Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,6,Mod(37,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.g (of order \(3\), degree \(2\), 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: | \(20.2083612964\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{79})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 79x^{2} + 6241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(-4.44410 + 7.69740i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.37 |
Dual form | 126.6.g.j.109.1 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | − | 3.46410i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | −18.0528 | + | 31.2683i | −0.322938 | + | 0.559345i | −0.981093 | − | 0.193538i | \(-0.938004\pi\) |
0.658155 | + | 0.752883i | \(0.271337\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −124.435 | − | 36.3731i | −0.959835 | − | 0.280566i | ||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 72.2111 | + | 125.073i | 0.228352 | + | 0.395517i | ||||
\(11\) | 77.7174 | + | 134.610i | 0.193658 | + | 0.335426i | 0.946460 | − | 0.322821i | \(-0.104631\pi\) |
−0.752801 | + | 0.658248i | \(0.771298\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1158.87 | 1.90185 | 0.950925 | − | 0.309422i | \(-0.100136\pi\) | ||||
0.950925 | + | 0.309422i | \(0.100136\pi\) | |||||||
\(14\) | −374.869 | + | 358.308i | −0.511164 | + | 0.488581i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | 619.040 | + | 1072.21i | 0.519513 | + | 0.899823i | 0.999743 | + | 0.0226804i | \(0.00722003\pi\) |
−0.480230 | + | 0.877143i | \(0.659447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 140.140 | − | 242.729i | 0.0890588 | − | 0.154254i | −0.818055 | − | 0.575140i | \(-0.804947\pi\) |
0.907114 | + | 0.420886i | \(0.138281\pi\) | |||||||
\(20\) | 577.689 | 0.322938 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 621.739 | 0.273874 | ||||||||
\(23\) | −1741.20 | + | 3015.84i | −0.686322 | + | 1.18874i | 0.286698 | + | 0.958021i | \(0.407443\pi\) |
−0.973019 | + | 0.230723i | \(0.925891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 910.694 | + | 1577.37i | 0.291422 | + | 0.504758i | ||||
\(26\) | 2317.74 | − | 4014.44i | 0.672405 | − | 1.16464i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 491.478 | + | 2015.20i | 0.118470 | + | 0.485762i | ||||
\(29\) | 5656.78 | 1.24903 | 0.624517 | − | 0.781011i | \(-0.285296\pi\) | ||||
0.624517 | + | 0.781011i | \(0.285296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1157.35 | + | 2004.59i | 0.216302 | + | 0.374646i | 0.953675 | − | 0.300840i | \(-0.0972671\pi\) |
−0.737372 | + | 0.675486i | \(0.763934\pi\) | |||||||
\(32\) | 512.000 | + | 886.810i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4952.32 | 0.734703 | ||||||||
\(35\) | 3383.72 | − | 3234.23i | 0.466900 | − | 0.446273i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1166.59 | − | 2020.59i | 0.140092 | − | 0.242646i | −0.787439 | − | 0.616392i | \(-0.788594\pi\) |
0.927531 | + | 0.373746i | \(0.121927\pi\) | |||||||
\(38\) | −560.558 | − | 970.916i | −0.0629741 | − | 0.109074i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1155.38 | − | 2001.17i | 0.114176 | − | 0.197758i | ||||
\(41\) | −3812.61 | −0.354211 | −0.177106 | − | 0.984192i | \(-0.556673\pi\) | ||||
−0.177106 | + | 0.984192i | \(0.556673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3925.73 | 0.323780 | 0.161890 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161890 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(44\) | 1243.48 | − | 2153.77i | 0.0968292 | − | 0.167713i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6964.78 | + | 12063.4i | 0.485303 | + | 0.840569i | ||||
\(47\) | −5558.23 | + | 9627.13i | −0.367022 | + | 0.635700i | −0.989098 | − | 0.147256i | \(-0.952956\pi\) |
0.622077 | + | 0.782956i | \(0.286289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14161.0 | + | 9052.14i | 0.842566 | + | 0.538594i | ||||
\(50\) | 7285.56 | 0.412133 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9270.96 | − | 16057.8i | −0.475462 | − | 0.823525i | ||||
\(53\) | −5593.10 | − | 9687.54i | −0.273504 | − | 0.473722i | 0.696253 | − | 0.717797i | \(-0.254849\pi\) |
−0.969757 | + | 0.244074i | \(0.921516\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5612.06 | −0.250159 | ||||||||
\(56\) | 7963.82 | + | 2327.88i | 0.339353 | + | 0.0991950i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11313.6 | − | 19595.7i | 0.441600 | − | 0.764874i | ||||
\(59\) | −3005.18 | − | 5205.12i | −0.112393 | − | 0.194671i | 0.804342 | − | 0.594167i | \(-0.202518\pi\) |
−0.916735 | + | 0.399497i | \(0.869185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7419.36 | − | 12850.7i | 0.255295 | − | 0.442183i | −0.709681 | − | 0.704523i | \(-0.751161\pi\) |
0.964975 | + | 0.262340i | \(0.0844942\pi\) | |||||||
\(62\) | 9258.81 | 0.305897 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −20920.8 | + | 36235.9i | −0.614179 | + | 1.06379i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21491.9 | + | 37225.1i | 0.584909 | + | 1.01309i | 0.994887 | + | 0.100997i | \(0.0322032\pi\) |
−0.409977 | + | 0.912096i | \(0.634463\pi\) | |||||||
\(68\) | 9904.64 | − | 17155.3i | 0.259757 | − | 0.449912i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4436.27 | − | 18190.0i | −0.108211 | − | 0.443698i | ||||
\(71\) | 19962.4 | 0.469967 | 0.234984 | − | 0.971999i | \(-0.424496\pi\) | ||||
0.234984 | + | 0.971999i | \(0.424496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −22775.3 | − | 39448.0i | −0.500215 | − | 0.866398i | −1.00000 | 0.000248463i | \(-0.999921\pi\) | |
0.499785 | − | 0.866150i | \(-0.333412\pi\) | |||||||
\(74\) | −4666.35 | − | 8082.36i | −0.0990599 | − | 0.171577i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4484.47 | −0.0890588 | ||||||||
\(77\) | −4774.54 | − | 19577.0i | −0.0917709 | − | 0.376288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −54496.0 | + | 94389.9i | −0.982419 | + | 1.70160i | −0.329534 | + | 0.944144i | \(0.606892\pi\) |
−0.652885 | + | 0.757457i | \(0.726442\pi\) | |||||||
\(80\) | −4621.51 | − | 8004.69i | −0.0807345 | − | 0.139836i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7625.22 | + | 13207.3i | −0.125233 | + | 0.216909i | ||||
\(83\) | −55829.0 | −0.889538 | −0.444769 | − | 0.895645i | \(-0.646714\pi\) | ||||
−0.444769 | + | 0.895645i | \(0.646714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44701.6 | −0.671082 | ||||||||
\(86\) | 7851.47 | − | 13599.1i | 0.114473 | − | 0.198274i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4973.91 | − | 8615.07i | −0.0684686 | − | 0.118591i | ||||
\(89\) | −47772.9 | + | 82745.1i | −0.639303 | + | 1.10731i | 0.346283 | + | 0.938130i | \(0.387444\pi\) |
−0.985586 | + | 0.169175i | \(0.945890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −144204. | − | 42151.6i | −1.82546 | − | 0.533594i | ||||
\(92\) | 55718.2 | 0.686322 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22232.9 | + | 38508.5i | 0.259523 | + | 0.449508i | ||||
\(95\) | 5059.82 | + | 8763.86i | 0.0575209 | + | 0.0996292i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15004.9 | 0.161922 | 0.0809609 | − | 0.996717i | \(-0.474201\pi\) | ||||
0.0809609 | + | 0.996717i | \(0.474201\pi\) | |||||||
\(98\) | 59679.5 | − | 30950.9i | 0.627712 | − | 0.325542i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14571.1 | − | 25237.9i | 0.145711 | − | 0.252379i | ||||
\(101\) | 13438.1 | + | 23275.4i | 0.131079 | + | 0.227036i | 0.924093 | − | 0.382168i | \(-0.124822\pi\) |
−0.793014 | + | 0.609204i | \(0.791489\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25957.6 | − | 44959.9i | 0.241086 | − | 0.417573i | −0.719938 | − | 0.694038i | \(-0.755830\pi\) |
0.961024 | + | 0.276466i | \(0.0891632\pi\) | |||||||
\(104\) | −74167.6 | −0.672405 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −44744.8 | −0.386793 | ||||||||
\(107\) | −12487.4 | + | 21628.8i | −0.105442 | + | 0.182630i | −0.913919 | − | 0.405898i | \(-0.866959\pi\) |
0.808477 | + | 0.588528i | \(0.200292\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1818.07 | + | 3148.99i | 0.0146570 | + | 0.0253867i | 0.873261 | − | 0.487253i | \(-0.162001\pi\) |
−0.858604 | + | 0.512640i | \(0.828668\pi\) | |||||||
\(110\) | −11224.1 | + | 19440.7i | −0.0884444 | + | 0.153190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 23991.6 | − | 22931.7i | 0.180724 | − | 0.172740i | ||||
\(113\) | −62175.0 | −0.458057 | −0.229028 | − | 0.973420i | \(-0.573555\pi\) | ||||
−0.229028 | + | 0.973420i | \(0.573555\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −62866.8 | − | 108889.i | −0.443279 | − | 0.767781i | ||||
