Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(5\) | −16.0000 | −0.286217 | −0.143108 | − | 0.989707i | \(-0.545710\pi\) | ||||
−0.143108 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 433.000 | 1.78189 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.00000 | −0.0199346 | −0.00996732 | − | 0.999950i | \(-0.503173\pi\) | ||||
−0.00996732 | + | 0.999950i | \(0.503173\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −684.000 | −1.12253 | −0.561265 | − | 0.827636i | \(-0.689685\pi\) | ||||
−0.561265 | + | 0.827636i | \(0.689685\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 416.000 | 0.477381 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2218.00 | −1.86140 | −0.930699 | − | 0.365786i | \(-0.880800\pi\) | ||||
−0.930699 | + | 0.365786i | \(0.880800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2698.00 | 1.71458 | 0.857290 | − | 0.514833i | \(-0.172146\pi\) | ||||
0.857290 | + | 0.514833i | \(0.172146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1274.00 | 0.630407 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3344.00 | 1.31809 | 0.659047 | − | 0.752101i | \(-0.270960\pi\) | ||||
0.659047 | + | 0.752101i | \(0.270960\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2869.00 | −0.918080 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4940.00 | −1.30412 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3254.00 | 0.718493 | 0.359247 | − | 0.933243i | \(-0.383034\pi\) | ||||
0.359247 | + | 0.933243i | \(0.383034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4788.00 | 0.894849 | 0.447425 | − | 0.894322i | \(-0.352341\pi\) | ||||
0.447425 | + | 0.894322i | \(0.352341\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 208.000 | 0.0332490 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 784.000 | 0.108180 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11470.0 | 1.37740 | 0.688698 | − | 0.725048i | \(-0.258182\pi\) | ||||
0.688698 | + | 0.725048i | \(0.258182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17784.0 | 1.87227 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13350.0 | 1.24029 | 0.620143 | − | 0.784489i | \(-0.287075\pi\) | ||||
0.620143 | + | 0.784489i | \(0.287075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 928.000 | 0.0765380 | 0.0382690 | − | 0.999267i | \(-0.487816\pi\) | ||||
0.0382690 | + | 0.999267i | \(0.487816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6928.00 | −0.510008 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1212.00 | 0.0800310 | 0.0400155 | − | 0.999199i | \(-0.487259\pi\) | ||||
0.0400155 | + | 0.999199i | \(0.487259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 57668.0 | 3.10463 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13110.0 | −0.641081 | −0.320541 | − | 0.947235i | \(-0.603865\pi\) | ||||
−0.320541 | + | 0.947235i | \(0.603865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 128.000 | 0.00570563 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −70148.0 | −2.85975 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34702.0 | −1.29785 | −0.648925 | − | 0.760852i | \(-0.724781\pi\) | ||||
−0.648925 | + | 0.760852i | \(0.724781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1032.00 | 0.0355104 | 0.0177552 | − | 0.999842i | \(-0.494348\pi\) | ||||
0.0177552 | + | 0.999842i | \(0.494348\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21217.0 | −0.673492 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10944.0 | 0.321287 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10108.0 | −0.275092 | −0.137546 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137546 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −86944.0 | −2.19845 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62720.0 | 1.47659 | 0.738295 | − | 0.674477i | \(-0.235631\pi\) | ||||
0.738295 | + | 0.674477i | \(0.235631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18926.0 | −0.415673 | −0.207836 | − | 0.978164i | \(-0.566642\pi\) | ||||
−0.207836 | + | 0.978164i | \(0.566642\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 74594.0 | 1.53127 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 392.000 | 0.00753458 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11400.0 | 0.205512 | 0.102756 | − | 0.994707i | \(-0.467234\pi\) | ||||
0.102756 | + | 0.994707i | \(0.467234\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23221.0 | 0.393250 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −88958.0 | −1.41739 | −0.708696 | − | 0.705514i | \(-0.750716\pi\) | ||||
−0.708696 | + | 0.705514i | \(0.750716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35488.0 | 0.532763 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −84604.0 | −1.19838 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19722.0 | 0.263922 | 0.131961 | − | 0.991255i | \(-0.457873\pi\) | ||||
0.131961 | + | 0.991255i | \(0.457873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 33516.0 | 0.424276 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −124488. | −1.49252 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −43168.0 | −0.490742 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17062.0 | 0.184120 | 0.0920599 | − | 0.995753i | \(-0.470655\pi\) | ||||
0.0920599 | + | 0.995753i | \(0.470655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3464.00 | −0.0355214 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −45904.0 | −0.447762 | −0.223881 | − | 0.974617i | \(-0.571873\pi\) | ||||
−0.223881 | + | 0.974617i | \(0.571873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −136012. | −1.26324 | −0.631618 | − | 0.775280i | \(-0.717609\pi\) | ||||
−0.631618 | + | 0.775280i | \(0.717609\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20384.0 | −0.180433 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 69156.0 | 0.583943 | 0.291971 | − | 0.956427i | \(-0.405689\pi\) | ||||
0.291971 | + | 0.956427i | \(0.405689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 146414. | 1.18037 | 0.590183 | − | 0.807270i | \(-0.299056\pi\) | ||||
0.590183 | + | 0.807270i | \(0.299056\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −298220. | −2.29736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −80186.0 | −0.590748 | −0.295374 | − | 0.955382i | \(-0.595444\pi\) | ||||
