Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(13.9059675764\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.177113.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 118x + 136 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(10.7777\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.3331 | 1.42894 | 0.714468 | − | 0.699668i | \(-0.246669\pi\) | ||||
0.714468 | + | 0.699668i | \(0.246669\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 533.432 | 1.04186 | ||||||||
\(5\) | −2071.63 | −1.48233 | −0.741167 | − | 0.671320i | \(-0.765728\pi\) | ||||
−0.741167 | + | 0.671320i | \(0.765728\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10517.1 | −1.65560 | −0.827800 | − | 0.561024i | \(-0.810408\pi\) | ||||
−0.827800 | + | 0.561024i | \(0.810408\pi\) | |||||||
\(8\) | 692.954 | 0.0598136 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −66982.2 | −2.11816 | ||||||||
\(11\) | 31620.5 | 0.651182 | 0.325591 | − | 0.945511i | \(-0.394437\pi\) | ||||
0.325591 | + | 0.945511i | \(0.394437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 47622.2 | 0.462449 | 0.231225 | − | 0.972900i | \(-0.425727\pi\) | ||||
0.231225 | + | 0.972900i | \(0.425727\pi\) | |||||||
\(14\) | −340051. | −2.36575 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −250712. | −0.956389 | ||||||||
\(17\) | −34440.3 | −0.100011 | −0.0500053 | − | 0.998749i | \(-0.515924\pi\) | ||||
−0.0500053 | + | 0.998749i | \(0.515924\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 763166. | 1.34347 | 0.671735 | − | 0.740792i | \(-0.265550\pi\) | ||||
0.671735 | + | 0.740792i | \(0.265550\pi\) | |||||||
\(20\) | −1.10507e6 | −1.54438 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.02239e6 | 0.930497 | ||||||||
\(23\) | −1.48534e6 | −1.10675 | −0.553377 | − | 0.832931i | \(-0.686661\pi\) | ||||
−0.553377 | + | 0.832931i | \(0.686661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.33851e6 | 1.19732 | ||||||||
\(26\) | 1.53977e6 | 0.660811 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.61016e6 | −1.72490 | ||||||||
\(29\) | −4.80506e6 | −1.26156 | −0.630780 | − | 0.775962i | \(-0.717265\pi\) | ||||
−0.630780 | + | 0.775962i | \(0.717265\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.82305e6 | −1.52142 | −0.760708 | − | 0.649094i | \(-0.775148\pi\) | ||||
−0.760708 | + | 0.649094i | \(0.775148\pi\) | |||||||
\(32\) | −8.46109e6 | −1.42643 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.11356e6 | −0.142909 | ||||||||
\(35\) | 2.17875e7 | 2.45415 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.43456e6 | 0.827587 | 0.413794 | − | 0.910371i | \(-0.364204\pi\) | ||||
0.413794 | + | 0.910371i | \(0.364204\pi\) | |||||||
\(38\) | 2.46755e7 | 1.91973 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.43554e6 | −0.0886637 | ||||||||
\(41\) | −1.22899e7 | −0.679237 | −0.339618 | − | 0.940563i | \(-0.610298\pi\) | ||||
−0.339618 | + | 0.940563i | \(0.610298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.74423e7 | 1.67014 | 0.835072 | − | 0.550140i | \(-0.185426\pi\) | ||||
0.835072 | + | 0.550140i | \(0.185426\pi\) | |||||||
\(44\) | 1.68674e7 | 0.678439 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.80258e7 | −1.58148 | ||||||||
\(47\) | −1.98234e7 | −0.592568 | −0.296284 | − | 0.955100i | \(-0.595747\pi\) | ||||
−0.296284 | + | 0.955100i | \(0.595747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.02560e7 | 1.74101 | ||||||||
\(50\) | 7.56113e7 | 1.71089 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.54032e7 | 0.481807 | ||||||||
\(53\) | −5.78978e7 | −1.00791 | −0.503953 | − | 0.863731i | \(-0.668122\pi\) | ||||
−0.503953 | + | 0.863731i | \(0.668122\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.55059e7 | −0.965269 | ||||||||
\(56\) | −7.28788e6 | −0.0990273 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.55363e8 | −1.80269 | ||||||||
\(59\) | 2.84988e7 | 0.306191 | 0.153095 | − | 0.988211i | \(-0.451076\pi\) | ||||
0.153095 | + | 0.988211i | \(0.451076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.45141e7 | 0.411636 | 0.205818 | − | 0.978590i | \(-0.434014\pi\) | ||||
0.205818 | + | 0.978590i | \(0.434014\pi\) | |||||||
\(62\) | −2.52944e8 | −2.17401 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.45209e8 | −1.08189 | ||||||||
\(65\) | −9.86553e7 | −0.685505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.81934e8 | −1.10301 | −0.551503 | − | 0.834173i | \(-0.685946\pi\) | ||||
−0.551503 | + | 0.834173i | \(0.685946\pi\) | |||||||
\(68\) | −1.83715e7 | −0.104197 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.04459e8 | 3.50683 | ||||||||
\(71\) | −1.53722e8 | −0.717915 | −0.358958 | − | 0.933354i | \(-0.616868\pi\) | ||||
−0.358958 | + | 0.933354i | \(0.616868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.55706e7 | 0.0641729 | 0.0320864 | − | 0.999485i | \(-0.489785\pi\) | ||||
0.0320864 | + | 0.999485i | \(0.489785\pi\) | |||||||
\(74\) | 3.05049e8 | 1.18257 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.07097e8 | 1.39971 | ||||||||
\(77\) | −3.32557e8 | −1.07810 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.26170e8 | −0.942154 | −0.471077 | − | 0.882092i | \(-0.656135\pi\) | ||||
−0.471077 | + | 0.882092i | \(0.656135\pi\) | |||||||
\(80\) | 5.19381e8 | 1.41769 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.97371e8 | −0.970586 | ||||||||
\(83\) | −5.01181e7 | −0.115916 | −0.0579580 | − | 0.998319i | \(-0.518459\pi\) | ||||
−0.0579580 | + | 0.998319i | \(0.518459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.13473e7 | 0.148249 | ||||||||
\(86\) | 1.21063e9 | 2.38653 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.19116e7 | 0.0389495 | ||||||||
\(89\) | 1.59066e8 | 0.268735 | 0.134367 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134367 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00848e8 | −0.765631 | ||||||||
\(92\) | −7.92329e8 | −1.15308 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.40953e8 | −0.846742 | ||||||||
\(95\) | −1.58099e9 | −1.99147 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.49373e8 | −0.171317 | −0.0856583 | − | 0.996325i | \(-0.527299\pi\) | ||||
−0.0856583 | + | 0.996325i | \(0.527299\pi\) | |||||||
\(98\) | 2.27160e9 | 2.48779 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.24743e9 | 1.24743 | ||||||||
\(101\) | 1.84265e9 | 1.76196 | 0.880981 | − | 0.473152i | \(-0.156884\pi\) | ||||
0.880981 | + | 0.473152i | \(0.156884\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.50430e8 | −0.306785 | −0.153392 | − | 0.988165i | \(-0.549020\pi\) | ||||
−0.153392 | + | 0.988165i | \(0.549020\pi\) | |||||||
\(104\) | 3.30000e7 | 0.0276607 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.87202e9 | −1.44023 | ||||||||
\(107\) | −7.93460e8 | −0.585192 | −0.292596 | − | 0.956236i | \(-0.594519\pi\) | ||||
−0.292596 | + | 0.956236i | \(0.594519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.09944e9 | 0.746020 | 0.373010 | − | 0.927827i | \(-0.378326\pi\) | ||||
