Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.11 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.k.2881.11 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.92048 | + | 3.32636i | 0.858863 | + | 1.48759i | 0.873014 | + | 0.487694i | \(0.162162\pi\) |
−0.0141515 | + | 0.999900i | \(0.504505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55336 | + | 0.693065i | 0.965080 | + | 0.261954i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.903316 | + | 1.56459i | −0.272360 | + | 0.471741i | −0.969466 | − | 0.245227i | \(-0.921137\pi\) |
0.697106 | + | 0.716968i | \(0.254471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.692713 | + | 1.19981i | −0.192124 | + | 0.332769i | −0.945954 | − | 0.324301i | \(-0.894871\pi\) |
0.753830 | + | 0.657070i | \(0.228204\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.833405 | + | 1.44350i | 0.202130 | + | 0.350100i | 0.949215 | − | 0.314629i | \(-0.101880\pi\) |
−0.747084 | + | 0.664729i | \(0.768547\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0802084 | − | 0.138925i | 0.0184011 | − | 0.0318716i | −0.856678 | − | 0.515851i | \(-0.827476\pi\) |
0.875079 | + | 0.483980i | \(0.160809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.60019 | − | 2.77161i | −0.333663 | − | 0.577921i | 0.649564 | − | 0.760307i | \(-0.274951\pi\) |
−0.983227 | + | 0.182386i | \(0.941618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87646 | + | 8.44627i | −0.975291 | + | 1.68925i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.78000 | + | 6.54716i | 0.701929 | + | 1.21578i | 0.967788 | + | 0.251765i | \(0.0810110\pi\) |
−0.265859 | + | 0.964012i | \(0.585656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.22021 | −0.578367 | −0.289184 | − | 0.957274i | \(-0.593384\pi\) | ||||
−0.289184 | + | 0.957274i | \(0.593384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.59829 | + | 9.82442i | 0.439190 | + | 1.66063i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.58395 | − | 2.74348i | 0.260399 | − | 0.451025i | −0.705949 | − | 0.708263i | \(-0.749479\pi\) |
0.966348 | + | 0.257238i | \(0.0828124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00329 | + | 10.3980i | −0.937556 | + | 1.62389i | −0.167545 | + | 0.985864i | \(0.553584\pi\) |
−0.770011 | + | 0.638030i | \(0.779750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45480 | − | 5.98389i | −0.526852 | − | 0.912535i | −0.999510 | − | 0.0312891i | \(-0.990039\pi\) |
0.472658 | − | 0.881246i | \(-0.343295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4384 | 1.66846 | 0.834232 | − | 0.551414i | \(-0.185911\pi\) | ||||
0.834232 | + | 0.551414i | \(0.185911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03932 | + | 3.53929i | 0.862760 | + | 0.505613i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.37450 | − | 2.38071i | −0.188802 | − | 0.327015i | 0.756049 | − | 0.654515i | \(-0.227127\pi\) |
−0.944851 | + | 0.327500i | \(0.893794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.93918 | −0.935679 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.0705 | 1.96202 | 0.981009 | − | 0.193964i | \(-0.0621344\pi\) | ||||
0.981009 | + | 0.193964i | \(0.0621344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.20285 | −1.17830 | −0.589152 | − | 0.808022i | \(-0.700538\pi\) | ||||
−0.589152 | + | 0.808022i | \(0.700538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.32136 | −0.660033 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3366 | 1.50716 | 0.753578 | − | 0.657359i | \(-0.228326\pi\) | ||||
0.753578 | + | 0.657359i | \(0.228326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.93289 | −0.822783 | −0.411391 | − | 0.911459i | \(-0.634957\pi\) | ||||
−0.411391 | + | 0.911459i | \(0.634957\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.22457 | − | 10.7813i | −0.728531 | − | 1.26185i | −0.957504 | − | 0.288420i | \(-0.906870\pi\) |
0.228973 | − | 0.973433i | \(-0.426463\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.39085 | + | 3.36891i | −0.386424 | + | 0.383922i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.0743 | −1.80850 | −0.904251 | − | 0.427001i | \(-0.859570\pi\) | ||||
−0.904251 | + | 0.427001i | \(0.859570\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.45280 | − | 2.51633i | −0.159466 | − | 0.276203i | 0.775210 | − | 0.631703i | \(-0.217644\pi\) |
−0.934676 | + | 0.355500i | \(0.884311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20107 | + | 5.54441i | −0.347205 | + | 0.601376i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.04034 | + | 8.73012i | −0.534275 | + | 0.925391i | 0.464923 | + | 0.885351i | \(0.346082\pi\) |
−0.999198 | + | 0.0400399i | \(0.987251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.60030 | + | 2.58347i | −0.272585 | + | 0.270821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.616153 | 0.0632160 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.18830 | + | 7.25435i | 0.425257 | + | 0.736567i | 0.996444 | − | 0.0842527i | \(-0.0268503\pi\) |
−0.571187 | + | 0.820820i | \(0.693517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.05750 | − | 7.02780i | 0.403736 | − | 0.699292i | −0.590437 | − | 0.807084i | \(-0.701045\pi\) |
0.994173 | + | 0.107792i | \(0.0343780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.76891 | − | 6.52794i | −0.371362 | − | 0.643217i | 0.618414 | − | 0.785853i | \(-0.287776\pi\) |
−0.989775 | + | 0.142635i | \(0.954442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.95731 | + | 5.12221i | −0.285894 | + | 0.495183i | −0.972826 | − | 0.231539i | \(-0.925624\pi\) |
0.686932 | + | 0.726722i | \(0.258957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.48409 | − | 7.76668i | −0.429498 | − | 0.743913i | 0.567331 | − | 0.823490i | \(-0.307976\pi\) |
−0.996829 | + | 0.0795776i | \(0.974643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.98131 | − | 13.8240i | 0.750819 | − | 1.30046i | −0.196608 | − | 0.980482i | \(-0.562993\pi\) |
