Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.193 |
Dual form | 1200.3.bg.i.1057.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.67423 | − | 3.67423i | 0.524891 | − | 0.524891i | −0.394154 | − | 0.919044i | \(-0.628962\pi\) |
0.919044 | + | 0.394154i | \(0.128962\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.00000 | −0.545455 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.12372 | − | 6.12372i | −0.471056 | − | 0.471056i | 0.431200 | − | 0.902256i | \(-0.358090\pi\) |
−0.902256 | + | 0.431200i | \(0.858090\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.0454 | + | 22.0454i | −1.29679 | + | 1.29679i | −0.366287 | + | 0.930502i | \(0.619371\pi\) |
−0.930502 | + | 0.366287i | \(0.880629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 25.0000i | − | 1.31579i | −0.753110 | − | 0.657895i | \(-0.771447\pi\) | ||
0.753110 | − | 0.657895i | \(-0.228553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.00000 | 0.428571 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.34847 | − | 7.34847i | −0.319499 | − | 0.319499i | 0.529076 | − | 0.848575i | \(-0.322539\pi\) |
−0.848575 | + | 0.529076i | \(0.822539\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.0000i | 1.44828i | 0.689655 | + | 0.724138i | \(0.257762\pi\) | ||||
−0.689655 | + | 0.724138i | \(0.742238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −49.0000 | −1.58065 | −0.790323 | − | 0.612691i | \(-0.790087\pi\) | ||||
−0.790323 | + | 0.612691i | \(0.790087\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.34847 | − | 7.34847i | −0.222681 | − | 0.222681i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89898 | + | 4.89898i | −0.132405 | + | 0.132405i | −0.770203 | − | 0.637798i | \(-0.779845\pi\) |
0.637798 | + | 0.770203i | \(0.279845\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 15.0000i | − | 0.384615i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −60.0000 | −1.46341 | −0.731707 | − | 0.681619i | \(-0.761276\pi\) | ||||
−0.731707 | + | 0.681619i | \(0.761276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.22474 | − | 1.22474i | −0.0284824 | − | 0.0284824i | 0.692722 | − | 0.721205i | \(-0.256411\pi\) |
−0.721205 | + | 0.692722i | \(0.756411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 51.4393 | − | 51.4393i | 1.09445 | − | 1.09445i | 0.0994059 | − | 0.995047i | \(-0.468306\pi\) |
0.995047 | − | 0.0994059i | \(-0.0316942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22.0000i | 0.448980i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −54.0000 | −1.05882 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.6969 | + | 14.6969i | 0.277301 | + | 0.277301i | 0.832031 | − | 0.554730i | \(-0.187178\pi\) |
−0.554730 | + | 0.832031i | \(0.687178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.6186 | − | 30.6186i | 0.537169 | − | 0.537169i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 78.0000i | 1.32203i | 0.750371 | + | 0.661017i | \(0.229875\pi\) | ||||
−0.750371 | + | 0.661017i | \(0.770125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0000 | −0.213115 | −0.106557 | − | 0.994307i | \(-0.533983\pi\) | ||||
−0.106557 | + | 0.994307i | \(0.533983\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.0227 | + | 11.0227i | 0.174964 | + | 0.174964i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.6640 | + | 52.6640i | −0.786030 | + | 0.786030i | −0.980841 | − | 0.194811i | \(-0.937591\pi\) |
0.194811 | + | 0.980841i | \(0.437591\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 18.0000i | − | 0.260870i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 60.0000 | 0.845070 | 0.422535 | − | 0.906347i | \(-0.361140\pi\) | ||||
0.422535 | + | 0.906347i | \(0.361140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63.6867 | − | 63.6867i | −0.872421 | − | 0.872421i | 0.120315 | − | 0.992736i | \(-0.461610\pi\) |
−0.992736 | + | 0.120315i | \(0.961610\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.0454 | + | 22.0454i | −0.286304 | + | 0.286304i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 106.000i | 1.34177i | 0.741560 | + | 0.670886i | \(0.234086\pi\) | ||||
−0.741560 | + | 0.670886i | \(0.765914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −80.8332 | − | 80.8332i | −0.973894 | − | 0.973894i | 0.0257743 | − | 0.999668i | \(-0.491795\pi\) |
−0.999668 | + | 0.0257743i | \(0.991795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −51.4393 | + | 51.4393i | −0.591256 | + | 0.591256i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 60.0000i | − | 0.674157i | −0.941476 | − | 0.337079i | \(-0.890561\pi\) | ||
0.941476 | − | 0.337079i | \(-0.109439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −45.0000 | −0.494505 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −60.0125 | − | 60.0125i | −0.645296 | − | 0.645296i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 121.250 | − | 121.250i | 1.25000 | − | 1.25000i | 0.294277 | − | 0.955720i | \(-0.404921\pi\) |
0.955720 | − | 0.294277i | \(-0.0950789\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 18.0000i | − | 0.181818i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −192.000 | −1.90099 | −0.950495 | − | 0.310740i | \(-0.899423\pi\) | ||||
−0.950495 | + | 0.310740i | \(0.899423\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −78.3837 | − | 78.3837i | −0.761007 | − | 0.761007i | 0.215498 | − | 0.976504i | \(-0.430863\pi\) |
−0.976504 | + | 0.215498i | \(0.930863\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 29.3939 | − | 29.3939i | 0.274709 | − | 0.274709i | −0.556283 | − | 0.830993i | \(-0.687773\pi\) |
0.830993 | + | 0.556283i | \(0.187773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.00000i | − | 0.00917431i | −0.999989 | − | 0.00458716i | \(-0.998540\pi\) | ||
0.999989 | − | 0.00458716i | \(-0.00146014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −0.108108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 58.7878 | + | 58.7878i | 0.520246 | + | 0.520246i | 0.917646 | − | 0.397400i | \(-0.130087\pi\) |
−0.397400 | + | 0.917646i | \(0.630087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.3712 | − | 18.3712i | 0.157019 | − | 0.157019i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 162.000i | 1.36134i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0000 | −0.702479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −73.4847 | − | 73.4847i | −0.597437 | − | 0.597437i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.6969 | + | 14.6969i | −0.115724 | + | 0.115724i | −0.762597 | − | 0.646873i | \(-0.776076\pi\) |
