Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.a (trivial) |
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: | yes |
Analytic conductor: | \(26.4633302691\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 15x + 11 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.723686\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44737 | −0.255862 | −0.127931 | − | 0.991783i | \(-0.540834\pi\) | ||||
−0.127931 | + | 0.991783i | \(0.540834\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −29.9051 | −0.934535 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −13.0263 | −0.147722 | ||||||||
\(7\) | 41.5023 | 0.320130 | 0.160065 | − | 0.987106i | \(-0.448830\pi\) | ||||
0.160065 | + | 0.987106i | \(0.448830\pi\) | |||||||
\(8\) | 89.5997 | 0.494973 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 36.1843 | 0.114425 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −269.146 | −0.539554 | ||||||||
\(13\) | 434.580 | 0.713201 | 0.356600 | − | 0.934257i | \(-0.383936\pi\) | ||||
0.356600 | + | 0.934257i | \(0.383936\pi\) | |||||||
\(14\) | −60.0692 | −0.0819090 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | 827.280 | 0.807890 | ||||||||
\(17\) | 474.359 | 0.398093 | 0.199046 | − | 0.979990i | \(-0.436216\pi\) | ||||
0.199046 | + | 0.979990i | \(0.436216\pi\) | |||||||
\(18\) | −117.237 | −0.0852872 | ||||||||
\(19\) | −2586.54 | −1.64375 | −0.821873 | − | 0.569671i | \(-0.807071\pi\) | ||||
−0.821873 | + | 0.569671i | \(0.807071\pi\) | |||||||
\(20\) | 747.628 | 0.417937 | ||||||||
\(21\) | 373.520 | 0.184827 | ||||||||
\(22\) | −175.132 | −0.0771452 | ||||||||
\(23\) | −3671.69 | −1.44726 | −0.723629 | − | 0.690189i | \(-0.757527\pi\) | ||||
−0.723629 | + | 0.690189i | \(0.757527\pi\) | |||||||
\(24\) | 806.397 | 0.285773 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −628.999 | −0.182481 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −1241.13 | −0.299173 | ||||||||
\(29\) | −4269.64 | −0.942749 | −0.471374 | − | 0.881933i | \(-0.656242\pi\) | ||||
−0.471374 | + | 0.881933i | \(0.656242\pi\) | |||||||
\(30\) | 325.659 | 0.0660632 | ||||||||
\(31\) | −8415.46 | −1.57280 | −0.786400 | − | 0.617717i | \(-0.788058\pi\) | ||||
−0.786400 | + | 0.617717i | \(0.788058\pi\) | |||||||
\(32\) | −4064.57 | −0.701681 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | −686.573 | −0.101857 | ||||||||
\(35\) | −1037.56 | −0.143167 | ||||||||
\(36\) | −2422.31 | −0.311512 | ||||||||
\(37\) | 13940.3 | 1.67405 | 0.837024 | − | 0.547166i | \(-0.184294\pi\) | ||||
0.837024 | + | 0.547166i | \(0.184294\pi\) | |||||||
\(38\) | 3743.68 | 0.420571 | ||||||||
\(39\) | 3911.22 | 0.411767 | ||||||||
\(40\) | −2239.99 | −0.221359 | ||||||||
\(41\) | 1771.24 | 0.164558 | 0.0822788 | − | 0.996609i | \(-0.473780\pi\) | ||||
0.0822788 | + | 0.996609i | \(0.473780\pi\) | |||||||
\(42\) | −540.623 | −0.0472902 | ||||||||
\(43\) | −11481.3 | −0.946932 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(44\) | −3618.52 | −0.281773 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | 5314.30 | 0.370298 | ||||||||
\(47\) | −11048.5 | −0.729556 | −0.364778 | − | 0.931094i | \(-0.618855\pi\) | ||||
−0.364778 | + | 0.931094i | \(0.618855\pi\) | |||||||
\(48\) | 7445.52 | 0.466436 | ||||||||
\(49\) | −15084.6 | −0.897517 | ||||||||
\(50\) | −904.607 | −0.0511723 | ||||||||
\(51\) | 4269.23 | 0.229839 | ||||||||
\(52\) | −12996.2 | −0.666511 | ||||||||
\(53\) | 20924.0 | 1.02319 | 0.511594 | − | 0.859227i | \(-0.329055\pi\) | ||||
0.511594 | + | 0.859227i | \(0.329055\pi\) | |||||||
\(54\) | −1055.13 | −0.0492406 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 3718.59 | 0.158456 | ||||||||
\(57\) | −23278.8 | −0.949017 | ||||||||
\(58\) | 6179.75 | 0.241213 | ||||||||
\(59\) | −33001.2 | −1.23424 | −0.617121 | − | 0.786868i | \(-0.711701\pi\) | ||||
−0.617121 | + | 0.786868i | \(0.711701\pi\) | |||||||
\(60\) | 6728.65 | 0.241296 | ||||||||
\(61\) | −32348.2 | −1.11308 | −0.556539 | − | 0.830821i | \(-0.687871\pi\) | ||||
−0.556539 | + | 0.830821i | \(0.687871\pi\) | |||||||
\(62\) | 12180.3 | 0.402419 | ||||||||
\(63\) | 3361.68 | 0.106710 | ||||||||
\(64\) | −20590.0 | −0.628357 | ||||||||
\(65\) | −10864.5 | −0.318953 | ||||||||
\(66\) | −1576.19 | −0.0445398 | ||||||||
\(67\) | 28892.8 | 0.786325 | 0.393163 | − | 0.919469i | \(-0.371381\pi\) | ||||
0.393163 | + | 0.919469i | \(0.371381\pi\) | |||||||
\(68\) | −14185.7 | −0.372032 | ||||||||
\(69\) | −33045.2 | −0.835575 | ||||||||
\(70\) | 1501.73 | 0.0366308 | ||||||||
\(71\) | −20476.5 | −0.482069 | −0.241034 | − | 0.970517i | \(-0.577487\pi\) | ||||
−0.241034 | + | 0.970517i | \(0.577487\pi\) | |||||||
\(72\) | 7257.58 | 0.164991 | ||||||||
\(73\) | −43333.2 | −0.951729 | −0.475864 | − | 0.879519i | \(-0.657865\pi\) | ||||
−0.475864 | + | 0.879519i | \(0.657865\pi\) | |||||||
\(74\) | −20176.8 | −0.428325 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | 77350.7 | 1.53614 | ||||||||
\(77\) | 5021.77 | 0.0965229 | ||||||||
\(78\) | −5660.99 | −0.105355 | ||||||||
\(79\) | −95301.8 | −1.71804 | −0.859020 | − | 0.511942i | \(-0.828926\pi\) | ||||
−0.859020 | + | 0.511942i | \(0.828926\pi\) | |||||||
\(80\) | −20682.0 | −0.361299 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −2563.64 | −0.0421040 | ||||||||
\(83\) | −16682.8 | −0.265811 | −0.132905 | − | 0.991129i | \(-0.542431\pi\) | ||||
−0.132905 | + | 0.991129i | \(0.542431\pi\) | |||||||
\(84\) | −11170.2 | −0.172728 | ||||||||
\(85\) | −11859.0 | −0.178033 | ||||||||
\(86\) | 16617.7 | 0.242284 | ||||||||
\(87\) | −38426.7 | −0.544296 | ||||||||
\(88\) | 10841.6 | 0.149240 | ||||||||
\(89\) | 143269. | 1.91724 | 0.958622 | − | 0.284681i | \(-0.0918877\pi\) | ||||
0.958622 | + | 0.284681i | \(0.0918877\pi\) | |||||||
\(90\) | 2930.93 | 0.0381416 | ||||||||
\(91\) | 18036.1 | 0.228317 | ||||||||
\(92\) | 109802. | 1.35251 | ||||||||
\(93\) | −75739.1 | −0.908057 | ||||||||
\(94\) | 15991.3 | 0.186665 | ||||||||
\(95\) | 64663.4 | 0.735105 | ||||||||
\(96\) | −36581.1 | −0.405116 | ||||||||
\(97\) | −128960. | −1.39163 | −0.695816 | − | 0.718220i | \(-0.744957\pi\) | ||||
−0.695816 | + | 0.718220i | \(0.744957\pi\) | |||||||
\(98\) | 21833.0 | 0.229640 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | −18690.7 | −0.186907 | ||||||||
\(101\) | 147088. | 1.43475 | 0.717373 | − | 0.696689i | \(-0.245344\pi\) | ||||
0.717373 | + | 0.696689i | \(0.245344\pi\) | |||||||
\(102\) | −6179.16 | −0.0588070 | ||||||||
\(103\) | 88889.0 | 0.825572 | 0.412786 | − | 0.910828i | \(-0.364556\pi\) | ||||
0.412786 | + | 0.910828i | \(0.364556\pi\) | |||||||
\(104\) | 38938.3 | 0.353015 | ||||||||
\(105\) | −9338.01 | −0.0826573 | ||||||||
\(106\) | −30284.8 | −0.261794 | ||||||||
\(107\) | 146352. | 1.23577 | 0.617886 | − | 0.786268i | \(-0.287989\pi\) | ||||
0.617886 | + | 0.786268i | \(0.287989\pi\) | |||||||
\(108\) | −21800.8 | −0.179851 | ||||||||
\(109\) | −111535. | −0.899174 | −0.449587 | − | 0.893236i | \(-0.648429\pi\) | ||||
−0.449587 | + | 0.893236i | \(0.648429\pi\) | |||||||
\(110\) | 4378.30 | 0.0345004 | ||||||||
\(111\) | 125463. | 0.966512 | ||||||||
\(112\) | 34334.0 | 0.258630 | ||||||||
\(113\) | −56633.9 | −0.417234 | −0.208617 | − | 0.977997i | \(-0.566896\pi\) | ||||
−0.208617 | + | 0.977997i | \(0.566896\pi\) | |||||||
