Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,10,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, 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("169.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(87.0410563117\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-24.3176\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.3176 | 0.942115 | 0.471057 | − | 0.882103i | \(-0.343872\pi\) | ||||
0.471057 | + | 0.882103i | \(0.343872\pi\) | |||||||
\(3\) | −195.094 | −1.39058 | −0.695292 | − | 0.718727i | \(-0.744725\pi\) | ||||
−0.695292 | + | 0.718727i | \(0.744725\pi\) | |||||||
\(4\) | −57.5590 | −0.112420 | ||||||||
\(5\) | 1277.14 | 0.913846 | 0.456923 | − | 0.889506i | \(-0.348951\pi\) | ||||
0.456923 | + | 0.889506i | \(0.348951\pi\) | |||||||
\(6\) | −4158.93 | −1.31009 | ||||||||
\(7\) | 2277.98 | 0.358599 | 0.179299 | − | 0.983795i | \(-0.442617\pi\) | ||||
0.179299 | + | 0.983795i | \(0.442617\pi\) | |||||||
\(8\) | −12141.6 | −1.04803 | ||||||||
\(9\) | 18378.5 | 0.933725 | ||||||||
\(10\) | 27225.6 | 0.860948 | ||||||||
\(11\) | 7177.94 | 0.147820 | 0.0739099 | − | 0.997265i | \(-0.476452\pi\) | ||||
0.0739099 | + | 0.997265i | \(0.476452\pi\) | |||||||
\(12\) | 11229.4 | 0.156329 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 48561.1 | 0.337841 | ||||||||
\(15\) | −249162. | −1.27078 | ||||||||
\(16\) | −229361. | −0.874942 | ||||||||
\(17\) | −447890. | −1.30062 | −0.650311 | − | 0.759668i | \(-0.725361\pi\) | ||||
−0.650311 | + | 0.759668i | \(0.725361\pi\) | |||||||
\(18\) | 391786. | 0.879677 | ||||||||
\(19\) | 528333. | 0.930071 | 0.465036 | − | 0.885292i | \(-0.346041\pi\) | ||||
0.465036 | + | 0.885292i | \(0.346041\pi\) | |||||||
\(20\) | −73510.8 | −0.102734 | ||||||||
\(21\) | −444419. | −0.498662 | ||||||||
\(22\) | 153017. | 0.139263 | ||||||||
\(23\) | 2.24354e6 | 1.67170 | 0.835851 | − | 0.548957i | \(-0.184975\pi\) | ||||
0.835851 | + | 0.548957i | \(0.184975\pi\) | |||||||
\(24\) | 2.36876e6 | 1.45737 | ||||||||
\(25\) | −322041. | −0.164885 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 254496. | 0.0921603 | ||||||||
\(28\) | −131118. | −0.0403136 | ||||||||
\(29\) | 5.98542e6 | 1.57146 | 0.785730 | − | 0.618569i | \(-0.212287\pi\) | ||||
0.785730 | + | 0.618569i | \(0.212287\pi\) | |||||||
\(30\) | −5.31153e6 | −1.19722 | ||||||||
\(31\) | −169630. | −0.0329894 | −0.0164947 | − | 0.999864i | \(-0.505251\pi\) | ||||
−0.0164947 | + | 0.999864i | \(0.505251\pi\) | |||||||
\(32\) | 1.32709e6 | 0.223731 | ||||||||
\(33\) | −1.40037e6 | −0.205556 | ||||||||
\(34\) | −9.54795e6 | −1.22534 | ||||||||
\(35\) | 2.90930e6 | 0.327704 | ||||||||
\(36\) | −1.05785e6 | −0.104969 | ||||||||
\(37\) | −1.26336e7 | −1.10820 | −0.554100 | − | 0.832450i | \(-0.686938\pi\) | ||||
−0.554100 | + | 0.832450i | \(0.686938\pi\) | |||||||
\(38\) | 1.12628e7 | 0.876234 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.55066e7 | −0.957736 | ||||||||
\(41\) | 2.76549e7 | 1.52843 | 0.764213 | − | 0.644964i | \(-0.223128\pi\) | ||||
0.764213 | + | 0.644964i | \(0.223128\pi\) | |||||||
\(42\) | −9.47396e6 | −0.469796 | ||||||||
\(43\) | −2.27606e7 | −1.01526 | −0.507628 | − | 0.861576i | \(-0.669478\pi\) | ||||
−0.507628 | + | 0.861576i | \(0.669478\pi\) | |||||||
\(44\) | −413155. | −0.0166179 | ||||||||
\(45\) | 2.34719e7 | 0.853281 | ||||||||
\(46\) | 4.78270e7 | 1.57493 | ||||||||
\(47\) | −5.32103e7 | −1.59058 | −0.795289 | − | 0.606230i | \(-0.792681\pi\) | ||||
−0.795289 | + | 0.606230i | \(0.792681\pi\) | |||||||
\(48\) | 4.47468e7 | 1.21668 | ||||||||
\(49\) | −3.51644e7 | −0.871407 | ||||||||
\(50\) | −6.86516e6 | −0.155341 | ||||||||
\(51\) | 8.73804e7 | 1.80862 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.18756e7 | 0.554904 | 0.277452 | − | 0.960740i | \(-0.410510\pi\) | ||||
0.277452 | + | 0.960740i | \(0.410510\pi\) | |||||||
\(54\) | 5.42525e6 | 0.0868256 | ||||||||
\(55\) | 9.16722e6 | 0.135085 | ||||||||
\(56\) | −2.76584e7 | −0.375821 | ||||||||
\(57\) | −1.03074e8 | −1.29334 | ||||||||
\(58\) | 1.27595e8 | 1.48050 | ||||||||
\(59\) | −1.14800e8 | −1.23341 | −0.616705 | − | 0.787194i | \(-0.711533\pi\) | ||||
−0.616705 | + | 0.787194i | \(0.711533\pi\) | |||||||
\(60\) | 1.43415e7 | 0.142861 | ||||||||
\(61\) | −7.80352e7 | −0.721616 | −0.360808 | − | 0.932640i | \(-0.617499\pi\) | ||||
−0.360808 | + | 0.932640i | \(0.617499\pi\) | |||||||
\(62\) | −3.61610e6 | −0.0310798 | ||||||||
\(63\) | 4.18659e7 | 0.334833 | ||||||||
\(64\) | 1.45723e8 | 1.08572 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.98526e7 | −0.193657 | ||||||||
\(67\) | −8.40538e7 | −0.509590 | −0.254795 | − | 0.966995i | \(-0.582008\pi\) | ||||
−0.254795 | + | 0.966995i | \(0.582008\pi\) | |||||||
\(68\) | 2.57801e7 | 0.146216 | ||||||||
\(69\) | −4.37700e8 | −2.32464 | ||||||||
\(70\) | 6.20193e7 | 0.308735 | ||||||||
\(71\) | −1.25752e8 | −0.587288 | −0.293644 | − | 0.955915i | \(-0.594868\pi\) | ||||
−0.293644 | + | 0.955915i | \(0.594868\pi\) | |||||||
\(72\) | −2.23145e8 | −0.978570 | ||||||||
\(73\) | 1.88250e8 | 0.775859 | 0.387929 | − | 0.921689i | \(-0.373190\pi\) | ||||
0.387929 | + | 0.921689i | \(0.373190\pi\) | |||||||
\(74\) | −2.69318e8 | −1.04405 | ||||||||
\(75\) | 6.28282e7 | 0.229287 | ||||||||
\(76\) | −3.04103e7 | −0.104558 | ||||||||
\(77\) | 1.63512e7 | 0.0530080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.28673e8 | −1.23824 | −0.619120 | − | 0.785297i | \(-0.712510\pi\) | ||||
−0.619120 | + | 0.785297i | \(0.712510\pi\) | |||||||
\(80\) | −2.92926e8 | −0.799562 | ||||||||
\(81\) | −4.11395e8 | −1.06188 | ||||||||
\(82\) | 5.89536e8 | 1.43995 | ||||||||
\(83\) | −2.43067e8 | −0.562180 | −0.281090 | − | 0.959681i | \(-0.590696\pi\) | ||||
−0.281090 | + | 0.959681i | \(0.590696\pi\) | |||||||
\(84\) | 2.55803e7 | 0.0560594 | ||||||||
\(85\) | −5.72018e8 | −1.18857 | ||||||||
\(86\) | −4.85202e8 | −0.956488 | ||||||||
\(87\) | −1.16772e9 | −2.18525 | ||||||||
\(88\) | −8.71520e7 | −0.154919 | ||||||||
\(89\) | −2.92716e8 | −0.494529 | −0.247265 | − | 0.968948i | \(-0.579532\pi\) | ||||
−0.247265 | + | 0.968948i | \(0.579532\pi\) | |||||||
\(90\) | 5.00366e8 | 0.803889 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.29136e8 | −0.187932 | ||||||||
\(93\) | 3.30937e7 | 0.0458746 | ||||||||
\(94\) | −1.13432e9 | −1.49851 | ||||||||
\(95\) | 6.74754e8 | 0.849942 | ||||||||
\(96\) | −2.58908e8 | −0.311117 | ||||||||
\(97\) | −1.14275e9 | −1.31063 | −0.655313 | − | 0.755358i | \(-0.727463\pi\) | ||||
−0.655313 | + | 0.755358i | \(0.727463\pi\) | |||||||
\(98\) | −7.49622e8 | −0.820965 | ||||||||
\(99\) | 1.31920e8 | 0.138023 | ||||||||
\(100\) | 1.85364e7 | 0.0185364 | ||||||||
\(101\) | −8.98629e8 | −0.859279 | −0.429640 | − | 0.903000i | \(-0.641359\pi\) | ||||
−0.429640 | + | 0.903000i | \(0.641359\pi\) | |||||||
\(102\) | 1.86274e9 | 1.70393 | ||||||||
\(103\) | 6.13518e8 | 0.537106 | 0.268553 | − | 0.963265i | \(-0.413455\pi\) | ||||
0.268553 | + | 0.963265i | \(0.413455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.67585e8 | −0.455700 | ||||||||
\(106\) | 6.79513e8 | 0.522783 | ||||||||
\(107\) | 1.46257e9 | 1.07868 | 0.539338 | − | 0.842090i | \(-0.318675\pi\) | ||||
0.539338 | + | 0.842090i | \(0.318675\pi\) | |||||||
\(108\) | −1.46485e7 | −0.0103607 | ||||||||
\(109\) | −7.17715e8 | −0.487005 | −0.243502 | − | 0.969900i | \(-0.578296\pi\) | ||||
−0.243502 | + | 0.969900i | \(0.578296\pi\) | |||||||