0.373010 | + | 0.927827i | \(0.378326\pi\) | |||||||
\(110\) | −2.11801e9 | −1.37931 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.63676e9 | 1.58340 | ||||||||
\(113\) | −2.91370e9 | −1.68109 | −0.840547 | − | 0.541739i | \(-0.817766\pi\) | ||||
−0.840547 | + | 0.541739i | \(0.817766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.07707e9 | 1.64058 | ||||||||
\(116\) | −2.56317e9 | −1.31437 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.21455e8 | 0.437527 | ||||||||
\(119\) | 3.62212e8 | 0.165578 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.35809e9 | −0.575962 | ||||||||
\(122\) | 1.43928e9 | 0.588202 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.17306e9 | −1.58510 | ||||||||
\(125\) | −7.98371e8 | −0.292489 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.58765e9 | 0.541551 | 0.270776 | − | 0.962643i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962643i | \(0.412720\pi\) | |||||||
\(128\) | −3.62989e8 | −0.119522 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.18984e9 | −0.979543 | ||||||||
\(131\) | 3.75999e9 | 1.11549 | 0.557745 | − | 0.830012i | \(-0.311667\pi\) | ||||
0.557745 | + | 0.830012i | \(0.311667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.02630e9 | −2.22425 | ||||||||
\(134\) | −5.88251e9 | −1.57613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.38655e7 | −0.00598199 | ||||||||
\(137\) | −9.88347e8 | −0.239699 | −0.119850 | − | 0.992792i | \(-0.538241\pi\) | ||||
−0.119850 | + | 0.992792i | \(0.538241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.71601e9 | 1.07154 | 0.535769 | − | 0.844364i | \(-0.320022\pi\) | ||||
0.535769 | + | 0.844364i | \(0.320022\pi\) | |||||||
\(140\) | 1.16222e10 | 2.55688 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.97031e9 | −1.02585 | ||||||||
\(143\) | 1.50584e9 | 0.301139 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.95428e9 | 1.87005 | ||||||||
\(146\) | 5.03445e8 | 0.0916990 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.03269e9 | 0.862229 | ||||||||
\(149\) | −4.36878e9 | −0.726143 | −0.363071 | − | 0.931761i | \(-0.618272\pi\) | ||||
−0.363071 | + | 0.931761i | \(0.618272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.47508e9 | 1.01356 | 0.506779 | − | 0.862076i | \(-0.330836\pi\) | ||||
0.506779 | + | 0.862076i | \(0.330836\pi\) | |||||||
\(152\) | 5.28839e8 | 0.0803577 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.07526e10 | −1.54053 | ||||||||
\(155\) | 1.62064e10 | 2.25525 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.50860e8 | −0.111766 | −0.0558830 | − | 0.998437i | \(-0.517797\pi\) | ||||
−0.0558830 | + | 0.998437i | \(0.517797\pi\) | |||||||
\(158\) | −1.05461e10 | −1.34628 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.75282e10 | 2.11445 | ||||||||
\(161\) | 1.56215e10 | 1.83234 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.54283e9 | −0.947889 | −0.473945 | − | 0.880555i | \(-0.657170\pi\) | ||||
−0.473945 | + | 0.880555i | \(0.657170\pi\) | |||||||
\(164\) | −6.55582e9 | −0.707669 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.62048e9 | −0.165637 | ||||||||
\(167\) | −4.57212e8 | −0.0454876 | −0.0227438 | − | 0.999741i | \(-0.507240\pi\) | ||||
−0.0227438 | + | 0.999741i | \(0.507240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.33663e9 | −0.786141 | ||||||||
\(170\) | 2.30688e9 | 0.211839 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.99729e10 | 1.74005 | ||||||||
\(173\) | −9.13108e9 | −0.775023 | −0.387511 | − | 0.921865i | \(-0.626665\pi\) | ||||
−0.387511 | + | 0.921865i | \(0.626665\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.45944e10 | −1.98228 | ||||||||
\(176\) | −7.92764e9 | −0.622783 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.14312e9 | 0.384005 | ||||||||
\(179\) | −1.84541e9 | −0.134355 | −0.0671777 | − | 0.997741i | \(-0.521399\pi\) | ||||
−0.0671777 | + | 0.997741i | \(0.521399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.02105e10 | −0.707123 | −0.353562 | − | 0.935411i | \(-0.615030\pi\) | ||||
−0.353562 | + | 0.935411i | \(0.615030\pi\) | |||||||
\(182\) | −1.61940e10 | −1.09404 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.02927e9 | −0.0661989 | ||||||||
\(185\) | −1.95449e10 | −1.22676 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.08902e9 | −0.0651251 | ||||||||
\(188\) | −1.05744e10 | −0.617372 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.11185e10 | −2.84569 | ||||||||
\(191\) | −1.00230e10 | −0.544938 | −0.272469 | − | 0.962164i | \(-0.587840\pi\) | ||||
−0.272469 | + | 0.962164i | \(0.587840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.87244e9 | 0.304657 | 0.152328 | − | 0.988330i | \(-0.451323\pi\) | ||||
0.152328 | + | 0.988330i | \(0.451323\pi\) | |||||||
\(194\) | −4.82970e9 | −0.244801 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.74768e10 | 1.81389 | ||||||||
\(197\) | 2.73628e10 | 1.29438 | 0.647191 | − | 0.762328i | \(-0.275944\pi\) | ||||
0.647191 | + | 0.762328i | \(0.275944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.21639e9 | 0.100186 | 0.0500930 | − | 0.998745i | \(-0.484048\pi\) | ||||
0.0500930 | + | 0.998745i | \(0.484048\pi\) | |||||||
\(200\) | 1.62048e9 | 0.0716158 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.95786e10 | 2.51773 | ||||||||
\(203\) | 5.05353e10 | 2.08864 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.54601e10 | 1.00686 | ||||||||
\(206\) | −1.13305e10 | −0.438376 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.19394e10 | −0.442281 | ||||||||
\(209\) | 2.41317e10 | 0.874843 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.35207e10 | −0.469599 | −0.234799 | − | 0.972044i | \(-0.575443\pi\) | ||||
−0.234799 | + | 0.972044i | \(0.575443\pi\) | |||||||
\(212\) | −3.08845e10 | −1.05010 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.56551e10 | −0.836202 | ||||||||
\(215\) | −7.75664e10 | −2.47571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.22758e10 | 2.51886 | ||||||||
\(218\) | 3.55482e10 | 1.06601 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.49429e10 | −1.00567 | ||||||||
\(221\) | −1.64012e9 | −0.0462499 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.97283e9 | −0.0805004 | −0.0402502 | − | 0.999190i | \(-0.512815\pi\) | ||||
−0.0402502 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(224\) | 8.89862e10 | 2.36160 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.42090e10 | −2.40218 | ||||||||
\(227\) | 3.34599e10 | 0.836388 | 0.418194 | − | 0.908358i | \(-0.362663\pi\) | ||||
0.418194 | + | 0.908358i | \(0.362663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.60785e10 | −1.82811 | −0.914055 | − | 0.405590i | \(-0.867066\pi\) | ||||
−0.914055 | + | 0.405590i | \(0.867066\pi\) | |||||||
\(230\) | 9.94914e10 | 2.34429 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.32969e9 | −0.0754584 | ||||||||
\(233\) | −6.49552e10 | −1.44382 | −0.721909 | − | 0.691988i | \(-0.756735\pi\) | ||||
