Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(127,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(62.7794529086\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.4 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.127 |
Dual form | 2304.3.b.q.127.5 |
$q$-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 \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.36433i | − 0.272865i | −0.990649 | − | 0.136433i | \(-0.956436\pi\) | ||||
0.990649 | − | 0.136433i | \(-0.0435637\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.24213i | − 0.177446i | −0.996056 | − | 0.0887232i | \(-0.971721\pi\) | ||||
0.996056 | − | 0.0887232i | \(-0.0282787\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.79796 | 0.527087 | 0.263544 | − | 0.964647i | \(-0.415109\pi\) | ||||
0.263544 | + | 0.964647i | \(0.415109\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 16.3830i | − 1.26023i | −0.776501 | − | 0.630116i | \(-0.783007\pi\) | ||||
0.776501 | − | 0.630116i | \(-0.216993\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.01086 | 0.294756 | 0.147378 | − | 0.989080i | \(-0.452917\pi\) | ||||
0.147378 | + | 0.989080i | \(0.452917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.1835 | 1.37808 | 0.689039 | − | 0.724725i | \(-0.258033\pi\) | ||||
0.689039 | + | 0.724725i | \(0.258033\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 25.1117i | 1.09181i | 0.837847 | + | 0.545906i | \(0.183814\pi\) | ||||
−0.837847 | + | 0.545906i | \(0.816186\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.1386 | 0.925545 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 32.7743i | 1.13015i | 0.825040 | + | 0.565074i | \(0.191152\pi\) | ||||
−0.825040 | + | 0.565074i | \(0.808848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.01836i | − 0.0328504i | −0.999865 | − | 0.0164252i | \(-0.994771\pi\) | ||||
0.999865 | − | 0.0164252i | \(-0.00522854\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.69466 | −0.0484189 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.9948i | 0.405264i | 0.979255 | + | 0.202632i | \(0.0649495\pi\) | ||||
−0.979255 | + | 0.202632i | \(0.935050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −72.5212 | −1.76881 | −0.884405 | − | 0.466720i | \(-0.845435\pi\) | ||||
−0.884405 | + | 0.466720i | \(0.845435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.4922 | −0.778888 | −0.389444 | − | 0.921050i | \(-0.627333\pi\) | ||||
−0.389444 | + | 0.921050i | \(0.627333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 54.6513i | 1.03116i | 0.856842 | + | 0.515579i | \(0.172423\pi\) | ||||
−0.856842 | + | 0.515579i | \(0.827577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.91030i | − 0.143824i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 20.5880 | 0.348949 | 0.174474 | − | 0.984662i | \(-0.444177\pi\) | ||||
0.174474 | + | 0.984662i | \(0.444177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 111.026i | − 1.82010i | −0.414499 | − | 0.910050i | \(-0.636043\pi\) | ||||
0.414499 | − | 0.910050i | \(-0.363957\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.3518 | −0.343873 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.9540 | 0.909762 | 0.454881 | − | 0.890552i | \(-0.349682\pi\) | ||||
0.454881 | + | 0.890552i | \(0.349682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 80.4576i | − 1.13320i | −0.823991 | − | 0.566602i | \(-0.808258\pi\) | ||||
0.823991 | − | 0.566602i | \(-0.191742\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −30.0525 | −0.411679 | −0.205839 | − | 0.978586i | \(-0.565992\pi\) | ||||
−0.205839 | + | 0.978586i | \(0.565992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.20179i | − 0.0935298i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 80.9441i | − 1.02461i | −0.858804 | − | 0.512304i | \(-0.828792\pi\) | ||||
0.858804 | − | 0.512304i | \(-0.171208\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 113.958 | 1.37299 | 0.686496 | − | 0.727134i | \(-0.259148\pi\) | ||||
0.686496 | + | 0.727134i | \(0.259148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 6.83644i | − 0.0804288i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −21.0637 | −0.236671 | −0.118335 | − | 0.992974i | \(-0.537756\pi\) | ||||
−0.118335 | + | 0.992974i | \(0.537756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.3498 | −0.223624 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 76.2681i | 0.755130i | 0.925983 | + | 0.377565i | \(0.123239\pi\) | ||||
−0.925983 | + | 0.377565i | \(0.876761\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 182.763i | 1.77440i | 0.461383 | + | 0.887201i | \(0.347353\pi\) | ||||
−0.461383 | + | 0.887201i | \(0.652647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 31.8533 | 0.297694 | 0.148847 | − | 0.988860i | \(-0.452444\pi\) | ||||
