Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(611,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.611");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bb (of order \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(44\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 611.14 | ||
Character | \(\chi\) | \(=\) | 756.611 |
Dual form | 756.2.bb.a.683.14 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.801193 | + | 1.16537i | −0.566529 | + | 0.824042i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.716179 | − | 1.86737i | −0.358089 | − | 0.933687i | ||||
\(5\) | −2.71842 | + | 1.56948i | −1.21571 | + | 0.701892i | −0.963998 | − | 0.265909i | \(-0.914328\pi\) |
−0.251715 | + | 0.967801i | \(0.580995\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.39714 | − | 1.11970i | −0.906034 | − | 0.423206i | ||||
\(8\) | 2.74998 | + | 0.661514i | 0.972265 | + | 0.233881i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.348953 | − | 4.42542i | 0.110348 | − | 1.39944i | ||||
\(11\) | 1.84616 | − | 3.19765i | 0.556639 | − | 0.964127i | −0.441135 | − | 0.897441i | \(-0.645424\pi\) |
0.997774 | − | 0.0666862i | \(-0.0212426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.398951 | − | 0.691003i | 0.110649 | − | 0.191650i | −0.805383 | − | 0.592755i | \(-0.798040\pi\) |
0.916032 | + | 0.401105i | \(0.131374\pi\) | |||||||
\(14\) | 3.22543 | − | 1.89646i | 0.862034 | − | 0.506851i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.97418 | + | 2.67475i | −0.743544 | + | 0.668687i | ||||
\(17\) | 2.63178 | − | 1.51946i | 0.638301 | − | 0.368523i | −0.145659 | − | 0.989335i | \(-0.546530\pi\) |
0.783960 | + | 0.620812i | \(0.213197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.92177 | + | 2.26423i | 0.899715 | + | 0.519451i | 0.877108 | − | 0.480294i | \(-0.159470\pi\) |
0.0226074 | + | 0.999744i | \(0.492803\pi\) | |||||||
\(20\) | 4.87768 | + | 3.95228i | 1.09068 | + | 0.883756i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.24731 | + | 4.71340i | 0.479129 | + | 1.00490i | ||||
\(23\) | 1.10618 | + | 1.91595i | 0.230654 | + | 0.399504i | 0.958001 | − | 0.286766i | \(-0.0925802\pi\) |
−0.727347 | + | 0.686270i | \(0.759247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.42653 | − | 4.20287i | 0.485305 | − | 0.840573i | ||||
\(26\) | 0.485638 | + | 1.01855i | 0.0952415 | + | 0.199755i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.374113 | + | 5.27826i | −0.0707007 | + | 0.997498i | ||||
\(29\) | −8.16616 | + | 4.71474i | −1.51642 | + | 0.875505i | −0.516604 | + | 0.856224i | \(0.672804\pi\) |
−0.999814 | + | 0.0192805i | \(0.993862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.16508i | 0.388860i | 0.980916 | + | 0.194430i | \(0.0622858\pi\) | ||||
−0.980916 | + | 0.194430i | \(0.937714\pi\) | |||||||
\(32\) | −0.734183 | − | 5.60901i | −0.129786 | − | 0.991542i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.337832 | + | 4.28438i | −0.0579377 | + | 0.734766i | ||||
\(35\) | 8.27376 | − | 0.718458i | 1.39852 | − | 0.121441i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.94414 | + | 5.09940i | −0.484013 | + | 0.838336i | −0.999831 | − | 0.0183623i | \(-0.994155\pi\) |
0.515818 | + | 0.856698i | \(0.327488\pi\) | |||||||
\(38\) | −5.78077 | + | 2.75622i | −0.937764 | + | 0.447119i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.51383 | + | 2.51777i | −1.34615 | + | 0.398094i | ||||
\(41\) | 9.25469 | + | 5.34320i | 1.44534 | + | 0.834467i | 0.998199 | − | 0.0599959i | \(-0.0191088\pi\) |
0.447141 | + | 0.894463i | \(0.352442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.01769 | − | 2.31962i | 0.612693 | − | 0.353738i | −0.161326 | − | 0.986901i | \(-0.551577\pi\) |
0.774019 | + | 0.633163i | \(0.218244\pi\) | |||||||
\(44\) | −7.29339 | − | 1.15739i | −1.09952 | − | 0.174483i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.11906 | − | 0.245944i | −0.459880 | − | 0.0362624i | ||||
\(47\) | 10.6006 | 1.54626 | 0.773128 | − | 0.634250i | \(-0.218691\pi\) | ||||
0.773128 | + | 0.634250i | \(0.218691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.49256 | + | 5.36814i | 0.641794 | + | 0.766877i | ||||
\(50\) | 2.95378 | + | 6.19511i | 0.417728 | + | 0.876121i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.57608 | − | 0.250109i | −0.218563 | − | 0.0346839i | ||||
\(53\) | 6.12081 | − | 3.53385i | 0.840758 | − | 0.485412i | −0.0167637 | − | 0.999859i | \(-0.505336\pi\) |
0.857522 | + | 0.514447i | \(0.172003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5900i | 1.56280i | ||||||||
\(56\) | −5.85140 | − | 4.66489i | −0.781926 | − | 0.623372i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.04826 | − | 13.2940i | 0.137643 | − | 1.74559i | ||||
\(59\) | −0.509408 | −0.0663192 | −0.0331596 | − | 0.999450i | \(-0.510557\pi\) | ||||
−0.0331596 | + | 0.999450i | \(0.510557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.56150 | 1.22422 | 0.612112 | − | 0.790771i | \(-0.290320\pi\) | ||||
0.612112 | + | 0.790771i | \(0.290320\pi\) | |||||||
\(62\) | −2.52312 | − | 1.73465i | −0.320437 | − | 0.220301i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.12480 | + | 3.63830i | 0.890600 | + | 0.454788i | ||||
\(65\) | 2.50458i | 0.310655i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.45608i | − | 0.910906i | −0.890260 | − | 0.455453i | \(-0.849477\pi\) | ||
0.890260 | − | 0.455453i | \(-0.150523\pi\) | |||||||
\(68\) | −4.72223 | − | 3.82632i | −0.572654 | − | 0.464009i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.79162 | + | 10.2176i | −0.692230 | + | 1.22124i | ||||
\(71\) | −2.15661 | −0.255942 | −0.127971 | − | 0.991778i | \(-0.540847\pi\) | ||||
−0.127971 | + | 0.991778i | \(0.540847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.27196 | + | 2.20310i | 0.148871 | + | 0.257853i | 0.930811 | − | 0.365502i | \(-0.119103\pi\) |
−0.781939 | + | 0.623355i | \(0.785769\pi\) | |||||||
\(74\) | −3.58387 | − | 7.51662i | −0.416616 | − | 0.873789i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41949 | − | 8.94500i | 0.162826 | − | 1.02606i | ||||
\(77\) | −8.00590 | + | 5.59807i | −0.912357 | + | 0.637959i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.3964i | − | 1.16969i | −0.811145 | − | 0.584846i | \(-0.801155\pi\) | ||
0.811145 | − | 0.584846i | \(-0.198845\pi\) | |||||||
\(80\) | 3.88709 | − | 11.9390i | 0.434590 | − | 1.33482i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.6416 | + | 6.50421i | −1.50646 | + | 0.718270i | ||||
\(83\) | −0.812599 | − | 1.40746i | −0.0891943 | − | 0.154489i | 0.817976 | − | 0.575252i | \(-0.195096\pi\) |
−0.907171 | + | 0.420763i | \(0.861763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.76952 | + | 8.26105i | −0.517327 | + | 0.896037i | ||||
\(86\) | −0.515736 | + | 6.54057i | −0.0556132 | + | 0.705287i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.19220 | − | 7.57221i | 0.766691 | − | 0.807200i | ||||
\(89\) | 1.73558 | + | 1.00204i | 0.183971 | + | 0.106216i | 0.589157 | − | 0.808019i | \(-0.299460\pi\) |
−0.405186 | + | 0.914234i | \(0.632793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73006 | + | 1.20973i | −0.181359 | + | 0.126814i | ||||
\(92\) | 2.78558 | − | 3.43781i | 0.290417 | − | 0.358417i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.49313 | + | 12.3536i | −0.876000 | + | 1.27418i | ||||
\(95\) | −14.2147 | −1.45839 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.88309 | − | 3.26161i | −0.191199 | − | 0.331167i | 0.754449 | − | 0.656359i | \(-0.227904\pi\) |
−0.945648 | + | 0.325192i | \(0.894571\pi\) | |||||||
\(98\) | −9.85528 | + | 0.934580i | −0.995534 | + | 0.0944069i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.58615 | − | 1.52123i | −0.958615 | − | 0.152123i | ||||
\(101\) | 14.8471 | + | 8.57197i | 1.47734 | + | 0.852943i | 0.999672 | − | 0.0255972i | \(-0.00814873\pi\) |
0.477668 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.78573 | − | 1.60834i | 0.274486 | − | 0.158475i | −0.356438 | − | 0.934319i | \(-0.616009\pi\) |
0.630925 | + | 0.775844i | \(0.282676\pi\) | |||||||
\(104\) | 1.55422 | − | 1.63634i | 0.152403 | − | 0.160456i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.785705 | + | 9.96432i | −0.0763144 | + | 0.967820i | ||||
\(107\) | −1.77960 | + | 3.08236i | −0.172041 | + | 0.297983i | −0.939133 | − | 0.343553i | \(-0.888369\pi\) |
0.767092 | + | 0.641537i | \(0.221703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.56961 | + | 4.45070i | 0.246124 | + | 0.426300i | 0.962447 | − | 0.271469i | \(-0.0875095\pi\) |
−0.716323 | + | 0.697769i | \(0.754176\pi\) | |||||||
\(110\) | −13.5067 | − | 9.28587i | −1.28781 | − | 0.885373i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.1244 | − | 3.08157i | 0.956668 | − | 0.291181i | ||||
\(113\) | 7.11141 | + | 4.10577i | 0.668985 | + | 0.386239i | 0.795692 | − | 0.605701i | \(-0.207107\pi\) |