\(116\) | −45254.2 | − | 78382.7i | −0.312259 | − | 0.540848i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24041.4 | −0.158948 | ||||||||
\(119\) | −38030.6 | − | 155936.i | −0.246187 | − | 1.00944i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 68445.5 | − | 118551.i | 0.424993 | − | 0.736109i | ||||
\(122\) | −29677.4 | − | 51402.8i | −0.180521 | − | 0.312671i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18517.6 | − | 32073.4i | 0.108151 | − | 0.187323i | ||||
\(125\) | −178592. | −1.02232 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 63550.3 | 0.349630 | 0.174815 | − | 0.984601i | \(-0.444067\pi\) | ||||
0.174815 | + | 0.984601i | \(0.444067\pi\) | |||||||
\(128\) | 8192.00 | − | 14189.0i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 83683.2 | + | 144944.i | 0.434290 | + | 0.752213i | ||||
\(131\) | 68148.5 | − | 118037.i | 0.346959 | − | 0.600950i | −0.638749 | − | 0.769415i | \(-0.720548\pi\) |
0.985708 | + | 0.168465i | \(0.0538810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26267.0 | + | 25106.6i | −0.128760 | + | 0.123072i | ||||
\(134\) | 171935. | 0.827187 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −39618.6 | − | 68621.4i | −0.183676 | − | 0.318136i | ||||
\(137\) | 167652. | + | 290381.i | 0.763144 | + | 1.32180i | 0.941222 | + | 0.337788i | \(0.109679\pi\) |
−0.178078 | + | 0.984016i | \(0.556988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 58195.2 | 0.255476 | 0.127738 | − | 0.991808i | \(-0.459228\pi\) | ||||
0.127738 | + | 0.991808i | \(0.459228\pi\) | |||||||
\(140\) | −71884.6 | − | 21012.3i | −0.309967 | − | 0.0906054i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 39924.9 | − | 69151.9i | 0.166158 | − | 0.287795i | ||||
\(143\) | 90064.3 | + | 155996.i | 0.368309 | + | 0.637930i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −102121. | + | 176878.i | −0.403360 | + | 0.698641i | ||||
\(146\) | −182202. | −0.707411 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −37330.8 | −0.140092 | ||||||||
\(149\) | 141529. | − | 245135.i | 0.522251 | − | 0.904566i | −0.477414 | − | 0.878679i | \(-0.658426\pi\) |
0.999665 | − | 0.0258870i | \(-0.00824101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 120779. | + | 209195.i | 0.431071 | + | 0.746637i | 0.996966 | − | 0.0778407i | \(-0.0248026\pi\) |
−0.565895 | + | 0.824477i | \(0.691469\pi\) | |||||||
\(152\) | −8968.93 | + | 15534.6i | −0.0314870 | + | 0.0545372i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −77365.9 | − | 22614.6i | −0.262874 | − | 0.0768398i | ||||
\(155\) | −83573.6 | −0.279409 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 107014. | + | 185354.i | 0.346492 | + | 0.600142i | 0.985624 | − | 0.168956i | \(-0.0540394\pi\) |
−0.639132 | + | 0.769097i | \(0.720706\pi\) | |||||||
\(158\) | 217984. | + | 377559.i | 0.694675 | + | 1.20321i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −36972.1 | −0.114176 | ||||||||
\(161\) | 326360. | − | 311942.i | 0.992277 | − | 0.948440i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −32233.0 | + | 55829.2i | −0.0950237 | + | 0.164586i | −0.909619 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(164\) | 30500.9 | + | 52829.1i | 0.0885529 | + | 0.153378i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −111658. | + | 193397.i | −0.314499 | + | 0.544729i | ||||
\(167\) | 442694. | 1.22832 | 0.614162 | − | 0.789180i | \(-0.289494\pi\) | ||||
0.614162 | + | 0.789180i | \(0.289494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 971685. | 2.61703 | ||||||||
\(170\) | −89403.2 | + | 154851.i | −0.237263 | + | 0.410952i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −31405.9 | − | 54396.6i | −0.0809449 | − | 0.140201i | ||||
\(173\) | −39299.5 | + | 68068.8i | −0.0998325 | + | 0.172915i | −0.911615 | − | 0.411045i | \(-0.865164\pi\) |
0.811783 | + | 0.583960i | \(0.198497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −55948.3 | − | 229404.i | −0.138099 | − | 0.566247i | ||||
\(176\) | −39791.3 | −0.0968292 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 191092. | + | 330980.i | 0.452055 | + | 0.782983i | ||||
\(179\) | −255214. | − | 442043.i | −0.595348 | − | 1.03117i | −0.993498 | − | 0.113853i | \(-0.963681\pi\) |
0.398149 | − | 0.917321i | \(-0.369653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22051.8 | −0.0500319 | −0.0250160 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250160 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(182\) | −434425. | + | 415233.i | −0.972156 | + | 0.929208i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 111436. | − | 193014.i | 0.242651 | − | 0.420285i | ||||
\(185\) | 42120.3 | + | 72954.5i | 0.0904820 | + | 0.156719i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −96220.4 | + | 166659.i | −0.201216 | + | 0.348517i | ||||
\(188\) | 177863. | 0.367022 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 40478.5 | 0.0813469 | ||||||||
\(191\) | −279076. | + | 483374.i | −0.553528 | + | 0.958738i | 0.444489 | + | 0.895784i | \(0.353385\pi\) |
−0.998016 | + | 0.0629535i | \(0.979948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24658.1 | + | 42709.1i | 0.0476504 | + | 0.0825330i | 0.888867 | − | 0.458166i | \(-0.151493\pi\) |
−0.841216 | + | 0.540699i | \(0.818160\pi\) | |||||||
\(194\) | 30009.9 | − | 51978.7i | 0.0572480 | − | 0.0991564i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12142.2 | − | 268638.i | 0.0225765 | − | 0.499490i | ||||
\(197\) | 941509. | 1.72846 | 0.864229 | − | 0.503099i | \(-0.167807\pi\) | ||||
0.864229 | + | 0.503099i | \(0.167807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −320006. | − | 554267.i | −0.572830 | − | 0.992170i | −0.996274 | − | 0.0862477i | \(-0.972512\pi\) |
0.423444 | − | 0.905922i | \(-0.360821\pi\) | |||||||
\(200\) | −58284.4 | − | 100952.i | −0.103033 | − | 0.178459i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 107505. | 0.185374 | ||||||||
\(203\) | −703900. | − | 205754.i | −1.19887 | − | 0.350436i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 68828.2 | − | 119214.i | 0.114388 | − | 0.198126i | ||||
\(206\) | −103830. | − | 179840.i | −0.170473 | − | 0.295268i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −148335. | + | 256924.i | −0.237731 | + | 0.411762i | ||||
\(209\) | 43565.1 | 0.0689879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 921869. | 1.42549 | 0.712743 | − | 0.701425i | \(-0.247452\pi\) | ||||
0.712743 | + | 0.701425i | \(0.247452\pi\) | |||||||
\(212\) | −89489.7 | + | 155001.i | −0.136752 | + | 0.236861i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 49949.5 | + | 86515.1i | 0.0745585 | + | 0.129139i | ||||
\(215\) | −70870.4 | + | 122751.i | −0.104561 | + | 0.181105i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −71101.5 | − | 291537.i | −0.102501 | − | 0.420285i | ||||
\(218\) | 14544.6 | 0.0207281 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 44896.5 | + | 77762.9i | 0.0625396 | + | 0.108322i | ||||
\(221\) | 717387. | + | 1.24255e6i | 0.988036 | + | 1.71133i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −837700. | −1.12805 | −0.564023 | − | 0.825759i | \(-0.690747\pi\) | ||||
−0.564023 | + | 0.825759i | \(0.690747\pi\) | |||||||
\(224\) | −31454.6 | − | 128973.i | −0.0418855 | − | 0.171743i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −124350. | + | 215380.i | −0.161948 | + | 0.280501i | ||||
\(227\) | −665344. | − | 1.15241e6i | −0.857002 | − | 1.48437i | −0.874775 | − | 0.484529i | \(-0.838991\pi\) |
0.0177731 | − | 0.999842i | \(-0.494342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −505317. | + | 875234.i | −0.636759 | + | 1.10290i | 0.349381 | + | 0.936981i | \(0.386392\pi\) |
−0.986140 | + | 0.165918i | \(0.946941\pi\) | |||||||
\(230\) | −502935. | −0.626891 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −362034. | −0.441600 | ||||||||
\(233\) | 743050. | − | 1.28700e6i | 0.896661 | − | 1.55306i | 0.0649249 | − | 0.997890i | \(-0.479319\pi\) |
0.831736 | − | 0.555172i | \(-0.187347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −200683. | − | 347593.i | −0.237050 | − | 0.410583i | ||||
\(236\) | −48082.8 | + | 83281.9i | −0.0561966 | + | 0.0973353i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −616241. | − | 180131.i | −0.705193 | − | 0.206132i | ||||
\(239\) | −875637. | −0.991584 | −0.495792 | − | 0.868441i | \(-0.665122\pi\) | ||||
−0.495792 | + | 0.868441i | \(0.665122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −726472. | − | 1.25829e6i | −0.805706 | − | 1.39552i | −0.915814 | − | 0.401604i | \(-0.868453\pi\) |
0.110108 | − | 0.993920i | \(-0.464880\pi\) | |||||||
