Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(68,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.68");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.c (of order \(2\), degree \(1\), 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: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 68.4 | ||
Character | \(\chi\) | \(=\) | 69.68 |
Dual form | 69.6.c.b.68.30 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 9.59549i | − | 1.69626i | −0.529789 | − | 0.848129i | \(-0.677729\pi\) | ||
0.529789 | − | 0.848129i | \(-0.322271\pi\) | |||||||
\(3\) | −8.65480 | − | 12.9651i | −0.555205 | − | 0.831713i | ||||
\(4\) | −60.0734 | −1.87729 | ||||||||
\(5\) | 42.3345 | 0.757303 | 0.378652 | − | 0.925539i | \(-0.376388\pi\) | ||||
0.378652 | + | 0.925539i | \(0.376388\pi\) | |||||||
\(6\) | −124.407 | + | 83.0470i | −1.41080 | + | 0.941772i | ||||
\(7\) | 238.780i | 1.84185i | 0.389744 | + | 0.920923i | \(0.372564\pi\) | ||||
−0.389744 | + | 0.920923i | \(0.627436\pi\) | |||||||
\(8\) | 269.378i | 1.48812i | ||||||||
\(9\) | −93.1890 | + | 224.421i | −0.383494 | + | 0.923543i | ||||
\(10\) | − | 406.221i | − | 1.28458i | ||||||
\(11\) | −261.465 | −0.651526 | −0.325763 | − | 0.945451i | \(-0.605621\pi\) | ||||
−0.325763 | + | 0.945451i | \(0.605621\pi\) | |||||||
\(12\) | 519.923 | + | 778.859i | 1.04228 | + | 1.56137i | ||||
\(13\) | −36.2446 | −0.0594819 | −0.0297409 | − | 0.999558i | \(-0.509468\pi\) | ||||
−0.0297409 | + | 0.999558i | \(0.509468\pi\) | |||||||
\(14\) | 2291.21 | 3.12425 | ||||||||
\(15\) | −366.397 | − | 548.873i | −0.420459 | − | 0.629859i | ||||
\(16\) | 662.466 | 0.646939 | ||||||||
\(17\) | −1880.68 | −1.57831 | −0.789155 | − | 0.614194i | \(-0.789481\pi\) | ||||
−0.789155 | + | 0.614194i | \(0.789481\pi\) | |||||||
\(18\) | 2153.43 | + | 894.194i | 1.56657 | + | 0.650505i | ||||
\(19\) | 1308.83i | 0.831762i | 0.909419 | + | 0.415881i | \(0.136527\pi\) | ||||
−0.909419 | + | 0.415881i | \(0.863473\pi\) | |||||||
\(20\) | −2543.18 | −1.42168 | ||||||||
\(21\) | 3095.82 | − | 2066.60i | 1.53189 | − | 1.02260i | ||||
\(22\) | 2508.89i | 1.10516i | ||||||||
\(23\) | 666.102 | − | 2447.99i | 0.262555 | − | 0.964917i | ||||
\(24\) | 3492.52 | − | 2331.41i | 1.23769 | − | 0.826211i | ||||
\(25\) | −1332.79 | −0.426492 | ||||||||
\(26\) | 347.784i | 0.100897i | ||||||||
\(27\) | 3716.18 | − | 734.110i | 0.981041 | − | 0.193799i | ||||
\(28\) | − | 14344.4i | − | 3.45769i | ||||||
\(29\) | 2237.25i | 0.493992i | 0.969017 | + | 0.246996i | \(0.0794434\pi\) | ||||
−0.969017 | + | 0.246996i | \(0.920557\pi\) | |||||||
\(30\) | −5266.70 | + | 3515.76i | −1.06840 | + | 0.713207i | ||||
\(31\) | −3176.90 | −0.593744 | −0.296872 | − | 0.954917i | \(-0.595943\pi\) | ||||
−0.296872 | + | 0.954917i | \(0.595943\pi\) | |||||||
\(32\) | 2263.42i | 0.390741i | ||||||||
\(33\) | 2262.93 | + | 3389.93i | 0.361731 | + | 0.541883i | ||||
\(34\) | 18046.0i | 2.67722i | ||||||||
\(35\) | 10108.7i | 1.39484i | ||||||||
\(36\) | 5598.18 | − | 13481.7i | 0.719931 | − | 1.73376i | ||||
\(37\) | − | 11958.2i | − | 1.43602i | −0.696033 | − | 0.718010i | \(-0.745053\pi\) | ||
0.696033 | − | 0.718010i | \(-0.254947\pi\) | |||||||
\(38\) | 12558.9 | 1.41088 | ||||||||
\(39\) | 313.689 | + | 469.915i | 0.0330247 | + | 0.0494719i | ||||
\(40\) | 11404.0i | 1.12696i | ||||||||
\(41\) | 13987.9i | 1.29955i | 0.760125 | + | 0.649777i | \(0.225138\pi\) | ||||
−0.760125 | + | 0.649777i | \(0.774862\pi\) | |||||||
\(42\) | −19830.0 | − | 29705.9i | −1.73460 | − | 2.59848i | ||||
\(43\) | 11520.1i | 0.950133i | 0.879950 | + | 0.475067i | \(0.157576\pi\) | ||||
−0.879950 | + | 0.475067i | \(0.842424\pi\) | |||||||
\(44\) | 15707.1 | 1.22311 | ||||||||
\(45\) | −3945.12 | + | 9500.76i | −0.290421 | + | 0.699403i | ||||
\(46\) | −23489.7 | − | 6391.57i | −1.63675 | − | 0.445362i | ||||
\(47\) | − | 104.625i | − | 0.00690864i | −0.999994 | − | 0.00345432i | \(-0.998900\pi\) | ||
0.999994 | − | 0.00345432i | \(-0.00109955\pi\) | |||||||
\(48\) | −5733.51 | − | 8588.96i | −0.359184 | − | 0.538068i | ||||
\(49\) | −40209.1 | −2.39240 | ||||||||
\(50\) | 12788.7i | 0.723440i | ||||||||
\(51\) | 16276.9 | + | 24383.2i | 0.876286 | + | 1.31270i | ||||
\(52\) | 2177.34 | 0.111665 | ||||||||
\(53\) | −3042.21 | −0.148765 | −0.0743823 | − | 0.997230i | \(-0.523699\pi\) | ||||
−0.0743823 | + | 0.997230i | \(0.523699\pi\) | |||||||
\(54\) | −7044.15 | − | 35658.6i | −0.328734 | − | 1.66410i | ||||
\(55\) | −11069.0 | −0.493403 | ||||||||
\(56\) | −64322.2 | −2.74089 | ||||||||
\(57\) | 16969.1 | − | 11327.7i | 0.691788 | − | 0.461799i | ||||
\(58\) | 21467.5 | 0.837938 | ||||||||
\(59\) | − | 42246.8i | − | 1.58003i | −0.613090 | − | 0.790013i | \(-0.710074\pi\) | ||
0.613090 | − | 0.790013i | \(-0.289926\pi\) | |||||||
\(60\) | 22010.7 | + | 32972.7i | 0.789325 | + | 1.18243i | ||||
\(61\) | − | 19631.7i | − | 0.675511i | −0.941234 | − | 0.337755i | \(-0.890332\pi\) | ||
0.941234 | − | 0.337755i | \(-0.109668\pi\) | |||||||
\(62\) | 30483.9i | 1.00714i | ||||||||
\(63\) | −53587.3 | − | 22251.7i | −1.70103 | − | 0.706337i | ||||
\(64\) | 42917.5 | 1.30974 | ||||||||
\(65\) | −1534.40 | −0.0450458 | ||||||||
\(66\) | 32528.0 | − | 21713.9i | 0.919174 | − | 0.613589i | ||||
\(67\) | 53147.1i | 1.44641i | 0.690631 | + | 0.723207i | \(0.257333\pi\) | ||||
−0.690631 | + | 0.723207i | \(0.742667\pi\) | |||||||
\(68\) | 112979. | 2.96295 | ||||||||
\(69\) | −37503.5 | + | 12550.8i | −0.948306 | + | 0.317356i | ||||
\(70\) | 96997.5 | 2.36600 | ||||||||
\(71\) | 7483.69i | 0.176185i | 0.996112 | + | 0.0880926i | \(0.0280772\pi\) | ||||
−0.996112 | + | 0.0880926i | \(0.971923\pi\) | |||||||
\(72\) | −60454.1 | − | 25103.1i | −1.37434 | − | 0.570684i | ||||
\(73\) | −3498.30 | −0.0768333 | −0.0384167 | − | 0.999262i | \(-0.512231\pi\) | ||||
−0.0384167 | + | 0.999262i | \(0.512231\pi\) | |||||||
\(74\) | −114744. | −2.43586 | ||||||||
\(75\) | 11535.0 | + | 17279.7i | 0.236790 | + | 0.354719i | ||||
\(76\) | − | 78625.9i | − | 1.56146i | ||||||
\(77\) | − | 62432.7i | − | 1.20001i | ||||||
\(78\) | 4509.07 | − | 3010.00i | 0.0839171 | − | 0.0560184i | ||||
\(79\) | − | 21637.3i | − | 0.390063i | −0.980797 | − | 0.195031i | \(-0.937519\pi\) | ||
0.980797 | − | 0.195031i | \(-0.0624808\pi\) | |||||||
\(80\) | 28045.2 | 0.489929 | ||||||||
\(81\) | −41680.6 | − | 41827.2i | −0.705865 | − | 0.708347i | ||||
\(82\) | 134221. | 2.20438 | ||||||||
\(83\) | 40321.6 | 0.642455 | 0.321228 | − | 0.947002i | \(-0.395905\pi\) | ||||
0.321228 | + | 0.947002i | \(0.395905\pi\) | |||||||
\(84\) | −185976. | + | 124147.i | −2.87581 | + | 1.91973i | ||||
\(85\) | −79617.7 | −1.19526 | ||||||||
\(86\) | 110541. | 1.61167 | ||||||||
\(87\) | 29006.2 | − | 19362.9i | 0.410860 | − | 0.274267i | ||||
\(88\) | − | 70433.0i | − | 0.969548i | ||||||
\(89\) | −25017.5 | −0.334788 | −0.167394 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167394 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(90\) | 91164.5 | + | 37855.3i | 1.18637 | + | 0.492630i | ||||
\(91\) | − | 8654.49i | − | 0.109556i | ||||||
\(92\) | −40015.0 | + | 147059.i | −0.492894 | + | 1.81143i | ||||
\(93\) | 27495.4 | + | 41188.9i | 0.329650 | + | 0.493825i | ||||
\(94\) | −1003.93 | −0.0117188 | ||||||||
\(95\) | 55408.7i | 0.629896i | ||||||||
\(96\) | 29345.5 | − | 19589.4i | 0.324985 | − | 0.216942i | ||||
\(97\) | 86126.2i | 0.929407i | 0.885466 | + | 0.464703i | \(0.153839\pi\) | ||||
−0.885466 | + | 0.464703i | \(0.846161\pi\) | |||||||
\(98\) | 385826.i | 4.05813i | ||||||||
\(99\) | 24365.7 | − | 58678.3i | 0.249856 | − | 0.601713i | ||||
\(100\) | 80065.0 | 0.800650 | ||||||||
\(101\) | − | 33574.1i | − | 0.327493i | −0.986502 | − | 0.163746i | \(-0.947642\pi\) | ||
0.986502 | − | 0.163746i | \(-0.0523578\pi\) | |||||||
\(102\) | 233969. | − | 156185.i | 2.22668 | − | 1.48641i | ||||
\(103\) | − | 146840.i | − | 1.36380i | −0.731446 | − | 0.681900i | \(-0.761154\pi\) | ||
0.731446 | − | 0.681900i | \(-0.238846\pi\) | |||||||
\(104\) | − | 9763.50i | − | 0.0885161i | ||||||
\(105\) | 131060. | − | 87488.4i | 1.16010 | − | 0.774421i | ||||
\(106\) | 29191.5i | 0.252343i | ||||||||
\(107\) | 154244. | 1.30242 | 0.651209 | − | 0.758899i | \(-0.274262\pi\) | ||||
0.651209 | + | 0.758899i | \(0.274262\pi\) | |||||||
\(108\) | −223244. | + | 44100.5i | −1.84170 | + | 0.363818i | ||||
\(109\) | 236967.i | 1.91039i | 0.295982 | + | 0.955194i | \(0.404353\pi\) | ||||
−0.295982 | + | 0.955194i | \(0.595647\pi\) | |||||||
\(110\) | 106213.i | 0.836939i | ||||||||
\(111\) | −155039. | + | 103495.i | −1.19436 | + | 0.797286i | ||||
\(112\) | 158184.i | 1.19156i | ||||||||
\(113\) | −186109. | −1.37110 | −0.685552 | − | 0.728024i | \(-0.740439\pi\) | ||||
−0.685552 | + | 0.728024i | \(0.740439\pi\) | |||||||
