Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,8,Mod(1,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(2.49908020387\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8.1 |
$q$-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 | ||||||||
\(3\) | −84.0000 | −1.79620 | −0.898100 | − | 0.439790i | \(-0.855053\pi\) | ||||
−0.898100 | + | 0.439790i | \(0.855053\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −82.0000 | −0.293372 | −0.146686 | − | 0.989183i | \(-0.546861\pi\) | ||||
−0.146686 | + | 0.989183i | \(0.546861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −456.000 | −0.502483 | −0.251242 | − | 0.967924i | \(-0.580839\pi\) | ||||
−0.251242 | + | 0.967924i | \(0.580839\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4869.00 | 2.22634 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2524.00 | −0.571762 | −0.285881 | − | 0.958265i | \(-0.592286\pi\) | ||||
−0.285881 | + | 0.958265i | \(0.592286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10778.0 | −1.36062 | −0.680309 | − | 0.732925i | \(-0.738155\pi\) | ||||
−0.680309 | + | 0.732925i | \(0.738155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6888.00 | 0.526955 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11150.0 | −0.550432 | −0.275216 | − | 0.961382i | \(-0.588749\pi\) | ||||
−0.275216 | + | 0.961382i | \(0.588749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4124.00 | 0.137937 | 0.0689685 | − | 0.997619i | \(-0.478029\pi\) | ||||
0.0689685 | + | 0.997619i | \(0.478029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38304.0 | 0.902561 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 81704.0 | 1.40022 | 0.700109 | − | 0.714036i | \(-0.253135\pi\) | ||||
0.700109 | + | 0.714036i | \(0.253135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −71401.0 | −0.913933 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −225288. | −2.20275 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 99798.0 | 0.759852 | 0.379926 | − | 0.925017i | \(-0.375949\pi\) | ||||
0.379926 | + | 0.925017i | \(0.375949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40480.0 | −0.244048 | −0.122024 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122024 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 212016. | 1.02700 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 37392.0 | 0.147415 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −419442. | −1.36134 | −0.680669 | − | 0.732591i | \(-0.738311\pi\) | ||||
−0.680669 | + | 0.732591i | \(0.738311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 905352. | 2.44394 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 141402. | 0.320414 | 0.160207 | − | 0.987083i | \(-0.448784\pi\) | ||||
0.160207 | + | 0.987083i | \(0.448784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −690428. | −1.32428 | −0.662138 | − | 0.749382i | \(-0.730351\pi\) | ||||
−0.662138 | + | 0.749382i | \(0.730351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −399258. | −0.653145 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −682032. | −0.958213 | −0.479107 | − | 0.877757i | \(-0.659039\pi\) | ||||
−0.479107 | + | 0.877757i | \(0.659039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −615607. | −0.747510 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 936600. | 0.988686 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.81312e6 | 1.67286 | 0.836432 | − | 0.548071i | \(-0.184638\pi\) | ||||
0.836432 | + | 0.548071i | \(0.184638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 206968. | 0.167739 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −346416. | −0.247763 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −966028. | −0.612361 | −0.306181 | − | 0.951973i | \(-0.599051\pi\) | ||||
−0.306181 | + | 0.951973i | \(0.599051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.88767e6 | 1.06481 | 0.532404 | − | 0.846490i | \(-0.321289\pi\) | ||||
0.532404 | + | 0.846490i | \(0.321289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.22026e6 | −1.11870 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 883796. | 0.399168 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96587e6 | 1.20473 | 0.602365 | − | 0.798220i | \(-0.294225\pi\) | ||||
0.602365 | + | 0.798220i | \(0.294225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.86314e6 | −2.51507 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.54823e6 | −0.844957 | −0.422479 | − | 0.906373i | \(-0.638840\pi\) | ||||
−0.422479 | + | 0.906373i | \(0.638840\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.68033e6 | −0.505549 | −0.252775 | − | 0.967525i | \(-0.581343\pi\) | ||||
−0.252775 | + | 0.967525i | \(0.581343\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.99768e6 | 1.64161 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.15094e6 | 0.287301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.03806e6 | 0.921464 | 0.460732 | − | 0.887539i | \(-0.347587\pi\) | ||||
0.460732 | + | 0.887539i | \(0.347587\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.27569e6 | 1.73024 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.38576e6 | −1.03389 | −0.516945 | − | 0.856019i | \(-0.672931\pi\) | ||||
−0.516945 | + | 0.856019i | \(0.672931\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 914300. | 0.161481 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.38303e6 | −1.36485 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.47305e6 | −0.973293 | −0.486647 | − | 0.873599i | \(-0.661780\pi\) | ||||
−0.486647 | + | 0.873599i | \(0.661780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.91477e6 | 0.683688 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.40032e6 | 0.438359 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −338168. | −0.0404669 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.06576e6 | −0.674814 | −0.337407 | − | 0.941359i | \(-0.609550\pi\) | ||||
−0.337407 | + | 0.941359i | \(0.609550\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.22894e7 | −1.27293 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.70069e6 | 0.936866 | 0.468433 | − | 0.883499i | \(-0.344819\pi\) | ||||
0.468433 | + | 0.883499i | \(0.344819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.10159e6 | 0.369847 | 0.184924 | − | 0.982753i | \(-0.440796\pi\) | ||||
0.184924 | + | 0.982753i | \(0.440796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.14093e6 | −0.264786 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 72900.0 | 0.00575287 | 0.00287643 | − | 0.999996i | \(-0.499084\pi\) | ||||
0.00287643 | + | 0.999996i | \(0.499084\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.55841e6 | 0.706957 | 0.353478 | − | 0.935443i | \(-0.384999\pi\) | ||||
