Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,6,Mod(1,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.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: | \(3.84921167551\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 24.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 94.0000 | 1.68152 | 0.840762 | − | 0.541406i | \(-0.182108\pi\) | ||||
0.840762 | + | 0.541406i | \(0.182108\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 144.000 | 1.11075 | 0.555376 | − | 0.831599i | \(-0.312574\pi\) | ||||
0.555376 | + | 0.831599i | \(0.312574\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −380.000 | −0.946895 | −0.473448 | − | 0.880822i | \(-0.656991\pi\) | ||||
−0.473448 | + | 0.880822i | \(0.656991\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 814.000 | 1.33588 | 0.667938 | − | 0.744217i | \(-0.267177\pi\) | ||||
0.667938 | + | 0.744217i | \(0.267177\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −846.000 | −0.970828 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −862.000 | −0.723411 | −0.361705 | − | 0.932292i | \(-0.617805\pi\) | ||||
−0.361705 | + | 0.932292i | \(0.617805\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1156.00 | −0.734639 | −0.367319 | − | 0.930095i | \(-0.619724\pi\) | ||||
−0.367319 | + | 0.930095i | \(0.619724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1296.00 | −0.641293 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −488.000 | −0.192354 | −0.0961768 | − | 0.995364i | \(-0.530661\pi\) | ||||
−0.0961768 | + | 0.995364i | \(0.530661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5711.00 | 1.82752 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5466.00 | −1.20691 | −0.603455 | − | 0.797397i | \(-0.706210\pi\) | ||||
−0.603455 | + | 0.797397i | \(0.706210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9560.00 | 1.78671 | 0.893354 | − | 0.449353i | \(-0.148346\pi\) | ||||
0.893354 | + | 0.449353i | \(0.148346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3420.00 | 0.546690 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13536.0 | 1.86776 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10506.0 | −1.26163 | −0.630817 | − | 0.775932i | \(-0.717280\pi\) | ||||
−0.630817 | + | 0.775932i | \(0.717280\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7326.00 | −0.771268 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5190.00 | −0.482178 | −0.241089 | − | 0.970503i | \(-0.577505\pi\) | ||||
−0.241089 | + | 0.970503i | \(0.577505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17084.0 | −1.40902 | −0.704512 | − | 0.709692i | \(-0.748834\pi\) | ||||
−0.704512 | + | 0.709692i | \(0.748834\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7614.00 | 0.560508 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3168.00 | 0.209190 | 0.104595 | − | 0.994515i | \(-0.466645\pi\) | ||||
0.104595 | + | 0.994515i | \(0.466645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3929.00 | 0.233772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7758.00 | 0.417661 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −24770.0 | −1.21126 | −0.605629 | − | 0.795747i | \(-0.707078\pi\) | ||||
−0.605629 | + | 0.795747i | \(0.707078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −35720.0 | −1.59223 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10404.0 | 0.424144 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17380.0 | 0.650010 | 0.325005 | − | 0.945712i | \(-0.394634\pi\) | ||||
0.325005 | + | 0.945712i | \(0.394634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4366.00 | 0.150231 | 0.0751154 | − | 0.997175i | \(-0.476067\pi\) | ||||
0.0751154 | + | 0.997175i | \(0.476067\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11664.0 | 0.370251 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 76516.0 | 2.24631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5284.00 | −0.143806 | −0.0719028 | − | 0.997412i | \(-0.522907\pi\) | ||||
−0.0719028 | + | 0.997412i | \(0.522907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4392.00 | 0.111055 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8360.00 | 0.196816 | 0.0984080 | − | 0.995146i | \(-0.468625\pi\) | ||||
0.0984080 | + | 0.995146i | \(0.468625\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 39466.0 | 0.866794 | 0.433397 | − | 0.901203i | \(-0.357315\pi\) | ||||
0.433397 | + | 0.901203i | \(0.357315\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −51399.0 | −1.05512 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −54720.0 | −1.05177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42376.0 | 0.763928 | 0.381964 | − | 0.924177i | \(-0.375248\pi\) | ||||
0.381964 | + | 0.924177i | \(0.375248\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −61828.0 | −0.985122 | −0.492561 | − | 0.870278i | \(-0.663939\pi\) | ||||
−0.492561 | + | 0.870278i | \(0.663939\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −81028.0 | −1.21643 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 49194.0 | 0.696809 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −63078.0 | −0.844117 | −0.422059 | − | 0.906568i | \(-0.638692\pi\) | ||||
−0.422059 | + | 0.906568i | \(0.638692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 117216. | 1.48383 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −86040.0 | −1.03156 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −108664. | −1.23531 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16318.0 | −0.176091 | −0.0880456 | − | 0.996116i | \(-0.528062\pi\) | ||||
−0.0880456 | + | 0.996116i | \(0.528062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30780.0 | −0.315632 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 134766. | 1.31455 | 0.657275 | − | 0.753651i | \(-0.271709\pi\) | ||||
0.657275 | + | 0.753651i | \(0.271709\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 45184.0 | 0.419654 | 0.209827 | − | 0.977739i | \(-0.432710\pi\) | ||||
0.209827 | + | 0.977739i | \(0.432710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −121824. | −1.07835 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 143124. | 1.20852 | 0.604259 | − | 0.796788i | \(-0.293469\pi\) | ||||
0.604259 | + | 0.796788i | \(0.293469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 153070. | 1.23402 | 0.617012 | − | 0.786953i | \(-0.288343\pi\) | ||||
0.617012 | + | 0.786953i | \(0.288343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 94554.0 | 0.728404 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −64494.0 | −0.475142 | −0.237571 | − | 0.971370i | \(-0.576351\pi\) | ||||
