Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.28530 | −0.160984 | −0.0804920 | − | 0.996755i | \(-0.525649\pi\) | ||||
−0.0804920 | + | 0.996755i | \(0.525649\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1994.92 | −0.974084 | ||||||||
\(5\) | 6136.55 | 0.878192 | 0.439096 | − | 0.898440i | \(-0.355299\pi\) | ||||
0.439096 | + | 0.898440i | \(0.355299\pi\) | |||||||
\(6\) | −1770.33 | −0.0929441 | ||||||||
\(7\) | −33718.8 | −0.758287 | −0.379143 | − | 0.925338i | \(-0.623781\pi\) | ||||
−0.379143 | + | 0.925338i | \(0.623781\pi\) | |||||||
\(8\) | 29453.9 | 0.317796 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −44706.7 | −0.141375 | ||||||||
\(11\) | 984083. | 1.84235 | 0.921174 | − | 0.389150i | \(-0.127231\pi\) | ||||
0.921174 | + | 0.389150i | \(0.127231\pi\) | |||||||
\(12\) | −484767. | −0.562388 | ||||||||
\(13\) | −2.05640e6 | −1.53610 | −0.768048 | − | 0.640393i | \(-0.778772\pi\) | ||||
−0.768048 | + | 0.640393i | \(0.778772\pi\) | |||||||
\(14\) | 245652. | 0.122072 | ||||||||
\(15\) | 1.49118e6 | 0.507025 | ||||||||
\(16\) | 3.87102e6 | 0.922924 | ||||||||
\(17\) | 6.23478e6 | 1.06501 | 0.532503 | − | 0.846428i | \(-0.321252\pi\) | ||||
0.532503 | + | 0.846428i | \(0.321252\pi\) | |||||||
\(18\) | −430190. | −0.0536613 | ||||||||
\(19\) | 175904. | 0.0162979 | 0.00814893 | − | 0.999967i | \(-0.497406\pi\) | ||||
0.00814893 | + | 0.999967i | \(0.497406\pi\) | |||||||
\(20\) | −1.22420e7 | −0.855433 | ||||||||
\(21\) | −8.19368e6 | −0.437797 | ||||||||
\(22\) | −7.16934e6 | −0.296589 | ||||||||
\(23\) | 8.59617e6 | 0.278485 | 0.139242 | − | 0.990258i | \(-0.455533\pi\) | ||||
0.139242 | + | 0.990258i | \(0.455533\pi\) | |||||||
\(24\) | 7.15730e6 | 0.183480 | ||||||||
\(25\) | −1.11708e7 | −0.228778 | ||||||||
\(26\) | 1.49815e7 | 0.247287 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 6.72665e7 | 0.738635 | ||||||||
\(29\) | −9.86614e7 | −0.893219 | −0.446610 | − | 0.894729i | \(-0.647369\pi\) | ||||
−0.446610 | + | 0.894729i | \(0.647369\pi\) | |||||||
\(30\) | −1.08637e7 | −0.0816228 | ||||||||
\(31\) | 3.66929e7 | 0.230193 | 0.115097 | − | 0.993354i | \(-0.463282\pi\) | ||||
0.115097 | + | 0.993354i | \(0.463282\pi\) | |||||||
\(32\) | −8.85232e7 | −0.466372 | ||||||||
\(33\) | 2.39132e8 | 1.06368 | ||||||||
\(34\) | −4.54223e7 | −0.171449 | ||||||||
\(35\) | −2.06917e8 | −0.665921 | ||||||||
\(36\) | −1.17798e8 | −0.324695 | ||||||||
\(37\) | 5.41747e8 | 1.28436 | 0.642181 | − | 0.766553i | \(-0.278030\pi\) | ||||
0.642181 | + | 0.766553i | \(0.278030\pi\) | |||||||
\(38\) | −1.28151e6 | −0.00262369 | ||||||||
\(39\) | −4.99704e8 | −0.886865 | ||||||||
\(40\) | 1.80746e8 | 0.279086 | ||||||||
\(41\) | −2.76260e8 | −0.372397 | −0.186199 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186199 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(42\) | 5.96934e7 | 0.0704783 | ||||||||
\(43\) | −4.46177e8 | −0.462839 | −0.231420 | − | 0.972854i | \(-0.574337\pi\) | ||||
−0.231420 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(44\) | −1.96317e9 | −1.79460 | ||||||||
\(45\) | 3.62357e8 | 0.292731 | ||||||||
\(46\) | −6.26257e7 | −0.0448316 | ||||||||
\(47\) | 1.06691e8 | 0.0678564 | 0.0339282 | − | 0.999424i | \(-0.489198\pi\) | ||||
0.0339282 | + | 0.999424i | \(0.489198\pi\) | |||||||
\(48\) | 9.40659e8 | 0.532850 | ||||||||
\(49\) | −8.40367e8 | −0.425002 | ||||||||
\(50\) | 8.13828e7 | 0.0368296 | ||||||||
\(51\) | 1.51505e9 | 0.614881 | ||||||||
\(52\) | 4.10235e9 | 1.49629 | ||||||||
\(53\) | −2.52362e8 | −0.0828910 | −0.0414455 | − | 0.999141i | \(-0.513196\pi\) | ||||
−0.0414455 | + | 0.999141i | \(0.513196\pi\) | |||||||
\(54\) | −1.04536e8 | −0.0309814 | ||||||||
\(55\) | 6.03888e9 | 1.61794 | ||||||||
\(56\) | −9.93152e8 | −0.240980 | ||||||||
\(57\) | 4.27446e7 | 0.00940957 | ||||||||
\(58\) | 7.18778e8 | 0.143794 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −2.97480e9 | −0.493885 | ||||||||
\(61\) | 1.18084e10 | 1.79009 | 0.895046 | − | 0.445974i | \(-0.147143\pi\) | ||||
0.895046 | + | 0.445974i | \(0.147143\pi\) | |||||||
\(62\) | −2.67319e8 | −0.0370574 | ||||||||
\(63\) | −1.99106e9 | −0.252762 | ||||||||
\(64\) | −7.28294e9 | −0.847846 | ||||||||
\(65\) | −1.26192e10 | −1.34899 | ||||||||
\(66\) | −1.74215e9 | −0.171236 | ||||||||
\(67\) | −3.55842e9 | −0.321992 | −0.160996 | − | 0.986955i | \(-0.551471\pi\) | ||||
−0.160996 | + | 0.986955i | \(0.551471\pi\) | |||||||
\(68\) | −1.24379e10 | −1.03741 | ||||||||
\(69\) | 2.08887e9 | 0.160783 | ||||||||
\(70\) | 1.50746e9 | 0.107203 | ||||||||
\(71\) | −3.31645e9 | −0.218149 | −0.109074 | − | 0.994034i | \(-0.534789\pi\) | ||||
−0.109074 | + | 0.994034i | \(0.534789\pi\) | |||||||
\(72\) | 1.73923e9 | 0.105932 | ||||||||
\(73\) | −8.37143e9 | −0.472633 | −0.236316 | − | 0.971676i | \(-0.575940\pi\) | ||||
−0.236316 | + | 0.971676i | \(0.575940\pi\) | |||||||
\(74\) | −3.94679e9 | −0.206762 | ||||||||
\(75\) | −2.71451e9 | −0.132085 | ||||||||
\(76\) | −3.50915e8 | −0.0158755 | ||||||||
\(77\) | −3.31821e10 | −1.39703 | ||||||||
\(78\) | 3.64050e9 | 0.142771 | ||||||||
\(79\) | −2.44696e9 | −0.0894700 | −0.0447350 | − | 0.998999i | \(-0.514244\pi\) | ||||
−0.0447350 | + | 0.998999i | \(0.514244\pi\) | |||||||
\(80\) | 2.37548e10 | 0.810505 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 2.01264e9 | 0.0599500 | ||||||||
\(83\) | 5.29385e10 | 1.47517 | 0.737585 | − | 0.675255i | \(-0.235966\pi\) | ||||
0.737585 | + | 0.675255i | \(0.235966\pi\) | |||||||
\(84\) | 1.63458e10 | 0.426451 | ||||||||
\(85\) | 3.82601e10 | 0.935280 | ||||||||
\(86\) | 3.25053e9 | 0.0745097 | ||||||||
\(87\) | −2.39747e10 | −0.515700 | ||||||||
\(88\) | 2.89851e10 | 0.585491 | ||||||||
\(89\) | 5.01235e10 | 0.951473 | 0.475737 | − | 0.879588i | \(-0.342182\pi\) | ||||
0.475737 | + | 0.879588i | \(0.342182\pi\) | |||||||
\(90\) | −2.63988e9 | −0.0471250 | ||||||||
\(91\) | 6.93393e10 | 1.16480 | ||||||||
\(92\) | −1.71487e10 | −0.271268 | ||||||||
\(93\) | 8.91637e9 | 0.132902 | ||||||||
\(94\) | −7.77278e8 | −0.0109238 | ||||||||
\(95\) | 1.07944e9 | 0.0143126 | ||||||||
\(96\) | −2.15111e10 | −0.269260 | ||||||||
\(97\) | −9.10022e10 | −1.07599 | −0.537994 | − | 0.842949i | \(-0.680818\pi\) | ||||
−0.537994 | + | 0.842949i | \(0.680818\pi\) | |||||||
\(98\) | 6.12233e9 | 0.0684184 | ||||||||
\(99\) | 5.81091e10 | 0.614116 | ||||||||
\(100\) | 2.22849e10 | 0.222849 | ||||||||
\(101\) | 8.70346e10 | 0.823995 | 0.411997 | − | 0.911185i | \(-0.364831\pi\) | ||||
0.411997 | + | 0.911185i | \(0.364831\pi\) | |||||||
\(102\) | −1.10376e10 | −0.0989860 | ||||||||
\(103\) | 7.17170e10 | 0.609561 | 0.304781 | − | 0.952423i | \(-0.401417\pi\) | ||||
0.304781 | + | 0.952423i | \(0.401417\pi\) | |||||||
\(104\) | −6.05689e10 | −0.488165 | ||||||||
\(105\) | −5.02809e10 | −0.384470 | ||||||||
\(106\) | 1.83854e9 | 0.0133441 | ||||||||
\(107\) | −1.58378e11 | −1.09165 | −0.545825 | − | 0.837899i | \(-0.683784\pi\) | ||||
−0.545825 | + | 0.837899i | \(0.683784\pi\) | |||||||
\(108\) | −2.86250e10 | −0.187463 | ||||||||
\(109\) | 7.66736e10 | 0.477310 | 0.238655 | − | 0.971104i | \(-0.423294\pi\) | ||||
0.238655 | + | 0.971104i | \(0.423294\pi\) | |||||||
\(110\) | −4.39951e10 | −0.260462 | ||||||||
\(111\) | 1.31645e11 | 0.741526 | ||||||||
\(112\) | −1.30526e11 | −0.699841 | ||||||||
\(113\) | −6.87594e10 | −0.351075 | −0.175538 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175538 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(114\) | −3.11408e8 | −0.00151479 | ||||||||