\(110\) | 1.95423e8 | 0.127265 | ||||||||
\(111\) | 2.46473e9 | 1.54105 | ||||||||
\(112\) | −5.22479e8 | −0.313753 | ||||||||
\(113\) | 9.27444e7 | 0.0535099 | 0.0267550 | − | 0.999642i | \(-0.491483\pi\) | ||||
0.0267550 | + | 0.999642i | \(0.491483\pi\) | |||||||
\(114\) | −2.19730e9 | −1.21848 | ||||||||
\(115\) | 2.86531e9 | 1.52768 | ||||||||
\(116\) | −3.44514e8 | −0.176663 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.44726e9 | −1.16201 | ||||||||
\(119\) | −1.02028e9 | −0.466401 | ||||||||
\(120\) | 3.02523e9 | 1.33181 | ||||||||
\(121\) | −2.30642e9 | −0.978149 | ||||||||
\(122\) | −1.66352e9 | −0.679845 | ||||||||
\(123\) | −5.39529e9 | −2.12540 | ||||||||
\(124\) | 9.76371e6 | 0.00370866 | ||||||||
\(125\) | −2.90570e9 | −1.06453 | ||||||||
\(126\) | 8.92481e8 | 0.315451 | ||||||||
\(127\) | 4.40060e9 | 1.50105 | 0.750524 | − | 0.660843i | \(-0.229801\pi\) | ||||
0.750524 | + | 0.660843i | \(0.229801\pi\) | |||||||
\(128\) | 2.42700e9 | 0.799144 | ||||||||
\(129\) | 4.44045e9 | 1.41180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.21951e9 | −0.361798 | −0.180899 | − | 0.983502i | \(-0.557901\pi\) | ||||
−0.180899 | + | 0.983502i | \(0.557901\pi\) | |||||||
\(132\) | 8.06038e7 | 0.0231086 | ||||||||
\(133\) | 1.20353e9 | 0.333522 | ||||||||
\(134\) | −1.79183e9 | −0.480092 | ||||||||
\(135\) | 3.25027e8 | 0.0842204 | ||||||||
\(136\) | 5.43812e9 | 1.36309 | ||||||||
\(137\) | 6.73258e9 | 1.63282 | 0.816411 | − | 0.577472i | \(-0.195961\pi\) | ||||
0.816411 | + | 0.577472i | \(0.195961\pi\) | |||||||
\(138\) | −9.33073e9 | −2.19008 | ||||||||
\(139\) | 4.12694e8 | 0.0937695 | 0.0468847 | − | 0.998900i | \(-0.485071\pi\) | ||||
0.0468847 | + | 0.998900i | \(0.485071\pi\) | |||||||
\(140\) | −1.67456e8 | −0.0368404 | ||||||||
\(141\) | 1.03810e10 | 2.21183 | ||||||||
\(142\) | −2.68073e9 | −0.553293 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.21531e9 | −0.816956 | ||||||||
\(145\) | 7.64421e9 | 1.43607 | ||||||||
\(146\) | 4.01305e9 | 0.730948 | ||||||||
\(147\) | 6.86035e9 | 1.21177 | ||||||||
\(148\) | 7.27175e8 | 0.124584 | ||||||||
\(149\) | −7.17339e9 | −1.19230 | −0.596151 | − | 0.802872i | \(-0.703304\pi\) | ||||
−0.596151 | + | 0.802872i | \(0.703304\pi\) | |||||||
\(150\) | 1.33935e9 | 0.216015 | ||||||||
\(151\) | −9.30445e9 | −1.45645 | −0.728223 | − | 0.685340i | \(-0.759654\pi\) | ||||
−0.728223 | + | 0.685340i | \(0.759654\pi\) | |||||||
\(152\) | −6.41483e9 | −0.974740 | ||||||||
\(153\) | −8.23155e9 | −1.21442 | ||||||||
\(154\) | 3.48569e8 | 0.0499396 | ||||||||
\(155\) | −2.16641e8 | −0.0301472 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.86131e9 | −0.769921 | −0.384961 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384961 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(158\) | −9.13830e9 | −1.16656 | ||||||||
\(159\) | −6.21873e9 | −0.771640 | ||||||||
\(160\) | 1.69488e9 | 0.204456 | ||||||||
\(161\) | 5.11074e9 | 0.599470 | ||||||||
\(162\) | −8.76996e9 | −1.00041 | ||||||||
\(163\) | −1.60676e10 | −1.78282 | −0.891409 | − | 0.453199i | \(-0.850283\pi\) | ||||
−0.891409 | + | 0.453199i | \(0.850283\pi\) | |||||||
\(164\) | −1.59179e9 | −0.171825 | ||||||||
\(165\) | −1.78847e9 | −0.187847 | ||||||||
\(166\) | −5.18162e9 | −0.529638 | ||||||||
\(167\) | 1.49042e9 | 0.148281 | 0.0741404 | − | 0.997248i | \(-0.476379\pi\) | ||||
0.0741404 | + | 0.997248i | \(0.476379\pi\) | |||||||
\(168\) | 5.39598e9 | 0.522611 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.21941e10 | −1.11977 | ||||||||
\(171\) | 9.70997e9 | 0.868431 | ||||||||
\(172\) | 1.31008e9 | 0.114135 | ||||||||
\(173\) | −6.62250e9 | −0.562101 | −0.281050 | − | 0.959693i | \(-0.590683\pi\) | ||||
−0.281050 | + | 0.959693i | \(0.590683\pi\) | |||||||
\(174\) | −2.48930e10 | −2.05876 | ||||||||
\(175\) | −7.33604e8 | −0.0591276 | ||||||||
\(176\) | −1.64634e9 | −0.129334 | ||||||||
\(177\) | 2.23967e10 | 1.71516 | ||||||||
\(178\) | −6.24002e9 | −0.465903 | ||||||||
\(179\) | 1.41019e10 | 1.02669 | 0.513344 | − | 0.858183i | \(-0.328406\pi\) | ||||
0.513344 | + | 0.858183i | \(0.328406\pi\) | |||||||
\(180\) | −1.35102e9 | −0.0959257 | ||||||||
\(181\) | 2.38898e10 | 1.65447 | 0.827234 | − | 0.561857i | \(-0.189913\pi\) | ||||
0.827234 | + | 0.561857i | \(0.189913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.52242e10 | 1.00347 | ||||||||
\(184\) | −2.72403e10 | −1.75199 | ||||||||
\(185\) | −1.61348e10 | −1.01272 | ||||||||
\(186\) | 7.05479e8 | 0.0432191 | ||||||||
\(187\) | −3.21493e9 | −0.192258 | ||||||||
\(188\) | 3.06273e9 | 0.178813 | ||||||||
\(189\) | 5.79737e8 | 0.0330486 | ||||||||
\(190\) | 1.43842e10 | 0.800743 | ||||||||
\(191\) | −2.32674e10 | −1.26502 | −0.632509 | − | 0.774553i | \(-0.717975\pi\) | ||||
−0.632509 | + | 0.774553i | \(0.717975\pi\) | |||||||
\(192\) | −2.84297e10 | −1.50979 | ||||||||
\(193\) | −8.87539e9 | −0.460447 | −0.230224 | − | 0.973138i | \(-0.573946\pi\) | ||||
−0.230224 | + | 0.973138i | \(0.573946\pi\) | |||||||
\(194\) | −2.43607e10 | −1.23476 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.02403e9 | 0.0979634 | ||||||||
\(197\) | 9.96936e9 | 0.471595 | 0.235798 | − | 0.971802i | \(-0.424230\pi\) | ||||
0.235798 | + | 0.971802i | \(0.424230\pi\) | |||||||
\(198\) | 2.81222e9 | 0.130034 | ||||||||
\(199\) | −5.92044e9 | −0.267618 | −0.133809 | − | 0.991007i | \(-0.542721\pi\) | ||||
−0.133809 | + | 0.991007i | \(0.542721\pi\) | |||||||
\(200\) | 3.91011e9 | 0.172804 | ||||||||
\(201\) | 1.63984e10 | 0.708628 | ||||||||
\(202\) | −1.91566e10 | −0.809540 | ||||||||
\(203\) | 1.36347e10 | 0.563524 | ||||||||
\(204\) | −5.02953e9 | −0.203325 | ||||||||
\(205\) | 3.53191e10 | 1.39675 | ||||||||
\(206\) | 1.30787e10 | 0.506015 | ||||||||
\(207\) | 4.12330e10 | 1.56091 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.79234e9 | 0.137483 | ||||||||
\(210\) | −1.20996e10 | −0.429322 | ||||||||
\(211\) | −3.18290e10 | −1.10548 | −0.552741 | − | 0.833353i | \(-0.686418\pi\) | ||||
−0.552741 | + | 0.833353i | \(0.686418\pi\) | |||||||
\(212\) | −1.83473e9 | −0.0623822 | ||||||||
\(213\) | 2.45334e10 | 0.816674 | ||||||||
\(214\) | 3.11786e10 | 1.01624 | ||||||||
\(215\) | −2.90685e10 | −0.927788 | ||||||||
\(216\) | −3.09000e9 | −0.0965865 | ||||||||
\(217\) | −3.86413e8 | −0.0118300 | ||||||||
\(218\) | −1.53000e10 | −0.458814 | ||||||||
\(219\) | −3.67264e10 | −1.07890 | ||||||||
\(220\) | −5.27656e8 | −0.0151862 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.25422e10 | 1.45184 | ||||||||
\(223\) | 2.33567e10 | 0.632470 | 0.316235 | − | 0.948681i | \(-0.397581\pi\) | ||||
0.316235 | + | 0.948681i | \(0.397581\pi\) | |||||||
\(224\) | 3.02309e9 | 0.0802298 | ||||||||
\(225\) | −5.91865e9 | −0.153958 | ||||||||
\(226\) | 1.97709e9 | 0.0504125 | ||||||||
\(227\) | −2.96928e10 | −0.742223 | −0.371112 | − | 0.928588i | \(-0.621023\pi\) | ||||
−0.371112 | + | 0.928588i | \(0.621023\pi\) | |||||||
\(228\) | 5.93285e9 | 0.145397 | ||||||||
\(229\) | −4.24937e10 | −1.02109 | −0.510546 | − | 0.859850i | \(-0.670557\pi\) | ||||
−0.510546 | + | 0.859850i | \(0.670557\pi\) | |||||||
\(230\) | 6.10817e10 | 1.43925 | ||||||||
\(231\) | −3.19001e9 | −0.0737121 | ||||||||
\(232\) | −7.26728e10 | −1.64693 | ||||||||
\(233\) | −3.84693e10 | −0.855092 | −0.427546 | − | 0.903994i | \(-0.640622\pi\) | ||||
−0.427546 | + | 0.903994i | \(0.640622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.79569e10 | −1.45354 | ||||||||
