Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(170.562223914\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −135.000 | −0.482991 | −0.241495 | − | 0.970402i | \(-0.577638\pi\) | ||||
−0.241495 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1080.00 | −0.341526 | ||||||||
\(11\) | 4197.00 | 0.950746 | 0.475373 | − | 0.879784i | \(-0.342313\pi\) | ||||
0.475373 | + | 0.879784i | \(0.342313\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | 2744.00 | 0.267261 | ||||||||
\(15\) | 3645.00 | 0.278855 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −12735.0 | −0.628677 | −0.314339 | − | 0.949311i | \(-0.601783\pi\) | ||||
−0.314339 | + | 0.949311i | \(0.601783\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −28213.0 | −0.943652 | −0.471826 | − | 0.881692i | \(-0.656405\pi\) | ||||
−0.471826 | + | 0.881692i | \(0.656405\pi\) | |||||||
\(20\) | −8640.00 | −0.241495 | ||||||||
\(21\) | −9261.00 | −0.218218 | ||||||||
\(22\) | 33576.0 | 0.672279 | ||||||||
\(23\) | −57039.0 | −0.977517 | −0.488759 | − | 0.872419i | \(-0.662550\pi\) | ||||
−0.488759 | + | 0.872419i | \(0.662550\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | −59900.0 | −0.766720 | ||||||||
\(26\) | 17576.0 | 0.196116 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −10269.0 | −0.0781871 | −0.0390936 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390936 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(30\) | 29160.0 | 0.197180 | ||||||||
\(31\) | 98276.0 | 0.592491 | 0.296245 | − | 0.955112i | \(-0.404265\pi\) | ||||
0.296245 | + | 0.955112i | \(0.404265\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −113319. | −0.548914 | ||||||||
\(34\) | −101880. | −0.444542 | ||||||||
\(35\) | −46305.0 | −0.182553 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −352033. | −1.14256 | −0.571278 | − | 0.820757i | \(-0.693552\pi\) | ||||
−0.571278 | + | 0.820757i | \(0.693552\pi\) | |||||||
\(38\) | −225704. | −0.667262 | ||||||||
\(39\) | −59319.0 | −0.160128 | ||||||||
\(40\) | −69120.0 | −0.170763 | ||||||||
\(41\) | 473172. | 1.07220 | 0.536100 | − | 0.844155i | \(-0.319897\pi\) | ||||
0.536100 | + | 0.844155i | \(0.319897\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | 891395. | 1.70974 | 0.854871 | − | 0.518841i | \(-0.173636\pi\) | ||||
0.854871 | + | 0.518841i | \(0.173636\pi\) | |||||||
\(44\) | 268608. | 0.475373 | ||||||||
\(45\) | −98415.0 | −0.160997 | ||||||||
\(46\) | −456312. | −0.691209 | ||||||||
\(47\) | 684984. | 0.962361 | 0.481180 | − | 0.876622i | \(-0.340208\pi\) | ||||
0.481180 | + | 0.876622i | \(0.340208\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −479200. | −0.542153 | ||||||||
\(51\) | 343845. | 0.362967 | ||||||||
\(52\) | 140608. | 0.138675 | ||||||||
\(53\) | 271002. | 0.250039 | 0.125019 | − | 0.992154i | \(-0.460101\pi\) | ||||
0.125019 | + | 0.992154i | \(0.460101\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −566595. | −0.459202 | ||||||||
\(56\) | 175616. | 0.133631 | ||||||||
\(57\) | 761751. | 0.544817 | ||||||||
\(58\) | −82152.0 | −0.0552866 | ||||||||
\(59\) | −954024. | −0.604752 | −0.302376 | − | 0.953189i | \(-0.597780\pi\) | ||||
−0.302376 | + | 0.953189i | \(0.597780\pi\) | |||||||
\(60\) | 233280. | 0.139427 | ||||||||
\(61\) | 3.19716e6 | 1.80347 | 0.901737 | − | 0.432285i | \(-0.142293\pi\) | ||||
0.901737 | + | 0.432285i | \(0.142293\pi\) | |||||||
\(62\) | 786208. | 0.418954 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −296595. | −0.133958 | ||||||||
\(66\) | −906552. | −0.388140 | ||||||||
\(67\) | −2.90202e6 | −1.17880 | −0.589398 | − | 0.807843i | \(-0.700635\pi\) | ||||
−0.589398 | + | 0.807843i | \(0.700635\pi\) | |||||||
\(68\) | −815040. | −0.314339 | ||||||||
\(69\) | 1.54005e6 | 0.564370 | ||||||||
\(70\) | −370440. | −0.129085 | ||||||||
\(71\) | −4.59977e6 | −1.52522 | −0.762609 | − | 0.646860i | \(-0.776082\pi\) | ||||
−0.762609 | + | 0.646860i | \(0.776082\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | 1.27711e6 | 0.384237 | 0.192118 | − | 0.981372i | \(-0.438464\pi\) | ||||
0.192118 | + | 0.981372i | \(0.438464\pi\) | |||||||
\(74\) | −2.81626e6 | −0.807909 | ||||||||
\(75\) | 1.61730e6 | 0.442666 | ||||||||
\(76\) | −1.80563e6 | −0.471826 | ||||||||
\(77\) | 1.43957e6 | 0.359348 | ||||||||
\(78\) | −474552. | −0.113228 | ||||||||
\(79\) | −1.92849e6 | −0.440072 | −0.220036 | − | 0.975492i | \(-0.570617\pi\) | ||||
−0.220036 | + | 0.975492i | \(0.570617\pi\) | |||||||
\(80\) | −552960. | −0.120748 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 3.78538e6 | 0.758159 | ||||||||
\(83\) | −355674. | −0.0682777 | −0.0341388 | − | 0.999417i | \(-0.510869\pi\) | ||||
−0.0341388 | + | 0.999417i | \(0.510869\pi\) | |||||||
\(84\) | −592704. | −0.109109 | ||||||||
\(85\) | 1.71922e6 | 0.303645 | ||||||||
\(86\) | 7.13116e6 | 1.20897 | ||||||||
\(87\) | 277263. | 0.0451413 | ||||||||
\(88\) | 2.14886e6 | 0.336140 | ||||||||
\(89\) | −217854. | −0.0327567 | −0.0163784 | − | 0.999866i | \(-0.505214\pi\) | ||||
−0.0163784 | + | 0.999866i | \(0.505214\pi\) | |||||||
\(90\) | −787320. | −0.113842 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −3.65050e6 | −0.488759 | ||||||||
\(93\) | −2.65345e6 | −0.342075 | ||||||||
\(94\) | 5.47987e6 | 0.680492 | ||||||||
\(95\) | 3.80876e6 | 0.455775 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −4.40076e6 | −0.489583 | −0.244792 | − | 0.969576i | \(-0.578720\pi\) | ||||
−0.244792 | + | 0.969576i | \(0.578720\pi\) | |||||||
\(98\) | 941192. | 0.101015 | ||||||||
\(99\) | 3.05961e6 | 0.316915 | ||||||||
\(100\) | −3.83360e6 | −0.383360 | ||||||||
\(101\) | −1.30268e7 | −1.25810 | −0.629049 | − | 0.777366i | \(-0.716555\pi\) | ||||
−0.629049 | + | 0.777366i | \(0.716555\pi\) | |||||||
\(102\) | 2.75076e6 | 0.256656 | ||||||||
\(103\) | −1.20237e7 | −1.08420 | −0.542098 | − | 0.840316i | \(-0.682370\pi\) | ||||
−0.542098 | + | 0.840316i | \(0.682370\pi\) | |||||||
\(104\) | 1.12486e6 | 0.0980581 | ||||||||
\(105\) | 1.25024e6 | 0.105397 | ||||||||
\(106\) | 2.16802e6 | 0.176804 | ||||||||
\(107\) | −1.08829e7 | −0.858821 | −0.429410 | − | 0.903110i | \(-0.641279\pi\) | ||||
−0.429410 | + | 0.903110i | \(0.641279\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | −2.15309e7 | −1.59246 | −0.796230 | − | 0.604994i | \(-0.793175\pi\) | ||||
−0.796230 | + | 0.604994i | \(0.793175\pi\) | |||||||
\(110\) | −4.53276e6 | −0.324705 | ||||||||
\(111\) | 9.50489e6 | 0.659655 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −1.51964e7 | −0.990755 | −0.495378 | − | 0.868678i | \(-0.664970\pi\) | ||||
−0.495378 | + | 0.868678i | \(0.664970\pi\) | |||||||
\(114\) | 6.09401e6 | 0.385244 | ||||||||
\(115\) | 7.70026e6 | 0.472132 | ||||||||
\(116\) | −657216. | −0.0390936 | ||||||||
\(117\) | 1.60161e6 | 0.0924500 | ||||||||
\(118\) | −7.63219e6 | −0.427624 | ||||||||
\(119\) | −4.36810e6 | −0.237618 | ||||||||
\(120\) | 1.86624e6 | 0.0985901 | ||||||||
\(121\) | −1.87236e6 | −0.0960818 | ||||||||
\(122\) | 2.55773e7 | 1.27525 | ||||||||
\(123\) | −1.27756e7 | −0.619035 | ||||||||
\(124\) | 6.28966e6 | 0.296245 | ||||||||
\(125\) | 1.86334e7 | 0.853309 | ||||||||
\(126\) | 2.00038e6 | 0.0890871 | ||||||||
\(127\) | 8.10709e6 | 0.351198 | 0.175599 | − | 0.984462i | \(-0.443814\pi\) | ||||
