Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, 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("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1595208.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} + 33x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.64654\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-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 | ||||||||
\(3\) | 28.9338 | 1.85610 | 0.928052 | − | 0.372451i | \(-0.121482\pi\) | ||||
0.928052 | + | 0.372451i | \(0.121482\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 146.828 | 1.13257 | 0.566283 | − | 0.824211i | \(-0.308381\pi\) | ||||
0.566283 | + | 0.824211i | \(0.308381\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 594.165 | 2.44512 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −191.129 | −0.476260 | −0.238130 | − | 0.971233i | \(-0.576534\pi\) | ||||
−0.238130 | + | 0.971233i | \(0.576534\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −83.9971 | −0.137850 | −0.0689249 | − | 0.997622i | \(-0.521957\pi\) | ||||
−0.0689249 | + | 0.997622i | \(0.521957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2000.23 | 1.67864 | 0.839322 | − | 0.543635i | \(-0.182952\pi\) | ||||
0.839322 | + | 0.543635i | \(0.182952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −677.481 | −0.430540 | −0.215270 | − | 0.976555i | \(-0.569063\pi\) | ||||
−0.215270 | + | 0.976555i | \(0.569063\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4248.29 | 2.10216 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1296.23 | 0.510931 | 0.255466 | − | 0.966818i | \(-0.417771\pi\) | ||||
0.255466 | + | 0.966818i | \(0.417771\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10160.5 | 2.68230 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3266.00 | −0.721143 | −0.360571 | − | 0.932732i | \(-0.617418\pi\) | ||||
−0.360571 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6157.98 | −1.15089 | −0.575445 | − | 0.817841i | \(-0.695171\pi\) | ||||
−0.575445 | + | 0.817841i | \(0.695171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5530.08 | −0.883989 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11369.5 | 1.36533 | 0.682667 | − | 0.730730i | \(-0.260820\pi\) | ||||
0.682667 | + | 0.730730i | \(0.260820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2430.36 | −0.255863 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10599.8 | −0.984774 | −0.492387 | − | 0.870376i | \(-0.663876\pi\) | ||||
−0.492387 | + | 0.870376i | \(0.663876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12926.2 | 1.06610 | 0.533052 | − | 0.846082i | \(-0.321045\pi\) | ||||
0.533052 | + | 0.846082i | \(0.321045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9521.88 | 0.628750 | 0.314375 | − | 0.949299i | \(-0.398205\pi\) | ||||
0.314375 | + | 0.949299i | \(0.398205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4751.45 | 0.282706 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 57874.4 | 3.11574 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14786.8 | −0.723078 | −0.361539 | − | 0.932357i | \(-0.617749\pi\) | ||||
−0.361539 | + | 0.932357i | \(0.617749\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19602.1 | −0.799126 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 38226.9 | 1.42968 | 0.714841 | − | 0.699287i | \(-0.246499\pi\) | ||||
0.714841 | + | 0.699287i | \(0.246499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3581.69 | −0.123243 | −0.0616217 | − | 0.998100i | \(-0.519627\pi\) | ||||
−0.0616217 | + | 0.998100i | \(0.519627\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 87240.0 | 2.76926 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21780.0 | 0.592748 | 0.296374 | − | 0.955072i | \(-0.404223\pi\) | ||||
0.296374 | + | 0.955072i | \(0.404223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 37504.9 | 0.948341 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51390.1 | −1.20986 | −0.604928 | − | 0.796280i | \(-0.706798\pi\) | ||||
−0.604928 | + | 0.796280i | \(0.706798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13305.9 | 0.292238 | 0.146119 | − | 0.989267i | \(-0.453322\pi\) | ||||
0.146119 | + | 0.989267i | \(0.453322\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −28063.1 | −0.539396 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15944.3 | −0.287434 | −0.143717 | − | 0.989619i | \(-0.545906\pi\) | ||||
−0.143717 | + | 0.989619i | \(0.545906\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 149601. | 2.53350 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −53305.0 | −0.849323 | −0.424662 | − | 0.905352i | \(-0.639607\pi\) | ||||
−0.424662 | + | 0.905352i | \(0.639607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −94497.8 | −1.33852 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −51330.4 | −0.686910 | −0.343455 | − | 0.939169i | \(-0.611597\pi\) | ||||
−0.343455 | + | 0.939169i | \(0.611597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12333.1 | −0.156124 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −178174. | −2.13617 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −80849.9 | −0.872469 | −0.436234 | − | 0.899833i | \(-0.643688\pi\) | ||||
−0.436234 | + | 0.899833i | \(0.643688\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −113562. | −1.16451 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 89471.2 | 0.872729 | 0.436365 | − | 0.899770i | \(-0.356266\pi\) | ||||
0.436365 | + | 0.899770i | \(0.356266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −44184.6 | −0.410372 | −0.205186 | − | 0.978723i | \(-0.565780\pi\) | ||||
−0.205186 | + | 0.978723i | \(0.565780\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 56446.0 | 0.476622 | 0.238311 | − | 0.971189i | \(-0.423406\pi\) | ||||
