Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,3,Mod(321,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.321");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.k (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: | \(50.1363686423\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 64 x^{14} - 16 x^{13} + 2252 x^{12} + 648 x^{11} - 30106 x^{10} + 12360 x^{9} + \cdots + 1535848276 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 460) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.8 | ||
Root | \(0.613622 + 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.321 |
Dual form | 1840.3.k.c.321.7 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.613622 | −0.204541 | −0.102270 | − | 0.994757i | \(-0.532611\pi\) | ||||
−0.102270 | + | 0.994757i | \(0.532611\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.35348i | − | 0.336211i | −0.985769 | − | 0.168106i | \(-0.946235\pi\) | ||
0.985769 | − | 0.168106i | \(-0.0537650\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.62347 | −0.958163 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.167613i | 0.0152375i | 0.999971 | + | 0.00761877i | \(0.00242515\pi\) | ||||
−0.999971 | + | 0.00761877i | \(0.997575\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.3530 | −1.79639 | −0.898194 | − | 0.439600i | \(-0.855120\pi\) | ||||
−0.898194 | + | 0.439600i | \(0.855120\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.37210i | − | 0.0914734i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 25.5778i | − | 1.50457i | −0.658835 | − | 0.752287i | \(-0.728951\pi\) | ||
0.658835 | − | 0.752287i | \(-0.271049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.3833i | 1.28333i | 0.766984 | + | 0.641666i | \(0.221756\pi\) | ||||
−0.766984 | + | 0.641666i | \(0.778244\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44415i | 0.0687688i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.84182 | − | 20.7879i | −0.427905 | − | 0.903824i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.8141 | 0.400524 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.2749 | 0.526720 | 0.263360 | − | 0.964698i | \(-0.415169\pi\) | ||||
0.263360 | + | 0.964698i | \(0.415169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.4857 | 1.27373 | 0.636867 | − | 0.770974i | \(-0.280230\pi\) | ||||
0.636867 | + | 0.770974i | \(0.280230\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.102851i | − | 0.00311670i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.26254 | 0.150358 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.29869i | − | 0.116181i | −0.998311 | − | 0.0580904i | \(-0.981499\pi\) | ||
0.998311 | − | 0.0580904i | \(-0.0185012\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.3299 | 0.367434 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29.5894 | −0.721693 | −0.360846 | − | 0.932625i | \(-0.617512\pi\) | ||||
−0.360846 | + | 0.932625i | \(0.617512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.9539i | 1.18497i | 0.805580 | + | 0.592487i | \(0.201854\pi\) | ||||
−0.805580 | + | 0.592487i | \(0.798146\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 19.2827i | − | 0.428504i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.5518 | 1.41600 | 0.707998 | − | 0.706214i | \(-0.249599\pi\) | ||||
0.707998 | + | 0.706214i | \(0.249599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 43.4611 | 0.886962 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.6951i | 0.307747i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 15.1926i | 0.286653i | 0.989675 | + | 0.143326i | \(0.0457799\pi\) | ||||
−0.989675 | + | 0.143326i | \(0.954220\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.374794 | −0.00681444 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 14.9621i | − | 0.262493i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 58.1119 | 0.984948 | 0.492474 | − | 0.870327i | \(-0.336093\pi\) | ||||
0.492474 | + | 0.870327i | \(0.336093\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 93.2439i | 1.52859i | 0.644867 | + | 0.764294i | \(0.276913\pi\) | ||||
−0.644867 | + | 0.764294i | \(0.723087\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.2951i | 0.322145i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 52.2190i | − | 0.803369i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 97.0102i | − | 1.44791i | −0.689845 | − | 0.723957i | \(-0.742321\pi\) | ||
0.689845 | − | 0.723957i | \(-0.257679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.03916 | + | 12.7559i | 0.0875240 | + | 0.184869i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1710 | 0.199592 | 0.0997960 | − | 0.995008i | \(-0.468181\pi\) | ||||
0.0997960 | + | 0.995008i | \(0.468181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −64.9345 | −0.889513 | −0.444757 | − | 0.895651i | \(-0.646710\pi\) | ||||
−0.444757 | + | 0.895651i | \(0.646710\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.06811 | 0.0409081 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.394473 | 0.00512303 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 110.968i | 1.40466i | 0.711851 | + | 0.702331i | \(0.247857\pi\) | ||||
−0.711851 | + | 0.702331i | \(0.752143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 70.9754 | 0.876240 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 4.10459i | − | 0.0494529i | −0.999694 | − | 0.0247265i | \(-0.992129\pi\) | ||
0.999694 | − | 0.0247265i | \(-0.00787148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 57.1936 | 0.672866 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.37300 | −0.107736 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 87.7504i | − | 0.985960i | −0.870041 | − | 0.492980i | \(-0.835908\pi\) | ||
0.870041 | − | 0.492980i | \(-0.164092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54.9609i | 0.603965i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.2293 | −0.260530 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −54.5227 | −0.573923 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 61.4252i | 0.633249i | 0.948551 | + | 0.316625i | \(0.102550\pi\) | ||||
−0.948551 | + | 0.316625i | \(0.897450\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.44540i | − | 0.0146000i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −37.9300 | −0.375544 | −0.187772 | − | 0.982213i | \(-0.560127\pi\) | ||||
−0.187772 | + | 0.982213i | \(0.560127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 121.156i | − | 1.17627i | −0.808763 | − | 0.588135i | \(-0.799862\pi\) | ||
0.808763 | − | 0.588135i | \(-0.200138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.22921 | −0.0307544 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 62.2820i | 0.582074i | 0.956712 | + | 0.291037i | \(0.0940004\pi\) | ||||