\(114\) | 33693.1 | 0.242817 | ||||||||
\(115\) | 91792.2 | 0.647234 | ||||||||
\(116\) | 127684. | 0.881031 | ||||||||
\(117\) | 35201.0 | 0.237734 | ||||||||
\(118\) | 47765.1 | 0.315795 | ||||||||
\(119\) | 19687.0 | 0.127442 | ||||||||
\(120\) | −20159.9 | −0.127802 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 46819.9 | 0.284794 | ||||||||
\(123\) | 15941.2 | 0.0950074 | ||||||||
\(124\) | 251665. | 1.46984 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −4865.61 | −0.0273030 | ||||||||
\(127\) | 79565.3 | 0.437738 | 0.218869 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218869 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(128\) | 159868. | 0.862454 | ||||||||
\(129\) | −103331. | −0.546712 | ||||||||
\(130\) | 15725.0 | 0.0816078 | ||||||||
\(131\) | 73365.2 | 0.373518 | 0.186759 | − | 0.982406i | \(-0.440202\pi\) | ||||
0.186759 | + | 0.982406i | \(0.440202\pi\) | |||||||
\(132\) | −32566.7 | −0.162682 | ||||||||
\(133\) | −107347. | −0.526213 | ||||||||
\(134\) | −41818.6 | −0.201190 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | 42502.4 | 0.197045 | ||||||||
\(137\) | −130737. | −0.595112 | −0.297556 | − | 0.954704i | \(-0.596171\pi\) | ||||
−0.297556 | + | 0.954704i | \(0.596171\pi\) | |||||||
\(138\) | 47828.7 | 0.213792 | ||||||||
\(139\) | −366480. | −1.60884 | −0.804420 | − | 0.594060i | \(-0.797524\pi\) | ||||
−0.804420 | + | 0.594060i | \(0.797524\pi\) | |||||||
\(140\) | 31028.3 | 0.133794 | ||||||||
\(141\) | −99436.5 | −0.421209 | ||||||||
\(142\) | 29637.0 | 0.123343 | ||||||||
\(143\) | 52584.2 | 0.215038 | ||||||||
\(144\) | 67009.6 | 0.269297 | ||||||||
\(145\) | 106741. | 0.421610 | ||||||||
\(146\) | 62719.2 | 0.243511 | ||||||||
\(147\) | −135761. | −0.518181 | ||||||||
\(148\) | −416886. | −1.56446 | ||||||||
\(149\) | 476119. | 1.75691 | 0.878455 | − | 0.477825i | \(-0.158575\pi\) | ||||
0.878455 | + | 0.477825i | \(0.158575\pi\) | |||||||
\(150\) | −8141.47 | −0.0295444 | ||||||||
\(151\) | 231635. | 0.826725 | 0.413362 | − | 0.910567i | \(-0.364354\pi\) | ||||
0.413362 | + | 0.910567i | \(0.364354\pi\) | |||||||
\(152\) | −231753. | −0.813610 | ||||||||
\(153\) | 38423.0 | 0.132698 | ||||||||
\(154\) | −7268.38 | −0.0246965 | ||||||||
\(155\) | 210386. | 0.703378 | ||||||||
\(156\) | −116966. | −0.384810 | ||||||||
\(157\) | −79283.9 | −0.256706 | −0.128353 | − | 0.991729i | \(-0.540969\pi\) | ||||
−0.128353 | + | 0.991729i | \(0.540969\pi\) | |||||||
\(158\) | 137937. | 0.439581 | ||||||||
\(159\) | 188316. | 0.590738 | ||||||||
\(160\) | 101614. | 0.313801 | ||||||||
\(161\) | −152383. | −0.463311 | ||||||||
\(162\) | −9496.21 | −0.0284291 | ||||||||
\(163\) | −303550. | −0.894872 | −0.447436 | − | 0.894316i | \(-0.647663\pi\) | ||||
−0.447436 | + | 0.894316i | \(0.647663\pi\) | |||||||
\(164\) | −52969.1 | −0.153785 | ||||||||
\(165\) | −27225.0 | −0.0778499 | ||||||||
\(166\) | 24146.2 | 0.0680108 | ||||||||
\(167\) | −547748. | −1.51981 | −0.759906 | − | 0.650033i | \(-0.774755\pi\) | ||||
−0.759906 | + | 0.650033i | \(0.774755\pi\) | |||||||
\(168\) | 33467.3 | 0.0914846 | ||||||||
\(169\) | −182433. | −0.491345 | ||||||||
\(170\) | 17164.3 | 0.0455517 | ||||||||
\(171\) | −209509. | −0.547915 | ||||||||
\(172\) | 343349. | 0.884941 | ||||||||
\(173\) | −350354. | −0.890003 | −0.445001 | − | 0.895530i | \(-0.646797\pi\) | ||||
−0.445001 | + | 0.895530i | \(0.646797\pi\) | |||||||
\(174\) | 55617.8 | 0.139264 | ||||||||
\(175\) | 25938.9 | 0.0640261 | ||||||||
\(176\) | 100101. | 0.243588 | ||||||||
\(177\) | −297011. | −0.712590 | ||||||||
\(178\) | −207364. | −0.490549 | ||||||||
\(179\) | 185899. | 0.433656 | 0.216828 | − | 0.976210i | \(-0.430429\pi\) | ||||
0.216828 | + | 0.976210i | \(0.430429\pi\) | |||||||
\(180\) | 60557.9 | 0.139312 | ||||||||
\(181\) | 247930. | 0.562513 | 0.281257 | − | 0.959633i | \(-0.409249\pi\) | ||||
0.281257 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(182\) | −26104.9 | −0.0584176 | ||||||||
\(183\) | −291134. | −0.642636 | ||||||||
\(184\) | −328982. | −0.716354 | ||||||||
\(185\) | −348508. | −0.748657 | ||||||||
\(186\) | 109623. | 0.232337 | ||||||||
\(187\) | 57397.4 | 0.120030 | ||||||||
\(188\) | 330407. | 0.681796 | ||||||||
\(189\) | 30255.2 | 0.0616091 | ||||||||
\(190\) | −93592.0 | −0.188085 | ||||||||
\(191\) | 715625. | 1.41939 | 0.709695 | − | 0.704509i | \(-0.248833\pi\) | ||||
0.709695 | + | 0.704509i | \(0.248833\pi\) | |||||||
\(192\) | −185310. | −0.362782 | ||||||||
\(193\) | 315860. | 0.610381 | 0.305191 | − | 0.952291i | \(-0.401280\pi\) | ||||
0.305191 | + | 0.952291i | \(0.401280\pi\) | |||||||
\(194\) | 186653. | 0.356065 | ||||||||
\(195\) | −97780.6 | −0.184148 | ||||||||
\(196\) | 451106. | 0.838761 | ||||||||
\(197\) | 139508. | 0.256115 | 0.128058 | − | 0.991767i | \(-0.459126\pi\) | ||||
0.128058 | + | 0.991767i | \(0.459126\pi\) | |||||||
\(198\) | −14185.7 | −0.0257151 | ||||||||
\(199\) | 183434. | 0.328358 | 0.164179 | − | 0.986431i | \(-0.447503\pi\) | ||||
0.164179 | + | 0.986431i | \(0.447503\pi\) | |||||||
\(200\) | 55999.8 | 0.0989946 | ||||||||
\(201\) | 260035. | 0.453985 | ||||||||
\(202\) | −212892. | −0.367096 | ||||||||
\(203\) | −177200. | −0.301802 | ||||||||
\(204\) | −127672. | −0.214793 | ||||||||
\(205\) | −44281.0 | −0.0735924 | ||||||||
\(206\) | −128655. | −0.211232 | ||||||||
\(207\) | −297407. | −0.482420 | ||||||||
\(208\) | 359519. | 0.576188 | ||||||||
\(209\) | −312971. | −0.495608 | ||||||||
\(210\) | 13515.6 | 0.0211488 | ||||||||
\(211\) | −341928. | −0.528723 | −0.264361 | − | 0.964424i | \(-0.585161\pi\) | ||||
−0.264361 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(212\) | −625735. | −0.956204 | ||||||||
\(213\) | −184288. | −0.278322 | ||||||||
\(214\) | −211825. | −0.316186 | ||||||||
\(215\) | 287032. | 0.423481 | ||||||||
\(216\) | 65318.2 | 0.0952576 | ||||||||
\(217\) | −349261. | −0.503501 | ||||||||
\(218\) | 161432. | 0.230064 | ||||||||
\(219\) | −389998. | −0.549481 | ||||||||
\(220\) | 90463.0 | 0.126013 | ||||||||
\(221\) | 206147. | 0.283920 | ||||||||
\(222\) | −181591. | −0.247293 | ||||||||
\(223\) | −1.01837e6 | −1.37133 | −0.685665 | − | 0.727917i | \(-0.740489\pi\) | ||||
−0.685665 | + | 0.727917i | \(0.740489\pi\) | |||||||
\(224\) | −168689. | −0.224629 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 81970.3 | 0.106754 | ||||||||
\(227\) | −362408. | −0.466802 | −0.233401 | − | 0.972381i | \(-0.574985\pi\) | ||||
−0.233401 | + | 0.972381i | \(0.574985\pi\) | |||||||
\(228\) | 696156. | 0.886889 | ||||||||
\(229\) | −1.38333e6 | −1.74315 | −0.871577 | − | 0.490258i | \(-0.836902\pi\) | ||||
−0.871577 | + | 0.490258i | \(0.836902\pi\) | |||||||
\(230\) | −132857. | −0.165602 | ||||||||
\(231\) | 45196.0 | 0.0557275 | ||||||||
\(232\) | −382558. | −0.466635 | ||||||||
\(233\) | 1.19085e6 | 1.43704 | 0.718519 | − | 0.695507i | \(-0.244820\pi\) | ||||
0.718519 | + | 0.695507i | \(0.244820\pi\) | |||||||
\(234\) | −50948.9 | −0.0608269 | ||||||||
\(235\) | 276213. | 0.326267 | ||||||||
\(236\) | 986906. | 1.15344 | ||||||||
\(237\) | −857716. | −0.991911 | ||||||||
\(238\) | −28494.3 | −0.0326074 | ||||||||
\(239\) | 638385. | 0.722916 | 0.361458 | − | 0.932388i | \(-0.382279\pi\) | ||||
0.361458 | + | 0.932388i | \(0.382279\pi\) | |||||||
