Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,6,Mod(1,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, 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("1008.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.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: | \(161.666890371\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1008.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −84.0000 | −1.50264 | −0.751319 | − | 0.659939i | \(-0.770582\pi\) | ||||
−0.751319 | + | 0.659939i | \(0.770582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −336.000 | −0.837255 | −0.418627 | − | 0.908158i | \(-0.637489\pi\) | ||||
−0.418627 | + | 0.908158i | \(0.637489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 584.000 | 0.958417 | 0.479208 | − | 0.877701i | \(-0.340924\pi\) | ||||
0.479208 | + | 0.877701i | \(0.340924\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1458.00 | 1.22359 | 0.611794 | − | 0.791017i | \(-0.290448\pi\) | ||||
0.611794 | + | 0.791017i | \(0.290448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −470.000 | −0.298685 | −0.149343 | − | 0.988786i | \(-0.547716\pi\) | ||||
−0.149343 | + | 0.988786i | \(0.547716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4200.00 | −1.65550 | −0.827751 | − | 0.561096i | \(-0.810380\pi\) | ||||
−0.827751 | + | 0.561096i | \(0.810380\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3931.00 | 1.25792 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4866.00 | −1.07443 | −0.537214 | − | 0.843446i | \(-0.680523\pi\) | ||||
−0.537214 | + | 0.843446i | \(0.680523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7372.00 | 1.37778 | 0.688892 | − | 0.724864i | \(-0.258097\pi\) | ||||
0.688892 | + | 0.724864i | \(0.258097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4116.00 | 0.567944 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14330.0 | 1.72085 | 0.860423 | − | 0.509581i | \(-0.170200\pi\) | ||||
0.860423 | + | 0.509581i | \(0.170200\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6222.00 | −0.578057 | −0.289028 | − | 0.957321i | \(-0.593332\pi\) | ||||
−0.289028 | + | 0.957321i | \(0.593332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3704.00 | −0.305492 | −0.152746 | − | 0.988265i | \(-0.548812\pi\) | ||||
−0.152746 | + | 0.988265i | \(0.548812\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1812.00 | −0.119650 | −0.0598251 | − | 0.998209i | \(-0.519054\pi\) | ||||
−0.0598251 | + | 0.998209i | \(0.519054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37242.0 | 1.82114 | 0.910570 | − | 0.413355i | \(-0.135643\pi\) | ||||
0.910570 | + | 0.413355i | \(0.135643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 28224.0 | 1.25809 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34302.0 | 1.28289 | 0.641445 | − | 0.767169i | \(-0.278335\pi\) | ||||
0.641445 | + | 0.767169i | \(0.278335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24476.0 | 0.842201 | 0.421101 | − | 0.907014i | \(-0.361644\pi\) | ||||
0.421101 | + | 0.907014i | \(0.361644\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −49056.0 | −1.44015 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17452.0 | 0.474961 | 0.237481 | − | 0.971392i | \(-0.423678\pi\) | ||||
0.237481 | + | 0.971392i | \(0.423678\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28224.0 | 0.664466 | 0.332233 | − | 0.943197i | \(-0.392198\pi\) | ||||
0.332233 | + | 0.943197i | \(0.392198\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3602.00 | 0.0791109 | 0.0395555 | − | 0.999217i | \(-0.487406\pi\) | ||||
0.0395555 | + | 0.999217i | \(0.487406\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16464.0 | 0.316453 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −42872.0 | −0.772869 | −0.386435 | − | 0.922317i | \(-0.626294\pi\) | ||||
−0.386435 | + | 0.922317i | \(0.626294\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −35202.0 | −0.560883 | −0.280441 | − | 0.959871i | \(-0.590481\pi\) | ||||
−0.280441 | + | 0.959871i | \(0.590481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −122472. | −1.83861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −26730.0 | −0.357704 | −0.178852 | − | 0.983876i | \(-0.557238\pi\) | ||||
−0.178852 | + | 0.983876i | \(0.557238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28616.0 | −0.362248 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 39480.0 | 0.448816 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16978.0 | −0.183213 | −0.0916067 | − | 0.995795i | \(-0.529200\pi\) | ||||
−0.0916067 | + | 0.995795i | \(0.529200\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −99204.0 | −0.967667 | −0.483833 | − | 0.875160i | \(-0.660756\pi\) | ||||
−0.483833 | + | 0.875160i | \(0.660756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 131644. | 1.22267 | 0.611333 | − | 0.791373i | \(-0.290634\pi\) | ||||
0.611333 | + | 0.791373i | \(0.290634\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 48852.0 | 0.412499 | 0.206250 | − | 0.978499i | \(-0.433874\pi\) | ||||
