Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.4 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.i.1471.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.400000 | 0.200000 | − | 0.979796i | \(-0.435906\pi\) | ||||
0.200000 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.5112i | 1.59193i | 0.605344 | + | 0.795964i | \(0.293036\pi\) | ||||
−0.605344 | + | 0.795964i | \(0.706964\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.3303 | −1.56387 | −0.781935 | − | 0.623360i | \(-0.785767\pi\) | ||||
−0.781935 | + | 0.623360i | \(0.785767\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410i | 0.230940i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −32.3303 | −1.90178 | −0.950891 | − | 0.309525i | \(-0.899830\pi\) | ||||
−0.950891 | + | 0.309525i | \(0.899830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.0942i | 1.47864i | 0.673353 | + | 0.739321i | \(0.264854\pi\) | ||||
−0.673353 | + | 0.739321i | \(0.735146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 10.2016i | − 0.443548i | −0.975098 | − | 0.221774i | \(-0.928815\pi\) | ||||
0.975098 | − | 0.221774i | \(-0.0711847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −21.0000 | −0.840000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.6606 | 0.781400 | 0.390700 | − | 0.920518i | \(-0.372233\pi\) | ||||
0.390700 | + | 0.920518i | \(0.372233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 27.7128i | − 0.893962i | −0.894544 | − | 0.446981i | \(-0.852499\pi\) | ||||
0.894544 | − | 0.446981i | \(-0.147501\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −30.3303 | −0.919100 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.6606 | 1.69353 | 0.846765 | − | 0.531967i | \(-0.178547\pi\) | ||||
0.846765 | + | 0.531967i | \(0.178547\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 35.2131i | − 0.902900i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 28.3303 | 0.690983 | 0.345491 | − | 0.938422i | \(-0.387712\pi\) | ||||
0.345491 | + | 0.938422i | \(0.387712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 48.8788i | − 1.13672i | −0.822781 | − | 0.568358i | \(-0.807579\pi\) | ||||
0.822781 | − | 0.568358i | \(-0.192421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.00000 | −0.133333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 91.2108i | − 1.94066i | −0.241792 | − | 0.970328i | \(-0.577735\pi\) | ||||
0.241792 | − | 0.970328i | \(-0.422265\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 55.9977i | − 1.09799i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 46.6606 | 0.880389 | 0.440194 | − | 0.897902i | \(-0.354910\pi\) | ||||
0.440194 | + | 0.897902i | \(0.354910\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35.0224i | 0.636771i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −48.6606 | −0.853695 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 41.9506i | − 0.711027i | −0.934671 | − | 0.355514i | \(-0.884306\pi\) | ||||
0.934671 | − | 0.355514i | \(-0.115694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3303 | −0.202136 | −0.101068 | − | 0.994880i | \(-0.532226\pi\) | ||||
−0.101068 | + | 0.994880i | \(0.532226\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −40.6606 | −0.625548 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 55.4256i | 0.827248i | 0.910448 | + | 0.413624i | \(0.135737\pi\) | ||||
−0.910448 | + | 0.413624i | \(0.864263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.6697 | 0.256083 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.2964i | 0.750654i | 0.926892 | + | 0.375327i | \(0.122470\pi\) | ||||
−0.926892 | + | 0.375327i | \(0.877530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.3394 | −0.292320 | −0.146160 | − | 0.989261i | \(-0.546692\pi\) | ||||
−0.146160 | + | 0.989261i | \(0.546692\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 36.3731i | − 0.484974i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 96.9948i | − 1.22778i | −0.789390 | − | 0.613891i | \(-0.789603\pi\) | ||||
0.789390 | − | 0.613891i | \(-0.210397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 63.8794i | − 0.769632i | −0.922993 | − | 0.384816i | \(-0.874265\pi\) | ||||
0.922993 | − | 0.384816i | \(-0.125735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −64.6606 | −0.760713 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 39.2493i | 0.451142i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9909 | 0.190909 | 0.0954545 | − | 0.995434i | \(-0.469570\pi\) | ||||
0.0954545 | + | 0.995434i | \(0.469570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 48.0000 | 0.516129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 56.1884i | 0.591457i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 95.3212 | 0.982693 | 0.491346 | − | 0.870964i | \(-0.336505\pi\) | ||||
0.491346 | + | 0.870964i | \(0.336505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 52.5336i | − 0.530643i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.33939 | −0.0132613 | −0.00663067 | − | 0.999978i | \(-0.502111\pi\) | ||||
−0.00663067 | + | 0.999978i | \(0.502111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29.2384i | 0.283868i | 0.989876 | + | 0.141934i | \(0.0453321\pi\) | ||||
−0.989876 | + | 0.141934i | \(0.954668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 92.5772i | − 0.865208i | −0.901584 | − | 0.432604i | \(-0.857595\pi\) | ||||
0.901584 | − | 0.432604i | \(-0.142405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −106.661 | −0.978538 | −0.489269 | − | 0.872133i | \(-0.662736\pi\) | ||||
−0.489269 | + | 0.872133i | \(0.662736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 108.531i | 0.977760i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −135.321 | −1.19753 | −0.598766 | − | 0.800924i | \(-0.704342\pi\) | ||||
