Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −1.08153 | −0.624424 | −0.312212 | − | 0.950012i | \(-0.601070\pi\) | ||||
−0.312212 | + | 0.950012i | \(0.601070\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.98271 | −1.33391 | −0.666954 | − | 0.745099i | \(-0.732402\pi\) | ||||
−0.666954 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(6\) | −1.08153 | −0.441534 | ||||||||
\(7\) | −1.13392 | −0.428580 | −0.214290 | − | 0.976770i | \(-0.568744\pi\) | ||||
−0.214290 | + | 0.976770i | \(0.568744\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.83028 | −0.610095 | ||||||||
\(10\) | −2.98271 | −0.943216 | ||||||||
\(11\) | −2.91322 | −0.878370 | −0.439185 | − | 0.898397i | \(-0.644733\pi\) | ||||
−0.439185 | + | 0.898397i | \(0.644733\pi\) | |||||||
\(12\) | −1.08153 | −0.312212 | ||||||||
\(13\) | −0.731076 | −0.202764 | −0.101382 | − | 0.994848i | \(-0.532326\pi\) | ||||
−0.101382 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(14\) | −1.13392 | −0.303052 | ||||||||
\(15\) | 3.22590 | 0.832925 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.72696 | 1.87406 | 0.937032 | − | 0.349244i | \(-0.113562\pi\) | ||||
0.937032 | + | 0.349244i | \(0.113562\pi\) | |||||||
\(18\) | −1.83028 | −0.431402 | ||||||||
\(19\) | −2.28749 | −0.524786 | −0.262393 | − | 0.964961i | \(-0.584512\pi\) | ||||
−0.262393 | + | 0.964961i | \(0.584512\pi\) | |||||||
\(20\) | −2.98271 | −0.666954 | ||||||||
\(21\) | 1.22637 | 0.267616 | ||||||||
\(22\) | −2.91322 | −0.621102 | ||||||||
\(23\) | 0.277997 | 0.0579665 | 0.0289832 | − | 0.999580i | \(-0.490773\pi\) | ||||
0.0289832 | + | 0.999580i | \(0.490773\pi\) | |||||||
\(24\) | −1.08153 | −0.220767 | ||||||||
\(25\) | 3.89656 | 0.779312 | ||||||||
\(26\) | −0.731076 | −0.143376 | ||||||||
\(27\) | 5.22412 | 1.00538 | ||||||||
\(28\) | −1.13392 | −0.214290 | ||||||||
\(29\) | 5.89169 | 1.09406 | 0.547030 | − | 0.837113i | \(-0.315758\pi\) | ||||
0.547030 | + | 0.837113i | \(0.315758\pi\) | |||||||
\(30\) | 3.22590 | 0.588967 | ||||||||
\(31\) | 7.72320 | 1.38713 | 0.693564 | − | 0.720395i | \(-0.256039\pi\) | ||||
0.693564 | + | 0.720395i | \(0.256039\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.15075 | 0.548476 | ||||||||
\(34\) | 7.72696 | 1.32516 | ||||||||
\(35\) | 3.38214 | 0.571686 | ||||||||
\(36\) | −1.83028 | −0.305047 | ||||||||
\(37\) | 2.82143 | 0.463839 | 0.231920 | − | 0.972735i | \(-0.425499\pi\) | ||||
0.231920 | + | 0.972735i | \(0.425499\pi\) | |||||||
\(38\) | −2.28749 | −0.371079 | ||||||||
\(39\) | 0.790684 | 0.126611 | ||||||||
\(40\) | −2.98271 | −0.471608 | ||||||||
\(41\) | −2.69161 | −0.420359 | −0.210180 | − | 0.977663i | \(-0.567405\pi\) | ||||
−0.210180 | + | 0.977663i | \(0.567405\pi\) | |||||||
\(42\) | 1.22637 | 0.189233 | ||||||||
\(43\) | 1.83122 | 0.279259 | 0.139629 | − | 0.990204i | \(-0.455409\pi\) | ||||
0.139629 | + | 0.990204i | \(0.455409\pi\) | |||||||
\(44\) | −2.91322 | −0.439185 | ||||||||
\(45\) | 5.45921 | 0.813810 | ||||||||
\(46\) | 0.277997 | 0.0409885 | ||||||||
\(47\) | −2.34973 | −0.342744 | −0.171372 | − | 0.985206i | \(-0.554820\pi\) | ||||
−0.171372 | + | 0.985206i | \(0.554820\pi\) | |||||||
\(48\) | −1.08153 | −0.156106 | ||||||||
\(49\) | −5.71423 | −0.816319 | ||||||||
\(50\) | 3.89656 | 0.551057 | ||||||||
\(51\) | −8.35697 | −1.17021 | ||||||||
\(52\) | −0.731076 | −0.101382 | ||||||||
\(53\) | 10.0741 | 1.38378 | 0.691891 | − | 0.722002i | \(-0.256778\pi\) | ||||
0.691891 | + | 0.722002i | \(0.256778\pi\) | |||||||
\(54\) | 5.22412 | 0.710912 | ||||||||
\(55\) | 8.68931 | 1.17167 | ||||||||
\(56\) | −1.13392 | −0.151526 | ||||||||
\(57\) | 2.47400 | 0.327689 | ||||||||
\(58\) | 5.89169 | 0.773617 | ||||||||
\(59\) | −4.81439 | −0.626780 | −0.313390 | − | 0.949625i | \(-0.601465\pi\) | ||||
−0.313390 | + | 0.949625i | \(0.601465\pi\) | |||||||
\(60\) | 3.22590 | 0.416462 | ||||||||
\(61\) | −10.2163 | −1.30807 | −0.654035 | − | 0.756465i | \(-0.726925\pi\) | ||||
−0.654035 | + | 0.756465i | \(0.726925\pi\) | |||||||
\(62\) | 7.72320 | 0.980848 | ||||||||
\(63\) | 2.07539 | 0.261474 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.18059 | 0.270469 | ||||||||
\(66\) | 3.15075 | 0.387831 | ||||||||
\(67\) | 6.42078 | 0.784423 | 0.392211 | − | 0.919875i | \(-0.371710\pi\) | ||||
0.392211 | + | 0.919875i | \(0.371710\pi\) | |||||||
\(68\) | 7.72696 | 0.937032 | ||||||||
\(69\) | −0.300664 | −0.0361957 | ||||||||
\(70\) | 3.38214 | 0.404243 | ||||||||
\(71\) | −8.65038 | −1.02661 | −0.513305 | − | 0.858206i | \(-0.671579\pi\) | ||||
−0.513305 | + | 0.858206i | \(0.671579\pi\) | |||||||
\(72\) | −1.83028 | −0.215701 | ||||||||
\(73\) | −2.20145 | −0.257661 | −0.128830 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128830 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(74\) | 2.82143 | 0.327984 | ||||||||
\(75\) | −4.21427 | −0.486621 | ||||||||
\(76\) | −2.28749 | −0.262393 | ||||||||
\(77\) | 3.30335 | 0.376452 | ||||||||
\(78\) | 0.790684 | 0.0895273 | ||||||||
\(79\) | 7.73841 | 0.870639 | 0.435320 | − | 0.900276i | \(-0.356635\pi\) | ||||
0.435320 | + | 0.900276i | \(0.356635\pi\) | |||||||
\(80\) | −2.98271 | −0.333477 | ||||||||
\(81\) | −0.159210 | −0.0176900 | ||||||||
\(82\) | −2.69161 | −0.297239 | ||||||||
\(83\) | 5.72485 | 0.628384 | 0.314192 | − | 0.949360i | \(-0.398266\pi\) | ||||
0.314192 | + | 0.949360i | \(0.398266\pi\) | |||||||
\(84\) | 1.22637 | 0.133808 | ||||||||
\(85\) | −23.0473 | −2.49983 | ||||||||
\(86\) | 1.83122 | 0.197466 | ||||||||
\(87\) | −6.37207 | −0.683158 | ||||||||
\(88\) | −2.91322 | −0.310551 | ||||||||
\(89\) | −7.04382 | −0.746644 | −0.373322 | − | 0.927702i | \(-0.621781\pi\) | ||||
−0.373322 | + | 0.927702i | \(0.621781\pi\) | |||||||
\(90\) | 5.45921 | 0.575451 | ||||||||
\(91\) | 0.828979 | 0.0869006 | ||||||||
\(92\) | 0.277997 | 0.0289832 | ||||||||
\(93\) | −8.35291 | −0.866156 | ||||||||
\(94\) | −2.34973 | −0.242356 | ||||||||
\(95\) | 6.82291 | 0.700016 | ||||||||
\(96\) | −1.08153 | −0.110384 | ||||||||
\(97\) | −10.8995 | −1.10667 | −0.553337 | − | 0.832958i | \(-0.686646\pi\) | ||||
−0.553337 | + | 0.832958i | \(0.686646\pi\) | |||||||
\(98\) | −5.71423 | −0.577225 | ||||||||
\(99\) | 5.33203 | 0.535889 | ||||||||
\(100\) | 3.89656 | 0.389656 | ||||||||
\(101\) | 7.85628 | 0.781729 | 0.390865 | − | 0.920448i | \(-0.372176\pi\) | ||||
0.390865 | + | 0.920448i | \(0.372176\pi\) | |||||||
\(102\) | −8.35697 | −0.827464 | ||||||||
\(103\) | 8.57974 | 0.845387 | 0.422694 | − | 0.906273i | \(-0.361085\pi\) | ||||
0.422694 | + | 0.906273i | \(0.361085\pi\) | |||||||
\(104\) | −0.731076 | −0.0716879 | ||||||||
\(105\) | −3.65790 | −0.356975 | ||||||||
\(106\) | 10.0741 | 0.978482 | ||||||||
\(107\) | −17.5513 | −1.69675 | −0.848376 | − | 0.529394i | \(-0.822419\pi\) | ||||
−0.848376 | + | 0.529394i | \(0.822419\pi\) | |||||||
\(108\) | 5.22412 | 0.502691 | ||||||||
\(109\) | −2.48069 | −0.237607 | −0.118803 | − | 0.992918i | \(-0.537906\pi\) | ||||
−0.118803 | + | 0.992918i | \(0.537906\pi\) | |||||||
\(110\) | 8.68931 | 0.828493 | ||||||||
\(111\) | −3.05147 | −0.289633 | ||||||||
\(112\) | −1.13392 | −0.107145 | ||||||||
