Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), 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: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.145 |
Dual form | 1008.3.cg.b.577.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50000 | − | 0.866025i | −0.300000 | − | 0.173205i | 0.342443 | − | 0.939539i | \(-0.388746\pi\) |
−0.642443 | + | 0.766334i | \(0.722079\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.136364 | + | 0.236189i | 0.926118 | − | 0.377235i | \(-0.123125\pi\) |
−0.789754 | + | 0.613424i | \(0.789792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.92820i | − | 0.532939i | −0.963843 | − | 0.266469i | \(-0.914143\pi\) | ||
0.963843 | − | 0.266469i | \(-0.0858571\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.0000 | − | 8.66025i | 0.882353 | − | 0.509427i | 0.0109194 | − | 0.999940i | \(-0.496524\pi\) |
0.871433 | + | 0.490514i | \(0.163191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.00000 | − | 5.19615i | −0.473684 | − | 0.273482i | 0.244096 | − | 0.969751i | \(-0.421509\pi\) |
−0.717781 | + | 0.696269i | \(0.754842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.0000 | + | 31.1769i | −0.782609 | + | 1.35552i | 0.147809 | + | 0.989016i | \(0.452778\pi\) |
−0.930417 | + | 0.366502i | \(0.880555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.0000 | − | 19.0526i | −0.440000 | − | 0.762102i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51.0000 | 1.75862 | 0.879310 | − | 0.476249i | \(-0.158004\pi\) | ||||
0.879310 | + | 0.476249i | \(0.158004\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5000 | − | 6.06218i | 0.338710 | − | 0.195554i | −0.320992 | − | 0.947082i | \(-0.604016\pi\) |
0.659701 | + | 0.751528i | \(0.270683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.0000 | + | 1.73205i | 0.342857 | + | 0.0494872i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.0000 | + | 19.0526i | −0.297297 | + | 0.514934i | −0.975517 | − | 0.219925i | \(-0.929419\pi\) |
0.678219 | + | 0.734859i | \(0.262752\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 24.2487i | 0.591432i | 0.955276 | + | 0.295716i | \(0.0955582\pi\) | ||||
−0.955276 | + | 0.295716i | \(0.904442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −0.232558 | −0.116279 | − | 0.993217i | \(-0.537097\pi\) | ||||
−0.116279 | + | 0.993217i | \(0.537097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 78.0000 | + | 45.0333i | 1.65957 | + | 0.958156i | 0.972911 | + | 0.231180i | \(0.0742588\pi\) |
0.686664 | + | 0.726975i | \(0.259075\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 35.5000 | − | 33.7750i | 0.724490 | − | 0.689286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25.5000 | + | 44.1673i | 0.481132 | + | 0.833345i | 0.999766 | − | 0.0216515i | \(-0.00689241\pi\) |
−0.518634 | + | 0.854997i | \(0.673559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.19615i | − | 0.0944755i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 64.5000 | − | 37.2391i | 1.09322 | − | 0.631171i | 0.158788 | − | 0.987313i | \(-0.449241\pi\) |
0.934432 | + | 0.356142i | \(0.115908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 60.0000 | + | 34.6410i | 0.983607 | + | 0.567886i | 0.903357 | − | 0.428889i | \(-0.141095\pi\) |
0.0802495 | + | 0.996775i | \(0.474428\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | + | 10.3923i | −0.0923077 | + | 0.159882i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.0000 | + | 58.8897i | 0.507463 | + | 0.878951i | 0.999963 | + | 0.00863871i | \(0.00274982\pi\) |
−0.492500 | + | 0.870312i | \(0.663917\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18.0000 | + | 10.3923i | −0.246575 | + | 0.142360i | −0.618195 | − | 0.786025i | \(-0.712136\pi\) |
0.371620 | + | 0.928385i | \(0.378803\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.5000 | − | 12.9904i | −0.214286 | − | 0.168706i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 62.5000 | − | 108.253i | 0.791139 | − | 1.37029i | −0.134123 | − | 0.990965i | \(-0.542822\pi\) |
0.925262 | − | 0.379329i | \(-0.123845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 154.153i | − | 1.85726i | −0.371008 | − | 0.928630i | \(-0.620988\pi\) | ||
0.371008 | − | 0.928630i | \(-0.379012\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30.0000 | −0.352941 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −63.0000 | − | 36.3731i | −0.707865 | − | 0.408686i | 0.102405 | − | 0.994743i | \(-0.467346\pi\) |
−0.810270 | + | 0.586057i | \(0.800680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.0000 | + | 45.0333i | 0.197802 | + | 0.494872i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.00000 | + | 15.5885i | 0.0947368 | + | 0.164089i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 147.224i | 1.51778i | 0.651221 | + | 0.758888i | \(0.274257\pi\) | ||||
−0.651221 | + | 0.758888i | \(0.725743\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.0000 | + | 10.3923i | −0.178218 | + | 0.102894i | −0.586455 | − | 0.809982i | \(-0.699477\pi\) |
0.408237 | + | 0.912876i | \(0.366144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 132.000 | + | 76.2102i | 1.28155 | + | 0.739905i | 0.977132 | − | 0.212632i | \(-0.0682037\pi\) |
0.304421 | + | 0.952538i | \(0.401537\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.5000 | − | 28.5788i | 0.154206 | − | 0.267092i | −0.778564 | − | 0.627565i | \(-0.784052\pi\) |
0.932769 | + | 0.360473i | \(0.117385\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0000 | + | 27.7128i | 0.146789 | + | 0.254246i | 0.930039 | − | 0.367461i | \(-0.119773\pi\) |
−0.783250 | + | 0.621707i | \(0.786440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 186.000 | 1.64602 | 0.823009 | − | 0.568029i | \(-0.192294\pi\) | ||||
