Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,6,Mod(1,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.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: | \(100.239887383\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.6667 | −1.88563 | −0.942816 | − | 0.333313i | \(-0.891833\pi\) | ||||
−0.942816 | + | 0.333313i | \(0.891833\pi\) | |||||||
\(3\) | −5.92758 | −0.380254 | −0.190127 | − | 0.981759i | \(-0.560890\pi\) | ||||
−0.190127 | + | 0.981759i | \(0.560890\pi\) | |||||||
\(4\) | 81.7795 | 2.55561 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 63.2280 | 0.717020 | ||||||||
\(7\) | 120.405 | 0.928748 | 0.464374 | − | 0.885639i | \(-0.346279\pi\) | ||||
0.464374 | + | 0.885639i | \(0.346279\pi\) | |||||||
\(8\) | −530.986 | −2.93331 | ||||||||
\(9\) | −207.864 | −0.855407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −442.746 | −1.10325 | −0.551624 | − | 0.834093i | \(-0.685992\pi\) | ||||
−0.551624 | + | 0.834093i | \(0.685992\pi\) | |||||||
\(12\) | −484.755 | −0.971782 | ||||||||
\(13\) | 891.643 | 1.46330 | 0.731648 | − | 0.681682i | \(-0.238751\pi\) | ||||
0.731648 | + | 0.681682i | \(0.238751\pi\) | |||||||
\(14\) | −1284.33 | −1.75128 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3046.94 | 2.97553 | ||||||||
\(17\) | −480.421 | −0.403181 | −0.201590 | − | 0.979470i | \(-0.564611\pi\) | ||||
−0.201590 | + | 0.979470i | \(0.564611\pi\) | |||||||
\(18\) | 2217.23 | 1.61298 | ||||||||
\(19\) | 117.717 | 0.0748090 | 0.0374045 | − | 0.999300i | \(-0.488091\pi\) | ||||
0.0374045 | + | 0.999300i | \(0.488091\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −713.708 | −0.353161 | ||||||||
\(22\) | 4722.66 | 2.08032 | ||||||||
\(23\) | 2134.63 | 0.841401 | 0.420701 | − | 0.907200i | \(-0.361784\pi\) | ||||
0.420701 | + | 0.907200i | \(0.361784\pi\) | |||||||
\(24\) | 3147.46 | 1.11540 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9510.93 | −2.75924 | ||||||||
\(27\) | 2672.53 | 0.705527 | ||||||||
\(28\) | 9846.63 | 2.37352 | ||||||||
\(29\) | 640.905 | 0.141514 | 0.0707569 | − | 0.997494i | \(-0.477459\pi\) | ||||
0.0707569 | + | 0.997494i | \(0.477459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1623.14 | −0.303355 | −0.151677 | − | 0.988430i | \(-0.548468\pi\) | ||||
−0.151677 | + | 0.988430i | \(0.548468\pi\) | |||||||
\(32\) | −15509.5 | −2.67745 | ||||||||
\(33\) | 2624.41 | 0.419515 | ||||||||
\(34\) | 5124.53 | 0.760251 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16999.0 | −2.18609 | ||||||||
\(37\) | −12094.0 | −1.45233 | −0.726167 | − | 0.687518i | \(-0.758700\pi\) | ||||
−0.726167 | + | 0.687518i | \(0.758700\pi\) | |||||||
\(38\) | −1255.65 | −0.141062 | ||||||||
\(39\) | −5285.28 | −0.556425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12573.4 | −1.16813 | −0.584067 | − | 0.811706i | \(-0.698539\pi\) | ||||
−0.584067 | + | 0.811706i | \(0.698539\pi\) | |||||||
\(42\) | 7612.94 | 0.665931 | ||||||||
\(43\) | 11083.8 | 0.914154 | 0.457077 | − | 0.889427i | \(-0.348896\pi\) | ||||
0.457077 | + | 0.889427i | \(0.348896\pi\) | |||||||
\(44\) | −36207.5 | −2.81947 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22769.6 | −1.58657 | ||||||||
\(47\) | 19979.2 | 1.31927 | 0.659633 | − | 0.751588i | \(-0.270712\pi\) | ||||
0.659633 | + | 0.751588i | \(0.270712\pi\) | |||||||
\(48\) | −18061.0 | −1.13146 | ||||||||
\(49\) | −2309.73 | −0.137427 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2847.74 | 0.153311 | ||||||||
\(52\) | 72918.1 | 3.73962 | ||||||||
\(53\) | −36909.9 | −1.80490 | −0.902450 | − | 0.430794i | \(-0.858233\pi\) | ||||
−0.902450 | + | 0.430794i | \(0.858233\pi\) | |||||||
\(54\) | −28507.2 | −1.33036 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −63933.1 | −2.72430 | ||||||||
\(57\) | −697.775 | −0.0284464 | ||||||||
\(58\) | −6836.37 | −0.266843 | ||||||||
\(59\) | −16033.2 | −0.599641 | −0.299820 | − | 0.953996i | \(-0.596927\pi\) | ||||
−0.299820 | + | 0.953996i | \(0.596927\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 43151.3 | 1.48480 | 0.742402 | − | 0.669955i | \(-0.233687\pi\) | ||||
0.742402 | + | 0.669955i | \(0.233687\pi\) | |||||||
\(62\) | 17313.6 | 0.572016 | ||||||||
\(63\) | −25027.8 | −0.794457 | ||||||||
\(64\) | 67933.2 | 2.07316 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −27993.9 | −0.791050 | ||||||||
\(67\) | 18063.3 | 0.491597 | 0.245799 | − | 0.969321i | \(-0.420950\pi\) | ||||
0.245799 | + | 0.969321i | \(0.420950\pi\) | |||||||
\(68\) | −39288.6 | −1.03037 | ||||||||
\(69\) | −12653.2 | −0.319946 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −26156.6 | −0.615794 | −0.307897 | − | 0.951420i | \(-0.599625\pi\) | ||||
−0.307897 | + | 0.951420i | \(0.599625\pi\) | |||||||
\(72\) | 110373. | 2.50917 | ||||||||
\(73\) | −15093.0 | −0.331488 | −0.165744 | − | 0.986169i | \(-0.553003\pi\) | ||||
−0.165744 | + | 0.986169i | \(0.553003\pi\) | |||||||
\(74\) | 129004. | 2.73857 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9626.81 | 0.191183 | ||||||||
\(77\) | −53308.6 | −1.02464 | ||||||||
\(78\) | 56376.8 | 1.04921 | ||||||||
\(79\) | 43779.0 | 0.789220 | 0.394610 | − | 0.918849i | \(-0.370880\pi\) | ||||
0.394610 | + | 0.918849i | \(0.370880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34669.3 | 0.587127 | ||||||||
\(82\) | 134117. | 2.20267 | ||||||||
\(83\) | 23599.3 | 0.376013 | 0.188007 | − | 0.982168i | \(-0.439797\pi\) | ||||
0.188007 | + | 0.982168i | \(0.439797\pi\) | |||||||
\(84\) | −58366.7 | −0.902541 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −118229. | −1.72376 | ||||||||
\(87\) | −3799.01 | −0.0538112 | ||||||||
\(88\) | 235092. | 3.23616 | ||||||||
\(89\) | 48842.2 | 0.653612 | 0.326806 | − | 0.945091i | \(-0.394028\pi\) | ||||
0.326806 | + | 0.945091i | \(0.394028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 107358. | 1.35903 | ||||||||
\(92\) | 174569. | 2.15029 | ||||||||
\(93\) | 9621.28 | 0.115352 | ||||||||
\(94\) | −213113. | −2.48765 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 91933.5 | 1.01811 | ||||||||
\(97\) | 13981.0 | 0.150873 | 0.0754363 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754363 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(98\) | 24637.4 | 0.259137 | ||||||||
\(99\) | 92030.8 | 0.943725 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 381.587 | 0.00372212 | 0.00186106 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00186106 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(102\) | −30376.1 | −0.289089 | ||||||||
\(103\) | −110235. | −1.02383 | −0.511913 | − | 0.859038i | \(-0.671063\pi\) | ||||
−0.511913 | + | 0.859038i | \(0.671063\pi\) | |||||||
\(104\) | −473449. | −4.29230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 393709. | 3.40338 | ||||||||
\(107\) | 124723. | 1.05314 | 0.526572 | − | 0.850131i | \(-0.323477\pi\) | ||||
0.526572 | + | 0.850131i | \(0.323477\pi\) | |||||||
\(108\) | 218558. | 1.80305 | ||||||||
\(109\) | 36391.5 | 0.293382 | 0.146691 | − | 0.989182i | \(-0.453138\pi\) | ||||