\(113\) | −11.6372 | −1.09474 | −0.547368 | − | 0.836892i | \(-0.684370\pi\) | ||||
−0.547368 | + | 0.836892i | \(0.684370\pi\) | |||||||
\(114\) | 2.47400 | 0.231711 | ||||||||
\(115\) | −0.829186 | −0.0773220 | ||||||||
\(116\) | 5.89169 | 0.547030 | ||||||||
\(117\) | 1.33808 | 0.123705 | ||||||||
\(118\) | −4.81439 | −0.443200 | ||||||||
\(119\) | −8.76173 | −0.803186 | ||||||||
\(120\) | 3.22590 | 0.294483 | ||||||||
\(121\) | −2.51312 | −0.228466 | ||||||||
\(122\) | −10.2163 | −0.924945 | ||||||||
\(123\) | 2.91107 | 0.262482 | ||||||||
\(124\) | 7.72320 | 0.693564 | ||||||||
\(125\) | 3.29124 | 0.294377 | ||||||||
\(126\) | 2.07539 | 0.184890 | ||||||||
\(127\) | −8.57468 | −0.760880 | −0.380440 | − | 0.924806i | \(-0.624227\pi\) | ||||
−0.380440 | + | 0.924806i | \(0.624227\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.98053 | −0.174376 | ||||||||
\(130\) | 2.18059 | 0.191250 | ||||||||
\(131\) | −12.4733 | −1.08980 | −0.544898 | − | 0.838502i | \(-0.683432\pi\) | ||||
−0.544898 | + | 0.838502i | \(0.683432\pi\) | |||||||
\(132\) | 3.15075 | 0.274238 | ||||||||
\(133\) | 2.59382 | 0.224913 | ||||||||
\(134\) | 6.42078 | 0.554670 | ||||||||
\(135\) | −15.5820 | −1.34109 | ||||||||
\(136\) | 7.72696 | 0.662582 | ||||||||
\(137\) | −13.9245 | −1.18965 | −0.594826 | − | 0.803854i | \(-0.702779\pi\) | ||||
−0.594826 | + | 0.803854i | \(0.702779\pi\) | |||||||
\(138\) | −0.300664 | −0.0255942 | ||||||||
\(139\) | 8.26207 | 0.700780 | 0.350390 | − | 0.936604i | \(-0.386049\pi\) | ||||
0.350390 | + | 0.936604i | \(0.386049\pi\) | |||||||
\(140\) | 3.38214 | 0.285843 | ||||||||
\(141\) | 2.54131 | 0.214017 | ||||||||
\(142\) | −8.65038 | −0.725924 | ||||||||
\(143\) | 2.12979 | 0.178102 | ||||||||
\(144\) | −1.83028 | −0.152524 | ||||||||
\(145\) | −17.5732 | −1.45938 | ||||||||
\(146\) | −2.20145 | −0.182194 | ||||||||
\(147\) | 6.18014 | 0.509729 | ||||||||
\(148\) | 2.82143 | 0.231920 | ||||||||
\(149\) | −10.0517 | −0.823468 | −0.411734 | − | 0.911304i | \(-0.635077\pi\) | ||||
−0.411734 | + | 0.911304i | \(0.635077\pi\) | |||||||
\(150\) | −4.21427 | −0.344093 | ||||||||
\(151\) | 12.4850 | 1.01601 | 0.508006 | − | 0.861354i | \(-0.330383\pi\) | ||||
0.508006 | + | 0.861354i | \(0.330383\pi\) | |||||||
\(152\) | −2.28749 | −0.185540 | ||||||||
\(153\) | −14.1425 | −1.14336 | ||||||||
\(154\) | 3.30335 | 0.266192 | ||||||||
\(155\) | −23.0361 | −1.85030 | ||||||||
\(156\) | 0.790684 | 0.0633053 | ||||||||
\(157\) | 5.48909 | 0.438077 | 0.219039 | − | 0.975716i | \(-0.429708\pi\) | ||||
0.219039 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(158\) | 7.73841 | 0.615635 | ||||||||
\(159\) | −10.8955 | −0.864067 | ||||||||
\(160\) | −2.98271 | −0.235804 | ||||||||
\(161\) | −0.315226 | −0.0248433 | ||||||||
\(162\) | −0.159210 | −0.0125087 | ||||||||
\(163\) | −3.97886 | −0.311648 | −0.155824 | − | 0.987785i | \(-0.549803\pi\) | ||||
−0.155824 | + | 0.987785i | \(0.549803\pi\) | |||||||
\(164\) | −2.69161 | −0.210180 | ||||||||
\(165\) | −9.39778 | −0.731616 | ||||||||
\(166\) | 5.72485 | 0.444334 | ||||||||
\(167\) | 20.8740 | 1.61528 | 0.807640 | − | 0.589676i | \(-0.200745\pi\) | ||||
0.807640 | + | 0.589676i | \(0.200745\pi\) | |||||||
\(168\) | 1.22637 | 0.0946164 | ||||||||
\(169\) | −12.4655 | −0.958887 | ||||||||
\(170\) | −23.0473 | −1.76765 | ||||||||
\(171\) | 4.18675 | 0.320169 | ||||||||
\(172\) | 1.83122 | 0.139629 | ||||||||
\(173\) | −3.22557 | −0.245236 | −0.122618 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122618 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(174\) | −6.37207 | −0.483065 | ||||||||
\(175\) | −4.41837 | −0.333998 | ||||||||
\(176\) | −2.91322 | −0.219593 | ||||||||
\(177\) | 5.20693 | 0.391376 | ||||||||
\(178\) | −7.04382 | −0.527957 | ||||||||
\(179\) | −11.1498 | −0.833375 | −0.416687 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416687 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(180\) | 5.45921 | 0.406905 | ||||||||
\(181\) | 5.32402 | 0.395732 | 0.197866 | − | 0.980229i | \(-0.436599\pi\) | ||||
0.197866 | + | 0.980229i | \(0.436599\pi\) | |||||||
\(182\) | 0.828979 | 0.0614480 | ||||||||
\(183\) | 11.0493 | 0.816790 | ||||||||
\(184\) | 0.277997 | 0.0204942 | ||||||||
\(185\) | −8.41549 | −0.618719 | ||||||||
\(186\) | −8.35291 | −0.612465 | ||||||||
\(187\) | −22.5104 | −1.64612 | ||||||||
\(188\) | −2.34973 | −0.171372 | ||||||||
\(189\) | −5.92371 | −0.430886 | ||||||||
\(190\) | 6.82291 | 0.494986 | ||||||||
\(191\) | −18.0496 | −1.30603 | −0.653013 | − | 0.757347i | \(-0.726495\pi\) | ||||
−0.653013 | + | 0.757347i | \(0.726495\pi\) | |||||||
\(192\) | −1.08153 | −0.0780530 | ||||||||
\(193\) | −23.7304 | −1.70815 | −0.854075 | − | 0.520149i | \(-0.825876\pi\) | ||||
−0.854075 | + | 0.520149i | \(0.825876\pi\) | |||||||
\(194\) | −10.8995 | −0.782536 | ||||||||
\(195\) | −2.35838 | −0.168887 | ||||||||
\(196\) | −5.71423 | −0.408160 | ||||||||
\(197\) | 5.26145 | 0.374863 | 0.187432 | − | 0.982278i | \(-0.439984\pi\) | ||||
0.187432 | + | 0.982278i | \(0.439984\pi\) | |||||||
\(198\) | 5.33203 | 0.378931 | ||||||||
\(199\) | −8.41324 | −0.596399 | −0.298199 | − | 0.954504i | \(-0.596386\pi\) | ||||
−0.298199 | + | 0.954504i | \(0.596386\pi\) | |||||||
\(200\) | 3.89656 | 0.275529 | ||||||||
\(201\) | −6.94429 | −0.489812 | ||||||||
\(202\) | 7.85628 | 0.552766 | ||||||||
\(203\) | −6.68069 | −0.468892 | ||||||||
\(204\) | −8.35697 | −0.585105 | ||||||||
\(205\) | 8.02830 | 0.560721 | ||||||||
\(206\) | 8.57974 | 0.597779 | ||||||||
\(207\) | −0.508814 | −0.0353650 | ||||||||
\(208\) | −0.731076 | −0.0506910 | ||||||||
\(209\) | 6.66396 | 0.460956 | ||||||||
\(210\) | −3.65790 | −0.252419 | ||||||||
\(211\) | 26.7402 | 1.84087 | 0.920437 | − | 0.390892i | \(-0.127833\pi\) | ||||
0.920437 | + | 0.390892i | \(0.127833\pi\) | |||||||
\(212\) | 10.0741 | 0.691891 | ||||||||
\(213\) | 9.35568 | 0.641041 | ||||||||
\(214\) | −17.5513 | −1.19978 | ||||||||
\(215\) | −5.46201 | −0.372506 | ||||||||
\(216\) | 5.22412 | 0.355456 | ||||||||
\(217\) | −8.75746 | −0.594495 | ||||||||
\(218\) | −2.48069 | −0.168013 | ||||||||
\(219\) | 2.38095 | 0.160890 | ||||||||
\(220\) | 8.68931 | 0.585833 | ||||||||
\(221\) | −5.64900 | −0.379993 | ||||||||
\(222\) | −3.05147 | −0.204801 | ||||||||
\(223\) | −20.4191 | −1.36736 | −0.683682 | − | 0.729780i | \(-0.739623\pi\) | ||||
−0.683682 | + | 0.729780i | \(0.739623\pi\) | |||||||
\(224\) | −1.13392 | −0.0757629 | ||||||||
\(225\) | −7.13181 | −0.475454 | ||||||||
\(226\) | −11.6372 | −0.774095 | ||||||||
\(227\) | 4.05376 | 0.269058 | 0.134529 | − | 0.990910i | \(-0.457048\pi\) | ||||
0.134529 | + | 0.990910i | \(0.457048\pi\) | |||||||
\(228\) | 2.47400 | 0.163844 | ||||||||
\(229\) | −18.0760 | −1.19450 | −0.597249 | − | 0.802056i | \(-0.703740\pi\) | ||||
−0.597249 | + | 0.802056i | \(0.703740\pi\) | |||||||
\(230\) | −0.829186 | −0.0546749 | ||||||||
\(231\) | −3.57269 | −0.235066 | ||||||||
\(232\) | 5.89169 | 0.386809 | ||||||||
\(233\) | 26.7595 | 1.75307 | 0.876536 | − | 0.481337i | \(-0.159849\pi\) | ||||
0.876536 | + | 0.481337i | \(0.159849\pi\) | |||||||
