Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,6,Mod(293,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.293");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(94.3056860500\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 293.20 | ||
Character | \(\chi\) | \(=\) | 588.293 |
Dual form | 588.6.f.c.293.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.39153 | + | 15.5262i | −0.0892665 | + | 0.996008i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −69.8984 | −1.25038 | −0.625190 | − | 0.780473i | \(-0.714978\pi\) | ||||
−0.625190 | + | 0.780473i | \(0.714978\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −239.127 | − | 43.2103i | −0.984063 | − | 0.177820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 465.771i | 1.16062i | 0.814395 | + | 0.580310i | \(0.197069\pi\) | ||||
−0.814395 | + | 0.580310i | \(0.802931\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 285.857i | 0.469127i | 0.972101 | + | 0.234563i | \(0.0753660\pi\) | ||||
−0.972101 | + | 0.234563i | \(0.924634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 97.2655 | − | 1085.26i | 0.111617 | − | 1.24539i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 898.214 | 0.753803 | 0.376901 | − | 0.926253i | \(-0.376990\pi\) | ||||
0.376901 | + | 0.926253i | \(0.376990\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2096.30i | 1.33220i | 0.745863 | + | 0.666100i | \(0.232037\pi\) | ||||
−0.745863 | + | 0.666100i | \(0.767963\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4901.65i | 1.93207i | 0.258409 | + | 0.966036i | \(0.416802\pi\) | ||||
−0.258409 | + | 0.966036i | \(0.583198\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1760.78 | 0.563450 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1003.65 | − | 3652.62i | 0.264954 | − | 0.964261i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5878.95i | 1.29809i | 0.760750 | + | 0.649045i | \(0.224831\pi\) | ||||
−0.760750 | + | 0.649045i | \(0.775169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3854.71i | 0.720423i | 0.932871 | + | 0.360211i | \(0.117295\pi\) | ||||
−0.932871 | + | 0.360211i | \(0.882705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7231.66 | − | 648.133i | −1.15599 | − | 0.103605i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3618.34 | −0.434515 | −0.217257 | − | 0.976114i | \(-0.569711\pi\) | ||||
−0.217257 | + | 0.976114i | \(0.569711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4438.28 | − | 397.778i | −0.467254 | − | 0.0418773i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17142.4 | 1.59262 | 0.796308 | − | 0.604891i | \(-0.206783\pi\) | ||||
0.796308 | + | 0.604891i | \(0.206783\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18567.3 | −1.53136 | −0.765680 | − | 0.643221i | \(-0.777598\pi\) | ||||
−0.765680 | + | 0.643221i | \(0.777598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16714.6 | + | 3020.33i | 1.23045 | + | 0.222343i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2422.15 | 0.159940 | 0.0799698 | − | 0.996797i | \(-0.474518\pi\) | ||||
0.0799698 | + | 0.996797i | \(0.474518\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1249.89 | + | 13945.9i | −0.0672894 | + | 0.750793i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7618.31i | 0.372537i | 0.982499 | + | 0.186268i | \(0.0596394\pi\) | ||||
−0.982499 | + | 0.186268i | \(0.940361\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 32556.6i | − | 1.45122i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −32547.6 | − | 2917.06i | −1.32688 | − | 0.118921i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10644.1 | −0.398089 | −0.199044 | − | 0.979990i | \(-0.563784\pi\) | ||||
−0.199044 | + | 0.979990i | \(0.563784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15624.4i | 0.537624i | 0.963193 | + | 0.268812i | \(0.0866310\pi\) | ||||
−0.963193 | + | 0.268812i | \(0.913369\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 19980.9i | − | 0.586586i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2973.20 | −0.0809165 | −0.0404582 | − | 0.999181i | \(-0.512882\pi\) | ||||
−0.0404582 | + | 0.999181i | \(0.512882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −76104.2 | − | 6820.79i | −1.92436 | − | 0.172469i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16268.3i | 0.382997i | 0.981493 | + | 0.191498i | \(0.0613347\pi\) | ||||
−0.981493 | + | 0.191498i | \(0.938665\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14677.7i | 0.322368i | 0.986924 | + | 0.161184i | \(0.0515312\pi\) | ||||
−0.986924 | + | 0.161184i | \(0.948469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2450.17 | + | 27338.3i | −0.0502972 | + | 0.561200i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −86199.9 | −1.55396 | −0.776978 | − | 0.629527i | \(-0.783249\pi\) | ||||
−0.776978 | + | 0.629527i | \(0.783249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 55314.7 | + | 20665.5i | 0.936760 | + | 0.349973i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2747.03 | 0.0437691 | 0.0218846 | − | 0.999761i | \(-0.493033\pi\) | ||||
0.0218846 | + | 0.999761i | \(0.493033\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −62783.7 | −0.942540 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −91277.9 | − | 8180.72i | −1.29291 | − | 0.115876i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 101804. | 1.36235 | 0.681173 | − | 0.732122i | \(-0.261470\pi\) | ||||
0.681173 | + | 0.732122i | \(0.261470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −59849.1 | − | 5363.94i | −0.717547 | − | 0.0643097i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 146528.i | − | 1.66576i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 23406.7i | − | 0.252587i | −0.991993 | − | 0.126294i | \(-0.959692\pi\) | ||
0.991993 | − | 0.126294i | \(-0.0403082\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20126.1 | − | 111378.i | 0.206382 | − | 1.14212i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62202.4 | 0.606741 | 0.303371 | − | 0.952873i | \(-0.401888\pi\) | ||||
0.303371 | + | 0.952873i | \(0.401888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 38730.7i | − | 0.359718i | −0.983692 | − | 0.179859i | \(-0.942436\pi\) | ||
0.983692 | − | 0.179859i | \(-0.0575641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 188678.i | − | 1.59317i | −0.604525 | − | 0.796586i | \(-0.706637\pi\) | ||
0.604525 | − | 0.796586i | \(-0.293363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 158294. | 1.27614 | 0.638071 | − | 0.769978i | \(-0.279733\pi\) | ||||
