Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(111,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([7, 0, 11]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.bb (of order \(14\), degree \(6\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 111.15 | ||
Character | \(\chi\) | \(=\) | 784.111 |
Dual form | 784.2.bb.b.671.15 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{11}{14}\right)\) |
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 | ||||||||
\(3\) | 0.977383 | + | 1.22560i | 0.564292 | + | 0.707600i | 0.979345 | − | 0.202197i | \(-0.0648083\pi\) |
−0.415053 | + | 0.909797i | \(0.636237\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.470082 | + | 0.374878i | −0.210227 | + | 0.167650i | −0.722943 | − | 0.690908i | \(-0.757211\pi\) |
0.512716 | + | 0.858558i | \(0.328640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.48039 | − | 2.19281i | −0.559536 | − | 0.828806i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.120747 | − | 0.529025i | 0.0402488 | − | 0.176342i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.53257 | − | 1.26277i | 1.66813 | − | 0.380740i | 0.718850 | − | 0.695165i | \(-0.244669\pi\) |
0.949282 | + | 0.314425i | \(0.101812\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.517931 | − | 0.118214i | 0.143648 | − | 0.0327868i | −0.150092 | − | 0.988672i | \(-0.547957\pi\) |
0.293740 | + | 0.955885i | \(0.405100\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.918900 | − | 0.209733i | −0.237259 | − | 0.0541528i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.00663338 | − | 0.0137744i | 0.00160883 | − | 0.00334077i | −0.900163 | − | 0.435553i | \(-0.856553\pi\) |
0.901772 | + | 0.432213i | \(0.142267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.54052 | 1.04167 | 0.520833 | − | 0.853658i | \(-0.325621\pi\) | ||||
0.520833 | + | 0.853658i | \(0.325621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.24060 | − | 3.95759i | 0.270722 | − | 0.863616i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.102508 | − | 0.212861i | −0.0213745 | − | 0.0443846i | 0.890008 | − | 0.455944i | \(-0.150698\pi\) |
−0.911383 | + | 0.411560i | \(0.864984\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.03216 | + | 4.52219i | −0.206432 | + | 0.904439i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00346 | − | 2.40954i | 0.962917 | − | 0.463717i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.07949 | − | 1.48300i | −0.571846 | − | 0.275387i | 0.125532 | − | 0.992090i | \(-0.459936\pi\) |
−0.697379 | + | 0.716703i | \(0.745650\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.84992 | 1.05068 | 0.525338 | − | 0.850893i | \(-0.323939\pi\) | ||||
0.525338 | + | 0.850893i | \(0.323939\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.95509 | + | 5.54650i | 1.21073 | + | 0.965522i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.51794 | + | 0.475836i | 0.256579 | + | 0.0804310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.35144 | + | 2.57712i | 0.879772 | + | 0.423676i | 0.818541 | − | 0.574448i | \(-0.194783\pi\) |
0.0612307 | + | 0.998124i | \(0.480497\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.651100 | + | 0.519235i | 0.104259 | + | 0.0831442i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.23297 | − | 0.983262i | 0.192558 | − | 0.153560i | −0.522465 | − | 0.852661i | \(-0.674988\pi\) |
0.715023 | + | 0.699101i | \(0.246416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.47172 | − | 4.36355i | −0.834429 | − | 0.665435i | 0.110079 | − | 0.993923i | \(-0.464890\pi\) |
−0.944508 | + | 0.328488i | \(0.893461\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.141559 | + | 0.293950i | 0.0211024 | + | 0.0438195i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.699308 | + | 3.06387i | 0.102005 | + | 0.446911i | 0.999976 | + | 0.00685856i | \(0.00218316\pi\) |
−0.897972 | + | 0.440053i | \(0.854960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.61688 | + | 6.49245i | −0.373839 | + | 0.927493i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0233652 | − | 0.00533296i | 0.00327178 | − | 0.000746763i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7318 | + | 5.16818i | −1.47413 | + | 0.709904i | −0.986593 | − | 0.163198i | \(-0.947819\pi\) |
−0.487537 | + | 0.873102i | \(0.662105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.12738 | + | 2.66764i | −0.286855 | + | 0.359705i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.43782 | + | 5.56486i | 0.587804 | + | 0.737083i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.17584 | − | 7.74426i | 0.804026 | − | 1.00822i | −0.195595 | − | 0.980685i | \(-0.562664\pi\) |
0.999621 | − | 0.0275323i | \(-0.00876491\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.48363 | + | 7.23382i | −0.446033 | + | 0.926196i | 0.549826 | + | 0.835279i | \(0.314694\pi\) |
−0.995858 | + | 0.0909169i | \(0.971020\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.33881 | + | 0.518390i | −0.168674 | + | 0.0653110i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.199154 | + | 0.249731i | −0.0247020 | + | 0.0309754i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.76147i | − | 0.703875i | −0.936024 | − | 0.351937i | \(-0.885523\pi\) | ||
0.936024 | − | 0.351937i | \(-0.114477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.160692 | − | 0.333681i | 0.0193451 | − | 0.0401705i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.23326 | − | 2.56090i | −0.146362 | − | 0.303923i | 0.814880 | − | 0.579629i | \(-0.196803\pi\) |
−0.961242 | + | 0.275706i | \(0.911088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.26962 | + | 0.746269i | 0.382680 | + | 0.0873442i | 0.409533 | − | 0.912295i | \(-0.365692\pi\) |
−0.0268533 | + | 0.999639i | \(0.508549\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.55121 | + | 3.15490i | −0.756469 | + | 0.364296i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.9594 | − | 10.2625i | −1.24894 | − | 1.16952i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.84700i | − | 0.882856i | −0.897297 | − | 0.441428i | \(-0.854472\pi\) | ||
0.897297 | − | 0.441428i | \(-0.145528\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.37675 | + | 3.07088i | 0.708528 | + | 0.341209i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.22440 | + | 14.1270i | −0.353924 | + | 1.55064i | 0.414106 | + | 0.910229i | \(0.364094\pi\) |
−0.768030 | + | 0.640414i | \(0.778763\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.00204547 | + | 0.00896179i | 0.000221862 | + | 0.000972043i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.19227 | − | 5.22368i | −0.127825 | − | 0.560037i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.67524 | − | 1.06709i | −0.495575 | − | 0.113112i | −0.0325735 | − | 0.999469i | \(-0.510370\pi\) |
−0.463001 | + | 0.886358i | \(0.653227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.02596 | − | 0.960723i | −0.107550 | − | 0.100711i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.71761 | + | 7.16966i | 0.592889 | + | 0.743459i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.13442 | + | 1.70214i | −0.218986 | + | 0.174636i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2524i | − | 1.34558i | −0.739833 | − | 0.672791i | \(-0.765095\pi\) | ||
0.739833 | − | 0.672791i | \(-0.234905\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.07934i | − | 0.309486i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.2089 | − | 8.14136i | 1.01583 | − | 0.810095i | 0.0339137 | − | 0.999425i | \(-0.489203\pi\) |
0.981914 | + | 0.189330i | \(0.0606314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.97069 | + | 7.48701i | 0.588310 | + | 0.737717i | 0.983505 | − | 0.180880i | \(-0.0578946\pi\) |
−0.395195 | + | 0.918597i | \(0.629323\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.900427 | + | 2.32546i | 0.0878727 | + | 0.226942i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.83564 | + | 1.10370i | 0.467479 | + | 0.106699i | 0.449770 | − | 0.893144i | \(-0.351506\pi\) |
0.0177083 | + | 0.999843i | \(0.494363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.07697 | − | 17.8624i | −0.390503 | − | 1.71090i | −0.662891 | − | 0.748716i | \(-0.730671\pi\) |