\(234\) | 1.33808 | 0.0874728 | ||||||||
\(235\) | 7.00857 | 0.457189 | ||||||||
\(236\) | −4.81439 | −0.313390 | ||||||||
\(237\) | −8.36936 | −0.543648 | ||||||||
\(238\) | −8.76173 | −0.567938 | ||||||||
\(239\) | 9.24933 | 0.598289 | 0.299145 | − | 0.954208i | \(-0.403299\pi\) | ||||
0.299145 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(240\) | 3.22590 | 0.208231 | ||||||||
\(241\) | −2.15772 | −0.138991 | −0.0694954 | − | 0.997582i | \(-0.522139\pi\) | ||||
−0.0694954 | + | 0.997582i | \(0.522139\pi\) | |||||||
\(242\) | −2.51312 | −0.161550 | ||||||||
\(243\) | −15.5002 | −0.994336 | ||||||||
\(244\) | −10.2163 | −0.654035 | ||||||||
\(245\) | 17.0439 | 1.08890 | ||||||||
\(246\) | 2.91107 | 0.185603 | ||||||||
\(247\) | 1.67233 | 0.106408 | ||||||||
\(248\) | 7.72320 | 0.490424 | ||||||||
\(249\) | −6.19162 | −0.392378 | ||||||||
\(250\) | 3.29124 | 0.208156 | ||||||||
\(251\) | 22.0796 | 1.39365 | 0.696827 | − | 0.717239i | \(-0.254595\pi\) | ||||
0.696827 | + | 0.717239i | \(0.254595\pi\) | |||||||
\(252\) | 2.07539 | 0.130737 | ||||||||
\(253\) | −0.809869 | −0.0509160 | ||||||||
\(254\) | −8.57468 | −0.538023 | ||||||||
\(255\) | 24.9264 | 1.56095 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.21757 | 0.450220 | 0.225110 | − | 0.974333i | \(-0.427726\pi\) | ||||
0.225110 | + | 0.974333i | \(0.427726\pi\) | |||||||
\(258\) | −1.98053 | −0.123302 | ||||||||
\(259\) | −3.19926 | −0.198792 | ||||||||
\(260\) | 2.18059 | 0.135234 | ||||||||
\(261\) | −10.7835 | −0.667480 | ||||||||
\(262\) | −12.4733 | −0.770602 | ||||||||
\(263\) | 15.3564 | 0.946918 | 0.473459 | − | 0.880816i | \(-0.343005\pi\) | ||||
0.473459 | + | 0.880816i | \(0.343005\pi\) | |||||||
\(264\) | 3.15075 | 0.193915 | ||||||||
\(265\) | −30.0481 | −1.84584 | ||||||||
\(266\) | 2.59382 | 0.159037 | ||||||||
\(267\) | 7.61814 | 0.466222 | ||||||||
\(268\) | 6.42078 | 0.392211 | ||||||||
\(269\) | −22.8657 | −1.39415 | −0.697073 | − | 0.717000i | \(-0.745515\pi\) | ||||
−0.697073 | + | 0.717000i | \(0.745515\pi\) | |||||||
\(270\) | −15.5820 | −0.948292 | ||||||||
\(271\) | −23.3920 | −1.42096 | −0.710482 | − | 0.703715i | \(-0.751523\pi\) | ||||
−0.710482 | + | 0.703715i | \(0.751523\pi\) | |||||||
\(272\) | 7.72696 | 0.468516 | ||||||||
\(273\) | −0.896569 | −0.0542628 | ||||||||
\(274\) | −13.9245 | −0.841211 | ||||||||
\(275\) | −11.3516 | −0.684525 | ||||||||
\(276\) | −0.300664 | −0.0180978 | ||||||||
\(277\) | 30.4657 | 1.83051 | 0.915253 | − | 0.402880i | \(-0.131991\pi\) | ||||
0.915253 | + | 0.402880i | \(0.131991\pi\) | |||||||
\(278\) | 8.26207 | 0.495526 | ||||||||
\(279\) | −14.1357 | −0.846279 | ||||||||
\(280\) | 3.38214 | 0.202122 | ||||||||
\(281\) | −3.16439 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(282\) | 2.54131 | 0.151333 | ||||||||
\(283\) | 22.7438 | 1.35198 | 0.675990 | − | 0.736910i | \(-0.263716\pi\) | ||||
0.675990 | + | 0.736910i | \(0.263716\pi\) | |||||||
\(284\) | −8.65038 | −0.513305 | ||||||||
\(285\) | −7.37921 | −0.437107 | ||||||||
\(286\) | 2.12979 | 0.125937 | ||||||||
\(287\) | 3.05206 | 0.180158 | ||||||||
\(288\) | −1.83028 | −0.107851 | ||||||||
\(289\) | 42.7060 | 2.51211 | ||||||||
\(290\) | −17.5732 | −1.03194 | ||||||||
\(291\) | 11.7881 | 0.691034 | ||||||||
\(292\) | −2.20145 | −0.128830 | ||||||||
\(293\) | 31.9816 | 1.86839 | 0.934193 | − | 0.356769i | \(-0.116122\pi\) | ||||
0.934193 | + | 0.356769i | \(0.116122\pi\) | |||||||
\(294\) | 6.18014 | 0.360433 | ||||||||
\(295\) | 14.3599 | 0.836067 | ||||||||
\(296\) | 2.82143 | 0.163992 | ||||||||
\(297\) | −15.2190 | −0.883097 | ||||||||
\(298\) | −10.0517 | −0.582280 | ||||||||
\(299\) | −0.203237 | −0.0117535 | ||||||||
\(300\) | −4.21427 | −0.243311 | ||||||||
\(301\) | −2.07645 | −0.119685 | ||||||||
\(302\) | 12.4850 | 0.718429 | ||||||||
\(303\) | −8.49684 | −0.488131 | ||||||||
\(304\) | −2.28749 | −0.131196 | ||||||||
\(305\) | 30.4724 | 1.74485 | ||||||||
\(306\) | −14.1425 | −0.808475 | ||||||||
\(307\) | −23.5117 | −1.34188 | −0.670941 | − | 0.741510i | \(-0.734110\pi\) | ||||
−0.670941 | + | 0.741510i | \(0.734110\pi\) | |||||||
\(308\) | 3.30335 | 0.188226 | ||||||||
\(309\) | −9.27929 | −0.527880 | ||||||||
\(310\) | −23.0361 | −1.30836 | ||||||||
\(311\) | −17.2273 | −0.976873 | −0.488437 | − | 0.872599i | \(-0.662433\pi\) | ||||
−0.488437 | + | 0.872599i | \(0.662433\pi\) | |||||||
\(312\) | 0.790684 | 0.0447636 | ||||||||
\(313\) | −9.55032 | −0.539816 | −0.269908 | − | 0.962886i | \(-0.586993\pi\) | ||||
−0.269908 | + | 0.962886i | \(0.586993\pi\) | |||||||
\(314\) | 5.48909 | 0.309767 | ||||||||
\(315\) | −6.19028 | −0.348783 | ||||||||
\(316\) | 7.73841 | 0.435320 | ||||||||
\(317\) | −5.00960 | −0.281367 | −0.140684 | − | 0.990055i | \(-0.544930\pi\) | ||||
−0.140684 | + | 0.990055i | \(0.544930\pi\) | |||||||
\(318\) | −10.8955 | −0.610988 | ||||||||
\(319\) | −17.1638 | −0.960990 | ||||||||
\(320\) | −2.98271 | −0.166739 | ||||||||
\(321\) | 18.9824 | 1.05949 | ||||||||
\(322\) | −0.315226 | −0.0175668 | ||||||||
\(323\) | −17.6753 | −0.983482 | ||||||||
\(324\) | −0.159210 | −0.00884500 | ||||||||
\(325\) | −2.84868 | −0.158016 | ||||||||
\(326\) | −3.97886 | −0.220369 | ||||||||
\(327\) | 2.68295 | 0.148367 | ||||||||
\(328\) | −2.69161 | −0.148619 | ||||||||
\(329\) | 2.66440 | 0.146893 | ||||||||
\(330\) | −9.39778 | −0.517331 | ||||||||
\(331\) | 12.8684 | 0.707312 | 0.353656 | − | 0.935375i | \(-0.384938\pi\) | ||||
0.353656 | + | 0.935375i | \(0.384938\pi\) | |||||||
\(332\) | 5.72485 | 0.314192 | ||||||||
\(333\) | −5.16401 | −0.282986 | ||||||||
\(334\) | 20.8740 | 1.14218 | ||||||||
\(335\) | −19.1513 | −1.04635 | ||||||||
\(336\) | 1.22637 | 0.0669039 | ||||||||
\(337\) | −7.29248 | −0.397247 | −0.198623 | − | 0.980076i | \(-0.563647\pi\) | ||||
−0.198623 | + | 0.980076i | \(0.563647\pi\) | |||||||
\(338\) | −12.4655 | −0.678035 | ||||||||
\(339\) | 12.5860 | 0.683579 | ||||||||
\(340\) | −23.0473 | −1.24991 | ||||||||
\(341\) | −22.4994 | −1.21841 | ||||||||
\(342\) | 4.18675 | 0.226394 | ||||||||
\(343\) | 14.4169 | 0.778438 | ||||||||
\(344\) | 1.83122 | 0.0987330 | ||||||||
\(345\) | 0.896793 | 0.0482817 | ||||||||
\(346\) | −3.22557 | −0.173408 | ||||||||
\(347\) | 14.7381 | 0.791185 | 0.395592 | − | 0.918426i | \(-0.370539\pi\) | ||||
0.395592 | + | 0.918426i | \(0.370539\pi\) | |||||||
\(348\) | −6.37207 | −0.341579 | ||||||||
\(349\) | −25.4287 | −1.36117 | −0.680584 | − | 0.732670i | \(-0.738274\pi\) | ||||
−0.680584 | + | 0.732670i | \(0.738274\pi\) | |||||||
\(350\) | −4.41837 | −0.236172 | ||||||||
\(351\) | −3.81923 | −0.203855 | ||||||||
\(352\) | −2.91322 | −0.155275 | ||||||||
\(353\) | −6.78268 | −0.361005 | −0.180503 | − | 0.983574i | \(-0.557772\pi\) | ||||
−0.180503 | + | 0.983574i | \(0.557772\pi\) | |||||||
\(354\) | 5.20693 | 0.276745 | ||||||||
\(355\) | 25.8016 | 1.36941 | ||||||||
\(356\) | −7.04382 | −0.373322 | ||||||||
\(357\) | 9.47611 | 0.501529 | ||||||||
\(358\) | −11.1498 | −0.589285 | ||||||||
\(359\) | −30.4679 | −1.60803 | −0.804016 | − | 0.594607i | \(-0.797308\pi\) | ||||
−0.804016 | + | 0.594607i | \(0.797308\pi\) | |||||||
\(360\) | 5.45921 | 0.287725 | ||||||||
