Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,7,Mod(113,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.113");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.e (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: | \(34.9682207102\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.2 | ||
Character | \(\chi\) | \(=\) | 152.113 |
Dual form | 152.7.e.a.113.29 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 48.7582i | − | 1.80586i | −0.429787 | − | 0.902930i | \(-0.641411\pi\) | ||
0.429787 | − | 0.902930i | \(-0.358589\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −200.006 | −1.60005 | −0.800023 | − | 0.599969i | \(-0.795180\pi\) | ||||
−0.800023 | + | 0.599969i | \(0.795180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −536.711 | −1.56476 | −0.782378 | − | 0.622804i | \(-0.785993\pi\) | ||||
−0.782378 | + | 0.622804i | \(0.785993\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1648.37 | −2.26113 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −528.705 | −0.397224 | −0.198612 | − | 0.980078i | \(-0.563643\pi\) | ||||
−0.198612 | + | 0.980078i | \(0.563643\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1938.33i | − | 0.882260i | −0.897443 | − | 0.441130i | \(-0.854578\pi\) | ||
0.897443 | − | 0.441130i | \(-0.145422\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9751.93i | 2.88946i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6548.79 | 1.33295 | 0.666476 | − | 0.745527i | \(-0.267802\pi\) | ||||
0.666476 | + | 0.745527i | \(0.267802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2289.83 | − | 6465.49i | −0.333843 | − | 0.942629i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26169.1i | 2.82573i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18877.3 | −1.55152 | −0.775758 | − | 0.631030i | \(-0.782632\pi\) | ||||
−0.775758 | + | 0.631030i | \(0.782632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24377.3 | 1.56015 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 44826.7i | 2.27743i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 21391.9i | − | 0.877113i | −0.898704 | − | 0.438556i | \(-0.855490\pi\) | ||
0.898704 | − | 0.438556i | \(-0.144510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 41792.2i | − | 1.40285i | −0.712746 | − | 0.701423i | \(-0.752549\pi\) | ||
0.712746 | − | 0.701423i | \(-0.247451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 25778.7i | 0.717331i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 107345. | 2.50368 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 25164.2i | − | 0.496797i | −0.968658 | − | 0.248398i | \(-0.920096\pi\) | ||
0.968658 | − | 0.248398i | \(-0.0799042\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −94509.4 | −1.59324 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13690.7i | 0.198644i | 0.995055 | + | 0.0993220i | \(0.0316674\pi\) | ||||
−0.995055 | + | 0.0993220i | \(0.968333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11123.7 | −0.139908 | −0.0699540 | − | 0.997550i | \(-0.522285\pi\) | ||||
−0.0699540 | + | 0.997550i | \(0.522285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 329683. | 3.61792 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −172525. | −1.66172 | −0.830860 | − | 0.556482i | \(-0.812151\pi\) | ||||
−0.830860 | + | 0.556482i | \(0.812151\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 170410. | 1.44846 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 319308.i | − | 2.40712i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 120834.i | − | 0.811640i | −0.913953 | − | 0.405820i | \(-0.866986\pi\) | ||
0.913953 | − | 0.405820i | \(-0.133014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 105744. | 0.635577 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −315246. | + | 111648.i | −1.70226 | + | 0.602875i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 30982.4i | − | 0.150855i | −0.997151 | − | 0.0754273i | \(-0.975968\pi\) | ||
0.997151 | − | 0.0754273i | \(-0.0240321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 96479.8 | 0.425057 | 0.212528 | − | 0.977155i | \(-0.431830\pi\) | ||||
0.212528 | + | 0.977155i | \(0.431830\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 884697. | 3.53812 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 387676.i | 1.41166i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 393271.i | 1.30758i | 0.756676 | + | 0.653790i | \(0.226822\pi\) | ||||
−0.756676 | + | 0.653790i | \(0.773178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 920424.i | 2.80182i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 259029.i | 0.723726i | 0.932231 | + | 0.361863i | \(0.117859\pi\) | ||||
−0.932231 | + | 0.361863i | \(0.882141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −24478.8 | −0.0629246 | −0.0314623 | − | 0.999505i | \(-0.510016\pi\) | ||||
−0.0314623 | + | 0.999505i | \(0.510016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.18860e6i | − | 2.81741i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 283762. | 0.621558 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 429564.i | 0.871257i | 0.900126 | + | 0.435629i | \(0.143474\pi\) | ||||
−0.900126 | + | 0.435629i | \(0.856526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 984011. | 1.85159 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.05440e6 | 1.84404 | 0.922022 | − | 0.387137i | \(-0.126536\pi\) | ||||
0.922022 | + | 0.387137i | \(0.126536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.30980e6 | −2.13278 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.04303e6 | −1.58394 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 442773.i | 0.628074i | 0.949411 | + | 0.314037i | \(0.101682\pi\) | ||||
−0.949411 | + | 0.314037i | \(0.898318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04032e6i | 1.38052i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.03771e6 | −2.53334 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 457980. | + | 1.29314e6i | 0.534165 | + | 1.50825i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 650087.i | 0.712289i | 0.934431 | + | 0.356144i | \(0.115909\pi\) | ||||
−0.934431 | + | 0.356144i | \(0.884091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 871500. | 0.898176 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 833712. | 0.809193 | 0.404596 | − | 0.914495i | \(-0.367412\pi\) | ||||
0.404596 | + | 0.914495i | \(0.367412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.91703e6i | − | 1.75436i | −0.480166 | − | 0.877178i | \(-0.659424\pi\) | ||
0.480166 | − | 0.877178i | \(-0.340576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.23397e6i | − | 4.52130i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 635712.i | − | 0.518930i | −0.965752 | − | 0.259465i | \(-0.916454\pi\) | ||
