Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(29,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.29");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.b (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: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 1880 x^{10} + 1266870 x^{8} + 399545800 x^{6} + 62009694600 x^{4} + 4432082624000 x^{2} + 109931031040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{8}\cdot 5^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.1 | ||
Root | \(-18.2420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.29 |
Dual form | 60.7.b.a.29.2 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −24.4963 | − | 11.3548i | −0.907270 | − | 0.420549i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −124.726 | − | 8.26448i | −0.997812 | − | 0.0661159i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 577.271i | 1.68301i | 0.540252 | + | 0.841503i | \(0.318329\pi\) | ||||
−0.540252 | + | 0.841503i | \(0.681671\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 471.136 | + | 556.302i | 0.646277 | + | 0.763103i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1964.28i | − | 1.47580i | −0.674912 | − | 0.737898i | \(-0.735819\pi\) | ||
0.674912 | − | 0.737898i | \(-0.264181\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2091.29i | − | 0.951885i | −0.879476 | − | 0.475943i | \(-0.842107\pi\) | ||
0.879476 | − | 0.475943i | \(-0.157893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2961.49 | + | 1618.70i | 0.877480 | + | 0.479614i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1153.08 | 0.234699 | 0.117350 | − | 0.993091i | \(-0.462560\pi\) | ||||
0.117350 | + | 0.993091i | \(0.462560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5613.44 | 0.818405 | 0.409202 | − | 0.912444i | \(-0.365807\pi\) | ||||
0.409202 | + | 0.912444i | \(0.365807\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6554.81 | − | 14141.0i | 0.707786 | − | 1.52694i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3383.70 | 0.278104 | 0.139052 | − | 0.990285i | \(-0.455594\pi\) | ||||
0.139052 | + | 0.990285i | \(0.455594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15488.4 | + | 2061.60i | 0.991257 | + | 0.131942i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5224.38 | − | 18977.0i | −0.265426 | − | 0.964131i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5725.09i | 0.234740i | 0.993088 | + | 0.117370i | \(0.0374464\pi\) | ||||
−0.993088 | + | 0.117370i | \(0.962554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36900.2 | 1.23864 | 0.619318 | − | 0.785140i | \(-0.287409\pi\) | ||||
0.619318 | + | 0.785140i | \(0.287409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −22304.1 | + | 48117.7i | −0.620644 | + | 1.33894i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4770.85 | − | 72001.0i | 0.111273 | − | 1.67932i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32609.3i | 0.643778i | 0.946777 | + | 0.321889i | \(0.104318\pi\) | ||||
−0.946777 | + | 0.321889i | \(0.895682\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −23746.2 | + | 51228.9i | −0.400314 | + | 0.863617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 56515.1i | 0.819998i | 0.912086 | + | 0.409999i | \(0.134471\pi\) | ||||
−0.912086 | + | 0.409999i | \(0.865529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 113328.i | − | 1.42538i | −0.701479 | − | 0.712690i | \(-0.747477\pi\) | ||
0.701479 | − | 0.712690i | \(-0.252523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −54165.6 | − | 73279.3i | −0.594410 | − | 0.804162i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 157774. | 1.51964 | 0.759822 | − | 0.650131i | \(-0.225286\pi\) | ||||
0.759822 | + | 0.650131i | \(0.225286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −215593. | −1.83251 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28246.1 | − | 13093.0i | −0.212935 | − | 0.0987024i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 109599. | 0.736175 | 0.368087 | − | 0.929791i | \(-0.380013\pi\) | ||||
0.368087 | + | 0.929791i | \(0.380013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16233.8 | + | 244998.i | −0.0975735 | + | 1.47257i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −137508. | − | 63739.6i | −0.742514 | − | 0.344179i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 227718.i | 1.10877i | 0.832261 | + | 0.554384i | \(0.187046\pi\) | ||||
−0.832261 | + | 0.554384i | \(0.812954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −271177. | −1.19471 | −0.597357 | − | 0.801976i | \(-0.703782\pi\) | ||||
−0.597357 | + | 0.801976i | \(0.703782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −321137. | + | 271973.i | −1.28431 | + | 1.08769i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17283.4 | + | 260840.i | −0.0629347 | + | 0.949803i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 219429.i | − | 0.729574i | −0.931091 | − | 0.364787i | \(-0.881142\pi\) | ||
0.931091 | − | 0.364787i | \(-0.118858\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −82888.0 | − | 38421.2i | −0.252316 | − | 0.116956i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 522399.i | − | 1.45958i | −0.683672 | − | 0.729789i | \(-0.739618\pi\) | ||
0.683672 | − | 0.729789i | \(-0.260382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1788.95i | − | 0.00459864i | −0.999997 | − | 0.00229932i | \(-0.999268\pi\) | ||
0.999997 | − | 0.00229932i | \(-0.000731898\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −355999. | − | 226369.i | −0.843850 | − | 0.536579i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.13392e6 | 2.48377 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 794759. | 1.61196 | 0.805979 | − | 0.591944i | \(-0.201639\pi\) | ||||
0.805979 | + | 0.591944i | \(0.201639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −87502.3 | + | 524188.i | −0.164651 | + | 0.986352i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 213226. | 0.372912 | 0.186456 | − | 0.982463i | \(-0.440300\pi\) | ||||
0.186456 | + | 0.982463i | \(0.440300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −143819. | − | 9529.58i | −0.234186 | − | 0.0155173i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 65007.3 | − | 140243.i | 0.0987198 | − | 0.212973i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.24220e6i | − | 1.76206i | −0.473061 | − | 0.881030i | \(-0.656851\pi\) | ||
0.473061 | − | 0.881030i | \(-0.343149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.20724e6 | 1.60203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −903919. | − | 418995.i | −1.12378 | − | 0.520907i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −700144. | − | 46392.2i | −0.816614 | − | 0.0541095i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 492715.i | − | 0.539859i | −0.962880 | − | 0.269929i | \(-0.913000\pi\) | ||
0.962880 | − | 0.269929i | \(-0.0870004\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.09273e6 | − | 925445.i | 1.12618 | − | 0.953773i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.37089e6i | 1.33057i | 0.746590 | + | 0.665284i | \(0.231690\pi\) | ||||
−0.746590 | + | 0.665284i | \(0.768310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 915262.i | 0.837595i | 0.908080 | + | 0.418797i | \(0.137548\pi\) | ||||
−0.908080 | + | 0.418797i | \(0.862452\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −934426. | + | 1.70959e6i | −0.807193 | + | 1.47680i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.02000e6 | 1.64892 | 0.824462 | − | 0.565917i | \(-0.191478\pi\) | ||||
0.824462 | + | 0.565917i | \(0.191478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −72909.5 | −0.0562995 | −0.0281497 | − | 0.999604i | \(-0.508962\pi\) | ||||