0.823009 | + | 0.568029i | \(0.192294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 54.0000 | − | 31.1769i | 0.469565 | − | 0.271104i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −75.0000 | + | 95.2628i | −0.630252 | + | 0.800528i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.0000 | − | 96.9948i | 0.462810 | − | 0.801610i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 81.4064i | 0.651251i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −131.000 | −1.03150 | −0.515748 | − | 0.856740i | \(-0.672486\pi\) | ||||
−0.515748 | + | 0.856740i | \(0.672486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 85.5000 | + | 49.3634i | 0.652672 | + | 0.376820i | 0.789479 | − | 0.613777i | \(-0.210351\pi\) |
−0.136807 | + | 0.990598i | \(0.543684\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 72.0000 | + | 10.3923i | 0.541353 | + | 0.0781376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −72.0000 | − | 124.708i | −0.525547 | − | 0.910275i | −0.999557 | − | 0.0297553i | \(-0.990527\pi\) |
0.474010 | − | 0.880520i | \(-0.342806\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 148.956i | 1.07163i | 0.844336 | + | 0.535814i | \(0.179995\pi\) | ||||
−0.844336 | + | 0.535814i | \(0.820005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.0000 | − | 10.3923i | 0.125874 | − | 0.0726735i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −76.5000 | − | 44.1673i | −0.527586 | − | 0.304602i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −75.0000 | + | 129.904i | −0.503356 | + | 0.871838i | 0.496637 | + | 0.867958i | \(0.334568\pi\) |
−0.999992 | + | 0.00387918i | \(0.998765\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −116.500 | − | 201.784i | −0.771523 | − | 1.33632i | −0.936728 | − | 0.350058i | \(-0.886162\pi\) |
0.165205 | − | 0.986259i | \(-0.447171\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.0000 | −0.135484 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 126.000 | − | 72.7461i | 0.802548 | − | 0.463351i | −0.0418135 | − | 0.999125i | \(-0.513314\pi\) |
0.844361 | + | 0.535774i | \(0.179980\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 36.0000 | − | 249.415i | 0.223602 | − | 1.54916i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −74.0000 | + | 128.172i | −0.453988 | + | 0.786330i | −0.998629 | − | 0.0523391i | \(-0.983332\pi\) |
0.544642 | + | 0.838669i | \(0.316666\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 27.7128i | − | 0.165945i | −0.996552 | − | 0.0829725i | \(-0.973559\pi\) | ||
0.996552 | − | 0.0829725i | \(-0.0264414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 121.000 | 0.715976 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 162.000 | + | 93.5307i | 0.936416 | + | 0.540640i | 0.888835 | − | 0.458227i | \(-0.151515\pi\) |
0.0475811 | + | 0.998867i | \(0.484849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 121.000 | + | 95.2628i | 0.691429 | + | 0.544359i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 81.0000 | + | 140.296i | 0.452514 | + | 0.783777i | 0.998541 | − | 0.0539901i | \(-0.0171939\pi\) |
−0.546028 | + | 0.837767i | \(0.683861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 259.808i | 1.43540i | 0.696352 | + | 0.717701i | \(0.254805\pi\) | ||||
−0.696352 | + | 0.717701i | \(0.745195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 33.0000 | − | 19.0526i | 0.178378 | − | 0.102987i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.0000 | + | 25.9808i | 0.240642 | + | 0.138935i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −48.0000 | + | 83.1384i | −0.251309 | + | 0.435280i | −0.963886 | − | 0.266314i | \(-0.914194\pi\) |
0.712578 | + | 0.701593i | \(0.247528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −147.500 | − | 255.477i | −0.764249 | − | 1.32372i | −0.940643 | − | 0.339398i | \(-0.889777\pi\) |
0.176394 | − | 0.984320i | \(-0.443557\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 330.000 | 1.67513 | 0.837563 | − | 0.546340i | \(-0.183979\pi\) | ||||
0.837563 | + | 0.546340i | \(0.183979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 102.000 | − | 58.8897i | 0.512563 | − | 0.295928i | −0.221324 | − | 0.975200i | \(-0.571038\pi\) |
0.733886 | + | 0.679272i | \(0.237704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −331.500 | + | 132.502i | −1.63300 | + | 0.652719i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.0000 | − | 36.3731i | 0.102439 | − | 0.177430i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 31.1769i | − | 0.149172i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −220.000 | −1.04265 | −0.521327 | − | 0.853357i | \(-0.674563\pi\) | ||||
−0.521327 | + | 0.853357i | \(0.674563\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.0000 | + | 8.66025i | 0.0697674 | + | 0.0402803i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −52.5000 | + | 66.6840i | −0.241935 | + | 0.307299i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −60.0000 | − | 103.923i | −0.271493 | − | 0.470240i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 150.688i | − | 0.675733i | −0.941194 | − | 0.337866i | \(-0.890295\pi\) | ||
0.941194 | − | 0.337866i | \(-0.109705\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 94.5000 | − | 54.5596i | 0.416300 | − | 0.240351i | −0.277193 | − | 0.960814i | \(-0.589404\pi\) |
0.693493 | + | 0.720464i | \(0.256071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −327.000 | − | 188.794i | −1.42795 | − | 0.824426i | −0.430989 | − | 0.902357i | \(-0.641835\pi\) |
−0.996959 | + | 0.0779313i | \(0.975169\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −105.000 | + | 181.865i | −0.450644 | + | 0.780538i | −0.998426 | − | 0.0560830i | \(-0.982139\pi\) |
0.547782 | + | 0.836621i | \(0.315472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −78.0000 | − | 135.100i | −0.331915 | − | 0.574893i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 120.000 | 0.502092 | 0.251046 | − | 0.967975i | \(-0.419225\pi\) | ||||
0.251046 | + | 0.967975i | \(0.419225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | + | 6.06218i | −0.0435685 | + | 0.0251543i | −0.521626 | − | 0.853174i | \(-0.674674\pi\) |
