Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, 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("294.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(47.1528430250\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 26.0000 | 0.465102 | 0.232551 | − | 0.972584i | \(-0.425293\pi\) | ||||
0.232551 | + | 0.972584i | \(0.425293\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −104.000 | −0.328877 | ||||||||
\(11\) | −358.000 | −0.892075 | −0.446037 | − | 0.895014i | \(-0.647165\pi\) | ||||
−0.446037 | + | 0.895014i | \(0.647165\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 332.000 | 0.544853 | 0.272427 | − | 0.962177i | \(-0.412174\pi\) | ||||
0.272427 | + | 0.962177i | \(0.412174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 234.000 | 0.268527 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 126.000 | 0.105742 | 0.0528711 | − | 0.998601i | \(-0.483163\pi\) | ||||
0.0528711 | + | 0.998601i | \(0.483163\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −2200.00 | −1.39810 | −0.699051 | − | 0.715072i | \(-0.746394\pi\) | ||||
−0.699051 | + | 0.715072i | \(0.746394\pi\) | |||||||
\(20\) | 416.000 | 0.232551 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1432.00 | 0.630792 | ||||||||
\(23\) | −2142.00 | −0.844306 | −0.422153 | − | 0.906525i | \(-0.638726\pi\) | ||||
−0.422153 | + | 0.906525i | \(0.638726\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | −2449.00 | −0.783680 | ||||||||
\(26\) | −1328.00 | −0.385270 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3610.00 | −0.797099 | −0.398549 | − | 0.917147i | \(-0.630486\pi\) | ||||
−0.398549 | + | 0.917147i | \(0.630486\pi\) | |||||||
\(30\) | −936.000 | −0.189877 | ||||||||
\(31\) | 5668.00 | 1.05932 | 0.529658 | − | 0.848211i | \(-0.322320\pi\) | ||||
0.529658 | + | 0.848211i | \(0.322320\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −3222.00 | −0.515040 | ||||||||
\(34\) | −504.000 | −0.0747710 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −2922.00 | −0.350894 | −0.175447 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175447 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(38\) | 8800.00 | 0.988607 | ||||||||
\(39\) | 2988.00 | 0.314571 | ||||||||
\(40\) | −1664.00 | −0.164438 | ||||||||
\(41\) | −2142.00 | −0.199003 | −0.0995015 | − | 0.995037i | \(-0.531725\pi\) | ||||
−0.0995015 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6388.00 | 0.526858 | 0.263429 | − | 0.964679i | \(-0.415146\pi\) | ||||
0.263429 | + | 0.964679i | \(0.415146\pi\) | |||||||
\(44\) | −5728.00 | −0.446037 | ||||||||
\(45\) | 2106.00 | 0.155034 | ||||||||
\(46\) | 8568.00 | 0.597014 | ||||||||
\(47\) | −6520.00 | −0.430530 | −0.215265 | − | 0.976556i | \(-0.569061\pi\) | ||||
−0.215265 | + | 0.976556i | \(0.569061\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9796.00 | 0.554145 | ||||||||
\(51\) | 1134.00 | 0.0610503 | ||||||||
\(52\) | 5312.00 | 0.272427 | ||||||||
\(53\) | −10702.0 | −0.523330 | −0.261665 | − | 0.965159i | \(-0.584271\pi\) | ||||
−0.261665 | + | 0.965159i | \(0.584271\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | −9308.00 | −0.414906 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19800.0 | −0.807194 | ||||||||
\(58\) | 14440.0 | 0.563634 | ||||||||
\(59\) | 42524.0 | 1.59039 | 0.795196 | − | 0.606353i | \(-0.207368\pi\) | ||||
0.795196 | + | 0.606353i | \(0.207368\pi\) | |||||||
\(60\) | 3744.00 | 0.134263 | ||||||||
\(61\) | −44840.0 | −1.54291 | −0.771456 | − | 0.636283i | \(-0.780471\pi\) | ||||
−0.771456 | + | 0.636283i | \(0.780471\pi\) | |||||||
\(62\) | −22672.0 | −0.749050 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 8632.00 | 0.253413 | ||||||||
\(66\) | 12888.0 | 0.364188 | ||||||||
\(67\) | −1448.00 | −0.0394077 | −0.0197039 | − | 0.999806i | \(-0.506272\pi\) | ||||
−0.0197039 | + | 0.999806i | \(0.506272\pi\) | |||||||
\(68\) | 2016.00 | 0.0528711 | ||||||||
\(69\) | −19278.0 | −0.487460 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4402.00 | −0.103634 | −0.0518172 | − | 0.998657i | \(-0.516501\pi\) | ||||
−0.0518172 | + | 0.998657i | \(0.516501\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 20500.0 | 0.450243 | 0.225121 | − | 0.974331i | \(-0.427722\pi\) | ||||
0.225121 | + | 0.974331i | \(0.427722\pi\) | |||||||
\(74\) | 11688.0 | 0.248120 | ||||||||
\(75\) | −22041.0 | −0.452458 | ||||||||
\(76\) | −35200.0 | −0.699051 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11952.0 | −0.222435 | ||||||||
\(79\) | 65236.0 | 1.17603 | 0.588017 | − | 0.808849i | \(-0.299909\pi\) | ||||
0.588017 | + | 0.808849i | \(0.299909\pi\) | |||||||
\(80\) | 6656.00 | 0.116276 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 8568.00 | 0.140716 | ||||||||
\(83\) | −102804. | −1.63800 | −0.819002 | − | 0.573791i | \(-0.805472\pi\) | ||||
−0.819002 | + | 0.573791i | \(0.805472\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3276.00 | 0.0491809 | ||||||||
\(86\) | −25552.0 | −0.372545 | ||||||||
\(87\) | −32490.0 | −0.460205 | ||||||||
\(88\) | 22912.0 | 0.315396 | ||||||||
\(89\) | −128006. | −1.71299 | −0.856496 | − | 0.516154i | \(-0.827363\pi\) | ||||
−0.856496 | + | 0.516154i | \(0.827363\pi\) | |||||||
\(90\) | −8424.00 | −0.109626 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −34272.0 | −0.422153 | ||||||||
\(93\) | 51012.0 | 0.611596 | ||||||||
\(94\) | 26080.0 | 0.304430 | ||||||||
\(95\) | −57200.0 | −0.650260 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −113324. | −1.22290 | −0.611452 | − | 0.791281i | \(-0.709414\pi\) | ||||
−0.611452 | + | 0.791281i | \(0.709414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −28998.0 | −0.297358 | ||||||||
\(100\) | −39184.0 | −0.391840 | ||||||||
\(101\) | −139714. | −1.36281 | −0.681407 | − | 0.731905i | \(-0.738632\pi\) | ||||
−0.681407 | + | 0.731905i | \(0.738632\pi\) | |||||||
\(102\) | −4536.00 | −0.0431691 | ||||||||
\(103\) | −142180. | −1.32052 | −0.660261 | − | 0.751036i | \(-0.729554\pi\) | ||||
−0.660261 | + | 0.751036i | \(0.729554\pi\) | |||||||
\(104\) | −21248.0 | −0.192635 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 42808.0 | 0.370050 | ||||||||
\(107\) | −198518. | −1.67626 | −0.838128 | − | 0.545473i | \(-0.816350\pi\) | ||||
−0.838128 | + | 0.545473i | \(0.816350\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 132538. | 1.06850 | 0.534250 | − | 0.845327i | \(-0.320594\pi\) | ||||
0.534250 | + | 0.845327i | \(0.320594\pi\) | |||||||
\(110\) | 37232.0 | 0.293383 | ||||||||
\(111\) | −26298.0 | −0.202589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 47026.0 | 0.346451 | 0.173226 | − | 0.984882i | \(-0.444581\pi\) | ||||
0.173226 | + | 0.984882i | \(0.444581\pi\) | |||||||
\(114\) | 79200.0 | 0.570773 | ||||||||
\(115\) | −55692.0 | −0.392689 | ||||||||
\(116\) | −57760.0 | −0.398549 | ||||||||
\(117\) | 26892.0 | 0.181618 | ||||||||
\(118\) | −170096. | −1.12458 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −14976.0 | −0.0949386 | ||||||||
\(121\) | −32887.0 | −0.204202 | ||||||||
\(122\) | 179360. | 1.09100 | ||||||||
