Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(1,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, 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("450.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(72.1727189158\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{4081}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1020 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(32.4414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −241.648 | −1.86397 | −0.931984 | − | 0.362500i | \(-0.881923\pi\) | ||||
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −653.296 | −1.62790 | −0.813951 | − | 0.580933i | \(-0.802688\pi\) | ||||
−0.813951 | + | 0.580933i | \(0.802688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 828.296 | 1.35934 | 0.679669 | − | 0.733519i | \(-0.262124\pi\) | ||||
0.679669 | + | 0.733519i | \(0.262124\pi\) | |||||||
\(14\) | 966.592 | 1.31802 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 2162.48 | 1.81481 | 0.907403 | − | 0.420262i | \(-0.138062\pi\) | ||||
0.907403 | + | 0.420262i | \(0.138062\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1254.24 | 0.797071 | 0.398535 | − | 0.917153i | \(-0.369519\pi\) | ||||
0.398535 | + | 0.917153i | \(0.369519\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2613.18 | 1.15110 | ||||||||
\(23\) | 3746.48 | 1.47674 | 0.738370 | − | 0.674396i | \(-0.235596\pi\) | ||||
0.738370 | + | 0.674396i | \(0.235596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3313.18 | −0.961197 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3866.37 | −0.931984 | ||||||||
\(29\) | −2466.70 | −0.544656 | −0.272328 | − | 0.962205i | \(-0.587794\pi\) | ||||
−0.272328 | + | 0.962205i | \(0.587794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1895.76 | −0.354306 | −0.177153 | − | 0.984183i | \(-0.556689\pi\) | ||||
−0.177153 | + | 0.984183i | \(0.556689\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8649.92 | −1.28326 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1050.45 | 0.126145 | 0.0630724 | − | 0.998009i | \(-0.479910\pi\) | ||||
0.0630724 | + | 0.998009i | \(0.479910\pi\) | |||||||
\(38\) | −5016.96 | −0.563614 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1960.56 | −0.182146 | −0.0910730 | − | 0.995844i | \(-0.529030\pi\) | ||||
−0.0910730 | + | 0.995844i | \(0.529030\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11017.6 | 0.908688 | 0.454344 | − | 0.890826i | \(-0.349874\pi\) | ||||
0.454344 | + | 0.890826i | \(0.349874\pi\) | |||||||
\(44\) | −10452.7 | −0.813951 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14985.9 | −1.04421 | ||||||||
\(47\) | −23064.8 | −1.52302 | −0.761509 | − | 0.648154i | \(-0.775541\pi\) | ||||
−0.761509 | + | 0.648154i | \(0.775541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41586.8 | 2.47437 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13252.7 | 0.679669 | ||||||||
\(53\) | −27329.4 | −1.33641 | −0.668205 | − | 0.743977i | \(-0.732937\pi\) | ||||
−0.668205 | + | 0.743977i | \(0.732937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 15465.5 | 0.659012 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9866.82 | 0.385130 | ||||||||
\(59\) | −35225.7 | −1.31744 | −0.658718 | − | 0.752390i | \(-0.728901\pi\) | ||||
−0.658718 | + | 0.752390i | \(0.728901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2685.33 | 0.0924002 | 0.0462001 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0462001 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(62\) | 7583.04 | 0.250532 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48125.1 | 1.30974 | 0.654869 | − | 0.755743i | \(-0.272724\pi\) | ||||
0.654869 | + | 0.755743i | \(0.272724\pi\) | |||||||
\(68\) | 34599.7 | 0.907403 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −27237.7 | −0.641245 | −0.320622 | − | 0.947207i | \(-0.603892\pi\) | ||||
−0.320622 | + | 0.947207i | \(0.603892\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6547.77 | −0.143809 | −0.0719046 | − | 0.997412i | \(-0.522908\pi\) | ||||
−0.0719046 | + | 0.997412i | \(0.522908\pi\) | |||||||
\(74\) | −4201.78 | −0.0891978 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20067.8 | 0.398535 | ||||||||
\(77\) | 157868. | 3.03436 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −65037.3 | −1.17245 | −0.586226 | − | 0.810148i | \(-0.699387\pi\) | ||||
−0.586226 | + | 0.810148i | \(0.699387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7842.23 | 0.128797 | ||||||||
\(83\) | −62567.2 | −0.996900 | −0.498450 | − | 0.866919i | \(-0.666097\pi\) | ||||
−0.498450 | + | 0.866919i | \(0.666097\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −44070.3 | −0.642539 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 41811.0 | 0.575551 | ||||||||
\(89\) | −17926.2 | −0.239891 | −0.119946 | − | 0.992780i | \(-0.538272\pi\) | ||||
−0.119946 | + | 0.992780i | \(0.538272\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −200156. | −2.53376 | ||||||||
\(92\) | 59943.7 | 0.738370 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 92259.2 | 1.07694 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 95974.9 | 1.03569 | 0.517843 | − | 0.855475i | \(-0.326735\pi\) | ||||
0.517843 | + | 0.855475i | \(0.326735\pi\) | |||||||
\(98\) | −166347. | −1.74965 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −41533.7 | −0.405133 | −0.202567 | − | 0.979269i | \(-0.564928\pi\) | ||||
−0.202567 | + | 0.979269i | \(0.564928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −41380.4 | −0.384328 | −0.192164 | − | 0.981363i | \(-0.561551\pi\) | ||||
−0.192164 | + | 0.981363i | \(0.561551\pi\) | |||||||
\(104\) | −53011.0 | −0.480598 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 109317. | 0.944985 | ||||||||
\(107\) | 11403.4 | 0.0962885 | 0.0481442 | − | 0.998840i | \(-0.484669\pi\) | ||||
0.0481442 | + | 0.998840i | \(0.484669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 98362.4 | 0.792981 | 0.396490 | − | 0.918039i | \(-0.370228\pi\) | ||||
0.396490 | + | 0.918039i | \(0.370228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −61861.9 | −0.465992 | ||||||||
