Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.30 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.29 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.47003 | 1.55184 | 0.775922 | − | 0.630829i | \(-0.217285\pi\) | ||||
0.775922 | + | 0.630829i | \(0.217285\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.11891i | − 1.54341i | −0.635981 | − | 0.771705i | \(-0.719404\pi\) | ||||
0.635981 | − | 0.771705i | \(-0.280596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.268602i | 0.0744968i | 0.999306 | + | 0.0372484i | \(0.0118593\pi\) | ||||
−0.999306 | + | 0.0372484i | \(0.988141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.96616i | 0.476864i | 0.971159 | + | 0.238432i | \(0.0766334\pi\) | ||||
−0.971159 | + | 0.238432i | \(0.923367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.909926 | −0.208751 | −0.104376 | − | 0.994538i | \(-0.533284\pi\) | ||||
−0.104376 | + | 0.994538i | \(0.533284\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.86455 | −1.22284 | −0.611421 | − | 0.791305i | \(-0.709402\pi\) | ||||
−0.611421 | + | 0.791305i | \(0.709402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.04110 | 1.40822 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.19959 | −1.33693 | −0.668466 | − | 0.743743i | \(-0.733049\pi\) | ||||
−0.668466 | + | 0.743743i | \(0.733049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.57491i | − 0.821678i | −0.911708 | − | 0.410839i | \(-0.865236\pi\) | ||||
0.911708 | − | 0.410839i | \(-0.134764\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.47003i | 0.586542i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.98312i | − 1.14802i | −0.818849 | − | 0.574009i | \(-0.805388\pi\) | ||||
0.818849 | − | 0.574009i | \(-0.194612\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 8.34605i | − 1.30343i | −0.758462 | − | 0.651717i | \(-0.774049\pi\) | ||||
0.758462 | − | 0.651717i | \(-0.225951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.25237 | 1.41097 | 0.705487 | − | 0.708723i | \(-0.250728\pi\) | ||||
0.705487 | + | 0.708723i | \(0.250728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.49316 | 0.947125 | 0.473562 | − | 0.880760i | \(-0.342968\pi\) | ||||
0.473562 | + | 0.880760i | \(0.342968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.54325 | 0.624063 | 0.312032 | − | 0.950072i | \(-0.398990\pi\) | ||||
0.312032 | + | 0.950072i | \(0.398990\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 17.7628i | − 2.39513i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 3.50524i | − 0.456344i | −0.973621 | − | 0.228172i | \(-0.926725\pi\) | ||||
0.973621 | − | 0.228172i | \(-0.0732748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.96254i | − 0.251278i | −0.992076 | − | 0.125639i | \(-0.959902\pi\) | ||||
0.992076 | − | 0.125639i | \(-0.0400980\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.932057i | 0.115607i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0280 | 1.34728 | 0.673641 | − | 0.739059i | \(-0.264729\pi\) | ||||
0.673641 | + | 0.739059i | \(0.264729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.20092 | −0.142523 | −0.0712616 | − | 0.997458i | \(-0.522703\pi\) | ||||
−0.0712616 | + | 0.997458i | \(0.522703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.01697 | −1.05536 | −0.527679 | − | 0.849444i | \(-0.676937\pi\) | ||||
−0.527679 | + | 0.849444i | \(0.676937\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.11891 | 0.583354 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 13.5570i | − 1.52528i | −0.646825 | − | 0.762638i | \(-0.723904\pi\) | ||||
0.646825 | − | 0.762638i | \(-0.276096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.96335i | 0.544799i | 0.962184 | + | 0.272399i | \(0.0878172\pi\) | ||||
−0.962184 | + | 0.272399i | \(0.912183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.82263i | 0.740019i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 18.2032i | − 1.92954i | −0.263100 | − | 0.964769i | \(-0.584745\pi\) | ||||
0.263100 | − | 0.964769i | \(-0.415255\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.268602 | −0.0281572 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.15747 | −0.323949 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.39139 | 0.344344 | 0.172172 | − | 0.985067i | \(-0.444922\pi\) | ||||
0.172172 | + | 0.985067i | \(0.444922\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.18671 | 0.814608 | 0.407304 | − | 0.913293i | \(-0.366469\pi\) | ||||
0.407304 | + | 0.913293i | \(0.366469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5624i | 1.63194i | 0.578093 | + | 0.815971i | \(0.303797\pi\) | ||||
−0.578093 | + | 0.815971i | \(0.696203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 15.1480i | − 1.46441i | −0.681083 | − | 0.732206i | \(-0.738491\pi\) | ||||
0.681083 | − | 0.732206i | \(-0.261509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.70038i | 0.737562i | 0.929516 | + | 0.368781i | \(0.120225\pi\) | ||||
