Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not 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: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{3}]$ |
Embedding invariants
Embedding label | 18.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.6.c.a.30.1 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.50000 | − | 9.52628i | −0.972272 | − | 1.68402i | −0.688659 | − | 0.725085i | \(-0.741800\pi\) |
−0.283613 | − | 0.958939i | \(-0.591533\pi\) | |||||||
\(3\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(4\) | −44.5000 | + | 77.0763i | −1.39062 | + | 2.40863i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 627.000 | 3.46372 | ||||||||
\(9\) | 121.500 | + | 210.444i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 38.0000 | − | 65.8179i | 0.0946895 | − | 0.164007i | −0.814789 | − | 0.579757i | \(-0.803148\pi\) |
0.909479 | + | 0.415750i | \(0.136481\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2024.50 | − | 3506.54i | −1.97705 | − | 3.42435i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 1336.50 | − | 2314.89i | 0.972272 | − | 1.68402i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −836.000 | −0.368256 | ||||||||
\(23\) | 2476.00 | + | 4288.56i | 0.975958 | + | 1.69041i | 0.676737 | + | 0.736225i | \(0.263393\pi\) |
0.299220 | + | 0.954184i | \(0.403273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1562.50 | − | 2706.33i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7282.00 | 1.60789 | 0.803944 | − | 0.594705i | \(-0.202731\pi\) | ||||
0.803944 | + | 0.594705i | \(0.202731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | −12237.5 | + | 21196.0i | −2.11260 | + | 3.65913i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −21627.0 | −2.78125 | ||||||||
\(37\) | 4443.00 | + | 7695.50i | 0.533546 | + | 0.924129i | 0.999232 | + | 0.0391791i | \(0.0124743\pi\) |
−0.465686 | + | 0.884950i | \(0.654192\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11748.0 | 0.968931 | 0.484465 | − | 0.874810i | \(-0.339014\pi\) | ||||
0.484465 | + | 0.874810i | \(0.339014\pi\) | |||||||
\(44\) | 3382.00 | + | 5857.80i | 0.263355 | + | 0.456145i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 27236.0 | − | 47174.1i | 1.89779 | − | 3.28707i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −34375.0 | −1.94454 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12275.0 | + | 21260.9i | −0.600250 | + | 1.03966i | 0.392533 | + | 0.919738i | \(0.371599\pi\) |
−0.992783 | + | 0.119925i | \(0.961735\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −40051.0 | − | 69370.4i | −1.56330 | − | 2.70772i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 139657. | 4.26199 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34682.0 | + | 60071.0i | −0.943881 | + | 1.63485i | −0.185904 | + | 0.982568i | \(0.559521\pi\) |
−0.757977 | + | 0.652281i | \(0.773812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2224.00 | −0.0523587 | −0.0261794 | − | 0.999657i | \(-0.508334\pi\) | ||||
−0.0261794 | + | 0.999657i | \(0.508334\pi\) | |||||||
\(72\) | 76180.5 | + | 131948.i | 1.73186 | + | 2.99967i | ||||
\(73\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(74\) | 48873.0 | − | 84650.5i | 1.03750 | − | 1.79701i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40084.0 | − | 69427.5i | −0.722609 | − | 1.25160i | −0.959951 | − | 0.280169i | \(-0.909609\pi\) |
0.237342 | − | 0.971426i | \(-0.423724\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29524.5 | + | 51137.9i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −64614.0 | − | 111915.i | −0.942064 | − | 1.63170i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23826.0 | − | 41267.8i | 0.327978 | − | 0.568074i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −440728. | −5.42877 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18468.0 | 0.189379 | ||||||||
