Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −26.0000 | −1.66790 | −0.833950 | − | 0.551839i | \(-0.813926\pi\) | ||||
−0.833950 | + | 0.551839i | \(0.813926\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000 | 0.169698 | 0.0848492 | − | 0.996394i | \(-0.472959\pi\) | ||||
0.0848492 | + | 0.996394i | \(0.472959\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 433.000 | 1.78189 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −768.000 | −1.91372 | −0.956862 | − | 0.290541i | \(-0.906165\pi\) | ||||
−0.956862 | + | 0.290541i | \(0.906165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.0000 | 0.0754917 | 0.0377459 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377459 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −650.000 | −0.745908 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 378.000 | 0.317227 | 0.158613 | − | 0.987341i | \(-0.449298\pi\) | ||||
0.158613 | + | 0.987341i | \(0.449298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1100.00 | 0.699051 | 0.349525 | − | 0.936927i | \(-0.386343\pi\) | ||||
0.349525 | + | 0.936927i | \(0.386343\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −572.000 | −0.283040 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1986.00 | 0.782816 | 0.391408 | − | 0.920217i | \(-0.371988\pi\) | ||||
0.391408 | + | 0.920217i | \(0.371988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4940.00 | −1.30412 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5610.00 | 1.23870 | 0.619352 | − | 0.785113i | \(-0.287395\pi\) | ||||
0.619352 | + | 0.785113i | \(0.287395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3988.00 | 0.745334 | 0.372667 | − | 0.927965i | \(-0.378443\pi\) | ||||
0.372667 | + | 0.927965i | \(0.378443\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 19968.0 | 3.19190 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 550.000 | 0.0758914 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 142.000 | 0.0170523 | 0.00852617 | − | 0.999964i | \(-0.497286\pi\) | ||||
0.00852617 | + | 0.999964i | \(0.497286\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1196.00 | −0.125913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1542.00 | 0.143260 | 0.0716300 | − | 0.997431i | \(-0.477180\pi\) | ||||
0.0716300 | + | 0.997431i | \(0.477180\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5026.00 | −0.414526 | −0.207263 | − | 0.978285i | \(-0.566456\pi\) | ||||
−0.207263 | + | 0.978285i | \(0.566456\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10825.0 | 0.796887 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −24738.0 | −1.63350 | −0.816752 | − | 0.576990i | \(-0.804227\pi\) | ||||
−0.816752 | + | 0.576990i | \(0.804227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16323.0 | −0.971202 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9828.00 | −0.529102 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14166.0 | 0.692720 | 0.346360 | − | 0.938102i | \(-0.387418\pi\) | ||||
0.346360 | + | 0.938102i | \(0.387418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19200.0 | −0.855844 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −28600.0 | −1.16595 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28380.0 | 1.06141 | 0.530704 | − | 0.847557i | \(-0.321928\pi\) | ||||
0.530704 | + | 0.847557i | \(0.321928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5522.00 | −0.190008 | −0.0950040 | − | 0.995477i | \(-0.530286\pi\) | ||||
−0.0950040 | + | 0.995477i | \(0.530286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9526.00 | 0.302384 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1150.00 | 0.0337609 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −24742.0 | −0.673361 | −0.336680 | − | 0.941619i | \(-0.609304\pi\) | ||||
−0.336680 | + | 0.941619i | \(0.609304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −51636.0 | −1.30566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −42372.0 | −0.997546 | −0.498773 | − | 0.866733i | \(-0.666216\pi\) | ||||
−0.498773 | + | 0.866733i | \(0.666216\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52126.0 | −1.14485 | −0.572423 | − | 0.819958i | \(-0.693997\pi\) | ||||
−0.572423 | + | 0.819958i | \(0.693997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16250.0 | −0.333580 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16896.0 | −0.324756 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39640.0 | 0.714605 | 0.357302 | − | 0.933989i | \(-0.383697\pi\) | ||||
0.357302 | + | 0.933989i | \(0.383697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23221.0 | 0.393250 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −59826.0 | −0.953223 | −0.476612 | − | 0.879114i | \(-0.658135\pi\) | ||||
−0.476612 | + | 0.879114i | \(0.658135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9450.00 | 0.141868 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −145860. | −2.06604 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 57690.0 | 0.772015 | 0.386007 | − | 0.922496i | \(-0.373854\pi\) | ||||
0.386007 | + | 0.922496i | \(0.373854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1012.00 | 0.0128108 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −103688. | −1.24314 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 27500.0 | 0.312625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −144382. | −1.55806 | −0.779029 | − | 0.626988i | \(-0.784288\pi\) | ||||
−0.779029 | + | 0.626988i | \(0.784288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −332544. | −3.41005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 141258. | 1.37787 | 0.688937 | − | 0.724821i | \(-0.258078\pi\) | ||||
0.688937 | + | 0.724821i | \(0.258078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −139814. | −1.29855 | −0.649273 | − | 0.760555i | \(-0.724927\pi\) | ||||
−0.649273 | + | 0.760555i | \(0.724927\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14300.0 | −0.126579 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 86418.0 | 0.729701 | 0.364850 | − | 0.931066i | \(-0.381120\pi\) | ||||
0.364850 | + | 0.931066i | \(0.381120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −218450. | −1.76111 | −0.880554 | − | 0.473947i | \(-0.842829\pi\) | ||||
−0.880554 | + | 0.473947i | \(0.842829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3692.00 | −0.0284416 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −28806.0 | −0.212220 | −0.106110 | − | 0.994354i | \(-0.533840\pi\) | ||||