0.206250 | + | 0.978499i | \(0.433874\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56374.0 | −0.454478 | −0.227239 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227239 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8742.00 | −0.0644043 | −0.0322021 | − | 0.999481i | \(-0.510252\pi\) | ||||
−0.0322021 | + | 0.999481i | \(0.510252\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 352800. | 2.48762 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −71442.0 | −0.462473 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −48155.0 | −0.299005 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −67704.0 | −0.387560 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −315992. | −1.73847 | −0.869234 | − | 0.494401i | \(-0.835388\pi\) | ||||
−0.869234 | + | 0.494401i | \(0.835388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −24666.0 | −0.125580 | −0.0627900 | − | 0.998027i | \(-0.520000\pi\) | ||||
−0.0627900 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23030.0 | 0.112892 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −303234. | −1.38031 | −0.690155 | − | 0.723662i | \(-0.742458\pi\) | ||||
−0.690155 | + | 0.723662i | \(0.742458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −250586. | −1.10007 | −0.550034 | − | 0.835142i | \(-0.685385\pi\) | ||||
−0.550034 | + | 0.835142i | \(0.685385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −196224. | −0.802439 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 408744. | 1.61448 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 60594.0 | 0.223596 | 0.111798 | − | 0.993731i | \(-0.464339\pi\) | ||||
0.111798 | + | 0.993731i | \(0.464339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −124448. | −0.444166 | −0.222083 | − | 0.975028i | \(-0.571286\pi\) | ||||
−0.222083 | + | 0.975028i | \(0.571286\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −619248. | −2.07031 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 76040.0 | 0.246203 | 0.123101 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123101 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 205800. | 0.625721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −124256. | −0.366310 | −0.183155 | − | 0.983084i | \(-0.558631\pi\) | ||||
−0.183155 | + | 0.983084i | \(0.558631\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −72420.0 | −0.200940 | −0.100470 | − | 0.994940i | \(-0.532035\pi\) | ||||
−0.100470 | + | 0.994940i | \(0.532035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30237.0 | −0.0814370 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 441552. | 1.12167 | 0.560837 | − | 0.827926i | \(-0.310479\pi\) | ||||
0.560837 | + | 0.827926i | \(0.310479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −192619. | −0.475449 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10692.0 | −0.0249417 | −0.0124709 | − | 0.999922i | \(-0.503970\pi\) | ||||
−0.0124709 | + | 0.999922i | \(0.503970\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −546064. | −1.23893 | −0.619465 | − | 0.785024i | \(-0.712651\pi\) | ||||
−0.619465 | + | 0.785024i | \(0.712651\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.20372e6 | −2.58581 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −489888. | −1.02445 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −575976. | −1.14241 | −0.571204 | − | 0.820808i | \(-0.693523\pi\) | ||||
−0.571204 | + | 0.820808i | \(0.693523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −413938. | −0.799912 | −0.399956 | − | 0.916534i | \(-0.630975\pi\) | ||||
−0.399956 | + | 0.916534i | \(0.630975\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 494946. | 0.908641 | 0.454320 | − | 0.890838i | \(-0.349882\pi\) | ||||
0.454320 | + | 0.890838i | \(0.349882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −520364. | −0.931482 | −0.465741 | − | 0.884921i | \(-0.654212\pi\) | ||||
−0.465741 | + | 0.884921i | \(0.654212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 238434. | 0.406095 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 522648. | 0.868610 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 157920. | 0.250076 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −183284. | −0.283412 | −0.141706 | − | 0.989909i | \(-0.545259\pi\) | ||||
−0.141706 | + | 0.989909i | \(0.545259\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 311136. | 0.459044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −361228. | −0.520753 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 851472. | 1.17271 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.27746e6 | 1.72023 | 0.860115 | − | 0.510100i | \(-0.170392\pi\) | ||||
0.860115 | + | 0.510100i | \(0.170392\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.28764e6 | −1.65856 | −0.829279 | − | 0.558835i | \(-0.811248\pi\) | ||||
−0.829279 | + | 0.558835i | \(0.811248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 350936. | 0.442221 | 0.221110 | − | 0.975249i | \(-0.429032\pi\) | ||||
0.221110 | + | 0.975249i | \(0.429032\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −836154. | −1.00901 | −0.504506 | − | 0.863408i | \(-0.668325\pi\) | ||||
