Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(127,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.3.g.b.127.6 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.36433 | 0.272865 | 0.136433 | − | 0.990649i | \(-0.456436\pi\) | ||||
0.136433 | + | 0.990649i | \(0.456436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.24213i | − 0.177446i | −0.996056 | − | 0.0887232i | \(-0.971721\pi\) | ||||
0.996056 | − | 0.0887232i | \(-0.0282787\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.79796i | − 0.527087i | −0.964647 | − | 0.263544i | \(-0.915109\pi\) | ||||
0.964647 | − | 0.263544i | \(-0.0848913\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.3830 | 1.26023 | 0.630116 | − | 0.776501i | \(-0.283007\pi\) | ||||
0.630116 | + | 0.776501i | \(0.283007\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 2.36308i | − 0.157539i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.01086 | −0.294756 | −0.147378 | − | 0.989080i | \(-0.547083\pi\) | ||||
−0.147378 | + | 0.989080i | \(0.547083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 26.1835i | − 1.37808i | −0.724725 | − | 0.689039i | \(-0.758033\pi\) | ||||
0.724725 | − | 0.689039i | \(-0.241967\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.15142 | −0.102449 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 25.1117i | − 1.09181i | −0.837847 | − | 0.545906i | \(-0.816186\pi\) | ||||
0.837847 | − | 0.545906i | \(-0.183814\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.1386 | −0.925545 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 32.7743 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.01836i | 0.0328504i | 0.999865 | + | 0.0164252i | \(0.00522854\pi\) | ||||
−0.999865 | + | 0.0164252i | \(0.994771\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.0424 | −0.304314 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.69466i | − 0.0484189i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.9948 | 0.405264 | 0.202632 | − | 0.979255i | \(-0.435050\pi\) | ||||
0.202632 | + | 0.979255i | \(0.435050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 28.3762i | − 0.727595i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −72.5212 | −1.76881 | −0.884405 | − | 0.466720i | \(-0.845435\pi\) | ||||
−0.884405 | + | 0.466720i | \(0.845435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 33.4922i | − 0.778888i | −0.921050 | − | 0.389444i | \(-0.872667\pi\) | ||||
0.921050 | − | 0.389444i | \(-0.127333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.09298 | −0.0909550 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 66.5640i | − 1.41626i | −0.706085 | − | 0.708128i | \(-0.749540\pi\) | ||||
0.706085 | − | 0.708128i | \(-0.250460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.4571 | 0.968513 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.67906i | 0.170178i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −54.6513 | −1.03116 | −0.515579 | − | 0.856842i | \(-0.672423\pi\) | ||||
−0.515579 | + | 0.856842i | \(0.672423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.91030i | − 0.143824i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −45.3511 | −0.795633 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 20.5880i | − 0.348949i | −0.984662 | − | 0.174474i | \(-0.944177\pi\) | ||||
0.984662 | − | 0.174474i | \(-0.0558226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 111.026 | 1.82010 | 0.910050 | − | 0.414499i | \(-0.136043\pi\) | ||||
0.910050 | + | 0.414499i | \(0.136043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.72638i | 0.0591488i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.3518 | 0.343873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 60.9540i | − 0.909762i | −0.890552 | − | 0.454881i | \(-0.849682\pi\) | ||||
0.890552 | − | 0.454881i | \(-0.150318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −43.4947 | −0.630358 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80.4576i | 1.13320i | 0.823991 | + | 0.566602i | \(0.191742\pi\) | ||||
−0.823991 | + | 0.566602i | \(0.808258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.0525 | 0.411679 | 0.205839 | − | 0.978586i | \(-0.434008\pi\) | ||||
0.205839 | + | 0.978586i | \(0.434008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 40.0773i | 0.534363i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.20179 | −0.0935298 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.9441i | 1.02461i | 0.858804 | + | 0.512304i | \(0.171208\pi\) | ||||
−0.858804 | + | 0.512304i | \(0.828792\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 113.958i | 1.37299i | 0.727134 | + | 0.686496i | \(0.240852\pi\) | ||||
−0.727134 | + | 0.686496i | \(0.759148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.83644 | −0.0804288 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 56.7667i | − 0.652491i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −21.0637 | −0.236671 | −0.118335 | − | 0.992974i | \(-0.537756\pi\) | ||||
−0.118335 | + | 0.992974i | \(0.537756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 20.3498i | − 0.223624i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.76386 | 0.0189662 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 35.7228i | − 0.376029i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 160.594 | 1.65561 | 0.827806 | − | 0.561014i | \(-0.189589\pi\) | ||||
0.827806 | + | 0.561014i | \(0.189589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.3939i | 0.175696i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −76.2681 | −0.755130 | −0.377565 | − | 0.925983i | \(-0.623239\pi\) | ||||
−0.377565 | + | 0.925983i | \(0.623239\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 182.763i | 1.77440i | 0.461383 | + | 0.887201i | \(0.347353\pi\) | ||||
−0.461383 | + | 0.887201i | \(0.652647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.93524 | −0.0279547 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 31.8533i | − 0.297694i | −0.988860 | − | 0.148847i | \(-0.952444\pi\) | ||||
0.988860 | − | 0.148847i | \(-0.0475562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3289 | 0.103935 | 0.0519676 | − | 0.998649i | \(-0.483451\pi\) | ||||
0.0519676 | + | 0.998649i | \(0.483451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 25.9717i | − 0.233979i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 49.9587 | 0.442113 | 0.221056 | − | 0.975261i | \(-0.429050\pi\) | ||||
