Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(5.29266605383\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.15207 | −1.61787 | −0.808936 | − | 0.587897i | \(-0.799956\pi\) | ||||
−0.808936 | + | 0.587897i | \(0.799956\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 51.7603 | 1.61751 | ||||||||
\(5\) | 95.5207 | 1.70873 | 0.854363 | − | 0.519677i | \(-0.173948\pi\) | ||||
0.854363 | + | 0.519677i | \(0.173948\pi\) | |||||||
\(6\) | 82.3686 | 0.934079 | ||||||||
\(7\) | −209.521 | −1.61615 | −0.808075 | − | 0.589079i | \(-0.799491\pi\) | ||||
−0.808075 | + | 0.589079i | \(0.799491\pi\) | |||||||
\(8\) | −180.848 | −0.999053 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −874.212 | −2.76450 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −465.843 | −0.933870 | ||||||||
\(13\) | −335.779 | −0.551055 | −0.275527 | − | 0.961293i | \(-0.588852\pi\) | ||||
−0.275527 | + | 0.961293i | \(0.588852\pi\) | |||||||
\(14\) | 1917.55 | 2.61472 | ||||||||
\(15\) | −859.686 | −0.986533 | ||||||||
\(16\) | −1.19832 | −0.00117023 | ||||||||
\(17\) | −799.124 | −0.670644 | −0.335322 | − | 0.942104i | \(-0.608845\pi\) | ||||
−0.335322 | + | 0.942104i | \(0.608845\pi\) | |||||||
\(18\) | −741.317 | −0.539291 | ||||||||
\(19\) | −658.175 | −0.418271 | −0.209135 | − | 0.977887i | \(-0.567065\pi\) | ||||
−0.209135 | + | 0.977887i | \(0.567065\pi\) | |||||||
\(20\) | 4944.18 | 2.76388 | ||||||||
\(21\) | 1885.69 | 0.933085 | ||||||||
\(22\) | 1107.40 | 0.487807 | ||||||||
\(23\) | −4119.66 | −1.62383 | −0.811917 | − | 0.583773i | \(-0.801576\pi\) | ||||
−0.811917 | + | 0.583773i | \(0.801576\pi\) | |||||||
\(24\) | 1627.63 | 0.576804 | ||||||||
\(25\) | 5999.20 | 1.91974 | ||||||||
\(26\) | 3073.07 | 0.891536 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −10844.9 | −2.61414 | ||||||||
\(29\) | 559.348 | 0.123506 | 0.0617529 | − | 0.998091i | \(-0.480331\pi\) | ||||
0.0617529 | + | 0.998091i | \(0.480331\pi\) | |||||||
\(30\) | 7867.90 | 1.59608 | ||||||||
\(31\) | −6052.31 | −1.13114 | −0.565571 | − | 0.824700i | \(-0.691344\pi\) | ||||
−0.565571 | + | 0.824700i | \(0.691344\pi\) | |||||||
\(32\) | 5798.10 | 1.00095 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 7313.64 | 1.08502 | ||||||||
\(35\) | −20013.6 | −2.76156 | ||||||||
\(36\) | 4192.59 | 0.539170 | ||||||||
\(37\) | −14053.3 | −1.68762 | −0.843810 | − | 0.536642i | \(-0.819692\pi\) | ||||
−0.843810 | + | 0.536642i | \(0.819692\pi\) | |||||||
\(38\) | 6023.66 | 0.676709 | ||||||||
\(39\) | 3022.01 | 0.318151 | ||||||||
\(40\) | −17274.7 | −1.70711 | ||||||||
\(41\) | 1846.27 | 0.171528 | 0.0857642 | − | 0.996315i | \(-0.472667\pi\) | ||||
0.0857642 | + | 0.996315i | \(0.472667\pi\) | |||||||
\(42\) | −17257.9 | −1.50961 | ||||||||
\(43\) | 1623.49 | 0.133900 | 0.0669498 | − | 0.997756i | \(-0.478673\pi\) | ||||
0.0669498 | + | 0.997756i | \(0.478673\pi\) | |||||||
\(44\) | −6263.00 | −0.487698 | ||||||||
\(45\) | 7737.17 | 0.569575 | ||||||||
\(46\) | 37703.4 | 2.62715 | ||||||||
\(47\) | 20728.1 | 1.36872 | 0.684361 | − | 0.729143i | \(-0.260081\pi\) | ||||
0.684361 | + | 0.729143i | \(0.260081\pi\) | |||||||
\(48\) | 10.7848 | 0.000675633 0 | ||||||||
\(49\) | 27091.9 | 1.61194 | ||||||||
\(50\) | −54905.1 | −3.10590 | ||||||||
\(51\) | 7192.12 | 0.387196 | ||||||||
\(52\) | −17380.0 | −0.891337 | ||||||||
\(53\) | −7585.46 | −0.370930 | −0.185465 | − | 0.982651i | \(-0.559379\pi\) | ||||
−0.185465 | + | 0.982651i | \(0.559379\pi\) | |||||||
\(54\) | 6671.86 | 0.311360 | ||||||||
\(55\) | −11558.0 | −0.515200 | ||||||||
\(56\) | 37891.4 | 1.61462 | ||||||||
\(57\) | 5923.58 | 0.241489 | ||||||||
\(58\) | −5119.19 | −0.199817 | ||||||||
\(59\) | 18468.5 | 0.690717 | 0.345359 | − | 0.938471i | \(-0.387757\pi\) | ||||
0.345359 | + | 0.938471i | \(0.387757\pi\) | |||||||
\(60\) | −44497.6 | −1.59573 | ||||||||
\(61\) | −16972.3 | −0.584005 | −0.292002 | − | 0.956418i | \(-0.594322\pi\) | ||||
−0.292002 | + | 0.956418i | \(0.594322\pi\) | |||||||
\(62\) | 55391.2 | 1.83004 | ||||||||
\(63\) | −16971.2 | −0.538717 | ||||||||
\(64\) | −53026.3 | −1.61823 | ||||||||
\(65\) | −32073.8 | −0.941601 | ||||||||
\(66\) | −9966.60 | −0.281635 | ||||||||
\(67\) | −5618.62 | −0.152912 | −0.0764561 | − | 0.997073i | \(-0.524361\pi\) | ||||
−0.0764561 | + | 0.997073i | \(0.524361\pi\) | |||||||
\(68\) | −41362.9 | −1.08477 | ||||||||
\(69\) | 37076.9 | 0.937521 | ||||||||
\(70\) | 183165. | 4.46785 | ||||||||
\(71\) | 3703.10 | 0.0871807 | 0.0435903 | − | 0.999049i | \(-0.486120\pi\) | ||||
0.0435903 | + | 0.999049i | \(0.486120\pi\) | |||||||
\(72\) | −14648.7 | −0.333018 | ||||||||
\(73\) | −19808.0 | −0.435044 | −0.217522 | − | 0.976055i | \(-0.569797\pi\) | ||||
−0.217522 | + | 0.976055i | \(0.569797\pi\) | |||||||
\(74\) | 128617. | 2.73035 | ||||||||
\(75\) | −53992.8 | −1.10836 | ||||||||
\(76\) | −34067.4 | −0.676557 | ||||||||
\(77\) | 25352.0 | 0.487288 | ||||||||
\(78\) | −27657.6 | −0.514728 | ||||||||
\(79\) | 64009.9 | 1.15393 | 0.576965 | − | 0.816769i | \(-0.304237\pi\) | ||||
0.576965 | + | 0.816769i | \(0.304237\pi\) | |||||||
\(80\) | −114.464 | −0.00199960 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −16897.2 | −0.277511 | ||||||||
\(83\) | −46390.2 | −0.739147 | −0.369573 | − | 0.929202i | \(-0.620496\pi\) | ||||
−0.369573 | + | 0.929202i | \(0.620496\pi\) | |||||||
\(84\) | 97603.7 | 1.50927 | ||||||||
\(85\) | −76332.9 | −1.14595 | ||||||||
\(86\) | −14858.3 | −0.216632 | ||||||||
\(87\) | −5034.13 | −0.0713061 | ||||||||
\(88\) | 21882.6 | 0.301226 | ||||||||
\(89\) | −53959.5 | −0.722093 | −0.361046 | − | 0.932548i | \(-0.617580\pi\) | ||||
−0.361046 | + | 0.932548i | \(0.617580\pi\) | |||||||
\(90\) | −70811.1 | −0.921500 | ||||||||
\(91\) | 70352.5 | 0.890587 | ||||||||
\(92\) | −213235. | −2.62657 | ||||||||
\(93\) | 54470.8 | 0.653065 | ||||||||
\(94\) | −189705. | −2.21442 | ||||||||
\(95\) | −62869.3 | −0.714710 | ||||||||
\(96\) | −52182.9 | −0.577897 | ||||||||
\(97\) | 145249. | 1.56741 | 0.783707 | − | 0.621130i | \(-0.213326\pi\) | ||||
0.783707 | + | 0.621130i | \(0.213326\pi\) | |||||||
\(98\) | −247947. | −2.60792 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 310521. | 3.10521 | ||||||||
\(101\) | −77215.1 | −0.753180 | −0.376590 | − | 0.926380i | \(-0.622903\pi\) | ||||
−0.376590 | + | 0.926380i | \(0.622903\pi\) | |||||||
\(102\) | −65822.7 | −0.626434 | ||||||||
\(103\) | −106203. | −0.986374 | −0.493187 | − | 0.869923i | \(-0.664168\pi\) | ||||
−0.493187 | + | 0.869923i | \(0.664168\pi\) | |||||||
\(104\) | 60724.9 | 0.550533 | ||||||||
\(105\) | 180122. | 1.59439 | ||||||||
\(106\) | 69422.6 | 0.600118 | ||||||||
\(107\) | 33750.8 | 0.284987 | 0.142493 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142493 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(108\) | −37733.3 | −0.311290 | ||||||||
\(109\) | −37977.1 | −0.306165 | −0.153083 | − | 0.988213i | \(-0.548920\pi\) | ||||
−0.153083 | + | 0.988213i | \(0.548920\pi\) | |||||||
\(110\) | 105780. | 0.833528 | ||||||||
\(111\) | 126480. | 0.974348 | ||||||||
\(112\) | 251.072 | 0.00189127 | ||||||||
\(113\) | 239549. | 1.76481 | 0.882407 | − | 0.470486i | \(-0.155922\pi\) | ||||
0.882407 | + | 0.470486i | \(0.155922\pi\) | |||||||
\(114\) | −54213.0 | −0.390698 | ||||||||