\(240\) | −186138. | −0.208596 | ||||||||
\(241\) | 301289. | 0.334150 | 0.167075 | − | 0.985944i | \(-0.446568\pi\) | ||||
0.167075 | + | 0.985944i | \(0.446568\pi\) | |||||||
\(242\) | −21191.0 | −0.0232601 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 967378. | 1.04021 | ||||||||
\(245\) | 377114. | 0.401382 | ||||||||
\(246\) | −23072.8 | −0.0243087 | ||||||||
\(247\) | −1.12406e6 | −1.17232 | ||||||||
\(248\) | −754023. | −0.778494 | ||||||||
\(249\) | −150145. | −0.153466 | ||||||||
\(250\) | 22615.2 | 0.0228850 | ||||||||
\(251\) | −285054. | −0.285590 | −0.142795 | − | 0.989752i | \(-0.545609\pi\) | ||||
−0.142795 | + | 0.989752i | \(0.545609\pi\) | |||||||
\(252\) | −100532. | −0.0997243 | ||||||||
\(253\) | −444274. | −0.436365 | ||||||||
\(254\) | −115161. | −0.112000 | ||||||||
\(255\) | −106731. | −0.102787 | ||||||||
\(256\) | 427492. | 0.407688 | ||||||||
\(257\) | −1.72616e6 | −1.63022 | −0.815112 | − | 0.579303i | \(-0.803325\pi\) | ||||
−0.815112 | + | 0.579303i | \(0.803325\pi\) | |||||||
\(258\) | 149559. | 0.139882 | ||||||||
\(259\) | 578554. | 0.535913 | ||||||||
\(260\) | 324904. | 0.298073 | ||||||||
\(261\) | −345841. | −0.314250 | ||||||||
\(262\) | −106187. | −0.0955690 | ||||||||
\(263\) | −1.29514e6 | −1.15459 | −0.577296 | − | 0.816535i | \(-0.695892\pi\) | ||||
−0.577296 | + | 0.816535i | \(0.695892\pi\) | |||||||
\(264\) | 97574.1 | 0.0861638 | ||||||||
\(265\) | −523100. | −0.457583 | ||||||||
\(266\) | 155371. | 0.134638 | ||||||||
\(267\) | 1.28942e6 | 1.10692 | ||||||||
\(268\) | −864042. | −0.734848 | ||||||||
\(269\) | −1.96289e6 | −1.65392 | −0.826960 | − | 0.562261i | \(-0.809932\pi\) | ||||
−0.826960 | + | 0.562261i | \(0.809932\pi\) | |||||||
\(270\) | 26378.4 | 0.0220211 | ||||||||
\(271\) | 436034. | 0.360659 | 0.180330 | − | 0.983606i | \(-0.442284\pi\) | ||||
0.180330 | + | 0.983606i | \(0.442284\pi\) | |||||||
\(272\) | 392427. | 0.321615 | ||||||||
\(273\) | 162325. | 0.131819 | ||||||||
\(274\) | 189226. | 0.152266 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 988220. | 0.780874 | ||||||||
\(277\) | −1.10131e6 | −0.862401 | −0.431201 | − | 0.902256i | \(-0.641910\pi\) | ||||
−0.431201 | + | 0.902256i | \(0.641910\pi\) | |||||||
\(278\) | 530433. | 0.411641 | ||||||||
\(279\) | −681652. | −0.524267 | ||||||||
\(280\) | −92964.8 | −0.0708636 | ||||||||
\(281\) | 1.21262e6 | 0.916135 | 0.458067 | − | 0.888917i | \(-0.348542\pi\) | ||||
0.458067 | + | 0.888917i | \(0.348542\pi\) | |||||||
\(282\) | 143922. | 0.107771 | ||||||||
\(283\) | 2.07749e6 | 1.54196 | 0.770979 | − | 0.636860i | \(-0.219767\pi\) | ||||
0.770979 | + | 0.636860i | \(0.219767\pi\) | |||||||
\(284\) | 612351. | 0.450510 | ||||||||
\(285\) | 581971. | 0.424413 | ||||||||
\(286\) | −76108.9 | −0.0550200 | ||||||||
\(287\) | 73510.5 | 0.0526799 | ||||||||
\(288\) | −329230. | −0.233894 | ||||||||
\(289\) | −1.19484e6 | −0.841522 | ||||||||
\(290\) | −154494. | −0.107874 | ||||||||
\(291\) | −1.16064e6 | −0.803460 | ||||||||
\(292\) | 1.29588e6 | 0.889424 | ||||||||
\(293\) | 1.75150e6 | 1.19190 | 0.595950 | − | 0.803021i | \(-0.296775\pi\) | ||||
0.595950 | + | 0.803021i | \(0.296775\pi\) | |||||||
\(294\) | 196497. | 0.132583 | ||||||||
\(295\) | 825031. | 0.551970 | ||||||||
\(296\) | 1.24905e6 | 0.828609 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −689121. | −0.449526 | ||||||||
\(299\) | −1.59564e6 | −1.03219 | ||||||||
\(300\) | −168216. | −0.107911 | ||||||||
\(301\) | −476499. | −0.303142 | ||||||||
\(302\) | −335261. | −0.211527 | ||||||||
\(303\) | 1.32380e6 | 0.828351 | ||||||||
\(304\) | −2.13979e6 | −1.32797 | ||||||||
\(305\) | 808706. | 0.497784 | ||||||||
\(306\) | −55612.4 | −0.0339522 | ||||||||
\(307\) | 2.76532e6 | 1.67456 | 0.837278 | − | 0.546777i | \(-0.184146\pi\) | ||||
0.837278 | + | 0.546777i | \(0.184146\pi\) | |||||||
\(308\) | −150177. | −0.0902040 | ||||||||
\(309\) | 800001. | 0.476644 | ||||||||
\(310\) | −304507. | −0.179967 | ||||||||
\(311\) | 138490. | 0.0811925 | 0.0405962 | − | 0.999176i | \(-0.487074\pi\) | ||||
0.0405962 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(312\) | 350444. | 0.203813 | ||||||||
\(313\) | 2.25033e6 | 1.29833 | 0.649165 | − | 0.760647i | \(-0.275118\pi\) | ||||
0.649165 | + | 0.760647i | \(0.275118\pi\) | |||||||
\(314\) | 114753. | 0.0656812 | ||||||||
\(315\) | −84042.1 | −0.0477222 | ||||||||
\(316\) | 2.85001e6 | 1.60557 | ||||||||
\(317\) | −300036. | −0.167697 | −0.0838486 | − | 0.996479i | \(-0.526721\pi\) | ||||
−0.0838486 | + | 0.996479i | \(0.526721\pi\) | |||||||
\(318\) | −272563. | −0.151147 | ||||||||
\(319\) | −516626. | −0.284249 | ||||||||
\(320\) | 514750. | 0.281010 | ||||||||
\(321\) | 1.31716e6 | 0.713473 | ||||||||
\(322\) | 220555. | 0.118544 | ||||||||
\(323\) | −1.22695e6 | −0.654363 | ||||||||
\(324\) | −196207. | −0.103837 | ||||||||
\(325\) | 271613. | 0.142640 | ||||||||
\(326\) | 439350. | 0.228963 | ||||||||
\(327\) | −1.00381e6 | −0.519139 | ||||||||
\(328\) | 158703. | 0.0814516 | ||||||||
\(329\) | −458538. | −0.233553 | ||||||||
\(330\) | 39404.7 | 0.0199188 | ||||||||
\(331\) | 637880. | 0.320014 | 0.160007 | − | 0.987116i | \(-0.448848\pi\) | ||||
0.160007 | + | 0.987116i | \(0.448848\pi\) | |||||||
\(332\) | 498900. | 0.248410 | ||||||||
\(333\) | 1.12916e6 | 0.558016 | ||||||||
\(334\) | 792796. | 0.388862 | ||||||||
\(335\) | −722319. | −0.351655 | ||||||||
\(336\) | 309006. | 0.149320 | ||||||||
\(337\) | 119077. | 0.0571153 | 0.0285576 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285576 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(338\) | 264048. | 0.125716 | ||||||||
\(339\) | −509705. | −0.240890 | ||||||||
\(340\) | 354644. | 0.166378 | ||||||||
\(341\) | −1.01827e6 | −0.474217 | ||||||||
\(342\) | 303238. | 0.140190 | ||||||||
\(343\) | −1.32357e6 | −0.607453 | ||||||||
\(344\) | −1.02872e6 | −0.468706 | ||||||||
\(345\) | 826130. | 0.373681 | ||||||||
\(346\) | 507092. | 0.227718 | ||||||||
\(347\) | −2.35817e6 | −1.05136 | −0.525681 | − | 0.850682i | \(-0.676189\pi\) | ||||
−0.525681 | + | 0.850682i | \(0.676189\pi\) | |||||||
\(348\) | 1.14916e6 | 0.508664 | ||||||||
\(349\) | 2.71913e6 | 1.19500 | 0.597499 | − | 0.801870i | \(-0.296161\pi\) | ||||
0.597499 | + | 0.801870i | \(0.296161\pi\) | |||||||
\(350\) | −37543.3 | −0.0163818 | ||||||||
\(351\) | 316809. | 0.137256 | ||||||||
\(352\) | −491813. | −0.211565 | ||||||||
\(353\) | −787647. | −0.336430 | −0.168215 | − | 0.985750i | \(-0.553800\pi\) | ||||
−0.168215 | + | 0.985750i | \(0.553800\pi\) | |||||||
\(354\) | 429885. | 0.182324 | ||||||||
\(355\) | 511911. | 0.215588 | ||||||||
\(356\) | −4.28448e6 | −1.79173 | ||||||||
\(357\) | 177183. | 0.0735784 | ||||||||
\(358\) | −269065. | −0.110956 | ||||||||
\(359\) | 3.28528e6 | 1.34535 | 0.672676 | − | 0.739937i | \(-0.265145\pi\) | ||||
0.672676 | + | 0.739937i | \(0.265145\pi\) | |||||||
\(360\) | −181439. | −0.0737862 | ||||||||
\(361\) | 4.21407e6 | 1.70190 | ||||||||
\(362\) | −358847. | −0.143926 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −539371. | −0.213370 | ||||||||
\(365\) | 1.08333e6 | 0.425626 | ||||||||
\(366\) | 421379. | 0.164426 | ||||||||
\(367\) | −700644. | −0.271539 | −0.135770 | − | 0.990740i | \(-0.543351\pi\) | ||||
−0.135770 | + | 0.990740i | \(0.543351\pi\) | |||||||
