Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.723686\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 | \(-0.459166\pi\) | ||||
0.127931 | + | 0.991783i | \(0.459166\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −29.9051 | −0.934535 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −13.0263 | −0.147722 | ||||||||
\(7\) | −41.5023 | −0.320130 | −0.160065 | − | 0.987106i | \(-0.551170\pi\) | ||||
−0.160065 | + | 0.987106i | \(0.551170\pi\) | |||||||
\(8\) | −89.5997 | −0.494973 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 269.146 | 0.539554 | ||||||||
\(13\) | −434.580 | −0.713201 | −0.356600 | − | 0.934257i | \(-0.616064\pi\) | ||||
−0.356600 | + | 0.934257i | \(0.616064\pi\) | |||||||
\(14\) | −60.0692 | −0.0819090 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 827.280 | 0.807890 | ||||||||
\(17\) | −474.359 | −0.398093 | −0.199046 | − | 0.979990i | \(-0.563784\pi\) | ||||
−0.199046 | + | 0.979990i | \(0.563784\pi\) | |||||||
\(18\) | 117.237 | 0.0852872 | ||||||||
\(19\) | −2586.54 | −1.64375 | −0.821873 | − | 0.569671i | \(-0.807071\pi\) | ||||
−0.821873 | + | 0.569671i | \(0.807071\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 373.520 | 0.184827 | ||||||||
\(22\) | 175.132 | 0.0771452 | ||||||||
\(23\) | 3671.69 | 1.44726 | 0.723629 | − | 0.690189i | \(-0.242473\pi\) | ||||
0.723629 | + | 0.690189i | \(0.242473\pi\) | |||||||
\(24\) | 806.397 | 0.285773 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −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 | \(0.656242\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2422.31 | −0.311512 | ||||||||
\(37\) | −13940.3 | −1.67405 | −0.837024 | − | 0.547166i | \(-0.815706\pi\) | ||||
−0.837024 | + | 0.547166i | \(0.815706\pi\) | |||||||
\(38\) | −3743.68 | −0.420571 | ||||||||
\(39\) | 3911.22 | 0.411767 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(-0.343003\pi\) | ||||
0.473466 | + | 0.880812i | \(0.343003\pi\) | |||||||
\(44\) | −3618.52 | −0.281773 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5314.30 | 0.370298 | ||||||||
\(47\) | 11048.5 | 0.729556 | 0.364778 | − | 0.931094i | \(-0.381145\pi\) | ||||
0.364778 | + | 0.931094i | \(0.381145\pi\) | |||||||
\(48\) | −7445.52 | −0.466436 | ||||||||
\(49\) | −15084.6 | −0.897517 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4269.23 | 0.229839 | ||||||||
\(52\) | 12996.2 | 0.666511 | ||||||||
\(53\) | −20924.0 | −1.02319 | −0.511594 | − | 0.859227i | \(-0.670945\pi\) | ||||
−0.511594 | + | 0.859227i | \(0.670945\pi\) | |||||||
\(54\) | −1055.13 | −0.0492406 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | \(0.711701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1576.19 | −0.0445398 | ||||||||
\(67\) | −28892.8 | −0.786325 | −0.393163 | − | 0.919469i | \(-0.628619\pi\) | ||||
−0.393163 | + | 0.919469i | \(0.628619\pi\) | |||||||
\(68\) | 14185.7 | 0.372032 | ||||||||
\(69\) | −33045.2 | −0.835575 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −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 | \(-0.342135\pi\) | ||||
0.475864 | + | 0.879519i | \(0.342135\pi\) | |||||||
\(74\) | −20176.8 | −0.428325 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(0.828926\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 2563.64 | 0.0421040 | ||||||||
\(83\) | 16682.8 | 0.265811 | 0.132905 | − | 0.991129i | \(-0.457569\pi\) | ||||
0.132905 | + | 0.991129i | \(0.457569\pi\) | |||||||
\(84\) | −11170.2 | −0.172728 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 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 | \(0.0918877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18036.1 | 0.228317 | ||||||||
\(92\) | −109802. | −1.35251 | ||||||||
\(93\) | 75739.1 | 0.908057 | ||||||||
\(94\) | 15991.3 | 0.186665 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −36581.1 | −0.405116 | ||||||||
\(97\) | 128960. | 1.39163 | 0.695816 | − | 0.718220i | \(-0.255043\pi\) | ||||
0.695816 | + | 0.718220i | \(0.255043\pi\) | |||||||
\(98\) | −21833.0 | −0.229640 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 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 | \(-0.635444\pi\) | ||||
−0.412786 | + | 0.910828i | \(0.635444\pi\) | |||||||
\(104\) | 38938.3 | 0.353015 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −30284.8 | −0.261794 | ||||||||
\(107\) | −146352. | −1.23577 | −0.617886 | − | 0.786268i | \(-0.712011\pi\) | ||||
−0.617886 | + | 0.786268i | \(0.712011\pi\) | |||||||
\(108\) | 21800.8 | 0.179851 | ||||||||
\(109\) | −111535. | −0.899174 | −0.449587 | − | 0.893236i | \(-0.648429\pi\) | ||||
−0.449587 | + | 0.893236i | \(0.648429\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 125463. | 0.966512 | ||||||||
\(112\) | −34334.0 | −0.258630 | ||||||||
\(113\) | 56633.9 | 0.417234 | 0.208617 | − | 0.977997i | \(-0.433104\pi\) | ||||
0.208617 | + | 0.977997i | \(0.433104\pi\) | |||||||
\(114\) | 33693.1 | 0.242817 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 127684. | 0.881031 | ||||||||
