Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,38,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(216.785095312\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 15934380 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3991.29\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 480412. | 1.29586 | 0.647931 | − | 0.761699i | \(-0.275635\pi\) | ||||
0.647931 | + | 0.761699i | \(0.275635\pi\) | |||||||
\(3\) | −3.45869e7 | −0.0515429 | −0.0257715 | − | 0.999668i | \(-0.508204\pi\) | ||||
−0.0257715 | + | 0.999668i | \(0.508204\pi\) | |||||||
\(4\) | 9.33565e10 | 0.679258 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.66160e13 | −0.0667925 | ||||||||
\(7\) | 5.42222e15 | 1.25853 | 0.629264 | − | 0.777191i | \(-0.283356\pi\) | ||||
0.629264 | + | 0.777191i | \(0.283356\pi\) | |||||||
\(8\) | −2.11777e16 | −0.415637 | ||||||||
\(9\) | −4.49088e17 | −0.997343 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.03285e18 | −0.0560108 | −0.0280054 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280054 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(12\) | −3.22892e18 | −0.0350109 | ||||||||
\(13\) | 1.23244e19 | 0.0303957 | 0.0151979 | − | 0.999885i | \(-0.495162\pi\) | ||||
0.0151979 | + | 0.999885i | \(0.495162\pi\) | |||||||
\(14\) | 2.60490e21 | 1.63088 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.30048e22 | −1.21787 | ||||||||
\(17\) | 5.41594e22 | 0.934047 | 0.467023 | − | 0.884245i | \(-0.345326\pi\) | ||||
0.467023 | + | 0.884245i | \(0.345326\pi\) | |||||||
\(18\) | −2.15747e23 | −1.29242 | ||||||||
\(19\) | −3.08845e23 | −0.680455 | −0.340228 | − | 0.940343i | \(-0.610504\pi\) | ||||
−0.340228 | + | 0.940343i | \(0.610504\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.87538e23 | −0.0648682 | ||||||||
\(22\) | −4.96192e23 | −0.0725822 | ||||||||
\(23\) | 2.61592e25 | 1.68136 | 0.840678 | − | 0.541535i | \(-0.182156\pi\) | ||||
0.840678 | + | 0.541535i | \(0.182156\pi\) | |||||||
\(24\) | 7.32473e23 | 0.0214232 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.92077e24 | 0.0393886 | ||||||||
\(27\) | 3.11065e25 | 0.102949 | ||||||||
\(28\) | 5.06199e26 | 0.854866 | ||||||||
\(29\) | 2.49238e26 | 0.219913 | 0.109957 | − | 0.993936i | \(-0.464929\pi\) | ||||
0.109957 | + | 0.993936i | \(0.464929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.34643e27 | −0.602859 | −0.301429 | − | 0.953489i | \(-0.597464\pi\) | ||||
−0.301429 | + | 0.953489i | \(0.597464\pi\) | |||||||
\(32\) | −8.14116e27 | −1.16255 | ||||||||
\(33\) | 3.57230e25 | 0.00288696 | ||||||||
\(34\) | 2.60188e28 | 1.21040 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.19253e28 | −0.677453 | ||||||||
\(37\) | −6.21792e28 | −0.605220 | −0.302610 | − | 0.953114i | \(-0.597858\pi\) | ||||
−0.302610 | + | 0.953114i | \(0.597858\pi\) | |||||||
\(38\) | −1.48373e29 | −0.881776 | ||||||||
\(39\) | −4.26262e26 | −0.00156668 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.53404e29 | −1.24352 | −0.621761 | − | 0.783207i | \(-0.713582\pi\) | ||||
−0.621761 | + | 0.783207i | \(0.713582\pi\) | |||||||
\(42\) | −9.00954e28 | −0.0840603 | ||||||||
\(43\) | −3.53994e29 | −0.213713 | −0.106856 | − | 0.994274i | \(-0.534078\pi\) | ||||
−0.106856 | + | 0.994274i | \(0.534078\pi\) | |||||||
\(44\) | −9.64230e28 | −0.0380457 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25672e31 | 2.17881 | ||||||||
\(47\) | −6.68978e29 | −0.0779115 | −0.0389557 | − | 0.999241i | \(-0.512403\pi\) | ||||
−0.0389557 | + | 0.999241i | \(0.512403\pi\) | |||||||
\(48\) | 7.95667e29 | 0.0627724 | ||||||||
\(49\) | 1.08383e31 | 0.583895 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.87321e30 | −0.0481435 | ||||||||
\(52\) | 1.15056e30 | 0.0206465 | ||||||||
\(53\) | −1.24128e32 | −1.56591 | −0.782956 | − | 0.622077i | \(-0.786289\pi\) | ||||
−0.782956 | + | 0.622077i | \(0.786289\pi\) | |||||||
\(54\) | 1.49439e31 | 0.133408 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.14830e32 | −0.523092 | ||||||||
\(57\) | 1.06820e31 | 0.0350726 | ||||||||
\(58\) | 1.19737e32 | 0.284977 | ||||||||
\(59\) | 6.57033e31 | 0.113979 | 0.0569895 | − | 0.998375i | \(-0.481850\pi\) | ||||
0.0569895 | + | 0.998375i | \(0.481850\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.06034e33 | −0.992758 | −0.496379 | − | 0.868106i | \(-0.665337\pi\) | ||||
−0.496379 | + | 0.868106i | \(0.665337\pi\) | |||||||
\(62\) | −1.12725e33 | −0.781222 | ||||||||
\(63\) | −2.43505e33 | −1.25519 | ||||||||
\(64\) | −7.49344e32 | −0.288637 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.71618e31 | 0.00374110 | ||||||||
\(67\) | 8.44869e33 | 1.39446 | 0.697229 | − | 0.716849i | \(-0.254416\pi\) | ||||
0.697229 | + | 0.716849i | \(0.254416\pi\) | |||||||
\(68\) | 5.05613e33 | 0.634459 | ||||||||
\(69\) | −9.04768e32 | −0.0866620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.04837e33 | −0.397932 | −0.198966 | − | 0.980006i | \(-0.563758\pi\) | ||||
−0.198966 | + | 0.980006i | \(0.563758\pi\) | |||||||
\(72\) | 9.51066e33 | 0.414533 | ||||||||
\(73\) | −9.36735e33 | −0.316333 | −0.158166 | − | 0.987412i | \(-0.550558\pi\) | ||||
−0.158166 | + | 0.987412i | \(0.550558\pi\) | |||||||
\(74\) | −2.98716e34 | −0.784282 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.88327e34 | −0.462205 | ||||||||
\(77\) | −5.60032e33 | −0.0704911 | ||||||||
\(78\) | −2.04781e32 | −0.00203021 | ||||||||
\(79\) | 1.51854e35 | 1.18940 | 0.594698 | − | 0.803949i | \(-0.297272\pi\) | ||||
0.594698 | + | 0.803949i | \(0.297272\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.01141e35 | 0.992037 | ||||||||
\(82\) | −4.09985e35 | −1.61143 | ||||||||
\(83\) | 1.43761e35 | 0.451541 | 0.225771 | − | 0.974180i | \(-0.427510\pi\) | ||||
0.225771 | + | 0.974180i | \(0.427510\pi\) | |||||||
\(84\) | −1.75079e34 | −0.0440623 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.70063e35 | −0.276942 | ||||||||
\(87\) | −8.62039e33 | −0.0113350 | ||||||||
\(88\) | 2.18734e34 | 0.0232802 | ||||||||
\(89\) | 2.28283e35 | 0.197133 | 0.0985664 | − | 0.995130i | \(-0.468574\pi\) | ||||
0.0985664 | + | 0.995130i | \(0.468574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.68253e34 | 0.0382539 | ||||||||
\(92\) | 2.44213e36 | 1.14208 | ||||||||
\(93\) | 8.11557e34 | 0.0310731 | ||||||||
\(94\) | −3.21385e35 | −0.100962 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.81578e35 | 0.0599212 | ||||||||
\(97\) | −7.07361e36 | −1.24269 | −0.621347 | − | 0.783535i | \(-0.713414\pi\) | ||||
−0.621347 | + | 0.783535i | \(0.713414\pi\) | |||||||
\(98\) | 5.20686e36 | 0.756647 | ||||||||
\(99\) | 4.63839e35 | 0.0558620 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.31355e37 | −1.09270 | −0.546350 | − | 0.837557i | \(-0.683983\pi\) | ||||
−0.546350 | + | 0.837557i | \(0.683983\pi\) | |||||||
\(102\) | −8.99911e35 | −0.0623873 | ||||||||
\(103\) | −2.33181e37 | −1.34960 | −0.674800 | − | 0.738000i | \(-0.735770\pi\) | ||||
−0.674800 | + | 0.738000i | \(0.735770\pi\) | |||||||
\(104\) | −2.61002e35 | −0.0126336 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.96327e37 | −2.02920 | ||||||||
\(107\) | −3.01693e36 | −0.0862909 | −0.0431454 | − | 0.999069i | \(-0.513738\pi\) | ||||
−0.0431454 | + | 0.999069i | \(0.513738\pi\) | |||||||
\(108\) | 2.90400e36 | 0.0699289 | ||||||||
