Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,3,Mod(97,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.b (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: | \(2.67030659073\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.97 |
Dual form | 98.3.b.b.97.3 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0.717439i | 0.239146i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 6.63103i | 1.32621i | 0.748528 | + | 0.663103i | \(0.230761\pi\) | ||||
−0.748528 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(6\) | 1.01461i | 0.169102i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 8.48528 | 0.942809 | ||||||||
\(10\) | 9.37769i | 0.937769i | ||||||||
\(11\) | −4.75736 | −0.432487 | −0.216244 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216244 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(12\) | 1.43488i | 0.119573i | ||||||||
\(13\) | − 15.2913i | − 1.17625i | −0.808769 | − | 0.588126i | \(-0.799866\pi\) | ||||
0.808769 | − | 0.588126i | \(-0.200134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.75736 | −0.317157 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − 3.76127i | − 0.221251i | −0.993862 | − | 0.110626i | \(-0.964715\pi\) | ||||
0.993862 | − | 0.110626i | \(-0.0352855\pi\) | |||||||
\(18\) | 12.0000 | 0.666667 | ||||||||
\(19\) | − 4.18154i | − 0.220081i | −0.993927 | − | 0.110041i | \(-0.964902\pi\) | ||||
0.993927 | − | 0.110041i | \(-0.0350981\pi\) | |||||||
\(20\) | 13.2621i | 0.663103i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.72792 | −0.305815 | ||||||||
\(23\) | −27.7279 | −1.20556 | −0.602781 | − | 0.797907i | \(-0.705941\pi\) | ||||
−0.602781 | + | 0.797907i | \(0.705941\pi\) | |||||||
\(24\) | 2.02922i | 0.0845510i | ||||||||
\(25\) | −18.9706 | −0.758823 | ||||||||
\(26\) | − 21.6251i | − 0.831736i | ||||||||
\(27\) | 12.5446i | 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.51472 | 0.121197 | 0.0605986 | − | 0.998162i | \(-0.480699\pi\) | ||||
0.0605986 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(30\) | −6.72792 | −0.224264 | ||||||||
\(31\) | − 48.8667i | − 1.57635i | −0.615454 | − | 0.788173i | \(-0.711027\pi\) | ||||
0.615454 | − | 0.788173i | \(-0.288973\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − 3.41311i | − 0.103428i | ||||||||
\(34\) | − 5.31925i | − 0.156448i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.9706 | 0.471405 | ||||||||
\(37\) | −2.94113 | −0.0794899 | −0.0397449 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397449 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(38\) | − 5.91359i | − 0.155621i | ||||||||
\(39\) | 10.9706 | 0.281296 | ||||||||
\(40\) | 18.7554i | 0.468885i | ||||||||
\(41\) | 27.9590i | 0.681927i | 0.940077 | + | 0.340963i | \(0.110753\pi\) | ||||
−0.940077 | + | 0.340963i | \(0.889247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4853 | −0.243844 | −0.121922 | − | 0.992540i | \(-0.538906\pi\) | ||||
−0.121922 | + | 0.992540i | \(0.538906\pi\) | |||||||
\(44\) | −9.51472 | −0.216244 | ||||||||
\(45\) | 56.2662i | 1.25036i | ||||||||
\(46\) | −39.2132 | −0.852461 | ||||||||
\(47\) | − 52.6790i | − 1.12083i | −0.828212 | − | 0.560415i | \(-0.810642\pi\) | ||||
0.828212 | − | 0.560415i | \(-0.189358\pi\) | |||||||
\(48\) | 2.86976i | 0.0597866i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −26.8284 | −0.536569 | ||||||||
\(51\) | 2.69848 | 0.0529115 | ||||||||
\(52\) | − 30.5826i | − 0.588126i | ||||||||
\(53\) | 55.9706 | 1.05605 | 0.528024 | − | 0.849229i | \(-0.322933\pi\) | ||||
0.528024 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(54\) | 17.7408i | 0.328533i | ||||||||
\(55\) | − 31.5462i | − 0.573567i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.0526316 | ||||||||
\(58\) | 4.97056 | 0.0856994 | ||||||||
\(59\) | 38.7206i | 0.656281i | 0.944629 | + | 0.328141i | \(0.106422\pi\) | ||||
−0.944629 | + | 0.328141i | \(0.893578\pi\) | |||||||
\(60\) | −9.51472 | −0.158579 | ||||||||
\(61\) | 90.5080i | 1.48374i | 0.670545 | + | 0.741869i | \(0.266060\pi\) | ||||
−0.670545 | + | 0.741869i | \(0.733940\pi\) | |||||||
\(62\) | − 69.1080i | − 1.11464i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 101.397 | 1.55995 | ||||||||
\(66\) | − 4.82687i | − 0.0731344i | ||||||||
\(67\) | −34.6396 | −0.517009 | −0.258505 | − | 0.966010i | \(-0.583230\pi\) | ||||
−0.258505 | + | 0.966010i | \(0.583230\pi\) | |||||||
\(68\) | − 7.52255i | − 0.110626i | ||||||||
\(69\) | − 19.8931i | − 0.288306i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.4264 | 0.513048 | 0.256524 | − | 0.966538i | \(-0.417423\pi\) | ||||
0.256524 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(72\) | 24.0000 | 0.333333 | ||||||||
\(73\) | 52.6069i | 0.720642i | 0.932828 | + | 0.360321i | \(0.117333\pi\) | ||||
−0.932828 | + | 0.360321i | \(0.882667\pi\) | |||||||
\(74\) | −4.15938 | −0.0562078 | ||||||||
\(75\) | − 13.6102i | − 0.181470i | ||||||||
\(76\) | − 8.36308i | − 0.110041i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15.5147 | 0.198907 | ||||||||
\(79\) | −33.7868 | −0.427681 | −0.213840 | − | 0.976869i | \(-0.568597\pi\) | ||||
−0.213840 | + | 0.976869i | \(0.568597\pi\) | |||||||
\(80\) | 26.5241i | 0.331552i | ||||||||
\(81\) | 67.3675 | 0.831698 | ||||||||
\(82\) | 39.5400i | 0.482195i | ||||||||
\(83\) | 127.577i | 1.53708i | 0.639803 | + | 0.768539i | \(0.279016\pi\) | ||||
−0.639803 | + | 0.768539i | \(0.720984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.9411 | 0.293425 | ||||||||
\(86\) | −14.8284 | −0.172424 | ||||||||
\(87\) | 2.52160i | 0.0289839i | ||||||||
\(88\) | −13.4558 | −0.152907 | ||||||||
\(89\) | 50.3314i | 0.565522i | 0.959190 | + | 0.282761i | \(0.0912503\pi\) | ||||
−0.959190 | + | 0.282761i | \(0.908750\pi\) | |||||||
\(90\) | 79.5724i | 0.884137i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −55.4558 | −0.602781 | ||||||||
\(93\) | 35.0589 | 0.376977 | ||||||||
\(94\) | − 74.4993i | − 0.792546i | ||||||||
\(95\) | 27.7279 | 0.291873 | ||||||||
\(96\) | 4.05845i | 0.0422755i | ||||||||
\(97\) | − 101.792i | − 1.04940i | −0.851287 | − | 0.524700i | \(-0.824177\pi\) | ||||
0.851287 | − | 0.524700i | \(-0.175823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40.3675 | −0.407753 | ||||||||
\(100\) | −37.9411 | −0.379411 | ||||||||
\(101\) | − 59.6793i | − 0.590884i | −0.955361 | − | 0.295442i | \(-0.904533\pi\) | ||||
0.955361 | − | 0.295442i | \(-0.0954669\pi\) | |||||||
\(102\) | 3.81623 | 0.0374141 | ||||||||
\(103\) | − 120.178i | − 1.16678i | −0.812193 | − | 0.583388i | \(-0.801727\pi\) | ||||
0.812193 | − | 0.583388i | \(-0.198273\pi\) | |||||||
\(104\) | − 43.2503i | − 0.415868i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 79.1543 | 0.746739 | ||||||||
\(107\) | −113.610 | −1.06178 | −0.530889 | − | 0.847442i | \(-0.678142\pi\) | ||||
−0.530889 | + | 0.847442i | \(0.678142\pi\) | |||||||
\(108\) | 25.0892i | 0.232308i | ||||||||
\(109\) | −145.309 | −1.33311 | −0.666553 | − | 0.745457i | \(-0.732231\pi\) | ||||
−0.666553 | + | 0.745457i | \(0.732231\pi\) | |||||||
\(110\) | − 44.6131i | − 0.405573i | ||||||||
\(111\) | − 2.11008i | − 0.0190097i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 34.5442 | 0.305700 | 0.152850 | − | 0.988249i | \(-0.451155\pi\) | ||||
0.152850 | + | 0.988249i | \(0.451155\pi\) | |||||||
\(114\) | 4.24264 | 0.0372161 | ||||||||
\(115\) | − 183.865i | − 1.59882i | ||||||||
\(116\) | 7.02944 | 0.0605986 | ||||||||