0.175599 | + | 0.984462i | \(0.443814\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −2.40677e7 | −0.987120 | ||||||||
\(130\) | −2.37276e6 | −0.0947223 | ||||||||
\(131\) | 8.57031e6 | 0.333079 | 0.166539 | − | 0.986035i | \(-0.446741\pi\) | ||||
0.166539 | + | 0.986035i | \(0.446741\pi\) | |||||||
\(132\) | −7.25242e6 | −0.274457 | ||||||||
\(133\) | −9.67706e6 | −0.356667 | ||||||||
\(134\) | −2.32161e7 | −0.833534 | ||||||||
\(135\) | 2.65720e6 | 0.0929516 | ||||||||
\(136\) | −6.52032e6 | −0.222271 | ||||||||
\(137\) | −2.62757e7 | −0.873036 | −0.436518 | − | 0.899695i | \(-0.643789\pi\) | ||||
−0.436518 | + | 0.899695i | \(0.643789\pi\) | |||||||
\(138\) | 1.23204e7 | 0.399070 | ||||||||
\(139\) | 725828. | 0.0229236 | 0.0114618 | − | 0.999934i | \(-0.496352\pi\) | ||||
0.0114618 | + | 0.999934i | \(0.496352\pi\) | |||||||
\(140\) | −2.96352e6 | −0.0912767 | ||||||||
\(141\) | −1.84946e7 | −0.555619 | ||||||||
\(142\) | −3.67981e7 | −1.07849 | ||||||||
\(143\) | 9.22081e6 | 0.263690 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 1.38632e6 | 0.0377636 | ||||||||
\(146\) | 1.02169e7 | 0.271696 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | −2.25301e7 | −0.571278 | ||||||||
\(149\) | 1.90708e7 | 0.472299 | 0.236150 | − | 0.971717i | \(-0.424114\pi\) | ||||
0.236150 | + | 0.971717i | \(0.424114\pi\) | |||||||
\(150\) | 1.29384e7 | 0.313012 | ||||||||
\(151\) | −7.41798e7 | −1.75334 | −0.876671 | − | 0.481091i | \(-0.840241\pi\) | ||||
−0.876671 | + | 0.481091i | \(0.840241\pi\) | |||||||
\(152\) | −1.44451e7 | −0.333631 | ||||||||
\(153\) | −9.28382e6 | −0.209559 | ||||||||
\(154\) | 1.15166e7 | 0.254098 | ||||||||
\(155\) | −1.32673e7 | −0.286167 | ||||||||
\(156\) | −3.79642e6 | −0.0800641 | ||||||||
\(157\) | 2.24399e7 | 0.462777 | 0.231388 | − | 0.972861i | \(-0.425673\pi\) | ||||
0.231388 | + | 0.972861i | \(0.425673\pi\) | |||||||
\(158\) | −1.54280e7 | −0.311178 | ||||||||
\(159\) | −7.31705e6 | −0.144360 | ||||||||
\(160\) | −4.42368e6 | −0.0853815 | ||||||||
\(161\) | −1.95644e7 | −0.369467 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | −5.02668e7 | −0.909127 | −0.454564 | − | 0.890714i | \(-0.650205\pi\) | ||||
−0.454564 | + | 0.890714i | \(0.650205\pi\) | |||||||
\(164\) | 3.02830e7 | 0.536100 | ||||||||
\(165\) | 1.52981e7 | 0.265120 | ||||||||
\(166\) | −2.84539e6 | −0.0482796 | ||||||||
\(167\) | 5.15138e7 | 0.855887 | 0.427943 | − | 0.903806i | \(-0.359238\pi\) | ||||
0.427943 | + | 0.903806i | \(0.359238\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 1.37538e7 | 0.214710 | ||||||||
\(171\) | −2.05673e7 | −0.314551 | ||||||||
\(172\) | 5.70493e7 | 0.854871 | ||||||||
\(173\) | 1.31669e7 | 0.193340 | 0.0966699 | − | 0.995316i | \(-0.469181\pi\) | ||||
0.0966699 | + | 0.995316i | \(0.469181\pi\) | |||||||
\(174\) | 2.21810e6 | 0.0319198 | ||||||||
\(175\) | −2.05457e7 | −0.289793 | ||||||||
\(176\) | 1.71909e7 | 0.237687 | ||||||||
\(177\) | 2.57586e7 | 0.349154 | ||||||||
\(178\) | −1.74283e6 | −0.0231625 | ||||||||
\(179\) | −6.29758e7 | −0.820707 | −0.410354 | − | 0.911926i | \(-0.634595\pi\) | ||||
−0.410354 | + | 0.911926i | \(0.634595\pi\) | |||||||
\(180\) | −6.29856e6 | −0.0804984 | ||||||||
\(181\) | 8.61178e6 | 0.107949 | 0.0539744 | − | 0.998542i | \(-0.482811\pi\) | ||||
0.0539744 | + | 0.998542i | \(0.482811\pi\) | |||||||
\(182\) | 6.02857e6 | 0.0741249 | ||||||||
\(183\) | −8.63233e7 | −1.04124 | ||||||||
\(184\) | −2.92040e7 | −0.345605 | ||||||||
\(185\) | 4.75245e7 | 0.551844 | ||||||||
\(186\) | −2.12276e7 | −0.241883 | ||||||||
\(187\) | −5.34488e7 | −0.597712 | ||||||||
\(188\) | 4.38390e7 | 0.481180 | ||||||||
\(189\) | −6.75127e6 | −0.0727393 | ||||||||
\(190\) | 3.04700e7 | 0.322282 | ||||||||
\(191\) | 1.15446e8 | 1.19884 | 0.599422 | − | 0.800433i | \(-0.295397\pi\) | ||||
0.599422 | + | 0.800433i | \(0.295397\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | 2.02053e6 | 0.0202309 | 0.0101154 | − | 0.999949i | \(-0.496780\pi\) | ||||
0.0101154 | + | 0.999949i | \(0.496780\pi\) | |||||||
\(194\) | −3.52061e7 | −0.346188 | ||||||||
\(195\) | 8.00806e6 | 0.0773404 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −1.02161e8 | −0.952032 | −0.476016 | − | 0.879437i | \(-0.657919\pi\) | ||||
−0.476016 | + | 0.879437i | \(0.657919\pi\) | |||||||
\(198\) | 2.44769e7 | 0.224093 | ||||||||
\(199\) | −1.76061e8 | −1.58372 | −0.791858 | − | 0.610705i | \(-0.790886\pi\) | ||||
−0.791858 | + | 0.610705i | \(0.790886\pi\) | |||||||
\(200\) | −3.06688e7 | −0.271076 | ||||||||
\(201\) | 7.83545e7 | 0.680578 | ||||||||
\(202\) | −1.04215e8 | −0.889609 | ||||||||
\(203\) | −3.52227e6 | −0.0295519 | ||||||||
\(204\) | 2.20061e7 | 0.181483 | ||||||||
\(205\) | −6.38782e7 | −0.517862 | ||||||||
\(206\) | −9.61895e7 | −0.766642 | ||||||||
\(207\) | −4.15814e7 | −0.325839 | ||||||||
\(208\) | 8.99891e6 | 0.0693375 | ||||||||
\(209\) | −1.18410e8 | −0.897173 | ||||||||
\(210\) | 1.00019e7 | 0.0745271 | ||||||||
\(211\) | −7.29003e6 | −0.0534245 | −0.0267123 | − | 0.999643i | \(-0.508504\pi\) | ||||
−0.0267123 | + | 0.999643i | \(0.508504\pi\) | |||||||
\(212\) | 1.73441e7 | 0.125019 | ||||||||
\(213\) | 1.24194e8 | 0.880585 | ||||||||
\(214\) | −8.70634e7 | −0.607278 | ||||||||
\(215\) | −1.20338e8 | −0.825789 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | 3.37087e7 | 0.223940 | ||||||||
\(218\) | −1.72247e8 | −1.12604 | ||||||||
\(219\) | −3.44820e7 | −0.221839 | ||||||||
\(220\) | −3.62621e7 | −0.229601 | ||||||||
\(221\) | −2.79788e7 | −0.174364 | ||||||||
\(222\) | 7.60391e7 | 0.466446 | ||||||||
\(223\) | −8.42454e7 | −0.508721 | −0.254360 | − | 0.967110i | \(-0.581865\pi\) | ||||
−0.254360 | + | 0.967110i | \(0.581865\pi\) | |||||||
\(224\) | 1.12394e7 | 0.0668153 | ||||||||
\(225\) | −4.36671e7 | −0.255573 | ||||||||
\(226\) | −1.21571e8 | −0.700570 | ||||||||
\(227\) | 2.74120e8 | 1.55543 | 0.777714 | − | 0.628618i | \(-0.216379\pi\) | ||||
0.777714 | + | 0.628618i | \(0.216379\pi\) | |||||||
\(228\) | 4.87521e7 | 0.272409 | ||||||||
\(229\) | −1.36185e8 | −0.749386 | −0.374693 | − | 0.927149i | \(-0.622252\pi\) | ||||
−0.374693 | + | 0.927149i | \(0.622252\pi\) | |||||||
\(230\) | 6.16021e7 | 0.333848 | ||||||||
\(231\) | −3.88684e7 | −0.207470 | ||||||||
\(232\) | −5.25773e6 | −0.0276433 | ||||||||
\(233\) | −1.92333e8 | −0.996113 | −0.498057 | − | 0.867145i | \(-0.665953\pi\) | ||||
−0.498057 | + | 0.867145i | \(0.665953\pi\) | |||||||
\(234\) | 1.28129e7 | 0.0653720 | ||||||||
\(235\) | −9.24728e7 | −0.464811 | ||||||||
\(236\) | −6.10575e7 | −0.302376 | ||||||||
\(237\) | 5.20693e7 | 0.254076 | ||||||||
\(238\) | −3.49448e7 | −0.168021 | ||||||||
\(239\) | 2.61286e7 | 0.123801 | 0.0619003 | − | 0.998082i | \(-0.480284\pi\) | ||||
0.0619003 | + | 0.998082i | \(0.480284\pi\) | |||||||
\(240\) | 1.49299e7 | 0.0697137 | ||||||||
\(241\) | 8.10060e7 | 0.372784 | 0.186392 | − | 0.982475i | \(-0.440321\pi\) | ||||
0.186392 | + | 0.982475i | \(0.440321\pi\) | |||||||
\(242\) | −1.49789e7 | −0.0679401 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 2.04618e8 | 0.901737 | ||||||||
\(245\) | −1.58826e7 | −0.0689987 | ||||||||
\(246\) | −1.02205e8 | −0.437724 | ||||||||
\(247\) | −6.19840e7 | −0.261722 | ||||||||
\(248\) | 5.03173e7 | 0.209477 | ||||||||
