Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1569,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.l (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1569.2 | ||
Character | \(\chi\) | \(=\) | 2240.1569 |
Dual form | 2240.2.l.c.1569.1 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.11575 | −1.79888 | −0.899441 | − | 0.437043i | \(-0.856026\pi\) | ||||
−0.899441 | + | 0.437043i | \(0.856026\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.660542 | + | 2.13628i | −0.295403 | + | 0.955373i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.70793 | 2.23598 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.780127i | − | 0.235217i | −0.993060 | − | 0.117609i | \(-0.962477\pi\) | ||
0.993060 | − | 0.117609i | \(-0.0375228\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.09141 | −0.857402 | −0.428701 | − | 0.903446i | \(-0.641029\pi\) | ||||
−0.428701 | + | 0.903446i | \(0.641029\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.05809 | − | 6.65612i | 0.531396 | − | 1.71860i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.31343i | 1.77377i | 0.461993 | + | 0.886883i | \(0.347134\pi\) | ||||
−0.461993 | + | 0.886883i | \(0.652866\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.207666i | − | 0.0476418i | −0.999716 | − | 0.0238209i | \(-0.992417\pi\) | ||
0.999716 | − | 0.0238209i | \(-0.00758314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.11575i | 0.679913i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.52875i | − | 0.318766i | −0.987217 | − | 0.159383i | \(-0.949049\pi\) | ||
0.987217 | − | 0.159383i | \(-0.0509505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.12737 | − | 2.82220i | −0.825474 | − | 0.564441i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.5530 | −2.22337 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.60641i | 0.669693i | 0.942273 | + | 0.334846i | \(0.108684\pi\) | ||||
−0.942273 | + | 0.334846i | \(0.891316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.94658 | 1.42725 | 0.713624 | − | 0.700529i | \(-0.247053\pi\) | ||||
0.713624 | + | 0.700529i | \(0.247053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.43068i | 0.423128i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.13628 | + | 0.660542i | 0.361097 | + | 0.111652i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70429 | 0.608981 | 0.304490 | − | 0.952515i | \(-0.401514\pi\) | ||||
0.304490 | + | 0.952515i | \(0.401514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.63207 | 1.54237 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.24284 | 0.974968 | 0.487484 | − | 0.873132i | \(-0.337915\pi\) | ||||
0.487484 | + | 0.873132i | \(0.337915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.61428 | 1.00867 | 0.504334 | − | 0.863509i | \(-0.331738\pi\) | ||||
0.504334 | + | 0.863509i | \(0.331738\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.43087 | + | 14.3300i | −0.660515 | + | 2.13619i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.61892i | 0.382009i | 0.981589 | + | 0.191005i | \(0.0611745\pi\) | ||||
−0.981589 | + | 0.191005i | \(0.938825\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 22.7868i | − | 3.19080i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.69448 | 1.19428 | 0.597140 | − | 0.802137i | \(-0.296304\pi\) | ||||
0.597140 | + | 0.802137i | \(0.296304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.66657 | + | 0.515307i | 0.224720 | + | 0.0694839i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.647035i | 0.0857019i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.6333i | 1.90510i | 0.304388 | + | 0.952548i | \(0.401548\pi\) | ||||
−0.304388 | + | 0.952548i | \(0.598452\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.37646i | − | 0.816423i | −0.912887 | − | 0.408211i | \(-0.866153\pi\) | ||
0.912887 | − | 0.408211i | \(-0.133847\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 6.70793i | − | 0.845119i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.04200 | − | 6.60411i | 0.253279 | − | 0.819139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.21281 | −0.881185 | −0.440593 | − | 0.897707i | \(-0.645232\pi\) | ||||
−0.440593 | + | 0.897707i | \(0.645232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.76321i | 0.573423i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.6433 | −1.73784 | −0.868921 | − | 0.494950i | \(-0.835186\pi\) | ||||
−0.868921 | + | 0.494950i | \(0.835186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.502306i | − | 0.0587905i | −0.999568 | − | 0.0293952i | \(-0.990642\pi\) | ||
0.999568 | − | 0.0293952i | \(-0.00935815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.8599 | + | 8.79329i | 1.48493 | + | 1.01536i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.780127 | −0.0889037 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.4410 | −1.28722 | −0.643608 | − | 0.765355i | \(-0.722563\pi\) | ||||
−0.643608 | + | 0.765355i | \(0.722563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15.8725 | 1.76361 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8372 | −1.51883 | −0.759415 | − | 0.650606i | \(-0.774515\pi\) | ||||
−0.759415 | + | 0.650606i | \(0.774515\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.6235 | − | 4.83083i | −1.69461 | − | 0.523977i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 11.2367i | − | 1.20470i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3744 | −1.73568 | −0.867839 | − | 0.496845i | \(-0.834492\pi\) | ||||
−0.867839 | + | 0.496845i | \(0.834492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.09141i | 0.324068i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.7596 | −2.56745 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.443631 | + | 0.137172i | 0.0455156 | + | 0.0140735i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2956i | 1.04536i | 0.852530 | + | 0.522678i | \(0.175067\pi\) | ||||
−0.852530 | + | 0.522678i | \(0.824933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.23304i | − | 0.525940i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.51019i | − | 0.150269i | −0.997173 | − | 0.0751345i | \(-0.976061\pi\) | ||
0.997173 | − | 0.0751345i | \(-0.0239386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.3376i | − | 1.21566i | −0.794068 | − | 0.607829i | \(-0.792041\pi\) | ||
0.794068 | − | 0.607829i | \(-0.207959\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.65612 | − | 2.05809i | −0.649571 | − | 0.200849i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.23235 | 0.795851 | 0.397925 | − | 0.917418i | \(-0.369730\pi\) | ||||
0.397925 | + | 0.917418i | \(0.369730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.05171i | 0.675431i | 0.941248 | + | 0.337715i | \(0.109654\pi\) | ||||
−0.941248 | + | 0.337715i | \(0.890346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.5416 | −1.09548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 7.44815i | − | 0.700663i | −0.936626 | − | 0.350332i | \(-0.886069\pi\) | ||