\(115\) | −393512. | −2.77469 | ||||||||
\(116\) | 28952.1 | 0.199772 | ||||||||
\(117\) | −27198.1 | −0.183685 | ||||||||
\(118\) | −169025. | −1.11749 | ||||||||
\(119\) | 167433. | 1.08386 | ||||||||
\(120\) | 155472. | 0.985599 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 155332. | 0.944845 | ||||||||
\(123\) | −16616.4 | −0.0990320 | ||||||||
\(124\) | −313270. | −1.82963 | ||||||||
\(125\) | 274545. | 1.57159 | ||||||||
\(126\) | 155321. | 0.871575 | ||||||||
\(127\) | 88793.2 | 0.488507 | 0.244253 | − | 0.969711i | \(-0.421457\pi\) | ||||
0.244253 | + | 0.969711i | \(0.421457\pi\) | |||||||
\(128\) | 299761. | 1.61715 | ||||||||
\(129\) | −14611.4 | −0.0773070 | ||||||||
\(130\) | 293542. | 1.52339 | ||||||||
\(131\) | 333640. | 1.69864 | 0.849318 | − | 0.527881i | \(-0.177013\pi\) | ||||
0.849318 | + | 0.527881i | \(0.177013\pi\) | |||||||
\(132\) | 56367.0 | 0.281572 | ||||||||
\(133\) | 137901. | 0.675988 | ||||||||
\(134\) | 51421.9 | 0.247392 | ||||||||
\(135\) | −69634.6 | −0.328844 | ||||||||
\(136\) | 144520. | 0.670009 | ||||||||
\(137\) | −377709. | −1.71932 | −0.859659 | − | 0.510869i | \(-0.829324\pi\) | ||||
−0.859659 | + | 0.510869i | \(0.829324\pi\) | |||||||
\(138\) | −339330. | −1.51679 | ||||||||
\(139\) | −365308. | −1.60370 | −0.801849 | − | 0.597527i | \(-0.796150\pi\) | ||||
−0.801849 | + | 0.597527i | \(0.796150\pi\) | |||||||
\(140\) | −1.03591e6 | −4.46685 | ||||||||
\(141\) | −186553. | −0.790232 | ||||||||
\(142\) | −33891.1 | −0.141047 | ||||||||
\(143\) | 40629.2 | 0.166149 | ||||||||
\(144\) | −97.0636 | −0.000390077 0 | ||||||||
\(145\) | 53429.3 | 0.211038 | ||||||||
\(146\) | 181284. | 0.703845 | ||||||||
\(147\) | −243827. | −0.930655 | ||||||||
\(148\) | −727405. | −2.72974 | ||||||||
\(149\) | 297568. | 1.09805 | 0.549023 | − | 0.835807i | \(-0.315000\pi\) | ||||
0.549023 | + | 0.835807i | \(0.315000\pi\) | |||||||
\(150\) | 494146. | 1.79319 | ||||||||
\(151\) | 318093. | 1.13530 | 0.567651 | − | 0.823269i | \(-0.307852\pi\) | ||||
0.567651 | + | 0.823269i | \(0.307852\pi\) | |||||||
\(152\) | 119030. | 0.417875 | ||||||||
\(153\) | −64729.0 | −0.223548 | ||||||||
\(154\) | −232023. | −0.788369 | ||||||||
\(155\) | −578121. | −1.93281 | ||||||||
\(156\) | 156420. | 0.514613 | ||||||||
\(157\) | −34489.6 | −0.111671 | −0.0558353 | − | 0.998440i | \(-0.517782\pi\) | ||||
−0.0558353 | + | 0.998440i | \(0.517782\pi\) | |||||||
\(158\) | −585823. | −1.86691 | ||||||||
\(159\) | 68269.1 | 0.214157 | ||||||||
\(160\) | 553839. | 1.71034 | ||||||||
\(161\) | 863153. | 2.62436 | ||||||||
\(162\) | −60046.7 | −0.179764 | ||||||||
\(163\) | −45865.7 | −0.135213 | −0.0676067 | − | 0.997712i | \(-0.521536\pi\) | ||||
−0.0676067 | + | 0.997712i | \(0.521536\pi\) | |||||||
\(164\) | 95563.7 | 0.277449 | ||||||||
\(165\) | 104022. | 0.297451 | ||||||||
\(166\) | 424566. | 1.19584 | ||||||||
\(167\) | 290943. | 0.807265 | 0.403633 | − | 0.914921i | \(-0.367747\pi\) | ||||
0.403633 | + | 0.914921i | \(0.367747\pi\) | |||||||
\(168\) | −341022. | −0.932201 | ||||||||
\(169\) | −258546. | −0.696339 | ||||||||
\(170\) | 698604. | 1.85399 | ||||||||
\(171\) | −53312.2 | −0.139424 | ||||||||
\(172\) | 84032.5 | 0.216584 | ||||||||
\(173\) | −139360. | −0.354016 | −0.177008 | − | 0.984209i | \(-0.556642\pi\) | ||||
−0.177008 | + | 0.984209i | \(0.556642\pi\) | |||||||
\(174\) | 46072.7 | 0.115364 | ||||||||
\(175\) | −1.25696e6 | −3.10259 | ||||||||
\(176\) | 144.996 | 0.000352838 0 | ||||||||
\(177\) | −166216. | −0.398786 | ||||||||
\(178\) | 493841. | 1.16825 | ||||||||
\(179\) | −599556. | −1.39861 | −0.699306 | − | 0.714823i | \(-0.746507\pi\) | ||||
−0.699306 | + | 0.714823i | \(0.746507\pi\) | |||||||
\(180\) | 400479. | 0.921294 | ||||||||
\(181\) | 130631. | 0.296380 | 0.148190 | − | 0.988959i | \(-0.452655\pi\) | ||||
0.148190 | + | 0.988959i | \(0.452655\pi\) | |||||||
\(182\) | −643871. | −1.44086 | ||||||||
\(183\) | 152751. | 0.337175 | ||||||||
\(184\) | 745031. | 1.62230 | ||||||||
\(185\) | −1.34238e6 | −2.88368 | ||||||||
\(186\) | −498520. | −1.05658 | ||||||||
\(187\) | 96694.0 | 0.202207 | ||||||||
\(188\) | 1.07289e6 | 2.21392 | ||||||||
\(189\) | 152741. | 0.311028 | ||||||||
\(190\) | 575384. | 1.15631 | ||||||||
\(191\) | 338243. | 0.670882 | 0.335441 | − | 0.942061i | \(-0.391115\pi\) | ||||
0.335441 | + | 0.942061i | \(0.391115\pi\) | |||||||
\(192\) | 477236. | 0.934287 | ||||||||
\(193\) | −329094. | −0.635955 | −0.317978 | − | 0.948098i | \(-0.603004\pi\) | ||||
−0.317978 | + | 0.948098i | \(0.603004\pi\) | |||||||
\(194\) | −1.32933e6 | −2.53588 | ||||||||
\(195\) | 288664. | 0.543634 | ||||||||
\(196\) | 1.40229e6 | 2.60733 | ||||||||
\(197\) | 517397. | 0.949858 | 0.474929 | − | 0.880024i | \(-0.342474\pi\) | ||||
0.474929 | + | 0.880024i | \(0.342474\pi\) | |||||||
\(198\) | 89699.4 | 0.162602 | ||||||||
\(199\) | −531436. | −0.951302 | −0.475651 | − | 0.879634i | \(-0.657788\pi\) | ||||
−0.475651 | + | 0.879634i | \(0.657788\pi\) | |||||||
\(200\) | −1.08494e6 | −1.91793 | ||||||||
\(201\) | 50567.5 | 0.0882839 | ||||||||
\(202\) | 706678. | 1.21855 | ||||||||
\(203\) | −117195. | −0.199604 | ||||||||
\(204\) | 372266. | 0.626294 | ||||||||
\(205\) | 176357. | 0.293095 | ||||||||
\(206\) | 971973. | 1.59583 | ||||||||
\(207\) | −333692. | −0.541278 | ||||||||
\(208\) | 402.369 | 0.000644861 0 | ||||||||
\(209\) | 79639.2 | 0.126113 | ||||||||
\(210\) | −1.64849e6 | −2.57951 | ||||||||
\(211\) | 409913. | 0.633848 | 0.316924 | − | 0.948451i | \(-0.397350\pi\) | ||||
0.316924 | + | 0.948451i | \(0.397350\pi\) | |||||||
\(212\) | −392626. | −0.599984 | ||||||||
\(213\) | −33327.9 | −0.0503338 | ||||||||
\(214\) | −308890. | −0.461072 | ||||||||
\(215\) | 155077. | 0.228798 | ||||||||
\(216\) | 131838. | 0.192268 | ||||||||
\(217\) | 1.26808e6 | 1.82810 | ||||||||
\(218\) | 347569. | 0.495336 | ||||||||
\(219\) | 178272. | 0.251173 | ||||||||
\(220\) | −598246. | −0.833342 | ||||||||
\(221\) | 268329. | 0.369561 | ||||||||
\(222\) | −1.15755e6 | −1.57637 | ||||||||
\(223\) | 269898. | 0.363444 | 0.181722 | − | 0.983350i | \(-0.441833\pi\) | ||||
0.181722 | + | 0.983350i | \(0.441833\pi\) | |||||||
\(224\) | −1.21482e6 | −1.61768 | ||||||||
\(225\) | 485935. | 0.639915 | ||||||||
\(226\) | −2.19237e6 | −2.85524 | ||||||||
\(227\) | −1.02146e6 | −1.31570 | −0.657852 | − | 0.753147i | \(-0.728535\pi\) | ||||
−0.657852 | + | 0.753147i | \(0.728535\pi\) | |||||||
\(228\) | 306606. | 0.390611 | ||||||||
\(229\) | 169276. | 0.213307 | 0.106654 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106654 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(230\) | 3.60145e6 | 4.48909 | ||||||||
\(231\) | −228168. | −0.281336 | ||||||||
\(232\) | −101157. | −0.123389 | ||||||||
\(233\) | −20445.6 | −0.0246723 | −0.0123361 | − | 0.999924i | \(-0.503927\pi\) | ||||
−0.0123361 | + | 0.999924i | \(0.503927\pi\) | |||||||
\(234\) | 248919. | 0.297179 | ||||||||
\(235\) | 1.97996e6 | 2.33877 | ||||||||
\(236\) | 955933. | 1.11724 | ||||||||
\(237\) | −576089. | −0.666222 | ||||||||
\(238\) | −1.53236e6 | −1.75355 | ||||||||
\(239\) | −933552. | −1.05717 | −0.528583 | − | 0.848881i | \(-0.677277\pi\) | ||||
−0.528583 | + | 0.848881i | \(0.677277\pi\) | |||||||
\(240\) | 1030.18 | 0.00115447 | ||||||||
\(241\) | −1.30259e6 | −1.44466 | −0.722331 | − | 0.691547i | \(-0.756929\pi\) | ||||
