Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,12,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(172.877215626\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −56.0000 | −1.23744 | −0.618718 | − | 0.785613i | \(-0.712348\pi\) | ||||
−0.618718 | + | 0.785613i | \(0.712348\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1088.00 | 0.531250 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −27984.0 | −0.629319 | −0.314659 | − | 0.949205i | \(-0.601890\pi\) | ||||
−0.314659 | + | 0.949205i | \(0.601890\pi\) | |||||||
\(8\) | 53760.0 | 0.580049 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 112028. | 0.209733 | 0.104867 | − | 0.994486i | \(-0.466558\pi\) | ||||
0.104867 | + | 0.994486i | \(0.466558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.09692e6 | 0.819384 | 0.409692 | − | 0.912224i | \(-0.365636\pi\) | ||||
0.409692 | + | 0.912224i | \(0.365636\pi\) | |||||||
\(14\) | 1.56710e6 | 0.778742 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.23878e6 | −1.24902 | ||||||||
\(17\) | −249566. | −0.0426301 | −0.0213150 | − | 0.999773i | \(-0.506785\pi\) | ||||
−0.0213150 | + | 0.999773i | \(0.506785\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.37124e7 | −1.27048 | −0.635242 | − | 0.772313i | \(-0.719100\pi\) | ||||
−0.635242 | + | 0.772313i | \(0.719100\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.27357e6 | −0.259531 | ||||||||
\(23\) | 4.13957e7 | 1.34107 | 0.670537 | − | 0.741877i | \(-0.266064\pi\) | ||||
0.670537 | + | 0.741877i | \(0.266064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.14276e7 | −1.01394 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.04466e7 | −0.334326 | ||||||||
\(29\) | 4.53385e6 | 0.0410467 | 0.0205233 | − | 0.999789i | \(-0.493467\pi\) | ||||
0.0205233 | + | 0.999789i | \(0.493467\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.65339e8 | −1.66461 | −0.832304 | − | 0.554320i | \(-0.812978\pi\) | ||||
−0.832304 | + | 0.554320i | \(0.812978\pi\) | |||||||
\(32\) | 1.83271e8 | 0.965539 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.39757e7 | 0.0527521 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.12137e8 | 0.502929 | 0.251465 | − | 0.967866i | \(-0.419088\pi\) | ||||
0.251465 | + | 0.967866i | \(0.419088\pi\) | |||||||
\(38\) | 7.67896e8 | 1.57214 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.26697e9 | 1.70787 | 0.853936 | − | 0.520379i | \(-0.174209\pi\) | ||||
0.853936 | + | 0.520379i | \(0.174209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.41295e7 | −0.0146572 | −0.00732861 | − | 0.999973i | \(-0.502333\pi\) | ||||
−0.00732861 | + | 0.999973i | \(0.502333\pi\) | |||||||
\(44\) | 1.21886e8 | 0.111421 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.31816e9 | −1.65949 | ||||||||
\(47\) | −2.65727e9 | −1.69004 | −0.845022 | − | 0.534732i | \(-0.820413\pi\) | ||||
−0.845022 | + | 0.534732i | \(0.820413\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.19422e9 | −0.603958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.19345e9 | 0.435298 | ||||||||
\(53\) | 2.40270e9 | 0.789191 | 0.394596 | − | 0.918855i | \(-0.370885\pi\) | ||||
0.394596 | + | 0.918855i | \(0.370885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50442e9 | −0.365035 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.53896e8 | −0.0507927 | ||||||||
\(59\) | −7.49874e9 | −1.36553 | −0.682766 | − | 0.730637i | \(-0.739223\pi\) | ||||
−0.682766 | + | 0.730637i | \(0.739223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.06483e9 | −0.616209 | −0.308105 | − | 0.951352i | \(-0.599695\pi\) | ||||
−0.308105 | + | 0.951352i | \(0.599695\pi\) | |||||||
\(62\) | 1.48590e10 | 2.05985 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.65830e8 | 0.0542297 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.87151e9 | −0.621786 | −0.310893 | − | 0.950445i | \(-0.600628\pi\) | ||||
−0.310893 | + | 0.950445i | \(0.600628\pi\) | |||||||
\(68\) | −2.71528e8 | −0.0226472 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.32837e10 | 0.873774 | 0.436887 | − | 0.899516i | \(-0.356081\pi\) | ||||
0.436887 | + | 0.899516i | \(0.356081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.88758e10 | 1.63027 | 0.815134 | − | 0.579273i | \(-0.196663\pi\) | ||||
0.815134 | + | 0.579273i | \(0.196663\pi\) | |||||||
\(74\) | −1.18797e10 | −0.622343 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.49191e10 | −0.674945 | ||||||||
\(77\) | −3.13499e9 | −0.131989 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.71003e10 | 0.990889 | 0.495445 | − | 0.868640i | \(-0.335005\pi\) | ||||
0.495445 | + | 0.868640i | \(0.335005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.09503e10 | −2.11338 | ||||||||
\(83\) | −3.43653e10 | −0.957613 | −0.478807 | − | 0.877920i | \(-0.658930\pi\) | ||||
−0.478807 | + | 0.877920i | \(0.658930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.91255e8 | 0.0181374 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.02263e9 | 0.121655 | ||||||||
\(89\) | 6.35004e10 | 1.20540 | 0.602700 | − | 0.797968i | \(-0.294091\pi\) | ||||
0.602700 | + | 0.797968i | \(0.294091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.06963e10 | −0.515653 | ||||||||
\(92\) | 4.50386e10 | 0.712445 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.48807e11 | 2.09132 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.96345e10 | −0.232153 | −0.116077 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116077 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(98\) | 6.68765e10 | 0.747360 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.21293e11 | 1.14834 | 0.574169 | − | 0.818737i | \(-0.305325\pi\) | ||||
0.574169 | + | 0.818737i | \(0.305325\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.32353e11 | −1.12494 | −0.562469 | − | 0.826818i | \(-0.690149\pi\) | ||||
−0.562469 | + | 0.826818i | \(0.690149\pi\) | |||||||
\(104\) | 5.89705e10 | 0.475282 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.34551e11 | −0.976574 | ||||||||
\(107\) | 1.93758e10 | 0.133552 | 0.0667759 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667759 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.32688e11 | 1.44853 | 0.724265 | − | 0.689522i | \(-0.242179\pi\) | ||||