0.478058 | + | 0.878329i | \(0.341341\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −82.5000 | + | 19.9186i | −0.336735 | + | 0.0813003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.0000 | + | 62.3538i | −0.145749 | + | 0.252445i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 136.832i | − | 0.545147i | −0.962135 | − | 0.272574i | \(-0.912125\pi\) | ||
0.962135 | − | 0.272574i | \(-0.0878749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −108.000 | −0.426877 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −117.000 | − | 67.5500i | −0.455253 | − | 0.262840i | 0.254793 | − | 0.966996i | \(-0.417993\pi\) |
−0.710046 | + | 0.704155i | \(0.751326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.0000 | − | 152.420i | 0.0849421 | − | 0.588496i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −81.0000 | − | 140.296i | −0.307985 | − | 0.533445i | 0.669937 | − | 0.742418i | \(-0.266321\pi\) |
−0.977921 | + | 0.208973i | \(0.932988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 88.3346i | − | 0.333338i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −334.500 | + | 193.124i | −1.24349 | + | 0.717932i | −0.969804 | − | 0.243886i | \(-0.921578\pi\) |
−0.273691 | + | 0.961818i | \(0.588244\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −187.500 | − | 108.253i | −0.691882 | − | 0.399458i | 0.112435 | − | 0.993659i | \(-0.464135\pi\) |
−0.804317 | + | 0.594201i | \(0.797468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.0000 | − | 57.1577i | 0.120000 | − | 0.207846i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 50.0000 | + | 86.6025i | 0.180505 | + | 0.312645i | 0.942053 | − | 0.335465i | \(-0.108893\pi\) |
−0.761547 | + | 0.648109i | \(0.775560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −228.000 | −0.811388 | −0.405694 | − | 0.914009i | \(-0.632970\pi\) | ||||
−0.405694 | + | 0.914009i | \(0.632970\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | + | 8.66025i | −0.0530035 | + | 0.0306016i | −0.526268 | − | 0.850319i | \(-0.676409\pi\) |
0.473264 | + | 0.880921i | \(0.343076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −63.0000 | − | 157.617i | −0.219512 | − | 0.549187i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | − | 9.52628i | 0.0190311 | − | 0.0329629i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 278.860i | 0.951741i | 0.879515 | + | 0.475871i | \(0.157867\pi\) | ||||
−0.879515 | + | 0.475871i | \(0.842133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −129.000 | −0.437288 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 216.000 | + | 124.708i | 0.722408 | + | 0.417082i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 65.0000 | − | 25.9808i | 0.215947 | − | 0.0863148i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −60.0000 | − | 103.923i | −0.196721 | − | 0.340731i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.7128i | 0.0902697i | 0.998981 | + | 0.0451349i | \(0.0143718\pi\) | ||||
−0.998981 | + | 0.0451349i | \(0.985628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 57.0000 | − | 32.9090i | 0.183280 | − | 0.105817i | −0.405553 | − | 0.914072i | \(-0.632921\pi\) |
0.588833 | + | 0.808255i | \(0.299588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 103.500 | + | 59.7558i | 0.330671 | + | 0.190913i | 0.656139 | − | 0.754640i | \(-0.272189\pi\) |
−0.325468 | + | 0.945553i | \(0.605522\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −100.500 | + | 174.071i | −0.317035 | + | 0.549120i | −0.979868 | − | 0.199647i | \(-0.936021\pi\) |
0.662833 | + | 0.748767i | \(0.269354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 76.5000 | + | 132.502i | 0.239812 | + | 0.415366i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −180.000 | −0.557276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −132.000 | + | 76.2102i | −0.406154 | + | 0.234493i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −624.000 | − | 90.0666i | −1.89666 | − | 0.273759i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 224.000 | − | 387.979i | 0.676737 | − | 1.17214i | −0.299221 | − | 0.954184i | \(-0.596727\pi\) |
0.975958 | − | 0.217959i | \(-0.0699400\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 117.779i | − | 0.351580i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −293.000 | −0.869436 | −0.434718 | − | 0.900567i | \(-0.643152\pi\) | ||||
−0.434718 | + | 0.900567i | \(0.643152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.5000 | + | 18.1865i | 0.0923754 | + | 0.0533329i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −143.000 | + | 311.769i | −0.416910 | + | 0.908948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −195.000 | − | 337.750i | −0.561960 | − | 0.973343i | −0.997325 | − | 0.0730890i | \(-0.976714\pi\) |
0.435366 | − | 0.900254i | \(-0.356619\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 138.564i | 0.397032i | 0.980098 | + | 0.198516i | \(0.0636121\pi\) | ||||
−0.980098 | + | 0.198516i | \(0.936388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 438.000 | − | 252.879i | 1.24079 | − | 0.716372i | 0.271537 | − | 0.962428i | \(-0.412468\pi\) |
0.969256 | + | 0.246056i | \(0.0791346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −150.000 | + | 259.808i | −0.417827 | + | 0.723698i | −0.995721 | − | 0.0924142i | \(-0.970542\pi\) |
0.577893 | + | 0.816112i | \(0.303875\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −126.500 | − | 219.104i | −0.350416 | − | 0.606937i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.0000 | 0.0986301 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 175.500 | − | 101.325i | 0.478202 | − | 0.276090i | −0.241465 | − | 0.970410i | \(-0.577628\pi\) |
0.719667 | + | 0.694320i | \(0.244295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −280.500 | − | 220.836i | −0.756065 | − | 0.595247i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −205.000 | + | 355.070i | −0.549598 | + | 0.951931i | 0.448704 | + | 0.893680i | \(0.351886\pi\) |
−0.998302 | + | 0.0582510i | \(0.981448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 353.338i | − | 0.937237i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 374.000 | 0.986807 | 0.493404 | − | 0.869800i | \(-0.335753\pi\) | ||||
