Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("336.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(53.8889634572\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −54.0000 | −0.965981 | −0.482991 | − | 0.875625i | \(-0.660450\pi\) | ||||
−0.482991 | + | 0.875625i | \(0.660450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −216.000 | −0.538235 | −0.269118 | − | 0.963107i | \(-0.586732\pi\) | ||||
−0.269118 | + | 0.963107i | \(0.586732\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 998.000 | 1.63784 | 0.818921 | − | 0.573906i | \(-0.194572\pi\) | ||||
0.818921 | + | 0.573906i | \(0.194572\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −486.000 | −0.557710 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1302.00 | 1.09267 | 0.546335 | − | 0.837567i | \(-0.316023\pi\) | ||||
0.546335 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −884.000 | −0.561783 | −0.280891 | − | 0.959740i | \(-0.590630\pi\) | ||||
−0.280891 | + | 0.959740i | \(0.590630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2268.00 | 0.893971 | 0.446986 | − | 0.894541i | \(-0.352498\pi\) | ||||
0.446986 | + | 0.894541i | \(0.352498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −209.000 | −0.0668800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1482.00 | −0.327230 | −0.163615 | − | 0.986524i | \(-0.552315\pi\) | ||||
−0.163615 | + | 0.986524i | \(0.552315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8360.00 | −1.56244 | −0.781218 | − | 0.624259i | \(-0.785401\pi\) | ||||
−0.781218 | + | 0.624259i | \(0.785401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1944.00 | −0.310750 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2646.00 | 0.365107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4714.00 | −0.566090 | −0.283045 | − | 0.959107i | \(-0.591345\pi\) | ||||
−0.283045 | + | 0.959107i | \(0.591345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8982.00 | 0.945609 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9786.00 | −0.909171 | −0.454585 | − | 0.890703i | \(-0.650213\pi\) | ||||
−0.454585 | + | 0.890703i | \(0.650213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19436.0 | −1.60301 | −0.801504 | − | 0.597989i | \(-0.795967\pi\) | ||||
−0.801504 | + | 0.597989i | \(0.795967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4374.00 | −0.321994 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22200.0 | −1.46591 | −0.732957 | − | 0.680275i | \(-0.761860\pi\) | ||||
−0.732957 | + | 0.680275i | \(0.761860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11718.0 | 0.630853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26790.0 | 1.31004 | 0.655018 | − | 0.755614i | \(-0.272661\pi\) | ||||
0.655018 | + | 0.755614i | \(0.272661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11664.0 | 0.519925 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7956.00 | −0.324345 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −28092.0 | −1.05064 | −0.525318 | − | 0.850906i | \(-0.676054\pi\) | ||||
−0.525318 | + | 0.850906i | \(0.676054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38866.0 | −1.33735 | −0.668675 | − | 0.743555i | \(-0.733138\pi\) | ||||
−0.668675 | + | 0.743555i | \(0.733138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −53892.0 | −1.58213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23948.0 | −0.651752 | −0.325876 | − | 0.945413i | \(-0.605659\pi\) | ||||
−0.325876 | + | 0.945413i | \(0.605659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20412.0 | 0.516134 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 20628.0 | 0.485636 | 0.242818 | − | 0.970072i | \(-0.421928\pi\) | ||||
0.242818 | + | 0.970072i | \(0.421928\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 290.000 | 0.00636929 | 0.00318464 | − | 0.999995i | \(-0.498986\pi\) | ||||
0.00318464 | + | 0.999995i | \(0.498986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1881.00 | −0.0386132 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10584.0 | 0.203434 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 99544.0 | 1.79452 | 0.897258 | − | 0.441506i | \(-0.145556\pi\) | ||||
0.897258 | + | 0.441506i | \(0.145556\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −19308.0 | −0.307639 | −0.153820 | − | 0.988099i | \(-0.549158\pi\) | ||||
−0.153820 | + | 0.988099i | \(0.549158\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −70308.0 | −1.05550 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13338.0 | −0.188926 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 36390.0 | 0.486975 | 0.243488 | − | 0.969904i | \(-0.421708\pi\) | ||||
0.243488 | + | 0.969904i | \(0.421708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48902.0 | −0.619046 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −75240.0 | −0.902072 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 47736.0 | 0.542671 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −79078.0 | −0.853348 | −0.426674 | − | 0.904405i | \(-0.640315\pi\) | ||||
−0.426674 | + | 0.904405i | \(0.640315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17496.0 | −0.179412 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 184626. | 1.80090 | 0.900450 | − | 0.434960i | \(-0.143238\pi\) | ||||
0.900450 | + | 0.434960i | \(0.143238\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −64592.0 | −0.599909 | −0.299955 | − | 0.953953i | \(-0.596972\pi\) | ||||
−0.299955 | + | 0.953953i | \(0.596972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23814.0 | 0.210794 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −149592. | −1.26313 | −0.631566 | − | 0.775322i | \(-0.717588\pi\) | ||||
−0.631566 | + | 0.775322i | \(0.717588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −63826.0 | −0.514555 | −0.257277 | − | 0.966338i | \(-0.582825\pi\) | ||||
−0.257277 | + | 0.966338i | \(0.582825\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −42426.0 | −0.326832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −71022.0 | −0.523235 | −0.261618 | − | 0.965172i | \(-0.584256\pi\) | ||||
−0.261618 | + | 0.965172i | \(0.584256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −122472. | −0.863559 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 80838.0 | 0.545948 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −63798.0 | −0.412990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −114395. | −0.710303 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −88074.0 | −0.524910 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 180036. | 1.03059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −269624. | −1.48337 | −0.741685 | − | 0.670749i | \(-0.765973\pi\) | ||||
−0.741685 | + | 0.670749i | \(0.765973\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −174924. | −0.925497 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −81180.0 | −0.413305 | −0.206653 | − | 0.978414i | \(-0.566257\pi\) | ||||
−0.206653 | + | 0.978414i | \(0.566257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 43316.0 | 0.212334 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −39366.0 | −0.185903 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −260910. | −1.18765 | −0.593826 | − | 0.804593i | \(-0.702383\pi\) | ||||
−0.593826 | + | 0.804593i | \(0.702383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 297964. | 1.30806 | 0.654029 | − | 0.756470i | \(-0.273078\pi\) | ||||
0.654029 | + | 0.756470i | \(0.273078\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −199800. | −0.846346 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −215568. | −0.881544 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 80028.0 | 0.316098 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −398970. | −1.47223 | −0.736113 | − | 0.676859i | \(-0.763341\pi\) | ||||
−0.736113 | + | 0.676859i | \(0.763341\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 224968. | 0.802931 | 0.401466 | − | 0.915874i | \(-0.368501\pi\) | ||||
0.401466 | + | 0.915874i | \(0.368501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 105462. | 0.364223 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 451440. | 1.50928 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −233218. | −0.755115 | −0.377557 | − | 0.925986i | \(-0.623236\pi\) | ||||
−0.377557 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 241110. | 0.756349 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −111132. | −0.337889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −466220. | −1.37443 | −0.687214 | − | 0.726455i | \(-0.741166\pi\) | ||||
−0.687214 | + | 0.726455i | \(0.741166\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 104976. | 0.300179 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 100848. | 0.279818 | 0.139909 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139909 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 624711. | 1.68253 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −71604.0 | −0.187261 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −668838. | −1.69905 | −0.849524 | − | 0.527550i | \(-0.823111\pi\) | ||||
−0.849524 | + | 0.527550i | \(0.823111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10241.0 | 0.0252783 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −252828. | −0.606585 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 614856. | 1.43430 | 0.717151 | − | 0.696917i | \(-0.245446\pi\) | ||||
0.717151 | + | 0.696917i | \(0.245446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 540686. | 1.22673 | 0.613365 | − | 0.789800i | \(-0.289816\pi\) | ||||
0.613365 | + | 0.789800i | \(0.289816\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −349794. | −0.772120 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 254556. | 0.546832 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −281232. | −0.588113 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 41916.0 | 0.0831374 | 0.0415687 | − | 0.999136i | \(-0.486764\pi\) | ||||
0.0415687 | + | 0.999136i | \(0.486764\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −533998. | −1.03192 | −0.515960 | − | 0.856612i | \(-0.672565\pi\) | ||||
−0.515960 | + | 0.856612i | \(0.672565\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −485028. | −0.913441 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 824886. | 1.51436 | 0.757179 | − | 0.653208i | \(-0.226577\pi\) | ||||
0.757179 | + | 0.653208i | \(0.226577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 399544. | 0.715207 | 0.357604 | − | 0.933873i | \(-0.383594\pi\) | ||||
0.357604 | + | 0.933873i | \(0.383594\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −215532. | −0.376289 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 72618.0 | 0.123681 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 528444. | 0.878242 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 183708. | 0.297990 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 190944. | 0.302371 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −868868. | −1.34353 | −0.671765 | − | 0.740764i | \(-0.734464\pi\) | ||||
−0.671765 | + | 0.740764i | \(0.734464\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 185652. | 0.280382 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.04954e6 | 1.54848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 409640. | 0.590545 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2610.00 | 0.00367731 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.29940e6 | 1.78962 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 626656. | 0.843853 | 0.421927 | − | 0.906630i | \(-0.361354\pi\) | ||||
0.421927 | + | 0.906630i | \(0.361354\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16929.0 | −0.0222933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 450396. | 0.580136 | 0.290068 | − | 0.957006i | \(-0.406322\pi\) | ||||
0.290068 | + | 0.957006i | \(0.406322\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.06453e6 | −1.34143 | −0.670717 | − | 0.741714i | \(-0.734013\pi\) | ||||
−0.670717 | + | 0.741714i | \(0.734013\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 95256.0 | 0.117453 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.43618e6 | 1.73308 | 0.866540 | − | 0.499108i | \(-0.166339\pi\) | ||||
0.866540 | + | 0.499108i | \(0.166339\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.19880e6 | 1.41605 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 895896. | 1.03606 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 997860. | 1.12999 | 0.564995 | − | 0.825094i | \(-0.308878\pi\) | ||||
0.564995 | + | 0.825094i | \(0.308878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −227974. | −0.252838 | −0.126419 | − | 0.991977i | \(-0.540348\pi\) | ||||
−0.126419 | + | 0.991977i | \(0.540348\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −129654. | −0.137997 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −882232. | −0.920111 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −173772. | −0.177616 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.51657e6 | −1.51942 | −0.759712 | − | 0.650260i | \(-0.774660\pi\) | ||||
−0.759712 | + | 0.650260i | \(0.774660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −489888. | −0.481167 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −632772. | −0.609392 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 455886. | 0.430550 | 0.215275 | − | 0.976553i | \(-0.430935\pi\) | ||||
0.215275 | + | 0.976553i | \(0.430935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 230986. | 0.213962 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −120042. | −0.109077 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 752652. | 0.670973 | 0.335486 | − | 0.942045i | \(-0.391099\pi\) | ||||
0.335486 | + | 0.942045i | \(0.391099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.44666e6 | −1.26547 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 327510. | 0.281155 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 143682. | 0.121066 | 0.0605329 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605329 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −757496. | −0.626552 | −0.313276 | − | 0.949662i | \(-0.601426\pi\) | ||||
−0.313276 | + | 0.949662i | \(0.601426\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −440118. | −0.357407 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 45144.0 | 0.0359972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.16214e6 | −0.910035 | −0.455018 | − | 0.890482i | \(-0.650367\pi\) | ||||
−0.455018 | + | 0.890482i | \(0.650367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −677160. | −0.520812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −414366. | −0.313053 | −0.156527 | − | 0.987674i | \(-0.550030\pi\) | ||||
−0.156527 | + | 0.987674i | \(0.550030\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −120428. | −0.0893843 | −0.0446922 | − | 0.999001i | \(-0.514231\pi\) | ||||
−0.0446922 | + | 0.999001i | \(0.514231\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 429624. | 0.313312 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 479514. | 0.343634 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 275347. | 0.193926 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −711702. | −0.492681 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.20159e6 | 1.49819 | 0.749094 | − | 0.662463i | \(-0.230489\pi\) | ||||
0.749094 | + | 0.662463i | \(0.230489\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51697e6 | 1.01490 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −157464. | −0.103583 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.26346e6 | 1.46418 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 952364. | 0.605880 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.66163e6 | 1.03975 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.09876e6 | 1.29186 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −110900. | −0.0671561 | −0.0335781 | − | 0.999436i | \(-0.510690\pi\) | ||||
−0.0335781 | + | 0.999436i | \(0.510690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −581328. | −0.346358 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 910608. | 0.533864 | 0.266932 | − | 0.963715i | \(-0.413990\pi\) | ||||
0.266932 | + | 0.963715i | \(0.413990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.12247e6 | 1.80152 | 0.900758 | − | 0.434322i | \(-0.143012\pi\) | ||||
0.900758 | + | 0.434322i | \(0.143012\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 214326. | 0.121702 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.76688e6 | −1.54647 | −0.773237 | − | 0.634117i | \(-0.781364\pi\) | ||||
−0.773237 | + | 0.634117i | \(0.781364\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 320112. | 0.176127 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.34633e6 | −0.729270 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.15097e6 | −0.613842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −208582. | −0.109539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −574434. | −0.297078 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.08780e6 | 0.554063 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.22257e6 | −1.61671 | −0.808356 | − | 0.588694i | \(-0.799642\pi\) | ||||
−0.808356 | + | 0.588694i | \(0.799642\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −381834. | −0.188697 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.29319e6 | 0.629580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.63306e6 | 0.783298 | 0.391649 | − | 0.920115i | \(-0.371905\pi\) | ||||
0.391649 | + | 0.920115i | \(0.371905\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −639198. | −0.302090 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.80576e6 | 0.840958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.10225e6 | −0.498576 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.03642e6 | −0.462073 | −0.231036 | − | 0.972945i | \(-0.574212\pi\) | ||||
−0.231036 | + | 0.972945i | \(0.574212\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.22999e6 | −1.85898 | −0.929491 | − | 0.368844i | \(-0.879754\pi\) | ||||
−0.929491 | + | 0.368844i | \(0.879754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 727542. | 0.315203 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 238806. | 0.102002 | 0.0510010 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510010 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.11391e6 | −0.469116 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −574182. | −0.238440 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.66428e6 | 1.09105 | 0.545523 | − | 0.838096i | \(-0.316331\pi\) | ||||
0.545523 | + | 0.838096i | \(0.316331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.69464e6 | −0.684400 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.02956e6 | −0.410094 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15660.0 | −0.00615261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71083e6 | 0.663044 | 0.331522 | − | 0.943448i | \(-0.392438\pi\) | ||||
0.331522 | + | 0.943448i | \(0.392438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −792666. | −0.303057 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.31271e6 | −0.495147 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.96649e6 | −1.47616 | −0.738081 | − | 0.674712i | \(-0.764268\pi\) | ||||
−0.738081 | + | 0.674712i | \(0.764268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.62032e6 | 0.595009 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.47904e6 | −0.535951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −828668. | −0.296335 | −0.148167 | − | 0.988962i | \(-0.547337\pi\) | ||||
−0.148167 | + | 0.988962i | \(0.547337\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.42662e6 | −0.856424 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.55686e6 | 0.890657 | 0.445329 | − | 0.895367i | \(-0.353087\pi\) | ||||
0.445329 | + | 0.895367i | \(0.353087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −571536. | −0.196513 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.57432e6 | −0.534336 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.91785e6 | 0.977664 | 0.488832 | − | 0.872378i | \(-0.337423\pi\) | ||||
0.488832 | + | 0.872378i | \(0.337423\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.95294e6 | 0.976815 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −730620. | −0.238622 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.37538e6 | −1.73347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.50715e6 | 0.798370 | 0.399185 | − | 0.916870i | \(-0.369293\pi\) | ||||
0.399185 | + | 0.916870i | \(0.369293\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 389844. | 0.122591 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 990666. | 0.307657 | 0.153828 | − | 0.988098i | \(-0.450840\pi\) | ||||
0.153828 | + | 0.988098i | \(0.450840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.34328e6 | −2.55902 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −354294. | −0.107331 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.01822e6 | 0.304689 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.51824e6 | 1.33555 | 0.667777 | − | 0.744362i | \(-0.267246\pi\) | ||||
0.667777 | + | 0.744362i | \(0.267246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.34819e6 | −0.685691 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.37651e6 | 0.397103 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.04263e6 | 0.297174 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.68168e6 | 0.755207 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −605220. | −0.168414 | −0.0842070 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842070 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.49893e6 | 1.23710 | 0.618549 | − | 0.785746i | \(-0.287721\pi\) | ||||
0.618549 | + | 0.785746i | \(0.287721\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.79820e6 | −0.488638 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −272118. | −0.0730777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.90443e6 | 0.505471 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.94011e6 | −0.508960 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.37594e6 | −1.39400 | −0.696998 | − | 0.717074i | \(-0.745481\pi\) | ||||
−0.696998 | + | 0.717074i | \(0.745481\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.98561e6 | −0.508950 | −0.254475 | − | 0.967079i | \(-0.581903\pi\) | ||||
−0.254475 | + | 0.967079i | \(0.581903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 720252. | 0.182499 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00491e6 | −0.502217 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.38727e6 | −0.838859 | −0.419429 | − | 0.907788i | \(-0.637770\pi\) | ||||
−0.419429 | + | 0.907788i | \(0.637770\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.14094e6 | −0.518318 | −0.259159 | − | 0.965835i | \(-0.583445\pi\) | ||||
−0.259159 | + | 0.965835i | \(0.583445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.96506e6 | −0.470409 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.59073e6 | −0.849990 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.97808e6 | −1.63350 | −0.816752 | − | 0.576990i | \(-0.804227\pi\) | ||||
−0.816752 | + | 0.576990i | \(0.804227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.11378e6 | 0.489348 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.02471e6 | 0.463573 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.64071e6 | 0.597987 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.17999e6 | −1.16021 | −0.580107 | − | 0.814540i | \(-0.696989\pi\) | ||||
−0.580107 | + | 0.814540i | \(0.696989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 949158. | 0.210284 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.83001e6 | −1.71597 | −0.857985 | − | 0.513674i | \(-0.828284\pi\) | ||||
−0.857985 | + | 0.513674i | \(0.828284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −165320. | −0.0358404 | −0.0179202 | − | 0.999839i | \(-0.505704\pi\) | ||||
−0.0179202 | + | 0.999839i | \(0.505704\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.06296e6 | 0.871385 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.79329e6 | 0.380504 | 0.190252 | − | 0.981735i | \(-0.439070\pi\) | ||||
0.190252 | + | 0.981735i | \(0.439070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.17345e6 | 0.246339 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.09896e6 | −0.435966 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.19818e6 | 0.862795 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 184756. | 0.0375720 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.16999e6 | 0.436678 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.59657e6 | 1.31365 | 0.656824 | − | 0.754044i | \(-0.271899\pi\) | ||||
0.656824 | + | 0.754044i | \(0.271899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.70457e6 | −0.927166 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00019e6 | −0.195080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.27021e6 | 0.824319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.97393e6 | 1.14140 | 0.570700 | − | 0.821159i | \(-0.306672\pi\) | ||||
0.570700 | + | 0.821159i | \(0.306672\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.19598e6 | −0.793526 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −381264. | −0.0713710 | −0.0356855 | − | 0.999363i | \(-0.511361\pi\) | ||||
−0.0356855 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.92956e6 | −0.357554 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 944784. | 0.173308 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.01077e6 | −0.183553 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.54351e6 | −0.277497 | −0.138748 | − | 0.990328i | \(-0.544308\pi\) | ||||
−0.138748 | + | 0.990328i | \(0.544308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 907632. | 0.161553 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.02300e6 | 0.708974 | 0.354487 | − | 0.935061i | \(-0.384656\pi\) | ||||
0.354487 | + | 0.935061i | \(0.384656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.96980e6 | −1.73964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.62240e6 | 0.971408 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.94715e6 | −0.333123 | −0.166562 | − | 0.986031i | \(-0.553266\pi\) | ||||
−0.166562 | + | 0.986031i | \(0.553266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14210.0 | −0.00240736 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −644436. | −0.108115 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.48797e6 | 0.579501 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.79520e6 | 0.789006 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.01954e6 | −0.980946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.38569e6 | 1.19206 | 0.596028 | − | 0.802963i | \(-0.296745\pi\) | ||||
0.596028 | + | 0.802963i | \(0.296745\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 329740. | 0.0527130 | 0.0263565 | − | 0.999653i | \(-0.491610\pi\) | ||||
0.0263565 | + | 0.999653i | \(0.491610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 92169.0 | 0.0145944 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.08847e7 | −1.70722 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.29252e6 | −0.200816 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.27545e6 | −0.350212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.76643e6 | −1.48908 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.07797e6 | 1.22016 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.53370e6 | 0.828095 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −518616. | −0.0768907 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 87086.0 | 0.0127925 | 0.00639625 | − | 0.999980i | \(-0.497964\pi\) | ||||
0.00639625 | + | 0.999980i | \(0.497964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.86617e6 | 0.708252 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.44660e6 | 0.497050 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.91531e6 | −0.988196 | −0.494098 | − | 0.869406i | \(-0.664502\pi\) | ||||
−0.494098 | + | 0.869406i | \(0.664502\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.14815e6 | −0.445784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.31009e6 | 0.183832 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.87766e6 | −0.678263 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.29100e6 | 0.315714 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.52258e6 | −0.207942 | −0.103971 | − | 0.994580i | \(-0.533155\pi\) | ||||
−0.103971 | + | 0.994580i | \(0.533155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.93971e7 | −2.62548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.53109e6 | −0.339547 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.86462e6 | 1.04570 | 0.522850 | − | 0.852425i | \(-0.324869\pi\) | ||||
0.522850 | + | 0.852425i | \(0.324869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.83519e6 | 0.505435 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.46321e6 | −0.189464 | −0.0947321 | − | 0.995503i | \(-0.530199\pi\) | ||||
−0.0947321 | + | 0.995503i | \(0.530199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.19855e6 | −1.18067 | −0.590336 | − | 0.807158i | \(-0.701005\pi\) | ||||
−0.590336 | + | 0.807158i | \(0.701005\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 377244. | 0.0479994 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −474012. | −0.0597888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.28939e6 | 0.411317 | 0.205658 | − | 0.978624i | \(-0.434066\pi\) | ||||
0.205658 | + | 0.978624i | \(0.434066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.80598e6 | −0.595780 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 946092. | 0.116277 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.78664e6 | −0.705107 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.36525e6 | −0.527375 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.12929e6 | −0.614416 | −0.307208 | − | 0.951642i | \(-0.599395\pi\) | ||||
−0.307208 | + | 0.951642i | \(0.599395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.39024e6 | 0.877749 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.42397e6 | 0.874315 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.75433e6 | −0.321647 | −0.160823 | − | 0.986983i | \(-0.551415\pi\) | ||||
−0.160823 | + | 0.986983i | \(0.551415\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.44509e6 | 0.398941 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.59590e6 | 0.412925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.88616e6 | 1.12580 | 0.562899 | − | 0.826525i | \(-0.309686\pi\) | ||||
0.562899 | + | 0.826525i | \(0.309686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.37039e7 | 1.54760 | 0.773798 | − | 0.633433i | \(-0.218355\pi\) | ||||
0.773798 | + | 0.633433i | \(0.218355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.93979e6 | −0.217251 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.17733e6 | 0.686139 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.85310e6 | 0.865107 | 0.432553 | − | 0.901608i | \(-0.357613\pi\) | ||||
0.432553 | + | 0.901608i | \(0.357613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 653562. | 0.0714075 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.21556e7 | −2.40094 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.46977e7 | 1.57978 | 0.789892 | − | 0.613246i | \(-0.210136\pi\) | ||||
0.789892 | + | 0.613246i | \(0.210136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.75600e6 | 0.507053 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.28370e6 | 0.664511 | 0.332256 | − | 0.943189i | \(-0.392190\pi\) | ||||
0.332256 | + | 0.943189i | \(0.392190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.26692e6 | 0.237799 | 0.118900 | − | 0.992906i | \(-0.462063\pi\) | ||||
0.118900 | + | 0.992906i | \(0.462063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.65337e6 | 0.172045 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.78311e6 | −0.184059 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.06882e6 | −0.928647 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.71850e6 | 0.174574 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.13763e6 | −0.618549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.17477e7 | 1.17457 | 0.587285 | − | 0.809380i | \(-0.300197\pi\) | ||||
0.587285 | + | 0.809380i | \(0.300197\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.81981e6 | −0.775688 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.45597e7 | 1.43291 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.39620e6 | 0.233978 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.67087e6 | 0.161879 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.93231e6 | 0.570268 | 0.285134 | − | 0.958488i | \(-0.407962\pi\) | ||||
0.285134 | + | 0.958488i | \(0.407962\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.94443e6 | 0.662383 | 0.331191 | − | 0.943564i | \(-0.392549\pi\) | ||||
0.331191 | + | 0.943564i | \(0.392549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.44590e6 | 0.894013 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.97050e6 | 0.466809 | 0.233404 | − | 0.972380i | \(-0.425013\pi\) | ||||
0.233404 | + | 0.972380i | \(0.425013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.06787e6 | 0.565490 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.68676e6 | 0.340951 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.83355e7 | −1.68271 | −0.841354 | − | 0.540484i | \(-0.818241\pi\) | ||||
−0.841354 | + | 0.540484i | \(0.818241\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.38372e6 | 0.399245 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23490.0 | 0.00212310 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.01402e6 | −0.808546 | −0.404273 | − | 0.914638i | \(-0.632475\pi\) | ||||
−0.404273 | + | 0.914638i | \(0.632475\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 699398. | 0.0622617 | 0.0311308 | − | 0.999515i | \(-0.490089\pi\) | ||||
0.0311308 | + | 0.999515i | \(0.490089\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.16946e7 | 1.03324 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.33906e6 | −0.205111 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.36118e6 | −0.292534 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.63990e6 | 0.487199 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.39506e6 | 0.719809 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.80603e6 | −0.494130 | −0.247065 | − | 0.968999i | \(-0.579466\pi\) | ||||
−0.247065 | + | 0.968999i | \(0.579466\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −152361. | −0.0128711 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 985074. | 0.0826033 | 0.0413016 | − | 0.999147i | \(-0.486850\pi\) | ||||
0.0413016 | + | 0.999147i | \(0.486850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.87482e6 | 0.322535 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.05356e6 | 0.334942 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.88208e7 | 1.54379 | 0.771894 | − | 0.635752i | \(-0.219310\pi\) | ||||
0.771894 | + | 0.635752i | \(0.219310\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.40891e7 | 1.14725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.58077e6 | −0.774477 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.67364e7 | 2.14563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.93385e7 | 1.54073 | 0.770366 | − | 0.637601i | \(-0.220073\pi\) | ||||
0.770366 | + | 0.637601i | \(0.220073\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 857304. | 0.0678113 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.60901e7 | −1.26356 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.27414e7 | −0.993423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.29256e7 | 1.00059 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.41489e6 | −0.108750 | −0.0543748 | − | 0.998521i | \(-0.517317\pi\) | ||||
−0.0543748 | + | 0.998521i | \(0.517317\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.16718e6 | 0.318019 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.07892e7 | 0.817554 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.04667e6 | −0.680676 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −754906. | −0.0563998 | −0.0281999 | − | 0.999602i | \(-0.508977\pi\) | ||||
−0.0281999 | + | 0.999602i | \(0.508977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.06306e6 | 0.598172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.89605e7 | −1.39677 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.16407e7 | 0.851555 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.98074e6 | 0.652400 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.08854e6 | −0.0785279 | −0.0392639 | − | 0.999229i | \(-0.512501\pi\) | ||||
−0.0392639 | + | 0.999229i | \(0.512501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.16501e6 | 0.226744 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.05177e6 | −0.145976 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 309738. | 0.0218851 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 755392. | 0.0530074 | 0.0265037 | − | 0.999649i | \(-0.491563\pi\) | ||||
0.0265037 | + | 0.999649i | \(0.491563\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.53057e7 | −1.75156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.56369e6 | 0.107495 | 0.0537477 | − | 0.998555i | \(-0.482883\pi\) | ||||
0.0537477 | + | 0.998555i | \(0.482883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.16689e6 | −0.0796728 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.17277e6 | 0.350796 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.05544e7 | 0.710922 | 0.355461 | − | 0.934691i | \(-0.384324\pi\) | ||||
0.355461 | + | 0.934691i | \(0.384324\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.94009e6 | −0.531227 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.73678e7 | −1.15418 | −0.577088 | − | 0.816682i | \(-0.695811\pi\) | ||||
−0.577088 | + | 0.816682i | \(0.695811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.15444e7 | 1.42214 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.56395e6 | −0.102546 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.33001e6 | 0.477419 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.80181e7 | 1.81276 | 0.906378 | − | 0.422467i | \(-0.138836\pi\) | ||||
0.906378 | + | 0.422467i | \(0.138836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.36491e7 | −0.877239 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.21483e7 | −0.775617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.01979e7 | −0.646801 | −0.323401 | − | 0.946262i | \(-0.604826\pi\) | ||||
−0.323401 | + | 0.946262i | \(0.604826\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.40899e6 | −0.277802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.57535e6 | 0.161204 | 0.0806018 | − | 0.996746i | \(-0.474316\pi\) | ||||
0.0806018 | + | 0.996746i | \(0.474316\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.12747e6 | 0.194483 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.69495e6 | −0.351833 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.80358e7 | −1.72078 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 971234. | 0.0592254 | 0.0296127 | − | 0.999561i | \(-0.490573\pi\) | ||||
0.0296127 | + | 0.999561i | \(0.490573\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.10297e6 | 0.248578 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.72921e7 | −1.04088 | −0.520439 | − | 0.853899i | \(-0.674232\pi\) | ||||
−0.520439 | + | 0.853899i | \(0.674232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.74724e6 | 0.104496 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.07887e6 | 0.123531 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.65082e6 | 0.510756 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.45565e6 | −0.261387 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.08038e6 | −0.0629755 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.25938e7 | 0.729427 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.65515e7 | 0.952576 | 0.476288 | − | 0.879289i | \(-0.341982\pi\) | ||||
0.476288 | + | 0.879289i | \(0.341982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.77387e6 | 0.387386 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.48008e6 | 0.197764 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.87883e7 | −2.19037 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.30199e7 | −0.730619 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.91057e6 | 0.162305 | 0.0811526 | − | 0.996702i | \(-0.474140\pi\) | ||||
0.0811526 | + | 0.996702i | \(0.474140\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.89044e7 | −1.60176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.94759e6 | 0.162325 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −62640.0 | −0.00342817 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00113e6 | 0.326395 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.29314e6 | 0.0698974 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.16252e7 | −0.624496 | −0.312248 | − | 0.950001i | \(-0.601082\pi\) | ||||
−0.312248 | + | 0.950001i | \(0.601082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.09020e7 | −1.64981 | −0.824906 | − | 0.565270i | \(-0.808772\pi\) | ||||
−0.824906 | + | 0.565270i | \(0.808772\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.81746e6 | −0.361740 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.51759e7 | 1.32767 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.71814e7 | 0.900542 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.96106e6 | −0.206349 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.22870e7 | −1.15397 | −0.576984 | − | 0.816755i | \(-0.695771\pi\) | ||||
−0.576984 | + | 0.816755i | \(0.695771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.64895e7 | 0.848610 | 0.424305 | − | 0.905519i | \(-0.360518\pi\) | ||||
0.424305 | + | 0.905519i | \(0.360518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 406296. | 0.0207830 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.37457e7 | 1.20732 | 0.603658 | − | 0.797244i | \(-0.293709\pi\) | ||||
0.603658 | + | 0.797244i | \(0.293709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.60865e7 | 1.31835 | 0.659173 | − | 0.751991i | \(-0.270906\pi\) | ||||
0.659173 | + | 0.751991i | \(0.270906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.04592e7 | −0.525409 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.12610e6 | 0.156096 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.44579e6 | −0.270299 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.09444e6 | −0.300691 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.00872e7 | −0.494729 | −0.247365 | − | 0.968922i | \(-0.579565\pi\) | ||||
−0.247365 | + | 0.968922i | \(0.579565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83148e7 | −0.892920 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.72929e6 | −0.180741 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.37344e7 | −1.62529 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.60536e6 | 0.268469 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.08385e6 | −0.0516061 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.06914e7 | −0.506068 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.43630e7 | −1.14646 | −0.573229 | − | 0.819395i | \(-0.694309\pi\) | ||||
−0.573229 | + | 0.819395i | \(0.694309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.86662e6 | 0.180890 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.45612e6 | 0.114234 | 0.0571172 | − | 0.998367i | \(-0.481809\pi\) | ||||
0.0571172 | + | 0.998367i | \(0.481809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.62982e6 | −0.399042 | −0.199521 | − | 0.979894i | \(-0.563939\pi\) | ||||
−0.199521 | + | 0.979894i | \(0.563939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.31563e6 | 0.198397 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.05199e7 | −0.480824 | −0.240412 | − | 0.970671i | \(-0.577283\pi\) | ||||
−0.240412 | + | 0.970671i | \(0.577283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.61173e7 | 1.64125 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.47812e6 | 0.111963 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.15015e7 | −0.965872 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.39001e7 | −1.06747 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.40532e6 | −0.284449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.82176e6 | −0.389525 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.14540e7 | −0.502872 | −0.251436 | − | 0.967874i | \(-0.580903\pi\) | ||||
−0.251436 | + | 0.967874i | \(0.580903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.98143e7 | 0.864980 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.18134e7 | −0.512786 | −0.256393 | − | 0.966573i | \(-0.582534\pi\) | ||||
−0.256393 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.63221e6 | −0.199934 | −0.0999670 | − | 0.994991i | \(-0.531874\pi\) | ||||
−0.0999670 | + | 0.994991i | \(0.531874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.36527e7 | 0.585950 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.47728e7 | −1.91075 | −0.955377 | − | 0.295388i | \(-0.904551\pi\) | ||||