0.724265 | + | 0.689522i | \(0.242179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.46602e11 | 0.786034 | ||||||||
\(113\) | 3.19485e11 | 1.63124 | 0.815621 | − | 0.578586i | \(-0.196395\pi\) | ||||
0.815621 | + | 0.578586i | \(0.196395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.93283e9 | 0.0218061 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.19929e11 | 1.68976 | ||||||||
\(119\) | 6.98385e9 | 0.0268279 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.72761e11 | −0.956012 | ||||||||
\(122\) | 2.27630e11 | 0.762520 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.88689e11 | −0.884323 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.61435e11 | 1.50792 | 0.753962 | − | 0.656918i | \(-0.228140\pi\) | ||||
0.753962 | + | 0.656918i | \(0.228140\pi\) | |||||||
\(128\) | −4.01426e11 | −1.03264 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.57850e11 | −1.03689 | −0.518443 | − | 0.855112i | \(-0.673488\pi\) | ||||
−0.518443 | + | 0.855112i | \(0.673488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.83728e11 | 0.799539 | ||||||||
\(134\) | 3.84805e11 | 0.769421 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.34167e10 | −0.0247275 | ||||||||
\(137\) | −4.20737e10 | −0.0744814 | −0.0372407 | − | 0.999306i | \(-0.511857\pi\) | ||||
−0.0372407 | + | 0.999306i | \(0.511857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.13653e11 | 1.33002 | 0.665009 | − | 0.746835i | \(-0.268428\pi\) | ||||
0.665009 | + | 0.746835i | \(0.268428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.43889e11 | −1.08124 | ||||||||
\(143\) | 1.22886e11 | 0.171852 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.61705e12 | −2.01735 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.30805e11 | 0.267181 | ||||||||
\(149\) | 1.56119e11 | 0.174153 | 0.0870763 | − | 0.996202i | \(-0.472248\pi\) | ||||
0.0870763 | + | 0.996202i | \(0.472248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.50139e11 | 0.570295 | 0.285147 | − | 0.958484i | \(-0.407957\pi\) | ||||
0.285147 | + | 0.958484i | \(0.407957\pi\) | |||||||
\(152\) | −7.37180e11 | −0.736943 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.75560e11 | 0.163328 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.87489e12 | 1.56866 | 0.784328 | − | 0.620346i | \(-0.213008\pi\) | ||||
0.784328 | + | 0.620346i | \(0.213008\pi\) | |||||||
\(158\) | −1.51762e12 | −1.22616 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.15842e12 | −0.843962 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.17731e12 | 1.48214 | 0.741068 | − | 0.671430i | \(-0.234320\pi\) | ||||
0.741068 | + | 0.671430i | \(0.234320\pi\) | |||||||
\(164\) | 1.37846e12 | 0.907307 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.92445e12 | 1.18499 | ||||||||
\(167\) | −1.18014e12 | −0.703058 | −0.351529 | − | 0.936177i | \(-0.614338\pi\) | ||||
−0.351529 | + | 0.936177i | \(0.614338\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.88923e11 | −0.328610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.53729e10 | −0.00778665 | ||||||||
\(173\) | 4.99181e11 | 0.244909 | 0.122454 | − | 0.992474i | \(-0.460923\pi\) | ||||
0.122454 | + | 0.992474i | \(0.460923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.86890e11 | −0.261961 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.55602e12 | −1.49161 | ||||||||
\(179\) | −3.21203e12 | −1.30643 | −0.653217 | − | 0.757171i | \(-0.726581\pi\) | ||||
−0.653217 | + | 0.757171i | \(0.726581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.93245e12 | −1.12201 | −0.561007 | − | 0.827811i | \(-0.689586\pi\) | ||||
−0.561007 | + | 0.827811i | \(0.689586\pi\) | |||||||
\(182\) | 1.71899e12 | 0.638089 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.22543e12 | 0.777887 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.79584e10 | −0.00894094 | ||||||||
\(188\) | −2.89111e12 | −0.897836 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.28642e12 | −0.650839 | −0.325419 | − | 0.945570i | \(-0.605505\pi\) | ||||
−0.325419 | + | 0.945570i | \(0.605505\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.86617e12 | −1.57685 | −0.788423 | − | 0.615133i | \(-0.789102\pi\) | ||||
−0.788423 | + | 0.615133i | \(0.789102\pi\) | |||||||
\(194\) | 1.09953e12 | 0.287275 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.29931e12 | −0.320853 | ||||||||
\(197\) | 5.41588e11 | 0.130048 | 0.0650242 | − | 0.997884i | \(-0.479288\pi\) | ||||
0.0650242 | + | 0.997884i | \(0.479288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12034e12 | −1.39022 | −0.695110 | − | 0.718903i | \(-0.744644\pi\) | ||||
−0.695110 | + | 0.718903i | \(0.744644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.79243e12 | −1.42100 | ||||||||
\(203\) | −1.26875e11 | −0.0258314 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.41176e12 | 1.39204 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.74654e12 | −1.02343 | ||||||||
\(209\) | −1.53617e12 | −0.266463 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.92054e12 | 0.316133 | 0.158067 | − | 0.987428i | \(-0.449474\pi\) | ||||
0.158067 | + | 0.987428i | \(0.449474\pi\) | |||||||
\(212\) | 2.61414e12 | 0.419258 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.08505e12 | −0.165262 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.42525e12 | 1.04757 | ||||||||
\(218\) | −1.30305e13 | −1.79246 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.73754e11 | −0.0349304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.97214e12 | −1.08948 | −0.544740 | − | 0.838605i | \(-0.683372\pi\) | ||||
−0.544740 | + | 0.838605i | \(0.683372\pi\) | |||||||
\(224\) | −5.12867e12 | −0.607632 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.78911e13 | −2.01856 | ||||||||
\(227\) | 1.08223e13 | 1.19173 | 0.595864 | − | 0.803086i | \(-0.296810\pi\) | ||||
0.595864 | + | 0.803086i | \(0.296810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.41898e12 | −0.883414 | −0.441707 | − | 0.897159i | \(-0.645627\pi\) | ||||
−0.441707 | + | 0.897159i | \(0.645627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.43740e11 | 0.0238091 | ||||||||
\(233\) | −1.69297e13 | −1.61507 | −0.807537 | − | 0.589817i | \(-0.799200\pi\) | ||||