0.238311 | + | 0.971189i | \(0.423406\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 52651.1 | 0.424465 | 0.212232 | − | 0.977219i | \(-0.431927\pi\) | ||||
0.212232 | + | 0.977219i | \(0.431927\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 328964. | 2.53420 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 78399.6 | 0.577587 | 0.288794 | − | 0.957391i | \(-0.406746\pi\) | ||||
0.288794 | + | 0.957391i | \(0.406746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −49908.1 | −0.337059 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 293690. | 1.90118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124521. | −0.773176 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −306691. | −1.82784 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −296102. | −1.62904 | −0.814522 | − | 0.580133i | \(-0.803001\pi\) | ||||
−0.814522 | + | 0.580133i | \(0.803001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 374004. | 1.97880 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 199030. | 1.01331 | 0.506653 | − | 0.862150i | \(-0.330883\pi\) | ||||
0.506653 | + | 0.862150i | \(0.330883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −99473.2 | −0.487615 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 361224. | 1.64428 | 0.822138 | − | 0.569288i | \(-0.192781\pi\) | ||||
0.822138 | + | 0.569288i | \(0.192781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 257315. | 1.12961 | 0.564805 | − | 0.825224i | \(-0.308951\pi\) | ||||
0.564805 | + | 0.825224i | \(0.308951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 275504. | 1.16702 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16054.3 | 0.0656524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 137477. | 0.524733 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −478333. | −1.76508 | −0.882540 | − | 0.470238i | \(-0.844168\pi\) | ||||
−0.882540 | + | 0.470238i | \(0.844168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 193483. | 0.690558 | 0.345279 | − | 0.938500i | \(-0.387784\pi\) | ||||
0.345279 | + | 0.938500i | \(0.387784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.18847e6 | 4.10449 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −460294. | −1.49034 | −0.745172 | − | 0.666873i | \(-0.767633\pi\) | ||||
−0.745172 | + | 0.666873i | \(0.767633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −427839. | −1.34211 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 190323. | 0.578663 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 372211. | 1.09729 | 0.548643 | − | 0.836057i | \(-0.315145\pi\) | ||||
0.548643 | + | 0.836057i | \(0.315145\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 423266. | 1.17442 | 0.587208 | − | 0.809436i | \(-0.300227\pi\) | ||||
0.587208 | + | 0.809436i | \(0.300227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −364237. | −0.980997 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −402535. | −1.05272 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −223915. | −0.568810 | −0.284405 | − | 0.958704i | \(-0.591796\pi\) | ||||
−0.284405 | + | 0.958704i | \(0.591796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.10605e6 | 2.65364 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 29324.8 | 0.0684072 | 0.0342036 | − | 0.999415i | \(-0.489111\pi\) | ||||
0.0342036 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −46594.3 | −0.105715 | −0.0528574 | − | 0.998602i | \(-0.516833\pi\) | ||||
−0.0528574 | + | 0.998602i | \(0.516833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −103632. | −0.228752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −382302. | −0.799472 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.49185e6 | 3.03788 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −327452. | −0.649477 | −0.324739 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324739 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 406622. | 0.785773 | 0.392887 | − | 0.919587i | \(-0.371476\pi\) | ||||
0.392887 | + | 0.919587i | \(0.371476\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 364071. | 0.668376 | 0.334188 | − | 0.942506i | \(-0.391538\pi\) | ||||
0.334188 | + | 0.942506i | \(0.391538\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −55181.3 | −0.0987777 | −0.0493889 | − | 0.998780i | \(-0.515727\pi\) | ||||
−0.0493889 | + | 0.998780i | \(0.515727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 630177. | 1.10020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −479540. | −0.816742 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 770174. | 1.24929 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 129486. | 0.205049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 831145. | 1.28520 | 0.642600 | − | 0.766202i | \(-0.277856\pi\) | ||||
0.642600 | + | 0.766202i | \(0.277856\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.48691e6 | −2.24562 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −904163. | −1.30346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 384989. | 0.542423 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −168014. | −0.231401 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −458628. | −0.617587 | −0.308793 | − | 0.951129i | \(-0.599925\pi\) | ||||
−0.308793 | + | 0.951129i | \(0.599925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22779.7 | −0.0293416 | −0.0146708 | − | 0.999892i | \(-0.504670\pi\) | ||||
−0.0146708 | + | 0.999892i | \(0.504670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.36560e6 | −1.72082 | −0.860408 | − | 0.509606i | \(-0.829791\pi\) | ||||
−0.860408 | + | 0.509606i | \(0.829791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −811971. | −1.00118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −673470. | −0.812696 | −0.406348 | − | 0.913718i | \(-0.633198\pi\) | ||||