−0.504506 | + | 0.863408i | \(0.668325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 152208. | 0.179791 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 774336. | 0.876869 | 0.438434 | − | 0.898763i | \(-0.355533\pi\) | ||||
0.438434 | + | 0.898763i | \(0.355533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.15285e6 | −1.27859 | −0.639293 | − | 0.768963i | \(-0.720773\pi\) | ||||
−0.639293 | + | 0.768963i | \(0.720773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −201684. | −0.214663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −274480. | −0.286265 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.35801e6 | 1.36056 | 0.680282 | − | 0.732951i | \(-0.261858\pi\) | ||||
0.680282 | + | 0.732951i | \(0.261858\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41120e6 | 1.38608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 317742. | 0.300083 | 0.150042 | − | 0.988680i | \(-0.452059\pi\) | ||||
0.150042 | + | 0.988680i | \(0.452059\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −702170. | −0.650418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.05101e6 | 0.936951 | 0.468475 | − | 0.883477i | \(-0.344804\pi\) | ||||
0.468475 | + | 0.883477i | \(0.344804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.12833e6 | −2.73651 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.18958e6 | −1.00234 | −0.501169 | − | 0.865349i | \(-0.667097\pi\) | ||||
−0.501169 | + | 0.865349i | \(0.667097\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.43008e6 | 1.18287 | 0.591435 | − | 0.806353i | \(-0.298562\pi\) | ||||
0.591435 | + | 0.806353i | \(0.298562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.32082e6 | −1.05320 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 63302.0 | 0.0495699 | 0.0247849 | − | 0.999693i | \(-0.492110\pi\) | ||||
0.0247849 | + | 0.999693i | \(0.492110\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 496614. | 0.375192 | 0.187596 | − | 0.982246i | \(-0.439930\pi\) | ||||
0.187596 | + | 0.982246i | \(0.439930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.15842e6 | 0.859803 | 0.429902 | − | 0.902876i | \(-0.358548\pi\) | ||||
0.429902 | + | 0.902876i | \(0.358548\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 304878. | 0.218485 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 705907. | 0.497168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.43886e6 | −0.979151 | −0.489575 | − | 0.871961i | \(-0.662848\pi\) | ||||
−0.489575 | + | 0.871961i | \(0.662848\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.88137e6 | −1.92772 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.45280e6 | −1.58666 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 181496. | 0.115465 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.05598e6 | −1.26552 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 989098. | 0.598954 | 0.299477 | − | 0.954104i | \(-0.403188\pi\) | ||||
0.299477 | + | 0.954104i | \(0.403188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.22050e6 | −1.30182 | −0.650909 | − | 0.759155i | \(-0.725612\pi\) | ||||
−0.650909 | + | 0.759155i | \(0.725612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.33008e6 | 1.34434 | 0.672171 | − | 0.740396i | \(-0.265362\pi\) | ||||
0.672171 | + | 0.740396i | \(0.265362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −427542. | −0.238963 | −0.119481 | − | 0.992836i | \(-0.538123\pi\) | ||||
−0.119481 | + | 0.992836i | \(0.538123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.63498e6 | 0.899569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −685260. | −0.365468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.29570e6 | 1.20561 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 88788.0 | 0.0452235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 396616. | 0.198976 | 0.0994879 | − | 0.995039i | \(-0.468280\pi\) | ||||
0.0994879 | + | 0.995039i | \(0.468280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.46597e6 | −0.713695 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.21819e6 | −1.54361 | −0.771805 | − | 0.635860i | \(-0.780646\pi\) | ||||
−0.771805 | + | 0.635860i | \(0.780646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.47699e6 | −1.15356 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.78018e6 | 1.23951 | 0.619755 | − | 0.784796i | \(-0.287232\pi\) | ||||
0.619755 | + | 0.784796i | \(0.287232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −338800. | −0.148895 | −0.0744475 | − | 0.997225i | \(-0.523719\pi\) | ||||
−0.0744475 | + | 0.997225i | \(0.523719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 362046. | 0.154642 | 0.0773209 | − | 0.997006i | \(-0.475363\pi\) | ||||
0.0773209 | + | 0.997006i | \(0.475363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.37082e6 | −0.998451 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 876528. | 0.358946 | 0.179473 | − | 0.983763i | \(-0.442561\pi\) | ||||
0.179473 | + | 0.983763i | \(0.442561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.25520e6 | −0.910787 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −302568. | −0.118875 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.98062e6 | −1.15516 | −0.577578 | − | 0.816335i | \(-0.696002\pi\) | ||||