0.947426 | − | 0.319974i | \(-0.103674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.14626 | − | 10.6456i | 0.573142 | − | 0.992710i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.12755 | + | 4.26338i | 0.103362 | + | 0.390824i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86804 | + | 6.69964i | 0.351640 | + | 0.609059i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.2557 | −1.63284 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.60913 | −0.763937 | −0.381968 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381968 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.964831 | + | 1.67114i | 0.0842976 | + | 0.146008i | 0.905092 | − | 0.425216i | \(-0.139802\pi\) |
−0.820794 | + | 0.571224i | \(0.806469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.301085 | − | 0.299136i | 0.0261074 | − | 0.0259384i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.85442 | + | 3.21195i | −0.158434 | + | 0.274416i | −0.934304 | − | 0.356477i | \(-0.883978\pi\) |
0.775870 | + | 0.630893i | \(0.217311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.134568 | + | 0.233079i | −0.0114139 | + | 0.0197695i | −0.871676 | − | 0.490083i | \(-0.836967\pi\) |
0.860262 | + | 0.509852i | \(0.170300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.25148 | − | 2.16762i | −0.104654 | − | 0.181266i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.5188 | + | 25.1473i | −1.20572 | + | 2.08837i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.15880 | + | 7.20325i | 0.340702 | + | 0.590113i | 0.984563 | − | 0.175029i | \(-0.0560019\pi\) |
−0.643861 | + | 0.765142i | \(0.722669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.87069 | − | 8.43628i | 0.396371 | − | 0.686535i | −0.596904 | − | 0.802313i | \(-0.703603\pi\) |
0.993275 | + | 0.115778i | \(0.0369360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.18434 | − | 10.7116i | −0.496738 | − | 0.860376i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.2580 | 1.93600 | 0.968001 | − | 0.250947i | \(-0.0807420\pi\) | ||||
0.968001 | + | 0.250947i | \(0.0807420\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.16496 | − | 8.18597i | −0.170623 | − | 0.645145i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.91401 | + | 6.77927i | −0.306569 | + | 0.530993i | −0.977609 | − | 0.210428i | \(-0.932514\pi\) |
0.671040 | + | 0.741421i | \(0.265848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.15395 | + | 3.73076i | −0.166678 | + | 0.288695i | −0.937250 | − | 0.348658i | \(-0.886637\pi\) |
0.770572 | + | 0.637353i | \(0.219971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.54030 | + | 9.59608i | 0.426177 | + | 0.738160i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3359 | 1.31803 | 0.659014 | − | 0.752131i | \(-0.270974\pi\) | ||||
0.659014 | + | 0.752131i | \(0.270974\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.3052 | + | 18.1867i | −1.38374 | + | 1.37478i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.68644 | − | 16.7774i | −0.723998 | − | 1.25400i | −0.959385 | − | 0.282100i | \(-0.908969\pi\) |
0.235387 | − | 0.971902i | \(-0.424364\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.89036 | 0.214839 | 0.107420 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107420 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.1677 | 0.894590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.01131 | −0.220209 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.70044 | 0.267755 | 0.133877 | − | 0.990998i | \(-0.457257\pi\) | ||||
0.133877 | + | 0.990998i | \(0.457257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7670 | −0.918991 | −0.459495 | − | 0.888180i | \(-0.651970\pi\) | ||||
−0.459495 | + | 0.888180i | \(0.651970\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.44715 | −0.174352 | −0.0871762 | − | 0.996193i | \(-0.527784\pi\) | ||||
−0.0871762 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24829 | − | 3.89415i | −0.159377 | − | 0.276049i | 0.775267 | − | 0.631633i | \(-0.217615\pi\) |
−0.934644 | + | 0.355584i | \(0.884282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.11411 | + | 19.3371i | 0.358940 | + | 1.35720i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −46.1167 | −3.22093 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.144907 | + | 0.250986i | 0.0100234 | + | 0.0173611i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09087 | + | 1.88945i | −0.0750987 | + | 0.130075i | −0.901129 | − | 0.433551i | \(-0.857261\pi\) |
0.826030 | + | 0.563625i | \(0.190594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.2697 | − | 22.9838i | 0.904988 | − | 1.56749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.22237 | − | 2.23182i | −0.558171 | − | 0.151506i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.30924 | −0.155336 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.87967 | + | 4.98773i | 0.192837 | + | 0.334003i | 0.946189 | − | 0.323614i | \(-0.104898\pi\) |
−0.753352 | + | 0.657617i | \(0.771564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.29135 | + | 14.3610i | −0.550316 | + | 0.953175i | 0.447935 | + | 0.894066i | \(0.352159\pi\) |
−0.998252 | + | 0.0591094i | \(0.981174\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.29688 | + | 12.6386i | 0.482191 | + | 0.835180i | 0.999791 | − | 0.0204432i | \(-0.00650771\pi\) |
−0.517600 | + | 0.855623i | \(0.673174\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.949438 | + | 1.64448i | −0.0621998 | + | 0.107733i | −0.895448 | − | 0.445165i | \(-0.853145\pi\) |
0.833249 | + | 0.552898i | \(0.186478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.9672 | + | 38.0483i | 1.43298 | + | 2.48200i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.46351 | + | 7.73103i | −0.288721 | + | 0.500079i | −0.973505 | − | 0.228667i | \(-0.926563\pi\) |
