Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, 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("98.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4037x + 70980 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(19.2603\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −179.327 | −1.27821 | −0.639103 | − | 0.769121i | \(-0.720694\pi\) | ||||
−0.639103 | + | 0.769121i | \(0.720694\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 168.288 | 0.120417 | 0.0602087 | − | 0.998186i | \(-0.480823\pi\) | ||||
0.0602087 | + | 0.998186i | \(0.480823\pi\) | |||||||
\(6\) | 2869.24 | 0.903829 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 12475.3 | 0.633812 | ||||||||
\(10\) | −2692.61 | −0.0851479 | ||||||||
\(11\) | 14493.8 | 0.298480 | 0.149240 | − | 0.988801i | \(-0.452317\pi\) | ||||
0.149240 | + | 0.988801i | \(0.452317\pi\) | |||||||
\(12\) | −45907.8 | −0.639103 | ||||||||
\(13\) | 109153. | 1.05997 | 0.529983 | − | 0.848008i | \(-0.322198\pi\) | ||||
0.529983 | + | 0.848008i | \(0.322198\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30178.7 | −0.153918 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −300416. | −0.872375 | −0.436188 | − | 0.899856i | \(-0.643672\pi\) | ||||
−0.436188 | + | 0.899856i | \(0.643672\pi\) | |||||||
\(18\) | −199605. | −0.448173 | ||||||||
\(19\) | 491792. | 0.865745 | 0.432872 | − | 0.901455i | \(-0.357500\pi\) | ||||
0.432872 | + | 0.901455i | \(0.357500\pi\) | |||||||
\(20\) | 43081.8 | 0.0602087 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −231901. | −0.211057 | ||||||||
\(23\) | −2.27046e6 | −1.69176 | −0.845880 | − | 0.533373i | \(-0.820924\pi\) | ||||
−0.845880 | + | 0.533373i | \(0.820924\pi\) | |||||||
\(24\) | 734525. | 0.451914 | ||||||||
\(25\) | −1.92480e6 | −0.985500 | ||||||||
\(26\) | −1.74645e6 | −0.749509 | ||||||||
\(27\) | 1.29253e6 | 0.468064 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.80273e6 | −0.998399 | −0.499199 | − | 0.866487i | \(-0.666372\pi\) | ||||
−0.499199 | + | 0.866487i | \(0.666372\pi\) | |||||||
\(30\) | 482859. | 0.108837 | ||||||||
\(31\) | −7.90737e6 | −1.53782 | −0.768908 | − | 0.639359i | \(-0.779200\pi\) | ||||
−0.768908 | + | 0.639359i | \(0.779200\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | −2.59913e6 | −0.381519 | ||||||||
\(34\) | 4.80666e6 | 0.616863 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.19368e6 | 0.316906 | ||||||||
\(37\) | 1.41551e7 | 1.24167 | 0.620835 | − | 0.783942i | \(-0.286794\pi\) | ||||
0.620835 | + | 0.783942i | \(0.286794\pi\) | |||||||
\(38\) | −7.86867e6 | −0.612174 | ||||||||
\(39\) | −1.95742e7 | −1.35486 | ||||||||
\(40\) | −689309. | −0.0425740 | ||||||||
\(41\) | −1.11075e7 | −0.613890 | −0.306945 | − | 0.951727i | \(-0.599307\pi\) | ||||
−0.306945 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.50738e6 | 0.379479 | 0.189740 | − | 0.981834i | \(-0.439236\pi\) | ||||
0.189740 | + | 0.981834i | \(0.439236\pi\) | |||||||
\(44\) | 3.71041e6 | 0.149240 | ||||||||
\(45\) | 2.09945e6 | 0.0763220 | ||||||||
\(46\) | 3.63274e7 | 1.19625 | ||||||||
\(47\) | 4.37456e7 | 1.30766 | 0.653828 | − | 0.756643i | \(-0.273162\pi\) | ||||
0.653828 | + | 0.756643i | \(0.273162\pi\) | |||||||
\(48\) | −1.17524e7 | −0.319552 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.07969e7 | 0.696853 | ||||||||
\(51\) | 5.38729e7 | 1.11508 | ||||||||
\(52\) | 2.79433e7 | 0.529983 | ||||||||
\(53\) | −5.51883e7 | −0.960740 | −0.480370 | − | 0.877066i | \(-0.659498\pi\) | ||||
−0.480370 | + | 0.877066i | \(0.659498\pi\) | |||||||
\(54\) | −2.06805e7 | −0.330971 | ||||||||
\(55\) | 2.43914e6 | 0.0359421 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.81917e7 | −1.10660 | ||||||||
\(58\) | 6.08436e7 | 0.705975 | ||||||||
\(59\) | 4.90092e7 | 0.526554 | 0.263277 | − | 0.964720i | \(-0.415197\pi\) | ||||
0.263277 | + | 0.964720i | \(0.415197\pi\) | |||||||
\(60\) | −7.72575e6 | −0.0769591 | ||||||||
\(61\) | 1.41890e8 | 1.31210 | 0.656052 | − | 0.754716i | \(-0.272225\pi\) | ||||
0.656052 | + | 0.754716i | \(0.272225\pi\) | |||||||
\(62\) | 1.26518e8 | 1.08740 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | 1.83692e7 | 0.127638 | ||||||||
\(66\) | 4.15862e7 | 0.269775 | ||||||||
\(67\) | −9.87576e7 | −0.598734 | −0.299367 | − | 0.954138i | \(-0.596776\pi\) | ||||
−0.299367 | + | 0.954138i | \(0.596776\pi\) | |||||||
\(68\) | −7.69066e7 | −0.436188 | ||||||||
\(69\) | 4.07156e8 | 2.16242 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.96024e8 | 1.38250 | 0.691248 | − | 0.722617i | \(-0.257061\pi\) | ||||
0.691248 | + | 0.722617i | \(0.257061\pi\) | |||||||
\(72\) | −5.10989e7 | −0.224086 | ||||||||
\(73\) | −4.60393e7 | −0.189747 | −0.0948737 | − | 0.995489i | \(-0.530245\pi\) | ||||
−0.0948737 | + | 0.995489i | \(0.530245\pi\) | |||||||
\(74\) | −2.26482e8 | −0.877993 | ||||||||
\(75\) | 3.45170e8 | 1.25967 | ||||||||
\(76\) | 1.25899e8 | 0.432872 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.13187e8 | 0.958028 | ||||||||
\(79\) | −5.52570e8 | −1.59612 | −0.798060 | − | 0.602579i | \(-0.794140\pi\) | ||||
−0.798060 | + | 0.602579i | \(0.794140\pi\) | |||||||
\(80\) | 1.10289e7 | 0.0301043 | ||||||||
\(81\) | −4.77339e8 | −1.23209 | ||||||||
\(82\) | 1.77721e8 | 0.434086 | ||||||||
\(83\) | 5.43217e8 | 1.25638 | 0.628191 | − | 0.778059i | \(-0.283796\pi\) | ||||
0.628191 | + | 0.778059i | \(0.283796\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.05566e7 | −0.105049 | ||||||||
\(86\) | −1.36118e8 | −0.268332 | ||||||||
\(87\) | 6.81933e8 | 1.27616 | ||||||||
\(88\) | −5.93666e7 | −0.105529 | ||||||||
\(89\) | −5.08661e8 | −0.859356 | −0.429678 | − | 0.902982i | \(-0.641373\pi\) | ||||
−0.429678 | + | 0.902982i | \(0.641373\pi\) | |||||||
\(90\) | −3.35912e7 | −0.0539678 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.81238e8 | −0.845880 | ||||||||
\(93\) | 1.41801e9 | 1.96565 | ||||||||
\(94\) | −6.99929e8 | −0.924653 | ||||||||
\(95\) | 8.27628e7 | 0.104251 | ||||||||
\(96\) | 1.88038e8 | 0.225957 | ||||||||
\(97\) | 1.18179e9 | 1.35540 | 0.677701 | − | 0.735338i | \(-0.262976\pi\) | ||||
0.677701 | + | 0.735338i | \(0.262976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.80815e8 | 0.189180 | ||||||||
\(100\) | −4.92750e8 | −0.492750 | ||||||||
\(101\) | 5.25710e8 | 0.502690 | 0.251345 | − | 0.967898i | \(-0.419127\pi\) | ||||
0.251345 | + | 0.967898i | \(0.419127\pi\) | |||||||
\(102\) | −8.61966e8 | −0.788478 | ||||||||
\(103\) | 1.48474e9 | 1.29982 | 0.649909 | − | 0.760012i | \(-0.274807\pi\) | ||||
0.649909 | + | 0.760012i | \(0.274807\pi\) | |||||||
\(104\) | −4.47092e8 | −0.374755 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.83014e8 | 0.679346 | ||||||||
\(107\) | 2.05930e9 | 1.51877 | 0.759385 | − | 0.650642i | \(-0.225500\pi\) | ||||
0.759385 | + | 0.650642i | \(0.225500\pi\) | |||||||
\(108\) | 3.30889e8 | 0.234032 | ||||||||
\(109\) | 1.62236e9 | 1.10085 | 0.550424 | − | 0.834886i | \(-0.314466\pi\) | ||||
0.550424 | + | 0.834886i | \(0.314466\pi\) | |||||||
\(110\) | −3.90262e7 | −0.0254149 | ||||||||
\(111\) | −2.53840e9 | −1.58711 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.79789e8 | −0.161428 | −0.0807139 | − | 0.996737i | \(-0.525720\pi\) | ||||
−0.0807139 | + | 0.996737i | \(0.525720\pi\) | |||||||
\(114\) | 1.41107e9 | 0.782485 | ||||||||