0.148847 | + | 0.988860i | \(0.452444\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 11.3289i | − 0.103935i | −0.998649 | − | 0.0519676i | \(-0.983451\pi\) | ||||
0.998649 | − | 0.0519676i | \(-0.0165493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −49.9587 | −0.442113 | −0.221056 | − | 0.975261i | \(-0.570950\pi\) | ||||
−0.221056 | + | 0.975261i | \(0.570950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 34.2605 | 0.297917 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 6.22412i | − 0.0523035i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −87.3837 | −0.722179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 65.6767i | − 0.525414i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 208.236i | − 1.63965i | −0.572614 | − | 0.819825i | \(-0.694071\pi\) | ||||
0.572614 | − | 0.819825i | \(-0.305929\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 220.549 | 1.68358 | 0.841791 | − | 0.539804i | \(-0.181502\pi\) | ||||
0.841791 | + | 0.539804i | \(0.181502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 32.5231i | − 0.244535i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.2664 | 0.111433 | 0.0557167 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557167 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 86.7117 | 0.623825 | 0.311912 | − | 0.950111i | \(-0.399030\pi\) | ||||
0.311912 | + | 0.950111i | \(0.399030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 94.9881i | − 0.664252i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 44.7148 | 0.308378 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 146.849i | 0.985561i | 0.870154 | + | 0.492780i | \(0.164019\pi\) | ||||
−0.870154 | + | 0.492780i | \(0.835981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 195.933i | − 1.29757i | −0.760972 | − | 0.648785i | \(-0.775277\pi\) | ||||
0.760972 | − | 0.648785i | \(-0.224723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.38938 | −0.00896374 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.65454i | − 0.0296468i | −0.999890 | − | 0.0148234i | \(-0.995281\pi\) | ||||
0.999890 | − | 0.0148234i | \(-0.00471860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 31.1918 | 0.193738 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 59.5489 | 0.365331 | 0.182665 | − | 0.983175i | \(-0.441528\pi\) | ||||
0.182665 | + | 0.983175i | \(0.441528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 209.012i | − 1.25157i | −0.779996 | − | 0.625785i | \(-0.784779\pi\) | ||||
0.779996 | − | 0.625785i | \(-0.215221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −99.4032 | −0.588185 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 96.7635i | − 0.559326i | −0.960098 | − | 0.279663i | \(-0.909777\pi\) | ||||
0.960098 | − | 0.279663i | \(-0.0902228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 28.7411i | − 0.164235i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 49.5039 | 0.276558 | 0.138279 | − | 0.990393i | \(-0.455843\pi\) | ||||
0.138279 | + | 0.990393i | \(0.455843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 141.417i | 0.781310i | 0.920537 | + | 0.390655i | \(0.127752\pi\) | ||||
−0.920537 | + | 0.390655i | \(0.872248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.4578 | 0.110582 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.0528 | 0.155362 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 380.039i | − 1.92913i | −0.263840 | − | 0.964566i | \(-0.584989\pi\) | ||||
0.263840 | − | 0.964566i | \(-0.415011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 77.6563i | 0.390233i | 0.980780 | + | 0.195116i | \(0.0625084\pi\) | ||||
−0.980780 | + | 0.195116i | \(0.937492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40.7098 | 0.200541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 98.9425i | 0.482646i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 151.811 | 0.726367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 191.446 | 0.907325 | 0.453662 | − | 0.891174i | \(-0.350117\pi\) | ||||
0.453662 | + | 0.891174i | \(0.350117\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 45.6943i | 0.212531i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.26493 | −0.00582919 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 82.0930i | − 0.371462i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 168.451i | − 0.755387i | −0.925931 | − | 0.377693i | \(-0.876717\pi\) | ||||
0.925931 | − | 0.377693i | \(-0.123283\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −113.516 | −0.500071 | −0.250036 | − | 0.968237i | \(-0.580442\pi\) | ||||
−0.250036 | + | 0.968237i | \(0.580442\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 117.618i | 0.513615i | 0.966463 | + | 0.256808i | \(0.0826707\pi\) | ||||
