i | \(0.465438\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.68158 | 0.412190 | ||||||||
\(130\) | 0.172095 | 0.0150937 | ||||||||
\(131\) | −12.9309 | −1.12978 | −0.564890 | − | 0.825166i | \(-0.691081\pi\) | ||||
−0.564890 | + | 0.825166i | \(0.691081\pi\) | |||||||
\(132\) | −15.9796 | −1.39084 | ||||||||
\(133\) | −15.9086 | −1.37945 | ||||||||
\(134\) | −7.84645 | −0.677830 | ||||||||
\(135\) | −0.167658 | −0.0144297 | ||||||||
\(136\) | −4.32305 | −0.370698 | ||||||||
\(137\) | −13.9638 | −1.19301 | −0.596506 | − | 0.802609i | \(-0.703445\pi\) | ||||
−0.596506 | + | 0.802609i | \(0.703445\pi\) | |||||||
\(138\) | 18.3913 | 1.56557 | ||||||||
\(139\) | −11.7947 | −1.00041 | −0.500207 | − | 0.865906i | \(-0.666743\pi\) | ||||
−0.500207 | + | 0.865906i | \(0.666743\pi\) | |||||||
\(140\) | −2.04891 | −0.173164 | ||||||||
\(141\) | −5.46839 | −0.460521 | ||||||||
\(142\) | −8.12981 | −0.682238 | ||||||||
\(143\) | 1.59905 | 0.133720 | ||||||||
\(144\) | 3.09749 | 0.258124 | ||||||||
\(145\) | −6.70113 | −0.556498 | ||||||||
\(146\) | 9.56163 | 0.791326 | ||||||||
\(147\) | −4.08602 | −0.337009 | ||||||||
\(148\) | 10.6398 | 0.874584 | ||||||||
\(149\) | 15.3095 | 1.25420 | 0.627102 | − | 0.778937i | \(-0.284241\pi\) | ||||
0.627102 | + | 0.778937i | \(0.284241\pi\) | |||||||
\(150\) | 11.1488 | 0.910295 | ||||||||
\(151\) | 19.2314 | 1.56503 | 0.782514 | − | 0.622633i | \(-0.213937\pi\) | ||||
0.782514 | + | 0.622633i | \(0.213937\pi\) | |||||||
\(152\) | 5.40761 | 0.438615 | ||||||||
\(153\) | −13.3906 | −1.08257 | ||||||||
\(154\) | −19.0378 | −1.53411 | ||||||||
\(155\) | 0.975061 | 0.0783188 | ||||||||
\(156\) | −0.610166 | −0.0488524 | ||||||||
\(157\) | −4.25207 | −0.339352 | −0.169676 | − | 0.985500i | \(-0.554272\pi\) | ||||
−0.169676 | + | 0.985500i | \(0.554272\pi\) | |||||||
\(158\) | 13.6598 | 1.08672 | ||||||||
\(159\) | 14.8094 | 1.17446 | ||||||||
\(160\) | 0.696459 | 0.0550599 | ||||||||
\(161\) | 21.9110 | 1.72683 | ||||||||
\(162\) | −8.69803 | −0.683382 | ||||||||
\(163\) | 20.9568 | 1.64146 | 0.820732 | − | 0.571314i | \(-0.193566\pi\) | ||||
0.820732 | + | 0.571314i | \(0.193566\pi\) | |||||||
\(164\) | −0.621738 | −0.0485495 | ||||||||
\(165\) | −11.1291 | −0.866402 | ||||||||
\(166\) | −13.2203 | −1.02609 | ||||||||
\(167\) | −10.0101 | −0.774604 | −0.387302 | − | 0.921953i | \(-0.626593\pi\) | ||||
−0.387302 | + | 0.921953i | \(0.626593\pi\) | |||||||
\(168\) | 7.26444 | 0.560464 | ||||||||
\(169\) | −12.9389 | −0.995303 | ||||||||
\(170\) | −3.01083 | −0.230920 | ||||||||
\(171\) | 16.7500 | 1.28091 | ||||||||
\(172\) | −1.89591 | −0.144562 | ||||||||
\(173\) | 6.49479 | 0.493789 | 0.246895 | − | 0.969042i | \(-0.420590\pi\) | ||||
0.246895 | + | 0.969042i | \(0.420590\pi\) | |||||||
\(174\) | 23.7590 | 1.80116 | ||||||||
\(175\) | 13.2825 | 1.00406 | ||||||||
\(176\) | 6.47128 | 0.487791 | ||||||||
\(177\) | 9.63789 | 0.724428 | ||||||||
\(178\) | 5.90688 | 0.442740 | ||||||||
\(179\) | −3.91627 | −0.292716 | −0.146358 | − | 0.989232i | \(-0.546755\pi\) | ||||
−0.146358 | + | 0.989232i | \(0.546755\pi\) | |||||||
\(180\) | 2.15727 | 0.160794 | ||||||||
\(181\) | −19.7376 | −1.46708 | −0.733542 | − | 0.679644i | \(-0.762134\pi\) | ||||
−0.733542 | + | 0.679644i | \(0.762134\pi\) | |||||||
\(182\) | −0.726941 | −0.0538845 | ||||||||
\(183\) | −24.0245 | −1.77594 | ||||||||
\(184\) | −7.44793 | −0.549069 | ||||||||
\(185\) | 7.41017 | 0.544806 | ||||||||
\(186\) | −3.45710 | −0.253487 | ||||||||
\(187\) | −27.9756 | −2.04578 | ||||||||
\(188\) | 2.21454 | 0.161512 | ||||||||
\(189\) | 0.708200 | 0.0515140 | ||||||||
\(190\) | 3.76618 | 0.273227 | ||||||||
\(191\) | −6.28499 | −0.454766 | −0.227383 | − | 0.973805i | \(-0.573017\pi\) | ||||
−0.227383 | + | 0.973805i | \(0.573017\pi\) | |||||||
\(192\) | −2.46931 | −0.178207 | ||||||||
\(193\) | 4.98373 | 0.358737 | 0.179369 | − | 0.983782i | \(-0.442595\pi\) | ||||
0.179369 | + | 0.983782i | \(0.442595\pi\) | |||||||
\(194\) | 4.65460 | 0.334181 | ||||||||
\(195\) | −0.424956 | −0.0304317 | ||||||||
\(196\) | 1.65472 | 0.118194 | ||||||||
\(197\) | −8.89301 | −0.633601 | −0.316800 | − | 0.948492i | \(-0.602609\pi\) | ||||
−0.316800 | + | 0.948492i | \(0.602609\pi\) | |||||||
\(198\) | 20.0447 | 1.42452 | ||||||||
\(199\) | −5.48201 | −0.388609 | −0.194305 | − | 0.980941i | \(-0.562245\pi\) | ||||
−0.194305 | + | 0.980941i | \(0.562245\pi\) | |||||||
\(200\) | −4.51494 | −0.319255 | ||||||||
\(201\) | 19.3753 | 1.36663 | ||||||||
\(202\) | −13.8748 | −0.976230 | ||||||||
\(203\) | 28.3060 | 1.98669 | ||||||||
\(204\) | 10.6749 | 0.747396 | ||||||||
\(205\) | −0.433015 | −0.0302431 | ||||||||
\(206\) | −3.48612 | −0.242890 | ||||||||
\(207\) | −23.0699 | −1.60347 | ||||||||
\(208\) | 0.247100 | 0.0171333 | ||||||||
\(209\) | 34.9941 | 2.42060 | ||||||||
\(210\) | 5.05939 | 0.349131 | ||||||||
\(211\) | −23.9300 | −1.64741 | −0.823705 | − | 0.567018i | \(-0.808097\pi\) | ||||
−0.823705 | + | 0.567018i | \(0.808097\pi\) | |||||||
\(212\) | −5.99737 | −0.411901 | ||||||||
\(213\) | 20.0750 | 1.37552 | ||||||||
\(214\) | −10.7045 | −0.731742 | ||||||||
\(215\) | −1.32042 | −0.0900521 | ||||||||
\(216\) | −0.240730 | −0.0163796 | ||||||||
\(217\) | −4.11872 | −0.279597 | ||||||||
\(218\) | 17.3569 | 1.17556 | ||||||||
\(219\) | −23.6106 | −1.59546 | ||||||||
\(220\) | 4.50698 | 0.303861 | ||||||||
\(221\) | −1.06823 | −0.0718566 | ||||||||
\(222\) | −26.2729 | −1.76332 | ||||||||
\(223\) | −18.6303 | −1.24758 | −0.623789 | − | 0.781593i | \(-0.714407\pi\) | ||||
−0.623789 | + | 0.781593i | \(0.714407\pi\) | |||||||
\(224\) | −2.94189 | −0.196563 | ||||||||
\(225\) | −13.9850 | −0.932333 | ||||||||
\(226\) | 12.1686 | 0.809445 | ||||||||
\(227\) | −11.4522 | −0.760108 | −0.380054 | − | 0.924964i | \(-0.624095\pi\) | ||||
−0.380054 | + | 0.924964i | \(0.624095\pi\) | |||||||
\(228\) | −13.3531 | −0.884328 | ||||||||
\(229\) | 8.16991 | 0.539883 | 0.269942 | − | 0.962877i | \(-0.412996\pi\) | ||||
0.269942 | + | 0.962877i | \(0.412996\pi\) | |||||||
\(230\) | −5.18718 | −0.342033 | ||||||||
\(231\) | 47.0102 | 3.09304 | ||||||||
\(232\) | −9.62171 | −0.631696 | ||||||||