\(115\) | −3.82092e8 | −0.203717 | ||||||||
\(116\) | −9.73498e8 | −0.499199 | ||||||||
\(117\) | 1.36172e9 | 0.671819 | ||||||||
\(118\) | −7.84147e8 | −0.372330 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.23612e8 | 0.0544183 | ||||||||
\(121\) | −2.14788e9 | −0.910910 | ||||||||
\(122\) | −2.27024e9 | −0.927797 | ||||||||
\(123\) | 1.99189e9 | 0.784679 | ||||||||
\(124\) | −2.02429e9 | −0.768908 | ||||||||
\(125\) | −6.52610e8 | −0.239089 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.04209e9 | −0.696558 | −0.348279 | − | 0.937391i | \(-0.613234\pi\) | ||||
−0.348279 | + | 0.937391i | \(0.613234\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | −1.52561e9 | −0.485053 | ||||||||
\(130\) | −2.93908e8 | −0.0902539 | ||||||||
\(131\) | −2.40237e9 | −0.712719 | −0.356359 | − | 0.934349i | \(-0.615982\pi\) | ||||
−0.356359 | + | 0.934349i | \(0.615982\pi\) | |||||||
\(132\) | −6.65378e8 | −0.190759 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.58012e9 | 0.423369 | ||||||||
\(135\) | 2.17518e8 | 0.0563630 | ||||||||
\(136\) | 1.23051e9 | 0.308431 | ||||||||
\(137\) | −1.93337e9 | −0.468891 | −0.234446 | − | 0.972129i | \(-0.575327\pi\) | ||||
−0.234446 | + | 0.972129i | \(0.575327\pi\) | |||||||
\(138\) | −6.51449e9 | −1.52906 | ||||||||
\(139\) | 8.99325e8 | 0.204338 | 0.102169 | − | 0.994767i | \(-0.467422\pi\) | ||||
0.102169 | + | 0.994767i | \(0.467422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.84478e9 | −1.67146 | ||||||||
\(142\) | −4.73638e9 | −0.977573 | ||||||||
\(143\) | 1.58205e9 | 0.316378 | ||||||||
\(144\) | 8.17583e8 | 0.158453 | ||||||||
\(145\) | −6.39954e8 | −0.120225 | ||||||||
\(146\) | 7.36629e8 | 0.134172 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.62371e9 | 0.620835 | ||||||||
\(149\) | −9.43719e9 | −1.56857 | −0.784286 | − | 0.620399i | \(-0.786971\pi\) | ||||
−0.784286 | + | 0.620399i | \(0.786971\pi\) | |||||||
\(150\) | −5.52272e9 | −0.890723 | ||||||||
\(151\) | 4.42810e9 | 0.693141 | 0.346571 | − | 0.938024i | \(-0.387346\pi\) | ||||
0.346571 | + | 0.938024i | \(0.387346\pi\) | |||||||
\(152\) | −2.01438e9 | −0.306087 | ||||||||
\(153\) | −3.74779e9 | −0.552922 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.33072e9 | −0.185180 | ||||||||
\(156\) | −5.01099e9 | −0.677428 | ||||||||
\(157\) | 5.24204e9 | 0.688576 | 0.344288 | − | 0.938864i | \(-0.388120\pi\) | ||||
0.344288 | + | 0.938864i | \(0.388120\pi\) | |||||||
\(158\) | 8.84112e9 | 1.12863 | ||||||||
\(159\) | 9.89678e9 | 1.22802 | ||||||||
\(160\) | −1.76463e8 | −0.0212870 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.63742e9 | 0.871222 | ||||||||
\(163\) | 8.97873e9 | 0.996256 | 0.498128 | − | 0.867104i | \(-0.334021\pi\) | ||||
0.498128 | + | 0.867104i | \(0.334021\pi\) | |||||||
\(164\) | −2.84353e9 | −0.306945 | ||||||||
\(165\) | −4.37404e8 | −0.0459415 | ||||||||
\(166\) | −8.69147e9 | −0.888396 | ||||||||
\(167\) | −1.16267e10 | −1.15673 | −0.578367 | − | 0.815777i | \(-0.696310\pi\) | ||||
−0.578367 | + | 0.815777i | \(0.696310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.30995e9 | 0.123528 | ||||||||
\(170\) | 8.08905e8 | 0.0742809 | ||||||||
\(171\) | 6.13526e9 | 0.548720 | ||||||||
\(172\) | 2.17789e9 | 0.189740 | ||||||||
\(173\) | 6.13714e9 | 0.520905 | 0.260452 | − | 0.965487i | \(-0.416128\pi\) | ||||
0.260452 | + | 0.965487i | \(0.416128\pi\) | |||||||
\(174\) | −1.09109e10 | −0.902381 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.49865e8 | 0.0746200 | ||||||||
\(177\) | −8.78869e9 | −0.673045 | ||||||||
\(178\) | 8.13857e9 | 0.607656 | ||||||||
\(179\) | 2.33469e10 | 1.69977 | 0.849885 | − | 0.526969i | \(-0.176672\pi\) | ||||
0.849885 | + | 0.526969i | \(0.176672\pi\) | |||||||
\(180\) | 5.37460e8 | 0.0381610 | ||||||||
\(181\) | 5.45222e9 | 0.377590 | 0.188795 | − | 0.982017i | \(-0.439542\pi\) | ||||
0.188795 | + | 0.982017i | \(0.439542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.54448e10 | −1.67714 | ||||||||
\(184\) | 9.29981e9 | 0.598127 | ||||||||
\(185\) | 2.38214e9 | 0.149518 | ||||||||
\(186\) | −2.26881e10 | −1.38992 | ||||||||
\(187\) | −4.35417e9 | −0.260386 | ||||||||
\(188\) | 1.11989e10 | 0.653828 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.32420e9 | −0.0737164 | ||||||||
\(191\) | 2.34598e10 | 1.27548 | 0.637741 | − | 0.770250i | \(-0.279869\pi\) | ||||
0.637741 | + | 0.770250i | \(0.279869\pi\) | |||||||
\(192\) | −3.00861e9 | −0.159776 | ||||||||
\(193\) | 8.76414e9 | 0.454675 | 0.227338 | − | 0.973816i | \(-0.426998\pi\) | ||||
0.227338 | + | 0.973816i | \(0.426998\pi\) | |||||||
\(194\) | −1.89087e10 | −0.958414 | ||||||||
\(195\) | −3.29411e9 | −0.163148 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.40897e10 | 0.666503 | 0.333252 | − | 0.942838i | \(-0.391854\pi\) | ||||
0.333252 | + | 0.942838i | \(0.391854\pi\) | |||||||
\(198\) | −2.89304e9 | −0.133771 | ||||||||
\(199\) | 1.45952e10 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(200\) | 7.88400e9 | 0.348427 | ||||||||
\(201\) | 1.77099e10 | 0.765306 | ||||||||
\(202\) | −8.41137e9 | −0.355456 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.37915e10 | 0.557538 | ||||||||
\(205\) | −1.86927e9 | −0.0739231 | ||||||||
\(206\) | −2.37558e10 | −0.919110 | ||||||||
\(207\) | −2.83247e10 | −1.07226 | ||||||||
\(208\) | 7.15347e9 | 0.264992 | ||||||||
\(209\) | 7.12793e9 | 0.258407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.18799e10 | 1.10725 | 0.553625 | − | 0.832766i | \(-0.313244\pi\) | ||||
0.553625 | + | 0.832766i | \(0.313244\pi\) | |||||||
\(212\) | −1.41282e10 | −0.480370 | ||||||||
\(213\) | −5.30852e10 | −1.76712 | ||||||||
\(214\) | −3.29487e10 | −1.07393 | ||||||||
\(215\) | 1.43169e9 | 0.0456959 | ||||||||
\(216\) | −5.29422e9 | −0.165486 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.59577e10 | −0.778417 | ||||||||
\(219\) | 8.25611e9 | 0.242536 | ||||||||
\(220\) | 6.24419e8 | 0.0179711 | ||||||||
\(221\) | −3.27914e10 | −0.924688 | ||||||||
\(222\) | 4.06144e10 | 1.12226 | ||||||||
\(223\) | 5.49341e10 | 1.48755 | 0.743773 | − | 0.668433i | \(-0.233035\pi\) | ||||
0.743773 | + | 0.668433i | \(0.233035\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.40126e10 | −0.624622 | ||||||||
\(226\) | 4.47663e9 | 0.114147 | ||||||||
\(227\) | 2.54176e10 | 0.635358 | 0.317679 | − | 0.948198i | \(-0.397097\pi\) | ||||
0.317679 | + | 0.948198i | \(0.397097\pi\) | |||||||
\(228\) | −2.25771e10 | −0.553300 | ||||||||
\(229\) | −3.95101e10 | −0.949399 | −0.474700 | − | 0.880148i | \(-0.657443\pi\) | ||||
−0.474700 | + | 0.880148i | \(0.657443\pi\) | |||||||
\(230\) | 6.11347e9 | 0.144050 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.55760e10 | 0.352987 | ||||||||
\(233\) | 1.03351e9 | 0.0229727 | 0.0114863 | − | 0.999934i | \(-0.496344\pi\) | ||||
0.0114863 | + | 0.999934i | \(0.496344\pi\) | |||||||
\(234\) | −2.17876e10 | −0.475048 | ||||||||
\(235\) | 7.36187e9 | 0.157465 | ||||||||
\(236\) | 1.25463e10 | 0.263277 | ||||||||
\(237\) | 9.90909e10 | 2.04017 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.53952e10 | 0.503455 | 0.251727 | − | 0.967798i | \(-0.419001\pi\) | ||||
0.251727 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(240\) | −1.97779e9 | −0.0384796 | ||||||||
\(241\) | 4.44854e10 | 0.849455 | 0.424728 | − | 0.905321i | \(-0.360370\pi\) | ||||