\(368\) | −3.03751e6 | −1.16923 | ||||||||
\(369\) | 143470. | 0.0548525 | ||||||||
\(370\) | 504420. | 0.191553 | ||||||||
\(371\) | 868394. | 0.327553 | ||||||||
\(372\) | 2.26499e6 | 0.848611 | ||||||||
\(373\) | −2.59078e6 | −0.964180 | −0.482090 | − | 0.876122i | \(-0.660122\pi\) | ||||
−0.482090 | + | 0.876122i | \(0.660122\pi\) | |||||||
\(374\) | −83075.4 | −0.0307109 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | −989943. | −0.361111 | ||||||||
\(377\) | −1.85550e6 | −0.672369 | ||||||||
\(378\) | −43790.5 | −0.0157634 | ||||||||
\(379\) | −672260. | −0.240402 | −0.120201 | − | 0.992750i | \(-0.538354\pi\) | ||||
−0.120201 | + | 0.992750i | \(0.538354\pi\) | |||||||
\(380\) | −1.93377e6 | −0.686982 | ||||||||
\(381\) | 716088. | 0.252728 | ||||||||
\(382\) | −1.03577e6 | −0.363168 | ||||||||
\(383\) | 2.41377e6 | 0.840813 | 0.420407 | − | 0.907336i | \(-0.361887\pi\) | ||||
0.420407 | + | 0.907336i | \(0.361887\pi\) | |||||||
\(384\) | 1.43881e6 | 0.497938 | ||||||||
\(385\) | −125544. | −0.0431664 | ||||||||
\(386\) | −457167. | −0.156173 | ||||||||
\(387\) | −929983. | −0.315644 | ||||||||
\(388\) | 3.85655e6 | 1.30053 | ||||||||
\(389\) | 3.01046e6 | 1.00869 | 0.504347 | − | 0.863501i | \(-0.331733\pi\) | ||||
0.504347 | + | 0.863501i | \(0.331733\pi\) | |||||||
\(390\) | 141525. | 0.0471163 | ||||||||
\(391\) | −1.74170e6 | −0.576143 | ||||||||
\(392\) | −1.35157e6 | −0.444247 | ||||||||
\(393\) | 660287. | 0.215651 | ||||||||
\(394\) | −201921. | −0.0655300 | ||||||||
\(395\) | 2.38255e6 | 0.768331 | ||||||||
\(396\) | −293100. | −0.0939243 | ||||||||
\(397\) | 871291. | 0.277452 | 0.138726 | − | 0.990331i | \(-0.455699\pi\) | ||||
0.138726 | + | 0.990331i | \(0.455699\pi\) | |||||||
\(398\) | −265498. | −0.0840142 | ||||||||
\(399\) | −966124. | −0.303809 | ||||||||
\(400\) | 517050. | 0.161578 | ||||||||
\(401\) | −2.01901e6 | −0.627014 | −0.313507 | − | 0.949586i | \(-0.601504\pi\) | ||||
−0.313507 | + | 0.949586i | \(0.601504\pi\) | |||||||
\(402\) | −376367. | −0.116157 | ||||||||
\(403\) | −3.65719e6 | −1.12172 | ||||||||
\(404\) | −4.39869e6 | −1.34082 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | 256474. | 0.0772196 | ||||||||
\(407\) | 1.68678e6 | 0.504744 | ||||||||
\(408\) | 382522. | 0.113764 | ||||||||
\(409\) | −346377. | −0.102386 | −0.0511930 | − | 0.998689i | \(-0.516302\pi\) | ||||
−0.0511930 | + | 0.998689i | \(0.516302\pi\) | |||||||
\(410\) | 64091.1 | 0.0188295 | ||||||||
\(411\) | −1.17664e6 | −0.343588 | ||||||||
\(412\) | −2.65824e6 | −0.771526 | ||||||||
\(413\) | −1.36963e6 | −0.395118 | ||||||||
\(414\) | 430458. | 0.123433 | ||||||||
\(415\) | 417069. | 0.118874 | ||||||||
\(416\) | −1.76638e6 | −0.500440 | ||||||||
\(417\) | −3.29832e6 | −0.928865 | ||||||||
\(418\) | 452985. | 0.126807 | ||||||||
\(419\) | −938584. | −0.261179 | −0.130589 | − | 0.991437i | \(-0.541687\pi\) | ||||
−0.130589 | + | 0.991437i | \(0.541687\pi\) | |||||||
\(420\) | 279254. | 0.0772461 | ||||||||
\(421\) | 4.88046e6 | 1.34201 | 0.671004 | − | 0.741454i | \(-0.265863\pi\) | ||||
0.671004 | + | 0.741454i | \(0.265863\pi\) | |||||||
\(422\) | 494897. | 0.135280 | ||||||||
\(423\) | −894929. | −0.243185 | ||||||||
\(424\) | 1.87479e6 | 0.506450 | ||||||||
\(425\) | 296474. | 0.0796186 | ||||||||
\(426\) | 266733. | 0.0712120 | ||||||||
\(427\) | −1.34253e6 | −0.356330 | ||||||||
\(428\) | −4.37666e6 | −1.15487 | ||||||||
\(429\) | 473258. | 0.124152 | ||||||||
\(430\) | −415442. | −0.108353 | ||||||||
\(431\) | −5.27493e6 | −1.36780 | −0.683902 | − | 0.729574i | \(-0.739718\pi\) | ||||
−0.683902 | + | 0.729574i | \(0.739718\pi\) | |||||||
\(432\) | 603087. | 0.155479 | ||||||||
\(433\) | −3.30374e6 | −0.846811 | −0.423405 | − | 0.905940i | \(-0.639165\pi\) | ||||
−0.423405 | + | 0.905940i | \(0.639165\pi\) | |||||||
\(434\) | 505510. | 0.128827 | ||||||||
\(435\) | 960668. | 0.243417 | ||||||||
\(436\) | 3.33546e6 | 0.840310 | ||||||||
\(437\) | 9.49695e6 | 2.37892 | ||||||||
\(438\) | 564473. | 0.140591 | ||||||||
\(439\) | 5.92591e6 | 1.46755 | 0.733777 | − | 0.679391i | \(-0.237756\pi\) | ||||
0.733777 | + | 0.679391i | \(0.237756\pi\) | |||||||
\(440\) | −271039. | −0.0667422 | ||||||||
\(441\) | −1.22185e6 | −0.299172 | ||||||||
\(442\) | −298371. | −0.0726442 | ||||||||
\(443\) | 2.36693e6 | 0.573029 | 0.286515 | − | 0.958076i | \(-0.407503\pi\) | ||||
0.286515 | + | 0.958076i | \(0.407503\pi\) | |||||||
\(444\) | −3.75198e6 | −0.903239 | ||||||||
\(445\) | −3.58173e6 | −0.857418 | ||||||||
\(446\) | 1.47396e6 | 0.350871 | ||||||||
\(447\) | 4.28507e6 | 1.01435 | ||||||||
\(448\) | −854532. | −0.201156 | ||||||||
\(449\) | −3.35144e6 | −0.784540 | −0.392270 | − | 0.919850i | \(-0.628310\pi\) | ||||
−0.392270 | + | 0.919850i | \(0.628310\pi\) | |||||||
\(450\) | −73273.2 | −0.0170574 | ||||||||
\(451\) | 214320. | 0.0496160 | ||||||||
\(452\) | 1.69364e6 | 0.389920 | ||||||||
\(453\) | 2.08471e6 | 0.477310 | ||||||||
\(454\) | 524539. | 0.119437 | ||||||||
\(455\) | −450902. | −0.102107 | ||||||||
\(456\) | −2.08578e6 | −0.469738 | ||||||||
\(457\) | 4.04376e6 | 0.905721 | 0.452861 | − | 0.891581i | \(-0.350404\pi\) | ||||
0.452861 | + | 0.891581i | \(0.350404\pi\) | |||||||
\(458\) | 2.00219e6 | 0.446006 | ||||||||
\(459\) | 345807. | 0.0766130 | ||||||||
\(460\) | −2.74506e6 | −0.604862 | ||||||||
\(461\) | −8.31607e6 | −1.82249 | −0.911247 | − | 0.411861i | \(-0.864879\pi\) | ||||
−0.911247 | + | 0.411861i | \(0.864879\pi\) | |||||||
\(462\) | −65415.4 | −0.0142585 | ||||||||
\(463\) | −5.54406e6 | −1.20192 | −0.600960 | − | 0.799279i | \(-0.705215\pi\) | ||||
−0.600960 | + | 0.799279i | \(0.705215\pi\) | |||||||
\(464\) | −3.53218e6 | −0.761637 | ||||||||
\(465\) | 1.89348e6 | 0.406095 | ||||||||
\(466\) | −1.72361e6 | −0.367683 | ||||||||
\(467\) | −5.54472e6 | −1.17649 | −0.588244 | − | 0.808684i | \(-0.700180\pi\) | ||||
−0.588244 | + | 0.808684i | \(0.700180\pi\) | |||||||
\(468\) | −1.05269e6 | −0.222170 | ||||||||
\(469\) | 1.19912e6 | 0.251726 | ||||||||
\(470\) | −399782. | −0.0834793 | ||||||||
\(471\) | −713555. | −0.148209 | ||||||||
\(472\) | −2.95690e6 | −0.610916 | ||||||||
\(473\) | −1.38923e6 | −0.285511 | ||||||||
\(474\) | 1.24143e6 | 0.253792 | ||||||||
\(475\) | −1.61659e6 | −0.328749 | ||||||||
\(476\) | −588741. | −0.119099 | ||||||||
\(477\) | 1.69484e6 | 0.341063 | ||||||||
\(478\) | −923980. | −0.184966 | ||||||||
\(479\) | 2.93070e6 | 0.583624 | 0.291812 | − | 0.956476i | \(-0.405742\pi\) | ||||
0.291812 | + | 0.956476i | \(0.405742\pi\) | |||||||
\(480\) | 914529. | 0.181173 | ||||||||
\(481\) | 6.05818e6 | 1.19393 | ||||||||
\(482\) | −436078. | −0.0854961 | ||||||||
\(483\) | −1.37145e6 | −0.267493 | ||||||||
\(484\) | −437841. | −0.0849577 | ||||||||
\(485\) | 3.22399e6 | 0.622357 | ||||||||
\(486\) | −85465.9 | −0.0164135 | ||||||||
\(487\) | −370838. | −0.0708536 | −0.0354268 | − | 0.999372i | \(-0.511279\pi\) | ||||
−0.0354268 | + | 0.999372i | \(0.511279\pi\) | |||||||
\(488\) | −2.89839e6 | −0.550944 | ||||||||
\(489\) | −2.73195e6 | −0.516655 | ||||||||
\(490\) | −545824. | −0.102698 | ||||||||
\(491\) | 592085. | 0.110836 | 0.0554179 | − | 0.998463i | \(-0.482351\pi\) | ||||
0.0554179 | + | 0.998463i | \(0.482351\pi\) | |||||||
\(492\) | −476722. | −0.0887877 | ||||||||