−0.577578 | + | 0.816335i | \(0.696002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.82486e6 | −0.688326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.91441e6 | 1.45678 | 0.728391 | − | 0.685162i | \(-0.240268\pi\) | ||||
0.728391 | + | 0.685162i | \(0.240268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.84174e6 | −1.02975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.60661e6 | −1.28974 | −0.644868 | − | 0.764294i | \(-0.723088\pi\) | ||||
−0.644868 | + | 0.764294i | \(0.723088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.66644e6 | −0.928826 | −0.464413 | − | 0.885619i | \(-0.653735\pi\) | ||||
−0.464413 | + | 0.885619i | \(0.653735\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.38298e6 | −0.475513 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 213366. | 0.0714910 | 0.0357455 | − | 0.999361i | \(-0.488619\pi\) | ||||
0.0357455 | + | 0.999361i | \(0.488619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.12360e6 | −2.02565 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.60125e6 | 1.16134 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.09408e6 | −1.30371 | −0.651854 | − | 0.758345i | \(-0.726008\pi\) | ||||
−0.651854 | + | 0.758345i | \(0.726008\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −942366. | −0.292657 | −0.146328 | − | 0.989236i | \(-0.546746\pi\) | ||||
−0.146328 | + | 0.989236i | \(0.546746\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.30525e6 | 1.32049 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.81488e6 | −1.44079 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.84561e6 | −1.43232 | −0.716160 | − | 0.697936i | \(-0.754102\pi\) | ||||
−0.716160 | + | 0.697936i | \(0.754102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.68080e6 | −0.484887 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.95697e6 | 0.842804 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.73485e6 | −0.482754 | −0.241377 | − | 0.970431i | \(-0.577599\pi\) | ||||
−0.241377 | + | 0.970431i | \(0.577599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.65145e6 | −0.454109 | −0.227055 | − | 0.973882i | \(-0.572910\pi\) | ||||
−0.227055 | + | 0.973882i | \(0.572910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.73140e6 | 1.53918 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19932e6 | −0.318322 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.14360e6 | 1.07445 | 0.537223 | − | 0.843440i | \(-0.319473\pi\) | ||||
0.537223 | + | 0.843440i | \(0.319473\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.03966e6 | −0.779121 | −0.389561 | − | 0.921001i | \(-0.627373\pi\) | ||||
−0.389561 | + | 0.921001i | \(0.627373\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.97400e6 | 0.494474 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.54271e6 | −0.629703 | −0.314852 | − | 0.949141i | \(-0.601955\pi\) | ||||
−0.314852 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.43210e6 | −0.588806 | −0.294403 | − | 0.955681i | \(-0.595121\pi\) | ||||
−0.294403 | + | 0.955681i | \(0.595121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.24532e6 | 0.537500 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.82853e6 | −0.428042 | −0.214021 | − | 0.976829i | \(-0.568656\pi\) | ||||
−0.214021 | + | 0.976829i | \(0.568656\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.09059e6 | 0.483981 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.40374e6 | 0.544327 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.58063e6 | 0.354030 | 0.177015 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177015 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.09604e6 | −1.11681 | −0.558407 | − | 0.829567i | \(-0.688587\pi\) | ||||
−0.558407 | + | 0.829567i | \(0.688587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.02338e6 | 1.52263 | 0.761313 | − | 0.648384i | \(-0.224555\pi\) | ||||
0.761313 | + | 0.648384i | \(0.224555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.24845e6 | −0.901443 | −0.450722 | − | 0.892665i | \(-0.648833\pi\) | ||||
−0.450722 | + | 0.892665i | \(0.648833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −855148. | −0.179518 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.24454e6 | 0.255775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.84757e6 | −0.375722 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 559284. | 0.111377 | 0.0556883 | − | 0.998448i | \(-0.482265\pi\) | ||||
0.0556883 | + | 0.998448i | \(0.482265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.36872e6 | 1.64929 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.42615e6 | 0.275303 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.32057e6 | 0.252312 | 0.126156 | − | 0.992010i | \(-0.459736\pi\) | ||||
0.126156 | + | 0.992010i | \(0.459736\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.27193e6 | 1.17408 | 0.587040 | − | 0.809558i | \(-0.300293\pi\) | ||||
