Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(53,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.bv (of order \(12\), degree \(4\), 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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 317.7 | ||
Character | \(\chi\) | \(=\) | 420.317 |
Dual form | 420.2.bv.c.53.7 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0801247 | − | 1.73020i | 0.0462600 | − | 0.998929i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.746108 | − | 2.10792i | −0.333670 | − | 0.942690i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.40557 | + | 1.10146i | −0.909221 | + | 0.416313i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98716 | − | 0.277263i | −0.995720 | − | 0.0924210i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.63993 | − | 1.52416i | 0.795968 | − | 0.459552i | −0.0460916 | − | 0.998937i | \(-0.514677\pi\) |
0.842059 | + | 0.539385i | \(0.181343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.512041 | − | 0.512041i | 0.142015 | − | 0.142015i | −0.632525 | − | 0.774540i | \(-0.717982\pi\) |
0.774540 | + | 0.632525i | \(0.217982\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.70690 | + | 1.12202i | −0.957116 | + | 0.289704i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.88873 | − | 1.04198i | −0.943155 | − | 0.252718i | −0.245700 | − | 0.969346i | \(-0.579018\pi\) |
−0.697455 | + | 0.716628i | \(0.745684\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.78739 | − | 3.34135i | −1.32772 | − | 0.766559i | −0.342773 | − | 0.939418i | \(-0.611366\pi\) |
−0.984947 | + | 0.172859i | \(0.944699\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.71300 | + | 4.25037i | 0.373806 | + | 0.927507i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.29376 | + | 0.614611i | −0.478282 | + | 0.128155i | −0.489902 | − | 0.871777i | \(-0.662968\pi\) |
0.0116206 | + | 0.999932i | \(0.496301\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.88664 | + | 3.14547i | −0.777329 | + | 0.629094i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.719065 | + | 5.14616i | −0.138384 | + | 0.990379i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.51556 | 1.58130 | 0.790650 | − | 0.612269i | \(-0.209743\pi\) | ||||
0.790650 | + | 0.612269i | \(0.209743\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.921008 | + | 1.59523i | 0.165418 | + | 0.286512i | 0.936804 | − | 0.349856i | \(-0.113769\pi\) |
−0.771386 | + | 0.636368i | \(0.780436\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.42558 | − | 4.68971i | −0.422239 | − | 0.816374i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.11661 | + | 4.24895i | 0.695834 | + | 0.718203i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.78938 | − | 0.747413i | 0.458572 | − | 0.122874i | −0.0221357 | − | 0.999755i | \(-0.507047\pi\) |
0.480707 | + | 0.876881i | \(0.340380\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.844905 | − | 0.926959i | −0.135293 | − | 0.148432i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.91355i | − | 1.39206i | −0.718012 | − | 0.696031i | \(-0.754948\pi\) | ||
0.718012 | − | 0.696031i | \(-0.245052\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.54399 | + | 7.54399i | −1.15045 | + | 1.15045i | −0.163984 | + | 0.986463i | \(0.552435\pi\) |
−0.986463 | + | 0.163984i | \(0.947565\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.64430 | + | 6.50356i | 0.245117 | + | 0.969493i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.95084 | − | 7.28063i | −0.284559 | − | 1.06199i | −0.949161 | − | 0.314791i | \(-0.898066\pi\) |
0.664602 | − | 0.747198i | \(-0.268601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.57357 | − | 5.29929i | 0.653367 | − | 0.757041i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.11442 | + | 6.64477i | −0.296077 | + | 0.930455i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.81412 | − | 10.5024i | 0.386549 | − | 1.44262i | −0.449161 | − | 0.893451i | \(-0.648277\pi\) |
0.835710 | − | 0.549171i | \(-0.185056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.18248 | − | 4.42756i | −0.698806 | − | 0.597012i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.24491 | + | 9.74561i | −0.827159 | + | 1.29084i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.06765 | + | 1.84923i | 0.138996 | + | 0.240749i | 0.927117 | − | 0.374772i | \(-0.122279\pi\) |
−0.788121 | + | 0.615521i | \(0.788946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12318 | − | 12.3377i | 0.912029 | − | 1.57968i | 0.100836 | − | 0.994903i | \(-0.467848\pi\) |
0.811193 | − | 0.584778i | \(-0.198818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.49123 | − | 2.62326i | 0.943806 | − | 0.330500i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.46138 | − | 0.697303i | −0.181262 | − | 0.0864898i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.03593 | − | 3.86614i | 0.126559 | − | 0.472325i | −0.873331 | − | 0.487126i | \(-0.838045\pi\) |
0.999890 | + | 0.0148018i | \(0.00471174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.879611 | + | 4.01790i | 0.105893 | + | 0.483698i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.41895i | − | 0.405755i | −0.979204 | − | 0.202878i | \(-0.934971\pi\) | ||
0.979204 | − | 0.202878i | \(-0.0650293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0196 | + | 2.95269i | 1.28975 | + | 0.345586i | 0.837564 | − | 0.546340i | \(-0.183979\pi\) |
0.452182 | + | 0.891926i | \(0.350646\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.13087 | + | 6.97669i | 0.592462 | + | 0.805599i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.67173 | + | 6.57426i | −0.532393 | + | 0.749206i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1569 | + | 7.01879i | 1.36776 | + | 0.789675i | 0.990641 | − | 0.136490i | \(-0.0435823\pi\) |
0.377117 | + | 0.926166i | \(0.376916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.84625 | + | 1.65646i | 0.982917 | + | 0.184051i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.995323 | − | 0.995323i | −0.109251 | − | 0.109251i | 0.650368 | − | 0.759619i | \(-0.274615\pi\) |
−0.759619 | + | 0.650368i | \(0.774615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.705000 | + | 8.97455i | 0.0764680 | + | 0.973427i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.682306 | − | 14.7336i | 0.0731509 | − | 1.57961i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.706248 | + | 1.22326i | −0.0748622 | + | 0.129665i | −0.901026 | − | 0.433764i | \(-0.857185\pi\) |
0.826164 | + | 0.563429i | \(0.190518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.667760 | + | 1.79575i | −0.0700003 | + | 0.188245i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.83386 | − | 1.46571i | 0.293858 | − | 0.151987i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.72528 | + | 14.6924i | −0.279608 | + | 1.50741i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.556234 | − | 0.556234i | −0.0564770 | − | 0.0564770i | 0.678304 | − | 0.734781i | \(-0.262715\pi\) |
−0.734781 | + | 0.678304i | \(0.762715\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.30847 | + | 3.82096i | −0.835033 | + | 0.384021i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.90475 | − | 1.67706i | 0.289034 | − | 0.166874i | −0.348472 | − | 0.937319i | \(-0.613299\pi\) |
0.637506 | + | 0.770445i | \(0.279966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.448028 | + | 1.67206i | 0.0441456 | + | 0.164753i | 0.984480 | − | 0.175499i | \(-0.0561540\pi\) |
−0.940334 | + | 0.340253i | \(0.889487\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.68135 | − | 6.78209i | 0.749623 | − | 0.661865i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.06095 | − | 7.69158i | −0.199240 | − | 0.743573i | −0.991128 | − | 0.132908i | \(-0.957569\pi\) |
0.791889 | − | 0.610666i | \(-0.209098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.12083 | − | 1.22446i | 0.203138 | − | 0.117282i | −0.394980 | − | 0.918690i | \(-0.629249\pi\) |
0.598119 | + | 0.801408i | \(0.295915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.06967 | − | 4.88607i | −0.101529 | − | 0.463765i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.01803 | − | 5.01803i | −0.472056 | − | 0.472056i | 0.430523 | − | 0.902580i | \(-0.358329\pi\) |