\(493\) | −2.02534e6 | −0.375301 | ||||||||
\(494\) | 1.62693e6 | 0.299952 | ||||||||
\(495\) | −245025. | −0.0449467 | ||||||||
\(496\) | −6.96194e6 | −1.27065 | ||||||||
\(497\) | −849819. | −0.154325 | ||||||||
\(498\) | 217315. | 0.0392661 | ||||||||
\(499\) | −6.23154e6 | −1.12032 | −0.560162 | − | 0.828383i | \(-0.689261\pi\) | ||||
−0.560162 | + | 0.828383i | \(0.689261\pi\) | |||||||
\(500\) | 467267. | 0.0835873 | ||||||||
\(501\) | −4.92974e6 | −0.877464 | ||||||||
\(502\) | 412579. | 0.0730714 | ||||||||
\(503\) | 6.58812e6 | 1.16102 | 0.580512 | − | 0.814251i | \(-0.302852\pi\) | ||||
0.580512 | + | 0.814251i | \(0.302852\pi\) | |||||||
\(504\) | 301206. | 0.0528186 | ||||||||
\(505\) | −3.67721e6 | −0.641638 | ||||||||
\(506\) | 643030. | 0.111649 | ||||||||
\(507\) | −1.64190e6 | −0.283678 | ||||||||
\(508\) | −2.37941e6 | −0.409082 | ||||||||
\(509\) | 8.26967e6 | 1.41479 | 0.707397 | − | 0.706816i | \(-0.249869\pi\) | ||||
0.707397 | + | 0.706816i | \(0.249869\pi\) | |||||||
\(510\) | 154479. | 0.0262993 | ||||||||
\(511\) | −1.79842e6 | −0.304677 | ||||||||
\(512\) | −5.73451e6 | −0.966765 | ||||||||
\(513\) | −1.88559e6 | −0.316339 | ||||||||
\(514\) | 2.49839e6 | 0.417112 | ||||||||
\(515\) | −2.22222e6 | −0.369207 | ||||||||
\(516\) | 3.09014e6 | 0.510921 | ||||||||
\(517\) | −1.33687e6 | −0.219969 | ||||||||
\(518\) | −837383. | −0.137120 | ||||||||
\(519\) | −3.15318e6 | −0.513843 | ||||||||
\(520\) | −973457. | −0.157873 | ||||||||
\(521\) | 1.99187e6 | 0.321490 | 0.160745 | − | 0.986996i | \(-0.448610\pi\) | ||||
0.160745 | + | 0.986996i | \(0.448610\pi\) | |||||||
\(522\) | 500560. | 0.0804044 | ||||||||
\(523\) | 7.99327e6 | 1.27782 | 0.638911 | − | 0.769281i | \(-0.279385\pi\) | ||||
0.638911 | + | 0.769281i | \(0.279385\pi\) | |||||||
\(524\) | −2.19399e6 | −0.349066 | ||||||||
\(525\) | 233450. | 0.0369655 | ||||||||
\(526\) | 1.87455e6 | 0.295416 | ||||||||
\(527\) | −3.99194e6 | −0.626121 | ||||||||
\(528\) | 900907. | 0.140636 | ||||||||
\(529\) | 7.04495e6 | 1.09456 | ||||||||
\(530\) | 757121. | 0.117078 | ||||||||
\(531\) | −2.67310e6 | −0.411414 | ||||||||
\(532\) | 3.21023e6 | 0.491764 | ||||||||
\(533\) | 769746. | 0.117363 | ||||||||
\(534\) | −1.86627e6 | −0.283219 | ||||||||
\(535\) | −3.65879e6 | −0.552654 | ||||||||
\(536\) | 2.58878e6 | 0.389210 | ||||||||
\(537\) | 1.67309e6 | 0.250371 | ||||||||
\(538\) | 2.84103e6 | 0.423175 | ||||||||
\(539\) | −1.82523e6 | −0.270611 | ||||||||
\(540\) | 545021. | 0.0804320 | ||||||||
\(541\) | −8.83361e6 | −1.29761 | −0.648806 | − | 0.760954i | \(-0.724731\pi\) | ||||
−0.648806 | + | 0.760954i | \(0.724731\pi\) | |||||||
\(542\) | −631103. | −0.0922789 | ||||||||
\(543\) | 2.23137e6 | 0.324767 | ||||||||
\(544\) | −1.92806e6 | −0.279334 | ||||||||
\(545\) | 2.78837e6 | 0.402123 | ||||||||
\(546\) | −234944. | −0.0337274 | ||||||||
\(547\) | 2.98240e6 | 0.426184 | 0.213092 | − | 0.977032i | \(-0.431647\pi\) | ||||
0.213092 | + | 0.977032i | \(0.431647\pi\) | |||||||
\(548\) | 3.90972e6 | 0.556153 | ||||||||
\(549\) | −2.62021e6 | −0.371026 | ||||||||
\(550\) | −109457. | −0.0154290 | ||||||||
\(551\) | 1.10436e7 | 1.54964 | ||||||||
\(552\) | −2.96084e6 | −0.413587 | ||||||||
\(553\) | −3.95524e6 | −0.549997 | ||||||||
\(554\) | 1.59400e6 | 0.220655 | ||||||||
\(555\) | −3.13657e6 | −0.432237 | ||||||||
\(556\) | 1.09596e7 | 1.50352 | ||||||||
\(557\) | 1.20831e7 | 1.65021 | 0.825105 | − | 0.564979i | \(-0.191116\pi\) | ||||
0.825105 | + | 0.564979i | \(0.191116\pi\) | |||||||
\(558\) | 986604. | 0.134140 | ||||||||
\(559\) | −4.98954e6 | −0.675353 | ||||||||
\(560\) | −858350. | −0.115663 | ||||||||
\(561\) | 516576. | 0.0692991 | ||||||||
\(562\) | −1.75511e6 | −0.234404 | ||||||||
\(563\) | −1.18255e7 | −1.57235 | −0.786176 | − | 0.618003i | \(-0.787942\pi\) | ||||
−0.786176 | + | 0.618003i | \(0.787942\pi\) | |||||||
\(564\) | 2.97366e6 | 0.393635 | ||||||||
\(565\) | 1.41585e6 | 0.186593 | ||||||||
\(566\) | −3.00690e6 | −0.394528 | ||||||||
\(567\) | 272296. | 0.0355700 | ||||||||
\(568\) | −1.83468e6 | −0.238611 | ||||||||
\(569\) | −1.13220e6 | −0.146603 | −0.0733014 | − | 0.997310i | \(-0.523353\pi\) | ||||
−0.0733014 | + | 0.997310i | \(0.523353\pi\) | |||||||
\(570\) | −842328. | −0.108591 | ||||||||
\(571\) | −2.92831e6 | −0.375860 | −0.187930 | − | 0.982182i | \(-0.560178\pi\) | ||||
−0.187930 | + | 0.982182i | \(0.560178\pi\) | |||||||
\(572\) | −1.57254e6 | −0.200961 | ||||||||
\(573\) | 6.44062e6 | 0.819485 | ||||||||
\(574\) | −106397. | −0.0134788 | ||||||||
\(575\) | −2.29480e6 | −0.289452 | ||||||||
\(576\) | −1.66779e6 | −0.209452 | ||||||||
\(577\) | 3.70459e6 | 0.463235 | 0.231617 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231617 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(578\) | 1.72938e6 | 0.215313 | ||||||||
\(579\) | 2.84274e6 | 0.352404 | ||||||||
\(580\) | −3.19210e6 | −0.394009 | ||||||||
\(581\) | −692373. | −0.0850941 | ||||||||
\(582\) | 1.67987e6 | 0.205574 | ||||||||
\(583\) | 2.53181e6 | 0.308503 | ||||||||
\(584\) | −3.88264e6 | −0.471080 | ||||||||
\(585\) | −880025. | −0.106318 | ||||||||
\(586\) | −2.53507e6 | −0.304962 | ||||||||
\(587\) | 6.77491e6 | 0.811537 | 0.405769 | − | 0.913976i | \(-0.367004\pi\) | ||||
0.405769 | + | 0.913976i | \(0.367004\pi\) | |||||||
\(588\) | 4.05995e6 | 0.484259 | ||||||||
\(589\) | 2.17669e7 | 2.58528 | ||||||||
\(590\) | −1.19413e6 | −0.141228 | ||||||||
\(591\) | 1.25558e6 | 0.147868 | ||||||||
\(592\) | 1.15325e7 | 1.35245 | ||||||||
\(593\) | 1.58897e7 | 1.85557 | 0.927787 | − | 0.373111i | \(-0.121709\pi\) | ||||
0.927787 | + | 0.373111i | \(0.121709\pi\) | |||||||
\(594\) | −127671. | −0.0148466 | ||||||||
\(595\) | −492174. | −0.0569936 | ||||||||
\(596\) | −1.42384e7 | −1.64189 | ||||||||
\(597\) | 1.65091e6 | 0.189578 | ||||||||
\(598\) | 2.30949e6 | 0.264097 | ||||||||
\(599\) | 4.74611e6 | 0.540469 | 0.270234 | − | 0.962795i | \(-0.412899\pi\) | ||||
0.270234 | + | 0.962795i | \(0.412899\pi\) | |||||||
\(600\) | 503998. | 0.0571546 | ||||||||
\(601\) | −2.55803e6 | −0.288882 | −0.144441 | − | 0.989513i | \(-0.546138\pi\) | ||||
−0.144441 | + | 0.989513i | \(0.546138\pi\) | |||||||
\(602\) | 689671. | 0.0775623 | ||||||||
\(603\) | 2.34031e6 | 0.262108 | ||||||||
\(604\) | −6.92706e6 | −0.772603 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | −1.91602e6 | −0.211943 | ||||||||
\(607\) | 1.28362e6 | 0.141405 | 0.0707025 | − | 0.997497i | \(-0.477476\pi\) | ||||
0.0707025 | + | 0.997497i | \(0.477476\pi\) | |||||||
\(608\) | 1.05132e7 | 1.15339 | ||||||||
\(609\) | −1.59480e6 | −0.174246 | ||||||||
\(610\) | −1.17050e6 | −0.127364 | ||||||||
\(611\) | −4.80146e6 | −0.520320 | ||||||||
\(612\) | −1.14905e6 | −0.124011 | ||||||||
\(613\) | 1.01402e7 | 1.08992 | 0.544960 | − | 0.838462i | \(-0.316545\pi\) | ||||
0.544960 | + | 0.838462i | \(0.316545\pi\) | |||||||
\(614\) | −4.00245e6 | −0.428455 | ||||||||
\(615\) | −398529. | −0.0424886 | ||||||||
\(616\) | 449950. | 0.0477763 | ||||||||
\(617\) | 1.44801e7 | 1.53130 | 0.765649 | − | 0.643259i | \(-0.222418\pi\) | ||||
0.765649 | + | 0.643259i | \(0.222418\pi\) | |||||||
\(618\) | −1.15790e6 | −0.121955 | ||||||||
\(619\) | 1.03997e6 | 0.109092 | 0.0545462 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545462 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(620\) | −6.29163e6 | −0.657331 | ||||||||