−0.955377 | + | 0.295388i | \(0.904551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.32116e7 | 0.560661 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.41718e6 | −0.0598039 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.96248e7 | 0.823525 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.32022e7 | −1.38551 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.03712e7 | 0.845347 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.23895e7 | 0.511276 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.48806e7 | 1.43144 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.57128e6 | 0.349805 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.91970e7 | −1.18500 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.08357e7 | 0.840986 | 0.420493 | − | 0.907296i | \(-0.361857\pi\) | ||||
0.420493 | + | 0.907296i | \(0.361857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.49547e7 | 0.600300 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.27869e6 | −0.210732 | −0.105366 | − | 0.994434i | \(-0.533601\pi\) | ||||
−0.105366 | + | 0.994434i | \(0.533601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.17053e6 | 0.165582 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.88889e7 | 0.745853 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.97782e6 | 0.156215 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.51286e7 | −0.981477 | −0.490738 | − | 0.871307i | \(-0.663273\pi\) | ||||
−0.490738 | + | 0.871307i | \(0.663273\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −998100. | −0.0387726 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.05867e7 | 0.795396 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 985226. | 0.0378601 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.23195e6 | −0.199970 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.38042e7 | 0.524774 | 0.262387 | − | 0.964963i | \(-0.415490\pi\) | ||||
0.262387 | + | 0.964963i | \(0.415490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.12248e6 | −0.0802547 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.19547e6 | 0.308226 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.51865e7 | 0.568106 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.73307e7 | −1.76114 | −0.880570 | − | 0.473915i | \(-0.842840\pi\) | ||||
−0.880570 | + | 0.473915i | \(0.842840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.81023e7 | 1.04011 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.25570e7 | −1.19859 | −0.599295 | − | 0.800528i | \(-0.704552\pi\) | ||||
−0.599295 | + | 0.800528i | \(0.704552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.21946e7 | −0.812773 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.92893e6 | 0.0702648 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.27117e6 | 0.190999 | 0.0954997 | − | 0.995429i | \(-0.469555\pi\) | ||||
0.0954997 | + | 0.995429i | \(0.469555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 289420. | 0.0104319 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.49019e7 | −0.892857 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.20579e6 | 0.292677 | 0.146338 | − | 0.989235i | \(-0.453251\pi\) | ||||
0.146338 | + | 0.989235i | \(0.453251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.26346e6 | −0.0803092 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.88101e6 | 0.101687 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.27846e7 | 0.448890 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.12604e7 | 1.44120 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.21170e7 | −0.421044 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.88359e7 | 0.996816 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.18118e7 | 0.406210 | 0.203105 | − | 0.979157i | \(-0.434897\pi\) | ||||
0.203105 | + | 0.979157i | \(0.434897\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.03587e7 | −0.354402 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.67702e7 | 1.25155 | 0.625774 | − | 0.780004i | \(-0.284783\pi\) | ||||
0.625774 | + | 0.780004i | \(0.284783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.46002e7 | −0.494399 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.87724e6 | −0.0632423 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.85183e7 | −0.620674 | −0.310337 | − | 0.950627i | \(-0.600442\pi\) | ||||
−0.310337 | + | 0.950627i | \(0.600442\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.86024e6 | −0.262107 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.16991e6 | −0.171518 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.72169e7 | −0.898370 | −0.449185 | − | 0.893439i | \(-0.648286\pi\) | ||||
−0.449185 | + | 0.893439i | \(0.648286\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.45438e7 | −1.46284 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.79020e6 | 0.319889 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.40808e7 | −1.43304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.63398e7 | −0.528522 | −0.264261 | − | 0.964451i | \(-0.585128\pi\) | ||||
−0.264261 | + | 0.964451i | \(0.585128\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.90031e7 | −0.933409 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.15754e7 | −0.690877 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.02062e7 | −0.962406 | −0.481203 | − | 0.876609i | \(-0.659800\pi\) | ||||
−0.481203 | + | 0.876609i | \(0.659800\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.43651e6 | −0.108944 |
(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 | 336.6.a.j.1.1 | 1 | ||
3.2 | odd | 2 | 1008.6.a.x.1.1 | 1 | |||
4.3 | odd | 2 | 42.6.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 126.6.a.k.1.1 | 1 | |||
20.3 | even | 4 | 1050.6.g.o.799.2 | 2 | |||
20.7 | even | 4 | 1050.6.g.o.799.1 | 2 | |||
20.19 | odd | 2 | 1050.6.a.n.1.1 | 1 | |||
28.3 | even | 6 | 294.6.e.h.79.1 | 2 | |||
28.11 | odd | 6 | 294.6.e.r.79.1 | 2 | |||
28.19 | even | 6 | 294.6.e.h.67.1 | 2 | |||
28.23 | odd | 6 | 294.6.e.r.67.1 | 2 | |||
28.27 | even | 2 | 294.6.a.h.1.1 | 1 | |||
84.83 | odd | 2 | 882.6.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
126.6.a.k.1.1 | 1 | 12.11 | even | 2 | |||
294.6.a.h.1.1 | 1 | 28.27 | even | 2 | |||
294.6.e.h.67.1 | 2 | 28.19 | even | 6 | |||
294.6.e.h.79.1 | 2 | 28.3 | even | 6 | |||
294.6.e.r.67.1 | 2 | 28.23 | odd | 6 | |||
294.6.e.r.79.1 | 2 | 28.11 | odd | 6 | |||
336.6.a.j.1.1 | 1 | 1.1 | even | 1 | trivial | ||
882.6.a.o.1.1 | 1 | 84.83 | odd | 2 | |||
1008.6.a.x.1.1 | 1 | 3.2 | odd | 2 | |||
1050.6.a.n.1.1 | 1 | 20.19 | odd | 2 | |||
1050.6.g.o.799.1 | 2 | 20.7 | even | 4 | |||
1050.6.g.o.799.2 | 2 | 20.3 | even | 4 |