\(117\) | −35201.0 | −0.237734 | ||||||||
\(118\) | −47765.1 | −0.315795 | ||||||||
\(119\) | 19687.0 | 0.127442 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −46819.9 | −0.284794 | ||||||||
\(123\) | −15941.2 | −0.0950074 | ||||||||
\(124\) | 251665. | 1.46984 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4865.61 | −0.0273030 | ||||||||
\(127\) | −79565.3 | −0.437738 | −0.218869 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218869 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(128\) | −159868. | −0.862454 | ||||||||
\(129\) | −103331. | −0.546712 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 42502.4 | 0.197045 | ||||||||
\(137\) | 130737. | 0.595112 | 0.297556 | − | 0.954704i | \(-0.403829\pi\) | ||||
0.297556 | + | 0.954704i | \(0.403829\pi\) | |||||||
\(138\) | −47828.7 | −0.213792 | ||||||||
\(139\) | −366480. | −1.60884 | −0.804420 | − | 0.594060i | \(-0.797524\pi\) | ||||
−0.804420 | + | 0.594060i | \(0.797524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −99436.5 | −0.421209 | ||||||||
\(142\) | −29637.0 | −0.123343 | ||||||||
\(143\) | −52584.2 | −0.215038 | ||||||||
\(144\) | 67009.6 | 0.269297 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 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 | \(0.158575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −116966. | −0.384810 | ||||||||
\(157\) | 79283.9 | 0.256706 | 0.128353 | − | 0.991729i | \(-0.459031\pi\) | ||||
0.128353 | + | 0.991729i | \(0.459031\pi\) | |||||||
\(158\) | −137937. | −0.439581 | ||||||||
\(159\) | 188316. | 0.590738 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −152383. | −0.463311 | ||||||||
\(162\) | 9496.21 | 0.0284291 | ||||||||
\(163\) | 303550. | 0.894872 | 0.447436 | − | 0.894316i | \(-0.352337\pi\) | ||||
0.447436 | + | 0.894316i | \(0.352337\pi\) | |||||||
\(164\) | −52969.1 | −0.153785 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24146.2 | 0.0680108 | ||||||||
\(167\) | 547748. | 1.51981 | 0.759906 | − | 0.650033i | \(-0.225245\pi\) | ||||
0.759906 | + | 0.650033i | \(0.225245\pi\) | |||||||
\(168\) | −33467.3 | −0.0914846 | ||||||||
\(169\) | −182433. | −0.491345 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −209509. | −0.547915 | ||||||||
\(172\) | −343349. | −0.884941 | ||||||||
\(173\) | 350354. | 0.890003 | 0.445001 | − | 0.895530i | \(-0.353203\pi\) | ||||
0.445001 | + | 0.895530i | \(0.353203\pi\) | |||||||
\(174\) | 55617.8 | 0.139264 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(0.430429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 109623. | 0.232337 | ||||||||
\(187\) | −57397.4 | −0.120030 | ||||||||
\(188\) | −330407. | −0.681796 | ||||||||
\(189\) | 30255.2 | 0.0616091 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(-0.598720\pi\) | ||||
−0.305191 | + | 0.952291i | \(0.598720\pi\) | |||||||
\(194\) | 186653. | 0.356065 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 451106. | 0.838761 | ||||||||
\(197\) | −139508. | −0.256115 | −0.128058 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128058 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(198\) | 14185.7 | 0.0257151 | ||||||||
\(199\) | 183434. | 0.328358 | 0.164179 | − | 0.986431i | \(-0.447503\pi\) | ||||
0.164179 | + | 0.986431i | \(0.447503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 260035. | 0.453985 | ||||||||
\(202\) | 212892. | 0.367096 | ||||||||
\(203\) | 177200. | 0.301802 | ||||||||
\(204\) | −127672. | −0.214793 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −128655. | −0.211232 | ||||||||
\(207\) | 297407. | 0.482420 | ||||||||
\(208\) | −359519. | −0.576188 | ||||||||
\(209\) | −312971. | −0.495608 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 65318.2 | 0.0952576 | ||||||||
\(217\) | 349261. | 0.503501 | ||||||||
\(218\) | −161432. | −0.230064 | ||||||||
\(219\) | −389998. | −0.549481 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 206147. | 0.283920 | ||||||||
\(222\) | 181591. | 0.247293 | ||||||||
\(223\) | 1.01837e6 | 1.37133 | 0.685665 | − | 0.727917i | \(-0.259511\pi\) | ||||
0.685665 | + | 0.727917i | \(0.259511\pi\) | |||||||
\(224\) | −168689. | −0.224629 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 81970.3 | 0.106754 | ||||||||
\(227\) | 362408. | 0.466802 | 0.233401 | − | 0.972381i | \(-0.425015\pi\) | ||||
0.233401 | + | 0.972381i | \(0.425015\pi\) | |||||||
\(228\) | −696156. | −0.886889 | ||||||||
\(229\) | −1.38333e6 | −1.74315 | −0.871577 | − | 0.490258i | \(-0.836902\pi\) | ||||
−0.871577 | + | 0.490258i | \(0.836902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45196.0 | 0.0557275 | ||||||||
\(232\) | 382558. | 0.466635 | ||||||||
\(233\) | −1.19085e6 | −1.43704 | −0.718519 | − | 0.695507i | \(-0.755180\pi\) | ||||
−0.718519 | + | 0.695507i | \(0.755180\pi\) | |||||||
\(234\) | −50948.9 | −0.0608269 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | \(0.382279\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −23072.8 | −0.0243087 | ||||||||