−0.126707 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.01410 | − | 3.47224i | −0.560818 | − | 0.323788i | ||||
\(116\) | 14.6526 | + | 11.8727i | 1.36046 | + | 1.10235i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.408134 | − | 0.593649i | 0.0375718 | − | 0.0546498i | ||||
\(119\) | −8.01009 | + | 0.695561i | −0.734283 | + | 0.0637620i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.31663 | − | 2.28047i | −0.119694 | − | 0.207316i | ||||
\(122\) | −7.66061 | + | 11.1427i | −0.693559 | + | 1.00881i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.04302 | − | 1.55059i | 0.363074 | − | 0.139247i | ||||
\(125\) | − | 0.461263i | − | 0.0412566i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.6020i | − | 1.47319i | −0.676333 | − | 0.736596i | \(-0.736432\pi\) | ||
0.676333 | − | 0.736596i | \(-0.263568\pi\) | |||||||
\(128\) | −9.94831 | + | 5.38805i | −0.879315 | + | 0.476241i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.91877 | − | 2.00665i | −0.255993 | − | 0.175995i | ||||
\(131\) | 5.74553 | + | 9.95156i | 0.501990 | + | 0.869471i | 0.999997 | + | 0.00229890i | \(0.000731762\pi\) |
−0.498008 | + | 0.867173i | \(0.665935\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.86577 | − | 9.81887i | −0.595338 | − | 0.851404i | ||||
\(134\) | 8.68910 | + | 5.97377i | 0.750624 | + | 0.516055i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.24250 | − | 2.43753i | 0.706789 | − | 0.209016i | ||||
\(137\) | −12.0589 | − | 6.96218i | −1.03026 | − | 0.594819i | −0.113199 | − | 0.993572i | \(-0.536110\pi\) |
−0.917058 | + | 0.398753i | \(0.869443\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1223 | − | 7.57615i | −1.11302 | − | 0.642601i | −0.173408 | − | 0.984850i | \(-0.555478\pi\) |
−0.939609 | + | 0.342249i | \(0.888811\pi\) | |||||||
\(140\) | −7.26712 | − | 14.9357i | −0.614184 | − | 1.26229i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.72786 | − | 2.51325i | 0.144999 | − | 0.210907i | ||||
\(143\) | −1.47306 | − | 2.55141i | −0.123183 | − | 0.213360i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.7994 | − | 25.6332i | 1.22902 | − | 2.12872i | ||||
\(146\) | −3.58651 | − | 0.282803i | −0.296822 | − | 0.0234049i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.6310 | + | 1.84573i | 0.956064 | + | 0.151718i | ||||
\(149\) | −15.6827 | + | 9.05441i | −1.28478 | + | 0.741766i | −0.977718 | − | 0.209924i | \(-0.932678\pi\) |
−0.307059 | + | 0.951690i | \(0.599345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0993 | + | 9.87226i | 1.39152 | + | 0.803393i | 0.993483 | − | 0.113977i | \(-0.0363590\pi\) |
0.398035 | + | 0.917370i | \(0.369692\pi\) | |||||||
\(152\) | 9.28697 | + | 8.82091i | 0.753272 | + | 0.715470i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.109546 | − | 13.8150i | −0.00882743 | − | 1.11324i | ||||
\(155\) | −3.39805 | − | 5.88560i | −0.272938 | − | 0.472743i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.62102 | −0.448606 | −0.224303 | − | 0.974519i | \(-0.572011\pi\) | ||||
−0.224303 | + | 0.974519i | \(0.572011\pi\) | |||||||
\(158\) | 12.1157 | + | 8.32956i | 0.963874 | + | 0.662664i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.7990 | + | 14.0953i | 0.853739 | + | 1.11433i | ||||
\(161\) | −0.506373 | − | 5.83139i | −0.0399078 | − | 0.459578i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.24708 | + | 1.87470i | 0.254331 | + | 0.146838i | 0.621746 | − | 0.783219i | \(-0.286424\pi\) |
−0.367415 | + | 0.930057i | \(0.619757\pi\) | |||||||
\(164\) | 3.34974 | − | 21.1087i | 0.261571 | − | 1.64831i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.29126 | + | 0.180670i | 0.177837 | + | 0.0140227i | ||||
\(167\) | 0.739116 | − | 1.28019i | 0.0571945 | − | 0.0990638i | −0.836011 | − | 0.548713i | \(-0.815118\pi\) |
0.893205 | + | 0.449650i | \(0.148451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.18168 | + | 10.7070i | 0.475514 | + | 0.823614i | ||||
\(170\) | −5.80588 | − | 12.1770i | −0.445291 | − | 0.933930i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.20898 | − | 5.84128i | −0.549680 | − | 0.445393i | ||||
\(173\) | − | 6.91237i | − | 0.525537i | −0.964859 | − | 0.262769i | \(-0.915364\pi\) | ||
0.964859 | − | 0.262769i | \(-0.0846356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5227 | + | 7.35789i | −0.795438 | + | 0.556204i | ||||
\(176\) | 3.06209 | + | 14.4484i | 0.230813 | + | 1.08909i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.55828 | + | 1.21977i | −0.191751 | + | 0.0914254i | ||||
\(179\) | −1.52346 | − | 2.63872i | −0.113869 | − | 0.197227i | 0.803458 | − | 0.595361i | \(-0.202991\pi\) |
−0.917327 | + | 0.398134i | \(0.869658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.27649 | −0.169210 | −0.0846049 | − | 0.996415i | \(-0.526963\pi\) | ||||
−0.0846049 | + | 0.996415i | \(0.526963\pi\) | |||||||
\(182\) | −0.0236725 | − | 2.98538i | −0.00175472 | − | 0.221291i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.77453 | + | 6.00059i | 0.130820 | + | 0.442369i | ||||
\(185\) | − | 18.4831i | − | 1.35890i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 11.2207i | − | 0.820538i | ||||||
\(188\) | −7.59192 | − | 19.7953i | −0.553698 | − | 1.44372i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.3887 | − | 16.5654i | 0.826223 | − | 1.20178i | ||||
\(191\) | −8.64042 | −0.625199 | −0.312599 | − | 0.949885i | \(-0.601200\pi\) | ||||
−0.312599 | + | 0.949885i | \(0.601200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9563 | 1.65243 | 0.826215 | − | 0.563355i | \(-0.190490\pi\) | ||||
0.826215 | + | 0.563355i | \(0.190490\pi\) | |||||||
\(194\) | 5.30971 | + | 0.418681i | 0.381215 | + | 0.0300595i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.80685 | − | 12.2338i | 0.486204 | − | 0.873845i | ||||
\(197\) | − | 6.30658i | − | 0.449325i | −0.974437 | − | 0.224663i | \(-0.927872\pi\) | ||
0.974437 | − | 0.224663i | \(-0.0721280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1317 | − | 6.42691i | 0.789108 | − | 0.455592i | −0.0505404 | − | 0.998722i | \(-0.516094\pi\) |
0.839648 | + | 0.543130i | \(0.182761\pi\) | |||||||
\(200\) | 9.45316 | − | 9.95262i | 0.668439 | − | 0.703757i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.8849 | + | 10.4346i | −1.53982 | + | 0.734173i | ||||
\(203\) | 24.8545 | − | 2.15826i | 1.74444 | − | 0.151480i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −33.5441 | −2.34282 | ||||||||
\(206\) | −0.357594 | + | 4.53501i | −0.0249147 | + | 0.315969i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.661709 | + | 3.12226i | 0.0458813 | + | 0.216490i | ||||
\(209\) | 14.4804 | − | 8.36029i | 1.00163 | − | 0.578293i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3528 | − | 7.13189i | −0.850402 | − | 0.490980i | 0.0103847 | − | 0.999946i | \(-0.496694\pi\) |
−0.860786 | + | 0.508966i | \(0.830028\pi\) | |||||||
\(212\) | −10.9826 | − | 8.89898i | −0.754290 | − | 0.611184i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.16629 | − | 4.54347i | −0.148085 | − | 0.310585i | ||||
\(215\) | −7.28118 | + | 12.6114i | −0.496572 | + | 0.860088i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.42424 | − | 5.19001i | 0.164568 | − | 0.352321i | ||||
\(218\) | −7.24547 | − | 0.571319i | −0.490725 | − | 0.0386946i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 21.6430 | − | 8.30055i | 1.45917 | − | 0.559623i | ||||
\(221\) | − | 2.42476i | − | 0.163107i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.96034 | − | 2.28651i | 0.265204 | − | 0.153116i | −0.361502 | − | 0.932371i | \(-0.617736\pi\) |
0.626706 | + | 0.779256i | \(0.284403\pi\) | |||||||
\(224\) | −4.52045 | + | 14.2676i | −0.302035 | + | 0.953297i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.4824 | + | 4.99791i | −0.697276 | + | 0.332456i | ||||
\(227\) | −3.22107 | + | 5.57906i | −0.213790 | + | 0.370295i | −0.952898 | − | 0.303292i | \(-0.901914\pi\) |
0.739108 | + | 0.673587i | \(0.235247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.29989 | + | 5.71557i | 0.218063 | + | 0.377696i | 0.954216 | − | 0.299120i | \(-0.0966930\pi\) |
−0.736153 | + | 0.676815i | \(0.763360\pi\) | |||||||
\(230\) | 8.86491 | − | 4.22672i | 0.584535 | − | 0.278702i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.5757 | + | 7.56341i | −1.67912 | + | 0.496562i | ||||
\(233\) | 4.20962 | + | 2.43043i | 0.275781 | + | 0.159222i | 0.631512 | − | 0.775366i | \(-0.282435\pi\) |
−0.355731 | + | 0.934589i | \(0.615768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.8169 | + | 16.6374i | −1.87980 | + | 1.08531i | ||||
\(236\) | 0.364827 | + | 0.951255i | 0.0237482 | + | 0.0619214i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.60704 | − | 9.89200i | 0.363451 | − | 0.641203i | ||||
\(239\) | 7.00661 | − | 12.1358i | 0.453220 | − | 0.785000i | −0.545364 | − | 0.838199i | \(-0.683608\pi\) |
