Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), 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: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 13.7 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.7.j.a.41.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 6.80225 | − | 18.6890i | 0.251935 | − | 0.692186i | −0.747670 | − | 0.664071i | \(-0.768827\pi\) |
0.999605 | − | 0.0281151i | \(-0.00895048\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.07240 | − | 34.4383i | −0.0485792 | − | 0.275506i | 0.950836 | − | 0.309694i | \(-0.100227\pi\) |
−0.999415 | + | 0.0341878i | \(0.989116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −223.008 | + | 386.261i | −0.650168 | + | 1.12612i | 0.332914 | + | 0.942957i | \(0.391968\pi\) |
−0.983082 | + | 0.183167i | \(0.941365\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 255.437 | + | 214.337i | 0.350394 | + | 0.294016i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 338.033 | + | 585.490i | 0.253969 | + | 0.439888i | 0.964615 | − | 0.263662i | \(-0.0849305\pi\) |
−0.710646 | + | 0.703550i | \(0.751597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 630.159 | + | 1731.35i | 0.286827 | + | 0.788050i | 0.996506 | + | 0.0835249i | \(0.0266178\pi\) |
−0.709679 | + | 0.704525i | \(0.751160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −684.924 | − | 120.771i | −0.202940 | − | 0.0357839i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3154.66 | − | 2647.08i | 0.642106 | − | 0.538791i | −0.262558 | − | 0.964916i | \(-0.584566\pi\) |
0.904664 | + | 0.426126i | \(0.140122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2252.47 | − | 6478.60i | 0.328396 | − | 0.944540i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5701.88 | + | 6795.24i | 0.615687 | + | 0.733748i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3207.53 | + | 18190.8i | −0.263626 | + | 1.49510i | 0.509295 | + | 0.860592i | \(0.329906\pi\) |
−0.772920 | + | 0.634503i | \(0.781205\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13533.6 | − | 4925.82i | 0.866149 | − | 0.315252i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18299.5 | − | 10565.2i | 0.929712 | − | 0.536770i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10737.6 | + | 12796.6i | −0.440264 | + | 0.524686i | −0.939854 | − | 0.341576i | \(-0.889039\pi\) |
0.499590 | + | 0.866262i | \(0.333484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29439.5 | + | 16996.9i | 0.988202 | + | 0.570539i | 0.904736 | − | 0.425972i | \(-0.140068\pi\) |
0.0834657 | + | 0.996511i | \(0.473401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13241.6 | − | 2334.86i | 0.368468 | − | 0.0649708i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14656.4 | + | 5334.48i | 0.341839 | + | 0.124419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5729.37i | − | 0.113110i | −0.998399 | − | 0.0565551i | \(-0.981988\pi\) | ||
0.998399 | − | 0.0565551i | \(-0.0180116\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36643.7 | 0.617739 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −21479.7 | + | 59015.1i | −0.311657 | + | 0.856271i | 0.680665 | + | 0.732595i | \(0.261691\pi\) |
−0.992323 | + | 0.123677i | \(0.960531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19195.5 | + | 108863.i | 0.241431 | + | 1.36922i | 0.828637 | + | 0.559786i | \(0.189117\pi\) |
−0.587206 | + | 0.809437i | \(0.699772\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5830.30 | − | 10098.4i | 0.0639813 | − | 0.110819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46760.9 | + | 39237.0i | 0.450390 | + | 0.377922i | 0.839581 | − | 0.543235i | \(-0.182801\pi\) |
−0.389190 | + | 0.921157i | \(0.627245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40640.4 | − | 70391.2i | −0.345437 | − | 0.598315i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28012.5 | − | 76963.7i | −0.211174 | − | 0.580197i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15076.1 | − | 2658.33i | −0.101266 | − | 0.0178559i | 0.122786 | − | 0.992433i | \(-0.460817\pi\) |
−0.224051 | + | 0.974577i | \(0.571928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18110.6 | − | 15196.6i | 0.108854 | − | 0.0913395i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −105757. | − | 86165.5i | −0.571063 | − | 0.465274i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −124978. | − | 148943.i | −0.608525 | − | 0.725212i | 0.370527 | − | 0.928822i | \(-0.379177\pi\) |
−0.979052 | + | 0.203610i | \(0.934733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 58204.5 | − | 330094.i | 0.256429 | − | 1.45428i | −0.535949 | − | 0.844250i | \(-0.680046\pi\) |
0.792378 | − | 0.610031i | \(-0.208843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −139755. | + | 50866.5i | −0.558914 | + | 0.203428i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 55798.0 | − | 32215.0i | 0.203179 | − | 0.117305i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63591.1 | + | 75785.0i | −0.211433 | + | 0.251976i | −0.861329 | − | 0.508047i | \(-0.830368\pi\) |
0.649897 | + | 0.760023i | \(0.274812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 318150. | + | 183684.i | 0.968467 | + | 0.559145i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −695029. | + | 122552.i | −1.94191 | + | 0.342410i | −0.941927 | + | 0.335816i | \(0.890988\pi\) |
−0.999978 | + | 0.00659391i | \(0.997901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −175843. | − | 64001.5i | −0.452018 | − | 0.164521i | 0.105971 | − | 0.994369i | \(-0.466205\pi\) |
−0.557989 | + | 0.829848i | \(0.688427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 286436.i | − | 0.678959i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −301536. | −0.660491 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −234966. | + | 645565.i | −0.476568 | + | 1.30936i | 0.435821 | + | 0.900033i | \(0.356458\pi\) |
−0.912389 | + | 0.409325i | \(0.865764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −30764.8 | − | 174476.i | −0.0578893 | − | 0.328307i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 334822. | − | 579928.i | 0.585571 | − | 1.01424i | −0.409233 | − | 0.912430i | \(-0.634204\pi\) |
0.994804 | − | 0.101808i | \(-0.0324629\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −110317. | − | 92567.2i | −0.179633 | − | 0.150730i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 166116. | + | 287721.i | 0.252262 | + | 0.436931i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −19415.8 | − | 53344.6i | −0.0275414 | − | 0.0756694i | 0.925160 | − | 0.379577i | \(-0.123931\pi\) |
−0.952701 | + | 0.303908i | \(0.901708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −809281. | − | 142698.i | −1.07393 | − | 0.189363i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 517911. | − | 434579.i | 0.643882 | − | 0.540281i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −236790. | − | 38230.6i | −0.276180 | − | 0.0445903i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 752838. | + | 897198.i | 0.824872 | + | 0.983044i | 0.999999 | − | 0.00150162i | \(-0.000477982\pi\) |
−0.175127 | + | 0.984546i | \(0.556034\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −39146.2 | + | 222009.i | −0.0403445 | + | 0.228805i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.36349e6 | − | 496271.i | 1.32339 | − | 0.481675i | 0.418849 | − | 0.908056i | \(-0.362434\pi\) |
0.904544 | + | 0.426381i | \(0.140212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −784403. | + | 452875.i | −0.717840 | + | 0.414445i | −0.813957 | − | 0.580925i | \(-0.802691\pi\) |
0.0961172 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 199392. | − | 237626.i | 0.172243 | − | 0.205271i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.12479e6 | + | 649398.i | 0.918164 | + | 0.530102i | 0.883049 | − | 0.469281i | \(-0.155487\pi\) |
0.0351149 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 228120. | − | 40223.8i | 0.176151 | − | 0.0310601i | −0.0848769 | − | 0.996391i | \(-0.527050\pi\) |
0.261028 | + | 0.965331i | \(0.415939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −107076. | − | 38972.6i | −0.0782932 | − | 0.0284964i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.22997e6i | − | 0.852431i | −0.904622 | − | 0.426216i | \(-0.859846\pi\) | ||
