Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,7,Mod(127,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.127");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.g (of order \(2\), degree \(1\), 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: | \(44.1703840550\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.127 |
Dual form | 192.7.g.b.127.1 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.0480000 | −0.0240000 | − | 0.999712i | \(-0.507640\pi\) | ||||
−0.0240000 | + | 0.999712i | \(0.507640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 200.918i | − 0.585766i | −0.956148 | − | 0.292883i | \(-0.905385\pi\) | ||||
0.956148 | − | 0.292883i | \(-0.0946147\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 644.323i | 0.484089i | 0.970265 | + | 0.242045i | \(0.0778181\pi\) | ||||
−0.970265 | + | 0.242045i | \(0.922182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2654.00 | 1.20801 | 0.604005 | − | 0.796980i | \(-0.293571\pi\) | ||||
0.604005 | + | 0.796980i | \(0.293571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 93.5307i | − 0.0277128i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7206.00 | −1.46672 | −0.733360 | − | 0.679840i | \(-0.762049\pi\) | ||||
−0.733360 | + | 0.679840i | \(0.762049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3540.31i | 0.516156i | 0.966124 | + | 0.258078i | \(0.0830891\pi\) | ||||
−0.966124 | + | 0.258078i | \(0.916911\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3132.00 | 0.338192 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 17459.1i | − 1.43495i | −0.696583 | − | 0.717476i | \(-0.745297\pi\) | ||||
0.696583 | − | 0.717476i | \(-0.254703\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15589.0 | −0.997696 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3788.00i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11550.0 | −0.473574 | −0.236787 | − | 0.971562i | \(-0.576094\pi\) | ||||
−0.236787 | + | 0.971562i | \(0.576094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8542.47i | 0.286747i | 0.989669 | + | 0.143373i | \(0.0457950\pi\) | ||||
−0.989669 | + | 0.143373i | \(0.954205\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10044.0 | −0.279489 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1205.51i | 0.0281168i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −22346.0 | −0.441158 | −0.220579 | − | 0.975369i | \(-0.570795\pi\) | ||||
−0.220579 | + | 0.975369i | \(0.570795\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41371.8i | 0.697445i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 103626. | 1.50355 | 0.751774 | − | 0.659421i | \(-0.229199\pi\) | ||||
0.751774 | + | 0.659421i | \(0.229199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 127389.i | − 1.60223i | −0.598507 | − | 0.801117i | \(-0.704239\pi\) | ||||
0.598507 | − | 0.801117i | \(-0.295761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1458.00 | 0.0160000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 160831.i | − 1.54909i | −0.632518 | − | 0.774546i | \(-0.717979\pi\) | ||||
0.632518 | − | 0.774546i | \(-0.282021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 77281.0 | 0.656878 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 112330.i | − 0.846812i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −168462. | −1.13155 | −0.565776 | − | 0.824559i | \(-0.691423\pi\) | ||||
−0.565776 | + | 0.824559i | \(0.691423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3865.94i | − 0.0232363i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −55188.0 | −0.298003 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 111593.i | 0.543349i | 0.962389 | + | 0.271675i | \(0.0875775\pi\) | ||||
−0.962389 | + | 0.271675i | \(0.912423\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 260470. | 1.14754 | 0.573770 | − | 0.819016i | \(-0.305480\pi\) | ||||
0.573770 | + | 0.819016i | \(0.305480\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 48823.0i | 0.195255i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15924.0 | −0.0579845 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 317083.i | − 1.05426i | −0.849784 | − | 0.527131i | \(-0.823268\pi\) | ||||
0.849784 | − | 0.527131i | \(-0.176732\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 272160. | 0.828470 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 708423.i | − 1.97933i | −0.143412 | − | 0.989663i | \(-0.545807\pi\) | ||||
0.143412 | − | 0.989663i | \(-0.454193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −395918. | −1.01774 | −0.508870 | − | 0.860844i | \(-0.669937\pi\) | ||||
−0.508870 | + | 0.860844i | \(0.669937\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 243008.i | − 0.576020i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 129456. | 0.283563 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 556743.i | − 1.12921i | −0.825362 | − | 0.564604i | \(-0.809029\pi\) | ||||
0.825362 | − | 0.564604i | \(-0.190971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 89145.2i | 0.155906i | 0.996957 | + | 0.0779531i | \(0.0248385\pi\) | ||||
−0.996957 | + | 0.0779531i | \(0.975162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43236.0 | 0.0704026 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 180047.i | − 0.273418i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −251886. | −0.357301 | −0.178650 | − | 0.983913i | \(-0.557173\pi\) | ||||
−0.178650 | + | 0.983913i | \(0.557173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 533236.i | − 0.707612i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −133164. | −0.165553 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 21241.9i | − 0.0247755i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 517474. | 0.566987 | 0.283494 | − | 0.958974i | \(-0.408507\pi\) | ||||
0.283494 | + | 0.958974i | \(0.408507\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 156570.i | − 0.161363i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.02382e6 | −0.993712 | −0.496856 | − | 0.867833i | \(-0.665512\pi\) | ||||
−0.496856 | + | 0.867833i | \(0.665512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 90960.4i | 0.0832416i | 0.999133 | + | 0.0416208i | \(0.0132521\pi\) | ||||
−0.999133 | + | 0.0416208i | \(0.986748\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18792.0 | −0.0162332 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.20282e6i | − 1.79815i | −0.437791 | − | 0.899077i | \(-0.644239\pi\) | ||||
0.437791 | − | 0.899077i | \(-0.355761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −952594. | −0.735577 | −0.367789 | − | 0.929909i | \(-0.619885\pi\) | ||||