0.998584 | + | 0.0531992i | \(0.0169418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.09728 | − | 3.63260i | 0.135098 | − | 0.233997i | −0.790537 | − | 0.612414i | \(-0.790198\pi\) |
0.925635 | + | 0.378418i | \(0.123532\pi\) | |||||||
\(242\) | 3.71247 | + | 0.292735i | 0.238647 | + | 0.0188177i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.84774 | − | 17.8549i | −0.438382 | − | 1.14304i | ||||
\(245\) | −20.6378 | − | 7.54186i | −1.31850 | − | 0.481832i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12919 | − | 1.80664i | 0.199105 | − | 0.114954i | ||||
\(248\) | −1.43223 | + | 5.95394i | −0.0909469 | + | 0.378075i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.537542 | + | 0.369561i | 0.0339972 | + | 0.0233731i | ||||
\(251\) | −4.07143 | −0.256986 | −0.128493 | − | 0.991710i | \(-0.541014\pi\) | ||||
−0.128493 | + | 0.991710i | \(0.541014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.16873 | 0.513564 | ||||||||
\(254\) | 19.3475 | + | 13.3014i | 1.21397 | + | 0.834606i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.69145 | − | 15.9103i | 0.105716 | − | 0.994396i | ||||
\(257\) | 22.8777 | − | 13.2084i | 1.42707 | − | 0.823920i | 0.430183 | − | 0.902742i | \(-0.358449\pi\) |
0.996889 | + | 0.0788211i | \(0.0251156\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.7673 | − | 8.92743i | 0.793321 | − | 0.554723i | ||||
\(260\) | 4.67699 | − | 1.79373i | 0.290055 | − | 0.111242i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.2005 | − | 1.27744i | −1.00087 | − | 0.0789206i | ||||
\(263\) | 1.36934 | − | 2.37177i | 0.0844373 | − | 0.146250i | −0.820714 | − | 0.571339i | \(-0.806424\pi\) |
0.905151 | + | 0.425090i | \(0.139757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0926 | + | 19.2130i | −0.681414 | + | 1.18024i | ||||
\(266\) | 16.9434 | − | 0.134353i | 1.03887 | − | 0.00823769i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.9233 | + | 5.33989i | −0.850501 | + | 0.326186i | ||||
\(269\) | −11.0850 | + | 6.39993i | −0.675865 | + | 0.390211i | −0.798295 | − | 0.602266i | \(-0.794265\pi\) |
0.122430 | + | 0.992477i | \(0.460931\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.3102 | + | 11.1488i | 1.17301 | + | 0.677240i | 0.954388 | − | 0.298569i | \(-0.0965093\pi\) |
0.218626 | + | 0.975809i | \(0.429843\pi\) | |||||||
\(272\) | −3.76321 | + | 11.5585i | −0.228178 | + | 0.700837i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.7750 | − | 8.47498i | 1.07383 | − | 0.511992i | ||||
\(275\) | −8.95952 | − | 15.5183i | −0.540280 | − | 0.935792i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.01753 | + | 15.6188i | −0.541811 | + | 0.938444i | 0.456989 | + | 0.889472i | \(0.348928\pi\) |
−0.998800 | + | 0.0489717i | \(0.984406\pi\) | |||||||
\(278\) | 19.3425 | − | 9.22236i | 1.16009 | − | 0.553121i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 23.2280 | + | 3.49747i | 1.38814 | + | 0.209014i | ||||
\(281\) | −6.29086 | + | 3.63203i | −0.375281 | + | 0.216669i | −0.675763 | − | 0.737119i | \(-0.736186\pi\) |
0.300482 | + | 0.953788i | \(0.402853\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.99707i | 0.594264i | 0.954836 | + | 0.297132i | \(0.0960302\pi\) | ||||
−0.954836 | + | 0.297132i | \(0.903970\pi\) | |||||||
\(284\) | 1.54452 | + | 4.02720i | 0.0916503 | + | 0.238970i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.15354 | + | 0.327514i | 0.245604 | + | 0.0193663i | ||||
\(287\) | −16.2020 | − | 23.1708i | −0.956375 | − | 1.36773i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.88248 | + | 6.72465i | −0.228381 | + | 0.395568i | ||||
\(290\) | 18.0151 | + | 37.7839i | 1.05788 | + | 2.21875i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.20306 | − | 3.95303i | 0.187445 | − | 0.231334i | ||||
\(293\) | 20.0527 | + | 11.5774i | 1.17149 | + | 0.676361i | 0.954031 | − | 0.299708i | \(-0.0968893\pi\) |
0.217460 | + | 0.976069i | \(0.430223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.38478 | − | 0.799505i | 0.0806252 | − | 0.0465490i | ||||
\(296\) | −11.4697 | + | 12.0757i | −0.666660 | + | 0.701884i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.01313 | − | 25.5305i | 0.116617 | − | 1.47894i | ||||
\(299\) | 1.76524 | 0.102087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.2282 | + | 1.06185i | −0.704824 | + | 0.0612038i | ||||
\(302\) | −25.2047 | + | 12.0174i | −1.45037 | + | 0.691523i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −17.7203 | + | 3.75551i | −1.01633 | + | 0.215393i | ||||
\(305\) | −25.9921 | + | 15.0066i | −1.48831 | + | 0.859273i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.4146i | 1.62171i | 0.585250 | + | 0.810853i | \(0.300996\pi\) | ||||
−0.585250 | + | 0.810853i | \(0.699004\pi\) | |||||||
\(308\) | 16.1873 | + | 10.9408i | 0.922359 | + | 0.623410i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.58140 | + | 0.755511i | 0.544187 | + | 0.0429102i | ||||
\(311\) | −4.59925 | −0.260799 | −0.130400 | − | 0.991462i | \(-0.541626\pi\) | ||||
−0.130400 | + | 0.991462i | \(0.541626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3503 | −1.20679 | −0.603395 | − | 0.797442i | \(-0.706186\pi\) | ||||
−0.603395 | + | 0.797442i | \(0.706186\pi\) | |||||||
\(314\) | 4.50352 | − | 6.55057i | 0.254149 | − | 0.369670i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.4141 | + | 7.44571i | −1.09213 | + | 0.418854i | ||||
\(317\) | − | 2.13460i | − | 0.119891i | −0.998202 | − | 0.0599457i | \(-0.980907\pi\) | ||
0.998202 | − | 0.0599457i | \(-0.0190927\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.8167i | 1.94936i | ||||||||
\(320\) | −25.0784 | + | 1.29179i | −1.40193 | + | 0.0722132i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.20144 | + | 4.08196i | 0.401320 | + | 0.227479i | ||||
\(323\) | 13.7617 | 0.765719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.93613 | − | 3.35348i | −0.107397 | − | 0.186017i | ||||
\(326\) | −4.78626 | + | 2.28205i | −0.265086 | + | 0.126391i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21.9156 | + | 20.8158i | 1.21009 | + | 1.14936i | ||||
\(329\) | −25.4111 | − | 11.8695i | −1.40096 | − | 0.654384i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.0079i | 1.59442i | 0.603704 | + | 0.797209i | \(0.293691\pi\) | ||||
−0.603704 | + | 0.797209i | \(0.706309\pi\) | |||||||
\(332\) | −2.04629 | + | 2.52542i | −0.112305 | + | 0.138600i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.899717 | + | 1.88702i | 0.0492303 | + | 0.103253i | ||||
\(335\) | 11.7022 | + | 20.2687i | 0.639358 | + | 1.10740i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.37475 | − | 11.0414i | 0.347255 | − | 0.601463i | −0.638506 | − | 0.769617i | \(-0.720447\pi\) |
0.985761 | + | 0.168154i | \(0.0537807\pi\) | |||||||
\(338\) | −17.4303 | − | 1.37441i | −0.948084 | − | 0.0747582i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.8423 | + | 2.99009i | 1.02187 | + | 0.162161i | ||||
\(341\) | 6.92317 | + | 3.99709i | 0.374911 | + | 0.216455i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.75860 | − | 17.8985i | −0.256940 | − | 0.966427i | ||||
\(344\) | 12.5830 | − | 3.72114i | 0.678432 | − | 0.200630i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.05547 | + | 5.53814i | 0.433065 | + | 0.297732i | ||||
\(347\) | −31.5387 | −1.69308 | −0.846542 | − | 0.532322i | \(-0.821319\pi\) | ||||
−0.846542 | + | 0.532322i | \(0.821319\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.19035 | + | 7.25790i | 0.224304 | + | 0.388507i | 0.956111 | − | 0.293006i | \(-0.0946557\pi\) |
−0.731806 | + | 0.681513i | \(0.761322\pi\) | |||||||
\(350\) | −0.143983 | − | 18.1579i | −0.00769619 | − | 0.970580i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.2911 | − | 8.00748i | −1.02822 | − | 0.426800i | ||||
\(353\) | −9.89067 | − | 5.71038i | −0.526427 | − | 0.303933i | 0.213133 | − | 0.977023i | \(-0.431633\pi\) |
−0.739560 | + | 0.673090i | \(0.764967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.86256 | − | 3.38475i | 0.311153 | − | 0.179644i | ||||
\(356\) | 0.628193 | − | 3.95861i | 0.0332942 | − | 0.209806i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.29567 | + | 0.338722i | 0.227033 | + | 0.0179020i | ||||
\(359\) | 1.41558 | − | 2.45186i | 0.0747117 | − | 0.129404i | −0.826249 | − | 0.563305i | \(-0.809530\pi\) |
0.900961 | + | 0.433900i | \(0.142863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.753506 | + | 1.30511i | 0.0396582 | + | 0.0686900i | ||||
\(362\) | 1.82391 | − | 2.65295i | 0.0958623 | − | 0.139436i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.49804 | + | 2.36428i | 0.183347 | + | 0.123922i | ||||
\(365\) | −6.91543 | − | 3.99262i | −0.361970 | − | 0.208983i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0829 | − | 13.9043i | −1.25712 | − | 0.725797i | −0.284604 | − | 0.958645i | \(-0.591862\pi\) |
−0.972513 | + | 0.232848i | \(0.925195\pi\) | |||||||
