Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 13062x^{6} + 45211107x^{4} + 45928424926x^{2} + 852972309225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(43.3581i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.a.193.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 81.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1783.68i | − 1.27630i | −0.769913 | − | 0.638149i | \(-0.779700\pi\) | ||||
0.769913 | − | 0.638149i | \(-0.220300\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4965.03 | −0.781593 | −0.390797 | − | 0.920477i | \(-0.627800\pi\) | ||||
−0.390797 | + | 0.920477i | \(0.627800\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 53705.0i | − 1.10598i | −0.833187 | − | 0.552991i | \(-0.813487\pi\) | ||||
0.833187 | − | 0.552991i | \(-0.186513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54228.9i | 0.526606i | 0.964713 | + | 0.263303i | \(0.0848118\pi\) | ||||
−0.964713 | + | 0.263303i | \(0.915188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −144478. | −0.736871 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −554662. | −1.61068 | −0.805339 | − | 0.592815i | \(-0.798017\pi\) | ||||
−0.805339 | + | 0.592815i | \(0.798017\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 650852.i | − 1.14575i | −0.819642 | − | 0.572876i | \(-0.805828\pi\) | ||||
0.819642 | − | 0.572876i | \(-0.194172\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 402168.i | 0.451253i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 183775. | 0.136934 | 0.0684669 | − | 0.997653i | \(-0.478189\pi\) | ||||
0.0684669 | + | 0.997653i | \(0.478189\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.22839e6 | −0.628937 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.02445e6i | − 0.531516i | −0.964040 | − | 0.265758i | \(-0.914378\pi\) | ||||
0.964040 | − | 0.265758i | \(-0.0856222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.43180e6 | −0.667413 | −0.333706 | − | 0.942677i | \(-0.608299\pi\) | ||||
−0.333706 | + | 0.942677i | \(0.608299\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.35011e6 | −0.638539 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.85603e6i | 0.997546i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.30084e6i | 0.114108i | 0.998371 | + | 0.0570542i | \(0.0181708\pi\) | ||||
−0.998371 | + | 0.0570542i | \(0.981829\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.39254e6 | 0.304036 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 157393. | 0.00869877 | 0.00434938 | − | 0.999991i | \(-0.498616\pi\) | ||||
0.00434938 | + | 0.999991i | \(0.498616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.10193e6i | 0.0937583i | 0.998901 | + | 0.0468792i | \(0.0149276\pi\) | ||||
−0.998901 | + | 0.0468792i | \(0.985072\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.17027e7i | 0.425433i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.73332e7 | −1.41490 | −0.707449 | − | 0.706764i | \(-0.750154\pi\) | ||||
−0.707449 | + | 0.706764i | \(0.750154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.57021e7 | −0.389112 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.49277e7i | 0.929925i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.00735e8i | − 1.75364i | −0.480820 | − | 0.876819i | \(-0.659661\pi\) | ||||
0.480820 | − | 0.876819i | \(-0.340339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.57926e7 | −1.41156 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.27190e7 | −0.661501 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.80263e7i | 0.193674i | 0.995300 | + | 0.0968372i | \(0.0308726\pi\) | ||||
−0.995300 | + | 0.0968372i | \(0.969127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.48498e7i | 0.507214i | 0.967307 | + | 0.253607i | \(0.0816169\pi\) | ||||
−0.967307 | + | 0.253607i | \(0.918383\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.25756e7 | 0.260531 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.67270e7 | 0.672106 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.13387e8i | 1.29369i | 0.762621 | + | 0.646846i | \(0.223912\pi\) | ||||
−0.762621 | + | 0.646846i | \(0.776088\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1.48858e7i | − 0.0790588i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.64615e8 | −0.768786 | −0.384393 | − | 0.923169i | \(-0.625589\pi\) | ||||
−0.384393 | + | 0.923169i | \(0.625589\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.58505e7 | −0.312612 | −0.156306 | − | 0.987709i | \(-0.549959\pi\) | ||||
−0.156306 | + | 0.987709i | \(0.549959\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.94998e7i | 0.363117i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.66647e8i | 0.864428i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.25335e8 | 1.22860 | 0.614298 | − | 0.789074i | \(-0.289439\pi\) | ||||
0.614298 | + | 0.789074i | \(0.289439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.06618e8i | 0.246592i | 0.992370 | + | 0.123296i | \(0.0393465\pi\) | ||||
−0.992370 | + | 0.123296i | \(0.960654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.89341e8i | 2.05570i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.63981e8 | −0.306871 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.02792e9 | −1.73662 | −0.868308 | − | 0.496025i | \(-0.834793\pi\) | ||||
−0.868308 | + | 0.496025i | \(0.834793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.69248e8i | − 0.411591i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.77976e8i | 0.385331i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.16091e9 | −1.46232 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.24259e8 | 0.715966 | 0.357983 | − | 0.933728i | \(-0.383465\pi\) | ||||
0.357983 | + | 0.933728i | \(0.383465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.52359e8i | 0.368660i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.25002e8i | 0.502013i | 0.967985 | + | 0.251006i | \(0.0807615\pi\) | ||||
−0.967985 | + | 0.251006i | \(0.919239\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.09299e9 | 0.956859 | 0.478429 | − | 0.878126i | \(-0.341206\pi\) | ||||
0.478429 | + | 0.878126i | \(0.341206\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.17339e8 | 0.575933 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.50815e9i | − 1.84981i | −0.380202 | − | 0.924904i | \(-0.624145\pi\) | ||||
0.380202 | − | 0.924904i | \(-0.375855\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.99633e9i | − 1.35461i | −0.735703 | − | 0.677304i | \(-0.763148\pi\) | ||||
0.735703 | − | 0.677304i | \(-0.236852\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.05368e8 | 0.0658805 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.75634e9 | −1.01334 | −0.506670 | − | 0.862140i | \(-0.669124\pi\) | ||||