0.272388 | − | 0.962187i | \(-0.412187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.07189 | + | 9.07756i | 0.196655 | + | 0.861604i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.48222 | + | 6.49402i | −0.139435 | + | 0.610906i | 0.856124 | + | 0.516770i | \(0.172866\pi\) |
−0.995559 | + | 0.0941358i | \(0.969991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.127984 | + | 0.0616340i | 0.0119346 | + | 0.00574740i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.288272i | − | 0.0266508i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0400246 | + | 0.00584568i | −0.00366905 | + | 0.000535873i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.1041 | − | 9.20003i | 1.73673 | − | 0.836367i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.41017 | + | 0.550105i | 0.217318 | + | 0.0496013i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.51445 | − | 5.22131i | −0.224899 | − | 0.467008i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.726717 | + | 1.50904i | −0.0644857 | + | 0.133906i | −0.930721 | − | 0.365731i | \(-0.880819\pi\) |
0.866235 | + | 0.499637i | \(0.166533\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 10.9710i | − | 0.965942i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1098 | + | 13.9313i | −0.970669 | + | 1.21718i | 0.00545948 | + | 0.999985i | \(0.498262\pi\) |
−0.976128 | + | 0.217195i | \(0.930309\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.72175 | − | 9.95652i | −0.582850 | − | 0.863340i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.44875 | + | 3.00837i | −0.124689 | + | 0.258919i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.5875 | + | 14.5302i | −0.989983 | + | 1.24140i | −0.0196056 | + | 0.999808i | \(0.506241\pi\) |
−0.970378 | + | 0.241592i | \(0.922330\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.243306 | − | 0.305096i | −0.0206370 | − | 0.0258779i | 0.771406 | − | 0.636343i | \(-0.219554\pi\) |
−0.792043 | + | 0.610465i | \(0.790982\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.07158 | + | 3.85165i | −0.258674 | + | 0.324367i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.71621 | − | 1.30806i | 0.227141 | − | 0.109385i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00356 | − | 0.457299i | 0.166386 | − | 0.0379766i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.5148 | + | 3.13837i | −0.867249 | + | 0.258849i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.0316917 | − | 0.138850i | −0.00259629 | − | 0.0113751i | 0.973613 | − | 0.228205i | \(-0.0732855\pi\) |
−0.976209 | + | 0.216830i | \(0.930428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.20129 | − | 17.0302i | −0.667412 | − | 1.38589i | −0.909526 | − | 0.415647i | \(-0.863555\pi\) |
0.242114 | − | 0.970248i | \(-0.422159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.00648603 | − | 0.00517243i | −0.000524364 | − | 0.000418166i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.74994 | + | 2.19301i | −0.220881 | + | 0.176146i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4714 | − | 13.9330i | −1.39437 | − | 1.11198i | −0.979352 | − | 0.202164i | \(-0.935203\pi\) |
−0.415022 | − | 0.909812i | \(-0.636226\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.8232 | − | 8.10164i | −1.33417 | − | 0.642502i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.315012 | + | 0.539900i | −0.0248264 | + | 0.0425501i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.05602 | − | 2.43709i | −0.239366 | − | 0.190888i | 0.496458 | − | 0.868061i | \(-0.334634\pi\) |
−0.735824 | + | 0.677173i | \(0.763205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.34872 | −0.416397 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.61377 | + | 4.14817i | 0.666554 | + | 0.320995i | 0.736384 | − | 0.676564i | \(-0.236532\pi\) |
−0.0698306 | + | 0.997559i | \(0.522246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4583 | + | 5.51803i | −0.881409 | + | 0.424464i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.548252 | − | 2.40205i | 0.0419259 | − | 0.183689i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.07147 | + | 8.45450i | 0.309548 | + | 0.642784i | 0.996470 | − | 0.0839475i | \(-0.0267528\pi\) |
−0.686922 | + | 0.726731i | \(0.741039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4443 | − | 4.43128i | 0.865110 | − | 0.334974i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.5275 | 1.16712 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.27697 | + | 6.80471i | −0.244933 | + | 0.508608i | −0.986801 | − | 0.161938i | \(-0.948226\pi\) |
0.741868 | + | 0.670545i | \(0.233940\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.86582 | + | 0.425860i | 0.138685 | + | 0.0316539i | 0.291300 | − | 0.956632i | \(-0.405912\pi\) |
−0.152615 | + | 0.988286i | \(0.548769\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2706 | + | 2.80069i | −0.907069 | + | 0.207033i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.48172 | + | 0.794680i | −0.255981 | + | 0.0584261i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0193058 | − | 0.0845841i | 0.00141178 | − | 0.00618540i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.6908 | − | 7.40460i | −0.923118 | − | 0.538606i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.6249 | + | 16.4478i | −1.49237 | + | 1.19012i | −0.560063 | + | 0.828450i | \(0.689223\pi\) |
−0.932305 | + | 0.361673i | \(0.882206\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.82962 | + | 4.80219i | 0.275662 | + | 0.345669i | 0.900319 | − | 0.435230i | \(-0.143333\pi\) |
−0.624658 | + | 0.780899i | \(0.714761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.500720 | −0.0358573 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.465162 | 0.0331414 | 0.0165707 | − | 0.999863i | \(-0.494725\pi\) | ||||
0.0165707 | + | 0.999863i | \(0.494725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6098 | + | 14.5582i | 0.822995 | + | 1.03200i | 0.998867 | + | 0.0475898i | \(0.0151540\pi\) |
−0.175872 | + | 0.984413i | \(0.556275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.06125 | − | 5.63116i | 0.498062 | − | 0.397191i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.30690 | + | 8.94817i | 0.0917263 | + | 0.628039i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.210994 | + | 0.924427i | −0.0147365 | + | 0.0645648i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.124986 | + | 0.0285273i | −0.00868715 | + | 0.00198279i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.1207 | − | 5.73364i | 1.73764 | − | 0.396604i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9566 | − | 4.78320i | −1.44271 | − | 0.329289i | −0.571663 | − | 0.820489i | \(-0.693702\pi\) |
−0.871047 | + | 0.491199i | \(0.836559\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.93327 | − | 4.01447i | 0.132465 | − | 0.275067i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.20795 | 0.286980 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.66018 | − | 12.8278i | −0.587891 | − | 0.870808i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.28104 | + | 4.73663i | 0.154139 | + | 0.320072i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.00180731 | − | 0.00791833i | 0.000121573 | − | 0.000532645i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.57519 | + | 4.61117i | −0.641202 | + | 0.308787i | −0.726086 | − | 0.687604i | \(-0.758662\pi\) |
0.0848835 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.26772 | + | 1.09208i | 0.151182 | + | 0.0728052i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.0968 | −0.670150 | −0.335075 | − | 0.942192i | \(-0.608762\pi\) | ||||
−0.335075 | + | 0.942192i | \(0.608762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1208 | + | 12.8559i | 1.06529 | + | 0.849542i | 0.989055 | − | 0.147548i | \(-0.0471380\pi\) |
0.0762369 | + | 0.997090i | \(0.475709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.86618 | − | 23.4622i | 0.122786 | − | 1.54370i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.6175 | − | 8.96571i | −1.21967 | − | 0.587363i | −0.290452 | − | 0.956890i | \(-0.593806\pi\) |