−0.966463 | + | 0.256808i | \(0.917329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 277.085 | 1.18921 | 0.594604 | − | 0.804019i | \(-0.297309\pi\) | ||||
0.594604 | + | 0.804019i | \(0.297309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −90.8150 | −0.386447 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 64.7470i | − 0.264273i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 428.964i | − 1.73670i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 452.914 | 1.80444 | 0.902219 | − | 0.431279i | \(-0.141937\pi\) | ||||
0.902219 | + | 0.431279i | \(0.141937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 145.596i | 0.575480i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 346.830 | 1.34953 | 0.674767 | − | 0.738031i | \(-0.264244\pi\) | ||||
0.674767 | + | 0.738031i | \(0.264244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.6254 | 0.0719127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 402.440i | − 1.53019i | −0.643917 | − | 0.765095i | \(-0.722692\pi\) | ||||
0.643917 | − | 0.765095i | \(-0.277308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 74.5622 | 0.281367 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 321.562i | 1.19540i | 0.801721 | + | 0.597699i | \(0.203918\pi\) | ||||
−0.801721 | + | 0.597699i | \(0.796082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 456.902i | 1.68599i | 0.537924 | + | 0.842993i | \(0.319209\pi\) | ||||
−0.537924 | + | 0.842993i | \(0.680791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 134.157 | 0.487843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 329.543i | 1.18969i | 0.803842 | + | 0.594843i | \(0.202786\pi\) | ||||
−0.803842 | + | 0.594843i | \(0.797214\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −175.064 | −0.623005 | −0.311503 | − | 0.950245i | \(-0.600832\pi\) | ||||
−0.311503 | + | 0.950245i | \(0.600832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 150.298 | 0.531087 | 0.265544 | − | 0.964099i | \(-0.414449\pi\) | ||||
0.265544 | + | 0.964099i | \(0.414449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 90.0804i | 0.313869i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −263.891 | −0.913119 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 160.435i | − 0.547561i | −0.961792 | − | 0.273781i | \(-0.911726\pi\) | ||||
0.961792 | − | 0.273781i | \(-0.0882742\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 28.0887i | − 0.0952159i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 411.405 | 1.37594 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.6015i | 0.138211i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −151.476 | −0.496642 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −168.120 | −0.547621 | −0.273811 | − | 0.961784i | \(-0.588284\pi\) | ||||
−0.273811 | + | 0.961784i | \(0.588284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 470.376i | 1.51246i | 0.654305 | + | 0.756231i | \(0.272961\pi\) | ||||
−0.654305 | + | 0.756231i | \(0.727039\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.4378 | −0.0621016 | −0.0310508 | − | 0.999518i | \(-0.509885\pi\) | ||||
−0.0310508 | + | 0.999518i | \(0.509885\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 242.195i | − 0.764021i | −0.924158 | − | 0.382011i | \(-0.875232\pi\) | ||||
0.924158 | − | 0.382011i | \(-0.124768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 190.024i | 0.595686i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 131.202 | 0.406197 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 379.080i | − 1.16640i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −82.6808 | −0.251309 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 440.951 | 1.33218 | 0.666090 | − | 0.745872i | \(-0.267967\pi\) | ||||
0.666090 | + | 0.745872i | \(0.267967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5.90443i | − 0.0173150i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 119.812i | − 0.349306i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.1029 | −0.0464060 | −0.0232030 | − | 0.999731i | \(-0.507386\pi\) | ||||
−0.0232030 | + | 0.999731i | \(0.507386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 274.843i | 0.787516i | 0.919214 | + | 0.393758i | \(0.128825\pi\) | ||||
−0.919214 | + | 0.393758i | \(0.871175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −165.428 | −0.468634 | −0.234317 | − | 0.972160i | \(-0.575285\pi\) | ||||
−0.234317 | + | 0.972160i | \(0.575285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −109.770 | −0.309212 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 688.519i | − 1.91788i | −0.283607 | − | 0.958941i | \(-0.591531\pi\) | ||||