\(117\) | − 129.751i | − 1.10898i | ||||||||
\(118\) | 54.7592i | 0.464061i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −13.4558 | −0.112132 | ||||||||
\(121\) | −98.3675 | −0.812955 | ||||||||
\(122\) | 127.998i | 1.04916i | ||||||||
\(123\) | −20.0589 | −0.163080 | ||||||||
\(124\) | − 97.7334i | − 0.788173i | ||||||||
\(125\) | 39.9814i | 0.319851i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −247.338 | −1.94754 | −0.973772 | − | 0.227526i | \(-0.926936\pi\) | ||||
−0.973772 | + | 0.227526i | \(0.926936\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − 7.52255i | − 0.0583143i | ||||||||
\(130\) | 143.397 | 1.10305 | ||||||||
\(131\) | 147.645i | 1.12706i | 0.826096 | + | 0.563529i | \(0.190557\pi\) | ||||
−0.826096 | + | 0.563529i | \(0.809443\pi\) | |||||||
\(132\) | − 6.82623i | − 0.0517139i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −48.9878 | −0.365581 | ||||||||
\(135\) | −83.1838 | −0.616176 | ||||||||
\(136\) | − 10.6385i | − 0.0782242i | ||||||||
\(137\) | −32.5736 | −0.237763 | −0.118882 | − | 0.992908i | \(-0.537931\pi\) | ||||
−0.118882 | + | 0.992908i | \(0.537931\pi\) | |||||||
\(138\) | − 28.1331i | − 0.203863i | ||||||||
\(139\) | − 68.5857i | − 0.493422i | −0.969089 | − | 0.246711i | \(-0.920650\pi\) | ||||
0.969089 | − | 0.246711i | \(-0.0793499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.7939 | 0.268042 | ||||||||
\(142\) | 51.5147 | 0.362780 | ||||||||
\(143\) | 72.7461i | 0.508714i | ||||||||
\(144\) | 33.9411 | 0.235702 | ||||||||
\(145\) | 23.3062i | 0.160732i | ||||||||
\(146\) | 74.3973i | 0.509571i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.88225 | −0.0397449 | ||||||||
\(149\) | 92.3970 | 0.620114 | 0.310057 | − | 0.950718i | \(-0.399652\pi\) | ||||
0.310057 | + | 0.950718i | \(0.399652\pi\) | |||||||
\(150\) | − 19.2478i | − 0.128318i | ||||||||
\(151\) | −91.7868 | −0.607860 | −0.303930 | − | 0.952694i | \(-0.598299\pi\) | ||||
−0.303930 | + | 0.952694i | \(0.598299\pi\) | |||||||
\(152\) | − 11.8272i | − 0.0778104i | ||||||||
\(153\) | − 31.9155i | − 0.208598i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 324.037 | 2.09056 | ||||||||
\(156\) | 21.9411 | 0.140648 | ||||||||
\(157\) | 8.45631i | 0.0538618i | 0.999637 | + | 0.0269309i | \(0.00857341\pi\) | ||||
−0.999637 | + | 0.0269309i | \(0.991427\pi\) | |||||||
\(158\) | −47.7817 | −0.302416 | ||||||||
\(159\) | 40.1555i | 0.252550i | ||||||||
\(160\) | 37.5108i | 0.234442i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 95.2721 | 0.588099 | ||||||||
\(163\) | 221.978 | 1.36183 | 0.680913 | − | 0.732364i | \(-0.261583\pi\) | ||||
0.680913 | + | 0.732364i | \(0.261583\pi\) | |||||||
\(164\) | 55.9180i | 0.340963i | ||||||||
\(165\) | 22.6325 | 0.137166 | ||||||||
\(166\) | 180.422i | 1.08688i | ||||||||
\(167\) | − 168.841i | − 1.01102i | −0.862820 | − | 0.505511i | \(-0.831304\pi\) | ||||
0.862820 | − | 0.505511i | \(-0.168696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64.8234 | −0.383570 | ||||||||
\(170\) | 35.2721 | 0.207483 | ||||||||
\(171\) | − 35.4815i | − 0.207494i | ||||||||
\(172\) | −20.9706 | −0.121922 | ||||||||
\(173\) | 164.341i | 0.949947i | 0.880000 | + | 0.474974i | \(0.157542\pi\) | ||||
−0.880000 | + | 0.474974i | \(0.842458\pi\) | |||||||
\(174\) | 3.56608i | 0.0204947i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.0294 | −0.108122 | ||||||||
\(177\) | −27.7797 | −0.156947 | ||||||||
\(178\) | 71.1794i | 0.399884i | ||||||||
\(179\) | 185.184 | 1.03455 | 0.517273 | − | 0.855820i | \(-0.326947\pi\) | ||||
0.517273 | + | 0.855820i | \(0.326947\pi\) | |||||||
\(180\) | 112.532i | 0.625180i | ||||||||
\(181\) | 155.086i | 0.856830i | 0.903582 | + | 0.428415i | \(0.140928\pi\) | ||||
−0.903582 | + | 0.428415i | \(0.859072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −64.9340 | −0.354831 | ||||||||
\(184\) | −78.4264 | −0.426230 | ||||||||
\(185\) | − 19.5027i | − 0.105420i | ||||||||
\(186\) | 49.5807 | 0.266563 | ||||||||
\(187\) | 17.8937i | 0.0956884i | ||||||||
\(188\) | − 105.358i | − 0.560415i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 39.2132 | 0.206385 | ||||||||
\(191\) | 248.095 | 1.29893 | 0.649465 | − | 0.760392i | \(-0.274993\pi\) | ||||
0.649465 | + | 0.760392i | \(0.274993\pi\) | |||||||
\(192\) | 5.73951i | 0.0298933i | ||||||||
\(193\) | 154.338 | 0.799679 | 0.399840 | − | 0.916585i | \(-0.369066\pi\) | ||||
0.399840 | + | 0.916585i | \(0.369066\pi\) | |||||||
\(194\) | − 143.955i | − 0.742038i | ||||||||
\(195\) | 72.7461i | 0.373057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −181.103 | −0.919303 | −0.459651 | − | 0.888099i | \(-0.652026\pi\) | ||||
−0.459651 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(198\) | −57.0883 | −0.288325 | ||||||||
\(199\) | 348.707i | 1.75229i | 0.482043 | + | 0.876147i | \(0.339895\pi\) | ||||
−0.482043 | + | 0.876147i | \(0.660105\pi\) | |||||||
\(200\) | −53.6569 | −0.268284 | ||||||||
\(201\) | − 24.8518i | − 0.123641i | ||||||||
\(202\) | − 84.3992i | − 0.417818i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.39697 | 0.0264557 | ||||||||
\(205\) | −185.397 | −0.904375 | ||||||||
\(206\) | − 169.957i | − 0.825035i | ||||||||
\(207\) | −235.279 | −1.13661 | ||||||||
\(208\) | − 61.1651i | − 0.294063i | ||||||||
\(209\) | 19.8931i | 0.0951823i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 364.073 | 1.72547 | 0.862733 | − | 0.505660i | \(-0.168751\pi\) | ||||
0.862733 | + | 0.505660i | \(0.168751\pi\) | |||||||
\(212\) | 111.941 | 0.528024 | ||||||||
\(213\) | 26.1337i | 0.122694i | ||||||||
\(214\) | −160.669 | −0.750790 | ||||||||
\(215\) | − 69.5282i | − 0.323387i | ||||||||
\(216\) | 35.4815i | 0.164266i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −205.497 | −0.942649 | ||||||||
\(219\) | −37.7422 | −0.172339 | ||||||||
\(220\) | − 63.0924i | − 0.286784i | ||||||||
\(221\) | −57.5147 | −0.260248 | ||||||||
\(222\) | − 2.98410i | − 0.0134419i | ||||||||
\(223\) | − 123.231i | − 0.552603i | −0.961071 | − | 0.276302i | \(-0.910891\pi\) | ||||
0.961071 | − | 0.276302i | \(-0.0891089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −160.971 | −0.715425 | ||||||||
\(226\) | 48.8528 | 0.216163 | ||||||||
\(227\) | − 76.3756i | − 0.336456i | −0.985748 | − | 0.168228i | \(-0.946195\pi\) | ||||
0.985748 | − | 0.168228i | \(-0.0538045\pi\) | |||||||
\(228\) | 6.00000 | 0.0263158 | ||||||||
\(229\) | − 357.286i | − 1.56020i | −0.625654 | − | 0.780101i | \(-0.715168\pi\) | ||||
0.625654 | − | 0.780101i | \(-0.284832\pi\) | |||||||
\(230\) | − 260.024i | − 1.13054i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.94113 | 0.0428497 | ||||||||
\(233\) | −273.073 | −1.17199 | −0.585994 | − | 0.810315i | \(-0.699296\pi\) | ||||
−0.585994 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(234\) | − 183.495i | − 0.784168i | ||||||||
\(235\) | 349.316 | 1.48645 | ||||||||
\(236\) | 77.4412i | 0.328141i | ||||||||
\(237\) | − 24.2400i | − 0.102278i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −265.103 | −1.10922 | −0.554608 | − | 0.832112i | \(-0.687132\pi\) | ||||
−0.554608 | + | 0.832112i | \(0.687132\pi\) | |||||||
\(240\) | −19.0294 | −0.0792893 | ||||||||
\(241\) | − 87.6383i | − 0.363644i | −0.983331 | − | 0.181822i | \(-0.941800\pi\) | ||||
0.983331 | − | 0.181822i | \(-0.0581995\pi\) | |||||||
\(242\) | −139.113 | −0.574846 | ||||||||
\(243\) | 161.234i | 0.663513i | ||||||||