−0.929220 | + | 0.369527i | \(0.879520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.47731 | − | 1.17812i | −0.0963690 | − | 0.0768518i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.61727 | − | 7.66952i | 0.624709 | − | 0.498189i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.90732 | + | 1.52104i | 0.123374 | + | 0.0983876i | 0.683233 | − | 0.730200i | \(-0.260573\pi\) |
−0.559859 | + | 0.828588i | \(0.689145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.37926 | + | 11.1701i | 0.346508 | + | 0.719532i | 0.999277 | − | 0.0380255i | \(-0.0121068\pi\) |
−0.652768 | + | 0.757558i | \(0.726393\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.23840 | − | 5.42580i | −0.0794436 | − | 0.348065i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.20373 | − | 4.03299i | −0.0769036 | − | 0.257659i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.35168 | − | 0.536755i | 0.149634 | − | 0.0341529i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.4656 | + | 9.85569i | −1.29695 | + | 0.624579i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.62267 | − | 8.30457i | 0.418019 | − | 0.524180i | −0.527583 | − | 0.849503i | \(-0.676902\pi\) |
0.945603 | + | 0.325323i | \(0.105473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.835930 | − | 1.04822i | −0.0525545 | − | 0.0659012i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.00898435 | + | 0.0112660i | −0.000562622 | + | 0.000705506i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0392 | + | 22.9231i | −0.688604 | + | 1.42990i | 0.203959 | + | 0.978979i | \(0.434619\pi\) |
−0.892563 | + | 0.450922i | \(0.851095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.27109 | − | 15.5499i | −0.141119 | − | 0.966222i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.15638 | + | 1.45006i | −0.0715783 | + | 0.0897563i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3223i | 0.944812i | 0.881381 | + | 0.472406i | \(0.156614\pi\) | ||||
−0.881381 | + | 0.472406i | \(0.843386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.10741 | − | 6.45259i | 0.190886 | − | 0.396380i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.26167 | − | 6.77293i | −0.199611 | − | 0.414497i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.4742 | − | 7.18379i | −1.91902 | − | 0.438003i | −0.998928 | − | 0.0462989i | \(-0.985257\pi\) |
−0.920091 | − | 0.391705i | \(-0.871886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.89788 | + | 1.39555i | −0.176034 | + | 0.0847734i | −0.519825 | − | 0.854273i | \(-0.674003\pi\) |
0.343792 | + | 0.939046i | \(0.388289\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.174703 | − | 2.19641i | 0.0105735 | − | 0.132933i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.3227i | 1.58732i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9688 | − | 5.76386i | −0.719134 | − | 0.346317i | 0.0382663 | − | 0.999268i | \(-0.487816\pi\) |
−0.757400 | + | 0.652951i | \(0.773531\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.706358 | − | 3.09475i | 0.0422885 | − | 0.185278i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.33185 | + | 18.9791i | 0.258417 | + | 1.13220i | 0.922944 | + | 0.384934i | \(0.125776\pi\) |
−0.664527 | + | 0.747264i | \(0.731367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.177804 | + | 0.779009i | 0.0105693 | + | 0.0463073i | 0.979938 | − | 0.199305i | \(-0.0638683\pi\) |
−0.969368 | + | 0.245612i | \(0.921011\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.17228 | − | 0.952296i | −0.247145 | − | 0.0564092i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.98139 | − | 1.24806i | −0.235014 | − | 0.0736709i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.5992 | + | 13.2910i | 0.623481 | + | 0.781821i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.2422 | − | 12.9527i | 0.952134 | − | 0.759301i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.330751i | 0.0193227i | 0.999953 | + | 0.00966134i | \(0.00307535\pi\) | ||||
−0.999953 | + | 0.00966134i | \(0.996925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.95563i | 0.346750i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.6393 | − | 19.6492i | 1.42972 | − | 1.14016i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0782556 | − | 0.0981294i | −0.00452564 | − | 0.00567497i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.46816 | + | 18.4582i | −0.0846236 | + | 1.06391i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.9561 | + | 4.55484i | 1.14645 | + | 0.261669i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.07421 | − | 4.70642i | −0.0615091 | − | 0.269489i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.19856 | − | 27.1577i | −0.353770 | − | 1.54997i | −0.768395 | − | 0.639976i | \(-0.778944\pi\) |
0.414624 | − | 0.909993i | \(-0.363913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.34042 | + | 14.6353i | −0.190030 | + | 0.832576i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7589 | + | 9.03380i | 1.06372 | + | 0.512260i | 0.882077 | − | 0.471105i | \(-0.156145\pi\) |
0.181642 | + | 0.983365i | \(0.441859\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.00551i | 0.452498i | 0.974069 | + | 0.226249i | \(0.0726464\pi\) | ||||
−0.974069 | + | 0.226249i | \(0.927354\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.435016 | − | 0.745575i | 0.0245104 | − | 0.0420084i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.4573 | − | 5.99912i | 0.699671 | − | 0.336944i | −0.0500047 | − | 0.998749i | \(-0.515924\pi\) |
0.749676 | + | 0.661805i | \(0.230209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.9102 | − | 4.31612i | −1.05877 | − | 0.241656i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.37357 | + | 7.00529i | 0.188294 | + | 0.390997i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0301190 | − | 0.0625428i | 0.00167587 | − | 0.00347997i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.46420i | 0.136689i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.9073 | − | 22.4551i | 0.990278 | − | 1.24177i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.68325 | − | 6.06919i | 0.313328 | − | 0.334605i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.92697 | + | 16.4605i | −0.435706 | + | 0.904752i | 0.561314 | + | 0.827603i | \(0.310296\pi\) |
−0.997020 | + | 0.0771491i | \(0.975418\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00953 | − | 2.51987i | 0.110121 | − | 0.138088i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.15985 | + | 2.70836i | 0.118005 | + | 0.147974i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.72562 | + | 12.1955i | −0.529788 | + | 0.664333i | −0.972655 | − | 0.232254i | \(-0.925390\pi\) |
0.442867 | + | 0.896587i | \(0.353961\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.40776 | + | 4.53054i | −0.510960 | + | 0.246065i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.3651 | − | 7.38712i | 1.75267 | − | 0.400035i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1108 | − | 3.87306i | 0.977889 | − | 0.209126i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0495511 | + | 0.217097i | 0.00266774 | + | 0.0116881i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.93676 | − | 14.4043i | −0.372385 | − | 0.773265i | 0.627601 | − | 0.778535i | \(-0.284037\pi\) |
−0.999986 | + | 0.00527002i | \(0.998322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.39975 | + | 5.90111i | 0.396100 | + | 0.315879i | 0.801204 | − | 0.598392i | \(-0.204193\pi\) |
−0.405104 | + | 0.914271i | \(0.632765\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.30661 | − | 1.83946i | 0.123118 | − | 0.0981830i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.1340 | − | 8.08158i | −0.539377 | − | 0.430139i | 0.315533 | − | 0.948915i | \(-0.397817\pi\) |
−0.854911 | + | 0.518775i | \(0.826388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.53976 | + | 0.741510i | 0.0817220 | + | 0.0393552i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0462839 | − | 0.0433407i | −0.00244960 | − | 0.00229383i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.16713 | + | 1.72823i | 0.114377 | + | 0.0912123i | 0.679008 | − | 0.734131i | \(-0.262410\pi\) |