0.283607 | − | 0.958941i | \(-0.408469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 324.574 | 0.899096 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.0015i | 0.112333i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 102.170i | 0.278393i | 0.990265 | + | 0.139196i | \(0.0444519\pi\) | ||||
−0.990265 | + | 0.139196i | \(0.955548\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 67.8838 | 0.182975 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 294.317i | − 0.789052i | −0.918885 | − | 0.394526i | \(-0.870909\pi\) | ||||
0.918885 | − | 0.394526i | \(-0.129091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 536.942 | 1.42425 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 81.1923 | 0.214228 | 0.107114 | − | 0.994247i | \(-0.465839\pi\) | ||||
0.107114 | + | 0.994247i | \(0.465839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 368.767i | − 0.947987i | −0.880528 | − | 0.473993i | \(-0.842812\pi\) | ||||
0.880528 | − | 0.473993i | \(-0.157188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 125.831i | 0.321819i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −110.434 | −0.279580 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 114.315i | 0.287947i | 0.989582 | + | 0.143973i | \(0.0459880\pi\) | ||||
−0.989582 | + | 0.143973i | \(0.954012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −39.9083 | −0.0995218 | −0.0497609 | − | 0.998761i | \(-0.515846\pi\) | ||||
−0.0497609 | + | 0.998761i | \(0.515846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6839 | −0.0413992 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 86.9391i | 0.213610i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 269.868 | 0.659825 | 0.329912 | − | 0.944012i | \(-0.392981\pi\) | ||||
0.329912 | + | 0.944012i | \(0.392981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 25.5728i | − 0.0619197i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 155.476i | − 0.374641i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.3559 | −0.0485821 | −0.0242910 | − | 0.999705i | \(-0.507733\pi\) | ||||
−0.0242910 | + | 0.999705i | \(0.507733\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 557.905i | − 1.32519i | −0.748978 | − | 0.662595i | \(-0.769455\pi\) | ||||
0.748978 | − | 0.662595i | \(-0.230545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 115.944 | 0.272810 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −137.908 | −0.322970 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 657.510i | 1.50460i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 381.087i | − 0.868080i | −0.900894 | − | 0.434040i | \(-0.857088\pi\) | ||||
0.900894 | − | 0.434040i | \(-0.142912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −599.838 | −1.35404 | −0.677018 | − | 0.735966i | \(-0.736728\pi\) | ||||
−0.677018 | + | 0.735966i | \(0.736728\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.7377i | 0.0645791i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −814.240 | −1.81345 | −0.906726 | − | 0.421720i | \(-0.861427\pi\) | ||||
−0.906726 | + | 0.421720i | \(0.861427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −420.475 | −0.932317 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.7637i | 0.0610191i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −111.281 | −0.243502 | −0.121751 | − | 0.992561i | \(-0.538851\pi\) | ||||
−0.121751 | + | 0.992561i | \(0.538851\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 507.833i | 1.10159i | 0.834641 | + | 0.550795i | \(0.185675\pi\) | ||||
−0.834641 | + | 0.550795i | \(0.814325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 397.302i | − 0.858103i | −0.903280 | − | 0.429052i | \(-0.858848\pi\) | ||||
0.903280 | − | 0.429052i | \(-0.141152\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −830.195 | −1.77772 | −0.888860 | − | 0.458179i | \(-0.848502\pi\) | ||||
−0.888860 | + | 0.458179i | \(0.848502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 75.7126i | − 0.161434i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −194.186 | −0.410542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 605.849 | 1.27547 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 219.103i | − 0.451759i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 177.070i | 0.363593i | 0.983336 | + | 0.181797i | \(0.0581913\pi\) | ||||
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −94.9463 | −0.193373 | −0.0966866 | − | 0.995315i | \(-0.530824\pi\) | ||||
−0.0966866 | + | 0.995315i | \(0.530824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 164.227i | 0.333118i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −99.9384 | −0.201083 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −744.720 | −1.49243 | −0.746213 | − | 0.665707i | \(-0.768130\pi\) | ||||
−0.746213 | + | 0.665707i | \(0.768130\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 578.757i | − 1.15061i | −0.817939 | − | 0.575305i | \(-0.804883\pi\) | ||||