−0.295374 | + | 0.955382i | \(0.595444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −53504.0 | −0.377261 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −296172. | −2.00023 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 108682. | 0.703542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −160987. | −0.999603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −347100. | −2.06867 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 95904.0 | 0.548987 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 274800. | 1.51185 | 0.755923 | − | 0.654661i | \(-0.227189\pi\) | ||||
0.755923 | + | 0.654661i | \(0.227189\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24128.0 | −0.127658 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −180742. | −0.920197 | −0.460099 | − | 0.887868i | \(-0.652186\pi\) | ||||
−0.460099 | + | 0.887868i | \(0.652186\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −132202. | −0.648051 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 79040.0 | 0.373261 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −209678. | −0.954446 | −0.477223 | − | 0.878782i | \(-0.658357\pi\) | ||||
−0.477223 | + | 0.878782i | \(0.658357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17242.0 | −0.0756921 | −0.0378461 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378461 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31512.0 | −0.133484 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5472.00 | 0.0223772 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −52064.0 | −0.205645 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −62426.0 | −0.238272 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −59358.0 | −0.219035 | −0.109518 | − | 0.993985i | \(-0.534931\pi\) | ||||
−0.109518 | + | 0.993985i | \(0.534931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −336344. | −1.20044 | −0.600221 | − | 0.799834i | \(-0.704921\pi\) | ||||
−0.600221 | + | 0.799834i | \(0.704921\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −960394. | −3.31681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −76608.0 | −0.256121 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −464588. | −1.50425 | −0.752123 | − | 0.659023i | \(-0.770970\pi\) | ||||
−0.752123 | + | 0.659023i | \(0.770970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 340860. | 1.06926 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −163856. | −0.498193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −314792. | −0.928014 | −0.464007 | − | 0.885831i | \(-0.653589\pi\) | ||||
−0.464007 | + | 0.885831i | \(0.653589\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3328.00 | −0.00951642 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 285724. | 0.792785 | 0.396393 | − | 0.918081i | \(-0.370262\pi\) | ||||
0.396393 | + | 0.918081i | \(0.370262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 96563.0 | 0.260072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.16823e6 | 3.05520 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 709148. | 1.80145 | 0.900724 | − | 0.434392i | \(-0.143037\pi\) | ||||
0.900724 | + | 0.434392i | \(0.143037\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 140581. | 0.347002 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 902252. | 2.16468 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 617148. | 1.43965 | 0.719825 | − | 0.694156i | \(-0.244222\pi\) | ||||
0.719825 | + | 0.694156i | \(0.244222\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −237828. | −0.539593 | −0.269797 | − | 0.962917i | \(-0.586956\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26832.0 | −0.0592278 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −183520. | −0.394234 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17744.0 | 0.0371063 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 242060. | 0.492911 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −133512. | −0.264812 | −0.132406 | − | 0.991196i | \(-0.542270\pi\) | ||||
−0.132406 | + | 0.991196i | \(0.542270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 270446. | 0.522622 | 0.261311 | − | 0.965255i | \(-0.415845\pi\) | ||||
0.261311 | + | 0.965255i | \(0.415845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −284544. | −0.535874 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −875102. | −1.60655 | −0.803273 | − | 0.595611i | \(-0.796910\pi\) | ||||
−0.803273 | + | 0.595611i | \(0.796910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −347620. | −0.622260 | −0.311130 | − | 0.950367i | \(-0.600708\pi\) | ||||
−0.311130 | + | 0.950367i | \(0.600708\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 262808. | 0.458826 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −159446. | −0.271565 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −213600. | −0.354990 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.44795e6 | 2.34870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21584.0 | −0.0341795 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 425380. | 0.657765 | 0.328883 | − | 0.944371i | \(-0.393328\pi\) | ||||
0.328883 | + | 0.944371i | \(0.393328\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.63072e6 | −2.46281 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14848.0 | −0.0219064 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −234612. | −0.338221 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 492076. | 0.693301 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.51711e6 | 2.08947 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 481592. | 0.648511 | 0.324255 | − | 0.945970i | \(-0.394886\pi\) | ||||
0.324255 | + | 0.945970i | \(0.394886\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.24228e6 | −1.63592 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6042.00 | 0.00778245 | 0.00389122 | − | 0.999992i | \(-0.498761\pi\) | ||||
0.00389122 | + | 0.999992i | \(0.498761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1804.00 | −0.00227325 | −0.00113663 | − | 0.999999i | \(-0.500362\pi\) | ||||
−0.00113663 | + | 0.999999i | \(0.500362\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10192.0 | −0.0125669 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.61153e6 | −1.94468 | −0.972339 | − | 0.233576i | \(-0.924957\pi\) | ||||
−0.972339 | + | 0.233576i | \(0.924957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19392.0 | −0.0229062 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −296400. | −0.342774 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −987096. | −1.11780 | −0.558901 | − | 0.829235i | \(-0.688777\pi\) | ||||
−0.558901 | + | 0.829235i | \(0.688777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 893510. | 0.990962 | 0.495481 | − | 0.868619i | \(-0.334992\pi\) | ||||