0.221056 | + | 0.975261i | \(0.429050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 34.2605i | − 0.297917i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −49.1490 | −0.420077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.22412i | 0.0523035i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 87.3837 | 0.722179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 125.610i | 1.02122i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −65.6767 | −0.525414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 208.236i | 1.63965i | 0.572614 | + | 0.819825i | \(0.305929\pi\) | ||||
−0.572614 | + | 0.819825i | \(0.694071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −58.0102 | −0.449691 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 220.549i | 1.68358i | 0.539804 | + | 0.841791i | \(0.318498\pi\) | ||||
−0.539804 | + | 0.841791i | \(0.681502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32.5231 | −0.244535 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.08924i | 0.0525129i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.2664 | 0.111433 | 0.0557167 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557167 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 86.7117i | 0.623825i | 0.950111 | + | 0.311912i | \(0.100970\pi\) | ||||
−0.950111 | + | 0.311912i | \(0.899030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −115.292 | −0.817675 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 94.9881i | − 0.664252i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 44.7148 | 0.308378 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 82.1982i | − 0.559171i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −146.849 | −0.985561 | −0.492780 | − | 0.870154i | \(-0.664019\pi\) | ||||
−0.492780 | + | 0.870154i | \(0.664019\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 195.933i | − 1.29757i | −0.760972 | − | 0.648785i | \(-0.775277\pi\) | ||||
0.760972 | − | 0.648785i | \(-0.224723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.0326 | 0.0982522 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.38938i | 0.00896374i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.65454 | 0.0296468 | 0.0148234 | − | 0.999890i | \(-0.495281\pi\) | ||||
0.0148234 | + | 0.999890i | \(0.495281\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 94.6589i | 0.595339i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.1918 | −0.193738 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 59.5489i | − 0.365331i | −0.983175 | − | 0.182665i | \(-0.941528\pi\) | ||||
0.983175 | − | 0.182665i | \(-0.0584725\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.7010 | −0.0830367 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 209.012i | 1.25157i | 0.779996 | + | 0.625785i | \(0.215221\pi\) | ||||
−0.779996 | + | 0.625785i | \(0.784779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 99.4032 | 0.588185 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 78.5504i | 0.459359i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −96.7635 | −0.559326 | −0.279663 | − | 0.960098i | \(-0.590223\pi\) | ||||
−0.279663 | + | 0.960098i | \(0.590223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.7411i | 0.164235i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.6594 | −0.201466 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 49.5039i | 0.276558i | 0.990393 | + | 0.138279i | \(0.0441571\pi\) | ||||
−0.990393 | + | 0.138279i | \(0.955843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 141.417 | 0.781310 | 0.390655 | − | 0.920537i | \(-0.372248\pi\) | ||||
0.390655 | + | 0.920537i | \(0.372248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 192.303i | − 1.05084i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.4578 | 0.110582 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.0528i | 0.155362i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.45427 | 0.0341496 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 116.994i | − 0.612533i | −0.951946 | − | 0.306267i | \(-0.900920\pi\) | ||||
0.951946 | − | 0.306267i | \(-0.0990799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −90.7357 | −0.470133 | −0.235067 | − | 0.971979i | \(-0.575531\pi\) | ||||
−0.235067 | + | 0.971979i | \(0.575531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 38.7144i | − 0.198535i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 380.039 | 1.92913 | 0.964566 | − | 0.263840i | \(-0.0849891\pi\) | ||||
0.964566 | + | 0.263840i | \(0.0849891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 77.6563i | 0.390233i | 0.980780 | + | 0.195116i | \(0.0625084\pi\) | ||||
−0.980780 | + | 0.195116i | \(0.937492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −105.576 | −0.525251 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 40.7098i | − 0.200541i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −98.9425 | −0.482646 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 75.3350i | 0.363937i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −151.811 | −0.726367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 191.446i | − 0.907325i | −0.891174 | − | 0.453662i | \(-0.850117\pi\) | ||||
0.891174 | − | 0.453662i | \(-0.149883\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 139.357 | 0.654256 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 45.6943i | − 0.212531i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.26493 | 0.00582919 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 52.0525i | − 0.237683i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82.0930 | −0.371462 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 168.451i | 0.755387i | 0.925931 | + | 0.377693i | \(0.123283\pi\) | ||||
−0.925931 | + | 0.377693i | \(0.876717\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 69.4158 | 0.308515 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 113.516i | − 0.500071i | −0.968237 | − | 0.250036i | \(-0.919558\pi\) | ||||
0.968237 | − | 0.250036i | \(-0.0804424\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 117.618 | 0.513615 | 0.256808 | − | 0.966463i | \(-0.417329\pi\) | ||||
0.256808 | + | 0.966463i | \(0.417329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.4739i | 0.0539994i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 277.085 | 1.18921 | 0.594604 | − | 0.804019i | \(-0.297309\pi\) | ||||
0.594604 | + | 0.804019i | \(0.297309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 90.8150i | − 0.386447i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 140.199 | 0.591558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 343.072i | − 1.43545i | −0.696327 | − | 0.717724i | \(-0.745184\pi\) | ||||
0.696327 | − | 0.717724i | \(-0.254816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −328.140 | −1.36157 | −0.680787 | − | 0.732481i | \(-0.738362\pi\) | ||||