−0.902580 | + | 0.430523i | \(0.858329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00694 | + | 4.37649i | 0.280399 | + | 0.408110i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.67152 | + | 1.38758i | −0.154532 | + | 0.128282i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.5023 | − | 1.77671i | 0.962746 | − | 0.162871i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.853861 | + | 1.47893i | −0.0776237 | + | 0.134448i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.4222 | − | 0.714195i | −1.39057 | − | 0.0643968i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.53026 | + | 5.84587i | 0.852412 | + | 0.522870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.74490 | − | 5.74490i | −0.509777 | − | 0.509777i | 0.404681 | − | 0.914458i | \(-0.367383\pi\) |
−0.914458 | + | 0.404681i | \(0.867383\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4481 | + | 13.6570i | 1.09600 | + | 1.20244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.12384 | − | 0.648847i | −0.0981900 | − | 0.0566900i | 0.450101 | − | 0.892978i | \(-0.351388\pi\) |
−0.548291 | + | 0.836288i | \(0.684721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.6024 | + | 1.66329i | 1.52632 | + | 0.144226i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.3842 | − | 2.32386i | 0.979795 | − | 0.200006i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.507990 | − | 0.136116i | −0.0434006 | − | 0.0116291i | 0.237053 | − | 0.971497i | \(-0.423818\pi\) |
−0.280454 | + | 0.959867i | \(0.590485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6744i | 1.49912i | 0.661936 | + | 0.749561i | \(0.269735\pi\) | ||||
−0.661936 | + | 0.749561i | \(0.730265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.7532 | + | 2.79198i | −1.07402 | + | 0.235127i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.571317 | − | 2.13218i | 0.0477759 | − | 0.178302i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.35353 | − | 17.9501i | −0.527632 | − | 1.49068i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.80235 | − | 8.33778i | −0.726006 | − | 0.687689i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3981 | + | 18.0100i | −0.851842 | + | 1.47543i | 0.0277017 | + | 0.999616i | \(0.491181\pi\) |
−0.879544 | + | 0.475818i | \(0.842152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.44655 | − | 9.43371i | −0.443234 | − | 0.767704i | 0.554693 | − | 0.832055i | \(-0.312836\pi\) |
−0.997927 | + | 0.0643508i | \(0.979502\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.3273 | + | 4.19077i | 0.915762 | + | 0.338803i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.67545 | − | 3.13163i | 0.214897 | − | 0.251538i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.58508 | + | 9.64763i | −0.206312 | + | 0.769965i | 0.782734 | + | 0.622356i | \(0.213824\pi\) |
−0.989046 | + | 0.147609i | \(0.952842\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.9458 | − | 5.71049i | −1.42320 | − | 0.452871i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.84084 | − | 4.00498i | 0.381511 | − | 0.315636i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.883109 | − | 3.29581i | −0.0691705 | − | 0.258148i | 0.922678 | − | 0.385572i | \(-0.125996\pi\) |
−0.991848 | + | 0.127424i | \(0.959329\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.07579 | + | 8.61195i | −0.628700 | + | 0.670440i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.6613 | + | 10.6613i | −0.824994 | + | 0.824994i | −0.986819 | − | 0.161825i | \(-0.948262\pi\) |
0.161825 | + | 0.986819i | \(0.448262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4756i | 0.959664i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.3614 | + | 11.5858i | 1.25119 | + | 0.885987i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.7718 | − | 4.49399i | 1.27514 | − | 0.341672i | 0.443140 | − | 0.896453i | \(-0.353865\pi\) |
0.831996 | + | 0.554781i | \(0.187198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.88500 | − | 11.8476i | 0.444864 | − | 0.895598i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.28507 | − | 1.69908i | 0.246921 | − | 0.127711i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.14090 | − | 12.3684i | −0.533736 | − | 0.924458i | −0.999223 | − | 0.0394031i | \(-0.987454\pi\) |
0.465488 | − | 0.885054i | \(-0.345879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.90010 | −0.438551 | −0.219275 | − | 0.975663i | \(-0.570369\pi\) | ||||
−0.219275 | + | 0.975663i | \(0.570369\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.7759 | − | 13.3130i | −1.53580 | − | 0.984129i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.65667 | − | 5.32214i | −0.268844 | − | 0.391292i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.8541 | + | 3.17630i | −0.866858 | + | 0.232274i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.93852 | − | 13.1715i | −0.286485 | − | 0.958085i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.55692 | + | 5.51769i | 0.691514 | + | 0.399246i | 0.804179 | − | 0.594387i | \(-0.202605\pi\) |
−0.112665 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6035 | − | 3.64505i | −0.979203 | − | 0.262377i | −0.266494 | − | 0.963837i | \(-0.585865\pi\) |
−0.712709 | + | 0.701460i | \(0.752532\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.32356 | + | 2.47260i | −0.0947824 | + | 0.177067i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.63139 | − | 1.63139i | 0.116232 | − | 0.116232i | −0.646599 | − | 0.762830i | \(-0.723809\pi\) |
0.762830 | + | 0.646599i | \(0.223809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.65354 | − | 5.57347i | 0.684321 | − | 0.395093i | −0.117160 | − | 0.993113i | \(-0.537379\pi\) |
0.801481 | + | 0.598020i | \(0.204046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.60618 | − | 2.10214i | −0.465964 | − | 0.148273i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.4848 | + | 9.37955i | −1.43775 | + | 0.658315i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.7890 | + | 6.65047i | −1.31228 | + | 0.464489i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.02223 | − | 1.19997i | 0.488079 | − | 0.0834035i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.3711 | −1.40910 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.72171 | 0.187370 | 0.0936852 | − | 0.995602i | \(-0.470135\pi\) | ||||
0.0936852 | + | 0.995602i | \(0.470135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.91546 | − | 0.273943i | −0.405321 | − | 0.0187702i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.5307 | + | 10.2735i | 1.46838 | + | 0.700646i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.97264 | − | 2.82300i | −0.269680 | − | 0.191638i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.99168 | − | 18.8295i | 0.404880 | − | 1.27238i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.52473 | + | 1.45765i | −0.169831 | + | 0.0980522i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0957 | − | 13.0957i | 0.876950 | − | 0.876950i | −0.116268 | − | 0.993218i | \(-0.537093\pi\) |
0.993218 | + | 0.116268i | \(0.0370931\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.4822 | − | 8.31841i | 0.832143 | − | 0.554560i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.2362 | − | 3.54662i | −0.878515 | − | 0.235397i | −0.208748 | − | 0.977969i | \(-0.566939\pi\) |
−0.669766 | + | 0.742572i | \(0.733606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3326 | − | 5.96554i | −0.682799 | − | 0.394214i | 0.118110 | − | 0.993001i | \(-0.462316\pi\) |
−0.800909 | + | 0.598787i | \(0.795650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.0004 | + | 8.60978i | 0.723775 | + | 0.566482i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.76217 | − | 2.61577i | 0.639541 | − | 0.171365i | 0.0755455 | − | 0.997142i | \(-0.475930\pi\) |
0.563996 | + | 0.825778i | \(0.309264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.8914 | + | 9.54435i | −0.906177 | + | 0.622605i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.1180 | − | 20.4714i | 0.852103 | − | 1.32976i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4204 | 1.38557 | 0.692784 | − | 0.721145i | \(-0.256384\pi\) | ||||
