Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,8,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(0.937155076452\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.00000 | 0.530330 | 0.265165 | − | 0.964203i | \(-0.414574\pi\) | ||||
0.265165 | + | 0.964203i | \(0.414574\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −92.0000 | −0.718750 | ||||||||
\(5\) | 390.000 | 1.39531 | 0.697653 | − | 0.716436i | \(-0.254228\pi\) | ||||
0.697653 | + | 0.716436i | \(0.254228\pi\) | |||||||
\(6\) | −162.000 | −0.306186 | ||||||||
\(7\) | −64.0000 | −0.0705240 | −0.0352620 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352620 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(8\) | −1320.00 | −0.911505 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2340.00 | 0.739973 | ||||||||
\(11\) | −948.000 | −0.214750 | −0.107375 | − | 0.994219i | \(-0.534245\pi\) | ||||
−0.107375 | + | 0.994219i | \(0.534245\pi\) | |||||||
\(12\) | 2484.00 | 0.414971 | ||||||||
\(13\) | −5098.00 | −0.643573 | −0.321787 | − | 0.946812i | \(-0.604283\pi\) | ||||
−0.321787 | + | 0.946812i | \(0.604283\pi\) | |||||||
\(14\) | −384.000 | −0.0374010 | ||||||||
\(15\) | −10530.0 | −0.805581 | ||||||||
\(16\) | 3856.00 | 0.235352 | ||||||||
\(17\) | 28386.0 | 1.40131 | 0.700653 | − | 0.713502i | \(-0.252892\pi\) | ||||
0.700653 | + | 0.713502i | \(0.252892\pi\) | |||||||
\(18\) | 4374.00 | 0.176777 | ||||||||
\(19\) | −8620.00 | −0.288317 | −0.144158 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144158 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(20\) | −35880.0 | −1.00288 | ||||||||
\(21\) | 1728.00 | 0.0407170 | ||||||||
\(22\) | −5688.00 | −0.113889 | ||||||||
\(23\) | −15288.0 | −0.262001 | −0.131001 | − | 0.991382i | \(-0.541819\pi\) | ||||
−0.131001 | + | 0.991382i | \(0.541819\pi\) | |||||||
\(24\) | 35640.0 | 0.526258 | ||||||||
\(25\) | 73975.0 | 0.946880 | ||||||||
\(26\) | −30588.0 | −0.341306 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 5888.00 | 0.0506891 | ||||||||
\(29\) | 36510.0 | 0.277983 | 0.138992 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138992 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(30\) | −63180.0 | −0.427224 | ||||||||
\(31\) | −276808. | −1.66883 | −0.834416 | − | 0.551135i | \(-0.814195\pi\) | ||||
−0.834416 | + | 0.551135i | \(0.814195\pi\) | |||||||
\(32\) | 192096. | 1.03632 | ||||||||
\(33\) | 25596.0 | 0.123986 | ||||||||
\(34\) | 170316. | 0.743155 | ||||||||
\(35\) | −24960.0 | −0.0984026 | ||||||||
\(36\) | −67068.0 | −0.239583 | ||||||||
\(37\) | 268526. | 0.871526 | 0.435763 | − | 0.900061i | \(-0.356479\pi\) | ||||
0.435763 | + | 0.900061i | \(0.356479\pi\) | |||||||
\(38\) | −51720.0 | −0.152903 | ||||||||
\(39\) | 137646. | 0.371567 | ||||||||
\(40\) | −514800. | −1.27183 | ||||||||
\(41\) | −629718. | −1.42693 | −0.713465 | − | 0.700691i | \(-0.752875\pi\) | ||||
−0.713465 | + | 0.700691i | \(0.752875\pi\) | |||||||
\(42\) | 10368.0 | 0.0215935 | ||||||||
\(43\) | 685772. | 1.31535 | 0.657673 | − | 0.753303i | \(-0.271541\pi\) | ||||
0.657673 | + | 0.753303i | \(0.271541\pi\) | |||||||
\(44\) | 87216.0 | 0.154352 | ||||||||
\(45\) | 284310. | 0.465102 | ||||||||
\(46\) | −91728.0 | −0.138947 | ||||||||
\(47\) | 583296. | 0.819495 | 0.409748 | − | 0.912199i | \(-0.365617\pi\) | ||||
0.409748 | + | 0.912199i | \(0.365617\pi\) | |||||||
\(48\) | −104112. | −0.135880 | ||||||||
\(49\) | −819447. | −0.995026 | ||||||||
\(50\) | 443850. | 0.502159 | ||||||||
\(51\) | −766422. | −0.809044 | ||||||||
\(52\) | 469016. | 0.462568 | ||||||||
\(53\) | −428058. | −0.394945 | −0.197473 | − | 0.980308i | \(-0.563273\pi\) | ||||
−0.197473 | + | 0.980308i | \(0.563273\pi\) | |||||||
\(54\) | −118098. | −0.102062 | ||||||||
\(55\) | −369720. | −0.299643 | ||||||||
\(56\) | 84480.0 | 0.0642830 | ||||||||
\(57\) | 232740. | 0.166460 | ||||||||
\(58\) | 219060. | 0.147423 | ||||||||
\(59\) | 1.30638e6 | 0.828109 | 0.414054 | − | 0.910252i | \(-0.364112\pi\) | ||||
0.414054 | + | 0.910252i | \(0.364112\pi\) | |||||||
\(60\) | 968760. | 0.579011 | ||||||||
\(61\) | 300662. | 0.169599 | 0.0847997 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0847997 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(62\) | −1.66085e6 | −0.885032 | ||||||||
\(63\) | −46656.0 | −0.0235080 | ||||||||
\(64\) | 659008. | 0.314240 | ||||||||
\(65\) | −1.98822e6 | −0.897982 | ||||||||
\(66\) | 153576. | 0.0657536 | ||||||||
\(67\) | −507244. | −0.206042 | −0.103021 | − | 0.994679i | \(-0.532851\pi\) | ||||
−0.103021 | + | 0.994679i | \(0.532851\pi\) | |||||||
\(68\) | −2.61151e6 | −1.00719 | ||||||||
\(69\) | 412776. | 0.151266 | ||||||||
\(70\) | −149760. | −0.0521858 | ||||||||
\(71\) | 5.56063e6 | 1.84383 | 0.921913 | − | 0.387397i | \(-0.126626\pi\) | ||||
0.921913 | + | 0.387397i | \(0.126626\pi\) | |||||||
\(72\) | −962280. | −0.303835 | ||||||||
\(73\) | 1.36908e6 | 0.411907 | 0.205954 | − | 0.978562i | \(-0.433970\pi\) | ||||
0.205954 | + | 0.978562i | \(0.433970\pi\) | |||||||
\(74\) | 1.61116e6 | 0.462196 | ||||||||
\(75\) | −1.99733e6 | −0.546681 | ||||||||
\(76\) | 793040. | 0.207228 | ||||||||
\(77\) | 60672.0 | 0.0151451 | ||||||||
\(78\) | 825876. | 0.197053 | ||||||||
\(79\) | −6.91372e6 | −1.57767 | −0.788836 | − | 0.614603i | \(-0.789316\pi\) | ||||
−0.788836 | + | 0.614603i | \(0.789316\pi\) | |||||||
\(80\) | 1.50384e6 | 0.328388 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −3.77831e6 | −0.756744 | ||||||||
\(83\) | −4.37675e6 | −0.840191 | −0.420096 | − | 0.907480i | \(-0.638003\pi\) | ||||
−0.420096 | + | 0.907480i | \(0.638003\pi\) | |||||||
\(84\) | −158976. | −0.0292654 | ||||||||
\(85\) | 1.10705e7 | 1.95525 | ||||||||
\(86\) | 4.11463e6 | 0.697568 | ||||||||
\(87\) | −985770. | −0.160494 | ||||||||
\(88\) | 1.25136e6 | 0.195746 | ||||||||
\(89\) | −8.52831e6 | −1.28232 | −0.641162 | − | 0.767405i | \(-0.721547\pi\) | ||||
−0.641162 | + | 0.767405i | \(0.721547\pi\) | |||||||
\(90\) | 1.70586e6 | 0.246658 | ||||||||
\(91\) | 326272. | 0.0453874 | ||||||||
\(92\) | 1.40650e6 | 0.188313 | ||||||||
\(93\) | 7.47382e6 | 0.963501 | ||||||||
\(94\) | 3.49978e6 | 0.434603 | ||||||||
\(95\) | −3.36180e6 | −0.402290 | ||||||||
\(96\) | −5.18659e6 | −0.598319 | ||||||||
\(97\) | −8.82681e6 | −0.981981 | −0.490990 | − | 0.871165i | \(-0.663365\pi\) | ||||
−0.490990 | + | 0.871165i | \(0.663365\pi\) | |||||||
\(98\) | −4.91668e6 | −0.527692 | ||||||||
\(99\) | −691092. | −0.0715835 | ||||||||
\(100\) | −6.80570e6 | −0.680570 | ||||||||
\(101\) | 1.19864e7 | 1.15762 | 0.578808 | − | 0.815464i | \(-0.303518\pi\) | ||||
0.578808 | + | 0.815464i | \(0.303518\pi\) | |||||||
\(102\) | −4.59853e6 | −0.429061 | ||||||||
\(103\) | 7.20939e6 | 0.650082 | 0.325041 | − | 0.945700i | \(-0.394622\pi\) | ||||
0.325041 | + | 0.945700i | \(0.394622\pi\) | |||||||
\(104\) | 6.72936e6 | 0.586620 | ||||||||
\(105\) | 673920. | 0.0568127 | ||||||||
\(106\) | −2.56835e6 | −0.209451 | ||||||||
\(107\) | 1.14261e7 | 0.901683 | 0.450842 | − | 0.892604i | \(-0.351124\pi\) | ||||
0.450842 | + | 0.892604i | \(0.351124\pi\) | |||||||
\(108\) | 1.81084e6 | 0.138324 | ||||||||
\(109\) | 4.02095e6 | 0.297397 | 0.148698 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148698 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(110\) | −2.21832e6 | −0.158909 | ||||||||
\(111\) | −7.25020e6 | −0.503176 | ||||||||
\(112\) | −246784. | −0.0165979 | ||||||||
\(113\) | −1.77063e7 | −1.15439 | −0.577197 | − | 0.816605i | \(-0.695853\pi\) | ||||
−0.577197 | + | 0.816605i | \(0.695853\pi\) | |||||||
\(114\) | 1.39644e6 | 0.0882786 | ||||||||
\(115\) | −5.96232e6 | −0.365572 | ||||||||
\(116\) | −3.35892e6 | −0.199801 | ||||||||