\(114\) | −108694. | − | 162827.i | −0.783330 | − | 1.17345i | ||||
\(115\) | 28199.1 | − | 103635.i | 0.198834 | − | 0.730735i | ||||
\(116\) | − | 134399.i | − | 0.927368i | ||||||
\(117\) | 3377.60 | − | 8134.04i | 0.0228109 | − | 0.0549341i | ||||
\(118\) | −405379. | −2.68013 | ||||||||
\(119\) | − | 449069.i | − | 2.90701i | ||||||
\(120\) | 147854. | − | 98699.3i | 0.937305 | − | 0.625693i | ||||
\(121\) | −92687.0 | −0.575513 | ||||||||
\(122\) | −188375. | −1.14584 | ||||||||
\(123\) | 181355. | − | 121063.i | 1.08086 | − | 0.721519i | ||||
\(124\) | 190847. | 1.11463 | ||||||||
\(125\) | −188718. | −1.08029 | ||||||||
\(126\) | −213516. | + | 514197.i | −1.19813 | + | 2.88538i | ||||
\(127\) | 111909. | 0.615679 | 0.307839 | − | 0.951438i | \(-0.400394\pi\) | ||||
0.307839 | + | 0.951438i | \(0.400394\pi\) | |||||||
\(128\) | − | 339385.i | − | 1.83091i | ||||||
\(129\) | 149359. | − | 99704.0i | 0.790238 | − | 0.527519i | ||||
\(130\) | 14723.3i | 0.0764094i | ||||||||
\(131\) | − | 45103.0i | − | 0.229629i | −0.993387 | − | 0.114815i | \(-0.963373\pi\) | ||
0.993387 | − | 0.114815i | \(-0.0366274\pi\) | |||||||
\(132\) | −135942. | − | 203645.i | −0.679075 | − | 1.01727i | ||||
\(133\) | −312523. | −1.53198 | ||||||||
\(134\) | 509973. | 2.45349 | ||||||||
\(135\) | 157323. | − | 31078.2i | 0.742946 | − | 0.146765i | ||||
\(136\) | − | 506614.i | − | 2.34871i | ||||||
\(137\) | 38559.8 | 0.175523 | 0.0877614 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877614 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(138\) | 120431. | + | 359864.i | 0.538318 | + | 1.60857i | ||||
\(139\) | −248892. | −1.09263 | −0.546317 | − | 0.837579i | \(-0.683971\pi\) | ||||
−0.546317 | + | 0.837579i | \(0.683971\pi\) | |||||||
\(140\) | − | 607262.i | − | 2.61852i | ||||||
\(141\) | −1356.48 | + | 905.512i | −0.00574601 | + | 0.00383572i | ||||
\(142\) | 71809.6 | 0.298856 | ||||||||
\(143\) | 9476.69 | 0.0387540 | ||||||||
\(144\) | −61734.6 | + | 148671.i | −0.248097 | + | 0.597477i | ||||
\(145\) | 94713.0i | 0.374102i | ||||||||
\(146\) | 33567.9i | 0.130329i | ||||||||
\(147\) | 348001. | + | 521316.i | 1.32827 | + | 1.98979i | ||||
\(148\) | 718368.i | 2.69583i | ||||||||
\(149\) | −271774. | −1.00286 | −0.501432 | − | 0.865197i | \(-0.667193\pi\) | ||||
−0.501432 | + | 0.865197i | \(0.667193\pi\) | |||||||
\(150\) | 165808. | − | 110684.i | 0.601695 | − | 0.401658i | ||||
\(151\) | 372890. | 1.33088 | 0.665439 | − | 0.746452i | \(-0.268244\pi\) | ||||
0.665439 | + | 0.746452i | \(0.268244\pi\) | |||||||
\(152\) | −352570. | −1.23776 | ||||||||
\(153\) | 175259. | − | 422064.i | 0.605272 | − | 1.45764i | ||||
\(154\) | −599073. | −2.03553 | ||||||||
\(155\) | −134493. | −0.449644 | ||||||||
\(156\) | −18844.4 | − | 28229.4i | −0.0619970 | − | 0.0928732i | ||||
\(157\) | 213649.i | 0.691754i | 0.938280 | + | 0.345877i | \(0.112418\pi\) | ||||
−0.938280 | + | 0.345877i | \(0.887582\pi\) | |||||||
\(158\) | −207620. | −0.661647 | ||||||||
\(159\) | 26329.7 | + | 39442.7i | 0.0825949 | + | 0.123730i | ||||
\(160\) | 95820.7i | 0.295910i | ||||||||
\(161\) | 584532. | + | 159052.i | 1.77723 | + | 0.483587i | ||||
\(162\) | −401352. | + | 399946.i | −1.20154 | + | 1.19733i | ||||
\(163\) | −558201. | −1.64559 | −0.822795 | − | 0.568338i | \(-0.807587\pi\) | ||||
−0.822795 | + | 0.568338i | \(0.807587\pi\) | |||||||
\(164\) | − | 840303.i | − | 2.43964i | ||||||
\(165\) | 95800.0 | + | 143511.i | 0.273940 | + | 0.410370i | ||||
\(166\) | − | 386906.i | − | 1.08977i | ||||||
\(167\) | 367432.i | 1.01950i | 0.860324 | + | 0.509748i | \(0.170261\pi\) | ||||
−0.860324 | + | 0.509748i | \(0.829739\pi\) | |||||||
\(168\) | 556696. | + | 833946.i | 1.52175 | + | 2.27963i | ||||
\(169\) | −369979. | −0.996462 | ||||||||
\(170\) | 763971.i | 2.02747i | ||||||||
\(171\) | −293729. | − | 121969.i | −0.768168 | − | 0.318976i | ||||
\(172\) | − | 692051.i | − | 1.78368i | ||||||
\(173\) | 308503.i | 0.783689i | 0.920031 | + | 0.391844i | \(0.128163\pi\) | ||||
−0.920031 | + | 0.391844i | \(0.871837\pi\) | |||||||
\(174\) | −185797. | − | 278329.i | −0.465228 | − | 0.696924i | ||||
\(175\) | − | 318243.i | − | 0.785532i | ||||||
\(176\) | −173212. | −0.421498 | ||||||||
\(177\) | −547736. | + | 365638.i | −1.31413 | + | 0.877239i | ||||
\(178\) | 240056.i | 0.567887i | ||||||||
\(179\) | 377659.i | 0.880982i | 0.897757 | + | 0.440491i | \(0.145196\pi\) | ||||
−0.897757 | + | 0.440491i | \(0.854804\pi\) | |||||||
\(180\) | 236997. | − | 570743.i | 0.545206 | − | 1.31298i | ||||
\(181\) | 71598.6i | 0.162446i | 0.996696 | + | 0.0812228i | \(0.0258825\pi\) | ||||
−0.996696 | + | 0.0812228i | \(0.974117\pi\) | |||||||
\(182\) | −83044.1 | −0.185836 | ||||||||
\(183\) | −254527. | + | 169908.i | −0.561831 | + | 0.375047i | ||||
\(184\) | 659435. | + | 179433.i | 1.43591 | + | 0.390714i | ||||
\(185\) | − | 506244.i | − | 1.08750i | ||||||
\(186\) | 395228. | − | 263832.i | 0.837654 | − | 0.559171i | ||||
\(187\) | 491732. | 1.02831 | ||||||||
\(188\) | 6285.21i | 0.0129696i | ||||||||
\(189\) | 175291. | + | 887351.i | 0.356948 | + | 1.80693i | ||||
\(190\) | 531674. | 1.06847 | ||||||||
\(191\) | 240272. | 0.476562 | 0.238281 | − | 0.971196i | \(-0.423416\pi\) | ||||
0.238281 | + | 0.971196i | \(0.423416\pi\) | |||||||
\(192\) | −371442. | − | 556431.i | −0.727174 | − | 1.08933i | ||||
\(193\) | 464503. | 0.897626 | 0.448813 | − | 0.893626i | \(-0.351847\pi\) | ||||
0.448813 | + | 0.893626i | \(0.351847\pi\) | |||||||
\(194\) | 826423. | 1.57651 | ||||||||
\(195\) | 13279.9 | + | 19893.7i | 0.0250097 | + | 0.0374652i | ||||
\(196\) | 2.41550e6 | 4.49124 | ||||||||
\(197\) | 284782.i | 0.522814i | 0.965229 | + | 0.261407i | \(0.0841864\pi\) | ||||
−0.965229 | + | 0.261407i | \(0.915814\pi\) | |||||||
\(198\) | −563047. | − | 233801.i | −1.02066 | − | 0.423821i | ||||
\(199\) | 201795.i | 0.361225i | 0.983554 | + | 0.180612i | \(0.0578080\pi\) | ||||
−0.983554 | + | 0.180612i | \(0.942192\pi\) | |||||||
\(200\) | − | 359023.i | − | 0.634670i | ||||||
\(201\) | 689059. | − | 459977.i | 1.20300 | − | 0.803057i | ||||
\(202\) | −322160. | −0.555512 | ||||||||
\(203\) | −534212. | −0.909857 | ||||||||
\(204\) | −977808. | − | 1.46478e6i | −1.64505 | − | 2.46433i | ||||
\(205\) | 592173.i | 0.984156i | ||||||||
\(206\) | −1.40900e6 | −2.31336 | ||||||||
\(207\) | 487307. | + | 377613.i | 0.790454 | + | 0.612521i | ||||
\(208\) | −24010.8 | −0.0384812 | ||||||||
\(209\) | − | 342213.i | − | 0.541915i | ||||||
\(210\) | −839494. | − | 1.25759e6i | −1.31362 | − | 1.96784i | ||||
\(211\) | 201305. | 0.311278 | 0.155639 | − | 0.987814i | \(-0.450256\pi\) | ||||
0.155639 | + | 0.987814i | \(0.450256\pi\) | |||||||
\(212\) | 182756. | 0.279275 | ||||||||
\(213\) | 97026.9 | − | 64769.8i | 0.146536 | − | 0.0978190i | ||||
\(214\) | − | 1.48005e6i | − | 2.20924i | ||||||
\(215\) | 487697.i | 0.719539i | ||||||||
\(216\) | 197753. | + | 1.00106e6i | 0.288396 | + | 1.45991i | ||||
\(217\) | − | 758581.i | − | 1.09358i | ||||||
\(218\) | 2.27381e6 | 3.24051 | ||||||||
\(219\) | 30277.1 | + | 45355.9i | 0.0426583 | + | 0.0639033i | ||||
\(220\) | 664953. | 0.926263 | ||||||||
\(221\) | 68164.4 | 0.0938808 | ||||||||
\(222\) | 993090. | + | 1.48768e6i | 1.35240 | + | 2.02594i | ||||
\(223\) | −95000.1 | −0.127927 | −0.0639635 | − | 0.997952i | \(-0.520374\pi\) | ||||
−0.0639635 | + | 0.997952i | \(0.520374\pi\) | |||||||
\(224\) | −540459. | −0.719686 | ||||||||
\(225\) | 124201. | − | 299105.i | 0.163557 | − | 0.393883i | ||||
\(226\) | 1.78580e6i | 2.32575i | ||||||||
\(227\) | 608206. | 0.783405 | 0.391702 | − | 0.920092i | \(-0.371886\pi\) | ||||
0.391702 | + | 0.920092i | \(0.371886\pi\) | |||||||
\(228\) | −1.01939e6 | + | 680491.i | −1.29869 | + | 0.866932i | ||||
\(229\) | − | 1.17155e6i | − | 1.47629i | −0.674643 | − | 0.738144i | \(-0.735703\pi\) | ||
0.674643 | − | 0.738144i | \(-0.264297\pi\) | |||||||
\(230\) | −994424. | − | 270584.i | −1.23952 | − | 0.337274i | ||||
\(231\) | −809448. | + | 540342.i | −0.998066 | + | 0.666253i | ||||
\(232\) | −602667. | −0.735118 | ||||||||
\(233\) | − | 1.20936e6i | − | 1.45937i | −0.683785 | − | 0.729683i | \(-0.739668\pi\) | ||
0.683785 | − | 0.729683i | \(-0.260332\pi\) | |||||||
\(234\) | −78050.1 | − | 32409.7i | −0.0931824 | − | 0.0386933i | ||||
\(235\) | − | 4429.27i | − | 0.00523194i | ||||||
\(236\) | 2.53791e6i | 2.96617i | ||||||||
\(237\) | −280530. | + | 187266.i | −0.324420 | + | 0.216565i | ||||
\(238\) | −4.30904e6 | −4.93103 | ||||||||
\(239\) | − | 1.09845e6i | − | 1.24390i | −0.783056 | − | 0.621951i | \(-0.786340\pi\) | ||
0.783056 | − | 0.621951i | \(-0.213660\pi\) | |||||||
\(240\) | −242725. | − | 363610.i | −0.272011 | − | 0.407481i | ||||