\(242\) | −273782. | − | 474204.i | −0.300515 | − | 0.520508i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −237419. | −0.255295 | ||||||||
\(245\) | −538691. | + | 279374.i | −0.573356 | + | 0.297352i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 162403. | − | 281291.i | 0.169376 | − | 0.293369i | ||||
\(248\) | −74070.4 | − | 128294.i | −0.0764743 | − | 0.132457i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −357184. | + | 618661.i | −0.361445 | + | 0.626041i | ||||
\(251\) | 198384. | 0.198757 | 0.0993786 | − | 0.995050i | \(-0.468315\pi\) | ||||
0.0993786 | + | 0.995050i | \(0.468315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −541284. | −0.531648 | ||||||||
\(254\) | 127101. | − | 220145.i | 0.123613 | − | 0.214104i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 239786. | − | 415321.i | 0.226460 | − | 0.392240i | −0.730297 | − | 0.683130i | \(-0.760618\pi\) |
0.956756 | + | 0.290890i | \(0.0939515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −218659. | + | 208999.i | −0.202543 | + | 0.193595i | ||||
\(260\) | 669466. | 0.614179 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −272594. | − | 472147.i | −0.245337 | − | 0.424936i | ||||
\(263\) | 227471. | + | 393992.i | 0.202786 | + | 0.351235i | 0.949425 | − | 0.313994i | \(-0.101667\pi\) |
−0.746639 | + | 0.665229i | \(0.768334\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 403884. | 0.353299 | ||||||||
\(266\) | 34437.7 | + | 141205.i | 0.0298422 | + | 0.122362i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 343871. | − | 595602.i | 0.292455 | − | 0.506546i | ||||
\(269\) | −430068. | − | 744900.i | −0.362374 | − | 0.627650i | 0.625977 | − | 0.779841i | \(-0.284700\pi\) |
−0.988351 | + | 0.152192i | \(0.951367\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −652790. | + | 1.13067e6i | −0.539946 | + | 0.935214i | 0.458960 | + | 0.888457i | \(0.348222\pi\) |
−0.998906 | + | 0.0467569i | \(0.985111\pi\) | |||||||
\(272\) | −316949. | −0.259757 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.34121e6 | 1.07925 | ||||||||
\(275\) | −141554. | + | 245178.i | −0.112873 | + | 0.195501i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 271554. | + | 470346.i | 0.212646 | + | 0.368314i | 0.952542 | − | 0.304408i | \(-0.0984586\pi\) |
−0.739896 | + | 0.672721i | \(0.765125\pi\) | |||||||
\(278\) | 116390. | − | 201594.i | 0.0903245 | − | 0.156447i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −216558. | + | 206991.i | −0.165074 | + | 0.157781i | ||||
\(281\) | −998089. | −0.754055 | −0.377028 | − | 0.926202i | \(-0.623054\pi\) | ||||
−0.377028 | + | 0.926202i | \(0.623054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −888660. | − | 1.53920e6i | −0.659583 | − | 1.14243i | −0.980724 | − | 0.195400i | \(-0.937399\pi\) |
0.321140 | − | 0.947032i | \(-0.395934\pi\) | |||||||
\(284\) | −159699. | − | 276608.i | −0.117492 | − | 0.203502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 720514. | 0.520868 | ||||||||
\(287\) | 474421. | + | 138676.i | 0.339984 | + | 0.0993796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −56493.2 | + | 97849.1i | −0.0397880 | + | 0.0689148i | ||||
\(290\) | 408482. | + | 707512.i | 0.285219 | + | 0.494014i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −364405. | + | 631167.i | −0.250108 | + | 0.433199i | ||||
\(293\) | 1.63987e6 | 1.11594 | 0.557969 | − | 0.829862i | \(-0.311581\pi\) | ||||
0.557969 | + | 0.829862i | \(0.311581\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 217007. | 0.145184 | ||||||||
\(296\) | −74661.6 | + | 129318.i | −0.0495300 | + | 0.0857884i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −566116. | − | 980541.i | −0.369287 | − | 0.639625i | ||||
\(299\) | −2.01782e6 | + | 3.49496e6i | −1.30528 | + | 2.26081i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −488498. | − | 142791.i | −0.310775 | − | 0.0908415i | ||||
\(302\) | 966231. | 0.609626 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 35875.7 | + | 62138.6i | 0.0222647 | + | 0.0385636i | ||||
\(305\) | 267880. | + | 463982.i | 0.164889 | + | 0.285595i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.38130e6 | 1.44201 | 0.721006 | − | 0.692928i | \(-0.243680\pi\) | ||||
0.721006 | + | 0.692928i | \(0.243680\pi\) | |||||||
\(308\) | −233071. | + | 222774.i | −0.139995 | + | 0.133810i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −167147. | + | 289507.i | −0.0987859 | + | 0.171102i | ||||
\(311\) | −622564. | − | 1.07831e6i | −0.364992 | − | 0.632184i | 0.623783 | − | 0.781597i | \(-0.285595\pi\) |
−0.988775 | + | 0.149413i | \(0.952262\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −831495. | + | 1.44019e6i | −0.479732 | + | 0.830921i | −0.999730 | − | 0.0232470i | \(-0.992600\pi\) |
0.519997 | + | 0.854168i | \(0.325933\pi\) | |||||||
\(314\) | 856115. | 0.490014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.74387e6 | 0.982419 | ||||||||
\(317\) | −1.31243e6 | + | 2.27319e6i | −0.733547 | + | 1.27054i | 0.221812 | + | 0.975090i | \(0.428803\pi\) |
−0.955358 | + | 0.295450i | \(0.904530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 439630. | + | 761462.i | 0.241886 | + | 0.418959i | ||||
\(320\) | −73944.2 | + | 128075.i | −0.0403672 | + | 0.0699181i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −427879. | − | 1.75443e6i | −0.229976 | − | 0.942967i | ||||
\(323\) | 347008. | 0.185069 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.05538e6 | + | 1.82796e6i | 0.554241 | + | 0.959974i | ||||
\(326\) | 128932. | + | 223317.i | 0.0671919 | + | 0.116380i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 244007. | 0.125233 | ||||||||
\(329\) | 1.04180e6 | − | 995780.i | 0.530636 | − | 0.507193i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −869428. | + | 1.50589e6i | −0.436178 | + | 0.755482i | −0.997391 | − | 0.0721894i | \(-0.977001\pi\) |
0.561213 | + | 0.827671i | \(0.310335\pi\) | |||||||
\(332\) | 446632. | + | 773589.i | 0.222385 | + | 0.385181i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 885389. | − | 1.53354e6i | 0.434278 | − | 0.752191i | ||||
\(335\) | −1.55196e6 | −0.755558 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 853564. | 0.409413 | 0.204706 | − | 0.978823i | \(-0.434376\pi\) | ||||
0.204706 | + | 0.978823i | \(0.434376\pi\) | |||||||
\(338\) | 1.94337e6 | − | 3.36602e6i | 0.925260 | − | 1.60260i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 357613. | + | 619403.i | 0.167771 | + | 0.290587i | ||||
\(341\) | −179892. | + | 311583.i | −0.0837774 | + | 0.145107i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.43287e6 | − | 1.64148e6i | −0.657613 | − | 0.753356i | ||||
\(344\) | −251247. | −0.114473 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 157198. | + | 272275.i | 0.0705922 | + | 0.122269i | ||||
\(347\) | −1.49250e6 | − | 2.58508e6i | −0.665411 | − | 1.15253i | −0.979174 | − | 0.203024i | \(-0.934923\pi\) |
0.313763 | − | 0.949501i | \(-0.398410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.87467e6 | 1.26335 | 0.631676 | − | 0.775233i | \(-0.282367\pi\) | ||||
0.631676 | + | 0.775233i | \(0.282367\pi\) | |||||||
\(350\) | −906576. | − | 264998.i | −0.395580 | − | 0.115631i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −79582.6 | + | 137841.i | −0.0342343 | + | 0.0592955i | ||||
\(353\) | 735546. | + | 1.27400e6i | 0.314176 | + | 0.544169i | 0.979262 | − | 0.202598i | \(-0.0649384\pi\) |
−0.665086 | + | 0.746767i | \(0.731605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −360377. | + | 624192.i | −0.151770 | + | 0.262874i | ||||
\(356\) | 1.52873e6 | 0.639303 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.04171e6 | −0.841950 | ||||||||
\(359\) | 1.53900e6 | − | 2.66562e6i | 0.630233 | − | 1.09160i | −0.357270 | − | 0.934001i | \(-0.616293\pi\) |
0.987504 | − | 0.157595i | \(-0.0503741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.19877e6 | + | 2.07633e6i | 0.484137 | + | 0.838550i | ||||
\(362\) | −44103.6 | + | 76389.6i | −0.0176890 | + | 0.0306382i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 569559. | + | 2.33536e6i | 0.225312 | + | 0.923846i | ||||
\(365\) | 1.64463e6 | 0.646154 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −808349. | − | 1.40010e6i | −0.313281 | − | 0.542618i | 0.665790 | − | 0.746139i | \(-0.268095\pi\) |
−0.979071 | + | 0.203521i | \(0.934761\pi\) | |||||||
\(368\) | −445746. | − | 772055.i | −0.171580 | − | 0.297186i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 336962. | 0.127961 | ||||||||
\(371\) | 343611. | + | 1.40890e6i | 0.129608 | + | 0.531431i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.38059e6 | − | 4.12331e6i | 0.885958 | − | 1.53452i | 0.0413462 | − | 0.999145i | \(-0.486835\pi\) |