0.353478 | + | 0.935443i | \(0.384999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.52331e7 | 2.44524 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.33890e6 | 0.608865 | 0.304433 | − | 0.952534i | \(-0.401533\pi\) | ||||
0.304433 | + | 0.952534i | \(0.401533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.69973e6 | −0.410785 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.24781e7 | −3.02920 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.08440e6 | 0.276583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.31166e7 | −0.673089 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.18778e7 | −0.575529 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.22611e7 | 0.561495 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.59794e7 | −1.55862 | −0.779311 | − | 0.626637i | \(-0.784431\pi\) | ||||
−0.779311 | + | 0.626637i | \(0.784431\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.79960e7 | 2.37867 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −676052. | −0.0262743 | −0.0131371 | − | 0.999914i | \(-0.504182\pi\) | ||||
−0.0131371 | + | 0.999914i | \(0.504182\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.88054e6 | −0.0693111 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.84736e7 | 0.646225 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.95841e7 | −0.982962 | −0.491481 | − | 0.870888i | \(-0.663544\pi\) | ||||
−0.491481 | + | 0.870888i | \(0.663544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.19084e7 | −1.00775 | −0.503876 | − | 0.863776i | \(-0.668093\pi\) | ||||
−0.503876 | + | 0.863776i | \(0.668093\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.72907e7 | 1.72114 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.72037e7 | 0.777949 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.18344e6 | −0.222919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.17110e7 | 1.34268 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.16603e7 | −0.288773 | −0.144386 | − | 0.989521i | \(-0.546121\pi\) | ||||
−0.144386 | + | 0.989521i | \(0.546121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.76295e7 | −0.416698 | −0.208349 | − | 0.978055i | \(-0.566809\pi\) | ||||
−0.208349 | + | 0.978055i | \(0.566809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.42894e7 | −1.22545 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.31936e6 | 0.0715968 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.34658e6 | 0.130885 | 0.0654427 | − | 0.997856i | \(-0.479154\pi\) | ||||
0.0654427 | + | 0.997856i | \(0.479154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.52302e8 | −3.00480 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.72570e7 | −0.703587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.04234e7 | 1.45454 | 0.727271 | − | 0.686351i | \(-0.240789\pi\) | ||||
0.727271 | + | 0.686351i | \(0.240789\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.73853e7 | −0.301293 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.14767e8 | 1.90682 | 0.953411 | − | 0.301673i | \(-0.0975451\pi\) | ||||
0.953411 | + | 0.301673i | \(0.0975451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.34168e7 | 0.851283 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00798e7 | 0.307095 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.33755e7 | −0.930594 | −0.465297 | − | 0.885155i | \(-0.654053\pi\) | ||||
−0.465297 | + | 0.885155i | \(0.654053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.25589e7 | 0.459236 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.11464e7 | 1.09992 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.13228e7 | −0.147559 | −0.0737796 | − | 0.997275i | \(-0.523506\pi\) | ||||
−0.0737796 | + | 0.997275i | \(0.523506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.22650e6 | −0.0655143 | −0.0327571 | − | 0.999463i | \(-0.510429\pi\) | ||||
−0.0327571 | + | 0.999463i | \(0.510429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.58564e8 | −1.91261 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.43942e7 | 0.399379 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.81426e7 | 0.314716 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.02731e8 | 1.10684 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.50301e7 | −0.882990 | −0.441495 | − | 0.897264i | \(-0.645552\pi\) | ||||
−0.441495 | + | 0.897264i | \(0.645552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15092e8 | 1.15237 | 0.576186 | − | 0.817319i | \(-0.304540\pi\) | ||||
0.576186 | + | 0.817319i | \(0.304540\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.42389e7 | −0.716985 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.38522e8 | −1.29088 | −0.645441 | − | 0.763810i | \(-0.723326\pi\) | ||||
−0.645441 | + | 0.763810i | \(0.723326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.19614e7 | −0.197548 | −0.0987742 | − | 0.995110i | \(-0.531492\pi\) | ||||
−0.0987742 | + | 0.995110i | \(0.531492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.49133e8 | −2.16394 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.55079e7 | −0.381813 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.15950e7 | −0.0940007 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.97817e8 | 3.11736 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.04090e7 | −0.0788671 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.10208e7 | −0.447187 | −0.223594 | − | 0.974682i | \(-0.571779\pi\) | ||||
−0.223594 | + | 0.974682i | \(0.571779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.14051e8 | 1.51771 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.66151e7 | 0.388506 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.84589e7 | 0.122630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.41147e8 | 0.908068 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.20175e8 | 0.748928 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.22448e7 | −0.255098 | −0.127549 | − | 0.991832i | \(-0.540711\pi\) | ||||
−0.127549 | + | 0.991832i | \(0.540711\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.47651e8 | −2.03472 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.39102e8 | −1.35673 | −0.678364 | − | 0.734726i | \(-0.737311\pi\) | ||||
−0.678364 | + | 0.734726i | \(0.737311\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.67889e7 | −0.257465 | −0.128733 | − | 0.991679i | \(-0.541091\pi\) | ||||
−0.128733 | + | 0.991679i | \(0.541091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.66793e7 | −0.516050 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.45225e8 | 1.78795 | 0.893977 | − | 0.448113i | \(-0.147904\pi\) | ||||
0.893977 | + | 0.448113i | \(0.147904\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.59266e7 | 0.281113 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.39197e8 | −1.65513 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.34413e8 | 1.11068 | 0.555340 | − | 0.831624i | \(-0.312588\pi\) | ||||