−0.722331 | + | 0.691547i | \(0.756929\pi\) | |||||||
\(242\) | −133995. | −0.147079 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −878493. | −0.944634 | ||||||||
\(245\) | 2.58784e6 | 2.75437 | ||||||||
\(246\) | 152075. | 0.160221 | ||||||||
\(247\) | 221001. | 0.230490 | ||||||||
\(248\) | 1.09455e6 | 1.13007 | ||||||||
\(249\) | 417511. | 0.426747 | ||||||||
\(250\) | −2.51266e6 | −2.54263 | ||||||||
\(251\) | −930872. | −0.932622 | −0.466311 | − | 0.884621i | \(-0.654417\pi\) | ||||
−0.466311 | + | 0.884621i | \(0.654417\pi\) | |||||||
\(252\) | −878434. | −0.871380 | ||||||||
\(253\) | 498478. | 0.489604 | ||||||||
\(254\) | −812642. | −0.790342 | ||||||||
\(255\) | 686996. | 0.661612 | ||||||||
\(256\) | −1.04659e6 | −0.998106 | ||||||||
\(257\) | −25313.6 | −0.0239067 | −0.0119534 | − | 0.999929i | \(-0.503805\pi\) | ||||
−0.0119534 | + | 0.999929i | \(0.503805\pi\) | |||||||
\(258\) | 133725. | 0.125073 | ||||||||
\(259\) | 2.94446e6 | 2.72745 | ||||||||
\(260\) | −1.66015e6 | −1.52305 | ||||||||
\(261\) | 45307.2 | 0.0411686 | ||||||||
\(262\) | −3.05350e6 | −2.74818 | ||||||||
\(263\) | −1.69322e6 | −1.50947 | −0.754735 | − | 0.656030i | \(-0.772235\pi\) | ||||
−0.754735 | + | 0.656030i | \(0.772235\pi\) | |||||||
\(264\) | −196943. | −0.173913 | ||||||||
\(265\) | −724568. | −0.633818 | ||||||||
\(266\) | −1.26208e6 | −1.09366 | ||||||||
\(267\) | 485636. | 0.416901 | ||||||||
\(268\) | −290821. | −0.247337 | ||||||||
\(269\) | 469365. | 0.395485 | 0.197742 | − | 0.980254i | \(-0.436639\pi\) | ||||
0.197742 | + | 0.980254i | \(0.436639\pi\) | |||||||
\(270\) | 637300. | 0.532028 | ||||||||
\(271\) | −2.18341e6 | −1.80598 | −0.902988 | − | 0.429666i | \(-0.858631\pi\) | ||||
−0.902988 | + | 0.429666i | \(0.858631\pi\) | |||||||
\(272\) | 957.603 | 0.000784808 0 | ||||||||
\(273\) | −633173. | −0.514181 | ||||||||
\(274\) | 3.45682e6 | 2.78164 | ||||||||
\(275\) | −725903. | −0.578825 | ||||||||
\(276\) | 1.91911e6 | 1.51645 | ||||||||
\(277\) | −84280.4 | −0.0659974 | −0.0329987 | − | 0.999455i | \(-0.510506\pi\) | ||||
−0.0329987 | + | 0.999455i | \(0.510506\pi\) | |||||||
\(278\) | 3.34333e6 | 2.59458 | ||||||||
\(279\) | −490237. | −0.377047 | ||||||||
\(280\) | 3.61941e6 | 2.75894 | ||||||||
\(281\) | 649515. | 0.490708 | 0.245354 | − | 0.969433i | \(-0.421096\pi\) | ||||
0.245354 | + | 0.969433i | \(0.421096\pi\) | |||||||
\(282\) | 1.70735e6 | 1.27849 | ||||||||
\(283\) | 1.54893e6 | 1.14965 | 0.574826 | − | 0.818276i | \(-0.305070\pi\) | ||||
0.574826 | + | 0.818276i | \(0.305070\pi\) | |||||||
\(284\) | 191674. | 0.141016 | ||||||||
\(285\) | 565824. | 0.412638 | ||||||||
\(286\) | −371841. | −0.268808 | ||||||||
\(287\) | −386832. | −0.277216 | ||||||||
\(288\) | 469646. | 0.333649 | ||||||||
\(289\) | −781258. | −0.550237 | ||||||||
\(290\) | −488989. | −0.341432 | ||||||||
\(291\) | −1.30724e6 | −0.904947 | ||||||||
\(292\) | −1.02527e6 | −0.703688 | ||||||||
\(293\) | −70276.6 | −0.0478236 | −0.0239118 | − | 0.999714i | \(-0.507612\pi\) | ||||
−0.0239118 | + | 0.999714i | \(0.507612\pi\) | |||||||
\(294\) | 2.23152e6 | 1.50568 | ||||||||
\(295\) | 1.76412e6 | 1.18025 | ||||||||
\(296\) | 2.54151e6 | 1.68602 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −2.72336e6 | −1.77650 | ||||||||
\(299\) | 1.38329e6 | 0.894821 | ||||||||
\(300\) | −2.79469e6 | −1.79279 | ||||||||
\(301\) | −340155. | −0.216402 | ||||||||
\(302\) | −2.91121e6 | −1.83678 | ||||||||
\(303\) | 694936. | 0.434849 | ||||||||
\(304\) | 788.702 | 0.000489473 0 | ||||||||
\(305\) | −1.62121e6 | −0.997904 | ||||||||
\(306\) | 592405. | 0.361672 | ||||||||
\(307\) | 1.43343e6 | 0.868022 | 0.434011 | − | 0.900908i | \(-0.357098\pi\) | ||||
0.434011 | + | 0.900908i | \(0.357098\pi\) | |||||||
\(308\) | 1.31223e6 | 0.788193 | ||||||||
\(309\) | 955823. | 0.569484 | ||||||||
\(310\) | 5.29100e6 | 3.12704 | ||||||||
\(311\) | −227879. | −0.133599 | −0.0667996 | − | 0.997766i | \(-0.521279\pi\) | ||||
−0.0667996 | + | 0.997766i | \(0.521279\pi\) | |||||||
\(312\) | −546524. | −0.317850 | ||||||||
\(313\) | −723760. | −0.417574 | −0.208787 | − | 0.977961i | \(-0.566952\pi\) | ||||
−0.208787 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(314\) | 315651. | 0.180669 | ||||||||
\(315\) | −1.62110e6 | −0.920519 | ||||||||
\(316\) | 3.31317e6 | 1.86649 | ||||||||
\(317\) | 1.26086e6 | 0.704723 | 0.352362 | − | 0.935864i | \(-0.385379\pi\) | ||||
0.352362 | + | 0.935864i | \(0.385379\pi\) | |||||||
\(318\) | −624804. | −0.346478 | ||||||||
\(319\) | −67681.1 | −0.0372384 | ||||||||
\(320\) | −5.06510e6 | −2.76512 | ||||||||
\(321\) | −303757. | −0.164537 | ||||||||
\(322\) | −7.89964e6 | −4.24588 | ||||||||
\(323\) | 525964. | 0.280511 | ||||||||
\(324\) | 339600. | 0.179723 | ||||||||
\(325\) | −2.01440e6 | −1.05788 | ||||||||
\(326\) | 419766. | 0.218758 | ||||||||
\(327\) | 341794. | 0.176765 | ||||||||
\(328\) | −333894. | −0.171366 | ||||||||
\(329\) | −4.34297e6 | −2.21206 | ||||||||
\(330\) | −952016. | −0.481238 | ||||||||
\(331\) | 433444. | 0.217452 | 0.108726 | − | 0.994072i | \(-0.465323\pi\) | ||||
0.108726 | + | 0.994072i | \(0.465323\pi\) | |||||||
\(332\) | −2.40117e6 | −1.19558 | ||||||||
\(333\) | −1.13832e6 | −0.562540 | ||||||||
\(334\) | −2.66273e6 | −1.30605 | ||||||||
\(335\) | −536694. | −0.261285 | ||||||||
\(336\) | −2259.65 | −0.00109192 | ||||||||
\(337\) | 3.80554e6 | 1.82533 | 0.912666 | − | 0.408706i | \(-0.134020\pi\) | ||||
0.912666 | + | 0.408706i | \(0.134020\pi\) | |||||||
\(338\) | 2.36623e6 | 1.12659 | ||||||||
\(339\) | −2.15594e6 | −1.01892 | ||||||||
\(340\) | −3.95101e6 | −1.85358 | ||||||||
\(341\) | 732330. | 0.341052 | ||||||||
\(342\) | 487917. | 0.225570 | ||||||||
\(343\) | −2.15490e6 | −0.988991 | ||||||||
\(344\) | −293605. | −0.133773 | ||||||||
\(345\) | 3.54161e6 | 1.60197 | ||||||||
\(346\) | 1.27543e6 | 0.572753 | ||||||||
\(347\) | 2.91029e6 | 1.29752 | 0.648759 | − | 0.760994i | \(-0.275288\pi\) | ||||
0.648759 | + | 0.760994i | \(0.275288\pi\) | |||||||
\(348\) | −260568. | −0.115338 | ||||||||
\(349\) | −4.13500e6 | −1.81724 | −0.908620 | − | 0.417625i | \(-0.862863\pi\) | ||||
−0.908620 | + | 0.417625i | \(0.862863\pi\) | |||||||
\(350\) | 1.15037e7 | 5.01960 | ||||||||
\(351\) | 244783. | 0.106050 | ||||||||
\(352\) | −701570. | −0.301797 | ||||||||
\(353\) | 499935. | 0.213539 | 0.106769 | − | 0.994284i | \(-0.465949\pi\) | ||||
0.106769 | + | 0.994284i | \(0.465949\pi\) | |||||||
\(354\) | 1.52122e6 | 0.645185 | ||||||||
\(355\) | 353723. | 0.148968 | ||||||||
\(356\) | −2.79296e6 | −1.16799 | ||||||||
\(357\) | −1.50690e6 | −0.625768 | ||||||||
\(358\) | 5.48718e6 | 2.26278 | ||||||||
\(359\) | −2.96365e6 | −1.21364 | −0.606822 | − | 0.794838i | \(-0.707556\pi\) | ||||
−0.606822 | + | 0.794838i | \(0.707556\pi\) | |||||||
\(360\) | −1.39925e6 | −0.569036 | ||||||||
\(361\) | −2.04290e6 | −0.825050 | ||||||||
\(362\) | −1.19554e6 | −0.479504 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 3.64147e6 | 1.44053 | ||||||||
\(365\) | −1.89207e6 | −0.743371 | ||||||||
\(366\) | −1.39799e6 | −0.545507 | ||||||||
\(367\) | 257505. | 0.0997976 | 0.0498988 | − | 0.998754i | \(-0.484110\pi\) | ||||
0.0498988 | + | 0.998754i | \(0.484110\pi\) | |||||||
\(368\) | 4936.65 | 0.00190026 | ||||||||