−0.237571 | + | 0.971370i | \(0.576351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −45872.0 | −0.323447 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 65934.0 | 0.445292 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −124128. | −0.803530 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16651.0 | −0.103390 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 46710.0 | 0.278386 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 243084. | 1.39149 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 33256.0 | 0.182962 | 0.0914810 | − | 0.995807i | \(-0.470840\pi\) | ||||
0.0914810 | + | 0.995807i | \(0.470840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 153756. | 0.813500 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149284. | −0.760038 | −0.380019 | − | 0.924979i | \(-0.624082\pi\) | ||||
−0.380019 | + | 0.924979i | \(0.624082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −166464. | −0.816002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −68526.0 | −0.323609 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 148602. | 0.676431 | 0.338215 | − | 0.941069i | \(-0.390177\pi\) | ||||
0.338215 | + | 0.941069i | \(0.390177\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −324012. | −1.42241 | −0.711204 | − | 0.702986i | \(-0.751850\pi\) | ||||
−0.711204 | + | 0.702986i | \(0.751850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28512.0 | −0.120776 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −309320. | −1.26493 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −513804. | −2.02945 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −35361.0 | −0.134968 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −59986.0 | −0.221352 | −0.110676 | − | 0.993857i | \(-0.535302\pi\) | ||||
−0.110676 | + | 0.993857i | \(0.535302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 91520.0 | 0.326643 | 0.163322 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163322 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −69822.0 | −0.241137 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 898640. | 3.00439 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 345550. | 1.11882 | 0.559412 | − | 0.828890i | \(-0.311027\pi\) | ||||
0.559412 | + | 0.828890i | \(0.311027\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 222930. | 0.699320 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −70272.0 | −0.213657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −634164. | −1.86953 | −0.934765 | − | 0.355266i | \(-0.884390\pi\) | ||||
−0.934765 | + | 0.355266i | \(0.884390\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 321480. | 0.919272 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −415848. | −1.15383 | −0.576917 | − | 0.816803i | \(-0.695744\pi\) | ||||
−0.576917 | + | 0.816803i | \(0.695744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 291303. | 0.784564 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −93636.0 | −0.244880 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −324282. | −0.823773 | −0.411887 | − | 0.911235i | \(-0.635130\pi\) | ||||
−0.411887 | + | 0.911235i | \(0.635130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 822384. | 2.02992 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −156420. | −0.375283 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 606828. | 1.41558 | 0.707788 | − | 0.706425i | \(-0.249693\pi\) | ||||
0.707788 | + | 0.706425i | \(0.249693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 463254. | 1.05105 | 0.525524 | − | 0.850779i | \(-0.323869\pi\) | ||||
0.525524 | + | 0.850779i | \(0.323869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −39294.0 | −0.0867358 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −987564. | −2.12147 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 327560. | 0.684994 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −104976. | −0.213764 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 955008. | 1.89419 | 0.947095 | − | 0.320953i | \(-0.104003\pi\) | ||||
0.947095 | + | 0.320953i | \(0.104003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −256126. | −0.494949 | −0.247474 | − | 0.968894i | \(-0.579601\pi\) | ||||
−0.247474 | + | 0.968894i | \(0.579601\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −688644. | −1.29691 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 111150. | 0.204053 | 0.102027 | − | 0.994782i | \(-0.467467\pi\) | ||||
0.102027 | + | 0.994782i | \(0.467467\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −516800. | −0.925102 | −0.462551 | − | 0.886593i | \(-0.653066\pi\) | ||||
−0.462551 | + | 0.886593i | \(0.653066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 47556.0 | 0.0830262 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −787104. | −1.34058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −487860. | −0.810794 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −39528.0 | −0.0641179 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 439280. | 0.695626 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 400972. | 0.620023 | 0.310012 | − | 0.950733i | \(-0.399667\pi\) | ||||
0.310012 | + | 0.950733i | \(0.399667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −75240.0 | −0.113632 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.60590e6 | −2.36931 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.37664e6 | 1.98459 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −355194. | −0.500444 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −701668. | −0.966387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −206168. | −0.277625 | −0.138813 | − | 0.990319i | \(-0.544329\pi\) | ||||
−0.138813 | + | 0.990319i | \(0.544329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 462591. | 0.609173 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 363468. | 0.468168 | 0.234084 | − | 0.972216i | \(-0.424791\pi\) | ||||
0.234084 | + | 0.972216i | \(0.424791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −589274. | −0.742555 | −0.371277 | − | 0.928522i | \(-0.621080\pi\) | ||||
−0.371277 | + | 0.928522i | \(0.621080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 492480. | 0.607238 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 730090. | 0.881022 | 0.440511 | − | 0.897747i | \(-0.354797\pi\) | ||||
0.440511 | + | 0.897747i | \(0.354797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 297792. | 0.351758 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −381384. | −0.441054 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 472496. | 0.535061 | 0.267531 | − | 0.963549i | \(-0.413792\pi\) | ||||