−0.406348 | + | 0.913718i | \(0.633198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −461330. | −0.533508 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −461339. | −0.522426 | −0.261213 | − | 0.965281i | \(-0.584123\pi\) | ||||
−0.261213 | + | 0.965281i | \(0.584123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −842868. | −0.934796 | −0.467398 | − | 0.884047i | \(-0.654809\pi\) | ||||
−0.467398 | + | 0.884047i | \(0.654809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.85951e6 | 2.02014 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 56906.4 | 0.0593498 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.54232e6 | −1.57643 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.34039e6 | 1.34291 | 0.671457 | − | 0.741044i | \(-0.265669\pi\) | ||||
0.671457 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −247747. | −0.243336 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −337841. | −0.319066 | −0.159533 | − | 0.987193i | \(-0.550999\pi\) | ||||
−0.159533 | + | 0.987193i | \(0.550999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.66937e6 | 1.54633 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.94054e6 | −1.76328 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −836410. | −0.745641 | −0.372821 | − | 0.927903i | \(-0.621609\pi\) | ||||
−0.372821 | + | 0.927903i | \(0.621609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.48518e6 | −1.27498 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −36624.0 | −0.0308592 | −0.0154296 | − | 0.999881i | \(-0.504912\pi\) | ||||
−0.0154296 | + | 0.999881i | \(0.504912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.92834e6 | −1.59500 | −0.797500 | − | 0.603319i | \(-0.793845\pi\) | ||||
−0.797500 | + | 0.603319i | \(0.793845\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −356844. | −0.289782 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.42694e6 | −1.11739 | −0.558696 | − | 0.829373i | \(-0.688698\pi\) | ||||
−0.558696 | + | 0.829373i | \(0.688698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.65885e6 | −2.81407 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.36724e6 | −1.78845 | −0.894223 | − | 0.447621i | \(-0.852271\pi\) | ||||
−0.894223 | + | 0.447621i | \(0.852271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.35021e6 | 1.00215 | 0.501077 | − | 0.865403i | \(-0.332937\pi\) | ||||
0.501077 | + | 0.865403i | \(0.332937\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.55634e6 | −1.11532 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.58108e6 | 1.81785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.33929e6 | −1.61939 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −506336. | −0.344564 | −0.172282 | − | 0.985048i | \(-0.555114\pi\) | ||||
−0.172282 | + | 0.985048i | \(0.555114\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.94197e6 | −1.27747 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −108880. | −0.0704317 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.89793e6 | 1.20743 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.58874e6 | 1.61988 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.15053e6 | 0.696712 | 0.348356 | − | 0.937362i | \(-0.386740\pi\) | ||||
0.348356 | + | 0.937362i | \(0.386740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.27843e6 | −0.761693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 742231. | 0.435149 | 0.217574 | − | 0.976044i | \(-0.430185\pi\) | ||||
0.217574 | + | 0.976044i | \(0.430185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.67101e6 | −0.964090 | −0.482045 | − | 0.876146i | \(-0.660106\pi\) | ||||
−0.482045 | + | 0.876146i | \(0.660106\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 646531. | 0.361361 | 0.180681 | − | 0.983542i | \(-0.442170\pi\) | ||||
0.180681 | + | 0.983542i | \(0.442170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 624227. | 0.343452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.63320e6 | 0.884660 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.35512e6 | −0.722723 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.52340e6 | 0.787851 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.39808e6 | 0.712101 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.73052e6 | −1.36986 | −0.684928 | − | 0.728610i | \(-0.740166\pi\) | ||||
−0.684928 | + | 0.728610i | \(0.740166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.75538e6 | 3.33841 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −390252. | −0.187185 | −0.0935923 | − | 0.995611i | \(-0.529835\pi\) | ||||
−0.0935923 | + | 0.995611i | \(0.529835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.26840e6 | 1.07206 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.17697e6 | 0.548123 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.77009e6 | −0.812382 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.23128e6 | −0.994788 | −0.497394 | − | 0.867525i | \(-0.665710\pi\) | ||||
−0.497394 | + | 0.867525i | \(0.665710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −502679. | −0.220916 | −0.110458 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110458 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −853455. | −0.369754 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.57148e6 | −1.95263 | −0.976316 | − | 0.216350i | \(-0.930585\pi\) | ||||
−0.976316 | + | 0.216350i | \(0.930585\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.49758e6 | 3.52878 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 448308. | 0.183586 | 0.0917931 | − | 0.995778i | \(-0.470740\pi\) | ||||
