Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −6.89244 | −0.442150 | −0.221075 | − | 0.975257i | \(-0.570957\pi\) | ||||
−0.221075 | + | 0.975257i | \(0.570957\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 48.4622 | 0.866919 | 0.433459 | − | 0.901173i | \(-0.357293\pi\) | ||||
0.433459 | + | 0.901173i | \(0.357293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −195.494 | −0.804503 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 163.506 | 0.407429 | 0.203714 | − | 0.979030i | \(-0.434699\pi\) | ||||
0.203714 | + | 0.979030i | \(0.434699\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 120.828 | 0.198295 | 0.0991473 | − | 0.995073i | \(-0.468389\pi\) | ||||
0.0991473 | + | 0.995073i | \(0.468389\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −334.023 | −0.383308 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 78.1920 | 0.0656206 | 0.0328103 | − | 0.999462i | \(-0.489554\pi\) | ||||
0.0328103 | + | 0.999462i | \(0.489554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2265.00 | 1.43941 | 0.719704 | − | 0.694281i | \(-0.244278\pi\) | ||||
0.719704 | + | 0.694281i | \(0.244278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 337.730 | 0.167117 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2451.95 | −0.966480 | −0.483240 | − | 0.875488i | \(-0.660540\pi\) | ||||
−0.483240 | + | 0.875488i | \(0.660540\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −776.413 | −0.248452 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3022.30 | 0.797862 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6985.27 | −1.54237 | −0.771185 | − | 0.636611i | \(-0.780336\pi\) | ||||
−0.771185 | + | 0.636611i | \(0.780336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2794.03 | 0.522188 | 0.261094 | − | 0.965313i | \(-0.415917\pi\) | ||||
0.261094 | + | 0.965313i | \(0.415917\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1126.95 | −0.180145 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2374.65 | −0.327664 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9459.44 | −1.13595 | −0.567977 | − | 0.823044i | \(-0.692274\pi\) | ||||
−0.567977 | + | 0.823044i | \(0.692274\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −832.803 | −0.0876760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10088.5 | 0.937271 | 0.468636 | − | 0.883392i | \(-0.344746\pi\) | ||||
0.468636 | + | 0.883392i | \(0.344746\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6934.29 | 0.571914 | 0.285957 | − | 0.958242i | \(-0.407689\pi\) | ||||
0.285957 | + | 0.958242i | \(0.407689\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9474.08 | −0.697439 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1165.76 | 0.0769778 | 0.0384889 | − | 0.999259i | \(-0.487746\pi\) | ||||
0.0384889 | + | 0.999259i | \(0.487746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −538.934 | −0.0290142 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8562.42 | −0.418704 | −0.209352 | − | 0.977840i | \(-0.567135\pi\) | ||||
−0.209352 | + | 0.977840i | \(0.567135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7923.85 | 0.353207 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15611.4 | −0.636435 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6220.26 | −0.232637 | −0.116318 | − | 0.993212i | \(-0.537109\pi\) | ||||
−0.116318 | + | 0.993212i | \(0.537109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 41928.9 | 1.44274 | 0.721371 | − | 0.692549i | \(-0.243512\pi\) | ||||
0.721371 | + | 0.692549i | \(0.243512\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9579.22 | 0.304074 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5855.62 | 0.171905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1812.09 | −0.0493166 | −0.0246583 | − | 0.999696i | \(-0.507850\pi\) | ||||
−0.0246583 | + | 0.999696i | \(0.507850\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16900.0 | 0.427329 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −56823.3 | −1.33777 | −0.668884 | − | 0.743367i | \(-0.733228\pi\) | ||||
−0.668884 | + | 0.743367i | \(0.733228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44299.5 | −0.972953 | −0.486476 | − | 0.873694i | \(-0.661718\pi\) | ||||
−0.486476 | + | 0.873694i | \(0.661718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5351.38 | 0.109853 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8011.78 | −0.153993 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 34912.4 | 0.629379 | 0.314690 | − | 0.949195i | \(-0.398100\pi\) | ||||
0.314690 | + | 0.949195i | \(0.398100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26674.1 | 0.451728 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 39652.9 | 0.631800 | 0.315900 | − | 0.948793i | \(-0.397694\pi\) | ||||
0.315900 | + | 0.948793i | \(0.397694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3789.36 | 0.0568877 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 48145.6 | 0.681960 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −126299. | −1.69015 | −0.845077 | − | 0.534645i | \(-0.820445\pi\) | ||||
−0.845077 | + | 0.534645i | \(0.820445\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5920.59 | −0.0749483 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −19257.7 | −0.230886 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 109767. | 1.24785 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −145513. | −1.57026 | −0.785130 | − | 0.619331i | \(-0.787404\pi\) | ||||
−0.785130 | + | 0.619331i | \(0.787404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −31964.4 | −0.327777 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −99545.5 | −0.970998 | −0.485499 | − | 0.874237i | \(-0.661362\pi\) | ||||
−0.485499 | + | 0.874237i | \(0.661362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −129791. | −1.20546 | −0.602729 | − | 0.797946i | \(-0.705920\pi\) | ||||
−0.602729 | + | 0.797946i | \(0.705920\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16367.1 | 0.144877 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −218811. | −1.84761 | −0.923804 | − | 0.382865i | \(-0.874938\pi\) | ||||
−0.923804 | + | 0.382865i | \(0.874938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −201627. | −1.62549 | −0.812743 | − | 0.582623i | \(-0.802026\pi\) | ||||
−0.812743 | + | 0.582623i | \(0.802026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 65198.6 | 0.502263 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 31803.9 | 0.234306 | 0.117153 | − | 0.993114i | \(-0.462623\pi\) | ||||