0.555340 | + | 0.831624i | \(0.312588\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.09557e8 | −0.504175 | −0.252087 | − | 0.967705i | \(-0.581117\pi\) | ||||
−0.252087 | + | 0.967705i | \(0.581117\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.02453e8 | −0.905112 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.04798e7 | 0.219299 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.44485e7 | −0.187680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.52404e8 | 1.85707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.94031e8 | −1.57280 | −0.786398 | − | 0.617720i | \(-0.788057\pi\) | ||||
−0.786398 | + | 0.617720i | \(0.788057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.06221e8 | −0.800591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.68012e7 | −0.290053 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.19064e8 | 1.17250 | 0.586248 | − | 0.810131i | \(-0.300604\pi\) | ||||
0.586248 | + | 0.810131i | \(0.300604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.91266e8 | 0.684050 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.85916e8 | 1.69169 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.19359e8 | 0.743549 | 0.371774 | − | 0.928323i | \(-0.378750\pi\) | ||||
0.371774 | + | 0.928323i | \(0.378750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.48676e8 | −0.490772 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.43736e8 | 1.74823 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.48033e8 | −0.463687 | −0.231844 | − | 0.972753i | \(-0.574476\pi\) | ||||
−0.231844 | + | 0.972753i | \(0.574476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.69934e8 | −1.12910 | −0.564549 | − | 0.825399i | \(-0.690950\pi\) | ||||
−0.564549 | + | 0.825399i | \(0.690950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.12841e8 | −1.22804 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.80216e8 | 0.522552 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.95860e8 | −1.11908 | −0.559541 | − | 0.828803i | \(-0.689023\pi\) | ||||
−0.559541 | + | 0.828803i | \(0.689023\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.97097e8 | −0.543332 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.97760e8 | −1.60714 | −0.803572 | − | 0.595208i | \(-0.797070\pi\) | ||||
−0.803572 | + | 0.595208i | \(0.797070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.05797e7 | 0.211336 | 0.105668 | − | 0.994401i | \(-0.466302\pi\) | ||||
0.105668 | + | 0.994401i | \(0.466302\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.84061e7 | 0.0726867 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.44793e7 | −0.161003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.86016e8 | −0.697025 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.09524e8 | 1.21210 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.54530e8 | 1.75243 | 0.876213 | − | 0.481924i | \(-0.160062\pi\) | ||||
0.876213 | + | 0.481924i | \(0.160062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.92143e7 | 0.179650 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.68627e8 | 1.25945 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.80606e8 | −1.90516 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.14835e8 | 0.665427 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.14858e8 | −1.68280 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.54789e8 | −0.312385 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.20472e8 | 1.61838 | 0.809188 | − | 0.587549i | \(-0.199907\pi\) | ||||
0.809188 | + | 0.587549i | \(0.199907\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.44534e8 | −0.664320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.53503e8 | 1.23193 | 0.615965 | − | 0.787773i | \(-0.288766\pi\) | ||||
0.615965 | + | 0.787773i | \(0.288766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.63587e8 | 1.22319 | 0.611594 | − | 0.791172i | \(-0.290529\pi\) | ||||
0.611594 | + | 0.791172i | \(0.290529\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.82062e8 | 0.328195 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.54718e8 | −0.625426 | −0.312713 | − | 0.949848i | \(-0.601238\pi\) | ||||
−0.312713 | + | 0.949848i | \(0.601238\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.51890e8 | −0.434454 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.12360e6 | −0.0103333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.59826e7 | −0.0759250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.69560e8 | 1.24351 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.02906e8 | −1.26984 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.11007e8 | 0.481486 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.05543e8 | −0.463100 | −0.231550 | − | 0.972823i | \(-0.574380\pi\) | ||||
−0.231550 | + | 0.972823i | \(0.574380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.04226e9 | −3.03080 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.43201e8 | −0.353434 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.54965e7 | 0.0505220 | 0.0252610 | − | 0.999681i | \(-0.491958\pi\) | ||||
0.0252610 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.84467e8 | −1.09364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02172e8 | 0.139537 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.56252e8 | 0.878095 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.62777e8 | 0.737853 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.90594e8 | −0.244882 | −0.122441 | − | 0.992476i | \(-0.539072\pi\) | ||||
−0.122441 | + | 0.992476i | \(0.539072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.60864e8 | 1.08404 | 0.542020 | − | 0.840366i | \(-0.317660\pi\) | ||||
0.542020 | + | 0.840366i | \(0.317660\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.42815e9 | 2.99710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.04544e9 | −1.26500 | −0.632498 | − | 0.774562i | \(-0.717970\pi\) | ||||
−0.632498 | + | 0.774562i | \(0.717970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.08955e8 | 0.247887 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.27090e8 | −0.496798 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.63303e8 | 0.870696 | 0.435348 | − | 0.900262i | \(-0.356625\pi\) | ||||
0.435348 | + | 0.900262i | \(0.356625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.76864e8 | −0.980973 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.10179e9 | 1.20900 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.37787e8 | 0.148314 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.38692e9 | −1.46460 | −0.732302 | − | 0.680980i | \(-0.761554\pi\) | ||||