−0.0281497 | + | 0.999604i | \(0.508962\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 370272. | − | 798806.i | 0.270740 | − | 0.584080i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −895459. | −0.620598 | −0.310299 | − | 0.950639i | \(-0.600429\pi\) | ||||
−0.310299 | + | 0.950639i | \(0.600429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −422036. | − | 27964.5i | −0.277496 | − | 0.0183871i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.16339e6 | − | 985284.i | 0.726386 | − | 0.615182i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 665638.i | 0.395000i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.08685e6 | −1.17797 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 641719. | − | 1.38441e6i | 0.344849 | − | 0.743960i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.91478e6 | − | 385140.i | −0.980365 | − | 0.197192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.54012e6i | − | 1.24006i | −0.784578 | − | 0.620030i | \(-0.787121\pi\) | ||
0.784578 | − | 0.620030i | \(-0.212879\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.28681e6 | + | 2.77611e6i | −0.599442 | + | 1.29320i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.17618e6i | − | 0.523192i | −0.965178 | − | 0.261596i | \(-0.915751\pi\) | ||
0.965178 | − | 0.261596i | \(-0.0842488\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.24048e6i | 1.37738i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 494784. | + | 2.41011e6i | 0.201101 | + | 0.979571i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.00301e6 | 1.16787 | 0.583936 | − | 0.811800i | \(-0.301512\pi\) | ||||
0.583936 | + | 0.811800i | \(0.301512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.49837e6 | −1.30263 | −0.651316 | − | 0.758807i | \(-0.725783\pi\) | ||||
−0.651316 | + | 0.758807i | \(0.725783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.86488e6 | − | 1.79150e6i | −1.37873 | − | 0.639085i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.10789e6 | −1.40479 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 47314.9 | − | 714070.i | 0.0155201 | − | 0.234227i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.28123e6 | + | 2.44802e6i | 1.66258 | + | 0.770660i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.24451e6i | 0.980822i | 0.871491 | + | 0.490411i | \(0.163153\pi\) | ||||
−0.871491 | + | 0.490411i | \(0.836847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.67601e6 | 0.777243 | 0.388622 | − | 0.921397i | \(-0.372951\pi\) | ||||
0.388622 | + | 0.921397i | \(0.372951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 543256. | + | 641459.i | 0.151681 | + | 0.179099i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.60244e6 | − | 304961.i | −1.23593 | − | 0.0818935i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.18905e6i | − | 0.307255i | −0.988129 | − | 0.153628i | \(-0.950904\pi\) | ||
0.988129 | − | 0.153628i | \(-0.0490956\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.68478e6 | − | 1.24448e6i | −0.667909 | − | 0.309597i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.95331e6i | 0.468051i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.72124e6i | − | 0.397446i | −0.980056 | − | 0.198723i | \(-0.936321\pi\) | ||
0.980056 | − | 0.198723i | \(-0.0636794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.17958e6 | − | 5.81722e6i | 0.707812 | − | 1.29498i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.57401e6 | −0.767372 | −0.383686 | − | 0.923464i | \(-0.625345\pi\) | ||||
−0.383686 | + | 0.923464i | \(0.625345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 453305. | 0.0939141 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.64469e6 | + | 3.12277e6i | 0.528916 | + | 0.624527i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.35434e6 | −0.454706 | −0.227353 | − | 0.973812i | \(-0.573007\pi\) | ||||
−0.227353 | + | 0.973812i | \(0.573007\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.19010e6 | + | 8.94100e6i | −0.222060 | + | 1.66829i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.58569e6 | − | 5.57824e6i | 0.466291 | − | 1.00595i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 721898.i | 0.125868i | 0.998018 | + | 0.0629342i | \(0.0200458\pi\) | ||||
−0.998018 | + | 0.0629342i | \(0.979954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.41728e6 | 1.41950 | 0.709751 | − | 0.704452i | \(-0.248807\pi\) | ||||
0.709751 | + | 0.704452i | \(0.248807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.64283e6 | + | 3.07917e6i | 1.08393 | + | 0.502435i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 269499. | − | 4.06724e6i | 0.0425639 | − | 0.642369i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.26497e6i | − | 0.346368i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.09549e7 | − | 3.01589e6i | 1.62264 | − | 0.446714i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.76598e6i | − | 0.971025i | −0.874230 | − | 0.485513i | \(-0.838633\pi\) | ||
0.874230 | − | 0.485513i | \(-0.161367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.56942e6i | − | 1.33111i | −0.746349 | − | 0.665554i | \(-0.768195\pi\) | ||
0.746349 | − | 0.665554i | \(-0.231805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.38517e6 | − | 6.19335e6i | 0.456537 | − | 0.835260i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 155980. | 0.0204019 | 0.0102010 | − | 0.999948i | \(-0.496753\pi\) | ||||
0.0102010 | + | 0.999948i | \(0.496753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 29316.1 | 0.00372003 | 0.00186002 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00186002 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.49157e6 | + | 5.37519e6i | −0.306821 | + | 0.661920i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.30493e6 | −0.395070 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 467068. | − | 7.04893e6i | 0.0542149 | − | 0.818204i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.59418e6 | + | 1.88236e6i | 0.179733 | + | 0.212222i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.10264e7i | − | 1.20780i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.23485e6 | 0.344355 | 0.172178 | − | 0.985066i | \(-0.444920\pi\) | ||||
0.172178 | + | 0.985066i | \(0.444920\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.93175e6 | + | 1.27968e7i | −0.613824 | + | 1.32423i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −936594. | + | 1.41350e7i | −0.0942402 | + | 1.42226i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.13014e7i | 2.08463i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20313.2 | + | 43822.7i | −0.00193395 | + | 0.00417221i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.41142e6i | − | 0.223407i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 977603.i | 0.0881552i | 0.999028 | + | 0.0440776i | \(0.0140349\pi\) | ||||
−0.999028 | + | 0.0440776i | \(0.985965\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.15027e6 | + | 9.58752e6i | 0.539942 | + | 0.841702i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.17072e7 | −1.00086 | −0.500432 | − | 0.865776i | \(-0.666825\pi\) | ||||
−0.500432 | + | 0.865776i | \(0.666825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.33434e6 | 0.610738 | 0.305369 | − | 0.952234i | \(-0.401220\pi\) | ||||
0.305369 | + | 0.952234i | \(0.401220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.77769e7 | − | 1.28755e7i | −2.25345 | − | 1.04455i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.54612e6 | 0.754673 | 0.377337 | − | 0.926076i | \(-0.376840\pi\) | ||||
