Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,6,Mod(1,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, 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("504.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.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: | \(80.8334451857\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{249}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 62 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(8.38987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.1 |
$q$-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 | ||||||||
\(5\) | 0.440532 | 0.00788048 | 0.00394024 | − | 0.999992i | \(-0.498746\pi\) | ||||
0.00394024 | + | 0.999992i | \(0.498746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 203.392 | 0.506818 | 0.253409 | − | 0.967359i | \(-0.418448\pi\) | ||||
0.253409 | + | 0.967359i | \(0.418448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −402.951 | −0.661294 | −0.330647 | − | 0.943755i | \(-0.607267\pi\) | ||||
−0.330647 | + | 0.943755i | \(0.607267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1761.53 | −1.47832 | −0.739160 | − | 0.673530i | \(-0.764777\pi\) | ||||
−0.739160 | + | 0.673530i | \(0.764777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1775.40 | 1.12827 | 0.564134 | − | 0.825683i | \(-0.309210\pi\) | ||||
0.564134 | + | 0.825683i | \(0.309210\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2710.72 | 1.06848 | 0.534239 | − | 0.845334i | \(-0.320598\pi\) | ||||
0.534239 | + | 0.845334i | \(0.320598\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3124.81 | −0.999938 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −781.595 | −0.172578 | −0.0862892 | − | 0.996270i | \(-0.527501\pi\) | ||||
−0.0862892 | + | 0.996270i | \(0.527501\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9655.74 | −1.80460 | −0.902300 | − | 0.431108i | \(-0.858123\pi\) | ||||
−0.902300 | + | 0.431108i | \(0.858123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.5861 | 0.00297854 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3788.80 | 0.454985 | 0.227493 | − | 0.973780i | \(-0.426947\pi\) | ||||
0.227493 | + | 0.973780i | \(0.426947\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18034.1 | 1.67546 | 0.837730 | − | 0.546084i | \(-0.183882\pi\) | ||||
0.837730 | + | 0.546084i | \(0.183882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13199.7 | −1.08866 | −0.544329 | − | 0.838872i | \(-0.683216\pi\) | ||||
−0.544329 | + | 0.838872i | \(0.683216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 26648.6 | 1.75966 | 0.879831 | − | 0.475286i | \(-0.157655\pi\) | ||||
0.879831 | + | 0.475286i | \(0.157655\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −22760.3 | −1.11298 | −0.556490 | − | 0.830854i | \(-0.687852\pi\) | ||||
−0.556490 | + | 0.830854i | \(0.687852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 89.6008 | 0.00399397 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1579.56 | −0.0590752 | −0.0295376 | − | 0.999564i | \(-0.509403\pi\) | ||||
−0.0295376 | + | 0.999564i | \(0.509403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35327.9 | −1.21561 | −0.607804 | − | 0.794087i | \(-0.707949\pi\) | ||||
−0.607804 | + | 0.794087i | \(0.707949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −177.513 | −0.00521131 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −48572.1 | −1.32190 | −0.660952 | − | 0.750428i | \(-0.729847\pi\) | ||||
−0.660952 | + | 0.750428i | \(0.729847\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12764.0 | −0.300498 | −0.150249 | − | 0.988648i | \(-0.548007\pi\) | ||||
−0.150249 | + | 0.988648i | \(0.548007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10152.3 | 0.222976 | 0.111488 | − | 0.993766i | \(-0.464438\pi\) | ||||
0.111488 | + | 0.993766i | \(0.464438\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9966.21 | 0.191559 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8703.14 | −0.156895 | −0.0784474 | − | 0.996918i | \(-0.524996\pi\) | ||||
−0.0784474 | + | 0.996918i | \(0.524996\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 26277.1 | 0.418680 | 0.209340 | − | 0.977843i | \(-0.432868\pi\) | ||||
0.209340 | + | 0.977843i | \(0.432868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −776.012 | −0.0116499 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −33598.5 | −0.449619 | −0.224809 | − | 0.974403i | \(-0.572176\pi\) | ||||
−0.224809 | + | 0.974403i | \(0.572176\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19744.6 | −0.249946 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 782.121 | 0.00889130 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23000.5 | 0.248203 | 0.124102 | − | 0.992270i | \(-0.460395\pi\) | ||||
0.124102 | + | 0.992270i | \(0.460395\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −57527.8 | −0.561144 | −0.280572 | − | 0.959833i | \(-0.590524\pi\) | ||||
−0.280572 | + | 0.959833i | \(0.590524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −167794. | −1.55842 | −0.779210 | − | 0.626763i | \(-0.784379\pi\) | ||||