−0.732302 | + | 0.680980i | \(0.761554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.88486e8 | 0.713351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.26782e8 | −0.840586 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.77105e8 | 0.476029 | 0.238015 | − | 0.971262i | \(-0.423503\pi\) | ||||
0.238015 | + | 0.971262i | \(0.423503\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.02994e9 | −1.00856 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.07562e9 | −1.03387 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.92468e8 | −0.370311 | −0.185156 | − | 0.982709i | \(-0.559279\pi\) | ||||
−0.185156 | + | 0.982709i | \(0.559279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.02227e9 | 2.79960 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.10409e9 | 1.91368 | 0.956839 | − | 0.290617i | \(-0.0938605\pi\) | ||||
0.956839 | + | 0.290617i | \(0.0938605\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.43774e7 | −0.0842860 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.36169e9 | −2.94829 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.26019e9 | −1.08546 | −0.542730 | − | 0.839907i | \(-0.682609\pi\) | ||||
−0.542730 | + | 0.839907i | \(0.682609\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.11000e8 | −0.770725 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.67884e7 | 0.0471939 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.31121e8 | −0.270332 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.81298e8 | −0.787107 | −0.393554 | − | 0.919302i | \(-0.628754\pi\) | ||||
−0.393554 | + | 0.919302i | \(0.628754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.57966e8 | 0.124497 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.09981e8 | 0.704737 | 0.352369 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352369 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.36293e8 | 0.332056 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.78606e8 | −0.507604 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.05867e9 | 0.778361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.55609e7 | −0.0257004 | −0.0128502 | − | 0.999917i | \(-0.504090\pi\) | ||||
−0.0128502 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.48507e9 | 1.76560 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.40509e8 | 0.307701 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.41633e8 | 0.303314 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.68031e9 | 1.81013 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.65360e9 | 1.76233 | 0.881163 | − | 0.472813i | \(-0.156761\pi\) | ||||
0.881163 | + | 0.472813i | \(0.156761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.12113e9 | −0.732264 | −0.366132 | − | 0.930563i | \(-0.619318\pi\) | ||||
−0.366132 | + | 0.930563i | \(0.619318\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.32081e9 | −2.13331 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.96121e8 | 0.503058 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.60778e8 | −0.535049 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.28511e9 | −1.39735 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.06344e9 | −0.639799 | −0.319900 | − | 0.947451i | \(-0.603649\pi\) | ||||
−0.319900 | + | 0.947451i | \(0.603649\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.05962e8 | −0.417901 | −0.208951 | − | 0.977926i | \(-0.567005\pi\) | ||||
−0.208951 | + | 0.977926i | \(0.567005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.87409e8 | 0.400408 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.36947e8 | 0.193142 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.48506e9 | 0.837760 | 0.418880 | − | 0.908042i | \(-0.362423\pi\) | ||||
0.418880 | + | 0.908042i | \(0.362423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.99739e9 | −1.66421 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.22153e8 | −0.394654 | −0.197327 | − | 0.980338i | \(-0.563226\pi\) | ||||
−0.197327 | + | 0.980338i | \(0.563226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.30790e8 | 0.285537 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.79462e8 | 0.518694 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.22968e9 | −0.641109 | −0.320554 | − | 0.947230i | \(-0.603869\pi\) | ||||
−0.320554 | + | 0.947230i | \(0.603869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.56899e8 | −0.183201 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.48088e9 | 0.748473 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.03011e8 | −0.200575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.85551e7 | −0.0434017 | −0.0217009 | − | 0.999765i | \(-0.506908\pi\) | ||||
−0.0217009 | + | 0.999765i | \(0.506908\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.51196e9 | 1.21246 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.10937e8 | 0.100277 | 0.0501384 | − | 0.998742i | \(-0.484034\pi\) | ||||
0.0501384 | + | 0.998742i | \(0.484034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.29775e9 | −1.54413 | −0.772066 | − | 0.635543i | \(-0.780776\pi\) | ||||
−0.772066 | + | 0.635543i | \(0.780776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.78826e8 | −0.128602 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.82873e7 | 0.0401134 | 0.0200567 | − | 0.999799i | \(-0.493615\pi\) | ||||
0.0200567 | + | 0.999799i | \(0.493615\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.35244e9 | −0.605357 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.33113e8 | −0.235096 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.74264e9 | 0.757171 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.94458e8 | −0.126065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.82807e9 | 3.72436 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.51507e9 | −1.87711 | −0.938557 | − | 0.345125i | \(-0.887836\pi\) | ||||
−0.938557 | + | 0.345125i | \(0.887836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.52075e9 | 1.85226 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.12959e9 | 1.26378 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.97392e8 | 0.197972 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.31338e9 | 1.29993 | 0.649964 | − | 0.759965i | \(-0.274784\pi\) | ||||
0.649964 | + | 0.759965i | \(0.274784\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.75557e9 | −2.61265 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.01694e9 | −1.53147 | −0.765737 | − | 0.643154i | \(-0.777626\pi\) | ||||
−0.765737 | + | 0.643154i | \(0.777626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.11275e9 | −0.418247 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00773e9 | 0.373443 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.16199e9 | 0.424577 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.70976e9 | 0.976290 | 0.488145 | − | 0.872763i | \(-0.337674\pi\) | ||||