0.377337 | + | 0.926076i | \(0.376840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.96786e7 | − | 1.30392e6i | −1.51632 | − | 0.100473i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.94686e7 | − | 9.02434e6i | −1.46248 | − | 0.677907i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.01433e7i | 0.742996i | 0.928434 | + | 0.371498i | \(0.121156\pi\) | ||||
−0.928434 | + | 0.371498i | \(0.878844\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.83607e6 | −0.131171 | −0.0655855 | − | 0.997847i | \(-0.520892\pi\) | ||||
−0.0655855 | + | 0.997847i | \(0.520892\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.09554e6 | − | 1.18471e7i | 0.564192 | − | 0.825644i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.68902e7 | + | 1.78176e6i | 1.82850 | + | 0.121158i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.17393e7i | − | 0.779027i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.22325e6 | − | 2.42114e6i | −0.338332 | − | 0.156828i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.54625e7i | 1.61020i | 0.593138 | + | 0.805101i | \(0.297889\pi\) | ||||
−0.593138 | + | 0.805101i | \(0.702111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.64654e6i | − | 0.410425i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.41483e6 | + | 1.86648e6i | 0.205944 | + | 0.112565i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.15777e6 | −0.0682058 | −0.0341029 | − | 0.999418i | \(-0.510857\pi\) | ||||
−0.0341029 | + | 0.999418i | \(0.510857\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.88244e7 | −1.08348 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.18488e6 | + | 2.69730e6i | −0.179131 | + | 0.151707i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.06176e7 | 1.68308 | 0.841539 | − | 0.540197i | \(-0.181650\pi\) | ||||
0.841539 | + | 0.540197i | \(0.181650\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.36700e7 | − | 905783.i | −0.734564 | − | 0.0486728i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.41049e7 | + | 3.04292e7i | −0.741032 | + | 1.59866i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.65595e7i | − | 0.850726i | −0.905023 | − | 0.425363i | \(-0.860146\pi\) | ||
0.905023 | − | 0.425363i | \(-0.139854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.07489e7 | 0.540076 | 0.270038 | − | 0.962850i | \(-0.412964\pi\) | ||||
0.270038 | + | 0.962850i | \(0.412964\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.95730e7 | − | 1.37080e7i | −1.45347 | − | 0.673731i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.04957e6 | − | 3.04236e7i | 0.194720 | − | 1.46289i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.05269e6i | 0.378880i | 0.981892 | + | 0.189440i | \(0.0606672\pi\) | ||||
−0.981892 | + | 0.189440i | \(0.939333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.73850e7 | + | 2.05277e7i | 0.800503 | + | 0.945207i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.58716e6i | 0.387018i | 0.981099 | + | 0.193509i | \(0.0619868\pi\) | ||||
−0.981099 | + | 0.193509i | \(0.938013\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.02701e7i | 0.894326i | 0.894452 | + | 0.447163i | \(0.147566\pi\) | ||||
−0.894452 | + | 0.447163i | \(0.852434\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.66242e7 | + | 9.08645e6i | 0.718134 | + | 0.392518i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.26245e7 | −1.38006 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.28080e7 | −0.944916 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.59468e6 | + | 1.20697e7i | −0.227037 | + | 0.489798i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.15378e7 | 0.458691 | 0.229345 | − | 0.973345i | \(-0.426341\pi\) | ||||
0.229345 | + | 0.973345i | \(0.426341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.88197e6 | − | 2.84024e7i | 0.0733071 | − | 1.10634i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.72762e7 | + | 1.02622e7i | −1.42286 | + | 0.391715i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 7.07630e6i | − | 0.264723i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.54208e7 | 2.39892 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.55662e7 | − | 3.35816e7i | 0.559569 | − | 1.20718i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.38230e7 | + | 2.24114e6i | 1.19210 | + | 0.0789895i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.88025e7i | 0.649831i | 0.945743 | + | 0.324915i | \(0.105336\pi\) | ||||
−0.945743 | + | 0.324915i | \(0.894664\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.03926e7 | − | 2.24205e7i | 0.352249 | − | 0.759924i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.99873e7i | − | 1.32935i | −0.747131 | − | 0.664677i | \(-0.768569\pi\) | ||
0.747131 | − | 0.664677i | \(-0.231431\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.56862e7i | 1.16377i | 0.813271 | + | 0.581885i | \(0.197685\pi\) | ||||
−0.813271 | + | 0.581885i | \(0.802315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.23020e7 | − | 3.12683e7i | 1.35341 | − | 1.00040i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.27131e7 | 1.02694 | 0.513469 | − | 0.858108i | \(-0.328360\pi\) | ||||
0.513469 | + | 0.858108i | \(0.328360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.12457e7 | 0.346429 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.94826e7 | − | 2.29368e7i | −1.49602 | − | 0.693453i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.47272e6 | 0.192079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.31141e6 | − | 3.23908e7i | 0.125594 | − | 0.943563i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.78601e6 | + | 827874.i | 0.0510788 | + | 0.0236767i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.10784e7i | 2.55757i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.47453e7 | 1.50960 | 0.754802 | − | 0.655953i | \(-0.227733\pi\) | ||||
0.754802 | + | 0.655953i | \(0.227733\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.81406e7 | + | 1.53634e7i | −0.491268 | + | 0.416059i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.81346e6 | + | 2.73686e7i | −0.0482364 | + | 0.727977i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.88792e7i | − | 1.27713i | −0.769568 | − | 0.638564i | \(-0.779529\pi\) | ||
0.769568 | − | 0.638564i | \(-0.220471\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.19354e7 | + | 1.01678e7i | 0.563050 | + | 0.260992i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.24825e7i | − | 1.82797i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 5.65402e7i | − | 1.40112i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00208e7 | + | 5.47717e6i | 0.244031 | + | 0.133383i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.06967e7 | −1.69204 | −0.846020 | − | 0.533150i | \(-0.821008\pi\) | ||||
−0.846020 | + | 0.533150i | \(0.821008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.99983e7 | −0.470454 | −0.235227 | − | 0.971940i | \(-0.575583\pi\) | ||||
−0.235227 | + | 0.971940i | \(0.575583\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.96864e7 | + | 1.09257e7i | −0.917742 | + | 0.252655i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 772050. | 0.0175518 | 0.00877590 | − | 0.999961i | \(-0.497207\pi\) | ||||
0.00877590 | + | 0.999961i | \(0.497207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.31736e6 | + | 6.51570e7i | −0.0965013 | + | 1.45638i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.55820e6 | − | 1.63057e7i | 0.166117 | − | 0.358372i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.53083e7i | − | 1.41151i | −0.708455 | − | 0.705756i | \(-0.750607\pi\) | ||
0.708455 | − | 0.705756i | \(-0.249393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.55352e7 | −0.330214 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.11201e7 | + | 2.36958e7i | 1.06874 | + | 0.495395i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14784.8 | + | 223130.i | −0.000304043 | + | 0.00458858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.64905e7i | 1.54742i | 0.633538 | + | 0.773712i | \(0.281602\pi\) | ||||
