Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,8,Mod(1,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.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: | \(94.9650477472\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5014x^{3} + 113222x^{2} - 625803x + 567036 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 76) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(15.8518\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.1 |
$q$-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 | ||||||||
\(3\) | −8.09048 | −0.173002 | −0.0865008 | − | 0.996252i | \(-0.527568\pi\) | ||||
−0.0865008 | + | 0.996252i | \(0.527568\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 276.339 | 0.988662 | 0.494331 | − | 0.869274i | \(-0.335413\pi\) | ||||
0.494331 | + | 0.869274i | \(0.335413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 720.800 | 0.794276 | 0.397138 | − | 0.917759i | \(-0.370003\pi\) | ||||
0.397138 | + | 0.917759i | \(0.370003\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2121.54 | −0.970070 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4974.98 | 1.12698 | 0.563491 | − | 0.826122i | \(-0.309458\pi\) | ||||
0.563491 | + | 0.826122i | \(0.309458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8085.05 | 1.02066 | 0.510330 | − | 0.859979i | \(-0.329523\pi\) | ||||
0.510330 | + | 0.859979i | \(0.329523\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2235.72 | −0.171040 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1375.87 | 0.0679215 | 0.0339608 | − | 0.999423i | \(-0.489188\pi\) | ||||
0.0339608 | + | 0.999423i | \(0.489188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5831.62 | −0.137411 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 55033.5 | 0.943147 | 0.471574 | − | 0.881827i | \(-0.343686\pi\) | ||||
0.471574 | + | 0.881827i | \(0.343686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1761.49 | −0.0225471 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 34858.2 | 0.340825 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −117756. | −0.896585 | −0.448292 | − | 0.893887i | \(-0.647968\pi\) | ||||
−0.448292 | + | 0.893887i | \(0.647968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 151040. | 0.910598 | 0.455299 | − | 0.890339i | \(-0.349532\pi\) | ||||
0.455299 | + | 0.890339i | \(0.349532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −40250.0 | −0.194970 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 199185. | 0.785271 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −76088.3 | −0.246952 | −0.123476 | − | 0.992348i | \(-0.539404\pi\) | ||||
−0.123476 | + | 0.992348i | \(0.539404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −65411.9 | −0.176576 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 420662. | 0.953212 | 0.476606 | − | 0.879117i | \(-0.341867\pi\) | ||||
0.476606 | + | 0.879117i | \(0.341867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 411546. | 0.789366 | 0.394683 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394683 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −586266. | −0.959072 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 791764. | 1.11238 | 0.556190 | − | 0.831055i | \(-0.312263\pi\) | ||||
0.556190 | + | 0.831055i | \(0.312263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −303991. | −0.369126 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11131.5 | −0.0117505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −800670. | −0.738734 | −0.369367 | − | 0.929284i | \(-0.620425\pi\) | ||||
−0.369367 | + | 0.929284i | \(0.620425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.37478e6 | 1.11421 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −55492.6 | −0.0396893 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.09461e6 | −1.96166 | −0.980831 | − | 0.194860i | \(-0.937575\pi\) | ||||
−0.980831 | + | 0.194860i | \(0.937575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.19949e6 | −1.24070 | −0.620350 | − | 0.784325i | \(-0.713010\pi\) | ||||
−0.620350 | + | 0.784325i | \(0.713010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.52921e6 | −0.770504 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.23422e6 | 1.00909 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 420260. | 0.170709 | 0.0853544 | − | 0.996351i | \(-0.472798\pi\) | ||||
0.0853544 | + | 0.996351i | \(0.472798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −445247. | −0.163166 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.69010e6 | −0.891999 | −0.446000 | − | 0.895033i | \(-0.647152\pi\) | ||||
−0.446000 | + | 0.895033i | \(0.647152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 598122. | 0.179953 | 0.0899766 | − | 0.995944i | \(-0.471321\pi\) | ||||
0.0899766 | + | 0.995944i | \(0.471321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14251.3 | 0.00390069 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.58597e6 | 0.895136 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.62187e6 | −0.598296 | −0.299148 | − | 0.954207i | \(-0.596702\pi\) | ||||
−0.299148 | + | 0.954207i | \(0.596702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.35780e6 | 0.911107 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.86850e6 | 1.12656 | 0.563280 | − | 0.826266i | \(-0.309539\pi\) | ||||
0.563280 | + | 0.826266i | \(0.309539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 380208. | 0.0671515 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 952705. | 0.155110 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.26993e6 | 0.942752 | 0.471376 | − | 0.881932i | \(-0.343757\pi\) | ||||
0.471376 | + | 0.881932i | \(0.343757\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.82770e6 | 0.810685 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.22199e6 | −0.157535 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.89541e6 | 0.226815 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21791e7 | 1.35492 | 0.677462 | − | 0.735558i | \(-0.263080\pi\) | ||||
0.677462 | + | 0.735558i | \(0.263080\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.05546e7 | −1.09325 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.80256e6 | 0.463819 | 0.231909 | − | 0.972737i | \(-0.425503\pi\) | ||||
0.231909 | + | 0.972737i | \(0.425503\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.18941e6 | −0.377766 | −0.188883 | − | 0.982000i | \(-0.560487\pi\) | ||||
−0.188883 | + | 0.982000i | \(0.560487\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.61151e6 | −0.135853 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.54409e7 | 1.21851 | 0.609255 | − | 0.792974i | \(-0.291469\pi\) | ||||