0.844612 | − | 0.535379i | \(-0.179831\pi\) | |||||||
\(374\) | 384881. | + | 666634.i | 0.142281 | + | 0.246439i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 355727. | − | 616136.i | 0.129762 | − | 0.224754i | ||||
\(377\) | 6.55547e6 | 2.37548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00193e6 | 0.358294 | 0.179147 | − | 0.983822i | \(-0.442666\pi\) | ||||
0.179147 | + | 0.983822i | \(0.442666\pi\) | |||||||
\(380\) | 80957.1 | − | 140222.i | 0.0287605 | − | 0.0498146i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.11630e6 | + | 1.93350e6i | 0.391403 | + | 0.677930i | ||||
\(383\) | −1.41076e6 | + | 2.44351e6i | −0.491424 | + | 0.851172i | −0.999951 | − | 0.00987425i | \(-0.996857\pi\) |
0.508527 | + | 0.861046i | \(0.330190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 698335. | + | 204128.i | 0.240111 | + | 0.0701859i | ||||
\(386\) | 197265. | 0.0673879 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −120040. | − | 207915.i | −0.0404804 | − | 0.0701142i | ||||
\(389\) | −621198. | − | 1.07595e6i | −0.208140 | − | 0.360510i | 0.742988 | − | 0.669304i | \(-0.233408\pi\) |
−0.951129 | + | 0.308795i | \(0.900074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.31148e6 | −1.42621 | ||||||||
\(392\) | −906304. | − | 579337.i | −0.297892 | − | 0.190422i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.88302e6 | − | 3.26148e6i | 0.611102 | − | 1.05846i | ||||
\(395\) | −1.96761e6 | − | 3.40800e6i | −0.634521 | − | 1.09902i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.37281e6 | + | 2.37778e6i | −0.437154 | + | 0.757173i | −0.997469 | − | 0.0711068i | \(-0.977347\pi\) |
0.560315 | + | 0.828280i | \(0.310680\pi\) | |||||||
\(398\) | −2.56005e6 | −0.810103 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −466276. | −0.145711 | ||||||||
\(401\) | −1.85668e6 | + | 3.21586e6i | −0.576601 | + | 0.998702i | 0.419265 | + | 0.907864i | \(0.362288\pi\) |
−0.995866 | + | 0.0908378i | \(0.971046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.34122e6 | + | 2.32306e6i | 0.411374 | + | 0.712521i | ||||
\(404\) | 215009. | − | 372407.i | 0.0655396 | − | 0.113518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.12055e6 | + | 2.02687e6i | −0.638461 | + | 0.610255i | ||||
\(407\) | 362656. | 0.108520 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.87970e6 | − | 3.25574e6i | −0.555623 | − | 0.962367i | −0.997855 | − | 0.0654664i | \(-0.979146\pi\) |
0.442232 | − | 0.896901i | \(-0.354187\pi\) | |||||||
\(410\) | −275313. | − | 476856.i | −0.0808847 | − | 0.140096i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −830643. | −0.241086 | ||||||||
\(413\) | 184622. | + | 757005.i | 0.0532609 | + | 0.218385i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.00787e6 | − | 1.74568e6i | 0.287266 | − | 0.497559i | ||||
\(416\) | 593341. | + | 1.02770e6i | 0.168101 | + | 0.291160i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 87130.2 | − | 150914.i | 0.0243909 | − | 0.0422463i | ||||
\(419\) | −4.60027e6 | −1.28011 | −0.640056 | − | 0.768328i | \(-0.721089\pi\) | ||||
−0.640056 | + | 0.768328i | \(0.721089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −404864. | −0.111328 | −0.0556639 | − | 0.998450i | \(-0.517728\pi\) | ||||
−0.0556639 | + | 0.998450i | \(0.517728\pi\) | |||||||
\(422\) | 1.84374e6 | − | 3.19345e6i | 0.503986 | − | 0.872929i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 357959. | + | 620003.i | 0.0966982 | + | 0.167486i | ||||
\(425\) | −1.12751e6 | + | 1.95291e6i | −0.302795 | + | 0.524457i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.39065e6 | + | 1.32921e6i | −0.369102 | + | 0.352796i | ||||
\(428\) | 399596. | 0.105442 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 283482. | + | 491004.i | 0.0739356 | + | 0.128060i | ||||
\(431\) | 47379.2 | + | 82063.2i | 0.0122856 | + | 0.0212792i | 0.872103 | − | 0.489323i | \(-0.162756\pi\) |
−0.859817 | + | 0.510602i | \(0.829423\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.31727e6 | 1.10660 | 0.553298 | − | 0.832983i | \(-0.313369\pi\) | ||||
0.553298 | + | 0.832983i | \(0.313369\pi\) | |||||||
\(434\) | −1.15212e6 | − | 336771.i | −0.293611 | − | 0.0858244i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29089.2 | − | 50383.9i | 0.00732850 | − | 0.0126933i | ||||
\(437\) | 488021. | + | 845277.i | 0.122246 | + | 0.211736i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.11184e6 | − | 1.92576e6i | 0.275346 | − | 0.476914i | −0.694876 | − | 0.719130i | \(-0.744541\pi\) |
0.970222 | + | 0.242216i | \(0.0778741\pi\) | |||||||
\(440\) | 359172. | 0.0884444 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.73909e6 | 1.39729 | ||||||||
\(443\) | −2.34213e6 | + | 4.05668e6i | −0.567024 | + | 0.982114i | 0.429835 | + | 0.902908i | \(0.358572\pi\) |
−0.996858 | + | 0.0792062i | \(0.974761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.72487e6 | − | 2.98756e6i | −0.412910 | − | 0.715182i | ||||
\(446\) | −1.67540e6 | + | 2.90188e6i | −0.398824 | + | 0.690784i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −509685. | − | 148984.i | −0.119979 | − | 0.0350707i | ||||
\(449\) | −897932. | −0.210198 | −0.105099 | − | 0.994462i | \(-0.533516\pi\) | ||||
−0.105099 | + | 0.994462i | \(0.533516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −296306. | − | 513217.i | −0.0685960 | − | 0.118812i | ||||
\(452\) | 497400. | + | 861522.i | 0.114514 | + | 0.198344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.32276e6 | −1.21198 | ||||||||
\(455\) | 3.92129e6 | − | 3.74805e6i | 0.887974 | − | 0.848745i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.99091e6 | + | 5.18040e6i | −0.669903 | + | 1.16031i | 0.308027 | + | 0.951377i | \(0.400331\pi\) |
−0.977931 | + | 0.208929i | \(0.933002\pi\) | |||||||
\(458\) | 2.02127e6 | + | 3.50094e6i | 0.450256 | + | 0.779867i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00587e6 | + | 1.74222e6i | −0.221639 | + | 0.383891i | ||||
\(461\) | −1.62507e6 | −0.356138 | −0.178069 | − | 0.984018i | \(-0.556985\pi\) | ||||
−0.178069 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.46295e6 | −1.83472 | −0.917359 | − | 0.398060i | \(-0.869683\pi\) | ||||
−0.917359 | + | 0.398060i | \(0.869683\pi\) | |||||||
\(464\) | −724068. | + | 1.25412e6i | −0.156129 | + | 0.270424i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.97220e6 | − | 5.14800e6i | −0.634035 | − | 1.09818i | ||||
\(467\) | 3.83297e6 | − | 6.63890e6i | 0.813286 | − | 1.40865i | −0.0972658 | − | 0.995258i | \(-0.531010\pi\) |
0.910552 | − | 0.413395i | \(-0.135657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.32035e6 | − | 5.41383e6i | −0.277177 | − | 1.13651i | ||||
\(470\) | −1.60546e6 | −0.335240 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 192331. | + | 333127.i | 0.0397370 | + | 0.0688265i | ||||
\(473\) | 305098. | + | 528445.i | 0.0627027 | + | 0.108604i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 510497. | 0.103815 | ||||||||
\(476\) | −1.85647e6 | + | 1.77446e6i | −0.375553 | + | 0.358962i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.75127e6 | + | 3.03330e6i | −0.350578 | + | 0.607219i | ||||
\(479\) | −1.20146e6 | − | 2.08099e6i | −0.239261 | − | 0.414412i | 0.721242 | − | 0.692683i | \(-0.243572\pi\) |
−0.960502 | + | 0.278272i | \(0.910238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.35192e6 | − | 2.34160e6i | 0.266434 | − | 0.461477i | ||||
\(482\) | −5.81178e6 | −1.13944 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.19026e6 | −0.424993 | ||||||||
\(485\) | −270881. | + | 469180.i | −0.0522907 | + | 0.0905701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 85150.8 | + | 147486.i | 0.0162692 | + | 0.0281791i | 0.874045 | − | 0.485844i | \(-0.161488\pi\) |
−0.857776 | + | 0.514023i | \(0.828154\pi\) | |||||||
\(488\) | −474839. | + | 822445.i | −0.0902603 | + | 0.156335i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −109600. | + | 2.42483e6i | −0.0206215 | + | 0.456237i | ||||
\(491\) | 5.77628e6 | 1.08130 | 0.540648 | − | 0.841249i | \(-0.318179\pi\) | ||||
0.540648 | + | 0.841249i | \(0.318179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50177e6 | + | 6.06525e6i | 0.648890 | + | 1.12391i | ||||
\(494\) | −649614. | − | 1.12516e6i | −0.119767 | − | 0.207443i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −592564. | −0.108151 | ||||||||
\(497\) | −2.48402e6 | − | 726095.i | −0.451091 | − | 0.131857i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −271801. | + | 470773.i | −0.0488652 | + | 0.0846369i | −0.889423 | − | 0.457084i | \(-0.848894\pi\) |
0.840558 | + | 0.541721i | \(0.182227\pi\) | |||||||
