Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,34,Mod(1,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(27.5931315524\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 65185566x - 173679864984 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{3}\cdot 7\cdot 11\cdot 29 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(9172.25\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.16957e7 | 0.290987 | 0.145494 | − | 0.989359i | \(-0.453523\pi\) | ||||
0.145494 | + | 0.989359i | \(0.453523\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.04966e11 | 1.77307 | 0.886535 | − | 0.462662i | \(-0.153106\pi\) | ||||
0.886535 | + | 0.462662i | \(0.153106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.12234e14 | 1.27646 | 0.638229 | − | 0.769846i | \(-0.279667\pi\) | ||||
0.638229 | + | 0.769846i | \(0.279667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.08836e15 | −0.915326 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12022e17 | 1.39124 | 0.695620 | − | 0.718410i | \(-0.255130\pi\) | ||||
0.695620 | + | 0.718410i | \(0.255130\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.20110e18 | −0.917435 | −0.458718 | − | 0.888582i | \(-0.651691\pi\) | ||||
−0.458718 | + | 0.888582i | \(0.651691\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.31252e19 | 0.515940 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.09205e19 | −0.453163 | −0.226582 | − | 0.973992i | \(-0.572755\pi\) | ||||
−0.226582 | + | 0.973992i | \(0.572755\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.28541e20 | 0.420382 | 0.210191 | − | 0.977660i | \(-0.432591\pi\) | ||||
0.210191 | + | 0.977660i | \(0.432591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.43500e21 | 0.371433 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.52550e22 | −0.858693 | −0.429346 | − | 0.903140i | \(-0.641256\pi\) | ||||
−0.429346 | + | 0.903140i | \(0.641256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49568e23 | 2.14377 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.31004e23 | −0.557336 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.22959e24 | 1.65447 | 0.827233 | − | 0.561859i | \(-0.189914\pi\) | ||||
0.827233 | + | 0.561859i | \(0.189914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.96021e24 | 1.47161 | 0.735806 | − | 0.677192i | \(-0.236803\pi\) | ||||
0.735806 | + | 0.677192i | \(0.236803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.59998e24 | 0.404833 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.78977e25 | 2.26325 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.07477e25 | −0.143215 | −0.0716074 | − | 0.997433i | \(-0.522813\pi\) | ||||
−0.0716074 | + | 0.997433i | \(0.522813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.77546e25 | −0.266962 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.45950e25 | 0.133727 | 0.0668635 | − | 0.997762i | \(-0.478701\pi\) | ||||
0.0668635 | + | 0.997762i | \(0.478701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.34669e26 | −0.820092 | −0.410046 | − | 0.912065i | \(-0.634487\pi\) | ||||
−0.410046 | + | 0.912065i | \(0.634487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.07828e27 | −1.62294 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.88377e27 | −0.741901 | −0.370950 | − | 0.928653i | \(-0.620968\pi\) | ||||
−0.370950 | + | 0.928653i | \(0.620968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.86547e27 | 0.629346 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.97259e27 | −0.131865 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.58827e27 | −0.233464 | −0.116732 | − | 0.993163i | \(-0.537242\pi\) | ||||
−0.116732 | + | 0.993163i | \(0.537242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.28266e29 | 2.46676 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.14671e28 | 0.122326 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.55330e29 | −0.937990 | −0.468995 | − | 0.883201i | \(-0.655384\pi\) | ||||
−0.468995 | + | 0.883201i | \(0.655384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.35869e29 | 1.86688 | 0.933440 | − | 0.358733i | \(-0.116791\pi\) | ||||
0.933440 | + | 0.358733i | \(0.116791\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.71086e29 | −1.16838 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.33159e30 | −1.62668 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.20034e29 | −0.385298 | −0.192649 | − | 0.981268i | \(-0.561708\pi\) | ||||
−0.192649 | + | 0.981268i | \(0.561708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.47926e29 | −0.249869 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.97143e30 | 0.845675 | 0.422837 | − | 0.906206i | \(-0.361034\pi\) | ||||
0.422837 | + | 0.906206i | \(0.361034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09019e30 | −0.916024 | −0.458012 | − | 0.888946i | \(-0.651438\pi\) | ||||
−0.458012 | + | 0.888946i | \(0.651438\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.41457e30 | 0.623811 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.37961e31 | 1.77586 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.81467e30 | −0.0887054 | −0.0443527 | − | 0.999016i | \(-0.514123\pi\) | ||||
−0.0443527 | + | 0.999016i | \(0.514123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.32747e31 | 0.753149 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.91242e31 | −0.846559 | −0.423279 | − | 0.905999i | \(-0.639121\pi\) | ||||
−0.423279 | + | 0.905999i | \(0.639121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.50038e31 | −0.803490 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.83726e31 | 0.481428 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.76955e32 | −1.21040 | −0.605199 | − | 0.796075i | \(-0.706906\pi\) | ||||
−0.605199 | + | 0.796075i | \(0.706906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47039e32 | −1.17107 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.29311e32 | 0.428220 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.19749e32 | 0.745367 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.13793e32 | 1.34518 | 0.672590 | − | 0.740016i | \(-0.265182\pi\) | ||||
0.672590 | + | 0.740016i | \(0.265182\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.07884e33 | −1.27344 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.19750e32 | 0.525913 | 0.262956 | − | 0.964808i | \(-0.415302\pi\) | ||||
0.262956 | + | 0.964808i | \(0.415302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.96344e33 | 1.81962 | 0.909812 | − | 0.415020i | \(-0.136225\pi\) | ||||
0.909812 | + | 0.415020i | \(0.136225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.47309e33 | 0.658577 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.09640e33 | −1.66890 | −0.834451 | − | 0.551082i | \(-0.814215\pi\) | ||||