0.684784 | + | 0.728746i | \(0.259897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1465 | − | 21.0383i | 0.782423 | − | 1.35520i | −0.148104 | − | 0.988972i | \(-0.547317\pi\) |
0.930527 | − | 0.366224i | \(-0.119350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.174600 | + | 26.8861i | −0.0111548 | + | 1.71769i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.111123 | + | 0.192470i | 0.00707057 | + | 0.0122466i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.64873 | −0.356545 | −0.178272 | − | 0.983981i | \(-0.557051\pi\) | ||||
−0.178272 | + | 0.983981i | \(0.557051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.78191 | 0.363506 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.7856 | − | 20.4132i | −0.735163 | − | 1.27334i | −0.954652 | − | 0.297724i | \(-0.903772\pi\) |
0.219489 | − | 0.975615i | \(-0.429561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.94580 | − | 5.90731i | 0.369454 | − | 0.367063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.8203 | + | 22.2053i | −0.790531 | + | 1.36924i | 0.135108 | + | 0.990831i | \(0.456862\pi\) |
−0.925639 | + | 0.378409i | \(0.876471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.27940 | − | 9.14419i | 0.324311 | − | 0.561723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.27239 | + | 14.3282i | 0.504376 | + | 0.873606i | 0.999987 | + | 0.00506090i | \(0.00161094\pi\) |
−0.495611 | + | 0.868545i | \(0.665056\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.90748 | + | 15.4282i | −0.541091 | + | 0.937197i | 0.457751 | + | 0.889081i | \(0.348655\pi\) |
−0.998842 | + | 0.0481166i | \(0.984678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.80996 | − | 15.2593i | −0.531260 | − | 0.920170i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.92191 | − | 5.06089i | 0.175560 | − | 0.304080i | −0.764795 | − | 0.644274i | \(-0.777160\pi\) |
0.940355 | + | 0.340194i | \(0.110493\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5591 | + | 18.2889i | 0.629905 | + | 1.09103i | 0.987570 | + | 0.157177i | \(0.0502394\pi\) |
−0.357666 | + | 0.933850i | \(0.616427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7762 | 0.759468 | 0.379734 | − | 0.925096i | \(-0.376016\pi\) | ||||
0.379734 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.5351 | + | 22.3892i | −1.33020 | + | 1.32159i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.11087 | − | 12.3164i | 0.418287 | − | 0.724494i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.93828 | + | 10.2854i | −0.346918 | + | 0.600880i | −0.985700 | − | 0.168508i | \(-0.946105\pi\) |
0.638782 | + | 0.769388i | \(0.279439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.9426 | + | 50.1301i | 1.68510 | + | 2.91869i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.43389 | 0.256419 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.67413 | − | 17.6734i | −0.269413 | − | 1.01868i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.6739 | − | 30.6120i | −1.01200 | − | 1.75284i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.93298 | 0.224467 | 0.112234 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112234 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.98221 | 0.112401 | 0.0562005 | − | 0.998420i | \(-0.482101\pi\) | ||||
0.0562005 | + | 0.998420i | \(0.482101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4995 | 1.15870 | 0.579349 | − | 0.815080i | \(-0.303307\pi\) | ||||
0.579349 | + | 0.815080i | \(0.303307\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.51416 | −0.534369 | −0.267184 | − | 0.963645i | \(-0.586093\pi\) | ||||
−0.267184 | + | 0.963645i | \(0.586093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6581 | −0.764709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.267384 | 0.0148777 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.75597 | − | 11.7017i | −0.374754 | − | 0.649093i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.2064 | + | 7.92756i | 1.61020 | + | 0.437061i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.52986 | −0.0840886 | −0.0420443 | − | 0.999116i | \(-0.513387\pi\) | ||||
−0.0420443 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.6921 | + | 41.0360i | 1.29444 | + | 2.24204i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6972 | − | 18.5281i | 0.582714 | − | 1.00929i | −0.412442 | − | 0.910984i | \(-0.635324\pi\) |
0.995156 | − | 0.0983063i | \(-0.0313425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.90887 | − | 5.03831i | 0.157524 | − | 0.272840i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9676 | + | 13.2227i | 0.700185 | + | 0.713961i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.14381 | 0.276134 | 0.138067 | − | 0.990423i | \(-0.455911\pi\) | ||||
0.138067 | + | 0.990423i | \(0.455911\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.207526 | + | 0.359446i | 0.0111086 | + | 0.0192407i | 0.871526 | − | 0.490349i | \(-0.163131\pi\) |
−0.860418 | + | 0.509590i | \(0.829797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.04122 | + | 10.4637i | −0.321542 | + | 0.556926i | −0.980806 | − | 0.194985i | \(-0.937534\pi\) |
0.659265 | + | 0.751911i | \(0.270868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.3145 | − | 23.0613i | −0.706658 | − | 1.22397i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.14926 | + | 14.1149i | −0.430102 | + | 0.744958i | −0.996882 | − | 0.0789113i | \(-0.974856\pi\) |
0.566780 | + | 0.823869i | \(0.308189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.48713 | + | 16.4322i | 0.499323 | + | 0.864852i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.9083 | − | 41.4104i | 1.25142 | − | 2.16752i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3500 | − | 30.0511i | 0.905664 | − | 1.56866i | 0.0856404 | − | 0.996326i | \(-0.472706\pi\) |