0.609255 | + | 0.792974i | \(0.291469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.21155e7 | 1.63570 | 0.817850 | − | 0.575432i | \(-0.195166\pi\) | ||||
0.817850 | + | 0.575432i | \(0.195166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 615591. | 0.0427230 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.04919e7 | −0.684036 | −0.342018 | − | 0.939693i | \(-0.611110\pi\) | ||||
−0.342018 | + | 0.939693i | \(0.611110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.52079e7 | 0.932454 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.71528e7 | −0.990112 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 991730. | 0.0539485 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.26330e6 | 0.270091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.40336e6 | −0.164907 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.20758e7 | −1.01095 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.77716e6 | −0.0769863 | −0.0384932 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384932 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.32960e6 | −0.136562 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.55541e7 | 0.604498 | 0.302249 | − | 0.953229i | \(-0.402263\pi\) | ||||
0.302249 | + | 0.953229i | \(0.402263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.94396e6 | 0.182219 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.63269e6 | 0.336961 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.72051e7 | 1.56844 | 0.784218 | − | 0.620485i | \(-0.213064\pi\) | ||||
0.784218 | + | 0.620485i | \(0.213064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.49244e7 | 1.73466 | 0.867329 | − | 0.497735i | \(-0.165835\pi\) | ||||
0.867329 | + | 0.497735i | \(0.165835\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.40575e6 | −0.192443 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.02230e7 | 1.15027 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.25407e7 | −0.886419 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.45943e6 | 0.0638593 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.28970e7 | −0.319402 | −0.159701 | − | 0.987165i | \(-0.551053\pi\) | ||||
−0.159701 | + | 0.987165i | \(0.551053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.86914e7 | 0.441796 | 0.220898 | − | 0.975297i | \(-0.429101\pi\) | ||||
0.220898 | + | 0.975297i | \(0.429101\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.91898e6 | −0.0658887 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.17384e7 | 0.900274 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.68724e7 | 1.79157 | 0.895784 | − | 0.444490i | \(-0.146615\pi\) | ||||
0.895784 | + | 0.444490i | \(0.146615\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.47780e6 | 0.127802 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.96681e7 | 0.749119 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.53832e7 | −1.18252 | −0.591262 | − | 0.806480i | \(-0.701370\pi\) | ||||
−0.591262 | + | 0.806480i | \(0.701370\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.11227e7 | −0.192759 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.93667e7 | 0.321772 | 0.160886 | − | 0.986973i | \(-0.448565\pi\) | ||||
0.160886 | + | 0.986973i | \(0.448565\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.61950e6 | 0.0417461 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.45517e7 | −0.222549 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.41324e7 | 0.207518 | 0.103759 | − | 0.994602i | \(-0.466913\pi\) | ||||
0.103759 | + | 0.994602i | \(0.466913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26968e6 | −0.0179086 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.50369e7 | 0.339370 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −613278. | −0.00799229 | −0.00399615 | − | 0.999992i | \(-0.501272\pi\) | ||||
−0.00399615 | + | 0.999992i | \(0.501272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.33331e7 | −0.919232 | −0.459616 | − | 0.888118i | \(-0.652013\pi\) | ||||
−0.459616 | + | 0.888118i | \(0.652013\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.77949e7 | 0.214643 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.10262e7 | −0.244152 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.84495e6 | 0.0765464 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.51258e7 | 0.270709 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.08428e7 | −0.112597 | −0.0562984 | − | 0.998414i | \(-0.517930\pi\) | ||||
−0.0562984 | + | 0.998414i | \(0.517930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.57865e8 | 1.58065 | 0.790326 | − | 0.612687i | \(-0.209911\pi\) | ||||
0.790326 | + | 0.612687i | \(0.209911\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.80759e7 | −0.174574 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.95231e7 | 0.368315 | 0.184157 | − | 0.982897i | \(-0.441044\pi\) | ||||
0.184157 | + | 0.982897i | \(0.441044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.52880e6 | −0.0587283 | −0.0293642 | − | 0.999569i | \(-0.509348\pi\) | ||||
−0.0293642 | + | 0.999569i | \(0.509348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.40010e6 | −0.0295329 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.48787e7 | −0.712136 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.16245e8 | 0.942405 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.16756e8 | −0.914919 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.41234e7 | 0.258548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.25402e8 | −0.918999 | −0.459500 | − | 0.888178i | \(-0.651971\pi\) | ||||
−0.459500 | + | 0.888178i | \(0.651971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.17642e7 | 0.154317 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.13726e8 | 0.780416 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.08870e8 | 0.723266 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.83909e6 | −0.0311322 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.11240e7 | 0.0693248 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.73524e8 | 1.65169 | 0.825844 | − | 0.563899i | \(-0.190699\pi\) | ||||
0.825844 | + | 0.563899i | \(0.190699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.73709e6 | 0.0218723 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.45717e8 | 0.826835 | 0.413418 | − | 0.910542i | \(-0.364335\pi\) | ||||
0.413418 | + | 0.910542i | \(0.364335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.70169e8 | 0.936391 | 0.468196 | − | 0.883625i | \(-0.344904\pi\) | ||||