\(249\) | 9.60320e6 | 0.0394201 | ||||||||
\(250\) | 1.49067e8 | 0.603381 | ||||||||
\(251\) | −4.92098e8 | −1.96423 | −0.982117 | − | 0.188270i | \(-0.939712\pi\) | ||||
−0.982117 | + | 0.188270i | \(0.939712\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | −2.39393e8 | −0.929371 | ||||||||
\(254\) | 6.48568e7 | 0.248335 | ||||||||
\(255\) | −4.64191e7 | −0.175310 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −4.01406e7 | −0.147509 | −0.0737544 | − | 0.997276i | \(-0.523498\pi\) | ||||
−0.0737544 | + | 0.997276i | \(0.523498\pi\) | |||||||
\(258\) | −1.92541e8 | −0.697999 | ||||||||
\(259\) | −1.20747e8 | −0.431845 | ||||||||
\(260\) | −1.89821e7 | −0.0669788 | ||||||||
\(261\) | −7.48610e6 | −0.0260624 | ||||||||
\(262\) | 6.85625e7 | 0.235522 | ||||||||
\(263\) | 7.44163e7 | 0.252245 | 0.126123 | − | 0.992015i | \(-0.459747\pi\) | ||||
0.126123 | + | 0.992015i | \(0.459747\pi\) | |||||||
\(264\) | −5.80193e7 | −0.194070 | ||||||||
\(265\) | −3.65853e7 | −0.120766 | ||||||||
\(266\) | −7.74165e7 | −0.252201 | ||||||||
\(267\) | 5.88206e6 | 0.0189121 | ||||||||
\(268\) | −1.85729e8 | −0.589398 | ||||||||
\(269\) | −2.94494e8 | −0.922453 | −0.461226 | − | 0.887283i | \(-0.652590\pi\) | ||||
−0.461226 | + | 0.887283i | \(0.652590\pi\) | |||||||
\(270\) | 2.12576e7 | 0.0657267 | ||||||||
\(271\) | 1.50668e8 | 0.459863 | 0.229932 | − | 0.973207i | \(-0.426150\pi\) | ||||
0.229932 | + | 0.973207i | \(0.426150\pi\) | |||||||
\(272\) | −5.21626e7 | −0.157169 | ||||||||
\(273\) | −2.03464e7 | −0.0605228 | ||||||||
\(274\) | −2.10206e8 | −0.617330 | ||||||||
\(275\) | −2.51400e8 | −0.728956 | ||||||||
\(276\) | 9.85634e7 | 0.282185 | ||||||||
\(277\) | 3.94010e8 | 1.11385 | 0.556926 | − | 0.830562i | \(-0.311981\pi\) | ||||
0.556926 | + | 0.830562i | \(0.311981\pi\) | |||||||
\(278\) | 5.80662e6 | 0.0162094 | ||||||||
\(279\) | 7.16432e7 | 0.197497 | ||||||||
\(280\) | −2.37082e7 | −0.0645423 | ||||||||
\(281\) | 4.42694e8 | 1.19023 | 0.595116 | − | 0.803640i | \(-0.297106\pi\) | ||||
0.595116 | + | 0.803640i | \(0.297106\pi\) | |||||||
\(282\) | −1.47957e8 | −0.392882 | ||||||||
\(283\) | −6.68393e7 | −0.175299 | −0.0876495 | − | 0.996151i | \(-0.527936\pi\) | ||||
−0.0876495 | + | 0.996151i | \(0.527936\pi\) | |||||||
\(284\) | −2.94385e8 | −0.762609 | ||||||||
\(285\) | −1.02836e8 | −0.263142 | ||||||||
\(286\) | 7.37665e7 | 0.186457 | ||||||||
\(287\) | 1.62298e8 | 0.405253 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −2.48158e8 | −0.604765 | ||||||||
\(290\) | 1.10905e7 | 0.0267029 | ||||||||
\(291\) | 1.18820e8 | 0.282661 | ||||||||
\(292\) | 8.17351e7 | 0.192118 | ||||||||
\(293\) | 2.91003e8 | 0.675867 | 0.337934 | − | 0.941170i | \(-0.390272\pi\) | ||||
0.337934 | + | 0.941170i | \(0.390272\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | 1.28793e8 | 0.292090 | ||||||||
\(296\) | −1.80241e8 | −0.403954 | ||||||||
\(297\) | −8.26096e7 | −0.182971 | ||||||||
\(298\) | 1.52566e8 | 0.333966 | ||||||||
\(299\) | −1.25315e8 | −0.271115 | ||||||||
\(300\) | 1.03507e8 | 0.221333 | ||||||||
\(301\) | 3.05748e8 | 0.646222 | ||||||||
\(302\) | −5.93439e8 | −1.23980 | ||||||||
\(303\) | 3.51725e8 | 0.726363 | ||||||||
\(304\) | −1.15560e8 | −0.235913 | ||||||||
\(305\) | −4.31616e8 | −0.871061 | ||||||||
\(306\) | −7.42705e7 | −0.148181 | ||||||||
\(307\) | −4.66264e8 | −0.919702 | −0.459851 | − | 0.887996i | \(-0.652097\pi\) | ||||
−0.459851 | + | 0.887996i | \(0.652097\pi\) | |||||||
\(308\) | 9.21325e7 | 0.179674 | ||||||||
\(309\) | 3.24640e8 | 0.625960 | ||||||||
\(310\) | −1.06138e8 | −0.202351 | ||||||||
\(311\) | −8.01986e8 | −1.51184 | −0.755919 | − | 0.654665i | \(-0.772810\pi\) | ||||
−0.755919 | + | 0.654665i | \(0.772810\pi\) | |||||||
\(312\) | −3.03713e7 | −0.0566139 | ||||||||
\(313\) | −2.28927e8 | −0.421981 | −0.210990 | − | 0.977488i | \(-0.567669\pi\) | ||||
−0.210990 | + | 0.977488i | \(0.567669\pi\) | |||||||
\(314\) | 1.79519e8 | 0.327233 | ||||||||
\(315\) | −3.37563e7 | −0.0608511 | ||||||||
\(316\) | −1.23424e8 | −0.220036 | ||||||||
\(317\) | −4.87643e7 | −0.0859795 | −0.0429897 | − | 0.999076i | \(-0.513688\pi\) | ||||
−0.0429897 | + | 0.999076i | \(0.513688\pi\) | |||||||
\(318\) | −5.85364e7 | −0.102078 | ||||||||
\(319\) | −4.30990e7 | −0.0743361 | ||||||||
\(320\) | −3.53894e7 | −0.0603738 | ||||||||
\(321\) | 2.93839e8 | 0.495840 | ||||||||
\(322\) | −1.56515e8 | −0.261253 | ||||||||
\(323\) | 3.59293e8 | 0.593252 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −1.31600e8 | −0.212650 | ||||||||
\(326\) | −4.02134e8 | −0.642850 | ||||||||
\(327\) | 5.81333e8 | 0.919407 | ||||||||
\(328\) | 2.42264e8 | 0.379080 | ||||||||
\(329\) | 2.34950e8 | 0.363738 | ||||||||
\(330\) | 1.22385e8 | 0.187468 | ||||||||
\(331\) | 7.97529e8 | 1.20878 | 0.604391 | − | 0.796688i | \(-0.293416\pi\) | ||||
0.604391 | + | 0.796688i | \(0.293416\pi\) | |||||||
\(332\) | −2.27631e7 | −0.0341388 | ||||||||
\(333\) | −2.56632e8 | −0.380852 | ||||||||
\(334\) | 4.12111e8 | 0.605203 | ||||||||
\(335\) | 3.91772e8 | 0.569347 | ||||||||
\(336\) | −3.79331e7 | −0.0545545 | ||||||||
\(337\) | 4.47244e8 | 0.636560 | 0.318280 | − | 0.947997i | \(-0.396895\pi\) | ||||
0.318280 | + | 0.947997i | \(0.396895\pi\) | |||||||
\(338\) | 3.86145e7 | 0.0543928 | ||||||||
\(339\) | 4.10303e8 | 0.572013 | ||||||||
\(340\) | 1.10030e8 | 0.151823 | ||||||||
\(341\) | 4.12464e8 | 0.563308 | ||||||||
\(342\) | −1.64538e8 | −0.222421 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 4.56394e8 | 0.604485 | ||||||||
\(345\) | −2.07907e8 | −0.272585 | ||||||||
\(346\) | 1.05335e8 | 0.136712 | ||||||||
\(347\) | −1.11624e9 | −1.43419 | −0.717094 | − | 0.696977i | \(-0.754528\pi\) | ||||
−0.717094 | + | 0.696977i | \(0.754528\pi\) | |||||||
\(348\) | 1.77448e7 | 0.0225707 | ||||||||
\(349\) | −5.83656e7 | −0.0734967 | −0.0367483 | − | 0.999325i | \(-0.511700\pi\) | ||||
−0.0367483 | + | 0.999325i | \(0.511700\pi\) | |||||||
\(350\) | −1.64366e8 | −0.204915 | ||||||||
\(351\) | −4.32436e7 | −0.0533761 | ||||||||
\(352\) | 1.37527e8 | 0.168070 | ||||||||
\(353\) | 1.17201e9 | 1.41814 | 0.709068 | − | 0.705140i | \(-0.249116\pi\) | ||||
0.709068 | + | 0.705140i | \(0.249116\pi\) | |||||||
\(354\) | 2.06069e8 | 0.246889 | ||||||||
\(355\) | 6.20969e8 | 0.736666 | ||||||||
\(356\) | −1.39427e7 | −0.0163784 | ||||||||
\(357\) | 1.17939e8 | 0.137189 | ||||||||
\(358\) | −5.03807e8 | −0.580328 | ||||||||
\(359\) | 2.76337e8 | 0.315216 | 0.157608 | − | 0.987502i | \(-0.449622\pi\) | ||||
0.157608 | + | 0.987502i | \(0.449622\pi\) | |||||||
\(360\) | −5.03885e7 | −0.0569210 | ||||||||
\(361\) | −9.78984e7 | −0.109522 | ||||||||
\(362\) | 6.88942e7 | 0.0763313 | ||||||||
\(363\) | 5.05538e7 | 0.0554728 | ||||||||
\(364\) | 4.82285e7 | 0.0524142 | ||||||||
\(365\) | −1.72410e8 | −0.185583 | ||||||||
\(366\) | −6.90586e8 | −0.736265 | ||||||||
\(367\) | 6.82458e8 | 0.720683 | 0.360342 | − | 0.932820i | \(-0.382660\pi\) | ||||
0.360342 | + | 0.932820i | \(0.382660\pi\) | |||||||
\(368\) | −2.33632e8 | −0.244379 | ||||||||
\(369\) | 3.44942e8 | 0.357400 | ||||||||
\(370\) | 3.80196e8 | 0.390212 | ||||||||
\(371\) | 9.29537e7 | 0.0945057 | ||||||||
\(372\) | −1.69821e8 | −0.171037 | ||||||||