\(247\) | 1.12406e6 | 1.17232 | ||||||||
\(248\) | 754023. | 0.778494 | ||||||||
\(249\) | −150145. | −0.153466 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 427492. | 0.407688 | ||||||||
\(257\) | 1.72616e6 | 1.63022 | 0.815112 | − | 0.579303i | \(-0.196675\pi\) | ||||
0.815112 | + | 0.579303i | \(0.196675\pi\) | |||||||
\(258\) | −149559. | −0.139882 | ||||||||
\(259\) | 578554. | 0.535913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −345841. | −0.314250 | ||||||||
\(262\) | 106187. | 0.0955690 | ||||||||
\(263\) | 1.29514e6 | 1.15459 | 0.577296 | − | 0.816535i | \(-0.304108\pi\) | ||||
0.577296 | + | 0.816535i | \(0.304108\pi\) | |||||||
\(264\) | 97574.1 | 0.0861638 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 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 | \(0.809932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 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 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 988220. | 0.780874 | ||||||||
\(277\) | 1.10131e6 | 0.862401 | 0.431201 | − | 0.902256i | \(-0.358090\pi\) | ||||
0.431201 | + | 0.902256i | \(0.358090\pi\) | |||||||
\(278\) | −530433. | −0.411641 | ||||||||
\(279\) | −681652. | −0.524267 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(-0.780233\pi\) | ||||
−0.770979 | + | 0.636860i | \(0.780233\pi\) | |||||||
\(284\) | 612351. | 0.450510 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −76108.9 | −0.0550200 | ||||||||
\(287\) | −73510.5 | −0.0526799 | ||||||||
\(288\) | 329230. | 0.233894 | ||||||||
\(289\) | −1.19484e6 | −0.841522 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.16064e6 | −0.803460 | ||||||||
\(292\) | −1.29588e6 | −0.889424 | ||||||||
\(293\) | −1.75150e6 | −1.19190 | −0.595950 | − | 0.803021i | \(-0.703225\pi\) | ||||
−0.595950 | + | 0.803021i | \(0.703225\pi\) | |||||||
\(294\) | 196497. | 0.132583 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.24905e6 | 0.828609 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 689121. | 0.449526 | ||||||||
\(299\) | −1.59564e6 | −1.03219 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −476499. | −0.303142 | ||||||||
\(302\) | 335261. | 0.211527 | ||||||||
\(303\) | −1.32380e6 | −0.828351 | ||||||||
\(304\) | −2.13979e6 | −1.32797 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −55612.4 | −0.0339522 | ||||||||
\(307\) | −2.76532e6 | −1.67456 | −0.837278 | − | 0.546777i | \(-0.815854\pi\) | ||||
−0.837278 | + | 0.546777i | \(0.815854\pi\) | |||||||
\(308\) | 150177. | 0.0902040 | ||||||||
\(309\) | 800001. | 0.476644 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(-0.724882\pi\) | ||||
−0.649165 | + | 0.760647i | \(0.724882\pi\) | |||||||
\(314\) | 114753. | 0.0656812 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.85001e6 | 1.60557 | ||||||||
\(317\) | 300036. | 0.167697 | 0.0838486 | − | 0.996479i | \(-0.473279\pi\) | ||||
0.0838486 | + | 0.996479i | \(0.473279\pi\) | |||||||
\(318\) | 272563. | 0.151147 | ||||||||
\(319\) | −516626. | −0.284249 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.31716e6 | 0.713473 | ||||||||
\(322\) | −220555. | −0.118544 | ||||||||
\(323\) | 1.22695e6 | 0.654363 | ||||||||
\(324\) | −196207. | −0.103837 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 439350. | 0.228963 | ||||||||
\(327\) | 1.00381e6 | 0.519139 | ||||||||
\(328\) | −158703. | −0.0814516 | ||||||||
\(329\) | −458538. | −0.233553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 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 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 309006. | 0.149320 | ||||||||
\(337\) | −119077. | −0.0571153 | −0.0285576 | − | 0.999592i | \(-0.509091\pi\) | ||||
−0.0285576 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(338\) | −264048. | −0.125716 | ||||||||
\(339\) | −509705. | −0.240890 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.01827e6 | −0.474217 | ||||||||
\(342\) | −303238. | −0.140190 | ||||||||
\(343\) | 1.32357e6 | 0.607453 | ||||||||
\(344\) | −1.02872e6 | −0.468706 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 507092. | 0.227718 | ||||||||
\(347\) | 2.35817e6 | 1.05136 | 0.525681 | − | 0.850682i | \(-0.323811\pi\) | ||||
0.525681 | + | 0.850682i | \(0.323811\pi\) | |||||||
\(348\) | −1.14916e6 | −0.508664 | ||||||||
\(349\) | 2.71913e6 | 1.19500 | 0.597499 | − | 0.801870i | \(-0.296161\pi\) | ||||
0.597499 | + | 0.801870i | \(0.296161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 316809. | 0.137256 | ||||||||
\(352\) | 491813. | 0.211565 | ||||||||
\(353\) | 787647. | 0.336430 | 0.168215 | − | 0.985750i | \(-0.446200\pi\) | ||||
0.168215 | + | 0.985750i | \(0.446200\pi\) | |||||||
\(354\) | 429885. | 0.182324 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −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 | \(0.265145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.21407e6 | 1.70190 | ||||||||