\(113\) | −10076.8 | −0.0742377 | −0.0371189 | − | 0.999311i | \(-0.511818\pi\) | ||||
−0.0371189 | + | 0.999311i | \(0.511818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39467.3 | −0.272328 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 140903. | 0.931568 | ||||||||
\(119\) | −522559. | −3.38274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 265745. | 1.65007 | ||||||||
\(122\) | −10741.3 | −0.0653368 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −30332.2 | −0.177153 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −255129. | −1.40362 | −0.701812 | − | 0.712362i | \(-0.747626\pi\) | ||||
−0.701812 | + | 0.712362i | \(0.747626\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 65433.3 | 0.333135 | 0.166568 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166568 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −303085. | −1.48571 | ||||||||
\(134\) | −192500. | −0.926124 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −138399. | −0.641631 | ||||||||
\(137\) | 67354.0 | 0.306593 | 0.153296 | − | 0.988180i | \(-0.451011\pi\) | ||||
0.153296 | + | 0.988180i | \(0.451011\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −93837.8 | −0.411946 | −0.205973 | − | 0.978558i | \(-0.566036\pi\) | ||||
−0.205973 | + | 0.978558i | \(0.566036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 108951. | 0.453429 | ||||||||
\(143\) | −541123. | −2.21287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 26191.1 | 0.101688 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16807.1 | 0.0630724 | ||||||||
\(149\) | −432235. | −1.59498 | −0.797489 | − | 0.603334i | \(-0.793839\pi\) | ||||
−0.797489 | + | 0.603334i | \(0.793839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −255822. | −0.913053 | −0.456527 | − | 0.889710i | \(-0.650907\pi\) | ||||
−0.456527 | + | 0.889710i | \(0.650907\pi\) | |||||||
\(152\) | −80271.4 | −0.281807 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −631471. | −2.14561 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −58837.3 | −0.190504 | −0.0952519 | − | 0.995453i | \(-0.530366\pi\) | ||||
−0.0952519 | + | 0.995453i | \(0.530366\pi\) | |||||||
\(158\) | 260149. | 0.829048 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −905330. | −2.75259 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 155006. | 0.456962 | 0.228481 | − | 0.973548i | \(-0.426624\pi\) | ||||
0.228481 | + | 0.973548i | \(0.426624\pi\) | |||||||
\(164\) | −31368.9 | −0.0910730 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 250269. | 0.704914 | ||||||||
\(167\) | 588656. | 1.63332 | 0.816658 | − | 0.577121i | \(-0.195824\pi\) | ||||
0.816658 | + | 0.577121i | \(0.195824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 314782. | 0.847798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 176281. | 0.454344 | ||||||||
\(173\) | −192049. | −0.487862 | −0.243931 | − | 0.969793i | \(-0.578437\pi\) | ||||
−0.243931 | + | 0.969793i | \(0.578437\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −167244. | −0.406976 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 71704.9 | 0.169629 | ||||||||
\(179\) | 350715. | 0.818130 | 0.409065 | − | 0.912505i | \(-0.365855\pi\) | ||||
0.409065 | + | 0.912505i | \(0.365855\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 524637. | 1.19032 | 0.595158 | − | 0.803608i | \(-0.297089\pi\) | ||||
0.595158 | + | 0.803608i | \(0.297089\pi\) | |||||||
\(182\) | 800625. | 1.79164 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −239775. | −0.522106 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41274e6 | −2.95433 | ||||||||
\(188\) | −369037. | −0.761509 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −63662.7 | −0.126270 | −0.0631352 | − | 0.998005i | \(-0.520110\pi\) | ||||
−0.0631352 | + | 0.998005i | \(0.520110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −717477. | −1.38648 | −0.693242 | − | 0.720705i | \(-0.743818\pi\) | ||||
−0.693242 | + | 0.720705i | \(0.743818\pi\) | |||||||
\(194\) | −383900. | −0.732341 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 665389. | 1.23719 | ||||||||
\(197\) | 287465. | 0.527740 | 0.263870 | − | 0.964558i | \(-0.415001\pi\) | ||||
0.263870 | + | 0.964558i | \(0.415001\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 643619. | 1.15212 | 0.576058 | − | 0.817409i | \(-0.304590\pi\) | ||||
0.576058 | + | 0.817409i | \(0.304590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 166135. | 0.286472 | ||||||||
\(203\) | 596074. | 1.01522 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 165522. | 0.271761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 212044. | 0.339834 | ||||||||
\(209\) | −819391. | −1.29755 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −873827. | −1.35120 | −0.675600 | − | 0.737269i | \(-0.736115\pi\) | ||||
−0.675600 | + | 0.737269i | \(0.736115\pi\) | |||||||
\(212\) | −437270. | −0.668205 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −45613.5 | −0.0680862 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 458107. | 0.660416 | ||||||||
\(218\) | −393449. | −0.560722 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.79117e6 | 2.46693 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −288496. | −0.388488 | −0.194244 | − | 0.980953i | \(-0.562225\pi\) | ||||
−0.194244 | + | 0.980953i | \(0.562225\pi\) | |||||||
\(224\) | 247448. | 0.329506 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 40307.0 | 0.0524940 | ||||||||
\(227\) | −125358. | −0.161469 | −0.0807343 | − | 0.996736i | \(-0.525727\pi\) | ||||
−0.0807343 | + | 0.996736i | \(0.525727\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −698183. | −0.879793 | −0.439897 | − | 0.898048i | \(-0.644985\pi\) | ||||
−0.439897 | + | 0.898048i | \(0.644985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 157869. | 0.192565 | ||||||||
\(233\) | −984588. | −1.18813 | −0.594066 | − | 0.804416i | \(-0.702478\pi\) | ||||
−0.594066 | + | 0.804416i | \(0.702478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −563611. | −0.658718 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.09024e6 | 2.39196 | ||||||||