−0.598766 | + | 0.800924i | \(0.704342\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 20.4032i | − 0.177419i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 60.9909 | 0.521290 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −185.642 | −1.53423 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 49.0695i | 0.398939i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −92.0000 | −0.736000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 84.6640i | − 0.666646i | −0.942813 | − | 0.333323i | \(-0.891830\pi\) | ||||
0.942813 | − | 0.333323i | \(-0.108170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 84.6606 | 0.656284 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 75.4474i | − 0.575935i | −0.957640 | − | 0.287967i | \(-0.907021\pi\) | ||||
0.957640 | − | 0.287967i | \(-0.0929794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 10.3923i | − 0.0769800i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −173.303 | −1.26499 | −0.632493 | − | 0.774566i | \(-0.717968\pi\) | ||||
−0.632493 | + | 0.774566i | \(0.717968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 230.156i | 1.65580i | 0.560875 | + | 0.827900i | \(0.310465\pi\) | ||||
−0.560875 | + | 0.827900i | \(0.689535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 157.982 | 1.12044 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 356.008i | − 2.48957i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 45.3212 | 0.312560 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 87.9818 | 0.590482 | 0.295241 | − | 0.955423i | \(-0.404600\pi\) | ||||
0.295241 | + | 0.955423i | \(0.404600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4032i | 0.135121i | 0.997715 | + | 0.0675603i | \(0.0215215\pi\) | ||||
−0.997715 | + | 0.0675603i | \(0.978478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 96.9909 | 0.633928 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 55.4256i | − 0.357585i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −170.312 | −1.08479 | −0.542395 | − | 0.840123i | \(-0.682482\pi\) | ||||
−0.542395 | + | 0.840123i | \(0.682482\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 80.8185i | 0.508293i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 250.178i | − 1.53484i | −0.641148 | − | 0.767418i | \(-0.721541\pi\) | ||||
0.641148 | − | 0.767418i | \(-0.278459\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −60.6606 | −0.367640 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 228.249i | 1.36676i | 0.730062 | + | 0.683381i | \(0.239491\pi\) | ||||
−0.730062 | + | 0.683381i | \(0.760509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 244.321 | 1.44569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 84.2826i | − 0.492881i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 39.3576 | 0.227500 | 0.113750 | − | 0.993509i | \(-0.463714\pi\) | ||||
0.113750 | + | 0.993509i | \(0.463714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 72.6606 | 0.410512 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 64.8644i | 0.362371i | 0.983449 | + | 0.181186i | \(0.0579935\pi\) | ||||
−0.983449 | + | 0.181186i | \(0.942007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6515 | −0.0754227 | −0.0377114 | − | 0.999289i | \(-0.512007\pi\) | ||||
−0.0377114 | + | 0.999289i | \(0.512007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 21.3567i | − 0.116703i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 125.321 | 0.677412 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 566.143i | − 3.02750i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 238.451i | − 1.24843i | −0.781251 | − | 0.624217i | \(-0.785418\pi\) | ||||
0.781251 | − | 0.624217i | \(-0.214582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 68.6424 | 0.355660 | 0.177830 | − | 0.984061i | \(-0.443092\pi\) | ||||
0.177830 | + | 0.984061i | \(0.443092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 70.4262i | − 0.361160i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −211.982 | −1.07605 | −0.538025 | − | 0.842929i | \(-0.680829\pi\) | ||||
−0.538025 | + | 0.842929i | \(0.680829\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 157.442i | − 0.791164i | −0.918431 | − | 0.395582i | \(-0.870543\pi\) | ||||
0.918431 | − | 0.395582i | \(-0.129457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −96.0000 | −0.477612 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 56.6606 | 0.276393 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.6048i | 0.147849i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −491.964 | −2.35389 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 205.876i | 0.975716i | 0.872923 | + | 0.487858i | \(0.162222\pi\) | ||||
−0.872923 | + | 0.487858i | \(0.837778\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −92.3121 | −0.433390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 97.7576i | − 0.454687i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 36.9609i | − 0.168771i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 657.285 | 2.97414 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 164.307i | − 0.736802i | −0.929667 | − | 0.368401i | \(-0.879905\pi\) | ||||
0.929667 | − | 0.368401i | \(-0.120095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 63.0000 | 0.280000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 282.086i | 1.24267i | 0.783545 | + | 0.621336i | \(0.213410\pi\) | ||||
−0.783545 | + | 0.621336i | \(0.786590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −93.6515 | −0.408959 | −0.204479 | − | 0.978871i | \(-0.565550\pi\) | ||||
−0.204479 | + | 0.978871i | \(0.565550\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −225.339 | −0.967122 | −0.483561 | − | 0.875311i | \(-0.660657\pi\) | ||||
−0.483561 | + | 0.875311i | \(0.660657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 182.422i | − 0.776263i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 168.000 | 0.708861 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 81.7720i | − 0.342142i | −0.985259 | − | 0.171071i | \(-0.945277\pi\) | ||||