0.424728 | + | 0.905321i | \(0.360370\pi\) | |||||||
\(242\) | 3.43660e10 | 0.644110 | ||||||||
\(243\) | 6.01590e10 | 1.10681 | ||||||||
\(244\) | 3.63239e10 | 0.656052 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.18702e10 | −0.554852 | ||||||||
\(247\) | 5.36807e10 | 0.917660 | ||||||||
\(248\) | 3.23886e10 | 0.543700 | ||||||||
\(249\) | −9.74136e10 | −1.60592 | ||||||||
\(250\) | 1.04418e10 | 0.169061 | ||||||||
\(251\) | −7.74824e10 | −1.23217 | −0.616086 | − | 0.787679i | \(-0.711283\pi\) | ||||
−0.616086 | + | 0.787679i | \(0.711283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.29076e10 | −0.504956 | ||||||||
\(254\) | 3.26734e10 | 0.492541 | ||||||||
\(255\) | 9.06618e9 | 0.134274 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −6.63813e10 | −0.949177 | −0.474588 | − | 0.880208i | \(-0.657403\pi\) | ||||
−0.474588 | + | 0.880208i | \(0.657403\pi\) | |||||||
\(258\) | 2.44097e10 | 0.342984 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.70252e9 | 0.0638191 | ||||||||
\(261\) | −4.74402e10 | −0.632797 | ||||||||
\(262\) | 3.84378e10 | 0.503968 | ||||||||
\(263\) | 7.44561e10 | 0.959620 | 0.479810 | − | 0.877372i | \(-0.340706\pi\) | ||||
0.479810 | + | 0.877372i | \(0.340706\pi\) | |||||||
\(264\) | 1.06461e10 | 0.134887 | ||||||||
\(265\) | −9.28756e9 | −0.115690 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.12168e10 | 1.09843 | ||||||||
\(268\) | −2.52820e10 | −0.299367 | ||||||||
\(269\) | −2.00175e10 | −0.233091 | −0.116545 | − | 0.993185i | \(-0.537182\pi\) | ||||
−0.116545 | + | 0.993185i | \(0.537182\pi\) | |||||||
\(270\) | −3.48029e9 | −0.0398547 | ||||||||
\(271\) | 1.45053e11 | 1.63367 | 0.816836 | − | 0.576869i | \(-0.195726\pi\) | ||||
0.816836 | + | 0.576869i | \(0.195726\pi\) | |||||||
\(272\) | −1.96881e10 | −0.218094 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.09339e10 | 0.331556 | ||||||||
\(275\) | −2.78977e10 | −0.294152 | ||||||||
\(276\) | 1.04232e11 | 1.08121 | ||||||||
\(277\) | 1.05211e11 | 1.07374 | 0.536871 | − | 0.843664i | \(-0.319606\pi\) | ||||
0.536871 | + | 0.843664i | \(0.319606\pi\) | |||||||
\(278\) | −1.43892e10 | −0.144489 | ||||||||
\(279\) | −9.86470e10 | −0.974687 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.15652e11 | 1.10656 | 0.553281 | − | 0.832995i | \(-0.313376\pi\) | ||||
0.553281 | + | 0.832995i | \(0.313376\pi\) | |||||||
\(282\) | 1.25516e11 | 1.18190 | ||||||||
\(283\) | −1.01339e11 | −0.939155 | −0.469578 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469578 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(284\) | 7.57821e10 | 0.691248 | ||||||||
\(285\) | −1.48416e10 | −0.133254 | ||||||||
\(286\) | −2.53127e10 | −0.223713 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.30813e10 | −0.112043 | ||||||||
\(289\) | −2.83379e10 | −0.238961 | ||||||||
\(290\) | 1.02393e10 | 0.0850116 | ||||||||
\(291\) | −2.11928e11 | −1.73248 | ||||||||
\(292\) | −1.17861e10 | −0.0948737 | ||||||||
\(293\) | 3.48160e10 | 0.275978 | 0.137989 | − | 0.990434i | \(-0.455936\pi\) | ||||
0.137989 | + | 0.990434i | \(0.455936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.24767e9 | 0.0634063 | ||||||||
\(296\) | −5.79794e10 | −0.438996 | ||||||||
\(297\) | 1.87337e10 | 0.139708 | ||||||||
\(298\) | 1.50995e11 | 1.10915 | ||||||||
\(299\) | −2.47828e11 | −1.79321 | ||||||||
\(300\) | 8.83636e10 | 0.629836 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.08497e10 | −0.490125 | ||||||||
\(303\) | −9.42743e10 | −0.642542 | ||||||||
\(304\) | 3.22301e10 | 0.216436 | ||||||||
\(305\) | 2.38785e10 | 0.158000 | ||||||||
\(306\) | 5.99647e10 | 0.390975 | ||||||||
\(307\) | 3.68120e10 | 0.236520 | 0.118260 | − | 0.992983i | \(-0.462268\pi\) | ||||
0.118260 | + | 0.992983i | \(0.462268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.66254e11 | −1.66144 | ||||||||
\(310\) | 2.12915e10 | 0.130942 | ||||||||
\(311\) | −6.01195e10 | −0.364413 | −0.182206 | − | 0.983260i | \(-0.558324\pi\) | ||||
−0.182206 | + | 0.983260i | \(0.558324\pi\) | |||||||
\(312\) | 8.01759e10 | 0.479014 | ||||||||
\(313\) | −9.53249e10 | −0.561380 | −0.280690 | − | 0.959798i | \(-0.590563\pi\) | ||||
−0.280690 | + | 0.959798i | \(0.590563\pi\) | |||||||
\(314\) | −8.38727e10 | −0.486897 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.41458e11 | −0.798060 | ||||||||
\(317\) | −1.10625e11 | −0.615298 | −0.307649 | − | 0.951500i | \(-0.599542\pi\) | ||||
−0.307649 | + | 0.951500i | \(0.599542\pi\) | |||||||
\(318\) | −1.58349e11 | −0.868344 | ||||||||
\(319\) | −5.51159e10 | −0.298002 | ||||||||
\(320\) | 2.82341e9 | 0.0150522 | ||||||||
\(321\) | −3.69288e11 | −1.94130 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.47742e11 | −0.755254 | ||||||||
\(324\) | −1.22199e11 | −0.616047 | ||||||||
\(325\) | −2.10099e11 | −1.04460 | ||||||||
\(326\) | −1.43660e11 | −0.704459 | ||||||||
\(327\) | −2.90933e11 | −1.40711 | ||||||||
\(328\) | 4.54965e10 | 0.217043 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.99846e9 | 0.0324855 | ||||||||
\(331\) | −4.41494e10 | −0.202162 | −0.101081 | − | 0.994878i | \(-0.532230\pi\) | ||||
−0.101081 | + | 0.994878i | \(0.532230\pi\) | |||||||
\(332\) | 1.39063e11 | 0.628191 | ||||||||
\(333\) | 1.76590e11 | 0.786985 | ||||||||
\(334\) | 1.86028e11 | 0.817934 | ||||||||
\(335\) | −1.66198e10 | −0.0720980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.39384e11 | 1.43336 | 0.716682 | − | 0.697400i | \(-0.245660\pi\) | ||||
0.716682 | + | 0.697400i | \(0.245660\pi\) | |||||||
\(338\) | −2.09592e10 | −0.0873475 | ||||||||
\(339\) | 5.01739e10 | 0.206338 | ||||||||
\(340\) | −1.29425e10 | −0.0525246 | ||||||||
\(341\) | −1.14608e11 | −0.459007 | ||||||||
\(342\) | −9.81642e10 | −0.388003 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.48462e10 | −0.134166 | ||||||||
\(345\) | 6.85196e10 | 0.260393 | ||||||||
\(346\) | −9.81942e10 | −0.368335 | ||||||||
\(347\) | 2.36437e11 | 0.875453 | 0.437726 | − | 0.899108i | \(-0.355784\pi\) | ||||
0.437726 | + | 0.899108i | \(0.355784\pi\) | |||||||
\(348\) | 1.74575e11 | 0.638080 | ||||||||
\(349\) | −2.70871e11 | −0.977346 | −0.488673 | − | 0.872467i | \(-0.662519\pi\) | ||||
−0.488673 | + | 0.872467i | \(0.662519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41084e11 | 0.496132 | ||||||||
\(352\) | −1.51978e10 | −0.0527643 | ||||||||
\(353\) | −1.88618e11 | −0.646544 | −0.323272 | − | 0.946306i | \(-0.604783\pi\) | ||||
−0.323272 | + | 0.946306i | \(0.604783\pi\) | |||||||
\(354\) | 1.40619e11 | 0.475915 | ||||||||
\(355\) | 4.98174e10 | 0.166477 | ||||||||
\(356\) | −1.30217e11 | −0.429678 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.73550e11 | −1.20192 | ||||||||
\(359\) | −5.65261e10 | −0.179607 | −0.0898037 | − | 0.995959i | \(-0.528624\pi\) | ||||
−0.0898037 | + | 0.995959i | \(0.528624\pi\) | |||||||
\(360\) | −8.59935e9 | −0.0269839 | ||||||||
\(361\) | −8.08287e10 | −0.250486 | ||||||||
\(362\) | −8.72356e10 | −0.266996 | ||||||||
\(363\) | 3.85173e11 | 1.16433 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.74788e9 | −0.0228489 | ||||||||
\(366\) | 4.07117e11 | 1.18592 | ||||||||
\(367\) | −5.33289e10 | −0.153450 | −0.0767248 | − | 0.997052i | \(-0.524446\pi\) | ||||
−0.0767248 | + | 0.997052i | \(0.524446\pi\) | |||||||
\(368\) | −1.48797e11 | −0.422940 | ||||||||