\(621\) | −2.67666e6 | −0.278525 | ||||||||
\(622\) | −200446. | −0.0207740 | ||||||||
\(623\) | 5.94599e6 | 0.613768 | ||||||||
\(624\) | 3.23567e6 | 0.332662 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −3.25706e6 | −0.332193 | ||||||||
\(627\) | −2.81674e6 | −0.286139 | ||||||||
\(628\) | 2.37099e6 | 0.239901 | ||||||||
\(629\) | 6.61270e6 | 0.666426 | ||||||||
\(630\) | 121640. | 0.0122103 | ||||||||
\(631\) | 1.25757e7 | 1.25736 | 0.628681 | − | 0.777664i | \(-0.283595\pi\) | ||||
0.628681 | + | 0.777664i | \(0.283595\pi\) | |||||||
\(632\) | −8.53902e6 | −0.850384 | ||||||||
\(633\) | −3.07735e6 | −0.305258 | ||||||||
\(634\) | 434264. | 0.0429073 | ||||||||
\(635\) | −1.98913e6 | −0.195763 | ||||||||
\(636\) | −5.63161e6 | −0.552065 | ||||||||
\(637\) | −6.55545e6 | −0.640109 | ||||||||
\(638\) | 747750. | 0.0727285 | ||||||||
\(639\) | −1.65859e6 | −0.160690 | ||||||||
\(640\) | −3.99669e6 | −0.385701 | ||||||||
\(641\) | 5.13372e6 | 0.493500 | 0.246750 | − | 0.969079i | \(-0.420637\pi\) | ||||
0.246750 | + | 0.969079i | \(0.420637\pi\) | |||||||
\(642\) | −1.90643e6 | −0.182550 | ||||||||
\(643\) | −1.80636e7 | −1.72296 | −0.861482 | − | 0.507788i | \(-0.830463\pi\) | ||||
−0.861482 | + | 0.507788i | \(0.830463\pi\) | |||||||
\(644\) | 4.55704e6 | 0.432981 | ||||||||
\(645\) | 2.58329e6 | 0.244497 | ||||||||
\(646\) | 1.77585e6 | 0.167426 | ||||||||
\(647\) | −298642. | −0.0280472 | −0.0140236 | − | 0.999902i | \(-0.504464\pi\) | ||||
−0.0140236 | + | 0.999902i | \(0.504464\pi\) | |||||||
\(648\) | 587864. | 0.0549970 | ||||||||
\(649\) | −3.99315e6 | −0.372138 | ||||||||
\(650\) | −393125. | −0.0364961 | ||||||||
\(651\) | −3.14335e6 | −0.290696 | ||||||||
\(652\) | 9.07770e6 | 0.836289 | ||||||||
\(653\) | 1.52761e6 | 0.140194 | 0.0700971 | − | 0.997540i | \(-0.477669\pi\) | ||||
0.0700971 | + | 0.997540i | \(0.477669\pi\) | |||||||
\(654\) | 1.45289e6 | 0.132828 | ||||||||
\(655\) | −1.83413e6 | −0.167042 | ||||||||
\(656\) | 1.46531e6 | 0.132944 | ||||||||
\(657\) | −3.50999e6 | −0.317243 | ||||||||
\(658\) | 663675. | 0.0597573 | ||||||||
\(659\) | 1.69648e7 | 1.52172 | 0.760862 | − | 0.648913i | \(-0.224776\pi\) | ||||
0.760862 | + | 0.648913i | \(0.224776\pi\) | |||||||
\(660\) | 814167. | 0.0727534 | ||||||||
\(661\) | −7.24635e6 | −0.645083 | −0.322542 | − | 0.946555i | \(-0.604537\pi\) | ||||
−0.322542 | + | 0.946555i | \(0.604537\pi\) | |||||||
\(662\) | −923249. | −0.0818793 | ||||||||
\(663\) | 1.85532e6 | 0.163921 | ||||||||
\(664\) | −1.49477e6 | −0.131569 | ||||||||
\(665\) | 2.68368e6 | 0.235330 | ||||||||
\(666\) | −1.63432e6 | −0.142775 | ||||||||
\(667\) | 1.56768e7 | 1.36440 | ||||||||
\(668\) | 1.63805e7 | 1.42032 | ||||||||
\(669\) | −9.16530e6 | −0.791738 | ||||||||
\(670\) | 1.04546e6 | 0.0899751 | ||||||||
\(671\) | −3.91414e6 | −0.335606 | ||||||||
\(672\) | −1.51820e6 | −0.129690 | ||||||||
\(673\) | −2.29001e7 | −1.94895 | −0.974473 | − | 0.224505i | \(-0.927923\pi\) | ||||
−0.974473 | + | 0.224505i | \(0.927923\pi\) | |||||||
\(674\) | −172348. | −0.0146136 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | 5.45568e6 | 0.459179 | ||||||||
\(677\) | 1.31898e7 | 1.10603 | 0.553015 | − | 0.833171i | \(-0.313477\pi\) | ||||
0.553015 | + | 0.833171i | \(0.313477\pi\) | |||||||
\(678\) | 737732. | 0.0616346 | ||||||||
\(679\) | −5.35212e6 | −0.445504 | ||||||||
\(680\) | −1.06256e6 | −0.0881213 | ||||||||
\(681\) | −3.26167e6 | −0.269508 | ||||||||
\(682\) | 1.47382e6 | 0.121334 | ||||||||
\(683\) | −2.11554e7 | −1.73528 | −0.867638 | − | 0.497196i | \(-0.834363\pi\) | ||||
−0.867638 | + | 0.497196i | \(0.834363\pi\) | |||||||
\(684\) | 6.26540e6 | 0.512046 | ||||||||
\(685\) | 3.26844e6 | 0.266142 | ||||||||
\(686\) | 1.91570e6 | 0.155424 | ||||||||
\(687\) | −1.24499e7 | −1.00641 | ||||||||
\(688\) | −9.49822e6 | −0.765017 | ||||||||
\(689\) | 9.09316e6 | 0.729738 | ||||||||
\(690\) | −1.19572e6 | −0.0956105 | ||||||||
\(691\) | −1.40736e7 | −1.12127 | −0.560636 | − | 0.828063i | \(-0.689443\pi\) | ||||
−0.560636 | + | 0.828063i | \(0.689443\pi\) | |||||||
\(692\) | 1.04774e7 | 0.831739 | ||||||||
\(693\) | 406764. | 0.0321743 | ||||||||
\(694\) | 3.41315e6 | 0.269003 | ||||||||
\(695\) | 9.16200e6 | 0.719495 | ||||||||
\(696\) | −3.44302e6 | −0.269412 | ||||||||
\(697\) | 840203. | 0.0655092 | ||||||||
\(698\) | −3.93560e6 | −0.305754 | ||||||||
\(699\) | 1.07177e7 | 0.829674 | ||||||||
\(700\) | −775706. | −0.0598346 | ||||||||
\(701\) | −5.70759e6 | −0.438690 | −0.219345 | − | 0.975647i | \(-0.570392\pi\) | ||||
−0.219345 | + | 0.975647i | \(0.570392\pi\) | |||||||
\(702\) | −458541. | −0.0351184 | ||||||||
\(703\) | −3.60571e7 | −2.75171 | ||||||||
\(704\) | −2.49139e6 | −0.189457 | ||||||||
\(705\) | 2.48591e6 | 0.188371 | ||||||||
\(706\) | 1.14002e6 | 0.0860796 | ||||||||
\(707\) | 6.10450e6 | 0.459306 | ||||||||
\(708\) | 8.88215e6 | 0.665940 | ||||||||
\(709\) | −6.05501e6 | −0.452375 | −0.226188 | − | 0.974084i | \(-0.572626\pi\) | ||||
−0.226188 | + | 0.974084i | \(0.572626\pi\) | |||||||
\(710\) | −740926. | −0.0551606 | ||||||||
\(711\) | −7.71945e6 | −0.572680 | ||||||||
\(712\) | 1.28369e7 | 0.948985 | ||||||||
\(713\) | 3.08989e7 | 2.27625 | ||||||||
\(714\) | −256449. | −0.0188259 | ||||||||
\(715\) | −1.31461e6 | −0.0961679 | ||||||||
\(716\) | −5.55934e6 | −0.405266 | ||||||||
\(717\) | 5.74546e6 | 0.417376 | ||||||||
\(718\) | −4.75502e6 | −0.344224 | ||||||||
\(719\) | −1.99372e6 | −0.143828 | −0.0719139 | − | 0.997411i | \(-0.522911\pi\) | ||||
−0.0719139 | + | 0.997411i | \(0.522911\pi\) | |||||||
\(720\) | −1.67524e6 | −0.120433 | ||||||||
\(721\) | 3.68909e6 | 0.264291 | ||||||||
\(722\) | −6.09933e6 | −0.435451 | ||||||||
\(723\) | 2.71160e6 | 0.192921 | ||||||||
\(724\) | −7.41438e6 | −0.525688 | ||||||||
\(725\) | −2.66852e6 | −0.188550 | ||||||||
\(726\) | −190719. | −0.0134293 | ||||||||
\(727\) | 1.66770e7 | 1.17026 | 0.585129 | − | 0.810940i | \(-0.301044\pi\) | ||||
0.585129 | + | 0.810940i | \(0.301044\pi\) | |||||||
\(728\) | 1.61603e6 | 0.113011 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.56798e6 | −0.108901 | ||||||||
\(731\) | −5.44624e6 | −0.376967 | ||||||||
\(732\) | 8.70640e6 | 0.600566 | ||||||||
\(733\) | −6.22120e6 | −0.427676 | −0.213838 | − | 0.976869i | \(-0.568596\pi\) | ||||
−0.213838 | + | 0.976869i | \(0.568596\pi\) | |||||||
\(734\) | 1.01409e6 | 0.0694764 | ||||||||
\(735\) | 3.39403e6 | 0.231738 | ||||||||
\(736\) | 1.49238e7 | 1.01551 | ||||||||
\(737\) | 3.49602e6 | 0.237086 | ||||||||
\(738\) | −207655. | −0.0140347 | ||||||||
\(739\) | 193628. | 0.0130424 | 0.00652118 | − | 0.999979i | \(-0.497924\pi\) | ||||
0.00652118 | + | 0.999979i | \(0.497924\pi\) | |||||||
\(740\) | 1.04222e7 | 0.699646 | ||||||||
\(741\) | −1.01165e7 | −0.676840 | ||||||||
\(742\) | −1.25689e6 | −0.0838083 | ||||||||
\(743\) | 1.49469e7 | 0.993295 | 0.496648 | − | 0.867952i | \(-0.334564\pi\) | ||||
0.496648 | + | 0.867952i | \(0.334564\pi\) | |||||||
\(744\) | −6.78620e6 | −0.449464 | ||||||||
\(745\) | −1.19030e7 | −0.785714 | ||||||||
\(746\) | 3.74982e6 | 0.246697 | ||||||||
\(747\) | −1.35130e6 | −0.0886036 | ||||||||
\(748\) | −1.71648e6 | −0.112172 | ||||||||
\(749\) | 6.07393e6 | 0.395608 | ||||||||