0.646873 | + | 0.762597i | \(0.276076\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.00000i | − | 0.0232558i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −0.0916031 | −0.0458015 | − | 0.998951i | \(-0.514584\pi\) | ||||
−0.0458015 | + | 0.998951i | \(0.514584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −91.8559 | − | 91.8559i | −0.690646 | − | 0.690646i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 80.8332 | − | 80.8332i | 0.590023 | − | 0.590023i | −0.347614 | − | 0.937638i | \(-0.613008\pi\) |
0.937638 | + | 0.347614i | \(0.113008\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 58.0000i | − | 0.417266i | −0.977994 | − | 0.208633i | \(-0.933099\pi\) | ||
0.977994 | − | 0.208633i | \(-0.0669014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 126.000 | 0.893617 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 36.7423 | + | 36.7423i | 0.256939 | + | 0.256939i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −26.9444 | + | 26.9444i | −0.183295 | + | 0.183295i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 234.000i | 1.57047i | 0.619198 | + | 0.785235i | \(0.287458\pi\) | ||||
−0.619198 | + | 0.785235i | \(0.712542\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −85.0000 | −0.562914 | −0.281457 | − | 0.959574i | \(-0.590818\pi\) | ||||
−0.281457 | + | 0.959574i | \(0.590818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −66.1362 | − | 66.1362i | −0.432263 | − | 0.432263i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −74.7094 | + | 74.7094i | −0.475856 | + | 0.475856i | −0.903804 | − | 0.427947i | \(-0.859237\pi\) |
0.427947 | + | 0.903804i | \(0.359237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 36.0000i | 0.226415i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −54.0000 | −0.335404 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −79.6084 | − | 79.6084i | −0.488395 | − | 0.488395i | 0.419404 | − | 0.907800i | \(-0.362239\pi\) |
−0.907800 | + | 0.419404i | \(0.862239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 176.363 | − | 176.363i | 1.05607 | − | 1.05607i | 0.0577355 | − | 0.998332i | \(-0.481612\pi\) |
0.998332 | − | 0.0577355i | \(-0.0183880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 94.0000i | − | 0.556213i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 75.0000 | 0.438596 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −80.8332 | − | 80.8332i | −0.467244 | − | 0.467244i | 0.433777 | − | 0.901020i | \(-0.357181\pi\) |
−0.901020 | + | 0.433777i | \(0.857181\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −95.5301 | + | 95.5301i | −0.539718 | + | 0.539718i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 42.0000i | − | 0.234637i | −0.993094 | − | 0.117318i | \(-0.962570\pi\) | ||
0.993094 | − | 0.117318i | \(-0.0374298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 145.000 | 0.801105 | 0.400552 | − | 0.916274i | \(-0.368818\pi\) | ||||
0.400552 | + | 0.916274i | \(0.368818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.9217 | − | 15.9217i | −0.0870037 | − | 0.0870037i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 132.272 | − | 132.272i | 0.707339 | − | 0.707339i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.0000i | 0.142857i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −294.000 | −1.53927 | −0.769634 | − | 0.638486i | \(-0.779561\pi\) | ||||
−0.769634 | + | 0.638486i | \(0.779561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.7196 | − | 25.7196i | −0.133262 | − | 0.133262i | 0.637329 | − | 0.770592i | \(-0.280039\pi\) |
−0.770592 | + | 0.637329i | \(0.780039\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.0454 | − | 22.0454i | 0.111906 | − | 0.111906i | −0.648937 | − | 0.760842i | \(-0.724786\pi\) |
0.760842 | + | 0.648937i | \(0.224786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 179.000i | − | 0.899497i | −0.893155 | − | 0.449749i | \(-0.851514\pi\) | ||
0.893155 | − | 0.449749i | \(-0.148486\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −129.000 | −0.641791 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 154.318 | + | 154.318i | 0.760186 | + | 0.760186i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.0454 | − | 22.0454i | 0.106500 | − | 0.106500i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 150.000i | 0.717703i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 85.0000 | 0.402844 | 0.201422 | − | 0.979505i | \(-0.435444\pi\) | ||||
0.201422 | + | 0.979505i | \(0.435444\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 73.4847 | + | 73.4847i | 0.344999 | + | 0.344999i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −180.037 | + | 180.037i | −0.829666 | + | 0.829666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 156.000i | − | 0.712329i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 270.000 | 1.22172 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 104.103 | + | 104.103i | 0.466831 | + | 0.466831i | 0.900886 | − | 0.434055i | \(-0.142918\pi\) |
−0.434055 | + | 0.900886i | \(0.642918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 373.000i | 1.62882i | 0.580289 | + | 0.814410i | \(0.302940\pi\) | ||||
−0.580289 | + | 0.814410i | \(0.697060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −54.0000 | −0.233766 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 220.454 | + | 220.454i | 0.946155 | + | 0.946155i | 0.998623 | − | 0.0524678i | \(-0.0167087\pi\) |
−0.0524678 | + | 0.998623i | \(0.516709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −129.823 | + | 129.823i | −0.547776 | + | 0.547776i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 36.0000i | 0.150628i | 0.997160 | + | 0.0753138i | \(0.0239959\pi\) | ||||
−0.997160 | + | 0.0753138i | \(0.976004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −97.0000 | −0.402490 | −0.201245 | − | 0.979541i | \(-0.564499\pi\) | ||||
−0.201245 | + | 0.979541i | \(0.564499\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −153.093 | + | 153.093i | −0.619810 | + | 0.619810i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 198.000i | − | 0.795181i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −288.000 | −1.14741 | −0.573705 | − | 0.819062i | \(-0.694494\pi\) | ||||