0.117153 | + | 0.993114i | \(0.462623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −118827. | −0.837859 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −23621.3 | −0.159529 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3831.41 | −0.0248022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −134317. | −0.834002 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −69534.1 | −0.414415 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −189071. | −1.08231 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −318115. | −1.75015 | −0.875075 | − | 0.483988i | \(-0.839188\pi\) | ||||
−0.875075 | + | 0.483988i | \(0.839188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −47794.2 | −0.252872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 305194. | 1.55381 | 0.776905 | − | 0.629618i | \(-0.216788\pi\) | ||||
0.776905 | + | 0.629618i | \(0.216788\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −110985. | −0.544045 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 146467. | 0.691681 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 180045. | 0.819556 | 0.409778 | − | 0.912185i | \(-0.365606\pi\) | ||||
0.409778 | + | 0.912185i | \(0.365606\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 323204. | 1.41886 | 0.709430 | − | 0.704776i | \(-0.248953\pi\) | ||||
0.709430 | + | 0.704776i | \(0.248953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8034.96 | −0.0340358 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19756.2 | 0.0807909 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −338522. | −1.33711 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16548.8 | −0.0631644 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −294159. | −1.08547 | −0.542733 | − | 0.839905i | \(-0.682610\pi\) | ||||
−0.542733 | + | 0.839905i | \(0.682610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −334962. | −1.19551 | −0.597754 | − | 0.801679i | \(-0.703940\pi\) | ||||
−0.597754 | + | 0.801679i | \(0.703940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15286.1 | −0.0527919 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 135405. | 0.452694 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 145150. | 0.469967 | 0.234984 | − | 0.971999i | \(-0.424496\pi\) | ||||
0.234984 | + | 0.971999i | \(0.424496\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 59016.0 | 0.185130 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 120146. | 0.365295 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 176221. | 0.519504 | 0.259752 | − | 0.965675i | \(-0.416359\pi\) | ||||
0.259752 | + | 0.965675i | \(0.416359\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −54614.7 | −0.156171 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −45460.7 | −0.126138 | −0.0630689 | − | 0.998009i | \(-0.520089\pi\) | ||||
−0.0630689 | + | 0.998009i | \(0.520089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −356693. | −0.960679 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −442794. | −1.15801 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 205842. | 0.522900 | 0.261450 | − | 0.965217i | \(-0.415799\pi\) | ||||
0.261450 | + | 0.965217i | \(0.415799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 38044.2 | 0.0939061 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 42872.8 | 0.102860 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 199205. | 0.464695 | 0.232348 | − | 0.972633i | \(-0.425359\pi\) | ||||
0.232348 | + | 0.972633i | \(0.425359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −198411. | −0.450162 | −0.225081 | − | 0.974340i | \(-0.572265\pi\) | ||||
−0.225081 | + | 0.974340i | \(0.572265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −288992. | −0.637909 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −458425. | −0.984780 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12784.8 | 0.0267357 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −148093. | −0.301563 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 372947. | 0.739714 | 0.369857 | − | 0.929089i | \(-0.379407\pi\) | ||||
0.369857 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 175020. | 0.338215 | 0.169108 | − | 0.985598i | \(-0.445911\pi\) | ||||
0.169108 | + | 0.985598i | \(0.445911\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40359.5 | −0.0760080 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −883770. | −1.62246 | −0.811229 | − | 0.584728i | \(-0.801201\pi\) | ||||
−0.811229 | + | 0.584728i | \(0.801201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 785843. | 1.40671 | 0.703353 | − | 0.710841i | \(-0.251686\pi\) | ||||
0.703353 | + | 0.710841i | \(0.251686\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12489.7 | 0.0218054 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 342278. | 0.582961 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 488909. | 0.812538 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 479343. | 0.777536 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 370340. | 0.586456 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −763861. | −1.18116 | −0.590579 | − | 0.806980i | \(-0.701101\pi\) | ||||
−0.590579 | + | 0.806980i | \(0.701101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 391652. | 0.591495 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 336051. | 0.495803 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −136907. | −0.197368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 305332. | 0.430191 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9447.82 | 0.0130122 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −204400. | −0.275245 | −0.137623 | − | 0.990485i | \(-0.543946\pi\) | ||||
−0.137623 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 151784. | 0.199881 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.00806e6 | −1.29844 | −0.649218 | − | 0.760603i | \(-0.724904\pi\) | ||||
−0.649218 | + | 0.760603i | \(0.724904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 244324. | 0.307877 | 0.153938 | − | 0.988080i | \(-0.450804\pi\) | ||||
0.153938 | + | 0.988080i | \(0.450804\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 55220.8 | 0.0680883 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20822.9 | 0.0251276 | 0.0125638 | − | 0.999921i | \(-0.496001\pi\) | ||||
0.0125638 | + | 0.999921i | \(0.496001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 56495.5 | 0.0667335 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −240632. | −0.278280 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −474033. | −0.536801 | −0.268401 | − | 0.963307i | \(-0.586495\pi\) | ||||
−0.268401 | + | 0.963307i | \(0.586495\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.70390e6 | −1.88974 | −0.944869 | − | 0.327450i | \(-0.893811\pi\) | ||||
