Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(289,320)]
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, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.289");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.f (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: | 8.0.73499483897856.45 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3721x^{4} + 13845841 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-2.02144 + 7.54412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.289 |
Dual form | 320.6.f.b.289.2 |
$q$-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 | ||||||||
\(3\) | −19.1311 | −1.22726 | −0.613631 | − | 0.789593i | \(-0.710292\pi\) | ||||
−0.613631 | + | 0.789593i | \(0.710292\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −55.2268 | − | 8.66025i | −0.987927 | − | 0.154919i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 121.499i | − | 0.937190i | −0.883413 | − | 0.468595i | \(-0.844760\pi\) | ||
0.883413 | − | 0.468595i | \(-0.155240\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 123.000 | 0.506173 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 298.000i | 0.742565i | 0.928520 | + | 0.371283i | \(0.121082\pi\) | ||||
−0.928520 | + | 0.371283i | \(0.878918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 485.996 | 0.797580 | 0.398790 | − | 0.917042i | \(-0.369430\pi\) | ||||
0.398790 | + | 0.917042i | \(0.369430\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1056.55 | + | 165.680i | 1.21245 | + | 0.190127i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 420.885i | − | 0.353216i | −0.984281 | − | 0.176608i | \(-0.943487\pi\) | ||
0.984281 | − | 0.176608i | \(-0.0565126\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2574.00i | 1.63578i | 0.575376 | + | 0.817889i | \(0.304856\pi\) | ||||
−0.575376 | + | 0.817889i | \(0.695144\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2324.41i | 1.15018i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 717.948i | − | 0.282992i | −0.989939 | − | 0.141496i | \(-0.954809\pi\) | ||
0.989939 | − | 0.141496i | \(-0.0451912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2975.00 | + | 956.556i | 0.952000 | + | 0.306098i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2295.74 | 0.606055 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3734.30i | 0.824545i | 0.911061 | + | 0.412273i | \(0.135265\pi\) | ||||
−0.911061 | + | 0.412273i | \(0.864735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6228.45 | −1.16406 | −0.582031 | − | 0.813167i | \(-0.697742\pi\) | ||||
−0.582031 | + | 0.813167i | \(0.697742\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5701.08i | − | 0.911322i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1052.21 | + | 6710.00i | −0.145189 | + | 0.925875i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5721.50 | 0.687077 | 0.343538 | − | 0.939139i | \(-0.388374\pi\) | ||||
0.343538 | + | 0.939139i | \(0.388374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9297.65 | −0.978840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11396.0 | 1.05875 | 0.529374 | − | 0.848388i | \(-0.322427\pi\) | ||||
0.529374 | + | 0.848388i | \(0.322427\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19150.3 | −1.57944 | −0.789721 | − | 0.613467i | \(-0.789775\pi\) | ||||
−0.789721 | + | 0.613467i | \(0.789775\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6792.90 | − | 1065.21i | −0.500062 | − | 0.0784160i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2286.39i | 0.150975i | 0.997147 | + | 0.0754876i | \(0.0240513\pi\) | ||||
−0.997147 | + | 0.0754876i | \(0.975949\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2045.00 | 0.121675 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8052.00i | 0.433489i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17230.8 | 0.842587 | 0.421294 | − | 0.906924i | \(-0.361576\pi\) | ||||
0.421294 | + | 0.906924i | \(0.361576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2580.76 | − | 16457.6i | 0.115038 | − | 0.733600i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 49243.5i | − | 2.00753i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 16378.0i | − | 0.612535i | −0.951946 | − | 0.306267i | \(-0.900920\pi\) | ||
0.951946 | − | 0.306267i | \(-0.0990802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 48736.4i | − | 1.67699i | −0.544913 | − | 0.838493i | \(-0.683437\pi\) | ||
0.544913 | − | 0.838493i | \(-0.316563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 14944.4i | − | 0.474380i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26840.0 | − | 4208.85i | −0.787951 | − | 0.123561i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8398.56 | −0.228569 | −0.114285 | − | 0.993448i | \(-0.536458\pi\) | ||||
−0.114285 | + | 0.993448i | \(0.536458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13735.2i | 0.347305i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29091.5 | 0.684890 | 0.342445 | − | 0.939538i | \(-0.388745\pi\) | ||||
0.342445 | + | 0.939538i | \(0.388745\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 420.885i | − | 0.00924392i | −0.999989 | − | 0.00462196i | \(-0.998529\pi\) | ||
0.999989 | − | 0.00462196i | \(-0.00147122\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −56915.1 | − | 18300.0i | −1.16835 | − | 0.375663i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 36206.7 | 0.695924 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31170.0 | 0.561913 | 0.280956 | − | 0.959721i | \(-0.409348\pi\) | ||||
0.280956 | + | 0.959721i | \(0.409348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73809.0 | −1.24996 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −106273. | −1.69328 | −0.846641 | − | 0.532164i | \(-0.821379\pi\) | ||||
−0.846641 | + | 0.532164i | \(0.821379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3644.97 | + | 23244.1i | −0.0547201 | + | 0.348952i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 71441.4i | − | 1.01193i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −99362.0 | −1.32967 | −0.664837 | − | 0.746988i | \(-0.731499\pi\) | ||||
−0.664837 | + | 0.746988i | \(0.731499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 59048.0i | − | 0.747484i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 119157. | 1.42861 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22291.5 | − | 142154.i | 0.253414 | − | 1.61603i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 180330.i | − | 1.94598i | −0.230845 | − | 0.972991i | \(-0.574149\pi\) | ||
0.230845 | − | 0.972991i | \(-0.425851\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 36654.0i | 0.375866i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 136340.i | 1.32990i | 0.746886 | + | 0.664952i | \(0.231548\pi\) | ||||
−0.746886 | + | 0.664952i | \(0.768452\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 98557.8i | 0.915372i | 0.889114 | + | 0.457686i | \(0.151322\pi\) | ||||
−0.889114 | + | 0.457686i | \(0.848678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20130.0 | − | 128370.i | 0.178185 | − | 1.13629i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −107115. | −0.904465 | −0.452232 | − | 0.891900i | \(-0.649372\pi\) | ||||