\(117\) | −3.71644e6 | −0.214524 | ||||||||
\(118\) | 7.83828e6 | 0.439171 | ||||||||
\(119\) | −1.81670e6 | −0.0988257 | ||||||||
\(120\) | 1.38996e7 | 0.734291 | ||||||||
\(121\) | −1.85885e7 | −0.953882 | ||||||||
\(122\) | 1.80397e6 | 0.0899436 | ||||||||
\(123\) | 1.70024e7 | 0.823838 | ||||||||
\(124\) | 2.54663e7 | 1.19947 | ||||||||
\(125\) | −1.61850e6 | −0.0741187 | ||||||||
\(126\) | −279936. | −0.0124670 | ||||||||
\(127\) | 1.67883e7 | 0.727267 | 0.363633 | − | 0.931542i | \(-0.381536\pi\) | ||||
0.363633 | + | 0.931542i | \(0.381536\pi\) | |||||||
\(128\) | −2.06342e7 | −0.869668 | ||||||||
\(129\) | −1.85158e7 | −0.759416 | ||||||||
\(130\) | −1.19293e7 | −0.476227 | ||||||||
\(131\) | 1.68268e7 | 0.653960 | 0.326980 | − | 0.945031i | \(-0.393969\pi\) | ||||
0.326980 | + | 0.945031i | \(0.393969\pi\) | |||||||
\(132\) | −2.35483e6 | −0.0891151 | ||||||||
\(133\) | 551680. | 0.0203332 | ||||||||
\(134\) | −3.04346e6 | −0.109270 | ||||||||
\(135\) | −7.67637e6 | −0.268527 | ||||||||
\(136\) | −3.74695e7 | −1.27730 | ||||||||
\(137\) | 2.80449e7 | 0.931820 | 0.465910 | − | 0.884832i | \(-0.345727\pi\) | ||||
0.465910 | + | 0.884832i | \(0.345727\pi\) | |||||||
\(138\) | 2.47666e6 | 0.0802212 | ||||||||
\(139\) | −1.18273e7 | −0.373537 | −0.186769 | − | 0.982404i | \(-0.559801\pi\) | ||||
−0.186769 | + | 0.982404i | \(0.559801\pi\) | |||||||
\(140\) | 2.29632e6 | 0.0707268 | ||||||||
\(141\) | −1.57490e7 | −0.473136 | ||||||||
\(142\) | 3.33638e7 | 0.977836 | ||||||||
\(143\) | 4.83290e6 | 0.138208 | ||||||||
\(144\) | 2.81102e6 | 0.0784505 | ||||||||
\(145\) | 1.42389e7 | 0.387872 | ||||||||
\(146\) | 8.21449e6 | 0.218447 | ||||||||
\(147\) | 2.21251e7 | 0.574479 | ||||||||
\(148\) | −2.47044e7 | −0.626409 | ||||||||
\(149\) | 2.07846e7 | 0.514743 | 0.257371 | − | 0.966313i | \(-0.417144\pi\) | ||||
0.257371 | + | 0.966313i | \(0.417144\pi\) | |||||||
\(150\) | −1.19840e7 | −0.289922 | ||||||||
\(151\) | 76112.0 | 0.00179901 | 0.000899505 | − | 1.00000i | \(-0.499714\pi\) | ||||
0.000899505 | 1.00000i | \(0.499714\pi\) | ||||||||
\(152\) | 1.13784e7 | 0.262802 | ||||||||
\(153\) | 2.06934e7 | 0.467102 | ||||||||
\(154\) | 364032. | 0.00803188 | ||||||||
\(155\) | −1.07955e8 | −2.32853 | ||||||||
\(156\) | −1.26634e7 | −0.267064 | ||||||||
\(157\) | −3.21825e7 | −0.663698 | −0.331849 | − | 0.943332i | \(-0.607672\pi\) | ||||
−0.331849 | + | 0.943332i | \(0.607672\pi\) | |||||||
\(158\) | −4.14823e7 | −0.836687 | ||||||||
\(159\) | 1.15576e7 | 0.228022 | ||||||||
\(160\) | 7.49174e7 | 1.44598 | ||||||||
\(161\) | 978432. | 0.0184774 | ||||||||
\(162\) | 3.18865e6 | 0.0589256 | ||||||||
\(163\) | 5.83435e7 | 1.05520 | 0.527601 | − | 0.849492i | \(-0.323092\pi\) | ||||
0.527601 | + | 0.849492i | \(0.323092\pi\) | |||||||
\(164\) | 5.79341e7 | 1.02561 | ||||||||
\(165\) | 9.98244e6 | 0.172999 | ||||||||
\(166\) | −2.62605e7 | −0.445579 | ||||||||
\(167\) | −2.58365e7 | −0.429266 | −0.214633 | − | 0.976695i | \(-0.568855\pi\) | ||||
−0.214633 | + | 0.976695i | \(0.568855\pi\) | |||||||
\(168\) | −2.28096e6 | −0.0371138 | ||||||||
\(169\) | −3.67589e7 | −0.585813 | ||||||||
\(170\) | 6.64232e7 | 1.03693 | ||||||||
\(171\) | −6.28398e6 | −0.0961055 | ||||||||
\(172\) | −6.30910e7 | −0.945405 | ||||||||
\(173\) | 6.35201e7 | 0.932716 | 0.466358 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466358 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(174\) | −5.91462e6 | −0.0851147 | ||||||||
\(175\) | −4.73440e6 | −0.0667777 | ||||||||
\(176\) | −3.65549e6 | −0.0505418 | ||||||||
\(177\) | −3.52723e7 | −0.478109 | ||||||||
\(178\) | −5.11699e7 | −0.680055 | ||||||||
\(179\) | −8.09559e7 | −1.05503 | −0.527513 | − | 0.849547i | \(-0.676875\pi\) | ||||
−0.527513 | + | 0.849547i | \(0.676875\pi\) | |||||||
\(180\) | −2.61565e7 | −0.334292 | ||||||||
\(181\) | 6.45032e7 | 0.808549 | 0.404274 | − | 0.914638i | \(-0.367524\pi\) | ||||
0.404274 | + | 0.914638i | \(0.367524\pi\) | |||||||
\(182\) | 1.95763e6 | 0.0240703 | ||||||||
\(183\) | −8.11787e6 | −0.0979182 | ||||||||
\(184\) | 2.01802e7 | 0.238815 | ||||||||
\(185\) | 1.04725e8 | 1.21605 | ||||||||
\(186\) | 4.48429e7 | 0.510973 | ||||||||
\(187\) | −2.69099e7 | −0.300931 | ||||||||
\(188\) | −5.36632e7 | −0.589012 | ||||||||
\(189\) | 1.25971e6 | 0.0135723 | ||||||||
\(190\) | −2.01708e7 | −0.213346 | ||||||||
\(191\) | 5.68274e7 | 0.590121 | 0.295060 | − | 0.955479i | \(-0.404660\pi\) | ||||
0.295060 | + | 0.955479i | \(0.404660\pi\) | |||||||
\(192\) | −1.77932e7 | −0.181426 | ||||||||
\(193\) | 1.16377e8 | 1.16524 | 0.582621 | − | 0.812744i | \(-0.302027\pi\) | ||||
0.582621 | + | 0.812744i | \(0.302027\pi\) | |||||||
\(194\) | −5.29609e7 | −0.520774 | ||||||||
\(195\) | 5.36819e7 | 0.518450 | ||||||||
\(196\) | 7.53891e7 | 0.715175 | ||||||||
\(197\) | −1.18816e8 | −1.10724 | −0.553622 | − | 0.832768i | \(-0.686755\pi\) | ||||
−0.553622 | + | 0.832768i | \(0.686755\pi\) | |||||||
\(198\) | −4.14655e6 | −0.0379629 | ||||||||
\(199\) | −9.50106e7 | −0.854646 | −0.427323 | − | 0.904099i | \(-0.640543\pi\) | ||||
−0.427323 | + | 0.904099i | \(0.640543\pi\) | |||||||
\(200\) | −9.76470e7 | −0.863086 | ||||||||
\(201\) | 1.36956e7 | 0.118958 | ||||||||
\(202\) | 7.19185e7 | 0.613919 | ||||||||
\(203\) | −2.33664e6 | −0.0196045 | ||||||||
\(204\) | 7.05108e7 | 0.581501 | ||||||||
\(205\) | −2.45590e8 | −1.99100 | ||||||||
\(206\) | 4.32564e7 | 0.344758 | ||||||||
\(207\) | −1.11450e7 | −0.0873337 | ||||||||
\(208\) | −1.96579e7 | −0.151466 | ||||||||
\(209\) | 8.17176e6 | 0.0619161 | ||||||||
\(210\) | 4.04352e6 | 0.0301295 | ||||||||
\(211\) | 1.79246e8 | 1.31360 | 0.656798 | − | 0.754067i | \(-0.271910\pi\) | ||||
0.656798 | + | 0.754067i | \(0.271910\pi\) | |||||||
\(212\) | 3.93813e7 | 0.283867 | ||||||||
\(213\) | −1.50137e8 | −1.06453 | ||||||||
\(214\) | 6.85565e7 | 0.478190 | ||||||||
\(215\) | 2.67451e8 | 1.83531 | ||||||||
\(216\) | 2.59816e7 | 0.175419 | ||||||||
\(217\) | 1.77157e7 | 0.117693 | ||||||||
\(218\) | 2.41257e7 | 0.157718 | ||||||||
\(219\) | −3.69652e7 | −0.237815 | ||||||||
\(220\) | 3.40142e7 | 0.215368 | ||||||||
\(221\) | −1.44712e8 | −0.901843 | ||||||||
\(222\) | −4.35012e7 | −0.266849 | ||||||||
\(223\) | −2.06537e8 | −1.24718 | −0.623592 | − | 0.781750i | \(-0.714327\pi\) | ||||
−0.623592 | + | 0.781750i | \(0.714327\pi\) | |||||||
\(224\) | −1.22941e7 | −0.0730853 | ||||||||
\(225\) | 5.39278e7 | 0.315627 | ||||||||
\(226\) | −1.06238e8 | −0.612209 | ||||||||
\(227\) | 4.33954e7 | 0.246237 | 0.123118 | − | 0.992392i | \(-0.460710\pi\) | ||||
0.123118 | + | 0.992392i | \(0.460710\pi\) | |||||||
\(228\) | −2.14121e7 | −0.119643 | ||||||||
\(229\) | −3.61931e7 | −0.199160 | −0.0995799 | − | 0.995030i | \(-0.531750\pi\) | ||||
−0.0995799 | + | 0.995030i | \(0.531750\pi\) | |||||||
\(230\) | −3.57739e7 | −0.193874 | ||||||||
\(231\) | −1.63814e6 | −0.00874400 | ||||||||
\(232\) | −4.81932e7 | −0.253383 | ||||||||
\(233\) | 9.22347e7 | 0.477693 | 0.238846 | − | 0.971057i | \(-0.423231\pi\) | ||||
0.238846 | + | 0.971057i | \(0.423231\pi\) | |||||||
\(234\) | −2.22987e7 | −0.113769 | ||||||||
\(235\) | 2.27485e8 | 1.14345 | ||||||||
\(236\) | −1.20187e8 | −0.595203 | ||||||||
\(237\) | 1.86670e8 | 0.910870 | ||||||||
\(238\) | −1.09002e7 | −0.0524102 | ||||||||
\(239\) | 4.98468e7 | 0.236181 | 0.118090 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118090 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(240\) | −4.06037e7 | −0.189595 | ||||||||
\(241\) | 1.99374e8 | 0.917506 | 0.458753 | − | 0.888564i | \(-0.348296\pi\) | ||||
0.458753 | + | 0.888564i | \(0.348296\pi\) | |||||||
\(242\) | −1.11531e8 | −0.505872 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −2.76609e7 | −0.121900 | ||||||||