−0.779210 | + | 0.626763i | \(0.784379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −67979.3 | −0.574007 | −0.287004 | − | 0.957929i | \(-0.592659\pi\) | ||||
−0.287004 | + | 0.957929i | \(0.592659\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 91585.8 | 0.738349 | 0.369175 | − | 0.929360i | \(-0.379640\pi\) | ||||
0.369175 | + | 0.929360i | \(0.379640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −154355. | −1.13717 | −0.568584 | − | 0.822625i | \(-0.692508\pi\) | ||||
−0.568584 | + | 0.822625i | \(0.692508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1194.16 | 0.00842012 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −86315.1 | −0.558752 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119683. | −0.743135 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2753.24 | −0.0157605 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −54085.3 | −0.297557 | −0.148778 | − | 0.988871i | \(-0.547534\pi\) | ||||
−0.148778 | + | 0.988871i | \(0.547534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −43981.5 | −0.223919 | −0.111960 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111960 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 86994.6 | 0.426445 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −79578.6 | −0.362239 | −0.181119 | − | 0.983461i | \(-0.557972\pi\) | ||||
−0.181119 | + | 0.983461i | \(0.557972\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −207284. | −0.909973 | −0.454987 | − | 0.890498i | \(-0.650356\pi\) | ||||
−0.454987 | + | 0.890498i | \(0.650356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −81957.1 | −0.335156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −344.318 | −0.00136000 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −382884. | −1.41287 | −0.706434 | − | 0.707779i | \(-0.749697\pi\) | ||||
−0.706434 | + | 0.707779i | \(0.749697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 50287.6 | 0.179481 | 0.0897406 | − | 0.995965i | \(-0.471396\pi\) | ||||
0.0897406 | + | 0.995965i | \(0.471396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4253.66 | −0.0142211 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 367616. | 1.19027 | 0.595135 | − | 0.803626i | \(-0.297099\pi\) | ||||
0.595135 | + | 0.803626i | \(0.297099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 132825. | 0.403847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −206972. | −0.610158 | −0.305079 | − | 0.952327i | \(-0.598683\pi\) | ||||
−0.305079 | + | 0.952327i | \(0.598683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −257285. | −0.713878 | −0.356939 | − | 0.934128i | \(-0.616180\pi\) | ||||
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −208923. | −0.562691 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 269032. | 0.683421 | 0.341710 | − | 0.939805i | \(-0.388994\pi\) | ||||
0.341710 | + | 0.939805i | \(0.388994\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −153115. | −0.377941 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −533998. | −1.24568 | −0.622841 | − | 0.782348i | \(-0.714022\pi\) | ||||
−0.622841 | + | 0.782348i | \(0.714022\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −629728. | −1.42875 | −0.714375 | − | 0.699763i | \(-0.753289\pi\) | ||||
−0.714375 | + | 0.699763i | \(0.753289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1669.09 | 0.00358550 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −358282. | −0.749239 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 452199. | 0.896903 | 0.448452 | − | 0.893807i | \(-0.351976\pi\) | ||||
0.448452 | + | 0.893807i | \(0.351976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −372356. | −0.719556 | −0.359778 | − | 0.933038i | \(-0.617148\pi\) | ||||
−0.359778 | + | 0.933038i | \(0.617148\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 250110. | 0.459161 | 0.229581 | − | 0.973290i | \(-0.426265\pi\) | ||||
0.229581 | + | 0.973290i | \(0.426265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −936025. | −1.67554 | −0.837770 | − | 0.546023i | \(-0.816141\pi\) | ||||
−0.837770 | + | 0.546023i | \(0.816141\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −38298.1 | −0.0652285 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7944.59 | 0.0132034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 361102. | 0.571827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 961698. | 1.48707 | 0.743537 | − | 0.668695i | \(-0.233147\pi\) | ||||
0.743537 | + | 0.668695i | \(0.233147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5814.88 | −0.00857916 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −473131. | −0.682075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 709812. | 0.977604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −624199. | −0.840545 | −0.420273 | − | 0.907398i | \(-0.638066\pi\) | ||||
−0.420273 | + | 0.907398i | \(0.638066\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −698450. | −0.899644 | −0.449822 | − | 0.893118i | \(-0.648513\pi\) | ||||
