Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(190,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.190");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.f (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1156923.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 190.3 | ||
Root | \(0.500000 - 1.51496i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.190 |
Dual form | 567.2.f.l.379.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33454 | + | 2.31149i | 0.943662 | + | 1.63447i | 0.758408 | + | 0.651780i | \(0.225977\pi\) |
0.185254 | + | 0.982691i | \(0.440689\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.56199 | + | 4.43750i | −1.28100 | + | 2.21875i | ||||
\(5\) | −0.727452 | + | 1.25998i | −0.325326 | + | 0.563482i | −0.981578 | − | 0.191060i | \(-0.938808\pi\) |
0.656252 | + | 0.754542i | \(0.272141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | −8.33816 | −2.94798 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.88325 | −1.22799 | ||||||||
\(11\) | −0.772548 | − | 1.33809i | −0.232932 | − | 0.403450i | 0.725738 | − | 0.687972i | \(-0.241499\pi\) |
−0.958670 | + | 0.284522i | \(0.908165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.94163 | + | 5.09505i | −0.815861 | + | 1.41311i | 0.0928478 | + | 0.995680i | \(0.470403\pi\) |
−0.908708 | + | 0.417432i | \(0.862930\pi\) | |||||||
\(14\) | 1.33454 | − | 2.31149i | 0.356671 | − | 0.617772i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.00362 | − | 10.3986i | −1.50090 | − | 2.59964i | ||||
\(17\) | 6.79306 | 1.64756 | 0.823780 | − | 0.566910i | \(-0.191861\pi\) | ||||
0.823780 | + | 0.566910i | \(0.191861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.24797 | −1.43338 | −0.716691 | − | 0.697391i | \(-0.754344\pi\) | ||||
−0.716691 | + | 0.697391i | \(0.754344\pi\) | |||||||
\(20\) | −3.72745 | − | 6.45614i | −0.833484 | − | 1.44364i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.06199 | − | 3.57147i | 0.439618 | − | 0.761441i | ||||
\(23\) | 1.45490 | − | 2.51997i | 0.303368 | − | 0.525450i | −0.673528 | − | 0.739161i | \(-0.735222\pi\) |
0.976897 | + | 0.213712i | \(0.0685554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.44163 | + | 2.49697i | 0.288325 | + | 0.499394i | ||||
\(26\) | −15.7029 | −3.07959 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.12398 | 0.968342 | ||||||||
\(29\) | 1.94163 | + | 3.36300i | 0.360551 | + | 0.624493i | 0.988052 | − | 0.154123i | \(-0.0492553\pi\) |
−0.627501 | + | 0.778616i | \(0.715922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 1.73205i | −0.179605 | + | 0.311086i | −0.941745 | − | 0.336327i | \(-0.890815\pi\) |
0.762140 | + | 0.647412i | \(0.224149\pi\) | |||||||
\(32\) | 7.68597 | − | 13.3125i | 1.35870 | − | 2.35334i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.06561 | + | 15.7021i | 1.55474 | + | 2.69289i | ||||
\(35\) | 1.45490 | 0.245924 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | −8.33816 | − | 14.4421i | −1.35263 | − | 2.34282i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.06561 | − | 10.5059i | 0.959057 | − | 1.66114i | ||||
\(41\) | −1.12398 | + | 1.94680i | −0.175537 | + | 0.304038i | −0.940347 | − | 0.340217i | \(-0.889499\pi\) |
0.764810 | + | 0.644256i | \(0.222833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.56561 | + | 6.17582i | 0.543750 | + | 0.941803i | 0.998684 | + | 0.0512782i | \(0.0163295\pi\) |
−0.454934 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(44\) | 7.91705 | 1.19354 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.76651 | 1.14511 | ||||||||
\(47\) | −2.66908 | − | 4.62298i | −0.389325 | − | 0.674331i | 0.603034 | − | 0.797716i | \(-0.293958\pi\) |
−0.992359 | + | 0.123385i | \(0.960625\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −3.84782 | + | 6.66461i | −0.544163 | + | 0.942519i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.0728 | − | 26.1069i | −2.09023 | − | 3.62038i | ||||
\(53\) | 9.79306 | 1.34518 | 0.672590 | − | 0.740015i | \(-0.265182\pi\) | ||||
0.672590 | + | 0.740015i | \(0.265182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24797 | 0.303116 | ||||||||
\(56\) | 4.16908 | + | 7.22106i | 0.557117 | + | 0.964954i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.18236 | + | 8.97610i | −0.680477 | + | 1.17862i | ||||
\(59\) | −2.33816 | + | 4.04981i | −0.304402 | + | 0.527240i | −0.977128 | − | 0.212652i | \(-0.931790\pi\) |
0.672726 | + | 0.739892i | \(0.265123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18236 | + | 2.04790i | 0.151385 | + | 0.262207i | 0.931737 | − | 0.363134i | \(-0.118293\pi\) |
−0.780352 | + | 0.625341i | \(0.784960\pi\) | |||||||
\(62\) | −5.33816 | −0.677947 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 17.0145 | 2.12681 | ||||||||
\(65\) | −4.27979 | − | 7.41281i | −0.530842 | − | 0.919445i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.68236 | + | 2.91393i | −0.205533 | + | 0.355993i | −0.950302 | − | 0.311329i | \(-0.899226\pi\) |
0.744770 | + | 0.667322i | \(0.232559\pi\) | |||||||
\(68\) | −17.4038 | + | 30.1442i | −2.11052 | + | 3.65552i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.94163 | + | 3.36300i | 0.232069 | + | 0.401955i | ||||
\(71\) | −1.36471 | −0.161962 | −0.0809808 | − | 0.996716i | \(-0.525805\pi\) | ||||
−0.0809808 | + | 0.996716i | \(0.525805\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.88325 | −0.220418 | −0.110209 | − | 0.993908i | \(-0.535152\pi\) | ||||
−0.110209 | + | 0.993908i | \(0.535152\pi\) | |||||||
\(74\) | 6.67270 | + | 11.5575i | 0.775685 | + | 1.34353i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.0072 | − | 27.7253i | 1.83616 | − | 3.18032i | ||||
\(77\) | −0.772548 | + | 1.33809i | −0.0880400 | + | 0.152490i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.68236 | − | 2.91393i | −0.189280 | − | 0.327842i | 0.755730 | − | 0.654883i | \(-0.227282\pi\) |
−0.945010 | + | 0.327040i | \(0.893949\pi\) | |||||||
\(80\) | 17.4694 | 1.95314 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 1.12398 | + | 1.94680i | 0.123373 | + | 0.213689i | 0.921096 | − | 0.389336i | \(-0.127295\pi\) |
−0.797723 | + | 0.603024i | \(0.793962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.94163 | + | 8.55915i | −0.535995 | + | 0.928370i | ||||
\(86\) | −9.51690 | + | 16.4837i | −1.02623 | + | 1.77749i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.44163 | + | 11.1572i | 0.686680 | + | 1.18936i | ||||
\(89\) | −0.793062 | −0.0840644 | −0.0420322 | − | 0.999116i | \(-0.513383\pi\) | ||||
−0.0420322 | + | 0.999116i | \(0.513383\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.88325 | 0.616733 | ||||||||
\(92\) | 7.45490 | + | 12.9123i | 0.777227 | + | 1.34620i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.12398 | − | 12.3391i | 0.734783 | − | 1.27268i | ||||
\(95\) | 4.54510 | − | 7.87234i | 0.466317 | − | 0.807685i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.12398 | − | 8.87500i | −0.520262 | − | 0.901120i | −0.999723 | − | 0.0235564i | \(-0.992501\pi\) |
0.479461 | − | 0.877563i | \(-0.340832\pi\) | |||||||
\(98\) | −2.66908 | −0.269618 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.7737 | −1.47737 | ||||||||
\(101\) | 4.54510 | + | 7.87234i | 0.452254 | + | 0.783327i | 0.998526 | − | 0.0542812i | \(-0.0172867\pi\) |
−0.546272 | + | 0.837608i | \(0.683953\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.00724 | + | 15.6010i | −0.887509 | + | 1.53721i | −0.0446993 | + | 0.999000i | \(0.514233\pi\) |
−0.842810 | + | 0.538211i | \(0.819100\pi\) | |||||||
\(104\) | 24.5278 | − | 42.4833i | 2.40514 | − | 4.16583i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.0692 | + | 22.6366i | 1.26940 | + | 2.19866i | ||||
\(107\) | 18.2214 | 1.76153 | 0.880765 | − | 0.473553i | \(-0.157029\pi\) | ||||
0.880765 | + | 0.473553i | \(0.157029\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.3792 | 1.56884 | 0.784421 | − | 0.620229i | \(-0.212960\pi\) | ||||
0.784421 | + | 0.620229i | \(0.212960\pi\) | |||||||
\(110\) | 3.00000 | + | 5.19615i | 0.286039 | + | 0.495434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.00362 | + | 10.3986i | −0.567289 | + | 0.982573i | ||||