0.495481 | + | 0.868619i | \(0.334992\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 596674. | 0.648219 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −38416.0 | −0.0408881 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.84543e6 | −1.92467 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.31291e6 | 2.36407 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −365946. | −0.366634 | −0.183317 | − | 0.983054i | \(-0.558683\pi\) | ||||
−0.183317 | + | 0.983054i | \(0.558683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26752.0 | −0.0262757 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −922688. | −0.888596 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.40459e6 | 1.32653 | 0.663266 | − | 0.748383i | \(-0.269170\pi\) | ||||
0.663266 | + | 0.748383i | \(0.269170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −562030. | −0.520607 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.40898e6 | 1.28028 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.09968e6 | 0.980341 | 0.490170 | − | 0.871627i | \(-0.336935\pi\) | ||||
0.490170 | + | 0.871627i | \(0.336935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 209760. | 0.183488 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −512772. | −0.440196 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −814948. | −0.686672 | −0.343336 | − | 0.939213i | \(-0.611557\pi\) | ||||
−0.343336 | + | 0.939213i | \(0.611557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.69906e6 | −1.40535 | −0.702675 | − | 0.711511i | \(-0.748011\pi\) | ||||
−0.702675 | + | 0.711511i | \(0.748011\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −871416. | −0.707651 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22952.0 | 0.0183016 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.36508e6 | 1.06895 | 0.534477 | − | 0.845183i | \(-0.320508\pi\) | ||||
0.534477 | + | 0.845183i | \(0.320508\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.07320e6 | 1.59453 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −715846. | −0.540821 | −0.270411 | − | 0.962745i | \(-0.587159\pi\) | ||||
−0.270411 | + | 0.962745i | \(0.587159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −217726. | −0.161601 | −0.0808005 | − | 0.996730i | \(-0.525748\pi\) | ||||
−0.0808005 | + | 0.996730i | \(0.525748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.12237e6 | 0.818508 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −654150. | −0.468784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.49967e6 | 2.46480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −443612. | −0.307094 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.50708e6 | −1.02557 | −0.512787 | − | 0.858516i | \(-0.671387\pi\) | ||||
−0.512787 | + | 0.858516i | \(0.671387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 555232. | 0.371466 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 39520.0 | 0.0259972 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.28730e6 | −1.47960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45472.0 | −0.0289286 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.19350e6 | 0.746822 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16512.0 | −0.0101637 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12502.0 | −0.00757066 | −0.00378533 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378533 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.53631e6 | 2.10695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −647432. | −0.379571 | −0.189786 | − | 0.981826i | \(-0.560779\pi\) | ||||
−0.189786 | + | 0.981826i | \(0.560779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −935978. | −0.540014 | −0.270007 | − | 0.962858i | \(-0.587026\pi\) | ||||
−0.270007 | + | 0.962858i | \(0.587026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 339472. | 0.192765 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −705942. | −0.394567 | −0.197284 | − | 0.980346i | \(-0.563212\pi\) | ||||
−0.197284 | + | 0.980346i | \(0.563212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26032.0 | −0.0143229 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.79806e6 | −0.973959 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.98416e6 | −3.19152 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.96240e6 | 1.03057 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.80676e6 | −1.96873 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −59388.0 | −0.0302489 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.14304e6 | 0.573445 | 0.286722 | − | 0.958014i | \(-0.407434\pi\) | ||||
0.286722 | + | 0.958014i | \(0.407434\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.96651e6 | 2.45437 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 161728. | 0.0787360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.36402e6 | −1.13390 | −0.566952 | − | 0.823751i | \(-0.691877\pi\) | ||||
−0.566952 | + | 0.823751i | \(0.691877\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.08484e6 | 0.985309 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −38304.0 | −0.0178385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.39110e6 | 0.629234 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −726240. | −0.323785 | −0.161892 | − | 0.986808i | \(-0.551760\pi\) | ||||
−0.161892 | + | 0.986808i | \(0.551760\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −136180. | −0.0598480 | −0.0299240 | − | 0.999552i | \(-0.509527\pi\) | ||||
−0.0299240 | + | 0.999552i | \(0.509527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.37896e6 | 1.46391 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.16907e6 | −0.499349 | −0.249674 | − | 0.968330i | \(-0.580324\pi\) | ||||
−0.249674 | + | 0.968330i | \(0.580324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.00352e6 | −0.422625 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.82573e6 | −1.17344 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4280.00 | −0.00175270 | −0.000876350 | − | 1.00000i | \(-0.500279\pi\) | ||||
−0.000876350 | 1.00000i | \(0.500279\pi\) | ||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.80310e6 | 1.93979 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.18566e6 | 1.66724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 302816. | 0.118973 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.44796e6 | 0.948722 | 0.474361 | − | 0.880330i | \(-0.342679\pi\) | ||||
0.474361 | + | 0.880330i | \(0.342679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.78055e6 | 2.21006 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 642390. | 0.242306 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 904514. | 0.336623 | 0.168311 | − | 0.985734i | \(-0.446169\pi\) | ||||