0.146691 | + | 0.989182i | \(0.453138\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 71688.3 | 0.552256 | ||||||||
\(112\) | 366866. | 2.76352 | ||||||||
\(113\) | −89912.1 | −0.662402 | −0.331201 | − | 0.943560i | \(-0.607454\pi\) | ||||
−0.331201 | + | 0.943560i | \(0.607454\pi\) | |||||||
\(114\) | 7442.98 | 0.0536395 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 52412.9 | 0.361654 | ||||||||
\(117\) | −185340. | −1.25171 | ||||||||
\(118\) | 171023. | 1.13070 | ||||||||
\(119\) | −57844.9 | −0.374454 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 34972.9 | 0.217154 | ||||||||
\(122\) | −460284. | −2.79979 | ||||||||
\(123\) | 74529.7 | 0.444188 | ||||||||
\(124\) | −132739. | −0.775257 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 266965. | 1.49805 | ||||||||
\(127\) | 159416. | 0.877044 | 0.438522 | − | 0.898720i | \(-0.355502\pi\) | ||||
0.438522 | + | 0.898720i | \(0.355502\pi\) | |||||||
\(128\) | −228324. | −1.23176 | ||||||||
\(129\) | −65700.4 | −0.347611 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −191343. | −0.974167 | −0.487084 | − | 0.873355i | \(-0.661939\pi\) | ||||
−0.487084 | + | 0.873355i | \(0.661939\pi\) | |||||||
\(132\) | 214623. | 1.07212 | ||||||||
\(133\) | 14173.6 | 0.0694787 | ||||||||
\(134\) | −192676. | −0.926972 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 255097. | 1.18265 | ||||||||
\(137\) | 279442. | 1.27201 | 0.636005 | − | 0.771685i | \(-0.280586\pi\) | ||||
0.636005 | + | 0.771685i | \(0.280586\pi\) | |||||||
\(138\) | 134968. | 0.603301 | ||||||||
\(139\) | 197654. | 0.867699 | 0.433850 | − | 0.900985i | \(-0.357155\pi\) | ||||
0.433850 | + | 0.900985i | \(0.357155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −118428. | −0.501657 | ||||||||
\(142\) | 279006. | 1.16116 | ||||||||
\(143\) | −394771. | −1.61438 | ||||||||
\(144\) | −633349. | −2.54529 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 160993. | 0.625065 | ||||||||
\(147\) | 13691.1 | 0.0522572 | ||||||||
\(148\) | −989044. | −3.71160 | ||||||||
\(149\) | 49298.1 | 0.181913 | 0.0909567 | − | 0.995855i | \(-0.471008\pi\) | ||||
0.0909567 | + | 0.995855i | \(0.471008\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 173320. | 0.618594 | 0.309297 | − | 0.950966i | \(-0.399906\pi\) | ||||
0.309297 | + | 0.950966i | \(0.399906\pi\) | |||||||
\(152\) | −62505.8 | −0.219438 | ||||||||
\(153\) | 99862.2 | 0.344884 | ||||||||
\(154\) | 568630. | 1.93209 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −432228. | −1.42201 | ||||||||
\(157\) | 41142.9 | 0.133213 | 0.0666064 | − | 0.997779i | \(-0.478783\pi\) | ||||
0.0666064 | + | 0.997779i | \(0.478783\pi\) | |||||||
\(158\) | −466979. | −1.48818 | ||||||||
\(159\) | 218786. | 0.686321 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 257019. | 0.781450 | ||||||||
\(162\) | −369808. | −1.10711 | ||||||||
\(163\) | −226902. | −0.668912 | −0.334456 | − | 0.942411i | \(-0.608553\pi\) | ||||
−0.334456 | + | 0.942411i | \(0.608553\pi\) | |||||||
\(164\) | −1.02825e6 | −2.98529 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −251727. | −0.709023 | ||||||||
\(167\) | −106692. | −0.296034 | −0.148017 | − | 0.988985i | \(-0.547289\pi\) | ||||
−0.148017 | + | 0.988985i | \(0.547289\pi\) | |||||||
\(168\) | 378969. | 1.03593 | ||||||||
\(169\) | 423734. | 1.14124 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24469.0 | −0.0639921 | ||||||||
\(172\) | 906432. | 2.33622 | ||||||||
\(173\) | 115853. | 0.294302 | 0.147151 | − | 0.989114i | \(-0.452990\pi\) | ||||
0.147151 | + | 0.989114i | \(0.452990\pi\) | |||||||
\(174\) | 40523.1 | 0.101468 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.34902e6 | −3.28275 | ||||||||
\(177\) | 95038.3 | 0.228016 | ||||||||
\(178\) | −520988. | −1.23247 | ||||||||
\(179\) | −593880. | −1.38537 | −0.692686 | − | 0.721239i | \(-0.743573\pi\) | ||||
−0.692686 | + | 0.721239i | \(0.743573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −738669. | −1.67592 | −0.837961 | − | 0.545731i | \(-0.816252\pi\) | ||||
−0.837961 | + | 0.545731i | \(0.816252\pi\) | |||||||
\(182\) | −1.14516e6 | −2.56264 | ||||||||
\(183\) | −255783. | −0.564603 | ||||||||
\(184\) | −1.13346e6 | −2.46809 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −102628. | −0.217512 | ||||||||
\(187\) | 212705. | 0.444808 | ||||||||
\(188\) | 1.63389e6 | 3.37153 | ||||||||
\(189\) | 321785. | 0.655256 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 847947. | 1.68184 | 0.840922 | − | 0.541157i | \(-0.182013\pi\) | ||||
0.840922 | + | 0.541157i | \(0.182013\pi\) | |||||||
\(192\) | −402679. | −0.788327 | ||||||||
\(193\) | 274628. | 0.530703 | 0.265352 | − | 0.964152i | \(-0.414512\pi\) | ||||
0.265352 | + | 0.964152i | \(0.414512\pi\) | |||||||
\(194\) | −149132. | −0.284490 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −188889. | −0.351210 | ||||||||
\(197\) | 172037. | 0.315833 | 0.157916 | − | 0.987452i | \(-0.449522\pi\) | ||||
0.157916 | + | 0.987452i | \(0.449522\pi\) | |||||||
\(198\) | −981670. | −1.77952 | ||||||||
\(199\) | −1.05743e6 | −1.89287 | −0.946433 | − | 0.322899i | \(-0.895342\pi\) | ||||
−0.946433 | + | 0.322899i | \(0.895342\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −107071. | −0.186932 | ||||||||
\(202\) | −4070.29 | −0.00701854 | ||||||||
\(203\) | 77167.9 | 0.131431 | ||||||||
\(204\) | 232886. | 0.391804 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.17585e6 | 1.93056 | ||||||||
\(207\) | −443712. | −0.719740 | ||||||||
\(208\) | 2.71679e6 | 4.35409 | ||||||||
\(209\) | −52118.5 | −0.0825328 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17241e6 | −1.81290 | −0.906449 | − | 0.422315i | \(-0.861218\pi\) | ||||
−0.906449 | + | 0.422315i | \(0.861218\pi\) | |||||||
\(212\) | −3.01847e6 | −4.61262 | ||||||||
\(213\) | 155045. | 0.234158 | ||||||||
\(214\) | −1.33039e6 | −1.98584 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.41908e6 | −2.06953 | ||||||||
\(217\) | −195433. | −0.281740 | ||||||||
\(218\) | −388179. | −0.553211 | ||||||||
\(219\) | 89464.9 | 0.126050 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −428364. | −0.589973 | ||||||||
\(222\) | −764681. | −1.04135 | ||||||||
\(223\) | −26647.3 | −0.0358832 | −0.0179416 | − | 0.999839i | \(-0.505711\pi\) | ||||
−0.0179416 | + | 0.999839i | \(0.505711\pi\) | |||||||
\(224\) | −1.86741e6 | −2.48668 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 959070. | 1.24905 | ||||||||
\(227\) | 641494. | 0.826282 | 0.413141 | − | 0.910667i | \(-0.364432\pi\) | ||||
0.413141 | + | 0.910667i | \(0.364432\pi\) | |||||||
\(228\) | −57063.7 | −0.0726980 | ||||||||
\(229\) | 790242. | 0.995799 | 0.497899 | − | 0.867235i | \(-0.334105\pi\) | ||||
0.497899 | + | 0.867235i | \(0.334105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 315991. | 0.389623 | ||||||||
\(232\) | −340311. | −0.415103 | ||||||||
\(233\) | −538442. | −0.649754 | −0.324877 | − | 0.945756i | \(-0.605323\pi\) | ||||
−0.324877 | + | 0.945756i | \(0.605323\pi\) | |||||||
\(234\) | 1.97698e6 | 2.36027 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.31119e6 | −1.53245 | ||||||||