−0.106110 | + | 0.994354i | \(0.533840\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 49650.0 | 0.350086 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 19918.0 | 0.134518 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8316.00 | 0.0538328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 428773. | 2.66234 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −40092.0 | −0.238943 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 216502. | 1.19111 | 0.595556 | − | 0.803314i | \(-0.296932\pi\) | ||||
0.595556 | + | 0.803314i | \(0.296932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 130676. | 0.691388 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −244608. | −1.24535 | −0.622676 | − | 0.782479i | \(-0.713955\pi\) | ||||
−0.622676 | + | 0.782479i | \(0.713955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24200.0 | 0.118628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −123500. | −0.583220 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −239502. | −1.09020 | −0.545102 | − | 0.838370i | \(-0.683509\pi\) | ||||
−0.545102 | + | 0.838370i | \(0.683509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 30860.0 | 0.135475 | 0.0677375 | − | 0.997703i | \(-0.478422\pi\) | ||||
0.0677375 | + | 0.997703i | \(0.478422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 643188. | 2.72452 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −35328.0 | −0.144470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 140250. | 0.553966 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 424398. | 1.61987 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 100950. | 0.372512 | 0.186256 | − | 0.982501i | \(-0.440365\pi\) | ||||
0.186256 | + | 0.982501i | \(0.440365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12452.0 | −0.0444423 | −0.0222212 | − | 0.999753i | \(-0.507074\pi\) | ||||
−0.0222212 | + | 0.999753i | \(0.507074\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 163674. | 0.565264 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 99700.0 | 0.333323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6022.00 | 0.0194981 | 0.00974903 | − | 0.999952i | \(-0.496897\pi\) | ||||
0.00974903 | + | 0.999952i | \(0.496897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −368316. | −1.15539 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 43692.0 | 0.132843 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −500866. | −1.47656 | −0.738282 | − | 0.674492i | \(-0.764363\pi\) | ||||
−0.738282 | + | 0.674492i | \(0.764363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 499200. | 1.42746 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −555258. | −1.54065 | −0.770324 | − | 0.637652i | \(-0.779906\pi\) | ||||
−0.770324 | + | 0.637652i | \(0.779906\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369177. | −0.994301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 476300. | 1.24563 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −417354. | −1.06020 | −0.530102 | − | 0.847934i | \(-0.677846\pi\) | ||||
−0.530102 | + | 0.847934i | \(0.677846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13750.0 | 0.0339397 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −737880. | −1.77032 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −52380.0 | −0.122189 | −0.0610946 | − | 0.998132i | \(-0.519459\pi\) | ||||
−0.0610946 | + | 0.998132i | \(0.519459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −546662. | −1.24029 | −0.620144 | − | 0.784488i | \(-0.712926\pi\) | ||||
−0.620144 | + | 0.784488i | \(0.712926\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 143572. | 0.316914 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3550.00 | 0.00762604 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −290304. | −0.607084 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −108680. | −0.221307 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 452028. | 0.896565 | 0.448283 | − | 0.893892i | \(-0.352036\pi\) | ||||
0.448283 | + | 0.893892i | \(0.352036\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 485594. | 0.938383 | 0.469191 | − | 0.883097i | \(-0.344545\pi\) | ||||
0.469191 | + | 0.883097i | \(0.344545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29900.0 | −0.0563099 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.01018e6 | −1.85452 | −0.927262 | − | 0.374414i | \(-0.877844\pi\) | ||||
−0.927262 | + | 0.374414i | \(0.877844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 807640. | 1.44572 | 0.722862 | − | 0.690993i | \(-0.242826\pi\) | ||||
0.722862 | + | 0.690993i | \(0.242826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 643292. | 1.12310 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 123420. | 0.210206 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38550.0 | 0.0640678 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 859938. | 1.39489 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −844800. | −1.33779 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 149552. | 0.231252 | 0.115626 | − | 0.993293i | \(-0.463113\pi\) | ||||
0.115626 | + | 0.993293i | \(0.463113\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.10167e6 | 1.66381 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −125650. | −0.185381 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 87736.0 | 0.126482 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.35528e6 | 1.90949 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17388.0 | 0.0239480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 443506. | 0.597224 | 0.298612 | − | 0.954375i | \(-0.403476\pi\) | ||||
0.298612 | + | 0.954375i | \(0.403476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 270625. | 0.356379 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 420018. | 0.541007 | 0.270504 | − | 0.962719i | \(-0.412810\pi\) | ||||
0.270504 | + | 0.962719i | \(0.412810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.05875e6 | −1.33415 | −0.667075 | − | 0.744990i | \(-0.732454\pi\) | ||||
−0.667075 | + | 0.744990i | \(0.732454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 439296. | 0.541661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.27345e6 | −1.53671 | −0.768353 | − | 0.640026i | \(-0.778923\pi\) | ||||
−0.768353 | + | 0.640026i | \(0.778923\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −618450. | −0.730525 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.03064e6 | −1.19189 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 370680. | 0.419763 | 0.209882 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209882 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −561298. | −0.622517 | −0.311258 | − | 0.950325i | \(-0.600750\pi\) | ||||