−0.807537 | + | 0.589817i | \(0.799200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.15863e12 | −0.725439 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.91096e11 | −0.0331979 | ||||||||
\(239\) | −6.99835e12 | −0.580506 | −0.290253 | − | 0.956950i | \(-0.593740\pi\) | ||||
−0.290253 | + | 0.956950i | \(0.593740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.06165e12 | −0.717982 | −0.358991 | − | 0.933341i | \(-0.616879\pi\) | ||||
−0.358991 | + | 0.933341i | \(0.616879\pi\) | |||||||
\(242\) | 1.52746e13 | 1.18300 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.42253e12 | −0.327361 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.50415e13 | −1.04101 | ||||||||
\(248\) | −1.42646e13 | −0.965553 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.59291e13 | −1.64279 | −0.821394 | − | 0.570362i | \(-0.806803\pi\) | ||||
−0.821394 | + | 0.570362i | \(0.806803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.63748e12 | 0.281267 | ||||||||
\(254\) | −3.14404e13 | −1.86596 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.15259e13 | 1.22360 | ||||||||
\(257\) | 8.77582e12 | 0.488265 | 0.244133 | − | 0.969742i | \(-0.421497\pi\) | ||||
0.244133 | + | 0.969742i | \(0.421497\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.93644e12 | −0.316503 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.56396e13 | 1.28308 | ||||||||
\(263\) | 8.38157e12 | 0.410742 | 0.205371 | − | 0.978684i | \(-0.434160\pi\) | ||||
0.205371 | + | 0.978684i | \(0.434160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.14888e13 | −0.989380 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.47621e12 | −0.330324 | ||||||||
\(269\) | 3.22500e13 | 1.39602 | 0.698011 | − | 0.716087i | \(-0.254068\pi\) | ||||
0.698011 | + | 0.716087i | \(0.254068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.89199e12 | −0.120189 | −0.0600947 | − | 0.998193i | \(-0.519140\pi\) | ||||
−0.0600947 | + | 0.998193i | \(0.519140\pi\) | |||||||
\(272\) | 1.30742e12 | 0.0532460 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.35613e12 | 0.0921660 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.73968e12 | −0.358844 | −0.179422 | − | 0.983772i | \(-0.557423\pi\) | ||||
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(278\) | −4.55645e13 | −1.64581 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.36930e12 | 0.319023 | 0.159512 | − | 0.987196i | \(-0.449008\pi\) | ||||
0.159512 | + | 0.987196i | \(0.449008\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.70902e13 | −1.54207 | −0.771036 | − | 0.636791i | \(-0.780261\pi\) | ||||
−0.771036 | + | 0.636791i | \(0.780261\pi\) | |||||||
\(284\) | 1.44527e13 | 0.464193 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.88161e12 | −0.212656 | ||||||||
\(287\) | −3.54549e13 | −1.07480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.42096e13 | −0.998183 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.14169e13 | 0.866080 | ||||||||
\(293\) | −1.11851e13 | −0.302600 | −0.151300 | − | 0.988488i | \(-0.548346\pi\) | ||||
−0.151300 | + | 0.988488i | \(0.548346\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.14045e13 | 0.291723 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.74264e12 | −0.215503 | ||||||||
\(299\) | 4.54079e13 | 1.09885 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.95401e11 | 0.00922406 | ||||||||
\(302\) | −3.08078e13 | −0.705704 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.18364e13 | 1.58686 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85767e13 | −1.01664 | −0.508320 | − | 0.861168i | \(-0.669733\pi\) | ||||
−0.508320 | + | 0.861168i | \(0.669733\pi\) | |||||||
\(308\) | −3.41087e12 | −0.0701191 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.18050e13 | −1.00969 | −0.504846 | − | 0.863209i | \(-0.668451\pi\) | ||||
−0.504846 | + | 0.863209i | \(0.668451\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.45673e13 | −0.462236 | −0.231118 | − | 0.972926i | \(-0.574238\pi\) | ||||
−0.231118 | + | 0.972926i | \(0.574238\pi\) | |||||||
\(314\) | −1.04994e14 | −1.94111 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.94851e13 | 0.526410 | ||||||||
\(317\) | −1.74942e13 | −0.306950 | −0.153475 | − | 0.988153i | \(-0.549046\pi\) | ||||
−0.153475 | + | 0.988153i | \(0.549046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07918e11 | 0.00860885 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.48714e13 | 1.04435 | ||||||||
\(323\) | 3.42215e12 | 0.0541609 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.21929e14 | −1.83405 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.81123e13 | 0.990648 | ||||||||
\(329\) | 7.43611e13 | 1.06358 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.84453e13 | −0.946868 | −0.473434 | − | 0.880829i | \(-0.656986\pi\) | ||||
−0.473434 | + | 0.880829i | \(0.656986\pi\) | |||||||
\(332\) | −3.73894e13 | −0.508732 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.60876e13 | 0.869990 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.69939e13 | 0.964921 | 0.482460 | − | 0.875918i | \(-0.339743\pi\) | ||||
0.482460 | + | 0.875918i | \(0.339743\pi\) | |||||||
\(338\) | 3.29797e13 | 0.406635 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.97254e13 | −0.349123 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.87526e13 | 1.00940 | ||||||||
\(344\) | −7.59605e11 | −0.00850190 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.79541e13 | −0.303059 | ||||||||
\(347\) | 1.29519e14 | 1.38204 | 0.691020 | − | 0.722836i | \(-0.257162\pi\) | ||||
0.691020 | + | 0.722836i | \(0.257162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.64763e13 | 0.377112 | 0.188556 | − | 0.982062i | \(-0.439619\pi\) | ||||
0.188556 | + | 0.982062i | \(0.439619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.05315e13 | 0.202505 | ||||||||
\(353\) | 1.03351e14 | 1.00358 | 0.501790 | − | 0.864989i | \(-0.332675\pi\) | ||||
0.501790 | + | 0.864989i | \(0.332675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.90884e13 | 0.640369 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.79874e14 | 1.61663 | ||||||||
\(359\) | 1.52982e14 | 1.35400 | 0.677002 | − | 0.735981i | \(-0.263279\pi\) | ||||
0.677002 | + | 0.735981i | \(0.263279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.15402e13 | 0.614130 | ||||||||