−0.680787 | + | 0.732481i | \(0.738362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 64.7470 | 0.264273 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 428.964i | − 1.73670i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 197.382 | 0.792697 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 452.914i | − 1.80444i | −0.431279 | − | 0.902219i | \(-0.641937\pi\) | ||||
0.431279 | − | 0.902219i | \(-0.358063\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −145.596 | −0.575480 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.8411i | 0.0464356i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −346.830 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 18.6254i | − 0.0719127i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −98.3229 | −0.376716 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 402.440i | 1.53019i | 0.643917 | + | 0.765095i | \(0.277308\pi\) | ||||
−0.643917 | + | 0.765095i | \(0.722692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −74.5622 | −0.281367 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.4834i | 0.136642i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 321.562 | 1.19540 | 0.597699 | − | 0.801721i | \(-0.296082\pi\) | ||||
0.597699 | + | 0.801721i | \(0.296082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 456.902i | − 1.68599i | −0.537924 | − | 0.842993i | \(-0.680791\pi\) | ||||
0.537924 | − | 0.842993i | \(-0.319209\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −35.2468 | −0.129109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 134.157i | 0.487843i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 329.543 | 1.18969 | 0.594843 | − | 0.803842i | \(-0.297214\pi\) | ||||
0.594843 | + | 0.803842i | \(0.297214\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 3.05509i | − 0.0109501i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −175.064 | −0.623005 | −0.311503 | − | 0.950245i | \(-0.600832\pi\) | ||||
−0.311503 | + | 0.950245i | \(0.600832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 150.298i | 0.531087i | 0.964099 | + | 0.265544i | \(0.0855515\pi\) | ||||
−0.964099 | + | 0.265544i | \(0.914449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −61.8736 | −0.217101 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 90.0804i | 0.313869i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −263.891 | −0.913119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 278.158i | − 0.955868i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 160.435 | 0.547561 | 0.273781 | − | 0.961792i | \(-0.411726\pi\) | ||||
0.273781 | + | 0.961792i | \(0.411726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 28.0887i | − 0.0952159i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 30.1271 | 0.101438 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 411.405i | − 1.37594i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.6015 | −0.138211 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 132.100i | 0.435974i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 151.476 | 0.496642 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 168.120i | 0.547621i | 0.961784 | + | 0.273811i | \(0.0882841\pi\) | ||||
−0.961784 | + | 0.273811i | \(0.911716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 316.555 | 1.02445 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 470.376i | − 1.51246i | −0.654305 | − | 0.756231i | \(-0.727039\pi\) | ||||
0.654305 | − | 0.756231i | \(-0.272961\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4378 | 0.0621016 | 0.0310508 | − | 0.999518i | \(-0.490115\pi\) | ||||
0.0310508 | + | 0.999518i | \(0.490115\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.08399i | 0.0161396i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −242.195 | −0.764021 | −0.382011 | − | 0.924158i | \(-0.624768\pi\) | ||||
−0.382011 | + | 0.924158i | \(0.624768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 190.024i | − 0.595686i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −55.1715 | −0.171874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 131.202i | 0.406197i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −379.080 | −1.16640 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 19.6223i | − 0.0600070i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −82.6808 | −0.251309 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 440.951i | 1.33218i | 0.745872 | + | 0.666090i | \(0.232033\pi\) | ||||
−0.745872 | + | 0.666090i | \(0.767967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −44.9843 | −0.135088 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 83.1612i | − 0.248242i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −250.841 | −0.744335 | −0.372167 | − | 0.928166i | \(-0.621385\pi\) | ||||
−0.372167 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 86.5310i | − 0.255254i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.90443 | 0.0173150 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 119.812i | − 0.349306i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −59.3409 | −0.172003 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1029i | 0.0464060i | 0.999731 | + | 0.0232030i | \(0.00738641\pi\) | ||||
−0.999731 | + | 0.0232030i | \(0.992614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −274.843 | −0.787516 | −0.393758 | − | 0.919214i | \(-0.628825\pi\) | ||||
−0.393758 | + | 0.919214i | \(0.628825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 85.1287i | 0.242532i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 165.428 | 0.468634 | 0.234317 | − | 0.972160i | \(-0.424715\pi\) | ||||
0.234317 | + | 0.972160i | \(0.424715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 109.770i | 0.309212i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.7805 | 0.0301974 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 688.519i | 1.91788i | 0.283607 | + | 0.958941i | \(0.408469\pi\) | ||||
−0.283607 | + | 0.958941i | \(0.591531\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −324.574 | −0.899096 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 151.353i | − 0.416950i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.0015 | 0.112333 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 102.170i | − 0.278393i | −0.990265 | − | 0.139196i | \(-0.955548\pi\) | ||||
0.990265 | − | 0.139196i | \(-0.0444519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 217.564 | 0.589603 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 67.8838i | 0.182975i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −294.317 | −0.789052 | −0.394526 | − | 0.918885i | \(-0.629091\pi\) | ||||