\(244\) | 181.016i | 0.741869i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.3675 | −0.115315 | ||||||||
\(247\) | −63.9411 | −0.258871 | ||||||||
\(248\) | − 138.216i | − 0.557322i | ||||||||
\(249\) | −91.5290 | −0.367586 | ||||||||
\(250\) | 56.5422i | 0.226169i | ||||||||
\(251\) | 495.655i | 1.97472i | 0.158491 | + | 0.987360i | \(0.449337\pi\) | ||||
−0.158491 | + | 0.987360i | \(0.550663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.912 | 0.521390 | ||||||||
\(254\) | −349.789 | −1.37712 | ||||||||
\(255\) | 17.8937i | 0.0701715i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 400.536i | − 1.55851i | −0.626709 | − | 0.779254i | \(-0.715598\pi\) | ||||
0.626709 | − | 0.779254i | \(-0.284402\pi\) | |||||||
\(258\) | − 10.6385i | − 0.0412345i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 202.794 | 0.779977 | ||||||||
\(261\) | 29.8234 | 0.114266 | ||||||||
\(262\) | 208.801i | 0.796950i | ||||||||
\(263\) | −32.3452 | −0.122986 | −0.0614928 | − | 0.998108i | \(-0.519586\pi\) | ||||
−0.0614928 | + | 0.998108i | \(0.519586\pi\) | |||||||
\(264\) | − 9.65375i | − 0.0365672i | ||||||||
\(265\) | 371.142i | 1.40054i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.1097 | −0.135242 | ||||||||
\(268\) | −69.2792 | −0.258505 | ||||||||
\(269\) | − 306.963i | − 1.14113i | −0.821253 | − | 0.570564i | \(-0.806725\pi\) | ||||
0.821253 | − | 0.570564i | \(-0.193275\pi\) | |||||||
\(270\) | −117.640 | −0.435702 | ||||||||
\(271\) | 75.9852i | 0.280388i | 0.990124 | + | 0.140194i | \(0.0447726\pi\) | ||||
−0.990124 | + | 0.140194i | \(0.955227\pi\) | |||||||
\(272\) | − 15.0451i | − 0.0553129i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −46.0660 | −0.168124 | ||||||||
\(275\) | 90.2498 | 0.328181 | ||||||||
\(276\) | − 39.7862i | − 0.144153i | ||||||||
\(277\) | 278.411 | 1.00509 | 0.502547 | − | 0.864550i | \(-0.332396\pi\) | ||||
0.502547 | + | 0.864550i | \(0.332396\pi\) | |||||||
\(278\) | − 96.9948i | − 0.348902i | ||||||||
\(279\) | − 414.648i | − 1.48619i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 394.690 | 1.40459 | 0.702296 | − | 0.711885i | \(-0.252158\pi\) | ||||
0.702296 | + | 0.711885i | \(0.252158\pi\) | |||||||
\(282\) | 53.4487 | 0.189534 | ||||||||
\(283\) | 146.396i | 0.517301i | 0.965971 | + | 0.258650i | \(0.0832778\pi\) | ||||
−0.965971 | + | 0.258650i | \(0.916722\pi\) | |||||||
\(284\) | 72.8528 | 0.256524 | ||||||||
\(285\) | 19.8931i | 0.0698003i | ||||||||
\(286\) | 102.879i | 0.359715i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 48.0000 | 0.166667 | ||||||||
\(289\) | 274.853 | 0.951048 | ||||||||
\(290\) | 32.9600i | 0.113655i | ||||||||
\(291\) | 73.0294 | 0.250960 | ||||||||
\(292\) | 105.214i | 0.360321i | ||||||||
\(293\) | − 299.678i | − 1.02279i | −0.859345 | − | 0.511396i | \(-0.829128\pi\) | ||||
0.859345 | − | 0.511396i | \(-0.170872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −256.757 | −0.870364 | ||||||||
\(296\) | −8.31876 | −0.0281039 | ||||||||
\(297\) | − 59.6793i | − 0.200940i | ||||||||
\(298\) | 130.669 | 0.438487 | ||||||||
\(299\) | 423.996i | 1.41805i | ||||||||
\(300\) | − 27.2204i | − 0.0907348i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −129.806 | −0.429822 | ||||||||
\(303\) | 42.8162 | 0.141308 | ||||||||
\(304\) | − 16.7262i | − 0.0550203i | ||||||||
\(305\) | −600.161 | −1.96774 | ||||||||
\(306\) | − 45.1353i | − 0.147501i | ||||||||
\(307\) | 20.9886i | 0.0683666i | 0.999416 | + | 0.0341833i | \(0.0108830\pi\) | ||||
−0.999416 | + | 0.0341833i | \(0.989117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 86.2203 | 0.279030 | ||||||||
\(310\) | 458.257 | 1.47825 | ||||||||
\(311\) | 182.039i | 0.585336i | 0.956214 | + | 0.292668i | \(0.0945430\pi\) | ||||
−0.956214 | + | 0.292668i | \(0.905457\pi\) | |||||||
\(312\) | 31.0294 | 0.0994533 | ||||||||
\(313\) | 97.9286i | 0.312871i | 0.987688 | + | 0.156435i | \(0.0500003\pi\) | ||||
−0.987688 | + | 0.156435i | \(0.950000\pi\) | |||||||
\(314\) | 11.9590i | 0.0380861i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −67.5736 | −0.213840 | ||||||||
\(317\) | −481.971 | −1.52041 | −0.760206 | − | 0.649682i | \(-0.774902\pi\) | ||||
−0.760206 | + | 0.649682i | \(0.774902\pi\) | |||||||
\(318\) | 56.7884i | 0.178580i | ||||||||
\(319\) | −16.7208 | −0.0524162 | ||||||||
\(320\) | 53.0482i | 0.165776i | ||||||||
\(321\) | − 81.5084i | − 0.253920i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.7279 | −0.0486933 | ||||||||
\(324\) | 134.735 | 0.415849 | ||||||||
\(325\) | 290.084i | 0.892567i | ||||||||
\(326\) | 313.924 | 0.962957 | ||||||||
\(327\) | − 104.250i | − 0.318808i | ||||||||
\(328\) | 79.0800i | 0.241098i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 32.0071 | 0.0969913 | ||||||||
\(331\) | 225.007 | 0.679780 | 0.339890 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339890 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(332\) | 255.155i | 0.768539i | ||||||||
\(333\) | −24.9563 | −0.0749438 | ||||||||
\(334\) | − 238.777i | − 0.714901i | ||||||||
\(335\) | − 229.696i | − 0.685661i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −264.368 | −0.784473 | −0.392237 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392237 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(338\) | −91.6741 | −0.271225 | ||||||||
\(339\) | 24.7833i | 0.0731071i | ||||||||
\(340\) | 49.8823 | 0.146713 | ||||||||
\(341\) | 232.476i | 0.681749i | ||||||||
\(342\) | − 50.1785i | − 0.146721i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −29.6569 | −0.0862118 | ||||||||
\(345\) | 131.912 | 0.382353 | ||||||||
\(346\) | 232.413i | 0.671714i | ||||||||
\(347\) | −191.257 | −0.551173 | −0.275586 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275586 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(348\) | 5.04319i | 0.0144919i | ||||||||
\(349\) | − 135.448i | − 0.388104i | −0.980991 | − | 0.194052i | \(-0.937837\pi\) | ||||
0.980991 | − | 0.194052i | \(-0.0621630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 191.823 | 0.546505 | ||||||||
\(352\) | −26.9117 | −0.0764537 | ||||||||
\(353\) | − 348.490i | − 0.987225i | −0.869682 | − | 0.493612i | \(-0.835676\pi\) | ||||
0.869682 | − | 0.493612i | \(-0.164324\pi\) | |||||||
\(354\) | −39.2864 | −0.110978 | ||||||||
\(355\) | 241.545i | 0.680407i | ||||||||
\(356\) | 100.663i | 0.282761i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 261.889 | 0.731535 | ||||||||
\(359\) | 304.831 | 0.849110 | 0.424555 | − | 0.905402i | \(-0.360431\pi\) | ||||
0.424555 | + | 0.905402i | \(0.360431\pi\) | |||||||
\(360\) | 159.145i | 0.442069i | ||||||||
\(361\) | 343.515 | 0.951564 | ||||||||
\(362\) | 219.325i | 0.605870i | ||||||||
\(363\) | − 70.5727i | − 0.194415i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −348.838 | −0.955720 | ||||||||
\(366\) | −91.8305 | −0.250903 | ||||||||
\(367\) | − 95.0042i | − 0.258867i | −0.991588 | − | 0.129434i | \(-0.958684\pi\) | ||||
0.991588 | − | 0.129434i | \(-0.0413159\pi\) | |||||||
\(368\) | −110.912 | −0.301390 | ||||||||
\(369\) | 237.240i | 0.642927i | ||||||||
\(370\) | − 27.5810i | − 0.0745432i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 70.1177 | 0.188489 | ||||||||
\(373\) | 253.558 | 0.679781 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(374\) | 25.3056i | 0.0676619i | ||||||||
\(375\) | −28.6842 | −0.0764912 | ||||||||
\(376\) | − 148.999i | − 0.396273i | ||||||||