−0.573705 | + | 0.819062i | \(0.694494\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.0908 | + | 44.0908i | 0.174272 | + | 0.174272i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 338.030 | − | 338.030i | 1.31529 | − | 1.31529i | 0.397832 | − | 0.917458i | \(-0.369763\pi\) |
0.917458 | − | 0.397832i | \(-0.130237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.0000i | 0.138996i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −126.000 | −0.482759 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 249.848 | + | 249.848i | 0.949992 | + | 0.949992i | 0.998808 | − | 0.0488156i | \(-0.0155447\pi\) |
−0.0488156 | + | 0.998808i | \(0.515545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 73.4847 | − | 73.4847i | 0.275224 | − | 0.275224i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 318.000i | 1.18216i | 0.806614 | + | 0.591078i | \(0.201297\pi\) | ||||
−0.806614 | + | 0.591078i | \(0.798703\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 226.000 | 0.833948 | 0.416974 | − | 0.908918i | \(-0.363091\pi\) | ||||
0.416974 | + | 0.908918i | \(0.363091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −55.1135 | − | 55.1135i | −0.201881 | − | 0.201881i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −380.896 | + | 380.896i | −1.37507 | + | 1.37507i | −0.522333 | + | 0.852742i | \(0.674938\pi\) |
−0.852742 | + | 0.522333i | \(0.825062\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 147.000i | − | 0.526882i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 126.000 | 0.448399 | 0.224199 | − | 0.974543i | \(-0.428023\pi\) | ||||
0.224199 | + | 0.974543i | \(0.428023\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −395.593 | − | 395.593i | −1.39785 | − | 1.39785i | −0.806171 | − | 0.591683i | \(-0.798464\pi\) |
−0.591683 | − | 0.806171i | \(-0.701536\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −220.454 | + | 220.454i | −0.768133 | + | 0.768133i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 683.000i | − | 2.36332i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 297.000 | 1.02062 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.0454 | + | 22.0454i | 0.0752403 | + | 0.0752403i | 0.743725 | − | 0.668485i | \(-0.233057\pi\) |
−0.668485 | + | 0.743725i | \(0.733057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.0454 | − | 22.0454i | 0.0742270 | − | 0.0742270i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 90.0000i | 0.301003i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.00000 | −0.0299003 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −235.151 | − | 235.151i | −0.776076 | − | 0.776076i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −86.9569 | + | 86.9569i | −0.283247 | + | 0.283247i | −0.834403 | − | 0.551155i | \(-0.814187\pi\) |
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 192.000i | − | 0.621359i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 246.000 | 0.790997 | 0.395498 | − | 0.918467i | \(-0.370572\pi\) | ||||
0.395498 | + | 0.918467i | \(0.370572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −37.9671 | − | 37.9671i | −0.121301 | − | 0.121301i | 0.643851 | − | 0.765151i | \(-0.277336\pi\) |
−0.765151 | + | 0.643851i | \(0.777336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6969 | − | 14.6969i | 0.0463626 | − | 0.0463626i | −0.683545 | − | 0.729908i | \(-0.739563\pi\) |
0.729908 | + | 0.683545i | \(0.239563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 252.000i | − | 0.789969i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 72.0000 | 0.224299 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 551.135 | + | 551.135i | 1.70630 | + | 1.70630i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.22474 | − | 1.22474i | 0.00374540 | − | 0.00374540i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 378.000i | − | 1.14894i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 178.000 | 0.537764 | 0.268882 | − | 0.963173i | \(-0.413346\pi\) | ||||
0.268882 | + | 0.963173i | \(0.413346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6969 | − | 14.6969i | −0.0441350 | − | 0.0441350i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 417.638 | − | 417.638i | 1.23928 | − | 1.23928i | 0.278987 | − | 0.960295i | \(-0.410001\pi\) |
0.960295 | − | 0.278987i | \(-0.0899987\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 144.000i | 0.424779i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 294.000 | 0.862170 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 260.871 | + | 260.871i | 0.760556 | + | 0.760556i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −448.257 | + | 448.257i | −1.29181 | + | 1.29181i | −0.358137 | + | 0.933669i | \(0.616588\pi\) |
−0.933669 | + | 0.358137i | \(0.883412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 542.000i | − | 1.55301i | −0.630112 | − | 0.776504i | \(-0.716991\pi\) | ||
0.630112 | − | 0.776504i | \(-0.283009\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 45.0000 | 0.128205 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 242.499 | + | 242.499i | 0.686967 | + | 0.686967i | 0.961561 | − | 0.274593i | \(-0.0885432\pi\) |
−0.274593 | + | 0.961561i | \(0.588543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −198.409 | + | 198.409i | −0.555767 | + | 0.555767i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 408.000i | 1.13649i | 0.822859 | + | 0.568245i | \(0.192377\pi\) | ||||
−0.822859 | + | 0.568245i | \(0.807623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −264.000 | −0.731302 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −104.103 | − | 104.103i | −0.286786 | − | 0.286786i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 199.633 | − | 199.633i | 0.543960 | − | 0.543960i | −0.380727 | − | 0.924687i | \(-0.624326\pi\) |
0.924687 | + | 0.380727i | \(0.124326\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 180.000i | − | 0.487805i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 108.000 | 0.291105 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 319.658 | + | 319.658i | 0.856993 | + | 0.856993i | 0.990983 | − | 0.133990i | \(-0.0427789\pi\) |