\(362\) | 1.64217e14 | 1.38842 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.33975e13 | −0.273941 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.49106e14 | −1.16905 | −0.584523 | − | 0.811377i | \(-0.698718\pi\) | ||||
−0.584523 | + | 0.811377i | \(0.698718\pi\) | |||||||
\(368\) | −2.16863e14 | −1.67503 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.72371e13 | −0.496653 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.61185e13 | 0.402446 | 0.201223 | − | 0.979545i | \(-0.435508\pi\) | ||||
0.201223 | + | 0.979545i | \(0.435508\pi\) | |||||||
\(374\) | 1.56567e12 | 0.0110638 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.42855e14 | −0.980308 | ||||||||
\(377\) | 4.97328e12 | 0.0336330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.57417e13 | 0.497530 | 0.248765 | − | 0.968564i | \(-0.419975\pi\) | ||||
0.248765 | + | 0.968564i | \(0.419975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.28040e14 | 0.805372 | ||||||||
\(383\) | 2.02071e13 | 0.125289 | 0.0626443 | − | 0.998036i | \(-0.480047\pi\) | ||||
0.0626443 | + | 0.998036i | \(0.480047\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.28505e14 | 1.95125 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.13623e13 | −0.123332 | ||||||||
\(389\) | −1.96148e14 | −1.11651 | −0.558253 | − | 0.829671i | \(-0.688528\pi\) | ||||
−0.558253 | + | 0.829671i | \(0.688528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.03310e13 | −0.0571701 | ||||||||
\(392\) | −6.42014e13 | −0.350325 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.03289e13 | −0.160927 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.12645e14 | −1.59112 | −0.795562 | − | 0.605872i | \(-0.792824\pi\) | ||||
−0.795562 | + | 0.605872i | \(0.792824\pi\) | |||||||
\(398\) | 3.42739e14 | 1.72031 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.29292e14 | 0.622696 | 0.311348 | − | 0.950296i | \(-0.399219\pi\) | ||||
0.311348 | + | 0.950296i | \(0.399219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.91056e14 | −1.36395 | ||||||||
\(404\) | 1.31967e14 | 0.610055 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.10501e12 | 0.0319648 | ||||||||
\(407\) | 2.37653e13 | 0.105481 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.70213e14 | 0.735385 | 0.367692 | − | 0.929948i | \(-0.380148\pi\) | ||||
0.367692 | + | 0.929948i | \(0.380148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.44000e14 | −0.597624 | ||||||||
\(413\) | 2.09845e14 | 0.859355 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.01034e14 | 0.791147 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.60258e13 | 0.329731 | ||||||||
\(419\) | −7.47406e13 | −0.282735 | −0.141367 | − | 0.989957i | \(-0.545150\pi\) | ||||
−0.141367 | + | 0.989957i | \(0.545150\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.85677e14 | −0.684239 | −0.342119 | − | 0.939656i | \(-0.611145\pi\) | ||||
−0.342119 | + | 0.939656i | \(0.611145\pi\) | |||||||
\(422\) | −1.07550e14 | −0.391195 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.29169e14 | 0.457769 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.13750e14 | 0.387792 | ||||||||
\(428\) | 2.10809e13 | 0.0709494 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.42728e14 | 1.11001 | 0.555003 | − | 0.831849i | \(-0.312717\pi\) | ||||
0.555003 | + | 0.831849i | \(0.312717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.77829e14 | −1.50865 | −0.754326 | − | 0.656500i | \(-0.772036\pi\) | ||||
−0.754326 | + | 0.656500i | \(0.772036\pi\) | |||||||
\(434\) | −4.15814e14 | −1.29630 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.53164e14 | 0.769532 | ||||||||
\(437\) | −5.67636e14 | −1.70381 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.50255e14 | −1.61068 | −0.805339 | − | 0.592814i | \(-0.798017\pi\) | ||||
−0.805339 | + | 0.592814i | \(0.798017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.53302e13 | 0.0432242 | ||||||||
\(443\) | 2.60772e13 | 0.0726173 | 0.0363087 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363087 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.02440e14 | 1.34816 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.30358e13 | −0.0341278 | ||||||||
\(449\) | 1.54203e14 | 0.398784 | 0.199392 | − | 0.979920i | \(-0.436103\pi\) | ||||
0.199392 | + | 0.979920i | \(0.436103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.41936e14 | 0.358197 | ||||||||
\(452\) | 3.47599e14 | 0.866598 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.06048e14 | −1.47469 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.76543e13 | −0.182233 | −0.0911163 | − | 0.995840i | \(-0.529044\pi\) | ||||
−0.0911163 | + | 0.995840i | \(0.529044\pi\) | |||||||
\(458\) | 4.71463e14 | 1.09317 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.59986e14 | −1.47632 | −0.738158 | − | 0.674627i | \(-0.764304\pi\) | ||||
−0.738158 | + | 0.674627i | \(0.764304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.96908e14 | 0.648525 | 0.324262 | − | 0.945967i | \(-0.394884\pi\) | ||||
0.324262 | + | 0.945967i | \(0.394884\pi\) | |||||||
\(464\) | −2.37519e13 | −0.0512683 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48065e14 | 1.99855 | ||||||||
\(467\) | −8.37123e14 | −1.74400 | −0.872000 | − | 0.489507i | \(-0.837177\pi\) | ||||
−0.872000 | + | 0.489507i | \(0.837177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.92292e14 | 0.391302 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.03132e14 | −0.792075 | ||||||||
\(473\) | −1.58291e12 | −0.00307410 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.59843e12 | 0.0142523 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.91907e14 | 0.718340 | ||||||||
\(479\) | −1.21855e14 | −0.220800 | −0.110400 | − | 0.993887i | \(-0.535213\pi\) | ||||
−0.110400 | + | 0.993887i | \(0.535213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.32698e14 | 0.412092 | ||||||||
\(482\) | 5.07452e14 | 0.888457 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.96764e14 | −0.507881 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.45308e13 | −0.156374 | −0.0781870 | − | 0.996939i | \(-0.524913\pi\) | ||||
−0.0781870 | + | 0.996939i | \(0.524913\pi\) | |||||||
\(488\) | −2.18525e14 | −0.357431 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.09824e14 | 0.331823 | 0.165911 | − | 0.986141i | \(-0.446943\pi\) | ||||