0.820024 | − | 0.572330i | \(-0.193960\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.85962 | − | 7.03143i | −0.0965465 | − | 0.365054i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.75329 | + | 13.4291i | 0.401450 | + | 0.695332i | 0.993901 | − | 0.110274i | \(-0.0351730\pi\) |
−0.592451 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.4738 | −0.539430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1820 | 0.831214 | 0.415607 | − | 0.909544i | \(-0.363569\pi\) | ||||
0.415607 | + | 0.909544i | \(0.363569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.17027 | − | 3.75902i | −0.110896 | − | 0.192077i | 0.805236 | − | 0.592955i | \(-0.202039\pi\) |
−0.916132 | + | 0.400877i | \(0.868705\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.7183 | − | 4.80931i | −0.903006 | − | 0.245105i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.7731 | − | 22.1237i | 0.647624 | − | 1.12172i | −0.336065 | − | 0.941839i | \(-0.609096\pi\) |
0.983689 | − | 0.179879i | \(-0.0575705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.66722 | − | 4.61975i | 0.134887 | − | 0.233631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.8703 | − | 53.4690i | −1.55326 | − | 2.69032i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.28225 | − | 3.95297i | 0.114543 | − | 0.198394i | −0.803054 | − | 0.595906i | \(-0.796793\pi\) |
0.917597 | + | 0.397512i | \(0.130126\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.668128 | + | 1.15723i | 0.0333647 | + | 0.0577894i | 0.882226 | − | 0.470827i | \(-0.156044\pi\) |
−0.848861 | + | 0.528616i | \(0.822711\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.23068 | − | 3.86366i | 0.111118 | − | 0.192463i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.86161 | + | 4.95645i | 0.141845 | + | 0.245682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.6664 | 1.02189 | 0.510944 | − | 0.859614i | \(-0.329296\pi\) | ||||
0.510944 | + | 0.859614i | \(0.329296\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.4806 | + | 10.4449i | 1.89350 | + | 0.513958i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.58015 | − | 9.66510i | 0.273919 | − | 0.474441i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.5227 | − | 18.2259i | 0.514069 | − | 0.890394i | −0.485797 | − | 0.874071i | \(-0.661471\pi\) |
0.999867 | − | 0.0163228i | \(-0.00519594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.51630 | − | 14.7507i | −0.415059 | − | 0.718903i | 0.580376 | − | 0.814349i | \(-0.302906\pi\) |
−0.995435 | + | 0.0954456i | \(0.969572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.2563 | −0.788544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.4982 | − | 6.37818i | −1.13716 | − | 0.308662i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2925 | + | 31.6836i | 0.881121 | + | 1.52615i | 0.850096 | + | 0.526627i | \(0.176544\pi\) |
0.0310244 | + | 0.999519i | \(0.490123\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6571 | −1.13689 | −0.568444 | − | 0.822722i | \(-0.692454\pi\) | ||||
−0.568444 | + | 0.822722i | \(0.692454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.513395 | −0.0245590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.7864 | −0.992082 | −0.496041 | − | 0.868299i | \(-0.665213\pi\) | ||||
−0.496041 | + | 0.868299i | \(0.665213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.42807 | 0.352918 | 0.176459 | − | 0.984308i | \(-0.443536\pi\) | ||||
0.176459 | + | 0.984308i | \(0.443536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.7194 | −1.83547 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.15800 | 0.385000 | 0.192500 | − | 0.981297i | \(-0.438340\pi\) | ||||
0.192500 | + | 0.981297i | \(0.438340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8457 | − | 18.7854i | −0.510705 | − | 0.884568i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.5873 | − | 3.68805i | −0.636985 | − | 0.172898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3058 | 0.669199 | 0.334600 | − | 0.942360i | \(-0.391399\pi\) | ||||
0.334600 | + | 0.942360i | \(0.391399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.71961 | − | 13.3708i | −0.359538 | − | 0.622738i | 0.628346 | − | 0.777934i | \(-0.283732\pi\) |
−0.987884 | + | 0.155196i | \(0.950399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5531 | + | 18.2785i | −0.490444 | + | 0.849474i | −0.999940 | − | 0.0109995i | \(-0.996499\pi\) |
0.509496 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.49896 | − | 6.06037i | 0.161912 | − | 0.280440i | −0.773642 | − | 0.633623i | \(-0.781567\pi\) |
0.935555 | + | 0.353182i | \(0.114900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.4998 | + | 8.55007i | 1.45453 | + | 0.394805i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4831 | 0.573974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.782265 | + | 1.35492i | 0.0358928 | + | 0.0621681i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.54406 | + | 2.67440i | −0.0705500 | + | 0.122196i | −0.899142 | − | 0.437656i | \(-0.855809\pi\) |
0.828592 | + | 0.559852i | \(0.189142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.19444 | + | 3.80089i | 0.100058 | + | 0.173305i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0871 | + | 27.8636i | −0.730475 | + | 1.26522i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.90011 | − | 8.48725i | −0.222045 | − | 0.384594i | 0.733384 | − | 0.679815i | \(-0.237940\pi\) |
−0.955429 | + | 0.295221i | \(0.904607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.98641 | − | 17.2970i | 0.450680 | − | 0.780601i | −0.547748 | − | 0.836643i | \(-0.684515\pi\) |
0.998428 | + | 0.0560419i | \(0.0178481\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.30055 | + | 10.9129i | −0.283762 | + | 0.491491i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.7022 | − | 4.80495i | −0.794052 | − | 0.215531i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1650 | − | 17.6062i | −0.455046 | − | 0.788163i | 0.543645 | − | 0.839315i | \(-0.317044\pi\) |