\(241\) | − | 716834.i | − | 0.795016i | −0.917599 | − | 0.397508i | \(-0.869875\pi\) | ||
0.917599 | − | 0.397508i | \(-0.130125\pi\) | |||||||
\(242\) | 889377.i | 0.976220i | ||||||||
\(243\) | −181557. | + | 902400.i | −0.197241 | + | 0.980355i | ||||
\(244\) | 1.17934e6i | 1.26813i | ||||||||
\(245\) | −1.70223e6 | −1.81177 | ||||||||
\(246\) | −1.16166e6 | − | 1.74019e6i | −1.22388 | − | 1.83341i | ||||
\(247\) | − | 47438.0i | − | 0.0494748i | ||||||
\(248\) | − | 855787.i | − | 0.883561i | ||||||
\(249\) | −348976. | − | 522775.i | −0.356695 | − | 0.534339i | ||||
\(250\) | 1.81084e6i | 1.83245i | ||||||||
\(251\) | 1.70891e6 | 1.71213 | 0.856063 | − | 0.516871i | \(-0.172903\pi\) | ||||
0.856063 | + | 0.516871i | \(0.172903\pi\) | |||||||
\(252\) | 3.21917e6 | + | 1.33674e6i | 3.19333 | + | 1.32600i | ||||
\(253\) | −174162. | + | 640064.i | −0.171062 | + | 0.628669i | ||||
\(254\) | − | 1.07382e6i | − | 1.04435i | ||||||
\(255\) | 689075. | + | 1.03225e6i | 0.663615 | + | 0.994113i | ||||
\(256\) | −1.88321e6 | −1.79597 | ||||||||
\(257\) | 136300.i | 0.128725i | 0.997927 | + | 0.0643623i | \(0.0205013\pi\) | ||||
−0.997927 | + | 0.0643623i | \(0.979499\pi\) | |||||||
\(258\) | −956708. | − | 1.43318e6i | −0.894809 | − | 1.34045i | ||||
\(259\) | 2.85538e6 | 2.64493 | ||||||||
\(260\) | 92176.5 | 0.0845643 | ||||||||
\(261\) | −502086. | − | 208487.i | −0.456223 | − | 0.189443i | ||||
\(262\) | −432785. | −0.389510 | ||||||||
\(263\) | 115648. | 0.103098 | 0.0515488 | − | 0.998670i | \(-0.483584\pi\) | ||||
0.0515488 | + | 0.998670i | \(0.483584\pi\) | |||||||
\(264\) | −913173. | + | 609583.i | −0.806386 | + | 0.538298i | ||||
\(265\) | −128791. | −0.112660 | ||||||||
\(266\) | 2.99881e6i | 2.59863i | ||||||||
\(267\) | 216522. | + | 324356.i | 0.185876 | + | 0.278447i | ||||
\(268\) | − | 3.19273e6i | − | 2.71535i | ||||||
\(269\) | − | 1.33952e6i | − | 1.12867i | −0.825545 | − | 0.564336i | \(-0.809132\pi\) | ||
0.825545 | − | 0.564336i | \(-0.190868\pi\) | |||||||
\(270\) | −298211. | − | 1.50959e6i | −0.248951 | − | 1.26023i | ||||
\(271\) | 598555. | 0.495086 | 0.247543 | − | 0.968877i | \(-0.420377\pi\) | ||||
0.247543 | + | 0.968877i | \(0.420377\pi\) | |||||||
\(272\) | −1.24589e6 | −1.02107 | ||||||||
\(273\) | −112207. | + | 74902.9i | −0.0911196 | + | 0.0608263i | ||||
\(274\) | − | 370000.i | − | 0.297732i | ||||||
\(275\) | 348477. | 0.277871 | ||||||||
\(276\) | 2.25296e6 | − | 753966.i | 1.78025 | − | 0.595771i | ||||
\(277\) | 804088. | 0.629657 | 0.314828 | − | 0.949149i | \(-0.398053\pi\) | ||||
0.314828 | + | 0.949149i | \(0.398053\pi\) | |||||||
\(278\) | 2.38824e6i | 1.85339i | ||||||||
\(279\) | 296052. | − | 712963.i | 0.227697 | − | 0.548348i | ||||
\(280\) | −2.72305e6 | −2.07568 | ||||||||
\(281\) | −193375. | −0.146095 | −0.0730475 | − | 0.997328i | \(-0.523272\pi\) | ||||
−0.0730475 | + | 0.997328i | \(0.523272\pi\) | |||||||
\(282\) | 8688.83 | + | 13016.1i | 0.00650637 | + | 0.00974672i | ||||
\(283\) | 1.88789e6i | 1.40123i | 0.713539 | + | 0.700615i | \(0.247091\pi\) | ||||
−0.713539 | + | 0.700615i | \(0.752909\pi\) | |||||||
\(284\) | − | 449571.i | − | 0.330752i | ||||||
\(285\) | 718381. | − | 479551.i | 0.523893 | − | 0.349722i | ||||
\(286\) | − | 90933.5i | − | 0.0657368i | ||||||
\(287\) | −3.34004e6 | −2.39358 | ||||||||
\(288\) | −507958. | − | 210926.i | −0.360867 | − | 0.149847i | ||||
\(289\) | 2.11710e6 | 1.49106 | ||||||||
\(290\) | 908818. | 0.634573 | ||||||||
\(291\) | 1.11664e6 | − | 745404.i | 0.773000 | − | 0.516011i | ||||
\(292\) | 210155. | 0.144239 | ||||||||
\(293\) | 974967. | 0.663469 | 0.331735 | − | 0.943373i | \(-0.392366\pi\) | ||||
0.331735 | + | 0.943373i | \(0.392366\pi\) | |||||||
\(294\) | 5.00228e6 | − | 3.33924e6i | 3.37520 | − | 2.25309i | ||||
\(295\) | − | 1.78850e6i | − | 1.19656i | ||||||
\(296\) | 3.22127e6 | 2.13697 | ||||||||
\(297\) | −971651. | + | 191944.i | −0.639174 | + | 0.126265i | ||||
\(298\) | 2.60780e6i | 1.70112i | ||||||||
\(299\) | −24142.6 | + | 88726.3i | −0.0156173 | + | 0.0573951i | ||||
\(300\) | −692946. | − | 1.03805e6i | −0.444525 | − | 0.665911i | ||||
\(301\) | −2.75077e6 | −1.75000 | ||||||||
\(302\) | − | 3.57806e6i | − | 2.25751i | ||||||
\(303\) | −435293. | + | 290577.i | −0.272380 | + | 0.181826i | ||||
\(304\) | 867055.i | 0.538100i | ||||||||
\(305\) | − | 831097.i | − | 0.511567i | ||||||
\(306\) | −4.04991e6 | − | 1.68169e6i | −2.47253 | − | 1.02670i | ||||
\(307\) | −2.41673e6 | −1.46346 | −0.731731 | − | 0.681593i | \(-0.761287\pi\) | ||||
−0.731731 | + | 0.681593i | \(0.761287\pi\) | |||||||
\(308\) | 3.75055e6i | 2.25278i | ||||||||
\(309\) | −1.90380e6 | + | 1.27087e6i | −1.13429 | + | 0.757189i | ||||
\(310\) | 1.29052e6i | 0.762713i | ||||||||
\(311\) | 1.22914e6i | 0.720610i | 0.932835 | + | 0.360305i | \(0.117327\pi\) | ||||
−0.932835 | + | 0.360305i | \(0.882673\pi\) | |||||||
\(312\) | −126585. | + | 84501.1i | −0.0736200 | + | 0.0491446i | ||||
\(313\) | 2.09149e6i | 1.20669i | 0.797480 | + | 0.603345i | \(0.206166\pi\) | ||||
−0.797480 | + | 0.603345i | \(0.793834\pi\) | |||||||
\(314\) | 2.05007e6 | 1.17339 | ||||||||
\(315\) | −2.26860e6 | − | 942016.i | −1.28819 | − | 0.534912i | ||||
\(316\) | 1.29982e6i | 0.732262i | ||||||||
\(317\) | − | 1.80590e6i | − | 1.00936i | −0.863308 | − | 0.504678i | \(-0.831611\pi\) | ||
0.863308 | − | 0.504678i | \(-0.168389\pi\) | |||||||
\(318\) | 378472. | − | 252647.i | 0.209877 | − | 0.140102i | ||||
\(319\) | − | 584963.i | − | 0.321849i | ||||||
\(320\) | 1.81689e6 | 0.991869 | ||||||||
\(321\) | −1.33495e6 | − | 1.99980e6i | −0.723109 | − | 1.08324i | ||||
\(322\) | 1.52618e6 | − | 5.60887e6i | 0.820289 | − | 3.01464i | ||||
\(323\) | − | 2.46149e6i | − | 1.31278i | ||||||
\(324\) | 2.50390e6 | + | 2.51270e6i | 1.32512 | + | 1.32978i | ||||
\(325\) | 48306.3 | 0.0253685 | ||||||||
\(326\) | 5.35621e6i | 2.79135i | ||||||||
\(327\) | 3.07231e6 | − | 2.05090e6i | 1.58889 | − | 1.06066i | ||||
\(328\) | −3.76805e6 | −1.93389 | ||||||||
\(329\) | 24982.5 | 0.0127247 | ||||||||
\(330\) | 1.37706e6 | − | 919248.i | 0.696094 | − | 0.464673i | ||||
\(331\) | 2.12287e6 | 1.06501 | 0.532505 | − | 0.846427i | \(-0.321251\pi\) | ||||
0.532505 | + | 0.846427i | \(0.321251\pi\) | |||||||
\(332\) | −2.42226e6 | −1.20608 | ||||||||
\(333\) | 2.68366e6 | + | 1.11437e6i | 1.32623 | + | 0.550705i | ||||
\(334\) | 3.52569e6 | 1.72933 | ||||||||
\(335\) | 2.24996e6i | 1.09537i | ||||||||
\(336\) | 2.05087e6 | − | 1.36905e6i | 0.991039 | − | 0.661562i | ||||
\(337\) | 2.65650e6i | 1.27419i | 0.770783 | + | 0.637097i | \(0.219865\pi\) | ||||
−0.770783 | + | 0.637097i | \(0.780135\pi\) | |||||||
\(338\) | 3.55013e6i | 1.69026i | ||||||||
\(339\) | 1.61073e6 | + | 2.41292e6i | 0.761244 | + | 1.14037i | ||||
\(340\) | 4.78291e6 | 2.24385 | ||||||||
\(341\) | 830648. | 0.386840 | ||||||||
\(342\) | −1.17035e6 | + | 2.81847e6i | −0.541065 | + | 1.30301i | ||||
\(343\) | − | 5.58795e6i | − | 2.56459i | ||||||
\(344\) | −3.10326e6 | −1.41391 | ||||||||
\(345\) | −1.58769e6 | + | 531330.i | −0.718156 | + | 0.240335i | ||||
\(346\) | 2.96023e6 | 1.32934 | ||||||||
\(347\) | 76257.0i | 0.0339982i | 0.999856 | + | 0.0169991i | \(0.00541124\pi\) | ||||
−0.999856 | + | 0.0169991i | \(0.994589\pi\) | |||||||
\(348\) | −1.74250e6 | + | 1.16320e6i | −0.771304 | + | 0.514880i | ||||
\(349\) | −3.01230e6 | −1.32384 | −0.661918 | − | 0.749576i | \(-0.730257\pi\) | ||||
−0.661918 | + | 0.749576i | \(0.730257\pi\) | |||||||
\(350\) | −3.05370e6 | −1.33247 | ||||||||
\(351\) | −134691. | + | 26607.5i | −0.0583542 | + | 0.0115275i | ||||
\(352\) | − | 591804.i | − | 0.254578i | ||||||
\(353\) | 307452.i | 0.131323i | 0.997842 | + | 0.0656614i | \(0.0209157\pi\) | ||||
−0.997842 | + | 0.0656614i | \(0.979084\pi\) | |||||||
\(354\) | 3.50847e6 | + | 5.25579e6i | 1.48802 | + | 2.22910i | ||||
\(355\) | 316818.i | 0.133426i | ||||||||
\(356\) | 1.50289e6 | 0.628495 | ||||||||
\(357\) | −5.82224e6 | + | 3.88660e6i | −2.41779 | + | 1.61398i | ||||
\(358\) | 3.62382e6 | 1.49437 | ||||||||
\(359\) | 1.84486e6 | 0.755488 | 0.377744 | − | 0.925910i | \(-0.376700\pi\) | ||||
0.377744 | + | 0.925910i | \(0.376700\pi\) | |||||||
\(360\) | −2.55930e6 | − | 1.06273e6i | −1.04079 | − | 0.432181i | ||||
\(361\) | 763064. | 0.308172 | ||||||||
\(362\) | 687024. | 0.275550 | ||||||||
\(363\) | 802187. | + | 1.20170e6i | 0.319528 | + | 0.478662i | ||||
\(364\) | 519905.i | 0.205670i | ||||||||
\(365\) | −148099. | −0.0581862 | ||||||||
\(366\) | 1.63035e6 | + | 2.44231e6i | 0.636177 | + | 0.953011i | ||||
\(367\) | 2.45837e6i | 0.952755i | 0.879241 | + | 0.476378i | \(0.158050\pi\) | ||||
−0.879241 | + | 0.476378i | \(0.841950\pi\) | |||||||
\(368\) | 441270. | − | 1.62171e6i | 0.169857 | − | 0.624243i | ||||