−0.564631 | + | 0.825343i | \(0.690982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.61631 | 0.0850690 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.9475 | + | 14.4220i | 1.57184 | + | 0.756957i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.81675 | + | 0.874900i | −0.0950930 | + | 0.0457944i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.28986 | − | 10.0325i | 0.119530 | − | 0.523693i | −0.879342 | − | 0.476191i | \(-0.842017\pi\) |
0.998871 | − | 0.0475016i | \(-0.0151259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.371293 | − | 0.770998i | −0.0193287 | − | 0.0401365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.2202 | + | 15.8820i | 1.41320 | + | 0.824552i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9550 | 0.619005 | 0.309502 | − | 0.950899i | \(-0.399838\pi\) | ||||
0.309502 | + | 0.950899i | \(0.399838\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.94165 | − | 8.18492i | 0.203546 | − | 0.422668i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.77027 | − | 0.404054i | −0.0911738 | − | 0.0208098i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.9222 | − | 2.49293i | 0.561038 | − | 0.128053i | 0.0674081 | − | 0.997725i | \(-0.478527\pi\) |
0.493629 | + | 0.869672i | \(0.335670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.55976 | + | 0.584249i | −0.131141 | + | 0.0299320i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.70012 | + | 16.2113i | −0.189067 | + | 0.828357i | 0.788043 | + | 0.615621i | \(0.211095\pi\) |
−0.977110 | + | 0.212736i | \(0.931763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.99900 | + | 0.715779i | 0.458632 | + | 0.0364795i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.96912 | + | 2.36779i | −0.150929 | + | 0.120362i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.77214 | + | 9.74595i | 0.394063 | + | 0.494139i | 0.938798 | − | 0.344469i | \(-0.111941\pi\) |
−0.544735 | + | 0.838608i | \(0.683370\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.00361200 | −0.000182667 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.9327 | −1.40902 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.94167 | + | 3.68873i | 0.148011 | + | 0.185600i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.53902 | + | 2.02480i | −0.127430 | + | 0.101622i | −0.685131 | − | 0.728420i | \(-0.740255\pi\) |
0.557701 | + | 0.830042i | \(0.311684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.63298 | − | 17.9695i | 0.282002 | − | 0.899600i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.282584 | − | 1.23808i | 0.0141116 | − | 0.0618269i | −0.967382 | − | 0.253322i | \(-0.918477\pi\) |
0.981493 | + | 0.191496i | \(0.0613338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.02986 | − | 0.691545i | 0.150928 | − | 0.0344483i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.14880 | + | 0.946937i | −0.206156 | + | 0.0470537i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.8615 | + | 7.50043i | 1.62889 | + | 0.371783i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4653 | − | 25.8844i | 0.616369 | − | 1.27990i | −0.326014 | − | 0.945365i | \(-0.605706\pi\) |
0.942382 | − | 0.334538i | \(-0.108580\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.1336 | −1.43705 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.1244 | − | 2.07793i | −1.28550 | − | 0.102248i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.78018 | − | 7.84962i | −0.185562 | − | 0.385323i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.136122 | − | 0.596391i | 0.00666595 | − | 0.0292054i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.6865 | − | 15.2594i | 1.54799 | − | 0.745471i | 0.551905 | − | 0.833907i | \(-0.313901\pi\) |
0.996082 | + | 0.0884361i | \(0.0281869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.4369 | + | 11.2866i | 1.14225 | + | 0.550077i | 0.906696 | − | 0.421785i | \(-0.138596\pi\) |
0.235551 | + | 0.971862i | \(0.424311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.70530 | 0.0829147 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0554436 | + | 0.0442148i | 0.00268941 | + | 0.00214473i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.0196 | − | 3.06995i | 1.01721 | − | 0.148565i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.25793 | + | 2.05051i | 0.205575 | + | 0.0989997i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5563 | − | 14.0007i | −0.845659 | − | 0.674390i | 0.101612 | − | 0.994824i | \(-0.467600\pi\) |
−0.947271 | + | 0.320434i | \(0.896171\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.3517 | − | 18.6224i | 1.12221 | − | 0.894935i | 0.126927 | − | 0.991912i | \(-0.459489\pi\) |
0.995287 | + | 0.0969770i | \(0.0309173\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.51871 | + | 2.00860i | 0.120763 | + | 0.0963050i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.465442 | − | 0.966500i | −0.0222651 | − | 0.0462339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.30520 | − | 18.8623i | −0.205476 | − | 0.900249i | −0.967534 | − | 0.252740i | \(-0.918668\pi\) |
0.762058 | − | 0.647509i | \(-0.224189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.11869 | + | 2.16833i | 0.148509 | + | 0.103254i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.9869 | − | 6.15958i | 1.28218 | − | 0.292650i | 0.473448 | − | 0.880822i | \(-0.343009\pi\) |
0.808736 | + | 0.588171i | \(0.200152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.59778 | − | 1.25102i | 0.123146 | − | 0.0593042i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.139200 | − | 0.174551i | 0.00658394 | − | 0.00825600i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.34377 | + | 1.68504i | 0.0634166 | + | 0.0795219i | 0.812528 | − | 0.582922i | \(-0.198091\pi\) |
−0.749111 | + | 0.662444i | \(0.769519\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.57986 | − | 6.99692i | 0.262745 | − | 0.329472i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.8563 | − | 26.6965i | 0.604044 | − | 1.25431i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.842441 | + | 0.0670076i | 0.0394942 | + | 0.00314137i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0661 | + | 21.4002i | −0.798319 | + | 1.00106i | 0.201448 | + | 0.979499i | \(0.435435\pi\) |
−0.999768 | + | 0.0215614i | \(0.993136\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 0.0849030i | − | 0.00396293i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.184354 | + | 0.382815i | −0.00858622 | + | 0.0178295i | −0.905218 | − | 0.424948i | \(-0.860292\pi\) |
0.896632 | + | 0.442777i | \(0.146007\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.7832 | + | 22.3916i | 0.501139 | + | 1.04063i | 0.986110 | + | 0.166096i | \(0.0531160\pi\) |
−0.484971 | + | 0.874530i | \(0.661170\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.37549 | − | 1.22692i | −0.249283 | − | 0.0568971i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.1510 | + | 7.29634i | −0.701105 | + | 0.337634i | −0.750247 | − | 0.661157i | \(-0.770066\pi\) |
0.0491422 | + | 0.998792i | \(0.484351\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.6338 | + | 8.52923i | −0.583376 | + | 0.393843i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 35.0309i | − | 1.61414i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.7828 | − | 17.2321i | −1.64530 | − | 0.792333i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.68655 | + | 20.5331i | −0.215034 | + | 0.942123i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.43826 | + | 6.30145i | 0.0658536 | + | 0.288523i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.99233 | + | 8.72898i | 0.0910320 | + | 0.398837i | 0.999831 | − | 0.0183974i | \(-0.00585641\pi\) |
−0.908799 | + | 0.417235i | \(0.862999\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.07633 | + | 0.702153i | 0.140269 | + | 0.0320154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.969588 | + | 0.141610i | −0.0441178 | + | 0.00644350i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.96805 | + | 6.22974i | 0.225587 | + | 0.282878i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.2801 | + | 14.5779i | −0.828350 | + | 0.660587i | −0.942990 | − | 0.332820i | \(-0.892000\pi\) |