−0.367789 | + | 0.929909i | \(0.619885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 348340.i | − 0.254703i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −121038. | −0.0838854 | −0.0419427 | − | 0.999120i | \(-0.513355\pi\) | ||||
−0.0419427 | + | 0.999120i | \(0.513355\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 104754.i | 0.0688777i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −644922. | −0.402670 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.44781e6i | 0.859156i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.35641e6 | 0.765658 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.61537e6i | 0.868074i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 187284. | 0.0958894 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.44941e6i | − 0.707590i | −0.935323 | − | 0.353795i | \(-0.884891\pi\) | ||||
0.935323 | − | 0.353795i | \(-0.115109\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.98580e6 | 0.925051 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 632787.i | − 0.281478i | −0.990047 | − | 0.140739i | \(-0.955052\pi\) | ||||
0.990047 | − | 0.140739i | \(-0.0449478\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 711312. | 0.302347 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22728.0i | 0.00923760i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.47821e6 | −1.74158 | −0.870789 | − | 0.491656i | \(-0.836392\pi\) | ||||
−0.870789 | + | 0.491656i | \(0.836392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.24905e6i | 0.837443i | 0.908115 | + | 0.418722i | \(0.137522\pi\) | ||||
−0.908115 | + | 0.418722i | \(0.862478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.50711e6 | 0.894368 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.71003e6i | 0.584785i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 69300.0 | 0.0227316 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.20469e6i | 0.379248i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.84051e6 | 0.556389 | 0.278194 | − | 0.960525i | \(-0.410264\pi\) | ||||
0.278194 | + | 0.960525i | \(0.410264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.14464e6i | 0.332460i | 0.986087 | + | 0.166230i | \(0.0531594\pi\) | ||||
−0.986087 | + | 0.166230i | \(0.946841\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.75106e6 | 0.488907 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 51254.8i | − 0.0137638i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.28775e6 | 1.36638 | 0.683191 | − | 0.730240i | \(-0.260592\pi\) | ||||
0.683191 | + | 0.730240i | \(0.260592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 2.62606e6i | − 0.653302i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.50784e6 | −0.840547 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.45869e6i | 1.49136i | 0.666306 | + | 0.745678i | \(0.267874\pi\) | ||||
−0.666306 | + | 0.745678i | \(0.732126\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 60264.0 | 0.0134155 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.97714e6i | 0.853927i | 0.904269 | + | 0.426964i | \(0.140417\pi\) | ||||
−0.904269 | + | 0.426964i | \(0.859583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.21691e6 | 0.459290 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 860296.i | − 0.172052i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.73548e6 | −1.10772 | −0.553862 | − | 0.832609i | \(-0.686846\pi\) | ||||
−0.553862 | + | 0.832609i | \(0.686846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.13211e6i | 0.584417i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.73956e6 | −0.313703 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.16883e6i | 1.42430i | 0.702029 | + | 0.712149i | \(0.252278\pi\) | ||||
−0.702029 | + | 0.712149i | \(0.747722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.24656e6 | −0.547505 | −0.273752 | − | 0.961800i | \(-0.588265\pi\) | ||||
−0.273752 | + | 0.961800i | \(0.588265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.06033e6i | 0.662533i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 134076. | 0.0211756 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.64299e6i | − 0.710024i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −761076. | −0.112731 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.11705e6i | 0.160314i | 0.996782 | + | 0.0801571i | \(0.0255422\pi\) | ||||
−0.996782 | + | 0.0801571i | \(0.974458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.12375e6 | 0.434514 | 0.217257 | − | 0.976114i | \(-0.430289\pi\) | ||||
0.217257 | + | 0.976114i | \(0.430289\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 248231.i | − 0.0334774i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.08530e7 | −1.41955 | −0.709777 | − | 0.704426i | \(-0.751204\pi\) | ||||
−0.709777 | + | 0.704426i | \(0.751204\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.99733e6i | 1.14171i | 0.821052 | + | 0.570853i | \(0.193388\pi\) | ||||
−0.821052 | + | 0.570853i | \(0.806612\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.94284e6 | 0.608679 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.32060e6i | 0.277404i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −621756. | −0.0721703 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.24255e6i | 0.478318i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.28110e6 | −0.249865 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.84129e6i | − 0.408912i | −0.978876 | − | 0.204456i | \(-0.934457\pi\) | ||||
0.978876 | − | 0.204456i | \(-0.0655426\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.10432e7 | 1.14276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 764333.i | 0.0769073i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.71634e6 | 0.167967 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.17175e6i | − 0.587592i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.91247e7 | −1.77181 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.51732e6i | − 0.317174i | −0.987345 | − | 0.158587i | \(-0.949306\pi\) | ||||
0.987345 | − | 0.158587i | \(-0.0506938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.78813e6 | 0.332565 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.62115e7i | 1.38595i | 0.720964 | + | 0.692973i | \(0.243699\pi\) | ||||
−0.720964 | + | 0.692973i | \(0.756301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.46861e7 | 1.22293 | 0.611463 | − | 0.791273i | \(-0.290582\pi\) | ||||
0.611463 | + | 0.791273i | \(0.290582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.01802e6i | 0.163715i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.10117e6 | −0.482331 | −0.241165 | − | 0.970484i | \(-0.577530\pi\) | ||||
−0.241165 | + | 0.970484i | \(0.577530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 964988.i | 0.0743564i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.67877e6 | 0.651948 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 2.63536e7i | − 1.93039i | −0.261528 | − | 0.965196i | \(-0.584226\pi\) | ||||
0.261528 | − | 0.965196i | \(-0.415774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.15214e6 | −0.153752 | −0.0768758 | − | 0.997041i | \(-0.524495\pi\) | ||||
−0.0768758 | + | 0.997041i | \(0.524495\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 920483.i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −463686. | −0.0315301 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.39599e6i | 0.623522i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.38964e6 | −0.0900125 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 7.99802e6i | − 0.505780i | −0.967495 | − | 0.252890i | \(-0.918619\pi\) | ||||
0.967495 | − | 0.252890i | \(-0.0813810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.12493e7 | 0.694645 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 673983.i | 0.0406470i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.86154e7 | −1.68578 | −0.842890 | − | 0.538086i | \(-0.819147\pi\) | ||||
−0.842890 | + | 0.538086i | \(0.819147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.48971e6i | 0.258416i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.80665e6 | 0.157858 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.49487e6i | − 0.0821744i | −0.999156 | − | 0.0410872i | \(-0.986918\pi\) | ||||
0.999156 | − | 0.0410872i | \(-0.0130821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.01077e6 | 0.0543145 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.92651e6i | − 0.206288i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 532290. | 0.0273459 | 0.0136729 | − | 0.999907i | \(-0.495648\pi\) | ||||
0.0136729 | + | 0.999907i | \(0.495648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 2.88563e7i | − 1.44988i | −0.688811 | − | 0.724941i | \(-0.741867\pi\) | ||||
0.688811 | − | 0.724941i | \(-0.258133\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.31233e6 | 0.408540 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.00443e7i | − 0.482974i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.82479e7 | 0.858567 | 0.429284 | − | 0.903170i | \(-0.358766\pi\) | ||||
0.429284 | + | 0.903170i | \(0.358766\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 2.07582e6i | − 0.0955823i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.52019e6 | 0.429069 | 0.214534 | − | 0.976716i | \(-0.431177\pi\) | ||||
0.214534 | + | 0.976716i | \(0.431177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.81369e7i | − 1.68262i | −0.540552 | − | 0.841310i | \(-0.681785\pi\) | ||||
0.540552 | − | 0.841310i | \(-0.318215\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 331128. | 0.0143041 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.08203e7i | − 0.880728i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.77889e7 | 1.15127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.06662e6i | 0.327350i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.68345e7 | −0.669266 | −0.334633 | − | 0.942349i | \(-0.608612\pi\) | ||||
−0.334633 | + | 0.942349i | \(0.608612\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 669555.i | − 0.0260808i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.44069e6 | 0.0931630 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.63364e7i | − 1.73344i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.55947e7 | −0.938535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1.59598e7i | − 0.573720i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.56282e6 | −0.0550820 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.39154e7i | 1.51775i | 0.651234 | + | 0.758877i | \(0.274252\pi\) | ||||
−0.651234 | + | 0.758877i | \(0.725748\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.41793e6 | −0.0480596 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.08371e7i | 1.69005i | 0.534726 | + | 0.845025i | \(0.320415\pi\) | ||||
−0.534726 | + | 0.845025i | \(0.679585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.30721e7 | 0.426298 | 0.213149 | − | 0.977020i | \(-0.431628\pi\) | ||||
0.213149 | + | 0.977020i | \(0.431628\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 292938.i | − 0.00937226i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.07723e6 | −0.159386 | −0.0796928 | − | 0.996819i | \(-0.525394\pi\) | ||||
−0.0796928 | + | 0.996819i | \(0.525394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 7.44193e6i | − 0.229252i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.43385e7 | 1.03816 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.55115e7i | − 0.757056i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.13732e7 | −1.20523 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.48495e7i | − 0.424686i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.23139e7 | −0.907406 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5.59418e7i | − 1.54260i | −0.636474 | − | 0.771298i | \(-0.719608\pi\) | ||||
0.636474 | − | 0.771298i | \(-0.280392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.43008e6 | 0.147053 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.90250e6i | 0.0506046i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.55737e7 | −0.668197 | −0.334099 | − | 0.942538i | \(-0.608432\pi\) | ||||
−0.334099 | + | 0.942538i | \(0.608432\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.88680e6i | − 0.0484313i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.50411e6 | −0.138811 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.91649e7i | − 0.970543i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.63296e6 | −0.0397666 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.96031e6i | − 0.118719i | −0.998237 | − | 0.0593595i | \(-0.981094\pi\) | ||||
0.998237 | − | 0.0593595i | \(-0.0189058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.06563e7 | 0.721179 | 0.360590 | − | 0.932725i | \(-0.382576\pi\) | ||||
0.360590 | + | 0.932725i | \(0.382576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 1.00533e7i | − 0.232482i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.33353e7 | −1.21252 | −0.606262 | − | 0.795265i | \(-0.707332\pi\) | ||||
−0.606262 | + | 0.795265i | \(0.707332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.25054e6i | 0.0950077i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.25692e7 | −0.496034 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.83885e7i | 0.613564i | 0.951780 | + | 0.306782i | \(0.0992522\pi\) | ||||
−0.951780 | + | 0.306782i | \(0.900748\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.45121e7 | 0.733583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.11443e7i | 0.442053i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.37551e6 | 0.0488515 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 5.75671e7i | − 1.16460i | −0.812974 | − | 0.582299i | \(-0.802153\pi\) | ||||
0.812974 | − | 0.582299i | \(-0.197847\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.51811e7 | −0.501183 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.38470e7i | 0.662825i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.68328e7 | 0.902451 | 0.451226 | − | 0.892410i | \(-0.350987\pi\) | ||||
0.451226 | + | 0.892410i | \(0.350987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.91947e6i | 0.0553618i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.06537e7 | −0.572083 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.92476e7i | 1.45569i | 0.685742 | + | 0.727845i | \(0.259478\pi\) | ||||
−0.685742 | + | 0.727845i | \(0.740522\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.25941e7 | 0.408527 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 2.00575e7i | − 0.357010i | −0.983939 | − | 0.178505i | \(-0.942874\pi\) | ||||
0.983939 | − | 0.178505i | \(-0.0571260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −776736. | −0.0136110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.09555e7i | 0.534078i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.79345e7 | 0.814328 | 0.407164 | − | 0.913355i | \(-0.366518\pi\) | ||||
0.407164 | + | 0.913355i | \(0.366518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25810e8i | 2.10468i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.86418e6 | 0.162511 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.34046e6i | 0.0542020i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.43785e7 | 0.549434 | 0.274717 | − | 0.961525i | \(-0.411416\pi\) | ||||
0.274717 | + | 0.961525i | \(0.411416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.10883e7i | 0.174560i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.09234e7 | 1.41008 | 0.705038 | − | 0.709170i | \(-0.250930\pi\) | ||||
0.705038 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.26717e7i | 0.346393i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −354294. | −0.00533333 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.43980e7i | − 0.213560i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.15454e8 | −1.68748 | −0.843739 | − | 0.536753i | \(-0.819651\pi\) | ||||
−0.843739 | + | 0.536753i | \(0.819651\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 6.98084e7i | − 1.00550i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.24209e7 | 0.318276 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 534871.i | − 0.00748350i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.50593e7 | −0.483498 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.40305e7i | 1.00640i | 0.864171 | + | 0.503198i | \(0.167843\pi\) | ||||
−0.864171 | + | 0.503198i | \(0.832157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.14811e8 | −1.53863 | −0.769317 | − | 0.638867i | \(-0.779404\pi\) | ||||
−0.769317 | + | 0.638867i | \(0.779404\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.90820e7i | 0.516364i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.12334e8 | 1.46334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.23331e7i | − 0.672191i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.66568e7 | −0.337626 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 3.42559e6i | − 0.0427862i | −0.999771 | − | 0.0213931i | \(-0.993190\pi\) | ||||
0.999771 | − | 0.0213931i | \(-0.00681016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.08786e8 | 1.34002 | 0.670008 | − | 0.742354i | \(-0.266291\pi\) | ||||
0.670008 | + | 0.742354i | \(0.266291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.08028e6i | 0.0131241i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.18106e7 | 0.740659 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.13400e8i | 1.34036i | 0.742199 | + | 0.670180i | \(0.233783\pi\) | ||||
−0.742199 | + | 0.670180i | \(0.766217\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.87793e7 | −0.218959 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.44463e7i | 0.281191i | 0.990067 | + | 0.140595i | \(0.0449017\pi\) | ||||
−0.990067 | + | 0.140595i | \(0.955098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.51132e6 | 0.0171504 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.86906e7i | 0.321231i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.03699e7 | 0.998354 | 0.499177 | − | 0.866500i | \(-0.333636\pi\) | ||||
0.499177 | + | 0.866500i | \(0.333636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.67686e7i | 0.727851i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.78432e7 | −0.191946 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.19942e6i | 0.0339654i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.82048e7 | −0.609832 | −0.304916 | − | 0.952379i | \(-0.598628\pi\) | ||||
−0.304916 | + | 0.952379i | \(0.598628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.72963e7i | 0.282271i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.73271e8 | −1.76858 | −0.884288 | − | 0.466942i | \(-0.845356\pi\) | ||||
−0.884288 | + | 0.466942i | \(0.845356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.25400e8i | 1.26344i | 0.775197 | + | 0.631719i | \(0.217650\pi\) | ||||
−0.775197 | + | 0.631719i | \(0.782350\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 798984. | 0.00794656 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.45905e8i | 1.43258i | 0.697800 | + | 0.716292i | \(0.254162\pi\) | ||||
−0.697800 | + | 0.716292i | \(0.745838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.37077e7 | −0.617551 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.24279e7i | 0.788881i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.20796e7 | 0.775625 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.51899e7i | − 0.514966i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.09363e7 | 0.377184 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 7.62417e6i | − 0.0693723i | −0.999398 | − | 0.0346861i | \(-0.988957\pi\) | ||||
0.999398 | − | 0.0346861i | \(-0.0110432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.93063e7 | −0.532924 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 5.46818e7i | − 0.485290i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.10484e6 | −0.0272154 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.71349e8i | − 1.48352i | −0.670665 | − | 0.741760i | \(-0.733991\pi\) | ||||
0.670665 | − | 0.741760i | \(-0.266009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.00681e8 | −0.861035 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3.30473e6i | − 0.0279185i | −0.999903 | − | 0.0139592i | \(-0.995556\pi\) | ||||
0.999903 | − | 0.0139592i | \(-0.00444351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.32293e7 | 0.694601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 939423.i | 0.00774543i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.42335e8 | −1.15942 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 1.26207e8i | − 1.01574i | −0.861435 | − | 0.507868i | \(-0.830434\pi\) | ||||
0.861435 | − | 0.507868i | \(-0.169566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.19974e7 | −0.493015 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 212336.i | 0.00166847i | 1.00000 | 0.000834236i | \(0.000265546\pi\) | |||||
−1.00000 | 0.000834236i | \(0.999734\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.14293e6 | 0.0476982 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.45582e7i | 0.265171i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.49792e8 | 1.13589 | 0.567944 | − | 0.823067i | \(-0.307739\pi\) | ||||
0.567944 | + | 0.823067i | \(0.307739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.95470e7i | 0.596158i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.34107e7 | 0.0993342 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 545762.i | − 0.00399560i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.03627e8 | 0.749899 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 8.94073e7i | − 0.639544i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.11422e8 | 0.787876 | 0.393938 | − | 0.919137i | \(-0.371113\pi\) | ||||
0.393938 | + | 0.919137i | \(0.371113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.69486e8i | 1.88379i | 0.335911 | + | 0.941894i | \(0.390956\pi\) | ||||
−0.335911 | + | 0.941894i | \(0.609044\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.88247e7 | −0.337413 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 6.15571e7i | − 0.420578i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.56783e8 | −1.05909 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.71170e7i | − 0.181116i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.75023e8 | 1.81630 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.32169e7i | 0.0863114i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.27339e8 | −0.822319 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.97939e7i | 0.317987i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.03425e8 | −1.91628 | −0.958142 | − | 0.286292i | \(-0.907577\pi\) | ||||
−0.958142 | + | 0.286292i | \(0.907577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5.06089e7i | − 0.316102i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.71556e6 | 0.0353077 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.92937e7i | − 0.117884i | −0.998261 | − | 0.0589418i | \(-0.981227\pi\) | ||||
0.998261 | − | 0.0589418i | \(-0.0187726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.32942e7 | −0.382514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 4.08906e7i | − 0.244438i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.11860e8 | −0.661452 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.09004e6i | 0.0122257i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.71693e8 | 0.993544 | 0.496772 | − | 0.867881i | \(-0.334518\pi\) | ||||
0.496772 | + | 0.867881i | \(0.334518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 3.38090e8i | − 1.93552i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.23771e7 | 0.409933 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.21392e8i | − 1.24062i | −0.784358 | − | 0.620308i | \(-0.787008\pi\) | ||||
0.784358 | − | 0.620308i | \(-0.212992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 726228. | 0.00402650 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.18640e7i | − 0.0650852i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.56991e8 | 1.39502 | 0.697511 | − | 0.716574i | \(-0.254291\pi\) | ||||
0.697511 | + | 0.716574i | \(0.254291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.71249e8i | − 1.45700i | −0.685045 | − | 0.728501i | \(-0.740218\pi\) | ||||
0.685045 | − | 0.728501i | \(-0.259782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.74131e7 | −0.0925574 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.72169e8i | 1.43165i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.41573e6 | −0.0177810 | −0.00889049 | − | 0.999960i | \(-0.502830\pi\) | ||||
−0.00889049 | + | 0.999960i | \(0.502830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.86944e7i | 0.250867i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.79109e7 | 0.0913247 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.08544e8i | − 0.547772i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.86953e6 | 0.0193282 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.32848e8i | − 1.15122i | −0.817725 | − | 0.575609i | \(-0.804765\pi\) | ||||
0.817725 | − | 0.575609i | \(-0.195235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.02430e7 | −0.148006 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 1.69182e8i | − 0.819580i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.86693e7 | −0.425216 | −0.212608 | − | 0.977138i | \(-0.568196\pi\) | ||||
−0.212608 | + | 0.977138i | \(0.568196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 8.68689e6i | − 0.0412395i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.40255e8 | −0.659165 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 2.37591e7i | − 0.110547i | −0.998471 | − | 0.0552737i | \(-0.982397\pi\) | ||||
0.998471 | − | 0.0552737i | \(-0.0176031\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.56421e8 | 1.18122 | 0.590609 | − | 0.806958i | \(-0.298888\pi\) | ||||
0.590609 | + | 0.806958i | \(0.298888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.70512e7i | 0.351421i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.13845e6 | −0.0367516 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.08193e8i | 0.930895i | 0.885076 | + | 0.465447i | \(0.154107\pi\) | ||||
−0.885076 | + | 0.465447i | \(0.845893\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.61746e7 | −0.160159 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 4.26846e8i | − 1.87132i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.59662e8 | −1.12727 | −0.563634 | − | 0.826024i | \(-0.690597\pi\) | ||||
−0.563634 | + | 0.826024i | \(0.690597\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 9.69222e6i | − 0.0416675i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.40534e8 | 0.598309 | 0.299155 | − | 0.954205i | \(-0.403295\pi\) | ||||
0.299155 | + | 0.954205i | \(0.403295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.58033e8i | 0.666307i | 0.942873 | + | 0.333154i | \(0.108113\pi\) | ||||
−0.942873 | + | 0.333154i | \(0.891887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.61349e7 | −0.276157 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.06084e7i | 0.209295i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.42454e8 | 0.993093 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.55589e7i | − 0.144260i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.61025e8 | 0.647056 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 2.49902e8i | − 0.994677i | −0.867556 | − | 0.497339i | \(-0.834311\pi\) | ||||
0.867556 | − | 0.497339i | \(-0.165689\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.98798e7 | 0.236086 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.69649e6i | 0.0339643i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.05104e8 | 0.793515 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.72147e8i | 0.659775i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.94095e7 | −0.111664 | −0.0558321 | − | 0.998440i | \(-0.517781\pi\) | ||||
−0.0558321 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.55925e8i | − 0.962675i | −0.876535 | − | 0.481337i | \(-0.840151\pi\) | ||||
0.876535 | − | 0.481337i | \(-0.159849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.19148e7 | −0.0444024 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 4.08342e8i | − 1.50769i | −0.657054 | − | 0.753844i | \(-0.728197\pi\) | ||||
0.657054 | − | 0.753844i | \(-0.271803\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.19016e7 | −0.263030 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.67550e7i | 0.0969756i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.06095e8 | −0.740164 | −0.370082 | − | 0.928999i | \(-0.620670\pi\) | ||||
−0.370082 | + | 0.928999i | \(0.620670\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.79672e6i | 0.0135109i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.62081e7 | 0.339247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 7.85056e7i | − 0.274312i | −0.990549 | − | 0.137156i | \(-0.956204\pi\) | ||||
0.990549 | − | 0.137156i | \(-0.0437961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50505e7 | 0.190615 | 0.0953074 | − | 0.995448i | \(-0.469617\pi\) | ||||
0.0953074 | + | 0.995448i | \(0.469617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.98125e8i | − 1.02296i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.26787e6 | −0.0145126 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.01652e8i | 0.679557i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.48295e7 | 0.183120 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.67827e8i | 0.555512i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.82818e7 | −0.158394 | −0.0791969 | − | 0.996859i | \(-0.525236\pi\) | ||||
−0.0791969 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.90511e7i | 0.192007i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.02892e8 | 1.29844 | 0.649221 | − | 0.760600i | \(-0.275095\pi\) | ||||
0.649221 | + | 0.760600i | \(0.275095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.03970e8i | − 0.332122i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.52713e8 | −0.800176 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.26946e8i | 0.398434i | 0.979955 | + | 0.199217i | \(0.0638398\pi\) | ||||
−0.979955 | + | 0.199217i | \(0.936160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.68693e7 | 0.0835958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.28934e8i | 0.706056i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.47098e8 | −1.36693 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.39216e8i | − 0.421944i | −0.977492 | − | 0.210972i | \(-0.932337\pi\) | ||||
0.977492 | − | 0.210972i | \(-0.0676629\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.14578e7 | −0.0945211 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1.34943e7i | − 0.0401973i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.46729e8 | −2.20528 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 9.51078e7i | − 0.278474i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.45981e8 | −1.29468 | −0.647340 | − | 0.762201i | \(-0.724119\pi\) | ||||
−0.647340 | + | 0.762201i | \(0.724119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.91118e7i | − 0.227706i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.50427e7 | −0.0429297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.05704e8i | 0.582083i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.59057e8 | −0.446288 | −0.223144 | − | 0.974786i | \(-0.571632\pi\) | ||||
−0.223144 | + | 0.974786i | \(0.571632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.35289e8i | 0.376403i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.49144e8 | 0.411468 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.02602e7i | − 0.0280697i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.10811e8 | 1.11451 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 3.34049e8i | − 0.898718i | −0.893351 | − | 0.449359i | \(-0.851652\pi\) | ||||
0.893351 | − | 0.449359i | \(-0.148348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82756e7 | 0.0487602 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 3.35486e7i | − 0.0887686i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.80053e8 | 0.472483 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.60960e8i | 0.679157i | 0.940578 | + | 0.339579i | \(0.110284\pi\) | ||||
−0.940578 | + | 0.339579i | \(0.889716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.17964e8i | 2.35003i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.56906e8 | 0.906238 | 0.453119 | − | 0.891450i | \(-0.350311\pi\) | ||||
0.453119 | + | 0.891450i | \(0.350311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 7.22815e6i | − 0.0182039i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.04304e8 | 0.510357 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.61653e7i | 0.213501i | 0.994286 | + | 0.106750i | \(0.0340446\pi\) | ||||
−0.994286 | + | 0.106750i | \(0.965955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.46469e8 | −0.359990 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.61364e7i | − 0.0637204i | −0.999492 | − | 0.0318602i | \(-0.989857\pi\) | ||||
0.999492 | − | 0.0318602i | \(-0.0101431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.10430e7 | −0.0267067 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2.16623e7i | − 0.0519688i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.42585e8 | −1.05330 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.80052e8i | 1.36945i | 0.728800 | + | 0.684727i | \(0.240078\pi\) | ||||
−0.728800 | + | 0.684727i | \(0.759922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.24677e8 | 0.292012 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.86786e6i | − 0.0159581i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.35602e8 | −0.773636 | −0.386818 | − | 0.922156i | \(-0.626426\pi\) | ||||
−0.386818 | + | 0.922156i | \(0.626426\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.75359e8i | 0.401054i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.34765e8 | 0.532696 | 0.266348 | − | 0.963877i | \(-0.414183\pi\) | ||||
0.266348 | + | 0.963877i | \(0.414183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.91393e8i | 0.430877i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.05063e7 | −0.0234675 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.96167e8i | 0.656372i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.78738e8 | 0.832837 | 0.416419 | − | 0.909173i | \(-0.363285\pi\) | ||||
0.416419 | + | 0.909173i | \(0.363285\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4.46070e8i | − 0.973285i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.34904e8 | 0.292070 | 0.146035 | − | 0.989279i | \(-0.453349\pi\) | ||||
0.146035 | + | 0.989279i | \(0.453349\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.33169e8i | − 0.286086i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.99877e7 | −0.149196 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.66868e8i | 0.776065i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.56453e8 | 0.958171 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.37513e7i | 0.0911394i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.17265e7 | −0.0655863 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 8.58679e7i | − 0.176160i | −0.996113 | − | 0.0880799i | \(-0.971927\pi\) | ||||
0.996113 | − | 0.0880799i | \(-0.0280731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.33027e7 | 0.0474434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.43187e7i | 0.0491373i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.91287e8 | 1.38624 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.57564e7i | 0.0313585i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.82735e8 | −1.74363 | −0.871817 | − | 0.489832i | \(-0.837058\pi\) | ||||
−0.871817 | + | 0.489832i | \(0.837058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.15895e9i | 2.27208i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.12083e7 | 0.119100 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.55099e8i | − 0.492677i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.10470e7 | 0.0403463 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.29758e6i | 0.0157881i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.19181e7 | 0.0602825 | 0.0301412 | − | 0.999546i | \(-0.490404\pi\) | ||||
0.0301412 | + | 0.999546i | \(0.490404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 8.59397e7i | − 0.161113i | −0.996750 | − | 0.0805567i | \(-0.974330\pi\) | ||||
0.996750 | − | 0.0805567i | \(-0.0256698\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.49825e8 | 0.837089 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 3.87521e7i | − 0.0715851i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.50996e8 | 0.827003 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.29576e8i | 0.235871i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.71027e8 | −1.39328 | −0.696642 | − | 0.717419i | \(-0.745324\pi\) | ||||
−0.696642 | + | 0.717419i | \(0.745324\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.04669e8i | − 0.367158i | −0.983005 | − | 0.183579i | \(-0.941232\pi\) | ||||
0.983005 | − | 0.183579i | \(-0.0587683\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.56576e8 | 0.278845 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.55414e8i | 0.451574i | 0.974177 | + | 0.225787i | \(0.0724953\pi\) | ||||
−0.974177 | + | 0.225787i | \(0.927505\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.29211e8 | 1.10442 | 0.552208 | − | 0.833706i | \(-0.313785\pi\) | ||||
0.552208 | + | 0.833706i | \(0.313785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.84457e8i | 0.495694i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.56887e8 | −0.963456 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.38628e7i | − 0.0409885i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.23589e7 | 0.0551845 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.24118e8i | 0.379481i | 0.981834 | + | 0.189741i | \(0.0607647\pi\) | ||||
−0.981834 | + | 0.189741i | \(0.939235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.61421e8 | −0.775728 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.48405e8i | 0.247723i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.33014e7 | −0.0220459 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.72527e8i | − 0.448496i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.94496e8 | 0.971461 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.90140e8i | 0.633042i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.09382e8 | −0.337359 | −0.168679 | − | 0.985671i | \(-0.553950\pi\) | ||||
−0.168679 | + | 0.985671i | \(0.553950\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.16177e6i | 0.00825849i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.32297e8 | −0.527940 | −0.263970 | − | 0.964531i | \(-0.585032\pi\) | ||||
−0.263970 | + | 0.964531i | \(0.585032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.58920e8i | 1.03957i | 0.854297 | + | 0.519784i | \(0.173988\pi\) | ||||
−0.854297 | + | 0.519784i | \(0.826012\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.24557e8 | 0.508488 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.00694e9i | 1.56665i | 0.621610 | + | 0.783327i | \(0.286479\pi\) | ||||
−0.621610 | + | 0.783327i | \(0.713521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.44129e7 | 0.0531707 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.33186e8i | 0.664686i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.58723e8 | 0.546637 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 8.41538e8i | − 1.27356i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.25746e8 | −0.188996 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.76287e7i | − 0.0561688i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.31416e8 | −1.08434 | −0.542170 | − | 0.840269i | \(-0.682397\pi\) | ||||
−0.542170 | + | 0.840269i | \(0.682397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 2.62425e8i | − 0.386401i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.16606e9 | −1.70528 | −0.852638 | − | 0.522502i | \(-0.824999\pi\) | ||||
−0.852638 | + | 0.522502i | \(0.824999\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 7.42439e7i | − 0.107840i | −0.998545 | − | 0.0539198i | \(-0.982828\pi\) | ||||
0.998545 | − | 0.0539198i | \(-0.0171715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.04373e7 | 0.0150577 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.35897e8i | − 0.338027i | −0.985614 | − | 0.169014i | \(-0.945942\pi\) | ||||
0.985614 | − | 0.169014i | \(-0.0540582\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.91213e8 | −0.414482 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.80466e7i | 0.0537877i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.69393e8 | 0.799572 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 4.90130e7i | − 0.0683663i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.22313e8 | 1.00080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 9.86656e7i | − 0.135796i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21394e9 | 1.65967 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.98982e8i | − 0.541864i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.94794e7 | 0.0262802 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.54036e8i | 0.340466i | 0.985404 | + | 0.170233i | \(0.0544520\pi\) | ||||
−0.985404 | + | 0.170233i | \(0.945548\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.48789e8 | 0.331237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.03209e9i | − 1.36509i | −0.730844 | − | 0.682544i | \(-0.760874\pi\) | ||||
0.730844 | − | 0.682544i | \(-0.239126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.74383e7 | −0.0754726 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.43620e7i | − 0.0318016i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.27138e8 | −0.164880 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.13004e9i | 1.45595i | 0.685602 | + | 0.727976i | \(0.259539\pi\) | ||||
−0.685602 | + | 0.727976i | \(0.740461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.84573e8 | −0.876276 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.88015e9i | − 2.39105i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.48352e8 | 0.440142 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.21034e7i | − 0.0277472i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.40049e9 | −1.74676 | −0.873382 | − | 0.487036i | \(-0.838078\pi\) | ||||
−0.873382 | + | 0.487036i | \(0.838078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.73599e8i | 0.339051i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.92472e8 | −0.975751 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.78579e7i | 0.0340812i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.55654e8 | 0.432324 | 0.216162 | − | 0.976357i | \(-0.430646\pi\) | ||||
0.216162 | + | 0.976357i | \(0.430646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.03774e8i | 0.246123i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.04392e8 | −0.125285 | −0.0626427 | − | 0.998036i | \(-0.519953\pi\) | ||||
−0.0626427 | + | 0.998036i | \(0.519953\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.80921e9i | − 2.15752i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.56646e6 | 0.00541108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.83576e8i | − 1.15813i | −0.815281 | − | 0.579066i | \(-0.803417\pi\) | ||||
0.815281 | − | 0.579066i | \(-0.196583\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.05077e9 | −1.22944 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 7.91462e7i | − 0.0920213i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.13478e8 | 0.362184 | 0.181092 | − | 0.983466i | \(-0.442037\pi\) | ||||
0.181092 | + | 0.983466i | \(0.442037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 6.70229e6i | − 0.00769508i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.16008e8 | 0.132359 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.99753e8i | 1.02016i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.14530e8 | 0.917776 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.35284e8i | 0.599384i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.87425e7 | −0.0208567 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3.95187e8i | − 0.437042i | −0.975832 | − | 0.218521i | \(-0.929877\pi\) | ||||
0.975832 | − | 0.218521i | \(-0.0701232\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.97685e8 | 0.437087 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.04334e8i | 0.223194i | 0.993754 | + | 0.111597i | \(0.0355966\pi\) | ||||
−0.993754 | + | 0.111597i | \(0.964403\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.51875e8 | 0.490546 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 6.44944e8i | − 0.695839i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.87988e7 | −0.0416040 | −0.0208020 | − | 0.999784i | \(-0.506622\pi\) | ||||
−0.0208020 | + | 0.999784i | \(0.506622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.62296e8i | − 0.172966i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.31480e8 | 0.245192 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.59099e8i | 0.799168i | 0.916697 | + | 0.399584i | \(0.130845\pi\) | ||||
−0.916697 | + | 0.399584i | \(0.869155\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.51181e7 | 0.0681386 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.03724e8i | − 0.523891i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.22409e9 | −2.29913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.08413e8i | 0.522391i | 0.965286 | + | 0.261195i | \(0.0841167\pi\) | ||||
−0.965286 | + | 0.261195i | \(0.915883\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.72046e8 | 0.890618 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 5.39840e7i | − 0.0548019i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.50556e8 | −0.151919 | −0.0759594 | − | 0.997111i | \(-0.524202\pi\) | ||||
−0.0759594 | + | 0.997111i | \(0.524202\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.46465e7i | 0.0849010i |
(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 | 192.7.g.b.127.2 | 2 | ||
3.2 | odd | 2 | 576.7.g.g.127.1 | 2 | |||
4.3 | odd | 2 | inner | 192.7.g.b.127.1 | 2 | ||
8.3 | odd | 2 | 48.7.g.b.31.2 | yes | 2 | ||
8.5 | even | 2 | 48.7.g.b.31.1 | ✓ | 2 | ||
12.11 | even | 2 | 576.7.g.g.127.2 | 2 | |||
16.3 | odd | 4 | 768.7.b.b.127.4 | 4 | |||
16.5 | even | 4 | 768.7.b.b.127.3 | 4 | |||
16.11 | odd | 4 | 768.7.b.b.127.1 | 4 | |||
16.13 | even | 4 | 768.7.b.b.127.2 | 4 | |||
24.5 | odd | 2 | 144.7.g.c.127.1 | 2 | |||
24.11 | even | 2 | 144.7.g.c.127.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.g.b.31.1 | ✓ | 2 | 8.5 | even | 2 | ||
48.7.g.b.31.2 | yes | 2 | 8.3 | odd | 2 | ||
144.7.g.c.127.1 | 2 | 24.5 | odd | 2 | |||
144.7.g.c.127.2 | 2 | 24.11 | even | 2 | |||
192.7.g.b.127.1 | 2 | 4.3 | odd | 2 | inner | ||
192.7.g.b.127.2 | 2 | 1.1 | even | 1 | trivial | ||
576.7.g.g.127.1 | 2 | 3.2 | odd | 2 | |||
576.7.g.g.127.2 | 2 | 12.11 | even | 2 | |||
768.7.b.b.127.1 | 4 | 16.11 | odd | 4 | |||
768.7.b.b.127.2 | 4 | 16.13 | even | 4 | |||
768.7.b.b.127.3 | 4 | 16.5 | even | 4 | |||
768.7.b.b.127.4 | 4 | 16.3 | odd | 4 |