0.965752 | − | 0.259465i | \(-0.0835462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 213031.i | 0.164499i | 0.996612 | + | 0.0822495i | \(0.0262104\pi\) | ||||
−0.996612 | + | 0.0822495i | \(0.973790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.22696e6 | −0.897146 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.40999e6i | − | 0.977192i | −0.872510 | − | 0.488596i | \(-0.837509\pi\) | ||
0.872510 | − | 0.488596i | \(-0.162491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.77557e6 | 2.48250 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.19507e6i | 1.99491i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.51481e6 | −2.08574 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.49203e6 | −0.842213 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 667536. | 0.358723 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.75052e6 | −0.896265 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.08186e6i | − | 1.50453i | −0.658858 | − | 0.752267i | \(-0.728960\pi\) | ||
0.658858 | − | 0.752267i | \(-0.271040\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 542370.i | 0.252654i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.57928e6 | 0.702500 | 0.351250 | − | 0.936282i | \(-0.385757\pi\) | ||||
0.351250 | + | 0.936282i | \(0.385757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.22898e6 | + | 3.47010e6i | 0.522384 | + | 1.47498i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.96560e6i | − | 3.64400i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 124358. | 0.0483629 | 0.0241815 | − | 0.999708i | \(-0.492302\pi\) | ||||
0.0241815 | + | 0.999708i | \(0.492302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.67389e6 | −1.36799 | −0.683994 | − | 0.729488i | \(-0.739758\pi\) | ||||
−0.683994 | + | 0.729488i | \(0.739758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.41200e6i | 3.00083i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.02480e6i | 0.350455i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.27851e6i | 1.40342i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 8.30889e6i | − | 2.61572i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.98841e6 | 0.601099 | 0.300550 | − | 0.953766i | \(-0.402830\pi\) | ||||
0.300550 | + | 0.953766i | \(0.402830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.64353e6i | − | 1.05826i | −0.848541 | − | 0.529129i | \(-0.822519\pi\) | ||
0.848541 | − | 0.529129i | \(-0.177481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.07948e7 | −3.01398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.35868e6i | 2.24462i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.40292e6 | −1.39614 | −0.698071 | − | 0.716029i | \(-0.745958\pi\) | ||||
−0.698071 | + | 0.716029i | \(0.745958\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.89168e6 | −1.46571 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.01317e7 | 2.42775 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.26230e6 | −1.21510 | −0.607551 | − | 0.794281i | \(-0.707848\pi\) | ||||
−0.607551 | + | 0.794281i | \(0.707848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.15590e6i | − | 1.14776i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.23985e6i | 1.55446i | 0.629216 | + | 0.777231i | \(0.283376\pi\) | ||||
−0.629216 | + | 0.777231i | \(0.716624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.06970e6 | 0.221617 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.77448e6 | + | 1.06575e7i | 0.754865 | + | 2.13141i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.04060e6i | − | 0.394113i | −0.980392 | − | 0.197056i | \(-0.936862\pi\) | ||
0.980392 | − | 0.197056i | \(-0.0631382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.30836e7 | −2.44125 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.51065e6 | −0.272422 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.60633e6i | − | 0.977507i | −0.872422 | − | 0.488753i | \(-0.837452\pi\) | ||
0.872422 | − | 0.488753i | \(-0.162548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.11913e6i | 1.03194i | 0.856607 | + | 0.515970i | \(0.172568\pi\) | ||||
−0.856607 | + | 0.515970i | \(0.827432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.70418e6i | − | 0.767593i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.03300e6i | 0.794898i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46238e6 | −0.529480 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 2.40590e7i | − | 3.56362i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.75957e6 | −1.11362 | −0.556810 | − | 0.830640i | \(-0.687975\pi\) | ||||
−0.556810 | + | 0.830640i | \(0.687975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.17937e6i | − | 0.442251i | −0.975245 | − | 0.221126i | \(-0.929027\pi\) | ||
0.975245 | − | 0.221126i | \(-0.0709731\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.89024e7 | 2.54926 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.92471e6 | 0.644142 | 0.322071 | − | 0.946715i | \(-0.395621\pi\) | ||||
0.322071 | + | 0.946715i | \(0.395621\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.04801e6 | 0.513668 | 0.256834 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256834 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.91752e7 | 2.36131 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.14813e7i | 1.37247i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.73823e6i | − | 0.317840i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.11167e7 | 3.50819 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.21065e6 | + | 3.41834e6i | 0.132611 | + | 0.374435i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.50695e6i | − | 0.373321i | −0.982424 | − | 0.186661i | \(-0.940234\pi\) | ||
0.982424 | − | 0.186661i | \(-0.0597665\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.26298e7 | 1.30695 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.22480e6 | 0.223859 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.24303e7i | 2.19511i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.19354e6i | 0.113633i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.26937e7i | − | 1.17601i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.26743e7i | − | 1.14290i | −0.820637 | − | 0.571449i | \(-0.806381\pi\) | ||
0.820637 | − | 0.571449i | \(-0.193619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.01828e7 | −3.52771 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.87026e6i | 0.330874i | 0.986220 | + | 0.165437i | \(0.0529034\pi\) | ||||
−0.986220 | + | 0.165437i | \(0.947097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.28607e6 | −0.773260 | −0.386630 | − | 0.922235i | \(-0.626361\pi\) | ||||