−0.944869 | + | 0.327450i | \(0.893811\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −918268. | −0.997594 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 116358. | 0.123846 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 273676. | 0.285427 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −273305. | −0.279351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 810918. | 0.812442 | 0.406221 | − | 0.913775i | \(-0.366846\pi\) | ||||
0.406221 | + | 0.913775i | \(0.366846\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −400909. | −0.393771 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26117.9 | −0.0251529 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.26657e6 | 1.19618 | 0.598088 | − | 0.801431i | \(-0.295927\pi\) | ||||
0.598088 | + | 0.801431i | \(0.295927\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 463512. | 0.429350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.36558e6 | 1.24084 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.96048e6 | −1.74773 | −0.873863 | − | 0.486172i | \(-0.838393\pi\) | ||||
−0.873863 | + | 0.486172i | \(0.838393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −414954. | −0.362982 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 870511. | 0.747302 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.49358e6 | 1.25848 | 0.629242 | − | 0.777209i | \(-0.283365\pi\) | ||||
0.629242 | + | 0.777209i | \(0.283365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.23626e6 | 1.02255 | 0.511275 | − | 0.859417i | \(-0.329173\pi\) | ||||
0.511275 | + | 0.859417i | \(0.329173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 40807.4 | 0.0331384 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −126948. | −0.101227 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 170150. | 0.133239 | 0.0666197 | − | 0.997778i | \(-0.478779\pi\) | ||||
0.0666197 | + | 0.997778i | \(0.478779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −546217. | −0.420102 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.29957e6 | 0.981824 | 0.490912 | − | 0.871209i | \(-0.336664\pi\) | ||||
0.490912 | + | 0.871209i | \(0.336664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 374032. | 0.277615 | 0.138807 | − | 0.990319i | \(-0.455673\pi\) | ||||
0.138807 | + | 0.990319i | \(0.455673\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −756561. | −0.551737 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −494335. | −0.354255 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41374e6 | −0.995694 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.00294e6 | 0.694291 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.15022e6 | −0.782728 | −0.391364 | − | 0.920236i | \(-0.627997\pi\) | ||||
−0.391364 | + | 0.920236i | \(0.627997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −301448. | −0.201677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 494163. | 0.325072 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −296266. | −0.191648 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −339780. | −0.216163 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 686112. | 0.429327 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.03197e6 | 1.25074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.61214e6 | −1.58179 | −0.790897 | − | 0.611949i | \(-0.790386\pi\) | ||||
−0.790897 | + | 0.611949i | \(0.790386\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 894578. | 0.532994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.40646e6 | −0.824566 | −0.412283 | − | 0.911056i | \(-0.635269\pi\) | ||||
−0.412283 | + | 0.911056i | \(0.635269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.37930e6 | 1.37274 | 0.686369 | − | 0.727253i | \(-0.259203\pi\) | ||||
0.686369 | + | 0.727253i | \(0.259203\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 464230. | 0.263607 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 563199. | 0.314785 | 0.157393 | − | 0.987536i | \(-0.449691\pi\) | ||||
0.157393 | + | 0.987536i | \(0.449691\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.14213e6 | −0.628405 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.50814e6 | 0.816921 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 177105. | 0.0944547 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −93812.8 | −0.0492667 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.38970e6 | 0.718709 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −57122.4 | −0.0290949 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 850649. | 0.426757 | 0.213378 | − | 0.976970i | \(-0.431553\pi\) | ||||
0.213378 | + | 0.976970i | \(0.431553\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.84927e6 | 0.913879 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −87818.0 | −0.0427535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.01506e6 | 1.92582 | 0.962912 | − | 0.269814i | \(-0.0869623\pi\) | ||||
0.962912 | + | 0.269814i | \(0.0869623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −219207. | −0.103599 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 456840. | 0.212754 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 819009. | 0.370460 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.39961e6 | 1.06984 | 0.534918 | − | 0.844904i | \(-0.320343\pi\) | ||||
0.534918 | + | 0.844904i | \(0.320343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 919171. | 0.403955 | 0.201977 | − | 0.979390i | \(-0.435263\pi\) | ||||
0.201977 | + | 0.979390i | \(0.435263\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 365179. | 0.158212 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.07684e6 | 0.459953 | 0.229976 | − | 0.973196i | \(-0.426135\pi\) | ||||
0.229976 | + | 0.973196i | \(0.426135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.75378e6 | −1.15974 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26407.8 | 0.0109663 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.24219e6 | −0.508688 | −0.254344 | − | 0.967114i | \(-0.581860\pi\) | ||||
−0.254344 | + | 0.967114i | \(0.581860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.65411e6 | 1.07189 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 925771. | 0.368754 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.14685e6 | −0.843471 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.17293e6 | 1.61725 | 0.808624 | − | 0.588326i | \(-0.200213\pi\) | ||||