−0.506670 | + | 0.862140i | \(0.669124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.27796e8i | − 0.174768i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3.55796e8i | − 0.175535i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.75392e9 | 1.25889 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.26281e8 | −0.223195 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.27488e7i | − 0.00502224i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.29269e9i | − 0.473587i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.66916e9 | 1.59266 | 0.796328 | − | 0.604865i | \(-0.206773\pi\) | ||||
0.796328 | + | 0.604865i | \(0.206773\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.70256e8 | 0.0541314 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.48941e9i | 1.62857i | 0.580468 | + | 0.814283i | \(0.302869\pi\) | ||||
−0.580468 | + | 0.814283i | \(0.697131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23150e9i | 0.895513i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.47921e8 | 0.245624 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.05978e9 | −0.742075 | −0.371037 | − | 0.928618i | \(-0.620998\pi\) | ||||
−0.371037 | + | 0.928618i | \(0.620998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 8.06711e9i | − 1.83295i | −0.400089 | − | 0.916476i | \(-0.631021\pi\) | ||||
0.400089 | − | 0.916476i | \(-0.368979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.83399e9i | 0.816892i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.91236e9 | 0.582416 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.61097e9 | −0.678373 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.27187e9i | 0.224654i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.06220e9i | − 1.00761i | −0.863817 | − | 0.503805i | \(-0.831933\pi\) | ||||
0.863817 | − | 0.503805i | \(-0.168067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.92499e9 | −0.927451 | −0.463726 | − | 0.885979i | \(-0.653488\pi\) | ||||
−0.463726 | + | 0.885979i | \(0.653488\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.63914e9 | 0.536892 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.12124e9i | 0.851818i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.68760e9i | 0.747103i | 0.927609 | + | 0.373551i | \(0.121860\pi\) | ||||
−0.927609 | + | 0.373551i | \(0.878140\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.15956e9 | −1.01246 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.12448e8 | −0.107027 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.56247e9i | 0.506239i | 0.967435 | + | 0.253120i | \(0.0814566\pi\) | ||||
−0.967435 | + | 0.253120i | \(0.918543\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.75920e9i | 0.814966i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.22032e9 | 0.121409 | 0.0607044 | − | 0.998156i | \(-0.480665\pi\) | ||||
0.0607044 | + | 0.998156i | \(0.480665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.66373e9 | 0.722687 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.27024e9i | 0.381918i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.24268e10i | − 1.90353i | −0.306821 | − | 0.951767i | \(-0.599265\pi\) | ||||
0.306821 | − | 0.951767i | \(-0.400735\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.09901e9 | 0.491573 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.46013e9 | 0.111818 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.72440e10i | 1.25545i | 0.778435 | + | 0.627725i | \(0.216014\pi\) | ||||
−0.778435 | + | 0.627725i | \(0.783986\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.90161e9i | 0.200949i | 0.994940 | + | 0.100474i | \(0.0320361\pi\) | ||||
−0.994940 | + | 0.100474i | \(0.967964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.44283e9 | 0.292840 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.32029e9 | 0.145636 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.97882e10i | 1.78138i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.63862e9i | − 0.150418i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.14739e9 | 0.0623824 | 0.0311912 | − | 0.999513i | \(-0.490070\pi\) | ||||
0.0311912 | + | 0.999513i | \(0.490070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.19936e10 | 1.65980 | 0.829900 | − | 0.557913i | \(-0.188398\pi\) | ||||
0.829900 | + | 0.557913i | \(0.188398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 7.83489e9i | − 0.388040i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.38558e9i | − 0.160153i | −0.996789 | − | 0.0800764i | \(-0.974484\pi\) | ||||
0.996789 | − | 0.0800764i | \(-0.0255164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.28755e9 | 0.329415 | 0.164707 | − | 0.986342i | \(-0.447332\pi\) | ||||
0.164707 | + | 0.986342i | \(0.447332\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.72843e10 | 0.746913 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.00515e10i | 0.415429i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.80739e8i | − 0.0111022i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.20575e9 | −0.0456446 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.49540e10 | −1.26718 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.58433e9i | 0.0550268i | 0.999621 | + | 0.0275134i | \(0.00875889\pi\) | ||||
−0.999621 | + | 0.0275134i | \(0.991241\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.33338e10i | 0.443859i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.74917e9 | 0.119664 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.70390e10 | 0.521645 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.14389e9i | 0.180487i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.00787e10i | − 0.848192i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82233e10 | 0.764250 | 0.382125 | − | 0.924111i | \(-0.375192\pi\) | ||||
0.382125 | + | 0.924111i | \(0.375192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.05948e9 | 0.209646 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.00872e10i | − 0.252147i | −0.992021 | − | 0.126073i | \(-0.959763\pi\) | ||||
0.992021 | − | 0.126073i | \(-0.0402375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.06314e9i | − 0.0736051i | −0.999323 | − | 0.0368025i | \(-0.988283\pi\) | ||||
0.999323 | − | 0.0368025i | \(-0.0117173\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.15984e10 | 0.499077 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.21496e10 | −0.936896 | −0.468448 | − | 0.883491i | \(-0.655187\pi\) | ||||
−0.468448 | + | 0.883491i | \(0.655187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.44273e10i | 1.80583i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.44521e10i | − 0.709330i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.33007e10 | 1.65142 | 0.825711 | − | 0.564093i | \(-0.190774\pi\) | ||||