0.936626 | − | 0.350332i | \(-0.113931\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.26583 | + | 1.00980i | 0.304541 | + | 0.0941646i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.7369 | −1.91713 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.31343 | 0.670421 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3914 | 0.944673 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.4512 | −1.75385 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.75531 | − | 6.95302i | 0.783099 | − | 0.621897i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.2620i | − | 1.26555i | −0.774336 | − | 0.632775i | \(-0.781916\pi\) | ||
0.774336 | − | 0.632775i | \(-0.218084\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.6085 | −1.81447 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 3.78753i | − | 0.330918i | −0.986217 | − | 0.165459i | \(-0.947089\pi\) | ||
0.986217 | − | 0.165459i | \(-0.0529105\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.207666 | −0.0180069 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.63123 | − | 24.6804i | 0.656792 | − | 2.12415i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.1281i | 1.63423i | 0.576477 | + | 0.817113i | \(0.304427\pi\) | ||||
−0.576477 | + | 0.817113i | \(0.695573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0683i | 1.10844i | 0.832372 | + | 0.554218i | \(0.186982\pi\) | ||||
−0.832372 | + | 0.554218i | \(0.813018\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 8.15992i | − | 0.687189i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.41169i | 0.201676i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.70429 | − | 2.38218i | −0.639806 | − | 0.197829i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.11575 | 0.256983 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.7098i | − | 1.04123i | −0.853793 | − | 0.520613i | \(-0.825703\pi\) | ||
0.853793 | − | 0.520613i | \(-0.174297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5732 | −1.67423 | −0.837114 | − | 0.547029i | \(-0.815759\pi\) | ||||
−0.837114 | + | 0.547029i | \(0.815759\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 49.0579i | 3.96610i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.24905 | + | 16.9761i | −0.421614 | + | 1.36355i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0900 | −1.12450 | −0.562251 | − | 0.826967i | \(-0.690064\pi\) | ||||
−0.562251 | + | 0.826967i | \(0.690064\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.0899 | −2.14837 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.52875 | −0.120482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0610878 | −0.00478477 | −0.00239238 | − | 0.999997i | \(-0.500762\pi\) | ||||
−0.00239238 | + | 0.999997i | \(0.500762\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.19262 | − | 1.60557i | −0.404245 | − | 0.124993i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3878i | 1.19074i | 0.803450 | + | 0.595372i | \(0.202995\pi\) | ||||
−0.803450 | + | 0.595372i | \(0.797005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.44320 | −0.264861 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1.39301i | − | 0.106526i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.82169 | −0.746729 | −0.373365 | − | 0.927685i | \(-0.621796\pi\) | ||||
−0.373365 | + | 0.927685i | \(0.621796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82220 | + | 4.12737i | −0.213338 | + | 0.312000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 45.5938i | − | 3.42704i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 7.54793i | − | 0.564159i | −0.959391 | − | 0.282079i | \(-0.908976\pi\) | ||
0.959391 | − | 0.282079i | \(-0.0910241\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.7551i | − | 1.31973i | −0.751386 | − | 0.659863i | \(-0.770614\pi\) | ||
0.751386 | − | 0.659863i | \(-0.229386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.8675i | 1.46865i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.44684 | + | 7.91339i | −0.179895 | + | 0.581804i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.70540 | 0.417221 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.5530i | 0.840356i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5484 | −0.763256 | −0.381628 | − | 0.924316i | \(-0.624636\pi\) | ||||
−0.381628 | + | 0.924316i | \(0.624636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.2499i | 0.737805i | 0.929468 | + | 0.368902i | \(0.120266\pi\) | ||||
−0.929468 | + | 0.368902i | \(0.879734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.36238 | + | 20.5768i | −0.455620 | + | 1.47353i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1196 | −0.863487 | −0.431743 | − | 0.901996i | \(-0.642101\pi\) | ||||
−0.431743 | + | 0.901996i | \(0.642101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.3840 | −1.37410 | −0.687048 | − | 0.726612i | \(-0.741094\pi\) | ||||
−0.687048 | + | 0.726612i | \(0.741094\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.4734 | 1.58515 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.60641 | 0.253120 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.12366 | + | 13.3364i | −0.288009 | + | 0.931457i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 10.2547i | − | 0.712754i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.162006 | −0.0112062 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.74843i | − | 0.464581i | −0.972646 | − | 0.232291i | \(-0.925378\pi\) | ||
0.972646 | − | 0.232291i | \(-0.0746221\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 45.6250 | 3.12617 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.36901 | + | 14.1299i | −0.297964 | + | 0.963654i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 7.94658i | − | 0.539449i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.56506i | 0.105757i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 22.6088i | − | 1.52083i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7700i | 1.25694i | 0.777836 | + | 0.628468i | \(0.216318\pi\) | ||||
−0.777836 | + | 0.628468i | \(0.783682\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.6861 | − | 18.9311i | −1.84574 | − | 1.26207i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.45729 | −0.163096 | −0.0815481 | − | 0.996669i | \(-0.525986\pi\) | ||||
−0.0815481 | + | 0.996669i | \(0.525986\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 16.3838i | − | 1.08267i | −0.840806 | − | 0.541336i | \(-0.817919\pi\) | ||
0.840806 | − | 0.541336i | \(-0.182081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.43068 | 0.159927 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7227i | 1.22656i | 0.789864 | + | 0.613282i | \(0.210151\pi\) | ||||
−0.789864 | + | 0.613282i | \(0.789849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.59475 | − | 1.72991i | −0.364961 | − | 0.112847i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 35.6474 | 2.31555 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.8849 | 1.28625 | 0.643123 | − | 0.765763i | \(-0.277638\pi\) | ||||