\(233\) | −29.0524 | −1.90328 | −0.951642 | − | 0.307209i | \(-0.900605\pi\) | ||||
−0.951642 | + | 0.307209i | \(0.900605\pi\) | |||||||
\(234\) | 0.765390 | 0.0500351 | ||||||||
\(235\) | 1.54234 | 0.100611 | ||||||||
\(236\) | −3.90307 | −0.254068 | ||||||||
\(237\) | −33.7303 | −2.19102 | ||||||||
\(238\) | 12.7179 | 0.824381 | ||||||||
\(239\) | 6.29282 | 0.407049 | 0.203524 | − | 0.979070i | \(-0.434760\pi\) | ||||
0.203524 | + | 0.979070i | \(0.434760\pi\) | |||||||
\(240\) | −1.71977 | −0.111011 | ||||||||
\(241\) | 1.21320 | 0.0781493 | 0.0390746 | − | 0.999236i | \(-0.487559\pi\) | ||||
0.0390746 | + | 0.999236i | \(0.487559\pi\) | |||||||
\(242\) | 30.8774 | 1.98488 | ||||||||
\(243\) | 22.2003 | 1.42415 | ||||||||
\(244\) | 9.72924 | 0.622851 | ||||||||
\(245\) | 1.15245 | 0.0736271 | ||||||||
\(246\) | 1.53526 | 0.0978847 | ||||||||
\(247\) | 1.33622 | 0.0850217 | ||||||||
\(248\) | 1.40003 | 0.0889017 | ||||||||
\(249\) | 32.6450 | 2.06879 | ||||||||
\(250\) | −6.62677 | −0.419114 | ||||||||
\(251\) | −30.7423 | −1.94044 | −0.970218 | − | 0.242234i | \(-0.922120\pi\) | ||||
−0.970218 | + | 0.242234i | \(0.922120\pi\) | |||||||
\(252\) | −9.11247 | −0.574032 | ||||||||
\(253\) | −48.1976 | −3.03016 | ||||||||
\(254\) | 2.44248 | 0.153255 | ||||||||
\(255\) | 7.43466 | 0.465577 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.7955 | −1.42194 | −0.710971 | − | 0.703222i | \(-0.751744\pi\) | ||||
−0.710971 | + | 0.703222i | \(0.751744\pi\) | |||||||
\(258\) | 4.68158 | 0.291463 | ||||||||
\(259\) | −31.3010 | −1.94495 | ||||||||
\(260\) | 0.172095 | 0.0106729 | ||||||||
\(261\) | −29.8031 | −1.84477 | ||||||||
\(262\) | −12.9309 | −0.798875 | ||||||||
\(263\) | −18.6455 | −1.14973 | −0.574867 | − | 0.818247i | \(-0.694946\pi\) | ||||
−0.574867 | + | 0.818247i | \(0.694946\pi\) | |||||||
\(264\) | −15.9796 | −0.983475 | ||||||||
\(265\) | −4.17692 | −0.256586 | ||||||||
\(266\) | −15.9086 | −0.975419 | ||||||||
\(267\) | −14.5859 | −0.892644 | ||||||||
\(268\) | −7.84645 | −0.479298 | ||||||||
\(269\) | −6.31721 | −0.385167 | −0.192584 | − | 0.981281i | \(-0.561687\pi\) | ||||
−0.192584 | + | 0.981281i | \(0.561687\pi\) | |||||||
\(270\) | −0.167658 | −0.0102034 | ||||||||
\(271\) | −21.6233 | −1.31352 | −0.656759 | − | 0.754100i | \(-0.728073\pi\) | ||||
−0.656759 | + | 0.754100i | \(0.728073\pi\) | |||||||
\(272\) | −4.32305 | −0.262123 | ||||||||
\(273\) | 1.79504 | 0.108641 | ||||||||
\(274\) | −13.9638 | −0.843587 | ||||||||
\(275\) | −29.2175 | −1.76188 | ||||||||
\(276\) | 18.3913 | 1.10702 | ||||||||
\(277\) | −18.4094 | −1.10611 | −0.553057 | − | 0.833144i | \(-0.686539\pi\) | ||||
−0.553057 | + | 0.833144i | \(0.686539\pi\) | |||||||
\(278\) | −11.7947 | −0.707400 | ||||||||
\(279\) | 4.33656 | 0.259623 | ||||||||
\(280\) | −2.04891 | −0.122446 | ||||||||
\(281\) | −16.6219 | −0.991577 | −0.495788 | − | 0.868443i | \(-0.665121\pi\) | ||||
−0.495788 | + | 0.868443i | \(0.665121\pi\) | |||||||
\(282\) | −5.46839 | −0.325638 | ||||||||
\(283\) | 3.84401 | 0.228503 | 0.114251 | − | 0.993452i | \(-0.463553\pi\) | ||||
0.114251 | + | 0.993452i | \(0.463553\pi\) | |||||||
\(284\) | −8.12981 | −0.482415 | ||||||||
\(285\) | −9.29987 | −0.550876 | ||||||||
\(286\) | 1.59905 | 0.0945540 | ||||||||
\(287\) | 1.82908 | 0.107967 | ||||||||
\(288\) | 3.09749 | 0.182521 | ||||||||
\(289\) | 1.68875 | 0.0993380 | ||||||||
\(290\) | −6.70113 | −0.393504 | ||||||||
\(291\) | −11.4937 | −0.673770 | ||||||||
\(292\) | 9.56163 | 0.559552 | ||||||||
\(293\) | 31.2539 | 1.82587 | 0.912936 | − | 0.408103i | \(-0.133809\pi\) | ||||
0.912936 | + | 0.408103i | \(0.133809\pi\) | |||||||
\(294\) | −4.08602 | −0.238301 | ||||||||
\(295\) | −2.71833 | −0.158267 | ||||||||
\(296\) | 10.6398 | 0.618424 | ||||||||
\(297\) | −1.55783 | −0.0903943 | ||||||||
\(298\) | 15.3095 | 0.886856 | ||||||||
\(299\) | −1.84038 | −0.106432 | ||||||||
\(300\) | 11.1488 | 0.643676 | ||||||||
\(301\) | 5.57755 | 0.321485 | ||||||||
\(302\) | 19.2314 | 1.10664 | ||||||||
\(303\) | 34.2613 | 1.96826 | ||||||||
\(304\) | 5.40761 | 0.310148 | ||||||||
\(305\) | 6.77602 | 0.387994 | ||||||||
\(306\) | −13.3906 | −0.765489 | ||||||||
\(307\) | 7.83720 | 0.447293 | 0.223646 | − | 0.974670i | \(-0.428204\pi\) | ||||
0.223646 | + | 0.974670i | \(0.428204\pi\) | |||||||
\(308\) | −19.0378 | −1.08478 | ||||||||
\(309\) | 8.60832 | 0.489710 | ||||||||
\(310\) | 0.975061 | 0.0553798 | ||||||||
\(311\) | −29.8325 | −1.69165 | −0.845824 | − | 0.533462i | \(-0.820891\pi\) | ||||
−0.845824 | + | 0.533462i | \(0.820891\pi\) | |||||||
\(312\) | −0.610166 | −0.0345439 | ||||||||
\(313\) | 16.7816 | 0.948551 | 0.474276 | − | 0.880376i | \(-0.342710\pi\) | ||||
0.474276 | + | 0.880376i | \(0.342710\pi\) | |||||||
\(314\) | −4.25207 | −0.239958 | ||||||||
\(315\) | −6.34647 | −0.357583 | ||||||||
\(316\) | 13.6598 | 0.768424 | ||||||||
\(317\) | −10.5987 | −0.595284 | −0.297642 | − | 0.954678i | \(-0.596200\pi\) | ||||
−0.297642 | + | 0.954678i | \(0.596200\pi\) | |||||||
\(318\) | 14.8094 | 0.830467 | ||||||||
\(319\) | −62.2647 | −3.48616 | ||||||||
\(320\) | 0.696459 | 0.0389333 | ||||||||
\(321\) | 26.4326 | 1.47532 | ||||||||
\(322\) | 21.9110 | 1.22105 | ||||||||
\(323\) | −23.3774 | −1.30075 | ||||||||
\(324\) | −8.69803 | −0.483224 | ||||||||
\(325\) | −1.11564 | −0.0618847 | ||||||||
\(326\) | 20.9568 | 1.16069 | ||||||||
\(327\) | −42.8596 | −2.37014 | ||||||||
\(328\) | −0.621738 | −0.0343297 | ||||||||
\(329\) | −6.51494 | −0.359180 | ||||||||
\(330\) | −11.1291 | −0.612638 | ||||||||
\(331\) | 35.8218 | 1.96894 | 0.984472 | − | 0.175541i | \(-0.0561676\pi\) | ||||
0.984472 | + | 0.175541i | \(0.0561676\pi\) | |||||||
\(332\) | −13.2203 | −0.725559 | ||||||||
\(333\) | 32.9566 | 1.80601 | ||||||||
\(334\) | −10.0101 | −0.547728 | ||||||||
\(335\) | −5.46473 | −0.298570 | ||||||||
\(336\) | 7.26444 | 0.396308 | ||||||||
\(337\) | 5.65042 | 0.307798 | 0.153899 | − | 0.988087i | \(-0.450817\pi\) | ||||
0.153899 | + | 0.988087i | \(0.450817\pi\) | |||||||
\(338\) | −12.9389 | −0.703786 | ||||||||
\(339\) | −30.0481 | −1.63199 | ||||||||