\(113\) | 3.74797 | − | 6.49167i | 0.352579 | − | 0.610685i | −0.634122 | − | 0.773233i | \(-0.718638\pi\) |
0.986701 | + | 0.162549i | \(0.0519714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.11675 | + | 3.66631i | 0.197388 | + | 0.341885i | ||||
\(116\) | −19.8977 | −1.84746 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.4815 | −1.14901 | ||||||||
\(119\) | −3.39653 | − | 5.88296i | −0.311359 | − | 0.539290i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.30634 | − | 7.45880i | 0.391485 | − | 0.678073i | ||||
\(122\) | −3.15580 | + | 5.46601i | −0.285713 | + | 0.494869i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.12398 | − | 8.87500i | −0.460147 | − | 0.796998i | ||||
\(125\) | −11.4694 | −1.02585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.13122 | −0.632793 | −0.316397 | − | 0.948627i | \(-0.602473\pi\) | ||||
−0.316397 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(128\) | 7.33454 | + | 12.7038i | 0.648288 | + | 1.12287i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.4231 | − | 19.7854i | 1.00187 | − | 1.73529i | ||||
\(131\) | 9.46214 | − | 16.3889i | 0.826711 | − | 1.43191i | −0.0738934 | − | 0.997266i | \(-0.523542\pi\) |
0.900605 | − | 0.434640i | \(-0.143124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.12398 | + | 5.41090i | 0.270884 | + | 0.469184i | ||||
\(134\) | −8.98068 | −0.775813 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −56.6416 | −4.85698 | ||||||||
\(137\) | −2.95490 | − | 5.11804i | −0.252454 | − | 0.437264i | 0.711747 | − | 0.702436i | \(-0.247904\pi\) |
−0.964201 | + | 0.265172i | \(0.914571\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.876017 | − | 1.51731i | 0.0743028 | − | 0.128696i | −0.826480 | − | 0.562966i | \(-0.809660\pi\) |
0.900783 | + | 0.434270i | \(0.142994\pi\) | |||||||
\(140\) | −3.72745 | + | 6.45614i | −0.315027 | + | 0.545643i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.82126 | − | 3.15452i | −0.152837 | − | 0.264721i | ||||
\(143\) | 9.09019 | 0.760160 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.64976 | −0.469187 | ||||||||
\(146\) | −2.51328 | − | 4.35312i | −0.208000 | − | 0.360267i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.8100 | + | 22.1875i | −1.05297 | + | 1.82380i | ||||
\(149\) | −3.04510 | + | 5.27426i | −0.249464 | + | 0.432084i | −0.963377 | − | 0.268150i | \(-0.913588\pi\) |
0.713913 | + | 0.700234i | \(0.246921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.317644 | − | 0.550175i | −0.0258495 | − | 0.0447726i | 0.852811 | − | 0.522219i | \(-0.174896\pi\) |
−0.878661 | + | 0.477447i | \(0.841562\pi\) | |||||||
\(152\) | 52.0965 | 4.22559 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.12398 | −0.332320 | ||||||||
\(155\) | −1.45490 | − | 2.51997i | −0.116861 | − | 0.202409i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.57691 | − | 4.46335i | 0.205660 | − | 0.356214i | −0.744683 | − | 0.667419i | \(-0.767399\pi\) |
0.950343 | + | 0.311205i | \(0.100733\pi\) | |||||||
\(158\) | 4.49034 | − | 7.77750i | 0.357232 | − | 0.618745i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11.1824 | + | 19.3684i | 0.884043 | + | 1.53121i | ||||
\(161\) | −2.90981 | −0.229325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.36471 | −0.420197 | −0.210098 | − | 0.977680i | \(-0.567378\pi\) | ||||
−0.210098 | + | 0.977680i | \(0.567378\pi\) | |||||||
\(164\) | −5.75927 | − | 9.97535i | −0.449724 | − | 0.778944i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 4.87602 | − | 8.44551i | 0.377318 | − | 0.653533i | −0.613353 | − | 0.789809i | \(-0.710180\pi\) |
0.990671 | + | 0.136275i | \(0.0435132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8063 | − | 18.7171i | −0.831257 | − | 1.43978i | ||||
\(170\) | −26.3792 | −2.02319 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −36.5403 | −2.78617 | ||||||||
\(173\) | 12.1558 | + | 21.0545i | 0.924189 | + | 1.60074i | 0.792861 | + | 0.609402i | \(0.208591\pi\) |
0.131327 | + | 0.991339i | \(0.458076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44163 | − | 2.49697i | 0.108977 | − | 0.188753i | ||||
\(176\) | −9.27617 | + | 16.0668i | −0.699217 | + | 1.21108i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.05837 | − | 1.83316i | −0.0793284 | − | 0.137401i | ||||
\(179\) | −13.5861 | −1.01547 | −0.507737 | − | 0.861512i | \(-0.669518\pi\) | ||||
−0.507737 | + | 0.861512i | \(0.669518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 7.85144 | + | 13.5991i | 0.581987 | + | 1.00803i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.1312 | + | 21.0119i | −0.894325 | + | 1.54902i | ||||
\(185\) | −3.63726 | + | 6.29992i | −0.267417 | + | 0.463179i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.24797 | − | 9.08974i | −0.383769 | − | 0.664708i | ||||
\(188\) | 27.3526 | 1.99490 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 24.2624 | 1.76018 | ||||||||
\(191\) | 7.65580 | + | 13.2602i | 0.553954 | + | 0.959477i | 0.997984 | + | 0.0634651i | \(0.0202151\pi\) |
−0.444030 | + | 0.896012i | \(0.646452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.18959 | − | 10.7207i | 0.445537 | − | 0.771692i | −0.552553 | − | 0.833478i | \(-0.686346\pi\) |
0.998089 | + | 0.0617858i | \(0.0196796\pi\) | |||||||
\(194\) | 13.6763 | − | 23.6881i | 0.981902 | − | 1.70070i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.56199 | − | 4.43750i | −0.182999 | − | 0.316964i | ||||
\(197\) | 5.72942 | 0.408205 | 0.204102 | − | 0.978950i | \(-0.434572\pi\) | ||||
0.204102 | + | 0.978950i | \(0.434572\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0145 | 0.851684 | 0.425842 | − | 0.904798i | \(-0.359978\pi\) | ||||
0.425842 | + | 0.904798i | \(0.359978\pi\) | |||||||
\(200\) | −12.0205 | − | 20.8201i | −0.849979 | − | 1.47221i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1312 | + | 21.0119i | −0.853550 | + | 1.47839i | ||||
\(203\) | 1.94163 | − | 3.36300i | 0.136276 | − | 0.236036i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.63529 | − | 2.83240i | −0.114213 | − | 0.197823i | ||||
\(206\) | −48.0821 | −3.35004 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 70.6416 | 4.89812 | ||||||||
\(209\) | 4.82685 | + | 8.36036i | 0.333880 | + | 0.578298i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.56561 | − | 11.3720i | 0.451995 | − | 0.782879i | −0.546515 | − | 0.837450i | \(-0.684046\pi\) |
0.998510 | + | 0.0545708i | \(0.0173791\pi\) | |||||||
\(212\) | −25.0897 | + | 43.4567i | −1.72317 | + | 2.98462i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24.3172 | + | 42.1186i | 1.66229 | + | 2.87917i | ||||
\(215\) | −10.3752 | −0.707586 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 21.8587 | + | 37.8603i | 1.48046 | + | 2.56423i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.75927 | + | 9.97535i | −0.388290 | + | 0.672538i | ||||
\(221\) | −19.9827 | + | 34.6110i | −1.34418 | + | 2.32819i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.635288 | + | 1.10035i | 0.0425420 | + | 0.0736849i | 0.886512 | − | 0.462705i | \(-0.153121\pi\) |
−0.843970 | + | 0.536390i | \(0.819788\pi\) | |||||||
\(224\) | −15.3719 | −1.02708 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.0072 | 1.33086 | ||||||||
\(227\) | −8.09743 | − | 14.0252i | −0.537445 | − | 0.930882i | −0.999041 | − | 0.0437919i | \(-0.986056\pi\) |
0.461595 | − | 0.887091i | \(-0.347277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.18236 | + | 10.7082i | −0.408542 | + | 0.707615i | −0.994727 | − | 0.102562i | \(-0.967296\pi\) |
0.586185 | + | 0.810177i | \(0.300629\pi\) | |||||||
\(230\) | −5.64976 | + | 9.78568i | −0.372534 | + | 0.645248i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.1896 | − | 28.0412i | −1.06290 | − | 1.84099i | ||||
\(233\) | −18.7931 | −1.23117 | −0.615587 | − | 0.788069i | \(-0.711081\pi\) | ||||
−0.615587 | + | 0.788069i | \(0.711081\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.76651 | 0.506631 | ||||||||
\(236\) | −11.9807 | − | 20.7512i | −0.779876 | − | 1.35078i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.06561 | − | 15.7021i | 0.587636 | − | 1.01782i | ||||
\(239\) | 10.5656 | − | 18.3002i | 0.683433 | − | 1.18374i | −0.290494 | − | 0.956877i | \(-0.593820\pi\) |