\(245\) | −3.19584e8 | −1.38837 | ||||||||
\(246\) | 1.02014e8 | 0.436906 | ||||||||
\(247\) | 4.39448e7 | 0.185553 | ||||||||
\(248\) | 3.65387e8 | 1.52115 | ||||||||
\(249\) | 1.18172e8 | 0.485085 | ||||||||
\(250\) | −9.71100e6 | −0.0393074 | ||||||||
\(251\) | −3.94678e8 | −1.57538 | −0.787689 | − | 0.616073i | \(-0.788723\pi\) | ||||
−0.787689 | + | 0.616073i | \(0.788723\pi\) | |||||||
\(252\) | 4.29235e6 | 0.0168964 | ||||||||
\(253\) | 1.44930e7 | 0.0562649 | ||||||||
\(254\) | 1.00730e8 | 0.385691 | ||||||||
\(255\) | −2.98905e8 | −1.12886 | ||||||||
\(256\) | −2.08158e8 | −0.775451 | ||||||||
\(257\) | −1.42885e8 | −0.525076 | −0.262538 | − | 0.964922i | \(-0.584559\pi\) | ||||
−0.262538 | + | 0.964922i | \(0.584559\pi\) | |||||||
\(258\) | −1.11095e8 | −0.402741 | ||||||||
\(259\) | −1.71857e7 | −0.0614635 | ||||||||
\(260\) | 1.82916e8 | 0.645425 | ||||||||
\(261\) | 2.66158e7 | 0.0926611 | ||||||||
\(262\) | 1.00961e8 | 0.346815 | ||||||||
\(263\) | 4.40241e8 | 1.49226 | 0.746131 | − | 0.665799i | \(-0.231909\pi\) | ||||
0.746131 | + | 0.665799i | \(0.231909\pi\) | |||||||
\(264\) | −3.37867e7 | −0.113014 | ||||||||
\(265\) | −1.66943e8 | −0.551070 | ||||||||
\(266\) | 3.31008e6 | 0.0107833 | ||||||||
\(267\) | 2.30264e8 | 0.740350 | ||||||||
\(268\) | 4.66664e7 | 0.148092 | ||||||||
\(269\) | 2.75405e8 | 0.862657 | 0.431329 | − | 0.902195i | \(-0.358045\pi\) | ||||
0.431329 | + | 0.902195i | \(0.358045\pi\) | |||||||
\(270\) | −4.60582e7 | −0.142408 | ||||||||
\(271\) | −4.24670e8 | −1.29616 | −0.648080 | − | 0.761572i | \(-0.724428\pi\) | ||||
−0.648080 | + | 0.761572i | \(0.724428\pi\) | |||||||
\(272\) | 1.09456e8 | 0.329800 | ||||||||
\(273\) | −8.80934e6 | −0.0262044 | ||||||||
\(274\) | 1.68269e8 | 0.494172 | ||||||||
\(275\) | −7.01283e7 | −0.203343 | ||||||||
\(276\) | −3.79754e7 | −0.108723 | ||||||||
\(277\) | 5.16158e8 | 1.45916 | 0.729581 | − | 0.683894i | \(-0.239715\pi\) | ||||
0.729581 | + | 0.683894i | \(0.239715\pi\) | |||||||
\(278\) | −7.09638e7 | −0.198098 | ||||||||
\(279\) | −2.01793e8 | −0.556277 | ||||||||
\(280\) | 3.29472e7 | 0.0896944 | ||||||||
\(281\) | −3.11043e8 | −0.836273 | −0.418137 | − | 0.908384i | \(-0.637317\pi\) | ||||
−0.418137 | + | 0.908384i | \(0.637317\pi\) | |||||||
\(282\) | −9.44940e7 | −0.250918 | ||||||||
\(283\) | −5.94308e8 | −1.55869 | −0.779344 | − | 0.626596i | \(-0.784448\pi\) | ||||
−0.779344 | + | 0.626596i | \(0.784448\pi\) | |||||||
\(284\) | −5.11578e8 | −1.32525 | ||||||||
\(285\) | 9.07686e7 | 0.232262 | ||||||||
\(286\) | 2.89974e7 | 0.0732957 | ||||||||
\(287\) | 4.03020e7 | 0.100633 | ||||||||
\(288\) | 1.40038e8 | 0.345440 | ||||||||
\(289\) | 3.95426e8 | 0.963658 | ||||||||
\(290\) | 8.54334e7 | 0.205700 | ||||||||
\(291\) | 2.38324e8 | 0.566947 | ||||||||
\(292\) | −1.25956e8 | −0.296058 | ||||||||
\(293\) | 1.15515e8 | 0.268288 | 0.134144 | − | 0.990962i | \(-0.457172\pi\) | ||||
0.134144 | + | 0.990962i | \(0.457172\pi\) | |||||||
\(294\) | 1.32750e8 | 0.304663 | ||||||||
\(295\) | 5.09488e8 | 1.15547 | ||||||||
\(296\) | −3.54454e8 | −0.794400 | ||||||||
\(297\) | 1.86595e7 | 0.0413287 | ||||||||
\(298\) | 1.24708e8 | 0.272984 | ||||||||
\(299\) | 7.79382e7 | 0.168617 | ||||||||
\(300\) | 1.83754e8 | 0.392927 | ||||||||
\(301\) | −4.38894e7 | −0.0927635 | ||||||||
\(302\) | 456672. | 0.000954070 0 | ||||||||
\(303\) | −3.23633e8 | −0.668350 | ||||||||
\(304\) | −3.32387e7 | −0.0678558 | ||||||||
\(305\) | 1.17258e8 | 0.236643 | ||||||||
\(306\) | 1.24160e8 | 0.247718 | ||||||||
\(307\) | −2.60600e8 | −0.514032 | −0.257016 | − | 0.966407i | \(-0.582739\pi\) | ||||
−0.257016 | + | 0.966407i | \(0.582739\pi\) | |||||||
\(308\) | −5.58182e6 | −0.0108855 | ||||||||
\(309\) | −1.94654e8 | −0.375325 | ||||||||
\(310\) | −6.47731e8 | −1.23489 | ||||||||
\(311\) | 5.76795e8 | 1.08733 | 0.543663 | − | 0.839303i | \(-0.317037\pi\) | ||||
0.543663 | + | 0.839303i | \(0.317037\pi\) | |||||||
\(312\) | −1.81693e8 | −0.338685 | ||||||||
\(313\) | −4.60074e8 | −0.848053 | −0.424026 | − | 0.905650i | \(-0.639384\pi\) | ||||
−0.424026 | + | 0.905650i | \(0.639384\pi\) | |||||||
\(314\) | −1.93095e8 | −0.351979 | ||||||||
\(315\) | −1.81958e7 | −0.0328009 | ||||||||
\(316\) | 6.36062e8 | 1.13395 | ||||||||
\(317\) | 6.25561e7 | 0.110297 | 0.0551483 | − | 0.998478i | \(-0.482437\pi\) | ||||
0.0551483 | + | 0.998478i | \(0.482437\pi\) | |||||||
\(318\) | 6.93454e7 | 0.120927 | ||||||||
\(319\) | −3.46115e7 | −0.0596970 | ||||||||
\(320\) | 2.57013e8 | 0.438460 | ||||||||
\(321\) | −3.08504e8 | −0.520587 | ||||||||
\(322\) | 5.87059e6 | 0.00979910 | ||||||||
\(323\) | −2.44687e8 | −0.404020 | ||||||||
\(324\) | −4.88926e7 | −0.0798611 | ||||||||
\(325\) | −3.77125e8 | −0.609387 | ||||||||
\(326\) | 3.50061e8 | 0.559606 | ||||||||
\(327\) | −1.08566e8 | −0.171702 | ||||||||
\(328\) | 8.31228e8 | 1.30065 | ||||||||
\(329\) | −3.73309e7 | −0.0577941 | ||||||||
\(330\) | 5.98946e7 | 0.0917464 | ||||||||
\(331\) | 6.84236e8 | 1.03707 | 0.518535 | − | 0.855057i | \(-0.326478\pi\) | ||||
0.518535 | + | 0.855057i | \(0.326478\pi\) | |||||||
\(332\) | 4.02661e8 | 0.603888 | ||||||||
\(333\) | 1.95755e8 | 0.290509 | ||||||||
\(334\) | −1.55019e8 | −0.227652 | ||||||||
\(335\) | −1.97825e8 | −0.287491 | ||||||||
\(336\) | 6.66317e6 | 0.00958282 | ||||||||
\(337\) | −6.26313e8 | −0.891429 | −0.445714 | − | 0.895175i | \(-0.647050\pi\) | ||||
−0.445714 | + | 0.895175i | \(0.647050\pi\) | |||||||
\(338\) | −2.20553e8 | −0.310674 | ||||||||
\(339\) | 4.78071e8 | 0.666489 | ||||||||
\(340\) | −1.01849e9 | −1.40534 | ||||||||
\(341\) | 2.62414e8 | 0.358382 | ||||||||
\(342\) | −3.77039e7 | −0.0509677 | ||||||||
\(343\) | 1.05151e8 | 0.140697 | ||||||||
\(344\) | −9.05219e8 | −1.19894 | ||||||||
\(345\) | 1.60983e8 | 0.211063 | ||||||||
\(346\) | 3.81120e8 | 0.494647 | ||||||||
\(347\) | −1.25340e9 | −1.61041 | −0.805203 | − | 0.593000i | \(-0.797943\pi\) | ||||
−0.805203 | + | 0.593000i | \(0.797943\pi\) | |||||||
\(348\) | 9.06908e7 | 0.115355 | ||||||||
\(349\) | 2.65350e8 | 0.334142 | 0.167071 | − | 0.985945i | \(-0.446569\pi\) | ||||
0.167071 | + | 0.985945i | \(0.446569\pi\) | |||||||
\(350\) | −2.84064e7 | −0.0354142 | ||||||||
\(351\) | 1.00344e8 | 0.123856 | ||||||||
\(352\) | −1.82107e8 | −0.222550 | ||||||||
\(353\) | −5.69636e8 | −0.689264 | −0.344632 | − | 0.938738i | \(-0.611996\pi\) | ||||
−0.344632 | + | 0.938738i | \(0.611996\pi\) | |||||||
\(354\) | −2.11634e8 | −0.253556 | ||||||||
\(355\) | 2.16865e9 | 2.57270 | ||||||||
\(356\) | 7.84605e8 | 0.921671 | ||||||||
\(357\) | 4.90510e7 | 0.0570570 | ||||||||
\(358\) | −4.85735e8 | −0.559512 | ||||||||
\(359\) | 9.32541e8 | 1.06374 | 0.531872 | − | 0.846825i | \(-0.321489\pi\) | ||||
0.531872 | + | 0.846825i | \(0.321489\pi\) | |||||||
\(360\) | −3.75289e8 | −0.423943 | ||||||||
\(361\) | −8.19567e8 | −0.916874 | ||||||||
\(362\) | 3.87019e8 | 0.428798 | ||||||||
\(363\) | 5.01889e8 | 0.550724 | ||||||||
\(364\) | −3.00170e7 | −0.0326222 | ||||||||
\(365\) | 5.33942e8 | 0.574737 | ||||||||
\(366\) | −4.87072e7 | −0.0519290 | ||||||||
\(367\) | −8.52565e8 | −0.900318 | −0.450159 | − | 0.892948i | \(-0.648633\pi\) | ||||
−0.450159 | + | 0.892948i | \(0.648633\pi\) | |||||||
\(368\) | −5.89505e7 | −0.0616624 | ||||||||
\(369\) | −4.59064e8 | −0.475643 | ||||||||
\(370\) | 6.28351e8 | 0.644906 | ||||||||
\(371\) | 2.73957e7 | 0.0278531 | ||||||||
\(372\) | −6.87591e8 | −0.692516 | ||||||||
\(373\) | 3.81183e8 | 0.380323 | 0.190162 | − | 0.981753i | \(-0.439099\pi\) | ||||
0.190162 | + | 0.981753i | \(0.439099\pi\) | |||||||
\(374\) | −1.61460e8 | −0.159593 | ||||||||
\(375\) | 4.36995e7 | 0.0427924 | ||||||||