0.114640 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 6.12743i | − | 0.277092i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.0316i | − | 1.03940i | −0.854348 | − | 0.519701i | \(-0.826043\pi\) | ||
0.854348 | − | 0.519701i | \(-0.173957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0408548 | + | 0.0325806i | −0.00184001 | + | 0.00146736i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.15438 | + | 1.44754i | 0.0518854 | + | 0.0650622i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.78987 | + | 6.49546i | −0.169999 | + | 0.291361i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.2438 | + | 5.76173i | 1.13007 | + | 0.257930i | 0.746372 | − | 0.665529i | \(-0.231794\pi\) |
0.383695 | + | 0.923460i | \(0.374651\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.33495 | + | 14.6114i | 0.148995 | + | 0.652788i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.46034 | + | 6.39816i | 0.0651133 | + | 0.285280i | 0.996993 | − | 0.0774865i | \(-0.0246895\pi\) |
−0.931880 | + | 0.362766i | \(0.881832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.74702 | + | 7.65421i | −0.0777415 | + | 0.340608i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.9621 | − | 8.65007i | −0.797723 | − | 0.384163i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.9425i | 1.28286i | 0.767183 | + | 0.641428i | \(0.221658\pi\) | ||||
−0.767183 | + | 0.641428i | \(0.778342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.20389 | − | 8.27444i | −0.141732 | − | 0.366040i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.7183 | − | 10.9406i | 1.00304 | − | 0.483038i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.61343 | − | 1.28123i | −0.247357 | − | 0.0564577i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.73794 | + | 16.0680i | 0.340314 | + | 0.706670i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.38244 | + | 13.2533i | −0.280158 | + | 0.581754i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.1910i | 1.23507i | 0.786543 | + | 0.617536i | \(0.211869\pi\) | ||||
−0.786543 | + | 0.617536i | \(0.788131\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.51846 | + | 4.41201i | −0.153852 | + | 0.192924i | −0.852784 | − | 0.522264i | \(-0.825088\pi\) |
0.698932 | + | 0.715188i | \(0.253659\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.6165 | + | 9.69511i | 0.725202 | + | 0.423129i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0388048 | − | 0.0805790i | 0.00169036 | − | 0.00351007i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.3055 | − | 17.9385i | 0.621977 | − | 0.779934i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.35120 | − | 4.20227i | −0.145430 | − | 0.182363i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.522358 | − | 0.655017i | 0.0226259 | − | 0.0283719i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.68690 | + | 1.29394i | −0.116165 | + | 0.0559420i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.5427 | + | 2.63455i | −0.498104 | + | 0.113689i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.27955 | + | 39.2245i | −0.270479 | + | 1.68952i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.16996 | − | 9.50722i | −0.0932939 | − | 0.408747i | 0.906619 | − | 0.421950i | \(-0.138654\pi\) |
−0.999913 | + | 0.0132031i | \(0.995797\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.30168 | + | 2.70297i | 0.0558605 | + | 0.115996i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.61271 | + | 6.86841i | 0.368928 | + | 0.294210i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.8866 | − | 16.6565i | 0.893045 | − | 0.712179i | −0.0652781 | − | 0.997867i | \(-0.520793\pi\) |
0.958323 | + | 0.285688i | \(0.0922220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.40624 | + | 2.71638i | 0.145375 | + | 0.115932i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.9825 | − | 6.73360i | −0.595673 | − | 0.286861i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.2070 | + | 11.6166i | −0.731716 | + | 0.493990i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.37693 | − | 3.49049i | −0.185791 | − | 0.148163i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.1878 | 0.685900 | 0.342950 | − | 0.939354i | \(-0.388574\pi\) | ||||
0.342950 | + | 0.939354i | \(0.388574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.34981 | − | 1.61318i | −0.141682 | − | 0.0682303i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.122535 | − | 0.0590099i | 0.00517344 | − | 0.00249140i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82099 | − | 12.3596i | 0.118891 | − | 0.520894i | −0.880050 | − | 0.474881i | \(-0.842491\pi\) |
0.998941 | − | 0.0460134i | \(-0.0146517\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.73770 | − | 3.60837i | −0.0731056 | − | 0.151805i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.70622 | − | 18.5292i | −0.113651 | − | 0.778151i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.3269 | −0.642535 | −0.321268 | − | 0.946988i | \(-0.604109\pi\) | ||||
−0.321268 | + | 0.946988i | \(0.604109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.4813 | − | 25.9177i | 0.522327 | − | 1.08462i | −0.458311 | − | 0.888792i | \(-0.651545\pi\) |
0.980638 | − | 0.195831i | \(-0.0627404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.3169 | − | 9.20207i | −1.68426 | − | 0.384422i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.06840 | − | 0.243856i | 0.0445555 | − | 0.0101695i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9234 | − | 4.31915i | 0.787793 | − | 0.179809i | 0.190346 | − | 0.981717i | \(-0.439039\pi\) |
0.597447 | + | 0.801908i | \(0.296182\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.14256 | + | 9.38715i | −0.0890415 | + | 0.390117i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.7513 | − | 13.8430i | 1.48322 | − | 0.574306i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.8484 | + | 42.1452i | −2.18876 | + | 1.74547i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.108067 | + | 0.135512i | 0.00446802 | + | 0.00560272i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −46.2068 | −1.90716 | −0.953580 | − | 0.301141i | \(-0.902633\pi\) | ||||
−0.953580 | + | 0.301141i | \(0.902633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.5617 | 1.09445 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.454641 | + | 0.570102i | 0.0187015 | + | 0.0234509i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.5710 | + | 21.1896i | −1.09114 | + | 0.870154i | −0.992165 | − | 0.124936i | \(-0.960127\pi\) |
−0.0989739 | + | 0.995090i | \(0.531556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0166234 | − | 0.0177523i | 0.000681495 | − | 0.000727774i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.49532 | + | 28.4578i | −0.265836 | + | 1.16470i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.6554 | + | 4.71446i | −0.843957 | + | 0.192628i | −0.622576 | − | 0.782560i | \(-0.713914\pi\) |
−0.221382 | + | 0.975187i | \(0.571057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2174 | + | 3.70152i | −0.661521 | + | 0.150988i | −0.540084 | − | 0.841611i | \(-0.681608\pi\) |
−0.121437 | + | 0.992599i | \(0.538750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.04796 | − | 0.695677i | −0.124122 | − | 0.0283301i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.53159 | + | 11.4865i | −0.224891 | + | 0.466991i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8869 | 1.61896 | 0.809479 | − | 0.587149i | \(-0.199750\pi\) | ||||
0.809479 | + | 0.587149i | \(0.199750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.68953 | + | 10.3475i | −0.392640 | + | 0.419303i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.724387 | + | 1.50421i | 0.0293056 | + | 0.0608536i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.58047 | + | 15.6871i | −0.144614 | + | 0.633594i | 0.849715 | + | 0.527243i | \(0.176774\pi\) |
−0.994329 | + | 0.106352i | \(0.966083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.33920 | + | 0.644924i | −0.0540017 | + | 0.0260059i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.1516 | − | 19.3360i | −1.61644 | − | 0.778437i | −0.616481 | − | 0.787370i | \(-0.711442\pi\) |