0.468196 | + | 0.883625i | \(0.344904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.90122e7 | −0.154860 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.20408e8 | −1.14151 | −0.570757 | − | 0.821119i | \(-0.693350\pi\) | ||||
−0.570757 | + | 0.821119i | \(0.693350\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.18796e8 | 1.09977 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.12122e7 | 0.103506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.50266e7 | −0.402867 | −0.201434 | − | 0.979502i | \(-0.564560\pi\) | ||||
−0.201434 | + | 0.979502i | \(0.564560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.65575e8 | −0.761967 | −0.380983 | − | 0.924582i | \(-0.624414\pi\) | ||||
−0.380983 | + | 0.924582i | \(0.624414\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.11492e8 | −0.498448 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.40047e7 | −0.364941 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.54554e7 | 0.234155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.74790e7 | −0.194896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.70250e8 | 1.07872 | 0.539359 | − | 0.842076i | \(-0.318667\pi\) | ||||
0.539359 | + | 0.842076i | \(0.318667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.73791e8 | 1.06291 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.07607e6 | −0.0116173 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.67907e7 | 0.208695 | 0.104347 | − | 0.994541i | \(-0.466725\pi\) | ||||
0.104347 | + | 0.994541i | \(0.466725\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.48444e7 | −0.196148 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.49825e8 | 0.869750 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.98253e6 | 0.0101097 | 0.00505487 | − | 0.999987i | \(-0.498391\pi\) | ||||
0.00505487 | + | 0.999987i | \(0.498391\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.21257e8 | −0.730358 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.07267e7 | −0.163098 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.74367e8 | −0.859407 | −0.429703 | − | 0.902970i | \(-0.641382\pi\) | ||||
−0.429703 | + | 0.902970i | \(0.641382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.28592e8 | 0.392483 | 0.196241 | − | 0.980556i | \(-0.437126\pi\) | ||||
0.196241 | + | 0.980556i | \(0.437126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.71489e7 | −0.140250 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.76340e6 | −0.0254102 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.63559e8 | −1.59316 | −0.796582 | − | 0.604531i | \(-0.793361\pi\) | ||||
−0.796582 | + | 0.604531i | \(0.793361\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.20439e8 | −0.883344 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.69126e8 | −1.26130 | −0.630648 | − | 0.776069i | \(-0.717211\pi\) | ||||
−0.630648 | + | 0.776069i | \(0.717211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.16530e8 | −0.567891 | −0.283946 | − | 0.958840i | \(-0.591644\pi\) | ||||
−0.283946 | + | 0.958840i | \(0.591644\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.53348e7 | −0.0392393 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.03213e8 | 0.757114 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.08446e8 | −0.995387 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.85349e7 | −0.234404 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.53977e8 | −0.822127 | −0.411063 | − | 0.911607i | \(-0.634843\pi\) | ||||
−0.411063 | + | 0.911607i | \(0.634843\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.55163e8 | −1.93942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73419e8 | 0.384104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.44948e8 | 0.962632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.96642e8 | 0.626975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.88550e7 | −0.0802414 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.07805e8 | −1.22663 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.23436e8 | 1.22972 | 0.614862 | − | 0.788635i | \(-0.289212\pi\) | ||||
0.614862 | + | 0.788635i | \(0.289212\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.38943e7 | 0.0653540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.17438e8 | −0.975432 | −0.487716 | − | 0.873002i | \(-0.662170\pi\) | ||||
−0.487716 | + | 0.873002i | \(0.662170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.03327e8 | −0.374791 | −0.187395 | − | 0.982285i | \(-0.560005\pi\) | ||||
−0.187395 | + | 0.982285i | \(0.560005\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.22581e8 | −0.761768 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.01407e6 | −0.00355114 | −0.00177557 | − | 0.999998i | \(-0.500565\pi\) | ||||
−0.00177557 | + | 0.999998i | \(0.500565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.85836e8 | −1.01044 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.24924e8 | −0.210804 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.43712e6 | 0.0155823 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.42418e7 | −0.0230129 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.78925e8 | −0.282978 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.70703e8 | 0.883537 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.89819e8 | −0.742399 | −0.371200 | − | 0.928553i | \(-0.621053\pi\) | ||||
−0.371200 | + | 0.928553i | \(0.621053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.61425e8 | 0.239560 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.16134e8 | 0.168773 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.87197e8 | 1.12041 | 0.560207 | − | 0.828352i | \(-0.310721\pi\) | ||||
0.560207 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.48844e7 | 0.118339 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.51423e8 | 1.02623 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.12726e8 | −1.08746 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.23039e8 | −0.161316 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.92885e8 | 0.376308 | 0.188154 | − | 0.982140i | \(-0.439750\pi\) | ||||
0.188154 | + | 0.982140i | \(0.439750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.32289e9 | 1.66584 | 0.832921 | − | 0.553392i | \(-0.186667\pi\) | ||||
0.832921 | + | 0.553392i | \(0.186667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81830e8 | 0.347866 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.07075e9 | −1.29562 | −0.647811 | − | 0.761801i | \(-0.724315\pi\) | ||||