\(377\) | − 53.7446i | − 0.142559i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 508.250 | 1.34103 | 0.670514 | − | 0.741897i | \(-0.266074\pi\) | ||||
0.670514 | + | 0.741897i | \(0.266074\pi\) | |||||||
\(380\) | 55.4558 | 0.145936 | ||||||||
\(381\) | − 177.450i | − 0.465748i | ||||||||
\(382\) | 350.860 | 0.918482 | ||||||||
\(383\) | − 477.761i | − 1.24742i | −0.781656 | − | 0.623709i | \(-0.785625\pi\) | ||||
0.781656 | − | 0.623709i | \(-0.214375\pi\) | |||||||
\(384\) | 8.11689i | 0.0211377i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 218.267 | 0.565459 | ||||||||
\(387\) | −88.9706 | −0.229898 | ||||||||
\(388\) | − 203.584i | − 0.524700i | ||||||||
\(389\) | 170.220 | 0.437584 | 0.218792 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218792 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(390\) | 102.879i | 0.263791i | ||||||||
\(391\) | 104.292i | 0.266732i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −105.926 | −0.269532 | ||||||||
\(394\) | −256.118 | −0.650045 | ||||||||
\(395\) | − 224.041i | − 0.567193i | ||||||||
\(396\) | −80.7351 | −0.203876 | ||||||||
\(397\) | − 244.550i | − 0.615995i | −0.951387 | − | 0.307997i | \(-0.900341\pi\) | ||||
0.951387 | − | 0.307997i | \(-0.0996588\pi\) | |||||||
\(398\) | 493.146i | 1.23906i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −75.8823 | −0.189706 | ||||||||
\(401\) | −417.573 | −1.04133 | −0.520664 | − | 0.853762i | \(-0.674316\pi\) | ||||
−0.520664 | + | 0.853762i | \(0.674316\pi\) | |||||||
\(402\) | − 35.1458i | − 0.0874273i | ||||||||
\(403\) | −747.235 | −1.85418 | ||||||||
\(404\) | − 119.359i | − 0.295442i | ||||||||
\(405\) | 446.716i | 1.10300i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.9920 | 0.0343784 | ||||||||
\(408\) | 7.63247 | 0.0187070 | ||||||||
\(409\) | 308.212i | 0.753574i | 0.926300 | + | 0.376787i | \(0.122971\pi\) | ||||
−0.926300 | + | 0.376787i | \(0.877029\pi\) | |||||||
\(410\) | −262.191 | −0.639490 | ||||||||
\(411\) | − 23.3696i | − 0.0568603i | ||||||||
\(412\) | − 240.356i | − 0.583388i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −332.735 | −0.803708 | ||||||||
\(415\) | −845.970 | −2.03848 | ||||||||
\(416\) | − 86.5006i | − 0.207934i | ||||||||
\(417\) | 49.2061 | 0.118000 | ||||||||
\(418\) | 28.1331i | 0.0673040i | ||||||||
\(419\) | 103.142i | 0.246163i | 0.992397 | + | 0.123081i | \(0.0392776\pi\) | ||||
−0.992397 | + | 0.123081i | \(0.960722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −165.220 | −0.392447 | −0.196224 | − | 0.980559i | \(-0.562868\pi\) | ||||
−0.196224 | + | 0.980559i | \(0.562868\pi\) | |||||||
\(422\) | 514.877 | 1.22009 | ||||||||
\(423\) | − 446.996i | − 1.05673i | ||||||||
\(424\) | 158.309 | 0.373369 | ||||||||
\(425\) | 71.3535i | 0.167891i | ||||||||
\(426\) | 36.9587i | 0.0867574i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −227.220 | −0.530889 | ||||||||
\(429\) | −52.1909 | −0.121657 | ||||||||
\(430\) | − 98.3277i | − 0.228669i | ||||||||
\(431\) | 594.536 | 1.37943 | 0.689717 | − | 0.724079i | \(-0.257735\pi\) | ||||
0.689717 | + | 0.724079i | \(0.257735\pi\) | |||||||
\(432\) | 50.1785i | 0.116154i | ||||||||
\(433\) | 40.6267i | 0.0938261i | 0.998899 | + | 0.0469131i | \(0.0149384\pi\) | ||||
−0.998899 | + | 0.0469131i | \(0.985062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.7208 | −0.0384386 | ||||||||
\(436\) | −290.617 | −0.666553 | ||||||||
\(437\) | 115.945i | 0.265321i | ||||||||
\(438\) | −53.3755 | −0.121862 | ||||||||
\(439\) | − 146.600i | − 0.333941i | −0.985962 | − | 0.166971i | \(-0.946602\pi\) | ||||
0.985962 | − | 0.166971i | \(-0.0533985\pi\) | |||||||
\(440\) | − 89.2261i | − 0.202787i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −81.3381 | −0.184023 | ||||||||
\(443\) | 107.360 | 0.242349 | 0.121174 | − | 0.992631i | \(-0.461334\pi\) | ||||
0.121174 | + | 0.992631i | \(0.461334\pi\) | |||||||
\(444\) | − 4.22016i | − 0.00950486i | ||||||||
\(445\) | −333.749 | −0.749999 | ||||||||
\(446\) | − 174.274i | − 0.390750i | ||||||||
\(447\) | 66.2892i | 0.148298i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 135.161 | 0.301028 | 0.150514 | − | 0.988608i | \(-0.451907\pi\) | ||||
0.150514 | + | 0.988608i | \(0.451907\pi\) | |||||||
\(450\) | −227.647 | −0.505882 | ||||||||
\(451\) | − 133.011i | − 0.294925i | ||||||||
\(452\) | 69.0883 | 0.152850 | ||||||||
\(453\) | − 65.8514i | − 0.145367i | ||||||||
\(454\) | − 108.011i | − 0.237910i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.48528 | 0.0186081 | ||||||||
\(457\) | 159.735 | 0.349530 | 0.174765 | − | 0.984610i | \(-0.444083\pi\) | ||||
0.174765 | + | 0.984610i | \(0.444083\pi\) | |||||||
\(458\) | − 505.279i | − 1.10323i | ||||||||
\(459\) | 47.1838 | 0.102797 | ||||||||
\(460\) | − 367.729i | − 0.799412i | ||||||||
\(461\) | − 310.250i | − 0.672993i | −0.941685 | − | 0.336497i | \(-0.890758\pi\) | ||||
0.941685 | − | 0.336497i | \(-0.109242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −326.014 | −0.704135 | −0.352067 | − | 0.935975i | \(-0.614521\pi\) | ||||
−0.352067 | + | 0.935975i | \(0.614521\pi\) | |||||||
\(464\) | 14.0589 | 0.0302993 | ||||||||
\(465\) | 232.476i | 0.499949i | ||||||||
\(466\) | −386.184 | −0.828721 | ||||||||
\(467\) | − 595.558i | − 1.27529i | −0.770332 | − | 0.637643i | \(-0.779910\pi\) | ||||
0.770332 | − | 0.637643i | \(-0.220090\pi\) | |||||||
\(468\) | − 259.502i | − 0.554491i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 494.007 | 1.05108 | ||||||||
\(471\) | −6.06688 | −0.0128809 | ||||||||
\(472\) | 109.518i | 0.232030i | ||||||||
\(473\) | 49.8823 | 0.105459 | ||||||||
\(474\) | − 34.2805i | − 0.0723217i | ||||||||
\(475\) | 79.3262i | 0.167002i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 474.926 | 0.995652 | ||||||||
\(478\) | −374.912 | −0.784334 | ||||||||
\(479\) | 506.680i | 1.05779i | 0.848688 | + | 0.528894i | \(0.177393\pi\) | ||||
−0.848688 | + | 0.528894i | \(0.822607\pi\) | |||||||
\(480\) | −26.9117 | −0.0560660 | ||||||||
\(481\) | 44.9736i | 0.0935002i | ||||||||
\(482\) | − 123.939i | − 0.257135i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −196.735 | −0.406477 | ||||||||
\(485\) | 674.985 | 1.39172 | ||||||||
\(486\) | 228.019i | 0.469175i | ||||||||
\(487\) | 211.302 | 0.433884 | 0.216942 | − | 0.976184i | \(-0.430392\pi\) | ||||
0.216942 | + | 0.976184i | \(0.430392\pi\) | |||||||
\(488\) | 255.995i | 0.524581i | ||||||||
\(489\) | 159.255i | 0.325676i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −784.161 | −1.59707 | −0.798534 | − | 0.601949i | \(-0.794391\pi\) | ||||
−0.798534 | + | 0.601949i | \(0.794391\pi\) | |||||||
\(492\) | −40.1177 | −0.0815401 | ||||||||
\(493\) | − 13.2198i | − 0.0268151i | ||||||||
\(494\) | −90.4264 | −0.183049 | ||||||||
\(495\) | − 267.678i | − 0.540764i | ||||||||
\(496\) | − 195.467i | − 0.394086i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −129.442 | −0.259923 | ||||||||
\(499\) | −171.492 | −0.343672 | −0.171836 | − | 0.985126i | \(-0.554970\pi\) | ||||
−0.171836 | + | 0.985126i | \(0.554970\pi\) | |||||||
\(500\) | 79.9628i | 0.159926i | ||||||||
\(501\) | 121.133 | 0.241782 | ||||||||
\(502\) | 700.962i | 1.39634i | ||||||||
\(503\) | 20.0883i | 0.0399370i | 0.999801 | + | 0.0199685i | \(0.00635659\pi\) | ||||
−0.999801 | + | 0.0199685i | \(0.993643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 395.735 | 0.783634 | ||||||||
\(506\) | 186.551 | 0.368678 | ||||||||
\(507\) | − 46.5068i | − 0.0917294i | ||||||||