−0.311258 | + | 0.950325i | \(0.600750\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 596674. | 0.648219 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −408075. | −0.434335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 50600.0 | 0.0527726 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.55548e6 | 1.58988 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 577152. | 0.578237 | 0.289119 | − | 0.957293i | \(-0.406638\pi\) | ||||
0.289119 | + | 0.957293i | \(0.406638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.52525e6 | −1.49809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −245700. | −0.236622 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −651462. | −0.615257 | −0.307628 | − | 0.951507i | \(-0.599535\pi\) | ||||
−0.307628 | + | 0.951507i | \(0.599535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3124.00 | 0.00289375 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.42913e6 | 2.20724 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −917574. | −0.817997 | −0.408999 | − | 0.912535i | \(-0.634122\pi\) | ||||
−0.408999 | + | 0.912535i | \(0.634122\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 354150. | 0.309794 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.49994e6 | −1.28764 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 735390. | 0.619637 | 0.309818 | − | 0.950796i | \(-0.399732\pi\) | ||||
0.309818 | + | 0.950796i | \(0.399732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.12131e6 | 0.927474 | 0.463737 | − | 0.885973i | \(-0.346508\pi\) | ||||
0.463737 | + | 0.885973i | \(0.346508\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26312.0 | −0.0213672 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −480000. | −0.382745 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.66034e6 | 1.30016 | 0.650082 | − | 0.759864i | \(-0.274735\pi\) | ||||
0.650082 | + | 0.759864i | \(0.274735\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.72680e6 | 1.32811 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.45210e6 | 1.09706 | 0.548531 | − | 0.836130i | \(-0.315187\pi\) | ||||
0.548531 | + | 0.836130i | \(0.315187\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 309014. | 0.229357 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −715000. | −0.521427 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 33924.0 | 0.0243110 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.27697e6 | −0.899367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.75393e6 | 2.59869 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.59301e6 | 1.08405 | 0.542024 | − | 0.840363i | \(-0.317658\pi\) | ||||
0.542024 | + | 0.840363i | \(0.317658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 709500. | 0.474676 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.79392e6 | 2.49573 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 91356.0 | 0.0590961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −110572. | −0.0703443 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.67271e6 | −2.29816 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −138050. | −0.0849741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.24726e6 | 0.755284 | 0.377642 | − | 0.925952i | \(-0.376735\pi\) | ||||
0.377642 | + | 0.925952i | \(0.376735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.63516e6 | 2.16585 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 665988. | 0.390450 | 0.195225 | − | 0.980758i | \(-0.437456\pi\) | ||||
0.195225 | + | 0.980758i | \(0.437456\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −591286. | −0.341143 | −0.170572 | − | 0.985345i | \(-0.554561\pi\) | ||||
−0.170572 | + | 0.985345i | \(0.554561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 238150. | 0.135230 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 516342. | 0.288595 | 0.144298 | − | 0.989534i | \(-0.453908\pi\) | ||||
0.144298 | + | 0.989534i | \(0.453908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.30848e6 | −2.37054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.24687e6 | −1.21707 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 415800. | 0.221757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28750.0 | 0.0150983 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.67970e6 | 2.93735 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −544236. | −0.277203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.29577e6 | −1.65343 | −0.826717 | − | 0.562619i | \(-0.809794\pi\) | ||||
−0.826717 | + | 0.562619i | \(0.809794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 61486.0 | 0.0303854 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −618550. | −0.301136 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.91098e6 | 0.916602 | 0.458301 | − | 0.888797i | \(-0.348458\pi\) | ||||
0.458301 | + | 0.888797i | \(0.348458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 748956. | 0.353962 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.06278e6 | −1.42636 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −728860. | −0.334510 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.29090e6 | −0.583909 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.42006e6 | 1.07895 | 0.539476 | − | 0.842001i | \(-0.318622\pi\) | ||||
0.539476 | + | 0.842001i | \(0.318622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.50727e6 | −1.10189 | −0.550944 | − | 0.834542i | \(-0.685732\pi\) | ||||
−0.550944 | + | 0.834542i | \(0.685732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −227240. | −0.0984503 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −413166. | −0.176477 | −0.0882384 | − | 0.996099i | \(-0.528124\pi\) | ||||
−0.0882384 | + | 0.996099i | \(0.528124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.05930e6 | −0.446116 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −216216. | −0.0897878 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.73772e6 | −0.711613 | −0.355806 | − | 0.934560i | \(-0.615794\pi\) | ||||
−0.355806 | + | 0.934560i | \(0.615794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.26610e6 | −0.511328 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.11481e7 | −4.44052 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.30315e6 | −0.511991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.16098e6 | −0.449944 | −0.224972 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224972 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 667686. | 0.255274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 311652. | 0.117553 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −343754. | −0.127931 | −0.0639655 | − | 0.997952i | \(-0.520375\pi\) | ||||