−0.647811 | + | 0.761801i | \(0.724315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.43381e8 | −0.881886 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.02357e6 | −0.00933316 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.11066e8 | 0.582970 | 0.291485 | − | 0.956575i | \(-0.405851\pi\) | ||||
0.291485 | + | 0.956575i | \(0.405851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.25826e7 | −0.0467261 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.65285e8 | 0.177913 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.57375e8 | 0.377392 | 0.188696 | − | 0.982036i | \(-0.439574\pi\) | ||||
0.188696 | + | 0.982036i | \(0.439574\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.92453e8 | −0.924683 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.77123e8 | −0.586759 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.92494e8 | −0.192060 | −0.0960300 | − | 0.995378i | \(-0.530614\pi\) | ||||
−0.0960300 | + | 0.995378i | \(0.530614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.78604e8 | 0.174897 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.52066e8 | −0.915108 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.22141e9 | −1.15245 | −0.576226 | − | 0.817291i | \(-0.695475\pi\) | ||||
−0.576226 | + | 0.817291i | \(0.695475\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.43781e7 | 0.0133188 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.37917e7 | −0.0580188 | −0.0290094 | − | 0.999579i | \(-0.509235\pi\) | ||||
−0.0290094 | + | 0.999579i | \(0.509235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.90944e8 | 0.884987 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.73112e8 | −0.765741 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.07082e9 | −1.78369 | −0.891845 | − | 0.452340i | \(-0.850589\pi\) | ||||
−0.891845 | + | 0.452340i | \(0.850589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.57192e7 | 0.0640600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.25840e8 | −0.104579 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.24526e8 | −0.591513 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.48707e9 | 1.19280 | 0.596398 | − | 0.802689i | \(-0.296598\pi\) | ||||
0.596398 | + | 0.802689i | \(0.296598\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.99991e7 | −0.0315242 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.94594e8 | 0.383039 | 0.191520 | − | 0.981489i | \(-0.438658\pi\) | ||||
0.191520 | + | 0.981489i | \(0.438658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.22117e9 | 0.929411 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.20423e9 | 0.900777 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.78538e8 | −0.278310 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.77741e9 | −1.28457 | −0.642284 | − | 0.766467i | \(-0.722013\pi\) | ||||
−0.642284 | + | 0.766467i | \(0.722013\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.81912e8 | −0.271342 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.23060e9 | −1.55810 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.62170e9 | 1.11379 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.44365e8 | −0.300098 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.25911e8 | 0.349271 | 0.174636 | − | 0.984633i | \(-0.444125\pi\) | ||||
0.174636 | + | 0.984633i | \(0.444125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.27157e9 | −0.830527 | −0.415264 | − | 0.909701i | \(-0.636311\pi\) | ||||
−0.415264 | + | 0.909701i | \(0.636311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.67976e9 | −1.07909 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.42359e6 | −0.00153144 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.58539e9 | −0.985459 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.25423e8 | −0.198998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.07412e9 | 1.24786 | 0.623928 | − | 0.781482i | \(-0.285536\pi\) | ||||
0.623928 | + | 0.781482i | \(0.285536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00301e9 | −1.18570 | −0.592851 | − | 0.805312i | \(-0.701998\pi\) | ||||
−0.592851 | + | 0.805312i | \(0.701998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.63270e8 | 0.153352 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.77475e8 | 0.216373 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.57162e8 | −0.427133 | −0.213566 | − | 0.976929i | \(-0.568508\pi\) | ||||
−0.213566 | + | 0.976929i | \(0.568508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.44930e8 | 0.358078 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.44853e7 | 0.0243110 | 0.0121555 | − | 0.999926i | \(-0.496131\pi\) | ||||
0.0121555 | + | 0.999926i | \(0.496131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.73263e9 | 0.932063 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.04343e8 | 0.0552570 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.40918e9 | −1.77741 | −0.888706 | − | 0.458477i | \(-0.848395\pi\) | ||||
−0.888706 | + | 0.458477i | \(0.848395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.09279e9 | 1.07425 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.51222e8 | −0.0764314 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.61042e9 | 0.801494 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.41561e9 | 1.67403 | 0.837013 | − | 0.547183i | \(-0.184300\pi\) | ||||
0.837013 | + | 0.547183i | \(0.184300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.79605e7 | 0.0231494 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.71518e9 | −0.815371 | −0.407686 | − | 0.913122i | \(-0.633664\pi\) | ||||
−0.407686 | + | 0.913122i | \(0.633664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.34891e9 | 1.09985 | 0.549924 | − | 0.835215i | \(-0.314657\pi\) | ||||
0.549924 | + | 0.835215i | \(0.314657\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.37684e8 | −0.155749 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.93983e9 | 0.881364 | 0.440682 | − | 0.897663i | \(-0.354737\pi\) | ||||
0.440682 | + | 0.897663i | \(0.354737\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.02923e8 | 0.135590 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.02840e8 | −0.309944 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.04743e9 | 0.889602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20821e7 | −0.00517266 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.69866e9 | 0.716624 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.99335e8 | −0.207595 | −0.103798 | − | 0.994598i | \(-0.533099\pi\) | ||||