\(369\) | −3.13919e6 | − | 1.30352e6i | −1.20019 | − | 0.498371i | ||||
\(370\) | −4.85765e6 | −1.84469 | ||||||||
\(371\) | − | 726420.i | − | 0.274002i | ||||||
\(372\) | −1.65174e6 | − | 2.47436e6i | −0.618849 | − | 0.927054i | ||||
\(373\) | 1.32615e6i | 0.493539i | 0.969074 | + | 0.246769i | \(0.0793690\pi\) | ||||
−0.969074 | + | 0.246769i | \(0.920631\pi\) | |||||||
\(374\) | − | 4.71841e6i | − | 1.74428i | ||||||
\(375\) | 1.63332e6 | + | 2.44676e6i | 0.599781 | + | 0.898489i | ||||
\(376\) | 28183.8 | 0.0102809 | ||||||||
\(377\) | − | 81088.2i | − | 0.0293836i | ||||||
\(378\) | 8.51456e6 | − | 1.68200e6i | 3.06502 | − | 0.605477i | ||||
\(379\) | − | 997226.i | − | 0.356612i | −0.983975 | − | 0.178306i | \(-0.942938\pi\) | ||
0.983975 | − | 0.178306i | \(-0.0570616\pi\) | |||||||
\(380\) | − | 3.32859e6i | − | 1.18250i | ||||||
\(381\) | −968546. | − | 1.45091e6i | −0.341828 | − | 0.512068i | ||||
\(382\) | − | 2.30553e6i | − | 0.808373i | ||||||
\(383\) | −5.12880e6 | −1.78656 | −0.893282 | − | 0.449496i | \(-0.851603\pi\) | ||||
−0.893282 | + | 0.449496i | \(0.851603\pi\) | |||||||
\(384\) | −4.40017e6 | + | 2.93731e6i | −1.52279 | + | 1.01653i | ||||
\(385\) | − | 2.64306e6i | − | 0.908773i | ||||||
\(386\) | − | 4.45713e6i | − | 1.52261i | ||||||
\(387\) | −2.58535e6 | − | 1.07355e6i | −0.877489 | − | 0.364370i | ||||
\(388\) | − | 5.17389e6i | − | 1.74477i | ||||||
\(389\) | −2.66611e6 | −0.893314 | −0.446657 | − | 0.894705i | \(-0.647386\pi\) | ||||
−0.446657 | + | 0.894705i | \(0.647386\pi\) | |||||||
\(390\) | 190889. | − | 127427.i | 0.0635507 | − | 0.0424229i | ||||
\(391\) | −1.25272e6 | + | 4.60388e6i | −0.414394 | + | 1.52294i | ||||
\(392\) | − | 1.08314e7i | − | 3.56017i | ||||||
\(393\) | −584766. | + | 390357.i | −0.190985 | + | 0.127491i | ||||
\(394\) | 2.73262e6 | 0.886827 | ||||||||
\(395\) | − | 916003.i | − | 0.295396i | ||||||
\(396\) | −1.46373e6 | + | 3.52500e6i | −0.469054 | + | 1.12959i | ||||
\(397\) | 656587. | 0.209082 | 0.104541 | − | 0.994521i | \(-0.466663\pi\) | ||||
0.104541 | + | 0.994521i | \(0.466663\pi\) | |||||||
\(398\) | 1.93632e6 | 0.612731 | ||||||||
\(399\) | 2.70482e6 | + | 4.05190e6i | 0.850563 | + | 1.27417i | ||||
\(400\) | −882926. | −0.275914 | ||||||||
\(401\) | −4.02814e6 | −1.25096 | −0.625480 | − | 0.780240i | \(-0.715097\pi\) | ||||
−0.625480 | + | 0.780240i | \(0.715097\pi\) | |||||||
\(402\) | −4.41371e6 | − | 6.61186e6i | −1.36219 | − | 2.04060i | ||||
\(403\) | 115145. | 0.0353170 | ||||||||
\(404\) | 2.01691e6i | 0.614800i | ||||||||
\(405\) | −1.76453e6 | − | 1.77073e6i | −0.534554 | − | 0.536433i | ||||
\(406\) | 5.12602e6i | 1.54335i | ||||||||
\(407\) | 3.12664e6i | 0.935605i | ||||||||
\(408\) | −6.56831e6 | + | 4.38464e6i | −1.95345 | + | 1.30402i | ||||
\(409\) | −2.84042e6 | −0.839603 | −0.419802 | − | 0.907616i | \(-0.637900\pi\) | ||||
−0.419802 | + | 0.907616i | \(0.637900\pi\) | |||||||
\(410\) | 5.68219e6 | 1.66938 | ||||||||
\(411\) | −333727. | − | 499933.i | −0.0974512 | − | 0.145985i | ||||
\(412\) | 8.82117e6i | 2.56025i | ||||||||
\(413\) | 1.00877e7 | 2.91017 | ||||||||
\(414\) | 3.62338e6 | − | 4.67595e6i | 1.03899 | − | 1.34081i | ||||
\(415\) | 1.70700e6 | 0.486534 | ||||||||
\(416\) | − | 82036.5i | − | 0.0232420i | ||||||
\(417\) | 2.15411e6 | + | 3.22692e6i | 0.606636 | + | 0.908758i | ||||
\(418\) | −3.28370e6 | −0.919228 | ||||||||
\(419\) | 730556. | 0.203291 | 0.101646 | − | 0.994821i | \(-0.467589\pi\) | ||||
0.101646 | + | 0.994821i | \(0.467589\pi\) | |||||||
\(420\) | −7.87322e6 | + | 5.25572e6i | −2.17786 | + | 1.45382i | ||||
\(421\) | − | 4.57249e6i | − | 1.25733i | −0.777678 | − | 0.628663i | \(-0.783603\pi\) | ||
0.777678 | − | 0.628663i | \(-0.216397\pi\) | |||||||
\(422\) | − | 1.93162e6i | − | 0.528009i | ||||||
\(423\) | 23480.2 | + | 9749.95i | 0.00638043 | + | 0.00264942i | ||||
\(424\) | − | 819505.i | − | 0.221379i | ||||||
\(425\) | 2.50654e6 | 0.673136 | ||||||||
\(426\) | −621498. | − | 931021.i | −0.165926 | − | 0.248562i | ||||
\(427\) | 4.68765e6 | 1.24419 | ||||||||
\(428\) | −9.26599e6 | −2.44502 | ||||||||
\(429\) | −82018.8 | − | 122867.i | −0.0215164 | − | 0.0322322i | ||||
\(430\) | 4.67970e6 | 1.22052 | ||||||||
\(431\) | −3.59508e6 | −0.932214 | −0.466107 | − | 0.884728i | \(-0.654344\pi\) | ||||
−0.466107 | + | 0.884728i | \(0.654344\pi\) | |||||||
\(432\) | 2.46184e6 | − | 486323.i | 0.634674 | − | 0.125376i | ||||
\(433\) | 2.87279e6i | 0.736351i | 0.929756 | + | 0.368175i | \(0.120017\pi\) | ||||
−0.929756 | + | 0.368175i | \(0.879983\pi\) | |||||||
\(434\) | −7.27895e6 | −1.85500 | ||||||||
\(435\) | 1.22797e6 | − | 819722.i | 0.311145 | − | 0.207703i | ||||
\(436\) | − | 1.42354e7i | − | 3.58636i | ||||||
\(437\) | 3.20400e6 | + | 871814.i | 0.802581 | + | 0.218384i | ||||
\(438\) | 435212. | − | 290523.i | 0.108397 | − | 0.0723595i | ||||
\(439\) | −2.20954e6 | −0.547193 | −0.273597 | − | 0.961845i | \(-0.588213\pi\) | ||||
−0.273597 | + | 0.961845i | \(0.588213\pi\) | |||||||
\(440\) | − | 2.98175e6i | − | 0.734242i | ||||||
\(441\) | 3.74704e6 | − | 9.02376e6i | 0.917471 | − | 2.20948i | ||||
\(442\) | − | 654071.i | − | 0.159246i | ||||||
\(443\) | 3.21150e6i | 0.777497i | 0.921344 | + | 0.388748i | \(0.127092\pi\) | ||||
−0.921344 | + | 0.388748i | \(0.872908\pi\) | |||||||
\(444\) | 9.31373e6 | − | 6.21733e6i | 2.24216 | − | 1.49674i | ||||
\(445\) | −1.05911e6 | −0.253536 | ||||||||
\(446\) | 911572.i | 0.216997i | ||||||||
\(447\) | 2.35215e6 | + | 3.52358e6i | 0.556796 | + | 0.834096i | ||||
\(448\) | 1.02479e7i | 2.41234i | ||||||||
\(449\) | − | 5.52846e6i | − | 1.29416i | −0.762421 | − | 0.647081i | \(-0.775990\pi\) | ||
0.762421 | − | 0.647081i | \(-0.224010\pi\) | |||||||
\(450\) | −2.87006e6 | − | 1.19177e6i | −0.668128 | − | 0.277435i | ||||
\(451\) | − | 3.65736e6i | − | 0.846693i | ||||||
\(452\) | 1.11802e7 | 2.57397 | ||||||||
\(453\) | −3.22729e6 | − | 4.83456e6i | −0.738910 | − | 1.10691i | ||||
\(454\) | − | 5.83604e6i | − | 1.32886i | ||||||
\(455\) | − | 366384.i | − | 0.0829675i | ||||||
\(456\) | 3.05142e6 | + | 4.57112e6i | 0.687211 | + | 1.02946i | ||||
\(457\) | 4.18096e6i | 0.936453i | 0.883609 | + | 0.468226i | \(0.155107\pi\) | ||||
−0.883609 | + | 0.468226i | \(0.844893\pi\) | |||||||
\(458\) | −1.12416e7 | −2.50417 | ||||||||
\(459\) | −6.98894e6 | + | 1.38063e6i | −1.54839 | + | 0.305875i | ||||
\(460\) | −1.69402e6 | + | 6.22568e6i | −0.373270 | + | 1.37180i | ||||
\(461\) | 2.12110e6i | 0.464847i | 0.972615 | + | 0.232423i | \(0.0746655\pi\) | ||||
−0.972615 | + | 0.232423i | \(0.925335\pi\) | |||||||
\(462\) | 5.18485e6 | + | 7.76705e6i | 1.13014 | + | 1.69298i | ||||
\(463\) | 5.07644e6 | 1.10054 | 0.550271 | − | 0.834986i | \(-0.314524\pi\) | ||||
0.550271 | + | 0.834986i | \(0.314524\pi\) | |||||||
\(464\) | 1.48210e6i | 0.319583i | ||||||||
\(465\) | 1.16401e6 | + | 1.74371e6i | 0.249645 | + | 0.373975i | ||||
\(466\) | −1.16044e7 | −2.47546 | ||||||||
\(467\) | 1.39124e6 | 0.295196 | 0.147598 | − | 0.989047i | \(-0.452846\pi\) | ||||
0.147598 | + | 0.989047i | \(0.452846\pi\) | |||||||
\(468\) | −202904. | + | 488640.i | −0.0428228 | + | 0.103127i | ||||
\(469\) | −1.26905e7 | −2.66407 | ||||||||
\(470\) | −42501.0 | −0.00887472 | ||||||||
\(471\) | 2.76998e6 | − | 1.84909e6i | 0.575341 | − | 0.384065i | ||||
\(472\) | 1.13804e7 | 2.35127 | ||||||||
\(473\) | − | 3.01210e6i | − | 0.619037i | ||||||
\(474\) | 1.79691e6 | + | 2.69182e6i | 0.367350 | + | 0.550301i | ||||
\(475\) | − | 1.74439e6i | − | 0.354740i | ||||||
\(476\) | 2.69771e7i | 5.45730i | ||||||||
\(477\) | 283501. | − | 682736.i | 0.0570504 | − | 0.137391i | ||||
\(478\) | −1.05402e7 | −2.10998 | ||||||||
\(479\) | −1.02165e6 | −0.203453 | −0.101727 | − | 0.994812i | \(-0.532437\pi\) | ||||
−0.101727 | + | 0.994812i | \(0.532437\pi\) | |||||||
\(480\) | 1.24233e6 | − | 829308.i | 0.246112 | − | 0.164291i | ||||
\(481\) | 433419.i | 0.0854171i | ||||||||
\(482\) | −6.87837e6 | −1.34855 | ||||||||
\(483\) | −2.99687e6 | − | 8.95509e6i | −0.584521 | − | 1.74664i | ||||
\(484\) | 5.56802e6 | 1.08041 | ||||||||
\(485\) | 3.64611e6i | 0.703843i | ||||||||
\(486\) | 8.65897e6 | + | 1.74213e6i | 1.66294 | + | 0.334573i | ||||
\(487\) | 7.39100e6 | 1.41215 | 0.706075 | − | 0.708138i | \(-0.250464\pi\) | ||||
0.706075 | + | 0.708138i | \(0.250464\pi\) | |||||||
\(488\) | 5.28834e6 | 1.00524 | ||||||||
\(489\) | 4.83112e6 | + | 7.23715e6i | 0.913641 | + | 1.36866i | ||||
\(490\) | 1.63338e7i | 3.07323i | ||||||||
\(491\) | − | 3.70147e6i | − | 0.692900i | −0.938068 | − | 0.346450i | \(-0.887387\pi\) | ||
0.938068 | − | 0.346450i | \(-0.112613\pi\) | |||||||
\(492\) | −1.08946e7 | + | 7.27265e6i | −2.02908 | + | 1.35450i | ||||
\(493\) | − | 4.20755e6i | − | 0.779672i | ||||||
\(494\) | −455191. | −0.0839220 | ||||||||