−0.834451 | + | 0.551082i | \(0.814215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.31361e33 | −1.28189 | −0.640947 | − | 0.767585i | \(-0.721458\pi\) | ||||
−0.640947 | + | 0.767585i | \(0.721458\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.33180e32 | −0.0416737 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.75830e33 | 0.500262 | 0.250131 | − | 0.968212i | \(-0.419526\pi\) | ||||
0.250131 | + | 0.968212i | \(0.419526\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.52784e34 | −1.52252 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.12000e34 | 0.839753 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.02044e34 | −0.578444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.17282e34 | 0.935546 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.18448e33 | 0.0389128 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.05529e34 | 2.02799 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.74550e34 | −0.531937 | −0.265968 | − | 0.963982i | \(-0.585692\pi\) | ||||
−0.265968 | + | 0.963982i | \(0.585692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.59392e34 | −0.238636 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.61531e34 | −0.187620 | −0.0938099 | − | 0.995590i | \(-0.529905\pi\) | ||||
−0.0938099 | + | 0.995590i | \(0.529905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.93203e34 | 0.536601 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.39749e35 | −0.988194 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.20499e35 | −0.668490 | −0.334245 | − | 0.942486i | \(-0.608481\pi\) | ||||
−0.334245 | + | 0.942486i | \(0.608481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.71862e35 | −0.750648 | −0.375324 | − | 0.926894i | \(-0.622469\pi\) | ||||
−0.375324 | + | 0.926894i | \(0.622469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.25655e34 | −0.215884 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.66683e35 | −1.27637 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.34882e36 | 2.93348 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.05560e35 | 0.183132 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.16022e33 | −0.00438676 | −0.00219338 | − | 0.999998i | \(-0.500698\pi\) | ||||
−0.00219338 | + | 0.999998i | \(0.500698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.88992e35 | −0.990326 | −0.495163 | − | 0.868800i | \(-0.664892\pi\) | ||||
−0.495163 | + | 0.868800i | \(0.664892\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.62636e35 | 0.414792 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.60572e36 | 2.60927 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.61326e36 | −0.944842 | −0.472421 | − | 0.881373i | \(-0.656620\pi\) | ||||
−0.472421 | + | 0.881373i | \(0.656620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.42937e35 | −0.0679349 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.83447e36 | −1.09609 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.86098e36 | −1.84874 | −0.924368 | − | 0.381501i | \(-0.875407\pi\) | ||||
−0.924368 | + | 0.381501i | \(0.875407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.78283e36 | 0.717797 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.82436e35 | 0.165435 | 0.0827175 | − | 0.996573i | \(-0.473640\pi\) | ||||
0.0827175 | + | 0.996573i | \(0.473640\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.11269e35 | −0.158313 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.68941e36 | −0.384787 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.05668e37 | −1.24791 | −0.623957 | − | 0.781459i | \(-0.714476\pi\) | ||||
−0.623957 | + | 0.781459i | \(0.714476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.80100e37 | 2.73644 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.37001e36 | −0.272943 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.19253e37 | 0.802405 | 0.401202 | − | 0.915989i | \(-0.368592\pi\) | ||||
0.401202 | + | 0.915989i | \(0.368592\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.20113e36 | 0.123296 | 0.0616481 | − | 0.998098i | \(-0.480364\pi\) | ||||
0.0616481 | + | 0.998098i | \(0.480364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.16261e37 | 0.543238 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.50200e36 | −0.253930 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.92772e37 | −0.630458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.59265e37 | −0.711416 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.41890e37 | 0.327265 | 0.163633 | − | 0.986521i | \(-0.447679\pi\) | ||||
0.163633 | + | 0.986521i | \(0.447679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.71061e36 | −0.0720693 | −0.0360346 | − | 0.999351i | \(-0.511473\pi\) | ||||
−0.0360346 | + | 0.999351i | \(0.511473\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.88899e37 | −0.473342 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.85371e37 | −0.672018 | −0.336009 | − | 0.941859i | \(-0.609077\pi\) | ||||
−0.336009 | + | 0.941859i | \(0.609077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.20691e38 | −1.41449 | −0.707245 | − | 0.706968i | \(-0.750062\pi\) | ||||
−0.707245 | + | 0.706968i | \(0.750062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.12825e37 | −0.112117 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.50236e38 | 2.11186 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.30281e37 | 0.237107 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.28506e38 | 0.785984 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.12062e38 | 0.584852 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.47609e37 | −0.378038 | −0.189019 | − | 0.981973i | \(-0.560531\pi\) | ||||
−0.189019 | + | 0.981973i | \(0.560531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.44675e37 | 0.246081 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.44450e38 | −1.45408 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.68938e38 | 1.87845 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.10435e38 | −0.266551 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00126e38 | 0.415748 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.55613e38 | −1.71101 | −0.855504 | − | 0.517797i | \(-0.826752\pi\) | ||||
−0.855504 | + | 0.517797i | \(0.826752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.26989e39 | −1.96225 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.31422e38 | −0.175486 | −0.0877430 | − | 0.996143i | \(-0.527965\pi\) | ||||
−0.0877430 | + | 0.996143i | \(0.527965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01200e39 | 1.16922 | 0.584610 | − | 0.811314i | \(-0.301247\pi\) | ||||
