Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1025,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.f (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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 37x^{4} + 22x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.7 | ||
Root | \(-0.676777i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1025 |
Dual form | 2736.2.f.g.1025.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 2.60938i | 1.16695i | 0.812131 | + | 0.583475i | \(0.198307\pi\) | ||||
−0.812131 | + | 0.583475i | \(0.801693\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.723074 | 0.273296 | 0.136648 | − | 0.990620i | \(-0.456367\pi\) | ||||
0.136648 | + | 0.990620i | \(0.456367\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.10683i | 1.53977i | 0.638184 | + | 0.769884i | \(0.279686\pi\) | ||||
−0.638184 | + | 0.769884i | \(0.720314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.91037i | − | 1.63924i | −0.572907 | − | 0.819621i | \(-0.694184\pi\) | ||
0.572907 | − | 0.819621i | \(-0.305816\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.27841i | 0.552595i | 0.961072 | + | 0.276297i | \(0.0891075\pi\) | ||||
−0.961072 | + | 0.276297i | \(0.910893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.22215 | + | 1.08324i | 0.968629 | + | 0.248513i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0606600i | 0.0126485i | 0.999980 | + | 0.00632424i | \(0.00201308\pi\) | ||||
−0.999980 | + | 0.00632424i | \(0.997987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.80886 | −0.361772 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.46807 | −0.458308 | −0.229154 | − | 0.973390i | \(-0.573596\pi\) | ||||
−0.229154 | + | 0.973390i | \(0.573596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.86012i | 1.59132i | 0.605741 | + | 0.795662i | \(0.292877\pi\) | ||||
−0.605741 | + | 0.795662i | \(0.707123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.88678i | 0.318923i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.03678i | − | 0.170445i | −0.996362 | − | 0.0852226i | \(-0.972840\pi\) | ||
0.996362 | − | 0.0852226i | \(-0.0271601\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9982 | 1.71762 | 0.858812 | − | 0.512291i | \(-0.171203\pi\) | ||||
0.858812 | + | 0.512291i | \(0.171203\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.413294 | −0.0630267 | −0.0315134 | − | 0.999503i | \(-0.510033\pi\) | ||||
−0.0315134 | + | 0.999503i | \(0.510033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.94744i | 0.284063i | 0.989862 | + | 0.142031i | \(0.0453634\pi\) | ||||
−0.989862 | + | 0.142031i | \(0.954637\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47716 | −0.925309 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.82659 | 0.937704 | 0.468852 | − | 0.883277i | \(-0.344668\pi\) | ||||
0.468852 | + | 0.883277i | \(0.344668\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.3257 | −1.79683 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.46623 | −0.711642 | −0.355821 | − | 0.934554i | \(-0.615799\pi\) | ||||
−0.355821 | + | 0.934554i | \(0.615799\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.54966 | 0.966635 | 0.483318 | − | 0.875445i | \(-0.339432\pi\) | ||||
0.483318 | + | 0.875445i | \(0.339432\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.4224 | 1.91291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.6040i | 1.53982i | 0.638150 | + | 0.769912i | \(0.279700\pi\) | ||||
−0.638150 | + | 0.769912i | \(0.720300\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3585 | −1.46669 | −0.733343 | − | 0.679858i | \(-0.762041\pi\) | ||||
−0.733343 | + | 0.679858i | \(0.762041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.3038 | −1.67413 | −0.837064 | − | 0.547105i | \(-0.815730\pi\) | ||||
−0.837064 | + | 0.547105i | \(0.815730\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.69262i | 0.420813i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.40074i | − | 1.05767i | −0.848726 | − | 0.528833i | \(-0.822630\pi\) | ||
0.848726 | − | 0.528833i | \(-0.177370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.01619i | 0.879891i | 0.898024 | + | 0.439946i | \(0.145002\pi\) | ||||
−0.898024 | + | 0.439946i | \(0.854998\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.94523 | −0.644851 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.2928 | −1.72703 | −0.863517 | − | 0.504319i | \(-0.831744\pi\) | ||||
−0.863517 | + | 0.504319i | \(0.831744\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.27364i | − | 0.447999i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82659 | + | 11.0172i | −0.290002 | + | 1.13034i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.783264i | − | 0.0795284i | −0.999209 | − | 0.0397642i | \(-0.987339\pi\) | ||
0.999209 | − | 0.0397642i | \(-0.0126607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.32967i | 0.231811i | 0.993260 | + | 0.115905i | \(0.0369770\pi\) | ||||
−0.993260 | + | 0.115905i | \(0.963023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7840i | 1.06257i | 0.847192 | + | 0.531287i | \(0.178292\pi\) | ||||