0.493404 | + | 0.869800i | \(0.335753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −249.000 | − | 143.760i | −0.650131 | − | 0.375353i | 0.138376 | − | 0.990380i | \(-0.455812\pi\) |
−0.788506 | + | 0.615027i | \(0.789145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.5000 | + | 33.7750i | 0.0350649 | + | 0.0877272i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −69.0000 | − | 119.512i | −0.177378 | − | 0.307228i | 0.763604 | − | 0.645685i | \(-0.223428\pi\) |
−0.940982 | + | 0.338458i | \(0.890095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 623.538i | 1.59473i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −187.500 | + | 108.253i | −0.474684 | + | 0.274059i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 534.000 | + | 308.305i | 1.34509 | + | 0.776587i | 0.987549 | − | 0.157311i | \(-0.0502826\pi\) |
0.357539 | + | 0.933898i | \(0.383616\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 258.000 | − | 446.869i | 0.643392 | − | 1.11439i | −0.341279 | − | 0.939962i | \(-0.610860\pi\) |
0.984671 | − | 0.174425i | \(-0.0558066\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.0000 | − | 72.7461i | −0.104218 | − | 0.180511i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −66.0000 | −0.162162 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 226.500 | − | 130.770i | 0.553790 | − | 0.319731i | −0.196859 | − | 0.980432i | \(-0.563074\pi\) |
0.750649 | + | 0.660701i | \(0.229741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −322.500 | + | 409.630i | −0.780872 | + | 0.991840i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −133.500 | + | 231.229i | −0.321687 | + | 0.557178i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 533.472i | 1.27320i | 0.771193 | + | 0.636601i | \(0.219660\pi\) | ||||
−0.771193 | + | 0.636601i | \(0.780340\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −76.0000 | −0.180523 | −0.0902613 | − | 0.995918i | \(-0.528770\pi\) | ||||
−0.0902613 | + | 0.995918i | \(0.528770\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −330.000 | − | 190.526i | −0.776471 | − | 0.448296i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −480.000 | − | 69.2820i | −1.12412 | − | 0.162253i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −303.000 | − | 524.811i | −0.703016 | − | 1.21766i | −0.967403 | − | 0.253243i | \(-0.918503\pi\) |
0.264386 | − | 0.964417i | \(-0.414831\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.6410i | − | 0.0800023i | −0.999200 | − | 0.0400012i | \(-0.987264\pi\) | ||
0.999200 | − | 0.0400012i | \(-0.0127362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 324.000 | − | 187.061i | 0.741419 | − | 0.428058i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −85.5000 | − | 49.3634i | −0.194761 | − | 0.112445i | 0.399449 | − | 0.916756i | \(-0.369202\pi\) |
−0.594209 | + | 0.804310i | \(0.702535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −310.500 | + | 537.802i | −0.700903 | + | 1.21400i | 0.267247 | + | 0.963628i | \(0.413886\pi\) |
−0.968150 | + | 0.250371i | \(0.919447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 63.0000 | + | 109.119i | 0.141573 | + | 0.245212i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −504.000 | −1.12249 | −0.561247 | − | 0.827648i | \(-0.689678\pi\) | ||||
−0.561247 | + | 0.827648i | \(0.689678\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −63.0000 | + | 36.3731i | −0.139690 | + | 0.0806498i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | − | 83.1384i | 0.0263736 | − | 0.182722i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 221.500 | − | 383.649i | 0.484683 | − | 0.839495i | −0.515162 | − | 0.857093i | \(-0.672268\pi\) |
0.999845 | + | 0.0175975i | \(0.00560174\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 180.133i | 0.390745i | 0.980729 | + | 0.195372i | \(0.0625915\pi\) | ||||
−0.980729 | + | 0.195372i | \(0.937408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −158.000 | −0.341253 | −0.170626 | − | 0.985336i | \(-0.554579\pi\) | ||||
−0.170626 | + | 0.985336i | \(0.554579\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000 | + | 10.3923i | 0.0385439 | + | 0.0222533i | 0.519148 | − | 0.854684i | \(-0.326249\pi\) |
−0.480604 | + | 0.876938i | \(0.659583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −374.000 | − | 294.449i | −0.797441 | − | 0.627822i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0000 | − | 25.9808i | −0.0317125 | − | 0.0549276i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 228.631i | 0.481328i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 357.000 | − | 206.114i | 0.745303 | − | 0.430301i | −0.0786914 | − | 0.996899i | \(-0.525074\pi\) |
0.823994 | + | 0.566598i | \(0.191741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 132.000 | + | 76.2102i | 0.274428 | + | 0.158441i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 127.500 | − | 220.836i | 0.262887 | − | 0.455333i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 57.5000 | + | 99.5929i | 0.118070 | + | 0.204503i | 0.919003 | − | 0.394251i | \(-0.128996\pi\) |
−0.800933 | + | 0.598754i | \(0.795663\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 273.000 | 0.556008 | 0.278004 | − | 0.960580i | \(-0.410327\pi\) | ||||
0.278004 | + | 0.960580i | \(0.410327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 765.000 | − | 441.673i | 1.55172 | − | 0.895888i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 233.000 | − | 403.568i | 0.466934 | − | 0.808753i | −0.532353 | − | 0.846523i | \(-0.678692\pi\) |
0.999286 | + | 0.0377695i | \(0.0120253\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 723.997i | 1.43936i | 0.694307 | + | 0.719679i | \(0.255711\pi\) | ||||
−0.694307 | + | 0.719679i | \(0.744289\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 0.0712871 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 307.500 | + | 177.535i | 0.604126 | + | 0.348792i | 0.770663 | − | 0.637243i | \(-0.219925\pi\) |