\(237\) | −259503. | −0.300104 | ||||||||
\(238\) | 617017. | 0.706082 | ||||||||
\(239\) | 420883. | 0.476614 | 0.238307 | − | 0.971190i | \(-0.423408\pi\) | ||||
0.238307 | + | 0.971190i | \(0.423408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 45463.9 | 0.0504225 | 0.0252113 | − | 0.999682i | \(-0.491974\pi\) | ||||
0.0252113 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(242\) | −373048. | −0.409473 | ||||||||
\(243\) | −854930. | −0.928784 | ||||||||
\(244\) | 3.52889e6 | 3.79458 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −794990. | −0.837575 | ||||||||
\(247\) | 104961. | 0.109468 | ||||||||
\(248\) | 861863. | 0.889834 | ||||||||
\(249\) | −139887. | −0.142981 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 682911. | 0.684194 | 0.342097 | − | 0.939665i | \(-0.388863\pi\) | ||||
0.342097 | + | 0.939665i | \(0.388863\pi\) | |||||||
\(252\) | −2.04676e6 | −2.03032 | ||||||||
\(253\) | −945099. | −0.928273 | ||||||||
\(254\) | −1.70045e6 | −1.65378 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 261610. | 0.249491 | ||||||||
\(257\) | −504722. | −0.476672 | −0.238336 | − | 0.971183i | \(-0.576602\pi\) | ||||
−0.238336 | + | 0.971183i | \(0.576602\pi\) | |||||||
\(258\) | 700809. | 0.655467 | ||||||||
\(259\) | −1.45618e6 | −1.34885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −133221. | −0.121052 | ||||||||
\(262\) | 2.04100e6 | 1.83692 | ||||||||
\(263\) | −1.45944e6 | −1.30105 | −0.650527 | − | 0.759483i | \(-0.725452\pi\) | ||||
−0.650527 | + | 0.759483i | \(0.725452\pi\) | |||||||
\(264\) | −1.39352e6 | −1.23057 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −151186. | −0.131011 | ||||||||
\(267\) | −289516. | −0.248539 | ||||||||
\(268\) | 1.47721e6 | 1.25633 | ||||||||
\(269\) | −969441. | −0.816847 | −0.408423 | − | 0.912793i | \(-0.633921\pi\) | ||||
−0.408423 | + | 0.912793i | \(0.633921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.88150e6 | −1.55626 | −0.778130 | − | 0.628104i | \(-0.783831\pi\) | ||||
−0.778130 | + | 0.628104i | \(0.783831\pi\) | |||||||
\(272\) | −1.46382e6 | −1.19968 | ||||||||
\(273\) | −636372. | −0.516779 | ||||||||
\(274\) | −2.98074e6 | −2.39854 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.03477e6 | −0.817658 | ||||||||
\(277\) | −1.19182e6 | −0.933280 | −0.466640 | − | 0.884447i | \(-0.654536\pi\) | ||||
−0.466640 | + | 0.884447i | \(0.654536\pi\) | |||||||
\(278\) | −2.10833e6 | −1.63616 | ||||||||
\(279\) | 337392. | 0.259492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.45386e6 | −1.09839 | −0.549197 | − | 0.835693i | \(-0.685066\pi\) | ||||
−0.549197 | + | 0.835693i | \(0.685066\pi\) | |||||||
\(282\) | 1.26324e6 | 0.945940 | ||||||||
\(283\) | −1.02913e6 | −0.763847 | −0.381923 | − | 0.924194i | \(-0.624738\pi\) | ||||
−0.381923 | + | 0.924194i | \(0.624738\pi\) | |||||||
\(284\) | −2.13907e6 | −1.57373 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.21092e6 | 3.04412 | ||||||||
\(287\) | −1.51389e6 | −1.08490 | ||||||||
\(288\) | 3.22385e6 | 2.29031 | ||||||||
\(289\) | −1.18905e6 | −0.837445 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −82873.8 | −0.0573700 | ||||||||
\(292\) | −1.23430e6 | −0.847155 | ||||||||
\(293\) | 787720. | 0.536047 | 0.268023 | − | 0.963412i | \(-0.413630\pi\) | ||||
0.268023 | + | 0.963412i | \(0.413630\pi\) | |||||||
\(294\) | −146040. | −0.0985379 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.42175e6 | 4.26014 | ||||||||
\(297\) | −1.18325e6 | −0.778370 | ||||||||
\(298\) | −525851. | −0.343022 | ||||||||
\(299\) | 1.90333e6 | 1.23122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.33455e6 | 0.849019 | ||||||||
\(302\) | −1.84876e6 | −1.16644 | ||||||||
\(303\) | −2261.89 | −0.00141535 | ||||||||
\(304\) | 358676. | 0.222596 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.06521e6 | −0.650324 | ||||||||
\(307\) | 1.55665e6 | 0.942637 | 0.471318 | − | 0.881963i | \(-0.343778\pi\) | ||||
0.471318 | + | 0.881963i | \(0.343778\pi\) | |||||||
\(308\) | −4.35955e6 | −2.61858 | ||||||||
\(309\) | 653426. | 0.389314 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.72339e6 | 1.59665 | 0.798323 | − | 0.602229i | \(-0.205721\pi\) | ||||
0.798323 | + | 0.602229i | \(0.205721\pi\) | |||||||
\(312\) | 2.80641e6 | 1.63217 | ||||||||
\(313\) | −144019. | −0.0830919 | −0.0415460 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415460 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(314\) | −438861. | −0.251190 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.58022e6 | 2.01694 | ||||||||
\(317\) | 577983. | 0.323048 | 0.161524 | − | 0.986869i | \(-0.448359\pi\) | ||||
0.161524 | + | 0.986869i | \(0.448359\pi\) | |||||||
\(318\) | −2.33374e6 | −1.29415 | ||||||||
\(319\) | −283758. | −0.156125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −739306. | −0.400463 | ||||||||
\(322\) | −2.74156e6 | −1.47353 | ||||||||
\(323\) | −56553.6 | −0.0301616 | ||||||||
\(324\) | 2.83524e6 | 1.50047 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.42031e6 | 1.26132 | ||||||||
\(327\) | −215713. | −0.111560 | ||||||||
\(328\) | 6.67628e6 | 3.42650 | ||||||||
\(329\) | 2.40558e6 | 1.22527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.98342e6 | 0.995050 | 0.497525 | − | 0.867450i | \(-0.334242\pi\) | ||||
0.497525 | + | 0.867450i | \(0.334242\pi\) | |||||||
\(332\) | 1.92994e6 | 0.960944 | ||||||||
\(333\) | 2.51391e6 | 1.24234 | ||||||||
\(334\) | 1.13806e6 | 0.558211 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.17463e6 | −1.05084 | ||||||||
\(337\) | 913445. | 0.438135 | 0.219067 | − | 0.975710i | \(-0.429699\pi\) | ||||
0.219067 | + | 0.975710i | \(0.429699\pi\) | |||||||
\(338\) | −4.51986e6 | −2.15196 | ||||||||
\(339\) | 532961. | 0.251881 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 718637. | 0.334675 | ||||||||
\(342\) | 261005. | 0.120666 | ||||||||
\(343\) | −2.30174e6 | −1.05638 | ||||||||
\(344\) | −5.88536e6 | −2.68150 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.23578e6 | −0.554946 | ||||||||
\(347\) | 2.80370e6 | 1.24999 | 0.624997 | − | 0.780627i | \(-0.285100\pi\) | ||||
0.624997 | + | 0.780627i | \(0.285100\pi\) | |||||||
\(348\) | −310682. | −0.137520 | ||||||||
\(349\) | 1.92703e6 | 0.846887 | 0.423444 | − | 0.905922i | \(-0.360821\pi\) | ||||
0.423444 | + | 0.905922i | \(0.360821\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.38294e6 | 1.03239 | ||||||||
\(352\) | 6.86675e6 | 2.95389 | ||||||||
\(353\) | −758405. | −0.323940 | −0.161970 | − | 0.986796i | \(-0.551785\pi\) | ||||
−0.161970 | + | 0.986796i | \(0.551785\pi\) | |||||||
\(354\) | −1.01375e6 | −0.429955 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.99429e6 | 1.67038 | ||||||||
\(357\) | 342880. | 0.142388 | ||||||||
\(358\) | 6.33477e6 | 2.61230 | ||||||||
\(359\) | 467609. | 0.191490 | 0.0957452 | − | 0.995406i | \(-0.469477\pi\) | ||||
0.0957452 | + | 0.995406i | \(0.469477\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46224e6 | −0.994404 | ||||||||