0.985259 | − | 0.171071i | \(-0.0547228\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 326.000 | 1.35270 | 0.676349 | − | 0.736582i | \(-0.263561\pi\) | ||||
0.676349 | + | 0.736582i | \(0.263561\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 571.164i | − 2.31240i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 110.642 | 0.444347 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 255.136i | 1.01648i | 0.861216 | + | 0.508240i | \(0.169704\pi\) | ||||
−0.861216 | + | 0.508240i | \(0.830296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 178.642 | 0.706097 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 111.995i | − 0.439198i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −129.652 | −0.504481 | −0.252240 | − | 0.967665i | \(-0.581167\pi\) | ||||
−0.252240 | + | 0.967665i | \(0.581167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −67.9818 | −0.260467 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 394.685i | 1.50070i | 0.661038 | + | 0.750352i | \(0.270116\pi\) | ||||
−0.661038 | + | 0.750352i | \(0.729884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 93.3212 | 0.352156 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.4291i | 0.110221i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.9818 | −0.104022 | −0.0520108 | − | 0.998647i | \(-0.516563\pi\) | ||||
−0.0520108 | + | 0.998647i | \(0.516563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 26.9500i | − 0.0994465i | −0.998763 | − | 0.0497233i | \(-0.984166\pi\) | ||||
0.998763 | − | 0.0497233i | \(-0.0158339\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 367.735i | − 1.33722i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 48.6788 | 0.175736 | 0.0878678 | − | 0.996132i | \(-0.471995\pi\) | ||||
0.0878678 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 83.1384i | 0.297987i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 113.303 | 0.403214 | 0.201607 | − | 0.979467i | \(-0.435384\pi\) | ||||
0.201607 | + | 0.979467i | \(0.435384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 238.992i | − 0.844493i | −0.906481 | − | 0.422246i | \(-0.861242\pi\) | ||||
0.906481 | − | 0.422246i | \(-0.138758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −97.3212 | −0.341478 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 756.248 | 2.61678 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 165.101i | 0.567358i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.37576 | −0.0183473 | −0.00917365 | − | 0.999958i | \(-0.502920\pi\) | ||||
−0.00917365 | + | 0.999958i | \(0.502920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 83.9012i | − 0.284411i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 90.9909 | 0.306367 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 207.402i | 0.693651i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.31990i | − 0.00765643i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.6606 | −0.0808544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 12.7122i | − 0.0414078i | −0.999786 | − | 0.0207039i | \(-0.993409\pi\) | ||||
0.999786 | − | 0.0207039i | \(-0.00659073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −50.6424 | −0.163891 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 172.061i | − 0.553250i | −0.960978 | − | 0.276625i | \(-0.910784\pi\) | ||||
0.960978 | − | 0.276625i | \(-0.0892161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.66061 | −0.0212799 | −0.0106399 | − | 0.999943i | \(-0.503387\pi\) | ||||
−0.0106399 | + | 0.999943i | \(0.503387\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −598.624 | −1.88840 | −0.944202 | − | 0.329366i | \(-0.893165\pi\) | ||||
−0.944202 | + | 0.329366i | \(0.893165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 396.815i | 1.24393i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 160.348 | 0.499528 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 908.294i | − 2.81206i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 426.936 | 1.31365 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 184.742i | − 0.564959i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 446.012i | 1.34747i | 0.738974 | + | 0.673734i | \(0.235311\pi\) | ||||
−0.738974 | + | 0.673734i | \(0.764689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −187.982 | −0.564510 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 110.851i | 0.330899i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.03637 | 0.0179121 | 0.00895603 | − | 0.999960i | \(-0.497149\pi\) | ||||
0.00895603 | + | 0.999960i | \(0.497149\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 234.383i | − 0.691396i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 485.285 | 1.42312 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 35.3394 | 0.102433 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 439.306i | − 1.26601i | −0.774147 | − | 0.633005i | \(-0.781821\pi\) | ||||
0.774147 | − | 0.633005i | \(-0.218179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 223.009 | 0.638995 | 0.319497 | − | 0.947587i | \(-0.396486\pi\) | ||||
0.319497 | + | 0.947587i | \(0.396486\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 105.639i | 0.300967i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −624.955 | −1.77041 | −0.885205 | − | 0.465202i | \(-0.845982\pi\) | ||||
−0.885205 | + | 0.465202i | \(0.845982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 106.593i | 0.300262i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 112.218i | − 0.312584i | −0.987711 | − | 0.156292i | \(-0.950046\pi\) | ||||
0.987711 | − | 0.156292i | \(-0.0499541\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −428.285 | −1.18638 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 321.542i | − 0.885791i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.6788 | −0.116928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 288.252i | − 0.785427i | −0.919661 | − | 0.392714i | \(-0.871536\pi\) | ||||