0.584610 | + | 0.811314i | \(0.301247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.16274e38 | 0.516752 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.43939e38 | 0.385435 | 0.192717 | − | 0.981254i | \(-0.438270\pi\) | ||||
0.192717 | + | 0.981254i | \(0.438270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.74458e39 | −1.31544 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.93706e37 | −0.0258121 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.91733e39 | 1.66502 | 0.832512 | − | 0.554008i | \(-0.186902\pi\) | ||||
0.832512 | + | 0.554008i | \(0.186902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.88758e36 | 0.00243115 | 0.00121558 | − | 0.999999i | \(-0.499613\pi\) | ||||
0.00121558 | + | 0.999999i | \(0.499613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.78912e39 | 0.776492 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.94344e39 | 1.11587 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.16337e39 | −0.385674 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.48829e38 | −0.246338 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.40071e39 | −0.610553 | −0.305276 | − | 0.952264i | \(-0.598749\pi\) | ||||
−0.305276 | + | 0.952264i | \(0.598749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.35461e39 | −1.19465 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.19335e39 | −0.233805 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.55258e39 | 0.267398 | 0.133699 | − | 0.991022i | \(-0.457315\pi\) | ||||
0.133699 | + | 0.991022i | \(0.457315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.20626e39 | −0.182808 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.13449e40 | −1.51438 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.41636e40 | 1.66688 | 0.833442 | − | 0.552607i | \(-0.186367\pi\) | ||||
0.833442 | + | 0.552607i | \(0.186367\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.98567e39 | −0.413947 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.83917e39 | −0.352210 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.46974e39 | −0.362552 | −0.181276 | − | 0.983432i | \(-0.558023\pi\) | ||||
−0.181276 | + | 0.983432i | \(0.558023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.70466e39 | 0.337703 | 0.168851 | − | 0.985642i | \(-0.445994\pi\) | ||||
0.168851 | + | 0.985642i | \(0.445994\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.35969e39 | −0.340766 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.29140e40 | 2.98250 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.48781e40 | 1.24423 | 0.622116 | − | 0.782925i | \(-0.286273\pi\) | ||||
0.622116 | + | 0.782925i | \(0.286273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.03276e40 | −1.34701 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.82873e38 | 0.0269579 | 0.0134789 | − | 0.999909i | \(-0.495709\pi\) | ||||
0.0134789 | + | 0.999909i | \(0.495709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.13055e40 | −1.09937 | −0.549686 | − | 0.835371i | \(-0.685253\pi\) | ||||
−0.549686 | + | 0.835371i | \(0.685253\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.93720e39 | 0.216892 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.12741e39 | 0.170697 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.19880e40 | −0.794643 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.76558e40 | 0.391430 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.43484e38 | 0.00878138 | 0.00439069 | − | 0.999990i | \(-0.498602\pi\) | ||||
0.00439069 | + | 0.999990i | \(0.498602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.39696e40 | −1.66312 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.89779e40 | −0.775387 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.55889e40 | 0.787795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.24549e40 | −1.04681 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.34459e40 | 0.153034 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.24182e41 | 3.31011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.15172e40 | −0.838918 | −0.419459 | − | 0.907774i | \(-0.637780\pi\) | ||||
−0.419459 | + | 0.907774i | \(0.637780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.42940e40 | 0.529487 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.61111e40 | −0.341397 | −0.170698 | − | 0.985323i | \(-0.554602\pi\) | ||||
−0.170698 | + | 0.985323i | \(0.554602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.08893e40 | 0.538778 | 0.269389 | − | 0.963031i | \(-0.413178\pi\) | ||||
0.269389 | + | 0.963031i | \(0.413178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.45488e41 | −2.07161 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.72792e41 | 1.47351 | 0.736756 | − | 0.676159i | \(-0.236357\pi\) | ||||
0.736756 | + | 0.676159i | \(0.236357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.72722e41 | 2.30176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.10570e41 | −0.485629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.80552e40 | −0.190502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.49326e41 | −1.96677 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.15283e41 | −0.373015 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.23657e41 | −0.947006 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.98182e40 | 0.105419 | 0.0527096 | − | 0.998610i | \(-0.483214\pi\) | ||||
0.0527096 | + | 0.998610i | \(0.483214\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.46882e40 | 0.131088 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.14603e41 | −0.683161 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.02227e41 | −0.201220 | −0.100610 | − | 0.994926i | \(-0.532079\pi\) | ||||
−0.100610 | + | 0.994926i | \(0.532079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.15391e40 | 0.145570 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.26370e42 | 2.04736 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.21609e41 | −0.473124 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.31476e41 | −0.443034 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.19238e42 | 1.44870 | 0.724348 | − | 0.689434i | \(-0.242141\pi\) | ||||
0.724348 | + | 0.689434i | \(0.242141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.44292e41 | −1.04349 | −0.521743 | − | 0.853103i | \(-0.674718\pi\) | ||||
−0.521743 | + | 0.853103i | \(0.674718\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.08463e41 | 0.511319 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.78690e41 | 0.346738 | 0.173369 | − | 0.984857i | \(-0.444535\pi\) | ||||