0.904622 | − | 0.426216i | \(-0.140154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 645938. | 0.424715 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −210126. | + | 577317.i | −0.131197 | + | 0.360460i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 318948. | + | 1.80884e6i | 0.189269 | + | 1.07340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 657248. | − | 1.13839e6i | 0.370999 | − | 0.642590i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 956824. | + | 802870.i | 0.514182 | + | 0.431450i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −525018. | − | 909357.i | −0.268809 | − | 0.465591i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 460147. | + | 1.26424e6i | 0.224639 | + | 0.617191i | 0.999896 | − | 0.0144557i | \(-0.00460154\pi\) |
−0.775256 | + | 0.631647i | \(0.782379\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.16511e6 | + | 381768.i | 1.00858 | + | 0.177840i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.40432e6 | + | 1.17836e6i | −0.624672 | + | 0.524162i | −0.899268 | − | 0.437397i | \(-0.855900\pi\) |
0.274596 | + | 0.961560i | \(0.411456\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00011e6 | + | 2.31482e6i | 0.850157 | + | 0.983925i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −474971. | − | 566048.i | −0.193048 | − | 0.230066i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −38396.2 | + | 217756.i | −0.0149323 | + | 0.0846854i | −0.991363 | − | 0.131145i | \(-0.958135\pi\) |
0.976431 | + | 0.215830i | \(0.0692458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.38012e6 | + | 866293.i | −0.886246 | + | 0.322567i | −0.744728 | − | 0.667368i | \(-0.767421\pi\) |
−0.141518 | + | 0.989936i | \(0.545198\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.05138e6 | − | 607015.i | 0.375062 | − | 0.216542i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −800672. | + | 954204.i | −0.273808 | + | 0.326312i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 505895. | + | 292079.i | 0.165942 | + | 0.0958067i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.59199e6 | + | 280711.i | −0.501173 | + | 0.0883704i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −529979. | − | 192897.i | −0.160214 | − | 0.0583131i | 0.260668 | − | 0.965428i | \(-0.416057\pi\) |
−0.420882 | + | 0.907115i | \(0.638279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.18209e6i | − | 0.924234i | −0.886819 | − | 0.462117i | \(-0.847090\pi\) | ||
0.886819 | − | 0.462117i | \(-0.152910\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.37319e6 | 0.383403 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 406576. | − | 1.11706e6i | 0.109181 | − | 0.299972i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −656962. | − | 3.72582e6i | −0.169762 | − | 0.962770i | −0.944017 | − | 0.329896i | \(-0.892986\pi\) |
0.774255 | − | 0.632874i | \(-0.218125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −152233. | + | 263675.i | −0.0378720 | + | 0.0655961i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.31110e6 | − | 5.29564e6i | −1.51226 | − | 1.26894i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 119764. | + | 207437.i | 0.0276543 | + | 0.0478986i | 0.879521 | − | 0.475859i | \(-0.157863\pi\) |
−0.851867 | + | 0.523758i | \(0.824530\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −160817. | − | 441841.i | −0.0357997 | − | 0.0983590i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.41774e6 | + | 249987.i | 0.304403 | + | 0.0536744i | 0.323763 | − | 0.946138i | \(-0.395052\pi\) |
−0.0193605 | + | 0.999813i | \(0.506163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.09709e6 | − | 920568.i | 0.227291 | − | 0.190720i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.96397e6 | − | 1.17209e6i | 0.392778 | − | 0.234408i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.13020e6 | − | 7.30568e6i | −1.18396 | − | 1.41099i | −0.890482 | − | 0.455019i | \(-0.849632\pi\) |
−0.293476 | − | 0.955966i | \(-0.594812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.11544e6 | + | 6.32598e6i | −0.208129 | + | 1.18036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.63374e6 | + | 1.32257e6i | −0.655290 | + | 0.238506i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.02397e6 | + | 1.74589e6i | −0.527253 | + | 0.304410i | −0.739897 | − | 0.672720i | \(-0.765126\pi\) |
0.212644 | + | 0.977130i | \(0.431792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.98204e6 | + | 2.36211e6i | −0.334255 | + | 0.398349i | −0.906826 | − | 0.421506i | \(-0.861502\pi\) |
0.572571 | + | 0.819855i | \(0.305946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.77322e6 | − | 3.33317e6i | −0.942030 | − | 0.543881i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −197310. | + | 34791.0i | −0.0311626 | + | 0.00549480i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.61622e6 | + | 952226.i | 0.400082 | + | 0.145618i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.42452e6i | 1.39596i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.12208e6 | 0.591584 | 0.295792 | − | 0.955252i | \(-0.404416\pi\) | ||||
0.295792 | + | 0.955252i | \(0.404416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.72786e6 | − | 4.74725e6i | 0.240346 | − | 0.660344i | −0.759605 | − | 0.650385i | \(-0.774608\pi\) |
0.999950 | − | 0.00995941i | \(-0.00317023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −222515. | − | 1.26195e6i | −0.0300093 | − | 0.170191i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.42997e6 | − | 7.67294e6i | 0.579432 | − | 1.00361i | −0.416113 | − | 0.909313i | \(-0.636608\pi\) |
0.995545 | − | 0.0942922i | \(-0.0300588\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.69142e6 | − | 3.93657e6i | −0.595312 | − | 0.499526i | 0.294623 | − | 0.955614i | \(-0.404806\pi\) |
−0.889935 | + | 0.456087i | \(0.849250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 983784. | + | 1.70396e6i | 0.121147 | + | 0.209832i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.54825e6 | − | 7.00125e6i | −0.304616 | − | 0.836926i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.16281e6 | + | 381362.i | 0.251048 | + | 0.0442666i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.71830e6 | + | 3.95912e6i | −0.531954 | + | 0.446363i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.55457e6 | − | 871180.i | 0.498894 | − | 0.0954266i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.25470e6 | + | 6.26231e6i | 0.559372 | + | 0.666634i | 0.969414 | − | 0.245433i | \(-0.0789302\pi\) |
−0.410041 | + | 0.912067i | \(0.634486\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.43738e6 | + | 1.38231e7i | −0.252223 | + | 1.43043i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.63249e6 | − | 1.32212e6i | 0.365501 | − | 0.133032i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.31305e7 | + | 7.58089e6i | −1.28500 | + | 0.741892i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.39225e6 | + | 2.85097e6i | −0.227758 | + | 0.271432i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.57095e6 | + | 3.79374e6i | 0.608767 | + | 0.351472i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.74211e6 | − | 659835.i | 0.337444 | − | 0.0595005i | −0.00235853 | − | 0.999997i | \(-0.500751\pi\) |
0.339803 | + | 0.940497i | \(0.389640\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.51277e6 | + | 1.64251e6i | 0.396183 | + | 0.144199i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.55988e7i | − | 1.33356i | −0.745254 | − | 0.666780i | \(-0.767672\pi\) | ||
0.745254 | − | 0.666780i | \(-0.232328\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.04778e7 | 1.70521 | 0.852603 | − | 0.522559i | \(-0.175023\pi\) | ||||
0.852603 | + | 0.522559i | \(0.175023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.05112e6 | + | 5.63541e6i | −0.166401 | + | 0.457183i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.88321e6 | − | 1.06802e7i | −0.148878 | − | 0.844330i | −0.964171 | − | 0.265281i | \(-0.914535\pi\) |
0.815293 | − | 0.579049i | \(-0.196576\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.06731e6 | − | 1.84863e6i | 0.0822404 | − | 0.142445i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.04667e7 | + | 8.78258e6i | 0.786256 | + | 0.659747i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.01761e6 | − | 1.76255e6i | −0.0745395 | − | 0.129106i | 0.826346 | − | 0.563162i | \(-0.190415\pi\) |