\(115\) | 5.27508e10 | 0.244563 | ||||||||
\(116\) | 1.96822e11 | 0.870071 | ||||||||
\(117\) | −1.21428e11 | −0.512032 | ||||||||
\(118\) | −5.20844e9 | −0.0209583 | ||||||||
\(119\) | −2.10229e11 | −0.807580 | ||||||||
\(120\) | 4.39212e10 | 0.161130 | ||||||||
\(121\) | 6.83107e11 | 2.39425 | ||||||||
\(122\) | −8.60275e10 | −0.288176 | ||||||||
\(123\) | −6.71312e10 | −0.215004 | ||||||||
\(124\) | −7.31995e10 | −0.224228 | ||||||||
\(125\) | −3.68187e11 | −1.07910 | ||||||||
\(126\) | 1.45055e10 | 0.0406907 | ||||||||
\(127\) | 3.88670e11 | 1.04390 | 0.521952 | − | 0.852975i | \(-0.325204\pi\) | ||||
0.521952 | + | 0.852975i | \(0.325204\pi\) | |||||||
\(128\) | 2.34354e11 | 0.602861 | ||||||||
\(129\) | −1.08421e11 | −0.267220 | ||||||||
\(130\) | 9.19346e10 | 0.217165 | ||||||||
\(131\) | −4.12904e11 | −0.935097 | −0.467549 | − | 0.883967i | \(-0.654863\pi\) | ||||
−0.467549 | + | 0.883967i | \(0.654863\pi\) | |||||||
\(132\) | −4.77050e11 | −1.03611 | ||||||||
\(133\) | −5.93127e9 | −0.0123584 | ||||||||
\(134\) | 2.59242e10 | 0.0518356 | ||||||||
\(135\) | 8.80529e10 | 0.169008 | ||||||||
\(136\) | 1.83639e11 | 0.338454 | ||||||||
\(137\) | 3.63576e11 | 0.643624 | 0.321812 | − | 0.946804i | \(-0.395708\pi\) | ||||
0.321812 | + | 0.946804i | \(0.395708\pi\) | |||||||
\(138\) | −1.52180e10 | −0.0258835 | ||||||||
\(139\) | 1.27317e11 | 0.208115 | 0.104057 | − | 0.994571i | \(-0.466817\pi\) | ||||
0.104057 | + | 0.994571i | \(0.466817\pi\) | |||||||
\(140\) | 4.12785e11 | 0.648663 | ||||||||
\(141\) | 2.59260e10 | 0.0391769 | ||||||||
\(142\) | 2.41614e10 | 0.0351185 | ||||||||
\(143\) | −2.02366e12 | −2.83002 | ||||||||
\(144\) | 2.28580e11 | 0.307641 | ||||||||
\(145\) | −6.05441e11 | −0.784418 | ||||||||
\(146\) | 6.09884e10 | 0.0760863 | ||||||||
\(147\) | −2.04209e11 | −0.245375 | ||||||||
\(148\) | −1.08074e12 | −1.25108 | ||||||||
\(149\) | 3.81557e11 | 0.425633 | 0.212816 | − | 0.977092i | \(-0.431736\pi\) | ||||
0.212816 | + | 0.977092i | \(0.431736\pi\) | |||||||
\(150\) | 1.97760e10 | 0.0212636 | ||||||||
\(151\) | 6.92029e10 | 0.0717383 | 0.0358691 | − | 0.999356i | \(-0.488580\pi\) | ||||
0.0358691 | + | 0.999356i | \(0.488580\pi\) | |||||||
\(152\) | 5.18106e9 | 0.00517939 | ||||||||
\(153\) | 3.68157e11 | 0.355002 | ||||||||
\(154\) | 2.41742e11 | 0.224899 | ||||||||
\(155\) | 2.25168e11 | 0.202154 | ||||||||
\(156\) | 9.96872e11 | 0.863881 | ||||||||
\(157\) | 1.78601e12 | 1.49429 | 0.747145 | − | 0.664661i | \(-0.231424\pi\) | ||||
0.747145 | + | 0.664661i | \(0.231424\pi\) | |||||||
\(158\) | 1.78268e10 | 0.0144032 | ||||||||
\(159\) | −6.13241e10 | −0.0478572 | ||||||||
\(160\) | −5.43228e11 | −0.409564 | ||||||||
\(161\) | −2.89853e11 | −0.211171 | ||||||||
\(162\) | −2.54023e10 | −0.0178871 | ||||||||
\(163\) | 1.34003e12 | 0.912182 | 0.456091 | − | 0.889933i | \(-0.349249\pi\) | ||||
0.456091 | + | 0.889933i | \(0.349249\pi\) | |||||||
\(164\) | 5.51118e11 | 0.362746 | ||||||||
\(165\) | 1.46745e12 | 0.934116 | ||||||||
\(166\) | −3.85673e11 | −0.237479 | ||||||||
\(167\) | −7.41664e11 | −0.441842 | −0.220921 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220921 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(168\) | −2.41336e11 | −0.139130 | ||||||||
\(169\) | 2.43660e12 | 1.35959 | ||||||||
\(170\) | −2.78736e11 | −0.150565 | ||||||||
\(171\) | 1.03869e10 | 0.00543262 | ||||||||
\(172\) | 8.90089e11 | 0.450844 | ||||||||
\(173\) | 3.52135e12 | 1.72765 | 0.863825 | − | 0.503791i | \(-0.168062\pi\) | ||||
0.863825 | + | 0.503791i | \(0.168062\pi\) | |||||||
\(174\) | 1.74663e11 | 0.0830195 | ||||||||
\(175\) | 3.76667e11 | 0.173480 | ||||||||
\(176\) | 3.80941e12 | 1.70035 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | −3.65165e11 | −0.153172 | ||||||||
\(179\) | 3.10316e12 | 1.26215 | 0.631077 | − | 0.775720i | \(-0.282613\pi\) | ||||
0.631077 | + | 0.775720i | \(0.282613\pi\) | |||||||
\(180\) | −7.22876e11 | −0.285144 | ||||||||
\(181\) | 2.94843e12 | 1.12813 | 0.564064 | − | 0.825731i | \(-0.309237\pi\) | ||||
0.564064 | + | 0.825731i | \(0.309237\pi\) | |||||||
\(182\) | −5.05158e11 | −0.187514 | ||||||||
\(183\) | 2.86943e12 | 1.03351 | ||||||||
\(184\) | 2.53191e11 | 0.0885014 | ||||||||
\(185\) | 3.32446e12 | 1.12792 | ||||||||
\(186\) | −6.49584e10 | −0.0213951 | ||||||||
\(187\) | 6.13554e12 | 1.96211 | ||||||||
\(188\) | −2.12841e11 | −0.0660978 | ||||||||
\(189\) | −4.83828e11 | −0.145932 | ||||||||
\(190\) | −7.86407e9 | −0.00230411 | ||||||||
\(191\) | 1.24738e12 | 0.355072 | 0.177536 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177536 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(192\) | −1.76975e12 | −0.489504 | ||||||||
\(193\) | 3.29097e12 | 0.884625 | 0.442313 | − | 0.896861i | \(-0.354158\pi\) | ||||
0.442313 | + | 0.896861i | \(0.354158\pi\) | |||||||
\(194\) | 6.62979e11 | 0.173217 | ||||||||
\(195\) | −3.06646e12 | −0.778838 | ||||||||
\(196\) | 1.67647e12 | 0.413987 | ||||||||
\(197\) | 6.40666e12 | 1.53839 | 0.769197 | − | 0.639012i | \(-0.220657\pi\) | ||||
0.769197 | + | 0.639012i | \(0.220657\pi\) | |||||||
\(198\) | −4.23342e11 | −0.0988629 | ||||||||
\(199\) | −7.08530e12 | −1.60941 | −0.804704 | − | 0.593676i | \(-0.797676\pi\) | ||||
−0.804704 | + | 0.593676i | \(0.797676\pi\) | |||||||
\(200\) | −3.29024e11 | −0.0727048 | ||||||||
\(201\) | −8.64695e11 | −0.185902 | ||||||||
\(202\) | −6.34074e11 | −0.132650 | ||||||||
\(203\) | 3.32675e12 | 0.677316 | ||||||||
\(204\) | −3.02241e12 | −0.598946 | ||||||||
\(205\) | −1.69528e12 | −0.327037 | ||||||||
\(206\) | −5.22480e11 | −0.0981296 | ||||||||
\(207\) | 5.07595e11 | 0.0928283 | ||||||||
\(208\) | −7.96036e12 | −1.41770 | ||||||||
\(209\) | 1.73104e11 | 0.0300263 | ||||||||
\(210\) | 3.66312e11 | 0.0618935 | ||||||||
\(211\) | 7.38091e12 | 1.21494 | 0.607472 | − | 0.794341i | \(-0.292184\pi\) | ||||
0.607472 | + | 0.794341i | \(0.292184\pi\) | |||||||
\(212\) | 5.03444e11 | 0.0807428 | ||||||||
\(213\) | −8.05898e11 | −0.125948 | ||||||||
\(214\) | 1.15383e12 | 0.175738 | ||||||||
\(215\) | −2.73799e12 | −0.406462 | ||||||||
\(216\) | 4.22632e11 | 0.0611599 | ||||||||
\(217\) | −1.23724e12 | −0.174552 | ||||||||
\(218\) | −5.58591e11 | −0.0768392 | ||||||||
\(219\) | −2.03426e12 | −0.272875 | ||||||||
\(220\) | −1.20471e13 | −1.57601 | ||||||||
\(221\) | −1.28212e13 | −1.63595 | ||||||||
\(222\) | −9.59071e11 | −0.119374 | ||||||||
\(223\) | 1.50922e13 | 1.83263 | 0.916315 | − | 0.400459i | \(-0.131149\pi\) | ||||
0.916315 | + | 0.400459i | \(0.131149\pi\) | |||||||
\(224\) | 2.98490e12 | 0.353644 | ||||||||
\(225\) | −6.59626e11 | −0.0762594 | ||||||||
\(226\) | 5.00933e11 | 0.0565175 | ||||||||
\(227\) | 1.46411e13 | 1.61224 | 0.806121 | − | 0.591751i | \(-0.201563\pi\) | ||||
0.806121 | + | 0.591751i | \(0.201563\pi\) | |||||||
\(228\) | −8.52723e10 | −0.00916571 | ||||||||
\(229\) | 1.33878e13 | 1.40480 | 0.702398 | − | 0.711784i | \(-0.252113\pi\) | ||||
0.702398 | + | 0.711784i | \(0.252113\pi\) | |||||||
\(230\) | −3.84306e11 | −0.0393708 | ||||||||
\(231\) | −8.06326e12 | −0.806575 | ||||||||
\(232\) | −2.90597e12 | −0.283861 | ||||||||
\(233\) | 1.61708e13 | 1.54268 | 0.771339 | − | 0.636425i | \(-0.219587\pi\) | ||||
0.771339 | + | 0.636425i | \(0.219587\pi\) | |||||||
\(234\) | 8.84640e11 | 0.0824289 | ||||||||
\(235\) | 6.54717e11 | 0.0595910 | ||||||||
\(236\) | −1.42622e12 | −0.126815 | ||||||||
\(237\) | −5.94611e11 | −0.0516555 | ||||||||
\(238\) | 1.53159e12 | 0.130007 | ||||||||