0.267531 | + | 0.963549i | \(0.413792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 993042. | 1.10135 | 0.550675 | − | 0.834720i | \(-0.314371\pi\) | ||||
0.550675 | + | 0.834720i | \(0.314371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 369326. | 0.393092 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −940984. | −0.981386 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 556452. | 0.568760 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.93653e6 | 1.94017 | 0.970086 | − | 0.242760i | \(-0.0780528\pi\) | ||||
0.970086 | + | 0.242760i | \(0.0780528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 185440. | 0.182139 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 729252. | 0.702307 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 735746. | 0.694856 | 0.347428 | − | 0.937707i | \(-0.387055\pi\) | ||||
0.347428 | + | 0.937707i | \(0.387055\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.51286e6 | −1.40136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −442746. | −0.402303 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −542984. | −0.484058 | −0.242029 | − | 0.970269i | \(-0.577813\pi\) | ||||
−0.242029 | + | 0.970269i | \(0.577813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.32838e6 | −2.03676 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 567702. | 0.487351 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 438614. | 0.369574 | 0.184787 | − | 0.982779i | \(-0.440840\pi\) | ||||
0.184787 | + | 0.982779i | \(0.440840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 644408. | 0.533013 | 0.266506 | − | 0.963833i | \(-0.414131\pi\) | ||||
0.266506 | + | 0.963833i | \(0.414131\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.05494e6 | −0.856688 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.17018e6 | −1.73047 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.41953e6 | −1.11159 | −0.555796 | − | 0.831319i | \(-0.687586\pi\) | ||||
−0.555796 | + | 0.831319i | \(0.687586\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 774360. | 0.595569 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 645242. | 0.487480 | 0.243740 | − | 0.969841i | \(-0.421626\pi\) | ||||
0.243740 | + | 0.969841i | \(0.421626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.93696e6 | 1.43766 | 0.718829 | − | 0.695187i | \(-0.244679\pi\) | ||||
0.718829 | + | 0.695187i | \(0.244679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 977976. | 0.713208 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −747360. | −0.535581 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −676813. | −0.476677 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 146862. | 0.101666 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.65429e6 | −1.12575 | −0.562876 | − | 0.826541i | \(-0.690305\pi\) | ||||
−0.562876 | + | 0.826541i | \(0.690305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.63372e6 | 1.09301 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 277020. | 0.182230 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −397232. | −0.256960 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.46010e6 | −1.56508 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.21289e6 | −0.758955 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 410404. | 0.252617 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.78236e6 | −1.68487 | −0.842436 | − | 0.538797i | \(-0.818879\pi\) | ||||
−0.842436 | + | 0.538797i | \(0.818879\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −406656. | −0.242287 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.00510e6 | 0.589259 | 0.294630 | − | 0.955611i | \(-0.404804\pi\) | ||||
0.294630 | + | 0.955611i | \(0.404804\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 535386. | 0.308892 | 0.154446 | − | 0.988001i | \(-0.450641\pi\) | ||||
0.154446 | + | 0.988001i | \(0.450641\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.09642e6 | 0.622585 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.96266e6 | 1.65590 | 0.827950 | − | 0.560802i | \(-0.189507\pi\) | ||||
0.827950 | + | 0.560802i | \(0.189507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.07708e6 | 1.14282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.28812e6 | −0.697738 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 996472. | 0.531446 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.64875e6 | 2.44134 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.37763e6 | −0.712464 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 456192. | 0.232358 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.55935e6 | 0.782300 | 0.391150 | − | 0.920327i | \(-0.372077\pi\) | ||||
0.391150 | + | 0.920327i | \(0.372077\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −850986. | −0.420544 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −496696. | −0.241812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.61557e6 | 1.73421 | 0.867106 | − | 0.498124i | \(-0.165978\pi\) | ||||
0.867106 | + | 0.498124i | \(0.165978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 580446. | 0.274323 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.63280e6 | −1.69183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.85443e6 | −0.851090 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 412848. | 0.186742 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.76488e6 | −0.786847 | −0.393424 | − | 0.919357i | \(-0.628709\pi\) | ||||
−0.393424 | + | 0.919357i | \(0.628709\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 553134. | 0.243090 | 0.121545 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121545 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −593406. | −0.257089 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.17408e6 | −0.501488 | −0.250744 | − | 0.968053i | \(-0.580675\pi\) | ||||
−0.250744 | + | 0.968053i | \(0.580675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 785840. | 0.330951 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.11715e6 | 0.463919 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.18975e6 | −0.487215 | −0.243607 | − | 0.969874i | \(-0.578331\pi\) | ||||
−0.243607 | + | 0.969874i | \(0.578331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.13976e6 | −0.460306 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 149859. | 0.0596920 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.70980e6 | 1.45753 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.35327e6 | −0.524469 | −0.262235 | − | 0.965004i | \(-0.584459\pi\) | ||||