−0.956712 | + | 0.291037i | \(0.906000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.133627i | − | 0.00122594i | −1.00000 | 0.000612968i | \(-0.999805\pi\) | |||
1.00000 | 0.000612968i | \(-0.000195114\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.63777i | 0.0237637i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 210.838i | 1.86583i | 0.360101 | + | 0.932913i | \(0.382742\pi\) | ||||
−0.360101 | + | 0.932913i | \(0.617258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 46.4833 | − | 22.0070i | 0.404202 | − | 0.191365i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 201.384 | 1.72123 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −60.1967 | −0.505855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.972 | 0.999768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.1567 | 0.147616 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 30.3950 | 0.239331 | 0.119665 | − | 0.992814i | \(-0.461818\pi\) | ||||
0.119665 | + | 0.992814i | \(0.461818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 31.2664i | − | 0.242375i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 120.707 | 0.921429 | 0.460715 | − | 0.887548i | \(-0.347593\pi\) | ||||
0.460715 | + | 0.887548i | \(0.347593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 57.3856 | 0.431470 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 24.1812i | 0.179120i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 43.8304i | − | 0.319930i | −0.987123 | − | 0.159965i | \(-0.948862\pi\) | ||
0.987123 | − | 0.159965i | \(-0.0511382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −194.276 | −1.39767 | −0.698834 | − | 0.715284i | \(-0.746297\pi\) | ||||
−0.698834 | + | 0.715284i | \(0.746297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −40.8377 | −0.289629 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.91427i | − | 0.0273725i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.1557i | 0.235556i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.6687 | −0.181420 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 198.743i | − | 1.33384i | −0.745127 | − | 0.666922i | \(-0.767611\pi\) | ||
0.745127 | − | 0.666922i | \(-0.232389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −150.390 | −0.995963 | −0.497981 | − | 0.867188i | \(-0.665925\pi\) | ||||
−0.497981 | + | 0.867188i | \(0.665925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 220.569i | 1.44163i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 88.2928i | 0.569631i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 156.829i | 0.998910i | 0.866340 | + | 0.499455i | \(0.166466\pi\) | ||||
−0.866340 | + | 0.499455i | \(0.833534\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.32252i | − | 0.0586322i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −48.9240 | + | 23.1625i | −0.303876 | + | 0.143867i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 224.124 | 1.37499 | 0.687497 | − | 0.726187i | \(-0.258709\pi\) | ||||
0.687497 | + | 0.726187i | \(0.258709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.229982 | 0.00139383 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 52.2597 | 0.312932 | 0.156466 | − | 0.987683i | \(-0.449990\pi\) | ||||
0.156466 | + | 0.987683i | \(0.449990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 376.364 | 2.22701 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 210.269i | − | 1.22964i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 165.785 | 0.958294 | 0.479147 | − | 0.877735i | \(-0.340946\pi\) | ||||
0.479147 | + | 0.877735i | \(0.340946\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.7674i | 0.0672422i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.6588 | −0.201462 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −46.4803 | −0.259667 | −0.129833 | − | 0.991536i | \(-0.541444\pi\) | ||||
−0.129833 | + | 0.991536i | \(0.541444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 251.378i | 1.38883i | 0.719576 | + | 0.694413i | \(0.244336\pi\) | ||||
−0.719576 | + | 0.694413i | \(0.755664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 57.2165i | − | 0.312659i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.61217 | 0.0519577 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.28716 | 0.0229260 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 25.4509i | − | 0.134661i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.75124i | 0.0353468i | 0.999844 | + | 0.0176734i | \(0.00562591\pi\) | ||||
−0.999844 | + | 0.0176734i | \(0.994374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 316.647 | 1.64066 | 0.820330 | − | 0.571890i | \(-0.193790\pi\) | ||||
0.820330 | + | 0.571890i | \(0.193790\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 32.0427i | 0.164322i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 161.256 | 0.818559 | 0.409280 | − | 0.912409i | \(-0.365780\pi\) | ||||
0.409280 | + | 0.912409i | \(0.365780\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 264.616i | 1.32973i | 0.746965 | + | 0.664864i | \(0.231510\pi\) | ||||
−0.746965 | + | 0.664864i | \(0.768490\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 59.5276i | 0.296157i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 35.9491i | − | 0.177089i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 66.1639i | − | 0.322751i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 84.8706 | + | 179.264i | 0.410003 | + | 0.866010i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.08696 | −0.0195548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 68.5753 | 0.325002 | 0.162501 | − | 0.986708i | \(-0.448044\pi\) | ||||
0.162501 | + | 0.986708i | \(0.448044\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.69566 | −0.0408247 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −113.936 | −0.529936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 92.9288i | − | 0.428244i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.8452 | 0.181942 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 597.318i | 2.70280i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 327.315 | 1.46778 | 0.733889 | − | 0.679269i | \(-0.237703\pi\) | ||||
0.733889 | + | 0.679269i | \(0.237703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 43.1173 | 0.191633 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 67.7935i | 0.298650i | 0.988788 | + | 0.149325i | \(0.0477100\pi\) | ||||
−0.988788 | + | 0.149325i | \(0.952290\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 334.659i | − | 1.46139i | −0.682703 | − | 0.730696i | \(-0.739196\pi\) | ||
0.682703 | − | 0.730696i | \(-0.260804\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.242058 | −0.00104787 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −401.337 | −1.72247 | −0.861237 | − | 0.508203i | \(-0.830310\pi\) | ||||