0.488145 | + | 0.872763i | \(0.337674\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.64045e9 | −3.42504 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.04579e8 | 0.106712 | 0.0533558 | − | 0.998576i | \(-0.483008\pi\) | ||||
0.0533558 | + | 0.998576i | \(0.483008\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.95456e8 | −0.274850 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.48701e9 | −1.52908 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.88202e8 | −0.0632575 | −0.0316287 | − | 0.999500i | \(-0.510069\pi\) | ||||
−0.0316287 | + | 0.999500i | \(0.510069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.66229e8 | 0.254030 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.29088e8 | −0.303841 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.36331e8 | −0.108503 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72145e9 | 0.547870 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.32355e9 | 1.67153 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.14963e9 | 1.28552 | 0.642758 | − | 0.766069i | \(-0.277790\pi\) | ||||
0.642758 | + | 0.766069i | \(0.277790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.51360e9 | 0.768318 | 0.384159 | − | 0.923267i | \(-0.374491\pi\) | ||||
0.384159 | + | 0.923267i | \(0.374491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.73494e9 | −0.824880 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.51352e8 | 0.134332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.27072e9 | 0.960613 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.70359e9 | −1.36332 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.52403e9 | −0.435962 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.97780e6 | −0.00168773 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.51112e8 | 0.265046 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.55379e9 | 0.427398 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.32416e9 | −0.359543 | −0.179772 | − | 0.983708i | \(-0.557536\pi\) | ||||
−0.179772 | + | 0.983708i | \(0.557536\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.39026e8 | 0.117677 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.83789e8 | −0.207401 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.58047e8 | 0.145786 | 0.0728929 | − | 0.997340i | \(-0.476777\pi\) | ||||
0.0728929 | + | 0.997340i | \(0.476777\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.19107e9 | 2.37062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.11567e8 | 0.104812 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.84136e9 | −0.463020 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.88912e9 | −0.717364 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.30331e9 | −0.809946 | −0.404973 | − | 0.914329i | \(-0.632719\pi\) | ||||
−0.404973 | + | 0.914329i | \(0.632719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.44143e9 | 1.80184 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.36398e9 | −0.565293 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.22011e8 | −0.0288152 | −0.0144076 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144076 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.65790e8 | −0.178624 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.77371e9 | −0.869417 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.00925e8 | 0.113993 | 0.0569967 | − | 0.998374i | \(-0.481848\pi\) | ||||
0.0569967 | + | 0.998374i | \(0.481848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.98702e9 | −1.57060 | −0.785300 | − | 0.619116i | \(-0.787491\pi\) | ||||
−0.785300 | + | 0.619116i | \(0.787491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.14253e9 | 1.58603 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.83375e9 | −1.27971 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.16573e9 | −1.76962 | −0.884809 | − | 0.465954i | \(-0.845711\pi\) | ||||
−0.884809 | + | 0.465954i | \(0.845711\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.66769e9 | −2.06989 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.45591e9 | 0.519512 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.57631e9 | −0.956479 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.30320e9 | 0.888682 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.53182e9 | 1.74104 | 0.870519 | − | 0.492135i | \(-0.163783\pi\) | ||||
0.870519 | + | 0.492135i | \(0.163783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.66940e8 | −0.0336632 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.16358e10 | 2.31868 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.71175e9 | −0.337092 | −0.168546 | − | 0.985694i | \(-0.553907\pi\) | ||||
−0.168546 | + | 0.985694i | \(0.553907\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.16921e8 | −0.0811417 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.84475e9 | 0.354836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.77362e9 | −0.907516 | −0.453758 | − | 0.891125i | \(-0.649917\pi\) | ||||
−0.453758 | + | 0.891125i | \(0.649917\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.89998e8 | 0.148445 | 0.0742224 | − | 0.997242i | \(-0.476353\pi\) | ||||
0.0742224 | + | 0.997242i | \(0.476353\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.44408e10 | 2.68214 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.07556e9 | 0.197465 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.82652e9 | −0.331485 | −0.165743 | − | 0.986169i | \(-0.553002\pi\) | ||||
−0.165743 | + | 0.986169i | \(0.553002\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.82266e9 | 0.685813 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.35094e9 | 1.30376 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.90339e9 | −1.21046 | −0.605231 | − | 0.796050i | \(-0.706919\pi\) | ||||
−0.605231 | + | 0.796050i | \(0.706919\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.73977e8 | 0.168844 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.69235e9 | −0.975649 | −0.487825 | − | 0.872942i | \(-0.662209\pi\) | ||||
−0.487825 | + | 0.872942i | \(0.662209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.28594e9 | −0.726321 | −0.363161 | − | 0.931727i | \(-0.618302\pi\) | ||||
−0.363161 | + | 0.931727i | \(0.618302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.84069e10 | −3.08433 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.95171e9 | 0.489064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.57279e9 | 0.749206 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.74354e8 | 0.141661 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.67678e9 | 0.749324 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.61602e8 | −0.0889869 | −0.0444935 | − | 0.999010i | \(-0.514167\pi\) | ||||