0.173369 | + | 0.984857i | \(0.444535\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.79762e42 | 1.49944 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.21391e41 | −0.168320 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.89278e41 | −0.269899 | −0.134950 | − | 0.990852i | \(-0.543087\pi\) | ||||
−0.134950 | + | 0.990852i | \(0.543087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.30141e42 | −0.823279 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.71410e41 | 0.272232 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.07939e42 | −1.62417 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.36076e42 | −0.655829 | −0.327914 | − | 0.944707i | \(-0.606346\pi\) | ||||
−0.327914 | + | 0.944707i | \(0.606346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.77799e41 | −0.122404 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.39427e41 | −0.298007 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.42419e42 | 1.26288 | 0.631440 | − | 0.775425i | \(-0.282464\pi\) | ||||
0.631440 | + | 0.775425i | \(0.282464\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.74765e42 | 0.590119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.90756e42 | −1.51786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.97551e42 | −0.559928 | −0.279964 | − | 0.960011i | \(-0.590322\pi\) | ||||
−0.279964 | + | 0.960011i | \(0.590322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.95656e41 | −0.154787 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.75888e42 | −1.13429 | −0.567146 | − | 0.823617i | \(-0.691952\pi\) | ||||
−0.567146 | + | 0.823617i | \(0.691952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.43958e43 | 3.14872 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.73826e42 | 0.750652 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.85205e42 | 0.710434 | 0.355217 | − | 0.934784i | \(-0.384407\pi\) | ||||
0.355217 | + | 0.934784i | \(0.384407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.29620e42 | 0.389128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.50453e41 | −0.0545949 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.09781e42 | −0.157281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.07957e42 | −0.933176 | −0.466588 | − | 0.884475i | \(-0.654517\pi\) | ||||
−0.466588 | + | 0.884475i | \(0.654517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.28700e42 | 0.156144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.99621e42 | −0.446444 | −0.223222 | − | 0.974768i | \(-0.571657\pi\) | ||||
−0.223222 | + | 0.974768i | \(0.571657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.31190e43 | −1.35011 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.40804e43 | 1.33539 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.27875e42 | −0.199246 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.22070e42 | 0.340369 | 0.170184 | − | 0.985412i | \(-0.445564\pi\) | ||||
0.170184 | + | 0.985412i | \(0.445564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.61432e42 | −0.194522 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.74334e43 | −1.19731 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.36688e43 | −1.50101 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.72868e42 | −0.218429 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.25752e42 | −0.284610 | −0.142305 | − | 0.989823i | \(-0.545451\pi\) | ||||
−0.142305 | + | 0.989823i | \(0.545451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.56053e43 | 1.78180 | 0.890902 | − | 0.454195i | \(-0.150073\pi\) | ||||
0.890902 | + | 0.454195i | \(0.150073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.46736e43 | 0.679081 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.26909e43 | −0.971480 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.01427e43 | 2.38300 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.01250e43 | −0.371408 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.50406e43 | −1.19041 | −0.595205 | − | 0.803574i | \(-0.702929\pi\) | ||||
−0.595205 | + | 0.803574i | \(0.702929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.65228e43 | 1.46425 | 0.732125 | − | 0.681170i | \(-0.238529\pi\) | ||||
0.732125 | + | 0.681170i | \(0.238529\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.92638e43 | 0.853606 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.33483e43 | −0.360979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.97854e42 | −0.124864 | −0.0624320 | − | 0.998049i | \(-0.519886\pi\) | ||||
−0.0624320 | + | 0.998049i | \(0.519886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.47573e43 | −0.576057 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.46629e43 | 1.39635 | 0.698174 | − | 0.715928i | \(-0.253996\pi\) | ||||
0.698174 | + | 0.715928i | \(0.253996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07052e44 | −2.14612 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.85633e40 | −0.00127649 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.27700e43 | 0.393820 | 0.196910 | − | 0.980422i | \(-0.436909\pi\) | ||||
0.196910 | + | 0.980422i | \(0.436909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15753e43 | 0.186046 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.92874e43 | −0.288172 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.49450e44 | −2.07638 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.89272e43 | −1.27849 | −0.639247 | − | 0.769002i | \(-0.720754\pi\) | ||||
−0.639247 | + | 0.769002i | \(0.720754\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.10030e43 | 0.252564 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.21100e44 | 1.35544 | 0.677720 | − | 0.735320i | \(-0.262968\pi\) | ||||
0.677720 | + | 0.735320i | \(0.262968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.96429e43 | 0.204701 | 0.102350 | − | 0.994748i | \(-0.467364\pi\) | ||||
0.102350 | + | 0.994748i | \(0.467364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.82288e43 | 0.759264 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.33961e44 | 1.21130 | 0.605650 | − | 0.795731i | \(-0.292913\pi\) | ||||
0.605650 | + | 0.795731i | \(0.292913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.83655e43 | −0.491817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50008e43 | −0.274937 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.55766e44 | −1.14094 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.31907e44 | 0.901205 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.35234e43 | 0.213695 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.06153e44 | 1.22646 | 0.613232 | − | 0.789903i | \(-0.289869\pi\) | ||||