−0.929516 | + | 0.368781i | \(0.879775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.5822i | − 1.37178i | −0.727706 | − | 0.685889i | \(-0.759413\pi\) | ||||
0.727706 | − | 0.685889i | \(-0.240587\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.3501 | −1.89766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.96616 | −0.180238 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2033 | −1.38211 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.08266 | 0.633492 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 13.7782i | − 1.22262i | −0.791392 | − | 0.611309i | \(-0.790643\pi\) | ||||
0.791392 | − | 0.611309i | \(-0.209357\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4226i | 0.997997i | 0.866603 | + | 0.498999i | \(0.166299\pi\) | ||||
−0.866603 | + | 0.498999i | \(0.833701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.909926i | − 0.0789006i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.89343i | 0.503510i | 0.967791 | + | 0.251755i | \(0.0810077\pi\) | ||||
−0.967791 | + | 0.251755i | \(0.918992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.67309 | −0.311547 | −0.155774 | − | 0.987793i | \(-0.549787\pi\) | ||||
−0.155774 | + | 0.987793i | \(0.549787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.37495 | 0.114979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.9828 | −2.07471 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.0240 | 1.88620 | 0.943102 | − | 0.332504i | \(-0.107894\pi\) | ||||
0.943102 | + | 0.332504i | \(0.107894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1.33860i | − 0.108934i | −0.998516 | − | 0.0544669i | \(-0.982654\pi\) | ||||
0.998516 | − | 0.0544669i | \(-0.0173459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 15.8751i | − 1.27512i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.7839i | 1.73854i | 0.494333 | + | 0.869272i | \(0.335412\pi\) | ||||
−0.494333 | + | 0.869272i | \(0.664588\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 5.86455i | − 0.462191i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.2710 | 1.58775 | 0.793875 | − | 0.608082i | \(-0.208061\pi\) | ||||
0.793875 | + | 0.608082i | \(0.208061\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.57632 | −0.508891 | −0.254445 | − | 0.967087i | \(-0.581893\pi\) | ||||
−0.254445 | + | 0.967087i | \(0.581893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9279 | 0.994450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.3399 | −1.01421 | −0.507105 | − | 0.861884i | \(-0.669284\pi\) | ||||
−0.507105 | + | 0.861884i | \(0.669284\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.04110i | 0.532257i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 9.82571i | − 0.734408i | −0.930140 | − | 0.367204i | \(-0.880315\pi\) | ||||
0.930140 | − | 0.367204i | \(-0.119685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.88753i | 0.363287i | 0.983364 | + | 0.181643i | \(0.0581417\pi\) | ||||
−0.983364 | + | 0.181643i | \(0.941858\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 24.2316i | − 1.78154i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0646 | 0.735997 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6129 | −0.840281 | −0.420141 | − | 0.907459i | \(-0.638019\pi\) | ||||
−0.420141 | + | 0.907459i | \(0.638019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8166 | −0.922562 | −0.461281 | − | 0.887254i | \(-0.652610\pi\) | ||||
−0.461281 | + | 0.887254i | \(0.652610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.69147 | 0.334253 | 0.167127 | − | 0.985935i | \(-0.446551\pi\) | ||||
0.167127 | + | 0.985935i | \(0.446551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 15.3555i | − 1.08852i | −0.838915 | − | 0.544262i | \(-0.816810\pi\) | ||||
0.838915 | − | 0.544262i | \(-0.183190\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 7.19959i | − 0.505312i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 28.9610i | − 2.02273i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.65783i | 0.322189i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.09850 | −0.350995 | −0.175497 | − | 0.984480i | \(-0.556153\pi\) | ||||
−0.175497 | + | 0.984480i | \(0.556153\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.1060 | 2.18961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.57491 | 0.310565 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.528115 | −0.0355249 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.5118i | 1.97625i | 0.153636 | + | 0.988127i | \(0.450902\pi\) | ||||
−0.153636 | + | 0.988127i | \(0.549098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.4769i | 0.960868i | 0.877031 | + | 0.480434i | \(0.159521\pi\) | ||||
−0.877031 | + | 0.480434i | \(0.840479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9120i | 0.787168i | 0.919289 | + | 0.393584i | \(0.128765\pi\) | ||||
−0.919289 | + | 0.393584i | \(0.871235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2938i | 0.870904i | 0.900212 | + | 0.435452i | \(0.143411\pi\) | ||||