0.973927 | − | 0.226863i | \(-0.0728470\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.18236 | − | 5.51200i | −0.204994 | − | 0.355059i | 0.745137 | − | 0.666911i | \(-0.232384\pi\) |
−0.950131 | + | 0.311852i | \(0.899051\pi\) | |||||||
\(242\) | 22.9879 | 1.47772 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.1167 | −0.775695 | ||||||||
\(245\) | −0.727452 | − | 1.25998i | −0.0464752 | − | 0.0804974i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.3792 | − | 31.8337i | 1.16944 | − | 2.02553i | ||||
\(248\) | 8.33816 | − | 14.4421i | 0.529474 | − | 0.917075i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.3063 | − | 26.5114i | −0.968058 | − | 1.67673i | ||||
\(251\) | 16.0145 | 1.01082 | 0.505412 | − | 0.862878i | \(-0.331340\pi\) | ||||
0.505412 | + | 0.862878i | \(0.331340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.49593 | −0.282657 | ||||||||
\(254\) | −9.51690 | − | 16.4837i | −0.597143 | − | 1.03428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.56199 | + | 4.43750i | −0.160124 | + | 0.277344i | ||||
\(257\) | 8.64450 | − | 14.9727i | 0.539229 | − | 0.933972i | −0.459717 | − | 0.888066i | \(-0.652049\pi\) |
0.998946 | − | 0.0459063i | \(-0.0146176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | − | 4.33013i | −0.155342 | − | 0.269061i | ||||
\(260\) | 43.8591 | 2.72003 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 50.5104 | 3.12054 | ||||||||
\(263\) | −6.77255 | − | 11.7304i | −0.417613 | − | 0.723327i | 0.578086 | − | 0.815976i | \(-0.303800\pi\) |
−0.995699 | + | 0.0926488i | \(0.970467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.12398 | + | 12.3391i | −0.437623 | + | 0.757985i | ||||
\(266\) | −8.33816 | + | 14.4421i | −0.511245 | + | 0.885503i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.62036 | − | 14.9309i | −0.526573 | − | 0.912050i | ||||
\(269\) | 12.7931 | 0.780007 | 0.390003 | − | 0.920813i | \(-0.372474\pi\) | ||||
0.390003 | + | 0.920813i | \(0.372474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −32.0145 | −1.94474 | −0.972370 | − | 0.233443i | \(-0.925001\pi\) | ||||
−0.972370 | + | 0.233443i | \(0.925001\pi\) | |||||||
\(272\) | −40.7830 | − | 70.6382i | −2.47283 | − | 4.28307i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.88687 | − | 13.6605i | 0.476463 | − | 0.825259i | ||||
\(275\) | 2.22745 | − | 3.85806i | 0.134320 | − | 0.232650i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.68959 | − | 11.5867i | −0.401939 | − | 0.696178i | 0.592021 | − | 0.805922i | \(-0.298330\pi\) |
−0.993960 | + | 0.109744i | \(0.964997\pi\) | |||||||
\(278\) | 4.67632 | 0.280467 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.1312 | −0.724979 | ||||||||
\(281\) | −5.38325 | − | 9.32407i | −0.321138 | − | 0.556227i | 0.659585 | − | 0.751630i | \(-0.270732\pi\) |
−0.980723 | + | 0.195403i | \(0.937399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3719 | − | 24.8929i | 0.854324 | − | 1.47973i | −0.0229473 | − | 0.999737i | \(-0.507305\pi\) |
0.877271 | − | 0.479995i | \(-0.159362\pi\) | |||||||
\(284\) | 3.49638 | − | 6.05591i | 0.207472 | − | 0.359352i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.1312 | + | 21.0119i | 0.717334 | + | 1.24246i | ||||
\(287\) | 2.24797 | 0.132693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.1457 | 1.71445 | ||||||||
\(290\) | −7.53983 | − | 13.0594i | −0.442754 | − | 0.766873i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.82488 | − | 8.35694i | 0.282355 | − | 0.489053i | ||||
\(293\) | 3.06561 | − | 5.30979i | 0.179095 | − | 0.310201i | −0.762476 | − | 0.647017i | \(-0.776016\pi\) |
0.941571 | + | 0.336815i | \(0.109350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.40180 | − | 5.89208i | −0.198060 | − | 0.343050i | ||||
\(296\) | −41.6908 | −2.42323 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.2552 | −0.941639 | ||||||||
\(299\) | 8.55957 | + | 14.8256i | 0.495013 | + | 0.857387i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.56561 | − | 6.17582i | 0.205518 | − | 0.355968i | ||||
\(302\) | 0.847817 | − | 1.46846i | 0.0487864 | − | 0.0845005i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 37.5104 | + | 64.9699i | 2.15137 | + | 3.72628i | ||||
\(305\) | −3.44043 | −0.196998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.76651 | −0.329112 | −0.164556 | − | 0.986368i | \(-0.552619\pi\) | ||||
−0.164556 | + | 0.986368i | \(0.552619\pi\) | |||||||
\(308\) | −3.95852 | − | 6.85636i | −0.225558 | − | 0.390678i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.88325 | − | 6.72599i | 0.220554 | − | 0.382011i | ||||
\(311\) | 2.66908 | − | 4.62298i | 0.151350 | − | 0.262145i | −0.780374 | − | 0.625313i | \(-0.784971\pi\) |
0.931724 | + | 0.363168i | \(0.118305\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.69366 | − | 6.39761i | −0.208778 | − | 0.361614i | 0.742552 | − | 0.669789i | \(-0.233615\pi\) |
−0.951330 | + | 0.308174i | \(0.900282\pi\) | |||||||
\(314\) | 13.7560 | 0.776295 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.2407 | 0.969867 | ||||||||
\(317\) | 5.51328 | + | 9.54928i | 0.309656 | + | 0.536341i | 0.978287 | − | 0.207254i | \(-0.0664526\pi\) |
−0.668631 | + | 0.743595i | \(0.733119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | −12.3772 | + | 21.4380i | −0.691907 | + | 1.19842i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.88325 | − | 6.72599i | −0.216405 | − | 0.374825i | ||||
\(323\) | −42.4428 | −2.36158 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.9629 | −0.940933 | ||||||||
\(326\) | −7.15942 | − | 12.4005i | −0.396524 | − | 0.686799i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.37195 | − | 16.2327i | 0.517479 | − | 0.896301i | ||||
\(329\) | −2.66908 | + | 4.62298i | −0.147151 | + | 0.254873i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.7665 | + | 27.3084i | 0.866606 | + | 1.50101i | 0.865444 | + | 0.501006i | \(0.167036\pi\) |
0.00116169 | + | 0.999999i | \(0.499630\pi\) | |||||||
\(332\) | −11.5185 | −0.632162 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 26.0289 | 1.42424 | ||||||||
\(335\) | −2.44767 | − | 4.23948i | −0.133730 | − | 0.231628i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3249 | + | 30.0076i | −0.943746 | + | 1.63462i | −0.185505 | + | 0.982643i | \(0.559392\pi\) |
−0.758242 | + | 0.651973i | \(0.773941\pi\) | |||||||
\(338\) | 28.8430 | − | 49.9575i | 1.56885 | − | 2.71733i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −25.3208 | − | 43.8569i | −1.37321 | − | 2.37848i | ||||
\(341\) | 3.09019 | 0.167343 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −29.7306 | − | 51.4949i | −1.60297 | − | 2.77642i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −32.4448 | + | 56.1960i | −1.74424 | + | 3.02112i | ||||
\(347\) | 1.34420 | − | 2.32822i | 0.0721603 | − | 0.124985i | −0.827688 | − | 0.561189i | \(-0.810344\pi\) |
0.899848 | + | 0.436204i | \(0.143677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.24073 | + | 3.88106i | 0.119943 | + | 0.207748i | 0.919745 | − | 0.392516i | \(-0.128395\pi\) |
−0.799802 | + | 0.600264i | \(0.795062\pi\) | |||||||
\(350\) | 7.69563 | 0.411349 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −23.7511 | −1.26594 | ||||||||
\(353\) | 15.5523 | + | 26.9374i | 0.827767 | + | 1.43373i | 0.899786 | + | 0.436332i | \(0.143723\pi\) |
−0.0720188 | + | 0.997403i | \(0.522944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.992763 | − | 1.71952i | 0.0526904 | − | 0.0912624i | ||||
\(356\) | 2.03182 | − | 3.51921i | 0.107686 | − | 0.186518i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.1312 | − | 31.4042i | −0.958265 | − | 1.65976i | ||||
\(359\) | 18.2214 | 0.961689 | 0.480845 | − | 0.876806i | \(-0.340330\pi\) | ||||
0.480845 | + | 0.876806i | \(0.340330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.0371 | 1.05458 | ||||||||
\(362\) | 2.66908 | + | 4.62298i | 0.140284 | + | 0.242978i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.0728 | + | 26.1069i | −0.790032 | + | 1.36838i | ||||
\(365\) | 1.36998 | − | 2.37287i | 0.0717079 | − | 0.124202i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1312 | + | 24.4760i | 0.737644 | + | 1.27764i | 0.953554 | + | 0.301223i | \(0.0973949\pi\) |