−0.262235 | + | 0.965004i | \(0.584459\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −420390. | −0.160726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.56688e6 | −1.34541 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.79306e6 | 1.03946 | 0.519731 | − | 0.854330i | \(-0.326032\pi\) | ||||
0.519731 | + | 0.854330i | \(0.326032\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.18776e6 | −0.803379 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.44932e6 | −1.61228 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.37304e6 | −1.20621 | −0.603105 | − | 0.797662i | \(-0.706070\pi\) | ||||
−0.603105 | + | 0.797662i | \(0.706070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −299304. | −0.105633 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.72781e6 | 1.64688 | 0.823442 | − | 0.567401i | \(-0.192051\pi\) | ||||
0.823442 | + | 0.567401i | \(0.192051\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.14368e6 | −1.76857 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.38380e6 | −0.469675 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 188254. | 0.0630769 | 0.0315384 | − | 0.999503i | \(-0.489959\pi\) | ||||
0.0315384 | + | 0.999503i | \(0.489959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 420656. | 0.139151 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.34356e6 | 0.438808 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.98334e6 | 1.28456 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −524578. | −0.167045 | −0.0835226 | − | 0.996506i | \(-0.526617\pi\) | ||||
−0.0835226 | + | 0.996506i | \(0.526617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.49818e6 | 0.471119 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.08653e6 | −0.958537 | −0.479269 | − | 0.877668i | \(-0.659098\pi\) | ||||
−0.479269 | + | 0.877668i | \(0.659098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.78184e6 | 2.38682 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 616734. | 0.186836 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.99228e6 | 1.19463 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.60196e6 | −1.36030 | −0.680150 | − | 0.733073i | \(-0.738085\pi\) | ||||
−0.680150 | + | 0.733073i | \(0.738085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.33742e6 | −0.390537 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.50272e6 | 0.722000 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.81183e6 | −1.65651 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.91611e6 | 0.821227 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.09492e6 | 0.582953 | 0.291476 | − | 0.956578i | \(-0.405854\pi\) | ||||
0.291476 | + | 0.956578i | \(0.405854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 987206. | 0.271458 | 0.135729 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135729 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 256608. | 0.0697299 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.92288e6 | −1.32205 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 628704. | 0.166869 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.78388e6 | 0.730310 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.25933e6 | 0.845152 | 0.422576 | − | 0.906327i | \(-0.361126\pi\) | ||||
0.422576 | + | 0.906327i | \(0.361126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.31461e6 | 1.87487 | 0.937436 | − | 0.348159i | \(-0.113193\pi\) | ||||
0.937436 | + | 0.348159i | \(0.113193\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.62424e6 | 1.17170 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 564128. | 0.141310 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.31419e6 | −1.81136 | −0.905681 | − | 0.423961i | \(-0.860639\pi\) | ||||
−0.905681 | + | 0.423961i | \(0.860639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 318249. | 0.0779239 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.07403e6 | −1.71261 | −0.856303 | − | 0.516474i | \(-0.827244\pi\) | ||||
−0.856303 | + | 0.516474i | \(0.827244\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.92933e6 | −1.41940 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 539874. | 0.127798 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.48079e6 | 1.75118 | 0.875591 | − | 0.483053i | \(-0.160472\pi\) | ||||
0.875591 | + | 0.483053i | \(0.160472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.97220e6 | 0.456572 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −823680. | −0.188588 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.10183e7 | 2.49509 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.97108e6 | 0.665463 | 0.332732 | − | 0.943022i | \(-0.392030\pi\) | ||||
0.332732 | + | 0.943022i | \(0.392030\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 628398. | 0.139220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.29078e6 | −1.81695 | −0.908475 | − | 0.417939i | \(-0.862753\pi\) | ||||
−0.908475 | + | 0.417939i | \(0.862753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 955064. | 0.207052 | 0.103526 | − | 0.994627i | \(-0.466987\pi\) | ||||
0.103526 | + | 0.994627i | \(0.466987\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.08776e6 | −1.73459 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.19018e6 | −1.73781 | −0.868903 | − | 0.494983i | \(-0.835174\pi\) | ||||
−0.868903 | + | 0.494983i | \(0.835174\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −760896. | −0.159732 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.10995e6 | −0.645953 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.49192e6 | 1.33420 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.60192e6 | −1.34257 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00637e6 | −0.403752 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.39774e6 | −0.676631 | −0.338315 | − | 0.941033i | \(-0.609857\pi\) | ||||
−0.338315 | + | 0.941033i | \(0.609857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.55188e6 | −1.68538 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 632448. | 0.123355 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.53389e6 | −0.296101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.94814e6 | 0.372219 | 0.186110 | − | 0.982529i | \(-0.440412\pi\) | ||||
0.186110 | + | 0.982529i | \(0.440412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.70748e6 | 1.07937 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.92574e6 | −0.734882 | −0.367441 | − | 0.930047i | \(-0.619766\pi\) | ||||
−0.367441 | + | 0.930047i | \(0.619766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.71169e6 | 0.873091 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.89332e6 | −0.530742 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.20384e6 | 0.218614 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.07102e6 | 0.372334 | 0.186167 | − | 0.982518i | \(-0.440393\pi\) | ||||