−0.449822 | + | 0.893118i | \(0.648513\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −987151. | −1.24393 | −0.621964 | − | 0.783046i | \(-0.713665\pi\) | ||||
−0.621964 | + | 0.783046i | \(0.713665\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.11183e6 | 1.34168 | 0.670839 | − | 0.741603i | \(-0.265934\pi\) | ||||
0.670839 | + | 0.741603i | \(0.265934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11739.6 | 0.0138670 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.50111e6 | −1.69988 | −0.849941 | − | 0.526878i | \(-0.823362\pi\) | ||||
−0.849941 | + | 0.526878i | \(0.823362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −172734. | −0.191574 | −0.0957869 | − | 0.995402i | \(-0.530537\pi\) | ||||
−0.0957869 | + | 0.995402i | \(0.530537\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1057.72 | 0.00112578 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −715400. | −0.746117 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 136981. | 0.137238 | 0.0686192 | − | 0.997643i | \(-0.478141\pi\) | ||||
0.0686192 | + | 0.997643i | \(0.478141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 551339. | 0.541524 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.97671e6 | 1.86686 | 0.933428 | − | 0.358765i | \(-0.116802\pi\) | ||||
0.933428 | + | 0.358765i | \(0.116802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 185651. | 0.171968 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −414337. | −0.369372 | −0.184686 | − | 0.982798i | \(-0.559127\pi\) | ||||
−0.184686 | + | 0.982798i | \(0.559127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10026.6 | −0.00877082 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −241748. | −0.203696 | −0.101848 | − | 0.994800i | \(-0.532476\pi\) | ||||
−0.101848 | + | 0.994800i | \(0.532476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 558814. | 0.462215 | 0.231107 | − | 0.972928i | \(-0.425765\pi\) | ||||
0.231107 | + | 0.972928i | \(0.425765\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −635561. | −0.506787 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 232158. | 0.181796 | 0.0908981 | − | 0.995860i | \(-0.471026\pi\) | ||||
0.0908981 | + | 0.995860i | \(0.471026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.85817e6 | −1.40385 | −0.701923 | − | 0.712253i | \(-0.747675\pi\) | ||||
−0.701923 | + | 0.712253i | \(0.747675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.42916e6 | 1.80297 | 0.901487 | − | 0.432805i | \(-0.142476\pi\) | ||||
0.901487 | + | 0.432805i | \(0.142476\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 883670. | 0.633265 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.68314e6 | 1.18543 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.61912e6 | 1.10182 | 0.550908 | − | 0.834566i | \(-0.314281\pi\) | ||||
0.550908 | + | 0.834566i | \(0.314281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −695.846 | −0.000465541 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.09229e6 | −0.706577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −646784. | −0.411474 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15563.1 | −0.00957958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 936495. | 0.567100 | 0.283550 | − | 0.958957i | \(-0.408488\pi\) | ||||
0.283550 | + | 0.958957i | \(0.408488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −48784.9 | −0.0286012 | −0.0143006 | − | 0.999898i | \(-0.504552\pi\) | ||||
−0.0143006 | + | 0.999898i | \(0.504552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.31634e6 | 0.759466 | 0.379733 | − | 0.925096i | \(-0.376016\pi\) | ||||
0.379733 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.08008e6 | 1.72153 | 0.860763 | − | 0.509006i | \(-0.169987\pi\) | ||||
0.860763 | + | 0.509006i | \(0.169987\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −158970. | −0.0874659 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.12743e6 | −1.66794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.25915e6 | 0.661253 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.30578e6 | 0.665090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.20819e6 | −1.60950 | −0.804749 | − | 0.593615i | \(-0.797700\pi\) | ||||
−0.804749 | + | 0.593615i | \(0.797700\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21397.6 | −0.0104172 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.77901e6 | 1.33295 | 0.666477 | − | 0.745525i | \(-0.267801\pi\) | ||||
0.666477 | + | 0.745525i | \(0.267801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.96390e6 | −0.914604 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.01762e6 | −1.34537 | −0.672684 | − | 0.739930i | \(-0.734859\pi\) | ||||
−0.672684 | + | 0.739930i | \(0.734859\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.35064e6 | 0.593574 | 0.296787 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296787 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −158501. | −0.0677011 | −0.0338506 | − | 0.999427i | \(-0.510777\pi\) | ||||