−0.215910 | + | 0.976413i | \(0.569272\pi\) | |||||||
\(368\) | −34.9388 | −1.82131 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.4163 | −1.00940 | ||||||||
\(371\) | −4.89653 | − | 8.48104i | −0.254215 | − | 0.440314i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.07691 | − | 1.86527i | 0.0557605 | − | 0.0965801i | −0.836798 | − | 0.547512i | \(-0.815575\pi\) |
0.892558 | + | 0.450932i | \(0.148908\pi\) | |||||||
\(374\) | 14.0072 | − | 24.2612i | 0.724297 | − | 1.25452i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.2552 | + | 38.5471i | 1.14772 | + | 1.98792i | ||||
\(377\) | −22.8462 | −1.17664 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.67237 | −0.394103 | −0.197052 | − | 0.980393i | \(-0.563137\pi\) | ||||
−0.197052 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(380\) | 23.2890 | + | 40.3377i | 1.19470 | + | 2.06928i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.4339 | + | 35.3926i | −1.04549 | + | 1.81084i | ||||
\(383\) | −8.90981 | + | 15.4322i | −0.455270 | + | 0.788551i | −0.998704 | − | 0.0509014i | \(-0.983791\pi\) |
0.543434 | + | 0.839452i | \(0.317124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.12398 | − | 1.94680i | −0.0572835 | − | 0.0992179i | ||||
\(386\) | 33.0410 | 1.68174 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 52.5104 | 2.66581 | ||||||||
\(389\) | −0.0901918 | − | 0.156217i | −0.00457291 | − | 0.00792051i | 0.863730 | − | 0.503955i | \(-0.168122\pi\) |
−0.868303 | + | 0.496035i | \(0.834789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.88325 | − | 17.1183i | 0.499818 | − | 0.865710i | ||||
\(392\) | 4.16908 | − | 7.22106i | 0.210570 | − | 0.364718i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.64614 | + | 13.2435i | 0.385207 | + | 0.667198i | ||||
\(395\) | 4.89533 | 0.246311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.3937 | −1.12391 | −0.561953 | − | 0.827169i | \(-0.689950\pi\) | ||||
−0.561953 | + | 0.827169i | \(0.689950\pi\) | |||||||
\(398\) | 16.0338 | + | 27.7713i | 0.803701 | + | 1.39205i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.3100 | − | 29.9817i | 0.865498 | − | 1.49909i | ||||
\(401\) | −6.04510 | + | 10.4704i | −0.301878 | + | 0.522867i | −0.976561 | − | 0.215240i | \(-0.930947\pi\) |
0.674684 | + | 0.738107i | \(0.264280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.88325 | − | 10.1901i | −0.293066 | − | 0.507605i | ||||
\(404\) | −46.5780 | −2.31734 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.3647 | 0.514392 | ||||||||
\(407\) | −3.86274 | − | 6.69046i | −0.191469 | − | 0.331634i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1824 | − | 17.6364i | 0.503485 | − | 0.872062i | −0.496507 | − | 0.868033i | \(-0.665384\pi\) |
0.999992 | − | 0.00402894i | \(-0.00128246\pi\) | |||||||
\(410\) | 4.36471 | − | 7.55990i | 0.215558 | − | 0.373357i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −46.1529 | − | 79.9392i | −2.27379 | − | 3.93832i | ||||
\(413\) | 4.67632 | 0.230106 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.27058 | −0.160546 | ||||||||
\(416\) | 45.2185 | + | 78.3208i | 2.21702 | + | 3.83999i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.8833 | + | 22.3145i | −0.630141 | + | 1.09144i | ||||
\(419\) | −5.48870 | + | 9.50670i | −0.268140 | + | 0.464433i | −0.968382 | − | 0.249474i | \(-0.919742\pi\) |
0.700241 | + | 0.713906i | \(0.253076\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.86471 | − | 6.69388i | −0.188355 | − | 0.326240i | 0.756347 | − | 0.654170i | \(-0.226982\pi\) |
−0.944702 | + | 0.327931i | \(0.893649\pi\) | |||||||
\(422\) | 35.0483 | 1.70612 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −81.6561 | −3.96557 | ||||||||
\(425\) | 9.79306 | + | 16.9621i | 0.475033 | + | 0.822782i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.18236 | − | 2.04790i | 0.0572182 | − | 0.0991049i | ||||
\(428\) | −46.6831 | + | 80.8575i | −2.25651 | + | 3.90840i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.8462 | − | 23.9823i | −0.667722 | − | 1.15653i | ||||
\(431\) | 27.1722 | 1.30884 | 0.654421 | − | 0.756131i | \(-0.272913\pi\) | ||||
0.654421 | + | 0.756131i | \(0.272913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.59820 | 0.220976 | 0.110488 | − | 0.993877i | \(-0.464759\pi\) | ||||
0.110488 | + | 0.993877i | \(0.464759\pi\) | |||||||
\(434\) | 2.66908 | + | 4.62298i | 0.128120 | + | 0.221910i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −41.9633 | + | 72.6826i | −2.00968 | + | 3.48087i | ||||
\(437\) | −9.09019 | + | 15.7447i | −0.434843 | + | 0.753170i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1240 | + | 20.9994i | 0.578646 | + | 1.00224i | 0.995635 | + | 0.0933329i | \(0.0297521\pi\) |
−0.416989 | + | 0.908912i | \(0.636915\pi\) | |||||||
\(440\) | −18.7439 | −0.893580 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −106.671 | −5.07380 | ||||||||
\(443\) | −15.0410 | − | 26.0518i | −0.714621 | − | 1.23776i | −0.963106 | − | 0.269124i | \(-0.913266\pi\) |
0.248485 | − | 0.968636i | \(-0.420067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.576915 | − | 0.999246i | 0.0273484 | − | 0.0473688i | ||||
\(446\) | −1.69563 | + | 2.93692i | −0.0802906 | + | 0.139067i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.50724 | − | 14.7350i | −0.401929 | − | 0.696162i | ||||
\(449\) | −29.3792 | −1.38649 | −0.693245 | − | 0.720702i | \(-0.743820\pi\) | ||||
−0.693245 | + | 0.720702i | \(0.743820\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.47332 | 0.163552 | ||||||||
\(452\) | 19.2045 | + | 33.2632i | 0.903304 | + | 1.56457i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.6127 | − | 37.4343i | 1.01433 | − | 1.75688i | ||||
\(455\) | −4.27979 | + | 7.41281i | −0.200639 | + | 0.347518i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | −33.0024 | −1.54210 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.6923 | −1.01141 | ||||||||
\(461\) | −4.25520 | − | 7.37023i | −0.198185 | − | 0.343266i | 0.749755 | − | 0.661715i | \(-0.230171\pi\) |
−0.947940 | + | 0.318449i | \(0.896838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.6968 | + | 20.2595i | −0.543598 | + | 0.941539i | 0.455096 | + | 0.890442i | \(0.349605\pi\) |
−0.998694 | + | 0.0510966i | \(0.983728\pi\) | |||||||
\(464\) | 23.3136 | − | 40.3803i | 1.08231 | − | 1.87461i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.0801 | − | 43.4400i | −1.16181 | − | 2.01232i | ||||
\(467\) | −25.8872 | −1.19792 | −0.598958 | − | 0.800780i | \(-0.704419\pi\) | ||||
−0.598958 | + | 0.800780i | \(0.704419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.36471 | 0.155368 | ||||||||
\(470\) | 10.3647 | + | 17.9522i | 0.478089 | + | 0.828074i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.4959 | − | 33.7679i | 0.897373 | − | 1.55430i | ||||
\(473\) | 5.50921 | − | 9.54223i | 0.253314 | − | 0.438752i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.00724 | − | 15.6010i | −0.413280 | − | 0.715823i | ||||
\(476\) | 34.8075 | 1.59540 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 56.4009 | 2.57972 | ||||||||
\(479\) | 5.90981 | + | 10.2361i | 0.270026 | + | 0.467699i | 0.968868 | − | 0.247577i | \(-0.0796344\pi\) |
−0.698842 | + | 0.715276i | \(0.746301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7081 | + | 25.4752i | −0.670633 | + | 1.16157i | ||||
\(482\) | 8.49396 | − | 14.7120i | 0.386889 | − | 0.670112i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0656 | + | 38.2188i | 1.00298 | + | 1.73722i | ||||
\(485\) | 14.9098 | 0.677020 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.8606 | 1.44374 | 0.721872 | − | 0.692027i | \(-0.243282\pi\) | ||||
0.721872 | + | 0.692027i | \(0.243282\pi\) | |||||||
\(488\) | −9.85867 | − | 17.0757i | −0.446281 | − | 0.772982i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.94163 | − | 3.36300i | 0.0877138 | − | 0.151925i | ||||
\(491\) | −7.76651 | + | 13.4520i | −0.350498 | + | 0.607080i | −0.986337 | − | 0.164742i | \(-0.947321\pi\) |
0.635839 | + | 0.771822i | \(0.280654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.1896 | + | 22.8450i | 0.594029 | + | 1.02889i | ||||