\(369\) | −1.38570e11 | −0.389091 | ||||||||
\(370\) | −3.81143e10 | −0.105726 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.63010e11 | 0.982823 | ||||||||
\(373\) | 3.62011e11 | 0.968349 | 0.484174 | − | 0.874972i | \(-0.339120\pi\) | ||||
0.484174 | + | 0.874972i | \(0.339120\pi\) | |||||||
\(374\) | 6.96668e10 | 0.184121 | ||||||||
\(375\) | 1.17031e11 | 0.305605 | ||||||||
\(376\) | −1.79182e11 | −0.462326 | ||||||||
\(377\) | −4.15080e11 | −1.05827 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.82450e11 | −0.454222 | −0.227111 | − | 0.973869i | \(-0.572928\pi\) | ||||
−0.227111 | + | 0.973869i | \(0.572928\pi\) | |||||||
\(380\) | 2.11873e10 | 0.0521253 | ||||||||
\(381\) | 3.66202e11 | 0.890345 | ||||||||
\(382\) | −3.75357e11 | −0.901903 | ||||||||
\(383\) | 4.67701e10 | 0.111064 | 0.0555320 | − | 0.998457i | \(-0.482315\pi\) | ||||
0.0555320 | + | 0.998457i | \(0.482315\pi\) | |||||||
\(384\) | 4.81378e10 | 0.112979 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.40226e11 | −0.321504 | ||||||||
\(387\) | 1.06132e11 | 0.240518 | ||||||||
\(388\) | 3.02539e11 | 0.677701 | ||||||||
\(389\) | 7.47331e11 | 1.65478 | 0.827389 | − | 0.561630i | \(-0.189825\pi\) | ||||
0.827389 | + | 0.561630i | \(0.189825\pi\) | |||||||
\(390\) | 5.27057e10 | 0.115363 | ||||||||
\(391\) | 6.82083e11 | 1.47585 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.30810e11 | 0.911002 | ||||||||
\(394\) | −2.25434e11 | −0.471289 | ||||||||
\(395\) | −9.29911e10 | −0.192200 | ||||||||
\(396\) | 4.62886e10 | 0.0945901 | ||||||||
\(397\) | 5.20994e11 | 1.05263 | 0.526315 | − | 0.850290i | \(-0.323573\pi\) | ||||
0.526315 | + | 0.850290i | \(0.323573\pi\) | |||||||
\(398\) | −2.33524e11 | −0.466506 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.26144e11 | −0.246375 | ||||||||
\(401\) | −2.80021e11 | −0.540805 | −0.270402 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270402 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(402\) | −2.83359e11 | −0.541153 | ||||||||
\(403\) | −8.63116e11 | −1.63003 | ||||||||
\(404\) | 1.34582e11 | 0.251345 | ||||||||
\(405\) | −8.03305e10 | −0.148366 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.05161e11 | 0.370613 | ||||||||
\(408\) | −2.20663e11 | −0.394239 | ||||||||
\(409\) | 1.02969e12 | 1.81950 | 0.909749 | − | 0.415159i | \(-0.136274\pi\) | ||||
0.909749 | + | 0.415159i | \(0.136274\pi\) | |||||||
\(410\) | 2.99083e10 | 0.0522715 | ||||||||
\(411\) | 3.46706e11 | 0.599340 | ||||||||
\(412\) | 3.80093e11 | 0.649909 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.53196e11 | 0.758201 | ||||||||
\(415\) | 9.14170e10 | 0.151290 | ||||||||
\(416\) | −1.14456e11 | −0.187377 | ||||||||
\(417\) | −1.61274e11 | −0.261187 | ||||||||
\(418\) | −1.14047e11 | −0.182722 | ||||||||
\(419\) | 7.23331e11 | 1.14650 | 0.573250 | − | 0.819381i | \(-0.305682\pi\) | ||||
0.573250 | + | 0.819381i | \(0.305682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04783e11 | −0.938275 | −0.469137 | − | 0.883125i | \(-0.655435\pi\) | ||||
−0.469137 | + | 0.883125i | \(0.655435\pi\) | |||||||
\(422\) | −5.10078e11 | −0.782944 | ||||||||
\(423\) | 5.45740e11 | 0.828809 | ||||||||
\(424\) | 2.26051e11 | 0.339673 | ||||||||
\(425\) | 5.78243e11 | 0.859726 | ||||||||
\(426\) | 8.49363e11 | 1.24954 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.27180e11 | 0.759385 | ||||||||
\(429\) | −2.83704e11 | −0.404397 | ||||||||
\(430\) | −2.29071e10 | −0.0323118 | ||||||||
\(431\) | −1.27204e12 | −1.77563 | −0.887813 | − | 0.460204i | \(-0.847776\pi\) | ||||
−0.887813 | + | 0.460204i | \(0.847776\pi\) | |||||||
\(432\) | 8.47075e10 | 0.117016 | ||||||||
\(433\) | 3.81300e11 | 0.521280 | 0.260640 | − | 0.965436i | \(-0.416066\pi\) | ||||
0.260640 | + | 0.965436i | \(0.416066\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.14761e11 | 0.153672 | ||||||||
\(436\) | 4.15323e11 | 0.550424 | ||||||||
\(437\) | −1.11659e12 | −1.46463 | ||||||||
\(438\) | −1.32098e11 | −0.171499 | ||||||||
\(439\) | 7.49056e11 | 0.962551 | 0.481276 | − | 0.876569i | \(-0.340174\pi\) | ||||
0.481276 | + | 0.876569i | \(0.340174\pi\) | |||||||
\(440\) | −9.99070e9 | −0.0127075 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.24663e11 | 0.653853 | ||||||||
\(443\) | 6.69286e10 | 0.0825648 | 0.0412824 | − | 0.999148i | \(-0.486856\pi\) | ||||
0.0412824 | + | 0.999148i | \(0.486856\pi\) | |||||||
\(444\) | −6.49831e11 | −0.793555 | ||||||||
\(445\) | −8.56017e10 | −0.103481 | ||||||||
\(446\) | −8.78946e11 | −1.05185 | ||||||||
\(447\) | 1.69235e12 | 2.00496 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.18015e11 | −0.833729 | −0.416865 | − | 0.908969i | \(-0.636871\pi\) | ||||
−0.416865 | + | 0.908969i | \(0.636871\pi\) | |||||||
\(450\) | 3.84201e11 | 0.441674 | ||||||||
\(451\) | −1.60991e11 | −0.183234 | ||||||||
\(452\) | −7.16261e10 | −0.0807139 | ||||||||
\(453\) | −7.94081e11 | −0.885977 | ||||||||
\(454\) | −4.06682e11 | −0.449266 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.61233e11 | 0.391242 | ||||||||
\(457\) | 1.66054e12 | 1.78085 | 0.890426 | − | 0.455128i | \(-0.150407\pi\) | ||||
0.890426 | + | 0.455128i | \(0.150407\pi\) | |||||||
\(458\) | 6.32162e11 | 0.671327 | ||||||||
\(459\) | −3.88298e11 | −0.408327 | ||||||||
\(460\) | −9.78156e10 | −0.101859 | ||||||||
\(461\) | −5.97375e11 | −0.616018 | −0.308009 | − | 0.951384i | \(-0.599663\pi\) | ||||
−0.308009 | + | 0.951384i | \(0.599663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.50336e11 | −0.657693 | −0.328847 | − | 0.944383i | \(-0.606660\pi\) | ||||
−0.328847 | + | 0.944383i | \(0.606660\pi\) | |||||||
\(464\) | −2.49215e11 | −0.249600 | ||||||||
\(465\) | 2.38634e11 | 0.236698 | ||||||||
\(466\) | −1.65361e10 | −0.0162441 | ||||||||
\(467\) | 1.14333e12 | 1.11236 | 0.556180 | − | 0.831062i | \(-0.312267\pi\) | ||||
0.556180 | + | 0.831062i | \(0.312267\pi\) | |||||||
\(468\) | 3.48601e11 | 0.335910 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.17790e11 | −0.111344 | ||||||||
\(471\) | −9.40042e11 | −0.880143 | ||||||||
\(472\) | −2.00742e11 | −0.186165 | ||||||||
\(473\) | 1.23304e11 | 0.113267 | ||||||||
\(474\) | −1.58545e12 | −1.44262 | ||||||||
\(475\) | −9.46602e11 | −0.853191 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.88493e11 | −0.608929 | ||||||||
\(478\) | −4.06322e11 | −0.355996 | ||||||||
\(479\) | −1.93813e11 | −0.168218 | −0.0841090 | − | 0.996457i | \(-0.526804\pi\) | ||||
−0.0841090 | + | 0.996457i | \(0.526804\pi\) | |||||||
\(480\) | 3.16447e10 | 0.0272092 | ||||||||
\(481\) | 1.54508e12 | 1.31613 | ||||||||
\(482\) | −7.11766e11 | −0.600656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.49857e11 | −0.455455 | ||||||||
\(485\) | 1.98882e11 | 0.163214 | ||||||||
\(486\) | −9.62543e11 | −0.782631 | ||||||||
\(487\) | 4.62927e11 | 0.372934 | 0.186467 | − | 0.982461i | \(-0.440296\pi\) | ||||
0.186467 | + | 0.982461i | \(0.440296\pi\) | |||||||
\(488\) | −5.81182e11 | −0.463899 | ||||||||
\(489\) | −1.61013e12 | −1.27342 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.20314e12 | 0.934222 | 0.467111 | − | 0.884199i | \(-0.345295\pi\) | ||||
0.467111 | + | 0.884199i | \(0.345295\pi\) | |||||||
\(492\) | 5.09923e11 | 0.392339 | ||||||||
\(493\) | 1.14240e12 | 0.870978 | ||||||||
\(494\) | −8.58891e11 | −0.648884 | ||||||||