\(500\) | 1.42874e6 | + | 2.47464e6i | 0.255580 | + | 0.442678i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 396769. | − | 687223.i | 0.0702713 | − | 0.121713i | ||||
\(503\) | 5.40086e6 | 0.951794 | 0.475897 | − | 0.879501i | \(-0.342124\pi\) | ||||
0.475897 | + | 0.879501i | \(0.342124\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −970378. | −0.169322 | ||||||||
\(506\) | −1.08257e6 | + | 1.87506e6i | −0.187966 | + | 0.325567i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −508402. | − | 880579.i | −0.0874074 | − | 0.151394i | ||||
\(509\) | 4.17209e6 | − | 7.22628e6i | 0.713772 | − | 1.23629i | −0.249659 | − | 0.968334i | \(-0.580319\pi\) |
0.963431 | − | 0.267955i | \(-0.0863480\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39919e6 | + | 5.73710e6i | 0.237042 | + | 0.971942i | ||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −959144. | − | 1.66129e6i | −0.160131 | − | 0.277355i | ||||
\(515\) | 937213. | + | 1.62330e6i | 0.155711 | + | 0.269700i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.72788e6 | −0.284307 | ||||||||
\(518\) | 286676. | + | 1.17546e6i | 0.0469426 | + | 0.192478i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.33893e6 | − | 2.31910e6i | 0.217145 | − | 0.376106i | ||||
\(521\) | −5.73919e6 | − | 9.94057e6i | −0.926310 | − | 1.60442i | −0.789441 | − | 0.613827i | \(-0.789629\pi\) |
−0.136870 | − | 0.990589i | \(-0.543704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.19367e6 | − | 3.79955e6i | 0.350685 | − | 0.607404i | −0.635685 | − | 0.771949i | \(-0.719282\pi\) |
0.986370 | + | 0.164545i | \(0.0526155\pi\) | |||||||
\(524\) | −2.18075e6 | −0.346959 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.81977e6 | 0.286782 | ||||||||
\(527\) | −1.43289e6 | + | 2.48184e6i | −0.224744 | + | 0.389267i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.84535e6 | − | 4.92829e6i | −0.442075 | − | 0.765697i | ||||
\(530\) | 807769. | − | 1.39910e6i | 0.124910 | − | 0.216350i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 558023. | + | 163114.i | 0.0854817 | + | 0.0249869i | ||||
\(533\) | −4.41832e6 | −0.673657 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −450864. | − | 780919.i | −0.0681022 | − | 0.117956i | ||||
\(536\) | −1.37548e6 | − | 2.38241e6i | −0.206797 | − | 0.358182i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.44055e6 | −0.512474 | ||||||||
\(539\) | −117957. | + | 2.60973e6i | −0.0174885 | + | 0.386922i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.61153e6 | + | 6.25535e6i | −0.530515 | + | 0.918879i | 0.468851 | + | 0.883277i | \(0.344668\pi\) |
−0.999366 | + | 0.0356020i | \(0.988665\pi\) | |||||||
\(542\) | 2.61116e6 | + | 4.52266e6i | 0.381799 | + | 0.661296i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −633897. | + | 1.09794e6i | −0.0918378 | + | 0.159068i | ||||
\(545\) | −131285. | −0.0189332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.54529e6 | 0.506622 | 0.253311 | − | 0.967385i | \(-0.418480\pi\) | ||||
0.253311 | + | 0.967385i | \(0.418480\pi\) | |||||||
\(548\) | 2.68243e6 | − | 4.64610e6i | 0.381572 | − | 0.660902i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 566214. | + | 980712.i | 0.0798131 | + | 0.138240i | ||||
\(551\) | 792739. | − | 1.37306e6i | 0.111237 | − | 0.192669i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.02144e7 | − | 9.76319e6i | 1.42037 | − | 1.35762i | ||||
\(554\) | 2.17243e6 | 0.300727 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −465562. | − | 806377.i | −0.0638691 | − | 0.110624i | ||||
\(557\) | 5.18314e6 | + | 8.97747e6i | 0.707873 | + | 1.22607i | 0.965645 | + | 0.259866i | \(0.0836783\pi\) |
−0.257772 | + | 0.966206i | \(0.582988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.54941e6 | 0.615780 | ||||||||
\(560\) | 283921. | + | 1.16416e6i | 0.0382585 | + | 0.156871i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.99618e6 | + | 3.45748e6i | −0.266599 | + | 0.461763i | ||||
\(563\) | −2.24141e6 | − | 3.88223e6i | −0.298023 | − | 0.516191i | 0.677660 | − | 0.735375i | \(-0.262994\pi\) |
−0.975684 | + | 0.219184i | \(0.929661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.12243e6 | − | 1.94411e6i | 0.147924 | − | 0.256212i | ||||
\(566\) | −7.10928e6 | −0.932792 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.27760e6 | −0.166158 | ||||||||
\(569\) | 3.24668e6 | − | 5.62341e6i | 0.420396 | − | 0.728147i | −0.575582 | − | 0.817744i | \(-0.695225\pi\) |
0.995978 | + | 0.0895969i | \(0.0285579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 248754. | + | 430854.i | 0.0319286 | + | 0.0553019i | 0.881548 | − | 0.472094i | \(-0.156502\pi\) |
−0.849620 | + | 0.527396i | \(0.823168\pi\) | |||||||
\(572\) | 1.44103e6 | − | 2.49593e6i | 0.184155 | − | 0.318965i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.42923e6 | − | 1.36609e6i | 0.181060 | − | 0.173061i | ||||
\(575\) | −6.34279e6 | −0.800038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.27561e6 | + | 5.67353e6i | 0.409594 | + | 0.709437i | 0.994844 | − | 0.101416i | \(-0.0323372\pi\) |
−0.585250 | + | 0.810853i | \(0.699004\pi\) | |||||||
\(578\) | 225973. | + | 391397.i | 0.0281343 | + | 0.0487301i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.26786e6 | 0.403360 | ||||||||
\(581\) | 6.94707e6 | + | 2.03067e6i | 0.853810 | + | 0.249574i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 869363. | − | 1.50578e6i | 0.105933 | − | 0.183481i | ||||
\(584\) | 1.45762e6 | + | 2.52467e6i | 0.176853 | + | 0.306318i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.27974e6 | − | 5.68067e6i | 0.394543 | − | 0.683369i | ||||
\(587\) | 30793.5 | 0.00368862 | 0.00184431 | − | 0.999998i | \(-0.499413\pi\) | ||||
0.00184431 | + | 0.999998i | \(0.499413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 648763. | 0.0770544 | ||||||||
\(590\) | 434014. | − | 751735.i | 0.0513303 | − | 0.0889067i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 298646. | + | 517271.i | 0.0350230 | + | 0.0606616i | ||||
\(593\) | 285468. | − | 494446.i | 0.0333366 | − | 0.0577407i | −0.848876 | − | 0.528592i | \(-0.822720\pi\) |
0.882212 | + | 0.470852i | \(0.156053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.56243e6 | + | 1.62593e6i | 0.644128 | + | 0.188283i | ||||
\(596\) | −4.52893e6 | −0.522251 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.07127e6 | + | 1.39799e7i | 0.922973 | + | 1.59864i | ||||
\(599\) | 4.53555e6 | + | 7.85581e6i | 0.516492 | + | 0.894590i | 0.999817 | + | 0.0191488i | \(0.00609561\pi\) |
−0.483325 | + | 0.875441i | \(0.660571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.36309e7 | −1.53936 | −0.769679 | − | 0.638431i | \(-0.779584\pi\) | ||||
−0.769679 | + | 0.638431i | \(0.779584\pi\) | |||||||
\(602\) | −1.47164e6 | + | 1.40662e6i | −0.165504 | + | 0.158193i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.93246e6 | − | 3.34712e6i | 0.215535 | − | 0.373318i | ||||
\(605\) | 2.47126e6 | + | 4.28035e6i | 0.274493 | + | 0.475435i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.97825e6 | − | 3.42644e6i | 0.217927 | − | 0.377460i | −0.736247 | − | 0.676713i | \(-0.763404\pi\) |
0.954174 | + | 0.299253i | \(0.0967373\pi\) | |||||||
\(608\) | 287006. | 0.0314870 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.14304e6 | 0.233188 | ||||||||
\(611\) | −6.44126e6 | + | 1.11566e7i | −0.698020 | + | 1.20901i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −661552. | − | 1.14584e6i | −0.0711070 | − | 0.123161i | 0.828280 | − | 0.560315i | \(-0.189320\pi\) |
−0.899387 | + | 0.437154i | \(0.855987\pi\) | |||||||
\(614\) | 4.76261e6 | − | 8.24908e6i | 0.509828 | − | 0.883049i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 305571. | + | 1.25293e6i | 0.0324459 | + | 0.133038i | ||||
\(617\) | −9.26370e6 | −0.979651 | −0.489826 | − | 0.871820i | \(-0.662940\pi\) | ||||
−0.489826 | + | 0.871820i | \(0.662940\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −334693. | − | 579705.i | −0.0351091 | − | 0.0608107i | 0.847937 | − | 0.530097i | \(-0.177845\pi\) |
−0.883046 | + | 0.469286i | \(0.844511\pi\) | |||||||
\(620\) | 668589. | + | 1.15803e6i | 0.0698521 | + | 0.120987i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.98051e6 | −0.516176 | ||||||||
\(623\) | 8.95430e6 | − | 8.55872e6i | 0.924297 | − | 0.883463i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 378164. | − | 654999.i | 0.0387240 | − | 0.0670719i | ||||
\(626\) | 3.32598e6 | + | 5.76077e6i | 0.339222 | + | 0.587550i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.71223e6 | − | 2.96567e6i | 0.173246 | − | 0.300071i | ||||