−0.166537 | + | 0.986035i | \(0.553259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 90.0000 | − | 114.315i | 0.176125 | − | 0.223709i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −132.000 | − | 228.631i | −0.256311 | − | 0.443943i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 270.200i | 0.522630i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 795.000 | − | 458.993i | 1.52591 | − | 0.880986i | 0.526384 | − | 0.850247i | \(-0.323547\pi\) |
0.999527 | − | 0.0307387i | \(-0.00978599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −420.000 | − | 242.487i | −0.803059 | − | 0.463646i | 0.0414805 | − | 0.999139i | \(-0.486793\pi\) |
−0.844540 | + | 0.535493i | \(0.820126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 105.000 | − | 181.865i | 0.199241 | − | 0.345096i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −383.500 | − | 664.241i | −0.724953 | − | 1.25565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 168.000 | 0.315197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.5000 | + | 28.5788i | −0.0925234 | + | 0.0534184i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 141.000 | + | 41.5692i | 0.261596 | + | 0.0771229i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.0000 | + | 53.6936i | −0.0573013 | + | 0.0992488i | −0.893253 | − | 0.449554i | \(-0.851583\pi\) |
0.835952 | + | 0.548803i | \(0.184916\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 55.4256i | − | 0.101698i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 802.000 | 1.46618 | 0.733090 | − | 0.680132i | \(-0.238078\pi\) | ||||
0.733090 | + | 0.680132i | \(0.238078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −459.000 | − | 265.004i | −0.833031 | − | 0.480951i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −125.000 | + | 866.025i | −0.226040 | + | 1.56605i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −55.5000 | − | 96.1288i | −0.0996409 | − | 0.172583i | 0.811895 | − | 0.583803i | \(-0.198436\pi\) |
−0.911536 | + | 0.411220i | \(0.865103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 69.2820i | 0.123939i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 166.500 | − | 96.1288i | 0.295737 | − | 0.170744i | −0.344789 | − | 0.938680i | \(-0.612050\pi\) |
0.640526 | + | 0.767936i | \(0.278716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −279.000 | − | 161.081i | −0.493805 | − | 0.285099i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −213.000 | + | 368.927i | −0.374341 | + | 0.648378i | −0.990228 | − | 0.139457i | \(-0.955464\pi\) |
0.615887 | + | 0.787834i | \(0.288798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −290.000 | − | 502.295i | −0.507881 | − | 0.879676i | −0.999958 | − | 0.00912412i | \(-0.997096\pi\) |
0.492077 | − | 0.870551i | \(-0.336238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 792.000 | 1.37739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −835.500 | + | 482.376i | −1.44801 | + | 0.836007i | −0.998363 | − | 0.0572006i | \(-0.981783\pi\) |
−0.449644 | + | 0.893208i | \(0.648449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 400.500 | + | 1001.99i | 0.689329 | + | 1.72460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −76.5000 | + | 132.502i | −0.131218 | + | 0.227276i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1002.86i | 1.70845i | 0.519907 | + | 0.854223i | \(0.325966\pi\) | ||||
−0.519907 | + | 0.854223i | \(0.674034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −126.000 | −0.213922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 762.000 | + | 439.941i | 1.28499 | + | 0.741890i | 0.977756 | − | 0.209743i | \(-0.0672629\pi\) |
0.307235 | + | 0.951634i | \(0.400596\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 195.000 | − | 77.9423i | 0.327731 | − | 0.130995i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 78.0000 | + | 135.100i | 0.130217 | + | 0.225543i | 0.923760 | − | 0.382972i | \(-0.125099\pi\) |
−0.793543 | + | 0.608514i | \(0.791766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1124.10i | − | 1.87038i | −0.354141 | − | 0.935192i | \(-0.615227\pi\) | ||
0.354141 | − | 0.935192i | \(-0.384773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −168.000 | + | 96.9948i | −0.277686 | + | 0.160322i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 346.500 | + | 200.052i | 0.570840 | + | 0.329575i | 0.757485 | − | 0.652853i | \(-0.226428\pi\) |
−0.186645 | + | 0.982427i | \(0.559761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 312.000 | − | 540.400i | 0.510638 | − | 0.884451i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 428.000 | + | 741.318i | 0.698206 | + | 1.20933i | 0.969088 | + | 0.246715i | \(0.0793512\pi\) |
−0.270883 | + | 0.962612i | \(0.587315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −444.000 | −0.719611 | −0.359806 | − | 0.933027i | \(-0.617157\pi\) | ||||
−0.359806 | + | 0.933027i | \(0.617157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 222.000 | − | 128.172i | 0.358643 | − | 0.207063i | −0.309842 | − | 0.950788i | \(-0.600276\pi\) |
0.668485 | + | 0.743725i | \(0.266943\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 504.000 | + | 72.7461i | 0.808989 | + | 0.116767i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −204.500 | + | 354.204i | −0.327200 | + | 0.566727i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 381.051i | 0.605805i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 85.0000 | 0.134707 | 0.0673534 | − | 0.997729i | \(-0.478545\pi\) | ||||
0.0673534 | + | 0.997729i | \(0.478545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 196.500 | + | 113.449i | 0.309449 | + | 0.178660i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −234.000 | − | 245.951i | −0.367347 | − | 0.386109i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −66.0000 | − | 114.315i | −0.102964 | − | 0.178339i | 0.809940 | − | 0.586512i | \(-0.199499\pi\) |