0.638071 | + | 0.769978i | \(0.279733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5035.02 | − | 56179.1i | 0.0387877 | − | 0.432780i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 168309.i | 1.23997i | 0.784615 | + | 0.619984i | \(0.212861\pi\) | ||||
−0.784615 | + | 0.619984i | \(0.787139\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 342618.i | − | 2.41582i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12352.0 | − | 68356.2i | 0.0834203 | − | 0.461650i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −55891.3 | −0.347041 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23854.1 | + | 266156.i | −0.142167 | + | 1.58626i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 95356.7 | 0.545854 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −120698. | −0.664036 | −0.332018 | − | 0.943273i | \(-0.607730\pi\) | ||||
−0.332018 | + | 0.943273i | \(0.607730\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25836.9 | − | 288280.i | 0.136699 | − | 1.52525i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −242876. | −1.23653 | −0.618267 | − | 0.785968i | \(-0.712165\pi\) | ||||
−0.618267 | + | 0.785968i | \(0.712165\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −70153.2 | + | 255312.i | −0.331294 | + | 1.20569i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 208676.i | − | 0.949887i | −0.880016 | − | 0.474944i | \(-0.842468\pi\) | ||
0.880016 | − | 0.474944i | \(-0.157532\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 202179.i | 0.887563i | 0.896135 | + | 0.443782i | \(0.146363\pi\) | ||||
−0.896135 | + | 0.443782i | \(0.853637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3370.48 | + | 37606.8i | −0.0142772 | + | 0.159301i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −133144. | −0.544478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 410929.i | − | 1.62310i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 501543.i | 1.85073i | 0.379081 | + | 0.925364i | \(0.376240\pi\) | ||||
−0.379081 | + | 0.925364i | \(0.623760\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 352128. | 1.25678 | 0.628389 | − | 0.777899i | \(-0.283715\pi\) | ||||
0.628389 | + | 0.777899i | \(0.283715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −214788. | − | 38812.1i | −0.741789 | − | 0.134041i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 269438.i | − | 0.900802i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 547248.i | − | 1.77188i | −0.463797 | − | 0.885941i | \(-0.653513\pi\) | ||
0.463797 | − | 0.885941i | \(-0.346487\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −118284. | − | 10601.1i | −0.371050 | − | 0.0332551i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −629293. | −1.85517 | −0.927585 | − | 0.373611i | \(-0.878119\pi\) | ||||
−0.927585 | + | 0.373611i | \(0.878119\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 505481. | + | 45303.4i | 1.44542 | + | 0.129545i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 588586. | 1.63312 | 0.816562 | − | 0.577258i | \(-0.195877\pi\) | ||||
0.816562 | + | 0.577258i | \(0.195877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 289579. | 0.779920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 90581.8 | − | 501282.i | 0.236892 | − | 1.31097i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −161240. | −0.409598 | −0.204799 | − | 0.978804i | \(-0.565654\pi\) | ||||
−0.204799 | + | 0.978804i | \(0.565654\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14811.6 | − | 165263.i | 0.0355360 | − | 0.396499i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 330630.i | 0.771275i | 0.922650 | + | 0.385638i | \(0.126018\pi\) | ||||
−0.922650 | + | 0.385638i | \(0.873982\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 421555.i | − | 0.956439i | −0.878240 | − | 0.478220i | \(-0.841282\pi\) | ||
0.878240 | − | 0.478220i | \(-0.158718\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −242588. | − | 21741.8i | −0.535477 | − | 0.0479918i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 252916. | 0.543309 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 418362.i | 0.874879i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 398002.i | − | 0.789408i | −0.918808 | − | 0.394704i | \(-0.870847\pi\) | ||
0.918808 | − | 0.394704i | \(-0.129153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 519175. | 1.00328 | 0.501638 | − | 0.865078i | \(-0.332731\pi\) | ||||
0.501638 | + | 0.865078i | \(0.332731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 310228. | + | 27804.0i | 0.584245 | + | 0.0523626i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 580266.i | 1.06527i | 0.846344 | + | 0.532637i | \(0.178799\pi\) | ||||
−0.846344 | + | 0.532637i | \(0.821201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 844112.i | − | 1.51101i | −0.655142 | − | 0.755505i | \(-0.727391\pi\) | ||
0.655142 | − | 0.755505i | \(-0.272609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4137.29 | − | 46162.5i | 0.00722313 | − | 0.0805934i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.19822e6 | −1.99138 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 211802. | − | 1.17212e6i | 0.343562 | − | 1.90128i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −976395. | −1.54618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.04382e6 | −1.61406 | −0.807032 | − | 0.590508i | \(-0.798927\pi\) | ||||
−0.807032 | + | 0.590508i | \(0.798927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −252585. | − | 22637.7i | −0.381468 | − | 0.0341888i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.29782e6 | 1.91478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −227890. | − | 20424.5i | −0.321081 | − | 0.0287767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 256761.i | 0.353629i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 185286.i | 0.249506i | 0.992188 | + | 0.124753i | \(0.0398138\pi\) | ||||
−0.992188 | + | 0.124753i | \(0.960186\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −421051. | − | 76083.9i | −0.554470 | − | 0.100193i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −877852. | −1.13072 | −0.565362 | − | 0.824843i | \(-0.691264\pi\) | ||||
−0.565362 | + | 0.824843i | \(0.691264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.22612e6i | − | 1.54505i | −0.634983 | − | 0.772526i | \(-0.718993\pi\) | ||
0.634983 | − | 0.772526i | \(-0.281007\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 75659.1i | − | 0.0913001i | −0.998957 | − | 0.0456501i | \(-0.985464\pi\) | ||