−0.0338506 | + | 0.999427i | \(0.510777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5622.96 | −0.00236807 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.54504e6 | 0.632709 | 0.316354 | − | 0.948641i | \(-0.397541\pi\) | ||||
0.316354 | + | 0.948641i | \(0.397541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 675948. | 0.272989 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4472.43 | 0.00175716 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.51991e6 | 0.976607 | 0.488304 | − | 0.872674i | \(-0.337616\pi\) | ||||
0.488304 | + | 0.872674i | \(0.337616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.11525e6 | −0.420667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.94012e6 | 1.09419 | 0.547096 | − | 0.837070i | \(-0.315733\pi\) | ||||
0.547096 | + | 0.837070i | \(0.315733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 314945. | 0.114125 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.62230e6 | 1.65295 | 0.826475 | − | 0.562973i | \(-0.190342\pi\) | ||||
0.826475 | + | 0.562973i | \(0.190342\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.60273e6 | 1.60331 | 0.801656 | − | 0.597785i | \(-0.203952\pi\) | ||||
0.801656 | + | 0.597785i | \(0.203952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4390.44 | 0.00150958 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.16928e6 | 1.06191 | 0.530953 | − | 0.847401i | \(-0.321834\pi\) | ||||
0.530953 | + | 0.847401i | \(0.321834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.77503e6 | −1.57955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3834.01 | −0.00123641 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.11443e6 | −0.991749 | −0.495874 | − | 0.868394i | \(-0.665152\pi\) | ||||
−0.495874 | + | 0.868394i | \(0.665152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.35836e6 | −1.97462 | −0.987312 | − | 0.158795i | \(-0.949239\pi\) | ||||
−0.987312 | + | 0.158795i | \(0.949239\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.89079e6 | 1.19337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 770612. | 0.230595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.46377e6 | 1.31945 | 0.659726 | − | 0.751507i | \(-0.270673\pi\) | ||||
0.659726 | + | 0.751507i | \(0.270673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −77398.3 | −0.0223283 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11575.9 | 0.00329940 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.96754e6 | 0.825773 | 0.412887 | − | 0.910782i | \(-0.364521\pi\) | ||||
0.412887 | + | 0.910782i | \(0.364521\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.81021e6 | 1.87264 | 0.936322 | − | 0.351143i | \(-0.114207\pi\) | ||||
0.936322 | + | 0.351143i | \(0.114207\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.50445e6 | 1.47823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73107e6 | −0.459457 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 675836. | 0.175246 | 0.0876230 | − | 0.996154i | \(-0.472073\pi\) | ||||
0.0876230 | + | 0.996154i | \(0.472073\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.24399e6 | −0.318859 | −0.159429 | − | 0.987209i | \(-0.550965\pi\) | ||||
−0.159429 | + | 0.987209i | \(0.550965\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.81262e6 | 1.20553 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 313929. | 0.0777445 | 0.0388723 | − | 0.999244i | \(-0.487623\pi\) | ||||
0.0388723 | + | 0.999244i | \(0.487623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.43067e6 | 0.830557 | 0.415279 | − | 0.909694i | \(-0.363684\pi\) | ||||
0.415279 | + | 0.909694i | \(0.363684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14801.2 | −0.00354321 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −363883. | −0.0851816 | −0.0425908 | − | 0.999093i | \(-0.513561\pi\) | ||||
−0.0425908 | + | 0.999093i | \(0.513561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.66799e6 | 0.849154 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8698.14 | −0.00196969 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.52131e6 | −1.23666 | −0.618332 | − | 0.785917i | \(-0.712191\pi\) | ||||
−0.618332 | + | 0.785917i | \(0.712191\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 300842. | 0.0659306 | 0.0329653 | − | 0.999456i | \(-0.489505\pi\) | ||||
0.0329653 | + | 0.999456i | \(0.489505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.80343e6 | −1.47494 | −0.737472 | − | 0.675378i | \(-0.763981\pi\) | ||||
−0.737472 | + | 0.675378i | \(0.763981\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.40398e6 | −0.510080 | −0.255040 | − | 0.966931i | \(-0.582089\pi\) | ||||
−0.255040 | + | 0.966931i | \(0.582089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.38003e6 | −0.499633 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.68471e6 | −0.551752 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.54778e6 | −1.12820 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.09265e6 | −1.01416 | −0.507078 | − | 0.861900i | \(-0.669274\pi\) | ||||