\(236\) | 6.60776e9 | 0.138660 | ||||||||
\(237\) | 8.36314e10 | 1.72188 | ||||||||
\(238\) | −2.17500e10 | −0.439403 | ||||||||
\(239\) | 1.98946e10 | 0.394407 | 0.197203 | − | 0.980363i | \(-0.436814\pi\) | ||||
0.197203 | + | 0.980363i | \(0.436814\pi\) | |||||||
\(240\) | 5.71479e10 | 1.11186 | ||||||||
\(241\) | 5.31240e10 | 1.01441 | 0.507206 | − | 0.861825i | \(-0.330678\pi\) | ||||
0.507206 | + | 0.861825i | \(0.330678\pi\) | |||||||
\(242\) | −4.91675e10 | −0.921529 | ||||||||
\(243\) | 7.52513e10 | 1.38448 | ||||||||
\(244\) | 4.49162e9 | 0.0811240 | ||||||||
\(245\) | −4.49098e10 | −0.796332 | ||||||||
\(246\) | −1.15015e11 | −2.00238 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.05958e9 | 0.0345738 | ||||||||
\(249\) | 4.74209e10 | 0.781758 | ||||||||
\(250\) | −6.19427e10 | −1.00291 | ||||||||
\(251\) | 1.26269e10 | 0.200801 | 0.100400 | − | 0.994947i | \(-0.467988\pi\) | ||||
0.100400 | + | 0.994947i | \(0.467988\pi\) | |||||||
\(252\) | −2.40976e9 | −0.0376418 | ||||||||
\(253\) | 1.61040e10 | 0.247111 | ||||||||
\(254\) | 9.38102e10 | 1.41416 | ||||||||
\(255\) | 1.11597e11 | 1.65280 | ||||||||
\(256\) | −2.28724e10 | −0.332837 | ||||||||
\(257\) | 1.11000e11 | 1.58717 | 0.793583 | − | 0.608461i | \(-0.208213\pi\) | ||||
0.793583 | + | 0.608461i | \(0.208213\pi\) | |||||||
\(258\) | 9.46598e10 | 1.33008 | ||||||||
\(259\) | −2.87790e10 | −0.397399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.10003e11 | 1.46731 | ||||||||
\(262\) | −2.59971e10 | −0.340855 | ||||||||
\(263\) | 7.01020e10 | 0.903503 | 0.451752 | − | 0.892144i | \(-0.350799\pi\) | ||||
0.451752 | + | 0.892144i | \(0.350799\pi\) | |||||||
\(264\) | 1.70028e10 | 0.215428 | ||||||||
\(265\) | 4.07096e10 | 0.507097 | ||||||||
\(266\) | 2.56564e10 | 0.314216 | ||||||||
\(267\) | 5.71071e10 | 0.687685 | ||||||||
\(268\) | 4.83805e9 | 0.0572880 | ||||||||
\(269\) | 7.41364e10 | 0.863269 | 0.431635 | − | 0.902049i | \(-0.357937\pi\) | ||||
0.431635 | + | 0.902049i | \(0.357937\pi\) | |||||||
\(270\) | 6.92880e9 | 0.0793453 | ||||||||
\(271\) | −8.92477e10 | −1.00516 | −0.502580 | − | 0.864531i | \(-0.667616\pi\) | ||||
−0.502580 | + | 0.864531i | \(0.667616\pi\) | |||||||
\(272\) | 1.02728e11 | 1.13797 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.43523e11 | 1.53831 | ||||||||
\(275\) | −2.31159e9 | −0.0243733 | ||||||||
\(276\) | 2.51936e10 | 0.261336 | ||||||||
\(277\) | −6.68313e10 | −0.682057 | −0.341028 | − | 0.940053i | \(-0.610775\pi\) | ||||
−0.341028 | + | 0.940053i | \(0.610775\pi\) | |||||||
\(278\) | 8.79765e9 | 0.0883416 | ||||||||
\(279\) | −3.11754e9 | −0.0308031 | ||||||||
\(280\) | −3.53236e10 | −0.343443 | ||||||||
\(281\) | 8.13670e10 | 0.778520 | 0.389260 | − | 0.921128i | \(-0.372731\pi\) | ||||
0.389260 | + | 0.921128i | \(0.372731\pi\) | |||||||
\(282\) | 2.21298e11 | 2.08380 | ||||||||
\(283\) | −1.19236e11 | −1.10502 | −0.552508 | − | 0.833507i | \(-0.686329\pi\) | ||||
−0.552508 | + | 0.833507i | \(0.686329\pi\) | |||||||
\(284\) | 7.23814e9 | 0.0660229 | ||||||||
\(285\) | −1.31640e11 | −1.18192 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.29972e10 | 0.548091 | ||||||||
\(288\) | 2.43900e10 | 0.208904 | ||||||||
\(289\) | 8.20174e10 | 0.691617 | ||||||||
\(290\) | 1.62956e11 | 1.35295 | ||||||||
\(291\) | 2.22943e11 | 1.82254 | ||||||||
\(292\) | −1.08355e10 | −0.0872219 | ||||||||
\(293\) | 6.95594e10 | 0.551381 | 0.275690 | − | 0.961246i | \(-0.411094\pi\) | ||||
0.275690 | + | 0.961246i | \(0.411094\pi\) | |||||||
\(294\) | 1.46246e11 | 1.14162 | ||||||||
\(295\) | −1.46615e11 | −1.12715 | ||||||||
\(296\) | 1.53392e11 | 1.16142 | ||||||||
\(297\) | 1.82676e9 | 0.0136231 | ||||||||
\(298\) | −1.52920e11 | −1.12328 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.61633e9 | −0.0257764 | ||||||||
\(301\) | −5.18482e10 | −0.364069 | ||||||||
\(302\) | −1.98349e11 | −1.37214 | ||||||||
\(303\) | 1.75317e11 | 1.19490 | ||||||||
\(304\) | −1.21179e11 | −0.813759 | ||||||||
\(305\) | −9.96618e10 | −0.659446 | ||||||||
\(306\) | −1.75477e11 | −1.14413 | ||||||||
\(307\) | 4.02660e10 | 0.258711 | 0.129356 | − | 0.991598i | \(-0.458709\pi\) | ||||
0.129356 | + | 0.991598i | \(0.458709\pi\) | |||||||
\(308\) | −9.41157e8 | −0.00595915 | ||||||||
\(309\) | −1.19693e11 | −0.746891 | ||||||||
\(310\) | −4.61827e9 | −0.0284022 | ||||||||
\(311\) | −1.78556e11 | −1.08231 | −0.541157 | − | 0.840921i | \(-0.682014\pi\) | ||||
−0.541157 | + | 0.840921i | \(0.682014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.44550e9 | 0.0556257 | 0.0278128 | − | 0.999613i | \(-0.491146\pi\) | ||||
0.0278128 | + | 0.999613i | \(0.491146\pi\) | |||||||
\(314\) | −1.24949e11 | −0.725354 | ||||||||
\(315\) | 5.34685e10 | 0.305985 | ||||||||
\(316\) | 2.46740e10 | 0.139203 | ||||||||
\(317\) | −5.42593e10 | −0.301792 | −0.150896 | − | 0.988550i | \(-0.548216\pi\) | ||||
−0.150896 | + | 0.988550i | \(0.548216\pi\) | |||||||
\(318\) | −1.32569e11 | −0.726974 | ||||||||
\(319\) | 4.29630e10 | 0.232293 | ||||||||
\(320\) | 1.86109e11 | 0.992183 | ||||||||
\(321\) | −2.85339e11 | −1.49999 | ||||||||
\(322\) | 1.08949e11 | 0.564769 | ||||||||
\(323\) | −2.36635e11 | −1.20967 | ||||||||
\(324\) | 2.36795e10 | 0.119377 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.42523e11 | −1.67962 | ||||||||
\(327\) | 1.40022e11 | 0.677221 | ||||||||
\(328\) | −3.35776e11 | −1.60183 | ||||||||
\(329\) | −1.21212e11 | −0.570379 | ||||||||
\(330\) | −3.81259e10 | −0.176973 | ||||||||
\(331\) | −6.66790e10 | −0.305325 | −0.152663 | − | 0.988278i | \(-0.548785\pi\) | ||||
−0.152663 | + | 0.988278i | \(0.548785\pi\) | |||||||
\(332\) | 1.39907e10 | 0.0632001 | ||||||||
\(333\) | −2.32186e11 | −1.03476 | ||||||||
\(334\) | 3.17722e10 | 0.139697 | ||||||||
\(335\) | −1.07348e11 | −0.465687 | ||||||||
\(336\) | 1.01932e11 | 0.436300 | ||||||||
\(337\) | 2.13457e11 | 0.901522 | 0.450761 | − | 0.892645i | \(-0.351153\pi\) | ||||
0.450761 | + | 0.892645i | \(0.351153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.80938e10 | −0.0744101 | ||||||||
\(340\) | 3.29247e10 | 0.133619 | ||||||||
\(341\) | −1.21759e9 | −0.00487649 | ||||||||
\(342\) | 2.06994e11 | 0.818162 | ||||||||
\(343\) | −1.72028e11 | −0.671084 | ||||||||
\(344\) | 2.76351e11 | 1.06402 | ||||||||
\(345\) | −5.59004e11 | −2.12437 | ||||||||
\(346\) | −1.41176e11 | −0.529564 | ||||||||
\(347\) | −9.49978e10 | −0.351748 | −0.175874 | − | 0.984413i | \(-0.556275\pi\) | ||||
−0.175874 | + | 0.984413i | \(0.556275\pi\) | |||||||
\(348\) | 6.72126e10 | 0.245665 | ||||||||
\(349\) | −2.52647e11 | −0.911590 | −0.455795 | − | 0.890085i | \(-0.650645\pi\) | ||||
−0.455795 | + | 0.890085i | \(0.650645\pi\) | |||||||
\(350\) | −1.56387e10 | −0.0557050 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.52580e9 | 0.0330719 | ||||||||
\(353\) | −4.50376e11 | −1.54379 | −0.771896 | − | 0.635749i | \(-0.780691\pi\) | ||||
−0.771896 | + | 0.635749i | \(0.780691\pi\) | |||||||
\(354\) | 4.77445e11 | 1.61588 | ||||||||
\(355\) | −1.60602e11 | −0.536691 | ||||||||
\(356\) | 1.68485e10 | 0.0555949 | ||||||||
\(357\) | 1.99051e11 | 0.648570 | ||||||||
\(358\) | 3.00619e11 | 0.967258 | ||||||||
\(359\) | −3.93740e11 | −1.25108 | −0.625539 | − | 0.780193i | \(-0.715121\pi\) | ||||
−0.625539 | + | 0.780193i | \(0.715121\pi\) | |||||||
\(360\) | −2.84988e11 | −0.894262 | ||||||||
\(361\) | −4.35522e10 | −0.134967 | ||||||||