0.165911 | + | 0.986141i | \(0.446943\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.13149e12 | −0.00174982 | ||||||||
\(494\) | 8.42321e14 | 1.28819 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.39005e15 | 2.07913 | ||||||||
\(497\) | −3.71732e14 | −0.549882 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.64936e14 | −0.383343 | −0.191671 | − | 0.981459i | \(-0.561391\pi\) | ||||
−0.191671 | + | 0.981459i | \(0.561391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.45203e15 | 2.03285 | ||||||||
\(503\) | −3.64546e14 | −0.504811 | −0.252405 | − | 0.967622i | \(-0.581222\pi\) | ||||
−0.252405 | + | 0.967622i | \(0.581222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.59699e14 | −0.348051 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.10842e14 | 0.801085 | ||||||||
\(509\) | −2.36671e14 | −0.307042 | −0.153521 | − | 0.988145i | \(-0.549061\pi\) | ||||
−0.153521 | + | 0.988145i | \(0.549061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.08062e14 | −1.02596 | ||||||||
\(512\) | −3.83327e14 | −0.481487 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.91446e14 | −0.604197 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.97689e14 | −0.354458 | ||||||||
\(518\) | 3.32441e14 | 0.391652 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.57734e14 | −0.294147 | −0.147073 | − | 0.989126i | \(-0.546985\pi\) | ||||
−0.147073 | + | 0.989126i | \(0.546985\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.48029e15 | 1.65420 | 0.827101 | − | 0.562053i | \(-0.189988\pi\) | ||||
0.827101 | + | 0.562053i | \(0.189988\pi\) | |||||||
\(524\) | −4.98141e14 | −0.550846 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.69368e14 | −0.508267 | ||||||||
\(527\) | 6.62196e13 | 0.0709624 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.60797e14 | 0.798477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.17496e14 | 0.424755 | ||||||||
\(533\) | 1.38977e15 | 1.39940 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.69413e14 | −0.360666 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.80600e15 | −1.72749 | ||||||||
\(539\) | −1.33786e14 | −0.126670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.21529e15 | −1.12744 | −0.563720 | − | 0.825966i | \(-0.690630\pi\) | ||||
−0.563720 | + | 0.825966i | \(0.690630\pi\) | |||||||
\(542\) | 1.61951e14 | 0.148727 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.57383e13 | −0.0411610 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.93440e14 | 0.430828 | 0.215414 | − | 0.976523i | \(-0.430890\pi\) | ||||
0.215414 | + | 0.976523i | \(0.430890\pi\) | |||||||
\(548\) | −4.57762e13 | −0.0395682 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.21701e13 | −0.0521492 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.58375e14 | −0.623585 | ||||||||
\(554\) | 5.45422e14 | 0.444047 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.85254e14 | 0.706572 | ||||||||
\(557\) | 5.15728e14 | 0.407584 | 0.203792 | − | 0.979014i | \(-0.434673\pi\) | ||||
0.203792 | + | 0.979014i | \(0.434673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.54990e13 | −0.0120099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.24681e14 | −0.394771 | ||||||||
\(563\) | 2.86863e14 | 0.213737 | 0.106868 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106868 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.63705e15 | 1.90822 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.14134e14 | 0.506832 | ||||||||
\(569\) | 5.24421e14 | 0.368606 | 0.184303 | − | 0.982869i | \(-0.440997\pi\) | ||||
0.184303 | + | 0.982869i | \(0.440997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.33323e15 | −0.919194 | −0.459597 | − | 0.888127i | \(-0.652006\pi\) | ||||
−0.459597 | + | 0.888127i | \(0.652006\pi\) | |||||||
\(572\) | 1.33700e14 | 0.0912963 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.98547e15 | 1.32999 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.21802e15 | −0.792844 | −0.396422 | − | 0.918068i | \(-0.629748\pi\) | ||||
−0.396422 | + | 0.918068i | \(0.629748\pi\) | |||||||
\(578\) | 1.91574e15 | 1.23519 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.61677e14 | 0.602644 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.69170e14 | 0.165519 | ||||||||
\(584\) | 1.55237e15 | 0.945634 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.26367e14 | 0.374448 | ||||||||
\(587\) | 7.51065e14 | 0.444803 | 0.222402 | − | 0.974955i | \(-0.428610\pi\) | ||||
0.222402 | + | 0.974955i | \(0.428610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.63844e15 | 2.11486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.11134e15 | −0.628170 | ||||||||
\(593\) | −1.95401e15 | −1.09427 | −0.547137 | − | 0.837043i | \(-0.684282\pi\) | ||||
−0.547137 | + | 0.837043i | \(0.684282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.69857e14 | 0.0925186 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.54284e15 | −1.35976 | ||||||||
\(599\) | −2.08899e15 | −1.10685 | −0.553425 | − | 0.832899i | \(-0.686679\pi\) | ||||
−0.553425 | + | 0.832899i | \(0.686679\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.78205e15 | −1.44729 | −0.723645 | − | 0.690173i | \(-0.757535\pi\) | ||||
−0.723645 | + | 0.690173i | \(0.757535\pi\) | |||||||
\(602\) | −2.21425e13 | −0.0114142 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.98551e14 | 0.302969 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.48334e15 | −1.22320 | −0.611601 | − | 0.791166i | \(-0.709474\pi\) | ||||
−0.611601 | + | 0.791166i | \(0.709474\pi\) | |||||||
\(608\) | −2.51309e15 | −1.22670 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.91482e15 | −1.38479 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.54510e15 | 1.65423 | 0.827116 | − | 0.562032i | \(-0.189980\pi\) | ||||
0.827116 | + | 0.562032i | \(0.189980\pi\) | |||||||
\(614\) | 2.72030e15 | 1.25803 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.68537e14 | −0.0765600 | ||||||||
\(617\) | 1.21585e14 | 0.0547410 | 0.0273705 | − | 0.999625i | \(-0.491287\pi\) | ||||
0.0273705 | + | 0.999625i | \(0.491287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.33849e15 | −0.591994 | −0.295997 | − | 0.955189i | \(-0.595652\pi\) | ||||