−0.721909 | + | 0.691988i | \(0.756735\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.10667e10 | 0.878384 | ||||||||
\(236\) | 1.52022e10 | 0.319008 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.17115e10 | 0.236600 | ||||||||
\(239\) | 3.98471e10 | 0.789963 | 0.394981 | − | 0.918689i | \(-0.370751\pi\) | ||||
0.394981 | + | 0.918689i | \(0.370751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.18614e10 | 0.226496 | 0.113248 | − | 0.993567i | \(-0.463875\pi\) | ||||
0.113248 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(242\) | −4.39113e10 | −0.823014 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.37452e10 | 0.428867 | ||||||||
\(245\) | −1.45544e11 | −2.58076 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.63436e10 | 0.621286 | ||||||||
\(248\) | −5.42101e9 | −0.0910014 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.58138e10 | −0.417948 | ||||||||
\(251\) | 6.51966e10 | 1.03680 | 0.518398 | − | 0.855139i | \(-0.326529\pi\) | ||||
0.518398 | + | 0.855139i | \(0.326529\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.69673e10 | −0.720698 | ||||||||
\(254\) | 5.13339e10 | 0.773842 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.26105e10 | 0.911102 | ||||||||
\(257\) | −3.80164e10 | −0.543591 | −0.271796 | − | 0.962355i | \(-0.587617\pi\) | ||||
−0.271796 | + | 0.962355i | \(0.587617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.92243e10 | −1.37015 | ||||||||
\(260\) | −5.26259e10 | −0.714199 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.21572e11 | 1.59397 | ||||||||
\(263\) | −3.53924e10 | −0.456152 | −0.228076 | − | 0.973643i | \(-0.573243\pi\) | ||||
−0.228076 | + | 0.973643i | \(0.573243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.19943e11 | 1.49406 | ||||||||
\(266\) | −2.59515e11 | −3.17831 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.70495e10 | −1.14918 | ||||||||
\(269\) | 6.44475e9 | 0.0750448 | 0.0375224 | − | 0.999296i | \(-0.488053\pi\) | ||||
0.0375224 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.68603e11 | 1.89890 | 0.949452 | − | 0.313912i | \(-0.101640\pi\) | ||||
0.949452 | + | 0.313912i | \(0.101640\pi\) | |||||||
\(272\) | 8.63458e9 | 0.0956491 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.19563e10 | −0.342515 | ||||||||
\(275\) | 7.39449e10 | 0.779671 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.87122e10 | −0.497140 | −0.248570 | − | 0.968614i | \(-0.579961\pi\) | ||||
−0.248570 | + | 0.968614i | \(0.579961\pi\) | |||||||
\(278\) | 1.52483e11 | 1.53116 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.50978e10 | 0.146792 | ||||||||
\(281\) | −1.51361e11 | −1.44822 | −0.724110 | − | 0.689684i | \(-0.757749\pi\) | ||||
−0.724110 | + | 0.689684i | \(0.757749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.14282e10 | −0.661959 | −0.330979 | − | 0.943638i | \(-0.607379\pi\) | ||||
−0.330979 | + | 0.943638i | \(0.607379\pi\) | |||||||
\(284\) | −8.20001e10 | −0.747966 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.86885e10 | 0.430308 | ||||||||
\(287\) | 1.29254e11 | 1.12454 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.17402e11 | −0.989998 | ||||||||
\(290\) | 3.21853e11 | 2.67219 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.30584e9 | 0.0668591 | ||||||||
\(293\) | −2.22271e11 | −1.76189 | −0.880945 | − | 0.473218i | \(-0.843092\pi\) | ||||
−0.880945 | + | 0.473218i | \(0.843092\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.90388e10 | −0.453878 | ||||||||
\(296\) | 6.53772e9 | 0.0495009 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.41256e11 | −1.03761 | ||||||||
\(299\) | −7.07352e10 | −0.511818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.93784e11 | −2.76509 | ||||||||
\(302\) | 2.09360e11 | 1.44831 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.91335e11 | −1.28488 | ||||||||
\(305\) | −9.22166e10 | −0.610183 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.24657e11 | 1.44343 | 0.721717 | − | 0.692188i | \(-0.243353\pi\) | ||||
0.721717 | + | 0.692188i | \(0.243353\pi\) | |||||||
\(308\) | −1.77396e11 | −1.12322 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.24005e11 | 3.22261 | ||||||||
\(311\) | 2.99889e11 | 1.81777 | 0.908886 | − | 0.417046i | \(-0.136934\pi\) | ||||
0.908886 | + | 0.417046i | \(0.136934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.50502e11 | 0.886325 | 0.443162 | − | 0.896441i | \(-0.353857\pi\) | ||||
0.443162 | + | 0.896441i | \(0.353857\pi\) | |||||||
\(314\) | −2.75110e10 | −0.159706 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.73989e11 | −0.981591 | ||||||||
\(317\) | 2.49896e11 | 1.38993 | 0.694966 | − | 0.719043i | \(-0.255420\pi\) | ||||
0.694966 | + | 0.719043i | \(0.255420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.51939e11 | −0.821504 | ||||||||
\(320\) | 3.00819e11 | 1.60373 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.05092e11 | 2.61830 | ||||||||
\(323\) | −2.62836e10 | −0.134361 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.11365e11 | 0.553698 | ||||||||
\(326\) | −2.76216e11 | −1.35447 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.51634e9 | −0.0406276 | ||||||||
\(329\) | 2.08485e11 | 0.981055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.32449e10 | 0.243810 | 0.121905 | − | 0.992542i | \(-0.461100\pi\) | ||||
0.121905 | + | 0.992542i | \(0.461100\pi\) | |||||||
\(332\) | −2.67346e10 | −0.120768 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.47831e10 | −0.0649989 | ||||||||
\(335\) | 3.76900e11 | 1.63502 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.54762e10 | 0.149831 | 0.0749156 | − | 0.997190i | \(-0.476131\pi\) | ||||
0.0749156 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(338\) | −2.69549e11 | −1.12334 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.80589e10 | 0.154455 | ||||||||
\(341\) | −2.47369e11 | −0.990719 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.14487e11 | −1.22681 | ||||||||
\(344\) | 2.59458e10 | 0.0998973 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.95236e11 | −1.10746 | ||||||||
\(347\) | −3.92158e11 | −1.45204 | −0.726019 | − | 0.687675i | \(-0.758632\pi\) | ||||
−0.726019 | + | 0.687675i | \(0.758632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.30145e10 | −0.299530 | −0.149765 | − | 0.988722i | \(-0.547852\pi\) | ||||
−0.149765 | + | 0.988722i | \(0.547852\pi\) | |||||||
\(350\) | −7.95213e11 | −2.83255 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.67544e11 | −0.928867 | ||||||||
\(353\) | −1.85625e11 | −0.636281 | −0.318141 | − | 0.948044i | \(-0.603058\pi\) | ||||
−0.318141 | + | 0.948044i | \(0.603058\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.18454e11 | 1.06419 | ||||||||
\(356\) | 8.48511e10 | 0.279984 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.96680e10 | −0.191985 | ||||||||
\(359\) | 3.92754e11 | 1.24794 | 0.623972 | − | 0.781447i | \(-0.285518\pi\) | ||||