\(376\) | −7.69951e8 | −0.746974 | ||||||||
\(377\) | −1.86128e8 | −0.178903 | ||||||||
\(378\) | 7.55827e6 | 0.00719782 | ||||||||
\(379\) | −1.48353e9 | −1.39978 | −0.699889 | − | 0.714251i | \(-0.746767\pi\) | ||||
−0.699889 | + | 0.714251i | \(0.746767\pi\) | |||||||
\(380\) | 3.09286e8 | 0.289146 | ||||||||
\(381\) | −4.53284e8 | −0.419888 | ||||||||
\(382\) | 3.40964e8 | 0.312959 | ||||||||
\(383\) | −7.61930e8 | −0.692978 | −0.346489 | − | 0.938054i | \(-0.612626\pi\) | ||||
−0.346489 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(384\) | 5.57124e8 | 0.502103 | ||||||||
\(385\) | 2.36621e7 | 0.0211320 | ||||||||
\(386\) | 6.98262e8 | 0.617963 | ||||||||
\(387\) | 4.99928e8 | 0.438449 | ||||||||
\(388\) | 8.12067e8 | 0.705799 | ||||||||
\(389\) | 1.60902e9 | 1.38592 | 0.692959 | − | 0.720977i | \(-0.256307\pi\) | ||||
0.692959 | + | 0.720977i | \(0.256307\pi\) | |||||||
\(390\) | 3.22092e8 | 0.274950 | ||||||||
\(391\) | −4.33965e8 | −0.367144 | ||||||||
\(392\) | 1.08167e9 | 0.906971 | ||||||||
\(393\) | −4.54323e8 | −0.377564 | ||||||||
\(394\) | −7.12896e8 | −0.587205 | ||||||||
\(395\) | −2.69635e9 | −2.20134 | ||||||||
\(396\) | 6.35805e7 | 0.0514506 | ||||||||
\(397\) | 1.88016e9 | 1.50809 | 0.754046 | − | 0.656822i | \(-0.228100\pi\) | ||||
0.754046 | + | 0.656822i | \(0.228100\pi\) | |||||||
\(398\) | −5.70064e8 | −0.453245 | ||||||||
\(399\) | −1.48954e7 | −0.0117394 | ||||||||
\(400\) | 2.85248e8 | 0.222850 | ||||||||
\(401\) | 2.68592e8 | 0.208012 | 0.104006 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104006 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(402\) | 8.21735e7 | 0.0630871 | ||||||||
\(403\) | 1.41117e9 | 1.07402 | ||||||||
\(404\) | −1.10275e9 | −0.832037 | ||||||||
\(405\) | 2.07262e8 | 0.155034 | ||||||||
\(406\) | −1.40198e7 | −0.0103969 | ||||||||
\(407\) | −2.54563e8 | −0.187161 | ||||||||
\(408\) | 1.01168e9 | 0.737448 | ||||||||
\(409\) | 8.99478e7 | 0.0650069 | 0.0325034 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325034 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(410\) | −1.47354e9 | −1.05589 | ||||||||
\(411\) | −7.57212e8 | −0.537986 | ||||||||
\(412\) | −6.63264e8 | −0.467247 | ||||||||
\(413\) | −8.36083e7 | −0.0584015 | ||||||||
\(414\) | −6.68697e7 | −0.0463157 | ||||||||
\(415\) | −1.70693e9 | −1.17232 | ||||||||
\(416\) | −9.79305e8 | −0.666947 | ||||||||
\(417\) | 3.19337e8 | 0.215662 | ||||||||
\(418\) | 4.90306e7 | 0.0328360 | ||||||||
\(419\) | 1.69054e9 | 1.12273 | 0.561367 | − | 0.827567i | \(-0.310276\pi\) | ||||
0.561367 | + | 0.827567i | \(0.310276\pi\) | |||||||
\(420\) | −6.20006e7 | −0.0408342 | ||||||||
\(421\) | −1.13333e9 | −0.740232 | −0.370116 | − | 0.928985i | \(-0.620682\pi\) | ||||
−0.370116 | + | 0.928985i | \(0.620682\pi\) | |||||||
\(422\) | 1.07548e9 | 0.696639 | ||||||||
\(423\) | 4.25223e8 | 0.273165 | ||||||||
\(424\) | 5.65037e8 | 0.359995 | ||||||||
\(425\) | 2.09985e9 | 1.32687 | ||||||||
\(426\) | −9.00822e8 | −0.564554 | ||||||||
\(427\) | −1.92424e7 | −0.0119608 | ||||||||
\(428\) | −1.05120e9 | −0.648085 | ||||||||
\(429\) | −1.30488e8 | −0.0797942 | ||||||||
\(430\) | 1.60471e9 | 0.973321 | ||||||||
\(431\) | 2.19943e9 | 1.32324 | 0.661621 | − | 0.749839i | \(-0.269869\pi\) | ||||
0.661621 | + | 0.749839i | \(0.269869\pi\) | |||||||
\(432\) | −7.58976e7 | −0.0452934 | ||||||||
\(433\) | −1.51738e8 | −0.0898227 | −0.0449114 | − | 0.998991i | \(-0.514301\pi\) | ||||
−0.0449114 | + | 0.998991i | \(0.514301\pi\) | |||||||
\(434\) | 1.06294e8 | 0.0624160 | ||||||||
\(435\) | −3.84450e8 | −0.223938 | ||||||||
\(436\) | −3.69927e8 | −0.213754 | ||||||||
\(437\) | 1.31783e8 | 0.0755393 | ||||||||
\(438\) | −2.21791e8 | −0.126120 | ||||||||
\(439\) | 9.90763e8 | 0.558912 | 0.279456 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279456 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(440\) | 4.88030e8 | 0.273126 | ||||||||
\(441\) | −5.97377e8 | −0.331675 | ||||||||
\(442\) | −8.68271e8 | −0.478275 | ||||||||
\(443\) | −1.77376e9 | −0.969351 | −0.484675 | − | 0.874694i | \(-0.661062\pi\) | ||||
−0.484675 | + | 0.874694i | \(0.661062\pi\) | |||||||
\(444\) | 6.67019e8 | 0.361658 | ||||||||
\(445\) | −3.32604e9 | −1.78924 | ||||||||
\(446\) | −1.23922e9 | −0.661419 | ||||||||
\(447\) | −5.61185e8 | −0.297187 | ||||||||
\(448\) | −4.21765e7 | −0.0221614 | ||||||||
\(449\) | −2.77010e8 | −0.144422 | −0.0722110 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722110 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(450\) | 3.23567e8 | 0.167386 | ||||||||
\(451\) | 5.96973e8 | 0.306434 | ||||||||
\(452\) | 1.62898e9 | 0.829720 | ||||||||
\(453\) | −2.05502e6 | −0.00103866 | ||||||||
\(454\) | 2.60372e8 | 0.130587 | ||||||||
\(455\) | 1.27246e8 | 0.0633293 | ||||||||
\(456\) | −3.07217e8 | −0.151729 | ||||||||
\(457\) | 2.94758e9 | 1.44464 | 0.722320 | − | 0.691559i | \(-0.243076\pi\) | ||||
0.722320 | + | 0.691559i | \(0.243076\pi\) | |||||||
\(458\) | −2.17159e8 | −0.105620 | ||||||||
\(459\) | −5.58722e8 | −0.269681 | ||||||||
\(460\) | 5.48533e8 | 0.262755 | ||||||||
\(461\) | −2.76687e9 | −1.31533 | −0.657667 | − | 0.753309i | \(-0.728457\pi\) | ||||
−0.657667 | + | 0.753309i | \(0.728457\pi\) | |||||||
\(462\) | −9.82886e6 | −0.00463721 | ||||||||
\(463\) | 4.63553e8 | 0.217053 | 0.108527 | − | 0.994094i | \(-0.465387\pi\) | ||||
0.108527 | + | 0.994094i | \(0.465387\pi\) | |||||||
\(464\) | 1.40783e8 | 0.0654238 | ||||||||
\(465\) | 2.91479e9 | 1.34438 | ||||||||
\(466\) | 5.53408e8 | 0.253335 | ||||||||
\(467\) | −4.17922e8 | −0.189883 | −0.0949415 | − | 0.995483i | \(-0.530266\pi\) | ||||
−0.0949415 | + | 0.995483i | \(0.530266\pi\) | |||||||
\(468\) | 3.41913e8 | 0.154189 | ||||||||
\(469\) | 3.24636e7 | 0.0145309 | ||||||||
\(470\) | 1.36491e9 | 0.606404 | ||||||||
\(471\) | 8.68927e8 | 0.383186 | ||||||||
\(472\) | −1.72442e9 | −0.754825 | ||||||||
\(473\) | −6.50112e8 | −0.282471 | ||||||||
\(474\) | 1.12002e9 | 0.483062 | ||||||||
\(475\) | −6.37664e8 | −0.273001 | ||||||||
\(476\) | 1.67137e8 | 0.0710310 | ||||||||
\(477\) | −3.12054e8 | −0.131648 | ||||||||
\(478\) | 2.99081e8 | 0.125254 | ||||||||
\(479\) | −1.50973e9 | −0.627660 | −0.313830 | − | 0.949479i | \(-0.601612\pi\) | ||||
−0.313830 | + | 0.949479i | \(0.601612\pi\) | |||||||
\(480\) | −2.02277e9 | −0.834838 | ||||||||
\(481\) | −1.36895e9 | −0.560891 | ||||||||
\(482\) | 1.19624e9 | 0.486581 | ||||||||
\(483\) | −2.64177e7 | −0.0106679 | ||||||||
\(484\) | 1.71014e9 | 0.685603 | ||||||||
\(485\) | −3.44246e9 | −1.37016 | ||||||||
\(486\) | −8.60934e7 | −0.0340207 | ||||||||
\(487\) | 9.29460e8 | 0.364653 | 0.182326 | − | 0.983238i | \(-0.441637\pi\) | ||||
0.182326 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(488\) | −3.96874e8 | −0.154591 | ||||||||
\(489\) | −1.57527e9 | −0.609221 | ||||||||
\(490\) | −1.91751e9 | −0.736293 | ||||||||
\(491\) | 5.12803e9 | 1.95508 | 0.977541 | − | 0.210743i | \(-0.0675885\pi\) | ||||
0.977541 | + | 0.210743i | \(0.0675885\pi\) | |||||||
\(492\) | −1.56422e9 | −0.592134 | ||||||||
\(493\) | 1.03637e9 | 0.389540 | ||||||||
\(494\) | 2.63669e8 | 0.0984043 | ||||||||
\(495\) | −2.69526e8 | −0.0998809 | ||||||||
\(496\) | −1.06737e9 | −0.392762 | ||||||||
\(497\) | −3.55880e8 | −0.130034 | ||||||||
\(498\) | 7.09033e8 | 0.257255 | ||||||||
\(499\) | −4.10649e8 | −0.147951 | −0.0739757 | − | 0.997260i | \(-0.523569\pi\) | ||||
−0.0739757 | + | 0.997260i | \(0.523569\pi\) | |||||||
\(500\) | 1.48902e8 | 0.0532728 | ||||||||
\(501\) | 6.97586e8 | 0.247837 | ||||||||
\(502\) | −2.36807e9 | −0.835470 | ||||||||
\(503\) | 5.02041e9 | 1.75894 | 0.879470 | − | 0.475954i | \(-0.157897\pi\) | ||||