\(100\) | 139062. | + | 240863.i | 1.39062 | + | 2.40863i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 270050. | 2.33442 | ||||||||
\(107\) | 32450.0 | + | 56205.0i | 0.274003 | + | 0.474587i | 0.969883 | − | 0.243571i | \(-0.0783189\pi\) |
−0.695880 | + | 0.718158i | \(0.744986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 109791. | − | 190164.i | 0.885117 | − | 1.53307i | 0.0395367 | − | 0.999218i | \(-0.487412\pi\) |
0.845580 | − | 0.533849i | \(-0.179255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 123202. | 0.907657 | 0.453828 | − | 0.891089i | \(-0.350058\pi\) | ||||
0.453828 | + | 0.891089i | \(0.350058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −324049. | + | 561269.i | −2.23597 | + | 3.87281i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77637.5 | + | 134472.i | 0.482068 | + | 0.834966i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −262064. | −1.44178 | −0.720888 | − | 0.693051i | \(-0.756266\pi\) | ||||
−0.720888 | + | 0.693051i | \(0.756266\pi\) | |||||||
\(128\) | −376514. | − | 652141.i | −2.03121 | − | 3.51817i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 763004. | 3.67083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 176725. | − | 306097.i | 0.804445 | − | 1.39334i | −0.112219 | − | 0.993683i | \(-0.535796\pi\) |
0.916665 | − | 0.399657i | \(-0.130871\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12232.0 | + | 21186.4i | 0.0509069 | + | 0.0881733i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 491954. | − | 852088.i | 1.97705 | − | 3.42435i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −790854. | −2.96785 | ||||||||
\(149\) | 168509. | + | 291866.i | 0.621810 | + | 1.07701i | 0.989149 | + | 0.146919i | \(0.0469356\pi\) |
−0.367339 | + | 0.930087i | \(0.619731\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 130812. | − | 226573.i | 0.466880 | − | 0.808660i | −0.532404 | − | 0.846490i | \(-0.678711\pi\) |
0.999284 | + | 0.0378305i | \(0.0120447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(158\) | −440924. | + | 763703.i | −1.40514 | + | 2.43378i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 649539. | 1.94454 | ||||||||
\(163\) | −331550. | − | 574261.i | −0.977417 | − | 1.69294i | −0.671716 | − | 0.740809i | \(-0.734442\pi\) |
−0.305702 | − | 0.952127i | \(-0.598891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −371293. | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −522786. | + | 905492.i | −1.34742 | + | 2.33380i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −307724. | −0.748824 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −292282. | + | 506247.i | −0.681820 | + | 1.18095i | 0.292605 | + | 0.956233i | \(0.405478\pi\) |
−0.974425 | + | 0.224713i | \(0.927856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.55245e6 | + | 2.68893e6i | 3.38044 | + | 5.85510i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −501524. | − | 868665.i | −0.994737 | − | 1.72294i | −0.586102 | − | 0.810237i | \(-0.699338\pi\) |
−0.408635 | − | 0.912698i | \(-0.633995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 192951. | − | 334201.i | 0.372867 | − | 0.645824i | −0.617138 | − | 0.786855i | \(-0.711708\pi\) |
0.990005 | + | 0.141030i | \(0.0450415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 385814. | 0.708292 | 0.354146 | − | 0.935190i | \(-0.384772\pi\) | ||||
0.354146 | + | 0.935190i | \(0.384772\pi\) | |||||||
\(198\) | −101574. | − | 175931.i | −0.184128 | − | 0.318919i | ||||
\(199\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(200\) | 979688. | − | 1.69687e6i | 1.73186 | − | 2.99967i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −601668. | + | 1.04212e6i | −0.975958 | + | 1.69041i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09705e6 | −1.69637 | −0.848186 | − | 0.529699i | \(-0.822305\pi\) | ||||
−0.848186 | + | 0.529699i | \(0.822305\pi\) | |||||||