\(362\) | 5.09273e11 | 1.55870 | ||||||||
\(363\) | 4.49969e11 | 1.36020 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.40422e11 | 0.709015 | ||||||||
\(366\) | 3.24543e11 | 0.945382 | ||||||||
\(367\) | −2.26305e11 | −0.651173 | −0.325586 | − | 0.945512i | \(-0.605562\pi\) | ||||
−0.325586 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(368\) | −5.14580e11 | −1.46264 | ||||||||
\(369\) | 5.08255e11 | 1.42713 | ||||||||
\(370\) | −3.43956e11 | −0.954103 | ||||||||
\(371\) | 7.26120e10 | 0.198988 | ||||||||
\(372\) | −1.90484e9 | −0.00515721 | ||||||||
\(373\) | 4.75023e11 | 1.27065 | 0.635323 | − | 0.772246i | \(-0.280867\pi\) | ||||
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(374\) | −6.85346e10 | −0.181129 | ||||||||
\(375\) | 5.66884e11 | 1.48031 | ||||||||
\(376\) | 6.46060e11 | 1.66697 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.23586e10 | 0.0311355 | ||||||||
\(379\) | 1.67293e11 | 0.416486 | 0.208243 | − | 0.978077i | \(-0.433225\pi\) | ||||
0.208243 | + | 0.978077i | \(0.433225\pi\) | |||||||
\(380\) | −3.88381e10 | −0.0955504 | ||||||||
\(381\) | −8.58528e11 | −2.08733 | ||||||||
\(382\) | −4.96005e11 | −1.19179 | ||||||||
\(383\) | 5.36589e11 | 1.27423 | 0.637114 | − | 0.770769i | \(-0.280128\pi\) | ||||
0.637114 | + | 0.770769i | \(0.280128\pi\) | |||||||
\(384\) | −4.73492e11 | −1.11128 | ||||||||
\(385\) | 2.08827e10 | 0.0484411 | ||||||||
\(386\) | −1.89202e11 | −0.433794 | ||||||||
\(387\) | −4.18306e11 | −0.947971 | ||||||||
\(388\) | 6.57755e10 | 0.147340 | ||||||||
\(389\) | 5.95613e11 | 1.31884 | 0.659418 | − | 0.751776i | \(-0.270803\pi\) | ||||
0.659418 | + | 0.751776i | \(0.270803\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00486e12 | −2.17425 | ||||||||
\(392\) | 4.26954e11 | 0.913258 | ||||||||
\(393\) | 2.37919e11 | 0.503110 | ||||||||
\(394\) | 2.12523e11 | 0.444297 | ||||||||
\(395\) | −5.47475e11 | −1.13156 | ||||||||
\(396\) | −7.59317e9 | −0.0155165 | ||||||||
\(397\) | 6.68797e11 | 1.35125 | 0.675627 | − | 0.737243i | \(-0.263873\pi\) | ||||
0.675627 | + | 0.737243i | \(0.263873\pi\) | |||||||
\(398\) | −1.26210e11 | −0.252127 | ||||||||
\(399\) | −2.34801e11 | −0.463791 | ||||||||
\(400\) | 7.38637e10 | 0.144265 | ||||||||
\(401\) | −4.27579e11 | −0.825785 | −0.412892 | − | 0.910780i | \(-0.635481\pi\) | ||||
−0.412892 | + | 0.910780i | \(0.635481\pi\) | |||||||
\(402\) | 3.49574e11 | 0.667609 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.17241e10 | 0.0966000 | ||||||||
\(405\) | −5.25408e11 | −0.970397 | ||||||||
\(406\) | 2.90658e11 | 0.530904 | ||||||||
\(407\) | −9.06830e10 | −0.163814 | ||||||||
\(408\) | −1.06094e12 | −1.89549 | ||||||||
\(409\) | 4.37893e10 | 0.0773772 | 0.0386886 | − | 0.999251i | \(-0.487682\pi\) | ||||
0.0386886 | + | 0.999251i | \(0.487682\pi\) | |||||||
\(410\) | 7.52919e11 | 1.31589 | ||||||||
\(411\) | −1.31348e12 | −2.27058 | ||||||||
\(412\) | −3.53135e10 | −0.0603813 | ||||||||
\(413\) | −2.61512e11 | −0.442299 | ||||||||
\(414\) | 8.78989e11 | 1.47056 | ||||||||
\(415\) | −3.10431e11 | −0.513746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.05139e10 | −0.130394 | ||||||||
\(418\) | 8.08437e10 | 0.129525 | ||||||||
\(419\) | −1.14243e11 | −0.181079 | −0.0905395 | − | 0.995893i | \(-0.528859\pi\) | ||||
−0.0905395 | + | 0.995893i | \(0.528859\pi\) | |||||||
\(420\) | 3.26696e10 | 0.0512297 | ||||||||
\(421\) | 5.06520e11 | 0.785828 | 0.392914 | − | 0.919575i | \(-0.371467\pi\) | ||||
0.392914 | + | 0.919575i | \(0.371467\pi\) | |||||||
\(422\) | −6.78518e11 | −1.04149 | ||||||||
\(423\) | −9.77926e11 | −1.48516 | ||||||||
\(424\) | −3.87023e11 | −0.581554 | ||||||||
\(425\) | 1.44239e11 | 0.214453 | ||||||||
\(426\) | 5.22993e11 | 0.769401 | ||||||||
\(427\) | −1.77763e11 | −0.258770 | ||||||||
\(428\) | −8.41842e10 | −0.121264 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.19670e11 | −0.874083 | ||||||||
\(431\) | 1.32605e11 | 0.185103 | 0.0925513 | − | 0.995708i | \(-0.470498\pi\) | ||||
0.0925513 | + | 0.995708i | \(0.470498\pi\) | |||||||
\(432\) | −5.83714e10 | −0.0806350 | ||||||||
\(433\) | 1.21346e12 | 1.65894 | 0.829469 | − | 0.558553i | \(-0.188643\pi\) | ||||
0.829469 | + | 0.558553i | \(0.188643\pi\) | |||||||
\(434\) | −8.23741e9 | −0.0111452 | ||||||||
\(435\) | −1.49134e12 | −1.99698 | ||||||||
\(436\) | 4.13110e10 | 0.0547490 | ||||||||
\(437\) | 1.18534e12 | 1.55480 | ||||||||
\(438\) | −7.82920e11 | −1.01644 | ||||||||
\(439\) | −7.26961e11 | −0.934159 | −0.467079 | − | 0.884215i | \(-0.654694\pi\) | ||||
−0.467079 | + | 0.884215i | \(0.654694\pi\) | |||||||
\(440\) | −1.11305e11 | −0.141572 | ||||||||
\(441\) | −6.46270e11 | −0.813655 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.02161e12 | −1.26028 | −0.630142 | − | 0.776480i | \(-0.717003\pi\) | ||||
−0.630142 | + | 0.776480i | \(0.717003\pi\) | |||||||
\(444\) | −1.41867e11 | −0.173244 | ||||||||
\(445\) | −3.73840e11 | −0.451924 | ||||||||
\(446\) | 4.97910e11 | 0.595859 | ||||||||
\(447\) | 1.39948e12 | 1.65800 | ||||||||
\(448\) | 3.31954e11 | 0.389339 | ||||||||
\(449\) | −5.91722e11 | −0.687083 | −0.343542 | − | 0.939137i | \(-0.611627\pi\) | ||||
−0.343542 | + | 0.939137i | \(0.611627\pi\) | |||||||
\(450\) | −1.26171e11 | −0.145046 | ||||||||
\(451\) | 1.98505e11 | 0.225932 | ||||||||
\(452\) | −5.33827e9 | −0.00601558 | ||||||||
\(453\) | 1.81524e12 | 2.02531 | ||||||||
\(454\) | −6.32979e11 | −0.699259 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.25149e12 | 1.35546 | ||||||||
\(457\) | 8.30664e11 | 0.890845 | 0.445423 | − | 0.895320i | \(-0.353053\pi\) | ||||
0.445423 | + | 0.895320i | \(0.353053\pi\) | |||||||
\(458\) | −9.05865e11 | −0.961986 | ||||||||
\(459\) | −1.13986e11 | −0.119866 | ||||||||
\(460\) | −1.64924e11 | −0.171741 | ||||||||
\(461\) | −8.73246e11 | −0.900497 | −0.450249 | − | 0.892903i | \(-0.648665\pi\) | ||||
−0.450249 | + | 0.892903i | \(0.648665\pi\) | |||||||
\(462\) | −6.80035e10 | −0.0694452 | ||||||||
\(463\) | −7.70415e11 | −0.779130 | −0.389565 | − | 0.920999i | \(-0.627375\pi\) | ||||
−0.389565 | + | 0.920999i | \(0.627375\pi\) | |||||||
\(464\) | −1.37282e12 | −1.37494 | ||||||||
\(465\) | 4.22652e10 | 0.0419223 | ||||||||
\(466\) | −8.20074e11 | −0.805595 | ||||||||
\(467\) | 4.50995e11 | 0.438779 | 0.219390 | − | 0.975637i | \(-0.429593\pi\) | ||||
0.219390 | + | 0.975637i | \(0.429593\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.91473e11 | −0.182738 | ||||||||
\(470\) | −1.44868e12 | −1.36940 | ||||||||
\(471\) | 1.14350e12 | 1.07064 | ||||||||
\(472\) | 1.39386e12 | 1.29265 | ||||||||
\(473\) | −1.63374e11 | −0.150075 | ||||||||
\(474\) | 1.78282e12 | 1.62221 | ||||||||
\(475\) | −1.70145e11 | −0.153355 | ||||||||
\(476\) | 5.87265e10 | 0.0524327 | ||||||||
\(477\) | 5.85827e11 | 0.518128 | ||||||||
\(478\) | 4.24105e11 | 0.371576 | ||||||||
\(479\) | 5.26966e11 | 0.457376 | 0.228688 | − | 0.973500i | \(-0.426556\pi\) | ||||
0.228688 | + | 0.973500i | \(0.426556\pi\) | |||||||
\(480\) | −3.30661e11 | −0.284313 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.13248e12 | 0.955692 | ||||||||
\(483\) | −9.97072e11 | −0.833613 | ||||||||
\(484\) | 1.32755e11 | 0.109963 | ||||||||
\(485\) | −1.45945e12 | −1.19771 | ||||||||
\(486\) | 1.60418e12 | 1.30434 | ||||||||
\(487\) | −1.88076e12 | −1.51514 | −0.757570 | − | 0.652754i | \(-0.773614\pi\) | ||||
−0.757570 | + | 0.652754i | \(0.773614\pi\) | |||||||
\(488\) | 9.47475e11 | 0.756273 | ||||||||