\(239\) | −3.64028e12 | −0.301958 | −0.150979 | − | 0.988537i | \(-0.548243\pi\) | ||||
−0.150979 | + | 0.988537i | \(0.548243\pi\) | |||||||
\(240\) | 5.77241e12 | 0.467945 | ||||||||
\(241\) | 2.03587e12 | 0.161308 | 0.0806540 | − | 0.996742i | \(-0.474299\pi\) | ||||
0.0806540 | + | 0.996742i | \(0.474299\pi\) | |||||||
\(242\) | −4.97664e12 | −0.385436 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −2.35568e13 | −1.74370 | ||||||||
\(245\) | −5.15696e12 | −0.373233 | ||||||||
\(246\) | 4.89071e11 | 0.0346122 | ||||||||
\(247\) | −3.61728e11 | −0.0250351 | ||||||||
\(248\) | 1.08075e12 | 0.0731544 | ||||||||
\(249\) | 1.28640e13 | 0.851689 | ||||||||
\(250\) | 2.68235e12 | 0.173718 | ||||||||
\(251\) | −7.68200e12 | −0.486708 | −0.243354 | − | 0.969937i | \(-0.578248\pi\) | ||||
−0.243354 | + | 0.969937i | \(0.578248\pi\) | |||||||
\(252\) | 3.97202e12 | 0.246212 | ||||||||
\(253\) | 8.45934e12 | 0.513066 | ||||||||
\(254\) | −2.83158e12 | −0.168052 | ||||||||
\(255\) | 9.29719e12 | 0.539984 | ||||||||
\(256\) | 1.32081e13 | 0.750795 | ||||||||
\(257\) | −3.17374e13 | −1.76579 | −0.882895 | − | 0.469571i | \(-0.844409\pi\) | ||||
−0.882895 | + | 0.469571i | \(0.844409\pi\) | |||||||
\(258\) | 7.89879e11 | 0.0430182 | ||||||||
\(259\) | −1.82671e13 | −0.973914 | ||||||||
\(260\) | 2.51743e13 | 1.31403 | ||||||||
\(261\) | −5.82586e12 | −0.297740 | ||||||||
\(262\) | 3.00813e12 | 0.150536 | ||||||||
\(263\) | −1.09978e13 | −0.538949 | −0.269474 | − | 0.963008i | \(-0.586850\pi\) | ||||
−0.269474 | + | 0.963008i | \(0.586850\pi\) | |||||||
\(264\) | 7.04338e12 | 0.338033 | ||||||||
\(265\) | −1.54864e12 | −0.0727943 | ||||||||
\(266\) | 4.32111e10 | 0.00198951 | ||||||||
\(267\) | 1.21800e13 | 0.549333 | ||||||||
\(268\) | 7.09877e12 | 0.313648 | ||||||||
\(269\) | 5.20193e12 | 0.225178 | 0.112589 | − | 0.993642i | \(-0.464086\pi\) | ||||
0.112589 | + | 0.993642i | \(0.464086\pi\) | |||||||
\(270\) | −6.41492e11 | −0.0272076 | ||||||||
\(271\) | −3.29168e13 | −1.36800 | −0.684001 | − | 0.729481i | \(-0.739761\pi\) | ||||
−0.684001 | + | 0.729481i | \(0.739761\pi\) | |||||||
\(272\) | 2.41350e13 | 0.982919 | ||||||||
\(273\) | 1.68494e13 | 0.672498 | ||||||||
\(274\) | −2.64876e12 | −0.103613 | ||||||||
\(275\) | −1.09930e13 | −0.421489 | ||||||||
\(276\) | −4.16713e12 | −0.156617 | ||||||||
\(277\) | −4.92559e13 | −1.81476 | −0.907380 | − | 0.420310i | \(-0.861921\pi\) | ||||
−0.907380 | + | 0.420310i | \(0.861921\pi\) | |||||||
\(278\) | −9.27539e11 | −0.0335032 | ||||||||
\(279\) | 2.16668e12 | 0.0767311 | ||||||||
\(280\) | −6.09453e12 | −0.211627 | ||||||||
\(281\) | 4.51468e13 | 1.53724 | 0.768621 | − | 0.639705i | \(-0.220943\pi\) | ||||
0.768621 | + | 0.639705i | \(0.220943\pi\) | |||||||
\(282\) | −1.88879e11 | −0.00630685 | ||||||||
\(283\) | −4.94712e13 | −1.62004 | −0.810022 | − | 0.586399i | \(-0.800545\pi\) | ||||
−0.810022 | + | 0.586399i | \(0.800545\pi\) | |||||||
\(284\) | 6.61607e12 | 0.212495 | ||||||||
\(285\) | 2.62305e11 | 0.00826341 | ||||||||
\(286\) | 1.47430e13 | 0.455588 | ||||||||
\(287\) | 9.31516e12 | 0.282384 | ||||||||
\(288\) | −5.22721e12 | −0.155457 | ||||||||
\(289\) | 4.60057e12 | 0.134237 | ||||||||
\(290\) | 4.41082e12 | 0.126279 | ||||||||
\(291\) | −2.21135e13 | −0.621222 | ||||||||
\(292\) | 1.67004e13 | 0.460384 | ||||||||
\(293\) | 3.97795e13 | 1.07619 | 0.538093 | − | 0.842886i | \(-0.319145\pi\) | ||||
0.538093 | + | 0.842886i | \(0.319145\pi\) | |||||||
\(294\) | 1.48773e12 | 0.0395014 | ||||||||
\(295\) | 4.38717e12 | 0.114331 | ||||||||
\(296\) | 1.59566e13 | 0.408165 | ||||||||
\(297\) | 1.41205e13 | 0.354560 | ||||||||
\(298\) | −2.77976e12 | −0.0685200 | ||||||||
\(299\) | −1.76771e13 | −0.427779 | ||||||||
\(300\) | 5.41524e12 | 0.128662 | ||||||||
\(301\) | 1.50446e13 | 0.350965 | ||||||||
\(302\) | −5.04164e11 | −0.0115487 | ||||||||
\(303\) | 2.11494e13 | 0.475734 | ||||||||
\(304\) | 6.80928e11 | 0.0150417 | ||||||||
\(305\) | 7.24626e13 | 1.57204 | ||||||||
\(306\) | −2.68214e12 | −0.0571496 | ||||||||
\(307\) | 9.32676e12 | 0.195195 | 0.0975977 | − | 0.995226i | \(-0.468884\pi\) | ||||
0.0975977 | + | 0.995226i | \(0.468884\pi\) | |||||||
\(308\) | 6.61958e13 | 1.36082 | ||||||||
\(309\) | 1.74272e13 | 0.351930 | ||||||||
\(310\) | −1.64042e12 | −0.0325435 | ||||||||
\(311\) | −4.41430e13 | −0.860359 | −0.430180 | − | 0.902743i | \(-0.641550\pi\) | ||||
−0.430180 | + | 0.902743i | \(0.641550\pi\) | |||||||
\(312\) | −1.47182e13 | −0.281842 | ||||||||
\(313\) | 9.01074e13 | 1.69538 | 0.847689 | − | 0.530494i | \(-0.177993\pi\) | ||||
0.847689 | + | 0.530494i | \(0.177993\pi\) | |||||||
\(314\) | −1.30116e13 | −0.240557 | ||||||||
\(315\) | −1.22183e13 | −0.221974 | ||||||||
\(316\) | 4.88150e12 | 0.0871513 | ||||||||
\(317\) | −4.48767e13 | −0.787400 | −0.393700 | − | 0.919239i | \(-0.628805\pi\) | ||||
−0.393700 | + | 0.919239i | \(0.628805\pi\) | |||||||
\(318\) | 4.46765e11 | 0.00770424 | ||||||||
\(319\) | −9.70909e13 | −1.64562 | ||||||||
\(320\) | −4.46922e13 | −0.744572 | ||||||||
\(321\) | −3.84858e13 | −0.630265 | ||||||||
\(322\) | 2.11166e12 | 0.0339952 | ||||||||
\(323\) | 1.09672e12 | 0.0173573 | ||||||||
\(324\) | −6.95587e12 | −0.108232 | ||||||||
\(325\) | 2.29716e13 | 0.351425 | ||||||||
\(326\) | −9.76250e12 | −0.146847 | ||||||||
\(327\) | 1.86317e13 | 0.275575 | ||||||||
\(328\) | −8.13694e12 | −0.118346 | ||||||||
\(329\) | −3.59751e12 | −0.0514546 | ||||||||
\(330\) | −1.06908e13 | −0.150378 | ||||||||
\(331\) | −4.88286e13 | −0.675493 | −0.337746 | − | 0.941237i | \(-0.609665\pi\) | ||||
−0.337746 | + | 0.941237i | \(0.609665\pi\) | |||||||
\(332\) | −1.05608e14 | −1.43694 | ||||||||
\(333\) | 3.19896e13 | 0.428120 | ||||||||
\(334\) | 5.40325e12 | 0.0711295 | ||||||||
\(335\) | −2.18364e13 | −0.282771 | ||||||||
\(336\) | −3.17179e13 | −0.404053 | ||||||||
\(337\) | −7.41414e13 | −0.929173 | −0.464586 | − | 0.885528i | \(-0.653797\pi\) | ||||
−0.464586 | + | 0.885528i | \(0.653797\pi\) | |||||||
\(338\) | −1.77514e13 | −0.218872 | ||||||||
\(339\) | −1.67085e13 | −0.202694 | ||||||||
\(340\) | −7.63259e13 | −0.911041 | ||||||||
\(341\) | 3.61088e13 | 0.424096 | ||||||||
\(342\) | −7.56720e10 | −0.000874564 0 | ||||||||
\(343\) | 9.50093e13 | 1.08056 | ||||||||
\(344\) | −1.31417e13 | −0.147088 | ||||||||
\(345\) | 1.28185e13 | 0.141199 | ||||||||
\(346\) | −2.56541e13 | −0.278124 | ||||||||
\(347\) | −2.14365e13 | −0.228740 | −0.114370 | − | 0.993438i | \(-0.536485\pi\) | ||||
−0.114370 | + | 0.993438i | \(0.536485\pi\) | |||||||
\(348\) | 4.78277e13 | 0.502336 | ||||||||
\(349\) | −8.64032e13 | −0.893285 | −0.446642 | − | 0.894713i | \(-0.647380\pi\) | ||||
−0.446642 | + | 0.894713i | \(0.647380\pi\) | |||||||
\(350\) | −2.74413e12 | −0.0279274 | ||||||||
\(351\) | −2.95070e13 | −0.295622 | ||||||||
\(352\) | −8.71142e13 | −0.859220 | ||||||||
\(353\) | −1.26783e14 | −1.23112 | −0.615558 | − | 0.788091i | \(-0.711070\pi\) | ||||
−0.615558 | + | 0.788091i | \(0.711070\pi\) | |||||||
\(354\) | −1.26565e12 | −0.0121003 | ||||||||
\(355\) | −2.03516e13 | −0.191577 | ||||||||
\(356\) | −9.99926e13 | −0.926815 | ||||||||
\(357\) | −5.10858e13 | −0.466256 | ||||||||
\(358\) | −2.26075e13 | −0.203187 | ||||||||
\(359\) | −7.94965e13 | −0.703604 | −0.351802 | − | 0.936074i | \(-0.614431\pi\) | ||||
−0.351802 | + | 0.936074i | \(0.614431\pi\) | |||||||
\(360\) | 1.06729e13 | 0.0930286 | ||||||||
\(361\) | −1.16459e14 | −0.999734 | ||||||||
\(362\) | −2.14802e13 | −0.181610 | ||||||||
\(363\) | 1.65995e14 | 1.38232 | ||||||||