−0.900886 | + | 0.434056i | \(0.857082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.25488e6 | + | 1.71851e7i | 0.446856 | + | 1.22773i | 0.934901 | + | 0.354909i | \(0.115488\pi\) |
−0.488045 | + | 0.872819i | \(0.662290\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.17000e7 | + | 2.06303e6i | 0.815396 | + | 0.143776i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.17737e6 | + | 1.82703e6i | −0.148059 | + | 0.124236i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.26361e7 | − | 182737.i | 0.838538 | − | 0.0121265i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.56075e6 | − | 1.02023e7i | −0.554516 | − | 0.660846i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.56964e6 | − | 1.45732e7i | 0.162499 | − | 0.921579i | −0.789106 | − | 0.614257i | \(-0.789456\pi\) |
0.951605 | − | 0.307322i | \(-0.0994330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.17348e7 | + | 4.27112e6i | −0.724627 | + | 0.263743i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.48039e6 | + | 1.43206e6i | −0.149589 | + | 0.0863654i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.29411e7 | − | 1.54226e7i | 0.762379 | − | 0.908568i | −0.235617 | − | 0.971846i | \(-0.575711\pi\) |
0.997996 | + | 0.0632783i | \(0.0201556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.21303e6 | + | 1.27769e6i | 0.127376 | + | 0.0735406i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.48557e6 | + | 967254.i | −0.308532 | + | 0.0544025i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.77771e6 | + | 1.37497e6i | 0.207664 | + | 0.0755835i | 0.443758 | − | 0.896147i | \(-0.353645\pi\) |
−0.236094 | + | 0.971730i | \(0.575867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 535339.i | 0.0287668i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.12903e6 | −0.0593159 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.28982e6 | + | 1.17862e7i | −0.220385 | + | 0.605503i | −0.999779 | − | 0.0210316i | \(-0.993305\pi\) |
0.779394 | + | 0.626534i | \(0.215527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.64876e6 | + | 2.63644e7i | 0.233577 | + | 1.32468i | 0.845590 | + | 0.533832i | \(0.179249\pi\) |
−0.612014 | + | 0.790847i | \(0.709640\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.17182e6 | + | 1.41540e7i | −0.401634 | + | 0.695651i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.45882e6 | + | 6.25869e6i | 0.358651 | + | 0.300944i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.74114e6 | + | 8.21189e6i | 0.223071 | + | 0.386370i | 0.955739 | − | 0.294216i | \(-0.0950585\pi\) |
−0.732668 | + | 0.680586i | \(0.761725\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.87688e6 | + | 1.06516e7i | 0.178513 | + | 0.490460i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.58733e7 | − | 6.32543e6i | −1.61678 | − | 0.285083i | −0.709217 | − | 0.704990i | \(-0.750951\pi\) |
−0.907567 | + | 0.419907i | \(0.862063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.21487e7 | − | 1.85850e7i | 0.977214 | − | 0.819980i | −0.00645240 | − | 0.999979i | \(-0.502054\pi\) |
0.983667 | + | 0.179999i | \(0.0576094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.32520e6 | + | 4.16532e6i | −0.100444 | + | 0.179934i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.80051e7 | − | 2.14576e7i | −0.761638 | − | 0.907685i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.24656e6 | + | 7.06958e6i | −0.0516439 | + | 0.292887i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.18887e7 | − | 7.96685e6i | 0.888264 | − | 0.323302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.36327e7 | + | 7.87085e6i | −0.541975 | + | 0.312910i | −0.745879 | − | 0.666081i | \(-0.767970\pi\) |
0.203904 | + | 0.978991i | \(0.434637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.37044e6 | + | 5.20848e6i | −0.170239 | + | 0.202883i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.23717e7 | + | 7.14280e6i | 0.472237 | + | 0.272646i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.35159e7 | + | 5.90975e6i | −1.25383 | + | 0.221083i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.63302e7 | − | 1.68628e7i | −1.69889 | − | 0.618344i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.88581e7i | − | 1.03738i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.17213e7 | −0.413121 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.75649e6 | − | 1.58158e7i | 0.198949 | − | 0.546609i | −0.799595 | − | 0.600539i | \(-0.794953\pi\) |
0.998545 | + | 0.0539304i | \(0.0171749\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.12809e6 | + | 1.77403e7i | 0.106024 | + | 0.601292i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.74940e7 | − | 4.76210e7i | 0.914023 | − | 1.58313i | 0.105697 | − | 0.994398i | \(-0.466293\pi\) |
0.808326 | − | 0.588736i | \(-0.200374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.65303e7 | − | 1.38706e7i | −0.539074 | − | 0.452337i | 0.332147 | − | 0.943228i | \(-0.392227\pi\) |
−0.871221 | + | 0.490891i | \(0.836671\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.60040e6 | + | 4.50403e6i | 0.0831973 | + | 0.144102i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.11556e7 | − | 3.06496e7i | −0.350198 | − | 0.962161i | −0.982306 | − | 0.187281i | \(-0.940033\pi\) |
0.632108 | − | 0.774880i | \(-0.282190\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.11219e7 | − | 1.96110e6i | −0.342616 | − | 0.0604125i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.97877e7 | − | 1.66039e7i | 0.598247 | − | 0.501989i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00436e7 | − | 2.64003e7i | −0.298044 | − | 0.783431i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.70566e7 | + | 2.03273e7i | 0.496869 | + | 0.592146i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 799988. | − | 4.53696e6i | 0.0228792 | − | 0.129754i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.55838e7 | + | 9.31173e6i | −0.718417 | + | 0.261482i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.59223e7 | + | 1.49662e7i | −0.714808 | + | 0.412695i | −0.812839 | − | 0.582489i | \(-0.802079\pi\) |
0.0980306 | + | 0.995183i | \(0.468746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.22802e6 | − | 1.46350e6i | 0.0332562 | − | 0.0396331i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.99606e6 | + | 1.72977e6i | 0.0796921 | + | 0.0460103i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −581576. | + | 102548.i | −0.0151956 | + | 0.00267939i | −0.181241 | − | 0.983439i | \(-0.558011\pi\) |
0.166045 | + | 0.986118i | \(0.446900\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.29869e7 | − | 8.36656e6i | −0.590041 | − | 0.214757i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29821e7i | 0.579597i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.62208e7 | −0.401967 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.39383e6 | − | 1.20720e7i | 0.107001 | − | 0.293982i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.17242e6 | + | 5.20194e7i | 0.219531 | + | 1.24502i | 0.872869 | + | 0.487955i | \(0.162257\pi\) |
−0.653338 | + | 0.757066i | \(0.726632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.33494e6 | + | 4.04424e6i | −0.0549288 | + | 0.0951395i | −0.892182 | − | 0.451675i | \(-0.850827\pi\) |
0.837254 | + | 0.546815i | \(0.184160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.98237e7 | + | 2.50250e7i | 0.689668 | + | 0.578700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.73778e7 | − | 3.00992e7i | −0.395067 | − | 0.684276i | 0.598043 | − | 0.801464i | \(-0.295945\pi\) |
−0.993110 | + | 0.117188i | \(0.962612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.44099e6 | + | 2.31914e7i | 0.188672 | + | 0.518373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.59750e7 | + | 6.34337e6i | 0.790673 | + | 0.139417i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.44752e7 | − | 1.21461e7i | 0.312853 | − | 0.262515i | −0.472817 | − | 0.881161i | \(-0.656763\pi\) |