−0.0639655 | + | 0.997952i | \(0.520375\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −406250. | −0.149182 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 258060. | 0.0935120 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 573140. | 0.204957 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.62905e6 | −1.98666 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.88055e6 | 1.00341 | 0.501704 | − | 0.865039i | \(-0.332707\pi\) | ||||
0.501704 | + | 0.865039i | \(0.332707\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −422400. | −0.145235 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.17626e6 | −0.738640 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.08559e6 | 1.03387 | 0.516933 | − | 0.856026i | \(-0.327074\pi\) | ||||
0.516933 | + | 0.856026i | \(0.327074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 750708. | 0.248330 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.35981e6 | 2.07712 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 991000. | 0.319581 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −885458. | −0.281963 | −0.140981 | − | 0.990012i | \(-0.545026\pi\) | ||||
−0.140981 | + | 0.990012i | \(0.545026\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −629200. | −0.197859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.75344e6 | −1.16565 | −0.582825 | − | 0.812598i | \(-0.698053\pi\) | ||||
−0.582825 | + | 0.812598i | \(0.698053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 183448. | 0.0562666 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 580525. | 0.175867 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −109056. | −0.0326335 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.94653e6 | −0.575377 | −0.287689 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287689 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.22705e6 | 1.81835 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 624360. | 0.180119 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.49565e6 | −0.426295 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −802360. | −0.225959 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.99166e6 | −0.832486 | −0.416243 | − | 0.909253i | \(-0.636654\pi\) | ||||
−0.416243 | + | 0.909253i | \(0.636654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.96660e6 | −1.09072 | −0.545360 | − | 0.838202i | \(-0.683607\pi\) | ||||
−0.545360 | + | 0.838202i | \(0.683607\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.07116e7 | −2.91073 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 236250. | 0.0634453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −121484. | −0.0322440 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 918528. | 0.240962 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.17115e6 | 1.34089 | 0.670446 | − | 0.741958i | \(-0.266103\pi\) | ||||
0.670446 | + | 0.741958i | \(0.266103\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.53485e6 | −1.16237 | −0.581183 | − | 0.813773i | \(-0.697410\pi\) | ||||
−0.581183 | + | 0.813773i | \(0.697410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.64650e6 | −0.923960 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.18460e6 | 0.547228 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.08220e6 | 0.268007 | 0.134004 | − | 0.990981i | \(-0.457217\pi\) | ||||
0.134004 | + | 0.990981i | \(0.457217\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.06786e6 | −1.73058 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.08079e6 | −0.261656 | −0.130828 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130828 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.44225e6 | 0.345255 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.62470e6 | −0.621314 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.61783e6 | 0.612810 | 0.306405 | − | 0.951901i | \(-0.400874\pi\) | ||||
0.306405 | + | 0.951901i | \(0.400874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18426e6 | −0.274160 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 323752. | 0.0741254 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25300.0 | 0.00572917 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.59046e6 | 0.356231 | 0.178115 | − | 0.984010i | \(-0.443000\pi\) | ||||
0.178115 | + | 0.984010i | \(0.443000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.86732e6 | −0.413701 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.25470e6 | −0.932431 | −0.466216 | − | 0.884671i | \(-0.654383\pi\) | ||||
−0.466216 | + | 0.884671i | \(0.654383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.26605e6 | −0.708061 | −0.354031 | − | 0.935234i | \(-0.615189\pi\) | ||||
−0.354031 | + | 0.935234i | \(0.615189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.59220e6 | −0.555950 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −601542. | −0.127636 | −0.0638181 | − | 0.997962i | \(-0.520328\pi\) | ||||
−0.0638181 | + | 0.997962i | \(0.520328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −544324. | −0.114268 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −156572. | −0.0325208 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.85997e6 | 0.793288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 687500. | 0.139810 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.13388e6 | 1.23435 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.57932e6 | 0.911931 | 0.455966 | − | 0.889997i | \(-0.349294\pi\) | ||||
0.455966 | + | 0.889997i | \(0.349294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6532.00 | 0.00128731 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.13599e6 | −0.221568 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.60955e6 | −0.696785 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.05226e6 | −1.34743 | −0.673714 | − | 0.738992i | \(-0.735302\pi\) | ||||
−0.673714 | + | 0.738992i | \(0.735302\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.30225e7 | 2.46276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.62349e6 | −0.491106 | −0.245553 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245553 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.12058e6 | 0.392950 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.31360e6 | −1.52502 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −932184. | −0.169282 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.61234e6 | −0.649437 | −0.324719 | − | 0.945811i | \(-0.605270\pi\) | ||||