0.998957 | − | 0.0456501i | \(-0.0145359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −169304. | −0.199985 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 119950. | − | 1.33836e6i | 0.138716 | − | 1.54775i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 658418.i | − | 0.745601i | −0.927911 | − | 0.372801i | \(-0.878397\pi\) | ||
0.927911 | − | 0.372801i | \(-0.121603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 567326.i | 0.629202i | 0.949224 | + | 0.314601i | \(0.101871\pi\) | ||||
−0.949224 | + | 0.314601i | \(0.898129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −397830. | + | 830072.i | −0.432197 | + | 0.901779i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −599241. | −0.624970 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3822.57 | + | 42651.0i | −0.00390712 | + | 0.0435944i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.83665e6 | −1.84010 | −0.920050 | − | 0.391800i | \(-0.871852\pi\) | ||||
−0.920050 | + | 0.391800i | \(0.871852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28305e6 | −2.24240 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 87365.3 | − | 974794.i | 0.0841373 | − | 0.938777i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −902411. | −0.852259 | −0.426129 | − | 0.904662i | \(-0.640123\pi\) | ||||
−0.426129 | + | 0.904662i | \(0.640123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 254031. | − | 1.40582e6i | 0.230827 | − | 1.27740i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 933055.i | 0.831798i | 0.909411 | + | 0.415899i | \(0.136533\pi\) | ||||
−0.909411 | + | 0.415899i | \(0.863467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 532508.i | − | 0.465813i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −141662. | + | 1.58062e6i | −0.121612 | + | 1.35691i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −533435. | −0.449470 | −0.224735 | − | 0.974420i | \(-0.572152\pi\) | ||||
−0.224735 | + | 0.974420i | \(0.572152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 798687.i | 0.660622i | 0.943872 | + | 0.330311i | \(0.107154\pi\) | ||||
−0.943872 | + | 0.330311i | \(0.892846\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 820120.i | 0.653951i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.18032e6 | 0.924271 | 0.462136 | − | 0.886809i | \(-0.347083\pi\) | ||||
0.462136 | + | 0.886809i | \(0.347083\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 166563. | − | 921766.i | 0.128106 | − | 0.708941i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.56254e6i | − | 1.18050i | −0.807221 | − | 0.590250i | \(-0.799029\pi\) | ||
0.807221 | − | 0.590250i | \(-0.200971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.08464e6i | 0.805044i | 0.915410 | + | 0.402522i | \(0.131866\pi\) | ||||
−0.915410 | + | 0.402522i | \(0.868134\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.27502e6 | + | 203898.i | 1.65911 | + | 0.148696i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −613068. | −0.431782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 363418. | + | 32571.1i | 0.251579 | + | 0.0225476i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.39243e6 | 0.947552 | 0.473776 | − | 0.880645i | \(-0.342891\pi\) | ||||
0.473776 | + | 0.880645i | \(0.342891\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 744007. | 0.497762 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.70128e6 | + | 467469.i | 1.11914 | + | 0.307512i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.40117e6 | −0.906386 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −86556.3 | + | 965768.i | −0.0541617 | + | 0.604319i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.09212e6i | − | 0.672234i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.19400e6i | 0.723034i | 0.932366 | + | 0.361517i | \(0.117741\pi\) | ||||
−0.932366 | + | 0.361517i | \(0.882259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 601341. | + | 53894.8i | 0.358282 | + | 0.0321108i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.62556e6 | 1.53929 | 0.769646 | − | 0.638470i | \(-0.220433\pi\) | ||||
0.769646 | + | 0.638470i | \(0.220433\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 887758.i | − | 0.512193i | −0.966651 | − | 0.256097i | \(-0.917563\pi\) | ||
0.966651 | − | 0.256097i | \(-0.0824365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.81415e6i | 1.01397i | 0.861955 | + | 0.506986i | \(0.169240\pi\) | ||||
−0.861955 | + | 0.506986i | \(0.830760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.73824e6 | −1.50659 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.92946e6 | + | 262551.i | 1.58681 | + | 0.142217i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.88293e6i | 1.00422i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 503331.i | 0.264329i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −220271. | + | 2.45771e6i | −0.113917 | + | 1.27105i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.55409e6 | −1.28135 | −0.640673 | − | 0.767814i | \(-0.721345\pi\) | ||||
−0.640673 | + | 0.767814i | \(0.721345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 865243. | + | 156350.i | 0.427590 | + | 0.0772656i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 207822. | 0.101176 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.68914e6 | 0.810196 | 0.405098 | − | 0.914273i | \(-0.367237\pi\) | ||||
0.405098 | + | 0.914273i | \(0.367237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.61320e6 | − | 234206.i | −1.23502 | − | 0.110688i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.79541e6 | −0.836138 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.31956e6 | + | 476762.i | 2.40618 | + | 0.215652i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 169943.i | 0.0757668i | 0.999282 | + | 0.0378834i | \(0.0120615\pi\) | ||||
−0.999282 | + | 0.0378834i | \(0.987938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.36988e6i | 1.04151i | 0.853706 | + | 0.520755i | \(0.174350\pi\) | ||||
−0.853706 | + | 0.520755i | \(0.825650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.04412e6 | + | 286899.i | 0.452361 | + | 0.124297i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.02957e6 | −0.866897 | −0.433448 | − | 0.901178i | \(-0.642703\pi\) | ||||
−0.433448 | + | 0.901178i | \(0.642703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.13712e6i | − | 0.478892i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 352368.i | − | 0.144298i | −0.997394 | − | 0.0721489i | \(-0.977014\pi\) | ||