0.613232 | + | 0.789903i | \(0.289869\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.36568e43 | 0.131390 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.14959e43 | −0.318947 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.92317e44 | 2.38510 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.57095e44 | −0.711108 | −0.355554 | − | 0.934656i | \(-0.615708\pi\) | ||||
−0.355554 | + | 0.934656i | \(0.615708\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.27158e44 | −0.537959 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.22476e44 | −1.67093 | −0.835464 | − | 0.549545i | \(-0.814801\pi\) | ||||
−0.835464 | + | 0.549545i | \(0.814801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.02715e44 | −0.749743 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.52663e44 | −2.25789 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.33496e44 | 1.07947 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.23722e44 | 0.374791 | 0.187395 | − | 0.982285i | \(-0.439995\pi\) | ||||
0.187395 | + | 0.982285i | \(0.439995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.69755e43 | 0.0481395 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.11832e44 | −0.296957 | −0.148478 | − | 0.988916i | \(-0.547438\pi\) | ||||
−0.148478 | + | 0.988916i | \(0.547438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.74927e44 | 0.932479 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.97707e43 | −0.0460670 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.64785e44 | −0.578162 | −0.289081 | − | 0.957305i | \(-0.593350\pi\) | ||||
−0.289081 | + | 0.957305i | \(0.593350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.71292e44 | −1.16927 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.22095e44 | −0.234294 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.79278e45 | 3.22632 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.11423e44 | −1.03216 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.29256e44 | −0.363127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.23370e44 | 0.926666 | 0.463333 | − | 0.886184i | \(-0.346653\pi\) | ||||
0.463333 | + | 0.886184i | \(0.346653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.27079e44 | 1.15417 | 0.577084 | − | 0.816685i | \(-0.304191\pi\) | ||||
0.577084 | + | 0.816685i | \(0.304191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.07698e44 | 0.796269 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.41905e44 | −0.666881 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.27191e44 | −0.262647 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.90376e44 | 0.858567 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.20169e44 | −0.122686 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.08314e45 | −2.95908 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.58728e44 | 0.233489 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.03159e45 | 0.875571 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.03419e45 | 0.825745 | 0.412873 | − | 0.910789i | \(-0.364525\pi\) | ||||
0.412873 | + | 0.910789i | \(0.364525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.77552e43 | 0.0358776 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.21455e45 | −2.27289 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.01840e45 | 0.677844 | 0.338922 | − | 0.940815i | \(-0.389938\pi\) | ||||
0.338922 | + | 0.940815i | \(0.389938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.72669e45 | −1.70880 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.17843e45 | 0.695508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.03667e44 | −0.113229 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.41066e44 | −0.0738903 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.74214e44 | −0.135357 | −0.0676783 | − | 0.997707i | \(-0.521559\pi\) | ||||
−0.0676783 | + | 0.997707i | \(0.521559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.61708e45 | 0.752381 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.18232e44 | −0.183455 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.73021e44 | −0.0715666 | −0.0357833 | − | 0.999360i | \(-0.511393\pi\) | ||||
−0.0357833 | + | 0.999360i | \(0.511393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.27364e45 | 0.886998 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.61221e45 | 0.961363 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.46685e45 | 1.20388 | 0.601939 | − | 0.798542i | \(-0.294395\pi\) | ||||
0.601939 | + | 0.798542i | \(0.294395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.55607e45 | 1.16540 | 0.582699 | − | 0.812688i | \(-0.301997\pi\) | ||||
0.582699 | + | 0.812688i | \(0.301997\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.07840e44 | 0.0952300 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.30284e45 | −1.84084 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.33881e45 | −0.369249 | −0.184625 | − | 0.982809i | \(-0.559107\pi\) | ||||
−0.184625 | + | 0.982809i | \(0.559107\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.05046e43 | −0.0209712 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.39107e45 | −1.08060 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.39686e45 | −0.324804 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.77562e45 | 1.48894 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.27700e45 | 0.265255 | 0.132628 | − | 0.991166i | \(-0.457659\pi\) | ||||
0.132628 | + | 0.991166i | \(0.457659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.15021e45 | 0.618640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.05305e45 | −0.195549 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.49368e45 | −1.31611 | −0.658056 | − | 0.752969i | \(-0.728621\pi\) | ||||
−0.658056 | + | 0.752969i | \(0.728621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.17329e45 | −1.02562 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.61849e45 | −0.411599 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.19178e46 | −1.77278 | −0.886388 | − | 0.462943i | \(-0.846793\pi\) | ||||
−0.886388 | + | 0.462943i | \(0.846793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.25892e45 | −0.177243 | −0.0886214 | − | 0.996065i | \(-0.528246\pi\) | ||||
−0.0886214 | + | 0.996065i | \(0.528246\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.64612e45 | 0.352674 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.31448e46 | 1.65879 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.28539e44 | 0.0631632 | 0.0315816 | − | 0.999501i | \(-0.489946\pi\) | ||||
0.0315816 | + | 0.999501i | \(0.489946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.42905e45 | 0.614523 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.34748e45 | 0.680646 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.85915e44 | −0.100171 | −0.0500854 | − | 0.998745i | \(-0.515949\pi\) | ||||