−0.900212 | + | 0.435452i | \(0.856589\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.5315 | 1.46979 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.7744 | 0.761624 | 0.380812 | − | 0.924652i | \(-0.375644\pi\) | ||||
0.380812 | + | 0.924652i | \(0.375644\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.3009 | −1.50094 | −0.750471 | − | 0.660903i | \(-0.770173\pi\) | ||||
−0.750471 | + | 0.660903i | \(0.770173\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.47003 | −0.221692 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.244408i | − 0.0155513i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 18.5562i | − 1.17126i | −0.810579 | − | 0.585629i | \(-0.800847\pi\) | ||||
0.810579 | − | 0.585629i | \(-0.199153\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0201i | 1.88735i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 12.7179i | − 0.793318i | −0.917966 | − | 0.396659i | \(-0.870169\pi\) | ||||
0.917966 | − | 0.396659i | \(-0.129831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.98312 | 0.433910 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.04929 | 0.249690 | 0.124845 | − | 0.992176i | \(-0.460157\pi\) | ||||
0.124845 | + | 0.992176i | \(0.460157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7652 | 0.968449 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.6641 | −1.38185 | −0.690926 | − | 0.722925i | \(-0.742797\pi\) | ||||
−0.690926 | + | 0.722925i | \(0.742797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0619260i | 0.00376174i | 0.999998 | + | 0.00188087i | \(0.000598699\pi\) | ||||
−0.999998 | + | 0.00188087i | \(0.999401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 36.0427i | − 2.17346i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9177i | 1.49716i | 0.663045 | + | 0.748580i | \(0.269264\pi\) | ||||
−0.663045 | + | 0.748580i | \(0.730736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.26290i | 0.492923i | 0.969153 | + | 0.246462i | \(0.0792679\pi\) | ||||
−0.969153 | + | 0.246462i | \(0.920732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.4764 | −1.39553 | −0.697763 | − | 0.716329i | \(-0.745821\pi\) | ||||
−0.697763 | + | 0.716329i | \(0.745821\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.34605 | 0.492652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.1342 | 0.772601 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.18958 | 0.361599 | 0.180800 | − | 0.983520i | \(-0.442131\pi\) | ||||
0.180800 | + | 0.983520i | \(0.442131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 12.1633i | − 0.708174i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.57523i | − 0.0910979i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.25237i | 0.533298i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 6.81007i | − 0.389944i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4140 | 1.45045 | 0.725226 | − | 0.688511i | \(-0.241735\pi\) | ||||
0.725226 | + | 0.688511i | \(0.241735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.55273 | 0.428276 | 0.214138 | − | 0.976803i | \(-0.431306\pi\) | ||||
0.214138 | + | 0.976803i | \(0.431306\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.49790 | 0.141190 | 0.0705948 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705948 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.9643 | 0.615815 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.8541i | 2.06343i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.78906i | − 0.0995460i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.89125i | 0.104908i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.49316i | 0.357980i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.6043 | −1.95699 | −0.978494 | − | 0.206275i | \(-0.933866\pi\) | ||||
−0.978494 | + | 0.206275i | \(0.933866\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.2674 | 2.09077 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.4308 | 1.00399 | 0.501995 | − | 0.864871i | \(-0.332600\pi\) | ||||
0.501995 | + | 0.864871i | \(0.332600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.4185 | −1.26819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 25.2141i | − 1.35356i | −0.736184 | − | 0.676782i | \(-0.763374\pi\) | ||||
0.736184 | − | 0.676782i | \(-0.236626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.82396i | 0.258221i | 0.991630 | + | 0.129110i | \(0.0412121\pi\) | ||||
−0.991630 | + | 0.129110i | \(0.958788\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 21.2660i | − 1.13187i | −0.824448 | − | 0.565937i | \(-0.808514\pi\) | ||||
0.824448 | − | 0.565937i | \(-0.191486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.16723 | −0.221174 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.9785 | 1.31832 | 0.659158 | − | 0.752004i | \(-0.270913\pi\) | ||||
0.659158 | + | 0.752004i | \(0.270913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1720 | −0.956423 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.2892 | −1.63775 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.8851i | 0.724795i | 0.932024 | + | 0.362397i | \(0.118042\pi\) | ||||