−0.998691 | + | 0.0511526i | \(0.983710\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.9595 | −1.06830 | −0.534151 | − | 0.845389i | \(-0.679369\pi\) | ||||
−0.534151 | + | 0.845389i | \(0.679369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.1693 | 1.38702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.03046 | + | 8.71302i | 0.222971 | + | 0.386198i | 0.955709 | − | 0.294314i | \(-0.0950910\pi\) |
−0.732737 | + | 0.680511i | \(0.761758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.42146 | − | 31.8425i | −0.372544 | − | 1.40863i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.4762 | − | 25.0735i | 0.637898 | − | 1.10487i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3325 | + | 17.8964i | −0.454423 | + | 0.787083i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.99821 | − | 13.8533i | −0.350408 | − | 0.606924i | 0.635913 | − | 0.771761i | \(-0.280624\pi\) |
−0.986321 | + | 0.164836i | \(0.947290\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7103 | − | 32.4072i | 0.818146 | − | 1.41707i | −0.0889016 | − | 0.996040i | \(-0.528336\pi\) |
0.907047 | − | 0.421029i | \(-0.138331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.68374 | − | 4.64838i | −0.116906 | − | 0.202487i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.37877 | − | 11.0484i | 0.277338 | − | 0.480364i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.31711 | − | 14.4057i | −0.360254 | − | 0.623978i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.7178 | −0.982175 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.9930 | + | 6.25195i | −0.473500 | + | 0.269291i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.229159 | − | 0.396916i | 0.00985233 | − | 0.0170647i | −0.861057 | − | 0.508508i | \(-0.830197\pi\) |
0.870910 | + | 0.491443i | \(0.163531\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.2232 | − | 29.8314i | 0.737760 | − | 1.27784i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2013 | + | 19.4011i | 0.478931 | + | 0.829533i | 0.999708 | − | 0.0241596i | \(-0.00769098\pi\) |
−0.520777 | + | 0.853693i | \(0.674358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.21275 | 0.0516650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.0436 | − | 11.1405i | −1.74535 | − | 0.473744i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.4155 | − | 18.0401i | −0.441317 | − | 0.764383i | 0.556471 | − | 0.830867i | \(-0.312155\pi\) |
−0.997787 | + | 0.0664841i | \(0.978822\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.57275 | 0.404884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.80605 | 0.371131 | 0.185565 | − | 0.982632i | \(-0.440588\pi\) | ||||
0.185565 | + | 0.982632i | \(0.440588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.3117 | 2.57940 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9857 | −0.795923 | −0.397962 | − | 0.917402i | \(-0.630282\pi\) | ||||
−0.397962 | + | 0.917402i | \(0.630282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7597 | 0.659523 | 0.329762 | − | 0.944064i | \(-0.393032\pi\) | ||||
0.329762 | + | 0.944064i | \(0.393032\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.2131 | 1.30167 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.9306 | − | 27.5927i | −0.663201 | − | 1.14870i | −0.979770 | − | 0.200128i | \(-0.935864\pi\) |
0.316569 | − | 0.948570i | \(-0.397469\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.96555 | − | 7.43199i | −0.0815449 | − | 0.308331i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.96644 | 0.205689 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.3597 | − | 35.2640i | −0.840333 | − | 1.45550i | −0.889613 | − | 0.456715i | \(-0.849026\pi\) |
0.0492799 | − | 0.998785i | \(-0.484307\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.258288 | + | 0.447368i | −0.0106426 | + | 0.0184335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.0693 | − | 24.3688i | 0.577759 | − | 1.00071i | −0.417977 | − | 0.908458i | \(-0.637261\pi\) |
0.995736 | − | 0.0922500i | \(-0.0294059\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0161 | + | 11.9383i | −0.492613 | + | 0.489425i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9926 | 1.34804 | 0.674020 | − | 0.738713i | \(-0.264566\pi\) | ||||
0.674020 | + | 0.738713i | \(0.264566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.98103 | − | 3.43124i | −0.0808079 | − | 0.139963i | 0.822789 | − | 0.568347i | \(-0.192417\pi\) |
−0.903597 | + | 0.428383i | \(0.859083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.8570 | + | 25.7330i | −0.604021 | + | 1.04620i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.0132 | + | 29.4676i | 0.690543 | + | 1.19605i | 0.971660 | + | 0.236382i | \(0.0759615\pi\) |
−0.281118 | + | 0.959673i | \(0.590705\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.92354 | + | 13.7240i | −0.320552 | + | 0.555212i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2967 | − | 26.4946i | −0.617827 | − | 1.07011i | −0.989881 | − | 0.141897i | \(-0.954680\pi\) |
0.372054 | − | 0.928211i | \(-0.378654\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.7646 | + | 32.5013i | −0.755435 | + | 1.30845i | 0.189723 | + | 0.981838i | \(0.439241\pi\) |
−0.945158 | + | 0.326614i | \(0.894092\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.92302 | + | 5.06282i | −0.117486 | + | 0.203492i | −0.918771 | − | 0.394791i | \(-0.870817\pi\) |
0.801285 | + | 0.598283i | \(0.204150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9203 | + | 18.7979i | −0.758028 | + | 0.753121i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.6774 | − | 18.4937i | −0.427095 | − | 0.739749i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.28028 | 0.210539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6347 | −1.02050 | −0.510251 | − | 0.860025i | \(-0.670448\pi\) | ||||