−0.103798 | + | 0.994598i | \(0.533099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.15177e8 | −0.252053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.20934e8 | −0.129599 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.36557e9 | 1.33956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.33245e9 | 0.915084 | 0.457542 | − | 0.889188i | \(-0.348730\pi\) | ||||
0.457542 | + | 0.889188i | \(0.348730\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.28982e8 | 0.204578 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.75314e9 | 0.668391 | 0.334196 | − | 0.942504i | \(-0.391535\pi\) | ||||
0.334196 | + | 0.942504i | \(0.391535\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.62018e8 | −0.0608974 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.91667e9 | −1.08086 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.93902e9 | −0.708493 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.10432e9 | −0.397872 | −0.198936 | − | 0.980012i | \(-0.563749\pi\) | ||||
−0.198936 | + | 0.980012i | \(0.563749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.56686e8 | −0.0556671 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.39626e9 | −0.839548 | −0.419774 | − | 0.907629i | \(-0.637891\pi\) | ||||
−0.419774 | + | 0.907629i | \(0.637891\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.32714e9 | 0.458560 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.11930e7 | −0.00722213 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.57893e9 | −0.530702 | −0.265351 | − | 0.964152i | \(-0.585488\pi\) | ||||
−0.265351 | + | 0.964152i | \(0.585488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.31126e8 | 0.142933 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.39092e8 | 0.0781907 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.15770e9 | −0.373483 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.93901e9 | 1.25363 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.14338e8 | −0.0359009 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.97045e9 | 0.920215 | 0.460108 | − | 0.887863i | \(-0.347811\pi\) | ||||
0.460108 | + | 0.887863i | \(0.347811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.32922e8 | −0.254594 | −0.127297 | − | 0.991865i | \(-0.540630\pi\) | ||||
−0.127297 | + | 0.991865i | \(0.540630\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.02724e7 | 0.00309822 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.07812e8 | 0.0618492 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.76141e8 | −0.110473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.56536e9 | 1.90295 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.40107e9 | 0.972905 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.26693e9 | 1.20469 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.96171e6 | 0.00138268 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.51235e9 | −0.415998 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.68340e8 | 0.235776 | 0.117888 | − | 0.993027i | \(-0.462388\pi\) | ||||
0.117888 | + | 0.993027i | \(0.462388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.93300e8 | 0.159028 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.11138e9 | 1.61715 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.78914e9 | −1.77362 | −0.886808 | − | 0.462139i | \(-0.847082\pi\) | ||||
−0.886808 | + | 0.462139i | \(0.847082\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.66631e9 | 1.20357 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.07691e8 | −0.205691 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.88984e9 | −0.475212 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.70112e8 | 0.0422386 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.20950e9 | 1.76771 | 0.883857 | − | 0.467757i | \(-0.154938\pi\) | ||||
0.883857 | + | 0.467757i | \(0.154938\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.32737e9 | 0.805674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.53790e7 | −0.0132426 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.85174e9 | 1.85433 | 0.927164 | − | 0.374655i | \(-0.122239\pi\) | ||||
0.927164 | + | 0.374655i | \(0.122239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.89932e9 | −0.676281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.14110e9 | 0.723671 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.52870e9 | −1.03058 | −0.515289 | − | 0.857017i | \(-0.672315\pi\) | ||||
−0.515289 | + | 0.857017i | \(0.672315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.34549e9 | −1.65118 | −0.825590 | − | 0.564271i | \(-0.809157\pi\) | ||||
−0.825590 | + | 0.564271i | \(0.809157\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.77237e7 | 0.0194794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.69411e7 | −0.0212653 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.37956e8 | 0.0732393 | 0.0366197 | − | 0.999329i | \(-0.488341\pi\) | ||||
0.0366197 | + | 0.999329i | \(0.488341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.27721e9 | −0.273455 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.23002e9 | 0.894799 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.98332e9 | −0.832540 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.73999e9 | −0.978886 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.74946e9 | 1.17326 | 0.586629 | − | 0.809856i | \(-0.300455\pi\) | ||||
0.586629 | + | 0.809856i | \(0.300455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.03599e9 | 0.208906 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.19761e8 | −0.0637190 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.26534e9 | 0.249181 | 0.124590 | − | 0.992208i | \(-0.460238\pi\) | ||||
0.124590 | + | 0.992208i | \(0.460238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.74054e8 | 0.0533368 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.28211e7 | 0.0101601 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.89338e9 | −1.88084 | −0.940418 | − | 0.340021i | \(-0.889566\pi\) | ||||
−0.940418 | + | 0.340021i | \(0.889566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.60429e9 | −1.42889 | −0.714443 | − | 0.699693i | \(-0.753320\pi\) | ||||
−0.714443 | + | 0.699693i | \(0.753320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.91599e8 | −0.165600 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.45446e9 | 0.267028 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.96147e9 | −0.900430 | −0.450215 | − | 0.892920i | \(-0.648653\pi\) | ||||
−0.450215 | + | 0.892920i | \(0.648653\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.86710e8 | 0.123201 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.40145e9 | 1.13536 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.04021e9 | 0.883765 | 0.441883 | − | 0.897073i | \(-0.354311\pi\) | ||||