\(368\) | −8.41466 | − | 2.73964i | −0.438644 | − | 0.142814i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.5396 | + | 14.8085i | 1.11979 | + | 0.769857i | ||||
\(371\) | −18.6293 | + | 1.61769i | −0.967184 | + | 0.0839861i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6595 | − | 27.1231i | −0.810821 | − | 1.40438i | −0.912290 | − | 0.409544i | \(-0.865688\pi\) |
0.101470 | − | 0.994839i | \(-0.467645\pi\) | |||||||
\(374\) | 13.0763 | + | 8.98994i | 0.676157 | + | 0.464859i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29.1515 | + | 7.01245i | 1.50337 | + | 0.361639i | ||||
\(377\) | 7.52380i | 0.387495i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.7198i | 1.37250i | 0.727364 | + | 0.686252i | \(0.240745\pi\) | ||||
−0.727364 | + | 0.686252i | \(0.759255\pi\) | |||||||
\(380\) | 10.1802 | + | 26.5441i | 0.522235 | + | 1.36168i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.92264 | − | 10.0693i | 0.354193 | − | 0.515190i | ||||
\(383\) | 3.72138 | + | 6.44562i | 0.190154 | + | 0.329356i | 0.945301 | − | 0.326199i | \(-0.105768\pi\) |
−0.755147 | + | 0.655555i | \(0.772435\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9773 | − | 27.7830i | 0.661386 | − | 1.41595i | ||||
\(386\) | −18.3924 | + | 26.7526i | −0.936150 | + | 1.36167i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.74202 | + | 5.85234i | −0.240740 | + | 0.297108i | ||||
\(389\) | 26.6043 | + | 15.3600i | 1.34889 | + | 0.778784i | 0.988093 | − | 0.153859i | \(-0.0491701\pi\) |
0.360801 | + | 0.932643i | \(0.382503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.82243 | + | 3.36158i | 0.294453 | + | 0.170003i | ||||
\(392\) | 8.80335 | + | 17.7342i | 0.444636 | + | 0.895711i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.34950 | + | 5.05279i | 0.370263 | + | 0.254556i | ||||
\(395\) | 16.3170 | + | 28.2619i | 0.820997 | + | 1.42201i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.16714 | + | 3.75359i | −0.108765 | + | 0.188387i | −0.915270 | − | 0.402840i | \(-0.868023\pi\) |
0.806505 | + | 0.591227i | \(0.201356\pi\) | |||||||
\(398\) | −1.42894 | + | 18.1218i | −0.0716262 | + | 0.908364i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.02469 | + | 18.9904i | 0.201235 | + | 0.949521i | ||||
\(401\) | 11.4437 | − | 6.60702i | 0.571471 | − | 0.329939i | −0.186266 | − | 0.982499i | \(-0.559639\pi\) |
0.757737 | + | 0.652560i | \(0.226305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.49608 | + | 0.863762i | 0.0745250 | + | 0.0430271i | ||||
\(404\) | 5.37391 | − | 33.8641i | 0.267362 | − | 1.68480i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.3981 | + | 30.6939i | −0.863453 | + | 1.52331i | ||||
\(407\) | 10.8707 | + | 18.8286i | 0.538841 | + | 0.933301i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.9859 | −1.18603 | −0.593014 | − | 0.805192i | \(-0.702062\pi\) | ||||
−0.593014 | + | 0.805192i | \(0.702062\pi\) | |||||||
\(410\) | 26.8753 | − | 39.0914i | 1.32728 | − | 1.93058i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.99846 | − | 4.05015i | −0.246257 | − | 0.199536i | ||||
\(413\) | 1.22112 | + | 0.570382i | 0.0600875 | + | 0.0280667i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.41796 | + | 2.55071i | 0.216869 | + | 0.125210i | ||||
\(416\) | −4.16875 | − | 1.73040i | −0.204390 | − | 0.0848397i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.85880 | + | 23.5733i | −0.0909167 | + | 1.15301i | ||||
\(419\) | −9.47883 | + | 16.4178i | −0.463071 | + | 0.802063i | −0.999112 | − | 0.0421291i | \(-0.986586\pi\) |
0.536041 | + | 0.844192i | \(0.319919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.69978 | − | 11.6044i | −0.326527 | − | 0.565562i | 0.655293 | − | 0.755375i | \(-0.272545\pi\) |
−0.981820 | + | 0.189813i | \(0.939212\pi\) | |||||||
\(422\) | 18.2083 | − | 8.68157i | 0.886365 | − | 0.422612i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.1698 | − | 5.66902i | 0.930969 | − | 0.275312i | ||||
\(425\) | − | 14.7480i | − | 0.715385i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.9202 | − | 10.7060i | −1.10919 | − | 0.518098i | ||||
\(428\) | 7.03044 | + | 1.11566i | 0.339829 | + | 0.0539276i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.86329 | − | 18.5894i | −0.427426 | − | 0.896461i | ||||
\(431\) | 8.82760 | + | 15.2899i | 0.425211 | + | 0.736486i | 0.996440 | − | 0.0843040i | \(-0.0268667\pi\) |
−0.571229 | + | 0.820790i | \(0.693533\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.5556 | 1.08395 | 0.541976 | − | 0.840394i | \(-0.317676\pi\) | ||||
0.541976 | + | 0.840394i | \(0.317676\pi\) | |||||||
\(434\) | 4.10600 | + | 6.98333i | 0.197094 | + | 0.335211i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.47082 | − | 7.98593i | 0.309896 | − | 0.382456i | ||||
\(437\) | 10.0186i | 0.479253i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.5109i | 1.59939i | 0.600408 | + | 0.799694i | \(0.295005\pi\) | ||||
−0.600408 | + | 0.799694i | \(0.704995\pi\) | |||||||
\(440\) | −7.66698 | + | 31.8724i | −0.365509 | + | 1.51946i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.82575 | + | 1.94270i | 0.134407 | + | 0.0924049i | ||||
\(443\) | 2.98342 | 0.141747 | 0.0708733 | − | 0.997485i | \(-0.477421\pi\) | ||||
0.0708733 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.29069 | −0.298208 | ||||||||
\(446\) | −0.508374 | + | 6.44720i | −0.0240722 | + | 0.305284i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.0053 | − | 16.6991i | −0.614444 | − | 0.788960i | ||||
\(449\) | − | 39.5688i | − | 1.86737i | −0.358099 | − | 0.933684i | \(-0.616575\pi\) | ||
0.358099 | − | 0.933684i | \(-0.383425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.1713 | − | 19.7288i | 1.60906 | − | 0.928994i | ||||
\(452\) | 2.57398 | − | 16.2201i | 0.121070 | − | 0.762931i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.92097 | − | 8.22364i | −0.184020 | − | 0.385955i | ||||
\(455\) | 2.80437 | − | 6.00383i | 0.131471 | − | 0.281464i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2088 | 1.36633 | 0.683165 | − | 0.730264i | \(-0.260603\pi\) | ||||
0.683165 | + | 0.730264i | \(0.260603\pi\) | |||||||
\(458\) | −9.30461 | − | 0.733686i | −0.434776 | − | 0.0342829i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.17681 | + | 13.7173i | −0.101494 | + | 0.639573i | ||||
\(461\) | 1.80514 | − | 1.04220i | 0.0840737 | − | 0.0485400i | −0.457374 | − | 0.889275i | \(-0.651210\pi\) |
0.541447 | + | 0.840735i | \(0.317877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8405 | − | 10.3002i | −0.829118 | − | 0.478692i | 0.0244325 | − | 0.999701i | \(-0.492222\pi\) |
−0.853551 | + | 0.521010i | \(0.825555\pi\) | |||||||
\(464\) | 11.6769 | − | 35.8649i | 0.542086 | − | 1.66499i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.20507 | + | 2.95853i | −0.287444 | + | 0.137051i | ||||
\(467\) | 7.00189 | − | 12.1276i | 0.324009 | − | 0.561199i | −0.657303 | − | 0.753627i | \(-0.728303\pi\) |
0.981311 | + | 0.192427i | \(0.0616360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.34855 | + | 17.8733i | −0.385500 | + | 0.825311i | ||||
\(470\) | 3.69911 | − | 46.9121i | 0.170627 | − | 2.16389i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.40086 | − | 0.336981i | −0.0644799 | − | 0.0155108i | ||||
\(473\) | − | 17.1296i | − | 0.787618i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.0325 | − | 10.9884i | 0.873273 | − | 0.504184i | ||||
\(476\) | 7.03553 | + | 14.4597i | 0.322473 | + | 0.662759i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.52907 | + | 17.8884i | 0.390110 | + | 0.818198i | ||||
\(479\) | 18.7706 | − | 32.5116i | 0.857650 | − | 1.48549i | −0.0165142 | − | 0.999864i | \(-0.505257\pi\) |
0.874164 | − | 0.485630i | \(-0.161410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.34913 | + | 4.06882i | 0.107111 | + | 0.185522i | ||||
\(482\) | 2.55300 | + | 5.35453i | 0.116286 | + | 0.243892i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.31555 | + | 4.09187i | −0.150707 | + | 0.185994i | ||||
\(485\) | 10.2381 | + | 5.91095i | 0.464887 | + | 0.268402i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.414665 | − | 0.239407i | 0.0187903 | − | 0.0108486i | −0.490575 | − | 0.871399i | \(-0.663213\pi\) |
0.509366 | + | 0.860550i | \(0.329880\pi\) | |||||||
\(488\) | 26.2939 | + | 6.32507i | 1.19027 | + | 0.286322i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 25.3240 | − | 18.0082i | 1.14402 | − | 0.813529i | ||||
\(491\) | −1.44107 | + | 2.49601i | −0.0650346 | + | 0.112643i | −0.896709 | − | 0.442620i | \(-0.854049\pi\) |
0.831675 | + | 0.555263i | \(0.187382\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.3277 | + | 24.8163i | −0.645288 | + | 1.11767i | ||||
\(494\) | −0.401681 | + | 5.09413i | −0.0180725 | + | 0.229196i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.79105 | − | 6.43934i | −0.260026 | − | 0.289135i | ||||