0.692784 | + | 0.721145i | \(0.256384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.02811 | − | 8.70894i | −0.323889 | − | 0.560992i | 0.657398 | − | 0.753544i | \(-0.271657\pi\) |
−0.981287 | + | 0.192552i | \(0.938324\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.57480 | − | 15.1730i | 0.229324 | − | 0.973350i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.5828 | − | 5.68688i | −0.931664 | − | 0.363321i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.67429 | + | 1.25247i | −0.297418 | + | 0.0796930i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.80185 | + | 1.64235i | −0.114188 | + | 0.104080i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.13237i | 0.323952i | 0.986795 | + | 0.161976i | \(0.0517867\pi\) | ||||
−0.986795 | + | 0.161976i | \(0.948213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.11859 | + | 5.11859i | −0.321803 | + | 0.321803i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.5842 | − | 0.500705i | 0.975922 | − | 0.0313554i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.90270 | − | 10.8330i | −0.181065 | − | 0.675745i | −0.995439 | − | 0.0954037i | \(-0.969586\pi\) |
0.814373 | − | 0.580341i | \(-0.197081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.88682 | + | 4.87035i | −0.365789 | + | 0.302629i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.4373 | − | 2.36105i | −1.57453 | − | 0.146145i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.68895 | + | 13.7673i | −0.227470 | + | 0.848931i | 0.753930 | + | 0.656955i | \(0.228156\pi\) |
−0.981400 | + | 0.191975i | \(0.938511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.2379 | + | 1.90402i | −1.48893 | + | 0.116963i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.05989 | + | 1.31996i | 0.126063 | + | 0.0807803i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.17746 | − | 12.4317i | −0.437618 | − | 0.757976i | 0.559888 | − | 0.828568i | \(-0.310844\pi\) |
−0.997505 | + | 0.0705927i | \(0.977511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.840888 | − | 1.45646i | 0.0510803 | − | 0.0884737i | −0.839355 | − | 0.543584i | \(-0.817067\pi\) |
0.890435 | + | 0.455110i | \(0.150400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.05349 | + | 1.29924i | 0.184806 | + | 0.0786335i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.46624 | + | 14.2277i | −0.329627 | + | 0.857962i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.03258 | + | 7.58569i | −0.122126 | + | 0.455780i | −0.999721 | − | 0.0236225i | \(-0.992480\pi\) |
0.877595 | + | 0.479403i | \(0.159147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.30890 | − | 5.02058i | −0.138230 | − | 0.300574i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.01304i | 0.478018i | 0.971017 | + | 0.239009i | \(0.0768225\pi\) | ||||
−0.971017 | + | 0.239009i | \(0.923177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.35822 | + | 0.363933i | 0.0807376 | + | 0.0216336i | 0.298962 | − | 0.954265i | \(-0.403360\pi\) |
−0.218224 | + | 0.975899i | \(0.570026\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.2023 | + | 5.89249i | 1.49286 | + | 0.349041i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.81791 | + | 21.4422i | 0.579533 | + | 1.26569i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.685955 | − | 0.396036i | −0.0403503 | − | 0.0232963i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00696 | + | 0.917826i | −0.0590292 | + | 0.0538039i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.47074 | + | 3.47074i | 0.202763 | + | 0.202763i | 0.801183 | − | 0.598420i | \(-0.204205\pi\) |
−0.598420 | + | 0.801183i | \(0.704205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.10144 | − | 3.63025i | 0.180573 | − | 0.211361i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.94530 | + | 14.6814i | 0.344981 | + | 0.851904i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.859793 | + | 1.48920i | −0.0497231 | + | 0.0861229i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.83822 | − | 26.4570i | 0.567066 | − | 1.52496i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.66890 | − | 5.16017i | −0.153324 | − | 0.296444i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.3215 | − | 5.80981i | −1.79347 | − | 0.332669i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7303 | + | 19.7303i | 1.12607 | + | 1.12607i | 0.990811 | + | 0.135254i | \(0.0431852\pi\) |
0.135254 | + | 0.990811i | \(0.456815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.92890 | − | 0.641204i | 0.166619 | − | 0.0364768i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.7702 | + | 13.7238i | −1.34789 | + | 0.778203i | −0.987950 | − | 0.154774i | \(-0.950535\pi\) |
−0.359937 | + | 0.932977i | \(0.617202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.10435 | + | 22.7817i | 0.345038 | + | 1.28770i | 0.892568 | + | 0.450913i | \(0.148902\pi\) |
−0.547530 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.1189 | − | 13.8337i | −0.626478 | − | 0.779439i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.31005 | + | 31.0135i | 0.466739 | + | 1.74189i | 0.651059 | + | 0.759027i | \(0.274325\pi\) |
−0.184320 | + | 0.982866i | \(0.559008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.4804 | − | 12.9791i | 1.25866 | − | 0.726690i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.4731 | + | 2.94957i | −0.751994 | + | 0.164629i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.0240 | + | 19.0240i | 1.05852 | + | 1.05852i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.379511 | + | 3.60073i | −0.0210515 | + | 0.199733i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.94863 | − | 3.76756i | −0.107759 | − | 0.208346i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.7122 | + | 15.3653i | 0.700847 | + | 0.847117i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9114 | − | 24.0952i | 0.764637 | − | 1.32439i | −0.175801 | − | 0.984426i | \(-0.556252\pi\) |
0.940438 | − | 0.339965i | \(-0.110415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.53956 | + | 1.45925i | −0.467965 | + | 0.0799664i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.92243 | + | 0.700906i | −0.487485 | + | 0.0382946i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.16934 | − | 5.16934i | −0.281592 | − | 0.281592i | 0.552152 | − | 0.833744i | \(-0.313807\pi\) |
−0.833744 | + | 0.552152i | \(0.813807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.08424 | + | 8.28011i | −0.493388 | + | 0.449714i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.86279 | + | 2.80753i | 0.263335 | + | 0.152036i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.16511 | + | 17.7854i | −0.278890 | + | 0.960323i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.81312 | − | 4.85194i | 0.420644 | − | 0.261220i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.8906 | + | 6.66941i | 1.33620 | + | 0.358033i | 0.855022 | − | 0.518592i | \(-0.173543\pi\) |
0.481175 | + | 0.876625i | \(0.340210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.4866i | − | 0.989563i | −0.869017 | − | 0.494782i | \(-0.835248\pi\) | ||
0.869017 | − | 0.494782i | \(-0.164752\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.26685 | + | 3.00323i | 0.120996 | + | 0.160301i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.80767 | − | 25.4066i | 0.362336 | − | 1.35226i | −0.508661 | − | 0.860967i | \(-0.669859\pi\) |
0.870997 | − | 0.491289i | \(-0.163474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.20688 | + | 2.55091i | −0.382501 | + | 0.135388i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.23257 | − | 18.3134i | −0.118160 | − | 0.969250i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.69610 | + | 8.13389i | −0.247851 | + | 0.429290i | −0.962929 | − | 0.269754i | \(-0.913058\pi\) |
0.715078 | + | 0.699044i | \(0.246391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8293 | + | 22.2210i | 0.675226 | + | 1.16953i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.49043 | + | 1.59585i | 0.130713 | + | 0.0837602i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.99778 | − | 25.4314i | −0.104568 | − | 1.33114i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.54474 | − | 13.2291i | 0.185034 | − | 0.690555i | −0.809590 | − | 0.586996i | \(-0.800310\pi\) |