\(495\) | 1.03151e6 | − | 2.48412e6i | 0.189217 | − | 0.455679i | ||||
\(496\) | −2.10459e6 | −0.384116 | ||||||||
\(497\) | −1.78696e6 | −0.324506 | ||||||||
\(498\) | −5.01628e6 | + | 3.34859e6i | −0.906377 | + | 0.605047i | ||||
\(499\) | −3.46388e6 | −0.622748 | −0.311374 | − | 0.950288i | \(-0.600789\pi\) | ||||
−0.311374 | + | 0.950288i | \(0.600789\pi\) | |||||||
\(500\) | 1.13370e7 | 2.02802 | ||||||||
\(501\) | 4.76380e6 | − | 3.18004e6i | 0.847928 | − | 0.566029i | ||||
\(502\) | − | 1.63979e7i | − | 2.90421i | ||||||
\(503\) | −79065.9 | −0.0139338 | −0.00696689 | − | 0.999976i | \(-0.502218\pi\) | ||||
−0.00696689 | + | 0.999976i | \(0.502218\pi\) | |||||||
\(504\) | 5.99413e6 | − | 1.44353e7i | 1.05111 | − | 2.53133i | ||||
\(505\) | − | 1.42135e6i | − | 0.248011i | ||||||
\(506\) | 6.14173e6 | + | 1.67117e6i | 1.06639 | + | 0.290165i | ||||
\(507\) | 3.20210e6 | + | 4.79683e6i | 0.553241 | + | 0.828771i | ||||
\(508\) | −6.72273e6 | −1.15581 | ||||||||
\(509\) | 1.50028e6i | 0.256672i | 0.991731 | + | 0.128336i | \(0.0409636\pi\) | ||||
−0.991731 | + | 0.128336i | \(0.959036\pi\) | |||||||
\(510\) | 9.90498e6 | − | 6.61201e6i | 1.68627 | − | 1.12566i | ||||
\(511\) | − | 835325.i | − | 0.141515i | ||||||
\(512\) | 7.20996e6i | 1.21551i | ||||||||
\(513\) | 960825. | + | 4.86385e6i | 0.161195 | + | 0.815993i | ||||
\(514\) | 1.30786e6 | 0.218350 | ||||||||
\(515\) | − | 6.21639e6i | − | 1.03281i | ||||||
\(516\) | −8.97253e6 | + | 5.98956e6i | −1.48351 | + | 0.990308i | ||||
\(517\) | 27355.9i | 0.00450116i | ||||||||
\(518\) | − | 2.73987e7i | − | 4.48648i | ||||||
\(519\) | 3.99978e6 | − | 2.67003e6i | 0.651804 | − | 0.435108i | ||||
\(520\) | − | 413333.i | − | 0.0670335i | ||||||
\(521\) | −1.32448e6 | −0.213771 | −0.106886 | − | 0.994271i | \(-0.534088\pi\) | ||||
−0.106886 | + | 0.994271i | \(0.534088\pi\) | |||||||
\(522\) | −2.00054e6 | + | 4.81776e6i | −0.321344 | + | 0.773872i | ||||
\(523\) | 7.72536e6i | 1.23499i | 0.786573 | + | 0.617497i | \(0.211853\pi\) | ||||
−0.786573 | + | 0.617497i | \(0.788147\pi\) | |||||||
\(524\) | 2.70949e6i | 0.431081i | ||||||||
\(525\) | −4.12606e6 | + | 2.75433e6i | −0.653338 | + | 0.436132i | ||||
\(526\) | − | 1.10970e6i | − | 0.174880i | ||||||
\(527\) | 5.97472e6 | 0.937112 | ||||||||
\(528\) | 1.49911e6 | + | 2.24571e6i | 0.234018 | + | 0.350566i | ||||
\(529\) | −5.54896e6 | − | 3.26122e6i | −0.862129 | − | 0.506688i | ||||
\(530\) | 1.23581e6i | 0.191100i | ||||||||
\(531\) | 9.48108e6 | + | 3.93694e6i | 1.45922 | + | 0.605930i | ||||
\(532\) | 1.87743e7 | 2.87597 | ||||||||
\(533\) | − | 506987.i | − | 0.0772999i | ||||||
\(534\) | 3.11235e6 | − | 2.07763e6i | 0.472319 | − | 0.315294i | ||||
\(535\) | 6.52987e6 | 0.986325 | ||||||||
\(536\) | −1.43167e7 | −2.15244 | ||||||||
\(537\) | 4.89639e6 | − | 3.26856e6i | 0.732724 | − | 0.489126i | ||||
\(538\) | −1.28533e7 | −1.91452 | ||||||||
\(539\) | 1.05133e7 | 1.55871 | ||||||||
\(540\) | −9.45092e6 | + | 1.86698e6i | −1.39473 | + | 0.275521i | ||||
\(541\) | 1.20047e6 | 0.176343 | 0.0881716 | − | 0.996105i | \(-0.471898\pi\) | ||||
0.0881716 | + | 0.996105i | \(0.471898\pi\) | |||||||
\(542\) | − | 5.74342e6i | − | 0.839794i | ||||||
\(543\) | 928285. | − | 619671.i | 0.135108 | − | 0.0901907i | ||||
\(544\) | − | 4.25676e6i | − | 0.616711i | ||||||
\(545\) | 1.00319e7i | 1.44674i | ||||||||
\(546\) | 718730. | + | 1.07668e6i | 0.103177 | + | 0.154562i | ||||
\(547\) | −7.08747e6 | −1.01280 | −0.506399 | − | 0.862299i | \(-0.669024\pi\) | ||||
−0.506399 | + | 0.862299i | \(0.669024\pi\) | |||||||
\(548\) | −2.31642e6 | −0.329508 | ||||||||
\(549\) | 4.40576e6 | + | 1.82945e6i | 0.623863 | + | 0.259054i | ||||
\(550\) | − | 3.34381e6i | − | 0.471340i | ||||||
\(551\) | −2.92818e6 | −0.410884 | ||||||||
\(552\) | −3.38090e6 | − | 1.01026e7i | −0.472264 | − | 1.41119i | ||||
\(553\) | 5.16655e6 | 0.718436 | ||||||||
\(554\) | − | 7.71561e6i | − | 1.06806i | ||||||
\(555\) | −6.56351e6 | + | 4.38143e6i | −0.904490 | + | 0.603787i | ||||
\(556\) | 1.49518e7 | 2.05119 | ||||||||
\(557\) | −1.19085e7 | −1.62637 | −0.813183 | − | 0.582008i | \(-0.802267\pi\) | ||||
−0.813183 | + | 0.582008i | \(0.802267\pi\) | |||||||
\(558\) | −6.84123e6 | − | 2.84076e6i | −0.930140 | − | 0.386233i | ||||
\(559\) | − | 417540.i | − | 0.0565157i | ||||||
\(560\) | 6.69664e6i | 0.902375i | ||||||||
\(561\) | −4.25584e6 | − | 6.37537e6i | −0.570924 | − | 0.855260i | ||||
\(562\) | 1.85553e6i | 0.247815i | ||||||||
\(563\) | −3.48037e6 | −0.462759 | −0.231379 | − | 0.972864i | \(-0.574324\pi\) | ||||
−0.231379 | + | 0.972864i | \(0.574324\pi\) | |||||||
\(564\) | 81488.5 | − | 54397.2i | 0.0107870 | − | 0.00720077i | ||||
\(565\) | −7.87883e6 | −1.03834 | ||||||||
\(566\) | 1.81152e7 | 2.37685 | ||||||||
\(567\) | 9.98750e6 | − | 9.95251e6i | 1.30467 | − | 1.30009i | ||||
\(568\) | −2.01594e6 | −0.262185 | ||||||||
\(569\) | −8.76497e6 | −1.13493 | −0.567466 | − | 0.823397i | \(-0.692076\pi\) | ||||
−0.567466 | + | 0.823397i | \(0.692076\pi\) | |||||||
\(570\) | −4.60153e6 | − | 6.89322e6i | −0.593219 | − | 0.888658i | ||||
\(571\) | 1.28771e7i | 1.65283i | 0.563058 | + | 0.826417i | \(0.309625\pi\) | ||||
−0.563058 | + | 0.826417i | \(0.690375\pi\) | |||||||
\(572\) | −569297. | −0.0727527 | ||||||||
\(573\) | −2.07951e6 | − | 3.11516e6i | −0.264590 | − | 0.396363i | ||||
\(574\) | 3.20494e7i | 4.06013i | ||||||||
\(575\) | −887771. | + | 3.26265e6i | −0.111978 | + | 0.411529i | ||||
\(576\) | −3.99944e6 | + | 9.63159e6i | −0.502277 | + | 1.20960i | ||||
\(577\) | 1.41805e7 | 1.77318 | 0.886589 | − | 0.462559i | \(-0.153069\pi\) | ||||
0.886589 | + | 0.462559i | \(0.153069\pi\) | |||||||
\(578\) | − | 2.03146e7i | − | 2.52923i | ||||||
\(579\) | −4.02018e6 | − | 6.02234e6i | −0.498367 | − | 0.746567i | ||||
\(580\) | − | 5.68973e6i | − | 0.702299i | ||||||
\(581\) | 9.62802e6i | 1.18330i | ||||||||
\(582\) | −7.15252e6 | − | 1.07147e7i | −0.875289 | − | 1.31121i | ||||
\(583\) | 795432. | 0.0969241 | ||||||||
\(584\) | − | 942365.i | − | 0.114337i | ||||||
\(585\) | 142989. | − | 344351.i | 0.0172748 | − | 0.0416018i | ||||
\(586\) | − | 9.35529e6i | − | 1.12542i | ||||||
\(587\) | 4.31162e6i | 0.516470i | 0.966082 | + | 0.258235i | \(0.0831409\pi\) | ||||
−0.966082 | + | 0.258235i | \(0.916859\pi\) | |||||||
\(588\) | −2.09056e7 | − | 3.13172e7i | −2.49356 | − | 3.73542i | ||||
\(589\) | − | 4.15802e6i | − | 0.493853i | ||||||
\(590\) | −1.71615e7 | −2.02967 | ||||||||
\(591\) | 3.69224e6 | − | 2.46473e6i | 0.434831 | − | 0.290269i | ||||
\(592\) | − | 7.92188e6i | − | 0.929018i | ||||||
\(593\) | 1.53560e7i | 1.79325i | 0.442787 | + | 0.896627i | \(0.353990\pi\) | ||||
−0.442787 | + | 0.896627i | \(0.646010\pi\) | |||||||
\(594\) | 1.84180e6 | + | 9.32347e6i | 0.214179 | + | 1.08421i | ||||
\(595\) | − | 1.90111e7i | − | 2.20148i | ||||||
\(596\) | 1.63264e7 | 1.88267 | ||||||||
\(597\) | 2.61630e6 | − | 1.74649e6i | 0.300436 | − | 0.200554i | ||||
\(598\) | 851373. | + | 231660.i | 0.0973569 | + | 0.0264910i | ||||
\(599\) | − | 8.95775e6i | − | 1.02007i | −0.860152 | − | 0.510037i | \(-0.829632\pi\) | ||
0.860152 | − | 0.510037i | \(-0.170368\pi\) | |||||||
\(600\) | −4.65479e6 | + | 3.10727e6i | −0.527863 | + | 0.352372i | ||||
\(601\) | 2.98822e6 | 0.337463 | 0.168732 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168732 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(602\) | 2.63950e7i | 2.96845i | ||||||||
\(603\) | −1.19273e7 | − | 4.95273e6i | −1.33583 | − | 0.554691i | ||||
\(604\) | −2.24008e7 | −2.49845 | ||||||||
\(605\) | −3.92386e6 | −0.435838 | ||||||||
\(606\) | 2.78823e6 | + | 4.17685e6i | 0.308423 | + | 0.462027i | ||||
\(607\) | −1.01901e7 | −1.12255 | −0.561277 | − | 0.827628i | \(-0.689690\pi\) | ||||
−0.561277 | + | 0.827628i | \(0.689690\pi\) | |||||||
\(608\) | −2.96243e6 | −0.325004 | ||||||||
\(609\) | 4.62349e6 | + | 6.92612e6i | 0.505158 | + | 0.756740i | ||||
\(610\) | −7.97478e6 | −0.867749 | ||||||||
\(611\) | 3792.11i | 0.000410939i | ||||||||
\(612\) | −1.05284e7 | + | 2.53548e7i | −1.13627 | + | 2.73642i | ||||
\(613\) | 6.67644e6i | 0.717619i | 0.933411 | + | 0.358809i | \(0.116817\pi\) | ||||
−0.933411 | + | 0.358809i | \(0.883183\pi\) | |||||||
\(614\) | 2.31897e7i | 2.48241i | ||||||||
\(615\) | 7.67760e6 | − | 5.12514e6i | 0.818536 | − | 0.546409i | ||||
\(616\) | 1.68180e7 | 1.78576 | ||||||||
\(617\) | 1.07353e7 | 1.13528 | 0.567638 | − | 0.823278i | \(-0.307857\pi\) | ||||
0.567638 | + | 0.823278i | \(0.307857\pi\) | |||||||
\(618\) | 1.21946e7 | + | 1.82679e7i | 1.28439 | + | 1.92405i | ||||
\(619\) | 1.50784e7i | 1.58172i | 0.612000 | + | 0.790858i | \(0.290365\pi\) | ||||
−0.612000 | + | 0.790858i | \(0.709635\pi\) | |||||||
\(620\) | 8.07943e6 | 0.844114 | ||||||||