0.997394 | − | 0.0721489i | \(-0.0229857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91837e6 | −0.774755 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 77774.3 | − | 867781.i | 0.0309791 | − | 0.345655i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.02595e6i | − | 0.403082i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.80805e6i | 0.700723i | 0.936615 | + | 0.350362i | \(0.113941\pi\) | ||||
−0.936615 | + | 0.350362i | \(0.886059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.09921e6 | − | 740728.i | −1.56723 | − | 0.283200i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.63970e6 | 1.35454 | 0.677272 | − | 0.735733i | \(-0.263162\pi\) | ||||
0.677272 | + | 0.735733i | \(0.263162\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −132692. | + | 1.48053e6i | −0.0487265 | + | 0.543675i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.68054e6 | −0.608968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.81458e6 | 1.72171 | 0.860856 | − | 0.508849i | \(-0.169929\pi\) | ||||
0.860856 | + | 0.508849i | \(0.169929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 167955. | − | 1.87399e6i | 0.0592762 | − | 0.661385i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.70544e6 | 1.29075 | 0.645376 | − | 0.763865i | \(-0.276701\pi\) | ||||
0.645376 | + | 0.763865i | \(0.276701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.43995e6 | + | 802299.i | 1.50696 | + | 0.272307i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.09914e6i | 0.368282i | 0.982900 | + | 0.184141i | \(0.0589503\pi\) | ||||
−0.982900 | + | 0.184141i | \(0.941050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40274e6i | 1.45640i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 337969. | − | 3.77095e6i | 0.110381 | − | 1.23160i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.02523e6 | 1.94304 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.54292e6i | − | 1.76507i | −0.470246 | − | 0.882535i | \(-0.655835\pi\) | ||
0.470246 | − | 0.882535i | \(-0.344165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.50177e6i | − | 1.08749i | −0.839250 | − | 0.543746i | \(-0.817005\pi\) | ||
0.839250 | − | 0.543746i | \(-0.182995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.10189e6 | −0.337970 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.86641e6 | − | 1.44449e6i | −1.17131 | − | 0.437599i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.68532e6i | − | 0.504307i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.96495e6i | 1.46760i | 0.679367 | + | 0.733799i | \(0.262254\pi\) | ||||
−0.679367 | + | 0.733799i | \(0.737746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.23996e6 | + | 290379.i | 0.946095 | + | 0.0847932i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −192013. | −0.0547281 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.13908e6 | − | 281338.i | −0.884020 | − | 0.0792297i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.93856e6 | 0.817711 | 0.408855 | − | 0.912599i | \(-0.365928\pi\) | ||||
0.408855 | + | 0.912599i | \(0.365928\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −90444.5 | −0.0248701 | −0.0124350 | − | 0.999923i | \(-0.503958\pi\) | ||||
−0.0124350 | + | 0.999923i | \(0.503958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −579201. | − | 104662.i | −0.157391 | − | 0.0284405i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.58156e6 | 0.424730 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 185273. | − | 2.06722e6i | 0.0486037 | − | 0.542305i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 295281.i | 0.0765672i | 0.999267 | + | 0.0382836i | \(0.0121890\pi\) | ||||
−0.999267 | + | 0.0382836i | \(0.987811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.22505e6i | 1.85191i | 0.377628 | + | 0.925957i | \(0.376740\pi\) | ||||
−0.377628 | + | 0.925957i | \(0.623260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.38017e6 | + | 571819.i | 1.61663 | + | 0.144889i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.02753e7 | −2.57390 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.59769e6i | 0.395668i | 0.980236 | + | 0.197834i | \(0.0633906\pi\) | ||||
−0.980236 | + | 0.197834i | \(0.936609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5.69173e6i | − | 1.37795i | −0.724783 | − | 0.688977i | \(-0.758060\pi\) | ||
0.724783 | − | 0.688977i | \(-0.241940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.11590e6 | −1.70345 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.78707e6 | − | 697911.i | −1.84334 | − | 0.165208i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.13493e6i | 1.67022i | 0.550082 | + | 0.835111i | \(0.314597\pi\) | ||||
−0.550082 | + | 0.835111i | \(0.685403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.98441e6i | 1.84842i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −489997. | + | 5.46723e6i | −0.112188 | + | 1.25176i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.94203e6 | 0.434976 | 0.217488 | − | 0.976063i | \(-0.430214\pi\) | ||||
0.217488 | + | 0.976063i | \(0.430214\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 901489. | − | 3.28083e6i | 0.199723 | − | 0.726862i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.10948e6 | 1.33891 | 0.669456 | − | 0.742852i | \(-0.266527\pi\) | ||||
0.669456 | + | 0.742852i | \(0.266527\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.08866e6 | 0.886398 | 0.443199 | − | 0.896423i | \(-0.353844\pi\) | ||||
0.443199 | + | 0.896423i | \(0.353844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.18335e6 | + | 374930.i | 0.897206 | + | 0.0804115i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −444247. | −0.0942611 | −0.0471306 | − | 0.998889i | \(-0.515008\pi\) | ||||
−0.0471306 | + | 0.998889i | \(0.515008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.49669e6 | + | 761511.i | 1.76481 | + | 0.158170i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.64810e6i | − | 1.77733i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.69112e6i | 0.750627i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 329190. | − | 1.82175e6i | 0.0662446 | − | 0.366600i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.50806e6 | −0.300317 | −0.150159 | − | 0.988662i | \(-0.547978\pi\) | ||||
−0.150159 | + | 0.988662i | \(0.547978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.03433e6i | − | 0.203843i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.63609e6i | 0.315830i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.85810e6 | 0.546078 | 0.273039 | − | 0.962003i | \(-0.411971\pi\) | ||||