0.168311 | + | 0.985734i | \(0.446169\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.49350e6 | −0.915655 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.22574e6 | −0.806530 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.23034e6 | 1.51279 | 0.756393 | − | 0.654117i | \(-0.226960\pi\) | ||||
0.756393 | + | 0.654117i | \(0.226960\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.14480e6 | −2.52161 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.55400e6 | 1.58634 | 0.793169 | − | 0.609002i | \(-0.208430\pi\) | ||||
0.793169 | + | 0.609002i | \(0.208430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6272.00 | −0.00215652 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 401824. | 0.136382 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.98541e6 | 1.33536 | 0.667680 | − | 0.744448i | \(-0.267287\pi\) | ||||
0.667680 | + | 0.744448i | \(0.267287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.41699e6 | −2.45350 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.69929e6 | 1.53480 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −182400. | −0.0588210 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −552420. | −0.175911 | −0.0879555 | − | 0.996124i | \(-0.528033\pi\) | ||||
−0.0879555 | + | 0.996124i | \(0.528033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.43725e6 | 1.08088 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38190.0 | 0.0118601 | 0.00593006 | − | 0.999982i | \(-0.498112\pi\) | ||||
0.00593006 | + | 0.999982i | \(0.498112\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.27499e6 | −1.00449 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −371536. | −0.112555 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −91760.0 | −0.0274579 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.92475e6 | −1.16012 | −0.580062 | − | 0.814573i | \(-0.696972\pi\) | ||||
−0.580062 | + | 0.814573i | \(0.696972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.45163e6 | 1.59192 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.70040e6 | 0.490541 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.42333e6 | 0.405681 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 448292. | 0.126247 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −598386. | −0.166512 | −0.0832562 | − | 0.996528i | \(-0.526532\pi\) | ||||
−0.0832562 | + | 0.996528i | \(0.526532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.61597e6 | −1.26928 | −0.634641 | − | 0.772807i | \(-0.718852\pi\) | ||||
−0.634641 | + | 0.772807i | \(0.718852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 524796. | 0.142607 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.36344e6 | 1.70891 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −50568.0 | −0.0134217 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −142272. | −0.0373230 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −61560.0 | −0.0159627 | −0.00798133 | − | 0.999968i | \(-0.502541\pi\) | ||||
−0.00798133 | + | 0.999968i | \(0.502541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.79727e6 | −0.973310 | −0.486655 | − | 0.873594i | \(-0.661783\pi\) | ||||
−0.486655 | + | 0.873594i | \(0.661783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.35366e6 | 0.342995 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.02211e6 | 2.25998 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.28852e6 | −0.566752 | −0.283376 | − | 0.959009i | \(-0.591455\pi\) | ||||
−0.283376 | + | 0.959009i | \(0.591455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.03963e6 | 0.254556 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.75976e6 | 1.15233 | 0.576163 | − | 0.817335i | \(-0.304549\pi\) | ||||
0.576163 | + | 0.817335i | \(0.304549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −315552. | −0.0755389 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.54331e6 | 0.365329 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.36715e6 | −1.02231 | −0.511155 | − | 0.859489i | \(-0.670782\pi\) | ||||
−0.511155 | + | 0.859489i | \(0.670782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −106800. | −0.0247246 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.74494e6 | 2.00222 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −536256. | −0.121435 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.44994e6 | 1.22068 | 0.610339 | − | 0.792140i | \(-0.291033\pi\) | ||||
0.610339 | + | 0.792140i | \(0.291033\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.09569e7 | 2.42749 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.66966e6 | −0.365911 | −0.182956 | − | 0.983121i | \(-0.558566\pi\) | ||||
−0.182956 | + | 0.983121i | \(0.558566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 70768.0 | 0.0153421 | 0.00767104 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767104 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.99181e6 | 0.427184 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.66083e6 | −1.20112 | −0.600562 | − | 0.799578i | \(-0.705056\pi\) | ||||
−0.600562 | + | 0.799578i | \(0.705056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 495292. | 0.103975 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.20793e7 | 2.50893 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7424.00 | −0.00152576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.74056e6 | −1.57412 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.67663e6 | −1.14234 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.44948e6 | −0.288652 | −0.144326 | − | 0.989530i | \(-0.546101\pi\) | ||||
−0.144326 | + | 0.989530i | \(0.546101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.84548e6 | −1.54617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.26026e6 | 0.830937 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −272992. | −0.0526982 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.07504e6 | 0.778591 | 0.389296 | − | 0.921113i | \(-0.372718\pi\) | ||||
0.389296 | + | 0.921113i | \(0.372718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.18459e6 | 1.54784 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −986100. | −0.184594 | −0.0922969 | − | 0.995732i | \(-0.529421\pi\) | ||||
−0.0922969 | + | 0.995732i | \(0.529421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.21737e6 | −1.33740 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 55424.0 | 0.0101668 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.07328e6 | −0.558099 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.98342e6 | −1.07572 | −0.537859 | − | 0.843035i | \(-0.680767\pi\) | ||||