\(621\) | 678260. | − | 9.58616e6i | 0.0705776 | − | 0.997506i | ||||
\(622\) | 1.17942e7 | 1.22234 | ||||||||
\(623\) | − | 5.97370e6i | − | 0.616628i | ||||||
\(624\) | 207809. | + | 311303.i | 0.0213650 | + | 0.0320053i | ||||
\(625\) | −3.82435e6 | −0.391613 | ||||||||
\(626\) | 2.00689e7 | 2.04686 | ||||||||
\(627\) | −4.43684e6 | + | 2.96179e6i | −0.450718 | + | 0.300874i | ||||
\(628\) | − | 1.28346e7i | − | 1.29862i | ||||||
\(629\) | 2.24895e7i | 2.26648i | ||||||||
\(630\) | −9.03911e6 | + | 2.17683e7i | −0.907348 | + | 2.18511i | ||||
\(631\) | 234707.i | 0.0234667i | 0.999931 | + | 0.0117334i | \(0.00373493\pi\) | ||||
−0.999931 | + | 0.0117334i | \(0.996265\pi\) | |||||||
\(632\) | 5.82860e6 | 0.580459 | ||||||||
\(633\) | −1.74226e6 | − | 2.60995e6i | −0.172823 | − | 0.258894i | ||||
\(634\) | −1.73285e7 | −1.71213 | ||||||||
\(635\) | 4.73760e6 | 0.466256 | ||||||||
\(636\) | −1.58172e6 | − | 2.36946e6i | −0.155055 | − | 0.232277i | ||||
\(637\) | 1.45736e6 | 0.142304 | ||||||||
\(638\) | −5.61301e6 | −0.545939 | ||||||||
\(639\) | −1.67950e6 | − | 697397.i | −0.162715 | − | 0.0675660i | ||||
\(640\) | − | 1.43677e7i | − | 1.38656i | ||||||
\(641\) | 1.01915e7 | 0.979701 | 0.489850 | − | 0.871807i | \(-0.337051\pi\) | ||||
0.489850 | + | 0.871807i | \(0.337051\pi\) | |||||||
\(642\) | −1.91891e7 | + | 1.28095e7i | −1.83745 | + | 1.22658i | ||||
\(643\) | − | 4.79332e6i | − | 0.457203i | −0.973520 | − | 0.228601i | \(-0.926585\pi\) | ||
0.973520 | − | 0.228601i | \(-0.0734152\pi\) | |||||||
\(644\) | −3.51148e7 | − | 9.55480e6i | −3.33638 | − | 0.907835i | ||||
\(645\) | 6.32306e6 | − | 4.22092e6i | 0.598450 | − | 0.399492i | ||||
\(646\) | −2.36192e7 | −2.22681 | ||||||||
\(647\) | 9.51131e6i | 0.893264i | 0.894718 | + | 0.446632i | \(0.147377\pi\) | ||||
−0.894718 | + | 0.446632i | \(0.852623\pi\) | |||||||
\(648\) | 1.12673e7 | − | 1.12278e7i | 1.05410 | − | 1.05041i | ||||
\(649\) | 1.10461e7i | 1.02943i | ||||||||
\(650\) | − | 463522.i | − | 0.0430316i | ||||||
\(651\) | −9.83510e6 | + | 6.56536e6i | −0.909549 | + | 0.607164i | ||||
\(652\) | 3.35330e7 | 3.08926 | ||||||||
\(653\) | − | 2.01707e7i | − | 1.85113i | −0.378585 | − | 0.925566i | \(-0.623589\pi\) | ||
0.378585 | − | 0.925566i | \(-0.376411\pi\) | |||||||
\(654\) | −1.96794e7 | − | 2.94803e7i | −1.79915 | − | 2.69518i | ||||
\(655\) | − | 1.90941e6i | − | 0.173899i | ||||||
\(656\) | 9.26653e6i | 0.840732i | ||||||||
\(657\) | 326003. | − | 785092.i | 0.0294651 | − | 0.0709589i | ||||
\(658\) | − | 239719.i | − | 0.0215843i | ||||||
\(659\) | 1.48161e7 | 1.32898 | 0.664491 | − | 0.747296i | \(-0.268648\pi\) | ||||
0.664491 | + | 0.747296i | \(0.268648\pi\) | |||||||
\(660\) | −5.75503e6 | − | 8.62120e6i | −0.514266 | − | 0.770385i | ||||
\(661\) | 1.86036e6i | 0.165613i | 0.996566 | + | 0.0828064i | \(0.0263883\pi\) | ||||
−0.996566 | + | 0.0828064i | \(0.973612\pi\) | |||||||
\(662\) | − | 2.03700e7i | − | 1.80653i | ||||||
\(663\) | −589949. | − | 883760.i | −0.0521231 | − | 0.0780819i | ||||
\(664\) | 1.08618e7i | 0.956050i | ||||||||
\(665\) | −1.32305e7 | −1.16017 | ||||||||
\(666\) | 1.06929e7 | − | 2.57511e7i | 0.934138 | − | 2.24962i | ||||
\(667\) | 5.47677e6 | + | 1.49024e6i | 0.476661 | + | 0.129700i | ||||
\(668\) | − | 2.20729e7i | − | 1.91389i | ||||||
\(669\) | 822206. | + | 1.23169e6i | 0.0710257 | + | 0.106399i | ||||
\(670\) | 2.15895e7 | 1.85804 | ||||||||
\(671\) | 5.13299e6i | 0.440113i | ||||||||
\(672\) | 4.67756e6 | + | 7.00712e6i | 0.399573 | + | 0.598572i | ||||
\(673\) | −1.03407e6 | −0.0880061 | −0.0440031 | − | 0.999031i | \(-0.514011\pi\) | ||||
−0.0440031 | + | 0.999031i | \(0.514011\pi\) | |||||||
\(674\) | 2.54905e7 | 2.16136 | ||||||||
\(675\) | −4.95287e6 | + | 978412.i | −0.418406 | + | 0.0826537i | ||||
\(676\) | 2.22259e7 | 1.87065 | ||||||||
\(677\) | 1.20130e7 | 1.00735 | 0.503676 | − | 0.863893i | \(-0.331981\pi\) | ||||
0.503676 | + | 0.863893i | \(0.331981\pi\) | |||||||
\(678\) | 2.31532e7 | − | 1.54558e7i | 1.93436 | − | 1.29127i | ||||
\(679\) | −2.05652e7 | −1.71182 | ||||||||
\(680\) | − | 2.14473e7i | − | 1.77869i | ||||||
\(681\) | −5.26390e6 | − | 7.88547e6i | −0.434951 | − | 0.651568i | ||||
\(682\) | − | 7.97047e6i | − | 0.656180i | ||||||
\(683\) | − | 6.04943e6i | − | 0.496207i | −0.968734 | − | 0.248104i | \(-0.920193\pi\) | ||
0.968734 | − | 0.248104i | \(-0.0798073\pi\) | |||||||
\(684\) | 1.76453e7 | + | 7.32707e6i | 1.44208 | + | 0.598811i | ||||
\(685\) | 1.63241e6 | 0.132924 | ||||||||
\(686\) | −5.36191e7 | −4.35020 | ||||||||
\(687\) | −1.51893e7 | + | 1.01395e7i | −1.22785 | + | 0.819643i | ||||
\(688\) | 7.63166e6i | 0.614679i | ||||||||
\(689\) | 110264. | 0.00884880 | ||||||||
\(690\) | 5.09837e6 | + | 1.52347e7i | 0.407670 | + | 1.21818i | ||||
\(691\) | −1.22344e6 | −0.0974736 | −0.0487368 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487368 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(692\) | − | 1.85328e7i | − | 1.47121i | ||||||
\(693\) | 1.40112e7 | + | 5.81805e6i | 1.10826 | + | 0.460197i | ||||
\(694\) | 731723. | 0.0576698 | ||||||||
\(695\) | −1.05367e7 | −0.827455 | ||||||||
\(696\) | 5.21596e6 | + | 7.81365e6i | 0.408142 | + | 0.611408i | ||||
\(697\) | − | 2.63068e7i | − | 2.05110i | ||||||
\(698\) | 2.89045e7i | 2.24557i | ||||||||
\(699\) | −1.56795e7 | + | 1.04667e7i | −1.21377 | + | 0.810248i | ||||
\(700\) | 1.91180e7i | 1.47467i | ||||||||
\(701\) | −494965. | −0.0380434 | −0.0190217 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190217 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(702\) | 255312. | + | 1.29243e6i | 0.0195537 | + | 0.0989838i | ||||
\(703\) | 1.56512e7 | 1.19443 | ||||||||
\(704\) | −1.12214e7 | −0.853329 | ||||||||
\(705\) | −57426.1 | + | 38334.4i | −0.00435147 | + | 0.00290480i | ||||
\(706\) | 2.95015e6 | 0.222757 | ||||||||
\(707\) | 8.01684e6 | 0.603191 | ||||||||
\(708\) | 3.29044e7 | − | 2.19651e7i | 2.46701 | − | 1.64684i | ||||
\(709\) | − | 1.61820e6i | − | 0.120897i | −0.998171 | − | 0.0604486i | \(-0.980747\pi\) | ||
0.998171 | − | 0.0604486i | \(-0.0192531\pi\) | |||||||
\(710\) | 3.04003e6 | 0.226325 | ||||||||
\(711\) | 4.85585e6 | + | 2.01635e6i | 0.360240 | + | 0.149587i | ||||
\(712\) | − | 6.73918e6i | − | 0.498204i | ||||||
\(713\) | −2.11614e6 | + | 7.77701e6i | −0.155891 | + | 0.572913i | ||||
\(714\) | 3.72938e7 | + | 5.58672e7i | 2.73774 | + | 4.10121i | ||||
\(715\) | 401191. | 0.0293485 | ||||||||
\(716\) | − | 2.26872e7i | − | 1.65386i | ||||||
\(717\) | −1.42416e7 | + | 9.50687e6i | −1.03457 | + | 0.690621i | ||||
\(718\) | − | 1.77023e7i | − | 1.28150i | ||||||
\(719\) | 1.10050e7i | 0.793902i | 0.917840 | + | 0.396951i | \(0.129932\pi\) | ||||
−0.917840 | + | 0.396951i | \(0.870068\pi\) | |||||||
\(720\) | −2.61351e6 | + | 6.29393e6i | −0.187885 | + | 0.452471i | ||||
\(721\) | 3.50624e7 | 2.51191 | ||||||||
\(722\) | − | 7.32197e6i | − | 0.522739i | ||||||
\(723\) | −9.29384e6 | + | 6.20405e6i | −0.661225 | + | 0.441397i | ||||
\(724\) | − | 4.30117e6i | − | 0.304958i | ||||||
\(725\) | − | 2.98178e6i | − | 0.210683i | ||||||
\(726\) | 1.15309e7 | − | 7.69738e6i | 0.811935 | − | 0.542002i | ||||
\(727\) | 1.01959e7i | 0.715469i | 0.933823 | + | 0.357734i | \(0.116451\pi\) | ||||
−0.933823 | + | 0.357734i | \(0.883549\pi\) | |||||||
\(728\) | 2.33133e6 | 0.163033 | ||||||||
\(729\) | 1.32711e7 | − | 5.45617e6i | 0.924884 | − | 0.380250i | ||||
\(730\) | 1.42108e6i | 0.0986988i | ||||||||
\(731\) | − | 2.16656e7i | − | 1.49960i | ||||||
\(732\) | 1.52903e7 | − | 1.02069e7i | 1.05472 | − | 0.704074i | ||||
\(733\) | − | 3.14789e6i | − | 0.216401i | −0.994129 | − | 0.108201i | \(-0.965491\pi\) | ||
0.994129 | − | 0.108201i | \(-0.0345089\pi\) | |||||||
\(734\) | 2.35892e7 | 1.61612 | ||||||||
\(735\) | 1.47325e7 | + | 2.20697e7i | 1.00591 | + | 1.50687i | ||||
\(736\) | 5.54082e6 | + | 1.50767e6i | 0.377033 | + | 0.102591i | ||||
\(737\) | − | 1.38961e7i | − | 0.942377i | ||||||
\(738\) | −1.25079e7 | + | 3.01220e7i | −0.845366 | + | 2.03584i | ||||
\(739\) | −2.23241e7 | −1.50371 | −0.751853 | − | 0.659330i | \(-0.770840\pi\) | ||||
−0.751853 | + | 0.659330i | \(0.770840\pi\) | |||||||
\(740\) | 3.04118e7i | 2.04156i | ||||||||
\(741\) | −615039. | + | 410566.i | −0.0411488 | + | 0.0274687i | ||||
\(742\) | −6.97036e6 | −0.464778 | ||||||||
\(743\) | −5.25688e6 | −0.349346 | −0.174673 | − | 0.984626i | \(-0.555887\pi\) | ||||
−0.174673 | + | 0.984626i | \(0.555887\pi\) | |||||||
\(744\) | −1.10954e7 | + | 7.40666e6i | −0.734869 | + | 0.490558i | ||||
\(745\) | −1.15054e7 | −0.759473 | ||||||||
\(746\) | 1.27251e7 | 0.837169 | ||||||||
\(747\) | −3.75754e6 | + | 9.04902e6i | −0.246378 | + | 0.593335i | ||||
\(748\) | −2.95400e7 | −1.93044 | ||||||||
\(749\) | 3.68305e7i | 2.39885i | ||||||||