0.825711 | + | 0.564093i | \(0.190774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.35832e10 | 0.259373 | 0.129686 | − | 0.991555i | \(-0.458603\pi\) | ||||
0.129686 | + | 0.991555i | \(0.458603\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.48678e9i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.80075e10i | 0.496623i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52950e10 | 0.603360 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.63606e9 | 0.142370 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 9.40336e9i | − 0.149538i | −0.997201 | − | 0.0747690i | \(-0.976178\pi\) | ||||
0.997201 | − | 0.0747690i | \(-0.0238219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.86963e9i | − 0.151446i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.01366e10 | 1.18686 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.20439e10 | −0.458190 | −0.229095 | − | 0.973404i | \(-0.573577\pi\) | ||||
−0.229095 | + | 0.973404i | \(0.573577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 6.45874e9i | − 0.0891864i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.32824e10i | 0.177172i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.93217e10 | 1.15121 | 0.575607 | − | 0.817726i | \(-0.304766\pi\) | ||||
0.575607 | + | 0.817726i | \(0.304766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.79680e11 | −2.23817 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.32615e10i | 1.00264i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.70480e10i | − 0.431400i | −0.976460 | − | 0.215700i | \(-0.930797\pi\) | ||||
0.976460 | − | 0.215700i | \(-0.0692033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.10018e11 | 1.23909 | 0.619546 | − | 0.784960i | \(-0.287317\pi\) | ||||
0.619546 | + | 0.784960i | \(0.287317\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.18091e10 | −0.237632 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.59709e10i | 0.695593i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.60128e10i | 0.877818i | 0.898532 | + | 0.438909i | \(0.144635\pi\) | ||||
−0.898532 | + | 0.438909i | \(0.855365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.25160e10 | 0.222471 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.40155e11 | 1.34101 | 0.670503 | − | 0.741907i | \(-0.266078\pi\) | ||||
0.670503 | + | 0.741907i | \(0.266078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.86732e10i | 0.636426i | 0.948019 | + | 0.318213i | \(0.103083\pi\) | ||||
−0.948019 | + | 0.318213i | \(0.896917\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.40339e10i | 0.844272i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.81461e8 | −0.00679890 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.89063e11 | 1.59428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 5.05650e10i | − 0.413363i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3.90112e10i | − 0.309233i | −0.987975 | − | 0.154616i | \(-0.950586\pi\) | ||||
0.987975 | − | 0.154616i | \(-0.0494141\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.21531e10 | 0.247186 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.85410e10 | 0.212846 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.96590e9i | 0.0721101i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.04361e10i | − 0.0732809i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.25251e10 | 0.289837 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.78346e10 | 0.647356 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.94107e11i | 1.24715i | 0.781765 | + | 0.623573i | \(0.214320\pi\) | ||||
−0.781765 | + | 0.623573i | \(0.785680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 8.85320e10i | − 0.552443i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.41999e11 | 0.860726 | 0.430363 | − | 0.902656i | \(-0.358386\pi\) | ||||
0.430363 | + | 0.902656i | \(0.358386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.96211e11 | −1.15551 | −0.577756 | − | 0.816209i | \(-0.696072\pi\) | ||||
−0.577756 | + | 0.816209i | \(0.696072\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 5.81044e10i | − 0.332515i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.32729e11i | 1.85065i | 0.379177 | + | 0.925324i | \(0.376207\pi\) | ||||
−0.379177 | + | 0.925324i | \(0.623793\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08723e11 | −0.587847 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.03160e11 | −1.06799 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.61003e11i | 1.84544i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6.66143e10i | − 0.331202i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.61703e11 | −0.782084 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.35011e11 | 1.10587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82155e11i | 1.29200i | 0.763338 | + | 0.646000i | \(0.223559\pi\) | ||||
−0.763338 | + | 0.646000i | \(0.776441\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 8.53484e9i | − 0.0380361i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.80614e11 | 1.65114 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.98725e11 | −1.26164 | −0.630822 | − | 0.775928i | \(-0.717282\pi\) | ||||
−0.630822 | + | 0.775928i | \(0.717282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.42263e11i | 0.585052i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.84305e11i | 0.738146i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.78318e11 | 1.08572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.65515e10 | −0.100903 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.84025e11i | 1.79219i | 0.443858 | + | 0.896097i | \(0.353609\pi\) | ||||
−0.443858 | + | 0.896097i | \(0.646391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.44115e10i | 0.0880806i | 0.999030 | + | 0.0440403i | \(0.0140230\pi\) | ||||
−0.999030 | + | 0.0440403i | \(0.985977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.88194e10 | −0.101345 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.28670e11 | −1.12661 | −0.563306 | − | 0.826248i | \(-0.690471\pi\) | ||||
−0.563306 | + | 0.826248i | \(0.690471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.93620e11i | 0.981201i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.23067e11i | − 0.726823i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.58376e11 | −1.45646 | −0.728228 | − | 0.685335i | \(-0.759656\pi\) | ||||