0.623972 | + | 0.781447i | \(0.285518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.59734e11 | 0.804909 | ||||||||
\(362\) | −3.30139e11 | −1.01043 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.67168e11 | −0.797679 | ||||||||
\(365\) | −3.22564e10 | −0.0951257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.97459e10 | 0.143140 | 0.0715698 | − | 0.997436i | \(-0.477199\pi\) | ||||
0.0715698 | + | 0.997436i | \(0.477199\pi\) | |||||||
\(368\) | 3.72393e11 | 1.05849 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.31947e11 | −1.75296 | ||||||||
\(371\) | 6.08917e11 | 1.66869 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.03156e11 | 1.07841 | 0.539204 | − | 0.842175i | \(-0.318725\pi\) | ||||
0.539204 | + | 0.842175i | \(0.318725\pi\) | |||||||
\(374\) | −3.52114e10 | −0.0930596 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.37367e10 | −0.0354436 | ||||||||
\(377\) | −2.28827e11 | −0.583407 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.41222e11 | −0.849494 | −0.424747 | − | 0.905312i | \(-0.639637\pi\) | ||||
−0.424747 | + | 0.905312i | \(0.639637\pi\) | |||||||
\(380\) | −8.43352e11 | −2.07483 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.24075e11 | −0.778682 | ||||||||
\(383\) | −3.16998e11 | −0.752770 | −0.376385 | − | 0.926463i | \(-0.622833\pi\) | ||||
−0.376385 | + | 0.926463i | \(0.622833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.88933e11 | 1.59810 | ||||||||
\(386\) | 1.89874e11 | 0.435335 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.96803e10 | −0.178488 | ||||||||
\(389\) | 1.11909e11 | 0.247795 | 0.123898 | − | 0.992295i | \(-0.460461\pi\) | ||||
0.123898 | + | 0.992295i | \(0.460461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.11556e10 | 0.110687 | ||||||||
\(392\) | 4.86842e10 | 0.104136 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.84725e11 | 1.84959 | ||||||||
\(395\) | 6.75702e11 | 1.39659 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.48788e11 | 0.704700 | 0.352350 | − | 0.935868i | \(-0.385383\pi\) | ||||
0.352350 | + | 0.935868i | \(0.385383\pi\) | |||||||
\(398\) | 7.16627e10 | 0.143159 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.86291e11 | −1.14510 | ||||||||
\(401\) | −2.54977e11 | −0.492437 | −0.246218 | − | 0.969214i | \(-0.579188\pi\) | ||||
−0.246218 | + | 0.969214i | \(0.579188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.72550e11 | −0.703578 | ||||||||
\(404\) | 9.82928e11 | 1.83572 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.63397e12 | 2.98453 | ||||||||
\(407\) | 2.98326e11 | 0.538910 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.68334e10 | 0.0474156 | 0.0237078 | − | 0.999719i | \(-0.492453\pi\) | ||||
0.0237078 | + | 0.999719i | \(0.492453\pi\) | |||||||
\(410\) | 8.23204e11 | 1.43873 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.86930e11 | −0.319626 | ||||||||
\(413\) | −2.99725e11 | −0.506930 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.03826e11 | 0.171826 | ||||||||
\(416\) | −4.02935e11 | −0.659653 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.80254e11 | 1.25009 | ||||||||
\(419\) | 8.67220e9 | 0.0137457 | 0.00687284 | − | 0.999976i | \(-0.497812\pi\) | ||||
0.00687284 | + | 0.999976i | \(0.497812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.68105e11 | −1.50194 | −0.750971 | − | 0.660335i | \(-0.770414\pi\) | ||||
−0.750971 | + | 0.660335i | \(0.770414\pi\) | |||||||
\(422\) | −4.37166e11 | −0.671027 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.01205e10 | −0.0602865 | ||||||||
\(425\) | −8.05389e10 | −0.119744 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.68160e11 | −0.681504 | ||||||||
\(428\) | −4.23257e11 | −0.609687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.50796e12 | −3.53764 | ||||||||
\(431\) | 1.38264e12 | 1.93001 | 0.965006 | − | 0.262227i | \(-0.0844570\pi\) | ||||
0.965006 | + | 0.262227i | \(0.0844570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.26247e12 | −1.72594 | −0.862971 | − | 0.505254i | \(-0.831399\pi\) | ||||
−0.862971 | + | 0.505254i | \(0.831399\pi\) | |||||||
\(434\) | 2.66024e12 | 3.59929 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.86474e11 | 0.777247 | ||||||||
\(437\) | −1.13356e12 | −1.48689 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.36242e11 | 0.560579 | 0.280290 | − | 0.959915i | \(-0.409570\pi\) | ||||
0.280290 | + | 0.959915i | \(0.409570\pi\) | |||||||
\(440\) | −4.53926e10 | −0.0577362 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.30302e10 | −0.0660881 | ||||||||
\(443\) | −5.07995e11 | −0.626675 | −0.313337 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313337 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.29526e11 | −0.398355 | ||||||||
\(446\) | −9.61208e10 | −0.115030 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.52718e12 | 1.79118 | ||||||||
\(449\) | −1.47077e12 | −1.70780 | −0.853899 | − | 0.520439i | \(-0.825768\pi\) | ||||
−0.853899 | + | 0.520439i | \(0.825768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88613e11 | −0.442307 | ||||||||
\(452\) | −1.55426e12 | −1.75146 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.08186e12 | 1.19515 | ||||||||
\(455\) | 1.03757e12 | 1.13492 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.11991e12 | −1.20105 | −0.600526 | − | 0.799605i | \(-0.705042\pi\) | ||||
−0.600526 | + | 0.799605i | \(0.705042\pi\) | |||||||
\(458\) | −2.45986e12 | −2.61225 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.64141e12 | 1.70925 | ||||||||
\(461\) | −1.72669e12 | −1.78057 | −0.890286 | − | 0.455402i | \(-0.849496\pi\) | ||||
−0.890286 | + | 0.455402i | \(0.849496\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.74673e11 | 0.277780 | 0.138890 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138890 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(464\) | 1.20468e12 | 1.20654 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.10021e12 | −2.06312 | ||||||||
\(467\) | −1.14495e12 | −1.11394 | −0.556971 | − | 0.830532i | \(-0.688036\pi\) | ||||
−0.556971 | + | 0.830532i | \(0.688036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.91342e12 | 1.82614 | ||||||||
\(470\) | 1.32782e12 | 1.25516 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.97484e10 | 0.0183144 | ||||||||
\(473\) | 1.18394e12 | 1.08757 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.78467e12 | 1.60856 | ||||||||
\(476\) | 1.93215e11 | 0.172508 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.28838e12 | 1.12881 | ||||||||
\(479\) | −9.32652e11 | −0.809487 | −0.404744 | − | 0.914430i | \(-0.632639\pi\) | ||||
−0.404744 | + | 0.914430i | \(0.632639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.49294e11 | 0.382717 | ||||||||
\(482\) | 3.83517e11 | 0.323648 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.24448e11 | −0.600071 | ||||||||
\(485\) | 3.09445e11 | 0.253949 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.02912e12 | −0.829059 | −0.414530 | − | 0.910036i | \(-0.636054\pi\) | ||||