0.587040 | + | 0.809558i | \(0.300293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.09463e6 | −1.31466 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.38298e6 | −0.251144 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.93785e6 | 0.707959 | 0.353979 | − | 0.935253i | \(-0.384828\pi\) | ||||
0.353979 | + | 0.935253i | \(0.384828\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.59830e6 | −1.33905 | −0.669525 | − | 0.742790i | \(-0.733502\pi\) | ||||
−0.669525 | + | 0.742790i | \(0.733502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.33314e6 | 1.45405 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.82664e6 | 1.33900 | 0.669501 | − | 0.742812i | \(-0.266508\pi\) | ||||
0.669501 | + | 0.742812i | \(0.266508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −176498. | −0.0299011 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.10581e7 | −1.83722 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 608832. | 0.100178 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.94454e6 | −1.44366 | −0.721828 | − | 0.692072i | \(-0.756698\pi\) | ||||
−0.721828 | + | 0.692072i | \(0.756698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.07481e6 | −0.651407 | −0.325704 | − | 0.945472i | \(-0.605601\pi\) | ||||
−0.325704 | + | 0.945472i | \(0.605601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.07484e7 | 1.68584 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.12037e7 | 1.74069 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.63365e6 | −0.554019 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.10357e6 | −0.619837 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −806736. | −0.119608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.18676e7 | −1.74329 | −0.871644 | − | 0.490140i | \(-0.836946\pi\) | ||||
−0.871644 | + | 0.490140i | \(0.836946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.73542e6 | 0.682915 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.37801e6 | 0.768516 | 0.384258 | − | 0.923226i | \(-0.374457\pi\) | ||||
0.384258 | + | 0.923226i | \(0.374457\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.28702e6 | 0.320916 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.10073e6 | 0.292117 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.64878e6 | 0.771466 | 0.385733 | − | 0.922611i | \(-0.373949\pi\) | ||||
0.385733 | + | 0.922611i | \(0.373949\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.16314e6 | −0.292789 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.56407e6 | 0.606850 | 0.303425 | − | 0.952855i | \(-0.401870\pi\) | ||||
0.303425 | + | 0.952855i | \(0.401870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 734328. | 0.0967763 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.00165e6 | −1.03609 | −0.518047 | − | 0.855352i | \(-0.673341\pi\) | ||||
−0.518047 | + | 0.855352i | \(0.673341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.37164e7 | 1.76055 | 0.880275 | − | 0.474464i | \(-0.157358\pi\) | ||||
0.880275 | + | 0.474464i | \(0.157358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.65102e7 | −2.08249 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.09797e6 | 0.762510 | 0.381255 | − | 0.924470i | \(-0.375492\pi\) | ||||
0.381255 | + | 0.924470i | \(0.375492\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.72490e6 | 0.211994 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.25133e7 | −1.52476 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.08462e6 | −0.968422 | −0.484211 | − | 0.874951i | \(-0.660893\pi\) | ||||
−0.484211 | + | 0.874951i | \(0.660893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.46484e6 | −0.411524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.41575e6 | −0.165330 | −0.0826649 | − | 0.996577i | \(-0.526343\pi\) | ||||
−0.0826649 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00113e6 | 0.694929 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.75460e6 | 0.996941 | 0.498470 | − | 0.866907i | \(-0.333895\pi\) | ||||
0.498470 | + | 0.866907i | \(0.333895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.70276e6 | 0.982813 | 0.491407 | − | 0.870930i | \(-0.336483\pi\) | ||||
0.491407 | + | 0.870930i | \(0.336483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.04502e6 | 0.449296 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.69578e7 | 1.86809 | 0.934045 | − | 0.357157i | \(-0.116254\pi\) | ||||
0.934045 | + | 0.357157i | \(0.116254\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.05821e6 | −0.114675 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.76743e7 | 1.89973 | 0.949866 | − | 0.312658i | \(-0.101220\pi\) | ||||
0.949866 | + | 0.312658i | \(0.101220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.70636e6 | 1.02646 | 0.513232 | − | 0.858250i | \(-0.328448\pi\) | ||||
0.513232 | + | 0.858250i | \(0.328448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.48739e7 | −1.56027 | −0.780133 | − | 0.625613i | \(-0.784849\pi\) | ||||
−0.780133 | + | 0.625613i | \(0.784849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.30977e6 | 0.135199 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.59724e6 | −0.675557 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.08931e7 | 2.10561 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.26353e7 | −1.26331 | −0.631656 | − | 0.775248i | \(-0.717625\pi\) | ||||