\(373\) | −1.10862e9 | −1.10612 | −0.553062 | − | 0.833140i | \(-0.686541\pi\) | ||||
−0.553062 | + | 0.833140i | \(0.686541\pi\) | |||||||
\(374\) | −4.27590e8 | −0.422647 | ||||||||
\(375\) | −5.03101e8 | −0.492658 | ||||||||
\(376\) | 3.50712e8 | 0.340246 | ||||||||
\(377\) | −2.25610e7 | −0.0216852 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | −8.56782e8 | −0.808413 | −0.404206 | − | 0.914668i | \(-0.632452\pi\) | ||||
−0.404206 | + | 0.914668i | \(0.632452\pi\) | |||||||
\(380\) | 2.43760e8 | 0.227887 | ||||||||
\(381\) | −2.18892e8 | −0.202764 | ||||||||
\(382\) | 9.23569e8 | 0.847711 | ||||||||
\(383\) | −1.04811e9 | −0.953259 | −0.476630 | − | 0.879104i | \(-0.658142\pi\) | ||||
−0.476630 | + | 0.879104i | \(0.658142\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | −1.94342e8 | −0.173562 | ||||||||
\(386\) | 1.61643e7 | 0.0143054 | ||||||||
\(387\) | 6.49827e8 | 0.569914 | ||||||||
\(388\) | −2.81649e8 | −0.244792 | ||||||||
\(389\) | −3.25143e8 | −0.280060 | −0.140030 | − | 0.990147i | \(-0.544720\pi\) | ||||
−0.140030 | + | 0.990147i | \(0.544720\pi\) | |||||||
\(390\) | 6.40645e7 | 0.0546879 | ||||||||
\(391\) | 7.26392e8 | 0.614543 | ||||||||
\(392\) | 6.02363e7 | 0.0505076 | ||||||||
\(393\) | −2.31398e8 | −0.192303 | ||||||||
\(394\) | −8.17284e8 | −0.673188 | ||||||||
\(395\) | 2.60347e8 | 0.212551 | ||||||||
\(396\) | 1.95815e8 | 0.158458 | ||||||||
\(397\) | 1.12836e9 | 0.905065 | 0.452532 | − | 0.891748i | \(-0.350521\pi\) | ||||
0.452532 | + | 0.891748i | \(0.350521\pi\) | |||||||
\(398\) | −1.40849e9 | −1.11986 | ||||||||
\(399\) | 2.61281e8 | 0.205922 | ||||||||
\(400\) | −2.45350e8 | −0.191680 | ||||||||
\(401\) | 3.93234e8 | 0.304541 | 0.152271 | − | 0.988339i | \(-0.451341\pi\) | ||||
0.152271 | + | 0.988339i | \(0.451341\pi\) | |||||||
\(402\) | 6.26836e8 | 0.481241 | ||||||||
\(403\) | 2.15912e8 | 0.164327 | ||||||||
\(404\) | −8.33718e8 | −0.629049 | ||||||||
\(405\) | −7.17445e7 | −0.0536656 | ||||||||
\(406\) | −2.81781e7 | −0.0208964 | ||||||||
\(407\) | −1.47748e9 | −1.08628 | ||||||||
\(408\) | 1.76049e8 | 0.128328 | ||||||||
\(409\) | −8.76131e8 | −0.633195 | −0.316597 | − | 0.948560i | \(-0.602540\pi\) | ||||
−0.316597 | + | 0.948560i | \(0.602540\pi\) | |||||||
\(410\) | −5.11026e8 | −0.366184 | ||||||||
\(411\) | 7.09444e8 | 0.504048 | ||||||||
\(412\) | −7.69516e8 | −0.542098 | ||||||||
\(413\) | −3.27230e8 | −0.228575 | ||||||||
\(414\) | −3.32651e8 | −0.230403 | ||||||||
\(415\) | 4.80160e7 | 0.0329775 | ||||||||
\(416\) | 7.19913e7 | 0.0490290 | ||||||||
\(417\) | −1.95974e7 | −0.0132349 | ||||||||
\(418\) | −9.47280e8 | −0.634397 | ||||||||
\(419\) | 1.50539e9 | 0.999772 | 0.499886 | − | 0.866091i | \(-0.333375\pi\) | ||||
0.499886 | + | 0.866091i | \(0.333375\pi\) | |||||||
\(420\) | 8.00150e7 | 0.0526986 | ||||||||
\(421\) | −1.45302e9 | −0.949042 | −0.474521 | − | 0.880244i | \(-0.657379\pi\) | ||||
−0.474521 | + | 0.880244i | \(0.657379\pi\) | |||||||
\(422\) | −5.83202e7 | −0.0377769 | ||||||||
\(423\) | 4.99353e8 | 0.320787 | ||||||||
\(424\) | 1.38753e8 | 0.0884020 | ||||||||
\(425\) | 7.62826e8 | 0.482019 | ||||||||
\(426\) | 9.93550e8 | 0.622667 | ||||||||
\(427\) | 1.09663e9 | 0.681649 | ||||||||
\(428\) | −6.96507e8 | −0.429410 | ||||||||
\(429\) | −2.48962e8 | −0.152241 | ||||||||
\(430\) | −9.62707e8 | −0.583921 | ||||||||
\(431\) | 7.01355e8 | 0.421956 | 0.210978 | − | 0.977491i | \(-0.432335\pi\) | ||||
0.210978 | + | 0.977491i | \(0.432335\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | −2.01359e9 | −1.19196 | −0.595981 | − | 0.802998i | \(-0.703237\pi\) | ||||
−0.595981 | + | 0.802998i | \(0.703237\pi\) | |||||||
\(434\) | 2.69669e8 | 0.158350 | ||||||||
\(435\) | −3.74305e7 | −0.0218029 | ||||||||
\(436\) | −1.37797e9 | −0.796230 | ||||||||
\(437\) | 1.60924e9 | 0.922436 | ||||||||
\(438\) | −2.75856e8 | −0.156864 | ||||||||
\(439\) | −3.23642e9 | −1.82574 | −0.912871 | − | 0.408248i | \(-0.866140\pi\) | ||||
−0.912871 | + | 0.408248i | \(0.866140\pi\) | |||||||
\(440\) | −2.90097e8 | −0.162352 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | −2.23830e8 | −0.123294 | ||||||||
\(443\) | 4.09585e8 | 0.223837 | 0.111918 | − | 0.993717i | \(-0.464300\pi\) | ||||
0.111918 | + | 0.993717i | \(0.464300\pi\) | |||||||
\(444\) | 6.08313e8 | 0.329827 | ||||||||
\(445\) | 2.94103e7 | 0.0158212 | ||||||||
\(446\) | −6.73964e8 | −0.359720 | ||||||||
\(447\) | −5.14912e8 | −0.272682 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | −2.07365e9 | −1.08112 | −0.540558 | − | 0.841307i | \(-0.681787\pi\) | ||||
−0.540558 | + | 0.841307i | \(0.681787\pi\) | |||||||
\(450\) | −3.49337e8 | −0.180718 | ||||||||
\(451\) | 1.98590e9 | 1.01939 | ||||||||
\(452\) | −9.72570e8 | −0.495378 | ||||||||
\(453\) | 2.00286e9 | 1.01229 | ||||||||
\(454\) | 2.19296e9 | 1.09985 | ||||||||
\(455\) | −1.01732e8 | −0.0506312 | ||||||||
\(456\) | 3.90017e8 | 0.192622 | ||||||||
\(457\) | −1.08948e9 | −0.533966 | −0.266983 | − | 0.963701i | \(-0.586027\pi\) | ||||
−0.266983 | + | 0.963701i | \(0.586027\pi\) | |||||||
\(458\) | −1.08948e9 | −0.529896 | ||||||||
\(459\) | 2.50663e8 | 0.120989 | ||||||||
\(460\) | 4.92817e8 | 0.236066 | ||||||||
\(461\) | −1.46678e9 | −0.697286 | −0.348643 | − | 0.937256i | \(-0.613358\pi\) | ||||
−0.348643 | + | 0.937256i | \(0.613358\pi\) | |||||||
\(462\) | −3.10947e8 | −0.146703 | ||||||||
\(463\) | 1.59802e7 | 0.00748252 | 0.00374126 | − | 0.999993i | \(-0.498809\pi\) | ||||
0.00374126 | + | 0.999993i | \(0.498809\pi\) | |||||||
\(464\) | −4.20618e7 | −0.0195468 | ||||||||
\(465\) | 3.58216e8 | 0.165219 | ||||||||
\(466\) | −1.53867e9 | −0.704358 | ||||||||
\(467\) | −2.86456e9 | −1.30152 | −0.650758 | − | 0.759285i | \(-0.725549\pi\) | ||||
−0.650758 | + | 0.759285i | \(0.725549\pi\) | |||||||
\(468\) | 1.02503e8 | 0.0462250 | ||||||||
\(469\) | −9.95392e8 | −0.445543 | ||||||||
\(470\) | −7.39783e8 | −0.328671 | ||||||||
\(471\) | −6.05876e8 | −0.267184 | ||||||||
\(472\) | −4.88460e8 | −0.213812 | ||||||||
\(473\) | 3.74118e9 | 1.62553 | ||||||||
\(474\) | 4.16555e8 | 0.179659 | ||||||||
\(475\) | 1.68996e9 | 0.723517 | ||||||||
\(476\) | −2.79559e8 | −0.118809 | ||||||||
\(477\) | 1.97560e8 | 0.0833462 | ||||||||
\(478\) | 2.09028e8 | 0.0875403 | ||||||||
\(479\) | −4.11927e9 | −1.71256 | −0.856281 | − | 0.516510i | \(-0.827231\pi\) | ||||
−0.856281 | + | 0.516510i | \(0.827231\pi\) | |||||||
\(480\) | 1.19439e8 | 0.0492950 | ||||||||
\(481\) | −7.73417e8 | −0.316888 | ||||||||
\(482\) | 6.48048e8 | 0.263598 | ||||||||
\(483\) | 5.28238e8 | 0.213312 | ||||||||
\(484\) | −1.19831e8 | −0.0480409 | ||||||||
\(485\) | 5.94102e8 | 0.236464 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | −1.12488e8 | −0.0441321 | −0.0220661 | − | 0.999757i | \(-0.507024\pi\) | ||||
−0.0220661 | + | 0.999757i | \(0.507024\pi\) | |||||||
\(488\) | 1.63695e9 | 0.637624 | ||||||||
\(489\) | 1.35720e9 | 0.524885 | ||||||||
\(490\) | −1.27061e8 | −0.0487894 | ||||||||
\(491\) | −1.52267e8 | −0.0580525 | −0.0290263 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290263 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(492\) | −8.17641e8 | −0.309517 | ||||||||
\(493\) | 1.30776e8 | 0.0491545 | ||||||||
\(494\) | −4.95872e8 | −0.185065 | ||||||||