0.919661 | − | 0.392714i | \(-0.128464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −84.9909 | −0.230328 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −391.248 | −1.04892 | −0.524462 | − | 0.851434i | \(-0.675733\pi\) | ||||
−0.524462 | + | 0.851434i | \(0.675733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 159.349i | − 0.424930i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −460.697 | −1.22201 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 412.197i | − 1.08759i | −0.839218 | − | 0.543795i | \(-0.816987\pi\) | ||||
0.839218 | − | 0.543795i | \(-0.183013\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 146.642 | 0.384888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 56.1884i | − 0.146706i | −0.997306 | − | 0.0733530i | \(-0.976630\pi\) | ||||
0.997306 | − | 0.0733530i | \(-0.0233700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 146.636i | 0.378906i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −401.267 | −1.03153 | −0.515767 | − | 0.856729i | \(-0.672493\pi\) | ||||
−0.515767 | + | 0.856729i | \(0.672493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 329.821i | 0.843532i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 130.679 | 0.332516 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 193.990i | − 0.491113i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 278.936 | 0.702610 | 0.351305 | − | 0.936261i | \(-0.385738\pi\) | ||||
0.351305 | + | 0.936261i | \(0.385738\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −467.982 | −1.16704 | −0.583518 | − | 0.812100i | \(-0.698324\pi\) | ||||
−0.583518 | + | 0.812100i | \(0.698324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 563.410i | 1.39804i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.0444444 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1097.26i | 2.69598i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −69.9636 | −0.171060 | −0.0855301 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855301 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 300.170i | − 0.730340i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 127.759i | − 0.307853i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −398.642 | −0.955977 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 111.233i | − 0.265472i | −0.991151 | − | 0.132736i | \(-0.957624\pi\) | ||||
0.991151 | − | 0.132736i | \(-0.0423762\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −436.606 | −1.03707 | −0.518535 | − | 0.855057i | \(-0.673522\pi\) | ||||
−0.518535 | + | 0.855057i | \(0.673522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 273.633i | 0.646885i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 678.936 | 1.59750 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 616.624 | 1.43735 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 664.060i | − 1.54074i | −0.637596 | − | 0.770371i | \(-0.720071\pi\) | ||||
0.637596 | − | 0.770371i | \(-0.279929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 116.055 | 0.268024 | 0.134012 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134012 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 78.4986i | 0.180457i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 286.606 | 0.655849 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 363.762i | 0.828615i | 0.910137 | + | 0.414308i | \(0.135976\pi\) | ||||
−0.910137 | + | 0.414308i | \(0.864024\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 723.299i | − 1.63273i | −0.577537 | − | 0.816365i | \(-0.695986\pi\) | ||||
0.577537 | − | 0.816365i | \(-0.304014\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.9818 | 0.0763636 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 152.389i | 0.340915i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −264.715 | −0.589566 | −0.294783 | − | 0.955564i | \(-0.595247\pi\) | ||||
−0.294783 | + | 0.955564i | \(0.595247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 496.098i | 1.10000i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.3394 | −0.0780119 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −277.927 | −0.608156 | −0.304078 | − | 0.952647i | \(-0.598348\pi\) | ||||
−0.304078 | + | 0.952647i | \(0.598348\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 167.993i | 0.365998i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −758.000 | −1.64425 | −0.822126 | − | 0.569306i | \(-0.807212\pi\) | ||||
−0.822126 | + | 0.569306i | \(0.807212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 499.593i | 1.07904i | 0.841974 | + | 0.539518i | \(0.181393\pi\) | ||||
−0.841974 | + | 0.539518i | \(0.818607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 96.0000 | 0.206452 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 419.888i | − 0.899117i | −0.893251 | − | 0.449558i | \(-0.851581\pi\) | ||||
0.893251 | − | 0.449558i | \(-0.148419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 294.989i | − 0.626304i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 855.927 | 1.80957 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 589.978i | − 1.24206i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −139.982 | −0.293463 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 690.850i | 1.44228i | 0.692791 | + | 0.721138i | \(0.256381\pi\) | ||||
−0.692791 | + | 0.721138i | \(0.743619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1273.91 | −2.64846 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 190.642 | 0.393077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 163.544i | − 0.335819i | −0.985802 | − | 0.167910i | \(-0.946298\pi\) | ||||
0.985802 | − | 0.167910i | \(-0.0537017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 433.321 | 0.886137 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 184.551i | − 0.375867i | −0.982182 | − | 0.187934i | \(-0.939821\pi\) | ||||