0.808624 | + | 0.588326i | \(0.200213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.97224e6 | −0.754037 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 419558. | 0.158255 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.72238e6 | 0.640999 | 0.320500 | − | 0.947249i | \(-0.396149\pi\) | ||||
0.320500 | + | 0.947249i | \(0.396149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.30316e6 | 0.478542 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −844020. | −0.305844 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.72998e6 | −0.618647 | −0.309324 | − | 0.950957i | \(-0.600103\pi\) | ||||
−0.309324 | + | 0.950957i | \(0.600103\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.19259e6 | 0.773830 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.34881e6 | −1.16652 | −0.583262 | − | 0.812284i | \(-0.698224\pi\) | ||||
−0.583262 | + | 0.812284i | \(0.698224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −388269. | −0.133500 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.35561e6 | −0.460106 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.18691e6 | 1.73794 | 0.868970 | − | 0.494864i | \(-0.164782\pi\) | ||||
0.868970 | + | 0.494864i | \(0.164782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −191723. | −0.0634209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.10353e6 | −0.687018 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.69193e6 | 0.545621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.30271e6 | 0.414830 | 0.207415 | − | 0.978253i | \(-0.433495\pi\) | ||||
0.207415 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 764957. | 0.240550 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.53036e6 | −0.475261 | −0.237631 | − | 0.971356i | \(-0.576371\pi\) | ||||
−0.237631 | + | 0.971356i | \(0.576371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 337598. | 0.103547 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.29269e6 | 0.391611 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.54667e6 | −0.462820 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.93690e6 | −0.868123 | −0.434062 | − | 0.900883i | \(-0.642920\pi\) | ||||
−0.434062 | + | 0.900883i | \(0.642920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.24095e6 | −0.362367 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 304793. | 0.0879284 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.92167e6 | 0.547719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.22766e6 | −0.627349 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.16465e6 | 0.324085 | 0.162043 | − | 0.986784i | \(-0.448192\pi\) | ||||
0.162043 | + | 0.986784i | \(0.448192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.58204e6 | 0.435022 | 0.217511 | − | 0.976058i | \(-0.430206\pi\) | ||||
0.217511 | + | 0.976058i | \(0.430206\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −227900. | −0.0619289 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −60709.3 | −0.0163036 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.05451e6 | −0.545305 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −136168. | −0.0357217 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.10233e6 | 1.58235 | 0.791174 | − | 0.611591i | \(-0.209470\pi\) | ||||
0.791174 | + | 0.611591i | \(0.209470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.08115e6 | 0.277118 | 0.138559 | − | 0.990354i | \(-0.455753\pi\) | ||||
0.138559 | + | 0.990354i | \(0.455753\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.33324e6 | 0.591203 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.55367e6 | −1.39116 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.04807e6 | −1.74546 | −0.872728 | − | 0.488207i | \(-0.837651\pi\) | ||||
−0.872728 | + | 0.488207i | \(0.837651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −469382. | −0.114929 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.32031e6 | 0.561742 | 0.280871 | − | 0.959746i | \(-0.409377\pi\) | ||||
0.280871 | + | 0.959746i | \(0.409377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.12075e6 | −1.46523 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.02747e6 | 0.479939 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45039e6 | −1.27589 | −0.637943 | − | 0.770084i | \(-0.720214\pi\) | ||||
−0.637943 | + | 0.770084i | \(0.720214\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.64952e6 | 0.381871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.30871e6 | 0.528595 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −286925. | −0.0649741 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.62676e6 | 1.48426 | 0.742132 | − | 0.670254i | \(-0.233815\pi\) | ||||
0.742132 | + | 0.670254i | \(0.233815\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 236319. | 0.0523561 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −606397. | −0.132894 | −0.0664469 | − | 0.997790i | \(-0.521166\pi\) | ||||
−0.0664469 | + | 0.997790i | \(0.521166\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.65855e6 | 0.793153 | 0.396576 | − | 0.918002i | \(-0.370198\pi\) | ||||
0.396576 | + | 0.918002i | \(0.370198\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −933271. | −0.200159 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.62712e6 | −1.19397 | −0.596986 | − | 0.802252i | \(-0.703635\pi\) | ||||
−0.596986 | + | 0.802252i | \(0.703635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 88792.5 | 0.0186399 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00044e6 | −0.207796 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.13380e6 | 0.233014 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.75857e6 | −0.357624 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.67390e6 | 0.336848 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.25107e6 | 0.846563 | 0.423281 | − | 0.905998i | \(-0.360878\pi\) | ||||
0.423281 | + | 0.905998i | \(0.360878\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.14297e6 | −0.225254 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −828098. | −0.161515 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.05187e6 | −1.36129 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.28756e6 | 1.01026 | 0.505130 | − | 0.863043i | \(-0.331445\pi\) | ||||
0.505130 | + | 0.863043i | \(0.331445\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.21459e6 | −0.229699 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.33842e6 | 0.624939 | 0.312469 | − | 0.949928i | \(-0.398844\pi\) | ||||
0.312469 | + | 0.949928i | \(0.398844\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −546192. | −0.101211 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.54907e6 | −0.284156 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.78434e6 | 0.505629 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.52847e6 | −0.454576 | −0.227288 | − | 0.973828i | \(-0.572986\pi\) | ||||