0.186167 | + | 0.982518i | \(0.440393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.74263e6 | 0.666167 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.16500e6 | −1.61515 | −0.807574 | − | 0.589766i | \(-0.799220\pi\) | ||||
−0.807574 | + | 0.589766i | \(0.799220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.26680e7 | 2.21045 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.62173e6 | −0.452968 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.91517e6 | 1.18307 | 0.591533 | − | 0.806281i | \(-0.298523\pi\) | ||||
0.591533 | + | 0.806281i | \(0.298523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.68310e6 | 0.962794 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 842724. | 0.141381 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.24730e6 | 0.705658 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.20384e6 | −0.198081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.91854e6 | 0.475606 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26077e6 | −0.364891 | −0.182445 | − | 0.983216i | \(-0.558401\pi\) | ||||
−0.182445 | + | 0.983216i | \(0.558401\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.25524e6 | 1.31970 | 0.659850 | − | 0.751397i | \(-0.270620\pi\) | ||||
0.659850 | + | 0.751397i | \(0.270620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.40146e6 | −1.17198 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.24072e6 | −1.29252 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.19820e6 | −0.963000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.40778e6 | 0.216670 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.22466e6 | −0.644130 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.34537e7 | 2.03215 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.46145e6 | −0.817283 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.49302e6 | −0.221357 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.90467e6 | 0.279786 | 0.139893 | − | 0.990167i | \(-0.455324\pi\) | ||||
0.139893 | + | 0.990167i | \(0.455324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.16929e6 | −0.606823 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.43886e7 | 2.07504 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.57060e6 | 0.224439 | 0.112220 | − | 0.993683i | \(-0.464204\pi\) | ||||
0.112220 | + | 0.993683i | \(0.464204\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 353646. | 0.0500770 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.31870e6 | 0.886642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.10214e6 | 0.848535 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.88808e6 | 1.22483 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.36849e6 | 0.323469 | 0.161735 | − | 0.986834i | \(-0.448291\pi\) | ||||
0.161735 | + | 0.986834i | \(0.448291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.39064e7 | −1.88228 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.94804e6 | −0.395482 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.64976e6 | 0.884168 | 0.442084 | − | 0.896974i | \(-0.354239\pi\) | ||||
0.442084 | + | 0.896974i | \(0.354239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.06244e6 | −0.798962 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 944784. | 0.123417 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.94565e6 | −1.15833 | −0.579164 | − | 0.815211i | \(-0.696621\pi\) | ||||
−0.579164 | + | 0.815211i | \(0.696621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.19526e6 | −0.538479 | −0.269239 | − | 0.963073i | \(-0.586772\pi\) | ||||
−0.269239 | + | 0.963073i | \(0.586772\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.59507e6 | −1.09361 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.78697e6 | −0.351530 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.24845e6 | −0.781326 | −0.390663 | − | 0.920534i | \(-0.627754\pi\) | ||||
−0.390663 | + | 0.920534i | \(0.627754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.30513e6 | 0.285759 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.90323e6 | −1.09423 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.41260e6 | 1.14693 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.19780e6 | 0.748769 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.55284e6 | −0.545365 | −0.272683 | − | 0.962104i | \(-0.587911\pi\) | ||||
−0.272683 | + | 0.962104i | \(0.587911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.10514e7 | −1.31259 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.00035e6 | −0.117810 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 210802. | 0.0246172 | 0.0123086 | − | 0.999924i | \(-0.496082\pi\) | ||||
0.0123086 | + | 0.999924i | \(0.496082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.16680e7 | −1.35116 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.65120e6 | 0.534108 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.05945e6 | 0.348398 | 0.174199 | − | 0.984710i | \(-0.444266\pi\) | ||||
0.174199 | + | 0.984710i | \(0.444266\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.37094e6 | 0.832409 | 0.416204 | − | 0.909271i | \(-0.363360\pi\) | ||||
0.416204 | + | 0.909271i | \(0.363360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −428004. | −0.0479352 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.56519e6 | −0.173852 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.12257e6 | 0.233824 | 0.116912 | − | 0.993142i | \(-0.462700\pi\) | ||||
0.116912 | + | 0.993142i | \(0.462700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.08394e6 | 0.773983 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.57875e6 | 0.279452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.09689e7 | −1.17899 | −0.589496 | − | 0.807771i | \(-0.700674\pi\) | ||||
−0.589496 | + | 0.807771i | \(0.700674\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.39074e6 | 0.468112 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.28953e6 | −0.770879 | −0.385440 | − | 0.922733i | \(-0.625950\pi\) | ||||
−0.385440 | + | 0.922733i | \(0.625950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.23675e6 | −0.234634 | −0.117317 | − | 0.993095i | \(-0.537429\pi\) | ||||
−0.117317 | + | 0.993095i | \(0.537429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 355752. | 0.0370185 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.08323e6 | −0.937606 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.00302e6 | 0.512309 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.95352e6 | −0.401620 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.05617e6 | 0.912679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.06160e6 | −0.706041 | −0.353020 | − | 0.935616i | \(-0.614845\pi\) | ||||