−0.633538 | + | 0.773712i | \(0.718398\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.14395e7 | + | 2.66263e7i | −0.625743 | + | 0.529946i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.32686e7i | 1.23899i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.27687e6i | 0.0631441i | 0.999501 | + | 0.0315721i | \(0.0100514\pi\) | ||||
−0.999501 | + | 0.0315721i | \(0.989949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.25317e7 | + | 3.11764e7i | 0.806527 | + | 0.591197i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.19728e7 | 0.223446 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.34796e7 | −0.431293 | −0.215647 | − | 0.976471i | \(-0.569186\pi\) | ||||
−0.215647 | + | 0.976471i | \(0.569186\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.88426e7 | + | 6.22234e7i | −0.521506 | + | 1.12507i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.17247e7 | −0.742672 | −0.371336 | − | 0.928499i | \(-0.621100\pi\) | ||||
−0.371336 | + | 0.928499i | \(0.621100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.41430e8 | − | 9.37130e6i | −2.47834 | − | 0.164217i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.30444e7 | − | 5.33928e7i | 1.08771 | − | 0.921190i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1.14875e7i | − | 0.195154i | −0.995228 | − | 0.0975772i | \(-0.968891\pi\) | ||
0.995228 | − | 0.0975772i | \(-0.0311093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.90166e6 | 0.0652708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.33553e7 | + | 2.88121e7i | −0.220028 | + | 0.474676i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.91274e7 | − | 6.56827e6i | −1.60843 | − | 0.106576i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.37851e7i | 0.699768i | 0.936793 | + | 0.349884i | \(0.113779\pi\) | ||||
−0.936793 | + | 0.349884i | \(0.886221\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.67950e7 | − | 7.93796e7i | 0.579256 | − | 1.24966i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.48066e7i | 1.47030i | 0.677905 | + | 0.735149i | \(0.262888\pi\) | ||||
−0.677905 | + | 0.735149i | \(0.737112\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.71692e7i | − | 1.17904i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.52460e7 | − | 6.46569e7i | 0.229504 | − | 0.973308i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.40539e7 | 0.950084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.61855e7 | −1.11353 | −0.556766 | − | 0.830669i | \(-0.687958\pi\) | ||||
−0.556766 | + | 0.830669i | \(0.687958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.35626e7 | − | 3.40986e7i | −1.05957 | − | 0.491147i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.31455e8 | −1.86606 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.65950e7 | − | 1.76220e6i | −0.372096 | − | 0.0246554i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.56971e7 | + | 3.97234e7i | 1.18184 | + | 0.547820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.04931e7i | − | 0.278590i | −0.990251 | − | 0.139295i | \(-0.955516\pi\) | ||
0.990251 | − | 0.139295i | \(-0.0444837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.38839e7 | 1.12417 | 0.562086 | − | 0.827079i | \(-0.309999\pi\) | ||||
0.562086 | + | 0.827079i | \(0.309999\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.43331e7 | + | 8.77700e7i | 0.982112 | + | 1.15964i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.78593e7 | + | 2.37718e6i | 0.232647 | + | 0.0309668i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.56543e8i | − | 2.01071i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00628e8 | + | 4.66444e7i | 1.27452 | + | 0.590782i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.73808e7i | 1.09140i | 0.837980 | + | 0.545700i | \(0.183736\pi\) | ||||
−0.837980 | + | 0.545700i | \(0.816264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.07750e7i | 0.748619i | 0.927304 | + | 0.374310i | \(0.122120\pi\) | ||||
−0.927304 | + | 0.374310i | \(0.877880\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.26717e6 | + | 1.69548e7i | −0.112585 | + | 0.205980i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.89942e7 | 0.227602 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.05339e7 | 0.833690 | 0.416845 | − | 0.908978i | \(-0.363136\pi\) | ||||
0.416845 | + | 0.908978i | \(0.363136\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.01574e8 | − | 1.19935e8i | −1.18431 | − | 1.39839i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.46818e7 | 1.08907 | 0.544534 | − | 0.838739i | \(-0.316706\pi\) | ||||
0.544534 | + | 0.838739i | \(0.316706\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.02661e7 | + | 1.54935e8i | −0.116500 | + | 1.75820i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.68408e7 | − | 7.94784e7i | 0.412484 | − | 0.889870i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.22686e7i | − | 0.687907i | −0.938987 | − | 0.343954i | \(-0.888234\pi\) | ||
0.938987 | − | 0.343954i | \(-0.111766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.11012e8 | 1.21015 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.55523e7 | − | 3.03856e7i | −0.705169 | − | 0.326869i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.50575e8 | − | 9.97724e6i | −1.59852 | − | 0.105920i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.06549e8i | − | 1.11635i | −0.829724 | − | 0.558174i | \(-0.811502\pi\) | ||
0.829724 | − | 0.558174i | \(-0.188498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.02411e6 | − | 2.18819e7i | −0.0622953 | − | 0.226281i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.54272e8i | − | 1.57465i | −0.616538 | − | 0.787325i | \(-0.711465\pi\) | ||
0.616538 | − | 0.787325i | \(-0.288535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.79213e7i | 0.281315i | 0.990058 | + | 0.140658i | \(0.0449217\pi\) | ||||
−0.990058 | + | 0.140658i | \(0.955078\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.09280e8 | + | 5.97302e7i | 1.08688 | + | 0.594067i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.44176e6 | −0.0337933 | −0.0168966 | − | 0.999857i | \(-0.505379\pi\) | ||||
−0.0168966 | + | 0.999857i | \(0.505379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.26670e8 | 1.22788 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.35014e7 | + | 2.91272e7i | −0.129216 | + | 0.278764i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.22608e8 | −2.10357 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.69431e7 | + | 1.15727e7i | 0.811250 | + | 0.107982i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.16363e7 | + | 6.09704e7i | 0.475773 | + | 0.561777i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.09773e7i | 0.463843i | 0.972735 | + | 0.231921i | \(0.0745012\pi\) | ||||
−0.972735 | + | 0.231921i | \(0.925499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.81955e7 | 0.612803 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.21795e7 | − | 4.78488e7i | 0.196838 | − | 0.424649i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.07203e6 | + | 6.14546e7i | −0.0356932 | + | 0.538678i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.88123e8i | 1.62875i | 0.580339 | + | 0.814375i | \(0.302920\pi\) | ||||
−0.580339 | + | 0.814375i | \(0.697080\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.95443e7 | + | 4.21639e7i | −0.167145 | + | 0.360591i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.88211e8i | − | 1.59001i | −0.606601 | − | 0.795006i | \(-0.707468\pi\) | ||