\(340\) | −3.01083 | −0.163285 | ||||||||
\(341\) | 9.05996 | 0.490624 | ||||||||
\(342\) | 16.7500 | 0.905737 | ||||||||
\(343\) | 15.7252 | 0.849082 | ||||||||
\(344\) | −1.89591 | −0.102221 | ||||||||
\(345\) | 12.8088 | 0.689600 | ||||||||
\(346\) | 6.49479 | 0.349162 | ||||||||
\(347\) | −6.06311 | −0.325485 | −0.162742 | − | 0.986669i | \(-0.552034\pi\) | ||||
−0.162742 | + | 0.986669i | \(0.552034\pi\) | |||||||
\(348\) | 23.7590 | 1.27361 | ||||||||
\(349\) | 11.9537 | 0.639864 | 0.319932 | − | 0.947440i | \(-0.396340\pi\) | ||||
0.319932 | + | 0.947440i | \(0.396340\pi\) | |||||||
\(350\) | 13.2825 | 0.709978 | ||||||||
\(351\) | −0.0594843 | −0.00317504 | ||||||||
\(352\) | 6.47128 | 0.344920 | ||||||||
\(353\) | −26.7512 | −1.42382 | −0.711911 | − | 0.702270i | \(-0.752170\pi\) | ||||
−0.711911 | + | 0.702270i | \(0.752170\pi\) | |||||||
\(354\) | 9.63789 | 0.512248 | ||||||||
\(355\) | −5.66208 | −0.300512 | ||||||||
\(356\) | 5.90688 | 0.313064 | ||||||||
\(357\) | −31.4045 | −1.66210 | ||||||||
\(358\) | −3.91627 | −0.206981 | ||||||||
\(359\) | 3.02557 | 0.159683 | 0.0798417 | − | 0.996808i | \(-0.474559\pi\) | ||||
0.0798417 | + | 0.996808i | \(0.474559\pi\) | |||||||
\(360\) | 2.15727 | 0.113698 | ||||||||
\(361\) | 10.2423 | 0.539066 | ||||||||
\(362\) | −19.7376 | −1.03738 | ||||||||
\(363\) | −76.2459 | −4.00187 | ||||||||
\(364\) | −0.726941 | −0.0381021 | ||||||||
\(365\) | 6.65929 | 0.348563 | ||||||||
\(366\) | −24.0245 | −1.25578 | ||||||||
\(367\) | −19.2019 | −1.00233 | −0.501165 | − | 0.865351i | \(-0.667095\pi\) | ||||
−0.501165 | + | 0.865351i | \(0.667095\pi\) | |||||||
\(368\) | −7.44793 | −0.388250 | ||||||||
\(369\) | −1.92582 | −0.100254 | ||||||||
\(370\) | 7.41017 | 0.385236 | ||||||||
\(371\) | 17.6436 | 0.916010 | ||||||||
\(372\) | −3.45710 | −0.179242 | ||||||||
\(373\) | −9.96496 | −0.515966 | −0.257983 | − | 0.966149i | \(-0.583058\pi\) | ||||
−0.257983 | + | 0.966149i | \(0.583058\pi\) | |||||||
\(374\) | −27.9756 | −1.44659 | ||||||||
\(375\) | 16.3635 | 0.845010 | ||||||||
\(376\) | 2.21454 | 0.114206 | ||||||||
\(377\) | −2.37752 | −0.122449 | ||||||||
\(378\) | 0.708200 | 0.0364259 | ||||||||
\(379\) | −1.37433 | −0.0705944 | −0.0352972 | − | 0.999377i | \(-0.511238\pi\) | ||||
−0.0352972 | + | 0.999377i | \(0.511238\pi\) | |||||||
\(380\) | 3.76618 | 0.193201 | ||||||||
\(381\) | −6.03124 | −0.308990 | ||||||||
\(382\) | −6.28499 | −0.321568 | ||||||||
\(383\) | 2.50631 | 0.128066 | 0.0640331 | − | 0.997948i | \(-0.479604\pi\) | ||||
0.0640331 | + | 0.997948i | \(0.479604\pi\) | |||||||
\(384\) | −2.46931 | −0.126011 | ||||||||
\(385\) | −13.2590 | −0.675744 | ||||||||
\(386\) | 4.98373 | 0.253665 | ||||||||
\(387\) | −5.87255 | −0.298519 | ||||||||
\(388\) | 4.65460 | 0.236302 | ||||||||
\(389\) | −1.84245 | −0.0934159 | −0.0467080 | − | 0.998909i | \(-0.514873\pi\) | ||||
−0.0467080 | + | 0.998909i | \(0.514873\pi\) | |||||||
\(390\) | −0.424956 | −0.0215185 | ||||||||
\(391\) | 32.1978 | 1.62831 | ||||||||
\(392\) | 1.65472 | 0.0835761 | ||||||||
\(393\) | 31.9305 | 1.61068 | ||||||||
\(394\) | −8.89301 | −0.448023 | ||||||||
\(395\) | 9.51350 | 0.478676 | ||||||||
\(396\) | 20.0447 | 1.00728 | ||||||||
\(397\) | −10.8483 | −0.544463 | −0.272231 | − | 0.962232i | \(-0.587762\pi\) | ||||
−0.272231 | + | 0.962232i | \(0.587762\pi\) | |||||||
\(398\) | −5.48201 | −0.274788 | ||||||||
\(399\) | 39.2833 | 1.96662 | ||||||||
\(400\) | −4.51494 | −0.225747 | ||||||||
\(401\) | 26.6113 | 1.32890 | 0.664451 | − | 0.747331i | \(-0.268665\pi\) | ||||
0.664451 | + | 0.747331i | \(0.268665\pi\) | |||||||
\(402\) | 19.3753 | 0.966353 | ||||||||
\(403\) | 0.345947 | 0.0172328 | ||||||||
\(404\) | −13.8748 | −0.690299 | ||||||||
\(405\) | −6.05782 | −0.301016 | ||||||||
\(406\) | 28.3060 | 1.40480 | ||||||||
\(407\) | 68.8529 | 3.41291 | ||||||||
\(408\) | 10.6749 | 0.528488 | ||||||||
\(409\) | 26.8595 | 1.32811 | 0.664057 | − | 0.747682i | \(-0.268833\pi\) | ||||
0.664057 | + | 0.747682i | \(0.268833\pi\) | |||||||
\(410\) | −0.433015 | −0.0213851 | ||||||||
\(411\) | 34.4810 | 1.70082 | ||||||||
\(412\) | −3.48612 | −0.171749 | ||||||||
\(413\) | 11.4824 | 0.565013 | ||||||||
\(414\) | −23.0699 | −1.13382 | ||||||||
\(415\) | −9.20741 | −0.451974 | ||||||||
\(416\) | 0.247100 | 0.0121151 | ||||||||
\(417\) | 29.1248 | 1.42625 | ||||||||
\(418\) | 34.9941 | 1.71162 | ||||||||
\(419\) | −13.3434 | −0.651866 | −0.325933 | − | 0.945393i | \(-0.605678\pi\) | ||||
−0.325933 | + | 0.945393i | \(0.605678\pi\) | |||||||
\(420\) | 5.05939 | 0.246873 | ||||||||
\(421\) | −8.43153 | −0.410928 | −0.205464 | − | 0.978665i | \(-0.565870\pi\) | ||||
−0.205464 | + | 0.978665i | \(0.565870\pi\) | |||||||
\(422\) | −23.9300 | −1.16490 | ||||||||
\(423\) | 6.85951 | 0.333521 | ||||||||
\(424\) | −5.99737 | −0.291258 | ||||||||
\(425\) | 19.5183 | 0.946778 | ||||||||
\(426\) | 20.0750 | 0.972637 | ||||||||
\(427\) | −28.6224 | −1.38513 | ||||||||
\(428\) | −10.7045 | −0.517419 | ||||||||
\(429\) | −3.94856 | −0.190638 | ||||||||
\(430\) | −1.32042 | −0.0636764 | ||||||||
\(431\) | −0.278983 | −0.0134381 | −0.00671907 | − | 0.999977i | \(-0.502139\pi\) | ||||
−0.00671907 | + | 0.999977i | \(0.502139\pi\) | |||||||
\(432\) | −0.240730 | −0.0115821 | ||||||||
\(433\) | −0.219535 | −0.0105502 | −0.00527509 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527509 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(434\) | −4.11872 | −0.197705 | ||||||||
\(435\) | 16.5472 | 0.793375 | ||||||||
\(436\) | 17.3569 | 0.831247 | ||||||||
\(437\) | −40.2755 | −1.92664 | ||||||||
\(438\) | −23.6106 | −1.12816 | ||||||||
\(439\) | −22.7700 | −1.08675 | −0.543377 | − | 0.839489i | \(-0.682854\pi\) | ||||
−0.543377 | + | 0.839489i | \(0.682854\pi\) | |||||||
\(440\) | 4.50698 | 0.214862 | ||||||||
\(441\) | 5.12548 | 0.244071 | ||||||||
\(442\) | −1.06823 | −0.0508103 | ||||||||
\(443\) | 16.1828 | 0.768866 | 0.384433 | − | 0.923153i | \(-0.374397\pi\) | ||||
0.384433 | + | 0.923153i | \(0.374397\pi\) | |||||||
\(444\) | −26.2729 | −1.24686 | ||||||||
\(445\) | 4.11390 | 0.195018 | ||||||||
\(446\) | −18.6303 | −0.882171 | ||||||||