0.273039 | + | 0.962003i | \(0.411971\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 875679. | − | 9.77054e6i | 0.165605 | − | 1.84776i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.95391e6i | − | 0.927352i | −0.886005 | − | 0.463676i | \(-0.846530\pi\) | ||
0.886005 | − | 0.463676i | \(-0.153470\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.28056e6i | 0.978503i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.40678e6 | + | 7.78517e6i | −0.258056 | + | 1.42809i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.98813e6 | −1.43613 | −0.718065 | − | 0.695976i | \(-0.754972\pi\) | ||||
−0.718065 | + | 0.695976i | \(0.754972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −819034. | + | 9.13853e6i | −0.145783 | + | 1.62660i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.57392e6 | 0.453602 | 0.226801 | − | 0.973941i | \(-0.427173\pi\) | ||||
0.226801 | + | 0.973941i | \(0.427173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.34784e6 | −0.758657 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −402957. | + | 4.49607e6i | −0.0696208 | + | 0.776807i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.29786e6 | 1.59070 | 0.795350 | − | 0.606150i | \(-0.207287\pi\) | ||||
0.795350 | + | 0.606150i | \(0.207287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.65697e6 | + | 2.10394e6i | 1.28459 | + | 0.352972i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.70721e6i | 0.449784i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.12816e6i | 0.185629i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 224370. | − | 2.50345e6i | 0.0365634 | − | 0.407963i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.09866e7 | 1.77325 | 0.886624 | − | 0.462490i | \(-0.153044\pi\) | ||||
0.886624 | + | 0.462490i | \(0.153044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 278694.i | − | 0.0445527i | −0.999752 | − | 0.0222763i | \(-0.992909\pi\) | ||
0.999752 | − | 0.0222763i | \(-0.00709137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46235e6i | 0.543057i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.75899e7 | −2.73290 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.54530e6 | + | 459936.i | 0.391744 | + | 0.0707883i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.90026e6i | 0.747139i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.31883e7i | 1.99207i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.13343e6 | − | 460080.i | −0.768196 | − | 0.0688491i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24150e6 | −0.182370 | −0.0911849 | − | 0.995834i | \(-0.529065\pi\) | ||||
−0.0911849 | + | 0.995834i | \(0.529065\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.54515e6 | + | 586605.i | 0.952621 | + | 0.0853780i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.10645e7 | −1.59566 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.28542e6 | −0.755286 | −0.377643 | − | 0.925951i | \(-0.623265\pi\) | ||||
−0.377643 | + | 0.925951i | \(0.623265\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 675135. | − | 3.73622e6i | 0.0956004 | − | 0.529056i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.23240e7 | −1.72931 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −351939. | + | 3.92683e6i | −0.0484993 | + | 0.541140i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.68636e6i | 1.04974i | 0.851182 | + | 0.524871i | \(0.175887\pi\) | ||||
−0.851182 | + | 0.524871i | \(0.824113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.30759e6i | − | 0.718402i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.49558e6 | − | 582162.i | −0.871386 | − | 0.0780974i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.56529e6 | 0.607012 | 0.303506 | − | 0.952830i | \(-0.401843\pi\) | ||||
0.303506 | + | 0.952830i | \(0.401843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.17645e7i | − | 1.55043i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.68731e6i | 0.606936i | 0.952842 | + | 0.303468i | \(0.0981446\pi\) | ||||
−0.952842 | + | 0.303468i | \(0.901855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.13561e6 | 0.659177 | 0.329589 | − | 0.944125i | \(-0.393090\pi\) | ||||
0.329589 | + | 0.944125i | \(0.393090\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.17947e6 | + | 553831.i | 0.786257 | + | 0.0704678i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.63073e6i | 1.08862i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 667514.i | − | 0.0834682i | −0.999129 | − | 0.0417341i | \(-0.986712\pi\) | ||
0.999129 | − | 0.0417341i | \(-0.0132882\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −722447. | + | 8.06083e6i | −0.0895590 | + | 0.999271i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.54839e6 | −0.432374 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −863382. | + | 4.77798e6i | −0.104307 | + | 0.577238i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.60922e6 | 1.15105 | 0.575523 | − | 0.817785i | \(-0.304798\pi\) | ||||
0.575523 | + | 0.817785i | \(0.304798\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.08062e6 | −0.959747 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00934e6 | − | 807456.i | −1.06102 | − | 0.0950934i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.00253e7 | −1.17074 | −0.585371 | − | 0.810766i | \(-0.699051\pi\) | ||||
−0.585371 | + | 0.810766i | \(0.699051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.31059e7 | + | 1.17461e6i | 1.50498 | + | 0.134883i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.96759e6i | − | 0.565690i | −0.959166 | − | 0.282845i | \(-0.908722\pi\) | ||
0.959166 | − | 0.282845i | \(-0.0912782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.91804e6i | 0.329538i | 0.986332 | + | 0.164769i | \(0.0526878\pi\) | ||||
−0.986332 | + | 0.164769i | \(0.947312\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 710973. | + | 128473.i | 0.0796269 | + | 0.0143886i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.90671e6 | 0.433933 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.53707e6i | 0.609969i | 0.952357 | + | 0.304985i | \(0.0986513\pi\) | ||||
−0.952357 | + | 0.304985i | \(0.901349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 692387.i | 0.0750319i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.39229e6 | −0.579591 | −0.289796 | − | 0.957089i | \(-0.593587\pi\) | ||||
−0.289796 | + | 0.957089i | \(0.593587\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.66736e6 | − | 1.86039e7i | 0.177763 | − | 1.98343i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.18727e7i | − | 1.25556i | −0.778392 | − | 0.627778i | \(-0.783965\pi\) | ||