−0.728228 | + | 0.685335i | \(0.759656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00920e11 | −0.312749 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.26288e10i | 0.128862i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.35293e11i | 0.398986i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.88051e11 | 1.69207 | 0.846034 | − | 0.533128i | \(-0.178984\pi\) | ||||
0.846034 | + | 0.533128i | \(0.178984\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.03265e9 | −0.00289959 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.00154e11i | 1.37063i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.61776e9i | 0.0177020i | 0.999961 | + | 0.00885098i | \(0.00281739\pi\) | ||||
−0.999961 | + | 0.00885098i | \(0.997183\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.04708e11 | −0.273426 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.09784e11 | 0.279899 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 5.36022e11i | − 1.33446i | −0.744851 | − | 0.667231i | \(-0.767479\pi\) | ||||
0.744851 | − | 0.667231i | \(-0.232521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3.78202e11i | − 0.919520i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.39762e11 | 1.28176 | 0.640882 | − | 0.767640i | \(-0.278569\pi\) | ||||
0.640882 | + | 0.767640i | \(0.278569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.75613e11 | 1.10327 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.37907e10i | − 0.0312528i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 1.54973e11i | − 0.343150i | −0.985171 | − | 0.171575i | \(-0.945114\pi\) | ||||
0.985171 | − | 0.171575i | \(-0.0548855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01933e11 | −0.220556 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.44643e11 | 0.940253 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 7.58662e11i | − 1.56806i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.94662e11i | − 0.999427i | −0.866191 | − | 0.499714i | \(-0.833439\pi\) | ||||
0.866191 | − | 0.499714i | \(-0.166561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.61751e11 | 0.517024 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.84391e11 | 0.935506 | 0.467753 | − | 0.883859i | \(-0.345064\pi\) | ||||
0.467753 | + | 0.883859i | \(0.345064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.86103e11i | − 0.351463i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 7.67816e10i | − 0.141811i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.98619e10 | 0.126202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.98035e11 | −0.703341 | −0.351671 | − | 0.936124i | \(-0.614386\pi\) | ||||
−0.351671 | + | 0.936124i | \(0.614386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.47842e11i | 0.428437i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 8.95011e10i | − 0.151375i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.90172e11 | 0.314725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.53436e11 | −1.05826 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.97991e10i | − 0.110633i | −0.998469 | − | 0.0553167i | \(-0.982383\pi\) | ||||
0.998469 | − | 0.0553167i | \(-0.0176169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 3.17674e11i | − 0.492847i | −0.969162 | − | 0.246423i | \(-0.920745\pi\) | ||||
0.969162 | − | 0.246423i | \(-0.0792554\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.10553e11 | 0.471633 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.81343e11 | 1.01301 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.72331e11i | − 0.396435i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.35901e11i | − 0.336258i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.99506e11 | 1.11603 | 0.558013 | − | 0.829832i | \(-0.311564\pi\) | ||||
0.558013 | + | 0.829832i | \(0.311564\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.63025e11 | 0.906430 | 0.453215 | − | 0.891401i | \(-0.350277\pi\) | ||||
0.453215 | + | 0.891401i | \(0.350277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.92489e11i | 0.391659i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.19610e11i | − 0.156892i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.31042e10 | −0.0553898 | −0.0276949 | − | 0.999616i | \(-0.508817\pi\) | ||||
−0.0276949 | + | 0.999616i | \(0.508817\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.03021e11 | 0.129704 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.49651e11i | 0.801426i | 0.916204 | + | 0.400713i | \(0.131238\pi\) | ||||
−0.916204 | + | 0.400713i | \(0.868762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.83348e12i | 2.21644i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.91039e11 | −0.581744 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.28210e10 | 0.0264988 | 0.0132494 | − | 0.999912i | \(-0.495782\pi\) | ||||
0.0132494 | + | 0.999912i | \(0.495782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 8.45279e9i | − 0.00962067i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.79924e11i | 0.535464i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.80253e11 | −0.525313 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.44749e12 | −1.55237 | −0.776183 | − | 0.630508i | \(-0.782847\pi\) | ||||
−0.776183 | + | 0.630508i | \(0.782847\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.94770e11i | − 0.309975i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.28905e11i | − 0.132927i | −0.997789 | − | 0.0664637i | \(-0.978828\pi\) | ||||
0.997789 | − | 0.0664637i | \(-0.0211717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.71037e12 | 1.72972 | 0.864860 | − | 0.502013i | \(-0.167407\pi\) | ||||
0.864860 | + | 0.502013i | \(0.167407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.95820e11 | 0.491797 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.91054e12i | − 1.85879i | −0.369092 | − | 0.929393i | \(-0.620331\pi\) | ||||
0.369092 | − | 0.929393i | \(-0.379669\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.05947e12i | − 1.01114i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.60695e11 | 0.431340 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.12884e11 | 0.103695 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.99502e11i | 0.720606i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.60924e11i | 0.584546i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.92498e12 | −1.67077 | −0.835385 | − | 0.549665i | \(-0.814756\pi\) | ||||
−0.835385 | + | 0.549665i | \(0.814756\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.05433e10 | −0.0600901 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.39083e10i | 0.0617918i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.11348e12i | − 0.913785i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.29897e12 | −1.85205 | −0.926026 | − | 0.377460i | \(-0.876798\pi\) | ||||