0.982182 | − | 0.187934i | \(-0.0601790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −732.624 | −1.48605 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 105.067i | − 0.212257i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 574.659i | 1.15162i | 0.817583 | + | 0.575811i | \(0.195314\pi\) | ||||
−0.817583 | + | 0.575811i | \(0.804686\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −395.339 | −0.789101 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 198.567i | − 0.394764i | −0.980327 | − | 0.197382i | \(-0.936756\pi\) | ||||
0.980327 | − | 0.197382i | \(-0.0632440\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.67879 | −0.00530453 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 423.177i | 0.834668i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 209.376 | 0.411347 | 0.205674 | − | 0.978621i | \(-0.434061\pi\) | ||||
0.205674 | + | 0.978621i | \(0.434061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 145.982 | 0.284565 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 58.4768i | 0.113547i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1597.21 | 3.08939 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 68.1693i | 0.131347i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −340.367 | −0.653295 | −0.326647 | − | 0.945146i | \(-0.605919\pi\) | ||||
−0.326647 | + | 0.945146i | \(0.605919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 237.022i | 0.453196i | 0.973988 | + | 0.226598i | \(0.0727604\pi\) | ||||
−0.973988 | + | 0.226598i | \(0.927240\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 895.964i | 1.70012i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 424.927 | 0.803265 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 125.852i | 0.237009i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −575.964 | −1.08061 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 185.154i | − 0.346083i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −112.348 | −0.209215 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 692.570 | 1.28017 | 0.640083 | − | 0.768306i | \(-0.278900\pi\) | ||||
0.640083 | + | 0.768306i | \(0.278900\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 23.6451i | − 0.0435453i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −213.321 | −0.391415 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 301.027i | − 0.550323i | −0.961398 | − | 0.275162i | \(-0.911269\pi\) | ||||
0.961398 | − | 0.275162i | \(-0.0887314\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.9909 | 0.0673787 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 636.632i | 1.15541i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 217.063i | 0.391104i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 82.6970 | 0.148469 | 0.0742343 | − | 0.997241i | \(-0.476349\pi\) | ||||
0.0742343 | + | 0.997241i | \(0.476349\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 993.721i | 1.77768i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 980.588 | 1.74793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 75.1290i | 0.133444i | 0.997772 | + | 0.0667220i | \(0.0212541\pi\) | ||||
−0.997772 | + | 0.0667220i | \(0.978746\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −270.642 | −0.479013 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 255.909 | 0.449752 | 0.224876 | − | 0.974387i | \(-0.427802\pi\) | ||||
0.224876 | + | 0.974387i | \(0.427802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 791.341i | − 1.38589i | −0.720992 | − | 0.692943i | \(-0.756314\pi\) | ||||
0.720992 | − | 0.692943i | \(-0.243686\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 413.009 | 0.720784 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 214.234i | 0.372580i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 384.642 | 0.666625 | 0.333312 | − | 0.942816i | \(-0.391834\pi\) | ||||
0.333312 | + | 0.942816i | \(0.391834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 118.892i | 0.205341i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 817.084i | 1.40152i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 121.982 | 0.208516 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 429.167i | − 0.731120i | −0.930788 | − | 0.365560i | \(-0.880878\pi\) | ||||
0.930788 | − | 0.365560i | \(-0.119122\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 778.570 | 1.32185 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 367.163i | − 0.621258i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −859.524 | −1.44945 | −0.724725 | − | 0.689038i | \(-0.758033\pi\) | ||||
−0.724725 | + | 0.689038i | \(0.758033\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 272.697 | 0.456779 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 745.228i | 1.24412i | 0.782970 | + | 0.622060i | \(0.213704\pi\) | ||||
−0.782970 | + | 0.622060i | \(0.786296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −52.6424 | −0.0875914 | −0.0437957 | − | 0.999041i | \(-0.513945\pi\) | ||||
−0.0437957 | + | 0.999041i | \(0.513945\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 166.277i | − 0.275749i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −371.285 | −0.613694 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 635.425i | 1.04683i | 0.852078 | + | 0.523414i | \(0.175342\pi\) | ||||
−0.852078 | + | 0.523414i | \(0.824658\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1854.34i | 3.03493i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 71.9818 | 0.117425 | 0.0587127 | − | 0.998275i | \(-0.481300\pi\) | ||||
0.0587127 | + | 0.998275i | \(0.481300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 98.1390i | 0.159576i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1173.23 | −1.90151 | −0.950754 | − | 0.309947i | \(-0.899689\pi\) | ||||
−0.950754 | + | 0.309947i | \(0.899689\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 97.6947i | − 0.157827i | −0.996881 | − | 0.0789133i | \(-0.974855\pi\) | ||||