\(494\) | 98.1110 | 4.41422 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.0145 | 1.07828 | ||||||||
\(497\) | 0.682356 | + | 1.18188i | 0.0306079 | + | 0.0530144i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3792 | + | 21.4414i | −0.554169 | + | 0.959848i | 0.443799 | + | 0.896126i | \(0.353630\pi\) |
−0.997968 | + | 0.0637218i | \(0.979703\pi\) | |||||||
\(500\) | 29.3845 | − | 50.8954i | 1.31411 | − | 2.27611i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.3719 | + | 37.0173i | 0.953877 | + | 1.65216i | ||||
\(503\) | −35.2995 | −1.57393 | −0.786964 | − | 0.616999i | \(-0.788348\pi\) | ||||
−0.786964 | + | 0.616999i | \(0.788348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.2254 | −0.588521 | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.2701 | − | 31.6448i | 0.810606 | − | 1.40401i | ||||
\(509\) | 0.0901918 | − | 0.156217i | 0.00399768 | − | 0.00692419i | −0.864020 | − | 0.503458i | \(-0.832061\pi\) |
0.868017 | + | 0.496534i | \(0.165394\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.941627 | + | 1.63095i | 0.0416551 | + | 0.0721488i | ||||
\(512\) | 15.6618 | 0.692162 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46.1457 | 2.03540 | ||||||||
\(515\) | −13.1047 | − | 22.6979i | −0.577461 | − | 1.00019i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.12398 | + | 7.14295i | −0.181373 | + | 0.314147i | ||||
\(518\) | 6.67270 | − | 11.5575i | 0.293182 | − | 0.507805i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 35.6855 | + | 61.8091i | 1.56491 | + | 2.71051i | ||||
\(521\) | −10.8567 | −0.475641 | −0.237820 | − | 0.971309i | \(-0.576433\pi\) | ||||
−0.237820 | + | 0.971309i | \(0.576433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.7439 | −1.78161 | −0.890803 | − | 0.454389i | \(-0.849857\pi\) | ||||
−0.890803 | + | 0.454389i | \(0.849857\pi\) | |||||||
\(524\) | 48.4839 | + | 83.9765i | 2.11803 | + | 3.66853i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0765 | − | 31.3094i | 0.788171 | − | 1.36515i | ||||
\(527\) | −6.79306 | + | 11.7659i | −0.295910 | + | 0.512532i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.26651 | + | 12.5860i | 0.315935 | + | 0.547216i | ||||
\(530\) | −38.0289 | −1.65187 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −32.0145 | −1.38800 | ||||||||
\(533\) | −6.61268 | − | 11.4535i | −0.286427 | − | 0.496106i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.2552 | + | 22.9587i | −0.573072 | + | 0.992591i | ||||
\(536\) | 14.0278 | − | 24.2968i | 0.605907 | − | 1.04946i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.0728 | + | 29.5710i | 0.736063 | + | 1.27490i | ||||
\(539\) | 1.54510 | 0.0665520 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2335 | −0.740926 | −0.370463 | − | 0.928847i | \(-0.620801\pi\) | ||||
−0.370463 | + | 0.928847i | \(0.620801\pi\) | |||||||
\(542\) | −42.7246 | − | 74.0011i | −1.83518 | − | 3.17862i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 52.2113 | − | 90.4326i | 2.23854 | − | 3.87727i | ||||
\(545\) | −11.9151 | + | 20.6375i | −0.510386 | + | 0.884014i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.9303 | + | 34.5203i | 0.852159 | + | 1.47598i | 0.879256 | + | 0.476350i | \(0.158040\pi\) |
−0.0270967 | + | 0.999633i | \(0.508626\pi\) | |||||||
\(548\) | 30.2818 | 1.29357 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.8905 | 0.507012 | ||||||||
\(551\) | −12.1312 | − | 21.0119i | −0.516807 | − | 0.895137i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.68236 | + | 2.91393i | −0.0715411 | + | 0.123913i | ||||
\(554\) | 17.8551 | − | 30.9259i | 0.758589 | − | 1.31391i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.48870 | + | 7.77465i | 0.190363 | + | 0.329719i | ||||
\(557\) | −28.5861 | −1.21123 | −0.605616 | − | 0.795757i | \(-0.707073\pi\) | ||||
−0.605616 | + | 0.795757i | \(0.707073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.9548 | −1.77450 | ||||||||
\(560\) | −8.73469 | − | 15.1289i | −0.369108 | − | 0.639314i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.3683 | − | 24.8867i | 0.606091 | − | 1.04978i | ||||
\(563\) | 12.0410 | − | 20.8557i | 0.507469 | − | 0.878962i | −0.492494 | − | 0.870316i | \(-0.663915\pi\) |
0.999963 | − | 0.00864587i | \(-0.00275210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.45293 | + | 9.44475i | 0.229407 | + | 0.397344i | ||||
\(566\) | 76.7197 | 3.22477 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.3792 | 0.477460 | ||||||||
\(569\) | −0.526554 | − | 0.912018i | −0.0220743 | − | 0.0382338i | 0.854777 | − | 0.518995i | \(-0.173694\pi\) |
−0.876852 | + | 0.480761i | \(0.840360\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.13122 | − | 14.0837i | 0.340281 | − | 0.589384i | −0.644204 | − | 0.764854i | \(-0.722811\pi\) |
0.984485 | + | 0.175470i | \(0.0561445\pi\) | |||||||
\(572\) | −23.2890 | + | 40.3377i | −0.973762 | + | 1.68660i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.00000 | + | 5.19615i | 0.125218 | + | 0.216883i | ||||
\(575\) | 8.38972 | 0.349875 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.3937 | 1.59835 | 0.799175 | − | 0.601099i | \(-0.205270\pi\) | ||||
0.799175 | + | 0.601099i | \(0.205270\pi\) | |||||||
\(578\) | 38.8961 | + | 67.3700i | 1.61786 | + | 2.80222i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.4746 | − | 25.0708i | 0.601027 | − | 1.04101i | ||||
\(581\) | 1.12398 | − | 1.94680i | 0.0466307 | − | 0.0807667i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.56561 | − | 13.1040i | −0.313336 | − | 0.542713i | ||||
\(584\) | 15.7029 | 0.649789 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.3647 | 0.676020 | ||||||||
\(587\) | −13.9774 | − | 24.2096i | −0.576909 | − | 0.999235i | −0.995831 | − | 0.0912132i | \(-0.970926\pi\) |
0.418923 | − | 0.908022i | \(-0.362408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.24797 | − | 10.8218i | 0.257443 | − | 0.445904i | ||||
\(590\) | 9.07966 | − | 15.7264i | 0.373804 | − | 0.647447i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.0181 | − | 51.9929i | −1.23374 | − | 2.13689i | ||||
\(593\) | −3.52249 | −0.144651 | −0.0723256 | − | 0.997381i | \(-0.523042\pi\) | ||||
−0.0723256 | + | 0.997381i | \(0.523042\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.88325 | 0.405174 | ||||||||
\(596\) | −15.6030 | − | 27.0252i | −0.639125 | − | 1.10700i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.8462 | + | 39.5707i | −0.934249 | + | 1.61817i | ||||
\(599\) | 2.97949 | − | 5.16062i | 0.121738 | − | 0.210857i | −0.798715 | − | 0.601710i | \(-0.794486\pi\) |
0.920453 | + | 0.390852i | \(0.127820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.430322 | + | 0.745340i | 0.0175532 | + | 0.0304031i | 0.874669 | − | 0.484721i | \(-0.161079\pi\) |
−0.857115 | + | 0.515125i | \(0.827746\pi\) | |||||||
\(602\) | 19.0338 | 0.775759 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.25520 | 0.132452 | ||||||||
\(605\) | 6.26531 | + | 10.8518i | 0.254721 | + | 0.441190i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4887 | − | 28.5593i | 0.669256 | − | 1.15918i | −0.308857 | − | 0.951108i | \(-0.599946\pi\) |
0.978113 | − | 0.208076i | \(-0.0667202\pi\) | |||||||
\(608\) | −48.0217 | + | 83.1760i | −1.94754 | + | 3.37323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.59139 | − | 7.95252i | −0.185900 | − | 0.321988i | ||||
\(611\) | 31.4057 | 1.27054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.9203 | −1.12769 | −0.563846 | − | 0.825880i | \(-0.690679\pi\) | ||||
−0.563846 | + | 0.825880i | \(0.690679\pi\) | |||||||
\(614\) | −7.69563 | − | 13.3292i | −0.310570 | − | 0.537924i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.44163 | − | 11.1572i | 0.259541 | − | 0.449537i | ||||
\(617\) | −20.6855 | + | 35.8284i | −0.832768 | + | 1.44240i | 0.0630670 | + | 0.998009i | \(0.479912\pi\) |
−0.895835 | + | 0.444387i | \(0.853422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.64252 | + | 9.77314i | 0.226792 | + | 0.392816i | 0.956856 | − | 0.290564i | \(-0.0938428\pi\) |
−0.730063 | + | 0.683379i | \(0.760509\pi\) | |||||||
\(620\) | 14.9098 | 0.598792 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.2480 | 0.571291 | ||||||||