−0.507078 | + | 0.861900i | \(0.669274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.52670e6 | −0.300879 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10132.4 | 0.00195596 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.33002e6 | −1.40050 | −0.700249 | − | 0.713899i | \(-0.746928\pi\) | ||||
−0.700249 | + | 0.713899i | \(0.746928\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.36290e6 | −0.255130 | −0.127565 | − | 0.991830i | \(-0.540716\pi\) | ||||
−0.127565 | + | 0.991830i | \(0.540716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.37680e6 | 0.255126 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −625436. | −0.113577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.05087e6 | 0.908060 | 0.454030 | − | 0.890986i | \(-0.349986\pi\) | ||||
0.454030 | + | 0.890986i | \(0.349986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.93004e6 | 1.04505 | 0.522526 | − | 0.852623i | \(-0.324990\pi\) | ||||
0.522526 | + | 0.852623i | \(0.324990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25342.9 | −0.00442208 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.01042e6 | 1.19936 | 0.599680 | − | 0.800240i | \(-0.295294\pi\) | ||||
0.599680 | + | 0.800240i | \(0.295294\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 497464. | 0.0842770 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −73918.9 | −0.0122811 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.42011e6 | 0.891829 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.40461e6 | 0.710908 | 0.355454 | − | 0.934694i | \(-0.384326\pi\) | ||||
0.355454 | + | 0.934694i | \(0.384326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.18270e6 | −1.14824 | −0.574121 | − | 0.818770i | \(-0.694656\pi\) | ||||
−0.574121 | + | 0.818770i | \(0.694656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.70089e7 | 2.66778 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 911672. | 0.141644 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.26686e6 | −1.10797 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29947.1 | −0.00452345 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 488344. | 0.0724026 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.23327e6 | 1.35632 | 0.678161 | − | 0.734914i | \(-0.262777\pi\) | ||||
0.678161 | + | 0.734914i | \(0.262777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40346.5 | 0.00581855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.61993e6 | −0.660187 | −0.330093 | − | 0.943948i | \(-0.607080\pi\) | ||||
−0.330093 | + | 0.943948i | \(0.607080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.38764e6 | −0.194715 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −426454. | −0.0593006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.71536e6 | −1.32685 | −0.663424 | − | 0.748244i | \(-0.730897\pi\) | ||||
−0.663424 | + | 0.748244i | \(0.730897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.31882e6 | 0.719923 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.70410e6 | −1.29028 | −0.645141 | − | 0.764064i | \(-0.723201\pi\) | ||||
−0.645141 | + | 0.764064i | \(0.723201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −67998.3 | −0.00896143 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.91242e6 | −1.02454 | −0.512270 | − | 0.858825i | \(-0.671195\pi\) | ||||
−0.512270 | + | 0.858825i | \(0.671195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.91956e6 | 1.01651 | 0.508254 | − | 0.861207i | \(-0.330291\pi\) | ||||
0.508254 | + | 0.861207i | \(0.330291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.47048e6 | −1.06841 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.81761e6 | −0.852497 | −0.426248 | − | 0.904606i | \(-0.640165\pi\) | ||||
−0.426248 | + | 0.904606i | \(0.640165\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.28758e6 | 0.158246 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.62925e6 | −0.564079 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.75763e6 | −0.689682 | −0.344841 | − | 0.938661i | \(-0.612067\pi\) | ||||
−0.344841 | + | 0.938661i | \(0.612067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.71428e7 | −2.03607 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.22350e6 | −0.142879 | −0.0714393 | − | 0.997445i | \(-0.522759\pi\) | ||||
−0.0714393 | + | 0.997445i | \(0.522759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38024.6 | −0.00440324 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 590873. | 0.0672864 | 0.0336432 | − | 0.999434i | \(-0.489289\pi\) | ||||
0.0336432 | + | 0.999434i | \(0.489289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.27472e7 | −1.43955 | −0.719776 | − | 0.694207i | \(-0.755755\pi\) | ||||
−0.719776 | + | 0.694207i | \(0.755755\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −52724.1 | −0.00585626 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.36918e6 | 0.811797 | 0.405899 | − | 0.913918i | \(-0.366959\pi\) | ||||