\(109\) | 3.05531e37 | 0.620391 | 0.310195 | − | 0.950673i | \(-0.399606\pi\) | ||||
0.310195 | + | 0.950673i | \(0.399606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.15059e36 | 0.0311948 | ||||||||
\(112\) | −1.24737e38 | −1.53272 | ||||||||
\(113\) | −4.21983e37 | −0.439890 | −0.219945 | − | 0.975512i | \(-0.570588\pi\) | ||||
−0.219945 | + | 0.975512i | \(0.570588\pi\) | |||||||
\(114\) | 5.13177e36 | 0.0454493 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.32680e37 | 0.149378 | ||||||||
\(117\) | −5.53472e36 | −0.0303150 | ||||||||
\(118\) | 3.15646e37 | 0.147701 | ||||||||
\(119\) | 2.93664e38 | 1.17552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.38973e38 | −0.996863 | ||||||||
\(122\) | −5.09400e38 | −1.28648 | ||||||||
\(123\) | 2.95166e37 | 0.0640947 | ||||||||
\(124\) | −2.19054e38 | −0.409497 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.16983e39 | −1.62655 | ||||||||
\(127\) | −1.09656e39 | −1.31724 | −0.658619 | − | 0.752476i | \(-0.728859\pi\) | ||||
−0.658619 | + | 0.752476i | \(0.728859\pi\) | |||||||
\(128\) | 7.58918e38 | 0.788516 | ||||||||
\(129\) | 1.22436e37 | 0.0110154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.36928e39 | −1.60360 | −0.801802 | − | 0.597590i | \(-0.796125\pi\) | ||||
−0.801802 | + | 0.597590i | \(0.796125\pi\) | |||||||
\(132\) | 3.33498e36 | 0.00196099 | ||||||||
\(133\) | −1.67463e39 | −0.856373 | ||||||||
\(134\) | 4.05885e39 | 1.80702 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.14697e39 | −0.388225 | ||||||||
\(137\) | −2.55274e39 | −0.754529 | −0.377265 | − | 0.926105i | \(-0.623135\pi\) | ||||
−0.377265 | + | 0.926105i | \(0.623135\pi\) | |||||||
\(138\) | −4.34661e38 | −0.112302 | ||||||||
\(139\) | −6.38958e39 | −1.44444 | −0.722219 | − | 0.691665i | \(-0.756878\pi\) | ||||
−0.722219 | + | 0.691665i | \(0.756878\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.31379e37 | 0.00401578 | ||||||||
\(142\) | −3.38612e39 | −0.515665 | ||||||||
\(143\) | −1.27292e37 | −0.00170249 | ||||||||
\(144\) | 1.03312e40 | 1.21463 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.50019e39 | −0.409923 | ||||||||
\(147\) | −3.74864e38 | −0.0300956 | ||||||||
\(148\) | −5.80483e39 | −0.411100 | ||||||||
\(149\) | −3.49035e39 | −0.218234 | −0.109117 | − | 0.994029i | \(-0.534802\pi\) | ||||
−0.109117 | + | 0.994029i | \(0.534802\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.43880e40 | −0.702953 | −0.351476 | − | 0.936197i | \(-0.614320\pi\) | ||||
−0.351476 | + | 0.936197i | \(0.614320\pi\) | |||||||
\(152\) | 6.54064e39 | 0.282823 | ||||||||
\(153\) | −2.43223e40 | −0.931565 | ||||||||
\(154\) | −2.69046e39 | −0.0913468 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.97943e37 | −0.00106418 | ||||||||
\(157\) | −3.81842e40 | −0.907277 | −0.453639 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453639 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(158\) | 7.29527e40 | 1.54129 | ||||||||
\(159\) | 4.29322e39 | 0.0807116 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.41841e41 | 2.11604 | ||||||||
\(162\) | 9.66305e40 | 1.28554 | ||||||||
\(163\) | 7.49639e40 | 0.889982 | 0.444991 | − | 0.895535i | \(-0.353207\pi\) | ||||
0.444991 | + | 0.895535i | \(0.353207\pi\) | |||||||
\(164\) | −7.96708e40 | −0.844672 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.90646e40 | 0.585135 | ||||||||
\(167\) | 1.87857e41 | 1.42421 | 0.712104 | − | 0.702074i | \(-0.247743\pi\) | ||||
0.712104 | + | 0.702074i | \(0.247743\pi\) | |||||||
\(168\) | 3.97163e39 | 0.0269617 | ||||||||
\(169\) | −1.64249e41 | −0.999076 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.38699e41 | 0.678648 | ||||||||
\(172\) | −3.30477e40 | −0.145166 | ||||||||
\(173\) | −2.98432e41 | −1.17759 | −0.588793 | − | 0.808284i | \(-0.700397\pi\) | ||||
−0.588793 | + | 0.808284i | \(0.700397\pi\) | |||||||
\(174\) | −4.14134e39 | −0.0146886 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.37605e40 | 0.0682136 | ||||||||
\(177\) | −2.27248e39 | −0.00587481 | ||||||||
\(178\) | 1.09670e41 | 0.255457 | ||||||||
\(179\) | 3.46258e41 | 0.727141 | 0.363570 | − | 0.931567i | \(-0.381558\pi\) | ||||
0.363570 | + | 0.931567i | \(0.381558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.05668e41 | 0.693613 | 0.346806 | − | 0.937937i | \(-0.387266\pi\) | ||||
0.346806 | + | 0.937937i | \(0.387266\pi\) | |||||||
\(182\) | 3.21037e40 | 0.0495717 | ||||||||
\(183\) | 3.66740e40 | 0.0511697 | ||||||||
\(184\) | −5.53993e41 | −0.698835 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.89882e40 | 0.0402664 | ||||||||
\(187\) | −5.59384e40 | −0.0523167 | ||||||||
\(188\) | −6.24534e40 | −0.0529220 | ||||||||
\(189\) | 1.68666e41 | 0.129564 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41675e42 | −0.895726 | −0.447863 | − | 0.894102i | \(-0.647815\pi\) | ||||
−0.447863 | + | 0.894102i | \(0.647815\pi\) | |||||||
\(192\) | 2.59175e40 | 0.0148772 | ||||||||
\(193\) | 1.28639e42 | 0.670751 | 0.335375 | − | 0.942085i | \(-0.391137\pi\) | ||||
0.335375 | + | 0.942085i | \(0.391137\pi\) | |||||||
\(194\) | −3.39825e42 | −1.61036 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.01183e42 | 0.396615 | ||||||||
\(197\) | −3.68135e41 | −0.131336 | −0.0656678 | − | 0.997842i | \(-0.520918\pi\) | ||||
−0.0656678 | + | 0.997842i | \(0.520918\pi\) | |||||||
\(198\) | 2.22834e41 | 0.0723894 | ||||||||
\(199\) | 3.12066e42 | 0.923557 | 0.461779 | − | 0.886995i | \(-0.347211\pi\) | ||||
0.461779 | + | 0.886995i | \(0.347211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.92214e41 | −0.0718744 | ||||||||
\(202\) | −6.31044e42 | −1.41599 | ||||||||
\(203\) | 1.35142e42 | 0.276767 | ||||||||
\(204\) | −1.74876e41 | −0.0327019 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.12023e43 | −1.74890 | ||||||||
\(207\) | −1.17478e43 | −1.67689 | ||||||||
\(208\) | −2.83520e41 | −0.0370179 | ||||||||
\(209\) | 3.18990e41 | 0.0381128 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.58037e42 | −0.759391 | −0.379695 | − | 0.925112i | \(-0.623971\pi\) | ||||
−0.379695 | + | 0.925112i | \(0.623971\pi\) | |||||||
\(212\) | −1.15882e43 | −1.06366 | ||||||||
\(213\) | 2.43782e41 | 0.0205106 | ||||||||
\(214\) | −1.44937e42 | −0.111821 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.58765e41 | −0.0427894 | ||||||||
\(217\) | −1.27228e43 | −0.758715 | ||||||||
\(218\) | 1.46781e43 | 0.803941 | ||||||||
\(219\) | 3.23988e41 | 0.0163047 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.67479e41 | 0.0283910 | ||||||||
\(222\) | 1.03317e42 | 0.0404242 | ||||||||
\(223\) | −4.00362e43 | −1.44149 | −0.720747 | − | 0.693198i | \(-0.756201\pi\) | ||||
−0.720747 | + | 0.693198i | \(0.756201\pi\) | |||||||
\(224\) | −4.41431e43 | −1.46310 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.02726e43 | −0.570037 | ||||||||
\(227\) | −3.89322e43 | −1.00886 | −0.504430 | − | 0.863453i | \(-0.668297\pi\) | ||||
−0.504430 | + | 0.863453i | \(0.668297\pi\) | |||||||
\(228\) | 9.97236e41 | 0.0238234 | ||||||||
\(229\) | −3.32118e43 | −0.731704 | −0.365852 | − | 0.930673i | \(-0.619222\pi\) | ||||
−0.365852 | + | 0.930673i | \(0.619222\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.93698e41 | 0.00363332 | ||||||||
\(232\) | −5.27830e42 | −0.0914043 | ||||||||