−0.295997 | + | 0.955189i | \(0.595652\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.90108e15 | 1.24943 | ||||||||
\(623\) | −1.77700e15 | −0.758581 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.37577e15 | 0.571988 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.03988e15 | 0.833348 | ||||||||
\(629\) | −5.29422e13 | −0.0214399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.23141e15 | −0.888010 | −0.444005 | − | 0.896024i | \(-0.646443\pi\) | ||||
−0.444005 | + | 0.896024i | \(0.646443\pi\) | |||||||
\(632\) | 1.45691e15 | 0.574764 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.79674e14 | 0.379831 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30997e15 | −0.494873 | ||||||||
\(638\) | −2.84434e13 | −0.0106529 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.53917e15 | −0.926773 | −0.463386 | − | 0.886156i | \(-0.653366\pi\) | ||||
−0.463386 | + | 0.886156i | \(0.653366\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.40215e15 | 0.503076 | 0.251538 | − | 0.967847i | \(-0.419064\pi\) | ||||
0.251538 | + | 0.967847i | \(0.419064\pi\) | |||||||
\(644\) | −1.26036e15 | −0.448355 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.91641e14 | −0.0670207 | ||||||||
\(647\) | 1.45024e15 | 0.502882 | 0.251441 | − | 0.967873i | \(-0.419096\pi\) | ||||
0.251441 | + | 0.967873i | \(0.419096\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.40069e14 | −0.286397 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.36891e15 | 0.787384 | ||||||||
\(653\) | 6.74967e14 | 0.222464 | 0.111232 | − | 0.993794i | \(-0.464520\pi\) | ||||
0.111232 | + | 0.993794i | \(0.464520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.63738e15 | −2.13317 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.16422e15 | −1.31611 | ||||||||
\(659\) | −3.55334e15 | −1.11370 | −0.556849 | − | 0.830614i | \(-0.687990\pi\) | ||||
−0.556849 | + | 0.830614i | \(0.687990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.08998e15 | 1.26070 | 0.630351 | − | 0.776310i | \(-0.282911\pi\) | ||||
0.630351 | + | 0.776310i | \(0.282911\pi\) | |||||||
\(662\) | 3.83294e15 | 1.17169 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.84748e15 | −0.555462 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.87682e14 | 0.0550466 | ||||||||
\(668\) | −1.28399e15 | −0.373500 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.55375e14 | −0.129239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.31714e14 | 0.0646948 | 0.0323474 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323474 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(674\) | −4.31166e15 | −1.19403 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.40748e14 | −0.174574 | ||||||||
\(677\) | −4.21442e15 | −1.13894 | −0.569469 | − | 0.822013i | \(-0.692851\pi\) | ||||
−0.569469 | + | 0.822013i | \(0.692851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.49452e14 | 0.146099 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.66462e15 | 0.432018 | ||||||||
\(683\) | −9.30314e14 | −0.239506 | −0.119753 | − | 0.992804i | \(-0.538210\pi\) | ||||
−0.119753 | + | 0.992804i | \(0.538210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.97015e15 | −1.24907 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.40216e13 | 0.0183072 | ||||||||
\(689\) | 2.63557e15 | 0.646650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.13309e15 | −0.756561 | −0.378280 | − | 0.925691i | \(-0.623485\pi\) | ||||
−0.378280 | + | 0.925691i | \(0.623485\pi\) | |||||||
\(692\) | 5.43109e14 | 0.130108 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.25305e15 | −1.71019 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.16193e14 | −0.0728067 | ||||||||
\(698\) | −2.04267e15 | −0.466653 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.21787e15 | 1.38737 | 0.693686 | − | 0.720278i | \(-0.255986\pi\) | ||||
0.693686 | + | 0.720278i | \(0.255986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.90891e15 | −0.638964 | ||||||||
\(704\) | 5.21860e13 | 0.0113738 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.78764e15 | −1.24187 | ||||||||
\(707\) | −3.39428e15 | −0.722670 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.38076e15 | −0.289444 | −0.144722 | − | 0.989472i | \(-0.546229\pi\) | ||||
−0.144722 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.41378e15 | 0.699191 | ||||||||
\(713\) | −1.09839e16 | −2.23236 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.49469e15 | −0.694043 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.56698e15 | −1.67550 | ||||||||
\(719\) | 1.22219e15 | 0.237209 | 0.118604 | − | 0.992942i | \(-0.462158\pi\) | ||||
0.118604 | + | 0.992942i | \(0.462158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.70376e15 | 0.707945 | ||||||||
\(722\) | −4.00625e15 | −0.759948 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.19051e15 | −0.596070 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.75213e15 | 1.41573 | 0.707867 | − | 0.706346i | \(-0.249658\pi\) | ||||
0.707867 | + | 0.706346i | \(0.249658\pi\) | |||||||
\(728\) | −1.65023e15 | −0.299104 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.52625e12 | 0.000624839 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.29426e15 | −1.44779 | −0.723895 | − | 0.689910i | \(-0.757650\pi\) | ||||
−0.723895 | + | 0.689910i | \(0.757650\pi\) | |||||||
\(734\) | 8.34994e15 | 1.44662 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.58665e15 | 1.29486 | ||||||||
\(737\) | −7.69802e14 | −0.130409 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.08381e14 | −0.0681587 | −0.0340793 | − | 0.999419i | \(-0.510850\pi\) | ||||
−0.0340793 | + | 0.999419i | \(0.510850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.76528e15 | 0.614576 | ||||||||
\(743\) | 1.87602e15 | 0.303948 | 0.151974 | − | 0.988384i | \(-0.451437\pi\) | ||||
0.151974 | + | 0.988384i | \(0.451437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.14264e15 | −0.498002 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.04187e13 | −0.00474987 | ||||||||
\(749\) | −5.42214e14 | −0.0840467 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.97525e15 | 1.52372 | 0.761858 | − | 0.647744i | \(-0.224287\pi\) | ||||
0.761858 | + | 0.647744i | \(0.224287\pi\) | |||||||