\(212\) | −1.09248e6 | − | 1.89222e6i | −1.66944 | − | 2.89156i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 356950. | − | 618256.i | 0.532811 | − | 0.922855i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.41540e6 | −3.44230 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 759375. | 1.00000 | ||||||||
\(226\) | −677611. | − | 1.17366e6i | −0.882489 | − | 1.52852i | ||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.56581e6 | 5.56927 | ||||||||
\(233\) | 639749. | + | 1.10808e6i | 0.772004 | + | 1.33715i | 0.936463 | + | 0.350767i | \(0.114079\pi\) |
−0.164458 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 723536. | 0.819342 | 0.409671 | − | 0.912233i | \(-0.365643\pi\) | ||||
0.409671 | + | 0.912233i | \(0.365643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(242\) | 854012. | − | 1.47919e6i | 0.937402 | − | 1.62363i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 376352. | 0.369652 | ||||||||
\(254\) | 1.44135e6 | + | 2.49649e6i | 1.40180 | + | 2.42799i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.90714e6 | + | 3.30326e6i | −1.81879 | + | 3.15023i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 884763. | + | 1.53245e6i | 0.803944 | + | 1.39247i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −765776. | + | 1.32636e6i | −0.682672 | + | 1.18242i | 0.291490 | + | 0.956574i | \(0.405849\pi\) |
−0.974162 | + | 0.225849i | \(0.927484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.08670e6 | − | 5.34632e6i | −2.62517 | − | 4.54692i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.88795e6 | −3.12856 | ||||||||
\(275\) | −118750. | − | 205681.i | −0.0946895 | − | 0.164007i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27572e6 | − | 2.20962e6i | 0.998982 | − | 1.73029i | 0.460423 | − | 0.887700i | \(-0.347698\pi\) |
0.538559 | − | 0.842588i | \(-0.318969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.54797e6 | 1.92499 | 0.962497 | − | 0.271294i | \(-0.0874515\pi\) | ||||
0.962497 | + | 0.271294i | \(0.0874515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(284\) | 98968.0 | − | 171418.i | 0.0728113 | − | 0.126113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.94742e6 | −4.22520 | ||||||||
\(289\) | 709928. | + | 1.22963e6i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.78576e6 | + | 4.82508e6i | 1.84805 | + | 3.20092i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.85360e6 | − | 3.21053e6i | 1.20914 | − | 2.09428i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.87786e6 | −1.81574 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.13495e6 | 4.01951 | ||||||||
\(317\) | 110857. | + | 192010.i | 0.0619605 | + | 0.107319i | 0.895342 | − | 0.445380i | \(-0.146931\pi\) |
−0.833381 | + | 0.552699i | \(0.813598\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 276716. | − | 479286.i | 0.152250 | − | 0.263705i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.62768e6 | − | 4.55128e6i | −1.39062 | − | 2.40863i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.64705e6 | + | 6.31688e6i | −1.90063 | + | 3.29199i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48574e6 | − | 2.57337e6i | −0.745371 | − | 1.29102i | −0.950021 | − | 0.312185i | \(-0.898939\pi\) |
0.204651 | − | 0.978835i | \(-0.434394\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.07965e6 | + | 1.87001e6i | −0.533546 | + | 0.924129i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.15965e6 | −1.99518 | −0.997590 | − | 0.0693859i | \(-0.977896\pi\) | ||||
−0.997590 | + | 0.0693859i | \(0.977896\pi\) | |||||||
\(338\) | 2.04211e6 | + | 3.53704e6i | 0.972272 | + | 1.68402i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.36600e6 | 3.35610 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.14908e6 | + | 1.99027e6i | −0.512304 | + | 0.887336i | 0.487595 | + | 0.873070i | \(0.337874\pi\) |
−0.999898 | + | 0.0142656i | \(0.995459\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 930050. | + | 1.61089e6i | 0.400083 | + | 0.692963i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.43020e6 | 2.65166 | ||||||||