−0.537859 | + | 0.843035i | \(0.680767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.42882e6 | −1.32229 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.49373e6 | −0.615700 | −0.307850 | − | 0.951435i | \(-0.599609\pi\) | ||||
−0.307850 | + | 0.951435i | \(0.599609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 734464. | 0.128157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.51064e6 | −0.433775 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.15711e6 | −0.369043 | −0.184522 | − | 0.982828i | \(-0.559074\pi\) | ||||
−0.184522 | + | 0.982828i | \(0.559074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 927374. | 0.157110 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.33281e7 | −2.23602 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.17619e6 | 0.361559 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9696.00 | −0.00159539 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.84378e7 | −3.00464 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.65817e6 | −1.07463 | −0.537317 | − | 0.843380i | \(-0.680562\pi\) | ||||
−0.537317 | + | 0.843380i | \(0.680562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.95223e6 | −0.951537 | −0.475768 | − | 0.879571i | \(-0.657830\pi\) | ||||
−0.475768 | + | 0.879571i | \(0.657830\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.65511e6 | −0.578764 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.06198e7 | −1.66567 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.74599e6 | 0.737374 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.50260e7 | −2.31263 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.13140e6 | −1.39226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.10650e6 | −0.167134 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.60458e7 | −2.40119 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19208.0 | −0.00284780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.39681e6 | 0.939659 | 0.469830 | − | 0.882757i | \(-0.344315\pi\) | ||||
0.469830 | + | 0.882757i | \(0.344315\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.18353e6 | 0.899988 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.34262e6 | −0.337840 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.51851e6 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 446856. | 0.0632757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.77929e6 | 1.23191 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −558600. | −0.0776762 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.77152e6 | 0.657543 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.02159e6 | −0.276093 | −0.138046 | − | 0.990426i | \(-0.544082\pi\) | ||||
−0.138046 | + | 0.990426i | \(0.544082\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −634752. | −0.0859161 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −461344. | −0.0618896 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.14678e6 | −1.08322 | −0.541608 | − | 0.840631i | \(-0.682184\pi\) | ||||
−0.541608 | + | 0.840631i | \(0.682184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.28298e6 | 0.169082 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.13783e6 | −0.148634 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.19824e7 | −1.55154 | −0.775772 | − | 0.631013i | \(-0.782639\pi\) | ||||
−0.775772 | + | 0.631013i | \(0.782639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.39582e6 | −0.179159 | −0.0895793 | − | 0.995980i | \(-0.528552\pi\) | ||||
−0.0895793 | + | 0.995980i | \(0.528552\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.47131e6 | 0.441679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.59394e6 | −1.21012 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.96784e6 | 0.246065 | 0.123033 | − | 0.992403i | \(-0.460738\pi\) | ||||
0.123033 | + | 0.992403i | \(0.460738\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.03160e6 | −0.871681 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.35894e6 | 0.535724 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 104880. | 0.0127797 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.73875e6 | 0.572498 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.18897e6 | 0.381993 | 0.190997 | − | 0.981591i | \(-0.438828\pi\) | ||||
0.190997 | + | 0.981591i | \(0.438828\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29180e7 | 1.53429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.27527e7 | 2.67956 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.67500e6 | 0.195604 | 0.0978022 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0978022 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.73891e6 | −0.201366 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.03812e6 | 1.03787 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.00635e7 | −1.14599 | −0.572994 | − | 0.819559i | \(-0.694218\pi\) | ||||
−0.572994 | + | 0.819559i | \(0.694218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.72798e6 | 0.195143 | 0.0975713 | − | 0.995229i | \(-0.468893\pi\) | ||||
0.0975713 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.37676e6 | −0.490185 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.57579e6 | 0.286103 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.69523e7 | −1.86748 | −0.933740 | − | 0.357953i | \(-0.883475\pi\) | ||||
−0.933740 | + | 0.357953i | \(0.883475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.14560e6 | 0.452943 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −829008. | −0.0898371 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.01942e7 | −1.09572 | −0.547861 | − | 0.836569i | \(-0.684558\pi\) | ||||
−0.547861 | + | 0.836569i | \(0.684558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.55360e6 | 0.592089 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.57452e7 | 1.66508 | 0.832540 | − | 0.553965i | \(-0.186886\pi\) | ||||
0.832540 | + | 0.553965i | \(0.186886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 332690. | 0.0348990 | 0.0174495 | − | 0.999848i | \(-0.494445\pi\) | ||||
0.0174495 | + | 0.999848i | \(0.494445\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.65194e7 | −1.71895 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −966378. | −0.0997532 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.43116e6 | 0.760951 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 561184. | 0.0570081 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.54405e7 | −2.56388 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.59720e6 | 0.359659 | 0.179830 | − | 0.983698i | \(-0.442445\pi\) | ||||