\(362\) | 7.87920e6 | 3.16017 | ||||||||
\(363\) | −207305. | −0.0825739 | ||||||||
\(364\) | 8.77967e6 | 3.47316 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.72837e6 | 1.06463 | ||||||||
\(367\) | 3.84424e6 | 1.48986 | 0.744930 | − | 0.667143i | \(-0.232483\pi\) | ||||
0.744930 | + | 0.667143i | \(0.232483\pi\) | |||||||
\(368\) | 6.50410e6 | 2.50362 | ||||||||
\(369\) | 2.61355e6 | 0.999229 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.44412e6 | −1.67630 | ||||||||
\(372\) | 786823. | 0.294795 | ||||||||
\(373\) | −3.10489e6 | −1.15551 | −0.577755 | − | 0.816210i | \(-0.696071\pi\) | ||||
−0.577755 | + | 0.816210i | \(0.696071\pi\) | |||||||
\(374\) | −2.26887e6 | −0.838745 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.06086e7 | −3.86982 | ||||||||
\(377\) | 571458. | 0.207077 | ||||||||
\(378\) | −3.43240e6 | −1.23557 | ||||||||
\(379\) | −1.92276e6 | −0.687586 | −0.343793 | − | 0.939046i | \(-0.611712\pi\) | ||||
−0.343793 | + | 0.939046i | \(0.611712\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −944949. | −0.333500 | ||||||||
\(382\) | −9.04484e6 | −3.17134 | ||||||||
\(383\) | −3.69535e6 | −1.28724 | −0.643619 | − | 0.765346i | \(-0.722568\pi\) | ||||
−0.643619 | + | 0.765346i | \(0.722568\pi\) | |||||||
\(384\) | 1.35341e6 | 0.468382 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.92939e6 | −1.00071 | ||||||||
\(387\) | −2.30393e6 | −0.781973 | ||||||||
\(388\) | 1.14336e6 | 0.385571 | ||||||||
\(389\) | −3.66232e6 | −1.22711 | −0.613554 | − | 0.789653i | \(-0.710261\pi\) | ||||
−0.613554 | + | 0.789653i | \(0.710261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.02552e6 | −0.339237 | ||||||||
\(392\) | 1.22644e6 | 0.403116 | ||||||||
\(393\) | 1.13420e6 | 0.370431 | ||||||||
\(394\) | −1.83508e6 | −0.595545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.52624e6 | 2.41179 | ||||||||
\(397\) | −599240. | −0.190820 | −0.0954102 | − | 0.995438i | \(-0.530416\pi\) | ||||
−0.0954102 | + | 0.995438i | \(0.530416\pi\) | |||||||
\(398\) | 1.12794e7 | 3.56925 | ||||||||
\(399\) | −84015.3 | −0.0264196 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 950637. | 0.295226 | 0.147613 | − | 0.989045i | \(-0.452841\pi\) | ||||
0.147613 | + | 0.989045i | \(0.452841\pi\) | |||||||
\(402\) | 1.14210e6 | 0.352485 | ||||||||
\(403\) | −1.44726e6 | −0.443898 | ||||||||
\(404\) | 31206.0 | 0.00951228 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −823130. | −0.247830 | ||||||||
\(407\) | 5.35458e6 | 1.60228 | ||||||||
\(408\) | −1.51211e6 | −0.449709 | ||||||||
\(409\) | 1.80612e6 | 0.533873 | 0.266937 | − | 0.963714i | \(-0.413989\pi\) | ||||
0.266937 | + | 0.963714i | \(0.413989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.65642e6 | −0.483688 | ||||||||
\(412\) | −9.01495e6 | −2.61650 | ||||||||
\(413\) | −1.93048e6 | −0.556915 | ||||||||
\(414\) | 4.73297e6 | 1.35717 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.38289e7 | −3.91791 | ||||||||
\(417\) | −1.17161e6 | −0.329946 | ||||||||
\(418\) | 555935. | 0.155627 | ||||||||
\(419\) | −5.78098e6 | −1.60867 | −0.804334 | − | 0.594177i | \(-0.797478\pi\) | ||||
−0.804334 | + | 0.594177i | \(0.797478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.09006e6 | −1.67462 | −0.837311 | − | 0.546727i | \(-0.815873\pi\) | ||||
−0.837311 | + | 0.546727i | \(0.815873\pi\) | |||||||
\(422\) | 1.25058e7 | 3.41846 | ||||||||
\(423\) | −4.15294e6 | −1.12851 | ||||||||
\(424\) | 1.95986e7 | 5.29433 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.65383e6 | −0.441536 | ||||||||
\(427\) | 5.19561e6 | 1.37901 | ||||||||
\(428\) | 1.01998e7 | 2.69142 | ||||||||
\(429\) | 2.34004e6 | 0.613874 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.90927e6 | −1.79159 | −0.895796 | − | 0.444465i | \(-0.853394\pi\) | ||||
−0.895796 | + | 0.444465i | \(0.853394\pi\) | |||||||
\(432\) | 8.14305e6 | 2.09932 | ||||||||
\(433\) | −3.78791e6 | −0.970911 | −0.485456 | − | 0.874261i | \(-0.661346\pi\) | ||||
−0.485456 | + | 0.874261i | \(0.661346\pi\) | |||||||
\(434\) | 2.08464e6 | 0.531259 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.97608e6 | 0.749770 | ||||||||
\(437\) | 251281. | 0.0629444 | ||||||||
\(438\) | −954300. | −0.237684 | ||||||||
\(439\) | 2.35490e6 | 0.583192 | 0.291596 | − | 0.956542i | \(-0.405814\pi\) | ||||
0.291596 | + | 0.956542i | \(0.405814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 480110. | 0.117556 | ||||||||
\(442\) | 4.56925e6 | 1.11247 | ||||||||
\(443\) | −5.17434e6 | −1.25270 | −0.626348 | − | 0.779544i | \(-0.715451\pi\) | ||||
−0.626348 | + | 0.779544i | \(0.715451\pi\) | |||||||
\(444\) | 5.86263e6 | 1.41135 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 284240. | 0.0676625 | ||||||||
\(447\) | −292219. | −0.0691734 | ||||||||
\(448\) | 8.17947e6 | 1.92544 | ||||||||
\(449\) | −713943. | −0.167128 | −0.0835638 | − | 0.996502i | \(-0.526630\pi\) | ||||
−0.0835638 | + | 0.996502i | \(0.526630\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.56681e6 | 1.28874 | ||||||||
\(452\) | −7.35297e6 | −1.69284 | ||||||||
\(453\) | −1.02737e6 | −0.235223 | ||||||||
\(454\) | −6.84266e6 | −1.55806 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 370508. | 0.0834422 | ||||||||
\(457\) | −3.40931e6 | −0.763617 | −0.381809 | − | 0.924241i | \(-0.624699\pi\) | ||||
−0.381809 | + | 0.924241i | \(0.624699\pi\) | |||||||
\(458\) | −8.42932e6 | −1.87771 | ||||||||
\(459\) | −1.28394e6 | −0.284455 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.02085e6 | −0.223722 | −0.111861 | − | 0.993724i | \(-0.535681\pi\) | ||||
−0.111861 | + | 0.993724i | \(0.535681\pi\) | |||||||
\(462\) | −3.37060e6 | −0.734687 | ||||||||
\(463\) | 606404. | 0.131465 | 0.0657324 | − | 0.997837i | \(-0.479062\pi\) | ||||
0.0657324 | + | 0.997837i | \(0.479062\pi\) | |||||||
\(464\) | 1.95280e6 | 0.421079 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.74342e6 | 1.22520 | ||||||||
\(467\) | −6.52897e6 | −1.38533 | −0.692664 | − | 0.721261i | \(-0.743563\pi\) | ||||
−0.692664 | + | 0.721261i | \(0.743563\pi\) | |||||||
\(468\) | −1.51570e7 | −3.19889 | ||||||||
\(469\) | 2.17490e6 | 0.456570 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −243878. | −0.0506548 | ||||||||
\(472\) | 8.51342e6 | 1.75893 | ||||||||
\(473\) | −4.90733e6 | −1.00854 | ||||||||
\(474\) | 2.76806e6 | 0.565886 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.73053e6 | −0.956957 | ||||||||
\(477\) | 7.67223e6 | 1.54392 | ||||||||
\(478\) | −4.48946e6 | −0.898719 | ||||||||
\(479\) | −6.39974e6 | −1.27445 | −0.637226 | − | 0.770677i | \(-0.719918\pi\) | ||||
−0.637226 | + | 0.770677i | \(0.719918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.07835e7 | −2.12520 | ||||||||
\(482\) | −484952. | −0.0950783 | ||||||||
\(483\) | −1.52350e6 | −0.297150 | ||||||||
\(484\) | 2.86007e6 | 0.554962 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.11932e6 | 1.75135 | ||||||||
\(487\) | −2.87162e6 | −0.548661 | −0.274331 | − | 0.961635i | \(-0.588456\pi\) | ||||
−0.274331 | + | 0.961635i | \(0.588456\pi\) | |||||||