\(239\) | −131049. | −0.148402 | −0.0742011 | − | 0.997243i | \(-0.523641\pi\) | ||||
−0.0742011 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.23632e6 | −1.37116 | −0.685579 | − | 0.727998i | \(-0.740451\pi\) | ||||
−0.685579 | + | 0.727998i | \(0.740451\pi\) | |||||||
\(242\) | −1.06298e6 | −1.16677 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 42965.3 | 0.0462001 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.03888e6 | 1.08349 | ||||||||
\(248\) | 121329. | 0.125266 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −611918. | −0.613068 | −0.306534 | − | 0.951860i | \(-0.599169\pi\) | ||||
−0.306534 | + | 0.951860i | \(0.599169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.44756e6 | −2.40399 | ||||||||
\(254\) | 1.02052e6 | 0.992513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.64515e6 | −1.55372 | −0.776858 | − | 0.629675i | \(-0.783188\pi\) | ||||
−0.776858 | + | 0.629675i | \(0.783188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −253838. | −0.235130 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −261733. | −0.235562 | ||||||||
\(263\) | 268273. | 0.239159 | 0.119580 | − | 0.992825i | \(-0.461845\pi\) | ||||
0.119580 | + | 0.992825i | \(0.461845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.21234e6 | 1.05056 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 770001. | 0.654869 | ||||||||
\(269\) | 947177. | 0.798087 | 0.399044 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399044 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 609159. | 0.503857 | 0.251929 | − | 0.967746i | \(-0.418935\pi\) | ||||
0.251929 | + | 0.967746i | \(0.418935\pi\) | |||||||
\(272\) | 553595. | 0.453701 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −269416. | −0.216794 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 741976. | 0.581019 | 0.290510 | − | 0.956872i | \(-0.406175\pi\) | ||||
0.290510 | + | 0.956872i | \(0.406175\pi\) | |||||||
\(278\) | 375351. | 0.291290 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 423084. | 0.319639 | 0.159820 | − | 0.987146i | \(-0.448909\pi\) | ||||
0.159820 | + | 0.987146i | \(0.448909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −445130. | −0.330385 | −0.165192 | − | 0.986261i | \(-0.552825\pi\) | ||||
−0.165192 | + | 0.986261i | \(0.552825\pi\) | |||||||
\(284\) | −435803. | −0.320622 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.16449e6 | 1.56473 | ||||||||
\(287\) | 473765. | 0.339514 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.25647e6 | 2.29352 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −104764. | −0.0719046 | ||||||||
\(293\) | 2.45992e6 | 1.67399 | 0.836994 | − | 0.547211i | \(-0.184311\pi\) | ||||
0.836994 | + | 0.547211i | \(0.184311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −67228.5 | −0.0445989 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.72894e6 | 1.12782 | ||||||||
\(299\) | 3.10320e6 | 2.00739 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.66238e6 | −1.69376 | ||||||||
\(302\) | 1.02329e6 | 0.645626 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 321086. | 0.199268 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 374253. | 0.226631 | 0.113315 | − | 0.993559i | \(-0.463853\pi\) | ||||
0.113315 | + | 0.993559i | \(0.463853\pi\) | |||||||
\(308\) | 2.52588e6 | 1.51718 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.22568e6 | −1.30485 | −0.652427 | − | 0.757851i | \(-0.726249\pi\) | ||||
−0.652427 | + | 0.757851i | \(0.726249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.05869e6 | 1.76471 | 0.882357 | − | 0.470580i | \(-0.155955\pi\) | ||||
0.882357 | + | 0.470580i | \(0.155955\pi\) | |||||||
\(314\) | 235349. | 0.134706 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04060e6 | −0.586226 | ||||||||
\(317\) | −520610. | −0.290981 | −0.145490 | − | 0.989360i | \(-0.546476\pi\) | ||||
−0.145490 | + | 0.989360i | \(0.546476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.61149e6 | 0.886646 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.62132e6 | 1.94638 | ||||||||
\(323\) | 2.71227e6 | 1.44653 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −620025. | −0.323121 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 125476. | 0.0643983 | ||||||||
\(329\) | 5.57357e6 | 2.83886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.12755e6 | −1.06736 | −0.533679 | − | 0.845687i | \(-0.679191\pi\) | ||||
−0.533679 | + | 0.845687i | \(0.679191\pi\) | |||||||
\(332\) | −1.00108e6 | −0.498450 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.35462e6 | −1.15493 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.08383e6 | −1.47916 | −0.739581 | − | 0.673067i | \(-0.764976\pi\) | ||||
−0.739581 | + | 0.673067i | \(0.764976\pi\) | |||||||
\(338\) | −1.25913e6 | −0.599484 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.23849e6 | 0.576776 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.98799e6 | −2.74819 | ||||||||
\(344\) | −705125. | −0.321270 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 768196. | 0.344970 | ||||||||
\(347\) | −4.04955e6 | −1.80544 | −0.902719 | − | 0.430231i | \(-0.858432\pi\) | ||||
−0.902719 | + | 0.430231i | \(0.858432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −493135. | −0.216722 | −0.108361 | − | 0.994112i | \(-0.534560\pi\) | ||||
−0.108361 | + | 0.994112i | \(0.534560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 668975. | 0.287775 | ||||||||
\(353\) | −1.34815e6 | −0.575841 | −0.287920 | − | 0.957654i | \(-0.592964\pi\) | ||||
−0.287920 | + | 0.957654i | \(0.592964\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −286820. | −0.119946 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.40286e6 | −0.578505 | ||||||||
\(359\) | −1.64749e6 | −0.674664 | −0.337332 | − | 0.941386i | \(-0.609524\pi\) | ||||
−0.337332 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −902980. | −0.364678 | ||||||||
\(362\) | −2.09855e6 | −0.841681 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.20250e6 | −1.26688 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27918.4 | −0.0108199 | −0.00540997 | − | 0.999985i | \(-0.501722\pi\) | ||||