0.817939 | − | 0.575305i | \(-0.195117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 104.055 | 0.206049 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 323.101i | − 0.634777i | −0.948296 | − | 0.317388i | \(-0.897194\pi\) | ||||
0.948296 | − | 0.317388i | \(-0.102806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.3290i | 0.0730509i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 249.349 | 0.484172 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 385.935i | − 0.746490i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −582.929 | −1.11887 | −0.559433 | − | 0.828875i | \(-0.688981\pi\) | ||||
−0.559433 | + | 0.828875i | \(0.688981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 227.111 | 0.434247 | 0.217124 | − | 0.976144i | \(-0.430332\pi\) | ||||
0.217124 | + | 0.976144i | \(0.430332\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 5.10288i | − 0.00968288i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −101.596 | −0.192053 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1188.12i | 2.22911i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 43.4582i | − 0.0812303i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 275.154 | 0.510491 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 551.391i | − 1.01921i | −0.860409 | − | 0.509603i | \(-0.829792\pi\) | ||||
0.860409 | − | 0.509603i | \(-0.170208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.4564 | −0.0283603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 745.659 | 1.36318 | 0.681590 | − | 0.731735i | \(-0.261289\pi\) | ||||
0.681590 | + | 0.731735i | \(0.261289\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 858.144i | 1.55743i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −100.543 | −0.181813 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 755.207i | 1.35585i | 0.735132 | + | 0.677924i | \(0.237120\pi\) | ||||
−0.735132 | + | 0.677924i | \(0.762880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 548.703i | 0.981580i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 699.309 | 1.24211 | 0.621056 | − | 0.783766i | \(-0.286704\pi\) | ||||
0.621056 | + | 0.783766i | \(0.286704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 68.1600i | 0.120637i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.8709 | 0.0630419 | 0.0315210 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315210 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −828.429 | −1.45084 | −0.725420 | − | 0.688307i | \(-0.758354\pi\) | ||||
−0.725420 | + | 0.688307i | \(0.758354\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 141.550i | − 0.243632i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 316.866i | 0.543510i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −645.149 | −1.09906 | −0.549531 | − | 0.835473i | \(-0.685193\pi\) | ||||
−0.549531 | + | 0.835473i | \(0.685193\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 26.6643i | − 0.0452704i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −203.619 | −0.343370 | −0.171685 | − | 0.985152i | \(-0.554921\pi\) | ||||
−0.171685 | + | 0.985152i | \(0.554921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.49172 | −0.0142718 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 603.605i | 1.00769i | 0.863795 | + | 0.503844i | \(0.168081\pi\) | ||||
−0.863795 | + | 0.503844i | \(0.831919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 626.271 | 1.04205 | 0.521024 | − | 0.853542i | \(-0.325550\pi\) | ||||
0.521024 | + | 0.853542i | \(0.325550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 119.220i | 0.197057i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 421.012i | 0.693595i | 0.937940 | + | 0.346797i | \(0.112731\pi\) | ||||
−0.937940 | + | 0.346797i | \(0.887269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1090.52 | −1.78481 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9743i | 0.0211652i | 0.999944 | + | 0.0105826i | \(0.00336861\pi\) | ||||
−0.999944 | + | 0.0105826i | \(0.996631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −423.164 | −0.685842 | −0.342921 | − | 0.939364i | \(-0.611416\pi\) | ||||
−0.342921 | + | 0.939364i | \(0.611416\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −625.820 | −1.01102 | −0.505509 | − | 0.862821i | \(-0.668695\pi\) | ||||
−0.505509 | + | 0.862821i | \(0.668695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.1637i | 0.0419963i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 488.861 | 0.782178 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 75.1367i | 0.119454i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 690.848i | 1.09485i | 0.836856 | + | 0.547423i | \(0.184391\pi\) | ||||