\(495\) | 3.04290e10 | 0.0227806 | ||||||||
\(496\) | −5.18217e11 | −0.384454 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.55862e12 | 1.13555 | ||||||||
\(499\) | 3.45574e11 | 0.249510 | 0.124755 | − | 0.992188i | \(-0.460185\pi\) | ||||
0.124755 | + | 0.992188i | \(0.460185\pi\) | |||||||
\(500\) | −1.67068e11 | −0.119544 | ||||||||
\(501\) | 2.08499e12 | 1.47854 | ||||||||
\(502\) | 1.23972e12 | 0.871277 | ||||||||
\(503\) | −1.55705e12 | −1.08454 | −0.542270 | − | 0.840204i | \(-0.682435\pi\) | ||||
−0.542270 | + | 0.840204i | \(0.682435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.84709e10 | 0.0605326 | ||||||||
\(506\) | 5.26521e11 | 0.357058 | ||||||||
\(507\) | −2.34910e11 | −0.157894 | ||||||||
\(508\) | −5.22774e11 | −0.348279 | ||||||||
\(509\) | −1.97093e12 | −1.30149 | −0.650746 | − | 0.759295i | \(-0.725544\pi\) | ||||
−0.650746 | + | 0.759295i | \(0.725544\pi\) | |||||||
\(510\) | −1.45059e11 | −0.0949464 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 6.35657e11 | 0.405224 | ||||||||
\(514\) | 1.06210e12 | 0.671169 | ||||||||
\(515\) | 2.49864e11 | 0.156521 | ||||||||
\(516\) | −3.90555e11 | −0.242526 | ||||||||
\(517\) | 6.34039e11 | 0.390309 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.10056e12 | −0.665824 | ||||||||
\(520\) | −7.52404e10 | −0.0451270 | ||||||||
\(521\) | −1.48877e12 | −0.885235 | −0.442617 | − | 0.896711i | \(-0.645950\pi\) | ||||
−0.442617 | + | 0.896711i | \(0.645950\pi\) | |||||||
\(522\) | 7.59044e11 | 0.447455 | ||||||||
\(523\) | 2.06845e12 | 1.20889 | 0.604446 | − | 0.796646i | \(-0.293394\pi\) | ||||
0.604446 | + | 0.796646i | \(0.293394\pi\) | |||||||
\(524\) | −6.15005e11 | −0.356359 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.19130e12 | −0.678554 | ||||||||
\(527\) | 2.37550e12 | 1.34155 | ||||||||
\(528\) | −1.70337e11 | −0.0953797 | ||||||||
\(529\) | 3.35384e12 | 1.86205 | ||||||||
\(530\) | 1.48601e11 | 0.0818050 | ||||||||
\(531\) | 6.11405e11 | 0.333737 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.21243e12 | −0.650703 | ||||||||
\(534\) | −1.45947e12 | −0.776710 | ||||||||
\(535\) | 3.46556e11 | 0.182886 | ||||||||
\(536\) | 4.04511e11 | 0.211684 | ||||||||
\(537\) | −4.18673e12 | −2.17266 | ||||||||
\(538\) | 3.20281e11 | 0.164820 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.56847e10 | 0.0281815 | ||||||||
\(541\) | −3.40957e12 | −1.71124 | −0.855622 | − | 0.517601i | \(-0.826825\pi\) | ||||
−0.855622 | + | 0.517601i | \(0.826825\pi\) | |||||||
\(542\) | −2.32085e12 | −1.15518 | ||||||||
\(543\) | −9.77733e11 | −0.482637 | ||||||||
\(544\) | 3.15009e11 | 0.154216 | ||||||||
\(545\) | 2.73024e11 | 0.132561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.65758e10 | 0.0461238 | 0.0230619 | − | 0.999734i | \(-0.492659\pi\) | ||||
0.0230619 | + | 0.999734i | \(0.492659\pi\) | |||||||
\(548\) | −4.94942e11 | −0.234446 | ||||||||
\(549\) | 1.77013e12 | 0.831627 | ||||||||
\(550\) | 4.46363e11 | 0.207997 | ||||||||
\(551\) | −1.87015e12 | −0.864359 | ||||||||
\(552\) | −1.66771e12 | −0.764530 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.68337e12 | −0.759251 | ||||||||
\(555\) | −4.27183e11 | −0.191116 | ||||||||
\(556\) | 2.30227e11 | 0.102169 | ||||||||
\(557\) | −8.96612e11 | −0.394690 | −0.197345 | − | 0.980334i | \(-0.563232\pi\) | ||||
−0.197345 | + | 0.980334i | \(0.563232\pi\) | |||||||
\(558\) | 1.57835e12 | 0.689207 | ||||||||
\(559\) | 9.28609e11 | 0.402235 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.80822e11 | 0.332828 | ||||||||
\(562\) | −1.85044e12 | −0.782457 | ||||||||
\(563\) | 4.25576e12 | 1.78521 | 0.892605 | − | 0.450839i | \(-0.148875\pi\) | ||||
0.892605 | + | 0.450839i | \(0.148875\pi\) | |||||||
\(564\) | −2.00826e12 | −0.835728 | ||||||||
\(565\) | −4.70853e10 | −0.0194387 | ||||||||
\(566\) | 1.62142e12 | 0.664083 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.21251e12 | −0.488786 | ||||||||
\(569\) | −4.79023e12 | −1.91581 | −0.957903 | − | 0.287092i | \(-0.907311\pi\) | ||||
−0.957903 | + | 0.287092i | \(0.907311\pi\) | |||||||
\(570\) | 2.37466e11 | 0.0942247 | ||||||||
\(571\) | 2.37883e12 | 0.936483 | 0.468242 | − | 0.883600i | \(-0.344888\pi\) | ||||
0.468242 | + | 0.883600i | \(0.344888\pi\) | |||||||
\(572\) | 4.05004e11 | 0.158189 | ||||||||
\(573\) | −4.20699e12 | −1.63033 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.37019e12 | 1.66723 | ||||||||
\(576\) | 2.09301e11 | 0.0792265 | ||||||||
\(577\) | −4.13934e12 | −1.55468 | −0.777339 | − | 0.629082i | \(-0.783431\pi\) | ||||
−0.777339 | + | 0.629082i | \(0.783431\pi\) | |||||||
\(578\) | 4.53407e11 | 0.168971 | ||||||||
\(579\) | −1.57165e12 | −0.581169 | ||||||||
\(580\) | −1.63828e11 | −0.0601123 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.39084e12 | 1.22505 | ||||||||
\(583\) | −7.99889e11 | −0.286762 | ||||||||
\(584\) | 1.88577e11 | 0.0670858 | ||||||||
\(585\) | 2.29162e11 | 0.0808987 | ||||||||
\(586\) | −5.57056e11 | −0.195146 | ||||||||
\(587\) | 3.51788e12 | 1.22295 | 0.611476 | − | 0.791263i | \(-0.290576\pi\) | ||||
0.611476 | + | 0.791263i | \(0.290576\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.88878e12 | −1.33136 | ||||||||
\(590\) | −1.31963e11 | −0.0448350 | ||||||||
\(591\) | −2.52666e12 | −0.851929 | ||||||||
\(592\) | 9.27670e11 | 0.310417 | ||||||||
\(593\) | −1.46555e10 | −0.00486691 | −0.00243346 | − | 0.999997i | \(-0.500775\pi\) | ||||
−0.00243346 | + | 0.999997i | \(0.500775\pi\) | |||||||
\(594\) | −2.99739e11 | −0.0987882 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.41592e12 | −0.784286 | ||||||||
\(597\) | −2.61733e12 | −0.843283 | ||||||||
\(598\) | 3.96525e12 | 1.26799 | ||||||||
\(599\) | −3.03476e12 | −0.963170 | −0.481585 | − | 0.876399i | \(-0.659939\pi\) | ||||
−0.481585 | + | 0.876399i | \(0.659939\pi\) | |||||||
\(600\) | −1.41382e12 | −0.445361 | ||||||||
\(601\) | −9.37778e11 | −0.293201 | −0.146600 | − | 0.989196i | \(-0.546833\pi\) | ||||
−0.146600 | + | 0.989196i | \(0.546833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.23203e12 | −0.379485 | ||||||||
\(604\) | 1.13359e12 | 0.346571 | ||||||||
\(605\) | −3.61463e11 | −0.109689 | ||||||||
\(606\) | 1.50839e12 | 0.454346 | ||||||||
\(607\) | 4.36820e12 | 1.30603 | 0.653015 | − | 0.757345i | \(-0.273504\pi\) | ||||
0.653015 | + | 0.757345i | \(0.273504\pi\) | |||||||
\(608\) | −5.15681e11 | −0.153044 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.82056e11 | −0.111723 | ||||||||
\(611\) | 4.77498e12 | 1.38607 | ||||||||
\(612\) | −9.59435e11 | −0.276461 | ||||||||
\(613\) | −1.25555e12 | −0.359138 | −0.179569 | − | 0.983745i | \(-0.557470\pi\) | ||||
−0.179569 | + | 0.983745i | \(0.557470\pi\) | |||||||
\(614\) | −5.88992e11 | −0.167245 | ||||||||
\(615\) | 3.35212e11 | 0.0944889 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.91635e12 | 1.64350 | 0.821751 | − | 0.569846i | \(-0.192997\pi\) | ||||
0.821751 | + | 0.569846i | \(0.192997\pi\) | |||||||
\(618\) | 4.26007e12 | 1.17481 | ||||||||
\(619\) | 8.44127e11 | 0.231100 | 0.115550 | − | 0.993302i | \(-0.463137\pi\) | ||||
0.115550 | + | 0.993302i | \(0.463137\pi\) | |||||||
\(620\) | −3.40664e11 | −0.0925899 | ||||||||
\(621\) | −2.93465e12 | −0.791851 | ||||||||
\(622\) | 9.61912e11 | 0.257679 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.28281e12 | −0.338714 | ||||||||