−0.00540997 | + | 0.999985i | \(0.501722\pi\) | |||||||
\(368\) | 959099. | 0.369185 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.60409e6 | 2.49103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.80536e6 | 1.04404 | 0.522019 | − | 0.852934i | \(-0.325179\pi\) | ||||
0.522019 | + | 0.852934i | \(0.325179\pi\) | |||||||
\(374\) | 5.65096e6 | 2.08902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.47615e6 | 0.538468 | ||||||||
\(377\) | −2.04316e6 | −0.740371 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.70014e6 | 0.607976 | 0.303988 | − | 0.952676i | \(-0.401682\pi\) | ||||
0.303988 | + | 0.952676i | \(0.401682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 254651. | 0.0892867 | ||||||||
\(383\) | −627913. | −0.218727 | −0.109363 | − | 0.994002i | \(-0.534881\pi\) | ||||
−0.109363 | + | 0.994002i | \(0.534881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.86991e6 | 0.980392 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.53560e6 | 0.517843 | ||||||||
\(389\) | −3.14339e6 | −1.05323 | −0.526616 | − | 0.850103i | \(-0.676540\pi\) | ||||
−0.526616 | + | 0.850103i | \(0.676540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.10169e6 | 2.68000 | ||||||||
\(392\) | −2.66156e6 | −0.874823 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.14986e6 | −0.373169 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.10773e6 | −0.352743 | −0.176371 | − | 0.984324i | \(-0.556436\pi\) | ||||
−0.176371 | + | 0.984324i | \(0.556436\pi\) | |||||||
\(398\) | −2.57448e6 | −0.814669 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.41563e6 | −0.750187 | −0.375093 | − | 0.926987i | \(-0.622389\pi\) | ||||
−0.375093 | + | 0.926987i | \(0.622389\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.57025e6 | −0.481622 | ||||||||
\(404\) | −664540. | −0.202567 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.38430e6 | −0.717869 | ||||||||
\(407\) | −686252. | −0.205351 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.69830e6 | 1.09319 | 0.546593 | − | 0.837398i | \(-0.315925\pi\) | ||||
0.546593 | + | 0.837398i | \(0.315925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −662087. | −0.192164 | ||||||||
\(413\) | 8.51222e6 | 2.45566 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −848175. | −0.240299 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.27756e6 | 0.917509 | ||||||||
\(419\) | 3.45478e6 | 0.961357 | 0.480679 | − | 0.876897i | \(-0.340390\pi\) | ||||
0.480679 | + | 0.876897i | \(0.340390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.83980e6 | −1.33083 | −0.665415 | − | 0.746474i | \(-0.731745\pi\) | ||||
−0.665415 | + | 0.746474i | \(0.731745\pi\) | |||||||
\(422\) | 3.49531e6 | 0.955442 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.74908e6 | 0.472493 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −648905. | −0.172231 | ||||||||
\(428\) | 182454. | 0.0481442 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.54923e6 | 1.43893 | 0.719464 | − | 0.694529i | \(-0.244387\pi\) | ||||
0.719464 | + | 0.694529i | \(0.244387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −814302. | −0.208721 | −0.104360 | − | 0.994540i | \(-0.533280\pi\) | ||||
−0.104360 | + | 0.994540i | \(0.533280\pi\) | |||||||
\(434\) | −1.83243e6 | −0.466984 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.57380e6 | 0.396490 | ||||||||
\(437\) | 4.69899e6 | 1.17707 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.02462e6 | −0.996697 | −0.498349 | − | 0.866977i | \(-0.666060\pi\) | ||||
−0.498349 | + | 0.866977i | \(0.666060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.16470e6 | −1.74438 | ||||||||
\(443\) | −4.46382e6 | −1.08068 | −0.540341 | − | 0.841446i | \(-0.681705\pi\) | ||||
−0.540341 | + | 0.841446i | \(0.681705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.15399e6 | 0.274703 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −989791. | −0.232996 | ||||||||
\(449\) | 4.66889e6 | 1.09294 | 0.546472 | − | 0.837477i | \(-0.315970\pi\) | ||||
0.546472 | + | 0.837477i | \(0.315970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.28082e6 | 0.296516 | ||||||||
\(452\) | −161228. | −0.0371189 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 501433. | 0.114176 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.71340e6 | −1.05571 | −0.527854 | − | 0.849335i | \(-0.677003\pi\) | ||||
−0.527854 | + | 0.849335i | \(0.677003\pi\) | |||||||
\(458\) | 2.79273e6 | 0.622108 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.23975e6 | −1.36746 | −0.683731 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683731 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.33992e6 | −0.724076 | −0.362038 | − | 0.932163i | \(-0.617919\pi\) | ||||
−0.362038 | + | 0.932163i | \(0.617919\pi\) | |||||||
\(464\) | −631476. | −0.136164 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.93835e6 | 0.840136 | ||||||||
\(467\) | 722497. | 0.153301 | 0.0766503 | − | 0.997058i | \(-0.475578\pi\) | ||||
0.0766503 | + | 0.997058i | \(0.475578\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.16293e7 | −2.44131 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.25444e6 | 0.465784 | ||||||||
\(473\) | −7.19774e6 | −1.47926 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.36095e6 | −1.69137 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 524197. | 0.104936 | ||||||||
\(479\) | 5.37714e6 | 1.07081 | 0.535405 | − | 0.844595i | \(-0.320159\pi\) | ||||
0.535405 | + | 0.844595i | \(0.320159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 870080. | 0.171473 | ||||||||
\(482\) | 4.94527e6 | 0.969556 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.25192e6 | 0.825034 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.72084e6 | −0.328790 | −0.164395 | − | 0.986395i | \(-0.552567\pi\) | ||||
−0.164395 | + | 0.986395i | \(0.552567\pi\) | |||||||
\(488\) | −171861. | −0.0326684 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.31449e6 | −1.36924 | −0.684621 | − | 0.728899i | \(-0.740032\pi\) | ||||