−0.0444935 | + | 0.999010i | \(0.514167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.12575e9 | 0.803238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.95031e9 | 0.457256 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.63501e9 | 1.01708 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.24073e10 | −1.88116 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.17445e9 | 0.775998 | 0.387999 | − | 0.921660i | \(-0.373166\pi\) | ||||
0.387999 | + | 0.921660i | \(0.373166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.04374e10 | −1.54830 | −0.774148 | − | 0.633004i | \(-0.781822\pi\) | ||||
−0.774148 | + | 0.633004i | \(0.781822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.75567e9 | −0.697835 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.71623e8 | −0.141037 | −0.0705185 | − | 0.997510i | \(-0.522465\pi\) | ||||
−0.0705185 | + | 0.997510i | \(0.522465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.43825e9 | 0.350125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.55055e9 | −0.220268 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.25223e9 | −1.01924 | −0.509619 | − | 0.860400i | \(-0.670214\pi\) | ||||
−0.509619 | + | 0.860400i | \(0.670214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.54363e7 | 0.00770814 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.18151e9 | −1.12552 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.81924e9 | 0.519851 | 0.259925 | − | 0.965629i | \(-0.416302\pi\) | ||||
0.259925 | + | 0.965629i | \(0.416302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.07881e10 | 1.45292 | 0.726459 | − | 0.687210i | \(-0.241165\pi\) | ||||
0.726459 | + | 0.687210i | \(0.241165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.00947e10 | −1.34523 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.54205e8 | 0.0203339 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.15390e9 | 1.06396 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.54857e9 | 0.458207 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.76448e9 | −0.608817 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.34833e9 | −0.802798 | −0.401399 | − | 0.915903i | \(-0.631476\pi\) | ||||
−0.401399 | + | 0.915903i | \(0.631476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.60858e10 | 2.01316 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.82566e9 | 1.09317 | 0.546584 | − | 0.837404i | \(-0.315928\pi\) | ||||
0.546584 | + | 0.837404i | \(0.315928\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.76599e9 | 0.339083 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.00846e10 | 2.43696 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.92331e9 | 0.591268 | 0.295634 | − | 0.955301i | \(-0.404469\pi\) | ||||
0.295634 | + | 0.955301i | \(0.404469\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.42590e9 | 0.288374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.93027e9 | 0.462459 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.95418e10 | −2.27613 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.68449e9 | −0.655418 | −0.327709 | − | 0.944779i | \(-0.606277\pi\) | ||||
−0.327709 | + | 0.944779i | \(0.606277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.60395e9 | 0.639628 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.61649e9 | 0.295646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.57663e9 | −0.176366 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.89989e10 | −3.21152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.70567e9 | −0.187017 | −0.0935085 | − | 0.995618i | \(-0.529808\pi\) | ||||
−0.0935085 | + | 0.995618i | \(0.529808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.72978e9 | −0.187779 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.69784e9 | −0.504936 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.42351e9 | −0.470760 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.52189e9 | 0.476495 | 0.238248 | − | 0.971204i | \(-0.423427\pi\) | ||||
0.238248 | + | 0.971204i | \(0.423427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.96613e10 | 2.05149 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.30738e9 | −0.341720 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.23070e9 | −0.228229 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.96907e10 | −1.99500 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.09206e9 | −0.310239 | −0.155120 | − | 0.987896i | \(-0.549576\pi\) | ||||
−0.155120 | + | 0.987896i | \(0.549576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.87033e9 | −0.185842 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.20280e9 | 0.905599 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.12568e9 | −0.694453 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44622e10 | 1.39593 | 0.697965 | − | 0.716132i | \(-0.254089\pi\) | ||||
0.697965 | + | 0.716132i | \(0.254089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.09288e9 | −0.104478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.69827e9 | 0.728924 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.15415e9 | 0.295814 | 0.147907 | − | 0.989001i | \(-0.452746\pi\) | ||||
0.147907 | + | 0.989001i | \(0.452746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.24030e9 | −0.393905 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.48585e9 | −0.688819 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.54236e10 | 1.40582 | 0.702912 | − | 0.711277i | \(-0.251883\pi\) | ||||
0.702912 | + | 0.711277i | \(0.251883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.73367e9 | 0.337111 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.59520e10 | −1.42677 | −0.713385 | − | 0.700772i | \(-0.752839\pi\) | ||||
−0.713385 | + | 0.700772i | \(0.752839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.56141e8 | 0.0847179 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.62233e10 | −2.30179 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.32424e7 | −0.00289072 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.13964e9 | 0.528936 | 0.264468 | − | 0.964395i | \(-0.414804\pi\) | ||||
0.264468 | + | 0.964395i | \(0.414804\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.30986e10 | 2.82506 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.44562e9 | 0.122248 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.42818e10 | −1.19660 | −0.598299 | − | 0.801273i | \(-0.704157\pi\) | ||||
−0.598299 | + | 0.801273i | \(0.704157\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.73226e10 | 1.43802 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.47536e10 | 1.21353 | 0.606767 | − | 0.794880i | \(-0.292466\pi\) | ||||