−0.394526 | + | 0.918885i | \(0.629091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 113.755i | 0.303348i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 536.942 | 1.42425 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 81.1923i | 0.214228i | 0.994247 | + | 0.107114i | \(0.0341610\pi\) | ||||
−0.994247 | + | 0.107114i | \(0.965839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 360.675 | 0.946653 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 198.838i | 0.519160i | 0.965722 | + | 0.259580i | \(0.0835841\pi\) | ||||
−0.965722 | + | 0.259580i | \(0.916416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.82559 | −0.0255210 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 100.477i | 0.259629i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 368.767 | 0.947987 | 0.473993 | − | 0.880528i | \(-0.342812\pi\) | ||||
0.473993 | + | 0.880528i | \(0.342812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 125.831i | 0.321819i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 382.002 | 0.972016 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 110.434i | 0.279580i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −114.315 | −0.287947 | −0.143973 | − | 0.989582i | \(-0.545988\pi\) | ||||
−0.143973 | + | 0.989582i | \(0.545988\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 56.3317i | 0.141182i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 39.9083 | 0.0995218 | 0.0497609 | − | 0.998761i | \(-0.484154\pi\) | ||||
0.0497609 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6839i | 0.0413992i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.2789 | 0.0303183 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 86.9391i | − 0.213610i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −269.868 | −0.659825 | −0.329912 | − | 0.944012i | \(-0.607019\pi\) | ||||
−0.329912 | + | 0.944012i | \(0.607019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 26.4421i | − 0.0643361i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.5728 | −0.0619197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 155.476i | 0.374641i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 150.189 | 0.360165 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 20.3559i | − 0.0485821i | −0.999705 | − | 0.0242910i | \(-0.992267\pi\) | ||||
0.999705 | − | 0.0242910i | \(-0.00773283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −557.905 | −1.32519 | −0.662595 | − | 0.748978i | \(-0.730545\pi\) | ||||
−0.662595 | + | 0.748978i | \(0.730545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 199.692i | 0.472085i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 115.944 | 0.272810 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 137.908i | − 0.322970i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −164.524 | −0.383506 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 376.569i | 0.873710i | 0.899532 | + | 0.436855i | \(0.143908\pi\) | ||||
−0.899532 | + | 0.436855i | \(0.856092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 602.876 | 1.39232 | 0.696162 | − | 0.717885i | \(-0.254890\pi\) | ||||
0.696162 | + | 0.717885i | \(0.254890\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 77.4483i | − 0.178042i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −657.510 | −1.50460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 381.087i | − 0.868080i | −0.900894 | − | 0.434040i | \(-0.857088\pi\) | ||||
0.900894 | − | 0.434040i | \(-0.142912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −142.371 | −0.322838 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 599.838i | 1.35404i | 0.735966 | + | 0.677018i | \(0.236728\pi\) | ||||
−0.735966 | + | 0.677018i | \(0.763272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.7377 | −0.0645791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 254.349i | 0.569014i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 814.240 | 1.81345 | 0.906726 | − | 0.421720i | \(-0.138573\pi\) | ||||
0.906726 | + | 0.421720i | \(0.138573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 420.475i | 0.932317i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −339.366 | −0.749152 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 27.7637i | − 0.0610191i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 111.281 | 0.243502 | 0.121751 | − | 0.992561i | \(-0.461149\pi\) | ||||
0.121751 | + | 0.992561i | \(0.461149\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 26.0372i | − 0.0567259i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 507.833 | 1.10159 | 0.550795 | − | 0.834641i | \(-0.314325\pi\) | ||||
0.550795 | + | 0.834641i | \(0.314325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 397.302i | 0.858103i | 0.903280 | + | 0.429052i | \(0.141152\pi\) | ||||
−0.903280 | + | 0.429052i | \(0.858848\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.40648 | 0.00517522 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 830.195i | − 1.77772i | −0.458179 | − | 0.888860i | \(-0.651498\pi\) | ||||
0.458179 | − | 0.888860i | \(-0.348502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −75.7126 | −0.161434 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 8.06190i | − 0.0171166i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −194.186 | −0.410542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 605.849i | 1.27547i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 163.954 | 0.343719 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 146.251i | 0.305325i | 0.988278 | + | 0.152662i | \(0.0487847\pi\) | ||||
−0.988278 | + | 0.152662i | \(0.951215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 245.660 | 0.510727 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 54.0258i | 0.111855i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 219.103 | 0.451759 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 177.070i | 0.363593i | 0.983336 | + | 0.181797i | \(0.0581913\pi\) | ||||
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −103.142 | −0.210924 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 94.9463i | 0.193373i | 0.995315 | + | 0.0966866i | \(0.0308245\pi\) | ||||
−0.995315 | + | 0.0966866i | \(0.969176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −164.227 | −0.333118 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.7309i | 0.0479412i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 99.9384 | 0.201083 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 744.720i | 1.49243i | 0.665707 | + | 0.746213i | \(0.268130\pi\) | ||||
−0.665707 | + | 0.746213i | \(0.731870\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 362.020 | 0.722594 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 578.757i | 1.15061i | 0.817939 | + | 0.575305i | \(0.195117\pi\) | ||||