0.785670 | + | 0.618646i | \(0.212318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.68986e7 | − | 2.91857e7i | −0.784312 | − | 0.620367i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.68046e7 | − | 2.00269e7i | −0.351324 | − | 0.418691i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.13632e6 | + | 6.44437e6i | −0.0233679 | + | 0.132526i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.25663e7 | − | 4.57375e6i | 0.254219 | − | 0.0925282i | −0.211767 | − | 0.977320i | \(-0.567922\pi\) |
0.465986 | + | 0.884792i | \(0.345700\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.81359e7 | + | 1.04708e7i | −0.360960 | + | 0.208400i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.38890e6 | − | 5.23049e6i | 0.0859476 | − | 0.102428i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.03291e7 | + | 4.63780e7i | 1.54791 | + | 0.893688i | 0.998301 | + | 0.0582673i | \(0.0185576\pi\) |
0.549611 | + | 0.835420i | \(0.314776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.05663e7 | + | 3.62639e6i | −0.389998 | + | 0.0687672i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.89217e7 | − | 1.05266e7i | −0.539759 | − | 0.196456i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.63765e7i | 0.851884i | 0.904750 | + | 0.425942i | \(0.140057\pi\) | ||||
−0.904750 | + | 0.425942i | \(0.859943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.67575e7 | 0.483805 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.18755e7 | − | 8.75773e7i | 0.567363 | − | 1.55882i | −0.241242 | − | 0.970465i | \(-0.577555\pi\) |
0.808605 | − | 0.588352i | \(-0.200223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.83105e6 | + | 1.03844e7i | 0.0320861 | + | 0.181969i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.84302e7 | + | 3.19220e7i | −0.317977 | + | 0.550753i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.54686e7 | + | 5.49346e7i | 1.11220 | + | 0.933249i | 0.998185 | − | 0.0602298i | \(-0.0191834\pi\) |
0.114018 | + | 0.993479i | \(0.463628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.80338e7 | + | 6.58765e7i | 0.636268 | + | 1.10205i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.24699e7 | + | 3.42609e7i | 0.205441 | + | 0.564444i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.36590e7 | + | 4.17171e6i | 0.383888 | + | 0.0676898i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.41889e7 | + | 2.02969e7i | −0.386584 | + | 0.324383i | −0.815281 | − | 0.579066i | \(-0.803417\pi\) |
0.428696 | + | 0.903449i | \(0.358973\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.68669e7 | − | 2.16341e7i | 0.895243 | − | 0.340581i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.07945e7 | − | 4.86170e7i | −0.632658 | − | 0.753972i | 0.350534 | − | 0.936550i | \(-0.386000\pi\) |
−0.983191 | + | 0.182578i | \(0.941556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.08760e7 | + | 6.16808e7i | −0.166170 | + | 0.942399i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.82183e6 | + | 2.11897e6i | −0.0876383 | + | 0.0318977i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.35449e6 | − | 1.93672e6i | 0.0497557 | − | 0.0287265i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.50643e7 | − | 7.75406e7i | 0.950983 | − | 1.13334i | −0.0399793 | − | 0.999201i | \(-0.512729\pi\) |
0.990963 | − | 0.134137i | \(-0.0428264\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.80846e6 | + | 2.19882e6i | 0.0548560 | + | 0.0316711i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.54021e7 | − | 1.50587e7i | 1.21232 | − | 0.213765i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.20049e7 | − | 8.00913e6i | −0.307876 | − | 0.112058i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.03748e7i | 0.694713i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.11157e8 | −1.51110 | −0.755549 | − | 0.655092i | \(-0.772630\pi\) | ||||
−0.755549 | + | 0.655092i | \(0.772630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.36936e7 | − | 6.50975e7i | 0.317529 | − | 0.872405i | −0.673551 | − | 0.739141i | \(-0.735232\pi\) |
0.991081 | − | 0.133264i | \(-0.0425459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.53451e6 | + | 2.00452e7i | 0.0466991 | + | 0.264844i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.96549e7 | − | 5.13637e7i | 0.386304 | − | 0.669098i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.14522e8 | + | 9.60957e7i | 1.47098 | + | 1.23430i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.23868e7 | + | 2.14545e7i | 0.156887 | + | 0.271736i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.34585e7 | − | 6.44518e7i | −0.293001 | − | 0.805014i | −0.995624 | − | 0.0934512i | \(-0.970210\pi\) |
0.702623 | − | 0.711562i | \(-0.252012\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.00887e8 | − | 1.77891e7i | −1.24271 | − | 0.219124i | −0.486636 | − | 0.873605i | \(-0.661776\pi\) |
−0.756079 | + | 0.654481i | \(0.772887\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.89989e6 | − | 7.46789e6i | 0.108123 | − | 0.0907257i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.10626e8 | + | 6.17546e7i | 1.32560 | + | 0.739989i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.19709e7 | − | 8.57716e7i | −0.850675 | − | 1.01379i | −0.999688 | − | 0.0249595i | \(-0.992054\pi\) |
0.149014 | − | 0.988835i | \(-0.452390\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.70640e6 | − | 2.66913e7i | 0.0548748 | − | 0.311210i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.83127e7 | + | 2.12241e7i | −0.670737 | + | 0.244128i | −0.654865 | − | 0.755746i | \(-0.727275\pi\) |
−0.0158716 | + | 0.999874i | \(0.505052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.71920e6 | + | 992578.i | −0.0195095 | + | 0.0112638i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.21010e6 | + | 8.59266e6i | −0.0807270 | + | 0.0962067i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.52284e7 | − | 3.76596e7i | −0.720606 | − | 0.416042i | 0.0943698 | − | 0.995537i | \(-0.469916\pi\) |
−0.814976 | + | 0.579495i | \(0.803250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.18136e7 | + | 7.37287e6i | −0.455815 | + | 0.0803724i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.94702e7 | − | 2.16454e7i | −0.639742 | − | 0.232847i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.87368e7i | 0.305073i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.52194e8 | 1.59459 | 0.797296 | − | 0.603589i | \(-0.206263\pi\) | ||||
0.797296 | + | 0.603589i | \(0.206263\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.97619e7 | − | 8.17700e7i | 0.307767 | − | 0.845583i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.75401e6 | + | 3.83039e7i | 0.0689380 | + | 0.390967i | 0.999680 | + | 0.0252907i | \(0.00805114\pi\) |
−0.930742 | + | 0.365676i | \(0.880838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.28131e7 | + | 7.41545e7i | −0.431354 | + | 0.747127i | −0.996990 | − | 0.0775277i | \(-0.975297\pi\) |
0.565636 | + | 0.824655i | \(0.308631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.81111e7 | − | 1.51970e7i | −0.180130 | − | 0.151147i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.27398e7 | + | 1.25989e8i | 0.714202 | + | 1.23703i | 0.963266 | + | 0.268548i | \(0.0865438\pi\) |
−0.249064 | + | 0.968487i | \(0.580123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.50914e7 | − | 4.14634e7i | −0.146289 | − | 0.401926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.41007e7 | − | 1.30660e7i | −0.709185 | − | 0.125049i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.72495e7 | + | 4.80380e7i | −0.540988 | + | 0.453943i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.42841e6 | − | 9.87739e7i | −0.0133283 | − | 0.921640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.28123e6 | − | 3.91042e6i | −0.0302330 | − | 0.0360303i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.23849e7 | + | 1.83664e8i | −0.294670 | + | 1.67116i | 0.373872 | + | 0.927480i | \(0.378030\pi\) |
−0.668542 | + | 0.743675i | \(0.733081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.91952e6 | − | 3.61041e6i | 0.0891365 | − | 0.0324430i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.41900e8 | + | 8.19260e7i | −1.25933 | + | 0.727077i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.63264e7 | − | 3.13746e7i | 0.230763 | − | 0.275013i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.44836e8 | − | 8.36209e7i | −1.25397 | − | 0.723983i | −0.282078 | − | 0.959391i | \(-0.591024\pi\) |