\(508\) | −494.676 | −0.973772 | ||||||||
\(509\) | 476.764i | 0.936668i | 0.883551 | + | 0.468334i | \(0.155146\pi\) | ||||
−0.883551 | + | 0.468334i | \(0.844854\pi\) | |||||||
\(510\) | 25.3056i | 0.0496187i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 52.4558 | 0.102253 | ||||||||
\(514\) | − 566.444i | − 1.10203i | ||||||||
\(515\) | 796.904 | 1.54739 | ||||||||
\(516\) | − 15.0451i | − 0.0291572i | ||||||||
\(517\) | 250.613i | 0.484744i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −117.905 | −0.227176 | ||||||||
\(520\) | 286.794 | 0.551527 | ||||||||
\(521\) | 854.274i | 1.63968i | 0.572592 | + | 0.819841i | \(0.305938\pi\) | ||||
−0.572592 | + | 0.819841i | \(0.694062\pi\) | |||||||
\(522\) | 42.1766 | 0.0807981 | ||||||||
\(523\) | 593.002i | 1.13385i | 0.823771 | + | 0.566923i | \(0.191866\pi\) | ||||
−0.823771 | + | 0.566923i | \(0.808134\pi\) | |||||||
\(524\) | 295.289i | 0.563529i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.7431 | −0.0869640 | ||||||||
\(527\) | −183.801 | −0.348769 | ||||||||
\(528\) | − 13.6525i | − 0.0258569i | ||||||||
\(529\) | 239.838 | 0.453379 | ||||||||
\(530\) | 524.875i | 0.990330i | ||||||||
\(531\) | 328.555i | 0.618748i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 427.529 | 0.802118 | ||||||||
\(534\) | −51.0669 | −0.0956309 | ||||||||
\(535\) | − 753.352i | − 1.40814i | ||||||||
\(536\) | −97.9756 | −0.182790 | ||||||||
\(537\) | 132.858i | 0.247408i | ||||||||
\(538\) | − 434.112i | − 0.806899i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −166.368 | −0.308088 | ||||||||
\(541\) | 855.191 | 1.58076 | 0.790380 | − | 0.612617i | \(-0.209883\pi\) | ||||
0.790380 | + | 0.612617i | \(0.209883\pi\) | |||||||
\(542\) | 107.459i | 0.198264i | ||||||||
\(543\) | −111.265 | −0.204908 | ||||||||
\(544\) | − 21.2770i | − 0.0391121i | ||||||||
\(545\) | − 963.546i | − 1.76797i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 415.897 | 0.760323 | 0.380161 | − | 0.924920i | \(-0.375868\pi\) | ||||
0.380161 | + | 0.924920i | \(0.375868\pi\) | |||||||
\(548\) | −65.1472 | −0.118882 | ||||||||
\(549\) | 767.986i | 1.39888i | ||||||||
\(550\) | 127.632 | 0.232059 | ||||||||
\(551\) | − 14.6969i | − 0.0266732i | ||||||||
\(552\) | − 56.2662i | − 0.101931i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 393.733 | 0.710709 | ||||||||
\(555\) | 13.9920 | 0.0252108 | ||||||||
\(556\) | − 137.171i | − 0.246711i | ||||||||
\(557\) | −584.220 | −1.04887 | −0.524435 | − | 0.851451i | \(-0.675723\pi\) | ||||
−0.524435 | + | 0.851451i | \(0.675723\pi\) | |||||||
\(558\) | − 586.400i | − 1.05090i | ||||||||
\(559\) | 160.333i | 0.286822i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8377 | −0.0228835 | ||||||||
\(562\) | 558.177 | 0.993197 | ||||||||
\(563\) | 911.147i | 1.61838i | 0.587548 | + | 0.809189i | \(0.300093\pi\) | ||||
−0.587548 | + | 0.809189i | \(0.699907\pi\) | |||||||
\(564\) | 75.5879 | 0.134021 | ||||||||
\(565\) | 229.063i | 0.405422i | ||||||||
\(566\) | 207.035i | 0.365787i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 103.029 | 0.181390 | ||||||||
\(569\) | 699.999 | 1.23023 | 0.615113 | − | 0.788439i | \(-0.289110\pi\) | ||||
0.615113 | + | 0.788439i | \(0.289110\pi\) | |||||||
\(570\) | 28.1331i | 0.0493563i | ||||||||
\(571\) | −562.463 | −0.985049 | −0.492525 | − | 0.870299i | \(-0.663926\pi\) | ||||
−0.492525 | + | 0.870299i | \(0.663926\pi\) | |||||||
\(572\) | 145.492i | 0.254357i | ||||||||
\(573\) | 177.993i | 0.310634i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 526.014 | 0.914807 | ||||||||
\(576\) | 67.8823 | 0.117851 | ||||||||
\(577\) | − 661.659i | − 1.14672i | −0.819302 | − | 0.573362i | \(-0.805639\pi\) | ||||
0.819302 | − | 0.573362i | \(-0.194361\pi\) | |||||||
\(578\) | 388.701 | 0.672492 | ||||||||
\(579\) | 110.728i | 0.191240i | ||||||||
\(580\) | 46.6124i | 0.0803662i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 103.279 | 0.177456 | ||||||||
\(583\) | −266.272 | −0.456727 | ||||||||
\(584\) | 148.795i | 0.254785i | ||||||||
\(585\) | 860.382 | 1.47074 | ||||||||
\(586\) | − 423.809i | − 0.723224i | ||||||||
\(587\) | 823.029i | 1.40209i | 0.713116 | + | 0.701046i | \(0.247283\pi\) | ||||
−0.713116 | + | 0.701046i | \(0.752717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204.338 | −0.346924 | ||||||||
\(590\) | −363.110 | −0.615440 | ||||||||
\(591\) | − 129.930i | − 0.219848i | ||||||||
\(592\) | −11.7645 | −0.0198725 | ||||||||
\(593\) | 622.256i | 1.04934i | 0.851307 | + | 0.524668i | \(0.175811\pi\) | ||||
−0.851307 | + | 0.524668i | \(0.824189\pi\) | |||||||
\(594\) | − 84.3992i | − 0.142086i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 184.794 | 0.310057 | ||||||||
\(597\) | −250.176 | −0.419055 | ||||||||
\(598\) | 599.620i | 1.00271i | ||||||||
\(599\) | −512.845 | −0.856168 | −0.428084 | − | 0.903739i | \(-0.640811\pi\) | ||||
−0.428084 | + | 0.903739i | \(0.640811\pi\) | |||||||
\(600\) | − 38.4955i | − 0.0641592i | ||||||||
\(601\) | − 680.160i | − 1.13171i | −0.824504 | − | 0.565857i | \(-0.808546\pi\) | ||||
0.824504 | − | 0.565857i | \(-0.191454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −293.927 | −0.487441 | ||||||||
\(604\) | −183.574 | −0.303930 | ||||||||
\(605\) | − 652.278i | − 1.07815i | ||||||||
\(606\) | 60.5513 | 0.0999196 | ||||||||
\(607\) | − 38.7381i | − 0.0638189i | −0.999491 | − | 0.0319095i | \(-0.989841\pi\) | ||||
0.999491 | − | 0.0319095i | \(-0.0101588\pi\) | |||||||
\(608\) | − 23.6544i | − 0.0389052i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −848.756 | −1.39140 | ||||||||
\(611\) | −805.529 | −1.31838 | ||||||||
\(612\) | − 63.8309i | − 0.104299i | ||||||||
\(613\) | 401.103 | 0.654329 | 0.327164 | − | 0.944967i | \(-0.393907\pi\) | ||||
0.327164 | + | 0.944967i | \(0.393907\pi\) | |||||||
\(614\) | 29.6823i | 0.0483425i | ||||||||
\(615\) | − 133.011i | − 0.216278i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −959.044 | −1.55437 | −0.777183 | − | 0.629275i | \(-0.783352\pi\) | ||||
−0.777183 | + | 0.629275i | \(0.783352\pi\) | |||||||
\(618\) | 121.934 | 0.197304 | ||||||||
\(619\) | − 1004.53i | − 1.62283i | −0.584469 | − | 0.811416i | \(-0.698697\pi\) | ||||
0.584469 | − | 0.811416i | \(-0.301303\pi\) | |||||||
\(620\) | 648.073 | 1.04528 | ||||||||
\(621\) | − 347.836i | − 0.560123i | ||||||||
\(622\) | 257.443i | 0.413895i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 43.8823 | 0.0703241 | ||||||||
\(625\) | −739.382 | −1.18301 | ||||||||
\(626\) | 138.492i | 0.221233i | ||||||||
\(627\) | −14.2721 | −0.0227625 | ||||||||
\(628\) | 16.9126i | 0.0269309i | ||||||||
\(629\) | 11.0624i | 0.0175873i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −386.514 | −0.612542 | −0.306271 | − | 0.951944i | \(-0.599081\pi\) | ||||
−0.306271 | + | 0.951944i | \(0.599081\pi\) | |||||||
\(632\) | −95.5635 | −0.151208 | ||||||||
\(633\) | 261.200i | 0.412639i | ||||||||
\(634\) | −681.609 | −1.07509 | ||||||||
\(635\) | − 1640.11i | − 2.58284i | ||||||||
\(636\) | 80.3109i | 0.126275i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −23.6468 | −0.0370639 | ||||||||
\(639\) | 309.088 | 0.483706 | ||||||||
\(640\) | 75.0215i | 0.117221i | ||||||||
\(641\) | −992.147 | −1.54781 | −0.773906 | − | 0.633301i | \(-0.781700\pi\) | ||||
−0.773906 | + | 0.633301i | \(0.781700\pi\) | |||||||
\(642\) | − 115.270i | − 0.179549i | ||||||||
\(643\) | − 944.986i | − 1.46965i | −0.678256 | − | 0.734826i | \(-0.737264\pi\) | ||||