−0.324719 | + | 0.945811i | \(0.605270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.44367e7 | 2.56965 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.15629e6 | −1.61361 | −0.806807 | − | 0.590815i | \(-0.798806\pi\) | ||||
−0.806807 | + | 0.590815i | \(0.798806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.53145e6 | 0.616204 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.59860e6 | 1.65840 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.26159e6 | −1.24233 | −0.621165 | − | 0.783679i | \(-0.713340\pi\) | ||||
−0.621165 | + | 0.783679i | \(0.713340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.14677e6 | −0.194279 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.43400e6 | −0.911646 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.49535e6 | −0.580728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.89988e7 | 3.12608 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.08512e7 | 1.76831 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.81020e6 | 0.937771 | 0.468886 | − | 0.883259i | \(-0.344656\pi\) | ||||
0.468886 | + | 0.883259i | \(0.344656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.17067e6 | −1.30618 | −0.653090 | − | 0.757280i | \(-0.726528\pi\) | ||||
−0.653090 | + | 0.757280i | \(0.726528\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −357500. | −0.0566080 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.50746e6 | 0.236440 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.49215e6 | −0.387199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22885e7 | 1.89132 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 70932.0 | 0.0108149 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.16045e6 | 0.326332 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.36188e6 | 0.203800 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.25361e7 | 1.85861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 817378. | 0.120069 | 0.0600343 | − | 0.998196i | \(-0.480879\pi\) | ||||
0.0600343 | + | 0.998196i | \(0.480879\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.42132e7 | 2.06868 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.46125e6 | −0.787591 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.50750e6 | −0.501221 | −0.250611 | − | 0.968088i | \(-0.580631\pi\) | ||||
−0.250611 | + | 0.968088i | \(0.580631\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.39103e6 | −0.338574 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.17100e6 | 0.865918 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 872080. | 0.121267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −92300.0 | −0.0127195 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.61490e6 | −1.31313 | −0.656563 | − | 0.754271i | \(-0.727991\pi\) | ||||
−0.656563 | + | 0.754271i | \(0.727991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −231196. | −0.0312933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.54790e6 | 1.01256 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.01941e6 | 0.268506 | 0.134253 | − | 0.990947i | \(-0.457136\pi\) | ||||
0.134253 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −720150. | −0.0949078 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 510862. | 0.0667338 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.37859e6 | 0.178507 | 0.0892533 | − | 0.996009i | \(-0.471552\pi\) | ||||
0.0892533 | + | 0.996009i | \(0.471552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.54295e6 | 1.09652 | 0.548261 | − | 0.836307i | \(-0.315290\pi\) | ||||
0.548261 | + | 0.836307i | \(0.315290\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.17527e7 | −1.49538 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.24125e6 | 0.156563 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.31458e6 | −0.289423 | −0.144711 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144711 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.26254e7 | −1.56513 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.31617e6 | −0.161760 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.08795e7 | −1.32568 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 497950. | 0.0601584 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 928338. | 0.111202 | 0.0556008 | − | 0.998453i | \(-0.482293\pi\) | ||||
0.0556008 | + | 0.998453i | \(0.482293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.38680e6 | 0.521026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.62646e7 | 3.09316 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −909486. | −0.106209 | −0.0531043 | − | 0.998589i | \(-0.516912\pi\) | ||||
−0.0531043 | + | 0.998589i | \(0.516912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 207900. | 0.0240748 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.09986e7 | −2.41132 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.51136e6 | 0.969241 | 0.484621 | − | 0.874724i | \(-0.338958\pi\) | ||||
0.484621 | + | 0.874724i | \(0.338958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.12498e6 | 0.691701 | 0.345851 | − | 0.938290i | \(-0.387590\pi\) | ||||
0.345851 | + | 0.938290i | \(0.387590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.07133e7 | −1.19986 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.07193e7 | 1.19064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.51646e6 | 0.497538 | 0.248769 | − | 0.968563i | \(-0.419974\pi\) | ||||
0.248769 | + | 0.968563i | \(0.419974\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.20892e6 | −0.350603 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.13795e6 | −0.123316 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.63979e6 | −1.03614 | −0.518068 | − | 0.855340i | \(-0.673349\pi\) | ||||
−0.518068 | + | 0.855340i | \(0.673349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.00230e6 | −0.106859 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.92650e6 | −1.04974 | −0.524872 | − | 0.851181i | \(-0.675887\pi\) | ||||
−0.524872 | + | 0.851181i | \(0.675887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.63322e6 | 0.800721 | 0.400360 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400360 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.81084e6 | −1.02089 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.26918e6 | 0.131010 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.19648e7 | 2.23130 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53676.0 | 0.00540946 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.80314e7 | −1.80284 | −0.901418 | − | 0.432949i | \(-0.857473\pi\) | ||||