−0.386630 | + | 0.922235i | \(0.626361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.38357e7i | − | 1.12245i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −497816. | −0.0393551 | −0.0196776 | − | 0.999806i | \(-0.506264\pi\) | ||||
−0.0196776 | + | 0.999806i | \(0.506264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.45059e7 | 2.65883 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.09448e7 | 1.57337 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.92128e7 | −1.40733 | −0.703666 | − | 0.710531i | \(-0.748455\pi\) | ||||
−0.703666 | + | 0.710531i | \(0.748455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.98986e6i | 0.713688i | 0.934164 | + | 0.356844i | \(0.116147\pi\) | ||||
−0.934164 | + | 0.356844i | \(0.883853\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.53000e7i | − | 1.06628i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.40830e7 | −2.31761 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.25322e7 | + | 4.43844e6i | −0.831644 | + | 0.294537i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.14107e7i | − | 3.33009i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.17603e6 | −0.137608 | −0.0688039 | − | 0.997630i | \(-0.521918\pi\) | ||||
−0.0688039 | + | 0.997630i | \(0.521918\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.98053e6 | 0.616300 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.38634e7i | 3.85151i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 679353.i | − | 0.0400217i | −0.999800 | − | 0.0200109i | \(-0.993630\pi\) | ||
0.999800 | − | 0.0200109i | \(-0.00637008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.35059e7i | 0.777366i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.52617e7i | 1.98327i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.30125e6 | 0.236444 | 0.118222 | − | 0.992987i | \(-0.462281\pi\) | ||||
0.118222 | + | 0.992987i | \(0.462281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.41676e7i | 1.29866i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.15888e7 | 1.13421 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.41857e7i | 1.24252i | 0.783606 | + | 0.621258i | \(0.213378\pi\) | ||||
−0.783606 | + | 0.621258i | \(0.786622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.72186e7 | −0.865145 | −0.432572 | − | 0.901599i | \(-0.642394\pi\) | ||||
−0.432572 | + | 0.901599i | \(0.642394\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.07242e7 | 2.49303 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.28884e7 | −0.619729 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.88436e6 | −0.182760 | −0.0913798 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913798 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.88888e7i | 3.17202i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.08519e7i | − | 1.39047i | −0.718781 | − | 0.695237i | \(-0.755300\pi\) | ||
0.718781 | − | 0.695237i | \(-0.244700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.00137e6 | 0.132422 | 0.0662109 | − | 0.997806i | \(-0.478909\pi\) | ||||
0.0662109 | + | 0.997806i | \(0.478909\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.30510e7 | − | 2.23303e7i | 2.72369 | − | 0.964628i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 7.34797e6i | − | 0.310829i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.87491e7 | 0.776759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.16971e7 | 1.28629 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.32041e7i | − | 1.71760i | −0.512310 | − | 0.858801i | \(-0.671210\pi\) | ||
0.512310 | − | 0.858801i | \(-0.328790\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.19665e6i | 0.241374i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.37001e7i | − | 0.904650i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.65904e7i | 1.36884i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.97020e6 | 0.218922 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.06503e7i | − | 1.46129i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.92965e7 | −0.680110 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.15697e7i | − | 1.43669i | −0.695689 | − | 0.718343i | \(-0.744901\pi\) | ||
0.695689 | − | 0.718343i | \(-0.255099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.34711e7 | −3.16812 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.96783e6 | 0.231642 | 0.115821 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115821 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.20071e6 | −0.300046 | −0.150023 | − | 0.988682i | \(-0.547935\pi\) | ||||
−0.150023 | + | 0.988682i | \(0.547935\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.76945e8 | −5.66116 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.11085e7i | 1.60441i | 0.597049 | + | 0.802204i | \(0.296340\pi\) | ||||
−0.597049 | + | 0.802204i | \(0.703660\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.13100e7i | 0.348410i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.09962e7 | −0.937116 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.49956e7 | − | 4.23411e7i | −0.444997 | − | 1.25648i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.72512e7i | − | 1.37646i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.03870e7 | 0.297062 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.25960e7 | 2.60019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.44088e6i | − | 0.0397323i | −0.999803 | − | 0.0198661i | \(-0.993676\pi\) | ||
0.999803 | − | 0.0198661i | \(-0.00632401\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.14799e7i | 1.12332i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 7.86566e7i | − | 2.09219i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.83356e7i | − | 1.78549i | −0.450563 | − | 0.892745i | \(-0.648777\pi\) | ||
0.450563 | − | 0.892745i | \(-0.351223\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.87485e7 | −1.76467 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.20957e7i | 0.557244i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.83174e7 | −0.701732 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.84090e8i | − | 4.48305i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.59872e7 | −0.621973 | −0.310987 | − | 0.950414i | \(-0.600659\pi\) | ||||
−0.310987 | + | 0.950414i | \(0.600659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.61563e7 | 0.380071 | 0.190035 | − | 0.981777i | \(-0.439140\pi\) | ||||
0.190035 | + | 0.981777i | \(0.439140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.68887e7 | 2.00929 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.13046e7 | 1.16636 | 0.583179 | − | 0.812343i | \(-0.301808\pi\) | ||||
0.583179 | + | 0.812343i | \(0.301808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.18074e7i | − | 1.15799i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.71376e8i | 3.76656i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.41259e7 | 0.305305 | 0.152652 | − | 0.988280i | \(-0.451219\pi\) | ||||