\(489\) | 3.13469e12 | 2.47916 | ||||||||
\(490\) | −9.57371e11 | −0.750236 | ||||||||
\(491\) | 1.68889e12 | 1.31140 | 0.655699 | − | 0.755022i | \(-0.272374\pi\) | ||||
0.655699 | + | 0.755022i | \(0.272374\pi\) | |||||||
\(492\) | 3.10547e11 | 0.238938 | ||||||||
\(493\) | −2.68081e12 | −2.04388 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.68480e11 | 0.126132 | ||||||||
\(496\) | 3.89064e10 | 0.0288638 | ||||||||
\(497\) | −2.86460e11 | −0.210601 | ||||||||
\(498\) | 1.01090e12 | 0.736506 | ||||||||
\(499\) | −1.60699e12 | −1.16027 | −0.580137 | − | 0.814519i | \(-0.697001\pi\) | ||||
−0.580137 | + | 0.814519i | \(0.697001\pi\) | |||||||
\(500\) | 1.67249e11 | 0.119674 | ||||||||
\(501\) | −2.90772e11 | −0.206197 | ||||||||
\(502\) | 2.69176e11 | 0.189177 | ||||||||
\(503\) | 2.73565e12 | 1.90548 | 0.952740 | − | 0.303786i | \(-0.0982507\pi\) | ||||
0.952740 | + | 0.303786i | \(0.0982507\pi\) | |||||||
\(504\) | −5.08321e11 | −0.350914 | ||||||||
\(505\) | −1.14767e12 | −0.785249 | ||||||||
\(506\) | 3.43299e11 | 0.232807 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.53294e11 | −0.168748 | ||||||||
\(509\) | −7.49256e11 | −0.494766 | −0.247383 | − | 0.968918i | \(-0.579571\pi\) | ||||
−0.247383 | + | 0.968918i | \(0.579571\pi\) | |||||||
\(510\) | 2.37898e12 | 1.55713 | ||||||||
\(511\) | 4.28830e11 | 0.278222 | ||||||||
\(512\) | −1.73021e12 | −1.11271 | ||||||||
\(513\) | 1.34459e11 | 0.0857157 | ||||||||
\(514\) | 2.36625e12 | 1.49529 | ||||||||
\(515\) | 7.83548e11 | 0.490832 | ||||||||
\(516\) | −2.55588e11 | −0.158714 | ||||||||
\(517\) | −3.81940e11 | −0.235119 | ||||||||
\(518\) | −6.13500e11 | −0.374396 | ||||||||
\(519\) | 1.29201e12 | 0.781649 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.07862e12 | 0.641355 | 0.320678 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320678 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(522\) | 2.34501e12 | 1.38238 | ||||||||
\(523\) | −2.69236e12 | −1.57353 | −0.786765 | − | 0.617253i | \(-0.788246\pi\) | ||||
−0.786765 | + | 0.617253i | \(0.788246\pi\) | |||||||
\(524\) | 7.01939e10 | 0.0406732 | ||||||||
\(525\) | 1.43121e11 | 0.0822219 | ||||||||
\(526\) | 1.49441e12 | 0.851204 | ||||||||
\(527\) | 7.59755e10 | 0.0429067 | ||||||||
\(528\) | 3.21190e11 | 0.179850 | ||||||||
\(529\) | 3.23232e12 | 1.79459 | ||||||||
\(530\) | 8.67832e11 | 0.477743 | ||||||||
\(531\) | −2.10985e12 | −1.15167 | ||||||||
\(532\) | −6.92740e10 | −0.0374945 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.21739e12 | 0.647878 | ||||||||
\(535\) | 1.86791e12 | 0.985743 | ||||||||
\(536\) | 1.02055e12 | 0.534064 | ||||||||
\(537\) | −2.75119e12 | −1.42770 | ||||||||
\(538\) | 1.58041e12 | 0.813299 | ||||||||
\(539\) | −2.52408e11 | −0.128811 | ||||||||
\(540\) | −1.87082e10 | −0.00946804 | ||||||||
\(541\) | −1.94584e12 | −0.976604 | −0.488302 | − | 0.872675i | \(-0.662384\pi\) | ||||
−0.488302 | + | 0.872675i | \(0.662384\pi\) | |||||||
\(542\) | −1.90255e12 | −0.946976 | ||||||||
\(543\) | −4.66074e12 | −2.30068 | ||||||||
\(544\) | −5.94392e11 | −0.290990 | ||||||||
\(545\) | −9.16622e11 | −0.445047 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.49274e11 | −0.357847 | −0.178924 | − | 0.983863i | \(-0.557261\pi\) | ||||
−0.178924 | + | 0.983863i | \(0.557261\pi\) | |||||||
\(548\) | −3.87520e11 | −0.183562 | ||||||||
\(549\) | −1.43417e12 | −0.673791 | ||||||||
\(550\) | −4.92777e10 | −0.0229625 | ||||||||
\(551\) | 3.16229e12 | 1.46157 | ||||||||
\(552\) | 5.31440e12 | 2.43629 | ||||||||
\(553\) | −9.76509e11 | −0.444031 | ||||||||
\(554\) | −1.42468e12 | −0.642576 | ||||||||
\(555\) | 3.14780e12 | 1.40828 | ||||||||
\(556\) | −2.37542e10 | −0.0105415 | ||||||||
\(557\) | −2.43252e12 | −1.07080 | −0.535399 | − | 0.844599i | \(-0.679839\pi\) | ||||
−0.535399 | + | 0.844599i | \(0.679839\pi\) | |||||||
\(558\) | −6.64586e10 | −0.0290200 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.67278e11 | −0.286722 | ||||||||
\(561\) | 6.27212e11 | 0.267351 | ||||||||
\(562\) | 1.73455e12 | 0.733455 | ||||||||
\(563\) | −2.26566e12 | −0.950401 | −0.475200 | − | 0.879878i | \(-0.657624\pi\) | ||||
−0.475200 | + | 0.879878i | \(0.657624\pi\) | |||||||
\(564\) | −5.97518e11 | −0.248654 | ||||||||
\(565\) | 1.18447e11 | 0.0488999 | ||||||||
\(566\) | −2.54183e12 | −1.04105 | ||||||||
\(567\) | −9.37149e11 | −0.380789 | ||||||||
\(568\) | 1.52683e12 | 0.615494 | ||||||||
\(569\) | 4.39567e12 | 1.75800 | 0.879002 | − | 0.476817i | \(-0.158210\pi\) | ||||
0.879002 | + | 0.476817i | \(0.158210\pi\) | |||||||
\(570\) | −2.80626e12 | −1.11350 | ||||||||
\(571\) | 2.81010e12 | 1.10626 | 0.553132 | − | 0.833094i | \(-0.313433\pi\) | ||||
0.553132 | + | 0.833094i | \(0.313433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.53931e12 | 1.75912 | ||||||||
\(574\) | 1.34295e12 | 0.516365 | ||||||||
\(575\) | −7.22513e11 | −0.275639 | ||||||||
\(576\) | 2.67818e12 | 1.01377 | ||||||||
\(577\) | 3.06576e12 | 1.15146 | 0.575728 | − | 0.817642i | \(-0.304719\pi\) | ||||
0.575728 | + | 0.817642i | \(0.304719\pi\) | |||||||
\(578\) | 1.74842e12 | 0.651583 | ||||||||
\(579\) | 1.73153e12 | 0.640291 | ||||||||
\(580\) | −4.39993e11 | −0.161443 | ||||||||
\(581\) | −5.53702e11 | −0.201597 | ||||||||
\(582\) | 4.75262e12 | 1.71704 | ||||||||
\(583\) | 2.28801e11 | 0.0820257 | ||||||||
\(584\) | −2.28567e12 | −0.813121 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.48284e12 | 0.519464 | ||||||||
\(587\) | −1.53677e12 | −0.534240 | −0.267120 | − | 0.963663i | \(-0.586072\pi\) | ||||
−0.267120 | + | 0.963663i | \(0.586072\pi\) | |||||||
\(588\) | −3.94875e11 | −0.136226 | ||||||||
\(589\) | −8.96210e10 | −0.0306825 | ||||||||
\(590\) | −3.12549e12 | −1.06190 | ||||||||
\(591\) | −1.94496e12 | −0.655793 | ||||||||
\(592\) | 2.89765e12 | 0.969611 | ||||||||
\(593\) | 3.34336e12 | 1.11029 | 0.555146 | − | 0.831753i | \(-0.312662\pi\) | ||||
0.555146 | + | 0.831753i | \(0.312662\pi\) | |||||||
\(594\) | 3.89421e10 | 0.0128345 | ||||||||
\(595\) | −1.30304e12 | −0.426219 | ||||||||
\(596\) | 4.12893e11 | 0.134038 | ||||||||
\(597\) | 1.15504e12 | 0.372145 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.97101e11 | −0.316460 | −0.158230 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158230 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(600\) | −7.62838e11 | −0.240299 | ||||||||
\(601\) | −2.24332e12 | −0.701386 | −0.350693 | − | 0.936491i | \(-0.614054\pi\) | ||||
−0.350693 | + | 0.936491i | \(0.614054\pi\) | |||||||
\(602\) | −1.10528e12 | −0.342995 | ||||||||
\(603\) | −1.54478e12 | −0.475817 | ||||||||
\(604\) | 5.35555e11 | 0.163733 | ||||||||
\(605\) | −2.94562e12 | −0.893878 | ||||||||
\(606\) | 3.73734e12 | 1.12573 | ||||||||
\(607\) | −5.75690e12 | −1.72123 | −0.860617 | − | 0.509253i | \(-0.829922\pi\) | ||||
−0.860617 | + | 0.509253i | \(0.829922\pi\) | |||||||
\(608\) | 7.01147e11 | 0.208086 | ||||||||
\(609\) | −2.66003e12 | −0.783627 | ||||||||
\(610\) | −2.12455e12 | −0.621274 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.73799e11 | 0.136525 | ||||||||
\(613\) | −3.44873e12 | −0.986479 | −0.493239 | − | 0.869894i | \(-0.664187\pi\) | ||||
−0.493239 | + | 0.869894i | \(0.664187\pi\) | |||||||
\(614\) | 8.58375e11 | 0.243736 | ||||||||
\(615\) | −6.89053e12 | −1.94229 | ||||||||
\(616\) | −1.98530e11 | −0.0555538 | ||||||||
\(617\) | 5.13402e12 | 1.42618 | 0.713089 | − | 0.701073i | \(-0.247295\pi\) | ||||