−0.414530 | + | 0.910036i | \(0.636054\pi\) | |||||||
\(488\) | 3.08462e10 | 0.0246214 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.70590e12 | −3.68774 | ||||||||
\(491\) | −1.72889e12 | −1.34246 | −0.671228 | − | 0.741251i | \(-0.734233\pi\) | ||||
−0.671228 | + | 0.741251i | \(0.734233\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.65487e11 | 0.126169 | ||||||||
\(494\) | 1.17510e12 | 0.887779 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.96133e12 | 1.45507 | ||||||||
\(497\) | 1.61671e12 | 1.18858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.39976e12 | 1.73267 | 0.866336 | − | 0.499462i | \(-0.166469\pi\) | ||||
0.866336 | + | 0.499462i | \(0.166469\pi\) | |||||||
\(500\) | −4.25876e11 | −0.304732 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.10801e12 | 1.48152 | ||||||||
\(503\) | −1.98201e12 | −1.38054 | −0.690271 | − | 0.723551i | \(-0.742509\pi\) | ||||
−0.690271 | + | 0.723551i | \(0.742509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.81728e12 | −2.61182 | ||||||||
\(506\) | −1.51860e12 | −1.02983 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.46905e11 | 0.564220 | ||||||||
\(509\) | 2.25559e12 | 1.48946 | 0.744731 | − | 0.667364i | \(-0.232578\pi\) | ||||
0.744731 | + | 0.667364i | \(0.232578\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.63757e11 | −0.106245 | ||||||||
\(512\) | 2.21024e12 | 1.42143 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.22919e12 | −0.776757 | ||||||||
\(515\) | 7.25959e11 | 0.454757 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.26827e11 | −0.385869 | ||||||||
\(518\) | −3.20823e12 | −1.95786 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.83636e10 | −0.0410025 | ||||||||
\(521\) | 7.71315e11 | 0.458630 | 0.229315 | − | 0.973352i | \(-0.426351\pi\) | ||||
0.229315 | + | 0.973352i | \(0.426351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.54315e12 | −0.901886 | −0.450943 | − | 0.892553i | \(-0.648912\pi\) | ||||
−0.450943 | + | 0.892553i | \(0.648912\pi\) | |||||||
\(524\) | 2.00570e12 | 1.16218 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.14435e12 | −0.651812 | ||||||||
\(527\) | 2.69428e11 | 0.152158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.05089e11 | 0.224905 | ||||||||
\(530\) | 3.87812e12 | 2.13491 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.28148e12 | −2.31735 | ||||||||
\(533\) | −5.85272e11 | −0.314113 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.64375e12 | 0.867450 | ||||||||
\(536\) | −1.26072e11 | −0.0659747 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.08379e11 | 0.107234 | ||||||||
\(539\) | 2.22153e12 | 1.13371 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.58683e12 | 1.80021 | 0.900105 | − | 0.435674i | \(-0.143490\pi\) | ||||
0.900105 | + | 0.435674i | \(0.143490\pi\) | |||||||
\(542\) | 5.45146e12 | 2.71341 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.91402e11 | 0.142658 | ||||||||
\(545\) | −2.27762e12 | −1.10585 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.61010e12 | −1.24656 | −0.623282 | − | 0.781997i | \(-0.714201\pi\) | ||||
−0.623282 | + | 0.781997i | \(0.714201\pi\) | |||||||
\(548\) | −5.27215e11 | −0.249733 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.39087e12 | 1.11410 | ||||||||
\(551\) | −3.66706e12 | −1.69487 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.43036e12 | 1.55983 | ||||||||
\(554\) | −1.57502e12 | −0.710382 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.51567e12 | 1.11639 | ||||||||
\(557\) | 1.44707e12 | 0.637002 | 0.318501 | − | 0.947923i | \(-0.396821\pi\) | ||||
0.318501 | + | 0.947923i | \(0.396821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.78308e12 | 0.772357 | ||||||||
\(560\) | −5.46238e12 | −2.34712 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.89397e12 | −2.06942 | ||||||||
\(563\) | 3.02936e12 | 1.27076 | 0.635380 | − | 0.772200i | \(-0.280844\pi\) | ||||
0.635380 | + | 0.772200i | \(0.280844\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.03610e12 | 2.49194 | ||||||||
\(566\) | −2.30950e12 | −0.945897 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.06522e11 | −0.0429411 | ||||||||
\(569\) | 8.23594e11 | 0.329388 | 0.164694 | − | 0.986345i | \(-0.447336\pi\) | ||||
0.164694 | + | 0.986345i | \(0.447336\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.54932e11 | −0.297198 | −0.148599 | − | 0.988898i | \(-0.547476\pi\) | ||||
−0.148599 | + | 0.988898i | \(0.547476\pi\) | |||||||
\(572\) | 8.03262e11 | 0.313744 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.17920e12 | 1.60690 | ||||||||
\(575\) | −3.47349e12 | −1.32514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.22193e12 | −1.58569 | −0.792847 | − | 0.609420i | \(-0.791402\pi\) | ||||
−0.792847 | + | 0.609420i | \(0.791402\pi\) | |||||||
\(578\) | −3.79597e12 | −1.41464 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.30993e12 | 1.94833 | ||||||||
\(581\) | 5.27098e11 | 0.191910 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.83076e12 | −0.656330 | ||||||||
\(584\) | 1.07897e10 | 0.00383841 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.18673e12 | −2.51763 | ||||||||
\(587\) | 2.52727e12 | 0.878578 | 0.439289 | − | 0.898346i | \(-0.355230\pi\) | ||||
0.439289 | + | 0.898346i | \(0.355230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.97028e12 | −2.04398 | ||||||||
\(590\) | −1.90891e12 | −0.648562 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.36535e12 | −0.791495 | ||||||||
\(593\) | 2.59659e12 | 0.862299 | 0.431150 | − | 0.902280i | \(-0.358108\pi\) | ||||
0.431150 | + | 0.902280i | \(0.358108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.50368e11 | −0.245441 | ||||||||
\(596\) | −2.33045e12 | −0.756538 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.28709e12 | −0.731355 | ||||||||
\(599\) | 3.56005e12 | 1.12989 | 0.564944 | − | 0.825129i | \(-0.308898\pi\) | ||||
0.564944 | + | 0.825129i | \(0.308898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.93346e12 | 0.604506 | 0.302253 | − | 0.953228i | \(-0.402261\pi\) | ||||
0.302253 | + | 0.953228i | \(0.402261\pi\) | |||||||
\(602\) | −1.27323e13 | −3.95114 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.45401e12 | 1.05598 | ||||||||
\(605\) | 2.81345e12 | 0.853769 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.32290e12 | 0.395528 | 0.197764 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197764 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(608\) | −6.45721e12 | −1.91637 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.98165e12 | −0.871912 | ||||||||
\(611\) | −9.44034e11 | −0.274033 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.74984e11 | −0.278885 | −0.139443 | − | 0.990230i | \(-0.544531\pi\) | ||||
−0.139443 | + | 0.990230i | \(0.544531\pi\) | |||||||
\(614\) | 7.26386e12 | 2.06257 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.30447e11 | −0.0644848 | ||||||||