\(625\) | 3.64956e12 | 0.956709 | ||||||||
\(626\) | 1.52520e12 | 0.396956 | ||||||||
\(627\) | −1.27823e12 | −0.330298 | ||||||||
\(628\) | 1.34196e12 | 0.344288 | ||||||||
\(629\) | −4.25243e12 | −1.08320 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.70645e11 | −0.118185 | −0.0590924 | − | 0.998253i | \(-0.518821\pi\) | ||||
−0.0590924 | + | 0.998253i | \(0.518821\pi\) | |||||||
\(632\) | 2.26333e12 | 0.564313 | ||||||||
\(633\) | −5.71694e12 | −1.41529 | ||||||||
\(634\) | 1.77000e12 | 0.435081 | ||||||||
\(635\) | −3.43659e11 | −0.0838777 | ||||||||
\(636\) | 2.53358e12 | 0.614012 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.81855e11 | 0.210719 | ||||||||
\(639\) | 3.69299e12 | 0.876243 | ||||||||
\(640\) | −4.51746e10 | −0.0106435 | ||||||||
\(641\) | 7.35770e11 | 0.172140 | 0.0860698 | − | 0.996289i | \(-0.472569\pi\) | ||||
0.0860698 | + | 0.996289i | \(0.472569\pi\) | |||||||
\(642\) | 5.90861e12 | 1.37271 | ||||||||
\(643\) | 2.51018e12 | 0.579103 | 0.289551 | − | 0.957162i | \(-0.406494\pi\) | ||||
0.289551 | + | 0.957162i | \(0.406494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.56742e11 | −0.0584087 | ||||||||
\(646\) | 2.36388e12 | 0.534046 | ||||||||
\(647\) | −1.18989e12 | −0.266955 | −0.133477 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133477 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(648\) | 1.95518e12 | 0.435611 | ||||||||
\(649\) | 7.10329e11 | 0.157166 | ||||||||
\(650\) | 3.36158e12 | 0.738641 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.29856e12 | 0.498128 | ||||||||
\(653\) | −4.19215e12 | −0.902250 | −0.451125 | − | 0.892461i | \(-0.648977\pi\) | ||||
−0.451125 | + | 0.892461i | \(0.648977\pi\) | |||||||
\(654\) | 4.65493e12 | 0.994977 | ||||||||
\(655\) | −4.04290e11 | −0.0858237 | ||||||||
\(656\) | −7.27944e11 | −0.153473 | ||||||||
\(657\) | −5.74355e11 | −0.120264 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.83674e11 | 0.0792461 | 0.0396230 | − | 0.999215i | \(-0.487384\pi\) | ||||
0.0396230 | + | 0.999215i | \(0.487384\pi\) | |||||||
\(660\) | −1.11975e11 | −0.0229707 | ||||||||
\(661\) | 7.20723e12 | 1.46846 | 0.734230 | − | 0.678901i | \(-0.237543\pi\) | ||||
0.734230 | + | 0.678901i | \(0.237543\pi\) | |||||||
\(662\) | 7.06390e11 | 0.142950 | ||||||||
\(663\) | 5.88041e12 | 1.18194 | ||||||||
\(664\) | −2.22502e12 | −0.444198 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.82544e12 | −0.556482 | ||||||||
\(667\) | 8.63394e12 | 1.68905 | ||||||||
\(668\) | −2.97644e12 | −0.578367 | ||||||||
\(669\) | −9.85119e12 | −1.90139 | ||||||||
\(670\) | 2.65916e11 | 0.0509810 | ||||||||
\(671\) | 2.05653e12 | 0.391636 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.29279e12 | −0.994529 | −0.497264 | − | 0.867599i | \(-0.665662\pi\) | ||||
−0.497264 | + | 0.867599i | \(0.665662\pi\) | |||||||
\(674\) | −5.43014e12 | −1.01354 | ||||||||
\(675\) | −2.48787e12 | −0.461277 | ||||||||
\(676\) | 3.35348e11 | 0.0617640 | ||||||||
\(677\) | −8.77680e11 | −0.160578 | −0.0802892 | − | 0.996772i | \(-0.525584\pi\) | ||||
−0.0802892 | + | 0.996772i | \(0.525584\pi\) | |||||||
\(678\) | −8.02782e11 | −0.145903 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.07080e11 | 0.0371405 | ||||||||
\(681\) | −4.55808e12 | −0.812119 | ||||||||
\(682\) | 1.83372e12 | 0.324567 | ||||||||
\(683\) | −1.02795e13 | −1.80749 | −0.903747 | − | 0.428068i | \(-0.859195\pi\) | ||||
−0.903747 | + | 0.428068i | \(0.859195\pi\) | |||||||
\(684\) | 1.57063e12 | 0.274360 | ||||||||
\(685\) | −3.25363e11 | −0.0564626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.08525e12 | 1.21353 | ||||||||
\(688\) | 5.57540e11 | 0.0948698 | ||||||||
\(689\) | −6.02399e12 | −1.01835 | ||||||||
\(690\) | −1.09631e12 | −0.184125 | ||||||||
\(691\) | −1.34749e12 | −0.224841 | −0.112420 | − | 0.993661i | \(-0.535860\pi\) | ||||
−0.112420 | + | 0.993661i | \(0.535860\pi\) | |||||||
\(692\) | 1.57111e12 | 0.260452 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.78299e12 | −0.619039 | ||||||||
\(695\) | 1.51346e11 | 0.0246059 | ||||||||
\(696\) | −2.79320e12 | −0.451191 | ||||||||
\(697\) | 3.33689e12 | 0.535543 | ||||||||
\(698\) | 4.33394e12 | 0.691088 | ||||||||
\(699\) | −1.85336e11 | −0.0293639 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.86975e12 | 1.07451 | 0.537254 | − | 0.843420i | \(-0.319462\pi\) | ||||
0.537254 | + | 0.843420i | \(0.319462\pi\) | |||||||
\(702\) | −2.25735e12 | −0.350818 | ||||||||
\(703\) | 6.96137e12 | 1.07497 | ||||||||
\(704\) | 2.43165e11 | 0.0373100 | ||||||||
\(705\) | −1.32019e12 | −0.201272 | ||||||||
\(706\) | 3.01789e12 | 0.457175 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.24990e12 | −0.336523 | ||||||||
\(709\) | −1.40987e12 | −0.209542 | −0.104771 | − | 0.994496i | \(-0.533411\pi\) | ||||
−0.104771 | + | 0.994496i | \(0.533411\pi\) | |||||||
\(710\) | −7.97078e11 | −0.117717 | ||||||||
\(711\) | −6.89349e12 | −1.01164 | ||||||||
\(712\) | 2.08347e12 | 0.303828 | ||||||||
\(713\) | 1.79534e13 | 2.60162 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.66240e11 | 0.0380975 | ||||||||
\(716\) | 5.97680e12 | 0.849885 | ||||||||
\(717\) | −4.55405e12 | −0.643519 | ||||||||
\(718\) | 9.04418e11 | 0.127002 | ||||||||
\(719\) | −6.92395e12 | −0.966216 | −0.483108 | − | 0.875561i | \(-0.660492\pi\) | ||||
−0.483108 | + | 0.875561i | \(0.660492\pi\) | |||||||
\(720\) | 1.37590e11 | 0.0190805 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.29326e12 | 0.177120 | ||||||||
\(723\) | −7.97745e12 | −1.08578 | ||||||||
\(724\) | 1.39577e12 | 0.188795 | ||||||||
\(725\) | 7.31950e12 | 0.983922 | ||||||||
\(726\) | −6.16277e12 | −0.823306 | ||||||||
\(727\) | 9.30979e12 | 1.23605 | 0.618024 | − | 0.786160i | \(-0.287934\pi\) | ||||
0.618024 | + | 0.786160i | \(0.287934\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.39269e12 | −0.182634 | ||||||||
\(730\) | 1.23966e11 | 0.0161566 | ||||||||
\(731\) | −2.55576e12 | −0.331048 | ||||||||
\(732\) | −6.51387e12 | −0.838570 | ||||||||
\(733\) | −8.26111e12 | −1.05699 | −0.528494 | − | 0.848937i | \(-0.677243\pi\) | ||||
−0.528494 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(734\) | 8.53263e11 | 0.108505 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.38075e12 | 0.299064 | ||||||||
\(737\) | −1.43137e12 | −0.178710 | ||||||||
\(738\) | 2.21712e12 | 0.275129 | ||||||||
\(739\) | 5.12673e12 | 0.632325 | 0.316163 | − | 0.948705i | \(-0.397606\pi\) | ||||
0.316163 | + | 0.948705i | \(0.397606\pi\) | |||||||
\(740\) | 6.09828e11 | 0.0747592 | ||||||||
\(741\) | −9.62642e12 | −1.17296 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.04980e12 | 0.126374 | 0.0631870 | − | 0.998002i | \(-0.479874\pi\) | ||||
0.0631870 | + | 0.998002i | \(0.479874\pi\) | |||||||
\(744\) | −5.80816e12 | −0.694961 | ||||||||
\(745\) | −1.58817e12 | −0.188883 | ||||||||
\(746\) | −5.79217e12 | −0.684726 | ||||||||
\(747\) | 6.77680e12 | 0.796310 | ||||||||
\(748\) | −1.11467e12 | −0.130193 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.87249e12 | −0.216095 | ||||||||
\(751\) | −1.15116e12 | −0.132055 | −0.0660277 | − | 0.997818i | \(-0.521033\pi\) | ||||
−0.0660277 | + | 0.997818i | \(0.521033\pi\) | |||||||
\(752\) | 2.86691e12 | 0.326914 | ||||||||
\(753\) | 1.38947e13 | 1.57497 | ||||||||