−0.353020 | + | 0.935616i | \(0.614845\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.60875e6 | −0.357971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.12606e6 | 0.307655 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.19821e6 | 0.312290 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 677160. | 0.0656053 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.80189e7 | 1.73214 | 0.866070 | − | 0.499922i | \(-0.166638\pi\) | ||||
0.866070 | + | 0.499922i | \(0.166638\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.07252e6 | 0.102301 | 0.0511505 | − | 0.998691i | \(-0.483711\pi\) | ||||
0.0511505 | + | 0.998691i | \(0.483711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44531e7 | 1.36792 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.03054e7 | 1.90701 | 0.953503 | − | 0.301385i | \(-0.0974489\pi\) | ||||
0.953503 | + | 0.301385i | \(0.0974489\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.60440e6 | −0.615491 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.23898e7 | −1.14580 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.97292e7 | 1.81061 | 0.905306 | − | 0.424759i | \(-0.139641\pi\) | ||||
0.905306 | + | 0.424759i | \(0.139641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.40327e7 | −1.27802 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.19675e6 | 0.288931 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.29511e7 | 1.16170 | 0.580848 | − | 0.814012i | \(-0.302721\pi\) | ||||
0.580848 | + | 0.814012i | \(0.302721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.01888e7 | 1.79725 | 0.898623 | − | 0.438721i | \(-0.144568\pi\) | ||||
0.898623 | + | 0.438721i | \(0.144568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.31501e6 | 0.557944 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.56476e7 | −1.37213 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.66741e6 | 0.232153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.85551e6 | 0.160287 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.65908e6 | −0.142253 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.83989e7 | −1.56587 | −0.782934 | − | 0.622105i | \(-0.786278\pi\) | ||||
−0.782934 | + | 0.622105i | \(0.786278\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.16332e6 | −0.351706 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.72791e6 | −0.396458 | −0.198229 | − | 0.980156i | \(-0.563519\pi\) | ||||
−0.198229 | + | 0.980156i | \(0.563519\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.34979e6 | −0.195594 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.27121e6 | −0.270297 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.38084e7 | −1.13264 | −0.566321 | − | 0.824184i | \(-0.691634\pi\) | ||||
−0.566321 | + | 0.824184i | \(0.691634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.39686e7 | 1.13743 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.30347e6 | 0.428714 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.01628e7 | −1.61809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.28964e7 | 1.02748 | 0.513742 | − | 0.857945i | \(-0.328259\pi\) | ||||
0.513742 | + | 0.857945i | \(0.328259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.43232e6 | −0.350589 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.04571e7 | −2.39181 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.47378e6 | 0.348813 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.57081e6 | −0.508658 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.81078e6 | −0.677204 | −0.338602 | − | 0.940930i | \(-0.609954\pi\) | ||||
−0.338602 | + | 0.940930i | \(0.609954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.21449e7 | 0.926845 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.68013e6 | −0.203087 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.94063e7 | 1.46014 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.83369e7 | 1.36997 | 0.684984 | − | 0.728558i | \(-0.259809\pi\) | ||||
0.684984 | + | 0.728558i | \(0.259809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.43246e6 | 0.254643 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.66528e6 | −0.343680 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.90761e7 | −2.12702 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.25246e6 | −0.308918 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.26238e7 | 1.63209 | 0.816044 | − | 0.577990i | \(-0.196163\pi\) | ||||
0.816044 | + | 0.577990i | \(0.196163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.50650e6 | 0.466132 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.93738e6 | −0.635864 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.12163e7 | −2.20565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.25658e7 | −0.881769 | −0.440885 | − | 0.897564i | \(-0.645335\pi\) | ||||
−0.440885 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.47264e7 | 1.01930 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 833534. | 0.0573012 | 0.0286506 | − | 0.999589i | \(-0.490879\pi\) | ||||
0.0286506 | + | 0.999589i | \(0.490879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.32393e6 | −0.226952 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.00792e6 | 0.136169 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.84188e6 | 0.595571 | 0.297786 | − | 0.954633i | \(-0.403752\pi\) | ||||
0.297786 | + | 0.954633i | \(0.403752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.46886e6 | 0.566603 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.62140e7 | −1.74205 | −0.871025 | − | 0.491239i | \(-0.836544\pi\) | ||||
−0.871025 | + | 0.491239i | \(0.836544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.63868e6 | −0.372209 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.00807e6 | −0.328374 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.06099e7 | 1.34236 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.17143e6 | 0.399288 | 0.199644 | − | 0.979869i | \(-0.436021\pi\) | ||||
0.199644 | + | 0.979869i | \(0.436021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.74288e7 | −1.12016 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.60288e6 | 0.549258 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.70734e6 | −0.425413 | −0.212706 | − | 0.977116i | \(-0.568228\pi\) | ||||
−0.212706 | + | 0.977116i | \(0.568228\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.66896e6 | −0.105158 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.08114e7 | −0.676734 | −0.338367 | − | 0.941014i | \(-0.609875\pi\) | ||||