\(623\) | 0.396531 | + | 0.686812i | 0.0158867 | + | 0.0275165i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.13529 | − | 1.96638i | 0.0454115 | − | 0.0786550i | ||||
\(626\) | 9.85867 | − | 17.0757i | 0.394032 | − | 0.682483i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.2041 | + | 22.8701i | 0.526900 | + | 0.912617i | ||||
\(629\) | 33.9653 | 1.35429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2624 | 1.28435 | 0.642174 | − | 0.766559i | \(-0.278033\pi\) | ||||
0.642174 | + | 0.766559i | \(0.278033\pi\) | |||||||
\(632\) | 14.0278 | + | 24.2968i | 0.557994 | + | 0.966474i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.7154 | + | 25.4878i | −0.584422 | + | 1.01225i | ||||
\(635\) | 5.18762 | − | 8.98522i | 0.205864 | − | 0.356568i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.94163 | − | 5.09505i | −0.116552 | − | 0.201873i | ||||
\(638\) | 16.0145 | 0.634019 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.3421 | −0.843621 | ||||||||
\(641\) | −18.9694 | − | 32.8559i | −0.749245 | − | 1.29773i | −0.948185 | − | 0.317719i | \(-0.897083\pi\) |
0.198939 | − | 0.980012i | \(-0.436250\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.4018 | + | 33.6049i | −0.765132 | + | 1.32525i | 0.175045 | + | 0.984561i | \(0.443993\pi\) |
−0.940177 | + | 0.340687i | \(0.889340\pi\) | |||||||
\(644\) | 7.45490 | − | 12.9123i | 0.293764 | − | 0.508815i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −56.6416 | − | 98.1062i | −2.22854 | − | 3.85994i | ||||
\(647\) | 43.7279 | 1.71912 | 0.859560 | − | 0.511035i | \(-0.170738\pi\) | ||||
0.859560 | + | 0.511035i | \(0.170738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.22536 | 0.283620 | ||||||||
\(650\) | −22.6377 | − | 39.2096i | −0.887923 | − | 1.53793i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.7443 | − | 23.8059i | 0.538270 | − | 0.932311i | ||||
\(653\) | −17.5994 | + | 30.4831i | −0.688718 | + | 1.19289i | 0.283535 | + | 0.958962i | \(0.408493\pi\) |
−0.972253 | + | 0.233932i | \(0.924841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.7665 | + | 23.8443i | 0.537902 | + | 0.931674i | ||||
\(656\) | 26.9919 | 1.05386 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.2480 | −0.555444 | ||||||||
\(659\) | −2.18642 | − | 3.78700i | −0.0851710 | − | 0.147520i | 0.820293 | − | 0.571943i | \(-0.193810\pi\) |
−0.905464 | + | 0.424423i | \(0.860477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3063 | − | 19.5832i | 0.439766 | − | 0.761696i | −0.557905 | − | 0.829904i | \(-0.688395\pi\) |
0.997671 | + | 0.0682081i | \(0.0217282\pi\) | |||||||
\(662\) | −42.0821 | + | 72.8883i | −1.63557 | + | 2.83288i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.37195 | − | 16.2327i | −0.363702 | − | 0.629951i | ||||
\(665\) | −9.09019 | −0.352503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2995 | 0.437519 | ||||||||
\(668\) | 24.9846 | + | 43.2746i | 0.966684 | + | 1.67435i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.53302 | − | 11.3155i | 0.252392 | − | 0.437157i | ||||
\(671\) | 1.82685 | − | 3.16420i | 0.0705249 | − | 0.122153i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8647 | − | 22.2823i | −0.495898 | − | 0.858921i | 0.504091 | − | 0.863651i | \(-0.331828\pi\) |
−0.999989 | + | 0.00472987i | \(0.998494\pi\) | |||||||
\(674\) | −92.4830 | −3.56231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 110.743 | 4.25935 | ||||||||
\(677\) | 17.0676 | + | 29.5619i | 0.655960 | + | 1.13616i | 0.981652 | + | 0.190681i | \(0.0610696\pi\) |
−0.325692 | + | 0.945476i | \(0.605597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.12398 | + | 8.87500i | −0.196640 | + | 0.340591i | ||||
\(680\) | 41.2041 | − | 71.3675i | 1.58010 | − | 2.73682i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.12398 | + | 7.14295i | 0.157915 | + | 0.273518i | ||||
\(683\) | 13.8075 | 0.528331 | 0.264165 | − | 0.964477i | \(-0.414904\pi\) | ||||
0.264165 | + | 0.964477i | \(0.414904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.59820 | 0.328520 | ||||||||
\(686\) | 1.33454 | + | 2.31149i | 0.0509530 | + | 0.0882531i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 42.8131 | − | 74.1545i | 1.63224 | − | 2.82711i | ||||
\(689\) | −28.8075 | + | 49.8961i | −1.09748 | + | 1.90089i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.635288 | + | 1.10035i | 0.0241675 | + | 0.0418593i | 0.877856 | − | 0.478924i | \(-0.158973\pi\) |
−0.853689 | + | 0.520784i | \(0.825640\pi\) | |||||||
\(692\) | −124.572 | −4.73553 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.17554 | 0.272380 | ||||||||
\(695\) | 1.27452 | + | 2.20753i | 0.0483453 | + | 0.0837365i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.63529 | + | 13.2247i | −0.289207 | + | 0.500921i | ||||
\(698\) | −5.98068 | + | 10.3588i | −0.226372 | + | 0.392088i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.38687 | + | 12.7944i | 0.279198 | + | 0.483584i | ||||
\(701\) | 15.0000 | 0.566542 | 0.283271 | − | 0.959040i | \(-0.408580\pi\) | ||||
0.283271 | + | 0.959040i | \(0.408580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.2398 | −1.17823 | ||||||||
\(704\) | −13.1445 | − | 22.7669i | −0.495402 | − | 0.858061i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −41.5104 | + | 71.8981i | −1.56226 | + | 2.70592i | ||||
\(707\) | 4.54510 | − | 7.87234i | 0.170936 | − | 0.296070i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | + | 26.8468i | 0.582115 | + | 1.00825i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 5.29952 | 0.198888 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.61268 | 0.247821 | ||||||||
\(713\) | 2.90981 | + | 5.03994i | 0.108973 | + | 0.188747i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.61268 | + | 11.4535i | −0.247300 | + | 0.428336i | ||||
\(716\) | 34.8075 | − | 60.2884i | 1.30082 | − | 2.25308i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.3172 | + | 42.1186i | 0.907510 | + | 1.57185i | ||||
\(719\) | −36.4428 | −1.35909 | −0.679544 | − | 0.733635i | \(-0.737822\pi\) | ||||
−0.679544 | + | 0.733635i | \(0.737822\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0145 | 0.670894 | ||||||||
\(722\) | 26.7403 | + | 46.3155i | 0.995170 | + | 1.72369i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.12398 | + | 8.87500i | −0.190431 | + | 0.329837i | ||||
\(725\) | −5.59820 | + | 9.69637i | −0.207912 | + | 0.360114i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.89049 | + | 13.6667i | 0.292642 | + | 0.506871i | 0.974434 | − | 0.224676i | \(-0.0721322\pi\) |
−0.681792 | + | 0.731547i | \(0.738799\pi\) | |||||||
\(728\) | −49.0555 | −1.81812 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.31315 | 0.270672 | ||||||||
\(731\) | 24.2214 | + | 41.9527i | 0.895861 | + | 1.55168i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3864 | + | 30.1142i | −0.642182 | + | 1.11229i | 0.342762 | + | 0.939422i | \(0.388637\pi\) |
−0.984945 | + | 0.172870i | \(0.944696\pi\) | |||||||
\(734\) | −37.7173 | + | 65.3284i | −1.39217 | + | 2.41131i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.3647 | − | 38.7368i | −0.824374 | − | 1.42786i | ||||
\(737\) | 5.19880 | 0.191500 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.635288 | 0.0233694 | 0.0116847 | − | 0.999932i | \(-0.496281\pi\) | ||||
0.0116847 | + | 0.999932i | \(0.496281\pi\) | |||||||
\(740\) | −18.6373 | − | 32.2807i | −0.685119 | − | 1.18666i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.0692 | − | 22.6366i | 0.479786 | − | 0.831015i | ||||
\(743\) | 24.9448 | − | 43.2057i | 0.915136 | − | 1.58506i | 0.108434 | − | 0.994104i | \(-0.465417\pi\) |
0.806702 | − | 0.590958i | \(-0.201250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.43032 | − | 7.67354i | −0.162314 | − | 0.281137i | ||||
\(746\) | 5.74874 | 0.210476 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 53.7810 | 1.96643 | ||||||||
\(749\) | −9.11071 | − | 15.7802i | −0.332898 | − | 0.576596i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.08415 | − | 15.7342i | 0.331485 | − | 0.574150i | −0.651318 | − | 0.758805i | \(-0.725784\pi\) |
0.982803 | + | 0.184655i | \(0.0591169\pi\) | |||||||
\(752\) | −32.0483 | + | 55.5092i | −1.16868 | + | 2.02421i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30.4891 | − | 52.8087i | −1.11035 | − | 1.92318i | ||||