\(362\) | 358847. | 0.143926 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −539371. | −0.213370 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 421379. | 0.164426 | ||||||||
\(367\) | 700644. | 0.271539 | 0.135770 | − | 0.990740i | \(-0.456649\pi\) | ||||
0.135770 | + | 0.990740i | \(0.456649\pi\) | |||||||
\(368\) | 3.03751e6 | 1.16923 | ||||||||
\(369\) | 143470. | 0.0548525 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 868394. | 0.327553 | ||||||||
\(372\) | −2.26499e6 | −0.848611 | ||||||||
\(373\) | 2.59078e6 | 0.964180 | 0.482090 | − | 0.876122i | \(-0.339878\pi\) | ||||
0.482090 | + | 0.876122i | \(0.339878\pi\) | |||||||
\(374\) | −83075.4 | −0.0307109 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −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 | \(0.538354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 716088. | 0.252728 | ||||||||
\(382\) | 1.03577e6 | 0.363168 | ||||||||
\(383\) | −2.41377e6 | −0.840813 | −0.420407 | − | 0.907336i | \(-0.638113\pi\) | ||||
−0.420407 | + | 0.907336i | \(0.638113\pi\) | |||||||
\(384\) | 1.43881e6 | 0.497938 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | \(0.331733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.74170e6 | −0.576143 | ||||||||
\(392\) | 1.35157e6 | 0.444247 | ||||||||
\(393\) | −660287. | −0.215651 | ||||||||
\(394\) | −201921. | −0.0655300 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −293100. | −0.0939243 | ||||||||
\(397\) | −871291. | −0.277452 | −0.138726 | − | 0.990331i | \(-0.544301\pi\) | ||||
−0.138726 | + | 0.990331i | \(0.544301\pi\) | |||||||
\(398\) | 265498. | 0.0840142 | ||||||||
\(399\) | −966124. | −0.303809 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | \(0.516302\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.17664e6 | −0.343588 | ||||||||
\(412\) | 2.65824e6 | 0.771526 | ||||||||
\(413\) | 1.36963e6 | 0.395118 | ||||||||
\(414\) | 430458. | 0.123433 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −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 | \(0.541687\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 266733. | 0.0712120 | ||||||||
\(427\) | 1.34253e6 | 0.356330 | ||||||||
\(428\) | 4.37666e6 | 1.15487 | ||||||||
\(429\) | 473258. | 0.124152 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | \(-0.360835\pi\) | ||||
0.423405 | + | 0.905940i | \(0.360835\pi\) | |||||||
\(434\) | 505510. | 0.128827 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(0.237756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.22185e6 | −0.299172 | ||||||||
\(442\) | 298371. | 0.0726442 | ||||||||
\(443\) | −2.36693e6 | −0.573029 | −0.286515 | − | 0.958076i | \(-0.592497\pi\) | ||||
−0.286515 | + | 0.958076i | \(0.592497\pi\) | |||||||
\(444\) | −3.75198e6 | −0.903239 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 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 | \(0.628310\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 214320. | 0.0496160 | ||||||||
\(452\) | −1.69364e6 | −0.389920 | ||||||||
\(453\) | −2.08471e6 | −0.477310 | ||||||||
\(454\) | 524539. | 0.119437 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.08578e6 | −0.469738 | ||||||||
\(457\) | −4.04376e6 | −0.905721 | −0.452861 | − | 0.891581i | \(-0.649596\pi\) | ||||
−0.452861 | + | 0.891581i | \(0.649596\pi\) | |||||||
\(458\) | −2.00219e6 | −0.446006 | ||||||||
\(459\) | 345807. | 0.0766130 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −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 | \(-0.294785\pi\) | ||||
0.600960 | + | 0.799279i | \(0.294785\pi\) | |||||||
\(464\) | −3.53218e6 | −0.761637 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.72361e6 | −0.367683 | ||||||||
\(467\) | 5.54472e6 | 1.17649 | 0.588244 | − | 0.808684i | \(-0.299820\pi\) | ||||
0.588244 | + | 0.808684i | \(0.299820\pi\) | |||||||
\(468\) | 1.05269e6 | 0.222170 | ||||||||
\(469\) | 1.19912e6 | 0.251726 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −713555. | −0.148209 | ||||||||
\(472\) | 2.95690e6 | 0.610916 | ||||||||
\(473\) | 1.38923e6 | 0.285511 | ||||||||
\(474\) | 1.24143e6 | 0.253792 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −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 | \(0.405742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.05818e6 | 1.19393 | ||||||||
\(482\) | 436078. | 0.0854961 | ||||||||
\(483\) | 1.37145e6 | 0.267493 | ||||||||
\(484\) | −437841. | −0.0849577 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −85465.9 | −0.0164135 | ||||||||
\(487\) | 370838. | 0.0708536 | 0.0354268 | − | 0.999372i | \(-0.488721\pi\) | ||||
0.0354268 | + | 0.999372i | \(0.488721\pi\) | |||||||
\(488\) | 2.89839e6 | 0.550944 | ||||||||
\(489\) | −2.73195e6 | −0.516655 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −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 | \(0.689261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.92974e6 | −0.877464 | ||||||||
\(502\) | −412579. | −0.0730714 | ||||||||
\(503\) | −6.58812e6 | −1.16102 | −0.580512 | − | 0.814251i | \(-0.697148\pi\) | ||||