−0.133990 | + | 0.990983i | \(0.542779\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 257.196 | − | 257.196i | 0.682219 | − | 0.682219i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 71.0000i | 0.187335i | 0.995604 | + | 0.0936675i | \(0.0298591\pi\) | ||||
−0.995604 | + | 0.0936675i | \(0.970141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.0000 | −0.0944882 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −58.7878 | − | 58.7878i | −0.153493 | − | 0.153493i | 0.626183 | − | 0.779676i | \(-0.284616\pi\) |
−0.779676 | + | 0.626183i | \(0.784616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.67423 | − | 3.67423i | 0.00949415 | − | 0.00949415i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 288.000i | 0.740360i | 0.928960 | + | 0.370180i | \(0.120704\pi\) | ||||
−0.928960 | + | 0.370180i | \(0.879296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 324.000 | 0.828645 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.6969 | − | 14.6969i | −0.0373968 | − | 0.0373968i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 74.7094 | − | 74.7094i | 0.188185 | − | 0.188185i | −0.606726 | − | 0.794911i | \(-0.707517\pi\) |
0.794911 | + | 0.606726i | \(0.207517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 225.000i | − | 0.563910i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.0000 | 0.0897756 | 0.0448878 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448878 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 300.062 | + | 300.062i | 0.744572 | + | 0.744572i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.3939 | − | 29.3939i | 0.0722208 | − | 0.0722208i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.0000i | 0.0317848i | 0.999874 | + | 0.0158924i | \(0.00505893\pi\) | ||||
−0.999874 | + | 0.0158924i | \(0.994941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 198.000 | 0.481752 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 286.590 | + | 286.590i | 0.693923 | + | 0.693923i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 71.0352 | − | 71.0352i | 0.170348 | − | 0.170348i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 144.000i | 0.343675i | 0.985125 | + | 0.171838i | \(0.0549705\pi\) | ||||
−0.985125 | + | 0.171838i | \(0.945030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 610.000 | 1.44893 | 0.724466 | − | 0.689311i | \(-0.242087\pi\) | ||||
0.724466 | + | 0.689311i | \(0.242087\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 154.318 | + | 154.318i | 0.364818 | + | 0.364818i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −47.7650 | + | 47.7650i | −0.111862 | + | 0.111862i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 90.0000i | 0.209790i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 402.000 | 0.932715 | 0.466357 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466357 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 292.714 | + | 292.714i | 0.676014 | + | 0.676014i | 0.959096 | − | 0.283082i | \(-0.0913568\pi\) |
−0.283082 | + | 0.959096i | \(0.591357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −183.712 | + | 183.712i | −0.420393 | + | 0.420393i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 119.000i | − | 0.271071i | −0.990773 | − | 0.135535i | \(-0.956725\pi\) | ||
0.990773 | − | 0.135535i | \(-0.0432754\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −66.0000 | −0.149660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 191.060 | + | 191.060i | 0.431287 | + | 0.431287i | 0.889066 | − | 0.457779i | \(-0.151355\pi\) |
−0.457779 | + | 0.889066i | \(0.651355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −286.590 | + | 286.590i | −0.641142 | + | 0.641142i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 84.0000i | 0.187082i | 0.995615 | + | 0.0935412i | \(0.0298187\pi\) | ||||
−0.995615 | + | 0.0935412i | \(0.970181\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 360.000 | 0.798226 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −104.103 | − | 104.103i | −0.229809 | − | 0.229809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −146.969 | + | 146.969i | −0.321596 | + | 0.321596i | −0.849379 | − | 0.527783i | \(-0.823023\pi\) |
0.527783 | + | 0.849379i | \(0.323023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 162.000i | − | 0.352941i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 516.000 | 1.11931 | 0.559653 | − | 0.828727i | \(-0.310934\pi\) | ||||
0.559653 | + | 0.828727i | \(0.310934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −524.191 | − | 524.191i | −1.13216 | − | 1.13216i | −0.989817 | − | 0.142344i | \(-0.954536\pi\) |
−0.142344 | − | 0.989817i | \(-0.545464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 507.044 | − | 507.044i | 1.08575 | − | 1.08575i | 0.0897872 | − | 0.995961i | \(-0.471381\pi\) |
0.995961 | − | 0.0897872i | \(-0.0286187\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 387.000i | 0.825160i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −183.000 | −0.388535 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.34847 | + | 7.34847i | 0.0155359 | + | 0.0155359i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −44.0908 | + | 44.0908i | −0.0924336 | + | 0.0924336i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 102.000i | − | 0.212944i | −0.994316 | − | 0.106472i | \(-0.966045\pi\) | ||
0.994316 | − | 0.106472i | \(-0.0339554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 60.0000 | 0.124740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −66.1362 | − | 66.1362i | −0.136928 | − | 0.136928i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −243.724 | + | 243.724i | −0.500460 | + | 0.500460i | −0.911581 | − | 0.411121i | \(-0.865138\pi\) |
0.411121 | + | 0.911581i | \(0.365138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 195.000i | − | 0.398773i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −444.000 | −0.904277 | −0.452138 | − | 0.891948i | \(-0.649339\pi\) | ||||
−0.452138 | + | 0.891948i | \(0.649339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −925.907 | − | 925.907i | −1.87811 | − | 1.87811i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 220.454 | − | 220.454i | 0.443570 | − | 0.443570i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 707.000i | − | 1.41683i | −0.705794 | − | 0.708417i | \(-0.749410\pi\) | ||
0.705794 | − | 0.708417i | \(-0.250590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 432.000 | 0.862275 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −176.363 | − | 176.363i | −0.350623 | − | 0.350623i | 0.509718 | − | 0.860341i | \(-0.329750\pi\) |