\(359\) | −2.13448e6 | − | 3.69703e6i | −0.874091 | − | 1.51397i | −0.857728 | − | 0.514104i | \(-0.828124\pi\) |
−0.0163636 | − | 0.999866i | \(-0.505209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23805e6 | − | 2.14436e6i | 0.500000 | − | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(368\) | 1.00253e7 | − | 1.73644e7i | 3.85904 | − | 6.68405i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −299651. | − | 519011.i | −0.111518 | − | 0.193154i | 0.804865 | − | 0.593458i | \(-0.202238\pi\) |
−0.916382 | + | 0.400304i | \(0.868904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.59273e6 | −1.99998 | −0.999991 | − | 0.00429827i | \(-0.998632\pi\) | ||||
−0.999991 | + | 0.00429827i | \(0.998632\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.51676e6 | + | 9.55532e6i | −1.93431 | + | 3.35032i | ||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.24492e6 | −1.45011 | ||||||||
\(387\) | 1.42738e6 | + | 2.47230e6i | 0.484465 | + | 0.839119i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 630059. | − | 1.09129e6i | 0.211109 | − | 0.365652i | −0.740953 | − | 0.671557i | \(-0.765626\pi\) |
0.952062 | + | 0.305905i | \(0.0989591\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.12198e6 | − | 3.67537e6i | −0.688652 | − | 1.19278i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −821826. | + | 1.42344e6i | −0.263355 | + | 0.456145i | ||||
\(397\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.26531e7 | −3.95410 | ||||||||
\(401\) | −3.01646e6 | − | 5.22467e6i | −0.936779 | − | 1.62255i | −0.771431 | − | 0.636313i | \(-0.780459\pi\) |
−0.165348 | − | 0.986235i | \(-0.552875\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 675336. | 0.202085 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.32367e7 | 3.79559 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.07477e6 | 0.570513 | 0.285257 | − | 0.958451i | \(-0.407921\pi\) | ||||
0.285257 | + | 0.958451i | \(0.407921\pi\) | |||||||
\(422\) | 6.03379e6 | + | 1.04508e7i | 1.64933 | + | 2.85673i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.69643e6 | + | 1.33306e7i | −2.07910 | + | 3.60110i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.77610e6 | −1.52414 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.66942e6 | − | 6.35563e6i | 0.951491 | − | 1.64803i | 0.209290 | − | 0.977854i | \(-0.432885\pi\) |
0.742201 | − | 0.670177i | \(-0.233782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.77140e6 | + | 1.69246e7i | 2.46173 | + | 4.26384i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.55245e6 | + | 4.42097e6i | 0.617942 | + | 1.07031i | 0.989861 | + | 0.142042i | \(0.0453668\pi\) |
−0.371918 | + | 0.928265i | \(0.621300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.99808e6 | 0.467732 | 0.233866 | − | 0.972269i | \(-0.424862\pi\) | ||||
0.233866 | + | 0.972269i | \(0.424862\pi\) | |||||||
\(450\) | −4.17656e6 | − | 7.23402e6i | −0.972272 | − | 1.68402i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.48249e6 | + | 9.49595e6i | −1.26221 | + | 2.18621i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.88984e6 | + | 5.00535e6i | 0.647267 | + | 1.12110i | 0.983773 | + | 0.179419i | \(0.0574216\pi\) |
−0.336505 | + | 0.941682i | \(0.609245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.88620e6 | 0.625711 | 0.312856 | − | 0.949801i | \(-0.398714\pi\) | ||||
0.312856 | + | 0.949801i | \(0.398714\pi\) | |||||||
\(464\) | −1.47424e7 | − | 2.55346e7i | −3.17888 | − | 5.50597i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.03724e6 | − | 1.21889e7i | 1.50120 | − | 2.60015i | ||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 446424. | − | 773229.i | 0.0917476 | − | 0.158911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.96565e6 | −1.20050 | ||||||||