−0.580512 | + | 0.814251i | \(0.697148\pi\) | |||||||
\(504\) | 301206. | 0.0528186 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 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 | \(0.249869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.79842e6 | −0.304677 | ||||||||
\(512\) | 5.73451e6 | 0.966765 | ||||||||
\(513\) | 1.88559e6 | 0.316339 | ||||||||
\(514\) | 2.49839e6 | 0.417112 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.09014e6 | 0.510921 | ||||||||
\(517\) | 1.33687e6 | 0.219969 | ||||||||
\(518\) | 837383. | 0.137120 | ||||||||
\(519\) | −3.15318e6 | −0.513843 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(-0.720615\pi\) | ||||
−0.638911 | + | 0.769281i | \(0.720615\pi\) | |||||||
\(524\) | −2.19399e6 | −0.349066 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.87455e6 | 0.295416 | ||||||||
\(527\) | 3.99194e6 | 0.626121 | ||||||||
\(528\) | −900907. | −0.140636 | ||||||||
\(529\) | 7.04495e6 | 1.09456 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.67310e6 | −0.411414 | ||||||||
\(532\) | −3.21023e6 | −0.491764 | ||||||||
\(533\) | −769746. | −0.117363 | ||||||||
\(534\) | −1.86627e6 | −0.283219 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.58878e6 | 0.389210 | ||||||||
\(537\) | −1.67309e6 | −0.250371 | ||||||||
\(538\) | −2.84103e6 | −0.423175 | ||||||||
\(539\) | −1.82523e6 | −0.270611 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −234944. | −0.0337274 | ||||||||
\(547\) | −2.98240e6 | −0.426184 | −0.213092 | − | 0.977032i | \(-0.568353\pi\) | ||||
−0.213092 | + | 0.977032i | \(0.568353\pi\) | |||||||
\(548\) | −3.90972e6 | −0.556153 | ||||||||
\(549\) | −2.62021e6 | −0.371026 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10436e7 | 1.54964 | ||||||||
\(552\) | 2.96084e6 | 0.413587 | ||||||||
\(553\) | 3.95524e6 | 0.549997 | ||||||||
\(554\) | 1.59400e6 | 0.220655 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.09596e7 | 1.50352 | ||||||||
\(557\) | −1.20831e7 | −1.65021 | −0.825105 | − | 0.564979i | \(-0.808884\pi\) | ||||
−0.825105 | + | 0.564979i | \(0.808884\pi\) | |||||||
\(558\) | −986604. | −0.134140 | ||||||||
\(559\) | −4.98954e6 | −0.675353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 516576. | 0.0692991 | ||||||||
\(562\) | 1.75511e6 | 0.234404 | ||||||||
\(563\) | 1.18255e7 | 1.57235 | 0.786176 | − | 0.618003i | \(-0.212058\pi\) | ||||
0.786176 | + | 0.618003i | \(0.212058\pi\) | |||||||
\(564\) | 2.97366e6 | 0.393635 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −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 | \(0.523353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −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 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.66779e6 | −0.209452 | ||||||||
\(577\) | −3.70459e6 | −0.463235 | −0.231617 | − | 0.972807i | \(-0.574402\pi\) | ||||
−0.231617 | + | 0.972807i | \(0.574402\pi\) | |||||||
\(578\) | −1.72938e6 | −0.215313 | ||||||||
\(579\) | 2.84274e6 | 0.352404 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −692373. | −0.0850941 | ||||||||
\(582\) | −1.67987e6 | −0.205574 | ||||||||
\(583\) | −2.53181e6 | −0.308503 | ||||||||
\(584\) | −3.88264e6 | −0.471080 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.53507e6 | −0.304962 | ||||||||
\(587\) | −6.77491e6 | −0.811537 | −0.405769 | − | 0.913976i | \(-0.632996\pi\) | ||||
−0.405769 | + | 0.913976i | \(0.632996\pi\) | |||||||
\(588\) | −4.05995e6 | −0.484259 | ||||||||
\(589\) | 2.17669e7 | 2.58528 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.25558e6 | 0.147868 | ||||||||
\(592\) | −1.15325e7 | −1.35245 | ||||||||
\(593\) | −1.58897e7 | −1.85557 | −0.927787 | − | 0.373111i | \(-0.878291\pi\) | ||||
−0.927787 | + | 0.373111i | \(0.878291\pi\) | |||||||
\(594\) | −127671. | −0.0148466 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −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 | \(0.412899\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.91602e6 | −0.211943 | ||||||||
\(607\) | −1.28362e6 | −0.141405 | −0.0707025 | − | 0.997497i | \(-0.522524\pi\) | ||||
−0.0707025 | + | 0.997497i | \(0.522524\pi\) | |||||||
\(608\) | −1.05132e7 | −1.15339 | ||||||||
\(609\) | −1.59480e6 | −0.174246 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.80146e6 | −0.520320 | ||||||||
\(612\) | 1.14905e6 | 0.124011 | ||||||||
\(613\) | −1.01402e7 | −1.08992 | −0.544960 | − | 0.838462i | \(-0.683455\pi\) | ||||
−0.544960 | + | 0.838462i | \(0.683455\pi\) | |||||||
\(614\) | −4.00245e6 | −0.428455 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 449950. | 0.0477763 | ||||||||
\(617\) | −1.44801e7 | −1.53130 | −0.765649 | − | 0.643259i | \(-0.777582\pi\) | ||||
−0.765649 | + | 0.643259i | \(0.777582\pi\) | |||||||
\(618\) | 1.15790e6 | 0.121955 | ||||||||
\(619\) | 1.03997e6 | 0.109092 | 0.0545462 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545462 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.67666e6 | −0.278525 | ||||||||