\(629\) | 2.88866e6 | 0.291118 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −666246. | −0.0666133 | −0.0333067 | − | 0.999445i | \(-0.510604\pi\) | ||||
−0.0333067 | + | 0.999445i | \(0.510604\pi\) | |||||||
\(632\) | 3.48774e6 | − | 6.04095e6i | 0.347338 | − | 0.601607i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.24972e6 | + | 9.09277e6i | 0.518696 | + | 0.898407i | ||||
\(635\) | −1.14726e6 | + | 1.98711e6i | −0.112909 | + | 0.195564i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.64108e7 | + | 1.04903e7i | 1.60243 | + | 1.02432i | ||||
\(638\) | 3.51704e6 | 0.342078 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 295777. | + | 512300.i | 0.0285439 | + | 0.0494396i | ||||
\(641\) | −1.05439e6 | − | 1.82625e6i | −0.101357 | − | 0.175556i | 0.810887 | − | 0.585203i | \(-0.198985\pi\) |
−0.912244 | + | 0.409647i | \(0.865652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.25977e7 | 1.20161 | 0.600806 | − | 0.799395i | \(-0.294846\pi\) | ||||
0.600806 | + | 0.799395i | \(0.294846\pi\) | |||||||
\(644\) | −6.93328e6 | − | 2.02664e6i | −0.658756 | − | 0.192558i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 694016. | − | 1.20207e6i | 0.0654317 | − | 0.113331i | ||||
\(647\) | 8.56496e6 | + | 1.48349e7i | 0.804386 | + | 1.39324i | 0.916705 | + | 0.399565i | \(0.130839\pi\) |
−0.112319 | + | 0.993672i | \(0.535828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 467109. | − | 809056.i | 0.0435318 | − | 0.0753992i | ||||
\(650\) | 8.44301e6 | 0.783815 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.03146e6 | 0.0950237 | ||||||||
\(653\) | −4.12762e6 | + | 7.14925e6i | −0.378806 | + | 0.656112i | −0.990889 | − | 0.134682i | \(-0.956999\pi\) |
0.612083 | + | 0.790794i | \(0.290332\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.46054e6 | + | 4.26178e6i | 0.224092 | + | 0.388139i | ||||
\(656\) | 488014. | − | 845265.i | 0.0442764 | − | 0.0766890i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.36587e6 | − | 5.60048e6i | −0.122983 | − | 0.504267i | ||||
\(659\) | 1.05417e7 | 0.945581 | 0.472790 | − | 0.881175i | \(-0.343247\pi\) | ||||
0.472790 | + | 0.881175i | \(0.343247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.23820e6 | − | 3.87668e6i | −0.199249 | − | 0.345109i | 0.749036 | − | 0.662529i | \(-0.230517\pi\) |
−0.948285 | + | 0.317420i | \(0.897184\pi\) | |||||||
\(662\) | 3.47771e6 | + | 6.02357e6i | 0.308424 | + | 0.534206i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.57306e6 | 0.314499 | ||||||||
\(665\) | −310848. | − | 1.27457e6i | −0.0272580 | − | 0.111766i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.84956e6 | + | 1.70599e7i | −0.857240 | + | 1.48478i | ||||
\(668\) | −3.54155e6 | − | 6.13415e6i | −0.307081 | − | 0.531880i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.10391e6 | + | 5.37614e6i | −0.267130 | + | 0.462683i | ||||
\(671\) | 2.30645e6 | 0.197760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.87165e7 | −1.59289 | −0.796447 | − | 0.604708i | \(-0.793290\pi\) | ||||
−0.796447 | + | 0.604708i | \(0.793290\pi\) | |||||||
\(674\) | 1.70713e6 | − | 2.95683e6i | 0.144749 | − | 0.250713i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.77348e6 | − | 1.34641e7i | −0.654258 | − | 1.13321i | ||||
\(677\) | 2.08116e6 | − | 3.60467e6i | 0.174515 | − | 0.302270i | −0.765478 | − | 0.643462i | \(-0.777497\pi\) |
0.939993 | + | 0.341192i | \(0.110831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.86714e6 | − | 545776.i | −0.155418 | − | 0.0454297i | ||||
\(680\) | 2.86090e6 | 0.237263 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 719570. | + | 1.24633e6i | 0.0592396 | + | 0.102606i | ||||
\(683\) | −6.43455e6 | − | 1.11450e7i | −0.527796 | − | 0.914170i | −0.999475 | − | 0.0323992i | \(-0.989685\pi\) |
0.471679 | − | 0.881770i | \(-0.343648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21063e7 | −0.985793 | ||||||||
\(686\) | −8.55199e6 | + | 1.68063e6i | −0.693836 | + | 0.136352i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −502494. | + | 870345.i | −0.0404725 | + | 0.0701004i | ||||
\(689\) | −6.48168e6 | − | 1.12266e7i | −0.520163 | − | 0.900949i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.64518e6 | − | 8.04569e6i | 0.370090 | − | 0.641015i | −0.619489 | − | 0.785006i | \(-0.712660\pi\) |
0.989579 | + | 0.143990i | \(0.0459934\pi\) | |||||||
\(692\) | 1.25758e6 | 0.0998325 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.19400e7 | −0.941033 | ||||||||
\(695\) | −1.05059e6 | + | 1.81967e6i | −0.0825029 | + | 0.142899i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.36016e6 | − | 4.08791e6i | −0.184018 | − | 0.318728i | ||||
\(698\) | 5.74934e6 | − | 9.95815e6i | 0.446662 | − | 0.773642i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.73113e6 | + | 2.61048e6i | −0.210668 | + | 0.201361i | ||||
\(701\) | −2.50809e7 | −1.92774 | −0.963870 | − | 0.266375i | \(-0.914174\pi\) | ||||
−0.963870 | + | 0.266375i | \(0.914174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −326970. | − | 566329.i | −0.0249528 | − | 0.0432196i | ||||
\(704\) | 318330. | + | 551364.i | 0.0242073 | + | 0.0419283i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.88437e6 | 0.444312 | ||||||||
\(707\) | −825564. | − | 3.38505e6i | −0.0621158 | − | 0.254693i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.96890e6 | + | 8.60639e6i | −0.371231 | + | 0.642991i | −0.989755 | − | 0.142774i | \(-0.954398\pi\) |
0.618524 | + | 0.785766i | \(0.287731\pi\) | |||||||
\(710\) | 1.44151e6 | + | 2.49677e6i | 0.107318 | + | 0.185880i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.05747e6 | − | 5.29569e6i | 0.226028 | − | 0.391491i | ||||
\(713\) | −8.06069e6 | −0.593811 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.50364e6 | −0.475764 | ||||||||
\(716\) | −4.08342e6 | + | 7.07269e6i | −0.297674 | + | 0.515587i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.15598e6 | − | 1.06625e7i | −0.445642 | − | 0.771875i | ||||
\(719\) | −7.00047e6 | + | 1.21252e7i | −0.505016 | + | 0.874713i | 0.494968 | + | 0.868911i | \(0.335180\pi\) |
−0.999983 | + | 0.00580117i | \(0.998153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.86536e6 | + | 4.65041e6i | −0.348559 | + | 0.333160i | ||||
\(722\) | 9.59017e6 | 0.684673 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 176414. | + | 305559.i | 0.0125080 | + | 0.0216645i | ||||
\(725\) | 5.15160e6 | + | 8.92283e6i | 0.363996 | + | 0.630460i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.27315e6 | 0.580544 | 0.290272 | − | 0.956944i | \(-0.406254\pi\) | ||||
0.290272 | + | 0.956944i | \(0.406254\pi\) | |||||||
\(728\) | 9.22903e6 | + | 2.69770e6i | 0.645398 | + | 0.188654i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.28926e6 | − | 5.69716e6i | 0.228450 | − | 0.395687i | ||||
\(731\) | 2.43019e6 | + | 4.20921e6i | 0.168208 | + | 0.291345i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.64295e6 | − | 2.84568e6i | 0.112945 | − | 0.195626i | −0.804012 | − | 0.594614i | \(-0.797305\pi\) |
0.916956 | + | 0.398988i | \(0.130638\pi\) | |||||||
\(734\) | −6.46679e6 | −0.443046 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.56597e6 | −0.242651 | ||||||||
\(737\) | −3.34059e6 | + | 5.78608e6i | −0.226545 | + | 0.392388i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.04564e6 | − | 8.73930e6i | −0.339864 | − | 0.588662i | 0.644543 | − | 0.764568i | \(-0.277048\pi\) |
−0.984407 | + | 0.175907i | \(0.943714\pi\) | |||||||
\(740\) | 673925. | − | 1.16727e6i | 0.0452410 | − | 0.0783597i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.56781e6 | + | 1.62751e6i | 0.371257 | + | 0.108521i | ||||
\(743\) | −1.73443e7 | −1.15261 | −0.576307 | − | 0.817233i | \(-0.695507\pi\) | ||||
−0.576307 | + | 0.817233i | \(0.695507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.10998e6 | + | 8.85074e6i | 0.337309 | + | 0.584237i | ||||
\(746\) | −9.52237e6 | − | 1.64932e7i | −0.626467 | − | 1.08507i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.07905e6 | 0.201216 | ||||||||
\(749\) | 2.34057e6 | − | 2.23717e6i | 0.152446 | − | 0.145711i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.79857e6 | − | 1.52396e7i | 0.569262 | − | 0.985990i | −0.427377 | − | 0.904073i | \(-0.640562\pi\) |
0.996639 | − | 0.0819170i | \(-0.0261042\pi\) | |||||||
\(752\) | −1.42291e6 | − | 2.46455e6i | −0.0917554 | − | 0.158925i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.31109e7 | − | 2.27088e7i | 0.839857 | − | 1.45468i | ||||
\(755\) | −8.72158e6 | −0.556836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.66480e6 | −0.295865 | −0.147932 | − | 0.988997i | \(-0.547262\pi\) | ||||
−0.147932 | + | 0.988997i | \(0.547262\pi\) | |||||||