0.405899 | + | 0.913918i | \(0.366959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.07381e7 | −1.16365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.05204e6 | −0.543020 | −0.271510 | − | 0.962436i | \(-0.587523\pi\) | ||||
−0.271510 | + | 0.962436i | \(0.587523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.04265e7 | −1.10262 | −0.551309 | − | 0.834301i | \(-0.685871\pi\) | ||||
−0.551309 | + | 0.834301i | \(0.685871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.84513e7 | 1.93553 | 0.967765 | − | 0.251856i | \(-0.0810410\pi\) | ||||
0.967765 | + | 0.251856i | \(0.0810410\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.64633e6 | −0.169940 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.76381e6 | 0.999814 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.67410e6 | −0.672614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.28762e6 | 0.228723 | 0.114362 | − | 0.993439i | \(-0.463518\pi\) | ||||
0.114362 | + | 0.993439i | \(0.463518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23826.3 | −0.00234489 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −967487. | −0.0944705 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.98845e6 | 0.671793 | 0.335897 | − | 0.941899i | \(-0.390961\pi\) | ||||
0.335897 | + | 0.941899i | \(0.390961\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.47461e7 | −1.40653 | −0.703265 | − | 0.710928i | \(-0.748275\pi\) | ||||
−0.703265 | + | 0.710928i | \(0.748275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.20477e6 | 0.300979 | 0.150490 | − | 0.988612i | \(-0.451915\pi\) | ||||
0.150490 | + | 0.988612i | \(0.451915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −321269. | −0.0299404 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.10963e6 | 0.193608 | 0.0968041 | − | 0.995303i | \(-0.469138\pi\) | ||||
0.0968041 | + | 0.995303i | \(0.469138\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19375.3 | −0.00176459 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.74852e7 | 1.56840 | 0.784202 | − | 0.620505i | \(-0.213072\pi\) | ||||
0.784202 | + | 0.620505i | \(0.213072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −973131. | −0.0866299 | −0.0433149 | − | 0.999061i | \(-0.513792\pi\) | ||||
−0.0433149 | + | 0.999061i | \(0.513792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 38323.9 | 0.00336059 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.11869e6 | −0.184396 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.18542e6 | −0.616092 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 651051. | 0.0554086 | 0.0277043 | − | 0.999616i | \(-0.491180\pi\) | ||||
0.0277043 | + | 0.999616i | \(0.491180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.62839e6 | 0.388113 | 0.194057 | − | 0.980990i | \(-0.437835\pi\) | ||||
0.194057 | + | 0.980990i | \(0.437835\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.12702e6 | 0.0938119 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.77222e7 | −1.45367 | −0.726836 | − | 0.686811i | \(-0.759010\pi\) | ||||
−0.726836 | + | 0.686811i | \(0.759010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35057.0 | −0.00285462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.17128e6 | 0.736007 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.41125e7 | 1.12437 | 0.562186 | − | 0.827011i | \(-0.309960\pi\) | ||||
0.562186 | + | 0.827011i | \(0.309960\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −91315.3 | −0.00717103 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.17676e7 | −2.47687 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.02386e6 | −0.0786947 | −0.0393474 | − | 0.999226i | \(-0.512528\pi\) | ||||
−0.0393474 | + | 0.999226i | \(0.512528\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.72664e6 | 0.513346 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.81886e6 | −0.212092 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.14313e6 | −0.533670 | −0.266835 | − | 0.963742i | \(-0.585978\pi\) | ||||
−0.266835 | + | 0.963742i | \(0.585978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.61740e7 | −1.92818 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36104.8 | −0.00264119 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.74905e7 | −1.26177 | −0.630884 | − | 0.775878i | \(-0.717307\pi\) | ||||
−0.630884 | + | 0.775878i | \(0.717307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.22193e6 | −0.589027 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44233e6 | 0.172568 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.07868e6 | −0.566897 | −0.283449 | − | 0.958987i | \(-0.591479\pi\) | ||||
−0.283449 | + | 0.958987i | \(0.591479\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.32516e7 | 1.60939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.42261e6 | −0.441521 | −0.220761 | − | 0.975328i | \(-0.570854\pi\) | ||||
−0.220761 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.87917e6 | −0.669965 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.45407e7 | −1.65301 | −0.826506 | − | 0.562927i | \(-0.809675\pi\) | ||||