\(617\) | 2.87228e12 | 0.797890 | 0.398945 | − | 0.916975i | \(-0.369376\pi\) | ||||
0.398945 | + | 0.916975i | \(0.369376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.16143e12 | −1.13929 | −0.569645 | − | 0.821891i | \(-0.692919\pi\) | ||||
−0.569645 | + | 0.821891i | \(0.692919\pi\) | |||||||
\(620\) | 8.64502e12 | 2.34965 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.69636e12 | 2.59748 | ||||||||
\(623\) | −1.67292e12 | −0.444917 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.91347e12 | −0.763750 | ||||||||
\(626\) | 4.86620e12 | 1.26650 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.53876e11 | −0.116444 | ||||||||
\(629\) | −3.24929e11 | −0.0827675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.22906e12 | −0.810855 | −0.405428 | − | 0.914127i | \(-0.632877\pi\) | ||||
−0.405428 | + | 0.914127i | \(0.632877\pi\) | |||||||
\(632\) | −2.26021e11 | −0.0563536 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.07993e12 | 1.98612 | ||||||||
\(635\) | −3.28903e12 | −0.802760 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.34574e12 | 0.805129 | ||||||||
\(638\) | −4.91265e12 | −1.17388 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.51978e11 | 0.177172 | ||||||||
\(641\) | −4.91306e12 | −1.14945 | −0.574727 | − | 0.818345i | \(-0.694892\pi\) | ||||
−0.574727 | + | 0.818345i | \(0.694892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.18575e12 | 0.273553 | 0.136777 | − | 0.990602i | \(-0.456326\pi\) | ||||
0.136777 | + | 0.990602i | \(0.456326\pi\) | |||||||
\(644\) | 8.33301e12 | 1.90904 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.49832e11 | −0.191994 | ||||||||
\(647\) | −6.72898e12 | −1.50966 | −0.754832 | − | 0.655919i | \(-0.772281\pi\) | ||||
−0.754832 | + | 0.655919i | \(0.772281\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.01147e11 | 0.199386 | ||||||||
\(650\) | 3.60078e12 | 0.791199 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.55702e12 | −0.987567 | ||||||||
\(653\) | −7.24926e11 | −0.156021 | −0.0780107 | − | 0.996953i | \(-0.524857\pi\) | ||||
−0.0780107 | + | 0.996953i | \(0.524857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.78929e12 | −1.65353 | ||||||||
\(656\) | 3.08122e12 | 0.649615 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.74098e12 | 1.40187 | ||||||||
\(659\) | 6.02523e12 | 1.24448 | 0.622242 | − | 0.782825i | \(-0.286222\pi\) | ||||
0.622242 | + | 0.782825i | \(0.286222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.74974e12 | 0.356506 | 0.178253 | − | 0.983985i | \(-0.442956\pi\) | ||||
0.178253 | + | 0.983985i | \(0.442956\pi\) | |||||||
\(662\) | 1.72158e12 | 0.348390 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.47296e10 | −0.00693335 | ||||||||
\(665\) | 1.66275e13 | 3.29708 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.13716e12 | 1.39624 | ||||||||
\(668\) | −2.43891e11 | −0.0473917 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.21864e13 | 2.33635 | ||||||||
\(671\) | 1.40756e12 | 0.268050 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.59466e12 | −0.675445 | −0.337722 | − | 0.941246i | \(-0.609656\pi\) | ||||
−0.337722 | + | 0.941246i | \(0.609656\pi\) | |||||||
\(674\) | 1.14706e12 | 0.214099 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.44702e12 | −0.819048 | ||||||||
\(677\) | 2.33912e12 | 0.427960 | 0.213980 | − | 0.976838i | \(-0.431357\pi\) | ||||
0.213980 | + | 0.976838i | \(0.431357\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.57097e12 | 0.283632 | ||||||||
\(680\) | 4.94404e10 | 0.00886732 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.99821e12 | −1.41567 | ||||||||
\(683\) | −4.03165e11 | −0.0708907 | −0.0354453 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354453 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.04748e12 | 0.355315 | ||||||||
\(686\) | −1.01683e13 | −1.75304 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.38721e12 | −1.59731 | ||||||||
\(689\) | −2.75722e12 | −0.466106 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.79472e12 | 1.30062 | 0.650308 | − | 0.759670i | \(-0.274640\pi\) | ||||
0.650308 | + | 0.759670i | \(0.274640\pi\) | |||||||
\(692\) | −4.87081e12 | −0.807465 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.26797e13 | −2.07487 | ||||||||
\(695\) | −9.76980e12 | −1.58838 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.23268e11 | 0.0679309 | ||||||||
\(698\) | −2.68412e12 | −0.428009 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.31194e13 | −2.06525 | ||||||||
\(701\) | 2.40116e12 | 0.375569 | 0.187784 | − | 0.982210i | \(-0.439869\pi\) | ||||
0.187784 | + | 0.982210i | \(0.439869\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.20013e12 | 1.11184 | ||||||||
\(704\) | −4.59159e12 | −0.704508 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00182e12 | −0.909206 | ||||||||
\(707\) | −1.93793e13 | −2.91710 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.36135e12 | −0.796830 | −0.398415 | − | 0.917205i | \(-0.630440\pi\) | ||||
−0.398415 | + | 0.917205i | \(0.630440\pi\) | |||||||
\(710\) | 1.02966e13 | 1.52066 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.10226e11 | 0.0160740 | ||||||||
\(713\) | 1.16199e13 | 1.68383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.11953e12 | −0.446388 | ||||||||
\(716\) | −9.84402e11 | −0.139979 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.26990e13 | 1.78323 | ||||||||
\(719\) | −5.40289e12 | −0.753956 | −0.376978 | − | 0.926222i | \(-0.623037\pi\) | ||||
−0.376978 | + | 0.926222i | \(0.623037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.68551e12 | 0.507912 | ||||||||
\(722\) | 8.39803e12 | 1.15016 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.44662e12 | −0.736722 | ||||||||
\(725\) | −1.12367e13 | −1.51049 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.15572e12 | 0.418980 | 0.209490 | − | 0.977811i | \(-0.432820\pi\) | ||||
0.209490 | + | 0.977811i | \(0.432820\pi\) | |||||||
\(728\) | −3.47065e11 | −0.0457951 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.04295e12 | −0.135929 | ||||||||
\(731\) | −1.28952e12 | −0.167032 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.20641e13 | −1.54357 | −0.771784 | − | 0.635885i | \(-0.780635\pi\) | ||||
−0.771784 | + | 0.635885i | \(0.780635\pi\) | |||||||
\(734\) | 1.60844e12 | 0.204537 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.25676e13 | 1.57871 | ||||||||
\(737\) | −5.75286e12 | −0.718257 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.39060e12 | 1.03489 | 0.517444 | − | 0.855717i | \(-0.326884\pi\) | ||||
0.517444 | + | 0.855717i | \(0.326884\pi\) | |||||||
\(740\) | −1.04259e13 | −1.27811 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.96882e13 | 2.38445 | ||||||||
\(743\) | −7.40995e11 | −0.0892001 | −0.0446001 | − | 0.999005i | \(-0.514201\pi\) | ||||
−0.0446001 | + | 0.999005i | \(0.514201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.05048e12 | 1.07639 | ||||||||