0.0917931 | + | 0.995778i | \(0.470740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.01712e6 | −0.814636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.60286e6 | −1.43510 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.56484e6 | 0.994018 | 0.497009 | − | 0.867745i | \(-0.334432\pi\) | ||||
0.497009 | + | 0.867745i | \(0.334432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.29801e6 | −2.40789 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.17112e6 | −0.818934 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −484728. | −0.180396 | −0.0901978 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901978 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 274335. | 0.0994094 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.26934e6 | −1.52673 | −0.763366 | − | 0.645966i | \(-0.776455\pi\) | ||||
−0.763366 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.56737e6 | −3.02367 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.27791e6 | −0.445147 | −0.222573 | − | 0.974916i | \(-0.571446\pi\) | ||||
−0.222573 | + | 0.974916i | \(0.571446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.68029e6 | 2.60676 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.37341e6 | 1.13030 | 0.565151 | − | 0.824987i | \(-0.308818\pi\) | ||||
0.565151 | + | 0.824987i | \(0.308818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.59276e6 | 0.857672 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.75870e6 | 1.88080 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.82804e6 | −0.582117 | −0.291058 | − | 0.956705i | \(-0.594007\pi\) | ||||
−0.291058 | + | 0.956705i | \(0.594007\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.87814e6 | −0.905064 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.34118e6 | 0.416511 | 0.208256 | − | 0.978074i | \(-0.433221\pi\) | ||||
0.208256 | + | 0.978074i | \(0.433221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 517252. | 0.158650 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.17305e6 | −0.650254 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −803937. | −0.237637 | −0.118818 | − | 0.992916i | \(-0.537911\pi\) | ||||
−0.118818 | + | 0.992916i | \(0.537911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.04516e7 | 3.05195 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.61278e6 | 1.61921 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.44511e6 | 2.09667 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.90295e6 | 1.08607 | 0.543035 | − | 0.839710i | \(-0.317275\pi\) | ||||
0.543035 | + | 0.839710i | \(0.317275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.04306e6 | 0.836769 | 0.418384 | − | 0.908270i | \(-0.362597\pi\) | ||||
0.418384 | + | 0.908270i | \(0.362597\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.65756e6 | 1.53737 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −525892. | −0.139581 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 464511. | 0.121858 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −772580. | −0.200332 | −0.100166 | − | 0.994971i | \(-0.531937\pi\) | ||||
−0.100166 | + | 0.994971i | \(0.531937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.83430e6 | −1.23912 | −0.619561 | − | 0.784948i | \(-0.712689\pi\) | ||||
−0.619561 | + | 0.784948i | \(0.712689\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −878171. | −0.219976 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.98655e6 | −1.23492 | −0.617460 | − | 0.786602i | \(-0.711838\pi\) | ||||
−0.617460 | + | 0.786602i | \(0.711838\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82314e6 | 0.691252 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.63238e6 | −1.84778 | −0.923891 | − | 0.382655i | \(-0.875010\pi\) | ||||
−0.923891 | + | 0.382655i | \(0.875010\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.38400e7 | −3.27617 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.92156e6 | 0.449819 | 0.224910 | − | 0.974380i | \(-0.427791\pi\) | ||||
0.224910 | + | 0.974380i | \(0.427791\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.02592e6 | 0.469009 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.59820e6 | 1.28175 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.64057e6 | −1.48735 | −0.743677 | − | 0.668539i | \(-0.766920\pi\) | ||||
−0.743677 | + | 0.668539i | \(0.766920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.03234e7 | 4.50262 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.78658e6 | 1.26815 | 0.634074 | − | 0.773272i | \(-0.281381\pi\) | ||||
0.634074 | + | 0.773272i | \(0.281381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.55738e6 | −0.988013 | −0.494007 | − | 0.869458i | \(-0.664468\pi\) | ||||
−0.494007 | + | 0.869458i | \(0.664468\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.02351e6 | 0.217171 | 0.108585 | − | 0.994087i | \(-0.465368\pi\) | ||||
0.108585 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.19791e6 | 0.671326 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.33181e7 | −2.76623 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.47057e6 | −0.507743 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.78581e6 | −1.76801 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.42421e6 | −1.08018 | −0.540092 | − | 0.841606i | \(-0.681610\pi\) | ||||
−0.540092 | + | 0.841606i | \(0.681610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −955009. | −0.188211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.50676e6 | 1.07406 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.76364e6 | 1.67441 | 0.837206 | − | 0.546888i | \(-0.184188\pi\) | ||||
0.837206 | + | 0.546888i | \(0.184188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.07695e7 | 2.03668 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.44420e6 | −0.457545 | −0.228772 | − | 0.973480i | \(-0.573471\pi\) | ||||