\(497\) | 5.16969 | + | 2.41475i | 0.231893 | + | 0.108316i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0701 | − | 8.70073i | 0.674631 | − | 0.389498i | −0.123198 | − | 0.992382i | \(-0.539315\pi\) |
0.797829 | + | 0.602884i | \(0.205982\pi\) | |||||||
\(500\) | −0.861351 | + | 0.330347i | −0.0385208 | + | 0.0147736i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.26200 | − | 4.74473i | 0.145590 | − | 0.211768i | ||||
\(503\) | −22.3882 | −0.998240 | −0.499120 | − | 0.866533i | \(-0.666343\pi\) | ||||
−0.499120 | + | 0.866533i | \(0.666343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −53.8141 | −2.39470 | ||||||||
\(506\) | −6.54473 | + | 9.51960i | −0.290949 | + | 0.423198i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −31.0022 | + | 11.8900i | −1.37550 | + | 0.527534i | ||||
\(509\) | −9.84296 | + | 5.68284i | −0.436282 | + | 0.251887i | −0.702019 | − | 0.712158i | \(-0.747718\pi\) |
0.265738 | + | 0.964045i | \(0.414385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.582262 | − | 6.70534i | −0.0257578 | − | 0.296627i | ||||
\(512\) | 17.1863 | + | 14.7184i | 0.759533 | + | 0.650469i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.93672 | + | 37.2435i | −0.129533 | + | 1.64274i | ||||
\(515\) | −5.04852 | + | 8.74430i | −0.222464 | + | 0.385320i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5704 | − | 33.8970i | 0.860707 | − | 1.49079i | ||||
\(518\) | 0.174696 | + | 22.0312i | 0.00767571 | + | 0.967997i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.65682 | + | 6.88755i | −0.0726562 | + | 0.302039i | ||||
\(521\) | −21.0799 | + | 12.1705i | −0.923529 | + | 0.533200i | −0.884759 | − | 0.466049i | \(-0.845677\pi\) |
−0.0387695 | + | 0.999248i | \(0.512344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.0137 | − | 20.7925i | −1.57477 | − | 0.909194i | −0.995571 | − | 0.0940077i | \(-0.970032\pi\) |
−0.579199 | − | 0.815186i | \(-0.696634\pi\) | |||||||
\(524\) | 14.4685 | − | 17.8562i | 0.632057 | − | 0.780050i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.66689 | + | 3.49604i | 0.0726797 | + | 0.152435i | ||||
\(527\) | 3.28976 | + | 5.69803i | 0.143304 | + | 0.248210i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.05275 | − | 15.6798i | 0.393598 | − | 0.681731i | ||||
\(530\) | −13.5029 | − | 28.3203i | −0.586529 | − | 1.23016i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.4184 | + | 19.8530i | −0.581761 | + | 0.860738i | ||||
\(533\) | 7.38434 | − | 4.26335i | 0.319851 | − | 0.184666i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 11.1722i | − | 0.483016i | ||||||
\(536\) | 4.93231 | − | 20.5041i | 0.213043 | − | 0.885642i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.42294 | − | 18.0457i | 0.0613473 | − | 0.778007i | ||||
\(539\) | 25.4594 | − | 4.45516i | 1.09661 | − | 0.191897i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.99498 | − | 17.3118i | 0.429718 | − | 0.744293i | −0.567130 | − | 0.823628i | \(-0.691946\pi\) |
0.996848 | + | 0.0793350i | \(0.0252797\pi\) | |||||||
\(542\) | −28.4637 | + | 13.5713i | −1.22262 | + | 0.582936i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.4549 | − | 13.6461i | −0.448249 | − | 0.585073i | ||||
\(545\) | −13.9706 | − | 8.06590i | −0.598433 | − | 0.345505i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5952 | + | 6.11715i | −0.453019 | + | 0.261551i | −0.709104 | − | 0.705104i | \(-0.750900\pi\) |
0.256085 | + | 0.966654i | \(0.417567\pi\) | |||||||
\(548\) | −4.36471 | + | 27.5046i | −0.186451 | + | 1.17494i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.2629 | + | 1.99203i | 1.07722 | + | 0.0849404i | ||||
\(551\) | −42.7011 | −1.81913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.6409 | + | 24.9217i | −0.495020 | + | 1.05978i | ||||
\(554\) | −10.9769 | − | 23.0225i | −0.466365 | − | 0.978131i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.74962 | + | 29.9301i | −0.201429 | + | 1.26932i | ||||
\(557\) | −6.58200 | + | 3.80012i | −0.278888 | + | 0.161016i | −0.632920 | − | 0.774217i | \(-0.718144\pi\) |
0.354032 | + | 0.935233i | \(0.384810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.70165i | − | 0.156563i | ||||||
\(560\) | −22.6859 | + | 24.2671i | −0.958656 | + | 1.02547i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.807534 | − | 10.2411i | 0.0340637 | − | 0.431997i | ||||
\(563\) | 17.0080 | 0.716801 | 0.358401 | − | 0.933568i | \(-0.383322\pi\) | ||||
0.358401 | + | 0.933568i | \(0.383322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.7757 | −1.08439 | ||||||||
\(566\) | −11.6503 | − | 8.00959i | −0.489699 | − | 0.336668i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.93064 | − | 1.42663i | −0.248844 | − | 0.0598600i | ||||
\(569\) | − | 4.41762i | − | 0.185196i | −0.995704 | − | 0.0925982i | \(-0.970483\pi\) | ||
0.995704 | − | 0.0925982i | \(-0.0295172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.912274i | − | 0.0381775i | −0.999818 | − | 0.0190887i | \(-0.993923\pi\) | ||
0.999818 | − | 0.0190887i | \(-0.00607651\pi\) | |||||||
\(572\) | −3.70947 | + | 4.57801i | −0.155101 | + | 0.191416i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 39.9836 | − | 0.317049i | 1.66888 | − | 0.0132334i | ||||
\(575\) | 10.7367 | 0.447750 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.46070 | + | 7.72616i | 0.185701 | + | 0.321644i | 0.943813 | − | 0.330481i | \(-0.107211\pi\) |
−0.758111 | + | 0.652125i | \(0.773878\pi\) | |||||||
\(578\) | −4.72610 | − | 9.91227i | −0.196580 | − | 0.412296i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −58.4658 | − | 9.27797i | −2.42766 | − | 0.385247i | ||||
\(581\) | 0.371982 | + | 4.28375i | 0.0154324 | + | 0.177720i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 26.0963i | − | 1.08080i | ||||||
\(584\) | 2.04048 | + | 6.89989i | 0.0844358 | + | 0.285520i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.5581 | + | 14.0931i | −1.22103 | + | 0.582180i | ||||
\(587\) | 6.93517 | + | 12.0121i | 0.286245 | + | 0.495791i | 0.972910 | − | 0.231183i | \(-0.0742596\pi\) |
−0.686665 | + | 0.726974i | \(0.740926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.90225 | + | 8.49095i | −0.201994 | + | 0.349864i | ||||
\(590\) | −0.177759 | + | 2.25434i | −0.00731823 | + | 0.0928098i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.88322 | − | 23.0413i | −0.200699 | − | 0.946993i | ||||
\(593\) | 14.8781 | + | 8.58990i | 0.610972 | + | 0.352745i | 0.773346 | − | 0.633984i | \(-0.218582\pi\) |
−0.162374 | + | 0.986729i | \(0.551915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.6831 | − | 14.4625i | 0.847924 | − | 0.592904i | ||||
\(596\) | 28.1396 | + | 22.8009i | 1.15264 | + | 0.933961i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.41430 | + | 2.05716i | −0.0578350 | + | 0.0841236i | ||||
\(599\) | −10.4271 | −0.426039 | −0.213020 | − | 0.977048i | \(-0.568330\pi\) | ||||
−0.213020 | + | 0.977048i | \(0.568330\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3792 | + | 23.1735i | 0.545750 | + | 0.945267i | 0.998559 | + | 0.0536595i | \(0.0170885\pi\) |
−0.452809 | + | 0.891607i | \(0.649578\pi\) | |||||||
\(602\) | 8.55974 | − | 15.1012i | 0.348869 | − | 0.615478i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.18909 | − | 39.0010i | 0.251830 | − | 1.58693i | ||||
\(605\) | 7.15831 | + | 4.13285i | 0.291026 | + | 0.168024i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.0574 | − | 15.0442i | 1.05764 | − | 0.610626i | 0.132858 | − | 0.991135i | \(-0.457585\pi\) |
0.924777 | + | 0.380509i | \(0.124251\pi\) | |||||||
\(608\) | 9.82081 | − | 23.6596i | 0.398286 | − | 0.959523i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.33651 | − | 42.3136i | 0.135091 | − | 1.71323i | ||||
\(611\) | 4.22912 | − | 7.32505i | 0.171092 | − | 0.296340i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.42095 | + | 5.92526i | 0.138171 | + | 0.239319i | 0.926804 | − | 0.375545i | \(-0.122544\pi\) |
−0.788633 | + | 0.614864i | \(0.789211\pi\) | |||||||
\(614\) | −33.1135 | − | 22.7656i | −1.33635 | − | 0.918744i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.7193 | + | 10.0986i | −1.03626 | + | 0.406882i | ||||
\(617\) | −3.69878 | − | 2.13549i | −0.148907 | − | 0.0859716i | 0.423695 | − | 0.905805i | \(-0.360733\pi\) |
−0.572602 | + | 0.819833i | \(0.694066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.4075 | + | 11.2049i | 0.780055 | + | 0.450365i | 0.836450 | − | 0.548044i | \(-0.184627\pi\) |
−0.0563948 | + | 0.998409i | \(0.517961\pi\) | |||||||
\(620\) | −8.55700 | + | 10.5606i | −0.343658 | + | 0.424123i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.68488 | − | 5.35983i | 0.147750 | − | 0.214909i | ||||
\(623\) | −3.03844 | − | 4.34534i | −0.121733 | − | 0.174092i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.8566 | + | 22.2682i | 0.514263 | + | 0.890729i | ||||
\(626\) | 17.1057 | − | 24.8810i | 0.683682 | − | 0.994445i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.02565 | + | 10.4966i | 0.160641 | + | 0.418858i | ||||