0.643123 | + | 0.765763i | \(0.277638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7523 | 1.46561 | 0.732803 | − | 0.680441i | \(-0.238212\pi\) | ||||
0.732803 | + | 0.680441i | \(0.238212\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7958 | −0.949153 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.660542 | − | 2.13628i | 0.0422005 | − | 0.136482i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.641979i | 0.0408482i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.1133 | 2.73220 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.48168i | 0.219762i | 0.993945 | + | 0.109881i | \(0.0350469\pi\) | ||||
−0.993945 | + | 0.109881i | \(0.964953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.19262 | −0.0749793 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 48.6790 | + | 15.0517i | 3.04840 | + | 0.942572i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.5841i | − | 1.34638i | −0.739469 | − | 0.673191i | \(-0.764923\pi\) | ||
0.739469 | − | 0.673191i | \(-0.235077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.70429i | − | 0.230173i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.1915i | 1.49742i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.07710i | 0.559718i | 0.960041 | + | 0.279859i | \(0.0902878\pi\) | ||||
−0.960041 | + | 0.279859i | \(0.909712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.74307 | + | 18.5738i | −0.352794 | + | 1.14098i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 51.0185 | 3.12228 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 31.6554i | − | 1.93006i | −0.262136 | − | 0.965031i | \(-0.584427\pi\) | ||
0.262136 | − | 0.965031i | \(-0.415573\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1433 | −0.616165 | −0.308082 | − | 0.951360i | \(-0.599687\pi\) | ||||
−0.308082 | + | 0.951360i | \(0.599687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 9.63207i | − | 0.582959i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.20168 | + | 3.21987i | −0.132766 | + | 0.194166i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.0993 | −1.50807 | −0.754036 | − | 0.656833i | \(-0.771896\pi\) | ||||
−0.754036 | + | 0.656833i | \(0.771896\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 53.3051 | 3.19129 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2025 | −0.727938 | −0.363969 | − | 0.931411i | \(-0.618579\pi\) | ||||
−0.363969 | + | 0.931411i | \(0.618579\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.6338 | −1.58322 | −0.791608 | − | 0.611029i | \(-0.790756\pi\) | ||||
−0.791608 | + | 0.611029i | \(0.790756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.38225 | − | 0.427394i | −0.0818772 | − | 0.0253166i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.24284i | − | 0.368503i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.4862 | −2.14625 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 32.0785i | − | 1.88047i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.5580 | 0.675228 | 0.337614 | − | 0.941285i | \(-0.390380\pi\) | ||||
0.337614 | + | 0.941285i | \(0.390380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.2608 | − | 9.66592i | −1.82008 | − | 0.562772i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.01280i | 0.522976i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.72599i | 0.273311i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.61428i | − | 0.381241i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.70537i | 0.270316i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.6219 | + | 4.21192i | 0.779988 | + | 0.241174i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.28984 | 0.301907 | 0.150954 | − | 0.988541i | \(-0.451766\pi\) | ||||
0.150954 | + | 0.988541i | \(0.451766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 38.4409i | 2.18682i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.05081 | −0.456519 | −0.228260 | − | 0.973600i | \(-0.573304\pi\) | ||||
−0.228260 | + | 0.973600i | \(0.573304\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.21760i | − | 0.181869i | −0.995857 | − | 0.0909347i | \(-0.971015\pi\) | ||
0.995857 | − | 0.0909347i | \(-0.0289855\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.3300 | + | 4.43087i | 0.807404 | + | 0.249651i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.3949 | 1.08932 | 0.544662 | − | 0.838656i | \(-0.316658\pi\) | ||||
0.544662 | + | 0.838656i | \(0.316658\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.81346 | 0.157523 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.6500 | −1.43164 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.51875 | 0.0845054 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7594 | + | 8.72458i | 0.707763 | + | 0.483953i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 21.9714i | − | 1.21502i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.61892 | 0.144386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1320i | 0.941662i | 0.882223 | + | 0.470831i | \(0.156046\pi\) | ||||
−0.882223 | + | 0.470831i | \(0.843954\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.8481 | 1.36167 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.76436 | − | 15.4086i | 0.260305 | − | 0.841860i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.5830i | − | 0.630965i | −0.948931 | − | 0.315482i | \(-0.897834\pi\) | ||
0.948931 | − | 0.315482i | \(-0.102166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.2066i | 1.26041i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 6.19934i | − | 0.335713i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.1755 | − | 3.14630i | −0.547832 | − | 0.169391i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.7866 | −0.901149 | −0.450575 | − | 0.892739i | \(-0.648781\pi\) | ||||
−0.450575 | + | 0.892739i | \(0.648781\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.8563i | 1.59817i | 0.601218 | + | 0.799085i | \(0.294682\pi\) | ||||
−0.601218 | + | 0.799085i | \(0.705318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 35.7150 | 1.90633 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.4892i | 0.717957i | 0.933346 | + | 0.358979i | \(0.116875\pi\) | ||||
−0.933346 | + | 0.358979i | \(0.883125\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.67253 | − | 31.2822i | 0.513364 | − | 1.66029i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.7868 | −1.20601 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.7437 | 0.672589 | 0.336295 | − | 0.941757i | \(-0.390826\pi\) | ||||
0.336295 | + | 0.941757i | \(0.390826\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9569 | 0.997730 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.3771 | −1.69935 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.07307 | + | 0.331794i | 0.0561668 | + | 0.0173669i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.6342i | − | 1.02490i | −0.858717 | − | 0.512449i | \(-0.828738\pi\) | ||