0.441883 | + | 0.897073i | \(0.354311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.40482e8 | −0.163037 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.84954e9 | −1.34538 | −0.672692 | − | 0.739922i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739922i | \(0.734862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.69511e9 | 0.456729 | 0.228365 | − | 0.973576i | \(-0.426662\pi\) | ||||
0.228365 | + | 0.973576i | \(0.426662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.91837e9 | 0.321448 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.51936e9 | 0.748805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.96280e9 | −0.976945 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.76075e8 | −0.0447291 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.04688e8 | −0.0167733 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.44546e9 | 0.862843 | 0.431422 | − | 0.902150i | \(-0.358012\pi\) | ||||
0.431422 | + | 0.902150i | \(0.358012\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.01456e9 | 0.158988 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.91100e8 | −0.0761135 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.45778e9 | −0.376752 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.70717e9 | 0.865302 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.19511e10 | −1.79228 | −0.896139 | − | 0.443773i | \(-0.853640\pi\) | ||||
−0.896139 | + | 0.443773i | \(0.853640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.08936e10 | 1.61597 | 0.807987 | − | 0.589200i | \(-0.200557\pi\) | ||||
0.807987 | + | 0.589200i | \(0.200557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.20101e8 | −0.135013 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.48672e9 | −0.215807 | −0.107903 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107903 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.53956e10 | −2.21076 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.80809e8 | −0.125126 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.66204e9 | 1.21737 | 0.608687 | − | 0.793411i | \(-0.291697\pi\) | ||||
0.608687 | + | 0.793411i | \(0.291697\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.29821e9 | 0.597644 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.26894e9 | −0.174567 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.47037e9 | 0.608477 | 0.304239 | − | 0.952596i | \(-0.401598\pi\) | ||||
0.304239 | + | 0.952596i | \(0.401598\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.62221e9 | 1.16122 | 0.580608 | − | 0.814183i | \(-0.302815\pi\) | ||||
0.580608 | + | 0.814183i | \(0.302815\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.99986e7 | −0.0119933 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.36621e9 | 0.180153 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.48054e9 | −0.845611 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.21294e9 | −0.285744 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.09424e10 | −1.39825 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.08380e9 | 0.263513 | 0.131757 | − | 0.991282i | \(-0.457938\pi\) | ||||
0.131757 | + | 0.991282i | \(0.457938\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.14025e7 | −0.00768463 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.68414e9 | 0.951777 | 0.475888 | − | 0.879506i | \(-0.342127\pi\) | ||||
0.475888 | + | 0.879506i | \(0.342127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.77871e9 | 1.07618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.17892e9 | −0.143044 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.90692e9 | −0.949587 | −0.474794 | − | 0.880097i | \(-0.657477\pi\) | ||||
−0.474794 | + | 0.880097i | \(0.657477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.30446e10 | 1.55065 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.37675e9 | −0.161997 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.47346e9 | −0.753996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.47299e10 | −1.69835 | −0.849175 | − | 0.528112i | \(-0.822900\pi\) | ||||
−0.849175 | + | 0.528112i | \(0.822900\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.60779e9 | −0.868345 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.51778e10 | 1.71499 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.78778e8 | 0.0647437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.78320e9 | 0.197484 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.76814e10 | 1.93867 | 0.969335 | − | 0.245744i | \(-0.0790323\pi\) | ||||
0.969335 | + | 0.245744i | \(0.0790323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.21889e8 | −0.0566546 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.77016e9 | −0.190261 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.46169e9 | 0.368400 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.52758e9 | −0.371719 | −0.185859 | − | 0.982576i | \(-0.559507\pi\) | ||||
−0.185859 | + | 0.982576i | \(0.559507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.56241e9 | 0.580390 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.31227e9 | 0.858828 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.11152e10 | 1.13722 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.87906e8 | 0.0696967 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.24573e10 | 1.24990 | 0.624949 | − | 0.780666i | \(-0.285120\pi\) | ||||
0.624949 | + | 0.780666i | \(0.285120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.01972e9 | −0.300050 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.33958e9 | 0.131821 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.07427e8 | 0.0202154 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.43981e10 | −1.38975 | −0.694873 | − | 0.719132i | \(-0.744540\pi\) | ||||
−0.694873 | + | 0.719132i | \(0.744540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.62848e9 | −0.824875 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.66235e8 | 0.0536150 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.94697e10 | −1.82598 | −0.912990 | − | 0.407983i | \(-0.866232\pi\) | ||||
−0.912990 | + | 0.407983i | \(0.866232\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.79638e8 | 0.0631353 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.09078e9 | 0.192386 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.90895e10 | −1.73996 | −0.869979 | − | 0.493089i | \(-0.835868\pi\) | ||||
−0.869979 | + | 0.493089i | \(0.835868\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.48660e8 | −0.0405092 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.60614e10 | −1.43655 | −0.718277 | − | 0.695758i | \(-0.755069\pi\) | ||||