\(754\) | 6.64128e12 | 0.748309 | ||||||||
\(755\) | 7.45198e11 | 0.0834662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.77630e12 | −0.528641 | −0.264320 | − | 0.964435i | \(-0.585148\pi\) | ||||
−0.264320 | + | 0.964435i | \(0.585148\pi\) | |||||||
\(758\) | 2.91920e12 | 0.321183 | ||||||||
\(759\) | 5.90123e12 | 0.645438 | ||||||||
\(760\) | −3.38996e11 | −0.0368582 | ||||||||
\(761\) | 1.16815e12 | 0.126260 | 0.0631301 | − | 0.998005i | \(-0.479892\pi\) | ||||
0.0631301 | + | 0.998005i | \(0.479892\pi\) | |||||||
\(762\) | −5.85923e12 | −0.629569 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.00572e12 | 0.637741 | ||||||||
\(765\) | −6.30710e11 | −0.0665814 | ||||||||
\(766\) | −7.48321e11 | −0.0785342 | ||||||||
\(767\) | 5.34951e12 | 0.558130 | ||||||||
\(768\) | −7.70205e11 | −0.0798879 | ||||||||
\(769\) | −1.52183e13 | −1.56927 | −0.784634 | − | 0.619959i | \(-0.787149\pi\) | ||||
−0.784634 | + | 0.619959i | \(0.787149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19040e13 | 1.21324 | ||||||||
\(772\) | 2.24362e12 | 0.227338 | ||||||||
\(773\) | 1.75227e13 | 1.76520 | 0.882600 | − | 0.470124i | \(-0.155791\pi\) | ||||
0.882600 | + | 0.470124i | \(0.155791\pi\) | |||||||
\(774\) | −1.69812e12 | −0.170072 | ||||||||
\(775\) | 1.52201e13 | 1.51552 | ||||||||
\(776\) | −4.84062e12 | −0.479207 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.19573e13 | −1.17010 | ||||||||
\(779\) | −5.46260e12 | −0.531472 | ||||||||
\(780\) | −8.43292e11 | −0.0815741 | ||||||||
\(781\) | 4.29051e12 | 0.412647 | ||||||||
\(782\) | −1.09133e13 | −1.04358 | ||||||||
\(783\) | −4.91515e12 | −0.467314 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.82175e11 | 0.0829165 | ||||||||
\(786\) | −6.89296e12 | −0.644176 | ||||||||
\(787\) | −1.12156e12 | −0.104216 | −0.0521081 | − | 0.998641i | \(-0.516594\pi\) | ||||
−0.0521081 | + | 0.998641i | \(0.516594\pi\) | |||||||
\(788\) | 3.60695e12 | 0.333252 | ||||||||
\(789\) | −1.33520e13 | −1.22659 | ||||||||
\(790\) | 1.48786e12 | 0.135906 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.40617e11 | −0.0668853 | ||||||||
\(793\) | 1.54878e13 | 1.39079 | ||||||||
\(794\) | −8.33591e12 | −0.744322 | ||||||||
\(795\) | 1.66551e12 | 0.147875 | ||||||||
\(796\) | 3.73638e12 | 0.329870 | ||||||||
\(797\) | −1.56799e13 | −1.37651 | −0.688257 | − | 0.725467i | \(-0.741624\pi\) | ||||
−0.688257 | + | 0.725467i | \(0.741624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.31419e13 | −1.14077 | ||||||||
\(800\) | 2.01830e12 | 0.174213 | ||||||||
\(801\) | −6.34571e12 | −0.544670 | ||||||||
\(802\) | 4.48033e12 | 0.382407 | ||||||||
\(803\) | −6.67284e11 | −0.0566358 | ||||||||
\(804\) | 4.53375e12 | 0.382653 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.38099e13 | 1.15261 | ||||||||
\(807\) | 3.58969e12 | 0.297938 | ||||||||
\(808\) | −2.15331e12 | −0.177728 | ||||||||
\(809\) | 1.31404e13 | 1.07855 | 0.539275 | − | 0.842130i | \(-0.318698\pi\) | ||||
0.539275 | + | 0.842130i | \(0.318698\pi\) | |||||||
\(810\) | 1.28529e12 | 0.104910 | ||||||||
\(811\) | −6.99946e12 | −0.568160 | −0.284080 | − | 0.958801i | \(-0.591688\pi\) | ||||
−0.284080 | + | 0.958801i | \(0.591688\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.60120e13 | −2.08817 | ||||||||
\(814\) | −3.28258e12 | −0.262063 | ||||||||
\(815\) | 1.51102e12 | 0.119966 | ||||||||
\(816\) | 3.53061e12 | 0.278769 | ||||||||
\(817\) | 4.18386e12 | 0.328532 | ||||||||
\(818\) | −1.64750e13 | −1.28658 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.78533e11 | −0.0369615 | ||||||||
\(821\) | 6.26383e11 | 0.0481167 | 0.0240583 | − | 0.999711i | \(-0.492341\pi\) | ||||
0.0240583 | + | 0.999711i | \(0.492341\pi\) | |||||||
\(822\) | −5.54730e12 | −0.423797 | ||||||||
\(823\) | 1.29677e13 | 0.985290 | 0.492645 | − | 0.870230i | \(-0.336030\pi\) | ||||
0.492645 | + | 0.870230i | \(0.336030\pi\) | |||||||
\(824\) | −6.08149e12 | −0.459555 | ||||||||
\(825\) | 5.00282e12 | 0.375987 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.65832e11 | 0.0718004 | 0.0359002 | − | 0.999355i | \(-0.488570\pi\) | ||||
0.0359002 | + | 0.999355i | \(0.488570\pi\) | |||||||
\(828\) | −7.25113e12 | −0.536129 | ||||||||
\(829\) | 1.92526e13 | 1.41578 | 0.707888 | − | 0.706325i | \(-0.249648\pi\) | ||||
0.707888 | + | 0.706325i | \(0.249648\pi\) | |||||||
\(830\) | −1.46267e12 | −0.106978 | ||||||||
\(831\) | −1.88671e13 | −1.37246 | ||||||||
\(832\) | 1.83129e12 | 0.132496 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.58038e12 | 0.184687 | ||||||||
\(835\) | −1.95664e12 | −0.139291 | ||||||||
\(836\) | 1.82475e12 | 0.129204 | ||||||||
\(837\) | −1.02205e13 | −0.719796 | ||||||||
\(838\) | −1.15733e13 | −0.810698 | ||||||||
\(839\) | 1.29497e13 | 0.902256 | 0.451128 | − | 0.892459i | \(-0.351022\pi\) | ||||
0.451128 | + | 0.892459i | \(0.351022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.64218e10 | −0.00319993 | ||||||||
\(842\) | 9.67653e12 | 0.663460 | ||||||||
\(843\) | −2.07396e13 | −1.41441 | ||||||||
\(844\) | 8.16125e12 | 0.553625 | ||||||||
\(845\) | 2.20450e11 | 0.0148749 | ||||||||
\(846\) | −8.73184e12 | −0.586056 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.61682e12 | −0.240185 | ||||||||
\(849\) | 1.81728e13 | 1.20043 | ||||||||
\(850\) | −9.25188e12 | −0.607918 | ||||||||
\(851\) | −3.21387e13 | −2.10061 | ||||||||
\(852\) | −1.35898e13 | −0.883558 | ||||||||
\(853\) | −1.06726e13 | −0.690241 | −0.345120 | − | 0.938558i | \(-0.612162\pi\) | ||||
−0.345120 | + | 0.938558i | \(0.612162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.03249e12 | 0.0660754 | ||||||||
\(856\) | −8.43488e12 | −0.536966 | ||||||||
\(857\) | −2.42456e13 | −1.53539 | −0.767697 | − | 0.640813i | \(-0.778598\pi\) | ||||
−0.767697 | + | 0.640813i | \(0.778598\pi\) | |||||||
\(858\) | 4.53927e12 | 0.285952 | ||||||||
\(859\) | 2.36434e13 | 1.48163 | 0.740817 | − | 0.671707i | \(-0.234439\pi\) | ||||
0.740817 | + | 0.671707i | \(0.234439\pi\) | |||||||
\(860\) | 3.66513e11 | 0.0228479 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.03526e13 | 1.25556 | ||||||||
\(863\) | −1.34443e13 | −0.825069 | −0.412534 | − | 0.910942i | \(-0.635356\pi\) | ||||
−0.412534 | + | 0.910942i | \(0.635356\pi\) | |||||||
\(864\) | −1.35532e12 | −0.0827428 | ||||||||
\(865\) | 1.03281e12 | 0.0627260 | ||||||||
\(866\) | −6.10080e12 | −0.368601 | ||||||||
\(867\) | 5.08176e12 | 0.305442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.00883e12 | −0.476409 | ||||||||
\(870\) | −1.83618e12 | −0.108662 | ||||||||
\(871\) | −1.07797e13 | −0.634638 | ||||||||
\(872\) | −6.64517e12 | −0.389208 | ||||||||
\(873\) | 1.47432e13 | 0.859070 | ||||||||
\(874\) | 1.78655e13 | 1.03565 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.11356e12 | 0.121268 | ||||||||
\(877\) | −2.24398e13 | −1.28092 | −0.640458 | − | 0.767993i | \(-0.721255\pi\) | ||||
−0.640458 | + | 0.767993i | \(0.721255\pi\) | |||||||
\(878\) | −1.19849e13 | −0.680626 | ||||||||
\(879\) | −6.24346e12 | −0.352757 | ||||||||
\(880\) | 1.59851e11 | 0.00898554 | ||||||||
\(881\) | −2.34578e13 | −1.31188 | −0.655942 | − | 0.754811i | \(-0.727728\pi\) | ||||
−0.655942 | + | 0.754811i | \(0.727728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.46146e13 | −1.36260 | −0.681302 | − | 0.732002i | \(-0.738586\pi\) | ||||