0.678256 | − | 0.734826i | \(-0.262736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.8823 | 0.0773368 | ||||||||
\(646\) | −22.2426 | −0.0344313 | ||||||||
\(647\) | 2.89088i | 0.00446812i | 0.999998 | + | 0.00223406i | \(0.000711124\pi\) | ||||
−0.999998 | + | 0.00223406i | \(0.999289\pi\) | |||||||
\(648\) | 190.544 | 0.294050 | ||||||||
\(649\) | − 184.208i | − 0.283833i | ||||||||
\(650\) | 410.241i | 0.631140i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 443.955 | 0.680913 | ||||||||
\(653\) | −323.059 | −0.494730 | −0.247365 | − | 0.968922i | \(-0.579565\pi\) | ||||
−0.247365 | + | 0.968922i | \(0.579565\pi\) | |||||||
\(654\) | − 147.432i | − 0.225431i | ||||||||
\(655\) | −979.036 | −1.49471 | ||||||||
\(656\) | 111.836i | 0.170482i | ||||||||
\(657\) | 446.384i | 0.679428i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 295.955 | 0.449098 | 0.224549 | − | 0.974463i | \(-0.427909\pi\) | ||||
0.224549 | + | 0.974463i | \(0.427909\pi\) | |||||||
\(660\) | 45.2649 | 0.0685832 | ||||||||
\(661\) | 20.7511i | 0.0313935i | 0.999877 | + | 0.0156968i | \(0.00499664\pi\) | ||||
−0.999877 | + | 0.0156968i | \(0.995003\pi\) | |||||||
\(662\) | 318.208 | 0.480677 | ||||||||
\(663\) | − 41.2633i | − 0.0622373i | ||||||||
\(664\) | 360.843i | 0.543439i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −35.2935 | −0.0529933 | ||||||||
\(667\) | −97.4558 | −0.146111 | ||||||||
\(668\) | − 337.681i | − 0.505511i | ||||||||
\(669\) | 88.4104 | 0.132153 | ||||||||
\(670\) | − 324.840i | − 0.484835i | ||||||||
\(671\) | − 430.579i | − 0.641698i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 627.044 | 0.931714 | 0.465857 | − | 0.884860i | \(-0.345746\pi\) | ||||
0.465857 | + | 0.884860i | \(0.345746\pi\) | |||||||
\(674\) | −373.872 | −0.554706 | ||||||||
\(675\) | − 237.979i | − 0.352561i | ||||||||
\(676\) | −129.647 | −0.191785 | ||||||||
\(677\) | 109.246i | 0.161368i | 0.996740 | + | 0.0806838i | \(0.0257104\pi\) | ||||
−0.996740 | + | 0.0806838i | \(0.974290\pi\) | |||||||
\(678\) | 35.0489i | 0.0516946i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 70.5442 | 0.103741 | ||||||||
\(681\) | 54.7948 | 0.0804623 | ||||||||
\(682\) | 328.771i | 0.482069i | ||||||||
\(683\) | 793.566 | 1.16188 | 0.580941 | − | 0.813946i | \(-0.302685\pi\) | ||||
0.580941 | + | 0.813946i | \(0.302685\pi\) | |||||||
\(684\) | − 70.9631i | − 0.103747i | ||||||||
\(685\) | − 215.996i | − 0.315323i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 256.331 | 0.373116 | ||||||||
\(688\) | −41.9411 | −0.0609609 | ||||||||
\(689\) | − 855.862i | − 1.24218i | ||||||||
\(690\) | 186.551 | 0.270364 | ||||||||
\(691\) | − 183.889i | − 0.266121i | −0.991108 | − | 0.133060i | \(-0.957520\pi\) | ||||
0.991108 | − | 0.133060i | \(-0.0424804\pi\) | |||||||
\(692\) | 328.682i | 0.474974i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −270.478 | −0.389738 | ||||||||
\(695\) | 454.794 | 0.654380 | ||||||||
\(696\) | 7.13215i | 0.0102473i | ||||||||
\(697\) | 105.161 | 0.150877 | ||||||||
\(698\) | − 191.553i | − 0.274431i | ||||||||
\(699\) | − 195.913i | − 0.280277i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1043.82 | −1.48905 | −0.744525 | − | 0.667595i | \(-0.767324\pi\) | ||||
−0.744525 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(702\) | 271.279 | 0.386438 | ||||||||
\(703\) | 12.2984i | 0.0174942i | ||||||||
\(704\) | −38.0589 | −0.0540609 | ||||||||
\(705\) | 250.613i | 0.355479i | ||||||||
\(706\) | − 492.840i | − 0.698073i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −55.5593 | −0.0784736 | ||||||||
\(709\) | −980.558 | −1.38301 | −0.691507 | − | 0.722369i | \(-0.743053\pi\) | ||||
−0.691507 | + | 0.722369i | \(0.743053\pi\) | |||||||
\(710\) | 341.596i | 0.481121i | ||||||||
\(711\) | −286.690 | −0.403221 | ||||||||
\(712\) | 142.359i | 0.199942i | ||||||||
\(713\) | 1354.97i | 1.90038i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −482.382 | −0.674660 | ||||||||
\(716\) | 370.368 | 0.517273 | ||||||||
\(717\) | − 190.195i | − 0.265265i | ||||||||
\(718\) | 431.095 | 0.600411 | ||||||||
\(719\) | 778.484i | 1.08273i | 0.840787 | + | 0.541366i | \(0.182093\pi\) | ||||
−0.840787 | + | 0.541366i | \(0.817907\pi\) | |||||||
\(720\) | 225.065i | 0.312590i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 485.803 | 0.672858 | ||||||||
\(723\) | 62.8751 | 0.0869642 | ||||||||
\(724\) | 310.173i | 0.428415i | ||||||||
\(725\) | −66.6762 | −0.0919672 | ||||||||
\(726\) | − 99.8049i | − 0.137472i | ||||||||
\(727\) | 735.255i | 1.01135i | 0.862723 | + | 0.505677i | \(0.168757\pi\) | ||||
−0.862723 | + | 0.505677i | \(0.831243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 490.632 | 0.673021 | ||||||||
\(730\) | −493.331 | −0.675796 | ||||||||
\(731\) | 39.4380i | 0.0539508i | ||||||||
\(732\) | −129.868 | −0.177415 | ||||||||
\(733\) | 478.860i | 0.653288i | 0.945147 | + | 0.326644i | \(0.105918\pi\) | ||||
−0.945147 | + | 0.326644i | \(0.894082\pi\) | |||||||
\(734\) | − 134.356i | − 0.183047i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −156.853 | −0.213115 | ||||||||
\(737\) | 164.793 | 0.223600 | ||||||||
\(738\) | 335.508i | 0.454618i | ||||||||
\(739\) | −19.9045 | −0.0269344 | −0.0134672 | − | 0.999909i | \(-0.504287\pi\) | ||||
−0.0134672 | + | 0.999909i | \(0.504287\pi\) | |||||||
\(740\) | − 39.0054i | − 0.0527100i | ||||||||
\(741\) | − 45.8739i | − 0.0619080i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.3095 | 0.0582901 | 0.0291450 | − | 0.999575i | \(-0.490722\pi\) | ||||
0.0291450 | + | 0.999575i | \(0.490722\pi\) | |||||||
\(744\) | 99.1615 | 0.133282 | ||||||||
\(745\) | 612.687i | 0.822399i | ||||||||
\(746\) | 358.586 | 0.480678 | ||||||||
\(747\) | 1082.53i | 1.44917i | ||||||||
\(748\) | 35.7875i | 0.0478442i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −40.5656 | −0.0540874 | ||||||||
\(751\) | 225.330 | 0.300040 | 0.150020 | − | 0.988683i | \(-0.452066\pi\) | ||||
0.150020 | + | 0.988683i | \(0.452066\pi\) | |||||||
\(752\) | − 210.716i | − 0.280207i | ||||||||
\(753\) | −355.602 | −0.472247 | ||||||||
\(754\) | − 76.0063i | − 0.100804i | ||||||||
\(755\) | − 608.641i | − 0.806147i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 935.779 | 1.23617 | 0.618084 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618084 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(758\) | 718.774 | 0.948250 | ||||||||
\(759\) | 94.6386i | 0.124689i | ||||||||
\(760\) | 78.4264 | 0.103193 | ||||||||
\(761\) | − 1402.71i | − 1.84325i | −0.388081 | − | 0.921625i | \(-0.626862\pi\) | ||||
0.388081 | − | 0.921625i | \(-0.373138\pi\) | |||||||
\(762\) | − 250.952i | − 0.329334i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 496.191 | 0.649465 | ||||||||
\(765\) | 211.632 | 0.276644 | ||||||||
\(766\) | − 675.656i | − 0.882058i | ||||||||
\(767\) | 592.087 | 0.771952 | ||||||||
\(768\) | 11.4790i | 0.0149466i | ||||||||
\(769\) | − 1.72330i | − 0.00224097i | −0.999999 | − | 0.00112048i | \(-0.999643\pi\) | ||||
0.999999 | − | 0.00112048i | \(-0.000356661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 287.360 | 0.372711 | ||||||||
\(772\) | 308.676 | 0.399840 | ||||||||
\(773\) | 224.258i | 0.290113i | 0.989423 | + | 0.145057i | \(0.0463364\pi\) | ||||
−0.989423 | + | 0.145057i | \(0.953664\pi\) | |||||||
\(774\) | −125.823 | −0.162563 | ||||||||
\(775\) | 927.029i | 1.19617i | ||||||||