0.858717 | − | 0.512449i | \(-0.171262\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 41.8765 | 2.18000 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.69448i | − | 0.451395i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0932918 | 0.00483046 | 0.00241523 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241523 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.2794 | + | 21.6639i | −1.40870 | + | 1.11872i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11.1489i | − | 0.574196i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.35354i | 0.429093i | 0.976714 | + | 0.214546i | \(0.0688273\pi\) | ||||
−0.976714 | + | 0.214546i | \(0.931173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.4369i | 2.27657i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5675i | 0.897659i | 0.893617 | + | 0.448830i | \(0.148159\pi\) | ||||
−0.893617 | + | 0.448830i | \(0.851841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.515307 | − | 1.66657i | 0.0262625 | − | 0.0849362i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 44.3681 | 2.25536 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.7337i | 1.00054i | 0.865870 | + | 0.500270i | \(0.166766\pi\) | ||||
−0.865870 | + | 0.500270i | \(0.833234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1804 | 0.565417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.8010i | 0.595282i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.55728 | − | 24.4412i | 0.380248 | − | 1.22977i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.4713 | −1.37874 | −0.689372 | − | 0.724408i | \(-0.742113\pi\) | ||||
−0.689372 | + | 0.724408i | \(0.742113\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.647035 | 0.0323923 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.20403 | 0.409690 | 0.204845 | − | 0.978794i | \(-0.434331\pi\) | ||||
0.204845 | + | 0.978794i | \(0.434331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.5661 | −1.22373 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.4844 | + | 33.9081i | −0.520976 | + | 1.68490i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.88981i | − | 0.143243i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.5743 | −1.06678 | −0.533389 | − | 0.845870i | \(-0.679082\pi\) | ||||
−0.533389 | + | 0.845870i | \(0.679082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 59.5986i | − | 2.93978i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.6333 | 0.720059 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.14005 | − | 29.5601i | 0.448668 | − | 1.45105i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 40.7175i | − | 1.99394i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.4499i | 0.901336i | 0.892692 | + | 0.450668i | \(0.148814\pi\) | ||||
−0.892692 | + | 0.450668i | \(0.851186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.05800i | 0.392723i | 0.980532 | + | 0.196362i | \(0.0629126\pi\) | ||||
−0.980532 | + | 0.196362i | \(0.937087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.5675i | 0.854163i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.6400 | − | 30.1852i | 1.00119 | − | 1.46420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.37646 | −0.308579 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 7.51424i | − | 0.362791i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.24841 | −0.0601340 | −0.0300670 | − | 0.999548i | \(-0.509572\pi\) | ||||
−0.0300670 | + | 0.999548i | \(0.509572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.23559i | 0.443834i | 0.975066 | + | 0.221917i | \(0.0712314\pi\) | ||||
−0.975066 | + | 0.221917i | \(0.928769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0047 | + | 7.42229i | 1.15094 | + | 0.355872i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.317469 | −0.0151866 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2320 | 0.870166 | 0.435083 | − | 0.900390i | \(-0.356719\pi\) | ||||
0.435083 | + | 0.900390i | \(0.356719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.70793 | −0.319425 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.5857 | 1.12059 | 0.560296 | − | 0.828292i | \(-0.310687\pi\) | ||||
0.560296 | + | 0.828292i | \(0.310687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.8159 | − | 34.9802i | 0.512725 | − | 1.65822i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.6006i | 1.87304i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.62083 | 0.0764917 | 0.0382458 | − | 0.999268i | \(-0.487823\pi\) | ||||
0.0382458 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.87021i | − | 0.229329i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 64.1012 | 3.01174 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.60411 | − | 2.04200i | −0.309605 | − | 0.0957306i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.4779i | − | 0.817581i | −0.912628 | − | 0.408790i | \(-0.865951\pi\) | ||
0.912628 | − | 0.408790i | \(-0.134049\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 84.4919i | − | 3.94375i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.5433i | − | 0.584200i | −0.956388 | − | 0.292100i | \(-0.905646\pi\) | ||
0.956388 | − | 0.292100i | \(-0.0943540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.1797i | − | 1.17020i | −0.810961 | − | 0.585101i | \(-0.801055\pi\) | ||
0.810961 | − | 0.585101i | \(-0.198945\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.3547 | − | 52.8934i | 0.758433 | − | 2.45287i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.98968 | −0.230895 | −0.115447 | − | 0.993314i | \(-0.536830\pi\) | ||||
−0.115447 | + | 0.993314i | \(0.536830\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.21281i | 0.333057i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 43.9009 | 2.02284 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.15998i | − | 0.237256i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.586074 | + | 0.857112i | −0.0268909 | + | 0.0393270i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 58.3219 | 2.67038 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.8772 | −1.54789 | −0.773945 | − | 0.633253i | \(-0.781719\pi\) | ||||
−0.773945 | + | 0.633253i | \(0.781719\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4515 | −0.522142 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.76321 | 0.216733 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.9942 | − | 6.80065i | −0.998705 | − | 0.308802i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2197i | 1.18813i | 0.804419 | + | 0.594063i | \(0.202477\pi\) | ||||
−0.804419 | + | 0.594063i | \(0.797523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.190335 | 0.00860723 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.912260i | − | 0.0411697i | −0.999788 | − | 0.0205849i | \(-0.993447\pi\) | ||