\(622\) | 200446. | 0.0207740 | ||||||||
\(623\) | −5.94599e6 | −0.613768 | ||||||||
\(624\) | 3.23567e6 | 0.332662 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.25706e6 | −0.332193 | ||||||||
\(627\) | 2.81674e6 | 0.286139 | ||||||||
\(628\) | −2.37099e6 | −0.239901 | ||||||||
\(629\) | 6.61270e6 | 0.666426 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.63161e6 | −0.552065 | ||||||||
\(637\) | 6.55545e6 | 0.640109 | ||||||||
\(638\) | −747750. | −0.0727285 | ||||||||
\(639\) | −1.65859e6 | −0.160690 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 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 | \(-0.169537\pi\) | ||||
0.861482 | + | 0.507788i | \(0.169537\pi\) | |||||||
\(644\) | 4.55704e6 | 0.432981 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.77585e6 | 0.167426 | ||||||||
\(647\) | 298642. | 0.0280472 | 0.0140236 | − | 0.999902i | \(-0.495536\pi\) | ||||
0.0140236 | + | 0.999902i | \(0.495536\pi\) | |||||||
\(648\) | −587864. | −0.0549970 | ||||||||
\(649\) | −3.99315e6 | −0.372138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.14335e6 | −0.290696 | ||||||||
\(652\) | −9.07770e6 | −0.836289 | ||||||||
\(653\) | −1.52761e6 | −0.140194 | −0.0700971 | − | 0.997540i | \(-0.522331\pi\) | ||||
−0.0700971 | + | 0.997540i | \(0.522331\pi\) | |||||||
\(654\) | 1.45289e6 | 0.132828 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | \(0.224776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.63432e6 | −0.142775 | ||||||||
\(667\) | −1.56768e7 | −1.36440 | ||||||||
\(668\) | −1.63805e7 | −1.42032 | ||||||||
\(669\) | −9.16530e6 | −0.791738 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.91414e6 | −0.335606 | ||||||||
\(672\) | 1.51820e6 | 0.129690 | ||||||||
\(673\) | 2.29001e7 | 1.94895 | 0.974473 | − | 0.224505i | \(-0.0720765\pi\) | ||||
0.974473 | + | 0.224505i | \(0.0720765\pi\) | |||||||
\(674\) | −172348. | −0.0146136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.45568e6 | 0.459179 | ||||||||
\(677\) | −1.31898e7 | −1.10603 | −0.553015 | − | 0.833171i | \(-0.686523\pi\) | ||||
−0.553015 | + | 0.833171i | \(0.686523\pi\) | |||||||
\(678\) | −737732. | −0.0616346 | ||||||||
\(679\) | −5.35212e6 | −0.445504 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.26167e6 | −0.269508 | ||||||||
\(682\) | −1.47382e6 | −0.121334 | ||||||||
\(683\) | 2.11554e7 | 1.73528 | 0.867638 | − | 0.497196i | \(-0.165637\pi\) | ||||
0.867638 | + | 0.497196i | \(0.165637\pi\) | |||||||
\(684\) | 6.26540e6 | 0.512046 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.91570e6 | 0.155424 | ||||||||
\(687\) | 1.24499e7 | 1.00641 | ||||||||
\(688\) | 9.49822e6 | 0.765017 | ||||||||
\(689\) | 9.09316e6 | 0.729738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.44302e6 | −0.269412 | ||||||||
\(697\) | −840203. | −0.0655092 | ||||||||
\(698\) | 3.93560e6 | 0.305754 | ||||||||
\(699\) | 1.07177e7 | 0.829674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | \(0.572626\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.71945e6 | −0.572680 | ||||||||
\(712\) | −1.28369e7 | −0.948985 | ||||||||
\(713\) | −3.08989e7 | −2.27625 | ||||||||
\(714\) | −256449. | −0.0188259 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −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 | \(0.522911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.68909e6 | 0.264291 | ||||||||
\(722\) | 6.09933e6 | 0.435451 | ||||||||
\(723\) | −2.71160e6 | −0.192921 | ||||||||
\(724\) | −7.41438e6 | −0.525688 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −190719. | −0.0134293 | ||||||||
\(727\) | −1.66770e7 | −1.17026 | −0.585129 | − | 0.810940i | \(-0.698956\pi\) | ||||
−0.585129 | + | 0.810940i | \(0.698956\pi\) | |||||||
\(728\) | −1.61603e6 | −0.113011 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.44624e6 | −0.376967 | ||||||||
\(732\) | −8.70640e6 | −0.600566 | ||||||||
\(733\) | 6.22120e6 | 0.427676 | 0.213838 | − | 0.976869i | \(-0.431404\pi\) | ||||
0.213838 | + | 0.976869i | \(0.431404\pi\) | |||||||
\(734\) | 1.01409e6 | 0.0694764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | \(0.497924\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.01165e7 | −0.676840 | ||||||||
\(742\) | 1.25689e6 | 0.0838083 | ||||||||
\(743\) | −1.49469e7 | −0.993295 | −0.496648 | − | 0.867952i | \(-0.665436\pi\) | ||||
−0.496648 | + | 0.867952i | \(0.665436\pi\) | |||||||
\(744\) | −6.78620e6 | −0.449464 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.74982e6 | 0.246697 | ||||||||
\(747\) | 1.35130e6 | 0.0886036 | ||||||||
\(748\) | 1.71648e6 | 0.112172 | ||||||||
\(749\) | 6.07393e6 | 0.395608 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −904784. | −0.0575759 | ||||||||
\(757\) | 2.87783e7 | 1.82527 | 0.912633 | − | 0.408780i | \(-0.134046\pi\) | ||||
0.912633 | + | 0.408780i | \(0.134046\pi\) | |||||||
\(758\) | −973009. | −0.0615098 | ||||||||