\(123\) | −19278.0 | −0.114894 | ||||||||
\(124\) | 90688.0 | 0.529658 | ||||||||
\(125\) | −144924. | −0.829593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 165548. | 0.910782 | 0.455391 | − | 0.890291i | \(-0.349499\pi\) | ||||
0.455391 | + | 0.890291i | \(0.349499\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 57492.0 | 0.304182 | ||||||||
\(130\) | −34528.0 | −0.179190 | ||||||||
\(131\) | −139308. | −0.709248 | −0.354624 | − | 0.935009i | \(-0.615391\pi\) | ||||
−0.354624 | + | 0.935009i | \(0.615391\pi\) | |||||||
\(132\) | −51552.0 | −0.257520 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5792.00 | 0.0278655 | ||||||||
\(135\) | 18954.0 | 0.0895089 | ||||||||
\(136\) | −8064.00 | −0.0373855 | ||||||||
\(137\) | −332842. | −1.51508 | −0.757542 | − | 0.652786i | \(-0.773600\pi\) | ||||
−0.757542 | + | 0.652786i | \(0.773600\pi\) | |||||||
\(138\) | 77112.0 | 0.344686 | ||||||||
\(139\) | 8556.00 | 0.0375607 | 0.0187804 | − | 0.999824i | \(-0.494022\pi\) | ||||
0.0187804 | + | 0.999824i | \(0.494022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −58680.0 | −0.248566 | ||||||||
\(142\) | 17608.0 | 0.0732806 | ||||||||
\(143\) | −118856. | −0.486050 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −93860.0 | −0.370732 | ||||||||
\(146\) | −82000.0 | −0.318370 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −46752.0 | −0.175447 | ||||||||
\(149\) | 69554.0 | 0.256659 | 0.128329 | − | 0.991732i | \(-0.459038\pi\) | ||||
0.128329 | + | 0.991732i | \(0.459038\pi\) | |||||||
\(150\) | 88164.0 | 0.319936 | ||||||||
\(151\) | 529240. | 1.88891 | 0.944453 | − | 0.328647i | \(-0.106593\pi\) | ||||
0.944453 | + | 0.328647i | \(0.106593\pi\) | |||||||
\(152\) | 140800. | 0.494303 | ||||||||
\(153\) | 10206.0 | 0.0352474 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 147368. | 0.492690 | ||||||||
\(156\) | 47808.0 | 0.157286 | ||||||||
\(157\) | 13040.0 | 0.0422210 | 0.0211105 | − | 0.999777i | \(-0.493280\pi\) | ||||
0.0211105 | + | 0.999777i | \(0.493280\pi\) | |||||||
\(158\) | −260944. | −0.831581 | ||||||||
\(159\) | −96318.0 | −0.302144 | ||||||||
\(160\) | −26624.0 | −0.0822192 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −351240. | −1.03546 | −0.517732 | − | 0.855543i | \(-0.673224\pi\) | ||||
−0.517732 | + | 0.855543i | \(0.673224\pi\) | |||||||
\(164\) | −34272.0 | −0.0995015 | ||||||||
\(165\) | −83772.0 | −0.239546 | ||||||||
\(166\) | 411216. | 1.15824 | ||||||||
\(167\) | 626128. | 1.73729 | 0.868644 | − | 0.495436i | \(-0.164992\pi\) | ||||
0.868644 | + | 0.495436i | \(0.164992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −261069. | −0.703135 | ||||||||
\(170\) | −13104.0 | −0.0347762 | ||||||||
\(171\) | −178200. | −0.466034 | ||||||||
\(172\) | 102208. | 0.263429 | ||||||||
\(173\) | −184826. | −0.469513 | −0.234757 | − | 0.972054i | \(-0.575429\pi\) | ||||
−0.234757 | + | 0.972054i | \(0.575429\pi\) | |||||||
\(174\) | 129960. | 0.325414 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −91648.0 | −0.223019 | ||||||||
\(177\) | 382716. | 0.918213 | ||||||||
\(178\) | 512024. | 1.21127 | ||||||||
\(179\) | −357522. | −0.834008 | −0.417004 | − | 0.908905i | \(-0.636920\pi\) | ||||
−0.417004 | + | 0.908905i | \(0.636920\pi\) | |||||||
\(180\) | 33696.0 | 0.0775170 | ||||||||
\(181\) | 696508. | 1.58026 | 0.790132 | − | 0.612937i | \(-0.210012\pi\) | ||||
0.790132 | + | 0.612937i | \(0.210012\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −403560. | −0.890800 | ||||||||
\(184\) | 137088. | 0.298507 | ||||||||
\(185\) | −75972.0 | −0.163202 | ||||||||
\(186\) | −204048. | −0.432464 | ||||||||
\(187\) | −45108.0 | −0.0943299 | ||||||||
\(188\) | −104320. | −0.215265 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 228800. | 0.459803 | ||||||||
\(191\) | 68670.0 | 0.136202 | 0.0681010 | − | 0.997678i | \(-0.478306\pi\) | ||||
0.0681010 | + | 0.997678i | \(0.478306\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 827222. | 1.59856 | 0.799280 | − | 0.600959i | \(-0.205215\pi\) | ||||
0.799280 | + | 0.600959i | \(0.205215\pi\) | |||||||
\(194\) | 453296. | 0.864724 | ||||||||
\(195\) | 77688.0 | 0.146308 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −143382. | −0.263226 | −0.131613 | − | 0.991301i | \(-0.542016\pi\) | ||||
−0.131613 | + | 0.991301i | \(0.542016\pi\) | |||||||
\(198\) | 115992. | 0.210264 | ||||||||
\(199\) | −542600. | −0.971286 | −0.485643 | − | 0.874157i | \(-0.661414\pi\) | ||||
−0.485643 | + | 0.874157i | \(0.661414\pi\) | |||||||
\(200\) | 156736. | 0.277073 | ||||||||
\(201\) | −13032.0 | −0.0227521 | ||||||||
\(202\) | 558856. | 0.963655 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 18144.0 | 0.0305251 | ||||||||
\(205\) | −55692.0 | −0.0925568 | ||||||||
\(206\) | 568720. | 0.933750 | ||||||||
\(207\) | −173502. | −0.281435 | ||||||||
\(208\) | 84992.0 | 0.136213 | ||||||||
\(209\) | 787600. | 1.24721 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12776e6 | 1.74385 | 0.871925 | − | 0.489640i | \(-0.162872\pi\) | ||||
0.871925 | + | 0.489640i | \(0.162872\pi\) | |||||||
\(212\) | −171232. | −0.261665 | ||||||||
\(213\) | −39618.0 | −0.0598334 | ||||||||
\(214\) | 794072. | 1.18529 | ||||||||
\(215\) | 166088. | 0.245043 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −530152. | −0.755543 | ||||||||
\(219\) | 184500. | 0.259948 | ||||||||
\(220\) | −148928. | −0.207453 | ||||||||
\(221\) | 41832.0 | 0.0576140 | ||||||||
\(222\) | 105192. | 0.143252 | ||||||||
\(223\) | 897976. | 1.20921 | 0.604606 | − | 0.796525i | \(-0.293331\pi\) | ||||
0.604606 | + | 0.796525i | \(0.293331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −198369. | −0.261227 | ||||||||
\(226\) | −188104. | −0.244978 | ||||||||
\(227\) | −467612. | −0.602311 | −0.301156 | − | 0.953575i | \(-0.597372\pi\) | ||||
−0.301156 | + | 0.953575i | \(0.597372\pi\) | |||||||
\(228\) | −316800. | −0.403597 | ||||||||
\(229\) | −446140. | −0.562189 | −0.281095 | − | 0.959680i | \(-0.590697\pi\) | ||||
−0.281095 | + | 0.959680i | \(0.590697\pi\) | |||||||
\(230\) | 222768. | 0.277673 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 231040. | 0.281817 | ||||||||
\(233\) | 701486. | 0.846504 | 0.423252 | − | 0.906012i | \(-0.360888\pi\) | ||||
0.423252 | + | 0.906012i | \(0.360888\pi\) | |||||||
\(234\) | −107568. | −0.128423 | ||||||||
\(235\) | −169520. | −0.200240 | ||||||||
\(236\) | 680384. | 0.795196 | ||||||||
\(237\) | 587124. | 0.678983 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −384198. | −0.435071 | −0.217536 | − | 0.976052i | \(-0.569802\pi\) | ||||
−0.217536 | + | 0.976052i | \(0.569802\pi\) | |||||||
\(240\) | 59904.0 | 0.0671317 | ||||||||
\(241\) | −953780. | −1.05780 | −0.528902 | − | 0.848683i | \(-0.677396\pi\) | ||||
−0.528902 | + | 0.848683i | \(0.677396\pi\) | |||||||
\(242\) | 131548. | 0.144393 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −717440. | −0.771456 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 77112.0 | 0.0812427 | ||||||||
\(247\) | −730400. | −0.761760 | ||||||||