0.713089 | + | 0.701073i | \(0.247295\pi\) | |||||||
\(618\) | −2.55158e12 | −0.703657 | ||||||||
\(619\) | −1.83851e12 | −0.503336 | −0.251668 | − | 0.967814i | \(-0.580979\pi\) | ||||
−0.251668 | + | 0.967814i | \(0.580979\pi\) | |||||||
\(620\) | 1.24696e10 | 0.00338915 | ||||||||
\(621\) | 5.70972e11 | 0.154065 | ||||||||
\(622\) | −3.80640e12 | −1.01966 | ||||||||
\(623\) | −6.66802e11 | −0.177338 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.08200e12 | −0.807928 | ||||||||
\(626\) | 2.01356e11 | 0.0524058 | ||||||||
\(627\) | −7.39861e11 | −0.191182 | ||||||||
\(628\) | 3.37371e11 | 0.0865544 | ||||||||
\(629\) | 5.65845e12 | 1.44135 | ||||||||
\(630\) | 1.13982e12 | 0.288273 | ||||||||
\(631\) | −3.01780e12 | −0.757805 | −0.378903 | − | 0.925437i | \(-0.623699\pi\) | ||||
−0.378903 | + | 0.925437i | \(0.623699\pi\) | |||||||
\(632\) | 5.20480e12 | 1.29771 | ||||||||
\(633\) | 6.20963e12 | 1.53727 | ||||||||
\(634\) | −1.15668e12 | −0.284322 | ||||||||
\(635\) | 5.62017e12 | 1.37173 | ||||||||
\(636\) | 3.57944e11 | 0.0867477 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.15868e11 | 0.218847 | ||||||||
\(639\) | −2.31113e12 | −0.548366 | ||||||||
\(640\) | 3.09962e12 | 0.730295 | ||||||||
\(641\) | 2.47728e12 | 0.579580 | 0.289790 | − | 0.957090i | \(-0.406415\pi\) | ||||
0.289790 | + | 0.957090i | \(0.406415\pi\) | |||||||
\(642\) | −6.08274e12 | −1.41316 | ||||||||
\(643\) | −5.96725e12 | −1.37665 | −0.688327 | − | 0.725401i | \(-0.741654\pi\) | ||||
−0.688327 | + | 0.725401i | \(0.741654\pi\) | |||||||
\(644\) | −2.94169e11 | −0.0673923 | ||||||||
\(645\) | 5.67107e12 | 1.29017 | ||||||||
\(646\) | −5.04449e12 | −1.13965 | ||||||||
\(647\) | −4.85153e12 | −1.08845 | −0.544227 | − | 0.838938i | \(-0.683177\pi\) | ||||
−0.544227 | + | 0.838938i | \(0.683177\pi\) | |||||||
\(648\) | 4.99501e12 | 1.11288 | ||||||||
\(649\) | −8.24027e11 | −0.182322 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.53867e10 | 0.0164506 | ||||||||
\(652\) | 9.24835e11 | 0.200424 | ||||||||
\(653\) | −1.50523e12 | −0.323961 | −0.161980 | − | 0.986794i | \(-0.551788\pi\) | ||||
−0.161980 | + | 0.986794i | \(0.551788\pi\) | |||||||
\(654\) | 2.98493e12 | 0.638020 | ||||||||
\(655\) | −1.55749e12 | −0.330628 | ||||||||
\(656\) | −6.34294e12 | −1.33728 | ||||||||
\(657\) | 3.45976e12 | 0.724439 | ||||||||
\(658\) | −2.58395e12 | −0.537362 | ||||||||
\(659\) | −3.29009e12 | −0.679552 | −0.339776 | − | 0.940506i | \(-0.610351\pi\) | ||||
−0.339776 | + | 0.940506i | \(0.610351\pi\) | |||||||
\(660\) | 1.02942e11 | 0.0211177 | ||||||||
\(661\) | −7.79224e12 | −1.58765 | −0.793827 | − | 0.608144i | \(-0.791914\pi\) | ||||
−0.793827 | + | 0.608144i | \(0.791914\pi\) | |||||||
\(662\) | −1.42144e12 | −0.287652 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.95124e12 | 0.589179 | ||||||||
\(665\) | 1.53708e12 | 0.304788 | ||||||||
\(666\) | −4.94966e12 | −0.974858 | ||||||||
\(667\) | 1.34285e13 | 2.62701 | ||||||||
\(668\) | −8.57871e10 | −0.0166697 | ||||||||
\(669\) | −4.55675e12 | −0.879503 | ||||||||
\(670\) | −2.28841e12 | −0.438730 | ||||||||
\(671\) | −5.60132e11 | −0.106669 | ||||||||
\(672\) | −5.89786e11 | −0.111566 | ||||||||
\(673\) | −6.76161e12 | −1.27052 | −0.635261 | − | 0.772297i | \(-0.719108\pi\) | ||||
−0.635261 | + | 0.772297i | \(0.719108\pi\) | |||||||
\(674\) | 4.55040e12 | 0.849337 | ||||||||
\(675\) | −8.19583e10 | −0.0151959 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.04459e12 | 1.10590 | 0.552952 | − | 0.833213i | \(-0.313501\pi\) | ||||
0.552952 | + | 0.833213i | \(0.313501\pi\) | |||||||
\(678\) | −3.85718e11 | −0.0701029 | ||||||||
\(679\) | −2.60316e12 | −0.469988 | ||||||||
\(680\) | 6.94523e12 | 1.24565 | ||||||||
\(681\) | 5.79287e12 | 1.03212 | ||||||||
\(682\) | −2.59562e10 | −0.00459421 | ||||||||
\(683\) | −3.24587e12 | −0.570740 | −0.285370 | − | 0.958417i | \(-0.592116\pi\) | ||||
−0.285370 | + | 0.958417i | \(0.592116\pi\) | |||||||
\(684\) | −5.58896e11 | −0.0976289 | ||||||||
\(685\) | 8.59843e12 | 1.49215 | ||||||||
\(686\) | −3.66724e12 | −0.632238 | ||||||||
\(687\) | 8.29025e12 | 1.41992 | ||||||||
\(688\) | 5.22039e12 | 0.888290 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.19166e13 | −2.00140 | ||||||||
\(691\) | 4.14584e12 | 0.691769 | 0.345885 | − | 0.938277i | \(-0.387579\pi\) | ||||
0.345885 | + | 0.938277i | \(0.387579\pi\) | |||||||
\(692\) | 3.81184e11 | 0.0631913 | ||||||||
\(693\) | 3.00511e11 | 0.0494949 | ||||||||
\(694\) | −2.02513e12 | −0.331387 | ||||||||
\(695\) | 5.27067e11 | 0.0856908 | ||||||||
\(696\) | 1.41780e13 | 2.29020 | ||||||||
\(697\) | −1.23863e13 | −1.98790 | ||||||||
\(698\) | −5.38583e12 | −0.858822 | ||||||||
\(699\) | 7.50512e12 | 1.18908 | ||||||||
\(700\) | 4.22255e10 | 0.00664711 | ||||||||
\(701\) | −5.47240e12 | −0.855947 | −0.427974 | − | 0.903791i | \(-0.640772\pi\) | ||||
−0.427974 | + | 0.903791i | \(0.640772\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.67473e12 | −1.03071 | ||||||||
\(704\) | 1.04599e12 | 0.160491 | ||||||||
\(705\) | 1.32580e13 | 2.02128 | ||||||||
\(706\) | −9.60094e12 | −1.45443 | ||||||||
\(707\) | −2.04706e12 | −0.308136 | ||||||||
\(708\) | −1.28913e12 | −0.192818 | ||||||||
\(709\) | −1.68810e12 | −0.250895 | −0.125447 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125447 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(710\) | −3.42366e12 | −0.505625 | ||||||||
\(711\) | −7.87838e12 | −1.15618 | ||||||||
\(712\) | 3.55406e12 | 0.518280 | ||||||||
\(713\) | −3.80571e11 | −0.0551484 | ||||||||
\(714\) | 4.24329e12 | 0.611028 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.11690e11 | −0.115420 | ||||||||
\(717\) | −3.88131e12 | −0.548456 | ||||||||
\(718\) | −8.39360e12 | −1.17866 | ||||||||
\(719\) | −3.99409e12 | −0.557363 | −0.278681 | − | 0.960384i | \(-0.589897\pi\) | ||||
−0.278681 | + | 0.960384i | \(0.589897\pi\) | |||||||
\(720\) | −5.38354e12 | −0.746572 | ||||||||
\(721\) | 1.39758e12 | 0.192605 | ||||||||
\(722\) | −9.28430e11 | −0.127154 | ||||||||
\(723\) | −1.03642e13 | −1.41062 | ||||||||
\(724\) | −1.37507e12 | −0.185995 | ||||||||
\(725\) | −1.92755e12 | −0.259111 | ||||||||
\(726\) | 9.59226e12 | 1.28146 | ||||||||
\(727\) | −1.96928e12 | −0.261459 | −0.130730 | − | 0.991418i | \(-0.541732\pi\) | ||||
−0.130730 | + | 0.991418i | \(0.541732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.58356e12 | −0.863350 | ||||||||
\(730\) | 5.12522e12 | 0.667974 | ||||||||
\(731\) | 1.01942e13 | 1.32046 | ||||||||
\(732\) | −8.76287e11 | −0.112810 | ||||||||
\(733\) | −2.48265e12 | −0.317649 | −0.158825 | − | 0.987307i | \(-0.550770\pi\) | ||||
−0.158825 | + | 0.987307i | \(0.550770\pi\) | |||||||
\(734\) | −4.82428e12 | −0.613479 | ||||||||
\(735\) | 8.76162e12 | 1.10737 | ||||||||
\(736\) | 2.97739e12 | 0.374012 | ||||||||
\(737\) | −6.03333e11 | −0.0753275 | ||||||||
\(738\) | 1.08348e13 | 1.34452 | ||||||||
\(739\) | 8.83198e12 | 1.08933 | 0.544664 | − | 0.838655i | \(-0.316657\pi\) | ||||
0.544664 | + | 0.838655i | \(0.316657\pi\) | |||||||
\(740\) | 9.28704e11 | 0.113850 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.54792e12 | 0.187469 | ||||||||
\(743\) | −5.88065e12 | −0.707906 | −0.353953 | − | 0.935263i | \(-0.615163\pi\) | ||||
−0.353953 | + | 0.935263i | \(0.615163\pi\) | |||||||
\(744\) | −4.01812e11 | −0.0480778 | ||||||||
\(745\) | −9.16141e12 | −1.08958 | ||||||||