0.999788 | − | 0.0205849i | \(-0.00655283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.3752 | −1.18788 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.1792 | + | 3.45664i | 0.502469 | + | 0.155364i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6433i | 0.656843i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.73724i | 0.435899i | 0.975960 | + | 0.217949i | \(0.0699368\pi\) | ||||
−0.975960 | + | 0.217949i | \(0.930063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 47.9446i | − | 2.14201i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.5199i | 0.513646i | 0.966458 | + | 0.256823i | \(0.0826757\pi\) | ||||
−0.966458 | + | 0.256823i | \(0.917324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.22618 | + | 0.997541i | 0.143563 | + | 0.0443900i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.7282 | 0.476454 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 10.5269i | − | 0.466598i | −0.972405 | − | 0.233299i | \(-0.925048\pi\) | ||
0.972405 | − | 0.233299i | \(-0.0749520\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.502306 | −0.0222207 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.39916i | 0.105925i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.3565 | + | 8.14949i | 1.16141 | + | 0.359109i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.04309 | 0.0898551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.6020 | 1.34328 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2935 | −0.889075 | −0.444538 | − | 0.895760i | \(-0.646632\pi\) | ||||
−0.444538 | + | 0.895760i | \(0.646632\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.0756 | 0.790392 | 0.395196 | − | 0.918597i | \(-0.370677\pi\) | ||||
0.395196 | + | 0.918597i | \(0.370677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.79329 | − | 12.8599i | 0.383771 | − | 0.561251i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 58.1167i | 2.53161i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.6629 | 0.898388 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 98.1592i | 4.25975i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.2992 | −0.835939 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.43781 | + | 17.5866i | −0.235097 | + | 0.760334i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.5175i | 1.01485i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.780127i | 0.0336025i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.588349i | 0.0252951i | 0.999920 | + | 0.0126475i | \(0.00402595\pi\) | ||||
−0.999920 | + | 0.0126475i | \(0.995974\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 55.3206i | 2.37403i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0644 | − | 4.65795i | −0.645288 | − | 0.199525i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5454 | −0.450890 | −0.225445 | − | 0.974256i | \(-0.572384\pi\) | ||||
−0.225445 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 42.7728i | − | 1.82550i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.748926 | 0.0319053 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4410i | 0.486522i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.62374 | − | 24.6562i | 0.323610 | − | 1.04660i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.3739 | 1.62596 | 0.812978 | − | 0.582295i | \(-0.197845\pi\) | ||||
0.812978 | + | 0.582295i | \(0.197845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.4474 | −0.864834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.7766 | −0.750530 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.4307 | 0.692473 | 0.346237 | − | 0.938147i | \(-0.387459\pi\) | ||||
0.346237 | + | 0.938147i | \(0.387459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.9113 | + | 4.91982i | 0.669395 | + | 0.206978i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 15.8725i | − | 0.666582i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.1733 | −0.761866 | −0.380933 | − | 0.924603i | \(-0.624397\pi\) | ||||
−0.380933 | + | 0.924603i | \(0.624397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.4832i | 0.522406i | 0.965284 | + | 0.261203i | \(0.0841192\pi\) | ||||
−0.965284 | + | 0.261203i | \(0.915881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.8662 | 1.37301 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.31444 | + | 6.30971i | −0.179925 | + | 0.263133i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0366i | 0.792505i | 0.918142 | + | 0.396252i | \(0.129689\pi\) | ||||
−0.918142 | + | 0.396252i | \(0.870311\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 31.9362i | − | 1.32722i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.8372i | 0.574064i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6.78280i | − | 0.280915i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.6976 | − | 44.2999i | 0.566327 | − | 1.83157i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.45396 | −0.183835 | −0.0919173 | − | 0.995767i | \(-0.529300\pi\) | ||||
−0.0919173 | + | 0.995767i | \(0.529300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.65023i | − | 0.0679966i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.7618 | 1.55331 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.4961i | − | 1.45765i | −0.684699 | − | 0.728826i | \(-0.740066\pi\) | ||
0.684699 | − | 0.728826i | \(-0.259934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.83083 | + | 15.6235i | −0.198045 | + | 0.640502i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 60.3958 | 2.47183 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.92977 | 0.0788483 | 0.0394242 | − | 0.999223i | \(-0.487448\pi\) | ||||
0.0394242 | + | 0.999223i | \(0.487448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.5646 | −1.69546 | −0.847728 | − | 0.530430i | \(-0.822030\pi\) | ||||
−0.847728 | + | 0.530430i | \(0.822030\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −48.3830 | −1.97031 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.86396 | + | 22.1989i | −0.279060 | + | 0.902515i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.1119i | − | 1.26279i | −0.775460 | − | 0.631396i | \(-0.782482\pi\) | ||
0.775460 | − | 0.631396i | \(-0.217518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.2367 | −0.455333 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 8.09616i | − | 0.327535i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.7427 | −1.16091 | −0.580453 | − | 0.814293i | \(-0.697125\pi\) | ||||
−0.580453 | + | 0.814293i | \(0.697125\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.8483 | − | 41.5531i | 0.518094 | − | 1.67558i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3.31564i | − | 0.133483i | −0.997770 | − | 0.0667414i | \(-0.978740\pi\) | ||
0.997770 | − | 0.0667414i | \(-0.0212602\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.0326i | 0.845374i | 0.906276 | + | 0.422687i | \(0.138913\pi\) | ||||