−0.452232 | + | 0.891900i | \(0.649372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 234766.i | − | 1.89264i | −0.323230 | − | 0.946321i | \(-0.604769\pi\) | ||
0.323230 | − | 0.946321i | \(-0.395231\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −109459. | −0.843224 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 27548.8i | − | 0.202958i | −0.994838 | − | 0.101479i | \(-0.967642\pi\) | ||
0.994838 | − | 0.101479i | \(-0.0323575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6217.62 | + | 39650.0i | −0.0438409 | + | 0.279575i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 59777.5 | 0.403713 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −51137.1 | −0.331031 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 72247.0 | 0.448597 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −218018. | −1.29936 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −156016. | − | 78591.8i | −0.893086 | − | 0.449886i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 160986.i | − | 0.885685i | −0.896599 | − | 0.442842i | \(-0.853970\pi\) | ||
0.896599 | − | 0.442842i | \(-0.146030\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 366366. | 1.93839 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 194590.i | 0.990700i | 0.868693 | + | 0.495350i | \(0.164960\pi\) | ||||
−0.868693 | + | 0.495350i | \(0.835040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 312738. | 1.53303 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −126786. | − | 19881.6i | −0.598739 | − | 0.0938897i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 26707.1i | − | 0.121569i | −0.998151 | − | 0.0607847i | \(-0.980640\pi\) | ||
0.998151 | − | 0.0607847i | \(-0.0193603\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 140690.i | 0.617627i | 0.951123 | + | 0.308813i | \(0.0999319\pi\) | ||||
−0.951123 | + | 0.308813i | \(0.900068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 43741.2i | − | 0.185286i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 144827.i | 0.592255i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32340.0 | − | 206234.i | 0.127738 | − | 0.814590i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −39123.2 | −0.149328 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 329343.i | 1.21530i | 0.794206 | + | 0.607648i | \(0.207887\pi\) | ||||
−0.794206 | + | 0.607648i | \(0.792113\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 134282. | 0.479266 | 0.239633 | − | 0.970864i | \(-0.422973\pi\) | ||||
0.239633 | + | 0.970864i | \(0.422973\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 51768.8i | − | 0.178789i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 343978. | + | 53940.0i | 1.15001 | + | 0.180336i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −413958. | −1.34032 | −0.670158 | − | 0.742218i | \(-0.733774\pi\) | ||||
−0.670158 | + | 0.742218i | \(0.733774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −329644. | −1.03408 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −87230.0 | −0.265217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −298618. | −0.880332 | −0.440166 | − | 0.897916i | \(-0.645080\pi\) | ||||
−0.440166 | + | 0.897916i | \(0.645080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −49372.8 | + | 314852.i | −0.141181 | + | 0.900320i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 248708.i | − | 0.690080i | −0.938588 | − | 0.345040i | \(-0.887865\pi\) | ||
0.938588 | − | 0.345040i | \(-0.112135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −135101. | −0.363866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 316602.i | 0.827987i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 751593. | 1.90927 | 0.954635 | − | 0.297779i | \(-0.0962459\pi\) | ||||
0.954635 | + | 0.297779i | \(0.0962459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 116221. | − | 361459.i | 0.286872 | − | 0.892205i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 313330.i | 0.751741i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 654422.i | − | 1.52660i | −0.646044 | − | 0.763300i | \(-0.723578\pi\) | ||
0.646044 | − | 0.763300i | \(-0.276422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 69025.7i | 0.156608i | 0.996930 | + | 0.0783041i | \(0.0249505\pi\) | ||||
−0.996930 | + | 0.0783041i | \(0.975049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 932383.i | 2.05810i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −315980. | − | 49549.6i | −0.678782 | − | 0.106441i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 125424. | 0.262286 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 278929.i | − | 0.567989i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 622693. | 1.23507 | 0.617534 | − | 0.786544i | \(-0.288132\pi\) | ||||
0.617534 | + | 0.786544i | \(0.288132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 656159.i | 1.26799i | 0.773337 | + | 0.633995i | \(0.218586\pi\) | ||||
−0.773337 | + | 0.633995i | \(0.781414\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 513479. | + | 80520.0i | 0.967022 | + | 0.151641i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −395601. | −0.726259 | −0.363129 | − | 0.931739i | \(-0.618292\pi\) | ||||
−0.363129 | + | 0.931739i | \(0.618292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2514.94 | 0.00450189 | 0.00225094 | − | 0.999997i | \(-0.499284\pi\) | ||||
0.00225094 | + | 0.999997i | \(0.499284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 160674. | 0.280515 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 453714. | 0.772755 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −629365. | − | 98692.3i | −1.04597 | − | 0.164021i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 88307.7i | − | 0.143243i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −767052. | −1.21467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.01981e6i | − | 1.57693i | −0.615078 | − | 0.788466i | \(-0.710875\pi\) | ||
0.615078 | − | 0.788466i | \(-0.289125\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −556554. | −0.840539 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.05761e6 | + | 165846.i | 1.56037 | + | 0.244686i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 756751.i | 1.09095i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8052.00i | 0.0113447i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 204548.i | − | 0.281718i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 88462.3i | 0.119123i | 0.998225 | + | 0.0595616i | \(0.0189703\pi\) | ||||
−0.998225 | + | 0.0595616i | \(0.981030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 365925. | + | 117656.i | 0.481877 | + | 0.154939i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 411836. | 0.530468 | 0.265234 | − | 0.964184i | \(-0.414551\pi\) | ||||
0.265234 | + | 0.964184i | \(0.414551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.26328e6i | − | 1.59188i | −0.605373 | − | 0.795942i | \(-0.706976\pi\) | ||
0.605373 | − | 0.795942i | \(-0.293024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −692675. | −0.854082 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.21341e6i | 1.46426i | 0.681165 | + | 0.732130i | \(0.261474\pi\) | ||||