−0.684621 | + | 0.728899i | \(0.740032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.33420e6 | −0.988444 | ||||||||
\(494\) | −4.15553e6 | −0.766142 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −485314. | −0.0885766 | ||||||||
\(497\) | 6.58193e6 | 1.19526 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.29878e6 | −1.31220 | −0.656098 | − | 0.754676i | \(-0.727794\pi\) | ||||
−0.656098 | + | 0.754676i | \(0.727794\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.44767e6 | 0.433505 | ||||||||
\(503\) | 923591. | 0.162764 | 0.0813822 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813822 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.79025e6 | 1.69988 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.08207e6 | −0.701812 | ||||||||
\(509\) | −8.81318e6 | −1.50778 | −0.753891 | − | 0.657000i | \(-0.771825\pi\) | ||||
−0.753891 | + | 0.657000i | \(0.771825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.58226e6 | 0.268056 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.58059e6 | 1.09864 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.50682e7 | 2.47933 | ||||||||
\(518\) | 1.01535e6 | 0.166262 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.66995e6 | −0.269531 | −0.134765 | − | 0.990878i | \(-0.543028\pi\) | ||||
−0.134765 | + | 0.990878i | \(0.543028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.85438e6 | 0.456308 | 0.228154 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228154 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(524\) | 1.04693e6 | 0.166568 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.07309e6 | −0.169111 | ||||||||
\(527\) | −4.09954e6 | −0.642997 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.59978e6 | 1.18076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.84936e6 | −0.742857 | ||||||||
\(533\) | −1.62392e6 | −0.247598 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.08000e6 | −0.463062 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.78871e6 | −0.564333 | ||||||||
\(539\) | −2.71685e7 | −4.02804 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.85655e6 | −1.15409 | −0.577044 | − | 0.816713i | \(-0.695794\pi\) | ||||
−0.577044 | + | 0.816713i | \(0.695794\pi\) | |||||||
\(542\) | −2.43664e6 | −0.356281 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.21438e6 | −0.320815 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.07748e7 | −1.53972 | −0.769860 | − | 0.638213i | \(-0.779674\pi\) | ||||
−0.769860 | + | 0.638213i | \(0.779674\pi\) | |||||||
\(548\) | 1.07766e6 | 0.153296 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.09384e6 | −0.434129 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.57161e7 | 2.18541 | ||||||||
\(554\) | −2.96791e6 | −0.410843 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.50140e6 | −0.205973 | ||||||||
\(557\) | −7.62158e6 | −1.04090 | −0.520448 | − | 0.853893i | \(-0.674235\pi\) | ||||
−0.520448 | + | 0.853893i | \(0.674235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.12581e6 | 1.23521 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.69233e6 | −0.226019 | ||||||||
\(563\) | −4.25551e6 | −0.565823 | −0.282911 | − | 0.959146i | \(-0.591300\pi\) | ||||
−0.282911 | + | 0.959146i | \(0.591300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.78052e6 | 0.233617 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.74321e6 | 0.226714 | ||||||||
\(569\) | −5.99899e6 | −0.776779 | −0.388389 | − | 0.921495i | \(-0.626968\pi\) | ||||
−0.388389 | + | 0.921495i | \(0.626968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.20283e6 | 1.18122 | 0.590611 | − | 0.806957i | \(-0.298887\pi\) | ||||
0.590611 | + | 0.806957i | \(0.298887\pi\) | |||||||
\(572\) | −8.65796e6 | −1.10643 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.89506e6 | −0.240073 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.03879e6 | 0.505024 | 0.252512 | − | 0.967594i | \(-0.418743\pi\) | ||||
0.252512 | + | 0.967594i | \(0.418743\pi\) | |||||||
\(578\) | −1.30259e7 | −1.62176 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.51192e7 | 1.85819 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.78542e7 | 2.17555 | ||||||||
\(584\) | 419058. | 0.0508442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.83969e6 | −1.18369 | ||||||||
\(587\) | 1.65997e7 | 1.98840 | 0.994200 | − | 0.107544i | \(-0.0342987\pi\) | ||||
0.994200 | + | 0.107544i | \(0.0342987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.37774e6 | −0.282407 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 268914. | 0.0315362 | ||||||||
\(593\) | −1.09900e7 | −1.28340 | −0.641698 | − | 0.766957i | \(-0.721770\pi\) | ||||
−0.641698 | + | 0.766957i | \(0.721770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.91577e6 | −0.797489 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.24128e7 | −1.41944 | ||||||||
\(599\) | −4.47167e6 | −0.509217 | −0.254608 | − | 0.967044i | \(-0.581947\pi\) | ||||
−0.254608 | + | 0.967044i | \(0.581947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.60311e7 | 1.81041 | 0.905206 | − | 0.424974i | \(-0.139717\pi\) | ||||
0.905206 | + | 0.424974i | \(0.139717\pi\) | |||||||
\(602\) | 1.06495e7 | 1.19767 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.09316e6 | −0.456527 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −720250. | −0.0793435 | −0.0396718 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396718 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(608\) | −1.28434e6 | −0.140904 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.91045e7 | −2.07030 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.46218e7 | −1.57163 | −0.785813 | − | 0.618464i | \(-0.787755\pi\) | ||||
−0.785813 | + | 0.618464i | \(0.787755\pi\) | |||||||
\(614\) | −1.49701e6 | −0.160252 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.01035e7 | −1.07281 | ||||||||
\(617\) | 4.57269e6 | 0.483569 | 0.241784 | − | 0.970330i | \(-0.422267\pi\) | ||||
0.241784 | + | 0.970330i | \(0.422267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.62486e6 | −0.485145 | −0.242573 | − | 0.970133i | \(-0.577991\pi\) | ||||