\(248\) | −362752. | −0.374525 | ||||||||
\(249\) | −925236. | −0.945702 | ||||||||
\(250\) | 579696. | 0.586611 | ||||||||
\(251\) | 569540. | 0.570611 | 0.285305 | − | 0.958437i | \(-0.407905\pi\) | ||||
0.285305 | + | 0.958437i | \(0.407905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 766836. | 0.753184 | ||||||||
\(254\) | −662192. | −0.644020 | ||||||||
\(255\) | 29484.0 | 0.0283946 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.06664e6 | 1.00736 | 0.503681 | − | 0.863890i | \(-0.331979\pi\) | ||||
0.503681 | + | 0.863890i | \(0.331979\pi\) | |||||||
\(258\) | −229968. | −0.215089 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 138112. | 0.126706 | ||||||||
\(261\) | −292410. | −0.265700 | ||||||||
\(262\) | 557232. | 0.501514 | ||||||||
\(263\) | −1.48243e6 | −1.32155 | −0.660777 | − | 0.750582i | \(-0.729773\pi\) | ||||
−0.660777 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(264\) | 206208. | 0.182094 | ||||||||
\(265\) | −278252. | −0.243402 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.15205e6 | −0.988996 | ||||||||
\(268\) | −23168.0 | −0.0197039 | ||||||||
\(269\) | −215110. | −0.181251 | −0.0906254 | − | 0.995885i | \(-0.528887\pi\) | ||||
−0.0906254 | + | 0.995885i | \(0.528887\pi\) | |||||||
\(270\) | −75816.0 | −0.0632924 | ||||||||
\(271\) | 1.93104e6 | 1.59723 | 0.798614 | − | 0.601843i | \(-0.205567\pi\) | ||||
0.798614 | + | 0.601843i | \(0.205567\pi\) | |||||||
\(272\) | 32256.0 | 0.0264355 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.33137e6 | 1.07133 | ||||||||
\(275\) | 876742. | 0.699101 | ||||||||
\(276\) | −308448. | −0.243730 | ||||||||
\(277\) | 2.03756e6 | 1.59555 | 0.797777 | − | 0.602953i | \(-0.206009\pi\) | ||||
0.797777 | + | 0.602953i | \(0.206009\pi\) | |||||||
\(278\) | −34224.0 | −0.0265594 | ||||||||
\(279\) | 459108. | 0.353105 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −639066. | −0.482814 | −0.241407 | − | 0.970424i | \(-0.577609\pi\) | ||||
−0.241407 | + | 0.970424i | \(0.577609\pi\) | |||||||
\(282\) | 234720. | 0.175763 | ||||||||
\(283\) | 37744.0 | 0.0280144 | 0.0140072 | − | 0.999902i | \(-0.495541\pi\) | ||||
0.0140072 | + | 0.999902i | \(0.495541\pi\) | |||||||
\(284\) | −70432.0 | −0.0518172 | ||||||||
\(285\) | −514800. | −0.375428 | ||||||||
\(286\) | 475424. | 0.343689 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.40398e6 | −0.988819 | ||||||||
\(290\) | 375440. | 0.262147 | ||||||||
\(291\) | −1.01992e6 | −0.706044 | ||||||||
\(292\) | 328000. | 0.225121 | ||||||||
\(293\) | −1.83921e6 | −1.25159 | −0.625795 | − | 0.779987i | \(-0.715225\pi\) | ||||
−0.625795 | + | 0.779987i | \(0.715225\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.10562e6 | 0.739695 | ||||||||
\(296\) | 187008. | 0.124060 | ||||||||
\(297\) | −260982. | −0.171680 | ||||||||
\(298\) | −278216. | −0.181485 | ||||||||
\(299\) | −711144. | −0.460023 | ||||||||
\(300\) | −352656. | −0.226229 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.11696e6 | −1.33566 | ||||||||
\(303\) | −1.25743e6 | −0.786821 | ||||||||
\(304\) | −563200. | −0.349525 | ||||||||
\(305\) | −1.16584e6 | −0.717611 | ||||||||
\(306\) | −40824.0 | −0.0249237 | ||||||||
\(307\) | −1.06472e6 | −0.644747 | −0.322374 | − | 0.946613i | \(-0.604481\pi\) | ||||
−0.322374 | + | 0.946613i | \(0.604481\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.27962e6 | −0.762403 | ||||||||
\(310\) | −589472. | −0.348385 | ||||||||
\(311\) | −1.00952e6 | −0.591853 | −0.295927 | − | 0.955211i | \(-0.595628\pi\) | ||||
−0.295927 | + | 0.955211i | \(0.595628\pi\) | |||||||
\(312\) | −191232. | −0.111218 | ||||||||
\(313\) | −1.44910e6 | −0.836058 | −0.418029 | − | 0.908434i | \(-0.637279\pi\) | ||||
−0.418029 | + | 0.908434i | \(0.637279\pi\) | |||||||
\(314\) | −52160.0 | −0.0298548 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.04378e6 | 0.588017 | ||||||||
\(317\) | 2.72311e6 | 1.52201 | 0.761003 | − | 0.648748i | \(-0.224707\pi\) | ||||
0.761003 | + | 0.648748i | \(0.224707\pi\) | |||||||
\(318\) | 385272. | 0.213648 | ||||||||
\(319\) | 1.29238e6 | 0.711072 | ||||||||
\(320\) | 106496. | 0.0581378 | ||||||||
\(321\) | −1.78666e6 | −0.967787 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −277200. | −0.147838 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −813068. | −0.426991 | ||||||||
\(326\) | 1.40496e6 | 0.732184 | ||||||||
\(327\) | 1.19284e6 | 0.616898 | ||||||||
\(328\) | 137088. | 0.0703582 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 335088. | 0.169385 | ||||||||
\(331\) | −1.10040e6 | −0.552055 | −0.276027 | − | 0.961150i | \(-0.589018\pi\) | ||||
−0.276027 | + | 0.961150i | \(0.589018\pi\) | |||||||
\(332\) | −1.64486e6 | −0.819002 | ||||||||
\(333\) | −236682. | −0.116965 | ||||||||
\(334\) | −2.50451e6 | −1.22845 | ||||||||
\(335\) | −37648.0 | −0.0183286 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.73512e6 | 0.832251 | 0.416125 | − | 0.909307i | \(-0.363388\pi\) | ||||
0.416125 | + | 0.909307i | \(0.363388\pi\) | |||||||
\(338\) | 1.04428e6 | 0.497191 | ||||||||
\(339\) | 423234. | 0.200024 | ||||||||
\(340\) | 52416.0 | 0.0245905 | ||||||||
\(341\) | −2.02914e6 | −0.944989 | ||||||||
\(342\) | 712800. | 0.329536 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −408832. | −0.186273 | ||||||||
\(345\) | −501228. | −0.226719 | ||||||||
\(346\) | 739304. | 0.331996 | ||||||||
\(347\) | 1.59145e6 | 0.709526 | 0.354763 | − | 0.934956i | \(-0.384562\pi\) | ||||
0.354763 | + | 0.934956i | \(0.384562\pi\) | |||||||
\(348\) | −519840. | −0.230103 | ||||||||
\(349\) | −2.33376e6 | −1.02563 | −0.512817 | − | 0.858498i | \(-0.671398\pi\) | ||||
−0.512817 | + | 0.858498i | \(0.671398\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 242028. | 0.104857 | ||||||||
\(352\) | 366592. | 0.157698 | ||||||||
\(353\) | 2.81081e6 | 1.20059 | 0.600296 | − | 0.799778i | \(-0.295049\pi\) | ||||
0.600296 | + | 0.799778i | \(0.295049\pi\) | |||||||
\(354\) | −1.53086e6 | −0.649275 | ||||||||
\(355\) | −114452. | −0.0482006 | ||||||||
\(356\) | −2.04810e6 | −0.856496 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.43009e6 | 0.589733 | ||||||||
\(359\) | 939310. | 0.384656 | 0.192328 | − | 0.981331i | \(-0.438396\pi\) | ||||
0.192328 | + | 0.981331i | \(0.438396\pi\) | |||||||
\(360\) | −134784. | −0.0548128 | ||||||||
\(361\) | 2.36390e6 | 0.954688 | ||||||||
\(362\) | −2.78603e6 | −1.11742 | ||||||||
\(363\) | −295983. | −0.117896 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 533000. | 0.209409 | ||||||||
\(366\) | 1.61424e6 | 0.629891 | ||||||||
\(367\) | 3.09851e6 | 1.20085 | 0.600424 | − | 0.799682i | \(-0.294999\pi\) | ||||
0.600424 | + | 0.799682i | \(0.294999\pi\) | |||||||
\(368\) | −548352. | −0.211077 | ||||||||
\(369\) | −173502. | −0.0663344 | ||||||||
\(370\) | 303888. | 0.115401 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 816192. | 0.305798 | ||||||||
\(373\) | −228266. | −0.0849511 | −0.0424756 | − | 0.999098i | \(-0.513524\pi\) | ||||
−0.0424756 | + | 0.999098i | \(0.513524\pi\) | |||||||