−0.861237 | + | 0.508203i | \(0.830310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 148.814i | 0.633253i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 68.0926i | − | 0.287310i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 421.040 | 1.76167 | 0.880837 | − | 0.473419i | \(-0.156980\pi\) | ||||
0.880837 | + | 0.473419i | \(0.156980\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 386.686i | − | 1.60451i | −0.596985 | − | 0.802253i | \(-0.703635\pi\) | ||
0.596985 | − | 0.802253i | \(-0.296365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −140.879 | −0.579751 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 97.1821i | 0.396661i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 569.424i | − | 2.30536i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.51867i | 0.0101151i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 433.551i | 1.72730i | 0.504095 | + | 0.863648i | \(0.331826\pi\) | ||||
−0.504095 | + | 0.863648i | \(0.668174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.48433 | − | 1.64962i | 0.0137720 | − | 0.00652022i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −35.0953 | −0.137628 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −270.409 | −1.05218 | −0.526088 | − | 0.850430i | \(-0.676342\pi\) | ||||
−0.526088 | + | 0.850430i | \(0.676342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1169 | −0.0390613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −131.722 | −0.504684 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 97.1155i | − | 0.369260i | −0.982808 | − | 0.184630i | \(-0.940891\pi\) | ||
0.982808 | − | 0.184630i | \(-0.0591087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.9717 | −0.128195 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 53.8456i | 0.201669i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 447.101 | 1.66208 | 0.831042 | − | 0.556209i | \(-0.187745\pi\) | ||||
0.831042 | + | 0.556209i | \(0.187745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1461 | 0.0448195 | 0.0224097 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224097 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 33.7252i | − | 0.123535i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.838065i | − | 0.00304751i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.18232 | −0.0187087 | −0.00935437 | − | 0.999956i | \(-0.502978\pi\) | ||||
−0.00935437 | + | 0.999956i | \(0.502978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −340.504 | −1.22044 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 362.929i | − | 1.29156i | −0.763523 | − | 0.645780i | \(-0.776532\pi\) | ||
0.763523 | − | 0.645780i | \(-0.223468\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 551.340i | − | 1.94820i | −0.226126 | − | 0.974098i | \(-0.572606\pi\) | ||
0.226126 | − | 0.974098i | \(-0.427394\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.4563 | 0.117391 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 69.6380i | 0.242641i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −365.222 | −1.26374 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 37.6918i | − | 0.129525i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 62.4364i | 0.213094i | 0.994308 | + | 0.106547i | \(0.0339794\pi\) | ||||
−0.994308 | + | 0.106547i | \(0.966021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129.942i | 0.440482i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.81259i | 0.00610300i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 229.836 | + | 485.462i | 0.768684 | + | 1.62362i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 119.919 | 0.398401 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.2747 | 0.0768140 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −208.500 | −0.683606 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 73.2150 | 0.238485 | 0.119243 | − | 0.992865i | \(-0.461953\pi\) | ||||
0.119243 | + | 0.992865i | \(0.461953\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 74.3439i | 0.240595i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 453.724 | 1.45892 | 0.729461 | − | 0.684023i | \(-0.239771\pi\) | ||||
0.729461 | + | 0.684023i | \(0.239771\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 88.0757i | 0.281392i | 0.990053 | + | 0.140696i | \(0.0449340\pi\) | ||||
−0.990053 | + | 0.140696i | \(0.955066\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −45.3813 | −0.144068 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.6220 | 0.0650535 | 0.0325267 | − | 0.999471i | \(-0.489645\pi\) | ||||
0.0325267 | + | 0.999471i | \(0.489645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.56027i | 0.00802592i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 38.2176i | − | 0.119058i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 623.670 | 1.93087 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 116.765 | 0.359277 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0819965i | 0.000250754i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 156.628i | − | 0.476074i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 38.9486 | 0.117669 | 0.0588347 | − | 0.998268i | \(-0.481262\pi\) | ||||
0.0588347 | + | 0.998268i | \(0.481262\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 37.0696i | 0.111320i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 216.921 | 0.647527 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 313.014i | − | 0.928825i | −0.885619 | − | 0.464412i | \(-0.846266\pi\) | ||
0.885619 | − | 0.464412i | \(-0.153734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 129.375i | − | 0.381637i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.61832i | 0.0194086i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 217.605i | − | 0.634418i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −28.5231 | + | 13.5040i | −0.0826758 | + | 0.0391419i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 300.671 | 0.866488 | 0.433244 | − | 0.901277i | \(-0.357369\pi\) | ||||
0.433244 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.08765 | 0.0203084 | 0.0101542 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101542 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −252.543 | −0.719496 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −577.956 | −1.63727 | −0.818635 | − | 0.574314i | \(-0.805269\pi\) | ||||
−0.818635 | + | 0.574314i | \(0.805269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.6874i | 0.0892603i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 36.9380 | 0.103468 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 204.788i | 0.570440i | 0.958462 | + | 0.285220i | \(0.0920667\pi\) | ||||