\(488\) | −2.29127e7 | −4.35539 | ||||||||
\(489\) | 1.34498e6 | 0.254357 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.25927e6 | −0.797319 | −0.398659 | − | 0.917099i | \(-0.630524\pi\) | ||||
−0.398659 | + | 0.917099i | \(0.630524\pi\) | |||||||
\(492\) | 6.09500e6 | 1.13517 | ||||||||
\(493\) | −307904. | −0.0570556 | ||||||||
\(494\) | −1.11959e6 | −0.206416 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.94561e6 | −0.902642 | ||||||||
\(497\) | −3.14937e6 | −0.571917 | ||||||||
\(498\) | 1.49213e6 | 0.269609 | ||||||||
\(499\) | −819085. | −0.147258 | −0.0736288 | − | 0.997286i | \(-0.523458\pi\) | ||||
−0.0736288 | + | 0.997286i | \(0.523458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 632426. | 0.112568 | ||||||||
\(502\) | −7.28444e6 | −1.29014 | ||||||||
\(503\) | −4.74111e6 | −0.835527 | −0.417763 | − | 0.908556i | \(-0.637186\pi\) | ||||
−0.417763 | + | 0.908556i | \(0.637186\pi\) | |||||||
\(504\) | 1.32894e7 | 2.33039 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.00811e7 | 1.75038 | ||||||||
\(507\) | −2.51171e6 | −0.433961 | ||||||||
\(508\) | 1.30369e7 | 2.24138 | ||||||||
\(509\) | −9.67261e6 | −1.65481 | −0.827407 | − | 0.561602i | \(-0.810185\pi\) | ||||
−0.827407 | + | 0.561602i | \(0.810185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.81727e6 | −0.307869 | ||||||||
\(512\) | 4.51583e6 | 0.761312 | ||||||||
\(513\) | 314601. | 0.0527797 | ||||||||
\(514\) | 5.38374e6 | 0.898828 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.37295e6 | −0.888358 | ||||||||
\(517\) | −8.84569e6 | −1.45548 | ||||||||
\(518\) | 1.55327e7 | 2.54344 | ||||||||
\(519\) | −686731. | −0.111910 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.94535e6 | 0.313980 | 0.156990 | − | 0.987600i | \(-0.449821\pi\) | ||||
0.156990 | + | 0.987600i | \(0.449821\pi\) | |||||||
\(522\) | 1.42103e6 | 0.228259 | ||||||||
\(523\) | 6.10286e6 | 0.975617 | 0.487809 | − | 0.872951i | \(-0.337796\pi\) | ||||
0.487809 | + | 0.872951i | \(0.337796\pi\) | |||||||
\(524\) | −1.56479e7 | −2.48959 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.55674e7 | 2.45331 | ||||||||
\(527\) | 779790. | 0.122307 | ||||||||
\(528\) | 7.99644e6 | 1.24828 | ||||||||
\(529\) | −1.87970e6 | −0.292044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.33273e6 | 0.512937 | ||||||||
\(532\) | 1.15911e6 | 0.177560 | ||||||||
\(533\) | −1.12110e7 | −1.70933 | ||||||||
\(534\) | 3.08820e6 | 0.468653 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.59134e6 | −1.44201 | ||||||||
\(537\) | 3.52027e6 | 0.526794 | ||||||||
\(538\) | 1.03408e7 | 1.54027 | ||||||||
\(539\) | 1.02263e6 | 0.151616 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.48331e6 | 1.09926 | 0.549630 | − | 0.835408i | \(-0.314769\pi\) | ||||
0.549630 | + | 0.835408i | \(0.314769\pi\) | |||||||
\(542\) | 2.00695e7 | 2.93453 | ||||||||
\(543\) | 4.37852e6 | 0.637276 | ||||||||
\(544\) | 7.45107e6 | 1.07950 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.78802e6 | 0.974455 | ||||||||
\(547\) | −1.01882e7 | −1.45590 | −0.727948 | − | 0.685632i | \(-0.759526\pi\) | ||||
−0.727948 | + | 0.685632i | \(0.759526\pi\) | |||||||
\(548\) | 2.28527e7 | 3.25076 | ||||||||
\(549\) | −8.96958e6 | −1.27011 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 75445.1 | 0.0105865 | ||||||||
\(552\) | 6.71866e6 | 0.938502 | ||||||||
\(553\) | 5.27119e6 | 0.732986 | ||||||||
\(554\) | 1.27129e7 | 1.75982 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.61641e7 | 2.21750 | ||||||||
\(557\) | −3.28894e6 | −0.449178 | −0.224589 | − | 0.974454i | \(-0.572104\pi\) | ||||
−0.224589 | + | 0.974454i | \(0.572104\pi\) | |||||||
\(558\) | −3.59887e6 | −0.489306 | ||||||||
\(559\) | 9.88283e6 | 1.33768 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.26082e6 | −0.169140 | ||||||||
\(562\) | 1.55080e7 | 2.07117 | ||||||||
\(563\) | 7.09348e6 | 0.943166 | 0.471583 | − | 0.881822i | \(-0.343683\pi\) | ||||
0.471583 | + | 0.881822i | \(0.343683\pi\) | |||||||
\(564\) | −9.68499e6 | −1.28204 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.09775e7 | 1.44033 | ||||||||
\(567\) | 4.17434e6 | 0.545293 | ||||||||
\(568\) | 1.38888e7 | 1.80631 | ||||||||
\(569\) | −2.13368e6 | −0.276279 | −0.138139 | − | 0.990413i | \(-0.544112\pi\) | ||||
−0.138139 | + | 0.990413i | \(0.544112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 69756.6 | 0.00895355 | 0.00447677 | − | 0.999990i | \(-0.498575\pi\) | ||||
0.00447677 | + | 0.999990i | \(0.498575\pi\) | |||||||
\(572\) | −3.22842e7 | −4.12572 | ||||||||
\(573\) | −5.02628e6 | −0.639528 | ||||||||
\(574\) | 1.61483e7 | 2.04573 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.41209e7 | −1.77339 | ||||||||
\(577\) | −1.02943e7 | −1.28723 | −0.643616 | − | 0.765349i | \(-0.722567\pi\) | ||||
−0.643616 | + | 0.765349i | \(0.722567\pi\) | |||||||
\(578\) | 1.26833e7 | 1.57911 | ||||||||
\(579\) | −1.62788e6 | −0.201802 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.84146e6 | 0.349222 | ||||||||
\(582\) | 883993. | 0.108179 | ||||||||
\(583\) | 1.63417e7 | 1.99125 | ||||||||
\(584\) | 8.01416e6 | 0.972358 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.40241e6 | −1.01079 | ||||||||
\(587\) | −5.84442e6 | −0.700077 | −0.350039 | − | 0.936735i | \(-0.613832\pi\) | ||||
−0.350039 | + | 0.936735i | \(0.613832\pi\) | |||||||
\(588\) | 1.11965e6 | 0.133549 | ||||||||
\(589\) | −191070. | −0.0226937 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.01977e6 | −0.120097 | ||||||||
\(592\) | −3.68498e7 | −4.32147 | ||||||||
\(593\) | −8.58492e6 | −1.00253 | −0.501267 | − | 0.865292i | \(-0.667133\pi\) | ||||
−0.501267 | + | 0.865292i | \(0.667133\pi\) | |||||||
\(594\) | 1.26215e7 | 1.46772 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.03158e6 | 0.464900 | ||||||||
\(597\) | 6.26802e6 | 0.719771 | ||||||||
\(598\) | −2.03023e7 | −2.32163 | ||||||||
\(599\) | −4.48945e6 | −0.511242 | −0.255621 | − | 0.966777i | \(-0.582280\pi\) | ||||
−0.255621 | + | 0.966777i | \(0.582280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.96161e6 | −0.447389 | −0.223694 | − | 0.974659i | \(-0.571812\pi\) | ||||
−0.223694 | + | 0.974659i | \(0.571812\pi\) | |||||||
\(602\) | −1.42353e7 | −1.60094 | ||||||||
\(603\) | −3.75470e6 | −0.420516 | ||||||||
\(604\) | 1.41740e7 | 1.58088 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24127.0 | 0.00266883 | ||||||||
\(607\) | 1.42627e7 | 1.57120 | 0.785599 | − | 0.618736i | \(-0.212355\pi\) | ||||
0.785599 | + | 0.618736i | \(0.212355\pi\) | |||||||
\(608\) | −1.82572e6 | −0.200297 | ||||||||
\(609\) | −457419. | −0.0499771 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.78143e7 | 1.93048 | ||||||||
\(612\) | 8.16668e6 | 0.881388 | ||||||||
\(613\) | −1.78171e7 | −1.91508 | −0.957538 | − | 0.288307i | \(-0.906907\pi\) | ||||
−0.957538 | + | 0.288307i | \(0.906907\pi\) | |||||||
\(614\) | −1.66044e7 | −1.77747 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.83061e7 | 3.00558 | ||||||||
\(617\) | −1.85246e7 | −1.95901 | −0.979504 | − | 0.201425i | \(-0.935443\pi\) | ||||