−0.836856 | + | 0.547423i | \(0.815609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −284.101 | −0.447403 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 777.491i | − 1.22055i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 369.160 | 0.575913 | 0.287957 | − | 0.957643i | \(-0.407024\pi\) | ||||
0.287957 | + | 0.957643i | \(0.407024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −666.030 | −1.03582 | −0.517909 | − | 0.855436i | \(-0.673289\pi\) | ||||
−0.517909 | + | 0.855436i | \(0.673289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 651.886i | 1.00755i | 0.863835 | + | 0.503776i | \(0.168056\pi\) | ||||
−0.863835 | + | 0.503776i | \(0.831944\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 119.368 | 0.183926 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 903.324i | − 1.38334i | −0.722212 | − | 0.691672i | \(-0.756874\pi\) | ||||
0.722212 | − | 0.691672i | \(-0.243126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 300.901i | − 0.459391i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −643.621 | −0.976664 | −0.488332 | − | 0.872658i | \(-0.662394\pi\) | ||||
−0.488332 | + | 0.872658i | \(0.662394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 860.187i | 1.30134i | 0.759360 | + | 0.650671i | \(0.225512\pi\) | ||||
−0.759360 | + | 0.650671i | \(0.774488\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −44.3722 | −0.0667250 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −823.017 | −1.23391 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1307.26i | − 1.93095i | −0.260489 | − | 0.965477i | \(-0.583884\pi\) | ||||
0.260489 | − | 0.965477i | \(-0.416116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 199.478i | − 0.293783i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 783.569 | 1.14725 | 0.573623 | − | 0.819120i | \(-0.305538\pi\) | ||||
0.573623 | + | 0.819120i | \(0.305538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 20.8283i | − 0.0304063i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 895.354 | 1.29950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1014.95 | 1.46882 | 0.734408 | − | 0.678708i | \(-0.237460\pi\) | ||||
0.734408 | + | 0.678708i | \(0.237460\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 118.303i | − 0.170220i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −363.394 | −0.521368 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 957.527i | 1.36595i | 0.730444 | + | 0.682973i | \(0.239313\pi\) | ||||
−0.730444 | + | 0.682973i | \(0.760687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 392.615i | 0.558485i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 94.7346 | 0.133995 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 65.7503i | 0.0927366i | 0.998924 | + | 0.0463683i | \(0.0147648\pi\) | ||||
−0.998924 | + | 0.0463683i | \(0.985235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.5728 | 0.0358665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −129.595 | −0.181251 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 758.352i | 1.04600i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 249.632i | 0.343373i | 0.985152 | + | 0.171686i | \(0.0549216\pi\) | ||||
−0.985152 | + | 0.171686i | \(0.945078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −167.825 | −0.229582 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 662.187i | − 0.903393i | −0.892172 | − | 0.451696i | \(-0.850819\pi\) | ||||
0.892172 | − | 0.451696i | \(-0.149181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 353.409 | 0.479524 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 98.7372 | 0.133609 | 0.0668046 | − | 0.997766i | \(-0.478720\pi\) | ||||
0.0668046 | + | 0.997766i | \(0.478720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 906.520i | 1.22008i | 0.792370 | + | 0.610041i | \(0.208847\pi\) | ||||
−0.792370 | + | 0.610041i | \(0.791153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 200.349 | 0.268925 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 39.5657i | − 0.0528248i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 286.284i | − 0.381204i | −0.981667 | − | 0.190602i | \(-0.938956\pi\) | ||||
0.981667 | − | 0.190602i | \(-0.0610440\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −267.316 | −0.354062 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1162.42i | 1.53556i | 0.640712 | + | 0.767781i | \(0.278639\pi\) | ||||
−0.640712 | + | 0.767781i | \(0.721361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −994.905 | −1.30737 | −0.653683 | − | 0.756769i | \(-0.726777\pi\) | ||||
−0.653683 | + | 0.756769i | \(0.726777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.0720 | −0.0184429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 927.633i | − 1.20004i | −0.799984 | − | 0.600021i | \(-0.795159\pi\) | ||||