−0.510251 | + | 0.860025i | \(0.670448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.5336 | − | 28.6371i | −0.656117 | − | 1.13643i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.43001 | + | 4.79435i | −0.334009 | + | 0.189959i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.9824 | − | 22.4861i | 0.512772 | − | 0.888147i | −0.487118 | − | 0.873336i | \(-0.661952\pi\) |
0.999890 | − | 0.0148113i | \(-0.00471476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.5634 | − | 39.0809i | 0.889812 | − | 1.54120i | 0.0497151 | − | 0.998763i | \(-0.484169\pi\) |
0.840097 | − | 0.542436i | \(-0.182498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.70324 | + | 4.68215i | 0.106275 | + | 0.184074i | 0.914259 | − | 0.405131i | \(-0.132774\pi\) |
−0.807983 | + | 0.589206i | \(0.799441\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6135 | + | 23.5792i | −0.534375 | + | 0.925564i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.9515 | − | 27.6288i | −0.624231 | − | 1.08120i | −0.988689 | − | 0.149980i | \(-0.952079\pi\) |
0.364458 | − | 0.931220i | \(-0.381254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.70587 | + | 6.41875i | −0.144800 | + | 0.250801i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.50215 | + | 4.33385i | 0.0974699 | + | 0.168823i | 0.910637 | − | 0.413208i | \(-0.135592\pi\) |
−0.813167 | + | 0.582031i | \(0.802258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.63406 | 0.374721 | 0.187361 | − | 0.982291i | \(-0.440007\pi\) | ||||
0.187361 | + | 0.982291i | \(0.440007\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.57326 | + | 0.427034i | 0.0610085 | + | 0.0165597i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0975 | − | 20.9534i | 0.468415 | − | 0.811319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.31308 | − | 14.3987i | 0.320923 | − | 0.555855i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5885 | + | 23.5359i | 0.523797 | + | 0.907243i | 0.999616 | + | 0.0276998i | \(0.00881825\pi\) |
−0.475819 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.0502 | 1.46239 | 0.731194 | − | 0.682169i | \(-0.238963\pi\) | ||||
0.731194 | + | 0.682169i | \(0.238963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.66651 | + | 21.4257i | 0.217461 | + | 0.822244i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0571 | + | 26.0797i | 0.576146 | + | 0.997913i | 0.995916 | + | 0.0902831i | \(0.0287772\pi\) |
−0.419771 | + | 0.907630i | \(0.637889\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2455 | −0.544293 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.80854 | 0.145094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3902 | −0.547429 | −0.273714 | − | 0.961811i | \(-0.588252\pi\) | ||||
−0.273714 | + | 0.961811i | \(0.588252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.03374 | −0.0392120 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0127 | −0.758034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.4170 | −0.544521 | −0.272261 | − | 0.962224i | \(-0.587771\pi\) | ||||
−0.272261 | + | 0.962224i | \(0.587771\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.254092 | − | 0.440100i | −0.00958325 | − | 0.0165987i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.2310 | − | 15.1324i | 0.572820 | − | 0.569113i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.4882 | 0.431448 | 0.215724 | − | 0.976454i | \(-0.430789\pi\) | ||||
0.215724 | + | 0.976454i | \(0.430789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.15296 | + | 8.92519i | 0.192980 | + | 0.334251i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.80686 | − | 8.32573i | 0.179766 | − | 0.311365i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.9451 | − | 31.0818i | 0.669240 | − | 1.15916i | −0.308877 | − | 0.951102i | \(-0.599953\pi\) |
0.978117 | − | 0.208055i | \(-0.0667134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.09910 | − | 19.2803i | −0.189901 | − | 0.718036i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −73.7321 | −2.73834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.03060 | + | 8.71326i | 0.186575 | + | 0.323157i | 0.944106 | − | 0.329642i | \(-0.106928\pi\) |
−0.757531 | + | 0.652799i | \(0.773595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.75850 | − | 9.97401i | 0.212986 | − | 0.368902i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.5690 | − | 28.6984i | −0.611992 | − | 1.06000i | −0.990904 | − | 0.134568i | \(-0.957035\pi\) |
0.378913 | − | 0.925432i | \(-0.376298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.1438 | + | 19.3017i | −0.410489 | + | 0.710987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9237 | − | 37.9729i | −0.806475 | − | 1.39686i | −0.915291 | − | 0.402793i | \(-0.868039\pi\) |
0.108816 | − | 0.994062i | \(-0.465294\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.50115 | − | 7.79622i | 0.165131 | − | 0.286016i | −0.771571 | − | 0.636144i | \(-0.780529\pi\) |
0.936702 | + | 0.350128i | \(0.113862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9738 | + | 27.6673i | −0.585233 | + | 1.01365i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1011 | + | 11.0293i | −0.405626 | + | 0.403000i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.59141 | + | 9.68460i | 0.204033 | + | 0.353396i | 0.949824 | − | 0.312784i | \(-0.101262\pi\) |
−0.745791 | + | 0.666180i | \(0.767928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.4162 | 1.36171 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.1431 | 1.53172 | 0.765859 | − | 0.643009i | \(-0.222314\pi\) | ||||
0.765859 | + | 0.643009i | \(0.222314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.14155 | + | 1.97721i | 0.0413810 | + | 0.0716740i | 0.885974 | − | 0.463735i | \(-0.153491\pi\) |
−0.844593 | + | 0.535409i | \(0.820158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.06670 | − | 22.9389i | −0.219629 | − | 0.830444i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.4396 | + | 18.0819i | −0.376951 | + | 0.652898i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.96676 | − | 15.5309i | 0.323350 | − | 0.560058i | −0.657827 | − | 0.753169i | \(-0.728524\pi\) |