0.994623 | − | 0.103559i | \(-0.0330231\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.47140 | + | 26.6262i | −0.128656 | + | 1.38610i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.79845 | + | 28.3641i | 0.249123 | + | 1.47259i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.60558 | + | 28.3844i | 0.393802 | + | 1.46969i | 0.823811 | + | 0.566865i | \(0.191844\pi\) |
−0.430008 | + | 0.902825i | \(0.641489\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.8781 | − | 16.0208i | 0.561743 | − | 0.827312i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.36032 | − | 4.36032i | 0.224568 | − | 0.224568i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.342505i | − | 0.0175933i | −0.999961 | − | 0.00879664i | \(-0.997200\pi\) | ||
0.999961 | − | 0.00879664i | \(-0.00280009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4001 | + | 9.47949i | −0.532814 | + | 0.485649i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.0334 | + | 6.70768i | −1.27915 | + | 0.342746i | −0.833528 | − | 0.552477i | \(-0.813683\pi\) |
−0.445618 | + | 0.895223i | \(0.647016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.3436 | + | 4.94253i | 0.883913 | + | 0.251895i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.6268 | − | 20.4434i | 1.25185 | − | 1.03920i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.6458 | − | 25.3673i | −0.742572 | − | 1.28617i | −0.951321 | − | 0.308203i | \(-0.900272\pi\) |
0.208749 | − | 0.977969i | \(-0.433061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.56022 | 0.483481 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.21268 | + | 1.89247i | −0.0611716 | + | 0.0954624i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.72467 | − | 30.8625i | 0.288040 | − | 1.55286i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.5081 | − | 7.37078i | 1.38059 | − | 0.369929i | 0.509257 | − | 0.860615i | \(-0.329920\pi\) |
0.871337 | + | 0.490686i | \(0.163254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.28820 | − | 30.3223i | 0.214679 | − | 1.51801i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.3395 | − | 12.8977i | −1.11558 | − | 0.644081i | −0.175311 | − | 0.984513i | \(-0.556093\pi\) |
−0.940269 | + | 0.340432i | \(0.889427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.28842 | + | 0.345231i | 0.0641807 | + | 0.0171972i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.10858 | − | 19.8831i | −0.154467 | − | 0.987998i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.22459 | − | 6.22459i | 0.308541 | − | 0.308541i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.1282 | − | 14.5078i | 1.24251 | − | 0.717364i | 0.272905 | − | 0.962041i | \(-0.412015\pi\) |
0.969605 | + | 0.244677i | \(0.0786820\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.276209 | + | 0.868017i | −0.0136244 | + | 0.0428161i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.60517 | − | 3.27248i | −0.226605 | − | 0.161028i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.35544 | + | 2.84068i | −0.0665360 | + | 0.139443i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.5801 | + | 1.41615i | 1.49752 | + | 0.0693494i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.0060 | −0.977359 | −0.488679 | − | 0.872463i | \(-0.662521\pi\) | ||||
−0.488679 | + | 0.872463i | \(0.662521\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.405902 | −0.0197825 | −0.00989124 | − | 0.999951i | \(-0.503149\pi\) | ||||
−0.00989124 | + | 0.999951i | \(0.503149\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.80882 | + | 22.2893i | 0.185191 | + | 1.08374i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.3916 | − | 8.18207i | 0.892125 | − | 0.396889i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.54584 | + | 37.5251i | −0.171595 | + | 1.81597i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.64332 | − | 1.15933i | −0.175901 | − | 0.0559730i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.8654 | − | 20.1295i | 1.67940 | − | 0.969605i | 0.717364 | − | 0.696698i | \(-0.245348\pi\) |
0.962041 | − | 0.272907i | \(-0.0879850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.70713 | + | 9.70713i | −0.466495 | + | 0.466495i | −0.900777 | − | 0.434282i | \(-0.857002\pi\) |
0.434282 | + | 0.900777i | \(0.357002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.5663 | + | 9.55461i | −1.51349 | + | 0.458108i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.3285 | + | 4.10727i | 0.733263 | + | 0.196477i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6016 | + | 6.12083i | 0.505987 | + | 0.292131i | 0.731182 | − | 0.682182i | \(-0.238969\pi\) |
−0.225196 | + | 0.974314i | \(0.572302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.1313 | + | 14.5617i | −0.720537 | + | 0.693416i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5633 | + | 2.83043i | −0.501879 | + | 0.134478i | −0.500872 | − | 0.865521i | \(-0.666987\pi\) |
−0.00100695 | + | 0.999999i | \(0.500321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.10547 | + | 0.576031i | 0.147213 | + | 0.0273065i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.3276 | + | 19.4337i | 1.43445 | + | 0.919184i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.4970 | 1.06170 | 0.530849 | − | 0.847467i | \(-0.321873\pi\) | ||||
0.530849 | + | 0.847467i | \(0.321873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5857 | − | 23.5311i | −0.639725 | − | 1.10804i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.7586 | + | 8.66774i | −0.787386 | + | 0.407246i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.28351 | + | 0.0677631i | 0.200814 | + | 0.00317678i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9896 | + | 4.82030i | −0.841517 | + | 0.225484i | −0.653732 | − | 0.756726i | \(-0.726798\pi\) |
−0.187785 | + | 0.982210i | \(0.560131\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.15845 | − | 19.2628i | 0.380804 | − | 0.899108i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.92233i | 0.275830i | 0.990444 | + | 0.137915i | \(0.0440402\pi\) | ||||
−0.990444 | + | 0.137915i | \(0.955960\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.3657 | − | 26.3657i | 1.22532 | − | 1.22532i | 0.259605 | − | 0.965715i | \(-0.416408\pi\) |
0.965715 | − | 0.259605i | \(-0.0835922\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.20396 | − | 4.87997i | −0.241328 | − | 0.226303i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4566 | − | 39.0245i | −0.483873 | − | 1.80584i | −0.585083 | − | 0.810973i | \(-0.698938\pi\) |
0.101210 | − | 0.994865i | \(-0.467729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.76640 | + | 10.4413i | 0.0815646 | + | 0.482136i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.4852 | + | 5.24570i | 0.759597 | + | 0.241709i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.41731 | + | 31.4138i | −0.387028 | + | 1.44441i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.0037 | − | 5.21743i | 1.51431 | − | 0.239392i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.3182 | + | 30.5922i | −0.518224 | + | 1.40072i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.363532 | − | 0.629656i | −0.0166102 | − | 0.0287697i | 0.857601 | − | 0.514316i | \(-0.171954\pi\) |
−0.874211 | + | 0.485546i | \(0.838621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04557 | − | 1.81098i | 0.0476740 | − | 0.0825738i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.54152 | − | 8.69650i | −0.297650 | − | 0.395704i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.757485 | + | 1.58751i | −0.0343956 | + | 0.0720850i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.72938 | − | 17.6503i | 0.214309 | − | 0.799812i | −0.772100 | − | 0.635501i | \(-0.780793\pi\) |
0.986409 | − | 0.164310i | \(-0.0525398\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.77316 | + | 1.26388i | −0.261071 | + | 0.0571545i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.6269i | 1.69808i | 0.528330 | + | 0.849039i | \(0.322818\pi\) | ||||