−0.926026 | + | 0.377460i | \(0.876798\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.69560e11 | 0.292277 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.35110e11i | 0.415505i | 0.978181 | + | 0.207753i | \(0.0666149\pi\) | ||||
−0.978181 | + | 0.207753i | \(0.933385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.12289e12i | 0.856101i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.28495e11 | 0.470521 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.17317e11 | 0.600878 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.06412e12i | − 0.768312i | −0.923268 | − | 0.384156i | \(-0.874492\pi\) | ||||
0.923268 | − | 0.384156i | \(-0.125508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 9.88461e10i | − 0.0700954i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.01345e12 | −1.40244 | −0.701220 | − | 0.712945i | \(-0.747361\pi\) | ||||
−0.701220 | + | 0.712945i | \(0.747361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.36436e11 | 0.640718 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 6.20762e11i | − 0.417243i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.34279e12i | − 0.886701i | −0.896348 | − | 0.443350i | \(-0.853790\pi\) | ||||
0.896348 | − | 0.443350i | \(-0.146210\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.76600e11 | 0.244336 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.45889e11 | 0.220500 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.94954e12i | − 1.22124i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.54203e12i | 1.56485i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.81657e12 | −1.09901 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.74500e12 | −1.03759 | −0.518796 | − | 0.854898i | \(-0.673619\pi\) | ||||
−0.518796 | + | 0.854898i | \(0.673619\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.62381e12i | 0.949026i | 0.880249 | + | 0.474513i | \(0.157376\pi\) | ||||
−0.880249 | + | 0.474513i | \(0.842624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4.94020e11i | − 0.283810i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.90349e12 | 1.07499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.76738e12 | −0.981249 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.18270e11i | − 0.0645581i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.53524e9i | 0.00458082i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.47374e12 | −2.36091 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.39676e12 | 0.724835 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.43280e11i | 0.430351i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 2.26145e12i | − 1.13501i | −0.823370 | − | 0.567505i | \(-0.807909\pi\) | ||||
0.823370 | − | 0.567505i | \(-0.192091\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.35031e11 | 0.116018 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.56082e12 | −1.72888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.08228e12i | 0.994480i | 0.867613 | + | 0.497240i | \(0.165653\pi\) | ||||
−0.867613 | + | 0.497240i | \(0.834347\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 3.59870e11i | − 0.169071i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.31762e12 | −0.608986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.11180e12 | −0.960263 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.87944e11i | − 0.0840832i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.69657e12i | − 0.746831i | −0.927664 | − | 0.373415i | \(-0.878187\pi\) | ||||
0.927664 | − | 0.373415i | \(-0.121813\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.13985e11 | −0.0493736 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.41284e12 | 1.02848 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.48379e11i | 0.0622423i | 0.999516 | + | 0.0311212i | \(0.00990778\pi\) | ||||
−0.999516 | + | 0.0311212i | \(0.990092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.13275e12i | 1.29332i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.13728e11 | −0.0868437 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.31992e11 | −0.372741 | −0.186370 | − | 0.982480i | \(-0.559672\pi\) | ||||
−0.186370 | + | 0.982480i | \(0.559672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.97476e12i | − 1.95844i | −0.202807 | − | 0.979219i | \(-0.565007\pi\) | ||||
0.202807 | − | 0.979219i | \(-0.434993\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.29388e10i | − 0.0360165i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.25748e11 | −0.0861228 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.93519e11 | 0.298034 | 0.149017 | − | 0.988835i | \(-0.452389\pi\) | ||||
0.149017 | + | 0.988835i | \(0.452389\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 2.59148e12i | − 0.958286i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.29362e11i | − 0.192735i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.40999e12 | −1.93949 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.34626e11 | −0.224035 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4.52536e11i | − 0.157319i | −0.996902 | − | 0.0786596i | \(-0.974936\pi\) | ||||
0.996902 | − | 0.0786596i | \(-0.0250640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.23359e12i | 0.764690i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.74232e11 | −0.0924643 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.09626e12 | −0.696144 | −0.348072 | − | 0.937468i | \(-0.613164\pi\) | ||||
−0.348072 | + | 0.937468i | \(0.613164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.91211e12i | − 1.60672i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.90292e11i | − 0.190188i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.30531e12 | −0.731659 | −0.365829 | − | 0.930682i | \(-0.619215\pi\) | ||||
−0.365829 | + | 0.930682i | \(0.619215\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.13269e12 | 0.666794 | 0.333397 | − | 0.942787i | \(-0.391805\pi\) | ||||
0.333397 | + | 0.942787i | \(0.391805\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.40003e12i | − 0.431230i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.38718e11i | 0.284863i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.72283e12 | −1.11308 | −0.556538 | − | 0.830822i | \(-0.687870\pi\) | ||||
−0.556538 | + | 0.830822i | \(0.687870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.14168e11 | 0.239848 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.56682e12i | − 0.745093i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.70140e12i | 1.91687i | 0.285305 | + | 0.958437i | \(0.407905\pi\) | ||||