−0.860341 | + | 0.509718i | \(0.829750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 115.126 | − | 115.126i | 0.227073 | − | 0.227073i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 666.000i | 1.30845i | 0.756301 | + | 0.654224i | \(0.227005\pi\) | ||||
−0.756301 | + | 0.654224i | \(0.772995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −468.000 | −0.915851 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 91.8559 | + | 91.8559i | 0.179056 | + | 0.179056i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −308.636 | + | 308.636i | −0.596974 | + | 0.596974i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 198.000i | − | 0.381503i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −558.000 | −1.07102 | −0.535509 | − | 0.844530i | \(-0.679880\pi\) | ||||
−0.535509 | + | 0.844530i | \(0.679880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 547.461 | + | 547.461i | 1.04677 | + | 1.04677i | 0.998851 | + | 0.0479193i | \(0.0152590\pi\) |
0.0479193 | + | 0.998851i | \(0.484741\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1080.22 | − | 1080.22i | 2.04976 | − | 2.04976i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 421.000i | − | 0.795841i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −234.000 | −0.440678 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 367.423 | + | 367.423i | 0.689350 | + | 0.689350i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.4393 | − | 51.4393i | 0.0957901 | − | 0.0957901i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 132.000i | − | 0.244898i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 803.000 | 1.48429 | 0.742144 | − | 0.670240i | \(-0.233809\pi\) | ||||
0.742144 | + | 0.670240i | \(0.233809\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 177.588 | + | 177.588i | 0.327050 | + | 0.327050i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 215.555 | − | 215.555i | 0.394068 | − | 0.394068i | −0.482067 | − | 0.876135i | \(-0.660114\pi\) |
0.876135 | + | 0.482067i | \(0.160114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 39.0000i | − | 0.0710383i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1050.00 | 1.90563 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 389.469 | + | 389.469i | 0.704284 | + | 0.704284i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −448.257 | + | 448.257i | −0.804770 | + | 0.804770i | −0.983837 | − | 0.179067i | \(-0.942692\pi\) |
0.179067 | + | 0.983837i | \(0.442692\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.0000i | 0.0268336i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 324.000 | 0.577540 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 257.196 | + | 257.196i | 0.456832 | + | 0.456832i | 0.897614 | − | 0.440782i | \(-0.145299\pi\) |
−0.440782 | + | 0.897614i | \(0.645299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −33.0681 | + | 33.0681i | −0.0583212 | + | 0.0583212i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 582.000i | − | 1.02285i | −0.859329 | − | 0.511424i | \(-0.829118\pi\) | ||
0.859329 | − | 0.511424i | \(-0.170882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −215.000 | −0.376532 | −0.188266 | − | 0.982118i | \(-0.560287\pi\) | ||||
−0.188266 | + | 0.982118i | \(0.560287\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −360.075 | − | 360.075i | −0.628403 | − | 0.628403i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −246.174 | + | 246.174i | −0.426644 | + | 0.426644i | −0.887484 | − | 0.460839i | \(-0.847548\pi\) |
0.460839 | + | 0.887484i | \(0.347548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 63.0000i | − | 0.108808i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −594.000 | −1.02238 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −88.1816 | − | 88.1816i | −0.151255 | − | 0.151255i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.6969 | + | 14.6969i | −0.0250374 | + | 0.0250374i | −0.719515 | − | 0.694477i | \(-0.755636\pi\) |
0.694477 | + | 0.719515i | \(0.255636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1225.00i | 2.07980i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.0000 | 0.0913706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −323.333 | − | 323.333i | −0.545249 | − | 0.545249i | 0.379814 | − | 0.925063i | \(-0.375988\pi\) |
−0.925063 | + | 0.379814i | \(0.875988\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 219.229 | − | 219.229i | 0.367218 | − | 0.367218i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 528.000i | − | 0.881469i | −0.897637 | − | 0.440735i | \(-0.854718\pi\) | ||
0.897637 | − | 0.440735i | \(-0.145282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 493.000 | 0.820300 | 0.410150 | − | 0.912018i | \(-0.365476\pi\) | ||||
0.410150 | + | 0.912018i | \(0.365476\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −157.992 | − | 157.992i | −0.262010 | − | 0.262010i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −729.948 | + | 729.948i | −1.20255 | + | 1.20255i | −0.229162 | + | 0.973388i | \(0.573598\pi\) |
−0.973388 | + | 0.229162i | \(0.926402\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 378.000i | 0.620690i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −630.000 | −1.03110 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −112.677 | − | 112.677i | −0.183812 | − | 0.183812i | 0.609203 | − | 0.793014i | \(-0.291490\pi\) |
−0.793014 | + | 0.609203i | \(0.791490\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −382.120 | + | 382.120i | −0.619320 | + | 0.619320i | −0.945357 | − | 0.326037i | \(-0.894287\pi\) |
0.326037 | + | 0.945357i | \(0.394287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 733.000i | 1.18417i | 0.805876 | + | 0.592084i | \(0.201695\pi\) | ||||
−0.805876 | + | 0.592084i | \(0.798305\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 54.0000 | 0.0869565 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −220.454 | − | 220.454i | −0.353859 | − | 0.353859i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −183.712 | + | 183.712i | −0.293001 | + | 0.293001i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 216.000i | − | 0.343402i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −647.000 | −1.02536 | −0.512678 | − | 0.858581i | \(-0.671347\pi\) | ||||