−0.528330 | + | 0.849039i | \(0.677182\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.1147 | − | 8.87305i | −1.49141 | − | 0.399622i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.2533 | + | 14.6627i | 0.640638 | + | 0.659041i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.76584 | + | 8.22455i | 0.168921 | + | 0.368921i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.10886 | + | 1.79490i | 0.139172 | + | 0.0803509i | 0.567969 | − | 0.823050i | \(-0.307729\pi\) |
−0.428797 | + | 0.903401i | \(0.641063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5919 | + | 19.3003i | 0.785947 | + | 0.862275i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0730 | + | 11.0730i | 0.493722 | + | 0.493722i | 0.909477 | − | 0.415754i | \(-0.136482\pi\) |
−0.415754 | + | 0.909477i | \(0.636482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.70237 | − | 4.87172i | −0.253752 | − | 0.216789i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.5853 | + | 0.999606i | 0.958636 | + | 0.0443941i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.1754 | + | 29.7487i | −0.761287 | + | 1.31859i | 0.180900 | + | 0.983502i | \(0.442099\pi\) |
−0.942187 | + | 0.335087i | \(0.891234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.7607 | + | 5.03472i | −1.31654 | + | 0.222723i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.3566 | − | 27.3802i | 0.942919 | − | 1.20887i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.19030 | − | 2.19195i | 0.140581 | − | 0.0965888i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2469 | − | 16.2469i | −0.714539 | − | 0.714539i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.43165 | − | 29.3786i | −0.282318 | − | 1.28958i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.1158 | + | 13.3459i | −1.01272 | + | 0.584696i | −0.911988 | − | 0.410217i | \(-0.865453\pi\) |
−0.100736 | + | 0.994913i | \(0.532120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.89247 | + | 25.7231i | 0.301387 | + | 1.12479i | 0.936011 | + | 0.351970i | \(0.114488\pi\) |
−0.634625 | + | 0.772821i | \(0.718845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −20.0272 | − | 11.1315i | −0.874060 | − | 0.485818i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.91935 | − | 7.16310i | −0.0836080 | − | 0.312029i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0350 | + | 8.68046i | −0.653696 | + | 0.377411i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.67653 | − | 5.81996i | −0.116151 | − | 0.252565i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.56410 | − | 4.56410i | −0.197693 | − | 0.197693i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.6755 | + | 10.0831i | −0.634479 | + | 0.435929i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.9719 | + | 11.3641i | −0.948158 | + | 0.490399i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.99692 | − | 20.9606i | 0.172160 | − | 0.902836i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.10742 | − | 7.11425i | 0.176592 | − | 0.305866i | −0.764119 | − | 0.645075i | \(-0.776826\pi\) |
0.940711 | + | 0.339209i | \(0.110159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.472743 | + | 10.2083i | −0.0202874 | + | 0.438081i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.16343 | − | 3.55695i | −0.178342 | − | 0.152363i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4125 | − | 22.4125i | −0.958288 | − | 0.958288i | 0.0408761 | − | 0.999164i | \(-0.486985\pi\) |
−0.999164 | + | 0.0408761i | \(0.986985\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.6989 | + | 34.8797i | −1.05412 | + | 1.48863i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −49.2829 | − | 28.4535i | −2.09952 | − | 1.21216i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.9752 | − | 3.49388i | −1.57235 | − | 0.148575i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.50134 | + | 5.90032i | −0.403310 | + | 0.250455i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.9630 | + | 9.63625i | 1.52380 | + | 0.408301i | 0.920991 | − | 0.389585i | \(-0.127382\pi\) |
0.602809 | + | 0.797886i | \(0.294048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.72566i | 0.326761i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.54581 | + | 20.7644i | 0.191924 | + | 0.876675i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.68038 | + | 21.1995i | −0.239399 | + | 0.893450i | 0.736717 | + | 0.676201i | \(0.236375\pi\) |
−0.976116 | + | 0.217249i | \(0.930292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.83360 | + | 14.3216i | −0.287492 | + | 0.602514i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.1048 | + | 5.75906i | −0.970312 | + | 0.241858i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.0396 | − | 22.5852i | 0.546648 | − | 0.946821i | −0.451854 | − | 0.892092i | \(-0.649237\pi\) |
0.998501 | − | 0.0547292i | \(-0.0174296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.341798 | + | 0.592011i | 0.0143038 | + | 0.0247749i | 0.873089 | − | 0.487561i | \(-0.162113\pi\) |
−0.858785 | + | 0.512336i | \(0.828780\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.3124 | − | 16.0932i | 0.430808 | − | 0.672305i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.98178 | − | 9.60373i | 0.291161 | − | 0.400503i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.48627 | + | 27.9391i | −0.311657 | + | 1.16312i | 0.615404 | + | 0.788212i | \(0.288993\pi\) |
−0.927061 | + | 0.374910i | \(0.877674\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.39663 | + | 23.2447i | −0.307394 | + | 0.966017i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.49063 | + | 1.29801i | 0.144816 | + | 0.0538507i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.57836 | − | 32.0149i | −0.355279 | − | 1.32592i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.17204 | + | 2.48814i | 0.172493 | + | 0.102872i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.5547 | − | 32.5547i | 1.34367 | − | 1.34367i | 0.451304 | − | 0.892370i | \(-0.350959\pi\) |
0.892370 | − | 0.451304i | \(-0.149041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.3097i | − | 0.507211i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.69191 | − | 2.95334i | −0.110730 | − | 0.121484i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.3500 | − | 9.47201i | 1.45165 | − | 0.388969i | 0.555053 | − | 0.831815i | \(-0.312698\pi\) |
0.896598 | + | 0.442846i | \(0.146031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.5810 | − | 20.8124i | −0.474776 | − | 0.853226i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.86971 | − | 17.1491i | −0.363013 | − | 0.701865i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8528 | − | 29.1898i | −0.688585 | − | 1.19266i | −0.972296 | − | 0.233754i | \(-0.924899\pi\) |
0.283711 | − | 0.958910i | \(-0.408434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.76968 | 0.316932 | 0.158466 | − | 0.987364i | \(-0.449345\pi\) | ||||
0.158466 | + | 0.987364i | \(0.449345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.16643 | + | 11.2616i | −0.169670 | + | 0.458606i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.75454 | + | 0.696427i | 0.152644 | + | 0.0283138i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.00880159 | − | 0.00235838i | 0.000357246 | − | 9.57237e-5i | −0.258640 | − | 0.965974i | \(-0.583274\pi\) |
0.258998 | + | 0.965878i | \(0.416608\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.5871 | + | 36.1943i | 0.591100 | + | 1.46667i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.72689 | − | 2.72907i | −0.191229 | − | 0.110406i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.9113 | + | 9.89035i | 1.49083 | + | 0.399467i | 0.910018 | − | 0.414568i | \(-0.136067\pi\) |
0.580815 | + | 0.814036i | \(0.302734\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0012 | + | 33.0416i | 0.403286 | + | 1.33237i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.3739 | − | 13.3739i | 0.538413 | − | 0.538413i | −0.384650 | − | 0.923063i | \(-0.625678\pi\) |
0.923063 | + | 0.384650i | \(0.125678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.2461 | + | 20.3493i | −1.41666 | + | 0.817908i | −0.996004 | − | 0.0893126i | \(-0.971533\pi\) |