\(752\) | 1.39209e16 | 2.11090 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.78504e14 | −0.0416187 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.09293e16 | −1.59795 | −0.798977 | − | 0.601361i | \(-0.794625\pi\) | ||||
−0.798977 | + | 0.601361i | \(0.794625\pi\) | |||||||
\(758\) | −4.24153e15 | −0.615662 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.39091e15 | 0.481615 | 0.240808 | − | 0.970573i | \(-0.422588\pi\) | ||||
0.240808 | + | 0.970573i | \(0.422588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.51153e15 | −0.911587 | ||||||||
\(764\) | −2.48763e15 | −0.345758 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.13160e15 | −0.155037 | ||||||||
\(767\) | −8.22553e15 | −1.11890 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.40507e15 | −0.858873 | −0.429437 | − | 0.903097i | \(-0.641288\pi\) | ||||
−0.429437 | + | 0.903097i | \(0.641288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.38239e15 | −0.837699 | ||||||||
\(773\) | 6.92865e15 | 0.902945 | 0.451473 | − | 0.892285i | \(-0.350899\pi\) | ||||
0.451473 | + | 0.892285i | \(0.350899\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.05555e15 | −0.134660 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.09843e16 | 1.38161 | ||||||||
\(779\) | −1.73732e16 | −2.16982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.48815e15 | 0.183259 | ||||||||
\(782\) | 5.78534e14 | 0.0707444 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.25627e15 | 0.754358 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.81869e15 | 0.332802 | 0.166401 | − | 0.986058i | \(-0.446785\pi\) | ||||
0.166401 | + | 0.986058i | \(0.446785\pi\) | |||||||
\(788\) | 5.89248e14 | 0.0690882 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.94046e15 | −1.02657 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.45880e15 | −0.504912 | ||||||||
\(794\) | 1.75081e16 | 1.96892 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.65893e15 | −0.738555 | ||||||||
\(797\) | 3.10085e15 | 0.341554 | 0.170777 | − | 0.985310i | \(-0.445372\pi\) | ||||
0.170777 | + | 0.985310i | \(0.445372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.63165e14 | 0.0720467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.24033e15 | −0.770547 | ||||||||
\(803\) | 3.23490e15 | 0.341921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.62991e16 | 1.68780 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.52073e15 | 0.666092 | ||||||||
\(809\) | −1.32956e16 | −1.34894 | −0.674468 | − | 0.738304i | \(-0.735627\pi\) | ||||
−0.674468 | + | 0.738304i | \(0.735627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.98127e15 | 0.698747 | 0.349373 | − | 0.936984i | \(-0.386394\pi\) | ||||
0.349373 | + | 0.936984i | \(0.386394\pi\) | |||||||
\(812\) | −1.38040e14 | −0.0137230 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.33086e15 | −0.130526 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.93750e14 | 0.0186218 | ||||||||
\(818\) | −9.53193e15 | −0.909992 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.46007e15 | −0.604436 | −0.302218 | − | 0.953239i | \(-0.597727\pi\) | ||||
−0.302218 | + | 0.953239i | \(0.597727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.54918e15 | 0.419985 | 0.209993 | − | 0.977703i | \(-0.432656\pi\) | ||||
0.209993 | + | 0.977703i | \(0.432656\pi\) | |||||||
\(824\) | −7.11529e15 | −0.652519 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.17513e16 | −1.06340 | ||||||||
\(827\) | −3.58820e15 | −0.322549 | −0.161275 | − | 0.986910i | \(-0.551560\pi\) | ||||
−0.161275 | + | 0.986910i | \(0.551560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.35990e16 | 1.20630 | 0.603152 | − | 0.797626i | \(-0.293911\pi\) | ||||
0.603152 | + | 0.797626i | \(0.293911\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.10979e14 | 0.0444350 | ||||||||
\(833\) | 2.98037e14 | 0.0257468 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.67136e15 | −0.141558 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.18547e15 | 0.349867 | ||||||||
\(839\) | 1.49622e16 | 1.24253 | 0.621263 | − | 0.783602i | \(-0.286620\pi\) | ||||
0.621263 | + | 0.783602i | \(0.286620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.21800e16 | −0.998315 | ||||||||
\(842\) | 1.03979e16 | 0.846702 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.08955e15 | 0.167946 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.63295e15 | 0.601636 | ||||||||
\(848\) | −1.25872e16 | −0.985718 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.78156e15 | 0.674465 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.31290e15 | 0.706098 | 0.353049 | − | 0.935605i | \(-0.385145\pi\) | ||||
0.353049 | + | 0.935605i | \(0.385145\pi\) | |||||||
\(854\) | −6.37001e15 | −0.479868 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.04165e15 | 0.0774666 | ||||||||
\(857\) | −2.01081e16 | −1.48585 | −0.742927 | − | 0.669373i | \(-0.766563\pi\) | ||||
−0.742927 | + | 0.669373i | \(0.766563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.78636e16 | −1.30319 | −0.651594 | − | 0.758568i | \(-0.725900\pi\) | ||||
−0.651594 | + | 0.758568i | \(0.725900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.91928e16 | −1.37356 | ||||||||
\(863\) | 2.51194e16 | 1.78628 | 0.893141 | − | 0.449776i | \(-0.148496\pi\) | ||||
0.893141 | + | 0.449776i | \(0.148496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.67584e16 | 1.86686 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.07867e15 | 0.556521 | ||||||||
\(869\) | 3.03599e15 | 0.207822 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.53752e15 | −0.509481 | ||||||||
\(872\) | 1.25093e16 | 0.840218 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.17876e16 | 2.10836 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.05249e16 | −0.685045 | −0.342522 | − | 0.939510i | \(-0.611281\pi\) | ||||
−0.342522 | + | 0.939510i | \(0.611281\pi\) | |||||||
\(878\) | 3.08143e16 | 1.99311 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.10050e16 | 1.33338 | 0.666691 | − | 0.745334i | \(-0.267710\pi\) | ||||
0.666691 | + | 0.745334i | \(0.267710\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.55181e16 | 0.972868 | 0.486434 | − | 0.873717i | \(-0.338297\pi\) | ||||
0.486434 | + | 0.873717i | \(0.338297\pi\) | |||||||