0.778392 | − | 0.627778i | \(-0.216035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.71087e6i | 0.703967i | 0.936006 | + | 0.351983i | \(0.114493\pi\) | ||||
−0.936006 | + | 0.351983i | \(0.885507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.79039e7 | + | 4.91953e6i | 1.86302 | + | 0.511911i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.21677e7 | −1.24597 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.35868e6 | − | 1.51597e7i | 0.138022 | − | 1.54001i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.25004e6 | −0.327539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.01133e7 | 1.01116 | 0.505580 | − | 0.862780i | \(-0.331279\pi\) | ||||
0.505580 | + | 0.862780i | \(0.331279\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.45251e6 | − | 1.62066e7i | 0.144082 | − | 1.60762i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.43661e6 | 0.830297 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 702957. | − | 3.89019e6i | 0.0681046 | − | 0.376893i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 8.43591e6i | − | 0.810937i | −0.914109 | − | 0.405468i | \(-0.867108\pi\) | ||
0.914109 | − | 0.405468i | \(-0.132892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.51051e7i | 1.44077i | 0.693573 | + | 0.720386i | \(0.256035\pi\) | ||||
−0.693573 | + | 0.720386i | \(0.743965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.80596e6 | + | 2.01503e7i | −0.170926 | + | 1.90714i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.08522e7 | −1.01919 | −0.509597 | − | 0.860413i | \(-0.670205\pi\) | ||||
−0.509597 | + | 0.860413i | \(0.670205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.95772e6i | − | 0.462030i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 590041.i | 0.0541501i | 0.999633 | + | 0.0270750i | \(0.00861931\pi\) | ||||
−0.999633 | + | 0.0270750i | \(0.991381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.69766e7 | 1.54614 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 634229. | − | 3.50984e6i | 0.0573235 | − | 0.317230i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.38679e7i | − | 1.24394i | −0.783042 | − | 0.621969i | \(-0.786333\pi\) | ||
0.783042 | − | 0.621969i | \(-0.213667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.62028e7i | − | 1.44240i | −0.692727 | − | 0.721200i | \(-0.743591\pi\) | ||
0.692727 | − | 0.721200i | \(-0.256409\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.98652e6 | − | 357290.i | −0.352217 | − | 0.0315672i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.88166e7 | −2.50800 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.87679e6 | − | 257831.i | −0.248510 | − | 0.0222725i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.27738e6 | −0.623977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.09799e7 | −0.934456 | −0.467228 | − | 0.884137i | \(-0.654747\pi\) | ||||
−0.467228 | + | 0.884137i | \(0.654747\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.76720e6 | − | 6.43145e6i | 0.149288 | − | 0.543312i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −190993. | −0.0160157 | −0.00800785 | − | 0.999968i | \(-0.502549\pi\) | ||||
−0.00800785 | + | 0.999968i | \(0.502549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.22156e6 | − | 1.36297e7i | 0.100936 | − | 1.12621i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.35316e7i | 1.10993i | 0.831873 | + | 0.554967i | \(0.187269\pi\) | ||||
−0.831873 | + | 0.554967i | \(0.812731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.45861e7i | 1.18772i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.90370e7 | + | 1.70618e6i | 1.53888 | + | 0.137922i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.17775e6 | −0.174767 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.88908e6i | − | 0.787881i | −0.919136 | − | 0.393941i | \(-0.871112\pi\) | ||
0.919136 | − | 0.393941i | \(-0.128888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.41320e7i | − | 1.10979i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.53975e7 | 1.20052 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.17470e6 | + | 105282.i | 0.0909357 | + | 0.00815005i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.46554e6i | 0.112643i | 0.998413 | + | 0.0563213i | \(0.0179371\pi\) | ||||
−0.998413 | + | 0.0563213i | \(0.982063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.58512e6i | − | 0.578861i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 235591. | − | 2.62865e6i | 0.0178520 | − | 0.199187i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.66337e6 | 0.124272 | 0.0621361 | − | 0.998068i | \(-0.480209\pi\) | ||||
0.0621361 | + | 0.998068i | \(0.480209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.06127e7 | + | 3.72473e6i | 1.52919 | + | 0.276325i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.88945e7 | −1.39191 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.30652e6 | 0.680805 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.02227e7 | + | 916207.i | 0.742625 | + | 0.0665573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.28664e6 | 0.525660 | 0.262830 | − | 0.964842i | \(-0.415344\pi\) | ||||
0.262830 | + | 0.964842i | \(0.415344\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.80843e6 | − | 789449.i | −0.626690 | − | 0.0561667i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.03515e7i | 0.731408i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.37534e6i | − | 0.166682i | −0.996521 | − | 0.0833411i | \(-0.973441\pi\) | ||
0.996521 | − | 0.0833411i | \(-0.0265591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.23343e7 | − | 7.33187e6i | −0.859598 | − | 0.510970i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.66774e7 | −1.15434 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.12018e7i | − | 1.45751i | −0.684774 | − | 0.728755i | \(-0.740099\pi\) | ||
0.684774 | − | 0.728755i | \(-0.259901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.38483e6i | − | 0.0939133i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8248.53 | 0.000555604 | 0.000277802 | − | 1.00000i | \(-0.499912\pi\) | ||||
0.000277802 | 1.00000i | \(0.499912\pi\) | ||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 833861. | − | 9.30395e6i | 0.0557889 | − | 0.622475i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.10286e7i | − | 1.39746i | −0.715386 | − | 0.698730i | \(-0.753749\pi\) | ||