−0.906276 | + | 0.422687i | \(0.861087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.6616i | 0.708736i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3744i | 0.656025i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.07035 | + | 23.2965i | 0.362814 | + | 0.931862i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.504770 | 0.0201586 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.0910i | 1.08019i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.91397 | −0.235432 | −0.117716 | − | 0.993047i | \(-0.537557\pi\) | ||||
−0.117716 | + | 0.993047i | \(0.537557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.0265i | 0.835727i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.4676 | + | 9.42066i | 1.20907 | + | 0.373847i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.09141 | 0.122486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −98.2263 | −3.88577 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.64380 | −0.183419 | −0.0917095 | − | 0.995786i | \(-0.529233\pi\) | ||||
−0.0917095 | + | 0.995786i | \(0.529233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.9654 | 0.747922 | 0.373961 | − | 0.927444i | \(-0.377999\pi\) | ||||
0.373961 | + | 0.927444i | \(0.377999\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.6128 | − | 44.0254i | 0.536002 | − | 1.73350i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.18211i | 0.360986i | 0.983576 | + | 0.180493i | \(0.0577693\pi\) | ||||
−0.983576 | + | 0.180493i | \(0.942231\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4159 | 0.448111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.7596i | 0.970405i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.20199 | 0.164437 | 0.0822184 | − | 0.996614i | \(-0.473800\pi\) | ||||
0.0822184 | + | 0.996614i | \(0.473800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.09121 | + | 2.50182i | 0.316150 | + | 0.0977542i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.36943i | − | 0.131454i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.48955i | − | 0.213843i | −0.994267 | − | 0.106921i | \(-0.965901\pi\) | ||
0.994267 | − | 0.106921i | \(-0.0340993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.5752i | − | 0.411329i | −0.978623 | − | 0.205664i | \(-0.934065\pi\) | ||
0.978623 | − | 0.205664i | \(-0.0659355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 70.4434i | 2.73580i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.137172 | − | 0.443631i | 0.00531930 | − | 0.0172033i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.51329 | 0.213475 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 58.4828i | − | 2.26108i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97445 | −0.192037 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.0174i | 1.61965i | 0.586670 | + | 0.809826i | \(0.300439\pi\) | ||||
−0.586670 | + | 0.809826i | \(0.699561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 47.6834 | + | 32.6049i | 1.83534 | + | 1.25496i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.86589 | −0.148578 | −0.0742891 | − | 0.997237i | \(-0.523669\pi\) | ||||
−0.0742891 | + | 0.997237i | \(0.523669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.2956 | 0.395108 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.65632 | 0.293391 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.61529 | −0.329655 | −0.164828 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164828 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.8630 | − | 12.6349i | −1.56130 | − | 0.482756i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 51.0479i | 1.94760i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.8782 | −1.02398 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.2087i | 1.33940i | 0.742631 | + | 0.669701i | \(0.233578\pi\) | ||||
−0.742631 | + | 0.669701i | \(0.766422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.23304 | −0.198787 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.9174 | − | 8.63213i | −1.05897 | − | 0.327435i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.6566i | 1.72937i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 58.3353i | − | 2.20644i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9933i | 1.32168i | 0.750527 | + | 0.660840i | \(0.229800\pi\) | ||||
−0.750527 | + | 0.660840i | \(0.770200\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.769253i | − | 0.0290129i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.4319 | + | 5.38997i | 0.656522 | + | 0.202998i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.51019 | −0.0567964 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 36.3304i | − | 1.36442i | −0.731158 | − | 0.682209i | \(-0.761020\pi\) | ||
0.731158 | − | 0.682209i | \(-0.238980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −76.7456 | −2.87818 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.1483i | − | 0.454959i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.15204 | − | 1.59302i | −0.192676 | − | 0.0595757i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −61.9564 | −2.31380 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.5471 | −0.393341 | −0.196670 | − | 0.980470i | \(-0.563013\pi\) | ||||
−0.196670 | + | 0.980470i | \(0.563013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3376 | −0.459475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −70.8906 | −2.63645 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.1780 | − | 14.8850i | 0.378002 | − | 0.552814i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 30.5631i | − | 1.13352i | −0.823883 | − | 0.566761i | \(-0.808196\pi\) | ||
0.823883 | − | 0.566761i | \(-0.191804\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.51731 | −0.0561968 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.3731i | 1.78914i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.32197 | 0.307379 | 0.153690 | − | 0.988119i | \(-0.450884\pi\) | ||||
0.153690 | + | 0.988119i | \(0.450884\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.05809 | + | 6.65612i | −0.0759137 | + | 0.245515i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.62691i | 0.207270i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.2933i | 0.746502i | 0.927730 | + | 0.373251i | \(0.121757\pi\) | ||||
−0.927730 | + | 0.373251i | \(0.878243\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2.00025i | − | 0.0734810i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 36.2809i | − | 1.33102i | −0.746391 | − | 0.665508i | \(-0.768215\pi\) | ||
0.746391 | − | 0.665508i | \(-0.231785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.1516 | + | 8.39535i | 0.994759 | + | 0.307582i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −92.8189 | −3.39607 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 8.23235i | − | 0.300803i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.28827 | 0.0835001 | 0.0417501 | − | 0.999128i | \(-0.486707\pi\) | ||||