\(758\) | 2.00386e6 | − | 3.47079e6i | 0.126676 | − | 0.219409i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −323828. | − | 560887.i | −0.0203367 | − | 0.0352242i | ||||
\(761\) | 9.13585e6 | − | 1.58238e7i | 0.571857 | − | 0.990485i | −0.424518 | − | 0.905419i | \(-0.639557\pi\) |
0.996375 | − | 0.0850658i | \(-0.0271101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −111693. | − | 457973.i | −0.00694566 | − | 0.0284792i | ||||
\(764\) | 8.93044e6 | 0.553528 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.64305e6 | + | 9.77404e6i | 0.347489 | + | 0.601869i | ||||
\(767\) | −3.48261e6 | − | 6.03205e6i | −0.213755 | − | 0.370234i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.31895e7 | −1.41409 | −0.707043 | − | 0.707171i | \(-0.749971\pi\) | ||||
−0.707043 | + | 0.707171i | \(0.749971\pi\) | |||||||
\(770\) | 2.10379e6 | − | 2.01085e6i | 0.127872 | − | 0.122223i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 394530. | − | 683346.i | 0.0238252 | − | 0.0412665i | ||||
\(773\) | 1.01074e6 | + | 1.75066e6i | 0.0608405 | + | 0.105379i | 0.894841 | − | 0.446384i | \(-0.147289\pi\) |
−0.834001 | + | 0.551763i | \(0.813955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.10799e6 | + | 3.65114e6i | −0.126070 | + | 0.218360i | ||||
\(776\) | −960317. | −0.0572480 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.96959e6 | −0.294355 | ||||||||
\(779\) | −534297. | + | 925430.i | −0.0315456 | + | 0.0546387i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.55143e6 | + | 2.68715e6i | 0.0910131 | + | 0.157639i | ||||
\(782\) | −8.62296e6 | + | 1.49354e7i | −0.504243 | + | 0.873374i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.81949e6 | + | 1.98085e6i | −0.221930 | + | 0.115097i | ||||
\(785\) | −7.72763e6 | −0.447582 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.88722e6 | − | 1.36611e7i | −0.453928 | − | 0.786227i | 0.544698 | − | 0.838632i | \(-0.316644\pi\) |
−0.998626 | + | 0.0524059i | \(0.983311\pi\) | |||||||
\(788\) | −7.53207e6 | − | 1.30459e7i | −0.432114 | − | 0.748444i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.57409e7 | −0.897348 | ||||||||
\(791\) | 7.73672e6 | + | 2.26149e6i | 0.439659 | + | 0.128515i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.59807e6 | − | 1.48923e7i | 0.485532 | − | 0.840966i | ||||
\(794\) | 5.49124e6 | + | 9.51111e6i | 0.309115 | + | 0.535402i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.12010e6 | + | 8.86827e6i | −0.286415 | + | 0.496085i | ||||
\(797\) | −1.22436e6 | −0.0682750 | −0.0341375 | − | 0.999417i | \(-0.510868\pi\) | ||||
−0.0341375 | + | 0.999417i | \(0.510868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.37631e7 | −0.762690 | ||||||||
\(800\) | −932551. | + | 1.61523e6i | −0.0515167 | + | 0.0892295i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.42670e6 | + | 1.28634e7i | 0.407718 | + | 0.706189i | ||||
\(803\) | 3.54007e6 | − | 6.13158e6i | 0.193742 | − | 0.335571i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.86221e6 | + | 1.58362e7i | 0.210061 | + | 0.861312i | ||||
\(806\) | 1.07297e7 | 0.581771 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −860037. | − | 1.48963e6i | −0.0463435 | − | 0.0802692i | ||||
\(809\) | −1.38662e7 | − | 2.40170e7i | −0.744882 | − | 1.29017i | −0.950250 | − | 0.311489i | \(-0.899172\pi\) |
0.205368 | − | 0.978685i | \(-0.434161\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.19246e7 | −0.636636 | −0.318318 | − | 0.947984i | \(-0.603118\pi\) | ||||
−0.318318 | + | 0.947984i | \(0.603118\pi\) | |||||||
\(812\) | 2.78018e6 | + | 1.13996e7i | 0.147973 | + | 0.606734i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 725313. | − | 1.25628e6i | 0.0383676 | − | 0.0664546i | ||||
\(815\) | −1.16379e6 | − | 2.01575e6i | −0.0613735 | − | 0.106302i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 550151. | − | 952889.i | 0.0288354 | − | 0.0499444i | ||||
\(818\) | −1.50376e7 | −0.785770 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.20250e6 | −0.114388 | ||||||||
\(821\) | 8.02312e6 | − | 1.38965e7i | 0.415418 | − | 0.719525i | −0.580054 | − | 0.814578i | \(-0.696969\pi\) |
0.995472 | + | 0.0950526i | \(0.0303019\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.61533e6 | + | 9.72603e6i | 0.288985 | + | 0.500537i | 0.973568 | − | 0.228398i | \(-0.0733489\pi\) |
−0.684583 | + | 0.728935i | \(0.740016\pi\) | |||||||
\(824\) | −1.66129e6 | + | 2.87743e6i | −0.0852367 | + | 0.147634i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.99159e6 | + | 874460.i | 0.152564 | + | 0.0445954i | ||||
\(827\) | 2.68427e7 | 1.36478 | 0.682389 | − | 0.730989i | \(-0.260941\pi\) | ||||
0.682389 | + | 0.730989i | \(0.260941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.40210e7 | − | 2.42850e7i | −0.708584 | − | 1.22730i | −0.965382 | − | 0.260839i | \(-0.916001\pi\) |
0.256798 | − | 0.966465i | \(-0.417332\pi\) | |||||||
\(830\) | −4.03147e6 | − | 6.98272e6i | −0.203127 | − | 0.351827i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.74673e6 | 0.237731 | ||||||||
\(833\) | −939564. | + | 2.07872e7i | −0.0469152 | + | 1.03797i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.99186e6 | + | 1.38423e7i | −0.396672 | + | 0.687056i | ||||
\(836\) | −348521. | − | 603656.i | −0.0172470 | − | 0.0298727i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.20054e6 | + | 1.59358e7i | −0.452588 | + | 0.783905i | ||||
\(839\) | 3.30603e7 | 1.62145 | 0.810723 | − | 0.585430i | \(-0.199074\pi\) | ||||
0.810723 | + | 0.585430i | \(0.199074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.14880e7 | 0.560086 | ||||||||
\(842\) | −809728. | + | 1.40249e6i | −0.0393604 | + | 0.0681741i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.37495e6 | − | 1.27738e7i | −0.356372 | − | 0.617254i | ||||
\(845\) | −1.75416e7 | + | 3.03830e7i | −0.845139 | + | 1.46382i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.28291e7 | + | 1.22623e7i | −0.614450 | + | 0.587305i | ||||
\(848\) | 2.86367e6 | 0.136752 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.51005e6 | + | 7.81164e6i | 0.214109 | + | 0.370847i | ||||
\(851\) | 4.06251e6 | + | 7.03648e6i | 0.192296 | + | 0.333067i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.73897e7 | 1.28889 | 0.644444 | − | 0.764652i | \(-0.277089\pi\) | ||||
0.644444 | + | 0.764652i | \(0.277089\pi\) | |||||||
\(854\) | 1.82322e6 | + | 7.47575e6i | 0.0855452 | + | 0.350760i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 799192. | − | 1.38424e6i | 0.0372792 | − | 0.0645695i | ||||
\(857\) | −1.48360e6 | − | 2.56968e6i | −0.0690027 | − | 0.119516i | 0.829460 | − | 0.558566i | \(-0.188648\pi\) |
−0.898463 | + | 0.439050i | \(0.855315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.98980e7 | − | 3.44643e7i | 0.920081 | − | 1.59363i | 0.120794 | − | 0.992678i | \(-0.461456\pi\) |
0.799287 | − | 0.600949i | \(-0.205211\pi\) | |||||||
\(860\) | 2.26785e6 | 0.104561 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 379034. | 0.0173744 | ||||||||
\(863\) | 3.59799e6 | − | 6.23190e6i | 0.164450 | − | 0.284835i | −0.772010 | − | 0.635610i | \(-0.780749\pi\) |
0.936460 | + | 0.350775i | \(0.114082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.41893e6 | − | 2.45766e6i | −0.0644794 | − | 0.111682i | ||||
\(866\) | 8.63453e6 | − | 1.49554e7i | 0.391241 | − | 0.677649i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.47084e6 | + | 3.31751e6i | −0.156364 | + | 0.149456i | ||||
\(869\) | −1.69411e7 | −0.761015 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.49063e7 | + | 4.31391e7i | 1.11241 | + | 1.92675i | ||||
\(872\) | −116357. | − | 201536.i | −0.00518203 | − | 0.00897554i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.90417e6 | 0.172882 | ||||||||
\(875\) | 2.22231e7 | + | 6.49594e6i | 0.981259 | + | 0.286828i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.25621e7 | + | 2.17582e7i | −0.551523 | + | 0.955266i | 0.446642 | + | 0.894713i | \(0.352620\pi\) |
−0.998165 | + | 0.0605532i | \(0.980714\pi\) | |||||||
\(878\) | −4.44734e6 | − | 7.70303e6i | −0.194699 | − | 0.337229i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 718343. | − | 1.24421e6i | 0.0312698 | − | 0.0541609i | ||||
\(881\) | −120262. | −0.00522022 | −0.00261011 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00261011 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.43497e7 | 1.05097 | 0.525487 | − | 0.850802i | \(-0.323883\pi\) | ||||
0.525487 | + | 0.850802i | \(0.323883\pi\) | |||||||
\(884\) | 1.14782e7 | − | 1.98808e7i | 0.494018 | − | 0.855664i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.36851e6 | + | 1.62267e7i | 0.400946 | + | 0.694459i | ||||