0.799984 | − | 0.600021i | \(-0.204841\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 23.5635i | − 0.0304045i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1898.86 | −2.43756 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 466.490i | − 0.597298i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.35031 | −0.00808957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 781.920 | 0.993545 | 0.496772 | − | 0.867881i | \(-0.334518\pi\) | ||||
0.496772 | + | 0.867881i | \(0.334518\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62.0550i | 0.0784513i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1818.94 | −2.29375 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1160.22i | − 1.45574i | −0.685718 | − | 0.727868i | \(-0.740511\pi\) | ||||
0.685718 | − | 0.727868i | \(-0.259489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 333.543i | − 0.417450i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −174.243 | −0.216991 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 42.5558i | − 0.0528644i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1512.26 | 1.86930 | 0.934651 | − | 0.355568i | \(-0.115712\pi\) | ||||
0.934651 | + | 0.355568i | \(0.115712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1586.92 | −1.95674 | −0.978371 | − | 0.206858i | \(-0.933676\pi\) | ||||
−0.978371 | + | 0.206858i | \(0.933676\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 81.2441i | − 0.0996860i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −876.942 | −1.07337 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1118.96i | 1.36292i | 0.731857 | + | 0.681459i | \(0.238654\pi\) | ||||
−0.731857 | + | 0.681459i | \(0.761346\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1628.26i | 1.97844i | 0.146438 | + | 0.989220i | \(0.453219\pi\) | ||||
−0.146438 | + | 0.989220i | \(0.546781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −421.552 | −0.509736 | −0.254868 | − | 0.966976i | \(-0.582032\pi\) | ||||
−0.254868 | + | 0.966976i | \(0.582032\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 475.263i | 0.573297i | 0.958036 | + | 0.286649i | \(0.0925412\pi\) | ||||
−0.958036 | + | 0.286649i | \(0.907459\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 237.801 | 0.285475 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −285.161 | −0.341510 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 653.590i | 0.779010i | 0.921024 | + | 0.389505i | \(0.127354\pi\) | ||||
−0.921024 | + | 0.389505i | \(0.872646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −233.154 | −0.277234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 135.618i | 0.160495i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 108.541i | 0.128148i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −376.544 | −0.442472 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 140.493i | 0.164705i | 0.996603 | + | 0.0823523i | \(0.0262433\pi\) | ||||
−0.996603 | + | 0.0823523i | \(0.973757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −562.796 | −0.656704 | −0.328352 | − | 0.944555i | \(-0.606493\pi\) | ||||
−0.328352 | + | 0.944555i | \(0.606493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 228.316 | 0.265792 | 0.132896 | − | 0.991130i | \(-0.457572\pi\) | ||||
0.132896 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 469.310i | − 0.540058i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 998.611i | − 1.14651i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −81.5787 | −0.0932328 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1406.66i | 1.60395i | 0.597359 | + | 0.801974i | \(0.296217\pi\) | ||||
−0.597359 | + | 0.801974i | \(0.703783\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −943.043 | −1.07042 | −0.535212 | − | 0.844718i | \(-0.679768\pi\) | ||||
−0.535212 | + | 0.844718i | \(0.679768\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1146.63 | −1.29856 | −0.649280 | − | 0.760549i | \(-0.724930\pi\) | ||||
−0.649280 | + | 0.760549i | \(0.724930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 894.171i | 1.00808i | 0.863679 | + | 0.504042i | \(0.168154\pi\) | ||||
−0.863679 | + | 0.504042i | \(0.831846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −258.655 | −0.290950 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1742.88i | − 1.95171i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 67.5395i | − 0.0754631i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.3761 | 0.0371258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 273.850i | 0.303940i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 192.939 | 0.213192 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1358.60 | 1.49790 | 0.748950 | − | 0.662626i | \(-0.230558\pi\) | ||||