−0.227288 | + | 0.973828i | \(0.572986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 313335. | 0.0557719 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.94498e6 | −1.04768 | −0.523842 | − | 0.851815i | \(-0.675502\pi\) | ||||
−0.523842 | + | 0.851815i | \(0.675502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.82420e6 | −0.841776 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.45849e6 | 0.424765 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 603525. | 0.103253 | 0.0516263 | − | 0.998666i | \(-0.483560\pi\) | ||||
0.0516263 | + | 0.998666i | \(0.483560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.17068e6 | 0.367741 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.84549e6 | 1.14845 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.28997e6 | −1.04503 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 190609. | 0.0313630 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.41875e6 | −0.231200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.03389e7 | 1.66870 | 0.834350 | − | 0.551235i | \(-0.185843\pi\) | ||||
0.834350 | + | 0.551235i | \(0.185843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.82310e6 | 1.41048 | 0.705240 | − | 0.708968i | \(-0.250839\pi\) | ||||
0.705240 | + | 0.708968i | \(0.250839\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −262218. | −0.0415206 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 218471. | 0.0342663 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −424266. | −0.0659172 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.21602e6 | 0.187157 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.21897e6 | 0.185856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.06041e7 | −1.60173 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.37301e6 | −0.205465 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 392577. | 0.0582041 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.16811e6 | −0.171590 | −0.0857949 | − | 0.996313i | \(-0.527343\pi\) | ||||
−0.0857949 | + | 0.996313i | \(0.527343\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.36753e6 | 0.199039 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.77130e6 | −1.40916 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.17075e6 | −1.31050 | −0.655249 | − | 0.755413i | \(-0.727436\pi\) | ||||
−0.655249 | + | 0.755413i | \(0.727436\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.19685e6 | −1.16069 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.58216e7 | −2.22010 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.71071e6 | −0.237883 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.15967e6 | 0.435421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.22421e6 | −0.850054 | −0.425027 | − | 0.905181i | \(-0.639735\pi\) | ||||
−0.425027 | + | 0.905181i | \(0.639735\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 837859. | 0.113407 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −88118.8 | −0.0118212 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.64042e6 | 0.749964 | 0.374982 | − | 0.927032i | \(-0.377649\pi\) | ||||
0.374982 | + | 0.927032i | \(0.377649\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54129e6 | 0.203125 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.30703e6 | −0.170737 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.05286e7 | −1.36330 | −0.681650 | − | 0.731678i | \(-0.738737\pi\) | ||||
−0.681650 | + | 0.731678i | \(0.738737\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.31395e6 | 0.938776 | 0.469388 | − | 0.882992i | \(-0.344475\pi\) | ||||
0.469388 | + | 0.882992i | \(0.344475\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.57052e6 | −0.327065 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.90373e6 | 0.240124 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.66534e6 | 0.333282 | 0.166641 | − | 0.986018i | \(-0.446708\pi\) | ||||
0.166641 | + | 0.986018i | \(0.446708\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.20631e6 | −0.149542 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.94299e6 | −0.238798 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.40000e6 | −0.170592 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.14474e6 | −0.138298 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.92431e6 | −0.589861 | −0.294931 | − | 0.955519i | \(-0.595297\pi\) | ||||
−0.294931 | + | 0.955519i | \(0.595297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.32847e6 | 0.751641 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.09133e6 | 0.717371 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.08735e6 | −0.594094 | −0.297047 | − | 0.954863i | \(-0.596002\pi\) | ||||
−0.297047 | + | 0.954863i | \(0.596002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −185678. | −0.0215015 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.41638e6 | −0.621975 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.64678e6 | 0.529157 | 0.264579 | − | 0.964364i | \(-0.414767\pi\) | ||||
0.264579 | + | 0.964364i | \(0.414767\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.35424e6 | −0.491730 | −0.245865 | − | 0.969304i | \(-0.579072\pi\) | ||||
−0.245865 | + | 0.969304i | \(0.579072\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 354254. | 0.0396754 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.50929e6 | −0.723012 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.25461e7 | −1.38209 | −0.691043 | − | 0.722813i | \(-0.742849\pi\) | ||||
−0.691043 | + | 0.722813i | \(0.742849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.35914e6 | −0.257756 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 140857. | 0.0152643 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.07637e6 | 0.438149 | 0.219075 | − | 0.975708i | \(-0.429696\pi\) | ||||
0.219075 | + | 0.975708i | \(0.429696\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.36978e6 | −0.359264 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.88533e6 | −0.939639 | −0.469819 | − | 0.882763i | \(-0.655681\pi\) | ||||
−0.469819 | + | 0.882763i | \(0.655681\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.28530e7 | 1.34827 | 0.674136 | − | 0.738607i | \(-0.264516\pi\) | ||||
0.674136 | + | 0.738607i | \(0.264516\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.41053e6 | −0.771117 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.18867e6 | 0.638818 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.73652e6 | −0.689819 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.55255e6 | −0.259302 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −739652. | −0.0745420 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −288616. | −0.0288567 | −0.0144283 | − | 0.999896i | \(-0.504593\pi\) | ||||