\(750\) | 203537. | 0.0132126 | ||||||||
\(751\) | −3.06276e6 | −0.198159 | −0.0990793 | − | 0.995080i | \(-0.531590\pi\) | ||||
−0.0990793 | + | 0.995080i | \(0.531590\pi\) | |||||||
\(752\) | −9.14020e6 | −0.589401 | ||||||||
\(753\) | −2.56548e6 | −0.164885 | ||||||||
\(754\) | 2.68560e6 | 0.172033 | ||||||||
\(755\) | −5.79086e6 | −0.369723 | ||||||||
\(756\) | −904784. | −0.0575759 | ||||||||
\(757\) | −2.87783e7 | −1.82527 | −0.912633 | − | 0.408780i | \(-0.865954\pi\) | ||||
−0.912633 | + | 0.408780i | \(0.865954\pi\) | |||||||
\(758\) | 973009. | 0.0615098 | ||||||||
\(759\) | −3.99847e6 | −0.251935 | ||||||||
\(760\) | 5.79382e6 | 0.363857 | ||||||||
\(761\) | 1.92089e6 | 0.120238 | 0.0601189 | − | 0.998191i | \(-0.480852\pi\) | ||||
0.0601189 | + | 0.998191i | \(0.480852\pi\) | |||||||
\(762\) | −1.03645e6 | −0.0646635 | ||||||||
\(763\) | −4.62895e6 | −0.287853 | ||||||||
\(764\) | −2.14008e7 | −1.32647 | ||||||||
\(765\) | −960576. | −0.0593442 | ||||||||
\(766\) | −3.49363e6 | −0.215132 | ||||||||
\(767\) | −1.43417e7 | −0.880262 | ||||||||
\(768\) | 3.84743e6 | 0.235379 | ||||||||
\(769\) | 1.51697e7 | 0.925043 | 0.462521 | − | 0.886608i | \(-0.346945\pi\) | ||||
0.462521 | + | 0.886608i | \(0.346945\pi\) | |||||||
\(770\) | 181709. | 0.0110446 | ||||||||
\(771\) | −1.55354e7 | −0.941211 | ||||||||
\(772\) | −9.44583e6 | −0.570423 | ||||||||
\(773\) | −1.17588e7 | −0.707809 | −0.353904 | − | 0.935282i | \(-0.615146\pi\) | ||||
−0.353904 | + | 0.935282i | \(0.615146\pi\) | |||||||
\(774\) | 1.34603e6 | 0.0807612 | ||||||||
\(775\) | −5.25966e6 | −0.314560 | ||||||||
\(776\) | −1.15548e7 | −0.688821 | ||||||||
\(777\) | 5.20699e6 | 0.309410 | ||||||||
\(778\) | −4.35726e6 | −0.258086 | ||||||||
\(779\) | −4.58138e6 | −0.270491 | ||||||||
\(780\) | 2.92414e6 | 0.172092 | ||||||||
\(781\) | −2.47765e6 | −0.145349 | ||||||||
\(782\) | 2.52088e6 | 0.147413 | ||||||||
\(783\) | −3.11256e6 | −0.181432 | ||||||||
\(784\) | −1.24791e7 | −0.725095 | ||||||||
\(785\) | 1.98210e6 | 0.114802 | ||||||||
\(786\) | −955680. | −0.0551768 | ||||||||
\(787\) | −1.07859e6 | −0.0620756 | −0.0310378 | − | 0.999518i | \(-0.509881\pi\) | ||||
−0.0310378 | + | 0.999518i | \(0.509881\pi\) | |||||||
\(788\) | −4.17202e6 | −0.239348 | ||||||||
\(789\) | −1.16563e7 | −0.666604 | ||||||||
\(790\) | −3.44843e6 | −0.196586 | ||||||||
\(791\) | −2.35043e6 | −0.133569 | ||||||||
\(792\) | 878167. | 0.0497467 | ||||||||
\(793\) | −1.40579e7 | −0.793849 | ||||||||
\(794\) | −1.26108e6 | −0.0709892 | ||||||||
\(795\) | −4.70790e6 | −0.264186 | ||||||||
\(796\) | −5.48562e6 | −0.306862 | ||||||||
\(797\) | 7.73047e6 | 0.431082 | 0.215541 | − | 0.976495i | \(-0.430848\pi\) | ||||
0.215541 | + | 0.976495i | \(0.430848\pi\) | |||||||
\(798\) | 1.39834e6 | 0.0777331 | ||||||||
\(799\) | −5.24095e6 | −0.290431 | ||||||||
\(800\) | −2.54036e6 | −0.140336 | ||||||||
\(801\) | 1.16048e7 | 0.639082 | ||||||||
\(802\) | 2.92225e6 | 0.160429 | ||||||||
\(803\) | −5.24331e6 | −0.286957 | ||||||||
\(804\) | −7.77637e6 | −0.424265 | ||||||||
\(805\) | 3.80958e6 | 0.207199 | ||||||||
\(806\) | 5.29332e6 | 0.287006 | ||||||||
\(807\) | −1.76660e7 | −0.954891 | ||||||||
\(808\) | 1.31791e7 | 0.710161 | ||||||||
\(809\) | −1.49228e6 | −0.0801639 | −0.0400819 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400819 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(810\) | 237405. | 0.0127139 | ||||||||
\(811\) | −7.38116e6 | −0.394069 | −0.197035 | − | 0.980397i | \(-0.563131\pi\) | ||||
−0.197035 | + | 0.980397i | \(0.563131\pi\) | |||||||
\(812\) | 5.29917e6 | 0.282045 | ||||||||
\(813\) | 3.92431e6 | 0.208227 | ||||||||
\(814\) | −2.44139e6 | −0.129145 | ||||||||
\(815\) | 7.58875e6 | 0.400199 | ||||||||
\(816\) | 3.53184e6 | 0.185685 | ||||||||
\(817\) | 2.96967e7 | 1.55652 | ||||||||
\(818\) | 501336. | 0.0261967 | ||||||||
\(819\) | 1.46092e6 | 0.0761057 | ||||||||
\(820\) | 1.32423e6 | 0.0687746 | ||||||||
\(821\) | −1.42454e7 | −0.737594 | −0.368797 | − | 0.929510i | \(-0.620230\pi\) | ||||
−0.368797 | + | 0.929510i | \(0.620230\pi\) | |||||||
\(822\) | 1.70303e6 | 0.0879109 | ||||||||
\(823\) | −1.91145e7 | −0.983702 | −0.491851 | − | 0.870679i | \(-0.663680\pi\) | ||||
−0.491851 | + | 0.870679i | \(0.663680\pi\) | |||||||
\(824\) | 7.96443e6 | 0.408636 | ||||||||
\(825\) | 680625. | 0.0348155 | ||||||||
\(826\) | 1.98236e6 | 0.101096 | ||||||||
\(827\) | −2.68783e7 | −1.36659 | −0.683294 | − | 0.730143i | \(-0.739453\pi\) | ||||
−0.683294 | + | 0.730143i | \(0.739453\pi\) | |||||||
\(828\) | 8.89398e6 | 0.450838 | ||||||||
\(829\) | 2.27066e7 | 1.14754 | 0.573768 | − | 0.819018i | \(-0.305481\pi\) | ||||
0.573768 | + | 0.819018i | \(0.305481\pi\) | |||||||
\(830\) | −603654. | −0.0304154 | ||||||||
\(831\) | −9.91177e6 | −0.497908 | ||||||||
\(832\) | −8.94801e6 | −0.448145 | ||||||||
\(833\) | −7.15549e6 | −0.357295 | ||||||||
\(834\) | 4.77389e6 | 0.237661 | ||||||||
\(835\) | 1.36937e7 | 0.679681 | ||||||||
\(836\) | 9.35943e6 | 0.463163 | ||||||||
\(837\) | −6.13487e6 | −0.302686 | ||||||||
\(838\) | 1.35848e6 | 0.0668257 | ||||||||
\(839\) | −1.54859e7 | −0.759505 | −0.379753 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379753 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(840\) | −836683. | −0.0409131 | ||||||||
\(841\) | −2.28136e6 | −0.111225 | ||||||||
\(842\) | −7.06383e6 | −0.343368 | ||||||||
\(843\) | 1.09136e7 | 0.528931 | ||||||||
\(844\) | 1.02254e7 | 0.494110 | ||||||||
\(845\) | 4.56082e6 | 0.219736 | ||||||||
\(846\) | 1.29529e6 | 0.0622218 | ||||||||
\(847\) | 607635. | 0.0291028 | ||||||||
\(848\) | 1.73100e7 | 0.826623 | ||||||||
\(849\) | 1.86974e7 | 0.890250 | ||||||||
\(850\) | −429108. | −0.0203713 | ||||||||
\(851\) | −5.11844e7 | −2.42278 | ||||||||
\(852\) | 5.51116e6 | 0.260102 | ||||||||
\(853\) | −3.77200e6 | −0.177500 | −0.0887502 | − | 0.996054i | \(-0.528287\pi\) | ||||
−0.0887502 | + | 0.996054i | \(0.528287\pi\) | |||||||
\(854\) | 1.94313e6 | 0.0911712 | ||||||||
\(855\) | 5.23774e6 | 0.245035 | ||||||||
\(856\) | 1.31131e7 | 0.611674 | ||||||||
\(857\) | −6.50207e6 | −0.302412 | −0.151206 | − | 0.988502i | \(-0.548316\pi\) | ||||
−0.151206 | + | 0.988502i | \(0.548316\pi\) | |||||||
\(858\) | −684980. | −0.0317658 | ||||||||
\(859\) | −1.10411e7 | −0.510538 | −0.255269 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255269 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(860\) | −8.58372e6 | −0.395758 | ||||||||
\(861\) | 661594. | 0.0304147 | ||||||||
\(862\) | 7.63479e6 | 0.349968 | ||||||||
\(863\) | −1.55955e6 | −0.0712808 | −0.0356404 | − | 0.999365i | \(-0.511347\pi\) | ||||
−0.0356404 | + | 0.999365i | \(0.511347\pi\) | |||||||
\(864\) | −2.96307e6 | −0.135039 | ||||||||
\(865\) | 8.75884e6 | 0.398021 | ||||||||
\(866\) | 4.78174e6 | 0.216666 | ||||||||
\(867\) | −1.07536e7 | −0.485853 | ||||||||
\(868\) | 1.04447e7 | 0.470539 | ||||||||
\(869\) | −1.15315e7 | −0.518009 | ||||||||
\(870\) | −1.39044e6 | −0.0622810 | ||||||||
\(871\) | 1.25562e7 | 0.560808 | ||||||||
\(872\) | −9.99348e6 | −0.445067 | ||||||||
\(873\) | −1.04457e7 | −0.463878 | ||||||||
\(874\) | −1.37456e7 | −0.608676 | ||||||||
\(875\) | −648473. | −0.0286333 | ||||||||
\(876\) | 1.16629e7 | 0.513509 | ||||||||