\(233\) | 7.95672e43 | 1.27248 | 0.636238 | − | 0.771493i | \(-0.280490\pi\) | ||||
0.636238 | + | 0.771493i | \(0.280490\pi\) | |||||||
\(234\) | −2.65894e42 | −0.0392840 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.13383e42 | 0.0774211 | ||||||||
\(237\) | −5.25218e42 | −0.0613049 | ||||||||
\(238\) | 1.41080e44 | 1.52332 | ||||||||
\(239\) | −1.42241e44 | −1.42123 | −0.710615 | − | 0.703581i | \(-0.751583\pi\) | ||||
−0.710615 | + | 0.703581i | \(0.751583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.48641e44 | 1.27299 | 0.636494 | − | 0.771282i | \(-0.280384\pi\) | ||||
0.636494 | + | 0.771282i | \(0.280384\pi\) | |||||||
\(242\) | −1.62846e44 | −1.29180 | ||||||||
\(243\) | −2.09636e43 | −0.154081 | ||||||||
\(244\) | −9.89897e43 | −0.674339 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.41801e43 | 0.0830579 | ||||||||
\(247\) | −3.80632e42 | −0.0206829 | ||||||||
\(248\) | 4.96920e43 | 0.250571 | ||||||||
\(249\) | −4.97227e42 | −0.0232738 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.84398e44 | 0.744377 | 0.372189 | − | 0.928157i | \(-0.378607\pi\) | ||||
0.372189 | + | 0.928157i | \(0.378607\pi\) | |||||||
\(252\) | −2.27328e44 | −0.852595 | ||||||||
\(253\) | −2.70185e43 | −0.0941741 | ||||||||
\(254\) | −5.26801e44 | −1.70696 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.67582e44 | 1.31044 | ||||||||
\(257\) | 2.92391e44 | 0.762433 | 0.381216 | − | 0.924486i | \(-0.375505\pi\) | ||||
0.381216 | + | 0.924486i | \(0.375505\pi\) | |||||||
\(258\) | 5.88196e42 | 0.0142744 | ||||||||
\(259\) | −3.37149e44 | −0.761687 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.11930e44 | −0.219329 | ||||||||
\(262\) | −1.13823e45 | −2.07805 | ||||||||
\(263\) | 4.07317e44 | 0.693029 | 0.346514 | − | 0.938045i | \(-0.387365\pi\) | ||||
0.346514 | + | 0.938045i | \(0.387365\pi\) | |||||||
\(264\) | −7.56533e41 | −0.00119993 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.04510e44 | −1.10974 | ||||||||
\(267\) | −7.89562e42 | −0.0101608 | ||||||||
\(268\) | 7.88740e44 | 0.947196 | ||||||||
\(269\) | −6.06370e44 | −0.679705 | −0.339853 | − | 0.940479i | \(-0.610377\pi\) | ||||
−0.339853 | + | 0.940479i | \(0.610377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.82672e45 | −1.78542 | −0.892711 | − | 0.450630i | \(-0.851200\pi\) | ||||
−0.892711 | + | 0.450630i | \(0.851200\pi\) | |||||||
\(272\) | −1.24593e45 | −1.13754 | ||||||||
\(273\) | −2.31128e42 | −0.00197172 | ||||||||
\(274\) | −1.22637e45 | −0.977766 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.44659e43 | −0.0588659 | ||||||||
\(277\) | −2.33400e45 | −1.52134 | −0.760668 | − | 0.649141i | \(-0.775128\pi\) | ||||
−0.760668 | + | 0.649141i | \(0.775128\pi\) | |||||||
\(278\) | −3.06963e45 | −1.87179 | ||||||||
\(279\) | 1.05375e45 | 0.601257 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00137e45 | −0.500643 | −0.250322 | − | 0.968163i | \(-0.580536\pi\) | ||||
−0.250322 | + | 0.968163i | \(0.580536\pi\) | |||||||
\(282\) | 1.11157e43 | 0.00520390 | ||||||||
\(283\) | 2.73703e45 | 1.20014 | 0.600069 | − | 0.799948i | \(-0.295140\pi\) | ||||
0.600069 | + | 0.799948i | \(0.295140\pi\) | |||||||
\(284\) | −6.58011e44 | −0.270299 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.11525e42 | −0.00220619 | ||||||||
\(287\) | −4.62734e45 | −1.56501 | ||||||||
\(288\) | 3.65609e45 | 1.15946 | ||||||||
\(289\) | −4.28857e44 | −0.127557 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.44655e44 | 0.0640521 | ||||||||
\(292\) | −8.74503e44 | −0.214871 | ||||||||
\(293\) | −1.07452e45 | −0.247836 | −0.123918 | − | 0.992292i | \(-0.539546\pi\) | ||||
−0.123918 | + | 0.992292i | \(0.539546\pi\) | |||||||
\(294\) | −1.80089e44 | −0.0389998 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.31681e45 | 0.251552 | ||||||||
\(297\) | −3.21283e43 | −0.00576625 | ||||||||
\(298\) | −1.67680e45 | −0.282801 | ||||||||
\(299\) | 3.22396e44 | 0.0511060 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.91943e45 | −0.268963 | ||||||||
\(302\) | −6.91215e45 | −0.910930 | ||||||||
\(303\) | 4.54316e44 | 0.0563209 | ||||||||
\(304\) | 7.10494e45 | 0.828704 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.16847e46 | −1.20718 | ||||||||
\(307\) | 1.41267e46 | 1.37398 | 0.686989 | − | 0.726668i | \(-0.258932\pi\) | ||||
0.686989 | + | 0.726668i | \(0.258932\pi\) | |||||||
\(308\) | −5.22826e44 | −0.0478817 | ||||||||
\(309\) | 8.06503e44 | 0.0695624 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.21153e46 | 0.927399 | 0.463700 | − | 0.885992i | \(-0.346522\pi\) | ||||
0.463700 | + | 0.885992i | \(0.346522\pi\) | |||||||
\(312\) | 9.02726e42 | 0.000651172 0 | ||||||||
\(313\) | −8.67864e45 | −0.590040 | −0.295020 | − | 0.955491i | \(-0.595326\pi\) | ||||
−0.295020 | + | 0.955491i | \(0.595326\pi\) | |||||||
\(314\) | −1.83441e46 | −1.17571 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.41766e46 | 0.807906 | ||||||||
\(317\) | 2.34417e46 | 1.26006 | 0.630031 | − | 0.776570i | \(-0.283042\pi\) | ||||
0.630031 | + | 0.776570i | \(0.283042\pi\) | |||||||
\(318\) | 2.06251e45 | 0.104591 | ||||||||
\(319\) | −2.57425e44 | −0.0123175 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.04346e44 | 0.00444768 | ||||||||
\(322\) | 6.81421e46 | 2.74209 | ||||||||
\(323\) | −1.67269e46 | −0.635577 | ||||||||
\(324\) | 1.87778e46 | 0.673849 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.60135e46 | 1.15329 | ||||||||
\(327\) | −1.05674e45 | −0.0319768 | ||||||||
\(328\) | 1.80732e46 | 0.516854 | ||||||||
\(329\) | −3.62734e45 | −0.0980538 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.11187e46 | 1.23527 | 0.617635 | − | 0.786465i | \(-0.288091\pi\) | ||||
0.617635 | + | 0.786465i | \(0.288091\pi\) | |||||||
\(332\) | 1.34211e46 | 0.306713 | ||||||||
\(333\) | 2.79239e46 | 0.603612 | ||||||||
\(334\) | 9.02488e46 | 1.84558 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.31428e45 | 0.0790009 | ||||||||
\(337\) | −2.29819e46 | −0.398320 | −0.199160 | − | 0.979967i | \(-0.563821\pi\) | ||||
−0.199160 | + | 0.979967i | \(0.563821\pi\) | |||||||
\(338\) | −7.89071e46 | −1.29466 | ||||||||
\(339\) | 1.45951e45 | 0.0226732 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.42350e45 | 0.0337666 | ||||||||
\(342\) | 6.66325e46 | 0.879433 | ||||||||
\(343\) | −4.18801e46 | −0.523680 | ||||||||
\(344\) | 7.49680e45 | 0.0888269 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.43370e47 | −1.52599 | ||||||||
\(347\) | 8.38076e46 | 0.845645 | 0.422822 | − | 0.906213i | \(-0.361039\pi\) | ||||
0.422822 | + | 0.906213i | \(0.361039\pi\) | |||||||
\(348\) | −8.04770e44 | −0.00769938 | ||||||||
\(349\) | 1.33845e47 | 1.21432 | 0.607158 | − | 0.794581i | \(-0.292310\pi\) | ||||
0.607158 | + | 0.794581i | \(0.292310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.83368e44 | 0.00312920 | ||||||||
\(352\) | 8.40857e45 | 0.0651153 | ||||||||
\(353\) | −1.44127e46 | −0.105904 | −0.0529520 | − | 0.998597i | \(-0.516863\pi\) | ||||
−0.0529520 | + | 0.998597i | \(0.516863\pi\) | |||||||
\(354\) | −1.09172e45 | −0.00761294 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.13117e46 | 0.133904 | ||||||||
\(357\) | −1.01569e46 | −0.0605900 | ||||||||
\(358\) | 1.66346e47 | 0.942274 | ||||||||