−0.242573 | + | 0.970133i | \(0.577991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.90273e6 | 0.922671 | ||||||||
\(623\) | 4.33184e6 | 0.447149 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.22348e7 | −1.24784 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −941397. | −0.0952519 | ||||||||
\(629\) | 2.27157e6 | 0.228928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.03670e7 | −1.03653 | −0.518263 | − | 0.855221i | \(-0.673421\pi\) | ||||
−0.518263 | + | 0.855221i | \(0.673421\pi\) | |||||||
\(632\) | 4.16239e6 | 0.414524 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.08244e6 | 0.205755 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.44462e7 | 3.36351 | ||||||||
\(638\) | −6.44595e6 | −0.626954 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.62432e6 | 0.444532 | 0.222266 | − | 0.974986i | \(-0.428655\pi\) | ||||
0.222266 | + | 0.974986i | \(0.428655\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.13460e7 | 1.08222 | 0.541111 | − | 0.840951i | \(-0.318004\pi\) | ||||
0.541111 | + | 0.840951i | \(0.318004\pi\) | |||||||
\(644\) | −1.44853e7 | −1.37630 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.08491e7 | −1.02285 | ||||||||
\(647\) | 1.10482e7 | 1.03760 | 0.518800 | − | 0.854895i | \(-0.326379\pi\) | ||||
0.518800 | + | 0.854895i | \(0.326379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.30128e7 | 2.14466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.48010e6 | 0.228481 | ||||||||
\(653\) | −1.37432e6 | −0.126126 | −0.0630631 | − | 0.998010i | \(-0.520087\pi\) | ||||
−0.0630631 | + | 0.998010i | \(0.520087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −501902. | −0.0455365 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.22943e7 | −2.00738 | ||||||||
\(659\) | 1.28061e7 | 1.14869 | 0.574344 | − | 0.818614i | \(-0.305257\pi\) | ||||
0.574344 | + | 0.818614i | \(0.305257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −104794. | −0.00932894 | −0.00466447 | − | 0.999989i | \(-0.501485\pi\) | ||||
−0.00466447 | + | 0.999989i | \(0.501485\pi\) | |||||||
\(662\) | 8.51021e6 | 0.754737 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.00430e6 | 0.352457 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.24146e6 | −0.804315 | ||||||||
\(668\) | 9.41850e6 | 0.816658 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.75432e6 | −0.150419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80490e7 | 1.53608 | 0.768042 | − | 0.640400i | \(-0.221231\pi\) | ||||
0.768042 | + | 0.640400i | \(0.221231\pi\) | |||||||
\(674\) | 1.23353e7 | 1.04593 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.03651e6 | 0.423899 | ||||||||
\(677\) | 1.29914e7 | 1.08939 | 0.544697 | − | 0.838633i | \(-0.316645\pi\) | ||||
0.544697 | + | 0.838633i | \(0.316645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.31922e7 | −1.93049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.95397e6 | −0.407842 | ||||||||
\(683\) | −3.91843e6 | −0.321411 | −0.160705 | − | 0.987002i | \(-0.551377\pi\) | ||||
−0.160705 | + | 0.987002i | \(0.551377\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.39520e7 | 1.94326 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.82050e6 | 0.227172 | ||||||||
\(689\) | −2.26368e7 | −1.81663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.11077e6 | −0.247840 | −0.123920 | − | 0.992292i | \(-0.539547\pi\) | ||||
−0.123920 | + | 0.992292i | \(0.539547\pi\) | |||||||
\(692\) | −3.07278e6 | −0.243931 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.61982e7 | 1.27664 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.23967e6 | −0.330560 | ||||||||
\(698\) | 1.97254e6 | 0.153245 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.94916e7 | −1.49814 | −0.749070 | − | 0.662490i | \(-0.769500\pi\) | ||||
−0.749070 | + | 0.662490i | \(0.769500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31751e6 | 0.100546 | ||||||||
\(704\) | −2.67590e6 | −0.203488 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.39261e6 | 0.407181 | ||||||||
\(707\) | 1.00366e7 | 0.755155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.13693e6 | −0.607918 | −0.303959 | − | 0.952685i | \(-0.598309\pi\) | ||||
−0.303959 | + | 0.952685i | \(0.598309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.14728e6 | 0.0848143 | ||||||||
\(713\) | −7.10243e6 | −0.523218 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.61144e6 | 0.409065 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.58997e6 | 0.477059 | ||||||||
\(719\) | 1.14993e7 | 0.829566 | 0.414783 | − | 0.909920i | \(-0.363857\pi\) | ||||
0.414783 | + | 0.909920i | \(0.363857\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.99951e6 | 0.716375 | ||||||||
\(722\) | 3.61192e6 | 0.257867 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.39419e6 | 0.595158 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.10897e7 | −1.47991 | −0.739953 | − | 0.672658i | \(-0.765152\pi\) | ||||
−0.739953 | + | 0.672658i | \(0.765152\pi\) | |||||||
\(728\) | 1.28100e7 | 0.895820 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.38253e7 | 1.64909 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.20274e7 | 1.51427 | 0.757134 | − | 0.653259i | \(-0.226599\pi\) | ||||
0.757134 | + | 0.653259i | \(0.226599\pi\) | |||||||
\(734\) | 111673. | 0.00765085 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.83640e6 | −0.261053 | ||||||||
\(737\) | −3.14399e7 | −2.13213 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.26088e7 | −0.849305 | −0.424653 | − | 0.905356i | \(-0.639604\pi\) | ||||
−0.424653 | + | 0.905356i | \(0.639604\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.64164e7 | −1.76142 | ||||||||
\(743\) | −5.90968e6 | −0.392728 | −0.196364 | − | 0.980531i | \(-0.562913\pi\) | ||||
−0.196364 | + | 0.980531i | \(0.562913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.12214e7 | −0.738247 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.26039e7 | −1.47716 | ||||||||
\(749\) | −2.75561e6 | −0.179479 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.15585e7 | −0.747830 | −0.373915 | − | 0.927463i | \(-0.621985\pi\) | ||||