\(369\) | 149548. | 0.0571761 | ||||||||
\(370\) | 1.22856e7 | 4.66542 | ||||||||
\(371\) | 1.58931e6 | 0.599479 | ||||||||
\(372\) | 2.81943e6 | 1.05634 | ||||||||
\(373\) | −1.28217e6 | −0.477169 | −0.238584 | − | 0.971122i | \(-0.576683\pi\) | ||||
−0.238584 | + | 0.971122i | \(0.576683\pi\) | |||||||
\(374\) | −884950. | −0.327145 | ||||||||
\(375\) | −2.47091e6 | −0.907358 | ||||||||
\(376\) | −3.74864e6 | −1.36743 | ||||||||
\(377\) | −187817. | −0.0680584 | ||||||||
\(378\) | −1.39789e6 | −0.503204 | ||||||||
\(379\) | 3.13440e6 | 1.12087 | 0.560436 | − | 0.828198i | \(-0.310634\pi\) | ||||
0.560436 | + | 0.828198i | \(0.310634\pi\) | |||||||
\(380\) | −3.25414e6 | −1.15605 | ||||||||
\(381\) | −799139. | −0.282040 | ||||||||
\(382\) | −3.09563e6 | −1.08540 | ||||||||
\(383\) | 875781. | 0.305069 | 0.152535 | − | 0.988298i | \(-0.451256\pi\) | ||||
0.152535 | + | 0.988298i | \(0.451256\pi\) | |||||||
\(384\) | −2.69785e6 | −0.933661 | ||||||||
\(385\) | 2.42164e6 | 0.832641 | ||||||||
\(386\) | 3.01189e6 | 1.02889 | ||||||||
\(387\) | 131503. | 0.0446332 | ||||||||
\(388\) | 7.51814e6 | 2.53531 | ||||||||
\(389\) | −1.95280e6 | −0.654312 | −0.327156 | − | 0.944970i | \(-0.606090\pi\) | ||||
−0.327156 | + | 0.944970i | \(0.606090\pi\) | |||||||
\(390\) | −2.64187e6 | −0.879530 | ||||||||
\(391\) | 3.29212e6 | 1.08901 | ||||||||
\(392\) | −4.89952e6 | −1.61042 | ||||||||
\(393\) | −3.00276e6 | −0.980708 | ||||||||
\(394\) | −4.73526e6 | −1.53675 | ||||||||
\(395\) | 6.11427e6 | 1.97175 | ||||||||
\(396\) | −507303. | −0.162566 | ||||||||
\(397\) | −1.70718e6 | −0.543629 | −0.271814 | − | 0.962350i | \(-0.587624\pi\) | ||||
−0.271814 | + | 0.962350i | \(0.587624\pi\) | |||||||
\(398\) | 4.86374e6 | 1.53909 | ||||||||
\(399\) | −1.24111e6 | −0.390282 | ||||||||
\(400\) | −7188.94 | −0.00224654 | ||||||||
\(401\) | 4.51630e6 | 1.40256 | 0.701280 | − | 0.712886i | \(-0.252612\pi\) | ||||
0.701280 | + | 0.712886i | \(0.252612\pi\) | |||||||
\(402\) | −462798. | −0.142832 | ||||||||
\(403\) | 2.03224e6 | 0.623321 | ||||||||
\(404\) | −3.99668e6 | −1.21828 | ||||||||
\(405\) | 626711. | 0.189858 | ||||||||
\(406\) | 1.07258e6 | 0.322934 | ||||||||
\(407\) | 1.70045e6 | 0.508836 | ||||||||
\(408\) | −1.30068e6 | −0.386830 | ||||||||
\(409\) | −721013. | −0.213125 | −0.106563 | − | 0.994306i | \(-0.533984\pi\) | ||||
−0.106563 | + | 0.994306i | \(0.533984\pi\) | |||||||
\(410\) | −1.61403e6 | −0.474190 | ||||||||
\(411\) | 3.39938e6 | 0.992648 | ||||||||
\(412\) | −5.49708e6 | −1.59547 | ||||||||
\(413\) | −3.86952e6 | −1.11630 | ||||||||
\(414\) | 3.05397e6 | 0.875718 | ||||||||
\(415\) | −4.43122e6 | −1.26300 | ||||||||
\(416\) | −1.94688e6 | −0.551576 | ||||||||
\(417\) | 3.28777e6 | 0.925895 | ||||||||
\(418\) | −728863. | −0.204035 | ||||||||
\(419\) | 3.89904e6 | 1.08498 | 0.542491 | − | 0.840061i | \(-0.317481\pi\) | ||||
0.542491 | + | 0.840061i | \(0.317481\pi\) | |||||||
\(420\) | 9.32318e6 | 2.57894 | ||||||||
\(421\) | −3.39665e6 | −0.933996 | −0.466998 | − | 0.884258i | \(-0.654665\pi\) | ||||
−0.466998 | + | 0.884258i | \(0.654665\pi\) | |||||||
\(422\) | −3.75155e6 | −1.02549 | ||||||||
\(423\) | 1.67898e6 | 0.456241 | ||||||||
\(424\) | 1.37181e6 | 0.370579 | ||||||||
\(425\) | −4.79410e6 | −1.28746 | ||||||||
\(426\) | 305020. | 0.0814336 | ||||||||
\(427\) | 3.55605e6 | 0.943840 | ||||||||
\(428\) | 1.74695e6 | 0.460969 | ||||||||
\(429\) | −365663. | −0.0959263 | ||||||||
\(430\) | −1.41928e6 | −0.370165 | ||||||||
\(431\) | −5.15196e6 | −1.33592 | −0.667958 | − | 0.744199i | \(-0.732832\pi\) | ||||
−0.667958 | + | 0.744199i | \(0.732832\pi\) | |||||||
\(432\) | 873.573 | 0.000225211 0 | ||||||||
\(433\) | −3.23450e6 | −0.829063 | −0.414531 | − | 0.910035i | \(-0.636055\pi\) | ||||
−0.414531 | + | 0.910035i | \(0.636055\pi\) | |||||||
\(434\) | −1.16056e7 | −2.95762 | ||||||||
\(435\) | −480864. | −0.121843 | ||||||||
\(436\) | −1.96571e6 | −0.495226 | ||||||||
\(437\) | 2.71146e6 | 0.679202 | ||||||||
\(438\) | −1.63156e6 | −0.406365 | ||||||||
\(439\) | 6.31060e6 | 1.56282 | 0.781411 | − | 0.624017i | \(-0.214500\pi\) | ||||
0.781411 | + | 0.624017i | \(0.214500\pi\) | |||||||
\(440\) | 2.09024e6 | 0.514712 | ||||||||
\(441\) | 2.19444e6 | 0.537314 | ||||||||
\(442\) | −2.45576e6 | −0.597903 | ||||||||
\(443\) | 2.87512e6 | 0.696061 | 0.348030 | − | 0.937483i | \(-0.386851\pi\) | ||||
0.348030 | + | 0.937483i | \(0.386851\pi\) | |||||||
\(444\) | 6.54664e6 | 1.57602 | ||||||||
\(445\) | −5.15425e6 | −1.23386 | ||||||||
\(446\) | −2.47013e6 | −0.588006 | ||||||||
\(447\) | −2.67811e6 | −0.633957 | ||||||||
\(448\) | 1.11101e7 | 2.61531 | ||||||||
\(449\) | −4.54361e6 | −1.06362 | −0.531809 | − | 0.846865i | \(-0.678487\pi\) | ||||
−0.531809 | + | 0.846865i | \(0.678487\pi\) | |||||||
\(450\) | −4.44731e6 | −1.03530 | ||||||||
\(451\) | −223399. | −0.0517178 | ||||||||
\(452\) | 1.23992e7 | 2.85461 | ||||||||
\(453\) | −2.86284e6 | −0.655467 | ||||||||
\(454\) | 9.34850e6 | 2.12864 | ||||||||
\(455\) | 6.72012e6 | 1.52177 | ||||||||
\(456\) | −1.07127e6 | −0.241260 | ||||||||
\(457\) | 2.78485e6 | 0.623751 | 0.311876 | − | 0.950123i | \(-0.399043\pi\) | ||||
0.311876 | + | 0.950123i | \(0.399043\pi\) | |||||||
\(458\) | −1.54922e6 | −0.345104 | ||||||||
\(459\) | 582561. | 0.129065 | ||||||||
\(460\) | −2.03683e7 | −4.48808 | ||||||||
\(461\) | −2.00495e6 | −0.439391 | −0.219695 | − | 0.975569i | \(-0.570506\pi\) | ||||
−0.219695 | + | 0.975569i | \(0.570506\pi\) | |||||||
\(462\) | 2.08821e6 | 0.455165 | ||||||||
\(463\) | −4.67402e6 | −1.01330 | −0.506650 | − | 0.862152i | \(-0.669116\pi\) | ||||
−0.506650 | + | 0.862152i | \(0.669116\pi\) | |||||||
\(464\) | −670.276 | −0.000144530 0 | ||||||||
\(465\) | 5.20309e6 | 1.11591 | ||||||||
\(466\) | 187119. | 0.0399166 | ||||||||
\(467\) | −1.41948e6 | −0.301188 | −0.150594 | − | 0.988596i | \(-0.548119\pi\) | ||||
−0.150594 | + | 0.988596i | \(0.548119\pi\) | |||||||
\(468\) | −1.40778e6 | −0.297112 | ||||||||
\(469\) | 1.17722e6 | 0.247129 | ||||||||
\(470\) | −1.81208e7 | −3.78383 | ||||||||
\(471\) | 310406. | 0.0644731 | ||||||||
\(472\) | −3.33998e6 | −0.690063 | ||||||||
\(473\) | −196443. | −0.0403722 | ||||||||
\(474\) | 5.27241e6 | 1.07786 | ||||||||
\(475\) | −3.94852e6 | −0.802973 | ||||||||
\(476\) | 8.66639e6 | 1.75316 | ||||||||
\(477\) | −614422. | −0.123643 | ||||||||
\(478\) | 8.54393e6 | 1.71036 | ||||||||
\(479\) | −3.60077e6 | −0.717062 | −0.358531 | − | 0.933518i | \(-0.616722\pi\) | ||||
−0.358531 | + | 0.933518i | \(0.616722\pi\) | |||||||
\(480\) | −4.98455e6 | −0.987467 | ||||||||
\(481\) | 4.71880e6 | 0.929970 | ||||||||
\(482\) | 1.19214e7 | 2.33728 | ||||||||
\(483\) | −7.76838e6 | −1.51517 | ||||||||
\(484\) | 757823. | 0.147046 | ||||||||
\(485\) | 1.38743e7 | 2.67828 | ||||||||
\(486\) | 540420. | 0.103787 | ||||||||
\(487\) | −5.57519e6 | −1.06521 | −0.532607 | − | 0.846363i | \(-0.678788\pi\) | ||||
−0.532607 | + | 0.846363i | \(0.678788\pi\) | |||||||
\(488\) | 3.06941e6 | 0.583452 | ||||||||
\(489\) | 412792. | 0.0780654 | ||||||||
\(490\) | −2.36841e7 | −4.45621 | ||||||||
\(491\) | −1.80948e6 | −0.338728 | −0.169364 | − | 0.985554i | \(-0.554171\pi\) | ||||
−0.169364 | + | 0.985554i | \(0.554171\pi\) | |||||||
\(492\) | −860073. | −0.160185 | ||||||||