\(359\) | 6.57303e46 | 0.353605 | 0.176802 | − | 0.984246i | \(-0.443425\pi\) | ||||
0.176802 | + | 0.984246i | \(0.443425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.10622e47 | −0.536981 | ||||||||
\(362\) | 1.94888e47 | 0.898826 | ||||||||
\(363\) | 1.17240e46 | 0.0513812 | ||||||||
\(364\) | 6.23858e45 | 0.0259842 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.76186e46 | 0.0663088 | ||||||||
\(367\) | −2.16797e47 | −0.775768 | −0.387884 | − | 0.921708i | \(-0.626794\pi\) | ||||
−0.387884 | + | 0.921708i | \(0.626794\pi\) | |||||||
\(368\) | −6.01789e47 | −2.04767 | ||||||||
\(369\) | 3.83253e47 | 1.24022 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.73051e47 | −1.97074 | ||||||||
\(372\) | 7.57641e45 | 0.0211066 | ||||||||
\(373\) | −2.47528e47 | −0.656163 | −0.328081 | − | 0.944649i | \(-0.606402\pi\) | ||||
−0.328081 | + | 0.944649i | \(0.606402\pi\) | |||||||
\(374\) | −2.68734e46 | −0.0677952 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.41674e46 | 0.0323829 | ||||||||
\(377\) | 3.07170e45 | 0.00668442 | ||||||||
\(378\) | 8.10293e46 | 0.167897 | ||||||||
\(379\) | 1.02737e47 | 0.202722 | 0.101361 | − | 0.994850i | \(-0.467680\pi\) | ||||
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.79267e46 | 0.0678943 | ||||||||
\(382\) | −6.80622e47 | −1.16074 | ||||||||
\(383\) | 1.22188e48 | 1.98541 | 0.992706 | − | 0.120559i | \(-0.0384687\pi\) | ||||
0.992706 | + | 0.120559i | \(0.0384687\pi\) | |||||||
\(384\) | −2.62487e46 | −0.0406424 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.17995e47 | 0.869200 | ||||||||
\(387\) | 1.58975e47 | 0.213145 | ||||||||
\(388\) | −6.60368e47 | −0.844110 | ||||||||
\(389\) | −1.16416e48 | −1.41888 | −0.709440 | − | 0.704766i | \(-0.751052\pi\) | ||||
−0.709440 | + | 0.704766i | \(0.751052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.41677e48 | 1.57047 | ||||||||
\(392\) | −2.29531e47 | −0.242688 | ||||||||
\(393\) | 8.19461e46 | 0.0826544 | ||||||||
\(394\) | −1.76857e47 | −0.170193 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.33024e46 | 0.0379447 | ||||||||
\(397\) | 1.33628e48 | 1.11756 | 0.558781 | − | 0.829315i | \(-0.311269\pi\) | ||||
0.558781 | + | 0.829315i | \(0.311269\pi\) | |||||||
\(398\) | 1.49920e48 | 1.19680 | ||||||||
\(399\) | 5.79202e46 | 0.0441399 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.54007e47 | 0.176472 | 0.0882358 | − | 0.996100i | \(-0.471877\pi\) | ||||
0.0882358 | + | 0.996100i | \(0.471877\pi\) | |||||||
\(402\) | −1.40383e47 | −0.0931393 | ||||||||
\(403\) | −2.89182e46 | −0.0183243 | ||||||||
\(404\) | −1.22628e48 | −0.742225 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.49240e47 | 0.358652 | ||||||||
\(407\) | 6.42216e46 | 0.0338988 | ||||||||
\(408\) | 3.96703e46 | 0.0200102 | ||||||||
\(409\) | −1.33788e48 | −0.644967 | −0.322484 | − | 0.946575i | \(-0.604518\pi\) | ||||
−0.322484 | + | 0.946575i | \(0.604518\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.82915e46 | 0.0388906 | ||||||||
\(412\) | −2.17690e48 | −0.916727 | ||||||||
\(413\) | 3.56257e47 | 0.143446 | ||||||||
\(414\) | −5.64377e48 | −2.17302 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00334e47 | −0.0353365 | ||||||||
\(417\) | 2.20996e47 | 0.0744505 | ||||||||
\(418\) | 1.53247e47 | 0.0493889 | ||||||||
\(419\) | 2.08239e48 | 0.642101 | 0.321050 | − | 0.947062i | \(-0.395964\pi\) | ||||
0.321050 | + | 0.947062i | \(0.395964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.42178e48 | −1.24847 | −0.624236 | − | 0.781236i | \(-0.714590\pi\) | ||||
−0.624236 | + | 0.781236i | \(0.714590\pi\) | |||||||
\(422\) | −3.64170e48 | −0.984065 | ||||||||
\(423\) | 3.00430e47 | 0.0777045 | ||||||||
\(424\) | 2.62876e48 | 0.650851 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.17116e47 | 0.0265789 | ||||||||
\(427\) | −5.74940e48 | −1.24941 | ||||||||
\(428\) | −2.81650e47 | −0.0586138 | ||||||||
\(429\) | 4.40263e44 | 8.77511e−5 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.37175e48 | 0.616631 | 0.308315 | − | 0.951284i | \(-0.400235\pi\) | ||||
0.308315 | + | 0.951284i | \(0.400235\pi\) | |||||||
\(432\) | −7.15601e47 | −0.125378 | ||||||||
\(433\) | −2.37577e48 | −0.398822 | −0.199411 | − | 0.979916i | \(-0.563903\pi\) | ||||
−0.199411 | + | 0.979916i | \(0.563903\pi\) | |||||||
\(434\) | −6.11220e48 | −0.983190 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.85233e48 | 0.421405 | ||||||||
\(437\) | −8.07916e48 | −1.14409 | ||||||||
\(438\) | 1.55648e47 | 0.0211286 | ||||||||
\(439\) | −2.31976e48 | −0.301890 | −0.150945 | − | 0.988542i | \(-0.548232\pi\) | ||||
−0.150945 | + | 0.988542i | \(0.548232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.86736e48 | −0.582344 | ||||||||
\(442\) | 3.20665e47 | 0.0367908 | ||||||||
\(443\) | 1.52174e49 | 1.67444 | 0.837222 | − | 0.546864i | \(-0.184178\pi\) | ||||
0.837222 | + | 0.546864i | \(0.184178\pi\) | |||||||
\(444\) | 2.00771e47 | 0.0211893 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.92339e49 | −1.86798 | ||||||||
\(447\) | 1.20720e47 | 0.0112484 | ||||||||
\(448\) | −4.06311e48 | −0.363258 | ||||||||
\(449\) | 1.92781e49 | 1.65390 | 0.826948 | − | 0.562279i | \(-0.190075\pi\) | ||||
0.826948 | + | 0.562279i | \(0.190075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.81436e47 | 0.0696506 | ||||||||
\(452\) | −3.93949e48 | −0.298799 | ||||||||
\(453\) | 4.97636e47 | 0.0362322 | ||||||||
\(454\) | −1.87035e49 | −1.30734 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.26221e47 | −0.0145775 | ||||||||
\(457\) | −1.19646e49 | −0.740367 | −0.370183 | − | 0.928959i | \(-0.620705\pi\) | ||||
−0.370183 | + | 0.928959i | \(0.620705\pi\) | |||||||
\(458\) | −1.59553e49 | −0.948187 | ||||||||
\(459\) | 1.68471e48 | 0.0961591 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.78549e49 | −1.46702 | −0.733508 | − | 0.679680i | \(-0.762119\pi\) | ||||
−0.733508 | + | 0.679680i | \(0.762119\pi\) | |||||||
\(462\) | 9.30548e46 | 0.00470828 | ||||||||
\(463\) | 1.11920e49 | 0.544075 | 0.272038 | − | 0.962287i | \(-0.412303\pi\) | ||||
0.272038 | + | 0.962287i | \(0.412303\pi\) | |||||||
\(464\) | −5.73369e48 | −0.267825 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.82250e49 | 1.64895 | ||||||||
\(467\) | 1.63248e49 | 0.676840 | 0.338420 | − | 0.940995i | \(-0.390108\pi\) | ||||
0.338420 | + | 0.940995i | \(0.390108\pi\) | |||||||
\(468\) | −5.16702e47 | −0.0205917 | ||||||||
\(469\) | 4.58106e49 | 1.75497 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32067e48 | 0.0467637 | ||||||||
\(472\) | −1.39145e48 | −0.0473739 | ||||||||
\(473\) | 3.65622e47 | 0.0119702 | ||||||||
\(474\) | −2.52321e48 | −0.0794427 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.74154e49 | 0.798485 | ||||||||
\(477\) | 5.57445e49 | 1.56175 | ||||||||
\(478\) | −6.83344e49 | −1.84172 | ||||||||
\(479\) | 2.63654e49 | 0.683639 | 0.341820 | − | 0.939766i | \(-0.388957\pi\) | ||||
0.341820 | + | 0.939766i | \(0.388957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.66319e47 | −0.0183961 | ||||||||
\(482\) | 7.14090e49 | 1.64962 | ||||||||
\(483\) | −4.90585e48 | −0.109067 | ||||||||
\(484\) | −3.16453e49 | −0.677127 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00712e49 | −0.199668 | ||||||||
\(487\) | 7.78447e49 | 1.48574 | 0.742871 | − | 0.669435i | \(-0.233464\pi\) | ||||