−0.912905 | + | 0.408173i | \(0.866166\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 713.605i | − | 1.10981i | −0.831915 | − | 0.554903i | \(-0.812755\pi\) | ||
0.831915 | − | 0.554903i | \(-0.187245\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 864.000 | − | 498.831i | 1.33539 | − | 0.770990i | 0.349274 | − | 0.937021i | \(-0.386428\pi\) |
0.986121 | + | 0.166031i | \(0.0530951\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 193.500 | + | 111.717i | 0.298151 | + | 0.172138i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −187.500 | + | 324.760i | −0.287136 | + | 0.497335i | −0.973125 | − | 0.230278i | \(-0.926037\pi\) |
0.685989 | + | 0.727612i | \(0.259370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −85.5000 | − | 148.090i | −0.130534 | − | 0.226092i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1038.00 | 1.57511 | 0.787557 | − | 0.616242i | \(-0.211346\pi\) | ||||
0.787557 | + | 0.616242i | \(0.211346\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 387.000 | − | 223.435i | 0.585477 | − | 0.338025i | −0.177830 | − | 0.984061i | \(-0.556908\pi\) |
0.763307 | + | 0.646036i | \(0.223574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −99.0000 | − | 77.9423i | −0.148872 | − | 0.117206i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −918.000 | + | 1590.02i | −1.37631 | + | 2.38384i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 207.846i | 0.309756i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1093.00 | 1.62407 | 0.812036 | − | 0.583608i | \(-0.198359\pi\) | ||||
0.812036 | + | 0.583608i | \(0.198359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1048.50 | + | 605.352i | 1.54874 | + | 0.894168i | 0.998238 | + | 0.0593371i | \(0.0188987\pi\) |
0.550506 | + | 0.834831i | \(0.314435\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −382.500 | − | 956.958i | −0.563328 | − | 1.40936i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.50000 | + | 2.59808i | 0.00219619 | + | 0.00380392i | 0.867121 | − | 0.498097i | \(-0.165968\pi\) |
−0.864925 | + | 0.501901i | \(0.832634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 249.415i | 0.364110i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 306.000 | − | 176.669i | 0.444122 | − | 0.256414i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 987.000 | + | 569.845i | 1.42836 | + | 0.824667i | 0.996992 | − | 0.0775070i | \(-0.0246960\pi\) |
0.431373 | + | 0.902174i | \(0.358029\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 129.000 | − | 223.435i | 0.185612 | − | 0.321489i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 210.000 | + | 363.731i | 0.301291 | + | 0.521852i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −447.000 | −0.637660 | −0.318830 | − | 0.947812i | \(-0.603290\pi\) | ||||
−0.318830 | + | 0.947812i | \(0.603290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 198.000 | − | 114.315i | 0.281650 | − | 0.162611i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 90.0000 | − | 114.315i | 0.127298 | − | 0.161691i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 211.000 | − | 365.463i | 0.297602 | − | 0.515462i | −0.677985 | − | 0.735076i | \(-0.737146\pi\) |
0.975587 | + | 0.219614i | \(0.0704797\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 436.477i | 0.612169i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0000 | −0.0503497 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 147.000 | + | 84.8705i | 0.204451 | + | 0.118040i | 0.598730 | − | 0.800951i | \(-0.295672\pi\) |
−0.394279 | + | 0.918991i | \(0.629006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1056.00 | − | 152.420i | −1.46463 | − | 0.211401i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −561.000 | − | 971.681i | −0.773793 | − | 1.34025i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.2295i | 0.0690914i | 0.999403 | + | 0.0345457i | \(0.0109984\pi\) | ||||
−0.999403 | + | 0.0345457i | \(0.989002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −150.000 | + | 86.6025i | −0.205198 | + | 0.118471i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 255.000 | + | 147.224i | 0.347885 | + | 0.200852i | 0.663754 | − | 0.747951i | \(-0.268962\pi\) |
−0.315868 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −102.000 | + | 176.669i | −0.138399 | + | 0.239714i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.0000 | + | 84.8705i | 0.0663058 | + | 0.114845i | 0.897272 | − | 0.441477i | \(-0.145545\pi\) |
−0.830967 | + | 0.556322i | \(0.812212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −180.000 | −0.242261 | −0.121131 | − | 0.992637i | \(-0.538652\pi\) | ||||
−0.121131 | + | 0.992637i | \(0.538652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 225.000 | − | 129.904i | 0.302013 | − | 0.174368i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.0000 | + | 228.631i | −0.0440587 | + | 0.305248i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 360.500 | − | 624.404i | 0.480027 | − | 0.831431i | −0.519711 | − | 0.854342i | \(-0.673960\pi\) |
0.999737 | + | 0.0229117i | \(0.00729366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 403.568i | 0.534527i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −644.000 | −0.850727 | −0.425363 | − | 0.905023i | \(-0.639854\pi\) | ||||
−0.425363 | + | 0.905023i | \(0.639854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 492.000 | + | 284.056i | 0.646518 | + | 0.373267i | 0.787121 | − | 0.616799i | \(-0.211571\pi\) |
−0.140603 | + | 0.990066i | \(0.544904\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −176.000 | − | 138.564i | −0.230668 | − | 0.181604i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −258.000 | − | 446.869i | −0.336375 | − | 0.582619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 275.396i | 0.358122i | 0.983838 | + | 0.179061i | \(0.0573060\pi\) | ||||
−0.983838 | + | 0.179061i | \(0.942694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 870.000 | − | 502.295i | 1.12549 | − | 0.649799i | 0.182690 | − | 0.983171i | \(-0.441520\pi\) |