0.606601 | − | 0.795006i | \(-0.292532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.60146e6i | 0.0550934i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.43941e8 | + | 1.06397e8i | −1.18678 | + | 0.877228i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.01566e8 | 2.45648 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.48935e8 | −1.19866 | −0.599329 | − | 0.800503i | \(-0.704566\pi\) | ||||
−0.599329 | + | 0.800503i | \(0.704566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.75499e7 | + | 4.05822e7i | 0.696214 | + | 0.322717i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.03064e8 | 0.809848 | 0.404924 | − | 0.914350i | \(-0.367298\pi\) | ||||
0.404924 | + | 0.914350i | \(0.367298\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.13297e7 | − | 1.70986e8i | 0.0879717 | − | 1.32766i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.11043e7 | − | 5.14720e6i | −0.0852054 | − | 0.0394955i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.52846e7i | − | 0.267566i | −0.991011 | − | 0.133783i | \(-0.957287\pi\) | ||
0.991011 | − | 0.133783i | \(-0.0427126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.03271e6 | 0.00773955 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.93267e7 | − | 1.06526e8i | −0.217226 | − | 0.789049i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.56417e6 | − | 1.14157e8i | 0.0553783 | − | 0.835762i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.09913e8i | − | 2.24269i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.76726e7 | + | 2.67331e7i | 0.412541 | + | 0.191226i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.46705e8i | 1.03736i | 0.854968 | + | 0.518681i | \(0.173577\pi\) | ||||
−0.854968 | + | 0.518681i | \(0.826423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.08549e6i | 0.0145782i | 0.999973 | + | 0.00728910i | \(0.00232021\pi\) | ||||
−0.999973 | + | 0.00728910i | \(0.997680\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.30677e8 | − | 2.05508e8i | 0.903067 | − | 1.42020i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.25488e7 | 0.290707 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.36586e8 | −0.922658 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.26680e8 | + | 1.07286e8i | −0.846104 | + | 0.716572i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.18190e8 | 0.780544 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.51948e8 | − | 1.66943e7i | −1.64532 | − | 0.109020i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.19702e6 | − | 1.76838e7i | 0.0529338 | − | 0.114197i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.23486e8i | 2.70441i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.27649e7 | 0.396392 | 0.198196 | − | 0.980162i | \(-0.436492\pi\) | ||||
0.198196 | + | 0.980162i | \(0.436492\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.06192e8 | − | 9.55767e7i | −1.28787 | − | 0.596970i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.09374e6 | + | 602559.i | 0.0561763 | + | 0.00372229i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.73173e8i | 1.05808i | 0.848598 | + | 0.529039i | \(0.177447\pi\) | ||||
−0.848598 | + | 0.529039i | \(0.822553\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.27761e8 | − | 1.50856e8i | −0.772116 | − | 0.911689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.21374e7i | 0.192113i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.58791e8i | 2.71294i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.27845e7 | + | 9.65722e7i | −0.308765 | + | 0.564902i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.17506e7 | −0.299468 | −0.149734 | − | 0.988726i | \(-0.547842\pi\) | ||||
−0.149734 | + | 0.988726i | \(0.547842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.37001e8 | −1.35680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.57183e7 | + | 5.54834e7i | −0.145665 | + | 0.314249i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.07620e7 | 0.508603 | 0.254301 | − | 0.967125i | \(-0.418154\pi\) | ||||
0.254301 | + | 0.967125i | \(0.418154\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.11687e8 | + | 7.40051e6i | 0.619240 | + | 0.0410314i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.02598e8 | − | 5.05126e7i | −1.66004 | − | 0.277109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.75126e8i | − | 0.950633i | −0.879815 | − | 0.475317i | \(-0.842333\pi\) | ||
0.879815 | − | 0.475317i | \(-0.157667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.10251e8 | −0.592209 | −0.296104 | − | 0.955156i | \(-0.595688\pi\) | ||||
−0.296104 | + | 0.955156i | \(0.595688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.68265e7 | + | 1.65741e8i | −0.408364 | + | 0.880982i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.24080e7 | + | 6.97583e6i | 0.275673 | + | 0.0366937i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.96873e6i | 0.0518934i | 0.999663 | + | 0.0259467i | \(0.00826003\pi\) | ||||
−0.999663 | + | 0.0259467i | \(0.991740\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.08659e8 | + | 2.34415e8i | −0.559796 | + | 1.20767i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.23089e8i | 0.627613i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.15285e8i | − | 1.08644i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.53248e8 | + | 1.13276e8i | −0.765470 | + | 0.565810i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.37250e8 | 1.17298 | 0.586492 | − | 0.809955i | \(-0.300509\pi\) | ||||
0.586492 | + | 0.809955i | \(0.300509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.07137e8 | 1.01371 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.82094e6 | − | 1.77113e6i | −0.0185101 | − | 0.00858001i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.60386e8 | −0.769135 | −0.384567 | − | 0.923097i | \(-0.625649\pi\) | ||||
−0.384567 | + | 0.923097i | \(0.625649\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.50115e6 | − | 8.30227e7i | 0.0261158 | − | 0.394136i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −718135. | − | 332879.i | −0.00337507 | − | 0.00156445i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.76259e8i | − | 1.28539i | −0.766121 | − | 0.642697i | \(-0.777815\pi\) | ||
0.766121 | − | 0.642697i | \(-0.222185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.13920e8 | −0.524777 | −0.262389 | − | 0.964962i | \(-0.584510\pi\) | ||||
−0.262389 | + | 0.964962i | \(0.584510\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.22069e8 | − | 1.03381e8i | 0.556739 | − | 0.471507i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.60286e8 | + | 1.72467e7i | 1.17540 | + | 0.0778827i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.44632e8i | − | 0.646691i | −0.946281 | − | 0.323346i | \(-0.895192\pi\) | ||
0.946281 | − | 0.323346i | \(-0.104808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.09584e7 | + | 3.75268e7i | 0.358435 | + | 0.166146i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.29952e8i | − | 1.44653i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 3.45683e8i | − | 1.50071i | −0.661035 | − | 0.750355i | \(-0.729882\pi\) | ||
0.661035 | − | 0.750355i | \(-0.270118\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.14808e7 | + | 1.67369e8i | −0.393282 | + | 0.719532i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.46558e8 | −1.47544 | −0.737718 | − | 0.675109i | \(-0.764096\pi\) | ||||
−0.737718 | + | 0.675109i | \(0.764096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.62514e7 | 0.279333 | 0.139667 | − | 0.990199i | \(-0.455397\pi\) | ||||
0.139667 | + | 0.990199i | \(0.455397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.76777e7 | − | 6.42124e7i | −0.0738162 | − | 0.268129i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.17085e8 | 2.96556 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.35640e8 | + | 6.38618e7i | 0.965182 | + | 0.261578i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.25203e8 | + | 2.70105e8i | −0.507938 | + | 1.09580i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.76010e7i | 0.151094i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.64322e7 | 0.184812 | 0.0924062 | − | 0.995721i | \(-0.470544\pi\) | ||||
0.0924062 | + | 0.995721i | \(0.470544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.92418e7 | − | 3.67311e7i | −0.312423 | − | 0.144818i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.09928e7 | + | 3.16820e8i | −0.0819876 | + | 1.23735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.50868e8i | 1.74434i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.90612e8 | − | 2.46121e8i | 1.11381 | − | 0.943293i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.05739e7i | 0.116085i | 0.998314 | + | 0.0580427i | \(0.0184859\pi\) | ||||
−0.998314 | + | 0.0580427i | \(0.981514\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.79228e7i | − | 0.0674176i | −0.999432 | − | 0.0337088i | \(-0.989268\pi\) | ||
0.999432 | − | 0.0337088i | \(-0.0107319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.83443e8 | − | 3.35619e8i | 0.683631 | − | 1.25074i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.35543e8 | −0.869674 | −0.434837 | − | 0.900509i | \(-0.643194\pi\) | ||||
−0.434837 | + | 0.900509i | \(0.643194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.47302e8 | 1.63631 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.41874e8 | − | 5.21806e8i | 0.876690 | − | 1.89133i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.09475e8 | −1.47058 | −0.735289 | − | 0.677754i | \(-0.762954\pi\) | ||||
−0.735289 | + | 0.677754i | \(0.762954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.72054e6 | + | 1.46701e8i | −0.0345913 | + | 0.522047i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 995197. | − | 842840.i | 0.00350924 | − | 0.00297200i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 4.99908e7i | − | 0.174676i | −0.996179 | − | 0.0873381i | \(-0.972164\pi\) | ||
0.996179 | − | 0.0873381i | \(-0.0278361\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.04661e8 | −0.708647 | −0.354323 | − | 0.935123i | \(-0.615289\pi\) | ||||
−0.354323 | + | 0.935123i | \(0.615289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.73812e7 | + | 5.90708e7i | −0.0939534 | + | 0.202690i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.67808e7 | − | 4.04173e8i | 0.0910667 | − | 1.37437i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.93719e7i | 0.0652823i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.11005e7 | − | 2.39476e7i | 0.0370736 | − | 0.0799806i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.32669e8i | 1.76315i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.22290e8i | − | 0.729246i | −0.931155 | − | 0.364623i | \(-0.881198\pi\) | ||
0.931155 | − | 0.364623i | \(-0.118802\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.17944e7 | − | 3.04694e8i | −0.135896 | − | 0.990723i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.74942e8 | −0.563805 | −0.281902 | − | 0.959443i | \(-0.590965\pi\) | ||||
−0.281902 | + | 0.959443i | \(0.590965\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.84430e8 | 0.908586 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.86782e8 | + | 1.32933e8i | 0.908053 | + | 0.420912i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.36393e8 | −0.428084 | −0.214042 | − | 0.976825i | \(-0.568663\pi\) | ||||
−0.214042 | + | 0.976825i | \(0.568663\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.74555e8 | − | 2.48183e7i | −1.16532 | − | 0.0772148i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.79664e8 | − | 8.32801e7i | −0.554104 | − | 0.256845i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.29205e8i | − | 0.700754i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.64003e8 | 0.497069 | 0.248535 | − | 0.968623i | \(-0.420051\pi\) | ||||
0.248535 | + | 0.968623i | \(0.420051\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.34233e8 | + | 6.30804e8i | 1.60521 | + | 1.89537i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.36340e8 | + | 2.89122e7i | 1.29978 | + | 0.0861246i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.51662e7i | 0.192453i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.33844e8 | − | 1.08394e8i | −0.684692 | − | 0.317377i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.66072e6i | 0.00772406i | 0.999993 | + | 0.00386203i | \(0.00122933\pi\) | ||||
−0.999993 | + | 0.00386203i | \(0.998771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.83050e8i | 0.526871i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.67247e8 | + | 2.55388e8i | 1.33346 | + | 0.728842i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.91373e8 | −2.23935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.59069e8 | −0.446322 | −0.223161 | − | 0.974782i | \(-0.571638\pi\) | ||||
−0.223161 | + | 0.974782i | \(0.571638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.74440e8 | + | 4.42126e8i | 1.04177 | + | 1.23009i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.24859e8 | 0.344470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.12363e8 | + | 3.39496e7i | 1.40171 | + | 0.0928788i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.15176e8 | − | 2.48474e8i | 0.312466 | − | 0.674098i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.30930e8i | − | 1.42840i | −0.699940 | − | 0.714201i | \(-0.746790\pi\) | ||
0.699940 | − | 0.714201i | \(-0.253210\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.28354e8 | −1.40968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.49769e7 | + | 2.08482e7i | 0.119008 | + | 0.0551638i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.18028e7 | + | 8.86724e7i | −0.0309722 | + | 0.232688i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.05344e8i | − | 0.274162i | −0.990560 | − | 0.137081i | \(-0.956228\pi\) | ||
0.990560 | − | 0.137081i | \(-0.0437720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.32832e8 | + | 1.98286e8i | −0.859098 | + | 0.511811i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.30675e8i | − | 0.334535i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.05103e8i | − | 1.28253i | −0.767319 | − | 0.641266i | \(-0.778410\pi\) | ||
0.767319 | − | 0.641266i | \(-0.221590\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.38477e8 | − | 3.48979e8i | −1.60799 | − | 0.878897i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.31020e8 | −1.07670 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.95184e8 | −0.979189 | −0.489594 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489594 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.33298e8 | + | 2.87570e8i | −0.327619 | + | 0.706788i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.65070e7 | −0.0890041 | −0.0445020 | − | 0.999009i | \(-0.514170\pi\) | ||||
−0.0445020 | + | 0.999009i | \(0.514170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.68142e7 | − | 4.04676e8i | 0.0648479 | − | 0.978676i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.00459e8 | + | 1.18618e8i | 0.241005 | + | 0.284570i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.16609e9i | 2.77515i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.56142e7 | −0.0840821 | −0.0420411 | − | 0.999116i | \(-0.513386\pi\) | ||||
−0.0420411 | + | 0.999116i | \(0.513386\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.89122e8 | − | 6.23738e8i | 0.677169 | − | 1.46089i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.33769e8 | − | 2.21158e7i | −0.775543 | − | 0.0513881i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.62243e8i | 1.52661i | 0.646035 | + | 0.763307i | \(0.276426\pi\) | ||||
−0.646035 | + | 0.763307i | \(0.723574\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.54702e7 | + | 1.62816e8i | −0.172604 | + | 0.372366i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.67728e8i | − | 0.607491i | −0.952753 | − | 0.303746i | \(-0.901763\pi\) | ||
0.952753 | − | 0.303746i | \(-0.0982373\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.20885e7i | − | 0.0947524i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.24571e7 | − | 8.44966e7i | −0.139508 | − | 0.188736i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.76224e8 | 1.05542 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.59472e8 | −0.350675 | −0.175337 | − | 0.984508i | \(-0.556102\pi\) | ||||
−0.175337 | + | 0.984508i | \(0.556102\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.83609e7 | + | 1.31462e7i | 0.0618810 | + | 0.0286839i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.52540e8 | −0.546754 | −0.273377 | − | 0.961907i | \(-0.588141\pi\) | ||||
−0.273377 | + | 0.961907i | \(0.588141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.71525e8 | + | 7.60735e7i | 1.22781 | + | 0.163429i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.61128e8 | + | 2.13748e8i | 0.983011 | + | 0.455657i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.17244e8i | 0.671090i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.02614e9 | −2.15404 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.08645e8 | − | 2.99100e7i | 0.226321 | − | 0.0623063i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.82684e6 | + | 1.48305e8i | −0.0203145 | + | 0.306583i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.29615e8i | 0.676212i | 0.941108 | + | 0.338106i | \(0.109786\pi\) | ||||
−0.941108 | + | 0.338106i | \(0.890214\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.50018e8 | − | 3.47657e8i | −1.52701 | − | 0.707816i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.16923e8i | − | 1.04447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.67111e8i | 1.13723i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.24578e8 | + | 1.77408e8i | 0.645978 | + | 0.353079i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.26420e8 | −1.23734 | −0.618672 | − | 0.785649i | \(-0.712329\pi\) | ||||
−0.618672 | + | 0.785649i | \(0.712329\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.81926e8 | 0.356659 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.91037e8 | − | 5.85244e8i | 1.34463 | − | 1.13878i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.51401e6 | −0.00678666 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.61431e7 | − | 2.43629e8i | 0.0309456 | − | 0.467027i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.88030e8 | + | 4.05646e8i | −0.357772 | + | 0.771838i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.89370e8i | 1.49085i | 0.666588 | + | 0.745427i | \(0.267754\pi\) | ||||
−0.666588 | + | 0.745427i | \(0.732246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.61805e8 | −0.678284 | −0.339142 | − | 0.940735i | \(-0.610137\pi\) | ||||
−0.339142 | + | 0.940735i | \(0.610137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.63307e8 | − | 1.22051e8i | −0.489995 | − | 0.227128i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.42251e7 | + | 2.14684e8i | −0.0262775 | + | 0.396576i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.36158e8i | − | 1.16654i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.68776e8 | + | 6.71591e8i | 1.03536 | + | 1.22251i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.19435e7i | − | 0.0938647i | −0.998898 | − | 0.0469323i | \(-0.985055\pi\) | ||
0.998898 | − | 0.0469323i | \(-0.0149445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.92402e7i | 0.0345153i | 0.999851 | + | 0.0172576i | \(0.00549355\pi\) | ||||
−0.999851 | + | 0.0172576i | \(0.994506\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.44654e8 | + | 6.99283e8i | −0.791882 | + | 1.24535i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.80571e7 | −0.138005 | −0.0690027 | − | 0.997616i | \(-0.521982\pi\) | ||||
−0.0690027 | + | 0.997616i | \(0.521982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.14440e8 | −0.376394 | −0.188197 | − | 0.982131i | \(-0.560264\pi\) | ||||
−0.188197 | + | 0.982131i | \(0.560264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.14368e7 | − | 1.97261e8i | 0.159337 | − | 0.343746i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.48595e8 | −0.430088 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.45773e8 | + | 2.95373e7i | 0.765693 | + | 0.0507355i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.92781e8 | − | 7.00255e8i | −0.328767 | − | 1.19421i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.80826e8i | − | 0.983468i | −0.870746 | − | 0.491734i | \(-0.836363\pi\) | ||
0.870746 | − | 0.491734i | \(-0.163637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.62047e8 | 0.944897 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.75057e7 | − | 2.10354e8i | 0.162760 | − | 0.351129i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.65392e7 | − | 3.74633e6i | −0.0937086 | − | 0.00620921i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.20468e9i | − | 1.98254i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.30163e8 | − | 4.96542e8i | 0.376108 | − | 0.811395i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.10340e8i | 0.179037i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.11351e9i | 1.79411i | 0.441921 | + | 0.897054i | \(0.354297\pi\) | ||||
−0.441921 | + | 0.897054i | \(0.645703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.04055e8 | − | 4.11349e8i | −0.486468 | − | 0.658130i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.01919e9 | 1.61925 | 0.809624 | − | 0.586949i | \(-0.199671\pi\) | ||||
0.809624 | + | 0.586949i | \(0.199671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.16974e8 | 0.342316 | 0.171158 | − | 0.985244i | \(-0.445249\pi\) | ||||
0.171158 | + | 0.985244i | \(0.445249\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.99180e8 | + | 3.70446e8i | 1.25209 | + | 0.580384i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.60488e7 | −0.102762 | −0.0513810 | − | 0.998679i | \(-0.516362\pi\) | ||||
−0.0513810 | + | 0.998679i | \(0.516362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.93649e8 | + | 1.94574e7i | 0.453711 | + | 0.0300633i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.58711e8 | + | 2.58980e8i | 0.857294 | + | 0.397383i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.56113e9i | − | 2.37892i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.58890e8 | −0.694470 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.74098e8 | − | 2.32136e8i | 0.411968 | − | 0.348899i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.22330e8 | − | 1.10534e9i | 0.331875 | − | 1.64996i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.63996e7i | 0.142915i | 0.997444 | + | 0.0714573i | \(0.0227650\pi\) | ||||
−0.997444 | + | 0.0714573i | \(0.977235\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.82633e8 | − | 1.31010e8i | −0.416156 | − | 0.192902i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.50201e8i | 0.804626i | 0.915502 | + | 0.402313i | \(0.131794\pi\) | ||||
−0.915502 | + | 0.402313i | \(0.868206\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.98530e8i | 0.288366i | 0.989551 | + | 0.144183i | \(0.0460553\pi\) | ||||
−0.989551 | + | 0.144183i | \(0.953945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.68606e8 | + | 6.74385e8i | −0.531780 | + | 0.972921i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.16431e9 | 1.66839 | 0.834197 | − | 0.551467i | \(-0.185932\pi\) | ||||
0.834197 | + | 0.551467i | \(0.185932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.46634e9 | 2.08703 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.02965e9 | + | 1.71879e8i | 1.45565 | + | 0.242991i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.85655e8 | 1.24368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.96611e6 | − | 9.00398e7i | 0.00832189 | − | 0.125593i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.03501e7 | + | 1.73343e8i | −0.111329 | + | 0.240176i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.11257e8i | 0.290758i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26377e8 | 0.172780 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.60257e9 | − | 7.42841e8i | −2.17647 | − | 1.00886i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.04986e9 | − | 6.95645e7i | −1.41640 | − | 0.0938516i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 3.90178e8i | − | 0.522927i | −0.965213 | − | 0.261464i | \(-0.915795\pi\) | ||
0.965213 | − | 0.261464i | \(-0.0842052\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.62626e8 | + | 6.45874e8i | −1.01536 | + | 0.859916i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.26135e8i | 1.09269i | 0.837561 | + | 0.546343i | \(0.183981\pi\) | ||||
−0.837561 | + | 0.546343i | \(0.816019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 4.18837e8i | − | 0.550342i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.03090e8 | − | 4.38953e8i | −1.04834 | − | 0.573001i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.78976e8 | 0.880535 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.12183e9 | 1.44538 | 0.722689 | − | 0.691173i | \(-0.242906\pi\) | ||||
0.722689 | + | 0.691173i | \(0.242906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.13499e8 | − | 4.60591e8i | 0.273286 | − | 0.589572i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.09249e9 | −1.38935 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.72273e7 | + | 5.05065e8i | −0.0849416 | + | 0.638149i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.09162e8 | + | 4.31213e8i | −0.639171 | + | 0.541318i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.13531e9i | − | 1.41601i | −0.706205 | − | 0.708007i | \(-0.749594\pi\) | ||
0.706205 | − | 0.708007i | \(-0.250406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.21022e9 | −1.49973 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.54048e8 | + | 9.79540e8i | −0.559058 | + | 1.20608i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.87188e7 | + | 2.82502e8i | −0.0229004 | + | 0.345610i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.58349e8i | − | 0.314042i | −0.987595 | − | 0.157021i | \(-0.949811\pi\) | ||
0.987595 | − | 0.157021i | \(-0.0501890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.05210e8 | − | 8.74180e8i | 0.489422 | − | 1.05585i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.16085e7i | − | 0.0499359i | −0.999688 | − | 0.0249679i | \(-0.992052\pi\) | ||
0.999688 | − | 0.0249679i | \(-0.00794837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.91230e8i | 0.228045i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.39129e9 | + | 2.85625e8i | −1.64862 | + | 0.338454i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.06748e8 | 0.949922 | 0.474961 | − | 0.880007i | \(-0.342462\pi\) | ||||
0.474961 | + | 0.880007i | \(0.342462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.74122e6 | −0.00437738 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.01350e8 | − | 3.71452e8i | −0.931710 | − | 0.431878i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.21593e8 | 0.718170 | 0.359085 | − | 0.933305i | \(-0.383089\pi\) | ||||
0.359085 | + | 0.933305i | \(0.383089\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.59173e7 | + | 8.43897e8i | −0.0642002 | + | 0.968901i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.75478e8 | − | 1.27693e8i | −0.314305 | − | 0.145690i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.73355e9i | 1.96554i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.74123e8 | 0.534221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.51697e8 | + | 1.12373e9i | 1.06566 | + | 1.25830i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.90863e7 | + | 1.19356e9i | −0.0880074 | + | 1.32820i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.47002e9i | 1.62571i | 0.582465 | + | 0.812856i | \(0.302088\pi\) | ||||
−0.582465 | + | 0.812856i | \(0.697912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.58558e8 | − | 7.34966e7i | −0.174267 | − | 0.0807785i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.08128e9i | 1.18108i | 0.807008 | + | 0.590541i | \(0.201085\pi\) | ||||
−0.807008 | + | 0.590541i | \(0.798915\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.01951e9i | − | 2.19234i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.73405e8 | + | 7.44498e8i | −0.510762 | + | 0.803248i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.28592e9 | 1.37889 | 0.689447 | − | 0.724336i | \(-0.257853\pi\) | ||||
0.689447 | + | 0.724336i | \(0.257853\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.44003e9 | −2.60044 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.43503e7 | − | 4.05597e7i | −0.0363851 | − | 0.0429623i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.47592e8 | 0.155383 | 0.0776915 | − | 0.996977i | \(-0.475245\pi\) | ||||
0.0776915 | + | 0.996977i | \(0.475245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.94549e7 | − | 1.28910e6i | −0.0203573 | − | 0.00134889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.03418e9 | − | 2.23108e9i | 1.07558 | − | 2.32041i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.83466e8i | − | 0.396404i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.60988e9 | −1.65414 | −0.827070 | − | 0.562099i | \(-0.809994\pi\) | ||||
−0.827070 | + | 0.562099i | \(0.809994\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.34106e9 | − | 6.21623e8i | −1.36962 | − | 0.634862i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.65649e6 | − | 242282.i | −0.00371189 | − | 0.000245953i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.54253e8i | − | 0.559271i | −0.960106 | − | 0.279635i | \(-0.909786\pi\) | ||
0.960106 | − | 0.279635i | \(-0.0902136\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.18826e8 | − | 1.70363e8i | 0.620686 | − | 0.170875i |
(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 | 60.7.b.a.29.1 | ✓ | 12 | |
3.2 | odd | 2 | inner | 60.7.b.a.29.11 | yes | 12 | |
4.3 | odd | 2 | 240.7.c.e.209.12 | 12 | |||
5.2 | odd | 4 | 300.7.g.i.101.6 | 12 | |||
5.3 | odd | 4 | 300.7.g.i.101.7 | 12 | |||
5.4 | even | 2 | inner | 60.7.b.a.29.12 | yes | 12 | |
12.11 | even | 2 | 240.7.c.e.209.2 | 12 | |||
15.2 | even | 4 | 300.7.g.i.101.5 | 12 | |||
15.8 | even | 4 | 300.7.g.i.101.8 | 12 | |||
15.14 | odd | 2 | inner | 60.7.b.a.29.2 | yes | 12 | |
20.19 | odd | 2 | 240.7.c.e.209.1 | 12 | |||
60.59 | even | 2 | 240.7.c.e.209.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.b.a.29.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
60.7.b.a.29.2 | yes | 12 | 15.14 | odd | 2 | inner | |
60.7.b.a.29.11 | yes | 12 | 3.2 | odd | 2 | inner | |
60.7.b.a.29.12 | yes | 12 | 5.4 | even | 2 | inner | |
240.7.c.e.209.1 | 12 | 20.19 | odd | 2 | |||
240.7.c.e.209.2 | 12 | 12.11 | even | 2 | |||
240.7.c.e.209.11 | 12 | 60.59 | even | 2 | |||
240.7.c.e.209.12 | 12 | 4.3 | odd | 2 | |||
300.7.g.i.101.5 | 12 | 15.2 | even | 4 | |||
300.7.g.i.101.6 | 12 | 5.2 | odd | 4 | |||
300.7.g.i.101.7 | 12 | 5.3 | odd | 4 | |||
300.7.g.i.101.8 | 12 | 15.8 | even | 4 |