−0.0500854 | + | 0.998745i | \(0.515949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.16569e44 | 0.0689952 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.14287e45 | −0.195565 | −0.0977826 | − | 0.995208i | \(-0.531175\pi\) | ||||
−0.0977826 | + | 0.995208i | \(0.531175\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.99540e45 | 0.864778 | 0.432389 | − | 0.901687i | \(-0.357671\pi\) | ||||
0.432389 | + | 0.901687i | \(0.357671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.83399e45 | 0.478580 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.98604e46 | −1.54502 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.96782e46 | 1.45199 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.43128e45 | 0.170185 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.77188e44 | 0.0648996 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.87168e46 | 1.17964 | 0.589818 | − | 0.807536i | \(-0.299199\pi\) | ||||
0.589818 | + | 0.807536i | \(0.299199\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.83895e45 | −0.110004 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.66093e46 | −0.943160 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.07094e46 | −0.577385 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.51197e46 | −0.774068 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.73888e46 | −1.81796 | −0.908980 | − | 0.416841i | \(-0.863137\pi\) | ||||
−0.908980 | + | 0.416841i | \(0.863137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.70674e45 | 0.171203 | 0.0856015 | − | 0.996329i | \(-0.472719\pi\) | ||||
0.0856015 | + | 0.996329i | \(0.472719\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.64267e45 | −0.423118 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.44855e46 | 1.43786 | 0.718928 | − | 0.695084i | \(-0.244633\pi\) | ||||
0.718928 | + | 0.695084i | \(0.244633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.29335e46 | −1.30497 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.45131e46 | 0.546606 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.14942e45 | −0.291782 | −0.145891 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145891 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.77205e45 | −0.332663 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.59007e46 | 0.838461 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.21169e46 | 0.680948 | 0.340474 | − | 0.940254i | \(-0.389412\pi\) | ||||
0.340474 | + | 0.940254i | \(0.389412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.77870e46 | −0.520928 | −0.260464 | − | 0.965484i | \(-0.583876\pi\) | ||||
−0.260464 | + | 0.965484i | \(0.583876\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.34187e45 | 0.120977 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.58867e46 | 0.951430 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.63082e46 | −1.42068 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.07327e46 | −0.497881 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.13616e47 | 2.59728 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.15371e46 | 0.251100 | 0.125550 | − | 0.992087i | \(-0.459930\pi\) | ||||
0.125550 | + | 0.992087i | \(0.459930\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.76511e46 | −1.19480 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.04683e46 | 1.58822 | 0.794112 | − | 0.607771i | \(-0.207936\pi\) | ||||
0.794112 | + | 0.607771i | \(0.207936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.13352e46 | 1.71707 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.85130e45 | −0.0510642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.01067e46 | −1.36687 | −0.683435 | − | 0.730011i | \(-0.739515\pi\) | ||||
−0.683435 | + | 0.730011i | \(0.739515\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.28979e46 | −1.18528 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.19562e46 | 0.340228 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.45015e46 | 0.214188 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.09406e46 | −0.154046 | −0.0770232 | − | 0.997029i | \(-0.524542\pi\) | ||||
−0.0770232 | + | 0.997029i | \(0.524542\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.21083e47 | −1.62549 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.03971e47 | −1.33095 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.96380e45 | −0.0606001 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.63159e45 | 0.112157 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.08980e46 | 0.676481 | 0.338240 | − | 0.941060i | \(-0.390168\pi\) | ||||
0.338240 | + | 0.941060i | \(0.390168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.68061e45 | −0.0602049 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.78500e46 | −0.382777 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.95570e46 | 0.671306 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.22329e47 | 1.12685 | 0.563425 | − | 0.826167i | \(-0.309484\pi\) | ||||
0.563425 | + | 0.826167i | \(0.309484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.23368e45 | 0.0811944 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.50525e47 | −1.26366 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.82327e47 | −2.26310 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.32937e46 | 0.484501 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.92469e46 | 0.360042 | 0.180021 | − | 0.983663i | \(-0.442384\pi\) | ||||
0.180021 | + | 0.983663i | \(0.442384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.32599e47 | 2.32268 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.06040e44 | 0.000707435 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.56434e47 | 3.54680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.32921e47 | −0.809611 | −0.404806 | − | 0.914403i | \(-0.632661\pi\) | ||||
−0.404806 | + | 0.914403i | \(0.632661\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.05689e46 | −0.527200 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.67965e46 | 0.371635 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.32699e47 | −1.76944 | −0.884721 | − | 0.466121i | \(-0.845651\pi\) | ||||
−0.884721 | + | 0.466121i | \(0.845651\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.38602e46 | 0.324705 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.10259e47 | −0.536042 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.02617e47 | −0.477074 | −0.238537 | − | 0.971133i | \(-0.576668\pi\) | ||||