0.179830 | + | 0.983698i | \(0.442445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.10599e7 | −1.09709 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.39680e6 | −0.432715 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.64228e6 | −0.160361 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.71578e7 | 2.63113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.46389e7 | −1.40723 | −0.703614 | − | 0.710583i | \(-0.748431\pi\) | ||||
−0.703614 | + | 0.710583i | \(0.748431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.38386e7 | 1.31997 | 0.659987 | − | 0.751277i | \(-0.270562\pi\) | ||||
0.659987 | + | 0.751277i | \(0.270562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 386048. | 0.0365378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.40358e7 | −1.31819 | −0.659093 | − | 0.752061i | \(-0.729060\pi\) | ||||
−0.659093 | + | 0.752061i | \(0.729060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 277616. | 0.0258722 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.09991e6 | 0.564119 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.61063e7 | −1.47813 | −0.739064 | − | 0.673635i | \(-0.764732\pi\) | ||||
−0.739064 | + | 0.673635i | \(0.764732\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.89187e6 | 0.263376 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.19496e6 | −0.740685 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.80075e6 | −0.430622 | −0.215311 | − | 0.976546i | \(-0.569076\pi\) | ||||
−0.215311 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.76565e7 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.94449e7 | −3.48504 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.11523e6 | 0.185483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.08814e7 | 0.947042 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.25214e7 | −1.08165 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8256.00 | −0.000707886 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.59225e6 | 0.561043 | 0.280521 | − | 0.959848i | \(-0.409493\pi\) | ||||
0.280521 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.41729e7 | 1.19729 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.77178e6 | −0.819411 | −0.409706 | − | 0.912218i | \(-0.634369\pi\) | ||||
−0.409706 | + | 0.912218i | \(0.634369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −836038. | −0.0695908 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −157092. | −0.0129803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.88663e7 | 1.54752 | 0.773758 | − | 0.633481i | \(-0.218374\pi\) | ||||
0.773758 | + | 0.633481i | \(0.218374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.35485e6 | 0.273178 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46904.0 | 0.00379156 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.96724e6 | 0.719632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.67018e6 | −0.690769 | −0.345385 | − | 0.938461i | \(-0.612252\pi\) | ||||
−0.345385 | + | 0.938461i | \(0.612252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 169736. | 0.0134258 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 275872. | 0.0216643 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.96103e7 | −2.30866 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.18997e7 | 3.24353 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.93482e6 | −0.609877 | −0.304938 | − | 0.952372i | \(-0.598636\pi\) | ||||
−0.304938 | + | 0.952372i | \(0.598636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.09461e7 | 2.36166 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 504192. | 0.0382053 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.24930e6 | 0.169238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.62600e7 | −1.96191 | −0.980956 | − | 0.194228i | \(-0.937780\pi\) | ||||
−0.980956 | + | 0.194228i | \(0.937780\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.93620e6 | 0.366200 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.60111e7 | 1.17950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −87552.0 | −0.00640473 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.56645e7 | 1.86438 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.20763e7 | 1.59259 | 0.796295 | − | 0.604909i | \(-0.206790\pi\) | ||||
0.796295 | + | 0.604909i | \(0.206790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.66459e6 | 0.477458 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.32313e7 | −1.65283 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.33573e6 | −0.659634 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.49245e6 | 0.595933 | 0.297966 | − | 0.954576i | \(-0.403692\pi\) | ||||
0.297966 | + | 0.954576i | \(0.403692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.11562e7 | −1.47441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.05830e6 | −0.142468 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.90713e7 | 1.31105 | 0.655526 | − | 0.755172i | \(-0.272447\pi\) | ||||
0.655526 | + | 0.755172i | \(0.272447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 998816. | 0.0681973 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 80864.0 | 0.00548386 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.46832e7 | 0.989032 | 0.494516 | − | 0.869169i | \(-0.335345\pi\) | ||||
0.494516 | + | 0.869169i | \(0.335345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.79812e7 | 3.21015 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.64265e7 | 1.09162 | 0.545812 | − | 0.837908i | \(-0.316221\pi\) | ||||
0.545812 | + | 0.837908i | \(0.316221\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 949728. | 0.0626915 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.85188e7 | −2.52564 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.38864e6 | −0.220710 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.44357e7 | −1.58097 | −0.790486 | − | 0.612479i | \(-0.790172\pi\) | ||||
−0.790486 | + | 0.612479i | \(0.790172\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.51460e6 | 0.611509 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.38150e6 | 0.343587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 295566. | 0.0187463 | 0.00937313 | − | 0.999956i | \(-0.497016\pi\) | ||||
0.00937313 | + | 0.999956i | \(0.497016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 695552. | 0.0438253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −473842. | −0.0296601 | −0.0148300 | − | 0.999890i | \(-0.504721\pi\) | ||||