0.996881 | − | 0.0789133i | \(-0.0251450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −53.0091 | −0.0853609 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 341.000 | 0.545600 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 852.106i | − 1.35902i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2025.84 | −3.22073 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 198.692i | 0.314885i | 0.987528 | + | 0.157443i | \(0.0503249\pi\) | ||||
−0.987528 | + | 0.157443i | \(0.949675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −356.588 | −0.563330 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 169.328i | − 0.266658i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 159.889i | − 0.250218i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 342.588 | 0.534458 | 0.267229 | − | 0.963633i | \(-0.413892\pi\) | ||||
0.267229 | + | 0.963633i | \(0.413892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 776.340i | − 1.20737i | −0.797222 | − | 0.603686i | \(-0.793698\pi\) | ||||
0.797222 | − | 0.603686i | \(-0.206302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 169.321 | 0.262514 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 755.430i | − 1.16759i | −0.811902 | − | 0.583794i | \(-0.801568\pi\) | ||||
0.811902 | − | 0.583794i | \(-0.198432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 734.606 | 1.13190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −681.339 | −1.04340 | −0.521699 | − | 0.853129i | \(-0.674702\pi\) | ||||
−0.521699 | + | 0.853129i | \(0.674702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 150.895i | − 0.230374i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 64.0182 | 0.0974402 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 65.9456i | 0.100069i | 0.998747 | + | 0.0500346i | \(0.0159332\pi\) | ||||
−0.998747 | + | 0.0500346i | \(0.984067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −161.615 | −0.244501 | −0.122250 | − | 0.992499i | \(-0.539011\pi\) | ||||
−0.122250 | + | 0.992499i | \(0.539011\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1138.45i | 1.71712i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 231.175i | − 0.346589i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 284.588 | 0.425393 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 215.919i | − 0.321786i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 451.248 | 0.670503 | 0.335251 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335251 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 109.119i | 0.161658i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 117.964 | 0.174245 | 0.0871223 | − | 0.996198i | \(-0.472233\pi\) | ||||
0.0871223 | + | 0.996198i | \(0.472233\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −488.588 | −0.717456 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 49.9268i | − 0.0730993i | −0.999332 | − | 0.0365496i | \(-0.988363\pi\) | ||||
0.999332 | − | 0.0365496i | \(-0.0116367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −346.606 | −0.505994 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 162.209i | − 0.236112i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −948.624 | −1.37681 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 725.047i | − 1.04927i | −0.851327 | − | 0.524636i | \(-0.824201\pi\) | ||||
0.851327 | − | 0.524636i | \(-0.175799\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 460.313i | 0.662320i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −915.927 | −1.31410 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 390.299i | − 0.558368i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −587.982 | −0.838776 | −0.419388 | − | 0.907807i | \(-0.637755\pi\) | ||||
−0.419388 | + | 0.907807i | \(0.637755\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1760.40i | 2.50413i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 315.964 | 0.448175 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 801.303 | 1.13019 | 0.565094 | − | 0.825027i | \(-0.308840\pi\) | ||||
0.565094 | + | 0.825027i | \(0.308840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 290.985i | 0.409261i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −282.715 | −0.396515 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 712.016i | − 0.995827i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 141.633 | 0.197536 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 328.740i | 0.457218i | 0.973518 | + | 0.228609i | \(0.0734177\pi\) | ||||
−0.973518 | + | 0.228609i | \(0.926582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 564.649i | 0.780980i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −475.873 | −0.656376 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 767.442i | − 1.05563i | −0.849360 | − | 0.527814i | \(-0.823012\pi\) | ||||
0.849360 | − | 0.527814i | \(-0.176988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1580.27i | 2.16179i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 60.2939 | 0.0822564 | 0.0411282 | − | 0.999154i | \(-0.486905\pi\) | ||||
0.0411282 | + | 0.999154i | \(0.486905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −970.570 | −1.31692 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 920.499i | − 1.24560i | −0.782381 | − | 0.622801i | \(-0.785995\pi\) | ||||
0.782381 | − | 0.622801i | \(-0.214005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 989.285 | 1.33507 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 598.273i | 0.805213i | 0.915373 | + | 0.402606i | \(0.131896\pi\) | ||||
−0.915373 | + | 0.402606i | \(0.868104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 175.964 | 0.236193 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 191.638i | 0.256544i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 150.450i | − 0.200334i | −0.994971 | − | 0.100167i | \(-0.968062\pi\) | ||||
0.994971 | − | 0.100167i | \(-0.0319376\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −441.909 | −0.586865 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40.8064i | 0.0540482i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 773.339 | 1.02158 | 0.510792 | − | 0.859704i | \(-0.329352\pi\) | ||||