−0.932024 | + | 0.362397i | \(0.881958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.54325i | 0.235874i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.513970i | 0.0266123i | 0.999911 | + | 0.0133062i | \(0.00423561\pi\) | ||||
−0.999911 | + | 0.0133062i | \(0.995764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.93383i | − 0.0995972i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.97711 | 0.409757 | 0.204878 | − | 0.978787i | \(-0.434320\pi\) | ||||
0.204878 | + | 0.978787i | \(0.434320\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.03401 | 0.410519 | 0.205259 | − | 0.978708i | \(-0.434196\pi\) | ||||
0.205259 | + | 0.978708i | \(0.434196\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.7628 | 0.905275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.60733 | −0.335005 | −0.167503 | − | 0.985872i | \(-0.553570\pi\) | ||||
−0.167503 | + | 0.985872i | \(0.553570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 11.5306i | − 0.583130i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 47.0430i | − 2.36699i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 17.4642i | − 0.876502i | −0.898853 | − | 0.438251i | \(-0.855598\pi\) | ||||
0.898853 | − | 0.438251i | \(-0.144402\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6133i | 0.929503i | 0.885441 | + | 0.464751i | \(0.153856\pi\) | ||||
−0.885441 | + | 0.464751i | \(0.846144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.22883 | 0.0612124 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.7460 | −1.77186 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.72844 | 0.184359 | 0.0921797 | − | 0.995742i | \(-0.470617\pi\) | ||||
0.0921797 | + | 0.995742i | \(0.470617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.50524 | 0.172482 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2230i | 0.845443i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 30.1591i | − 1.47337i | −0.676237 | − | 0.736684i | \(-0.736391\pi\) | ||||
0.676237 | − | 0.736684i | \(-0.263609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.17416i | − 0.203436i | −0.994813 | − | 0.101718i | \(-0.967566\pi\) | ||||
0.994813 | − | 0.101718i | \(-0.0324340\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.8439i | 0.671529i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.96254 | 0.0949740 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.3147 | −0.978524 | −0.489262 | − | 0.872137i | \(-0.662734\pi\) | ||||
−0.489262 | + | 0.872137i | \(0.662734\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.5740 | 1.80569 | 0.902847 | − | 0.429963i | \(-0.141473\pi\) | ||||
0.902847 | + | 0.429963i | \(0.141473\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.33630 | 0.255270 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2219i | 0.583317i | 0.956522 | + | 0.291659i | \(0.0942072\pi\) | ||||
−0.956522 | + | 0.291659i | \(0.905793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.13132i | 0.101262i | 0.998717 | + | 0.0506311i | \(0.0161233\pi\) | ||||
−0.998717 | + | 0.0506311i | \(0.983877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 63.1657i | − 2.99434i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 24.6873i | − 1.16506i | −0.812807 | − | 0.582532i | \(-0.802062\pi\) | ||||
0.812807 | − | 0.582532i | \(-0.197938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.7227 | −2.01173 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.932057 | −0.0436955 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.2814 | −1.55684 | −0.778419 | − | 0.627745i | \(-0.783978\pi\) | ||||
−0.778419 | + | 0.627745i | \(0.783978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.2279 | 0.709233 | 0.354617 | − | 0.935012i | \(-0.384611\pi\) | ||||
0.354617 | + | 0.935012i | \(0.384611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.21883i | 0.149592i | 0.997199 | + | 0.0747959i | \(0.0238305\pi\) | ||||
−0.997199 | + | 0.0747959i | \(0.976169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.5827i | 1.04500i | 0.852638 | + | 0.522502i | \(0.175001\pi\) | ||||
−0.852638 | + | 0.522502i | \(0.824999\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0280i | 0.509225i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 47.3621i | − 2.17771i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.40688 | −0.293968 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.0140 | −1.27999 | −0.639995 | − | 0.768379i | \(-0.721064\pi\) | ||||
−0.639995 | + | 0.768379i | \(0.721064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87568 | 0.0855237 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.7682 | 0.534368 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.55321i | − 0.115697i | −0.998325 | − | 0.0578485i | \(-0.981576\pi\) | ||||
0.998325 | − | 0.0578485i | \(-0.0184240\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.803432i | 0.0362584i | 0.999836 | + | 0.0181292i | \(0.00577102\pi\) | ||||