−0.826506 | + | 0.562927i | \(0.809675\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.53250e7 | 1.01842 | 0.509212 | − | 0.860641i | \(-0.329937\pi\) | ||||
0.509212 | + | 0.860641i | \(0.329937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −168673. | −0.0111341 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.33099e6 | −0.216954 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.24971e7 | −0.808554 | −0.404277 | − | 0.914637i | \(-0.632477\pi\) | ||||
−0.404277 | + | 0.914637i | \(0.632477\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22153.3 | 0.00141440 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.56124e7 | −0.990217 | −0.495108 | − | 0.868831i | \(-0.664872\pi\) | ||||
−0.495108 | + | 0.868831i | \(0.664872\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.82820e7 | −1.14436 | −0.572179 | − | 0.820128i | \(-0.693902\pi\) | ||||
−0.572179 | + | 0.820128i | \(0.693902\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.48770e6 | 0.279070 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 636485. | 0.0390661 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.32020e7 | 0.805051 | 0.402526 | − | 0.915409i | \(-0.368132\pi\) | ||||
0.402526 | + | 0.915409i | \(0.368132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.45645e7 | 0.876689 | 0.438344 | − | 0.898807i | \(-0.355565\pi\) | ||||
0.438344 | + | 0.898807i | \(0.355565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.01723e7 | 1.80449 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.20177e7 | 1.89037 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.59610e6 | −0.152298 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 161947. | 0.00937990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.78163e7 | 1.02537 | 0.512685 | − | 0.858577i | \(-0.328651\pi\) | ||||
0.512685 | + | 0.858577i | \(0.328651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.56339e6 | −0.429809 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.42354e7 | 0.803874 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.29429e7 | 1.27939 | 0.639696 | − | 0.768628i | \(-0.279060\pi\) | ||||
0.639696 | + | 0.768628i | \(0.279060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.69424e7 | −2.60134 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.06490e6 | 0.113008 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 58513.9 | 0.00318251 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.92525e6 | −0.157142 | −0.0785710 | − | 0.996909i | \(-0.525036\pi\) | ||||
−0.0785710 | + | 0.996909i | \(0.525036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.22818e6 | 0.385902 | 0.192951 | − | 0.981208i | \(-0.438194\pi\) | ||||
0.192951 | + | 0.981208i | \(0.438194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −91177.8 | −0.00480834 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.34347e7 | −1.22830 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.85795e7 | −1.47978 | −0.739890 | − | 0.672728i | \(-0.765122\pi\) | ||||
−0.739890 | + | 0.672728i | \(0.765122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.31774e6 | 0.0678157 | 0.0339078 | − | 0.999425i | \(-0.489205\pi\) | ||||
0.0339078 | + | 0.999425i | \(0.489205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.02202e7 | 1.53650 | 0.768252 | − | 0.640147i | \(-0.221127\pi\) | ||||
0.768252 | + | 0.640147i | \(0.221127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.04061e6 | −0.406352 | −0.203176 | − | 0.979142i | \(-0.565126\pi\) | ||||
−0.203176 | + | 0.979142i | \(0.565126\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.22944e6 | −0.211189 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −113342. | −0.00562570 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.62114e6 | 0.226644 | 0.113322 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113322 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.99003e7 | −0.970217 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −92037.4 | −0.00443427 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.86445e6 | −0.280879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.02704e7 | 0.486142 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.20395e7 | 1.03712 | 0.518559 | − | 0.855042i | \(-0.326468\pi\) | ||||
0.518559 | + | 0.855042i | \(0.326468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.48477e7 | 0.690569 | 0.345284 | − | 0.938498i | \(-0.387782\pi\) | ||||
0.345284 | + | 0.938498i | \(0.387782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −668744. | −0.0309227 | −0.0154613 | − | 0.999880i | \(-0.504922\pi\) | ||||
−0.0154613 | + | 0.999880i | \(0.504922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.09838e7 | 0.502024 | 0.251012 | − | 0.967984i | \(-0.419237\pi\) | ||||
0.251012 | + | 0.967984i | \(0.419237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 118517. | 0.00538569 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.77015e6 | −0.0795171 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.95722e7 | 0.874166 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −134909. | −0.00595690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.15400e7 | 1.82376 | 0.911879 | − | 0.410460i | \(-0.134632\pi\) | ||||