\(447\) | −37.8039 | −1.78806 | ||||||||
\(448\) | −2.94189 | −0.138991 | ||||||||
\(449\) | 30.1522 | 1.42297 | 0.711486 | − | 0.702700i | \(-0.248022\pi\) | ||||
0.711486 | + | 0.702700i | \(0.248022\pi\) | |||||||
\(450\) | −13.9850 | −0.659259 | ||||||||
\(451\) | −4.02344 | −0.189456 | ||||||||
\(452\) | 12.1686 | 0.572364 | ||||||||
\(453\) | −47.4882 | −2.23119 | ||||||||
\(454\) | −11.4522 | −0.537478 | ||||||||
\(455\) | −0.506285 | −0.0237350 | ||||||||
\(456\) | −13.3531 | −0.625315 | ||||||||
\(457\) | 12.3632 | 0.578324 | 0.289162 | − | 0.957280i | \(-0.406623\pi\) | ||||
0.289162 | + | 0.957280i | \(0.406623\pi\) | |||||||
\(458\) | 8.16991 | 0.381755 | ||||||||
\(459\) | 1.04069 | 0.0485750 | ||||||||
\(460\) | −5.18718 | −0.241854 | ||||||||
\(461\) | −28.6537 | −1.33453 | −0.667267 | − | 0.744819i | \(-0.732536\pi\) | ||||
−0.667267 | + | 0.744819i | \(0.732536\pi\) | |||||||
\(462\) | 47.0102 | 2.18711 | ||||||||
\(463\) | 12.4083 | 0.576664 | 0.288332 | − | 0.957531i | \(-0.406899\pi\) | ||||
0.288332 | + | 0.957531i | \(0.406899\pi\) | |||||||
\(464\) | −9.62171 | −0.446677 | ||||||||
\(465\) | −2.40773 | −0.111656 | ||||||||
\(466\) | −29.0524 | −1.34583 | ||||||||
\(467\) | 0.477760 | 0.0221081 | 0.0110541 | − | 0.999939i | \(-0.496481\pi\) | ||||
0.0110541 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(468\) | 0.765390 | 0.0353801 | ||||||||
\(469\) | 23.0834 | 1.06589 | ||||||||
\(470\) | 1.54234 | 0.0711427 | ||||||||
\(471\) | 10.4997 | 0.483799 | ||||||||
\(472\) | −3.90307 | −0.179653 | ||||||||
\(473\) | −12.2689 | −0.564127 | ||||||||
\(474\) | −33.7303 | −1.54928 | ||||||||
\(475\) | −24.4151 | −1.12024 | ||||||||
\(476\) | 12.7179 | 0.582926 | ||||||||
\(477\) | −18.5768 | −0.850572 | ||||||||
\(478\) | 6.29282 | 0.287827 | ||||||||
\(479\) | 32.8108 | 1.49916 | 0.749581 | − | 0.661913i | \(-0.230255\pi\) | ||||
0.749581 | + | 0.661913i | \(0.230255\pi\) | |||||||
\(480\) | −1.71977 | −0.0784966 | ||||||||
\(481\) | 2.62909 | 0.119876 | ||||||||
\(482\) | 1.21320 | 0.0552599 | ||||||||
\(483\) | −54.1050 | −2.46186 | ||||||||
\(484\) | 30.8774 | 1.40352 | ||||||||
\(485\) | 3.24174 | 0.147200 | ||||||||
\(486\) | 22.2003 | 1.00703 | ||||||||
\(487\) | −37.9687 | −1.72053 | −0.860264 | − | 0.509849i | \(-0.829701\pi\) | ||||
−0.860264 | + | 0.509849i | \(0.829701\pi\) | |||||||
\(488\) | 9.72924 | 0.440422 | ||||||||
\(489\) | −51.7488 | −2.34016 | ||||||||
\(490\) | 1.15245 | 0.0520622 | ||||||||
\(491\) | 17.0848 | 0.771026 | 0.385513 | − | 0.922702i | \(-0.374024\pi\) | ||||
0.385513 | + | 0.922702i | \(0.374024\pi\) | |||||||
\(492\) | 1.53526 | 0.0692150 | ||||||||
\(493\) | 41.5951 | 1.87335 | ||||||||
\(494\) | 1.33622 | 0.0601194 | ||||||||
\(495\) | 13.9603 | 0.627470 | ||||||||
\(496\) | 1.40003 | 0.0628630 | ||||||||
\(497\) | 23.9170 | 1.07282 | ||||||||
\(498\) | 32.6450 | 1.46286 | ||||||||
\(499\) | −7.42496 | −0.332387 | −0.166193 | − | 0.986093i | \(-0.553148\pi\) | ||||
−0.166193 | + | 0.986093i | \(0.553148\pi\) | |||||||
\(500\) | −6.62677 | −0.296358 | ||||||||
\(501\) | 24.7180 | 1.10432 | ||||||||
\(502\) | −30.7423 | −1.37210 | ||||||||
\(503\) | −4.26539 | −0.190184 | −0.0950922 | − | 0.995468i | \(-0.530315\pi\) | ||||
−0.0950922 | + | 0.995468i | \(0.530315\pi\) | |||||||
\(504\) | −9.11247 | −0.405902 | ||||||||
\(505\) | −9.66326 | −0.430009 | ||||||||
\(506\) | −48.1976 | −2.14265 | ||||||||
\(507\) | 31.9502 | 1.41896 | ||||||||
\(508\) | 2.44248 | 0.108368 | ||||||||
\(509\) | 24.5941 | 1.09012 | 0.545058 | − | 0.838398i | \(-0.316508\pi\) | ||||
0.545058 | + | 0.838398i | \(0.316508\pi\) | |||||||
\(510\) | 7.43466 | 0.329212 | ||||||||
\(511\) | −28.1293 | −1.24437 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.30177 | −0.0574746 | ||||||||
\(514\) | −22.7955 | −1.00546 | ||||||||
\(515\) | −2.42794 | −0.106988 | ||||||||
\(516\) | 4.68158 | 0.206095 | ||||||||
\(517\) | 14.3309 | 0.630273 | ||||||||
\(518\) | −31.3010 | −1.37529 | ||||||||
\(519\) | −16.0376 | −0.703974 | ||||||||
\(520\) | 0.172095 | 0.00754687 | ||||||||
\(521\) | −27.1394 | −1.18900 | −0.594498 | − | 0.804097i | \(-0.702649\pi\) | ||||
−0.594498 | + | 0.804097i | \(0.702649\pi\) | |||||||
\(522\) | −29.8031 | −1.30445 | ||||||||
\(523\) | −40.6113 | −1.77581 | −0.887903 | − | 0.460030i | \(-0.847839\pi\) | ||||
−0.887903 | + | 0.460030i | \(0.847839\pi\) | |||||||
\(524\) | −12.9309 | −0.564890 | ||||||||
\(525\) | −32.7985 | −1.43145 | ||||||||
\(526\) | −18.6455 | −0.812984 | ||||||||
\(527\) | −6.05238 | −0.263646 | ||||||||
\(528\) | −15.9796 | −0.695422 | ||||||||
\(529\) | 32.4717 | 1.41181 | ||||||||
\(530\) | −4.17692 | −0.181434 | ||||||||
\(531\) | −12.0897 | −0.524649 | ||||||||
\(532\) | −15.9086 | −0.689725 | ||||||||
\(533\) | −0.153631 | −0.00665451 | ||||||||
\(534\) | −14.5859 | −0.631195 | ||||||||
\(535\) | −7.45522 | −0.322317 | ||||||||
\(536\) | −7.84645 | −0.338915 | ||||||||
\(537\) | 9.67049 | 0.417312 | ||||||||
\(538\) | −6.31721 | −0.272354 | ||||||||
\(539\) | 10.7082 | 0.461233 | ||||||||
\(540\) | −0.167658 | −0.00721487 | ||||||||
\(541\) | 12.2652 | 0.527324 | 0.263662 | − | 0.964615i | \(-0.415070\pi\) | ||||
0.263662 | + | 0.964615i | \(0.415070\pi\) | |||||||
\(542\) | −21.6233 | −0.928798 | ||||||||
\(543\) | 48.7382 | 2.09156 | ||||||||
\(544\) | −4.32305 | −0.185349 | ||||||||
\(545\) | 12.0884 | 0.517810 | ||||||||
\(546\) | 1.79504 | 0.0768208 | ||||||||
\(547\) | −40.8139 | −1.74508 | −0.872538 | − | 0.488546i | \(-0.837528\pi\) | ||||
−0.872538 | + | 0.488546i | \(0.837528\pi\) | |||||||
\(548\) | −13.9638 | −0.596506 | ||||||||
\(549\) | 30.1362 | 1.28618 | ||||||||
\(550\) | −29.2175 | −1.24584 | ||||||||
\(551\) | −52.0305 | −2.21657 | ||||||||
\(552\) | 18.3913 | 0.782784 | ||||||||
\(553\) | −40.1857 | −1.70887 | ||||||||
\(554\) | −18.4094 | −0.782140 | ||||||||
\(555\) | −18.2980 | −0.776707 | ||||||||
\(556\) | −11.7947 | −0.500207 | ||||||||
\(557\) | −29.3130 | −1.24203 | −0.621017 | − | 0.783797i | \(-0.713280\pi\) | ||||
−0.621017 | + | 0.783797i | \(0.713280\pi\) | |||||||
\(558\) | 4.33656 | 0.183581 | ||||||||
\(559\) | −0.468479 | −0.0198146 | ||||||||
\(560\) | −2.04891 | −0.0865821 | ||||||||
\(561\) | 69.0805 | 2.91658 | ||||||||
\(562\) | −16.6219 | −0.701151 | ||||||||
\(563\) | −19.5949 | −0.825828 | −0.412914 | − | 0.910770i | \(-0.635489\pi\) | ||||
−0.412914 | + | 0.910770i | \(0.635489\pi\) | |||||||
\(564\) | −5.46839 | −0.230261 | ||||||||
\(565\) | 8.47496 | 0.356544 | ||||||||
\(566\) | 3.84401 | 0.161576 | ||||||||
\(567\) | 25.5887 | 1.07462 | ||||||||
\(568\) | −8.12981 | −0.341119 | ||||||||
\(569\) | 2.12297 | 0.0889996 | 0.0444998 | − | 0.999009i | \(-0.485831\pi\) | ||||
0.0444998 | + | 0.999009i | \(0.485831\pi\) | |||||||
\(570\) | −9.29987 | −0.389528 | ||||||||
\(571\) | −34.2072 | −1.43153 | −0.715763 | − | 0.698343i | \(-0.753921\pi\) | ||||
−0.715763 | + | 0.698343i | \(0.753921\pi\) | |||||||
\(572\) | 1.59905 | 0.0668598 | ||||||||
\(573\) | 15.5196 | 0.648339 | ||||||||
\(574\) | 1.82908 | 0.0763445 | ||||||||
\(575\) | 33.6270 | 1.40234 | ||||||||
\(576\) | 3.09749 | 0.129062 | ||||||||
\(577\) | −27.7876 | −1.15681 | −0.578406 | − | 0.815749i | \(-0.696325\pi\) | ||||
−0.578406 | + | 0.815749i | \(0.696325\pi\) | |||||||
\(578\) | 1.68875 | 0.0702426 | ||||||||
\(579\) | −12.3064 | −0.511436 | ||||||||
\(580\) | −6.70113 | −0.278249 | ||||||||
\(581\) | 38.8927 | 1.61354 | ||||||||
\(582\) | −11.4937 | −0.476427 | ||||||||
\(583\) | −38.8106 | −1.60737 | ||||||||
\(584\) | 9.56163 | 0.395663 | ||||||||
\(585\) | 0.533063 | 0.0220394 | ||||||||
\(586\) | 31.2539 | 1.29109 | ||||||||
\(587\) | 32.8144 | 1.35440 | 0.677199 | − | 0.735800i | \(-0.263194\pi\) | ||||
0.677199 | + | 0.735800i | \(0.263194\pi\) | |||||||
\(588\) | −4.08602 | −0.168505 | ||||||||
\(589\) | 7.57080 | 0.311949 | ||||||||
\(590\) | −2.71833 | −0.111912 | ||||||||
\(591\) | 21.9596 | 0.903297 | ||||||||
\(592\) | 10.6398 | 0.437292 | ||||||||
\(593\) | −26.4635 | −1.08673 | −0.543364 | − | 0.839497i | \(-0.682850\pi\) | ||||
−0.543364 | + | 0.839497i | \(0.682850\pi\) | |||||||
\(594\) | −1.55783 | −0.0639184 | ||||||||
\(595\) | 8.85752 | 0.363123 | ||||||||
\(596\) | 15.3095 | 0.627102 | ||||||||
\(597\) | 13.5368 | 0.554023 | ||||||||
\(598\) | −1.84038 | −0.0752589 | ||||||||
\(599\) | −16.3840 | −0.669434 | −0.334717 | − | 0.942319i | \(-0.608641\pi\) | ||||
−0.334717 | + | 0.942319i | \(0.608641\pi\) | |||||||
\(600\) | 11.1488 | 0.455148 | ||||||||
\(601\) | 5.75079 | 0.234580 | 0.117290 | − | 0.993098i | \(-0.462579\pi\) | ||||
0.117290 | + | 0.993098i | \(0.462579\pi\) | |||||||
\(602\) | 5.57755 | 0.227324 | ||||||||
\(603\) | −24.3043 | −0.989747 | ||||||||
\(604\) | 19.2314 | 0.782514 | ||||||||
\(605\) | 21.5049 | 0.874297 | ||||||||
\(606\) | 34.2613 | 1.39177 | ||||||||
\(607\) | −6.89203 | −0.279739 | −0.139869 | − | 0.990170i | \(-0.544668\pi\) | ||||
−0.139869 | + | 0.990170i | \(0.544668\pi\) | |||||||
\(608\) | 5.40761 | 0.219308 | ||||||||
\(609\) | −69.8963 | −2.83234 | ||||||||
\(610\) | 6.77602 | 0.274353 | ||||||||
\(611\) | 0.547213 | 0.0221379 | ||||||||
\(612\) | −13.3906 | −0.541283 | ||||||||
\(613\) | −38.3962 | −1.55081 | −0.775405 | − | 0.631465i | \(-0.782454\pi\) | ||||
−0.775405 | + | 0.631465i | \(0.782454\pi\) | |||||||
\(614\) | 7.83720 | 0.316284 | ||||||||
\(615\) | 1.06925 | 0.0431162 | ||||||||
\(616\) | −19.0378 | −0.767054 | ||||||||
\(617\) | 30.5710 | 1.23074 | 0.615372 | − | 0.788237i | \(-0.289006\pi\) | ||||
0.615372 | + | 0.788237i | \(0.289006\pi\) | |||||||
\(618\) | 8.60832 | 0.346277 | ||||||||
\(619\) | −7.12931 | −0.286551 | −0.143276 | − | 0.989683i | \(-0.545764\pi\) | ||||
−0.143276 | + | 0.989683i | \(0.545764\pi\) | |||||||
\(620\) | 0.975061 | 0.0391594 | ||||||||
\(621\) | 1.79294 | 0.0719481 | ||||||||
\(622\) | −29.8325 | −1.19618 | ||||||||
\(623\) | −17.3774 | −0.696211 | ||||||||
\(624\) | −0.610166 | −0.0244262 | ||||||||
\(625\) | 17.9594 | 0.718378 | ||||||||
\(626\) | 16.7816 | 0.670727 | ||||||||
\(627\) | −86.4114 | −3.45094 | ||||||||
\(628\) | −4.25207 | −0.169676 | ||||||||
\(629\) | −45.9962 | −1.83399 | ||||||||
\(630\) | −6.34647 | −0.252849 | ||||||||
\(631\) | 5.51858 | 0.219691 | 0.109846 | − | 0.993949i | \(-0.464964\pi\) | ||||
0.109846 | + | 0.993949i | \(0.464964\pi\) | |||||||
\(632\) | 13.6598 | 0.543358 | ||||||||
\(633\) | 59.0906 | 2.34864 | ||||||||
\(634\) | −10.5987 | −0.420929 | ||||||||
\(635\) | 1.70109 | 0.0675057 | ||||||||
\(636\) | 14.8094 | 0.587229 | ||||||||
\(637\) | 0.408882 | 0.0162005 | ||||||||
\(638\) | −62.2647 | −2.46508 | ||||||||
\(639\) | −25.1820 | −0.996184 | ||||||||
\(640\) | 0.696459 | 0.0275300 | ||||||||
\(641\) | 24.0020 | 0.948020 | 0.474010 | − | 0.880519i | \(-0.342806\pi\) | ||||
0.474010 | + | 0.880519i | \(0.342806\pi\) | |||||||
\(642\) | 26.4326 | 1.04321 | ||||||||
\(643\) | −1.14708 | −0.0452363 | −0.0226182 | − | 0.999744i | \(-0.507200\pi\) | ||||
−0.0226182 | + | 0.999744i | \(0.507200\pi\) | |||||||
\(644\) | 21.9110 | 0.863415 | ||||||||
\(645\) | 3.26053 | 0.128383 | ||||||||
\(646\) | −23.3774 | −0.919770 | ||||||||
\(647\) | 17.1933 | 0.675937 | 0.337969 | − | 0.941157i | \(-0.390260\pi\) | ||||
0.337969 | + | 0.941157i | \(0.390260\pi\) | |||||||
\(648\) | −8.69803 | −0.341691 | ||||||||
\(649\) | −25.2579 | −0.991458 | ||||||||
\(650\) | −1.11564 | −0.0437591 | ||||||||
\(651\) | 10.1704 | 0.398610 | ||||||||
\(652\) | 20.9568 | 0.820732 | ||||||||
\(653\) | 29.6101 | 1.15873 | 0.579367 | − | 0.815067i | \(-0.303300\pi\) | ||||
0.579367 | + | 0.815067i | \(0.303300\pi\) | |||||||
\(654\) | −42.8596 | −1.67594 | ||||||||
\(655\) | −9.00586 | −0.351888 | ||||||||
\(656\) | −0.621738 | −0.0242748 | ||||||||
\(657\) | 29.6170 | 1.15547 | ||||||||
\(658\) | −6.51494 | −0.253979 | ||||||||
\(659\) | −25.6107 | −0.997650 | −0.498825 | − | 0.866703i | \(-0.666235\pi\) | ||||
−0.498825 | + | 0.866703i | \(0.666235\pi\) | |||||||
\(660\) | −11.1291 | −0.433201 | ||||||||
\(661\) | 13.1870 | 0.512913 | 0.256457 | − | 0.966556i | \(-0.417445\pi\) | ||||
0.256457 | + | 0.966556i | \(0.417445\pi\) | |||||||
\(662\) | 35.8218 | 1.39225 | ||||||||
\(663\) | 2.63778 | 0.102443 | ||||||||
\(664\) | −13.2203 | −0.513047 | ||||||||
\(665\) | −11.0797 | −0.429652 | ||||||||
\(666\) | 32.9566 | 1.27704 | ||||||||
\(667\) | 71.6618 | 2.77476 | ||||||||
\(668\) | −10.0101 | −0.387302 | ||||||||
\(669\) | 46.0040 | 1.77862 | ||||||||
\(670\) | −5.46473 | −0.211121 | ||||||||
\(671\) | 62.9606 | 2.43057 | ||||||||
\(672\) | 7.26444 | 0.280232 | ||||||||
\(673\) | 40.5333 | 1.56245 | 0.781223 | − | 0.624252i | \(-0.214596\pi\) | ||||
0.781223 | + | 0.624252i | \(0.214596\pi\) | |||||||
\(674\) | 5.65042 | 0.217646 | ||||||||
\(675\) | 1.08688 | 0.0418341 | ||||||||
\(676\) | −12.9389 | −0.497652 | ||||||||
\(677\) | −39.0396 | −1.50041 | −0.750207 | − | 0.661203i | \(-0.770046\pi\) | ||||
−0.750207 | + | 0.661203i | \(0.770046\pi\) | |||||||
\(678\) | −30.0481 | −1.15399 | ||||||||
\(679\) | −13.6933 | −0.525502 | ||||||||
\(680\) | −3.01083 | −0.115460 | ||||||||
\(681\) | 28.2790 | 1.08365 | ||||||||
\(682\) | 9.05996 | 0.346924 | ||||||||
\(683\) | 25.0002 | 0.956605 | 0.478303 | − | 0.878195i | \(-0.341252\pi\) | ||||
0.478303 | + | 0.878195i | \(0.341252\pi\) | |||||||
\(684\) | 16.7500 | 0.640453 | ||||||||
\(685\) | −9.72525 | −0.371583 | ||||||||
\(686\) | 15.7252 | 0.600392 | ||||||||
\(687\) | −20.1740 | −0.769688 | ||||||||
\(688\) | −1.89591 | −0.0722808 | ||||||||
\(689\) | −1.48195 | −0.0564578 | ||||||||
\(690\) | 12.8088 | 0.487621 | ||||||||
\(691\) | −51.0081 | −1.94044 | −0.970219 | − | 0.242230i | \(-0.922121\pi\) | ||||
−0.970219 | + | 0.242230i | \(0.922121\pi\) | |||||||
\(692\) | 6.49479 | 0.246895 | ||||||||
\(693\) | −58.9693 | −2.24006 | ||||||||
\(694\) | −6.06311 | −0.230152 | ||||||||
\(695\) | −8.21454 | −0.311595 | ||||||||
\(696\) | 23.7590 | 0.900582 | ||||||||
\(697\) | 2.68780 | 0.101808 | ||||||||
\(698\) | 11.9537 | 0.452452 | ||||||||
\(699\) | 71.7393 | 2.71343 | ||||||||
\(700\) | 13.2825 | 0.502030 | ||||||||
\(701\) | −37.1792 | −1.40424 | −0.702120 | − | 0.712059i | \(-0.747763\pi\) | ||||
−0.702120 | + | 0.712059i | \(0.747763\pi\) | |||||||
\(702\) | −0.0594843 | −0.00224509 | ||||||||
\(703\) | 57.5357 | 2.17000 | ||||||||
\(704\) | 6.47128 | 0.243895 | ||||||||
\(705\) | −3.80851 | −0.143437 | ||||||||
\(706\) | −26.7512 | −1.00679 | ||||||||
\(707\) | 40.8183 | 1.53513 | ||||||||
\(708\) | 9.63789 | 0.362214 | ||||||||
\(709\) | 41.5877 | 1.56186 | 0.780930 | − | 0.624618i | \(-0.214745\pi\) | ||||
0.780930 | + | 0.624618i | \(0.214745\pi\) | |||||||
\(710\) | −5.66208 | −0.212494 | ||||||||
\(711\) | 42.3111 | 1.58679 | ||||||||
\(712\) | 5.90688 | 0.221370 | ||||||||
\(713\) | −10.4273 | −0.390505 | ||||||||
\(714\) | −31.4045 | −1.17528 | ||||||||
\(715\) | 1.11368 | 0.0416491 | ||||||||
\(716\) | −3.91627 | −0.146358 | ||||||||
\(717\) | −15.5389 | −0.580312 | ||||||||
\(718\) | 3.02557 | 0.112913 | ||||||||
\(719\) | −22.0324 | −0.821670 | −0.410835 | − | 0.911710i | \(-0.634763\pi\) | ||||
−0.410835 | + | 0.911710i | \(0.634763\pi\) | |||||||
\(720\) | 2.15727 | 0.0803969 | ||||||||
\(721\) | 10.2558 | 0.381946 | ||||||||
\(722\) | 10.2423 | 0.381177 | ||||||||
\(723\) | −2.99577 | −0.111414 | ||||||||
\(724\) | −19.7376 | −0.733542 | ||||||||
\(725\) | 43.4415 | 1.61338 | ||||||||
\(726\) | −76.2459 | −2.82975 | ||||||||
\(727\) | −8.48485 | −0.314686 | −0.157343 | − | 0.987544i | \(-0.550293\pi\) | ||||
−0.157343 | + | 0.987544i | \(0.550293\pi\) | |||||||
\(728\) | −0.726941 | −0.0269422 | ||||||||
\(729\) | −28.7254 | −1.06390 | ||||||||
\(730\) | 6.65929 | 0.246471 | ||||||||
\(731\) | 8.19610 | 0.303144 | ||||||||
\(732\) | −24.0245 | −0.887971 | ||||||||
\(733\) | 28.9346 | 1.06872 | 0.534362 | − | 0.845256i | \(-0.320552\pi\) | ||||
0.534362 | + | 0.845256i | \(0.320552\pi\) | |||||||
\(734\) | −19.2019 | −0.708755 | ||||||||
\(735\) | −2.84575 | −0.104967 | ||||||||
\(736\) | −7.44793 | −0.274534 | ||||||||
\(737\) | −50.7766 | −1.87038 | ||||||||
\(738\) | −1.92582 | −0.0708906 | ||||||||
\(739\) | −31.0629 | −1.14267 | −0.571333 | − | 0.820718i | \(-0.693574\pi\) | ||||
−0.571333 | + | 0.820718i | \(0.693574\pi\) | |||||||
\(740\) | 7.41017 | 0.272403 | ||||||||
\(741\) | −3.29954 | −0.121212 | ||||||||
\(742\) | 17.6436 | 0.647717 | ||||||||
\(743\) | 12.7090 | 0.466247 | 0.233124 | − | 0.972447i | \(-0.425105\pi\) | ||||
0.233124 | + | 0.972447i | \(0.425105\pi\) | |||||||
\(744\) | −3.45710 | −0.126743 | ||||||||
\(745\) | 10.6625 | 0.390642 | ||||||||
\(746\) | −9.96496 | −0.364843 | ||||||||
\(747\) | −40.9498 | −1.49827 | ||||||||
\(748\) | −27.9756 | −1.02289 | ||||||||
\(749\) | 31.4913 | 1.15067 | ||||||||
\(750\) | 16.3635 | 0.597512 | ||||||||
\(751\) | 12.9330 | 0.471933 | 0.235967 | − | 0.971761i | \(-0.424174\pi\) | ||||
0.235967 | + | 0.971761i | \(0.424174\pi\) | |||||||
\(752\) | 2.21454 | 0.0807560 | ||||||||
\(753\) | 75.9122 | 2.76639 | ||||||||
\(754\) | −2.37752 | −0.0865843 | ||||||||
\(755\) | 13.3939 | 0.487453 | ||||||||
\(756\) | 0.708200 | 0.0257570 | ||||||||
\(757\) | 12.1514 | 0.441651 | 0.220825 | − | 0.975313i | \(-0.429125\pi\) | ||||
0.220825 | + | 0.975313i | \(0.429125\pi\) | |||||||
\(758\) | −1.37433 | −0.0499177 | ||||||||
\(759\) | 119.015 | 4.31997 | ||||||||
\(760\) | 3.76618 | 0.136614 | ||||||||
\(761\) | 22.4820 | 0.814971 | 0.407486 | − | 0.913212i | \(-0.366406\pi\) | ||||
0.407486 | + | 0.913212i | \(0.366406\pi\) | |||||||
\(762\) | −6.03124 | −0.218489 | ||||||||
\(763\) | −51.0622 | −1.84858 | ||||||||
\(764\) | −6.28499 | −0.227383 | ||||||||
\(765\) | −9.32600 | −0.337182 | ||||||||
\(766\) | 2.50631 | 0.0905565 | ||||||||
\(767\) | −0.964449 | −0.0348243 | ||||||||
\(768\) | −2.46931 | −0.0891035 | ||||||||
\(769\) | −39.1107 | −1.41037 | −0.705183 | − | 0.709025i | \(-0.749135\pi\) | ||||
−0.705183 | + | 0.709025i | \(0.749135\pi\) | |||||||
\(770\) | −13.2590 | −0.477823 | ||||||||
\(771\) | 56.2890 | 2.02720 | ||||||||
\(772\) | 4.98373 | 0.179369 | ||||||||
\(773\) | −37.5363 | −1.35009 | −0.675043 | − | 0.737778i | \(-0.735875\pi\) | ||||
−0.675043 | + | 0.737778i | \(0.735875\pi\) | |||||||
\(774\) | −5.87255 | −0.211085 | ||||||||
\(775\) | −6.32104 | −0.227058 | ||||||||
\(776\) | 4.65460 | 0.167090 | ||||||||
\(777\) | 77.2920 | 2.77283 | ||||||||
\(778\) | −1.84245 | −0.0660550 | ||||||||
\(779\) | −3.36211 | −0.120460 | ||||||||
\(780\) | −0.424956 | −0.0152159 | ||||||||
\(781\) | −52.6102 | −1.88254 | ||||||||
\(782\) | 32.1978 | 1.15139 | ||||||||
\(783\) | 2.31623 | 0.0827753 | ||||||||
\(784\) | 1.65472 | 0.0590972 | ||||||||
\(785\) | −2.96139 | −0.105697 | ||||||||
\(786\) | 31.9305 | 1.13892 | ||||||||
\(787\) | −40.7619 | −1.45300 | −0.726502 | − | 0.687164i | \(-0.758855\pi\) | ||||
−0.726502 | + | 0.687164i | \(0.758855\pi\) | |||||||
\(788\) | −8.89301 | −0.316800 | ||||||||
\(789\) | 46.0416 | 1.63912 | ||||||||
\(790\) | 9.51350 | 0.338475 | ||||||||
\(791\) | −35.7988 | −1.27286 | ||||||||
\(792\) | 20.0447 | 0.712258 | ||||||||
\(793\) | 2.40410 | 0.0853720 | ||||||||
\(794\) | −10.8483 | −0.384993 | ||||||||
\(795\) | 10.3141 | 0.365804 | ||||||||
\(796\) | −5.48201 | −0.194305 | ||||||||
\(797\) | 26.4335 | 0.936322 | 0.468161 | − | 0.883643i | \(-0.344917\pi\) | ||||
0.468161 | + | 0.883643i | \(0.344917\pi\) | |||||||
\(798\) | 39.2833 | 1.39061 | ||||||||
\(799\) | −9.57357 | −0.338688 | ||||||||
\(800\) | −4.51494 | −0.159627 | ||||||||
\(801\) | 18.2965 | 0.646475 | ||||||||
\(802\) | 26.6113 | 0.939676 | ||||||||
\(803\) | 61.8760 | 2.18356 | ||||||||
\(804\) | 19.3753 | 0.683315 | ||||||||
\(805\) | 15.2601 | 0.537849 | ||||||||
\(806\) | 0.345947 | 0.0121854 | ||||||||
\(807\) | 15.5992 | 0.549116 | ||||||||
\(808\) | −13.8748 | −0.488115 | ||||||||
\(809\) | −14.4091 | −0.506596 | −0.253298 | − | 0.967388i | \(-0.581515\pi\) | ||||
−0.253298 | + | 0.967388i | \(0.581515\pi\) | |||||||
\(810\) | −6.05782 | −0.212850 | ||||||||
\(811\) | 12.3035 | 0.432036 | 0.216018 | − | 0.976389i | \(-0.430693\pi\) | ||||
0.216018 | + | 0.976389i | \(0.430693\pi\) | |||||||
\(812\) | 28.3060 | 0.993346 | ||||||||
\(813\) | 53.3945 | 1.87263 | ||||||||
\(814\) | 68.8529 | 2.41329 | ||||||||
\(815\) | 14.5956 | 0.511260 | ||||||||
\(816\) | 10.6749 | 0.373698 | ||||||||
\(817\) | −10.2523 | −0.358684 | ||||||||
\(818\) | 26.8595 | 0.939119 | ||||||||
\(819\) | −2.25169 | −0.0786805 | ||||||||
\(820\) | −0.433015 | −0.0151215 | ||||||||
\(821\) | 54.7857 | 1.91203 | 0.956017 | − | 0.293312i | \(-0.0947575\pi\) | ||||
0.956017 | + | 0.293312i | \(0.0947575\pi\) | |||||||
\(822\) | 34.4810 | 1.20266 | ||||||||
\(823\) | 9.26606 | 0.322994 | 0.161497 | − | 0.986873i | \(-0.448368\pi\) | ||||
0.161497 | + | 0.986873i | \(0.448368\pi\) | |||||||
\(824\) | −3.48612 | −0.121445 | ||||||||
\(825\) | 72.1469 | 2.51183 | ||||||||
\(826\) | 11.4824 | 0.399524 | ||||||||
\(827\) | −40.6307 | −1.41287 | −0.706433 | − | 0.707780i | \(-0.749697\pi\) | ||||
−0.706433 | + | 0.707780i | \(0.749697\pi\) | |||||||
\(828\) | −23.0699 | −0.801734 | ||||||||
\(829\) | −10.2587 | −0.356300 | −0.178150 | − | 0.984003i | \(-0.557011\pi\) | ||||
−0.178150 | + | 0.984003i | \(0.557011\pi\) | |||||||
\(830\) | −9.20741 | −0.319594 | ||||||||
\(831\) | 45.4585 | 1.57694 | ||||||||
\(832\) | 0.247100 | 0.00856665 | ||||||||
\(833\) | −7.15344 | −0.247852 | ||||||||
\(834\) | 29.1248 | 1.00851 | ||||||||
\(835\) | −6.97162 | −0.241263 | ||||||||
\(836\) | 34.9941 | 1.21030 | ||||||||
\(837\) | −0.337028 | −0.0116494 | ||||||||
\(838\) | −13.3434 | −0.460939 | ||||||||
\(839\) | 25.3075 | 0.873711 | 0.436855 | − | 0.899532i | \(-0.356092\pi\) | ||||
0.436855 | + | 0.899532i | \(0.356092\pi\) | |||||||
\(840\) | 5.05939 | 0.174565 | ||||||||
\(841\) | 63.5773 | 2.19232 | ||||||||
\(842\) | −8.43153 | −0.290570 | ||||||||
\(843\) | 41.0445 | 1.41365 | ||||||||
\(844\) | −23.9300 | −0.823705 | ||||||||
\(845\) | −9.01145 | −0.310003 | ||||||||
\(846\) | 6.85951 | 0.235835 | ||||||||
\(847\) | −90.8380 | −3.12123 | ||||||||
\(848\) | −5.99737 | −0.205950 | ||||||||
\(849\) | −9.49205 | −0.325766 | ||||||||
\(850\) | 19.5183 | 0.669473 | ||||||||
\(851\) | −79.2443 | −2.71646 | ||||||||
\(852\) | 20.0750 | 0.687759 | ||||||||
\(853\) | −35.4844 | −1.21496 | −0.607482 | − | 0.794334i | \(-0.707820\pi\) | ||||
−0.607482 | + | 0.794334i | \(0.707820\pi\) | |||||||
\(854\) | −28.6224 | −0.979437 | ||||||||
\(855\) | 11.6657 | 0.398959 | ||||||||
\(856\) | −10.7045 | −0.365871 | ||||||||
\(857\) | −34.9964 | −1.19545 | −0.597727 | − | 0.801699i | \(-0.703929\pi\) | ||||
−0.597727 | + | 0.801699i | \(0.703929\pi\) | |||||||
\(858\) | −3.94856 | −0.134801 | ||||||||
\(859\) | 45.4198 | 1.54970 | 0.774852 | − | 0.632143i | \(-0.217825\pi\) | ||||
0.774852 | + | 0.632143i | \(0.217825\pi\) | |||||||
\(860\) | −1.32042 | −0.0450260 | ||||||||
\(861\) | −4.51657 | −0.153924 | ||||||||
\(862\) | −0.278983 | −0.00950220 | ||||||||
\(863\) | 16.9731 | 0.577772 | 0.288886 | − | 0.957363i | \(-0.406715\pi\) | ||||
0.288886 | + | 0.957363i | \(0.406715\pi\) | |||||||
\(864\) | −0.240730 | −0.00818979 | ||||||||
\(865\) | 4.52335 | 0.153799 | ||||||||
\(866\) | −0.219535 | −0.00746010 | ||||||||
\(867\) | −4.17004 | −0.141622 | ||||||||
\(868\) | −4.11872 | −0.139799 | ||||||||
\(869\) | 88.3964 | 2.99864 | ||||||||
\(870\) | 16.5472 | 0.561001 | ||||||||
\(871\) | −1.93886 | −0.0656957 | ||||||||
\(872\) | 17.3569 | 0.587780 | ||||||||
\(873\) | 14.4176 | 0.487961 | ||||||||
\(874\) | −40.2755 | −1.36234 | ||||||||
\(875\) | 19.4952 | 0.659059 | ||||||||
\(876\) | −23.6106 | −0.797729 | ||||||||
\(877\) | −12.9442 | −0.437094 | −0.218547 | − | 0.975826i | \(-0.570132\pi\) | ||||
−0.218547 | + | 0.975826i | \(0.570132\pi\) | |||||||
\(878\) | −22.7700 | −0.768451 | ||||||||
\(879\) | −77.1755 | −2.60307 | ||||||||
\(880\) | 4.50698 | 0.151930 | ||||||||
\(881\) | 1.04540 | 0.0352205 | 0.0176103 | − | 0.999845i | \(-0.494394\pi\) | ||||
0.0176103 | + | 0.999845i | \(0.494394\pi\) | |||||||
\(882\) | 5.12548 | 0.172584 | ||||||||
\(883\) | −16.3441 | −0.550022 | −0.275011 | − | 0.961441i | \(-0.588682\pi\) | ||||
−0.275011 | + | 0.961441i | \(0.588682\pi\) | |||||||
\(884\) | −1.06823 | −0.0359283 | ||||||||
\(885\) | 6.71240 | 0.225635 | ||||||||
\(886\) | 16.1828 | 0.543670 | ||||||||
\(887\) | 27.6199 | 0.927385 | 0.463692 | − | 0.885996i | \(-0.346524\pi\) | ||||
0.463692 | + | 0.885996i | \(0.346524\pi\) | |||||||
\(888\) | −26.2729 | −0.881660 | ||||||||
\(889\) | −7.18551 | −0.240994 | ||||||||
\(890\) | 4.11390 | 0.137898 | ||||||||
\(891\) | −56.2874 | −1.88570 | ||||||||
\(892\) | −18.6303 | −0.623789 | ||||||||
\(893\) | 11.9754 | 0.400741 | ||||||||
\(894\) | −37.8039 | −1.26435 | ||||||||
\(895\) | −2.72752 | −0.0911711 | ||||||||
\(896\) | −2.94189 | −0.0982817 | ||||||||
\(897\) | 4.54448 | 0.151736 | ||||||||
\(898\) | 30.1522 | 1.00619 | ||||||||
\(899\) | −13.4706 | −0.449271 | ||||||||
\(900\) | −13.9850 | −0.466166 | ||||||||
\(901\) | 25.9269 | 0.863750 | ||||||||
\(902\) | −4.02344 | −0.133966 | ||||||||
\(903\) | −13.7727 | −0.458327 | ||||||||
\(904\) | 12.1686 | 0.404723 | ||||||||
\(905\) | −13.7464 | −0.456947 | ||||||||
\(906\) | −47.4882 | −1.57769 | ||||||||
\(907\) | −9.40241 | −0.312202 | −0.156101 | − | 0.987741i | \(-0.549893\pi\) | ||||
−0.156101 | + | 0.987741i | \(0.549893\pi\) | |||||||
\(908\) | −11.4522 | −0.380054 | ||||||||
\(909\) | −42.9772 | −1.42546 | ||||||||
\(910\) | −0.506285 | −0.0167832 | ||||||||
\(911\) | −23.0408 | −0.763376 | −0.381688 | − | 0.924291i | \(-0.624657\pi\) | ||||
−0.381688 | + | 0.924291i | \(0.624657\pi\) | |||||||
\(912\) | −13.3531 | −0.442164 | ||||||||
\(913\) | −85.5523 | −2.83137 | ||||||||
\(914\) | 12.3632 | 0.408937 | ||||||||
\(915\) | −16.7321 | −0.553146 | ||||||||
\(916\) | 8.16991 | 0.269942 | ||||||||
\(917\) | 38.0414 | 1.25624 | ||||||||
\(918\) | 1.04069 | 0.0343477 | ||||||||
\(919\) | 3.25112 | 0.107245 | 0.0536223 | − | 0.998561i | \(-0.482923\pi\) | ||||
0.0536223 | + | 0.998561i | \(0.482923\pi\) | |||||||
\(920\) | −5.18718 | −0.171016 | ||||||||
\(921\) | −19.3525 | −0.637686 | ||||||||
\(922\) | −28.6537 | −0.943658 | ||||||||
\(923\) | −2.00888 | −0.0661230 | ||||||||
\(924\) | 47.0102 | 1.54652 | ||||||||
\(925\) | −48.0380 | −1.57948 | ||||||||
\(926\) | 12.4083 | 0.407763 | ||||||||
\(927\) | −10.7982 | −0.354660 | ||||||||
\(928\) | −9.62171 | −0.315848 | ||||||||
\(929\) | −20.5269 | −0.673466 | −0.336733 | − | 0.941600i | \(-0.609322\pi\) | ||||
−0.336733 | + | 0.941600i | \(0.609322\pi\) | |||||||
\(930\) | −2.40773 | −0.0789525 | ||||||||
\(931\) | 8.94809 | 0.293262 | ||||||||
\(932\) | −29.0524 | −0.951642 | ||||||||
\(933\) | 73.6657 | 2.41171 | ||||||||
\(934\) | 0.477760 | 0.0156328 | ||||||||
\(935\) | −19.4839 | −0.637192 | ||||||||
\(936\) | 0.765390 | 0.0250175 | ||||||||
\(937\) | 16.8798 | 0.551440 | 0.275720 | − | 0.961238i | \(-0.411084\pi\) | ||||
0.275720 | + | 0.961238i | \(0.411084\pi\) | |||||||
\(938\) | 23.0834 | 0.753700 | ||||||||
\(939\) | −41.4389 | −1.35231 | ||||||||
\(940\) | 1.54234 | 0.0503055 | ||||||||
\(941\) | 31.8413 | 1.03800 | 0.518999 | − | 0.854775i | \(-0.326305\pi\) | ||||
0.518999 | + | 0.854775i | \(0.326305\pi\) | |||||||
\(942\) | 10.4997 | 0.342098 | ||||||||
\(943\) | 4.63066 | 0.150795 | ||||||||
\(944\) | −3.90307 | −0.127034 | ||||||||
\(945\) | 0.493232 | 0.0160449 | ||||||||
\(946\) | −12.2689 | −0.398898 | ||||||||
\(947\) | 15.7039 | 0.510307 | 0.255154 | − | 0.966901i | \(-0.417874\pi\) | ||||
0.255154 | + | 0.966901i | \(0.417874\pi\) | |||||||
\(948\) | −33.7303 | −1.09551 | ||||||||
\(949\) | 2.36268 | 0.0766958 | ||||||||
\(950\) | −24.4151 | −0.792129 | ||||||||
\(951\) | 26.1715 | 0.848670 | ||||||||
\(952\) | 12.7179 | 0.412191 | ||||||||
\(953\) | 20.5730 | 0.666425 | 0.333212 | − | 0.942852i | \(-0.391867\pi\) | ||||
0.333212 | + | 0.942852i | \(0.391867\pi\) | |||||||
\(954\) | −18.5768 | −0.601445 | ||||||||
\(955\) | −4.37724 | −0.141644 | ||||||||
\(956\) | 6.29282 | 0.203524 | ||||||||
\(957\) | 153.751 | 4.97006 | ||||||||
\(958\) | 32.8108 | 1.06007 | ||||||||
\(959\) | 41.0801 | 1.32655 | ||||||||
\(960\) | −1.71977 | −0.0555054 | ||||||||
\(961\) | −29.0399 | −0.936772 | ||||||||
\(962\) | 2.62909 | 0.0847652 | ||||||||
\(963\) | −33.1569 | −1.06847 | ||||||||
\(964\) | 1.21320 | 0.0390746 | ||||||||
\(965\) | 3.47097 | 0.111734 | ||||||||
\(966\) | −54.1050 | −1.74080 | ||||||||
\(967\) | 22.2325 | 0.714950 | 0.357475 | − | 0.933923i | \(-0.383638\pi\) | ||||
0.357475 | + | 0.933923i | \(0.383638\pi\) | |||||||
\(968\) | 30.8774 | 0.992438 | ||||||||
\(969\) | 57.7259 | 1.85442 | ||||||||
\(970\) | 3.24174 | 0.104086 | ||||||||
\(971\) | −29.5759 | −0.949134 | −0.474567 | − | 0.880219i | \(-0.657395\pi\) | ||||
−0.474567 | + | 0.880219i | \(0.657395\pi\) | |||||||
\(972\) | 22.2003 | 0.712075 | ||||||||
\(973\) | 34.6988 | 1.11239 | ||||||||
\(974\) | −37.9687 | −1.21660 | ||||||||
\(975\) | 2.75487 | 0.0882264 | ||||||||
\(976\) | 9.72924 | 0.311425 | ||||||||
\(977\) | 46.6229 | 1.49160 | 0.745800 | − | 0.666170i | \(-0.232067\pi\) | ||||
0.745800 | + | 0.666170i | \(0.232067\pi\) | |||||||
\(978\) | −51.7488 | −1.65474 | ||||||||
\(979\) | 38.2251 | 1.22168 | ||||||||
\(980\) | 1.15245 | 0.0368135 | ||||||||
\(981\) | 53.7629 | 1.71652 | ||||||||
\(982\) | 17.0848 | 0.545198 | ||||||||
\(983\) | 34.5085 | 1.10065 | 0.550326 | − | 0.834950i | \(-0.314504\pi\) | ||||
0.550326 | + | 0.834950i | \(0.314504\pi\) | |||||||
\(984\) | 1.53526 | 0.0489424 | ||||||||
\(985\) | −6.19362 | −0.197345 | ||||||||
\(986\) | 41.5951 | 1.32466 | ||||||||
\(987\) | 16.0874 | 0.512067 | ||||||||
\(988\) | 1.33622 | 0.0425109 | ||||||||
\(989\) | 14.1206 | 0.449009 | ||||||||
\(990\) | 13.9603 | 0.443688 | ||||||||
\(991\) | 28.4311 | 0.903145 | 0.451573 | − | 0.892234i | \(-0.350863\pi\) | ||||
0.451573 | + | 0.892234i | \(0.350863\pi\) | |||||||
\(992\) | 1.40003 | 0.0444509 | ||||||||
\(993\) | −88.4551 | −2.80704 | ||||||||
\(994\) | 23.9170 | 0.758601 | ||||||||
\(995\) | −3.81799 | −0.121039 | ||||||||
\(996\) | 32.6450 | 1.03440 | ||||||||
\(997\) | −34.1080 | −1.08021 | −0.540105 | − | 0.841598i | \(-0.681616\pi\) | ||||
−0.540105 | + | 0.841598i | \(0.681616\pi\) | |||||||
\(998\) | −7.42496 | −0.235033 | ||||||||
\(999\) | −2.56131 | −0.0810362 |
(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 | 8038.2.a.a.1.14 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8038.2.a.a.1.14 | ✓ | 75 | 1.1 | even | 1 | trivial |