\(361\) | −13.7674 | −0.724600 | ||||||||
\(362\) | 5.32402 | 0.279824 | ||||||||
\(363\) | 2.71803 | 0.142659 | ||||||||
\(364\) | 0.828979 | 0.0434503 | ||||||||
\(365\) | 6.56630 | 0.343696 | ||||||||
\(366\) | 11.0493 | 0.577558 | ||||||||
\(367\) | 24.6983 | 1.28924 | 0.644620 | − | 0.764503i | \(-0.277016\pi\) | ||||
0.644620 | + | 0.764503i | \(0.277016\pi\) | |||||||
\(368\) | 0.277997 | 0.0144916 | ||||||||
\(369\) | 4.92641 | 0.256459 | ||||||||
\(370\) | −8.41549 | −0.437501 | ||||||||
\(371\) | −11.4232 | −0.593061 | ||||||||
\(372\) | −8.35291 | −0.433078 | ||||||||
\(373\) | −10.4154 | −0.539289 | −0.269644 | − | 0.962960i | \(-0.586906\pi\) | ||||
−0.269644 | + | 0.962960i | \(0.586906\pi\) | |||||||
\(374\) | −22.5104 | −1.16398 | ||||||||
\(375\) | −3.55958 | −0.183816 | ||||||||
\(376\) | −2.34973 | −0.121178 | ||||||||
\(377\) | −4.30728 | −0.221836 | ||||||||
\(378\) | −5.92371 | −0.304683 | ||||||||
\(379\) | −21.4886 | −1.10379 | −0.551897 | − | 0.833912i | \(-0.686096\pi\) | ||||
−0.551897 | + | 0.833912i | \(0.686096\pi\) | |||||||
\(380\) | 6.82291 | 0.350008 | ||||||||
\(381\) | 9.27381 | 0.475112 | ||||||||
\(382\) | −18.0496 | −0.923500 | ||||||||
\(383\) | −18.9808 | −0.969875 | −0.484938 | − | 0.874549i | \(-0.661158\pi\) | ||||
−0.484938 | + | 0.874549i | \(0.661158\pi\) | |||||||
\(384\) | −1.08153 | −0.0551918 | ||||||||
\(385\) | −9.85294 | −0.502152 | ||||||||
\(386\) | −23.7304 | −1.20785 | ||||||||
\(387\) | −3.35166 | −0.170374 | ||||||||
\(388\) | −10.8995 | −0.553337 | ||||||||
\(389\) | 1.81540 | 0.0920444 | 0.0460222 | − | 0.998940i | \(-0.485346\pi\) | ||||
0.0460222 | + | 0.998940i | \(0.485346\pi\) | |||||||
\(390\) | −2.35838 | −0.119421 | ||||||||
\(391\) | 2.14808 | 0.108633 | ||||||||
\(392\) | −5.71423 | −0.288612 | ||||||||
\(393\) | 13.4903 | 0.680495 | ||||||||
\(394\) | 5.26145 | 0.265068 | ||||||||
\(395\) | −23.0814 | −1.16135 | ||||||||
\(396\) | 5.33203 | 0.267944 | ||||||||
\(397\) | 7.94724 | 0.398861 | 0.199430 | − | 0.979912i | \(-0.436091\pi\) | ||||
0.199430 | + | 0.979912i | \(0.436091\pi\) | |||||||
\(398\) | −8.41324 | −0.421718 | ||||||||
\(399\) | −2.80530 | −0.140441 | ||||||||
\(400\) | 3.89656 | 0.194828 | ||||||||
\(401\) | −25.5334 | −1.27508 | −0.637538 | − | 0.770419i | \(-0.720047\pi\) | ||||
−0.637538 | + | 0.770419i | \(0.720047\pi\) | |||||||
\(402\) | −6.94429 | −0.346350 | ||||||||
\(403\) | −5.64625 | −0.281260 | ||||||||
\(404\) | 7.85628 | 0.390865 | ||||||||
\(405\) | 0.474877 | 0.0235968 | ||||||||
\(406\) | −6.68069 | −0.331557 | ||||||||
\(407\) | −8.21945 | −0.407423 | ||||||||
\(408\) | −8.35697 | −0.413732 | ||||||||
\(409\) | 9.59658 | 0.474520 | 0.237260 | − | 0.971446i | \(-0.423751\pi\) | ||||
0.237260 | + | 0.971446i | \(0.423751\pi\) | |||||||
\(410\) | 8.02830 | 0.396490 | ||||||||
\(411\) | 15.0598 | 0.742848 | ||||||||
\(412\) | 8.57974 | 0.422694 | ||||||||
\(413\) | 5.45911 | 0.268625 | ||||||||
\(414\) | −0.508814 | −0.0250069 | ||||||||
\(415\) | −17.0756 | −0.838207 | ||||||||
\(416\) | −0.731076 | −0.0358439 | ||||||||
\(417\) | −8.93572 | −0.437584 | ||||||||
\(418\) | 6.66396 | 0.325945 | ||||||||
\(419\) | −14.0049 | −0.684184 | −0.342092 | − | 0.939667i | \(-0.611135\pi\) | ||||
−0.342092 | + | 0.939667i | \(0.611135\pi\) | |||||||
\(420\) | −3.65790 | −0.178487 | ||||||||
\(421\) | 13.7078 | 0.668079 | 0.334040 | − | 0.942559i | \(-0.391588\pi\) | ||||
0.334040 | + | 0.942559i | \(0.391588\pi\) | |||||||
\(422\) | 26.7402 | 1.30169 | ||||||||
\(423\) | 4.30067 | 0.209106 | ||||||||
\(424\) | 10.0741 | 0.489241 | ||||||||
\(425\) | 30.1086 | 1.46048 | ||||||||
\(426\) | 9.35568 | 0.453284 | ||||||||
\(427\) | 11.5845 | 0.560612 | ||||||||
\(428\) | −17.5513 | −0.848376 | ||||||||
\(429\) | −2.30344 | −0.111211 | ||||||||
\(430\) | −5.46201 | −0.263402 | ||||||||
\(431\) | −32.6504 | −1.57271 | −0.786356 | − | 0.617773i | \(-0.788035\pi\) | ||||
−0.786356 | + | 0.617773i | \(0.788035\pi\) | |||||||
\(432\) | 5.22412 | 0.251345 | ||||||||
\(433\) | 13.3901 | 0.643489 | 0.321745 | − | 0.946827i | \(-0.395731\pi\) | ||||
0.321745 | + | 0.946827i | \(0.395731\pi\) | |||||||
\(434\) | −8.75746 | −0.420372 | ||||||||
\(435\) | 19.0060 | 0.911270 | ||||||||
\(436\) | −2.48069 | −0.118803 | ||||||||
\(437\) | −0.635916 | −0.0304200 | ||||||||
\(438\) | 2.38095 | 0.113766 | ||||||||
\(439\) | −24.4386 | −1.16639 | −0.583196 | − | 0.812332i | \(-0.698198\pi\) | ||||
−0.583196 | + | 0.812332i | \(0.698198\pi\) | |||||||
\(440\) | 8.68931 | 0.414246 | ||||||||
\(441\) | 10.4587 | 0.498032 | ||||||||
\(442\) | −5.64900 | −0.268695 | ||||||||
\(443\) | 17.5279 | 0.832775 | 0.416388 | − | 0.909187i | \(-0.363296\pi\) | ||||
0.416388 | + | 0.909187i | \(0.363296\pi\) | |||||||
\(444\) | −3.05147 | −0.144816 | ||||||||
\(445\) | 21.0097 | 0.995955 | ||||||||
\(446\) | −20.4191 | −0.966873 | ||||||||
\(447\) | 10.8713 | 0.514194 | ||||||||
\(448\) | −1.13392 | −0.0535725 | ||||||||
\(449\) | −20.4080 | −0.963112 | −0.481556 | − | 0.876415i | \(-0.659928\pi\) | ||||
−0.481556 | + | 0.876415i | \(0.659928\pi\) | |||||||
\(450\) | −7.13181 | −0.336197 | ||||||||
\(451\) | 7.84127 | 0.369231 | ||||||||
\(452\) | −11.6372 | −0.547368 | ||||||||
\(453\) | −13.5029 | −0.634422 | ||||||||
\(454\) | 4.05376 | 0.190252 | ||||||||
\(455\) | −2.47260 | −0.115917 | ||||||||
\(456\) | 2.47400 | 0.115855 | ||||||||
\(457\) | −2.60763 | −0.121980 | −0.0609898 | − | 0.998138i | \(-0.519426\pi\) | ||||
−0.0609898 | + | 0.998138i | \(0.519426\pi\) | |||||||
\(458\) | −18.0760 | −0.844638 | ||||||||
\(459\) | 40.3666 | 1.88415 | ||||||||
\(460\) | −0.829186 | −0.0386610 | ||||||||
\(461\) | 30.6105 | 1.42567 | 0.712837 | − | 0.701330i | \(-0.247410\pi\) | ||||
0.712837 | + | 0.701330i | \(0.247410\pi\) | |||||||
\(462\) | −3.57269 | −0.166216 | ||||||||
\(463\) | −10.9539 | −0.509073 | −0.254536 | − | 0.967063i | \(-0.581923\pi\) | ||||
−0.254536 | + | 0.967063i | \(0.581923\pi\) | |||||||
\(464\) | 5.89169 | 0.273515 | ||||||||
\(465\) | 24.9143 | 1.15537 | ||||||||
\(466\) | 26.7595 | 1.23961 | ||||||||
\(467\) | 31.9401 | 1.47801 | 0.739005 | − | 0.673700i | \(-0.235296\pi\) | ||||
0.739005 | + | 0.673700i | \(0.235296\pi\) | |||||||
\(468\) | 1.33808 | 0.0618526 | ||||||||
\(469\) | −7.28062 | −0.336188 | ||||||||
\(470\) | 7.00857 | 0.323281 | ||||||||
\(471\) | −5.93664 | −0.273546 | ||||||||
\(472\) | −4.81439 | −0.221600 | ||||||||
\(473\) | −5.33477 | −0.245293 | ||||||||
\(474\) | −8.36936 | −0.384417 | ||||||||
\(475\) | −8.91334 | −0.408972 | ||||||||
\(476\) | −8.76173 | −0.401593 | ||||||||
\(477\) | −18.4384 | −0.844238 | ||||||||
\(478\) | 9.24933 | 0.423055 | ||||||||
\(479\) | 3.95132 | 0.180540 | 0.0902702 | − | 0.995917i | \(-0.471227\pi\) | ||||
0.0902702 | + | 0.995917i | \(0.471227\pi\) | |||||||
\(480\) | 3.22590 | 0.147242 | ||||||||
\(481\) | −2.06268 | −0.0940499 | ||||||||
\(482\) | −2.15772 | −0.0982814 | ||||||||
\(483\) | 0.340927 | 0.0155127 | ||||||||
\(484\) | −2.51312 | −0.114233 | ||||||||
\(485\) | 32.5100 | 1.47620 | ||||||||
\(486\) | −15.5002 | −0.703102 | ||||||||