−0.999960 | + | 0.00893318i | \(0.997156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.5643 | −0.866743 | −0.433371 | − | 0.901215i | \(-0.642676\pi\) | ||||
−0.433371 | + | 0.901215i | \(0.642676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.02580 | − | 0.818044i | −0.0411637 | − | 0.0328270i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.58126 | + | 11.8317i | 0.183544 | + | 0.474025i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.7563 | − | 8.55099i | −0.710253 | − | 0.342040i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 31.5797 | + | 25.1840i | 1.26117 | + | 1.00575i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0709964 | − | 0.0566177i | 0.00283081 | − | 0.00225750i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6690 | − | 22.0653i | −1.10148 | − | 0.878405i | −0.108203 | − | 0.994129i | \(-0.534510\pi\) |
−0.993281 | + | 0.115724i | \(0.963081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6203 | − | 30.3594i | −0.581105 | − | 1.20668i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.224090 | − | 0.981804i | −0.00889275 | − | 0.0389617i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.587859 | + | 3.67200i | −0.0232918 | + | 0.145490i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.50369 | + | 0.343208i | −0.0594852 | + | 0.0135771i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.149827 | − | 0.0721528i | 0.00591781 | − | 0.00284987i | −0.430922 | − | 0.902389i | \(-0.641812\pi\) |
0.436840 | + | 0.899539i | \(0.356097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.6992 | − | 33.4797i | 1.05291 | − | 1.32031i | 0.107582 | − | 0.994196i | \(-0.465689\pi\) |
0.945331 | − | 0.326114i | \(-0.105739\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.11278 | + | 5.15726i | 0.161941 | + | 0.203067i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.44553 | + | 4.32055i | −0.135458 | + | 0.169858i | −0.844934 | − | 0.534871i | \(-0.820360\pi\) |
0.709476 | + | 0.704729i | \(0.248932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.3890 | − | 50.6444i | 0.957353 | − | 1.98796i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.25742 | − | 23.1516i | 0.284441 | − | 0.907382i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.9289 | + | 19.9742i | −0.623344 | + | 0.781649i | −0.988811 | − | 0.149175i | \(-0.952338\pi\) |
0.365466 | + | 0.930825i | \(0.380910\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10.7137i | − | 0.418617i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.789590 | − | 1.63960i | 0.0308048 | − | 0.0639669i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.91741 | − | 8.13459i | −0.152601 | − | 0.316878i | 0.810628 | − | 0.585561i | \(-0.199126\pi\) |
−0.963229 | + | 0.268683i | \(0.913412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.38856 | − | 0.773416i | −0.131800 | − | 0.0300824i | 0.156112 | − | 0.987739i | \(-0.450104\pi\) |
−0.287912 | + | 0.957657i | \(0.592961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0114711 | − | 0.00552421i | 0.000445502 | − | 0.000214542i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.89225 | + | 2.16054i | 0.267270 | + | 0.0837823i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.807523i | 0.0312674i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0101 | − | 7.22847i | −0.580323 | − | 0.279469i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1387 | + | 44.4207i | −0.391401 | + | 1.71484i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.03339 | − | 13.2901i | −0.116929 | − | 0.512297i | −0.999141 | − | 0.0414454i | \(-0.986804\pi\) |
0.882212 | − | 0.470852i | \(-0.156053\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.73203 | + | 25.1137i | 0.220626 | + | 0.966626i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.4123 | + | 6.94141i | 1.16884 | + | 0.266780i | 0.762528 | − | 0.646955i | \(-0.223958\pi\) |
0.406311 | + | 0.913735i | \(0.366815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.0602 | + | 19.6188i | −1.11523 | + | 0.752901i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.86846 | − | 12.3747i | −0.378160 | − | 0.474198i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.6111 | + | 12.4495i | −0.597343 | + | 0.476365i | −0.874874 | − | 0.484351i | \(-0.839056\pi\) |
0.277530 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.1743i | − | 0.426947i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.3228i | 1.23319i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.94740 | + | 3.94542i | −0.188481 | + | 0.150308i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.808127 | − | 1.01336i | −0.0307426 | − | 0.0385500i | 0.766223 | − | 0.642575i | \(-0.222134\pi\) |
−0.796965 | + | 0.604025i | \(0.793563\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.75243 | + | 4.55864i | −0.256504 | + | 0.173168i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.228748 | + | 0.0522101i | 0.00867689 | + | 0.00198044i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.00536503 | − | 0.0235057i | −0.000203215 | − | 0.000890344i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.20804 | − | 31.5805i | −0.272633 | − | 1.19448i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.19084 | − | 35.8864i | 0.309364 | − | 1.35541i | −0.546175 | − | 0.837671i | \(-0.683916\pi\) |
0.855538 | − | 0.517740i | \(-0.173226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.2983 | + | 11.7015i | 0.916429 | + | 0.441329i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.96206i | − | 0.111558i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.9657 | − | 10.3339i | −1.23980 | − | 0.388647i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8366 | − | 17.7396i | 1.38343 | − | 0.666223i | 0.413699 | − | 0.910414i | \(-0.364237\pi\) |
0.969727 | + | 0.244191i | \(0.0785223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.15126 | − | 0.947497i | −0.155684 | − | 0.0355339i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.599667 | − | 1.24522i | −0.0224577 | − | 0.0466339i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.786480 | + | 1.63314i | −0.0294127 | + | 0.0610761i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.82424i | 0.142819i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5798 | − | 25.8063i | 0.767497 | − | 0.962411i | −0.232451 | − | 0.972608i | \(-0.574674\pi\) |
0.999948 | + | 0.0101970i | \(0.00324586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.57866 | − | 24.1763i | 0.282244 | − | 0.900374i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.43252 | + | 17.5103i | −0.313609 | + | 0.651216i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.88495 | − | 12.3953i | 0.367118 | − | 0.460351i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.8787 | − | 17.4034i | −0.514734 | − | 0.645456i | 0.454747 | − | 0.890620i | \(-0.349730\pi\) |
−0.969482 | + | 0.245164i | \(0.921158\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.6780 | − | 23.4215i | 0.691778 | − | 0.867463i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0964011 | + | 0.0464243i | −0.00356552 | + | 0.00171707i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.8704 | + | 6.13299i | −0.992480 | + | 0.226527i | −0.687778 | − | 0.725921i | \(-0.741414\pi\) |
−0.304702 | + | 0.952448i | \(0.598557\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.76633 | − | 5.41707i | 0.138923 | − | 0.199812i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.27542 | − | 31.8757i | −0.267994 | − | 1.17416i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7143 | + | 32.6310i | 0.578058 | + | 1.20035i | 0.960992 | + | 0.276575i | \(0.0891994\pi\) |
−0.382934 | + | 0.923776i | \(0.625086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.95633 | + | 2.35760i | 0.108604 | + | 0.0866085i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.2699 | + | 23.3419i | −1.07381 | + | 0.856333i | −0.990129 | − | 0.140160i | \(-0.955238\pi\) |