\(759\) | −3.99847e6 | −0.251935 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −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 | \(0.346945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.55354e7 | −0.941211 | ||||||||
\(772\) | 9.44583e6 | 0.570423 | ||||||||
\(773\) | 1.17588e7 | 0.707809 | 0.353904 | − | 0.935282i | \(-0.384854\pi\) | ||||
0.353904 | + | 0.935282i | \(0.384854\pi\) | |||||||
\(774\) | 1.34603e6 | 0.0807612 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.15548e7 | −0.688821 | ||||||||
\(777\) | −5.20699e6 | −0.309410 | ||||||||
\(778\) | 4.35726e6 | 0.258086 | ||||||||
\(779\) | −4.58138e6 | −0.270491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.47765e6 | −0.145349 | ||||||||
\(782\) | −2.52088e6 | −0.147413 | ||||||||
\(783\) | 3.11256e6 | 0.181432 | ||||||||
\(784\) | −1.24791e7 | −0.725095 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −955680. | −0.0551768 | ||||||||
\(787\) | 1.07859e6 | 0.0620756 | 0.0310378 | − | 0.999518i | \(-0.490119\pi\) | ||||
0.0310378 | + | 0.999518i | \(0.490119\pi\) | |||||||
\(788\) | 4.17202e6 | 0.239348 | ||||||||
\(789\) | −1.16563e7 | −0.666604 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.35043e6 | −0.133569 | ||||||||
\(792\) | −878167. | −0.0497467 | ||||||||
\(793\) | 1.40579e7 | 0.793849 | ||||||||
\(794\) | −1.26108e6 | −0.0709892 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.48562e6 | −0.306862 | ||||||||
\(797\) | −7.73047e6 | −0.431082 | −0.215541 | − | 0.976495i | \(-0.569152\pi\) | ||||
−0.215541 | + | 0.976495i | \(0.569152\pi\) | |||||||
\(798\) | −1.39834e6 | −0.0777331 | ||||||||
\(799\) | −5.24095e6 | −0.290431 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.16048e7 | 0.639082 | ||||||||
\(802\) | −2.92225e6 | −0.160429 | ||||||||
\(803\) | 5.24331e6 | 0.286957 | ||||||||
\(804\) | −7.77637e6 | −0.424265 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | \(0.512762\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.53184e6 | 0.185685 | ||||||||
\(817\) | −2.96967e7 | −1.55652 | ||||||||
\(818\) | −501336. | −0.0261967 | ||||||||
\(819\) | 1.46092e6 | 0.0761057 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −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 | \(-0.336320\pi\) | ||||
0.491851 | + | 0.870679i | \(0.336320\pi\) | |||||||
\(824\) | 7.96443e6 | 0.408636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.98236e6 | 0.101096 | ||||||||
\(827\) | 2.68783e7 | 1.36659 | 0.683294 | − | 0.730143i | \(-0.260547\pi\) | ||||
0.683294 | + | 0.730143i | \(0.260547\pi\) | |||||||
\(828\) | −8.89398e6 | −0.450838 | ||||||||
\(829\) | 2.27066e7 | 1.14754 | 0.573768 | − | 0.819018i | \(-0.305481\pi\) | ||||
0.573768 | + | 0.819018i | \(0.305481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.91177e6 | −0.497908 | ||||||||
\(832\) | 8.94801e6 | 0.448145 | ||||||||
\(833\) | 7.15549e6 | 0.357295 | ||||||||
\(834\) | 4.77389e6 | 0.237661 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | \(0.623991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.28136e6 | −0.111225 | ||||||||
\(842\) | 7.06383e6 | 0.343368 | ||||||||
\(843\) | −1.09136e7 | −0.528931 | ||||||||
\(844\) | 1.02254e7 | 0.494110 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.29529e6 | 0.0622218 | ||||||||
\(847\) | −607635. | −0.0291028 | ||||||||
\(848\) | −1.73100e7 | −0.826623 | ||||||||
\(849\) | 1.86974e7 | 0.890250 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.11844e7 | −2.42278 | ||||||||
\(852\) | −5.51116e6 | −0.260102 | ||||||||
\(853\) | 3.77200e6 | 0.177500 | 0.0887502 | − | 0.996054i | \(-0.471713\pi\) | ||||
0.0887502 | + | 0.996054i | \(0.471713\pi\) | |||||||
\(854\) | 1.94313e6 | 0.0911712 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.31131e7 | 0.611674 | ||||||||
\(857\) | 6.50207e6 | 0.302412 | 0.151206 | − | 0.988502i | \(-0.451684\pi\) | ||||
0.151206 | + | 0.988502i | \(0.451684\pi\) | |||||||
\(858\) | 684980. | 0.0317658 | ||||||||
\(859\) | −1.10411e7 | −0.510538 | −0.255269 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255269 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 661594. | 0.0304147 | ||||||||
\(862\) | −7.63479e6 | −0.349968 | ||||||||
\(863\) | 1.55955e6 | 0.0712808 | 0.0356404 | − | 0.999365i | \(-0.488653\pi\) | ||||
0.0356404 | + | 0.999365i | \(0.488653\pi\) | |||||||
\(864\) | −2.96307e6 | −0.135039 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.78174e6 | 0.216666 | ||||||||
\(867\) | 1.07536e7 | 0.485853 | ||||||||
\(868\) | −1.04447e7 | −0.470539 | ||||||||
\(869\) | −1.15315e7 | −0.518009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.25562e7 | 0.560808 | ||||||||
\(872\) | 9.99348e6 | 0.445067 | ||||||||
\(873\) | 1.04457e7 | 0.463878 | ||||||||
\(874\) | −1.37456e7 | −0.608676 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.16629e7 | 0.513509 | ||||||||
\(877\) | −2.78476e7 | −1.22261 | −0.611307 | − | 0.791393i | \(-0.709356\pi\) | ||||
−0.611307 | + | 0.791393i | \(0.709356\pi\) | |||||||
\(878\) | 8.57700e6 | 0.375491 | ||||||||