−0.338367 | + | 0.941014i | \(0.609875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.20421e7 | 1.37070 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.56327e6 | −0.405477 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.41473e7 | 0.868332 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.33048e7 | −0.811322 | −0.405661 | − | 0.914024i | \(-0.632959\pi\) | ||||
−0.405661 | + | 0.914024i | \(0.632959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.62171e6 | −0.401176 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.29053e7 | −0.776818 | −0.388409 | − | 0.921487i | \(-0.626975\pi\) | ||||
−0.388409 | + | 0.921487i | \(0.626975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.45972e7 | 3.26525 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.36158e7 | 0.809077 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.99964e6 | 0.354227 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.17680e6 | −0.186364 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.98471e6 | 0.232270 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.24817e7 | 1.88133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.77705e6 | 0.390035 | 0.195018 | − | 0.980800i | \(-0.437524\pi\) | ||||
0.195018 | + | 0.980800i | \(0.437524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.88686e6 | 0.279471 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.28714e6 | −0.527765 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.55392e6 | 0.200690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.09554e7 | 1.17592 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.49551e7 | 0.833956 | 0.416978 | − | 0.908916i | \(-0.363089\pi\) | ||||
0.416978 | + | 0.908916i | \(0.363089\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.73082e6 | −0.151330 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.10932e6 | −0.281372 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.49971e7 | −0.820763 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.60557e6 | −0.359270 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.94753e6 | −0.213374 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.65841e6 | −0.465122 | −0.232561 | − | 0.972582i | \(-0.574710\pi\) | ||||
−0.232561 | + | 0.972582i | \(0.574710\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.98323e7 | −1.05881 | −0.529407 | − | 0.848368i | \(-0.677586\pi\) | ||||
−0.529407 | + | 0.848368i | \(0.677586\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.79967e6 | −0.307735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.96114e7 | −3.14366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.97491e7 | 1.03512 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.49450e6 | 0.494609 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.02228e7 | 1.56486 | 0.782431 | − | 0.622737i | \(-0.213979\pi\) | ||||
0.782431 | + | 0.622737i | \(0.213979\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.64692e7 | −1.36220 | −0.681100 | − | 0.732190i | \(-0.738498\pi\) | ||||
−0.681100 | + | 0.732190i | \(0.738498\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.95316e7 | 0.999087 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.81882e6 | 0.448380 | 0.224190 | − | 0.974545i | \(-0.428026\pi\) | ||||
0.224190 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.31053e7 | −1.16768 | −0.583841 | − | 0.811868i | \(-0.698451\pi\) | ||||
−0.583841 | + | 0.811868i | \(0.698451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.27758e7 | 0.641778 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.38680e6 | −0.169113 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.90897e7 | −1.94020 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.96924e6 | −0.343852 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.65084e7 | 1.30010 | 0.650052 | − | 0.759890i | \(-0.274747\pi\) | ||||
0.650052 | + | 0.759890i | \(0.274747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.36601e6 | 0.456630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.80718e6 | −0.281447 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.73825e7 | 1.31926 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.39774e6 | −0.114840 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.74327e7 | −0.830032 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.12693e6 | 0.242680 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.84201e6 | −0.369024 | −0.184512 | − | 0.982830i | \(-0.559070\pi\) | ||||
−0.184512 | + | 0.982830i | \(0.559070\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.80178e6 | −0.411771 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.26563e7 | −1.05375 | −0.526875 | − | 0.849943i | \(-0.676636\pi\) | ||||
−0.526875 | + | 0.849943i | \(0.676636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.67391e7 | −1.23641 | −0.618207 | − | 0.786016i | \(-0.712140\pi\) | ||||
−0.618207 | + | 0.786016i | \(0.712140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.72624e6 | 0.309218 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.29957e7 | −0.593983 | −0.296992 | − | 0.954880i | \(-0.595983\pi\) | ||||
−0.296992 | + | 0.954880i | \(0.595983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.04825e7 | −1.38519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.09132e6 | 0.275210 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.61029e7 | −0.723359 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.30118e6 | −0.192106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.32176e6 | −0.0586971 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.50041e7 | 1.54561 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.16845e6 | −0.139107 | −0.0695533 | − | 0.997578i | \(-0.522157\pi\) | ||||
−0.0695533 | + | 0.997578i | \(0.522157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.48886e7 | 0.649953 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.85811e7 | 1.67469 | 0.837346 | − | 0.546673i | \(-0.184106\pi\) | ||||
0.837346 | + | 0.546673i | \(0.184106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.31224e7 | −0.998000 | −0.499000 | − | 0.866602i | \(-0.666299\pi\) | ||||
−0.499000 | + | 0.866602i | \(0.666299\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.47035e7 | −0.631047 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.62602e7 | −1.12070 | −0.560350 | − | 0.828256i | \(-0.689333\pi\) | ||||