0.715386 | − | 0.698730i | \(-0.246251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.50570e7i | − | 2.31411i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −656890. | − | 118700.i | −0.0430716 | − | 0.00778305i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.24333e7 | −0.804426 | −0.402213 | − | 0.915546i | \(-0.631759\pi\) | ||||
−0.402213 | + | 0.915546i | \(0.631759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.55575e6 | − | 2.85162e7i | 0.164259 | − | 1.83275i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.46132e7 | −1.57145 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.56314e7 | −0.991421 | −0.495710 | − | 0.868488i | \(-0.665092\pi\) | ||||
−0.495710 | + | 0.868488i | \(0.665092\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.17692e6 | − | 3.54471e7i | 0.200172 | − | 2.23345i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.54527e6 | 0.221915 | 0.110958 | − | 0.993825i | \(-0.464608\pi\) | ||||
0.110958 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.50133e7 | + | 2.71291e6i | 0.927518 | + | 0.167603i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.04269e6i | − | 0.186754i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 4.01821e6i | − | 0.245028i | −0.992467 | − | 0.122514i | \(-0.960904\pi\) | ||
0.992467 | − | 0.122514i | \(-0.0390957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.25573e6 | − | 1.40110e7i | 0.0760782 | − | 0.848857i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.96681e7 | −1.78584 | −0.892918 | − | 0.450219i | \(-0.851346\pi\) | ||||
−0.892918 | + | 0.450219i | \(0.851346\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.78729e6i | 0.405922i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.59355e7i | 2.12168i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.57728e6 | −0.444514 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.14735e7 | + | 5.90038e6i | 1.25170 | + | 0.343934i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.82517e7i | 2.21553i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 6.48183e6i | − | 0.373045i | −0.982451 | − | 0.186522i | \(-0.940278\pi\) | ||
0.982451 | − | 0.186522i | \(-0.0597217\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.44868e7 | − | 1.29837e6i | −0.828477 | − | 0.0742517i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.46634e6 | −0.252214 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.26783e6 | + | 740999.i | 0.463953 | + | 0.0415815i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.52053e7 | 1.96319 | 0.981594 | − | 0.190979i | \(-0.0611663\pi\) | ||||
0.981594 | + | 0.190979i | \(0.0611663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.17561e6 | 0.120563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.43440e7 | − | 4.39896e6i | −1.34064 | − | 0.242253i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.83645e6 | −0.374147 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 742290. | − | 8.28224e6i | 0.0401227 | − | 0.447676i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.62772e7i | 0.874397i | 0.899365 | + | 0.437198i | \(0.144029\pi\) | ||||
−0.899365 | + | 0.437198i | \(0.855971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 823682.i | − | 0.0439752i | −0.999758 | − | 0.0219876i | \(-0.993001\pi\) | ||
0.999758 | − | 0.0219876i | \(-0.00699943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.24006e7 | − | 1.11139e6i | −0.657985 | − | 0.0589715i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.39865e7 | 2.31967 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.89226e7i | − | 2.04008i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.33763e6i | 0.224592i | 0.993675 | + | 0.112296i | \(0.0358205\pi\) | ||||
−0.993675 | + | 0.112296i | \(0.964179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.01908e7 | 0.524454 | 0.262227 | − | 0.965006i | \(-0.415543\pi\) | ||||
0.262227 | + | 0.965006i | \(0.415543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.27334e7 | − | 1.14122e6i | −0.651341 | − | 0.0583760i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.90780e7i | 0.969996i | 0.874515 | + | 0.484998i | \(0.161180\pi\) | ||||
−0.874515 | + | 0.484998i | \(0.838820\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.64200e6i | − | 0.285133i | −0.989785 | − | 0.142566i | \(-0.954465\pi\) | ||
0.989785 | − | 0.142566i | \(-0.0455354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.64244e6 | + | 1.83259e7i | −0.0825065 | + | 0.920581i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.11412e7 | −2.04202 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.40798e7 | + | 3.86876e6i | 0.694675 | + | 0.190879i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.11858e7 | 0.548608 | 0.274304 | − | 0.961643i | \(-0.411552\pi\) | ||||
0.274304 | + | 0.961643i | \(0.411552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40509e7 | −0.685037 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.42604e7 | + | 2.17432e6i | 1.17579 | + | 0.105379i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.02411e7 | −0.975196 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.68404e7 | − | 1.50931e6i | −0.801830 | − | 0.0718635i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.77358e7i | − | 0.839514i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.52648e6i | − | 0.401233i | −0.979670 | − | 0.200617i | \(-0.935705\pi\) | ||
0.979670 | − | 0.200617i | \(-0.0642946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.33152e6 | + | 3.50388e7i | −0.296205 | + | 1.63921i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.71350e7 | 1.26205 | 0.631027 | − | 0.775761i | \(-0.282634\pi\) | ||||
0.631027 | + | 0.775761i | \(0.282634\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.17238e7i | 1.00451i | 0.864720 | + | 0.502254i | \(0.167496\pi\) | ||||
−0.864720 | + | 0.502254i | \(0.832504\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.77634e7i | − | 0.811895i | −0.913896 | − | 0.405948i | \(-0.866942\pi\) | ||
0.913896 | − | 0.405948i | \(-0.133058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.12704e7 | 0.512153 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 853101. | − | 9.51863e6i | 0.0385437 | − | 0.430058i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.01494e7i | − | 1.80355i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 849909.i | − | 0.0379601i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.01141e6 | + | 5.59719e6i | −0.0449152 | + | 0.248562i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −621725. | −0.0272960 | −0.0136480 | − | 0.999907i | \(-0.504344\pi\) | ||||