−0.817939 | + | 0.575305i | \(0.804883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −104.055 | −0.206049 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 172.171i | − 0.339589i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −323.101 | −0.634777 | −0.317388 | − | 0.948296i | \(-0.602806\pi\) | ||||
−0.317388 | + | 0.948296i | \(0.602806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 37.3290i | − 0.0730509i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 136.053 | 0.265211 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 249.349i | 0.484172i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −385.935 | −0.746490 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 167.599i | 0.322927i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −582.929 | −1.11887 | −0.559433 | − | 0.828875i | \(-0.688981\pi\) | ||||
−0.559433 | + | 0.828875i | \(0.688981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 227.111i | 0.434247i | 0.976144 | + | 0.217124i | \(0.0696675\pi\) | ||||
−0.976144 | + | 0.217124i | \(0.930332\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 49.7810 | 0.0948209 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 5.10288i | − 0.00968288i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −101.596 | −0.192053 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 61.7639i | 0.116316i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1188.12 | −2.22911 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 43.4582i | − 0.0812303i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 85.7433 | 0.159671 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 275.154i | − 0.510491i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 551.391 | 1.01921 | 0.509603 | − | 0.860409i | \(-0.329792\pi\) | ||||
0.509603 | + | 0.860409i | \(0.329792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 244.942i | − 0.451090i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4564 | 0.0283603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 745.659i | − 1.36318i | −0.731735 | − | 0.681590i | \(-0.761289\pi\) | ||||
0.731735 | − | 0.681590i | \(-0.238711\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −333.078 | −0.606700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 858.144i | − 1.55743i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 100.543 | 0.181813 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 35.4339i | − 0.0638448i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 755.207 | 1.35585 | 0.677924 | − | 0.735132i | \(-0.262880\pi\) | ||||
0.677924 | + | 0.735132i | \(0.262880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 548.703i | − 0.981580i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 50.3209 | 0.0896985 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 699.309i | 1.24211i | 0.783766 | + | 0.621056i | \(0.213296\pi\) | ||||
−0.783766 | + | 0.621056i | \(0.786704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 68.1600 | 0.120637 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 11.1791i | − 0.0197163i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.8709 | 0.0630419 | 0.0315210 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315210 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 828.429i | − 1.45084i | −0.688307 | − | 0.725420i | \(-0.741646\pi\) | ||||
0.688307 | − | 0.725420i | \(-0.258354\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −202.639 | −0.353646 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 581.049i | 1.01052i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −471.333 | −0.816867 | −0.408434 | − | 0.912788i | \(-0.633925\pi\) | ||||
−0.408434 | + | 0.912788i | \(0.633925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 157.159i | 0.271432i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 141.550 | 0.243632 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 316.866i | 0.543510i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −67.0553 | −0.114624 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 645.149i | 1.09906i | 0.835473 | + | 0.549531i | \(0.185193\pi\) | ||||
−0.835473 | + | 0.549531i | \(0.814807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.6643 | 0.0452704 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 658.247i | − 1.11379i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 203.619 | 0.343370 | 0.171685 | − | 0.985152i | \(-0.445079\pi\) | ||||
0.171685 | + | 0.985152i | \(0.445079\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.49172i | 0.0142718i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 134.505 | 0.225301 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 603.605i | − 1.00769i | −0.863795 | − | 0.503844i | \(-0.831919\pi\) | ||||
0.863795 | − | 0.503844i | \(-0.168081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −626.271 | −1.04205 | −0.521024 | − | 0.853542i | \(-0.674450\pi\) | ||||
−0.521024 | + | 0.853542i | \(0.674450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 182.862i | 0.303254i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 119.220 | 0.197057 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 421.012i | − 0.693595i | −0.937940 | − | 0.346797i | \(-0.887269\pi\) | ||||
0.937940 | − | 0.346797i | \(-0.112731\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −70.5114 | −0.115782 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1090.52i | − 1.78481i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9743 | 0.0211652 | 0.0105826 | − | 0.999944i | \(-0.496631\pi\) | ||||
0.0105826 | + | 0.999944i | \(0.496631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 171.373i | 0.278656i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −423.164 | −0.685842 | −0.342921 | − | 0.939364i | \(-0.611416\pi\) | ||||
−0.342921 | + | 0.939364i | \(0.611416\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 625.820i | − 1.01102i | −0.862821 | − | 0.505509i | \(-0.831305\pi\) | ||||
0.862821 | − | 0.505509i | \(-0.168695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 130.484 | 0.210119 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.1637i | 0.0419963i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 488.861 | 0.782178 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 262.944i | 0.419368i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −75.1367 | −0.119454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 690.848i | 1.09485i | 0.836856 | + | 0.547423i | \(0.184391\pi\) | ||||