−0.718277 | + | 0.695758i | \(0.755069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.56395e9 | −0.315780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.24503e10 | −1.09284 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.11298e10 | 0.967833 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.54515e10 | −1.33116 | −0.665579 | − | 0.746327i | \(-0.731815\pi\) | ||||
−0.665579 | + | 0.746327i | \(0.731815\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.18645e9 | −0.186620 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.16516e9 | 0.436787 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.26828e10 | −1.06262 | −0.531312 | − | 0.847176i | \(-0.678301\pi\) | ||||
−0.531312 | + | 0.847176i | \(0.678301\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.21510e9 | −0.183885 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.77060e10 | 1.45638 | 0.728190 | − | 0.685375i | \(-0.240362\pi\) | ||||
0.728190 | + | 0.685375i | \(0.240362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.59408e10 | 1.29920 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.06629e8 | −0.0651416 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.50201e10 | −2.00219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.88518e9 | 0.149489 | 0.0747446 | − | 0.997203i | \(-0.476186\pi\) | ||||
0.0747446 | + | 0.997203i | \(0.476186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.59464e8 | −0.0361045 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.99272e8 | 0.0544525 | 0.0272262 | − | 0.999629i | \(-0.491333\pi\) | ||||
0.0272262 | + | 0.999629i | \(0.491333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.66056e8 | −0.0205314 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.43718e8 | 0.0339338 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.88532e9 | 0.218682 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.33832e10 | −1.00527 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.10477e9 | −0.305579 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.40063e10 | 1.77126 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.19911e10 | −1.60818 | −0.804092 | − | 0.594505i | \(-0.797348\pi\) | ||||
−0.804092 | + | 0.594505i | \(0.797348\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.41301e7 | −0.00174900 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.56255e9 | −0.543314 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.77830e10 | −1.26633 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.79007e9 | 0.126353 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.41708e10 | 0.991496 | 0.495748 | − | 0.868466i | \(-0.334894\pi\) | ||||
0.495748 | + | 0.868466i | \(0.334894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.08937e9 | 0.0755546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.33019e10 | −0.914536 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.97565e9 | 0.202804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.09619e10 | 0.740626 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.21976e9 | 0.148679 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.00198e10 | −1.32935 | −0.664677 | − | 0.747131i | \(-0.731431\pi\) | ||||
−0.664677 | + | 0.747131i | \(0.731431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.19672e9 | 0.407933 | 0.203967 | − | 0.978978i | \(-0.434617\pi\) | ||||
0.203967 | + | 0.978978i | \(0.434617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.04037e9 | −0.0679001 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.80680e10 | −1.16912 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.82279e9 | 0.181093 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.23637e10 | −0.786422 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.36180e10 | −0.858839 | −0.429419 | − | 0.903105i | \(-0.641282\pi\) | ||||
−0.429419 | + | 0.903105i | \(0.641282\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.96103e9 | 0.622880 | 0.311440 | − | 0.950266i | \(-0.399189\pi\) | ||||
0.311440 | + | 0.950266i | \(0.399189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.09001e7 | 0.00439601 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.53194e10 | −1.55663 | −0.778313 | − | 0.627876i | \(-0.783924\pi\) | ||||
−0.778313 | + | 0.627876i | \(0.783924\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.10063e10 | −1.28059 | −0.640294 | − | 0.768130i | \(-0.721187\pi\) | ||||
−0.640294 | + | 0.768130i | \(0.721187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.55946e9 | 0.275620 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.18253e8 | −0.0250716 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.35179e9 | 0.318124 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.26499e9 | 0.310355 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.76564e10 | 1.03213 | 0.516066 | − | 0.856549i | \(-0.327396\pi\) | ||||
0.516066 | + | 0.856549i | \(0.327396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.38332e9 | −0.196136 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.79545e9 | 0.218206 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.23872e8 | 0.0412727 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.79379e9 | 0.214526 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.75183e9 | 0.0982461 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.18740e9 | −0.232912 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.73063e9 | −0.0954734 | −0.0477367 | − | 0.998860i | \(-0.515201\pi\) | ||||
−0.0477367 | + | 0.998860i | \(0.515201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.02120e9 | −0.220026 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.07792e8 | −0.00584995 | −0.00292498 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292498 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.21663e10 | 0.654911 | 0.327455 | − | 0.944867i | \(-0.393809\pi\) | ||||
0.327455 | + | 0.944867i | \(0.393809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.45314e9 | −0.130982 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.32114e10 | 1.22932 | 0.614659 | − | 0.788793i | \(-0.289293\pi\) | ||||
0.614659 | + | 0.788793i | \(0.289293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.90535e9 | 0.205165 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.30452e9 | 0.172203 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.30438e10 | −0.674270 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.39782e9 | 0.174236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.58385e10 | −1.31437 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.59122e10 | −0.802976 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.30902e10 | −1.15593 | −0.577963 | − | 0.816063i | \(-0.696152\pi\) | ||||