−0.971896 | + | 0.235409i | \(0.924357\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.69145e6 | − | 827229.i | 0.0401218 | − | 0.00707456i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.82318e8 | − | 6.63584e7i | −1.54023 | − | 0.560598i | −0.574129 | − | 0.818765i | \(-0.694659\pi\) |
−0.966100 | + | 0.258167i | \(0.916881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.87922e7i | 0.574114i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.88334e6 | 0.0649972 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.07660e8 | − | 2.95793e8i | 0.876969 | − | 2.40945i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.90633e7 | − | 1.08113e8i | −0.153425 | − | 0.870116i | −0.960212 | − | 0.279273i | \(-0.909906\pi\) |
0.806787 | − | 0.590843i | \(-0.201205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.43158e7 | − | 2.47958e7i | 0.113842 | − | 0.197181i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.12783e8 | + | 9.46364e7i | 0.886218 | + | 0.743625i | 0.967448 | − | 0.253070i | \(-0.0814403\pi\) |
−0.0812298 | + | 0.996695i | \(0.525885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53704e7 | − | 4.39428e7i | −0.196994 | − | 0.341204i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.74183e6 | − | 2.67655e7i | −0.0747510 | − | 0.205377i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.11515e7 | − | 1.25459e7i | −0.539549 | − | 0.0951370i | −0.102769 | − | 0.994705i | \(-0.532770\pi\) |
−0.436780 | + | 0.899568i | \(0.643881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.39355e7 | − | 5.36483e7i | 0.479159 | − | 0.402062i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.72288e7 | − | 1.42353e8i | −0.201686 | − | 1.05442i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.03595e7 | + | 2.42635e7i | 0.149054 | + | 0.177636i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.16619e6 | + | 4.06415e7i | −0.0518581 | + | 0.294102i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.78235e8 | + | 6.48723e7i | −1.27494 | + | 0.464042i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.18148e8 | + | 6.82127e7i | −0.835435 | + | 0.482338i | −0.855710 | − | 0.517456i | \(-0.826879\pi\) |
0.0202752 | + | 0.999794i | \(0.493546\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.25515e7 | − | 5.07109e7i | 0.297447 | − | 0.354484i | −0.596534 | − | 0.802588i | \(-0.703456\pi\) |
0.893982 | + | 0.448104i | \(0.147900\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.10639e8 | + | 6.38774e7i | 0.764593 | + | 0.441438i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.37864e8 | − | 2.43091e7i | 0.941931 | − | 0.166088i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.81510e8 | − | 6.60641e7i | −1.22612 | − | 0.446271i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 6.48332e7i | − | 0.433026i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.15711e8 | −0.764177 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.55340e7 | − | 4.26793e7i | 0.101443 | − | 0.278712i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.20592e7 | + | 6.83911e7i | 0.0778745 | + | 0.441648i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.74756e7 | − | 4.75891e7i | 0.175461 | − | 0.303907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.79778e8 | + | 1.50851e8i | 1.13539 | + | 0.952703i | 0.999278 | − | 0.0379907i | \(-0.0120957\pi\) |
0.136109 | + | 0.990694i | \(0.456540\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.06631e7 | + | 5.31101e7i | 0.191521 | + | 0.331724i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.77048e6 | − | 7.61182e6i | −0.0171145 | − | 0.0470218i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.35585e8 | + | 2.39073e7i | 0.828418 | + | 0.146072i | 0.571751 | − | 0.820427i | \(-0.306264\pi\) |
0.256667 | + | 0.966500i | \(0.417376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.56192e7 | − | 7.18430e7i | 0.517433 | − | 0.434178i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.87177e7 | + | 9.83885e7i | 0.351006 | + | 0.588152i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.96957e8 | − | 2.34724e8i | −1.16465 | − | 1.38798i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −691939. | + | 3.92418e6i | −0.00404752 | + | 0.0229546i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.42537e8 | + | 5.18791e7i | −0.824824 | + | 0.300211i | −0.719733 | − | 0.694251i | \(-0.755736\pi\) |
−0.105091 | + | 0.994463i | \(0.533513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.76383e8 | + | 1.01835e8i | −1.00977 | + | 0.582990i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.55923e7 | − | 4.24173e7i | 0.201590 | − | 0.240245i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.86415e8 | + | 1.65362e8i | 1.60499 | + | 0.926639i | 0.990469 | + | 0.137736i | \(0.0439825\pi\) |
0.614517 | + | 0.788903i | \(0.289351\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.23581e7 | + | 7.46887e6i | −0.234850 | + | 0.0414104i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.42538e7 | + | 2.70262e7i | 0.407352 | + | 0.148264i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.84830e7i | 0.100331i | 0.998741 | + | 0.0501656i | \(0.0159749\pi\) | ||||
−0.998741 | + | 0.0501656i | \(0.984025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28016e8 | 0.687632 | 0.343816 | − | 0.939037i | \(-0.388280\pi\) | ||||
0.343816 | + | 0.939037i | \(0.388280\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.80394e7 | − | 7.70376e7i | 0.149041 | − | 0.409486i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.61953e7 | + | 2.61987e8i | 0.242993 | + | 1.37808i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.89897e7 | − | 6.75322e7i | 0.202966 | − | 0.351547i | −0.746517 | − | 0.665366i | \(-0.768275\pi\) |
0.949483 | + | 0.313819i | \(0.101609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.69682e7 | − | 6.45840e7i | −0.396530 | − | 0.332728i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.49336e8 | + | 2.58657e8i | 0.761439 | + | 1.31885i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.53980e6 | − | 9.72553e6i | −0.0178638 | − | 0.0490803i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.11578e7 | + | 3.73069e6i | 0.105682 | + | 0.0186347i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.31639e8 | − | 1.10458e8i | 0.650836 | − | 0.546116i | −0.256489 | − | 0.966547i | \(-0.582566\pi\) |
0.907324 | + | 0.420431i | \(0.138121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.76428e8 | − | 1.52442e8i | 0.863419 | − | 0.746033i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.13266e8 | − | 1.34985e8i | −0.548702 | − | 0.653918i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.31073e7 | + | 1.31048e8i | −0.110812 | + | 0.628444i | 0.877927 | + | 0.478794i | \(0.158926\pi\) |
−0.988739 | + | 0.149650i | \(0.952185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.03566e7 | − | 2.19680e7i | 0.286533 | − | 0.104289i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.05483e8 | + | 6.09005e7i | −0.495745 | + | 0.286219i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.10976e6 | − | 7.28133e6i | 0.0284278 | − | 0.0338790i | −0.751643 | − | 0.659570i | \(-0.770738\pi\) |
0.780071 | + | 0.625691i | \(0.215183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.32996e8 | + | 1.34521e8i | 1.07331 | + | 0.619677i | 0.929084 | − | 0.369868i | \(-0.120597\pi\) |
0.144227 | + | 0.989545i | \(0.453930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.24871e7 | + | 5.72836e6i | −0.148170 | + | 0.0261263i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.31952e7 | − | 1.57218e7i | −0.195060 | − | 0.0709962i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.24763e8i | 0.557854i | 0.960312 | + | 0.278927i | \(0.0899788\pi\) | ||||
−0.960312 | + | 0.278927i | \(0.910021\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.48180e8 | −0.656052 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.84661e7 | + | 1.05685e8i | −0.168638 | + | 0.463328i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.19266e7 | + | 4.07916e8i | 0.312254 | + | 1.77088i | 0.587221 | + | 0.809427i | \(0.300222\pi\) |
−0.274967 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.18393e7 | − | 3.78267e7i | 0.0938886 | − | 0.162620i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.78802e8 | + | 1.50033e8i | 0.761234 | + | 0.638751i | 0.938448 | − | 0.345421i | \(-0.112264\pi\) |