\(776\) | − 287.911i | − 0.371019i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 240.728 | 0.309419 | ||||||||
\(779\) | 116.912 | 0.150079 | ||||||||
\(780\) | 145.492i | 0.186529i | ||||||||
\(781\) | −173.294 | −0.221887 | ||||||||
\(782\) | 147.492i | 0.188608i | ||||||||
\(783\) | 44.0908i | 0.0563101i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.0740 | −0.0714319 | ||||||||
\(786\) | −149.802 | −0.190588 | ||||||||
\(787\) | 70.2034i | 0.0892038i | 0.999005 | + | 0.0446019i | \(0.0142019\pi\) | ||||
−0.999005 | + | 0.0446019i | \(0.985798\pi\) | |||||||
\(788\) | −362.205 | −0.459651 | ||||||||
\(789\) | − 23.2057i | − 0.0294116i | ||||||||
\(790\) | − 316.842i | − 0.401066i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −114.177 | −0.144162 | ||||||||
\(793\) | 1383.98 | 1.74525 | ||||||||
\(794\) | − 345.846i | − 0.435574i | ||||||||
\(795\) | −266.272 | −0.334933 | ||||||||
\(796\) | 697.413i | 0.876147i | ||||||||
\(797\) | − 1305.38i | − 1.63787i | −0.573889 | − | 0.818933i | \(-0.694566\pi\) | ||||
0.573889 | − | 0.818933i | \(-0.305434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −198.140 | −0.247985 | ||||||||
\(800\) | −107.314 | −0.134142 | ||||||||
\(801\) | 427.076i | 0.533179i | ||||||||
\(802\) | −590.537 | −0.736330 | ||||||||
\(803\) | − 250.270i | − 0.311668i | ||||||||
\(804\) | − 49.7036i | − 0.0618204i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1056.75 | −1.31110 | ||||||||
\(807\) | 220.227 | 0.272897 | ||||||||
\(808\) | − 168.798i | − 0.208909i | ||||||||
\(809\) | 762.765 | 0.942849 | 0.471424 | − | 0.881907i | \(-0.343740\pi\) | ||||
0.471424 | + | 0.881907i | \(0.343740\pi\) | |||||||
\(810\) | 631.752i | 0.779941i | ||||||||
\(811\) | − 1214.98i | − 1.49813i | −0.662498 | − | 0.749064i | \(-0.730504\pi\) | ||||
0.662498 | − | 0.749064i | \(-0.269496\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.5147 | −0.0670538 | ||||||||
\(814\) | 19.7877 | 0.0243092 | ||||||||
\(815\) | 1471.94i | 1.80606i | ||||||||
\(816\) | 10.7939 | 0.0132279 | ||||||||
\(817\) | 43.8446i | 0.0536654i | ||||||||
\(818\) | 435.877i | 0.532857i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −370.794 | −0.452188 | ||||||||
\(821\) | −583.368 | −0.710557 | −0.355279 | − | 0.934760i | \(-0.615614\pi\) | ||||
−0.355279 | + | 0.934760i | \(0.615614\pi\) | |||||||
\(822\) | − 33.0496i | − 0.0402063i | ||||||||
\(823\) | 1030.74 | 1.25242 | 0.626210 | − | 0.779655i | \(-0.284605\pi\) | ||||
0.626210 | + | 0.779655i | \(0.284605\pi\) | |||||||
\(824\) | − 339.915i | − 0.412518i | ||||||||
\(825\) | 64.7487i | 0.0784833i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 152.102 | 0.183920 | 0.0919599 | − | 0.995763i | \(-0.470687\pi\) | ||||
0.0919599 | + | 0.995763i | \(0.470687\pi\) | |||||||
\(828\) | −470.558 | −0.568307 | ||||||||
\(829\) | 614.410i | 0.741146i | 0.928803 | + | 0.370573i | \(0.120839\pi\) | ||||
−0.928803 | + | 0.370573i | \(0.879161\pi\) | |||||||
\(830\) | −1196.38 | −1.44142 | ||||||||
\(831\) | 199.743i | 0.240365i | ||||||||
\(832\) | − 122.330i | − 0.147032i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 69.5879 | 0.0834387 | ||||||||
\(835\) | 1119.59 | 1.34082 | ||||||||
\(836\) | 39.7862i | 0.0475911i | ||||||||
\(837\) | 613.014 | 0.732395 | ||||||||
\(838\) | 145.865i | 0.174063i | ||||||||
\(839\) | 1546.14i | 1.84284i | 0.388568 | + | 0.921420i | \(0.372970\pi\) | ||||
−0.388568 | + | 0.921420i | \(0.627030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −828.647 | −0.985311 | ||||||||
\(842\) | −233.657 | −0.277502 | ||||||||
\(843\) | 283.166i | 0.335903i | ||||||||
\(844\) | 728.146 | 0.862733 | ||||||||
\(845\) | − 429.846i | − 0.508693i | ||||||||
\(846\) | − 632.148i | − 0.747219i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 223.882 | 0.264012 | ||||||||
\(849\) | −105.030 | −0.123711 | ||||||||
\(850\) | 100.909i | 0.118717i | ||||||||
\(851\) | 81.5513 | 0.0958300 | ||||||||
\(852\) | 52.2674i | 0.0613468i | ||||||||
\(853\) | 1235.15i | 1.44800i | 0.689798 | + | 0.724002i | \(0.257699\pi\) | ||||
−0.689798 | + | 0.724002i | \(0.742301\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 235.279 | 0.275180 | ||||||||
\(856\) | −321.338 | −0.375395 | ||||||||
\(857\) | − 1100.68i | − 1.28434i | −0.766561 | − | 0.642172i | \(-0.778034\pi\) | ||||
0.766561 | − | 0.642172i | \(-0.221966\pi\) | |||||||
\(858\) | −73.8091 | −0.0860246 | ||||||||
\(859\) | − 591.771i | − 0.688906i | −0.938803 | − | 0.344453i | \(-0.888064\pi\) | ||||
0.938803 | − | 0.344453i | \(-0.111936\pi\) | |||||||
\(860\) | − 139.056i | − 0.161694i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 840.801 | 0.975407 | ||||||||
\(863\) | −64.7271 | −0.0750024 | −0.0375012 | − | 0.999297i | \(-0.511940\pi\) | ||||
−0.0375012 | + | 0.999297i | \(0.511940\pi\) | |||||||
\(864\) | 70.9631i | 0.0821332i | ||||||||
\(865\) | −1089.75 | −1.25983 | ||||||||
\(866\) | 57.4548i | 0.0663451i | ||||||||
\(867\) | 197.190i | 0.227440i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 160.736 | 0.184967 | ||||||||
\(870\) | −23.6468 | −0.0271802 | ||||||||
\(871\) | 529.684i | 0.608133i | ||||||||
\(872\) | −410.995 | −0.471324 | ||||||||
\(873\) | − 863.732i | − 0.989384i | ||||||||
\(874\) | 163.972i | 0.187611i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −75.4844 | −0.0861694 | ||||||||
\(877\) | −304.192 | −0.346855 | −0.173427 | − | 0.984847i | \(-0.555484\pi\) | ||||
−0.173427 | + | 0.984847i | \(0.555484\pi\) | |||||||
\(878\) | − 207.324i | − 0.236132i | ||||||||
\(879\) | 215.001 | 0.244597 | ||||||||
\(880\) | − 126.185i | − 0.143392i | ||||||||
\(881\) | − 863.732i | − 0.980400i | −0.871610 | − | 0.490200i | \(-0.836924\pi\) | ||||
0.871610 | − | 0.490200i | \(-0.163076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −567.456 | −0.642645 | −0.321323 | − | 0.946970i | \(-0.604127\pi\) | ||||
−0.321323 | + | 0.946970i | \(0.604127\pi\) | |||||||
\(884\) | −115.029 | −0.130124 | ||||||||
\(885\) | − 184.208i | − 0.208144i | ||||||||
\(886\) | 151.831 | 0.171366 | ||||||||
\(887\) | 889.761i | 1.00311i | 0.865125 | + | 0.501556i | \(0.167239\pi\) | ||||
−0.865125 | + | 0.501556i | \(0.832761\pi\) | |||||||
\(888\) | − 5.96820i | − 0.00672095i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −471.993 | −0.530329 | ||||||||
\(891\) | −320.492 | −0.359699 | ||||||||
\(892\) | − 246.461i | − 0.276302i | ||||||||
\(893\) | −220.279 | −0.246673 | ||||||||
\(894\) | 93.7471i | 0.104862i | ||||||||
\(895\) | 1227.96i | 1.37202i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −304.191 | −0.339120 | ||||||||
\(898\) | 191.147 | 0.212859 | ||||||||
\(899\) | − 171.753i | − 0.191049i | ||||||||
\(900\) | −321.941 | −0.357712 | ||||||||
\(901\) | − 210.521i | − 0.233652i | ||||||||
\(902\) | − 188.106i | − 0.208543i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 97.7056 | 0.108081 | ||||||||
\(905\) | −1028.38 | −1.13633 | ||||||||
\(906\) | − 93.1280i | − 0.102790i | ||||||||
\(907\) | 373.978 | 0.412324 | 0.206162 | − | 0.978518i | \(-0.433903\pi\) | ||||
0.206162 | + | 0.978518i | \(0.433903\pi\) | |||||||
\(908\) | − 152.751i | − 0.168228i | ||||||||
\(909\) | − 506.395i | − 0.557091i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1133.75 | 1.24451 | 0.622256 | − | 0.782814i | \(-0.286216\pi\) | ||||
0.622256 | + | 0.782814i | \(0.286216\pi\) | |||||||
\(912\) | 12.0000 | 0.0131579 | ||||||||