\(374\) | 180432. | 0.0667013 | ||||||||
\(375\) | −1.30432e6 | −0.478966 | ||||||||
\(376\) | 417280. | 0.152215 | ||||||||
\(377\) | −1.19852e6 | −0.434302 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.03669e6 | −0.370725 | −0.185362 | − | 0.982670i | \(-0.559346\pi\) | ||||
−0.185362 | + | 0.982670i | \(0.559346\pi\) | |||||||
\(380\) | −915200. | −0.325130 | ||||||||
\(381\) | 1.48993e6 | 0.525840 | ||||||||
\(382\) | −274680. | −0.0963094 | ||||||||
\(383\) | −211776. | −0.0737700 | −0.0368850 | − | 0.999320i | \(-0.511744\pi\) | ||||
−0.0368850 | + | 0.999320i | \(0.511744\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.30889e6 | −1.13035 | ||||||||
\(387\) | 517428. | 0.175619 | ||||||||
\(388\) | −1.81318e6 | −0.611452 | ||||||||
\(389\) | 1.41325e6 | 0.473526 | 0.236763 | − | 0.971567i | \(-0.423914\pi\) | ||||
0.236763 | + | 0.971567i | \(0.423914\pi\) | |||||||
\(390\) | −310752. | −0.103455 | ||||||||
\(391\) | −269892. | −0.0892788 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.25377e6 | −0.409484 | ||||||||
\(394\) | 573528. | 0.186129 | ||||||||
\(395\) | 1.69614e6 | 0.546976 | ||||||||
\(396\) | −463968. | −0.148679 | ||||||||
\(397\) | −1.09034e6 | −0.347203 | −0.173602 | − | 0.984816i | \(-0.555541\pi\) | ||||
−0.173602 | + | 0.984816i | \(0.555541\pi\) | |||||||
\(398\) | 2.17040e6 | 0.686803 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −626944. | −0.195920 | ||||||||
\(401\) | 2.64253e6 | 0.820651 | 0.410325 | − | 0.911939i | \(-0.365415\pi\) | ||||
0.410325 | + | 0.911939i | \(0.365415\pi\) | |||||||
\(402\) | 52128.0 | 0.0160881 | ||||||||
\(403\) | 1.88178e6 | 0.577172 | ||||||||
\(404\) | −2.23542e6 | −0.681407 | ||||||||
\(405\) | 170586. | 0.0516780 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.04608e6 | 0.313024 | ||||||||
\(408\) | −72576.0 | −0.0215845 | ||||||||
\(409\) | 6.25427e6 | 1.84871 | 0.924354 | − | 0.381536i | \(-0.124605\pi\) | ||||
0.924354 | + | 0.381536i | \(0.124605\pi\) | |||||||
\(410\) | 222768. | 0.0654475 | ||||||||
\(411\) | −2.99558e6 | −0.874734 | ||||||||
\(412\) | −2.27488e6 | −0.660261 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 694008. | 0.199005 | ||||||||
\(415\) | −2.67290e6 | −0.761839 | ||||||||
\(416\) | −339968. | −0.0963174 | ||||||||
\(417\) | 77004.0 | 0.0216857 | ||||||||
\(418\) | −3.15040e6 | −0.881911 | ||||||||
\(419\) | −973924. | −0.271013 | −0.135506 | − | 0.990776i | \(-0.543266\pi\) | ||||
−0.135506 | + | 0.990776i | \(0.543266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 864618. | 0.237749 | 0.118875 | − | 0.992909i | \(-0.462071\pi\) | ||||
0.118875 | + | 0.992909i | \(0.462071\pi\) | |||||||
\(422\) | −4.51102e6 | −1.23309 | ||||||||
\(423\) | −528120. | −0.143510 | ||||||||
\(424\) | 684928. | 0.185025 | ||||||||
\(425\) | −308574. | −0.0828680 | ||||||||
\(426\) | 158472. | 0.0423086 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.17629e6 | −0.838128 | ||||||||
\(429\) | −1.06970e6 | −0.280621 | ||||||||
\(430\) | −664352. | −0.173271 | ||||||||
\(431\) | −3.66046e6 | −0.949166 | −0.474583 | − | 0.880211i | \(-0.657401\pi\) | ||||
−0.474583 | + | 0.880211i | \(0.657401\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −4.93667e6 | −1.26536 | −0.632681 | − | 0.774413i | \(-0.718045\pi\) | ||||
−0.632681 | + | 0.774413i | \(0.718045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −844740. | −0.214042 | ||||||||
\(436\) | 2.12061e6 | 0.534250 | ||||||||
\(437\) | 4.71240e6 | 1.18043 | ||||||||
\(438\) | −738000. | −0.183811 | ||||||||
\(439\) | 731304. | 0.181108 | 0.0905538 | − | 0.995892i | \(-0.471136\pi\) | ||||
0.0905538 | + | 0.995892i | \(0.471136\pi\) | |||||||
\(440\) | 595712. | 0.146691 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −167328. | −0.0407392 | ||||||||
\(443\) | 4.86620e6 | 1.17810 | 0.589048 | − | 0.808098i | \(-0.299503\pi\) | ||||
0.589048 | + | 0.808098i | \(0.299503\pi\) | |||||||
\(444\) | −420768. | −0.101294 | ||||||||
\(445\) | −3.32816e6 | −0.796716 | ||||||||
\(446\) | −3.59190e6 | −0.855042 | ||||||||
\(447\) | 625986. | 0.148182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.71987e6 | 1.33897 | 0.669484 | − | 0.742827i | \(-0.266515\pi\) | ||||
0.669484 | + | 0.742827i | \(0.266515\pi\) | |||||||
\(450\) | 793476. | 0.184715 | ||||||||
\(451\) | 766836. | 0.177526 | ||||||||
\(452\) | 752416. | 0.173226 | ||||||||
\(453\) | 4.76316e6 | 1.09056 | ||||||||
\(454\) | 1.87045e6 | 0.425898 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.26720e6 | 0.285386 | ||||||||
\(457\) | −6.82034e6 | −1.52762 | −0.763811 | − | 0.645440i | \(-0.776674\pi\) | ||||
−0.763811 | + | 0.645440i | \(0.776674\pi\) | |||||||
\(458\) | 1.78456e6 | 0.397528 | ||||||||
\(459\) | 91854.0 | 0.0203501 | ||||||||
\(460\) | −891072. | −0.196344 | ||||||||
\(461\) | −7.45934e6 | −1.63474 | −0.817369 | − | 0.576115i | \(-0.804568\pi\) | ||||
−0.817369 | + | 0.576115i | \(0.804568\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.23848e6 | −1.13567 | −0.567836 | − | 0.823142i | \(-0.692219\pi\) | ||||
−0.567836 | + | 0.823142i | \(0.692219\pi\) | |||||||
\(464\) | −924160. | −0.199275 | ||||||||
\(465\) | 1.32631e6 | 0.284455 | ||||||||
\(466\) | −2.80594e6 | −0.598569 | ||||||||
\(467\) | 8.95995e6 | 1.90114 | 0.950568 | − | 0.310516i | \(-0.100502\pi\) | ||||
0.950568 | + | 0.310516i | \(0.100502\pi\) | |||||||
\(468\) | 430272. | 0.0908089 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 678080. | 0.141591 | ||||||||
\(471\) | 117360. | 0.0243763 | ||||||||
\(472\) | −2.72154e6 | −0.562288 | ||||||||
\(473\) | −2.28690e6 | −0.469997 | ||||||||
\(474\) | −2.34850e6 | −0.480114 | ||||||||
\(475\) | 5.38780e6 | 1.09566 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −866862. | −0.174443 | ||||||||
\(478\) | 1.53679e6 | 0.307642 | ||||||||
\(479\) | −1.75354e6 | −0.349201 | −0.174601 | − | 0.984639i | \(-0.555863\pi\) | ||||
−0.174601 | + | 0.984639i | \(0.555863\pi\) | |||||||
\(480\) | −239616. | −0.0474693 | ||||||||
\(481\) | −970104. | −0.191186 | ||||||||
\(482\) | 3.81512e6 | 0.747981 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −526192. | −0.102101 | ||||||||
\(485\) | −2.94642e6 | −0.568776 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | 927568. | 0.177224 | 0.0886122 | − | 0.996066i | \(-0.471757\pi\) | ||||
0.0886122 | + | 0.996066i | \(0.471757\pi\) | |||||||
\(488\) | 2.86976e6 | 0.545502 | ||||||||
\(489\) | −3.16116e6 | −0.597825 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.43733e6 | 1.57943 | 0.789716 | − | 0.613472i | \(-0.210228\pi\) | ||||
0.789716 | + | 0.613472i | \(0.210228\pi\) | |||||||
\(492\) | −308448. | −0.0574472 | ||||||||
\(493\) | −454860. | −0.0842870 | ||||||||
\(494\) | 2.92160e6 | 0.538646 | ||||||||
\(495\) | −753948. | −0.138302 | ||||||||
\(496\) | 1.45101e6 | 0.264829 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.70094e6 | 0.668712 | ||||||||
\(499\) | 1.33278e6 | 0.239611 | 0.119806 | − | 0.992797i | \(-0.461773\pi\) | ||||
0.119806 | + | 0.992797i | \(0.461773\pi\) | |||||||