0.742871 | + | 0.669435i | \(0.233464\pi\) | |||||||
\(488\) | 2.24556e49 | 0.412628 | ||||||||
\(489\) | −2.59277e48 | −0.0458723 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.85282e49 | 1.61642 | 0.808208 | − | 0.588897i | \(-0.200438\pi\) | ||||
0.808208 | + | 0.588897i | \(0.200438\pi\) | |||||||
\(492\) | 2.75557e48 | 0.0435368 | ||||||||
\(493\) | 1.34986e49 | 0.205409 | ||||||||
\(494\) | −1.82860e48 | −0.0268022 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.39792e49 | 0.734201 | ||||||||
\(497\) | −3.82178e49 | −0.500809 | ||||||||
\(498\) | −2.38874e48 | −0.0301596 | ||||||||
\(499\) | 1.25338e50 | 1.52483 | 0.762415 | − | 0.647088i | \(-0.224013\pi\) | ||||
0.762415 | + | 0.647088i | \(0.224013\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.49741e48 | −0.0734078 | ||||||||
\(502\) | 8.85871e49 | 0.964610 | ||||||||
\(503\) | 1.11020e50 | 1.16518 | 0.582589 | − | 0.812767i | \(-0.302040\pi\) | ||||
0.582589 | + | 0.812767i | \(0.302040\pi\) | |||||||
\(504\) | 5.15688e49 | 0.521702 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.29800e49 | −0.122037 | ||||||||
\(507\) | 5.68087e48 | 0.0514953 | ||||||||
\(508\) | −1.02371e50 | −0.894745 | ||||||||
\(509\) | −1.38813e50 | −1.16991 | −0.584955 | − | 0.811066i | \(-0.698888\pi\) | ||||
−0.584955 | + | 0.811066i | \(0.698888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.07918e49 | −0.398114 | ||||||||
\(512\) | 1.20327e50 | 0.909639 | ||||||||
\(513\) | −9.60711e48 | −0.0700521 | ||||||||
\(514\) | 1.40468e50 | 0.988007 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.14302e48 | 0.00748228 | ||||||||
\(517\) | 6.90952e47 | 0.00436388 | ||||||||
\(518\) | −1.61970e50 | −0.987041 | ||||||||
\(519\) | 1.03219e49 | 0.0606962 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.33871e50 | −1.28079 | −0.640396 | − | 0.768045i | \(-0.721230\pi\) | ||||
−0.640396 | + | 0.768045i | \(0.721230\pi\) | |||||||
\(522\) | −5.37724e49 | −0.284220 | ||||||||
\(523\) | 1.30285e50 | 0.664679 | 0.332340 | − | 0.943160i | \(-0.392162\pi\) | ||||
0.332340 | + | 0.943160i | \(0.392162\pi\) | |||||||
\(524\) | −2.21188e50 | −1.08926 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.95680e50 | 0.898070 | ||||||||
\(527\) | −1.27081e50 | −0.563098 | ||||||||
\(528\) | −8.21803e47 | −0.00351593 | ||||||||
\(529\) | 4.42241e50 | 1.82696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.95065e49 | −0.113676 | ||||||||
\(532\) | −1.56337e50 | −0.581698 | ||||||||
\(533\) | −1.05177e49 | −0.0377977 | ||||||||
\(534\) | −3.79315e48 | −0.0131670 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.78924e50 | −0.579589 | ||||||||
\(537\) | −1.19760e49 | −0.0374789 | ||||||||
\(538\) | −2.91307e50 | −0.880804 | ||||||||
\(539\) | −1.11943e49 | −0.0327044 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.31273e50 | −1.44933 | −0.724667 | − | 0.689099i | \(-0.758007\pi\) | ||||
−0.724667 | + | 0.689099i | \(0.758007\pi\) | |||||||
\(542\) | −8.77579e50 | −2.31366 | ||||||||
\(543\) | −1.40308e49 | −0.0357508 | ||||||||
\(544\) | −4.40920e50 | −1.08588 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.11037e48 | −0.00255507 | ||||||||
\(547\) | 7.47732e49 | 0.166334 | 0.0831669 | − | 0.996536i | \(-0.473497\pi\) | ||||
0.0831669 | + | 0.996536i | \(0.473497\pi\) | |||||||
\(548\) | −2.38315e50 | −0.512520 | ||||||||
\(549\) | 4.76186e50 | 0.990121 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.69761e49 | −0.149641 | ||||||||
\(552\) | 1.91609e49 | 0.0360200 | ||||||||
\(553\) | 8.23388e50 | 1.49689 | ||||||||
\(554\) | −1.12128e51 | −1.97144 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.96509e50 | −0.981146 | ||||||||
\(557\) | −3.60496e50 | −0.573560 | −0.286780 | − | 0.957996i | \(-0.592585\pi\) | ||||
−0.286780 | + | 0.957996i | \(0.592585\pi\) | |||||||
\(558\) | 5.06234e50 | 0.779146 | ||||||||
\(559\) | −4.36275e48 | −0.00649594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.93474e48 | 0.00269655 | ||||||||
\(562\) | −4.81071e50 | −0.648764 | ||||||||
\(563\) | 3.94055e50 | 0.514223 | 0.257112 | − | 0.966382i | \(-0.417229\pi\) | ||||
0.257112 | + | 0.966382i | \(0.417229\pi\) | |||||||
\(564\) | 2.16007e48 | 0.00272775 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.31490e51 | 1.55521 | ||||||||
\(567\) | 1.09063e51 | 1.24851 | ||||||||
\(568\) | 1.49268e50 | 0.165396 | ||||||||
\(569\) | −1.14686e50 | −0.123008 | −0.0615040 | − | 0.998107i | \(-0.519590\pi\) | ||||
−0.0615040 | + | 0.998107i | \(0.519590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.48184e51 | 1.48948 | 0.744739 | − | 0.667356i | \(-0.232574\pi\) | ||||
0.744739 | + | 0.667356i | \(0.232574\pi\) | |||||||
\(572\) | −1.18835e48 | −0.00115643 | ||||||||
\(573\) | 4.90010e49 | 0.0461683 | ||||||||
\(574\) | −2.22303e51 | −2.02803 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.36521e50 | 0.287870 | ||||||||
\(577\) | −1.51306e51 | −1.25344 | −0.626722 | − | 0.779243i | \(-0.715604\pi\) | ||||
−0.626722 | + | 0.779243i | \(0.715604\pi\) | |||||||
\(578\) | −2.06028e50 | −0.165296 | ||||||||
\(579\) | −4.44922e49 | −0.0345725 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.79505e50 | 0.568278 | ||||||||
\(582\) | 1.17535e50 | 0.0830027 | ||||||||
\(583\) | 1.28206e50 | 0.0877079 | ||||||||
\(584\) | 1.98379e50 | 0.131480 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.16213e50 | −0.321161 | ||||||||
\(587\) | −8.72797e50 | −0.526148 | −0.263074 | − | 0.964776i | \(-0.584736\pi\) | ||||
−0.263074 | + | 0.964776i | \(0.584736\pi\) | |||||||
\(588\) | −3.49960e49 | −0.0204427 | ||||||||
\(589\) | 7.24683e50 | 0.410218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.27327e49 | 0.00676942 | ||||||||
\(592\) | 1.43042e51 | 0.737077 | ||||||||
\(593\) | −4.58679e49 | −0.0229085 | −0.0114543 | − | 0.999934i | \(-0.503646\pi\) | ||||
−0.0114543 | + | 0.999934i | \(0.503646\pi\) | |||||||
\(594\) | −1.54348e49 | −0.00747226 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.25846e50 | −0.148237 | ||||||||
\(597\) | −1.07934e50 | −0.0476028 | ||||||||
\(598\) | 1.54883e50 | 0.0662263 | ||||||||
\(599\) | −2.10919e51 | −0.874420 | −0.437210 | − | 0.899360i | \(-0.644033\pi\) | ||||
−0.437210 | + | 0.899360i | \(0.644033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.46594e51 | −0.961179 | −0.480589 | − | 0.876946i | \(-0.659577\pi\) | ||||
−0.480589 | + | 0.876946i | \(0.659577\pi\) | |||||||
\(602\) | −9.22119e50 | −0.348539 | ||||||||
\(603\) | −3.79420e51 | −1.39075 | ||||||||
\(604\) | −1.34321e51 | −0.477486 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.18259e50 | 0.0729841 | ||||||||
\(607\) | 4.33541e51 | 1.40618 | 0.703088 | − | 0.711103i | \(-0.251804\pi\) | ||||
0.703088 | + | 0.711103i | \(0.251804\pi\) | |||||||
\(608\) | 2.51436e51 | 0.791063 | ||||||||
\(609\) | −4.67416e49 | −0.0142654 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.24472e48 | −0.00236817 | ||||||||
\(612\) | −2.27065e51 | −0.632773 | ||||||||
\(613\) | 1.36136e51 | 0.368091 | 0.184046 | − | 0.982918i | \(-0.441081\pi\) | ||||
0.184046 | + | 0.982918i | \(0.441081\pi\) | |||||||
\(614\) | 6.78662e51 | 1.78049 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.18602e50 | 0.0292988 | ||||||||