−0.958462 | + | 0.285220i | \(0.907933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −233.545 | −0.646940 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −74.2310 | −0.204493 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 145.198i | − | 0.397802i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 160.597i | 0.437593i | 0.975770 | + | 0.218797i | \(0.0702132\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 255.163 | 0.691500 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.7555 | 0.0963759 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.71586i | − | 0.00996208i | −0.999988 | − | 0.00498104i | \(-0.998414\pi\) | ||
0.999988 | − | 0.00498104i | \(-0.00158552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.86050i | 0.0182947i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −356.715 | −0.946193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 207.746i | − | 0.548142i | −0.961709 | − | 0.274071i | \(-0.911630\pi\) | ||
0.961709 | − | 0.274071i | \(-0.0883704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.6510 | −0.0489528 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 417.212i | 1.08933i | 0.838655 | + | 0.544663i | \(0.183342\pi\) | ||||
−0.838655 | + | 0.544663i | \(0.816658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.882069i | 0.00229109i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 439.399i | − | 1.13540i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 235.791i | 0.606148i | 0.952967 | + | 0.303074i | \(0.0980129\pi\) | ||||
−0.952967 | + | 0.303074i | \(0.901987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −531.709 | + | 251.732i | −1.35987 | + | 0.643815i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −74.0686 | −0.188470 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −248.133 | −0.628184 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 319.562 | 0.804942 | 0.402471 | − | 0.915433i | \(-0.368151\pi\) | ||||
0.402471 | + | 0.915433i | \(0.368151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −35.2130 | −0.0882532 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 250.400i | 0.624440i | 0.950010 | + | 0.312220i | \(0.101073\pi\) | ||||
−0.950010 | + | 0.312220i | \(0.898927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −922.112 | −2.28812 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 158.706i | 0.391866i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.720516 | 0.00177031 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −389.521 | −0.952375 | −0.476188 | − | 0.879344i | \(-0.657982\pi\) | ||||
−0.476188 | + | 0.879344i | \(0.657982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.8953i | 0.0654387i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 136.765i | − | 0.331151i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.17815 | 0.0221160 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 119.212 | 0.285880 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 589.258i | 1.40634i | 0.711020 | + | 0.703171i | \(0.248233\pi\) | ||||
−0.711020 | + | 0.703171i | \(0.751767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 665.934i | 1.58179i | 0.611952 | + | 0.790895i | \(0.290385\pi\) | ||||
−0.611952 | + | 0.790895i | \(0.709615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −573.908 | −1.35676 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 127.889i | 0.300915i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 219.448 | 0.513929 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.40188i | 0.00559879i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 171.958i | − | 0.398975i | −0.979900 | − | 0.199488i | \(-0.936072\pi\) | ||
0.979900 | − | 0.199488i | \(-0.0639277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 513.166i | − | 1.18514i | −0.805519 | − | 0.592570i | \(-0.798113\pi\) | ||
0.805519 | − | 0.592570i | \(-0.201887\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 20.9587i | − | 0.0481808i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 506.879 | − | 239.976i | 1.15991 | − | 0.549144i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −65.3345 | −0.148826 | −0.0744128 | − | 0.997228i | \(-0.523708\pi\) | ||||
−0.0744128 | + | 0.997228i | \(0.523708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −374.786 | −0.849854 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 159.582 | 0.360230 | 0.180115 | − | 0.983646i | \(-0.442353\pi\) | ||||
0.180115 | + | 0.983646i | \(0.442353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 196.216 | 0.440935 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 121.953i | 0.272825i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −546.515 | −1.21718 | −0.608592 | − | 0.793484i | \(-0.708265\pi\) | ||||
−0.608592 | + | 0.793484i | \(0.708265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.95957i | − | 0.0109968i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 92.2828 | 0.203715 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −122.896 | −0.270102 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 253.821i | − | 0.555408i | −0.960667 | − | 0.277704i | \(-0.910427\pi\) | ||
0.960667 | − | 0.277704i | \(-0.0895734\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 276.602i | − | 0.602618i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −380.491 | −0.825360 | −0.412680 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 245.745 | 0.530767 | 0.265384 | − | 0.964143i | \(-0.414501\pi\) | ||||
0.265384 | + | 0.964143i | \(0.414501\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 54.1784i | − | 0.116513i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 609.764i | − | 1.30571i | −0.757485 | − | 0.652853i | \(-0.773572\pi\) | ||
0.757485 | − | 0.652853i | \(-0.226428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −228.311 | −0.486805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 96.2337i | − | 0.204318i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.54053 | −0.0180561 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 121.916i | − | 0.256666i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 131.013i | − | 0.274660i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 476.721i | − | 0.995241i | −0.867395 | − | 0.497621i | \(-0.834207\pi\) | ||
0.867395 | − | 0.497621i | \(-0.165793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100.387i | 0.208706i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.0208 | − | 14.2130i | 0.0621549 | − | 0.0294266i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −137.351 | −0.283198 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −561.472 | −1.15292 | −0.576460 | − | 0.817126i | \(-0.695566\pi\) | ||||
−0.576460 | + | 0.817126i | \(0.695566\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −137.527 | −0.281242 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −55.5940 | −0.113226 | −0.0566130 | − | 0.998396i | \(-0.518030\pi\) | ||||