−0.577963 | + | 0.816063i | \(0.696152\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.86385e9 | 0.142229 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.17232e9 | 0.304112 | 0.152056 | − | 0.988372i | \(-0.451411\pi\) | ||||
0.152056 | + | 0.988372i | \(0.451411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.18206e10 | 0.577801 | 0.288901 | − | 0.957359i | \(-0.406710\pi\) | ||||
0.288901 | + | 0.957359i | \(0.406710\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.91868e9 | 0.335523 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.11165e10 | −1.97826 | −0.989129 | − | 0.147049i | \(-0.953022\pi\) | ||||
−0.989129 | + | 0.147049i | \(0.953022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.28098e9 | −0.0611484 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.16800e10 | 1.02680 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.43071e9 | 0.255197 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.69473e8 | −0.00790168 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.59985e9 | −0.166537 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.77859e10 | −0.816428 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.10162e9 | −0.0501759 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.39998e9 | −0.108468 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.02648e10 | −0.908810 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.36671e10 | 0.608204 | 0.304102 | − | 0.952639i | \(-0.401644\pi\) | ||||
0.304102 | + | 0.952639i | \(0.401644\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.01889e10 | −0.449937 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.65765e10 | 1.60283 | 0.801417 | − | 0.598106i | \(-0.204080\pi\) | ||||
0.801417 | + | 0.598106i | \(0.204080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.91957e10 | 1.26961 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.91744e9 | 0.212210 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.12114e10 | 0.480138 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.71530e9 | 0.157903 | 0.0789514 | − | 0.996878i | \(-0.474843\pi\) | ||||
0.0789514 | + | 0.996878i | \(0.474843\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.04390e9 | −0.212744 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.17496e10 | −0.910427 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34029e8 | 0.00556805 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.88801e9 | 0.366459 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.28521e10 | −1.34434 | −0.672168 | − | 0.740398i | \(-0.734637\pi\) | ||||
−0.672168 | + | 0.740398i | \(0.734637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.08507e9 | −0.0846832 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.18632e9 | 0.168751 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.89153e9 | 0.0756786 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.29737e10 | 0.912310 | 0.456155 | − | 0.889900i | \(-0.349226\pi\) | ||||
0.456155 | + | 0.889900i | \(0.349226\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.64501e9 | 0.0648394 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.00811e10 | 0.394407 | 0.197204 | − | 0.980363i | \(-0.436814\pi\) | ||||
0.197204 | + | 0.980363i | \(0.436814\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.31505e10 | 0.899020 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.94324e9 | 0.267640 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.75260e10 | 0.670589 | 0.335295 | − | 0.942113i | \(-0.391164\pi\) | ||||
0.335295 | + | 0.942113i | \(0.391164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83584e9 | 0.183671 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62948e7 | 0.000614353 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.66888e10 | −0.998859 | −0.499429 | − | 0.866355i | \(-0.666457\pi\) | ||||
−0.499429 | + | 0.866355i | \(0.666457\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.99630e9 | −0.111320 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.73969e9 | 0.174807 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.40254e10 | 1.24577 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.69946e9 | −0.170811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.27585e10 | −1.18204 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.36244e10 | 1.56273 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.40155e10 | −0.854080 | −0.427040 | − | 0.904233i | \(-0.640444\pi\) | ||||
−0.427040 | + | 0.904233i | \(0.640444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.63508e7 | −0.00269576 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.24355e10 | 1.13698 | 0.568491 | − | 0.822689i | \(-0.307527\pi\) | ||||
0.568491 | + | 0.822689i | \(0.307527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.95895e10 | 1.37780 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.15223e8 | 0.00398127 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.53419e10 | −0.526317 | −0.263158 | − | 0.964753i | \(-0.584764\pi\) | ||||
−0.263158 | + | 0.964753i | \(0.584764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.11928e10 | 1.06247 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.69189e10 | −1.58674 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.48494e9 | 0.217755 | 0.108878 | − | 0.994055i | \(-0.465274\pi\) | ||||
0.108878 | + | 0.994055i | \(0.465274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.09218e10 | 0.364139 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.61726e9 | −0.152853 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.26488e10 | 0.744489 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.82059e10 | −1.24702 | −0.623510 | − | 0.781816i | \(-0.714294\pi\) | ||||
−0.623510 | + | 0.781816i | \(0.714294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.96287e9 | 0.128436 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.80416e9 | −0.0580625 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.90627e10 | 1.56790 | 0.783950 | − | 0.620824i | \(-0.213202\pi\) | ||||
0.783950 | + | 0.620824i | \(0.213202\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.65230e9 | −0.0841673 |
(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 | 304.8.a.g.1.3 | 5 | ||
4.3 | odd | 2 | 76.8.a.a.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.a.a.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
304.8.a.g.1.3 | 5 | 1.1 | even | 1 | trivial |