−0.0144283 | + | 0.999896i | \(0.504593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.26487e6 | 0.522250 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.54166e7 | −1.51724 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 290109. | 0.0283278 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.11086e7 | 1.07624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.94591e7 | −1.87058 | −0.935291 | − | 0.353880i | \(-0.884862\pi\) | ||||
−0.935291 | + | 0.353880i | \(0.884862\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.30171e7 | −1.24161 | −0.620805 | − | 0.783965i | \(-0.713194\pi\) | ||||
−0.620805 | + | 0.783965i | \(0.713194\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.31621e6 | −0.219219 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.42864e6 | 0.603751 | 0.301876 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301876 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.01705e6 | −0.0947829 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 943627. | 0.0872666 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.00202e7 | −0.919592 | −0.459796 | − | 0.888025i | \(-0.652077\pi\) | ||||
−0.459796 | + | 0.888025i | \(0.652077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.47904e7 | 1.34703 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.66030e6 | 0.782743 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.49356e7 | −1.33971 | −0.669854 | − | 0.742493i | \(-0.733643\pi\) | ||||
−0.669854 | + | 0.742493i | \(0.733643\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.35055e6 | 0.120229 | 0.0601143 | − | 0.998191i | \(-0.480853\pi\) | ||||
0.0601143 | + | 0.998191i | \(0.480853\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −65118.5 | −0.00575335 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.37857e6 | −0.471643 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.71276e7 | 1.49067 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.40882e6 | 0.121700 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.85561e6 | 0.587814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.59401e6 | 0.561193 | 0.280596 | − | 0.959826i | \(-0.409468\pi\) | ||||
0.280596 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.34655e6 | −0.198231 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.42517e7 | −1.19508 | −0.597538 | − | 0.801840i | \(-0.703854\pi\) | ||||
−0.597538 | + | 0.801840i | \(0.703854\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.13012e6 | 0.593502 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.94797e6 | 0.574104 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.65006e6 | 0.627499 | 0.313749 | − | 0.949506i | \(-0.398415\pi\) | ||||
0.313749 | + | 0.949506i | \(0.398415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.72536e6 | 0.710489 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.68399e6 | −0.136128 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.03458e6 | −0.0830266 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.38655e7 | −1.10469 | −0.552344 | − | 0.833616i | \(-0.686267\pi\) | ||||
−0.552344 | + | 0.833616i | \(0.686267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.56626e6 | 0.123888 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.56632e7 | 1.23004 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 788837. | 0.0615042 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −143521. | −0.0111102 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.38825e6 | 0.183563 | 0.0917814 | − | 0.995779i | \(-0.470744\pi\) | ||||
0.0917814 | + | 0.995779i | \(0.470744\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.14256e7 | −1.63510 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −389392. | −0.0295063 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.87773e6 | 0.367003 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.55641e7 | 1.16281 | 0.581404 | − | 0.813615i | \(-0.302504\pi\) | ||||
0.581404 | + | 0.813615i | \(0.302504\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.82518e6 | −0.506337 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.85083e6 | −0.504684 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 957427. | 0.0700391 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.26724e6 | 0.237347 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82555e7 | 1.31696 | 0.658478 | − | 0.752600i | \(-0.271200\pi\) | ||||
0.658478 | + | 0.752600i | \(0.271200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.35977e6 | 0.455620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.17440e7 | 0.835548 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.42346e6 | 0.383205 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.11427e6 | −0.148362 | −0.0741812 | − | 0.997245i | \(-0.523634\pi\) | ||||
−0.0741812 | + | 0.997245i | \(0.523634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −152693. | −0.0106414 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 542206. | 0.0375293 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.12932e6 | −0.146380 | −0.0731898 | − | 0.997318i | \(-0.523318\pi\) | ||||
−0.0731898 | + | 0.997318i | \(0.523318\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −801990. | −0.0547584 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −296288. | −0.0200930 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.08671e6 | 0.544704 | 0.272352 | − | 0.962198i | \(-0.412198\pi\) | ||||
0.272352 | + | 0.962198i | \(0.412198\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.88630e6 | −0.126202 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.18944e7 | −0.790442 | −0.395221 | − | 0.918586i | \(-0.629332\pi\) | ||||
−0.395221 | + | 0.918586i | \(0.629332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.42556e7 | −0.941010 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.75191e6 | −0.508285 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.07217e7 | 0.698331 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.85538e7 | −1.20042 | −0.600211 | − | 0.799842i | \(-0.704917\pi\) | ||||
−0.600211 | + | 0.799842i | \(0.704917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.58921e6 | −0.359222 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.62330e7 | −1.03641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.32534e6 | −0.591459 | −0.295730 | − | 0.955272i | \(-0.595563\pi\) | ||||