\(487\) | 2.21635 | 0.100432 | 0.0502161 | − | 0.998738i | \(-0.484009\pi\) | ||||
0.0502161 | + | 0.998738i | \(0.484009\pi\) | |||||||
\(488\) | −10.2163 | −0.462472 | ||||||||
\(489\) | 4.30327 | 0.194601 | ||||||||
\(490\) | 17.0439 | 0.769965 | ||||||||
\(491\) | −0.638437 | −0.0288123 | −0.0144061 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144061 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(492\) | 2.91107 | 0.131241 | ||||||||
\(493\) | 45.5249 | 2.05034 | ||||||||
\(494\) | 1.67233 | 0.0752415 | ||||||||
\(495\) | −15.9039 | −0.714827 | ||||||||
\(496\) | 7.72320 | 0.346782 | ||||||||
\(497\) | 9.80880 | 0.439985 | ||||||||
\(498\) | −6.19162 | −0.277453 | ||||||||
\(499\) | 1.84868 | 0.0827583 | 0.0413791 | − | 0.999144i | \(-0.486825\pi\) | ||||
0.0413791 | + | 0.999144i | \(0.486825\pi\) | |||||||
\(500\) | 3.29124 | 0.147189 | ||||||||
\(501\) | −22.5760 | −1.00862 | ||||||||
\(502\) | 22.0796 | 0.985462 | ||||||||
\(503\) | 14.9232 | 0.665392 | 0.332696 | − | 0.943034i | \(-0.392042\pi\) | ||||
0.332696 | + | 0.943034i | \(0.392042\pi\) | |||||||
\(504\) | 2.07539 | 0.0924451 | ||||||||
\(505\) | −23.4330 | −1.04276 | ||||||||
\(506\) | −0.809869 | −0.0360031 | ||||||||
\(507\) | 13.4819 | 0.598752 | ||||||||
\(508\) | −8.57468 | −0.380440 | ||||||||
\(509\) | −39.3398 | −1.74371 | −0.871854 | − | 0.489766i | \(-0.837082\pi\) | ||||
−0.871854 | + | 0.489766i | \(0.837082\pi\) | |||||||
\(510\) | 24.9264 | 1.10376 | ||||||||
\(511\) | 2.49626 | 0.110428 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.9501 | −0.527610 | ||||||||
\(514\) | 7.21757 | 0.318354 | ||||||||
\(515\) | −25.5909 | −1.12767 | ||||||||
\(516\) | −1.98053 | −0.0871880 | ||||||||
\(517\) | 6.84529 | 0.301056 | ||||||||
\(518\) | −3.19926 | −0.140567 | ||||||||
\(519\) | 3.48856 | 0.153131 | ||||||||
\(520\) | 2.18059 | 0.0956251 | ||||||||
\(521\) | −4.87042 | −0.213377 | −0.106688 | − | 0.994293i | \(-0.534025\pi\) | ||||
−0.106688 | + | 0.994293i | \(0.534025\pi\) | |||||||
\(522\) | −10.7835 | −0.471980 | ||||||||
\(523\) | 17.3383 | 0.758152 | 0.379076 | − | 0.925366i | \(-0.376242\pi\) | ||||
0.379076 | + | 0.925366i | \(0.376242\pi\) | |||||||
\(524\) | −12.4733 | −0.544898 | ||||||||
\(525\) | 4.77862 | 0.208556 | ||||||||
\(526\) | 15.3564 | 0.669572 | ||||||||
\(527\) | 59.6769 | 2.59957 | ||||||||
\(528\) | 3.15075 | 0.137119 | ||||||||
\(529\) | −22.9227 | −0.996640 | ||||||||
\(530\) | −30.0481 | −1.30521 | ||||||||
\(531\) | 8.81170 | 0.382395 | ||||||||
\(532\) | 2.59382 | 0.112456 | ||||||||
\(533\) | 1.96777 | 0.0852337 | ||||||||
\(534\) | 7.61814 | 0.329669 | ||||||||
\(535\) | 52.3506 | 2.26331 | ||||||||
\(536\) | 6.42078 | 0.277335 | ||||||||
\(537\) | 12.0589 | 0.520379 | ||||||||
\(538\) | −22.8657 | −0.985810 | ||||||||
\(539\) | 16.6468 | 0.717031 | ||||||||
\(540\) | −15.5820 | −0.670544 | ||||||||
\(541\) | −29.1340 | −1.25257 | −0.626283 | − | 0.779595i | \(-0.715425\pi\) | ||||
−0.626283 | + | 0.779595i | \(0.715425\pi\) | |||||||
\(542\) | −23.3920 | −1.00477 | ||||||||
\(543\) | −5.75811 | −0.247104 | ||||||||
\(544\) | 7.72696 | 0.331291 | ||||||||
\(545\) | 7.39917 | 0.316946 | ||||||||
\(546\) | −0.896569 | −0.0383696 | ||||||||
\(547\) | 28.2825 | 1.20927 | 0.604637 | − | 0.796501i | \(-0.293318\pi\) | ||||
0.604637 | + | 0.796501i | \(0.293318\pi\) | |||||||
\(548\) | −13.9245 | −0.594826 | ||||||||
\(549\) | 18.6988 | 0.798046 | ||||||||
\(550\) | −11.3516 | −0.484032 | ||||||||
\(551\) | −13.4772 | −0.574147 | ||||||||
\(552\) | −0.300664 | −0.0127971 | ||||||||
\(553\) | −8.77471 | −0.373139 | ||||||||
\(554\) | 30.4657 | 1.29436 | ||||||||
\(555\) | 9.10165 | 0.386343 | ||||||||
\(556\) | 8.26207 | 0.350390 | ||||||||
\(557\) | 40.8589 | 1.73125 | 0.865623 | − | 0.500696i | \(-0.166923\pi\) | ||||
0.865623 | + | 0.500696i | \(0.166923\pi\) | |||||||
\(558\) | −14.1357 | −0.598410 | ||||||||
\(559\) | −1.33876 | −0.0566237 | ||||||||
\(560\) | 3.38214 | 0.142922 | ||||||||
\(561\) | 24.3457 | 1.02788 | ||||||||
\(562\) | −3.16439 | −0.133482 | ||||||||
\(563\) | −32.1670 | −1.35568 | −0.677838 | − | 0.735211i | \(-0.737083\pi\) | ||||
−0.677838 | + | 0.735211i | \(0.737083\pi\) | |||||||
\(564\) | 2.54131 | 0.107009 | ||||||||
\(565\) | 34.7104 | 1.46028 | ||||||||
\(566\) | 22.7438 | 0.955995 | ||||||||
\(567\) | 0.180531 | 0.00758157 | ||||||||
\(568\) | −8.65038 | −0.362962 | ||||||||
\(569\) | −4.64164 | −0.194588 | −0.0972939 | − | 0.995256i | \(-0.531019\pi\) | ||||
−0.0972939 | + | 0.995256i | \(0.531019\pi\) | |||||||
\(570\) | −7.37921 | −0.309081 | ||||||||
\(571\) | −32.1457 | −1.34526 | −0.672628 | − | 0.739981i | \(-0.734835\pi\) | ||||
−0.672628 | + | 0.739981i | \(0.734835\pi\) | |||||||
\(572\) | 2.12979 | 0.0890509 | ||||||||
\(573\) | 19.5213 | 0.815514 | ||||||||
\(574\) | 3.05206 | 0.127391 | ||||||||
\(575\) | 1.08323 | 0.0451740 | ||||||||
\(576\) | −1.83028 | −0.0762618 | ||||||||
\(577\) | −27.9159 | −1.16215 | −0.581076 | − | 0.813849i | \(-0.697368\pi\) | ||||
−0.581076 | + | 0.813849i | \(0.697368\pi\) | |||||||
\(578\) | 42.7060 | 1.77633 | ||||||||
\(579\) | 25.6652 | 1.06661 | ||||||||
\(580\) | −17.5732 | −0.729688 | ||||||||
\(581\) | −6.49150 | −0.269313 | ||||||||
\(582\) | 11.7881 | 0.488635 | ||||||||
\(583\) | −29.3481 | −1.21547 | ||||||||
\(584\) | −2.20145 | −0.0910968 | ||||||||
\(585\) | −3.99109 | −0.165011 | ||||||||
\(586\) | 31.9816 | 1.32115 | ||||||||
\(587\) | −11.5842 | −0.478133 | −0.239066 | − | 0.971003i | \(-0.576841\pi\) | ||||
−0.239066 | + | 0.971003i | \(0.576841\pi\) | |||||||
\(588\) | 6.18014 | 0.254865 | ||||||||
\(589\) | −17.6667 | −0.727945 | ||||||||
\(590\) | 14.3599 | 0.591189 | ||||||||
\(591\) | −5.69044 | −0.234073 | ||||||||
\(592\) | 2.82143 | 0.115960 | ||||||||
\(593\) | 29.7714 | 1.22256 | 0.611282 | − | 0.791413i | \(-0.290654\pi\) | ||||
0.611282 | + | 0.791413i | \(0.290654\pi\) | |||||||
\(594\) | −15.2190 | −0.624444 | ||||||||
\(595\) | 26.1337 | 1.07138 | ||||||||
\(596\) | −10.0517 | −0.411734 | ||||||||
\(597\) | 9.09921 | 0.372406 | ||||||||
\(598\) | −0.203237 | −0.00831099 | ||||||||
\(599\) | −21.5261 | −0.879532 | −0.439766 | − | 0.898112i | \(-0.644939\pi\) | ||||
−0.439766 | + | 0.898112i | \(0.644939\pi\) | |||||||
\(600\) | −4.21427 | −0.172047 | ||||||||
\(601\) | 25.0311 | 1.02104 | 0.510520 | − | 0.859866i | \(-0.329453\pi\) | ||||
0.510520 | + | 0.859866i | \(0.329453\pi\) | |||||||
\(602\) | −2.07645 | −0.0846299 | ||||||||
\(603\) | −11.7518 | −0.478572 | ||||||||
\(604\) | 12.4850 | 0.508006 | ||||||||
\(605\) | 7.49592 | 0.304752 | ||||||||
\(606\) | −8.49684 | −0.345160 | ||||||||
\(607\) | −9.77988 | −0.396953 | −0.198476 | − | 0.980106i | \(-0.563599\pi\) | ||||
−0.198476 | + | 0.980106i | \(0.563599\pi\) | |||||||
\(608\) | −2.28749 | −0.0927699 | ||||||||
\(609\) | 7.22539 | 0.292788 | ||||||||
\(610\) | 30.4724 | 1.23379 | ||||||||
\(611\) | 1.71783 | 0.0694960 | ||||||||
\(612\) | −14.1425 | −0.571678 | ||||||||
\(613\) | −12.6469 | −0.510804 | −0.255402 | − | 0.966835i | \(-0.582208\pi\) | ||||
−0.255402 | + | 0.966835i | \(0.582208\pi\) | |||||||