\(364\) | −1.38327e14 | −1.13461 | ||||||||
\(365\) | −5.13717e13 | −0.415062 | ||||||||
\(366\) | −2.09047e13 | −0.166379 | ||||||||
\(367\) | 1.31070e14 | 1.02764 | 0.513820 | − | 0.857898i | \(-0.328230\pi\) | ||||
0.513820 | + | 0.857898i | \(0.328230\pi\) | |||||||
\(368\) | 3.32760e13 | 0.257020 | ||||||||
\(369\) | −1.63129e13 | −0.124132 | ||||||||
\(370\) | −2.42197e13 | −0.181576 | ||||||||
\(371\) | 8.50937e12 | 0.0628552 | ||||||||
\(372\) | −1.77875e13 | −0.129458 | ||||||||
\(373\) | 1.07548e14 | 0.771264 | 0.385632 | − | 0.922653i | \(-0.373983\pi\) | ||||
0.385632 | + | 0.922653i | \(0.373983\pi\) | |||||||
\(374\) | −4.46992e13 | −0.315869 | ||||||||
\(375\) | −8.94694e13 | −0.623021 | ||||||||
\(376\) | 3.14248e12 | 0.0215645 | ||||||||
\(377\) | 2.02887e14 | 1.37207 | ||||||||
\(378\) | 3.52484e12 | 0.0234928 | ||||||||
\(379\) | 1.38488e14 | 0.909695 | 0.454848 | − | 0.890569i | \(-0.349694\pi\) | ||||
0.454848 | + | 0.890569i | \(0.349694\pi\) | |||||||
\(380\) | −2.15341e12 | −0.0139417 | ||||||||
\(381\) | 9.44469e13 | 0.602699 | ||||||||
\(382\) | −9.08757e12 | −0.0571610 | ||||||||
\(383\) | −1.26680e14 | −0.785445 | −0.392723 | − | 0.919657i | \(-0.628467\pi\) | ||||
−0.392723 | + | 0.919657i | \(0.628467\pi\) | |||||||
\(384\) | 5.69480e13 | 0.348062 | ||||||||
\(385\) | −2.03624e14 | −1.22686 | ||||||||
\(386\) | −2.39757e13 | −0.142410 | ||||||||
\(387\) | −2.63463e13 | −0.154280 | ||||||||
\(388\) | 1.81543e14 | 1.04810 | ||||||||
\(389\) | −9.22822e13 | −0.525285 | −0.262643 | − | 0.964893i | \(-0.584594\pi\) | ||||
−0.262643 | + | 0.964893i | \(0.584594\pi\) | |||||||
\(390\) | 2.23401e13 | 0.125380 | ||||||||
\(391\) | 5.35952e13 | 0.296588 | ||||||||
\(392\) | −2.47521e13 | −0.135064 | ||||||||
\(393\) | −1.00336e14 | −0.539879 | ||||||||
\(394\) | −4.66745e13 | −0.247657 | ||||||||
\(395\) | −1.50159e13 | −0.0785719 | ||||||||
\(396\) | −1.15923e14 | −0.598201 | ||||||||
\(397\) | −1.42869e14 | −0.727094 | −0.363547 | − | 0.931576i | \(-0.618434\pi\) | ||||
−0.363547 | + | 0.931576i | \(0.618434\pi\) | |||||||
\(398\) | 5.16185e13 | 0.259089 | ||||||||
\(399\) | −1.44130e12 | −0.00713515 | ||||||||
\(400\) | −4.32425e13 | −0.211145 | ||||||||
\(401\) | −1.62373e14 | −0.782021 | −0.391011 | − | 0.920386i | \(-0.627874\pi\) | ||||
−0.391011 | + | 0.920386i | \(0.627874\pi\) | |||||||
\(402\) | 6.29957e12 | 0.0299273 | ||||||||
\(403\) | −7.54551e13 | −0.353599 | ||||||||
\(404\) | −1.73627e14 | −0.802640 | ||||||||
\(405\) | 2.13968e13 | 0.0975769 | ||||||||
\(406\) | −2.42364e13 | −0.109037 | ||||||||
\(407\) | 5.33124e14 | 2.36624 | ||||||||
\(408\) | 4.46242e13 | 0.195407 | ||||||||
\(409\) | −3.19251e14 | −1.37928 | −0.689642 | − | 0.724150i | \(-0.742232\pi\) | ||||
−0.689642 | + | 0.724150i | \(0.742232\pi\) | |||||||
\(410\) | 1.23507e13 | 0.0526476 | ||||||||
\(411\) | 8.83490e13 | 0.371596 | ||||||||
\(412\) | −1.43070e14 | −0.593764 | ||||||||
\(413\) | −2.41064e13 | −0.0987205 | ||||||||
\(414\) | −3.69798e12 | −0.0149439 | ||||||||
\(415\) | 3.24860e14 | 1.29548 | ||||||||
\(416\) | 1.82039e14 | 0.716392 | ||||||||
\(417\) | 3.09379e13 | 0.120155 | ||||||||
\(418\) | −1.26111e12 | −0.00483376 | ||||||||
\(419\) | −1.20423e14 | −0.455548 | −0.227774 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227774 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(420\) | 1.00307e14 | 0.374506 | ||||||||
\(421\) | 3.74027e14 | 1.37833 | 0.689163 | − | 0.724607i | \(-0.257978\pi\) | ||||
0.689163 | + | 0.724607i | \(0.257978\pi\) | |||||||
\(422\) | −5.37721e13 | −0.195586 | ||||||||
\(423\) | 6.30001e12 | 0.0226188 | ||||||||
\(424\) | −7.43307e12 | −0.0263424 | ||||||||
\(425\) | −6.96476e13 | −0.243650 | ||||||||
\(426\) | 5.87121e12 | 0.0202756 | ||||||||
\(427\) | −3.98164e14 | −1.35740 | ||||||||
\(428\) | 3.15952e14 | 1.06336 | ||||||||
\(429\) | −4.91750e14 | −1.63391 | ||||||||
\(430\) | 1.99471e13 | 0.0654339 | ||||||||
\(431\) | 2.55097e14 | 0.826191 | 0.413096 | − | 0.910688i | \(-0.364447\pi\) | ||||
0.413096 | + | 0.910688i | \(0.364447\pi\) | |||||||
\(432\) | 5.55450e13 | 0.177617 | ||||||||
\(433\) | −5.01589e13 | −0.158367 | −0.0791835 | − | 0.996860i | \(-0.525231\pi\) | ||||
−0.0791835 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(434\) | 9.01368e12 | 0.0281001 | ||||||||
\(435\) | −1.47122e14 | −0.452884 | ||||||||
\(436\) | −1.52958e14 | −0.464940 | ||||||||
\(437\) | 1.51210e12 | 0.00453871 | ||||||||
\(438\) | 1.48202e13 | 0.0439284 | ||||||||
\(439\) | 7.04081e13 | 0.206095 | 0.103048 | − | 0.994676i | \(-0.467141\pi\) | ||||
0.103048 | + | 0.994676i | \(0.467141\pi\) | |||||||
\(440\) | 1.77869e14 | 0.514174 | ||||||||
\(441\) | −4.96228e13 | −0.141667 | ||||||||
\(442\) | 9.34061e13 | 0.263362 | ||||||||
\(443\) | 1.17079e14 | 0.326030 | 0.163015 | − | 0.986624i | \(-0.447878\pi\) | ||||
0.163015 | + | 0.986624i | \(0.447878\pi\) | |||||||
\(444\) | −2.62621e14 | −0.722309 | ||||||||
\(445\) | 3.07586e14 | 0.835576 | ||||||||
\(446\) | −1.09951e14 | −0.295024 | ||||||||
\(447\) | 9.27184e13 | 0.245739 | ||||||||
\(448\) | 2.45572e14 | 0.642910 | ||||||||
\(449\) | −5.74915e13 | −0.148679 | −0.0743393 | − | 0.997233i | \(-0.523685\pi\) | ||||
−0.0743393 | + | 0.997233i | \(0.523685\pi\) | |||||||
\(450\) | 4.80557e12 | 0.0122765 | ||||||||
\(451\) | −2.71863e14 | −0.686086 | ||||||||
\(452\) | 1.37170e14 | 0.341977 | ||||||||
\(453\) | 1.68163e13 | 0.0414181 | ||||||||
\(454\) | −1.06665e14 | −0.259545 | ||||||||
\(455\) | 4.25504e14 | 1.02292 | ||||||||
\(456\) | 1.25900e12 | 0.00299032 | ||||||||
\(457\) | 2.90433e14 | 0.681565 | 0.340783 | − | 0.940142i | \(-0.389308\pi\) | ||||
0.340783 | + | 0.940142i | \(0.389308\pi\) | |||||||
\(458\) | −9.75340e13 | −0.226150 | ||||||||
\(459\) | 8.94623e13 | 0.204960 | ||||||||
\(460\) | −1.05234e14 | −0.238225 | ||||||||
\(461\) | −4.64431e14 | −1.03888 | −0.519441 | − | 0.854506i | \(-0.673860\pi\) | ||||
−0.519441 | + | 0.854506i | \(0.673860\pi\) | |||||||
\(462\) | 5.87433e13 | 0.129846 | ||||||||
\(463\) | 1.51143e14 | 0.330135 | 0.165068 | − | 0.986282i | \(-0.447216\pi\) | ||||
0.165068 | + | 0.986282i | \(0.447216\pi\) | |||||||
\(464\) | −3.81921e14 | −0.824374 | ||||||||
\(465\) | 5.47158e13 | 0.116714 | ||||||||
\(466\) | −1.17810e14 | −0.248346 | ||||||||
\(467\) | 5.53556e14 | 1.15324 | 0.576619 | − | 0.817013i | \(-0.304372\pi\) | ||||
0.576619 | + | 0.817013i | \(0.304372\pi\) | |||||||
\(468\) | 2.42240e14 | 0.498762 | ||||||||
\(469\) | 1.19986e14 | 0.244162 | ||||||||
\(470\) | −4.76981e12 | −0.00959319 | ||||||||
\(471\) | 4.33999e14 | 0.862729 | ||||||||
\(472\) | 2.10573e13 | 0.0413735 | ||||||||
\(473\) | −4.39075e14 | −0.852711 | ||||||||
\(474\) | 4.33192e12 | 0.00831571 | ||||||||
\(475\) | −1.96499e12 | −0.00372860 | ||||||||
\(476\) | 4.19392e14 | 0.786650 | ||||||||
\(477\) | −1.49018e13 | −0.0276303 | ||||||||
\(478\) | 2.65205e13 | 0.0486104 | ||||||||
\(479\) | 9.79817e14 | 1.77541 | 0.887707 | − | 0.460409i | \(-0.152297\pi\) | ||||
0.887707 | + | 0.460409i | \(0.152297\pi\) | |||||||
\(480\) | −1.32004e14 | −0.236462 | ||||||||
\(481\) | −1.11405e15 | −1.97290 | ||||||||
\(482\) | −1.48319e13 | −0.0259680 | ||||||||
\(483\) | −7.04342e13 | −0.121920 | ||||||||
\(484\) | −1.36275e15 | −2.33220 | ||||||||
\(485\) | −5.58440e14 | −0.944925 | ||||||||
\(486\) | −6.17275e12 | −0.0103271 | ||||||||
\(487\) | 1.35144e14 | 0.223557 | 0.111778 | − | 0.993733i | \(-0.464345\pi\) | ||||
0.111778 | + | 0.993733i | \(0.464345\pi\) | |||||||