\(887\) | −1.41383e7 | + | 2.44883e7i | −0.603377 | + | 1.04508i | 0.388929 | + | 0.921268i | \(0.372845\pi\) |
−0.992306 | + | 0.123812i | \(0.960488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.90786e6 | − | 2.31152e6i | −0.335587 | − | 0.0980941i | ||||
\(890\) | −1.37989e7 | −0.583943 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.70160e6 | + | 1.16075e7i | 0.282011 | + | 0.488458i | ||||
\(893\) | 1.55786e6 | + | 2.69828e6i | 0.0653730 | + | 0.113229i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.84293e7 | 0.769042 | ||||||||
\(896\) | −1.53547e6 | + | 1.46763e6i | −0.0638955 | + | 0.0610727i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.79586e6 | + | 3.11053e6i | −0.0743161 | + | 0.128719i | ||||
\(899\) | 6.54688e6 | + | 1.13395e7i | 0.270169 | + | 0.467946i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.92471e6 | − | 1.19940e7i | 0.284178 | − | 0.492210i | ||||
\(902\) | −2.37045e6 | −0.0970094 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.97920e6 | 0.161948 | ||||||||
\(905\) | 398096. | − | 689523.i | 0.0161572 | − | 0.0279851i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.21584e7 | + | 2.10590e7i | 0.490748 | + | 0.850000i | 0.999943 | − | 0.0106507i | \(-0.00339029\pi\) |
−0.509195 | + | 0.860651i | \(0.670057\pi\) | |||||||
\(908\) | −1.06455e7 | + | 1.84386e7i | −0.428501 | + | 0.742186i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.14106e6 | − | 2.10798e7i | −0.205802 | − | 0.843847i | ||||
\(911\) | 3.36224e7 | 1.34225 | 0.671123 | − | 0.741346i | \(-0.265812\pi\) | ||||
0.671123 | + | 0.741346i | \(0.265812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.33888e6 | − | 7.51517e6i | −0.172267 | − | 0.298374i | ||||
\(914\) | 1.19636e7 | + | 2.07216e7i | 0.473693 | + | 0.820461i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.61701e7 | 0.636759 | ||||||||
\(917\) | −1.27734e7 | + | 1.22091e7i | −0.501629 | + | 0.479468i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.06874e6 | − | 7.04727e6i | 0.158917 | − | 0.275253i | −0.775561 | − | 0.631272i | \(-0.782533\pi\) |
0.934479 | + | 0.356019i | \(0.115866\pi\) | |||||||
\(920\) | 4.02348e6 | + | 6.96887e6i | 0.156723 | + | 0.271452i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.25013e6 | + | 5.62939e6i | −0.125914 | + | 0.218089i | ||||
\(923\) | 2.31338e7 | 0.893807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.24962e6 | 0.163304 | ||||||||
\(926\) | −1.69259e7 | + | 2.93165e7i | −0.648671 | + | 1.12353i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.89627e6 | + | 5.01649e6i | 0.110400 | + | 0.191219i | ||||
\(929\) | 1.79027e7 | − | 3.10084e7i | 0.680580 | − | 1.17880i | −0.294224 | − | 0.955736i | \(-0.595061\pi\) |
0.974804 | − | 0.223063i | \(-0.0716054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.18173e6 | − | 2.16872e6i | 0.158118 | − | 0.0820029i | ||||
\(932\) | −2.37776e7 | −0.896661 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.53319e7 | − | 2.65556e7i | −0.575080 | − | 0.996068i | ||||
\(935\) | −3.47409e6 | − | 6.01730e6i | −0.129961 | − | 0.225098i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.65849e7 | 1.73339 | 0.866694 | − | 0.498840i | \(-0.166241\pi\) | ||||
0.866694 | + | 0.498840i | \(0.166241\pi\) | |||||||
\(938\) | −2.13947e7 | − | 6.25382e6i | −0.793963 | − | 0.232080i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.21093e6 | + | 5.56149e6i | −0.118525 | + | 0.205292i | ||||
\(941\) | −1.03362e6 | − | 1.79029e6i | −0.0380529 | − | 0.0659096i | 0.846372 | − | 0.532593i | \(-0.178782\pi\) |
−0.884425 | + | 0.466683i | \(0.845449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.63850e6 | − | 1.14982e7i | 0.243103 | − | 0.421067i | ||||
\(944\) | 1.53865e6 | 0.0561966 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.44078e6 | 0.0886750 | ||||||||
\(947\) | 1.18386e7 | − | 2.05051e7i | 0.428970 | − | 0.742998i | −0.567812 | − | 0.823158i | \(-0.692210\pi\) |
0.996782 | + | 0.0801602i | \(0.0255432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.63936e7 | − | 4.57150e7i | −0.951334 | − | 1.64776i | ||||
\(950\) | 1.02099e6 | − | 1.76841e6i | 0.0367041 | − | 0.0635734i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.43396e6 | + | 9.97993e6i | 0.0870403 | + | 0.356891i | ||||
\(953\) | 3.40521e6 | 0.121454 | 0.0607270 | − | 0.998154i | \(-0.480658\pi\) | ||||
0.0607270 | + | 0.998154i | \(0.480658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00762e7 | − | 1.74525e7i | −0.357510 | − | 0.619226i | ||||
\(956\) | 7.00510e6 | + | 1.21332e7i | 0.247896 | + | 0.429368i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.61170e6 | −0.338366 | ||||||||
\(959\) | −1.02996e7 | − | 4.22315e7i | −0.361639 | − | 1.48283i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.16357e7 | − | 2.01535e7i | 0.406427 | − | 0.703952i | ||||
\(962\) | −5.40769e6 | − | 9.36639e6i | −0.188397 | − | 0.326313i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.16236e7 | + | 2.01326e7i | −0.402853 | + | 0.697762i | ||||
\(965\) | −1.78059e6 | −0.0615525 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.44238e6 | 0.0496036 | 0.0248018 | − | 0.999692i | \(-0.492105\pi\) | ||||
0.0248018 | + | 0.999692i | \(0.492105\pi\) | |||||||
\(968\) | −4.38051e6 | + | 7.58727e6i | −0.150258 | + | 0.260254i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.08352e6 | + | 1.87672e6i | 0.0369751 | + | 0.0640427i | ||||
\(971\) | −2.57977e6 | + | 4.46830e6i | −0.0878078 | + | 0.152088i | −0.906584 | − | 0.422025i | \(-0.861319\pi\) |
0.818776 | + | 0.574113i | \(0.194653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.24151e6 | − | 2.11674e6i | −0.245215 | − | 0.0716779i | ||||
\(974\) | 681206. | 0.0230081 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.89936e6 | + | 3.28978e6i | 0.0638237 | + | 0.110546i | ||||
\(977\) | −3.48825e6 | − | 6.04183e6i | −0.116915 | − | 0.202503i | 0.801628 | − | 0.597823i | \(-0.203967\pi\) |
−0.918544 | + | 0.395319i | \(0.870634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.48511e7 | −0.495225 | ||||||||
\(980\) | 8.18065e6 | + | 5.22932e6i | 0.272096 | + | 0.173932i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.15526e7 | − | 2.00096e7i | 0.382296 | − | 0.662156i | ||||
\(983\) | −1.40784e7 | − | 2.43845e7i | −0.464696 | − | 0.804878i | 0.534491 | − | 0.845174i | \(-0.320503\pi\) |
−0.999188 | + | 0.0402961i | \(0.987170\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.69968e7 | + | 2.94394e7i | −0.558184 | + | 0.966804i | ||||
\(986\) | 2.80142e7 | 0.917669 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.19691e6 | −0.169376 | ||||||||
\(989\) | −6.83547e6 | + | 1.18394e7i | −0.222217 | + | 0.384891i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.17022e7 | + | 2.02687e7i | 0.378514 | + | 0.655606i | 0.990846 | − | 0.134995i | \(-0.0431018\pi\) |
−0.612332 | + | 0.790601i | \(0.709768\pi\) | |||||||
\(992\) | −1.18513e6 | + | 2.05270e6i | −0.0382372 | + | 0.0662287i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.48330e6 | + | 7.15271e6i | −0.240230 | + | 0.229617i | ||||
\(995\) | 2.31080e7 | 0.739954 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.15142e7 | + | 3.72637e7i | 0.685468 | + | 1.18727i | 0.973290 | + | 0.229581i | \(0.0737356\pi\) |
−0.287822 | + | 0.957684i | \(0.592931\pi\) | |||||||
\(998\) | 1.08720e6 | + | 1.88309e6i | 0.0345529 | + | 0.0598474i | ||||
\(999\) | 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 | 126.6.g.j.37.1 | 4 | ||
3.2 | odd | 2 | 14.6.c.a.9.1 | ✓ | 4 | ||
7.2 | even | 3 | 882.6.a.ba.1.2 | 2 | |||
7.4 | even | 3 | inner | 126.6.g.j.109.1 | 4 | ||
7.5 | odd | 6 | 882.6.a.bi.1.1 | 2 | |||
12.11 | even | 2 | 112.6.i.d.65.2 | 4 | |||
21.2 | odd | 6 | 98.6.a.h.1.2 | 2 | |||
21.5 | even | 6 | 98.6.a.g.1.1 | 2 | |||
21.11 | odd | 6 | 14.6.c.a.11.1 | yes | 4 | ||
21.17 | even | 6 | 98.6.c.e.67.2 | 4 | |||
21.20 | even | 2 | 98.6.c.e.79.2 | 4 | |||
84.11 | even | 6 | 112.6.i.d.81.2 | 4 | |||
84.23 | even | 6 | 784.6.a.s.1.1 | 2 | |||
84.47 | odd | 6 | 784.6.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.a.9.1 | ✓ | 4 | 3.2 | odd | 2 | ||
14.6.c.a.11.1 | yes | 4 | 21.11 | odd | 6 | ||
98.6.a.g.1.1 | 2 | 21.5 | even | 6 | |||
98.6.a.h.1.2 | 2 | 21.2 | odd | 6 | |||
98.6.c.e.67.2 | 4 | 21.17 | even | 6 | |||
98.6.c.e.79.2 | 4 | 21.20 | even | 2 | |||
112.6.i.d.65.2 | 4 | 12.11 | even | 2 | |||
112.6.i.d.81.2 | 4 | 84.11 | even | 6 | |||
126.6.g.j.37.1 | 4 | 1.1 | even | 1 | trivial | ||
126.6.g.j.109.1 | 4 | 7.4 | even | 3 | inner | ||
784.6.a.s.1.1 | 2 | 84.23 | even | 6 | |||
784.6.a.bb.1.2 | 2 | 84.47 | odd | 6 | |||
882.6.a.ba.1.2 | 2 | 7.2 | even | 3 | |||
882.6.a.bi.1.1 | 2 | 7.5 | odd | 6 |