−0.681165 | + | 0.732130i | \(0.738526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19800.7 | − | 126270.i | 0.0233890 | − | 0.149152i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −596317. | −0.689614 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −570738. | −0.646312 | −0.323156 | − | 0.946346i | \(-0.604744\pi\) | ||||
−0.323156 | + | 0.946346i | \(0.604744\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −724680. | −0.803718 | −0.401859 | − | 0.915702i | \(-0.631636\pi\) | ||||
−0.401859 | + | 0.915702i | \(0.631636\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 854186. | 0.927976 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −112939. | − | 17710.2i | −0.120207 | − | 0.0188499i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.25095e6i | 1.30466i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.03313e6 | 2.07810 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 562046.i | − | 0.563103i | −0.959546 | − | 0.281551i | \(-0.909151\pi\) | ||
0.959546 | − | 0.281551i | \(-0.0908490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 213949. | 0.210140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 69732.4 | − | 444686.i | 0.0671559 | − | 0.428256i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 453714.i | − | 0.428498i | −0.976779 | − | 0.214249i | \(-0.931270\pi\) | ||
0.976779 | − | 0.214249i | \(-0.0687305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 695156.i | − | 0.643921i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 459319.i | 0.417362i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.89769e6i | 1.69175i | 0.533380 | + | 0.845876i | \(0.320921\pi\) | ||||
−0.533380 | + | 0.845876i | \(0.679079\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −951600. | − | 149223.i | −0.832415 | − | 0.130533i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.90091e6 | 1.63186 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 341612.i | 0.287841i | 0.989589 | + | 0.143921i | \(0.0459710\pi\) | ||||
−0.989589 | + | 0.143921i | \(0.954029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −528366. | −0.437030 | −0.218515 | − | 0.975834i | \(-0.570121\pi\) | ||||
−0.218515 | + | 0.975834i | \(0.570121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.12965e6i | 0.917359i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −285054. | + | 886550.i | −0.227298 | + | 0.706922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 691329. | 0.541359 | 0.270680 | − | 0.962670i | \(-0.412752\pi\) | ||||
0.270680 | + | 0.962670i | \(0.412752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −766100. | −0.589217 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 387728. | 0.292928 | 0.146464 | − | 0.989216i | \(-0.453211\pi\) | ||||
0.146464 | + | 0.989216i | \(0.453211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −208128. | −0.154477 | −0.0772384 | − | 0.997013i | \(-0.524610\pi\) | ||||
−0.0772384 | + | 0.997013i | \(0.524610\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −426461. | + | 2.71956e6i | −0.311005 | + | 1.98329i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.38460e6i | − | 0.992248i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.24271e6 | 0.875238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.44992e6i | 2.38823i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.04872e6 | −1.39416 | −0.697080 | − | 0.716993i | \(-0.745518\pi\) | ||||
−0.697080 | + | 0.716993i | \(0.745518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −141838. | + | 904505.i | −0.0948935 | + | 0.605140i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 684129.i | 0.450036i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 348920.i | − | 0.225708i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.32674e6i | 1.48024i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.60834e6i | − | 1.63214i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −422070. | + | 2.69156e6i | −0.259797 | + | 1.65674i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 877755. | 0.531530 | 0.265765 | − | 0.964038i | \(-0.414376\pi\) | ||||
0.265765 | + | 0.964038i | \(0.414376\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.88552e6i | − | 1.12340i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.96427e6 | 1.73787 | 0.868935 | − | 0.494926i | \(-0.164805\pi\) | ||||
0.868935 | + | 0.494926i | \(0.164805\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.58612e6i | − | 0.915116i | −0.889180 | − | 0.457558i | \(-0.848724\pi\) | ||
0.889180 | − | 0.457558i | \(-0.151276\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −129422. | + | 825330.i | −0.0734906 | + | 0.468653i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 754884. | 0.421922 | 0.210961 | − | 0.977494i | \(-0.432341\pi\) | ||||
0.210961 | + | 0.977494i | \(0.432341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.11282e6 | −0.612278 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.04923e6 | 1.11002 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.08336e6 | 0.577784 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.44584e6 | + | 464882.i | 0.759296 | + | 0.244138i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.49133e6i | 2.32277i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 277794. | 0.141492 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 194226.i | − | 0.0974400i | −0.998812 | − | 0.0487200i | \(-0.984486\pi\) | ||
0.998812 | − | 0.0487200i | \(-0.0155142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 703744. | 0.347780 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 463826. | + | 72733.7i | 0.225810 | + | 0.0354098i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.47312e6i | − | 1.18623i | −0.805116 | − | 0.593117i | \(-0.797897\pi\) | ||
0.805116 | − | 0.593117i | \(-0.202103\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 527040.i | 0.249083i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.85608e6i | − | 0.864392i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.29050e6i | − | 1.05122i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 118950. | − | 758549.i | 0.0538043 | − | 0.343112i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.39126e6 | −1.06611 | −0.533056 | − | 0.846080i | \(-0.678956\pi\) | ||||
−0.533056 | + | 0.846080i | \(0.678956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.38607e6i | − | 1.04862i | −0.851527 | − | 0.524311i | \(-0.824323\pi\) | ||
0.851527 | − | 0.524311i | \(-0.175677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.11572e6 | 0.483378 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.80164e6i | − | 1.19667i | −0.801245 | − | 0.598336i | \(-0.795829\pi\) | ||
0.801245 | − | 0.598336i | \(-0.204171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.60663e6 | − | 251940.i | −0.676621 | − | 0.106103i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 978310. | 0.406262 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.18973e6 | −1.71574 | −0.857868 | − | 0.513871i | \(-0.828211\pi\) | ||||