\(614\) | −23.5117 | −0.948854 | ||||||||
\(615\) | −8.68288 | −0.350128 | ||||||||
\(616\) | 3.30335 | 0.133096 | ||||||||
\(617\) | 12.4909 | 0.502865 | 0.251433 | − | 0.967875i | \(-0.419098\pi\) | ||||
0.251433 | + | 0.967875i | \(0.419098\pi\) | |||||||
\(618\) | −9.27929 | −0.373268 | ||||||||
\(619\) | −2.13541 | −0.0858295 | −0.0429148 | − | 0.999079i | \(-0.513664\pi\) | ||||
−0.0429148 | + | 0.999079i | \(0.513664\pi\) | |||||||
\(620\) | −23.0361 | −0.925151 | ||||||||
\(621\) | 1.45229 | 0.0582784 | ||||||||
\(622\) | −17.2273 | −0.690754 | ||||||||
\(623\) | 7.98710 | 0.319997 | ||||||||
\(624\) | 0.790684 | 0.0316527 | ||||||||
\(625\) | −29.2996 | −1.17198 | ||||||||
\(626\) | −9.55032 | −0.381708 | ||||||||
\(627\) | −7.20730 | −0.287832 | ||||||||
\(628\) | 5.48909 | 0.219039 | ||||||||
\(629\) | 21.8010 | 0.869265 | ||||||||
\(630\) | −6.19028 | −0.246627 | ||||||||
\(631\) | −22.6430 | −0.901404 | −0.450702 | − | 0.892674i | \(-0.648826\pi\) | ||||
−0.450702 | + | 0.892674i | \(0.648826\pi\) | |||||||
\(632\) | 7.73841 | 0.307818 | ||||||||
\(633\) | −28.9205 | −1.14949 | ||||||||
\(634\) | −5.00960 | −0.198957 | ||||||||
\(635\) | 25.5758 | 1.01494 | ||||||||
\(636\) | −10.8955 | −0.432033 | ||||||||
\(637\) | 4.17754 | 0.165520 | ||||||||
\(638\) | −17.1638 | −0.679523 | ||||||||
\(639\) | 15.8326 | 0.626330 | ||||||||
\(640\) | −2.98271 | −0.117902 | ||||||||
\(641\) | 17.2774 | 0.682416 | 0.341208 | − | 0.939988i | \(-0.389164\pi\) | ||||
0.341208 | + | 0.939988i | \(0.389164\pi\) | |||||||
\(642\) | 18.9824 | 0.749174 | ||||||||
\(643\) | −36.5920 | −1.44305 | −0.721523 | − | 0.692390i | \(-0.756558\pi\) | ||||
−0.721523 | + | 0.692390i | \(0.756558\pi\) | |||||||
\(644\) | −0.315226 | −0.0124216 | ||||||||
\(645\) | 5.90735 | 0.232602 | ||||||||
\(646\) | −17.6753 | −0.695426 | ||||||||
\(647\) | −9.12560 | −0.358764 | −0.179382 | − | 0.983779i | \(-0.557410\pi\) | ||||
−0.179382 | + | 0.983779i | \(0.557410\pi\) | |||||||
\(648\) | −0.159210 | −0.00625436 | ||||||||
\(649\) | 14.0254 | 0.550545 | ||||||||
\(650\) | −2.84868 | −0.111735 | ||||||||
\(651\) | 9.47150 | 0.371217 | ||||||||
\(652\) | −3.97886 | −0.155824 | ||||||||
\(653\) | −39.8566 | −1.55971 | −0.779855 | − | 0.625960i | \(-0.784707\pi\) | ||||
−0.779855 | + | 0.625960i | \(0.784707\pi\) | |||||||
\(654\) | 2.68295 | 0.104912 | ||||||||
\(655\) | 37.2042 | 1.45369 | ||||||||
\(656\) | −2.69161 | −0.105090 | ||||||||
\(657\) | 4.02929 | 0.157197 | ||||||||
\(658\) | 2.66440 | 0.103869 | ||||||||
\(659\) | 22.3262 | 0.869705 | 0.434852 | − | 0.900502i | \(-0.356801\pi\) | ||||
0.434852 | + | 0.900502i | \(0.356801\pi\) | |||||||
\(660\) | −9.39778 | −0.365808 | ||||||||
\(661\) | −28.2513 | −1.09885 | −0.549423 | − | 0.835544i | \(-0.685153\pi\) | ||||
−0.549423 | + | 0.835544i | \(0.685153\pi\) | |||||||
\(662\) | 12.8684 | 0.500145 | ||||||||
\(663\) | 6.10958 | 0.237277 | ||||||||
\(664\) | 5.72485 | 0.222167 | ||||||||
\(665\) | −7.73661 | −0.300013 | ||||||||
\(666\) | −5.16401 | −0.200101 | ||||||||
\(667\) | 1.63788 | 0.0634188 | ||||||||
\(668\) | 20.8740 | 0.807640 | ||||||||
\(669\) | 22.0840 | 0.853815 | ||||||||
\(670\) | −19.1513 | −0.739880 | ||||||||
\(671\) | 29.7625 | 1.14897 | ||||||||
\(672\) | 1.22637 | 0.0473082 | ||||||||
\(673\) | −43.1383 | −1.66286 | −0.831429 | − | 0.555631i | \(-0.812477\pi\) | ||||
−0.831429 | + | 0.555631i | \(0.812477\pi\) | |||||||
\(674\) | −7.29248 | −0.280896 | ||||||||
\(675\) | 20.3561 | 0.783507 | ||||||||
\(676\) | −12.4655 | −0.479443 | ||||||||
\(677\) | −13.9912 | −0.537726 | −0.268863 | − | 0.963178i | \(-0.586648\pi\) | ||||
−0.268863 | + | 0.963178i | \(0.586648\pi\) | |||||||
\(678\) | 12.5860 | 0.483364 | ||||||||
\(679\) | 12.3591 | 0.474298 | ||||||||
\(680\) | −23.0473 | −0.883823 | ||||||||
\(681\) | −4.38428 | −0.168006 | ||||||||
\(682\) | −22.4994 | −0.861548 | ||||||||
\(683\) | 37.9890 | 1.45361 | 0.726805 | − | 0.686844i | \(-0.241005\pi\) | ||||
0.726805 | + | 0.686844i | \(0.241005\pi\) | |||||||
\(684\) | 4.18675 | 0.160084 | ||||||||
\(685\) | 41.5328 | 1.58689 | ||||||||
\(686\) | 14.4169 | 0.550439 | ||||||||
\(687\) | 19.5499 | 0.745874 | ||||||||
\(688\) | 1.83122 | 0.0698147 | ||||||||
\(689\) | −7.36492 | −0.280581 | ||||||||
\(690\) | 0.896793 | 0.0341403 | ||||||||
\(691\) | −37.6898 | −1.43379 | −0.716894 | − | 0.697182i | \(-0.754437\pi\) | ||||
−0.716894 | + | 0.697182i | \(0.754437\pi\) | |||||||
\(692\) | −3.22557 | −0.122618 | ||||||||
\(693\) | −6.04607 | −0.229671 | ||||||||
\(694\) | 14.7381 | 0.559452 | ||||||||
\(695\) | −24.6434 | −0.934776 | ||||||||
\(696\) | −6.37207 | −0.241533 | ||||||||
\(697\) | −20.7980 | −0.787780 | ||||||||
\(698\) | −25.4287 | −0.962490 | ||||||||
\(699\) | −28.9413 | −1.09466 | ||||||||
\(700\) | −4.41837 | −0.166999 | ||||||||
\(701\) | 13.6542 | 0.515714 | 0.257857 | − | 0.966183i | \(-0.416984\pi\) | ||||
0.257857 | + | 0.966183i | \(0.416984\pi\) | |||||||
\(702\) | −3.81923 | −0.144147 | ||||||||
\(703\) | −6.45397 | −0.243416 | ||||||||
\(704\) | −2.91322 | −0.109796 | ||||||||
\(705\) | −7.58001 | −0.285480 | ||||||||
\(706\) | −6.78268 | −0.255269 | ||||||||
\(707\) | −8.90836 | −0.335034 | ||||||||
\(708\) | 5.20693 | 0.195688 | ||||||||
\(709\) | 3.21091 | 0.120588 | 0.0602942 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602942 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(710\) | 25.8016 | 0.968316 | ||||||||
\(711\) | −14.1635 | −0.531172 | ||||||||
\(712\) | −7.04382 | −0.263978 | ||||||||
\(713\) | 2.14703 | 0.0804069 | ||||||||
\(714\) | 9.47611 | 0.354634 | ||||||||
\(715\) | −6.35254 | −0.237572 | ||||||||
\(716\) | −11.1498 | −0.416687 | ||||||||
\(717\) | −10.0035 | −0.373586 | ||||||||
\(718\) | −30.4679 | −1.13705 | ||||||||
\(719\) | 27.2625 | 1.01672 | 0.508359 | − | 0.861145i | \(-0.330252\pi\) | ||||
0.508359 | + | 0.861145i | \(0.330252\pi\) | |||||||
\(720\) | 5.45921 | 0.203453 | ||||||||
\(721\) | −9.72871 | −0.362316 | ||||||||
\(722\) | −13.7674 | −0.512370 | ||||||||
\(723\) | 2.33365 | 0.0867893 | ||||||||
\(724\) | 5.32402 | 0.197866 | ||||||||
\(725\) | 22.9574 | 0.852615 | ||||||||
\(726\) | 2.71803 | 0.100875 | ||||||||
\(727\) | 6.03486 | 0.223821 | 0.111910 | − | 0.993718i | \(-0.464303\pi\) | ||||
0.111910 | + | 0.993718i | \(0.464303\pi\) | |||||||
\(728\) | 0.828979 | 0.0307240 | ||||||||
\(729\) | 17.2416 | 0.638577 | ||||||||
\(730\) | 6.56630 | 0.243030 | ||||||||
\(731\) | 14.1498 | 0.523349 | ||||||||
\(732\) | 11.0493 | 0.408395 | ||||||||
\(733\) | −46.7308 | −1.72604 | −0.863020 | − | 0.505170i | \(-0.831430\pi\) | ||||
−0.863020 | + | 0.505170i | \(0.831430\pi\) | |||||||
\(734\) | 24.6983 | 0.911630 | ||||||||
\(735\) | −18.4336 | −0.679932 | ||||||||
\(736\) | 0.277997 | 0.0102471 | ||||||||
\(737\) | −18.7052 | −0.689013 | ||||||||
\(738\) | 4.92641 | 0.181344 | ||||||||
\(739\) | 1.82661 | 0.0671928 | 0.0335964 | − | 0.999435i | \(-0.489304\pi\) | ||||
0.0335964 | + | 0.999435i | \(0.489304\pi\) | |||||||
\(740\) | −8.41549 | −0.309360 | ||||||||
\(741\) | −1.80868 | −0.0664435 | ||||||||
\(742\) | −11.4232 | −0.419358 | ||||||||