0.606767 | + | 0.794880i | \(0.292466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.35863e9 | −0.355234 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.45173e9 | 0.359512 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.04118e10 | 0.833190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.97592e10 | 1.56685 | 0.783424 | − | 0.621487i | \(-0.213471\pi\) | ||||
0.783424 | + | 0.621487i | \(0.213471\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.68014e10 | −2.10604 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.01370e10 | 0.789374 | 0.394687 | − | 0.918816i | \(-0.370853\pi\) | ||||
0.394687 | + | 0.918816i | \(0.370853\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.89031e9 | 0.223043 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.60663e10 | −1.22869 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.83142e8 | 0.0441970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.43174e9 | 0.483114 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.24833e10 | −1.67376 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.20420e8 | −0.0383981 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27882e10 | −0.935188 | −0.467594 | − | 0.883943i | \(-0.654879\pi\) | ||||
−0.467594 | + | 0.883943i | \(0.654879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.84261e10 | −1.33556 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.25854e9 | −0.305945 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.03453e10 | −1.44880 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.24888e10 | 0.881524 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.38617e9 | −0.516791 | −0.258396 | − | 0.966039i | \(-0.583194\pi\) | ||||
−0.258396 | + | 0.966039i | \(0.583194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.60466e9 | 0.527431 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.15173e10 | −2.16688 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.24114e9 | 0.289054 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.05508e9 | 0.206413 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.24348e10 | 0.832875 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.53742e10 | 1.02087 | 0.510437 | − | 0.859915i | \(-0.329484\pi\) | ||||
0.510437 | + | 0.859915i | \(0.329484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.77882e9 | 0.643744 | 0.321872 | − | 0.946783i | \(-0.395688\pi\) | ||||
0.321872 | + | 0.946783i | \(0.395688\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.10745e10 | 2.02809 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.59472e9 | −0.426722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.84733e9 | −0.182667 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.39300e10 | 1.52212 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.83470e10 | 1.15708 | 0.578540 | − | 0.815654i | \(-0.303623\pi\) | ||||
0.578540 | + | 0.815654i | \(0.303623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.16960e10 | −1.98201 | −0.991004 | − | 0.133829i | \(-0.957273\pi\) | ||||
−0.991004 | + | 0.133829i | \(0.957273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.51382e10 | −0.938608 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.12845e9 | −0.376774 | −0.188387 | − | 0.982095i | \(-0.560326\pi\) | ||||
−0.188387 | + | 0.982095i | \(0.560326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.24652e10 | −0.759904 | −0.379952 | − | 0.925006i | \(-0.624060\pi\) | ||||
−0.379952 | + | 0.925006i | \(0.624060\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.32522e10 | 2.01010 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.86402e9 | 0.411454 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.41091e9 | −0.559409 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.11966e9 | 0.537575 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.82237e10 | −1.06530 | −0.532648 | − | 0.846337i | \(-0.678803\pi\) | ||||
−0.532648 | + | 0.846337i | \(0.678803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.29024e9 | −0.422625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.02118e10 | 2.88675 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.38017e9 | −0.249743 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.98117e9 | 0.338216 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.76870e9 | −0.379602 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.42701e10 | −1.90617 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.48619e10 | −1.37155 | −0.685777 | − | 0.727812i | \(-0.740537\pi\) | ||||
−0.685777 | + | 0.727812i | \(0.740537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.64654e9 | −0.0900930 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.96761e10 | 1.61055 | 0.805275 | − | 0.592902i | \(-0.202018\pi\) | ||||
0.805275 | + | 0.592902i | \(0.202018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.14772e10 | 0.617819 | 0.308910 | − | 0.951091i | \(-0.400036\pi\) | ||||
0.308910 | + | 0.951091i | \(0.400036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.41626e9 | 0.289194 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.13485e10 | 1.13066 | 0.565328 | − | 0.824866i | \(-0.308750\pi\) | ||||
0.565328 | + | 0.824866i | \(0.308750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.19679e9 | 0.273010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.40254e10 | 1.25200 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.01921e10 | −0.526858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.19661e10 | −1.63918 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.95342e10 | −1.50236 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.59108e9 | −0.282142 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.92753e9 | −0.396862 | −0.198431 | − | 0.980115i | \(-0.563585\pi\) | ||||
−0.198431 | + | 0.980115i | \(0.563585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.33805e10 | −3.14771 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.32045e9 | 0.360680 | 0.180340 | − | 0.983604i | \(-0.442280\pi\) | ||||
0.180340 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.54988e9 | −0.173521 | −0.0867604 | − | 0.996229i | \(-0.527651\pi\) | ||||
−0.0867604 | + | 0.996229i | \(0.527651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.65400e9 | −0.322687 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.80634e9 | 0.279364 | 0.139682 | − | 0.990196i | \(-0.455392\pi\) | ||||
0.139682 | + | 0.990196i | \(0.455392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.64066e10 | 0.783182 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.08878e10 | −0.989285 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.81270e9 | −0.132173 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.28466e8 | 0.0432898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.39709e10 | 3.42206 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.03982e9 | −0.185440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.02163e10 | −0.920798 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.64462e10 | −1.19524 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.28573e8 | 0.0192201 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.78240e10 | 0.793196 | 0.396598 | − | 0.917992i | \(-0.370191\pi\) | ||||