\(617\) | −3.77980e51 | −0.906136 | −0.453068 | − | 0.891476i | \(-0.649671\pi\) | ||||
−0.453068 | + | 0.891476i | \(0.649671\pi\) | |||||||
\(618\) | 3.87454e50 | 0.0901432 | ||||||||
\(619\) | 6.56261e50 | 0.148183 | 0.0740917 | − | 0.997251i | \(-0.476394\pi\) | ||||
0.0740917 | + | 0.997251i | \(0.476394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.13722e50 | 0.173094 | ||||||||
\(622\) | 5.82033e51 | 1.20178 | ||||||||
\(623\) | 1.23780e51 | 0.248097 | ||||||||
\(624\) | 9.80609e48 | 0.00190801 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.16932e51 | −0.764610 | ||||||||
\(627\) | −1.10329e49 | −0.00196445 | ||||||||
\(628\) | −3.56474e51 | −0.616275 | ||||||||
\(629\) | −3.36759e51 | −0.565304 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.19436e51 | 0.505640 | 0.252820 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252820 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(632\) | −3.21593e51 | −0.494357 | ||||||||
\(633\) | 2.62182e50 | 0.0391412 | ||||||||
\(634\) | 1.12617e52 | 1.63287 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.00800e50 | 0.0548240 | ||||||||
\(637\) | 1.33575e50 | 0.0177479 | ||||||||
\(638\) | −1.23670e50 | −0.0159618 | ||||||||
\(639\) | 3.16534e51 | 0.396875 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.48064e52 | −1.75217 | −0.876085 | − | 0.482157i | \(-0.839853\pi\) | ||||
−0.876085 | + | 0.482157i | \(0.839853\pi\) | |||||||
\(642\) | 5.01292e49 | 0.00576358 | ||||||||
\(643\) | −6.82003e51 | −0.761874 | −0.380937 | − | 0.924601i | \(-0.624399\pi\) | ||||
−0.380937 | + | 0.924601i | \(0.624399\pi\) | |||||||
\(644\) | 1.32418e52 | 1.43733 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.03579e51 | −0.823620 | ||||||||
\(647\) | 2.43296e51 | 0.242329 | 0.121165 | − | 0.992632i | \(-0.461337\pi\) | ||||
0.121165 | + | 0.992632i | \(0.461337\pi\) | |||||||
\(648\) | −4.25971e51 | −0.412328 | ||||||||
\(649\) | −6.78614e49 | −0.00638405 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.40044e50 | 0.0391064 | ||||||||
\(652\) | 6.99837e51 | 0.604528 | ||||||||
\(653\) | −5.92349e51 | −0.497375 | −0.248687 | − | 0.968584i | \(-0.579999\pi\) | ||||
−0.248687 | + | 0.968584i | \(0.579999\pi\) | |||||||
\(654\) | −5.07670e50 | −0.0414375 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.96324e52 | 1.51444 | ||||||||
\(657\) | 4.20676e51 | 0.315492 | ||||||||
\(658\) | −1.74262e51 | −0.127064 | ||||||||
\(659\) | 2.77432e51 | 0.196687 | 0.0983437 | − | 0.995153i | \(-0.468646\pi\) | ||||
0.0983437 | + | 0.995153i | \(0.468646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.53847e52 | 1.03124 | 0.515622 | − | 0.856816i | \(-0.327561\pi\) | ||||
0.515622 | + | 0.856816i | \(0.327561\pi\) | |||||||
\(662\) | 2.45580e52 | 1.60074 | ||||||||
\(663\) | −2.30861e49 | −0.00146336 | ||||||||
\(664\) | −3.04454e51 | −0.187677 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.34150e52 | 0.782198 | ||||||||
\(667\) | 6.51988e51 | 0.369753 | ||||||||
\(668\) | 1.75377e52 | 0.967404 | ||||||||
\(669\) | 1.38473e51 | 0.0742988 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09517e51 | 0.0556051 | ||||||||
\(672\) | 1.52678e51 | 0.0754125 | ||||||||
\(673\) | 8.54768e50 | 0.0410742 | 0.0205371 | − | 0.999789i | \(-0.493462\pi\) | ||||
0.0205371 | + | 0.999789i | \(0.493462\pi\) | |||||||
\(674\) | −1.10408e52 | −0.516168 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.53337e52 | −0.678630 | ||||||||
\(677\) | 3.33629e52 | 1.43673 | 0.718363 | − | 0.695669i | \(-0.244892\pi\) | ||||
0.718363 | + | 0.695669i | \(0.244892\pi\) | |||||||
\(678\) | 7.01167e50 | 0.0293814 | ||||||||
\(679\) | −3.83547e52 | −1.56397 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.34655e51 | 0.0519996 | ||||||||
\(682\) | 1.16428e51 | 0.0437568 | ||||||||
\(683\) | −3.41377e52 | −1.24868 | −0.624340 | − | 0.781153i | \(-0.714632\pi\) | ||||
−0.624340 | + | 0.781153i | \(0.714632\pi\) | |||||||
\(684\) | 1.29484e52 | 0.460977 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.01197e52 | −0.678618 | ||||||||
\(687\) | 1.14869e51 | 0.0377142 | ||||||||
\(688\) | 8.14359e51 | 0.260273 | ||||||||
\(689\) | −1.52980e51 | −0.0475970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.92716e52 | 1.74784 | 0.873922 | − | 0.486066i | \(-0.161569\pi\) | ||||
0.873922 | + | 0.486066i | \(0.161569\pi\) | |||||||
\(692\) | −2.78606e52 | −0.799884 | ||||||||
\(693\) | 2.51504e51 | 0.0703039 | ||||||||
\(694\) | 4.02621e52 | 1.09584 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.82560e50 | 0.00471124 | ||||||||
\(697\) | −4.62198e52 | −1.16151 | ||||||||
\(698\) | 6.43007e52 | 1.57359 | ||||||||
\(699\) | −2.75199e51 | −0.0655871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.09077e52 | 0.924744 | 0.462372 | − | 0.886686i | \(-0.346998\pi\) | ||||
0.462372 | + | 0.886686i | \(0.346998\pi\) | |||||||
\(702\) | 1.84174e50 | 0.00405502 | ||||||||
\(703\) | 1.92038e52 | 0.411825 | ||||||||
\(704\) | 7.73958e50 | 0.0161668 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.92401e51 | −0.137237 | ||||||||
\(707\) | −7.12235e52 | −1.37519 | ||||||||
\(708\) | −2.12150e50 | −0.00399051 | ||||||||
\(709\) | −8.44115e52 | −1.54684 | −0.773422 | − | 0.633891i | \(-0.781457\pi\) | ||||
−0.773422 | + | 0.633891i | \(0.781457\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.81960e52 | −1.18624 | ||||||||
\(712\) | −4.83452e51 | −0.0819357 | ||||||||
\(713\) | −6.13807e52 | −1.01362 | ||||||||
\(714\) | −4.87951e51 | −0.0785162 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.23254e52 | 0.493916 | ||||||||
\(717\) | 4.91969e51 | 0.0732544 | ||||||||
\(718\) | 3.15776e52 | 0.458223 | ||||||||
\(719\) | −2.81946e52 | −0.398733 | −0.199367 | − | 0.979925i | \(-0.563888\pi\) | ||||
−0.199367 | + | 0.979925i | \(0.563888\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.26436e53 | −1.69851 | ||||||||
\(722\) | −5.31442e52 | −0.695853 | ||||||||
\(723\) | −5.14105e51 | −0.0656135 | ||||||||
\(724\) | 3.78717e52 | 0.471142 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.63236e51 | 0.0665830 | ||||||||
\(727\) | −6.98427e52 | −0.804886 | −0.402443 | − | 0.915445i | \(-0.631839\pi\) | ||||
−0.402443 | + | 0.915445i | \(0.631839\pi\) | |||||||
\(728\) | −1.41521e51 | −0.0158997 | ||||||||
\(729\) | −8.98455e52 | −0.984095 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.91721e52 | −0.199618 | ||||||||
\(732\) | 3.42375e51 | 0.0347574 | ||||||||
\(733\) | −3.54513e52 | −0.350921 | −0.175460 | − | 0.984487i | \(-0.556141\pi\) | ||||
−0.175460 | + | 0.984487i | \(0.556141\pi\) | |||||||
\(734\) | −1.04152e53 | −1.00529 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.12966e53 | −1.95466 | ||||||||
\(737\) | −8.72620e51 | −0.0781046 | ||||||||
\(738\) | 1.84119e53 | 1.60715 | ||||||||
\(739\) | 1.51689e53 | 1.29131 | 0.645655 | − | 0.763629i | \(-0.276584\pi\) | ||||
0.645655 | + | 0.763629i | \(0.276584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31649e50 | 0.00106606 | ||||||||
\(742\) | −3.23341e53 | −2.55381 | ||||||||
\(743\) | −1.52901e53 | −1.17793 | −0.588964 | − | 0.808159i | \(-0.700464\pi\) | ||||
−0.588964 | + | 0.808159i | \(0.700464\pi\) | |||||||
\(744\) | −1.71869e51 | −0.0129151 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.18916e53 | −0.850296 | ||||||||