\(746\) | 1.30353e13 | 1.54098 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.80918e11 | −0.0678512 | ||||||||
\(749\) | 8.34491e12 | 0.968843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.41125e13 | 1.61891 | 0.809457 | − | 0.587180i | \(-0.199762\pi\) | ||||
0.809457 | + | 0.587180i | \(0.199762\pi\) | |||||||
\(752\) | 4.96996e12 | 0.566726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.39871e12 | −0.833652 | ||||||||
\(755\) | −1.34139e13 | −1.50243 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.66623e12 | 0.627138 | 0.313569 | − | 0.949565i | \(-0.398475\pi\) | ||||
0.313569 | + | 0.949565i | \(0.398475\pi\) | |||||||
\(758\) | −1.10328e13 | −1.21387 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.09556e12 | −0.119117 | ||||||||
\(761\) | 1.34131e13 | 1.44977 | 0.724883 | − | 0.688872i | \(-0.241894\pi\) | ||||
0.724883 | + | 0.688872i | \(0.241894\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.15629e13 | −1.23511 | ||||||||
\(764\) | −5.34658e12 | −0.567749 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.02495e13 | −1.07566 | ||||||||
\(767\) | 1.35717e12 | 0.141598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.64729e12 | −0.685450 | −0.342725 | − | 0.939436i | \(-0.611350\pi\) | ||||
−0.342725 | + | 0.939436i | \(0.611350\pi\) | |||||||
\(770\) | 2.22754e13 | 2.28358 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.13255e12 | 0.317409 | ||||||||
\(773\) | −1.79549e13 | −1.80874 | −0.904369 | − | 0.426752i | \(-0.859658\pi\) | ||||
−0.904369 | + | 0.426752i | \(0.859658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.82943e13 | −1.82162 | ||||||||
\(776\) | −1.03509e11 | −0.0102471 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.61838e12 | 0.354083 | ||||||||
\(779\) | −9.37924e12 | −0.912534 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.86077e12 | −0.467493 | ||||||||
\(782\) | 1.65402e12 | 0.158165 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.76140e13 | −1.66508 | ||||||||
\(785\) | 1.76266e12 | 0.165675 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.36005e12 | 0.869745 | 0.434873 | − | 0.900492i | \(-0.356793\pi\) | ||||
0.434873 | + | 0.900492i | \(0.356793\pi\) | |||||||
\(788\) | 1.45962e13 | 1.34856 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.18476e13 | 1.99563 | ||||||||
\(791\) | 3.06437e13 | 2.78322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.11986e12 | 0.190361 | ||||||||
\(794\) | 1.12774e13 | 1.00697 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.18229e12 | 0.104380 | ||||||||
\(797\) | 1.60113e13 | 1.40561 | 0.702803 | − | 0.711384i | \(-0.251931\pi\) | ||||
0.702803 | + | 0.711384i | \(0.251931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.82724e11 | 0.0592631 | ||||||||
\(800\) | −1.97863e13 | −1.70789 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.24419e12 | −0.703661 | ||||||||
\(803\) | 4.92350e11 | 0.0417882 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.23619e13 | −2.71614 | ||||||||
\(806\) | −1.20457e13 | −1.00537 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.27687e12 | 0.105389 | ||||||||
\(809\) | −1.53912e13 | −1.26329 | −0.631645 | − | 0.775258i | \(-0.717620\pi\) | ||||
−0.631645 | + | 0.775258i | \(0.717620\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.81531e13 | −1.47352 | −0.736760 | − | 0.676154i | \(-0.763645\pi\) | ||||
−0.736760 | + | 0.676154i | \(0.763645\pi\) | |||||||
\(812\) | 2.69571e13 | 2.17606 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.64581e12 | 0.770068 | ||||||||
\(815\) | 1.76975e13 | 1.40509 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.85747e13 | 2.24379 | ||||||||
\(818\) | 8.67609e11 | 0.0677539 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.35812e13 | 1.04900 | ||||||||
\(821\) | −2.20209e13 | −1.69157 | −0.845786 | − | 0.533523i | \(-0.820868\pi\) | ||||
−0.845786 | + | 0.533523i | \(0.820868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.72414e13 | −1.31000 | −0.655002 | − | 0.755627i | \(-0.727332\pi\) | ||||
−0.655002 | + | 0.755627i | \(0.727332\pi\) | |||||||
\(824\) | −2.42832e11 | −0.0183499 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.69105e12 | −0.724370 | ||||||||
\(827\) | 3.54008e12 | 0.263171 | 0.131585 | − | 0.991305i | \(-0.457993\pi\) | ||||
0.131585 | + | 0.991305i | \(0.457993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.85206e13 | 1.36194 | 0.680971 | − | 0.732310i | \(-0.261558\pi\) | ||||
0.680971 | + | 0.732310i | \(0.261558\pi\) | |||||||
\(830\) | 3.35702e12 | 0.245529 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.91517e12 | −0.500320 | ||||||||
\(833\) | −2.41964e12 | −0.174120 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.47171e11 | 0.0674279 | ||||||||
\(836\) | 1.28726e13 | 0.911462 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.80399e11 | 0.0196417 | ||||||||
\(839\) | −1.10025e13 | −0.766591 | −0.383295 | − | 0.923626i | \(-0.625211\pi\) | ||||
−0.383295 | + | 0.923626i | \(0.625211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.58144e12 | 0.591532 | ||||||||
\(842\) | −3.13019e13 | −2.14618 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.21235e12 | −0.489256 | ||||||||
\(845\) | 1.72704e13 | 1.16532 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.42832e13 | 0.953563 | ||||||||
\(848\) | 1.45156e13 | 0.963951 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.60407e12 | −0.171107 | ||||||||
\(851\) | −1.40135e13 | −0.915936 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.48235e13 | −0.958693 | −0.479347 | − | 0.877626i | \(-0.659126\pi\) | ||||
−0.479347 | + | 0.877626i | \(0.659126\pi\) | |||||||
\(854\) | −1.51371e13 | −0.973826 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.49832e11 | −0.0350024 | ||||||||
\(857\) | 7.68399e12 | 0.486601 | 0.243301 | − | 0.969951i | \(-0.421770\pi\) | ||||
0.243301 | + | 0.969951i | \(0.421770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.90428e12 | −0.119333 | −0.0596667 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596667 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(860\) | −4.13764e13 | −2.57934 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.47050e13 | 2.75786 | ||||||||
\(863\) | −3.09626e12 | −0.190015 | −0.0950077 | − | 0.995477i | \(-0.530288\pi\) | ||||
−0.0950077 | + | 0.995477i | \(0.530288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.89162e13 | 1.14884 | ||||||||
\(866\) | −4.08197e13 | −2.46626 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.38885e13 | 2.62429 | ||||||||
\(869\) | −1.03137e13 | −0.613513 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.66411e12 | −0.510084 | ||||||||
\(872\) | 7.61858e11 | 0.0446221 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.66516e13 | −2.12467 | ||||||||
\(875\) | 8.39656e12 | 0.484245 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.14925e12 | 0.236849 | 0.118425 | − | 0.992963i | \(-0.462216\pi\) | ||||