\(488\) | 3.47802e14 | 0.568884 | ||||||||
\(489\) | 3.25626e14 | 0.526648 | ||||||||
\(490\) | 3.75700e13 | 0.0600845 | ||||||||
\(491\) | 4.49871e14 | 0.711443 | 0.355721 | − | 0.934592i | \(-0.384235\pi\) | ||||
0.355721 | + | 0.934592i | \(0.384235\pi\) | |||||||
\(492\) | 1.33922e14 | 0.209432 | ||||||||
\(493\) | −6.15132e14 | −0.951284 | ||||||||
\(494\) | 2.63530e12 | 0.00403024 | ||||||||
\(495\) | 3.56590e14 | 0.539312 | ||||||||
\(496\) | 1.42039e14 | 0.212451 | ||||||||
\(497\) | 1.11827e14 | 0.165419 | ||||||||
\(498\) | −9.37185e13 | −0.137108 | ||||||||
\(499\) | −7.83753e14 | −1.13403 | −0.567017 | − | 0.823706i | \(-0.691903\pi\) | ||||
−0.567017 | + | 0.823706i | \(0.691903\pi\) | |||||||
\(500\) | 7.34505e14 | 1.05114 | ||||||||
\(501\) | −1.80224e14 | −0.255098 | ||||||||
\(502\) | 5.59657e13 | 0.0783522 | ||||||||
\(503\) | 2.94819e14 | 0.408255 | 0.204127 | − | 0.978944i | \(-0.434564\pi\) | ||||
0.204127 | + | 0.978944i | \(0.434564\pi\) | |||||||
\(504\) | −5.86446e13 | −0.0803268 | ||||||||
\(505\) | 5.34093e14 | 0.723626 | ||||||||
\(506\) | −6.16288e13 | −0.0825954 | ||||||||
\(507\) | 5.92094e14 | 0.784959 | ||||||||
\(508\) | −7.75368e14 | −1.01685 | ||||||||
\(509\) | −1.18940e15 | −1.54306 | −0.771528 | − | 0.636195i | \(-0.780507\pi\) | ||||
−0.771528 | + | 0.636195i | \(0.780507\pi\) | |||||||
\(510\) | −6.77329e13 | −0.0869288 | ||||||||
\(511\) | 2.82275e14 | 0.358391 | ||||||||
\(512\) | −5.76182e14 | −0.723727 | ||||||||
\(513\) | 2.52403e12 | 0.00313652 | ||||||||
\(514\) | 2.31216e14 | 0.284264 | ||||||||
\(515\) | 4.40095e14 | 0.535312 | ||||||||
\(516\) | 2.16292e14 | 0.260295 | ||||||||
\(517\) | 1.04993e14 | 0.125015 | ||||||||
\(518\) | 1.33081e14 | 0.156785 | ||||||||
\(519\) | 8.55689e14 | 0.997460 | ||||||||
\(520\) | −3.71685e14 | −0.428703 | ||||||||
\(521\) | 1.62699e15 | 1.85685 | 0.928427 | − | 0.371515i | \(-0.121161\pi\) | ||||
0.928427 | + | 0.371515i | \(0.121161\pi\) | |||||||
\(522\) | 4.24431e13 | 0.0479313 | ||||||||
\(523\) | 5.12180e14 | 0.572352 | 0.286176 | − | 0.958177i | \(-0.407616\pi\) | ||||
0.286176 | + | 0.958177i | \(0.407616\pi\) | |||||||
\(524\) | 8.23712e14 | 0.910864 | ||||||||
\(525\) | 9.15301e13 | 0.100158 | ||||||||
\(526\) | 8.01220e13 | 0.0867621 | ||||||||
\(527\) | 2.28772e14 | 0.245157 | ||||||||
\(528\) | 9.25686e14 | 0.981696 | ||||||||
\(529\) | −8.78916e14 | −0.922446 | ||||||||
\(530\) | 1.12823e13 | 0.0117187 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | 1.18324e13 | 0.0120382 | ||||||||
\(533\) | 5.68100e14 | 0.572038 | ||||||||
\(534\) | −8.87351e13 | −0.0884338 | ||||||||
\(535\) | −9.71894e14 | −0.958679 | ||||||||
\(536\) | −1.04809e14 | −0.102328 | ||||||||
\(537\) | 7.54068e14 | 0.728705 | ||||||||
\(538\) | −3.78976e13 | −0.0362501 | ||||||||
\(539\) | −8.26990e14 | −0.783001 | ||||||||
\(540\) | −1.75659e14 | −0.164628 | ||||||||
\(541\) | 4.66542e14 | 0.432819 | 0.216409 | − | 0.976303i | \(-0.430565\pi\) | ||||
0.216409 | + | 0.976303i | \(0.430565\pi\) | |||||||
\(542\) | 2.39809e14 | 0.220226 | ||||||||
\(543\) | 7.16468e14 | 0.651325 | ||||||||
\(544\) | −5.51923e14 | −0.496689 | ||||||||
\(545\) | 4.70512e14 | 0.419170 | ||||||||
\(546\) | −1.22753e14 | −0.108261 | ||||||||
\(547\) | 3.44855e14 | 0.301097 | 0.150548 | − | 0.988603i | \(-0.451896\pi\) | ||||
0.150548 | + | 0.988603i | \(0.451896\pi\) | |||||||
\(548\) | −7.25307e14 | −0.626944 | ||||||||
\(549\) | 6.97272e14 | 0.596697 | ||||||||
\(550\) | 8.00874e13 | 0.0678530 | ||||||||
\(551\) | −1.73549e13 | −0.0145576 | ||||||||
\(552\) | 6.15254e13 | 0.0510963 | ||||||||
\(553\) | 8.25086e13 | 0.0678439 | ||||||||
\(554\) | 3.58844e14 | 0.292147 | ||||||||
\(555\) | 8.07844e14 | 0.651203 | ||||||||
\(556\) | −2.53987e14 | −0.202721 | ||||||||
\(557\) | −4.50069e14 | −0.355693 | −0.177846 | − | 0.984058i | \(-0.556913\pi\) | ||||
−0.177846 | + | 0.984058i | \(0.556913\pi\) | |||||||
\(558\) | −1.57849e13 | −0.0123525 | ||||||||
\(559\) | 9.17516e14 | 0.710965 | ||||||||
\(560\) | −8.00983e14 | −0.614595 | ||||||||
\(561\) | 1.49094e15 | 1.13283 | ||||||||
\(562\) | −3.28908e14 | −0.247471 | ||||||||
\(563\) | 1.65669e15 | 1.23437 | 0.617186 | − | 0.786817i | \(-0.288273\pi\) | ||||
0.617186 | + | 0.786817i | \(0.288273\pi\) | |||||||
\(564\) | −5.17204e13 | −0.0381616 | ||||||||
\(565\) | −4.21946e14 | −0.308312 | ||||||||
\(566\) | 3.60413e14 | 0.260801 | ||||||||
\(567\) | −1.17570e14 | −0.0842541 | ||||||||
\(568\) | −9.76825e13 | −0.0693268 | ||||||||
\(569\) | −1.00863e15 | −0.708946 | −0.354473 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354473 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(570\) | −1.91097e12 | −0.00133028 | ||||||||
\(571\) | 1.20071e15 | 0.827828 | 0.413914 | − | 0.910316i | \(-0.364161\pi\) | ||||
0.413914 | + | 0.910316i | \(0.364161\pi\) | |||||||
\(572\) | 4.03705e15 | 2.75668 | ||||||||
\(573\) | 3.03114e14 | 0.205001 | ||||||||
\(574\) | −6.78638e13 | −0.0454593 | ||||||||
\(575\) | −9.60262e13 | −0.0637113 | ||||||||
\(576\) | −4.30050e14 | −0.282615 | ||||||||
\(577\) | 9.68634e14 | 0.630511 | 0.315256 | − | 0.949007i | \(-0.397910\pi\) | ||||
0.315256 | + | 0.949007i | \(0.397910\pi\) | |||||||
\(578\) | −3.35165e13 | −0.0216100 | ||||||||
\(579\) | 7.99707e14 | 0.510738 | ||||||||
\(580\) | 1.20781e15 | 0.764090 | ||||||||
\(581\) | −1.78502e15 | −1.11860 | ||||||||
\(582\) | 1.61104e14 | 0.100007 | ||||||||
\(583\) | −2.48346e14 | −0.152714 | ||||||||
\(584\) | −2.46571e14 | −0.150201 | ||||||||
\(585\) | −7.45150e14 | −0.449662 | ||||||||
\(586\) | −2.89806e14 | −0.173249 | ||||||||
\(587\) | −2.05902e15 | −1.21942 | −0.609708 | − | 0.792626i | \(-0.708713\pi\) | ||||
−0.609708 | + | 0.792626i | \(0.708713\pi\) | |||||||
\(588\) | 4.07382e14 | 0.239016 | ||||||||
\(589\) | 6.45442e12 | 0.00375165 | ||||||||
\(590\) | −3.19619e13 | −0.0184054 | ||||||||
\(591\) | 1.55682e15 | 0.888192 | ||||||||
\(592\) | 2.09712e15 | 1.18537 | ||||||||
\(593\) | −2.19888e15 | −1.23140 | −0.615702 | − | 0.787979i | \(-0.711127\pi\) | ||||
−0.615702 | + | 0.787979i | \(0.711127\pi\) | |||||||
\(594\) | −1.02872e14 | −0.0570785 | ||||||||
\(595\) | −1.29008e15 | −0.709210 | ||||||||
\(596\) | −7.61177e14 | −0.414602 | ||||||||
\(597\) | −1.72173e15 | −0.929192 | ||||||||
\(598\) | 1.28783e14 | 0.0688656 | ||||||||
\(599\) | −1.59947e15 | −0.847481 | −0.423740 | − | 0.905784i | \(-0.639283\pi\) | ||||
−0.423740 | + | 0.905784i | \(0.639283\pi\) | |||||||
\(600\) | −7.99529e13 | −0.0419762 | ||||||||
\(601\) | −2.27264e15 | −1.18228 | −0.591142 | − | 0.806568i | \(-0.701323\pi\) | ||||
−0.591142 | + | 0.806568i | \(0.701323\pi\) | |||||||
\(602\) | −1.09604e14 | −0.0564997 | ||||||||
\(603\) | −2.10121e14 | −0.107331 | ||||||||
\(604\) | −1.38055e14 | −0.0698791 | ||||||||
\(605\) | 4.19192e15 | 2.10261 | ||||||||
\(606\) | −1.54080e14 | −0.0765855 | ||||||||
\(607\) | 6.48922e14 | 0.319635 | 0.159818 | − | 0.987147i | \(-0.448909\pi\) | ||||
0.159818 | + | 0.987147i | \(0.448909\pi\) | |||||||
\(608\) | −1.55716e13 | −0.00760086 | ||||||||
\(609\) | 8.08399e14 | 0.391049 | ||||||||
\(610\) | −5.27912e14 | −0.253074 | ||||||||
\(611\) | −2.19399e14 | −0.104234 | ||||||||
\(612\) | −7.34446e14 | −0.345802 | ||||||||
\(613\) | −2.15085e15 | −1.00364 | −0.501819 | − | 0.864973i | \(-0.667336\pi\) | ||||
−0.501819 | + | 0.864973i | \(0.667336\pi\) | |||||||
\(614\) | −6.79483e13 | −0.0314233 | ||||||||
\(615\) | −4.11954e14 | −0.188815 | ||||||||