−0.979504 | + | 0.201425i | \(0.935443\pi\) | |||||||
\(618\) | −6.96993e6 | −0.734103 | ||||||||
\(619\) | 1.04691e7 | 1.09820 | 0.549102 | − | 0.835755i | \(-0.314970\pi\) | ||||
0.549102 | + | 0.835755i | \(0.314970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.70487e6 | 0.593631 | ||||||||
\(622\) | −2.90497e7 | −3.01069 | ||||||||
\(623\) | 5.88083e6 | 0.607041 | ||||||||
\(624\) | −1.61040e7 | −1.65566 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.53621e6 | 0.156681 | ||||||||
\(627\) | 308937. | 0.0313835 | ||||||||
\(628\) | 3.36465e6 | 0.340440 | ||||||||
\(629\) | 5.81023e6 | 0.585553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −60149.4 | −0.00601392 | −0.00300696 | − | 0.999995i | \(-0.500957\pi\) | ||||
−0.00300696 | + | 0.999995i | \(0.500957\pi\) | |||||||
\(632\) | −2.32460e7 | −2.31502 | ||||||||
\(633\) | 6.94956e6 | 0.689363 | ||||||||
\(634\) | −6.16520e6 | −0.609150 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.78922e7 | 1.75397 | ||||||||
\(637\) | −2.05946e6 | −0.201096 | ||||||||
\(638\) | 3.02677e6 | 0.294394 | ||||||||
\(639\) | 5.43701e6 | 0.526754 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.40256e7 | 1.34827 | 0.674136 | − | 0.738608i | \(-0.264516\pi\) | ||||
0.674136 | + | 0.738608i | \(0.264516\pi\) | |||||||
\(642\) | 7.88600e6 | 0.755125 | ||||||||
\(643\) | −5.64945e6 | −0.538863 | −0.269432 | − | 0.963020i | \(-0.586836\pi\) | ||||
−0.269432 | + | 0.963020i | \(0.586836\pi\) | |||||||
\(644\) | 2.10189e7 | 1.99708 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 603243. | 0.0568736 | ||||||||
\(647\) | 1.55564e7 | 1.46100 | 0.730498 | − | 0.682915i | \(-0.239288\pi\) | ||||
0.730498 | + | 0.682915i | \(0.239288\pi\) | |||||||
\(648\) | −1.84089e7 | −1.72222 | ||||||||
\(649\) | 7.09865e6 | 0.661552 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.15845e6 | 0.107133 | ||||||||
\(652\) | −1.85559e7 | −1.70948 | ||||||||
\(653\) | −2.45452e6 | −0.225260 | −0.112630 | − | 0.993637i | \(-0.535928\pi\) | ||||
−0.112630 | + | 0.993637i | \(0.535928\pi\) | |||||||
\(654\) | 2.30096e6 | 0.210361 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.83104e7 | −3.47582 | ||||||||
\(657\) | 3.13729e6 | 0.283557 | ||||||||
\(658\) | −2.56597e7 | −2.31040 | ||||||||
\(659\) | 158118. | 0.0141830 | 0.00709150 | − | 0.999975i | \(-0.497743\pi\) | ||||
0.00709150 | + | 0.999975i | \(0.497743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.69262e7 | −1.50680 | −0.753398 | − | 0.657565i | \(-0.771587\pi\) | ||||
−0.753398 | + | 0.657565i | \(0.771587\pi\) | |||||||
\(662\) | −2.11567e7 | −1.87630 | ||||||||
\(663\) | 2.53916e6 | 0.224340 | ||||||||
\(664\) | −1.25309e7 | −1.10296 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.68152e7 | −2.34259 | ||||||||
\(667\) | 1.36809e6 | 0.119070 | ||||||||
\(668\) | −8.72523e6 | −0.756547 | ||||||||
\(669\) | 157954. | 0.0136447 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.91050e7 | −1.63810 | ||||||||
\(672\) | 1.10692e7 | 0.945570 | ||||||||
\(673\) | 6.52562e6 | 0.555373 | 0.277686 | − | 0.960672i | \(-0.410432\pi\) | ||||
0.277686 | + | 0.960672i | \(0.410432\pi\) | |||||||
\(674\) | −9.74349e6 | −0.826161 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.46527e7 | 2.91656 | ||||||||
\(677\) | 1.82770e7 | 1.53261 | 0.766306 | − | 0.642476i | \(-0.222093\pi\) | ||||
0.766306 | + | 0.642476i | \(0.222093\pi\) | |||||||
\(678\) | −5.68496e6 | −0.474956 | ||||||||
\(679\) | 1.68338e6 | 0.140123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.80251e6 | −0.314197 | ||||||||
\(682\) | −7.66552e6 | −0.631075 | ||||||||
\(683\) | −8.58042e6 | −0.703812 | −0.351906 | − | 0.936035i | \(-0.614466\pi\) | ||||
−0.351906 | + | 0.936035i | \(0.614466\pi\) | |||||||
\(684\) | −2.00106e6 | −0.163539 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.45521e7 | 1.99195 | ||||||||
\(687\) | −4.68422e6 | −0.378657 | ||||||||
\(688\) | 3.37719e7 | 2.72009 | ||||||||
\(689\) | −3.29104e7 | −2.64111 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.16287e7 | −1.72320 | −0.861601 | − | 0.507586i | \(-0.830538\pi\) | ||||
−0.861601 | + | 0.507586i | \(0.830538\pi\) | |||||||
\(692\) | 9.47444e6 | 0.752122 | ||||||||
\(693\) | 1.10809e7 | 0.876483 | ||||||||
\(694\) | −2.99064e7 | −2.35703 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.01722e6 | 0.157845 | ||||||||
\(697\) | 6.04052e6 | 0.470969 | ||||||||
\(698\) | −2.05552e7 | −1.59692 | ||||||||
\(699\) | 3.19166e6 | 0.247072 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.16485e7 | −1.66392 | −0.831959 | − | 0.554837i | \(-0.812781\pi\) | ||||
−0.831959 | + | 0.554837i | \(0.812781\pi\) | |||||||
\(702\) | −2.54182e7 | −1.94672 | ||||||||
\(703\) | −1.42367e6 | −0.108648 | ||||||||
\(704\) | −3.00771e7 | −2.28720 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.08971e6 | 0.610831 | ||||||||
\(707\) | 45944.8 | 0.00345691 | ||||||||
\(708\) | 7.77219e6 | 0.582720 | ||||||||
\(709\) | 1.15365e7 | 0.861904 | 0.430952 | − | 0.902375i | \(-0.358178\pi\) | ||||
0.430952 | + | 0.902375i | \(0.358178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.10006e6 | −0.675104 | ||||||||
\(712\) | −2.59345e7 | −1.91725 | ||||||||
\(713\) | −3.46480e6 | −0.255243 | ||||||||
\(714\) | −3.65742e6 | −0.268491 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.85672e7 | −3.54047 | ||||||||
\(717\) | −2.49482e6 | −0.181235 | ||||||||
\(718\) | −4.98787e6 | −0.361081 | ||||||||
\(719\) | 1.16519e7 | 0.840570 | 0.420285 | − | 0.907392i | \(-0.361930\pi\) | ||||
0.420285 | + | 0.907392i | \(0.361930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.32728e7 | −0.950876 | ||||||||
\(722\) | 2.62641e7 | 1.87508 | ||||||||
\(723\) | −269491. | −0.0191734 | ||||||||
\(724\) | −6.04080e7 | −4.28300 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.21127e6 | 0.155704 | ||||||||
\(727\) | 8.27347e6 | 0.580566 | 0.290283 | − | 0.956941i | \(-0.406251\pi\) | ||||
0.290283 | + | 0.956941i | \(0.406251\pi\) | |||||||
\(728\) | −5.70055e7 | −3.98647 | ||||||||
\(729\) | −3.35697e6 | −0.233953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.32492e6 | −0.368570 | ||||||||
\(732\) | −2.09178e7 | −1.44290 | ||||||||
\(733\) | 2.68922e7 | 1.84870 | 0.924350 | − | 0.381545i | \(-0.124608\pi\) | ||||
0.924350 | + | 0.381545i | \(0.124608\pi\) | |||||||
\(734\) | −4.10055e7 | −2.80933 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.31069e7 | −2.25281 | ||||||||
\(737\) | −7.99744e6 | −0.542353 | ||||||||
\(738\) | −2.78781e7 | −1.88418 | ||||||||
\(739\) | 2.29150e7 | 1.54351 | 0.771753 | − | 0.635922i | \(-0.219380\pi\) | ||||
0.771753 | + | 0.635922i | \(0.219380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −622166. | −0.0416256 | ||||||||
\(742\) | 4.74043e7 | 3.16088 | ||||||||
\(743\) | −7.03515e6 | −0.467521 | −0.233761 | − | 0.972294i | \(-0.575103\pi\) | ||||
−0.233761 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(744\) | −5.10876e6 | −0.338363 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.31191e7 | 2.17887 | ||||||||