0.118425 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(878\) | 1.41051e13 | 0.801032 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.64231e13 | 0.923173 | ||||||||
\(881\) | 1.36244e13 | 0.761948 | 0.380974 | − | 0.924586i | \(-0.375589\pi\) | ||||
0.380974 | + | 0.924586i | \(0.375589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.83775e13 | −1.01734 | −0.508668 | − | 0.860963i | \(-0.669862\pi\) | ||||
−0.508668 | + | 0.860963i | \(0.669862\pi\) | |||||||
\(884\) | −8.74892e11 | −0.0481858 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.64251e13 | −0.895479 | ||||||||
\(887\) | 2.97823e13 | 1.61548 | 0.807741 | − | 0.589538i | \(-0.200690\pi\) | ||||
0.807741 | + | 0.589538i | \(0.200690\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.66975e13 | −0.896592 | ||||||||
\(890\) | −1.06546e13 | −0.569223 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.58580e12 | −0.0838700 | ||||||||
\(893\) | −1.51286e13 | −0.796097 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.82301e12 | 0.199160 | ||||||||
\(896\) | 3.81760e12 | 0.197881 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.75546e13 | −2.44033 | ||||||||
\(899\) | 3.75902e13 | 1.91936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.99401e12 | 0.100801 | ||||||||
\(902\) | −1.25651e13 | −0.632028 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.01906e12 | −0.100552 | ||||||||
\(905\) | 2.11524e13 | 1.04819 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.49542e13 | −1.71501 | −0.857504 | − | 0.514477i | \(-0.827986\pi\) | ||||
−0.857504 | + | 0.514477i | \(0.827986\pi\) | |||||||
\(908\) | 1.78486e13 | 0.871398 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.35479e13 | 1.62173 | ||||||||
\(911\) | −2.02274e13 | −0.972989 | −0.486494 | − | 0.873684i | \(-0.661725\pi\) | ||||
−0.486494 | + | 0.873684i | \(0.661725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.58476e12 | −0.0754824 | ||||||||
\(914\) | −3.62104e13 | −1.71623 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.05827e13 | −1.90463 | ||||||||
\(917\) | −3.95442e13 | −1.84681 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.43929e12 | 0.205302 | 0.102651 | − | 0.994717i | \(-0.467268\pi\) | ||||
0.102651 | + | 0.994717i | \(0.467268\pi\) | |||||||
\(920\) | 2.13227e12 | 0.0981290 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.58292e13 | −2.54432 | ||||||||
\(923\) | −7.32057e12 | −0.331999 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.20628e13 | 0.990884 | ||||||||
\(926\) | 8.88104e12 | 0.396930 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.06560e13 | 1.79953 | ||||||||
\(929\) | 1.16451e13 | 0.512948 | 0.256474 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256474 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.36170e13 | 2.33899 | ||||||||
\(932\) | −3.46492e13 | −1.50425 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.70200e13 | −1.59175 | ||||||||
\(935\) | 2.25604e12 | 0.0965372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.68375e12 | −0.283265 | −0.141632 | − | 0.989919i | \(-0.545235\pi\) | ||||
−0.141632 | + | 0.989919i | \(0.545235\pi\) | |||||||
\(938\) | 6.18670e13 | 2.60943 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.19063e13 | 0.915152 | ||||||||
\(941\) | 2.77843e13 | 1.15517 | 0.577586 | − | 0.816330i | \(-0.303995\pi\) | ||||
0.577586 | + | 0.816330i | \(0.303995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.82547e13 | 0.751748 | ||||||||
\(944\) | −7.14498e12 | −0.292838 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.82806e13 | 1.55406 | ||||||||
\(947\) | 2.02254e13 | 0.817189 | 0.408595 | − | 0.912716i | \(-0.366019\pi\) | ||||
0.408595 | + | 0.912716i | \(0.366019\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.41504e11 | 0.0296767 | ||||||||
\(950\) | 5.77040e13 | 2.29853 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.50996e11 | 0.00990379 | ||||||||
\(953\) | 1.95165e13 | 0.766450 | 0.383225 | − | 0.923655i | \(-0.374813\pi\) | ||||
0.383225 | + | 0.923655i | \(0.374813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.07639e13 | 0.807781 | ||||||||
\(956\) | 2.12557e13 | 0.823030 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.01556e13 | −1.15671 | ||||||||
\(959\) | 1.03946e13 | 0.396846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.47604e13 | 1.31471 | ||||||||
\(962\) | 1.45271e13 | 0.546878 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.32727e12 | 0.235977 | ||||||||
\(965\) | −1.21655e13 | −0.451603 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.20323e13 | 1.54584 | 0.772919 | − | 0.634504i | \(-0.218796\pi\) | ||||
0.772919 | + | 0.634504i | \(0.218796\pi\) | |||||||
\(968\) | −9.41094e11 | −0.0344504 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00053e13 | 0.362876 | ||||||||
\(971\) | −8.15237e12 | −0.294305 | −0.147152 | − | 0.989114i | \(-0.547011\pi\) | ||||
−0.147152 | + | 0.989114i | \(0.547011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.95988e13 | −1.77404 | ||||||||
\(974\) | −3.32747e13 | −1.18467 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.11602e13 | −0.393684 | ||||||||
\(977\) | 1.48575e13 | 0.521699 | 0.260849 | − | 0.965379i | \(-0.415997\pi\) | ||||
0.260849 | + | 0.965379i | \(0.415997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.02977e12 | 0.174995 | ||||||||
\(980\) | −7.76379e13 | −2.68879 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.59004e13 | −1.91828 | ||||||||
\(983\) | 8.38233e12 | 0.286335 | 0.143167 | − | 0.989698i | \(-0.454271\pi\) | ||||
0.143167 | + | 0.989698i | \(0.454271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.66855e13 | −1.91871 | ||||||||
\(986\) | 5.35073e12 | 0.180288 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.93868e13 | 0.647293 | ||||||||
\(989\) | −5.56146e13 | −1.84844 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.54621e13 | 1.16797 | 0.583986 | − | 0.811763i | \(-0.301492\pi\) | ||||
0.583986 | + | 0.811763i | \(0.301492\pi\) | |||||||
\(992\) | 6.61915e13 | 2.17020 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.22733e13 | 1.69840 | ||||||||
\(995\) | −4.59152e12 | −0.148509 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.17955e13 | 1.33968 | 0.669841 | − | 0.742505i | \(-0.266362\pi\) | ||||
0.669841 | + | 0.742505i | \(0.266362\pi\) | |||||||
\(998\) | 7.75919e13 | 2.47588 | ||||||||
\(999\) | 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 | 27.10.a.c.1.3 | yes | 3 | |
3.2 | odd | 2 | 27.10.a.b.1.1 | ✓ | 3 | ||
9.2 | odd | 6 | 81.10.c.h.28.3 | 6 | |||
9.4 | even | 3 | 81.10.c.g.55.1 | 6 | |||
9.5 | odd | 6 | 81.10.c.h.55.3 | 6 | |||
9.7 | even | 3 | 81.10.c.g.28.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.10.a.b.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
27.10.a.c.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
81.10.c.g.28.1 | 6 | 9.7 | even | 3 | |||
81.10.c.g.55.1 | 6 | 9.4 | even | 3 | |||
81.10.c.h.28.3 | 6 | 9.2 | odd | 6 | |||
81.10.c.h.55.3 | 6 | 9.5 | odd | 6 |