−0.285305 | + | 0.958437i | \(0.592095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.27398e10 | −0.00640987 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.02429e12 | 0.284537 | 0.142268 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142268 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 3.15002e12i | − 0.862393i | −0.902258 | − | 0.431196i | \(-0.858092\pi\) | ||||
0.902258 | − | 0.431196i | \(-0.141908\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.76655e10i | 0.0263529i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.10365e12 | 1.35733 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.70495e12 | −1.23338 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.83127e12i | 0.731607i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 7.21530e11i | − 0.183792i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.99605e12 | 0.501233 | 0.250617 | − | 0.968086i | \(-0.419367\pi\) | ||||
0.250617 | + | 0.968086i | \(0.419367\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.28331e11 | 0.0317697 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.32829e12i | − 2.03270i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.51506e11i | − 0.204909i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.08004e12 | 0.256262 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.10597e12 | 1.66250 | 0.831252 | − | 0.555896i | \(-0.187625\pi\) | ||||
0.831252 | + | 0.555896i | \(0.187625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.13065e12i | − 0.260843i | −0.991459 | − | 0.130422i | \(-0.958367\pi\) | ||||
0.991459 | − | 0.130422i | \(-0.0416331\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.03683e11i | − 0.0690878i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.14088e12 | −1.15337 | −0.576685 | − | 0.816967i | \(-0.695654\pi\) | ||||
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.68102e11 | 0.214200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 1.38016e12i | − 0.301172i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.23628e11i | − 0.112697i | −0.998411 | − | 0.0563486i | \(-0.982054\pi\) | ||||
0.998411 | − | 0.0563486i | \(-0.0179458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.79136e12 | 2.07854 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.97655e11 | 0.104204 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.73828e12i | 0.565579i | 0.959182 | + | 0.282789i | \(0.0912598\pi\) | ||||
−0.959182 | + | 0.282789i | \(0.908740\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.53582e12i | 0.312920i | 0.987684 | + | 0.156460i | \(0.0500082\pi\) | ||||
−0.987684 | + | 0.156460i | \(0.949992\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.43638e12 | −0.489704 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.76396e12 | 1.14294 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.72043e11i | − 0.0727825i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 2.28609e12i | − 0.441240i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.94571e12 | 0.560969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.06140e12 | −1.70266 | −0.851329 | − | 0.524632i | \(-0.824203\pi\) | ||||
−0.851329 | + | 0.524632i | \(0.824203\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 6.52818e11i | − 0.121039i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8.23814e12i | − 1.50723i | −0.657315 | − | 0.753616i | \(-0.728308\pi\) | ||||
0.657315 | − | 0.753616i | \(-0.271692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.09947e12 | −0.559594 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.17061e11 | −0.145577 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.99109e12i | − 0.350104i | −0.984559 | − | 0.175052i | \(-0.943991\pi\) | ||||
0.984559 | − | 0.175052i | \(-0.0560094\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.45767e12i | 0.947109i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.48115e11 | −0.0424959 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.46276e12 | 0.923476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 6.48604e11i | − 0.108225i | −0.998535 | − | 0.0541126i | \(-0.982767\pi\) | ||||
0.998535 | − | 0.0541126i | \(-0.0172330\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.74947e12i | − 0.288143i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.43891e13 | −2.33939 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.72999e10 | −0.0140109 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.41412e12i | 0.540917i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 9.56476e12i | − 1.49604i | −0.663677 | − | 0.748019i | \(-0.731005\pi\) | ||||
0.663677 | − | 0.748019i | \(-0.268995\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.46657e11 | 0.130740 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.83861e12 | 1.04260 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.60665e12i | − 0.392370i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 5.02818e12i | − 0.747314i | −0.927567 | − | 0.373657i | \(-0.878104\pi\) | ||||
0.927567 | − | 0.373657i | \(-0.121896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.79062e12 | −0.409532 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.30679e11 | −0.0913914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5.19473e12i | − 0.743336i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 6.74736e12i | − 0.953449i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.87923e11 | −0.0541334 | −0.0270667 | − | 0.999634i | \(-0.508617\pi\) | ||||
−0.0270667 | + | 0.999634i | \(0.508617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.42672e12 | −0.747874 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.10024e12i | − 0.149749i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.48682e12i | 0.334290i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.21943e12 | 0.161902 | 0.0809510 | − | 0.996718i | \(-0.474204\pi\) | ||||
0.0809510 | + | 0.996718i | \(0.474204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.16586e12i | − 0.151014i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.25774e12i | 0.160925i | 0.996758 | + | 0.0804626i | \(0.0256397\pi\) | ||||
−0.996758 | + | 0.0804626i | \(0.974360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.26861e12 | 0.286725 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.14599e13 | 1.43080 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.08922e13i | 1.34343i | 0.740812 | + | 0.671713i | \(0.234441\pi\) | ||||
−0.740812 | + | 0.671713i | \(0.765559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2.85889e12i | − 0.348350i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.60817e12 | −0.915863 | −0.457932 | − | 0.888987i | \(-0.651410\pi\) | ||||
−0.457932 | + | 0.888987i | \(0.651410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.08130e13 | −1.28601 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.99521e11i | − 0.0821974i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.24530e13i | 1.44580i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.34422e13 | −1.54202 | −0.771010 | − | 0.636823i | \(-0.780248\pi\) | ||||
−0.771010 | + | 0.636823i | \(0.780248\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.61672e11 | −0.0863358 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.05683e13i | 1.18370i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.22512e12i | − 0.135597i | −0.997699 | − | 0.0677983i | \(-0.978403\pi\) | ||||
0.997699 | − | 0.0677983i | \(-0.0215974\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.99440e11 | −0.0874375 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.86163e12 | 0.201216 | 0.100608 | − | 0.994926i | \(-0.467921\pi\) | ||||
0.100608 | + | 0.994926i | \(0.467921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.91186e12i | 1.05875i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6.49106e12i | − 0.685235i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.77545e11 | −0.101990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.61673e13 | −1.66713 | −0.833564 | − | 0.552422i | \(-0.813704\pi\) | ||||
−0.833564 | + | 0.552422i | \(0.813704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.59555e12i | 0.264536i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.51715e13i | 1.52834i | 0.645012 | + | 0.764172i | \(0.276852\pi\) | ||||
−0.645012 | + | 0.764172i | \(0.723148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.21560e12 | 0.419761 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.23158e11 | −0.0514918 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.02439e11i | − 0.00996664i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.84063e12i | 0.850263i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.07588e12 | 0.102290 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.01449e13 | 0.953526 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.28839e13i | − 1.19718i | −0.801055 | − | 0.598590i | \(-0.795728\pi\) | ||||
0.801055 | − | 0.598590i | \(-0.204272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 7.23506e12i | − 0.664654i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.72027e12 | 0.792019 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.97444e12 | −0.267101 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.45540e13i | 1.29221i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.41358e12i | 0.387462i | 0.981055 | + | 0.193731i | \(0.0620589\pi\) | ||||
−0.981055 | + | 0.193731i | \(0.937941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.62539e13 | 2.27894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.74418e12 | 0.578872 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.07355e12i | 0.345743i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.62752e12i | 0.136598i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.00089e12 | −0.249069 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.24867e13 | −1.02490 | −0.512449 | − | 0.858718i | \(-0.671262\pi\) | ||||
−0.512449 | + | 0.858718i | \(0.671262\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.75694e12i | 0.467302i | 0.972321 | + | 0.233651i | \(0.0750674\pi\) | ||||
−0.972321 | + | 0.233651i | \(0.924933\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 8.91150e12i | − 0.715391i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.13799e12 | 0.646112 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.36804e12 | 0.107424 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.76654e12i | 0.137197i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.15601e13i | − 0.888009i | −0.896025 | − | 0.444004i | \(-0.853557\pi\) | ||||
0.896025 | − | 0.444004i | \(-0.146443\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.28159e13 | −0.973758 | −0.486879 | − | 0.873469i | \(-0.661865\pi\) | ||||
−0.486879 | + | 0.873469i | \(0.661865\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.34364e12 | 0.401601 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.88099e13i | 1.39834i | 0.714957 | + | 0.699169i | \(0.246446\pi\) | ||||
−0.714957 | + | 0.699169i | \(0.753554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.05174e13i | 0.773413i | 0.922203 | + | 0.386707i | \(0.126387\pi\) | ||||
−0.922203 | + | 0.386707i | \(0.873613\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.96704e12 | 0.506808 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.70935e12 | 0.626734 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.17667e12i | − 0.154954i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.82380e12i | − 0.128444i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.13441e13 | 1.48713 | 0.743564 | − | 0.668665i | \(-0.233134\pi\) | ||||
0.743564 | + | 0.668665i | \(0.233134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.04087e13 | 0.717491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.13526e13i | − 0.774230i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.36696e13i | − 0.922364i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.61300e12 | 0.174447 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.56253e12 | 0.367441 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.39063e11i | 0.0156253i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.81634e13i | 1.17470i | 0.809334 | + | 0.587348i | \(0.199828\pi\) | ||||
−0.809334 | + | 0.587348i | \(0.800172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.61674e12 | 0.487441 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.86744e13 | 1.81585 | 0.907927 | − | 0.419128i | \(-0.137664\pi\) | ||||
0.907927 | + | 0.419128i | \(0.137664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.97255e12i | 0.562273i | 0.959668 | + | 0.281136i | \(0.0907113\pi\) | ||||
−0.959668 | + | 0.281136i | \(0.909289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.32983e10i | 0.00392535i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.96293e13 | 1.20463 | 0.602317 | − | 0.798257i | \(-0.294244\pi\) | ||||
0.602317 | + | 0.798257i | \(0.294244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00023e13 | −2.42948 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.53141e13i | − 0.920459i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.28426e13i | − 1.35880i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.15717e13 | −0.681265 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.09576e12 | −0.238655 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.41825e12i | 0.370152i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.82741e13i | 1.04313i | 0.853211 | + | 0.521565i | \(0.174652\pi\) | ||||
−0.853211 | + | 0.521565i | \(0.825348\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.15991e12 | −0.178535 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.46604e12 | 0.0819888 | 0.0409944 | − | 0.999159i | \(-0.486947\pi\) | ||||
0.0409944 | + | 0.999159i | \(0.486947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 9.47248e11i | − 0.0524373i | −0.999656 | − | 0.0262187i | \(-0.991653\pi\) | ||||
0.999656 | − | 0.0262187i | \(-0.00834661\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.60440e12i | − 0.142713i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.51475e12 | 0.299136 | 0.149568 | − | 0.988751i | \(-0.452212\pi\) | ||||
0.149568 | + | 0.988751i | \(0.452212\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.31825e13 | −1.24481 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.31182e12i | − 0.122887i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.08069e13i | 1.62112i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.07578e13 | 1.60233 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.07238e11 | 0.0416328 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.94751e12i | 0.354741i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.58741e13i | 2.82455i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.45327e11 | −0.0423087 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.17555e12 | 0.256471 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.24027e13i | 1.58982i | 0.606725 | + | 0.794912i | \(0.292483\pi\) | ||||
−0.606725 | + | 0.794912i | \(0.707517\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3.44454e12i | − 0.167338i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.85811e12 | 0.137482 | 0.0687410 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687410 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.72592e12 | 0.272726 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 7.92460e12i | − 0.373751i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.72551e13i | − 1.27288i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.84172e13 | 0.851734 | 0.425867 | − | 0.904786i | \(-0.359969\pi\) | ||||
0.425867 | + | 0.904786i | \(0.359969\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.57226e13 | 0.720040 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 8.92686e12i | − 0.404847i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.59795e12i | − 0.0717670i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.17109e12 | −0.318953 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.37811e13 | −1.48800 | −0.744000 | − | 0.668179i | \(-0.767074\pi\) | ||||
−0.744000 | + | 0.668179i | \(0.767074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02197e13i | 0.445826i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.15020e13i | − 0.496940i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.31326e13 | 2.27357 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.50959e13 | −1.91121 | −0.955606 | − | 0.294649i | \(-0.904797\pi\) | ||||
−0.955606 | + | 0.294649i | \(0.904797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.58931e13i | 0.667136i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.11150e13i | − 0.877887i | −0.898515 | − | 0.438943i | \(-0.855353\pi\) | ||||
0.898515 | − | 0.438943i | \(-0.144647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.89249e10 | 0.00119116 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.70646e12 | −0.191978 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.89150e12i | 0.0764244i | 0.999270 | + | 0.0382122i | \(0.0121663\pi\) | ||||
−0.999270 | + | 0.0382122i | \(0.987834\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.11329e12i | − 0.164623i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.69510e13 | 1.06847 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.36004e12 | 0.367587 | 0.183793 | − | 0.982965i | \(-0.441162\pi\) | ||||
0.183793 | + | 0.982965i | \(0.441162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.04658e12i | − 0.0796186i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.80658e12i | 0.339393i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.51919e13 | 0.580001 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.46624e13 | −0.554560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.64560e13i | 0.616602i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 5.70664e13i | − 2.11840i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.61523e13 | 0.961814 | 0.480907 | − | 0.876772i | \(-0.340308\pi\) | ||||
0.480907 | + | 0.876772i | \(0.340308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.92412e13 | 1.06546 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.18913e13i | 0.429281i | 0.976693 | + | 0.214640i | \(0.0688579\pi\) | ||||
−0.976693 | + | 0.214640i | \(0.931142\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00534e13i | 1.43262i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.39576e12 | −0.191219 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.37020e12 | 0.118340 | 0.0591699 | − | 0.998248i | \(-0.481155\pi\) | ||||
0.0591699 | + | 0.998248i | \(0.481155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.52044e13i | 1.92067i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.30979e13i | 0.451536i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.94392e13 | −1.68881 | −0.844404 | − | 0.535706i | \(-0.820045\pi\) | ||||
−0.844404 | + | 0.535706i | \(0.820045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.03879e12 | −0.204403 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.90359e13i | − 0.638477i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.86281e11i | 0.0128387i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.33144e13 | −1.09724 | −0.548619 | − | 0.836073i | \(-0.684846\pi\) | ||||
−0.548619 | + | 0.836073i | \(0.684846\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.28546e13 | 0.745936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.29987e13i | − 0.420431i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.18744e12i | − 0.0380612i | −0.999819 | − | 0.0190306i | \(-0.993942\pi\) | ||||
0.999819 | − | 0.0190306i | \(-0.00605799\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.91322e11 | −0.0219602 |
(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 | 384.10.d.a.193.1 | ✓ | 8 | |
4.3 | odd | 2 | 384.10.d.b.193.5 | yes | 8 | ||
8.3 | odd | 2 | 384.10.d.b.193.4 | yes | 8 | ||
8.5 | even | 2 | inner | 384.10.d.a.193.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.a.193.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
384.10.d.a.193.8 | yes | 8 | 8.5 | even | 2 | inner | |
384.10.d.b.193.4 | yes | 8 | 8.3 | odd | 2 | ||
384.10.d.b.193.5 | yes | 8 | 4.3 | odd | 2 |