\(746\) | 1.01264e13 | 1.19710 | ||||||||
\(747\) | −4.46722e12 | −0.524921 | ||||||||
\(748\) | 1.85048e11 | 0.0216136 | ||||||||
\(749\) | 3.33171e12 | 0.386811 | ||||||||
\(750\) | 1.20846e13 | 1.39462 | ||||||||
\(751\) | −9.39265e12 | −1.07748 | −0.538739 | − | 0.842473i | \(-0.681099\pi\) | ||||
−0.538739 | + | 0.842473i | \(0.681099\pi\) | |||||||
\(752\) | 1.22043e13 | 1.39166 | ||||||||
\(753\) | −2.46343e12 | −0.279230 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.18831e13 | −1.33097 | ||||||||
\(756\) | −3.33690e10 | −0.00371531 | ||||||||
\(757\) | 1.20690e13 | 1.33579 | 0.667897 | − | 0.744254i | \(-0.267195\pi\) | ||||
0.667897 | + | 0.744254i | \(0.267195\pi\) | |||||||
\(758\) | 3.56628e12 | 0.392378 | ||||||||
\(759\) | −3.14179e12 | −0.343628 | ||||||||
\(760\) | −8.19263e12 | −0.890762 | ||||||||
\(761\) | −1.73414e12 | −0.187436 | −0.0937182 | − | 0.995599i | \(-0.529875\pi\) | ||||
−0.0937182 | + | 0.995599i | \(0.529875\pi\) | |||||||
\(762\) | −1.83018e13 | −1.96651 | ||||||||
\(763\) | −1.63494e12 | −0.174639 | ||||||||
\(764\) | 1.33924e12 | 0.142213 | ||||||||
\(765\) | −1.05128e13 | −1.10980 | ||||||||
\(766\) | 1.14388e13 | 1.20047 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.46226e12 | 0.462839 | ||||||||
\(769\) | 1.87490e13 | 1.93335 | 0.966675 | − | 0.256006i | \(-0.0824068\pi\) | ||||
0.966675 | + | 0.256006i | \(0.0824068\pi\) | |||||||
\(770\) | 4.45170e11 | 0.0456371 | ||||||||
\(771\) | −2.16553e13 | −2.20709 | ||||||||
\(772\) | 5.10858e11 | 0.0517634 | ||||||||
\(773\) | 2.23308e12 | 0.224956 | 0.112478 | − | 0.993654i | \(-0.464121\pi\) | ||||
0.112478 | + | 0.993654i | \(0.464121\pi\) | |||||||
\(774\) | −8.91729e12 | −0.893097 | ||||||||
\(775\) | 5.46278e10 | 0.00543947 | ||||||||
\(776\) | 1.38749e13 | 1.37357 | ||||||||
\(777\) | 5.61460e12 | 0.552617 | ||||||||
\(778\) | 1.26971e13 | 1.24250 | ||||||||
\(779\) | 1.46110e13 | 1.42154 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.02638e11 | −0.0868129 | ||||||||
\(782\) | −2.14212e13 | −2.04839 | ||||||||
\(783\) | 1.52327e12 | 0.144826 | ||||||||
\(784\) | 8.06534e12 | 0.762431 | ||||||||
\(785\) | −7.48571e12 | −0.703590 | ||||||||
\(786\) | 5.07188e12 | 0.473988 | ||||||||
\(787\) | −7.05497e12 | −0.655555 | −0.327777 | − | 0.944755i | \(-0.606300\pi\) | ||||
−0.327777 | + | 0.944755i | \(0.606300\pi\) | |||||||
\(788\) | −5.73826e11 | −0.0530166 | ||||||||
\(789\) | −1.36765e13 | −1.25640 | ||||||||
\(790\) | −1.16709e13 | −1.06606 | ||||||||
\(791\) | 2.11270e11 | 0.0191886 | ||||||||
\(792\) | −1.60172e12 | −0.144652 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.42572e13 | 1.27304 | ||||||||
\(795\) | −7.94219e12 | −0.705161 | ||||||||
\(796\) | 3.40774e11 | 0.0300855 | ||||||||
\(797\) | 1.16654e13 | 1.02409 | 0.512045 | − | 0.858959i | \(-0.328888\pi\) | ||||
0.512045 | + | 0.858959i | \(0.328888\pi\) | |||||||
\(798\) | −5.00540e12 | −0.436944 | ||||||||
\(799\) | 2.38323e13 | 2.06874 | ||||||||
\(800\) | −4.27379e11 | −0.0368900 | ||||||||
\(801\) | −5.37969e12 | −0.461755 | ||||||||
\(802\) | −9.11497e12 | −0.777984 | ||||||||
\(803\) | 1.35125e12 | 0.114687 | ||||||||
\(804\) | −9.43873e11 | −0.0796638 | ||||||||
\(805\) | 6.52712e12 | 0.547823 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.44635e13 | −1.20045 | ||||||||
\(808\) | 1.09108e13 | 0.900548 | ||||||||
\(809\) | −1.37043e13 | −1.12483 | −0.562415 | − | 0.826855i | \(-0.690128\pi\) | ||||
−0.562415 | + | 0.826855i | \(0.690128\pi\) | |||||||
\(810\) | −1.12005e13 | −0.914225 | ||||||||
\(811\) | −2.07440e12 | −0.168383 | −0.0841917 | − | 0.996450i | \(-0.526831\pi\) | ||||
−0.0841917 | + | 0.996450i | \(0.526831\pi\) | |||||||
\(812\) | −7.84797e11 | −0.0633512 | ||||||||
\(813\) | 1.74117e13 | 1.39776 | ||||||||
\(814\) | −1.93315e12 | −0.154332 | ||||||||
\(815\) | −2.05206e13 | −1.62922 | ||||||||
\(816\) | −2.00416e13 | −1.58244 | ||||||||
\(817\) | −1.20252e13 | −0.944261 | ||||||||
\(818\) | 9.33483e11 | 0.0728982 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.03293e12 | −0.157022 | ||||||||
\(821\) | 1.51952e13 | 1.16724 | 0.583622 | − | 0.812026i | \(-0.301635\pi\) | ||||
0.583622 | + | 0.812026i | \(0.301635\pi\) | |||||||
\(822\) | −2.80003e13 | −2.13914 | ||||||||
\(823\) | 8.32881e12 | 0.632825 | 0.316412 | − | 0.948622i | \(-0.397522\pi\) | ||||
0.316412 | + | 0.948622i | \(0.397522\pi\) | |||||||
\(824\) | −7.44912e12 | −0.562901 | ||||||||
\(825\) | 4.50977e11 | 0.0338931 | ||||||||
\(826\) | −5.57481e12 | −0.416697 | ||||||||
\(827\) | 1.50997e13 | 1.12252 | 0.561258 | − | 0.827641i | \(-0.310317\pi\) | ||||
0.561258 | + | 0.827641i | \(0.310317\pi\) | |||||||
\(828\) | −2.37333e12 | −0.175477 | ||||||||
\(829\) | −9.65383e12 | −0.709912 | −0.354956 | − | 0.934883i | \(-0.615504\pi\) | ||||
−0.354956 | + | 0.934883i | \(0.615504\pi\) | |||||||
\(830\) | −6.61764e12 | −0.484007 | ||||||||
\(831\) | 1.30384e13 | 0.948458 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.57498e13 | 1.13337 | ||||||||
\(834\) | −1.71637e12 | −0.122846 | ||||||||
\(835\) | 1.90347e12 | 0.135506 | ||||||||
\(836\) | −2.18283e11 | −0.0154558 | ||||||||
\(837\) | −4.31701e10 | −0.00304032 | ||||||||
\(838\) | −2.43540e12 | −0.170597 | ||||||||
\(839\) | −1.96235e13 | −1.36725 | −0.683623 | − | 0.729835i | \(-0.739597\pi\) | ||||
−0.683623 | + | 0.729835i | \(0.739597\pi\) | |||||||
\(840\) | 6.89141e12 | 0.477586 | ||||||||
\(841\) | 2.13181e13 | 1.46949 | ||||||||
\(842\) | 1.07978e13 | 0.740340 | ||||||||
\(843\) | −1.58742e13 | −1.08260 | ||||||||
\(844\) | 1.83204e12 | 0.124278 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.08471e13 | −1.39919 | ||||||||
\(847\) | −5.25399e12 | −0.350763 | ||||||||
\(848\) | −7.31102e12 | −0.485508 | ||||||||
\(849\) | 2.32622e13 | 1.53662 | ||||||||
\(850\) | 3.07483e12 | 0.202040 | ||||||||
\(851\) | −2.83439e13 | −1.85258 | ||||||||
\(852\) | −1.41211e12 | −0.0918104 | ||||||||
\(853\) | 1.66671e13 | 1.07793 | 0.538963 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538963 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(854\) | −3.78947e12 | −0.243791 | ||||||||
\(855\) | 1.24010e13 | 0.793613 | ||||||||
\(856\) | −1.77580e13 | −1.13048 | ||||||||
\(857\) | −8.56434e12 | −0.542351 | −0.271175 | − | 0.962530i | \(-0.587412\pi\) | ||||
−0.271175 | + | 0.962530i | \(0.587412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.87649e12 | 0.117592 | 0.0587958 | − | 0.998270i | \(-0.481274\pi\) | ||||
0.0587958 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(860\) | 1.67315e12 | 0.104302 | ||||||||
\(861\) | −1.22904e13 | −0.762167 | ||||||||
\(862\) | 2.82683e12 | 0.174388 | ||||||||
\(863\) | −2.54184e11 | −0.0155991 | −0.00779956 | − | 0.999970i | \(-0.502483\pi\) | ||||
−0.00779956 | + | 0.999970i | \(0.502483\pi\) | |||||||
\(864\) | 3.37740e11 | 0.0206192 | ||||||||
\(865\) | −8.45785e12 | −0.513674 | ||||||||
\(866\) | 2.58681e13 | 1.56291 | ||||||||
\(867\) | −1.60011e13 | −0.961753 | ||||||||
\(868\) | 2.22415e10 | 0.00132992 | ||||||||
\(869\) | −3.07699e12 | −0.183036 | ||||||||
\(870\) | −3.17918e13 | −1.88139 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.71425e12 | 0.510394 | ||||||||
\(873\) | −2.10021e13 | −1.22376 | ||||||||
\(874\) | 2.52685e13 | 1.46480 | ||||||||
\(875\) | −6.61913e12 | −0.381737 | ||||||||
\(876\) | 2.11393e12 | 0.121289 | ||||||||
\(877\) | 2.88730e13 | 1.64814 | 0.824069 | − | 0.566490i | \(-0.191699\pi\) | ||||
