Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
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: | \( x^{8} - 4x^{7} - 384x^{6} + 506x^{5} + 49869x^{4} + 29654x^{3} - 2235516x^{2} - 1528906x + 34180205 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.7 | ||
Root | \(-10.3099 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.b.161.2 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 21.6198i | 1.38691i | 0.720499 | + | 0.693456i | \(0.243913\pi\) | ||||
−0.720499 | + | 0.693456i | \(0.756087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 169.466 | 1.30718 | 0.653592 | − | 0.756847i | \(-0.273261\pi\) | ||||
0.653592 | + | 0.756847i | \(0.273261\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −224.417 | −0.923525 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 512.594i | − 1.27730i | −0.769498 | − | 0.638649i | \(-0.779494\pi\) | ||||
0.769498 | − | 0.638649i | \(-0.220506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 36.4873i | 0.0598802i | 0.999552 | + | 0.0299401i | \(0.00953166\pi\) | ||||
−0.999552 | + | 0.0299401i | \(0.990468\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −540.496 | −0.620246 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1260.81 | −1.05810 | −0.529052 | − | 0.848589i | \(-0.677452\pi\) | ||||
−0.529052 | + | 0.848589i | \(0.677452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 790.251i | 0.502205i | 0.967960 | + | 0.251103i | \(0.0807932\pi\) | ||||
−0.967960 | + | 0.251103i | \(0.919207\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3663.82i | 1.81295i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4995.19 | −1.96894 | −0.984470 | − | 0.175554i | \(-0.943828\pi\) | ||||
−0.984470 | + | 0.175554i | \(0.943828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 401.768i | 0.106064i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 934.435i | − 0.206326i | −0.994664 | − | 0.103163i | \(-0.967104\pi\) | ||||
0.994664 | − | 0.103163i | \(-0.0328963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6690.60 | −1.25043 | −0.625217 | − | 0.780451i | \(-0.714989\pi\) | ||||
−0.625217 | + | 0.780451i | \(0.714989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11082.2 | 1.77150 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4236.64i | 0.584590i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4305.71i | 0.517059i | 0.966003 | + | 0.258530i | \(0.0832379\pi\) | ||||
−0.966003 | + | 0.258530i | \(0.916762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −788.849 | −0.0830486 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10359.3 | −0.962430 | −0.481215 | − | 0.876603i | \(-0.659804\pi\) | ||||
−0.481215 | + | 0.876603i | \(0.659804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6371.59i | 0.525505i | 0.964863 | + | 0.262752i | \(0.0846303\pi\) | ||||
−0.964863 | + | 0.262752i | \(0.915370\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 5610.42i | − 0.413013i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22120.7 | −1.46068 | −0.730338 | − | 0.683085i | \(-0.760638\pi\) | ||||
−0.730338 | + | 0.683085i | \(0.760638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11911.6 | 0.708730 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 27258.6i | − 1.46750i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23246.6i | 1.13676i | 0.822766 | + | 0.568380i | \(0.192430\pi\) | ||||
−0.822766 | + | 0.568380i | \(0.807570\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12814.9 | 0.571225 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17085.1 | −0.696515 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 27758.9i | − 1.03818i | −0.854720 | − | 0.519089i | \(-0.826271\pi\) | ||||
0.854720 | − | 0.519089i | \(-0.173729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 39950.3i | − 1.37466i | −0.726345 | − | 0.687330i | \(-0.758783\pi\) | ||||
0.726345 | − | 0.687330i | \(-0.241217\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −38030.9 | −1.20722 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −912.183 | −0.0267793 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55415.0i | 1.50814i | 0.656797 | + | 0.754068i | \(0.271911\pi\) | ||||
−0.656797 | + | 0.754068i | \(0.728089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 107995.i | − 2.73075i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −39874.7 | −0.938752 | −0.469376 | − | 0.882998i | \(-0.655521\pi\) | ||||
−0.469376 | + | 0.882998i | \(0.655521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −435.947 | −0.00957473 | −0.00478736 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478736 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 13512.4i | − 0.277382i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 86867.1i | − 1.66966i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61654.1 | 1.11146 | 0.555730 | − | 0.831363i | \(-0.312439\pi\) | ||||
0.555730 | + | 0.831363i | \(0.312439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63219.4 | −1.07063 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2943.22i | 0.0468952i | 0.999725 | + | 0.0234476i | \(0.00746428\pi\) | ||||
−0.999725 | + | 0.0234476i | \(0.992536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 31520.3i | − 0.473199i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20202.3 | 0.286156 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 64783.7 | 0.866943 | 0.433472 | − | 0.901167i | \(-0.357288\pi\) | ||||
0.433472 | + | 0.901167i | \(0.357288\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6183.35i | 0.0782745i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 144650.i | − 1.73424i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19756.3 | −0.224593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 159041. | 1.71625 | 0.858123 | − | 0.513445i | \(-0.171631\pi\) | ||||
0.858123 | + | 0.513445i | \(0.171631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 115035.i | 1.17962i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66973.7i | 0.653282i | 0.945148 | + | 0.326641i | \(0.105917\pi\) | ||||
−0.945148 | + | 0.326641i | \(0.894083\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −145452. | −1.35091 | −0.675454 | − | 0.737402i | \(-0.736052\pi\) | ||||
−0.675454 | + | 0.737402i | \(0.736052\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −91595.5 | −0.810776 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 67124.0i | 0.566785i | 0.959004 | + | 0.283392i | \(0.0914599\pi\) | ||||
−0.959004 | + | 0.283392i | \(0.908540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 102861.i | − 0.829247i | −0.909993 | − | 0.414624i | \(-0.863913\pi\) | ||||