−0.512678 | + | 0.858581i | \(0.671347\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 104.103 | + | 104.103i | 0.164460 | + | 0.164460i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 134.722 | − | 134.722i | 0.211494 | − | 0.211494i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 180.000i | 0.281690i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −636.000 | −0.992200 | −0.496100 | − | 0.868265i | \(-0.665235\pi\) | ||||
−0.496100 | + | 0.868265i | \(0.665235\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −396.817 | − | 396.817i | −0.617134 | − | 0.617134i | 0.327661 | − | 0.944795i | \(-0.393740\pi\) |
−0.944795 | + | 0.327661i | \(0.893740\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3939 | − | 29.3939i | 0.0454310 | − | 0.0454310i | −0.684026 | − | 0.729457i | \(-0.739773\pi\) |
0.729457 | + | 0.684026i | \(0.239773\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 468.000i | − | 0.721109i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −441.000 | −0.677419 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 521.741 | + | 521.741i | 0.798991 | + | 0.798991i | 0.982936 | − | 0.183945i | \(-0.0588869\pi\) |
−0.183945 | + | 0.982936i | \(0.558887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 191.060 | − | 191.060i | 0.290807 | − | 0.290807i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000i | 0.0546282i | 0.999627 | + | 0.0273141i | \(0.00869543\pi\) | ||||
−0.999627 | + | 0.0273141i | \(0.991305\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1022.00 | −1.54614 | −0.773071 | − | 0.634319i | \(-0.781280\pi\) | ||||
−0.773071 | + | 0.634319i | \(0.781280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 330.681 | + | 330.681i | 0.498765 | + | 0.498765i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 308.636 | − | 308.636i | 0.462722 | − | 0.462722i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 255.000i | 0.381166i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 78.0000 | 0.116244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −857.321 | − | 857.321i | −1.27388 | − | 1.27388i | −0.944035 | − | 0.329845i | \(-0.893003\pi\) |
−0.329845 | − | 0.944035i | \(-0.606997\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −536.438 | + | 536.438i | −0.792376 | + | 0.792376i | −0.981880 | − | 0.189504i | \(-0.939312\pi\) |
0.189504 | + | 0.981880i | \(0.439312\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 891.000i | − | 1.31222i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −764.241 | − | 764.241i | −1.11895 | − | 1.11895i | −0.991896 | − | 0.127051i | \(-0.959449\pi\) |
−0.127051 | − | 0.991896i | \(-0.540551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −456.830 | + | 456.830i | −0.664963 | + | 0.664963i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 180.000i | − | 0.261248i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 842.000 | 1.21852 | 0.609262 | − | 0.792969i | \(-0.291466\pi\) | ||||
0.609262 | + | 0.792969i | \(0.291466\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −66.1362 | − | 66.1362i | −0.0954347 | − | 0.0954347i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1322.72 | − | 1322.72i | 1.89774 | − | 1.89774i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 540.000i | 0.772532i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −534.000 | −0.761769 | −0.380884 | − | 0.924623i | \(-0.624380\pi\) | ||||
−0.380884 | + | 0.924623i | \(0.624380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 122.474 | + | 122.474i | 0.174217 | + | 0.174217i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −705.453 | + | 705.453i | −0.997812 | + | 0.997812i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 743.000i | − | 1.04795i | −0.851732 | − | 0.523977i | \(-0.824448\pi\) | ||
0.851732 | − | 0.523977i | \(-0.175552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −318.000 | −0.447257 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 360.075 | + | 360.075i | 0.505014 | + | 0.505014i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.0908 | + | 44.0908i | −0.0614935 | + | 0.0614935i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 906.000i | 1.26008i | 0.776561 | + | 0.630042i | \(0.216962\pi\) | ||||
−0.776561 | + | 0.630042i | \(0.783038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −576.000 | −0.798890 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −118.800 | − | 118.800i | −0.164316 | − | 0.164316i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 74.7094 | − | 74.7094i | 0.102764 | − | 0.102764i | −0.653855 | − | 0.756619i | \(-0.726850\pi\) |
0.756619 | + | 0.653855i | \(0.226850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.0000 | 0.0738714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 631.968 | + | 631.968i | 0.862167 | + | 0.862167i | 0.991590 | − | 0.129423i | \(-0.0413124\pi\) |
−0.129423 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 315.984 | − | 315.984i | 0.428744 | − | 0.428744i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 470.000i | 0.635995i | 0.948092 | + | 0.317997i | \(0.103010\pi\) | ||||
−0.948092 | + | 0.317997i | \(0.896990\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −375.000 | −0.506073 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −249.848 | − | 249.848i | −0.336269 | − | 0.336269i | 0.518692 | − | 0.854961i | \(-0.326419\pi\) |
−0.854961 | + | 0.518692i | \(0.826419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 242.499 | − | 242.499i | 0.324631 | − | 0.324631i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 216.000i | − | 0.288385i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1282.00 | −1.70706 | −0.853529 | − | 0.521046i | \(-0.825542\pi\) | ||||
−0.853529 | + | 0.521046i | \(0.825542\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −352.727 | − | 352.727i | −0.468428 | − | 0.468428i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −106.553 | + | 106.553i | −0.140757 | + | 0.140757i | −0.773974 | − | 0.633217i | \(-0.781734\pi\) |
0.633217 | + | 0.773974i | \(0.281734\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 108.000i | 0.142292i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −768.000 | −1.00920 | −0.504599 | − | 0.863354i | \(-0.668360\pi\) | ||||