0.0417501 | + | 0.999128i | \(0.486707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 10.8481i | − | 0.395325i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.5895 | − | 43.9502i | 0.494572 | − | 1.59951i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.3190 | −0.811198 | −0.405599 | − | 0.914051i | \(-0.632937\pi\) | ||||
−0.405599 | + | 0.914051i | \(0.632937\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.71591 | 0.134879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.99267 | 0.108484 | 0.0542421 | − | 0.998528i | \(-0.482726\pi\) | ||||
0.0542421 | + | 0.998528i | \(0.482726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.05171 | 0.255289 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −104.801 | − | 32.4048i | −3.78910 | − | 1.17160i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 45.2376i | − | 1.63343i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.713327 | −0.0257232 | −0.0128616 | − | 0.999917i | \(-0.504094\pi\) | ||||
−0.0128616 | + | 0.999917i | \(0.504094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 67.2509i | 2.42198i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.6727 | 0.923381 | 0.461691 | − | 0.887041i | \(-0.347243\pi\) | ||||
0.461691 | + | 0.887041i | \(0.347243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.7985 | − | 22.4269i | −1.17816 | − | 0.805597i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.5416i | 0.414054i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.29642i | − | 0.0464492i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4237i | 0.408770i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 41.6648i | − | 1.48898i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.30701 | − | 30.1001i | 0.332181 | − | 1.07432i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.9846 | −1.49659 | −0.748294 | − | 0.663367i | \(-0.769127\pi\) | ||||
−0.748294 | + | 0.663367i | \(0.769127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 28.2820i | − | 1.00687i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.44815 | −0.264826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.7123i | 0.700003i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.8940 | − | 57.8715i | 0.634635 | − | 2.05249i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.5201 | 0.797705 | 0.398852 | − | 0.917015i | \(-0.369409\pi\) | ||||
0.398852 | + | 0.917015i | \(0.369409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.1533 | −0.677595 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −109.838 | −3.88093 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.391863 | −0.0138285 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00980 | − | 3.26583i | 0.0355909 | − | 0.115106i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 98.6304i | 3.47195i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.11472 | 0.320457 | 0.160228 | − | 0.987080i | \(-0.448777\pi\) | ||||
0.160228 | + | 0.987080i | \(0.448777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.04562i | − | 0.317635i | −0.987308 | − | 0.158817i | \(-0.949232\pi\) | ||
0.987308 | − | 0.158817i | \(-0.0507681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.6042 | 1.10841 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0403511 | − | 0.130501i | 0.00141344 | − | 0.00457123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.37356i | − | 0.0480547i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.7369i | 0.724607i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 36.8007i | − | 1.28435i | −0.766557 | − | 0.642177i | \(-0.778032\pi\) | ||
0.766557 | − | 0.642177i | \(-0.221968\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35.1816i | − | 1.22635i | −0.789946 | − | 0.613177i | \(-0.789891\pi\) | ||
0.789946 | − | 0.613177i | \(-0.210109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.85988 | − | 10.0323i | 0.238831 | − | 0.349281i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.7117 | 0.581123 | 0.290561 | − | 0.956856i | \(-0.406158\pi\) | ||||
0.290561 | + | 0.956856i | \(0.406158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.9691i | 1.42292i | 0.702729 | + | 0.711458i | \(0.251965\pi\) | ||||
−0.702729 | + | 0.711458i | \(0.748035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 78.2033 | 2.71284 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 7.31343i | − | 0.253395i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.8726 | − | 10.1643i | −1.13760 | − | 0.351750i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −91.8067 | −3.17330 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.1392 | 1.14409 | 0.572046 | − | 0.820221i | \(-0.306150\pi\) | ||||
0.572046 | + | 0.820221i | \(0.306150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9938 | 0.551512 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.0199 | 1.30947 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.27438 | − | 7.35563i | 0.0782409 | − | 0.253041i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.3914i | − | 0.357053i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 82.9844 | 2.84802 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 5.66293i | − | 0.194123i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.6954 | −0.845554 | −0.422777 | − | 0.906234i | \(-0.638945\pi\) | ||||
−0.422777 | + | 0.906234i | \(0.638945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.97585 | + | 0.920138i | 0.101772 | + | 0.0314681i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.8936i | 1.08946i | 0.838610 | + | 0.544732i | \(0.183368\pi\) | ||||
−0.838610 | + | 0.544732i | \(0.816632\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9029i | 0.883794i | 0.897066 | + | 0.441897i | \(0.145694\pi\) | ||||
−0.897066 | + | 0.441897i | \(0.854306\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.4512i | 0.662893i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.68267i | − | 0.0572788i | −0.999590 | − | 0.0286394i | \(-0.990883\pi\) | ||
0.999590 | − | 0.0286394i | \(-0.00911745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.48764 | − | 20.9819i | 0.220586 | − | 0.713405i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 113.682 | 3.86085 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.92546i | 0.302775i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.2977 | 0.755530 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 69.0619i | 2.33739i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.95302 | − | 8.75531i | −0.235055 | − | 0.295983i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1199 | 0.611864 | 0.305932 | − | 0.952053i | \(-0.401032\pi\) | ||||
0.305932 | + | 0.952053i | \(0.401032\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −36.0120 | −1.21465 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0698 | −0.777242 | −0.388621 | − | 0.921398i | \(-0.627048\pi\) | ||||
−0.388621 | + | 0.921398i | \(0.627048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.3787 | −0.887715 | −0.443857 | − | 0.896097i | \(-0.646390\pi\) | ||||