−0.228772 | + | 0.973480i | \(0.573471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.53277e6 | −1.21054 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.54550e6 | −1.37024 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.77888e6 | −1.03894 | −0.519472 | − | 0.854487i | \(-0.673871\pi\) | ||||
−0.519472 | + | 0.854487i | \(0.673871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.22467e7 | 2.17984 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.58777e6 | 0.984733 | 0.492367 | − | 0.870388i | \(-0.336132\pi\) | ||||
0.492367 | + | 0.870388i | \(0.336132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.05388e7 | −1.82083 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.32211e6 | −1.59485 | −0.797425 | − | 0.603418i | \(-0.793805\pi\) | ||||
−0.797425 | + | 0.603418i | \(0.793805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.95367e6 | 0.330978 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.88357e6 | −1.15484 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.81990e6 | −0.299449 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.47871e6 | −1.05577 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.51696e6 | 1.21324 | 0.606622 | − | 0.794991i | \(-0.292524\pi\) | ||||
0.606622 | + | 0.794991i | \(0.292524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −618460. | −0.0988683 | −0.0494342 | − | 0.998777i | \(-0.515742\pi\) | ||||
−0.0494342 | + | 0.998777i | \(0.515742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.23174e7 | −1.93193 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.75613e6 | −0.738949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.27131e7 | 3.49575 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 890350. | 0.135751 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 848477. | 0.126971 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −908138. | −0.134642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.78044e6 | −1.14291 | −0.571454 | − | 0.820634i | \(-0.693620\pi\) | ||||
−0.571454 | + | 0.820634i | \(0.693620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.34815e6 | −0.196218 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.38809e6 | 0.912857 | 0.456428 | − | 0.889760i | \(-0.349128\pi\) | ||||
0.456428 | + | 0.889760i | \(0.349128\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.12811e6 | −0.301345 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.21265e6 | 0.310481 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34107e6 | −0.325538 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.07422e6 | 1.10271 | 0.551356 | − | 0.834270i | \(-0.314110\pi\) | ||||
0.551356 | + | 0.834270i | \(0.314110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.08576e6 | −0.146962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10615e7 | −1.48390 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.02445e6 | 0.668064 | 0.334032 | − | 0.942562i | \(-0.391591\pi\) | ||||
0.334032 | + | 0.942562i | \(0.391591\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.19656e7 | 2.86936 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.36647e6 | 1.08333 | 0.541666 | − | 0.840594i | \(-0.317794\pi\) | ||||
0.541666 | + | 0.840594i | \(0.317794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 831558. | 0.106734 | 0.0533670 | − | 0.998575i | \(-0.483005\pi\) | ||||
0.0533670 | + | 0.998575i | \(0.483005\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.47443e6 | −1.20550 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63868e6 | 0.705080 | 0.352540 | − | 0.935797i | \(-0.385318\pi\) | ||||
0.352540 | + | 0.935797i | \(0.385318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.17651e7 | 1.45848 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.82667e6 | −0.961915 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.82619e6 | 0.344373 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.13074e6 | −0.494803 | −0.247402 | − | 0.968913i | \(-0.579577\pi\) | ||||
−0.247402 | + | 0.968913i | \(0.579577\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.17191e6 | 0.495504 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.05340e7 | 1.24057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.07710e6 | 0.242561 | 0.121280 | − | 0.992618i | \(-0.461300\pi\) | ||||
0.121280 | + | 0.992618i | \(0.461300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.59660e6 | −0.183342 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.44039e7 | 1.64026 | 0.820128 | − | 0.572180i | \(-0.193902\pi\) | ||||
0.820128 | + | 0.572180i | \(0.193902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.16092e7 | 1.31104 | 0.655522 | − | 0.755176i | \(-0.272449\pi\) | ||||
0.655522 | + | 0.755176i | \(0.272449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.29409e7 | 1.44934 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.75662e7 | 1.93511 | 0.967557 | − | 0.252654i | \(-0.0813035\pi\) | ||||
0.967557 | + | 0.252654i | \(0.0813035\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.38749e7 | −1.51596 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −799810. | −0.0866730 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.76294e7 | −1.89490 | −0.947449 | − | 0.319906i | \(-0.896349\pi\) | ||||
−0.947449 | + | 0.319906i | \(0.896349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.44774e6 | 0.681859 | 0.340930 | − | 0.940089i | \(-0.389258\pi\) | ||||
0.340930 | + | 0.940089i | \(0.389258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.48717e7 | 1.56003 | 0.780017 | − | 0.625758i | \(-0.215210\pi\) | ||||
0.780017 | + | 0.625758i | \(0.215210\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.31704e7 | 1.37047 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.53674e6 | −0.777971 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.74653e6 | 0.380592 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.27418e7 | 2.29191 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.05549e6 | 0.505464 | 0.252732 | − | 0.967536i | \(-0.418671\pi\) | ||||