−0.857868 | + | 0.513871i | \(0.828211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.14938e6 | −1.67577 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.38217e6 | −0.550546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3644.97 | + | 23244.1i | −0.00143206 | + | 0.00913232i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.46783e6i | − | 1.34398i | −0.740560 | − | 0.671991i | \(-0.765439\pi\) | ||
0.740560 | − | 0.671991i | \(-0.234561\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.40171e6 | 0.535910 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.09352e6i | − | 0.789664i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.84265e6 | −0.685759 | −0.342880 | − | 0.939379i | \(-0.611402\pi\) | ||||
−0.342880 | + | 0.939379i | \(0.611402\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.98476e6 | + | 1.50355e6i | 1.09605 | + | 0.552128i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.81486e6i | 0.657641i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.94721e6i | − | 1.41154i | −0.708443 | − | 0.705768i | \(-0.750602\pi\) | ||
0.708443 | − | 0.705768i | \(-0.249398\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.07985e6i | 1.08697i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.51953e6i | − | 1.57433i | −0.616741 | − | 0.787166i | \(-0.711547\pi\) | ||
0.616741 | − | 0.787166i | \(-0.288453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.99958e6 | − | 313559.i | −0.687523 | − | 0.107812i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.35548e6 | −0.799470 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5.72440e6i | − | 1.91803i | −0.283353 | − | 0.959016i | \(-0.591447\pi\) | ||
0.283353 | − | 0.959016i | \(-0.408553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −302174. | −0.0999573 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.72273e6i | − | 1.21585i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.72142e6 | − | 269940.i | −0.555129 | − | 0.0870511i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.58558e6 | 0.504909 | 0.252454 | − | 0.967609i | \(-0.418762\pi\) | ||||
0.252454 | + | 0.967609i | \(0.418762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.98304e6 | −1.88144 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.73054e6 | −1.15854 | −0.579269 | − | 0.815136i | \(-0.696662\pi\) | ||||
−0.579269 | + | 0.815136i | \(0.696662\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.02700e6 | −0.928432 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.07624e6 | + | 639205.i | 1.23487 | + | 0.193643i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70501e6i | 0.510199i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.02334e6 | −0.598082 | −0.299041 | − | 0.954240i | \(-0.596667\pi\) | ||||
−0.299041 | + | 0.954240i | \(0.596667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 510936.i | 0.149198i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.98991e6 | −0.574061 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.86914e6 | + | 920355.i | 1.67284 | + | 0.262322i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.69156e6i | − | 0.757990i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.38701e6i | − | 1.49904i | −0.661983 | − | 0.749519i | \(-0.730285\pi\) | ||
0.661983 | − | 0.749519i | \(-0.269715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.52112e6i | 0.418271i | 0.977887 | + | 0.209135i | \(0.0670650\pi\) | ||||
−0.977887 | + | 0.209135i | \(0.932935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 281226.i | 0.0764195i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 402600. | − | 1.25213e6i | 0.108119 | − | 0.336262i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.92143e6 | −1.57165 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 2.77070e6i | − | 0.726852i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −837627. | −0.217199 | −0.108599 | − | 0.994086i | \(-0.534637\pi\) | ||||
−0.108599 | + | 0.994086i | \(0.534637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.25277e6i | − | 0.577426i | −0.957416 | − | 0.288713i | \(-0.906773\pi\) | ||
0.957416 | − | 0.288713i | \(-0.0932274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −618701. | + | 3.94548e6i | −0.156768 | + | 0.999716i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.84800e6 | 0.462912 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.39465e6 | 0.345385 | 0.172692 | − | 0.984976i | \(-0.444753\pi\) | ||||
0.172692 | + | 0.984976i | \(0.444753\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 251535. | 0.0615888 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.67982e6 | 1.37507 | 0.687536 | − | 0.726150i | \(-0.258692\pi\) | ||||
0.687536 | + | 0.726150i | \(0.258692\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.48745e6 | + | 860500.i | 1.31362 | + | 0.205992i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 6.30069e6i | − | 1.49149i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.07534e6 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341724\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.39601e6i | 0.786190i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.56897e6 | −0.588185 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −511371. | + | 3.26103e6i | −0.115800 | + | 0.738459i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.22059e6i | 0.497368i | 0.968585 | + | 0.248684i | \(0.0799980\pi\) | ||||
−0.968585 | + | 0.248684i | \(0.920002\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 966240.i | − | 0.214069i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.18822e6i | − | 0.479556i | −0.970828 | − | 0.239778i | \(-0.922925\pi\) | ||
0.970828 | − | 0.239778i | \(-0.0770747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.23618e6i | − | 1.78556i | −0.450497 | − | 0.892778i | \(-0.648753\pi\) | ||
0.450497 | − | 0.892778i | \(-0.351247\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.58068e6 | − | 1.03193e6i | −1.41136 | − | 0.221319i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.79680e6 | −1.01779 | −0.508897 | − | 0.860827i | \(-0.669947\pi\) | ||||
−0.508897 | + | 0.860827i | \(0.669947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.02042e6i | 0.214213i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.91948e6 | 1.64492 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.70678e6i | − | 1.17284i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.46218e6 | + | 7.65765e6i | −0.500709 | + | 1.55726i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.11938e6 | 0.426495 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.41529e6 | −0.680124 | −0.340062 | − | 0.940403i | \(-0.610448\pi\) | ||||
−0.340062 | + | 0.940403i | \(0.610448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78062e6 | 0.547999 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.66881e6 | 0.325491 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.56170e6 | + | 9.95905e6i | −0.301470 | + | 1.92249i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 922166.i | 0.176192i | 0.996112 | + | 0.0880961i | \(0.0280783\pi\) | ||||