\(750\) | 2.34778e7 | − | 1.56725e7i | 1.52407 | − | 1.01738i | ||||
\(751\) | 1.06147e7i | 0.686766i | 0.939196 | + | 0.343383i | \(0.111573\pi\) | ||||
−0.939196 | + | 0.343383i | \(0.888427\pi\) | |||||||
\(752\) | − | 69310.8i | − | 0.00446947i | ||||||
\(753\) | −1.47903e7 | − | 2.21563e7i | −0.950582 | − | 1.42400i | ||||
\(754\) | −778081. | −0.0498421 | ||||||||
\(755\) | 1.57861e7 | 1.00788 | ||||||||
\(756\) | −1.05303e7 | − | 5.33062e7i | −0.670097 | − | 3.39213i | ||||
\(757\) | 1.03081e7i | 0.653791i | 0.945061 | + | 0.326895i | \(0.106002\pi\) | ||||
−0.945061 | + | 0.326895i | \(0.893998\pi\) | |||||||
\(758\) | −9.56887e6 | −0.604906 | ||||||||
\(759\) | 9.80585e6 | − | 3.28158e6i | 0.617847 | − | 0.206766i | ||||
\(760\) | −1.49259e7 | −0.937360 | ||||||||
\(761\) | − | 6.30344e6i | − | 0.394563i | −0.980347 | − | 0.197281i | \(-0.936789\pi\) | ||
0.980347 | − | 0.197281i | \(-0.0632112\pi\) | |||||||
\(762\) | −1.39222e7 | + | 9.29367e6i | −0.868600 | + | 0.579829i | ||||
\(763\) | −5.65830e7 | −3.51864 | ||||||||
\(764\) | −1.44340e7 | −0.894648 | ||||||||
\(765\) | 7.41950e6 | − | 1.78679e7i | 0.458375 | − | 1.10387i | ||||
\(766\) | 4.92133e7i | 3.03048i | ||||||||
\(767\) | 1.53122e6i | 0.0939829i | ||||||||
\(768\) | 1.62988e7 | + | 2.44160e7i | 0.997129 | + | 1.49373i | ||||
\(769\) | − | 9.63731e6i | − | 0.587679i | −0.955855 | − | 0.293839i | \(-0.905067\pi\) | ||
0.955855 | − | 0.293839i | \(-0.0949331\pi\) | |||||||
\(770\) | −2.53615e7 | −1.54151 | ||||||||
\(771\) | 1.76714e6 | − | 1.17964e6i | 0.107062 | − | 0.0714686i | ||||
\(772\) | −2.79043e7 | −1.68511 | ||||||||
\(773\) | 5.63328e6 | 0.339088 | 0.169544 | − | 0.985523i | \(-0.445771\pi\) | ||||
0.169544 | + | 0.985523i | \(0.445771\pi\) | |||||||
\(774\) | −1.03012e7 | + | 2.48077e7i | −0.618066 | + | 1.48845i | ||||
\(775\) | 4.23413e6 | 0.253227 | ||||||||
\(776\) | −2.32005e7 | −1.38307 | ||||||||
\(777\) | −2.47127e7 | − | 3.70203e7i | −1.46848 | − | 2.19982i | ||||
\(778\) | 2.55826e7i | 1.51529i | ||||||||
\(779\) | −1.83078e7 | −1.08092 | ||||||||
\(780\) | −797769. | − | 1.19508e6i | −0.0469505 | − | 0.0703332i | ||||
\(781\) | − | 1.95672e6i | − | 0.114789i | ||||||
\(782\) | 4.41765e7 | + | 1.20205e7i | 2.58330 | + | 0.702919i | ||||
\(783\) | 1.64239e6 | + | 8.31403e6i | 0.0957352 | + | 0.484626i | ||||
\(784\) | −2.66371e7 | −1.54774 | ||||||||
\(785\) | 9.04473e6i | 0.523867i | ||||||||
\(786\) | 3.74566e6 | + | 5.61111e6i | 0.216258 | + | 0.323961i | ||||
\(787\) | − | 2.04060e7i | − | 1.17441i | −0.809438 | − | 0.587206i | \(-0.800228\pi\) | ||
0.809438 | − | 0.587206i | \(-0.199772\pi\) | |||||||
\(788\) | − | 1.71078e7i | − | 0.981475i | ||||||
\(789\) | −1.00091e6 | − | 1.49939e6i | −0.0572404 | − | 0.0857477i | ||||
\(790\) | −8.78950e6 | −0.501068 | ||||||||
\(791\) | − | 4.44391e7i | − | 2.52536i | ||||||
\(792\) | 1.58066e7 | + | 6.56358e6i | 0.895420 | + | 0.371816i | ||||
\(793\) | 711541.i | 0.0401806i | ||||||||
\(794\) | − | 6.30027e6i | − | 0.354657i | ||||||
\(795\) | 1.11466e6 | + | 1.66979e6i | 0.0625494 | + | 0.0937008i | ||||
\(796\) | − | 1.21225e7i | − | 0.678126i | ||||||
\(797\) | −9.56128e6 | −0.533175 | −0.266588 | − | 0.963811i | \(-0.585896\pi\) | ||||
−0.266588 | + | 0.963811i | \(0.585896\pi\) | |||||||
\(798\) | 3.88799e7 | − | 2.59541e7i | 2.16132 | − | 1.44277i | ||||
\(799\) | 196767.i | 0.0109040i | ||||||||
\(800\) | − | 3.01665e6i | − | 0.166648i | ||||||
\(801\) | 2.33136e6 | − | 5.61446e6i | 0.128389 | − | 0.309191i | ||||
\(802\) | 3.86519e7i | 2.12195i | ||||||||
\(803\) | 914683. | 0.0500590 | ||||||||
\(804\) | −4.13941e7 | + | 2.76324e7i | −2.25839 | + | 1.50757i | ||||
\(805\) | 2.47459e7 | + | 6.73340e6i | 1.34590 | + | 0.366222i | ||||
\(806\) | − | 1.10488e6i | − | 0.0599068i | ||||||
\(807\) | −1.73670e7 | + | 1.15932e7i | −0.938731 | + | 0.626645i | ||||
\(808\) | 9.04414e6 | 0.487348 | ||||||||
\(809\) | 341566.i | 0.0183486i | 0.999958 | + | 0.00917430i | \(0.00292031\pi\) | ||||
−0.999958 | + | 0.00917430i | \(0.997080\pi\) | |||||||
\(810\) | −1.69911e7 | + | 1.69315e7i | −0.909930 | + | 0.906742i | ||||
\(811\) | 8.80736e6 | 0.470212 | 0.235106 | − | 0.971970i | \(-0.424456\pi\) | ||||
0.235106 | + | 0.971970i | \(0.424456\pi\) | |||||||
\(812\) | 3.20919e7 | 1.70807 | ||||||||
\(813\) | −5.18037e6 | − | 7.76034e6i | −0.274874 | − | 0.411770i | ||||
\(814\) | 3.00017e7 | 1.58703 | ||||||||
\(815\) | −2.36312e7 | −1.24621 | ||||||||
\(816\) | 1.07829e7 | + | 1.61531e7i | 0.566904 | + | 0.849238i | ||||
\(817\) | −1.50778e7 | −0.790285 | ||||||||
\(818\) | 2.72552e7i | 1.42418i | ||||||||
\(819\) | 1.94225e6 | + | 806504.i | 0.101180 | + | 0.0420143i | ||||
\(820\) | − | 3.55739e7i | − | 1.84755i | ||||||
\(821\) | − | 2.18380e7i | − | 1.13072i | −0.824844 | − | 0.565360i | \(-0.808737\pi\) | ||
0.824844 | − | 0.565360i | \(-0.191263\pi\) | |||||||
\(822\) | −4.79710e6 | + | 3.20228e6i | −0.247628 | + | 0.165302i | ||||
\(823\) | 1.80035e7 | 0.926525 | 0.463262 | − | 0.886221i | \(-0.346679\pi\) | ||||
0.463262 | + | 0.886221i | \(0.346679\pi\) | |||||||
\(824\) | 3.95554e7 | 2.02950 | ||||||||
\(825\) | −3.01600e6 | − | 4.51805e6i | −0.154275 | − | 0.231109i | ||||
\(826\) | − | 9.67966e7i | − | 4.93639i | ||||||
\(827\) | −3.11461e7 | −1.58358 | −0.791790 | − | 0.610793i | \(-0.790851\pi\) | ||||
−0.791790 | + | 0.610793i | \(0.790851\pi\) | |||||||
\(828\) | −2.92742e7 | − | 2.26845e7i | −1.48392 | − | 1.14988i | ||||
\(829\) | 1.92259e7 | 0.971631 | 0.485815 | − | 0.874061i | \(-0.338523\pi\) | ||||
0.485815 | + | 0.874061i | \(0.338523\pi\) | |||||||
\(830\) | − | 1.63795e7i | − | 0.825287i | ||||||
\(831\) | −6.95921e6 | − | 1.04251e7i | −0.349589 | − | 0.523694i | ||||
\(832\) | −1.55553e6 | −0.0779057 | ||||||||
\(833\) | 7.56203e7 | 3.77595 | ||||||||
\(834\) | 3.09639e7 | − | 2.06698e7i | 1.54149 | − | 1.02901i | ||||
\(835\) | 1.55550e7i | 0.772067i | ||||||||
\(836\) | 2.05579e7i | 1.01733i | ||||||||
\(837\) | −1.18059e7 | + | 2.33219e6i | −0.582487 | + | 0.115067i | ||||
\(838\) | − | 7.01005e6i | − | 0.344835i | ||||||
\(839\) | 7.59547e6 | 0.372520 | 0.186260 | − | 0.982500i | \(-0.440363\pi\) | ||||
0.186260 | + | 0.982500i | \(0.440363\pi\) | |||||||
\(840\) | 2.35675e7 | + | 3.53047e7i | 1.15243 | + | 1.72637i | ||||
\(841\) | 1.55059e7 | 0.755972 | ||||||||
\(842\) | −4.38753e7 | −2.13275 | ||||||||
\(843\) | 1.67362e6 | + | 2.50713e6i | 0.0811127 | + | 0.121509i | ||||
\(844\) | −1.20931e7 | −0.584361 | ||||||||
\(845\) | −1.56629e7 | −0.754624 | ||||||||
\(846\) | 93555.5 | − | 225304.i | 0.00449411 | − | 0.0108229i | ||||
\(847\) | − | 2.21318e7i | − | 1.06001i | ||||||
\(848\) | −2.01536e6 | −0.0962417 | ||||||||
\(849\) | 2.44767e7 | − | 1.63393e7i | 1.16542 | − | 0.777971i | ||||
\(850\) | − | 2.40515e7i | − | 1.14181i | ||||||
\(851\) | −2.92735e7 | − | 7.96536e6i | −1.38564 | − | 0.377035i | ||||
\(852\) | −5.82874e6 | + | 3.89094e6i | −0.275091 | + | 0.183635i | ||||
\(853\) | 2.93401e7 | 1.38067 | 0.690333 | − | 0.723492i | \(-0.257464\pi\) | ||||
0.690333 | + | 0.723492i | \(0.257464\pi\) | |||||||
\(854\) | − | 4.49803e7i | − | 2.11046i | ||||||
\(855\) | −1.24349e7 | − | 5.16348e6i | −0.581736 | − | 0.241561i | ||||
\(856\) | 4.15501e7i | 1.93815i | ||||||||
\(857\) | 3.67696e7i | 1.71016i | 0.518497 | + | 0.855079i | \(0.326492\pi\) | ||||
−0.518497 | + | 0.855079i | \(0.673508\pi\) | |||||||
\(858\) | −1.17896e6 | + | 787011.i | −0.0546742 | + | 0.0364974i | ||||
\(859\) | −8.06409e6 | −0.372883 | −0.186442 | − | 0.982466i | \(-0.559695\pi\) | ||||
−0.186442 | + | 0.982466i | \(0.559695\pi\) | |||||||
\(860\) | − | 2.92977e7i | − | 1.35079i | ||||||
\(861\) | 2.89074e7 | + | 4.33041e7i | 1.32893 | + | 1.99077i | ||||
\(862\) | 3.44966e7i | 1.58128i | ||||||||
\(863\) | − | 4.88529e6i | − | 0.223287i | −0.993748 | − | 0.111644i | \(-0.964389\pi\) | ||
0.993748 | − | 0.111644i | \(-0.0356115\pi\) | |||||||
\(864\) | 1.66160e6 | + | 8.41126e6i | 0.0757254 | + | 0.383333i | ||||
\(865\) | 1.30603e7i | 0.593490i | ||||||||
\(866\) | 2.75659e7 | 1.24904 | ||||||||
\(867\) | −1.83230e7 | − | 2.74484e7i | −0.827846 | − | 1.24014i | ||||
\(868\) | 4.55705e7i | 2.05298i | ||||||||
\(869\) | 5.65739e6i | 0.254136i | ||||||||
\(870\) | −7.86563e6 | − | 1.17829e7i | −0.352318 | − | 0.527783i | ||||
\(871\) | − | 1.92629e6i | − | 0.0860354i | ||||||
\(872\) | −6.38337e7 | −2.84288 | ||||||||
\(873\) | −1.93285e7 | − | 8.02601e6i | −0.858347 | − | 0.356422i | ||||
\(874\) | 8.36548e6 | − | 3.07440e7i | 0.370435 | − | 1.36139i | ||||
\(875\) | − | 4.50622e7i | − | 1.98972i | ||||||
\(876\) | −1.81885e6 | − | 2.72468e6i | −0.0800822 | − | 0.119965i | ||||
\(877\) | 1.34241e7 | 0.589367 | 0.294683 | − | 0.955595i | \(-0.404786\pi\) | ||||