−0.847192 | + | 0.531287i | \(0.821708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.4224 | 1.10424 | 0.552122 | − | 0.833763i | \(-0.313818\pi\) | ||||
0.552122 | + | 0.833763i | \(0.313818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.5672i | − | 1.10794i | −0.832537 | − | 0.553969i | \(-0.813112\pi\) | ||
0.832537 | − | 0.553969i | \(-0.186888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.76272 | −0.730255 | −0.365128 | − | 0.930958i | \(-0.618975\pi\) | ||||
−0.365128 | + | 0.930958i | \(0.618975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.158285 | −0.0147601 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.64746i | 0.151022i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.0798 | −1.37089 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.32689i | 0.744780i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5672i | 1.02643i | 0.858262 | + | 0.513213i | \(0.171545\pi\) | ||||
−0.858262 | + | 0.513213i | \(0.828455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.39843i | − | 0.733774i | −0.930266 | − | 0.366887i | \(-0.880424\pi\) | ||
0.930266 | − | 0.366887i | \(-0.119576\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.05293 | + | 0.783264i | 0.264723 | + | 0.0679176i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.4166i | 1.57344i | 0.617310 | + | 0.786720i | \(0.288222\pi\) | ||||
−0.617310 | + | 0.786720i | \(0.711778\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2532 | −1.12412 | −0.562060 | − | 0.827097i | \(-0.689991\pi\) | ||||
−0.562060 | + | 0.827097i | \(0.689991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.1833 | 2.52405 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.44012i | − | 0.534823i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 14.6289i | − | 1.19845i | −0.800582 | − | 0.599223i | \(-0.795476\pi\) | ||
0.800582 | − | 0.599223i | \(-0.204524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.00330i | − | 0.488541i | −0.969707 | − | 0.244271i | \(-0.921451\pi\) | ||
0.969707 | − | 0.244271i | \(-0.0785485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.1194 | −1.85699 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3585 | 1.62479 | 0.812393 | − | 0.583110i | \(-0.198164\pi\) | ||||
0.812393 | + | 0.583110i | \(0.198164\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0438617i | 0.00345678i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.31657 | 0.181448 | 0.0907239 | − | 0.995876i | \(-0.471082\pi\) | ||||
0.0907239 | + | 0.995876i | \(0.471082\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.40236 | −0.185900 | −0.0929499 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929499 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.9325 | −1.68711 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.93429 | 0.603233 | 0.301616 | − | 0.953429i | \(-0.402474\pi\) | ||||
0.301616 | + | 0.953429i | \(0.402474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.30794 | −0.0988710 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.82475 | 0.435362 | 0.217681 | − | 0.976020i | \(-0.430151\pi\) | ||||
0.217681 | + | 0.976020i | \(0.430151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.12971i | 0.0839703i | 0.999118 | + | 0.0419852i | \(0.0133682\pi\) | ||||
−0.999118 | + | 0.0419852i | \(0.986632\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.70535 | 0.198901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6354 | −0.850868 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1560i | 1.24137i | 0.784062 | + | 0.620683i | \(0.213145\pi\) | ||||
−0.784062 | + | 0.620683i | \(0.786855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4273i | 1.47039i | 0.677855 | + | 0.735196i | \(0.262910\pi\) | ||||
−0.677855 | + | 0.735196i | \(0.737090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.76065i | 0.125441i | 0.998031 | + | 0.0627207i | \(0.0199777\pi\) | ||||
−0.998031 | + | 0.0627207i | \(0.980022\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.41329 | −0.312850 | −0.156425 | − | 0.987690i | \(-0.549997\pi\) | ||||
−0.156425 | + | 0.987690i | \(0.549997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.78459 | −0.125254 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.6984i | 2.00438i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.53193 | + | 21.5618i | −0.382652 | + | 1.49146i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 6.70451i | − | 0.461557i | −0.973006 | − | 0.230779i | \(-0.925873\pi\) | ||
0.973006 | − | 0.230779i | \(-0.0741273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.07844i | − | 0.0735490i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.40652i | 0.434903i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4662 | 0.905836 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.54381i | − | 0.103381i | −0.998663 | − | 0.0516904i | \(-0.983539\pi\) | ||
0.998663 | − | 0.0516904i | \(-0.0164609\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.6532 | 1.70266 | 0.851331 | − | 0.524630i | \(-0.175796\pi\) | ||||
0.851331 | + | 0.524630i | \(0.175796\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.59350 | −0.633956 | −0.316978 | − | 0.948433i | \(-0.602668\pi\) | ||||
−0.316978 | + | 0.948433i | \(0.602668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.12811i | 0.270442i | 0.990815 | + | 0.135221i | \(0.0431744\pi\) | ||||
−0.990815 | + | 0.135221i | \(0.956826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.08160 | −0.331487 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.87330i | 0.638651i | 0.947645 | + | 0.319325i | \(0.103456\pi\) | ||||
−0.947645 | + | 0.319325i | \(0.896544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.3111i | − | 0.986275i | −0.869951 | − | 0.493138i | \(-0.835850\pi\) | ||
0.869951 | − | 0.493138i | \(-0.164150\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 16.9014i | − | 1.07979i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.40236 | − | 24.9545i | 0.407372 | − | 1.58782i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.0611i | 0.824409i | 0.911091 | + | 0.412204i | \(0.135241\pi\) | ||||
−0.911091 | + | 0.412204i | \(0.864759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.309780 | −0.0194757 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.4005 | −1.08541 | −0.542707 | − | 0.839922i | \(-0.682601\pi\) | ||||
−0.542707 | + | 0.839922i | \(0.682601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.749667i | − | 0.0465821i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.7502i | − | 0.909537i | −0.890610 | − | 0.454769i | \(-0.849722\pi\) | ||
0.890610 | − | 0.454769i | \(-0.150278\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.8132i | 1.09425i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1259 | −1.04418 | −0.522092 | − | 0.852889i | \(-0.674848\pi\) | ||||
−0.522092 | + | 0.852889i | \(0.674848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6532 | 1.55832 | 0.779160 | − | 0.626825i | \(-0.215646\pi\) | ||||
0.779160 | + | 0.626825i | \(0.215646\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 9.23755i | − | 0.557045i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.5460 | 1.29457 | 0.647286 | − | 0.762247i | \(-0.275904\pi\) | ||||
0.647286 | + | 0.762247i | \(0.275904\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.7152 | 1.17611 | 0.588055 | − | 0.808821i | \(-0.299894\pi\) | ||||
0.588055 | + | 0.808821i | \(0.299894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.5192 | −1.10085 | −0.550425 | − | 0.834885i | \(-0.685534\pi\) | ||||
−0.550425 | + | 0.834885i | \(0.685534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.95249 | 0.469420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8089 | 0.694639 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.16973 | −0.418860 | −0.209430 | − | 0.977824i | \(-0.567161\pi\) | ||||
−0.209430 | + | 0.977824i | \(0.567161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 14.2635i | − | 0.830450i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.358523 | 0.0207339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.298842 | −0.0172250 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.6999i | 1.12801i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.9344i | − | 1.19479i | −0.801948 | − | 0.597394i | \(-0.796203\pi\) | ||
0.801948 | − | 0.597394i | \(-0.203797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.9469i | − | 0.677444i | −0.940886 | − | 0.338722i | \(-0.890005\pi\) | ||
0.940886 | − | 0.338722i | \(-0.109995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0639 | 0.625367 | 0.312683 | − | 0.949857i | \(-0.398772\pi\) | ||||
0.312683 | + | 0.949857i | \(0.398772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.82659 | −0.158757 | −0.0793785 | − | 0.996845i | \(-0.525294\pi\) | ||||
−0.0793785 | + | 0.996845i | \(0.525294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.6040i | − | 0.705689i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.46807 | + | 9.61979i | −0.137327 | + | 0.535259i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6910i | 0.593032i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.40814i | 0.0776333i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7512i | 1.19556i | 0.801662 | + | 0.597778i | \(0.203949\pi\) | ||||
−0.801662 | + | 0.597778i | \(0.796051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −32.8886 | −1.79690 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.8543i | − | 0.645747i | −0.946442 | − | 0.322873i | \(-0.895351\pi\) | ||
0.946442 | − | 0.322873i | \(-0.104649\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.2471 | −2.45027 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.74499 | −0.526180 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.0344660i | 0.00185023i | 1.00000 | 0.000925117i | \(0.000294474\pi\) | |||||
−1.00000 | 0.000925117i | \(0.999706\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.5374 | 1.42051 | 0.710256 | − | 0.703943i | \(-0.248579\pi\) | ||||
0.710256 | + | 0.703943i | \(0.248579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8130i | 1.32067i | 0.750973 | + | 0.660333i | \(0.229585\pi\) | ||||
−0.750973 | + | 0.660333i | \(0.770415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 32.2481i | − | 1.71155i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.40421i | − | 0.285223i | −0.989779 | − | 0.142612i | \(-0.954450\pi\) | ||
0.989779 | − | 0.142612i | \(-0.0455500\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.6532 | + | 9.14723i | 0.876483 | + | 0.481433i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 37.3239i | − | 1.95362i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5856 | 1.49216 | 0.746079 | − | 0.665858i | \(-0.231934\pi\) | ||||
0.746079 | + | 0.665858i | \(0.231934\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.93613 | 0.256271 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.54381i | 0.0799352i | 0.999201 | + | 0.0399676i | \(0.0127255\pi\) | ||||
−0.999201 | + | 0.0399676i | \(0.987275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.5872i | 0.751278i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 5.14983i | − | 0.264529i | −0.991214 | − | 0.132264i | \(-0.957775\pi\) | ||
0.991214 | − | 0.132264i | \(-0.0422248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.2508 | 0.779280 | 0.389640 | − | 0.920967i | \(-0.372599\pi\) | ||||
0.389640 | + | 0.920967i | \(0.372599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.63545 | −0.491068 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 29.6420i | − | 1.50291i | −0.659784 | − | 0.751455i | \(-0.729352\pi\) | ||
0.659784 | − | 0.751455i | \(-0.270648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.138208 | −0.00698948 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.5301 | 1.23424 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0026 | −1.05409 | −0.527045 | − | 0.849837i | \(-0.676700\pi\) | ||||
−0.527045 | + | 0.849837i | \(0.676700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.9982 | 0.748972 | 0.374486 | − | 0.927232i | \(-0.377819\pi\) | ||||
0.374486 | + | 0.927232i | \(0.377819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 52.3665 | 2.60856 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.29465 | 0.262446 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0929271i | 0.00459495i | 0.999997 | + | 0.00229747i | \(0.000731310\pi\) | ||||
−0.999997 | + | 0.00229747i | \(0.999269\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.95249 | −0.194489 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.9173 | −1.02679 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.6887i | − | 1.35268i | −0.736590 | − | 0.676340i | \(-0.763565\pi\) | ||
0.736590 | − | 0.676340i | \(-0.236435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.8692i | − | 0.578469i | −0.957258 | − | 0.289235i | \(-0.906599\pi\) | ||
0.957258 | − | 0.289235i | \(-0.0934007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.12132i | − | 0.199913i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.45897 | 0.264178 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5455 | 0.796967 | 0.398484 | − | 0.917175i | \(-0.369537\pi\) | ||||
0.398484 | + | 0.917175i | \(0.369537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.3979i | 1.79723i | 0.438740 | + | 0.898614i | \(0.355425\pi\) | ||||
−0.438740 | + | 0.898614i | \(0.644575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0657094 | + | 0.256116i | −0.00314331 | + | 0.0122517i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5454i | 1.07603i | 0.842935 | + | 0.538016i | \(0.180826\pi\) | ||||
−0.842935 | + | 0.538016i | \(0.819174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.86503i | 0.278656i | 0.990246 | + | 0.139328i | \(0.0444942\pi\) | ||||
−0.990246 | + | 0.139328i | \(0.955506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 42.5141i | − | 2.01536i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3604 | 0.630514 | 0.315257 | − | 0.949006i | \(-0.397909\pi\) | ||||
0.315257 | + | 0.949006i | \(0.397909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.1658i | 2.64474i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.1515 | 0.522792 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.65058 | 0.217545 | 0.108772 | − | 0.994067i | \(-0.465308\pi\) | ||||
0.108772 | + | 0.994067i | \(0.465308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.3953i | − | 0.810181i | −0.914277 | − | 0.405091i | \(-0.867240\pi\) | ||
0.914277 | − | 0.405091i | \(-0.132760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8931 | −1.43572 | −0.717861 | − | 0.696186i | \(-0.754879\pi\) | ||||
−0.717861 | + | 0.696186i | \(0.754879\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.8891i | 1.42938i | 0.699444 | + | 0.714688i | \(0.253431\pi\) | ||||
−0.699444 | + | 0.714688i | \(0.746569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.11363i | 0.420828i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.11062i | − | 0.0970466i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.63729 | − | 1.95943i | −0.350423 | − | 0.0899049i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 23.1951i | − | 1.05981i | −0.848057 | − | 0.529906i | \(-0.822227\pi\) | ||
0.848057 | − | 0.529906i | \(-0.177773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.12774 | −0.279401 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.04383 | 0.0928057 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.41740i | − | 0.290800i | −0.989373 | − | 0.145400i | \(-0.953553\pi\) | ||
0.989373 | − | 0.145400i | \(-0.0464469\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 35.8720i | − | 1.61888i | −0.587203 | − | 0.809440i | \(-0.699771\pi\) | ||
0.587203 | − | 0.809440i | \(-0.300229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.62326i | − | 0.253259i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.93613 | −0.400840 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5916 | 0.787509 | 0.393754 | − | 0.919216i | \(-0.371176\pi\) | ||||
0.393754 | + | 0.919216i | \(0.371176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 42.3605i | − | 1.88876i | −0.328852 | − | 0.944382i | \(-0.606662\pi\) | ||
0.328852 | − | 0.944382i | \(-0.393338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.07900 | −0.270512 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.4881 | −1.04109 | −0.520546 | − | 0.853834i | \(-0.674272\pi\) | ||||
−0.520546 | + | 0.853834i | \(0.674272\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3427 | −0.457533 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.1394 | −1.23997 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.94523 | −0.437391 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0774 | −0.441499 | −0.220750 | − | 0.975331i | \(-0.570850\pi\) | ||||
−0.220750 | + | 0.975331i | \(0.570850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 30.9578i | − | 1.35369i | −0.736126 | − | 0.676845i | \(-0.763347\pi\) | ||
0.736126 | − | 0.676845i | \(-0.236653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.1870 | −0.879357 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9963 | 0.999840 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 65.0032i | − | 2.81560i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.8054i | 1.28860i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 33.0778i | − | 1.42476i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.34942 | 0.315976 | 0.157988 | − | 0.987441i | \(-0.449499\pi\) | ||||
0.157988 | + | 0.987441i | \(0.449499\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.1833 | 1.29291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.6675i | − | 1.26849i | −0.773132 | − | 0.634245i | \(-0.781311\pi\) | ||
0.773132 | − | 0.634245i | \(-0.218689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4206 | − | 2.67351i | −0.443930 | − | 0.113895i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.79743i | − | 0.289056i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11.2849i | − | 0.478157i | −0.971000 | − | 0.239079i | \(-0.923155\pi\) | ||
0.971000 | − | 0.239079i | \(-0.0768453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.44272i | 0.103316i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.5940 | −1.66869 | −0.834343 | − | 0.551245i | \(-0.814153\pi\) | ||||
−0.834343 | + | 0.551245i | \(0.814153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 20.2559i | − | 0.852171i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.18511 | 0.133527 | 0.0667634 | − | 0.997769i | \(-0.478733\pi\) | ||||
0.0667634 | + | 0.997769i | \(0.478733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.5856 | −1.02888 | −0.514438 | − | 0.857527i | \(-0.672000\pi\) | ||||
−0.514438 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.109725i | − | 0.00457587i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.5697 | −0.981221 | −0.490611 | − | 0.871379i | \(-0.663226\pi\) | ||||
−0.490611 | + | 0.871379i | \(0.663226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.79630i | 0.240471i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.8623i | 1.44385i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.9676i | 0.989251i | 0.869106 | + | 0.494625i | \(0.164695\pi\) | ||||
−0.869106 | + | 0.494625i | \(0.835305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.59764 | + | 37.4088i | −0.395464 | + | 1.54140i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.67611i | − | 0.109895i | −0.998489 | − | 0.0549474i | \(-0.982501\pi\) | ||
0.998489 | − | 0.0549474i | \(-0.0174991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.29884 | −0.176235 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.3110 | −1.15676 | −0.578378 | − | 0.815769i | \(-0.696314\pi\) | ||||
−0.578378 | + | 0.815769i | \(0.696314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.1745i | − | 1.23084i | −0.788198 | − | 0.615422i | \(-0.788986\pi\) | ||
0.788198 | − | 0.615422i | \(-0.211014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 39.3488i | − | 1.59976i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 31.9352i | − | 1.29621i | −0.761551 | − | 0.648105i | \(-0.775562\pi\) | ||
0.761551 | − | 0.648105i | \(-0.224438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5101 | 0.465647 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.8844 | 1.69170 | 0.845848 | − | 0.533424i | \(-0.179095\pi\) | ||||
0.845848 | + | 0.533424i | \(0.179095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.71971i | 0.230267i | 0.993350 | + | 0.115133i | \(0.0367296\pi\) | ||||
−0.993350 | + | 0.115133i | \(0.963270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.1376 | 0.889787 | 0.444893 | − | 0.895584i | \(-0.353242\pi\) | ||||
0.444893 | + | 0.895584i | \(0.353242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.7809 | −0.471992 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7723 | −1.23089 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.36220 | 0.0941872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.02607 | 0.0408470 | 0.0204235 | − | 0.999791i | \(-0.493499\pi\) | ||||
0.0204235 | + | 0.999791i | \(0.493499\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.1833 | −1.19779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.2824i | 1.51680i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.0737 | 1.58282 | 0.791409 | − | 0.611288i | \(-0.209348\pi\) | ||||
0.791409 | + | 0.611288i | \(0.209348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7144 | 0.540845 | 0.270422 | − | 0.962742i | \(-0.412837\pi\) | ||||
0.270422 | + | 0.962742i | \(0.412837\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 8.25771i | − | 0.324644i | −0.986738 | − | 0.162322i | \(-0.948102\pi\) | ||
0.986738 | − | 0.162322i | \(-0.0518983\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27.9151i | − | 1.09576i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.23831i | 0.0484587i | 0.999706 | + | 0.0242293i | \(0.00771320\pi\) | ||||
−0.999706 | + | 0.0242293i | \(0.992287\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.9147 | 0.856278 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.8849 | −1.67056 | −0.835280 | − | 0.549825i | \(-0.814694\pi\) | ||||
−0.835280 | + | 0.549825i | \(0.814694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 50.6359i | − | 1.96951i | −0.173950 | − | 0.984754i | \(-0.555653\pi\) | ||
0.173950 | − | 0.984754i | \(-0.444347\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.04383 | + | 7.96626i | −0.0792564 | + | 0.308918i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.149713i | − | 0.00579690i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.5549i | 1.48839i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 41.5450i | − | 1.60144i | −0.599037 | − | 0.800721i | \(-0.704450\pi\) | ||
0.599037 | − | 0.800721i | \(-0.295550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.8266 | 1.33849 | 0.669247 | − | 0.743040i | \(-0.266617\pi\) | ||||
0.669247 | + | 0.743040i | \(0.266617\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 0.566358i | − | 0.0217348i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.8448 | 1.63941 | 0.819705 | − | 0.572786i | \(-0.194137\pi\) | ||||
0.819705 | + | 0.572786i | \(0.194137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.0560 | −1.83613 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 40.3476i | − | 1.53712i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.4278 | 1.23361 | 0.616806 | − | 0.787115i | \(-0.288426\pi\) | ||||
0.616806 | + | 0.787115i | \(0.288426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 34.5825i | − | 1.31179i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.0583i | 0.949150i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.3983i | 0.543814i | 0.962323 | + | 0.271907i | \(0.0876544\pi\) | ||||
−0.962323 | + | 0.271907i | \(0.912346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12308 | − | 4.37744i | 0.0423578 | − | 0.165098i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.68453i | 0.0633531i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.6458 | 1.78938 | 0.894688 | − | 0.446691i | \(-0.147398\pi\) | ||||
0.894688 | + | 0.446691i | \(0.147398\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.537454 | −0.0201278 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 78.7596i | 2.94544i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.7314i | 0.549389i | 0.961532 | + | 0.274695i | \(0.0885768\pi\) | ||||
−0.961532 | + | 0.274695i | \(0.911423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.79760i | 0.290398i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.46439 | 0.165803 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1723 | 0.896502 | 0.448251 | − | 0.893908i | \(-0.352047\pi\) | ||||
0.448251 | + | 0.893908i | \(0.352047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 0.941652i | − | 0.0348283i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.7134 | 1.35604 | 0.678020 | − | 0.735044i | \(-0.262838\pi\) | ||||
0.678020 | + | 0.735044i | \(0.262838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −64.3665 | −2.37097 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0425 | 0.553346 | 0.276673 | − | 0.960964i | \(-0.410768\pi\) | ||||
0.276673 | + | 0.960964i | \(0.410768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.4709 | −0.384139 | −0.192070 | − | 0.981381i | \(-0.561520\pi\) | ||||
−0.192070 | + | 0.981381i | \(0.561520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.1723 | 1.39853 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.25924 | 0.301786 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9209i | 0.909376i | 0.890651 | + | 0.454688i | \(0.150249\pi\) | ||||
−0.890651 | + | 0.454688i | \(0.849751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.6649 | 0.570103 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.66104 | 0.242100 | 0.121050 | − | 0.992646i | \(-0.461374\pi\) | ||||
0.121050 | + | 0.992646i | \(0.461374\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.3148i | 1.38891i | 0.719535 | + | 0.694456i | \(0.244355\pi\) | ||||
−0.719535 | + | 0.694456i | \(0.755645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.36396i | − | 0.302796i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.3074i | 1.16655i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.6373 | 0.744200 | 0.372100 | − | 0.928193i | \(-0.378638\pi\) | ||||
0.372100 | + | 0.928193i | \(0.378638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.83493 | −0.0659977 | −0.0329988 | − | 0.999455i | \(-0.510506\pi\) | ||||
−0.0329988 | + | 0.999455i | \(0.510506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 16.0267i | − | 0.575696i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.4359 | + | 11.9137i | 1.66374 | + | 0.426851i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 63.1129i | − | 2.25836i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.1231i | 1.89605i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9732i | 0.462443i | 0.972901 | + | 0.231222i | \(0.0742723\pi\) | ||||
−0.972901 | + | 0.231222i | \(0.925728\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.61302 | −0.199576 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 44.6213i | − | 1.58455i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.7306 | 0.840580 | 0.420290 | − | 0.907390i | \(-0.361928\pi\) | ||||
0.420290 | + | 0.907390i | \(0.361928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.43705 | −0.156972 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 73.0469i | − | 2.57777i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.114452 | −0.00403389 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.1252i | 0.707563i | 0.935328 | + | 0.353781i | \(0.115104\pi\) | ||||
−0.935328 | + | 0.353781i | \(0.884896\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3268i | 0.924460i | 0.886760 | + | 0.462230i | \(0.152951\pi\) | ||||
−0.886760 | + | 0.462230i | \(0.847049\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.04481i | 0.211740i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.74499 | − | 0.447697i | −0.0610495 | − | 0.0156629i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.43567i | 0.0850055i | 0.999096 | + | 0.0425028i | \(0.0135331\pi\) | ||||
−0.999096 | + | 0.0425028i | \(0.986467\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.4803 | 1.44591 | 0.722956 | − | 0.690894i | \(-0.242783\pi\) | ||||
0.722956 | + | 0.690894i | \(0.242783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4779 | −0.955501 | −0.477751 | − | 0.878496i | \(-0.658548\pi\) | ||||
−0.477751 | + | 0.878496i | \(0.658548\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 53.5625i | − | 1.86030i | −0.367178 | − | 0.930151i | \(-0.619676\pi\) | ||
0.367178 | − | 0.930151i | \(-0.380324\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 14.7576i | − | 0.511321i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 6.26866i | − | 0.216936i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.4104 | 1.74036 | 0.870180 | − | 0.492734i | \(-0.164003\pi\) | ||||
0.870180 | + | 0.492734i | \(0.164003\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.9087 | −0.789954 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 57.2301i | − | 1.96877i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9038 | −0.374658 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0628909 | 0.00215587 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.4943 | 1.24954 | 0.624770 | − | 0.780809i | \(-0.285193\pi\) | ||||
0.624770 | + | 0.780809i | \(0.285193\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.50822 | −0.222317 | −0.111158 | − | 0.993803i | \(-0.535456\pi\) | ||||
−0.111158 | + | 0.993803i | \(0.535456\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.7194 | −0.809294 | −0.404647 | − | 0.914473i | \(-0.632606\pi\) | ||||
−0.404647 | + | 0.914473i | \(0.632606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.6970 | −0.942817 | −0.471409 | − | 0.881915i | \(-0.656254\pi\) | ||||
−0.471409 | + | 0.881915i | \(0.656254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.7036i | 0.703943i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.0080 | 1.62856 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 74.4943 | 2.52414 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.02096i | 0.203546i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.1701i | 1.25515i | 0.778558 | + | 0.627573i | \(0.215952\pi\) | ||||
−0.778558 | + | 0.627573i | \(0.784048\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 54.4435i | − | 1.83425i | −0.398603 | − | 0.917124i | \(-0.630505\pi\) | ||
0.398603 | − | 0.917124i | \(-0.369495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2886 | 1.12025 | 0.560126 | − | 0.828408i | \(-0.310753\pi\) | ||||
0.560126 | + | 0.828408i | \(0.310753\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.0281 | 1.24328 | 0.621640 | − | 0.783303i | \(-0.286467\pi\) | ||||
0.621640 | + | 0.783303i | \(0.286467\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.36396i | 0.280518i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.10954 | + | 8.22237i | −0.0705931 | + | 0.275151i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.1990i | 0.508046i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 21.8673i | − | 0.729317i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5537i | 0.518170i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.94783 | −0.0979891 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.1538i | 0.702401i | 0.936300 | + | 0.351200i | \(0.114226\pi\) | ||||
−0.936300 | + | 0.351200i | \(0.885774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.7689 | −1.41700 | −0.708498 | − | 0.705712i | \(-0.750627\pi\) | ||||
−0.708498 | + | 0.705712i | \(0.750627\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.9374 | −1.35483 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 6.07269i | − | 0.200538i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.36506 | −0.308925 | −0.154462 | − | 0.987999i | \(-0.549365\pi\) | ||||
−0.154462 | + | 0.987999i | \(0.549365\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 73.0434i | 2.40425i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.87539i | 0.0616623i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.7164i | 0.351592i | 0.984427 | + | 0.175796i | \(0.0562499\pi\) | ||||
−0.984427 | + | 0.175796i | \(0.943750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.3476 | − | 7.01633i | −0.896281 | − | 0.229951i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 30.3613i | − | 0.992921i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.3256 | 0.598672 | 0.299336 | − | 0.954148i | \(-0.403235\pi\) | ||||
0.299336 | + | 0.954148i | \(0.403235\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.9865 | −0.423347 | −0.211673 | − | 0.977340i | \(-0.567891\pi\) | ||||
−0.211673 | + | 0.977340i | \(0.567891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.667148i | 0.0217253i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1.34528i | − | 0.0437158i | −0.999761 | − | 0.0218579i | \(-0.993042\pi\) | ||
0.999761 | − | 0.0218579i | \(-0.00695814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 84.5404i | 2.74430i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.85030 | 0.319083 | 0.159541 | − | 0.987191i | \(-0.448998\pi\) | ||||
0.159541 | + | 0.987191i | \(0.448998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.7665 | −1.44861 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3166i | 0.430015i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −47.5016 | −1.53231 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53.3027 | −1.71587 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.6951 | −1.01925 | −0.509623 | − | 0.860398i | \(-0.670215\pi\) | ||||
−0.509623 | + | 0.860398i | \(0.670215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.6769 | −0.920285 | −0.460143 | − | 0.887845i | \(-0.652202\pi\) | ||||
−0.460143 | + | 0.887845i | \(0.652202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.58303 | −0.307218 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8905 | 0.828309 | 0.414155 | − | 0.910207i | \(-0.364077\pi\) | ||||
0.414155 | + | 0.910207i | \(0.364077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 83.2047i | − | 2.65923i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −58.8849 | −1.87814 | −0.939069 | − | 0.343729i | \(-0.888310\pi\) | ||||
−0.939069 | + | 0.343729i | \(0.888310\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.59422 | −0.146384 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.0250704i | − | 0.000797192i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.5118i | 0.715110i | 0.933892 | + | 0.357555i | \(0.116390\pi\) | ||||
−0.933892 | + | 0.357555i | \(0.883610\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11.5160i | − | 0.365080i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.8928 | 0.756693 | 0.378346 | − | 0.925664i | \(-0.376493\pi\) | ||||
0.378346 | + | 0.925664i | \(0.376493\pi\) | |||||||
\(998\) | 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 | 2736.2.f.g.1025.7 | 8 | ||
3.2 | odd | 2 | 2736.2.f.h.1025.2 | 8 | |||
4.3 | odd | 2 | 1368.2.f.c.1025.7 | yes | 8 | ||
12.11 | even | 2 | 1368.2.f.d.1025.2 | yes | 8 | ||
19.18 | odd | 2 | 2736.2.f.h.1025.7 | 8 | |||
57.56 | even | 2 | inner | 2736.2.f.g.1025.2 | 8 | ||
76.75 | even | 2 | 1368.2.f.d.1025.7 | yes | 8 | ||
228.227 | odd | 2 | 1368.2.f.c.1025.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.f.c.1025.2 | ✓ | 8 | 228.227 | odd | 2 | ||
1368.2.f.c.1025.7 | yes | 8 | 4.3 | odd | 2 | ||
1368.2.f.d.1025.2 | yes | 8 | 12.11 | even | 2 | ||
1368.2.f.d.1025.7 | yes | 8 | 76.75 | even | 2 | ||
2736.2.f.g.1025.2 | 8 | 57.56 | even | 2 | inner | ||
2736.2.f.g.1025.7 | 8 | 1.1 | even | 1 | trivial | ||
2736.2.f.h.1025.2 | 8 | 3.2 | odd | 2 | |||
2736.2.f.h.1025.7 | 8 | 19.18 | odd | 2 |