−0.901418 | + | 0.432949i | \(0.857473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.88835e6 | −0.385706 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.41255e6 | 0.532681 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −750858. | −0.0733178 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.83471e7 | −1.77752 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.30190e6 | 0.894184 | 0.447092 | − | 0.894488i | \(-0.352460\pi\) | ||||
0.447092 | + | 0.894488i | \(0.352460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.38332e7 | −1.31946 | −0.659730 | − | 0.751503i | \(-0.729329\pi\) | ||||
−0.659730 | + | 0.751503i | \(0.729329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.26690e6 | 0.309198 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.48997e7 | 1.39932 | 0.699658 | − | 0.714478i | \(-0.253336\pi\) | ||||
0.699658 | + | 0.714478i | \(0.253336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.17958e7 | −2.03124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.28114e6 | −0.210959 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.93306e7 | 1.77403 | 0.887016 | − | 0.461738i | \(-0.152774\pi\) | ||||
0.887016 | + | 0.461738i | \(0.152774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.11520e6 | −0.556939 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.25706e7 | −2.03999 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.06110e6 | −0.364276 | −0.182138 | − | 0.983273i | \(-0.558302\pi\) | ||||
−0.182138 | + | 0.983273i | \(0.558302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.35152e7 | 1.20315 | 0.601575 | − | 0.798816i | \(-0.294540\pi\) | ||||
0.601575 | + | 0.798816i | \(0.294540\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −452088. | −0.0399429 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 605000. | 0.0530519 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.11415e7 | 0.969678 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.15312e7 | −0.996111 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.24090e6 | 0.363623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43520e7 | 1.22144 | 0.610722 | − | 0.791845i | \(-0.290879\pi\) | ||||
0.610722 | + | 0.791845i | \(0.290879\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.08750e6 | −0.260824 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.89530e6 | −0.158930 | −0.0794650 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794650 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.17640e6 | −0.264400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09205e7 | −0.902347 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.91641e6 | 0.239220 | 0.119610 | − | 0.992821i | \(-0.461836\pi\) | ||||
0.119610 | + | 0.992821i | \(0.461836\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.98755e6 | −0.487554 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.75275e7 | 2.22523 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 651636. | 0.0522946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.44278e7 | 1.14949 | 0.574743 | − | 0.818334i | \(-0.305102\pi\) | ||||
0.574743 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.31597e6 | −0.578680 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 771500. | 0.0605862 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 582876. | 0.0454458 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.31096e7 | 2.56307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.58679e7 | 1.21962 | 0.609811 | − | 0.792547i | \(-0.291246\pi\) | ||||
0.609811 | + | 0.792547i | \(0.291246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 156200. | 0.0119205 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.60797e7 | 1.21844 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.10768e6 | 0.233823 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 301810. | 0.0225485 | 0.0112743 | − | 0.999936i | \(-0.496411\pi\) | ||||
0.0112743 | + | 0.999936i | \(0.496411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.71641e7 | 1.27335 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.92017e6 | 0.583459 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −883200. | −0.0646091 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.63768e6 | −0.700123 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.12677e7 | −1.53426 | −0.767130 | − | 0.641492i | \(-0.778316\pi\) | ||||
−0.767130 | + | 0.641492i | \(0.778316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.07591e6 | −0.220361 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.45937e7 | 1.03830 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.50625e6 | 0.247741 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.55009e7 | −1.08773 | −0.543863 | − | 0.839174i | \(-0.683039\pi\) | ||||
−0.543863 | + | 0.839174i | \(0.683039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.11562e7 | −1.47441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.89983e6 | −0.131499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.21850e7 | 0.837653 | 0.418827 | − | 0.908066i | \(-0.362441\pi\) | ||||
0.418827 | + | 0.908066i | \(0.362441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.06100e7 | 0.724428 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.90019e7 | 1.28863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.90282e7 | −1.95528 | −0.977641 | − | 0.210282i | \(-0.932562\pi\) | ||||
−0.977641 | + | 0.210282i | \(0.932562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.31560e6 | −0.0880194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.61145e7 | −1.07089 | −0.535445 | − | 0.844570i | \(-0.679856\pi\) | ||||
−0.535445 | + | 0.844570i | \(0.679856\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.52375e6 | 0.166593 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.59047e7 | −1.69854 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.90120e6 | 0.123829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.92431e6 | 0.189201 | 0.0946005 | − | 0.995515i | \(-0.469843\pi\) | ||||
0.0946005 | + | 0.995515i | \(0.469843\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.50060e7 | −0.964442 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −311300. | −0.0198752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.60325e7 | −1.65111 | −0.825557 | − | 0.564319i | \(-0.809139\pi\) | ||||
−0.825557 | + | 0.564319i | \(0.809139\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.96564e7 | 2.49867 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63263e7 | 1.02194 | 0.510970 | − | 0.859598i | \(-0.329286\pi\) | ||||