\(500\) | −2.31878e6 | −0.414797 | ||||||||
\(501\) | 5.63515e6 | 1.00302 | ||||||||
\(502\) | −2.27816e6 | −0.403483 | ||||||||
\(503\) | 3.64494e6 | 0.642349 | 0.321174 | − | 0.947020i | \(-0.395922\pi\) | ||||
0.321174 | + | 0.947020i | \(0.395922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.63256e6 | −0.633848 | ||||||||
\(506\) | −3.06734e6 | −0.532582 | ||||||||
\(507\) | −2.34962e6 | −0.405955 | ||||||||
\(508\) | 2.64877e6 | 0.455391 | ||||||||
\(509\) | −3.26166e6 | −0.558013 | −0.279007 | − | 0.960289i | \(-0.590005\pi\) | ||||
−0.279007 | + | 0.960289i | \(0.590005\pi\) | |||||||
\(510\) | −117936. | −0.0200780 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −1.60380e6 | −0.269065 | ||||||||
\(514\) | −4.26657e6 | −0.712313 | ||||||||
\(515\) | −3.69668e6 | −0.614177 | ||||||||
\(516\) | 919872. | 0.152091 | ||||||||
\(517\) | 2.33416e6 | 0.384065 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.66343e6 | −0.271074 | ||||||||
\(520\) | −552448. | −0.0895948 | ||||||||
\(521\) | −2.18741e6 | −0.353050 | −0.176525 | − | 0.984296i | \(-0.556486\pi\) | ||||
−0.176525 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(522\) | 1.16964e6 | 0.187878 | ||||||||
\(523\) | 1.03890e7 | 1.66081 | 0.830406 | − | 0.557159i | \(-0.188109\pi\) | ||||
0.830406 | + | 0.557159i | \(0.188109\pi\) | |||||||
\(524\) | −2.22893e6 | −0.354624 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.92972e6 | 0.934480 | ||||||||
\(527\) | 714168. | 0.112014 | ||||||||
\(528\) | −824832. | −0.128760 | ||||||||
\(529\) | −1.84818e6 | −0.287147 | ||||||||
\(530\) | 1.11301e6 | 0.172111 | ||||||||
\(531\) | 3.44444e6 | 0.530131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −711144. | −0.108428 | ||||||||
\(534\) | 4.60822e6 | 0.699326 | ||||||||
\(535\) | −5.16147e6 | −0.779630 | ||||||||
\(536\) | 92672.0 | 0.0139327 | ||||||||
\(537\) | −3.21770e6 | −0.481515 | ||||||||
\(538\) | 860440. | 0.128164 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 303264. | 0.0447545 | ||||||||
\(541\) | 1.27724e7 | 1.87620 | 0.938101 | − | 0.346363i | \(-0.112583\pi\) | ||||
0.938101 | + | 0.346363i | \(0.112583\pi\) | |||||||
\(542\) | −7.72414e6 | −1.12941 | ||||||||
\(543\) | 6.26857e6 | 0.912366 | ||||||||
\(544\) | −129024. | −0.0186928 | ||||||||
\(545\) | 3.44599e6 | 0.496961 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.22238e6 | −0.746278 | −0.373139 | − | 0.927776i | \(-0.621719\pi\) | ||||
−0.373139 | + | 0.927776i | \(0.621719\pi\) | |||||||
\(548\) | −5.32547e6 | −0.757542 | ||||||||
\(549\) | −3.63204e6 | −0.514304 | ||||||||
\(550\) | −3.50697e6 | −0.494339 | ||||||||
\(551\) | 7.94200e6 | 1.11443 | ||||||||
\(552\) | 1.23379e6 | 0.172343 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.15025e6 | −1.12823 | ||||||||
\(555\) | −683748. | −0.0942245 | ||||||||
\(556\) | 136896. | 0.0187804 | ||||||||
\(557\) | −5.74047e6 | −0.783988 | −0.391994 | − | 0.919968i | \(-0.628215\pi\) | ||||
−0.391994 | + | 0.919968i | \(0.628215\pi\) | |||||||
\(558\) | −1.83643e6 | −0.249683 | ||||||||
\(559\) | 2.12082e6 | 0.287061 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −405972. | −0.0544614 | ||||||||
\(562\) | 2.55626e6 | 0.341401 | ||||||||
\(563\) | −2.30448e6 | −0.306409 | −0.153204 | − | 0.988195i | \(-0.548959\pi\) | ||||
−0.153204 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(564\) | −938880. | −0.124283 | ||||||||
\(565\) | 1.22268e6 | 0.161135 | ||||||||
\(566\) | −150976. | −0.0198092 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 281728. | 0.0366403 | ||||||||
\(569\) | −5.12150e6 | −0.663157 | −0.331578 | − | 0.943428i | \(-0.607581\pi\) | ||||
−0.331578 | + | 0.943428i | \(0.607581\pi\) | |||||||
\(570\) | 2.05920e6 | 0.265468 | ||||||||
\(571\) | −2.38637e6 | −0.306300 | −0.153150 | − | 0.988203i | \(-0.548942\pi\) | ||||
−0.153150 | + | 0.988203i | \(0.548942\pi\) | |||||||
\(572\) | −1.90170e6 | −0.243025 | ||||||||
\(573\) | 618030. | 0.0786363 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.24576e6 | 0.661666 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −5.24151e6 | −0.655416 | −0.327708 | − | 0.944779i | \(-0.606276\pi\) | ||||
−0.327708 | + | 0.944779i | \(0.606276\pi\) | |||||||
\(578\) | 5.61592e6 | 0.699200 | ||||||||
\(579\) | 7.44500e6 | 0.922929 | ||||||||
\(580\) | −1.50176e6 | −0.185366 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.07966e6 | 0.499249 | ||||||||
\(583\) | 3.83132e6 | 0.466849 | ||||||||
\(584\) | −1.31200e6 | −0.159185 | ||||||||
\(585\) | 699192. | 0.0844708 | ||||||||
\(586\) | 7.35684e6 | 0.885008 | ||||||||
\(587\) | 9.11548e6 | 1.09190 | 0.545952 | − | 0.837816i | \(-0.316168\pi\) | ||||
0.545952 | + | 0.837816i | \(0.316168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.24696e7 | −1.48103 | ||||||||
\(590\) | −4.42250e6 | −0.523043 | ||||||||
\(591\) | −1.29044e6 | −0.151974 | ||||||||
\(592\) | −748032. | −0.0877235 | ||||||||
\(593\) | 3.05043e6 | 0.356225 | 0.178112 | − | 0.984010i | \(-0.443001\pi\) | ||||
0.178112 | + | 0.984010i | \(0.443001\pi\) | |||||||
\(594\) | 1.04393e6 | 0.121396 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.11286e6 | 0.128329 | ||||||||
\(597\) | −4.88340e6 | −0.560772 | ||||||||
\(598\) | 2.84458e6 | 0.325285 | ||||||||
\(599\) | 1.43408e7 | 1.63308 | 0.816539 | − | 0.577290i | \(-0.195890\pi\) | ||||
0.816539 | + | 0.577290i | \(0.195890\pi\) | |||||||
\(600\) | 1.41062e6 | 0.159968 | ||||||||
\(601\) | −3.12662e6 | −0.353092 | −0.176546 | − | 0.984292i | \(-0.556492\pi\) | ||||
−0.176546 | + | 0.984292i | \(0.556492\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −117288. | −0.0131359 | ||||||||
\(604\) | 8.46784e6 | 0.944453 | ||||||||
\(605\) | −855062. | −0.0949750 | ||||||||
\(606\) | 5.02970e6 | 0.556366 | ||||||||
\(607\) | 1.15098e7 | 1.26794 | 0.633969 | − | 0.773359i | \(-0.281425\pi\) | ||||
0.633969 | + | 0.773359i | \(0.281425\pi\) | |||||||
\(608\) | 2.25280e6 | 0.247152 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.66336e6 | 0.507428 | ||||||||
\(611\) | −2.16464e6 | −0.234576 | ||||||||
\(612\) | 163296. | 0.0176237 | ||||||||
\(613\) | −1.21782e7 | −1.30898 | −0.654488 | − | 0.756072i | \(-0.727116\pi\) | ||||
−0.654488 | + | 0.756072i | \(0.727116\pi\) | |||||||
\(614\) | 4.25888e6 | 0.455905 | ||||||||
\(615\) | −501228. | −0.0534377 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.77629e6 | 0.187845 | 0.0939226 | − | 0.995580i | \(-0.470059\pi\) | ||||
0.0939226 | + | 0.995580i | \(0.470059\pi\) | |||||||
\(618\) | 5.11848e6 | 0.539101 | ||||||||
\(619\) | −5.95516e6 | −0.624694 | −0.312347 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312347 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(620\) | 2.35789e6 | 0.246345 | ||||||||
\(621\) | −1.56152e6 | −0.162487 | ||||||||
\(622\) | 4.03808e6 | 0.418503 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 764928. | 0.0786428 | ||||||||
\(625\) | 3.88510e6 | 0.397834 | ||||||||
\(626\) | 5.79638e6 | 0.591182 | ||||||||
\(627\) | 7.08840e6 | 0.720078 | ||||||||