\(493\) | −446989. | −0.0828284 | ||||||||
\(494\) | −2.02262e6 | −0.372903 | ||||||||
\(495\) | −936198. | −0.171733 | ||||||||
\(496\) | 7252.58 | 0.00132370 | ||||||||
\(497\) | −775877. | −0.140897 | ||||||||
\(498\) | −3.82109e6 | −0.690421 | ||||||||
\(499\) | −5.94504e6 | −1.06882 | −0.534409 | − | 0.845226i | \(-0.679466\pi\) | ||||
−0.534409 | + | 0.845226i | \(0.679466\pi\) | |||||||
\(500\) | 1.42106e7 | 2.54206 | ||||||||
\(501\) | −2.61848e6 | −0.466075 | ||||||||
\(502\) | 8.51940e6 | 1.50886 | ||||||||
\(503\) | 6.57296e6 | 1.15835 | 0.579176 | − | 0.815202i | \(-0.303374\pi\) | ||||
0.579176 | + | 0.815202i | \(0.303374\pi\) | |||||||
\(504\) | 3.06920e6 | 0.538207 | ||||||||
\(505\) | −7.37564e6 | −1.28698 | ||||||||
\(506\) | −4.56211e6 | −0.792117 | ||||||||
\(507\) | 2.32691e6 | 0.402031 | ||||||||
\(508\) | 4.59597e6 | 0.790165 | ||||||||
\(509\) | 1.76650e6 | 0.302218 | 0.151109 | − | 0.988517i | \(-0.451716\pi\) | ||||
0.151109 | + | 0.988517i | \(0.451716\pi\) | |||||||
\(510\) | −6.28743e6 | −1.07040 | ||||||||
\(511\) | 4.15018e6 | 0.703096 | ||||||||
\(512\) | −13882.8 | −0.00234046 | ||||||||
\(513\) | 479810. | 0.0804962 | ||||||||
\(514\) | 231671. | 0.0386780 | ||||||||
\(515\) | −1.01445e7 | −1.68544 | ||||||||
\(516\) | −756293. | −0.125045 | ||||||||
\(517\) | −2.50810e6 | −0.412685 | ||||||||
\(518\) | −2.69479e7 | −4.41266 | ||||||||
\(519\) | 1.25424e6 | 0.204391 | ||||||||
\(520\) | 5.80048e6 | 0.940709 | ||||||||
\(521\) | 9.74164e6 | 1.57231 | 0.786154 | − | 0.618031i | \(-0.212069\pi\) | ||||
0.786154 | + | 0.618031i | \(0.212069\pi\) | |||||||
\(522\) | −414655. | −0.0666055 | ||||||||
\(523\) | 6.30069e6 | 1.00724 | 0.503621 | − | 0.863925i | \(-0.332001\pi\) | ||||
0.503621 | + | 0.863925i | \(0.332001\pi\) | |||||||
\(524\) | 1.72693e7 | 2.74756 | ||||||||
\(525\) | 1.13126e7 | 1.79128 | ||||||||
\(526\) | 1.54965e7 | 2.44213 | ||||||||
\(527\) | 4.83655e6 | 0.758593 | ||||||||
\(528\) | −1304.97 | −0.000203711 0 | ||||||||
\(529\) | 1.05352e7 | 1.63683 | ||||||||
\(530\) | 6.63130e6 | 1.02544 | ||||||||
\(531\) | 1.49594e6 | 0.230239 | ||||||||
\(532\) | 7.13782e6 | 1.09342 | ||||||||
\(533\) | −619939. | −0.0945215 | ||||||||
\(534\) | −4.44457e6 | −0.674492 | ||||||||
\(535\) | 3.22390e6 | 0.486964 | ||||||||
\(536\) | 1.01611e6 | 0.152767 | ||||||||
\(537\) | 5.39600e6 | 0.807489 | ||||||||
\(538\) | −4.29566e6 | −0.639844 | ||||||||
\(539\) | −3.27812e6 | −0.486019 | ||||||||
\(540\) | −3.60431e6 | −0.531909 | ||||||||
\(541\) | −1.12441e7 | −1.65169 | −0.825847 | − | 0.563894i | \(-0.809303\pi\) | ||||
−0.825847 | + | 0.563894i | \(0.809303\pi\) | |||||||
\(542\) | 1.99827e7 | 2.92184 | ||||||||
\(543\) | −1.17567e6 | −0.171115 | ||||||||
\(544\) | −4.63340e6 | −0.671278 | ||||||||
\(545\) | −3.62760e6 | −0.523153 | ||||||||
\(546\) | 5.79484e6 | 0.831879 | ||||||||
\(547\) | 60699.0 | 0.00867388 | 0.00433694 | − | 0.999991i | \(-0.498620\pi\) | ||||
0.00433694 | + | 0.999991i | \(0.498620\pi\) | |||||||
\(548\) | −1.95504e7 | −2.78101 | ||||||||
\(549\) | −1.37476e6 | −0.194668 | ||||||||
\(550\) | 6.64351e6 | 0.936464 | ||||||||
\(551\) | −368149. | −0.0516589 | ||||||||
\(552\) | −6.70528e6 | −0.936633 | ||||||||
\(553\) | −1.34114e7 | −1.86492 | ||||||||
\(554\) | 771340. | 0.106775 | ||||||||
\(555\) | 1.20814e7 | 1.66489 | ||||||||
\(556\) | −1.89085e7 | −2.59400 | ||||||||
\(557\) | 2.28778e6 | 0.312447 | 0.156224 | − | 0.987722i | \(-0.450068\pi\) | ||||
0.156224 | + | 0.987722i | \(0.450068\pi\) | |||||||
\(558\) | 4.48668e6 | 0.610014 | ||||||||
\(559\) | −545134. | −0.0737860 | ||||||||
\(560\) | 23982.6 | 0.00323166 | ||||||||
\(561\) | −870246. | −0.116744 | ||||||||
\(562\) | −5.94441e6 | −0.793904 | ||||||||
\(563\) | −5.37938e6 | −0.715256 | −0.357628 | − | 0.933864i | \(-0.616414\pi\) | ||||
−0.357628 | + | 0.933864i | \(0.616414\pi\) | |||||||
\(564\) | −9.65605e6 | −1.27821 | ||||||||
\(565\) | 2.28819e7 | 3.01558 | ||||||||
\(566\) | −1.41759e7 | −1.85999 | ||||||||
\(567\) | −1.37467e6 | −0.179572 | ||||||||
\(568\) | −669699. | −0.0870981 | ||||||||
\(569\) | −6.95488e6 | −0.900552 | −0.450276 | − | 0.892889i | \(-0.648674\pi\) | ||||
−0.450276 | + | 0.892889i | \(0.648674\pi\) | |||||||
\(570\) | −5.17846e6 | −0.667596 | ||||||||
\(571\) | −3.19590e6 | −0.410206 | −0.205103 | − | 0.978740i | \(-0.565753\pi\) | ||||
−0.205103 | + | 0.978740i | \(0.565753\pi\) | |||||||
\(572\) | 2.10298e6 | 0.268748 | ||||||||
\(573\) | −3.04419e6 | −0.387334 | ||||||||
\(574\) | 3.54031e6 | 0.448500 | ||||||||
\(575\) | −2.47146e7 | −3.11734 | ||||||||
\(576\) | −4.29513e6 | −0.539411 | ||||||||
\(577\) | 2.54992e6 | 0.318851 | 0.159425 | − | 0.987210i | \(-0.449036\pi\) | ||||
0.159425 | + | 0.987210i | \(0.449036\pi\) | |||||||
\(578\) | 7.15012e6 | 0.890213 | ||||||||
\(579\) | 2.96184e6 | 0.367169 | ||||||||
\(580\) | 2.76552e6 | 0.341355 | ||||||||
\(581\) | 9.71970e6 | 1.19457 | ||||||||
\(582\) | 1.19640e7 | 1.46409 | ||||||||
\(583\) | 917841. | 0.111840 | ||||||||
\(584\) | 3.58223e6 | 0.434632 | ||||||||
\(585\) | −2.59798e6 | −0.313867 | ||||||||
\(586\) | 643177. | 0.0773724 | ||||||||
\(587\) | −1.96757e6 | −0.235687 | −0.117843 | − | 0.993032i | \(-0.537598\pi\) | ||||
−0.117843 | + | 0.993032i | \(0.537598\pi\) | |||||||
\(588\) | −1.26206e7 | −1.50534 | ||||||||
\(589\) | 3.98348e6 | 0.473124 | ||||||||
\(590\) | −1.61453e7 | −1.90949 | ||||||||
\(591\) | −4.65658e6 | −0.548401 | ||||||||
\(592\) | 16840.3 | 0.00197490 | ||||||||
\(593\) | −8.41413e6 | −0.982590 | −0.491295 | − | 0.870993i | \(-0.663476\pi\) | ||||
−0.491295 | + | 0.870993i | \(0.663476\pi\) | |||||||
\(594\) | −807295. | −0.0938785 | ||||||||
\(595\) | 1.59933e7 | 1.85202 | ||||||||
\(596\) | 1.54022e7 | 1.77610 | ||||||||
\(597\) | 4.78293e6 | 0.549235 | ||||||||
\(598\) | −1.26600e7 | −1.44771 | ||||||||
\(599\) | −1.00298e7 | −1.14216 | −0.571078 | − | 0.820896i | \(-0.693475\pi\) | ||||
−0.571078 | + | 0.820896i | \(0.693475\pi\) | |||||||
\(600\) | 9.76448e6 | 1.10732 | ||||||||
\(601\) | −1.42206e7 | −1.60595 | −0.802977 | − | 0.596010i | \(-0.796752\pi\) | ||||
−0.802977 | + | 0.596010i | \(0.796752\pi\) | |||||||
\(602\) | 3.11312e6 | 0.350111 | ||||||||
\(603\) | −455108. | −0.0509708 | ||||||||
\(604\) | 1.64646e7 | 1.83636 | ||||||||
\(605\) | 1.39852e6 | 0.155339 | ||||||||
\(606\) | −6.36010e6 | −0.703530 | ||||||||
\(607\) | 1.51717e7 | 1.67133 | 0.835665 | − | 0.549240i | \(-0.185083\pi\) | ||||
0.835665 | + | 0.549240i | \(0.185083\pi\) | |||||||
\(608\) | −3.81617e6 | −0.418667 | ||||||||
\(609\) | 1.05476e6 | 0.115241 | ||||||||
\(610\) | 1.48374e7 | 1.61448 | ||||||||
\(611\) | −6.96006e6 | −0.754241 | ||||||||
\(612\) | −3.35040e6 | −0.361591 | ||||||||
\(613\) | −1.52884e7 | −1.64328 | −0.821638 | − | 0.570010i | \(-0.806939\pi\) | ||||
−0.821638 | + | 0.570010i | \(0.806939\pi\) | |||||||
\(614\) | −1.31189e7 | −1.40435 | ||||||||
\(615\) | −1.58721e6 | −0.169218 | ||||||||
\(616\) | −4.58486e6 | −0.486826 | ||||||||
\(617\) | −1.81989e6 | −0.192457 | −0.0962284 | − | 0.995359i | \(-0.530678\pi\) | ||||
−0.0962284 | + | 0.995359i | \(0.530678\pi\) | |||||||
\(618\) | −8.74775e6 | −0.921352 | ||||||||
\(619\) | 1.39678e7 | 1.46521 | 0.732606 | − | 0.680653i | \(-0.238304\pi\) | ||||
0.732606 | + | 0.680653i | \(0.238304\pi\) | |||||||