−0.420655 | + | 0.907221i | \(0.638200\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.51352 | − | 12.2460i | −0.0607356 | − | 0.491415i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.351563 | − | 3.72054i | 0.0140851 | − | 0.149060i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.21201 | − | 24.4507i | 0.208480 | − | 0.978027i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.63222 | + | 35.2459i | −0.0651848 | + | 1.40759i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.6259 | −0.463557 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9314 | 0.514789 | 0.257395 | − | 0.966306i | \(-0.417136\pi\) | ||||
0.257395 | + | 0.966306i | \(0.417136\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.218076 | − | 4.70910i | 0.00866776 | − | 0.187170i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.82346 | + | 16.3961i | −0.310465 | + | 0.650659i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.371596 | − | 5.05531i | −0.0147232 | − | 0.200299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.947949 | + | 10.2130i | −0.0375003 | + | 0.404018i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.71838 | − | 0.992107i | 0.0678719 | − | 0.0391859i | −0.465680 | − | 0.884953i | \(-0.654190\pi\) |
0.533552 | + | 0.845767i | \(0.320857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.02169 | + | 3.02169i | −0.119164 | + | 0.119164i | −0.764174 | − | 0.645010i | \(-0.776853\pi\) |
0.645010 | + | 0.764174i | \(0.276853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.5003 | − | 36.4293i | 0.767823 | − | 1.43440i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.3963 | − | 5.46518i | −0.801862 | − | 0.214858i | −0.165461 | − | 0.986216i | \(-0.552911\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.63704 | + | 3.25455i | 0.221273 | + | 0.127752i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.20265 | + | 6.64725i | −0.203908 | + | 0.260526i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.47134 | + | 0.394244i | −0.0575779 | + | 0.0154279i | −0.287493 | − | 0.957783i | \(-0.592822\pi\) |
0.229915 | + | 0.973211i | \(0.426155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.529213 | + | 2.85306i | −0.0206781 | + | 0.111478i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32.0986 | − | 11.8755i | −1.25229 | − | 0.463307i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.8543 | 1.12400 | 0.562002 | − | 0.827136i | \(-0.310031\pi\) | ||||
0.562002 | + | 0.827136i | \(0.310031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.34839 | − | 9.26369i | −0.208028 | − | 0.360316i | 0.743065 | − | 0.669219i | \(-0.233371\pi\) |
−0.951093 | + | 0.308903i | \(0.900038\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.31973 | + | 4.48506i | 0.0900908 | + | 0.174185i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.62720 | − | 38.3454i | −0.373327 | − | 1.48697i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5326 | + | 5.23376i | −0.756307 | + | 0.202652i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.6088 | − | 23.7073i | −0.835444 | − | 0.916579i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 43.4275i | − | 1.67650i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.9024 | − | 25.9024i | 0.998464 | − | 0.998464i | −0.00153521 | − | 0.999999i | \(-0.500489\pi\) |
0.999999 | + | 0.00153521i | \(0.000488674\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.3923 | − | 22.2631i | −0.515472 | − | 0.856907i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.01599 | + | 11.2558i | 0.115914 | + | 0.432597i | 0.999354 | − | 0.0359478i | \(-0.0114450\pi\) |
−0.883440 | + | 0.468545i | \(0.844778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.95073 | + | 0.725393i | 0.0748622 | + | 0.0278380i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.19689 | + | 22.6170i | −0.275785 | + | 0.866685i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.94076 | − | 18.4392i | 0.189053 | − | 0.705556i | −0.804673 | − | 0.593718i | \(-0.797660\pi\) |
0.993726 | − | 0.111838i | \(-0.0356737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0920952 | + | 1.17236i | 0.00351878 | + | 0.0447936i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1495 | + | 17.3995i | −0.425378 | + | 0.663831i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.93674 | − | 6.81863i | −0.149978 | − | 0.259769i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.0814 | + | 36.5141i | −0.801976 | + | 1.38906i | 0.116338 | + | 0.993210i | \(0.462885\pi\) |
−0.918314 | + | 0.395854i | \(0.870449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.7780 | − | 18.3431i | 0.599357 | − | 0.696795i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 37.2562 | − | 13.1870i | 1.41321 | − | 0.500211i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.28775 | + | 34.6624i | −0.351799 | + | 1.31293i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.74360 | − | 17.1001i | −0.141596 | − | 0.646784i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.0274102i | − | 0.00103527i | −1.00000 | 0.000517635i | \(-0.999835\pi\) | |||
1.00000 | 0.000517635i | \(-0.000164768\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6406 | − | 4.99474i | −0.703045 | − | 0.188380i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.4005 | + | 24.7997i | 0.580018 | + | 0.934009i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.14039 | + | 7.23376i | −0.193324 | + | 0.272054i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.5893 | − | 14.1966i | −0.923471 | − | 0.533166i | −0.0387299 | − | 0.999250i | \(-0.512331\pi\) |
−0.884741 | + | 0.466084i | \(0.845665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.3686 | − | 24.3369i | −1.28892 | − | 0.912705i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.09302 | − | 3.09302i | −0.115834 | − | 0.115834i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.92074 | + | 0.386550i | −0.184025 | + | 0.0144562i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.71630 | − | 37.0614i | 0.0640964 | − | 1.38408i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.78490 | − | 11.7518i | 0.253034 | − | 0.438268i | −0.711326 | − | 0.702863i | \(-0.751905\pi\) |
0.964360 | + | 0.264595i | \(0.0852382\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.91948 | − | 3.52879i | −0.108727 | − | 0.131419i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.4711 | + | 8.00181i | −0.575375 | + | 0.297591i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.0970 | + | 26.7855i | −1.22919 | + | 0.994787i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.5270 | − | 11.5270i | −0.427515 | − | 0.427515i | 0.460266 | − | 0.887781i | \(-0.347754\pi\) |
−0.887781 | + | 0.460266i | \(0.847754\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9659 | − | 7.40084i | −0.961700 | − | 0.274105i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.1972 | − | 21.4758i | 1.37579 | − | 0.794312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.45107 | + | 12.8796i | 0.127468 | + | 0.475718i | 0.999916 | − | 0.0129901i | \(-0.00413499\pi\) |
−0.872447 | + | 0.488708i | \(0.837468\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.0079 | + | 24.7755i | −0.406031 | + | 0.913859i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.15785 | − | 11.7853i | −0.116321 | − | 0.434116i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.3089 | − | 14.6121i | 0.931003 | − | 0.537515i | 0.0438740 | − | 0.999037i | \(-0.486030\pi\) |
0.887129 | + | 0.461522i | \(0.152697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.79250 | + | 8.18780i | 0.0658491 | + | 0.300786i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.8645 | − | 12.8645i | −0.471952 | − | 0.471952i | 0.430594 | − | 0.902546i | \(-0.358304\pi\) |
−0.902546 | + | 0.430594i | \(0.858304\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.7216 | + | 8.48088i | 1.67511 | + | 0.310715i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.69722 | + | 3.24916i | 0.0986863 | + | 0.118880i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.4297 | + | 16.2326i | 0.490712 | + | 0.593127i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.6527 | + | 18.4510i | −0.388721 | + | 0.673285i | −0.992278 | − | 0.124035i | \(-0.960416\pi\) |