−0.0566130 | + | 0.998396i | \(0.518030\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 390.697i | − | 0.792489i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.23202 | 0.00652934 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 33.3512i | − | 0.0671051i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −761.749 | −1.52655 | −0.763275 | − | 0.646074i | \(-0.776410\pi\) | ||||
−0.763275 | + | 0.646074i | \(0.776410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.0677 | −0.0640074 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 742.151i | 1.47545i | 0.675101 | + | 0.737725i | \(0.264100\pi\) | ||||
−0.675101 | + | 0.737725i | \(0.735900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 84.8139i | − | 0.167948i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −230.945 | −0.455513 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 783.302 | 1.53890 | 0.769452 | − | 0.638704i | \(-0.220529\pi\) | ||||
0.769452 | + | 0.638704i | \(0.220529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 152.822i | 0.299064i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 263.685i | 0.514005i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 270.913 | 0.526044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.1549i | 0.0215763i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −101.729 | −0.196010 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 816.170i | 1.56655i | 0.621678 | + | 0.783273i | \(0.286451\pi\) | ||||
−0.621678 | + | 0.783273i | \(0.713549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 533.298i | − | 1.01969i | −0.860266 | − | 0.509845i | \(-0.829703\pi\) | ||
0.860266 | − | 0.509845i | \(-0.170297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 7.22073i | − | 0.0137538i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1009.96i | − | 1.91643i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −335.277 | + | 409.182i | −0.633794 | + | 0.773502i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −501.127 | −0.943741 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 691.002 | 1.29644 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −139.267 | −0.260312 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.5213 | 0.0531124 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.28465i | 0.0135151i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 397.274 | 0.734332 | 0.367166 | − | 0.930155i | \(-0.380328\pi\) | ||||
0.367166 | + | 0.930155i | \(0.380328\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 154.251i | − | 0.284071i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.298799 | 0.000548255 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 123.740 | 0.226215 | 0.113108 | − | 0.993583i | \(-0.463919\pi\) | ||||
0.113108 | + | 0.993583i | \(0.463919\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 804.086i | − | 1.46464i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 372.452i | 0.675956i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 261.161 | 0.472263 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.89824 | −0.0106275 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 826.982i | − | 1.48471i | −0.670008 | − | 0.742354i | \(-0.733709\pi\) | ||
0.670008 | − | 0.742354i | \(-0.266291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1189.93i | − | 2.12867i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.63070 | −0.00468930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 114.429i | − | 0.203249i | −0.994823 | − | 0.101624i | \(-0.967596\pi\) | ||
0.994823 | − | 0.101624i | \(-0.0324039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −471.449 | −0.834423 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 167.039i | − | 0.294602i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 218.123i | 0.383345i | 0.981459 | + | 0.191672i | \(0.0613911\pi\) | ||||
−0.981459 | + | 0.191672i | \(0.938609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 893.615i | 1.56500i | 0.622651 | + | 0.782500i | \(0.286056\pi\) | ||||
−0.622651 | + | 0.782500i | \(0.713944\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4.14271i | − | 0.00722985i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 49.2091 | + | 103.940i | 0.0855811 | + | 0.180765i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 218.968 | 0.379495 | 0.189747 | − | 0.981833i | \(-0.439233\pi\) | ||||
0.189747 | + | 0.981833i | \(0.439233\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −194.302 | −0.335582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.66007 | −0.0166266 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.54648 | −0.00436789 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 450.309i | 0.769758i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 383.491 | 0.653307 | 0.326653 | − | 0.945144i | \(-0.394079\pi\) | ||||
0.326653 | + | 0.945144i | \(0.394079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 962.793i | 1.63462i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −98.9503 | −0.167429 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 453.370 | 0.764537 | 0.382269 | − | 0.924051i | \(-0.375143\pi\) | ||||
0.382269 | + | 0.924051i | \(0.375143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 134.604i | − | 0.226225i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 162.374i | − | 0.271983i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 195.922 | 0.327082 | 0.163541 | − | 0.986537i | \(-0.447708\pi\) | ||||
0.163541 | + | 0.986537i | \(0.447708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −354.949 | −0.590597 | −0.295299 | − | 0.955405i | \(-0.595419\pi\) | ||||
−0.295299 | + | 0.955405i | \(0.595419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 836.565i | 1.38734i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 270.501i | 0.447110i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −476.386 | −0.784820 | −0.392410 | − | 0.919790i | \(-0.628359\pi\) | ||||
−0.392410 | + | 0.919790i | \(0.628359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.0592i | 0.0362219i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1554.19 | −2.54368 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 548.445i | 0.894690i | 0.894361 | + | 0.447345i | \(0.147630\pi\) | ||||
−0.894361 | + | 0.447345i | \(0.852370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 40.5996i | 0.0660157i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 784.342i | − | 1.27122i | −0.772011 | − | 0.635609i | \(-0.780749\pi\) | ||
0.772011 | − | 0.635609i | \(-0.219251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 551.280i | − | 0.890597i | −0.895382 | − | 0.445298i | \(-0.853098\pi\) | ||