\(913\) | − 606.932i | − 0.664766i | ||||||||
\(914\) | 225.899 | 0.247155 | ||||||||
\(915\) | − 430.579i | − 0.470578i | ||||||||
\(916\) | − 714.572i | − 0.780101i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 66.7279 | 0.0726884 | ||||||||
\(919\) | 456.302 | 0.496521 | 0.248260 | − | 0.968693i | \(-0.420141\pi\) | ||||
0.248260 | + | 0.968693i | \(0.420141\pi\) | |||||||
\(920\) | − 520.048i | − 0.565269i | ||||||||
\(921\) | −15.0580 | −0.0163496 | ||||||||
\(922\) | − 438.759i | − 0.475878i | ||||||||
\(923\) | − 557.007i | − 0.603474i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.7948 | 0.0603187 | ||||||||
\(926\) | −461.054 | −0.497898 | ||||||||
\(927\) | − 1019.74i | − 1.10005i | ||||||||
\(928\) | 19.8823 | 0.0214248 | ||||||||
\(929\) | 951.540i | 1.02426i | 0.858907 | + | 0.512131i | \(0.171144\pi\) | ||||
−0.858907 | + | 0.512131i | \(0.828856\pi\) | |||||||
\(930\) | 328.771i | 0.353518i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −546.146 | −0.585994 | ||||||||
\(933\) | −130.602 | −0.139981 | ||||||||
\(934\) | − 842.246i | − 0.901763i | ||||||||
\(935\) | −118.654 | −0.126903 | ||||||||
\(936\) | − 366.991i | − 0.392084i | ||||||||
\(937\) | 1295.71i | 1.38283i | 0.722460 | + | 0.691413i | \(0.243011\pi\) | ||||
−0.722460 | + | 0.691413i | \(0.756989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −70.2578 | −0.0748219 | ||||||||
\(940\) | 698.632 | 0.743225 | ||||||||
\(941\) | − 1356.89i | − 1.44197i | −0.692952 | − | 0.720984i | \(-0.743690\pi\) | ||||
0.692952 | − | 0.720984i | \(-0.256310\pi\) | |||||||
\(942\) | −8.57987 | −0.00910814 | ||||||||
\(943\) | − 775.245i | − 0.822105i | ||||||||
\(944\) | 154.882i | 0.164070i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70.5442 | 0.0745710 | ||||||||
\(947\) | −709.462 | −0.749168 | −0.374584 | − | 0.927193i | \(-0.622214\pi\) | ||||
−0.374584 | + | 0.927193i | \(0.622214\pi\) | |||||||
\(948\) | − 48.4799i | − 0.0511392i | ||||||||
\(949\) | 804.426 | 0.847657 | ||||||||
\(950\) | 112.184i | 0.118089i | ||||||||
\(951\) | − 345.784i | − 0.363601i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 936.603 | 0.982794 | 0.491397 | − | 0.870936i | \(-0.336486\pi\) | ||||
0.491397 | + | 0.870936i | \(0.336486\pi\) | |||||||
\(954\) | 671.647 | 0.704032 | ||||||||
\(955\) | 1645.13i | 1.72265i | ||||||||
\(956\) | −530.205 | −0.554608 | ||||||||
\(957\) | − 11.9961i | − 0.0125351i | ||||||||
\(958\) | 716.554i | 0.747969i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −38.0589 | −0.0396447 | ||||||||
\(961\) | −1426.95 | −1.48486 | ||||||||
\(962\) | 63.6023i | 0.0661146i | ||||||||
\(963\) | −964.014 | −1.00105 | ||||||||
\(964\) | − 175.277i | − 0.181822i | ||||||||
\(965\) | 1023.42i | 1.06054i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1374.37 | 1.42127 | 0.710635 | − | 0.703561i | \(-0.248408\pi\) | ||||
0.710635 | + | 0.703561i | \(0.248408\pi\) | |||||||
\(968\) | −278.225 | −0.287423 | ||||||||
\(969\) | − 11.2838i | − 0.0116448i | ||||||||
\(970\) | 954.573 | 0.984096 | ||||||||
\(971\) | 31.4617i | 0.0324014i | 0.999869 | + | 0.0162007i | \(0.00515706\pi\) | ||||
−0.999869 | + | 0.0162007i | \(0.994843\pi\) | |||||||
\(972\) | 322.467i | 0.331757i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 298.825 | 0.306802 | ||||||||
\(975\) | −208.118 | −0.213454 | ||||||||
\(976\) | 362.032i | 0.370935i | ||||||||
\(977\) | −541.897 | −0.554654 | −0.277327 | − | 0.960776i | \(-0.589449\pi\) | ||||
−0.277327 | + | 0.960776i | \(0.589449\pi\) | |||||||
\(978\) | 225.221i | 0.230288i | ||||||||
\(979\) | − 239.445i | − 0.244581i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1232.98 | −1.25687 | ||||||||
\(982\) | −1108.97 | −1.12930 | ||||||||
\(983\) | 22.4198i | 0.0228075i | 0.999935 | + | 0.0114038i | \(0.00363001\pi\) | ||||
−0.999935 | + | 0.0114038i | \(0.996370\pi\) | |||||||
\(984\) | −56.7351 | −0.0576576 | ||||||||
\(985\) | − 1200.90i | − 1.21918i | ||||||||
\(986\) | − 18.6957i | − 0.0189611i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −127.882 | −0.129435 | ||||||||
\(989\) | 290.735 | 0.293969 | ||||||||
\(990\) | − 378.554i | − 0.382378i | ||||||||
\(991\) | 678.035 | 0.684193 | 0.342096 | − | 0.939665i | \(-0.388863\pi\) | ||||
0.342096 | + | 0.939665i | \(0.388863\pi\) | |||||||
\(992\) | − 276.432i | − 0.278661i | ||||||||
\(993\) | 161.429i | 0.162567i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2312.28 | −2.32390 | ||||||||
\(996\) | −183.058 | −0.183793 | ||||||||
\(997\) | 876.163i | 0.878799i | 0.898292 | + | 0.439400i | \(0.144809\pi\) | ||||
−0.898292 | + | 0.439400i | \(0.855191\pi\) | |||||||
\(998\) | −242.527 | −0.243013 | ||||||||
\(999\) | − 36.8953i | − 0.0369322i |
(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 | 98.3.b.b.97.4 | 4 | ||
3.2 | odd | 2 | 882.3.c.f.685.1 | 4 | |||
4.3 | odd | 2 | 784.3.c.e.97.2 | 4 | |||
7.2 | even | 3 | 98.3.d.a.31.1 | 4 | |||
7.3 | odd | 6 | 98.3.d.a.19.1 | 4 | |||
7.4 | even | 3 | 14.3.d.a.5.1 | yes | 4 | ||
7.5 | odd | 6 | 14.3.d.a.3.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 98.3.b.b.97.3 | 4 | ||
21.2 | odd | 6 | 882.3.n.b.325.2 | 4 | |||
21.5 | even | 6 | 126.3.n.c.73.2 | 4 | |||
21.11 | odd | 6 | 126.3.n.c.19.2 | 4 | |||
21.17 | even | 6 | 882.3.n.b.19.2 | 4 | |||
21.20 | even | 2 | 882.3.c.f.685.2 | 4 | |||
28.3 | even | 6 | 784.3.s.c.705.2 | 4 | |||
28.11 | odd | 6 | 112.3.s.b.33.1 | 4 | |||
28.19 | even | 6 | 112.3.s.b.17.1 | 4 | |||
28.23 | odd | 6 | 784.3.s.c.129.2 | 4 | |||
28.27 | even | 2 | 784.3.c.e.97.3 | 4 | |||
35.4 | even | 6 | 350.3.k.a.201.2 | 4 | |||
35.12 | even | 12 | 350.3.i.a.199.3 | 8 | |||
35.18 | odd | 12 | 350.3.i.a.299.3 | 8 | |||
35.19 | odd | 6 | 350.3.k.a.101.2 | 4 | |||
35.32 | odd | 12 | 350.3.i.a.299.2 | 8 | |||
35.33 | even | 12 | 350.3.i.a.199.2 | 8 | |||
56.5 | odd | 6 | 448.3.s.d.129.1 | 4 | |||
56.11 | odd | 6 | 448.3.s.c.257.2 | 4 | |||
56.19 | even | 6 | 448.3.s.c.129.2 | 4 | |||
56.53 | even | 6 | 448.3.s.d.257.1 | 4 | |||
84.11 | even | 6 | 1008.3.cg.l.145.2 | 4 | |||
84.47 | odd | 6 | 1008.3.cg.l.577.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.1 | ✓ | 4 | 7.5 | odd | 6 | ||
14.3.d.a.5.1 | yes | 4 | 7.4 | even | 3 | ||
98.3.b.b.97.3 | 4 | 7.6 | odd | 2 | inner | ||
98.3.b.b.97.4 | 4 | 1.1 | even | 1 | trivial | ||
98.3.d.a.19.1 | 4 | 7.3 | odd | 6 | |||
98.3.d.a.31.1 | 4 | 7.2 | even | 3 | |||
112.3.s.b.17.1 | 4 | 28.19 | even | 6 | |||
112.3.s.b.33.1 | 4 | 28.11 | odd | 6 | |||
126.3.n.c.19.2 | 4 | 21.11 | odd | 6 | |||
126.3.n.c.73.2 | 4 | 21.5 | even | 6 | |||
350.3.i.a.199.2 | 8 | 35.33 | even | 12 | |||
350.3.i.a.199.3 | 8 | 35.12 | even | 12 | |||
350.3.i.a.299.2 | 8 | 35.32 | odd | 12 | |||
350.3.i.a.299.3 | 8 | 35.18 | odd | 12 | |||
350.3.k.a.101.2 | 4 | 35.19 | odd | 6 | |||
350.3.k.a.201.2 | 4 | 35.4 | even | 6 | |||
448.3.s.c.129.2 | 4 | 56.19 | even | 6 | |||
448.3.s.c.257.2 | 4 | 56.11 | odd | 6 | |||
448.3.s.d.129.1 | 4 | 56.5 | odd | 6 | |||
448.3.s.d.257.1 | 4 | 56.53 | even | 6 | |||
784.3.c.e.97.2 | 4 | 4.3 | odd | 2 | |||
784.3.c.e.97.3 | 4 | 28.27 | even | 2 | |||
784.3.s.c.129.2 | 4 | 28.23 | odd | 6 | |||
784.3.s.c.705.2 | 4 | 28.3 | even | 6 | |||
882.3.c.f.685.1 | 4 | 3.2 | odd | 2 | |||
882.3.c.f.685.2 | 4 | 21.20 | even | 2 | |||
882.3.n.b.19.2 | 4 | 21.17 | even | 6 | |||
882.3.n.b.325.2 | 4 | 21.2 | odd | 6 | |||
1008.3.cg.l.145.2 | 4 | 84.11 | even | 6 | |||
1008.3.cg.l.577.2 | 4 | 84.47 | odd | 6 |