\(747\) | −4.90543e6 | −0.321644 | ||||||||
\(748\) | 1.73949e7 | 1.13676 | ||||||||
\(749\) | 1.50172e7 | 0.978105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.11756e7 | −1.37005 | −0.685023 | − | 0.728522i | \(-0.740208\pi\) | ||||
−0.685023 | + | 0.728522i | \(0.740208\pi\) | |||||||
\(752\) | 6.08754e7 | 3.92552 | ||||||||
\(753\) | −4.04801e6 | −0.260168 | ||||||||
\(754\) | −6.09560e6 | −0.390470 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.63154e7 | 1.67458 | ||||||||
\(757\) | −6.10083e6 | −0.386945 | −0.193473 | − | 0.981106i | \(-0.561975\pi\) | ||||
−0.193473 | + | 0.981106i | \(0.561975\pi\) | |||||||
\(758\) | 2.05096e7 | 1.29653 | ||||||||
\(759\) | 5.60215e6 | 0.352980 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.42795e6 | −0.277167 | −0.138583 | − | 0.990351i | \(-0.544255\pi\) | ||||
−0.138583 | + | 0.990351i | \(0.544255\pi\) | |||||||
\(762\) | 1.00795e7 | 0.628858 | ||||||||
\(763\) | 4.38170e6 | 0.272478 | ||||||||
\(764\) | 6.93447e7 | 4.29814 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.94174e7 | 2.42726 | ||||||||
\(767\) | −1.42959e7 | −0.877453 | ||||||||
\(768\) | −1.55071e6 | −0.0948699 | ||||||||
\(769\) | −3.30798e6 | −0.201719 | −0.100860 | − | 0.994901i | \(-0.532159\pi\) | ||||
−0.100860 | + | 0.994901i | \(0.532159\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.99178e6 | 0.181257 | ||||||||
\(772\) | 2.24590e7 | 1.35627 | ||||||||
\(773\) | 1.66539e7 | 1.00246 | 0.501232 | − | 0.865313i | \(-0.332880\pi\) | ||||
0.501232 | + | 0.865313i | \(0.332880\pi\) | |||||||
\(774\) | 2.45754e7 | 1.47451 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.42373e6 | −0.442556 | ||||||||
\(777\) | 8.63160e6 | 0.512907 | ||||||||
\(778\) | 3.90651e7 | 2.31387 | ||||||||
\(779\) | −1.48010e6 | −0.0873869 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15807e7 | 0.679373 | ||||||||
\(782\) | 1.09390e7 | 0.639676 | ||||||||
\(783\) | 1.71284e6 | 0.0998417 | ||||||||
\(784\) | −7.03763e6 | −0.408918 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.20982e7 | −0.698497 | ||||||||
\(787\) | −1.03913e7 | −0.598045 | −0.299022 | − | 0.954246i | \(-0.596661\pi\) | ||||
−0.299022 | + | 0.954246i | \(0.596661\pi\) | |||||||
\(788\) | 1.40691e7 | 0.807146 | ||||||||
\(789\) | 8.65092e6 | 0.494732 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.08258e7 | −0.615205 | ||||||||
\(792\) | −4.88670e7 | −2.76824 | ||||||||
\(793\) | 3.84755e7 | 2.17271 | ||||||||
\(794\) | 6.39195e6 | 0.359817 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.64763e7 | −4.83743 | ||||||||
\(797\) | −1.68557e6 | −0.0939940 | −0.0469970 | − | 0.998895i | \(-0.514965\pi\) | ||||
−0.0469970 | + | 0.998895i | \(0.514965\pi\) | |||||||
\(798\) | 896170. | 0.0498176 | ||||||||
\(799\) | −9.59841e6 | −0.531903 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.01525e7 | −0.559104 | ||||||||
\(802\) | −1.01402e7 | −0.556687 | ||||||||
\(803\) | 6.68236e6 | 0.365714 | ||||||||
\(804\) | −8.75625e6 | −0.477725 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.54375e7 | 0.837029 | ||||||||
\(807\) | 5.74644e6 | 0.310609 | ||||||||
\(808\) | −202617. | −0.0109181 | ||||||||
\(809\) | 8.48627e6 | 0.455875 | 0.227937 | − | 0.973676i | \(-0.426802\pi\) | ||||
0.227937 | + | 0.973676i | \(0.426802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14182e7 | −0.609601 | −0.304801 | − | 0.952416i | \(-0.598590\pi\) | ||||
−0.304801 | + | 0.952416i | \(0.598590\pi\) | |||||||
\(812\) | 6.31075e6 | 0.335885 | ||||||||
\(813\) | 1.11528e7 | 0.591775 | ||||||||
\(814\) | −5.71160e7 | −3.02132 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.67689e6 | 0.456183 | ||||||||
\(817\) | 1.30475e6 | 0.0683869 | ||||||||
\(818\) | −1.92654e7 | −1.00669 | ||||||||
\(819\) | −2.23158e7 | −1.16253 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.66175e7 | 1.89597 | 0.947983 | − | 0.318320i | \(-0.103119\pi\) | ||||
0.947983 | + | 0.318320i | \(0.103119\pi\) | |||||||
\(822\) | 1.76686e7 | 0.912057 | ||||||||
\(823\) | 1.27704e7 | 0.657212 | 0.328606 | − | 0.944467i | \(-0.393421\pi\) | ||||
0.328606 | + | 0.944467i | \(0.393421\pi\) | |||||||
\(824\) | 5.85331e7 | 3.00319 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.05919e7 | 1.05014 | ||||||||
\(827\) | −3.02070e7 | −1.53583 | −0.767917 | − | 0.640549i | \(-0.778707\pi\) | ||||
−0.767917 | + | 0.640549i | \(0.778707\pi\) | |||||||
\(828\) | −3.62866e7 | −1.83937 | ||||||||
\(829\) | −3.87577e6 | −0.195872 | −0.0979359 | − | 0.995193i | \(-0.531224\pi\) | ||||
−0.0979359 | + | 0.995193i | \(0.531224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.06462e6 | 0.354884 | ||||||||
\(832\) | 6.05721e7 | 3.03364 | ||||||||
\(833\) | 1.10965e6 | 0.0554079 | ||||||||
\(834\) | 1.24973e7 | 0.622158 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.26223e6 | −0.210922 | ||||||||
\(837\) | −4.33789e6 | −0.214025 | ||||||||
\(838\) | 6.16643e7 | 3.03336 | ||||||||
\(839\) | −3.49516e6 | −0.171420 | −0.0857102 | − | 0.996320i | \(-0.527316\pi\) | ||||
−0.0857102 | + | 0.996320i | \(0.527316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.01004e7 | −0.979974 | ||||||||
\(842\) | 6.49612e7 | 3.15772 | ||||||||
\(843\) | 8.61789e6 | 0.417669 | ||||||||
\(844\) | −9.58791e7 | −4.63306 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.42984e7 | 2.12795 | ||||||||
\(847\) | 4.21090e6 | 0.201682 | ||||||||
\(848\) | −1.12462e8 | −5.37054 | ||||||||
\(849\) | 6.10028e6 | 0.290456 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.58163e7 | −1.22200 | ||||||||
\(852\) | 1.26795e7 | 0.598417 | ||||||||
\(853\) | 3.02315e7 | 1.42261 | 0.711307 | − | 0.702881i | \(-0.248104\pi\) | ||||
0.711307 | + | 0.702881i | \(0.248104\pi\) | |||||||
\(854\) | −5.54203e7 | −2.60030 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.62262e7 | −3.08920 | ||||||||
\(857\) | 4.90078e6 | 0.227936 | 0.113968 | − | 0.993484i | \(-0.463644\pi\) | ||||
0.113968 | + | 0.993484i | \(0.463644\pi\) | |||||||
\(858\) | −2.49606e7 | −1.15754 | ||||||||
\(859\) | −3.90589e7 | −1.80608 | −0.903040 | − | 0.429557i | \(-0.858670\pi\) | ||||
−0.903040 | + | 0.429557i | \(0.858670\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.97372e6 | 0.412539 | ||||||||
\(862\) | 7.36995e7 | 3.37828 | ||||||||
\(863\) | 3.66262e7 | 1.67404 | 0.837019 | − | 0.547173i | \(-0.184296\pi\) | ||||
0.837019 | + | 0.547173i | \(0.184296\pi\) | |||||||
\(864\) | −4.14495e7 | −1.88901 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.04046e7 | 1.83078 | ||||||||
\(867\) | 7.04820e6 | 0.318442 | ||||||||
\(868\) | −1.59824e7 | −0.720018 | ||||||||
\(869\) | −1.93830e7 | −0.870704 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.61060e7 | 0.719353 | ||||||||
\(872\) | −1.93234e7 | −0.860580 | ||||||||
\(873\) | −2.90615e6 | −0.129057 | ||||||||
\(874\) | −2.68036e6 | −0.118690 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.31640e6 | 0.322134 | ||||||||
\(877\) | 3.05781e7 | 1.34249 | 0.671246 | − | 0.741235i | \(-0.265759\pi\) | ||||