−0.0836785 | + | 0.996493i | \(0.526667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0669497 | + | 0.0533906i | 0.00245285 | + | 0.00195608i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.08422 | + | 3.41158i | 0.259198 | + | 0.124823i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.73843 | − | 12.2376i | −0.173138 | − | 0.447151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.87218 | − | 1.49302i | −0.0683169 | − | 0.0544809i | 0.588736 | − | 0.808325i | \(-0.299626\pi\) |
−0.657053 | + | 0.753844i | \(0.728197\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.6510 | 0.606795 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2395 | + | 4.93109i | 0.372654 | + | 0.179461i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.80434 | − | 2.79522i | 0.210962 | − | 0.101594i | −0.325419 | − | 0.945570i | \(-0.605505\pi\) |
0.536381 | + | 0.843976i | \(0.319791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.467678 | − | 2.04903i | 0.0169756 | − | 0.0743751i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.63303 | − | 9.62059i | −0.167947 | − | 0.348746i | 0.799960 | − | 0.600053i | \(-0.204854\pi\) |
−0.967907 | + | 0.251307i | \(0.919140\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.1333 | + | 35.3833i | −1.19951 | + | 1.28096i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.00498799 | 0.000180341 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.28318 | − | 4.74107i | 0.0824408 | − | 0.171190i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.17361 | − | 1.40909i | −0.222626 | − | 0.0508129i | 0.109753 | − | 0.993959i | \(-0.464994\pi\) |
−0.332379 | + | 0.943146i | \(0.607851\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.8840 | + | 8.87501i | −1.40037 | + | 0.319626i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.0641 | − | 3.21005i | 0.505852 | − | 0.115457i | 0.0380238 | − | 0.999277i | \(-0.487894\pi\) |
0.467828 | + | 0.883819i | \(0.345037\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.03806 | + | 26.4545i | −0.216894 | + | 0.950273i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.8382 | − | 17.9816i | 0.604067 | − | 0.645087i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.59833 | − | 4.46452i | 0.200581 | − | 0.159958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0570 | − | 12.6110i | −0.359866 | − | 0.451258i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.9815 | −0.678342 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.4362 | 0.479558 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3793 | − | 16.7771i | −0.476920 | − | 0.598039i | 0.483930 | − | 0.875106i | \(-0.339209\pi\) |
−0.960850 | + | 0.277068i | \(0.910637\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.7790 | + | 14.9757i | −0.668549 | + | 0.533150i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4345 | − | 6.36347i | 0.584342 | − | 0.226259i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.949136 | + | 4.15844i | −0.0337048 | + | 0.147670i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.9454 | − | 2.49822i | 0.388194 | − | 0.0886028i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.4157 | − | 11.5070i | 1.78581 | − | 0.407601i | 0.803571 | − | 0.595209i | \(-0.202931\pi\) |
0.982244 | + | 0.187609i | \(0.0600737\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0468416 | + | 0.0106913i | 0.00165714 | + | 0.000378231i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.12904 | + | 2.34447i | −0.0398926 | + | 0.0828379i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.0318 | 0.671616 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0543151 | − | 0.371888i | −0.00191435 | − | 0.0131073i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.9579 | − | 45.5961i | −0.772956 | − | 1.60506i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.86145 | + | 43.2058i | −0.346710 | + | 1.51904i | 0.437887 | + | 0.899030i | \(0.355727\pi\) |
−0.784597 | + | 0.620006i | \(0.787130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7628 | − | 8.55413i | 0.623737 | − | 0.300376i | −0.0951925 | − | 0.995459i | \(-0.530347\pi\) |
0.718930 | + | 0.695083i | \(0.244632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.54272 | − | 2.18766i | −0.159320 | − | 0.0767245i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.35019 | 0.0823236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.8444 | − | 19.8128i | −0.869197 | − | 0.693161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.632128 | + | 0.426756i | −0.0220883 | + | 0.0149121i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.2010 | − | 19.8413i | −1.43792 | − | 0.692468i | −0.457471 | − | 0.889224i | \(-0.651245\pi\) |
−0.980452 | + | 0.196757i | \(0.936959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.5899 | + | 28.3820i | 1.24059 | + | 0.989334i | 0.999824 | + | 0.0187491i | \(0.00596837\pi\) |
0.240761 | + | 0.970584i | \(0.422603\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.2611 | + | 25.7274i | −1.12319 | + | 0.895712i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.3608 | + | 9.05991i | 0.395052 | + | 0.315044i | 0.800789 | − | 0.598946i | \(-0.204414\pi\) |
−0.405737 | + | 0.913990i | \(0.632985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.5540 | + | 48.9105i | 0.818065 | + | 1.69873i | 0.709572 | + | 0.704633i | \(0.248889\pi\) |
0.108494 | + | 0.994097i | \(0.465397\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.63389 | − | 20.3024i | −0.160748 | − | 0.704283i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0720707 | + | 0.0791127i | 0.00249710 | + | 0.00274109i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.60424 | + | 1.27913i | −0.193943 | + | 0.0442661i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.2699 | − | 14.0956i | 1.01171 | − | 0.487216i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0997 | + | 12.6647i | −0.348682 | + | 0.437233i | −0.924985 | − | 0.380002i | \(-0.875923\pi\) |
0.576304 | + | 0.817236i | \(0.304495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7973 | − | 13.5393i | −0.372319 | − | 0.466874i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.0269 | + | 23.8590i | −0.655321 | + | 0.821746i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.31776 | − | 6.88940i | 0.114134 | − | 0.237003i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −48.4555 | − | 28.2720i | −1.66495 | − | 0.971438i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.780970 | + | 0.979306i | −0.0268028 | + | 0.0336097i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.40329i | − | 0.0481042i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.0511 | + | 47.8660i | −0.789253 | + | 1.63890i | −0.0201333 | + | 0.999797i | \(0.506409\pi\) |
−0.769120 | + | 0.639104i | \(0.779305\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.642751 | + | 1.33469i | 0.0219816 | + | 0.0456453i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.9322 | − | 10.2555i | −1.53486 | − | 0.350321i | −0.630190 | − | 0.776441i | \(-0.717023\pi\) |
−0.904667 | + | 0.426120i | \(0.859880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.1725 | + | 15.9750i | −1.13183 | + | 0.545061i | −0.903528 | − | 0.428530i | \(-0.859032\pi\) |
−0.228302 | + | 0.973590i | \(0.573317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.36172 | − | 6.09943i | −0.0804871 | − | 0.207868i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 58.1443i | − | 1.97925i | −0.143659 | − | 0.989627i | \(-0.545887\pi\) | ||
0.143659 | − | 0.989627i | \(-0.454113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.08333 | − | 2.44800i | −0.172838 | − | 0.0832346i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.92992 | + | 25.9807i | −0.201391 | + | 0.882351i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.90897 | − | 43.4140i | −0.336139 | − | 1.47272i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.681088 | − | 2.98404i | −0.0230778 | − | 0.101110i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.01088 | − | 1.60019i | −0.237282 | − | 0.0541581i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.72699 | + | 13.2433i | −0.261220 | + | 0.447705i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.5741 | − | 17.0213i | −0.458364 | − | 0.574770i | 0.497915 | − | 0.867226i | \(-0.334099\pi\) |