−0.373915 | + | 0.927463i | \(0.621985\pi\) | |||||||
\(752\) | −5.90459e6 | −0.380755 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.17265e6 | 0.523521 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.64988e7 | 1.68068 | 0.840342 | − | 0.542057i | \(-0.182354\pi\) | ||||
0.840342 | + | 0.542057i | \(0.182354\pi\) | |||||||
\(758\) | −6.80056e6 | −0.429904 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.54716e6 | −0.0968442 | −0.0484221 | − | 0.998827i | \(-0.515419\pi\) | ||||
−0.0484221 | + | 0.998827i | \(0.515419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.37691e7 | −1.47809 | ||||||||
\(764\) | −1.01860e6 | −0.0631352 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.51165e6 | 0.154663 | ||||||||
\(767\) | −2.91773e7 | −1.79084 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.16191e7 | 0.708529 | 0.354265 | − | 0.935145i | \(-0.384731\pi\) | ||||
0.354265 | + | 0.935145i | \(0.384731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.14796e7 | −0.693242 | ||||||||
\(773\) | −1.16233e7 | −0.699649 | −0.349824 | − | 0.936815i | \(-0.613759\pi\) | ||||
−0.349824 | + | 0.936815i | \(0.613759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.14239e6 | −0.366171 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.25736e7 | 0.744748 | ||||||||
\(779\) | −2.45901e6 | −0.145183 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.77943e7 | 1.04388 | ||||||||
\(782\) | −3.24068e7 | −1.89504 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.06462e7 | 0.618594 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.03314e7 | 1.17012 | 0.585059 | − | 0.810991i | \(-0.301071\pi\) | ||||
0.585059 | + | 0.810991i | \(0.301071\pi\) | |||||||
\(788\) | 4.59945e6 | 0.263870 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.43503e6 | 0.138377 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.22425e6 | 0.125603 | ||||||||
\(794\) | 4.43092e6 | 0.249427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.02979e7 | 0.576058 | ||||||||
\(797\) | −6.32170e6 | −0.352523 | −0.176262 | − | 0.984343i | \(-0.556401\pi\) | ||||
−0.176262 | + | 0.984343i | \(0.556401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.98772e7 | −2.76398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.66252e6 | 0.530462 | ||||||||
\(803\) | 4.27764e6 | 0.234107 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.28100e6 | 0.340558 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.65816e6 | 0.143236 | ||||||||
\(809\) | 1.84549e7 | 0.991380 | 0.495690 | − | 0.868499i | \(-0.334915\pi\) | ||||
0.495690 | + | 0.868499i | \(0.334915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.00263e7 | 1.60306 | 0.801530 | − | 0.597954i | \(-0.204020\pi\) | ||||
0.801530 | + | 0.597954i | \(0.204020\pi\) | |||||||
\(812\) | 9.53719e6 | 0.507610 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.74501e6 | 0.145205 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.38187e7 | 0.724289 | ||||||||
\(818\) | −1.47932e7 | −0.772999 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.51609e7 | 1.30277 | 0.651387 | − | 0.758746i | \(-0.274188\pi\) | ||||
0.651387 | + | 0.758746i | \(0.274188\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.97388e6 | −0.410365 | −0.205182 | − | 0.978724i | \(-0.565779\pi\) | ||||
−0.205182 | + | 0.978724i | \(0.565779\pi\) | |||||||
\(824\) | 2.64835e6 | 0.135880 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.40489e7 | −1.73641 | ||||||||
\(827\) | −1.37135e7 | −0.697243 | −0.348622 | − | 0.937264i | \(-0.613350\pi\) | ||||
−0.348622 | + | 0.937264i | \(0.613350\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.62566e7 | −0.821569 | −0.410785 | − | 0.911732i | \(-0.634745\pi\) | ||||
−0.410785 | + | 0.911732i | \(0.634745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.39270e6 | 0.169917 | ||||||||
\(833\) | 8.99307e7 | 4.49051 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.31103e7 | −0.648777 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.38191e7 | −0.679782 | ||||||||
\(839\) | 2.36734e7 | 1.16106 | 0.580532 | − | 0.814237i | \(-0.302844\pi\) | ||||
0.580532 | + | 0.814237i | \(0.302844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44265e7 | −0.703350 | ||||||||
\(842\) | 1.93592e7 | 0.941039 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.39812e7 | −0.675600 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.42168e7 | −3.07567 | ||||||||
\(848\) | −6.99632e6 | −0.334103 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.93547e6 | 0.186283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.53714e7 | −1.19391 | −0.596956 | − | 0.802274i | \(-0.703623\pi\) | ||||
−0.596956 | + | 0.802274i | \(0.703623\pi\) | |||||||
\(854\) | 2.59562e6 | 0.121786 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −729817. | −0.0340431 | ||||||||
\(857\) | 2.37850e7 | 1.10624 | 0.553122 | − | 0.833100i | \(-0.313436\pi\) | ||||
0.553122 | + | 0.833100i | \(0.313436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.55700e6 | −0.395675 | −0.197838 | − | 0.980235i | \(-0.563392\pi\) | ||||
−0.197838 | + | 0.980235i | \(0.563392\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.21969e7 | −1.01748 | ||||||||
\(863\) | 3.91623e7 | 1.78995 | 0.894977 | − | 0.446113i | \(-0.147192\pi\) | ||||
0.894977 | + | 0.446113i | \(0.147192\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.25721e6 | 0.147588 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.32971e6 | 0.330208 | ||||||||
\(869\) | 4.24886e7 | 1.90864 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.98618e7 | 1.78038 | ||||||||
\(872\) | −6.29519e6 | −0.280361 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.87960e7 | −0.832311 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.35047e7 | −1.03194 | −0.515972 | − | 0.856605i | \(-0.672569\pi\) | ||||
−0.515972 | + | 0.856605i | \(0.672569\pi\) | |||||||
\(878\) | 1.60985e7 | 0.704771 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.50902e7 | −1.95723 | −0.978617 | − | 0.205691i | \(-0.934056\pi\) | ||||
−0.978617 | + | 0.205691i | \(0.934056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.95876e7 | 0.845434 | 0.422717 | − | 0.906262i | \(-0.361076\pi\) | ||||