0.510970 | + | 0.859598i | \(0.329286\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.80590e6 | −0.298857 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.09185e6 | 0.252794 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.30548e6 | 0.0801275 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.58132e7 | 1.57408 | 0.787040 | − | 0.616902i | \(-0.211612\pi\) | ||||
0.787040 | + | 0.616902i | \(0.211612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.69380e7 | 1.02619 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.90592e7 | 1.14725 | 0.573624 | − | 0.819119i | \(-0.305537\pi\) | ||||
0.573624 | + | 0.819119i | \(0.305537\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.49250e6 | 0.149067 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −81224.0 | −0.00482649 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.69620e6 | 0.100146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.25417e7 | 1.90903 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.77134e7 | −1.61542 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 150550. | 0.00871980 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.73411e7 | −0.998021 | −0.499011 | − | 0.866596i | \(-0.666303\pi\) | ||||
−0.499011 | + | 0.866596i | \(0.666303\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.38569e7 | 1.36434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −633732. | −0.0360134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −254012. | −0.0143440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.20790e6 | −0.516705 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.58169e7 | 1.43965 | 0.719827 | − | 0.694153i | \(-0.244221\pi\) | ||||
0.719827 | + | 0.694153i | \(0.244221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.35096e6 | −0.518190 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.49798e7 | 1.37565 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00328e7 | 2.19092 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.09230e6 | 0.0594090 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.91201e7 | −1.03349 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.88489e6 | 0.477288 | 0.238644 | − | 0.971107i | \(-0.423297\pi\) | ||||
0.238644 | + | 0.971107i | \(0.423297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.46396e7 | −1.31547 | −0.657735 | − | 0.753249i | \(-0.728485\pi\) | ||||
−0.657735 | + | 0.753249i | \(0.728485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.91540e7 | −1.54693 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.25216e7 | −0.660340 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.52860e6 | −0.289774 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 438196. | 0.0228275 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.13768e7 | −0.589062 | −0.294531 | − | 0.955642i | \(-0.595163\pi\) | ||||
−0.294531 | + | 0.955642i | \(0.595163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.30783e7 | 0.673057 | 0.336529 | − | 0.941673i | \(-0.390747\pi\) | ||||
0.336529 | + | 0.941673i | \(0.390747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.24800e7 | 0.638381 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.57188e7 | −1.81607 | −0.908037 | − | 0.418891i | \(-0.862419\pi\) | ||||
−0.908037 | + | 0.418891i | \(0.862419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.61880e7 | −0.818103 | −0.409052 | − | 0.912511i | \(-0.634140\pi\) | ||||
−0.409052 | + | 0.912511i | \(0.634140\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.31689e7 | −2.16854 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.17009e6 | −0.308091 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.38814e7 | −0.688999 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.97007e7 | −0.972005 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.55497e7 | 1.25309 | 0.626543 | − | 0.779387i | \(-0.284469\pi\) | ||||
0.626543 | + | 0.779387i | \(0.284469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09610e7 | 0.534390 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.77547e7 | −1.82979 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.22942e6 | −0.444665 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.43301e6 | 0.451795 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.03436e6 | −0.382545 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 282012. | 0.0133488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.22953e7 | 1.04916 | 0.524579 | − | 0.851362i | \(-0.324223\pi\) | ||||
0.524579 | + | 0.851362i | \(0.324223\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.19075e7 | 0.557064 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.96872e7 | 0.915656 | 0.457828 | − | 0.889041i | \(-0.348628\pi\) | ||||
0.457828 | + | 0.889041i | \(0.348628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.77582e6 | 0.313313 | 0.156657 | − | 0.987653i | \(-0.449928\pi\) | ||||
0.156657 | + | 0.987653i | \(0.449928\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −882024. | −0.0405483 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.63804e7 | 1.20574 | 0.602871 | − | 0.797839i | \(-0.294023\pi\) | ||||
0.602871 | + | 0.797839i | \(0.294023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.04338e7 | −0.474138 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.32013e7 | 1.50006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.04435e7 | −1.36756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.13813e6 | −0.0508332 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.25174e7 | −2.77629 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 343750. | 0.0151783 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.95161e7 | −1.29587 | −0.647934 | − | 0.761697i | \(-0.724367\pi\) | ||||
−0.647934 | + | 0.761697i | \(0.724367\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.14182e7 | −1.80808 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.48565e7 | −0.644877 | −0.322438 | − | 0.946590i | \(-0.604502\pi\) | ||||
−0.322438 | + | 0.946590i | \(0.604502\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.45340e7 | −0.627313 | −0.313656 | − | 0.949537i | \(-0.601554\pi\) | ||||
−0.313656 | + | 0.949537i | \(0.601554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.84470e7 | −0.791713 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.72028e7 | 0.734160 | 0.367080 | − | 0.930189i | \(-0.380358\pi\) | ||||