0.942796 | + | 0.333372i | \(0.108186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −231.000 | − | 133.368i | −0.298065 | − | 0.172088i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 126.000 | − | 218.238i | 0.161746 | − | 0.280152i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −252.000 | −0.321019 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −690.000 | + | 398.372i | −0.876747 | + | 0.506190i | −0.869585 | − | 0.493784i | \(-0.835613\pi\) |
−0.00716264 | + | 0.999974i | \(0.502280\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1209.00 | + | 483.242i | −1.52845 | + | 0.610926i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 240.000 | − | 415.692i | 0.302648 | − | 0.524202i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 545.596i | − | 0.684562i | −0.939598 | − | 0.342281i | \(-0.888801\pi\) | ||
0.939598 | − | 0.342281i | \(-0.111199\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1560.00 | 1.95244 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −54.0000 | − | 31.1769i | −0.0672478 | − | 0.0388255i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −270.000 | + | 342.946i | −0.335404 | + | 0.426020i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0000 | + | 41.5692i | 0.0296663 | + | 0.0513835i | 0.880477 | − | 0.474088i | \(-0.157222\pi\) |
−0.850811 | + | 0.525472i | \(0.823889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 436.477i | 0.538196i | 0.963113 | + | 0.269098i | \(0.0867255\pi\) | ||||
−0.963113 | + | 0.269098i | \(0.913274\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 222.000 | − | 128.172i | 0.272393 | − | 0.157266i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 90.0000 | + | 51.9615i | 0.110159 | + | 0.0636004i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 595.500 | − | 1031.44i | 0.725335 | − | 1.25632i | −0.233501 | − | 0.972357i | \(-0.575018\pi\) |
0.958836 | − | 0.283960i | \(-0.0916484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −125.000 | − | 216.506i | −0.151883 | − | 0.263070i | 0.780036 | − | 0.625734i | \(-0.215200\pi\) |
−0.931920 | + | 0.362664i | \(0.881867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1137.00 | −1.37485 | −0.687424 | − | 0.726256i | \(-0.741259\pi\) | ||||
−0.687424 | + | 0.726256i | \(0.741259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 63.0000 | − | 36.3731i | 0.0759952 | − | 0.0438758i | −0.461521 | − | 0.887129i | \(-0.652696\pi\) |
0.537516 | + | 0.843253i | \(0.319363\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 240.000 | − | 814.064i | 0.288115 | − | 0.977268i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | + | 41.5692i | −0.0287425 | + | 0.0497835i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1416.82i | 1.68870i | 0.535794 | + | 0.844349i | \(0.320012\pi\) | ||||
−0.535794 | + | 0.844349i | \(0.679988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1760.00 | 2.09275 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −181.500 | − | 104.789i | −0.214793 | − | 0.124011i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −112.000 | + | 775.959i | −0.132231 | + | 0.916126i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −396.000 | − | 685.892i | −0.465335 | − | 0.805984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 872.954i | − | 1.02339i | −0.859166 | − | 0.511696i | \(-0.829017\pi\) | ||
0.859166 | − | 0.511696i | \(-0.170983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 600.000 | − | 346.410i | 0.700117 | − | 0.404213i | −0.107274 | − | 0.994229i | \(-0.534212\pi\) |
0.807391 | + | 0.590017i | \(0.200879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 771.000 | + | 445.137i | 0.897555 | + | 0.518204i | 0.876406 | − | 0.481573i | \(-0.159934\pi\) |
0.0211491 | + | 0.999776i | \(0.493268\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −315.000 | + | 545.596i | −0.365006 | + | 0.632209i | −0.988777 | − | 0.149398i | \(-0.952266\pi\) |
0.623771 | + | 0.781607i | \(0.285600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −162.000 | − | 280.592i | −0.187283 | − | 0.324384i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 375.000 | 0.431530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 408.000 | − | 235.559i | 0.468427 | − | 0.270447i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −211.500 | − | 529.142i | −0.241714 | − | 0.604733i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −820.000 | + | 1420.28i | −0.935006 | + | 1.61948i | −0.160382 | + | 0.987055i | \(0.551273\pi\) |
−0.774624 | + | 0.632422i | \(0.782061\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1267.86i | 1.43912i | 0.694432 | + | 0.719558i | \(0.255656\pi\) | ||||
−0.694432 | + | 0.719558i | \(0.744344\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −226.000 | −0.255946 | −0.127973 | − | 0.991778i | \(-0.540847\pi\) | ||||
−0.127973 | + | 0.991778i | \(0.540847\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.00000 | + | 3.46410i | 0.00676437 | + | 0.00390541i | 0.503378 | − | 0.864066i | \(-0.332090\pi\) |
−0.496614 | + | 0.867972i | \(0.665424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 851.500 | − | 340.348i | 0.957818 | − | 0.382844i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −468.000 | − | 810.600i | −0.524076 | − | 0.907727i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 280.592i | − | 0.313511i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 535.500 | − | 309.171i | 0.595662 | − | 0.343906i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 765.000 | + | 441.673i | 0.849057 | + | 0.490203i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 225.000 | − | 389.711i | 0.248619 | − | 0.430620i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 572.000 | + | 990.733i | 0.630650 | + | 1.09232i | 0.987419 | + | 0.158126i | \(0.0505452\pi\) |
−0.356768 | + | 0.934193i | \(0.616121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −480.000 | −0.526894 | −0.263447 | − | 0.964674i | \(-0.584859\pi\) | ||||