−0.999836 | + | 0.0181292i | \(0.994229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 14.1556i | − 0.637534i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1.20092i | − 0.0538687i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.6029 | −1.45950 | −0.729752 | − | 0.683712i | \(-0.760365\pi\) | ||||
−0.729752 | + | 0.683712i | \(0.760365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.6962 | 0.521508 | 0.260754 | − | 0.965405i | \(-0.416029\pi\) | ||||
0.260754 | + | 0.965405i | \(0.416029\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.4081 | 1.26414 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.0087 | 1.77335 | 0.886676 | − | 0.462391i | \(-0.153008\pi\) | ||||
0.886676 | + | 0.462391i | \(0.153008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 9.01697i | − 0.398887i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 57.4720i | 2.53252i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 33.2379i | − 1.46180i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.13277i | 0.224871i | 0.993659 | + | 0.112435i | \(0.0358651\pi\) | ||||
−0.993659 | + | 0.112435i | \(0.964135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.3652 | −1.54641 | −0.773207 | − | 0.634154i | \(-0.781348\pi\) | ||||
−0.773207 | + | 0.634154i | \(0.781348\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.99500 | 0.391829 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3929 | 0.495344 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.24177 | 0.0971018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 52.5640i | − 2.27254i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.11891i | 0.220487i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.7038i | 1.32006i | 0.751240 | + | 0.660029i | \(0.229456\pi\) | ||||
−0.751240 | + | 0.660029i | \(0.770544\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.7205i | 1.14458i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.21526 | 0.0947175 | 0.0473588 | − | 0.998878i | \(-0.484920\pi\) | ||||
0.0473588 | + | 0.998878i | \(0.484920\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.55110 | 0.279086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5570 | 0.576500 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.88158 | 0.376325 | 0.188162 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188162 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.48521i | 0.105113i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.9398i | 1.21967i | 0.792529 | + | 0.609834i | \(0.208764\pi\) | ||||
−0.792529 | + | 0.609834i | \(0.791236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 50.6007i | − 2.12879i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.8816i | 1.29463i | 0.762224 | + | 0.647313i | \(0.224107\pi\) | ||||
−0.762224 | + | 0.647313i | \(0.775893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.5945 | 1.32219 | 0.661094 | − | 0.750303i | \(-0.270092\pi\) | ||||
0.661094 | + | 0.750303i | \(0.270092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41.2928 | −1.72203 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.6007 | −1.56534 | −0.782669 | − | 0.622438i | \(-0.786142\pi\) | ||||
−0.782669 | + | 0.622438i | \(0.786142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.96335 | −0.205915 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 23.2565i | − 0.963186i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.0321i | 0.909361i | 0.890655 | + | 0.454680i | \(0.150246\pi\) | ||||
−0.890655 | + | 0.454680i | \(0.849754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.16283i | 0.171526i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17.8392i | − 0.732569i | −0.930503 | − | 0.366284i | \(-0.880630\pi\) | ||||
0.930503 | − | 0.366284i | \(-0.119370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.82263 | −0.279701 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.5363 | 0.798230 | 0.399115 | − | 0.916901i | \(-0.369317\pi\) | ||||
0.399115 | + | 0.916901i | \(0.369317\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.1240 | −0.820877 | −0.410438 | − | 0.911888i | \(-0.634624\pi\) | ||||
−0.410438 | + | 0.911888i | \(0.634624\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −52.7557 | −2.14483 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 15.3972i | − 0.624951i | −0.949926 | − | 0.312476i | \(-0.898842\pi\) | ||||
0.949926 | − | 0.312476i | \(-0.101158\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.74408i | 0.0705578i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 37.9629i | − 1.53331i | −0.642061 | − | 0.766653i | \(-0.721921\pi\) | ||||
0.642061 | − | 0.766653i | \(-0.278079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 43.0532i | − 1.73326i | −0.498953 | − | 0.866629i | \(-0.666282\pi\) | ||||
0.498953 | − | 0.866629i | \(-0.333718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.75463 | 0.271491 | 0.135746 | − | 0.990744i | \(-0.456657\pi\) | ||||