0.911879 | + | 0.410460i | \(0.134632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.03497e7 | −1.75146 | −0.875730 | − | 0.482801i | \(-0.839619\pi\) | ||||
−0.875730 | + | 0.482801i | \(0.839619\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.10878e7 | −0.910183 | −0.455092 | − | 0.890445i | \(-0.650394\pi\) | ||||
−0.455092 | + | 0.890445i | \(0.650394\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.52443e6 | −0.150411 | −0.0752056 | − | 0.997168i | \(-0.523961\pi\) | ||||
−0.0752056 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.65018e6 | −0.112466 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.73119e7 | 1.98537 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −235244. | −0.00981658 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.54687e6 | 0.311435 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00929e7 | 1.64534 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −277415. | −0.0112592 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.95093e7 | −1.19108 | −0.595540 | − | 0.803325i | \(-0.703062\pi\) | ||||
−0.595540 | + | 0.803325i | \(0.703062\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32643e7 | −0.529527 | −0.264763 | − | 0.964313i | \(-0.585294\pi\) | ||||
−0.264763 | + | 0.964313i | \(0.585294\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.34455e6 | 0.212195 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.15509e6 | −0.0846336 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.89419e7 | 0.739834 | 0.369917 | − | 0.929065i | \(-0.379386\pi\) | ||||
0.369917 | + | 0.929065i | \(0.379386\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.14327e6 | 0.198717 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.18393e7 | −0.454957 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.92211e7 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.26274e6 | 0.161181 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −157835. | −0.00590437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.46944e6 | −0.240723 | −0.120362 | − | 0.992730i | \(-0.538405\pi\) | ||||
−0.120362 | + | 0.992730i | \(0.538405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.11564e7 | 1.51518 | 0.757588 | − | 0.652733i | \(-0.226378\pi\) | ||||
0.757588 | + | 0.652733i | \(0.226378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.88854e7 | 1.79019 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.00657e7 | 1.08942 | 0.544711 | − | 0.838624i | \(-0.316639\pi\) | ||||
0.544711 | + | 0.838624i | \(0.316639\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.09089e6 | −0.147453 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.95724e7 | −1.05476 | −0.527381 | − | 0.849629i | \(-0.676826\pi\) | ||||
−0.527381 | + | 0.849629i | \(0.676826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 199208. | 0.00706803 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.89935e6 | −0.136913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.46041e7 | 2.25658 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −164035. | −0.00567045 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.49436e7 | 1.20172 | 0.600858 | − | 0.799356i | \(-0.294826\pi\) | ||||
0.600858 | + | 0.799356i | \(0.294826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.13425e7 | 0.386065 | 0.193032 | − | 0.981192i | \(-0.438168\pi\) | ||||
0.193032 | + | 0.981192i | \(0.438168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.01569e7 | −0.343938 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.24082e7 | −1.42139 | −0.710694 | − | 0.703501i | \(-0.751619\pi\) | ||||
−0.710694 | + | 0.703501i | \(0.751619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.83366e6 | −0.227875 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.98560e7 | 1.31556 | 0.657779 | − | 0.753211i | \(-0.271496\pi\) | ||||
0.657779 | + | 0.753211i | \(0.271496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 110182. | 0.00361841 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.57806e7 | −1.16321 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.81338e7 | 0.910007 | 0.455004 | − | 0.890490i | \(-0.349638\pi\) | ||||
0.455004 | + | 0.890490i | \(0.349638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −412349. | −0.0132041 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.67938e7 | 1.80952 | 0.904760 | − | 0.425922i | \(-0.140050\pi\) | ||||
0.904760 | + | 0.425922i | \(0.140050\pi\) | |||||||
\(998\) | 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 | 504.6.a.t.1.1 | 2 | ||
3.2 | odd | 2 | 168.6.a.h.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 1008.6.a.bu.1.1 | 2 | |||
12.11 | even | 2 | 336.6.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.a.h.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
336.6.a.w.1.2 | 2 | 12.11 | even | 2 | |||
504.6.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1008.6.a.bu.1.1 | 2 | 4.3 | odd | 2 |