−0.631656 | + | 0.775248i | \(0.717625\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.65433e7 | 2.61229 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.40218e6 | 0.136917 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.23398e6 | −0.599267 | −0.299634 | − | 0.954054i | \(-0.596864\pi\) | ||||
−0.299634 | + | 0.954054i | \(0.596864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.06874e7 | −1.01940 | −0.509701 | − | 0.860352i | \(-0.670244\pi\) | ||||
−0.509701 | + | 0.860352i | \(0.670244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.83258e7 | 1.72109 | 0.860544 | − | 0.509376i | \(-0.170124\pi\) | ||||
0.860544 | + | 0.509376i | \(0.170124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.15255e7 | −1.07411 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.28857e6 | 0.668897 | 0.334448 | − | 0.942414i | \(-0.391450\pi\) | ||||
0.334448 | + | 0.942414i | \(0.391450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.07194e6 | 0.188701 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.54337e6 | 0.407534 | 0.203767 | − | 0.979019i | \(-0.434681\pi\) | ||||
0.203767 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.10021e7 | −1.86964 | −0.934821 | − | 0.355120i | \(-0.884440\pi\) | ||||
−0.934821 | + | 0.355120i | \(0.884440\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.93452e6 | −0.169636 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.04372e7 | 1.77872 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.22394e6 | −0.705137 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.46923e6 | 0.295253 | 0.147627 | − | 0.989043i | \(-0.452837\pi\) | ||||
0.147627 | + | 0.989043i | \(0.452837\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.80916e7 | 1.51707 | 0.758536 | − | 0.651631i | \(-0.225915\pi\) | ||||
0.758536 | + | 0.651631i | \(0.225915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 831922. | 0.0692481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.67752e6 | 0.383675 | 0.191838 | − | 0.981427i | \(-0.438555\pi\) | ||||
0.191838 | + | 0.981427i | \(0.438555\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.54717e7 | 2.07411 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.17493e7 | 1.74541 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.68960e7 | −1.34614 | −0.673069 | − | 0.739579i | \(-0.735024\pi\) | ||||
−0.673069 | + | 0.739579i | \(0.735024\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.10492e7 | 1.65300 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.07168e6 | −0.707303 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.40964e6 | −0.185207 | −0.0926035 | − | 0.995703i | \(-0.529519\pi\) | ||||
−0.0926035 | + | 0.995703i | \(0.529519\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.73510e6 | −0.513991 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.86100e6 | 0.365744 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.77010e6 | −0.431090 | −0.215545 | − | 0.976494i | \(-0.569153\pi\) | ||||
−0.215545 | + | 0.976494i | \(0.569153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.09624e7 | −2.28092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.64828e7 | 1.20578 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.43716e7 | −1.03677 | −0.518385 | − | 0.855147i | \(-0.673467\pi\) | ||||
−0.518385 | + | 0.855147i | \(0.673467\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.45056e6 | −0.462124 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.91282e7 | −1.35154 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.40705e7 | 0.987353 | 0.493676 | − | 0.869646i | \(-0.335653\pi\) | ||||
0.493676 | + | 0.869646i | \(0.335653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.40043e6 | −0.373796 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.75000e6 | −0.257793 | −0.128897 | − | 0.991658i | \(-0.541144\pi\) | ||||
−0.128897 | + | 0.991658i | \(0.541144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.86387e6 | −0.397664 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.61318e7 | −1.76019 | −0.880093 | − | 0.474802i | \(-0.842520\pi\) | ||||
−0.880093 | + | 0.474802i | \(0.842520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −159072. | −0.0105711 | −0.00528557 | − | 0.999986i | \(-0.501682\pi\) | ||||
−0.00528557 | + | 0.999986i | \(0.501682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.08990e6 | −0.335984 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.39375e6 | −0.155910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.65311e7 | 1.71654 | 0.858272 | − | 0.513196i | \(-0.171539\pi\) | ||||
0.858272 | + | 0.513196i | \(0.171539\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.04536e7 | 0.667421 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.52032e7 | −0.964260 | −0.482130 | − | 0.876100i | \(-0.660137\pi\) | ||||
−0.482130 | + | 0.876100i | \(0.660137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.71380e6 | −0.295059 | −0.147530 | − | 0.989058i | \(-0.547132\pi\) | ||||