0.603556 | + | 0.797320i | \(0.293750\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.88000 | + | 0.411229i | 0.323605 | + | 0.0149860i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.8218 | + | 18.5195i | −0.575813 | + | 0.673992i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4939 | + | 18.4939i | 0.672174 | + | 0.672174i | 0.958217 | − | 0.286043i | \(-0.0923401\pi\) |
−0.286043 | + | 0.958217i | \(0.592340\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.44604 | + | 9.26629i | 0.306572 | + | 0.336345i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.7628 | − | 17.1835i | −1.07890 | − | 0.622903i | −0.148300 | − | 0.988942i | \(-0.547380\pi\) |
−0.930599 | + | 0.366039i | \(0.880714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.75311 | + | 5.28153i | −0.135872 | + | 0.191204i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.382363 | − | 27.0039i | 0.0138244 | − | 0.976328i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.49356 | + | 0.400199i | 0.0539294 | + | 0.0144503i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.44100i | − | 0.304390i | −0.988350 | − | 0.152195i | \(-0.951366\pi\) | ||
0.988350 | − | 0.152195i | \(-0.0486342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9758 | + | 4.15425i | −0.683398 | + | 0.149612i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.28472 | − | 23.4549i | 0.226046 | − | 0.843614i | −0.755937 | − | 0.654644i | \(-0.772818\pi\) |
0.981983 | − | 0.188970i | \(-0.0605149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.59739 | − | 3.30310i | −0.308827 | − | 0.118651i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.95499 | + | 10.5756i | 0.285384 | + | 0.379397i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.7833 | + | 51.5862i | −1.06710 | + | 1.84827i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.21104 | − | 9.02578i | −0.186466 | − | 0.322968i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.12324 | + | 43.8224i | −0.218827 | + | 1.56609i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.2652 | − | 1.74905i | 0.794678 | − | 0.0624263i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.522746 | − | 1.95091i | 0.0186339 | − | 0.0695426i | −0.955983 | − | 0.293423i | \(-0.905206\pi\) |
0.974617 | + | 0.223880i | \(0.0718724\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.5246 | + | 7.48571i | 0.837499 | + | 0.266498i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.5984 | + | 6.54408i | 0.625727 | + | 0.232681i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67005 | − | 9.96477i | −0.0948163 | − | 0.353859i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.35227 | + | 42.0890i | 0.0479602 | + | 1.49274i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.5999 | − | 10.5999i | 0.375468 | − | 0.375468i | −0.493996 | − | 0.869464i | \(-0.664464\pi\) |
0.869464 | + | 0.493996i | \(0.164464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.3451i | 1.07353i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.44884 | − | 3.45825i | 0.0865255 | − | 0.122191i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.5913 | − | 9.00076i | 1.18541 | − | 0.317630i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0540 | − | 7.21595i | −0.424846 | − | 0.254329i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.0844 | + | 11.4223i | −0.777408 | + | 0.402085i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.50317 | + | 4.33563i | 0.0880069 | + | 0.152432i | 0.906669 | − | 0.421844i | \(-0.138617\pi\) |
−0.818662 | + | 0.574276i | \(0.805284\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.45712 | 0.226740 | 0.113370 | − | 0.993553i | \(-0.463835\pi\) | ||||
0.113370 | + | 0.993553i | \(0.463835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.45259 | − | 1.57160i | −0.0860160 | − | 0.0551184i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.28840 | + | 4.32055i | −0.220273 | + | 0.151342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68.8672 | − | 18.4529i | 2.40936 | − | 0.645585i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.49260 | − | 5.17903i | 0.0870985 | − | 0.180970i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.96631 | + | 4.59935i | 0.278026 | + | 0.160518i | 0.632530 | − | 0.774536i | \(-0.282017\pi\) |
−0.354503 | + | 0.935055i | \(0.615350\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6038 | + | 3.37717i | 0.439340 | + | 0.117721i | 0.471707 | − | 0.881755i | \(-0.343638\pi\) |
−0.0323671 | + | 0.999476i | \(0.510305\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24.1787 | + | 10.5977i | 0.841795 | + | 0.368963i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.73603 | + | 8.73603i | −0.303782 | + | 0.303782i | −0.842491 | − | 0.538710i | \(-0.818912\pi\) |
0.538710 | + | 0.842491i | \(0.318912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.6216 | + | 13.6379i | −0.820411 | + | 0.473665i | −0.850558 | − | 0.525881i | \(-0.823736\pi\) |
0.0301471 | + | 0.999545i | \(0.490402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.9619 | + | 4.12457i | 0.449643 | + | 0.143080i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.3071 | + | 15.8419i | −0.807544 | + | 0.548889i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.4276 | + | 14.5186i | 1.05299 | + | 0.502438i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.87158 | + | 3.59258i | −0.306647 | + | 0.124178i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.7675 | 0.786022 | 0.393011 | − | 0.919534i | \(-0.371433\pi\) | ||||
0.393011 | + | 0.919534i | \(0.371433\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.5147 | 1.50051 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.8641 | + | 0.642042i | 0.477506 | + | 0.0221131i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.2976 | − | 9.30817i | 0.904665 | − | 0.320211i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.425043 | − | 4.49817i | 0.0146046 | − | 0.154559i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.738502 | − | 2.32082i | 0.0253453 | − | 0.0796504i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.93881 | + | 3.42877i | −0.203580 | + | 0.117537i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.75252 | − | 7.75252i | 0.265441 | − | 0.265441i | −0.561819 | − | 0.827260i | \(-0.689898\pi\) |
0.827260 | + | 0.561819i | \(0.189898\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.2145 | − | 43.1328i | 0.417727 | − | 1.47511i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −54.0758 | − | 14.4896i | −1.84719 | − | 0.494954i | −0.847819 | − | 0.530285i | \(-0.822085\pi\) |
−0.999376 | + | 0.0353310i | \(0.988751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4633 | + | 8.35040i | 0.493482 | + | 0.284912i | 0.726018 | − | 0.687676i | \(-0.241369\pi\) |
−0.232536 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.8859 | − | 15.2689i | 1.29115 | − | 0.520362i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.0073 | + | 9.38019i | −1.19166 | + | 0.319305i | −0.799543 | − | 0.600609i | \(-0.794925\pi\) |
−0.392121 | + | 0.919914i | \(0.628258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.9865 | − | 32.0006i | −0.747565 | − | 1.08805i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.740183 | + | 1.15511i | −0.0251379 | + | 0.0392294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.7911 | 1.45159 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.44919 | − | 2.51006i | −0.0491038 | − | 0.0850502i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.50734 | + | 1.81578i | 0.0510156 | + | 0.0614550i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.3647 | − | 3.56547i | −0.992709 | − | 0.120535i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.2427 | − | 9.71119i | 1.22383 | − | 0.327924i | 0.411654 | − | 0.911340i | \(-0.364951\pi\) |
0.812173 | + | 0.583416i | \(0.198284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.28315 | − | 5.72697i | 0.211925 | − | 0.193166i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.3229i | 1.29113i | 0.763704 | + | 0.645566i | \(0.223379\pi\) | ||||
−0.763704 | + | 0.645566i | \(0.776621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.7904 | − | 14.7904i | 0.497735 | − | 0.497735i | −0.412997 | − | 0.910732i | \(-0.635518\pi\) |