0.909993 | − | 0.414624i | \(-0.136087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −93088.6 | −0.717116 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −60698.8 | −0.447182 | −0.223591 | − | 0.974683i | \(-0.571778\pi\) | ||||
−0.223591 | + | 0.974683i | \(0.571778\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 124880.i | − 0.880537i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 8188.36i | − 0.0553009i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −213665. | −1.38314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −101702. | −0.631489 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 223965.i | − 1.33481i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 15625.0i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −318984. | −1.75493 | −0.877464 | − | 0.479642i | \(-0.840767\pi\) | ||||
−0.877464 | + | 0.479642i | \(0.840767\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −137753. | −0.728829 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 359449.i | − 1.83003i | −0.403417 | − | 0.915016i | \(-0.632178\pi\) | ||||
0.403417 | − | 0.915016i | \(-0.367822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 133920.i | 0.656475i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10044.2 | −0.0474331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 289504. | 1.31781 | 0.658906 | − | 0.752225i | \(-0.271019\pi\) | ||||
0.658906 | + | 0.752225i | \(0.271019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 318184.i | 1.39682i | 0.715696 | + | 0.698412i | \(0.246109\pi\) | ||||
−0.715696 | + | 0.698412i | \(0.753891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 478245.i | − 2.02583i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18703.2 | 0.0764849 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23360.9 | 0.0922718 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 257527.i | 0.982946i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 464507.i | 1.71406i | 0.515266 | + | 0.857030i | \(0.327693\pi\) | ||||
−0.515266 | + | 0.857030i | \(0.672307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13229.4 | −0.0472171 | −0.0236085 | − | 0.999721i | \(-0.507516\pi\) | ||||
−0.0236085 | + | 0.999721i | \(0.507516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 282948. | 0.977186 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 167265.i | − 0.559211i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 125487.i | 0.406303i | 0.979147 | + | 0.203152i | \(0.0651184\pi\) | ||||
−0.979147 | + | 0.203152i | \(0.934882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −502587. | −1.57659 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −846513. | −2.57377 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 449649.i | 1.32558i | 0.748807 | + | 0.662788i | \(0.230627\pi\) | ||||
−0.748807 | + | 0.662788i | \(0.769373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 277055.i | 0.792239i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 157771. | 0.437760 | 0.218880 | − | 0.975752i | \(-0.429760\pi\) | ||||
0.218880 | + | 0.975752i | \(0.429760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 369962. | 0.996414 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 177346.i | − 0.463799i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 253753.i | − 0.644608i | −0.946636 | − | 0.322304i | \(-0.895543\pi\) | ||||
0.946636 | − | 0.322304i | \(-0.104457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −105916. | −0.261437 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 600142. | 1.43986 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 166500.i | − 0.388403i | −0.980962 | − | 0.194201i | \(-0.937788\pi\) | ||||
0.980962 | − | 0.194201i | \(-0.0622115\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 639995.i | 1.45204i | 0.687671 | + | 0.726022i | \(0.258633\pi\) | ||||
−0.687671 | + | 0.726022i | \(0.741367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 863718. | 1.90653 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −107643. | −0.231236 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 646286.i | 1.35151i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 68086.0i | 0.138645i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 126967. | 0.251829 | 0.125915 | − | 0.992041i | \(-0.459813\pi\) | ||||
0.125915 | + | 0.992041i | \(0.459813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 287272. | 0.555137 | 0.277568 | − | 0.960706i | \(-0.410471\pi\) | ||||
0.277568 | + | 0.960706i | \(0.410471\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 19721.2i | − 0.0371405i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 500809.i | − 0.919405i | −0.888073 | − | 0.459702i | \(-0.847956\pi\) | ||||
0.888073 | − | 0.459702i | \(-0.152044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 858127. | 1.53610 | 0.768049 | − | 0.640392i | \(-0.221228\pi\) | ||||
0.768049 | + | 0.640392i | \(0.221228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.19806e6 | −2.09165 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 158355.i | − 0.269706i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 258982.i | − 0.430412i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.12100e6 | 1.81837 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 405078. | 0.641465 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 982183.i | − 1.51875i | −0.650653 | − | 0.759375i | \(-0.725505\pi\) | ||||
0.650653 | − | 0.759375i | \(-0.274495\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 862083.i | − 1.30197i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −159290. | −0.235013 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.13383e6 | −1.63455 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 9425.09i | − 0.0132793i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 46003.7i | − 0.0633595i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −188728. | −0.254141 | −0.127071 | − | 0.991894i | \(-0.540557\pi\) | ||||
−0.127071 | + | 0.991894i | \(0.540557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 140260. | 0.184705 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 517079.i | 0.666027i | 0.942922 | + | 0.333014i | \(0.108066\pi\) | ||||
−0.942922 | + | 0.333014i | \(0.891934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 160000.i | 0.201619i | 0.994906 | + | 0.100809i | \(0.0321432\pi\) | ||||
−0.994906 | + | 0.100809i | \(0.967857\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.87805e6 | 2.31568 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.49124e6 | 1.79953 | 0.899765 | − | 0.436375i | \(-0.143738\pi\) | ||||
0.899765 | + | 0.436375i | \(0.143738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 553017.i | − 0.653235i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.33295e6i | 1.54150i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 142742. | 0.161643 | 0.0808215 | − | 0.996729i | \(-0.474246\pi\) | ||||
0.0808215 | + | 0.996729i | \(0.474246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12428.9 | −0.0137844 | −0.00689222 | − | 0.999976i | \(-0.502194\pi\) | ||||
−0.00689222 | + | 0.999976i | \(0.502194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.26916e6i | − 1.37880i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 297791.i | 0.316954i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28834.2 | −0.0300722 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −63632.0 | −0.0650395 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 759309.i | 0.760736i | 0.924835 | + | 0.380368i | \(0.124203\pi\) | ||||
−0.924835 | + | 0.380368i | \(0.875797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.56051e6i | 2.51492i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 681464. | 0.656285 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 500270. | 0.472468 | 0.236234 | − | 0.971696i | \(-0.424087\pi\) | ||||
0.236234 | + | 0.971696i | \(0.424087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 729670.i | 0.675891i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 209703.i | 0.190547i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 549782. | 0.490119 | 0.245059 | − | 0.969508i | \(-0.421193\pi\) | ||||
0.245059 | + | 0.969508i | \(0.421193\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −581164. | −0.508375 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.40061e6i | 1.20237i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.02271e6i | 0.861731i | 0.902416 | + | 0.430865i | \(0.141792\pi\) | ||||
−0.902416 | + | 0.430865i | \(0.858208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.12050e6 | −0.926807 | −0.463404 | − | 0.886147i | \(-0.653372\pi\) | ||||
−0.463404 | + | 0.886147i | \(0.653372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −133683. | −0.108560 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 320371.i | 0.255459i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 323208.i | 0.253095i | 0.991961 | + | 0.126547i | \(0.0403896\pi\) | ||||
−0.991961 | + | 0.126547i | \(0.959610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50148e6 | 1.15481 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 325436. | 0.245867 | 0.122933 | − | 0.992415i | \(-0.460770\pi\) | ||||
0.122933 | + | 0.992415i | \(0.460770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.41107e6i | − 1.78955i | −0.446518 | − | 0.894775i | \(-0.647336\pi\) | ||||
0.446518 | − | 0.894775i | \(-0.352664\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 427127.i | − 0.311491i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.75554e6 | −1.25807 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 169793. | 0.119585 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.43843e6i | 2.38028i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.89437e6i | 1.28913i | 0.764550 | + | 0.644565i | \(0.222961\pi\) | ||||
−0.764550 | + | 0.644565i | \(0.777039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 693972. | 0.464287 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 205944. | 0.135475 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 182261.i | − 0.117901i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07977e6i | 0.686932i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.44796e6 | −0.906045 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 998757. | 0.614767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.37530e6i | − 0.832823i | −0.909176 | − | 0.416411i | \(-0.863288\pi\) | ||||
0.909176 | − | 0.416411i | \(-0.136712\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3.14464e6i | − 1.87359i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.60469e6 | −1.52705 | −0.763527 | − | 0.645776i | \(-0.776534\pi\) | ||||
−0.763527 | + | 0.645776i | \(0.776534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 780226. | 0.450152 | 0.225076 | − | 0.974341i | \(-0.427737\pi\) | ||||
0.225076 | + | 0.974341i | \(0.427737\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 950773.i | − 0.539884i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.28045e6i | 0.715673i | 0.933784 | + | 0.357836i | \(0.116485\pi\) | ||||
−0.933784 | + | 0.357836i | \(0.883515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −478986. | −0.263540 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.45121e6 | −0.786081 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 996359.i | − 0.531386i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 22804.6i | − 0.0119760i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.22383e6 | 1.15009 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.74870e6 | −1.90937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.35495e6i | 1.18144i | 0.806876 | + | 0.590721i | \(0.201157\pi\) | ||||
−0.806876 | + | 0.590721i | \(0.798843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 966273.i | − 0.477517i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.38537e6 | −0.674459 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.10943e6 | −1.97109 | −0.985546 | − | 0.169411i | \(-0.945814\pi\) | ||||
−0.985546 | + | 0.169411i | \(0.945814\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.31230e6i | − 0.620202i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.42956e6i | 1.59718i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −829599. | −0.380744 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.69988e6 | 1.22123 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.41845e6i | − 0.632398i | −0.948693 | − | 0.316199i | \(-0.897593\pi\) | ||||
0.948693 | − | 0.316199i | \(-0.102407\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.03977e6i | 0.896434i | 0.893925 | + | 0.448217i | \(0.147941\pi\) | ||||
−0.893925 | + | 0.448217i | \(0.852059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14659.5 | −0.00635112 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 129749. | 0.0554201 | 0.0277101 | − | 0.999616i | \(-0.491178\pi\) | ||||
0.0277101 | + | 0.999616i | \(0.491178\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 996866.i | − 0.419823i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.61939e6i | − 1.91829i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.54034e6 | 0.630782 | 0.315391 | − | 0.948962i | \(-0.397864\pi\) | ||||
0.315391 | + | 0.948962i | \(0.397864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.85160e6 | 0.747790 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.19878e6i | − 0.875819i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 10898.7i | − 0.00428195i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.89303e6 | −0.733655 | −0.366828 | − | 0.930289i | \(-0.619556\pi\) | ||||
−0.366828 | + | 0.930289i | \(0.619556\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.32479e6 | 0.888829 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.93950e6i | 1.48596i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.29601e6i | − 1.22664i | −0.789836 | − | 0.613319i | \(-0.789834\pi\) | ||||
0.789836 | − | 0.613319i | \(-0.210166\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 337810. | 0.124049 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34095.0 | 0.0123549 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.38042e6i | 0.493643i | 0.969061 | + | 0.246821i | \(0.0793861\pi\) | ||||
−0.969061 | + | 0.246821i | \(0.920614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 6.89637e6i | − 2.43393i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.13515e6 | −1.09210 | −0.546049 | − | 0.837753i | \(-0.683869\pi\) | ||||
−0.546049 | + | 0.837753i | \(0.683869\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.17168e6 | 0.746696 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.42989e6i | − 0.485317i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4.57462e6i | − 1.53279i | −0.642372 | − | 0.766393i | \(-0.722050\pi\) | ||||
0.642372 | − | 0.766393i | \(-0.277950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.29800e6 | 2.08334 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.77122e6 | 2.53809 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.54135e6i | 0.497060i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.13071e6i | 0.678496i | 0.940697 | + | 0.339248i | \(0.110173\pi\) | ||||
−0.940697 | + | 0.339248i | \(0.889827\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.89534e6 | −0.910473 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.03442e6 | −0.631799 | −0.315900 | − | 0.948793i | \(-0.602306\pi\) | ||||
−0.315900 | + | 0.948793i | \(0.602306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 244122.i | − 0.0748763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.58049e6i | − 0.478799i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.20708e6 | 0.660438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.79858e6 | −1.41842 | −0.709210 | − | 0.704997i | \(-0.750948\pi\) | ||||
−0.709210 | + | 0.704997i | \(0.750948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.25903e6i | 1.82769i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.70418e6i | − 1.35709i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −73580.6 | −0.0209722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.87908e6 | −1.93727 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.63789e6i | − 0.455773i | −0.973688 | − | 0.227887i | \(-0.926818\pi\) | ||||
0.973688 | − | 0.227887i | \(-0.0731816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 6.15276e6i | − 1.69186i | −0.533293 | − | 0.845931i | \(-0.679046\pi\) | ||||
0.533293 | − | 0.845931i | \(-0.320954\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.96425e6 | 1.34897 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 788008. | 0.211621 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.77020e6i | − 1.79693i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 404360.i | 0.106078i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.74591e6 | −1.74923 | −0.874616 | − | 0.484817i | \(-0.838886\pi\) | ||||
−0.874616 | + | 0.484817i | \(0.838886\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.05459e6 | 1.55190 | 0.775952 | − | 0.630792i | \(-0.217270\pi\) | ||||
0.775952 | + | 0.630792i | \(0.217270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 505058.i | 0.127973i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.94746e6i | − 0.988812i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.84810e6 | −1.69593 | −0.847967 | − | 0.530049i | \(-0.822174\pi\) | ||||
−0.847967 | + | 0.530049i | \(0.822174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.67317e6 | −0.654530 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.22271e6i | − 1.02231i | −0.859489 | − | 0.511154i | \(-0.829218\pi\) | ||||
0.859489 | − | 0.511154i | \(-0.170782\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.61959e6i | 0.387709i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.00425e7 | −2.37725 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 733420. | 0.171687 | 0.0858434 | − | 0.996309i | \(-0.472642\pi\) | ||||
0.0858434 | + | 0.996309i | \(0.472642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.31010e6i | 1.22931i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 286018.i | − 0.0654859i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −154584. | −0.0350054 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.36667e6 | −1.20203 | −0.601014 | − | 0.799239i | \(-0.705236\pi\) | ||||
−0.601014 | + | 0.799239i | \(0.705236\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 506555.i | − 0.112226i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.80941e6i | 0.396538i | 0.980148 | + | 0.198269i | \(0.0635320\pi\) | ||||
−0.980148 | + | 0.198269i | \(0.936468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.86270e6 | 1.05421 | 0.527103 | − | 0.849802i | \(-0.323278\pi\) | ||||
0.527103 | + | 0.849802i | \(0.323278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.61624e6 | 0.775576 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.18481e6i | 1.73667i | 0.495981 | + | 0.868334i | \(0.334809\pi\) | ||||
−0.495981 | + | 0.868334i | \(0.665191\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.39094e6i | 1.97141i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.71301e6 | −0.563507 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.26604e6 | 0.671226 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 493907.i | − 0.100441i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5.21692e6i | − 1.04983i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.20370e6 | −1.03627 | −0.518136 | − | 0.855298i | \(-0.673374\pi\) | ||||
−0.518136 | + | 0.855298i | \(0.673374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −157104. | −0.0309616 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.83015e7i | − 3.56959i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.97602e6i | 0.767528i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.82182e6 | 0.730211 | 0.365105 | − | 0.930966i | \(-0.381033\pi\) | ||||
0.365105 | + | 0.930966i | \(0.381033\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.72133e6 | −1.83846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.68377e6i | 0.876782i | 0.898784 | + | 0.438391i | \(0.144451\pi\) | ||||
−0.898784 | + | 0.438391i | \(0.855549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.17815e6i | 0.218314i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.87587e6 | −0.527541 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.75739e6 | −1.22712 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 129527.i | 0.0232867i | 0.999932 | + | 0.0116433i | \(0.00370628\pi\) | ||||
−0.999932 | + | 0.0116433i | \(0.996294\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.41098e6i | 0.607135i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.59305e6 | −0.809434 | −0.404717 | − | 0.914442i | \(-0.632630\pi\) | ||||
−0.404717 | + | 0.914442i | \(0.632630\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.67434e6 | −0.292157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.99851e6i | 1.38194i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7.25700e6i | − 1.24155i | −0.783991 | − | 0.620773i | \(-0.786819\pi\) | ||||
0.783991 | − | 0.620773i | \(-0.213181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −73878.0 | −0.0125159 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −317498. | −0.0532657 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.63629e6i | − 0.604145i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.13389e7i | 1.86572i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.48609e6 | 0.894015 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.82096e6 | 0.616706 | 0.308353 | − | 0.951272i | \(-0.400222\pi\) | ||||
0.308353 | + | 0.951272i | \(0.400222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.14789e6i | 0.503228i | 0.967828 | + | 0.251614i | \(0.0809613\pi\) | ||||
−0.967828 | + | 0.251614i | \(0.919039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 2.28989e6i | − 0.362590i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.43559e6 | 1.32309 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.85156e7 | 2.87672 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.22956e6i | 0.958784i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 377982.i | − 0.0576306i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.67810e6 | −0.253474 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.59971e6 | 0.538681 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 6.10583e6i | − 0.905259i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.65423e6i | 0.977472i | 0.872432 | + | 0.488736i | \(0.162542\pi\) | ||||
−0.872432 | + | 0.488736i | \(0.837458\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.38366e7 | −2.01386 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.57152e6 | 0.370851 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.73564e6i | 0.390923i | 0.980711 | + | 0.195461i | \(0.0626204\pi\) | ||||
−0.980711 | + | 0.195461i | \(0.937380\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.96551e6i | 1.26953i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 738438. | 0.103618 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.04483e7 | 1.45288 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 2.32722e6i | − 0.320704i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8.08022e6i | − 1.10353i | −0.833999 | − | 0.551766i | \(-0.813954\pi\) | ||||
0.833999 | − | 0.551766i | \(-0.186046\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −232482. | −0.0314674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.39726e7 | −1.87443 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8.04656e6i | − 1.06989i | −0.844887 | − | 0.534945i | \(-0.820332\pi\) | ||||
0.844887 | − | 0.534945i | \(-0.179668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.51747e6i | − 0.199986i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.07135e7 | −1.39951 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.03321e6 | −0.651725 | −0.325862 | − | 0.945417i | \(-0.605655\pi\) | ||||
−0.325862 | + | 0.945417i | \(0.605655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.04770e7i | 1.34476i | 0.740205 | + | 0.672381i | \(0.234728\pi\) | ||||
−0.740205 | + | 0.672381i | \(0.765272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.74499e6i | 0.349265i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12199e6 | 0.393788 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.04045e6 | 0.755318 | 0.377659 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377659 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.21077e6i | 0.769926i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 498776.i | 0.0613006i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.19161e7 | 1.45198 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 204709. | 0.0247313 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.24894e6i | − 0.149605i | −0.997198 | − | 0.0748026i | \(-0.976167\pi\) | ||||
0.997198 | − | 0.0748026i | \(-0.0238327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5.28725e6i | − 0.627974i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.08274e7 | 1.27513 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.62448e6 | −0.656819 | −0.328410 | − | 0.944535i | \(-0.606513\pi\) | ||||
−0.328410 | + | 0.944535i | \(0.606513\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 5.34162e6i | − 0.618558i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.85525e7i | 2.13043i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.21046e7 | 1.37842 | 0.689211 | − | 0.724560i | \(-0.257957\pi\) | ||||
0.689211 | + | 0.724560i | \(0.257957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.35567e7 | −1.53098 | −0.765488 | − | 0.643450i | \(-0.777502\pi\) | ||||
−0.765488 | + | 0.643450i | \(0.777502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.24360e7i | − 1.39280i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2.54255e6i | − 0.282410i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.54199e6 | 1.05116 | 0.525578 | − | 0.850745i | \(-0.323849\pi\) | ||||
0.525578 | + | 0.850745i | \(0.323849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.42360e6 | 0.374059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 807125.i | − 0.0874657i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.07109e6i | 0.867523i | 0.901028 | + | 0.433762i | \(0.142814\pi\) | ||||
−0.901028 | + | 0.433762i | \(0.857186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.59914e6 | 0.596943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 277031. | 0.0292964 | 0.0146482 | − | 0.999893i | \(-0.495337\pi\) | ||||
0.0146482 | + | 0.999893i | \(0.495337\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.49138e6i | 0.680943i | 0.940255 | + | 0.340471i | \(0.110587\pi\) | ||||
−0.940255 | + | 0.340471i | \(0.889413\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.00691e6i | − 0.208833i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.09786e7 | 1.13325 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.75772e6i | 0.889656i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5.42869e6i | − 0.547103i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.43239e7 | 1.43215 | 0.716074 | − | 0.698025i | \(-0.245937\pi\) | ||||
0.716074 | + | 0.698025i | \(0.245937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.12346e7 | 2.10637 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 7.97460e6i | − 0.784828i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 434623.i | 0.0424389i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.94854e6 | 0.866962 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.52078e7 | −1.46191 | −0.730956 | − | 0.682425i | \(-0.760925\pi\) | ||||
−0.730956 | + | 0.682425i | \(0.760925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.09843e6i | 0.200155i | 0.994980 | + | 0.100078i | \(0.0319091\pi\) | ||||
−0.994980 | + | 0.100078i | \(0.968091\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.44382e6i | − 0.325942i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.04496e7 | 0.981384 | 0.490692 | − | 0.871333i | \(-0.336744\pi\) | ||||
0.490692 | + | 0.871333i | \(0.336744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.42290e7 | −1.32606 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.45131e7i | − 2.26697i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.78680e6i | 0.531075i | 0.964101 | + | 0.265537i | \(0.0855494\pi\) | ||||
−0.964101 | + | 0.265537i | \(0.914451\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.98622e6 | 0.818415 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 97833.7 | 0.00884250 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.05285e6i | 0.542933i | 0.962448 | + | 0.271467i | \(0.0875087\pi\) | ||||
−0.962448 | + | 0.271467i | \(0.912491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 5.13781e6i | − 0.457377i | −0.973500 | − | 0.228689i | \(-0.926556\pi\) | ||||
0.973500 | − | 0.228689i | \(-0.0734438\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 994592. | 0.0878741 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.34801e6 | −0.293584 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.66768e6i | 0.406243i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 4.08027e6i | − 0.352471i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.04783e7 | −1.75585 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.06833e6 | −0.0909214 | −0.0454607 | − | 0.998966i | \(-0.514476\pi\) | ||||
−0.0454607 | + | 0.998966i | \(0.514476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 251105.i | − 0.0212127i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.78231e7i | − 1.49456i | −0.664510 | − | 0.747279i | \(-0.731360\pi\) | ||||
0.664510 | − | 0.747279i | \(-0.268640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.69520e7 | 2.24345 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.11792e7 | −0.923721 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.21938e7i | 1.00020i | 0.865968 | + | 0.500099i | \(0.166703\pi\) | ||||
−0.865968 | + | 0.500099i | \(0.833297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.23761e6i | 0.589344i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.45917e6 | −0.279628 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −848205. | −0.0680695 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 7.75412e6i | − 0.617785i | −0.951097 | − | 0.308893i | \(-0.900042\pi\) | ||||
0.951097 | − | 0.308893i | \(-0.0999583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.94944e7i | 1.54198i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.95460e6 | −0.624678 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.30611e7 | 1.01835 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.22404e7i | 2.49579i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.02808e7i | 1.55880i | 0.626528 | + | 0.779399i | \(0.284476\pi\) | ||||
−0.626528 | + | 0.779399i | \(0.715524\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.40259e6 | −0.259670 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.19561e7 | 0.905979 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.13497e7i | 0.853960i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 2.36091e6i | − 0.176386i | −0.996103 | − | 0.0881928i | \(-0.971891\pi\) | ||||
0.996103 | − | 0.0881928i | \(-0.0281092\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.38362e7 | −1.02646 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.34208e7 | 2.46203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 467580.i | 0.0342051i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.08606e6i | 0.224185i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.33349e6 | −0.312619 | −0.156310 | − | 0.987708i | \(-0.549960\pi\) | ||||
−0.156310 | + | 0.987708i | \(0.549960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.46491e7 | −1.76589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 268710.i | − 0.0191178i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 584022.i | 0.0412652i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.45026e6 | 0.312284 | 0.156142 | − | 0.987735i | \(-0.450094\pi\) | ||||
0.156142 | + | 0.987735i | \(0.450094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.20768e7 | 0.841650 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 8.03339e6i | − 0.556039i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 838509.i | 0.0576432i | 0.999585 | + | 0.0288216i | \(0.00917547\pi\) | ||||
−0.999585 | + | 0.0288216i | \(0.990825\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.43818e6 | −0.439587 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.84054e7 | 1.92634 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.44547e7i | − 1.64722i | −0.567158 | − | 0.823609i | \(-0.691957\pi\) | ||||
0.567158 | − | 0.823609i | \(-0.308043\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 623389.i | − 0.0417075i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.34515e7 | −0.893920 | −0.446960 | − | 0.894554i | \(-0.647493\pi\) | ||||
−0.446960 | + | 0.894554i | \(0.647493\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.16127e7 | −0.766551 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 660509.i | − 0.0433089i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.13752e7i | 0.740892i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.02598e7 | 1.95779 | 0.978896 | − | 0.204359i | \(-0.0655111\pi\) | ||||
0.978896 | + | 0.204359i | \(0.0655111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.64161e7 | −1.05507 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 330736.i | − 0.0211161i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.18417e7i | 1.38531i | 0.721269 | + | 0.692655i | \(0.243559\pi\) | ||||
−0.721269 | + | 0.692655i | \(0.756441\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.53577e7 | −3.48798 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.66377e6 | −0.166738 | −0.0833692 | − | 0.996519i | \(-0.526568\pi\) | ||||
−0.0833692 | + | 0.996519i | \(0.526568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.74314e7i | − 1.08398i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.07369e6i | 0.437011i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.01285e6 | 0.0621664 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.79300e6 | 0.109336 | 0.0546681 | − | 0.998505i | \(-0.482590\pi\) | ||||
0.0546681 | + | 0.998505i | \(0.482590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08158e7i | 0.655271i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.03672e7i | − 1.82792i | −0.405810 | − | 0.913958i | \(-0.633010\pi\) | ||||
0.405810 | − | 0.913958i | \(-0.366990\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.18162e6 | 0.250087 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.57753e7 | −0.937402 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 8.18642e6i | − 0.483337i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04395e7i | 1.19907i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 375426. | 0.0218837 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.13718e6 | −0.181704 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.37601e7i | 0.791925i | 0.918267 | + | 0.395962i | \(0.129589\pi\) | ||||
−0.918267 | + | 0.395962i | \(0.870411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.18862e7i | 0.679752i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.02864e7 | −0.584549 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.45768e6 | 0.0823150 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.25647e7i | − 0.705071i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.94451e6i | − 0.108434i | −0.998529 | − | 0.0542169i | \(-0.982734\pi\) | ||||
0.998529 | − | 0.0542169i | \(-0.0172662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.78901e7 | 1.54555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.45385e7 | −0.800644 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 223464.i | 0.0122298i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.11628e7i | − 1.15102i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.21108e7 | −1.19514 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.71536e6 | 0.253305 | 0.126652 | − | 0.991947i | \(-0.459577\pi\) | ||||
0.126652 | + | 0.991947i | \(0.459577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 7.50002e6i | − 0.400415i | −0.979754 | − | 0.200207i | \(-0.935838\pi\) | ||||
0.979754 | − | 0.200207i | \(-0.0641616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.42251e7i | − 1.28540i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.12412e7 | −0.592816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.03516e6 | −0.263911 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.38765e6i | − 0.0722885i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.84972e7i | − 1.47552i | −0.675063 | − | 0.737760i | \(-0.735884\pi\) | ||||
0.675063 | − | 0.737760i | \(-0.264116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.20948e6 | −0.319562 | −0.159781 | − | 0.987152i | \(-0.551079\pi\) | ||||
−0.159781 | + | 0.987152i | \(0.551079\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.92637e6 | −0.354300 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.27490e7i | 0.648207i | 0.946022 | + | 0.324104i | \(0.105063\pi\) | ||||
−0.946022 | + | 0.324104i | \(0.894937\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.60957e7i | 1.31881i | 0.751787 | + | 0.659406i | \(0.229192\pi\) | ||||
−0.751787 | + | 0.659406i | \(0.770808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.98771e6 | −0.351020 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.50183e7 | −0.749910 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.94428e6i | 0.195772i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.68807e6i | − 0.132626i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.88675e7 | −1.41581 | −0.707903 | − | 0.706310i | \(-0.750359\pi\) | ||||
−0.707903 | + | 0.706310i | \(0.750359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.96380e7 | 0.957430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.03587e6i | 0.340996i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.24904e6i | 0.445610i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.72350e7 | −0.825472 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.21269e7 | 2.48195 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2.15078e7i | − 1.01806i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.83501e7i | 0.863505i | 0.901992 | + | 0.431753i | \(0.142105\pi\) | ||||
−0.901992 | + | 0.431753i | \(0.857895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.43364e6 | 0.207417 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.16867e7 | −1.00865 | −0.504327 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504327 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 7.71806e6i | − 0.356883i | −0.983951 | − | 0.178441i | \(-0.942895\pi\) | ||||
0.983951 | − | 0.178441i | \(-0.0571055\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 3.79545e7i | − 1.74484i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.51914e7 | 1.15140 | 0.575700 | − | 0.817661i | \(-0.304730\pi\) | ||||
0.575700 | + | 0.817661i | \(0.304730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.34382e6 | 0.288277 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.67090e6i | 0.165854i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 3.16035e7i | − 1.41967i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.02194e6 | −0.0903075 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.56914e7 | −1.58500 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 2.64790e6i | − 0.116918i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.45084e7i | − 0.636971i | −0.947928 | − | 0.318485i | \(-0.896826\pi\) | ||||
0.947928 | − | 0.318485i | \(-0.103174\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.09560e7 | −1.78791 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.13732e7 | 1.79589 | 0.897943 | − | 0.440111i | \(-0.145061\pi\) | ||||
0.897943 | + | 0.440111i | \(0.145061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.77268e6i | 0.249158i | 0.992210 | + | 0.124579i | \(0.0397581\pi\) | ||||
−0.992210 | + | 0.124579i | \(0.960242\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.50036e7i | 0.643926i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.78721e6 | −0.417686 | −0.208843 | − | 0.977949i | \(-0.566970\pi\) | ||||
−0.208843 | + | 0.977949i | \(0.566970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.40568e7 | −2.29401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.24059e7i | 1.36751i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.74809e7i | − 0.733560i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.16251e6 | 0.173699 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.94045e6 | 0.163518 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.25193e6i | 0.257997i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.93096e7i | − 1.20281i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.33444e7 | −0.952714 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.59999e7 | −0.649374 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.90645e6i | 0.0769497i | 0.999260 | + | 0.0384749i | \(0.0122500\pi\) | ||||
−0.999260 | + | 0.0384749i | \(0.987750\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1.50300e7i | − 0.603323i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.24825e6 | 0.249438 | 0.124719 | − | 0.992192i | \(-0.460197\pi\) | ||||
0.124719 | + | 0.992192i | \(0.460197\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.50868e6 | 0.0598991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.15929e7i | 0.852627i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6.09142e7i | − 2.39219i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.90166e6 | 0.152391 | 0.0761957 | − | 0.997093i | \(-0.475723\pi\) | ||||
0.0761957 | + | 0.997093i | \(0.475723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.97338e7 | 1.15505 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.45492e6i | − 0.0562127i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.69107e6i | − 0.103412i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.26418e7 | 1.24760 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.94138e6 | 0.111818 | 0.0559090 | − | 0.998436i | \(-0.482194\pi\) | ||||
0.0559090 | + | 0.998436i | \(0.482194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.41318e6i | 0.355928i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.63129e7i | − 2.11789i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.61571e7 | −0.604415 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.73011e7 | 1.01585 | 0.507926 | − | 0.861401i | \(-0.330412\pi\) | ||||
0.507926 | + | 0.861401i | \(0.330412\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.68683e7i | 0.624322i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.99537e6i | − 0.110275i | −0.998479 | − | 0.0551374i | \(-0.982440\pi\) | ||||
0.998479 | − | 0.0551374i | \(-0.0175597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.17465e7 | 1.89497 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.70215e6 | −0.0620038 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.96401e7i | − 1.07400i | −0.843582 | − | 0.537000i | \(-0.819558\pi\) | ||||
0.843582 | − | 0.537000i | \(-0.180442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 15906.5i | 0 0.000573337i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.76831e7 | −0.992575 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.57409e7 | 0.918101 | 0.459051 | − | 0.888410i | \(-0.348190\pi\) | ||||
0.459051 | + | 0.888410i | \(0.348190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.17416e6i | 0.112621i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.03556e7i | − 0.365506i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.90611e7 | 1.72262 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.61349e7 | 0.563584 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.50637e7i | − 0.523440i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.18180e6i | 0.248265i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.11539e7 | 0.727487 | 0.363743 | − | 0.931499i | \(-0.381499\pi\) | ||||
0.363743 | + | 0.931499i | \(0.381499\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.15411e7 | 0.736985 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.18119e7i | 1.42315i | 0.702608 | + | 0.711577i | \(0.252019\pi\) | ||||
−0.702608 | + | 0.711577i | \(0.747981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.39213e7i | 1.82590i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 493031. | 0.0166097 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.93721e7 | −1.31963 | −0.659815 | − | 0.751428i | \(-0.729365\pi\) | ||||
−0.659815 | + | 0.751428i | \(0.729365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.32078e7i | − 1.10734i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.30837e7i | 0.765831i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.10636e6 | −0.234565 | −0.117283 | − | 0.993099i | \(-0.537418\pi\) | ||||
−0.117283 | + | 0.993099i | \(0.537418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.25202e7 | 0.411170 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 8.10462e7i | − 2.64813i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.18273e7i | − 1.03469i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.70666e6 | −0.0875487 | −0.0437744 | − | 0.999041i | \(-0.513938\pi\) | ||||
−0.0437744 | + | 0.999041i | \(0.513938\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.09137e7 | −1.63856 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.14532e7i | 0.686964i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.58535e7i | 0.505112i | 0.967582 | + | 0.252556i | \(0.0812713\pi\) | ||||
−0.967582 | + | 0.252556i | \(0.918729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.72990e6 | −0.0548412 |
(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 | 320.6.d.b.161.7 | yes | 8 | |
4.3 | odd | 2 | 320.6.d.a.161.2 | ✓ | 8 | ||
8.3 | odd | 2 | 320.6.d.a.161.7 | yes | 8 | ||
8.5 | even | 2 | inner | 320.6.d.b.161.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.a.161.2 | ✓ | 8 | 4.3 | odd | 2 | ||
320.6.d.a.161.7 | yes | 8 | 8.3 | odd | 2 | ||
320.6.d.b.161.2 | yes | 8 | 8.5 | even | 2 | inner | |
320.6.d.b.161.7 | yes | 8 | 1.1 | even | 1 | trivial |