0.367080 | + | 0.930189i | \(0.380358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.76304e6 | 0.202130 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78337e7 | −0.752572 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.72118e7 | −1.14190 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.30950e6 | −0.0546447 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.37526e6 | −0.0985665 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.23727e7 | 0.923249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.35475e6 | 0.219749 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.87487e6 | 0.117327 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.36666e7 | −0.554674 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.44434e7 | −1.39023 | −0.695116 | − | 0.718897i | \(-0.744647\pi\) | ||||
−0.695116 | + | 0.718897i | \(0.744647\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.11647e7 | 2.45522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 983748. | 0.0392724 | 0.0196362 | − | 0.999807i | \(-0.493749\pi\) | ||||
0.0196362 | + | 0.999807i | \(0.493749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.59464e7 | 1.82421 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.58930e6 | 0.141728 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.38138e6 | −0.211334 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.08857e7 | −1.20634 | −0.603168 | − | 0.797614i | \(-0.706095\pi\) | ||||
−0.603168 | + | 0.797614i | \(0.706095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.24287e7 | −1.25974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.94911e6 | −0.0753065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 88750.0 | 0.00341047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.05395e7 | −2.31387 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.20874e7 | −1.21982 | −0.609909 | − | 0.792472i | \(-0.708794\pi\) | ||||
−0.609909 | + | 0.792472i | \(0.708794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.79553e7 | −0.678920 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.73157e7 | −0.651232 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.25760e6 | −0.271496 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.52520e7 | 0.567515 | 0.283757 | − | 0.958896i | \(-0.408419\pi\) | ||||
0.283757 | + | 0.958896i | \(0.408419\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.53734e7 | 0.568993 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.48166e6 | −0.128178 | −0.0640889 | − | 0.997944i | \(-0.520414\pi\) | ||||
−0.0640889 | + | 0.997944i | \(0.520414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.06241e6 | 0.112146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.71700e6 | −0.0989715 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.54010e7 | −0.920398 | −0.460199 | − | 0.887816i | \(-0.652222\pi\) | ||||
−0.460199 | + | 0.887816i | \(0.652222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.39780e6 | −0.0864265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.34249e7 | −0.481348 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.97352e7 | −1.77391 | −0.886955 | − | 0.461856i | \(-0.847184\pi\) | ||||
−0.886955 | + | 0.461856i | \(0.847184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.13007e7 | 0.400956 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.12020e8 | 3.95383 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.26904e6 | −0.185006 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.27250e7 | −0.444477 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.74190e7 | 1.30025 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.21398e7 | 0.419658 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.05173e7 | −1.04949 | −0.524747 | − | 0.851258i | \(-0.675840\pi\) | ||||
−0.524747 | + | 0.851258i | \(0.675840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.08108e7 | −0.369869 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.19854e7 | 1.08869 | 0.544344 | − | 0.838862i | \(-0.316779\pi\) | ||||
0.544344 | + | 0.838862i | \(0.316779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 678920. | 0.0229899 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −747500. | −0.0251825 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.90786e6 | 0.0974623 | 0.0487312 | − | 0.998812i | \(-0.484482\pi\) | ||||
0.0487312 | + | 0.998812i | \(0.484482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.43059e7 | −1.47742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.45888e7 | −3.13810 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.49621e7 | −1.15402 | −0.577010 | − | 0.816737i | \(-0.695781\pi\) | ||||
−0.577010 | + | 0.816737i | \(0.695781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.52544e7 | −0.829368 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.41501e7 | 0.462347 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.98164e6 | −0.324497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.00465e6 | −0.0971874 | −0.0485937 | − | 0.998819i | \(-0.515474\pi\) | ||||
−0.0485937 | + | 0.998819i | \(0.515474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.56900e7 | 2.75776 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.01910e7 | 0.646547 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.20789e7 | −1.02207 | −0.511035 | − | 0.859560i | \(-0.670738\pi\) | ||||
−0.511035 | + | 0.859560i | \(0.670738\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −701480. | −0.0222383 |
(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 | 320.6.a.a.1.1 | 1 | ||
4.3 | odd | 2 | 320.6.a.p.1.1 | 1 | |||
8.3 | odd | 2 | 10.6.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 80.6.a.h.1.1 | 1 | |||
24.5 | odd | 2 | 720.6.a.r.1.1 | 1 | |||
24.11 | even | 2 | 90.6.a.f.1.1 | 1 | |||
40.3 | even | 4 | 50.6.b.d.49.2 | 2 | |||
40.13 | odd | 4 | 400.6.c.a.49.2 | 2 | |||
40.19 | odd | 2 | 50.6.a.g.1.1 | 1 | |||
40.27 | even | 4 | 50.6.b.d.49.1 | 2 | |||
40.29 | even | 2 | 400.6.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 400.6.c.a.49.1 | 2 | |||
56.27 | even | 2 | 490.6.a.j.1.1 | 1 | |||
120.59 | even | 2 | 450.6.a.h.1.1 | 1 | |||
120.83 | odd | 4 | 450.6.c.o.199.1 | 2 | |||
120.107 | odd | 4 | 450.6.c.o.199.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
50.6.a.g.1.1 | 1 | 40.19 | odd | 2 | |||
50.6.b.d.49.1 | 2 | 40.27 | even | 4 | |||
50.6.b.d.49.2 | 2 | 40.3 | even | 4 | |||
80.6.a.h.1.1 | 1 | 8.5 | even | 2 | |||
90.6.a.f.1.1 | 1 | 24.11 | even | 2 | |||
320.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
320.6.a.p.1.1 | 1 | 4.3 | odd | 2 | |||
400.6.a.a.1.1 | 1 | 40.29 | even | 2 | |||
400.6.c.a.49.1 | 2 | 40.37 | odd | 4 | |||
400.6.c.a.49.2 | 2 | 40.13 | odd | 4 | |||
450.6.a.h.1.1 | 1 | 120.59 | even | 2 | |||
450.6.c.o.199.1 | 2 | 120.83 | odd | 4 | |||
450.6.c.o.199.2 | 2 | 120.107 | odd | 4 | |||
490.6.a.j.1.1 | 1 | 56.27 | even | 2 | |||
720.6.a.r.1.1 | 1 | 24.5 | odd | 2 |