0.879470 | + | 0.475954i | \(0.157897\pi\) | |||||||
\(504\) | 6.15859e7 | 0.0214277 | ||||||||
\(505\) | 4.67470e9 | 1.61523 | ||||||||
\(506\) | 8.69581e7 | 0.0298389 | ||||||||
\(507\) | 9.92491e8 | 0.338219 | ||||||||
\(508\) | −1.54452e9 | −0.522723 | ||||||||
\(509\) | −3.24926e9 | −1.09212 | −0.546062 | − | 0.837745i | \(-0.683874\pi\) | ||||
−0.546062 | + | 0.837745i | \(0.683874\pi\) | |||||||
\(510\) | −1.79343e9 | −0.598671 | ||||||||
\(511\) | −8.76212e7 | −0.0290493 | ||||||||
\(512\) | 1.39223e9 | 0.458423 | ||||||||
\(513\) | 1.69667e8 | 0.0554866 | ||||||||
\(514\) | −8.57312e8 | −0.278463 | ||||||||
\(515\) | 2.81166e9 | 0.907064 | ||||||||
\(516\) | 1.70346e9 | 0.545830 | ||||||||
\(517\) | −5.52965e8 | −0.175987 | ||||||||
\(518\) | −1.03114e8 | −0.0325959 | ||||||||
\(519\) | −1.71504e9 | −0.538504 | ||||||||
\(520\) | 2.62445e9 | 0.818515 | ||||||||
\(521\) | −2.10950e9 | −0.653503 | −0.326752 | − | 0.945110i | \(-0.605954\pi\) | ||||
−0.326752 | + | 0.945110i | \(0.605954\pi\) | |||||||
\(522\) | 1.59695e8 | 0.0491410 | ||||||||
\(523\) | −5.28911e9 | −1.61669 | −0.808345 | − | 0.588709i | \(-0.799636\pi\) | ||||
−0.808345 | + | 0.588709i | \(0.799636\pi\) | |||||||
\(524\) | −1.54806e9 | −0.470034 | ||||||||
\(525\) | 1.27829e8 | 0.0385542 | ||||||||
\(526\) | 2.64144e9 | 0.791391 | ||||||||
\(527\) | −7.85747e9 | −2.33854 | ||||||||
\(528\) | 9.86982e7 | 0.0291803 | ||||||||
\(529\) | −3.17110e9 | −0.931355 | ||||||||
\(530\) | −1.00166e9 | −0.292249 | ||||||||
\(531\) | 9.52351e8 | 0.276036 | ||||||||
\(532\) | −5.07546e7 | −0.0146145 | ||||||||
\(533\) | 3.21030e9 | 0.918334 | ||||||||
\(534\) | 1.38159e9 | 0.392630 | ||||||||
\(535\) | 4.45617e9 | 1.25812 | ||||||||
\(536\) | 6.69562e8 | 0.187808 | ||||||||
\(537\) | 2.18581e9 | 0.609119 | ||||||||
\(538\) | 1.65243e9 | 0.457493 | ||||||||
\(539\) | 7.76836e8 | 0.213682 | ||||||||
\(540\) | 7.06226e8 | 0.193004 | ||||||||
\(541\) | 3.04614e9 | 0.827101 | 0.413551 | − | 0.910481i | \(-0.364288\pi\) | ||||
0.413551 | + | 0.910481i | \(0.364288\pi\) | |||||||
\(542\) | −2.54802e9 | −0.687393 | ||||||||
\(543\) | −1.74159e9 | −0.466816 | ||||||||
\(544\) | 5.45284e9 | 1.45220 | ||||||||
\(545\) | 1.56817e9 | 0.414959 | ||||||||
\(546\) | −5.28561e7 | −0.0138970 | ||||||||
\(547\) | −4.85537e9 | −1.26843 | −0.634215 | − | 0.773157i | \(-0.718677\pi\) | ||||
−0.634215 | + | 0.773157i | \(0.718677\pi\) | |||||||
\(548\) | −2.58013e9 | −0.669746 | ||||||||
\(549\) | 2.19183e8 | 0.0565331 | ||||||||
\(550\) | −4.20770e8 | −0.107839 | ||||||||
\(551\) | −3.14716e8 | −0.0801472 | ||||||||
\(552\) | −5.44864e8 | −0.137880 | ||||||||
\(553\) | 4.42478e8 | 0.111264 | ||||||||
\(554\) | 3.09695e9 | 0.773838 | ||||||||
\(555\) | −2.82758e9 | −0.702084 | ||||||||
\(556\) | 1.08811e9 | 0.268480 | ||||||||
\(557\) | 1.27762e9 | 0.313263 | 0.156631 | − | 0.987657i | \(-0.449937\pi\) | ||||
0.156631 | + | 0.987657i | \(0.449937\pi\) | |||||||
\(558\) | −1.21076e9 | −0.295011 | ||||||||
\(559\) | −3.49607e9 | −0.846522 | ||||||||
\(560\) | −9.62458e7 | −0.0231592 | ||||||||
\(561\) | 7.26568e8 | 0.173743 | ||||||||
\(562\) | −1.86626e9 | −0.443501 | ||||||||
\(563\) | 4.71265e9 | 1.11297 | 0.556487 | − | 0.830856i | \(-0.312149\pi\) | ||||
0.556487 | + | 0.830856i | \(0.312149\pi\) | |||||||
\(564\) | 1.44891e9 | 0.340066 | ||||||||
\(565\) | −6.90546e9 | −1.61073 | ||||||||
\(566\) | −3.56585e9 | −0.826619 | ||||||||
\(567\) | −3.40122e7 | −0.00783600 | ||||||||
\(568\) | −7.34003e9 | −1.68066 | ||||||||
\(569\) | 4.57800e9 | 1.04180 | 0.520898 | − | 0.853619i | \(-0.325597\pi\) | ||||
0.520898 | + | 0.853619i | \(0.325597\pi\) | |||||||
\(570\) | 5.44612e8 | 0.123176 | ||||||||
\(571\) | 4.95119e9 | 1.11297 | 0.556485 | − | 0.830858i | \(-0.312150\pi\) | ||||
0.556485 | + | 0.830858i | \(0.312150\pi\) | |||||||
\(572\) | −4.44627e8 | −0.0993367 | ||||||||
\(573\) | −1.53434e9 | −0.340706 | ||||||||
\(574\) | 2.41812e8 | 0.0533686 | ||||||||
\(575\) | −1.13093e9 | −0.248084 | ||||||||
\(576\) | 4.80417e8 | 0.104747 | ||||||||
\(577\) | 8.51847e9 | 1.84606 | 0.923031 | − | 0.384725i | \(-0.125704\pi\) | ||||
0.923031 | + | 0.384725i | \(0.125704\pi\) | |||||||
\(578\) | 2.37256e9 | 0.511057 | ||||||||
\(579\) | −3.14218e9 | −0.672753 | ||||||||
\(580\) | −1.30998e9 | −0.278783 | ||||||||
\(581\) | 2.80112e8 | 0.0592536 | ||||||||
\(582\) | 1.42994e9 | 0.300669 | ||||||||
\(583\) | 4.05799e8 | 0.0848147 | ||||||||
\(584\) | −1.80719e9 | −0.375455 | ||||||||
\(585\) | −1.44941e9 | −0.299327 | ||||||||
\(586\) | 6.93088e8 | 0.142281 | ||||||||
\(587\) | −5.62247e8 | −0.114735 | −0.0573673 | − | 0.998353i | \(-0.518271\pi\) | ||||
−0.0573673 | + | 0.998353i | \(0.518271\pi\) | |||||||
\(588\) | −2.03551e9 | −0.412907 | ||||||||
\(589\) | 2.38608e9 | 0.481152 | ||||||||
\(590\) | 3.05693e9 | 0.612778 | ||||||||
\(591\) | 3.20803e9 | 0.639268 | ||||||||
\(592\) | 1.03544e9 | 0.205115 | ||||||||
\(593\) | 3.62110e9 | 0.713099 | 0.356549 | − | 0.934277i | \(-0.383953\pi\) | ||||
0.356549 | + | 0.934277i | \(0.383953\pi\) | |||||||
\(594\) | 1.11957e8 | 0.0219179 | ||||||||
\(595\) | −7.08515e8 | −0.137892 | ||||||||
\(596\) | −1.91219e9 | −0.369971 | ||||||||
\(597\) | 2.56529e9 | 0.493430 | ||||||||
\(598\) | 4.67629e8 | 0.0894227 | ||||||||
\(599\) | −7.48104e9 | −1.42222 | −0.711112 | − | 0.703079i | \(-0.751808\pi\) | ||||
−0.711112 | + | 0.703079i | \(0.751808\pi\) | |||||||
\(600\) | 2.63647e9 | 0.498303 | ||||||||
\(601\) | −5.81270e9 | −1.09224 | −0.546119 | − | 0.837707i | \(-0.683895\pi\) | ||||
−0.546119 | + | 0.837707i | \(0.683895\pi\) | |||||||
\(602\) | −2.63336e8 | −0.0491953 | ||||||||
\(603\) | −3.69781e8 | −0.0686806 | ||||||||
\(604\) | −7.00230e6 | −0.00129304 | ||||||||
\(605\) | −7.24950e9 | −1.33096 | ||||||||
\(606\) | −1.94180e9 | −0.354446 | ||||||||
\(607\) | 3.84051e9 | 0.696993 | 0.348497 | − | 0.937310i | \(-0.386692\pi\) | ||||
0.348497 | + | 0.937310i | \(0.386692\pi\) | |||||||
\(608\) | −1.65587e9 | −0.298788 | ||||||||
\(609\) | 6.30893e7 | 0.0113187 | ||||||||
\(610\) | 7.03549e8 | 0.125499 | ||||||||
\(611\) | −2.97364e9 | −0.527405 | ||||||||
\(612\) | −1.90379e9 | −0.335730 | ||||||||
\(613\) | 1.70484e9 | 0.298932 | 0.149466 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149466 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(614\) | −1.56360e9 | −0.272606 | ||||||||
\(615\) | 6.63093e9 | 1.14951 | ||||||||
\(616\) | −8.00870e7 | −0.0138048 | ||||||||
\(617\) | −2.80809e9 | −0.481297 | −0.240649 | − | 0.970612i | \(-0.577360\pi\) | ||||
−0.240649 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(618\) | −1.16792e9 | −0.199046 | ||||||||
\(619\) | −2.54365e9 | −0.431063 | −0.215532 | − | 0.976497i | \(-0.569148\pi\) | ||||
−0.215532 | + | 0.976497i | \(0.569148\pi\) | |||||||
\(620\) | 9.93187e9 | 1.67363 | ||||||||
\(621\) | 3.00914e8 | 0.0504222 | ||||||||
\(622\) | 3.46077e9 | 0.576642 | ||||||||
\(623\) | 5.45812e8 | 0.0904346 | ||||||||
\(624\) | 5.30763e8 | 0.0874489 | ||||||||
\(625\) | −6.41051e9 | −1.05030 | ||||||||
\(626\) | −2.76045e9 | −0.449748 | ||||||||
\(627\) | −2.20638e8 | −0.0357473 | ||||||||
\(628\) | 2.96079e9 | 0.477033 | ||||||||
\(629\) | 7.62238e9 | 1.22127 | ||||||||
\(630\) | −1.09175e8 | −0.0173953 | ||||||||
\(631\) | −1.51146e8 | −0.0239494 | −0.0119747 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119747 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(632\) | 9.12611e9 | 1.43806 | ||||||||
\(633\) | −4.83965e9 | −0.758405 | ||||||||
\(634\) | 3.75337e8 | 0.0584936 | ||||||||
\(635\) | 6.54744e9 | 1.01476 | ||||||||
\(636\) | −1.06330e9 | −0.163891 | ||||||||
\(637\) | 4.17754e9 | 0.640373 | ||||||||