\(629\) | 17.8940i | 0.713481i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.90962i | − | 0.235258i | −0.993058 | − | 0.117629i | \(-0.962471\pi\) | ||
0.993058 | − | 0.117629i | \(-0.0375294\pi\) | |||||||
\(632\) | 6.87740 | − | 28.5900i | 0.273568 | − | 1.13725i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.48761 | + | 1.71023i | 0.0987955 | + | 0.0679219i | ||||
\(635\) | 26.0565 | + | 45.1312i | 1.03402 | + | 1.79098i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.50171 | − | 0.962749i | 0.217986 | − | 0.0381455i | ||||
\(638\) | −40.5743 | − | 27.8949i | −1.60635 | − | 1.10437i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.5872 | − | 30.2606i | 0.734725 | − | 1.19616i | ||||
\(641\) | 6.47169 | + | 3.73643i | 0.255616 | + | 0.147580i | 0.622333 | − | 0.782752i | \(-0.286185\pi\) |
−0.366717 | + | 0.930333i | \(0.619518\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.9307 | + | 9.19760i | 0.628246 | + | 0.362718i | 0.780073 | − | 0.625689i | \(-0.215182\pi\) |
−0.151826 | + | 0.988407i | \(0.548515\pi\) | |||||||
\(644\) | −10.5267 | + | 5.12191i | −0.414812 | + | 0.201831i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.0257 | + | 16.0374i | −0.433802 | + | 0.630984i | ||||
\(647\) | −1.76191 | − | 3.05173i | −0.0692680 | − | 0.119976i | 0.829311 | − | 0.558787i | \(-0.188733\pi\) |
−0.898579 | + | 0.438811i | \(0.855400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.940449 | + | 1.62891i | −0.0369159 | + | 0.0639402i | ||||
\(650\) | 5.45926 | + | 0.430473i | 0.214130 | + | 0.0168845i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.17528 | − | 7.40613i | 0.0460276 | − | 0.290047i | ||||
\(653\) | 6.32176 | − | 3.64987i | 0.247390 | − | 0.142830i | −0.371179 | − | 0.928561i | \(-0.621046\pi\) |
0.618568 | + | 0.785731i | \(0.287713\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.2375 | − | 18.0350i | −1.22055 | − | 0.704685i | ||||
\(656\) | −41.8168 | + | 8.86235i | −1.63267 | + | 0.346017i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 34.1915 | − | 20.1037i | 1.33293 | − | 0.783722i | ||||
\(659\) | −21.3105 | − | 36.9109i | −0.830139 | − | 1.43784i | −0.897927 | − | 0.440144i | \(-0.854927\pi\) |
0.0677880 | − | 0.997700i | \(-0.478406\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.9175 | 0.580225 | 0.290113 | − | 0.956992i | \(-0.406307\pi\) | ||||
0.290113 | + | 0.956992i | \(0.406307\pi\) | |||||||
\(662\) | −33.8050 | − | 23.2409i | −1.31387 | − | 0.903284i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.30358 | − | 4.40804i | −0.0505885 | − | 0.171065i | ||||
\(665\) | 34.0745 | + | 15.9161i | 1.32135 | + | 0.617200i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0664 | − | 10.4307i | −0.699535 | − | 0.403877i | ||||
\(668\) | −2.91993 | − | 0.463364i | −0.112975 | − | 0.0179281i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −32.9963 | − | 2.60182i | −1.27476 | − | 0.100517i | ||||
\(671\) | 17.6521 | − | 30.5743i | 0.681451 | − | 1.18031i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.11649 | + | 15.7902i | 0.351415 | + | 0.608668i | 0.986498 | − | 0.163776i | \(-0.0523673\pi\) |
−0.635083 | + | 0.772444i | \(0.719034\pi\) | |||||||
\(674\) | 7.75990 | + | 16.2752i | 0.298900 | + | 0.626898i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.5668 | − | 19.2116i | 0.598721 | − | 0.738908i | ||||
\(677\) | 24.2358i | 0.931456i | 0.884928 | + | 0.465728i | \(0.154208\pi\) | ||||
−0.884928 | + | 0.465728i | \(0.845792\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.862021 | + | 9.92704i | 0.0330813 | + | 0.380965i | ||||
\(680\) | −18.5809 | + | 19.5626i | −0.712545 | + | 0.750193i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.2049 | + | 4.86562i | −0.390766 | + | 0.186314i | ||||
\(683\) | −17.8152 | − | 30.8568i | −0.681678 | − | 1.18070i | −0.974468 | − | 0.224524i | \(-0.927917\pi\) |
0.292790 | − | 0.956177i | \(-0.405416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.7080 | 1.67000 | ||||||||
\(686\) | 24.6709 | + | 8.79461i | 0.941941 | + | 0.335780i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.74494 | + | 17.6453i | −0.219024 | + | 0.672720i | ||||
\(689\) | − | 5.63934i | − | 0.214842i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.77976i | 0.372039i | 0.982546 | + | 0.186020i | \(0.0595588\pi\) | ||||
−0.982546 | + | 0.186020i | \(0.940441\pi\) | |||||||
\(692\) | −12.9080 | + | 4.95049i | −0.490688 | + | 0.188189i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.2686 | − | 36.7542i | 0.959181 | − | 1.39517i | ||||
\(695\) | 47.5624 | 1.80415 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.4751 | 1.23008 | ||||||||
\(698\) | −11.8154 | − | 0.931668i | −0.447221 | − | 0.0352642i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.2760 | + | 14.3802i | 0.804158 | + | 0.543520i | ||||
\(701\) | 13.9885i | 0.528337i | 0.964476 | + | 0.264169i | \(0.0850976\pi\) | ||||
−0.964476 | + | 0.264169i | \(0.914902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.0925 | + | 13.3324i | −0.870949 | + | 0.502842i | ||||
\(704\) | 24.7875 | − | 16.0657i | 0.934216 | − | 0.605498i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5791 | − | 6.95118i | 0.548690 | − | 0.261611i | ||||
\(707\) | −25.9925 | − | 37.1725i | −0.977550 | − | 1.39801i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.5365 | 1.44727 | 0.723633 | − | 0.690184i | \(-0.242471\pi\) | ||||
0.723633 | + | 0.690184i | \(0.242471\pi\) | |||||||
\(710\) | −0.752554 | + | 9.54390i | −0.0282429 | + | 0.358176i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.10994 | + | 3.90369i | 0.154027 | + | 0.146297i | ||||
\(713\) | −4.14820 | + | 2.39496i | −0.155351 | + | 0.0896921i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00876 | + | 4.62386i | 0.299511 | + | 0.172923i | ||||
\(716\) | −3.83640 | + | 4.73467i | −0.143373 | + | 0.176943i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.72317 | + | 3.61410i | 0.0643083 | + | 0.134877i | ||||
\(719\) | −11.8394 | + | 20.5064i | −0.441534 | + | 0.764760i | −0.997804 | − | 0.0662424i | \(-0.978899\pi\) |
0.556269 | + | 0.831002i | \(0.312232\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.47865 | + | 0.736249i | −0.315761 | + | 0.0274193i | ||||
\(722\) | −2.12464 | − | 0.167532i | −0.0790710 | − | 0.00623489i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.63037 | + | 4.25105i | 0.0605922 | + | 0.157989i | ||||
\(725\) | 45.7617i | 1.69955i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5627 | + | 13.6039i | −0.873892 | + | 0.504542i | −0.868640 | − | 0.495444i | \(-0.835005\pi\) |
−0.00525253 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(728\) | −5.55787 | + | 2.18227i | −0.205989 | + | 0.0808804i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.1935 | − | 4.86017i | 0.377278 | − | 0.179883i | ||||
\(731\) | 7.04913 | − | 12.2095i | 0.260722 | − | 0.451583i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.77399 | − | 10.0008i | −0.213267 | − | 0.369390i | 0.739468 | − | 0.673192i | \(-0.235077\pi\) |
−0.952735 | + | 0.303802i | \(0.901744\pi\) | |||||||
\(734\) | 35.4987 | − | 16.9255i | 1.31028 | − | 0.624732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.93447 | − | 7.61122i | 0.366189 | − | 0.280553i | ||||
\(737\) | −23.8419 | − | 13.7651i | −0.878229 | − | 0.507046i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.71192 | + | 5.02983i | −0.320473 | + | 0.185025i | −0.651603 | − | 0.758560i | \(-0.725903\pi\) |
0.331130 | + | 0.943585i | \(0.392570\pi\) | |||||||
\(740\) | −34.5148 | + | 13.2372i | −1.26879 | + | 0.486608i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.0405 | − | 23.0061i | 0.478730 | − | 0.844581i | ||||
\(743\) | 22.8644 | − | 39.6022i | 0.838812 | − | 1.45286i | −0.0520771 | − | 0.998643i | \(-0.516584\pi\) |
0.890889 | − | 0.454221i | \(-0.150082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.4214 | − | 49.2273i | 1.04128 | − | 1.80355i | ||||
\(746\) | 44.1548 | + | 3.48169i | 1.61662 | + | 0.127474i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.9532 | + | 8.03601i | −0.766126 | + | 0.293826i | ||||
\(749\) | 7.71727 | − | 5.39624i | 0.281983 | − | 0.197174i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.42335 | + | 3.70852i | −0.234391 | + | 0.135326i | −0.612596 | − | 0.790396i | \(-0.709875\pi\) |
0.378205 | + | 0.925722i | \(0.376541\pi\) | |||||||
\(752\) | −31.5281 | + | 28.3539i | −1.14971 | + | 1.03396i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.76801 | − | 6.02802i | −0.319312 | − | 0.219527i | ||||
\(755\) | −61.9772 | −2.25558 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.6722 | −1.11480 | −0.557401 | − | 0.830244i | \(-0.688201\pi\) | ||||
−0.557401 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(758\) | −31.1385 | − | 21.4077i | −1.13100 | − | 0.777563i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −39.0901 | − | 9.40320i | −1.41795 | − | 0.341090i | ||||