\(628\) | 208640. | 0.0211105 | ||||||||
\(629\) | −368172. | −0.0371043 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.45351e7 | −1.45327 | −0.726633 | − | 0.687026i | \(-0.758916\pi\) | ||||
−0.726633 | + | 0.687026i | \(0.758916\pi\) | |||||||
\(632\) | −4.17510e6 | −0.415791 | ||||||||
\(633\) | 1.01498e7 | 1.00681 | ||||||||
\(634\) | −1.08924e7 | −1.07622 | ||||||||
\(635\) | 4.30425e6 | 0.423607 | ||||||||
\(636\) | −1.54109e6 | −0.151072 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.16952e6 | −0.502804 | ||||||||
\(639\) | −356562. | −0.0345448 | ||||||||
\(640\) | −425984. | −0.0411096 | ||||||||
\(641\) | −1.07349e7 | −1.03194 | −0.515970 | − | 0.856607i | \(-0.672568\pi\) | ||||
−0.515970 | + | 0.856607i | \(0.672568\pi\) | |||||||
\(642\) | 7.14665e6 | 0.684329 | ||||||||
\(643\) | 1.62815e7 | 1.55298 | 0.776492 | − | 0.630127i | \(-0.216997\pi\) | ||||
0.776492 | + | 0.630127i | \(0.216997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.49479e6 | 0.141476 | ||||||||
\(646\) | 1.10880e6 | 0.104537 | ||||||||
\(647\) | −7.91947e6 | −0.743765 | −0.371882 | − | 0.928280i | \(-0.621288\pi\) | ||||
−0.371882 | + | 0.928280i | \(0.621288\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −1.52236e7 | −1.41875 | ||||||||
\(650\) | 3.25227e6 | 0.301928 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.61984e6 | −0.517732 | ||||||||
\(653\) | 1.34478e6 | 0.123415 | 0.0617076 | − | 0.998094i | \(-0.480345\pi\) | ||||
0.0617076 | + | 0.998094i | \(0.480345\pi\) | |||||||
\(654\) | −4.77137e6 | −0.436213 | ||||||||
\(655\) | −3.62201e6 | −0.329873 | ||||||||
\(656\) | −548352. | −0.0497508 | ||||||||
\(657\) | 1.66050e6 | 0.150081 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.02235e7 | 1.81402 | 0.907010 | − | 0.421109i | \(-0.138359\pi\) | ||||
0.907010 | + | 0.421109i | \(0.138359\pi\) | |||||||
\(660\) | −1.34035e6 | −0.119773 | ||||||||
\(661\) | 7.17802e6 | 0.639001 | 0.319500 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319500 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(662\) | 4.40162e6 | 0.390362 | ||||||||
\(663\) | 376488. | 0.0332635 | ||||||||
\(664\) | 6.57946e6 | 0.579122 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 946728. | 0.0827065 | ||||||||
\(667\) | 7.73262e6 | 0.672995 | ||||||||
\(668\) | 1.00180e7 | 0.868644 | ||||||||
\(669\) | 8.08178e6 | 0.698139 | ||||||||
\(670\) | 150592. | 0.0129603 | ||||||||
\(671\) | 1.60527e7 | 1.37639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.61217e6 | 0.818057 | 0.409029 | − | 0.912522i | \(-0.365868\pi\) | ||||
0.409029 | + | 0.912522i | \(0.365868\pi\) | |||||||
\(674\) | −6.94047e6 | −0.588490 | ||||||||
\(675\) | −1.78532e6 | −0.150819 | ||||||||
\(676\) | −4.17710e6 | −0.351567 | ||||||||
\(677\) | −9.66815e6 | −0.810722 | −0.405361 | − | 0.914157i | \(-0.632854\pi\) | ||||
−0.405361 | + | 0.914157i | \(0.632854\pi\) | |||||||
\(678\) | −1.69294e6 | −0.141438 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −209664. | −0.0173881 | ||||||||
\(681\) | −4.20851e6 | −0.347745 | ||||||||
\(682\) | 8.11658e6 | 0.668208 | ||||||||
\(683\) | 389854. | 0.0319779 | 0.0159890 | − | 0.999872i | \(-0.494910\pi\) | ||||
0.0159890 | + | 0.999872i | \(0.494910\pi\) | |||||||
\(684\) | −2.85120e6 | −0.233017 | ||||||||
\(685\) | −8.65389e6 | −0.704669 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.01526e6 | −0.324580 | ||||||||
\(688\) | 1.63533e6 | 0.131715 | ||||||||
\(689\) | −3.55306e6 | −0.285138 | ||||||||
\(690\) | 2.00491e6 | 0.160314 | ||||||||
\(691\) | 3.73985e6 | 0.297961 | 0.148980 | − | 0.988840i | \(-0.452401\pi\) | ||||
0.148980 | + | 0.988840i | \(0.452401\pi\) | |||||||
\(692\) | −2.95722e6 | −0.234757 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.36578e6 | −0.501711 | ||||||||
\(695\) | 222456. | 0.0174696 | ||||||||
\(696\) | 2.07936e6 | 0.162707 | ||||||||
\(697\) | −269892. | −0.0210430 | ||||||||
\(698\) | 9.33504e6 | 0.725233 | ||||||||
\(699\) | 6.31337e6 | 0.488730 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.49886e7 | 1.92064 | 0.960322 | − | 0.278893i | \(-0.0899674\pi\) | ||||
0.960322 | + | 0.278893i | \(0.0899674\pi\) | |||||||
\(702\) | −968112. | −0.0741452 | ||||||||
\(703\) | 6.42840e6 | 0.490585 | ||||||||
\(704\) | −1.46637e6 | −0.111509 | ||||||||
\(705\) | −1.52568e6 | −0.115609 | ||||||||
\(706\) | −1.12433e7 | −0.848947 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.12346e6 | 0.459107 | ||||||||
\(709\) | −9.83584e6 | −0.734845 | −0.367423 | − | 0.930054i | \(-0.619760\pi\) | ||||
−0.367423 | + | 0.930054i | \(0.619760\pi\) | |||||||
\(710\) | 457808. | 0.0340830 | ||||||||
\(711\) | 5.28412e6 | 0.392011 | ||||||||
\(712\) | 8.19238e6 | 0.605634 | ||||||||
\(713\) | −1.21409e7 | −0.894387 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.09026e6 | −0.226063 | ||||||||
\(716\) | −5.72035e6 | −0.417004 | ||||||||
\(717\) | −3.45778e6 | −0.251188 | ||||||||
\(718\) | −3.75724e6 | −0.271993 | ||||||||
\(719\) | −2.13624e7 | −1.54109 | −0.770546 | − | 0.637384i | \(-0.780017\pi\) | ||||
−0.770546 | + | 0.637384i | \(0.780017\pi\) | |||||||
\(720\) | 539136. | 0.0387585 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.45560e6 | −0.675066 | ||||||||
\(723\) | −8.58402e6 | −0.610724 | ||||||||
\(724\) | 1.11441e7 | 0.790132 | ||||||||
\(725\) | 8.84089e6 | 0.624670 | ||||||||
\(726\) | 1.18393e6 | 0.0833653 | ||||||||
\(727\) | 6.53025e6 | 0.458241 | 0.229120 | − | 0.973398i | \(-0.426415\pi\) | ||||
0.229120 | + | 0.973398i | \(0.426415\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.13200e6 | −0.148074 | ||||||||
\(731\) | 804888. | 0.0557111 | ||||||||
\(732\) | −6.45696e6 | −0.445400 | ||||||||
\(733\) | −1.66571e7 | −1.14509 | −0.572545 | − | 0.819873i | \(-0.694044\pi\) | ||||
−0.572545 | + | 0.819873i | \(0.694044\pi\) | |||||||
\(734\) | −1.23940e7 | −0.849128 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.19341e6 | 0.149254 | ||||||||
\(737\) | 518384. | 0.0351547 | ||||||||
\(738\) | 694008. | 0.0469055 | ||||||||
\(739\) | −2.39536e7 | −1.61347 | −0.806733 | − | 0.590917i | \(-0.798766\pi\) | ||||
−0.806733 | + | 0.590917i | \(0.798766\pi\) | |||||||
\(740\) | −1.21555e6 | −0.0816008 | ||||||||
\(741\) | −6.57360e6 | −0.439803 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.48982e6 | −0.497736 | −0.248868 | − | 0.968537i | \(-0.580059\pi\) | ||||
−0.248868 | + | 0.968537i | \(0.580059\pi\) | |||||||
\(744\) | −3.26477e6 | −0.216232 | ||||||||
\(745\) | 1.80840e6 | 0.119373 | ||||||||
\(746\) | 913064. | 0.0600695 | ||||||||
\(747\) | −8.32712e6 | −0.546001 | ||||||||
\(748\) | −721728. | −0.0471650 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.21726e6 | 0.338680 | ||||||||
\(751\) | −4.71845e6 | −0.305281 | −0.152640 | − | 0.988282i | \(-0.548778\pi\) | ||||
−0.152640 | + | 0.988282i | \(0.548778\pi\) | |||||||
\(752\) | −1.66912e6 | −0.107632 | ||||||||
\(753\) | 5.12586e6 | 0.329442 | ||||||||
\(754\) | 4.79408e6 | 0.307098 | ||||||||