0.510792 | + | 0.859704i | \(0.329352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 309.418i | 0.407665i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 389.652 | 0.512026 | 0.256013 | − | 0.966673i | \(-0.417591\pi\) | ||||
0.256013 | + | 0.966673i | \(0.417591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 193.982 | 0.253571 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 852.869i | 1.11195i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.9818 | −0.0207826 | −0.0103913 | − | 0.999946i | \(-0.503308\pi\) | ||||
−0.0103913 | + | 0.999946i | \(0.503308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 224.563i | − 0.291262i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 833.303 | 1.07801 | 0.539006 | − | 0.842302i | \(-0.318800\pi\) | ||||
0.539006 | + | 0.842302i | \(0.318800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 581.969i | 0.750928i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 795.918i | 1.02172i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −933.285 | −1.19499 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 117.748i | − 0.150381i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −340.624 | −0.433916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1498.72i | 1.90434i | 0.305565 | + | 0.952171i | \(0.401155\pi\) | ||||
−0.305565 | + | 0.952171i | \(0.598845\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −683.615 | −0.866432 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 250.679 | 0.316114 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 161.637i | 0.203317i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −800.715 | −1.00466 | −0.502331 | − | 0.864676i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864676i | \(0.667524\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2948.87i | 3.69071i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −50.9727 | −0.0636364 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 373.679i | − 0.465353i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 48.4659i | − 0.0600569i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 243.394 | 0.300858 | 0.150429 | − | 0.988621i | \(-0.451935\pi\) | ||||
0.150429 | + | 0.988621i | \(0.451935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 750.597i | − 0.925521i | −0.886483 | − | 0.462760i | \(-0.846859\pi\) | ||||
0.886483 | − | 0.462760i | \(-0.153141\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.6788 | 0.0574155 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 500.356i | − 0.613934i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1373.21 | 1.68080 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1203.98 | −1.46648 | −0.733241 | − | 0.679969i | \(-0.761993\pi\) | ||||
−0.733241 | + | 0.679969i | \(0.761993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1385.51i | − 1.68349i | −0.539873 | − | 0.841746i | \(-0.681528\pi\) | ||||
0.539873 | − | 0.841746i | \(-0.318472\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 636.936 | 0.772044 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 120.608i | 0.145839i | 0.997338 | + | 0.0729193i | \(0.0232315\pi\) | ||||
−0.997338 | + | 0.0729193i | \(0.976768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 814.936 | 0.983035 | 0.491518 | − | 0.870868i | \(-0.336442\pi\) | ||||
0.491518 | + | 0.870868i | \(0.336442\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 84.3141i | 0.101461i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 456.499i | 0.546705i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −144.000 | −0.172043 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1267.35i | − 1.51055i | −0.655406 | − | 0.755276i | \(-0.727503\pi\) | ||||
0.655406 | − | 0.755276i | \(-0.272497\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −327.497 | −0.389414 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 196.247i | 0.232795i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 488.642 | 0.578275 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 413.945 | 0.487568 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 639.239i | − 0.751162i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 824.330 | 0.966390 | 0.483195 | − | 0.875513i | \(-0.339476\pi\) | ||||
0.483195 | + | 0.875513i | \(0.339476\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 168.565i | − 0.197152i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1054.83 | 1.23084 | 0.615418 | − | 0.788201i | \(-0.288987\pi\) | ||||
0.615418 | + | 0.788201i | \(0.288987\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 288.189i | − 0.335493i | −0.985830 | − | 0.167747i | \(-0.946351\pi\) | ||||
0.985830 | − | 0.167747i | \(-0.0536491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 497.338i | − 0.576290i | −0.957587 | − | 0.288145i | \(-0.906961\pi\) | ||||
0.957587 | − | 0.288145i | \(-0.0930385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 78.7152 | 0.0910002 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1309.86i | 1.51080i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1698.50 | 1.95454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1126.82i | − 1.29371i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −285.964 | −0.327564 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −822.624 | −0.937998 | −0.468999 | − | 0.883199i | \(-0.655385\pi\) | ||||
−0.468999 | + | 0.883199i | \(0.655385\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 9.31109i | − 0.0105928i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1017.47 | 1.15490 | 0.577452 | − | 0.816425i | \(-0.304047\pi\) | ||||
0.577452 | + | 0.816425i | \(0.304047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1333.58i | − 1.51029i | −0.655559 | − | 0.755144i | \(-0.727567\pi\) | ||||