\(495\) | −4.13048e8 | −0.153067 | ||||||||
\(496\) | 4.02538e8 | 0.148123 | ||||||||
\(497\) | −1.57772e9 | −0.576478 | ||||||||
\(498\) | 7.68256e7 | 0.0278742 | ||||||||
\(499\) | 3.33132e9 | 1.20023 | 0.600116 | − | 0.799913i | \(-0.295121\pi\) | ||||
0.600116 | + | 0.799913i | \(0.295121\pi\) | |||||||
\(500\) | 1.19254e9 | 0.426655 | ||||||||
\(501\) | −1.39087e9 | −0.494146 | ||||||||
\(502\) | −3.93678e9 | −1.38892 | ||||||||
\(503\) | −1.50448e9 | −0.527108 | −0.263554 | − | 0.964645i | \(-0.584895\pi\) | ||||
−0.263554 | + | 0.964645i | \(0.584895\pi\) | |||||||
\(504\) | 1.28024e8 | 0.0445435 | ||||||||
\(505\) | 1.75862e9 | 0.607649 | ||||||||
\(506\) | −1.91514e9 | −0.657164 | ||||||||
\(507\) | −1.30324e8 | −0.0444116 | ||||||||
\(508\) | 5.18854e8 | 0.175599 | ||||||||
\(509\) | 1.43003e9 | 0.480655 | 0.240327 | − | 0.970692i | \(-0.422745\pi\) | ||||
0.240327 | + | 0.970692i | \(0.422745\pi\) | |||||||
\(510\) | −3.71353e8 | −0.123963 | ||||||||
\(511\) | 4.38049e8 | 0.145228 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 5.55316e8 | 0.181606 | ||||||||
\(514\) | −3.21125e8 | −0.104305 | ||||||||
\(515\) | 1.62320e9 | 0.523656 | ||||||||
\(516\) | −1.54033e9 | −0.493560 | ||||||||
\(517\) | 2.87488e9 | 0.914961 | ||||||||
\(518\) | −9.65979e8 | −0.305361 | ||||||||
\(519\) | −3.55506e8 | −0.111625 | ||||||||
\(520\) | −1.51857e8 | −0.0473611 | ||||||||
\(521\) | −1.26240e8 | −0.0391080 | −0.0195540 | − | 0.999809i | \(-0.506225\pi\) | ||||
−0.0195540 | + | 0.999809i | \(0.506225\pi\) | |||||||
\(522\) | −5.98888e7 | −0.0184289 | ||||||||
\(523\) | −5.95449e8 | −0.182007 | −0.0910037 | − | 0.995851i | \(-0.529008\pi\) | ||||
−0.0910037 | + | 0.995851i | \(0.529008\pi\) | |||||||
\(524\) | 5.48500e8 | 0.166539 | ||||||||
\(525\) | 5.54734e8 | 0.167312 | ||||||||
\(526\) | 5.95331e8 | 0.178364 | ||||||||
\(527\) | −1.25154e9 | −0.372485 | ||||||||
\(528\) | −4.64155e8 | −0.137228 | ||||||||
\(529\) | −1.51378e8 | −0.0444598 | ||||||||
\(530\) | −2.92682e8 | −0.0853947 | ||||||||
\(531\) | −6.95483e8 | −0.201584 | ||||||||
\(532\) | −6.19332e8 | −0.178333 | ||||||||
\(533\) | 1.03956e9 | 0.297375 | ||||||||
\(534\) | 4.70565e7 | 0.0133729 | ||||||||
\(535\) | 1.46920e9 | 0.414802 | ||||||||
\(536\) | −1.48583e9 | −0.416767 | ||||||||
\(537\) | 1.70035e9 | 0.473836 | ||||||||
\(538\) | −2.35596e9 | −0.652272 | ||||||||
\(539\) | 4.93773e8 | 0.135821 | ||||||||
\(540\) | 1.70061e8 | 0.0464758 | ||||||||
\(541\) | −1.19809e8 | −0.0325311 | −0.0162655 | − | 0.999868i | \(-0.505178\pi\) | ||||
−0.0162655 | + | 0.999868i | \(0.505178\pi\) | |||||||
\(542\) | 1.20535e9 | 0.325173 | ||||||||
\(543\) | −2.32518e8 | −0.0623243 | ||||||||
\(544\) | −4.17300e8 | −0.111135 | ||||||||
\(545\) | 2.90666e9 | 0.769143 | ||||||||
\(546\) | −1.62771e8 | −0.0427960 | ||||||||
\(547\) | 6.05138e9 | 1.58088 | 0.790440 | − | 0.612540i | \(-0.209852\pi\) | ||||
0.790440 | + | 0.612540i | \(0.209852\pi\) | |||||||
\(548\) | −1.68164e9 | −0.436518 | ||||||||
\(549\) | 2.33073e9 | 0.601158 | ||||||||
\(550\) | −2.01120e9 | −0.515450 | ||||||||
\(551\) | 2.89719e8 | 0.0737814 | ||||||||
\(552\) | 7.88507e8 | 0.199535 | ||||||||
\(553\) | −6.61473e8 | −0.166331 | ||||||||
\(554\) | 3.15208e9 | 0.787613 | ||||||||
\(555\) | −1.28316e9 | −0.318607 | ||||||||
\(556\) | 4.64530e7 | 0.0114618 | ||||||||
\(557\) | −7.71199e9 | −1.89092 | −0.945461 | − | 0.325736i | \(-0.894388\pi\) | ||||
−0.945461 | + | 0.325736i | \(0.894388\pi\) | |||||||
\(558\) | 5.73146e8 | 0.139651 | ||||||||
\(559\) | 1.95839e9 | 0.474197 | ||||||||
\(560\) | −1.89665e8 | −0.0456383 | ||||||||
\(561\) | 1.44312e9 | 0.345089 | ||||||||
\(562\) | 3.54155e9 | 0.841621 | ||||||||
\(563\) | −1.03973e8 | −0.0245552 | −0.0122776 | − | 0.999925i | \(-0.503908\pi\) | ||||
−0.0122776 | + | 0.999925i | \(0.503908\pi\) | |||||||
\(564\) | −1.18365e9 | −0.277810 | ||||||||
\(565\) | 2.05152e9 | 0.478526 | ||||||||
\(566\) | −5.34714e8 | −0.123955 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | −2.35508e9 | −0.539246 | ||||||||
\(569\) | 6.29152e9 | 1.43174 | 0.715868 | − | 0.698236i | \(-0.246031\pi\) | ||||
0.715868 | + | 0.698236i | \(0.246031\pi\) | |||||||
\(570\) | −8.22691e8 | −0.186069 | ||||||||
\(571\) | −8.55133e9 | −1.92224 | −0.961119 | − | 0.276133i | \(-0.910947\pi\) | ||||
−0.961119 | + | 0.276133i | \(0.910947\pi\) | |||||||
\(572\) | 5.90132e8 | 0.131845 | ||||||||
\(573\) | −3.11705e9 | −0.692153 | ||||||||
\(574\) | 1.29838e9 | 0.286557 | ||||||||
\(575\) | 3.41664e9 | 0.749482 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 6.59657e9 | 1.42956 | 0.714781 | − | 0.699348i | \(-0.246526\pi\) | ||||
0.714781 | + | 0.699348i | \(0.246526\pi\) | |||||||
\(578\) | −1.98527e9 | −0.427633 | ||||||||
\(579\) | −5.45544e7 | −0.0116803 | ||||||||
\(580\) | 8.87242e7 | 0.0188818 | ||||||||
\(581\) | −1.21996e8 | −0.0258065 | ||||||||
\(582\) | 9.50564e8 | 0.199871 | ||||||||
\(583\) | 1.13740e9 | 0.237723 | ||||||||
\(584\) | 6.53881e8 | 0.135848 | ||||||||
\(585\) | −2.16218e8 | −0.0446525 | ||||||||
\(586\) | 2.32803e9 | 0.477910 | ||||||||
\(587\) | 5.25537e9 | 1.07243 | 0.536216 | − | 0.844081i | \(-0.319853\pi\) | ||||
0.536216 | + | 0.844081i | \(0.319853\pi\) | |||||||
\(588\) | −2.03297e8 | −0.0412393 | ||||||||
\(589\) | −2.77266e9 | −0.559105 | ||||||||
\(590\) | 1.03035e9 | 0.206538 | ||||||||
\(591\) | 2.75833e9 | 0.549656 | ||||||||
\(592\) | −1.44193e9 | −0.285639 | ||||||||
\(593\) | 2.40969e9 | 0.474537 | 0.237269 | − | 0.971444i | \(-0.423748\pi\) | ||||
0.237269 | + | 0.971444i | \(0.423748\pi\) | |||||||
\(594\) | −6.60876e8 | −0.129380 | ||||||||
\(595\) | 5.89694e8 | 0.114767 | ||||||||
\(596\) | 1.22053e9 | 0.236150 | ||||||||
\(597\) | 4.75365e9 | 0.914359 | ||||||||
\(598\) | −1.00252e9 | −0.191707 | ||||||||
\(599\) | 1.02623e10 | 1.95096 | 0.975482 | − | 0.220080i | \(-0.0706319\pi\) | ||||
0.975482 | + | 0.220080i | \(0.0706319\pi\) | |||||||
\(600\) | 8.28058e8 | 0.156506 | ||||||||
\(601\) | −2.12909e9 | −0.400067 | −0.200034 | − | 0.979789i | \(-0.564105\pi\) | ||||
−0.200034 | + | 0.979789i | \(0.564105\pi\) | |||||||
\(602\) | 2.44599e9 | 0.456948 | ||||||||
\(603\) | −2.11557e9 | −0.392932 | ||||||||
\(604\) | −4.74751e9 | −0.876671 | ||||||||
\(605\) | 2.52769e8 | 0.0464066 | ||||||||
\(606\) | 2.81380e9 | 0.513616 | ||||||||
\(607\) | 4.97253e9 | 0.902438 | 0.451219 | − | 0.892413i | \(-0.350989\pi\) | ||||
0.451219 | + | 0.892413i | \(0.350989\pi\) | |||||||
\(608\) | −9.24484e8 | −0.166816 | ||||||||
\(609\) | 9.51012e7 | 0.0170618 | ||||||||
\(610\) | −3.45293e9 | −0.615933 | ||||||||
\(611\) | 1.50491e9 | 0.266911 | ||||||||
\(612\) | −5.94164e8 | −0.104780 | ||||||||
\(613\) | 2.23562e8 | 0.0392000 | 0.0196000 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0196000 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(614\) | −3.73011e9 | −0.650328 | ||||||||
\(615\) | 1.72471e9 | 0.298988 | ||||||||
\(616\) | 7.37060e8 | 0.127049 | ||||||||
\(617\) | −4.15176e9 | −0.711597 | −0.355798 | − | 0.934563i | \(-0.615791\pi\) | ||||
−0.355798 | + | 0.934563i | \(0.615791\pi\) | |||||||
\(618\) | 2.59712e9 | 0.442621 | ||||||||
\(619\) | 4.08459e9 | 0.692200 | 0.346100 | − | 0.938198i | \(-0.387506\pi\) | ||||