0.671246 | + | 0.741235i | \(0.265759\pi\) | |||||||
\(878\) | −2.51191e7 | −1.09969 | ||||||||
\(879\) | −4.66927e6 | −0.203834 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.07731e7 | −0.467629 | −0.233815 | − | 0.972281i | \(-0.575121\pi\) | ||||
−0.233815 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(882\) | −5.12121e6 | −0.221667 | ||||||||
\(883\) | −2.56044e7 | −1.10513 | −0.552563 | − | 0.833471i | \(-0.686350\pi\) | ||||
−0.552563 | + | 0.833471i | \(0.686350\pi\) | |||||||
\(884\) | −3.50314e7 | −1.50774 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.51934e7 | 2.36212 | ||||||||
\(887\) | 1.57569e7 | 0.672453 | 0.336227 | − | 0.941781i | \(-0.390849\pi\) | ||||
0.336227 | + | 0.941781i | \(0.390849\pi\) | |||||||
\(888\) | −3.80654e7 | −1.61994 | ||||||||
\(889\) | 1.91944e7 | 0.814553 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.53497e7 | −0.647746 | ||||||||
\(892\) | −2.17920e6 | −0.0917034 | ||||||||
\(893\) | 2.35188e6 | 0.0986930 | ||||||||
\(894\) | 3.11702e6 | 0.130436 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.74912e7 | −1.14399 | ||||||||
\(897\) | −1.12821e7 | −0.468177 | ||||||||
\(898\) | 7.61545e6 | 0.315141 | ||||||||
\(899\) | −1.04028e6 | −0.0429289 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.77323e7 | 0.727701 | ||||||||
\(902\) | −5.93798e7 | −2.43009 | ||||||||
\(903\) | −7.91063e6 | −0.322843 | ||||||||
\(904\) | 4.77420e7 | 1.94303 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.09587e7 | 0.443544 | ||||||||
\(907\) | 1.31837e7 | 0.532131 | 0.266065 | − | 0.963955i | \(-0.414276\pi\) | ||||
0.266065 | + | 0.963955i | \(0.414276\pi\) | |||||||
\(908\) | 5.24611e7 | 2.11165 | ||||||||
\(909\) | −79318.1 | −0.00318392 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.28956e7 | −0.514808 | −0.257404 | − | 0.966304i | \(-0.582867\pi\) | ||||
−0.257404 | + | 0.966304i | \(0.582867\pi\) | |||||||
\(912\) | −2.12608e6 | −0.0846433 | ||||||||
\(913\) | −1.04485e7 | −0.414836 | ||||||||
\(914\) | 3.63662e7 | 1.43990 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.46256e7 | 2.54487 | ||||||||
\(917\) | −2.30385e7 | −0.904756 | ||||||||
\(918\) | 1.36955e7 | 0.536377 | ||||||||
\(919\) | 4.43910e7 | 1.73383 | 0.866914 | − | 0.498459i | \(-0.166100\pi\) | ||||
0.866914 | + | 0.498459i | \(0.166100\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.22715e6 | −0.358442 | ||||||||
\(922\) | 1.08891e7 | 0.421858 | ||||||||
\(923\) | −2.33223e7 | −0.901089 | ||||||||
\(924\) | 2.58416e7 | 0.995725 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.46836e6 | −0.247894 | ||||||||
\(927\) | 2.29138e7 | 0.875787 | ||||||||
\(928\) | −9.94008e6 | −0.378896 | ||||||||
\(929\) | 2.76819e7 | 1.05234 | 0.526170 | − | 0.850379i | \(-0.323628\pi\) | ||||
0.526170 | + | 0.850379i | \(0.323628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −271894. | −0.0102808 | ||||||||
\(932\) | −4.40335e7 | −1.66052 | ||||||||
\(933\) | −1.61431e7 | −0.607132 | ||||||||
\(934\) | 6.96429e7 | 2.61222 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.84130e7 | 3.67166 | ||||||||
\(937\) | 7.81376e6 | 0.290744 | 0.145372 | − | 0.989377i | \(-0.453562\pi\) | ||||
0.145372 | + | 0.989377i | \(0.453562\pi\) | |||||||
\(938\) | −2.31991e7 | −0.860923 | ||||||||
\(939\) | 853684. | 0.0315961 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.76275e7 | −0.648958 | −0.324479 | − | 0.945893i | \(-0.605189\pi\) | ||||
−0.324479 | + | 0.945893i | \(0.605189\pi\) | |||||||
\(942\) | 2.60139e6 | 0.0955163 | ||||||||
\(943\) | −2.68395e7 | −0.982869 | ||||||||
\(944\) | −4.88524e7 | −1.78425 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.23452e7 | 1.90173 | ||||||||
\(947\) | −4.10115e7 | −1.48604 | −0.743021 | − | 0.669268i | \(-0.766608\pi\) | ||||
−0.743021 | + | 0.669268i | \(0.766608\pi\) | |||||||
\(948\) | −2.12221e7 | −0.766949 | ||||||||
\(949\) | −1.34576e7 | −0.485066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.42604e6 | −0.122840 | ||||||||
\(952\) | 3.07148e7 | 1.09839 | ||||||||
\(953\) | 2.62994e7 | 0.938022 | 0.469011 | − | 0.883192i | \(-0.344611\pi\) | ||||
0.469011 | + | 0.883192i | \(0.344611\pi\) | |||||||
\(954\) | −8.18378e7 | −2.91127 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.44196e7 | 1.21804 | ||||||||
\(957\) | 1.68200e6 | 0.0593671 | ||||||||
\(958\) | 6.82644e7 | 2.40315 | ||||||||
\(959\) | 3.36461e7 | 1.18138 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.59946e7 | −0.907976 | ||||||||
\(962\) | 1.15025e8 | 4.00734 | ||||||||
\(963\) | −2.59254e7 | −0.900866 | ||||||||
\(964\) | 3.71802e6 | 0.128860 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.62508e7 | 0.560315 | ||||||||
\(967\) | −3.92036e6 | −0.134822 | −0.0674109 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674109 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(968\) | −1.85701e7 | −0.636981 | ||||||||
\(969\) | 335226. | 0.0114691 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.97706e6 | −0.101331 | −0.0506653 | − | 0.998716i | \(-0.516134\pi\) | ||||
−0.0506653 | + | 0.998716i | \(0.516134\pi\) | |||||||
\(972\) | −6.99157e7 | −2.37361 | ||||||||
\(973\) | 2.37985e7 | 0.805874 | ||||||||
\(974\) | 3.06308e7 | 1.03457 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.31479e8 | 4.41808 | ||||||||
\(977\) | 1.41516e7 | 0.474318 | 0.237159 | − | 0.971471i | \(-0.423784\pi\) | ||||
0.237159 | + | 0.971471i | \(0.423784\pi\) | |||||||
\(978\) | −1.43466e7 | −0.479624 | ||||||||
\(979\) | −2.16247e7 | −0.721096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.56447e6 | −0.250961 | ||||||||
\(982\) | 4.54326e7 | 1.50345 | ||||||||
\(983\) | 8.13535e6 | 0.268530 | 0.134265 | − | 0.990945i | \(-0.457133\pi\) | ||||
0.134265 | + | 0.990945i | \(0.457133\pi\) | |||||||
\(984\) | −3.95742e7 | −1.30294 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.28434e6 | 0.107586 | ||||||||
\(987\) | −1.42593e7 | −0.465913 | ||||||||
\(988\) | 8.58367e6 | 0.279757 | ||||||||
\(989\) | 2.36599e7 | 0.769170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.88149e6 | −0.254932 | −0.127466 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127466 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(992\) | 2.51740e7 | 0.812218 | ||||||||
\(993\) | −1.17569e7 | −0.378372 | ||||||||
\(994\) | 3.35936e7 | 1.07843 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.14399e7 | −0.365403 | ||||||||
\(997\) | 3.12716e7 | 0.996352 | 0.498176 | − | 0.867076i | \(-0.334003\pi\) | ||||
0.498176 | + | 0.867076i | \(0.334003\pi\) | |||||||
\(998\) | 8.73698e6 | 0.277674 | ||||||||
\(999\) | −3.23217e7 | −1.02466 |
(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 | 625.6.a.c.1.1 | 22 | ||
5.4 | even | 2 | 625.6.a.d.1.22 | 22 | |||
25.4 | even | 10 | 25.6.d.a.16.1 | yes | 44 | ||
25.19 | even | 10 | 25.6.d.a.11.1 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.6.d.a.11.1 | ✓ | 44 | 25.19 | even | 10 | ||
25.6.d.a.16.1 | yes | 44 | 25.4 | even | 10 | ||
625.6.a.c.1.1 | 22 | 1.1 | even | 1 | trivial | ||
625.6.a.d.1.22 | 22 | 5.4 | even | 2 |