0.135746 | + | 0.990744i | \(0.456657\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.2032 | 0.729297 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.6285 | −0.425138 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.7299 | 0.547448 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.96735i | 0.0783189i | 0.999233 | + | 0.0391594i | \(0.0124680\pi\) | ||||
−0.999233 | + | 0.0391594i | \(0.987532\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 47.8108i | − 1.89731i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 0.268602i | − 0.0106424i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 30.2998i | − 1.19677i | −0.801209 | − | 0.598385i | \(-0.795809\pi\) | ||||
0.801209 | − | 0.598385i | \(-0.204191\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.85901 | −0.152185 | −0.0760923 | − | 0.997101i | \(-0.524244\pi\) | ||||
−0.0760923 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.4004 | −1.31310 | −0.656552 | − | 0.754281i | \(-0.727986\pi\) | ||||
−0.656552 | + | 0.754281i | \(0.727986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.9430 | −0.704326 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.9899 | 1.05620 | 0.528098 | − | 0.849184i | \(-0.322905\pi\) | ||||
0.528098 | + | 0.849184i | \(0.322905\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.6367i | 1.54874i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 13.1888i | − 0.513763i | −0.966443 | − | 0.256881i | \(-0.917305\pi\) | ||||
0.966443 | − | 0.256881i | \(-0.0826950\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 33.5767i | − 1.30598i | −0.757366 | − | 0.652990i | \(-0.773514\pi\) | ||||
0.757366 | − | 0.652990i | \(-0.226486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 3.15747i | − 0.122441i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.2224 | 1.63486 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0461 | −0.387824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5269 | 0.521424 | 0.260712 | − | 0.965417i | \(-0.416043\pi\) | ||||
0.260712 | + | 0.965417i | \(0.416043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.3388 | 0.973850 | 0.486925 | − | 0.873444i | \(-0.338118\pi\) | ||||
0.486925 | + | 0.873444i | \(0.338118\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.39139i | 0.130150i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 4.74712i | − 0.181644i | −0.995867 | − | 0.0908218i | \(-0.971051\pi\) | ||||
0.995867 | − | 0.0908218i | \(-0.0289494\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.4504i | 0.781369i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.22033i | 0.0464908i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.8908 | 1.78381 | 0.891904 | − | 0.452224i | \(-0.149369\pi\) | ||||
0.891904 | + | 0.452224i | \(0.149369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.7457 | −0.483472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.4097 | 0.621561 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8394 | 0.447166 | 0.223583 | − | 0.974685i | \(-0.428225\pi\) | ||||
0.223583 | + | 0.974685i | \(0.428225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.35412i | 0.239650i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.18671i | 0.307893i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 3.55487i | − 0.133506i | −0.997770 | − | 0.0667530i | \(-0.978736\pi\) | ||||
0.997770 | − | 0.0667530i | \(-0.0212639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.8298i | 1.00478i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.77112 | 0.178430 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.174626 | −0.00651246 | −0.00325623 | − | 0.999995i | \(-0.501036\pi\) | ||||
−0.00325623 | + | 0.999995i | \(0.501036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5624 | −0.616816 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −50.6930 | −1.88269 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.37928i | 0.310770i | 0.987854 | + | 0.155385i | \(0.0496619\pi\) | ||||
−0.987854 | + | 0.155385i | \(0.950338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.1917i | 0.672843i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 15.6312i | − 0.577351i | −0.957427 | − | 0.288676i | \(-0.906785\pi\) | ||||
0.957427 | − | 0.288676i | \(-0.0932149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 56.4512i | − 2.07941i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4382 | 0.935760 | 0.467880 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467880 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.0542 | −1.21264 | −0.606320 | − | 0.795220i | \(-0.707355\pi\) | ||||
−0.606320 | + | 0.795220i | \(0.707355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 79.8941 | 2.92709 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1480 | 0.553496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.4075i | 1.47449i | 0.675625 | + | 0.737246i | \(0.263874\pi\) | ||||
−0.675625 | + | 0.737246i | \(0.736126\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.64498i | − 0.169048i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0219i | 1.09116i | 0.838057 | + | 0.545582i | \(0.183691\pi\) | ||||