−0.0148300 | + | 0.999890i | \(0.504721\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.17429e6 | −0.446136 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.53663e7 | 0.949327 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.37362e7 | 1.45687 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.33241e7 | 1.42229 | 0.711145 | − | 0.703045i | \(-0.248177\pi\) | ||||
0.711145 | + | 0.703045i | \(0.248177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.65194e7 | −2.21253 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.55583e7 | −0.936511 | −0.468255 | − | 0.883593i | \(-0.655117\pi\) | ||||
−0.468255 | + | 0.883593i | \(0.655117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.37368e7 | −0.821543 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.46128e7 | 0.868321 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.60183e7 | 2.12657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −501760. | −0.0294353 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.60748e7 | −0.937001 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.43341e6 | 0.430540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.66843e6 | −0.383784 | −0.191892 | − | 0.981416i | \(-0.561462\pi\) | ||||
−0.191892 | + | 0.981416i | \(0.561462\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.85917e7 | −1.63511 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.92911e6 | 0.223282 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −705888. | −0.0398614 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.45376e6 | −0.306040 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.22461e7 | 0.682892 | 0.341446 | − | 0.939901i | \(-0.389083\pi\) | ||||
0.341446 | + | 0.939901i | \(0.389083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.68822e6 | −0.148969 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.53963e6 | 0.470281 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 151408. | 0.00828629 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.62170e6 | 0.142591 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.11886e7 | 1.14530 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.91495e7 | −1.56588 | −0.782941 | − | 0.622095i | \(-0.786282\pi\) | ||||
−0.782941 | + | 0.622095i | \(0.786282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.58849e6 | −0.405138 | −0.202569 | − | 0.979268i | \(-0.564929\pi\) | ||||
−0.202569 | + | 0.979268i | \(0.564929\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.41755e7 | 2.34398 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.03667e6 | 0.265613 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.50374e6 | 0.131230 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.45124e7 | 0.756015 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.98849e6 | 0.310070 | 0.155035 | − | 0.987909i | \(-0.450451\pi\) | ||||
0.155035 | + | 0.987909i | \(0.450451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 817960. | 0.0420952 | 0.0210476 | − | 0.999778i | \(-0.493300\pi\) | ||||
0.0210476 | + | 0.999778i | \(0.493300\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −596752. | −0.0305252 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.51963e6 | −0.128107 | −0.0640535 | − | 0.997946i | \(-0.520403\pi\) | ||||
−0.0640535 | + | 0.997946i | \(0.520403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.61006e7 | 0.813684 | 0.406842 | − | 0.913499i | \(-0.366630\pi\) | ||||
0.406842 | + | 0.913499i | \(0.366630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.54921e7 | −1.78291 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.32542e6 | −0.265914 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.57158e6 | −0.226908 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.36527e7 | −1.16699 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.58167e7 | −1.26618 | −0.633091 | − | 0.774077i | \(-0.718214\pi\) | ||||
−0.633091 | + | 0.774077i | \(0.718214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.92263e6 | −0.483768 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.86120e7 | 0.902036 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.54501e6 | −0.0744370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.88836e6 | 0.377814 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.66088e6 | 0.269535 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.83557e7 | 1.81554 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.54270e7 | 0.725954 | 0.362977 | − | 0.931798i | \(-0.381760\pi\) | ||||
0.362977 | + | 0.931798i | \(0.381760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.86917e7 | −0.874449 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.60517e6 | 0.167677 | 0.0838384 | − | 0.996479i | \(-0.473282\pi\) | ||||
0.0838384 | + | 0.996479i | \(0.473282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.06995e6 | −0.188194 | −0.0940970 | − | 0.995563i | \(-0.529996\pi\) | ||||
−0.0940970 | + | 0.995563i | \(0.529996\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.70079e7 | 0.781885 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.25111e6 | 0.331419 | 0.165710 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165710 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.13464e7 | −0.515604 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.09913e7 | −4.11105 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −91200.0 | −0.00409681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.91387e6 | 0.308799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.38785e6 | 0.328082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.69930e6 | −0.207497 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.37414e6 | −0.104233 | −0.0521167 | − | 0.998641i | \(-0.516597\pi\) | ||||
−0.0521167 | + | 0.998641i | \(0.516597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.91841e7 | 1.71056 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.03558e7 | 1.31766 | 0.658828 | − | 0.752293i | \(-0.271052\pi\) | ||||
0.658828 | + | 0.752293i | \(0.271052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.53338e6 | −0.0661832 | −0.0330916 | − | 0.999452i | \(-0.510535\pi\) | ||||
−0.0330916 | + | 0.999452i | \(0.510535\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.44360e7 | −0.619569 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.92379e7 | −1.24778 | −0.623888 | − | 0.781514i | \(-0.714448\pi\) | ||||