−0.956279 | + | 0.292456i | \(0.905528\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.405368 | + | 0.323270i | −0.0136727 | + | 0.0109036i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.8583i | − | 0.601660i | −0.953678 | − | 0.300830i | \(-0.902736\pi\) | ||
0.953678 | − | 0.300830i | \(-0.0972636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.5907i | − | 0.894847i | −0.894322 | − | 0.447423i | \(-0.852342\pi\) | ||
0.894322 | − | 0.447423i | \(-0.147658\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.29921 | + | 5.82093i | −0.245360 | + | 0.195668i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.2089 | + | 30.3570i | 0.812855 | + | 1.01929i | 0.999322 | + | 0.0368271i | \(0.0117251\pi\) |
−0.186466 | + | 0.982461i | \(0.559703\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.38488 | − | 0.640421i | 0.147064 | − | 0.0214790i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39.1577 | + | 8.93748i | 1.31183 | + | 0.299417i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.17522 | + | 13.9116i | 0.106255 | + | 0.465533i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.01049 | − | 4.42723i | −0.0337769 | − | 0.147986i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0437816 | − | 0.191820i | 0.00146183 | − | 0.00640468i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0148 | − | 8.67545i | −0.600826 | − | 0.289342i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.182107i | 0.00606685i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.0573 | + | 16.2414i | −0.800578 | + | 0.540479i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.03673 | + | 0.499264i | −0.0344621 | + | 0.0165961i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.6798 | + | 4.49179i | 0.653458 | + | 0.149148i | 0.536382 | − | 0.843975i | \(-0.319791\pi\) |
0.117076 | + | 0.993123i | \(0.462648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.07429 | − | 6.38382i | −0.101968 | − | 0.211738i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9113 | − | 35.1167i | 0.560296 | − | 1.16347i | −0.407842 | − | 0.913052i | \(-0.633719\pi\) |
0.968139 | − | 0.250415i | \(-0.0805671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 82.2305i | 2.72143i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.71827 | − | 5.91653i | 0.155981 | − | 0.195594i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.9956 | + | 3.73802i | 1.55193 | + | 0.123440i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.39717 | − | 11.2073i | 0.178036 | − | 0.369696i | −0.792785 | − | 0.609502i | \(-0.791369\pi\) |
0.970821 | + | 0.239806i | \(0.0770838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.2260 | − | 34.1404i | 0.897128 | − | 1.12496i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.941482 | − | 1.18058i | −0.0309892 | − | 0.0388593i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1778 | + | 21.5403i | −0.564802 | + | 0.708239i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.68176 | − | 2.25461i | 0.153769 | − | 0.0740513i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.982385 | − | 0.224223i | 0.0322310 | − | 0.00735651i | −0.206375 | − | 0.978473i | \(-0.566167\pi\) |
0.238606 | + | 0.971116i | \(0.423310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8820 | + | 29.4791i | −0.389416 | + | 0.966139i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.26279 | + | 31.8204i | 0.237773 | + | 1.04175i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0226334 | + | 0.0469988i | 0.000740192 | + | 0.00153702i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.7844 | − | 21.3598i | −0.875007 | − | 0.697795i | 0.0792267 | − | 0.996857i | \(-0.474755\pi\) |
−0.954234 | + | 0.299062i | \(0.903326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.81155 | + | 7.82445i | −0.320188 | + | 0.255341i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.1990 | + | 27.2728i | 1.11485 | + | 0.889067i | 0.994611 | − | 0.103677i | \(-0.0330609\pi\) |
0.120244 | + | 0.992744i | \(0.461632\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.335688 | − | 0.161659i | −0.0109315 | − | 0.00526434i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.74153 | − | 1.27672i | 0.284362 | − | 0.0415316i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.6938 | − | 18.0977i | −0.737450 | − | 0.588097i | 0.181070 | − | 0.983470i | \(-0.442044\pi\) |
−0.918521 | + | 0.395373i | \(0.870615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.78166 | 0.0578350 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.5281 | + | 9.40422i | 0.633241 | + | 0.304953i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.9750 | − | 17.3246i | 1.16534 | − | 0.561200i | 0.251736 | − | 0.967796i | \(-0.418998\pi\) |
0.913608 | + | 0.406596i | \(0.133284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.52948 | − | 15.4637i | 0.114211 | − | 0.500392i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.1926 | − | 27.3948i | −0.426457 | − | 0.885548i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.0161 | + | 3.89873i | 1.58281 | + | 0.125897i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.22159 | 0.103922 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.16777 | − | 2.42490i | 0.0376309 | − | 0.0781414i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.60047 | − | 0.821783i | −0.115903 | − | 0.0264541i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.1536 | − | 8.48006i | 1.19478 | − | 0.272700i | 0.421536 | − | 0.906812i | \(-0.361491\pi\) |
0.773242 | + | 0.634111i | \(0.218634\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.106090 | − | 0.0242144i | 0.00340811 | − | 0.000777878i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.23374 | + | 18.5492i | −0.135867 | + | 0.595273i | 0.860451 | + | 0.509534i | \(0.170182\pi\) |
−0.996318 | + | 0.0857387i | \(0.972675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.308831 | + | 0.985187i | −0.00990066 | + | 0.0315837i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.02012 | + | 2.40847i | −0.0967213 | + | 0.0771327i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.7015 | + | 35.9906i | 0.918244 | + | 1.15144i | 0.988089 | + | 0.153883i | \(0.0491780\pi\) |
−0.0698454 | + | 0.997558i | \(0.522251\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.2136 | −0.869750 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.94191 | −0.317421 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.2035 | + | 22.8264i | 0.580600 | + | 0.728049i | 0.982215 | − | 0.187759i | \(-0.0601225\pi\) |
−0.401615 | + | 0.915809i | \(0.631551\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.218664 | + | 0.174379i | −0.00696723 | + | 0.00555618i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.9931 | + | 1.03347i | 0.413575 | + | 0.0328957i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.367932 | + | 1.61202i | −0.0116996 | + | 0.0512591i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.95126 | + | 0.445363i | −0.0619839 | + | 0.0141474i | −0.253400 | − | 0.967361i | \(-0.581549\pi\) |
0.191417 | + | 0.981509i | \(0.438692\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.9217 | + | 6.37294i | −0.886068 | + | 0.202239i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.9151 | − | 2.49130i | −0.346032 | − | 0.0789794i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.5121 | − | 48.8233i | 0.744635 | − | 1.54625i | −0.0903080 | − | 0.995914i | \(-0.528785\pi\) |
0.834943 | − | 0.550336i | \(-0.185501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.9854 | 1.04361 |
(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 | 784.2.bb.b.111.15 | yes | 120 | |
4.3 | odd | 2 | inner | 784.2.bb.b.111.6 | ✓ | 120 | |
49.34 | odd | 14 | inner | 784.2.bb.b.671.6 | yes | 120 | |
196.83 | even | 14 | inner | 784.2.bb.b.671.15 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.2.bb.b.111.6 | ✓ | 120 | 4.3 | odd | 2 | inner | |
784.2.bb.b.111.15 | yes | 120 | 1.1 | even | 1 | trivial | |
784.2.bb.b.671.6 | yes | 120 | 49.34 | odd | 14 | inner | |
784.2.bb.b.671.15 | yes | 120 | 196.83 | even | 14 | inner |