0.981177 | + | 0.193111i | \(0.0618577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.4807 | − | 30.2775i | −0.628737 | − | 1.08901i | −0.987805 | − | 0.155694i | \(-0.950239\pi\) |
0.359068 | − | 0.933311i | \(-0.383095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.7032 | − | 27.1988i | 0.564077 | − | 0.977009i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.963028 | + | 1.66801i | 0.0345041 | + | 0.0597628i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.26259 | − | 10.8471i | 0.224093 | − | 0.388141i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.5870 | + | 80.6910i | 1.66276 | + | 2.87998i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.3564 | 1.01079 | 0.505397 | − | 0.862887i | \(-0.331346\pi\) | ||||
0.505397 | + | 0.862887i | \(0.331346\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.9601 | − | 29.7662i | 1.06526 | − | 1.05836i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.37494 | − | 11.0417i | 0.226381 | − | 0.392103i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.51922 | − | 16.4878i | 0.337188 | − | 0.584027i | −0.646715 | − | 0.762732i | \(-0.723857\pi\) |
0.983903 | + | 0.178705i | \(0.0571908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.53283 | + | 16.5113i | 0.337247 | + | 0.584129i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.4910 | 0.793691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.0717 | − | 22.9224i | 0.813172 | − | 0.807908i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4529 | + | 18.1050i | 0.367505 | + | 0.636538i | 0.989175 | − | 0.146742i | \(-0.0468787\pi\) |
−0.621670 | + | 0.783280i | \(0.713545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.5392 | −0.615884 | −0.307942 | − | 0.951405i | \(-0.599640\pi\) | ||||
−0.307942 | + | 0.951405i | \(0.599640\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.0671 | −1.05320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.10842 | −0.0387786 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.9762 | 1.22068 | 0.610339 | − | 0.792140i | \(-0.291033\pi\) | ||||
0.610339 | + | 0.792140i | \(0.291033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.4235 | 1.06050 | 0.530249 | − | 0.847842i | \(-0.322099\pi\) | ||||
0.530249 | + | 0.847842i | \(0.322099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.6276 | −0.891158 | −0.445579 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445579 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9403 | + | 41.4658i | 0.831481 | + | 1.44017i | 0.896864 | + | 0.442307i | \(0.145840\pi\) |
−0.0653833 | + | 0.997860i | \(0.520827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.0757689 | + | 11.6674i | −0.00262524 | + | 0.404252i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.5465 | −0.572614 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.8466 | − | 37.8394i | −0.754227 | − | 1.30636i | −0.945758 | − | 0.324873i | \(-0.894678\pi\) |
0.191530 | − | 0.981487i | \(-0.438655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0769 | + | 24.3818i | −0.485409 | + | 0.840753i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.2800 | + | 36.8581i | −0.732055 | + | 1.26796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.23322 | + | 19.7874i | 0.179816 | + | 0.679904i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1385 | −0.347543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.33994 | + | 14.4452i | 0.285554 | + | 0.494594i | 0.972743 | − | 0.231884i | \(-0.0744890\pi\) |
−0.687189 | + | 0.726478i | \(0.741156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.21452 | − | 12.4959i | 0.246443 | − | 0.426852i | −0.716093 | − | 0.698005i | \(-0.754071\pi\) |
0.962536 | + | 0.271152i | \(0.0874048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3867 | + | 19.7223i | 0.388508 | + | 0.672915i | 0.992249 | − | 0.124265i | \(-0.0396573\pi\) |
−0.603741 | + | 0.797180i | \(0.706324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.97266 | + | 10.3450i | −0.203312 | + | 0.352146i | −0.949594 | − | 0.313484i | \(-0.898504\pi\) |
0.746282 | + | 0.665630i | \(0.231837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.2933 | + | 57.6656i | 1.13200 | + | 1.96069i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.5202 | − | 25.1497i | 0.492563 | − | 0.853145i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.54572 | + | 14.8016i | −0.289561 | + | 0.501534i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −46.6134 | − | 12.6524i | −1.57582 | − | 0.427729i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.3099 | + | 49.0342i | 0.955957 | + | 1.65577i | 0.732163 | + | 0.681130i | \(0.238511\pi\) |
0.223794 | + | 0.974636i | \(0.428156\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.41130 | 0.216002 | 0.108001 | − | 0.994151i | \(-0.465555\pi\) | ||||
0.108001 | + | 0.994151i | \(0.465555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.7180 | 0.865481 | 0.432741 | − | 0.901518i | \(-0.357547\pi\) | ||||
0.432741 | + | 0.901518i | \(0.357547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.99472 | − | 17.3114i | −0.335590 | − | 0.581259i | 0.648008 | − | 0.761633i | \(-0.275602\pi\) |
−0.983598 | + | 0.180375i | \(0.942269\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.9822 | − | 5.96669i | −0.737261 | − | 0.200116i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.917456 | − | 1.58908i | 0.0307015 | − | 0.0531766i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.2051 | − | 64.4412i | 1.24363 | − | 2.15403i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.1724 | − | 21.0832i | −0.405973 | − | 0.703166i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29104 | − | 3.96819i | 0.0763254 | − | 0.132200i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.55087 | + | 9.61439i | 0.184517 | + | 0.319593i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1517 | − | 21.0474i | 0.403491 | − | 0.698866i | −0.590654 | − | 0.806925i | \(-0.701130\pi\) |