0.252732 | + | 0.967536i | \(0.418671\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.40482e7 | 2.38547 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −399108. | −0.0389710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.05342e7 | −2.95824 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.66243e6 | 0.640453 | 0.320226 | − | 0.947341i | \(-0.396241\pi\) | ||||
0.320226 | + | 0.947341i | \(0.396241\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.29414e6 | 0.314206 | 0.157103 | − | 0.987582i | \(-0.449784\pi\) | ||||
0.157103 | + | 0.987582i | \(0.449784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.79219e6 | 0.450063 | 0.225032 | − | 0.974351i | \(-0.427751\pi\) | ||||
0.225032 | + | 0.974351i | \(0.427751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.30627e6 | −0.680901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.61609e7 | −2.41936 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.27962e7 | 1.17435 | 0.587177 | − | 0.809459i | \(-0.300239\pi\) | ||||
0.587177 | + | 0.809459i | \(0.300239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.90588e6 | 0.714556 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.06887e6 | 0.275274 | 0.137637 | − | 0.990483i | \(-0.456049\pi\) | ||||
0.137637 | + | 0.990483i | \(0.456049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.79240e6 | −0.159563 | −0.0797814 | − | 0.996812i | \(-0.525422\pi\) | ||||
−0.0797814 | + | 0.996812i | \(0.525422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.86128e6 | −0.429504 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.23349e6 | −0.368454 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.32698e7 | −1.14631 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 684564. | 0.0586959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.37614e7 | 1.17119 | 0.585593 | − | 0.810605i | \(-0.300862\pi\) | ||||
0.585593 | + | 0.810605i | \(0.300862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.01097e7 | 1.68629 | 0.843147 | − | 0.537684i | \(-0.180700\pi\) | ||||
0.843147 | + | 0.537684i | \(0.180700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.18710e7 | −0.988129 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −659104. | −0.0544611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.08331e6 | 0.498986 | 0.249493 | − | 0.968377i | \(-0.419736\pi\) | ||||
0.249493 | + | 0.968377i | \(0.419736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.95120e7 | −3.19401 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.24205e6 | 0.0996761 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.23063e7 | −1.77719 | −0.888593 | − | 0.458697i | \(-0.848316\pi\) | ||||
−0.888593 | + | 0.458697i | \(0.848316\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.66741e7 | −1.31889 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.12020e7 | −1.65308 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.94860e7 | −1.50845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.01349e7 | −1.54758 | −0.773792 | − | 0.633439i | \(-0.781643\pi\) | ||||
−0.773792 | + | 0.633439i | \(0.781643\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.70265e6 | −0.587830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.31369e7 | 0.988424 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.09436e6 | −0.530027 | −0.265013 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265013 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.47356e6 | −0.702812 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.98215e6 | −0.588026 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.33483e7 | −0.969677 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.57591e7 | 1.13686 | 0.568432 | − | 0.822730i | \(-0.307550\pi\) | ||||
0.568432 | + | 0.822730i | \(0.307550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.48753e6 | −0.464774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.43874e7 | −1.73508 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.93222e7 | 1.35588 | 0.677939 | − | 0.735118i | \(-0.262873\pi\) | ||||
0.677939 | + | 0.735118i | \(0.262873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.74496e7 | 1.21610 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.58554e7 | 1.78961 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.53614e6 | 0.518071 | 0.259035 | − | 0.965868i | \(-0.416595\pi\) | ||||
0.259035 | + | 0.965868i | \(0.416595\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.16278e6 | −0.282302 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.08996e6 | 0.410207 | 0.205104 | − | 0.978740i | \(-0.434247\pi\) | ||||
0.205104 | + | 0.978740i | \(0.434247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.64652e6 | 0.110159 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.29284e6 | 0.351736 | 0.175868 | − | 0.984414i | \(-0.443727\pi\) | ||||
0.175868 | + | 0.984414i | \(0.443727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.16720e7 | −2.07670 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.28785e6 | 0.539806 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.58109e7 | −1.02296 | −0.511478 | − | 0.859296i | \(-0.670902\pi\) | ||||
−0.511478 | + | 0.859296i | \(0.670902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.87827e7 | 2.49259 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.01450e7 | −1.27770 | −0.638849 | − | 0.769332i | \(-0.720589\pi\) | ||||
−0.638849 | + | 0.769332i | \(0.720589\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.16826e6 | −0.451657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.10320e7 | −1.31650 | −0.658248 | − | 0.752801i | \(-0.728702\pi\) | ||||