\(638\) | −2.07669e8 | −0.0316591 | ||||||||
\(639\) | 4.05370e9 | 0.614609 | ||||||||
\(640\) | −8.04735e9 | −1.21345 | ||||||||
\(641\) | −1.23625e10 | −1.85397 | −0.926987 | − | 0.375094i | \(-0.877610\pi\) | ||||
−0.926987 | + | 0.375094i | \(0.877610\pi\) | |||||||
\(642\) | −1.85102e9 | −0.276083 | ||||||||
\(643\) | 2.86744e9 | 0.425359 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(644\) | −9.00157e7 | −0.0132806 | ||||||||
\(645\) | −7.22118e9 | −1.05962 | ||||||||
\(646\) | −1.46812e9 | −0.214264 | ||||||||
\(647\) | −4.10640e9 | −0.596068 | −0.298034 | − | 0.954555i | \(-0.596331\pi\) | ||||
−0.298034 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(648\) | −7.01502e8 | −0.101278 | ||||||||
\(649\) | −1.23845e9 | −0.177837 | ||||||||
\(650\) | −2.26275e9 | −0.323176 | ||||||||
\(651\) | −4.78324e8 | −0.0679499 | ||||||||
\(652\) | −5.36760e9 | −0.758427 | ||||||||
\(653\) | 6.91100e9 | 0.971280 | 0.485640 | − | 0.874159i | \(-0.338587\pi\) | ||||
0.485640 | + | 0.874159i | \(0.338587\pi\) | |||||||
\(654\) | −6.51394e8 | −0.0910587 | ||||||||
\(655\) | 6.56244e9 | 0.912475 | ||||||||
\(656\) | −2.42819e9 | −0.335830 | ||||||||
\(657\) | 9.98061e8 | 0.137302 | ||||||||
\(658\) | −2.23986e8 | −0.0306499 | ||||||||
\(659\) | 3.42444e9 | 0.466112 | 0.233056 | − | 0.972463i | \(-0.425127\pi\) | ||||
0.233056 | + | 0.972463i | \(0.425127\pi\) | |||||||
\(660\) | −9.18384e8 | −0.124343 | ||||||||
\(661\) | −6.76437e9 | −0.911008 | −0.455504 | − | 0.890234i | \(-0.650541\pi\) | ||||
−0.455504 | + | 0.890234i | \(0.650541\pi\) | |||||||
\(662\) | 4.10541e9 | 0.549989 | ||||||||
\(663\) | 3.90722e9 | 0.520679 | ||||||||
\(664\) | 5.77731e9 | 0.765839 | ||||||||
\(665\) | 2.15155e8 | 0.0283711 | ||||||||
\(666\) | 1.17453e9 | 0.154065 | ||||||||
\(667\) | −5.58165e8 | −0.0728320 | ||||||||
\(668\) | 2.37696e9 | 0.308535 | ||||||||
\(669\) | 5.57650e9 | 0.720062 | ||||||||
\(670\) | −1.18695e9 | −0.152465 | ||||||||
\(671\) | −2.85028e8 | −0.0364215 | ||||||||
\(672\) | 3.31942e8 | 0.0421958 | ||||||||
\(673\) | −1.74959e9 | −0.221250 | −0.110625 | − | 0.993862i | \(-0.535285\pi\) | ||||
−0.110625 | + | 0.993862i | \(0.535285\pi\) | |||||||
\(674\) | −3.75788e9 | −0.472752 | ||||||||
\(675\) | −1.45605e9 | −0.182227 | ||||||||
\(676\) | 3.38182e9 | 0.421053 | ||||||||
\(677\) | 8.30011e9 | 1.02807 | 0.514036 | − | 0.857769i | \(-0.328150\pi\) | ||||
0.514036 | + | 0.857769i | \(0.328150\pi\) | |||||||
\(678\) | 2.86842e9 | 0.353459 | ||||||||
\(679\) | 5.64916e8 | 0.0692532 | ||||||||
\(680\) | −1.46131e10 | −1.78222 | ||||||||
\(681\) | −1.17168e9 | −0.142165 | ||||||||
\(682\) | 1.57448e9 | 0.190061 | ||||||||
\(683\) | −1.21232e10 | −1.45594 | −0.727969 | − | 0.685610i | \(-0.759536\pi\) | ||||
−0.727969 | + | 0.685610i | \(0.759536\pi\) | |||||||
\(684\) | 5.78126e8 | 0.0690759 | ||||||||
\(685\) | 1.09375e10 | 1.30017 | ||||||||
\(686\) | 6.30908e8 | 0.0746160 | ||||||||
\(687\) | 9.77213e8 | 0.114985 | ||||||||
\(688\) | 2.64434e9 | 0.309569 | ||||||||
\(689\) | 2.18224e9 | 0.254176 | ||||||||
\(690\) | 9.65896e8 | 0.111933 | ||||||||
\(691\) | 8.21846e9 | 0.947583 | 0.473791 | − | 0.880637i | \(-0.342885\pi\) | ||||
0.473791 | + | 0.880637i | \(0.342885\pi\) | |||||||
\(692\) | −5.84385e9 | −0.670390 | ||||||||
\(693\) | 4.42299e7 | 0.00504835 | ||||||||
\(694\) | −7.52038e9 | −0.854046 | ||||||||
\(695\) | −4.61265e9 | −0.521199 | ||||||||
\(696\) | 1.30122e9 | 0.146291 | ||||||||
\(697\) | −1.78752e10 | −1.99957 | ||||||||
\(698\) | 1.59210e9 | 0.177205 | ||||||||
\(699\) | −2.49034e9 | −0.275796 | ||||||||
\(700\) | 4.35565e8 | 0.0479965 | ||||||||
\(701\) | 4.72231e9 | 0.517775 | 0.258888 | − | 0.965907i | \(-0.416644\pi\) | ||||
0.258888 | + | 0.965907i | \(0.416644\pi\) | |||||||
\(702\) | 6.02064e8 | 0.0656844 | ||||||||
\(703\) | −2.31469e9 | −0.251275 | ||||||||
\(704\) | −6.24740e8 | −0.0674831 | ||||||||
\(705\) | −6.14211e9 | −0.660170 | ||||||||
\(706\) | −3.41781e9 | −0.365537 | ||||||||
\(707\) | −7.67131e8 | −0.0816397 | ||||||||
\(708\) | 3.24505e9 | 0.343641 | ||||||||
\(709\) | 2.78975e9 | 0.293970 | 0.146985 | − | 0.989139i | \(-0.453043\pi\) | ||||
0.146985 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(710\) | 1.30119e10 | 1.36438 | ||||||||
\(711\) | −5.04010e9 | −0.525891 | ||||||||
\(712\) | 1.12574e10 | 1.16885 | ||||||||
\(713\) | 4.23184e9 | 0.437236 | ||||||||
\(714\) | 2.94306e8 | 0.0302591 | ||||||||
\(715\) | 1.88483e9 | 0.192842 | ||||||||
\(716\) | 7.44794e9 | 0.758299 | ||||||||
\(717\) | −1.34586e9 | −0.136359 | ||||||||
\(718\) | 5.59524e9 | 0.564136 | ||||||||
\(719\) | 1.51985e9 | 0.152493 | 0.0762463 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762463 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(720\) | 1.09630e9 | 0.109463 | ||||||||
\(721\) | −4.61401e8 | −0.0458464 | ||||||||
\(722\) | −4.91740e9 | −0.486246 | ||||||||
\(723\) | −5.38310e9 | −0.529722 | ||||||||
\(724\) | −5.93429e9 | −0.581144 | ||||||||
\(725\) | 2.70083e9 | 0.263217 | ||||||||
\(726\) | 3.01133e9 | 0.292066 | ||||||||
\(727\) | −8.11761e9 | −0.783534 | −0.391767 | − | 0.920065i | \(-0.628136\pi\) | ||||
−0.391767 | + | 0.920065i | \(0.628136\pi\) | |||||||
\(728\) | −4.30679e8 | −0.0413708 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 3.20365e9 | 0.304800 | ||||||||
\(731\) | 1.94663e10 | 1.84320 | ||||||||
\(732\) | 7.46844e8 | 0.0703787 | ||||||||
\(733\) | −1.03241e10 | −0.968249 | −0.484124 | − | 0.874999i | \(-0.660862\pi\) | ||||
−0.484124 | + | 0.874999i | \(0.660862\pi\) | |||||||
\(734\) | −5.11539e9 | −0.477466 | ||||||||
\(735\) | 8.62878e9 | 0.801574 | ||||||||
\(736\) | −2.93676e9 | −0.271517 | ||||||||
\(737\) | 4.80867e8 | 0.0442475 | ||||||||
\(738\) | −2.75439e9 | −0.252248 | ||||||||
\(739\) | −1.35365e10 | −1.23382 | −0.616908 | − | 0.787035i | \(-0.711615\pi\) | ||||
−0.616908 | + | 0.787035i | \(0.711615\pi\) | |||||||
\(740\) | −9.63471e9 | −0.874033 | ||||||||
\(741\) | −1.18651e9 | −0.107129 | ||||||||
\(742\) | 1.64374e8 | 0.0147713 | ||||||||
\(743\) | −1.71936e10 | −1.53782 | −0.768910 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768910 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(744\) | −9.86544e9 | −0.878236 | ||||||||
\(745\) | 8.10601e9 | 0.718224 | ||||||||
\(746\) | 2.28710e9 | 0.201697 | ||||||||
\(747\) | −3.19065e9 | −0.280064 | ||||||||
\(748\) | 2.47571e9 | 0.216294 | ||||||||
\(749\) | −7.31269e8 | −0.0635903 | ||||||||
\(750\) | 2.62197e8 | 0.0226941 | ||||||||
\(751\) | 1.12478e10 | 0.969013 | 0.484506 | − | 0.874788i | \(-0.338999\pi\) | ||||
0.484506 | + | 0.874788i | \(0.338999\pi\) | |||||||
\(752\) | 2.24919e9 | 0.192870 | ||||||||
\(753\) | 1.06563e10 | 0.909545 | ||||||||
\(754\) | −1.11677e9 | −0.0948775 | ||||||||
\(755\) | 2.96837e7 | 0.00251017 | ||||||||
\(756\) | −1.15894e8 | −0.00975512 | ||||||||
\(757\) | 1.63068e10 | 1.36626 | 0.683131 | − | 0.730296i | \(-0.260618\pi\) | ||||
0.683131 | + | 0.730296i | \(0.260618\pi\) | |||||||
\(758\) | −8.90118e9 | −0.742345 | ||||||||
\(759\) | −3.91312e8 | −0.0324845 | ||||||||
\(760\) | 4.43758e9 | 0.366689 | ||||||||
\(761\) | 6.14069e9 | 0.505093 | 0.252546 | − | 0.967585i | \(-0.418732\pi\) | ||||
0.252546 | + | 0.967585i | \(0.418732\pi\) | |||||||
\(762\) | −2.71970e9 | −0.222679 | ||||||||
\(763\) | −2.57341e8 | −0.0209736 | ||||||||
\(764\) | −5.22812e9 | −0.424149 | ||||||||
\(765\) | 8.07042e9 | 0.651750 | ||||||||
\(766\) | −4.57158e9 | −0.367507 | ||||||||
\(767\) | −6.65993e9 | −0.532949 | ||||||||
\(768\) | 5.62028e9 | 0.447707 | ||||||||
\(769\) | 2.45069e10 | 1.94333 | 0.971664 | − | 0.236368i | \(-0.0759569\pi\) | ||||
0.971664 | + | 0.236368i | \(0.0759569\pi\) | |||||||