0.655559 | − | 0.755144i | \(-0.272433\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 145.321 | 0.164205 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1422.95i | 1.60423i | 0.597170 | + | 0.802115i | \(0.296292\pi\) | ||||
−0.597170 | + | 0.802115i | \(0.703708\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 157.601i | 0.176881i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2562.50 | 2.86954 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 129.729i | 0.144948i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −359.230 | −0.400480 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 627.989i | − 0.698542i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1508.55 | −1.67431 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.3030 | −0.0301691 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1055.57i | 1.16380i | 0.813260 | + | 0.581901i | \(0.197691\pi\) | ||||
−0.813260 | + | 0.581901i | \(0.802309\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.01818 | 0.00442044 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 239.851i | − 0.263283i | −0.991297 | − | 0.131641i | \(-0.957975\pi\) | ||||
0.991297 | − | 0.131641i | \(-0.0420247\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1118.61 | 1.22520 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 42.7134i | − 0.0466813i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 690.850i | 0.751741i | 0.926672 | + | 0.375871i | \(0.122656\pi\) | ||||
−0.926672 | + | 0.375871i | \(0.877344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.0182 | 0.0239068 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1083.53i | − 1.17392i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1315.87 | −1.42257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 87.7152i | − 0.0946227i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 918.900 | 0.989128 | 0.494564 | − | 0.869141i | \(-0.335328\pi\) | ||||
0.494564 | + | 0.869141i | \(0.335328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 298.018 | 0.319419 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 1132.29i | − 1.21100i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 513.891 | 0.548443 | 0.274221 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274221 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 11.5365i | − 0.0122860i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −525.855 | −0.558825 | −0.279413 | − | 0.960171i | \(-0.590140\pi\) | ||||
−0.279413 | + | 0.960171i | \(0.590140\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 289.015i | − 0.306484i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1822.53i | 1.92453i | 0.272110 | + | 0.962266i | \(0.412279\pi\) | ||||
−0.272110 | + | 0.962266i | \(0.587721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 433.836 | 0.457151 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1036.85i | − 1.09027i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1394.04 | −1.46279 | −0.731394 | − | 0.681955i | \(-0.761130\pi\) | ||||
−0.731394 | + | 0.681955i | \(0.761130\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 476.902i | − 0.499374i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −687.303 | −0.718185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 193.000 | 0.200832 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 277.732i | 0.288403i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 137.285 | 0.142264 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1199.92i | − 1.24086i | −0.784260 | − | 0.620432i | \(-0.786957\pi\) | ||||
0.784260 | − | 0.620432i | \(-0.213043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1573.21 | 1.62354 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1067.52i | 1.09940i | 0.835362 | + | 0.549700i | \(0.185258\pi\) | ||||
−0.835362 | + | 0.549700i | \(0.814742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 739.475i | 0.758436i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −399.945 | −0.409361 | −0.204680 | − | 0.978829i | \(-0.565615\pi\) | ||||
−0.204680 | + | 0.978829i | \(0.565615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 297.531i | 0.303914i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 319.982 | 0.326179 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 15.3820i | − 0.0156480i | −0.999969 | − | 0.00782401i | \(-0.997510\pi\) | ||||
0.999969 | − | 0.00782401i | \(-0.00249049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −423.964 | −0.430420 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −498.642 | −0.504188 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1242.69i | 1.25398i | 0.779028 | + | 0.626989i | \(0.215713\pi\) | ||||
−0.779028 | + | 0.626989i | \(0.784287\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −772.515 | −0.777961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 314.883i | − 0.316466i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −604.330 | −0.606149 | −0.303074 | − | 0.952967i | \(-0.598013\pi\) | ||||
−0.303074 | + | 0.952967i | \(0.598013\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 325.594i | − 0.325920i |
(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 | 2352.3.m.i.1471.4 | 4 | ||
4.3 | odd | 2 | inner | 2352.3.m.i.1471.1 | 4 | ||
7.6 | odd | 2 | 336.3.m.b.127.2 | ✓ | 4 | ||
21.20 | even | 2 | 1008.3.m.e.127.3 | 4 | |||
28.27 | even | 2 | 336.3.m.b.127.3 | yes | 4 | ||
56.13 | odd | 2 | 1344.3.m.b.127.4 | 4 | |||
56.27 | even | 2 | 1344.3.m.b.127.1 | 4 | |||
84.83 | odd | 2 | 1008.3.m.e.127.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.m.b.127.2 | ✓ | 4 | 7.6 | odd | 2 | ||
336.3.m.b.127.3 | yes | 4 | 28.27 | even | 2 | ||
1008.3.m.e.127.2 | 4 | 84.83 | odd | 2 | |||
1008.3.m.e.127.3 | 4 | 21.20 | even | 2 | |||
1344.3.m.b.127.1 | 4 | 56.27 | even | 2 | |||
1344.3.m.b.127.4 | 4 | 56.13 | odd | 2 | |||
2352.3.m.i.1471.1 | 4 | 4.3 | odd | 2 | inner | ||
2352.3.m.i.1471.4 | 4 | 1.1 | even | 1 | trivial |