\(620\) | −2.99237e7 | −3.12634 | ||||||||
\(621\) | 3.00323e6 | 0.312507 | ||||||||
\(622\) | 2.08557e6 | 0.216147 | ||||||||
\(623\) | 1.13056e7 | 1.16701 | ||||||||
\(624\) | −3621.32 | −0.000372311 0 | ||||||||
\(625\) | 7.47727e6 | 0.765672 | ||||||||
\(626\) | 6.62390e6 | 0.675582 | ||||||||
\(627\) | −716753. | −0.0728116 | ||||||||
\(628\) | −1.78519e6 | −0.180628 | ||||||||
\(629\) | 1.12303e7 | 1.13179 | ||||||||
\(630\) | 1.48364e7 | 1.48928 | ||||||||
\(631\) | −1.64990e7 | −1.64962 | −0.824808 | − | 0.565413i | \(-0.808717\pi\) | ||||
−0.824808 | + | 0.565413i | \(0.808717\pi\) | |||||||
\(632\) | −1.15761e7 | −1.15284 | ||||||||
\(633\) | −3.68921e6 | −0.365952 | ||||||||
\(634\) | −1.15395e7 | −1.14015 | ||||||||
\(635\) | 8.48159e6 | 0.834724 | ||||||||
\(636\) | 3.53363e6 | 0.346401 | ||||||||
\(637\) | −9.09688e6 | −0.888268 | ||||||||
\(638\) | 619422. | 0.0602470 | ||||||||
\(639\) | 299951. | 0.0290602 | ||||||||
\(640\) | 2.86333e7 | 2.76326 | ||||||||
\(641\) | 1.14852e7 | 1.10406 | 0.552030 | − | 0.833824i | \(-0.313853\pi\) | ||||
0.552030 | + | 0.833824i | \(0.313853\pi\) | |||||||
\(642\) | 2.78001e6 | 0.266200 | ||||||||
\(643\) | −5.83065e6 | −0.556147 | −0.278073 | − | 0.960560i | \(-0.589696\pi\) | ||||
−0.278073 | + | 0.960560i | \(0.589696\pi\) | |||||||
\(644\) | 4.46771e7 | 4.24493 | ||||||||
\(645\) | −1.39569e6 | −0.132096 | ||||||||
\(646\) | −4.81365e6 | −0.453830 | ||||||||
\(647\) | −1.27091e7 | −1.19359 | −0.596795 | − | 0.802394i | \(-0.703559\pi\) | ||||
−0.596795 | + | 0.802394i | \(0.703559\pi\) | |||||||
\(648\) | −1.18654e6 | −0.111006 | ||||||||
\(649\) | −2.23468e6 | −0.208259 | ||||||||
\(650\) | 1.84359e7 | 1.71152 | ||||||||
\(651\) | −1.14128e7 | −1.05545 | ||||||||
\(652\) | −2.37403e6 | −0.218709 | ||||||||
\(653\) | −8.01118e6 | −0.735214 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(654\) | −3.12812e6 | −0.285983 | ||||||||
\(655\) | 3.18696e7 | 2.90250 | ||||||||
\(656\) | −2212.42 | −0.000200728 0 | ||||||||
\(657\) | −1.60445e6 | −0.145015 | ||||||||
\(658\) | 3.97472e7 | 3.57883 | ||||||||
\(659\) | 1.48896e7 | 1.33558 | 0.667790 | − | 0.744350i | \(-0.267241\pi\) | ||||
0.667790 | + | 0.744350i | \(0.267241\pi\) | |||||||
\(660\) | 5.38421e6 | 0.481130 | ||||||||
\(661\) | −1.15205e7 | −1.02558 | −0.512788 | − | 0.858515i | \(-0.671387\pi\) | ||||
−0.512788 | + | 0.858515i | \(0.671387\pi\) | |||||||
\(662\) | −3.96691e6 | −0.351809 | ||||||||
\(663\) | −2.41496e6 | −0.213366 | ||||||||
\(664\) | 8.38956e6 | 0.738447 | ||||||||
\(665\) | 1.31724e7 | 1.15508 | ||||||||
\(666\) | 1.04180e7 | 0.910118 | ||||||||
\(667\) | −2.30432e6 | −0.200553 | ||||||||
\(668\) | 1.50593e7 | 1.30576 | ||||||||
\(669\) | −2.42908e6 | −0.209835 | ||||||||
\(670\) | 4.91186e6 | 0.422726 | ||||||||
\(671\) | 2.05365e6 | 0.176084 | ||||||||
\(672\) | 1.09334e7 | 0.933968 | ||||||||
\(673\) | −1.68386e7 | −1.43308 | −0.716538 | − | 0.697548i | \(-0.754274\pi\) | ||||
−0.716538 | + | 0.697548i | \(0.754274\pi\) | |||||||
\(674\) | −3.48286e7 | −2.95315 | ||||||||
\(675\) | −4.37342e6 | −0.369455 | ||||||||
\(676\) | −1.33824e7 | −1.12634 | ||||||||
\(677\) | −6.56811e6 | −0.550768 | −0.275384 | − | 0.961334i | \(-0.588805\pi\) | ||||
−0.275384 | + | 0.961334i | \(0.588805\pi\) | |||||||
\(678\) | 1.97314e7 | 1.64848 | ||||||||
\(679\) | −3.04327e7 | −2.53318 | ||||||||
\(680\) | 1.38046e7 | 1.14486 | ||||||||
\(681\) | 9.19317e6 | 0.759622 | ||||||||
\(682\) | −6.70233e6 | −0.551779 | ||||||||
\(683\) | −1.01525e7 | −0.832761 | −0.416381 | − | 0.909190i | \(-0.636702\pi\) | ||||
−0.416381 | + | 0.909190i | \(0.636702\pi\) | |||||||
\(684\) | −2.75946e6 | −0.225519 | ||||||||
\(685\) | −3.60790e7 | −2.93784 | ||||||||
\(686\) | 1.97218e7 | 1.60006 | ||||||||
\(687\) | −1.52348e6 | −0.123153 | ||||||||
\(688\) | −1945.46 | −0.000156693 0 | ||||||||
\(689\) | 2.54704e6 | 0.204403 | ||||||||
\(690\) | −3.24131e7 | −2.59178 | ||||||||
\(691\) | −1.01356e7 | −0.807521 | −0.403760 | − | 0.914865i | \(-0.632297\pi\) | ||||
−0.403760 | + | 0.914865i | \(0.632297\pi\) | |||||||
\(692\) | −7.21332e6 | −0.572625 | ||||||||
\(693\) | 2.05351e6 | 0.162429 | ||||||||
\(694\) | −2.66352e7 | −2.09922 | ||||||||
\(695\) | −3.48945e7 | −2.74028 | ||||||||
\(696\) | 910413. | 0.0712386 | ||||||||
\(697\) | −1.47540e6 | −0.115034 | ||||||||
\(698\) | 3.78438e7 | 2.94006 | ||||||||
\(699\) | 184010. | 0.0142445 | ||||||||
\(700\) | −6.50605e7 | −5.01848 | ||||||||
\(701\) | 9.16091e6 | 0.704115 | 0.352058 | − | 0.935978i | \(-0.385482\pi\) | ||||
0.352058 | + | 0.935978i | \(0.385482\pi\) | |||||||
\(702\) | −2.24027e6 | −0.171576 | ||||||||
\(703\) | 9.24955e6 | 0.705882 | ||||||||
\(704\) | 6.41618e6 | 0.487916 | ||||||||
\(705\) | −1.78197e7 | −1.35029 | ||||||||
\(706\) | −4.57544e6 | −0.345478 | ||||||||
\(707\) | 1.61782e7 | 1.21725 | ||||||||
\(708\) | −8.60340e6 | −0.645040 | ||||||||
\(709\) | −8.97668e6 | −0.670656 | −0.335328 | − | 0.942101i | \(-0.608847\pi\) | ||||
−0.335328 | + | 0.942101i | \(0.608847\pi\) | |||||||
\(710\) | −3.23730e6 | −0.241011 | ||||||||
\(711\) | 5.18480e6 | 0.384643 | ||||||||
\(712\) | 9.75847e6 | 0.721409 | ||||||||
\(713\) | 2.49334e7 | 1.83679 | ||||||||
\(714\) | 1.37912e7 | 1.01241 | ||||||||
\(715\) | 3.88093e6 | 0.283903 | ||||||||
\(716\) | −3.10332e7 | −2.26227 | ||||||||
\(717\) | 8.40196e6 | 0.610356 | ||||||||
\(718\) | 2.71235e7 | 1.96352 | ||||||||
\(719\) | 7.92637e6 | 0.571811 | 0.285905 | − | 0.958258i | \(-0.407706\pi\) | ||||
0.285905 | + | 0.958258i | \(0.407706\pi\) | |||||||
\(720\) | −9271.58 | −0.000666534 0 | ||||||||
\(721\) | 2.22516e7 | 1.59413 | ||||||||
\(722\) | 1.86968e7 | 1.33482 | ||||||||
\(723\) | 1.17233e7 | 0.834076 | ||||||||
\(724\) | 6.76148e6 | 0.479397 | ||||||||
\(725\) | 3.35564e6 | 0.237099 | ||||||||
\(726\) | 1.20596e6 | 0.0849163 | ||||||||
\(727\) | 1.78172e7 | 1.25027 | 0.625135 | − | 0.780516i | \(-0.285044\pi\) | ||||
0.625135 | + | 0.780516i | \(0.285044\pi\) | |||||||
\(728\) | −1.27231e7 | −0.889744 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.73164e7 | 1.20268 | ||||||||
\(731\) | −1.29737e6 | −0.0897989 | ||||||||
\(732\) | 7.90644e6 | 0.545385 | ||||||||
\(733\) | 1.81797e7 | 1.24976 | 0.624882 | − | 0.780719i | \(-0.285147\pi\) | ||||
0.624882 | + | 0.780719i | \(0.285147\pi\) | |||||||
\(734\) | −2.35670e6 | −0.161460 | ||||||||
\(735\) | −2.32905e7 | −1.59023 | ||||||||
\(736\) | −2.38862e7 | −1.62537 | ||||||||
\(737\) | 679852. | 0.0461048 | ||||||||
\(738\) | −1.36867e6 | −0.0925037 | ||||||||
\(739\) | −1.38291e7 | −0.931502 | −0.465751 | − | 0.884916i | \(-0.654216\pi\) | ||||
−0.465751 | + | 0.884916i | \(0.654216\pi\) | |||||||
\(740\) | −6.94822e7 | −4.66438 | ||||||||
\(741\) | −1.98901e6 | −0.133073 | ||||||||
\(742\) | −1.45455e7 | −0.969881 | ||||||||
\(743\) | −7.07226e6 | −0.469987 | −0.234994 | − | 0.971997i | \(-0.575507\pi\) | ||||
−0.234994 | + | 0.971997i | \(0.575507\pi\) | |||||||
\(744\) | −9.85093e6 | −0.652447 | ||||||||
\(745\) | 2.84239e7 | 1.87626 | ||||||||
\(746\) | 1.17345e7 | 0.771998 | ||||||||
\(747\) | −3.75760e6 | −0.246382 | ||||||||
\(748\) | 5.00491e6 | 0.327071 | ||||||||
\(749\) | −7.07149e6 | −0.460582 | ||||||||
\(750\) | 2.26139e7 | 1.46799 | ||||||||