−0.147530 | + | 0.989058i | \(0.547132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.76233e6 | 0.171776 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.00324e7 | 1.22954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.58977e6 | −0.0969434 | −0.0484717 | − | 0.998825i | \(-0.515435\pi\) | ||||
−0.0484717 | + | 0.998825i | \(0.515435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.69095e6 | 0.583334 | 0.291667 | − | 0.956520i | \(-0.405790\pi\) | ||||
0.291667 | + | 0.956520i | \(0.405790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.89793e7 | 1.73314 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.92434e6 | 0.172657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.48326e6 | −0.556327 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.38736e6 | −0.369954 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.57170e6 | 0.0904549 | 0.0452275 | − | 0.998977i | \(-0.485599\pi\) | ||||
0.0452275 | + | 0.998977i | \(0.485599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 428358. | 0.0243425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.42940e7 | 0.807180 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.25298e6 | 0.125635 | 0.0628175 | − | 0.998025i | \(-0.479991\pi\) | ||||
0.0628175 | + | 0.998025i | \(0.479991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.64190e6 | −0.146403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.21027e6 | −0.0662360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.72872e7 | −0.940232 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.37938e7 | 1.27818 | 0.639090 | − | 0.769132i | \(-0.279311\pi\) | ||||
0.639090 | + | 0.769132i | \(0.279311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.32300e6 | −0.284187 | −0.142093 | − | 0.989853i | \(-0.545383\pi\) | ||||
−0.142093 | + | 0.989853i | \(0.545383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.04375e7 | 0.550431 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.74088e6 | 0.0912460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.48802e7 | −0.770464 | −0.385232 | − | 0.922820i | \(-0.625879\pi\) | ||||
−0.385232 | + | 0.922820i | \(0.625879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00601e7 | −1.03236 | −0.516182 | − | 0.856479i | \(-0.672647\pi\) | ||||
−0.516182 | + | 0.856479i | \(0.672647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.21539e7 | 0.617949 | 0.308975 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308975 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.21197e7 | 1.62325 | 0.811625 | − | 0.584179i | \(-0.198583\pi\) | ||||
0.811625 | + | 0.584179i | \(0.198583\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.50066e6 | 0.174798 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.08328e6 | 0.301941 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.01320e6 | −0.0496922 | −0.0248461 | − | 0.999691i | \(-0.507910\pi\) | ||||
−0.0248461 | + | 0.999691i | \(0.507910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.16681e6 | 0.154394 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.53991e6 | 0.122370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.35960e6 | 0.113013 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.01860e7 | −2.84886 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 234824. | 0.0110502 | 0.00552510 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552510 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.83802e7 | −1.31997 | −0.659985 | − | 0.751279i | \(-0.729437\pi\) | ||||
−0.659985 | + | 0.751279i | \(0.729437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00081e7 | −1.84997 | −0.924986 | − | 0.380001i | \(-0.875924\pi\) | ||||
−0.924986 | + | 0.380001i | \(0.875924\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.08030e7 | −0.950823 | −0.475411 | − | 0.879764i | \(-0.657701\pi\) | ||||
−0.475411 | + | 0.879764i | \(0.657701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.70904e7 | −1.68547 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.44050e7 | 0.647088 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.01920e7 | 0.455211 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.31750e6 | 0.146484 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.03559e7 | 1.33273 | 0.666367 | − | 0.745624i | \(-0.267848\pi\) | ||||
0.666367 | + | 0.745624i | \(0.267848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.58936e7 | 1.12396 | 0.561981 | − | 0.827150i | \(-0.310039\pi\) | ||||
0.561981 | + | 0.827150i | \(0.310039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.88813e7 | 0.814950 | 0.407475 | − | 0.913216i | \(-0.366409\pi\) | ||||
0.407475 | + | 0.913216i | \(0.366409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.34431e7 | −1.00048 | −0.500238 | − | 0.865888i | \(-0.666754\pi\) | ||||