−0.504599 | + | 0.863354i | \(0.668360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.67423 | − | 3.67423i | −0.00481551 | − | 0.00481551i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 477.650 | − | 477.650i | 0.622752 | − | 0.622752i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 491.000i | 0.638492i | 0.947672 | + | 0.319246i | \(0.103430\pi\) | ||||
−0.947672 | + | 0.319246i | \(0.896570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 828.000 | 1.07393 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −793.635 | − | 793.635i | −1.02669 | − | 1.02669i | −0.999634 | − | 0.0270605i | \(-0.991385\pi\) |
−0.0270605 | − | 0.999634i | \(-0.508615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.0908 | + | 44.0908i | −0.0567449 | + | 0.0567449i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1500.00i | 1.92555i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −360.000 | −0.460948 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −154.318 | − | 154.318i | −0.197085 | − | 0.197085i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −378.446 | + | 378.446i | −0.480872 | + | 0.480872i | −0.905410 | − | 0.424538i | \(-0.860436\pi\) |
0.424538 | + | 0.905410i | \(0.360436\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 612.000i | 0.775665i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 432.000 | 0.546144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 79.6084 | + | 79.6084i | 0.100389 | + | 0.100389i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 617.271 | − | 617.271i | 0.774494 | − | 0.774494i | −0.204395 | − | 0.978889i | \(-0.565523\pi\) |
0.978889 | + | 0.204395i | \(0.0655227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2268.00i | 2.83855i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 180.000 | 0.224719 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 382.120 | + | 382.120i | 0.475866 | + | 0.475866i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −389.469 | + | 389.469i | −0.482613 | + | 0.482613i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 348.000i | 0.430161i | 0.976596 | + | 0.215080i | \(0.0690013\pi\) | ||||
−0.976596 | + | 0.215080i | \(0.930999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1045.00 | −1.28853 | −0.644266 | − | 0.764801i | \(-0.722837\pi\) | ||||
−0.644266 | + | 0.764801i | \(0.722837\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 276.792 | + | 276.792i | 0.340458 | + | 0.340458i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.6186 | + | 30.6186i | −0.0374769 | + | 0.0374769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 135.000i | − | 0.164835i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 606.000 | 0.738124 | 0.369062 | − | 0.929405i | \(-0.379679\pi\) | ||||
0.369062 | + | 0.929405i | \(0.379679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 302.512 | + | 302.512i | 0.367572 | + | 0.367572i | 0.866591 | − | 0.499019i | \(-0.166306\pi\) |
−0.499019 | + | 0.866591i | \(0.666306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −396.817 | + | 396.817i | −0.479827 | + | 0.479827i | −0.905076 | − | 0.425249i | \(-0.860187\pi\) |
0.425249 | + | 0.905076i | \(0.360187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 406.000i | 0.489747i | 0.969555 | + | 0.244873i | \(0.0787464\pi\) | ||||
−0.969555 | + | 0.244873i | \(0.921254\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −933.000 | −1.12274 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −484.999 | − | 484.999i | −0.582232 | − | 0.582232i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 180.037 | − | 180.037i | 0.215099 | − | 0.215099i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 462.000i | − | 0.550656i | −0.961350 | − | 0.275328i | \(-0.911214\pi\) | ||
0.961350 | − | 0.275328i | \(-0.0887864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −923.000 | −1.09750 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 154.318 | + | 154.318i | 0.183058 | + | 0.183058i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −312.310 | + | 312.310i | −0.368725 | + | 0.368725i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 969.000i | − | 1.14134i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 72.0000 | 0.0846063 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −285.366 | − | 285.366i | −0.334543 | − | 0.334543i | 0.519766 | − | 0.854309i | \(-0.326019\pi\) |
−0.854309 | + | 0.519766i | \(0.826019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −191.060 | + | 191.060i | −0.222941 | + | 0.222941i | −0.809736 | − | 0.586795i | \(-0.800389\pi\) |
0.586795 | + | 0.809736i | \(0.300389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 410.000i | − | 0.477299i | −0.971106 | − | 0.238650i | \(-0.923295\pi\) | ||
0.971106 | − | 0.238650i | \(-0.0767047\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −540.000 | −0.627178 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1116.97 | − | 1116.97i | −1.29428 | − | 1.29428i | −0.932111 | − | 0.362174i | \(-0.882035\pi\) |
−0.362174 | − | 0.932111i | \(-0.617965\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 836.501 | − | 836.501i | 0.964822 | − | 0.964822i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 636.000i | − | 0.731876i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 645.000 | 0.740528 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 363.749 | + | 363.749i | 0.416666 | + | 0.416666i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −180.037 | + | 180.037i | −0.205288 | + | 0.205288i | −0.802261 | − | 0.596973i | \(-0.796370\pi\) |
0.596973 | + | 0.802261i | \(0.296370\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.0000i | 0.0614334i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −120.000 | −0.136209 | −0.0681044 | − | 0.997678i | \(-0.521695\pi\) | ||||
−0.0681044 | + | 0.997678i | \(0.521695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −584.203 | − | 584.203i | −0.661612 | − | 0.661612i | 0.294148 | − | 0.955760i | \(-0.404964\pi\) |
−0.955760 | + | 0.294148i | \(0.904964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −198.409 | + | 198.409i | −0.223685 | + | 0.223685i | −0.810048 | − | 0.586363i | \(-0.800559\pi\) |
0.586363 | + | 0.810048i | \(0.300559\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 108.000i | 0.121485i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 54.0000 | 0.0606061 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1285.98 | − | 1285.98i | −1.44007 | − | 1.44007i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −110.227 | + | 110.227i | −0.122884 | + | 0.122884i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2058.00i | − | 2.28921i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −648.000 | −0.719201 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.0227 | − | 11.0227i | −0.0122068 | − | 0.0122068i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1033.68 | − | 1033.68i | 1.13967 | − | 1.13967i | 0.151166 | − | 0.988508i | \(-0.451697\pi\) |
0.988508 | − | 0.151166i | \(-0.0483028\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 576.000i | − | 0.633663i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1218.00 | −1.33699 | −0.668496 | − | 0.743716i | \(-0.733062\pi\) | ||||
−0.668496 | + | 0.743716i | \(0.733062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 484.999 | + | 484.999i | 0.531215 | + | 0.531215i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.0908 | + | 44.0908i | −0.0480816 | + | 0.0480816i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 469.000i | − | 0.510337i | −0.966897 | − | 0.255169i | \(-0.917869\pi\) | ||
0.966897 | − | 0.255169i | \(-0.0821310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −213.000 | −0.231270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −367.423 | − | 367.423i | −0.398075 | − | 0.398075i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 235.151 | − | 235.151i | 0.253669 | − | 0.253669i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 474.000i | 0.510226i | 0.966911 | + | 0.255113i | \(0.0821127\pi\) | ||||
−0.966911 | + | 0.255113i | \(0.917887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 550.000 | 0.590763 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 301.287 | + | 301.287i | 0.322923 | + | 0.322923i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −709.127 | + | 709.127i | −0.756806 | + | 0.756806i | −0.975740 | − | 0.218934i | \(-0.929742\pi\) |
0.218934 | + | 0.975740i | \(0.429742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 93.0000i | − | 0.0990415i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 990.000 | 1.05207 | 0.526036 | − | 0.850462i | \(-0.323678\pi\) | ||||
0.526036 | + | 0.850462i | \(0.323678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 440.908 | + | 440.908i | 0.467559 | + | 0.467559i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1036.13 | + | 1036.13i | −1.09412 | + | 1.09412i | −0.0990391 | + | 0.995084i | \(0.531577\pi\) |
−0.995084 | + | 0.0990391i | \(0.968423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 780.000i | 0.821918i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.0000 | 0.0378549 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −631.968 | − | 631.968i | −0.663136 | − | 0.663136i | 0.292982 | − | 0.956118i | \(-0.405352\pi\) |
−0.956118 | + | 0.292982i | \(0.905352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 308.636 | − | 308.636i | 0.322503 | − | 0.322503i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 594.000i | − | 0.619395i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1440.00 | 1.49844 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 88.1816 | + | 88.1816i | 0.0915697 | + | 0.0915697i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 563.383 | − | 563.383i | 0.582609 | − | 0.582609i | −0.353011 | − | 0.935619i | \(-0.614842\pi\) |
0.935619 | + | 0.353011i | \(0.114842\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1350.00i | 1.39319i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1338.00 | −1.37796 | −0.688980 | − | 0.724780i | \(-0.741941\pi\) | ||||
−0.688980 | + | 0.724780i | \(0.741941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −213.106 | − | 213.106i | −0.219019 | − | 0.219019i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −301.287 | + | 301.287i | −0.308380 | + | 0.308380i | −0.844281 | − | 0.535901i | \(-0.819972\pi\) |
0.535901 | + | 0.844281i | \(0.319972\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 360.000i | 0.367722i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | 0.00305810 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −426.211 | − | 426.211i | −0.433582 | − | 0.433582i | 0.456263 | − | 0.889845i | \(-0.349188\pi\) |
−0.889845 | + | 0.456263i | \(0.849188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 462.954 | − | 462.954i | 0.469051 | − | 0.469051i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0000i | 0.0182002i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −83.0000 | −0.0837538 | −0.0418769 | − | 0.999123i | \(-0.513334\pi\) | ||||
−0.0418769 | + | 0.999123i | \(0.513334\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 218.005 | + | 218.005i | 0.219541 | + | 0.219541i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 573.181 | − | 573.181i | 0.574905 | − | 0.574905i | −0.358590 | − | 0.933495i | \(-0.616742\pi\) |
0.933495 | + | 0.358590i | \(0.116742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 36.0000i | − | 0.0360360i |
(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 | 1200.3.bg.i.193.2 | 4 | ||
4.3 | odd | 2 | 300.3.k.c.193.1 | yes | 4 | ||
5.2 | odd | 4 | inner | 1200.3.bg.i.1057.2 | 4 | ||
5.3 | odd | 4 | inner | 1200.3.bg.i.1057.1 | 4 | ||
5.4 | even | 2 | inner | 1200.3.bg.i.193.1 | 4 | ||
12.11 | even | 2 | 900.3.l.d.793.1 | 4 | |||
20.3 | even | 4 | 300.3.k.c.157.2 | yes | 4 | ||
20.7 | even | 4 | 300.3.k.c.157.1 | ✓ | 4 | ||
20.19 | odd | 2 | 300.3.k.c.193.2 | yes | 4 | ||
60.23 | odd | 4 | 900.3.l.d.757.2 | 4 | |||
60.47 | odd | 4 | 900.3.l.d.757.1 | 4 | |||
60.59 | even | 2 | 900.3.l.d.793.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.k.c.157.1 | ✓ | 4 | 20.7 | even | 4 | ||
300.3.k.c.157.2 | yes | 4 | 20.3 | even | 4 | ||
300.3.k.c.193.1 | yes | 4 | 4.3 | odd | 2 | ||
300.3.k.c.193.2 | yes | 4 | 20.19 | odd | 2 | ||
900.3.l.d.757.1 | 4 | 60.47 | odd | 4 | |||
900.3.l.d.757.2 | 4 | 60.23 | odd | 4 | |||
900.3.l.d.793.1 | 4 | 12.11 | even | 2 | |||
900.3.l.d.793.2 | 4 | 60.59 | even | 2 | |||
1200.3.bg.i.193.1 | 4 | 5.4 | even | 2 | inner | ||
1200.3.bg.i.193.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.i.1057.1 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.i.1057.2 | 4 | 5.2 | odd | 4 | inner |