−0.238537 | + | 0.971133i | \(0.576668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.52403e46 | −0.112226 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.30680e47 | 0.981059 | 0.490530 | − | 0.871424i | \(-0.336803\pi\) | ||||
0.490530 | + | 0.871424i | \(0.336803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.91182e45 | −0.00777803 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.99078e47 | 0.774878 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.71989e47 | −2.13028 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.87651e47 | 1.02519 | 0.512597 | − | 0.858629i | \(-0.328683\pi\) | ||||
0.512597 | + | 0.858629i | \(0.328683\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.20852e46 | −0.177663 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.37810e47 | −1.75592 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.30633e47 | −0.408292 | −0.204146 | − | 0.978940i | \(-0.565442\pi\) | ||||
−0.204146 | + | 0.978940i | \(0.565442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.16172e47 | −0.347627 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00969e47 | 0.289295 | 0.144648 | − | 0.989483i | \(-0.453795\pi\) | ||||
0.144648 | + | 0.989483i | \(0.453795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.96367e47 | −1.63628 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.79879e47 | 0.735455 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.41898e47 | 0.860545 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.46600e47 | 1.07680 | 0.538399 | − | 0.842690i | \(-0.319029\pi\) | ||||
0.538399 | + | 0.842690i | \(0.319029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.36844e46 | 0.0778093 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.83555e47 | −1.29158 | −0.645788 | − | 0.763516i | \(-0.723471\pi\) | ||||
−0.645788 | + | 0.763516i | \(0.723471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.48748e48 | 3.15480 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.61707e46 | −0.0531947 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.88557e46 | 0.0562165 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.30010e47 | 1.17654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.15043e47 | −0.922092 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.75965e47 | −1.67527 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.26390e47 | 1.19560 | 0.597801 | − | 0.801644i | \(-0.296041\pi\) | ||||
0.597801 | + | 0.801644i | \(0.296041\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.07291e47 | 0.485042 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.21809e47 | 0.638563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.17950e48 | −1.71274 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.64722e46 | −0.120453 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.44974e47 | 0.728306 | 0.364153 | − | 0.931339i | \(-0.381359\pi\) | ||||
0.364153 | + | 0.931339i | \(0.381359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62194e47 | 0.336202 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.00410e47 | 1.10791 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.07923e48 | −1.27441 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.71476e48 | −1.94344 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.69744e46 | −0.105498 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.45844e47 | 0.778928 | 0.389464 | − | 0.921042i | \(-0.372660\pi\) | ||||
0.389464 | + | 0.921042i | \(0.372660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.28203e47 | 0.228811 | 0.114406 | − | 0.993434i | \(-0.463504\pi\) | ||||
0.114406 | + | 0.993434i | \(0.463504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.02071e47 | 0.0982672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.54569e48 | −3.27794 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.88303e47 | −0.344752 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.25702e48 | 1.07191 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.49028e47 | 0.613530 | 0.306765 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306765 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.29285e48 | −1.01730 | −0.508652 | − | 0.860972i | \(-0.669856\pi\) | ||||
−0.508652 | + | 0.860972i | \(0.669856\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.14801e48 | 0.867870 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.67722e48 | 1.21828 | 0.609141 | − | 0.793062i | \(-0.291514\pi\) | ||||
0.609141 | + | 0.793062i | \(0.291514\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.42330e48 | 0.993451 | 0.496725 | − | 0.867908i | \(-0.334536\pi\) | ||||
0.496725 | + | 0.867908i | \(0.334536\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.39750e47 | 0.362056 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.42371e47 | −0.285197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.73347e47 | 0.293328 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.37683e48 | −0.820182 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.05174e48 | −0.602329 | −0.301165 | − | 0.953572i | \(-0.597375\pi\) | ||||
−0.301165 | + | 0.953572i | \(0.597375\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.15499e48 | 1.73726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.48154e46 | 0.00784440 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.51286e47 | −0.280700 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.43864e48 | 1.19419 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.79196e47 | −0.319903 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.71433e47 | 0.122977 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.01265e48 | 0.441368 | 0.220684 | − | 0.975345i | \(-0.429171\pi\) | ||||
0.220684 | + | 0.975345i | \(0.429171\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.62700e48 | −0.682254 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.70633e48 | 1.49541 | 0.747705 | − | 0.664031i | \(-0.231156\pi\) | ||||
0.747705 | + | 0.664031i | \(0.231156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.78239e48 | −1.46852 | −0.734259 | − | 0.678869i | \(-0.762470\pi\) | ||||
−0.734259 | + | 0.678869i | \(0.762470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.32939e47 | 0.0496706 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.35247e48 | −1.56516 | −0.782578 | − | 0.622552i | \(-0.786096\pi\) | ||||
−0.782578 | + | 0.622552i | \(0.786096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.39258e48 | −2.21264 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.94003e47 | −0.231231 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.84750e47 | −0.123410 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.14465e48 | 0.353486 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.14087e48 | −1.23128 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.04077e48 | 2.58865 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.09991e48 | 1.13053 | 0.565264 | − | 0.824910i | \(-0.308774\pi\) | ||||