−0.263447 | + | 0.964674i | \(0.584859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 400.500 | − | 231.229i | 0.438664 | − | 0.253263i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −684.000 | − | 98.7269i | −0.745911 | − | 0.107663i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −871.000 | + | 1508.62i | −0.947769 | + | 1.64158i | −0.197660 | + | 0.980271i | \(0.563334\pi\) |
−0.750109 | + | 0.661314i | \(0.769999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 484.000 | 0.523243 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1005.00 | − | 580.237i | −1.08181 | − | 0.624582i | −0.150425 | − | 0.988621i | \(-0.548064\pi\) |
−0.931384 | + | 0.364039i | \(0.881397\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −495.000 | + | 119.512i | −0.531686 | + | 0.128369i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.0000 | − | 77.9423i | −0.0481283 | − | 0.0833607i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1331.95i | 1.42150i | 0.703444 | + | 0.710751i | \(0.251645\pi\) | ||||
−0.703444 | + | 0.710751i | \(0.748355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −703.500 | + | 406.166i | −0.747609 | + | 0.431632i | −0.824829 | − | 0.565382i | \(-0.808729\pi\) |
0.0772204 | + | 0.997014i | \(0.475395\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −756.000 | − | 436.477i | −0.801697 | − | 0.462860i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 645.000 | − | 1117.17i | 0.681098 | − | 1.17970i | −0.293548 | − | 0.955944i | \(-0.594836\pi\) |
0.974646 | − | 0.223752i | \(-0.0718307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.0000 | + | 124.708i | 0.0758693 | + | 0.131410i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −174.000 | −0.182581 | −0.0912907 | − | 0.995824i | \(-0.529099\pi\) | ||||
−0.0912907 | + | 0.995824i | \(0.529099\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 144.000 | − | 83.1384i | 0.150785 | − | 0.0870560i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 792.000 | + | 623.538i | 0.825860 | + | 0.650196i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.000 | + | 704.945i | −0.423517 | + | 0.733553i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 510.955i | 0.529487i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.0000 | −0.0423992 | −0.0211996 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0211996 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 853.500 | + | 492.768i | 0.878991 | + | 0.507486i | 0.870326 | − | 0.492477i | \(-0.163908\pi\) |
0.00866523 | + | 0.999962i | \(0.497242\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −387.000 | − | 968.216i | −0.397739 | − | 0.995084i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 639.000 | + | 1106.78i | 0.654043 | + | 1.13284i | 0.982133 | + | 0.188189i | \(0.0602618\pi\) |
−0.328090 | + | 0.944647i | \(0.606405\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 218.238i | − | 0.222920i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −201.000 | + | 116.047i | −0.204476 | + | 0.118054i | −0.598742 | − | 0.800942i | \(-0.704332\pi\) |
0.394266 | + | 0.918997i | \(0.370999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −495.000 | − | 285.788i | −0.502538 | − | 0.290140i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 180.000 | − | 311.769i | 0.182002 | − | 0.315237i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −416.500 | − | 721.399i | −0.420283 | − | 0.727951i | 0.575684 | − | 0.817672i | \(-0.304736\pi\) |
−0.995967 | + | 0.0897213i | \(0.971402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −204.000 | −0.205025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1014.00 | − | 585.433i | 1.01705 | − | 0.587195i | 0.103803 | − | 0.994598i | \(-0.466899\pi\) |
0.913248 | + | 0.407403i | \(0.133566\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1008.3.cg.b.145.1 | 2 | ||
3.2 | odd | 2 | 336.3.bh.b.145.1 | 2 | |||
4.3 | odd | 2 | 252.3.z.b.145.1 | 2 | |||
7.3 | odd | 6 | inner | 1008.3.cg.b.577.1 | 2 | ||
12.11 | even | 2 | 84.3.m.a.61.1 | ✓ | 2 | ||
21.2 | odd | 6 | 2352.3.f.c.97.1 | 2 | |||
21.5 | even | 6 | 2352.3.f.c.97.2 | 2 | |||
21.17 | even | 6 | 336.3.bh.b.241.1 | 2 | |||
28.3 | even | 6 | 252.3.z.b.73.1 | 2 | |||
28.11 | odd | 6 | 1764.3.z.e.325.1 | 2 | |||
28.19 | even | 6 | 1764.3.d.c.685.1 | 2 | |||
28.23 | odd | 6 | 1764.3.d.c.685.2 | 2 | |||
28.27 | even | 2 | 1764.3.z.e.901.1 | 2 | |||
60.23 | odd | 4 | 2100.3.be.c.649.2 | 4 | |||
60.47 | odd | 4 | 2100.3.be.c.649.1 | 4 | |||
60.59 | even | 2 | 2100.3.bd.b.901.1 | 2 | |||
84.11 | even | 6 | 588.3.m.a.325.1 | 2 | |||
84.23 | even | 6 | 588.3.d.a.97.2 | 2 | |||
84.47 | odd | 6 | 588.3.d.a.97.1 | 2 | |||
84.59 | odd | 6 | 84.3.m.a.73.1 | yes | 2 | ||
84.83 | odd | 2 | 588.3.m.a.313.1 | 2 | |||
420.59 | odd | 6 | 2100.3.bd.b.1501.1 | 2 | |||
420.143 | even | 12 | 2100.3.be.c.1249.1 | 4 | |||
420.227 | even | 12 | 2100.3.be.c.1249.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.3.m.a.61.1 | ✓ | 2 | 12.11 | even | 2 | ||
84.3.m.a.73.1 | yes | 2 | 84.59 | odd | 6 | ||
252.3.z.b.73.1 | 2 | 28.3 | even | 6 | |||
252.3.z.b.145.1 | 2 | 4.3 | odd | 2 | |||
336.3.bh.b.145.1 | 2 | 3.2 | odd | 2 | |||
336.3.bh.b.241.1 | 2 | 21.17 | even | 6 | |||
588.3.d.a.97.1 | 2 | 84.47 | odd | 6 | |||
588.3.d.a.97.2 | 2 | 84.23 | even | 6 | |||
588.3.m.a.313.1 | 2 | 84.83 | odd | 2 | |||
588.3.m.a.325.1 | 2 | 84.11 | even | 6 | |||
1008.3.cg.b.145.1 | 2 | 1.1 | even | 1 | trivial | ||
1008.3.cg.b.577.1 | 2 | 7.3 | odd | 6 | inner | ||
1764.3.d.c.685.1 | 2 | 28.19 | even | 6 | |||
1764.3.d.c.685.2 | 2 | 28.23 | odd | 6 | |||
1764.3.z.e.325.1 | 2 | 28.11 | odd | 6 | |||
1764.3.z.e.901.1 | 2 | 28.27 | even | 2 | |||
2100.3.bd.b.901.1 | 2 | 60.59 | even | 2 | |||
2100.3.bd.b.1501.1 | 2 | 420.59 | odd | 6 | |||
2100.3.be.c.649.1 | 4 | 60.47 | odd | 4 | |||
2100.3.be.c.649.2 | 4 | 60.23 | odd | 4 | |||
2100.3.be.c.1249.1 | 4 | 420.143 | even | 12 | |||
2100.3.be.c.1249.2 | 4 | 420.227 | even | 12 | |||
2352.3.f.c.97.1 | 2 | 21.2 | odd | 6 | |||
2352.3.f.c.97.2 | 2 | 21.5 | even | 6 |