\(761\) | 4.88598 | − | 2.82092i | 0.177117 | − | 0.102258i | −0.408821 | − | 0.912615i | \(-0.634060\pi\) |
0.585937 | + | 0.810356i | \(0.300726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.17629 | − | 13.5461i | −0.0425845 | − | 0.490403i | ||||
\(764\) | 6.18808 | + | 16.1349i | 0.223877 | + | 0.583740i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.4931 | − | 0.827399i | −0.379130 | − | 0.0298951i | ||||
\(767\) | −0.203229 | + | 0.352003i | −0.00733816 | + | 0.0127101i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.33932 | + | 5.78387i | −0.120419 | + | 0.208572i | −0.919933 | − | 0.392076i | \(-0.871757\pi\) |
0.799514 | + | 0.600647i | \(0.205090\pi\) | |||||||
\(770\) | 21.9801 | + | 37.3829i | 0.792108 | + | 1.34719i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.4408 | − | 42.8680i | −0.591718 | − | 1.54285i | ||||
\(773\) | 11.7948 | − | 6.80973i | 0.424230 | − | 0.244929i | −0.272656 | − | 0.962112i | \(-0.587902\pi\) |
0.696885 | + | 0.717183i | \(0.254569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.09955 | + | 5.25363i | 0.326866 | + | 0.188716i | ||||
\(776\) | −3.02087 | − | 10.2151i | −0.108443 | − | 0.366700i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.2153 | + | 18.6976i | −1.40594 | + | 0.670341i | ||||
\(779\) | 24.1965 | + | 41.9096i | 0.866929 | + | 1.50157i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.98145 | + | 6.89608i | −0.142468 | + | 0.246761i | ||||
\(782\) | −8.58239 | + | 4.09202i | −0.306906 | + | 0.146330i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.7201 | − | 3.94933i | −0.990003 | − | 0.141048i | ||||
\(785\) | 15.2803 | − | 8.82207i | 0.545376 | − | 0.314873i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.7977i | 0.670065i | 0.942207 | + | 0.335032i | \(0.108747\pi\) | ||||
−0.942207 | + | 0.335032i | \(0.891253\pi\) | |||||||
\(788\) | −11.7767 | + | 4.51664i | −0.419529 | + | 0.160898i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −46.0086 | − | 3.62787i | −1.63691 | − | 0.129074i | ||||
\(791\) | −12.4498 | − | 17.8047i | −0.442665 | − | 0.633064i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.81457 | − | 6.60703i | 0.135459 | − | 0.234622i | ||||
\(794\) | −2.63803 | − | 5.53287i | −0.0936202 | − | 0.196354i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.9738 | − | 16.1843i | −0.707951 | − | 0.573638i | ||||
\(797\) | −26.5106 | − | 15.3059i | −0.939054 | − | 0.542163i | −0.0493904 | − | 0.998780i | \(-0.515728\pi\) |
−0.889664 | + | 0.456616i | \(0.849061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.8985 | − | 16.1072i | 0.986977 | − | 0.569832i | ||||
\(800\) | −25.3554 | − | 10.5247i | −0.896450 | − | 0.372105i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.46898 | + | 18.6297i | −0.0518716 | + | 0.657836i | ||||
\(803\) | 9.39297 | 0.331471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.5288 | + | 15.0574i | 0.371091 | + | 0.530704i | ||||
\(806\) | −2.20525 | + | 1.05145i | −0.0776767 | + | 0.0370357i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35.1587 | + | 33.3943i | 1.23688 | + | 1.17481i | ||||
\(809\) | 0.871099 | − | 0.502929i | 0.0306262 | − | 0.0176821i | −0.484609 | − | 0.874731i | \(-0.661038\pi\) |
0.515235 | + | 0.857049i | \(0.327705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.9915i | − | 1.33406i | −0.745030 | − | 0.667031i | \(-0.767565\pi\) | ||
0.745030 | − | 0.667031i | \(-0.232435\pi\) | |||||||
\(812\) | −21.8305 | − | 44.8670i | −0.766102 | − | 1.57452i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −30.6519 | − | 2.41696i | −1.07435 | − | 0.0847143i | ||||
\(815\) | −11.7692 | −0.412258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.0086 | 0.734998 | ||||||||
\(818\) | 19.2174 | − | 27.9525i | 0.671919 | − | 0.977336i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.0236 | + | 62.6395i | 0.838940 | + | 2.18747i | ||||
\(821\) | 53.1065i | 1.85343i | 0.375767 | + | 0.926714i | \(0.377379\pi\) | ||||
−0.375767 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.76362i | − | 0.166049i | −0.996547 | − | 0.0830247i | \(-0.973542\pi\) | ||
0.996547 | − | 0.0830247i | \(-0.0264580\pi\) | |||||||
\(824\) | 8.72466 | − | 2.58011i | 0.303938 | − | 0.0898825i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.64306 | + | 0.966073i | −0.0571694 | + | 0.0336140i | ||||
\(827\) | −2.02105 | −0.0702787 | −0.0351393 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351393 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.51810 | − | 2.62943i | −0.0527259 | − | 0.0913240i | 0.838458 | − | 0.544967i | \(-0.183458\pi\) |
−0.891184 | + | 0.453643i | \(0.850124\pi\) | |||||||
\(830\) | −6.51217 | + | 3.10495i | −0.226041 | + | 0.107774i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.35653 | − | 3.47175i | 0.185704 | − | 0.120361i | ||||
\(833\) | 19.9801 | + | 7.30151i | 0.692270 | + | 0.252982i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.64011i | 0.160577i | ||||||||
\(836\) | −25.9824 | − | 21.0529i | −0.898619 | − | 0.728131i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.5385 | − | 24.2002i | −0.398590 | − | 0.835982i | ||||
\(839\) | 14.7757 | + | 25.5923i | 0.510114 | + | 0.883543i | 0.999931 | + | 0.0117180i | \(0.00373004\pi\) |
−0.489818 | + | 0.871825i | \(0.662937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.9575 | − | 51.8879i | 1.03302 | − | 1.78924i | ||||
\(842\) | 18.8912 | + | 1.48961i | 0.651034 | + | 0.0513352i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.47110 | + | 28.1750i | −0.153902 | + | 0.969824i | ||||
\(845\) | −33.6087 | − | 19.4040i | −1.15618 | − | 0.667518i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.602712 | + | 6.94084i | 0.0207094 | + | 0.238490i | ||||
\(848\) | −8.75221 | + | 26.8819i | −0.300552 | + | 0.923129i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.1869 | + | 11.8160i | 0.589507 | + | 0.405287i | ||||
\(851\) | −13.0270 | −0.446558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.4280 | − | 18.0618i | −0.357048 | − | 0.618426i | 0.630418 | − | 0.776256i | \(-0.282884\pi\) |
−0.987466 | + | 0.157830i | \(0.949550\pi\) | |||||||
\(854\) | 30.8400 | − | 18.1330i | 1.05532 | − | 0.620499i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.93290 | + | 7.29921i | −0.236962 | + | 0.249482i | ||||
\(857\) | −19.1033 | − | 11.0293i | −0.652557 | − | 0.376754i | 0.136878 | − | 0.990588i | \(-0.456293\pi\) |
−0.789435 | + | 0.613834i | \(0.789626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.7963 | − | 27.0178i | 1.59667 | − | 0.921836i | 0.604544 | − | 0.796572i | \(-0.293355\pi\) |
0.992123 | − | 0.125265i | \(-0.0399781\pi\) | |||||||
\(860\) | 28.7648 | + | 4.56469i | 0.980871 | + | 0.155655i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.8910 | − | 1.96270i | −0.847790 | − | 0.0668498i | ||||
\(863\) | −14.8916 | + | 25.7931i | −0.506917 | + | 0.878007i | 0.493051 | + | 0.870001i | \(0.335882\pi\) |
−0.999968 | + | 0.00800595i | \(0.997452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8488 | + | 18.7907i | 0.368871 | + | 0.638903i | ||||
\(866\) | −18.0714 | + | 26.2856i | −0.614091 | + | 0.893222i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.4279 | − | 0.809985i | −0.387887 | − | 0.0274927i | ||||
\(869\) | −33.2442 | − | 19.1935i | −1.12773 | − | 0.651096i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.15218 | − | 2.97461i | −0.174575 | − | 0.100791i | ||||
\(872\) | 4.12219 | + | 13.9392i | 0.139595 | + | 0.472040i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.6754 | − | 8.02681i | −0.394925 | − | 0.271511i | ||||
\(875\) | −0.516475 | + | 1.10571i | −0.0174600 | + | 0.0373799i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.43528 | − | 9.41418i | −0.183536 | − | 0.317894i | 0.759546 | − | 0.650454i | \(-0.225421\pi\) |
−0.943082 | + | 0.332559i | \(0.892088\pi\) | |||||||
\(878\) | −39.0526 | − | 26.8487i | −1.31796 | − | 0.906100i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31.0005 | − | 34.4709i | −1.04503 | − | 1.16201i | ||||
\(881\) | − | 40.5406i | − | 1.36585i | −0.730490 | − | 0.682923i | \(-0.760708\pi\) | ||
0.730490 | − | 0.682923i | \(-0.239292\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.8427i | − | 0.634106i | −0.948408 | − | 0.317053i | \(-0.897307\pi\) | ||
0.948408 | − | 0.317053i | \(-0.102693\pi\) | |||||||
\(884\) | −4.52794 | + | 1.73656i | −0.152291 | + | 0.0584069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.39030 | + | 3.47679i | −0.0803035 | + | 0.116805i | ||||
\(887\) | −1.05971 | − | 1.83546i | −0.0355814 | − | 0.0616289i | 0.847686 | − | 0.530498i | \(-0.177995\pi\) |
−0.883268 | + | 0.468869i | \(0.844662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5892 | + | 39.7974i | −0.623463 | + | 1.33476i | ||||