−0.996112 | + | 0.0880961i | \(0.971922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.71289e6 | 1.08040 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.75918e6i | 1.07810i | 0.842275 | + | 0.539048i | \(0.181216\pi\) | ||||
−0.842275 | + | 0.539048i | \(0.818784\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.57171e6 | 0.291243 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 317433. | − | 2.02428e6i | 0.0582290 | − | 0.371329i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.53459e6i | − | 0.641872i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.04215e6i | 0.726709i | 0.931651 | + | 0.363355i | \(0.118369\pi\) | ||||
−0.931651 | + | 0.363355i | \(0.881631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.75807e6i | 0.846909i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.42790e6i | 1.13279i | 0.824134 | + | 0.566395i | \(0.191662\pi\) | ||||
−0.824134 | + | 0.566395i | \(0.808338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.18074e6 | − | 7.52963e6i | 0.206028 | − | 1.31385i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.58463e6 | 0.446559 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.67839e6i | − | 1.48472i | −0.670001 | − | 0.742360i | \(-0.733707\pi\) | ||
0.670001 | − | 0.742360i | \(-0.266293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −51137.1 | −0.00866330 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.90922e6i | 0.991373i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 853535. | − | 5.44303e6i | 0.141809 | − | 0.904321i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −681344. | −0.112109 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.43788e7 | −2.34317 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.06563e6 | 0.656197 | 0.328098 | − | 0.944644i | \(-0.393592\pi\) | ||||
0.328098 | + | 0.944644i | \(0.393592\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.29913e6 | −0.687268 | −0.343634 | − | 0.939104i | \(-0.611658\pi\) | ||||
−0.343634 | + | 0.939104i | \(0.611658\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.22343e6 | + | 6.91513e6i | −0.352067 | + | 1.09497i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.62146e6i | 0.411166i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.92089e6 | 0.919916 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.01449e6i | − | 0.310049i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.53841e6 | 0.844437 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.91563e6 | + | 927645.i | 0.893545 | + | 0.140119i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.25198e7i | 1.87354i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 609410.i | 0.0903520i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 2.98051e6i | − | 0.437821i | −0.975745 | − | 0.218911i | \(-0.929750\pi\) | ||
0.975745 | − | 0.218911i | \(-0.0702503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.32054e6i | − | 0.192199i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.03313e6 | + | 1.29654e7i | −0.293207 | + | 1.86979i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 841980. | 0.120319 | 0.0601594 | − | 0.998189i | \(-0.480839\pi\) | ||||
0.0601594 | + | 0.998189i | \(0.480839\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 5.99458e6i | − | 0.848844i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.61209e6 | −1.34877 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.78712e6i | − | 0.526619i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.04505e6 | + | 947940.i | 0.833043 | + | 0.130632i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.95114e6 | −1.08590 | −0.542952 | − | 0.839764i | \(-0.682693\pi\) | ||||
−0.542952 | + | 0.839764i | \(0.682693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.30695e6 | −1.25973 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.39950e6 | −0.321894 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.88079e6 | 0.648962 | 0.324481 | − | 0.945892i | \(-0.394810\pi\) | ||||
0.324481 | + | 0.945892i | \(0.394810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −238580. | + | 1.52143e6i | −0.0314422 | + | 0.200508i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.96772e6i | 1.17145i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.06257e6 | 0.914497 | 0.457248 | − | 0.889339i | \(-0.348835\pi\) | ||||
0.457248 | + | 0.889339i | \(0.348835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.72095e6i | − | 0.220891i | −0.993882 | − | 0.110445i | \(-0.964772\pi\) | ||
0.993882 | − | 0.110445i | \(-0.0352278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.19128e7 | −1.51575 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 686758. | − | 2.13590e6i | 0.0866232 | − | 0.269408i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.57279e7i | − | 1.96666i | −0.181823 | − | 0.983331i | \(-0.558200\pi\) | ||
0.181823 | − | 0.983331i | \(-0.441800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1.25531e7i | − | 1.55616i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.29121e7i | 1.58693i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.13477e6i | 0.625676i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.30132e6 | − | 517688.i | −0.398839 | − | 0.0625430i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.31369e7 | 1.57361 | 0.786804 | − | 0.617203i | \(-0.211734\pi\) | ||||
0.786804 | + | 0.617203i | \(0.211734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.60320e7i | − | 1.90415i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.56829e6 | 0.891310 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.44213e6i | 1.10264i | 0.834294 | + | 0.551319i | \(0.185875\pi\) | ||||
−0.834294 | + | 0.551319i | \(0.814125\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.82414e6 | + | 442860.i | 0.327034 | + | 0.0512831i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −48113.6 | −0.00552500 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.05602e7 | 1.20256 | 0.601279 | − | 0.799039i | \(-0.294658\pi\) | ||||
0.601279 | + | 0.799039i | \(0.294658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00758e7 | −1.13787 | −0.568937 | − | 0.822381i | \(-0.692645\pi\) | ||||
−0.568937 | + | 0.822381i | \(0.692645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.03302e6 | −0.115696 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.98997e6 | − | 625677.i | −0.443181 | − | 0.0694964i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 4.22464e6i | − | 0.465391i | −0.972550 | − | 0.232696i | \(-0.925245\pi\) | ||
0.972550 | − | 0.232696i | \(-0.0747546\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.68006e6 | −0.948373 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.11118e6i | 0.120415i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.47741e6 | 1.01868 | 0.509341 | − | 0.860565i | \(-0.329889\pi\) | ||||
0.509341 | + | 0.860565i | \(0.329889\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.20405e7 | + | 1.88809e6i | 1.28368 | + | 0.201296i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.41901e7i | 1.50063i | 0.661081 | + | 0.750315i | \(0.270098\pi\) | ||||
−0.661081 | + | 0.750315i | \(0.729902\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.32823e6i | − | 0.768728i | −0.923182 | − | 0.384364i | \(-0.874421\pi\) | ||