\(747\) | −6.45615e52 | −0.450342 | ||||||||
\(748\) | −5.22221e51 | −0.0355365 | ||||||||
\(749\) | −1.63584e52 | −0.108600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.42568e53 | 0.900916 | 0.450458 | − | 0.892798i | \(-0.351261\pi\) | ||||
0.450458 | + | 0.892798i | \(0.351261\pi\) | |||||||
\(752\) | 1.53897e52 | 0.0948858 | ||||||||
\(753\) | −6.37778e51 | −0.0383674 | ||||||||
\(754\) | 1.47568e51 | 0.00866209 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.57461e52 | 0.0880075 | ||||||||
\(757\) | 2.82784e53 | 1.54234 | 0.771171 | − | 0.636628i | \(-0.219671\pi\) | ||||
0.771171 | + | 0.636628i | \(0.219671\pi\) | |||||||
\(758\) | 4.93559e52 | 0.262699 | ||||||||
\(759\) | 9.34487e50 | 0.00485401 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.71288e52 | 0.183694 | 0.0918470 | − | 0.995773i | \(-0.470723\pi\) | ||||
0.0918470 | + | 0.995773i | \(0.470723\pi\) | |||||||
\(762\) | 1.82204e52 | 0.0879817 | ||||||||
\(763\) | 1.65666e53 | 0.780780 | ||||||||
\(764\) | −1.32263e53 | −0.608429 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.87005e53 | 2.57282 | ||||||||
\(767\) | 8.09750e50 | 0.00346447 | ||||||||
\(768\) | −1.61722e52 | −0.0675441 | ||||||||
\(769\) | −6.15158e52 | −0.250813 | −0.125406 | − | 0.992105i | \(-0.540023\pi\) | ||||
−0.125406 | + | 0.992105i | \(0.540023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.01129e52 | −0.0392980 | ||||||||
\(772\) | 1.20093e53 | 0.455613 | ||||||||
\(773\) | 2.28656e53 | 0.846960 | 0.423480 | − | 0.905905i | \(-0.360808\pi\) | ||||
0.423480 | + | 0.905905i | \(0.360808\pi\) | |||||||
\(774\) | 7.63732e52 | 0.276206 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.49803e53 | 0.516510 | ||||||||
\(777\) | 1.16610e52 | 0.0392596 | ||||||||
\(778\) | −5.59277e53 | −1.83867 | ||||||||
\(779\) | 2.63570e53 | 0.846161 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.27989e51 | 0.0222885 | ||||||||
\(782\) | 6.80632e53 | 2.03511 | ||||||||
\(783\) | 7.75294e51 | 0.0226399 | ||||||||
\(784\) | −2.49334e53 | −0.711106 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.93679e52 | 0.107109 | ||||||||
\(787\) | −7.05791e52 | −0.187561 | −0.0937807 | − | 0.995593i | \(-0.529895\pi\) | ||||
−0.0937807 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(788\) | −3.43678e52 | −0.0892108 | ||||||||
\(789\) | −1.40879e52 | −0.0357207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.28809e53 | −0.553614 | ||||||||
\(792\) | −9.82306e51 | −0.0232183 | ||||||||
\(793\) | −1.30680e52 | −0.0301756 | ||||||||
\(794\) | 6.41963e53 | 1.44821 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.91333e53 | 0.627334 | ||||||||
\(797\) | 8.88567e53 | 1.86944 | 0.934719 | − | 0.355387i | \(-0.115651\pi\) | ||||
0.934719 | + | 0.355387i | \(0.115651\pi\) | |||||||
\(798\) | 2.78256e52 | 0.0571993 | ||||||||
\(799\) | −3.62314e52 | −0.0727729 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.02519e53 | −0.196609 | ||||||||
\(802\) | 1.22028e53 | 0.228683 | ||||||||
\(803\) | 9.67504e51 | 0.0177180 | ||||||||
\(804\) | −2.72801e52 | −0.0488213 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.38926e52 | −0.0237458 | ||||||||
\(807\) | 2.09725e52 | 0.0350340 | ||||||||
\(808\) | 2.78180e53 | 0.454167 | ||||||||
\(809\) | 3.72232e53 | 0.593972 | 0.296986 | − | 0.954882i | \(-0.404019\pi\) | ||||
0.296986 | + | 0.954882i | \(0.404019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.96718e53 | −0.909668 | −0.454834 | − | 0.890576i | \(-0.650301\pi\) | ||||
−0.454834 | + | 0.890576i | \(0.650301\pi\) | |||||||
\(812\) | 1.26164e53 | 0.187996 | ||||||||
\(813\) | 6.31808e52 | 0.0920259 | ||||||||
\(814\) | 3.08528e52 | 0.0439282 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.30929e52 | 0.0586324 | ||||||||
\(817\) | 1.09330e53 | 0.145422 | ||||||||
\(818\) | −6.42736e53 | −0.835788 | ||||||||
\(819\) | −3.00104e52 | −0.0381522 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.74697e52 | 0.106294 | 0.0531471 | − | 0.998587i | \(-0.483075\pi\) | ||||
0.0531471 | + | 0.998587i | \(0.483075\pi\) | |||||||
\(822\) | 4.24163e52 | 0.0503969 | ||||||||
\(823\) | −1.05135e54 | −1.22138 | −0.610692 | − | 0.791869i | \(-0.709108\pi\) | ||||
−0.610692 | + | 0.791869i | \(0.709108\pi\) | |||||||
\(824\) | 4.93825e53 | 0.560945 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.71150e53 | 0.185886 | ||||||||
\(827\) | 1.54483e53 | 0.164069 | 0.0820347 | − | 0.996629i | \(-0.473858\pi\) | ||||
0.0820347 | + | 0.996629i | \(0.473858\pi\) | |||||||
\(828\) | −1.09673e54 | −1.13904 | ||||||||
\(829\) | 2.69934e53 | 0.274156 | 0.137078 | − | 0.990560i | \(-0.456229\pi\) | ||||
0.137078 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.07259e52 | 0.0784141 | ||||||||
\(832\) | −9.23518e51 | −0.00877332 | ||||||||
\(833\) | 5.86997e53 | 0.545385 | ||||||||
\(834\) | 1.06169e53 | 0.0964776 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.97798e52 | 0.0258884 | ||||||||
\(837\) | −7.29891e52 | −0.0620636 | ||||||||
\(838\) | 1.00041e54 | 0.832074 | ||||||||
\(839\) | 2.43290e54 | 1.97937 | 0.989686 | − | 0.143252i | \(-0.0457561\pi\) | ||||
0.989686 | + | 0.143252i | \(0.0457561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22236e54 | −0.951638 | ||||||||
\(842\) | −2.12428e54 | −1.61785 | ||||||||
\(843\) | 3.46344e52 | 0.0258046 | ||||||||
\(844\) | −7.07677e53 | −0.515822 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.44330e53 | 0.100694 | ||||||||
\(847\) | −1.83798e54 | −1.25458 | ||||||||
\(848\) | 2.85555e54 | 1.90707 | ||||||||
\(849\) | −9.46656e52 | −0.0618586 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.62656e54 | −1.01759 | ||||||||
\(852\) | 2.27586e52 | 0.0139320 | ||||||||
\(853\) | −9.59321e53 | −0.574654 | −0.287327 | − | 0.957832i | \(-0.592767\pi\) | ||||
−0.287327 | + | 0.957832i | \(0.592767\pi\) | |||||||
\(854\) | −2.76208e54 | −1.61907 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.38917e52 | 0.0358657 | ||||||||
\(857\) | −3.59352e52 | −0.0197413 | −0.00987063 | − | 0.999951i | \(-0.503142\pi\) | ||||
−0.00987063 | + | 0.999951i | \(0.503142\pi\) | |||||||
\(858\) | 2.11508e50 | 0.000113713 0 | ||||||||
\(859\) | 8.55580e53 | 0.450181 | 0.225091 | − | 0.974338i | \(-0.427732\pi\) | ||||
0.225091 | + | 0.974338i | \(0.427732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.60046e53 | 0.0806651 | ||||||||
\(862\) | 1.61983e54 | 0.799068 | ||||||||
\(863\) | −1.56057e54 | −0.753502 | −0.376751 | − | 0.926315i | \(-0.622959\pi\) | ||||
−0.376751 | + | 0.926315i | \(0.622959\pi\) | |||||||
\(864\) | −2.53243e53 | −0.119683 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.14135e54 | −0.516818 | ||||||||
\(867\) | 1.48329e52 | 0.00657464 | ||||||||
\(868\) | −1.18776e54 | −0.515363 | ||||||||
\(869\) | −1.56842e53 | −0.0666190 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.04125e53 | 0.0423855 | ||||||||
\(872\) | −6.47046e53 | −0.257858 | ||||||||
\(873\) | 3.17667e54 | 1.23939 | ||||||||
\(874\) | −3.88132e54 | −1.48258 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.02464e52 | 0.0110751 | ||||||||
\(877\) | 3.37270e54 | 1.20916 | 0.604581 | − | 0.796544i | \(-0.293341\pi\) | ||||
0.604581 | + | 0.796544i | \(0.293341\pi\) | |||||||
\(878\) | −1.11444e54 | −0.391208 | ||||||||