−0.0136480 | + | 0.999907i | \(0.504344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.93760e6 | + | 2.16191e7i | −0.0845847 | + | 0.943769i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.18993e7 | 1.38465 | 0.692327 | − | 0.721584i | \(-0.256586\pi\) | ||||
0.692327 | + | 0.721584i | \(0.256586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.60937e7 | −0.694633 | −0.347316 | − | 0.937748i | \(-0.612907\pi\) | ||||
−0.347316 | + | 0.937748i | \(0.612907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.03531e6 | + | 1.15516e7i | −0.0444335 | + | 0.495775i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.19434e7 | 0.936471 | 0.468235 | − | 0.883604i | \(-0.344890\pi\) | ||||
0.468235 | + | 0.883604i | \(0.344890\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.62541e6 | + | 2.57640e7i | −0.406186 | + | 1.08722i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.07754e6i | 0.213071i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.31105e7i | − | 0.964387i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.94977e6 | − | 2.17549e7i | 0.0809100 | − | 0.902768i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.26616e7 | −0.935173 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.84288e6i | 0.280819i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.94660e7i | 1.19591i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.41122e7 | 0.973238 | 0.486619 | − | 0.873614i | \(-0.338230\pi\) | ||||
0.486619 | + | 0.873614i | \(0.338230\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.48743e7 | − | 2.68779e6i | −0.597071 | − | 0.107891i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.16994e7i | 0.467056i | 0.972350 | + | 0.233528i | \(0.0750271\pi\) | ||||
−0.972350 | + | 0.233528i | \(0.924973\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.27949e6i | 0.0507994i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.69565e7 | + | 1.51971e6i | 0.669550 | + | 0.0600080i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.35972e7 | 0.531080 | 0.265540 | − | 0.964100i | \(-0.414450\pi\) | ||||
0.265540 | + | 0.964100i | \(0.414450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.85383e7 | − | 1.66148e6i | −0.720147 | − | 0.0645427i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.65039e6 | −0.179674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.37110e6 | −0.244827 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.67357e6 | + | 9.26156e6i | −0.0639651 | + | 0.353985i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.13421e7 | −0.431177 | −0.215589 | − | 0.976484i | \(-0.569167\pi\) | ||||
−0.215589 | + | 0.976484i | \(0.569167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.65354e6 | + | 4.07651e7i | −0.137407 | + | 1.53315i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.92428e7i | − | 1.09393i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.45048e7i | − | 0.911806i | −0.890029 | − | 0.455903i | \(-0.849316\pi\) | ||
0.890029 | − | 0.455903i | \(-0.150684\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.37835e7 | + | 1.23534e6i | 0.510149 | + | 0.0457217i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.41453e6 | 0.199336 | 0.0996682 | − | 0.995021i | \(-0.468222\pi\) | ||||
0.0996682 | + | 0.995021i | \(0.468222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.40260e7i | 3.07705i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.00820e7i | − | 1.09001i | −0.838432 | − | 0.545006i | \(-0.816527\pi\) | ||
0.838432 | − | 0.545006i | \(-0.183473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.19573e6 | −0.151231 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.81669e7 | − | 2.52444e6i | −1.00992 | − | 0.0905137i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.03196e7i | − | 0.724742i | −0.932034 | − | 0.362371i | \(-0.881967\pi\) | ||
0.932034 | − | 0.362371i | \(-0.118033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.78197e7i | 0.987060i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.81034e6 | − | 4.25146e7i | 0.134488 | − | 1.50058i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.37704e7 | 0.480991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.15286e6 | + | 4.51182e7i | −0.283299 | + | 1.56778i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.62895e7 | −1.25448 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.69494e7 | −0.926792 | −0.463396 | − | 0.886151i | \(-0.653369\pi\) | ||||
−0.463396 | + | 0.886151i | \(0.653369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.92347e7 | − | 2.62014e6i | −1.00021 | − | 0.0896428i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.42537e7 | −1.16590 | −0.582948 | − | 0.812510i | \(-0.698101\pi\) | ||||
−0.582948 | + | 0.812510i | \(0.698101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.81483e6 | − | 700399.i | −0.263274 | − | 0.0235958i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.50876e7i | − | 0.840858i | −0.907325 | − | 0.420429i | \(-0.861880\pi\) | ||
0.907325 | − | 0.420429i | \(-0.138120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.74171e7i | 1.58117i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.78525e7 | − | 6.83995e6i | −1.25580 | − | 0.226924i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.36116e7 | −0.779367 | −0.389684 | − | 0.920949i | \(-0.627416\pi\) | ||||
−0.389684 | + | 0.920949i | \(0.627416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.05596e7i | − | 1.33200i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 9.10105e7i | − | 2.95870i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.17500e7 | −0.703519 | −0.351760 | − | 0.936090i | \(-0.614417\pi\) | ||||
−0.351760 | + | 0.936090i | \(0.614417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.55409e6 | − | 3.96554e7i | 0.114381 | − | 1.27623i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.90021e7i | 1.88934i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.35621e7i | 1.38794i | 0.720004 | + | 0.693970i | \(0.244140\pi\) | ||||
−0.720004 | + | 0.693970i | \(0.755860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.63153e6 | + | 1.32164e7i | −0.115127 | + | 0.418986i |
(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 | 588.6.f.c.293.20 | yes | 40 | |
3.2 | odd | 2 | inner | 588.6.f.c.293.22 | yes | 40 | |
7.6 | odd | 2 | inner | 588.6.f.c.293.21 | yes | 40 | |
21.20 | even | 2 | inner | 588.6.f.c.293.19 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.6.f.c.293.19 | ✓ | 40 | 21.20 | even | 2 | inner | |
588.6.f.c.293.20 | yes | 40 | 1.1 | even | 1 | trivial | |
588.6.f.c.293.21 | yes | 40 | 7.6 | odd | 2 | inner | |
588.6.f.c.293.22 | yes | 40 | 3.2 | odd | 2 | inner |