0.994145 | + | 0.108059i | \(0.0344635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7871 | + | 34.2723i | 0.655577 | + | 1.13549i | 0.981749 | + | 0.190183i | \(0.0609080\pi\) |
−0.326171 | + | 0.945311i | \(0.605759\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.24936 | 0.173728 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.30536 | + | 4.93571i | 0.0431067 | + | 0.162991i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9220 | − | 22.3815i | 0.426257 | − | 0.738298i | −0.570280 | − | 0.821450i | \(-0.693165\pi\) |
0.996537 | + | 0.0831519i | \(0.0264987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.80251 | − | 8.31818i | 0.158076 | − | 0.273796i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4481 | + | 26.7569i | 0.507930 | + | 0.879761i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.8506 | −1.66836 | −0.834178 | − | 0.551496i | \(-0.814057\pi\) | ||||
−0.834178 | + | 0.551496i | \(0.814057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.976100 | − | 0.555132i | 0.0319904 | − | 0.0181937i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.78315 | − | 10.0167i | −0.189129 | − | 0.327581i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7623 | 1.07030 | 0.535149 | − | 0.844758i | \(-0.320256\pi\) | ||||
0.535149 | + | 0.844758i | \(0.320256\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.6793 | −1.65210 | −0.826048 | − | 0.563599i | \(-0.809416\pi\) | ||||
−0.826048 | + | 0.563599i | \(0.809416\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.4256 | 1.25131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5255 | −0.374530 | −0.187265 | − | 0.982309i | \(-0.559962\pi\) | ||||
−0.187265 | + | 0.982309i | \(0.559962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.2474 | 0.559873 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.7747 | 1.48279 | 0.741395 | − | 0.671069i | \(-0.234165\pi\) | ||||
0.741395 | + | 0.671069i | \(0.234165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.10661 | + | 12.3090i | 0.229965 | + | 0.398310i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.96111 | + | 6.91605i | −0.224786 | + | 0.223331i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.6302 | −0.665491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.5188 | − | 42.4678i | −0.789287 | − | 1.36709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.07666 | − | 7.06098i | 0.131097 | − | 0.227066i | −0.793003 | − | 0.609218i | \(-0.791484\pi\) |
0.924100 | + | 0.382152i | \(0.124817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.1137 | − | 24.4457i | 0.452932 | − | 0.784501i | −0.545635 | − | 0.838023i | \(-0.683712\pi\) |
0.998567 | + | 0.0535223i | \(0.0170448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.505141 | + | 0.501871i | −0.0161941 | + | 0.0160893i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.6502 | 0.500694 | 0.250347 | − | 0.968156i | \(-0.419455\pi\) | ||||
0.250347 | + | 0.968156i | \(0.419455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.10603 | − | 15.7721i | −0.291030 | − | 0.504079i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.47581 | + | 2.55617i | −0.0470710 | + | 0.0815293i | −0.888601 | − | 0.458681i | \(-0.848322\pi\) |
0.841530 | + | 0.540210i | \(0.181655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.69970 | − | 8.14012i | −0.149745 | − | 0.259366i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.0567 | + | 19.1507i | −0.351582 | + | 0.608958i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8182 | − | 27.3979i | −0.502482 | − | 0.870324i | −0.999996 | − | 0.00286819i | \(-0.999087\pi\) |
0.497514 | − | 0.867456i | \(-0.334246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.63557 | − | 14.9572i | 0.273766 | − | 0.474176i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.792608 | − | 1.37284i | 0.0251021 | − | 0.0434782i | −0.853201 | − | 0.521582i | \(-0.825342\pi\) |
0.878304 | + | 0.478103i | \(0.158676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.q.k.2305.11 | 22 | ||
3.2 | odd | 2 | 1008.2.q.k.625.2 | 22 | |||
4.3 | odd | 2 | 1512.2.q.c.793.11 | 22 | |||
7.4 | even | 3 | 3024.2.t.l.1873.1 | 22 | |||
9.2 | odd | 6 | 1008.2.t.k.961.10 | 22 | |||
9.7 | even | 3 | 3024.2.t.l.289.1 | 22 | |||
12.11 | even | 2 | 504.2.q.d.121.10 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.k.193.10 | 22 | |||
28.11 | odd | 6 | 1512.2.t.d.361.1 | 22 | |||
36.7 | odd | 6 | 1512.2.t.d.289.1 | 22 | |||
36.11 | even | 6 | 504.2.t.d.457.2 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.k.529.2 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.k.2881.11 | 22 | ||
84.11 | even | 6 | 504.2.t.d.193.2 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.d.25.10 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.c.1369.11 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.10 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.d.121.10 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.d.193.2 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.d.457.2 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.k.529.2 | 22 | 63.11 | odd | 6 | |||
1008.2.q.k.625.2 | 22 | 3.2 | odd | 2 | |||
1008.2.t.k.193.10 | 22 | 21.11 | odd | 6 | |||
1008.2.t.k.961.10 | 22 | 9.2 | odd | 6 | |||
1512.2.q.c.793.11 | 22 | 4.3 | odd | 2 | |||
1512.2.q.c.1369.11 | 22 | 252.151 | odd | 6 | |||
1512.2.t.d.289.1 | 22 | 36.7 | odd | 6 | |||
1512.2.t.d.361.1 | 22 | 28.11 | odd | 6 | |||
3024.2.q.k.2305.11 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.k.2881.11 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.l.289.1 | 22 | 9.7 | even | 3 | |||
3024.2.t.l.1873.1 | 22 | 7.4 | even | 3 |