−0.658248 | + | 0.752801i | \(0.728702\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.73066e6 | 0.480734 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.21095e6 | −0.197081 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.09332e6 | −0.249609 | −0.124804 | − | 0.992181i | \(-0.539830\pi\) | ||||
−0.124804 | + | 0.992181i | \(0.539830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.77503e6 | −0.592219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.09247e7 | 0.657599 | 0.328799 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328799 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.83011e7 | 2.87015 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.18114e6 | 0.423984 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.82213e6 | 0.576206 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.31843e7 | −1.93432 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.38257e7 | −0.795700 | −0.397850 | − | 0.917450i | \(-0.630244\pi\) | ||||
−0.397850 | + | 0.917450i | \(0.630244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.42005e7 | −1.38399 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.15113e7 | 0.654156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 300852. | 0.0169891 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.38429e6 | 0.0771937 | 0.0385969 | − | 0.999255i | \(-0.487711\pi\) | ||||
0.0385969 | + | 0.999255i | \(0.487711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.90460e7 | 1.05545 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.04987e7 | −1.67958 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.54313e6 | −0.139181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.05967e6 | −0.0572780 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.08074e7 | −1.11776 | −0.558878 | − | 0.829250i | \(-0.688768\pi\) | ||||
−0.558878 | + | 0.829250i | \(0.688768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.24363e7 | 1.19784 | 0.598919 | − | 0.800810i | \(-0.295597\pi\) | ||||
0.598919 | + | 0.800810i | \(0.295597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.57942e7 | −2.96049 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.75726e6 | −0.459000 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.32791e6 | −0.381742 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.30693e7 | 0.676698 | 0.338349 | − | 0.941021i | \(-0.390131\pi\) | ||||
0.338349 | + | 0.941021i | \(0.390131\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09593e7 | 1.07864 | 0.539321 | − | 0.842100i | \(-0.318681\pi\) | ||||
0.539321 | + | 0.842100i | \(0.318681\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.54670e6 | −0.231171 | −0.115585 | − | 0.993298i | \(-0.536874\pi\) | ||||
−0.115585 | + | 0.993298i | \(0.536874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.05898e7 | −1.04055 | −0.520277 | − | 0.853997i | \(-0.674171\pi\) | ||||
−0.520277 | + | 0.853997i | \(0.674171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.12867e7 | −2.07399 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.50401e6 | 0.474564 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.25683e7 | −3.08703 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.09532e7 | −0.537200 | −0.268600 | − | 0.963252i | \(-0.586561\pi\) | ||||
−0.268600 | + | 0.963252i | \(0.586561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.84438e6 | −0.479953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.84932e7 | −3.31954 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.82831e7 | −0.875673 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.90666e7 | 1.86010 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.47375e7 | 0.697592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.27066e7 | 0.597939 | 0.298970 | − | 0.954263i | \(-0.403357\pi\) | ||||
0.298970 | + | 0.954263i | \(0.403357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.46258e6 | 0.347086 | 0.173543 | − | 0.984826i | \(-0.444478\pi\) | ||||
0.173543 | + | 0.984826i | \(0.444478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.13390e7 | −0.524315 | −0.262158 | − | 0.965025i | \(-0.584434\pi\) | ||||
−0.262158 | + | 0.965025i | \(0.584434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50309e7 | −2.07015 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.61275e7 | 0.737121 | 0.368561 | − | 0.929604i | \(-0.379851\pi\) | ||||
0.368561 | + | 0.929604i | \(0.379851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.46805e7 | 3.37411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.04742e6 | 0.136894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.82945e6 | −0.0817101 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.80381e7 | −2.13329 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.89336e7 | 1.70933 | 0.854663 | − | 0.519182i | \(-0.173763\pi\) | ||||
0.854663 | + | 0.519182i | \(0.173763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.46502e7 | −0.639546 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.57060e7 | 1.54989 | 0.774946 | − | 0.632027i | \(-0.217777\pi\) | ||||
0.774946 | + | 0.632027i | \(0.217777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.48264e7 | 1.50317 | 0.751583 | − | 0.659638i | \(-0.229291\pi\) | ||||
0.751583 | + | 0.659638i | \(0.229291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.97196e6 | −0.425571 | −0.212785 | − | 0.977099i | \(-0.568253\pi\) | ||||