\(755\) | 0.924283 | 0.0336381 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.4959 | −0.526864 | −0.263432 | − | 0.964678i | \(-0.584854\pi\) | ||||
−0.263432 | + | 0.964678i | \(0.584854\pi\) | |||||||
\(758\) | −10.2391 | − | 17.7346i | −0.371900 | − | 0.644150i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −37.8977 | + | 65.6408i | −1.37470 | + | 2.38104i | ||||
\(761\) | 11.0020 | − | 19.0560i | 0.398821 | − | 0.690779i | −0.594760 | − | 0.803904i | \(-0.702753\pi\) |
0.993581 | + | 0.113125i | \(0.0360861\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.18959 | − | 14.1848i | −0.296483 | − | 0.513524i | ||||
\(764\) | −78.4564 | −2.83845 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47.5620 | −1.71848 | ||||||||
\(767\) | −13.7560 | − | 23.8261i | −0.496700 | − | 0.860309i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.8176 | + | 23.9329i | −0.498277 | + | 0.863041i | −0.999998 | − | 0.00198843i | \(-0.999367\pi\) |
0.501721 | + | 0.865029i | \(0.332700\pi\) | |||||||
\(770\) | 3.00000 | − | 5.19615i | 0.108112 | − | 0.187256i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.7154 | + | 54.9326i | 1.14146 | + | 1.97707i | ||||
\(773\) | 22.0636 | 0.793574 | 0.396787 | − | 0.917911i | \(-0.370125\pi\) | ||||
0.396787 | + | 0.917911i | \(0.370125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.76651 | −0.207139 | ||||||||
\(776\) | 42.7246 | + | 74.0011i | 1.53372 | + | 2.65649i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.240729 | − | 0.416955i | 0.00863056 | − | 0.0149486i | ||||
\(779\) | 7.02261 | − | 12.1635i | 0.251611 | − | 0.435803i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.05431 | + | 1.82611i | 0.0377260 | + | 0.0653434i | ||||
\(782\) | 52.7584 | 1.88664 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0072 | 0.428830 | ||||||||
\(785\) | 3.74916 | + | 6.49374i | 0.133813 | + | 0.231772i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0072 | − | 22.5292i | 0.463658 | − | 0.803079i | −0.535482 | − | 0.844547i | \(-0.679870\pi\) |
0.999140 | + | 0.0414676i | \(0.0132033\pi\) | |||||||
\(788\) | −14.6787 | + | 25.4243i | −0.522908 | + | 0.905704i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.53302 | + | 11.3155i | 0.232434 | + | 0.402588i | ||||
\(791\) | −7.49593 | −0.266525 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.9122 | −0.494037 | ||||||||
\(794\) | −29.8852 | − | 51.7627i | −1.06059 | − | 1.83699i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.7810 | + | 53.3142i | −1.09100 | + | 1.88967i | ||||
\(797\) | 15.4376 | − | 26.7386i | 0.546826 | − | 0.947131i | −0.451663 | − | 0.892189i | \(-0.649169\pi\) |
0.998490 | − | 0.0549426i | \(-0.0174976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.1312 | − | 31.4042i | −0.641436 | − | 1.11100i | ||||
\(800\) | 44.3212 | 1.56699 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.2697 | −1.13948 | ||||||||
\(803\) | 1.45490 | + | 2.51997i | 0.0513425 | + | 0.0889277i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.11675 | − | 3.66631i | 0.0746055 | − | 0.129221i | ||||
\(806\) | 15.7029 | − | 27.1982i | 0.553110 | − | 0.958015i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −37.8977 | − | 65.6408i | −1.33324 | − | 2.30923i | ||||
\(809\) | −43.8567 | −1.54192 | −0.770960 | − | 0.636884i | \(-0.780223\pi\) | ||||
−0.770960 | + | 0.636884i | \(0.780223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2706 | 0.395763 | 0.197882 | − | 0.980226i | \(-0.436594\pi\) | ||||
0.197882 | + | 0.980226i | \(0.436594\pi\) | |||||||
\(812\) | 9.94886 | + | 17.2319i | 0.349137 | + | 0.604722i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.3100 | − | 17.8574i | 0.361364 | − | 0.625901i | ||||
\(815\) | 3.90257 | − | 6.75945i | 0.136701 | − | 0.236773i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.2778 | − | 38.5863i | −0.779402 | − | 1.34996i | ||||
\(818\) | 54.3550 | 1.90048 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.7584 | 0.585228 | ||||||||
\(821\) | 17.2029 | + | 29.7962i | 0.600384 | + | 1.03990i | 0.992763 | + | 0.120092i | \(0.0383190\pi\) |
−0.392378 | + | 0.919804i | \(0.628348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.27058 | + | 2.20070i | −0.0442895 | + | 0.0767116i | −0.887320 | − | 0.461154i | \(-0.847436\pi\) |
0.843031 | + | 0.537865i | \(0.180769\pi\) | |||||||
\(824\) | 75.1038 | − | 130.084i | 2.61636 | − | 4.53167i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.24073 | + | 10.8093i | 0.217143 | + | 0.376102i | ||||
\(827\) | −7.90586 | −0.274914 | −0.137457 | − | 0.990508i | \(-0.543893\pi\) | ||||
−0.137457 | + | 0.990508i | \(0.543893\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.2624 | −1.39837 | −0.699186 | − | 0.714940i | \(-0.746454\pi\) | ||||
−0.699186 | + | 0.714940i | \(0.746454\pi\) | |||||||
\(830\) | −4.36471 | − | 7.55990i | −0.151501 | − | 0.262408i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −50.0502 | + | 86.6896i | −1.73518 | + | 3.00542i | ||||
\(833\) | −3.39653 | + | 5.88296i | −0.117683 | + | 0.203833i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.09414 | + | 12.2874i | 0.245503 | + | 0.425223i | ||||
\(836\) | −49.4654 | −1.71080 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.2995 | −1.01214 | ||||||||
\(839\) | −10.5258 | − | 18.2312i | −0.363390 | − | 0.629410i | 0.625126 | − | 0.780524i | \(-0.285047\pi\) |
−0.988516 | + | 0.151113i | \(0.951714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.96017 | − | 12.0554i | 0.240006 | − | 0.415702i | ||||
\(842\) | 10.3152 | − | 17.8665i | 0.355486 | − | 0.615720i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.6421 | + | 58.2698i | 1.15801 | + | 2.00573i | ||||
\(845\) | 31.4444 | 1.08172 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.61268 | −0.295935 | ||||||||
\(848\) | −58.7938 | − | 101.834i | −2.01899 | − | 3.49699i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26.1385 | + | 45.2731i | −0.896542 | + | 1.55286i | ||||
\(851\) | 7.27452 | − | 12.5998i | 0.249367 | − | 0.431917i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7367 | + | 22.0605i | 0.436095 | + | 0.755339i | 0.997384 | − | 0.0722810i | \(-0.0230278\pi\) |
−0.561289 | + | 0.827620i | \(0.689694\pi\) | |||||||
\(854\) | 6.31160 | 0.215979 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −151.933 | −5.19296 | ||||||||
\(857\) | −17.6445 | − | 30.5612i | −0.602725 | − | 1.04395i | −0.992407 | − | 0.123000i | \(-0.960748\pi\) |
0.389682 | − | 0.920949i | \(-0.372585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0145 | − | 20.8097i | 0.409929 | − | 0.710017i | −0.584953 | − | 0.811067i | \(-0.698887\pi\) |
0.994881 | + | 0.101050i | \(0.0322203\pi\) | |||||||
\(860\) | 26.5813 | − | 46.0401i | 0.906414 | − | 1.56996i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.2624 | + | 62.8084i | 1.23510 | + | 2.13926i | ||||
\(863\) | −39.8365 | −1.35605 | −0.678025 | − | 0.735039i | \(-0.737164\pi\) | ||||
−0.678025 | + | 0.735039i | \(0.737164\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.3711 | −1.20265 | ||||||||
\(866\) | 6.13649 | + | 10.6287i | 0.208526 | + | 0.361178i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.12398 | + | 8.87500i | −0.173919 | + | 0.301237i | ||||
\(869\) | −2.59940 | + | 4.50230i | −0.0881787 | + | 0.152730i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.89773 | − | 17.1434i | −0.335372 | − | 0.580881i | ||||
\(872\) | −136.572 | −4.62492 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −48.5249 | −1.64138 | ||||||||
\(875\) | 5.73469 | + | 9.93277i | 0.193868 | + | 0.335789i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.50000 | − | 16.4545i | 0.320792 | − | 0.555628i | −0.659860 | − | 0.751389i | \(-0.729384\pi\) |
0.980652 | + | 0.195761i | \(0.0627176\pi\) | |||||||
\(878\) | −32.3599 | + | 56.0489i | −1.09209 | + | 1.89156i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.4959 | − | 23.3756i | −0.454948 | − | 0.787993i | ||||
\(881\) | −1.28505 | −0.0432944 | −0.0216472 | − | 0.999766i | \(-0.506891\pi\) | ||||