0.396598 | + | 0.917992i | \(0.370191\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.72326e10 | 2.08578 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.87703e10 | 0.822538 | 0.411269 | − | 0.911514i | \(-0.365086\pi\) | ||||
0.411269 | + | 0.911514i | \(0.365086\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.35937e10 | 0.591138 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.30023e10 | 0.561107 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.08280e8 | 0.0132024 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.75844e10 | 1.59736 | 0.798681 | − | 0.601754i | \(-0.205531\pi\) | ||||
0.798681 | + | 0.601754i | \(0.205531\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.89197e10 | −2.90693 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.74648e10 | 1.14966 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.99486e10 | 1.24417 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.99707e10 | 0.823404 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.92372e10 | −0.787205 | −0.393602 | − | 0.919281i | \(-0.628771\pi\) | ||||
−0.393602 | + | 0.919281i | \(0.628771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.53876e9 | −0.103109 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.48943e10 | −2.21279 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.30769e9 | −0.0923289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.04732e9 | 0.0415900 | 0.0207950 | − | 0.999784i | \(-0.493380\pi\) | ||||
0.0207950 | + | 0.999784i | \(0.493380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.57413e10 | −2.19709 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.97861e9 | −0.312150 | −0.156075 | − | 0.987745i | \(-0.549884\pi\) | ||||
−0.156075 | + | 0.987745i | \(0.549884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15531e10 | 0.448650 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.42397e9 | −0.324717 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.26943e9 | −0.163360 | −0.0816799 | − | 0.996659i | \(-0.526029\pi\) | ||||
−0.0816799 | + | 0.996659i | \(0.526029\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.81106e10 | 0.687860 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.97963e10 | 1.12339 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.06048e10 | −0.396897 | −0.198449 | − | 0.980111i | \(-0.563590\pi\) | ||||
−0.198449 | + | 0.980111i | \(0.563590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.97247e9 | 0.259045 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.11588e10 | 0.780367 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.34904e10 | 0.493922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.58740e10 | −0.940441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.54950e8 | 0.0128078 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.43750e9 | −0.338074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.65090e10 | −0.587123 | −0.293562 | − | 0.955940i | \(-0.594841\pi\) | ||||
−0.293562 | + | 0.955940i | \(0.594841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.86254e9 | 0.136377 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.46094e10 | −0.862649 | −0.431324 | − | 0.902197i | \(-0.641954\pi\) | ||||
−0.431324 | + | 0.902197i | \(0.641954\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.45503e10 | 0.506379 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.46430e10 | −2.23360 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.53886e10 | −0.870979 | −0.435489 | − | 0.900194i | \(-0.643425\pi\) | ||||
−0.435489 | + | 0.900194i | \(0.643425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.63380e10 | 0.556492 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.65399e10 | 1.57392 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.87585e10 | 0.629884 | 0.314942 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314942 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.13588e10 | 0.378709 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.61246e10 | −0.864846 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.64107e10 | −1.85428 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.59792e9 | −0.117434 | −0.0587170 | − | 0.998275i | \(-0.518701\pi\) | ||||
−0.0587170 | + | 0.998275i | \(0.518701\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.56656e10 | 0.831821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.80083e9 | 0.0579552 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.34287e10 | −0.429143 | −0.214571 | − | 0.976708i | \(-0.568835\pi\) | ||||
−0.214571 | + | 0.976708i | \(0.568835\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.44952e10 | 2.99868 |
(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 | 8.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 72.8.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 16.8.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 200.8.c.a.49.2 | 2 | |||
5.3 | odd | 4 | 200.8.c.a.49.1 | 2 | |||
5.4 | even | 2 | 200.8.a.i.1.1 | 1 | |||
7.6 | odd | 2 | 392.8.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 64.8.a.a.1.1 | 1 | |||
8.5 | even | 2 | 64.8.a.g.1.1 | 1 | |||
12.11 | even | 2 | 144.8.a.g.1.1 | 1 | |||
16.3 | odd | 4 | 256.8.b.c.129.2 | 2 | |||
16.5 | even | 4 | 256.8.b.e.129.2 | 2 | |||
16.11 | odd | 4 | 256.8.b.c.129.1 | 2 | |||
16.13 | even | 4 | 256.8.b.e.129.1 | 2 | |||
20.3 | even | 4 | 400.8.c.b.49.2 | 2 | |||
20.7 | even | 4 | 400.8.c.b.49.1 | 2 | |||
20.19 | odd | 2 | 400.8.a.b.1.1 | 1 | |||
24.5 | odd | 2 | 576.8.a.j.1.1 | 1 | |||
24.11 | even | 2 | 576.8.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.8.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
64.8.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
64.8.a.g.1.1 | 1 | 8.5 | even | 2 | |||
72.8.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
144.8.a.g.1.1 | 1 | 12.11 | even | 2 | |||
200.8.a.i.1.1 | 1 | 5.4 | even | 2 | |||
200.8.c.a.49.1 | 2 | 5.3 | odd | 4 | |||
200.8.c.a.49.2 | 2 | 5.2 | odd | 4 | |||
256.8.b.c.129.1 | 2 | 16.11 | odd | 4 | |||
256.8.b.c.129.2 | 2 | 16.3 | odd | 4 | |||
256.8.b.e.129.1 | 2 | 16.13 | even | 4 | |||
256.8.b.e.129.2 | 2 | 16.5 | even | 4 | |||
392.8.a.d.1.1 | 1 | 7.6 | odd | 2 | |||
400.8.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
400.8.c.b.49.1 | 2 | 20.7 | even | 4 | |||
400.8.c.b.49.2 | 2 | 20.3 | even | 4 | |||
576.8.a.j.1.1 | 1 | 24.5 | odd | 2 | |||
576.8.a.k.1.1 | 1 | 24.11 | even | 2 |