−0.177214 | + | 0.984172i | \(0.556708\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.87719e7 | − | 1.53757e8i | −0.374286 | − | 0.648282i | 0.615934 | − | 0.787798i | \(-0.288779\pi\) |
−0.990220 | + | 0.139516i | \(0.955445\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.33494e8 | + | 3.66772e8i | 0.557426 | + | 1.53151i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.49348e7 | + | 4.39668e6i | 0.103120 | + | 0.0181828i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.44257e8 | − | 1.21046e8i | 0.590876 | − | 0.495804i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.46998e7 | − | 9.10464e7i | 0.0596360 | − | 0.369369i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.51661e7 | − | 1.80742e7i | −0.0609427 | − | 0.0726286i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00033e7 | − | 5.67314e7i | 0.0398157 | − | 0.225806i | −0.958407 | − | 0.285406i | \(-0.907871\pi\) |
0.998222 | + | 0.0596002i | \(0.0189826\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.52780e8 | − | 5.56075e7i | 0.602360 | − | 0.219241i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.07442e7 | − | 2.35237e7i | 0.159127 | − | 0.0918722i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.62617e7 | − | 1.14720e8i | 0.372422 | − | 0.443835i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.03804e8 | − | 1.17666e8i | −0.781107 | − | 0.450972i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.17444e8 | + | 7.36066e7i | −1.58498 | + | 0.279475i | −0.895578 | − | 0.444904i | \(-0.853238\pi\) |
−0.689402 | + | 0.724379i | \(0.742127\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.15666e8 | − | 1.14893e8i | −1.18740 | − | 0.432176i | −0.328587 | − | 0.944474i | \(-0.606572\pi\) |
−0.858808 | + | 0.512297i | \(0.828795\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 7.68810e7i | − | 0.286510i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.54236e8 | 1.67714 | 0.838570 | − | 0.544795i | \(-0.183392\pi\) | ||||
0.838570 | + | 0.544795i | \(0.183392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.49581e7 | − | 1.23521e8i | 0.164465 | − | 0.451864i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.23626e7 | + | 2.96963e8i | 0.189792 | + | 1.07636i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.53576e8 | − | 2.66002e8i | 0.551550 | − | 0.955312i | −0.446613 | − | 0.894727i | \(-0.647370\pi\) |
0.998163 | − | 0.0605852i | \(-0.0192967\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.91085e7 | + | 4.12069e7i | 0.174756 | + | 0.146638i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.11989e7 | − | 5.40381e7i | −0.110013 | − | 0.190548i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.48749e7 | − | 1.50768e8i | −0.191742 | − | 0.526807i | 0.806149 | − | 0.591712i | \(-0.201548\pi\) |
−0.997891 | + | 0.0649050i | \(0.979326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.86882e8 | − | 5.05850e7i | −0.993342 | − | 0.175153i | −0.346724 | − | 0.937967i | \(-0.612706\pi\) |
−0.646618 | + | 0.762814i | \(0.723817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.15598e8 | − | 9.69986e7i | 0.396654 | − | 0.332832i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.75729e7 | − | 8.29369e7i | 0.229778 | − | 0.282022i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.98339e8 | − | 2.36371e8i | −0.668391 | − | 0.796557i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.31231e7 | − | 7.44248e7i | 0.0438286 | − | 0.248565i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.12942e8 | − | 7.75046e7i | 0.704845 | − | 0.256543i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.66525e8 | + | 2.69348e8i | −1.53049 | + | 0.883627i | −0.531147 | + | 0.847279i | \(0.678239\pi\) |
−0.999339 | + | 0.0363475i | \(0.988428\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.95616e8 | − | 2.33126e8i | 0.636051 | − | 0.758016i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.40832e8 | + | 2.54515e8i | 1.42072 | + | 0.820251i | 0.996360 | − | 0.0852450i | \(-0.0271673\pi\) |
0.424356 | + | 0.905496i | \(0.360501\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.14441e8 | + | 9.07098e7i | −1.64334 | + | 0.289764i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.91526e8 | − | 1.06107e8i | −0.923072 | − | 0.335971i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.66985e8i | − | 0.837962i | −0.907995 | − | 0.418981i | \(-0.862387\pi\) | ||
0.907995 | − | 0.418981i | \(-0.137613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.73230e6 | 0.0240568 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.39295e8 | − | 3.82710e8i | 0.429601 | − | 1.18032i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.89786e6 | − | 2.77772e7i | −0.0149744 | − | 0.0849240i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.28318e7 | − | 1.43469e8i | 0.251051 | − | 0.434834i | −0.712764 | − | 0.701404i | \(-0.752557\pi\) |
0.963816 | + | 0.266570i | \(0.0858903\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.70236e7 | − | 6.46304e7i | −0.231432 | − | 0.194195i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.42867e7 | + | 7.67068e7i | 0.131922 | + | 0.228496i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.84562e7 | + | 2.43031e8i | 0.261234 | + | 0.717735i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.12413e8 | − | 3.74541e7i | −0.621941 | − | 0.109665i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.64789e8 | + | 3.06094e8i | −1.05898 | + | 0.888588i | −0.994009 | − | 0.109299i | \(-0.965139\pi\) |
−0.0649695 | + | 0.997887i | \(0.520695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.71183e7 | − | 1.29052e7i | −0.106837 | − | 0.0371450i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.72890e7 | − | 3.25217e7i | −0.0778789 | − | 0.0928124i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.12379e8 | + | 6.37336e8i | −0.318001 | + | 1.80347i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.06996e8 | + | 1.11737e8i | −0.861378 | + | 0.313516i | −0.734671 | − | 0.678424i | \(-0.762663\pi\) |
−0.126708 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.98388e8 | + | 1.14539e8i | −0.551959 | + | 0.318673i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.03616e8 | + | 4.81011e8i | −1.11353 | + | 1.32705i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.77232e7 | + | 2.17795e7i | 0.103202 | + | 0.0595840i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.98623e7 | + | 7.02880e6i | −0.108145 | + | 0.0190688i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.27355e8 | − | 1.91942e8i | −1.41879 | − | 0.516396i | −0.485090 | − | 0.874464i | \(-0.661213\pi\) |
−0.933695 | + | 0.358069i | \(0.883435\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.03979e8i | − | 1.07784i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.63721e8 | 0.962394 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.22845e7 | + | 2.26075e8i | −0.215926 | + | 0.593251i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.76851e7 | − | 2.13723e8i | −0.0980769 | − | 0.556222i | −0.993761 | − | 0.111531i | \(-0.964425\pi\) |
0.895684 | − | 0.444691i | \(-0.146686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.82720e8 | − | 3.16480e8i | 0.471633 | − | 0.816891i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.48724e8 | + | 2.92614e8i | 0.892749 | + | 0.749105i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.18782e7 | − | 5.52146e7i | −0.0809434 | − | 0.140198i | 0.822712 | − | 0.568458i | \(-0.192460\pi\) |
−0.903655 | + | 0.428260i | \(0.859127\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.93344e7 | + | 5.31208e7i | 0.0486932 | + | 0.133783i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.58673e7 | − | 1.16142e7i | −0.164538 | − | 0.0290126i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.46050e8 | − | 2.90370e8i | 0.857443 | − | 0.719480i | −0.103973 | − | 0.994580i | \(-0.533156\pi\) |
0.961416 | + | 0.275100i | \(0.0887111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.25388e7 | − | 2.37400e8i | 0.202863 | − | 0.583479i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.07292e8 | − | 3.66216e8i | −0.749177 | − | 0.892834i | 0.247935 | − | 0.968777i | \(-0.420248\pi\) |