−0.0216472 | + | 0.999766i | \(0.506891\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.9348 | −0.872776 | −0.436388 | − | 0.899759i | \(-0.643742\pi\) | ||||
−0.436388 | + | 0.899759i | \(0.643742\pi\) | |||||||
\(884\) | −102.391 | − | 177.346i | −3.44377 | − | 5.96479i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40.1457 | − | 69.5344i | 1.34872 | − | 2.33605i | ||||
\(887\) | −20.5596 | + | 35.6102i | −0.690323 | + | 1.19567i | 0.281409 | + | 0.959588i | \(0.409198\pi\) |
−0.971732 | + | 0.236086i | \(0.924135\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.56561 | + | 6.17582i | 0.119587 | + | 0.207130i | ||||
\(890\) | 3.07966 | 0.103231 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.51041 | −0.217985 | ||||||||
\(893\) | 16.6763 | + | 28.8842i | 0.558052 | + | 0.966574i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.88325 | − | 17.1183i | 0.330361 | − | 0.572202i | ||||
\(896\) | 7.33454 | − | 12.7038i | 0.245030 | − | 0.424404i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.2077 | − | 67.9097i | −1.30838 | − | 2.26618i | ||||
\(899\) | −7.76651 | −0.259028 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.5249 | 2.21627 | ||||||||
\(902\) | 4.63529 | + | 8.02855i | 0.154338 | + | 0.267322i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31.2511 | + | 54.1286i | −1.03940 | + | 1.80029i | ||||
\(905\) | −1.45490 | + | 2.51997i | −0.0483626 | + | 0.0837666i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.6824 | − | 28.8947i | −0.553929 | − | 0.959432i | −0.997986 | − | 0.0634341i | \(-0.979795\pi\) |
0.444057 | − | 0.895998i | \(-0.353539\pi\) | |||||||
\(908\) | 82.9822 | 2.75386 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.8462 | −0.757343 | ||||||||
\(911\) | 10.4959 | + | 18.1795i | 0.347746 | + | 0.602313i | 0.985849 | − | 0.167638i | \(-0.0536139\pi\) |
−0.638103 | + | 0.769951i | \(0.720281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.73666 | − | 3.00799i | 0.0574751 | − | 0.0995498i | ||||
\(914\) | −1.33454 | + | 2.31149i | −0.0441426 | + | 0.0764573i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.6783 | − | 54.8684i | −1.04668 | − | 1.81290i | ||||
\(917\) | −18.9243 | −0.624935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.6353 | 0.812643 | 0.406322 | − | 0.913730i | \(-0.366811\pi\) | ||||
0.406322 | + | 0.913730i | \(0.366811\pi\) | |||||||
\(920\) | −17.6498 | − | 30.5703i | −0.581895 | − | 1.00787i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.3575 | − | 19.6717i | 0.374039 | − | 0.647854i | ||||
\(923\) | 4.01447 | − | 6.95327i | 0.132138 | − | 0.228870i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.20814 | + | 12.4849i | 0.237002 | + | 0.410500i | ||||
\(926\) | −62.4395 | −2.05189 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 59.6932 | 1.95952 | ||||||||
\(929\) | −23.4940 | − | 40.6927i | −0.770812 | − | 1.33509i | −0.937119 | − | 0.349011i | \(-0.886518\pi\) |
0.166307 | − | 0.986074i | \(-0.446816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.12398 | − | 5.41090i | 0.102384 | − | 0.177335i | ||||
\(932\) | 48.1477 | − | 83.3942i | 1.57713 | − | 2.73167i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.5475 | − | 59.8380i | −1.13043 | − | 1.95796i | ||||
\(935\) | 15.2706 | 0.499401 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.6416 | 1.91574 | 0.957869 | − | 0.287205i | \(-0.0927260\pi\) | ||||
0.957869 | + | 0.287205i | \(0.0927260\pi\) | |||||||
\(938\) | 4.49034 | + | 7.77750i | 0.146615 | + | 0.253944i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.8977 | + | 34.4639i | −0.648992 | + | 1.12409i | ||||
\(941\) | 11.8659 | − | 20.5524i | 0.386818 | − | 0.669988i | −0.605202 | − | 0.796072i | \(-0.706908\pi\) |
0.992020 | + | 0.126084i | \(0.0402410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.27058 | + | 5.66480i | 0.106505 | + | 0.184471i | ||||
\(944\) | 56.1496 | 1.82752 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.4090 | 0.956170 | ||||||||
\(947\) | 8.06758 | + | 13.9735i | 0.262161 | + | 0.454077i | 0.966816 | − | 0.255474i | \(-0.0822314\pi\) |
−0.704655 | + | 0.709550i | \(0.748898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.53983 | − | 9.59527i | 0.179831 | − | 0.311476i | ||||
\(950\) | 24.0410 | − | 41.6403i | 0.779994 | − | 1.35099i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 28.3208 | + | 49.0531i | 0.917883 | + | 1.58982i | ||||
\(953\) | 20.3792 | 0.660147 | 0.330073 | − | 0.943955i | \(-0.392927\pi\) | ||||
0.330073 | + | 0.943955i | \(0.392927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.2769 | −0.720864 | ||||||||
\(956\) | 54.1380 | + | 93.7698i | 1.75095 | + | 3.03273i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.7737 | + | 27.3209i | −0.509627 | + | 0.882699i | ||||
\(959\) | −2.95490 | + | 5.11804i | −0.0954188 | + | 0.165270i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | −78.5144 | −2.53140 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32.6127 | 1.05038 | ||||||||
\(965\) | 9.00526 | + | 15.5976i | 0.289890 | + | 0.502104i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1167 | + | 20.9868i | −0.389648 | + | 0.674891i | −0.992402 | − | 0.123037i | \(-0.960737\pi\) |
0.602754 | + | 0.797927i | \(0.294070\pi\) | |||||||
\(968\) | −35.9069 | + | 62.1926i | −1.15409 | + | 1.99895i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.8977 | + | 34.4639i | 0.638878 | + | 1.10657i | ||||
\(971\) | 48.3445 | 1.55145 | 0.775724 | − | 0.631072i | \(-0.217385\pi\) | ||||
0.775724 | + | 0.631072i | \(0.217385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.75203 | −0.0561676 | ||||||||
\(974\) | 42.5193 | + | 73.6456i | 1.36241 | + | 2.35976i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1968 | − | 24.5896i | 0.454429 | − | 0.787095i | ||||
\(977\) | 13.6763 | − | 23.6881i | 0.437544 | − | 0.757849i | −0.559955 | − | 0.828523i | \(-0.689182\pi\) |
0.997499 | + | 0.0706741i | \(0.0225150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.612679 | + | 1.06119i | 0.0195813 | + | 0.0339158i | ||||
\(980\) | 7.45490 | 0.238138 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.4588 | −1.32301 | ||||||||
\(983\) | 8.53786 | + | 14.7880i | 0.272315 | + | 0.471664i | 0.969454 | − | 0.245272i | \(-0.0788773\pi\) |
−0.697139 | + | 0.716936i | \(0.745544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.16788 | + | 7.21898i | −0.132800 | + | 0.230016i | ||||
\(986\) | −35.2041 | + | 60.9752i | −1.12113 | + | 1.94185i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 94.1746 | + | 163.115i | 2.99609 | + | 5.18939i | ||||
\(989\) | 20.7505 | 0.659827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1231 | 1.21102 | 0.605510 | − | 0.795838i | \(-0.292969\pi\) | ||||
0.605510 | + | 0.795838i | \(0.292969\pi\) | |||||||
\(992\) | 15.3719 | + | 26.6250i | 0.488060 | + | 0.845345i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.82126 | + | 3.15452i | −0.0577669 | + | 0.100055i | ||||
\(995\) | −8.73995 | + | 15.1380i | −0.277075 | + | 0.479908i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.82488 | − | 6.62489i | −0.121135 | − | 0.209812i | 0.799080 | − | 0.601224i | \(-0.205320\pi\) |
−0.920216 | + | 0.391412i | \(0.871987\pi\) | |||||||
\(998\) | −66.0821 | −2.09179 | ||||||||
\(999\) | 0 | 0 |
(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 | 567.2.f.l.190.3 | 6 | ||
3.2 | odd | 2 | 567.2.f.m.190.1 | 6 | |||
9.2 | odd | 6 | 567.2.f.m.379.1 | 6 | |||
9.4 | even | 3 | 567.2.a.f.1.1 | yes | 3 | ||
9.5 | odd | 6 | 567.2.a.e.1.3 | ✓ | 3 | ||
9.7 | even | 3 | inner | 567.2.f.l.379.3 | 6 | ||
36.23 | even | 6 | 9072.2.a.bu.1.2 | 3 | |||
36.31 | odd | 6 | 9072.2.a.cb.1.2 | 3 | |||
63.13 | odd | 6 | 3969.2.a.n.1.1 | 3 | |||
63.41 | even | 6 | 3969.2.a.o.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.a.e.1.3 | ✓ | 3 | 9.5 | odd | 6 | ||
567.2.a.f.1.1 | yes | 3 | 9.4 | even | 3 | ||
567.2.f.l.190.3 | 6 | 1.1 | even | 1 | trivial | ||
567.2.f.l.379.3 | 6 | 9.7 | even | 3 | inner | ||
567.2.f.m.190.1 | 6 | 3.2 | odd | 2 | |||
567.2.f.m.379.1 | 6 | 9.2 | odd | 6 | |||
3969.2.a.n.1.1 | 3 | 63.13 | odd | 6 | |||
3969.2.a.o.1.3 | 3 | 63.41 | even | 6 | |||
9072.2.a.bu.1.2 | 3 | 36.23 | even | 6 | |||
9072.2.a.cb.1.2 | 3 | 36.31 | odd | 6 |