\(755\) | 1.37602e7 | 0.878534 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.67397e7 | −1.69597 | −0.847983 | − | 0.530024i | \(-0.822183\pi\) | ||||
−0.847983 | + | 0.530024i | \(0.822183\pi\) | |||||||
\(758\) | 4.14677e6 | 0.262142 | ||||||||
\(759\) | 6.90152e6 | 0.434851 | ||||||||
\(760\) | 3.66080e6 | 0.229902 | ||||||||
\(761\) | −1.44331e7 | −0.903435 | −0.451718 | − | 0.892161i | \(-0.649189\pi\) | ||||
−0.451718 | + | 0.892161i | \(0.649189\pi\) | |||||||
\(762\) | −5.95973e6 | −0.371825 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.09872e6 | 0.0681010 | ||||||||
\(765\) | 265356. | 0.0163936 | ||||||||
\(766\) | 847104. | 0.0521633 | ||||||||
\(767\) | 1.41180e7 | 0.866530 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | −8.55510e6 | −0.521686 | −0.260843 | − | 0.965381i | \(-0.584001\pi\) | ||||
−0.260843 | + | 0.965381i | \(0.584001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.59978e6 | 0.581601 | ||||||||
\(772\) | 1.32356e7 | 0.799280 | ||||||||
\(773\) | 1.92272e7 | 1.15735 | 0.578677 | − | 0.815557i | \(-0.303569\pi\) | ||||
0.578677 | + | 0.815557i | \(0.303569\pi\) | |||||||
\(774\) | −2.06971e6 | −0.124182 | ||||||||
\(775\) | −1.38809e7 | −0.830165 | ||||||||
\(776\) | 7.25274e6 | 0.432362 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.65298e6 | −0.334833 | ||||||||
\(779\) | 4.71240e6 | 0.278227 | ||||||||
\(780\) | 1.24301e6 | 0.0731539 | ||||||||
\(781\) | 1.57592e6 | 0.0924497 | ||||||||
\(782\) | 1.07957e6 | 0.0631296 | ||||||||
\(783\) | −2.63169e6 | −0.153402 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 339040. | 0.0196371 | ||||||||
\(786\) | 5.01509e6 | 0.289549 | ||||||||
\(787\) | −2.53316e7 | −1.45789 | −0.728947 | − | 0.684570i | \(-0.759990\pi\) | ||||
−0.728947 | + | 0.684570i | \(0.759990\pi\) | |||||||
\(788\) | −2.29411e6 | −0.131613 | ||||||||
\(789\) | −1.33419e7 | −0.762999 | ||||||||
\(790\) | −6.78454e6 | −0.386770 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.85587e6 | 0.105132 | ||||||||
\(793\) | −1.48869e7 | −0.840661 | ||||||||
\(794\) | 4.36134e6 | 0.245510 | ||||||||
\(795\) | −2.50427e6 | −0.140528 | ||||||||
\(796\) | −8.68160e6 | −0.485643 | ||||||||
\(797\) | −3.13162e7 | −1.74632 | −0.873158 | − | 0.487437i | \(-0.837932\pi\) | ||||
−0.873158 | + | 0.487437i | \(0.837932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −821520. | −0.0455251 | ||||||||
\(800\) | 2.50778e6 | 0.138536 | ||||||||
\(801\) | −1.03685e7 | −0.570997 | ||||||||
\(802\) | −1.05701e7 | −0.580288 | ||||||||
\(803\) | −7.33900e6 | −0.401650 | ||||||||
\(804\) | −208512. | −0.0113760 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.52710e6 | −0.408122 | ||||||||
\(807\) | −1.93599e6 | −0.104645 | ||||||||
\(808\) | 8.94170e6 | 0.481827 | ||||||||
\(809\) | 484890. | 0.0260479 | 0.0130239 | − | 0.999915i | \(-0.495854\pi\) | ||||
0.0130239 | + | 0.999915i | \(0.495854\pi\) | |||||||
\(810\) | −682344. | −0.0365419 | ||||||||
\(811\) | −5.32623e6 | −0.284359 | −0.142180 | − | 0.989841i | \(-0.545411\pi\) | ||||
−0.142180 | + | 0.989841i | \(0.545411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.73793e7 | 0.922161 | ||||||||
\(814\) | −4.18430e6 | −0.221341 | ||||||||
\(815\) | −9.13224e6 | −0.481596 | ||||||||
\(816\) | 290304. | 0.0152626 | ||||||||
\(817\) | −1.40536e7 | −0.736601 | ||||||||
\(818\) | −2.50171e7 | −1.30723 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −891072. | −0.0462784 | ||||||||
\(821\) | 3.21777e7 | 1.66609 | 0.833043 | − | 0.553209i | \(-0.186597\pi\) | ||||
0.833043 | + | 0.553209i | \(0.186597\pi\) | |||||||
\(822\) | 1.19823e7 | 0.618530 | ||||||||
\(823\) | −8.07408e6 | −0.415521 | −0.207761 | − | 0.978180i | \(-0.566618\pi\) | ||||
−0.207761 | + | 0.978180i | \(0.566618\pi\) | |||||||
\(824\) | 9.09952e6 | 0.466875 | ||||||||
\(825\) | 7.89068e6 | 0.403626 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.04922e6 | −0.409251 | −0.204626 | − | 0.978840i | \(-0.565598\pi\) | ||||
−0.204626 | + | 0.978840i | \(0.565598\pi\) | |||||||
\(828\) | −2.77603e6 | −0.140718 | ||||||||
\(829\) | −1.35889e7 | −0.686751 | −0.343375 | − | 0.939198i | \(-0.611570\pi\) | ||||
−0.343375 | + | 0.939198i | \(0.611570\pi\) | |||||||
\(830\) | 1.06916e7 | 0.538701 | ||||||||
\(831\) | 1.83381e7 | 0.921193 | ||||||||
\(832\) | 1.35987e6 | 0.0681067 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −308016. | −0.0153341 | ||||||||
\(835\) | 1.62793e7 | 0.808017 | ||||||||
\(836\) | 1.26016e7 | 0.623606 | ||||||||
\(837\) | 4.13197e6 | 0.203865 | ||||||||
\(838\) | 3.89570e6 | 0.191635 | ||||||||
\(839\) | −3.67721e6 | −0.180349 | −0.0901744 | − | 0.995926i | \(-0.528742\pi\) | ||||
−0.0901744 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.47905e6 | −0.364633 | ||||||||
\(842\) | −3.45847e6 | −0.168114 | ||||||||
\(843\) | −5.75159e6 | −0.278753 | ||||||||
\(844\) | 1.80441e7 | 0.871925 | ||||||||
\(845\) | −6.78779e6 | −0.327029 | ||||||||
\(846\) | 2.11248e6 | 0.101477 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.73971e6 | −0.130832 | ||||||||
\(849\) | 339696. | 0.0161741 | ||||||||
\(850\) | 1.23430e6 | 0.0585965 | ||||||||
\(851\) | 6.25892e6 | 0.296262 | ||||||||
\(852\) | −633888. | −0.0299167 | ||||||||
\(853\) | −3.25379e7 | −1.53115 | −0.765573 | − | 0.643349i | \(-0.777544\pi\) | ||||
−0.765573 | + | 0.643349i | \(0.777544\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.63320e6 | −0.216753 | ||||||||
\(856\) | 1.27052e7 | 0.592646 | ||||||||
\(857\) | 1.12723e7 | 0.524278 | 0.262139 | − | 0.965030i | \(-0.415572\pi\) | ||||
0.262139 | + | 0.965030i | \(0.415572\pi\) | |||||||
\(858\) | 4.27882e6 | 0.198429 | ||||||||
\(859\) | −7.69694e6 | −0.355906 | −0.177953 | − | 0.984039i | \(-0.556948\pi\) | ||||
−0.177953 | + | 0.984039i | \(0.556948\pi\) | |||||||
\(860\) | 2.65741e6 | 0.122521 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.46418e7 | 0.671162 | ||||||||
\(863\) | −4.58785e6 | −0.209692 | −0.104846 | − | 0.994488i | \(-0.533435\pi\) | ||||
−0.104846 | + | 0.994488i | \(0.533435\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −4.80548e6 | −0.218372 | ||||||||
\(866\) | 1.97467e7 | 0.894746 | ||||||||
\(867\) | −1.26358e7 | −0.570895 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.33545e7 | −1.04911 | ||||||||
\(870\) | 3.37896e6 | 0.151351 | ||||||||
\(871\) | −480736. | −0.0214714 | ||||||||
\(872\) | −8.48243e6 | −0.377771 | ||||||||
\(873\) | −9.17924e6 | −0.407635 | ||||||||
\(874\) | −1.88496e7 | −0.834687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.95200e6 | 0.129974 | ||||||||
\(877\) | −1.14666e7 | −0.503424 | −0.251712 | − | 0.967802i | \(-0.580994\pi\) | ||||
−0.251712 | + | 0.967802i | \(0.580994\pi\) | |||||||
\(878\) | −2.92522e6 | −0.128062 | ||||||||
\(879\) | −1.65529e7 | −0.722606 | ||||||||
\(880\) | −2.38285e6 | −0.103726 | ||||||||
\(881\) | −3.02550e7 | −1.31328 | −0.656640 | − | 0.754204i | \(-0.728023\pi\) | ||||
−0.656640 | + | 0.754204i | \(0.728023\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.83052e6 | 0.424302 | 0.212151 | − | 0.977237i | \(-0.431953\pi\) | ||||