−0.838057 | + | 0.545582i | \(0.816309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 13.9651i | − 0.506234i | −0.967436 | − | 0.253117i | \(-0.918544\pi\) | ||||
0.967436 | − | 0.253117i | \(-0.0814557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.70038 | −0.278772 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.941516 | 0.0339962 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9999 | 0.649094 | 0.324547 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324547 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.2134 | 0.978798 | 0.489399 | − | 0.872060i | \(-0.337216\pi\) | ||||
0.489399 | + | 0.872060i | \(0.337216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 32.2124i | − 1.15710i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.59429i | 0.272094i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.14741i | 0.219972i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 75.5908i | 2.69795i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.45794 | −0.123262 | −0.0616312 | − | 0.998099i | \(-0.519630\pi\) | ||||
−0.0616312 | + | 0.998099i | \(0.519630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.5822 | 0.518484 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.527143 | 0.0187194 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.2671 | 1.56802 | 0.784010 | − | 0.620748i | \(-0.213171\pi\) | ||||
0.784010 | + | 0.620748i | \(0.213171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.7666i | 0.451650i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 46.1571i | 1.62885i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 20.3501i | − 0.717248i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.4191i | 0.506949i | 0.967342 | + | 0.253475i | \(0.0815734\pi\) | ||||
−0.967342 | + | 0.253475i | \(0.918427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.3314 | −0.854389 | −0.427195 | − | 0.904160i | \(-0.640498\pi\) | ||||
−0.427195 | + | 0.904160i | \(0.640498\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 70.3410 | 2.46394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.41897 | −0.294543 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.63626 | −0.126906 | −0.0634532 | − | 0.997985i | \(-0.520211\pi\) | ||||
−0.0634532 | + | 0.997985i | \(0.520211\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.408592i | 0.0142426i | 0.999975 | + | 0.00712132i | \(0.00226681\pi\) | ||||
−0.999975 | + | 0.00712132i | \(0.997733\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 39.3528i | − 1.36843i | −0.729280 | − | 0.684215i | \(-0.760145\pi\) | ||||
0.729280 | − | 0.684215i | \(-0.239855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 37.5641i | − 1.30465i | −0.757938 | − | 0.652327i | \(-0.773793\pi\) | ||||
0.757938 | − | 0.652327i | \(-0.226207\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.96616i | − 0.0681234i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.8200 | −0.789719 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.7770 | −1.23516 | −0.617579 | − | 0.786509i | \(-0.711887\pi\) | ||||
−0.617579 | + | 0.786509i | \(0.711887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8342 | 0.787385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 44.8600 | 1.54323 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 15.2033i | − 0.522390i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.9528i | 1.40384i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.3988i | 1.79410i | 0.441929 | + | 0.897050i | \(0.354294\pi\) | ||||
−0.441929 | + | 0.897050i | \(0.645706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.1325i | 0.653553i | 0.945102 | + | 0.326777i | \(0.105963\pi\) | ||||
−0.945102 | + | 0.326777i | \(0.894037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1998 | 0.416253 | 0.208127 | − | 0.978102i | \(-0.433263\pi\) | ||||
0.208127 | + | 0.978102i | \(0.433263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.3575 | −1.06742 | −0.533711 | − | 0.845667i | \(-0.679203\pi\) | ||||
−0.533711 | + | 0.845667i | \(0.679203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.2897 | −1.57390 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −69.3968 | −2.35413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.96214i | 0.100368i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.08266i | 0.239438i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.64956i | 0.157004i | 0.996914 | + | 0.0785022i | \(0.0250138\pi\) | ||||
−0.996914 | + | 0.0785022i | \(0.974986\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.3414i | 1.46021i | 0.683336 | + | 0.730104i | \(0.260528\pi\) | ||||
−0.683336 | + | 0.730104i | \(0.739472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.420653 | −0.0141561 | −0.00707805 | − | 0.999975i | \(-0.502253\pi\) | ||||
−0.00707805 | + | 0.999975i | \(0.502253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.5102 | 0.487204 | 0.243602 | − | 0.969875i | \(-0.421671\pi\) | ||||