−0.295730 | + | 0.955272i | \(0.595563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.76324e6 | 0.174106 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.00756e6 | 0.501232 | 0.250616 | − | 0.968087i | \(-0.419367\pi\) | ||||
0.250616 | + | 0.968087i | \(0.419367\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.87974e6 | 0.614376 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −740797. | −0.0457663 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −751584. | −0.0461306 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.02720e7 | 1.23618 | 0.618089 | − | 0.786108i | \(-0.287907\pi\) | ||||
0.618089 | + | 0.786108i | \(0.287907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.72973e6 | −0.528889 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.87881e6 | −0.173286 | −0.0866431 | − | 0.996239i | \(-0.527614\pi\) | ||||
−0.0866431 | + | 0.996239i | \(0.527614\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.16932e6 | −0.129739 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.19473e6 | −0.189838 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.28503e7 | 1.34911 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.29094e6 | −0.545045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.11116e7 | −1.23060 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.03428e6 | 0.407423 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.03508e7 | 1.17124 | 0.585618 | − | 0.810587i | \(-0.300852\pi\) | ||||
0.585618 | + | 0.810587i | \(0.300852\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.35125e7 | 0.772758 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.55839e6 | −0.0885595 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.06620e6 | 0.286088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.86005e6 | 0.160493 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.24765e7 | 1.25338 | 0.626689 | − | 0.779269i | \(-0.284410\pi\) | ||||
0.626689 | + | 0.779269i | \(0.284410\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 91153.3 | 0.00505133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.46908e7 | 1.35973 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.24322e6 | −0.396409 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.82253e6 | 0.316681 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.02944e7 | −0.556439 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.15427e6 | −0.0620062 | −0.0310031 | − | 0.999519i | \(-0.509870\pi\) | ||||
−0.0310031 | + | 0.999519i | \(0.509870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.26698e7 | 1.21031 | 0.605154 | − | 0.796108i | \(-0.293112\pi\) | ||||
0.605154 | + | 0.796108i | \(0.293112\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.52082e6 | −0.452121 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.54007e6 | 0.450368 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.57061e7 | 0.823217 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.15744e6 | 0.0602961 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.41657e6 | 0.125124 | 0.0625622 | − | 0.998041i | \(-0.480073\pi\) | ||||
0.0625622 | + | 0.998041i | \(0.480073\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.10169e6 | −0.108161 | −0.0540804 | − | 0.998537i | \(-0.517223\pi\) | ||||
−0.0540804 | + | 0.998537i | \(0.517223\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 874982. | 0.0447574 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.53997e7 | −0.782977 | −0.391489 | − | 0.920183i | \(-0.628040\pi\) | ||||
−0.391489 | + | 0.920183i | \(0.628040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.33839e7 | 1.18177 | 0.590883 | − | 0.806757i | \(-0.298779\pi\) | ||||
0.590883 | + | 0.806757i | \(0.298779\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.17275e6 | −0.0589118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 187739. | 0.00937436 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.20313e6 | −0.109351 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.44439e6 | 0.416634 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.03016e7 | 0.995695 | 0.497848 | − | 0.867265i | \(-0.334124\pi\) | ||||
0.497848 | + | 0.867265i | \(0.334124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.82829e7 | 1.37890 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.95721e6 | −0.434114 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.72862e7 | −0.832831 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.58153e6 | 0.315223 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.57800e6 | −0.122748 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.31941e7 | 1.09788 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.35163e7 | −1.57719 | −0.788594 | − | 0.614914i | \(-0.789191\pi\) | ||||
−0.788594 | + | 0.614914i | \(0.789191\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.14588e7 | −1.00390 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.30661e7 | −1.07281 | −0.536405 | − | 0.843961i | \(-0.680218\pi\) | ||||
−0.536405 | + | 0.843961i | \(0.680218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.85609e7 | −1.78305 | −0.891527 | − | 0.452968i | \(-0.850365\pi\) | ||||
−0.891527 | + | 0.452968i | \(0.850365\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.40717e6 | 0.156634 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.86892e7 | 1.76833 | 0.884163 | − | 0.467179i | \(-0.154729\pi\) | ||||
0.884163 | + | 0.467179i | \(0.154729\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.97555e6 | 0.453311 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.74414e6 | 0.440247 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.70838e6 | 0.256427 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −218952. | −0.00977922 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.84469e7 | 1.26328 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.26449e6 | 0.409073 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.17369e7 | 0.954332 | 0.477166 | − | 0.878813i | \(-0.341664\pi\) | ||||
0.477166 | + | 0.878813i | \(0.341664\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.92781e6 | 0.346084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.42086e6 | 0.365525 | 0.182762 | − | 0.983157i | \(-0.441496\pi\) | ||||
0.182762 | + | 0.983157i | \(0.441496\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.22954e7 | −1.39392 | −0.696962 | − | 0.717108i | \(-0.745465\pi\) | ||||
−0.696962 | + | 0.717108i | \(0.745465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.07771e6 | 0.0891716 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.21800e7 | −1.80010 | −0.900052 | − | 0.435782i | \(-0.856472\pi\) | ||||