0.346100 | + | 0.938198i | \(0.387506\pi\) | |||||||
\(620\) | −8.49105e8 | −0.143084 | ||||||||
\(621\) | 1.12270e9 | 0.188123 | ||||||||
\(622\) | −6.41588e9 | −1.06903 | ||||||||
\(623\) | −7.47239e7 | −0.0123809 | ||||||||
\(624\) | −2.42971e8 | −0.0400320 | ||||||||
\(625\) | 2.16418e9 | 0.354580 | ||||||||
\(626\) | −1.83142e9 | −0.298386 | ||||||||
\(627\) | 3.19707e9 | 0.517983 | ||||||||
\(628\) | 1.43615e9 | 0.231388 | ||||||||
\(629\) | 4.48314e9 | 0.718299 | ||||||||
\(630\) | −2.70051e8 | −0.0430282 | ||||||||
\(631\) | −1.01736e10 | −1.61202 | −0.806009 | − | 0.591903i | \(-0.798377\pi\) | ||||
−0.806009 | + | 0.591903i | \(0.798377\pi\) | |||||||
\(632\) | −9.87389e8 | −0.155589 | ||||||||
\(633\) | 1.96831e8 | 0.0308447 | ||||||||
\(634\) | −3.90115e8 | −0.0607967 | ||||||||
\(635\) | −1.09446e9 | −0.169625 | ||||||||
\(636\) | −4.68291e8 | −0.0721799 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | −3.44792e8 | −0.0525636 | ||||||||
\(639\) | −3.35323e9 | −0.508406 | ||||||||
\(640\) | −2.83116e8 | −0.0426907 | ||||||||
\(641\) | 3.92635e9 | 0.588824 | 0.294412 | − | 0.955679i | \(-0.404876\pi\) | ||||
0.294412 | + | 0.955679i | \(0.404876\pi\) | |||||||
\(642\) | 2.35071e9 | 0.350612 | ||||||||
\(643\) | 5.24722e9 | 0.778379 | 0.389189 | − | 0.921158i | \(-0.372755\pi\) | ||||
0.389189 | + | 0.921158i | \(0.372755\pi\) | |||||||
\(644\) | −1.25212e9 | −0.184733 | ||||||||
\(645\) | 3.24913e9 | 0.476770 | ||||||||
\(646\) | 2.87434e9 | 0.419493 | ||||||||
\(647\) | 8.70304e9 | 1.26330 | 0.631649 | − | 0.775254i | \(-0.282378\pi\) | ||||
0.631649 | + | 0.775254i | \(0.282378\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | −4.00404e9 | −0.574966 | ||||||||
\(650\) | −1.05280e9 | −0.150366 | ||||||||
\(651\) | −9.10134e8 | −0.129292 | ||||||||
\(652\) | −3.21708e9 | −0.454564 | ||||||||
\(653\) | 1.32545e10 | 1.86281 | 0.931403 | − | 0.363990i | \(-0.118586\pi\) | ||||
0.931403 | + | 0.363990i | \(0.118586\pi\) | |||||||
\(654\) | 4.65066e9 | 0.650119 | ||||||||
\(655\) | −1.15699e9 | −0.160874 | ||||||||
\(656\) | 1.93811e9 | 0.268050 | ||||||||
\(657\) | 9.31014e8 | 0.128079 | ||||||||
\(658\) | 1.87960e9 | 0.257202 | ||||||||
\(659\) | 1.32355e10 | 1.80153 | 0.900764 | − | 0.434308i | \(-0.143007\pi\) | ||||
0.900764 | + | 0.434308i | \(0.143007\pi\) | |||||||
\(660\) | 9.79076e8 | 0.132560 | ||||||||
\(661\) | 4.15598e9 | 0.559716 | 0.279858 | − | 0.960041i | \(-0.409713\pi\) | ||||
0.279858 | + | 0.960041i | \(0.409713\pi\) | |||||||
\(662\) | 6.38023e9 | 0.854739 | ||||||||
\(663\) | 7.55427e8 | 0.100669 | ||||||||
\(664\) | −1.82105e8 | −0.0241398 | ||||||||
\(665\) | 1.30640e9 | 0.172267 | ||||||||
\(666\) | −2.05306e9 | −0.269303 | ||||||||
\(667\) | 5.85733e8 | 0.0764293 | ||||||||
\(668\) | 3.29689e9 | 0.427943 | ||||||||
\(669\) | 2.27463e9 | 0.293710 | ||||||||
\(670\) | 3.13418e9 | 0.402589 | ||||||||
\(671\) | 1.34185e10 | 1.71465 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −2.50664e9 | −0.316986 | −0.158493 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158493 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(674\) | 3.57795e9 | 0.450116 | ||||||||
\(675\) | 1.17901e9 | 0.147555 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | −3.73190e9 | −0.462243 | −0.231121 | − | 0.972925i | \(-0.574239\pi\) | ||||
−0.231121 | + | 0.972925i | \(0.574239\pi\) | |||||||
\(678\) | 3.28242e9 | 0.404474 | ||||||||
\(679\) | −1.50946e9 | −0.185045 | ||||||||
\(680\) | 8.80243e8 | 0.107355 | ||||||||
\(681\) | −7.40124e9 | −0.898027 | ||||||||
\(682\) | 3.29971e9 | 0.398319 | ||||||||
\(683\) | −8.40851e8 | −0.100983 | −0.0504913 | − | 0.998725i | \(-0.516079\pi\) | ||||
−0.0504913 | + | 0.998725i | \(0.516079\pi\) | |||||||
\(684\) | −1.31631e9 | −0.157275 | ||||||||
\(685\) | 3.54722e9 | 0.421668 | ||||||||
\(686\) | 3.22829e8 | 0.0381802 | ||||||||
\(687\) | 3.67700e9 | 0.432658 | ||||||||
\(688\) | 3.65115e9 | 0.427436 | ||||||||
\(689\) | 5.95391e8 | 0.0693482 | ||||||||
\(690\) | −1.66326e9 | −0.192747 | ||||||||
\(691\) | 7.01310e9 | 0.808606 | 0.404303 | − | 0.914625i | \(-0.367514\pi\) | ||||
0.404303 | + | 0.914625i | \(0.367514\pi\) | |||||||
\(692\) | 8.42680e8 | 0.0966699 | ||||||||
\(693\) | 1.04945e9 | 0.119783 | ||||||||
\(694\) | −8.92995e9 | −1.01412 | ||||||||
\(695\) | −9.79868e7 | −0.0110719 | ||||||||
\(696\) | 1.41959e8 | 0.0159599 | ||||||||
\(697\) | −6.02585e9 | −0.674067 | ||||||||
\(698\) | −4.66924e8 | −0.0519700 | ||||||||
\(699\) | 5.19300e9 | 0.575106 | ||||||||
\(700\) | −1.31492e9 | −0.144896 | ||||||||
\(701\) | 4.56598e9 | 0.500635 | 0.250317 | − | 0.968164i | \(-0.419465\pi\) | ||||
0.250317 | + | 0.968164i | \(0.419465\pi\) | |||||||
\(702\) | −3.45948e8 | −0.0377426 | ||||||||
\(703\) | 9.93191e9 | 1.07817 | ||||||||
\(704\) | 1.10022e9 | 0.118843 | ||||||||
\(705\) | 2.49677e9 | 0.268359 | ||||||||
\(706\) | 9.37604e9 | 1.00277 | ||||||||
\(707\) | −4.46821e9 | −0.475516 | ||||||||
\(708\) | 1.64855e9 | 0.174577 | ||||||||
\(709\) | −3.91082e9 | −0.412103 | −0.206051 | − | 0.978541i | \(-0.566061\pi\) | ||||
−0.206051 | + | 0.978541i | \(0.566061\pi\) | |||||||
\(710\) | 4.96775e9 | 0.520901 | ||||||||
\(711\) | −1.40587e9 | −0.146691 | ||||||||
\(712\) | −1.11541e8 | −0.0115813 | ||||||||
\(713\) | −5.60556e9 | −0.579170 | ||||||||
\(714\) | 9.43511e8 | 0.0970070 | ||||||||
\(715\) | −1.24481e9 | −0.127360 | ||||||||
\(716\) | −4.03045e9 | −0.410354 | ||||||||
\(717\) | −7.05471e8 | −0.0714763 | ||||||||
\(718\) | 2.21069e9 | 0.222891 | ||||||||
\(719\) | −5.06745e9 | −0.508438 | −0.254219 | − | 0.967147i | \(-0.581818\pi\) | ||||
−0.254219 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(720\) | −4.03108e8 | −0.0402492 | ||||||||
\(721\) | −4.12413e9 | −0.409787 | ||||||||
\(722\) | −7.83187e8 | −0.0774436 | ||||||||
\(723\) | −2.18716e9 | −0.215227 | ||||||||
\(724\) | 5.51154e8 | 0.0539744 | ||||||||
\(725\) | 6.15113e8 | 0.0599476 | ||||||||
\(726\) | 4.04430e8 | 0.0392252 | ||||||||
\(727\) | 1.52509e10 | 1.47206 | 0.736031 | − | 0.676948i | \(-0.236698\pi\) | ||||
0.736031 | + | 0.676948i | \(0.236698\pi\) | |||||||
\(728\) | 3.85828e8 | 0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.37928e9 | −0.131227 | ||||||||
\(731\) | −1.13519e10 | −1.07488 | ||||||||
\(732\) | −5.52469e9 | −0.520618 | ||||||||
\(733\) | −1.09604e10 | −1.02793 | −0.513963 | − | 0.857812i | \(-0.671823\pi\) | ||||
−0.513963 | + | 0.857812i | \(0.671823\pi\) | |||||||
\(734\) | 5.45966e9 | 0.509600 | ||||||||
\(735\) | 4.28831e8 | 0.0398364 | ||||||||
\(736\) | −1.86905e9 | −0.172802 | ||||||||
\(737\) | −1.21798e10 | −1.12073 | ||||||||
\(738\) | 2.75954e9 | 0.252720 | ||||||||
\(739\) | −1.25222e10 | −1.14136 | −0.570682 | − | 0.821171i | \(-0.693321\pi\) | ||||
−0.570682 | + | 0.821171i | \(0.693321\pi\) | |||||||
\(740\) | 3.04157e9 | 0.275922 | ||||||||
\(741\) | 1.67357e9 | 0.151105 | ||||||||
\(742\) | 7.43629e8 | 0.0668256 | ||||||||
\(743\) | 7.60040e9 | 0.679791 | 0.339896 | − | 0.940463i | \(-0.389608\pi\) | ||||
0.339896 | + | 0.940463i | \(0.389608\pi\) | |||||||
\(744\) | −1.35857e9 | −0.120942 | ||||||||
\(745\) | −2.57456e9 | −0.228116 | ||||||||
\(746\) | −8.86900e9 | −0.782147 | ||||||||
\(747\) | −2.59286e8 | −0.0227592 | ||||||||