\(884\) | −2.97845e14 | −0.0185568 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.46032e15 | −0.0898593 | ||||||||
\(887\) | 7.61183e15 | 0.465489 | 0.232744 | − | 0.972538i | \(-0.425229\pi\) | ||||
0.232744 | + | 0.972538i | \(0.425229\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.57112e16 | −0.948964 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.76169e15 | −0.578786 | ||||||||
\(893\) | 3.64376e16 | 2.14717 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.12335e16 | 0.649863 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.63537e15 | −0.493470 | ||||||||
\(899\) | −1.20301e15 | −0.0683266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.99632e14 | −0.0336433 | ||||||||
\(902\) | −7.94842e15 | −0.443246 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.71755e16 | 0.946200 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.39103e16 | 1.29344 | 0.646719 | − | 0.762728i | \(-0.276141\pi\) | ||||
0.646719 | + | 0.762728i | \(0.276141\pi\) | |||||||
\(908\) | 1.17747e16 | 0.633105 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.44923e16 | −1.29324 | −0.646618 | − | 0.762814i | \(-0.723817\pi\) | ||||
−0.646618 | + | 0.762814i | \(0.723817\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.84987e15 | −0.200843 | ||||||||
\(914\) | 4.34864e15 | 0.225501 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.15985e15 | −0.469314 | ||||||||
\(917\) | 1.28125e16 | 0.652532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.21575e16 | −1.61826 | −0.809128 | − | 0.587632i | \(-0.800060\pi\) | ||||
−0.809128 | + | 0.587632i | \(0.800060\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.69592e16 | 1.82685 | ||||||||
\(923\) | 1.45712e16 | 0.715956 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.66268e16 | −0.802508 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.30925e14 | 0.0396322 | ||||||||
\(929\) | 1.27739e16 | 0.605672 | 0.302836 | − | 0.953043i | \(-0.402067\pi\) | ||||
0.302836 | + | 0.953043i | \(0.402067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.63757e16 | 0.767319 | ||||||||
\(932\) | −1.84196e16 | −0.858008 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.68789e16 | 2.15809 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.11554e15 | −0.0504565 | −0.0252283 | − | 0.999682i | \(-0.508031\pi\) | ||||
−0.0252283 | + | 0.999682i | \(0.508031\pi\) | |||||||
\(938\) | −1.07684e16 | −0.484211 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.97991e16 | 1.75845 | 0.879226 | − | 0.476405i | \(-0.158060\pi\) | ||||
0.879226 | + | 0.476405i | \(0.158060\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.24471e16 | 2.29038 | ||||||||
\(944\) | 3.92843e16 | 1.70558 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.86427e13 | 0.00380401 | ||||||||
\(947\) | −3.26979e16 | −1.39507 | −0.697534 | − | 0.716552i | \(-0.745719\pi\) | ||||
−0.697534 | + | 0.716552i | \(0.745719\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.16745e16 | 1.33581 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.75452e14 | 0.0155615 | ||||||||
\(953\) | −2.74452e15 | −0.113098 | −0.0565491 | − | 0.998400i | \(-0.518010\pi\) | ||||
−0.0565491 | + | 0.998400i | \(0.518010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.61420e15 | −0.308394 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.82390e15 | 0.273226 | ||||||||
\(959\) | 1.17739e15 | 0.0468725 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.49963e16 | 1.77092 | ||||||||
\(962\) | −1.30311e16 | −0.509938 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.85907e15 | −0.381428 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.81335e15 | −0.297161 | −0.148580 | − | 0.988900i | \(-0.547470\pi\) | ||||
−0.148580 | + | 0.988900i | \(0.547470\pi\) | |||||||
\(968\) | −1.46637e16 | −0.554533 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.79623e16 | −1.78318 | −0.891588 | − | 0.452848i | \(-0.850408\pi\) | ||||
−0.891588 | + | 0.452848i | \(0.850408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.27693e16 | −0.837005 | ||||||||
\(974\) | 5.29373e15 | 0.193503 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.12948e16 | 0.769660 | ||||||||
\(977\) | 4.28901e16 | 1.54148 | 0.770738 | − | 0.637152i | \(-0.219888\pi\) | ||||
0.770738 | + | 0.637152i | \(0.219888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.11382e15 | 0.252812 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.17501e16 | −0.410610 | ||||||||
\(983\) | −1.90984e16 | −0.663671 | −0.331836 | − | 0.943337i | \(-0.607668\pi\) | ||||
−0.331836 | + | 0.943337i | \(0.607668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.33637e13 | 0.00216530 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.63651e16 | −0.553039 | ||||||||
\(989\) | −5.84903e14 | −0.0196564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.64435e15 | −0.254060 | −0.127030 | − | 0.991899i | \(-0.540544\pi\) | ||||
−0.127030 | + | 0.991899i | \(0.540544\pi\) | |||||||
\(992\) | −4.86291e16 | −1.60724 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.08170e16 | 0.680445 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.72891e16 | −1.52033 | −0.760164 | − | 0.649731i | \(-0.774882\pi\) | ||||
−0.760164 | + | 0.649731i | \(0.774882\pi\) | |||||||
\(998\) | 1.48364e16 | 0.474362 | ||||||||
\(999\) | 0 | 0 |
(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 | 225.12.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 75.12.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 225.12.b.b.199.1 | 2 | |||
5.3 | odd | 4 | 225.12.b.b.199.2 | 2 | |||
5.4 | even | 2 | 45.12.a.b.1.1 | 1 | |||
15.2 | even | 4 | 75.12.b.b.49.2 | 2 | |||
15.8 | even | 4 | 75.12.b.b.49.1 | 2 | |||
15.14 | odd | 2 | 15.12.a.a.1.1 | ✓ | 1 | ||
60.59 | even | 2 | 240.12.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.12.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
45.12.a.b.1.1 | 1 | 5.4 | even | 2 | |||
75.12.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
75.12.b.b.49.1 | 2 | 15.8 | even | 4 | |||
75.12.b.b.49.2 | 2 | 15.2 | even | 4 | |||
225.12.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.12.b.b.199.1 | 2 | 5.2 | odd | 4 | |||
225.12.b.b.199.2 | 2 | 5.3 | odd | 4 | |||
240.12.a.e.1.1 | 1 | 60.59 | even | 2 |