−0.997112 | + | 0.0759422i | \(0.975804\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.42479e6 | + | 1.94229e7i | −0.00828256 | + | 0.0469727i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.09826e8 | − | 7.63705e7i | 0.503383 | − | 0.183216i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.01674e8 | + | 2.89641e8i | −1.19392 | + | 0.689311i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.41730e8 | − | 4.07258e8i | 0.806795 | − | 0.961501i | −0.193011 | − | 0.981197i | \(-0.561825\pi\) |
0.999806 | + | 0.0196960i | \(0.00626984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.54879e8 | − | 1.47154e8i | −0.596965 | − | 0.344658i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.09586e8 | + | 1.93229e7i | −0.254632 | + | 0.0448986i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.26422e8 | + | 2.64396e8i | 1.67456 | + | 0.609491i | 0.992549 | − | 0.121848i | \(-0.0388820\pi\) |
0.682014 | + | 0.731339i | \(0.261104\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.48365e8i | 0.568022i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.59652e8 | −1.04298 | −0.521489 | − | 0.853258i | \(-0.674623\pi\) | ||||
−0.521489 | + | 0.853258i | \(0.674623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.53357e7 | + | 9.70842e7i | −0.0795501 | + | 0.218562i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.33855e6 | − | 4.72902e7i | −0.0186254 | − | 0.105630i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.79116e8 | − | 3.10239e8i | 0.396962 | − | 0.687559i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.08851e8 | − | 2.59157e8i | −0.679156 | − | 0.569880i | 0.236603 | − | 0.971606i | \(-0.423966\pi\) |
−0.915760 | + | 0.401726i | \(0.868410\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.00204e8 | − | 3.46764e8i | −0.436828 | − | 0.756608i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.32298e7 | − | 1.46248e8i | −0.115243 | − | 0.316629i | 0.868639 | − | 0.495446i | \(-0.164995\pi\) |
−0.983882 | + | 0.178817i | \(0.942773\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.82146e8 | + | 8.50153e7i | 1.03579 | + | 0.182638i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.89324e7 | − | 3.26682e7i | 0.0829943 | − | 0.0696405i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.33953e8 | + | 2.72088e8i | 0.706435 | + | 0.575569i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.06696e8 | − | 3.65506e8i | −0.643806 | − | 0.767259i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.12942e7 | + | 3.47616e8i | −0.127683 | + | 0.724128i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.24322e8 | + | 4.52493e7i | −0.257002 | + | 0.0935412i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.65510e8 | + | 3.26498e8i | −1.16016 | + | 0.669816i | −0.951341 | − | 0.308139i | \(-0.900294\pi\) |
−0.208815 | + | 0.977955i | \(0.566961\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.13938e7 | − | 6.12488e7i | 0.104636 | − | 0.124700i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.75089e8 | + | 2.74293e8i | 0.959944 | + | 0.554224i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.08185e8 | − | 1.07240e8i | 1.21960 | − | 0.215048i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.00050e7 | + | 3.64151e6i | 0.0199119 | + | 0.00724736i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.18018e8i | 0.233117i | 0.993184 | + | 0.116558i | \(0.0371862\pi\) | ||||
−0.993184 | + | 0.116558i | \(0.962814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.51378e8 | 0.492819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.47421e6 | − | 1.77877e7i | 0.0125976 | − | 0.0346117i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.19684e7 | − | 1.24589e8i | −0.0424279 | − | 0.240620i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.44049e8 | + | 2.49501e8i | −0.276136 | + | 0.478282i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.91092e8 | + | 1.60345e8i | 0.363598 | + | 0.305095i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.14574e8 | + | 8.91268e8i | 0.971857 | + | 1.68331i | 0.689940 | + | 0.723866i | \(0.257637\pi\) |
0.281917 | + | 0.959439i | \(0.409030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23069e7 | + | 8.87624e7i | 0.0605665 | + | 0.166405i | 0.966285 | − | 0.257474i | \(-0.0828903\pi\) |
−0.905719 | + | 0.423879i | \(0.860668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.24348e8 | + | 9.24567e7i | 0.975771 | + | 0.172055i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.41651e6 | − | 5.38409e6i | 0.0118529 | − | 0.00994580i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.48516e8 | + | 1.20851e8i | 1.37257 | + | 0.221607i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.76135e8 | − | 2.09910e8i | −0.320623 | − | 0.382103i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.43559e7 | − | 3.64980e8i | 0.116294 | − | 0.659538i | −0.869807 | − | 0.493392i | \(-0.835757\pi\) |
0.986101 | − | 0.166146i | \(-0.0531322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.87342e8 | + | 2.50172e8i | −1.23303 | + | 0.448786i | −0.874634 | − | 0.484784i | \(-0.838898\pi\) |
−0.358395 | + | 0.933570i | \(0.616676\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.67705e8 | − | 9.68248e7i | 0.298666 | − | 0.172435i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.92893e7 | − | 1.18328e8i | 0.175544 | − | 0.209205i | −0.671097 | − | 0.741369i | \(-0.734177\pi\) |
0.846641 | + | 0.532164i | \(0.178621\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.39830e8 | − | 1.38466e8i | −0.420959 | − | 0.243041i | 0.274528 | − | 0.961579i | \(-0.411478\pi\) |
−0.695488 | + | 0.718538i | \(0.744812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.85723e8 | − | 3.27479e7i | 0.323640 | − | 0.0570664i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.14538e8 | − | 1.14482e8i | −0.544174 | − | 0.198063i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.03427e7i | − | 0.0864723i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.18306e8 | 1.22499 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.02876e8 | − | 5.57398e8i | 0.343515 | − | 0.943799i | −0.640851 | − | 0.767665i | \(-0.721419\pi\) |
0.984366 | − | 0.176134i | \(-0.0563592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.48338e7 | + | 3.10978e8i | 0.0921850 | + | 0.522807i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.62235e8 | + | 6.27409e8i | −0.604655 | + | 1.04729i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.83648e7 | − | 3.21919e7i | −0.0635861 | − | 0.0533551i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.93143e8 | + | 5.07738e8i | 0.482424 | + | 0.835583i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.96674e8 | − | 5.40358e8i | −0.321384 | − | 0.882996i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.04222e8 | + | 1.83771e7i | 0.169110 | + | 0.0298187i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.21353e7 | + | 5.21377e7i | −0.100113 | + | 0.0840050i | −0.691470 | − | 0.722405i | \(-0.743037\pi\) |
0.591357 | + | 0.806410i | \(0.298592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.22907e7 | − | 6.05185e7i | −0.0836617 | − | 0.0968255i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.51435e8 | + | 7.76349e8i | 1.03497 | + | 1.23343i | 0.971893 | + | 0.235422i | \(0.0756473\pi\) |
0.0630781 | + | 0.998009i | \(0.479908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.24825e8 | + | 7.07918e8i | −0.196935 | + | 1.11687i | 0.712702 | + | 0.701467i | \(0.247471\pi\) |
−0.909637 | + | 0.415405i | \(0.863640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.23496e8 | + | 1.90537e8i | −0.820171 | + | 0.298518i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.55263e8 | − | 3.20581e8i | 0.863905 | − | 0.498776i | −0.00141285 | − | 0.999999i | \(-0.500450\pi\) |
0.865318 | + | 0.501223i | \(0.167116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.14370e8 | + | 2.55477e8i | −0.331220 | + | 0.394732i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.23644e8 | + | 7.13860e7i | 0.189721 | + | 0.109536i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.57398e8 | + | 8.06517e7i | −0.697004 | + | 0.122901i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.71283e8 | − | 6.23417e7i | −0.259214 | − | 0.0943462i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.90539e8i | 0.586979i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.68332e8 | 0.699085 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.05304e8 | − | 5.64068e8i | 0.304368 | − | 0.836244i | −0.689360 | − | 0.724419i | \(-0.742108\pi\) |