\(770\) | 1.41972e8 | 0.0112069 | ||||||||
\(771\) | 3.85791e9 | 0.303153 | ||||||||
\(772\) | −1.07067e10 | −0.837518 | ||||||||
\(773\) | −1.01722e10 | −0.792110 | −0.396055 | − | 0.918227i | \(-0.629621\pi\) | ||||
−0.396055 | + | 0.918227i | \(0.629621\pi\) | |||||||
\(774\) | 2.99957e9 | 0.232523 | ||||||||
\(775\) | −2.04769e10 | −1.58018 | ||||||||
\(776\) | 1.16514e10 | 0.895080 | ||||||||
\(777\) | 4.64013e8 | 0.0354860 | ||||||||
\(778\) | 9.65411e9 | 0.734994 | ||||||||
\(779\) | 5.42817e9 | 0.411408 | ||||||||
\(780\) | −4.93874e9 | −0.372636 | ||||||||
\(781\) | −5.27148e9 | −0.395962 | ||||||||
\(782\) | −2.60379e9 | −0.194707 | ||||||||
\(783\) | −7.18626e8 | −0.0534979 | ||||||||
\(784\) | −3.15979e9 | −0.234181 | ||||||||
\(785\) | −1.25512e10 | −0.926062 | ||||||||
\(786\) | −2.72594e9 | −0.200234 | ||||||||
\(787\) | −9.79135e9 | −0.716030 | −0.358015 | − | 0.933716i | \(-0.616546\pi\) | ||||
−0.358015 | + | 0.933716i | \(0.616546\pi\) | |||||||
\(788\) | 1.09311e10 | 0.795832 | ||||||||
\(789\) | −1.18865e10 | −0.861558 | ||||||||
\(790\) | −1.61781e10 | −1.16744 | ||||||||
\(791\) | 1.13320e9 | 0.0814124 | ||||||||
\(792\) | 9.12241e8 | 0.0652487 | ||||||||
\(793\) | −1.53277e9 | −0.109150 | ||||||||
\(794\) | 1.12809e10 | 0.799786 | ||||||||
\(795\) | 4.50745e9 | 0.318160 | ||||||||
\(796\) | 8.74098e9 | 0.614277 | ||||||||
\(797\) | −9.75782e9 | −0.682729 | −0.341365 | − | 0.939931i | \(-0.610889\pi\) | ||||
−0.341365 | + | 0.939931i | \(0.610889\pi\) | |||||||
\(798\) | −8.93722e7 | −0.00622576 | ||||||||
\(799\) | 1.65574e10 | 1.14836 | ||||||||
\(800\) | 1.42103e10 | 0.981270 | ||||||||
\(801\) | −6.21714e9 | −0.427442 | ||||||||
\(802\) | 1.61155e9 | 0.110315 | ||||||||
\(803\) | −1.29789e9 | −0.0884572 | ||||||||
\(804\) | −1.25999e9 | −0.0855012 | ||||||||
\(805\) | 3.81588e8 | 0.0257816 | ||||||||
\(806\) | 8.46700e9 | 0.569583 | ||||||||
\(807\) | −7.43592e9 | −0.498055 | ||||||||
\(808\) | −1.58221e10 | −1.05517 | ||||||||
\(809\) | −2.78706e9 | −0.185066 | −0.0925330 | − | 0.995710i | \(-0.529496\pi\) | ||||
−0.0925330 | + | 0.995710i | \(0.529496\pi\) | |||||||
\(810\) | 1.24357e9 | 0.0822192 | ||||||||
\(811\) | −7.99983e9 | −0.526633 | −0.263316 | − | 0.964710i | \(-0.584816\pi\) | ||||
−0.263316 | + | 0.964710i | \(0.584816\pi\) | |||||||
\(812\) | 2.14971e8 | 0.0140907 | ||||||||
\(813\) | 1.14661e10 | 0.748339 | ||||||||
\(814\) | −1.52738e9 | −0.0992569 | ||||||||
\(815\) | 2.27540e10 | 1.47233 | ||||||||
\(816\) | −2.95532e9 | −0.190410 | ||||||||
\(817\) | −5.91135e9 | −0.379236 | ||||||||
\(818\) | 5.39687e8 | 0.0344751 | ||||||||
\(819\) | 2.37852e8 | 0.0151291 | ||||||||
\(820\) | 2.25943e10 | 1.43103 | ||||||||
\(821\) | −1.02402e10 | −0.645813 | −0.322906 | − | 0.946431i | \(-0.604660\pi\) | ||||
−0.322906 | + | 0.946431i | \(0.604660\pi\) | |||||||
\(822\) | −4.54327e9 | −0.285310 | ||||||||
\(823\) | 2.78682e10 | 1.74265 | 0.871324 | − | 0.490707i | \(-0.163262\pi\) | ||||
0.871324 | + | 0.490707i | \(0.163262\pi\) | |||||||
\(824\) | −9.51640e9 | −0.592553 | ||||||||
\(825\) | 1.89346e9 | 0.117400 | ||||||||
\(826\) | −5.01650e8 | −0.0309721 | ||||||||
\(827\) | 2.35125e10 | 1.44554 | 0.722769 | − | 0.691090i | \(-0.242869\pi\) | ||||
0.722769 | + | 0.691090i | \(0.242869\pi\) | |||||||
\(828\) | 1.02534e9 | 0.0627711 | ||||||||
\(829\) | −1.28598e10 | −0.783960 | −0.391980 | − | 0.919974i | \(-0.628210\pi\) | ||||
−0.391980 | + | 0.919974i | \(0.628210\pi\) | |||||||
\(830\) | −1.02416e10 | −0.621719 | ||||||||
\(831\) | −1.39363e10 | −0.842448 | ||||||||
\(832\) | −3.35962e9 | −0.202236 | ||||||||
\(833\) | −2.32608e10 | −1.39434 | ||||||||
\(834\) | 1.91602e9 | 0.114372 | ||||||||
\(835\) | −1.00762e10 | −0.598957 | ||||||||
\(836\) | −7.51802e8 | −0.0445022 | ||||||||
\(837\) | 5.44841e9 | 0.321167 | ||||||||
\(838\) | 1.01433e10 | 0.595420 | ||||||||
\(839\) | −7.99832e9 | −0.467554 | −0.233777 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233777 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(840\) | −8.89574e8 | −0.0517851 | ||||||||
\(841\) | −1.59169e10 | −0.922725 | ||||||||
\(842\) | −6.79996e9 | −0.392567 | ||||||||
\(843\) | 8.39816e9 | 0.482822 | ||||||||
\(844\) | −1.64907e10 | −0.944147 | ||||||||
\(845\) | −1.43360e10 | −0.817389 | ||||||||
\(846\) | 2.55134e9 | 0.144868 | ||||||||
\(847\) | 1.18966e9 | 0.0672716 | ||||||||
\(848\) | −1.65059e9 | −0.0929510 | ||||||||
\(849\) | 1.60463e10 | 0.899909 | ||||||||
\(850\) | 1.25991e10 | 0.703678 | ||||||||
\(851\) | −4.10523e9 | −0.228341 | ||||||||
\(852\) | 1.38126e10 | 0.765133 | ||||||||
\(853\) | 4.20827e9 | 0.232157 | 0.116079 | − | 0.993240i | \(-0.462968\pi\) | ||||
0.116079 | + | 0.993240i | \(0.462968\pi\) | |||||||
\(854\) | −1.15454e8 | −0.00634318 | ||||||||
\(855\) | −2.45075e9 | −0.134097 | ||||||||
\(856\) | −1.50824e10 | −0.821888 | ||||||||
\(857\) | 3.19307e10 | 1.73291 | 0.866453 | − | 0.499259i | \(-0.166394\pi\) | ||||
0.866453 | + | 0.499259i | \(0.166394\pi\) | |||||||
\(858\) | −7.82930e8 | −0.0423173 | ||||||||
\(859\) | 2.18002e10 | 1.17350 | 0.586752 | − | 0.809767i | \(-0.300406\pi\) | ||||
0.586752 | + | 0.809767i | \(0.300406\pi\) | |||||||
\(860\) | −2.46055e10 | −1.31913 | ||||||||
\(861\) | −1.08815e9 | −0.0581004 | ||||||||
\(862\) | 1.31966e10 | 0.701755 | ||||||||
\(863\) | 1.04728e10 | 0.554657 | 0.277329 | − | 0.960775i | \(-0.410551\pi\) | ||||
0.277329 | + | 0.960775i | \(0.410551\pi\) | |||||||
\(864\) | −3.78103e9 | −0.199440 | ||||||||
\(865\) | 2.47728e10 | 1.30142 | ||||||||
\(866\) | −9.10427e8 | −0.0476357 | ||||||||
\(867\) | −1.06765e10 | −0.556368 | ||||||||
\(868\) | −1.62985e9 | −0.0845916 | ||||||||
\(869\) | 6.55421e9 | 0.338806 | ||||||||
\(870\) | −2.30670e9 | −0.118761 | ||||||||
\(871\) | 2.58593e9 | 0.132603 | ||||||||
\(872\) | −5.30765e9 | −0.271078 | ||||||||
\(873\) | −6.43475e9 | −0.327327 | ||||||||
\(874\) | 7.90695e8 | 0.0400608 | ||||||||
\(875\) | 1.03584e8 | 0.00522714 | ||||||||
\(876\) | 3.40080e9 | 0.170929 | ||||||||
\(877\) | −1.77787e10 | −0.890024 | −0.445012 | − | 0.895525i | \(-0.646801\pi\) | ||||
−0.445012 | + | 0.895525i | \(0.646801\pi\) | |||||||
\(878\) | 5.94458e9 | 0.296408 | ||||||||
\(879\) | −3.11890e9 | −0.154896 | ||||||||
\(880\) | −1.42564e9 | −0.0705213 | ||||||||
\(881\) | −7.64253e9 | −0.376549 | −0.188274 | − | 0.982116i | \(-0.560289\pi\) | ||||
−0.188274 | + | 0.982116i | \(0.560289\pi\) | |||||||
\(882\) | −3.58426e9 | −0.175897 | ||||||||
\(883\) | −2.76375e10 | −1.35094 | −0.675472 | − | 0.737386i | \(-0.736060\pi\) | ||||
−0.675472 | + | 0.737386i | \(0.736060\pi\) | |||||||
\(884\) | 1.33135e10 | 0.648200 | ||||||||
\(885\) | −1.37562e10 | −0.667108 | ||||||||
\(886\) | −1.06425e10 | −0.514076 | ||||||||
\(887\) | 3.23087e10 | 1.55449 | 0.777243 | − | 0.629200i | \(-0.216617\pi\) | ||||
0.777243 | + | 0.629200i | \(0.216617\pi\) | |||||||
\(888\) | 9.57027e9 | 0.458647 | ||||||||
\(889\) | −1.07445e9 | −0.0512897 | ||||||||
\(890\) | −1.99562e10 | −0.948886 | ||||||||
\(891\) | −5.03806e8 | −0.0238612 | ||||||||
\(892\) | 1.90014e10 | 0.896414 | ||||||||
\(893\) | −5.02801e9 | −0.236274 | ||||||||
\(894\) | −3.36711e9 | −0.157607 | ||||||||
\(895\) | −3.15728e10 | −1.47208 | ||||||||
\(896\) | 1.32059e9 | 0.0613325 | ||||||||
\(897\) | −2.10433e9 | −0.0973511 | ||||||||
\(898\) | −1.66206e9 | −0.0765914 | ||||||||
\(899\) | −1.01063e10 | −0.463908 | ||||||||
\(900\) | −4.96136e9 | −0.226857 | ||||||||
\(901\) | −1.21509e10 | −0.553439 | ||||||||
\(902\) | 3.58184e9 | 0.162511 | ||||||||
\(903\) | 1.18501e9 | 0.0535570 | ||||||||
\(904\) | 2.33723e10 | 1.05223 | ||||||||
\(905\) | 2.51562e10 | 1.12817 | ||||||||