0.152652 | + | 0.988280i | \(0.451219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.65592e7 | + | 2.96098e7i | −0.777097 | + | 0.629381i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.27489e7i | 1.52092i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.89589e6 | 0.100682 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.40272e7 | 1.49759 | 0.748796 | − | 0.662801i | \(-0.230632\pi\) | ||||
0.748796 | + | 0.662801i | \(0.230632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.25674e7i | − | 0.449160i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.48532e7i | 1.27002i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.98987e6i | 0.0576137i | 0.999585 | + | 0.0288068i | \(0.00917077\pi\) | ||||
−0.999585 | + | 0.0288068i | \(0.990829\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.53522e7i | 1.61853i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.14645e7 | −0.773842 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.44308e7i | 0.265078i | 0.991178 | + | 0.132539i | \(0.0423130\pi\) | ||||
−0.991178 | + | 0.132539i | \(0.957687\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50266e8 | −2.71698 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.74178e7i | 0.310024i | 0.987913 | + | 0.155012i | \(0.0495417\pi\) | ||||
−0.987913 | + | 0.155012i | \(0.950458\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.67540e7 | −0.994523 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.83359e7 | 0.316351 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.88799e7 | 1.17016 | 0.585078 | − | 0.810977i | \(-0.301064\pi\) | ||||
0.585078 | + | 0.810977i | \(0.301064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.23624e8 | −2.06810 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 7.70031e7i | − | 1.26862i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.59153e7i | − | 1.39405i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.93049e7 | 0.787986 | 0.393993 | − | 0.919113i | \(-0.371093\pi\) | ||||
0.393993 | + | 0.919113i | \(0.371093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.69196e8 | − | 5.99228e7i | 2.66362 | − | 0.943352i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.12174e7i | 1.41463i | 0.706896 | + | 0.707317i | \(0.250095\pi\) | ||||
−0.706896 | + | 0.707317i | \(0.749905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.10068e7 | −1.23767 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.96808e8 | −2.96263 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.33045e7i | 0.197340i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.61534e7i | − | 0.382260i | −0.981565 | − | 0.191130i | \(-0.938785\pi\) | ||
0.981565 | − | 0.191130i | \(-0.0612152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.06348e6i | − | 0.0873367i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.66286e7i | 0.236051i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.10886e8 | −2.95056 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.79133e8i | 2.47039i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.37278e7 | −0.186621 | −0.0933103 | − | 0.995637i | \(-0.529745\pi\) | ||||
−0.0933103 | + | 0.995637i | \(0.529745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.13850e8i | 1.52577i | 0.646537 | + | 0.762883i | \(0.276217\pi\) | ||||
−0.646537 | + | 0.762883i | \(0.723783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.84384e8 | 3.75737 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.59642e8 | 2.07960 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.17818e7 | −0.665110 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.99676e7 | 0.632873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.26676e7i | 0.408024i | 0.978968 | + | 0.204012i | \(0.0653982\pi\) | ||||
−0.978968 | + | 0.204012i | \(0.934602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.83622e7i | − | 0.595720i | −0.954610 | − | 0.297860i | \(-0.903727\pi\) | ||
0.954610 | − | 0.297860i | \(-0.0962729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.08612e8 | 2.53438 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.32259e7 | + | 1.22051e8i | 0.517964 | + | 1.46250i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 9.35805e7i | − | 1.10609i | −0.833150 | − | 0.553047i | \(-0.813465\pi\) | ||
0.833150 | − | 0.553047i | \(-0.186535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.80898e8 | −3.27516 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.44279e8 | 1.65956 | 0.829780 | − | 0.558090i | \(-0.188466\pi\) | ||||
0.829780 | + | 0.558090i | \(0.188466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.85571e7i | − | 1.00495i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 9.69512e7i | − | 1.08550i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.26362e8i | − | 1.39597i | −0.716112 | − | 0.697986i | \(-0.754080\pi\) | ||
0.716112 | − | 0.697986i | \(-0.245920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.23836e6i | − | 0.0789061i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.77652e8 | −1.91107 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.08070e8i | − | 2.20890i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.45899e7 | −0.467184 | −0.233592 | − | 0.972335i | \(-0.575048\pi\) | ||||
−0.233592 | + | 0.972335i | \(0.575048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.93561e8i | 3.03571i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.77217e7 | 0.691234 | 0.345617 | − | 0.938376i | \(-0.387670\pi\) | ||||
0.345617 | + | 0.938376i | \(0.387670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.21686e6 | −0.0122602 | −0.00613009 | − | 0.999981i | \(-0.501951\pi\) | ||||
−0.00613009 | + | 0.999981i | \(0.501951\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.07554e8 | 4.05347 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.06509e6 | −0.0202763 | −0.0101382 | − | 0.999949i | \(-0.503227\pi\) | ||||
−0.0101382 | + | 0.999949i | \(0.503227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.11073e8i | − | 2.04604i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.63437e8i | 2.52124i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.88114e6 | 0.0555748 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.58200e7 | − | 1.57611e8i | −0.520846 | − | 1.47064i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.99180e8i | 1.83523i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.15904e8 | 1.96451 | 0.982253 | − | 0.187560i | \(-0.0600579\pi\) | ||||
0.982253 | + | 0.187560i | \(0.0600579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.87765e7 | −0.438304 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.94002e8i | − | 4.38417i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1.30021e8i | − | 1.13969i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.33297e8i | 1.15407i | 0.816720 | + | 0.577035i | \(0.195790\pi\) | ||||
−0.816720 | + | 0.577035i | \(0.804210\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.56580e8i | 2.19430i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.16823e8 | 0.986926 | 0.493463 | − | 0.869767i | \(-0.335731\pi\) | ||||
0.493463 | + | 0.869767i | \(0.335731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.40091e8i | − | 1.16915i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.74305e8 | −1.43712 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.39024e8i | − | 1.13245i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.10771e8 | −1.69632 | −0.848161 | − | 0.529738i | \(-0.822290\pi\) | ||||
−0.848161 | + | 0.529738i | \(0.822290\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.53002e8 | 2.80714 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.05595e8 | 0.829734 | 0.414867 | − | 0.909882i | \(-0.363828\pi\) | ||||
0.414867 | + | 0.909882i | \(0.363828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.66747e8 | −1.29475 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5.21568e7i | − | 0.400209i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.87764e8i | 1.42384i | 0.702263 | + | 0.711918i | \(0.252173\pi\) | ||||
−0.702263 | + | 0.711918i | \(0.747827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.31380e7 | 0.0984617 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.89826e8 | − | 1.02646e8i | 2.14677 | − | 0.760306i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.83418e8i | 2.80705i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.12147e7 | 0.660075 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.94962e7 | −0.711712 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.60813e6i | 0.0467267i | 0.999727 | + | 0.0233634i | \(0.00743746\pi\) | ||||
−0.999727 | + | 0.0233634i | \(0.992563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 9.32891e7i | − | 0.652118i | −0.945349 | − | 0.326059i | \(-0.894279\pi\) | ||
0.945349 | − | 0.326059i | \(-0.105721\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.37933e8i | 4.40856i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.73688e8i | − | 1.86992i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.08317e8 | 1.40720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.10703e7i | 0.341102i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.65371e7 | 0.175256 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.27146e8i | 0.830312i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.73355e8 | −1.76524 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.00966e7 | −0.575363 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.22147e7 | −0.203452 | −0.101726 | − | 0.994812i | \(-0.532437\pi\) | ||||
−0.101726 | + | 0.994812i | \(0.532437\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.98358e8 | 1.86354 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 4.26074e7i | − | 0.263206i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.39680e8i | − | 0.853436i | −0.904385 | − | 0.426718i | \(-0.859670\pi\) | ||
0.904385 | − | 0.426718i | \(-0.140330\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.59034e8 | −0.961110 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.38309e8 | + | 4.89839e7i | −0.826791 | + | 0.292818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.30552e8i | − | 1.36330i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.45400e8 | 1.43547 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.37604e8 | 0.796282 | 0.398141 | − | 0.917324i | \(-0.369655\pi\) | ||||
0.398141 | + | 0.917324i | \(0.369655\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.15613e7i | 0.123435i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.68819e8i | 0.956168i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.37756e7i | − | 0.133231i | −0.997779 | − | 0.0666156i | \(-0.978780\pi\) | ||
0.997779 | − | 0.0666156i | \(-0.0212201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.82006e8i | 1.56355i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.28130e8 | −2.89729 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.31155e7i | − | 0.125478i | −0.998030 | − | 0.0627389i | \(-0.980016\pi\) | ||
0.998030 | − | 0.0627389i | \(-0.0199835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.45006e7 | −0.400177 | −0.200088 | − | 0.979778i | \(-0.564123\pi\) | ||||
−0.200088 | + | 0.979778i | \(0.564123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.78343e8i | 2.01104i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.60178e8 | −2.42060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.89442e8 | −0.986164 | −0.493082 | − | 0.869983i | \(-0.664130\pi\) | ||||
−0.493082 | + | 0.869983i | \(0.664130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.55021e8 | −0.798645 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.65909e8 | −2.88548 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.38858e7i | 0.322403i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 6.39033e8i | − | 3.19195i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.84968e7 | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.70207e8 | + | 9.56971e7i | −1.32236 | + | 0.468331i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.40120e8i | − | 1.16323i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.12533e7 | 0.101921 | 0.0509604 | − | 0.998701i | \(-0.483772\pi\) | ||||
0.0509604 | + | 0.998701i | \(0.483772\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.02982e8 | 3.33729 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.97374e8i | − | 0.927613i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.83752e8i | 1.78554i | 0.450511 | + | 0.892771i | \(0.351242\pi\) | ||||
−0.450511 | + | 0.892771i | \(0.648758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.20417e8i | 1.93668i | 0.249643 | + | 0.968338i | \(0.419687\pi\) | ||||
−0.249643 | + | 0.968338i | \(0.580313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.48255e8i | − | 2.95661i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.98415e8 | 1.34758 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.10423e7i | 0.407078i | 0.979067 | + | 0.203539i | \(0.0652443\pi\) | ||||
−0.979067 | + | 0.203539i | \(0.934756\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.59807e8 | 2.47848 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.34409e8i | 1.46607i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.54414e8 | −1.10449 | −0.552243 | − | 0.833683i | \(-0.686228\pi\) | ||||
−0.552243 | + | 0.833683i | \(0.686228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.33511e8 | −0.573974 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.53267e8 | −0.652521 | −0.326260 | − | 0.945280i | \(-0.605789\pi\) | ||||
−0.326260 | + | 0.945280i | \(0.605789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.38743e8 | −1.42823 | −0.714116 | − | 0.700028i | \(-0.753171\pi\) | ||||
−0.714116 | + | 0.700028i | \(0.753171\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 8.46207e8i | − | 3.53347i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.37641e8i | − | 0.982782i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.07820e7 | −0.126083 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.66672e8 | − | 5.90290e7i | 0.676177 | − | 0.239476i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.64795e8i | − | 0.662206i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.40484e8 | 1.35522 | 0.677609 | − | 0.735423i | \(-0.263016\pi\) | ||||
0.677609 | + | 0.735423i | \(0.263016\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.70993e8 | −0.674166 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.16390e8i | 2.40732i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.30310e8i | − | 1.27792i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4.26975e8i | − | 1.63644i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.82902e8i | 0.694457i | 0.937781 | + | 0.347229i | \(0.112877\pi\) | ||||
−0.937781 | + | 0.347229i | \(0.887123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.80050e8 | −0.677268 | −0.338634 | − | 0.940918i | \(-0.609965\pi\) | ||||
−0.338634 | + | 0.940918i | \(0.609965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.08477e8i | − | 0.404259i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.45601e8 | −0.906811 | −0.453406 | − | 0.891304i | \(-0.649791\pi\) | ||||
−0.453406 | + | 0.891304i | \(0.649791\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.63805e7i | 0.0599230i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.09366e9 | 3.96406 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.72102e8 | 1.69549 | 0.847747 | − | 0.530401i | \(-0.177959\pi\) | ||||
0.847747 | + | 0.530401i | \(0.177959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.15866e8 | −1.12403 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.03500e7 | 0.142281 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.43351e8i | − | 0.850308i | −0.905121 | − | 0.425154i | \(-0.860220\pi\) | ||
0.905121 | − | 0.425154i | \(-0.139780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.16910e8i | 0.751060i | 0.926810 | + | 0.375530i | \(0.122539\pi\) | ||||
−0.926810 | + | 0.375530i | \(0.877461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.18922e8 | −2.12371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.45803e8 | − | 6.94040e8i | −0.835838 | − | 2.36004i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.03821e8i | 1.36086i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.17974e8 | −2.06392 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.10093e7 | −0.168843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.67917e8i | − | 1.20699i | −0.797366 | − | 0.603496i | \(-0.793774\pi\) | ||
0.797366 | − | 0.603496i | \(-0.206226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.09276e9i | 3.55313i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.47209e8i | − | 1.11899i | −0.828834 | − | 0.559494i | \(-0.810995\pi\) | ||
0.828834 | − | 0.559494i | \(-0.189005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.48909e8i | − | 1.11456i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.88707e8 | 0.597512 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.46683e7i | − | 0.0460382i | −0.999735 | − | 0.0230191i | \(-0.992672\pi\) | ||
0.999735 | − | 0.0230191i | \(-0.00732785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.48723e7 | −0.0773829 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.52773e8i | 1.39640i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.34217e8 | −0.716078 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.15880e7 | 0.0351216 | 0.0175608 | − | 0.999846i | \(-0.494410\pi\) | ||||
0.0175608 | + | 0.999846i | \(0.494410\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.67744e8 | −1.40543 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.34800e8 | 2.18884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.96578e7i | 0.264783i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.42726e7i | 0.0710699i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.56644e8 | 0.454737 | 0.227368 | − | 0.973809i | \(-0.426988\pi\) | ||||
0.227368 | + | 0.973809i | \(0.426988\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.62699e8 | + | 5.76219e7i | −0.468295 | + | 0.165852i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1.68245e9i | − | 4.80148i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.47463e8 | −1.26619 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.53434e8 | −0.711092 | −0.355546 | − | 0.934659i | \(-0.615705\pi\) | ||||
−0.355546 | + | 0.934659i | \(0.615705\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 7.08078e8i | − | 1.97003i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.88924e8i | 2.17654i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.04966e8i | − | 0.560744i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.36781e8i | 2.54145i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.92521e7 | 0.186314 | 0.0931572 | − | 0.995651i | \(-0.470304\pi\) | ||||
0.0931572 | + | 0.995651i | \(0.470304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.02889e9i | 2.74514i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.87088e8 | 1.28882 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.21478e8i | − | 1.36843i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.61429e8 | −0.680377 | −0.340189 | − | 0.940357i | \(-0.610491\pi\) | ||||
−0.340189 | + | 0.940357i | \(0.610491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.86576e7 | −0.0739702 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.28465e7 | −0.186491 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.79496e8 | 1.47143 | 0.735714 | − | 0.677293i | \(-0.236847\pi\) | ||||
0.735714 | + | 0.677293i | \(0.236847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.66183e9i | 4.18527i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.07925e8i | − | 0.519402i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.04122e8 | 0.257993 | 0.128997 | − | 0.991645i | \(-0.458824\pi\) | ||||
0.128997 | + | 0.991645i | \(0.458824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.16411e8 | + | 6.11049e8i | 0.531892 | + | 1.50183i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.31519e8i | − | 0.320643i | −0.987065 | − | 0.160321i | \(-0.948747\pi\) | ||
0.987065 | − | 0.160321i | \(-0.0512531\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.97693e8 | −0.961787 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.73804e9 | −4.16963 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.41194e8i | 0.811999i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.65619e8i | 0.627105i | 0.949571 | + | 0.313552i | \(0.101519\pi\) | ||||
−0.949571 | + | 0.313552i | \(0.898481\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06099e8i | 0.248501i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.28728e8i | 1.69326i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.34318e8 | 0.540154 | 0.270077 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270077 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4.86633e8i | − | 1.11295i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.90283e8 | −0.658670 | −0.329335 | − | 0.944213i | \(-0.606825\pi\) | ||||
−0.329335 | + | 0.944213i | \(0.606825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.14336e8i | − | 0.257401i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.15902e9 | 4.82251 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00539e7 | −0.133093 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.11713e8 | −0.465552 | −0.232776 | − | 0.972530i | \(-0.574781\pi\) | ||||
−0.232776 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.31241e7 | −0.0722737 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.33497e8i | − | 0.289024i | −0.989503 | − | 0.144512i | \(-0.953839\pi\) | ||
0.989503 | − | 0.144512i | \(-0.0461613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.01878e9i | − | 2.18865i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.58526e8 | 1.40381 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.85173e7 | − | 3.13495e7i | 0.187247 | − | 0.0663160i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.36950e8i | − | 0.287481i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.58928e8 | 1.99756 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.08061e9 | 2.23389 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.03802e8i | − | 0.623257i | −0.950204 | − | 0.311628i | \(-0.899126\pi\) | ||
0.950204 | − | 0.311628i | \(-0.100874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 2.09722e8i | − | 0.426984i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.56756e8i | 1.52907i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.87009e8i | − | 0.375011i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.17837e9 | 2.34520 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.29670e8i | 1.24376i | 0.783111 | + | 0.621882i | \(0.213632\pi\) | ||||
−0.783111 | + | 0.621882i | \(0.786368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.12983e9 | −2.21499 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.29851e8i | − | 1.42016i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.29420e7 | 0.0249952 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.02639e9 | −3.88451 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.17925e9 | 2.24381 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.12103e8 | 1.34492 | 0.672461 | − | 0.740133i | \(-0.265237\pi\) | ||||
0.672461 | + | 0.740133i | \(0.265237\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.04655e8i | 1.32103i | 0.750811 | + | 0.660517i | \(0.229663\pi\) | ||||
−0.750811 | + | 0.660517i | \(0.770337\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.39546e8i | 1.56233i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.05249e9 | 1.94422 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.54713e7 | + | 7.19199e7i | 0.0467074 | + | 0.131881i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.71483e9i | − | 3.12154i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.77996e8 | −1.58658 | −0.793292 | − | 0.608842i | \(-0.791634\pi\) | ||||
−0.793292 | + | 0.608842i | \(0.791634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.48972e6 | −0.00805414 | −0.00402707 | − | 0.999992i | \(-0.501282\pi\) | ||||
−0.00402707 | + | 0.999992i | \(0.501282\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.28417e8i | 1.11914i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.93291e8i | 0.695341i | 0.937617 | + | 0.347671i | \(0.113027\pi\) | ||||
−0.937617 | + | 0.347671i | \(0.886973\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.43942e7i | 0.0779224i | 0.999241 | + | 0.0389612i | \(0.0124049\pi\) | ||||
−0.999241 | + | 0.0389612i | \(0.987595\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.89395e8i | 0.330038i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.11598e9 | 1.93073 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.44801e9i | − | 2.48721i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.87340e9 | 3.19488 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.12436e8i | 1.20631i | 0.797623 | + | 0.603157i | \(0.206091\pi\) | ||||
−0.797623 | + | 0.603157i | \(0.793909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.37210e8 | 0.230673 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.50428e9 | −2.51100 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.13947e8 | −0.354597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.00790e8 | 1.31786 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.46341e8i | − | 0.239136i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.75033e8i | 0.770788i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.78089e8 | −0.931425 | −0.465712 | − | 0.884936i | \(-0.654202\pi\) | ||||
−0.465712 | + | 0.884936i | \(0.654202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.54918e8 | − | 2.13156e9i | −1.20782 | − | 3.41035i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.48564e8i | − | 1.34816i | −0.738657 | − | 0.674081i | \(-0.764540\pi\) | ||
0.738657 | − | 0.674081i | \(-0.235460\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.64312e8 | −0.259233 | −0.129617 | − | 0.991564i | \(-0.541375\pi\) | ||||
−0.129617 | + | 0.991564i | \(0.541375\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.58274e8 | −0.561314 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.18996e8i | 1.11865i | 0.828948 | + | 0.559325i | \(0.188940\pi\) | ||||
−0.828948 | + | 0.559325i | \(0.811060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.08133e8i | 0.630599i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 9.14172e8i | − | 1.40272i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.27113e8i | − | 0.346084i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.62288e8 | 1.15363 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.07158e9i | − | 1.61058i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.39523e8 | 1.40244 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.53997e8i | − | 0.969566i | −0.874635 | − | 0.484783i | \(-0.838899\pi\) | ||
0.874635 | − | 0.484783i | \(-0.161101\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.10656e9 | −3.10175 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.17967e9 | −1.72517 | −0.862587 | − | 0.505908i | \(-0.831158\pi\) | ||||
−0.862587 | + | 0.505908i | \(0.831158\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.21584e7 | −0.0757603 | −0.0378802 | − | 0.999282i | \(-0.512061\pi\) | ||||
−0.0378802 | + | 0.999282i | \(0.512061\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.02138e8 | 0.435889 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 5.01621e8i | − | 0.718795i | −0.933185 | − | 0.359397i | \(-0.882982\pi\) | ||
0.933185 | − | 0.359397i | \(-0.117018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.65407e9i | 2.35423i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.20252e8 | −0.735496 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.95053e8 | + | 1.11546e9i | 0.554754 | + | 1.56638i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.12130e9i | 1.56406i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.78408e9 | 2.47194 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.94014e8 | −1.23045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.91320e8i | − | 1.08188i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.91096e8i | − | 0.395342i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.22386e9i | − | 1.65115i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.42613e9i | 1.91133i | 0.294456 | + | 0.955665i | \(0.404862\pi\) | ||||
−0.294456 | + | 0.955665i | \(0.595138\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.37426e9 | −1.82969 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.19743e9i | − | 1.58378i | −0.610661 | − | 0.791892i | \(-0.709096\pi\) | ||
0.610661 | − | 0.791892i | \(-0.290904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.57467e8 | −0.732499 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.40864e8i | 1.22818i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.47620e8 | −1.09924 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.78298e8 | 1.13161 | 0.565803 | − | 0.824541i | \(-0.308566\pi\) | ||||
0.565803 | + | 0.824541i | \(0.308566\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.02687e9 | −2.59446 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.02083e8 | 0.638514 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.13437e8i | − | 0.775077i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.15997e9i | 3.96683i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.54253e8 | −0.566567 | −0.283283 | − | 0.959036i | \(-0.591424\pi\) | ||||
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.90210e8 | − | 1.10178e9i | −0.483559 | − | 1.36536i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 3.39739e8i | − | 0.418312i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.92496e8 | 0.847193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.42133e8 | −0.172773 | −0.0863863 | − | 0.996262i | \(-0.527532\pi\) | ||||
−0.0863863 | + | 0.996262i | \(0.527532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.48610e8i | 0.541842i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 6.11671e8i | − | 0.734090i | −0.930203 | − | 0.367045i | \(-0.880370\pi\) | ||
0.930203 | − | 0.367045i | \(-0.119630\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.58444e8i | − | 0.308199i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.81194e9i | 5.70197i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.46500e9 | 1.72499 | 0.862496 | − | 0.506065i | \(-0.168900\pi\) | ||||
0.862496 | + | 0.506065i | \(0.168900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.74478e7i | 0.0555159i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.49196e9 | 2.89734 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.21057e8i | − | 0.717551i | −0.933424 | − | 0.358776i | \(-0.883194\pi\) | ||
0.933424 | − | 0.358776i | \(-0.116806\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.55196e9 | 1.78185 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.51456e8 | 0.629180 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.67444e7 | −0.0756761 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.59082e8 | −0.967975 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.04789e9i | 1.17337i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.35893e8i | 0.707623i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.85908e8 | −0.316189 | −0.158095 | − | 0.987424i | \(-0.550535\pi\) | ||||
−0.158095 | + | 0.987424i | \(0.550535\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.06448e9 | + | 7.31161e8i | −2.26902 | + | 0.803603i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.35318e8i | − | 0.693958i | −0.937873 | − | 0.346979i | \(-0.887208\pi\) | ||
0.937873 | − | 0.346979i | \(-0.112792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.97182e9 | 2.14057 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.30389e9 | −2.48569 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.25172e9i | − | 1.34222i | −0.741358 | − | 0.671109i | \(-0.765818\pi\) | ||
0.741358 | − | 0.671109i | \(-0.234182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.34096e8i | − | 0.249486i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3.51153e8i | − | 0.371954i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.11393e9i | 1.17273i | 0.810047 | + | 0.586365i | \(0.199441\pi\) | ||||
−0.810047 | + | 0.586365i | \(0.800559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.84970e8 | −1.03066 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.51482e9i | − | 4.69557i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.09985e8 | 0.217070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.45307e7i | 0.0560299i | 0.999608 | + | 0.0280150i | \(0.00891860\pi\) | ||||
−0.999608 | + | 0.0280150i | \(0.991081\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.02547e7 | −0.0717510 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.09626e8 | −0.821893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.27388e9 | 1.28541 | 0.642706 | − | 0.766113i | \(-0.277812\pi\) | ||||
0.642706 | + | 0.766113i | \(0.277812\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.12803e9 | 1.13142 |
(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 | 152.7.e.a.113.2 | ✓ | 30 | |
4.3 | odd | 2 | 304.7.e.f.113.29 | 30 | |||
19.18 | odd | 2 | inner | 152.7.e.a.113.29 | yes | 30 | |
76.75 | even | 2 | 304.7.e.f.113.2 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.7.e.a.113.2 | ✓ | 30 | 1.1 | even | 1 | trivial | |
152.7.e.a.113.29 | yes | 30 | 19.18 | odd | 2 | inner | |
304.7.e.f.113.2 | 30 | 76.75 | even | 2 | |||
304.7.e.f.113.29 | 30 | 4.3 | odd | 2 |