0.212151 | + | 0.977237i | \(0.431953\pi\) | |||||||
\(884\) | 669312. | 0.0288070 | ||||||||
\(885\) | 9.95062e6 | 0.427063 | ||||||||
\(886\) | −1.94648e7 | −0.833039 | ||||||||
\(887\) | 2.32272e7 | 0.991263 | 0.495631 | − | 0.868533i | \(-0.334937\pi\) | ||||
0.495631 | + | 0.868533i | \(0.334937\pi\) | |||||||
\(888\) | 1.68307e6 | 0.0716259 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.33126e7 | 0.563363 | ||||||||
\(891\) | −2.34884e6 | −0.0991194 | ||||||||
\(892\) | 1.43676e7 | 0.604606 | ||||||||
\(893\) | 1.43440e7 | 0.601924 | ||||||||
\(894\) | −2.50394e6 | −0.104781 | ||||||||
\(895\) | −9.29557e6 | −0.387899 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.40030e6 | −0.265594 | ||||||||
\(898\) | −2.28795e7 | −0.946793 | ||||||||
\(899\) | −2.04615e7 | −0.844380 | ||||||||
\(900\) | −3.17390e6 | −0.130613 | ||||||||
\(901\) | −1.34845e6 | −0.0553380 | ||||||||
\(902\) | −3.06734e6 | −0.125530 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00966e6 | −0.122489 | ||||||||
\(905\) | 1.81092e7 | 0.734984 | ||||||||
\(906\) | −1.90526e7 | −0.771143 | ||||||||
\(907\) | 3.05501e7 | 1.23309 | 0.616544 | − | 0.787321i | \(-0.288532\pi\) | ||||
0.616544 | + | 0.787321i | \(0.288532\pi\) | |||||||
\(908\) | −7.48179e6 | −0.301156 | ||||||||
\(909\) | −1.13168e7 | −0.454271 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.21502e7 | 0.884265 | 0.442133 | − | 0.896950i | \(-0.354222\pi\) | ||||
0.442133 | + | 0.896950i | \(0.354222\pi\) | |||||||
\(912\) | −5.06880e6 | −0.201799 | ||||||||
\(913\) | 3.68038e7 | 1.46122 | ||||||||
\(914\) | 2.72814e7 | 1.08019 | ||||||||
\(915\) | −1.04926e7 | −0.414313 | ||||||||
\(916\) | −7.13824e6 | −0.281095 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −367416. | −0.0143897 | ||||||||
\(919\) | −1.26723e7 | −0.494955 | −0.247477 | − | 0.968894i | \(-0.579602\pi\) | ||||
−0.247477 | + | 0.968894i | \(0.579602\pi\) | |||||||
\(920\) | 3.56429e6 | 0.138836 | ||||||||
\(921\) | −9.58248e6 | −0.372245 | ||||||||
\(922\) | 2.98374e7 | 1.15593 | ||||||||
\(923\) | −1.46146e6 | −0.0564656 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.15598e6 | 0.274989 | ||||||||
\(926\) | 2.09539e7 | 0.803042 | ||||||||
\(927\) | −1.15166e7 | −0.440174 | ||||||||
\(928\) | 3.69664e6 | 0.140909 | ||||||||
\(929\) | −4.02840e7 | −1.53142 | −0.765709 | − | 0.643187i | \(-0.777612\pi\) | ||||
−0.765709 | + | 0.643187i | \(0.777612\pi\) | |||||||
\(930\) | −5.30525e6 | −0.201140 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.12238e7 | 0.423252 | ||||||||
\(933\) | −9.08568e6 | −0.341707 | ||||||||
\(934\) | −3.58398e7 | −1.34431 | ||||||||
\(935\) | −1.17281e6 | −0.0438731 | ||||||||
\(936\) | −1.72109e6 | −0.0642116 | ||||||||
\(937\) | 1.34104e7 | 0.498992 | 0.249496 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249496 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.30419e7 | −0.482698 | ||||||||
\(940\) | −2.71232e6 | −0.100120 | ||||||||
\(941\) | −2.73213e7 | −1.00584 | −0.502918 | − | 0.864334i | \(-0.667740\pi\) | ||||
−0.502918 | + | 0.864334i | \(0.667740\pi\) | |||||||
\(942\) | −469440. | −0.0172366 | ||||||||
\(943\) | 4.58816e6 | 0.168020 | ||||||||
\(944\) | 1.08861e7 | 0.397598 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.14762e6 | 0.332338 | ||||||||
\(947\) | 8.71745e6 | 0.315874 | 0.157937 | − | 0.987449i | \(-0.449516\pi\) | ||||
0.157937 | + | 0.987449i | \(0.449516\pi\) | |||||||
\(948\) | 9.39398e6 | 0.339492 | ||||||||
\(949\) | 6.80600e6 | 0.245316 | ||||||||
\(950\) | −2.15512e7 | −0.774752 | ||||||||
\(951\) | 2.45080e7 | 0.878731 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.62984e7 | −0.581315 | −0.290658 | − | 0.956827i | \(-0.593874\pi\) | ||||
−0.290658 | + | 0.956827i | \(0.593874\pi\) | |||||||
\(954\) | 3.46745e6 | 0.123350 | ||||||||
\(955\) | 1.78542e6 | 0.0633479 | ||||||||
\(956\) | −6.14717e6 | −0.217536 | ||||||||
\(957\) | 1.16314e7 | 0.410538 | ||||||||
\(958\) | 7.01414e6 | 0.246923 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 958464. | 0.0335659 | ||||||||
\(961\) | 3.49707e6 | 0.122151 | ||||||||
\(962\) | 3.88042e6 | 0.135189 | ||||||||
\(963\) | −1.60800e7 | −0.558752 | ||||||||
\(964\) | −1.52605e7 | −0.528902 | ||||||||
\(965\) | 2.15078e7 | 0.743493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.49067e6 | −0.188825 | −0.0944124 | − | 0.995533i | \(-0.530097\pi\) | ||||
−0.0944124 | + | 0.995533i | \(0.530097\pi\) | |||||||
\(968\) | 2.10477e6 | 0.0721964 | ||||||||
\(969\) | −2.49480e6 | −0.0853545 | ||||||||
\(970\) | 1.17857e7 | 0.402185 | ||||||||
\(971\) | 4.51675e7 | 1.53737 | 0.768685 | − | 0.639628i | \(-0.220911\pi\) | ||||
0.768685 | + | 0.639628i | \(0.220911\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.71027e6 | −0.125317 | ||||||||
\(975\) | −7.31761e6 | −0.246523 | ||||||||
\(976\) | −1.14790e7 | −0.385728 | ||||||||
\(977\) | −2.38010e7 | −0.797737 | −0.398868 | − | 0.917008i | \(-0.630597\pi\) | ||||
−0.398868 | + | 0.917008i | \(0.630597\pi\) | |||||||
\(978\) | 1.26446e7 | 0.422726 | ||||||||
\(979\) | 4.58261e7 | 1.52812 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.07356e7 | 0.356166 | ||||||||
\(982\) | −3.37493e7 | −1.11683 | ||||||||
\(983\) | 9.36478e6 | 0.309111 | 0.154555 | − | 0.987984i | \(-0.450606\pi\) | ||||
0.154555 | + | 0.987984i | \(0.450606\pi\) | |||||||
\(984\) | 1.23379e6 | 0.0406213 | ||||||||
\(985\) | −3.72793e6 | −0.122427 | ||||||||
\(986\) | 1.81944e6 | 0.0595999 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.16864e7 | −0.380880 | ||||||||
\(989\) | −1.36831e7 | −0.444830 | ||||||||
\(990\) | 3.01579e6 | 0.0977943 | ||||||||
\(991\) | −4.33916e7 | −1.40353 | −0.701764 | − | 0.712409i | \(-0.747604\pi\) | ||||
−0.701764 | + | 0.712409i | \(0.747604\pi\) | |||||||
\(992\) | −5.80403e6 | −0.187262 | ||||||||
\(993\) | −9.90364e6 | −0.318729 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.41076e7 | −0.451747 | ||||||||
\(996\) | −1.48038e7 | −0.472851 | ||||||||
\(997\) | 4.35294e6 | 0.138690 | 0.0693449 | − | 0.997593i | \(-0.477909\pi\) | ||||
0.0693449 | + | 0.997593i | \(0.477909\pi\) | |||||||
\(998\) | −5.33112e6 | −0.169431 | ||||||||
\(999\) | −2.13014e6 | −0.0675296 |
(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 | 294.6.a.g.1.1 | yes | 1 | |
3.2 | odd | 2 | 882.6.a.p.1.1 | 1 | |||
7.2 | even | 3 | 294.6.e.j.67.1 | 2 | |||
7.3 | odd | 6 | 294.6.e.q.79.1 | 2 | |||
7.4 | even | 3 | 294.6.e.j.79.1 | 2 | |||
7.5 | odd | 6 | 294.6.e.q.67.1 | 2 | |||
7.6 | odd | 2 | 294.6.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 882.6.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.6.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
294.6.a.g.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
294.6.e.j.67.1 | 2 | 7.2 | even | 3 | |||
294.6.e.j.79.1 | 2 | 7.4 | even | 3 | |||
294.6.e.q.67.1 | 2 | 7.5 | odd | 6 | |||
294.6.e.q.79.1 | 2 | 7.3 | odd | 6 | |||
882.6.a.p.1.1 | 1 | 3.2 | odd | 2 | |||
882.6.a.t.1.1 | 1 | 21.20 | even | 2 |