\(751\) | −653678. | −0.0422926 | −0.0211463 | − | 0.999776i | \(-0.506732\pi\) | ||||
−0.0211463 | + | 0.999776i | \(0.506732\pi\) | |||||||
\(752\) | −24838.8 | −0.00160172 | ||||||||
\(753\) | 8.37785e6 | 0.538449 | ||||||||
\(754\) | 1.71892e6 | 0.110110 | ||||||||
\(755\) | 3.03845e7 | 1.93992 | ||||||||
\(756\) | 7.90590e6 | 0.503092 | ||||||||
\(757\) | 2.72250e7 | 1.72674 | 0.863372 | − | 0.504569i | \(-0.168348\pi\) | ||||
0.863372 | + | 0.504569i | \(0.168348\pi\) | |||||||
\(758\) | −2.86862e7 | −1.81343 | ||||||||
\(759\) | −4.48631e6 | −0.282673 | ||||||||
\(760\) | 1.13698e7 | 0.714033 | ||||||||
\(761\) | −5.41780e6 | −0.339126 | −0.169563 | − | 0.985519i | \(-0.554236\pi\) | ||||
−0.169563 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(762\) | 7.31378e6 | 0.456304 | ||||||||
\(763\) | 7.95700e6 | 0.494809 | ||||||||
\(764\) | 1.75076e7 | 1.08516 | ||||||||
\(765\) | −6.18296e6 | −0.381982 | ||||||||
\(766\) | −8.01521e6 | −0.493563 | ||||||||
\(767\) | −6.20131e6 | −0.380623 | ||||||||
\(768\) | 9.41931e6 | 0.576257 | ||||||||
\(769\) | 2.96407e7 | 1.80748 | 0.903739 | − | 0.428084i | \(-0.140811\pi\) | ||||
0.903739 | + | 0.428084i | \(0.140811\pi\) | |||||||
\(770\) | −2.21630e7 | −1.34711 | ||||||||
\(771\) | 227822. | 0.0138026 | ||||||||
\(772\) | −1.70340e7 | −1.02866 | ||||||||
\(773\) | 1.87755e7 | 1.13017 | 0.565083 | − | 0.825034i | \(-0.308844\pi\) | ||||
0.565083 | + | 0.825034i | \(0.308844\pi\) | |||||||
\(774\) | −1.20352e6 | −0.0722108 | ||||||||
\(775\) | −3.63090e7 | −2.17150 | ||||||||
\(776\) | −2.62680e7 | −1.56593 | ||||||||
\(777\) | −2.65001e7 | −1.57469 | ||||||||
\(778\) | 1.78722e7 | 1.05859 | ||||||||
\(779\) | −1.21517e6 | −0.0717453 | ||||||||
\(780\) | 1.49414e7 | 0.879333 | ||||||||
\(781\) | −448076. | −0.0262860 | ||||||||
\(782\) | −3.01297e7 | −1.76188 | ||||||||
\(783\) | −407765. | −0.0237687 | ||||||||
\(784\) | −32464.7 | −0.00188634 | ||||||||
\(785\) | −3.29447e6 | −0.190814 | ||||||||
\(786\) | 2.74815e7 | 1.58666 | ||||||||
\(787\) | −1.54112e7 | −0.886951 | −0.443475 | − | 0.896286i | \(-0.646255\pi\) | ||||
−0.443475 | + | 0.896286i | \(0.646255\pi\) | |||||||
\(788\) | 2.67807e7 | 1.53641 | ||||||||
\(789\) | 1.52390e7 | 0.871493 | ||||||||
\(790\) | −5.59582e7 | −3.19004 | ||||||||
\(791\) | −5.01906e7 | −2.85221 | ||||||||
\(792\) | 1.77249e6 | 0.100409 | ||||||||
\(793\) | 5.69894e6 | 0.321819 | ||||||||
\(794\) | 1.56242e7 | 0.879522 | ||||||||
\(795\) | 6.52111e6 | 0.365935 | ||||||||
\(796\) | −2.75073e7 | −1.53874 | ||||||||
\(797\) | 2.10597e7 | 1.17437 | 0.587186 | − | 0.809452i | \(-0.300236\pi\) | ||||
0.587186 | + | 0.809452i | \(0.300236\pi\) | |||||||
\(798\) | 1.13587e7 | 0.631427 | ||||||||
\(799\) | −1.65643e7 | −0.917925 | ||||||||
\(800\) | 3.47840e7 | 1.92156 | ||||||||
\(801\) | −4.37072e6 | −0.240698 | ||||||||
\(802\) | −4.13334e7 | −2.26916 | ||||||||
\(803\) | 2.39677e6 | 0.131171 | ||||||||
\(804\) | 2.61739e6 | 0.142800 | ||||||||
\(805\) | 8.24490e7 | 4.48431 | ||||||||
\(806\) | −1.85992e7 | −1.00845 | ||||||||
\(807\) | −4.22428e6 | −0.228333 | ||||||||
\(808\) | 1.39642e7 | 0.752467 | ||||||||
\(809\) | 1.95659e7 | 1.05106 | 0.525532 | − | 0.850774i | \(-0.323866\pi\) | ||||
0.525532 | + | 0.850774i | \(0.323866\pi\) | |||||||
\(810\) | −5.73570e6 | −0.307167 | ||||||||
\(811\) | 1.29945e7 | 0.693758 | 0.346879 | − | 0.937910i | \(-0.387241\pi\) | ||||
0.346879 | + | 0.937910i | \(0.387241\pi\) | |||||||
\(812\) | −6.06605e6 | −0.322861 | ||||||||
\(813\) | 1.96507e7 | 1.04268 | ||||||||
\(814\) | −1.55626e7 | −0.823232 | ||||||||
\(815\) | −4.38113e6 | −0.231042 | ||||||||
\(816\) | −8618.43 | −0.000453109 0 | ||||||||
\(817\) | −1.06854e6 | −0.0560063 | ||||||||
\(818\) | 6.59876e6 | 0.344809 | ||||||||
\(819\) | 5.69856e6 | 0.296862 | ||||||||
\(820\) | 9.12830e6 | 0.474084 | ||||||||
\(821\) | −3.50872e7 | −1.81673 | −0.908367 | − | 0.418175i | \(-0.862670\pi\) | ||||
−0.908367 | + | 0.418175i | \(0.862670\pi\) | |||||||
\(822\) | −3.11114e7 | −1.60598 | ||||||||
\(823\) | 1.38494e7 | 0.712742 | 0.356371 | − | 0.934345i | \(-0.384014\pi\) | ||||
0.356371 | + | 0.934345i | \(0.384014\pi\) | |||||||
\(824\) | 1.92065e7 | 0.985440 | ||||||||
\(825\) | 6.53313e6 | 0.334184 | ||||||||
\(826\) | 3.54141e7 | 1.80604 | ||||||||
\(827\) | 2.31031e7 | 1.17464 | 0.587322 | − | 0.809353i | \(-0.300182\pi\) | ||||
0.587322 | + | 0.809353i | \(0.300182\pi\) | |||||||
\(828\) | −1.72720e7 | −0.875522 | ||||||||
\(829\) | −1.28103e6 | −0.0647401 | −0.0323701 | − | 0.999476i | \(-0.510306\pi\) | ||||
−0.0323701 | + | 0.999476i | \(0.510306\pi\) | |||||||
\(830\) | 4.05548e7 | 2.04337 | ||||||||
\(831\) | 758523. | 0.0381036 | ||||||||
\(832\) | 1.78051e7 | 0.891735 | ||||||||
\(833\) | −2.16498e7 | −1.08104 | ||||||||
\(834\) | −3.00899e7 | −1.49798 | ||||||||
\(835\) | 2.77910e7 | 1.37939 | ||||||||
\(836\) | 4.12215e6 | 0.203990 | ||||||||
\(837\) | 4.41213e6 | 0.217688 | ||||||||
\(838\) | −3.56843e7 | −1.75536 | ||||||||
\(839\) | 1.98332e7 | 0.972721 | 0.486361 | − | 0.873758i | \(-0.338324\pi\) | ||||
0.486361 | + | 0.873758i | \(0.338324\pi\) | |||||||
\(840\) | −3.25747e7 | −1.59288 | ||||||||
\(841\) | −2.01983e7 | −0.984746 | ||||||||
\(842\) | 3.10863e7 | 1.51109 | ||||||||
\(843\) | −5.84564e6 | −0.283311 | ||||||||
\(844\) | 2.12172e7 | 1.02526 | ||||||||
\(845\) | −2.46965e7 | −1.18985 | ||||||||
\(846\) | −1.53661e7 | −0.738139 | ||||||||
\(847\) | −3.06759e6 | −0.146923 | ||||||||
\(848\) | 9089.78 | 0.000434074 0 | ||||||||
\(849\) | −1.39404e7 | −0.663751 | ||||||||
\(850\) | 4.38760e7 | 2.08295 | ||||||||
\(851\) | 5.78948e7 | 2.74041 | ||||||||
\(852\) | −1.72507e6 | −0.0814154 | ||||||||
\(853\) | −2.65097e7 | −1.24747 | −0.623737 | − | 0.781634i | \(-0.714386\pi\) | ||||
−0.623737 | + | 0.781634i | \(0.714386\pi\) | |||||||
\(854\) | −3.25452e7 | −1.52701 | ||||||||
\(855\) | −5.09242e6 | −0.238237 | ||||||||
\(856\) | −6.10376e6 | −0.284717 | ||||||||
\(857\) | −1.96831e7 | −0.915465 | −0.457733 | − | 0.889090i | \(-0.651338\pi\) | ||||
−0.457733 | + | 0.889090i | \(0.651338\pi\) | |||||||
\(858\) | 3.34657e6 | 0.155196 | ||||||||
\(859\) | −1.74273e7 | −0.805835 | −0.402917 | − | 0.915236i | \(-0.632004\pi\) | ||||
−0.402917 | + | 0.915236i | \(0.632004\pi\) | |||||||
\(860\) | 8.02684e6 | 0.370083 | ||||||||
\(861\) | 3.48149e6 | 0.160051 | ||||||||
\(862\) | 4.71511e7 | 2.16134 | ||||||||
\(863\) | −6.02685e6 | −0.275463 | −0.137732 | − | 0.990470i | \(-0.543981\pi\) | ||||
−0.137732 | + | 0.990470i | \(0.543981\pi\) | |||||||
\(864\) | −4.22682e6 | −0.192632 | ||||||||
\(865\) | −1.33118e7 | −0.604916 | ||||||||
\(866\) | 2.96024e7 | 1.34132 | ||||||||
\(867\) | 7.03132e6 | 0.317679 | ||||||||
\(868\) | 6.56365e7 | 2.95696 | ||||||||
\(869\) | −7.74520e6 | −0.347923 | ||||||||
\(870\) | 4.40090e6 | 0.197126 | ||||||||
\(871\) | 1.88661e6 | 0.0842630 | ||||||||
\(872\) | 6.86809e6 | 0.305875 | ||||||||
\(873\) | 1.17652e7 | 0.522472 | ||||||||
\(874\) | −2.48154e7 | −1.09886 | ||||||||
\(875\) | −5.75229e7 | −2.53993 | ||||||||
\(876\) | 9.22741e6 | 0.406274 | ||||||||
\(877\) | −5.71518e6 | −0.250917 | −0.125459 | − | 0.992099i | \(-0.540040\pi\) | ||||
−0.125459 | + | 0.992099i | \(0.540040\pi\) | |||||||
\(878\) | −5.77551e7 | −2.52845 | ||||||||
\(879\) | 632490. | 0.0276109 | ||||||||