\(879\) | 1.57635e7 | 0.688144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −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 | \(-0.446005\pi\) | ||||
0.168817 | + | 0.985647i | \(0.446005\pi\) | |||||||
\(884\) | −6.16485e6 | −0.265333 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.42583e6 | −0.146616 | ||||||||
\(887\) | −2.39652e7 | −1.02276 | −0.511379 | − | 0.859355i | \(-0.670865\pi\) | ||||
−0.511379 | + | 0.859355i | \(0.670865\pi\) | |||||||
\(888\) | −1.12414e7 | −0.478397 | ||||||||
\(889\) | 3.30214e6 | 0.140133 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −3.04544e7 | −1.28156 | ||||||||
\(893\) | −2.85774e7 | −1.19920 | ||||||||
\(894\) | −6.20209e6 | −0.259534 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.63487e6 | 0.276098 | ||||||||
\(897\) | 1.43608e7 | 0.595933 | ||||||||
\(898\) | −4.85078e6 | −0.200734 | ||||||||
\(899\) | 3.59309e7 | 1.48276 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.92548e6 | 0.407324 | ||||||||
\(902\) | 310201. | 0.0126948 | ||||||||
\(903\) | 4.28849e6 | 0.175019 | ||||||||
\(904\) | −5.07438e6 | −0.206520 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.01735e6 | −0.122125 | ||||||||
\(907\) | 5.48830e6 | 0.221523 | 0.110762 | − | 0.993847i | \(-0.464671\pi\) | ||||
0.110762 | + | 0.993847i | \(0.464671\pi\) | |||||||
\(908\) | −1.08378e7 | −0.436243 | ||||||||
\(909\) | 1.19142e7 | 0.478249 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | \(0.543189\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.48879e7 | 0.966805 | ||||||||
\(922\) | −1.20365e7 | −0.466306 | ||||||||
\(923\) | 8.89866e6 | 0.343812 | ||||||||
\(924\) | −1.35159e6 | −0.0520793 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 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 | \(0.666070\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.90168e7 | 1.47529 | ||||||||
\(932\) | 3.56126e7 | 1.34296 | ||||||||
\(933\) | −1.24641e6 | −0.0468765 | ||||||||
\(934\) | 8.02527e6 | 0.301018 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.15400e6 | 0.117672 | ||||||||
\(937\) | 216082. | 0.00804027 | 0.00402013 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402013 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(938\) | 1.73557e6 | 0.0644071 | ||||||||
\(939\) | 2.02530e7 | 0.749592 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.01074e6 | 0.0730513 | ||||||||
\(947\) | 4.18343e7 | 1.51585 | 0.757927 | − | 0.652339i | \(-0.226212\pi\) | ||||
0.757927 | + | 0.652339i | \(0.226212\pi\) | |||||||
\(948\) | −2.56501e7 | −0.926976 | ||||||||
\(949\) | −1.88317e7 | −0.678774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.70033e6 | −0.0968200 | ||||||||
\(952\) | −1.76395e6 | −0.0630802 | ||||||||
\(953\) | 1.37691e7 | 0.491104 | 0.245552 | − | 0.969383i | \(-0.421031\pi\) | ||||
0.245552 | + | 0.969383i | \(0.421031\pi\) | |||||||
\(954\) | −2.45307e6 | −0.0872648 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.90910e7 | −0.675590 | ||||||||
\(957\) | 4.64963e6 | 0.164111 | ||||||||
\(958\) | 4.24182e6 | 0.149327 | ||||||||
\(959\) | −5.42590e6 | −0.190513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.21908e7 | 1.47370 | ||||||||
\(962\) | 8.76844e6 | 0.305481 | ||||||||
\(963\) | −1.18545e7 | −0.411924 | ||||||||
\(964\) | −9.01009e6 | −0.312275 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.98500e6 | 0.0684412 | ||||||||
\(967\) | 4.56284e7 | 1.56917 | 0.784584 | − | 0.620022i | \(-0.212877\pi\) | ||||
0.784584 | + | 0.620022i | \(0.212877\pi\) | |||||||
\(968\) | −1.31183e6 | −0.0449976 | ||||||||
\(969\) | −1.10425e7 | −0.377797 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.67610e7 | −0.899246 | ||||||||
\(977\) | 1.12269e7 | 0.376289 | 0.188145 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188145 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(978\) | −3.95415e6 | −0.132192 | ||||||||
\(979\) | 1.73356e7 | 0.578071 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.03431e6 | −0.299725 | ||||||||
\(982\) | 856967. | 0.0283586 | ||||||||
\(983\) | 1.92294e7 | 0.634718 | 0.317359 | − | 0.948305i | \(-0.397204\pi\) | ||||
0.317359 | + | 0.948305i | \(0.397204\pi\) | |||||||
\(984\) | 1.42832e6 | 0.0470261 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.93142e6 | 0.0960252 | ||||||||
\(987\) | 4.12684e6 | 0.134842 | ||||||||
\(988\) | −3.36151e7 | −1.09557 | ||||||||
\(989\) | 4.21556e7 | 1.37046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.49010e6 | 0.143419 | ||||||||
\(997\) | −2.88621e7 | −0.919583 | −0.459791 | − | 0.888027i | \(-0.652076\pi\) | ||||
−0.459791 | + | 0.888027i | \(0.652076\pi\) | |||||||
\(998\) | −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 | 825.6.a.i.1.2 | 3 | ||
5.4 | even | 2 | 165.6.a.b.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 495.6.a.d.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.b.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
495.6.a.d.1.2 | 3 | 15.14 | odd | 2 | |||
825.6.a.i.1.2 | 3 | 1.1 | even | 1 | trivial |