0.895382 | − | 0.445298i | \(-0.146902\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −106.431 | − | 224.804i | −0.171386 | − | 0.362003i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −206.519 | −0.331491 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.50785 | 0.00399975 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −109.951 | −0.174803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 636.749i | 1.00911i | 0.863379 | + | 0.504555i | \(0.168344\pi\) | ||||
−0.863379 | + | 0.504555i | \(0.831656\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −42.0793 | −0.0664760 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 67.9652i | 0.107032i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1014.95 | −1.59333 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −122.203 | −0.191242 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1157.64i | − | 1.80599i | −0.429655 | − | 0.902993i | \(-0.641365\pi\) | ||
0.429655 | − | 0.902993i | \(-0.358635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 709.420i | 1.10330i | 0.834077 | + | 0.551648i | \(0.186001\pi\) | ||||
−0.834077 | + | 0.551648i | \(0.813999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 69.9138 | 0.108394 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 809.209 | 1.25071 | 0.625355 | − | 0.780341i | \(-0.284954\pi\) | ||||
0.625355 | + | 0.780341i | \(0.284954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.74031i | 0.0150082i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 57.0232i | 0.0875932i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 313.648 | 0.480319 | 0.240159 | − | 0.970733i | \(-0.422800\pi\) | ||||
0.240159 | + | 0.970733i | \(0.422800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 269.910i | 0.412076i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 559.960 | 0.852299 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1138.57i | − | 1.72772i | −0.503731 | − | 0.863860i | \(-0.668040\pi\) | ||
0.503731 | − | 0.863860i | \(-0.331960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 295.689i | 0.447336i | 0.974665 | + | 0.223668i | \(0.0718031\pi\) | ||||
−0.974665 | + | 0.223668i | \(0.928197\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 366.528i | − | 0.552832i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 128.318i | 0.192959i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −150.333 | − | 317.533i | −0.225386 | − | 0.476062i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −200.847 | −0.300220 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.6289 | −0.0232919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −464.696 | −0.690485 | −0.345242 | − | 0.938514i | \(-0.612203\pi\) | ||||
−0.345242 | + | 0.938514i | \(0.612203\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −54.0707 | −0.0801048 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 15.9301i | − | 0.0235304i | −0.999931 | − | 0.0117652i | \(-0.996255\pi\) | ||
0.999931 | − | 0.0117652i | \(-0.00374506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 144.563 | 0.212905 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 41.5996i | − | 0.0610860i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −541.640 | −0.793031 | −0.396515 | − | 0.918028i | \(-0.629781\pi\) | ||||
−0.396515 | + | 0.918028i | \(0.629781\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 98.0079 | 0.143077 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 205.354i | 0.298914i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 354.793i | − | 0.514940i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1177.74 | −1.70440 | −0.852200 | − | 0.523216i | \(-0.824732\pi\) | ||||
−0.852200 | + | 0.523216i | \(0.824732\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.40173 | −0.00490870 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 434.414i | − | 0.625056i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 756.831i | 1.08584i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 246.269 | 0.352316 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 146.183i | − | 0.208535i | −0.994549 | − | 0.104268i | \(-0.966750\pi\) | ||
0.994549 | − | 0.104268i | \(-0.0332499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 104.816 | 0.149099 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 91.3158i | − | 0.129526i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 89.2673i | 0.126262i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 394.795i | − | 0.556833i | −0.960460 | − | 0.278417i | \(-0.910190\pi\) | ||
0.960460 | − | 0.278417i | \(-0.0898096\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 956.931i | − | 1.34590i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −388.612 | − | 820.827i | −0.545037 | − | 1.15123i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.75258 | 0.0122414 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −258.360 | −0.360334 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 916.745 | 1.27503 | 0.637514 | − | 0.770439i | \(-0.279963\pi\) | ||||
0.637514 | + | 0.770439i | \(0.279963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −285.138 | −0.395475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 237.279i | 0.328187i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −76.3744 | −0.105344 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1076.69i | − | 1.48100i | −0.672057 | − | 0.740500i | \(-0.734589\pi\) | ||
0.672057 | − | 0.740500i | \(-0.265411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −552.332 | −0.757657 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1303.29 | 1.78288 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.0078i | − | 0.0313885i | −0.999877 | − | 0.0156942i | \(-0.995004\pi\) | ||
0.999877 | − | 0.0156942i | \(-0.00499584\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 59.6330i | − | 0.0811334i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.2602 | 0.0220626 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 846.184 | 1.14504 | 0.572520 | − | 0.819891i | \(-0.305966\pi\) | ||||
0.572520 | + | 0.819891i | \(0.305966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 349.411i | 0.471540i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 792.433i | 1.06653i | 0.845948 | + | 0.533266i | \(0.179035\pi\) | ||||
−0.845948 | + | 0.533266i | \(0.820965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 444.402 | 0.596513 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.3958i | 0.0473840i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 146.579 | 0.195700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 882.680i | 1.17534i | 0.809101 | + | 0.587670i | \(0.199955\pi\) | ||||
−0.809101 | + | 0.587670i | \(0.800045\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 266.037i | − | 0.353302i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 336.283i | − | 0.445408i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 490.893i | − | 0.648472i | −0.945976 | − | 0.324236i | \(-0.894893\pi\) | ||