−0.443857 | + | 0.896097i | \(0.646390\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 97.4011 | + | 30.1166i | 3.27410 | + | 1.01236i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 16.5725i | − | 0.556450i | −0.960516 | − | 0.278225i | \(-0.910254\pi\) | ||
0.960516 | − | 0.278225i | \(-0.0897460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.2620 | −0.478333 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 12.3826i | − | 0.414831i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.543860 | 0.0181996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.1245 | + | 4.98572i | 0.538982 | + | 0.166654i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 14.7250i | − | 0.491654i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.6586i | 0.955818i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.5865i | 2.11837i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.6085i | 0.685807i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.9298 | + | 11.7280i | 1.26083 | + | 0.389852i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.6465 | 0.585941 | 0.292971 | − | 0.956121i | \(-0.405356\pi\) | ||||
0.292971 | + | 0.956121i | \(0.405356\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 10.1302i | − | 0.335998i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.6942 | 0.586235 | 0.293117 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293117 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7948i | 0.357255i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42.4425 | − | 13.1233i | −1.40311 | − | 0.433843i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.78753 | −0.125075 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.5650 | 1.00825 | 0.504123 | − | 0.863632i | \(-0.331816\pi\) | ||||
0.504123 | + | 0.863632i | \(0.331816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.4818 | −0.543095 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.2685 | 1.49003 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.2890 | − | 10.4542i | −0.502698 | − | 0.343733i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 82.7596i | − | 2.71818i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.4220 | −1.88396 | −0.941978 | − | 0.335676i | \(-0.891035\pi\) | ||||
−0.941978 | + | 0.335676i | \(0.891035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.207666i | 0.00680596i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.0843 | 0.821224 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.76866 | + | 12.1883i | −0.123248 | + | 0.398601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 57.8853i | − | 1.89103i | −0.325580 | − | 0.945515i | \(-0.605559\pi\) | ||
0.325580 | − | 0.945515i | \(-0.394441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0253i | 0.327162i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 20.5689i | − | 0.670529i | −0.942124 | − | 0.335264i | \(-0.891174\pi\) | ||
0.942124 | − | 0.335264i | \(-0.108826\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 9.54374i | − | 0.310787i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.6804 | − | 7.63123i | −0.802853 | − | 0.248244i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.78499 | −0.0905001 | −0.0452500 | − | 0.998976i | \(-0.514408\pi\) | ||||
−0.0452500 | + | 0.998976i | \(0.514408\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.55283i | 0.0504071i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.4296 | −1.95956 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.3339i | − | 0.431929i | −0.976401 | − | 0.215964i | \(-0.930710\pi\) | ||
0.976401 | − | 0.215964i | \(-0.0692895\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.96766 | − | 22.5343i | 0.225468 | − | 0.729194i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.76604 | −0.283366 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.1281 | 0.617680 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.1481 | 1.03704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 55.2220 | 1.77950 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.8967 | − | 6.77050i | −0.704879 | − | 0.217950i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.48530i | 0.112080i | 0.998429 | + | 0.0560399i | \(0.0178474\pi\) | ||||
−0.998429 | + | 0.0560399i | \(0.982153\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.73204 | −0.152015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 29.9970i | − | 0.962651i | −0.876542 | − | 0.481325i | \(-0.840156\pi\) | ||
0.876542 | − | 0.481325i | \(-0.159844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0683 | 0.418949 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −39.7551 | − | 27.1836i | −1.27318 | − | 0.870573i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 31.8837i | − | 1.02005i | −0.860160 | − | 0.510025i | \(-0.829636\pi\) | ||
0.860160 | − | 0.510025i | \(-0.170364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7741i | 0.408261i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.3023i | 1.51025i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.0621i | 1.66052i | 0.557373 | + | 0.830262i | \(0.311809\pi\) | ||||
−0.557373 | + | 0.830262i | \(0.688191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.00552 | − | 25.8909i | 0.255077 | − | 0.824952i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.15992 | −0.259733 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.1116i | − | 0.321529i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.1169 | −0.543737 | −0.271869 | − | 0.962334i | \(-0.587642\pi\) | ||||
−0.271869 | + | 0.962334i | \(0.587642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 53.3792i | − | 1.69394i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.8039 | − | 41.4096i | 0.405912 | − | 1.31277i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5800 | 0.588435 | 0.294217 | − | 0.955738i | \(-0.404941\pi\) | ||||
0.294217 | + | 0.955738i | \(0.404941\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −42.7956 | −1.35399 |
(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 | 2240.2.l.c.1569.2 | yes | 24 | |
4.3 | odd | 2 | inner | 2240.2.l.c.1569.23 | yes | 24 | |
5.4 | even | 2 | 2240.2.l.d.1569.23 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.l.d.1569.1 | yes | 24 | ||
8.5 | even | 2 | 2240.2.l.d.1569.24 | yes | 24 | ||
20.19 | odd | 2 | 2240.2.l.d.1569.2 | yes | 24 | ||
40.19 | odd | 2 | inner | 2240.2.l.c.1569.24 | yes | 24 | |
40.29 | even | 2 | inner | 2240.2.l.c.1569.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.l.c.1569.1 | ✓ | 24 | 40.29 | even | 2 | inner | |
2240.2.l.c.1569.2 | yes | 24 | 1.1 | even | 1 | trivial | |
2240.2.l.c.1569.23 | yes | 24 | 4.3 | odd | 2 | inner | |
2240.2.l.c.1569.24 | yes | 24 | 40.19 | odd | 2 | inner | |
2240.2.l.d.1569.1 | yes | 24 | 8.3 | odd | 2 | ||
2240.2.l.d.1569.2 | yes | 24 | 20.19 | odd | 2 | ||
2240.2.l.d.1569.23 | yes | 24 | 5.4 | even | 2 | ||
2240.2.l.d.1569.24 | yes | 24 | 8.5 | even | 2 |