−0.623888 | + | 0.781514i | \(0.714448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.34652e7 | −0.571424 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −185768. | −0.00783929 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.26998e6 | 0.137220 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.87437e6 | −0.412052 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.94697e7 | 2.46783 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.55802e7 | 0.642943 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.90780e7 | 1.19331 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.18227e6 | 0.0482501 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.80525e6 | 0.154441 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.48227e7 | −1.80917 | −0.904587 | − | 0.426289i | \(-0.859821\pi\) | ||||
−0.904587 | + | 0.426289i | \(0.859821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.98764e7 | −0.797864 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.62906e7 | −1.44877 | −0.724384 | − | 0.689397i | \(-0.757876\pi\) | ||||
−0.724384 | + | 0.689397i | \(0.757876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 711664. | 0.0282552 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 429312. | 0.0169520 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.85636e6 | 0.347802 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.25350e7 | 1.27076 | 0.635378 | − | 0.772201i | \(-0.280844\pi\) | ||||
0.635378 | + | 0.772201i | \(0.280844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 325052. | 0.0126271 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.29005e7 | −1.65752 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.29074e7 | −1.26456 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.88932e7 | −2.25095 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.46676e7 | −1.69806 | −0.849030 | − | 0.528344i | \(-0.822813\pi\) | ||||
−0.849030 | + | 0.528344i | \(0.822813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.47790e6 | 0.244940 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.68332e7 | 0.633087 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −283904. | −0.0106204 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.56680e7 | 0.582995 | 0.291498 | − | 0.956572i | \(-0.405846\pi\) | ||||
0.291498 | + | 0.956572i | \(0.405846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.43354e7 | 0.900689 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.01175e7 | 0.740627 | 0.370313 | − | 0.928907i | \(-0.379250\pi\) | ||||
0.370313 | + | 0.928907i | \(0.379250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.46424e7 | 1.63481 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.87296e6 | −0.141079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.84518e6 | 0.320503 | 0.160251 | − | 0.987076i | \(-0.448769\pi\) | ||||
0.160251 | + | 0.987076i | \(0.448769\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.29454e7 | 0.466605 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.83545e7 | 0.658099 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.14364e7 | −1.12124 | −0.560622 | − | 0.828072i | \(-0.689438\pi\) | ||||
−0.560622 | + | 0.828072i | \(0.689438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.13619e6 | 0.0757935 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 676832. | 0.0238892 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.02742e7 | 0.360747 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.70421e6 | −0.199245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.99445e7 | 1.04052 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.32714e6 | −0.149583 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.52158e6 | −0.327449 | −0.163724 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163724 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.55588e8 | 5.32313 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.06520e7 | −0.362564 | −0.181282 | − | 0.983431i | \(-0.558025\pi\) | ||||
−0.181282 | + | 0.983431i | \(0.558025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 844858. | 0.0286089 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.10223e7 | −1.71889 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.72931e7 | 0.914779 | 0.457389 | − | 0.889266i | \(-0.348785\pi\) | ||||
0.457389 | + | 0.889266i | \(0.348785\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −157776. | −0.00526119 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.33973e7 | 2.10328 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.04764e7 | 0.345802 | 0.172901 | − | 0.984939i | \(-0.444686\pi\) | ||||
0.172901 | + | 0.984939i | \(0.444686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.40016e7 | 0.459820 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.54409e6 | 0.0504521 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.10323e6 | 0.100884 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.88230e6 | 0.0608843 | 0.0304422 | − | 0.999537i | \(-0.490308\pi\) | ||||
0.0304422 | + | 0.999537i | \(0.490308\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.97190e7 | −0.956449 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.56192e6 | 0.178101 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.71518e7 | −0.865090 | −0.432545 | − | 0.901612i | \(-0.642384\pi\) | ||||
−0.432545 | + | 0.901612i | \(0.642384\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.66618e7 | −1.79629 |
(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 | 448.6.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 448.6.a.o.1.1 | 1 | |||
8.3 | odd | 2 | 112.6.a.b.1.1 | 1 | |||
8.5 | even | 2 | 28.6.a.b.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 252.6.a.a.1.1 | 1 | |||
24.11 | even | 2 | 1008.6.a.l.1.1 | 1 | |||
40.13 | odd | 4 | 700.6.e.b.449.2 | 2 | |||
40.29 | even | 2 | 700.6.a.b.1.1 | 1 | |||
40.37 | odd | 4 | 700.6.e.b.449.1 | 2 | |||
56.5 | odd | 6 | 196.6.e.i.165.1 | 2 | |||
56.13 | odd | 2 | 196.6.a.a.1.1 | 1 | |||
56.27 | even | 2 | 784.6.a.m.1.1 | 1 | |||
56.37 | even | 6 | 196.6.e.a.165.1 | 2 | |||
56.45 | odd | 6 | 196.6.e.i.177.1 | 2 | |||
56.53 | even | 6 | 196.6.e.a.177.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.6.a.b.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
112.6.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
196.6.a.a.1.1 | 1 | 56.13 | odd | 2 | |||
196.6.e.a.165.1 | 2 | 56.37 | even | 6 | |||
196.6.e.a.177.1 | 2 | 56.53 | even | 6 | |||
196.6.e.i.165.1 | 2 | 56.5 | odd | 6 | |||
196.6.e.i.177.1 | 2 | 56.45 | odd | 6 | |||
252.6.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
448.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.6.a.o.1.1 | 1 | 4.3 | odd | 2 | |||
700.6.a.b.1.1 | 1 | 40.29 | even | 2 | |||
700.6.e.b.449.1 | 2 | 40.37 | odd | 4 | |||
700.6.e.b.449.2 | 2 | 40.13 | odd | 4 | |||
784.6.a.m.1.1 | 1 | 56.27 | even | 2 | |||
1008.6.a.l.1.1 | 1 | 24.11 | even | 2 |