−0.681302 | + | 0.732002i | \(0.738586\pi\) | |||||||
\(884\) | −8.39461e12 | −0.462344 | ||||||||
\(885\) | −1.47903e12 | −0.0810463 | ||||||||
\(886\) | −1.07086e12 | −0.0583821 | ||||||||
\(887\) | −1.00413e13 | −0.544669 | −0.272334 | − | 0.962203i | \(-0.587796\pi\) | ||||
−0.272334 | + | 0.962203i | \(0.587796\pi\) | |||||||
\(888\) | 1.03973e13 | 0.561128 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.36963e12 | 0.0731724 | ||||||||
\(891\) | −6.91845e12 | −0.367755 | ||||||||
\(892\) | 1.40631e13 | 0.743773 | ||||||||
\(893\) | 2.15137e13 | 1.13210 | ||||||||
\(894\) | −2.70776e13 | −1.41772 | ||||||||
\(895\) | 3.92901e12 | 0.204682 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.44424e13 | 2.29209 | ||||||||
\(898\) | 1.14882e13 | 0.589535 | ||||||||
\(899\) | 3.00696e13 | 1.53535 | ||||||||
\(900\) | −6.14721e12 | −0.312311 | ||||||||
\(901\) | 1.65795e13 | 0.838126 | ||||||||
\(902\) | 2.57585e12 | 0.129566 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.14602e12 | 0.0570733 | ||||||||
\(905\) | 9.17546e11 | 0.0454683 | ||||||||
\(906\) | 1.27053e13 | 0.626481 | ||||||||
\(907\) | −4.19206e12 | −0.205681 | −0.102841 | − | 0.994698i | \(-0.532793\pi\) | ||||
−0.102841 | + | 0.994698i | \(0.532793\pi\) | |||||||
\(908\) | 6.50691e12 | 0.317679 | ||||||||
\(909\) | 6.55841e12 | 0.318611 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.27191e13 | −1.57387 | −0.786935 | − | 0.617036i | \(-0.788333\pi\) | ||||
−0.786935 | + | 0.617036i | \(0.788333\pi\) | |||||||
\(912\) | −5.77973e12 | −0.276650 | ||||||||
\(913\) | 7.87327e12 | 0.375005 | ||||||||
\(914\) | −2.65687e13 | −1.25925 | ||||||||
\(915\) | −4.28206e12 | −0.201957 | ||||||||
\(916\) | −1.01146e13 | −0.474700 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.21277e12 | 0.288731 | ||||||||
\(919\) | 3.99412e11 | 0.0184715 | 0.00923573 | − | 0.999957i | \(-0.497060\pi\) | ||||
0.00923573 | + | 0.999957i | \(0.497060\pi\) | |||||||
\(920\) | 1.56505e12 | 0.0720249 | ||||||||
\(921\) | −6.60141e12 | −0.302321 | ||||||||
\(922\) | 9.55800e12 | 0.435590 | ||||||||
\(923\) | 3.23120e13 | 1.46540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.72458e13 | −1.22366 | ||||||||
\(926\) | 1.04054e13 | 0.465059 | ||||||||
\(927\) | 1.85226e13 | 0.823840 | ||||||||
\(928\) | 3.98745e12 | 0.176494 | ||||||||
\(929\) | 2.25881e13 | 0.994968 | 0.497484 | − | 0.867473i | \(-0.334257\pi\) | ||||
0.497484 | + | 0.867473i | \(0.334257\pi\) | |||||||
\(930\) | −3.81815e12 | −0.167371 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.64578e11 | 0.0114863 | ||||||||
\(933\) | 1.07811e13 | 0.465795 | ||||||||
\(934\) | −1.82933e13 | −0.786557 | ||||||||
\(935\) | −7.32756e11 | −0.0313550 | ||||||||
\(936\) | −5.57762e12 | −0.237524 | ||||||||
\(937\) | 2.21481e13 | 0.938658 | 0.469329 | − | 0.883023i | \(-0.344496\pi\) | ||||
0.469329 | + | 0.883023i | \(0.344496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.70944e13 | 0.717559 | ||||||||
\(940\) | 1.88464e12 | 0.0787323 | ||||||||
\(941\) | −5.09190e12 | −0.211703 | −0.105851 | − | 0.994382i | \(-0.533757\pi\) | ||||
−0.105851 | + | 0.994382i | \(0.533757\pi\) | |||||||
\(942\) | 1.50407e13 | 0.622355 | ||||||||
\(943\) | 2.52193e13 | 1.03856 | ||||||||
\(944\) | 3.21187e12 | 0.131639 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.97287e12 | −0.0800917 | ||||||||
\(947\) | 1.20342e13 | 0.486229 | 0.243114 | − | 0.969998i | \(-0.421831\pi\) | ||||
0.243114 | + | 0.969998i | \(0.421831\pi\) | |||||||
\(948\) | 2.53673e13 | 1.02008 | ||||||||
\(949\) | −5.02534e12 | −0.201126 | ||||||||
\(950\) | 1.51456e13 | 0.603297 | ||||||||
\(951\) | 1.98380e13 | 0.786478 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.76503e13 | 1.08588 | 0.542940 | − | 0.839772i | \(-0.317311\pi\) | ||||
0.542940 | + | 0.839772i | \(0.317311\pi\) | |||||||
\(954\) | 1.10159e13 | 0.430578 | ||||||||
\(955\) | 3.94802e12 | 0.153590 | ||||||||
\(956\) | 6.50116e12 | 0.251727 | ||||||||
\(957\) | 9.88380e12 | 0.380908 | ||||||||
\(958\) | 3.10100e12 | 0.118948 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.06315e11 | −0.0192398 | ||||||||
\(961\) | 3.60869e13 | 1.36488 | ||||||||
\(962\) | −2.47213e13 | −0.930642 | ||||||||
\(963\) | 2.56904e13 | 0.962614 | ||||||||
\(964\) | 1.13883e13 | 0.424728 | ||||||||
\(965\) | 1.47490e12 | 0.0547508 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.75896e13 | 1.01467 | 0.507337 | − | 0.861748i | \(-0.330630\pi\) | ||||
0.507337 | + | 0.861748i | \(0.330630\pi\) | |||||||
\(968\) | 8.79771e12 | 0.322055 | ||||||||
\(969\) | 2.64942e13 | 0.965371 | ||||||||
\(970\) | −3.18211e12 | −0.115410 | ||||||||
\(971\) | −3.98756e13 | −1.43953 | −0.719766 | − | 0.694217i | \(-0.755751\pi\) | ||||
−0.719766 | + | 0.694217i | \(0.755751\pi\) | |||||||
\(972\) | 1.54007e13 | 0.553404 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −7.40683e12 | −0.263704 | ||||||||
\(975\) | 3.76765e13 | 1.33521 | ||||||||
\(976\) | 9.29892e12 | 0.328026 | ||||||||
\(977\) | −1.41342e13 | −0.496301 | −0.248151 | − | 0.968721i | \(-0.579823\pi\) | ||||
−0.248151 | + | 0.968721i | \(0.579823\pi\) | |||||||
\(978\) | 2.57621e13 | 0.900444 | ||||||||
\(979\) | −7.37242e12 | −0.256500 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.02394e13 | 0.697730 | ||||||||
\(982\) | −1.92503e13 | −0.660595 | ||||||||
\(983\) | 7.41532e11 | 0.0253302 | 0.0126651 | − | 0.999920i | \(-0.495968\pi\) | ||||
0.0126651 | + | 0.999920i | \(0.495968\pi\) | |||||||
\(984\) | −8.15877e12 | −0.277426 | ||||||||
\(985\) | 2.37112e12 | 0.0802585 | ||||||||
\(986\) | −1.82784e13 | −0.615875 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.37423e13 | 0.458830 | ||||||||
\(989\) | −1.93157e13 | −0.641987 | ||||||||
\(990\) | −4.86864e11 | −0.0161083 | ||||||||
\(991\) | −3.88208e13 | −1.27859 | −0.639297 | − | 0.768960i | \(-0.720775\pi\) | ||||
−0.639297 | + | 0.768960i | \(0.720775\pi\) | |||||||
\(992\) | 8.29148e12 | 0.271850 | ||||||||
\(993\) | 7.91719e12 | 0.258404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.45621e12 | 0.0794440 | ||||||||
\(996\) | −2.49379e13 | −0.802958 | ||||||||
\(997\) | 4.33172e13 | 1.38846 | 0.694229 | − | 0.719755i | \(-0.255746\pi\) | ||||
0.694229 | + | 0.719755i | \(0.255746\pi\) | |||||||
\(998\) | −5.52918e12 | −0.176430 | ||||||||
\(999\) | 1.82960e13 | 0.581180 |
(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 | 98.10.a.h.1.1 | 3 | ||
7.2 | even | 3 | 98.10.c.l.67.3 | 6 | |||
7.3 | odd | 6 | 14.10.c.b.9.1 | ✓ | 6 | ||
7.4 | even | 3 | 98.10.c.l.79.3 | 6 | |||
7.5 | odd | 6 | 14.10.c.b.11.1 | yes | 6 | ||
7.6 | odd | 2 | 98.10.a.g.1.3 | 3 | |||
21.5 | even | 6 | 126.10.g.e.109.2 | 6 | |||
21.17 | even | 6 | 126.10.g.e.37.2 | 6 | |||
28.3 | even | 6 | 112.10.i.a.65.3 | 6 | |||
28.19 | even | 6 | 112.10.i.a.81.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.c.b.9.1 | ✓ | 6 | 7.3 | odd | 6 | ||
14.10.c.b.11.1 | yes | 6 | 7.5 | odd | 6 | ||
98.10.a.g.1.3 | 3 | 7.6 | odd | 2 | |||
98.10.a.h.1.1 | 3 | 1.1 | even | 1 | trivial | ||
98.10.c.l.67.3 | 6 | 7.2 | even | 3 | |||
98.10.c.l.79.3 | 6 | 7.4 | even | 3 | |||
112.10.i.a.65.3 | 6 | 28.3 | even | 6 | |||
112.10.i.a.81.3 | 6 | 28.19 | even | 6 | |||
126.10.g.e.37.2 | 6 | 21.17 | even | 6 | |||
126.10.g.e.109.2 | 6 | 21.5 | even | 6 |