−0.560350 | + | 0.828256i | \(0.689333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.78886e6 | 0.203225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.49318e6 | −0.105211 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.66221e6 | −0.153679 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.70418e7 | 2.38032 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.57509e6 | 0.148356 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.22550e7 | −2.15639 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.13517e7 | 0.876236 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.21409e7 | 0.903598 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.35459e7 | 1.76736 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.13213e7 | 1.26422 | 0.632109 | − | 0.774879i | \(-0.282189\pi\) | ||||
0.632109 | + | 0.774879i | \(0.282189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.09160e7 | 0.438183 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.49877e6 | 0.179596 | 0.0897982 | − | 0.995960i | \(-0.471378\pi\) | ||||
0.0897982 | + | 0.995960i | \(0.471378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.34946e7 | 0.932807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.69364e6 | −0.145848 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.14969e7 | −0.844214 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.03824e6 | −0.118668 | −0.0593340 | − | 0.998238i | \(-0.518898\pi\) | ||||
−0.0593340 | + | 0.998238i | \(0.518898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.50412e7 | 0.972761 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.80504e6 | 0.262922 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.99998e7 | −2.30566 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.65990e6 | 0.139885 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −193966. | −0.00737371 | −0.00368686 | − | 0.999993i | \(-0.501174\pi\) | ||||
−0.00368686 | + | 0.999993i | \(0.501174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.54192e6 | −0.171738 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.04586e6 | −0.340209 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.07906e7 | 1.15183 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.23213e7 | −1.20265 | −0.601326 | − | 0.799003i | \(-0.705361\pi\) | ||||
−0.601326 | + | 0.799003i | \(0.705361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.81847e6 | −0.178339 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.50288e7 | −1.65774 | −0.828870 | − | 0.559442i | \(-0.811016\pi\) | ||||
−0.828870 | + | 0.559442i | \(0.811016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.53272e6 | 0.0927487 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.86774e6 | −0.359450 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.04495e7 | 0.378635 | 0.189318 | − | 0.981916i | \(-0.439372\pi\) | ||||
0.189318 | + | 0.981916i | \(0.439372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.21253e7 | 1.15793 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.66640e7 | −0.956034 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.31343e7 | 1.53847 | 0.769237 | − | 0.638963i | \(-0.220636\pi\) | ||||
0.769237 | + | 0.638963i | \(0.220636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.97708e7 | 3.18512 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.86937e7 | −0.659805 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.13987e7 | 0.751347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.27644e7 | 2.19233 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.15930e7 | 0.402839 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.40758e7 | −0.832268 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.43982e7 | −0.495157 | −0.247579 | − | 0.968868i | \(-0.579635\pi\) | ||||
−0.247579 | + | 0.968868i | \(0.579635\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.96825e6 | −0.306830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.00272e6 | 0.102204 | 0.0511019 | − | 0.998693i | \(-0.483727\pi\) | ||||
0.0511019 | + | 0.998693i | \(0.483727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.66577e7 | −1.57994 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.18388e7 | −1.40951 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.75164e7 | −1.25743 | −0.628716 | − | 0.777635i | \(-0.716419\pi\) | ||||
−0.628716 | + | 0.777635i | \(0.716419\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.39696e7 | 0.799291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.23987e7 | 0.411342 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.57244e6 | −0.0849105 | −0.0424553 | − | 0.999098i | \(-0.513518\pi\) | ||||
−0.0424553 | + | 0.999098i | \(0.513518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04481e7 | 0.343121 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.10573e6 | −0.134152 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.33699e6 | 0.271031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.41887e7 | −1.75277 | −0.876385 | − | 0.481611i | \(-0.840052\pi\) | ||||
−0.876385 | + | 0.481611i | \(0.840052\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.40341e7 | −0.451661 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.85792e7 | −1.55558 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.52674e7 | 1.12366 | 0.561830 | − | 0.827253i | \(-0.310097\pi\) | ||||
0.561830 | + | 0.827253i | \(0.310097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.65887e6 | 0.242801 |
(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 | 24.6.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 72.6.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.6.a.e.1.1 | 1 | |||
5.2 | odd | 4 | 600.6.f.b.49.2 | 2 | |||
5.3 | odd | 4 | 600.6.f.b.49.1 | 2 | |||
5.4 | even | 2 | 600.6.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 192.6.a.a.1.1 | 1 | |||
8.5 | even | 2 | 192.6.a.i.1.1 | 1 | |||
12.11 | even | 2 | 144.6.a.b.1.1 | 1 | |||
16.3 | odd | 4 | 768.6.d.o.385.2 | 2 | |||
16.5 | even | 4 | 768.6.d.d.385.2 | 2 | |||
16.11 | odd | 4 | 768.6.d.o.385.1 | 2 | |||
16.13 | even | 4 | 768.6.d.d.385.1 | 2 | |||
24.5 | odd | 2 | 576.6.a.bg.1.1 | 1 | |||
24.11 | even | 2 | 576.6.a.bf.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.6.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
48.6.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
72.6.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
144.6.a.b.1.1 | 1 | 12.11 | even | 2 | |||
192.6.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
192.6.a.i.1.1 | 1 | 8.5 | even | 2 | |||
576.6.a.bf.1.1 | 1 | 24.11 | even | 2 | |||
576.6.a.bg.1.1 | 1 | 24.5 | odd | 2 | |||
600.6.a.d.1.1 | 1 | 5.4 | even | 2 | |||
600.6.f.b.49.1 | 2 | 5.3 | odd | 4 | |||
600.6.f.b.49.2 | 2 | 5.2 | odd | 4 | |||
768.6.d.d.385.1 | 2 | 16.13 | even | 4 | |||
768.6.d.d.385.2 | 2 | 16.5 | even | 4 | |||
768.6.d.o.385.1 | 2 | 16.11 | odd | 4 | |||
768.6.d.o.385.2 | 2 | 16.3 | odd | 4 |