\(906\) | −1.23301e7 | −0.000550832 0 | ||||||||
\(907\) | 2.27142e10 | 1.01082 | 0.505409 | − | 0.862880i | \(-0.331342\pi\) | ||||
0.505409 | + | 0.862880i | \(0.331342\pi\) | |||||||
\(908\) | −3.99238e9 | −0.176983 | ||||||||
\(909\) | 8.73810e9 | 0.385872 | ||||||||
\(910\) | 7.63476e8 | 0.0335854 | ||||||||
\(911\) | 7.50925e9 | 0.329065 | 0.164533 | − | 0.986372i | \(-0.447388\pi\) | ||||
0.164533 | + | 0.986372i | \(0.447388\pi\) | |||||||
\(912\) | 8.97445e8 | 0.0391765 | ||||||||
\(913\) | 4.14916e9 | 0.180431 | ||||||||
\(914\) | 1.76855e10 | 0.766136 | ||||||||
\(915\) | −3.16597e9 | −0.136626 | ||||||||
\(916\) | 3.32976e9 | 0.143146 | ||||||||
\(917\) | −1.07691e9 | −0.0461199 | ||||||||
\(918\) | −3.35233e9 | −0.143020 | ||||||||
\(919\) | −2.49374e10 | −1.05986 | −0.529928 | − | 0.848043i | \(-0.677781\pi\) | ||||
−0.529928 | + | 0.848043i | \(0.677781\pi\) | |||||||
\(920\) | 7.87026e9 | 0.333221 | ||||||||
\(921\) | 7.03619e9 | 0.296776 | ||||||||
\(922\) | −1.66012e10 | −0.697561 | ||||||||
\(923\) | −2.83481e10 | −1.18664 | ||||||||
\(924\) | 1.50709e8 | 0.00628475 | ||||||||
\(925\) | 1.98642e10 | 0.825230 | ||||||||
\(926\) | 2.78132e9 | 0.115110 | ||||||||
\(927\) | 5.25565e9 | 0.216694 | ||||||||
\(928\) | 7.01342e9 | 0.288079 | ||||||||
\(929\) | −8.66205e9 | −0.354459 | −0.177229 | − | 0.984170i | \(-0.556713\pi\) | ||||
−0.177229 | + | 0.984170i | \(0.556713\pi\) | |||||||
\(930\) | 1.74887e10 | 0.712965 | ||||||||
\(931\) | 7.06363e9 | 0.286883 | ||||||||
\(932\) | −8.48559e9 | −0.343342 | ||||||||
\(933\) | −1.55735e10 | −0.627768 | ||||||||
\(934\) | −2.50753e9 | −0.100701 | ||||||||
\(935\) | −1.04949e10 | −0.419891 | ||||||||
\(936\) | 4.90570e9 | 0.195540 | ||||||||
\(937\) | 2.82655e10 | 1.12245 | 0.561226 | − | 0.827663i | \(-0.310330\pi\) | ||||
0.561226 | + | 0.827663i | \(0.310330\pi\) | |||||||
\(938\) | 1.94782e8 | 0.00770616 | ||||||||
\(939\) | 1.24220e10 | 0.489623 | ||||||||
\(940\) | −2.09287e10 | −0.821853 | ||||||||
\(941\) | −4.67082e10 | −1.82738 | −0.913691 | − | 0.406410i | \(-0.866780\pi\) | ||||
−0.913691 | + | 0.406410i | \(0.866780\pi\) | |||||||
\(942\) | 5.21356e9 | 0.203215 | ||||||||
\(943\) | 9.62713e9 | 0.373857 | ||||||||
\(944\) | 5.03740e9 | 0.194897 | ||||||||
\(945\) | 4.91288e8 | 0.0189376 | ||||||||
\(946\) | −3.90067e9 | −0.149803 | ||||||||
\(947\) | −4.67392e10 | −1.78837 | −0.894184 | − | 0.447701i | \(-0.852243\pi\) | ||||
−0.894184 | + | 0.447701i | \(0.852243\pi\) | |||||||
\(948\) | −1.71737e10 | −0.654688 | ||||||||
\(949\) | −6.97958e9 | −0.265093 | ||||||||
\(950\) | −3.82599e9 | −0.144781 | ||||||||
\(951\) | −1.68902e9 | −0.0636798 | ||||||||
\(952\) | 2.39805e9 | 0.0900801 | ||||||||
\(953\) | 3.82420e10 | 1.43125 | 0.715625 | − | 0.698484i | \(-0.246142\pi\) | ||||
0.715625 | + | 0.698484i | \(0.246142\pi\) | |||||||
\(954\) | −1.87233e9 | −0.0698171 | ||||||||
\(955\) | 2.21627e10 | 0.823399 | ||||||||
\(956\) | −4.58591e9 | −0.169755 | ||||||||
\(957\) | 9.34510e8 | 0.0344661 | ||||||||
\(958\) | −9.05837e9 | −0.332867 | ||||||||
\(959\) | −1.79487e9 | −0.0657157 | ||||||||
\(960\) | −6.93935e9 | −0.253145 | ||||||||
\(961\) | 4.91101e10 | 1.78500 | ||||||||
\(962\) | −8.21367e9 | −0.297457 | ||||||||
\(963\) | 8.32961e9 | 0.300561 | ||||||||
\(964\) | −1.83424e10 | −0.659457 | ||||||||
\(965\) | 4.53870e10 | 1.62587 | ||||||||
\(966\) | −1.58506e8 | −0.00565752 | ||||||||
\(967\) | −4.90012e10 | −1.74267 | −0.871333 | − | 0.490692i | \(-0.836744\pi\) | ||||
−0.871333 | + | 0.490692i | \(0.836744\pi\) | |||||||
\(968\) | 2.45368e10 | 0.869468 | ||||||||
\(969\) | 6.60656e9 | 0.233261 | ||||||||
\(970\) | −2.06547e10 | −0.726639 | ||||||||
\(971\) | 2.72929e10 | 0.956713 | 0.478357 | − | 0.878166i | \(-0.341233\pi\) | ||||
0.478357 | + | 0.878166i | \(0.341233\pi\) | |||||||
\(972\) | 1.32010e9 | 0.0461078 | ||||||||
\(973\) | 7.56947e8 | 0.0263433 | ||||||||
\(974\) | 5.57676e9 | 0.193386 | ||||||||
\(975\) | 1.01824e10 | 0.351830 | ||||||||
\(976\) | 1.15935e9 | 0.0399155 | ||||||||
\(977\) | 3.94482e9 | 0.135331 | 0.0676653 | − | 0.997708i | \(-0.478445\pi\) | ||||
0.0676653 | + | 0.997708i | \(0.478445\pi\) | |||||||
\(978\) | −9.45165e9 | −0.323088 | ||||||||
\(979\) | 8.08484e9 | 0.275380 | ||||||||
\(980\) | 2.94018e10 | 0.997889 | ||||||||
\(981\) | 2.93127e9 | 0.0991322 | ||||||||
\(982\) | 3.07682e10 | 1.03684 | ||||||||
\(983\) | 4.74320e8 | 0.0159270 | 0.00796351 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796351 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(984\) | −2.24431e10 | −0.750933 | ||||||||
\(985\) | −4.63383e10 | −1.54494 | ||||||||
\(986\) | 6.21824e9 | 0.206585 | ||||||||
\(987\) | 1.00794e9 | 0.0333674 | ||||||||
\(988\) | −4.04292e9 | −0.133366 | ||||||||
\(989\) | −1.04841e10 | −0.344622 | ||||||||
\(990\) | −1.61716e9 | −0.0529698 | ||||||||
\(991\) | 1.22197e10 | 0.398843 | 0.199421 | − | 0.979914i | \(-0.436094\pi\) | ||||
0.199421 | + | 0.979914i | \(0.436094\pi\) | |||||||
\(992\) | −5.31737e10 | −1.72944 | ||||||||
\(993\) | −1.84744e10 | −0.598752 | ||||||||
\(994\) | −2.13528e9 | −0.0689609 | ||||||||
\(995\) | −3.70541e10 | −1.19249 | ||||||||
\(996\) | −1.08718e10 | −0.348655 | ||||||||
\(997\) | −3.60690e10 | −1.15266 | −0.576330 | − | 0.817217i | \(-0.695516\pi\) | ||||
−0.576330 | + | 0.817217i | \(0.695516\pi\) | |||||||
\(998\) | −2.46390e9 | −0.0784631 | ||||||||
\(999\) | −5.28540e9 | −0.167725 |
(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 | 3.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.8.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.8.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 75.8.b.c.49.2 | 2 | |||
5.3 | odd | 4 | 75.8.b.c.49.1 | 2 | |||
5.4 | even | 2 | 75.8.a.a.1.1 | 1 | |||
7.2 | even | 3 | 147.8.e.b.67.1 | 2 | |||
7.3 | odd | 6 | 147.8.e.a.79.1 | 2 | |||
7.4 | even | 3 | 147.8.e.b.79.1 | 2 | |||
7.5 | odd | 6 | 147.8.e.a.67.1 | 2 | |||
7.6 | odd | 2 | 147.8.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 192.8.a.a.1.1 | 1 | |||
8.5 | even | 2 | 192.8.a.i.1.1 | 1 | |||
9.2 | odd | 6 | 81.8.c.c.28.1 | 2 | |||
9.4 | even | 3 | 81.8.c.a.55.1 | 2 | |||
9.5 | odd | 6 | 81.8.c.c.55.1 | 2 | |||
9.7 | even | 3 | 81.8.c.a.28.1 | 2 | |||
11.10 | odd | 2 | 363.8.a.b.1.1 | 1 | |||
12.11 | even | 2 | 144.8.a.b.1.1 | 1 | |||
13.12 | even | 2 | 507.8.a.a.1.1 | 1 | |||
15.2 | even | 4 | 225.8.b.f.199.1 | 2 | |||
15.8 | even | 4 | 225.8.b.f.199.2 | 2 | |||
15.14 | odd | 2 | 225.8.a.i.1.1 | 1 | |||
21.20 | even | 2 | 441.8.a.a.1.1 | 1 | |||
24.5 | odd | 2 | 576.8.a.w.1.1 | 1 | |||
24.11 | even | 2 | 576.8.a.x.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.8.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
75.8.a.a.1.1 | 1 | 5.4 | even | 2 | |||
75.8.b.c.49.1 | 2 | 5.3 | odd | 4 | |||
75.8.b.c.49.2 | 2 | 5.2 | odd | 4 | |||
81.8.c.a.28.1 | 2 | 9.7 | even | 3 | |||
81.8.c.a.55.1 | 2 | 9.4 | even | 3 | |||
81.8.c.c.28.1 | 2 | 9.2 | odd | 6 | |||
81.8.c.c.55.1 | 2 | 9.5 | odd | 6 | |||
144.8.a.b.1.1 | 1 | 12.11 | even | 2 | |||
147.8.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
147.8.e.a.67.1 | 2 | 7.5 | odd | 6 | |||
147.8.e.a.79.1 | 2 | 7.3 | odd | 6 | |||
147.8.e.b.67.1 | 2 | 7.2 | even | 3 | |||
147.8.e.b.79.1 | 2 | 7.4 | even | 3 | |||
192.8.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
192.8.a.i.1.1 | 1 | 8.5 | even | 2 | |||
225.8.a.i.1.1 | 1 | 15.14 | odd | 2 | |||
225.8.b.f.199.1 | 2 | 15.2 | even | 4 | |||
225.8.b.f.199.2 | 2 | 15.8 | even | 4 | |||
363.8.a.b.1.1 | 1 | 11.10 | odd | 2 | |||
441.8.a.a.1.1 | 1 | 21.20 | even | 2 | |||
507.8.a.a.1.1 | 1 | 13.12 | even | 2 | |||
576.8.a.w.1.1 | 1 | 24.5 | odd | 2 | |||
576.8.a.x.1.1 | 1 | 24.11 | even | 2 |