0.748950 | + | 0.662626i | \(0.230558\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 273.950i | − 0.298745i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1704.73i | 1.85498i | 0.373849 | + | 0.927490i | \(0.378038\pi\) | ||||
−0.373849 | + | 0.927490i | \(0.621962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1318.14 | −1.42810 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 346.958i | 0.375090i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1351.05 | 1.45431 | 0.727154 | − | 0.686475i | \(-0.240843\pi\) | ||||
0.727154 | + | 0.686475i | \(0.240843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1242.59 | 1.33469 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 39.6374i | − 0.0423930i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −672.646 | −0.717872 | −0.358936 | − | 0.933362i | \(-0.616860\pi\) | ||||
−0.358936 | + | 0.933362i | \(0.616860\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 528.671i | 0.561818i | 0.959734 | + | 0.280909i | \(0.0906359\pi\) | ||||
−0.959734 | + | 0.280909i | \(0.909364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1821.13i | − 1.93121i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 661.066 | 0.698063 | 0.349032 | − | 0.937111i | \(-0.386511\pi\) | ||||
0.349032 | + | 0.937111i | \(0.386511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 492.351i | 0.518811i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1545.41 | 1.62163 | 0.810815 | − | 0.585303i | \(-0.199024\pi\) | ||||
0.810815 | + | 0.585303i | \(0.199024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −159.618 | −0.167139 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 18.9627i | − 0.0197735i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 959.963 | 0.998921 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 123.793i | 0.128283i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 161.279i | − 0.166782i | −0.996517 | − | 0.0833912i | \(-0.973425\pi\) | ||||
0.996517 | − | 0.0833912i | \(-0.0265751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.20412 | −0.00432969 | −0.00216484 | − | 0.999998i | \(-0.500689\pi\) | ||||
−0.00216484 | + | 0.999998i | \(0.500689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 107.707i | − 0.110696i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1348.19 | 1.37993 | 0.689967 | − | 0.723841i | \(-0.257625\pi\) | ||||
0.689967 | + | 0.723841i | \(0.257625\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −122.126 | −0.124746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 984.262i | − 1.00128i | −0.865655 | − | 0.500642i | \(-0.833097\pi\) | ||||
0.865655 | − | 0.500642i | \(-0.166903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −518.497 | −0.526393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 841.045i | − 0.850399i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1013.87i | 1.02308i | 0.859259 | + | 0.511541i | \(0.170925\pi\) | ||||
−0.859259 | + | 0.511541i | \(0.829075\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 105.948 | 0.106481 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 311.310i | 0.312246i | 0.987738 | + | 0.156123i | \(0.0498997\pi\) | ||||
−0.987738 | + | 0.156123i | \(0.950100\pi\) | |||||||
\(998\) | 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 | 2304.3.b.q.127.4 | 8 | ||
3.2 | odd | 2 | 768.3.b.f.127.7 | 8 | |||
4.3 | odd | 2 | 2304.3.b.t.127.4 | 8 | |||
8.3 | odd | 2 | inner | 2304.3.b.q.127.5 | 8 | ||
8.5 | even | 2 | 2304.3.b.t.127.5 | 8 | |||
12.11 | even | 2 | 768.3.b.e.127.3 | 8 | |||
16.3 | odd | 4 | 1152.3.g.c.127.5 | 8 | |||
16.5 | even | 4 | 1152.3.g.f.127.4 | 8 | |||
16.11 | odd | 4 | 1152.3.g.f.127.3 | 8 | |||
16.13 | even | 4 | 1152.3.g.c.127.6 | 8 | |||
24.5 | odd | 2 | 768.3.b.e.127.2 | 8 | |||
24.11 | even | 2 | 768.3.b.f.127.6 | 8 | |||
48.5 | odd | 4 | 384.3.g.a.127.3 | ✓ | 8 | ||
48.11 | even | 4 | 384.3.g.a.127.7 | yes | 8 | ||
48.29 | odd | 4 | 384.3.g.b.127.6 | yes | 8 | ||
48.35 | even | 4 | 384.3.g.b.127.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.g.a.127.3 | ✓ | 8 | 48.5 | odd | 4 | ||
384.3.g.a.127.7 | yes | 8 | 48.11 | even | 4 | ||
384.3.g.b.127.2 | yes | 8 | 48.35 | even | 4 | ||
384.3.g.b.127.6 | yes | 8 | 48.29 | odd | 4 | ||
768.3.b.e.127.2 | 8 | 24.5 | odd | 2 | |||
768.3.b.e.127.3 | 8 | 12.11 | even | 2 | |||
768.3.b.f.127.6 | 8 | 24.11 | even | 2 | |||
768.3.b.f.127.7 | 8 | 3.2 | odd | 2 | |||
1152.3.g.c.127.5 | 8 | 16.3 | odd | 4 | |||
1152.3.g.c.127.6 | 8 | 16.13 | even | 4 | |||
1152.3.g.f.127.3 | 8 | 16.11 | odd | 4 | |||
1152.3.g.f.127.4 | 8 | 16.5 | even | 4 | |||
2304.3.b.q.127.4 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.b.q.127.5 | 8 | 8.3 | odd | 2 | inner | ||
2304.3.b.t.127.4 | 8 | 4.3 | odd | 2 | |||
2304.3.b.t.127.5 | 8 | 8.5 | even | 2 |