0.923182 | − | 0.384364i | \(-0.125579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.64822e6i | − | 0.171509i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.20724e7i | 1.24616i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.93562e6 | + | 5.69151e6i | 0.812608 | + | 0.582811i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.46746e7 | 1.49072 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.40809e6i | − | 0.242687i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.90206e6 | 0.890056 | 0.445028 | − | 0.895517i | \(-0.353194\pi\) | ||||
0.445028 | + | 0.895517i | \(0.353194\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.95101e7i | 1.93531i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.39418e6 | + | 8.89075e6i | −0.137210 | + | 0.874992i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 993862. | 0.0970459 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.57826e6 | 0.346673 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.64056e6 | −0.446093 | −0.223046 | − | 0.974808i | \(-0.571600\pi\) | ||||
−0.223046 | + | 0.974808i | \(0.571600\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.33925e7 | −1.27742 | −0.638712 | − | 0.769446i | \(-0.720533\pi\) | ||||
−0.638712 | + | 0.769446i | \(0.720533\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.02332e7 | − | 3.17282e6i | −1.91499 | − | 0.300294i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.50695e6i | − | 0.705022i | −0.935808 | − | 0.352511i | \(-0.885328\pi\) | ||
0.935808 | − | 0.352511i | \(-0.114672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.88064e6 | 0.454847 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.44775e7i | − | 1.33888i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.28654e6 | 0.852258 | 0.426129 | − | 0.904662i | \(-0.359877\pi\) | ||||
0.426129 | + | 0.904662i | \(0.359877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.68520e6 | − | 1.07466e7i | 0.153479 | − | 0.978740i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 51768.8i | − | 0.00467902i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.14194e6i | − | 0.192130i | −0.995375 | − | 0.0960648i | \(-0.969374\pi\) | ||
0.995375 | − | 0.0960648i | \(-0.0306256\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.13285e6i | 0.456936i | 0.973551 | + | 0.228468i | \(0.0733716\pi\) | ||||
−0.973551 | + | 0.228468i | \(0.926628\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.91324e6i | 0.345742i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.72715e7 | − | 2.70839e6i | −1.51453 | − | 0.237497i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.68104e6 | 0.233339 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 1.69238e6i | − | 0.146195i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.45235e7 | 1.24527 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.02549e7i | 0.872754i | 0.899764 | + | 0.436377i | \(0.143739\pi\) | ||||
−0.899764 | + | 0.436377i | \(0.856261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.82981e6 | + | 2.19600e6i | 0.576965 | + | 0.185512i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.81369e7 | −1.52087 | −0.760433 | − | 0.649416i | \(-0.775013\pi\) | ||||
−0.760433 | + | 0.649416i | \(0.775013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.19099e7 | −1.82375 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.87888e6 | −0.651024 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.29609e7 | 1.06313 | 0.531563 | − | 0.847019i | \(-0.321605\pi\) | ||||
0.531563 | + | 0.847019i | \(0.321605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −231290. | + | 1.47495e6i | −0.0188335 | + | 0.120102i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.41680e7i | 1.95366i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.37408e6 | 0.672031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.77055e7i | 1.41063i | 0.708894 | + | 0.705315i | \(0.249194\pi\) | ||||
−0.708894 | + | 0.705315i | \(0.750806\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.45342e6 | 0.352258 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.21841e6 | − | 7.76986e6i | 0.0956824 | − | 0.610170i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4.79640e6i | − | 0.373967i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 2.32139e7i | − | 1.79703i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.73670e6i | 0.671510i | 0.941949 | + | 0.335755i | \(0.108991\pi\) | ||||
−0.941949 | + | 0.335755i | \(0.891009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.47271e7i | 1.12391i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −378810. | + | 2.41569e6i | −0.0287044 | + | 0.183049i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.65652e7 | 1.24637 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.22402e6i | 0.614425i | 0.951641 | + | 0.307212i | \(0.0993962\pi\) | ||||
−0.951641 | + | 0.307212i | \(0.900604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.83391e6 | 0.284425 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.47171e6i | 0.329420i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.25424e6 | − | 7.99832e6i | 0.0917518 | − | 0.585105i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.09189e7 | 0.793195 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.63870e7 | −1.18216 | −0.591082 | − | 0.806612i | \(-0.701299\pi\) | ||||
−0.591082 | + | 0.806612i | \(0.701299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.19747e7 | 0.857877 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.38639e7 | 0.986373 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.57207e6 | + | 1.11095e7i | −0.252392 | + | 0.784967i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.04002e7i | − | 1.43152i | −0.698346 | − | 0.715760i | \(-0.746080\pi\) | ||
0.698346 | − | 0.715760i | \(-0.253920\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59405e6 | 0.111092 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.06005e6i | 0.557885i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.29292e6 | −0.432606 | −0.216303 | − | 0.976326i | \(-0.569400\pi\) | ||||
−0.216303 | + | 0.976326i | \(0.569400\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.16065e6 | + | 338816.i | 0.147525 | + | 0.0231338i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.50277e6i | − | 0.169728i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.24400e7i | 0.837934i | 0.908002 | + | 0.418967i | \(0.137608\pi\) | ||||
−0.908002 | + | 0.418967i | \(0.862392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.39321e7i | − | 1.60117i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.80211e7i | 1.19759i | 0.800901 | + | 0.598796i | \(0.204354\pi\) | ||||
−0.800901 | + | 0.598796i | \(0.795646\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.85219e6 | − | 1.81885e7i | 0.188273 | − | 1.20062i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.30716e7 | −0.857094 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.30144e7i | 0.847655i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.44062e7 | −0.932074 | −0.466037 | − | 0.884765i | \(-0.654319\pi\) | ||||