0.824069 | + | 0.566490i | \(0.191699\pi\) | |||||||
\(878\) | −1.54971e13 | −0.880085 | ||||||||
\(879\) | −1.35706e13 | −0.766742 | ||||||||
\(880\) | −2.10260e12 | −0.118191 | ||||||||
\(881\) | −1.43284e13 | −0.801317 | −0.400659 | − | 0.916227i | \(-0.631219\pi\) | ||||
−0.400659 | + | 0.916227i | \(0.631219\pi\) | |||||||
\(882\) | −1.37769e13 | −0.766556 | ||||||||
\(883\) | 3.54065e12 | 0.196001 | 0.0980007 | − | 0.995186i | \(-0.468755\pi\) | ||||
0.0980007 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.86037e13 | 1.56739 | ||||||||
\(886\) | −2.17783e13 | −1.18733 | ||||||||
\(887\) | 1.07018e13 | 0.580497 | 0.290249 | − | 0.956951i | \(-0.406262\pi\) | ||||
0.290249 | + | 0.956951i | \(0.406262\pi\) | |||||||
\(888\) | −2.99259e13 | −1.61506 | ||||||||
\(889\) | 1.00245e13 | 0.538274 | ||||||||
\(890\) | −7.96937e12 | −0.425764 | ||||||||
\(891\) | −2.95297e12 | −0.156967 | ||||||||
\(892\) | −1.34439e12 | −0.0711022 | ||||||||
\(893\) | −2.81127e13 | −1.47935 | ||||||||
\(894\) | 2.98336e13 | 1.56202 | ||||||||
\(895\) | 1.80101e13 | 0.938235 | ||||||||
\(896\) | 5.52866e12 | 0.286572 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.26141e13 | −0.647311 | ||||||||
\(899\) | −1.01531e12 | −0.0518416 | ||||||||
\(900\) | 3.40671e11 | 0.0173079 | ||||||||
\(901\) | −1.42768e13 | −0.721720 | ||||||||
\(902\) | 4.23165e12 | 0.212853 | ||||||||
\(903\) | 1.01152e13 | 0.506269 | ||||||||
\(904\) | −1.12607e12 | −0.0560799 | ||||||||
\(905\) | 3.05106e13 | 1.51193 | ||||||||
\(906\) | 3.86966e13 | 1.90808 | ||||||||
\(907\) | 2.74516e13 | 1.34690 | 0.673448 | − | 0.739234i | \(-0.264812\pi\) | ||||
0.673448 | + | 0.739234i | \(0.264812\pi\) | |||||||
\(908\) | 1.70909e12 | 0.0834406 | ||||||||
\(909\) | −1.65155e13 | −0.802331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.57903e13 | 0.759550 | 0.379775 | − | 0.925079i | \(-0.376001\pi\) | ||||
0.379775 | + | 0.925079i | \(0.376001\pi\) | |||||||
\(912\) | 2.36412e13 | 1.13160 | ||||||||
\(913\) | −1.74472e12 | −0.0831013 | ||||||||
\(914\) | 1.77078e13 | 0.839279 | ||||||||
\(915\) | 1.94434e13 | 0.917016 | ||||||||
\(916\) | 2.44589e12 | 0.114791 | ||||||||
\(917\) | −2.77803e12 | −0.129740 | ||||||||
\(918\) | −2.42991e12 | −0.112927 | ||||||||
\(919\) | 3.33575e13 | 1.54267 | 0.771335 | − | 0.636429i | \(-0.219589\pi\) | ||||
0.771335 | + | 0.636429i | \(0.219589\pi\) | |||||||
\(920\) | −3.47896e13 | −1.60105 | ||||||||
\(921\) | −7.85564e12 | −0.359760 | ||||||||
\(922\) | −1.86155e13 | −0.848372 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.83614e11 | 0.00828670 | ||||||||
\(925\) | 4.06853e12 | 0.182726 | ||||||||
\(926\) | −1.64234e13 | −0.734030 | ||||||||
\(927\) | 1.12756e13 | 0.501509 | ||||||||
\(928\) | 7.94322e12 | 0.351585 | ||||||||
\(929\) | 5.90953e12 | 0.260305 | 0.130152 | − | 0.991494i | \(-0.458453\pi\) | ||||
0.130152 | + | 0.991494i | \(0.458453\pi\) | |||||||
\(930\) | 9.00994e11 | 0.0394956 | ||||||||
\(931\) | −1.85785e13 | −0.810471 | ||||||||
\(932\) | 2.21425e12 | 0.0961293 | ||||||||
\(933\) | 3.48352e13 | 1.50505 | ||||||||
\(934\) | 9.61415e12 | 0.413380 | ||||||||
\(935\) | −4.10591e12 | −0.175694 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.94135e13 | 1.24657 | 0.623287 | − | 0.781993i | \(-0.285797\pi\) | ||||
0.623287 | + | 0.781993i | \(0.285797\pi\) | |||||||
\(938\) | −4.08175e12 | −0.172160 | ||||||||
\(939\) | −1.84276e12 | −0.0773522 | ||||||||
\(940\) | 3.91153e12 | 0.163407 | ||||||||
\(941\) | 1.78277e13 | 0.741212 | 0.370606 | − | 0.928790i | \(-0.379150\pi\) | ||||
0.370606 | + | 0.928790i | \(0.379150\pi\) | |||||||
\(942\) | 2.43768e13 | 1.00867 | ||||||||
\(943\) | 6.20448e13 | 2.55507 | ||||||||
\(944\) | 2.63306e13 | 1.07916 | ||||||||
\(945\) | 7.40404e11 | 0.0302013 | ||||||||
\(946\) | −3.48275e12 | −0.141388 | ||||||||
\(947\) | 2.20380e13 | 0.890427 | 0.445213 | − | 0.895425i | \(-0.353128\pi\) | ||||
0.445213 | + | 0.895425i | \(0.353128\pi\) | |||||||
\(948\) | −4.81374e12 | −0.193573 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.62709e12 | −0.144478 | ||||||||
\(951\) | 1.05856e13 | 0.419667 | ||||||||
\(952\) | 1.23879e13 | 0.488801 | ||||||||
\(953\) | 3.10318e13 | 1.21868 | 0.609340 | − | 0.792909i | \(-0.291435\pi\) | ||||
0.609340 | + | 0.792909i | \(0.291435\pi\) | |||||||
\(954\) | 1.24884e13 | 0.488136 | ||||||||
\(955\) | −2.97156e13 | −1.15603 | ||||||||
\(956\) | −1.14511e12 | −0.0443391 | ||||||||
\(957\) | −8.38180e12 | −0.323023 | ||||||||
\(958\) | 1.12337e13 | 0.430900 | ||||||||
\(959\) | 1.53367e13 | 0.585527 | ||||||||
\(960\) | −3.63086e13 | −1.37971 | ||||||||
\(961\) | −2.64108e13 | −0.998912 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.68799e13 | 1.00719 | ||||||||
\(964\) | −3.05776e12 | −0.114040 | ||||||||
\(965\) | −1.13351e13 | −0.420778 | ||||||||
\(966\) | −2.12552e13 | −0.785359 | ||||||||
\(967\) | −3.86641e13 | −1.42196 | −0.710982 | − | 0.703210i | \(-0.751749\pi\) | ||||
−0.710982 | + | 0.703210i | \(0.751749\pi\) | |||||||
\(968\) | 2.80038e13 | 1.02513 | ||||||||
\(969\) | 4.61660e13 | 1.68215 | ||||||||
\(970\) | −3.11120e13 | −1.12838 | ||||||||
\(971\) | 2.91204e13 | 1.05126 | 0.525631 | − | 0.850713i | \(-0.323829\pi\) | ||||
0.525631 | + | 0.850713i | \(0.323829\pi\) | |||||||
\(972\) | −4.33138e12 | −0.155643 | ||||||||
\(973\) | 9.40108e11 | 0.0336256 | ||||||||
\(974\) | −4.00933e13 | −1.42744 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.78982e13 | 0.631372 | ||||||||
\(977\) | 2.43957e13 | 0.856618 | 0.428309 | − | 0.903632i | \(-0.359109\pi\) | ||||
0.428309 | + | 0.903632i | \(0.359109\pi\) | |||||||
\(978\) | 6.68241e13 | 2.33565 | ||||||||
\(979\) | −2.10110e12 | −0.0731012 | ||||||||
\(980\) | 2.58496e12 | 0.0895235 | ||||||||
\(981\) | −1.31905e13 | −0.454729 | ||||||||
\(982\) | 3.60031e13 | 1.23549 | ||||||||
\(983\) | −1.65480e13 | −0.565268 | −0.282634 | − | 0.959228i | \(-0.591208\pi\) | ||||
−0.282634 | + | 0.959228i | \(0.591208\pi\) | |||||||
\(984\) | 6.55077e13 | 2.22748 | ||||||||
\(985\) | 1.27323e13 | 0.430965 | ||||||||
\(986\) | −5.71485e13 | −1.92557 | ||||||||
\(987\) | 2.36477e13 | 0.793160 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.10643e13 | −1.69721 | ||||||||
\(990\) | 3.59159e12 | 0.118831 | ||||||||
\(991\) | −6.37548e12 | −0.209982 | −0.104991 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104991 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(992\) | −2.25115e11 | −0.00738077 | ||||||||
\(993\) | 1.30086e13 | 0.424581 | ||||||||
\(994\) | −6.10664e12 | −0.198410 | ||||||||
\(995\) | −7.56122e12 | −0.244561 | ||||||||
\(996\) | −2.72950e12 | −0.0878851 | ||||||||
\(997\) | 1.52049e13 | 0.487366 | 0.243683 | − | 0.969855i | \(-0.421644\pi\) | ||||
0.243683 | + | 0.969855i | \(0.421644\pi\) | |||||||
\(998\) | −3.42572e13 | −1.09311 | ||||||||
\(999\) | −3.21519e12 | −0.102132 |
(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 | 169.10.a.b.1.4 | 5 | ||
13.12 | even | 2 | 13.10.a.b.1.2 | ✓ | 5 | ||
39.38 | odd | 2 | 117.10.a.e.1.4 | 5 | |||
52.51 | odd | 2 | 208.10.a.h.1.5 | 5 | |||
65.64 | even | 2 | 325.10.a.b.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.10.a.b.1.2 | ✓ | 5 | 13.12 | even | 2 | ||
117.10.a.e.1.4 | 5 | 39.38 | odd | 2 | |||
169.10.a.b.1.4 | 5 | 1.1 | even | 1 | trivial | ||
208.10.a.h.1.5 | 5 | 52.51 | odd | 2 | |||
325.10.a.b.1.4 | 5 | 65.64 | even | 2 |