\(748\) | −3.42072e9 | −0.298856 | ||||||||
\(749\) | −3.73284e9 | −0.324604 | ||||||||
\(750\) | −4.02481e9 | −0.348362 | ||||||||
\(751\) | −5.51279e9 | −0.474932 | −0.237466 | − | 0.971396i | \(-0.576317\pi\) | ||||
−0.237466 | + | 0.971396i | \(0.576317\pi\) | |||||||
\(752\) | 2.80569e9 | 0.240590 | ||||||||
\(753\) | 1.32866e10 | 1.13405 | ||||||||
\(754\) | −1.80488e8 | −0.0153338 | ||||||||
\(755\) | 1.00143e10 | 0.846848 | ||||||||
\(756\) | −4.32081e8 | −0.0363696 | ||||||||
\(757\) | 3.18779e9 | 0.267088 | 0.133544 | − | 0.991043i | \(-0.457364\pi\) | ||||
0.133544 | + | 0.991043i | \(0.457364\pi\) | |||||||
\(758\) | −6.85426e9 | −0.571634 | ||||||||
\(759\) | 6.46360e9 | 0.536573 | ||||||||
\(760\) | 1.95008e9 | 0.161141 | ||||||||
\(761\) | 1.15651e10 | 0.951268 | 0.475634 | − | 0.879643i | \(-0.342219\pi\) | ||||
0.475634 | + | 0.879643i | \(0.342219\pi\) | |||||||
\(762\) | −1.75113e9 | −0.143376 | ||||||||
\(763\) | −7.38508e9 | −0.601893 | ||||||||
\(764\) | 7.38856e9 | 0.599422 | ||||||||
\(765\) | 1.25332e9 | 0.101215 | ||||||||
\(766\) | −8.38488e9 | −0.674056 | ||||||||
\(767\) | −2.09599e9 | −0.167728 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | −4.91430e9 | −0.389690 | −0.194845 | − | 0.980834i | \(-0.562420\pi\) | ||||
−0.194845 | + | 0.980834i | \(0.562420\pi\) | |||||||
\(770\) | −1.55474e9 | −0.122727 | ||||||||
\(771\) | 1.08380e9 | 0.0851643 | ||||||||
\(772\) | 1.29314e8 | 0.0101154 | ||||||||
\(773\) | 8.20751e9 | 0.639121 | 0.319561 | − | 0.947566i | \(-0.396465\pi\) | ||||
0.319561 | + | 0.947566i | \(0.396465\pi\) | |||||||
\(774\) | 5.19862e9 | 0.402990 | ||||||||
\(775\) | −5.88673e9 | −0.454274 | ||||||||
\(776\) | −2.25319e9 | −0.173094 | ||||||||
\(777\) | 3.26018e9 | 0.249326 | ||||||||
\(778\) | −2.60114e9 | −0.198032 | ||||||||
\(779\) | −1.33496e10 | −1.01178 | ||||||||
\(780\) | 5.12516e8 | 0.0386702 | ||||||||
\(781\) | −1.93052e10 | −1.45009 | ||||||||
\(782\) | 5.81113e9 | 0.434547 | ||||||||
\(783\) | 2.02125e8 | 0.0150471 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −3.02938e9 | −0.223517 | ||||||||
\(786\) | −1.85119e9 | −0.135979 | ||||||||
\(787\) | 2.95314e9 | 0.215960 | 0.107980 | − | 0.994153i | \(-0.465562\pi\) | ||||
0.107980 | + | 0.994153i | \(0.465562\pi\) | |||||||
\(788\) | −6.53827e9 | −0.476016 | ||||||||
\(789\) | −2.00924e9 | −0.145634 | ||||||||
\(790\) | 2.08277e9 | 0.150296 | ||||||||
\(791\) | −5.21237e9 | −0.374470 | ||||||||
\(792\) | 1.56652e9 | 0.112047 | ||||||||
\(793\) | 7.02416e9 | 0.500194 | ||||||||
\(794\) | 9.02685e9 | 0.639977 | ||||||||
\(795\) | 9.87802e8 | 0.0697244 | ||||||||
\(796\) | −1.12679e10 | −0.791858 | ||||||||
\(797\) | 2.51364e10 | 1.75873 | 0.879364 | − | 0.476151i | \(-0.157968\pi\) | ||||
0.879364 | + | 0.476151i | \(0.157968\pi\) | |||||||
\(798\) | 2.09024e9 | 0.145609 | ||||||||
\(799\) | −8.72327e9 | −0.605014 | ||||||||
\(800\) | −1.96280e9 | −0.135538 | ||||||||
\(801\) | −1.58816e8 | −0.0109189 | ||||||||
\(802\) | 3.14587e9 | 0.215343 | ||||||||
\(803\) | 5.36003e9 | 0.365311 | ||||||||
\(804\) | 5.01469e9 | 0.340289 | ||||||||
\(805\) | 2.64119e9 | 0.178449 | ||||||||
\(806\) | 1.72730e9 | 0.116197 | ||||||||
\(807\) | 7.95135e9 | 0.532578 | ||||||||
\(808\) | −6.66974e9 | −0.444805 | ||||||||
\(809\) | −3.78645e9 | −0.251428 | −0.125714 | − | 0.992067i | \(-0.540122\pi\) | ||||
−0.125714 | + | 0.992067i | \(0.540122\pi\) | |||||||
\(810\) | −5.73956e8 | −0.0379473 | ||||||||
\(811\) | −1.42483e10 | −0.937974 | −0.468987 | − | 0.883205i | \(-0.655381\pi\) | ||||
−0.468987 | + | 0.883205i | \(0.655381\pi\) | |||||||
\(812\) | −2.25425e8 | −0.0147760 | ||||||||
\(813\) | −4.06804e9 | −0.265502 | ||||||||
\(814\) | −1.18199e10 | −0.768116 | ||||||||
\(815\) | 6.78602e9 | 0.439100 | ||||||||
\(816\) | 1.40839e9 | 0.0907417 | ||||||||
\(817\) | −2.51489e10 | −1.61340 | ||||||||
\(818\) | −7.00905e9 | −0.447736 | ||||||||
\(819\) | 5.49353e8 | 0.0349428 | ||||||||
\(820\) | −4.08821e9 | −0.258931 | ||||||||
\(821\) | 1.47716e10 | 0.931596 | 0.465798 | − | 0.884891i | \(-0.345767\pi\) | ||||
0.465798 | + | 0.884891i | \(0.345767\pi\) | |||||||
\(822\) | 5.67555e9 | 0.356416 | ||||||||
\(823\) | 1.69875e10 | 1.06226 | 0.531129 | − | 0.847291i | \(-0.321768\pi\) | ||||
0.531129 | + | 0.847291i | \(0.321768\pi\) | |||||||
\(824\) | −6.15613e9 | −0.383321 | ||||||||
\(825\) | 6.78781e9 | 0.420863 | ||||||||
\(826\) | −2.61784e9 | −0.161627 | ||||||||
\(827\) | 1.71925e10 | 1.05699 | 0.528493 | − | 0.848938i | \(-0.322757\pi\) | ||||
0.528493 | + | 0.848938i | \(0.322757\pi\) | |||||||
\(828\) | −2.66121e9 | −0.162920 | ||||||||
\(829\) | −1.31925e10 | −0.804239 | −0.402120 | − | 0.915587i | \(-0.631726\pi\) | ||||
−0.402120 | + | 0.915587i | \(0.631726\pi\) | |||||||
\(830\) | 3.84128e8 | 0.0233186 | ||||||||
\(831\) | −1.06383e10 | −0.643083 | ||||||||
\(832\) | 5.75930e8 | 0.0346688 | ||||||||
\(833\) | −1.49826e9 | −0.0898110 | ||||||||
\(834\) | −1.56779e8 | −0.00935850 | ||||||||
\(835\) | −6.95437e9 | −0.413385 | ||||||||
\(836\) | −7.57824e9 | −0.448587 | ||||||||
\(837\) | −1.93437e9 | −0.114025 | ||||||||
\(838\) | 1.20431e10 | 0.706945 | ||||||||
\(839\) | 2.23722e10 | 1.30780 | 0.653901 | − | 0.756581i | \(-0.273131\pi\) | ||||
0.653901 | + | 0.756581i | \(0.273131\pi\) | |||||||
\(840\) | 6.40120e8 | 0.0372635 | ||||||||
\(841\) | −1.71444e10 | −0.993887 | ||||||||
\(842\) | −1.16242e10 | −0.671074 | ||||||||
\(843\) | −1.19527e10 | −0.687181 | ||||||||
\(844\) | −4.66562e8 | −0.0267123 | ||||||||
\(845\) | −6.51619e8 | −0.0371531 | ||||||||
\(846\) | 3.99483e9 | 0.226831 | ||||||||
\(847\) | −6.42220e8 | −0.0363155 | ||||||||
\(848\) | 1.11002e9 | 0.0625096 | ||||||||
\(849\) | 1.80466e9 | 0.101209 | ||||||||
\(850\) | 6.10261e9 | 0.340839 | ||||||||
\(851\) | 2.00796e10 | 1.11687 | ||||||||
\(852\) | 7.94840e9 | 0.440292 | ||||||||
\(853\) | −9.13574e9 | −0.503990 | −0.251995 | − | 0.967728i | \(-0.581087\pi\) | ||||
−0.251995 | + | 0.967728i | \(0.581087\pi\) | |||||||
\(854\) | 8.77300e9 | 0.481999 | ||||||||
\(855\) | 2.77658e9 | 0.151925 | ||||||||
\(856\) | −5.57206e9 | −0.303639 | ||||||||
\(857\) | −9.30815e9 | −0.505162 | −0.252581 | − | 0.967576i | \(-0.581279\pi\) | ||||
−0.252581 | + | 0.967576i | \(0.581279\pi\) | |||||||
\(858\) | −1.99169e9 | −0.107651 | ||||||||
\(859\) | −2.40324e10 | −1.29366 | −0.646832 | − | 0.762632i | \(-0.723907\pi\) | ||||
−0.646832 | + | 0.762632i | \(0.723907\pi\) | |||||||
\(860\) | −7.70165e9 | −0.412895 | ||||||||
\(861\) | −4.38205e9 | −0.233973 | ||||||||
\(862\) | 5.61084e9 | 0.298368 | ||||||||
\(863\) | 2.08803e9 | 0.110586 | 0.0552929 | − | 0.998470i | \(-0.482391\pi\) | ||||
0.0552929 | + | 0.998470i | \(0.482391\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | −1.77753e9 | −0.0933813 | ||||||||
\(866\) | −1.61087e10 | −0.842845 | ||||||||
\(867\) | 6.70028e9 | 0.349161 | ||||||||
\(868\) | 2.15735e9 | 0.111970 | ||||||||
\(869\) | −8.09389e9 | −0.418397 | ||||||||
\(870\) | −2.99444e8 | −0.0154169 | ||||||||
\(871\) | −6.37573e9 | −0.326939 | ||||||||
\(872\) | −1.10238e10 | −0.563020 | ||||||||
\(873\) | −3.20815e9 | −0.163194 | ||||||||
\(874\) | 1.28739e10 | 0.652261 | ||||||||
\(875\) | 6.39125e9 | 0.322521 | ||||||||