−0.466037 | + | 0.884765i | \(0.654319\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.07526e7i | 0.691075i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.41599e6 | − | 1.16292e6i | −0.473480 | − | 0.0742476i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.45449e6 | 0.409376 | 0.204688 | − | 0.978827i | \(-0.434382\pi\) | ||||
0.204688 | + | 0.978827i | \(0.434382\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.09308e6 | −0.257897 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.63016e7 | 1.64635 | 0.823173 | − | 0.567791i | \(-0.192202\pi\) | ||||
0.823173 | + | 0.567791i | \(0.192202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.85238e7 | −1.77376 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −448331. | + | 2.85903e6i | −0.0276978 | + | 0.176630i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7.95964e6i | − | 0.488546i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.12180e6 | 0.0684070 | 0.0342035 | − | 0.999415i | \(-0.489111\pi\) | ||||
0.0342035 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.68006e6i | 0.525880i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.26128e7 | 0.759213 | 0.379607 | − | 0.925148i | \(-0.376059\pi\) | ||||
0.379607 | + | 0.925148i | \(0.376059\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.85297e7 | − | 5.95787e6i | −1.10819 | − | 0.356317i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.32991e7i | 0.790260i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.93333e7i | 1.73188i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.66927e6i | 0.508575i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.57297e6i | 0.499720i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.28616e7 | + | 3.58498e6i | 1.32413 | + | 0.207641i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.48088e7 | −1.42781 | −0.713904 | − | 0.700244i | \(-0.753075\pi\) | ||||
−0.713904 | + | 0.700244i | \(0.753075\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.63050e7i | − | 2.07622i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.34715e6 | −0.190210 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.36857e7i | − | 1.33753i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.82052e7 | + | 2.85480e6i | 1.02159 | + | 0.160198i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.93080e7 | −1.07669 | −0.538346 | − | 0.842724i | \(-0.680951\pi\) | ||||
−0.538346 | + | 0.842724i | \(0.680951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 962307. | 0.0533269 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.22215e7 | −0.673045 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 125424. | 0.00686421 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.81743e6 | + | 755434.i | 0.262015 | + | 0.0410872i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.53543e6i | − | 0.353257i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 177650. | 0.00954320 | 0.00477160 | − | 0.999989i | \(-0.498481\pi\) | ||||
0.00477160 | + | 0.999989i | \(0.498481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.14345e7i | − | 0.610470i | −0.952277 | − | 0.305235i | \(-0.901265\pi\) | ||
0.952277 | − | 0.305235i | \(-0.0987350\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.01082e7 | 0.536350 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.64917e7 | + | 2.58611e6i | 0.869704 | + | 0.136380i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.92928e7i | − | 2.58362i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 7.26290e6i | − | 0.378356i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.67695e6i | − | 0.190384i | −0.995459 | − | 0.0951920i | \(-0.969654\pi\) | ||
0.995459 | − | 0.0951920i | \(-0.0303465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.62394e7i | − | 1.35038i | −0.737646 | − | 0.675188i | \(-0.764063\pi\) | ||
0.737646 | − | 0.675188i | \(-0.235937\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.45340e6 | − | 1.69607e7i | 0.278954 | − | 0.867579i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.67039e6 | 0.339147 | 0.169573 | − | 0.985518i | \(-0.445761\pi\) | ||||
0.169573 | + | 0.985518i | \(0.445761\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.11275e6i | 0.460535i | 0.973127 | + | 0.230268i | \(0.0739602\pi\) | ||||
−0.973127 | + | 0.230268i | \(0.926040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.32259e7 | −0.664390 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 860709.i | − | 0.0429778i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.15388e6 | + | 1.37354e7i | −0.106907 | + | 0.681748i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.42989e7 | −0.705486 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.00667e7 | 0.984171 | 0.492085 | − | 0.870547i | \(-0.336235\pi\) | ||||
0.492085 | + | 0.870547i | \(0.336235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.56614e6 | 0.320125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.41767e6 | −0.359500 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.46120e6 | + | 1.17001e6i | 0.359473 | + | 0.0563699i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.77794e6i | − | 0.420421i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.98171e6 | 0.189584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.10774e6i | − | 0.194437i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.94245e7 | 1.85521 | 0.927605 | − | 0.373561i | \(-0.121863\pi\) | ||||
0.927605 | + | 0.373561i | \(0.121863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.74185e6 | − | 1.74849e7i | 0.128271 | − | 0.817991i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.62668e7i | 1.68678i | 0.537306 | + | 0.843388i | \(0.319442\pi\) | ||||
−0.537306 | + | 0.843388i | \(0.680558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.42739e7i | 0.660025i | 0.943977 | + | 0.330012i | \(0.107053\pi\) | ||||
−0.943977 | + | 0.330012i | \(0.892947\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.64890e7i | 1.21775i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.33238e6i | 0.289428i | 0.989474 | + | 0.144714i | \(0.0462262\pi\) | ||||
−0.989474 | + | 0.144714i | \(0.953774\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.15081e7 | − | 6.50898e6i | −1.88622 | − | 0.295783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.37745e7 | −1.07415 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.28866e6i | 0.417257i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.08167e6 | −0.182302 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.21806e7i | − | 0.985003i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.54882e6 | + | 1.89558e7i | −0.421628 | + | 0.836991i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.21218e7 | 0.971229 | 0.485614 | − | 0.874173i | \(-0.338596\pi\) | ||||
0.485614 | + | 0.874173i | \(0.338596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.91942e7 | 1.71100 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.31837e7 | −1.44040 | −0.720202 | − | 0.693764i | \(-0.755951\pi\) | ||||
−0.720202 | + | 0.693764i | \(0.755951\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.60307e7 | −1.12353 | −0.561764 | − | 0.827298i | \(-0.689877\pi\) | ||||