\(743\) | −18.5274 | −0.679703 | −0.339852 | − | 0.940479i | \(-0.610377\pi\) | ||||
−0.339852 | + | 0.940479i | \(0.610377\pi\) | |||||||
\(744\) | −8.35291 | −0.306232 | ||||||||
\(745\) | 29.9814 | 1.09843 | ||||||||
\(746\) | −10.4154 | −0.381335 | ||||||||
\(747\) | −10.4781 | −0.383374 | ||||||||
\(748\) | −22.5104 | −0.823061 | ||||||||
\(749\) | 19.9017 | 0.727194 | ||||||||
\(750\) | −3.55958 | −0.129978 | ||||||||
\(751\) | −34.9022 | −1.27360 | −0.636799 | − | 0.771030i | \(-0.719742\pi\) | ||||
−0.636799 | + | 0.771030i | \(0.719742\pi\) | |||||||
\(752\) | −2.34973 | −0.0856859 | ||||||||
\(753\) | −23.8799 | −0.870231 | ||||||||
\(754\) | −4.30728 | −0.156862 | ||||||||
\(755\) | −37.2390 | −1.35527 | ||||||||
\(756\) | −5.92371 | −0.215443 | ||||||||
\(757\) | −51.3967 | −1.86805 | −0.934023 | − | 0.357214i | \(-0.883727\pi\) | ||||
−0.934023 | + | 0.357214i | \(0.883727\pi\) | |||||||
\(758\) | −21.4886 | −0.780500 | ||||||||
\(759\) | 0.875901 | 0.0317932 | ||||||||
\(760\) | 6.82291 | 0.247493 | ||||||||
\(761\) | 38.7851 | 1.40596 | 0.702980 | − | 0.711210i | \(-0.251852\pi\) | ||||
0.702980 | + | 0.711210i | \(0.251852\pi\) | |||||||
\(762\) | 9.27381 | 0.335955 | ||||||||
\(763\) | 2.81289 | 0.101834 | ||||||||
\(764\) | −18.0496 | −0.653013 | ||||||||
\(765\) | 42.1831 | 1.52513 | ||||||||
\(766\) | −18.9808 | −0.685806 | ||||||||
\(767\) | 3.51968 | 0.127088 | ||||||||
\(768\) | −1.08153 | −0.0390265 | ||||||||
\(769\) | −16.1838 | −0.583604 | −0.291802 | − | 0.956479i | \(-0.594255\pi\) | ||||
−0.291802 | + | 0.956479i | \(0.594255\pi\) | |||||||
\(770\) | −9.85294 | −0.355075 | ||||||||
\(771\) | −7.80605 | −0.281128 | ||||||||
\(772\) | −23.7304 | −0.854075 | ||||||||
\(773\) | −24.5627 | −0.883459 | −0.441729 | − | 0.897148i | \(-0.645635\pi\) | ||||
−0.441729 | + | 0.897148i | \(0.645635\pi\) | |||||||
\(774\) | −3.35166 | −0.120473 | ||||||||
\(775\) | 30.0939 | 1.08101 | ||||||||
\(776\) | −10.8995 | −0.391268 | ||||||||
\(777\) | 3.46011 | 0.124131 | ||||||||
\(778\) | 1.81540 | 0.0650852 | ||||||||
\(779\) | 6.15703 | 0.220598 | ||||||||
\(780\) | −2.35838 | −0.0844436 | ||||||||
\(781\) | 25.2005 | 0.901745 | ||||||||
\(782\) | 2.14808 | 0.0768150 | ||||||||
\(783\) | 30.7789 | 1.09995 | ||||||||
\(784\) | −5.71423 | −0.204080 | ||||||||
\(785\) | −16.3724 | −0.584355 | ||||||||
\(786\) | 13.4903 | 0.481182 | ||||||||
\(787\) | 37.8219 | 1.34821 | 0.674103 | − | 0.738637i | \(-0.264530\pi\) | ||||
0.674103 | + | 0.738637i | \(0.264530\pi\) | |||||||
\(788\) | 5.26145 | 0.187432 | ||||||||
\(789\) | −16.6085 | −0.591278 | ||||||||
\(790\) | −23.0814 | −0.821201 | ||||||||
\(791\) | 13.1956 | 0.469182 | ||||||||
\(792\) | 5.33203 | 0.189465 | ||||||||
\(793\) | 7.46893 | 0.265229 | ||||||||
\(794\) | 7.94724 | 0.282037 | ||||||||
\(795\) | 32.4980 | 1.15259 | ||||||||
\(796\) | −8.41324 | −0.298199 | ||||||||
\(797\) | −2.13168 | −0.0755081 | −0.0377540 | − | 0.999287i | \(-0.512020\pi\) | ||||
−0.0377540 | + | 0.999287i | \(0.512020\pi\) | |||||||
\(798\) | −2.80530 | −0.0993067 | ||||||||
\(799\) | −18.1563 | −0.642323 | ||||||||
\(800\) | 3.89656 | 0.137764 | ||||||||
\(801\) | 12.8922 | 0.455523 | ||||||||
\(802\) | −25.5334 | −0.901615 | ||||||||
\(803\) | 6.41333 | 0.226322 | ||||||||
\(804\) | −6.94429 | −0.244906 | ||||||||
\(805\) | 0.940227 | 0.0331386 | ||||||||
\(806\) | −5.64625 | −0.198881 | ||||||||
\(807\) | 24.7300 | 0.870538 | ||||||||
\(808\) | 7.85628 | 0.276383 | ||||||||
\(809\) | −15.6387 | −0.549826 | −0.274913 | − | 0.961469i | \(-0.588649\pi\) | ||||
−0.274913 | + | 0.961469i | \(0.588649\pi\) | |||||||
\(810\) | 0.474877 | 0.0166855 | ||||||||
\(811\) | 37.2490 | 1.30799 | 0.653995 | − | 0.756499i | \(-0.273092\pi\) | ||||
0.653995 | + | 0.756499i | \(0.273092\pi\) | |||||||
\(812\) | −6.68069 | −0.234446 | ||||||||
\(813\) | 25.2993 | 0.887284 | ||||||||
\(814\) | −8.21945 | −0.288091 | ||||||||
\(815\) | 11.8678 | 0.415711 | ||||||||
\(816\) | −8.35697 | −0.292553 | ||||||||
\(817\) | −4.18890 | −0.146551 | ||||||||
\(818\) | 9.59658 | 0.335536 | ||||||||
\(819\) | −1.51727 | −0.0530176 | ||||||||
\(820\) | 8.02830 | 0.280360 | ||||||||
\(821\) | −36.3634 | −1.26909 | −0.634546 | − | 0.772885i | \(-0.718813\pi\) | ||||
−0.634546 | + | 0.772885i | \(0.718813\pi\) | |||||||
\(822\) | 15.0598 | 0.525273 | ||||||||
\(823\) | 13.0658 | 0.455447 | 0.227723 | − | 0.973726i | \(-0.426872\pi\) | ||||
0.227723 | + | 0.973726i | \(0.426872\pi\) | |||||||
\(824\) | 8.57974 | 0.298890 | ||||||||
\(825\) | 12.2771 | 0.427434 | ||||||||
\(826\) | 5.45911 | 0.189947 | ||||||||
\(827\) | −18.3079 | −0.636628 | −0.318314 | − | 0.947985i | \(-0.603117\pi\) | ||||
−0.318314 | + | 0.947985i | \(0.603117\pi\) | |||||||
\(828\) | −0.508814 | −0.0176825 | ||||||||
\(829\) | −51.4908 | −1.78835 | −0.894174 | − | 0.447719i | \(-0.852236\pi\) | ||||
−0.894174 | + | 0.447719i | \(0.852236\pi\) | |||||||
\(830\) | −17.0756 | −0.592702 | ||||||||
\(831\) | −32.9497 | −1.14301 | ||||||||
\(832\) | −0.731076 | −0.0253455 | ||||||||
\(833\) | −44.1537 | −1.52983 | ||||||||
\(834\) | −8.93572 | −0.309419 | ||||||||
\(835\) | −62.2611 | −2.15464 | ||||||||
\(836\) | 6.66396 | 0.230478 | ||||||||
\(837\) | 40.3469 | 1.39459 | ||||||||
\(838\) | −14.0049 | −0.483791 | ||||||||
\(839\) | 11.6875 | 0.403497 | 0.201748 | − | 0.979437i | \(-0.435338\pi\) | ||||
0.201748 | + | 0.979437i | \(0.435338\pi\) | |||||||
\(840\) | −3.65790 | −0.126210 | ||||||||
\(841\) | 5.71207 | 0.196968 | ||||||||
\(842\) | 13.7078 | 0.472403 | ||||||||
\(843\) | 3.42239 | 0.117874 | ||||||||
\(844\) | 26.7402 | 0.920437 | ||||||||
\(845\) | 37.1811 | 1.27907 | ||||||||
\(846\) | 4.30067 | 0.147860 | ||||||||
\(847\) | 2.84967 | 0.0979158 | ||||||||
\(848\) | 10.0741 | 0.345946 | ||||||||
\(849\) | −24.5982 | −0.844209 | ||||||||
\(850\) | 30.1086 | 1.03272 | ||||||||
\(851\) | 0.784349 | 0.0268871 | ||||||||
\(852\) | 9.35568 | 0.320520 | ||||||||
\(853\) | 2.33987 | 0.0801156 | 0.0400578 | − | 0.999197i | \(-0.487246\pi\) | ||||
0.0400578 | + | 0.999197i | \(0.487246\pi\) | |||||||
\(854\) | 11.5845 | 0.396413 | ||||||||
\(855\) | −12.4879 | −0.427076 | ||||||||
\(856\) | −17.5513 | −0.599892 | ||||||||
\(857\) | 11.8398 | 0.404441 | 0.202221 | − | 0.979340i | \(-0.435184\pi\) | ||||
0.202221 | + | 0.979340i | \(0.435184\pi\) | |||||||
\(858\) | −2.30344 | −0.0786381 | ||||||||
\(859\) | 42.6766 | 1.45611 | 0.728053 | − | 0.685521i | \(-0.240426\pi\) | ||||
0.728053 | + | 0.685521i | \(0.240426\pi\) | |||||||
\(860\) | −5.46201 | −0.186253 | ||||||||
\(861\) | −3.30091 | −0.112495 | ||||||||
\(862\) | −32.6504 | −1.11208 | ||||||||
\(863\) | −3.29402 | −0.112130 | −0.0560649 | − | 0.998427i | \(-0.517855\pi\) | ||||
−0.0560649 | + | 0.998427i | \(0.517855\pi\) | |||||||
\(864\) | 5.22412 | 0.177728 | ||||||||
\(865\) | 9.62094 | 0.327122 | ||||||||
\(866\) | 13.3901 | 0.455016 | ||||||||
\(867\) | −46.1879 | −1.56862 | ||||||||
\(868\) | −8.75746 | −0.297248 | ||||||||
\(869\) | −22.5437 | −0.764744 | ||||||||
\(870\) | 19.0060 | 0.644365 | ||||||||
\(871\) | −4.69407 | −0.159053 | ||||||||