\(880\) | 13850.1 | 0.000602903 0 | ||||||||
\(881\) | 1.76619e7 | 0.766649 | 0.383324 | − | 0.923614i | \(-0.374779\pi\) | ||||
0.383324 | + | 0.923614i | \(0.374779\pi\) | |||||||
\(882\) | −2.00837e7 | −0.869306 | ||||||||
\(883\) | 2.70117e7 | 1.16587 | 0.582936 | − | 0.812518i | \(-0.301904\pi\) | ||||
0.582936 | + | 0.812518i | \(0.301904\pi\) | |||||||
\(884\) | 1.38888e7 | 0.597769 | ||||||||
\(885\) | −1.58771e7 | −0.681416 | ||||||||
\(886\) | −2.63133e7 | −1.12614 | ||||||||
\(887\) | 1.30141e7 | 0.555398 | 0.277699 | − | 0.960668i | \(-0.410428\pi\) | ||||
0.277699 | + | 0.960668i | \(0.410428\pi\) | |||||||
\(888\) | −2.28736e7 | −0.973425 | ||||||||
\(889\) | −1.86040e7 | −0.789500 | ||||||||
\(890\) | 4.71720e7 | 1.99623 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 1.39700e7 | 0.587875 | ||||||||
\(893\) | −1.36427e7 | −0.572496 | ||||||||
\(894\) | 2.45103e7 | 1.02566 | ||||||||
\(895\) | −5.72700e7 | −2.38984 | ||||||||
\(896\) | −6.28061e7 | −2.61355 | ||||||||
\(897\) | −1.24496e7 | −0.516625 | ||||||||
\(898\) | 4.15834e7 | 1.72080 | ||||||||
\(899\) | −3.38535e6 | −0.139703 | ||||||||
\(900\) | 2.51522e7 | 1.03507 | ||||||||
\(901\) | 6.06172e6 | 0.248762 | ||||||||
\(902\) | 2.04456e6 | 0.0836727 | ||||||||
\(903\) | 3.06140e6 | 0.124940 | ||||||||
\(904\) | −4.33220e7 | −1.76314 | ||||||||
\(905\) | 1.24779e7 | 0.506431 | ||||||||
\(906\) | 2.62009e7 | 1.06046 | ||||||||
\(907\) | 9.84123e6 | 0.397220 | 0.198610 | − | 0.980079i | \(-0.436357\pi\) | ||||
0.198610 | + | 0.980079i | \(0.436357\pi\) | |||||||
\(908\) | −5.28713e7 | −2.12816 | ||||||||
\(909\) | −6.25442e6 | −0.251060 | ||||||||
\(910\) | −6.15030e7 | −2.46203 | ||||||||
\(911\) | 7.41735e6 | 0.296110 | 0.148055 | − | 0.988979i | \(-0.452699\pi\) | ||||
0.148055 | + | 0.988979i | \(0.452699\pi\) | |||||||
\(912\) | −7098.32 | −0.000282598 0 | ||||||||
\(913\) | 5.61321e6 | 0.222861 | ||||||||
\(914\) | −2.54871e7 | −1.00915 | ||||||||
\(915\) | 1.45909e7 | 0.576140 | ||||||||
\(916\) | 8.76177e6 | 0.345027 | ||||||||
\(917\) | −6.99046e7 | −2.74525 | ||||||||
\(918\) | −5.33164e6 | −0.208811 | ||||||||
\(919\) | 1.15896e7 | 0.452667 | 0.226333 | − | 0.974050i | \(-0.427326\pi\) | ||||
0.226333 | + | 0.974050i | \(0.427326\pi\) | |||||||
\(920\) | 7.11659e7 | 2.77206 | ||||||||
\(921\) | −1.29009e7 | −0.501153 | ||||||||
\(922\) | 1.83494e7 | 0.710878 | ||||||||
\(923\) | −1.24342e6 | −0.0480413 | ||||||||
\(924\) | −1.18101e7 | −0.455063 | ||||||||
\(925\) | −8.43087e7 | −3.23980 | ||||||||
\(926\) | 4.27769e7 | 1.63939 | ||||||||
\(927\) | −8.60240e6 | −0.328791 | ||||||||
\(928\) | 3.24316e6 | 0.123623 | ||||||||
\(929\) | 1.17151e7 | 0.445357 | 0.222679 | − | 0.974892i | \(-0.428520\pi\) | ||||
0.222679 | + | 0.974892i | \(0.428520\pi\) | |||||||
\(930\) | −4.76190e7 | −1.80540 | ||||||||
\(931\) | −1.78312e7 | −0.674228 | ||||||||
\(932\) | −1.05827e6 | −0.0399077 | ||||||||
\(933\) | 2.05091e6 | 0.0771336 | ||||||||
\(934\) | 1.29912e7 | 0.487284 | ||||||||
\(935\) | 9.23628e6 | 0.345516 | ||||||||
\(936\) | 4.91871e6 | 0.183511 | ||||||||
\(937\) | 9.18288e6 | 0.341688 | 0.170844 | − | 0.985298i | \(-0.445351\pi\) | ||||
0.170844 | + | 0.985298i | \(0.445351\pi\) | |||||||
\(938\) | −1.07740e7 | −0.399823 | ||||||||
\(939\) | 6.51384e6 | 0.241087 | ||||||||
\(940\) | 1.02484e8 | 3.78299 | ||||||||
\(941\) | 3.24899e6 | 0.119612 | 0.0598059 | − | 0.998210i | \(-0.480952\pi\) | ||||
0.0598059 | + | 0.998210i | \(0.480952\pi\) | |||||||
\(942\) | −2.84086e6 | −0.104309 | ||||||||
\(943\) | −7.60601e6 | −0.278534 | ||||||||
\(944\) | −22131.0 | −0.000808299 0 | ||||||||
\(945\) | 1.45899e7 | 0.531462 | ||||||||
\(946\) | 1.79786e6 | 0.0653171 | ||||||||
\(947\) | 3.50906e7 | 1.27150 | 0.635750 | − | 0.771895i | \(-0.280691\pi\) | ||||
0.635750 | + | 0.771895i | \(0.280691\pi\) | |||||||
\(948\) | −2.98186e7 | −1.07762 | ||||||||
\(949\) | 6.65109e6 | 0.239733 | ||||||||
\(950\) | 3.61372e7 | 1.29911 | ||||||||
\(951\) | −1.13477e7 | −0.406872 | ||||||||
\(952\) | −3.02799e7 | −1.08283 | ||||||||
\(953\) | −3.27415e7 | −1.16780 | −0.583898 | − | 0.811827i | \(-0.698473\pi\) | ||||
−0.583898 | + | 0.811827i | \(0.698473\pi\) | |||||||
\(954\) | 5.62323e6 | 0.200039 | ||||||||
\(955\) | 3.23092e7 | 1.14635 | ||||||||
\(956\) | −4.83209e7 | −1.70998 | ||||||||
\(957\) | 609130. | 0.0214996 | ||||||||
\(958\) | 3.29545e7 | 1.16011 | ||||||||
\(959\) | 7.91379e7 | 2.77868 | ||||||||
\(960\) | 4.55859e7 | 1.59644 | ||||||||
\(961\) | 8.00132e6 | 0.279482 | ||||||||
\(962\) | −4.31868e7 | −1.50457 | ||||||||
\(963\) | 2.73382e6 | 0.0949956 | ||||||||
\(964\) | −6.74227e7 | −2.33676 | ||||||||
\(965\) | −3.14353e7 | −1.08667 | ||||||||
\(966\) | 7.10967e7 | 2.45136 | ||||||||
\(967\) | −3.94890e7 | −1.35803 | −0.679016 | − | 0.734124i | \(-0.737593\pi\) | ||||
−0.679016 | + | 0.734124i | \(0.737593\pi\) | |||||||
\(968\) | −2.64779e6 | −0.0908230 | ||||||||
\(969\) | −4.73367e6 | −0.161953 | ||||||||
\(970\) | −1.26978e8 | −4.33312 | ||||||||
\(971\) | 1.43971e7 | 0.490033 | 0.245017 | − | 0.969519i | \(-0.421207\pi\) | ||||
0.245017 | + | 0.969519i | \(0.421207\pi\) | |||||||
\(972\) | −3.05640e6 | −0.103763 | ||||||||
\(973\) | 7.65396e7 | 2.59182 | ||||||||
\(974\) | 5.10245e7 | 1.72338 | ||||||||
\(975\) | 1.81296e7 | 0.610769 | ||||||||
\(976\) | 20338.2 | 0.000683421 0 | ||||||||
\(977\) | −4.55108e7 | −1.52538 | −0.762690 | − | 0.646764i | \(-0.776122\pi\) | ||||
−0.762690 | + | 0.646764i | \(0.776122\pi\) | |||||||
\(978\) | −3.77790e6 | −0.126300 | ||||||||
\(979\) | 6.52910e6 | 0.217719 | ||||||||
\(980\) | 1.33947e8 | 4.45522 | ||||||||
\(981\) | −3.07615e6 | −0.102055 | ||||||||
\(982\) | 1.65605e7 | 0.548018 | ||||||||
\(983\) | −3.34028e7 | −1.10255 | −0.551276 | − | 0.834323i | \(-0.685859\pi\) | ||||
−0.551276 | + | 0.834323i | \(0.685859\pi\) | |||||||
\(984\) | 3.00505e6 | 0.0989382 | ||||||||
\(985\) | 4.94222e7 | 1.62305 | ||||||||
\(986\) | 4.09087e6 | 0.134006 | ||||||||
\(987\) | 3.90867e7 | 1.27713 | ||||||||
\(988\) | 1.14391e7 | 0.372820 | ||||||||
\(989\) | −6.68823e6 | −0.217431 | ||||||||
\(990\) | 8.56815e6 | 0.277843 | ||||||||
\(991\) | 4.23892e7 | 1.37111 | 0.685553 | − | 0.728023i | \(-0.259560\pi\) | ||||
0.685553 | + | 0.728023i | \(0.259560\pi\) | |||||||
\(992\) | −3.50919e7 | −1.13221 | ||||||||
\(993\) | −3.90100e6 | −0.125546 | ||||||||
\(994\) | 7.10088e6 | 0.227953 | ||||||||
\(995\) | −5.07632e7 | −1.62551 | ||||||||
\(996\) | 2.16105e7 | 0.690267 | ||||||||
\(997\) | 3.39103e7 | 1.08042 | 0.540212 | − | 0.841529i | \(-0.318344\pi\) | ||||
0.540212 | + | 0.841529i | \(0.318344\pi\) | |||||||
\(998\) | 5.44094e7 | 1.72921 | ||||||||
\(999\) | 1.02449e7 | 0.324783 |
(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 | 33.6.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 99.6.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 528.6.a.s.1.2 | 2 | |||
5.4 | even | 2 | 825.6.a.e.1.2 | 2 | |||
11.10 | odd | 2 | 363.6.a.j.1.2 | 2 | |||
33.32 | even | 2 | 1089.6.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.6.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
363.6.a.j.1.2 | 2 | 11.10 | odd | 2 | |||
528.6.a.s.1.2 | 2 | 4.3 | odd | 2 | |||
825.6.a.e.1.2 | 2 | 5.4 | even | 2 | |||
1089.6.a.j.1.1 | 2 | 33.32 | even | 2 |