\(616\) | −9.77344e14 | −0.443970 | ||||||||
\(617\) | 1.76381e15 | 0.794114 | 0.397057 | − | 0.917794i | \(-0.370031\pi\) | ||||
0.397057 | + | 0.917794i | \(0.370031\pi\) | |||||||
\(618\) | −1.26963e14 | −0.0566552 | ||||||||
\(619\) | −1.42359e15 | −0.629630 | −0.314815 | − | 0.949153i | \(-0.601943\pi\) | ||||
−0.314815 | + | 0.949153i | \(0.601943\pi\) | |||||||
\(620\) | −4.49193e14 | −0.196915 | ||||||||
\(621\) | 1.23346e14 | 0.0535944 | ||||||||
\(622\) | 3.21595e14 | 0.138504 | ||||||||
\(623\) | −1.69011e15 | −0.721489 | ||||||||
\(624\) | −1.93437e15 | −0.818509 | ||||||||
\(625\) | −1.71395e15 | −0.718882 | ||||||||
\(626\) | −6.56460e14 | −0.272929 | ||||||||
\(627\) | 4.20642e13 | 0.0173357 | ||||||||
\(628\) | −3.56295e15 | −1.45556 | ||||||||
\(629\) | 3.37767e15 | 1.36785 | ||||||||
\(630\) | 8.90138e13 | 0.0357342 | ||||||||
\(631\) | 1.68693e12 | 0.000671327 0 | 0.000335664 | − | 1.00000i | \(-0.499893\pi\) | ||||
0.000335664 | 1.00000i | \(0.499893\pi\) | ||||||||
\(632\) | −7.20725e13 | −0.0284332 | ||||||||
\(633\) | 1.79356e15 | 0.701448 | ||||||||
\(634\) | 3.26941e14 | 0.126759 | ||||||||
\(635\) | 2.38510e15 | 0.916749 | ||||||||
\(636\) | 1.22337e14 | 0.0466169 | ||||||||
\(637\) | 1.72813e15 | 0.652843 | ||||||||
\(638\) | 7.07337e14 | 0.264919 | ||||||||
\(639\) | −1.95833e14 | −0.0727162 | ||||||||
\(640\) | 1.43813e15 | 0.529428 | ||||||||
\(641\) | 1.34445e15 | 0.490709 | 0.245355 | − | 0.969433i | \(-0.421096\pi\) | ||||
0.245355 | + | 0.969433i | \(0.421096\pi\) | |||||||
\(642\) | 2.80381e14 | 0.101463 | ||||||||
\(643\) | −1.23473e15 | −0.443008 | −0.221504 | − | 0.975159i | \(-0.571097\pi\) | ||||
−0.221504 | + | 0.975159i | \(0.571097\pi\) | |||||||
\(644\) | 5.78234e14 | 0.205699 | ||||||||
\(645\) | −6.65331e14 | −0.234671 | ||||||||
\(646\) | −7.98995e12 | −0.00279425 | ||||||||
\(647\) | 9.70146e14 | 0.336406 | 0.168203 | − | 0.985752i | \(-0.446204\pi\) | ||||
0.168203 | + | 0.985752i | \(0.446204\pi\) | |||||||
\(648\) | 1.02700e14 | 0.0353107 | ||||||||
\(649\) | 7.03545e14 | 0.239853 | ||||||||
\(650\) | −1.67355e14 | −0.0565739 | ||||||||
\(651\) | −3.00650e14 | −0.100778 | ||||||||
\(652\) | −2.67325e15 | −0.888542 | ||||||||
\(653\) | −4.52761e15 | −1.49227 | −0.746133 | − | 0.665796i | \(-0.768092\pi\) | ||||
−0.746133 | + | 0.665796i | \(0.768092\pi\) | |||||||
\(654\) | −1.35738e14 | −0.0443631 | ||||||||
\(655\) | −2.53381e15 | −0.821195 | ||||||||
\(656\) | −1.06941e15 | −0.343695 | ||||||||
\(657\) | −4.94324e14 | −0.157544 | ||||||||
\(658\) | 2.62089e13 | 0.00828336 | ||||||||
\(659\) | 3.99949e15 | 1.25353 | 0.626766 | − | 0.779208i | \(-0.284378\pi\) | ||||
0.626766 | + | 0.779208i | \(0.284378\pi\) | |||||||
\(660\) | −2.92745e15 | −0.909908 | ||||||||
\(661\) | 1.04030e15 | 0.320666 | 0.160333 | − | 0.987063i | \(-0.448743\pi\) | ||||
0.160333 | + | 0.987063i | \(0.448743\pi\) | |||||||
\(662\) | 3.55731e14 | 0.108743 | ||||||||
\(663\) | −3.11554e15 | −0.944516 | ||||||||
\(664\) | 1.55925e15 | 0.468803 | ||||||||
\(665\) | −3.63976e13 | −0.0108531 | ||||||||
\(666\) | −2.33054e14 | −0.0689205 | ||||||||
\(667\) | −8.48110e14 | −0.248748 | ||||||||
\(668\) | 1.47956e15 | 0.430391 | ||||||||
\(669\) | 3.66739e15 | 1.05807 | ||||||||
\(670\) | 1.59085e14 | 0.0455216 | ||||||||
\(671\) | 1.16204e16 | 3.29797 | ||||||||
\(672\) | 7.25331e14 | 0.204176 | ||||||||
\(673\) | −3.14094e15 | −0.876955 | −0.438477 | − | 0.898742i | \(-0.644482\pi\) | ||||
−0.438477 | + | 0.898742i | \(0.644482\pi\) | |||||||
\(674\) | 5.40143e14 | 0.149582 | ||||||||
\(675\) | −1.60289e14 | −0.0440284 | ||||||||
\(676\) | −4.86084e15 | −1.32435 | ||||||||
\(677\) | 1.53188e15 | 0.413988 | 0.206994 | − | 0.978342i | \(-0.433632\pi\) | ||||
0.206994 | + | 0.978342i | \(0.433632\pi\) | |||||||
\(678\) | 1.21727e14 | 0.0326304 | ||||||||
\(679\) | 3.06849e15 | 0.815907 | ||||||||
\(680\) | 1.12691e15 | 0.297228 | ||||||||
\(681\) | 3.55778e15 | 0.930829 | ||||||||
\(682\) | −2.63064e14 | −0.0682727 | ||||||||
\(683\) | −3.66393e15 | −0.943264 | −0.471632 | − | 0.881796i | \(-0.656335\pi\) | ||||
−0.471632 | + | 0.881796i | \(0.656335\pi\) | |||||||
\(684\) | −2.07212e13 | −0.00529183 | ||||||||
\(685\) | 2.23110e15 | 0.565225 | ||||||||
\(686\) | −6.92172e14 | −0.173953 | ||||||||
\(687\) | 3.25323e15 | 0.811060 | ||||||||
\(688\) | −1.72716e15 | −0.427166 | ||||||||
\(689\) | 5.18957e14 | 0.127329 | ||||||||
\(690\) | −9.33863e13 | −0.0227307 | ||||||||
\(691\) | −6.93874e15 | −1.67553 | −0.837763 | − | 0.546034i | \(-0.816137\pi\) | ||||
−0.837763 | + | 0.546034i | \(0.816137\pi\) | |||||||
\(692\) | −7.02483e15 | −1.68288 | ||||||||
\(693\) | −1.95937e15 | −0.465676 | ||||||||
\(694\) | 1.56171e14 | 0.0368235 | ||||||||
\(695\) | 7.81285e14 | 0.182765 | ||||||||
\(696\) | −7.06150e14 | −0.163888 | ||||||||
\(697\) | −1.72242e15 | −0.396605 | ||||||||
\(698\) | 6.29474e14 | 0.143805 | ||||||||
\(699\) | 3.92952e15 | 0.890665 | ||||||||
\(700\) | −7.51422e14 | −0.168984 | ||||||||
\(701\) | 3.04592e15 | 0.679625 | 0.339813 | − | 0.940493i | \(-0.389636\pi\) | ||||
0.339813 | + | 0.940493i | \(0.389636\pi\) | |||||||
\(702\) | 2.14968e14 | 0.0475904 | ||||||||
\(703\) | 9.52954e13 | 0.0209323 | ||||||||
\(704\) | −7.16701e15 | −1.56203 | ||||||||
\(705\) | 1.59096e14 | 0.0344049 | ||||||||
\(706\) | 9.23651e14 | 0.198190 | ||||||||
\(707\) | −2.93471e15 | −0.624824 | ||||||||
\(708\) | −3.46571e14 | −0.0732166 | ||||||||
\(709\) | 3.77463e15 | 0.791262 | 0.395631 | − | 0.918410i | \(-0.370526\pi\) | ||||
0.395631 | + | 0.918410i | \(0.370526\pi\) | |||||||
\(710\) | 1.48267e14 | 0.0308408 | ||||||||
\(711\) | −1.44490e14 | −0.0298233 | ||||||||
\(712\) | 1.47633e15 | 0.302374 | ||||||||
\(713\) | 3.15418e14 | 0.0641053 | ||||||||
\(714\) | 3.72175e14 | 0.0750598 | ||||||||
\(715\) | −1.24183e16 | −2.48530 | ||||||||
\(716\) | −6.19057e15 | −1.22944 | ||||||||
\(717\) | −8.84588e14 | −0.174335 | ||||||||
\(718\) | 5.79156e14 | 0.113269 | ||||||||
\(719\) | −1.02169e16 | −1.98294 | −0.991472 | − | 0.130321i | \(-0.958399\pi\) | ||||
−0.991472 | + | 0.130321i | \(0.958399\pi\) | |||||||
\(720\) | 1.40269e15 | 0.270168 | ||||||||
\(721\) | −2.41821e15 | −0.462222 | ||||||||
\(722\) | 8.48441e14 | 0.160941 | ||||||||
\(723\) | 4.94716e14 | 0.0931312 | ||||||||
\(724\) | −5.88189e15 | −1.09889 | ||||||||
\(725\) | 1.10213e15 | 0.204349 | ||||||||
\(726\) | −1.20932e15 | −0.222531 | ||||||||
\(727\) | 9.05981e15 | 1.65455 | 0.827275 | − | 0.561797i | \(-0.189890\pi\) | ||||
0.827275 | + | 0.561797i | \(0.189890\pi\) | |||||||
\(728\) | 2.04231e15 | 0.370169 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 3.74258e14 | 0.0668184 | ||||||||
\(731\) | −2.78181e15 | −0.492927 | ||||||||
\(732\) | −5.72430e15 | −1.00673 | ||||||||
\(733\) | 5.86732e15 | 1.02416 | 0.512080 | − | 0.858938i | \(-0.328875\pi\) | ||||
0.512080 | + | 0.858938i | \(0.328875\pi\) | |||||||
\(734\) | −9.54887e14 | −0.165434 | ||||||||
\(735\) | −1.25314e15 | −0.215486 | ||||||||
\(736\) | −7.60960e14 | −0.129878 | ||||||||
\(737\) | −3.50178e15 | −0.593222 | ||||||||
\(738\) | 1.18844e14 | 0.0199833 | ||||||||
\(739\) | −1.14387e16 | −1.90912 | −0.954560 | − | 0.298018i | \(-0.903674\pi\) | ||||
−0.954560 | + | 0.298018i | \(0.903674\pi\) | |||||||
\(740\) | −6.63205e15 | −1.09869 | ||||||||
\(741\) | −8.78999e13 | −0.0144540 | ||||||||
\(742\) | −6.19933e13 | −0.0101187 | ||||||||
\(743\) | 1.91244e15 | 0.309848 | 0.154924 | − | 0.987926i | \(-0.450487\pi\) | ||||