\(879\) | 3.71644e52 | 0.0127742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.67513e54 | 0.552069 | 0.276034 | − | 0.961148i | \(-0.410980\pi\) | ||||
0.276034 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(882\) | −2.33834e54 | −0.754637 | ||||||||
\(883\) | −1.42002e54 | −0.448767 | −0.224383 | − | 0.974501i | \(-0.572037\pi\) | ||||
−0.224383 | + | 0.974501i | \(0.572037\pi\) | |||||||
\(884\) | 6.23135e52 | 0.0192848 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.31060e54 | 2.16985 | ||||||||
\(887\) | −1.98874e54 | −0.578085 | −0.289042 | − | 0.957316i | \(-0.593337\pi\) | ||||
−0.289042 | + | 0.957316i | \(0.593337\pi\) | |||||||
\(888\) | −4.55446e52 | −0.0129657 | ||||||||
\(889\) | −5.94580e54 | −1.65778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.07748e53 | −0.0555647 | ||||||||
\(892\) | −3.73764e54 | −0.979147 | ||||||||
\(893\) | 2.06611e53 | 0.0530153 | ||||||||
\(894\) | 5.79955e52 | 0.0145764 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.11502e54 | 0.992370 | ||||||||
\(897\) | −1.11507e52 | −0.00263415 | ||||||||
\(898\) | 9.26145e54 | 2.14322 | ||||||||
\(899\) | −5.84819e53 | −0.132577 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.72271e54 | −1.46263 | ||||||||
\(902\) | 4.23452e53 | 0.0902575 | ||||||||
\(903\) | 6.63874e52 | 0.0138632 | ||||||||
\(904\) | 8.93665e53 | 0.182835 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.39070e53 | 0.0469520 | ||||||||
\(907\) | 6.36503e54 | 1.22480 | 0.612401 | − | 0.790547i | \(-0.290204\pi\) | ||||
0.612401 | + | 0.790547i | \(0.290204\pi\) | |||||||
\(908\) | −3.63458e54 | −0.685276 | ||||||||
\(909\) | 5.89899e54 | 1.08980 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.93922e54 | 0.521365 | 0.260683 | − | 0.965425i | \(-0.416052\pi\) | ||||
0.260683 | + | 0.965425i | \(0.416052\pi\) | |||||||
\(912\) | −2.45738e53 | −0.0427138 | ||||||||
\(913\) | −1.48484e53 | −0.0252912 | ||||||||
\(914\) | −5.74791e54 | −0.959413 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.10053e54 | −0.497016 | ||||||||
\(917\) | −1.28467e55 | −2.01818 | ||||||||
\(918\) | 8.09354e53 | 0.124609 | ||||||||
\(919\) | −7.57823e54 | −1.14349 | −0.571743 | − | 0.820433i | \(-0.693733\pi\) | ||||
−0.571743 | + | 0.820433i | \(0.693733\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.88598e53 | −0.0708189 | ||||||||
\(922\) | −1.33818e55 | −1.90105 | ||||||||
\(923\) | −8.68666e52 | −0.0120954 | ||||||||
\(924\) | 1.80830e52 | 0.00246796 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.37676e54 | 0.705046 | ||||||||
\(927\) | 1.04719e55 | 1.34602 | ||||||||
\(928\) | −2.02909e54 | −0.255660 | ||||||||
\(929\) | 6.55047e53 | 0.0809062 | 0.0404531 | − | 0.999181i | \(-0.487120\pi\) | ||||
0.0404531 | + | 0.999181i | \(0.487120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.34737e54 | −0.397314 | ||||||||
\(932\) | 7.42812e54 | 0.864340 | ||||||||
\(933\) | −4.19031e53 | −0.0478009 | ||||||||
\(934\) | 7.84263e54 | 0.877091 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.17213e53 | 0.0126000 | ||||||||
\(937\) | 3.87596e54 | 0.408505 | 0.204253 | − | 0.978918i | \(-0.434524\pi\) | ||||
0.204253 | + | 0.978918i | \(0.434524\pi\) | |||||||
\(938\) | 2.20080e55 | 2.27419 | ||||||||
\(939\) | 3.00168e53 | 0.0304124 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.38620e55 | −1.35027 | −0.675133 | − | 0.737696i | \(-0.735914\pi\) | ||||
−0.675133 | + | 0.737696i | \(0.735914\pi\) | |||||||
\(942\) | 6.34468e53 | 0.0605993 | ||||||||
\(943\) | −2.23244e55 | −2.09080 | ||||||||
\(944\) | −1.51149e54 | −0.138811 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.75649e53 | 0.0155117 | ||||||||
\(947\) | 8.86598e53 | 0.0767807 | 0.0383903 | − | 0.999263i | \(-0.487777\pi\) | ||||
0.0383903 | + | 0.999263i | \(0.487777\pi\) | |||||||
\(948\) | −4.90325e53 | −0.0416419 | ||||||||
\(949\) | −1.15447e53 | −0.00961515 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.10776e53 | −0.0649473 | ||||||||
\(952\) | −6.21913e54 | −0.488592 | ||||||||
\(953\) | −1.94425e55 | −1.49807 | −0.749036 | − | 0.662530i | \(-0.769483\pi\) | ||||
−0.749036 | + | 0.662530i | \(0.769483\pi\) | |||||||
\(954\) | 2.67803e55 | 2.02381 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.32791e55 | −0.965382 | ||||||||
\(957\) | 8.90355e51 | 0.000634881 0 | ||||||||
\(958\) | 1.26662e55 | 0.885902 | ||||||||
\(959\) | −1.38415e55 | −0.949597 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.64324e54 | −0.636561 | ||||||||
\(962\) | −3.68148e53 | −0.0238388 | ||||||||
\(963\) | 1.35486e54 | 0.0860616 | ||||||||
\(964\) | 1.38766e55 | 0.864687 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.35683e54 | −0.141335 | ||||||||
\(967\) | −6.67380e54 | −0.392630 | −0.196315 | − | 0.980541i | \(-0.562897\pi\) | ||||
−0.196315 | + | 0.980541i | \(0.562897\pi\) | |||||||
\(968\) | 7.17867e54 | 0.414333 | ||||||||
\(969\) | 5.78532e53 | 0.0327595 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.90466e52 | −0.00212827 | −0.00106414 | − | 0.999999i | \(-0.500339\pi\) | ||||
−0.00106414 | + | 0.999999i | \(0.500339\pi\) | |||||||
\(972\) | −1.95709e54 | −0.104661 | ||||||||
\(973\) | −3.46457e55 | −1.81787 | ||||||||
\(974\) | 3.73975e55 | 1.92532 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.43930e55 | 1.20905 | ||||||||
\(977\) | 6.49911e54 | 0.316085 | 0.158043 | − | 0.987432i | \(-0.449482\pi\) | ||||
0.158043 | + | 0.987432i | \(0.449482\pi\) | |||||||
\(978\) | −1.24560e54 | −0.0594441 | ||||||||
\(979\) | −2.35782e53 | −0.0110416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.37210e55 | −0.618743 | ||||||||
\(982\) | 4.73341e55 | 2.09465 | ||||||||
\(983\) | −1.39076e55 | −0.603967 | −0.301984 | − | 0.953313i | \(-0.597649\pi\) | ||||
−0.301984 | + | 0.953313i | \(0.597649\pi\) | |||||||
\(984\) | −6.25095e53 | −0.0266402 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.48488e54 | 0.266182 | ||||||||
\(987\) | 1.25459e53 | 0.00505398 | ||||||||
\(988\) | −3.55345e53 | −0.0140490 | ||||||||
\(989\) | −9.26022e54 | −0.359327 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.28319e55 | 1.60105 | 0.800525 | − | 0.599300i | \(-0.204554\pi\) | ||||
0.800525 | + | 0.599300i | \(0.204554\pi\) | |||||||
\(992\) | 1.91026e55 | 0.700853 | ||||||||
\(993\) | −1.76804e54 | −0.0636695 | ||||||||
\(994\) | −1.83603e55 | −0.648980 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.64193e53 | −0.0158089 | ||||||||
\(997\) | 3.24811e55 | 1.08585 | 0.542925 | − | 0.839781i | \(-0.317317\pi\) | ||||
0.542925 | + | 0.839781i | \(0.317317\pi\) | |||||||
\(998\) | 6.02137e55 | 1.97597 | ||||||||
\(999\) | −1.93418e54 | −0.0623067 |
(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 | 25.38.a.a.1.2 | 2 | ||
5.2 | odd | 4 | 25.38.b.a.24.4 | 4 | |||
5.3 | odd | 4 | 25.38.b.a.24.1 | 4 | |||
5.4 | even | 2 | 1.38.a.a.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 9.38.a.a.1.2 | 2 | |||
20.19 | odd | 2 | 16.38.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.38.a.a.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
9.38.a.a.1.2 | 2 | 15.14 | odd | 2 | |||
16.38.a.b.1.1 | 2 | 20.19 | odd | 2 | |||
25.38.a.a.1.2 | 2 | 1.1 | even | 1 | trivial | ||
25.38.b.a.24.1 | 4 | 5.3 | odd | 4 | |||
25.38.b.a.24.4 | 4 | 5.2 | odd | 4 |