0.243602 | + | 0.969875i | \(0.421671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7782 | 0.462106 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.90830 | −0.197714 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 34.0955i | − 1.13969i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.9375i | 1.09853i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.93276i | 0.297593i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.9599i | 0.563765i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.1284 | 1.00040 | 0.500198 | − | 0.865911i | \(-0.333260\pi\) | ||||
0.500198 | + | 0.865911i | \(0.333260\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.1934 | −0.503379 | −0.251689 | − | 0.967808i | \(-0.580986\pi\) | ||||
−0.251689 | + | 0.967808i | \(0.580986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4070 | 0.840848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.4226 | −0.377207 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.7985i | 1.27984i | 0.768440 | + | 0.639922i | \(0.221033\pi\) | ||||
−0.768440 | + | 0.639922i | \(0.778967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.322570i | − 0.0106175i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 49.1688i | − 1.61666i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.7700i | 1.43605i | 0.696019 | + | 0.718023i | \(0.254953\pi\) | ||||
−0.696019 | + | 0.718023i | \(0.745047\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.909926 | 0.0298216 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.9245 | 1.14215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7605 | 0.580209 | 0.290104 | − | 0.956995i | \(-0.406310\pi\) | ||||
0.290104 | + | 0.956995i | \(0.406310\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.6364 | −1.06392 | −0.531958 | − | 0.846771i | \(-0.678544\pi\) | ||||
−0.531958 | + | 0.846771i | \(0.678544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.9458i | 1.59390i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 14.9843i | − 0.486925i | −0.969910 | − | 0.243462i | \(-0.921717\pi\) | ||||
0.969910 | − | 0.243462i | \(-0.0782832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.42198i | − 0.0786208i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.1053i | 0.748453i | 0.927337 | + | 0.374226i | \(0.122092\pi\) | ||||
−0.927337 | + | 0.374226i | \(0.877908\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.2971 | −1.30398 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.89343 | −0.190309 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0702 | 0.324846 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.4741 | −1.43167 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.1604i | 0.809103i | 0.914515 | + | 0.404552i | \(0.132572\pi\) | ||||
−0.914515 | + | 0.404552i | \(0.867428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0973i | 0.773318i | 0.922223 | + | 0.386659i | \(0.126371\pi\) | ||||
−0.922223 | + | 0.386659i | \(0.873629\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3.67309i | − 0.117754i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.9215i | 0.989267i | 0.869102 | + | 0.494634i | \(0.164698\pi\) | ||||
−0.869102 | + | 0.494634i | \(0.835302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −93.1807 | −2.97807 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.67927 | 0.0535602 | 0.0267801 | − | 0.999641i | \(-0.491475\pi\) | ||||
0.0267801 | + | 0.999641i | \(0.491475\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.2795 | 0.518709 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −54.2610 | −1.72540 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.63921i | 0.242667i | 0.992612 | + | 0.121334i | \(0.0387171\pi\) | ||||
−0.992612 | + | 0.121334i | \(0.961283\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 53.2841i | − 1.68922i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.4039i | 1.81800i | 0.416798 | + | 0.908999i | \(0.363152\pi\) | ||||
−0.416798 | + | 0.908999i | \(0.636848\pi\) | |||||||
\(998\) | 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 | 6048.2.j.c.5615.30 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.3 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.29 | yes | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.4 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.3 | ✓ | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.4 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.30 | yes | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.29 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.3 | ✓ | 32 | 8.5 | even | 2 | ||
1512.2.j.c.323.4 | yes | 32 | 12.11 | even | 2 | ||
1512.2.j.c.323.29 | yes | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.30 | yes | 32 | 24.5 | odd | 2 | ||
6048.2.j.c.5615.3 | 32 | 3.2 | odd | 2 | inner | ||
6048.2.j.c.5615.4 | 32 | 8.3 | odd | 2 | inner | ||
6048.2.j.c.5615.29 | 32 | 24.11 | even | 2 | inner | ||
6048.2.j.c.5615.30 | 32 | 1.1 | even | 1 | trivial |