0.154924 | + | 0.987926i | \(0.450487\pi\) | |||||||
\(744\) | 2.62622e14 | 0.0422357 | ||||||||
\(745\) | 2.34145e15 | 0.373787 | ||||||||
\(746\) | −7.83518e14 | −0.124161 | ||||||||
\(747\) | 3.12596e15 | 0.491723 | ||||||||
\(748\) | −1.22399e16 | −1.91126 | ||||||||
\(749\) | 5.34032e15 | 0.827784 | ||||||||
\(750\) | 6.51812e14 | 0.100296 | ||||||||
\(751\) | 8.64165e15 | 1.32001 | 0.660005 | − | 0.751261i | \(-0.270554\pi\) | ||||
0.660005 | + | 0.751261i | \(0.270554\pi\) | |||||||
\(752\) | 4.13005e14 | 0.0626263 | ||||||||
\(753\) | −1.86673e15 | −0.281001 | ||||||||
\(754\) | −1.47809e15 | −0.220881 | ||||||||
\(755\) | 4.24667e14 | 0.0630000 | ||||||||
\(756\) | 9.65201e14 | 0.142150 | ||||||||
\(757\) | 7.45030e14 | 0.108930 | 0.0544649 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544649 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(758\) | −1.00893e15 | −0.146446 | ||||||||
\(759\) | 2.05562e15 | 0.296219 | ||||||||
\(760\) | 3.17938e13 | 0.00454850 | ||||||||
\(761\) | 1.21503e16 | 1.72573 | 0.862865 | − | 0.505434i | \(-0.168668\pi\) | ||||
0.862865 | + | 0.505434i | \(0.168668\pi\) | |||||||
\(762\) | −6.88074e14 | −0.0970248 | ||||||||
\(763\) | −2.58535e15 | −0.361938 | ||||||||
\(764\) | −2.48844e15 | −0.345870 | ||||||||
\(765\) | 2.25922e15 | 0.311760 | ||||||||
\(766\) | 9.22904e14 | 0.126444 | ||||||||
\(767\) | −1.47017e15 | −0.199983 | ||||||||
\(768\) | 3.20957e15 | 0.433472 | ||||||||
\(769\) | 1.05690e16 | 1.41723 | 0.708614 | − | 0.705596i | \(-0.249321\pi\) | ||||
0.708614 | + | 0.705596i | \(0.249321\pi\) | |||||||
\(770\) | 1.48346e15 | 0.197505 | ||||||||
\(771\) | −7.71218e15 | −1.01948 | ||||||||
\(772\) | −6.56524e15 | −0.861699 | ||||||||
\(773\) | −1.01248e15 | −0.131947 | −0.0659736 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659736 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(774\) | 1.91941e14 | 0.0248366 | ||||||||
\(775\) | −4.09889e14 | −0.0526632 | ||||||||
\(776\) | −2.68037e15 | −0.341945 | ||||||||
\(777\) | −4.43890e15 | −0.562289 | ||||||||
\(778\) | 6.72304e14 | 0.0845625 | ||||||||
\(779\) | −4.85952e13 | −0.00606928 | ||||||||
\(780\) | 6.11736e15 | 0.758654 | ||||||||
\(781\) | −3.26366e15 | −0.401906 | ||||||||
\(782\) | −3.90457e14 | −0.0477459 | ||||||||
\(783\) | −1.41568e15 | −0.171900 | ||||||||
\(784\) | −3.25308e15 | −0.392244 | ||||||||
\(785\) | 1.09599e16 | 1.31227 | ||||||||
\(786\) | 7.30976e14 | 0.0869118 | ||||||||
\(787\) | −3.03453e14 | −0.0358286 | −0.0179143 | − | 0.999840i | \(-0.505703\pi\) | ||||
−0.0179143 | + | 0.999840i | \(0.505703\pi\) | |||||||
\(788\) | −1.27808e16 | −1.49852 | ||||||||
\(789\) | −2.67246e15 | −0.311162 | ||||||||
\(790\) | 1.09395e14 | 0.0126488 | ||||||||
\(791\) | 2.31849e15 | 0.266216 | ||||||||
\(792\) | 1.71154e15 | 0.195164 | ||||||||
\(793\) | −2.42827e16 | −2.74975 | ||||||||
\(794\) | 1.04084e15 | 0.117050 | ||||||||
\(795\) | −3.76319e14 | −0.0420278 | ||||||||
\(796\) | 1.41346e16 | 1.56770 | ||||||||
\(797\) | 5.23026e14 | 0.0576106 | 0.0288053 | − | 0.999585i | \(-0.490830\pi\) | ||||
0.0288053 | + | 0.999585i | \(0.490830\pi\) | |||||||
\(798\) | 1.05003e13 | 0.00114864 | ||||||||
\(799\) | 6.65196e14 | 0.0722674 | ||||||||
\(800\) | 9.88877e14 | 0.106696 | ||||||||
\(801\) | 2.95974e15 | 0.317158 | ||||||||
\(802\) | 1.18293e15 | 0.125893 | ||||||||
\(803\) | −8.23817e15 | −0.870754 | ||||||||
\(804\) | 1.72500e15 | 0.181085 | ||||||||
\(805\) | −1.77870e15 | −0.185449 | ||||||||
\(806\) | 5.49713e14 | 0.0569237 | ||||||||
\(807\) | 1.26407e15 | 0.130007 | ||||||||
\(808\) | 2.56351e15 | 0.261862 | ||||||||
\(809\) | 1.63033e16 | 1.65409 | 0.827046 | − | 0.562135i | \(-0.190020\pi\) | ||||
0.827046 | + | 0.562135i | \(0.190020\pi\) | |||||||
\(810\) | −1.55882e14 | −0.0157083 | ||||||||
\(811\) | 7.45401e15 | 0.746063 | 0.373031 | − | 0.927819i | \(-0.378318\pi\) | ||||
0.373031 | + | 0.927819i | \(0.378318\pi\) | |||||||
\(812\) | −6.63661e15 | −0.659763 | ||||||||
\(813\) | −7.99878e15 | −0.789816 | ||||||||
\(814\) | −3.88397e15 | −0.380927 | ||||||||
\(815\) | 8.22314e15 | 0.801071 | ||||||||
\(816\) | 5.86480e15 | 0.567489 | ||||||||
\(817\) | −7.84842e13 | −0.00754329 | ||||||||
\(818\) | 2.32584e15 | 0.222043 | ||||||||
\(819\) | 4.09441e15 | 0.388267 | ||||||||
\(820\) | 3.38196e15 | 0.318561 | ||||||||
\(821\) | 9.56085e15 | 0.894559 | 0.447280 | − | 0.894394i | \(-0.352393\pi\) | ||||
0.447280 | + | 0.894394i | \(0.352393\pi\) | |||||||
\(822\) | −6.43649e14 | −0.0598211 | ||||||||
\(823\) | 1.47807e15 | 0.136457 | 0.0682285 | − | 0.997670i | \(-0.478265\pi\) | ||||
0.0682285 | + | 0.997670i | \(0.478265\pi\) | |||||||
\(824\) | 2.11235e15 | 0.193716 | ||||||||
\(825\) | −2.67130e15 | −0.243347 | ||||||||
\(826\) | 1.75623e14 | 0.0158924 | ||||||||
\(827\) | 6.56307e14 | 0.0589966 | 0.0294983 | − | 0.999565i | \(-0.490609\pi\) | ||||
0.0294983 | + | 0.999565i | \(0.490609\pi\) | |||||||
\(828\) | −1.01261e15 | −0.0904226 | ||||||||
\(829\) | −6.73203e15 | −0.597167 | −0.298584 | − | 0.954383i | \(-0.596514\pi\) | ||||
−0.298584 | + | 0.954383i | \(0.596514\pi\) | |||||||
\(830\) | −2.36670e15 | −0.208552 | ||||||||
\(831\) | −1.19692e16 | −1.04775 | ||||||||
\(832\) | 1.49766e16 | 1.30237 | ||||||||
\(833\) | −5.23950e15 | −0.452629 | ||||||||
\(834\) | −2.25392e14 | −0.0193431 | ||||||||
\(835\) | −4.55126e15 | −0.388022 | ||||||||
\(836\) | −3.45329e14 | −0.0292482 | ||||||||
\(837\) | 5.26503e14 | 0.0443007 | ||||||||
\(838\) | 8.77321e14 | 0.0733359 | ||||||||
\(839\) | −8.01856e15 | −0.665895 | −0.332947 | − | 0.942945i | \(-0.608043\pi\) | ||||
−0.332947 | + | 0.942945i | \(0.608043\pi\) | |||||||
\(840\) | −1.48097e15 | −0.122183 | ||||||||
\(841\) | −2.46644e15 | −0.202159 | ||||||||
\(842\) | −2.72490e15 | −0.221888 | ||||||||
\(843\) | 1.09707e16 | 0.887527 | ||||||||
\(844\) | −1.47244e16 | −1.18346 | ||||||||
\(845\) | 1.49523e16 | 1.19398 | ||||||||
\(846\) | −4.58975e13 | −0.00364126 | ||||||||
\(847\) | −2.30336e16 | −1.81553 | ||||||||
\(848\) | −9.76901e14 | −0.0765021 | ||||||||
\(849\) | −1.20215e16 | −0.935333 | ||||||||
\(850\) | 5.07404e14 | 0.0392238 | ||||||||
\(851\) | 4.65695e15 | 0.357675 | ||||||||
\(852\) | 1.60770e15 | 0.122684 | ||||||||
\(853\) | 2.59125e16 | 1.96467 | 0.982333 | − | 0.187139i | \(-0.0599215\pi\) | ||||
0.982333 | + | 0.187139i | \(0.0599215\pi\) | |||||||
\(854\) | 2.90075e15 | 0.218520 | ||||||||
\(855\) | 6.37401e13 | 0.00477088 | ||||||||
\(856\) | −4.66485e15 | −0.346922 | ||||||||
\(857\) | −2.30391e16 | −1.70244 | −0.851218 | − | 0.524813i | \(-0.824135\pi\) | ||||
−0.851218 | + | 0.524813i | \(0.824135\pi\) | |||||||
\(858\) | 3.58255e15 | 0.263034 | ||||||||
\(859\) | −9.62049e15 | −0.701834 | −0.350917 | − | 0.936406i | \(-0.614130\pi\) | ||||
−0.350917 | + | 0.936406i | \(0.614130\pi\) | |||||||
\(860\) | 5.46208e15 | 0.395928 | ||||||||
\(861\) | 2.26358e15 | 0.163034 | ||||||||
\(862\) | −1.85846e15 | −0.133004 | ||||||||
\(863\) | −1.14684e16 | −0.815536 | −0.407768 | − | 0.913085i | \(-0.633693\pi\) | ||||
−0.407768 | + | 0.913085i | \(0.633693\pi\) | |||||||
\(864\) | −1.27021e15 | −0.0897533 | ||||||||
\(865\) | 2.16090e16 | 1.51721 | ||||||||
\(866\) | 3.65423e14 | 0.0254945 | ||||||||
\(867\) | 1.11794e15 | 0.0775019 | ||||||||
\(868\) | 2.46820e15 | 0.170029 | ||||||||
\(869\) | −2.40801e15 | −0.164835 | ||||||||
\(870\) | 1.07183e15 | 0.0729071 | ||||||||
\(871\) | 7.31751e15 | 0.494611 | ||||||||
\(872\) | 2.25834e15 | 0.151687 | ||||||||