\(890\) | 5.04006 | − | 7.33099i | 0.168943 | − | 0.245735i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.10608 | − | 5.75790i | −0.237929 | − | 0.192789i | ||||
\(893\) | 41.5731 | + | 24.0022i | 1.39119 | + | 0.803204i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.28282 | + | 4.78209i | 0.276864 | + | 0.159848i | ||||
\(896\) | 29.8805 | − | 1.77681i | 0.998237 | − | 0.0593590i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46.1123 | + | 31.7023i | 1.53879 | + | 1.05792i | ||||
\(899\) | −10.2078 | − | 17.6804i | −0.340449 | − | 0.589675i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7391 | − | 18.6007i | 0.357771 | − | 0.619678i | ||||
\(902\) | −4.38644 | + | 55.6289i | −0.146052 | + | 1.85224i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.8402 | + | 15.9951i | 0.560097 | + | 0.531989i | ||||
\(905\) | 6.18844 | − | 3.57290i | 0.205711 | − | 0.118767i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.4300 | − | 9.48585i | −0.545548 | − | 0.314972i | 0.201776 | − | 0.979432i | \(-0.435329\pi\) |
−0.747324 | + | 0.664459i | \(0.768662\pi\) | |||||||
\(908\) | 12.7250 | + | 2.01934i | 0.422296 | + | 0.0670143i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.74985 | + | 8.07836i | 0.157456 | + | 0.267795i | ||||
\(911\) | 7.63448 | + | 13.2233i | 0.252942 | + | 0.438108i | 0.964334 | − | 0.264687i | \(-0.0852686\pi\) |
−0.711393 | + | 0.702795i | \(0.751935\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00076 | −0.198596 | ||||||||
\(914\) | −23.4019 | + | 34.0391i | −0.774066 | + | 1.12591i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.30980 | − | 10.2555i | 0.274564 | − | 0.338851i | ||||
\(917\) | −2.63012 | − | 30.2885i | −0.0868543 | − | 1.00022i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.7046 | − | 6.75766i | −0.386099 | − | 0.222914i | 0.294369 | − | 0.955692i | \(-0.404890\pi\) |
−0.680469 | + | 0.732777i | \(0.738224\pi\) | |||||||
\(920\) | −14.2417 | − | 13.5270i | −0.469536 | − | 0.445972i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.231719 | + | 2.93866i | −0.00763125 | + | 0.0967796i | ||||
\(923\) | −0.860382 | + | 1.49022i | −0.0283198 | + | 0.0490513i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.2881 | + | 24.7476i | 0.469789 | + | 0.813698i | ||||
\(926\) | 26.2973 | − | 12.5383i | 0.864181 | − | 0.412035i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 32.4405 | + | 42.3426i | 1.06491 | + | 1.38996i | ||||
\(929\) | − | 3.85010i | − | 0.126318i | −0.998003 | − | 0.0631589i | \(-0.979883\pi\) | ||
0.998003 | − | 0.0631589i | \(-0.0201175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.46405 | + | 31.2248i | 0.179077 | + | 1.02335i | ||||
\(932\) | 1.52367 | − | 9.60156i | 0.0499096 | − | 0.314509i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.52331 | + | 17.8764i | 0.278891 | + | 0.584932i | ||||
\(935\) | 17.6106 | + | 30.5025i | 0.575929 | + | 0.997538i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.7523 | −1.78868 | −0.894340 | − | 0.447389i | \(-0.852354\pi\) | ||||
−0.894340 | + | 0.447389i | \(0.852354\pi\) | |||||||
\(938\) | −14.1402 | − | 24.0491i | −0.461694 | − | 0.785231i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51.7063 | + | 41.8965i | 1.68647 | + | 1.36651i | ||||
\(941\) | − | 0.543104i | − | 0.0177047i | −0.999961 | − | 0.00885234i | \(-0.997182\pi\) | ||
0.999961 | − | 0.00885234i | \(-0.00281783\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.6421i | 0.769892i | ||||||||
\(944\) | 1.51507 | − | 1.36254i | 0.0493113 | − | 0.0443468i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.9623 | + | 13.7241i | 0.649030 | + | 0.446209i | ||||
\(947\) | −37.8464 | −1.22984 | −0.614921 | − | 0.788589i | \(-0.710812\pi\) | ||||
−0.614921 | + | 0.788589i | \(0.710812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.02980 | 0.0658900 | ||||||||
\(950\) | −2.44313 | + | 30.9838i | −0.0792657 | + | 1.00525i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22.4877 | − | 3.38601i | −0.728831 | − | 0.109741i | ||||
\(953\) | 55.2382i | 1.78934i | 0.446726 | + | 0.894671i | \(0.352590\pi\) | ||||
−0.446726 | + | 0.894671i | \(0.647410\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.4883 | − | 13.5609i | 0.760062 | − | 0.438822i | ||||
\(956\) | −27.6801 | − | 4.39256i | −0.895238 | − | 0.142066i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.8492 | + | 47.9228i | 0.738225 | + | 1.54832i | ||||
\(959\) | 21.1112 | + | 30.1916i | 0.681717 | + | 0.974937i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.3124 | 0.848788 | ||||||||
\(962\) | −6.62380 | − | 0.522299i | −0.213560 | − | 0.0168396i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.28546 | − | 1.31482i | −0.266857 | − | 0.0423476i | ||||
\(965\) | −62.4048 | + | 36.0294i | −2.00888 | + | 1.15983i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.0909 | − | 7.55803i | −0.420975 | − | 0.243050i | 0.274519 | − | 0.961582i | \(-0.411481\pi\) |
−0.695494 | + | 0.718532i | \(0.744815\pi\) | |||||||
\(968\) | −2.11215 | − | 7.14223i | −0.0678870 | − | 0.229560i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.0911 | + | 7.19533i | −0.484547 | + | 0.231028i | ||||
\(971\) | 24.1097 | − | 41.7592i | 0.773716 | − | 1.34012i | −0.161797 | − | 0.986824i | \(-0.551729\pi\) |
0.935513 | − | 0.353292i | \(-0.114938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.9730 | + | 32.8541i | 0.736479 | + | 1.05325i | ||||
\(974\) | −0.0532289 | + | 0.675049i | −0.00170556 | + | 0.0216300i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.4376 | + | 25.5746i | −0.910265 | + | 0.818623i | ||||
\(977\) | 37.7372i | 1.20732i | 0.797242 | + | 0.603660i | \(0.206292\pi\) | ||||
−0.797242 | + | 0.603660i | \(0.793708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.40831 | − | 3.69984i | 0.204811 | − | 0.118247i | ||||
\(980\) | 0.696884 | + | 43.9399i | 0.0222612 | + | 1.40361i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.75420 | − | 3.67917i | −0.0559787 | − | 0.117407i | ||||
\(983\) | −19.0627 | + | 33.0176i | −0.608006 | + | 1.05310i | 0.383563 | + | 0.923515i | \(0.374697\pi\) |
−0.991569 | + | 0.129582i | \(0.958636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.89804 | + | 17.1439i | 0.315378 | + | 0.546250i | ||||
\(986\) | −17.4410 | − | 36.5798i | −0.555433 | − | 1.16494i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.61472 | − | 4.54949i | −0.178628 | − | 0.144739i | ||||
\(989\) | 8.88856 | + | 5.13181i | 0.282640 | + | 0.163182i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4040 | + | 18.7085i | −1.02935 | + | 0.594294i | −0.916798 | − | 0.399352i | \(-0.869235\pi\) |
−0.112550 | + | 0.993646i | \(0.535902\pi\) | |||||||
\(992\) | 12.1440 | − | 1.58957i | 0.385571 | − | 0.0504688i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.95600 | + | 4.08993i | −0.220631 | + | 0.129725i | ||||
\(995\) | −20.1738 | + | 34.9421i | −0.639553 | + | 1.10774i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.33397 | − | 4.04255i | 0.0739174 | − | 0.128029i | −0.826698 | − | 0.562647i | \(-0.809783\pi\) |
0.900615 | + | 0.434618i | \(0.143117\pi\) | |||||||
\(998\) | −1.93449 | + | 24.5332i | −0.0612353 | + | 0.776586i | ||||
\(999\) | 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 | 756.2.bb.a.611.14 | 88 | ||
3.2 | odd | 2 | 252.2.bb.a.23.31 | yes | 88 | ||
4.3 | odd | 2 | inner | 756.2.bb.a.611.31 | 88 | ||
7.4 | even | 3 | 756.2.o.a.179.16 | 88 | |||
9.2 | odd | 6 | 756.2.o.a.359.3 | 88 | |||
9.7 | even | 3 | 252.2.o.a.191.42 | yes | 88 | ||
12.11 | even | 2 | 252.2.bb.a.23.14 | yes | 88 | ||
21.11 | odd | 6 | 252.2.o.a.95.29 | ✓ | 88 | ||
28.11 | odd | 6 | 756.2.o.a.179.3 | 88 | |||
36.7 | odd | 6 | 252.2.o.a.191.29 | yes | 88 | ||
36.11 | even | 6 | 756.2.o.a.359.16 | 88 | |||
63.11 | odd | 6 | inner | 756.2.bb.a.683.31 | 88 | ||
63.25 | even | 3 | 252.2.bb.a.11.14 | yes | 88 | ||
84.11 | even | 6 | 252.2.o.a.95.42 | yes | 88 | ||
252.11 | even | 6 | inner | 756.2.bb.a.683.14 | 88 | ||
252.151 | odd | 6 | 252.2.bb.a.11.31 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.o.a.95.29 | ✓ | 88 | 21.11 | odd | 6 | ||
252.2.o.a.95.42 | yes | 88 | 84.11 | even | 6 | ||
252.2.o.a.191.29 | yes | 88 | 36.7 | odd | 6 | ||
252.2.o.a.191.42 | yes | 88 | 9.7 | even | 3 | ||
252.2.bb.a.11.14 | yes | 88 | 63.25 | even | 3 | ||
252.2.bb.a.11.31 | yes | 88 | 252.151 | odd | 6 | ||
252.2.bb.a.23.14 | yes | 88 | 12.11 | even | 2 | ||
252.2.bb.a.23.31 | yes | 88 | 3.2 | odd | 2 | ||
756.2.o.a.179.3 | 88 | 28.11 | odd | 6 | |||
756.2.o.a.179.16 | 88 | 7.4 | even | 3 | |||
756.2.o.a.359.3 | 88 | 9.2 | odd | 6 | |||
756.2.o.a.359.16 | 88 | 36.11 | even | 6 | |||
756.2.bb.a.611.14 | 88 | 1.1 | even | 1 | trivial | ||
756.2.bb.a.611.31 | 88 | 4.3 | odd | 2 | inner | ||
756.2.bb.a.683.14 | 88 | 252.11 | even | 6 | inner | ||
756.2.bb.a.683.31 | 88 | 63.11 | odd | 6 | inner |