0.945976 | − | 0.324236i | \(-0.105107\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.13806 | + | 1.01224i | −0.00281694 | + | 0.00133365i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −852.432 | −1.12015 | −0.560073 | − | 0.828443i | \(-0.689227\pi\) | ||||
−0.560073 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.314488 | −0.000412173 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −493.207 | −0.644715 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1357.09 | −1.76935 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 323.724i | − | 0.420968i | −0.977597 | − | 0.210484i | \(-0.932496\pi\) | ||
0.977597 | − | 0.210484i | \(-0.0675039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 165.929 | 0.215213 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 224.753i | 0.290754i | 0.989376 | + | 0.145377i | \(0.0464396\pi\) | ||||
−0.989376 | + | 0.145377i | \(0.953560\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −197.429 | −0.254747 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.20794 | 0.00798962 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 721.487i | − | 0.926171i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.37525i | 0.00304129i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 165.185 | 0.210964 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −350.680 | −0.446726 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 387.295i | 0.492116i | 0.969255 | + | 0.246058i | \(0.0791354\pi\) | ||||
−0.969255 | + | 0.246058i | \(0.920865\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 59.5922i | 0.0755287i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 496.204 | 0.627312 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2177.53i | − | 2.74594i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.8458 | 0.0262211 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 143.007i | 0.179432i | 0.995967 | + | 0.0897161i | \(0.0285960\pi\) | ||||
−0.995967 | + | 0.0897161i | \(0.971404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1702.25i | − | 2.13047i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 756.713i | 0.944710i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 10.8839i | − | 0.0135540i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −51.7930 | − | 109.397i | −0.0643391 | − | 0.135897i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −274.351 | −0.339964 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −757.216 | −0.935990 | −0.467995 | − | 0.883731i | \(-0.655024\pi\) | ||||
−0.467995 | + | 0.883731i | \(0.655024\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.16598 | −0.0100690 | −0.00503451 | − | 0.999987i | \(-0.501603\pi\) | ||||
−0.00503451 | + | 0.999987i | \(0.501603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.45310 | −0.00916740 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 501.157i | 0.614916i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1242.42 | −1.52071 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 473.953i | − | 0.578697i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 98.3490 | 0.119792 | 0.0598959 | − | 0.998205i | \(-0.480923\pi\) | ||||
0.0598959 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −786.402 | −0.955531 | −0.477765 | − | 0.878487i | \(-0.658553\pi\) | ||||
−0.477765 | + | 0.878487i | \(0.658553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.514255i | 0.000623339i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1566.53i | 1.89423i | 0.320895 | + | 0.947115i | \(0.396016\pi\) | ||||
−0.320895 | + | 0.947115i | \(0.603984\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 376.874 | 0.454613 | 0.227307 | − | 0.973823i | \(-0.427008\pi\) | ||||
0.227307 | + | 0.973823i | \(0.427008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.17999 | 0.00382670 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1111.64i | − | 1.33450i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 116.856i | 0.139948i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 427.005 | 0.510161 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 511.907i | 0.610139i | 0.952330 | + | 0.305070i | \(0.0986797\pi\) | ||||
−0.952330 | + | 0.305070i | \(0.901320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −607.678 | −0.722566 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 222.701i | 0.264177i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 841.576i | 0.995948i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 284.705i | − | 0.336133i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 338.314i | 0.398485i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −89.3610 | + | 42.3070i | −0.105007 | + | 0.0497144i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −833.730 | −0.977409 | −0.488704 | − | 0.872449i | \(-0.662530\pi\) | ||||
−0.488704 | + | 0.872449i | \(0.662530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 470.175 | 0.549912 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 76.9417 | 0.0897803 | 0.0448902 | − | 0.998992i | \(-0.485706\pi\) | ||||
0.0448902 | + | 0.998992i | \(0.485706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1173.16 | 1.36572 | 0.682862 | − | 0.730548i | \(-0.260735\pi\) | ||||
0.682862 | + | 0.730548i | \(0.260735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 42.7314i | − | 0.0496300i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.6403 | 0.0482506 | 0.0241253 | − | 0.999709i | \(-0.492320\pi\) | ||||
0.0241253 | + | 0.999709i | \(0.492320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 370.706i | 0.428562i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 224.108 | 0.258487 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.5997 | −0.0214036 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2265.48i | 2.60101i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 529.698i | − | 0.606756i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.3127 | −0.0300716 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 855.659 | 0.975665 | 0.487833 | − | 0.872937i | \(-0.337788\pi\) | ||||
0.487833 | + | 0.872937i | \(0.337788\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 38.3123i | − | 0.0435863i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 660.677i | 0.749917i | 0.927042 | + | 0.374958i | \(0.122343\pi\) | ||||
−0.927042 | + | 0.374958i | \(0.877657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 249.768 | 0.282863 | 0.141431 | − | 0.989948i | \(-0.454830\pi\) | ||||
0.141431 | + | 0.989948i | \(0.454830\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 79.7354i | − | 0.0900965i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1459.55 | 1.64549 | 0.822747 | − | 0.568408i | \(-0.192440\pi\) | ||||