0.422717 | + | 0.906262i | \(0.361076\pi\) | |||||||
\(884\) | 2.86588e7 | 1.23347 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.78553e7 | 0.764157 | ||||||||
\(887\) | 9.54399e6 | 0.407306 | 0.203653 | − | 0.979043i | \(-0.434719\pi\) | ||||
0.203653 | + | 0.979043i | \(0.434719\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.16515e7 | 2.61631 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.61594e6 | −0.194244 | ||||||||
\(893\) | −2.89288e7 | −1.21395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.95916e6 | 0.164753 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.86756e7 | −0.772828 | ||||||||
\(899\) | 4.67628e6 | 0.192975 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.90992e7 | −2.42532 | ||||||||
\(902\) | −5.12330e6 | −0.209668 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 644912. | 0.0262470 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.08034e7 | −0.436054 | −0.218027 | − | 0.975943i | \(-0.569962\pi\) | ||||
−0.218027 | + | 0.975943i | \(0.569962\pi\) | |||||||
\(908\) | −2.00573e6 | −0.0807343 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.88914e7 | 1.55259 | 0.776296 | − | 0.630368i | \(-0.217096\pi\) | ||||
0.776296 | + | 0.630368i | \(0.217096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.08749e7 | 1.62286 | ||||||||
\(914\) | 1.88536e7 | 0.746498 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.11709e7 | −0.439897 | ||||||||
\(917\) | −1.58118e7 | −0.620953 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.89714e7 | 1.13157 | 0.565785 | − | 0.824553i | \(-0.308573\pi\) | ||||
0.565785 | + | 0.824553i | \(0.308573\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.49590e7 | 0.966941 | ||||||||
\(923\) | −2.25609e7 | −0.871668 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.33597e7 | 0.511999 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.52590e6 | 0.0962824 | ||||||||
\(929\) | 3.61023e7 | 1.37245 | 0.686224 | − | 0.727391i | \(-0.259267\pi\) | ||||
0.686224 | + | 0.727391i | \(0.259267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.21599e7 | 1.97225 | ||||||||
\(932\) | −1.57534e7 | −0.594066 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.88999e6 | −0.108400 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.02966e7 | 0.383129 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(938\) | 4.65173e7 | 1.72627 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.55696e7 | −0.573195 | −0.286597 | − | 0.958051i | \(-0.592524\pi\) | ||||
−0.286597 | + | 0.958051i | \(0.592524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.34519e6 | −0.268982 | ||||||||
\(944\) | −9.01778e6 | −0.329359 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.87910e7 | 1.04599 | ||||||||
\(947\) | −3.54260e7 | −1.28365 | −0.641826 | − | 0.766850i | \(-0.721823\pi\) | ||||
−0.641826 | + | 0.766850i | \(0.721823\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.42350e6 | −0.195485 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.34438e7 | 1.19598 | ||||||||
\(953\) | 5.47490e6 | 0.195274 | 0.0976369 | − | 0.995222i | \(-0.468872\pi\) | ||||
0.0976369 | + | 0.995222i | \(0.468872\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.09679e6 | −0.0742011 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.15086e7 | −0.757177 | ||||||||
\(959\) | −1.62760e7 | −0.571479 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50352e7 | −0.874467 | ||||||||
\(962\) | −3.48032e6 | −0.121250 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.97811e7 | −0.685579 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.65533e7 | 0.569269 | 0.284635 | − | 0.958636i | \(-0.408128\pi\) | ||||
0.284635 | + | 0.958636i | \(0.408128\pi\) | |||||||
\(968\) | −1.70077e7 | −0.583387 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.83751e6 | −0.0625435 | −0.0312718 | − | 0.999511i | \(-0.509956\pi\) | ||||
−0.0312718 | + | 0.999511i | \(0.509956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.26757e7 | 0.767855 | ||||||||
\(974\) | 6.88338e6 | 0.232490 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 687445. | 0.0231001 | ||||||||
\(977\) | 516874. | 0.0173240 | 0.00866200 | − | 0.999962i | \(-0.497243\pi\) | ||||
0.00866200 | + | 0.999962i | \(0.497243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.17111e7 | 0.390519 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.92580e7 | 0.968201 | ||||||||
\(983\) | −4.15798e7 | −1.37246 | −0.686229 | − | 0.727386i | \(-0.740735\pi\) | ||||
−0.686229 | + | 0.727386i | \(0.740735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.13368e7 | 0.698935 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.66221e7 | 0.541744 | ||||||||
\(989\) | 4.12771e7 | 1.34190 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.61859e7 | −0.523544 | −0.261772 | − | 0.965130i | \(-0.584307\pi\) | ||||
−0.261772 | + | 0.965130i | \(0.584307\pi\) | |||||||
\(992\) | 1.94126e6 | 0.0626331 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.63277e7 | −0.845176 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.74426e7 | 0.874355 | 0.437178 | − | 0.899375i | \(-0.355978\pi\) | ||||
0.437178 | + | 0.899375i | \(0.355978\pi\) | |||||||
\(998\) | 2.91951e7 | 0.927863 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.6.a.y.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 450.6.a.bd.1.1 | yes | 2 | ||
5.2 | odd | 4 | 450.6.c.p.199.1 | 4 | |||
5.3 | odd | 4 | 450.6.c.p.199.4 | 4 | |||
5.4 | even | 2 | 450.6.a.bf.1.2 | yes | 2 | ||
15.2 | even | 4 | 450.6.c.q.199.3 | 4 | |||
15.8 | even | 4 | 450.6.c.q.199.2 | 4 | |||
15.14 | odd | 2 | 450.6.a.ba.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.a.y.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
450.6.a.ba.1.2 | yes | 2 | 15.14 | odd | 2 | ||
450.6.a.bd.1.1 | yes | 2 | 3.2 | odd | 2 | ||
450.6.a.bf.1.2 | yes | 2 | 5.4 | even | 2 | ||
450.6.c.p.199.1 | 4 | 5.2 | odd | 4 | |||
450.6.c.p.199.4 | 4 | 5.3 | odd | 4 | |||
450.6.c.q.199.2 | 4 | 15.8 | even | 4 | |||
450.6.c.q.199.3 | 4 | 15.2 | even | 4 |