−0.212785 | + | 0.977099i | \(0.568253\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.34761e7 | −1.84500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.85930e7 | −1.20661 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.45089e6 | −0.270702 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.15030e6 | −0.130729 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.01120e7 | 0.829956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.95771e7 | −1.21379 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.49143e7 | 2.24112 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.17790e7 | −0.879064 | −0.439532 | − | 0.898227i | \(-0.644856\pi\) | ||||
−0.439532 | + | 0.898227i | \(0.644856\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.31606e7 | 2.13393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.45704e7 | −1.77931 | −0.889653 | − | 0.456637i | \(-0.849054\pi\) | ||||
−0.889653 | + | 0.456637i | \(0.849054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.01881e7 | 0.404499 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.92232e7 | 1.14764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.05848e7 | −1.97575 | −0.987873 | − | 0.155264i | \(-0.950377\pi\) | ||||
−0.987873 | + | 0.155264i | \(0.950377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.32893e7 | 1.29317 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.31662e6 | 0.166778 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.62529e7 | −1.00341 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.61614e6 | 0.365563 | 0.182781 | − | 0.983154i | \(-0.441490\pi\) | ||||
0.182781 | + | 0.983154i | \(0.441490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.21902e6 | −0.121716 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.14756e7 | 0.807682 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.07884e7 | −1.14562 | −0.572808 | − | 0.819690i | \(-0.694146\pi\) | ||||
−0.572808 | + | 0.819690i | \(0.694146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.83486e7 | −1.78945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.94367e7 | 1.45186 | 0.725932 | − | 0.687766i | \(-0.241409\pi\) | ||||
0.725932 | + | 0.687766i | \(0.241409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37397e7 | −0.503152 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.02857e7 | 0.735045 | 0.367523 | − | 0.930015i | \(-0.380206\pi\) | ||||
0.367523 | + | 0.930015i | \(0.380206\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.11765e6 | −0.0402849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.87066e7 | 0.670724 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.23933e6 | −0.258206 | −0.129103 | − | 0.991631i | \(-0.541210\pi\) | ||||
−0.129103 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.80613e7 | 0.637482 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.30377e7 | 1.86225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.29152e6 | 0.324548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.35382e7 | 1.16540 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.74626e7 | 1.63224 | 0.816122 | − | 0.577880i | \(-0.196120\pi\) | ||||
0.816122 | + | 0.577880i | \(0.196120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.92088e7 | −1.34145 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.13308e7 | 0.385668 | 0.192834 | − | 0.981231i | \(-0.438232\pi\) | ||||
0.192834 | + | 0.981231i | \(0.438232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.77811e7 | 1.27936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.09471e7 | −1.37242 | −0.686210 | − | 0.727404i | \(-0.740727\pi\) | ||||
−0.686210 | + | 0.727404i | \(0.740727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.81072e6 | 0.327148 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.12835e7 | 1.03787 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.17862e7 | 0.389036 | 0.194518 | − | 0.980899i | \(-0.437686\pi\) | ||||
0.194518 | + | 0.980899i | \(0.437686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.04517e7 | 1.32173 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.67553e7 | 0.544706 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.78243e7 | 1.54691 | 0.773454 | − | 0.633853i | \(-0.218527\pi\) | ||||
0.773454 | + | 0.633853i | \(0.218527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.90043e7 | −2.54260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.93264e6 | 0.189021 | 0.0945105 | − | 0.995524i | \(-0.469871\pi\) | ||||
0.0945105 | + | 0.995524i | \(0.469871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.15521e8 | 3.66223 |
(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 | 400.6.a.ba.1.4 | 4 | ||
4.3 | odd | 2 | 200.6.a.j.1.1 | 4 | |||
5.2 | odd | 4 | 80.6.c.d.49.1 | 8 | |||
5.3 | odd | 4 | 80.6.c.d.49.8 | 8 | |||
5.4 | even | 2 | 400.6.a.z.1.1 | 4 | |||
15.2 | even | 4 | 720.6.f.n.289.5 | 8 | |||
15.8 | even | 4 | 720.6.f.n.289.6 | 8 | |||
20.3 | even | 4 | 40.6.c.a.9.1 | ✓ | 8 | ||
20.7 | even | 4 | 40.6.c.a.9.8 | yes | 8 | ||
20.19 | odd | 2 | 200.6.a.k.1.4 | 4 | |||
40.3 | even | 4 | 320.6.c.j.129.8 | 8 | |||
40.13 | odd | 4 | 320.6.c.i.129.1 | 8 | |||
40.27 | even | 4 | 320.6.c.j.129.1 | 8 | |||
40.37 | odd | 4 | 320.6.c.i.129.8 | 8 | |||
60.23 | odd | 4 | 360.6.f.b.289.6 | 8 | |||
60.47 | odd | 4 | 360.6.f.b.289.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.1 | ✓ | 8 | 20.3 | even | 4 | ||
40.6.c.a.9.8 | yes | 8 | 20.7 | even | 4 | ||
80.6.c.d.49.1 | 8 | 5.2 | odd | 4 | |||
80.6.c.d.49.8 | 8 | 5.3 | odd | 4 | |||
200.6.a.j.1.1 | 4 | 4.3 | odd | 2 | |||
200.6.a.k.1.4 | 4 | 20.19 | odd | 2 | |||
320.6.c.i.129.1 | 8 | 40.13 | odd | 4 | |||
320.6.c.i.129.8 | 8 | 40.37 | odd | 4 | |||
320.6.c.j.129.1 | 8 | 40.27 | even | 4 | |||
320.6.c.j.129.8 | 8 | 40.3 | even | 4 | |||
360.6.f.b.289.5 | 8 | 60.47 | odd | 4 | |||
360.6.f.b.289.6 | 8 | 60.23 | odd | 4 | |||
400.6.a.z.1.1 | 4 | 5.4 | even | 2 | |||
400.6.a.ba.1.4 | 4 | 1.1 | even | 1 | trivial | ||
720.6.f.n.289.5 | 8 | 15.2 | even | 4 | |||
720.6.f.n.289.6 | 8 | 15.8 | even | 4 |