0.822747 | + | 0.568408i | \(0.192440\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 71.5339i | − | 0.0804656i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.8964i | 0.0133517i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1622.75i | 1.81719i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 103.933i | − | 0.116126i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −141.033 | − | 297.890i | −0.157227 | − | 0.332096i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 603.140 | 0.670901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 388.593 | 0.431291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −73.5848 | −0.0814893 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −562.097 | −0.621102 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 504.127i | 0.555818i | 0.960607 | + | 0.277909i | \(0.0896414\pi\) | ||||
−0.960607 | + | 0.277909i | \(0.910359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 327.088 | 0.359832 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 95.1985i | − | 0.104499i | −0.998634 | − | 0.0522494i | \(-0.983361\pi\) | ||
0.998634 | − | 0.0522494i | \(-0.0166391\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.687983 | 0.000753541 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 127.940 | 0.139825 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 284.082i | − | 0.309795i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 897.170i | 0.976246i | 0.872775 | + | 0.488123i | \(0.162318\pi\) | ||||
−0.872775 | + | 0.488123i | \(0.837682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.9264 | −0.0487800 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −330.937 | −0.358545 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.4935i | 0.0232362i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1044.78i | 1.12706i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −193.891 | −0.208709 | −0.104354 | − | 0.994540i | \(-0.533278\pi\) | ||||
−0.104354 | + | 0.994540i | \(0.533278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1059.73i | 1.13827i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −278.415 | −0.298409 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.58639i | 0.0102528i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1049.54i | 1.12011i | 0.828455 | + | 0.560056i | \(0.189220\pi\) | ||||
−0.828455 | + | 0.560056i | \(0.810780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 54.0452i | − | 0.0575561i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1194.28i | 1.26917i | 0.772855 | + | 0.634583i | \(0.218828\pi\) | ||||
−0.772855 | + | 0.634583i | \(0.781172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 291.214 | + | 615.103i | 0.308816 | + | 0.652283i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 56.9098 | 0.0602221 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −273.098 | −0.288382 | −0.144191 | − | 0.989550i | \(-0.546058\pi\) | ||||
−0.144191 | + | 0.989550i | \(0.546058\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1516.42 | 1.59791 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.6541 | −0.0133061 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 222.571i | 0.233548i | 0.993159 | + | 0.116774i | \(0.0372554\pi\) | ||||
−0.993159 | + | 0.116774i | \(0.962745\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0962 | −0.0158076 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.57104i | − | 0.00164163i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −103.154 | −0.107564 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 598.124 | 0.622398 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 537.087i | − | 0.557722i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 708.045i | 0.733726i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1285.39 | 1.32926 | 0.664629 | − | 0.747174i | \(-0.268590\pi\) | ||||
0.664629 | + | 0.747174i | \(0.268590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −382.698 | −0.394941 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1108.87i | 1.14198i | 0.820956 | + | 0.570991i | \(0.193441\pi\) | ||||
−0.820956 | + | 0.570991i | \(0.806559\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 457.224i | 0.469911i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −71.6497 | −0.0734868 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 520.016i | − | 0.532258i | −0.963937 | − | 0.266129i | \(-0.914255\pi\) | ||
0.963937 | − | 0.266129i | \(-0.0857447\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.7081 | 0.0150236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.15233i | 0.00117465i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1523.16i | − | 1.54950i | −0.632269 | − | 0.774749i | \(-0.717876\pi\) | ||
0.632269 | − | 0.774749i | \(-0.282124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 360.580i | 0.366071i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 96.1105i | 0.0973764i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1059.23 | − | 501.479i | 1.07101 | − | 0.507056i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1084.41 | −1.09426 | −0.547131 | − | 0.837047i | \(-0.684280\pi\) | ||||
−0.547131 | + | 0.837047i | \(0.684280\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.8997 | −0.0240682 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −591.699 | −0.594672 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −805.761 | −0.808185 | −0.404093 | − | 0.914718i | \(-0.632413\pi\) | ||||
−0.404093 | + | 0.914718i | \(0.632413\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 46.4867i | − | 0.0465332i |
(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 | 1840.3.k.c.321.8 | 16 | ||
4.3 | odd | 2 | 460.3.f.a.321.10 | yes | 16 | ||
12.11 | even | 2 | 4140.3.d.a.2161.6 | 16 | |||
20.3 | even | 4 | 2300.3.d.b.1149.14 | 32 | |||
20.7 | even | 4 | 2300.3.d.b.1149.19 | 32 | |||
20.19 | odd | 2 | 2300.3.f.e.1701.7 | 16 | |||
23.22 | odd | 2 | inner | 1840.3.k.c.321.7 | 16 | ||
92.91 | even | 2 | 460.3.f.a.321.9 | ✓ | 16 | ||
276.275 | odd | 2 | 4140.3.d.a.2161.11 | 16 | |||
460.183 | odd | 4 | 2300.3.d.b.1149.20 | 32 | |||
460.367 | odd | 4 | 2300.3.d.b.1149.13 | 32 | |||
460.459 | even | 2 | 2300.3.f.e.1701.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.3.f.a.321.9 | ✓ | 16 | 92.91 | even | 2 | ||
460.3.f.a.321.10 | yes | 16 | 4.3 | odd | 2 | ||
1840.3.k.c.321.7 | 16 | 23.22 | odd | 2 | inner | ||
1840.3.k.c.321.8 | 16 | 1.1 | even | 1 | trivial | ||
2300.3.d.b.1149.13 | 32 | 460.367 | odd | 4 | |||
2300.3.d.b.1149.14 | 32 | 20.3 | even | 4 | |||
2300.3.d.b.1149.19 | 32 | 20.7 | even | 4 | |||
2300.3.d.b.1149.20 | 32 | 460.183 | odd | 4 | |||
2300.3.f.e.1701.7 | 16 | 20.19 | odd | 2 | |||
2300.3.f.e.1701.8 | 16 | 460.459 | even | 2 | |||
4140.3.d.a.2161.6 | 16 | 12.11 | even | 2 | |||
4140.3.d.a.2161.11 | 16 | 276.275 | odd | 2 |