\(876\) | −2.20685e9 | −0.110920 | ||||||||
\(877\) | −3.28101e10 | −1.64251 | −0.821256 | − | 0.570560i | \(-0.806726\pi\) | ||||
−0.821256 | + | 0.570560i | \(0.806726\pi\) | |||||||
\(878\) | −2.58914e10 | −1.29099 | ||||||||
\(879\) | −7.85709e9 | −0.390212 | ||||||||
\(880\) | −2.32077e9 | −0.114800 | ||||||||
\(881\) | 4.25886e9 | 0.209835 | 0.104917 | − | 0.994481i | \(-0.466542\pi\) | ||||
0.104917 | + | 0.994481i | \(0.466542\pi\) | |||||||
\(882\) | 6.86129e8 | 0.0336718 | ||||||||
\(883\) | 2.84443e10 | 1.39038 | 0.695188 | − | 0.718828i | \(-0.255321\pi\) | ||||
0.695188 | + | 0.718828i | \(0.255321\pi\) | |||||||
\(884\) | −1.79064e9 | −0.0871818 | ||||||||
\(885\) | −3.47742e9 | −0.168638 | ||||||||
\(886\) | 3.27668e9 | 0.158276 | ||||||||
\(887\) | −9.78539e9 | −0.470810 | −0.235405 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235405 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(888\) | 4.86650e9 | 0.233223 | ||||||||
\(889\) | 2.78073e9 | 0.132740 | ||||||||
\(890\) | 2.35282e8 | 0.0111873 | ||||||||
\(891\) | 2.23046e9 | 0.105638 | ||||||||
\(892\) | −5.39171e9 | −0.254360 | ||||||||
\(893\) | −1.93255e10 | −0.908133 | ||||||||
\(894\) | −4.11929e9 | −0.192815 | ||||||||
\(895\) | 8.50174e9 | 0.396394 | ||||||||
\(896\) | 7.19323e8 | 0.0334077 | ||||||||
\(897\) | 3.38350e9 | 0.156528 | ||||||||
\(898\) | −1.65892e10 | −0.764465 | ||||||||
\(899\) | −1.00920e9 | −0.0463251 | ||||||||
\(900\) | −2.79469e9 | −0.127787 | ||||||||
\(901\) | −3.45121e9 | −0.157194 | ||||||||
\(902\) | 1.58872e10 | 0.720817 | ||||||||
\(903\) | −8.25521e9 | −0.373096 | ||||||||
\(904\) | −7.78056e9 | −0.350285 | ||||||||
\(905\) | −1.16259e9 | −0.0521383 | ||||||||
\(906\) | 1.60228e10 | 0.715799 | ||||||||
\(907\) | −1.40669e10 | −0.625998 | −0.312999 | − | 0.949753i | \(-0.601334\pi\) | ||||
−0.312999 | + | 0.949753i | \(0.601334\pi\) | |||||||
\(908\) | 1.75437e10 | 0.777714 | ||||||||
\(909\) | −9.49657e9 | −0.419366 | ||||||||
\(910\) | −8.13857e8 | −0.0358017 | ||||||||
\(911\) | 4.24394e10 | 1.85975 | 0.929875 | − | 0.367876i | \(-0.119915\pi\) | ||||
0.929875 | + | 0.367876i | \(0.119915\pi\) | |||||||
\(912\) | 3.12013e9 | 0.136204 | ||||||||
\(913\) | −1.49276e9 | −0.0649147 | ||||||||
\(914\) | −8.71586e9 | −0.377571 | ||||||||
\(915\) | 1.16536e10 | 0.502907 | ||||||||
\(916\) | −8.71584e9 | −0.374693 | ||||||||
\(917\) | 2.93962e9 | 0.125892 | ||||||||
\(918\) | 2.00530e9 | 0.0855521 | ||||||||
\(919\) | −4.22209e10 | −1.79442 | −0.897209 | − | 0.441606i | \(-0.854409\pi\) | ||||
−0.897209 | + | 0.441606i | \(0.854409\pi\) | |||||||
\(920\) | 3.94254e9 | 0.166924 | ||||||||
\(921\) | 1.25891e10 | 0.530990 | ||||||||
\(922\) | −1.17342e10 | −0.493056 | ||||||||
\(923\) | −1.01057e10 | −0.423019 | ||||||||
\(924\) | −2.48758e9 | −0.103735 | ||||||||
\(925\) | 2.10868e10 | 0.876020 | ||||||||
\(926\) | 1.27841e8 | 0.00529094 | ||||||||
\(927\) | −8.76527e9 | −0.361398 | ||||||||
\(928\) | −3.36495e8 | −0.0138217 | ||||||||
\(929\) | −5.03682e9 | −0.206111 | −0.103055 | − | 0.994676i | \(-0.532862\pi\) | ||||
−0.103055 | + | 0.994676i | \(0.532862\pi\) | |||||||
\(930\) | 2.86573e9 | 0.116827 | ||||||||
\(931\) | −3.31923e9 | −0.134807 | ||||||||
\(932\) | −1.23093e10 | −0.498057 | ||||||||
\(933\) | 2.16536e10 | 0.872860 | ||||||||
\(934\) | −2.29165e10 | −0.920310 | ||||||||
\(935\) | 7.21559e9 | 0.288690 | ||||||||
\(936\) | 8.20026e8 | 0.0326860 | ||||||||
\(937\) | −2.72484e10 | −1.08206 | −0.541032 | − | 0.841002i | \(-0.681966\pi\) | ||||
−0.541032 | + | 0.841002i | \(0.681966\pi\) | |||||||
\(938\) | −7.96314e9 | −0.315046 | ||||||||
\(939\) | 6.18104e9 | 0.243631 | ||||||||
\(940\) | −5.91826e9 | −0.232406 | ||||||||
\(941\) | 2.08440e10 | 0.815487 | 0.407743 | − | 0.913097i | \(-0.366316\pi\) | ||||
0.407743 | + | 0.913097i | \(0.366316\pi\) | |||||||
\(942\) | −4.84701e9 | −0.188928 | ||||||||
\(943\) | −2.69893e10 | −1.04809 | ||||||||
\(944\) | −3.90768e9 | −0.151188 | ||||||||
\(945\) | 9.11421e8 | 0.0351324 | ||||||||
\(946\) | 2.99295e10 | 1.14942 | ||||||||
\(947\) | −4.02745e10 | −1.54101 | −0.770505 | − | 0.637434i | \(-0.779996\pi\) | ||||
−0.770505 | + | 0.637434i | \(0.779996\pi\) | |||||||
\(948\) | 3.33244e9 | 0.127038 | ||||||||
\(949\) | 2.80581e9 | 0.106568 | ||||||||
\(950\) | 1.35197e10 | 0.511603 | ||||||||
\(951\) | 1.31664e9 | 0.0496403 | ||||||||
\(952\) | −2.23647e9 | −0.0840105 | ||||||||
\(953\) | −1.77964e10 | −0.666052 | −0.333026 | − | 0.942918i | \(-0.608070\pi\) | ||||
−0.333026 | + | 0.942918i | \(0.608070\pi\) | |||||||
\(954\) | 1.58048e9 | 0.0589346 | ||||||||
\(955\) | −1.55852e10 | −0.579031 | ||||||||
\(956\) | 1.67223e9 | 0.0619003 | ||||||||
\(957\) | 1.16367e9 | 0.0429180 | ||||||||
\(958\) | −3.29542e10 | −1.21096 | ||||||||
\(959\) | −9.01257e9 | −0.329977 | ||||||||
\(960\) | 9.55515e8 | 0.0348569 | ||||||||
\(961\) | −1.78544e10 | −0.648955 | ||||||||
\(962\) | −6.18733e9 | −0.224074 | ||||||||
\(963\) | −7.93365e9 | −0.286274 | ||||||||
\(964\) | 5.18438e9 | 0.186392 | ||||||||
\(965\) | −2.72772e8 | −0.00977134 | ||||||||
\(966\) | 4.22591e9 | 0.150834 | ||||||||
\(967\) | −1.37616e8 | −0.00489414 | −0.00244707 | − | 0.999997i | \(-0.500779\pi\) | ||||
−0.00244707 | + | 0.999997i | \(0.500779\pi\) | |||||||
\(968\) | −9.58649e8 | −0.0339700 | ||||||||
\(969\) | −9.70090e9 | −0.342514 | ||||||||
\(970\) | 4.75282e9 | 0.167205 | ||||||||
\(971\) | 1.07329e10 | 0.376226 | 0.188113 | − | 0.982147i | \(-0.439763\pi\) | ||||
0.188113 | + | 0.982147i | \(0.439763\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 2.48959e8 | 0.00866429 | ||||||||
\(974\) | −8.99904e8 | −0.0312061 | ||||||||
\(975\) | 3.55321e9 | 0.122773 | ||||||||
\(976\) | 1.30956e10 | 0.450868 | ||||||||
\(977\) | −1.34908e10 | −0.462814 | −0.231407 | − | 0.972857i | \(-0.574333\pi\) | ||||
−0.231407 | + | 0.972857i | \(0.574333\pi\) | |||||||
\(978\) | 1.08576e10 | 0.371150 | ||||||||
\(979\) | −9.14333e8 | −0.0311433 | ||||||||
\(980\) | −1.01649e9 | −0.0344993 | ||||||||
\(981\) | −1.56960e10 | −0.530820 | ||||||||
\(982\) | −1.21814e9 | −0.0410493 | ||||||||
\(983\) | 3.52787e10 | 1.18461 | 0.592305 | − | 0.805714i | \(-0.298218\pi\) | ||||
0.592305 | + | 0.805714i | \(0.298218\pi\) | |||||||
\(984\) | −6.54113e9 | −0.218862 | ||||||||
\(985\) | 1.37917e10 | 0.459822 | ||||||||
\(986\) | 1.04621e9 | 0.0347574 | ||||||||
\(987\) | −6.34364e9 | −0.210004 | ||||||||
\(988\) | −3.96697e9 | −0.130861 | ||||||||
\(989\) | −5.08443e10 | −1.67130 | ||||||||
\(990\) | −3.30438e9 | −0.108235 | ||||||||
\(991\) | 4.46894e10 | 1.45864 | 0.729318 | − | 0.684175i | \(-0.239838\pi\) | ||||
0.729318 | + | 0.684175i | \(0.239838\pi\) | |||||||
\(992\) | 3.22031e9 | 0.104739 | ||||||||
\(993\) | −2.15333e10 | −0.697891 | ||||||||
\(994\) | −1.26218e10 | −0.407631 | ||||||||
\(995\) | 2.37682e10 | 0.764920 | ||||||||
\(996\) | 6.14605e8 | 0.0197101 | ||||||||
\(997\) | −5.95582e10 | −1.90330 | −0.951652 | − | 0.307177i | \(-0.900616\pi\) | ||||
−0.951652 | + | 0.307177i | \(0.900616\pi\) | |||||||
\(998\) | 2.66506e10 | 0.848692 | ||||||||
\(999\) | 6.92907e9 | 0.219885 |
(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 | 546.8.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |