Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1121,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 35 x^{10} - 120 x^{9} + 362 x^{8} - 794 x^{7} + 1463 x^{6} - 2048 x^{5} + 2258 x^{4} + \cdots + 61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.12 | ||
Root | \(0.500000 - 0.234551i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1121 |
Dual form | 2240.2.b.h.1121.1 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.32646i | 1.92053i | 0.279085 | + | 0.960267i | \(0.409969\pi\) | ||||
−0.279085 | + | 0.960267i | \(0.590031\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.06534 | −2.68845 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.78873i | − 1.14235i | −0.820830 | − | 0.571173i | \(-0.806489\pi\) | ||||
0.820830 | − | 0.571173i | \(-0.193511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.49865i | 1.24770i | 0.781544 | + | 0.623850i | \(0.214433\pi\) | ||||
−0.781544 | + | 0.623850i | \(0.785567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.32646 | −0.858888 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.58941 | −0.628024 | −0.314012 | − | 0.949419i | \(-0.601673\pi\) | ||||
−0.314012 | + | 0.949419i | \(0.601673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.09856i | 1.16969i | 0.811145 | + | 0.584845i | \(0.198845\pi\) | ||||
−0.811145 | + | 0.584845i | \(0.801155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.32646i | 0.725893i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.16036 | −0.450466 | −0.225233 | − | 0.974305i | \(-0.572314\pi\) | ||||
−0.225233 | + | 0.974305i | \(0.572314\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 16.8497i | − 3.24272i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 0.164774i | − 0.0305978i | −0.999883 | − | 0.0152989i | \(-0.995130\pi\) | ||||
0.999883 | − | 0.0152989i | \(-0.00486998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.36151 | −1.14256 | −0.571281 | − | 0.820755i | \(-0.693553\pi\) | ||||
−0.571281 | + | 0.820755i | \(0.693553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.6031 | 2.19391 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000i | 0.169031i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.95666i | − 1.30807i | −0.756465 | − | 0.654034i | \(-0.773075\pi\) | ||||
0.756465 | − | 0.654034i | \(-0.226925\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.9646 | −2.39625 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.23582 | 0.505350 | 0.252675 | − | 0.967551i | \(-0.418690\pi\) | ||||
0.252675 | + | 0.967551i | \(0.418690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.69371i | − 1.32578i | −0.748717 | − | 0.662889i | \(-0.769330\pi\) | ||||
0.748717 | − | 0.662889i | \(-0.230670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 8.06534i | − 1.20231i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3012 | −1.79431 | −0.897154 | − | 0.441718i | \(-0.854369\pi\) | ||||
−0.897154 | + | 0.441718i | \(0.854369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 8.61357i | − 1.20614i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.26428i | 0.860465i | 0.902718 | + | 0.430232i | \(0.141568\pi\) | ||||
−0.902718 | + | 0.430232i | \(0.858432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.78873 | 0.510873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.9602 | −2.24643 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.88394i | 0.896212i | 0.893980 | + | 0.448106i | \(0.147901\pi\) | ||||
−0.893980 | + | 0.448106i | \(0.852099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.08623i | 1.03534i | 0.855582 | + | 0.517668i | \(0.173200\pi\) | ||||
−0.855582 | + | 0.517668i | \(0.826800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.06534 | −1.01614 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.49865 | −0.557989 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.05793i | 0.251416i | 0.992067 | + | 0.125708i | \(0.0401202\pi\) | ||||
−0.992067 | + | 0.125708i | \(0.959880\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 7.18635i | − 0.865135i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7699 | −1.51551 | −0.757757 | − | 0.652537i | \(-0.773705\pi\) | ||||
−0.757757 | + | 0.652537i | \(0.773705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.80848 | 0.913913 | 0.456957 | − | 0.889489i | \(-0.348939\pi\) | ||||
0.456957 | + | 0.889489i | \(0.348939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.32646i | − 0.384107i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.78873i | − 0.431766i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.08065 | −0.684126 | −0.342063 | − | 0.939677i | \(-0.611126\pi\) | ||||
−0.342063 | + | 0.939677i | \(0.611126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.8537 | 3.53930 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 17.7985i | − 1.95364i | −0.214069 | − | 0.976818i | \(-0.568672\pi\) | ||||
0.214069 | − | 0.976818i | \(-0.431328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.58941i | − 0.280861i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.548115 | 0.0587641 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.16036 | 0.440997 | 0.220499 | − | 0.975387i | \(-0.429232\pi\) | ||||
0.220499 | + | 0.975387i | \(0.429232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.49865i | 0.471587i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 21.1613i | − 2.19433i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.09856 | −0.523101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.338793 | −0.0343992 | −0.0171996 | − | 0.999852i | \(-0.505475\pi\) | ||||
−0.0171996 | + | 0.999852i | \(0.505475\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 30.5574i | 3.07114i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9111i | 1.28470i | 0.766412 | + | 0.642350i | \(0.222040\pi\) | ||||
−0.766412 | + | 0.642350i | \(0.777960\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3012 | 1.21207 | 0.606035 | − | 0.795438i | \(-0.292759\pi\) | ||||
0.606035 | + | 0.795438i | \(0.292759\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.32646 | −0.324629 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 13.7284i | − 1.32717i | −0.748100 | − | 0.663586i | \(-0.769034\pi\) | ||||
0.748100 | − | 0.663586i | \(-0.230966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.29180i | 0.411080i | 0.978649 | + | 0.205540i | \(0.0658950\pi\) | ||||
−0.978649 | + | 0.205540i | \(0.934105\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.4675 | 2.51219 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.2924 | −1.25044 | −0.625220 | − | 0.780448i | \(-0.714991\pi\) | ||||
−0.625220 | + | 0.780448i | \(0.714991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.16036i | − 0.201455i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 36.2831i | − 3.35438i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.58941 | −0.237371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.35449 | −0.304954 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7638i | 0.970541i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.7836 | 1.84425 | 0.922123 | − | 0.386896i | \(-0.126453\pi\) | ||||
0.922123 | + | 0.386896i | \(0.126453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.9193 | 2.54620 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5517i | 1.27138i | 0.771943 | + | 0.635692i | \(0.219285\pi\) | ||||
−0.771943 | + | 0.635692i | \(0.780715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.09856i | 0.442101i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.8497 | 1.45019 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.08623 | −0.690853 | −0.345427 | − | 0.938446i | \(-0.612266\pi\) | ||||
−0.345427 | + | 0.938446i | \(0.612266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 9.53686i | − 0.808906i | −0.914559 | − | 0.404453i | \(-0.867462\pi\) | ||||
0.914559 | − | 0.404453i | \(-0.132538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 40.9193i | − 3.44603i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.0442 | 1.42531 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.164774 | 0.0136838 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.32646i | 0.274362i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.79482i | 0.474730i | 0.971421 | + | 0.237365i | \(0.0762838\pi\) | ||||
−0.971421 | + | 0.237365i | \(0.923716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.11648 | 0.334994 | 0.167497 | − | 0.985873i | \(-0.446432\pi\) | ||||
0.167497 | + | 0.985873i | \(0.446432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.8845 | 1.68841 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.36151i | − 0.510969i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.8591i | 1.42531i | 0.701516 | + | 0.712654i | \(0.252507\pi\) | ||||
−0.701516 | + | 0.712654i | \(0.747493\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.8379 | −1.65255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.16036 | −0.170260 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.5269i | 1.68611i | 0.537824 | + | 0.843057i | \(0.319246\pi\) | ||||
−0.537824 | + | 0.843057i | \(0.680754\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.6031i | 0.981148i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.62970 | 0.358257 | 0.179128 | − | 0.983826i | \(-0.442672\pi\) | ||||
0.179128 | + | 0.983826i | \(0.442672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.23785 | −0.556758 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 41.1216i | − 3.14465i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.82472i | 0.746960i | 0.927638 | + | 0.373480i | \(0.121836\pi\) | ||||
−0.927638 | + | 0.373480i | \(0.878164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.8991 | −1.72120 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.45410i | 0.108685i | 0.998522 | + | 0.0543424i | \(0.0173062\pi\) | ||||
−0.998522 | + | 0.0543424i | \(0.982694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1639i | 1.20146i | 0.799453 | + | 0.600728i | \(0.205123\pi\) | ||||
−0.799453 | + | 0.600728i | \(0.794877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.8985 | −1.98840 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.95666 | 0.584986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.81058i | 0.717421i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 16.8497i | − 1.22563i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0537 | −0.727460 | −0.363730 | − | 0.931504i | \(-0.618497\pi\) | ||||
−0.363730 | + | 0.931504i | \(0.618497\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.13803 | 0.657770 | 0.328885 | − | 0.944370i | \(-0.393327\pi\) | ||||
0.328885 | + | 0.944370i | \(0.393327\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 14.9646i | − 1.07164i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.1777i | − 1.43760i | −0.695217 | − | 0.718800i | \(-0.744692\pi\) | ||||
0.695217 | − | 0.718800i | \(-0.255308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8011 | −0.978336 | −0.489168 | − | 0.872189i | \(-0.662700\pi\) | ||||
−0.489168 | + | 0.872189i | \(0.662700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.84561 | −0.482852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.164774i | − 0.0115649i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.23582i | 0.225999i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.4240 | 1.21105 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.3171 | 1.33619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 7.44801i | − 0.512742i | −0.966578 | − | 0.256371i | \(-0.917473\pi\) | ||||
0.966578 | − | 0.256371i | \(-0.0825270\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 42.4787i | − 2.91059i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.69371 | 0.592906 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.36151 | −0.431848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.9746i | 1.75520i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 11.6488i | − 0.783586i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.5009 | −1.90856 | −0.954282 | − | 0.298908i | \(-0.903378\pi\) | ||||
−0.954282 | + | 0.298908i | \(0.903378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.06534 | 0.537689 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.74630i | − 0.580512i | −0.956949 | − | 0.290256i | \(-0.906260\pi\) | ||||
0.956949 | − | 0.290256i | \(-0.0937405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.51513i | 0.100122i | 0.998746 | + | 0.0500612i | \(0.0159416\pi\) | ||||
−0.998746 | + | 0.0500612i | \(0.984058\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.6031 | 0.829221 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.33586 | 0.415076 | 0.207538 | − | 0.978227i | \(-0.433455\pi\) | ||||
0.207538 | + | 0.978227i | \(0.433455\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 12.3012i | − 0.802439i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 20.2270i | − 1.31389i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.57864 | 0.360852 | 0.180426 | − | 0.983589i | \(-0.442252\pi\) | ||||
0.180426 | + | 0.983589i | \(0.442252\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.2762 | −1.49935 | −0.749675 | − | 0.661806i | \(-0.769790\pi\) | ||||
−0.749675 | + | 0.661806i | \(0.769790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 55.4111i | 3.55463i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.9366 | −1.45942 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 59.2059 | 3.75202 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 15.3659i | − 0.969890i | −0.874545 | − | 0.484945i | \(-0.838840\pi\) | ||||
0.874545 | − | 0.484945i | \(-0.161160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.18502i | 0.514588i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.61357 | 0.539403 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.48529 | −0.279785 | −0.139892 | − | 0.990167i | \(-0.544676\pi\) | ||||
−0.139892 | + | 0.990167i | \(0.544676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.95666i | − 0.494403i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.32896i | 0.0822606i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.76164 | 0.108627 | 0.0543137 | − | 0.998524i | \(-0.482703\pi\) | ||||
0.0543137 | + | 0.998524i | \(0.482703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.26428 | −0.384811 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.8393i | 0.846950i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.09033i | − 0.249392i | −0.992195 | − | 0.124696i | \(-0.960204\pi\) | ||||
0.992195 | − | 0.124696i | \(-0.0397956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.98287 | −0.241942 | −0.120971 | − | 0.992656i | \(-0.538601\pi\) | ||||
−0.120971 | + | 0.992656i | \(0.538601\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.9646 | −0.905698 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.78873i | 0.228469i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.38618i | 0.323624i | 0.986822 | + | 0.161812i | \(0.0517338\pi\) | ||||
−0.986822 | + | 0.161812i | \(0.948266\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 51.3078 | 3.07172 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0969 | 1.31819 | 0.659096 | − | 0.752059i | \(-0.270939\pi\) | ||||
0.659096 | + | 0.752059i | \(0.270939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1846i | 0.962072i | 0.876701 | + | 0.481036i | \(0.159739\pi\) | ||||
−0.876701 | + | 0.481036i | \(0.840261\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 16.9602i | − 1.00463i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.23582 | 0.191004 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2950 | −0.605586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.12698i | − 0.0660648i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.07611i | 0.238129i | 0.992887 | + | 0.119065i | \(0.0379896\pi\) | ||||
−0.992887 | + | 0.119065i | \(0.962010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.88394 | −0.400798 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −63.8388 | −3.70431 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 9.71870i | − 0.562047i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.69371i | − 0.501097i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −42.9482 | −2.46731 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.08623 | −0.463016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 11.3719i | − 0.649028i | −0.945881 | − | 0.324514i | \(-0.894799\pi\) | ||||
0.945881 | − | 0.324514i | \(-0.105201\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.9193i | 2.32782i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.6165 | −1.67940 | −0.839699 | − | 0.543052i | \(-0.817269\pi\) | ||||
−0.839699 | + | 0.543052i | \(0.817269\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.5113 | −1.83764 | −0.918822 | − | 0.394671i | \(-0.870858\pi\) | ||||
−0.918822 | + | 0.394671i | \(0.870858\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 8.06534i | − 0.454430i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.1898i | 1.47096i | 0.677544 | + | 0.735482i | \(0.263044\pi\) | ||||
−0.677544 | + | 0.735482i | \(0.736956\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.624285 | −0.0349533 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.6669 | 2.54888 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 13.2023i | − 0.734594i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.49865i | − 0.249540i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2765 | −0.789492 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3012 | −0.678185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.6714i | 1.68585i | 0.538029 | + | 0.842927i | \(0.319169\pi\) | ||||
−0.538029 | + | 0.842927i | \(0.680831\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 64.1732i | 3.51667i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.05793 | −0.112437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.78095 | −0.260435 | −0.130217 | − | 0.991485i | \(-0.541568\pi\) | ||||
−0.130217 | + | 0.991485i | \(0.541568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 44.2165i | − 2.40151i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.1021i | 1.30520i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.18635 | 0.386900 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.22062i | 0.387623i | 0.981039 | + | 0.193812i | \(0.0620850\pi\) | ||||
−0.981039 | + | 0.193812i | \(0.937915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.0366i | 1.55429i | 0.629320 | + | 0.777146i | \(0.283334\pi\) | ||||
−0.629320 | + | 0.777146i | \(0.716666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 75.8007 | 4.04594 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.03715 | −0.374550 | −0.187275 | − | 0.982308i | \(-0.559966\pi\) | ||||
−0.187275 | + | 0.982308i | \(0.559966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 12.7699i | − 0.677758i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 8.61357i | − 0.455879i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.87446 | −0.415598 | −0.207799 | − | 0.978172i | \(-0.566630\pi\) | ||||
−0.207799 | + | 0.978172i | \(0.566630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.99533 | −0.368175 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 11.1586i | − 0.585674i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.80848i | 0.408714i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.86379 | 0.514886 | 0.257443 | − | 0.966294i | \(-0.417120\pi\) | ||||
0.257443 | + | 0.966294i | \(0.417120\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.0980 | −1.35861 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.26428i | 0.325225i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 28.7241i | − 1.48728i | −0.668581 | − | 0.743639i | \(-0.733098\pi\) | ||||
0.668581 | − | 0.743639i | \(-0.266902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.32646 | 0.171778 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.741261 | 0.0381769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.32584i | 0.0681039i | 0.999420 | + | 0.0340520i | \(0.0108412\pi\) | ||||
−0.999420 | + | 0.0340520i | \(0.989159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 69.1358i | 3.54194i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.0542666 | −0.00277290 | −0.00138645 | − | 0.999999i | \(-0.500441\pi\) | ||||
−0.00138645 | + | 0.999999i | \(0.500441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.78873 | 0.193092 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 70.1178i | 3.56429i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 11.4865i | − 0.582386i | −0.956664 | − | 0.291193i | \(-0.905948\pi\) | ||||
0.956664 | − | 0.291193i | \(-0.0940522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.59406 | 0.282904 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.4055 | −2.44174 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.08065i | − 0.305950i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6782i | 1.08800i | 0.839085 | + | 0.544000i | \(0.183091\pi\) | ||||
−0.839085 | + | 0.544000i | \(0.816909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.9602 | −0.849070 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.6650 | 1.18177 | 0.590887 | − | 0.806754i | \(-0.298778\pi\) | ||||
0.590887 | + | 0.806754i | \(0.298778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 28.6182i | − 1.42557i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.8537i | 1.58282i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −30.1457 | −1.49427 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.9319 | −1.52948 | −0.764741 | − | 0.644338i | \(-0.777133\pi\) | ||||
−0.764741 | + | 0.644338i | \(0.777133\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 26.8985i | − 1.32681i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.88394i | 0.338736i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7985 | 0.873693 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.7240 | 1.55353 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4123i | 0.606381i | 0.952930 | + | 0.303190i | \(0.0980518\pi\) | ||||
−0.952930 | + | 0.303190i | \(0.901948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8984i | 1.45716i | 0.684962 | + | 0.728578i | \(0.259819\pi\) | ||||
−0.684962 | + | 0.728578i | \(0.740181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 99.2130 | 4.82390 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.58941 | 0.125605 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.08623i | 0.391320i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 56.6968i | 2.73735i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.8670 | 0.667947 | 0.333974 | − | 0.942582i | \(-0.391610\pi\) | ||||
0.333974 | + | 0.942582i | \(0.391610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0695 | −0.580022 | −0.290011 | − | 0.957023i | \(-0.593659\pi\) | ||||
−0.290011 | + | 0.957023i | \(0.593659\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.548115i | 0.0262801i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 11.0147i | − 0.526906i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.6996 | 1.32203 | 0.661016 | − | 0.750372i | \(-0.270126\pi\) | ||||
0.661016 | + | 0.750372i | \(0.270126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.06534 | −0.384064 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.21001i | 0.0574893i | 0.999587 | + | 0.0287446i | \(0.00915096\pi\) | ||||
−0.999587 | + | 0.0287446i | \(0.990849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.16036i | 0.197220i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.2762 | −0.911735 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2432 | 0.672176 | 0.336088 | − | 0.941831i | \(-0.390896\pi\) | ||||
0.336088 | + | 0.941831i | \(0.390896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 12.2596i | − 0.577284i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6933i | 0.643368i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.49865 | −0.210900 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.62385 | −0.403406 | −0.201703 | − | 0.979447i | \(-0.564648\pi\) | ||||
−0.201703 | + | 0.979447i | \(0.564648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 43.6307i | 2.03651i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 31.2313i | − 1.45459i | −0.686326 | − | 0.727294i | \(-0.740778\pi\) | ||||
0.686326 | − | 0.727294i | \(-0.259222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0612 | −0.746427 | −0.373214 | − | 0.927745i | \(-0.621744\pi\) | ||||
−0.373214 | + | 0.927745i | \(0.621744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.1613 | 0.981333 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 38.9918i | − 1.80433i | −0.431395 | − | 0.902163i | \(-0.641978\pi\) | ||||
0.431395 | − | 0.902163i | \(-0.358022\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.05793i | 0.0950262i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −59.4075 | −2.73735 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.9382 | −1.51450 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.09856i | − 0.233938i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 50.5235i | − 2.31331i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.4743 | −1.71225 | −0.856123 | − | 0.516772i | \(-0.827134\pi\) | ||||
−0.856123 | + | 0.516772i | \(0.827134\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.7942 | 1.63208 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 7.18635i | − 0.326990i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.338793i | − 0.0153838i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.8490 | −0.763503 | −0.381751 | − | 0.924265i | \(-0.624679\pi\) | ||||
−0.381751 | + | 0.924265i | \(0.624679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −71.6082 | −3.23824 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.18660i | 0.279197i | 0.990208 | + | 0.139599i | \(0.0445813\pi\) | ||||
−0.990208 | + | 0.139599i | \(0.955419\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.426668i | 0.0192162i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.5574 | −1.37345 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.7699 | −0.572810 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7169i | 0.658821i | 0.944187 | + | 0.329410i | \(0.106850\pi\) | ||||
−0.944187 | + | 0.329410i | \(0.893150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.4005i | 0.688044i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.9698 | 0.801234 | 0.400617 | − | 0.916246i | \(-0.368796\pi\) | ||||
0.400617 | + | 0.916246i | \(0.368796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9111 | −0.574535 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 24.0764i | − 1.06927i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 36.5442i | − 1.61979i | −0.586574 | − | 0.809896i | \(-0.699524\pi\) | ||||
0.586574 | − | 0.809896i | \(-0.300476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.80848 | 0.345427 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 85.9090 | 3.79298 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.3012i | 0.542054i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.6058i | 2.04972i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.6816 | −1.43456 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.71262 | −0.162653 | −0.0813264 | − | 0.996688i | \(-0.525916\pi\) | ||||
−0.0813264 | + | 0.996688i | \(0.525916\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.8921i | 0.476280i | 0.971231 | + | 0.238140i | \(0.0765377\pi\) | ||||
−0.971231 | + | 0.238140i | \(0.923462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.32646i | − 0.145179i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.4726 | 0.717556 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3328 | −0.797080 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 55.5213i | − 2.40942i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.5568i | 0.630525i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.7284 | 0.593530 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.83701 | −0.208733 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.78873i | − 0.163192i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9421i | 0.900370i | 0.892935 | + | 0.450185i | \(0.148642\pi\) | ||||
−0.892935 | + | 0.450185i | \(0.851358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −53.7687 | −2.30744 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.29180 | −0.183840 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.72882i | 0.159433i | 0.996818 | + | 0.0797164i | \(0.0254015\pi\) | ||||
−0.996818 | + | 0.0797164i | \(0.974599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 65.2182i | − 2.78345i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.840111 | 0.0357899 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.08065 | −0.258575 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.4675i | 1.12348i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 0.983640i | − 0.0416782i | −0.999783 | − | 0.0208391i | \(-0.993366\pi\) | ||||
0.999783 | − | 0.0208391i | \(-0.00663376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.1100 | 1.65418 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.6345 | −1.37783 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7.97634i | − 0.336163i | −0.985773 | − | 0.168081i | \(-0.946243\pi\) | ||||
0.985773 | − | 0.168081i | \(-0.0537571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 13.2924i | − 0.559214i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.8537 | 1.33773 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.7001 | −1.66431 | −0.832157 | − | 0.554540i | \(-0.812894\pi\) | ||||
−0.832157 | + | 0.554540i | \(0.812894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.8606i | 1.91921i | 0.281356 | + | 0.959603i | \(0.409216\pi\) | ||||
−0.281356 | + | 0.959603i | \(0.590784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 33.4432i | − 1.39711i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.16036 | 0.0900932 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.0877 | 1.00278 | 0.501392 | − | 0.865220i | \(-0.332821\pi\) | ||||
0.501392 | + | 0.865220i | \(0.332821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.3973i | 1.26327i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 17.7985i | − 0.738405i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7337 | 0.982948 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.2831 | 1.50012 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.9561i | 1.11260i | 0.830983 | + | 0.556298i | \(0.187779\pi\) | ||||
−0.830983 | + | 0.556298i | \(0.812221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 32.4346i | − 1.33644i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 67.1203 | 2.76096 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.13361 | 0.251877 | 0.125939 | − | 0.992038i | \(-0.459806\pi\) | ||||
0.125939 | + | 0.992038i | \(0.459806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.58941i | − 0.106155i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 45.9089i | − 1.87893i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6746 | −0.599589 | −0.299795 | − | 0.954004i | \(-0.596918\pi\) | ||||
−0.299795 | + | 0.954004i | \(0.596918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.84333 | 0.115982 | 0.0579909 | − | 0.998317i | \(-0.481531\pi\) | ||||
0.0579909 | + | 0.998317i | \(0.481531\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 16.5979i | − 0.675918i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.35449i | − 0.136380i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.58677 | 0.389115 | 0.194557 | − | 0.980891i | \(-0.437673\pi\) | ||||
0.194557 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.548115 | 0.0222107 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 55.3386i | − 2.23876i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5376i | 0.789117i | 0.918871 | + | 0.394559i | \(0.129103\pi\) | ||||
−0.918871 | + | 0.394559i | \(0.870897\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.7638 | −0.434039 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.6597 | 1.39535 | 0.697673 | − | 0.716416i | \(-0.254219\pi\) | ||||
0.697673 | + | 0.716416i | \(0.254219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5053i | 0.462436i | 0.972902 | + | 0.231218i | \(0.0742710\pi\) | ||||
−0.972902 | + | 0.231218i | \(0.925729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 36.4013i | 1.46073i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.16036 | 0.166681 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 64.2575i | 2.56620i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.6031i | 0.821498i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5523 | 0.658936 | 0.329468 | − | 0.944167i | \(-0.393131\pi\) | ||||
0.329468 | + | 0.944167i | \(0.393131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.7755 | 0.984739 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.7836i | 0.824772i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.49865i | 0.178243i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 102.994 | 4.07438 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.2781 | 1.47240 | 0.736198 | − | 0.676766i | \(-0.236619\pi\) | ||||
0.736198 | + | 0.676766i | \(0.236619\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.89360i | 0.0746761i | 0.999303 | + | 0.0373381i | \(0.0118878\pi\) | ||||
−0.999303 | + | 0.0373381i | \(0.988112\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.9193i | 1.13870i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.0019 | −0.786354 | −0.393177 | − | 0.919463i | \(-0.628624\pi\) | ||||
−0.393177 | + | 0.919463i | \(0.628624\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.0814 | 1.02378 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 21.1613i | − 0.829377i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 14.1109i | − 0.552203i | −0.961128 | − | 0.276102i | \(-0.910957\pi\) | ||||
0.961128 | − | 0.276102i | \(-0.0890426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5517 | −0.568580 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −62.9780 | −2.45701 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.20106i | 0.124695i | 0.998054 | + | 0.0623477i | \(0.0198588\pi\) | ||||
−0.998054 | + | 0.0623477i | \(0.980141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 3.88158i | − 0.150976i | −0.997147 | − | 0.0754879i | \(-0.975949\pi\) | ||||
0.997147 | − | 0.0754879i | \(-0.0240514\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 38.7494 | 1.50490 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.09856 | −0.197714 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.355971i | 0.0137833i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 94.8072i | − 3.66546i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.6366 | 1.18271 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.53366 | −0.0976655 | −0.0488327 | − | 0.998807i | \(-0.515550\pi\) | ||||
−0.0488327 | + | 0.998807i | \(0.515550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.8497i | 0.648544i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.0982i | 1.19520i | 0.801795 | + | 0.597600i | \(0.203879\pi\) | ||||
−0.801795 | + | 0.597600i | \(0.796121\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.338793 | −0.0130017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.0942 | 1.11489 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6342i | 0.483435i | 0.970347 | + | 0.241718i | \(0.0777107\pi\) | ||||
−0.970347 | + | 0.241718i | \(0.922289\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.08623i | − 0.308959i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.04001 | −0.192288 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.1808 | −1.07360 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 7.57863i | − 0.288305i | −0.989555 | − | 0.144152i | \(-0.953954\pi\) | ||||
0.989555 | − | 0.144152i | \(-0.0460456\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.5574i | 1.16078i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.53686 | 0.361754 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.37886 | −0.317372 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.0760i | 0.797167i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8028i | 0.747942i | 0.927440 | + | 0.373971i | \(0.122004\pi\) | ||||
−0.927440 | + | 0.373971i | \(0.877996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.5675 | 1.53003 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.9193 | 1.54111 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.9111i | 0.485571i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.8494i | 1.45902i | 0.683971 | + | 0.729509i | \(0.260252\pi\) | ||||
−0.683971 | + | 0.729509i | \(0.739748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 49.0425 | 1.83924 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.7432 | 0.514685 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.0442i | 0.637416i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.5571i | 0.693028i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5862 | −1.51361 | −0.756805 | − | 0.653641i | \(-0.773241\pi\) | ||||
−0.756805 | + | 0.653641i | \(0.773241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3012 | 0.458119 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 77.4273i | − 2.87955i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.164774i | 0.00611956i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.75047 | −0.361625 | −0.180812 | − | 0.983518i | \(-0.557873\pi\) | ||||
−0.180812 | + | 0.983518i | \(0.557873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −88.7618 | −3.28747 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.5116i | 0.832621i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.2532i | 1.56066i | 0.625369 | + | 0.780330i | \(0.284949\pi\) | ||||
−0.625369 | + | 0.780330i | \(0.715051\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.32646 | −0.122698 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.79693 | 0.287204 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 28.4031i | − 1.04482i | −0.852693 | − | 0.522412i | \(-0.825032\pi\) | ||||
0.852693 | − | 0.522412i | \(-0.174968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 76.2978i | − 2.80287i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.5443 | 0.570265 | 0.285132 | − | 0.958488i | \(-0.407962\pi\) | ||||
0.285132 | + | 0.958488i | \(0.407962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.79482 | −0.212306 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 143.551i | 5.25225i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 13.7284i | − 0.501624i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.73572 | −0.0633373 | −0.0316687 | − | 0.999498i | \(-0.510082\pi\) | ||||
−0.0316687 | + | 0.999498i | \(0.510082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 51.1142 | 1.86271 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.11648i | 0.149814i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 18.9267i | − 0.687903i | −0.938987 | − | 0.343952i | \(-0.888234\pi\) | ||||
0.938987 | − | 0.343952i | \(-0.111766\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.2272 | −0.988283 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2341 | 0.443487 | 0.221743 | − | 0.975105i | \(-0.428825\pi\) | ||||
0.221743 | + | 0.975105i | \(0.428825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.29180i | 0.155373i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.8845i | 0.755080i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.9684 | −1.11820 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1640 | −0.402586 | −0.201293 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201293 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 14.9201i | − 0.537336i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 47.4529i | − 1.70676i | −0.521287 | − | 0.853381i | \(-0.674548\pi\) | ||||
0.521287 | − | 0.853381i | \(-0.325452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.36151 | 0.228512 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.4675 | 0.949517 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.4980i | 0.591103i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.3819i | 1.73124i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.77639 | −0.0992200 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.8591 | −0.637417 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.6866i | 0.951275i | 0.879641 | + | 0.475638i | \(0.157783\pi\) | ||||
−0.879641 | + | 0.475638i | \(0.842217\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.86003i | 0.208623i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.2924 | −0.472622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.3771 | −1.29179 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 20.8379i | − 0.739043i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0143i | 0.354726i | 0.984145 | + | 0.177363i | \(0.0567567\pi\) | ||||
−0.984145 | + | 0.177363i | \(0.943243\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.8527 | 1.12687 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.5547 | −1.18560 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 29.5842i | − 1.04401i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.16036i | − 0.0761427i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.6063 | 0.478966 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.6455 | 0.690699 | 0.345350 | − | 0.938474i | \(-0.387760\pi\) | ||||
0.345350 | + | 0.938474i | \(0.387760\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.8354i | 1.22324i | 0.791153 | + | 0.611618i | \(0.209481\pi\) | ||||
−0.791153 | + | 0.611618i | \(0.790519\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 13.2488i | − 0.464657i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.5269 | −0.754053 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.3254 | 1.55075 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 36.2831i | − 1.26784i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 42.6418i | − 1.48821i | −0.668064 | − | 0.744104i | \(-0.732877\pi\) | ||||
0.668064 | − | 0.744104i | \(-0.267123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.1802 | 0.459433 | 0.229717 | − | 0.973258i | \(-0.426220\pi\) | ||||
0.229717 | + | 0.973258i | \(0.426220\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.6031 | −0.438783 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.2431i | 0.947334i | 0.880704 | + | 0.473667i | \(0.157070\pi\) | ||||
−0.880704 | + | 0.473667i | \(0.842930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 39.0178i | − 1.35514i | −0.735457 | − | 0.677572i | \(-0.763032\pi\) | ||||
0.735457 | − | 0.677572i | \(-0.236968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.9169 | −0.621531 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.58941 | −0.0897177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.62970i | 0.160217i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 107.189i | 3.70500i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.5202 | −0.432247 | −0.216123 | − | 0.976366i | \(-0.569341\pi\) | ||||
−0.216123 | + | 0.976366i | \(0.569341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9728 | 0.999064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 73.5045i | 2.53163i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 7.23785i | − 0.248990i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.35449 | −0.115262 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −53.8373 | −1.84769 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.1893i | 0.589240i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 16.1155i | − 0.551786i | −0.961188 | − | 0.275893i | \(-0.911027\pi\) | ||||
0.961188 | − | 0.275893i | \(-0.0889735\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41.1216 | 1.40633 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.3966 | 0.457618 | 0.228809 | − | 0.973471i | \(-0.426517\pi\) | ||||
0.228809 | + | 0.973471i | \(0.426517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 51.5860i | − 1.76009i | −0.474890 | − | 0.880045i | \(-0.657512\pi\) | ||||
0.474890 | − | 0.880045i | \(-0.342488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.7638i | 0.366830i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.9388 | −0.712765 | −0.356382 | − | 0.934340i | \(-0.615990\pi\) | ||||
−0.356382 | + | 0.934340i | \(0.615990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.82472 | −0.334051 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 34.2458i | − 1.16305i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.0379i | 0.781509i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.25789 | −0.313692 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.73248 | 0.0924805 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.00000i | − 0.0338062i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 5.78490i | − 0.195342i | −0.995219 | − | 0.0976710i | \(-0.968861\pi\) | ||||
0.995219 | − | 0.0976710i | \(-0.0311393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.5590 | −0.457335 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.47470 | −0.251829 | −0.125915 | − | 0.992041i | \(-0.540187\pi\) | ||||
−0.125915 | + | 0.992041i | \(0.540187\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 46.3587i | − 1.56009i | −0.625721 | − | 0.780047i | \(-0.715195\pi\) | ||||
0.625721 | − | 0.780047i | \(-0.284805\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 22.8991i | − 0.769746i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.43749 | 0.115420 | 0.0577099 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577099 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.7836 | 0.697060 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 120.685i | − 4.04311i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 62.7182i | − 2.09878i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.45410 | −0.0486053 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.3289 | 1.07943 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.04821i | 0.0349599i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 16.2208i | − 0.540393i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.9193 | 0.962374 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.1639 | −0.537308 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.3061i | 1.23873i | 0.785104 | + | 0.619364i | \(0.212610\pi\) | ||||
−0.785104 | + | 0.619364i | \(0.787390\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 104.132i | − 3.45385i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8886 | −0.758333 | −0.379167 | − | 0.925328i | \(-0.623789\pi\) | ||||
−0.379167 | + | 0.925328i | \(0.623789\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67.4337 | −2.23173 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 26.8985i | − 0.889238i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5517i | 0.480538i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.4410 | 1.33403 | 0.667013 | − | 0.745046i | \(-0.267573\pi\) | ||||
0.667013 | + | 0.745046i | \(0.267573\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.8282 | 1.24648 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 57.4475i | − 1.89091i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.95666i | 0.261613i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −99.2130 | −3.25858 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.0701 | −0.396007 | −0.198004 | − | 0.980201i | \(-0.563446\pi\) | ||||
−0.198004 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.09856i | 0.167099i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 98.5182i | − 3.22534i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.81058 | −0.320840 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.3045 | −0.532646 | −0.266323 | − | 0.963884i | \(-0.585809\pi\) | ||||
−0.266323 | + | 0.963884i | \(0.585809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 108.147i | − 3.52926i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.3378i | 0.695593i | 0.937570 | + | 0.347796i | \(0.113070\pi\) | ||||
−0.937570 | + | 0.347796i | \(0.886930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.99053 | −0.227643 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.8497 | 0.548119 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.3715i | 0.661984i | 0.943634 | + | 0.330992i | \(0.107383\pi\) | ||||
−0.943634 | + | 0.330992i | \(0.892617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.1276i | 1.14029i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −87.1193 | −2.82504 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.9301 | 1.35825 | 0.679124 | − | 0.734024i | \(-0.262360\pi\) | ||||
0.679124 | + | 0.734024i | \(0.262360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 10.0537i | − 0.325330i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.07666i | − 0.0671289i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.08623 | −0.261118 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.46883 | 0.305446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 110.724i | 3.56803i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.13803i | 0.294164i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.1592 | 1.19496 | 0.597480 | − | 0.801884i | \(-0.296169\pi\) | ||||
0.597480 | + | 0.801884i | \(0.296169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.9168 | 1.41081 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 7.96541i | − 0.255622i | −0.991799 | − | 0.127811i | \(-0.959205\pi\) | ||||
0.991799 | − | 0.127811i | \(-0.0407951\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.53686i | − 0.305738i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.9646 | 0.479250 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.7944 | 0.345344 | 0.172672 | − | 0.984979i | \(-0.444760\pi\) | ||||
0.172672 | + | 0.984979i | \(0.444760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 15.7625i | − 0.503771i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 34.6148i | − 1.10517i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.44703 | 0.141838 | 0.0709192 | − | 0.997482i | \(-0.477407\pi\) | ||||
0.0709192 | + | 0.997482i | \(0.477407\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.1777 | 0.642914 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 40.9193i | − 1.30248i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.7815i | 0.597218i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.79041 | 0.279237 | 0.139618 | − | 0.990205i | \(-0.455412\pi\) | ||||
0.139618 | + | 0.990205i | \(0.455412\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −102.027 | −3.23774 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 13.8011i | − 0.437525i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.07611i | 0.129092i | 0.997915 | + | 0.0645459i | \(0.0205599\pi\) | ||||
−0.997915 | + | 0.0645459i | \(0.979440\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −134.067 | −4.24169 |
(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 | 2240.2.b.h.1121.12 | yes | 12 | |
4.3 | odd | 2 | 2240.2.b.g.1121.1 | ✓ | 12 | ||
8.3 | odd | 2 | 2240.2.b.g.1121.12 | yes | 12 | ||
8.5 | even | 2 | inner | 2240.2.b.h.1121.1 | yes | 12 | |
16.3 | odd | 4 | 8960.2.a.ch.1.6 | 6 | |||
16.5 | even | 4 | 8960.2.a.cb.1.6 | 6 | |||
16.11 | odd | 4 | 8960.2.a.cc.1.1 | 6 | |||
16.13 | even | 4 | 8960.2.a.ce.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.b.g.1121.1 | ✓ | 12 | 4.3 | odd | 2 | ||
2240.2.b.g.1121.12 | yes | 12 | 8.3 | odd | 2 | ||
2240.2.b.h.1121.1 | yes | 12 | 8.5 | even | 2 | inner | |
2240.2.b.h.1121.12 | yes | 12 | 1.1 | even | 1 | trivial | |
8960.2.a.cb.1.6 | 6 | 16.5 | even | 4 | |||
8960.2.a.cc.1.1 | 6 | 16.11 | odd | 4 | |||
8960.2.a.ce.1.1 | 6 | 16.13 | even | 4 | |||
8960.2.a.ch.1.6 | 6 | 16.3 | odd | 4 |