\(872\) | −2.48069 | −0.0840067 | ||||||||
\(873\) | 19.9491 | 0.675176 | ||||||||
\(874\) | −0.635916 | −0.0215102 | ||||||||
\(875\) | −3.73198 | −0.126164 | ||||||||
\(876\) | 2.38095 | 0.0804448 | ||||||||
\(877\) | −52.5111 | −1.77317 | −0.886587 | − | 0.462562i | \(-0.846930\pi\) | ||||
−0.886587 | + | 0.462562i | \(0.846930\pi\) | |||||||
\(878\) | −24.4386 | −0.824763 | ||||||||
\(879\) | −34.5892 | −1.16666 | ||||||||
\(880\) | 8.68931 | 0.292916 | ||||||||
\(881\) | 29.9596 | 1.00936 | 0.504682 | − | 0.863305i | \(-0.331610\pi\) | ||||
0.504682 | + | 0.863305i | \(0.331610\pi\) | |||||||
\(882\) | 10.4587 | 0.352162 | ||||||||
\(883\) | −26.0284 | −0.875926 | −0.437963 | − | 0.898993i | \(-0.644300\pi\) | ||||
−0.437963 | + | 0.898993i | \(0.644300\pi\) | |||||||
\(884\) | −5.64900 | −0.189996 | ||||||||
\(885\) | −15.5308 | −0.522060 | ||||||||
\(886\) | 17.5279 | 0.588861 | ||||||||
\(887\) | −49.5212 | −1.66276 | −0.831379 | − | 0.555706i | \(-0.812448\pi\) | ||||
−0.831379 | + | 0.555706i | \(0.812448\pi\) | |||||||
\(888\) | −3.05147 | −0.102401 | ||||||||
\(889\) | 9.72297 | 0.326098 | ||||||||
\(890\) | 21.0097 | 0.704246 | ||||||||
\(891\) | 0.463814 | 0.0155384 | ||||||||
\(892\) | −20.4191 | −0.683682 | ||||||||
\(893\) | 5.37498 | 0.179867 | ||||||||
\(894\) | 10.8713 | 0.363590 | ||||||||
\(895\) | 33.2566 | 1.11165 | ||||||||
\(896\) | −1.13392 | −0.0378815 | ||||||||
\(897\) | 0.219808 | 0.00733917 | ||||||||
\(898\) | −20.4080 | −0.681023 | ||||||||
\(899\) | 45.5028 | 1.51760 | ||||||||
\(900\) | −7.13181 | −0.237727 | ||||||||
\(901\) | 77.8421 | 2.59330 | ||||||||
\(902\) | 7.84127 | 0.261086 | ||||||||
\(903\) | 2.24576 | 0.0747341 | ||||||||
\(904\) | −11.6372 | −0.387048 | ||||||||
\(905\) | −15.8800 | −0.527870 | ||||||||
\(906\) | −13.5029 | −0.448604 | ||||||||
\(907\) | −32.4478 | −1.07741 | −0.538706 | − | 0.842494i | \(-0.681086\pi\) | ||||
−0.538706 | + | 0.842494i | \(0.681086\pi\) | |||||||
\(908\) | 4.05376 | 0.134529 | ||||||||
\(909\) | −14.3792 | −0.476929 | ||||||||
\(910\) | −2.47260 | −0.0819660 | ||||||||
\(911\) | 52.1417 | 1.72753 | 0.863765 | − | 0.503894i | \(-0.168100\pi\) | ||||
0.863765 | + | 0.503894i | \(0.168100\pi\) | |||||||
\(912\) | 2.47400 | 0.0819222 | ||||||||
\(913\) | −16.6778 | −0.551954 | ||||||||
\(914\) | −2.60763 | −0.0862526 | ||||||||
\(915\) | −32.9570 | −1.08952 | ||||||||
\(916\) | −18.0760 | −0.597249 | ||||||||
\(917\) | 14.1437 | 0.467065 | ||||||||
\(918\) | 40.3666 | 1.33229 | ||||||||
\(919\) | −26.4609 | −0.872865 | −0.436433 | − | 0.899737i | \(-0.643758\pi\) | ||||
−0.436433 | + | 0.899737i | \(0.643758\pi\) | |||||||
\(920\) | −0.829186 | −0.0273374 | ||||||||
\(921\) | 25.4287 | 0.837904 | ||||||||
\(922\) | 30.6105 | 1.00810 | ||||||||
\(923\) | 6.32408 | 0.208160 | ||||||||
\(924\) | −3.57269 | −0.117533 | ||||||||
\(925\) | 10.9939 | 0.361476 | ||||||||
\(926\) | −10.9539 | −0.359969 | ||||||||
\(927\) | −15.7034 | −0.515766 | ||||||||
\(928\) | 5.89169 | 0.193404 | ||||||||
\(929\) | 51.5944 | 1.69276 | 0.846379 | − | 0.532581i | \(-0.178778\pi\) | ||||
0.846379 | + | 0.532581i | \(0.178778\pi\) | |||||||
\(930\) | 24.9143 | 0.816972 | ||||||||
\(931\) | 13.0712 | 0.428393 | ||||||||
\(932\) | 26.7595 | 0.876536 | ||||||||
\(933\) | 18.6320 | 0.609983 | ||||||||
\(934\) | 31.9401 | 1.04511 | ||||||||
\(935\) | 67.1419 | 2.19578 | ||||||||
\(936\) | 1.33808 | 0.0437364 | ||||||||
\(937\) | −31.7036 | −1.03571 | −0.517855 | − | 0.855468i | \(-0.673269\pi\) | ||||
−0.517855 | + | 0.855468i | \(0.673269\pi\) | |||||||
\(938\) | −7.28062 | −0.237721 | ||||||||
\(939\) | 10.3290 | 0.337074 | ||||||||
\(940\) | 7.00857 | 0.228594 | ||||||||
\(941\) | −8.22125 | −0.268005 | −0.134003 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134003 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(942\) | −5.93664 | −0.193426 | ||||||||
\(943\) | −0.748261 | −0.0243667 | ||||||||
\(944\) | −4.81439 | −0.156695 | ||||||||
\(945\) | 17.6687 | 0.574763 | ||||||||
\(946\) | −5.33477 | −0.173448 | ||||||||
\(947\) | −19.8767 | −0.645906 | −0.322953 | − | 0.946415i | \(-0.604676\pi\) | ||||
−0.322953 | + | 0.946415i | \(0.604676\pi\) | |||||||
\(948\) | −8.36936 | −0.271824 | ||||||||
\(949\) | 1.60943 | 0.0522443 | ||||||||
\(950\) | −8.91334 | −0.289187 | ||||||||
\(951\) | 5.41806 | 0.175693 | ||||||||
\(952\) | −8.76173 | −0.283969 | ||||||||
\(953\) | −7.75630 | −0.251251 | −0.125626 | − | 0.992078i | \(-0.540094\pi\) | ||||
−0.125626 | + | 0.992078i | \(0.540094\pi\) | |||||||
\(954\) | −18.4384 | −0.596966 | ||||||||
\(955\) | 53.8369 | 1.74212 | ||||||||
\(956\) | 9.24933 | 0.299145 | ||||||||
\(957\) | 18.5633 | 0.600065 | ||||||||
\(958\) | 3.95132 | 0.127661 | ||||||||
\(959\) | 15.7892 | 0.509861 | ||||||||
\(960\) | 3.22590 | 0.104116 | ||||||||
\(961\) | 28.6479 | 0.924125 | ||||||||
\(962\) | −2.06268 | −0.0665033 | ||||||||
\(963\) | 32.1239 | 1.03518 | ||||||||
\(964\) | −2.15772 | −0.0694954 | ||||||||
\(965\) | 70.7809 | 2.27852 | ||||||||
\(966\) | 0.340927 | 0.0109692 | ||||||||
\(967\) | −8.03035 | −0.258239 | −0.129119 | − | 0.991629i | \(-0.541215\pi\) | ||||
−0.129119 | + | 0.991629i | \(0.541215\pi\) | |||||||
\(968\) | −2.51312 | −0.0807748 | ||||||||
\(969\) | 19.1165 | 0.614110 | ||||||||
\(970\) | 32.5100 | 1.04383 | ||||||||
\(971\) | 30.6975 | 0.985130 | 0.492565 | − | 0.870276i | \(-0.336059\pi\) | ||||
0.492565 | + | 0.870276i | \(0.336059\pi\) | |||||||
\(972\) | −15.5002 | −0.497168 | ||||||||
\(973\) | −9.36850 | −0.300340 | ||||||||
\(974\) | 2.21635 | 0.0710163 | ||||||||
\(975\) | 3.08095 | 0.0986693 | ||||||||
\(976\) | −10.2163 | −0.327017 | ||||||||
\(977\) | 3.99588 | 0.127840 | 0.0639198 | − | 0.997955i | \(-0.479640\pi\) | ||||
0.0639198 | + | 0.997955i | \(0.479640\pi\) | |||||||
\(978\) | 4.30327 | 0.137604 | ||||||||
\(979\) | 20.5202 | 0.655830 | ||||||||
\(980\) | 17.0439 | 0.544448 | ||||||||
\(981\) | 4.54036 | 0.144963 | ||||||||
\(982\) | −0.638437 | −0.0203734 | ||||||||
\(983\) | −14.6984 | −0.468806 | −0.234403 | − | 0.972140i | \(-0.575314\pi\) | ||||
−0.234403 | + | 0.972140i | \(0.575314\pi\) | |||||||
\(984\) | 2.91107 | 0.0928016 | ||||||||
\(985\) | −15.6934 | −0.500033 | ||||||||
\(986\) | 45.5249 | 1.44981 | ||||||||
\(987\) | −2.88164 | −0.0917235 | ||||||||
\(988\) | 1.67233 | 0.0532038 | ||||||||
\(989\) | 0.509075 | 0.0161877 | ||||||||
\(990\) | −15.9039 | −0.505459 | ||||||||
\(991\) | 20.5451 | 0.652636 | 0.326318 | − | 0.945260i | \(-0.394192\pi\) | ||||
0.326318 | + | 0.945260i | \(0.394192\pi\) | |||||||
\(992\) | 7.72320 | 0.245212 | ||||||||
\(993\) | −13.9176 | −0.441663 | ||||||||
\(994\) | 9.80880 | 0.311116 | ||||||||
\(995\) | 25.0943 | 0.795541 | ||||||||
\(996\) | −6.19162 | −0.196189 | ||||||||
\(997\) | 61.2662 | 1.94032 | 0.970160 | − | 0.242464i | \(-0.0779557\pi\) | ||||
0.970160 | + | 0.242464i | \(0.0779557\pi\) | |||||||
\(998\) | 1.84868 | 0.0585189 | ||||||||
\(999\) | 14.7395 | 0.466336 |
(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 | 8042.2.a.a.1.26 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.26 | ✓ | 67 | 1.1 | even | 1 | trivial |