−0.500238 | + | 0.865888i | \(0.666754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.54836e7 | 0.657079 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 851640. | 0.0357378 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 898128. | 0.0374784 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.58722e7 | −1.48033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.42988e7 | 2.22833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.58694e7 | 1.86166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.60873e6 | 0.226384 | 0.113192 | − | 0.993573i | \(-0.463892\pi\) | ||||
0.113192 | + | 0.993573i | \(0.463892\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.16215e7 | 0.863156 | 0.431578 | − | 0.902076i | \(-0.357957\pi\) | ||||
0.431578 | + | 0.902076i | \(0.357957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.18279e7 | 0.469602 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.20863e6 | 0.0474648 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.51695e7 | −1.76424 | −0.882119 | − | 0.471028i | \(-0.843883\pi\) | ||||
−0.882119 | + | 0.471028i | \(0.843883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.64828e7 | 0.636835 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.63312e7 | 2.16469 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.28729e7 | 0.869524 | 0.434762 | − | 0.900545i | \(-0.356832\pi\) | ||||
0.434762 | + | 0.900545i | \(0.356832\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12847e6 | −0.0426693 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.11506e7 | 1.53938 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.79616e7 | −0.668336 | −0.334168 | − | 0.942514i | \(-0.608455\pi\) | ||||
−0.334168 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.79697e7 | 0.661558 | 0.330779 | − | 0.943708i | \(-0.392689\pi\) | ||||
0.330779 | + | 0.943708i | \(0.392689\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.61324e7 | 0.956974 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.32115e7 | 1.56576 | 0.782879 | − | 0.622174i | \(-0.213750\pi\) | ||||
0.782879 | + | 0.622174i | \(0.213750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.10357e6 | 0.0758213 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.50965e6 | 0.267848 | 0.133924 | − | 0.990992i | \(-0.457242\pi\) | ||||
0.133924 | + | 0.990992i | \(0.457242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.83820e7 | 1.71662 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.48585e7 | 0.521708 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.57172e7 | 0.898288 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.47708e7 | 1.20198 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.69305e7 | 0.582242 | 0.291121 | − | 0.956686i | \(-0.405972\pi\) | ||||
0.291121 | + | 0.956686i | \(0.405972\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.86144e7 | 0.973949 | 0.486974 | − | 0.873416i | \(-0.338101\pi\) | ||||
0.486974 | + | 0.873416i | \(0.338101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22787e7 | 0.415787 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.69445e7 | −1.23826 | −0.619132 | − | 0.785287i | \(-0.712515\pi\) | ||||
−0.619132 | + | 0.785287i | \(0.712515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.98128e6 | 0.299489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.88787e7 | −1.28330 | −0.641650 | − | 0.766998i | \(-0.721750\pi\) | ||||
−0.641650 | + | 0.766998i | \(0.721750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.15755e7 | −1.36536 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.55568e7 | 0.505743 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.49212e7 | −0.806092 | −0.403046 | − | 0.915180i | \(-0.632049\pi\) | ||||
−0.403046 | + | 0.915180i | \(0.632049\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.37106e7 | 1.39968 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.01956e7 | 0.324845 | 0.162422 | − | 0.986721i | \(-0.448069\pi\) | ||||
0.162422 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 112.6.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 126.6.a.f.1.1 | 1 | |||
12.11 | even | 2 | 14.6.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 784.6.a.i.1.1 | 1 | |||
24.5 | odd | 2 | 448.6.a.l.1.1 | 1 | |||
24.11 | even | 2 | 448.6.a.e.1.1 | 1 | |||
28.27 | even | 2 | 882.6.a.x.1.1 | 1 | |||
60.23 | odd | 4 | 350.6.c.d.99.2 | 2 | |||
60.47 | odd | 4 | 350.6.c.d.99.1 | 2 | |||
60.59 | even | 2 | 350.6.a.i.1.1 | 1 | |||
84.11 | even | 6 | 98.6.c.c.79.1 | 2 | |||
84.23 | even | 6 | 98.6.c.c.67.1 | 2 | |||
84.47 | odd | 6 | 98.6.c.d.67.1 | 2 | |||
84.59 | odd | 6 | 98.6.c.d.79.1 | 2 | |||
84.83 | odd | 2 | 98.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
98.6.a.a.1.1 | 1 | 84.83 | odd | 2 | |||
98.6.c.c.67.1 | 2 | 84.23 | even | 6 | |||
98.6.c.c.79.1 | 2 | 84.11 | even | 6 | |||
98.6.c.d.67.1 | 2 | 84.47 | odd | 6 | |||
98.6.c.d.79.1 | 2 | 84.59 | odd | 6 | |||
112.6.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
126.6.a.f.1.1 | 1 | 4.3 | odd | 2 | |||
350.6.a.i.1.1 | 1 | 60.59 | even | 2 | |||
350.6.c.d.99.1 | 2 | 60.47 | odd | 4 | |||
350.6.c.d.99.2 | 2 | 60.23 | odd | 4 | |||
448.6.a.e.1.1 | 1 | 24.11 | even | 2 | |||
448.6.a.l.1.1 | 1 | 24.5 | odd | 2 | |||
784.6.a.i.1.1 | 1 | 21.20 | even | 2 | |||
882.6.a.x.1.1 | 1 | 28.27 | even | 2 | |||
1008.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial |