Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,24,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.a (trivial) |
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: | yes |
Analytic conductor: | \(214.530583901\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 618312 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 4) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-785.828\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 387210. | 1.26198 | 0.630990 | − | 0.775791i | \(-0.282649\pi\) | ||||
0.630990 | + | 0.775791i | \(0.282649\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09186e8 | 1.91592 | 0.957961 | − | 0.286900i | \(-0.0926246\pi\) | ||||
0.957961 | + | 0.286900i | \(0.0926246\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.31949e8 | −0.139911 | −0.0699557 | − | 0.997550i | \(-0.522286\pi\) | ||||
−0.0699557 | + | 0.997550i | \(0.522286\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.57885e10 | 0.592592 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.52441e12 | −1.61097 | −0.805485 | − | 0.592617i | \(-0.798095\pi\) | ||||
−0.805485 | + | 0.592617i | \(0.798095\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.20818e12 | −0.496490 | −0.248245 | − | 0.968697i | \(-0.579854\pi\) | ||||
−0.248245 | + | 0.968697i | \(0.579854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.09989e13 | 2.41785 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.42698e14 | −1.00985 | −0.504923 | − | 0.863164i | \(-0.668479\pi\) | ||||
−0.504923 | + | 0.863164i | \(0.668479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.73906e14 | −0.736369 | −0.368185 | − | 0.929753i | \(-0.620021\pi\) | ||||
−0.368185 | + | 0.929753i | \(0.620021\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.83418e14 | −0.176565 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.74397e14 | 0.0381653 | 0.0190827 | − | 0.999818i | \(-0.493925\pi\) | ||||
0.0190827 | + | 0.999818i | \(0.493925\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.18379e16 | 2.67075 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.48513e16 | −0.514141 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.76214e16 | 1.02922 | 0.514609 | − | 0.857425i | \(-0.327937\pi\) | ||||
0.514609 | + | 0.857425i | \(0.327937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.20141e17 | −0.849239 | −0.424620 | − | 0.905372i | \(-0.639592\pi\) | ||||
−0.424620 | + | 0.905372i | \(0.639592\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.90269e17 | −2.03301 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.53113e17 | −0.268059 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.03997e18 | −0.960952 | −0.480476 | − | 0.877008i | \(-0.659536\pi\) | ||||
−0.480476 | + | 0.877008i | \(0.659536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.24224e18 | −0.626560 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.44857e18 | 1.26243 | 0.631214 | − | 0.775609i | \(-0.282557\pi\) | ||||
0.631214 | + | 0.775609i | \(0.282557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.59241e18 | −0.589520 | −0.294760 | − | 0.955571i | \(-0.595240\pi\) | ||||
−0.294760 | + | 0.955571i | \(0.595240\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.16702e19 | 1.13536 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.37780e19 | −0.812946 | −0.406473 | − | 0.913663i | \(-0.633241\pi\) | ||||
−0.406473 | + | 0.913663i | \(0.633241\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.68330e19 | −0.980425 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.52541e19 | −1.27440 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.46557e19 | −0.217187 | −0.108593 | − | 0.994086i | \(-0.534635\pi\) | ||||
−0.108593 | + | 0.994086i | \(0.534635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.18886e20 | −3.08649 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.44780e20 | −0.929282 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.80044e19 | 0.207244 | 0.103622 | − | 0.994617i | \(-0.466957\pi\) | ||||
0.103622 | + | 0.994617i | \(0.466957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.58529e20 | 0.466462 | 0.233231 | − | 0.972421i | \(-0.425070\pi\) | ||||
0.233231 | + | 0.972421i | \(0.425070\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.08343e19 | −0.0829103 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.71107e20 | −0.951235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.69567e20 | −0.469718 | −0.234859 | − | 0.972029i | \(-0.575463\pi\) | ||||
−0.234859 | + | 0.972029i | \(0.575463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.75283e19 | 0.0481638 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.33886e21 | −0.687487 | −0.343743 | − | 0.939064i | \(-0.611695\pi\) | ||||
−0.343743 | + | 0.939064i | \(0.611695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.99578e21 | −1.11763 | −0.558814 | − | 0.829293i | \(-0.688743\pi\) | ||||
−0.558814 | + | 0.829293i | \(0.688743\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.23279e22 | 3.37044 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.11579e21 | 0.225393 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.35321e21 | 0.805198 | 0.402599 | − | 0.915377i | \(-0.368107\pi\) | ||||
0.402599 | + | 0.915377i | \(0.368107\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10027e22 | −1.24143 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.08227e22 | −0.922439 | −0.461219 | − | 0.887286i | \(-0.652588\pi\) | ||||
−0.461219 | + | 0.887286i | \(0.652588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.98504e22 | −1.93479 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.61837e22 | 1.29885 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.80097e22 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.34822e21 | 0.0694646 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.65196e22 | −1.07172 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.82158e22 | −1.41083 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.49638e22 | 0.354352 | 0.177176 | − | 0.984179i | \(-0.443304\pi\) | ||||
0.177176 | + | 0.984179i | \(0.443304\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.50448e22 | −0.954647 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.15528e22 | −0.370599 | −0.185300 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185300 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.58995e23 | 1.13176 | 0.565881 | − | 0.824487i | \(-0.308536\pi\) | ||||
0.565881 | + | 0.824487i | \(0.308536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.92871e22 | −0.338285 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.18100e23 | −1.46100 | −0.730499 | − | 0.682914i | \(-0.760712\pi\) | ||||
−0.730499 | + | 0.682914i | \(0.760712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.49191e23 | −0.924968 | −0.462484 | − | 0.886628i | \(-0.653042\pi\) | ||||
−0.462484 | + | 0.886628i | \(0.653042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02688e23 | −1.21270 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.93004e23 | −0.473330 | −0.236665 | − | 0.971591i | \(-0.576054\pi\) | ||||
−0.236665 | + | 0.971591i | \(0.576054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.64814e22 | 0.0731217 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.78979e23 | −0.294216 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.04448e23 | 0.141289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.42841e24 | 1.59522 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.72253e24 | 1.59316 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.16635e24 | 3.20103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.65775e24 | 1.06115 | 0.530575 | − | 0.847638i | \(-0.321976\pi\) | ||||
0.530575 | + | 0.847638i | \(0.321976\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.39102e24 | −0.743962 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.16608e24 | 0.970630 | 0.485315 | − | 0.874339i | \(-0.338705\pi\) | ||||
0.485315 | + | 0.874339i | \(0.338705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73680e23 | 0.103026 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.10669e24 | −0.985053 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.36579e24 | −0.365678 | −0.182839 | − | 0.983143i | \(-0.558529\pi\) | ||||
−0.182839 | + | 0.983143i | \(0.558529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.01914e24 | 0.230975 | 0.115488 | − | 0.993309i | \(-0.463157\pi\) | ||||
0.115488 | + | 0.993309i | \(0.463157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.33499e24 | −1.02592 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.89060e24 | 0.799830 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.41454e25 | 1.97190 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.03900e25 | −1.23728 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.32992e25 | 1.35576 | 0.677881 | − | 0.735171i | \(-0.262898\pi\) | ||||
0.677881 | + | 0.735171i | \(0.262898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.75843e25 | −1.53776 | −0.768882 | − | 0.639391i | \(-0.779186\pi\) | ||||
−0.768882 | + | 0.639391i | \(0.779186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.96090e24 | −0.598426 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.51317e25 | −1.62708 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.12704e25 | 0.629640 | 0.314820 | − | 0.949151i | \(-0.398056\pi\) | ||||
0.314820 | + | 0.949151i | \(0.398056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.67483e24 | −0.274085 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.27650e23 | −0.00533976 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.39967e25 | 0.508006 | 0.254003 | − | 0.967203i | \(-0.418253\pi\) | ||||
0.254003 | + | 0.967203i | \(0.418253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.23476e26 | −3.89509 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.01925e25 | 1.37848 | 0.689238 | − | 0.724535i | \(-0.257946\pi\) | ||||
0.689238 | + | 0.724535i | \(0.257946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.14615e25 | −0.753498 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.08596e25 | −0.436366 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.29563e25 | 0.237110 | 0.118555 | − | 0.992948i | \(-0.462174\pi\) | ||||
0.118555 | + | 0.992948i | \(0.462174\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.33037e25 | −0.373669 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.85878e25 | 0.261538 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.22455e25 | 0.275063 | 0.137531 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137531 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.15496e26 | 1.25679 | 0.628395 | − | 0.777895i | \(-0.283712\pi\) | ||||
0.628395 | + | 0.777895i | \(0.283712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.13841e25 | 0.588665 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.17548e26 | −1.84111 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.17531e26 | 1.62683 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.08704e25 | 0.0719342 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.24365e26 | −1.31544 | −0.657720 | − | 0.753262i | \(-0.728479\pi\) | ||||
−0.657720 | + | 0.753262i | \(0.728479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.97440e26 | 1.02689 | 0.513447 | − | 0.858121i | \(-0.328368\pi\) | ||||
0.513447 | + | 0.858121i | \(0.328368\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.59859e26 | −1.20044 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.41560e26 | −0.992347 | −0.496174 | − | 0.868223i | \(-0.665262\pi\) | ||||
−0.496174 | + | 0.868223i | \(0.665262\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.29101e26 | −1.20370 | −0.601850 | − | 0.798609i | \(-0.705569\pi\) | ||||
−0.601850 | + | 0.798609i | \(0.705569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.81821e26 | −0.592775 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.94954e25 | −0.143999 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.30580e26 | 2.41871 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.72934e24 | 0.0226164 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.69987e26 | 1.18627 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.06204e27 | −1.98104 | −0.990518 | − | 0.137387i | \(-0.956130\pi\) | ||||
−0.990518 | + | 0.137387i | \(0.956130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.18420e26 | −0.867594 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.51482e26 | −1.12947 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.79367e25 | 0.118818 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.16000e27 | −1.41042 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.57801e26 | 0.501378 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.37454e26 | −0.431943 | −0.215971 | − | 0.976400i | \(-0.569292\pi\) | ||||
−0.215971 | + | 0.976400i | \(0.569292\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.77619e27 | 1.58267 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.76894e27 | 1.42369 | 0.711846 | − | 0.702335i | \(-0.247859\pi\) | ||||
0.711846 | + | 0.702335i | \(0.247859\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.02884e27 | −0.748581 | −0.374291 | − | 0.927311i | \(-0.622114\pi\) | ||||
−0.374291 | + | 0.927311i | \(0.622114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.32046e26 | 0.284441 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.28652e27 | −0.767050 | −0.383525 | − | 0.923530i | \(-0.625290\pi\) | ||||
−0.383525 | + | 0.923530i | \(0.625290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.88217e27 | −1.55754 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.07282e27 | 1.01614 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.39893e26 | 0.0622614 | 0.0311307 | − | 0.999515i | \(-0.490089\pi\) | ||||
0.0311307 | + | 0.999515i | \(0.490089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.54422e26 | 0.345522 | 0.172761 | − | 0.984964i | \(-0.444731\pi\) | ||||
0.172761 | + | 0.984964i | \(0.444731\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.86220e27 | −1.05251 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.61309e27 | −1.87842 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.19956e27 | 0.365600 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.19066e27 | −1.16410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.52129e27 | 0.638814 | 0.319407 | − | 0.947618i | \(-0.396516\pi\) | ||||
0.319407 | + | 0.947618i | \(0.396516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.65853e26 | −0.0614831 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.15584e28 | −2.44166 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.52365e27 | −1.06658 | −0.533292 | − | 0.845931i | \(-0.679045\pi\) | ||||
−0.533292 | + | 0.845931i | \(0.679045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.61206e26 | 0.134448 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.77249e27 | 0.609906 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.10056e28 | −1.62976 | −0.814880 | − | 0.579630i | \(-0.803197\pi\) | ||||
−0.814880 | + | 0.579630i | \(0.803197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.06576e27 | −0.416113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.97354e27 | −0.868108 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.38900e27 | 0.387187 | 0.193593 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193593 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.30721e28 | −1.37151 | −0.685753 | − | 0.727834i | \(-0.740527\pi\) | ||||
−0.685753 | + | 0.727834i | \(0.740527\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.09256e26 | 0.0876629 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.85341e28 | −4.30250 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.72270e27 | 0.140505 | 0.0702526 | − | 0.997529i | \(-0.477619\pi\) | ||||
0.0702526 | + | 0.997529i | \(0.477619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.70245e27 | −0.503252 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.49530e27 | 0.587565 | 0.293783 | − | 0.955872i | \(-0.405086\pi\) | ||||
0.293783 | + | 0.955872i | \(0.405086\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.48272e28 | 0.945178 | 0.472589 | − | 0.881283i | \(-0.343319\pi\) | ||||
0.472589 | + | 0.881283i | \(0.343319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.02860e28 | −1.78043 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.25613e27 | −0.176628 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.95146e26 | 0.0197894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.66622e27 | 0.447185 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.04503e28 | 1.30201 | 0.651004 | − | 0.759074i | \(-0.274348\pi\) | ||||
0.651004 | + | 0.759074i | \(0.274348\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.00418e28 | 0.397064 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.26396e28 | 0.828265 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.59497e26 | −0.0189487 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.62946e27 | 0.0824806 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.60897e28 | −0.467689 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.31621e28 | 0.893704 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.06055e28 | −1.51503 | −0.757515 | − | 0.652818i | \(-0.773587\pi\) | ||||
−0.757515 | + | 0.652818i | \(0.773587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.15644e28 | 1.42826 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.87533e28 | 1.91179 | 0.955894 | − | 0.293711i | \(-0.0948903\pi\) | ||||
0.955894 | + | 0.293711i | \(0.0948903\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.40764e28 | 1.48225 | 0.741123 | − | 0.671369i | \(-0.234294\pi\) | ||||
0.741123 | + | 0.671369i | \(0.234294\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.54196e27 | −0.158850 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.50150e28 | −0.259623 | −0.129812 | − | 0.991539i | \(-0.541437\pi\) | ||||
−0.129812 | + | 0.991539i | \(0.541437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.03083e29 | −1.65804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.23171e29 | −1.84375 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.33556e28 | 0.743619 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.02142e29 | −1.32600 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.64891e28 | −1.16729 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.00848e28 | 0.113740 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.74199e28 | −0.814386 | −0.407193 | − | 0.913342i | \(-0.633492\pi\) | ||||
−0.407193 | + | 0.913342i | \(0.633492\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.80185e28 | −0.569452 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.82269e28 | −0.899943 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.10595e29 | −1.80179 | −0.900896 | − | 0.434035i | \(-0.857089\pi\) | ||||
−0.900896 | + | 0.434035i | \(0.857089\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.47330e28 | −0.597332 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.83144e29 | 1.36810 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.96729e28 | 0.277084 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.41260e28 | 0.0922781 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.83300e29 | 1.73164 | 0.865821 | − | 0.500354i | \(-0.166797\pi\) | ||||
0.865821 | + | 0.500354i | \(0.166797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.13553e28 | 0.293828 | 0.146914 | − | 0.989149i | \(-0.453066\pi\) | ||||
0.146914 | + | 0.989149i | \(0.453066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.76458e28 | 0.255266 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.28041e28 | 0.214821 | 0.107410 | − | 0.994215i | \(-0.465744\pi\) | ||||
0.107410 | + | 0.994215i | \(0.465744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.80071e29 | −1.31717 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.04432e28 | 0.178304 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.32369e28 | 0.137415 | 0.0687076 | − | 0.997637i | \(-0.478112\pi\) | ||||
0.0687076 | + | 0.997637i | \(0.478112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.18024e29 | −0.457761 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.53095e29 | 2.01314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.26675e29 | −2.14129 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.37619e29 | 0.441590 | 0.220795 | − | 0.975320i | \(-0.429135\pi\) | ||||
0.220795 | + | 0.975320i | \(0.429135\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.48179e29 | 0.748104 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.07272e28 | 0.0303869 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.64990e29 | −1.50449 | −0.752244 | − | 0.658884i | \(-0.771029\pi\) | ||||
−0.752244 | + | 0.658884i | \(0.771029\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.61325e30 | 4.03964 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.16942e29 | −0.510996 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18752e29 | 0.706484 | 0.353242 | − | 0.935532i | \(-0.385079\pi\) | ||||
0.353242 | + | 0.935532i | \(0.385079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.41899e29 | 1.33915 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.44375e29 | −0.676465 | −0.338233 | − | 0.941063i | \(-0.609829\pi\) | ||||
−0.338233 | + | 0.941063i | \(0.609829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.33408e29 | 0.431835 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00415e29 | −0.349345 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.77881e29 | 1.44217 | 0.721083 | − | 0.692849i | \(-0.243645\pi\) | ||||
0.721083 | + | 0.692849i | \(0.243645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.48861e28 | −0.0385411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.38726e29 | 1.22491 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.11982e30 | 1.54270 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.44903e30 | 1.88359 | 0.941793 | − | 0.336192i | \(-0.109139\pi\) | ||||
0.941793 | + | 0.336192i | \(0.109139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.05972e29 | 0.130017 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.88431e29 | 1.02911 | 0.514557 | − | 0.857456i | \(-0.327956\pi\) | ||||
0.514557 | + | 0.857456i | \(0.327956\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.85432e29 | 0.421639 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.30161e30 | −2.37848 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.58535e30 | 1.54806 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.16570e29 | −0.569068 | −0.284534 | − | 0.958666i | \(-0.591839\pi\) | ||||
−0.284534 | + | 0.958666i | \(0.591839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.28849e29 | −0.461478 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.51367e28 | −0.0289959 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.26396e30 | −1.76732 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.94623e29 | 0.291486 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.89006e29 | −0.271954 | −0.135977 | − | 0.990712i | \(-0.543417\pi\) | ||||
−0.135977 | + | 0.990712i | \(0.543417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.64655e30 | 1.08976 | 0.544879 | − | 0.838515i | \(-0.316576\pi\) | ||||
0.544879 | + | 0.838515i | \(0.316576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.68655e29 | −0.481745 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.54320e30 | −2.69705 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.16035e29 | −0.0652633 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.89369e30 | 1.00937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.94618e30 | 1.48857 | 0.744287 | − | 0.667859i | \(-0.232789\pi\) | ||||
0.744287 | + | 0.667859i | \(0.232789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.55571e30 | 1.22434 | 0.612168 | − | 0.790728i | \(-0.290298\pi\) | ||||
0.612168 | + | 0.790728i | \(0.290298\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.47726e30 | 2.48850 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.52080e28 | −0.0281037 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.96935e30 | −0.805341 | −0.402671 | − | 0.915345i | \(-0.631918\pi\) | ||||
−0.402671 | + | 0.915345i | \(0.631918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.49697e30 | −0.580992 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.63340e30 | 1.33866 | 0.669330 | − | 0.742966i | \(-0.266581\pi\) | ||||
0.669330 | + | 0.742966i | \(0.266581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.76738e30 | −1.31795 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.14959e30 | 1.71094 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.30596e29 | −0.293717 | −0.146858 | − | 0.989158i | \(-0.546916\pi\) | ||||
−0.146858 | + | 0.989158i | \(0.546916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.78147e30 | −2.03373 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.80881e30 | −1.94063 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.91216e29 | 0.133089 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.15005e30 | 1.32671 | 0.663354 | − | 0.748306i | \(-0.269132\pi\) | ||||
0.663354 | + | 0.748306i | \(0.269132\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.11925e30 | 0.519203 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.91029e30 | 0.445183 | 0.222592 | − | 0.974912i | \(-0.428548\pi\) | ||||
0.222592 | + | 0.974912i | \(0.428548\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.39782e30 | 0.531661 | 0.265831 | − | 0.964020i | \(-0.414354\pi\) | ||||
0.265831 | + | 0.964020i | \(0.414354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.73125e30 | −2.05334 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.20935e29 | 0.164879 | 0.0824394 | − | 0.996596i | \(-0.473729\pi\) | ||||
0.0824394 | + | 0.996596i | \(0.473729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.43699e29 | 0.0657189 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.36400e30 | 0.794592 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.47632e30 | 0.949699 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.19044e31 | −1.96666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.17618e29 | −0.128703 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.01484e30 | −1.35238 | −0.676191 | − | 0.736726i | \(-0.736371\pi\) | ||||
−0.676191 | + | 0.736726i | \(0.736371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.33642e30 | 0.477103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.94272e28 | −0.00673867 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.22207e30 | 0.678911 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.18875e31 | −1.47403 | −0.737014 | − | 0.675877i | \(-0.763765\pi\) | ||||
−0.737014 | + | 0.675877i | \(0.763765\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.41967e30 | 0.641093 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.78471e30 | −0.540031 | −0.270015 | − | 0.962856i | \(-0.587029\pi\) | ||||
−0.270015 | + | 0.962856i | \(0.587029\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.64943e30 | −1.03935 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.77902e31 | −1.82903 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.79977e29 | 0.0961872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.40022e31 | −1.31232 | −0.656160 | − | 0.754622i | \(-0.727820\pi\) | ||||
−0.656160 | + | 0.754622i | \(0.727820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.94350e31 | 1.73961 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.41798e30 | −0.634240 | −0.317120 | − | 0.948385i | \(-0.602716\pi\) | ||||
−0.317120 | + | 0.948385i | \(0.602716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.69227e30 | −0.710039 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.21822e31 | −0.950899 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.56637e30 | 0.639061 | 0.319530 | − | 0.947576i | \(-0.396475\pi\) | ||||
0.319530 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.19276e30 | 0.156369 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.55300e30 | 0.378597 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.32595e31 | 2.16837 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.10034e31 | 1.30963 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.01679e30 | 0.299227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.85808e31 | 1.06030 | 0.530151 | − | 0.847903i | \(-0.322135\pi\) | ||||
0.530151 | + | 0.847903i | \(0.322135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.92489e31 | −1.59713 | −0.798564 | − | 0.601910i | \(-0.794407\pi\) | ||||
−0.798564 | + | 0.601910i | \(0.794407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.02342e30 | −0.471563 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.71438e31 | 0.857601 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.08501e31 | −0.998543 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.67809e30 | 0.122811 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.42718e31 | −0.626782 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.65420e31 | −2.79916 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.61367e30 | 0.347123 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.09046e31 | 1.57943 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.50213e31 | −1.29588 | −0.647938 | − | 0.761693i | \(-0.724368\pi\) | ||||
−0.647938 | + | 0.761693i | \(0.724368\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.47211e31 | 1.58604 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.21272e31 | −1.77217 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.82542e30 | 0.0594990 | 0.0297495 | − | 0.999557i | \(-0.490529\pi\) | ||||
0.0297495 | + | 0.999557i | \(0.490529\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.84410e30 | 0.276421 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.52840e31 | −0.757884 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.91827e30 | −0.112656 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.42367e31 | −2.32344 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.56099e31 | 0.677756 | 0.338878 | − | 0.940830i | \(-0.389953\pi\) | ||||
0.338878 | + | 0.940830i | \(0.389953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.15251e31 | 0.292691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.42302e31 | 2.05303 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.17127e31 | −1.44387 | −0.721935 | − | 0.691961i | \(-0.756747\pi\) | ||||
−0.721935 | + | 0.691961i | \(0.756747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.03737e31 | −0.906862 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.05340e30 | 0.173690 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.42387e31 | −0.916243 | −0.458122 | − | 0.888889i | \(-0.651478\pi\) | ||||
−0.458122 | + | 0.888889i | \(0.651478\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.85052e31 | −0.964880 | −0.482440 | − | 0.875929i | \(-0.660249\pi\) | ||||
−0.482440 | + | 0.875929i | \(0.660249\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.68764e31 | −1.66006 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.55243e30 | 0.101930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.95368e31 | 0.873789 | 0.436894 | − | 0.899513i | \(-0.356078\pi\) | ||||
0.436894 | + | 0.899513i | \(0.356078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.64507e31 | 1.29592 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.92166e30 | 0.129060 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.23413e31 | 0.349881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.74400e31 | −0.563694 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.70339e31 | 0.825648 | 0.412824 | − | 0.910811i | \(-0.364542\pi\) | ||||
0.412824 | + | 0.910811i | \(0.364542\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.49212e31 | 0.625353 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.35345e31 | −1.25232 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.33571e32 | −1.72021 | −0.860107 | − | 0.510113i | \(-0.829604\pi\) | ||||
−0.860107 | + | 0.510113i | \(0.829604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.18490e31 | 0.270699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.27431e32 | −1.51904 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.93052e31 | −1.13910 | −0.569552 | − | 0.821955i | \(-0.692883\pi\) | ||||
−0.569552 | + | 0.821955i | \(0.692883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.44615e31 | 0.159645 | 0.0798227 | − | 0.996809i | \(-0.474565\pi\) | ||||
0.0798227 | + | 0.996809i | \(0.474565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.61964e31 | −0.278351 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.98803e32 | 3.05632 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.96312e31 | 0.784175 | 0.392088 | − | 0.919928i | \(-0.371753\pi\) | ||||
0.392088 | + | 0.919928i | \(0.371753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.91651e31 | −0.181724 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.42024e31 | 0.403619 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.28683e31 | 0.376999 | 0.188500 | − | 0.982073i | \(-0.439638\pi\) | ||||
0.188500 | + | 0.982073i | \(0.439638\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.60330e32 | 3.05236 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.17493e32 | 0.958810 | 0.479405 | − | 0.877594i | \(-0.340853\pi\) | ||||
0.479405 | + | 0.877594i | \(0.340853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.82548e32 | 1.43527 | 0.717637 | − | 0.696417i | \(-0.245224\pi\) | ||||
0.717637 | + | 0.696417i | \(0.245224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.59003e30 | −0.0196223 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.31822e31 | 0.0962442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.92005e32 | 3.46218 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.20705e32 | 1.49705 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.48402e32 | 0.970414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.49211e31 | 0.535400 | 0.267700 | − | 0.963502i | \(-0.413736\pi\) | ||||
0.267700 | + | 0.963502i | \(0.413736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.11232e32 | −2.50003 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.46779e32 | 2.03308 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.60851e31 | 0.486771 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.46930e31 | −0.407399 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.48524e31 | 0.236004 | 0.118002 | − | 0.993013i | \(-0.462351\pi\) | ||||
0.118002 | + | 0.993013i | \(0.462351\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.69068e32 | −1.36595 | −0.682976 | − | 0.730441i | \(-0.739314\pi\) | ||||
−0.682976 | + | 0.730441i | \(0.739314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.90982e32 | −1.42537 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.10364e31 | −0.383072 | −0.191536 | − | 0.981486i | \(-0.561347\pi\) | ||||
−0.191536 | + | 0.981486i | \(0.561347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.31786e31 | −0.333864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.40500e31 | 0.149946 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.49897e32 | −1.06233 | −0.531166 | − | 0.847268i | \(-0.678246\pi\) | ||||
−0.531166 | + | 0.847268i | \(0.678246\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.53113e32 | 1.85965 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.67130e32 | −0.662297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.39914e32 | −0.535400 | −0.267700 | − | 0.963502i | \(-0.586264\pi\) | ||||
−0.267700 | + | 0.963502i | \(0.586264\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.05101e32 | 0.757967 | 0.378984 | − | 0.925403i | \(-0.376274\pi\) | ||||
0.378984 | + | 0.925403i | \(0.376274\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.77265e32 | 0.632729 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.72500e31 | 0.197391 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17930e31 | 0.0392804 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.69386e32 | −0.545103 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.41664e32 | −0.751455 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.12434e31 | −0.153980 | −0.0769900 | − | 0.997032i | \(-0.524531\pi\) | ||||
−0.0769900 | + | 0.997032i | \(0.524531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.72835e32 | −1.37314 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.07886e31 | −0.198698 | −0.0993490 | − | 0.995053i | \(-0.531676\pi\) | ||||
−0.0993490 | + | 0.995053i | \(0.531676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.82722e31 | −0.0495779 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.84952e32 | 1.79667 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.04620e31 | −0.0265324 | −0.0132662 | − | 0.999912i | \(-0.504223\pi\) | ||||
−0.0132662 | + | 0.999912i | \(0.504223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.85705e32 | −0.700610 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.98377e32 | −0.944694 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.70181e31 | 0.107831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.91309e32 | 1.53347 | 0.766734 | − | 0.641965i | \(-0.221880\pi\) | ||||
0.766734 | + | 0.641965i | \(0.221880\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.22484e31 | 0.133566 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.13191e32 | 0.442531 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.34803e32 | −1.27486 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.98154e32 | −0.968002 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.87851e32 | −0.917339 | −0.458669 | − | 0.888607i | \(-0.651674\pi\) | ||||
−0.458669 | + | 0.888607i | \(0.651674\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.88851e32 | 0.707616 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.11601e33 | −1.96558 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.04145e31 | 0.0518511 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.32445e31 | −0.0383609 | −0.0191805 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191805 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.98647e32 | 0.477153 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.09521e31 | −0.0324115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.02304e33 | 1.53241 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.41678e31 | 0.0785725 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.46511e32 | −1.18919 | −0.594594 | − | 0.804026i | \(-0.702687\pi\) | ||||
−0.594594 | + | 0.804026i | \(0.702687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.16376e32 | −0.158346 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.30841e32 | 0.436042 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.15292e33 | 2.74879 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.29417e33 | 1.60083 | 0.800415 | − | 0.599446i | \(-0.204612\pi\) | ||||
0.800415 | + | 0.599446i | \(0.204612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.24448e31 | −0.0868242 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.12630e32 | 0.595325 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.02612e32 | −0.565636 | −0.282818 | − | 0.959174i | \(-0.591269\pi\) | ||||
−0.282818 | + | 0.959174i | \(0.591269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.17344e33 | −2.37052 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.15815e32 | 0.756702 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.75747e32 | −0.692426 | −0.346213 | − | 0.938156i | \(-0.612533\pi\) | ||||
−0.346213 | + | 0.938156i | \(0.612533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.64480e32 | 0.461379 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.22735e33 | −1.18194 | −0.590971 | − | 0.806693i | \(-0.701255\pi\) | ||||
−0.590971 | + | 0.806693i | \(0.701255\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.78201e33 | 2.59753 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.03782e32 | −0.546630 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.32832e32 | 0.204410 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.58023e32 | 0.730533 | 0.365267 | − | 0.930903i | \(-0.380978\pi\) | ||||
0.365267 | + | 0.930903i | \(0.380978\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.76268e32 | 0.806171 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.67838e33 | −2.94623 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.90201e32 | −0.303170 | −0.151585 | − | 0.988444i | \(-0.548438\pi\) | ||||
−0.151585 | + | 0.988444i | \(0.548438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.02941e32 | −0.0775904 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.45216e33 | −1.79319 | −0.896593 | − | 0.442855i | \(-0.853965\pi\) | ||||
−0.896593 | + | 0.442855i | \(0.853965\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.82395e32 | 0.129414 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.66531e33 | −1.14654 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.54007e32 | −0.102895 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.56496e32 | −0.620198 | −0.310099 | − | 0.950704i | \(-0.600362\pi\) | ||||
−0.310099 | + | 0.950704i | \(0.600362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.13881e33 | −1.34601 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.64837e33 | 1.00691 | 0.503454 | − | 0.864022i | \(-0.332062\pi\) | ||||
0.503454 | + | 0.864022i | \(0.332062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.82502e33 | −2.26811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.94747e32 | 0.169671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.66335e33 | −0.929613 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04098e33 | 1.10752 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00427e33 | −0.529163 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.35760e33 | 1.20634 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.91155e32 | 0.393145 | 0.196572 | − | 0.980489i | \(-0.437019\pi\) | ||||
0.196572 | + | 0.980489i | \(0.437019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.26149e33 | −2.05672 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.41269e32 | 0.0662242 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.08590e32 | −0.231593 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.18709e33 | −0.525126 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.89061e32 | 0.210181 | 0.105090 | − | 0.994463i | \(-0.466487\pi\) | ||||
0.105090 | + | 0.994463i | \(0.466487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.96610e33 | 0.820950 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.00473e33 | −0.407640 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.56681e33 | 1.80046 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.67025e31 | −0.0102306 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.31226e33 | 0.488622 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.88048e33 | 1.40436 | 0.702179 | − | 0.712000i | \(-0.252211\pi\) | ||||
0.702179 | + | 0.712000i | \(0.252211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.12171e33 | −1.44990 | −0.724949 | − | 0.688803i | \(-0.758137\pi\) | ||||
−0.724949 | + | 0.688803i | \(0.758137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.06164e33 | −1.73081 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.92792e33 | 0.973299 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.34322e33 | 0.434105 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.31004e32 | 0.0411641 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.87333e32 | 0.148895 | 0.0744474 | − | 0.997225i | \(-0.476281\pi\) | ||||
0.0744474 | + | 0.997225i | \(0.476281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.29803e33 | −0.979842 | −0.489921 | − | 0.871767i | \(-0.662974\pi\) | ||||
−0.489921 | + | 0.871767i | \(0.662974\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.87929e34 | −5.42967 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.54431e32 | −0.155788 | −0.0778940 | − | 0.996962i | \(-0.524820\pi\) | ||||
−0.0778940 | + | 0.996962i | \(0.524820\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.38218e33 | 1.47089 | 0.735446 | − | 0.677583i | \(-0.236973\pi\) | ||||
0.735446 | + | 0.677583i | \(0.236973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.67047e32 | 0.177315 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.82901e33 | 0.990078 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.04996e34 | 2.64105 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.78425e33 | 0.436628 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.71028e32 | 0.112146 | 0.0560730 | − | 0.998427i | \(-0.482142\pi\) | ||||
0.0560730 | + | 0.998427i | \(0.482142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.55929e32 | 0.0592878 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.28947e33 | 0.741495 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.58130e33 | −1.44364 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.04552e33 | −0.223190 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.74122e33 | 1.19280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.81368e32 | −0.0366750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.73307e33 | 1.52208 | 0.761041 | − | 0.648704i | \(-0.224689\pi\) | ||||
0.761041 | + | 0.648704i | \(0.224689\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.36354e33 | −0.836043 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.06846e33 | −0.572322 | −0.286161 | − | 0.958182i | \(-0.592379\pi\) | ||||
−0.286161 | + | 0.958182i | \(0.592379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.27658e33 | −1.13973 | −0.569864 | − | 0.821739i | \(-0.693004\pi\) | ||||
−0.569864 | + | 0.821739i | \(0.693004\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.26081e33 | −0.222901 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.01784e33 | −0.347347 | −0.173674 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173674 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.71027e33 | 0.454283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.53004e32 | 0.0249738 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.16051e33 | −1.29715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50646e33 | 0.233210 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.39269e33 | 0.209986 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.04955e33 | −0.447861 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.10079e33 | 1.01581 | 0.507903 | − | 0.861414i | \(-0.330421\pi\) | ||||
0.507903 | + | 0.861414i | \(0.330421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.17907e34 | 1.64311 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.35471e33 | 0.862726 | 0.431363 | − | 0.902178i | \(-0.358033\pi\) | ||||
0.431363 | + | 0.902178i | \(0.358033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.03451e33 | −0.533633 | −0.266817 | − | 0.963747i | \(-0.585972\pi\) | ||||
−0.266817 | + | 0.963747i | \(0.585972\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.88830e33 | 0.501086 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.96616e33 | 0.874726 | 0.437363 | − | 0.899285i | \(-0.355913\pi\) | ||||
0.437363 | + | 0.899285i | \(0.355913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.21339e33 | −0.148467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.67727e34 | 1.99990 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.15168e33 | 0.598628 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.65344e33 | 0.526998 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.16643e32 | −0.0239128 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.12407e33 | −0.874051 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.09134e33 | 0.219325 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.01815e33 | 0.104089 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.41601e34 | 2.40791 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.14289e33 | −0.208217 | −0.104109 | − | 0.994566i | \(-0.533199\pi\) | ||||
−0.104109 | + | 0.994566i | \(0.533199\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.31817e33 | −0.219614 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.44743e33 | 0.595559 | 0.297780 | − | 0.954635i | \(-0.403754\pi\) | ||||
0.297780 | + | 0.954635i | \(0.403754\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.64983e34 | 1.48602 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.28407e34 | 1.12784 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.58546e33 | −0.135802 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.53028e34 | −1.27833 | −0.639164 | − | 0.769071i | \(-0.720719\pi\) | ||||
−0.639164 | + | 0.769071i | \(0.720719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.34671e34 | −1.91194 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.29531e33 | 0.341330 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.31105e34 | −2.56647 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.87008e33 | 0.670673 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.50103e34 | −1.84475 | −0.922376 | − | 0.386294i | \(-0.873755\pi\) | ||||
−0.922376 | + | 0.386294i | \(0.873755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00330e34 | 0.721954 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.43662e34 | 2.41264 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.55044e34 | 3.11688 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.75099e33 | −0.584860 | −0.292430 | − | 0.956287i | \(-0.594464\pi\) | ||||
−0.292430 | + | 0.956287i | \(0.594464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.86831e34 | 1.87056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.18186e34 | −0.752115 | −0.376057 | − | 0.926596i | \(-0.622720\pi\) | ||||
−0.376057 | + | 0.926596i | \(0.622720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.75818e32 | 0.0481809 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.27394e33 | 0.137820 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.79192e34 | 1.65150 | 0.825750 | − | 0.564037i | \(-0.190752\pi\) | ||||
0.825750 | + | 0.564037i | \(0.190752\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.61100e33 | 0.554891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.81396e33 | −0.327639 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.61770e33 | −0.474049 | −0.237024 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237024 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.69340e34 | −2.52028 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.99148e34 | −2.09241 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.99691e32 | 0.0511625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.57957e33 | −0.278793 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.77463e34 | −0.865775 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.13017e34 | 1.96745 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.60088e34 | −1.20981 | −0.604903 | − | 0.796299i | \(-0.706788\pi\) | ||||
−0.604903 | + | 0.796299i | \(0.706788\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.06598e34 | 0.938432 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.04930e33 | 0.357057 | 0.178528 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178528 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.45961e32 | −0.0323161 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.95503e34 | −1.67339 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.25035e34 | 0.929958 | 0.464979 | − | 0.885322i | \(-0.346062\pi\) | ||||
0.464979 | + | 0.885322i | \(0.346062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.74543e34 | 1.10818 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.39020e34 | −0.548129 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.27108e33 | −0.203018 | −0.101509 | − | 0.994835i | \(-0.532367\pi\) | ||||
−0.101509 | + | 0.994835i | \(0.532367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.05310e34 | −1.90126 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.90494e33 | 0.143538 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.26505e32 | −0.0224992 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.12466e34 | −1.79812 | −0.899058 | − | 0.437829i | \(-0.855748\pi\) | ||||
−0.899058 | + | 0.437829i | \(0.855748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.99778e34 | −1.02774 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.88432e34 | −2.30619 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.33679e34 | 0.437591 | 0.218796 | − | 0.975771i | \(-0.429787\pi\) | ||||
0.218796 | + | 0.975771i | \(0.429787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.54450e34 | 0.494065 |
(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 | 64.24.a.f.1.2 | 2 | ||
4.3 | odd | 2 | 64.24.a.e.1.1 | 2 | |||
8.3 | odd | 2 | 4.24.a.a.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 16.24.a.c.1.1 | 2 | |||
24.11 | even | 2 | 36.24.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.24.a.a.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
16.24.a.c.1.1 | 2 | 8.5 | even | 2 | |||
36.24.a.e.1.2 | 2 | 24.11 | even | 2 | |||
64.24.a.e.1.1 | 2 | 4.3 | odd | 2 | |||
64.24.a.f.1.2 | 2 | 1.1 | even | 1 | trivial |