−0.836856 | + | 0.547423i | \(0.815609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −331.593 | −0.523844 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 284.101i | 0.447403i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 777.491 | 1.22055 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 241.373i | − 0.377735i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −369.160 | −0.575913 | −0.287957 | − | 0.957643i | \(-0.592976\pi\) | ||||
−0.287957 | + | 0.957643i | \(0.592976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 666.030i | 1.03582i | 0.855436 | + | 0.517909i | \(0.173289\pi\) | ||||
−0.855436 | + | 0.517909i | \(0.826711\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.1448 | −0.122705 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 651.886i | − 1.00755i | −0.863835 | − | 0.503776i | \(-0.831944\pi\) | ||||
0.863835 | − | 0.503776i | \(-0.168056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −119.368 | −0.183926 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.19093i | − 0.00336549i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −903.324 | −1.38334 | −0.691672 | − | 0.722212i | \(-0.743126\pi\) | ||||
−0.691672 | + | 0.722212i | \(0.743126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 300.901i | 0.459391i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −90.1576 | −0.137226 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 643.621i | − 0.976664i | −0.872658 | − | 0.488332i | \(-0.837606\pi\) | ||||
0.872658 | − | 0.488332i | \(-0.162394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 860.187 | 1.30134 | 0.650671 | − | 0.759360i | \(-0.274488\pi\) | ||||
0.650671 | + | 0.759360i | \(0.274488\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 142.189i | 0.214463i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −44.3722 | −0.0667250 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 823.017i | − 1.23391i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 291.766 | 0.436123 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 643.725i | − 0.959351i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 866.535 | 1.28757 | 0.643785 | − | 0.765206i | \(-0.277363\pi\) | ||||
0.643785 | + | 0.765206i | \(0.277363\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 120.232i | − 0.178121i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1307.26 | 1.93095 | 0.965477 | − | 0.260489i | \(-0.0838838\pi\) | ||||
0.965477 | + | 0.260489i | \(0.0838838\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 199.478i | − 0.293783i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −196.616 | −0.288716 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 783.569i | − 1.14725i | −0.819120 | − | 0.573623i | \(-0.805538\pi\) | ||||
0.819120 | − | 0.573623i | \(-0.194462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.8283 | 0.0304063 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 203.720i | − 0.296536i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −895.354 | −1.29950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1014.95i | − 1.46882i | −0.678708 | − | 0.734408i | \(-0.737460\pi\) | ||||
0.678708 | − | 0.734408i | \(-0.262540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.6054 | 0.0311766 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 118.303i | 0.170220i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 363.394 | 0.521368 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 479.926i | − 0.686590i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 957.527 | 1.36595 | 0.682973 | − | 0.730444i | \(-0.260687\pi\) | ||||
0.682973 | + | 0.730444i | \(0.260687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 392.615i | − 0.558485i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −157.296 | −0.223115 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 94.7346i | 0.133995i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 65.7503 | 0.0927366 | 0.0463683 | − | 0.998924i | \(-0.485235\pi\) | ||||
0.0463683 | + | 0.998924i | \(0.485235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 242.832i | − 0.341536i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.5728 | 0.0358665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 129.595i | − 0.181251i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −594.219 | −0.828757 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 573.085i | 0.797058i | 0.917156 | + | 0.398529i | \(0.130479\pi\) | ||||
−0.917156 | + | 0.398529i | \(0.869521\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 227.015 | 0.314861 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 568.354i | 0.786106i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −758.352 | −1.04600 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 249.632i | 0.343373i | 0.985152 | + | 0.171686i | \(0.0549216\pi\) | ||||
−0.985152 | + | 0.171686i | \(0.945078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 167.825i | 0.229582i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 662.187 | 0.903393 | 0.451696 | − | 0.892172i | \(-0.350819\pi\) | ||||
0.451696 | + | 0.892172i | \(0.350819\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 112.145i | − 0.152578i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −353.409 | −0.479524 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 98.7372i | − 0.133609i | −0.997766 | − | 0.0668046i | \(-0.978720\pi\) | ||||
0.997766 | − | 0.0668046i | \(-0.0212804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −742.988 | −1.00268 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 906.520i | − 1.22008i | −0.792370 | − | 0.610041i | \(-0.791153\pi\) | ||||
0.792370 | − | 0.610041i | \(-0.208847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −200.349 | −0.268925 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 341.875i | − 0.457664i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −39.5657 | −0.0528248 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 286.284i | 0.381204i | 0.981667 | + | 0.190602i | \(0.0610440\pi\) | ||||
−0.981667 | + | 0.190602i | \(0.938956\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −784.470 | −1.04179 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 267.316i | − 0.354062i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1162.42 | 1.53556 | 0.767781 | − | 0.640712i | \(-0.221361\pi\) | ||||
0.767781 | + | 0.640712i | \(0.221361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 252.180i | 0.332253i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −994.905 | −1.30737 | −0.653683 | − | 0.756769i | \(-0.726777\pi\) | ||||