0.910732 | + | 0.412997i | \(0.135518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.03254 | − | 5.65697i | −0.202782 | − | 0.190157i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.221528 | + | 0.826754i | 0.00743818 | + | 0.0277597i | 0.969545 | − | 0.244912i | \(-0.0787592\pi\) |
−0.962107 | + | 0.272672i | \(0.912093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.1475 | + | 7.49200i | 0.675727 | + | 0.251274i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.8782 | − | 9.11019i | 0.866951 | − | 0.305203i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0369 | + | 48.6543i | −0.436263 | + | 1.62815i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7437 | + | 24.2806i | −0.693385 | + | 0.811611i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.50773 | + | 1.60693i | 0.0837305 | + | 0.0536539i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.84290 | + | 13.5843i | 0.261575 | + | 0.453062i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.8867 | + | 37.9089i | −0.729152 | + | 1.26293i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −44.9876 | − | 19.1419i | −1.49709 | − | 0.637003i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.40211 | + | 12.4369i | 0.146331 | + | 0.413417i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2353 | − | 45.6627i | 0.406266 | − | 1.51621i | −0.395443 | − | 0.918491i | \(-0.629409\pi\) |
0.801709 | − | 0.597715i | \(-0.203925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.14195 | + | 4.20427i | −0.303219 | + | 0.139447i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.5777i | − | 1.07935i | −0.841875 | − | 0.539673i | \(-0.818548\pi\) | ||
0.841875 | − | 0.539673i | \(-0.181452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.14461 | − | 1.11055i | −0.137167 | − | 0.0367537i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.5617 | + | 53.7269i | −0.415279 | + | 1.77616i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.41815 | + | 0.322989i | 0.112877 | + | 0.0106660i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0821 | + | 9.86237i | 0.563487 | + | 0.325329i | 0.754544 | − | 0.656250i | \(-0.227858\pi\) |
−0.191057 | + | 0.981579i | \(0.561191\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.7181 | − | 32.5563i | 1.17695 | − | 1.07277i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.75064 | − | 1.75064i | −0.0576232 | − | 0.0576232i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.49037 | + | 11.6789i | −0.279162 | + | 0.383998i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.874731 | − | 5.11895i | −0.0287299 | − | 0.168128i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.4160 | + | 38.8256i | −0.735444 | + | 1.27383i | 0.219085 | + | 0.975706i | \(0.429693\pi\) |
−0.954528 | + | 0.298120i | \(0.903641\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −44.1759 | + | 15.3871i | −1.44781 | + | 0.504293i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.8402 | + | 42.2268i | 0.715016 | + | 1.38244i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.5398 | + | 22.6176i | 0.508206 | + | 0.739675i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.1180 | − | 20.1180i | −0.657228 | − | 0.657228i | 0.297495 | − | 0.954723i | \(-0.403849\pi\) |
−0.954723 | + | 0.297495i | \(0.903849\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39.9060 | − | 8.73634i | 1.30228 | − | 0.285100i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.7949 | − | 17.7794i | 1.00389 | − | 0.579593i | 0.0944896 | − | 0.995526i | \(-0.469878\pi\) |
0.909395 | + | 0.415933i | \(0.136545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.47836 | + | 20.4455i | 0.178400 | + | 0.665798i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.8259 | + | 18.1294i | −0.807585 | + | 0.589751i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.02075 | − | 7.54155i | −0.0656657 | − | 0.245068i | 0.925289 | − | 0.379262i | \(-0.123822\pi\) |
−0.990955 | + | 0.134194i | \(0.957155\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.15438 | − | 4.13058i | 0.232241 | − | 0.134084i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 54.3253 | − | 11.8931i | 1.76162 | − | 0.385659i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.66000 | − | 9.66000i | −0.312918 | − | 0.312918i | 0.533121 | − | 0.846039i | \(-0.321019\pi\) |
−0.846039 | + | 0.533121i | \(0.821019\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.50034 | − | 24.2620i | 0.145628 | − | 0.785100i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.6551 | − | 39.9355i | −0.667686 | − | 1.29093i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.37193 | − | 0.232095i | 0.0443021 | − | 0.00749474i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8035 | − | 23.9083i | 0.445274 | − | 0.771237i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.02381 | + | 23.5474i | 0.129665 | + | 0.758804i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.46623 | + | 31.3947i | 0.0793906 | + | 1.01063i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.2478 | − | 11.2478i | −0.361704 | − | 0.361704i | 0.502736 | − | 0.864440i | \(-0.332327\pi\) |
−0.864440 | + | 0.502736i | \(0.832327\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.4395 | − | 31.3909i | 1.10636 | − | 1.00842i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.4447 | + | 13.5358i | 0.752375 | + | 0.434384i | 0.826551 | − | 0.562861i | \(-0.190300\pi\) |
−0.0741766 | + | 0.997245i | \(0.523633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.4676 | − | 42.5170i | −0.624103 | − | 1.36303i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.19957 | + | 0.945136i | 0.198545 | + | 0.0302686i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.8489 | − | 8.26594i | −0.986944 | − | 0.264451i | −0.270978 | − | 0.962586i | \(-0.587347\pi\) |
−0.715966 | + | 0.698135i | \(0.754014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.30575i | 0.137612i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.67475 | + | 3.06963i | −0.213108 | + | 0.0980058i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.40257 | − | 27.6268i | 0.236105 | − | 0.881157i | −0.741542 | − | 0.670906i | \(-0.765905\pi\) |
0.977648 | − | 0.210251i | \(-0.0674280\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.65603 | − | 2.22164i | −0.148353 | − | 0.0707874i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.6036 | − | 20.7635i | 0.878632 | − | 0.660909i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.6675 | − | 21.9407i | 0.402802 | − | 0.697674i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.37664 | + | 16.2408i | 0.297859 | + | 0.515907i | 0.975646 | − | 0.219352i | \(-0.0703942\pi\) |
−0.677787 | + | 0.735258i | \(0.737061\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.5747 | − | 26.0000i | −1.28760 | − | 0.825085i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.9510 | − | 16.1905i | −0.600787 | − | 0.513272i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.26414 | + | 27.1101i | −0.230058 | + | 0.858587i | 0.750257 | + | 0.661146i | \(0.229930\pi\) |
−0.980315 | + | 0.197441i | \(0.936737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.84056 | + | 14.8920i | 0.0582327 | + | 0.471164i |
(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 | 420.2.bv.c.317.7 | yes | 48 | |
3.2 | odd | 2 | inner | 420.2.bv.c.317.5 | yes | 48 | |
5.3 | odd | 4 | inner | 420.2.bv.c.233.12 | yes | 48 | |
7.4 | even | 3 | inner | 420.2.bv.c.137.3 | yes | 48 | |
15.8 | even | 4 | inner | 420.2.bv.c.233.3 | yes | 48 | |
21.11 | odd | 6 | inner | 420.2.bv.c.137.12 | yes | 48 | |
35.18 | odd | 12 | inner | 420.2.bv.c.53.5 | ✓ | 48 | |
105.53 | even | 12 | inner | 420.2.bv.c.53.7 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bv.c.53.5 | ✓ | 48 | 35.18 | odd | 12 | inner | |
420.2.bv.c.53.7 | yes | 48 | 105.53 | even | 12 | inner | |
420.2.bv.c.137.3 | yes | 48 | 7.4 | even | 3 | inner | |
420.2.bv.c.137.12 | yes | 48 | 21.11 | odd | 6 | inner | |
420.2.bv.c.233.3 | yes | 48 | 15.8 | even | 4 | inner | |
420.2.bv.c.233.12 | yes | 48 | 5.3 | odd | 4 | inner | |
420.2.bv.c.317.5 | yes | 48 | 3.2 | odd | 2 | inner | |
420.2.bv.c.317.7 | yes | 48 | 1.1 | even | 1 | trivial |