\(478\) | −3.97945e6 | − | 6.89261e6i | −0.796623 | − | 1.37979i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.38195e7 | −2.68150 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.38073e6 | − | 2.39150e6i | 0.263807 | − | 0.456928i | −0.703443 | − | 0.710752i | \(-0.748355\pi\) |
0.967250 | + | 0.253824i | \(0.0816883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.82732e6 | 1.65244 | 0.826219 | − | 0.563349i | \(-0.190487\pi\) | ||||
0.826219 | + | 0.563349i | \(0.190487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.56018e6 | + | 9.63052e6i | 0.999626 | + | 1.73140i | 0.523489 | + | 0.852032i | \(0.324630\pi\) |
0.476137 | + | 0.879371i | \(0.342037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.06994e6 | − | 3.58523e6i | −0.359402 | − | 0.622503i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.16618e7 | − | 2.01989e7i | 2.00497 | − | 3.47271i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.78601e7 | 3.01099 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 9.73239e6 | − | 1.68570e7i | 1.56330 | − | 2.70772i | ||||
\(523\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.68471e7 | 2.65497 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.04298e6 | + | 1.56629e7i | −1.40499 | + | 2.43351i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.17456e7 | + | 3.76645e7i | −3.26934 | + | 5.66266i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.56306e6 | − | 9.63551e6i | −0.817186 | − | 1.41541i | −0.907748 | − | 0.419517i | \(-0.862200\pi\) |
0.0905619 | − | 0.995891i | \(-0.471134\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.23604e6 | −0.319529 | −0.159765 | − | 0.987155i | \(-0.551074\pi\) | ||||
−0.159765 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(548\) | 1.57285e7 | + | 2.72426e7i | 2.23736 | + | 3.87523i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.30625e6 | + | 2.26249e6i | −0.184128 | + | 0.318919i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.80660e7 | −3.88513 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.11974e6 | + | 5.40355e6i | −0.426070 | + | 0.737975i | −0.996520 | − | 0.0833578i | \(-0.973436\pi\) |
0.570450 | + | 0.821332i | \(0.306769\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.40139e7 | − | 2.42727e7i | −1.87162 | − | 3.24174i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.39445e6 | −0.181356 | ||||||||
\(569\) | −5.23689e6 | − | 9.07056e6i | −0.678099 | − | 1.17450i | −0.975553 | − | 0.219765i | \(-0.929471\pi\) |
0.297454 | − | 0.954736i | \(-0.403862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.16956e6 | + | 5.48984e6i | −0.406826 | + | 0.704644i | −0.994532 | − | 0.104431i | \(-0.966698\pi\) |
0.587706 | + | 0.809075i | \(0.300031\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.54750e7 | 1.95192 | ||||||||
\(576\) | 1.69683e7 | + | 2.93900e7i | 2.13100 | + | 3.69099i | ||||
\(577\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(578\) | 7.80921e6 | − | 1.35260e7i | 0.972272 | − | 1.68402i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 932900. | + | 1.61583e6i | 0.113675 | + | 0.196890i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.79897e7 | − | 3.11591e7i | 2.10970 | − | 3.65410i | ||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.99946e7 | −3.45882 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.58878e6 | − | 6.21596e6i | 0.408677 | − | 0.707849i | −0.586065 | − | 0.810264i | \(-0.699324\pi\) |
0.994742 | + | 0.102415i | \(0.0326569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.68555e7 | −1.88776 | ||||||||
\(604\) | 1.16423e7 | + | 2.01650e7i | 1.29851 | + | 2.24909i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.77570e6 | + | 1.52000e7i | −0.943258 | + | 1.63377i | −0.184057 | + | 0.982916i | \(0.558923\pi\) |
−0.759201 | + | 0.650856i | \(0.774410\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.14899e6 | −0.756017 | −0.378008 | − | 0.925802i | \(-0.623391\pi\) | ||||