−0.653683 | + | 0.756769i | \(0.726777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 14.0720i | − 0.0184429i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.5093 | 0.0268096 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 337.293i | − 0.439756i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −614.473 | −0.799055 | −0.399527 | − | 0.916721i | \(-0.630826\pi\) | ||||
−0.399527 | + | 0.916721i | \(0.630826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 600.727i | 0.779153i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 927.633 | 1.20004 | 0.600021 | − | 0.799984i | \(-0.295159\pi\) | ||||
0.600021 | + | 0.799984i | \(0.295159\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 23.5635i | − 0.0304045i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.2601 | −0.0415188 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1898.86i | 2.43756i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 466.490 | 0.597298 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 170.300i | 0.217497i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.35031 | 0.00808957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 781.920i | − 0.993545i | −0.867881 | − | 0.496772i | \(-0.834518\pi\) | ||||
0.867881 | − | 0.496772i | \(-0.165482\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 697.047 | 0.883456 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 62.0550i | − 0.0784513i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1818.94 | 2.29375 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 129.146i | 0.162447i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1160.22 | −1.45574 | −0.727868 | − | 0.685718i | \(-0.759489\pi\) | ||||
−0.727868 | + | 0.685718i | \(0.759489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 333.543i | 0.417450i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 63.1910 | 0.0788902 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 174.243i | − 0.216991i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.5558 | −0.0528644 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 556.962i | − 0.690163i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1512.26 | 1.86930 | 0.934651 | − | 0.355568i | \(-0.115712\pi\) | ||||
0.934651 | + | 0.355568i | \(0.115712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1586.92i | − 1.95674i | −0.206858 | − | 0.978371i | \(-0.566324\pi\) | ||||
0.206858 | − | 0.978371i | \(-0.433676\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −791.378 | −0.973405 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 81.2441i | − 0.0996860i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −876.942 | −1.07337 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 61.0493i | 0.0745412i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1118.96 | −1.36292 | −0.681459 | − | 0.731857i | \(-0.738654\pi\) | ||||
−0.681459 | + | 0.731857i | \(0.738654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1628.26i | 1.97844i | 0.146438 | + | 0.989220i | \(0.453219\pi\) | ||||
−0.146438 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 232.366 | 0.281656 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 421.552i | 0.509736i | 0.966976 | + | 0.254868i | \(0.0820321\pi\) | ||||
−0.966976 | + | 0.254868i | \(0.917968\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −475.263 | −0.573297 | −0.286649 | − | 0.958036i | \(-0.592541\pi\) | ||||
−0.286649 | + | 0.958036i | \(0.592541\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 570.786i | − 0.686866i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −237.801 | −0.285475 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 285.161i | 0.341510i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.29157 | −0.00632207 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 653.590i | − 0.779010i | −0.921024 | − | 0.389505i | \(-0.872646\pi\) | ||||
0.921024 | − | 0.389505i | \(-0.127354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 233.154 | 0.277234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 303.221i | 0.359692i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 135.618 | 0.160495 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 108.541i | − 0.128148i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 260.323 | 0.306623 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 376.544i | − 0.442472i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 140.493 | 0.164705 | 0.0823523 | − | 0.996603i | \(-0.473757\pi\) | ||||
0.0823523 | + | 0.996603i | \(0.473757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 107.168i | 0.125343i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −562.796 | −0.656704 | −0.328352 | − | 0.944555i | \(-0.606493\pi\) | ||||
−0.328352 | + | 0.944555i | \(0.606493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 228.316i | 0.265792i | 0.991130 | + | 0.132896i | \(0.0424277\pi\) | ||||
−0.991130 | + | 0.132896i | \(0.957572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 156.024 | 0.181212 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 892.187i | 1.03382i | 0.856040 | + | 0.516910i | \(0.172918\pi\) | ||||
−0.856040 | + | 0.516910i | \(0.827082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −132.017 | −0.152621 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 457.073i | 0.527189i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 469.310 | 0.540058 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 998.611i | − 1.14651i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −481.783 | −0.551871 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 81.5787i | 0.0932328i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1406.66 | −1.60395 | −0.801974 | − | 0.597359i | \(-0.796217\pi\) | ||||
−0.801974 | + | 0.597359i | \(0.796217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 277.882i | − 0.316135i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 943.043 | 1.07042 | 0.535212 | − | 0.844718i | \(-0.320232\pi\) | ||||
0.535212 | + | 0.844718i | \(0.320232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1146.63i | 1.29856i | 0.760549 | + | 0.649280i | \(0.224930\pi\) | ||||
−0.760549 | + | 0.649280i | \(0.775070\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −48.6511 | −0.0549729 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 894.171i | − 1.00808i | −0.863679 | − | 0.504042i | \(-0.831846\pi\) | ||||