0.294683 | + | 0.955595i | \(0.404786\pi\) | |||||||
\(878\) | 2.12016e7i | 0.928182i | ||||||||
\(879\) | −8.43814e6 | − | 1.26406e7i | −0.368362 | − | 0.551816i | ||||
\(880\) | −7.33284e6 | −0.319202 | ||||||||
\(881\) | −3.49780e7 | −1.51829 | −0.759146 | − | 0.650921i | \(-0.774383\pi\) | ||||
−0.759146 | + | 0.650921i | \(0.774383\pi\) | |||||||
\(882\) | −8.65874e7 | − | 3.59547e7i | −3.74786 | − | 1.55627i | ||||
\(883\) | 1.13880e6 | 0.0491527 | 0.0245764 | − | 0.999698i | \(-0.492176\pi\) | ||||
0.0245764 | + | 0.999698i | \(0.492176\pi\) | |||||||
\(884\) | −4.09487e6 | −0.176242 | ||||||||
\(885\) | −2.31881e7 | + | 1.54791e7i | −0.995194 | + | 0.664336i | ||||
\(886\) | 3.08159e7 | 1.31884 | ||||||||
\(887\) | 8.31249e6i | 0.354750i | 0.984143 | + | 0.177375i | \(0.0567605\pi\) | ||||
−0.984143 | + | 0.177375i | \(0.943239\pi\) | |||||||
\(888\) | −2.78794e7 | − | 4.17642e7i | −1.18646 | − | 1.77734i | ||||
\(889\) | 2.67216e7i | 1.13399i | ||||||||
\(890\) | 1.01626e7i | 0.430063i | ||||||||
\(891\) | 1.08980e7 | + | 1.09363e7i | 0.459889 | + | 0.461507i | ||||
\(892\) | 5.70698e6 | 0.240156 | ||||||||
\(893\) | 136937. | 0.00574635 | ||||||||
\(894\) | 3.38105e7 | − | 2.25700e7i | 1.41484 | − | 0.944470i | ||||
\(895\) | 1.59880e7i | 0.667171i | ||||||||
\(896\) | 8.10385e7 | 3.37226 | ||||||||
\(897\) | 1.35930e6 | − | 454897.i | 0.0564070 | − | 0.0188769i | ||||
\(898\) | −5.30483e7 | −2.19523 | ||||||||
\(899\) | − | 7.10752e6i | − | 0.293305i | ||||||
\(900\) | −7.46118e6 | + | 1.79683e7i | −0.307045 | + | 0.739435i | ||||
\(901\) | 5.72142e6 | 0.234797 | ||||||||
\(902\) | −3.50941e7 | −1.43621 | ||||||||
\(903\) | 2.38073e7 | + | 3.56641e7i | 0.971609 | + | 1.45550i | ||||
\(904\) | − | 5.01336e7i | − | 2.04037i | ||||||
\(905\) | 3.03109e6i | 0.123021i | ||||||||
\(906\) | −4.63900e7 | + | 3.09674e7i | −1.87760 | + | 1.25338i | ||||
\(907\) | − | 356480.i | − | 0.0143886i | −0.999974 | − | 0.00719428i | \(-0.997710\pi\) | ||
0.999974 | − | 0.00719428i | \(-0.00229003\pi\) | |||||||
\(908\) | −3.65370e7 | −1.47068 | ||||||||
\(909\) | 7.53474e6 | + | 3.12874e6i | 0.302454 | + | 0.125591i | ||||
\(910\) | −3.51563e6 | −0.140734 | ||||||||
\(911\) | −5.11410e6 | −0.204161 | −0.102081 | − | 0.994776i | \(-0.532550\pi\) | ||||
−0.102081 | + | 0.994776i | \(0.532550\pi\) | |||||||
\(912\) | 1.12415e7 | − | 7.50418e6i | 0.447545 | − | 0.298756i | ||||
\(913\) | −1.05427e7 | −0.418577 | ||||||||
\(914\) | 4.01184e7 | 1.58847 | ||||||||
\(915\) | −1.07753e7 | + | 7.19298e6i | −0.425477 | + | 0.284025i | ||||
\(916\) | 7.03788e7i | 2.77143i | ||||||||
\(917\) | 1.07697e7 | 0.422941 | ||||||||
\(918\) | 1.32478e7 | + | 6.70623e7i | 0.518844 | + | 2.62647i | ||||
\(919\) | − | 4.08757e7i | − | 1.59653i | −0.602307 | − | 0.798265i | \(-0.705752\pi\) | ||
0.602307 | − | 0.798265i | \(-0.294248\pi\) | |||||||
\(920\) | 2.79169e7 | + | 7.59623e6i | 1.08742 | + | 0.295889i | ||||
\(921\) | 2.09163e7 | + | 3.13332e7i | 0.812522 | + | 1.21718i | ||||
\(922\) | 2.03530e7 | 0.788500 | ||||||||
\(923\) | − | 271243.i | − | 0.0104798i | ||||||
\(924\) | 4.86263e7 | − | 3.24602e7i | 1.87366 | − | 1.25075i | ||||
\(925\) | 1.59377e7i | 0.612450i | ||||||||
\(926\) | − | 4.87110e7i | − | 1.86681i | ||||||
\(927\) | 3.29539e7 | + | 1.36839e7i | 1.25953 | + | 0.523009i | ||||
\(928\) | −5.06383e6 | −0.193023 | ||||||||
\(929\) | 2.72339e7i | 1.03531i | 0.855590 | + | 0.517654i | \(0.173195\pi\) | ||||
−0.855590 | + | 0.517654i | \(0.826805\pi\) | |||||||
\(930\) | 1.67318e7 | − | 1.11692e7i | 0.634358 | − | 0.423462i | ||||
\(931\) | − | 5.26268e7i | − | 1.98991i | ||||||
\(932\) | 7.26501e7i | 2.73966i | ||||||||
\(933\) | 1.59360e7 | − | 1.06380e7i | 0.599341 | − | 0.400087i | ||||
\(934\) | − | 1.33496e7i | − | 0.500729i | ||||||
\(935\) | 2.08172e7 | 0.778743 | ||||||||
\(936\) | 2.19113e6 | + | 909851.i | 0.0817484 | + | 0.0339454i | ||||
\(937\) | − | 2.55993e7i | − | 0.952529i | −0.879302 | − | 0.476265i | \(-0.841990\pi\) | ||
0.879302 | − | 0.476265i | \(-0.158010\pi\) | |||||||
\(938\) | 1.21771e8i | 4.51896i | ||||||||
\(939\) | 2.71165e7 | − | 1.81015e7i | 1.00362 | − | 0.669961i | ||||
\(940\) | 266081.i | 0.00982189i | ||||||||
\(941\) | −6.34978e6 | −0.233768 | −0.116884 | − | 0.993146i | \(-0.537291\pi\) | ||||
−0.116884 | + | 0.993146i | \(0.537291\pi\) | |||||||
\(942\) | −1.77429e7 | − | 2.65794e7i | −0.651474 | − | 0.975927i | ||||
\(943\) | 3.42423e7 | + | 9.31739e6i | 1.25396 | + | 0.341205i | ||||
\(944\) | − | 2.79871e7i | − | 1.02218i | ||||||
\(945\) | 7.42087e6 | + | 3.75656e7i | 0.270318 | + | 1.36839i | ||||
\(946\) | −2.89026e7 | −1.05005 | ||||||||
\(947\) | − | 7.94723e6i | − | 0.287966i | −0.989580 | − | 0.143983i | \(-0.954009\pi\) | ||
0.989580 | − | 0.143983i | \(-0.0459910\pi\) | |||||||
\(948\) | 1.68524e7 | − | 1.12497e7i | 0.609032 | − | 0.406556i | ||||
\(949\) | 126794. | 0.00457019 | ||||||||
\(950\) | −1.67383e7 | −0.601730 | ||||||||
\(951\) | −2.34137e7 | + | 1.56297e7i | −0.839495 | + | 0.560400i | ||||
\(952\) | 1.20969e8 | 4.32597 | ||||||||
\(953\) | −9.43634e6 | −0.336567 | −0.168283 | − | 0.985739i | \(-0.553822\pi\) | ||||
−0.168283 | + | 0.985739i | \(0.553822\pi\) | |||||||
\(954\) | −6.55119e6 | − | 2.72033e6i | −0.233050 | − | 0.0967722i | ||||
\(955\) | 1.01718e7 | 0.360902 | ||||||||
\(956\) | 6.59877e7i | 2.33517i | ||||||||
\(957\) | −7.58412e6 | + | 5.06274e6i | −0.267686 | + | 0.178692i | ||||
\(958\) | 9.80325e6i | 0.345109i | ||||||||
\(959\) | 9.20732e6i | 0.323286i | ||||||||
\(960\) | −1.57248e7 | − | 2.35562e7i | −0.550691 | − | 0.824951i | ||||
\(961\) | −1.85365e7 | −0.647468 | ||||||||
\(962\) | 4.15886e6 | 0.144890 | ||||||||
\(963\) | −1.43739e7 | + | 3.46157e7i | −0.499469 | + | 1.20284i | ||||
\(964\) | 4.30627e7i | 1.49248i | ||||||||
\(965\) | 1.96645e7 | 0.679775 | ||||||||
\(966\) | −8.59285e7 | + | 2.87565e7i | −2.96275 | + | 0.991500i | ||||
\(967\) | −3.60068e7 | −1.23828 | −0.619139 | − | 0.785282i | \(-0.712518\pi\) | ||||
−0.619139 | + | 0.785282i | \(0.712518\pi\) | |||||||
\(968\) | − | 2.49679e7i | − | 0.856432i | ||||||
\(969\) | −3.19135e7 | + | 2.13037e7i | −1.09186 | + | 0.728862i | ||||
\(970\) | 3.49862e7 | 1.19390 | ||||||||
\(971\) | −4.18592e7 | −1.42476 | −0.712382 | − | 0.701792i | \(-0.752383\pi\) | ||||
−0.712382 | + | 0.701792i | \(0.752383\pi\) | |||||||
\(972\) | 1.09068e7 | − | 5.42102e7i | 0.370280 | − | 1.84041i | ||||
\(973\) | − | 5.94306e7i | − | 2.01246i | ||||||
\(974\) | − | 7.09202e7i | − | 2.39537i | ||||||
\(975\) | −418081. | − | 626297.i | −0.0140847 | − | 0.0210993i | ||||
\(976\) | − | 1.30053e7i | − | 0.437015i | ||||||
\(977\) | 2.38899e7 | 0.800715 | 0.400358 | − | 0.916359i | \(-0.368886\pi\) | ||||
0.400358 | + | 0.916359i | \(0.368886\pi\) | |||||||
\(978\) | 6.94440e7 | − | 4.63569e7i | 2.32160 | − | 1.54977i | ||||
\(979\) | 6.54121e6 | 0.218123 | ||||||||
\(980\) | 1.02259e8 | 3.40123 | ||||||||
\(981\) | −5.31803e7 | − | 2.20827e7i | −1.76433 | − | 0.732622i | ||||
\(982\) | −3.55174e7 | −1.17534 | ||||||||
\(983\) | 4.55466e7 | 1.50339 | 0.751696 | − | 0.659510i | \(-0.229236\pi\) | ||||
0.751696 | + | 0.659510i | \(0.229236\pi\) | |||||||
\(984\) | 3.26117e7 | + | 4.88532e7i | 1.07371 | + | 1.60844i | ||||
\(985\) | 1.20561e7i | 0.395929i | ||||||||
\(986\) | −4.03735e7 | −1.32253 | ||||||||
\(987\) | −216218. | − | 323901.i | −0.00706480 | − | 0.0105833i | ||||
\(988\) | 2.84976e6i | 0.0928787i | ||||||||
\(989\) | 2.82010e7 | + | 7.67355e6i | 0.916799 | + | 0.249463i | ||||
\(990\) | −2.38363e7 | − | 9.89784e6i | −0.772950 | − | 0.320961i | ||||
\(991\) | 5.41729e7 | 1.75226 | 0.876129 | − | 0.482077i | \(-0.160117\pi\) | ||||
0.876129 | + | 0.482077i | \(0.160117\pi\) | |||||||
\(992\) | − | 7.19064e6i | − | 0.232000i | ||||||
\(993\) | −1.83730e7 | − | 2.75233e7i | −0.591299 | − | 0.885782i | ||||
\(994\) | 1.71467e7i | 0.550447i | ||||||||
\(995\) | 8.54290e6i | 0.273557i | ||||||||
\(996\) | 2.09642e7 | + | 3.14049e7i | 0.669621 | + | 1.00311i | ||||
\(997\) | 1.04983e7 | 0.334489 | 0.167244 | − | 0.985915i | \(-0.446513\pi\) | ||||
0.167244 | + | 0.985915i | \(0.446513\pi\) | |||||||
\(998\) | 3.32377e7i | 1.05634i | ||||||||
\(999\) | −8.77861e6 | − | 4.44387e7i | −0.278299 | − | 1.40879i |
(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 | 69.6.c.b.68.4 | yes | 32 | |
3.2 | odd | 2 | inner | 69.6.c.b.68.29 | yes | 32 | |
23.22 | odd | 2 | inner | 69.6.c.b.68.3 | ✓ | 32 | |
69.68 | even | 2 | inner | 69.6.c.b.68.30 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.c.b.68.3 | ✓ | 32 | 23.22 | odd | 2 | inner | |
69.6.c.b.68.4 | yes | 32 | 1.1 | even | 1 | trivial | |
69.6.c.b.68.29 | yes | 32 | 3.2 | odd | 2 | inner | |
69.6.c.b.68.30 | yes | 32 | 69.68 | even | 2 | inner |