−0.378008 | + | 0.925802i | \(0.623391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.88281e6 | − | 8.45728e6i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.99786e7 | 1.99752 | 0.998760 | − | 0.0497844i | \(-0.0158534\pi\) | ||||
0.998760 | + | 0.0497844i | \(0.0158534\pi\) | |||||||
\(632\) | −2.51327e7 | − | 4.35311e7i | −2.50291 | − | 4.33517i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.21943e6 | − | 2.11211e6i | 0.120485 | − | 0.208686i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.08775e6 | −0.592114 | ||||||||
\(639\) | −270216. | − | 468028.i | −0.0261794 | − | 0.0453440i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.74814e6 | − | 9.95607e6i | 0.552563 | − | 0.957068i | −0.445525 | − | 0.895269i | \(-0.646983\pi\) |
0.998089 | − | 0.0617984i | \(-0.0196836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | −1.85119e7 | + | 3.20635e7i | −1.73186 | + | 2.99967i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.90159e7 | 5.43688 | ||||||||
\(653\) | −5.48862e6 | − | 9.50658e6i | −0.503710 | − | 0.872451i | −0.999991 | − | 0.00428929i | \(-0.998635\pi\) |
0.496281 | − | 0.868162i | \(-0.334699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.02232e7 | −1.81400 | −0.907000 | − | 0.421131i | \(-0.861633\pi\) | ||||
−0.907000 | + | 0.421131i | \(0.861633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | −1.63431e7 | + | 2.83071e7i | −1.44941 | + | 2.51044i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.37523e7 | 2.07501 | ||||||||
\(667\) | 1.80302e7 | + | 3.12293e7i | 1.56923 | + | 2.71799i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.38435e6 | 0.117817 | 0.0589085 | − | 0.998263i | \(-0.481238\pi\) | ||||
0.0589085 | + | 0.998263i | \(0.481238\pi\) | |||||||
\(674\) | 2.28781e7 | + | 3.96260e7i | 1.93986 | + | 3.35993i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.65225e7 | − | 2.86179e7i | 1.39062 | − | 2.40863i | ||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.06574e7 | − | 1.84592e7i | 0.874179 | − | 1.51412i | 0.0165451 | − | 0.999863i | \(-0.494733\pi\) |
0.857634 | − | 0.514260i | \(-0.171933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.37838e7 | − | 4.11948e7i | −1.91563 | − | 3.31796i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.52798e7 | 1.99239 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.88600e6 | 0.375542 | 0.187771 | − | 0.982213i | \(-0.439874\pi\) | ||||
0.187771 | + | 0.982213i | \(0.439874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.30697e6 | − | 9.19193e6i | 0.403566 | − | 0.698997i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.16124e6 | + | 1.24036e7i | 0.535023 | + | 0.926688i | 0.999162 | + | 0.0409253i | \(0.0130306\pi\) |
−0.464139 | + | 0.885763i | \(0.653636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.74041e6 | − | 1.68709e7i | 0.722609 | − | 1.25160i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.60131e7 | − | 4.50560e7i | −1.89631 | − | 3.28451i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.34793e7 | + | 4.06674e7i | −1.69971 | + | 2.94398i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.72371e7 | −1.94454 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13781e7 | − | 1.97075e7i | 0.803944 | − | 1.39247i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.21200e8 | −8.24724 | ||||||||
\(737\) | 2.63583e6 | + | 4.56539e6i | 0.178751 | + | 0.309606i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.32447e6 | − | 2.29404e6i | 0.0892133 | − | 0.154522i | −0.817966 | − | 0.575267i | \(-0.804898\pi\) |
0.907179 | + | 0.420745i | \(0.138231\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.49502e7 | 1.65807 | 0.829033 | − | 0.559199i | \(-0.188891\pi\) | ||||
0.829033 | + | 0.559199i | \(0.188891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.29616e6 | + | 5.70912e6i | −0.216851 | + | 0.375597i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.25544e7 | − | 2.17448e7i | −0.812260 | − | 1.40688i | −0.911278 | − | 0.411791i | \(-0.864903\pi\) |
0.0990181 | − | 0.995086i | \(-0.468430\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.78870e7 | −1.13448 | −0.567242 | − | 0.823551i | \(-0.691989\pi\) | ||||
−0.567242 | + | 0.823551i | \(0.691989\pi\) | |||||||
\(758\) | 3.07600e7 | + | 5.32779e7i | 1.94453 | + | 3.36802i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.92713e7 | 5.53322 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.71726e7 | + | 2.97439e7i | 1.03704 | + | 1.79620i | ||||
\(773\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(774\) | 1.57012e7 | − | 2.71953e7i | 0.942064 | − | 1.63170i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.38613e7 | −0.821022 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −84512.0 | + | 146379.i | −0.00495782 | + | 0.00858720i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(788\) | −1.71687e7 | + | 2.97371e7i | −0.984969 | + | 1.70602i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.15794e7 | 0.655956 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.82422e7 | + | 6.62374e7i | 2.11260 | + | 3.65913i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.31811e7 | + | 5.74713e7i | −1.82161 | + | 3.15512i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.18534e6 | + | 1.59095e7i | −0.493428 | + | 0.854643i | −0.999971 | − | 0.00757189i | \(-0.997590\pi\) |
0.506543 | + | 0.862215i | \(0.330923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.71435e6 | − | 6.43344e6i | −0.196481 | − | 0.340316i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.77941e7 | − | 3.08202e7i | −0.921334 | − | 1.59580i | −0.797354 | − | 0.603512i | \(-0.793768\pi\) |
−0.123980 | − | 0.992285i | \(-0.539566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.54338e6 | + | 6.13731e6i | −0.182355 | + | 0.315848i | −0.942682 | − | 0.333692i | \(-0.891705\pi\) |
0.760327 | + | 0.649540i | \(0.225039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.68552e7 | −1.87385 | −0.936926 | − | 0.349527i | \(-0.886342\pi\) | ||||
−0.936926 | + | 0.349527i | \(0.886342\pi\) | |||||||
\(828\) | −5.35485e7 | − | 9.27486e7i | −2.71438 | − | 4.70145i | ||||
\(829\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.25164e7 | 1.58530 | ||||||||
\(842\) | −1.14113e7 | − | 1.97649e7i | −0.554694 | − | 0.960758i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.88188e7 | − | 8.45567e7i | 2.35902 | − | 4.08594i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.94030e7 | 4.74690 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.20017e7 | + | 3.81081e7i | −1.04144 | + | 1.80382i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.03461e7 | + | 3.52406e7i | 0.949069 | + | 1.64384i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.07273e7 | −3.70043 | ||||||||
\(863\) | −1.38071e7 | − | 2.39146e7i | −0.631068 | − | 1.09304i | −0.987334 | − | 0.158657i | \(-0.949284\pi\) |
0.356266 | − | 0.934385i | \(-0.384050\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.09277e6 | −0.273694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.88390e7 | − | 1.19233e8i | 3.06579 | − | 5.31011i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.16714e7 | + | 3.75359e7i | 0.951453 | + | 1.64797i | 0.742283 | + | 0.670086i | \(0.233743\pi\) |
0.209170 | + | 0.977879i | \(0.432924\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.94011e7 | −1.70062 | −0.850308 | − | 0.526286i | \(-0.823584\pi\) | ||||
−0.850308 | + | 0.526286i | \(0.823584\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.80770e7 | − | 4.86307e7i | 1.20162 | − | 2.08126i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.24386e6 | + | 3.88648e6i | 0.0946895 | + | 0.164007i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.09895e7 | − | 1.90343e7i | −0.454763 | − | 0.787673i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.37922e7 | + | 5.85298e7i | −1.39062 | + | 2.40863i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.72477e7 | 3.14387 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.24173e7 | + | 3.88280e7i | −0.904828 | + | 1.56721i | −0.0836802 | + | 0.996493i | \(0.526667\pi\) |
−0.821148 | + | 0.570715i | \(0.806666\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.87850e7 | 1.94756 | 0.973778 | − | 0.227498i | \(-0.0730547\pi\) | ||||
0.973778 | + | 0.227498i | \(0.0730547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.17883e7 | − | 5.50589e7i | 1.25864 | − | 2.18003i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.53358e7 | − | 4.38829e7i | −0.989569 | − | 1.71398i | −0.619543 | − | 0.784962i | \(-0.712682\pi\) |
−0.370026 | − | 0.929022i | \(-0.620651\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77688e7 | 1.06709 | ||||||||
\(926\) | −1.58741e7 | − | 2.74947e7i | −0.608361 | − | 1.05371i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.91135e7 | + | 1.54349e8i | −3.39683 | + | 5.88348i | ||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.13875e8 | −4.29427 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.82133e6 | −0.356814 | ||||||||
\(947\) | 2.75004e7 | + | 4.76322e7i | 0.996471 | + | 1.72594i | 0.570923 | + | 0.821003i | \(0.306585\pi\) |
0.425548 | + | 0.904936i | \(0.360081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.97130e6 | −0.355647 | −0.177824 | − | 0.984062i | \(-0.556906\pi\) | ||||
−0.177824 | + | 0.984062i | \(0.556906\pi\) | |||||||
\(954\) | 3.28111e7 | + | 5.68304e7i | 1.16721 | + | 2.02167i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.21974e7 | + | 5.57674e7i | −1.13940 | + | 1.97350i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.43146e7 | + | 2.47936e7i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.88535e6 | + | 1.36578e7i | −0.274003 | + | 0.474587i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00222e7 | 0.688566 | 0.344283 | − | 0.938866i | \(-0.388122\pi\) | ||||
0.344283 | + | 0.938866i | \(0.388122\pi\) | |||||||
\(968\) | 4.86787e7 | + | 8.43140e7i | 1.66975 | + | 2.89209i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.03761e7 | −1.02597 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.49909e7 | − | 4.32854e7i | 0.837616 | − | 1.45079i | −0.0542674 | − | 0.998526i | \(-0.517282\pi\) |
0.891883 | − | 0.452266i | \(-0.149384\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.33584e7 | 1.77023 | ||||||||
\(982\) | −4.85503e7 | − | 8.40916e7i | −1.60662 | − | 2.78275i | ||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.90880e7 | + | 5.03820e7i | 0.945636 | + | 1.63789i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.86572e7 | − | 4.96357e7i | 0.926936 | − | 1.60550i | 0.138519 | − | 0.990360i | \(-0.455766\pi\) |
0.788417 | − | 0.615141i | \(-0.210901\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(998\) | 6.11620e7 | − | 1.05936e8i | 1.94382 | − | 3.36679i | ||||
\(999\) | 0 | 0 |
(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 | 49.6.c.a.18.1 | 2 | ||
7.2 | even | 3 | inner | 49.6.c.a.30.1 | 2 | ||
7.3 | odd | 6 | 49.6.a.b.1.1 | ✓ | 1 | ||
7.4 | even | 3 | 49.6.a.b.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | inner | 49.6.c.a.30.1 | 2 | ||
7.6 | odd | 2 | CM | 49.6.c.a.18.1 | 2 | ||
21.11 | odd | 6 | 441.6.a.a.1.1 | 1 | |||
21.17 | even | 6 | 441.6.a.a.1.1 | 1 | |||
28.3 | even | 6 | 784.6.a.g.1.1 | 1 | |||
28.11 | odd | 6 | 784.6.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.b.1.1 | ✓ | 1 | 7.3 | odd | 6 | ||
49.6.a.b.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
49.6.c.a.18.1 | 2 | 1.1 | even | 1 | trivial | ||
49.6.c.a.18.1 | 2 | 7.6 | odd | 2 | CM | ||
49.6.c.a.30.1 | 2 | 7.2 | even | 3 | inner | ||
49.6.c.a.30.1 | 2 | 7.5 | odd | 6 | inner | ||
441.6.a.a.1.1 | 1 | 21.11 | odd | 6 | |||
441.6.a.a.1.1 | 1 | 21.17 | even | 6 | |||
784.6.a.g.1.1 | 1 | 28.3 | even | 6 | |||
784.6.a.g.1.1 | 1 | 28.11 | odd | 6 |