0.863679 | − | 0.504042i | \(-0.168154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 258.655 | 0.290950 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 52.1816i | − 0.0585652i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1742.88 | −1.95171 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 67.5395i | 0.0754631i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −712.574 | −0.794397 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.3761i | 0.0371258i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 273.850 | 0.303940 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 72.0559i | 0.0797961i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 192.939 | 0.213192 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1358.60i | 1.49790i | 0.662626 | + | 0.748950i | \(0.269442\pi\) | ||||
−0.662626 | + | 0.748950i | \(0.730558\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 228.804 | 0.251710 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 804.510i | 0.883106i | 0.897235 | + | 0.441553i | \(0.145572\pi\) | ||||
−0.897235 | + | 0.441553i | \(0.854428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 660.726 | 0.723686 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 262.364i | − 0.286736i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 273.950 | 0.298745 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1704.73i | 1.85498i | 0.373849 | + | 0.927490i | \(0.378038\pi\) | ||||
−0.373849 | + | 0.927490i | \(0.621962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 291.192 | 0.316169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1318.14i | 1.42810i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −346.958 | −0.375090 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 548.290i | − 0.591467i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1351.05 | −1.45431 | −0.727154 | − | 0.686475i | \(-0.759157\pi\) | ||||
−0.727154 | + | 0.686475i | \(0.759157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1242.59i | − 1.33469i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −814.715 | −0.873220 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.6374i | 0.0423930i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 672.646 | 0.717872 | 0.358936 | − | 0.933362i | \(-0.383140\pi\) | ||||
0.358936 | + | 0.933362i | \(0.383140\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 33.6672i | − 0.0358544i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 528.671 | 0.561818 | 0.280909 | − | 0.959734i | \(-0.409364\pi\) | ||||
0.280909 | + | 0.959734i | \(0.409364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1821.13i | 1.93121i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.80573 | 0.00931823 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 661.066i | 0.698063i | 0.937111 | + | 0.349032i | \(0.113489\pi\) | ||||
−0.937111 | + | 0.349032i | \(0.886511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 492.351 | 0.518811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 419.494i | 0.441108i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1545.41 | 1.62163 | 0.810815 | − | 0.585303i | \(-0.199024\pi\) | ||||
0.810815 | + | 0.585303i | \(0.199024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 159.618i | − 0.167139i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −329.131 | −0.343920 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 18.9627i | − 0.0197735i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 959.963 | 0.998921 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 95.5598i | 0.0992313i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −123.793 | −0.128283 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 161.279i | − 0.166782i | −0.996517 | − | 0.0833912i | \(-0.973425\pi\) | ||||
0.996517 | − | 0.0833912i | \(-0.0265751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 227.248 | 0.234518 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.20412i | 0.00432969i | 0.999998 | + | 0.00216484i | \(0.000689091\pi\) | ||||
−0.999998 | + | 0.00216484i | \(0.999311\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 107.707 | 0.110696 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 656.586i | 0.673422i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1348.19 | −1.37993 | −0.689967 | − | 0.723841i | \(-0.742375\pi\) | ||||
−0.689967 | + | 0.723841i | \(0.742375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 122.126i | 0.124746i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.9868 | −0.0346451 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 984.262i | 1.00128i | 0.865655 | + | 0.500642i | \(0.166903\pi\) | ||||
−0.865655 | + | 0.500642i | \(0.833097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 518.497 | 0.526393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 143.207i | 0.145094i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −841.045 | −0.850399 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1013.87i | − 1.02308i | −0.859259 | − | 0.511541i | \(-0.829075\pi\) | ||||
0.859259 | − | 0.511541i | \(-0.170925\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 763.750 | 0.769134 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 105.948i | 0.106481i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 311.310 | 0.312246 | 0.156123 | − | 0.987738i | \(-0.450100\pi\) | ||||
0.156123 | + | 0.987738i | \(0.450100\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 77.9151i | 0.0779931i |
(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 | 384.3.g.b.127.2 | yes | 8 | |
3.2 | odd | 2 | 1152.3.g.c.127.5 | 8 | |||
4.3 | odd | 2 | inner | 384.3.g.b.127.6 | yes | 8 | |
8.3 | odd | 2 | 384.3.g.a.127.3 | ✓ | 8 | ||
8.5 | even | 2 | 384.3.g.a.127.7 | yes | 8 | ||
12.11 | even | 2 | 1152.3.g.c.127.6 | 8 | |||
16.3 | odd | 4 | 768.3.b.e.127.2 | 8 | |||
16.5 | even | 4 | 768.3.b.e.127.3 | 8 | |||
16.11 | odd | 4 | 768.3.b.f.127.7 | 8 | |||
16.13 | even | 4 | 768.3.b.f.127.6 | 8 | |||
24.5 | odd | 2 | 1152.3.g.f.127.3 | 8 | |||
24.11 | even | 2 | 1152.3.g.f.127.4 | 8 | |||
48.5 | odd | 4 | 2304.3.b.t.127.4 | 8 | |||
48.11 | even | 4 | 2304.3.b.q.127.4 | 8 | |||
48.29 | odd | 4 | 2304.3.b.q.127.5 | 8 | |||
48.35 | even | 4 | 2304.3.b.t.127.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.3 | ✓ | 8 | 8.3 | odd | 2 | ||
384.3.g.a.127.7 | yes | 8 | 8.5 | even | 2 | ||
384.3.g.b.127.2 | yes | 8 | 1.1 | even | 1 | trivial | |
384.3.g.b.127.6 | yes | 8 | 4.3 | odd | 2 | inner | |
768.3.b.e.127.2 | 8 | 16.3 | odd | 4 | |||
768.3.b.e.127.3 | 8 | 16.5 | even | 4 | |||
768.3.b.f.127.6 | 8 | 16.13 | even | 4 | |||
768.3.b.f.127.7 | 8 | 16.11 | odd | 4 | |||
1152.3.g.c.127.5 | 8 | 3.2 | odd | 2 | |||
1152.3.g.c.127.6 | 8 | 12.11 | even | 2 | |||
1152.3.g.f.127.3 | 8 | 24.5 | odd | 2 | |||
1152.3.g.f.127.4 | 8 | 24.11 | even | 2 | |||
2304.3.b.q.127.4 | 8 | 48.11 | even | 4 | |||
2304.3.b.q.127.5 | 8 | 48.29 | odd | 4 | |||
2304.3.b.t.127.4 | 8 | 48.5 | odd | 4 | |||
2304.3.b.t.127.5 | 8 | 48.35 | even | 4 |