\(877\) | 2.78476e7 | 1.22261 | 0.611307 | − | 0.791393i | \(-0.290644\pi\) | ||||
0.611307 | + | 0.791393i | \(0.290644\pi\) | |||||||
\(878\) | −8.57700e6 | −0.375491 | ||||||||
\(879\) | 1.57635e7 | 0.688144 | ||||||||
\(880\) | −2.50252e6 | −0.108936 | ||||||||
\(881\) | −1.52851e7 | −0.663481 | −0.331740 | − | 0.943371i | \(-0.607636\pi\) | ||||
−0.331740 | + | 0.943371i | \(0.607636\pi\) | |||||||
\(882\) | 1.76847e6 | 0.0765467 | ||||||||
\(883\) | −7.82254e6 | −0.337634 | −0.168817 | − | 0.985647i | \(-0.553995\pi\) | ||||
−0.168817 | + | 0.985647i | \(0.553995\pi\) | |||||||
\(884\) | −6.16485e6 | −0.265333 | ||||||||
\(885\) | 7.42528e6 | 0.318680 | ||||||||
\(886\) | −3.42583e6 | −0.146616 | ||||||||
\(887\) | 2.39652e7 | 1.02276 | 0.511379 | − | 0.859355i | \(-0.329135\pi\) | ||||
0.511379 | + | 0.859355i | \(0.329135\pi\) | |||||||
\(888\) | 1.12414e7 | 0.478397 | ||||||||
\(889\) | 3.30214e6 | 0.140133 | ||||||||
\(890\) | 5.18409e6 | 0.219380 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 3.04544e7 | 1.28156 | ||||||||
\(893\) | 2.85774e7 | 1.19920 | ||||||||
\(894\) | −6.20209e6 | −0.259534 | ||||||||
\(895\) | −4.64748e6 | −0.193937 | ||||||||
\(896\) | 6.63487e6 | 0.276098 | ||||||||
\(897\) | −1.43608e7 | −0.595933 | ||||||||
\(898\) | 4.85078e6 | 0.200734 | ||||||||
\(899\) | 3.59309e7 | 1.48276 | ||||||||
\(900\) | −1.51395e6 | −0.0623023 | ||||||||
\(901\) | 9.92548e6 | 0.407324 | ||||||||
\(902\) | −310201. | −0.0126948 | ||||||||
\(903\) | −4.28849e6 | −0.175019 | ||||||||
\(904\) | −5.07438e6 | −0.206520 | ||||||||
\(905\) | −6.19825e6 | −0.251564 | ||||||||
\(906\) | −3.01735e6 | −0.122125 | ||||||||
\(907\) | −5.48830e6 | −0.221523 | −0.110762 | − | 0.993847i | \(-0.535329\pi\) | ||||
−0.110762 | + | 0.993847i | \(0.535329\pi\) | |||||||
\(908\) | 1.08378e7 | 0.436243 | ||||||||
\(909\) | 1.19142e7 | 0.478249 | ||||||||
\(910\) | 652623. | 0.0261251 | ||||||||
\(911\) | −918823. | −0.0366806 | −0.0183403 | − | 0.999832i | \(-0.505838\pi\) | ||||
−0.0183403 | + | 0.999832i | \(0.505838\pi\) | |||||||
\(912\) | −1.92581e7 | −0.766702 | ||||||||
\(913\) | −2.01861e6 | −0.0801450 | ||||||||
\(914\) | −5.85282e6 | −0.231739 | ||||||||
\(915\) | 7.27835e6 | 0.287396 | ||||||||
\(916\) | 4.13685e7 | 1.62904 | ||||||||
\(917\) | 3.04482e6 | 0.119574 | ||||||||
\(918\) | −500512. | −0.0196023 | ||||||||
\(919\) | −6.92636e6 | −0.270530 | −0.135265 | − | 0.990809i | \(-0.543189\pi\) | ||||
−0.135265 | + | 0.990809i | \(0.543189\pi\) | |||||||
\(920\) | 8.22455e6 | 0.320363 | ||||||||
\(921\) | 2.48879e7 | 0.966805 | ||||||||
\(922\) | 1.20365e7 | 0.466306 | ||||||||
\(923\) | −8.89866e6 | −0.343812 | ||||||||
\(924\) | −1.35159e6 | −0.0520793 | ||||||||
\(925\) | 8.71269e6 | 0.334810 | ||||||||
\(926\) | 8.02432e6 | 0.307525 | ||||||||
\(927\) | 7.20001e6 | 0.275191 | ||||||||
\(928\) | 1.73542e7 | 0.661509 | ||||||||
\(929\) | −2.62196e7 | −0.996752 | −0.498376 | − | 0.866961i | \(-0.666070\pi\) | ||||
−0.498376 | + | 0.866961i | \(0.666070\pi\) | |||||||
\(930\) | −2.74057e6 | −0.103904 | ||||||||
\(931\) | 3.90168e7 | 1.47529 | ||||||||
\(932\) | −3.56126e7 | −1.34296 | ||||||||
\(933\) | 1.24641e6 | 0.0468765 | ||||||||
\(934\) | 8.02527e6 | 0.301018 | ||||||||
\(935\) | −1.43493e6 | −0.0536788 | ||||||||
\(936\) | 3.15400e6 | 0.117672 | ||||||||
\(937\) | −216082. | −0.00804027 | −0.00402013 | − | 0.999992i | \(-0.501280\pi\) | ||||
−0.00402013 | + | 0.999992i | \(0.501280\pi\) | |||||||
\(938\) | −1.73557e6 | −0.0644071 | ||||||||
\(939\) | 2.02530e7 | 0.749592 | ||||||||
\(940\) | −8.26017e6 | −0.304908 | ||||||||
\(941\) | 2.94074e7 | 1.08264 | 0.541318 | − | 0.840818i | \(-0.317926\pi\) | ||||
0.541318 | + | 0.840818i | \(0.317926\pi\) | |||||||
\(942\) | 1.03278e6 | 0.0379211 | ||||||||
\(943\) | −6.50344e6 | −0.238157 | ||||||||
\(944\) | −2.73012e7 | −0.997132 | ||||||||
\(945\) | −756379. | −0.0275524 | ||||||||
\(946\) | 2.01074e6 | 0.0730513 | ||||||||
\(947\) | −4.18343e7 | −1.51585 | −0.757927 | − | 0.652339i | \(-0.773788\pi\) | ||||
−0.757927 | + | 0.652339i | \(0.773788\pi\) | |||||||
\(948\) | 2.56501e7 | 0.926976 | ||||||||
\(949\) | −1.88317e7 | −0.678774 | ||||||||
\(950\) | 2.33980e6 | 0.0841143 | ||||||||
\(951\) | −2.70033e6 | −0.0968200 | ||||||||
\(952\) | 1.76395e6 | 0.0630802 | ||||||||
\(953\) | −1.37691e7 | −0.491104 | −0.245552 | − | 0.969383i | \(-0.578969\pi\) | ||||
−0.245552 | + | 0.969383i | \(0.578969\pi\) | |||||||
\(954\) | −2.45307e6 | −0.0872648 | ||||||||
\(955\) | −1.78906e7 | −0.634771 | ||||||||
\(956\) | −1.90910e7 | −0.675590 | ||||||||
\(957\) | −4.64963e6 | −0.164111 | ||||||||
\(958\) | −4.24182e6 | −0.149327 | ||||||||
\(959\) | −5.42590e6 | −0.190513 | ||||||||
\(960\) | 4.63275e6 | 0.162241 | ||||||||
\(961\) | 4.21908e7 | 1.47370 | ||||||||
\(962\) | −8.76844e6 | −0.305481 | ||||||||
\(963\) | 1.18545e7 | 0.411924 | ||||||||
\(964\) | −9.01009e6 | −0.312275 | ||||||||
\(965\) | −7.89650e6 | −0.272971 | ||||||||
\(966\) | 1.98500e6 | 0.0684412 | ||||||||
\(967\) | −4.56284e7 | −1.56917 | −0.784584 | − | 0.620022i | \(-0.787123\pi\) | ||||
−0.784584 | + | 0.620022i | \(0.787123\pi\) | |||||||
\(968\) | 1.31183e6 | 0.0449976 | ||||||||
\(969\) | −1.10425e7 | −0.377797 | ||||||||
\(970\) | −4.66632e6 | −0.159237 | ||||||||
\(971\) | 9.15569e6 | 0.311633 | 0.155816 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155816 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(972\) | −1.76587e6 | −0.0599504 | ||||||||
\(973\) | −1.52097e7 | −0.515039 | ||||||||
\(974\) | 536741. | 0.0181287 | ||||||||
\(975\) | 2.44451e6 | 0.0823533 | ||||||||
\(976\) | −2.67610e7 | −0.899246 | ||||||||
\(977\) | −1.12269e7 | −0.376289 | −0.188145 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188145 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(978\) | 3.95415e6 | 0.132192 | ||||||||
\(979\) | 1.73356e7 | 0.578071 | ||||||||
\(980\) | −1.12776e7 | −0.375105 | ||||||||
\(981\) | −9.03431e6 | −0.299725 | ||||||||
\(982\) | −856967. | −0.0283586 | ||||||||
\(983\) | −1.92294e7 | −0.634718 | −0.317359 | − | 0.948305i | \(-0.602796\pi\) | ||||
−0.317359 | + | 0.948305i | \(0.602796\pi\) | |||||||
\(984\) | 1.42832e6 | 0.0470261 | ||||||||
\(985\) | −3.48771e6 | −0.114538 | ||||||||
\(986\) | 2.93142e6 | 0.0960252 | ||||||||
\(987\) | −4.12684e6 | −0.134842 | ||||||||
\(988\) | 3.36151e7 | 1.09557 | ||||||||
\(989\) | 4.21556e7 | 1.37046 | ||||||||
\(990\) | 354642. | 0.0115001 | ||||||||
\(991\) | 4.87732e7 | 1.57760 | 0.788801 | − | 0.614649i | \(-0.210702\pi\) | ||||
0.788801 | + | 0.614649i | \(0.210702\pi\) | |||||||
\(992\) | 3.42052e7 | 1.10360 | ||||||||
\(993\) | 5.74092e6 | 0.184760 | ||||||||
\(994\) | 1.23000e6 | 0.0394858 | ||||||||
\(995\) | −4.58586e6 | −0.146846 | ||||||||
\(996\) | 4.49010e6 | 0.143419 | ||||||||
\(997\) | 2.88621e7 | 0.919583 | 0.459791 | − | 0.888027i | \(-0.347924\pi\) | ||||
0.459791 | + | 0.888027i | \(0.347924\pi\) | |||||||
\(998\) | 9.01935e6 | 0.286648 | ||||||||
\(999\) | 1.01625e7 | 0.322171 |
(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 | 165.6.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.d.1.2 | 3 | |||
5.4 | even | 2 | 825.6.a.i.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.d.1.2 | 3 | 3.2 | odd | 2 | |||
825.6.a.i.1.2 | 3 | 5.4 | even | 2 |