\(873\) | −5.37359e15 | −0.358663 | ||||||||
\(874\) | −1.10161e13 | −0.000730659 0 | ||||||||
\(875\) | 1.24148e16 | 0.818270 | ||||||||
\(876\) | 4.05819e15 | 0.265803 | ||||||||
\(877\) | −4.36497e15 | −0.284108 | −0.142054 | − | 0.989859i | \(-0.545371\pi\) | ||||
−0.142054 | + | 0.989859i | \(0.545371\pi\) | |||||||
\(878\) | −5.12944e14 | −0.0331780 | ||||||||
\(879\) | 9.66641e15 | 0.621336 | ||||||||
\(880\) | 2.33766e16 | 1.49323 | ||||||||
\(881\) | −7.32263e15 | −0.464836 | −0.232418 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232418 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(882\) | 3.61517e14 | 0.0228061 | ||||||||
\(883\) | 9.83832e15 | 0.616790 | 0.308395 | − | 0.951258i | \(-0.400208\pi\) | ||||
0.308395 | + | 0.951258i | \(0.400208\pi\) | |||||||
\(884\) | 2.55773e16 | 1.59355 | ||||||||
\(885\) | 1.06608e15 | 0.0660090 | ||||||||
\(886\) | −8.52954e14 | −0.0524856 | ||||||||
\(887\) | 1.98191e16 | 1.21200 | 0.606001 | − | 0.795464i | \(-0.292773\pi\) | ||||
0.606001 | + | 0.795464i | \(0.292773\pi\) | |||||||
\(888\) | 3.87745e15 | 0.235654 | ||||||||
\(889\) | −1.31055e16 | −0.791579 | ||||||||
\(890\) | −2.24086e15 | −0.134514 | ||||||||
\(891\) | 3.43128e15 | 0.204705 | ||||||||
\(892\) | −3.01077e16 | −1.78514 | ||||||||
\(893\) | 1.87674e13 | 0.00110591 | ||||||||
\(894\) | −6.75481e14 | −0.0395601 | ||||||||
\(895\) | 1.90427e16 | 1.10841 | ||||||||
\(896\) | −7.90214e15 | −0.457142 | ||||||||
\(897\) | −4.29554e15 | −0.246979 | ||||||||
\(898\) | 4.18843e14 | 0.0239349 | ||||||||
\(899\) | −3.62017e15 | −0.205613 | ||||||||
\(900\) | 1.31590e15 | 0.0742831 | ||||||||
\(901\) | −1.57342e15 | −0.0882794 | ||||||||
\(902\) | 1.98060e15 | 0.110449 | ||||||||
\(903\) | 3.65583e15 | 0.202630 | ||||||||
\(904\) | −2.02523e15 | −0.111570 | ||||||||
\(905\) | 1.80932e16 | 0.990713 | ||||||||
\(906\) | −1.22512e14 | −0.00666765 | ||||||||
\(907\) | 2.93743e16 | 1.58901 | 0.794505 | − | 0.607257i | \(-0.207730\pi\) | ||||
0.794505 | + | 0.607257i | \(0.207730\pi\) | |||||||
\(908\) | −2.92078e16 | −1.57046 | ||||||||
\(909\) | 5.13931e15 | 0.274665 | ||||||||
\(910\) | −3.09993e15 | −0.164674 | ||||||||
\(911\) | 4.72649e15 | 0.249567 | 0.124784 | − | 0.992184i | \(-0.460176\pi\) | ||||
0.124784 | + | 0.992184i | \(0.460176\pi\) | |||||||
\(912\) | 1.65465e14 | 0.00868432 | ||||||||
\(913\) | 5.20958e16 | 2.71778 | ||||||||
\(914\) | −2.11589e15 | −0.109721 | ||||||||
\(915\) | 1.76084e16 | 0.907621 | ||||||||
\(916\) | −2.67076e16 | −1.36839 | ||||||||
\(917\) | 1.39226e16 | 0.709072 | ||||||||
\(918\) | −6.51760e14 | −0.0329953 | ||||||||
\(919\) | 1.45271e16 | 0.731046 | 0.365523 | − | 0.930802i | \(-0.380890\pi\) | ||||
0.365523 | + | 0.930802i | \(0.380890\pi\) | |||||||
\(920\) | 1.55372e15 | 0.0777212 | ||||||||
\(921\) | 2.26640e15 | 0.112696 | ||||||||
\(922\) | 3.38352e15 | 0.167243 | ||||||||
\(923\) | 6.81994e15 | 0.335097 | ||||||||
\(924\) | 1.60856e16 | 0.785671 | ||||||||
\(925\) | −6.05176e15 | −0.293834 | ||||||||
\(926\) | −1.10112e15 | −0.0531465 | ||||||||
\(927\) | 4.23482e15 | 0.203187 | ||||||||
\(928\) | 8.73382e15 | 0.416572 | ||||||||
\(929\) | −2.01875e15 | −0.0957185 | −0.0478592 | − | 0.998854i | \(-0.515240\pi\) | ||||
−0.0478592 | + | 0.998854i | \(0.515240\pi\) | |||||||
\(930\) | −3.98621e14 | −0.0187890 | ||||||||
\(931\) | −1.47824e14 | −0.00692661 | ||||||||
\(932\) | −3.22596e16 | −1.50270 | ||||||||
\(933\) | −1.07268e16 | −0.496729 | ||||||||
\(934\) | −4.03282e15 | −0.185653 | ||||||||
\(935\) | 3.76511e16 | 1.72311 | ||||||||
\(936\) | −3.57653e15 | −0.162722 | ||||||||
\(937\) | −4.90720e15 | −0.221955 | −0.110978 | − | 0.993823i | \(-0.535398\pi\) | ||||
−0.110978 | + | 0.993823i | \(0.535398\pi\) | |||||||
\(938\) | −8.74132e14 | −0.0393062 | ||||||||
\(939\) | 2.18961e16 | 0.978827 | ||||||||
\(940\) | −1.30611e15 | −0.0580466 | ||||||||
\(941\) | −2.30046e15 | −0.101642 | −0.0508208 | − | 0.998708i | \(-0.516184\pi\) | ||||
−0.0508208 | + | 0.998708i | \(0.516184\pi\) | |||||||
\(942\) | −3.16182e15 | −0.138885 | ||||||||
\(943\) | −2.37478e15 | −0.103707 | ||||||||
\(944\) | 2.76749e15 | 0.120154 | ||||||||
\(945\) | −2.96904e15 | −0.128157 | ||||||||
\(946\) | 3.19879e15 | 0.137273 | ||||||||
\(947\) | −1.29652e16 | −0.553167 | −0.276583 | − | 0.960990i | \(-0.589202\pi\) | ||||
−0.276583 | + | 0.960990i | \(0.589202\pi\) | |||||||
\(948\) | 1.18620e15 | 0.0503168 | ||||||||
\(949\) | 1.72150e16 | 0.726009 | ||||||||
\(950\) | 1.43155e13 | 0.000600244 0 | ||||||||
\(951\) | −1.09050e16 | −0.454606 | ||||||||
\(952\) | −6.19208e15 | −0.256645 | ||||||||
\(953\) | −3.89460e16 | −1.60491 | −0.802457 | − | 0.596710i | \(-0.796474\pi\) | ||||
−0.802457 | + | 0.596710i | \(0.796474\pi\) | |||||||
\(954\) | 1.08564e14 | 0.00444804 | ||||||||
\(955\) | 7.65464e15 | 0.311822 | ||||||||
\(956\) | 7.26208e15 | 0.294132 | ||||||||
\(957\) | −2.35931e16 | −0.950100 | ||||||||
\(958\) | −7.13826e15 | −0.285813 | ||||||||
\(959\) | −1.22594e16 | −0.488051 | ||||||||
\(960\) | −1.08602e16 | −0.429879 | ||||||||
\(961\) | −2.40621e16 | −0.947011 | ||||||||
\(962\) | 8.11617e15 | 0.317606 | ||||||||
\(963\) | −9.35205e15 | −0.363883 | ||||||||
\(964\) | −4.06140e15 | −0.157128 | ||||||||
\(965\) | 2.01952e16 | 0.776871 | ||||||||
\(966\) | 5.13135e14 | 0.0196271 | ||||||||
\(967\) | −6.35337e15 | −0.241634 | −0.120817 | − | 0.992675i | \(-0.538551\pi\) | ||||
−0.120817 | + | 0.992675i | \(0.538551\pi\) | |||||||
\(968\) | 2.01202e16 | 0.760882 | ||||||||
\(969\) | 2.66503e14 | 0.0100212 | ||||||||
\(970\) | 4.06841e15 | 0.152118 | ||||||||
\(971\) | −4.09349e16 | −1.52190 | −0.760952 | − | 0.648808i | \(-0.775268\pi\) | ||||
−0.760952 | + | 0.648808i | \(0.775268\pi\) | |||||||
\(972\) | −1.69028e15 | −0.0624875 | ||||||||
\(973\) | −4.29296e15 | −0.157811 | ||||||||
\(974\) | −9.84566e14 | −0.0359891 | ||||||||
\(975\) | 5.58210e15 | 0.202896 | ||||||||
\(976\) | 4.57104e16 | 1.65212 | ||||||||
\(977\) | 7.17746e14 | 0.0257959 | 0.0128980 | − | 0.999917i | \(-0.495894\pi\) | ||||
0.0128980 | + | 0.999917i | \(0.495894\pi\) | |||||||
\(978\) | −2.37229e15 | −0.0847820 | ||||||||
\(979\) | 4.93257e16 | 1.75295 | ||||||||
\(980\) | 1.02877e16 | 0.363560 | ||||||||
\(981\) | 4.52750e15 | 0.159103 | ||||||||
\(982\) | −3.27745e15 | −0.114531 | ||||||||
\(983\) | 2.84140e16 | 0.987387 | 0.493694 | − | 0.869636i | \(-0.335646\pi\) | ||||
0.493694 | + | 0.869636i | \(0.335646\pi\) | |||||||
\(984\) | −1.97728e15 | −0.0683273 | ||||||||
\(985\) | 3.93148e16 | 1.35101 | ||||||||
\(986\) | 4.48142e15 | 0.153141 | ||||||||
\(987\) | −8.74194e14 | −0.0297073 | ||||||||
\(988\) | 7.21620e14 | 0.0243863 | ||||||||
\(989\) | −3.83541e15 | −0.128894 | ||||||||
\(990\) | −2.59786e15 | −0.0868206 | ||||||||
\(991\) | −6.22968e15 | −0.207043 | −0.103522 | − | 0.994627i | \(-0.533011\pi\) | ||||
−0.103522 | + | 0.994627i | \(0.533011\pi\) | |||||||
\(992\) | −3.24817e15 | −0.107356 | ||||||||
\(993\) | −1.18654e16 | −0.389996 | ||||||||
\(994\) | −8.14693e14 | −0.0266298 | ||||||||
\(995\) | −4.34793e16 | −1.41337 | ||||||||
\(996\) | −2.56628e16 | −0.829617 | ||||||||
\(997\) | 5.19909e16 | 1.67149 | 0.835745 | − | 0.549118i | \(-0.185036\pi\) | ||||
0.835745 | + | 0.549118i | \(0.185036\pi\) | |||||||
\(998\) | 5.70988e15 | 0.182561 | ||||||||
\(999\) | 7.77348e15 | 0.247175 |
(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 | 177.12.a.d.1.13 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.13 | ✓ | 28 | 1.1 | even | 1 | trivial |