−0.561764 | + | 0.827298i | \(0.689877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.71351e6 | − | 1.73042e7i | 0.116459 | − | 0.742665i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 7.63560e6i | − | 0.325862i | −0.986637 | − | 0.162931i | \(-0.947905\pi\) | ||
0.986637 | − | 0.162931i | \(-0.0520949\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.95597e7 | −0.830055 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.19951e7i | − | 0.928178i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.88517e6 | −0.246962 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.66746e6 | + | 3.61416e7i | −0.236500 | + | 1.50817i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.67523e6i | 0.277004i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.32589e7i | − | 0.959821i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.25217e6i | − | 0.297616i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.45131e7i | − | 1.81664i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 597780. | − | 3.81207e6i | 0.0242616 | − | 0.154717i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.88224e7 | −1.16335 | −0.581677 | − | 0.813420i | \(-0.697603\pi\) | ||||
−0.581677 | + | 0.813420i | \(0.697603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.67698e7i | 0.673161i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.97947e6 | −0.158865 | −0.0794327 | − | 0.996840i | \(-0.525311\pi\) | ||||
−0.0794327 | + | 0.996840i | \(0.525311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3.16695e7i | − | 1.25737i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.07467e6 | − | 5.14925e7i | 0.318840 | − | 2.03325i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.36425e7 | 0.928474 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.36872e6 | 0.326866 | 0.163433 | − | 0.986554i | \(-0.447743\pi\) | ||||
0.163433 | + | 0.986554i | \(0.447743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.67924e7 | −0.652326 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.41384e7 | 0.546254 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.70215e7 | + | 5.47293e6i | 0.654097 | + | 0.210313i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.21226e7i | 0.463337i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.07236e7 | −0.407662 | −0.203831 | − | 0.979006i | \(-0.565339\pi\) | ||||
−0.203831 | + | 0.979006i | \(0.565339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.26383e6i | 0.199034i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.67099e7 | −2.13282 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.92675e6 | − | 1.08620e6i | −0.259120 | − | 0.0406332i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.87357e7i | − | 0.697141i | −0.937283 | − | 0.348570i | \(-0.886667\pi\) | ||
0.937283 | − | 0.348570i | \(-0.113333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.03443e7i | 1.12309i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.01934e7i | − | 1.11157i | −0.831326 | − | 0.555786i | \(-0.812418\pi\) | ||
0.831326 | − | 0.555786i | \(-0.187582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.18174e6i | − | 0.299617i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.41560e6 | + | 1.54044e7i | −0.0879925 | + | 0.561132i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.26775e7 | −0.459365 | −0.229683 | − | 0.973266i | \(-0.573769\pi\) | ||||
−0.229683 | + | 0.973266i | \(0.573769\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 204548.i | − | 0.00737276i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.44418e7 | −0.517809 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.17212e7i | − | 1.13140i | −0.824610 | − | 0.565702i | \(-0.808605\pi\) | ||
0.824610 | − | 0.565702i | \(-0.191395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.43893e7 | − | 5.39268e6i | −1.22016 | − | 0.191336i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.12895e7 | 0.751426 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.24488e6 | −0.113934 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.01645e7 | 0.355040 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.31752e7 | −0.457815 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.68251e6 | − | 3.62376e7i | 0.196436 | − | 1.25268i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.25308e7i | − | 1.46264i | −0.682034 | − | 0.731320i | \(-0.738904\pi\) | ||
0.682034 | − | 0.731320i | \(-0.261096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.07258e7 | −0.709092 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.55507e7i | − | 0.869671i | −0.900510 | − | 0.434836i | \(-0.856806\pi\) | ||
0.900510 | − | 0.434836i | \(-0.143194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.70937e7 | 0.578834 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.76605e7 | − | 8.89372e6i | −0.931855 | − | 0.299621i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 9.11824e6i | − | 0.305615i | −0.988256 | − | 0.152807i | \(-0.951169\pi\) | ||
0.988256 | − | 0.152807i | \(-0.0488314\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.96099e7i | − | 0.987370i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.88762e7i | − | 0.958004i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.75759e7i | − | 0.910218i | −0.890436 | − | 0.455109i | \(-0.849600\pi\) | ||
0.890436 | − | 0.455109i | \(-0.150400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.18478e7 | + | 3.42600e6i | 0.717491 | + | 0.112512i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.31451e6 | −0.173648 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.37489e7i | 0.446969i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.53539e7 | 0.820089 | 0.410045 | − | 0.912065i | \(-0.365513\pi\) | ||||
0.410045 | + | 0.912065i | \(0.365513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.71576e6i | 0.119584i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −138892. | − | 21780.0i | −0.00444754 | − | 0.000697429i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.16445e7 | −0.371006 | −0.185503 | − | 0.982644i | \(-0.559392\pi\) | ||||
−0.185503 | + | 0.982644i | \(0.559392\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.31350e7 | 0.416407 |
(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.f.b.289.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 320.6.f.b.289.5 | yes | 8 | |
5.4 | even | 2 | inner | 320.6.f.b.289.7 | yes | 8 | |
8.3 | odd | 2 | inner | 320.6.f.b.289.4 | yes | 8 | |
8.5 | even | 2 | inner | 320.6.f.b.289.8 | yes | 8 | |
20.19 | odd | 2 | inner | 320.6.f.b.289.3 | yes | 8 | |
40.19 | odd | 2 | inner | 320.6.f.b.289.6 | yes | 8 | |
40.29 | even | 2 | inner | 320.6.f.b.289.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.f.b.289.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
320.6.f.b.289.2 | yes | 8 | 40.29 | even | 2 | inner | |
320.6.f.b.289.3 | yes | 8 | 20.19 | odd | 2 | inner | |
320.6.f.b.289.4 | yes | 8 | 8.3 | odd | 2 | inner | |
320.6.f.b.289.5 | yes | 8 | 4.3 | odd | 2 | inner | |
320.6.f.b.289.6 | yes | 8 | 40.19 | odd | 2 | inner | |
320.6.f.b.289.7 | yes | 8 | 5.4 | even | 2 | inner | |
320.6.f.b.289.8 | yes | 8 | 8.5 | even | 2 | inner |