−0.900052 | + | 0.435782i | \(0.856472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.55876e7 | 0.661494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.36137e6 | 0.184047 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.64045e6 | 0.110802 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.65393e6 | 0.402853 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.04200e6 | 0.0847371 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.95171e7 | −0.805407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −669512. | −0.0274756 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.34191e6 | 0.0955766 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.61542e6 | −0.390254 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.64517e6 | 0.308581 | 0.154291 | − | 0.988026i | \(-0.450691\pi\) | ||||
0.154291 | + | 0.988026i | \(0.450691\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.94606e7 | 0.781170 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.93310e7 | −1.57014 | −0.785072 | − | 0.619405i | \(-0.787374\pi\) | ||||
−0.785072 | + | 0.619405i | \(0.787374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.48347e6 | 0.257413 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.40052e7 | −0.553015 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.49545e7 | −0.587285 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.52204e7 | 1.37564 | 0.687822 | − | 0.725880i | \(-0.258567\pi\) | ||||
0.687822 | + | 0.725880i | \(0.258567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.80040e7 | 0.699391 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.86587e6 | −0.265272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.34443e6 | 0.282230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.53734e7 | 0.969794 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.66300e7 | −0.632199 | −0.316099 | − | 0.948726i | \(-0.602373\pi\) | ||||
−0.316099 | + | 0.948726i | \(0.602373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.43826e6 | 0.205630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.69393e6 | 0.364582 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 619582. | 0.0231777 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.07121e7 | 0.770681 | 0.385341 | − | 0.922774i | \(-0.374084\pi\) | ||||
0.385341 | + | 0.922774i | \(0.374084\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.63992e7 | −0.606957 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.09797e7 | 0.404219 | 0.202110 | − | 0.979363i | \(-0.435220\pi\) | ||||
0.202110 | + | 0.979363i | \(0.435220\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.47364e7 | −0.905853 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.17689e6 | −0.261431 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.71723e6 | −0.0984581 | −0.0492290 | − | 0.998788i | \(-0.515676\pi\) | ||||
−0.0492290 | + | 0.998788i | \(0.515676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.35264e6 | −0.192931 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.88182e6 | −0.139182 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.24083e6 | −0.329594 | −0.164797 | − | 0.986328i | \(-0.552697\pi\) | ||||
−0.164797 | + | 0.986328i | \(0.552697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.80739e7 | 0.641272 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.87209e6 | 0.277850 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.82219e6 | −0.309763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.08225e7 | −0.727320 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.27763e7 | 1.48641 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.48183e6 | 0.293205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.50444e7 | −0.517379 | −0.258690 | − | 0.965960i | \(-0.583291\pi\) | ||||
−0.258690 | + | 0.965960i | \(0.583291\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.22068e6 | −0.0417632 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.27894e7 | −0.775685 | −0.387842 | − | 0.921726i | \(-0.626780\pi\) | ||||
−0.387842 | + | 0.921726i | \(0.626780\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.58370e7 | −0.536279 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 646600. | 0.0217833 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.96682e7 | −1.32955 | −0.664777 | − | 0.747042i | \(-0.731474\pi\) | ||||
−0.664777 | + | 0.747042i | \(0.731474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.06507e7 | −0.688617 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.94170e7 | 1.30771 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.77093e7 | 0.914621 | 0.457310 | − | 0.889307i | \(-0.348813\pi\) | ||||
0.457310 | + | 0.889307i | \(0.348813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.28294e7 | −1.40654 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 393713. | 0.0128643 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.70025e7 | −0.552743 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.78535e7 | 1.54785 | 0.773926 | − | 0.633276i | \(-0.218290\pi\) | ||||
0.773926 | + | 0.633276i | \(0.218290\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.86305e6 | −0.188691 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.80837e7 | 1.21950 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.48289e7 | 1.74691 | 0.873457 | − | 0.486902i | \(-0.161873\pi\) | ||||
0.873457 | + | 0.486902i | \(0.161873\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.85892e7 | −0.906335 |
(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 | 448.6.a.x.1.1 | 2 | ||
4.3 | odd | 2 | 448.6.a.r.1.2 | 2 | |||
8.3 | odd | 2 | 112.6.a.j.1.1 | 2 | |||
8.5 | even | 2 | 56.6.a.d.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 504.6.a.m.1.2 | 2 | |||
24.11 | even | 2 | 1008.6.a.bi.1.2 | 2 | |||
56.5 | odd | 6 | 392.6.i.h.361.2 | 4 | |||
56.13 | odd | 2 | 392.6.a.e.1.1 | 2 | |||
56.27 | even | 2 | 784.6.a.q.1.2 | 2 | |||
56.37 | even | 6 | 392.6.i.k.361.1 | 4 | |||
56.45 | odd | 6 | 392.6.i.h.177.2 | 4 | |||
56.53 | even | 6 | 392.6.i.k.177.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.d.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
112.6.a.j.1.1 | 2 | 8.3 | odd | 2 | |||
392.6.a.e.1.1 | 2 | 56.13 | odd | 2 | |||
392.6.i.h.177.2 | 4 | 56.45 | odd | 6 | |||
392.6.i.h.361.2 | 4 | 56.5 | odd | 6 | |||
392.6.i.k.177.1 | 4 | 56.53 | even | 6 | |||
392.6.i.k.361.1 | 4 | 56.37 | even | 6 | |||
448.6.a.r.1.2 | 2 | 4.3 | odd | 2 | |||
448.6.a.x.1.1 | 2 | 1.1 | even | 1 | trivial | ||
504.6.a.m.1.2 | 2 | 24.5 | odd | 2 | |||
784.6.a.q.1.2 | 2 | 56.27 | even | 2 | |||
1008.6.a.bi.1.2 | 2 | 24.11 | even | 2 |