0.565264 | + | 0.824910i | \(0.308774\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.62172e45 | 0.00255527 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.48110e48 | 0.634660 | 0.317330 | − | 0.948315i | \(-0.397214\pi\) | ||||
0.317330 | + | 0.948315i | \(0.397214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.54154e48 | −1.61186 | −0.805932 | − | 0.592008i | \(-0.798336\pi\) | ||||
−0.805932 | + | 0.592008i | \(0.798336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.03874e48 | −0.483947 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.77603e48 | −0.863566 | −0.431783 | − | 0.901977i | \(-0.642115\pi\) | ||||
−0.431783 | + | 0.901977i | \(0.642115\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.08138e48 | −0.678995 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.93475e48 | 1.04781 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.52419e48 | −0.311882 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.21438e48 | 1.42272 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.20604e48 | 0.229238 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.32888e49 | 2.43473 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.99008e47 | 0.105797 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.78892e48 | −0.304609 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.33161e48 | 0.218613 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.08989e48 | −0.172530 | −0.0862649 | − | 0.996272i | \(-0.527493\pi\) | ||||
−0.0862649 | + | 0.996272i | \(0.527493\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.15351e48 | −0.481382 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.98086e48 | 0.880462 | 0.440231 | − | 0.897885i | \(-0.354897\pi\) | ||||
0.440231 | + | 0.897885i | \(0.354897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.29520e48 | −1.17777 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.03338e48 | 0.963199 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.81292e48 | −0.239489 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.03793e49 | −1.32271 | −0.661353 | − | 0.750075i | \(-0.730018\pi\) | ||||
−0.661353 | + | 0.750075i | \(0.730018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.98553e48 | −0.244114 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.54044e48 | −0.775852 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.68229e48 | −0.307020 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.50790e49 | −1.66555 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.49398e49 | 1.59252 | 0.796261 | − | 0.604953i | \(-0.206808\pi\) | ||||
0.796261 | + | 0.604953i | \(0.206808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.57160e48 | 0.264566 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.00041e48 | −0.0993420 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.16620e49 | −1.11785 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.00299e48 | 0.740541 | 0.370270 | − | 0.928924i | \(-0.379265\pi\) | ||||
0.370270 | + | 0.928924i | \(0.379265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.75495e48 | 0.156777 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.01488e48 | −0.432545 | −0.216273 | − | 0.976333i | \(-0.569390\pi\) | ||||
−0.216273 | + | 0.976333i | \(0.569390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37880e48 | −0.114830 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.56846e49 | −1.26139 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.00367e48 | 0.543940 | 0.271970 | − | 0.962306i | \(-0.412325\pi\) | ||||
0.271970 | + | 0.962306i | \(0.412325\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.12040e49 | 0.840392 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.91842e48 | 0.428773 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.82156e48 | 0.127471 | 0.0637353 | − | 0.997967i | \(-0.479699\pi\) | ||||
0.0637353 | + | 0.997967i | \(0.479699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.58383e48 | 0.580264 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.02561e49 | 0.669782 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.35241e49 | −0.853300 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.91206e49 | 1.16564 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.59323e49 | 1.52759 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.24479e48 | −0.127784 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.21827e48 | 0.232059 | 0.116029 | − | 0.993246i | \(-0.462983\pi\) | ||||
0.116029 | + | 0.993246i | \(0.462983\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.04259e48 | −0.0554336 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.43768e49 | −0.738831 | −0.369415 | − | 0.929264i | \(-0.620442\pi\) | ||||
−0.369415 | + | 0.929264i | \(0.620442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.92888e49 | −0.958171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.19180e49 | −0.572306 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.59531e49 | 1.66908 | 0.834539 | − | 0.550949i | \(-0.185734\pi\) | ||||
0.834539 | + | 0.550949i | \(0.185734\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.75184e49 | −1.68395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.70375e49 | 1.17335 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.32449e49 | −0.555797 | −0.277898 | − | 0.960610i | \(-0.589638\pi\) | ||||
−0.277898 | + | 0.960610i | \(0.589638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.93633e49 | −1.19153 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.02198e48 | −0.275567 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.85541e49 | 0.704207 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.86373e49 | 1.78548 | 0.892738 | − | 0.450576i | \(-0.148781\pi\) | ||||
0.892738 | + | 0.450576i | \(0.148781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.63886e47 | 0.0306756 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.30141e49 | −2.50799 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.00393e49 | −0.998206 | −0.499103 | − | 0.866543i | \(-0.666337\pi\) | ||||
−0.499103 | + | 0.866543i | \(0.666337\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.48276e48 | 0.0798187 |
(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 | 4.34.a.a.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 16.34.a.d.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.34.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.34.a.d.1.2 | 3 | 4.3 | odd | 2 |