0.993728 | − | 0.111825i | \(-0.0356696\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.43654e7 | + | 3.08322e8i | 0.0800490 | + | 0.453981i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.93538e8 | − | 1.02804e9i | 0.868002 | − | 1.50342i | 0.00396761 | − | 0.999992i | \(-0.498737\pi\) |
0.864035 | − | 0.503432i | \(-0.167930\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.42884e8 | − | 2.03804e8i | −0.352790 | − | 0.296026i | 0.449119 | − | 0.893472i | \(-0.351738\pi\) |
−0.801909 | + | 0.597446i | \(0.796182\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.76127e7 | + | 1.17109e8i | 0.0975435 | + | 0.168950i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.54042e7 | + | 1.52222e8i | 0.0793911 | + | 0.218125i | 0.973038 | − | 0.230646i | \(-0.0740840\pi\) |
−0.893647 | + | 0.448771i | \(0.851862\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.90944e8 | − | 1.04199e8i | −0.841087 | − | 0.148306i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.17543e7 | − | 7.69910e7i | 0.129716 | − | 0.108845i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.59529e8 | − | 2.14565e8i | 0.504869 | − | 0.301303i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.84883e7 | + | 9.35387e7i | 0.109480 | + | 0.130474i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17536e8 | + | 6.66578e8i | −0.162852 | + | 0.923579i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.33612e8 | + | 1.94219e8i | −0.734424 | + | 0.267308i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.45969e7 | + | 3.15215e7i | −0.0746438 | + | 0.0430956i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.30299e8 | + | 7.51161e8i | −0.856018 | + | 1.02016i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.33827e7 | + | 5.39145e7i | 0.125986 | + | 0.0727378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.47053e8 | − | 1.49358e8i | 1.13524 | − | 0.200174i | 0.425719 | − | 0.904855i | \(-0.360021\pi\) |
0.709524 | + | 0.704681i | \(0.248910\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.54657e8 | + | 1.65481e8i | 0.605329 | + | 0.220322i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.52488e8i | − | 0.730748i | −0.930861 | − | 0.365374i | \(-0.880941\pi\) | ||
0.930861 | − | 0.365374i | \(-0.119059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.52723e8 | 0.594868 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.97313e7 | + | 2.19060e8i | −0.104080 | + | 0.285956i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.41982e8 | − | 8.05218e8i | −0.184130 | − | 1.04425i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.29474e8 | + | 3.97461e8i | −0.295656 | + | 0.512092i | −0.975137 | − | 0.221601i | \(-0.928872\pi\) |
0.679481 | + | 0.733693i | \(0.262205\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.56425e8 | − | 2.15166e8i | −0.328233 | − | 0.275420i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.50159e8 | − | 1.12611e9i | −0.826827 | − | 1.43211i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.82218e7 | − | 7.75388e7i | −0.0356582 | − | 0.0979702i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.97434e8 | − | 5.24457e7i | −0.373380 | − | 0.0658370i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.66549e8 | + | 6.43211e8i | −0.956077 | + | 0.802244i | −0.980310 | − | 0.197462i | \(-0.936730\pi\) |
0.0242333 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.47578e8 | + | 1.04739e8i | −0.678573 | + | 0.129795i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.02969e8 | − | 8.37766e8i | −0.865549 | − | 1.03152i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.69063e7 | − | 9.58804e7i | 0.0206830 | − | 0.117299i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.40992e8 | − | 2.69699e8i | 0.900730 | − | 0.327839i | 0.150185 | − | 0.988658i | \(-0.452013\pi\) |
0.750545 | + | 0.660819i | \(0.229791\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.71671e8 | + | 2.14584e8i | −0.448913 | + | 0.259180i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.53611e8 | − | 4.21417e8i | 0.424382 | − | 0.505759i | −0.510911 | − | 0.859634i | \(-0.670692\pi\) |
0.935293 | + | 0.353875i | \(0.115136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.00464e9 | − | 5.80027e8i | −1.19805 | − | 0.691692i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.24564e8 | − | 5.72294e7i | 0.384596 | − | 0.0678147i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.29502e8 | − | 1.56326e8i | −0.505726 | − | 0.184069i | 0.0765415 | − | 0.997066i | \(-0.475612\pi\) |
−0.582268 | + | 0.812997i | \(0.697834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.44776e8i | − | 0.403402i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.48695e8 | −0.754221 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.32818e8 | − | 1.18916e9i | 0.500065 | − | 1.37392i | −0.391147 | − | 0.920328i | \(-0.627921\pi\) |
0.891211 | − | 0.453588i | \(-0.149856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.50309e7 | − | 1.41957e8i | −0.0287387 | − | 0.162985i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.12305e8 | + | 1.94518e8i | −0.128134 | + | 0.221934i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.55479e7 | − | 6.33922e7i | −0.0856577 | − | 0.0718754i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.34039e8 | + | 2.32162e8i | 0.151029 | + | 0.261590i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.48123e8 | + | 4.06965e8i | 0.165861 | + | 0.455699i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.73980e8 | − | 3.06773e7i | −0.193605 | − | 0.0341378i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.98276e8 | − | 1.66373e8i | 0.219275 | − | 0.183994i | −0.526532 | − | 0.850155i | \(-0.676508\pi\) |
0.745808 | + | 0.666161i | \(0.232064\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.61714e8 | + | 8.12321e6i | −0.617368 | + | 0.00892804i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.14728e8 | − | 1.36728e8i | −0.125318 | − | 0.149348i | 0.699737 | − | 0.714400i | \(-0.253300\pi\) |
−0.825055 | + | 0.565052i | \(0.808856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.96170e8 | − | 1.11254e9i | 0.212958 | − | 1.20775i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.95920e8 | − | 1.80500e8i | 0.535054 | − | 0.194744i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.02575e9 | − | 5.92216e8i | 1.09991 | − | 0.635033i | 0.163713 | − | 0.986508i | \(-0.447653\pi\) |
0.936197 | + | 0.351475i | \(0.114320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.46695e7 | − | 2.94000e7i | 0.0262914 | − | 0.0313328i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.68920e7 | + | 3.86201e7i | 0.0708544 | + | 0.0409078i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.92242e8 | + | 1.04428e8i | −0.623503 | + | 0.109940i | −0.476469 | − | 0.879191i | \(-0.658084\pi\) |
−0.147034 | + | 0.989131i | \(0.546973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.91143e8 | − | 1.05968e8i | −0.304648 | − | 0.110883i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.41476e8i | 0.563155i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.04187e9 | −2.11077 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.54552e8 | + | 1.79837e9i | −0.672548 | + | 1.84781i | −0.164749 | + | 0.986335i | \(0.552682\pi\) |
−0.507799 | + | 0.861476i | \(0.669541\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.03375e8 | + | 5.86267e8i | 0.105576 | + | 0.598753i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.07080e8 | + | 1.85469e8i | −0.108703 | + | 0.188279i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.61974e8 | + | 8.07192e8i | 0.970684 | + | 0.814501i | 0.982658 | − | 0.185428i | \(-0.0593671\pi\) |
−0.0119739 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.05321e7 | − | 1.04845e8i | −0.0607141 | − | 0.105160i |
(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 | 76.7.j.a.13.7 | ✓ | 60 | |
19.3 | odd | 18 | inner | 76.7.j.a.41.7 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.j.a.13.7 | ✓ | 60 | 1.1 | even | 1 | trivial | |
76.7.j.a.41.7 | yes | 60 | 19.3 | odd | 18 | inner |